LMFDB - Embedded newform 414.2.i.e.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(55,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("414.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.i (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:	$3.30580664368$
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:	no (minimal twist has level 138)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			127.1
Root			$0.142315 + 0.989821i$ of defining polynomial
Character	$\chi$	$=$	414.127
Dual form			414.2.i.e.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{10}{11}\right)$

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			0
$3$		0			0
$4$	0.415415	−	0.909632i	0.207708	−	0.454816i
$5$	−0.186393	+	0.0547299i	−0.0833574	+	0.0244759i	−0.323145	−	0.946349i	$-0.604740\pi$
$5$	−0.186393	+	0.0547299i	−0.0833574	+	0.0244759i	0.239788	+	0.970825i	$0.422922\pi$
$6$		0			0
$7$	−1.27819	−	1.47511i	−0.483110	−	0.557539i	0.460901	−	0.887451i	$-0.347526\pi$
$7$	−1.27819	−	1.47511i	−0.483110	−	0.557539i	−0.944012	+	0.329913i	$0.892981\pi$
$8$	0.142315	+	0.989821i	0.0503159	+	0.349955i
$9$		0			0
$10$	0.127214	−	0.146813i	0.0402287	−	0.0464264i
$11$	−5.30154	−	3.40709i	−1.59847	−	1.02728i	−0.967962	−	0.251097i	$-0.919209\pi$
$11$	−5.30154	−	3.40709i	−1.59847	−	1.02728i	−0.630512	−	0.776180i	$-0.717155\pi$
$12$		0			0
$13$	−3.15177	+	3.63733i	−0.874143	+	1.00881i	0.125717	+	0.992066i	$0.459877\pi$
$13$	−3.15177	+	3.63733i	−0.874143	+	1.00881i	−0.999860	+	0.0167483i	$0.994669\pi$
$14$	1.87279	+	0.549899i	0.500523	+	0.146967i
$15$		0			0
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	1.33259	+	2.91797i	0.323201	+	0.707712i	0.999584	−	0.0288381i	$-0.00918071\pi$
$17$	1.33259	+	2.91797i	0.323201	+	0.707712i	−0.676383	+	0.736550i	$0.736453\pi$
$18$		0			0
$19$	0.357028	−	0.781782i	0.0819078	−	0.179353i	−0.864247	−	0.503068i	$-0.832205\pi$
$19$	0.357028	−	0.781782i	0.0819078	−	0.179353i	0.946155	+	0.323715i	$0.104932\pi$
$20$	−0.0276463	+	0.192284i	−0.00618191	+	0.0429961i
$21$		0			0
$22$	6.30195			1.34358
$23$	−3.37782	−	3.40446i	−0.704324	−	0.709878i
$23$	−3.37782	−	3.40446i	−0.704324	−	0.709878i
$24$		0			0
$25$	−4.17452	+	2.68280i	−0.834904	+	0.536560i
$26$	0.684944	−	4.76389i	0.134329	−	0.934276i
$27$		0			0
$28$	−1.87279	+	0.549899i	−0.353923	+	0.103921i
$29$	−2.25047	−	4.92785i	−0.417902	−	0.915079i	−0.995137	−	0.0985003i	$-0.968595\pi$
$29$	−2.25047	−	4.92785i	−0.417902	−	0.915079i	0.577235	−	0.816578i	$-0.304132\pi$
$30$		0			0
$31$	0.144265	+	1.00339i	0.0259108	+	0.180214i	0.998667	−	0.0516171i	$-0.0164375\pi$
$31$	0.144265	+	1.00339i	0.0259108	+	0.180214i	−0.972756	+	0.231831i	$0.925528\pi$
$32$	0.959493	+	0.281733i	0.169616	+	0.0498038i
$33$		0			0
$34$	−2.69862	−	1.73430i	−0.462810	−	0.297430i
$35$	0.318978	+	0.204995i	0.0539171	+	0.0346504i
$36$		0			0
$37$	−6.61126	−	1.94124i	−1.08688	−	0.319138i	−0.311255	−	0.950326i	$-0.600749\pi$
$37$	−6.61126	−	1.94124i	−1.08688	−	0.319138i	−0.775630	+	0.631188i	$0.782567\pi$
$38$	0.122312	+	0.850701i	0.0198417	+	0.138002i
$39$		0			0
$40$	−0.0806993	−	0.176707i	−0.0127597	−	0.0279398i
$41$	−0.932638	+	0.273847i	−0.145654	+	0.0427677i	−0.353747	−	0.935341i	$-0.615092\pi$
$41$	−0.932638	+	0.273847i	−0.145654	+	0.0427677i	0.208093	+	0.978109i	$0.433274\pi$
$42$		0			0
$43$	0.731899	−	5.09047i	0.111614	−	0.776290i	−0.854737	−	0.519061i	$-0.826282\pi$
$43$	0.731899	−	5.09047i	0.111614	−	0.776290i	0.966351	−	0.257228i	$-0.0828093\pi$
$44$	−5.30154	+	3.40709i	−0.799237	+	0.513638i
$45$		0			0
$46$	4.68219	+	1.03782i	0.690352	+	0.153019i
$47$	7.41216			1.08117			0.540587	−	0.841288i	$-0.318202\pi$
$47$	7.41216			1.08117			0.540587	+	0.841288i	$0.318202\pi$
$48$		0			0
$49$	0.454025	−	3.15781i	0.0648607	−	0.451116i
$50$	2.06140	−	4.51383i	0.291526	−	0.638352i
$51$		0			0
$52$	1.99934	+	4.37795i	0.277259	+	0.607112i
$53$	1.31494	+	1.51752i	0.180621	+	0.208447i	0.838839	−	0.544380i	$-0.183235\pi$
$53$	1.31494	+	1.51752i	0.180621	+	0.208447i	−0.658218	+	0.752827i	$0.728690\pi$
$54$		0			0
$55$	1.17464	+	0.344905i	0.158388	+	0.0465070i
$56$	1.27819	−	1.47511i	0.170805	−	0.197120i
$57$		0			0
$58$	4.55742	+	2.92887i	0.598418	+	0.384580i
$59$	−5.63325	+	6.50112i	−0.733387	+	0.846373i	−0.992849	−	0.119380i	$-0.961909\pi$
$59$	−5.63325	+	6.50112i	−0.733387	+	0.846373i	0.259462	+	0.965753i	$0.416455\pi$
$60$		0			0
$61$	−1.72487	−	11.9968i	−0.220848	−	1.53603i	−0.734844	−	0.678236i	$-0.762745\pi$
$61$	−1.72487	−	11.9968i	−0.220848	−	1.53603i	0.513996	−	0.857792i	$-0.328165\pi$
$62$	−0.663836	−	0.766107i	−0.0843072	−	0.0972957i
$63$		0			0
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	0.388396	−	0.850468i	0.0481746	−	0.105488i
$66$		0			0
$67$	5.96723	−	3.83491i	0.729014	−	0.468509i	−0.122748	−	0.992438i	$-0.539171\pi$
$67$	5.96723	−	3.83491i	0.729014	−	0.468509i	0.851762	+	0.523929i	$0.175534\pi$
$68$	3.20786			0.389010
$69$		0			0
$70$	−0.379170			−0.0453194
$71$	−0.933267	+	0.599775i	−0.110758	+	0.0711801i	−0.594847	−	0.803839i	$-0.702788\pi$
$71$	−0.933267	+	0.599775i	−0.110758	+	0.0711801i	0.484089	+	0.875019i	$0.339151\pi$
$72$		0			0
$73$	−5.47763	+	11.9943i	−0.641109	+	1.40383i	0.258017	+	0.966141i	$0.416931\pi$
$73$	−5.47763	+	11.9943i	−0.641109	+	1.40383i	−0.899125	+	0.437692i	$0.855796\pi$
$74$	6.61126	−	1.94124i	0.768543	−	0.225665i
$75$		0			0
$76$	−0.562819	−	0.649528i	−0.0645598	−	0.0745060i
$77$	1.75054	+	12.1753i	0.199492	+	1.38750i
$78$		0			0
$79$	−0.739858	+	0.853842i	−0.0832405	+	0.0960647i	−0.795842	−	0.605504i	$-0.792971\pi$
$79$	−0.739858	+	0.853842i	−0.0832405	+	0.0960647i	0.712601	+	0.701569i	$0.247517\pi$
$80$	0.163423	+	0.105026i	0.0182713	+	0.0117422i
$81$		0			0
$82$	0.636532	−	0.734597i	0.0702932	−	0.0811227i
$83$	3.84482	+	1.12894i	0.422024	+	0.123918i	0.485847	−	0.874044i	$-0.338511\pi$
$83$	3.84482	+	1.12894i	0.422024	+	0.123918i	−0.0638230	+	0.997961i	$0.520329\pi$
$84$		0			0
$85$	−0.408086	−	0.470956i	−0.0442631	−	0.0510824i
$86$	2.13640	+	4.67807i	0.230374	+	0.504450i
$87$		0			0
$88$	2.61792	−	5.73246i	0.279072	−	0.611082i
$89$	−1.35933	+	9.45436i	−0.144089	+	1.00216i	0.781575	+	0.623812i	$0.214417\pi$
$89$	−1.35933	+	9.45436i	−0.144089	+	1.00216i	−0.925663	+	0.378348i	$0.876492\pi$
$90$		0			0
$91$	9.39402			0.984760
$92$	−4.50000	+	1.65831i	−0.469157	+	0.172891i
$93$		0			0
$94$	−6.23551	+	4.00732i	−0.643143	+	0.413323i
$95$	−0.0237606	+	0.165259i	−0.00243779	+	0.0169552i
