LMFDB - Embedded newform 112.2.w.c.37.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,2,Mod(37,112)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("112.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	112.w (of order $12$, degree $4$, 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:	$0.894324502638$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.11
Character	$\chi$	$=$	112.37
Dual form			112.2.w.c.109.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39181 - 0.250740i) q^{2} +(-2.46036 - 0.659252i) q^{3} +(1.87426 - 0.697963i) q^{4} +(1.87532 - 0.502490i) q^{5} +(-3.58965 - 0.300642i) q^{6} +(0.364450 - 2.62053i) q^{7} +(2.43360 - 1.44138i) q^{8} +(3.02070 + 1.74400i) q^{9} +O(q^{10})$	\(q+(1.39181 - 0.250740i) q^{2} +(-2.46036 - 0.659252i) q^{3} +(1.87426 - 0.697963i) q^{4} +(1.87532 - 0.502490i) q^{5} +(-3.58965 - 0.300642i) q^{6} +(0.364450 - 2.62053i) q^{7} +(2.43360 - 1.44138i) q^{8} +(3.02070 + 1.74400i) q^{9} +(2.48409 - 1.16959i) q^{10} +(-1.37168 + 5.11917i) q^{11} +(-5.07149 + 0.481633i) q^{12} +(-3.61173 + 3.61173i) q^{13} +(-0.149826 - 3.73866i) q^{14} -4.94523 q^{15} +(3.02569 - 2.61633i) q^{16} +(-0.294815 - 0.510634i) q^{17} +(4.64152 + 1.66990i) q^{18} +(-0.137946 - 0.514822i) q^{19} +(3.16411 - 2.25070i) q^{20} +(-2.62427 + 6.20719i) q^{21} +(-0.625532 + 7.46884i) q^{22} +(0.378033 + 0.218258i) q^{23} +(-6.93778 + 1.94197i) q^{24} +(-1.06581 + 0.615344i) q^{25} +(-4.12123 + 5.93245i) q^{26} +(-0.878939 - 0.878939i) q^{27} +(-1.14596 - 5.16592i) q^{28} +(2.68976 - 2.68976i) q^{29} +(-6.88281 + 1.23997i) q^{30} +(3.94118 + 6.82633i) q^{31} +(3.55517 - 4.40009i) q^{32} +(6.74965 - 11.6907i) q^{33} +(-0.538362 - 0.636783i) q^{34} +(-0.633329 - 5.09746i) q^{35} +(6.87881 + 1.16037i) q^{36} +(-2.90863 + 0.779365i) q^{37} +(-0.321081 - 0.681944i) q^{38} +(11.2672 - 6.50513i) q^{39} +(3.83950 - 3.92591i) q^{40} -2.95135i q^{41} +(-2.09609 + 9.29722i) q^{42} +(-7.67329 - 7.67329i) q^{43} +(1.00211 + 10.5520i) q^{44} +(6.54110 + 1.75268i) q^{45} +(0.580875 + 0.208985i) q^{46} +(2.01771 - 3.49478i) q^{47} +(-9.16913 + 4.44242i) q^{48} +(-6.73435 - 1.91011i) q^{49} +(-1.32911 + 1.12368i) q^{50} +(0.388715 + 1.45070i) q^{51} +(-4.24847 + 9.29018i) q^{52} +(0.244374 - 0.912017i) q^{53} +(-1.44370 - 1.00293i) q^{54} +10.2893i q^{55} +(-2.89026 - 6.90264i) q^{56} +1.35759i q^{57} +(3.06920 - 4.41806i) q^{58} +(0.00753382 - 0.0281166i) q^{59} +(-9.26864 + 3.45159i) q^{60} +(0.529990 + 1.97795i) q^{61} +(7.19700 + 8.51273i) q^{62} +(5.67110 - 7.28022i) q^{63} +(3.84483 - 7.01550i) q^{64} +(-4.95829 + 8.58801i) q^{65} +(6.46288 - 17.9637i) q^{66} +(-6.24795 - 1.67413i) q^{67} +(-0.908964 - 0.751291i) q^{68} +(-0.786212 - 0.786212i) q^{69} +(-2.15961 - 6.93588i) q^{70} +2.05630i q^{71} +(9.86494 - 0.109777i) q^{72} +(6.85664 - 3.95868i) q^{73} +(-3.85283 + 1.81403i) q^{74} +(3.02794 - 0.811334i) q^{75} +(-0.617873 - 0.868628i) q^{76} +(12.9150 + 5.46021i) q^{77} +(14.0507 - 11.8790i) q^{78} +(-6.53028 + 11.3108i) q^{79} +(4.35946 - 6.42683i) q^{80} +(-3.64893 - 6.32013i) q^{81} +(-0.740020 - 4.10771i) q^{82} +(10.1551 - 10.1551i) q^{83} +(-0.586173 + 13.4655i) q^{84} +(-0.809460 - 0.809460i) q^{85} +(-12.6038 - 8.75575i) q^{86} +(-8.39101 + 4.84455i) q^{87} +(4.04056 + 14.4351i) q^{88} +(-3.35262 - 1.93564i) q^{89} +(9.54343 + 0.799284i) q^{90} +(8.14836 + 10.7810i) q^{91} +(0.860868 + 0.145218i) q^{92} +(-5.19647 - 19.3935i) q^{93} +(1.93199 - 5.36999i) q^{94} +(-0.517385 - 0.896137i) q^{95} +(-11.6478 + 8.48206i) q^{96} -12.0556 q^{97} +(-9.85186 - 0.969932i) q^{98} +(-13.0712 + 13.0712i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{8}+O(q^{10}) $ 48 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^8	$ 48 q - 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 24 q^{13} - 34 q^{14} - 40 q^{15} + 16 q^{16} + 8 q^{17} + 18 q^{18} - 4 q^{19} - 16 q^{20} - 8 q^{21} + 18 q^{24} - 10 q^{26} - 24 q^{27} - 10 q^{28} + 24 q^{29} - 4 q^{30} + 28 q^{31} + 16 q^{32} + 16 q^{33} - 44 q^{34} + 28 q^{35} - 72 q^{36} - 24 q^{37} + 20 q^{38} + 26 q^{40} + 6 q^{42} - 40 q^{43} + 6 q^{44} - 28 q^{45} - 14 q^{46} - 20 q^{47} + 56 q^{48} + 56 q^{50} + 24 q^{51} - 16 q^{52} - 16 q^{53} + 64 q^{54} + 40 q^{56} - 6 q^{58} - 20 q^{59} + 46 q^{60} + 8 q^{61} + 24 q^{62} - 16 q^{63} + 80 q^{64} + 8 q^{65} - 20 q^{66} + 48 q^{67} - 40 q^{69} + 82 q^{70} - 32 q^{72} - 8 q^{74} - 4 q^{75} - 36 q^{76} - 20 q^{77} + 116 q^{78} - 36 q^{79} - 28 q^{80} + 2 q^{82} - 8 q^{83} + 28 q^{84} - 20 q^{86} - 42 q^{88} - 20 q^{90} + 64 q^{91} + 76 q^{92} + 8 q^{93} - 72 q^{94} - 4 q^{95} - 120 q^{96} - 48 q^{97} - 2 q^{98} - 24 q^{99}+O(q^{100}) $ 48 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 24 * q^13 - 34 * q^14 - 40 * q^15 + 16 * q^16 + 8 * q^17 + 18 * q^18 - 4 * q^19 - 16 * q^20 - 8 * q^21 + 18 * q^24 - 10 * q^26 - 24 * q^27 - 10 * q^28 + 24 * q^29 - 4 * q^30 + 28 * q^31 + 16 * q^32 + 16 * q^33 - 44 * q^34 + 28 * q^35 - 72 * q^36 - 24 * q^37 + 20 * q^38 + 26 * q^40 + 6 * q^42 - 40 * q^43 + 6 * q^44 - 28 * q^45 - 14 * q^46 - 20 * q^47 + 56 * q^48 + 56 * q^50 + 24 * q^51 - 16 * q^52 - 16 * q^53 + 64 * q^54 + 40 * q^56 - 6 * q^58 - 20 * q^59 + 46 * q^60 + 8 * q^61 + 24 * q^62 - 16 * q^63 + 80 * q^64 + 8 * q^65 - 20 * q^66 + 48 * q^67 - 40 * q^69 + 82 * q^70 - 32 * q^72 - 8 * q^74 - 4 * q^75 - 36 * q^76 - 20 * q^77 + 116 * q^78 - 36 * q^79 - 28 * q^80 + 2 * q^82 - 8 * q^83 + 28 * q^84 - 20 * q^86 - 42 * q^88 - 20 * q^90 + 64 * q^91 + 76 * q^92 + 8 * q^93 - 72 * q^94 - 4 * q^95 - 120 * q^96 - 48 * q^97 - 2 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.39181	−	0.250740i	0.984157	−	0.177300i
$2$	1.39181	−	0.250740i	0.984157	−	0.177300i
$3$	−2.46036	−	0.659252i	−1.42049	−	0.380619i	−0.534833	−	0.844958i	$-0.679626\pi$
$3$	−2.46036	−	0.659252i	−1.42049	−	0.380619i	−0.885658	+	0.464338i	$0.846292\pi$
$4$	1.87426	−	0.697963i	0.937130	−	0.348982i
$5$	1.87532	−	0.502490i	0.838668	−	0.224720i	0.186176	−	0.982516i	$-0.440391\pi$
$5$	1.87532	−	0.502490i	0.838668	−	0.224720i	0.652491	+	0.757796i	$0.273724\pi$
$6$	−3.58965	−	0.300642i	−1.46547	−	0.122736i
$7$	0.364450	−	2.62053i	0.137749	−	0.990467i
$7$	0.364450	−	2.62053i	0.137749	−	0.990467i
$8$	2.43360	−	1.44138i	0.860408	−	0.509606i
$9$	3.02070	+	1.74400i	1.00690	+	0.581333i
$10$	2.48409	−	1.16959i	0.785538	−	0.369856i
$11$	−1.37168	+	5.11917i	−0.413576	+	1.54349i	0.374094	+	0.927391i	$0.377954\pi$
$11$	−1.37168	+	5.11917i	−0.413576	+	1.54349i	−0.787670	+	0.616097i	$0.788713\pi$
$12$	−5.07149	+	0.481633i	−1.46401	+	0.139036i
$13$	−3.61173	+	3.61173i	−1.00171	+	1.00171i	−0.00171617	+	0.999999i	$0.500546\pi$
$13$	−3.61173	+	3.61173i	−1.00171	+	1.00171i	−0.999999	+	0.00171617i	$0.999454\pi$
$14$	−0.149826	−	3.73866i	−0.0400427	−	0.999198i
$15$	−4.94523			−1.27685
$16$	3.02569	−	2.61633i	0.756424	−	0.654082i
$17$	−0.294815	−	0.510634i	−0.0715031	−	0.123847i	0.828057	−	0.560644i	$-0.189446\pi$
$17$	−0.294815	−	0.510634i	−0.0715031	−	0.123847i	−0.899560	+	0.436797i	$0.856113\pi$
$18$	4.64152	+	1.66990i	1.09402	+	0.393600i
$19$	−0.137946	−	0.514822i	−0.0316470	−	0.118108i	0.948295	−	0.317389i	$-0.102806\pi$
$19$	−0.137946	−	0.514822i	−0.0316470	−	0.118108i	−0.979942	+	0.199281i	$0.936139\pi$
$20$	3.16411	−	2.25070i	0.707517	−	0.503272i
$21$	−2.62427	+	6.20719i	−0.572663	+	1.35452i
$22$	−0.625532	+	7.46884i	−0.133364	+	1.59236i
$23$	0.378033	+	0.218258i	0.0788254	+	0.0455098i	0.538895	−	0.842373i	$-0.318842\pi$
$23$	0.378033	+	0.218258i	0.0788254	+	0.0455098i	−0.460069	+	0.887883i	$0.652175\pi$
$24$	−6.93778	+	1.94197i	−1.41617	+	0.396402i
$25$	−1.06581	+	0.615344i	−0.213161	+	0.123069i
$26$	−4.12123	+	5.93245i	−0.808241	+	1.16345i
$27$	−0.878939	−	0.878939i	−0.169152	−	0.169152i
$28$	−1.14596	−	5.16592i	−0.216566	−	0.976268i
$29$	2.68976	−	2.68976i	0.499476	−	0.499476i	−0.411799	−	0.911275i	$-0.635099\pi$
$29$	2.68976	−	2.68976i	0.499476	−	0.499476i	0.911275	+	0.411799i	$0.135099\pi$
$30$	−6.88281	+	1.23997i	−1.25662	+	0.226386i
$31$	3.94118	+	6.82633i	0.707857	+	1.22605i	0.965650	+	0.259845i	$0.0836714\pi$
$31$	3.94118	+	6.82633i	0.707857	+	1.22605i	−0.257793	+	0.966200i	$0.582995\pi$
$32$	3.55517	−	4.40009i	0.628471	−	0.777833i
$33$	6.74965	−	11.6907i	1.17496	−	2.03510i
$34$	−0.538362	−	0.636783i	−0.0923284	−	0.109207i
$35$	−0.633329	−	5.09746i	−0.107052	−	0.861628i
$36$	6.87881	+	1.16037i	1.14647	+	0.193395i
$37$	−2.90863	+	0.779365i	−0.478176	+	0.128127i	−0.489853	−	0.871805i	$-0.662950\pi$
$37$	−2.90863	+	0.779365i	−0.478176	+	0.128127i	0.0116774	+	0.999932i	$0.496283\pi$
$38$	−0.321081	−	0.681944i	−0.0520862	−	0.110626i
$39$	11.2672	−	6.50513i	1.80420	−	1.04165i
$40$	3.83950	−	3.92591i	0.607078	−	0.620741i
$41$		−	2.95135i		−	0.460923i	−0.973081	−	0.230461i	$-0.925976\pi$
$41$		−	2.95135i		−	0.460923i	0.973081	−	0.230461i	$-0.0740235\pi$
$42$	−2.09609	+	9.29722i	−0.323434	+	1.43459i
$43$	−7.67329	−	7.67329i	−1.17017	−	1.17017i	−0.982170	−	0.187996i	$-0.939801\pi$
$43$	−7.67329	−	7.67329i	−1.17017	−	1.17017i	−0.187996	−	0.982170i	$-0.560199\pi$
$44$	1.00211	+	10.5520i	0.151074	+	1.59078i
$45$	6.54110	+	1.75268i	0.975090	+	0.261275i
$46$	0.580875	+	0.208985i	0.0856454	+	0.0308131i
$47$	2.01771	−	3.49478i	0.294314	−	0.509766i	−0.680511	−	0.732738i	$-0.738242\pi$
$47$	2.01771	−	3.49478i	0.294314	−	0.509766i	0.974825	+	0.222971i	$0.0715756\pi$
$48$	−9.16913	+	4.44242i	−1.32345	+	0.641208i
$49$	−6.73435	−	1.91011i	−0.962050	−	0.272872i
$50$	−1.32911	+	1.12368i	−0.187964	+	0.158912i
$51$	0.388715	+	1.45070i	0.0544310	+	0.203139i
$52$	−4.24847	+	9.29018i	−0.589156	+	1.28832i
$53$	0.244374	−	0.912017i	0.0335674	−	0.125275i	−0.947109	−	0.320912i	$-0.896011\pi$
$53$	0.244374	−	0.912017i	0.0335674	−	0.125275i	0.980676	+	0.195637i	$0.0626773\pi$
$54$	−1.44370	−	1.00293i	−0.196463	−	0.136481i
$55$			10.2893i			1.38741i
