LMFDB - Embedded newform 138.2.e.b.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(13,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("138.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.e (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			25.1
Root			$-0.841254 - 0.540641i$ of defining polynomial
Character	$\chi$	$=$	138.25
Dual form			138.2.e.b.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 + 0.540641i) q^{2} +(0.142315 + 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.186393 + 0.0547299i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-1.27819 + 1.47511i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})$	\(q+(0.841254 + 0.540641i) q^{2} +(0.142315 + 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.186393 + 0.0547299i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-1.27819 + 1.47511i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(0.127214 + 0.146813i) q^{10} +(5.30154 - 3.40709i) q^{11} +(-0.841254 + 0.540641i) q^{12} +(-3.15177 - 3.63733i) q^{13} +(-1.87279 + 0.549899i) q^{14} +(-0.0276463 + 0.192284i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-1.33259 + 2.91797i) q^{17} +(-0.959493 - 0.281733i) q^{18} +(0.357028 + 0.781782i) q^{19} +(0.0276463 + 0.192284i) q^{20} +(-1.64200 - 1.05525i) q^{21} +6.30195 q^{22} +(3.37782 - 3.40446i) q^{23} -1.00000 q^{24} +(-4.17452 - 2.68280i) q^{25} +(-0.684944 - 4.76389i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(-1.87279 - 0.549899i) q^{28} +(2.25047 - 4.92785i) q^{29} +(-0.127214 + 0.146813i) q^{30} +(0.144265 - 1.00339i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(4.12690 + 4.76270i) q^{33} +(-2.69862 + 1.73430i) q^{34} +(-0.318978 + 0.204995i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-6.61126 + 1.94124i) q^{37} +(-0.122312 + 0.850701i) q^{38} +(3.15177 - 3.63733i) q^{39} +(-0.0806993 + 0.176707i) q^{40} +(0.932638 + 0.273847i) q^{41} +(-0.810827 - 1.77546i) q^{42} +(0.731899 + 5.09047i) q^{43} +(5.30154 + 3.40709i) q^{44} -0.194262 q^{45} +(4.68219 - 1.03782i) q^{46} -7.41216 q^{47} +(-0.841254 - 0.540641i) q^{48} +(0.454025 + 3.15781i) q^{49} +(-2.06140 - 4.51383i) q^{50} +(-3.07792 - 0.903759i) q^{51} +(1.99934 - 4.37795i) q^{52} +(-1.31494 + 1.51752i) q^{53} +(0.142315 - 0.989821i) q^{54} +(1.17464 - 0.344905i) q^{55} +(-1.27819 - 1.47511i) q^{56} +(-0.723014 + 0.464653i) q^{57} +(4.55742 - 2.92887i) q^{58} +(5.63325 + 6.50112i) q^{59} +(-0.186393 + 0.0547299i) q^{60} +(-1.72487 + 11.9968i) q^{61} +(0.663836 - 0.766107i) q^{62} +(0.810827 - 1.77546i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-0.388396 - 0.850468i) q^{65} +(0.896861 + 6.23781i) q^{66} +(5.96723 + 3.83491i) q^{67} -3.20786 q^{68} +(3.85052 + 2.85894i) q^{69} -0.379170 q^{70} +(0.933267 + 0.599775i) q^{71} +(-0.142315 - 0.989821i) q^{72} +(-5.47763 - 11.9943i) q^{73} +(-6.61126 - 1.94124i) q^{74} +(2.06140 - 4.51383i) q^{75} +(-0.562819 + 0.649528i) q^{76} +(-1.75054 + 12.1753i) q^{77} +(4.61792 - 1.35595i) q^{78} +(-0.739858 - 0.853842i) q^{79} +(-0.163423 + 0.105026i) q^{80} +(0.841254 - 0.540641i) q^{81} +(0.636532 + 0.734597i) q^{82} +(-3.84482 + 1.12894i) q^{83} +(0.277777 - 1.93198i) q^{84} +(-0.408086 + 0.470956i) q^{85} +(-2.13640 + 4.67807i) q^{86} +(5.19797 + 1.52626i) q^{87} +(2.61792 + 5.73246i) q^{88} +(1.35933 + 9.45436i) q^{89} +(-0.163423 - 0.105026i) q^{90} +9.39402 q^{91} +(4.50000 + 1.65831i) q^{92} +1.01371 q^{93} +(-6.23551 - 4.00732i) q^{94} +(0.0237606 + 0.165259i) q^{95} +(-0.415415 - 0.909632i) q^{96} +(1.07554 + 0.315806i) q^{97} +(-1.32529 + 2.90199i) q^{98} +(-4.12690 + 4.76270i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} - q^{8} - q^{9}+O(q^{10}) $ 10 * q - q^2 + q^3 - q^4 - 2 * q^5 + q^6 - q^8 - q^9	$ 10 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} - q^{8} - q^{9} + 9 q^{10} + 11 q^{11} + q^{12} + 13 q^{13} - 11 q^{14} + 13 q^{15} - q^{16} - 24 q^{17} - q^{18} - 14 q^{19} - 13 q^{20} + 11 q^{21} + 22 q^{22} - 10 q^{23} - 10 q^{24} - 43 q^{25} - 9 q^{26} + q^{27} - 11 q^{28} + 13 q^{29} - 9 q^{30} + 8 q^{31} - q^{32} + 22 q^{33} + 9 q^{34} - q^{36} - 13 q^{37} - 3 q^{38} - 13 q^{39} + 9 q^{40} - 10 q^{41} - 8 q^{43} + 11 q^{44} - 2 q^{45} + q^{46} - 8 q^{47} + q^{48} + 29 q^{49} + 23 q^{50} - 9 q^{51} + 2 q^{52} - 35 q^{53} + q^{54} - 11 q^{55} + 3 q^{57} + 13 q^{58} + 37 q^{59} + 2 q^{60} - 2 q^{61} + 8 q^{62} - q^{64} + 37 q^{65} + 14 q^{67} - 2 q^{68} - q^{69} - 22 q^{70} + 44 q^{71} - q^{72} - 49 q^{73} - 13 q^{74} - 23 q^{75} + 8 q^{76} + 44 q^{77} + 20 q^{78} - 8 q^{79} - 2 q^{80} - q^{81} + 12 q^{82} - 17 q^{83} - 11 q^{84} - 37 q^{85} + 14 q^{86} - 2 q^{87} + 59 q^{89} - 2 q^{90} + 66 q^{91} + 45 q^{92} + 36 q^{93} - 19 q^{94} - 28 q^{95} + q^{96} - 21 q^{97} - 26 q^{98} - 22 q^{99}+O(q^{100}) $ 10 * q - q^2 + q^3 - q^4 - 2 * q^5 + q^6 - q^8 - q^9 + 9 * q^10 + 11 * q^11 + q^12 + 13 * q^13 - 11 * q^14 + 13 * q^15 - q^16 - 24 * q^17 - q^18 - 14 * q^19 - 13 * q^20 + 11 * q^21 + 22 * q^22 - 10 * q^23 - 10 * q^24 - 43 * q^25 - 9 * q^26 + q^27 - 11 * q^28 + 13 * q^29 - 9 * q^30 + 8 * q^31 - q^32 + 22 * q^33 + 9 * q^34 - q^36 - 13 * q^37 - 3 * q^38 - 13 * q^39 + 9 * q^40 - 10 * q^41 - 8 * q^43 + 11 * q^44 - 2 * q^45 + q^46 - 8 * q^47 + q^48 + 29 * q^49 + 23 * q^50 - 9 * q^51 + 2 * q^52 - 35 * q^53 + q^54 - 11 * q^55 + 3 * q^57 + 13 * q^58 + 37 * q^59 + 2 * q^60 - 2 * q^61 + 8 * q^62 - q^64 + 37 * q^65 + 14 * q^67 - 2 * q^68 - q^69 - 22 * q^70 + 44 * q^71 - q^72 - 49 * q^73 - 13 * q^74 - 23 * q^75 + 8 * q^76 + 44 * q^77 + 20 * q^78 - 8 * q^79 - 2 * q^80 - q^81 + 12 * q^82 - 17 * q^83 - 11 * q^84 - 37 * q^85 + 14 * q^86 - 2 * q^87 + 59 * q^89 - 2 * q^90 + 66 * q^91 + 45 * q^92 + 36 * q^93 - 19 * q^94 - 28 * q^95 + q^96 - 21 * q^97 - 26 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$e\left(\frac{1}{11}\right)$

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 $

$2$	0.841254	+	0.540641i	0.594856	+	0.382291i
$2$	0.841254	+	0.540641i	0.594856	+	0.382291i
$3$	0.142315	+	0.989821i	0.0821655	+	0.571474i
$3$	0.142315	+	0.989821i	0.0821655	+	0.571474i
$4$	0.415415	+	0.909632i	0.207708	+	0.454816i
$5$	0.186393	+	0.0547299i	0.0833574	+	0.0244759i	0.323145	−	0.946349i	$-0.395260\pi$
$5$	0.186393	+	0.0547299i	0.0833574	+	0.0244759i	−0.239788	+	0.970825i	$0.577078\pi$
$6$	−0.415415	+	0.909632i	−0.169592	+	0.371356i
$7$	−1.27819	+	1.47511i	−0.483110	+	0.557539i	−0.944012	−	0.329913i	$-0.892981\pi$
$7$	−1.27819	+	1.47511i	−0.483110	+	0.557539i	0.460901	+	0.887451i	$0.347526\pi$
$8$	−0.142315	+	0.989821i	−0.0503159	+	0.349955i
$9$	−0.959493	+	0.281733i	−0.319831	+	0.0939109i
$10$	0.127214	+	0.146813i	0.0402287	+	0.0464264i
$11$	5.30154	−	3.40709i	1.59847	−	1.02728i	0.630512	−	0.776180i	$-0.282845\pi$
$11$	5.30154	−	3.40709i	1.59847	−	1.02728i	0.967962	−	0.251097i	$-0.0807913\pi$
$12$	−0.841254	+	0.540641i	−0.242849	+	0.156070i
$13$	−3.15177	−	3.63733i	−0.874143	−	1.00881i	−0.999860	−	0.0167483i	$-0.994669\pi$
$13$	−3.15177	−	3.63733i	−0.874143	−	1.00881i	0.125717	−	0.992066i	$-0.459877\pi$
$14$	−1.87279	+	0.549899i	−0.500523	+	0.146967i
$15$	−0.0276463	+	0.192284i	−0.00713825	+	0.0496476i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	−1.33259	+	2.91797i	−0.323201	+	0.707712i	−0.999584	−	0.0288381i	$-0.990819\pi$
$17$	−1.33259	+	2.91797i	−0.323201	+	0.707712i	0.676383	+	0.736550i	$0.263547\pi$
$18$	−0.959493	−	0.281733i	−0.226155	−	0.0664050i
$19$	0.357028	+	0.781782i	0.0819078	+	0.179353i	0.946155	−	0.323715i	$-0.104932\pi$
$19$	0.357028	+	0.781782i	0.0819078	+	0.179353i	−0.864247	+	0.503068i	$0.832205\pi$
$20$	0.0276463	+	0.192284i	0.00618191	+	0.0429961i
$21$	−1.64200	−	1.05525i	−0.358314	−	0.230274i
$22$	6.30195			1.34358
$23$	3.37782	−	3.40446i	0.704324	−	0.709878i
$23$	3.37782	−	3.40446i	0.704324	−	0.709878i
$24$	−1.00000			−0.204124
$25$	−4.17452	−	2.68280i	−0.834904	−	0.536560i
$26$	−0.684944	−	4.76389i	−0.134329	−	0.934276i
