LMFDB - Embedded newform 115.2.l.a.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(7,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("115.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.l (of order $44$, degree $20$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$10$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.5
Character	$\chi$	$=$	115.17
Dual form			115.2.l.a.88.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.117766 + 0.0439246i) q^{2} +(-0.632714 + 0.345488i) q^{3} +(-1.49956 + 1.29938i) q^{4} +(2.23369 + 0.103094i) q^{5} +(0.0593371 - 0.0684786i) q^{6} +(1.63018 + 2.17766i) q^{7} +(0.239998 - 0.439523i) q^{8} +(-1.34096 + 2.08657i) q^{9} +O(q^{10})$	\(q+(-0.117766 + 0.0439246i) q^{2} +(-0.632714 + 0.345488i) q^{3} +(-1.49956 + 1.29938i) q^{4} +(2.23369 + 0.103094i) q^{5} +(0.0593371 - 0.0684786i) q^{6} +(1.63018 + 2.17766i) q^{7} +(0.239998 - 0.439523i) q^{8} +(-1.34096 + 2.08657i) q^{9} +(-0.267582 + 0.0859729i) q^{10} +(-0.561740 + 0.256538i) q^{11} +(0.499874 - 1.34021i) q^{12} +(3.04488 + 2.27937i) q^{13} +(-0.287633 - 0.184850i) q^{14} +(-1.44891 + 0.706484i) q^{15} +(0.555805 - 3.86571i) q^{16} +(-0.459814 - 6.42904i) q^{17} +(0.0662679 - 0.304629i) q^{18} +(-4.66003 - 5.37796i) q^{19} +(-3.48351 + 2.74781i) q^{20} +(-1.78379 - 0.814630i) q^{21} +(0.0548858 - 0.0548858i) q^{22} +(4.61146 + 1.31697i) q^{23} +0.361009i q^{24} +(4.97874 + 0.460561i) q^{25} +(-0.458705 - 0.134688i) q^{26} +(0.281842 - 3.94066i) q^{27} +(-5.27414 - 1.14732i) q^{28} +(1.70881 + 1.48069i) q^{29} +(0.139600 - 0.146843i) q^{30} +(-9.09095 + 2.66934i) q^{31} +(0.317241 + 1.45833i) q^{32} +(0.266790 - 0.356390i) q^{33} +(0.336544 + 0.736927i) q^{34} +(3.41680 + 5.03228i) q^{35} +(-0.700393 - 4.87134i) q^{36} +(0.939469 - 0.204369i) q^{37} +(0.785020 + 0.428653i) q^{38} +(-2.71404 - 0.390220i) q^{39} +(0.581393 - 0.957017i) q^{40} +(8.00163 - 5.14234i) q^{41} +(0.245853 + 0.0175837i) q^{42} +(-1.71366 - 3.13834i) q^{43} +(0.509024 - 1.11461i) q^{44} +(-3.21040 + 4.52251i) q^{45} +(-0.600923 + 0.0474612i) q^{46} +(4.70878 + 4.70878i) q^{47} +(0.983891 + 2.63791i) q^{48} +(-0.112601 + 0.383482i) q^{49} +(-0.606559 + 0.164451i) q^{50} +(2.51209 + 3.90888i) q^{51} +(-7.52774 + 0.538395i) q^{52} +(4.07640 - 3.05156i) q^{53} +(0.139900 + 0.476457i) q^{54} +(-1.28120 + 0.515115i) q^{55} +(1.34837 - 0.193867i) q^{56} +(4.80649 + 1.79273i) q^{57} +(-0.266279 - 0.0993171i) q^{58} +(-3.63885 + 0.523187i) q^{59} +(1.25473 - 2.94209i) q^{60} +(0.885509 + 3.01577i) q^{61} +(0.953358 - 0.713675i) q^{62} +(-6.72983 + 0.481327i) q^{63} +(4.12148 + 6.41316i) q^{64} +(6.56634 + 5.40532i) q^{65} +(-0.0157646 + 0.0536894i) q^{66} +(-0.430384 - 1.15391i) q^{67} +(9.04326 + 9.04326i) q^{68} +(-3.37274 + 0.759937i) q^{69} +(-0.623425 - 0.442552i) q^{70} +(-2.54704 + 5.57724i) q^{71} +(0.595269 + 1.09015i) q^{72} +(-11.4132 - 0.816286i) q^{73} +(-0.101661 + 0.0653336i) q^{74} +(-3.30924 + 1.42869i) q^{75} +(13.9760 + 2.00944i) q^{76} +(-1.47439 - 0.805077i) q^{77} +(0.336763 - 0.0732582i) q^{78} +(-0.152203 - 1.05860i) q^{79} +(1.64003 - 8.57749i) q^{80} +(-1.90795 - 4.17782i) q^{81} +(-0.716448 + 0.957063i) q^{82} +(-1.28696 - 5.91605i) q^{83} +(3.73341 - 1.09623i) q^{84} +(-0.364285 - 14.4079i) q^{85} +(0.339662 + 0.294319i) q^{86} +(-1.59275 - 0.346482i) q^{87} +(-0.0220620 + 0.308467i) q^{88} +(6.64802 + 1.95203i) q^{89} +(0.179427 - 0.673614i) q^{90} +10.3465i q^{91} +(-8.62641 + 4.01714i) q^{92} +(4.82975 - 4.82975i) q^{93} +(-0.761367 - 0.347705i) q^{94} +(-9.85463 - 12.4931i) q^{95} +(-0.704560 - 0.813106i) q^{96} +(1.25467 - 5.76763i) q^{97} +(-0.00358374 - 0.0501072i) q^{98} +(0.217985 - 1.51612i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8}+O(q^{10}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23} - 10 q^{25} - 28 q^{26} - 26 q^{27} + 66 q^{28} - 22 q^{30} - 40 q^{31} - 46 q^{32} - 14 q^{35} - 12 q^{36} + 66 q^{37} - 22 q^{38} - 22 q^{40} - 8 q^{41} + 198 q^{42} - 22 q^{43} - 76 q^{46} + 52 q^{47} + 18 q^{48} - 82 q^{50} - 44 q^{51} + 158 q^{52} - 22 q^{53} - 10 q^{55} + 88 q^{56} + 66 q^{57} - 58 q^{58} - 22 q^{60} + 44 q^{61} + 38 q^{62} - 22 q^{63} - 22 q^{65} + 132 q^{66} - 22 q^{67} + 32 q^{70} + 132 q^{71} - 28 q^{72} + 34 q^{73} + 38 q^{75} + 132 q^{76} - 10 q^{77} + 22 q^{78} + 176 q^{80} - 48 q^{81} - 50 q^{82} - 22 q^{83} + 202 q^{85} - 46 q^{87} - 110 q^{88} + 396 q^{90} + 50 q^{92} - 36 q^{93} + 68 q^{95} + 148 q^{96} - 88 q^{97} - 50 q^{98}+O(q^{100}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{22}\right)$

Coefficient data

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

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

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

$2$	−0.117766	+	0.0439246i	−0.0832734	+	0.0310594i	−0.390756	−	0.920494i	$-0.627786\pi$
$2$	−0.117766	+	0.0439246i	−0.0832734	+	0.0310594i	0.307482	+	0.951554i	$0.400514\pi$
$3$	−0.632714	+	0.345488i	−0.365298	+	0.199468i	−0.651405	−	0.758730i	$-0.725820\pi$
$3$	−0.632714	+	0.345488i	−0.365298	+	0.199468i	0.286108	+	0.958197i	$0.407638\pi$
$4$	−1.49956	+	1.29938i	−0.749780	+	0.649688i
$5$	2.23369	+	0.103094i	0.998937	+	0.0461051i
$5$	2.23369	+	0.103094i	0.998937	+	0.0461051i
$6$	0.0593371	−	0.0684786i	0.0242243	−	0.0279563i
$7$	1.63018	+	2.17766i	0.616148	+	0.823078i	0.994734	−	0.102488i	$-0.0326804\pi$
$7$	1.63018	+	2.17766i	0.616148	+	0.823078i	−0.378586	+	0.925566i	$0.623590\pi$
$8$	0.239998	−	0.439523i	0.0848521	−	0.155395i
$9$	−1.34096	+	2.08657i	−0.446986	+	0.695523i
$10$	−0.267582	+	0.0859729i	−0.0846169	+	0.0271870i
$11$	−0.561740	+	0.256538i	−0.169371	+	0.0773492i	−0.498296	−	0.867007i	$-0.666041\pi$
$11$	−0.561740	+	0.256538i	−0.169371	+	0.0773492i	0.328925	+	0.944356i	$0.393314\pi$
$12$	0.499874	−	1.34021i	0.144301	−	0.386886i
$13$	3.04488	+	2.27937i	0.844499	+	0.632184i	0.931385	−	0.364034i	$-0.118601\pi$
$13$	3.04488	+	2.27937i	0.844499	+	0.632184i	−0.0868869	+	0.996218i	$0.527692\pi$
$14$	−0.287633	−	0.184850i	−0.0768731	−	0.0494033i
$15$	−1.44891	+	0.706484i	−0.374106	+	0.182413i
$16$	0.555805	−	3.86571i	0.138951	−	0.966427i
$17$	−0.459814	−	6.42904i	−0.111521	−	1.55927i	−0.677918	−	0.735138i	$-0.737117\pi$
$17$	−0.459814	−	6.42904i	−0.111521	−	1.55927i	0.566396	−	0.824133i	$-0.308337\pi$
$18$	0.0662679	−	0.304629i	0.0156195	−	0.0718017i
$19$	−4.66003	−	5.37796i	−1.06908	−	1.23379i	−0.971118	−	0.238599i	$-0.923312\pi$
$19$	−4.66003	−	5.37796i	−1.06908	−	1.23379i	−0.0979660	−	0.995190i	$-0.531234\pi$
$20$	−3.48351	+	2.74781i	−0.778936	+	0.614428i
$21$	−1.78379	−	0.814630i	−0.389255	−	0.177767i
$22$	0.0548858	−	0.0548858i	0.0117017	−	0.0117017i
$23$	4.61146	+	1.31697i	0.961556	+	0.274608i
$23$	4.61146	+	1.31697i	0.961556	+	0.274608i
$24$			0.361009i			0.0736907i
$25$	4.97874	+	0.460561i	0.995749	+	0.0921122i
$26$	−0.458705	−	0.134688i	−0.0899595	−	0.0264145i
$27$	0.281842	−	3.94066i	0.0542405	−	0.758381i
$28$	−5.27414	−	1.14732i	−0.996719	−	0.216823i
$29$	1.70881	+	1.48069i	0.317318	+	0.274958i	0.798926	−	0.601429i	$-0.205402\pi$
$29$	1.70881	+	1.48069i	0.317318	+	0.274958i	−0.481608	+	0.876387i	$0.659947\pi$
$30$	0.139600	−	0.146843i	0.0254874	−	0.0268097i
$31$	−9.09095	+	2.66934i	−1.63278	+	0.479428i	−0.964413	−	0.264401i	$-0.914826\pi$
$31$	−9.09095	+	2.66934i	−1.63278	+	0.479428i	−0.668370	+	0.743829i	$0.733008\pi$
$32$	0.317241	+	1.45833i	0.0560808	+	0.257799i
$33$	0.266790	−	0.356390i	0.0464422	−	0.0620395i
$34$	0.336544	+	0.736927i	0.0577167	+	0.126382i
$35$	3.41680	+	5.03228i	0.577545	+	0.850610i
$36$	−0.700393	−	4.87134i	−0.116732	−	0.811891i
$37$	0.939469	−	0.204369i	0.154448	−	0.0335981i	−0.134677	−	0.990890i	$-0.543000\pi$
$37$	0.939469	−	0.204369i	0.154448	−	0.0335981i	0.289124	+	0.957292i	$0.406636\pi$
$38$	0.785020	+	0.428653i	0.127347	+	0.0695367i
$39$	−2.71404	−	0.390220i	−0.434594	−	0.0624851i
$40$	0.581393	−	0.957017i	0.0919264	−	0.151318i
$41$	8.00163	−	5.14234i	1.24965	−	0.803098i	0.262813	−	0.964847i	$-0.415350\pi$
$41$	8.00163	−	5.14234i	1.24965	−	0.803098i	0.986832	+	0.161749i	$0.0517134\pi$
$42$	0.245853	+	0.0175837i	0.0379359	+	0.00271323i
$43$	−1.71366	−	3.13834i	−0.261331	−	0.478592i	0.713762	−	0.700389i	$-0.246990\pi$
$43$	−1.71366	−	3.13834i	−0.261331	−	0.478592i	−0.975093	+	0.221796i	$0.928808\pi$
$44$	0.509024	−	1.11461i	0.0767382	−	0.168033i
$45$	−3.21040	+	4.52251i	−0.478578	+	0.674175i
$46$	−0.600923	+	0.0474612i	−0.0886012	+	0.00699777i
$47$	4.70878	+	4.70878i	0.686846	+	0.686846i	0.961533	−	0.274688i	$-0.0885745\pi$
$47$	4.70878	+	4.70878i	0.686846	+	0.686846i	−0.274688	+	0.961533i	$0.588574\pi$
$48$	0.983891	+	2.63791i	0.142012	+	0.380750i
$49$	−0.112601	+	0.383482i	−0.0160858	+	0.0547832i
$50$	−0.606559	+	0.164451i	−0.0857803	+	0.0232568i
$51$	2.51209	+	3.90888i	0.351763	+	0.547353i
$52$	−7.52774	+	0.538395i	−1.04391	+	0.0746619i
$53$	4.07640	−	3.05156i	0.559937	−	0.419164i	−0.281466	−	0.959571i	$-0.590821\pi$
$53$	4.07640	−	3.05156i	0.559937	−	0.419164i	0.841403	+	0.540408i	$0.181730\pi$
$54$	0.139900	+	0.476457i	0.0190380	+	0.0648376i
$55$	−1.28120	+	0.515115i	−0.172757	+	0.0694581i
$56$	1.34837	−	0.193867i	0.180184	−	0.0259065i
$57$	4.80649	+	1.79273i	0.636635	+	0.237453i
$58$	−0.266279	−	0.0993171i	−0.0349642	−	0.0130410i
$59$	−3.63885	+	0.523187i	−0.473738	+	0.0681132i	−0.375049	−	0.927005i	$-0.622374\pi$
$59$	−3.63885	+	0.523187i	−0.473738	+	0.0681132i	−0.0986891	+	0.995118i	$0.531465\pi$
$60$	1.25473	−	2.94209i	0.161985	−	0.379822i
$61$	0.885509	+	3.01577i	0.113378	+	0.386130i	0.996557	−	0.0829055i	$-0.0264200\pi$
$61$	0.885509	+	3.01577i	0.113378	+	0.386130i	−0.883180	+	0.469035i	$0.844602\pi$
$62$	0.953358	−	0.713675i	0.121077	−	0.0906368i
