LMFDB - Embedded newform 112.2.w.c.109.11

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			109.11
Character	$\chi$	$=$	112.109
Dual form			112.2.w.c.37.11

$q$-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 $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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	−0.885658	−	0.464338i	$-0.846292\pi$
$3$	−2.46036	+	0.659252i	−1.42049	+	0.380619i	−0.534833	+	0.844958i	$0.679626\pi$
$4$	1.87426	+	0.697963i	0.937130	+	0.348982i
$5$	1.87532	+	0.502490i	0.838668	+	0.224720i	0.652491	−	0.757796i	$-0.273724\pi$
$5$	1.87532	+	0.502490i	0.838668	+	0.224720i	0.186176	+	0.982516i	$0.440391\pi$
$6$	−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	−0.787670	−	0.616097i	$-0.788713\pi$
$11$	−1.37168	−	5.11917i	−0.413576	−	1.54349i	0.374094	−	0.927391i	$-0.377954\pi$
$12$	−5.07149	−	0.481633i	−1.46401	−	0.139036i
$13$	−3.61173	−	3.61173i	−1.00171	−	1.00171i	−0.999999	−	0.00171617i	$-0.999454\pi$
$13$	−3.61173	−	3.61173i	−1.00171	−	1.00171i	−0.00171617	−	0.999999i	$-0.500546\pi$
$14$	−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	−0.899560	−	0.436797i	$-0.856113\pi$
$17$	−0.294815	+	0.510634i	−0.0715031	+	0.123847i	0.828057	+	0.560644i	$0.189446\pi$
$18$	4.64152	−	1.66990i	1.09402	−	0.393600i
$19$	−0.137946	+	0.514822i	−0.0316470	+	0.118108i	−0.979942	−	0.199281i	$-0.936139\pi$
$19$	−0.137946	+	0.514822i	−0.0316470	+	0.118108i	0.948295	+	0.317389i	$0.102806\pi$
$20$	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	−0.460069	−	0.887883i	$-0.652175\pi$
$23$	0.378033	−	0.218258i	0.0788254	−	0.0455098i	0.538895	+	0.842373i	$0.318842\pi$
$24$	−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	0.911275	−	0.411799i	$-0.135099\pi$
$29$	2.68976	+	2.68976i	0.499476	+	0.499476i	−0.411799	+	0.911275i	$0.635099\pi$
$30$	−6.88281	−	1.23997i	−1.25662	−	0.226386i
$31$	3.94118	−	6.82633i	0.707857	−	1.22605i	−0.257793	−	0.966200i	$-0.582995\pi$
$31$	3.94118	−	6.82633i	0.707857	−	1.22605i	0.965650	−	0.259845i	$-0.0836714\pi$
$32$	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	0.0116774	−	0.999932i	$-0.496283\pi$
$37$	−2.90863	−	0.779365i	−0.478176	−	0.128127i	−0.489853	+	0.871805i	$0.662950\pi$
$38$	−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	$0.0740235\pi$
$41$			2.95135i			0.460923i	−0.973081	+	0.230461i	$0.925976\pi$
$42$	−2.09609	−	9.29722i	−0.323434	−	1.43459i
$43$	−7.67329	+	7.67329i	−1.17017	+	1.17017i	−0.187996	+	0.982170i	$0.560199\pi$
$43$	−7.67329	+	7.67329i	−1.17017	+	1.17017i	−0.982170	+	0.187996i	$0.939801\pi$
$44$	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	0.974825	−	0.222971i	$-0.0715756\pi$
$47$	2.01771	+	3.49478i	0.294314	+	0.509766i	−0.680511	+	0.732738i	$0.738242\pi$
$48$	−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	0.980676	−	0.195637i	$-0.0626773\pi$
$53$	0.244374	+	0.912017i	0.0335674	+	0.125275i	−0.947109	+	0.320912i	$0.896011\pi$
$54$	−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	0.966415	−	0.256988i	$-0.0827302\pi$
$59$	0.00753382	+	0.0281166i	0.000980820	+	0.00366047i	−0.965434	+	0.260649i	$0.916064\pi$
$60$	−9.26864	−	3.45159i	−1.19658	−	0.445598i
$61$	0.529990	−	1.97795i	0.0678583	−	0.253251i	−0.923661	−	0.383211i	$-0.874818\pi$
$61$	0.529990	−	1.97795i	0.0678583	−	0.253251i	0.991519	+	0.129960i	$0.0414850\pi$
$62$	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	−0.619414	−	0.785065i	$-0.712630\pi$
$67$	−6.24795	+	1.67413i	−0.763309	+	0.204528i	−0.143895	+	0.989593i	$0.545963\pi$
$68$	−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	$-0.961063\pi$
$71$		−	2.05630i		−	0.244037i	0.992528	−	0.122019i	$-0.0389368\pi$
$72$	9.86494	+	0.109777i	1.16259	+	0.0129373i
$73$	6.85664	+	3.95868i	0.802509	+	0.463329i	0.844348	−	0.535796i	$-0.179988\pi$