$56$	−2.89026	−	6.90264i	−0.386227	−	0.922404i
$57$			1.35759i			0.179817i
$58$	3.06920	−	4.41806i	0.403006	−	0.580119i
$59$	0.00753382	−	0.0281166i	0.000980820	−	0.00366047i	−0.965434	−	0.260649i	$-0.916064\pi$
$59$	0.00753382	−	0.0281166i	0.000980820	−	0.00366047i	0.966415	+	0.256988i	$0.0827302\pi$
$60$	−9.26864	+	3.45159i	−1.19658	+	0.445598i
$61$	0.529990	+	1.97795i	0.0678583	+	0.253251i	0.991519	−	0.129960i	$-0.0414850\pi$
$61$	0.529990	+	1.97795i	0.0678583	+	0.253251i	−0.923661	+	0.383211i	$0.874818\pi$
$62$	7.19700	+	8.51273i	0.914020	+	1.08112i
$63$	5.67110	−	7.28022i	0.714491	−	0.917222i
$64$	3.84483	−	7.01550i	0.480604	−	0.876938i
$65$	−4.95829	+	8.58801i	−0.615000	+	1.06521i
$66$	6.46288	−	17.9637i	0.795526	−	2.21117i
$67$	−6.24795	−	1.67413i	−0.763309	−	0.204528i	−0.143895	−	0.989593i	$-0.545963\pi$
$67$	−6.24795	−	1.67413i	−0.763309	−	0.204528i	−0.619414	+	0.785065i	$0.712630\pi$
$68$	−0.908964	−	0.751291i	−0.110228	−	0.0911074i
$69$	−0.786212	−	0.786212i	−0.0946488	−	0.0946488i
$70$	−2.15961	−	6.93588i	−0.258123	−	0.828996i
$71$			2.05630i			0.244037i	0.992528	+	0.122019i	$0.0389368\pi$
$71$			2.05630i			0.244037i	−0.992528	+	0.122019i	$0.961063\pi$
$72$	9.86494	−	0.109777i	1.16259	−	0.0129373i
$73$	6.85664	−	3.95868i	0.802509	−	0.463329i	−0.0418389	−	0.999124i	$-0.513322\pi$
$73$	6.85664	−	3.95868i	0.802509	−	0.463329i	0.844348	+	0.535796i	$0.179988\pi$
$74$	−3.85283	+	1.81403i	−0.447883	+	0.210877i
$75$	3.02794	−	0.811334i	0.349636	−	0.0936847i
$76$	−0.617873	−	0.868628i	−0.0708749	−	0.0996384i
$77$	12.9150	+	5.46021i	1.47180	+	0.622248i
$78$	14.0507	−	11.8790i	1.59093	−	1.34504i
$79$	−6.53028	+	11.3108i	−0.734714	+	1.27256i	0.220135	+	0.975469i	$0.429350\pi$
$79$	−6.53028	+	11.3108i	−0.734714	+	1.27256i	−0.954849	+	0.297092i	$0.903983\pi$
$80$	4.35946	−	6.42683i	0.487402	−	0.718541i
$81$	−3.64893	−	6.32013i	−0.405437	−	0.702237i
$82$	−0.740020	−	4.10771i	−0.0817215	−	0.453620i
$83$	10.1551	−	10.1551i	1.11467	−	1.11467i	0.122161	−	0.992510i	$-0.461018\pi$
$83$	10.1551	−	10.1551i	1.11467	−	1.11467i	0.992510	−	0.122161i	$-0.0389824\pi$
$84$	−0.586173	+	13.4655i	−0.0639567	+	1.46921i
$85$	−0.809460	−	0.809460i	−0.0877983	−	0.0877983i
$86$	−12.6038	−	8.75575i	−1.35910	−	0.944157i
$87$	−8.39101	+	4.84455i	−0.899611	+	0.519391i
$88$	4.04056	+	14.4351i	0.430726	+	1.53879i
$89$	−3.35262	−	1.93564i	−0.355377	−	0.205177i	0.311674	−	0.950189i	$-0.399110\pi$
$89$	−3.35262	−	1.93564i	−0.355377	−	0.205177i	−0.667051	+	0.745012i	$0.732444\pi$
$90$	9.54343	+	0.799284i	1.00597	+	0.0842519i
$91$	8.14836	+	10.7810i	0.854180	+	1.13015i
$92$	0.860868	+	0.145218i	0.0897517	+	0.0151400i
$93$	−5.19647	−	19.3935i	−0.538849	−	2.01101i
$94$	1.93199	−	5.36999i	0.199269	−	0.553872i
$95$	−0.517385	−	0.896137i	−0.0530826	−	0.0919418i
$96$	−11.6478	+	8.48206i	−1.18880	+	0.865697i
$97$	−12.0556			−1.22406			−0.612029	−	0.790836i	$-0.709646\pi$
$97$	−12.0556			−1.22406			−0.612029	+	0.790836i	$0.709646\pi$
$98$	−9.85186	−	0.969932i	−0.995189	−	0.0979779i
$99$	−13.0712	+	13.0712i	−1.31371	+	1.31371i
$100$	−1.56811	+	1.89721i	−0.156811	+	0.189721i
$101$	−0.694969	+	2.59366i	−0.0691520	+	0.258079i	−0.991844	−	0.127460i	$-0.959318\pi$
$101$	−0.694969	+	2.59366i	−0.0691520	+	0.258079i	0.922692	+	0.385539i	$0.125984\pi$
$102$	0.904765	+	1.92163i	0.0895851	+	0.190270i
$103$	0.0773103	+	0.0446351i	0.00761761	+	0.00439803i	0.503804	−	0.863818i	$-0.331933\pi$
$103$	0.0773103	+	0.0446351i	0.00761761	+	0.00439803i	−0.496186	+	0.868216i	$0.665267\pi$
$104$	−3.58363	+	13.9954i	−0.351404	+	1.37236i
$105$	−1.80229	+	12.9591i	−0.175886	+	1.26468i
$106$	0.111443	−	1.33063i	0.0108243	−	0.129242i
$107$	14.0802	−	3.77279i	1.36119	−	0.364729i	0.496935	−	0.867788i	$-0.334459\pi$
$107$	14.0802	−	3.77279i	1.36119	−	0.364729i	0.864252	+	0.503059i	$0.167792\pi$
$108$	−2.26083	−	1.03389i	−0.217548	−	0.0994863i
$109$	−6.68404	−	1.79098i	−0.640215	−	0.171545i	−0.0759141	−	0.997114i	$-0.524187\pi$
$109$	−6.68404	−	1.79098i	−0.640215	−	0.171545i	−0.564301	+	0.825569i	$0.690854\pi$
$110$	2.57994	+	14.3208i	0.245988	+	1.36543i
$111$	7.67008			0.728012
$112$	−5.75345	−	8.88244i	−0.543650	−	0.839312i
$113$	7.51142			0.706615			0.353307	−	0.935507i	$-0.385057\pi$
$113$	7.51142			0.706615			0.353307	+	0.935507i	$0.385057\pi$
$114$	0.340402	+	1.88950i	0.0318815	+	0.176968i
$115$	0.818604	+	0.219344i	0.0763353	+	0.0204540i
$116$	3.16395	−	6.91866i	0.293766	−	0.642381i
$117$	−17.2088	+	4.61109i	−1.59095	+	0.426295i
$118$	0.00343568	−	0.0410219i	0.000316280	−	0.00377638i
$119$	−1.44558	+	0.586470i	−0.132516	+	0.0537616i
$120$	−12.0347	+	7.12797i	−1.09861	+	0.650691i
$121$	−14.7981	−	8.54370i	−1.34528	−	0.776700i
$122$	1.23360	+	2.62004i	0.111684	+	0.237207i
$123$	−1.94568	+	7.26138i	−0.175436	+	0.654737i
$124$	12.1513	+	10.0435i	1.09122	+	0.901934i
$125$	−8.55366	+	8.55366i	−0.765063	+	0.765063i
$126$	6.06764	−	11.5546i	0.540548	−	1.02937i
$127$	4.25202			0.377306			0.188653	−	0.982044i	$-0.439588\pi$
$127$	4.25202			0.377306			0.188653	+	0.982044i	$0.439588\pi$
$128$	3.59221	−	10.7283i	0.317509	−	0.948255i
$129$	13.8204	+	23.9377i	1.21682	+	2.10760i
$130$	−4.74763	+	13.1961i	−0.416395	+	1.15737i
$131$	1.31046	+	4.89071i	0.114496	+	0.427304i	0.999249	−	0.0387565i	$-0.0123397\pi$
$131$	1.31046	+	4.89071i	0.114496	+	0.427304i	−0.884753	+	0.466060i	$0.845673\pi$
$132$	4.49089	−	26.6225i	0.390882	−	2.31719i
$133$	−1.39938	+	0.173865i	−0.121342	+	0.0150760i
$134$	−9.11572	−	0.763463i	−0.787479	−	0.0659531i
$135$	−2.08995	−	1.20663i	−0.179874	−	0.103850i
$136$	−1.45348	−	0.817740i	−0.124635	−	0.0701206i
$137$	0.241507	−	0.139434i	0.0206333	−	0.0119127i	−0.489648	−	0.871920i	$-0.662875\pi$
$137$	0.241507	−	0.139434i	0.0206333	−	0.0119127i	0.510281	+	0.860008i	$0.329541\pi$
$138$	−1.29139	−	0.897121i	−0.109930	−	0.0763681i
$139$	−12.1095	−	12.1095i	−1.02712	−	1.02712i	−0.999622	−	0.0274943i	$-0.991247\pi$
$139$	−12.1095	−	12.1095i	−1.02712	−	1.02712i	−0.0274943	−	0.999622i	$-0.508753\pi$
$140$	−4.74486	−	9.11192i	−0.401014	−	0.770098i
$141$	−7.26825	+	7.26825i	−0.612097	+	0.612097i
$142$	0.515595	+	2.86197i	0.0432678	+	0.240171i
$143$	−13.5349	−	23.4432i	−1.13185	−	1.96042i
$144$	13.7026	−	2.62632i	1.14188	−	0.218860i
$145$	3.69258	−	6.39573i	0.306652	−	0.531136i
$146$	8.55052	−	7.22896i	0.707646	−	0.598273i
$147$	15.3097	+	9.13919i	1.26272	+	0.753788i
$148$	−4.90756	+	3.49085i	−0.403399	+	0.286946i
$149$	21.1901	−	5.67786i	1.73596	−	0.465149i	0.754417	−	0.656396i	$-0.227920\pi$
$149$	21.1901	−	5.67786i	1.73596	−	0.465149i	0.981542	+	0.191247i	$0.0612532\pi$
$150$	4.01088	−	1.88845i	0.327487	−	0.154191i
$151$	8.08773	−	4.66946i	0.658170	−	0.379995i	−0.133409	−	0.991061i	$-0.542592\pi$
$151$	8.08773	−	4.66946i	0.658170	−	0.379995i	0.791580	+	0.611066i	$0.209259\pi$
$152$	−1.07776	−	1.05404i	−0.0874179	−	0.0854937i
$153$		−	2.05663i		−	0.166269i
$154$	19.3443	+	4.36125i	1.55881	+	0.351439i
$155$	10.8211	+	10.8211i	0.869174	+	0.869174i
$156$	16.5773	−	20.0564i	1.32725	−	1.60580i
$157$	−11.2775	−	3.02179i	−0.900040	−	0.241165i	−0.221007	−	0.975272i	$-0.570934\pi$
$157$	−11.2775	−	3.02179i	−0.900040	−	0.241165i	−0.679034	+	0.734107i	$0.737601\pi$
$158$	−6.25283	+	17.3798i	−0.497449	+	1.38266i
$159$	−1.20250	+	2.08279i	−0.0953643	+	0.165176i
$160$	4.45607	−	10.0380i	0.352283	−	0.793574i
$161$	0.709725	−	0.911103i	0.0559341	−	0.0718050i
$162$	−6.66332	−	7.88148i	−0.523520	−	0.619228i
$163$	3.82793	+	14.2860i	0.299826	+	1.11897i	0.937308	+	0.348502i	$0.113310\pi$
$163$	3.82793	+	14.2860i	0.299826	+	1.11897i	−0.637482	+	0.770466i	$0.720024\pi$
$164$	−2.05993	−	5.53159i	−0.160854	−	0.431944i
$165$	6.78326	−	25.3155i	0.528076	−	1.97081i
$166$	11.5877	−	16.6803i	0.899380	−	1.29464i
$167$			0.426814i			0.0330279i	0.999864	+	0.0165139i	$0.00525679\pi$
$167$			0.426814i			0.0330279i	−0.999864	+	0.0165139i	$0.994743\pi$
$168$	2.56050	+	18.8884i	0.197547	+	1.45727i
$169$		−	13.0892i		−	1.00686i
$170$	−1.32958	−	0.923649i	−0.101974	−	0.0708407i
$171$	0.481156	−	1.79570i	0.0367949	−	0.137320i
$172$	−19.7374	−	9.02606i	−1.50496	−	0.688231i
$173$	1.08986	+	4.06740i	0.0828603	+	0.309239i	0.994900	−	0.100862i	$-0.0321601\pi$
$173$	1.08986	+	4.06740i	0.0828603	+	0.309239i	−0.912040	+	0.410101i	$0.865493\pi$
$174$	−10.4640	+	8.84665i	−0.793271	+	0.670663i
$175$	1.22409	+	3.01724i	0.0925327	+	0.228082i
$176$	9.24315	+	19.0778i	0.696729	+	1.43804i
$177$	−0.0370719	+	0.0642104i	−0.00278649	+	0.00482635i
$178$	−5.15155	−	1.85340i	−0.386125	−	0.138918i
$179$	−13.5720	−	3.63660i	−1.01442	−	0.271812i	−0.286943	−	0.957948i	$-0.592639\pi$
$179$	−13.5720	−	3.63660i	−1.01442	−	0.271812i	−0.727474	+	0.686135i	$0.759306\pi$
$180$	13.4830	−	1.28047i	1.00497	−	0.0954404i
$181$	10.0681	+	10.0681i	0.748356	+	0.748356i	0.974170	−	0.225814i	$-0.0725042\pi$
$181$	10.0681	+	10.0681i	0.748356	+	0.748356i	−0.225814	+	0.974170i	$0.572504\pi$
$182$	14.0442	+	12.9619i	1.04102	+	0.960800i
$183$		−	5.21587i		−	0.385568i
$184$	1.23457	−	0.0137383i	0.0910141	−	0.00101280i
$185$	−5.06298	+	2.92311i	−0.372238	+	0.214911i
$186$	−12.0952	−	25.6890i	−0.886863	−	1.88361i
$187$	3.01842	−	0.808782i	0.220728	−	0.0591440i
$188$	1.34249	−	7.95842i	0.0979110	−	0.580427i
$189$	−2.62362	+	1.98296i	−0.190840	+	0.144239i
$190$	−0.944798	−	1.11752i	−0.0685429	−	0.0810736i
$191$	−4.82250	+	8.35282i	−0.348944	+	0.604389i	−0.986062	−	0.166377i	$-0.946793\pi$
$191$	−4.82250	+	8.35282i	−0.348944	+	0.604389i	0.637118	+	0.770766i	$0.280126\pi$
$192$	−14.0847	+	14.7260i	−1.01647	+	1.06275i
$193$	9.77970	+	16.9389i	0.703959	+	1.21929i	0.967066	+	0.254525i	$0.0819193\pi$
$193$	9.77970	+	16.9389i	0.703959	+	1.21929i	−0.263108	+	0.964767i	$0.584747\pi$
$194$	−16.7790	+	3.02281i	−1.20466	+	0.217025i
$195$	17.8609	−	17.8609i	1.27904	−	1.27904i
$196$	−13.9551	+	1.12030i	−0.996793	+	0.0800211i