$63$	−6.72983	+	0.481327i	−0.847879	+	0.0606415i
$64$	4.12148	+	6.41316i	0.515186	+	0.801644i
$65$	6.56634	+	5.40532i	0.814454	+	0.670447i
$66$	−0.0157646	+	0.0536894i	−0.00194049	+	0.00660871i
$67$	−0.430384	−	1.15391i	−0.0525798	−	0.140972i	0.908005	−	0.418960i	$-0.137605\pi$
$67$	−0.430384	−	1.15391i	−0.0525798	−	0.140972i	−0.960585	+	0.277988i	$0.910332\pi$
$68$	9.04326	+	9.04326i	1.09666	+	1.09666i
$69$	−3.37274	+	0.759937i	−0.406030	+	0.0914856i
$70$	−0.623425	−	0.442552i	−0.0745136	−	0.0528950i
$71$	−2.54704	+	5.57724i	−0.302278	+	0.661897i	−0.998431	−	0.0559966i	$-0.982166\pi$
$71$	−2.54704	+	5.57724i	−0.302278	+	0.661897i	0.696153	+	0.717894i	$0.254894\pi$
$72$	0.595269	+	1.09015i	0.0701532	+	0.128476i
$73$	−11.4132	−	0.816286i	−1.33581	−	0.0955390i	−0.614920	−	0.788589i	$-0.710812\pi$
$73$	−11.4132	−	0.816286i	−1.33581	−	0.0955390i	−0.720889	+	0.693050i	$0.756266\pi$
$74$	−0.101661	+	0.0653336i	−0.0118179	+	0.00759488i
$75$	−3.30924	+	1.42869i	−0.382118	+	0.164971i
$76$	13.9760	+	2.00944i	1.60316	+	0.230499i
$77$	−1.47439	−	0.805077i	−0.168022	−	0.0917470i
$78$	0.336763	−	0.0732582i	0.0381309	−	0.00829486i
$79$	−0.152203	−	1.05860i	−0.0171242	−	0.119101i	0.979466	−	0.201608i	$-0.0646166\pi$
$79$	−0.152203	−	1.05860i	−0.0171242	−	0.119101i	−0.996591	+	0.0825063i	$0.973708\pi$
$80$	1.64003	−	8.57749i	0.183361	−	0.958993i
$81$	−1.90795	−	4.17782i	−0.211994	−	0.464203i
$82$	−0.716448	+	0.957063i	−0.0791185	+	0.105690i
$83$	−1.28696	−	5.91605i	−0.141262	−	0.649371i	−0.992257	−	0.124198i	$-0.960364\pi$
$83$	−1.28696	−	5.91605i	−0.141262	−	0.649371i	0.850995	−	0.525173i	$-0.175999\pi$
$84$	3.73341	−	1.09623i	0.407349	−	0.119608i
$85$	−0.364285	−	14.4079i	−0.0395123	−	1.56275i
$86$	0.339662	+	0.294319i	0.0366267	+	0.0317372i
$87$	−1.59275	−	0.346482i	−0.170761	−	0.0371468i
$88$	−0.0220620	+	0.308467i	−0.00235181	+	0.0328827i
$89$	6.64802	+	1.95203i	0.704688	+	0.206915i	0.614393	−	0.789000i	$-0.289401\pi$
$89$	6.64802	+	1.95203i	0.704688	+	0.206915i	0.0902949	+	0.995915i	$0.471219\pi$
$90$	0.179427	−	0.673614i	0.0189133	−	0.0710052i
$91$			10.3465i			1.08461i
$92$	−8.62641	+	4.01714i	−0.899365	+	0.418816i
$93$	4.82975	−	4.82975i	0.500821	−	0.500821i
$94$	−0.761367	−	0.347705i	−0.0785290	−	0.0358630i
$95$	−9.85463	−	12.4931i	−1.01106	−	1.28177i
$96$	−0.704560	−	0.813106i	−0.0719089	−	0.0829872i
$97$	1.25467	−	5.76763i	0.127393	−	0.585614i	−0.868548	−	0.495604i	$-0.834947\pi$
$97$	1.25467	−	5.76763i	0.127393	−	0.585614i	0.995941	−	0.0900096i	$-0.0286898\pi$
$98$	−0.00358374	−	0.0501072i	−0.000362012	−	0.00506160i
$99$	0.217985	−	1.51612i	0.0219083	−	0.152376i
$100$	−8.06436	+	5.77862i	−0.806436	+	0.577862i
$101$	−8.38242	−	5.38705i	−0.834082	−	0.536032i	0.0524909	−	0.998621i	$-0.483284\pi$
$101$	−8.38242	−	5.38705i	−0.834082	−	0.536032i	−0.886572	+	0.462590i	$0.846920\pi$
$102$	−0.467536	−	0.349993i	−0.0462929	−	0.0346544i
$103$	1.78320	−	4.78094i	0.175704	−	0.471080i	−0.819008	−	0.573782i	$-0.805476\pi$
$103$	1.78320	−	4.78094i	0.175704	−	0.471080i	0.994712	+	0.102701i	$0.0327486\pi$
$104$	1.73260	−	0.791253i	0.169896	−	0.0775888i
$105$	−3.90045	−	2.00353i	−0.380645	−	0.195524i
$106$	−0.346025	+	0.538425i	−0.0336089	+	0.0522965i
$107$	−0.409157	+	0.749315i	−0.0395547	+	0.0724390i	−0.896709	−	0.442621i	$-0.854049\pi$
$107$	−0.409157	+	0.749315i	−0.0395547	+	0.0724390i	0.857154	+	0.515060i	$0.172230\pi$
$108$	4.69776	+	6.27548i	0.452042	+	0.603858i
$109$	−1.33010	+	1.53502i	−0.127400	+	0.147028i	−0.815866	−	0.578241i	$-0.803739\pi$
$109$	−1.33010	+	1.53502i	−0.127400	+	0.147028i	0.688465	+	0.725269i	$0.258285\pi$
$110$	0.128256	−	0.116939i	0.0122288	−	0.0111497i
$111$	−0.523809	+	0.453883i	−0.0497177	+	0.0430806i
$112$	9.32425	−	5.09143i	0.881059	−	0.481095i
$113$	−12.5513	+	4.68138i	−1.18072	+	0.440387i	−0.861729	−	0.507370i	$-0.830618\pi$
$113$	−12.5513	+	4.68138i	−1.18072	+	0.440387i	−0.318995	+	0.947757i	$0.603345\pi$
$114$	−0.644788			−0.0603899
$115$	10.1648	+	3.41713i	0.947873	+	0.318649i
$116$	−4.48644			−0.416556
$117$	−8.83912	+	3.29682i	−0.817177	+	0.304791i
$118$	0.405553	−	0.221449i	0.0373342	−	0.0203860i
$119$	13.2507	−	11.4818i	1.21469	−	1.05253i
$120$	−0.0372180	+	0.806383i	−0.00339752	+	0.0736123i
$121$	−6.95373	+	8.02503i	−0.632157	+	0.729548i
$122$	−0.236750	−	0.316260i	−0.0214343	−	0.0286329i
$123$	−3.28613	+	6.01810i	−0.296300	+	0.542634i
$124$	10.1639	−	15.8154i	0.912749	−	1.42026i
$125$	11.0735	+	1.54203i	0.990443	+	0.137923i
$126$	0.771406	−	0.352289i	0.0687223	−	0.0313844i
$127$	−6.78488	+	18.1910i	−0.602061	+	1.61419i	0.174863	+	0.984593i	$0.444052\pi$
$127$	−6.78488	+	18.1910i	−0.602061	+	1.61419i	−0.776924	+	0.629594i	$0.783221\pi$
$128$	−3.15659	−	2.36299i	−0.279006	−	0.208861i
$129$	2.16852	+	1.39362i	0.190927	+	0.122702i
$130$	−1.01072	−	0.348141i	−0.0886460	−	0.0305340i
$131$	1.49196	−	10.3768i	0.130353	−	0.906627i	−0.814740	−	0.579826i	$-0.803120\pi$
$131$	1.49196	−	10.3768i	0.130353	−	0.906627i	0.945093	−	0.326801i	$-0.105971\pi$
$132$	0.0630167	+	0.881089i	0.00548490	+	0.0766889i
$133$	4.11470	−	18.9150i	0.356790	−	1.64014i
$134$	0.101370	+	0.116987i	0.00875700	+	0.0101061i
$135$	1.03581	−	8.77316i	0.0891480	−	0.755074i
$136$	−2.93607	−	1.34086i	−0.251766	−	0.114978i
$137$	−8.66517	+	8.66517i	−0.740315	+	0.740315i	−0.972639	−	0.232324i	$-0.925367\pi$
$137$	−8.66517	+	8.66517i	−0.740315	+	0.740315i	0.232324	+	0.972639i	$0.425367\pi$
$138$	0.363815	−	0.237641i	0.0309700	−	0.0202294i
$139$		−	4.26863i		−	0.362060i	−0.983478	−	0.181030i	$-0.942057\pi$
$139$		−	4.26863i		−	0.362060i	0.983478	−	0.181030i	$-0.0579432\pi$
$140$	−11.6625	−	3.10649i	−0.985663	−	0.262546i
$141$	−4.60614	−	1.35248i	−0.387907	−	0.113900i
$142$	0.0549778	−	0.768690i	0.00461363	−	0.0645070i
$143$	−2.29518	−	0.499286i	−0.191933	−	0.0417524i
$144$	7.32076	+	6.34347i	0.610063	+	0.528623i
$145$	3.66431	+	3.48358i	0.304304	+	0.289296i
$146$	1.37994	−	0.405188i	0.114205	−	0.0335336i
$147$	−0.0612446	−	0.281537i	−0.00505137	−	0.0232208i
$148$	−1.14324	+	1.52719i	−0.0939736	+	0.125534i
$149$	0.558230	+	1.22235i	0.0457320	+	0.100139i	0.931119	−	0.364716i	$-0.118834\pi$
$149$	0.558230	+	1.22235i	0.0457320	+	0.100139i	−0.885387	+	0.464855i	$0.846107\pi$
$150$	0.326963	−	0.313609i	0.0266964	−	0.0256061i
$151$	0.709389	+	4.93391i	0.0577293	+	0.401516i	0.998113	+	0.0614010i	$0.0195569\pi$
$151$	0.709389	+	4.93391i	0.0577293	+	0.401516i	−0.940384	+	0.340115i	$0.889534\pi$
$152$	−3.48214	+	0.757493i	−0.282439	+	0.0614408i
$153$	14.0312	+	7.66163i	1.13436	+	0.619406i
$154$	0.208996	+	0.0300491i	0.0168414	+	0.00242142i
$155$	−20.5816	+	5.02526i	−1.65315	+	0.403639i
$156$	4.57690	−	2.94140i	0.366445	−	0.235500i
$157$	18.0453	+	1.29062i	1.44017	+	0.103003i	0.769449	−	0.638708i	$-0.220531\pi$
$157$	18.0453	+	1.29062i	1.44017	+	0.103003i	0.670720	+	0.741711i	$0.265985\pi$
$158$	0.0644229	+	0.117982i	0.00512521	+	0.00938612i
$159$	−1.52492	+	3.33911i	−0.120934	+	0.264809i
$160$	0.558273	+	3.29017i	0.0441353	+	0.260111i
$161$	4.64957	+	12.1891i	0.366437	+	0.960635i
$162$	0.408201	+	0.408201i	0.0320713	+	0.0320713i
$163$	−1.14640	−	3.07362i	−0.0897929	−	0.240744i	0.884289	−	0.466940i	$-0.154644\pi$
$163$	−1.14640	−	3.07362i	−0.0897929	−	0.240744i	−0.974082	+	0.226196i	$0.927371\pi$
$164$	−5.31710	+	18.1084i	−0.415196	+	1.41403i
$165$	0.632668	−	0.768560i	0.0492532	−	0.0598323i
$166$	0.411421	+	0.640183i	0.0319324	+	0.0496879i
$167$	0.421174	−	0.0301230i	0.0325914	−	0.00233098i	−0.0550340	−	0.998484i	$-0.517527\pi$
$167$	0.421174	−	0.0301230i	0.0325914	−	0.00233098i	0.0876254	+	0.996153i	$0.472072\pi$
$168$	−0.786155	+	0.588508i	−0.0606532	+	0.0454044i
$169$	0.413258	+	1.40743i	0.0317891	+	0.108264i
$170$	0.675761	+	1.68076i	0.0518285	+	0.128909i
$171$	17.4704	−	2.51186i	1.33599	−	0.192087i
$172$	6.64762	+	2.47944i	0.506877	+	0.189055i
$173$	3.06702	+	1.14394i	0.233181	+	0.0869721i	0.463339	−	0.886181i	$-0.346651\pi$
$173$	3.06702	+	1.14394i	0.233181	+	0.0869721i	−0.230157	+	0.973153i	$0.573924\pi$
$174$	0.202792	−	0.0291570i	0.0153736	−	0.00221039i
$175$	7.11328	+	11.5928i	0.537713	+	0.876333i
$176$	0.679484	+	2.31411i	0.0512180	+	0.174433i
$177$	2.12160	−	1.58821i	0.159469	−	0.119377i
$178$	−0.868655	+	0.0621274i	−0.0651084	+	0.00465665i
$179$	−2.93098	−	4.56070i	−0.219072	−	0.340882i	0.714271	−	0.699870i	$-0.246759\pi$
$179$	−2.93098	−	4.56070i	−0.219072	−	0.340882i	−0.933342	+	0.358987i	$0.883122\pi$
$180$	−1.06225	−	10.9533i	−0.0791758	−	0.816409i
$181$	−6.16927	+	21.0106i	−0.458558	+	1.56171i	0.328300	+	0.944573i	$0.393524\pi$
$181$	−6.16927	+	21.0106i	−0.458558	+	1.56171i	−0.786859	+	0.617133i	$0.788294\pi$
$182$	−0.454465	−	1.21847i	−0.0336872	−	0.0903189i
$183$	−1.60219	−	1.60219i	−0.118437	−	0.118437i
$184$	1.68558	−	1.71077i	0.124263	−	0.126120i
$185$	2.11955	−	0.359643i	0.155833	−	0.0264415i
$186$	−0.356637	+	0.780926i	−0.0261499	+	0.0572603i
$187$	1.90759	+	3.49349i	0.139497	+	0.255469i
$188$	−13.1796	−	0.942621i	−0.961218	−	0.0687477i
$189$	9.04087	−	5.81021i	0.657627	−	0.422631i
$190$	1.70930	+	1.03841i	0.124006	+	0.0753341i
$191$	7.40450	+	1.06461i	0.535771	+	0.0770322i	0.404889	−	0.914366i	$-0.367310\pi$
$191$	7.40450	+	1.06461i	0.535771	+	0.0770322i	0.130882	+	0.991398i	$0.458219\pi$
$192$	−4.82339	−	2.63377i	−0.348098	−	0.190076i
$193$	−16.3194	+	3.55008i	−1.17470	+	0.255540i	−0.757228	−	0.653150i	$-0.773447\pi$
$193$	−16.3194	+	3.55008i	−1.17470	+	0.255540i	−0.417471	+	0.908690i	$0.637083\pi$
$194$	0.105583	+	0.734344i	0.00758039	+	0.0527228i
$195$	−6.02209	−	1.15143i	−0.431251	−	0.0824557i
$196$	−0.329436	−	0.721365i	−0.0235312	−	0.0515261i
$197$	12.0960	−	16.1584i	0.861806	−	1.15124i	−0.125450	−	0.992100i	$-0.540037\pi$
$197$	12.0960	−	16.1584i	0.861806	−	1.15124i	0.987256	−	0.159138i	$-0.0508716\pi$