$73$	6.85664	+	3.95868i	0.802509	+	0.463329i	−0.0418389	+	0.999124i	$0.513322\pi$
$74$	−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	−0.954849	−	0.297092i	$-0.903983\pi$
$79$	−6.53028	−	11.3108i	−0.734714	−	1.27256i	0.220135	−	0.975469i	$-0.429350\pi$
$80$	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	0.992510	+	0.122161i	$0.0389824\pi$
$83$	10.1551	+	10.1551i	1.11467	+	1.11467i	0.122161	+	0.992510i	$0.461018\pi$
$84$	−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	−0.667051	−	0.745012i	$-0.732444\pi$
$89$	−3.35262	+	1.93564i	−0.355377	+	0.205177i	0.311674	+	0.950189i	$0.399110\pi$
$90$	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	0.922692	−	0.385539i	$-0.125984\pi$
$101$	−0.694969	−	2.59366i	−0.0691520	−	0.258079i	−0.991844	+	0.127460i	$0.959318\pi$
$102$	0.904765	−	1.92163i	0.0895851	−	0.190270i
$103$	0.0773103	−	0.0446351i	0.00761761	−	0.00439803i	−0.496186	−	0.868216i	$-0.665267\pi$
$103$	0.0773103	−	0.0446351i	0.00761761	−	0.00439803i	0.503804	+	0.863818i	$0.331933\pi$
$104$	−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	0.864252	−	0.503059i	$-0.167792\pi$
$107$	14.0802	+	3.77279i	1.36119	+	0.364729i	0.496935	+	0.867788i	$0.334459\pi$
$108$	−2.26083	+	1.03389i	−0.217548	+	0.0994863i
$109$	−6.68404	+	1.79098i	−0.640215	+	0.171545i	−0.564301	−	0.825569i	$-0.690854\pi$
$109$	−6.68404	+	1.79098i	−0.640215	+	0.171545i	−0.0759141	+	0.997114i	$0.524187\pi$
$110$	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	−0.884753	−	0.466060i	$-0.845673\pi$
$131$	1.31046	−	4.89071i	0.114496	−	0.427304i	0.999249	+	0.0387565i	$0.0123397\pi$
$132$	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	0.510281	−	0.860008i	$-0.329541\pi$
$137$	0.241507	+	0.139434i	0.0206333	+	0.0119127i	−0.489648	+	0.871920i	$0.662875\pi$
$138$	−1.29139	+	0.897121i	−0.109930	+	0.0763681i
$139$	−12.1095	+	12.1095i	−1.02712	+	1.02712i	−0.0274943	+	0.999622i	$0.508753\pi$
$139$	−12.1095	+	12.1095i	−1.02712	+	1.02712i	−0.999622	+	0.0274943i	$0.991247\pi$
$140$	−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	0.981542	−	0.191247i	$-0.0612532\pi$
$149$	21.1901	+	5.67786i	1.73596	+	0.465149i	0.754417	+	0.656396i	$0.227920\pi$
$150$	4.01088	+	1.88845i	0.327487	+	0.154191i
$151$	8.08773	+	4.66946i	0.658170	+	0.379995i	0.791580	−	0.611066i	$-0.209259\pi$
$151$	8.08773	+	4.66946i	0.658170	+	0.379995i	−0.133409	+	0.991061i	$0.542592\pi$
$152$	−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	−0.679034	−	0.734107i	$-0.737601\pi$
$157$	−11.2775	+	3.02179i	−0.900040	+	0.241165i	−0.221007	+	0.975272i	$0.570934\pi$
$158$	−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	−0.637482	−	0.770466i	$-0.720024\pi$
$163$	3.82793	−	14.2860i	0.299826	−	1.11897i	0.937308	−	0.348502i	$-0.113310\pi$
$164$	−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	$-0.994743\pi$
$167$		−	0.426814i		−	0.0330279i	0.999864	−	0.0165139i	$-0.00525679\pi$
$168$	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	−0.912040	−	0.410101i	$-0.865493\pi$
$173$	1.08986	−	4.06740i	0.0828603	−	0.309239i	0.994900	+	0.100862i	$0.0321601\pi$
$174$	−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	−0.727474	−	0.686135i	$-0.759306\pi$
$179$	−13.5720	+	3.63660i	−1.01442	+	0.271812i	−0.286943	+	0.957948i	$0.592639\pi$
$180$	13.4830	+	1.28047i	1.00497	+	0.0954404i
$181$	10.0681	−	10.0681i	0.748356	−	0.748356i	−0.225814	−	0.974170i	$-0.572504\pi$
$181$	10.0681	−	10.0681i	0.748356	−	0.748356i	0.974170	+	0.225814i	$0.0725042\pi$
$182$	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	0.637118	−	0.770766i	$-0.280126\pi$
$191$	−4.82250	−	8.35282i	−0.348944	−	0.604389i	−0.986062	+	0.166377i	$0.946793\pi$
$192$	−14.0847	−	14.7260i	−1.01647	−	1.06275i
$193$	9.77970	−	16.9389i	0.703959	−	1.21929i	−0.263108	−	0.964767i	$-0.584747\pi$