$197$	−8.33252	−	8.33252i	−0.593668	−	0.593668i	0.344953	−	0.938620i	$-0.387895\pi$
$197$	−8.33252	−	8.33252i	−0.593668	−	0.593668i	−0.938620	+	0.344953i	$0.887895\pi$
$198$	−14.9152	+	21.4702i	−1.05998	+	1.52582i
$199$	−2.34374	+	1.35316i	−0.166144	+	0.0959230i	−0.580766	−	0.814070i	$-0.697247\pi$
$199$	−2.34374	+	1.35316i	−0.166144	+	0.0959230i	0.414623	+	0.909993i	$0.363914\pi$
$200$	−1.70680	+	3.03374i	−0.120689	+	0.214518i
$201$	14.2686	+	8.23795i	1.00643	+	0.581060i
$202$	−0.316930	+	3.78413i	−0.0222991	+	0.266251i
$203$	−6.06831	−	8.02888i	−0.425912	−	0.563517i
$204$	1.74109	+	2.44769i	0.121901	+	0.171372i
$205$	−1.48302	−	5.53471i	−0.103579	−	0.386561i
$206$	0.118793	+	0.0427388i	0.00827669	+	0.00297775i
$207$	0.761282	+	1.31858i	0.0529128	+	0.0916476i
$208$	−1.47852	+	20.3775i	−0.102517	+	1.41292i
$209$	2.82468			0.195387
$210$	0.740924	+	18.4885i	0.0511286	+	1.27583i
$211$	11.9853	−	11.9853i	0.825100	−	0.825100i	−0.161734	−	0.986834i	$-0.551709\pi$
$211$	11.9853	−	11.9853i	0.825100	−	0.825100i	0.986834	+	0.161734i	$0.0517087\pi$
$212$	−0.178534	−	1.87992i	−0.0122617	−	0.129113i
$213$	1.35562	−	5.05923i	0.0928854	−	0.346653i
$214$	18.6510	−	8.78147i	1.27496	−	0.600289i
$215$	−18.2456	−	10.5341i	−1.24434	−	0.718420i
$216$	−3.40587	−	0.872100i	−0.231740	−	0.0593389i
$217$	19.3250	−	7.84013i	1.31186	−	0.532223i
$218$	−9.75197	−	0.816750i	−0.660487	−	0.0553173i
$219$	−19.4796	+	5.21954i	−1.31631	+	0.352704i
$220$	7.18157	+	19.2849i	0.484181	+	1.30019i
$221$	2.90907	+	0.779483i	0.195685	+	0.0524337i
$222$	10.6753	−	1.92319i	0.716478	−	0.129076i
$223$	2.50874			0.167998			0.0839988	−	0.996466i	$-0.473231\pi$
$223$	2.50874			0.167998			0.0839988	+	0.996466i	$0.473231\pi$
$224$	−10.2349	−	10.9200i	−0.683847	−	0.729626i
$225$	−4.29264			−0.286176
$226$	10.4545	−	1.88341i	0.695420	−	0.125283i
$227$	−18.3064	−	4.90519i	−1.21504	−	0.325569i	−0.406303	−	0.913739i	$-0.633182\pi$
$227$	−18.3064	−	4.90519i	−1.21504	−	0.325569i	−0.808738	+	0.588170i	$0.799849\pi$
$228$	0.947547	+	2.54447i	0.0627529	+	0.168512i
$229$	25.1003	−	6.72559i	1.65867	−	0.444440i	0.696650	−	0.717412i	$-0.254673\pi$
$229$	25.1003	−	6.72559i	1.65867	−	0.444440i	0.962022	+	0.272972i	$0.0880066\pi$
$230$	1.19434	+	0.100029i	0.0787524	+	0.00659569i
$231$	−28.1760	−	21.9483i	−1.85385	−	1.44410i
$232$	2.66883	−	10.4228i	0.175217	−	0.684289i
$233$	12.2405	+	7.06704i	0.801900	+	0.462977i	0.844135	−	0.536130i	$-0.180114\pi$
$233$	12.2405	+	7.06704i	0.801900	+	0.462977i	−0.0422348	+	0.999108i	$0.513448\pi$
$234$	−22.7952	+	10.7327i	−1.49017	+	0.701617i
$235$	2.02776	−	7.56771i	0.132277	−	0.493663i
$236$	−0.00550402	−	0.0579561i	−0.000358281	−	0.00377262i
$237$	23.5235	−	23.5235i	1.52802	−	1.52802i
$238$	−1.86492	+	1.17872i	−0.120885	+	0.0764049i
$239$	−2.15987			−0.139710			−0.0698550	−	0.997557i	$-0.522254\pi$
$239$	−2.15987			−0.139710			−0.0698550	+	0.997557i	$0.522254\pi$
$240$	−14.9628	+	12.9383i	−0.965842	+	0.835166i
$241$	4.85611	+	8.41103i	0.312809	+	0.541802i	0.978969	−	0.204007i	$-0.0653966\pi$
$241$	4.85611	+	8.41103i	0.312809	+	0.541802i	−0.666160	+	0.745809i	$0.732063\pi$
$242$	−22.7384	−	8.18072i	−1.46168	−	0.525876i
$243$	5.77627	+	21.5573i	0.370548	+	1.38290i
$244$	2.37388	+	3.33728i	0.151972	+	0.213647i
$245$	−13.5889	−	0.198113i	−0.868160	−	0.0126570i
$246$	−0.887298	+	10.5943i	−0.0565720	+	0.675468i
$247$	2.35762	+	1.36117i	0.150012	+	0.0866094i
$248$	19.4306	+	10.9318i	1.23385	+	0.694171i
$249$	−31.6801	+	18.2905i	−2.00765	+	1.15912i
$250$	−9.76031	+	14.0498i	−0.617296	+	0.888587i
$251$	−10.1748	−	10.1748i	−0.642228	−	0.642228i	0.308875	−	0.951103i	$-0.400048\pi$
$251$	−10.1748	−	10.1748i	−0.642228	−	0.642228i	−0.951103	+	0.308875i	$0.900048\pi$
$252$	5.54778	−	17.6032i	0.349477	−	1.10890i
$253$	−1.63584	+	1.63584i	−0.102844	+	0.102844i
$254$	5.91800	−	1.06615i	0.371328	−	0.0668962i
$255$	1.45793	+	2.52520i	0.0912990	+	0.158134i
$256$	2.30965	−	15.8324i	0.144353	−	0.989526i
$257$	−13.2555	+	22.9591i	−0.826853	+	1.43215i	0.0736418	+	0.997285i	$0.476538\pi$
$257$	−13.2555	+	22.9591i	−0.826853	+	1.43215i	−0.900495	+	0.434867i	$0.856795\pi$
$258$	25.2375	+	29.8514i	1.57122	+	1.85847i
$259$	0.982297	+	7.90619i	0.0610370	+	0.491267i
$260$	−3.29900	+	19.5569i	−0.204595	+	1.21286i
$261$	12.8159	−	3.43401i	0.793283	−	0.212560i
$262$	3.05021	+	6.47835i	0.188443	+	0.400234i
$263$	−17.9812	+	10.3814i	−1.10877	+	0.640146i	−0.938509	−	0.345254i	$-0.887793\pi$
$263$	−17.9812	+	10.3814i	−1.10877	+	0.640146i	−0.170256	+	0.985400i	$0.554460\pi$
$264$	−0.424861	−	38.1794i	−0.0261484	−	2.34978i
$265$		−	1.83312i		−	0.112607i
$266$	−1.90407	+	0.592866i	−0.116746	+	0.0363510i
$267$	6.97259	+	6.97259i	0.426716	+	0.426716i
$268$	−12.8788	+	1.22308i	−0.786696	+	0.0747116i
$269$	24.1792	+	6.47880i	1.47423	+	0.395019i	0.904380	−	0.426728i	$-0.140334\pi$
$269$	24.1792	+	6.47880i	1.47423	+	0.395019i	0.569852	+	0.821747i	$0.307000\pi$
$270$	−3.21136	−	1.15537i	−0.195437	−	0.0703134i
$271$	2.82072	−	4.88563i	0.171347	−	0.296781i	−0.767544	−	0.640996i	$-0.778522\pi$
$271$	2.82072	−	4.88563i	0.171347	−	0.296781i	0.938891	+	0.344215i	$0.111855\pi$
$272$	−2.22801	−	0.773691i	−0.135093	−	0.0469119i
$273$	−12.9405	−	31.8969i	−0.783198	−	1.93049i
$274$	0.301170	−	0.254621i	0.0181943	−	0.0153822i
$275$	−1.68811	−	6.30010i	−0.101797	−	0.379910i
$276$	−2.02231	−	0.924818i	−0.121729	−	0.0556675i
$277$	−4.95063	+	18.4760i	−0.297455	+	1.11012i	0.641793	+	0.766878i	$0.278191\pi$
$277$	−4.95063	+	18.4760i	−0.297455	+	1.11012i	−0.939248	+	0.343239i	$0.888476\pi$
$278$	−19.8905	−	13.8178i	−1.19295	−	0.828736i
$279$			27.4937i			1.64600i
$280$	−8.88866	−	11.4923i	−0.531199	−	0.686797i
$281$			20.6400i			1.23128i	0.788029	+	0.615639i	$0.211102\pi$
$281$			20.6400i			1.23128i	−0.788029	+	0.615639i	$0.788898\pi$
$282$	−8.29357	+	11.9384i	−0.493875	+	0.710924i
$283$	6.14544	−	22.9351i	0.365309	−	1.36335i	−0.501693	−	0.865046i	$-0.667289\pi$
$283$	6.14544	−	22.9351i	0.365309	−	1.36335i	0.867002	−	0.498305i	$-0.166044\pi$
$284$	1.43522	+	3.85403i	0.0851646	+	0.228695i
$285$	0.682175	+	2.54591i	0.0404085	+	0.150807i
$286$	−24.7162	−	29.2347i	−1.46150	−	1.72868i
$287$	−7.73409	−	1.07562i	−0.456529	−	0.0634918i
$288$	18.4128	−	7.09112i	1.08499	−	0.417848i
$289$	8.32617	−	14.4213i	0.489775	−	0.848315i
$290$	3.53569	−	9.82750i	0.207623	−	0.577091i
$291$	29.6611	+	7.94766i	1.73876	+	0.465900i
$292$	10.0881	−	12.2053i	0.590361	−	0.714260i
$293$	20.5268	+	20.5268i	1.19919	+	1.19919i	0.974410	+	0.224778i	$0.0721656\pi$
$293$	20.5268	+	20.5268i	1.19919	+	1.19919i	0.224778	+	0.974410i	$0.427834\pi$
$294$	23.5997	+	8.88125i	1.37636	+	0.517965i
$295$		−	0.0565132i		−	0.00329033i
$296$	−5.95508	+	6.08911i	−0.346132	+	0.353922i
$297$	5.70506	−	3.29382i	0.331041	−	0.191127i
$298$	28.0689	−	13.2157i	1.62598	−	0.765564i
$299$	−2.15364	+	0.577067i	−0.124548	+	0.0333726i
$300$	5.10886	−	3.63404i	0.294960	−	0.209811i
$301$	−22.9046	+	17.3116i	−1.32020	+	0.997822i
$302$	10.0858	−	8.52690i	0.580370	−	0.490668i
$303$	3.41975	−	5.92318i	0.196460	−	0.340278i
$304$	−1.76432	−	1.19678i	−0.101191	−	0.0686401i
$305$	1.98780	+	3.44297i	0.113821	+	0.197144i
$306$	−0.515678	−	2.86243i	−0.0294794	−	0.163634i
$307$	−6.03127	+	6.03127i	−0.344223	+	0.344223i	−0.857952	−	0.513730i	$-0.828263\pi$
$307$	−6.03127	+	6.03127i	−0.344223	+	0.344223i	0.513730	+	0.857952i	$0.328263\pi$
$308$	28.0171	+	1.21962i	1.59642	+	0.0694945i
$309$	−0.160786	−	0.160786i	−0.00914677	−	0.00914677i
$310$	17.7742	+	12.3477i	1.00951	+	0.701299i
$311$	13.8721	−	8.00907i	0.786616	−	0.454153i	−0.0521541	−	0.998639i	$-0.516609\pi$
$311$	13.8721	−	8.00907i	0.786616	−	0.454153i	0.838770	+	0.544486i	$0.183275\pi$
$312$	18.0435	−	32.0713i	1.02151	−	1.81568i
$313$	−15.3757	−	8.87715i	−0.869085	−	0.501766i	−0.00204070	−	0.999998i	$-0.500650\pi$
$313$	−15.3757	−	8.87715i	−0.869085	−	0.501766i	−0.867044	+	0.498232i	$0.833983\pi$
$314$	−16.4538	−	1.37804i	−0.928539	−	0.0777673i
$315$	6.97687	−	16.5024i	0.393102	−	0.929805i
$316$	−4.34493	+	25.7572i	−0.244421	+	1.44896i
$317$	−4.02311	−	15.0144i	−0.225960	−	0.843295i	−0.982018	−	0.188790i	$-0.939544\pi$
$317$	−4.02311	−	15.0144i	−0.225960	−	0.843295i	0.756057	−	0.654505i	$-0.227123\pi$
$318$	−1.15141	+	3.20036i	−0.0645678	+	0.179467i
$319$	10.0799	+	17.4588i	0.564364	+	0.977506i
$320$	3.68507	−	15.0883i	0.206002	−	0.843461i
$321$	−37.1297			−2.07238
$322$	0.759351	−	1.44604i	0.0423170	−	0.0805845i
$323$	−0.222217	+	0.222217i	−0.0123645	+	0.0123645i
$324$	−11.2503	−	9.29875i	−0.625015	−	0.516597i
$325$	1.62695	−	6.07187i	0.0902471	−	0.336807i
$326$	8.90981	+	18.9236i	0.493469	+	1.04808i
$327$	15.2645	+	8.81294i	0.844126	+	0.487356i
$328$	−4.25402	−	7.18240i	−0.234889	−	0.396582i
$329$	−8.42282	−	6.56115i	−0.464365	−	0.361728i
$330$	3.09340	−	36.9351i	0.170286	−	2.03321i
$331$	−14.6818	+	3.93399i	−0.806987	+	0.216232i	−0.638649	−	0.769498i	$-0.720507\pi$
$331$	−14.6818	+	3.93399i	−0.806987	+	0.216232i	−0.168338	+	0.985729i	$0.553840\pi$
$332$	11.9454	−	26.1213i	0.655592	−	1.43359i
$333$	−10.1453	−	2.71842i	−0.555959	−	0.148969i
$334$	0.107019	+	0.594043i	0.00585583	+	0.0325046i
$335$	−12.5581			−0.686124
$336$	8.29980	+	25.6470i	0.452791	+	1.39916i
$337$	18.9202			1.03065			0.515325	−	0.856995i	$-0.327671\pi$
$337$	18.9202			1.03065			0.515325	+	0.856995i	$0.327671\pi$
$338$	−3.28199	−	18.2177i	−0.178517	−	0.990913i
$339$	−18.4808	−	4.95192i	−1.00374	−	0.268951i
$340$	−2.08211	−	0.952165i	−0.112918	−	0.0516384i
$341$	−40.3512	+	10.8121i	−2.18514	+	0.585506i
$342$	0.219423	−	2.61991i	0.0118651	−	0.141669i
$343$	−7.45983	+	16.9514i	−0.402793	+	0.915291i
$344$	−29.7339	−	7.61359i	−1.60314	−	0.410497i
$345$	−1.86946	−	1.07933i	−0.100648	−	0.0581094i
$346$	2.53673	+	5.38777i	0.136376	+	0.289648i
$347$	−1.58787	+	5.92600i	−0.0852412	+	0.318125i	−0.995360	−	0.0962234i	$-0.969324\pi$