$96$		0			0
$97$	1.07554	−	0.315806i	0.109204	−	0.0320653i	−0.226674	−	0.973971i	$-0.572785\pi$
$97$	1.07554	−	0.315806i	0.109204	−	0.0320653i	0.335878	+	0.941905i	$0.390967\pi$
$98$	1.32529	+	2.90199i	0.133875	+	0.293145i
$99$		0			0
$100$	0.706204	+	4.91175i	0.0706204	+	0.491175i
$101$	12.0622	+	3.54178i	1.20023	+	0.352420i	0.819942	−	0.572447i	$-0.194006\pi$
$101$	12.0622	+	3.54178i	1.20023	+	0.352420i	0.380290	+	0.924867i	$0.375824\pi$
$102$		0			0
$103$	16.3172	+	10.4864i	1.60778	+	1.03326i	0.963222	+	0.268706i	$0.0865959\pi$
$103$	16.3172	+	10.4864i	1.60778	+	1.03326i	0.644560	+	0.764553i	$0.277040\pi$
$104$	−4.04885	−	2.60204i	−0.397023	−	0.255151i
$105$		0			0
$106$	−1.92663	−	0.565710i	−0.187131	−	0.0549466i
$107$	0.437753	+	3.04464i	0.0423191	+	0.294336i	0.999979	+	0.00643501i	$0.00204834\pi$
$107$	0.437753	+	3.04464i	0.0423191	+	0.294336i	−0.957660	+	0.287901i	$0.907043\pi$
$108$		0			0
$109$	0.809766	+	1.77314i	0.0775615	+	0.169836i	0.944440	−	0.328683i	$-0.106605\pi$
$109$	0.809766	+	1.77314i	0.0775615	+	0.169836i	−0.866879	+	0.498519i	$0.833877\pi$
$110$	−1.17464	+	0.344905i	−0.111997	+	0.0328854i
$111$		0			0
$112$	−0.277777	+	1.93198i	−0.0262475	+	0.182555i
$113$	14.4268	−	9.27157i	1.35716	−	0.872196i	0.359034	−	0.933325i	$-0.383106\pi$
$113$	14.4268	−	9.27157i	1.35716	−	0.872196i	0.998130	+	0.0611286i	$0.0194700\pi$
$114$		0			0
$115$	0.815927	+	0.449698i	0.0760856	+	0.0419346i
$116$	−5.41741			−0.502994
$117$		0			0
$118$	1.22422	−	8.51465i	0.112699	−	0.783837i
$119$	2.60102	−	5.69544i	0.238435	−	0.522100i
$120$		0			0
$121$	11.9285	+	26.1197i	1.08441	+	2.37452i
$122$	7.93700	+	9.15979i	0.718582	+	0.829288i
$123$		0			0
$124$	0.972643	+	0.285594i	0.0873459	+	0.0256471i
$125$	1.26734	−	1.46259i	0.113355	−	0.130818i
$126$		0			0
$127$	−18.1810	−	11.6842i	−1.61330	−	1.03681i	−0.960113	−	0.279613i	$-0.909794\pi$
$127$	−18.1810	−	11.6842i	−1.61330	−	1.03681i	−0.653190	−	0.757194i	$-0.726570\pi$
$128$	0.654861	−	0.755750i	0.0578821	−	0.0667995i
$129$		0			0
$130$	0.133058	+	0.925442i	0.0116700	+	0.0811666i
$131$	−9.79482	−	11.3038i	−0.855777	−	0.987620i	0.144221	−	0.989546i	$-0.453932\pi$
$131$	−9.79482	−	11.3038i	−0.855777	−	0.987620i	−0.999998	+	0.00192587i	$0.999387\pi$
$132$		0			0
$133$	−1.60956	+	0.472610i	−0.139567	+	0.0409805i
$134$	−2.94665	+	6.45226i	−0.254552	+	0.557390i
$135$		0			0
$136$	−2.69862	+	1.73430i	−0.231405	+	0.148715i
$137$	−18.1570			−1.55126			−0.775628	−	0.631190i	$-0.782567\pi$
$137$	−18.1570			−1.55126			−0.775628	+	0.631190i	$0.782567\pi$
$138$		0			0
$139$	−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
$141$		0			0
$142$	0.460852	−	1.00912i	0.0386738	−	0.0846839i
$143$	29.1019	−	8.54510i	2.43363	−	0.714577i
$144$		0			0
$145$	0.689173	+	0.795348i	0.0572327	+	0.0660500i
$146$	−1.87655	−	13.0517i	−0.155305	−	1.08017i
$147$		0			0
$148$	−4.51223	+	5.20739i	−0.370903	+	0.428045i
$149$	−13.1516	−	8.45201i	−1.07742	−	0.692415i	−0.123459	−	0.992350i	$-0.539399\pi$
$149$	−13.1516	−	8.45201i	−1.07742	−	0.692415i	−0.953960	+	0.299934i	$0.903035\pi$
$150$		0			0
$151$	−13.5583	+	15.6472i	−1.10336	+	1.27335i	−0.144491	+	0.989506i	$0.546154\pi$
$151$	−13.5583	+	15.6472i	−1.10336	+	1.27335i	−0.958871	+	0.283842i	$0.908391\pi$
$152$	0.824635	+	0.242135i	0.0668867	+	0.0196397i
$153$		0			0
$154$	−8.05509	−	9.29606i	−0.649097	−	0.749098i
$155$	−0.0818052	−	0.179129i	−0.00657076	−	0.0143879i
$156$		0			0
$157$	−1.65182	+	3.61698i	−0.131830	+	0.288666i	−0.964023	−	0.265819i	$-0.914358\pi$
$157$	−1.65182	+	3.61698i	−0.131830	+	0.288666i	0.832193	+	0.554485i	$0.187085\pi$
$158$	0.160787	−	1.11829i	0.0127915	−	0.0889668i
$159$		0			0
$160$	−0.194262			−0.0153577
$161$	−0.704449	+	9.33420i	−0.0555183	+	0.735638i
$162$		0			0
$163$	20.6215	−	13.2526i	1.61520	−	1.03803i	0.656217	−	0.754572i	$-0.272156\pi$
$163$	20.6215	−	13.2526i	1.61520	−	1.03803i	0.958985	−	0.283455i	$-0.0914807\pi$
$164$	−0.138332	+	0.962117i	−0.0108019	+	0.0751288i
$165$		0			0
$166$	−3.84482	+	1.12894i	−0.298416	+	0.0876229i
$167$	0.811902	+	1.77782i	0.0628268	+	0.137572i	0.938441	−	0.345440i	$-0.112270\pi$
$167$	0.811902	+	1.77782i	0.0628268	+	0.137572i	−0.875614	+	0.483011i	$0.839543\pi$
$168$		0			0
$169$	−1.44646	−	10.0604i	−0.111266	−	0.773874i
$170$	0.597922	+	0.175566i	0.0458585	+	0.0134653i
$171$		0			0
$172$	−4.32641	−	2.78042i	−0.329886	−	0.212005i
$173$	−5.16669	−	3.32043i	−0.392816	−	0.252447i	0.329292	−	0.944228i	$-0.393190\pi$
$173$	−5.16669	−	3.32043i	−0.392816	−	0.252447i	−0.722108	+	0.691781i	$0.756826\pi$
$174$		0			0
$175$	9.29325	+	2.72875i	0.702504	+	0.206274i
$176$	0.896861	+	6.23781i	0.0676034	+	0.470192i
$177$		0			0
$178$	−3.96787	−	8.68842i	−0.297404	−	0.651225i
$179$	6.20879	−	1.82307i	0.464067	−	0.136262i	−0.0413370	−	0.999145i	$-0.513162\pi$
$179$	6.20879	−	1.82307i	0.464067	−	0.136262i	0.505404	+	0.862883i	$0.331344\pi$
$180$		0			0
$181$	−0.464155	+	3.22827i	−0.0345004	+	0.239955i	−0.999773	−	0.0212879i	$-0.993223\pi$
$181$	−0.464155	+	3.22827i	−0.0345004	+	0.239955i	0.965273	+	0.261243i	$0.0841324\pi$
$182$	−7.90275	+	5.07879i	−0.585791	+	0.376465i
$183$		0			0
$184$	2.88909	−	3.82794i	0.212987	−	0.282200i
$185$	1.33853			0.0984110
$186$		0			0
$187$	2.87700	−	20.0100i	0.210387	−	1.46328i
$188$	3.07912	−	6.74234i	0.224568	−	0.491736i
$189$		0			0
$190$	−0.0693569	−	0.151870i	−0.00503167	−	0.0110178i
$191$	−14.9659	−	17.2716i	−1.08290	−	1.24973i	−0.966538	−	0.256523i	$-0.917423\pi$
$191$	−14.9659	−	17.2716i	−1.08290	−	1.24973i	−0.116359	−	0.993207i	$-0.537122\pi$
$192$		0			0
$193$	16.2552	+	4.77294i	1.17007	+	0.343564i	0.808339	−	0.588718i	$-0.200367\pi$
$193$	16.2552	+	4.77294i	1.17007	+	0.343564i	0.361733	+	0.932282i	$0.382185\pi$
$194$	−0.734062	+	0.847152i	−0.0527025	+	0.0608220i
$195$		0			0
$196$	−2.68384	−	1.72480i	−0.191703	−	0.123200i
$197$	0.821721	−	0.948317i	0.0585452	−	0.0675648i	−0.725722	−	0.687989i	$-0.758494\pi$
$197$	0.821721	−	0.948317i	0.0585452	−	0.0675648i	0.784267	+	0.620424i	$0.213039\pi$
$198$		0			0
$199$	−3.53140	−	24.5614i	−0.250334	−	1.74111i	−0.596206	−	0.802832i	$-0.703326\pi$
$199$	−3.53140	−	24.5614i	−0.250334	−	1.74111i	0.345872	−	0.938282i	$-0.387583\pi$
$200$	−3.24959	−	3.75023i	−0.229781	−	0.265181i
$201$		0			0
$202$	−12.0622	+	3.54178i	−0.848692	+	0.249198i
$203$	−4.39258	+	9.61842i	−0.308299	+	0.675081i
$204$		0			0
$205$	0.158849	−	0.102086i	0.0110945	−	0.00713002i
$206$	−19.3963			−1.35140
$207$		0			0