$193$	9.77970	−	16.9389i	0.703959	−	1.21929i	0.967066	−	0.254525i	$-0.0819193\pi$
$194$	−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	−0.938620	−	0.344953i	$-0.887895\pi$
$197$	−8.33252	+	8.33252i	−0.593668	+	0.593668i	0.344953	+	0.938620i	$0.387895\pi$
$198$	−14.9152	−	21.4702i	−1.05998	−	1.52582i
$199$	−2.34374	−	1.35316i	−0.166144	−	0.0959230i	0.414623	−	0.909993i	$-0.363914\pi$
$199$	−2.34374	−	1.35316i	−0.166144	−	0.0959230i	−0.580766	+	0.814070i	$0.697247\pi$
$200$	−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	0.986834	−	0.161734i	$-0.0517087\pi$
$211$	11.9853	+	11.9853i	0.825100	+	0.825100i	−0.161734	+	0.986834i	$0.551709\pi$
$212$	−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	−0.808738	−	0.588170i	$-0.799849\pi$
$227$	−18.3064	+	4.90519i	−1.21504	+	0.325569i	−0.406303	+	0.913739i	$0.633182\pi$
$228$	0.947547	−	2.54447i	0.0627529	−	0.168512i
$229$	25.1003	+	6.72559i	1.65867	+	0.444440i	0.962022	−	0.272972i	$-0.0880066\pi$
$229$	25.1003	+	6.72559i	1.65867	+	0.444440i	0.696650	+	0.717412i	$0.254673\pi$
$230$	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	−0.0422348	−	0.999108i	$-0.513448\pi$
$233$	12.2405	−	7.06704i	0.801900	−	0.462977i	0.844135	+	0.536130i	$0.180114\pi$
$234$	−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	−0.666160	−	0.745809i	$-0.732063\pi$
$241$	4.85611	−	8.41103i	0.312809	−	0.541802i	0.978969	+	0.204007i	$0.0653966\pi$
$242$	−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	−0.951103	−	0.308875i	$-0.900048\pi$
$251$	−10.1748	+	10.1748i	−0.642228	+	0.642228i	0.308875	+	0.951103i	$0.400048\pi$
$252$	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	−0.900495	−	0.434867i	$-0.856795\pi$
$257$	−13.2555	−	22.9591i	−0.826853	−	1.43215i	0.0736418	−	0.997285i	$-0.476538\pi$
$258$	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	−0.170256	−	0.985400i	$-0.554460\pi$
$263$	−17.9812	−	10.3814i	−1.10877	−	0.640146i	−0.938509	+	0.345254i	$0.887793\pi$
$264$	−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	0.569852	−	0.821747i	$-0.307000\pi$
$269$	24.1792	−	6.47880i	1.47423	−	0.395019i	0.904380	+	0.426728i	$0.140334\pi$
$270$	−3.21136	+	1.15537i	−0.195437	+	0.0703134i
$271$	2.82072	+	4.88563i	0.171347	+	0.296781i	0.938891	−	0.344215i	$-0.111855\pi$
$271$	2.82072	+	4.88563i	0.171347	+	0.296781i	−0.767544	+	0.640996i	$0.778522\pi$
$272$	−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	−0.939248	−	0.343239i	$-0.888476\pi$
$277$	−4.95063	−	18.4760i	−0.297455	−	1.11012i	0.641793	−	0.766878i	$-0.278191\pi$
$278$	−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	$-0.788898\pi$
$281$		−	20.6400i		−	1.23128i	0.788029	−	0.615639i	$-0.211102\pi$
$282$	−8.29357	−	11.9384i	−0.493875	−	0.710924i
$283$	6.14544	+	22.9351i	0.365309	+	1.36335i	0.867002	+	0.498305i	$0.166044\pi$
$283$	6.14544	+	22.9351i	0.365309	+	1.36335i	−0.501693	+	0.865046i	$0.667289\pi$
$284$	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	0.224778	−	0.974410i	$-0.427834\pi$
$293$	20.5268	−	20.5268i	1.19919	−	1.19919i	0.974410	−	0.224778i	$-0.0721656\pi$
$294$	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	0.513730	−	0.857952i	$-0.328263\pi$
$307$	−6.03127	−	6.03127i	−0.344223	−	0.344223i	−0.857952	+	0.513730i	$0.828263\pi$
$308$	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	0.838770	−	0.544486i	$-0.183275\pi$
$311$	13.8721	+	8.00907i	0.786616	+	0.454153i	−0.0521541	+	0.998639i	$0.516609\pi$
$312$	18.0435	+	32.0713i	1.02151	+	1.81568i
$313$	−15.3757	+	8.87715i	−0.869085	+	0.501766i	−0.867044	−	0.498232i	$-0.833983\pi$
$313$	−15.3757	+	8.87715i	−0.869085	+	0.501766i	−0.00204070	+	0.999998i	$0.500650\pi$
$314$	−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	0.756057	+	0.654505i	$0.227123\pi$
$317$	−4.02311	+	15.0144i	−0.225960	+	0.843295i	−0.982018	+	0.188790i	$0.939544\pi$