$347$	−1.58787	+	5.92600i	−0.0852412	+	0.318125i	0.910119	+	0.414348i	$0.135990\pi$
$348$	−12.3456	+	14.9366i	−0.661794	+	0.800684i
$349$	−2.94202	+	2.94202i	−0.157483	+	0.157483i	−0.781450	−	0.623968i	$-0.785520\pi$
$349$	−2.94202	+	2.94202i	−0.157483	+	0.157483i	0.623968	+	0.781450i	$0.285520\pi$
$350$	2.46025	+	3.89249i	0.131506	+	0.208062i
$351$	6.34899			0.338884
$352$	17.6483	+	24.2350i	0.940655	+	1.29173i
$353$	−13.0287	−	22.5663i	−0.693446	−	1.20108i	−0.970702	−	0.240288i	$-0.922758\pi$
$353$	−13.0287	−	22.5663i	−0.693446	−	1.20108i	0.277256	−	0.960796i	$-0.410575\pi$
$354$	−0.0354968	+	0.0986639i	−0.00188664	+	0.00524393i
$355$	1.03327	+	3.85621i	0.0548402	+	0.204666i
$356$	−7.63469	−	1.28788i	−0.404638	−	0.0682574i
$357$	3.94328	−	0.489929i	0.208700	−	0.0259298i
$358$	−19.8014	−	1.65842i	−1.04654	−	0.0876500i
$359$	25.7055	+	14.8411i	1.35668	+	0.783282i	0.989175	−	0.146739i	$-0.0468776\pi$
$359$	25.7055	+	14.8411i	1.35668	+	0.783282i	0.367508	+	0.930020i	$0.380211\pi$
$360$	18.4447	−	5.16290i	0.972123	−	0.272109i
$361$	16.2085	−	9.35796i	0.853077	−	0.492524i
$362$	16.5373	+	11.4884i	0.869184	+	0.603817i
$363$	30.7763	+	30.7763i	1.61534	+	1.61534i
$364$	22.7968	+	14.5190i	1.19488	+	0.761005i
$365$	10.8692	−	10.8692i	0.568919	−	0.568919i
$366$	−1.30783	−	7.25949i	−0.0683612	−	0.379460i
$367$	2.21998	+	3.84511i	0.115882	+	0.200713i	0.918132	−	0.396275i	$-0.129697\pi$
$367$	2.21998	+	3.84511i	0.115882	+	0.200713i	−0.802250	+	0.596988i	$0.796364\pi$
$368$	1.71485	−	0.328678i	0.0893925	−	0.0171335i
$369$	5.14714	−	8.91512i	0.267950	−	0.464102i
$370$	−6.31375	+	5.33790i	−0.328236	+	0.277504i
$371$	−2.30090	−	0.972775i	−0.119457	−	0.0505039i
$372$	−23.2755	−	32.7215i	−1.20678	−	1.69653i
$373$	−17.6779	+	4.73679i	−0.915328	+	0.245261i	−0.685587	−	0.727990i	$-0.740455\pi$
$373$	−17.6779	+	4.73679i	−0.915328	+	0.245261i	−0.229741	+	0.973252i	$0.573788\pi$
$374$	3.99826	−	1.88251i	0.206745	−	0.0973421i
$375$	26.6841	−	15.4061i	1.37796	−	0.795567i
$376$	−0.127006	−	11.4132i	−0.00654984	−	0.588591i
$377$			19.4294i			1.00066i
$378$	−3.15436	+	3.41774i	−0.162243	+	0.175790i
$379$	1.71717	+	1.71717i	0.0882050	+	0.0882050i	0.749833	−	0.661628i	$-0.230134\pi$
$379$	1.71717	+	1.71717i	0.0882050	+	0.0882050i	−0.661628	+	0.749833i	$0.730134\pi$
$380$	−1.59519	−	1.31848i	−0.0818313	−	0.0676365i
$381$	−10.4615	−	2.80315i	−0.535960	−	0.143610i
$382$	−4.61761	+	12.8347i	−0.236258	+	0.656681i
$383$	5.88728	−	10.1971i	0.300826	−	0.521046i	−0.675497	−	0.737363i	$-0.736071\pi$
$383$	5.88728	−	10.1971i	0.300826	−	0.521046i	0.976323	+	0.216316i	$0.0694043\pi$
$384$	−15.9108	+	24.0273i	−0.811943	+	1.22614i
$385$	26.9635	+	3.74995i	1.37419	+	0.191115i
$386$	17.8587	+	21.1236i	0.908986	+	1.07516i
$387$	−9.79646	−	36.5609i	−0.497982	−	1.85849i
$388$	−22.5953	+	8.41434i	−1.14710	+	0.427173i
$389$	4.04561	−	15.0984i	0.205120	−	0.765520i	−0.784292	−	0.620391i	$-0.786974\pi$
$389$	4.04561	−	15.0984i	0.205120	−	0.765520i	0.989413	−	0.145128i	$-0.0463595\pi$
$390$	20.3804	−	29.3373i	1.03200	−	1.48555i
$391$		−	0.257382i		−	0.0130164i
$392$	−19.1419	+	5.05834i	−0.966813	+	0.255485i
$393$		−	12.8969i		−	0.650560i
$394$	−13.6866	−	9.50797i	−0.689519	−	0.479005i
$395$	−6.56280	+	24.4927i	−0.330210	+	1.23236i
$396$	−15.3757	+	33.6222i	−0.772656	+	1.68958i
$397$	−0.836855	−	3.12318i	−0.0420005	−	0.156748i	0.941741	−	0.336340i	$-0.109189\pi$
$397$	−0.836855	−	3.12318i	−0.0420005	−	0.156748i	−0.983741	+	0.179592i	$0.942522\pi$
$398$	−2.92275	+	2.47101i	−0.146504	+	0.123861i
$399$	3.55760	+	0.494774i	0.178103	+	0.0247697i
$400$	−1.61486	+	4.65034i	−0.0807432	+	0.232517i
$401$	−2.37385	+	4.11163i	−0.118544	+	0.205325i	−0.919191	−	0.393812i	$-0.871156\pi$
$401$	−2.37385	+	4.11163i	−0.118544	+	0.205325i	0.800647	+	0.599137i	$0.204489\pi$
$402$	21.9247	+	7.88796i	1.09350	+	0.393415i
$403$	−38.8894	−	10.4204i	−1.93722	−	0.519076i
$404$	0.507727	+	5.34625i	0.0252604	+	0.265986i
$405$	−10.0187	−	10.0187i	−0.497834	−	0.497834i
$406$	−10.4591	−	9.65309i	−0.519076	−	0.479075i
$407$		−	15.9588i		−	0.791048i
$408$	3.03700	+	2.97015i	0.150354	+	0.147044i
$409$	−2.68361	+	1.54938i	−0.132696	+	0.0766121i	−0.564879	−	0.825174i	$-0.691077\pi$
$409$	−2.68361	+	1.54938i	−0.132696	+	0.0766121i	0.432182	+	0.901786i	$0.357744\pi$
$410$	−3.45185	−	7.33140i	−0.170475	−	0.362072i
$411$	−0.686118	+	0.183845i	−0.0338437	+	0.00906839i
$412$	0.176053	+	0.0296980i	0.00867352	+	0.00146312i
$413$	−0.0709347	−	0.0299897i	−0.00349047	−	0.00147570i
$414$	1.39018	+	1.64433i	0.0683236	+	0.0808142i
$415$	13.9413	−	24.1470i	0.684349	−	1.18533i
$416$	3.05163	+	28.7323i	0.149618	+	1.40872i
$417$	21.8106	+	37.7770i	1.06807	+	1.84995i
$418$	3.93141	−	0.708259i	0.192291	−	0.0346421i
$419$	2.62329	−	2.62329i	0.128156	−	0.128156i	−0.640119	−	0.768276i	$-0.721115\pi$
$419$	2.62329	−	2.62329i	0.128156	−	0.128156i	0.768276	+	0.640119i	$0.221115\pi$
$420$	5.66703	+	25.5467i	0.276523	+	1.24655i
$421$	−3.44059	−	3.44059i	−0.167684	−	0.167684i	0.618276	−	0.785961i	$-0.287831\pi$
$421$	−3.44059	−	3.44059i	−0.167684	−	0.167684i	−0.785961	+	0.618276i	$0.787831\pi$
$422$	13.6760	−	19.6864i	0.665738	−	0.958318i
$423$	12.1898	−	7.03778i	0.592688	−	0.342189i
$424$	−0.719855	−	2.57172i	−0.0349593	−	0.124894i
$425$	0.628432	+	0.362825i	0.0304834	+	0.0175996i
$426$	0.618208	−	7.38139i	0.0299523	−	0.357629i
$427$	5.37643	−	0.667990i	0.260184	−	0.0323263i
$428$	23.7567	−	16.8987i	1.14832	−	0.816828i
$429$	17.8459	+	66.6018i	0.861608	+	3.21556i
$430$	−28.0357	−	10.0866i	−1.35200	−	0.486417i
$431$	11.3945	+	19.7358i	0.548853	+	0.950642i	0.998353	+	0.0573616i	$0.0182688\pi$
$431$	11.3945	+	19.7358i	0.548853	+	0.950642i	−0.449500	+	0.893280i	$0.648398\pi$
$432$	−4.95899	−	0.359808i	−0.238590	−	0.0173113i
$433$	−16.6448			−0.799899			−0.399950	−	0.916537i	$-0.630972\pi$
$433$	−16.6448			−0.799899			−0.399950	+	0.916537i	$0.630972\pi$
$434$	24.9308	−	15.7575i	1.19672	−	0.756384i
$435$	−13.3015	+	13.3015i	−0.637757	+	0.637757i
$436$	−13.7777	+	1.30845i	−0.659830	+	0.0626633i
$437$	0.0602155	−	0.224727i	0.00288050	−	0.0107502i
$438$	−25.8031	+	12.1489i	−1.23292	+	0.580497i
$439$	−26.7406	−	15.4387i	−1.27626	−	0.736847i	−0.300099	−	0.953908i	$-0.597020\pi$
$439$	−26.7406	−	15.4387i	−1.27626	−	0.736847i	−0.976158	+	0.217061i	$0.930353\pi$
$440$	14.8309	+	25.0401i	0.707033	+	1.19374i
$441$	−17.0112	−	17.5146i	−0.810057	−	0.834026i
$442$	4.24431	+	0.355471i	0.201881	+	0.0169080i
$443$	−13.7414	+	3.68200i	−0.652874	+	0.174937i	−0.570028	−	0.821625i	$-0.693068\pi$
$443$	−13.7414	+	3.68200i	−0.652874	+	0.174937i	−0.0828461	+	0.996562i	$0.526401\pi$
$444$	14.3757	−	5.35343i	0.682241	−	0.254063i
$445$	−7.25987	−	1.94528i	−0.344151	−	0.0922149i
$446$	3.49168	−	0.629041i	0.165336	−	0.0297860i
$447$	−55.8784			−2.64296
$448$	−16.9831	−	12.6323i	−0.802375	−	0.596820i
$449$	14.7633			0.696725			0.348363	−	0.937360i	$-0.386738\pi$
$449$	14.7633			0.696725			0.348363	+	0.937360i	$0.386738\pi$
$450$	−5.97453	+	1.07633i	−0.281642	+	0.0507389i
$451$	15.1084	+	4.04830i	0.711429	+	0.190627i
$452$	14.0783	−	5.24269i	0.662189	−	0.246596i
$453$	−22.9771	+	6.15670i	−1.07956	+	0.289267i
$454$	−26.7090	−	2.23694i	−1.25351	−	0.104985i
$455$	20.6981	+	16.1232i	0.970341	+	0.755869i
$456$	1.95680	+	3.30383i	0.0916358	+	0.154716i
$457$	−1.80328	−	1.04112i	−0.0843539	−	0.0487017i	0.457230	−	0.889349i	$-0.348842\pi$
$457$	−1.80328	−	1.04112i	−0.0843539	−	0.0487017i	−0.541584	+	0.840647i	$0.682175\pi$
$458$	33.2484	−	15.6544i	1.55359	−	0.731481i
$459$	−0.189692	+	0.707941i	−0.00885407	+	0.0330439i
$460$	1.68737	−	0.160248i	0.0786741	−	0.00747158i
$461$	10.5211	−	10.5211i	0.490015	−	0.490015i	−0.418296	−	0.908311i	$-0.637372\pi$
$461$	10.5211	−	10.5211i	0.490015	−	0.490015i	0.908311	+	0.418296i	$0.137372\pi$
$462$	−44.7189	−	23.4830i	−2.08051	−	1.09253i
$463$	26.5483			1.23380			0.616902	−	0.787040i	$-0.288387\pi$
$463$	26.5483			1.23380			0.616902	+	0.787040i	$0.288387\pi$
$464$	1.10110	−	15.1757i	0.0511171	−	0.704513i
$465$	−19.4901	−	33.7578i	−0.903830	−	1.56548i
$466$	18.8084	+	6.76679i	0.871282	+	0.313466i
$467$	2.50402	+	9.34512i	0.115872	+	0.432440i	0.999351	−	0.0360311i	$-0.0114715\pi$
$467$	2.50402	+	9.34512i	0.115872	+	0.432440i	−0.883479	+	0.468472i	$0.844805\pi$
$468$	−29.0354	+	20.6535i	−1.34216	+	0.954708i
$469$	−6.66419	+	15.7628i	−0.307724	+	0.727859i
$470$	0.924729	−	11.0412i	0.0426546	−	0.509294i
$471$	25.7546	+	14.8694i	1.18671	+	0.685146i
$472$	−0.0221925	−	0.0792837i	−0.00102149	−	0.00364933i
$473$	49.8062	−	28.7556i	2.29009	−	1.32218i
$474$	26.8419	−	38.6385i	1.23289	−	1.77472i
$475$	0.463816	+	0.463816i	0.0212813	+	0.0212813i
$476$	−2.30005	+	2.10816i	−0.105423	+	0.0966273i
$477$	2.32874	−	2.32874i	0.106626	−	0.106626i
$478$	−3.00612	+	0.541564i	−0.137497	+	0.0247706i
$479$	1.94642	+	3.37130i	0.0889342	+	0.154039i	0.907061	−	0.420999i	$-0.138321\pi$
$479$	1.94642	+	3.37130i	0.0889342	+	0.154039i	−0.818127	+	0.575038i	$0.804987\pi$
$480$	−17.5811	+	21.7594i	−0.802465	+	0.993178i
$481$	7.69033	−	13.3200i	0.350649	−	0.607342i
$482$	8.86775	+	10.4889i	0.403915	+	0.477757i
$483$	−2.34683	+	1.77376i	−0.106784	+	0.0807087i
$484$	−33.6987	−	5.68456i	−1.53176	−	0.258389i
$485$	−22.6080	+	6.05780i	−1.02658	+	0.275070i
$486$	13.4447	+	28.5553i	0.609866	+	1.29530i
$487$	−2.49944	+	1.44305i	−0.113260	+	0.0653909i	−0.555560	−	0.831476i	$-0.687496\pi$
$487$	−2.49944	+	1.44305i	−0.113260	+	0.0653909i	0.442300	+	0.896867i	$0.354163\pi$
$488$	4.14077	+	4.04962i	0.187444	+	0.183318i
$489$		−	37.6724i		−	1.70360i
$490$	−18.9628	+	3.13153i	−0.856650	+	0.141468i
$491$	10.1200	+	10.1200i	0.456710	+	0.456710i	0.897574	−	0.440864i	$-0.145328\pi$
$491$	10.1200	+	10.1200i	0.456710	+	0.456710i	−0.440864	+	0.897574i	$0.645328\pi$
$492$	1.42147	+	14.9677i	0.0640847	+	0.674797i