$208$	4.81288			0.333713
$209$	−4.55640	+	2.92822i	−0.315173	+	0.202549i
$210$		0			0
$211$	3.01519	−	6.60235i	0.207575	−	0.454525i	−0.776998	−	0.629503i	$-0.783258\pi$
$211$	3.01519	−	6.60235i	0.207575	−	0.454525i	0.984572	+	0.174979i	$0.0559856\pi$
$212$	1.92663	−	0.565710i	0.132321	−	0.0388531i
$213$		0			0
$214$	−2.01432	−	2.32464i	−0.137696	−	0.158909i
$215$	0.142180	+	0.988884i	0.00969660	+	0.0674413i
$216$		0			0
$217$	1.29571	−	1.49533i	0.0879583	−	0.101509i
$218$	−1.63985	−	1.05387i	−0.111065	−	0.0713769i
$219$		0			0
$220$	0.801699	−	0.925210i	0.0540505	−	0.0623776i
$221$	−14.8137	−	4.34968i	−0.996474	−	0.292591i
$222$		0			0
$223$	−13.5780	−	15.6698i	−0.909250	−	1.04933i	−0.998577	−	0.0533276i	$-0.983017\pi$
$223$	−13.5780	−	15.6698i	−0.909250	−	1.04933i	0.0893275	−	0.996002i	$-0.471528\pi$
$224$	−0.810827	−	1.77546i	−0.0541757	−	0.118628i
$225$		0			0
$226$	−7.12405	+	15.5995i	−0.473884	+	1.03766i
$227$	−2.99578	+	20.8361i	−0.198837	+	1.38294i	0.608829	+	0.793301i	$0.291639\pi$
$227$	−2.99578	+	20.8361i	−0.198837	+	1.38294i	−0.807666	+	0.589640i	$0.799270\pi$
$228$		0			0
$229$	−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
$231$		0			0
$232$	4.55742	−	2.92887i	0.299209	−	0.192290i
$233$	−2.05368	+	14.2837i	−0.134541	+	0.935756i	0.804989	+	0.593290i	$0.202171\pi$
$233$	−2.05368	+	14.2837i	−0.134541	+	0.935756i	−0.939530	+	0.342466i	$0.888738\pi$
$234$		0			0
$235$	−1.38157	+	0.405667i	−0.0901239	+	0.0264628i
$236$	3.57349	+	7.82485i	0.232614	+	0.509354i
$237$		0			0
$238$	0.891070	+	6.19753i	0.0577595	+	0.401726i
$239$	−9.41935	−	2.76577i	−0.609287	−	0.178903i	−0.0374888	−	0.999297i	$-0.511936\pi$
$239$	−9.41935	−	2.76577i	−0.609287	−	0.178903i	−0.571798	+	0.820394i	$0.693754\pi$
$240$		0			0
$241$	−12.5379	−	8.05765i	−0.807640	−	0.519039i	0.0704608	−	0.997515i	$-0.477553\pi$
$241$	−12.5379	−	8.05765i	−0.807640	−	0.519039i	−0.878101	+	0.478476i	$0.841189\pi$
$242$	−24.1562	−	15.5243i	−1.55282	−	0.997938i
$243$		0			0
$244$	−11.6292	−	3.41464i	−0.744482	−	0.218600i
$245$	0.0881997	+	0.613442i	0.00563487	+	0.0391914i
$246$		0			0
$247$	1.71833	+	3.76262i	0.109335	+	0.239410i
$248$	−0.972643	+	0.285594i	−0.0617629	+	0.0181352i
$249$		0			0
$250$	−0.275420	+	1.91559i	−0.0174191	+	0.121152i
$251$	1.80424	−	1.15952i	0.113883	−	0.0731880i	−0.482460	−	0.875918i	$-0.660256\pi$
$251$	1.80424	−	1.15952i	0.113883	−	0.0731880i	0.596342	+	0.802730i	$0.296620\pi$
$252$		0			0
$253$	6.30836	+	29.5574i	0.396603	+	1.85826i
$254$	21.6118			1.35604
$255$		0			0
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	6.58383	−	14.4166i	0.410688	−	0.899281i	−0.585386	−	0.810755i	$-0.699057\pi$
$257$	6.58383	−	14.4166i	0.410688	−	0.899281i	0.996074	−	0.0885261i	$-0.0282157\pi$
$258$		0			0
$259$	5.58690	+	12.2336i	0.347153	+	0.760159i
$260$	−0.612268	−	0.706595i	−0.0379712	−	0.0438211i
$261$		0			0
$262$	14.3512	+	4.21390i	0.886622	+	0.260336i
$263$	0.0855299	−	0.0987067i	0.00527400	−	0.00608652i	−0.753106	−	0.657899i	$-0.771445\pi$
$263$	0.0855299	−	0.0987067i	0.00527400	−	0.00608652i	0.758380	+	0.651812i	$0.225991\pi$
$264$		0			0
$265$	−0.328149	−	0.210888i	−0.0201580	−	0.0129548i
$266$	1.09854	−	1.26778i	0.0673557	−	0.0777326i
$267$		0			0
$268$	−1.00948	−	7.02107i	−0.0616636	−	0.428880i
$269$	−15.6962	−	18.1144i	−0.957016	−	1.10446i	−0.994456	−	0.105157i	$-0.966466\pi$
$269$	−15.6962	−	18.1144i	−0.957016	−	1.10446i	0.0374396	−	0.999299i	$-0.488080\pi$
$270$		0			0
$271$	−3.09137	+	0.907707i	−0.187787	+	0.0551393i	−0.374274	−	0.927318i	$-0.622108\pi$
$271$	−3.09137	+	0.907707i	−0.187787	+	0.0551393i	0.186487	+	0.982457i	$0.440290\pi$
$272$	1.33259	−	2.91797i	0.0808003	−	0.176928i
$273$		0			0
$274$	15.2746	−	9.81641i	0.922775	−	0.593031i
$275$	31.2719			1.88577
$276$		0			0
$277$	−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			0
$280$	−0.157513	+	0.344905i	−0.00941319	+	0.0206120i
$281$	9.32483	−	2.73802i	0.556273	−	0.163336i	0.00850036	−	0.999964i	$-0.497294\pi$
$281$	9.32483	−	2.73802i	0.556273	−	0.163336i	0.547772	+	0.836627i	$0.315476\pi$
$282$		0			0
$283$	−13.0872	−	15.1035i	−0.777955	−	0.897808i	0.219005	−	0.975724i	$-0.429719\pi$
$283$	−13.0872	−	15.1035i	−0.777955	−	0.897808i	−0.996960	+	0.0779160i	$0.975173\pi$
$284$	0.157881	+	1.09809i	0.00936850	+	0.0651594i
$285$		0			0
$286$	−19.8623	+	22.9223i	−1.17448	+	1.35542i
$287$	1.59604	+	1.02571i	0.0942114	+	0.0605460i
$288$		0			0
$289$	4.39387	−	5.07080i	0.258463	−	0.298282i
$290$	−1.00977	−	0.296494i	−0.0592955	−	0.0174107i
$291$		0			0
$292$	8.63495	+	9.96526i	0.505322	+	0.583173i
$293$	7.42848	+	16.2661i	0.433977	+	0.950276i	0.992665	+	0.120898i	$0.0385775\pi$
$293$	7.42848	+	16.2661i	0.433977	+	0.950276i	−0.558688	+	0.829378i	$0.688695\pi$
$294$		0			0
$295$	0.694192	−	1.52007i	0.0404174	−	0.0885018i
$296$	0.980602	−	6.82023i	0.0569963	−	0.396418i
$297$		0			0
$298$	15.6333			0.905613
$299$	23.0292	−	1.55621i	1.33182	−	0.0899979i
$300$		0			0
$301$	−8.44451	+	5.42696i	−0.486733	+	0.312805i
$302$	2.94651	−	20.4934i	0.169553	−	1.17926i
$303$		0			0
$304$	−0.824635	+	0.242135i	−0.0472960	+	0.0138874i
$305$	0.978086	+	2.14171i	0.0560050	+	0.122634i
$306$		0			0
$307$	1.78091	+	12.3865i	0.101642	+	0.706935i	0.975379	+	0.220536i	$0.0707807\pi$
$307$	1.78091	+	12.3865i	0.101642	+	0.706935i	−0.873737	+	0.486399i	$0.838310\pi$
$308$	11.8022	+	3.46544i	0.672493	+	0.197462i
$309$		0			0
$310$	0.165663	+	0.106465i	0.00940903	+	0.00604682i
$311$	−4.59133	−	2.95067i	−0.260350	−	0.167317i	0.403954	−	0.914779i	$-0.367636\pi$
$311$	−4.59133	−	2.95067i	−0.260350	−	0.167317i	−0.664304	+	0.747462i	$0.731272\pi$
$312$		0			0
$313$	22.9543	+	6.73999i	1.29745	+	0.380967i	0.856307	−	0.516468i	$-0.172753\pi$
$313$	22.9543	+	6.73999i	1.29745	+	0.380967i	0.441147	+	0.897435i	$0.354572\pi$
$314$	−0.565888	−	3.93584i	−0.0319349	−	0.222112i
$315$		0			0
$316$	0.469334	+	1.02770i	0.0264021	+	0.0578125i
$317$	−15.4695	+	4.54224i	−0.868852	+	0.255118i	−0.685627	−	0.727953i	$-0.740472\pi$
$317$	−15.4695	+	4.54224i	−0.868852	+	0.255118i	−0.183225	+	0.983071i	$0.558654\pi$
$318$		0			0
$319$	−4.85866	+	33.7927i	−0.272033	+	1.89203i
$320$	0.163423	−	0.105026i	0.00913565	−	0.00587112i
$321$		0			0
$322$	−4.45383	−	8.23328i	−0.248202	−	0.458823i
$323$	2.75699			0.153403
$324$		0			0
$325$	3.39887	−	23.6397i	0.188536	−	1.31129i
$326$	−10.1830	+	22.2977i	−0.563985	+	1.23495i
$327$		0			0
$328$	−0.403788	−	0.884172i	−0.0222955	−	0.0488203i