$318$	−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	−0.168338	−	0.985729i	$-0.553840\pi$
$331$	−14.6818	−	3.93399i	−0.806987	−	0.216232i	−0.638649	+	0.769498i	$0.720507\pi$
$332$	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	0.910119	−	0.414348i	$-0.135990\pi$
$347$	−1.58787	−	5.92600i	−0.0852412	−	0.318125i	−0.995360	+	0.0962234i	$0.969324\pi$
$348$	−12.3456	−	14.9366i	−0.661794	−	0.800684i
$349$	−2.94202	−	2.94202i	−0.157483	−	0.157483i	0.623968	−	0.781450i	$-0.285520\pi$
$349$	−2.94202	−	2.94202i	−0.157483	−	0.157483i	−0.781450	+	0.623968i	$0.785520\pi$
$350$	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	0.277256	+	0.960796i	$0.410575\pi$
$353$	−13.0287	+	22.5663i	−0.693446	+	1.20108i	−0.970702	+	0.240288i	$0.922758\pi$
$354$	−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	0.367508	−	0.930020i	$-0.380211\pi$
$359$	25.7055	−	14.8411i	1.35668	−	0.783282i	0.989175	+	0.146739i	$0.0468776\pi$
$360$	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	−0.802250	−	0.596988i	$-0.796364\pi$
$367$	2.21998	−	3.84511i	0.115882	−	0.200713i	0.918132	+	0.396275i	$0.129697\pi$
$368$	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	−0.229741	−	0.973252i	$-0.573788\pi$
$373$	−17.6779	−	4.73679i	−0.915328	−	0.245261i	−0.685587	+	0.727990i	$0.740455\pi$
$374$	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	−0.661628	−	0.749833i	$-0.730134\pi$
$379$	1.71717	−	1.71717i	0.0882050	−	0.0882050i	0.749833	+	0.661628i	$0.230134\pi$
$380$	−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	0.976323	−	0.216316i	$-0.0694043\pi$
$383$	5.88728	+	10.1971i	0.300826	+	0.521046i	−0.675497	+	0.737363i	$0.736071\pi$
$384$	−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	0.989413	+	0.145128i	$0.0463595\pi$
$389$	4.04561	+	15.0984i	0.205120	+	0.765520i	−0.784292	+	0.620391i	$0.786974\pi$
$390$	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	−0.983741	−	0.179592i	$-0.942522\pi$
$397$	−0.836855	+	3.12318i	−0.0420005	+	0.156748i	0.941741	+	0.336340i	$0.109189\pi$
$398$	−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	0.800647	−	0.599137i	$-0.204489\pi$
$401$	−2.37385	−	4.11163i	−0.118544	−	0.205325i	−0.919191	+	0.393812i	$0.871156\pi$
$402$	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	0.432182	−	0.901786i	$-0.357744\pi$
$409$	−2.68361	−	1.54938i	−0.132696	−	0.0766121i	−0.564879	+	0.825174i	$0.691077\pi$
$410$	−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	0.768276	−	0.640119i	$-0.221115\pi$
$419$	2.62329	+	2.62329i	0.128156	+	0.128156i	−0.640119	+	0.768276i	$0.721115\pi$
$420$	5.66703	−	25.5467i	0.276523	−	1.24655i
$421$	−3.44059	+	3.44059i	−0.167684	+	0.167684i	−0.785961	−	0.618276i	$-0.787831\pi$
$421$	−3.44059	+	3.44059i	−0.167684	+	0.167684i	0.618276	+	0.785961i	$0.287831\pi$
$422$	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	−0.449500	−	0.893280i	$-0.648398\pi$
$431$	11.3945	−	19.7358i	0.548853	−	0.950642i	0.998353	−	0.0573616i	$-0.0182688\pi$
$432$	−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	−0.976158	−	0.217061i	$-0.930353\pi$
$439$	−26.7406	+	15.4387i	−1.27626	+	0.736847i	−0.300099	+	0.953908i	$0.597020\pi$
$440$	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	−0.0828461	−	0.996562i	$-0.526401\pi$
$443$	−13.7414	−	3.68200i	−0.652874	−	0.174937i	−0.570028	+	0.821625i	$0.693068\pi$
$444$	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	−0.541584	−	0.840647i	$-0.682175\pi$
$457$	−1.80328	+	1.04112i	−0.0843539	+	0.0487017i	0.457230	+	0.889349i	$0.348842\pi$
$458$	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	0.908311	−	0.418296i	$-0.137372\pi$
$461$	10.5211	+	10.5211i	0.490015	+	0.490015i	−0.418296	+	0.908311i	$0.637372\pi$
$462$	−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	−0.883479	−	0.468472i	$-0.844805\pi$