$27$	−0.415415	−	0.909632i	−0.0799467	−	0.175059i
$28$	−1.87279	−	0.549899i	−0.353923	−	0.103921i
$29$	2.25047	−	4.92785i	0.417902	−	0.915079i	−0.577235	−	0.816578i	$-0.695868\pi$
$29$	2.25047	−	4.92785i	0.417902	−	0.915079i	0.995137	−	0.0985003i	$-0.0314045\pi$
$30$	−0.127214	+	0.146813i	−0.0232261	+	0.0268043i
$31$	0.144265	−	1.00339i	0.0259108	−	0.180214i	−0.972756	−	0.231831i	$-0.925528\pi$
$31$	0.144265	−	1.00339i	0.0259108	−	0.180214i	0.998667	+	0.0516171i	$0.0164375\pi$
$32$	−0.959493	+	0.281733i	−0.169616	+	0.0498038i
$33$	4.12690	+	4.76270i	0.718401	+	0.829079i
$34$	−2.69862	+	1.73430i	−0.462810	+	0.297430i
$35$	−0.318978	+	0.204995i	−0.0539171	+	0.0346504i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	−6.61126	+	1.94124i	−1.08688	+	0.319138i	−0.775630	−	0.631188i	$-0.782567\pi$
$37$	−6.61126	+	1.94124i	−1.08688	+	0.319138i	−0.311255	+	0.950326i	$0.600749\pi$
$38$	−0.122312	+	0.850701i	−0.0198417	+	0.138002i
$39$	3.15177	−	3.63733i	0.504687	−	0.582439i
$40$	−0.0806993	+	0.176707i	−0.0127597	+	0.0279398i
$41$	0.932638	+	0.273847i	0.145654	+	0.0427677i	0.353747	−	0.935341i	$-0.384908\pi$
$41$	0.932638	+	0.273847i	0.145654	+	0.0427677i	−0.208093	+	0.978109i	$0.566726\pi$
$42$	−0.810827	−	1.77546i	−0.125113	−	0.273960i
$43$	0.731899	+	5.09047i	0.111614	+	0.776290i	0.966351	+	0.257228i	$0.0828093\pi$
$43$	0.731899	+	5.09047i	0.111614	+	0.776290i	−0.854737	+	0.519061i	$0.826282\pi$
$44$	5.30154	+	3.40709i	0.799237	+	0.513638i
$45$	−0.194262			−0.0289588
$46$	4.68219	−	1.03782i	0.690352	−	0.153019i
$47$	−7.41216			−1.08117			−0.540587	−	0.841288i	$-0.681798\pi$
$47$	−7.41216			−1.08117			−0.540587	+	0.841288i	$0.681798\pi$
$48$	−0.841254	−	0.540641i	−0.121424	−	0.0780348i
$49$	0.454025	+	3.15781i	0.0648607	+	0.451116i
$50$	−2.06140	−	4.51383i	−0.291526	−	0.638352i
$51$	−3.07792	−	0.903759i	−0.430995	−	0.126552i
$52$	1.99934	−	4.37795i	0.277259	−	0.607112i
$53$	−1.31494	+	1.51752i	−0.180621	+	0.208447i	−0.838839	−	0.544380i	$-0.816765\pi$
$53$	−1.31494	+	1.51752i	−0.180621	+	0.208447i	0.658218	+	0.752827i	$0.271310\pi$
$54$	0.142315	−	0.989821i	0.0193666	−	0.134698i
$55$	1.17464	−	0.344905i	0.158388	−	0.0465070i
$56$	−1.27819	−	1.47511i	−0.170805	−	0.197120i
$57$	−0.723014	+	0.464653i	−0.0957656	+	0.0615448i
$58$	4.55742	−	2.92887i	0.598418	−	0.384580i
$59$	5.63325	+	6.50112i	0.733387	+	0.846373i	0.992849	−	0.119380i	$-0.0380907\pi$
$59$	5.63325	+	6.50112i	0.733387	+	0.846373i	−0.259462	+	0.965753i	$0.583545\pi$
$60$	−0.186393	+	0.0547299i	−0.0240632	+	0.00706560i
$61$	−1.72487	+	11.9968i	−0.220848	+	1.53603i	0.513996	+	0.857792i	$0.328165\pi$
$61$	−1.72487	+	11.9968i	−0.220848	+	1.53603i	−0.734844	+	0.678236i	$0.762745\pi$
$62$	0.663836	−	0.766107i	0.0843072	−	0.0972957i
$63$	0.810827	−	1.77546i	0.102155	−	0.223687i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	−0.388396	−	0.850468i	−0.0481746	−	0.105488i
$66$	0.896861	+	6.23781i	0.110396	+	0.767821i
$67$	5.96723	+	3.83491i	0.729014	+	0.468509i	0.851762	−	0.523929i	$-0.175534\pi$
$67$	5.96723	+	3.83491i	0.729014	+	0.468509i	−0.122748	+	0.992438i	$0.539171\pi$
$68$	−3.20786			−0.389010
$69$	3.85052	+	2.85894i	0.463548	+	0.344175i
$70$	−0.379170			−0.0453194
$71$	0.933267	+	0.599775i	0.110758	+	0.0711801i	0.594847	−	0.803839i	$-0.297212\pi$
$71$	0.933267	+	0.599775i	0.110758	+	0.0711801i	−0.484089	+	0.875019i	$0.660849\pi$
$72$	−0.142315	−	0.989821i	−0.0167720	−	0.116652i
$73$	−5.47763	−	11.9943i	−0.641109	−	1.40383i	−0.899125	−	0.437692i	$-0.855796\pi$
$73$	−5.47763	−	11.9943i	−0.641109	−	1.40383i	0.258017	−	0.966141i	$-0.416931\pi$
$74$	−6.61126	−	1.94124i	−0.768543	−	0.225665i
$75$	2.06140	−	4.51383i	0.238030	−	0.521212i
$76$	−0.562819	+	0.649528i	−0.0645598	+	0.0745060i
$77$	−1.75054	+	12.1753i	−0.199492	+	1.38750i
$78$	4.61792	−	1.35595i	0.522877	−	0.153531i
$79$	−0.739858	−	0.853842i	−0.0832405	−	0.0960647i	0.712601	−	0.701569i	$-0.247517\pi$
$79$	−0.739858	−	0.853842i	−0.0832405	−	0.0960647i	−0.795842	+	0.605504i	$0.792971\pi$
$80$	−0.163423	+	0.105026i	−0.0182713	+	0.0117422i
$81$	0.841254	−	0.540641i	0.0934726	−	0.0600712i
$82$	0.636532	+	0.734597i	0.0702932	+	0.0811227i
$83$	−3.84482	+	1.12894i	−0.422024	+	0.123918i	−0.485847	−	0.874044i	$-0.661489\pi$
$83$	−3.84482	+	1.12894i	−0.422024	+	0.123918i	0.0638230	+	0.997961i	$0.479671\pi$
$84$	0.277777	−	1.93198i	0.0303080	−	0.210797i
$85$	−0.408086	+	0.470956i	−0.0442631	+	0.0510824i
$86$	−2.13640	+	4.67807i	−0.230374	+	0.504450i
$87$	5.19797	+	1.52626i	0.557281	+	0.163632i
$88$	2.61792	+	5.73246i	0.279072	+	0.611082i
$89$	1.35933	+	9.45436i	0.144089	+	1.00216i	0.925663	+	0.378348i	$0.123508\pi$
$89$	1.35933	+	9.45436i	0.144089	+	1.00216i	−0.781575	+	0.623812i	$0.785583\pi$
$90$	−0.163423	−	0.105026i	−0.0172263	−	0.0110707i
$91$	9.39402			0.984760
$92$	4.50000	+	1.65831i	0.469157	+	0.172891i
$93$	1.01371			0.105116
$94$	−6.23551	−	4.00732i	−0.643143	−	0.413323i
$95$	0.0237606	+	0.165259i	0.00243779	+	0.0169552i
$96$	−0.415415	−	0.909632i	−0.0423981	−	0.0928389i
$97$	1.07554	+	0.315806i	0.109204	+	0.0320653i	0.335878	−	0.941905i	$-0.390967\pi$
$97$	1.07554	+	0.315806i	0.109204	+	0.0320653i	−0.226674	+	0.973971i	$0.572785\pi$
$98$	−1.32529	+	2.90199i	−0.133875	+	0.293145i
$99$	−4.12690	+	4.76270i	−0.414769	+	0.478669i
$100$	0.706204	−	4.91175i	0.0706204	−	0.491175i
$101$	−12.0622	+	3.54178i	−1.20023	+	0.352420i	−0.819942	−	0.572447i	$-0.805994\pi$
$101$	−12.0622	+	3.54178i	−1.20023	+	0.352420i	−0.380290	+	0.924867i	$0.624176\pi$
$102$	−2.10070	−	2.42434i	−0.208000	−	0.240045i
$103$	16.3172	−	10.4864i	1.60778	−	1.03326i	0.644560	−	0.764553i	$-0.277040\pi$
$103$	16.3172	−	10.4864i	1.60778	−	1.03326i	0.963222	−	0.268706i	$-0.0865959\pi$
$104$	4.04885	−	2.60204i	0.397023	−	0.255151i
$105$	−0.248303	−	0.286557i	−0.0242319	−	0.0279651i
$106$	−1.92663	+	0.565710i	−0.187131	+	0.0549466i
$107$	−0.437753	+	3.04464i	−0.0423191	+	0.294336i	0.957660	+	0.287901i	$0.0929574\pi$
$107$	−0.437753	+	3.04464i	−0.0423191	+	0.294336i	−0.999979	+	0.00643501i	$0.997952\pi$
$108$	0.654861	−	0.755750i	0.0630140	−	0.0727220i
$109$	0.809766	−	1.77314i	0.0775615	−	0.169836i	−0.866879	−	0.498519i	$-0.833877\pi$
$109$	0.809766	−	1.77314i	0.0775615	−	0.169836i	0.944440	+	0.328683i	$0.106605\pi$
$110$	1.17464	+	0.344905i	0.111997	+	0.0328854i
$111$	−2.86236	−	6.26770i	−0.271683	−	0.594904i
$112$	−0.277777	−	1.93198i	−0.0262475	−	0.182555i
$113$	−14.4268	−	9.27157i	−1.35716	−	0.872196i	−0.359034	−	0.933325i	$-0.616894\pi$
$113$	−14.4268	−	9.27157i	−1.35716	−	0.872196i	−0.998130	+	0.0611286i	$0.980530\pi$
$114$	−0.859449			−0.0804947
$115$	0.815927	−	0.449698i	0.0760856	−	0.0419346i
$116$	5.41741			0.502994
$117$	4.04885	+	2.60204i	0.374317	+	0.240559i
$118$	1.22422	+	8.51465i	0.112699	+	0.783837i
$119$	−2.60102	−	5.69544i	−0.238435	−	0.522100i
$120$	−0.186393	−	0.0547299i	−0.0170153	−	0.00499613i
$121$	11.9285	−	26.1197i	1.08441	−	2.37452i
$122$	−7.93700	+	9.15979i	−0.718582	+	0.829288i
$123$	−0.138332	+	0.962117i	−0.0124729	+	0.0867512i
$124$	0.972643	−	0.285594i	0.0873459	−	0.0256471i
$125$	−1.26734	−	1.46259i	−0.113355	−	0.130818i
$126$	1.64200	−	1.05525i	0.146281	−	0.0940091i
$127$	−18.1810	+	11.6842i	−1.61330	+	1.03681i	−0.653190	+	0.757194i	$0.726570\pi$
$127$	−18.1810	+	11.6842i	−1.61330	+	1.03681i	−0.960113	+	0.279613i	$0.909794\pi$
$128$	−0.654861	−	0.755750i	−0.0578821	−	0.0667995i
$129$	−4.93450	+	1.44890i	−0.434458	+	0.127568i
$130$	0.133058	−	0.925442i	0.0116700	−	0.0811666i
$131$	9.79482	−	11.3038i	0.855777	−	0.987620i	−0.144221	−	0.989546i	$-0.546068\pi$
$131$	9.79482	−	11.3038i	0.855777	−	0.987620i	0.999998	+	0.00192587i	$0.000613023\pi$
$132$	−2.61792	+	5.73246i	−0.227861	+	0.498946i
$133$	−1.60956	−	0.472610i	−0.139567	−	0.0409805i
$134$	2.94665	+	6.45226i	0.254552	+	0.557390i
$135$	−0.0276463	−	0.192284i	−0.00237942	−	0.0165492i