$329$	−9.47415	−	10.9337i	−0.522327	−	0.602797i
$330$		0			0
$331$	0.496914	+	0.145907i	0.0273129	+	0.00801979i	0.295360	−	0.955386i	$-0.404560\pi$
$331$	0.496914	+	0.145907i	0.0273129	+	0.00801979i	−0.268048	+	0.963406i	$0.586378\pi$
$332$	2.62412	−	3.02840i	0.144017	−	0.166205i
$333$		0			0
$334$	−1.64418	−	1.05665i	−0.0899653	−	0.0578172i
$335$	−0.902365	+	1.04139i	−0.0493015	+	0.0568970i
$336$		0			0
$337$	0.0754437	+	0.524723i	0.00410968	+	0.0285835i	0.991773	−	0.128008i	$-0.0408584\pi$
$337$	0.0754437	+	0.524723i	0.00410968	+	0.0285835i	−0.987663	+	0.156592i	$0.949949\pi$
$338$	6.65588	+	7.68130i	0.362032	+	0.417808i
$339$		0			0
$340$	−0.597922	+	0.175566i	−0.0324269	+	0.00952139i
$341$	2.65380	−	5.81102i	0.143712	−	0.314684i
$342$		0			0
$343$	−16.7324	+	10.7533i	−0.903467	+	0.580623i
$344$	5.14282			0.277282
$345$		0			0
$346$	6.14165			0.330177
$347$	−22.5562	+	14.4960i	−1.21088	+	0.778185i	−0.980805	−	0.194989i	$-0.937533\pi$
$347$	−22.5562	+	14.4960i	−1.21088	+	0.778185i	−0.230073	+	0.973173i	$0.573897\pi$
$348$		0			0
$349$	0.605377	−	1.32559i	0.0324051	−	0.0709573i	−0.892737	−	0.450578i	$-0.851218\pi$
$349$	0.605377	−	1.32559i	0.0324051	−	0.0709573i	0.925142	+	0.379620i	$0.123945\pi$
$350$	−9.29325	+	2.72875i	−0.496745	+	0.145858i
$351$		0			0
$352$	−4.12690	−	4.76270i	−0.219964	−	0.253853i
$353$	3.19550	+	22.2252i	0.170079	+	1.18293i	0.878713	+	0.477350i	$0.158403\pi$
$353$	3.19550	+	22.2252i	0.170079	+	1.18293i	−0.708634	+	0.705576i	$0.750688\pi$
$354$		0			0
$355$	0.141129	−	0.162871i	0.00749034	−	0.00864431i
$356$	8.03530	+	5.16397i	0.425870	+	0.273690i
$357$		0			0
$358$	−4.23754	+	4.89039i	−0.223961	+	0.258465i
$359$	0.162153	+	0.0476124i	0.00855811	+	0.00251289i	0.286009	−	0.958227i	$-0.407671\pi$
$359$	0.162153	+	0.0476124i	0.00855811	+	0.00251289i	−0.277451	+	0.960740i	$0.589490\pi$
$360$		0			0
$361$	11.9586	+	13.8010i	0.629402	+	0.726369i
$362$	−1.35486	−	2.96673i	−0.0712099	−	0.155928i
$363$		0			0
$364$	3.90242	−	8.54510i	0.204542	−	0.447885i
$365$	0.364543	−	2.53545i	0.0190810	−	0.132712i
$366$		0			0
$367$	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			0
$370$	−1.12605	+	0.723667i	−0.0585404	+	0.0376216i
$371$	0.557767	−	3.87936i	0.0289578	−	0.201406i
$372$		0			0
$373$	26.2789	−	7.71619i	1.36067	−	0.399529i	0.481672	−	0.876352i	$-0.340030\pi$
$373$	26.2789	−	7.71619i	1.36067	−	0.399529i	0.879000	+	0.476822i	$0.158211\pi$
$374$	8.39794	+	18.3889i	0.434247	+	0.950868i
$375$		0			0
$376$	1.05486	+	7.33672i	0.0544003	+	0.378362i
$377$	25.0172	+	7.34571i	1.28845	+	0.378323i
$378$		0			0
$379$	−2.30170	−	1.47921i	−0.118230	−	0.0759821i	0.480189	−	0.877165i	$-0.340568\pi$
$379$	−2.30170	−	1.47921i	−0.118230	−	0.0759821i	−0.598420	+	0.801183i	$0.704204\pi$
$380$	0.140454	+	0.0902643i	0.00720514	+	0.00463046i
$381$		0			0
$382$	21.9279	+	6.43861i	1.12193	+	0.329428i
$383$	−2.05088	−	14.2642i	−0.104795	−	0.728867i	−0.972688	−	0.232116i	$-0.925435\pi$
$383$	−2.05088	−	14.2642i	−0.104795	−	0.728867i	0.867893	−	0.496751i	$-0.165474\pi$
$384$		0			0
$385$	−0.992638	−	2.17357i	−0.0505895	−	0.110776i
$386$	−16.2552	+	4.77294i	−0.827365	+	0.242936i
$387$		0			0
$388$	0.159527	−	1.10953i	0.00809875	−	0.0563280i
$389$	−0.911952	+	0.586076i	−0.0462378	+	0.0297152i	−0.563556	−	0.826078i	$-0.690567\pi$
$389$	−0.911952	+	0.586076i	−0.0462378	+	0.0297152i	0.517318	+	0.855793i	$0.326931\pi$
$390$		0			0
$391$	5.43285	−	14.3931i	0.274751	−	0.727893i
$392$	3.19028			0.161134
$393$		0			0
$394$	−0.178577	+	1.24203i	−0.00899658	+	0.0625726i
$395$	0.0911736	−	0.199642i	0.00458744	−	0.0100451i
$396$		0			0
$397$	−11.2262	−	24.5819i	−0.563427	−	1.23373i	−0.950224	−	0.311568i	$-0.899146\pi$
$397$	−11.2262	−	24.5819i	−0.563427	−	1.23373i	0.386797	−	0.922165i	$-0.373581\pi$
$398$	16.2497	+	18.7532i	0.814524	+	0.940011i
$399$		0			0
$400$	4.76126	+	1.39803i	0.238063	+	0.0699015i
$401$	6.07324	−	7.00889i	0.303283	−	0.350007i	−0.583567	−	0.812065i	$-0.698343\pi$
$401$	6.07324	−	7.00889i	0.303283	−	0.350007i	0.886850	+	0.462058i	$0.152889\pi$
$402$		0			0
$403$	−4.10434	−	2.63770i	−0.204452	−	0.131393i
$404$	8.23252	−	9.50084i	0.409583	−	0.472684i
$405$		0			0
$406$	−1.50483	−	10.4663i	−0.0746836	−	0.519436i
$407$	28.4359	+	32.8167i	1.40951	+	1.62666i
$408$		0			0
$409$	−35.2765	+	10.3581i	−1.74431	+	0.512175i	−0.989595	−	0.143879i	$-0.954042\pi$
$409$	−35.2765	+	10.3581i	−1.74431	+	0.512175i	−0.754714	+	0.656054i	$0.772224\pi$
$410$	−0.0784406	+	0.171761i	−0.00387390	+	0.00848267i
$411$		0			0
$412$	16.3172	−	10.4864i	0.803891	−	0.516630i
$413$	16.7902			0.826193
$414$		0			0
$415$	−0.778434			−0.0382118
$416$	−4.04885	+	2.60204i	−0.198511	+	0.127575i
$417$		0			0
$418$	2.24997	−	4.92675i	0.110050	−	0.240975i
$419$	−25.4226	+	7.46473i	−1.24197	+	0.364676i	−0.835756	−	0.549101i	$-0.814970\pi$
$419$	−25.4226	+	7.46473i	−1.24197	+	0.364676i	−0.406217	+	0.913777i	$0.633152\pi$
$420$		0			0
$421$	−6.51649	−	7.52043i	−0.317594	−	0.366523i	0.574396	−	0.818577i	$-0.305237\pi$
$421$	−6.51649	−	7.52043i	−0.317594	−	0.366523i	−0.891991	+	0.452054i	$0.850691\pi$
$422$	1.03296	+	7.18439i	0.0502837	+	0.349731i
$423$		0			0
$424$	−1.31494	+	1.51752i	−0.0638591	+	0.0736973i
$425$	−13.3913	−	8.60605i	−0.649572	−	0.417455i
$426$		0			0
$427$	−15.4918	+	17.8785i	−0.749702	+	0.865202i
$428$	2.95135	+	0.866594i	0.142659	+	0.0418884i
$429$		0			0
$430$	−0.654241	−	0.755034i	−0.0315503	−	0.0364110i
$431$	−3.64438	−	7.98009i	−0.175544	−	0.384387i	0.801324	−	0.598230i	$-0.204129\pi$
$431$	−3.64438	−	7.98009i	−0.175544	−	0.384387i	−0.976868	+	0.213843i	$0.931402\pi$
$432$		0			0
$433$	−3.31942	+	7.26851i	−0.159521	+	0.349303i	−0.972468	−	0.233035i	$-0.925134\pi$
$433$	−3.31942	+	7.26851i	−0.159521	+	0.349303i	0.812947	+	0.582337i	$0.197862\pi$
$434$	−0.281584	+	1.95846i	−0.0135165	+	0.0940091i
$435$		0			0
$436$	1.94929			0.0933542
$437$	−3.86752	+	1.42523i	−0.185008	+	0.0681782i
$438$		0			0
$439$	−1.18670	+	0.762644i	−0.0566380	+	0.0363990i	−0.568653	−	0.822577i	$-0.692535\pi$
$439$	−1.18670	+	0.762644i	−0.0566380	+	0.0363990i	0.512015	+	0.858976i	$0.328899\pi$
$440$	−0.174226	+	1.21177i	−0.00830589	+	0.0577687i
$441$		0			0
$442$	14.8137	−	4.34968i	0.704614	−	0.206893i
$443$	−5.23153	−	11.4554i	−0.248557	−	0.544265i	0.743693	−	0.668522i	$-0.233073\pi$
$443$	−5.23153	−	11.4554i	−0.248557	−	0.544265i	−0.992250	+	0.124257i	$0.960345\pi$
$444$		0			0
$445$	−0.264066	−	1.83662i	−0.0125179	−	0.0870641i