$467$	2.50402	−	9.34512i	0.115872	−	0.432440i	0.999351	+	0.0360311i	$0.0114715\pi$
$468$	−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	−0.818127	−	0.575038i	$-0.804987\pi$
$479$	1.94642	−	3.37130i	0.0889342	−	0.154039i	0.907061	+	0.420999i	$0.138321\pi$
$480$	−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	0.442300	−	0.896867i	$-0.354163\pi$
$487$	−2.49944	−	1.44305i	−0.113260	−	0.0653909i	−0.555560	+	0.831476i	$0.687496\pi$
$488$	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	−0.440864	−	0.897574i	$-0.645328\pi$
$491$	10.1200	−	10.1200i	0.456710	−	0.456710i	0.897574	+	0.440864i	$0.145328\pi$
$492$	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	0.761265	+	0.648440i	$0.224578\pi$
$499$	−4.96424	+	18.5268i	−0.222230	+	0.829373i	−0.983495	+	0.180933i	$0.942088\pi$
$500$	−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	$0.190906\pi$
$503$			25.3179i			1.12887i	−0.825477	+	0.564436i	$0.809094\pi$
$504$	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	−0.977450	−	0.211167i	$-0.932274\pi$
$509$	−0.572369	+	2.13611i	−0.0253698	+	0.0946814i	0.952080	+	0.305849i	$0.0989402\pi$
$510$	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	0.291981	−	0.956424i	$-0.405686\pi$
$521$	−8.90915	−	5.14370i	−0.390317	−	0.225349i	−0.682297	+	0.731075i	$0.739019\pi$
$522$	16.9762	+	7.99293i	0.743028	+	0.349841i
$523$	−6.30777	−	1.69016i	−0.275819	−	0.0739056i	0.118258	−	0.992983i	$-0.462269\pi$
$523$	−6.30777	−	1.69016i	−0.275819	−	0.0739056i	−0.394077	+	0.919077i	$0.628936\pi$
$524$	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	−0.993297	−	0.115593i	$-0.963123\pi$
$541$	−1.75097	+	6.53469i	−0.0752799	+	0.280948i	0.918017	+	0.396542i	$0.129790\pi$
$542$	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	0.667898	−	0.744253i	$-0.267194\pi$
$547$	−1.78581	−	1.78581i	−0.0763555	−	0.0763555i	−0.744253	+	0.667898i	$0.767194\pi$
$548$	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	−0.186719	−	0.982413i	$-0.559785\pi$
$557$	3.36982	−	0.902940i	0.142784	−	0.0382588i	0.329503	+	0.944155i	$0.393119\pi$
$558$	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	0.669893	−	0.742458i	$-0.266340\pi$
$563$	38.4688	−	10.3077i	1.62127	−	0.434417i	0.951373	+	0.308041i	$0.0996734\pi$
$564$	−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	−0.659868	+	0.751381i	$0.729388\pi$
$569$	−39.1325	+	22.5931i	−1.64052	+	0.947153i	−0.980649	+	0.195772i	$0.937279\pi$
$570$	1.58782	−	3.37237i	0.0665063	−	0.141253i
$571$	6.44226	+	24.0429i	0.269600	+	1.00616i	0.959374	+	0.282137i	$0.0910433\pi$
$571$	6.44226	+	24.0429i	0.269600	+	1.00616i	−0.689774	+	0.724025i	$0.742290\pi$
$572$	−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	−0.957080	−	0.289825i	$-0.906403\pi$
$577$	−5.46579	+	9.46703i	−0.227544	+	0.394118i	0.729536	+	0.683943i	$0.239736\pi$
$578$	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	−0.843896	−	0.536507i	$-0.819744\pi$
$587$	−7.44744	+	7.44744i	−0.307389	+	0.307389i	0.536507	+	0.843896i	$0.319744\pi$
$588$	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	0.999750	+	0.0223792i	$0.00712412\pi$
$593$	12.6447	+	21.9013i	0.519256	+	0.899377i	−0.480494	+	0.876998i	$0.659543\pi$
$594$	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	0.781422	−	0.624003i	$-0.214495\pi$
$599$	15.4613	+	8.92656i	0.631730	+	0.364729i	−0.149692	+	0.988733i	$0.547828\pi$
$600$	6.19935	+	6.33888i	0.253088	+	0.258784i
$601$		−	15.3921i		−	0.627855i	−0.949447	−	0.313928i	$-0.898355\pi$
$601$		−	15.3921i		−	0.627855i	0.949447	−	0.313928i	$-0.101645\pi$
$602$	−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	−0.990445	−	0.137905i	$-0.955963\pi$
$607$	−15.1434	−	26.2292i	−0.614652	−	1.06461i	0.375793	−	0.926704i	$-0.377370\pi$