$198$	0.0409236	+	0.188123i	0.00290831	+	0.0133693i
$199$	−19.0873	+	5.60453i	−1.35306	+	0.397295i	−0.876312	−	0.481744i	$-0.840004\pi$
$199$	−19.0873	+	5.60453i	−1.35306	+	0.397295i	−0.476750	+	0.879039i	$0.658185\pi$
$200$	1.39732	−	2.07774i	0.0988051	−	0.146918i
$201$	0.670971	+	0.581400i	0.0473267	+	0.0410088i
$202$	1.22379	+	0.266219i	0.0861056	+	0.0187311i
$203$	−0.438784	+	6.13500i	−0.0307966	+	0.430593i
$204$	−8.84613	−	2.59746i	−0.619353	−	0.181859i
$205$	18.4033	−	10.6615i	1.28534	−	0.744629i
$206$			0.641361i			0.0446857i
$207$	−8.93173	+	7.85613i	−0.620798	+	0.546039i
$208$	10.5037	−	10.5037i	0.728304	−	0.728304i
$209$	3.99738	+	1.82554i	0.276504	+	0.126275i
$210$	0.547346	+	0.0646226i	0.0377705	+	0.00445939i
$211$	−4.31657	−	4.98159i	−0.297165	−	0.342947i	0.587457	−	0.809255i	$-0.300129\pi$
$211$	−4.31657	−	4.98159i	−0.297165	−	0.342947i	−0.884622	+	0.466309i	$0.845584\pi$
$212$	−2.14769	+	9.87277i	−0.147504	+	0.678065i
$213$	−0.315322	−	4.40878i	−0.0216055	−	0.302084i
$214$	0.0152716	−	0.106216i	0.00104394	−	0.00726078i
$215$	−3.50425	−	7.18675i	−0.238988	−	0.490132i
$216$	−1.66437	−	1.06963i	−0.113246	−	0.0727789i
$217$	−20.6328	−	15.4455i	−1.40064	−	1.04851i
$218$	0.0892160	−	0.239197i	0.00604247	−	0.0162005i
$219$	7.50329	−	3.42664i	0.507025	−	0.231551i
$220$	1.25191	−	2.43721i	0.0844038	−	0.164316i
$221$	13.2541	−	20.6238i	0.891566	−	1.38730i
$222$	0.0417504	−	0.0764602i	0.00280211	−	0.00513167i
$223$	4.52229	+	6.04107i	0.302835	+	0.404540i	0.925984	−	0.377563i	$-0.123238\pi$
$223$	4.52229	+	6.04107i	0.302835	+	0.404540i	−0.623149	+	0.782103i	$0.714147\pi$
$224$	−2.65860	+	3.06818i	−0.177635	+	0.205002i
$225$	−7.63727	+	9.77090i	−0.509152	+	0.651394i
$226$	1.27249	−	1.10262i	0.0846447	−	0.0733450i
$227$	8.01834	−	4.37834i	0.532196	−	0.290601i	−0.190594	−	0.981669i	$-0.561041\pi$
$227$	8.01834	−	4.37834i	0.532196	−	0.290601i	0.722790	+	0.691068i	$0.242860\pi$
$228$	−9.53704	+	3.55713i	−0.631606	+	0.235577i
$229$	3.47411			0.229576			0.114788	−	0.993390i	$-0.463381\pi$
$229$	3.47411			0.229576			0.114788	+	0.993390i	$0.463381\pi$
$230$	−1.34717	+	0.0440620i	−0.0888296	+	0.00290536i
$231$	1.21101			0.0796787
$232$	1.06091	−	0.395699i	0.0696522	−	0.0259789i
$233$	2.83654	−	1.54887i	0.185828	−	0.101470i	−0.383642	−	0.923482i	$-0.625330\pi$
$233$	2.83654	−	1.54887i	0.185828	−	0.101470i	0.569470	+	0.822012i	$0.307149\pi$
$234$	0.896140	−	0.776510i	0.0585825	−	0.0507620i
$235$	10.0325	+	11.0034i	0.654448	+	0.717782i
$236$	4.77685	−	5.51278i	0.310947	−	0.358852i
$237$	0.462034	+	0.617205i	0.0300123	+	0.0400918i
$238$	−1.05615	+	1.93420i	−0.0684602	+	0.125375i
$239$	−5.95060	+	9.25931i	−0.384912	+	0.598935i	−0.978603	−	0.205758i	$-0.934034\pi$
$239$	−5.95060	+	9.25931i	−0.384912	+	0.598935i	0.593691	+	0.804693i	$0.297670\pi$
$240$	1.92575	+	5.99371i	0.124307	+	0.386893i
$241$	−13.0609	+	5.96471i	−0.841326	+	0.384221i	−0.788988	−	0.614409i	$-0.789395\pi$
$241$	−13.0609	+	5.96471i	−0.841326	+	0.384221i	−0.0523383	+	0.998629i	$0.516667\pi$
$242$	0.466419	−	1.25052i	0.0299826	−	0.0803864i
$243$	12.1387	+	9.08694i	0.778700	+	0.582928i
$244$	−5.24649	−	3.37171i	−0.335872	−	0.215852i
$245$	−0.291049	+	0.844972i	−0.0185945	+	0.0539833i
$246$	0.122653	−	0.853072i	0.00782008	−	0.0543899i
$247$	−1.93088	−	26.9972i	−0.122859	−	1.71779i
$248$	−1.00857	+	4.63632i	−0.0640443	+	0.294407i
$249$	2.85820	+	3.29854i	0.181131	+	0.209037i
$250$	−1.37182	+	0.304799i	−0.0867614	+	0.0192772i
$251$	−19.2350	−	8.78434i	−1.21410	−	0.554462i	−0.297677	−	0.954667i	$-0.596212\pi$
$251$	−19.2350	−	8.78434i	−1.21410	−	0.554462i	−0.916426	+	0.400204i	$0.868939\pi$
$252$	9.46636	−	9.46636i	0.596325	−	0.596325i
$253$	−2.92830	+	0.443218i	−0.184101	+	0.0278649i
$254$		−	2.44031i		−	0.153118i
$255$	5.20824	+	8.99022i	0.326153	+	0.562989i
$256$	−14.1535	−	4.15585i	−0.884596	−	0.259741i
$257$	−0.834999	+	11.6748i	−0.0520858	+	0.728254i	0.902570	+	0.430543i	$0.141678\pi$
$257$	−0.834999	+	11.6748i	−0.0520858	+	0.728254i	−0.954656	+	0.297711i	$0.903777\pi$
$258$	−0.316593	−	0.0688706i	−0.0197102	−	0.00428770i
$259$	1.97655	+	1.71269i	0.122817	+	0.106421i
$260$	−16.8702	+	0.426540i	−1.04624	+	0.0264529i
$261$	−5.38101	+	1.58001i	−0.333076	+	0.0978001i
$262$	0.280095	+	1.28757i	0.0173043	+	0.0795466i
$263$	0.220835	−	0.295001i	0.0136173	−	0.0181905i	−0.793681	−	0.608334i	$-0.791838\pi$
$263$	0.220835	−	0.295001i	0.0136173	−	0.0181905i	0.807298	+	0.590144i	$0.200929\pi$
$264$	−0.0926127	−	0.202793i	−0.00569992	−	0.0124811i
$265$	9.42002	−	6.39598i	0.578667	−	0.392902i
$266$	0.346259	+	2.40828i	0.0212305	+	0.147661i
$267$	−4.88070	+	1.06173i	−0.298694	+	0.0649769i
$268$	2.14474	+	1.17112i	0.131011	+	0.0715375i
$269$	−22.9526	−	3.30008i	−1.39944	−	0.201209i	−0.599062	−	0.800702i	$-0.704460\pi$
$269$	−22.9526	−	3.30008i	−1.39944	−	0.201209i	−0.800380	+	0.599493i	$0.795369\pi$
$270$	0.263374	+	1.07868i	0.0160285	+	0.0656464i
$271$	6.68378	−	4.29541i	0.406011	−	0.260927i	−0.321658	−	0.946856i	$-0.604240\pi$
$271$	6.68378	−	4.29541i	0.406011	−	0.260927i	0.727669	+	0.685929i	$0.240604\pi$
$272$	−25.1084	−	1.79578i	−1.52242	−	0.108885i
$273$	−3.57459	−	6.54637i	−0.216344	−	0.396205i
$274$	0.639851	−	1.40108i	0.0386548	−	0.0846423i
$275$	−2.91491	+	1.01852i	−0.175776	+	0.0614192i
$276$	4.07018	−	5.52202i	0.244996	−	0.332387i
$277$	3.49088	+	3.49088i	0.209747	+	0.209747i	0.804160	−	0.594413i	$-0.202616\pi$
$277$	3.49088	+	3.49088i	0.209747	+	0.209747i	−0.594413	+	0.804160i	$0.702616\pi$
$278$	0.187498	+	0.502701i	0.0112454	+	0.0301500i
$279$	6.62080	−	22.5484i	0.396377	−	1.34994i
$280$	3.03183	−	0.294028i	0.181186	−	0.0175716i
$281$	−8.76040	−	13.6314i	−0.522601	−	0.813184i	0.475171	−	0.879894i	$-0.342386\pi$
$281$	−8.76040	−	13.6314i	−0.522601	−	0.813184i	−0.997772	+	0.0667097i	$0.978750\pi$
$282$	0.601855	−	0.0430456i	0.0358400	−	0.00256333i
$283$	21.5316	−	16.1184i	1.27992	−	0.958138i	0.279925	−	0.960022i	$-0.409691\pi$
$283$	21.5316	−	16.1184i	1.27992	−	0.958138i	0.999998	+	0.00188372i	$0.000599606\pi$
$284$	−3.42749	−	11.6730i	−0.203384	−	0.692664i
$285$	10.5514	+	4.49992i	0.625010	+	0.266552i
$286$	0.292226	−	0.0420157i	0.0172797	−	0.00248444i
$287$	24.2423	+	9.04192i	1.43098	+	0.533728i
$288$	−3.46832	−	1.29362i	−0.204373	−	0.0762271i
$289$	−24.2941	+	3.49297i	−1.42907	+	0.205469i
$290$	−0.584547	−	0.249295i	−0.0343258	−	0.0146391i
$291$	1.19880	+	4.08274i	0.0702749	+	0.239334i
$292$	18.1754	−	13.6059i	1.06363	−	0.796226i
$293$	26.8751	−	1.92215i	1.57006	−	0.112293i	0.741021	−	0.671482i	$-0.234342\pi$
$293$	26.8751	−	1.92215i	1.57006	−	0.112293i	0.829040	+	0.559189i	$0.188887\pi$
$294$	0.0195789	+	0.0304654i	0.00114187	+	0.00177678i
$295$	−8.18200	+	0.793494i	−0.476374	+	0.0461990i
$296$	0.135646	−	0.461967i	0.00788425	−	0.0268513i
$297$	0.852609	+	2.28593i	0.0494734	+	0.132643i
$298$	−0.119432	−	0.119432i	−0.00691851	−	0.00691851i
$299$	11.0395	+	14.5213i	0.638430	+	0.839786i
$300$	3.10599	−	6.44236i	0.179325	−	0.371950i
$301$	4.04066	−	8.84782i	0.232900	−	0.509980i
$302$	−0.300262	−	0.549889i	−0.0172781	−	0.0316426i
$303$	7.16484	+	0.512439i	0.411609	+	0.0294389i
$304$	−23.3797	+	15.0252i	−1.34092	+	0.861755i
$305$	1.66705	+	6.82758i	0.0954547	+	0.390946i
$306$	−1.98894	−	0.285967i	−0.113700	−	0.0163476i
$307$	13.0399	+	7.12032i	0.744226	+	0.406378i	0.806156	−	0.591703i	$-0.201544\pi$
$307$	13.0399	+	7.12032i	0.744226	+	0.406378i	−0.0619308	+	0.998080i	$0.519726\pi$
$308$	3.25703	−	0.708524i	0.185587	−	0.0403719i
$309$	0.523503	+	3.64105i	0.0297811	+	0.207132i
$310$	2.20308	−	1.49584i	0.125127	−	0.0849582i
$311$	−6.00521	−	13.1496i	−0.340524	−	0.745643i	0.659457	−	0.751742i	$-0.270786\pi$
$311$	−6.00521	−	13.1496i	−0.340524	−	0.745643i	−0.999981	+	0.00609842i	$0.998059\pi$
$312$	−0.822874	+	1.09923i	−0.0465861	+	0.0622317i
$313$	3.71571	+	17.0808i	0.210024	+	0.965466i	0.954591	+	0.297919i	$0.0962924\pi$
$313$	3.71571	+	17.0808i	0.210024	+	0.965466i	−0.744567	+	0.667548i	$0.767344\pi$
$314$	−2.18182	+	0.640639i	−0.123127	+	0.0361533i
$315$	−15.0820	+	0.381329i	−0.849774	+	0.0214855i
$316$	1.60375	+	1.38966i	0.0902182	+	0.0781745i
$317$	−26.5519	−	5.77602i	−1.49130	−	0.324413i	−0.608273	−	0.793728i	$-0.708138\pi$
$317$	−26.5519	−	5.77602i	−1.49130	−	0.324413i	−0.883031	+	0.469314i	$0.844501\pi$
$318$	0.0329154	−	0.460217i	0.00184580	−	0.0258077i
$319$	−1.33976	−	0.393390i	−0.0750123	−	0.0220256i
$320$	8.54496	+	14.7499i	0.477678	+	0.824545i
$321$		−	0.615461i		−	0.0343517i
$322$	−1.08296	−	1.23123i	−0.0603512	−	0.0686140i
$323$	−32.4324	+	32.4324i	−1.80459	+	1.80459i
$324$	8.28964	+	3.78575i	0.460536	+	0.210320i
$325$	14.1099	+	12.7508i	0.782677	+	0.707285i
$326$	0.270015	+	0.311614i	0.0149547	+	0.0172587i
$327$	0.311243	−	1.43076i	0.0172118	−	0.0791212i
$328$	−0.339802	−	4.75106i	−0.0187624	−	0.262333i
$329$	−2.57798	+	17.9302i	−0.142129	+	0.988526i
$330$	−0.0407484	+	0.118300i	−0.00224312	+	0.00651222i
$331$	20.5708	+	13.2200i	1.13067	+	0.726638i	0.965700	−	0.259660i	$-0.0836107\pi$
$331$	20.5708	+	13.2200i	1.13067	+	0.726638i	0.164971	+	0.986298i	$0.447247\pi$
$332$	9.61705	+	7.19923i	0.527804	+	0.395109i
$333$	−0.833358	+	2.23432i	−0.0456677	+	0.122440i
$334$	−0.0482770	+	0.0220474i	−0.00264160	+	0.00120638i
$335$	−0.842385	−	2.62184i	−0.0460244	−	0.143246i
$336$	−4.14056	+	6.44284i	−0.225886	+	0.351486i
$337$	4.46310	−	8.17356i	0.243121	−	0.445242i	−0.727416	−	0.686197i	$-0.759279\pi$
$337$	4.46310	−	8.17356i	0.243121	−	0.445242i	0.970536	+	0.240955i	$0.0774606\pi$
$338$	−0.110489	−	0.147595i	−0.00600979	−	0.00802814i
$339$	6.32400	−	7.29829i	0.343473	−	0.396388i
$340$	19.2675	+	21.1321i	1.04493	+	1.14605i
$341$	4.42196	−	3.83165i	0.239463	−	0.207496i