$136$	−2.69862	−	1.73430i	−0.231405	−	0.148715i
$137$	18.1570			1.55126			0.775628	−	0.631190i	$-0.217433\pi$
$137$	18.1570			1.55126			0.775628	+	0.631190i	$0.217433\pi$
$138$	1.69360	+	4.48684i	0.144169	+	0.381945i
$139$	−7.36718			−0.624876			−0.312438	−	0.949938i	$-0.601146\pi$
$139$	−7.36718			−0.624876			−0.312438	+	0.949938i	$0.601146\pi$
$140$	−0.318978	−	0.204995i	−0.0269585	−	0.0173252i
$141$	−1.05486	−	7.33672i	−0.0888353	−	0.617863i
$142$	0.460852	+	1.00912i	0.0386738	+	0.0846839i
$143$	−29.1019	−	8.54510i	−2.43363	−	0.714577i
$144$	0.415415	−	0.909632i	0.0346179	−	0.0758027i
$145$	0.689173	−	0.795348i	0.0572327	−	0.0660500i
$146$	1.87655	−	13.0517i	0.155305	−	1.08017i
$147$	−3.06106	+	0.898807i	−0.252472	+	0.0741324i
$148$	−4.51223	−	5.20739i	−0.370903	−	0.428045i
$149$	13.1516	−	8.45201i	1.07742	−	0.692415i	0.123459	−	0.992350i	$-0.460601\pi$
$149$	13.1516	−	8.45201i	1.07742	−	0.692415i	0.953960	+	0.299934i	$0.0969648\pi$
$150$	4.17452	−	2.68280i	0.340848	−	0.219050i
$151$	−13.5583	−	15.6472i	−1.10336	−	1.27335i	−0.958871	−	0.283842i	$-0.908391\pi$
$151$	−13.5583	−	15.6472i	−1.10336	−	1.27335i	−0.144491	−	0.989506i	$-0.546154\pi$
$152$	−0.824635	+	0.242135i	−0.0668867	+	0.0196397i
$153$	0.456526	−	3.17521i	0.0369080	−	0.256700i
$154$	−8.05509	+	9.29606i	−0.649097	+	0.749098i
$155$	0.0818052	−	0.179129i	0.00657076	−	0.0143879i
$156$	4.61792	+	1.35595i	0.369730	+	0.108562i
$157$	−1.65182	−	3.61698i	−0.131830	−	0.288666i	0.832193	−	0.554485i	$-0.187085\pi$
$157$	−1.65182	−	3.61698i	−0.131830	−	0.288666i	−0.964023	+	0.265819i	$0.914358\pi$
$158$	−0.160787	−	1.11829i	−0.0127915	−	0.0889668i
$159$	−1.68921	−	1.08559i	−0.133963	−	0.0860928i
$160$	−0.194262			−0.0153577
$161$	0.704449	+	9.33420i	0.0555183	+	0.735638i
$162$	1.00000			0.0785674
$163$	20.6215	+	13.2526i	1.61520	+	1.03803i	0.958985	+	0.283455i	$0.0914807\pi$
$163$	20.6215	+	13.2526i	1.61520	+	1.03803i	0.656217	+	0.754572i	$0.272156\pi$
$164$	0.138332	+	0.962117i	0.0108019	+	0.0751288i
$165$	0.508563	+	1.11360i	0.0395915	+	0.0866934i
$166$	−3.84482	−	1.12894i	−0.298416	−	0.0876229i
$167$	−0.811902	+	1.77782i	−0.0628268	+	0.137572i	−0.938441	−	0.345440i	$-0.887730\pi$
$167$	−0.811902	+	1.77782i	−0.0628268	+	0.137572i	0.875614	+	0.483011i	$0.160457\pi$
$168$	1.27819	−	1.47511i	0.0986145	−	0.113807i
$169$	−1.44646	+	10.0604i	−0.111266	+	0.773874i
$170$	−0.597922	+	0.175566i	−0.0458585	+	0.0134653i
$171$	−0.562819	−	0.649528i	−0.0430399	−	0.0496706i
$172$	−4.32641	+	2.78042i	−0.329886	+	0.212005i
$173$	5.16669	−	3.32043i	0.392816	−	0.252447i	−0.329292	−	0.944228i	$-0.606810\pi$
$173$	5.16669	−	3.32043i	0.392816	−	0.252447i	0.722108	+	0.691781i	$0.243174\pi$
$174$	3.54765	+	4.09421i	0.268947	+	0.310381i
$175$	9.29325	−	2.72875i	0.702504	−	0.206274i
$176$	−0.896861	+	6.23781i	−0.0676034	+	0.470192i
$177$	−5.63325	+	6.50112i	−0.423421	+	0.488654i
$178$	−3.96787	+	8.68842i	−0.297404	+	0.651225i
$179$	−6.20879	−	1.82307i	−0.464067	−	0.136262i	0.0413370	−	0.999145i	$-0.486838\pi$
$179$	−6.20879	−	1.82307i	−0.464067	−	0.136262i	−0.505404	+	0.862883i	$0.668656\pi$
$180$	−0.0806993	−	0.176707i	−0.00601497	−	0.0131709i
$181$	−0.464155	−	3.22827i	−0.0345004	−	0.239955i	0.965273	−	0.261243i	$-0.0841324\pi$
$181$	−0.464155	−	3.22827i	−0.0345004	−	0.239955i	−0.999773	+	0.0212879i	$0.993223\pi$
$182$	7.90275	+	5.07879i	0.585791	+	0.376465i
$183$	−12.1201			−0.895946
$184$	2.88909	+	3.82794i	0.212987	+	0.282200i
$185$	−1.33853			−0.0984110
$186$	0.852783	+	0.548050i	0.0625291	+	0.0401850i
$187$	2.87700	+	20.0100i	0.210387	+	1.46328i
$188$	−3.07912	−	6.74234i	−0.224568	−	0.491736i
$189$	1.87279	+	0.549899i	0.136225	+	0.0399993i
$190$	−0.0693569	+	0.151870i	−0.00503167	+	0.0110178i
$191$	14.9659	−	17.2716i	1.08290	−	1.24973i	0.116359	−	0.993207i	$-0.462878\pi$
$191$	14.9659	−	17.2716i	1.08290	−	1.24973i	0.966538	−	0.256523i	$-0.0825768\pi$
$192$	0.142315	−	0.989821i	0.0102707	−	0.0714342i
$193$	16.2552	−	4.77294i	1.17007	−	0.343564i	0.361733	−	0.932282i	$-0.382185\pi$
$193$	16.2552	−	4.77294i	1.17007	−	0.343564i	0.808339	+	0.588718i	$0.200367\pi$
$194$	0.734062	+	0.847152i	0.0527025	+	0.0608220i
$195$	0.786537	−	0.505477i	0.0563251	−	0.0361979i
$196$	−2.68384	+	1.72480i	−0.191703	+	0.123200i
$197$	−0.821721	−	0.948317i	−0.0585452	−	0.0675648i	0.725722	−	0.687989i	$-0.241506\pi$
$197$	−0.821721	−	0.948317i	−0.0585452	−	0.0675648i	−0.784267	+	0.620424i	$0.786961\pi$
$198$	−6.04668	+	1.77546i	−0.429719	+	0.126177i
$199$	−3.53140	+	24.5614i	−0.250334	+	1.74111i	0.345872	+	0.938282i	$0.387583\pi$
$199$	−3.53140	+	24.5614i	−0.250334	+	1.74111i	−0.596206	+	0.802832i	$0.703326\pi$
$200$	3.24959	−	3.75023i	0.229781	−	0.265181i
$201$	−2.94665	+	6.45226i	−0.207841	+	0.455107i
$202$	−12.0622	−	3.54178i	−0.848692	−	0.249198i
$203$	4.39258	+	9.61842i	0.308299	+	0.675081i
$204$	−0.456526	−	3.17521i	−0.0319632	−	0.222309i
$205$	0.158849	+	0.102086i	0.0110945	+	0.00713002i
$206$	19.3963			1.35140
$207$	−2.28185	+	4.21819i	−0.158600	+	0.293185i
$208$	4.81288			0.333713
$209$	4.55640	+	2.92822i	0.315173	+	0.202549i
$210$	−0.0539615	−	0.375310i	−0.00372370	−	0.0258989i
$211$	3.01519	+	6.60235i	0.207575	+	0.454525i	0.984572	−	0.174979i	$-0.0559856\pi$
$211$	3.01519	+	6.60235i	0.207575	+	0.454525i	−0.776998	+	0.629503i	$0.783258\pi$
$212$	−1.92663	−	0.565710i	−0.132321	−	0.0388531i
$213$	−0.460852	+	1.00912i	−0.0315771	+	0.0691441i
$214$	−2.01432	+	2.32464i	−0.137696	+	0.158909i
$215$	−0.142180	+	0.988884i	−0.00969660	+	0.0674413i
$216$	0.959493	−	0.281733i	0.0652852	−	0.0191695i
$217$	1.29571	+	1.49533i	0.0879583	+	0.101509i
$218$	1.63985	−	1.05387i	0.111065	−	0.0713769i
$219$	11.0927	−	7.12885i	0.749576	−	0.481723i
$220$	0.801699	+	0.925210i	0.0540505	+	0.0623776i
$221$	14.8137	−	4.34968i	0.996474	−	0.292591i
$222$	0.980602	−	6.82023i	0.0658137	−	0.457744i
$223$	−13.5780	+	15.6698i	−0.909250	+	1.04933i	0.0893275	+	0.996002i	$0.471528\pi$
$223$	−13.5780	+	15.6698i	−0.909250	+	1.04933i	−0.998577	+	0.0533276i	$0.983017\pi$
$224$	0.810827	−	1.77546i	0.0541757	−	0.118628i
$225$	4.76126	+	1.39803i	0.317417	+	0.0932021i
$226$	−7.12405	−	15.5995i	−0.473884	−	1.03766i
$227$	2.99578	+	20.8361i	0.198837	+	1.38294i	0.807666	+	0.589640i	$0.200730\pi$
$227$	2.99578	+	20.8361i	0.198837	+	1.38294i	−0.608829	+	0.793301i	$0.708361\pi$
$228$	−0.723014	−	0.464653i	−0.0478828	−	0.0307724i
$229$	−1.91595			−0.126609			−0.0633047	−	0.997994i	$-0.520164\pi$
$229$	−1.91595			−0.126609			−0.0633047	+	0.997994i	$0.520164\pi$
$230$	0.929527	+	0.0628131i	0.0612912	+	0.00414177i
$231$	−12.3005			−0.809311
$232$	4.55742	+	2.92887i	0.299209	+	0.192290i
$233$	2.05368	+	14.2837i	0.134541	+	0.935756i	0.939530	+	0.342466i	$0.111262\pi$
$233$	2.05368	+	14.2837i	0.134541	+	0.935756i	−0.804989	+	0.593290i	$0.797829\pi$
$234$	1.99934	+	4.37795i	0.130701	+	0.286196i
$235$	−1.38157	−	0.405667i	−0.0901239	−	0.0264628i
$236$	−3.57349	+	7.82485i	−0.232614	+	0.509354i
$237$	0.739858	−	0.853842i	0.0480589	−	0.0554630i
$238$	0.891070	−	6.19753i	0.0577595	−	0.401726i
$239$	9.41935	−	2.76577i	0.609287	−	0.178903i	0.0374888	−	0.999297i	$-0.488064\pi$
$239$	9.41935	−	2.76577i	0.609287	−	0.178903i	0.571798	+	0.820394i	$0.306246\pi$
$240$	−0.127214	−	0.146813i	−0.00821165	−	0.00947675i
$241$	−12.5379	+	8.05765i	−0.807640	+	0.519039i	−0.878101	−	0.478476i	$-0.841189\pi$
$241$	−12.5379	+	8.05765i	−0.807640	+	0.519039i	0.0704608	+	0.997515i	$0.477553\pi$
$242$	24.1562	−	15.5243i	1.55282	−	0.997938i
$243$	0.654861	+	0.755750i	0.0420093	+	0.0484814i
$244$	−11.6292	+	3.41464i	−0.744482	+	0.218600i
$245$	−0.0881997	+	0.613442i	−0.00563487	+	0.0391914i
$246$	−0.636532	+	0.734597i	−0.0405838	+	0.0468362i
$247$	1.71833	−	3.76262i	0.109335	−	0.239410i
$248$	0.972643	+	0.285594i	0.0617629	+	0.0181352i
$249$	−1.66463	−	3.64502i	−0.105491	−	0.230994i
$250$	−0.275420	−	1.91559i	−0.0174191	−	0.121152i