$608$	−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	0.998637	+	0.0521982i	$0.0166228\pi$
$613$	3.95872	+	14.7741i	0.159891	+	0.596722i	−0.838746	+	0.544523i	$0.816711\pi$
$614$	−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	$-0.709241\pi$
$617$		−	39.3266i		−	1.58323i	0.611020	−	0.791615i	$-0.290759\pi$
$618$	−0.264098	+	0.183467i	−0.0106236	+	0.00738014i
$619$	−1.39109	−	5.19162i	−0.0559127	−	0.208669i	0.932318	−	0.361639i	$-0.117783\pi$
$619$	−1.39109	−	5.19162i	−0.0559127	−	0.208669i	−0.988231	+	0.152970i	$0.951116\pi$
$620$	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	$-0.952415\pi$
$631$		−	7.48252i		−	0.297875i	0.988847	−	0.148937i	$-0.0475853\pi$
$632$	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	−0.944241	−	0.329256i	$-0.893202\pi$
$641$	−4.73385	+	8.19927i	−0.186976	+	0.323852i	0.757265	+	0.653108i	$0.226535\pi$
$642$	−51.6774	−	9.30989i	−2.03954	−	0.367432i
$643$	−20.6140	−	20.6140i	−0.812939	−	0.812939i	0.172135	−	0.985073i	$-0.444934\pi$
$643$	−20.6140	−	20.6140i	−0.812939	−	0.812939i	−0.985073	+	0.172135i	$0.944934\pi$
$644$	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	−0.230252	−	0.973131i	$-0.573955\pi$
$647$	−30.2216	−	17.4485i	−1.18813	−	0.685970i	−0.957882	+	0.287161i	$0.907288\pi$
$648$	−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	−0.401562	−	0.915832i	$-0.631533\pi$
$653$	10.3267	−	38.5399i	0.404117	−	1.50818i	0.805679	−	0.592353i	$-0.201801\pi$
$654$	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	0.565205	−	0.824951i	$-0.308797\pi$
$659$	−6.66795	−	6.66795i	−0.259746	−	0.259746i	−0.824951	+	0.565205i	$0.808797\pi$
$660$	−4.95568	+	52.1822i	−0.192900	+	2.03119i
$661$	0.649564	+	2.42421i	0.0252651	+	0.0942907i	0.977407	−	0.211365i	$-0.0677909\pi$
$661$	0.649564	+	2.42421i	0.0252651	+	0.0942907i	−0.952142	+	0.305656i	$0.901124\pi$
$662$	−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	0.568399	−	0.822753i	$-0.307563\pi$
$677$	16.8935	+	4.52660i	0.649270	+	0.173971i	0.0808713	+	0.996725i	$0.474230\pi$
$678$	−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	−0.909970	−	0.414675i	$-0.863895\pi$
$683$	−8.60472	−	32.1132i	−0.329250	−	1.22878i	0.580719	−	0.814104i	$-0.302771\pi$
$684$	−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	−0.853458	−	0.521161i	$-0.825499\pi$
$691$	3.84416	−	14.3466i	0.146239	−	0.545771i	0.999697	−	0.0246098i	$-0.00783432\pi$
$692$	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	0.176785	−	0.984249i	$-0.443430\pi$
$701$	−21.3787	−	21.3787i	−0.807464	−	0.807464i	−0.984249	+	0.176785i	$0.943430\pi$
$702$	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	−0.000522056	−	1.00000i	$-0.500166\pi$
$709$	−13.3395	−	3.57430i	−0.500974	−	0.134236i	−0.500452	+	0.865764i	$0.666833\pi$
$710$	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	0.900011	+	0.435866i	$0.143558\pi$
$719$	22.1881	+	38.4309i	0.827477	+	1.43323i	−0.0725344	+	0.997366i	$0.523109\pi$
$720$	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	$-0.991467\pi$
$727$		−	1.44539i		−	0.0536067i	0.999641	−	0.0268033i	$-0.00853279\pi$
$728$	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	−0.439807	−	0.898093i	$-0.644953\pi$
$733$	10.5622	−	39.4186i	0.390123	−	1.45596i	0.829930	−	0.557868i	$-0.188380\pi$
$734$	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	−0.454229	−	0.890885i	$-0.650085\pi$
$739$	−10.9326	+	2.92937i	−0.402161	+	0.107759i	0.0520685	+	0.998644i	$0.483419\pi$
$740$	−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	$-0.943246\pi$
$743$		−	9.66874i		−	0.354712i	0.984147	−	0.177356i	$-0.0567544\pi$
$744$	−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	0.757319	+	0.653045i	$0.226509\pi$
$751$	25.8756	+	44.8178i	0.944213	+	1.63542i	0.186893	+	0.982380i	$0.440158\pi$