$342$	−1.94709	+	1.06319i	−0.105287	+	0.0574909i
$343$	16.8224	−	6.27443i	0.908324	−	0.338787i
$344$	−1.79065			−0.0965454
$345$	−7.61199	+	1.34975i	−0.409816	+	0.0726683i
$346$	−0.411439			−0.0221191
$347$	15.8844	−	5.92458i	0.852720	−	0.318048i	0.115174	−	0.993345i	$-0.463257\pi$
$347$	15.8844	−	5.92458i	0.852720	−	0.318048i	0.737546	+	0.675297i	$0.235985\pi$
$348$	2.83864	−	1.55001i	0.152167	−	0.0830894i
$349$	−11.1268	+	9.64143i	−0.595604	+	0.516094i	−0.899678	−	0.436554i	$-0.856199\pi$
$349$	−11.1268	+	9.64143i	−0.595604	+	0.516094i	0.304073	+	0.952649i	$0.401653\pi$
$350$	−1.34691	−	1.05279i	−0.0719956	−	0.0562742i
$351$	9.84041	−	11.3564i	0.525242	−	0.606162i
$352$	−0.552325	−	0.737820i	−0.0294390	−	0.0393260i
$353$	2.00832	−	3.67796i	0.106892	−	0.195758i	−0.818758	−	0.574138i	$-0.805337\pi$
$353$	2.00832	−	3.67796i	0.106892	−	0.195758i	0.925650	+	0.378381i	$0.123519\pi$
$354$	−0.180091	+	0.280228i	−0.00957175	+	0.0148939i
$355$	−6.26428	+	12.1953i	−0.332474	+	0.647257i
$356$	−12.5055	+	5.71108i	−0.662791	+	0.302687i
$357$	−4.41708	+	11.8426i	−0.233776	+	0.626779i
$358$	0.545498	+	0.408354i	0.0288304	+	0.0215822i
$359$	−8.79431	−	5.65176i	−0.464146	−	0.298288i	0.287589	−	0.957754i	$-0.407146\pi$
$359$	−8.79431	−	5.65176i	−0.464146	−	0.298288i	−0.751735	+	0.659466i	$0.770783\pi$
$360$	1.21726	+	2.49644i	0.0641552	+	0.131574i
$361$	−4.50261	+	31.3163i	−0.236979	+	1.64823i
$362$	−0.196350	−	2.74533i	−0.0103199	−	0.144291i
$363$	1.62717	−	7.47998i	0.0854043	−	0.392597i
$364$	−13.4440	−	15.5152i	−0.704656	−	0.813217i
$365$	−25.4093	−	2.99996i	−1.32998	−	0.157025i
$366$	0.259059	+	0.118308i	0.0135412	+	0.00618408i
$367$	15.6615	−	15.6615i	0.817525	−	0.817525i	−0.168224	−	0.985749i	$-0.553803\pi$
$367$	15.6615	−	15.6615i	0.817525	−	0.817525i	0.985749	+	0.168224i	$0.0538031\pi$
$368$	7.65411	−	17.0946i	0.398998	−	0.891117i
$369$			23.5916i			1.22813i
$370$	−0.233815	+	0.135454i	−0.0121555	+	0.00704194i
$371$	13.2905	+	3.90244i	0.690008	+	0.202605i
$372$	−0.966837	+	13.5181i	−0.0501282	+	0.700883i
$373$	−1.42452	−	0.309885i	−0.0737586	−	0.0160452i	0.175535	−	0.984473i	$-0.443835\pi$
$373$	−1.42452	−	0.309885i	−0.0737586	−	0.0160452i	−0.249293	+	0.968428i	$0.580198\pi$
$374$	−0.378100	−	0.327626i	−0.0195511	−	0.0169411i
$375$	−7.53911	+	2.85009i	−0.389318	+	0.147178i
$376$	3.19972	−	0.939521i	0.165013	−	0.0484521i
$377$	1.82808	+	8.40356i	0.0941510	+	0.432805i
$378$	−0.809499	+	1.08136i	−0.0416362	+	0.0556194i
$379$	−5.48223	−	12.0044i	−0.281603	−	0.616625i	0.714987	−	0.699138i	$-0.246433\pi$
$379$	−5.48223	−	12.0044i	−0.281603	−	0.616625i	−0.996590	+	0.0825130i	$0.973705\pi$
$380$	31.0109	+	5.92932i	1.59082	+	0.304168i
$381$	−1.99187	−	13.8538i	−0.102047	−	0.709751i
$382$	−0.918763	+	0.199865i	−0.0470080	+	0.0102260i
$383$	−6.72004	−	3.66942i	−0.343378	−	0.187499i	0.298301	−	0.954472i	$-0.403580\pi$
$383$	−6.72004	−	3.66942i	−0.343378	−	0.187499i	−0.641679	+	0.766973i	$0.721762\pi$
$384$	2.81360	+	0.404535i	0.143581	+	0.0206439i
$385$	−3.21033	−	1.95029i	−0.163613	−	0.0993961i
$386$	1.76595	−	1.13490i	0.0898843	−	0.0577651i
$387$	8.84632	+	0.632701i	0.449684	+	0.0321620i
$388$	5.61286	+	10.2792i	0.284950	+	0.521847i
$389$	9.55541	−	20.9234i	0.484478	−	1.06086i	−0.496729	−	0.867905i	$-0.665466\pi$
$389$	9.55541	−	20.9234i	0.484478	−	1.06086i	0.981208	−	0.192954i	$-0.0618069\pi$
$390$	0.759776	−	0.128918i	0.0384727	−	0.00652801i
$391$	6.34647	−	30.2528i	0.320955	−	1.52995i
$392$	0.141526	+	0.141526i	0.00714812	+	0.00714812i
$393$	2.64108	+	7.08102i	0.133225	+	0.357190i
$394$	−0.714754	+	2.43423i	−0.0360088	+	0.122635i
$395$	−0.230840	−	2.38027i	−0.0116148	−	0.119764i
$396$	1.64312	+	2.55675i	0.0825701	+	0.128482i
$397$	−31.3625	+	2.24309i	−1.57404	+	0.112578i	−0.830847	−	0.556500i	$-0.812144\pi$
$397$	−31.3625	+	2.24309i	−1.57404	+	0.112578i	−0.743192	+	0.669078i	$0.766689\pi$
$398$	2.00166	−	1.49843i	0.100334	−	0.0751094i
$399$	3.93147	+	13.3894i	0.196820	+	0.670306i
$400$	4.54760	−	18.9904i	0.227380	−	0.949519i
$401$	−25.0184	+	3.59711i	−1.24936	+	0.179631i	−0.735074	−	0.677987i	$-0.762852\pi$
$401$	−25.0184	+	3.59711i	−1.24936	+	0.179631i	−0.514287	+	0.857618i	$0.671943\pi$
$402$	−0.104556	−	0.0389972i	−0.00521476	−	0.00194500i
$403$	−33.7653	−	12.5938i	−1.68197	−	0.627342i
$404$	19.5697	−	2.81370i	0.973631	−	0.139987i
$405$	−3.83105	−	9.52866i	−0.190367	−	0.473483i
$406$	−0.217803	−	0.741770i	−0.0108094	−	0.0368134i
$407$	−0.475309	+	0.355812i	−0.0235602	+	0.0176369i
$408$	2.32094	−	0.165997i	0.114904	−	0.00821808i
$409$	8.01231	+	12.4674i	0.396183	+	0.616473i	0.980842	−	0.194807i	$-0.0624079\pi$
$409$	8.01231	+	12.4674i	0.396183	+	0.616473i	−0.584659	+	0.811279i	$0.698772\pi$
$410$	−1.69899	+	2.06392i	−0.0839072	+	0.101930i
$411$	2.48886	−	8.47629i	0.122767	−	0.418104i
$412$	3.53823	+	9.48636i	0.174316	+	0.467359i
$413$	−7.07129	−	7.07129i	−0.347955	−	0.347955i
$414$	0.706780	−	1.31751i	0.0347364	−	0.0647521i
$415$	−2.26476	−	13.3473i	−0.111173	−	0.655194i
$416$	−2.35812	+	5.16357i	−0.115616	+	0.253165i
$417$	1.47476	+	2.70082i	0.0722193	+	0.132260i
$418$	−0.550943	−	0.0394042i	−0.0269475	−	0.00192732i
$419$	30.0434	−	19.3077i	1.46772	−	0.943245i	0.469540	−	0.882911i	$-0.344420\pi$
$419$	30.0434	−	19.3077i	1.46772	−	0.943245i	0.998178	−	0.0603340i	$-0.0192166\pi$
$420$	8.45230	−	2.06374i	0.412430	−	0.100700i
$421$	−24.3888	−	3.50658i	−1.18864	−	0.170900i	−0.480513	−	0.876988i	$-0.659549\pi$
$421$	−24.3888	−	3.50658i	−1.18864	−	0.170900i	−0.708124	+	0.706088i	$0.750458\pi$
$422$	0.727161	+	0.397060i	0.0353977	+	0.0193286i
$423$	−16.1395	+	3.51092i	−0.784727	+	0.170707i
$424$	−0.362902	−	2.52404i	−0.0176241	−	0.122578i
$425$	0.671669	−	32.2203i	0.0325807	−	1.56291i
$426$	0.230788	+	0.505355i	0.0111817	+	0.0244845i
$427$	−5.12378	+	6.84457i	−0.247957	+	0.331232i
$428$	−0.360086	−	1.65529i	−0.0174054	−	0.0800115i
$429$	1.62469	−	0.477052i	0.0784408	−	0.0230323i
$430$	0.728358	+	0.692435i	0.0351245	+	0.0333922i
$431$	28.4348	+	24.6389i	1.36966	+	1.18681i	0.961795	+	0.273771i	$0.0882710\pi$
$431$	28.4348	+	24.6389i	1.36966	+	1.18681i	0.407862	+	0.913044i	$0.366274\pi$
$432$	−15.0768	−	3.27976i	−0.725383	−	0.157797i
$433$	−1.50680	+	21.0679i	−0.0724124	+	1.01246i	0.823237	+	0.567698i	$0.192166\pi$
$433$	−1.50680	+	21.0679i	−0.0724124	+	1.01246i	−0.895650	+	0.444760i	$0.853289\pi$
$434$	3.10828	+	0.912674i	0.149202	+	0.0438098i
$435$	−3.52199	−	0.938137i	−0.168867	−	0.0449802i
$436$		−	4.03015i		−	0.193009i
$437$	−14.4069	−	30.9374i	−0.689176	−	1.47994i
$438$	−0.733122	+	0.733122i	−0.0350299	+	0.0350299i
$439$	−4.45739	−	2.03562i	−0.212740	−	0.0971549i	0.306195	−	0.951969i	$-0.400944\pi$
$439$	−4.45739	−	2.03562i	−0.212740	−	0.0971549i	−0.518935	+	0.854814i	$0.673671\pi$
$440$	−0.0810807	+	0.686745i	−0.00386537	+	0.0327393i
$441$	−0.649170	−	0.749182i	−0.0309129	−	0.0356753i
$442$	−0.654995	+	3.01097i	−0.0311550	+	0.143217i
$443$	−0.522882	−	7.31085i	−0.0248429	−	0.347349i	−0.994637	−	0.103425i	$-0.967020\pi$
$443$	−0.522882	−	7.31085i	−0.0248429	−	0.347349i	0.969794	−	0.243924i	$-0.0784347\pi$
$444$	0.195718	−	1.36125i	0.00928836	−	0.0646020i
$445$	14.6484	+	5.04561i	0.694399	+	0.239185i
$446$	−0.797925	−	0.512795i	−0.0377829	−	0.0242816i
$447$	−0.775508	−	0.580538i	−0.0366803	−	0.0274585i
$448$	−7.24693	+	19.4298i	−0.342385	+	0.917970i
$449$	−9.25366	+	4.22600i	−0.436707	+	0.199438i	−0.621623	−	0.783317i	$-0.713526\pi$
$449$	−9.25366	+	4.22600i	−0.436707	+	0.199438i	0.184915	+	0.982754i	$0.440799\pi$
$450$	0.470231	−	1.48615i	0.0221669	−	0.0700577i
$451$	−3.17563	+	4.94138i	−0.149535	+	0.232681i
$452$	12.7385	−	23.3288i	0.599168	−	1.09729i
$453$	−2.15345	−	2.87667i	−0.101178	−	0.135158i
$454$	−0.751974	+	0.867824i	−0.0352919	+	0.0407290i
$455$	−1.06666	+	23.1109i	−0.0500060	+	1.08345i
$456$	1.94149	−	1.68231i	0.0909188	−	0.0787816i
$457$	9.62320	−	5.25466i	0.450154	−	0.245803i	−0.238145	−	0.971230i	$-0.576539\pi$
$457$	9.62320	−	5.25466i	0.450154	−	0.245803i	0.688299	+	0.725427i	$0.258358\pi$
$458$	−0.409134	+	0.152599i	−0.0191176	+	0.00713048i
$459$	−25.4643			−1.18857
$460$	−19.6829	+	8.08371i	−0.917718	+	0.376905i
$461$	11.8245			0.550721			0.275360	−	0.961341i	$-0.411203\pi$
$461$	11.8245			0.550721			0.275360	+	0.961341i	$0.411203\pi$
$462$	−0.142616	+	0.0531932i	−0.00663511	+	0.00247477i
$463$	−13.2872	+	7.25535i	−0.617508	+	0.337185i	−0.757370	−	0.652986i	$-0.773516\pi$
$463$	−13.2872	+	7.25535i	−0.617508	+	0.337185i	0.139862	+	0.990171i	$0.455334\pi$
$464$	6.67370	−	5.78279i	0.309819	−	0.268459i
$465$	11.2861	−	10.2902i	0.523379	−	0.477198i
$466$	−0.266015	+	0.306998i	−0.0123229	+	0.0142214i
$467$	−14.6417	−	19.5591i	−0.677539	−	0.905087i	0.321587	−	0.946880i	$-0.395784\pi$
$467$	−14.6417	−	19.5591i	−0.677539	−	0.905087i	−0.999126	+	0.0417935i	$0.986693\pi$
$468$	8.97098	−	16.4291i	0.414684	−	0.759437i
$469$	1.81121	−	2.81830i	0.0836339	−	0.130137i
$470$	−1.66481	−	0.855157i	−0.0767920	−	0.0394454i
$471$	−11.8634	+	5.41783i	−0.546636	+	0.249640i
$472$	−0.643363	+	1.72492i	−0.0296132	+	0.0793960i
$473$	1.76774	+	1.32331i	0.0812807	+	0.0608460i
$474$	−0.0815226	−	0.0523914i	−0.00374445	−	0.00240642i
$475$	−20.7242	−	28.9217i	−0.950892	−	1.32702i
$476$	−4.95104	+	34.4352i	−0.226930	+	1.57834i
$477$	0.901006	+	12.5977i	0.0412542	+	0.576809i
$478$	0.294069	−	1.35181i	0.0134504	−	0.0618305i
$479$	13.4018	+	15.4665i	0.612344	+	0.706683i	0.974234	−	0.225538i	$-0.0724140\pi$
$479$	13.4018	+	15.4665i	0.612344	+	0.706683i	−0.361890	+	0.932221i	$0.617869\pi$
$480$	−1.48994	−	1.88886i	−0.0680063	−	0.0862144i
$481$	3.32641	+	1.51912i	0.151671	+	0.0692659i
$482$	1.27614	−	1.27614i	0.0581265	−	0.0581265i
$483$	−7.15304	−	6.10584i	−0.325474	−	0.277825i