$251$	−1.80424	−	1.15952i	−0.113883	−	0.0731880i	0.482460	−	0.875918i	$-0.339744\pi$
$251$	−1.80424	−	1.15952i	−0.113883	−	0.0731880i	−0.596342	+	0.802730i	$0.703380\pi$
$252$	1.95185			0.122955
$253$	6.30836	−	29.5574i	0.396603	−	1.85826i
$254$	−21.6118			−1.35604
$255$	−0.524239	−	0.336908i	−0.0328291	−	0.0210980i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−6.58383	−	14.4166i	−0.410688	−	0.899281i	−0.996074	−	0.0885261i	$-0.971784\pi$
$257$	−6.58383	−	14.4166i	−0.410688	−	0.899281i	0.585386	−	0.810755i	$-0.300943\pi$
$258$	−4.93450	−	1.44890i	−0.307208	−	0.0902045i
$259$	5.58690	−	12.2336i	0.347153	−	0.760159i
$260$	0.612268	−	0.706595i	0.0379712	−	0.0438211i
$261$	−0.770978	+	5.36227i	−0.0477223	+	0.331916i
$262$	14.3512	−	4.21390i	0.886622	−	0.260336i
$263$	−0.0855299	−	0.0987067i	−0.00527400	−	0.00608652i	0.753106	−	0.657899i	$-0.228555\pi$
$263$	−0.0855299	−	0.0987067i	−0.00527400	−	0.00608652i	−0.758380	+	0.651812i	$0.774009\pi$
$264$	−5.30154	+	3.40709i	−0.326287	+	0.209692i
$265$	−0.328149	+	0.210888i	−0.0201580	+	0.0129548i
$266$	−1.09854	−	1.26778i	−0.0673557	−	0.0777326i
$267$	−9.16467	+	2.69099i	−0.560869	+	0.164686i
$268$	−1.00948	+	7.02107i	−0.0616636	+	0.428880i
$269$	15.6962	−	18.1144i	0.957016	−	1.10446i	−0.0374396	−	0.999299i	$-0.511920\pi$
$269$	15.6962	−	18.1144i	0.957016	−	1.10446i	0.994456	−	0.105157i	$-0.0335344\pi$
$270$	0.0806993	−	0.176707i	0.00491120	−	0.0107540i
$271$	−3.09137	−	0.907707i	−0.187787	−	0.0551393i	0.186487	−	0.982457i	$-0.440290\pi$
$271$	−3.09137	−	0.907707i	−0.187787	−	0.0551393i	−0.374274	+	0.927318i	$0.622108\pi$
$272$	−1.33259	−	2.91797i	−0.0808003	−	0.176928i
$273$	1.33691	+	9.29840i	0.0809133	+	0.562765i
$274$	15.2746	+	9.81641i	0.922775	+	0.593031i
$275$	−31.2719			−1.88577
$276$	−1.00102	+	4.69020i	−0.0602541	+	0.282317i
$277$	−13.0026			−0.781250			−0.390625	−	0.920550i	$-0.627741\pi$
$277$	−13.0026			−0.781250			−0.390625	+	0.920550i	$0.627741\pi$
$278$	−6.19766	−	3.98300i	−0.371711	−	0.238884i
$279$	0.144265	+	1.00339i	0.00863694	+	0.0600712i
$280$	−0.157513	−	0.344905i	−0.00941319	−	0.0206120i
$281$	−9.32483	−	2.73802i	−0.556273	−	0.163336i	−0.00850036	−	0.999964i	$-0.502706\pi$
$281$	−9.32483	−	2.73802i	−0.556273	−	0.163336i	−0.547772	+	0.836627i	$0.684524\pi$
$282$	3.07912	−	6.74234i	0.183359	−	0.401500i
$283$	−13.0872	+	15.1035i	−0.777955	+	0.897808i	−0.996960	−	0.0779160i	$-0.975173\pi$
$283$	−13.0872	+	15.1035i	−0.777955	+	0.897808i	0.219005	+	0.975724i	$0.429719\pi$
$284$	−0.157881	+	1.09809i	−0.00936850	+	0.0651594i
$285$	−0.160195	+	0.0470375i	−0.00948913	+	0.00278626i
$286$	−19.8623	−	22.9223i	−1.17448	−	1.35542i
$287$	−1.59604	+	1.02571i	−0.0942114	+	0.0605460i
$288$	0.841254	−	0.540641i	0.0495713	−	0.0318576i
$289$	4.39387	+	5.07080i	0.258463	+	0.298282i
$290$	1.00977	−	0.296494i	0.0592955	−	0.0174107i
$291$	−0.159527	+	1.10953i	−0.00935163	+	0.0650420i
$292$	8.63495	−	9.96526i	0.505322	−	0.583173i
$293$	−7.42848	+	16.2661i	−0.433977	+	0.950276i	0.558688	+	0.829378i	$0.311305\pi$
$293$	−7.42848	+	16.2661i	−0.433977	+	0.950276i	−0.992665	+	0.120898i	$0.961422\pi$
$294$	−3.06106	−	0.898807i	−0.178524	−	0.0524195i
$295$	0.694192	+	1.52007i	0.0404174	+	0.0885018i
$296$	−0.980602	−	6.82023i	−0.0569963	−	0.396418i
$297$	−5.30154	−	3.40709i	−0.307626	−	0.197699i
$298$	15.6333			0.905613
$299$	−23.0292	−	1.55621i	−1.33182	−	0.0899979i
$300$	4.96226			0.286496
$301$	−8.44451	−	5.42696i	−0.486733	−	0.312805i
$302$	−2.94651	−	20.4934i	−0.169553	−	1.17926i
$303$	−5.22235	−	11.4354i	−0.300016	−	0.656944i
$304$	−0.824635	−	0.242135i	−0.0472960	−	0.0138874i
$305$	−0.978086	+	2.14171i	−0.0560050	+	0.122634i
$306$	2.10070	−	2.42434i	0.120089	−	0.138590i
$307$	1.78091	−	12.3865i	0.101642	−	0.706935i	−0.873737	−	0.486399i	$-0.838310\pi$
$307$	1.78091	−	12.3865i	0.101642	−	0.706935i	0.975379	−	0.220536i	$-0.0707807\pi$
$308$	−11.8022	+	3.46544i	−0.672493	+	0.197462i
$309$	12.7019	+	14.6588i	0.722585	+	0.833907i
$310$	0.165663	−	0.106465i	0.00940903	−	0.00604682i
$311$	4.59133	−	2.95067i	0.260350	−	0.167317i	−0.403954	−	0.914779i	$-0.632364\pi$
$311$	4.59133	−	2.95067i	0.260350	−	0.167317i	0.664304	+	0.747462i	$0.268728\pi$
$312$	3.15177	+	3.63733i	0.178434	+	0.205923i
$313$	22.9543	−	6.73999i	1.29745	−	0.380967i	0.441147	−	0.897435i	$-0.354572\pi$
$313$	22.9543	−	6.73999i	1.29745	−	0.380967i	0.856307	+	0.516468i	$0.172753\pi$
$314$	0.565888	−	3.93584i	0.0319349	−	0.222112i
$315$	0.248303	−	0.286557i	0.0139903	−	0.0161457i
$316$	0.469334	−	1.02770i	0.0264021	−	0.0578125i
$317$	15.4695	+	4.54224i	0.868852	+	0.255118i	0.685627	−	0.727953i	$-0.259528\pi$
$317$	15.4695	+	4.54224i	0.868852	+	0.255118i	0.183225	+	0.983071i	$0.441346\pi$
$318$	−0.834139	−	1.82651i	−0.0467762	−	0.102426i
$319$	−4.85866	−	33.7927i	−0.272033	−	1.89203i
$320$	−0.163423	−	0.105026i	−0.00913565	−	0.00587112i
$321$	−3.07594			−0.171682
$322$	−4.45383	+	8.23328i	−0.248202	+	0.458823i
$323$	−2.75699			−0.153403
$324$	0.841254	+	0.540641i	0.0467363	+	0.0300356i
$325$	3.39887	+	23.6397i	0.188536	+	1.31129i
$326$	10.1830	+	22.2977i	0.563985	+	1.23495i
$327$	1.87033	+	0.549179i	0.103430	+	0.0303697i
$328$	−0.403788	+	0.884172i	−0.0222955	+	0.0488203i
$329$	9.47415	−	10.9337i	0.522327	−	0.602797i
$330$	−0.174226	+	1.21177i	−0.00959081	+	0.0667056i
$331$	0.496914	−	0.145907i	0.0273129	−	0.00801979i	−0.268048	−	0.963406i	$-0.586378\pi$
$331$	0.496914	−	0.145907i	0.0273129	−	0.00801979i	0.295360	+	0.955386i	$0.404560\pi$
$332$	−2.62412	−	3.02840i	−0.144017	−	0.166205i
$333$	5.79655	−	3.72521i	0.317649	−	0.204140i
$334$	−1.64418	+	1.05665i	−0.0899653	+	0.0578172i
$335$	0.902365	+	1.04139i	0.0493015	+	0.0568970i
$336$	1.87279	−	0.549899i	0.102169	−	0.0299995i
$337$	0.0754437	−	0.524723i	0.00410968	−	0.0285835i	−0.987663	−	0.156592i	$-0.949949\pi$
$337$	0.0754437	−	0.524723i	0.00410968	−	0.0285835i	0.991773	+	0.128008i	$0.0408584\pi$
$338$	−6.65588	+	7.68130i	−0.362032	+	0.417808i
$339$	7.12405	−	15.5995i	0.386925	−	0.847248i
$340$	−0.597922	−	0.175566i	−0.0324269	−	0.00952139i
$341$	−2.65380	−	5.81102i	−0.143712	−	0.314684i
$342$	−0.122312	−	0.850701i	−0.00661389	−	0.0460006i
$343$	−16.7324	−	10.7533i	−0.903467	−	0.580623i
$344$	−5.14282			−0.277282
$345$	0.561240	+	0.743623i	0.0302161	+	0.0400353i
$346$	6.14165			0.330177
$347$	22.5562	+	14.4960i	1.21088	+	0.778185i	0.980805	−	0.194989i	$-0.0624670\pi$
$347$	22.5562	+	14.4960i	1.21088	+	0.778185i	0.230073	+	0.973173i	$0.426103\pi$
$348$	0.770978	+	5.36227i	0.0413287	+	0.287448i
$349$	0.605377	+	1.32559i	0.0324051	+	0.0709573i	0.925142	−	0.379620i	$-0.123945\pi$
$349$	0.605377	+	1.32559i	0.0324051	+	0.0709573i	−0.892737	+	0.450578i	$0.851218\pi$
$350$	9.29325	+	2.72875i	0.496745	+	0.145858i
$351$	−1.99934	+	4.37795i	−0.106717	+	0.233678i
$352$	−4.12690	+	4.76270i	−0.219964	+	0.253853i
$353$	−3.19550	+	22.2252i	−0.170079	+	1.18293i	0.708634	+	0.705576i	$0.249312\pi$
$353$	−3.19550	+	22.2252i	−0.170079	+	1.18293i	−0.878713	+	0.477350i	$0.841597\pi$
$354$	−8.25376	+	2.42352i	−0.438682	+	0.128809i
$355$	0.141129	+	0.162871i	0.00749034	+	0.00864431i
$356$	−8.03530	+	5.16397i	−0.425870	+	0.273690i
$357$	5.26731	−	3.38509i	0.278775	−	0.179158i
$358$	−4.23754	−	4.89039i	−0.223961	−	0.258465i
$359$	−0.162153	+	0.0476124i	−0.00855811	+	0.00251289i	−0.286009	−	0.958227i	$-0.592329\pi$
$359$	−0.162153	+	0.0476124i	−0.00855811	+	0.00251289i	0.277451	+	0.960740i	$0.410510\pi$
$360$	0.0276463	−	0.192284i	0.00145709	−	0.0101343i
$361$	11.9586	−	13.8010i	0.629402	−	0.726369i
$362$	1.35486	−	2.96673i	0.0712099	−	0.155928i
$363$	27.5514	+	8.08983i	1.44608	+	0.424606i
$364$	3.90242	+	8.54510i	0.204542	+	0.447885i
$365$	−0.364543	−	2.53545i	−0.0190810	−	0.132712i
$366$	−10.1961	−	6.55264i	−0.532959	−	0.342512i
$367$	17.8312			0.930782			0.465391	−	0.885105i	$-0.345914\pi$
$367$	17.8312			0.930782			0.465391	+	0.885105i	$0.345914\pi$
$368$	0.360914	+	4.78223i	0.0188139	+	0.249291i