$446$	19.8943	+	5.84149i	0.942022	+	0.276603i
$447$		0			0
$448$	1.64200	+	1.05525i	0.0775772	+	0.0498558i
$449$	32.2649	+	20.7354i	1.52267	+	0.978562i	0.991329	+	0.131406i	$0.0419493\pi$
$449$	32.2649	+	20.7354i	1.52267	+	0.978562i	0.531344	+	0.847156i	$0.321687\pi$
$450$		0			0
$451$	5.87744	+	1.72577i	0.276758	+	0.0812634i
$452$	−2.44059	−	16.9747i	−0.114796	−	0.798421i
$453$		0			0
$454$	−8.74464	−	19.1481i	−0.410406	−	0.898664i
$455$	−1.75098	+	0.514133i	−0.0820871	+	0.0241029i
$456$		0			0
$457$	−3.79066	+	26.3646i	−0.177319	+	1.23328i	0.685614	+	0.727966i	$0.259534\pi$
$457$	−3.79066	+	26.3646i	−0.177319	+	1.23328i	−0.862933	+	0.505318i	$0.831375\pi$
$458$	1.61180	−	1.03584i	0.0753144	−	0.0484016i
$459$		0			0
$460$	0.748008	−	0.555382i	0.0348761	−	0.0258948i
$461$	−7.65301			−0.356436			−0.178218	−	0.983991i	$-0.557033\pi$
$461$	−7.65301			−0.356436			−0.178218	+	0.983991i	$0.557033\pi$
$462$		0			0
$463$	0.590819	−	4.10924i	0.0274577	−	0.190972i	−0.971476	−	0.237137i	$-0.923791\pi$
$463$	0.590819	−	4.10924i	0.0274577	−	0.190972i	0.998934	+	0.0461649i	$0.0147000\pi$
$464$	−2.25047	+	4.92785i	−0.104476	+	0.228770i
$465$		0			0
$466$	−5.99468	−	13.1265i	−0.277698	−	0.608074i
$467$	−21.0312	−	24.2712i	−0.973206	−	1.12314i	−0.992367	−	0.123323i	$-0.960645\pi$
$467$	−21.0312	−	24.2712i	−0.973206	−	1.12314i	0.0191607	−	0.999816i	$-0.493901\pi$
$468$		0			0
$469$	−13.2842	−	3.90058i	−0.613406	−	0.180112i
$470$	0.942934	−	1.08820i	0.0434943	−	0.0501951i
$471$		0			0
$472$	−7.23664	−	4.65071i	−0.333093	−	0.214066i
$473$	−21.2239	+	24.4937i	−0.975876	+	1.12622i
$474$		0			0
$475$	0.606946	+	4.22140i	0.0278486	+	0.193691i
$476$	−4.10025	−	4.73194i	−0.187935	−	0.216888i
$477$		0			0
$478$	9.41935	−	2.76577i	0.430831	−	0.126503i
$479$	−0.754017	+	1.65107i	−0.0344519	+	0.0754391i	−0.926076	−	0.377338i	$-0.876839\pi$
$479$	−0.754017	+	1.65107i	−0.0344519	+	0.0754391i	0.891624	+	0.452777i	$0.149567\pi$
$480$		0			0
$481$	27.8981	−	17.9290i	1.27204	−	0.817492i
$482$	14.9039			0.678853
$483$		0			0
$484$	28.7146			1.30521
$485$	−0.183188	+	0.117728i	−0.00831815	+	0.00534575i
$486$		0			0
$487$	−6.72443	+	14.7245i	−0.304713	+	0.667229i	−0.998602	−	0.0528530i	$-0.983169\pi$
$487$	−6.72443	+	14.7245i	−0.304713	+	0.667229i	0.693889	+	0.720082i	$0.255896\pi$
$488$	11.6292	−	3.41464i	0.526428	−	0.154573i
$489$		0			0
$490$	−0.405850	−	0.468376i	−0.0183344	−	0.0211591i
$491$	−0.202307	−	1.40708i	−0.00913000	−	0.0635006i	0.984747	−	0.173992i	$-0.0556667\pi$
$491$	−0.202307	−	1.40708i	−0.00913000	−	0.0635006i	−0.993877	+	0.110491i	$0.964758\pi$
$492$		0			0
$493$	11.3804	−	13.1336i	0.512546	−	0.591509i
$494$	−3.47978	−	2.23632i	−0.156563	−	0.100617i
$495$		0			0
$496$	0.663836	−	0.766107i	0.0298071	−	0.0343992i
$497$	2.07763	+	0.610046i	0.0931942	+	0.0273643i
$498$		0			0
$499$	−13.4737	−	15.5495i	−0.603167	−	0.696092i	0.369253	−	0.929329i	$-0.379614\pi$
$499$	−13.4737	−	15.5495i	−0.603167	−	0.696092i	−0.972420	+	0.233237i	$0.925068\pi$
$500$	−0.803947	−	1.76040i	−0.0359536	−	0.0787274i
$501$		0			0
$502$	−0.890944	+	1.95089i	−0.0397648	+	0.0870727i
$503$	2.10448	−	14.6370i	0.0938342	−	0.652631i	−0.887569	−	0.460674i	$-0.847608\pi$
$503$	2.10448	−	14.6370i	0.0938342	−	0.652631i	0.981403	−	0.191957i	$-0.0614833\pi$
$504$		0			0
$505$	−2.44214			−0.108674
$506$	−21.2869	−	21.4547i	−0.946316	−	0.953778i
$507$		0			0
$508$	−18.1810	+	11.6842i	−0.806652	+	0.518403i
$509$	4.71769	−	32.8122i	0.209108	−	1.45438i	−0.566969	−	0.823739i	$-0.691884\pi$
$509$	4.71769	−	32.8122i	0.209108	−	1.45438i	0.776077	−	0.630638i	$-0.217207\pi$
$510$		0			0
$511$	24.6944	−	7.25094i	1.09242	−	0.320763i
$512$	−0.415415	−	0.909632i	−0.0183589	−	0.0402004i
$513$		0			0
$514$	2.25552	+	15.6875i	0.0994866	+	0.691945i
$515$	−3.61533	−	1.06156i	−0.159311	−	0.0467778i
$516$		0			0
$517$	−39.2959	−	25.2539i	−1.72823	−	1.11067i
$518$	−11.3140	−	7.27106i	−0.497108	−	0.319472i
$519$		0			0
$520$	0.897086	+	0.263408i	0.0393398	+	0.0115512i
$521$	−4.12229	−	28.6712i	−0.180601	−	1.25611i	−0.855347	−	0.518056i	$-0.826656\pi$
$521$	−4.12229	−	28.6712i	−0.180601	−	1.25611i	0.674746	−	0.738050i	$-0.264253\pi$
$522$		0			0
$523$	13.9867	+	30.6266i	0.611595	+	1.33921i	0.921477	+	0.388432i	$0.126983\pi$
$523$	13.9867	+	30.6266i	0.611595	+	1.33921i	−0.309882	+	0.950775i	$0.600290\pi$
$524$	−14.3512	+	4.21390i	−0.626937	+	0.184085i
$525$		0			0
$526$	−0.0185874	+	0.129278i	−0.000810450	+	0.00563680i
$527$	−2.73561	+	1.75807i	−0.119165	+	0.0765827i
$528$		0			0
$529$	−0.180643	+	22.9993i	−0.00785404	+	0.999969i
$530$	0.390071			0.0169436
$531$		0			0
$532$	−0.238735	+	1.66044i	−0.0103505	+	0.0719892i
$533$	1.94338	−	4.25542i	0.0841773	−	0.184323i
$534$		0			0
$535$	−0.248226	−	0.543540i	−0.0107318	−	0.0234993i
$536$	4.64510	+	5.36073i	0.200638	+	0.231548i
$537$		0			0
$538$	22.9979	+	6.75279i	0.991510	+	0.291134i
$539$	−13.1660	+	15.1944i	−0.567099	+	0.654467i
$540$		0			0
$541$	−33.8175	−	21.7332i	−1.45393	−	0.934383i	−0.999039	−	0.0438352i	$-0.986042\pi$
$541$	−33.8175	−	21.7332i	−1.45393	−	0.934383i	−0.454890	−	0.890548i	$-0.650321\pi$
$542$	2.10988	−	2.43493i	0.0906271	−	0.104589i
$543$		0			0
$544$	0.456526	+	3.17521i	0.0195734	+	0.136136i
$545$	−0.247978	−	0.286182i	−0.0106222	−	0.0122587i
$546$		0			0
$547$	−21.7806	+	6.39537i	−0.931272	+	0.273446i	−0.711969	−	0.702211i	$-0.752196\pi$
$547$	−21.7806	+	6.39537i	−0.931272	+	0.273446i	−0.219303	+	0.975657i	$0.570378\pi$
$548$	−7.54269	+	16.5162i	−0.322208	+	0.705536i
$549$		0			0
$550$	−26.3076	+	16.9069i	−1.12176	+	0.720912i
$551$	−4.65598			−0.198352
$552$		0			0
$553$	2.20519			0.0937741
$554$	10.9385	−	7.02973i	0.464731	−	0.298665i
$555$		0			0
$556$	−3.06044	+	6.70142i	−0.129791	+	0.284203i
$557$	3.79597	−	1.11460i	0.160841	−	0.0472270i	−0.200321	−	0.979730i	$-0.564198\pi$
$557$	3.79597	−	1.11460i	0.160841	−	0.0472270i	0.361162	+	0.932503i	$0.382380\pi$
$558$		0			0
$559$	16.2090	+	18.7061i	0.685566	+	0.791185i
$560$	−0.0539615	−	0.375310i	−0.00228029	−	0.0158598i
$561$		0			0
$562$	−6.36426	+	7.34475i	−0.268460	+	0.309820i
$563$	22.8941	+	14.7132i	0.964873	+	0.620086i	0.925342	−	0.379132i	$-0.123777\pi$
$563$	22.8941	+	14.7132i	0.964873	+	0.620086i	0.0395303	+	0.999218i	$0.487414\pi$
$564$		0			0
$565$	−2.18163	+	2.51773i	−0.0917818	+	0.105922i
$566$	19.1752	+	5.63035i	0.805995	+	0.236661i
$567$		0			0
$568$	−0.726488	−	0.838411i	−0.0304827	−	0.0351790i