$484$		−	21.0695i		−	0.957705i
$485$	3.39715	−	12.7537i	0.154257	−	0.579118i
$486$	−1.82868	−	0.536948i	−0.0829504	−	0.0243564i
$487$	−0.784175	+	10.9642i	−0.0355344	+	0.496835i	0.948255	+	0.317509i	$0.102846\pi$
$487$	−0.784175	+	10.9642i	−0.0355344	+	0.496835i	−0.983790	+	0.179326i	$0.942608\pi$
$488$	1.53802	+	0.334576i	0.0696230	+	0.0151455i
$489$	1.78724	+	1.54865i	0.0808219	+	0.0700325i
$490$	−0.00283920	−	0.112294i	−0.000128262	−	0.00507290i
$491$	26.7418	−	7.85210i	1.20684	−	0.354360i	0.384376	−	0.923177i	$-0.374417\pi$
$491$	26.7418	−	7.85210i	1.20684	−	0.354360i	0.822464	+	0.568817i	$0.192599\pi$
$492$	−2.89202	−	13.2944i	−0.130383	−	0.599359i
$493$	8.73370	−	11.6669i	0.393346	−	0.525449i
$494$	1.41323	+	3.09455i	0.0635844	+	0.139230i
$495$	0.643213	−	3.36406i	0.0289103	−	0.151203i
$496$	5.26611	+	36.6266i	0.236455	+	1.64458i
$497$	−16.2975	+	3.54530i	−0.731041	+	0.159028i
$498$	−0.481488	−	0.262912i	−0.0215760	−	0.0117814i
$499$	16.2115	+	2.33086i	0.725725	+	0.104344i	0.495270	−	0.868739i	$-0.335069\pi$
$499$	16.2115	+	2.33086i	0.725725	+	0.104344i	0.230456	+	0.973083i	$0.425978\pi$
$500$	−18.6090	+	12.0763i	−0.832221	+	0.540067i
$501$	−0.256076	+	0.164570i	−0.0114406	+	0.00735244i
$502$	2.65109	+	0.189609i	0.118324	+	0.00846268i
$503$	13.9216	+	25.4956i	0.620735	+	1.13679i	0.979133	+	0.203223i	$0.0651416\pi$
$503$	13.9216	+	25.4956i	0.620735	+	1.13679i	−0.358397	+	0.933569i	$0.616677\pi$
$504$	−1.40359	+	3.07344i	−0.0625209	+	0.136902i
$505$	−18.1683	−	12.8972i	−0.808481	−	0.573917i
$506$	0.325387	−	0.180821i	0.0144652	−	0.00803845i
$507$	−0.747724	−	0.747724i	−0.0332076	−	0.0332076i
$508$	−13.4626	−	36.0945i	−0.597305	−	1.60144i
$509$	9.68205	−	32.9740i	0.429149	−	1.46155i	−0.407194	−	0.913342i	$-0.633493\pi$
$509$	9.68205	−	32.9740i	0.429149	−	1.46155i	0.836343	−	0.548207i	$-0.184689\pi$
$510$	−1.00825	−	0.829976i	−0.0446459	−	0.0367519i
$511$	−16.8279	−	26.1847i	−0.744421	−	1.15834i
$512$	9.71540	−	0.694859i	0.429364	−	0.0307087i
$513$	−22.5061	+	16.8479i	−0.993669	+	0.743852i
$514$	−0.414476	−	1.41158i	−0.0182818	−	0.0622620i
$515$	4.47600	−	10.4953i	0.197236	−	0.462479i
$516$	−5.06266	+	0.727901i	−0.222871	+	0.0320441i
$517$	−3.85309	−	1.43713i	−0.169459	−	0.0632048i
$518$	−0.308000	−	0.114878i	−0.0135327	−	0.00504745i
$519$	−2.33577	+	0.335832i	−0.102529	+	0.0147414i
$520$	3.95167	−	1.58879i	0.173292	−	0.0696732i
$521$	5.03381	+	17.1436i	0.220535	+	0.751074i	0.993216	+	0.116280i	$0.0370969\pi$
$521$	5.03381	+	17.1436i	0.220535	+	0.751074i	−0.772681	+	0.634794i	$0.781085\pi$
$522$	0.564301	−	0.422431i	0.0246988	−	0.0184893i
$523$	24.8621	−	1.77817i	1.08714	−	0.0777539i	0.483756	−	0.875203i	$-0.339272\pi$
$523$	24.8621	−	1.77817i	1.08714	−	0.0777539i	0.603386	+	0.797449i	$0.293818\pi$
$524$	11.2461	+	17.4993i	0.491288	+	0.764459i
$525$	−8.50585	−	4.87738i	−0.371226	−	0.212866i
$526$	−0.0130491	+	0.0444413i	−0.000568969	+	0.00193773i
$527$	21.3415	+	57.2187i	0.929648	+	2.49248i
$528$	−1.22942	−	1.22942i	−0.0535035	−	0.0535035i
$529$	19.5312	+	12.1464i	0.849181	+	0.528102i
$530$	−0.828421	+	1.16700i	−0.0359843	+	0.0506913i
$531$	3.78787	−	8.29428i	0.164380	−	0.359941i
$532$	18.4074	+	33.7107i	0.798063	+	1.46154i
$533$	36.0853	+	2.58087i	1.56303	+	0.111790i
$534$	0.528146	−	0.339419i	0.0228551	−	0.0146881i
$535$	−0.991179	+	1.63155i	−0.0428524	+	0.0705383i
$536$	−0.610460	−	0.0877709i	−0.0263679	−	0.00379112i
$537$	3.43014	+	1.87300i	0.148021	+	0.0808258i
$538$	2.84800	−	0.619543i	0.122786	−	0.0267104i
$539$	−0.0351256	−	0.244304i	−0.00151297	−	0.0105229i
$540$	9.84638	+	14.5018i	0.423721	+	0.624057i
$541$	−5.02827	−	11.0104i	−0.216182	−	0.473373i	0.770208	−	0.637793i	$-0.220152\pi$
$541$	−5.02827	−	11.0104i	−0.216182	−	0.473373i	−0.986391	+	0.164419i	$0.947425\pi$
$542$	−0.598451	+	0.799437i	−0.0257057	+	0.0343388i
$543$	−3.35553	−	15.4251i	−0.144000	−	0.661956i
$544$	9.22981	−	2.71012i	0.395725	−	0.116195i
$545$	−3.12928	+	3.29163i	−0.134044	+	0.140998i
$546$	0.708513	+	0.613930i	0.0303216	+	0.0262738i
$547$	−32.6220	−	7.09649i	−1.39482	−	0.303424i	−0.548521	−	0.836137i	$-0.684809\pi$
$547$	−32.6220	−	7.09649i	−1.39482	−	0.303424i	−0.846296	+	0.532713i	$0.821173\pi$
$548$	1.73463	−	24.2532i	0.0740995	−	1.03605i
$549$	−7.48004	−	2.19634i	−0.319240	−	0.0937374i
$550$	0.298541	−	0.247984i	0.0127298	−	0.0105741i
$551$		−	16.0900i		−	0.685457i
$552$	−0.475440	+	1.66478i	−0.0202361	+	0.0708578i
$553$	2.05715	−	2.05715i	0.0874787	−	0.0874787i
$554$	−0.564444	−	0.257773i	−0.0239809	−	0.0109517i
$555$	−1.21682	+	0.959832i	−0.0516511	+	0.0407426i
$556$	5.54655	+	6.40106i	0.235226	+	0.271466i
$557$	−7.56086	+	34.7567i	−0.320364	+	1.47269i	0.482167	+	0.876079i	$0.339850\pi$
$557$	−7.56086	+	34.7567i	−0.320364	+	1.47269i	−0.802531	+	0.596610i	$0.796514\pi$
$558$	0.210720	+	2.94626i	0.00892051	+	0.124725i
$559$	1.93554	−	13.4620i	0.0818645	−	0.569380i
$560$	21.3524	−	10.4114i	0.902303	−	0.439962i
$561$	−2.41392	−	1.55133i	−0.101916	−	0.0654973i
$562$	1.63044	+	1.22053i	0.0687758	+	0.0514849i
$563$	−11.8365	+	31.7350i	−0.498850	+	1.33747i	0.406829	+	0.913504i	$0.366635\pi$
$563$	−11.8365	+	31.7350i	−0.498850	+	1.33747i	−0.905679	+	0.423964i	$0.860638\pi$
$564$	8.66456	−	3.95697i	0.364844	−	0.166619i
$565$	−28.5182	+	9.16278i	−1.19977	+	0.385481i
$566$	−1.82771	+	2.84397i	−0.0768244	+	0.119541i
$567$	5.98759	−	10.9654i	0.251455	−	0.460505i
$568$	1.84004	+	2.45801i	0.0772066	+	0.103136i
$569$	−21.7247	+	25.0717i	−0.910748	+	1.05106i	0.0877430	+	0.996143i	$0.472035\pi$
$569$	−21.7247	+	25.0717i	−0.910748	+	1.05106i	−0.998491	+	0.0549161i	$0.982511\pi$
$570$	−1.44026	−	0.0664739i	−0.0603257	−	0.00278428i
$571$	−13.4016	+	11.6126i	−0.560841	+	0.485971i	−0.888533	−	0.458813i	$-0.848275\pi$
$571$	−13.4016	+	11.6126i	−0.560841	+	0.485971i	0.327692	+	0.944785i	$0.393729\pi$
$572$	4.09052	−	2.23359i	0.171033	−	0.0933912i
$573$	−5.05274	+	1.88457i	−0.211081	+	0.0787292i
$574$	−3.25209			−0.135740
$575$	22.3527	+	8.68074i	0.932174	+	0.362012i
$576$	−18.9082			−0.787843
$577$	−18.1799	+	6.78077i	−0.756841	+	0.282287i	−0.698114	−	0.715987i	$-0.745977\pi$
$577$	−18.1799	+	6.78077i	−0.756841	+	0.282287i	−0.0587274	+	0.998274i	$0.518704\pi$
$578$	2.70761	−	1.47846i	0.112622	−	0.0614960i
$579$	9.09903	−	7.88436i	0.378143	−	0.327663i
$580$	−10.0213	−	0.462526i	−0.416113	−	0.0192054i
$581$	10.7852	−	12.4468i	0.447445	−	0.516379i
$582$	−0.320511	−	0.428152i	−0.0132856	−	0.0177475i
$583$	−1.50704	+	2.75994i	−0.0624152	+	0.114305i
$584$	−3.09791	+	4.82045i	−0.128193	+	0.199471i
$585$	−20.0837	+	6.45282i	−0.830361	+	0.266791i
$586$	−3.08056	+	1.40684i	−0.127257	+	0.0581161i
$587$	−7.11065	+	19.0644i	−0.293488	+	0.786872i	0.703599	+	0.710597i	$0.251575\pi$
$587$	−7.11065	+	19.0644i	−0.293488	+	0.786872i	−0.997087	+	0.0762744i	$0.975698\pi$
$588$	0.457662	+	0.342602i	0.0188737	+	0.0141286i
$589$	56.7197	+	36.4515i	2.33710	+	1.50196i
$590$	0.928710	−	0.452838i	0.0382344	−	0.0186430i
$591$	−2.07079	+	14.4027i	−0.0851811	+	0.592447i
$592$	−0.267869	−	3.74530i	−0.0110094	−	0.153931i
$593$	5.45388	−	25.0711i	0.223964	−	1.02955i	−0.718575	−	0.695450i	$-0.755205\pi$
$593$	5.45388	−	25.0711i	0.223964	−	1.02955i	0.942539	−	0.334096i	$-0.108431\pi$
$594$	−0.200817	−	0.231755i	−0.00823963	−	0.00950904i
$595$	30.7816	−	24.2807i	1.26192	−	0.995410i
$596$	−2.42539	−	1.10764i	−0.0993480	−	0.0453707i
$597$	10.1405	−	10.1405i	0.415023	−	0.415023i
$598$	−1.93792	−	1.22521i	−0.0792475	−	0.0501026i
$599$		−	23.3489i		−	0.954012i	−0.878900	−	0.477006i	$-0.841722\pi$
$599$		−	23.3489i		−	0.954012i	0.878900	−	0.477006i	$-0.158278\pi$
$600$	−0.166267	+	1.79737i	−0.00678781	+	0.0733774i
$601$	14.6694	+	4.30731i	0.598376	+	0.175699i	0.566874	−	0.823805i	$-0.308153\pi$
$601$	14.6694	+	4.30731i	0.598376	+	0.175699i	0.0315019	+	0.999504i	$0.489971\pi$
$602$	−0.0872175	+	1.21946i	−0.00355472	+	0.0497015i
$603$	2.98483	+	0.649310i	0.121552	+	0.0264420i
$604$	−7.47477	−	6.47693i	−0.304144	−	0.263543i
$605$	−16.3598	+	17.2085i	−0.665121	+	0.699627i
$606$	−0.866286	+	0.254364i	−0.0351904	+	0.0103328i
$607$	7.83249	+	36.0054i	0.317911	+	1.46141i	0.807711	+	0.589578i	$0.200706\pi$
$607$	7.83249	+	36.0054i	0.317911	+	1.46141i	−0.489800	+	0.871835i	$0.662930\pi$
$608$	6.36451	−	8.50199i	0.258115	−	0.344801i
$609$	−1.84195	−	4.03330i	−0.0746394	−	0.163437i
$610$	−0.496221	−	0.730835i	−0.0200914	−	0.0295907i
$611$	3.60463	+	25.0707i	0.145828	+	1.01425i
$612$	−30.9960	+	6.74277i	−1.25294	+	0.272560i
$613$	−16.9533	−	9.25719i	−0.684736	−	0.373894i	0.0989145	−	0.995096i	$-0.468463\pi$
$613$	−16.9533	−	9.25719i	−0.684736	−	0.373894i	−0.783651	+	0.621202i	$0.786645\pi$
$614$	−1.84842	−	0.265762i	−0.0745960	−	0.0107253i
$615$	−7.96063	+	13.1038i	−0.321004	+	0.528396i
$616$	−0.707700	+	0.454811i	−0.0285141	+	0.0183249i
$617$	27.5579	+	1.97098i	1.10944	+	0.0793488i	0.614010	−	0.789298i	$-0.289556\pi$
$617$	27.5579	+	1.97098i	1.10944	+	0.0793488i	0.495431	+	0.868647i	$0.335010\pi$
$618$	−0.221583	−	0.405798i	−0.00891336	−	0.0163236i
$619$	0.180591	−	0.395439i	0.00725856	−	0.0158940i	−0.905968	−	0.423346i	$-0.860855\pi$
$619$	0.180591	−	0.395439i	0.00725856	−	0.0158940i	0.913227	+	0.407452i	$0.133583\pi$
$620$	24.3336	−	34.2789i	0.977260	−	1.37667i
$621$	6.48945	−	17.8010i	0.260413	−	0.714331i
$622$	1.28480	+	1.28480i	0.0515158	+	0.0515158i
$623$	6.58657	+	17.6593i	0.263885	+	0.707504i
$624$	−3.01695	+	10.2748i	−0.120775	+	0.411321i
$625$	24.5758	+	4.58603i	0.983031	+	0.183441i
$626$	−1.18785	−	1.84834i	−0.0474762	−	0.0738744i
$627$	−3.15990	+	0.226001i	−0.126194	+	0.00902560i
$628$	−28.7369	+	21.5122i	−1.14673	+	0.858431i
$629$	−1.74588	−	5.94591i	−0.0696127	−	0.237079i
$630$	1.75940	−	0.707378i	0.0700962	−	0.0281826i