$369$	−0.972011			−0.0506009
$370$	−1.12605	−	0.723667i	−0.0585404	−	0.0376216i
$371$	−0.557767	−	3.87936i	−0.0289578	−	0.201406i
$372$	0.421108	+	0.922099i	0.0218335	+	0.0478086i
$373$	26.2789	+	7.71619i	1.36067	+	0.399529i	0.879000	−	0.476822i	$-0.158211\pi$
$373$	26.2789	+	7.71619i	1.36067	+	0.399529i	0.481672	+	0.876352i	$0.340030\pi$
$374$	−8.39794	+	18.3889i	−0.434247	+	0.950868i
$375$	1.26734	−	1.46259i	0.0654453	−	0.0755279i
$376$	1.05486	−	7.33672i	0.0544003	−	0.378362i
$377$	−25.0172	+	7.34571i	−1.28845	+	0.378323i
$378$	1.27819	+	1.47511i	0.0657430	+	0.0758714i
$379$	−2.30170	+	1.47921i	−0.118230	+	0.0759821i	−0.598420	−	0.801183i	$-0.704204\pi$
$379$	−2.30170	+	1.47921i	−0.118230	+	0.0759821i	0.480189	+	0.877165i	$0.340568\pi$
$380$	−0.140454	+	0.0902643i	−0.00720514	+	0.00463046i
$381$	−14.1527	−	16.3331i	−0.725066	−	0.836770i
$382$	21.9279	−	6.43861i	1.12193	−	0.329428i
$383$	2.05088	−	14.2642i	0.104795	−	0.728867i	−0.867893	−	0.496751i	$-0.834526\pi$
$383$	2.05088	−	14.2642i	0.104795	−	0.728867i	0.972688	−	0.232116i	$-0.0745649\pi$
$384$	0.654861	−	0.755750i	0.0334182	−	0.0385667i
$385$	−0.992638	+	2.17357i	−0.0505895	+	0.110776i
$386$	16.2552	+	4.77294i	0.827365	+	0.242936i
$387$	−2.13640	−	4.67807i	−0.108600	−	0.237800i
$388$	0.159527	+	1.10953i	0.00809875	+	0.0563280i
$389$	0.911952	+	0.586076i	0.0462378	+	0.0297152i	0.563556	−	0.826078i	$-0.309433\pi$
$389$	0.911952	+	0.586076i	0.0462378	+	0.0297152i	−0.517318	+	0.855793i	$0.673069\pi$
$390$	0.934959			0.0473435
$391$	5.43285	+	14.3931i	0.274751	+	0.727893i
$392$	−3.19028			−0.161134
$393$	12.5827	+	8.08642i	0.634714	+	0.407906i
$394$	−0.178577	−	1.24203i	−0.00899658	−	0.0625726i
$395$	−0.0911736	−	0.199642i	−0.00458744	−	0.0100451i
$396$	−6.04668	−	1.77546i	−0.303857	−	0.0892204i
$397$	−11.2262	+	24.5819i	−0.563427	+	1.23373i	0.386797	+	0.922165i	$0.373581\pi$
$397$	−11.2262	+	24.5819i	−0.563427	+	1.23373i	−0.950224	+	0.311568i	$0.899146\pi$
$398$	−16.2497	+	18.7532i	−0.814524	+	0.940011i
$399$	0.238735	−	1.66044i	0.0119517	−	0.0831259i
$400$	4.76126	−	1.39803i	0.238063	−	0.0699015i
$401$	−6.07324	−	7.00889i	−0.303283	−	0.350007i	0.583567	−	0.812065i	$-0.301657\pi$
$401$	−6.07324	−	7.00889i	−0.303283	−	0.350007i	−0.886850	+	0.462058i	$0.847111\pi$
$402$	−5.96723	+	3.83491i	−0.297619	+	0.191268i
$403$	−4.10434	+	2.63770i	−0.204452	+	0.131393i
$404$	−8.23252	−	9.50084i	−0.409583	−	0.472684i
$405$	0.186393	−	0.0547299i	0.00926193	−	0.00271955i
$406$	−1.50483	+	10.4663i	−0.0746836	+	0.519436i
$407$	−28.4359	+	32.8167i	−1.40951	+	1.62666i
$408$	1.33259	−	2.91797i	0.0659732	−	0.144461i
$409$	−35.2765	−	10.3581i	−1.74431	−	0.512175i	−0.754714	−	0.656054i	$-0.772224\pi$
$409$	−35.2765	−	10.3581i	−1.74431	−	0.512175i	−0.989595	+	0.143879i	$0.954042\pi$
$410$	0.0784406	+	0.171761i	0.00387390	+	0.00848267i
$411$	2.58401	+	17.9722i	0.127460	+	0.886502i
$412$	16.3172	+	10.4864i	0.803891	+	0.516630i
$413$	−16.7902			−0.826193
$414$	−4.20014	+	2.31491i	−0.206426	+	0.113772i
$415$	−0.778434			−0.0382118
$416$	4.04885	+	2.60204i	0.198511	+	0.127575i
$417$	−1.04846	−	7.29219i	−0.0513432	−	0.357100i
$418$	2.24997	+	4.92675i	0.110050	+	0.240975i
$419$	25.4226	+	7.46473i	1.24197	+	0.364676i	0.835756	−	0.549101i	$-0.185030\pi$
$419$	25.4226	+	7.46473i	1.24197	+	0.364676i	0.406217	+	0.913777i	$0.366848\pi$
$420$	0.157513	−	0.344905i	0.00768584	−	0.0168296i
$421$	−6.51649	+	7.52043i	−0.317594	+	0.366523i	−0.891991	−	0.452054i	$-0.850691\pi$
$421$	−6.51649	+	7.52043i	−0.317594	+	0.366523i	0.574396	+	0.818577i	$0.305237\pi$
$422$	−1.03296	+	7.18439i	−0.0502837	+	0.349731i
$423$	7.11192	−	2.08825i	0.345793	−	0.101534i
$424$	−1.31494	−	1.51752i	−0.0638591	−	0.0736973i
$425$	13.3913	−	8.60605i	0.649572	−	0.417455i
$426$	−0.933267	+	0.599775i	−0.0452170	+	0.0290592i
$427$	−15.4918	−	17.8785i	−0.749702	−	0.865202i
$428$	−2.95135	+	0.866594i	−0.142659	+	0.0418884i
$429$	4.31648	−	30.0218i	0.208402	−	1.44947i
$430$	−0.654241	+	0.755034i	−0.0315503	+	0.0364110i
$431$	3.64438	−	7.98009i	0.175544	−	0.384387i	−0.801324	−	0.598230i	$-0.795871\pi$
$431$	3.64438	−	7.98009i	0.175544	−	0.384387i	0.976868	+	0.213843i	$0.0685981\pi$
$432$	0.959493	+	0.281733i	0.0461636	+	0.0135549i
$433$	−3.31942	−	7.26851i	−0.159521	−	0.349303i	0.812947	−	0.582337i	$-0.197862\pi$
$433$	−3.31942	−	7.26851i	−0.159521	−	0.349303i	−0.972468	+	0.233035i	$0.925134\pi$
$434$	0.281584	+	1.95846i	0.0135165	+	0.0940091i
$435$	0.885331	+	0.568968i	0.0424484	+	0.0272799i
$436$	1.94929			0.0933542
$437$	3.86752	+	1.42523i	0.185008	+	0.0681782i
$438$	13.1859			0.630048
$439$	−1.18670	−	0.762644i	−0.0566380	−	0.0363990i	0.512015	−	0.858976i	$-0.328899\pi$
$439$	−1.18670	−	0.762644i	−0.0566380	−	0.0363990i	−0.568653	+	0.822577i	$0.692535\pi$
$440$	0.174226	+	1.21177i	0.00830589	+	0.0577687i
$441$	−1.32529	−	2.90199i	−0.0631092	−	0.138190i
$442$	14.8137	+	4.34968i	0.704614	+	0.206893i
$443$	5.23153	−	11.4554i	0.248557	−	0.544265i	−0.743693	−	0.668522i	$-0.766927\pi$
$443$	5.23153	−	11.4554i	0.248557	−	0.544265i	0.992250	+	0.124257i	$0.0396547\pi$
$444$	4.51223	−	5.20739i	0.214141	−	0.247132i
$445$	−0.264066	+	1.83662i	−0.0125179	+	0.0870641i
$446$	−19.8943	+	5.84149i	−0.942022	+	0.276603i
$447$	10.2376	+	11.8149i	0.484224	+	0.558824i
$448$	1.64200	−	1.05525i	0.0775772	−	0.0498558i
$449$	−32.2649	+	20.7354i	−1.52267	+	0.978562i	−0.531344	+	0.847156i	$0.678313\pi$
$449$	−32.2649	+	20.7354i	−1.52267	+	0.978562i	−0.991329	+	0.131406i	$0.958051\pi$
$450$	3.24959	+	3.75023i	0.153187	+	0.176787i
$451$	5.87744	−	1.72577i	0.276758	−	0.0812634i
$452$	2.44059	−	16.9747i	0.114796	−	0.798421i
$453$	13.5583	−	15.6472i	0.637026	−	0.735168i
$454$	−8.74464	+	19.1481i	−0.410406	+	0.898664i
$455$	1.75098	+	0.514133i	0.0820871	+	0.0241029i
$456$	−0.357028	−	0.781782i	−0.0167194	−	0.0366103i
$457$	−3.79066	−	26.3646i	−0.177319	−	1.23328i	−0.862933	−	0.505318i	$-0.831375\pi$
$457$	−3.79066	−	26.3646i	−0.177319	−	1.23328i	0.685614	−	0.727966i	$-0.259534\pi$
$458$	−1.61180	−	1.03584i	−0.0753144	−	0.0484016i
$459$	3.20786			0.149730
$460$	0.748008	+	0.555382i	0.0348761	+	0.0258948i
$461$	7.65301			0.356436			0.178218	−	0.983991i	$-0.442967\pi$
$461$	7.65301			0.356436			0.178218	+	0.983991i	$0.442967\pi$
$462$	−10.3478	−	6.65013i	−0.481423	−	0.309392i
$463$	0.590819	+	4.10924i	0.0274577	+	0.190972i	0.998934	−	0.0461649i	$-0.0147000\pi$
$463$	0.590819	+	4.10924i	0.0274577	+	0.190972i	−0.971476	+	0.237137i	$0.923791\pi$
$464$	2.25047	+	4.92785i	0.104476	+	0.228770i
$465$	0.188947	+	0.0554799i	0.00876222	+	0.00257282i
$466$	−5.99468	+	13.1265i	−0.277698	+	0.608074i
$467$	21.0312	−	24.2712i	0.973206	−	1.12314i	−0.0191607	−	0.999816i	$-0.506099\pi$
$467$	21.0312	−	24.2712i	0.973206	−	1.12314i	0.992367	−	0.123323i	$-0.0393551\pi$
$468$	−0.684944	+	4.76389i	−0.0316616	+	0.220211i
$469$	−13.2842	+	3.90058i	−0.613406	+	0.180112i
$470$	−0.942934	−	1.08820i	−0.0434943	−	0.0501951i
$471$	3.34509	−	2.14976i	0.154133	−	0.0990555i
$472$	−7.23664	+	4.65071i	−0.333093	+	0.214066i
$473$	21.2239	+	24.4937i	0.975876	+	1.12622i
$474$	1.08403	−	0.318300i	0.0497911	−	0.0146200i
$475$	0.606946	−	4.22140i	0.0278486	−	0.193691i
$476$	4.10025	−	4.73194i	0.187935	−	0.216888i
$477$	0.834139	−	1.82651i	0.0381926	−	0.0836302i
$478$	9.41935	+	2.76577i	0.430831	+	0.126503i
$479$	0.754017	+	1.65107i	0.0344519	+	0.0754391i	0.926076	−	0.377338i	$-0.123161\pi$
$479$	0.754017	+	1.65107i	0.0344519	+	0.0754391i	−0.891624	+	0.452777i	$0.850433\pi$
$480$	−0.0276463	−	0.192284i	−0.00126188	−	0.00877654i
$481$	27.8981	+	17.9290i	1.27204	+	0.817492i
$482$	−14.9039			−0.678853
$483$	−9.13893	+	2.02567i	−0.415836	+	0.0921713i
$484$	28.7146			1.30521
$485$	0.183188	+	0.117728i	0.00831815	+	0.00534575i
$486$	0.142315	+	0.989821i	0.00645553	+	0.0448992i
$487$	−6.72443	−	14.7245i	−0.304713	−	0.667229i	0.693889	−	0.720082i	$-0.255896\pi$