$569$	8.57486	+	18.7763i	0.359477	+	0.787144i	0.999818	+	0.0190542i	$0.00606550\pi$
$569$	8.57486	+	18.7763i	0.359477	+	0.787144i	−0.640342	+	0.768090i	$0.721207\pi$
$570$		0			0
$571$	12.6110	−	27.6142i	0.527753	−	1.15562i	−0.438667	−	0.898650i	$-0.644549\pi$
$571$	12.6110	−	27.6142i	0.527753	−	1.15562i	0.966420	−	0.256968i	$-0.0827235\pi$
$572$	4.31648	−	30.0218i	0.180481	−	1.25527i
$573$		0			0
$574$	−1.89722			−0.0791884
$575$	23.2343	+	5.14995i	0.968936	+	0.214768i
$576$		0			0
$577$	−11.8754	+	7.63182i	−0.494377	+	0.317717i	−0.763964	−	0.645259i	$-0.776749\pi$
$577$	−11.8754	+	7.63182i	−0.494377	+	0.317717i	0.269586	+	0.962976i	$0.413113\pi$
$578$	−0.954880	+	6.64134i	−0.0397178	+	0.276243i
$579$		0			0
$580$	1.00977	−	0.296494i	0.0419283	−	0.0123112i
$581$	−3.24910	−	7.11454i	−0.134795	−	0.295161i
$582$		0			0
$583$	−1.80087	−	12.5253i	−0.0745843	−	0.518745i
$584$	−12.6518	−	3.71491i	−0.523536	−	0.153724i
$585$		0			0
$586$	−15.0434	−	9.66778i	−0.621435	−	0.399372i
$587$	−30.7510	−	19.7625i	−1.26923	−	0.815685i	−0.279711	−	0.960084i	$-0.590239\pi$
$587$	−30.7510	−	19.7625i	−1.26923	−	0.815685i	−0.989520	+	0.144399i	$0.953875\pi$
$588$		0			0
$589$	0.835937	+	0.245453i	0.0344442	+	0.0101137i
$590$	0.237820	+	1.65407i	0.00979088	+	0.0680970i
$591$		0			0
$592$	2.86236	+	6.26770i	0.117642	+	0.257601i
$593$	6.37440	−	1.87169i	0.261765	−	0.0768612i	−0.148216	−	0.988955i	$-0.547353\pi$
$593$	6.37440	−	1.87169i	0.261765	−	0.0768612i	0.409982	+	0.912094i	$0.365535\pi$
$594$		0			0
$595$	−0.173101	+	1.20394i	−0.00709644	+	0.0493568i
$596$	−13.1516	+	8.45201i	−0.538710	+	0.346208i
$597$		0			0
$598$	−18.5321	+	13.7597i	−0.757833	+	0.562677i
$599$	−28.0099			−1.14445			−0.572226	−	0.820096i	$-0.693920\pi$
$599$	−28.0099			−1.14445			−0.572226	+	0.820096i	$0.693920\pi$
$600$		0			0
$601$	−2.50280	+	17.4074i	−0.102091	+	0.710061i	0.872913	+	0.487876i	$0.162228\pi$
$601$	−2.50280	+	17.4074i	−0.102091	+	0.710061i	−0.975004	+	0.222185i	$0.928681\pi$
$602$	4.16994	−	9.13089i	0.169954	−	0.372147i
$603$		0			0
$604$	8.60082	+	18.8332i	0.349962	+	0.766311i
$605$	−3.65291	−	4.21568i	−0.148512	−	0.171392i
$606$		0			0
$607$	22.6391	+	6.64743i	0.918891	+	0.269811i	0.706779	−	0.707435i	$-0.250148\pi$
$607$	22.6391	+	6.64743i	0.918891	+	0.269811i	0.212112	+	0.977245i	$0.431966\pi$
$608$	0.562819	−	0.649528i	0.0228253	−	0.0263418i
$609$		0			0
$610$	−1.98071	−	1.27293i	−0.0801967	−	0.0515393i
$611$	−23.3614	+	26.9605i	−0.945101	+	1.09070i
$612$		0			0
$613$	−4.69550	−	32.6579i	−0.189650	−	1.31904i	−0.832916	−	0.553399i	$-0.813330\pi$
$613$	−4.69550	−	32.6579i	−0.189650	−	1.31904i	0.643267	−	0.765642i	$-0.277579\pi$
$614$	−8.19485	−	9.45736i	−0.330717	−	0.381668i
$615$		0			0
$616$	−11.8022	+	3.46544i	−0.475524	+	0.139627i
$617$	15.8099	−	34.6189i	0.636484	−	1.39371i	−0.266418	−	0.963858i	$-0.585840\pi$
$617$	15.8099	−	34.6189i	0.636484	−	1.39371i	0.902901	−	0.429848i	$-0.141433\pi$
$618$		0			0
$619$	−7.14317	+	4.59063i	−0.287108	+	0.184513i	−0.676265	−	0.736658i	$-0.736403\pi$
$619$	−7.14317	+	4.59063i	−0.287108	+	0.184513i	0.389157	+	0.921171i	$0.372766\pi$
$620$	−0.196924			−0.00790866
$621$		0			0
$622$	5.45773			0.218835
$623$	15.6837	−	10.0793i	0.628354	−	0.403818i
$624$		0			0
$625$	10.1508	−	22.2272i	0.406033	−	0.889087i
$626$	−22.9543	+	6.73999i	−0.917438	+	0.269384i
$627$		0			0
$628$	2.60393	+	3.00510i	0.103908	+	0.119916i
$629$	−3.14563	−	21.8784i	−0.125425	−	0.872347i
$630$		0			0
$631$	−7.29960	+	8.42419i	−0.290593	+	0.335362i	−0.882209	−	0.470858i	$-0.843945\pi$
$631$	−7.29960	+	8.42419i	−0.290593	+	0.335362i	0.591617	+	0.806220i	$0.298490\pi$
$632$	−0.950444	−	0.610813i	−0.0378066	−	0.0242968i
$633$		0			0
$634$	10.5580	−	12.1846i	0.419313	−	0.483912i
$635$	4.02828	+	1.18281i	0.159858	+	0.0469384i
$636$		0			0
$637$	10.0550	+	11.6041i	0.398395	+	0.459772i
$638$	−14.1824	−	31.0551i	−0.561485	−	1.22948i
$639$		0			0
$640$	−0.0806993	+	0.176707i	−0.00318992	+	0.00698495i
$641$	−5.38460	+	37.4507i	−0.212679	+	1.47921i	0.551482	+	0.834187i	$0.314063\pi$
$641$	−5.38460	+	37.4507i	−0.212679	+	1.47921i	−0.764160	+	0.645026i	$0.776846\pi$
$642$		0			0
$643$	−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			0
$646$	−2.31933	+	1.49054i	−0.0912528	+	0.0586446i
$647$	−1.55788	+	10.8353i	−0.0612465	+	0.425979i	0.936011	+	0.351970i	$0.114488\pi$
$647$	−1.55788	+	10.8353i	−0.0612465	+	0.425979i	−0.997258	+	0.0740083i	$0.976421\pi$
$648$		0			0
$649$	52.0148	−	15.2729i	2.04176	−	0.599515i
$650$	9.92126	+	21.7245i	0.389144	+	0.852106i
$651$		0			0
$652$	−3.48854	−	24.2633i	−0.136622	−	0.950226i
$653$	5.55361	+	1.63069i	0.217329	+	0.0638137i	0.388585	−	0.921413i	$-0.372964\pi$
$653$	5.55361	+	1.63069i	0.217329	+	0.0638137i	−0.171255	+	0.985227i	$0.554782\pi$
$654$		0			0
$655$	2.44434	+	1.57088i	0.0955083	+	0.0613794i
$656$	0.817708	+	0.525509i	0.0319261	+	0.0205177i
$657$		0			0
$658$	13.8814	+	4.07594i	0.541153	+	0.158897i
$659$	−1.18327	−	8.22980i	−0.0460935	−	0.320588i	−0.999803	−	0.0198575i	$-0.993679\pi$
$659$	−1.18327	−	8.22980i	−0.0460935	−	0.320588i	0.953709	−	0.300730i	$-0.0972303\pi$
$660$		0			0
$661$	−5.05499	−	11.0689i	−0.196616	−	0.430530i	0.785486	−	0.618880i	$-0.212413\pi$
$661$	−5.05499	−	11.0689i	−0.196616	−	0.430530i	−0.982102	+	0.188350i	$0.939686\pi$
$662$	−0.496914	+	0.145907i	−0.0193131	+	0.00567085i
$663$		0			0
$664$	−0.570276	+	3.96635i	−0.0221310	+	0.153924i
$665$	0.274145	−	0.176182i	0.0106309	−	0.00683206i
$666$		0			0
$667$	−9.17495	+	24.3070i	−0.355255	+	0.941172i
$668$	1.95444			0.0756194
$669$		0			0
$670$	0.196103	−	1.36392i	0.00757611	−	0.0526930i
$671$	−31.7296	+	69.4781i	−1.22491	+	2.68217i
$672$		0			0
$673$	2.02362	+	4.43110i	0.0780047	+	0.170807i	0.944616	−	0.328177i	$-0.106434\pi$
$673$	2.02362	+	4.43110i	0.0780047	+	0.170807i	−0.866612	+	0.498983i	$0.833707\pi$
$674$	−0.347154	−	0.400637i	−0.0133719	−	0.0154320i
$675$		0			0
$676$	−9.75211	−	2.86348i	−0.375081	−	0.110134i
$677$	−13.1011	+	15.1195i	−0.503517	+	0.581090i	−0.949427	−	0.313988i	$-0.898335\pi$
$677$	−13.1011	+	15.1195i	−0.503517	+	0.581090i	0.445910	+	0.895078i	$0.352880\pi$
$678$		0			0
$679$	−1.84059	−	1.18287i	−0.0706353	−	0.0453946i
$680$	0.408086	−	0.470956i	0.0156494	−	0.0180604i
$681$		0			0
$682$	0.909153	+	6.32330i	0.0348133	+	0.242131i
$683$	−15.7090	−	18.1292i	−0.601089	−	0.693693i	0.370913	−	0.928668i	$-0.379045\pi$
$683$	−15.7090	−	18.1292i	−0.601089	−	0.693693i	−0.972002	+	0.234974i	$0.924499\pi$