$493$	−2.16647	−	0.580503i	−0.0975727	−	0.0261445i
$494$	3.62266	+	1.30334i	0.162991	+	0.0586402i
$495$	−17.9446	+	31.0809i	−0.806549	+	1.39698i
$496$	29.7847	+	10.3430i	1.33737	+	0.464413i
$497$	5.38858	+	0.749418i	0.241711	+	0.0336160i
$498$	−39.5065	+	33.4004i	−1.77033	+	1.49671i
$499$	−4.96424	−	18.5268i	−0.222230	−	0.829373i	−0.983495	−	0.180933i	$-0.942088\pi$
$499$	−4.96424	−	18.5268i	−0.222230	−	0.829373i	0.761265	−	0.648440i	$-0.224578\pi$
$500$	−10.0616	+	22.0019i	−0.449970	+	0.983956i
$501$	0.281378	−	1.05012i	0.0125710	−	0.0469158i
$502$	−16.7126	−	11.6101i	−0.745920	−	0.518186i
$503$		−	25.3179i		−	1.12887i	−0.825477	−	0.564436i	$-0.809094\pi$
$503$		−	25.3179i		−	1.12887i	0.825477	−	0.564436i	$-0.190906\pi$
$504$	3.30761	−	25.8914i	0.147333	−	1.15329i
$505$			5.21315i			0.231982i
$506$	−1.86660	+	2.68694i	−0.0829806	+	0.119449i
$507$	−8.62911	+	32.2043i	−0.383232	+	1.43024i
$508$	7.96939	−	2.96775i	0.353584	−	0.131673i
$509$	−0.572369	−	2.13611i	−0.0253698	−	0.0946814i	0.952080	−	0.305849i	$-0.0989402\pi$
$509$	−0.572369	−	2.13611i	−0.0253698	−	0.0946814i	−0.977450	+	0.211167i	$0.932274\pi$
$510$	2.66232	+	3.14904i	0.117890	+	0.139442i
$511$	−7.87494	−	19.4108i	−0.348367	−	0.858682i
$512$	−0.755222	−	22.6148i	−0.0333764	−	0.999443i
$513$	−0.331251	+	0.573743i	−0.0146251	+	0.0253314i
$514$	−12.6923	+	35.2784i	−0.559833	+	1.55606i
$515$	0.167410	+	0.0448574i	0.00737697	+	0.00197665i
$516$	42.6108	+	35.2193i	1.87583	+	1.55044i
$517$	15.1227	+	15.1227i	0.665097	+	0.665097i
$518$	3.34956	+	10.7576i	0.147171	+	0.472662i
$519$		−	10.7258i		−	0.470809i
$520$	0.312102	+	28.0466i	0.0136866	+	1.22992i
$521$	−8.90915	+	5.14370i	−0.390317	+	0.225349i	−0.682297	−	0.731075i	$-0.739019\pi$
$521$	−8.90915	+	5.14370i	−0.390317	+	0.225349i	0.291981	+	0.956424i	$0.405686\pi$
$522$	16.9762	−	7.99293i	0.743028	−	0.349841i
$523$	−6.30777	+	1.69016i	−0.275819	+	0.0739056i	−0.394077	−	0.919077i	$-0.628936\pi$
$523$	−6.30777	+	1.69016i	−0.275819	+	0.0739056i	0.118258	+	0.992983i	$0.462269\pi$
$524$	5.86969	+	8.25181i	0.256418	+	0.360482i
$525$	−1.02259	−	8.23049i	−0.0446295	−	0.359208i
$526$	−22.4233	+	18.9575i	−0.977701	+	0.826588i
$527$	2.32384	−	4.02501i	0.101228	−	0.175332i
$528$	−10.1644	−	53.0319i	−0.442350	−	2.30792i
$529$	−11.4047	−	19.7536i	−0.495858	−	0.858851i
$530$	−0.459635	−	2.55135i	−0.0199653	−	0.110823i
$531$	0.0717927	−	0.0717927i	0.00311554	−	0.00311554i
$532$	−2.50145	+	1.30258i	−0.108452	+	0.0564741i
$533$	10.6595	+	10.6595i	0.461713	+	0.461713i
$534$	11.4528	+	7.95621i	0.495612	+	0.344299i
$535$	24.5091	−	14.1503i	1.05962	−	0.611773i
$536$	−17.6181	+	4.93151i	−0.760986	+	0.213009i
$537$	30.9946	+	17.8947i	1.33751	+	0.772214i
$538$	35.2773	+	2.95456i	1.52091	+	0.127380i
$539$	19.0155	−	31.8542i	0.819056	−	1.37206i
$540$	−4.75929	−	0.802834i	−0.204807	−	0.0345485i
$541$	−1.75097	−	6.53469i	−0.0752799	−	0.280948i	0.918017	−	0.396542i	$-0.129790\pi$
$541$	−1.75097	−	6.53469i	−0.0752799	−	0.280948i	−0.993297	+	0.115593i	$0.963123\pi$
$542$	2.70088	−	7.50713i	0.116013	−	0.322459i
$543$	−18.1338	−	31.4086i	−0.778195	−	1.34787i
$544$	−3.29495	−	0.518180i	−0.141270	−	0.0222168i
$545$	−13.4346			−0.575477
$546$	−26.0086	−	41.1496i	−1.11306	−	1.76104i
$547$	−1.78581	+	1.78581i	−0.0763555	+	0.0763555i	−0.744253	−	0.667898i	$-0.767194\pi$
$547$	−1.78581	+	1.78581i	−0.0763555	+	0.0763555i	0.667898	+	0.744253i	$0.267194\pi$
$548$	0.355327	−	0.429899i	0.0151788	−	0.0183644i
$549$	−1.84860	+	6.89909i	−0.0788965	+	0.294446i
$550$	−3.92921	−	8.34526i	−0.167542	−	0.355843i
$551$	−1.75579	−	1.01370i	−0.0747991	−	0.0431853i
$552$	−3.04656	−	0.780095i	−0.129670	−	0.0332030i
$553$	27.2603	+	21.2350i	1.15922	+	0.903004i
$554$	−2.25766	+	26.9564i	−0.0959188	+	1.14527i
$555$	14.3838	−	3.85414i	0.610560	−	0.163599i
$556$	−31.1484	−	14.2444i	−1.32099	−	0.604096i
$557$	3.36982	+	0.902940i	0.142784	+	0.0382588i	0.329503	−	0.944155i	$-0.393119\pi$
$557$	3.36982	+	0.902940i	0.142784	+	0.0382588i	−0.186719	+	0.982413i	$0.559785\pi$
$558$	6.89376	+	38.2659i	0.291836	+	1.61993i
$559$	55.4278			2.34435
$560$	−15.2529	−	13.7664i	−0.644552	−	0.581735i
$561$	−7.95959			−0.336054
$562$	5.17526	+	28.7269i	0.218305	+	1.21177i
$563$	38.4688	+	10.3077i	1.62127	+	0.434417i	0.951373	−	0.308041i	$-0.0996734\pi$
$563$	38.4688	+	10.3077i	1.62127	+	0.434417i	0.669893	+	0.742458i	$0.266340\pi$
$564$	−8.54961	+	18.6956i	−0.360004	+	0.787225i
$565$	14.0863	−	3.77441i	0.592615	−	0.158791i
$566$	2.80253	−	33.4622i	0.117799	−	1.40652i
$567$	−17.8920	+	7.25876i	−0.751391	+	0.304839i
$568$	2.96391	+	5.00420i	0.124363	+	0.209972i
$569$	−39.1325	−	22.5931i	−1.64052	−	0.947153i	−0.980649	−	0.195772i	$-0.937279\pi$
$569$	−39.1325	−	22.5931i	−1.64052	−	0.947153i	−0.659868	−	0.751381i	$-0.729388\pi$
$570$	1.58782	+	3.37237i	0.0665063	+	0.141253i
$571$	6.44226	−	24.0429i	0.269600	−	1.00616i	−0.689774	−	0.724025i	$-0.742290\pi$
$571$	6.44226	−	24.0429i	0.269600	−	1.00616i	0.959374	−	0.282137i	$-0.0910433\pi$
$572$	−41.7305	−	34.4918i	−1.74484	−	1.44217i
$573$	17.3717	−	17.3717i	0.725714	−	0.725714i
$574$	−11.0341	+	0.442188i	−0.460553	+	0.0184566i
$575$	−0.537214			−0.0224034
$576$	23.8491	−	14.4863i	0.993713	−	0.603596i
$577$	−5.46579	−	9.46703i	−0.227544	−	0.394118i	0.729536	−	0.683943i	$-0.239736\pi$
$577$	−5.46579	−	9.46703i	−0.227544	−	0.394118i	−0.957080	+	0.289825i	$0.906403\pi$
$578$	7.97242	−	22.1594i	0.331609	−	0.921712i
$579$	−12.8946	−	48.1232i	−0.535881	−	1.99993i
$580$	2.45686	−	14.5645i	0.102016	−	0.604760i
$581$	−22.9108	−	30.3129i	−0.950500	−	1.25759i
$582$	43.2753	+	3.62441i	1.79382	+	0.150236i
$583$	4.33357	+	2.50199i	0.179478	+	0.103622i
$584$	10.9804	−	19.5169i	0.454370	−	0.807615i
$585$	−29.9550	+	17.2945i	−1.23848	+	0.715040i
$586$	33.7162	+	23.4225i	1.39280	+	0.967573i
$587$	−7.44744	−	7.44744i	−0.307389	−	0.307389i	0.536507	−	0.843896i	$-0.319744\pi$
$587$	−7.44744	−	7.44744i	−0.307389	−	0.307389i	−0.843896	+	0.536507i	$0.819744\pi$
$588$	35.0732	+	6.44360i	1.44639	+	0.265730i
$589$	2.97067	−	2.97067i	0.122404	−	0.122404i
$590$	−0.0141701	−	0.0786556i	−0.000583374	−	0.00323820i
$591$	15.0078	+	25.9943i	0.617338	+	1.06926i
$592$	−6.76155	+	9.96805i	−0.277898	+	0.409684i
$593$	12.6447	−	21.9013i	0.519256	−	0.899377i	−0.480494	−	0.876998i	$-0.659543\pi$
$593$	12.6447	−	21.9013i	0.519256	−	0.899377i	0.999750	−	0.0223792i	$-0.00712412\pi$
$594$	7.11446	−	6.01485i	0.291910	−	0.246792i
$595$	−2.41622	+	1.82621i	−0.0990555	+	0.0748672i
$596$	35.7528	−	25.4317i	1.46449	−	1.04172i
$597$	6.65853	−	1.78415i	0.272516	−	0.0730203i
$598$	−2.85276	+	1.34317i	−0.116658	+	0.0549263i
$599$	15.4613	−	8.92656i	0.631730	−	0.364729i	−0.149692	−	0.988733i	$-0.547828\pi$
$599$	15.4613	−	8.92656i	0.631730	−	0.364729i	0.781422	+	0.624003i	$0.214495\pi$
$600$	6.19935	−	6.33888i	0.253088	−	0.258784i
$601$			15.3921i			0.627855i	0.949447	+	0.313928i	$0.101645\pi$
$601$			15.3921i			0.627855i	−0.949447	+	0.313928i	$0.898355\pi$
$602$	−27.5381	+	29.8375i	−1.12237	+	1.21608i
$603$	−15.9535	−	15.9535i	−0.649676	−	0.649676i
$604$	11.8994	−	14.3967i	0.484180	−	0.585794i
$605$	−32.0443	−	8.58625i	−1.30279	−	0.349081i
$606$	3.27446	−	9.10140i	0.133016	−	0.369719i
$607$	−15.1434	+	26.2292i	−0.614652	+	1.06461i	0.375793	+	0.926704i	$0.377370\pi$
$607$	−15.1434	+	26.2292i	−0.614652	+	1.06461i	−0.990445	+	0.137905i	$0.955963\pi$
$608$	−2.75568	−	1.22330i	−0.111758	−	0.0496115i
$609$	9.63719	+	23.7545i	0.390519	+	0.962581i
$610$	3.62992	+	4.29353i	0.146971	+	0.173840i
$611$	5.33478	+	19.9097i	0.215822	+	0.805459i
$612$	−1.43545	−	3.85465i	−0.0580247	−	0.155815i
$613$	3.95872	−	14.7741i	0.159891	−	0.596722i	−0.838746	−	0.544523i	$-0.816711\pi$
$613$	3.95872	−	14.7741i	0.159891	−	0.596722i	0.998637	−	0.0521982i	$-0.0166228\pi$
$614$	−6.88209	+	9.90664i	−0.277738	+	0.399800i
$615$			14.5951i			0.588531i
$616$	39.3003	−	5.32753i	1.58345	−	0.214652i
$617$			39.3266i			1.58323i	0.611020	+	0.791615i	$0.290759\pi$
$617$			39.3266i			1.58323i	−0.611020	+	0.791615i	$0.709241\pi$
$618$	−0.264098	−	0.183467i	−0.0106236	−	0.00738014i
$619$	−1.39109	+	5.19162i	−0.0559127	+	0.208669i	−0.988231	−	0.152970i	$-0.951116\pi$
$619$	−1.39109	+	5.19162i	−0.0559127	+	0.208669i	0.932318	+	0.361639i	$0.117783\pi$
$620$	27.8344	+	12.7289i	1.11785	+	0.511203i
$621$	−0.140433	−	0.524103i	−0.00563538	−	0.0210315i
$622$	17.2991	−	14.6254i	0.693632	−	0.586424i
$623$	−6.29426	+	8.08020i	−0.252174	+	0.323726i
$624$	17.0716	−	49.1613i	0.683411	−	1.96803i
$625$	−8.66598	+	15.0099i	−0.346639	+	0.600397i
$626$	−23.6258	−	8.50000i	−0.944279	−	0.339728i
$627$	−6.94973	−	1.86217i	−0.277545	−	0.0743681i
$628$	−23.2460	+	2.20764i	−0.927617	+	0.0880946i
$629$	1.25548	+	1.25548i	0.0500592	+	0.0500592i
$630$	5.57265	−	24.7175i	0.222020	−	0.984770i
$631$			7.48252i			0.297875i	0.988847	+	0.148937i	$0.0475853\pi$
$631$			7.48252i			0.297875i	−0.988847	+	0.148937i	$0.952415\pi$
$632$	0.411052	+	36.9385i	0.0163508	+	1.46934i
$633$	−37.3894	+	21.5868i	−1.48610	+	0.857998i
$634$	−9.36411	−	19.8885i	−0.371896	−	0.789872i
$635$	7.97389	−	2.13660i	0.316434	−	0.0847883i
$636$	−0.800084	+	4.74298i	−0.0317254	+	0.188072i
$637$	31.2215	−	17.4239i	1.23704	−	0.690360i
$638$	18.4068	+	21.7719i	0.728734	+	0.861958i
$639$	−3.58618	+	6.21144i	−0.141867	+	0.245721i
$640$	1.34567	−	21.9240i	0.0531925	−	0.866622i
$641$	−4.73385	−	8.19927i	−0.186976	−	0.323852i	0.757265	−	0.653108i	$-0.226535\pi$
$641$	−4.73385	−	8.19927i	−0.186976	−	0.323852i	−0.944241	+	0.329256i	$0.893202\pi$
$642$	−51.6774	+	9.30989i	−2.03954	+	0.367432i
$643$	−20.6140	+	20.6140i	−0.812939	+	0.812939i	−0.985073	−	0.172135i	$-0.944934\pi$
$643$	−20.6140	+	20.6140i	−0.812939	+	0.812939i	0.172135	+	0.985073i	$0.444934\pi$
$644$	0.694292	−	2.20301i	0.0273589	−	0.0868106i
$645$	37.9462	+	37.9462i	1.49413	+	1.49413i
$646$	−0.253565	+	0.365002i	−0.00997638	+	0.0143608i