$487$	−6.72443	−	14.7245i	−0.304713	−	0.667229i	−0.998602	+	0.0528530i	$0.983169\pi$
$488$	−11.6292	−	3.41464i	−0.526428	−	0.154573i
$489$	−10.1830	+	22.2977i	−0.460491	+	1.00834i
$490$	−0.405850	+	0.468376i	−0.0183344	+	0.0211591i
$491$	0.202307	−	1.40708i	0.00913000	−	0.0635006i	−0.984747	−	0.173992i	$-0.944333\pi$
$491$	0.202307	−	1.40708i	0.00913000	−	0.0635006i	0.993877	+	0.110491i	$0.0352424\pi$
$492$	−0.932638	+	0.273847i	−0.0420466	+	0.0123460i
$493$	11.3804	+	13.1336i	0.512546	+	0.591509i
$494$	3.47978	−	2.23632i	0.156563	−	0.100617i
$495$	−1.02989	+	0.661868i	−0.0462899	+	0.0297487i
$496$	0.663836	+	0.766107i	0.0298071	+	0.0343992i
$497$	−2.07763	+	0.610046i	−0.0931942	+	0.0273643i
$498$	0.570276	−	3.96635i	0.0255547	−	0.177737i
$499$	−13.4737	+	15.5495i	−0.603167	+	0.696092i	−0.972420	−	0.233237i	$-0.925068\pi$
$499$	−13.4737	+	15.5495i	−0.603167	+	0.696092i	0.369253	+	0.929329i	$0.379614\pi$
$500$	0.803947	−	1.76040i	0.0359536	−	0.0787274i
$501$	−1.87527	−	0.550628i	−0.0837808	−	0.0246002i
$502$	−0.890944	−	1.95089i	−0.0397648	−	0.0870727i
$503$	−2.10448	−	14.6370i	−0.0938342	−	0.652631i	−0.981403	−	0.191957i	$-0.938517\pi$
$503$	−2.10448	−	14.6370i	−0.0938342	−	0.652631i	0.887569	−	0.460674i	$-0.152392\pi$
$504$	1.64200	+	1.05525i	0.0731405	+	0.0470045i
$505$	−2.44214			−0.108674
$506$	21.2869	−	21.4547i	0.946316	−	0.953778i
$507$	−10.1638			−0.451391
$508$	−18.1810	−	11.6842i	−0.806652	−	0.518403i
$509$	−4.71769	−	32.8122i	−0.209108	−	1.45438i	−0.776077	−	0.630638i	$-0.782793\pi$
$509$	−4.71769	−	32.8122i	−0.209108	−	1.45438i	0.566969	−	0.823739i	$-0.308116\pi$
$510$	−0.258872	−	0.566850i	−0.0114630	−	0.0251006i
$511$	24.6944	+	7.25094i	1.09242	+	0.320763i
$512$	0.415415	−	0.909632i	0.0183589	−	0.0402004i
$513$	0.562819	−	0.649528i	0.0248491	−	0.0286774i
$514$	2.25552	−	15.6875i	0.0994866	−	0.691945i
$515$	3.61533	−	1.06156i	0.159311	−	0.0467778i
$516$	−3.36783	−	3.88668i	−0.148260	−	0.171102i
$517$	−39.2959	+	25.2539i	−1.72823	+	1.11067i
$518$	11.3140	−	7.27106i	0.497108	−	0.319472i
$519$	4.02193	+	4.64155i	0.176543	+	0.203742i
$520$	0.897086	−	0.263408i	0.0393398	−	0.0115512i
$521$	4.12229	−	28.6712i	0.180601	−	1.25611i	−0.674746	−	0.738050i	$-0.735747\pi$
$521$	4.12229	−	28.6712i	0.180601	−	1.25611i	0.855347	−	0.518056i	$-0.173344\pi$
$522$	−3.54765	+	4.09421i	−0.155276	+	0.179198i
$523$	13.9867	−	30.6266i	0.611595	−	1.33921i	−0.309882	−	0.950775i	$-0.600290\pi$
$523$	13.9867	−	30.6266i	0.611595	−	1.33921i	0.921477	−	0.388432i	$-0.126983\pi$
$524$	14.3512	+	4.21390i	0.626937	+	0.184085i
$525$	4.02354	+	8.81032i	0.175602	+	0.384514i
$526$	−0.0185874	−	0.129278i	−0.000810450	−	0.00563680i
$527$	2.73561	+	1.75807i	0.119165	+	0.0765827i
$528$	−6.30195			−0.274257
$529$	−0.180643	−	22.9993i	−0.00785404	−	0.999969i
$530$	−0.390071			−0.0169436
$531$	−7.23664	−	4.65071i	−0.314043	−	0.201823i
$532$	−0.238735	−	1.66044i	−0.0103505	−	0.0719892i
$533$	−1.94338	−	4.25542i	−0.0841773	−	0.184323i
$534$	−9.16467	−	2.69099i	−0.396594	−	0.116451i
$535$	−0.248226	+	0.543540i	−0.0107318	+	0.0234993i
$536$	−4.64510	+	5.36073i	−0.200638	+	0.231548i
$537$	0.920906	−	6.40504i	0.0397400	−	0.276398i
$538$	22.9979	−	6.75279i	0.991510	−	0.291134i
$539$	13.1660	+	15.1944i	0.567099	+	0.654467i
$540$	0.163423	−	0.105026i	0.00703262	−	0.00451959i
$541$	−33.8175	+	21.7332i	−1.45393	+	0.934383i	−0.454890	+	0.890548i	$0.650321\pi$
$541$	−33.8175	+	21.7332i	−1.45393	+	0.934383i	−0.999039	+	0.0438352i	$0.986042\pi$
$542$	−2.10988	−	2.43493i	−0.0906271	−	0.104589i
$543$	3.12935	−	0.918861i	0.134293	−	0.0394321i
$544$	0.456526	−	3.17521i	0.0195734	−	0.136136i
$545$	0.247978	−	0.286182i	0.0106222	−	0.0122587i
$546$	−3.90242	+	8.54510i	−0.167008	+	0.365696i
$547$	−21.7806	−	6.39537i	−0.931272	−	0.273446i	−0.219303	−	0.975657i	$-0.570378\pi$
$547$	−21.7806	−	6.39537i	−0.931272	−	0.273446i	−0.711969	+	0.702211i	$0.752196\pi$
$548$	7.54269	+	16.5162i	0.322208	+	0.705536i
$549$	−1.72487	−	11.9968i	−0.0736159	−	0.512010i
$550$	−26.3076	−	16.9069i	−1.12176	−	0.720912i
$551$	4.65598			0.198352
$552$	−3.37782	+	3.40446i	−0.143770	+	0.144903i
$553$	2.20519			0.0937741
$554$	−10.9385	−	7.02973i	−0.464731	−	0.298665i
$555$	−0.190493	−	1.32491i	−0.00808599	−	0.0562393i
$556$	−3.06044	−	6.70142i	−0.129791	−	0.284203i
$557$	−3.79597	−	1.11460i	−0.160841	−	0.0472270i	0.200321	−	0.979730i	$-0.435802\pi$
$557$	−3.79597	−	1.11460i	−0.160841	−	0.0472270i	−0.361162	+	0.932503i	$0.617620\pi$
$558$	−0.421108	+	0.922099i	−0.0178269	+	0.0390355i
$559$	16.2090	−	18.7061i	0.685566	−	0.791185i
$560$	0.0539615	−	0.375310i	0.00228029	−	0.0158598i
$561$	−19.3969	+	5.69544i	−0.818938	+	0.240462i
$562$	−6.36426	−	7.34475i	−0.268460	−	0.309820i
$563$	−22.8941	+	14.7132i	−0.964873	+	0.620086i	−0.925342	−	0.379132i	$-0.876223\pi$
$563$	−22.8941	+	14.7132i	−0.964873	+	0.620086i	−0.0395303	+	0.999218i	$0.512586\pi$
$564$	6.23551	−	4.00732i	0.262562	−	0.168738i
$565$	−2.18163	−	2.51773i	−0.0917818	−	0.105922i
$566$	−19.1752	+	5.63035i	−0.805995	+	0.236661i
$567$	−0.277777	+	1.93198i	−0.0116655	+	0.0811356i
$568$	−0.726488	+	0.838411i	−0.0304827	+	0.0351790i
$569$	−8.57486	+	18.7763i	−0.359477	+	0.787144i	0.640342	+	0.768090i	$0.278793\pi$
$569$	−8.57486	+	18.7763i	−0.359477	+	0.787144i	−0.999818	+	0.0190542i	$0.993935\pi$
$570$	−0.160195	−	0.0470375i	−0.00670983	−	0.00197018i
$571$	12.6110	+	27.6142i	0.527753	+	1.15562i	0.966420	+	0.256968i	$0.0827235\pi$
$571$	12.6110	+	27.6142i	0.527753	+	1.15562i	−0.438667	+	0.898650i	$0.644549\pi$
$572$	−4.31648	−	30.0218i	−0.180481	−	1.25527i
$573$	19.2257	+	12.3556i	0.803165	+	0.516162i
$574$	−1.89722			−0.0791884
$575$	−23.2343	+	5.14995i	−0.968936	+	0.214768i
$576$	1.00000			0.0416667
$577$	−11.8754	−	7.63182i	−0.494377	−	0.317717i	0.269586	−	0.962976i	$-0.413113\pi$
$577$	−11.8754	−	7.63182i	−0.494377	−	0.317717i	−0.763964	+	0.645259i	$0.776749\pi$
$578$	0.954880	+	6.64134i	0.0397178	+	0.276243i
$579$	7.03771	+	15.4104i	0.292477	+	0.640436i
$580$	1.00977	+	0.296494i	0.0419283	+	0.0123112i
$581$	3.24910	−	7.11454i	0.134795	−	0.295161i
$582$	−0.734062	+	0.847152i	−0.0304278	+	0.0351156i
$583$	−1.80087	+	12.5253i	−0.0745843	+	0.518745i
$584$	12.6518	−	3.71491i	0.523536	−	0.153724i
$585$	0.612268	+	0.706595i	0.0253142	+	0.0292141i
$586$	−15.0434	+	9.66778i	−0.621435	+	0.399372i
$587$	30.7510	−	19.7625i	1.26923	−	0.815685i	0.279711	−	0.960084i	$-0.409761\pi$
$587$	30.7510	−	19.7625i	1.26923	−	0.815685i	0.989520	+	0.144399i	$0.0461249\pi$
$588$	−2.08919	−	2.41106i	−0.0861568	−	0.0994303i
$589$	0.835937	−	0.245453i	0.0344442	−	0.0101137i
$590$	−0.237820	+	1.65407i	−0.00979088	+	0.0680970i
$591$	0.821721	−	0.948317i	0.0338011	−	0.0390085i
$592$	2.86236	−	6.26770i	0.117642	−	0.257601i
$593$	−6.37440	−	1.87169i	−0.261765	−	0.0768612i	0.148216	−	0.988955i	$-0.452647\pi$
$593$	−6.37440	−	1.87169i	−0.261765	−	0.0768612i	−0.409982	+	0.912094i	$0.634465\pi$
$594$	−2.61792	−	5.73246i	−0.107415	−	0.235205i
$595$	−0.173101	−	1.20394i	−0.00709644	−	0.0493568i
$596$	13.1516	+	8.45201i	0.538710	+	0.346208i
$597$	−24.8140			−1.01557
$598$	−18.5321	−	13.7597i	−0.757833	−	0.562677i
$599$	28.0099			1.14445			0.572226	−	0.820096i	$-0.306080\pi$
$599$	28.0099			1.14445			0.572226	+	0.820096i	$0.306080\pi$
$600$	4.17452	+	2.68280i	0.170424	+	0.109525i
$601$	−2.50280	−	17.4074i	−0.102091	−	0.710061i	−0.975004	−	0.222185i	$-0.928681\pi$
$601$	−2.50280	−	17.4074i	−0.102091	−	0.710061i	0.872913	−	0.487876i	$-0.162228\pi$
$602$	−4.16994	−	9.13089i	−0.169954	−	0.372147i
$603$	−6.80594	−	1.99840i	−0.277159	−	0.0813813i
$604$	8.60082	−	18.8332i	0.349962	−	0.766311i
$605$	3.65291	−	4.21568i	0.148512	−	0.171392i
$606$	1.78910	−	12.4435i	0.0726772	−	0.505481i
$607$	22.6391	−	6.64743i	0.918891	−	0.269811i	0.212112	−	0.977245i	$-0.431966\pi$
$607$	22.6391	−	6.64743i	0.918891	−	0.269811i	0.706779	+	0.707435i	$0.250148\pi$