$631$	21.6466	−	3.11231i	0.861738	−	0.123899i	0.302745	−	0.953072i	$-0.402097\pi$
$631$	21.6466	−	3.11231i	0.861738	−	0.123899i	0.558993	+	0.829172i	$0.311188\pi$
$632$	−0.501807	−	0.187164i	−0.0199608	−	0.00744499i
$633$	4.45224	+	1.66060i	0.176961	+	0.0660029i
$634$	3.38063	−	0.486062i	0.134262	−	0.0193040i
$635$	−17.0307	+	39.9335i	−0.675843	+	1.58471i
$636$	−2.05205	−	6.98864i	−0.0813691	−	0.277118i
$637$	−1.21695	+	0.911000i	−0.0482175	+	0.0360951i
$638$	0.175059	−	0.0125204i	0.00693063	−	0.000495689i
$639$	−8.22184	−	12.7934i	−0.325251	−	0.506100i
$640$	−6.80723	−	5.60362i	−0.269079	−	0.221502i
$641$	−3.50910	+	11.9509i	−0.138601	+	0.472032i	−0.999313	−	0.0370604i	$-0.988201\pi$
$641$	−3.50910	+	11.9509i	−0.138601	+	0.472032i	0.860712	+	0.509092i	$0.170019\pi$
$642$	0.0270339	+	0.0724806i	0.00106694	+	0.00286058i
$643$	−12.4473	−	12.4473i	−0.490875	−	0.490875i	0.417707	−	0.908582i	$-0.362834\pi$
$643$	−12.4473	−	12.4473i	−0.490875	−	0.490875i	−0.908582	+	0.417707i	$0.862834\pi$
$644$	−22.8105	−	12.2367i	−0.898860	−	0.482195i
$645$	4.70013	+	3.33648i	0.185067	+	0.131374i
$646$	2.39486	−	5.24402i	0.0942247	−	0.206323i
$647$	−15.6647	−	28.6877i	−0.615842	−	1.12783i	−0.980468	−	0.196677i	$-0.936985\pi$
$647$	−15.6647	−	28.6877i	−0.615842	−	1.12783i	0.364626	−	0.931154i	$-0.381197\pi$
$648$	−2.29415	−	0.164081i	−0.0901229	−	0.00644572i
$649$	1.90987	−	1.22740i	0.0749690	−	0.0481796i
$650$	−2.22174	−	0.881839i	−0.0871440	−	0.0345886i
$651$	18.3909	+	2.64421i	0.720795	+	0.103635i
$652$	5.71288	+	3.11947i	0.223734	+	0.122168i
$653$	11.5904	−	2.52133i	0.453566	−	0.0986672i	0.0200217	−	0.999800i	$-0.493626\pi$
$653$	11.5904	−	2.52133i	0.453566	−	0.0986672i	0.433544	+	0.901132i	$0.357263\pi$
$654$	0.0261916	+	0.182167i	0.00102417	+	0.00712328i
$655$	4.40237	−	23.0248i	0.172015	−	0.899653i
$656$	−15.4314	−	33.7901i	−0.602496	−	1.31928i
$657$	17.0078	−	22.7198i	0.663537	−	0.886382i
$658$	−0.483979	−	2.22482i	−0.0188675	−	0.0867324i
$659$	8.59127	−	2.52262i	0.334668	−	0.0982675i	−0.110081	−	0.993923i	$-0.535111\pi$
$659$	8.59127	−	2.52262i	0.334668	−	0.0982675i	0.444749	+	0.895655i	$0.353293\pi$
$660$	0.0499247	+	1.97458i	0.00194332	+	0.0768603i
$661$	18.0545	+	15.6443i	0.702237	+	0.608492i	0.931012	−	0.364987i	$-0.118927\pi$
$661$	18.0545	+	15.6443i	0.702237	+	0.608492i	−0.228775	+	0.973479i	$0.573472\pi$
$662$	−3.00323	−	0.653312i	−0.116724	−	0.0253917i
$663$	−1.26078	+	17.6281i	−0.0489648	+	0.684618i
$664$	−2.90911	−	0.854192i	−0.112895	−	0.0331491i
$665$	11.1410	−	41.8260i	0.432029	−	1.62194i
$666$		−	0.299732i		−	0.0116144i
$667$	5.93008	+	9.07862i	0.229614	+	0.351526i
$668$	−0.592434	+	0.592434i	−0.0229220	+	0.0229220i
$669$	−4.94844	−	2.25987i	−0.191318	−	0.0873718i
$670$	0.214368	+	0.271763i	0.00828175	+	0.0104991i
$671$	−1.27109	−	1.46691i	−0.0490697	−	0.0566295i
$672$	0.622111	−	2.85980i	0.0239984	−	0.110319i
$673$	−3.27514	−	45.7925i	−0.126247	−	1.76517i	−0.527832	−	0.849349i	$-0.676995\pi$
$673$	−3.27514	−	45.7925i	−0.126247	−	1.76517i	0.401585	−	0.915822i	$-0.368459\pi$
$674$	−0.166583	+	1.15861i	−0.00641654	+	0.0446280i
$675$	3.21813	−	19.4897i	0.123866	−	0.750160i
$676$	−2.44848	−	1.57354i	−0.0941724	−	0.0605209i
$677$	−20.9097	−	15.6528i	−0.803623	−	0.601585i	0.116510	−	0.993189i	$-0.462829\pi$
$677$	−20.9097	−	15.6528i	−0.803623	−	0.601585i	−0.920134	+	0.391605i	$0.871920\pi$
$678$	−0.424180	+	1.13727i	−0.0162906	+	0.0436767i
$679$	14.6053	−	6.67000i	0.560499	−	0.255971i
$680$	−6.42003	−	3.29775i	−0.246197	−	0.126463i
$681$	−3.56065	+	5.54048i	−0.136444	+	0.212312i
$682$	−0.352455	+	0.645473i	−0.0134962	+	0.0247164i
$683$	22.1646	+	29.6084i	0.848104	+	1.13293i	0.989721	+	0.143013i	$0.0456791\pi$
$683$	22.1646	+	29.6084i	0.848104	+	1.13293i	−0.141617	+	0.989922i	$0.545230\pi$
$684$	−22.9340	+	26.4673i	−0.876905	+	1.01200i
$685$	−20.2486	+	18.4620i	−0.773660	+	0.705395i
$686$	−1.70551	+	1.47783i	−0.0651167	+	0.0564240i
$687$	−2.19812	+	1.20026i	−0.0838635	+	0.0457930i
$688$	−13.0844	+	4.88022i	−0.498837	+	0.186057i
$689$	19.3678			0.737854
$690$	0.837150	−	0.493309i	0.0318697	−	0.0187800i
$691$	−30.8094			−1.17205			−0.586023	−	0.810295i	$-0.699307\pi$
$691$	−30.8094			−1.17205			−0.586023	+	0.810295i	$0.699307\pi$
$692$	−6.08559	+	2.26981i	−0.231339	+	0.0862851i
$693$	3.65694	−	1.99684i	0.138916	−	0.0758537i
$694$	−1.61042	+	1.39543i	−0.0611305	+	0.0529699i
$695$	0.440071	−	9.53479i	0.0166928	−	0.361675i
$696$	−0.534544	+	0.616897i	−0.0202618	+	0.0233834i
$697$	−36.7395	−	49.0783i	−1.39161	−	1.85897i
$698$	0.886868	−	1.62418i	0.0335684	−	0.0614760i
$699$	−1.25960	+	1.95998i	−0.0476425	+	0.0741332i
$700$	−25.7302	−	8.14127i	−0.972510	−	0.307711i
$701$	−11.7865	+	5.38269i	−0.445168	+	0.203301i	−0.625370	−	0.780328i	$-0.715052\pi$
$701$	−11.7865	+	5.38269i	−0.445168	+	0.203301i	0.180202	+	0.983630i	$0.442325\pi$
$702$	−0.660042	+	1.76964i	−0.0249117	+	0.0667908i
$703$	−5.47704	−	4.10006i	−0.206571	−	0.154637i
$704$	−3.96042	−	2.54521i	−0.149264	−	0.0959262i
$705$	−10.1493	−	3.49590i	−0.382243	−	0.131663i
$706$	−0.0749594	+	0.521354i	−0.00282113	+	0.0196214i
$707$	−1.93364	−	27.0359i	−0.0727222	−	1.01679i
$708$	−1.11778	+	5.13836i	−0.0420088	+	0.193112i
$709$	9.99640	+	11.5365i	0.375423	+	0.433261i	0.911748	−	0.410751i	$-0.134733\pi$
$709$	9.99640	+	11.5365i	0.375423	+	0.433261i	−0.536325	+	0.844012i	$0.680188\pi$
$710$	0.202051	−	1.71135i	0.00758283	−	0.0642257i
$711$	2.41294	+	1.10195i	0.0904921	+	0.0413264i
$712$	2.45347	−	2.45347i	0.0919479	−	0.0919479i
$713$	−45.4380	+	0.337026i	−1.70167	+	0.0126217i
$714$		−	1.58868i		−	0.0594550i
$715$	−5.07525	−	1.35187i	−0.189803	−	0.0505570i
$716$	10.3212	+	3.03059i	0.385723	+	0.113258i
$717$	0.566046	−	7.91436i	0.0211394	−	0.295567i
$718$	1.28393	+	0.279301i	0.0479157	+	0.0104234i
$719$	13.3539	+	11.5712i	0.498018	+	0.431535i	0.867302	−	0.497781i	$-0.165852\pi$
$719$	13.3539	+	11.5712i	0.498018	+	0.431535i	−0.369285	+	0.929316i	$0.620397\pi$
$720$	15.6983	+	14.9241i	0.585042	+	0.556188i
$721$	13.3182	−	3.91057i	0.495995	−	0.145637i
$722$	−0.845300	−	3.88578i	−0.0314588	−	0.144614i
$723$	6.20308	−	8.28634i	0.230695	−	0.308172i
$724$	−18.0495	−	39.5229i	−0.670804	−	1.46886i
$725$	7.82579	+	8.15901i	0.290642	+	0.303018i
$726$	0.136929	+	0.952363i	0.00508192	+	0.0353455i
$727$	33.6362	−	7.31711i	1.24750	−	0.271376i	0.460125	−	0.887854i	$-0.347805\pi$
$727$	33.6362	−	7.31711i	1.24750	−	0.271376i	0.787372	+	0.616478i	$0.211441\pi$
$728$	4.54753	+	2.48314i	0.168543	+	0.0920312i
$729$	2.81858	+	0.405251i	0.104392	+	0.0150093i
$730$	3.12414	−	0.762799i	0.115629	−	0.0282325i
$731$	−19.3885	+	12.4603i	−0.717111	+	0.460859i
$732$	4.48442	+	0.320732i	0.165749	+	0.0118546i
$733$	19.1578	+	35.0848i	0.707608	+	1.29589i	0.945826	+	0.324675i	$0.105255\pi$
$733$	19.1578	+	35.0848i	0.707608	+	1.29589i	−0.238218	+	0.971212i	$0.576563\pi$
$734$	−1.15648	+	2.53233i	−0.0426863	+	0.0934699i
$735$	−0.107777	−	0.635180i	−0.00397540	−	0.0234290i
$736$	−0.457643	+	7.14285i	−0.0168690	+	0.263289i
$737$	0.537785	+	0.537785i	0.0198096	+	0.0198096i
$738$	−1.03625	−	2.77830i	−0.0381450	−	0.102271i
$739$	−8.24574	+	28.0824i	−0.303325	+	1.03303i	0.656941	+	0.753942i	$0.271850\pi$
$739$	−8.24574	+	28.0824i	−0.303325	+	1.03303i	−0.960266	+	0.279087i	$0.909968\pi$
$740$	−2.71108	+	3.29340i	−0.0996614	+	0.121068i
$741$	10.5489	+	16.4144i	0.387524	+	0.602999i
$742$	−1.73659	+	0.124203i	−0.0637521	+	0.00455964i
$743$	7.57308	−	5.66914i	0.277829	−	0.207980i	−0.451272	−	0.892387i	$-0.649029\pi$
$743$	7.57308	−	5.66914i	0.277829	−	0.207980i	0.729101	+	0.684406i	$0.239939\pi$
$744$	−0.963658	−	3.28192i	−0.0353294	−	0.120321i
$745$	1.12089	+	2.78791i	0.0410664	+	0.102141i
$746$	0.181372	−	0.0260773i	0.00664049	−	0.000954758i
$747$	14.0700	+	5.24785i	0.514795	+	0.192009i
$748$	−7.39990	−	2.76002i	−0.270567	−	0.100916i
$749$	−2.29875	+	0.330510i	−0.0839945	+	0.0120766i
$750$	0.762664	−	0.666798i	0.0278486	−	0.0243480i
$751$	1.29055	+	4.39521i	0.0470929	+	0.160384i	0.979682	−	0.200555i	$-0.0642746\pi$
$751$	1.29055	+	4.39521i	0.0470929	+	0.160384i	−0.932590	+	0.360939i	$0.882456\pi$
$752$	20.8199	−	15.5856i	0.759224	−	0.568348i
$753$	15.2052	−	1.08749i	0.554107	−	0.0396305i
$754$	−0.584409	−	0.909359i	−0.0212829	−	0.0331169i
$755$	1.07590	+	11.0940i	0.0391559	+	0.403751i
$756$	−6.00767	+	20.4603i	−0.218497	+	0.744132i
$757$	1.70676	+	4.57599i	0.0620331	+	0.166317i	0.964269	−	0.264926i	$-0.0853477\pi$
$757$	1.70676	+	4.57599i	0.0620331	+	0.166317i	−0.902236	+	0.431244i	$0.858075\pi$
$758$	1.17291	+	1.17291i	0.0426020	+	0.0426020i
$759$	1.69965	−	1.29212i	0.0616934	−	0.0469011i
$760$	−7.85611	+	1.33302i	−0.284971	+	0.0483536i
$761$	14.8164	−	32.4434i	0.537094	−	1.17607i	−0.425459	−	0.904977i	$-0.639887\pi$
$761$	14.8164	−	32.4434i	0.537094	−	1.17607i	0.962553	−	0.271093i	$-0.0873852\pi$
$762$	0.843097	+	1.54402i	0.0305422	+	0.0559338i
$763$	−5.51104	−	0.394157i	−0.199513	−	0.0142695i
$764$	−12.4868	+	8.02478i	−0.451757	+	0.290326i
$765$	30.5515	+	18.5602i	1.10459	+	0.671047i
$766$	0.952573	+	0.136959i	0.0344179	+	0.00494854i
$767$	−12.2724	−	6.70124i	−0.443131	−	0.241968i
$768$	10.3909	−	2.26041i	0.374951	−	0.0815656i
$769$	2.19063	+	15.2362i	0.0789962	+	0.549431i	0.990433	+	0.137991i	$0.0440646\pi$
$769$	2.19063	+	15.2362i	0.0789962	+	0.549431i	−0.911437	+	0.411439i	$0.865026\pi$
$770$	0.463734	+	0.0886666i	0.0167118	+	0.00319532i
$771$	−3.50519	−	7.67530i	−0.126236	−	0.276419i
$772$	19.8591	−	26.5286i	0.714744	−	0.954786i
$773$	−8.43419	−	38.7713i	−0.303357	−	1.39451i	−0.836260	−	0.548333i	$-0.815263\pi$
$773$	−8.43419	−	38.7713i	−0.303357	−	1.39451i	0.532904	−	0.846176i	$-0.321101\pi$
$774$	−1.06959	+	0.314060i	−0.0384456	+	0.0112887i