$647$	−30.2216	+	17.4485i	−1.18813	+	0.685970i	−0.957882	−	0.287161i	$-0.907288\pi$
$647$	−30.2216	+	17.4485i	−1.18813	+	0.685970i	−0.230252	+	0.973131i	$0.573955\pi$
$648$	−17.9898	−	10.1212i	−0.706705	−	0.397598i
$649$	0.133600	+	0.0771338i	0.00524425	+	0.00302777i
$650$	0.741946	−	8.85882i	0.0291015	−	0.347471i
$651$	−52.7151	+	6.54954i	−2.06607	+	0.256697i
$652$	17.1456	+	24.1040i	0.671475	+	0.943984i
$653$	10.3267	+	38.5399i	0.404117	+	1.50818i	0.805679	+	0.592353i	$0.201801\pi$
$653$	10.3267	+	38.5399i	0.404117	+	1.50818i	−0.401562	+	0.915832i	$0.631533\pi$
$654$	23.4549	+	8.43851i	0.917161	+	0.329972i
$655$	4.91507	+	8.51315i	0.192048	+	0.332636i
$656$	−7.72169	−	8.92987i	−0.301481	−	0.348653i
$657$	27.6157			1.07739
$658$	−13.3681	−	7.01993i	−0.521143	−	0.273665i
$659$	−6.66795	+	6.66795i	−0.259746	+	0.259746i	−0.824951	−	0.565205i	$-0.808797\pi$
$659$	−6.66795	+	6.66795i	−0.259746	+	0.259746i	0.565205	+	0.824951i	$0.308797\pi$
$660$	−4.95568	−	52.1822i	−0.192900	−	2.03119i
$661$	0.649564	−	2.42421i	0.0252651	−	0.0942907i	−0.952142	−	0.305656i	$-0.901124\pi$
$661$	0.649564	−	2.42421i	0.0252651	−	0.0942907i	0.977407	+	0.211365i	$0.0677909\pi$
$662$	−19.4479	+	9.15668i	−0.755864	+	0.355885i
$663$	−6.64349	−	3.83562i	−0.258012	−	0.148963i
$664$	10.0761	−	39.3510i	0.391030	−	1.52711i
$665$	−2.53692	+	1.02923i	−0.0983774	+	0.0399117i
$666$	−14.8019	−	1.23969i	−0.573563	−	0.0480372i
$667$	1.60388	−	0.429758i	0.0621024	−	0.0166403i
$668$	0.297901	+	0.799960i	0.0115261	+	0.0309514i
$669$	−6.17241	−	1.65389i	−0.238639	−	0.0639432i
$670$	−17.4785	+	3.14882i	−0.675254	+	0.121650i
$671$	−10.8524			−0.418954
$672$	17.9825	+	33.6146i	0.693688	+	1.29671i
$673$	−36.8448			−1.42026			−0.710131	−	0.704070i	$-0.751364\pi$
$673$	−36.8448			−1.42026			−0.710131	+	0.704070i	$0.751364\pi$
$674$	26.3333	−	4.74405i	1.01432	−	0.182734i
$675$	1.47763	+	0.395930i	0.0568740	+	0.0152393i
$676$	−9.13581	−	24.5326i	−0.351377	−	0.943563i
$677$	16.8935	−	4.52660i	0.649270	−	0.173971i	0.0808713	−	0.996725i	$-0.474230\pi$
$677$	16.8935	−	4.52660i	0.649270	−	0.173971i	0.568399	+	0.822753i	$0.307563\pi$
$678$	−26.9634	−	2.25824i	−1.03552	−	0.0867274i
$679$	−4.39366	+	31.5920i	−0.168613	+	1.21239i
$680$	−3.13665	−	0.803162i	−0.120285	−	0.0307999i
$681$	41.8067	+	24.1371i	1.60204	+	0.924936i
$682$	−53.4501	+	25.1660i	−2.04671	+	0.963655i
$683$	−8.60472	+	32.1132i	−0.329250	+	1.22878i	0.580719	+	0.814104i	$0.302771\pi$
$683$	−8.60472	+	32.1132i	−0.329250	+	1.22878i	−0.909970	+	0.414675i	$0.863895\pi$
$684$	−0.351520	−	3.70143i	−0.0134407	−	0.141528i
$685$	0.382838	−	0.382838i	0.0146275	−	0.0146275i
$686$	−6.13225	+	25.4636i	−0.234130	+	0.972205i
$687$	−66.1896			−2.52529
$688$	−43.2929	−	3.14119i	−1.65053	−	0.119757i
$689$	2.41135	+	4.17658i	0.0918650	+	0.159115i
$690$	−2.87256	−	1.03348i	−0.109357	−	0.0393438i
$691$	3.84416	+	14.3466i	0.146239	+	0.545771i	0.999697	+	0.0246098i	$0.00783432\pi$
$691$	3.84416	+	14.3466i	0.146239	+	0.545771i	−0.853458	+	0.521161i	$0.825499\pi$
$692$	4.88157	+	6.86269i	0.185570	+	0.260880i
$693$	29.4898	+	39.0174i	1.12022	+	1.48215i
$694$	−0.724122	+	8.64600i	−0.0274873	+	0.328198i
$695$	−28.7941	−	16.6243i	−1.09222	−	0.630595i
$696$	−13.4375	+	23.8844i	−0.509348	+	0.905335i
$697$	−1.50706	+	0.870101i	−0.0570839	+	0.0329574i
$698$	−3.35705	+	4.83241i	−0.127066	+	0.182909i
$699$	−25.4571	−	25.4571i	−0.962874	−	0.962874i
$700$	4.40019	+	4.80072i	0.166312	+	0.181450i
$701$	−21.3787	+	21.3787i	−0.807464	+	0.807464i	−0.984249	−	0.176785i	$-0.943430\pi$
$701$	−21.3787	+	21.3787i	−0.807464	+	0.807464i	0.176785	+	0.984249i	$0.443430\pi$
$702$	8.83657	−	1.59194i	0.333515	−	0.0600840i
$703$	0.802467	+	1.38991i	0.0302656	+	0.0524216i
$704$	30.6397	+	29.3054i	1.15478	+	1.10449i
$705$	−9.97805	+	17.2825i	−0.375795	+	0.650897i
$706$	−23.7917	−	28.1412i	−0.895412	−	1.05911i
$707$	6.54348	+	2.76645i	0.246093	+	0.104043i
$708$	−0.0246658	+	0.146222i	−0.000926998	+	0.00549535i
$709$	−13.3395	+	3.57430i	−0.500974	+	0.134236i	−0.500452	−	0.865764i	$-0.666833\pi$
$709$	−13.3395	+	3.57430i	−0.500974	+	0.134236i	−0.000522056		1.00000i	$0.500166\pi$
$710$	2.40501	+	5.10802i	0.0902586	+	0.191701i
$711$	−39.4520	+	22.7776i	−1.47956	+	0.854227i
$712$	−10.9489	+	0.121840i	−0.410329	+	0.00456614i
$713$			3.44077i			0.128858i
$714$	5.36544	−	1.67062i	0.200797	−	0.0625215i
$715$	−37.1623	−	37.1623i	−1.38979	−	1.38979i
$716$	−27.9756	+	2.65681i	−1.04550	+	0.0992897i
$717$	5.31405	+	1.42390i	0.198457	+	0.0531764i
$718$	39.4983	+	14.2105i	1.47407	+	0.530332i
$719$	22.1881	−	38.4309i	0.827477	−	1.43323i	−0.0725344	−	0.997366i	$-0.523109\pi$
$719$	22.1881	−	38.4309i	0.827477	−	1.43323i	0.900011	−	0.435866i	$-0.143558\pi$
$720$	24.3770	−	11.8106i	0.908476	−	0.440155i
$721$	0.145143	−	0.186327i	0.00540542	−	0.00693917i
$722$	20.2127	−	17.0886i	0.752238	−	0.635972i
$723$	−6.40280	−	23.8956i	−0.238123	−	0.888686i
$724$	25.8974	+	11.8431i	0.962470	+	0.440144i
$725$	−1.21164	+	4.52189i	−0.0449991	+	0.167939i
$726$	50.5516	+	35.1179i	1.87614	+	1.30335i
$727$			1.44539i			0.0536067i	0.999641	+	0.0268033i	$0.00853279\pi$
$727$			1.44539i			0.0536067i	−0.999641	+	0.0268033i	$0.991467\pi$
$728$	35.3693	+	14.4916i	1.31087	+	0.537096i
$729$		−	34.9533i		−	1.29457i
$730$	12.4025	−	17.8531i	0.459036	−	0.660774i
$731$	−1.65605	+	6.18045i	−0.0612511	+	0.228592i
$732$	−3.64049	−	9.77590i	−0.134556	−	0.361327i
$733$	10.5622	+	39.4186i	0.390123	+	1.45596i	0.829930	+	0.557868i	$0.188380\pi$
$733$	10.5622	+	39.4186i	0.390123	+	1.45596i	−0.439807	+	0.898093i	$0.644953\pi$
$734$	4.05390	+	4.79502i	0.149632	+	0.176987i
$735$	33.3029	+	9.44591i	1.22840	+	0.348418i
$736$	2.30432	−	0.887437i	0.0849385	−	0.0327114i
$737$	17.1404	−	29.6880i	0.631373	−	1.09357i
$738$	4.92846	−	13.6987i	0.181419	−	0.504257i
$739$	−10.9326	−	2.92937i	−0.402161	−	0.107759i	0.0520685	−	0.998644i	$-0.483419\pi$
$739$	−10.9326	−	2.92937i	−0.402161	−	0.107759i	−0.454229	+	0.890885i	$0.650085\pi$
$740$	−7.44911	+	9.01244i	−0.273835	+	0.331304i
$741$	−4.90325	−	4.90325i	−0.180125	−	0.180125i
$742$	−3.44633	−	0.776987i	−0.126519	−	0.0285241i
$743$			9.66874i			0.354712i	0.984147	+	0.177356i	$0.0567544\pi$
$743$			9.66874i			0.354712i	−0.984147	+	0.177356i	$0.943246\pi$
$744$	−40.5996	−	39.7059i	−1.48845	−	1.45569i
$745$	36.8851	−	21.2956i	1.35136	−	0.780210i
$746$	−23.4166	+	11.0253i	−0.857342	+	0.403663i
$747$	48.3861	−	12.9650i	1.77036	−	0.474365i
$748$	5.09279	−	3.62261i	0.186211	−	0.132456i
$749$	−4.75515	−	38.2727i	−0.173749	−	1.39845i
$750$	33.2763	−	28.1331i	1.21508	−	1.02728i
$751$	25.8756	−	44.8178i	0.944213	−	1.63542i	0.186893	−	0.982380i	$-0.440158\pi$
$751$	25.8756	−	44.8178i	0.944213	−	1.63542i	0.757319	−	0.653045i	$-0.226509\pi$
$752$	−3.03851	−	15.8531i	−0.110803	−	0.578105i
$753$	18.3259	+	31.7415i	0.667834	+	1.15672i
$754$	4.87172	+	27.0420i	0.177418	+	0.984811i
$755$	12.8207	−	12.8207i	0.466594	−	0.466594i
$756$	−3.53330	+	5.54776i	−0.128505	+	0.201770i
$757$	−28.2783	−	28.2783i	−1.02779	−	1.02779i	−0.999603	−	0.0281911i	$-0.991025\pi$
$757$	−28.2783	−	28.2783i	−1.02779	−	1.02779i	−0.0281911	−	0.999603i	$-0.508975\pi$
$758$	2.82053	+	1.95941i	0.102446	+	0.0711688i
$759$	5.10318	−	2.94632i	0.185234	−	0.106945i
$760$	−2.55079	−	1.43509i	−0.0925267	−	0.0520563i
$761$	−4.94191	−	2.85321i	−0.179144	−	0.103429i	0.407746	−	0.913095i	$-0.366315\pi$
$761$	−4.94191	−	2.85321i	−0.179144	−	0.103429i	−0.586891	+	0.809666i	$0.699648\pi$
$762$	−15.2633	−	1.27833i	−0.552930	−	0.0463092i
$763$	−7.12933	+	16.8630i	−0.258099	+	0.610482i
$764$	−3.20866	+	19.0213i	−0.116085	+	0.688166i
$765$	−1.03343	−	3.85683i	−0.0373639	−	0.139444i
$766$	5.63716	−	15.6685i	0.203679	−	0.566127i
$767$	0.0743395	+	0.128760i	0.00268425	+	0.00464925i
$768$	−16.1201	+	37.4308i	−0.581686	+	1.35067i
$769$	39.6503			1.42983			0.714914	−	0.699212i	$-0.246466\pi$
$769$	39.6503			1.42983			0.714914	+	0.699212i	$0.246466\pi$
$770$	38.4683	−	1.54161i	1.38630	−	0.0555557i
$771$	47.7491	−	47.7491i	1.71964	−	1.71964i
$772$	30.1525	+	24.9221i	1.08521	+	0.896966i
$773$	5.74604	−	21.4445i	0.206671	−	0.771305i	−0.782263	−	0.622948i	$-0.785935\pi$
$773$	5.74604	−	21.4445i	0.206671	−	0.771305i	0.988934	−	0.148357i	$-0.0473985\pi$
$774$	−22.8021	−	48.4294i	−0.819603	−	1.74076i
$775$	−8.40108	−	4.85037i	−0.301776	−	0.174230i
$776$	−29.3384	+	17.3767i	−1.05319	+	0.623786i
$777$	2.79536	−	20.0997i	0.100283	−	0.721072i
$778$	1.84494	−	22.0285i	0.0661442	−	0.789759i
$779$	−1.51942	+	0.407126i	−0.0544387	+	0.0145868i
$780$	21.0096	−	45.9421i	0.752266	−	1.64499i
$781$	−10.5265	−	2.82057i	−0.376669	−	0.100928i
$782$	−0.0645360	−	0.358227i	−0.00230780	−	0.0128102i
$783$	−4.72827			−0.168975
$784$	−25.3736	+	11.8399i	−0.906198	+	0.422853i
$785$	−22.6673			−0.809029
$786$	−3.23376	−	17.9499i	−0.115344	−	0.640253i
$787$	18.8470	+	5.05004i	0.671823	+	0.180014i	0.578576	−	0.815629i	$-0.303609\pi$
$787$	18.8470	+	5.05004i	0.671823	+	0.180014i	0.0932471	+	0.995643i	$0.470275\pi$
$788$	−21.4331	−	9.80151i	−0.763522	−	0.349164i
$789$	51.0841	−	13.6880i	1.81864	−	0.487304i
$790$	−2.99286	+	35.7347i	−0.106481	+	1.27138i
$791$	2.73754	−	19.6839i	0.0973357	−	0.699879i
$792$	−12.9695	+	50.6509i	−0.460853	+	1.79980i
$793$	−9.05801	−	5.22965i	−0.321659	−	0.185710i
$794$	−1.94785	−	4.13704i	−0.0691265	−	0.146818i
$795$	−1.20849	+	4.51013i	−0.0428606	+	0.159958i
$796$	−3.44833	+	4.17202i	−0.122223	+	0.147873i
$797$	−2.54421	+	2.54421i	−0.0901206	+	0.0901206i	−0.750730	−	0.660609i	$-0.770298\pi$
$797$	−2.54421	+	2.54421i	−0.0901206	+	0.0901206i	0.660609	+	0.750730i	$0.270298\pi$
$798$	5.07556	−	0.203402i	0.179673	−	0.00720036i
$799$	−2.37941			−0.0841774
$800$	−1.08156	+	6.87730i	−0.0382388	+	0.243149i
$801$	−6.75150	−	11.6939i	−0.238553	−	0.413185i
$802$	−2.27300	+	6.31782i	−0.0802623	+	0.223090i