$752$	−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	−0.0281911	+	0.999603i	$0.508975\pi$
$757$	−28.2783	+	28.2783i	−1.02779	+	1.02779i	−0.999603	+	0.0281911i	$0.991025\pi$
$758$	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	−0.586891	−	0.809666i	$-0.699648\pi$
$761$	−4.94191	+	2.85321i	−0.179144	+	0.103429i	0.407746	+	0.913095i	$0.366315\pi$
$762$	−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	0.988934	+	0.148357i	$0.0473985\pi$
$773$	5.74604	+	21.4445i	0.206671	+	0.771305i	−0.782263	+	0.622948i	$0.785935\pi$
$774$	−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	0.0932471	−	0.995643i	$-0.470275\pi$
$787$	18.8470	−	5.05004i	0.671823	−	0.180014i	0.578576	+	0.815629i	$0.303609\pi$
$788$	−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	0.660609	−	0.750730i	$-0.270298\pi$
$797$	−2.54421	−	2.54421i	−0.0901206	−	0.0901206i	−0.750730	+	0.660609i	$0.770298\pi$
$798$	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	0.119620	−	0.992820i	$-0.461832\pi$
$809$	−19.3519	−	11.1728i	−0.680378	−	0.392816i	−0.799997	+	0.600004i	$0.795166\pi$
$810$	−16.4562	+	11.4320i	−0.578212	+	0.401681i
$811$	31.7484	−	31.7484i	1.11484	−	1.11484i	0.122349	−	0.992487i	$-0.460957\pi$
$811$	31.7484	−	31.7484i	1.11484	−	1.11484i	0.992487	−	0.122349i	$-0.0390426\pi$
$812$	−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	0.956708	−	0.291050i	$-0.0940047\pi$
$821$	46.9829	+	12.5890i	1.63972	+	0.439361i	0.683008	+	0.730411i	$0.260671\pi$
$822$	−0.908847	−	0.427913i	−0.0316997	−	0.0149252i
$823$	−16.7248	−	9.65608i	−0.582991	−	0.336590i	0.179330	−	0.983789i	$-0.442607\pi$
$823$	−16.7248	−	9.65608i	−0.582991	−	0.336590i	−0.762321	+	0.647199i	$0.775940\pi$
$824$	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	−0.409025	−	0.912523i	$-0.634131\pi$
$827$	14.4794	−	14.4794i	0.503498	−	0.503498i	0.912523	+	0.409025i	$0.134131\pi$
$828$	2.34716	−	1.94001i	0.0815694	−	0.0674201i
$829$	−1.38085	+	0.369998i	−0.0479589	+	0.0128505i	−0.282719	−	0.959203i	$-0.591236\pi$
$829$	−1.38085	+	0.369998i	−0.0479589	+	0.0128505i	0.234760	+	0.972053i	$0.424570\pi$
$830$	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	$0.257772\pi$
$839$			41.9512i			1.44832i	−0.689634	+	0.724158i	$0.742228\pi$
$840$	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	−0.204960	+	0.978770i	$0.565706\pi$
$853$	−34.5722	+	34.5722i	−1.18373	+	1.18373i	−0.978770	+	0.204960i	$0.934294\pi$
$854$	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	0.371591	−	0.928396i	$-0.378812\pi$
$857$	−7.21992	−	4.16842i	−0.246628	−	0.142391i	−0.618219	+	0.786006i	$0.712146\pi$
$858$	41.5378	−	88.2222i	1.41808	−	3.01186i
$859$	12.6163	+	3.38053i	0.430463	+	0.115342i	0.467543	−	0.883970i	$-0.345139\pi$
$859$	12.6163	+	3.38053i	0.430463	+	0.115342i	−0.0370807	+	0.999312i	$0.511806\pi$
$860$	−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	−0.888669	−	0.458549i	$-0.848369\pi$
$863$	−24.7192	−	42.8148i	−0.841450	−	1.45743i	0.0472194	−	0.998885i	$-0.484964\pi$
$864$	−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	0.168966	+	0.985622i	$0.445957\pi$
$877$	−13.9238	+	51.9644i	−0.470174	+	1.75471i	−0.639140	+	0.769091i	$0.720709\pi$
$878$	−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	0.457514	−	0.889202i	$-0.348740\pi$
$883$	−12.8278	−	12.8278i	−0.431688	−	0.431688i	−0.889202	+	0.457514i	$0.848740\pi$
$884$	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	0.559207	−	0.829028i	$-0.311106\pi$
$887$	46.3646	−	26.7686i	1.55677	−	0.898801i	0.997563	−	0.0697733i	$-0.0222276\pi$
$888$	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	0.916123	+	0.400897i	$0.131302\pi$
$907$	9.73321	+	36.3248i	0.323186	+	1.20615i	−0.592937	+	0.805249i	$0.702032\pi$
$908$	−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	−0.734187	−	0.678947i	$-0.762437\pi$