$775$	−46.4909	+	9.10304i	−1.67000	+	0.326991i
$776$	−2.23389	−	1.93568i	−0.0801920	−	0.0694867i
$777$	−1.84230	−	0.400768i	−0.0660922	−	0.0143775i
$778$	−0.206253	+	2.88379i	−0.00739453	+	0.103389i
$779$	−64.9431	−	19.0690i	−2.32683	−	0.683219i
$780$	10.5266	−	6.09832i	0.376914	−	0.218355i
$781$		−	3.78638i		−	0.135487i
$782$	0.581443	+	3.84153i	0.0207923	+	0.137373i
$783$	6.31653	−	6.31653i	0.225734	−	0.225734i
$784$	1.41985	+	0.648422i	0.0507088	+	0.0231579i
$785$	40.1745	+	4.74321i	1.43389	+	0.169293i
$786$	−0.622062	−	0.717897i	−0.0221882	−	0.0256065i
$787$	−0.837822	+	3.85141i	−0.0298651	+	0.137288i	−0.989665	−	0.143396i	$-0.954198\pi$
$787$	−0.837822	+	3.85141i	−0.0298651	+	0.137288i	0.959800	+	0.280684i	$0.0905613\pi$
$788$	2.85712	+	39.9478i	0.101781	+	1.42308i
$789$	−0.0378061	+	0.262947i	−0.00134593	+	0.00936116i
$790$	0.131738	+	0.270176i	0.00468701	+	0.00961244i
$791$	−30.6552	−	19.7009i	−1.08997	−	0.700483i
$792$	−0.614053	−	0.459674i	−0.0218194	−	0.0163338i
$793$	−4.17778	+	11.2011i	−0.148357	+	0.397762i
$794$	3.59492	−	1.64175i	0.127579	−	0.0582634i
$795$	−3.75045	+	7.30133i	−0.133015	+	0.258952i
$796$	21.3401	−	33.2059i	0.756381	−	1.17695i
$797$	−3.59226	+	6.57874i	−0.127244	+	0.233031i	−0.933533	−	0.358492i	$-0.883291\pi$
$797$	−3.59226	+	6.57874i	−0.127244	+	0.233031i	0.806288	+	0.591523i	$0.201473\pi$
$798$	−1.05112	−	1.40413i	−0.0372091	−	0.0497056i
$799$	28.1077	−	32.4381i	0.994381	−	1.14758i
$800$	0.907810	+	7.40678i	0.0320959	+	0.261869i
$801$	−12.9878	+	11.2540i	−0.458900	+	0.397639i
$802$	2.78833	−	1.52254i	0.0984593	−	0.0537628i
$803$	6.62064	−	2.46937i	0.233637	−	0.0871422i
$804$	−1.76162			−0.0621275
$805$	9.12907	+	27.7060i	0.321757	+	0.976508i
$806$	4.52959			0.159548
$807$	15.6626	−	5.84183i	0.551348	−	0.205642i
$808$	−4.37950	+	2.39139i	−0.154070	+	0.0841287i
$809$	−15.6593	+	13.5688i	−0.550551	+	0.477055i	−0.885150	−	0.465305i	$-0.845945\pi$
$809$	−15.6593	+	13.5688i	−0.550551	+	0.477055i	0.334599	+	0.942361i	$0.391399\pi$
$810$	0.869712	+	0.953878i	0.0305586	+	0.0335159i
$811$	22.2083	−	25.6298i	0.779840	−	0.899983i	−0.217258	−	0.976114i	$-0.569711\pi$
$811$	22.2083	−	25.6298i	0.779840	−	0.899983i	0.997098	+	0.0761311i	$0.0242567\pi$
$812$	−7.31369	−	9.76994i	−0.256660	−	0.342858i
$813$	−2.74491	+	5.02693i	−0.0962683	+	0.176302i
$814$	0.0403466	−	0.0627805i	0.00141415	−	0.00220045i
$815$	−2.24383	−	6.98369i	−0.0785979	−	0.244628i
$816$	16.5068	−	7.53842i	0.577855	−	0.263897i
$817$	−8.89215	+	23.8408i	−0.311097	+	0.834083i
$818$	−1.49121	−	1.11630i	−0.0521388	−	0.0390306i
$819$	−21.5887	−	13.8742i	−0.754370	−	0.484804i
$820$	−13.7436	+	39.9003i	−0.479948	+	1.39338i
$821$	−0.259729	+	1.80645i	−0.00906460	+	0.0630457i	−0.993852	−	0.110720i	$-0.964684\pi$
$821$	−0.259729	+	1.80645i	−0.00906460	+	0.0630457i	0.984787	+	0.173765i	$0.0555935\pi$
$822$	0.0792131	+	1.10754i	0.00276287	+	0.0386300i
$823$	−4.13227	+	18.9957i	−0.144042	+	0.662150i	0.847329	+	0.531068i	$0.178209\pi$
$823$	−4.13227	+	18.9957i	−0.144042	+	0.662150i	−0.991371	+	0.131083i	$0.958155\pi$
$824$	−1.67337	−	1.93117i	−0.0582947	−	0.0672757i
$825$	1.49242	−	1.65150i	0.0519594	−	0.0574979i
$826$	1.14336	+	0.522156i	0.0397827	+	0.0181681i
$827$	−4.04210	+	4.04210i	−0.140558	+	0.140558i	−0.773884	−	0.633327i	$-0.781689\pi$
$827$	−4.04210	+	4.04210i	−0.140558	+	0.140558i	0.633327	+	0.773884i	$0.281689\pi$
$828$	3.18560	−	23.3864i	0.110707	−	0.812734i
$829$			12.5769i			0.436812i	0.975858	+	0.218406i	$0.0700857\pi$
$829$			12.5769i			0.436812i	−0.975858	+	0.218406i	$0.929914\pi$
$830$	0.852987	+	1.47239i	0.0296076	+	0.0511073i
$831$	−3.41479	−	1.00267i	−0.118458	−	0.0347823i
$832$	−2.06852	+	28.9217i	−0.0717131	+	1.00268i
$833$	2.51720	+	0.547583i	0.0872157	+	0.0189726i
$834$	−0.292310	−	0.253288i	−0.0101219	−	0.00877064i
$835$	0.943878	−	0.0238648i	0.0326642	−	0.000825874i
$836$	−8.36637	+	2.45659i	−0.289357	+	0.0849629i
$837$	7.95677	+	36.5767i	0.275026	+	1.26428i
$838$	−2.69002	+	3.59345i	−0.0929253	+	0.124134i
$839$	−1.90354	−	4.16818i	−0.0657176	−	0.143901i	0.873923	−	0.486064i	$-0.161568\pi$
$839$	−1.90354	−	4.16818i	−0.0657176	−	0.143901i	−0.939641	+	0.342163i	$0.888841\pi$
$840$	−1.81670	+	1.23350i	−0.0626821	+	0.0425597i
$841$	−3.39955	−	23.6444i	−0.117226	−	0.815323i
$842$	3.02621	−	0.658311i	0.104290	−	0.0226869i
$843$	10.2523	+	5.59820i	0.353109	+	0.192812i
$844$	12.9459	+	1.86134i	0.445617	+	0.0640700i
$845$	0.777993	+	3.18636i	0.0267638	+	0.109614i
$846$	1.74647	−	1.12239i	0.0600449	−	0.0385885i
$847$	−28.8116	−	2.06064i	−0.989977	−	0.0708046i
$848$	−9.53074	−	17.4543i	−0.327287	−	0.599381i
$849$	−8.05466	+	17.6373i	−0.276435	+	0.605309i
$850$	1.33616	+	3.82397i	0.0458300	+	0.131161i
$851$	4.60147	+	0.294817i	0.157737	+	0.0101062i
$852$	6.20150	+	6.20150i	0.212460	+	0.212460i
$853$	13.3124	+	35.6920i	0.455808	+	1.22207i	0.938194	+	0.346110i	$0.112498\pi$
$853$	13.3124	+	35.6920i	0.455808	+	1.22207i	−0.482385	+	0.875959i	$0.660230\pi$
$854$	0.302764	−	1.03112i	0.0103604	−	0.0352842i
$855$	39.2824	−	3.80963i	1.34343	−	0.130287i
$856$	0.231145	+	0.359668i	0.00790036	+	0.0122932i
$857$	56.6143	−	4.04913i	1.93391	−	0.138316i	0.949448	−	0.313926i	$-0.101644\pi$
$857$	56.6143	−	4.04913i	1.93391	−	0.138316i	0.984460	+	0.175610i	$0.0561898\pi$
$858$	−0.170380	+	0.127545i	−0.00581666	+	0.00435430i
$859$	0.769304	+	2.62001i	0.0262483	+	0.0893935i	0.971575	−	0.236730i	$-0.0760757\pi$
$859$	0.769304	+	2.62001i	0.0262483	+	0.0893935i	−0.945327	+	0.326123i	$0.894257\pi$
$860$	14.5931	+	6.22362i	0.497621	+	0.212224i
$861$	−18.4623	+	2.65448i	−0.629195	+	0.0904646i
$862$	−4.43092	−	1.65265i	−0.150918	−	0.0562894i
$863$	−39.2165	−	14.6270i	−1.33495	−	0.497909i	−0.422224	−	0.906491i	$-0.638751\pi$
$863$	−39.2165	−	14.6270i	−1.33495	−	0.497909i	−0.912722	+	0.408582i	$0.866023\pi$
$864$	5.83621	−	0.839121i	0.198552	−	0.0285475i
$865$	6.73284	+	2.87140i	0.228923	+	0.0976305i
$866$	−0.747947	−	2.54727i	−0.0254163	−	0.0865599i
$867$	14.1645	−	10.6034i	0.481051	−	0.360110i
$868$	51.0096	−	3.64828i	1.73138	−	0.123831i
$869$	0.357069	+	0.555611i	0.0121127	+	0.0188478i
$870$	0.455980	−	0.0442212i	0.0154592	−	0.00149924i
$871$	1.31971	−	4.49451i	0.0447166	−	0.152291i
$872$	0.355455	+	0.953011i	0.0120372	+	0.0322730i
$873$	10.3521	+	10.3521i	0.350366	+	0.350366i
$874$	3.05556	+	3.01057i	0.103356	+	0.101834i
$875$	14.6937	+	26.6281i	0.496738	+	0.900193i
$876$	−6.79914	+	14.8880i	−0.229722	+	0.503020i
$877$	2.33116	+	4.26919i	0.0787176	+	0.144160i	0.914073	−	0.405550i	$-0.132920\pi$
$877$	2.33116	+	4.26919i	0.0787176	+	0.144160i	−0.835355	+	0.549710i	$0.814738\pi$
$878$	0.614344	+	0.0439388i	0.0207331	+	0.00148286i
$879$	−16.3402	+	10.5012i	−0.551141	+	0.354197i
$880$	1.27918	+	5.23905i	0.0431213	+	0.176608i
$881$	10.1114	+	1.45379i	0.340660	+	0.0489795i	0.310522	−	0.950566i	$-0.399496\pi$
$881$	10.1114	+	1.45379i	0.340660	+	0.0489795i	0.0301381	+	0.999546i	$0.490405\pi$
$882$	0.109358	+	0.0597139i	0.00368227	+	0.00201067i
$883$	34.1939	−	7.43842i	1.15072	−	0.250323i	0.403548	−	0.914958i	$-0.367777\pi$
$883$	34.1939	−	7.43842i	1.15072	−	0.250323i	0.747168	+	0.664636i	$0.231413\pi$
$884$	6.92272	+	48.1486i	0.232836	+	1.61941i
$885$	4.90272	−	3.32884i	0.164803	−	0.111898i
$886$	0.382704	+	0.838004i	0.0128572	+	0.0281533i
$887$	−15.7262	+	21.0078i	−0.528035	+	0.705372i	−0.982682	−	0.185300i	$-0.940674\pi$
$887$	−15.7262	+	21.0078i	−0.528035	+	0.705372i	0.454647	+	0.890672i	$0.349765\pi$
$888$	0.0737791	+	0.339157i	0.00247586	+	0.0113814i
$889$	−50.6743	+	14.8793i	−1.69956	+	0.499036i
$890$	−1.94671	+	0.0492201i	−0.0652539	+	0.00164986i
$891$	2.14354	+	1.85739i	0.0718114	+	0.0622249i
$892$	−14.6311	−	3.18279i	−0.489884	−	0.106568i
$893$	3.38058	−	47.2667i	0.113127	−	1.58172i
$894$	0.116829	+	0.0343040i	0.00390734	+	0.00114730i
$895$	−6.07672	−	10.4893i	−0.203122	−	0.350620i
$896$		−	10.7261i		−	0.358333i
$897$	−12.0018	−	5.37380i	−0.400727	−	0.179426i
$898$	0.904145	−	0.904145i	0.0301717	−	0.0301717i
$899$	−19.4872	−	8.89951i	−0.649935	−	0.296815i
$900$	−1.24353	−	24.5757i	−0.0414509	−	0.819191i
$901$	−21.4930	−	24.8042i	−0.716034	−	0.826348i
$902$	0.156935	−	0.721417i	0.00522535	−	0.0240206i
$903$	0.500231	+	6.99415i	0.0166467	+	0.232751i
$904$	−0.954701	+	6.64009i	−0.0317529	+	0.220846i
$905$	−15.9463	+	46.2952i	−0.530074	+	1.53890i
$906$	0.379960	+	0.244186i	0.0126233	+	0.00811253i
$907$	25.8231	+	19.3309i	0.857441	+	0.641872i	0.934817	−	0.355130i	$-0.115563\pi$
$907$	25.8231	+	19.3309i	0.857441	+	0.641872i	−0.0773760	+	0.997002i	$0.524654\pi$
$908$	−6.33486	+	16.9844i	−0.210230	+	0.563648i
$909$	22.4809	−	10.2667i	0.745645	−	0.340525i
$910$	−0.889518	−	2.76853i	−0.0294872	−	0.0917760i
$911$	−25.1565	+	39.1443i	−0.833473	+	1.29691i	0.119187	+	0.992872i	$0.461971\pi$
$911$	−25.1565	+	39.1443i	−0.833473	+	1.29691i	−0.952660	+	0.304037i	$0.901665\pi$
$912$	9.60163	−	17.5841i	0.317942	−	0.582267i
$913$	2.24063	+	2.99313i	0.0741541	+	0.0990582i
$914$	−0.902480	+	1.04152i	−0.0298514	+	0.0344503i
$915$	−3.41361	−	3.74396i	−0.112851	−	0.123772i
$916$	−5.20964	+	4.51418i	−0.172131	+	0.149153i
$917$	25.0293	−	13.6671i	0.826541	−	0.451326i
$918$	2.99883	−	1.11851i	0.0989763	−	0.0369162i
$919$	3.95933			0.130606			0.0653032	−	0.997865i	$-0.479199\pi$
$919$	3.95933			0.130606			0.0653032	+	0.997865i	$0.479199\pi$
$920$	3.94144	−	3.64757i	0.129945	−	0.120257i
$921$	−10.7105			−0.352923
$922$	−1.39253	+	0.519385i	−0.0458604	+	0.0171050i
$923$	−20.4681	+	11.1764i	−0.673714	+	0.367876i
$924$	−1.81598	+	1.57356i	−0.0597415	+	0.0517663i
$925$	4.77150	−	0.584818i	0.156886	−	0.0192287i
$926$	1.24610	−	1.43807i	0.0409492	−	0.0472579i
$927$	7.58458	+	10.1318i	0.249110	+	0.332772i
$928$	−1.61724	+	2.96175i	−0.0530885	+	0.0972244i