$684$		0			0
$685$	3.38433	−	0.993730i	0.129309	−	0.0379685i
$686$	8.26256	−	18.0925i	0.315466	−	0.690774i
$687$		0			0
$688$	−4.32641	+	2.78042i	−0.164943	+	0.106002i
$689$	−9.66410			−0.368173
$690$		0			0
$691$	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
$693$		0			0
$694$	11.1383	−	24.3896i	0.422806	−	0.925816i
$695$	1.37319	−	0.403204i	0.0520880	−	0.0152944i
$696$		0			0
$697$	−2.04191	−	2.35648i	−0.0773427	−	0.0892582i
$698$	0.207393	+	1.44245i	0.00784994	+	0.0545975i
$699$		0			0
$700$	6.34271	−	7.31988i	0.239732	−	0.276665i
$701$	13.4451	+	8.64063i	0.507814	+	0.326352i	0.769335	−	0.638846i	$-0.220588\pi$
$701$	13.4451	+	8.64063i	0.507814	+	0.326352i	−0.261521	+	0.965198i	$0.584224\pi$
$702$		0			0
$703$	−3.87803	+	4.47549i	−0.146263	+	0.168796i
$704$	6.04668	+	1.77546i	0.227893	+	0.0669153i
$705$		0			0
$706$	−14.7041	−	16.9694i	−0.553394	−	0.638651i
$707$	−10.1932	−	22.3201i	−0.383356	−	0.839434i
$708$		0			0
$709$	2.66064	−	5.82599i	0.0999224	−	0.218800i	−0.853068	−	0.521800i	$-0.825261\pi$
$709$	2.66064	−	5.82599i	0.0999224	−	0.218800i	0.952991	+	0.303000i	$0.0979882\pi$
$710$	−0.0306702	+	0.213316i	−0.00115103	+	0.00800561i
$711$		0			0
$712$	−9.55158			−0.357960
$713$	2.92868	−	3.88041i	0.109680	−	0.145322i
$714$		0			0
$715$	−4.95672	+	3.18549i	−0.185371	+	0.119131i
$716$	0.920906	−	6.40504i	0.0344159	−	0.239368i
$717$		0			0
$718$	−0.162153	+	0.0476124i	−0.00605149	+	0.00177688i
$719$	17.3216	+	37.9290i	0.645986	+	1.41451i	0.895024	+	0.446019i	$0.147159\pi$
$719$	17.3216	+	37.9290i	0.645986	+	1.41451i	−0.249037	+	0.968494i	$0.580114\pi$
$720$		0			0
$721$	−5.38785	−	37.4733i	−0.200654	−	1.39558i
$722$	−17.5216	−	5.14482i	−0.652088	−	0.191470i
$723$		0			0
$724$	2.74372	+	1.76328i	0.101969	+	0.0655318i
$725$	22.6151	+	14.5338i	0.839903	+	0.539773i
$726$		0			0
$727$	9.60066	+	2.81901i	0.356069	+	0.104551i	0.454875	−	0.890555i	$-0.349684\pi$
$727$	9.60066	+	2.81901i	0.356069	+	0.104551i	−0.0988057	+	0.995107i	$0.531502\pi$
$728$	1.33691	+	9.29840i	0.0495491	+	0.344622i
$729$		0			0
$730$	1.06409	+	2.33004i	0.0393839	+	0.0862388i
$731$	15.8292	−	4.64787i	0.585463	−	0.171908i
$732$		0			0
$733$	3.32462	−	23.1232i	0.122798	−	0.854076i	−0.831565	−	0.555427i	$-0.812555\pi$
$733$	3.32462	−	23.1232i	0.122798	−	0.854076i	0.954363	−	0.298649i	$-0.0965360\pi$
$734$	−15.0006	+	9.64029i	−0.553682	+	0.355830i
$735$		0			0
$736$	−2.28185	−	4.21819i	−0.0841101	−	0.155485i
$737$	−44.7014			−1.64660
$738$		0			0
$739$	−3.80336	+	26.4530i	−0.139909	+	0.973088i	0.792033	+	0.610479i	$0.209023\pi$
$739$	−3.80336	+	26.4530i	−0.139909	+	0.973088i	−0.931941	+	0.362609i	$0.881886\pi$
$740$	0.556048	−	1.21757i	0.0204407	−	0.0447589i
$741$		0			0
$742$	1.62811	+	3.56507i	0.0597700	+	0.130878i
$743$	−9.93499	−	11.4656i	−0.364479	−	0.420632i	0.543656	−	0.839308i	$-0.317040\pi$
$743$	−9.93499	−	11.4656i	−0.364479	−	0.420632i	−0.908135	+	0.418676i	$0.862494\pi$
$744$		0			0
$745$	2.91394	+	0.855609i	0.106758	+	0.0313471i
$746$	−17.9356	+	20.6987i	−0.656667	+	0.757835i
$747$		0			0
$748$	−17.0066	−	10.9295i	−0.621823	−	0.399621i
$749$	3.93164	−	4.53735i	0.143659	−	0.165791i
$750$		0			0
$751$	−3.08374	−	21.4478i	−0.112527	−	0.782643i	−0.965447	−	0.260601i	$-0.916079\pi$
$751$	−3.08374	−	21.4478i	−0.112527	−	0.782643i	0.852920	−	0.522042i	$-0.174830\pi$
$752$	−4.85393	−	5.60174i	−0.177005	−	0.204274i
$753$		0			0
$754$	−25.0172	+	7.34571i	−0.911072	+	0.267515i
$755$	1.67081	−	3.65856i	0.0608070	−	0.133149i
$756$		0			0
$757$	−3.40872	+	2.19065i	−0.123892	+	0.0796206i	−0.601119	−	0.799159i	$-0.705278\pi$
$757$	−3.40872	+	2.19065i	−0.123892	+	0.0796206i	0.477227	+	0.878780i	$0.341642\pi$
$758$	2.73604			0.0993774
$759$		0			0
$760$	−0.166958			−0.00605620
$761$	37.1929	−	23.9024i	1.34824	−	0.866461i	0.350695	−	0.936490i	$-0.385945\pi$
$761$	37.1929	−	23.9024i	1.34824	−	0.866461i	0.997545	+	0.0700285i	$0.0223090\pi$
$762$		0			0
$763$	1.58054	−	3.46090i	0.0572194	−	0.125293i
$764$	−21.9279	+	6.43861i	−0.793323	+	0.232941i
$765$		0			0
$766$	9.43713	+	10.8910i	0.340977	+	0.393509i
$767$	−5.89204	−	40.9800i	−0.212749	−	1.47970i
$768$		0			0
$769$	−5.76963	+	6.65850i	−0.208058	+	0.240112i	−0.850182	−	0.526489i	$-0.823508\pi$
$769$	−5.76963	+	6.65850i	−0.208058	+	0.240112i	0.642124	+	0.766601i	$0.278054\pi$
$770$	2.01018	+	1.29187i	0.0724419	+	0.0465556i
$771$		0			0
$772$	11.0943	−	12.8035i	0.399291	−	0.460806i
$773$	−0.608433	−	0.178652i	−0.0218838	−	0.00642566i	0.270772	−	0.962643i	$-0.412721\pi$
$773$	−0.608433	−	0.178652i	−0.0218838	−	0.00642566i	−0.292656	+	0.956218i	$0.594539\pi$
$774$		0			0
$775$	−3.29413	−	3.80163i	−0.118329	−	0.136558i
$776$	0.465657	+	1.01965i	0.0167161	+	0.0366031i
$777$		0			0
$778$	0.450326	−	0.986077i	0.0161450	−	0.0353526i
$779$	−0.118889	+	0.826890i	−0.00425964	+	0.0296264i
$780$		0			0
$781$	6.99124			0.250166
$782$	3.21112	+	15.0455i	0.114829	+	0.538026i
$783$		0			0
$784$	−2.68384	+	1.72480i	−0.0958514	+	0.0615999i
$785$	0.109930	−	0.764583i	0.00392359	−	0.0272891i
$786$		0			0
$787$	−15.3336	+	4.50235i	−0.546584	+	0.160491i	−0.543355	−	0.839503i	$-0.682846\pi$
$787$	−15.3336	+	4.50235i	−0.546584	+	0.160491i	−0.00322916	+	0.999995i	$0.501028\pi$
$788$	−0.521264	−	1.14141i	−0.0185693	−	0.0406610i
$789$		0			0
$790$	0.0312347	+	0.217242i	0.00111128	+	0.00772912i
$791$	−32.1168	−	9.43035i	−1.14194	−	0.335305i
$792$		0			0
$793$	49.0726	+	31.5371i	1.74262	+	1.11991i
$794$	22.7341	+	14.6103i	0.806802	+	0.518500i
$795$		0			0
$796$	−23.8089	−	6.99091i	−0.843883	−	0.247786i
$797$	−5.83086	−	40.5546i	−0.206540	−	1.43652i	−0.784337	−	0.620335i	$-0.786996\pi$
$797$	−5.83086	−	40.5546i	−0.206540	−	1.43652i	0.577797	−	0.816181i	$-0.303913\pi$
$798$		0			0
$799$	9.87740	+	21.6285i	0.349437	+	0.765161i
$800$	−4.76126	+	1.39803i	−0.168336	+	0.0494279i
$801$		0			0
$802$	−1.31984	+	9.17969i	−0.0466052	+	0.324146i
$803$	69.9057	−	44.9257i	2.46692	−	1.58539i
$804$		0			0
$805$	−0.379555	−	1.77838i	−0.0133776	−	0.0626797i
$806$	4.87884			0.171850
$807$		0			0
$808$	−1.78910	+	12.4435i	−0.0629403	+	0.437759i
$809$	11.7254	−	25.6750i	0.412242	−	0.902685i	−0.583638	−	0.812014i	$-0.698371\pi$
$809$	11.7254	−	25.6750i	0.412242	−	0.902685i	0.995881	−	0.0906713i	$-0.0289013\pi$
$810$		0			0
$811$	−1.50266	−	3.29037i	−0.0527657	−	0.115541i	0.881413	−	0.472347i	$-0.156593\pi$
$811$	−1.50266	−	3.29037i	−0.0527657	−	0.115541i	−0.934178	+	0.356806i	$0.883866\pi$