$919$	−15.5605	+	8.98389i	−0.513295	+	0.296351i	0.220892	+	0.975298i	$0.429103\pi$
$920$	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	0.566286	−	0.824209i	$-0.308380\pi$
$929$	−13.1258	−	22.7345i	−0.430642	−	0.745894i	−0.996929	+	0.0783141i	$0.975046\pi$
$930$	−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	$0.285010\pi$
$937$			47.7798i			1.56090i	−0.625219	+	0.780449i	$0.714990\pi$
$938$	−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	−0.865082	−	0.501630i	$-0.832734\pi$
$941$	−41.8248	+	11.2069i	−1.36345	+	0.365335i	−0.498368	+	0.866966i	$0.666067\pi$
$942$	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	−0.841999	−	0.539478i	$-0.818621\pi$
$947$	4.82935	−	18.0234i	0.156933	−	0.585681i	0.998932	−	0.0462023i	$-0.0147119\pi$
$948$	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	$0.180700\pi$
$953$			33.1972i			1.07536i	−0.843148	+	0.537681i	$0.819300\pi$
$954$	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	$0.0684619\pi$
$967$			13.2736i			0.426850i	−0.976959	+	0.213425i	$0.931538\pi$
$968$	−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	−0.470934	−	0.882169i	$-0.656083\pi$
$971$	−41.1279	−	11.0202i	−1.31986	−	0.353655i	−0.848925	+	0.528514i	$0.822750\pi$
$972$	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	0.150949	+	0.988542i	$0.451767\pi$
$977$	−24.4001	+	42.2622i	−0.780628	+	1.35209i	−0.931577	+	0.363545i	$0.881566\pi$
$978$	−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	−0.465222	−	0.885194i	$-0.654025\pi$
$983$	−45.9141	−	26.5085i	−1.46443	−	0.845491i	−0.999212	+	0.0397033i	$0.987359\pi$
$984$	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	−0.734747	−	0.678341i	$-0.762699\pi$
$991$	6.92839	−	12.0003i	0.220088	−	0.381203i	0.954834	+	0.297139i	$0.0960324\pi$
$992$	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	−0.984520	−	0.175273i	$-0.943919\pi$
$997$	−6.93196	−	25.8704i	−0.219537	−	0.819325i	0.764982	−	0.644051i	$-0.222748\pi$
$998$	−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.109.11	yes	48
4.3	odd	2		448.2.ba.c.81.11		48
7.2	even	3	inner	112.2.w.c.93.6	yes	48
7.3	odd	6		784.2.m.k.589.3		24
7.4	even	3		784.2.m.j.589.3		24
7.5	odd	6		784.2.x.o.765.6		48
7.6	odd	2		784.2.x.o.557.11		48
8.3	odd	2		896.2.ba.e.417.2		48
8.5	even	2		896.2.ba.f.417.11		48
16.3	odd	4		896.2.ba.e.865.11		48
16.5	even	4	inner	112.2.w.c.53.6	yes	48
16.11	odd	4		448.2.ba.c.305.2		48
16.13	even	4		896.2.ba.f.865.2		48
28.23	odd	6		448.2.ba.c.401.2		48
56.37	even	6		896.2.ba.f.289.2		48
56.51	odd	6		896.2.ba.e.289.11		48
112.5	odd	12		784.2.x.o.373.11		48
112.37	even	12	inner	112.2.w.c.37.11	✓	48
112.51	odd	12		896.2.ba.e.737.2		48
112.53	even	12		784.2.m.j.197.3		24
112.69	odd	4		784.2.x.o.165.6		48
112.93	even	12		896.2.ba.f.737.11		48
112.101	odd	12		784.2.m.k.197.3		24
112.107	odd	12		448.2.ba.c.177.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.11	✓	48	112.37	even	12	inner
112.2.w.c.53.6	yes	48	16.5	even	4	inner
112.2.w.c.93.6	yes	48	7.2	even	3	inner
112.2.w.c.109.11	yes	48	1.1	even	1	trivial
448.2.ba.c.81.11		48	4.3	odd	2
448.2.ba.c.177.11		48	112.107	odd	12
448.2.ba.c.305.2		48	16.11	odd	4
448.2.ba.c.401.2		48	28.23	odd	6
784.2.m.j.197.3		24	112.53	even	12
784.2.m.j.589.3		24	7.4	even	3
784.2.m.k.197.3		24	112.101	odd	12
784.2.m.k.589.3		24	7.3	odd	6
784.2.x.o.165.6		48	112.69	odd	4
784.2.x.o.373.11		48	112.5	odd	12
784.2.x.o.557.11		48	7.6	odd	2
784.2.x.o.765.6		48	7.5	odd	6
896.2.ba.e.289.11		48	56.51	odd	6
896.2.ba.e.417.2		48	8.3	odd	2
896.2.ba.e.737.2		48	112.51	odd	12
896.2.ba.e.865.11		48	16.3	odd	4
896.2.ba.f.289.2		48	56.37	even	6
896.2.ba.f.417.11		48	8.5	even	2
896.2.ba.f.737.11		48	112.93	even	12
896.2.ba.f.865.2		48	16.13	even	4

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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