$608$	−0.562819	−	0.649528i	−0.0228253	−	0.0263418i
$609$	−8.89539	+	5.71672i	−0.360459	+	0.231653i
$610$	−1.98071	+	1.27293i	−0.0801967	+	0.0515393i
$611$	23.3614	+	26.9605i	0.945101	+	1.09070i
$612$	3.07792	−	0.903759i	0.124418	−	0.0365323i
$613$	−4.69550	+	32.6579i	−0.189650	+	1.31904i	0.643267	+	0.765642i	$0.277579\pi$
$613$	−4.69550	+	32.6579i	−0.189650	+	1.31904i	−0.832916	+	0.553399i	$0.813330\pi$
$614$	8.19485	−	9.45736i	0.330717	−	0.381668i
$615$	−0.0784406	+	0.171761i	−0.00316303	+	0.00692607i
$616$	−11.8022	−	3.46544i	−0.475524	−	0.139627i
$617$	−15.8099	−	34.6189i	−0.636484	−	1.39371i	−0.902901	−	0.429848i	$-0.858567\pi$
$617$	−15.8099	−	34.6189i	−0.636484	−	1.39371i	0.266418	−	0.963858i	$-0.414160\pi$
$618$	2.76038	+	19.1989i	0.111039	+	0.772292i
$619$	−7.14317	−	4.59063i	−0.287108	−	0.184513i	0.389157	−	0.921171i	$-0.372766\pi$
$619$	−7.14317	−	4.59063i	−0.287108	−	0.184513i	−0.676265	+	0.736658i	$0.736403\pi$
$620$	0.196924			0.00790866
$621$	−4.50000	−	1.65831i	−0.180579	−	0.0665458i
$622$	5.45773			0.218835
$623$	−15.6837	−	10.0793i	−0.628354	−	0.403818i
$624$	0.684944	+	4.76389i	0.0274197	+	0.190708i
$625$	10.1508	+	22.2272i	0.406033	+	0.889087i
$626$	22.9543	+	6.73999i	0.917438	+	0.269384i
$627$	−2.24997	+	4.92675i	−0.0898552	+	0.196755i
$628$	2.60393	−	3.00510i	0.103908	−	0.119916i
$629$	3.14563	−	21.8784i	0.125425	−	0.872347i
$630$	0.363811	−	0.106824i	0.0144946	−	0.00425599i
$631$	−7.29960	−	8.42419i	−0.290593	−	0.335362i	0.591617	−	0.806220i	$-0.298490\pi$
$631$	−7.29960	−	8.42419i	−0.290593	−	0.335362i	−0.882209	+	0.470858i	$0.843945\pi$
$632$	0.950444	−	0.610813i	0.0378066	−	0.0242968i
$633$	−6.10604	+	3.92412i	−0.242693	+	0.155970i
$634$	10.5580	+	12.1846i	0.419313	+	0.483912i
$635$	−4.02828	+	1.18281i	−0.159858	+	0.0469384i
$636$	0.285763	−	1.98753i	0.0113313	−	0.0788106i
$637$	10.0550	−	11.6041i	0.398395	−	0.459772i
$638$	14.1824	−	31.0551i	0.561485	−	1.22948i
$639$	−1.06444	−	0.312548i	−0.0421086	−	0.0123642i
$640$	−0.0806993	−	0.176707i	−0.00318992	−	0.00698495i
$641$	5.38460	+	37.4507i	0.212679	+	1.47921i	0.764160	+	0.645026i	$0.223154\pi$
$641$	5.38460	+	37.4507i	0.212679	+	1.47921i	−0.551482	+	0.834187i	$0.685937\pi$
$642$	−2.58765	−	1.66298i	−0.102126	−	0.0656326i
$643$	−22.3733			−0.882317			−0.441158	−	0.897429i	$-0.645432\pi$
$643$	−22.3733			−0.882317			−0.441158	+	0.897429i	$0.645432\pi$
$644$	−8.19804	+	4.51835i	−0.323048	+	0.178048i
$645$	−0.999053			−0.0393377
$646$	−2.31933	−	1.49054i	−0.0912528	−	0.0586446i
$647$	1.55788	+	10.8353i	0.0612465	+	0.425979i	0.997258	+	0.0740083i	$0.0235791\pi$
$647$	1.55788	+	10.8353i	0.0612465	+	0.425979i	−0.936011	+	0.351970i	$0.885512\pi$
$648$	0.415415	+	0.909632i	0.0163190	+	0.0357337i
$649$	52.0148	+	15.2729i	2.04176	+	0.599515i
$650$	−9.92126	+	21.7245i	−0.389144	+	0.852106i
$651$	−1.29571	+	1.49533i	−0.0507828	+	0.0586064i
$652$	−3.48854	+	24.2633i	−0.136622	+	0.950226i
$653$	−5.55361	+	1.63069i	−0.217329	+	0.0638137i	−0.388585	−	0.921413i	$-0.627036\pi$
$653$	−5.55361	+	1.63069i	−0.217329	+	0.0638137i	0.171255	+	0.985227i	$0.445218\pi$
$654$	1.27652	+	1.47318i	0.0499157	+	0.0576058i
$655$	2.44434	−	1.57088i	0.0955083	−	0.0613794i
$656$	−0.817708	+	0.525509i	−0.0319261	+	0.0205177i
$657$	8.63495	+	9.96526i	0.336881	+	0.388782i
$658$	13.8814	−	4.07594i	0.541153	−	0.158897i
$659$	1.18327	−	8.22980i	0.0460935	−	0.320588i	−0.953709	−	0.300730i	$-0.902770\pi$
$659$	1.18327	−	8.22980i	0.0460935	−	0.320588i	0.999803	−	0.0198575i	$-0.00632124\pi$
$660$	−0.801699	+	0.925210i	−0.0312061	+	0.0360137i
$661$	−5.05499	+	11.0689i	−0.196616	+	0.430530i	−0.982102	−	0.188350i	$-0.939686\pi$
$661$	−5.05499	+	11.0689i	−0.196616	+	0.430530i	0.785486	+	0.618880i	$0.212413\pi$
$662$	0.496914	+	0.145907i	0.0193131	+	0.00567085i
$663$	6.41361	+	14.0439i	0.249084	+	0.545418i
$664$	−0.570276	−	3.96635i	−0.0221310	−	0.153924i
$665$	−0.274145	−	0.176182i	−0.0106309	−	0.00683206i
$666$	6.89037			0.266996
$667$	−9.17495	−	24.3070i	−0.355255	−	0.941172i
$668$	−1.95444			−0.0756194
$669$	−17.4427	−	11.2097i	−0.674373	−	0.433393i
$670$	0.196103	+	1.36392i	0.00757611	+	0.0526930i
$671$	31.7296	+	69.4781i	1.22491	+	2.68217i
$672$	1.87279	+	0.549899i	0.0722443	+	0.0212128i
$673$	2.02362	−	4.43110i	0.0780047	−	0.170807i	−0.866612	−	0.498983i	$-0.833707\pi$
$673$	2.02362	−	4.43110i	0.0780047	−	0.170807i	0.944616	+	0.328177i	$0.106434\pi$
$674$	0.347154	−	0.400637i	0.0133719	−	0.0154320i
$675$	−0.706204	+	4.91175i	−0.0271818	+	0.189053i
$676$	−9.75211	+	2.86348i	−0.375081	+	0.110134i
$677$	13.1011	+	15.1195i	0.503517	+	0.581090i	0.949427	−	0.313988i	$-0.101665\pi$
$677$	13.1011	+	15.1195i	0.503517	+	0.581090i	−0.445910	+	0.895078i	$0.647120\pi$
$678$	14.4268	−	9.27157i	0.554060	−	0.356073i
$679$	−1.84059	+	1.18287i	−0.0706353	+	0.0453946i
$680$	−0.408086	−	0.470956i	−0.0156494	−	0.0180604i
$681$	−20.1977	+	5.93057i	−0.773977	+	0.227260i
$682$	0.909153	−	6.32330i	0.0348133	−	0.242131i
$683$	15.7090	−	18.1292i	0.601089	−	0.693693i	−0.370913	−	0.928668i	$-0.620955\pi$
$683$	15.7090	−	18.1292i	0.601089	−	0.693693i	0.972002	+	0.234974i	$0.0755006\pi$
$684$	0.357028	−	0.781782i	0.0136513	−	0.0298922i
$685$	3.38433	+	0.993730i	0.129309	+	0.0379685i
$686$	−8.26256	−	18.0925i	−0.315466	−	0.690774i
$687$	−0.272668	−	1.89645i	−0.0104029	−	0.0723540i
$688$	−4.32641	−	2.78042i	−0.164943	−	0.106002i
$689$	9.66410			0.368173
$690$	0.0701117	+	0.929005i	0.00266911	+	0.0353666i
$691$	16.5438			0.629356			0.314678	−	0.949199i	$-0.398104\pi$
$691$	16.5438			0.629356			0.314678	+	0.949199i	$0.398104\pi$
$692$	5.16669	+	3.32043i	0.196408	+	0.126224i
$693$	−1.75054	−	12.1753i	−0.0664974	−	0.462500i
$694$	11.1383	+	24.3896i	0.422806	+	0.925816i
$695$	−1.37319	−	0.403204i	−0.0520880	−	0.0152944i
$696$	−2.25047	+	4.92785i	−0.0853040	+	0.186790i
$697$	−2.04191	+	2.35648i	−0.0773427	+	0.0892582i
$698$	−0.207393	+	1.44245i	−0.00784994	+	0.0545975i
$699$	−13.8460	+	4.06556i	−0.523705	+	0.153774i
$700$	6.34271	+	7.31988i	0.239732	+	0.276665i
$701$	−13.4451	+	8.64063i	−0.507814	+	0.326352i	−0.769335	−	0.638846i	$-0.779412\pi$
$701$	−13.4451	+	8.64063i	−0.507814	+	0.326352i	0.261521	+	0.965198i	$0.415776\pi$
$702$	−4.04885	+	2.60204i	−0.152814	+	0.0982076i
$703$	−3.87803	−	4.47549i	−0.146263	−	0.168796i
$704$	−6.04668	+	1.77546i	−0.227893	+	0.0669153i
$705$	0.204919	−	1.42524i	0.00771770	−	0.0536778i
$706$	−14.7041	+	16.9694i	−0.553394	+	0.638651i
$707$	10.1932	−	22.3201i	0.383356	−	0.839434i
$708$	−8.25376	−	2.42352i	−0.310195	−	0.0910816i
$709$	2.66064	+	5.82599i	0.0999224	+	0.218800i	0.952991	−	0.303000i	$-0.0979882\pi$
$709$	2.66064	+	5.82599i	0.0999224	+	0.218800i	−0.853068	+	0.521800i	$0.825261\pi$
$710$	0.0306702	+	0.213316i	0.00115103	+	0.00800561i
$711$	0.950444	+	0.610813i	0.0356444	+	0.0229073i
$712$	−9.55158			−0.357960
$713$	−2.92868	−	3.88041i	−0.109680	−	0.145322i
$714$	6.26126			0.234322
$715$	−4.95672	−	3.18549i	−0.185371	−	0.119131i
$716$	−0.920906	−	6.40504i	−0.0344159	−	0.239368i
$717$	4.07813	+	8.92987i	0.152301	+	0.333492i
$718$	−0.162153	−	0.0476124i	−0.00605149	−	0.00177688i
$719$	−17.3216	+	37.9290i	−0.645986	+	1.41451i	0.249037	+	0.968494i	$0.419886\pi$
$719$	−17.3216	+	37.9290i	−0.645986	+	1.41451i	−0.895024	+	0.446019i	$0.852841\pi$
$720$	0.127214	−	0.146813i	0.00474100	−	0.00547141i
$721$	−5.38785	+	37.4733i	−0.200654	+	1.39558i
$722$	17.5216	−	5.14482i	0.652088	−	0.191470i
$723$	−9.75997	−	11.2636i	−0.362977	−	0.418898i
$724$	2.74372	−	1.76328i	0.101969	−	0.0655318i
$725$	−22.6151	+	14.5338i	−0.839903	+	0.539773i
$726$	18.8040	+	21.7010i	0.697884	+	0.805401i
$727$	9.60066	−	2.81901i	0.356069	−	0.104551i	−0.0988057	−	0.995107i	$-0.531502\pi$
$727$	9.60066	−	2.81901i	0.356069	−	0.104551i	0.454875	+	0.890555i	$0.349684\pi$
$728$	−1.33691	+	9.29840i	−0.0495491	+	0.344622i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	1.06409	−	2.33004i	0.0393839	−	0.0862388i