$929$	−6.52609	+	10.1548i	−0.214114	+	0.333168i	−0.931652	−	0.363351i	$-0.881632\pi$
$929$	−6.52609	+	10.1548i	−0.214114	+	0.333168i	0.717538	+	0.696519i	$0.245269\pi$
$930$	−0.877126	+	1.70758i	−0.0287621	+	0.0559938i
$931$	2.58707	−	1.18148i	0.0847879	−	0.0387213i
$932$	−2.24100	+	6.00834i	−0.0734063	+	0.196810i
$933$	8.34260	+	6.24519i	0.273124	+	0.204458i
$934$	2.58343	+	1.66027i	0.0845324	+	0.0543257i
$935$	3.90081	+	8.00004i	0.127570	+	0.261629i
$936$	−0.672341	+	4.67623i	−0.0219761	+	0.152847i
$937$	−3.68910	−	51.5804i	−0.120518	−	1.68506i	−0.594166	−	0.804343i	$-0.702518\pi$
$937$	−3.68910	−	51.5804i	−0.120518	−	1.68506i	0.473648	−	0.880714i	$-0.342937\pi$
$938$	−0.0895071	+	0.411458i	−0.00292251	+	0.0134346i
$939$	−8.25221	−	9.52356i	−0.269301	−	0.310790i
$940$	−29.3419	−	3.46426i	−0.957027	−	0.112992i
$941$	−8.39703	−	3.83480i	−0.273735	−	0.125011i	0.273818	−	0.961782i	$-0.411713\pi$
$941$	−8.39703	−	3.83480i	−0.273735	−	0.125011i	−0.547553	+	0.836771i	$0.684441\pi$
$942$	1.15913	−	1.15913i	0.0377666	−	0.0377666i
$943$	43.6716	−	13.1757i	1.42214	−	0.429061i
$944$			14.3575i			0.467297i
$945$	20.7935	−	12.0462i	0.676413	−	0.391862i
$946$	−0.266306	−	0.0781945i	−0.00865836	−	0.00254232i
$947$	−0.742267	+	10.3783i	−0.0241204	+	0.337248i	0.971035	+	0.238936i	$0.0767987\pi$
$947$	−0.742267	+	10.3783i	−0.0241204	+	0.337248i	−0.995156	+	0.0983115i	$0.968656\pi$
$948$	−1.49483	−	0.325180i	−0.0485498	−	0.0105614i
$949$	−32.8911	−	28.5003i	−1.06769	−	0.925160i
$950$	3.71099	+	2.49570i	0.120400	+	0.0809713i
$951$	18.7953	−	5.51881i	0.609480	−	0.178960i
$952$	−1.86638	−	8.57959i	−0.0604896	−	0.278066i
$953$	10.4164	−	13.9147i	0.337420	−	0.450741i	−0.599453	−	0.800410i	$-0.704615\pi$
$953$	10.4164	−	13.9147i	0.337420	−	0.450741i	0.936873	+	0.349669i	$0.113706\pi$
$954$	−0.659457	−	1.44401i	−0.0213507	−	0.0467515i
$955$	16.4296	+	3.14136i	0.531649	+	0.101652i
$956$	−3.10805	−	21.6170i	−0.100522	−	0.699142i
$957$	0.983599	−	0.213969i	0.0317952	−	0.00691663i
$958$	−2.25764	−	1.23277i	−0.0729411	−	0.0398288i
$959$	−32.9955	−	4.74404i	−1.06548	−	0.153193i
$960$	−10.5024	−	6.38029i	−0.338965	−	0.205923i
$961$	49.4411	−	31.7739i	1.59487	−	1.02496i
$962$	−0.458466	−	0.0327901i	−0.0147815	−	0.00105720i
$963$	−1.01484	−	1.85853i	−0.0327026	−	0.0598904i
$964$	11.8352	−	25.9155i	0.381186	−	0.834681i
$965$	−36.8186	+	6.24733i	−1.18523	+	0.201109i
$966$	1.11058	+	0.404869i	0.0357324	+	0.0130264i
$967$	−20.1459	−	20.1459i	−0.647848	−	0.647848i	0.304625	−	0.952472i	$-0.401469\pi$
$967$	−20.1459	−	20.1459i	−0.647848	−	0.647848i	−0.952472	+	0.304625i	$0.901469\pi$
$968$	1.85831	+	4.98232i	0.0597283	+	0.160138i
$969$	9.31543	−	31.7254i	0.299255	−	1.01917i
$970$	0.160132	+	1.65118i	0.00514154	+	0.0530162i
$971$	−0.883082	−	1.37410i	−0.0283394	−	0.0440970i	0.826795	−	0.562504i	$-0.190162\pi$
$971$	−0.883082	−	1.37410i	−0.0283394	−	0.0440970i	−0.855134	+	0.518407i	$0.826525\pi$
$972$	−30.0101	+	2.14637i	−0.962575	+	0.0688447i
$973$	9.29562	−	6.95861i	0.298004	−	0.223083i
$974$	−0.389249	−	1.32566i	−0.0124723	−	0.0424769i
$975$	−13.3328	−	3.19278i	−0.426990	−	0.102251i
$976$	12.1502	−	1.74694i	0.388920	−	0.0559183i
$977$	12.4856	+	4.65689i	0.399450	+	0.148987i	0.541157	−	0.840921i	$-0.317986\pi$
$977$	12.4856	+	4.65689i	0.399450	+	0.148987i	−0.141707	+	0.989909i	$0.545259\pi$
$978$	−0.278501	−	0.103875i	−0.00890548	−	0.00332157i
$979$	−4.23523	+	0.608934i	−0.135359	+	0.0194616i
$980$	−0.661490	−	1.64527i	−0.0211305	−	0.0525562i
$981$	−1.41931	−	4.83374i	−0.0453152	−	0.154329i
$982$	−2.80438	+	2.09934i	−0.0894915	+	0.0669925i
$983$	−57.3876	+	4.10444i	−1.83038	+	0.130911i	−0.943560	−	0.331202i	$-0.892546\pi$
$983$	−57.3876	+	4.10444i	−1.83038	+	0.130911i	−0.886821	+	0.462114i	$0.847091\pi$
$984$	1.85643	+	2.88866i	0.0591809	+	0.0920872i
$985$	28.6846	−	34.8458i	0.913968	−	1.11028i
$986$	−0.516074	+	1.75759i	−0.0164352	+	0.0559730i
$987$	−4.56356	−	12.2354i	−0.145260	−	0.389457i
$988$	37.9750	+	37.9750i	1.20814	+	1.20814i
$989$	−3.76938	−	16.7292i	−0.119859	−	0.531957i
$990$	0.0720162	+	0.424426i	0.00228882	+	0.0134892i
$991$	−12.3900	+	27.1304i	−0.393583	+	0.861826i	0.604298	+	0.796758i	$0.293454\pi$
$991$	−12.3900	+	27.1304i	−0.393583	+	0.861826i	−0.997881	+	0.0650674i	$0.979274\pi$
$992$	−6.77682	−	12.4108i	−0.215164	−	0.394044i
$993$	−17.5828	−	1.25754i	−0.557972	−	0.0399070i
$994$	1.76357	−	1.13338i	0.0559370	−	0.0359485i
$995$	−43.2129	+	10.5510i	−1.36994	+	0.334489i
$996$	−8.57210	−	1.23248i	−0.271617	−	0.0390527i
$997$	22.2990	+	12.1762i	0.706218	+	0.385624i	0.791861	−	0.610702i	$-0.209113\pi$
$997$	22.2990	+	12.1762i	0.706218	+	0.385624i	−0.0856428	+	0.996326i	$0.527294\pi$
$998$	−2.01155	+	0.437586i	−0.0636745	+	0.0138515i
$999$	−0.540568	−	3.75973i	−0.0171028	−	0.118953i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.l.a.17.5	✓	200
5.2	odd	4		575.2.r.b.293.5		200
5.3	odd	4	inner	115.2.l.a.63.6	yes	200
5.4	even	2		575.2.r.b.132.6		200
23.19	odd	22	inner	115.2.l.a.42.6	yes	200
115.19	odd	22		575.2.r.b.157.5		200
115.42	even	44		575.2.r.b.318.6		200
115.88	even	44	inner	115.2.l.a.88.5	yes	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.l.a.17.5	✓	200	1.1	even	1	trivial
115.2.l.a.42.6	yes	200	23.19	odd	22	inner
115.2.l.a.63.6	yes	200	5.3	odd	4	inner
115.2.l.a.88.5	yes	200	115.88	even	44	inner
575.2.r.b.132.6		200	5.4	even	2
575.2.r.b.157.5		200	115.19	odd	22
575.2.r.b.293.5		200	5.2	odd	4
575.2.r.b.318.6		200	115.42	even	44

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.117766 + 0.0439246i) q^{2} +(-0.632714 + 0.345488i) q^{3} +(-1.49956 + 1.29938i) q^{4} +(2.23369 + 0.103094i) q^{5} +(0.0593371 - 0.0684786i) q^{6} +(1.63018 + 2.17766i) q^{7} +(0.239998 - 0.439523i) q^{8} +(-1.34096 + 2.08657i) q^{9} +O(q^{10})\)	\(q+(-0.117766 + 0.0439246i) q^{2} +(-0.632714 + 0.345488i) q^{3} +(-1.49956 + 1.29938i) q^{4} +(2.23369 + 0.103094i) q^{5} +(0.0593371 - 0.0684786i) q^{6} +(1.63018 + 2.17766i) q^{7} +(0.239998 - 0.439523i) q^{8} +(-1.34096 + 2.08657i) q^{9} +(-0.267582 + 0.0859729i) q^{10} +(-0.561740 + 0.256538i) q^{11} +(0.499874 - 1.34021i) q^{12} +(3.04488 + 2.27937i) q^{13} +(-0.287633 - 0.184850i) q^{14} +(-1.44891 + 0.706484i) q^{15} +(0.555805 - 3.86571i) q^{16} +(-0.459814 - 6.42904i) q^{17} +(0.0662679 - 0.304629i) q^{18} +(-4.66003 - 5.37796i) q^{19} +(-3.48351 + 2.74781i) q^{20} +(-1.78379 - 0.814630i) q^{21} +(0.0548858 - 0.0548858i) q^{22} +(4.61146 + 1.31697i) q^{23} +0.361009i q^{24} +(4.97874 + 0.460561i) q^{25} +(-0.458705 - 0.134688i) q^{26} +(0.281842 - 3.94066i) q^{27} +(-5.27414 - 1.14732i) q^{28} +(1.70881 + 1.48069i) q^{29} +(0.139600 - 0.146843i) q^{30} +(-9.09095 + 2.66934i) q^{31} +(0.317241 + 1.45833i) q^{32} +(0.266790 - 0.356390i) q^{33} +(0.336544 + 0.736927i) q^{34} +(3.41680 + 5.03228i) q^{35} +(-0.700393 - 4.87134i) q^{36} +(0.939469 - 0.204369i) q^{37} +(0.785020 + 0.428653i) q^{38} +(-2.71404 - 0.390220i) q^{39} +(0.581393 - 0.957017i) q^{40} +(8.00163 - 5.14234i) q^{41} +(0.245853 + 0.0175837i) q^{42} +(-1.71366 - 3.13834i) q^{43} +(0.509024 - 1.11461i) q^{44} +(-3.21040 + 4.52251i) q^{45} +(-0.600923 + 0.0474612i) q^{46} +(4.70878 + 4.70878i) q^{47} +(0.983891 + 2.63791i) q^{48} +(-0.112601 + 0.383482i) q^{49} +(-0.606559 + 0.164451i) q^{50} +(2.51209 + 3.90888i) q^{51} +(-7.52774 + 0.538395i) q^{52} +(4.07640 - 3.05156i) q^{53} +(0.139900 + 0.476457i) q^{54} +(-1.28120 + 0.515115i) q^{55} +(1.34837 - 0.193867i) q^{56} +(4.80649 + 1.79273i) q^{57} +(-0.266279 - 0.0993171i) q^{58} +(-3.63885 + 0.523187i) q^{59} +(1.25473 - 2.94209i) q^{60} +(0.885509 + 3.01577i) q^{61} +(0.953358 - 0.713675i) q^{62} +(-6.72983 + 0.481327i) q^{63} +(4.12148 + 6.41316i) q^{64} +(6.56634 + 5.40532i) q^{65} +(-0.0157646 + 0.0536894i) q^{66} +(-0.430384 - 1.15391i) q^{67} +(9.04326 + 9.04326i) q^{68} +(-3.37274 + 0.759937i) q^{69} +(-0.623425 - 0.442552i) q^{70} +(-2.54704 + 5.57724i) q^{71} +(0.595269 + 1.09015i) q^{72} +(-11.4132 - 0.816286i) q^{73} +(-0.101661 + 0.0653336i) q^{74} +(-3.30924 + 1.42869i) q^{75} +(13.9760 + 2.00944i) q^{76} +(-1.47439 - 0.805077i) q^{77} +(0.336763 - 0.0732582i) q^{78} +(-0.152203 - 1.05860i) q^{79} +(1.64003 - 8.57749i) q^{80} +(-1.90795 - 4.17782i) q^{81} +(-0.716448 + 0.957063i) q^{82} +(-1.28696 - 5.91605i) q^{83} +(3.73341 - 1.09623i) q^{84} +(-0.364285 - 14.4079i) q^{85} +(0.339662 + 0.294319i) q^{86} +(-1.59275 - 0.346482i) q^{87} +(-0.0220620 + 0.308467i) q^{88} +(6.64802 + 1.95203i) q^{89} +(0.179427 - 0.673614i) q^{90} +10.3465i q^{91} +(-8.62641 + 4.01714i) q^{92} +(4.82975 - 4.82975i) q^{93} +(-0.761367 - 0.347705i) q^{94} +(-9.85463 - 12.4931i) q^{95} +(-0.704560 - 0.813106i) q^{96} +(1.25467 - 5.76763i) q^{97} +(-0.00358374 - 0.0501072i) q^{98} +(0.217985 - 1.51612i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8}+O(q^{10}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23} - 10 q^{25} - 28 q^{26} - 26 q^{27} + 66 q^{28} - 22 q^{30} - 40 q^{31} - 46 q^{32} - 14 q^{35} - 12 q^{36} + 66 q^{37} - 22 q^{38} - 22 q^{40} - 8 q^{41} + 198 q^{42} - 22 q^{43} - 76 q^{46} + 52 q^{47} + 18 q^{48} - 82 q^{50} - 44 q^{51} + 158 q^{52} - 22 q^{53} - 10 q^{55} + 88 q^{56} + 66 q^{57} - 58 q^{58} - 22 q^{60} + 44 q^{61} + 38 q^{62} - 22 q^{63} - 22 q^{65} + 132 q^{66} - 22 q^{67} + 32 q^{70} + 132 q^{71} - 28 q^{72} + 34 q^{73} + 38 q^{75} + 132 q^{76} - 10 q^{77} + 22 q^{78} + 176 q^{80} - 48 q^{81} - 50 q^{82} - 22 q^{83} + 202 q^{85} - 46 q^{87} - 110 q^{88} + 396 q^{90} + 50 q^{92} - 36 q^{93} + 68 q^{95} + 148 q^{96} - 88 q^{97} - 50 q^{98}+O(q^{100}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Introduction

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