$803$	10.8601	+	40.5303i	0.383244	+	1.43028i
$804$	32.4928	+	5.48113i	1.14593	+	0.193305i
$805$	0.873139	−	2.06524i	0.0307741	−	0.0727900i
$806$	−56.7394	−	4.75205i	−1.99856	−	0.167384i
$807$	−55.2185	−	31.8804i	−1.94378	−	1.12224i
$808$	2.04718	+	7.31365i	0.0720195	+	0.257293i
$809$	−19.3519	+	11.1728i	−0.680378	+	0.392816i	−0.799997	−	0.600004i	$-0.795166\pi$
$809$	−19.3519	+	11.1728i	−0.680378	+	0.392816i	0.119620	+	0.992820i	$0.461832\pi$
$810$	−16.4562	−	11.4320i	−0.578212	−	0.401681i
$811$	31.7484	+	31.7484i	1.11484	+	1.11484i	0.992487	+	0.122349i	$0.0390426\pi$
$811$	31.7484	+	31.7484i	1.11484	+	1.11484i	0.122349	+	0.992487i	$0.460957\pi$
$812$	−16.9774	−	10.8127i	−0.595792	−	0.379453i
$813$	−10.1609	+	10.1609i	−0.356357	+	0.356357i
$814$	−4.00151	−	22.2116i	−0.140253	−	0.778516i
$815$	14.3572	+	24.8673i	0.502909	+	0.871065i
$816$	4.97165	+	3.37238i	0.174043	+	0.118057i
$817$	−2.89188	+	5.00888i	−0.101174	+	0.175238i
$818$	−3.34658	+	2.82933i	−0.117010	+	0.0989253i
$819$	5.81173	+	46.7767i	0.203078	+	1.63451i
$820$	−6.64259	−	9.33839i	−0.231969	−	0.326111i
$821$	46.9829	−	12.5890i	1.63972	−	0.439361i	0.683008	−	0.730411i	$-0.260671\pi$
$821$	46.9829	−	12.5890i	1.63972	−	0.439361i	0.956708	+	0.291050i	$0.0940047\pi$
$822$	−0.908847	+	0.427913i	−0.0316997	+	0.0149252i
$823$	−16.7248	+	9.65608i	−0.582991	+	0.336590i	−0.762321	−	0.647199i	$-0.775940\pi$
$823$	−16.7248	+	9.65608i	−0.582991	+	0.336590i	0.179330	+	0.983789i	$0.442607\pi$
$824$	0.252479	−	0.00280958i	0.00879551	−	9.78765e-5i
$825$			16.6134i			0.578405i
$826$	−0.106247	−	0.0239538i	−0.00369681	−	0.000833458i
$827$	14.4794	+	14.4794i	0.503498	+	0.503498i	0.912523	−	0.409025i	$-0.134131\pi$
$827$	14.4794	+	14.4794i	0.503498	+	0.503498i	−0.409025	+	0.912523i	$0.634131\pi$
$828$	2.34716	+	1.94001i	0.0815694	+	0.0674201i
$829$	−1.38085	−	0.369998i	−0.0479589	−	0.0128505i	0.234760	−	0.972053i	$-0.424570\pi$
$829$	−1.38085	−	0.369998i	−0.0479589	−	0.0128505i	−0.282719	+	0.959203i	$0.591236\pi$
$830$	13.3489	−	37.1036i	0.463349	−	1.28788i
$831$	24.3607	−	42.1940i	0.845064	−	1.46369i
$832$	11.4516	+	39.2246i	0.397013	+	1.35987i
$833$	1.01002	+	4.00192i	0.0349952	+	0.138658i
$834$	39.8284	+	47.1096i	1.37914	+	1.63127i
$835$	0.214470	+	0.800412i	0.00742203	+	0.0276994i
$836$	5.29418	−	1.97152i	0.183103	−	0.0681865i
$837$	2.53587	−	9.46399i	0.0876524	−	0.327123i
$838$	2.99336	−	4.30888i	0.103404	−	0.148848i
$839$		−	41.9512i		−	1.44832i	−0.689634	−	0.724158i	$-0.742228\pi$
$839$		−	41.9512i		−	1.44832i	0.689634	−	0.724158i	$-0.257772\pi$
$840$	14.2930	+	34.1351i	0.493155	+	1.17777i
$841$			14.5304i			0.501048i
$842$	−5.65134	−	3.92595i	−0.194758	−	0.135297i
$843$	13.6069	−	50.7818i	0.468648	−	1.74902i
$844$	14.0982	−	30.8288i	0.485281	−	1.06117i
$845$	−6.57721	−	24.5465i	−0.226263	−	0.844425i
$846$	15.2012	−	12.8517i	0.522628	−	0.441851i
$847$	−27.7822	+	35.6652i	−0.954608	+	1.22547i
$848$	−1.64673	−	3.39885i	−0.0565491	−	0.116717i
$849$	−30.2400	+	52.3773i	−1.03784	+	1.79758i
$850$	0.965631	+	0.347410i	0.0331209	+	0.0119161i
$851$	−1.26966	−	0.340204i	−0.0435234	−	0.0116621i
$852$	−0.990381	−	10.4285i	−0.0339299	−	0.357274i
$853$	−34.5722	−	34.5722i	−1.18373	−	1.18373i	−0.978770	−	0.204960i	$-0.934294\pi$
$853$	−34.5722	−	34.5722i	−1.18373	−	1.18373i	−0.204960	−	0.978770i	$-0.565706\pi$
$854$	7.31547	−	2.27780i	0.250330	−	0.0779447i
$855$		−	3.60928i		−	0.123435i
$856$	28.8276	−	29.4764i	0.985308	−	1.00748i
$857$	−7.21992	+	4.16842i	−0.246628	+	0.142391i	−0.618219	−	0.786006i	$-0.712146\pi$
$857$	−7.21992	+	4.16842i	−0.246628	+	0.142391i	0.371591	+	0.928396i	$0.378812\pi$
$858$	41.5378	+	88.2222i	1.41808	+	3.01186i
$859$	12.6163	−	3.38053i	0.430463	−	0.115342i	−0.0370807	−	0.999312i	$-0.511806\pi$
$859$	12.6163	−	3.38053i	0.430463	−	0.115342i	0.467543	+	0.883970i	$0.345139\pi$
$860$	−41.5494	−	7.00888i	−1.41682	−	0.239001i
$861$	18.3196	+	7.74513i	0.624329	+	0.263953i
$862$	20.8075	+	24.6114i	0.708706	+	0.838269i
$863$	−24.7192	+	42.8148i	−0.841450	+	1.45743i	0.0472194	+	0.998885i	$0.484964\pi$
$863$	−24.7192	+	42.8148i	−0.841450	+	1.45743i	−0.888669	+	0.458549i	$0.848369\pi$
$864$	−6.99219	+	0.742633i	−0.237879	+	0.0252649i
$865$	4.08766	+	7.08003i	0.138985	+	0.240728i
$866$	−23.1664	+	4.17352i	−0.787226	+	0.141822i
$867$	−29.9927	+	29.9927i	−1.01861	+	1.01861i
$868$	30.7479	−	28.1826i	1.04365	−	0.956578i
$869$	−48.9443	−	48.9443i	−1.66032	−	1.66032i
$870$	−15.1779	+	21.8483i	−0.514579	+	0.740727i
$871$	28.6125	−	16.5194i	0.969497	−	0.559739i
$872$	−18.8478	+	5.27572i	−0.638266	+	0.178658i
$873$	−36.4162	−	21.0249i	−1.23250	−	0.711585i
$874$	0.0274603	−	0.327876i	0.000928860	−	0.0110906i
$875$	19.2977	+	25.5325i	0.652383	+	0.863156i
$876$	−32.8667	+	23.3788i	−1.11046	+	0.789897i
$877$	−13.9238	−	51.9644i	−0.470174	−	1.75471i	−0.639140	−	0.769091i	$-0.720709\pi$
$877$	−13.9238	−	51.9644i	−0.470174	−	1.75471i	0.168966	−	0.985622i	$-0.445957\pi$
$878$	−41.0888	−	14.7827i	−1.38668	−	0.498893i
$879$	−36.9710	−	64.0357i	−1.24700	−	2.15987i
$880$	26.9203	+	31.1324i	0.907481	+	1.04947i
$881$	26.2319			0.883776			0.441888	−	0.897070i	$-0.354309\pi$
$881$	26.2319			0.883776			0.441888	+	0.897070i	$0.354309\pi$
$882$	−28.0679	−	20.1115i	−0.945096	−	0.677190i
$883$	−12.8278	+	12.8278i	−0.431688	+	0.431688i	−0.889202	−	0.457514i	$-0.848740\pi$
$883$	−12.8278	+	12.8278i	−0.431688	+	0.431688i	0.457514	+	0.889202i	$0.348740\pi$
$884$	5.99640	−	0.569471i	0.201681	−	0.0191534i
$885$	−0.0372565	+	0.139043i	−0.00125236	+	0.00467388i
$886$	−18.2022	+	8.57015i	−0.611514	+	0.287920i
$887$	46.3646	+	26.7686i	1.55677	+	0.898801i	0.997563	+	0.0697733i	$0.0222276\pi$
$887$	46.3646	+	26.7686i	1.55677	+	0.898801i	0.559207	+	0.829028i	$0.311106\pi$
$888$	18.6659	−	11.0555i	0.626387	−	0.370999i
$889$	1.54965	−	11.1425i	0.0519736	−	0.373709i
$890$	−10.5921	−	0.887113i	−0.355048	−	0.0297361i
$891$	37.3590	−	10.0103i	1.25157	−	0.335358i
$892$	4.70203	−	1.75101i	0.157436	−	0.0586281i
$893$	−2.07752	−	0.556671i	−0.0695217	−	0.0186283i
$894$	−77.7720	+	14.0109i	−2.60109	+	0.468596i
$895$	−27.2791			−0.911841
$896$	−26.8046	−	13.3234i	−0.895479	−	0.445104i
$897$	5.67918			0.189622
$898$	20.5477	−	3.70176i	0.685687	−	0.123529i
$899$	28.9620	+	7.76035i	0.965937	+	0.258822i
$900$	−8.04551	+	2.99610i	−0.268184	+	0.0998701i
$901$	−0.537752	+	0.144090i	−0.0179151	+	0.00480034i
$902$	22.0431	+	1.84616i	0.733956	+	0.0614705i
$903$	67.7664	−	27.4928i	2.25512	−	0.914903i
$904$	18.2798	−	10.8268i	0.607977	−	0.360095i
$905$	23.9400	+	13.8218i	0.795793	+	0.459451i
$906$	−30.4360	+	14.3302i	−1.01117	+	0.476090i
$907$	9.73321	−	36.3248i	0.323186	−	1.20615i	−0.592937	−	0.805249i	$-0.702032\pi$
$907$	9.73321	−	36.3248i	0.323186	−	1.20615i	0.916123	−	0.400897i	$-0.131302\pi$
$908$	−37.7346	+	3.58361i	−1.25227	+	0.118926i
$909$	−6.62263	+	6.62263i	−0.219659	+	0.219659i
$910$	32.8505	+	17.2506i	1.08898	+	0.571853i
$911$	18.6202			0.616914			0.308457	−	0.951238i	$-0.400187\pi$
$911$	18.6202			0.616914			0.308457	+	0.951238i	$0.400187\pi$
$912$	3.55190	+	4.10765i	0.117615	+	0.136018i
$913$	38.0563	+	65.9155i	1.25948	+	2.18148i
$914$	−2.77087	−	0.996891i	−0.0916523	−	0.0329742i
$915$	−2.62092	−	9.78142i	−0.0866450	−	0.323364i
$916$	42.3502	−	30.1246i	1.39929	−	0.995344i
$917$	13.2939	−	1.65168i	0.439002	−	0.0545434i
$918$	−0.0865062	+	1.03288i	−0.00285513	+	0.0340902i
$919$	−15.5605	−	8.98389i	−0.513295	−	0.296351i	0.220892	−	0.975298i	$-0.429103\pi$
$919$	−15.5605	−	8.98389i	−0.513295	−	0.296351i	−0.734187	+	0.678947i	$0.762437\pi$
$920$	2.30832	−	0.646125i	0.0761029	−	0.0213021i
$921$	18.8152	−	10.8630i	0.619983	−	0.357947i
$922$	12.0053	−	17.2814i	0.395372	−	0.569132i
$923$	−7.42679	−	7.42679i	−0.244456	−	0.244456i
$924$	−68.1283	−	21.4711i	−2.24126	−	0.706347i
$925$	2.62046	−	2.62046i	0.0861602	−	0.0861602i
$926$	36.9501	−	6.65671i	1.21426	−	0.218753i
$927$	0.155687	+	0.269658i	0.00511344	+	0.00885674i
$928$	−2.27263	−	21.3977i	−0.0746028	−	0.702415i
$929$	−13.1258	+	22.7345i	−0.430642	+	0.745894i	−0.996929	−	0.0783141i	$-0.975046\pi$
$929$	−13.1258	+	22.7345i	−0.430642	+	0.745894i	0.566286	+	0.824209i	$0.308380\pi$
$930$	−35.5908	−	42.0974i	−1.16707	−	1.38043i
$931$	−0.0543870	+	3.73048i	−0.00178246	+	0.122262i
$932$	27.8744	+	4.70207i	0.913055	+	0.154021i
$933$	−39.4104	+	10.5600i	−1.29024	+	0.345719i
$934$	5.82830	+	12.3788i	0.190708	+	0.405045i
$935$	5.25408	−	3.03345i	0.171827	−	0.0992043i
$936$	−35.2330	+	36.0260i	−1.15163	+	1.17755i
$937$		−	47.7798i		−	1.56090i	−0.625219	−	0.780449i	$-0.714990\pi$
$937$		−	47.7798i		−	1.56090i	0.625219	−	0.780449i	$-0.285010\pi$
$938$	−5.32291	+	23.6098i	−0.173799	+	0.770887i
$939$	31.9775	+	31.9775i	1.04355	+	1.04355i
$940$	−1.48143	−	15.5991i	−0.0483190	−	0.508788i
$941$	−41.8248	−	11.2069i	−1.36345	−	0.365335i	−0.498368	−	0.866966i	$-0.666067\pi$
$941$	−41.8248	−	11.2069i	−1.36345	−	0.365335i	−0.865082	+	0.501630i	$0.832734\pi$
$942$	39.5737	+	14.2377i	1.28938	+	0.463888i
$943$	0.644154	−	1.11571i	0.0209765	−	0.0363324i
$944$	−0.0507672	−	0.104783i	−0.00165233	−	0.00341040i
$945$	−3.92370	+	5.03701i	−0.127638	+	0.163854i
$946$	62.1105	−	52.5107i	2.01939	−	1.70727i
$947$	4.82935	+	18.0234i	0.156933	+	0.585681i	0.998932	+	0.0462023i	$0.0147119\pi$
$947$	4.82935	+	18.0234i	0.156933	+	0.585681i	−0.841999	+	0.539478i	$0.818621\pi$
$948$	27.6706	−	60.5077i	0.898699	−	1.96520i
$949$	−10.4666	+	39.0620i	−0.339762	+	1.26801i
$950$	0.761840	+	0.529246i	0.0247174	+	0.0171710i
$951$			39.5932i			1.28390i
$952$	−2.67263	+	3.51087i	−0.0866206	+	0.113788i
$953$		−	33.1972i		−	1.07536i	−0.843148	−	0.537681i	$-0.819300\pi$
$953$		−	33.1972i		−	1.07536i	0.843148	−	0.537681i	$-0.180700\pi$
$954$	2.65725	−	3.82506i	0.0860316	−	0.123841i
$955$	−4.84652	+	18.0875i	−0.156830	+	0.585296i
$956$	−4.04815	+	1.50751i	−0.130926	+	0.0487562i