$731$	−15.8292	−	4.64787i	−0.585463	−	0.171908i
$732$	−5.03489	−	11.0249i	−0.186095	−	0.407491i
$733$	3.32462	+	23.1232i	0.122798	+	0.854076i	0.954363	+	0.298649i	$0.0965360\pi$
$733$	3.32462	+	23.1232i	0.122798	+	0.854076i	−0.831565	+	0.555427i	$0.812555\pi$
$734$	15.0006	+	9.64029i	0.553682	+	0.355830i
$735$	−0.619750			−0.0228598
$736$	−2.28185	+	4.21819i	−0.0841101	+	0.155485i
$737$	44.7014			1.64660
$738$	−0.817708	−	0.525509i	−0.0301002	−	0.0193442i
$739$	−3.80336	−	26.4530i	−0.139909	−	0.973088i	−0.931941	−	0.362609i	$-0.881886\pi$
$739$	−3.80336	−	26.4530i	−0.139909	−	0.973088i	0.792033	−	0.610479i	$-0.209023\pi$
$740$	−0.556048	−	1.21757i	−0.0204407	−	0.0447589i
$741$	3.96887	+	1.16536i	0.145800	+	0.0428108i
$742$	1.62811	−	3.56507i	0.0597700	−	0.130878i
$743$	9.93499	−	11.4656i	0.364479	−	0.420632i	−0.543656	−	0.839308i	$-0.682960\pi$
$743$	9.93499	−	11.4656i	0.364479	−	0.420632i	0.908135	+	0.418676i	$0.137506\pi$
$744$	−0.144265	+	1.00339i	−0.00528902	+	0.0367860i
$745$	2.91394	−	0.855609i	0.106758	−	0.0313471i
$746$	17.9356	+	20.6987i	0.656667	+	0.757835i
$747$	3.37102	−	2.16642i	0.123339	−	0.0792653i
$748$	−17.0066	+	10.9295i	−0.621823	+	0.399621i
$749$	−3.93164	−	4.53735i	−0.143659	−	0.165791i
$750$	1.85689	−	0.545233i	0.0678042	−	0.0199091i
$751$	−3.08374	+	21.4478i	−0.112527	+	0.782643i	0.852920	+	0.522042i	$0.174830\pi$
$751$	−3.08374	+	21.4478i	−0.112527	+	0.782643i	−0.965447	+	0.260601i	$0.916079\pi$
$752$	4.85393	−	5.60174i	0.177005	−	0.204274i
$753$	0.890944	−	1.95089i	0.0324678	−	0.0710946i
$754$	−25.0172	−	7.34571i	−0.911072	−	0.267515i
$755$	−1.67081	−	3.65856i	−0.0608070	−	0.133149i
$756$	0.277777	+	1.93198i	0.0101027	+	0.0702655i
$757$	−3.40872	−	2.19065i	−0.123892	−	0.0796206i	0.477227	−	0.878780i	$-0.341642\pi$
$757$	−3.40872	−	2.19065i	−0.123892	−	0.0796206i	−0.601119	+	0.799159i	$0.705278\pi$
$758$	−2.73604			−0.0993774
$759$	30.1543	+	2.03769i	1.09453	+	0.0739634i
$760$	−0.166958			−0.00605620
$761$	−37.1929	−	23.9024i	−1.34824	−	0.866461i	−0.350695	−	0.936490i	$-0.614055\pi$
$761$	−37.1929	−	23.9024i	−1.34824	−	0.866461i	−0.997545	+	0.0700285i	$0.977691\pi$
$762$	−3.07568	−	21.3918i	−0.111420	−	0.774944i
$763$	1.58054	+	3.46090i	0.0572194	+	0.125293i
$764$	21.9279	+	6.43861i	0.793323	+	0.232941i
$765$	0.258872	−	0.566850i	0.00935953	−	0.0204945i

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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 + 0.540641i) q^{2} +(0.142315 + 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.186393 + 0.0547299i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-1.27819 + 1.47511i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})\)	\(q+(0.841254 + 0.540641i) q^{2} +(0.142315 + 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.186393 + 0.0547299i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-1.27819 + 1.47511i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(0.127214 + 0.146813i) q^{10} +(5.30154 - 3.40709i) q^{11} +(-0.841254 + 0.540641i) q^{12} +(-3.15177 - 3.63733i) q^{13} +(-1.87279 + 0.549899i) q^{14} +(-0.0276463 + 0.192284i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-1.33259 + 2.91797i) q^{17} +(-0.959493 - 0.281733i) q^{18} +(0.357028 + 0.781782i) q^{19} +(0.0276463 + 0.192284i) q^{20} +(-1.64200 - 1.05525i) q^{21} +6.30195 q^{22} +(3.37782 - 3.40446i) q^{23} -1.00000 q^{24} +(-4.17452 - 2.68280i) q^{25} +(-0.684944 - 4.76389i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(-1.87279 - 0.549899i) q^{28} +(2.25047 - 4.92785i) q^{29} +(-0.127214 + 0.146813i) q^{30} +(0.144265 - 1.00339i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(4.12690 + 4.76270i) q^{33} +(-2.69862 + 1.73430i) q^{34} +(-0.318978 + 0.204995i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-6.61126 + 1.94124i) q^{37} +(-0.122312 + 0.850701i) q^{38} +(3.15177 - 3.63733i) q^{39} +(-0.0806993 + 0.176707i) q^{40} +(0.932638 + 0.273847i) q^{41} +(-0.810827 - 1.77546i) q^{42} +(0.731899 + 5.09047i) q^{43} +(5.30154 + 3.40709i) q^{44} -0.194262 q^{45} +(4.68219 - 1.03782i) q^{46} -7.41216 q^{47} +(-0.841254 - 0.540641i) q^{48} +(0.454025 + 3.15781i) q^{49} +(-2.06140 - 4.51383i) q^{50} +(-3.07792 - 0.903759i) q^{51} +(1.99934 - 4.37795i) q^{52} +(-1.31494 + 1.51752i) q^{53} +(0.142315 - 0.989821i) q^{54} +(1.17464 - 0.344905i) q^{55} +(-1.27819 - 1.47511i) q^{56} +(-0.723014 + 0.464653i) q^{57} +(4.55742 - 2.92887i) q^{58} +(5.63325 + 6.50112i) q^{59} +(-0.186393 + 0.0547299i) q^{60} +(-1.72487 + 11.9968i) q^{61} +(0.663836 - 0.766107i) q^{62} +(0.810827 - 1.77546i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-0.388396 - 0.850468i) q^{65} +(0.896861 + 6.23781i) q^{66} +(5.96723 + 3.83491i) q^{67} -3.20786 q^{68} +(3.85052 + 2.85894i) q^{69} -0.379170 q^{70} +(0.933267 + 0.599775i) q^{71} +(-0.142315 - 0.989821i) q^{72} +(-5.47763 - 11.9943i) q^{73} +(-6.61126 - 1.94124i) q^{74} +(2.06140 - 4.51383i) q^{75} +(-0.562819 + 0.649528i) q^{76} +(-1.75054 + 12.1753i) q^{77} +(4.61792 - 1.35595i) q^{78} +(-0.739858 - 0.853842i) q^{79} +(-0.163423 + 0.105026i) q^{80} +(0.841254 - 0.540641i) q^{81} +(0.636532 + 0.734597i) q^{82} +(-3.84482 + 1.12894i) q^{83} +(0.277777 - 1.93198i) q^{84} +(-0.408086 + 0.470956i) q^{85} +(-2.13640 + 4.67807i) q^{86} +(5.19797 + 1.52626i) q^{87} +(2.61792 + 5.73246i) q^{88} +(1.35933 + 9.45436i) q^{89} +(-0.163423 - 0.105026i) q^{90} +9.39402 q^{91} +(4.50000 + 1.65831i) q^{92} +1.01371 q^{93} +(-6.23551 - 4.00732i) q^{94} +(0.0237606 + 0.165259i) q^{95} +(-0.415415 - 0.909632i) q^{96} +(1.07554 + 0.315806i) q^{97} +(-1.32529 + 2.90199i) q^{98} +(-4.12690 + 4.76270i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} - q^{8} - q^{9}+O(q^{10}) \) 10 * q - q^2 + q^3 - q^4 - 2 * q^5 + q^6 - q^8 - q^9	\( 10 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} - q^{8} - q^{9} + 9 q^{10} + 11 q^{11} + q^{12} + 13 q^{13} - 11 q^{14} + 13 q^{15} - q^{16} - 24 q^{17} - q^{18} - 14 q^{19} - 13 q^{20} + 11 q^{21} + 22 q^{22} - 10 q^{23} - 10 q^{24} - 43 q^{25} - 9 q^{26} + q^{27} - 11 q^{28} + 13 q^{29} - 9 q^{30} + 8 q^{31} - q^{32} + 22 q^{33} + 9 q^{34} - q^{36} - 13 q^{37} - 3 q^{38} - 13 q^{39} + 9 q^{40} - 10 q^{41} - 8 q^{43} + 11 q^{44} - 2 q^{45} + q^{46} - 8 q^{47} + q^{48} + 29 q^{49} + 23 q^{50} - 9 q^{51} + 2 q^{52} - 35 q^{53} + q^{54} - 11 q^{55} + 3 q^{57} + 13 q^{58} + 37 q^{59} + 2 q^{60} - 2 q^{61} + 8 q^{62} - q^{64} + 37 q^{65} + 14 q^{67} - 2 q^{68} - q^{69} - 22 q^{70} + 44 q^{71} - q^{72} - 49 q^{73} - 13 q^{74} - 23 q^{75} + 8 q^{76} + 44 q^{77} + 20 q^{78} - 8 q^{79} - 2 q^{80} - q^{81} + 12 q^{82} - 17 q^{83} - 11 q^{84} - 37 q^{85} + 14 q^{86} - 2 q^{87} + 59 q^{89} - 2 q^{90} + 66 q^{91} + 45 q^{92} + 36 q^{93} - 19 q^{94} - 28 q^{95} + q^{96} - 21 q^{97} - 26 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q - q^2 + q^3 - q^4 - 2 * q^5 + q^6 - q^8 - q^9 + 9 * q^10 + 11 * q^11 + q^12 + 13 * q^13 - 11 * q^14 + 13 * q^15 - q^16 - 24 * q^17 - q^18 - 14 * q^19 - 13 * q^20 + 11 * q^21 + 22 * q^22 - 10 * q^23 - 10 * q^24 - 43 * q^25 - 9 * q^26 + q^27 - 11 * q^28 + 13 * q^29 - 9 * q^30 + 8 * q^31 - q^32 + 22 * q^33 + 9 * q^34 - q^36 - 13 * q^37 - 3 * q^38 - 13 * q^39 + 9 * q^40 - 10 * q^41 - 8 * q^43 + 11 * q^44 - 2 * q^45 + q^46 - 8 * q^47 + q^48 + 29 * q^49 + 23 * q^50 - 9 * q^51 + 2 * q^52 - 35 * q^53 + q^54 - 11 * q^55 + 3 * q^57 + 13 * q^58 + 37 * q^59 + 2 * q^60 - 2 * q^61 + 8 * q^62 - q^64 + 37 * q^65 + 14 * q^67 - 2 * q^68 - q^69 - 22 * q^70 + 44 * q^71 - q^72 - 49 * q^73 - 13 * q^74 - 23 * q^75 + 8 * q^76 + 44 * q^77 + 20 * q^78 - 8 * q^79 - 2 * q^80 - q^81 + 12 * q^82 - 17 * q^83 - 11 * q^84 - 37 * q^85 + 14 * q^86 - 2 * q^87 + 59 * q^89 - 2 * q^90 + 66 * q^91 + 45 * q^92 + 36 * q^93 - 19 * q^94 - 28 * q^95 + q^96 - 21 * q^97 - 26 * q^98 - 22 * q^99

Introduction

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