$957$	−13.2903	−	49.6002i	−0.429615	−	1.60335i
$958$	3.55436	+	4.20416i	0.114836	+	0.135830i
$959$	−0.277374	−	0.683694i	−0.00895688	−	0.0220776i
$960$	−19.0136	+	34.6933i	−0.613661	+	1.11972i
$961$	−15.5659	+	26.9609i	−0.502124	+	0.869705i
$962$	7.36360	−	20.4672i	0.237412	−	0.659890i
$963$	49.1118	+	13.1595i	1.58261	+	0.424058i
$964$	14.9722	+	12.3751i	0.482222	+	0.398574i
$965$	26.8517	+	26.8517i	0.864387	+	0.864387i
$966$	−2.82158	+	3.05717i	−0.0907829	+	0.0983629i
$967$		−	13.2736i		−	0.426850i	−0.976959	−	0.213425i	$-0.931538\pi$
$967$		−	13.2736i		−	0.426850i	0.976959	−	0.213425i	$-0.0684619\pi$
$968$	−48.3275	+	0.537788i	−1.55330	+	0.0172852i
$969$	0.693232	−	0.400238i	0.0222698	−	0.0128575i
$970$	−29.9471	+	14.1000i	−0.961543	+	0.452724i
$971$	−41.1279	+	11.0202i	−1.31986	+	0.353655i	−0.848925	−	0.528514i	$-0.822750\pi$
$971$	−41.1279	+	11.0202i	−1.31986	+	0.353655i	−0.470934	+	0.882169i	$0.656083\pi$
$972$	25.8725	+	36.3724i	0.829860	+	1.16665i
$973$	−36.1467	+	27.3200i	−1.15881	+	0.875840i
$974$	−3.11691	+	2.63516i	−0.0998722	+	0.0844359i
$975$	−8.00579	+	13.8664i	−0.256390	+	0.444081i
$976$	6.77855	+	4.59804i	0.216976	+	0.147180i
$977$	−24.4001	−	42.2622i	−0.780628	−	1.35209i	−0.931577	−	0.363545i	$-0.881566\pi$
$977$	−24.4001	−	42.2622i	−0.780628	−	1.35209i	0.150949	−	0.988542i	$-0.451767\pi$
$978$	−9.44596	−	52.4327i	−0.302049	−	1.67661i
$979$	14.5076	−	14.5076i	0.463664	−	0.463664i
$980$	−25.6073	+	9.11321i	−0.817996	+	0.291111i
$981$	−17.0670	−	17.0670i	−0.544907	−	0.544907i
$982$	16.6226	+	11.5476i	0.530449	+	0.368500i
$983$	−45.9141	+	26.5085i	−1.46443	+	0.845491i	−0.999212	−	0.0397033i	$-0.987359\pi$
$983$	−45.9141	+	26.5085i	−1.46443	+	0.845491i	−0.465222	+	0.885194i	$0.654025\pi$
$984$	5.73141	+	20.4758i	0.182711	+	0.652744i
$985$	−19.8131	−	11.4391i	−0.631299	−	0.364481i
$986$	−3.16086	−	0.264729i	−0.100662	−	0.00843069i
$987$	16.3977	+	21.6956i	0.521946	+	0.690578i
$988$	5.36885	+	0.905659i	0.170806	+	0.0288128i
$989$	−1.22601	−	4.57551i	−0.0389847	−	0.145493i
$990$	−17.1822	+	47.7581i	−0.546086	+	1.51785i
$991$	6.92839	+	12.0003i	0.220088	+	0.381203i	0.954834	−	0.297139i	$-0.0960324\pi$
$991$	6.92839	+	12.0003i	0.220088	+	0.381203i	−0.734747	+	0.678341i	$0.762699\pi$
$992$	44.0480	+	6.92720i	1.39853	+	0.219939i
$993$	38.7162			1.22862
$994$	7.68778	−	0.308087i	0.243842	−	0.00977191i
$995$	−3.71531	+	3.71531i	−0.117783	+	0.117783i
$996$	−46.6106	+	56.3927i	−1.47691	+	1.78687i
$997$	−6.93196	+	25.8704i	−0.219537	+	0.819325i	0.764982	+	0.644051i	$0.222748\pi$
$997$	−6.93196	+	25.8704i	−0.219537	+	0.819325i	−0.984520	+	0.175273i	$0.943919\pi$
$998$	−11.5547	−	24.5410i	−0.365757	−	0.776832i
$999$	3.24152	+	1.87149i	0.102557	+	0.0592114i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.2.w.c.37.11	✓	48
4.3	odd	2		448.2.ba.c.177.11		48
7.2	even	3		784.2.m.j.197.3		24
7.3	odd	6		784.2.x.o.165.6		48
7.4	even	3	inner	112.2.w.c.53.6	yes	48
7.5	odd	6		784.2.m.k.197.3		24
7.6	odd	2		784.2.x.o.373.11		48
8.3	odd	2		896.2.ba.e.737.2		48
8.5	even	2		896.2.ba.f.737.11		48
16.3	odd	4		448.2.ba.c.401.2		48
16.5	even	4		896.2.ba.f.289.2		48
16.11	odd	4		896.2.ba.e.289.11		48
16.13	even	4	inner	112.2.w.c.93.6	yes	48
28.11	odd	6		448.2.ba.c.305.2		48
56.11	odd	6		896.2.ba.e.865.11		48
56.53	even	6		896.2.ba.f.865.2		48
112.11	odd	12		896.2.ba.e.417.2		48
112.13	odd	4		784.2.x.o.765.6		48
112.45	odd	12		784.2.x.o.557.11		48
112.53	even	12		896.2.ba.f.417.11		48
112.61	odd	12		784.2.m.k.589.3		24
112.67	odd	12		448.2.ba.c.81.11		48
112.93	even	12		784.2.m.j.589.3		24
112.109	even	12	inner	112.2.w.c.109.11	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.11	✓	48	1.1	even	1	trivial
112.2.w.c.53.6	yes	48	7.4	even	3	inner
112.2.w.c.93.6	yes	48	16.13	even	4	inner
112.2.w.c.109.11	yes	48	112.109	even	12	inner
448.2.ba.c.81.11		48	112.67	odd	12
448.2.ba.c.177.11		48	4.3	odd	2
448.2.ba.c.305.2		48	28.11	odd	6
448.2.ba.c.401.2		48	16.3	odd	4
784.2.m.j.197.3		24	7.2	even	3
784.2.m.j.589.3		24	112.93	even	12
784.2.m.k.197.3		24	7.5	odd	6
784.2.m.k.589.3		24	112.61	odd	12
784.2.x.o.165.6		48	7.3	odd	6
784.2.x.o.373.11		48	7.6	odd	2
784.2.x.o.557.11		48	112.45	odd	12
784.2.x.o.765.6		48	112.13	odd	4
896.2.ba.e.289.11		48	16.11	odd	4
896.2.ba.e.417.2		48	112.11	odd	12
896.2.ba.e.737.2		48	8.3	odd	2
896.2.ba.e.865.11		48	56.11	odd	6
896.2.ba.f.289.2		48	16.5	even	4
896.2.ba.f.417.11		48	112.53	even	12
896.2.ba.f.737.11		48	8.5	even	2
896.2.ba.f.865.2		48	56.53	even	6

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:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	112.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39181 - 0.250740i) q^{2} +(-2.46036 - 0.659252i) q^{3} +(1.87426 - 0.697963i) q^{4} +(1.87532 - 0.502490i) q^{5} +(-3.58965 - 0.300642i) q^{6} +(0.364450 - 2.62053i) q^{7} +(2.43360 - 1.44138i) q^{8} +(3.02070 + 1.74400i) q^{9} +O(q^{10})\)	\(q+(1.39181 - 0.250740i) q^{2} +(-2.46036 - 0.659252i) q^{3} +(1.87426 - 0.697963i) q^{4} +(1.87532 - 0.502490i) q^{5} +(-3.58965 - 0.300642i) q^{6} +(0.364450 - 2.62053i) q^{7} +(2.43360 - 1.44138i) q^{8} +(3.02070 + 1.74400i) q^{9} +(2.48409 - 1.16959i) q^{10} +(-1.37168 + 5.11917i) q^{11} +(-5.07149 + 0.481633i) q^{12} +(-3.61173 + 3.61173i) q^{13} +(-0.149826 - 3.73866i) q^{14} -4.94523 q^{15} +(3.02569 - 2.61633i) q^{16} +(-0.294815 - 0.510634i) q^{17} +(4.64152 + 1.66990i) q^{18} +(-0.137946 - 0.514822i) q^{19} +(3.16411 - 2.25070i) q^{20} +(-2.62427 + 6.20719i) q^{21} +(-0.625532 + 7.46884i) q^{22} +(0.378033 + 0.218258i) q^{23} +(-6.93778 + 1.94197i) q^{24} +(-1.06581 + 0.615344i) q^{25} +(-4.12123 + 5.93245i) q^{26} +(-0.878939 - 0.878939i) q^{27} +(-1.14596 - 5.16592i) q^{28} +(2.68976 - 2.68976i) q^{29} +(-6.88281 + 1.23997i) q^{30} +(3.94118 + 6.82633i) q^{31} +(3.55517 - 4.40009i) q^{32} +(6.74965 - 11.6907i) q^{33} +(-0.538362 - 0.636783i) q^{34} +(-0.633329 - 5.09746i) q^{35} +(6.87881 + 1.16037i) q^{36} +(-2.90863 + 0.779365i) q^{37} +(-0.321081 - 0.681944i) q^{38} +(11.2672 - 6.50513i) q^{39} +(3.83950 - 3.92591i) q^{40} -2.95135i q^{41} +(-2.09609 + 9.29722i) q^{42} +(-7.67329 - 7.67329i) q^{43} +(1.00211 + 10.5520i) q^{44} +(6.54110 + 1.75268i) q^{45} +(0.580875 + 0.208985i) q^{46} +(2.01771 - 3.49478i) q^{47} +(-9.16913 + 4.44242i) q^{48} +(-6.73435 - 1.91011i) q^{49} +(-1.32911 + 1.12368i) q^{50} +(0.388715 + 1.45070i) q^{51} +(-4.24847 + 9.29018i) q^{52} +(0.244374 - 0.912017i) q^{53} +(-1.44370 - 1.00293i) q^{54} +10.2893i q^{55} +(-2.89026 - 6.90264i) q^{56} +1.35759i q^{57} +(3.06920 - 4.41806i) q^{58} +(0.00753382 - 0.0281166i) q^{59} +(-9.26864 + 3.45159i) q^{60} +(0.529990 + 1.97795i) q^{61} +(7.19700 + 8.51273i) q^{62} +(5.67110 - 7.28022i) q^{63} +(3.84483 - 7.01550i) q^{64} +(-4.95829 + 8.58801i) q^{65} +(6.46288 - 17.9637i) q^{66} +(-6.24795 - 1.67413i) q^{67} +(-0.908964 - 0.751291i) q^{68} +(-0.786212 - 0.786212i) q^{69} +(-2.15961 - 6.93588i) q^{70} +2.05630i q^{71} +(9.86494 - 0.109777i) q^{72} +(6.85664 - 3.95868i) q^{73} +(-3.85283 + 1.81403i) q^{74} +(3.02794 - 0.811334i) q^{75} +(-0.617873 - 0.868628i) q^{76} +(12.9150 + 5.46021i) q^{77} +(14.0507 - 11.8790i) q^{78} +(-6.53028 + 11.3108i) q^{79} +(4.35946 - 6.42683i) q^{80} +(-3.64893 - 6.32013i) q^{81} +(-0.740020 - 4.10771i) q^{82} +(10.1551 - 10.1551i) q^{83} +(-0.586173 + 13.4655i) q^{84} +(-0.809460 - 0.809460i) q^{85} +(-12.6038 - 8.75575i) q^{86} +(-8.39101 + 4.84455i) q^{87} +(4.04056 + 14.4351i) q^{88} +(-3.35262 - 1.93564i) q^{89} +(9.54343 + 0.799284i) q^{90} +(8.14836 + 10.7810i) q^{91} +(0.860868 + 0.145218i) q^{92} +(-5.19647 - 19.3935i) q^{93} +(1.93199 - 5.36999i) q^{94} +(-0.517385 - 0.896137i) q^{95} +(-11.6478 + 8.48206i) q^{96} -12.0556 q^{97} +(-9.85186 - 0.969932i) q^{98} +(-13.0712 + 13.0712i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{8}+O(q^{10}) \) 48 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^8	\( 48 q - 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 24 q^{13} - 34 q^{14} - 40 q^{15} + 16 q^{16} + 8 q^{17} + 18 q^{18} - 4 q^{19} - 16 q^{20} - 8 q^{21} + 18 q^{24} - 10 q^{26} - 24 q^{27} - 10 q^{28} + 24 q^{29} - 4 q^{30} + 28 q^{31} + 16 q^{32} + 16 q^{33} - 44 q^{34} + 28 q^{35} - 72 q^{36} - 24 q^{37} + 20 q^{38} + 26 q^{40} + 6 q^{42} - 40 q^{43} + 6 q^{44} - 28 q^{45} - 14 q^{46} - 20 q^{47} + 56 q^{48} + 56 q^{50} + 24 q^{51} - 16 q^{52} - 16 q^{53} + 64 q^{54} + 40 q^{56} - 6 q^{58} - 20 q^{59} + 46 q^{60} + 8 q^{61} + 24 q^{62} - 16 q^{63} + 80 q^{64} + 8 q^{65} - 20 q^{66} + 48 q^{67} - 40 q^{69} + 82 q^{70} - 32 q^{72} - 8 q^{74} - 4 q^{75} - 36 q^{76} - 20 q^{77} + 116 q^{78} - 36 q^{79} - 28 q^{80} + 2 q^{82} - 8 q^{83} + 28 q^{84} - 20 q^{86} - 42 q^{88} - 20 q^{90} + 64 q^{91} + 76 q^{92} + 8 q^{93} - 72 q^{94} - 4 q^{95} - 120 q^{96} - 48 q^{97} - 2 q^{98} - 24 q^{99}+O(q^{100}) \) 48 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 24 * q^13 - 34 * q^14 - 40 * q^15 + 16 * q^16 + 8 * q^17 + 18 * q^18 - 4 * q^19 - 16 * q^20 - 8 * q^21 + 18 * q^24 - 10 * q^26 - 24 * q^27 - 10 * q^28 + 24 * q^29 - 4 * q^30 + 28 * q^31 + 16 * q^32 + 16 * q^33 - 44 * q^34 + 28 * q^35 - 72 * q^36 - 24 * q^37 + 20 * q^38 + 26 * q^40 + 6 * q^42 - 40 * q^43 + 6 * q^44 - 28 * q^45 - 14 * q^46 - 20 * q^47 + 56 * q^48 + 56 * q^50 + 24 * q^51 - 16 * q^52 - 16 * q^53 + 64 * q^54 + 40 * q^56 - 6 * q^58 - 20 * q^59 + 46 * q^60 + 8 * q^61 + 24 * q^62 - 16 * q^63 + 80 * q^64 + 8 * q^65 - 20 * q^66 + 48 * q^67 - 40 * q^69 + 82 * q^70 - 32 * q^72 - 8 * q^74 - 4 * q^75 - 36 * q^76 - 20 * q^77 + 116 * q^78 - 36 * q^79 - 28 * q^80 + 2 * q^82 - 8 * q^83 + 28 * q^84 - 20 * q^86 - 42 * q^88 - 20 * q^90 + 64 * q^91 + 76 * q^92 + 8 * q^93 - 72 * q^94 - 4 * q^95 - 120 * q^96 - 48 * q^97 - 2 * q^98 - 24 * q^99

Introduction

L-functions

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