$812$	6.92448	+	7.99127i	0.243001	+	0.280439i
$813$		0			0
$814$	−41.6638	−	12.2336i	−1.46032	−	0.428788i
$815$	−3.11839	+	3.59881i	−0.109232	+	0.126061i
$816$		0			0
$817$	−3.71833	−	2.38963i	−0.130088	−	0.0836024i
$818$	24.0764	−	27.7857i	0.841813	−	0.971504i
$819$		0			0
$820$	−0.0268725	−	0.186903i	−0.000938430	−	0.00652692i
$821$	20.2317	+	23.3487i	0.706092	+	0.814874i	0.989562	−	0.144107i	$-0.0460311\pi$
$821$	20.2317	+	23.3487i	0.706092	+	0.814874i	−0.283470	+	0.958981i	$0.591486\pi$
$822$		0			0
$823$	−3.84377	+	1.12863i	−0.133985	+	0.0393416i	−0.348038	−	0.937481i	$-0.613152\pi$
$823$	−3.84377	+	1.12863i	−0.133985	+	0.0393416i	0.214052	+	0.976822i	$0.431334\pi$
$824$	−8.05752	+	17.6435i	−0.280697	+	0.614641i
$825$		0			0
$826$	−14.1248	+	9.07748i	−0.491466	+	0.315846i
$827$	26.0104			0.904469			0.452234	−	0.891899i	$-0.350627\pi$
$827$	26.0104			0.904469			0.452234	+	0.891899i	$0.350627\pi$
$828$		0			0
$829$	39.4460			1.37002			0.685008	−	0.728535i	$-0.259798\pi$
$829$	39.4460			1.37002			0.685008	+	0.728535i	$0.259798\pi$
$830$	0.654861	−	0.420853i	0.0227305	−	0.0146080i
$831$		0			0
$832$	1.99934	−	4.37795i	0.0693147	−	0.151778i
$833$	9.81944	−	2.88325i	0.340223	−	0.0998986i
$834$		0			0
$835$	−0.248632	−	0.286937i	−0.00860428	−	0.00992986i
$836$	0.770806	+	5.36107i	0.0266589	+	0.185417i
$837$		0			0
$838$	17.3511	−	20.0242i	0.599383	−	0.691725i
$839$	−2.74335	−	1.76304i	−0.0947110	−	0.0608670i	0.492428	−	0.870353i	$-0.336109\pi$
$839$	−2.74335	−	1.76304i	−0.0947110	−	0.0608670i	−0.587139	+	0.809486i	$0.699746\pi$
$840$		0			0
$841$	−0.228106	+	0.263249i	−0.00786573	+	0.00907754i
$842$	9.54787	+	2.80351i	0.329041	+	0.0966152i
$843$		0			0
$844$	−4.75316	−	5.48543i	−0.163610	−	0.188816i
$845$	0.820212	+	1.79601i	0.0282162	+	0.0617848i
$846$		0			0
$847$	23.2826	−	50.9817i	0.799998	−	1.75175i
$848$	0.285763	−	1.98753i	0.00981316	−	0.0682520i
$849$		0			0
$850$	15.9182			0.545991
$851$	15.7228	+	29.0649i	0.538970	+	0.996332i
$852$		0			0
$853$	−6.49153	+	4.17185i	−0.222266	+	0.142842i	−0.647035	−	0.762460i	$-0.723991\pi$
$853$	−6.49153	+	4.17185i	−0.222266	+	0.142842i	0.424770	+	0.905301i	$0.360355\pi$
$854$	3.36670	−	23.4159i	0.115206	−	0.801275i
$855$		0			0
$856$	−2.95135	+	0.866594i	−0.100875	+	0.0296196i
$857$	−1.92561	−	4.21649i	−0.0657775	−	0.144033i	0.873888	−	0.486127i	$-0.161591\pi$
$857$	−1.92561	−	4.21649i	−0.0657775	−	0.144033i	−0.939665	+	0.342095i	$0.888864\pi$
$858$		0			0
$859$	6.99219	+	48.6318i	0.238571	+	1.65929i	0.659130	+	0.752029i	$0.270925\pi$
$859$	6.99219	+	48.6318i	0.238571	+	1.65929i	−0.420559	+	0.907265i	$0.638166\pi$
$860$	0.958584	+	0.281466i	0.0326875	+	0.00959790i
$861$		0			0
$862$	7.38021	+	4.74297i	0.251371	+	0.161546i
$863$	34.3280	+	22.0613i	1.16854	+	0.750975i	0.973245	−	0.229770i	$-0.0737972\pi$
$863$	34.3280	+	22.0613i	1.16854	+	0.750975i	0.195295	+	0.980745i	$0.437434\pi$
$864$		0			0
$865$	1.14476	+	0.336132i	0.0389230	+	0.0114288i
$866$	−1.13718	−	7.90928i	−0.0386430	−	0.268768i
$867$		0			0
$868$	−0.821940	−	1.79980i	−0.0278985	−	0.0610891i
$869$	6.83150	−	2.00591i	0.231743	−	0.0680458i
$870$		0			0
$871$	−4.85849	+	33.7915i	−0.164624	+	1.14498i
$872$	−1.63985	+	1.05387i	−0.0555323	+	0.0356885i
$873$		0			0
$874$	2.48302	−	3.28992i	0.0839895	−	0.111283i
$875$	−3.77739			−0.127699
$876$		0			0
$877$	−3.64997	+	25.3861i	−0.123251	+	0.857228i	0.830583	+	0.556894i	$0.188007\pi$
$877$	−3.64997	+	25.3861i	−0.123251	+	0.857228i	−0.953834	+	0.300334i	$0.902902\pi$
$878$	0.585997	−	1.28315i	0.0197764	−	0.0433043i
$879$		0			0
$880$	−0.508563	−	1.11360i	−0.0171436	−	0.0375393i
$881$	28.1778	+	32.5190i	0.949336	+	1.09559i	0.995318	+	0.0966497i	$0.0308127\pi$
$881$	28.1778	+	32.5190i	0.949336	+	1.09559i	−0.0459826	+	0.998942i	$0.514642\pi$
$882$		0			0
$883$	9.63039	+	2.82774i	0.324089	+	0.0951610i	0.439730	−	0.898130i	$-0.355074\pi$
$883$	9.63039	+	2.82774i	0.324089	+	0.0951610i	−0.115641	+	0.993291i	$0.536892\pi$
$884$	−10.1104	+	11.6681i	−0.340050	+	0.392439i
$885$		0			0
$886$	10.5943	+	6.80856i	0.355923	+	0.228738i
$887$	−6.89056	+	7.95213i	−0.231362	+	0.267007i	−0.859546	−	0.511059i	$-0.829253\pi$
$887$	−6.89056	+	7.95213i	−0.231362	+	0.267007i	0.628183	+	0.778065i	$0.283799\pi$
$888$		0			0
$889$	6.00326	+	41.7536i	0.201343	+	1.40037i
$890$	1.21510	+	1.40230i	0.0407302	+	0.0470051i
$891$		0			0
$892$	−19.8943	+	5.84149i	−0.666110	+	0.195588i
$893$	2.64635	−	5.79469i	0.0885566	−	0.193912i
$894$		0			0
$895$	−1.05750	+	0.679612i	−0.0353482	+	0.0227169i
$896$	−1.95185			−0.0652067
$897$		0			0
$898$	−38.3533			−1.27987
$899$	4.61988	−	2.96901i	0.154081	−	0.0990221i
$900$		0			0
$901$	−2.67580	+	5.85919i	−0.0891439	+	0.195198i
$902$	−5.87744	+	1.72577i	−0.195697	+	0.0574619i
$903$		0			0
$904$	11.2304	+	12.9605i	0.373516	+	0.431060i
$905$	−0.0901675	−	0.627129i	−0.00299727	−	0.0208465i
$906$		0			0
$907$	−25.5472	+	29.4830i	−0.848281	+	0.978968i	−0.999955	−	0.00946225i	$-0.996988\pi$
$907$	−25.5472	+	29.4830i	−0.848281	+	0.978968i	0.151674	+	0.988431i	$0.451533\pi$
$908$	17.7087	+	11.3807i	0.587684	+	0.377681i
$909$		0			0
$910$	1.19505	−	1.37917i	0.0396157	−	0.0457189i
$911$	−21.8445	−	6.41412i	−0.723740	−	0.212509i	−0.100942	−	0.994892i	$-0.532186\pi$
$911$	−21.8445	−	6.41412i	−0.723740	−	0.212509i	−0.622798	+	0.782383i	$0.714004\pi$
$912$		0			0
$913$	−16.5371	−	19.0848i	−0.547297	−	0.631615i
$914$	−11.0649	−	24.2287i	−0.365993	−	0.801414i
$915$		0			0
$916$	−0.795914	+	1.74281i	−0.0262977	+	0.0575840i
$917$	−4.15474	+	28.8969i	−0.137202	+	0.954258i
$918$		0			0
$919$	−21.7361			−0.717007			−0.358504	−	0.933528i	$-0.616713\pi$
$919$	−21.7361			−0.717007			−0.358504	+	0.933528i	$0.616713\pi$
$920$	−0.329003	+	0.871621i	−0.0108469	+	0.0287365i
$921$		0			0
$922$	6.43813	−	4.13753i	0.212028	−	0.136262i
$923$	0.759861	−	5.28495i	0.0250111	−	0.173956i
$924$		0			0
$925$	32.8068	−	9.63295i	1.07868	−	0.316729i
$926$	1.72459	+	3.77633i	0.0566736	+	0.124098i
$927$		0			0
$928$	−0.770978	−	5.36227i	−0.0253086	−	0.176025i
$929$	−39.1306	−	11.4898i	−1.28383	−	0.376967i	−0.432520	−	0.901625i	$-0.642375\pi$
$929$	−39.1306	−	11.4898i	−1.28383	−	0.376967i	−0.851314	+	0.524657i	$0.824194\pi$
$930$		0			0
$931$	−2.30662	−	1.48238i	−0.0755964	−	0.0485829i
$932$	12.1398	+	7.80176i	0.397651	+	0.255555i
$933$		0			0
$934$	30.8146	+	9.04797i	1.00828	+	0.296059i
$935$	0.558892	+	3.88718i	0.0182777	+	0.127124i
$936$		0			0
$937$	−3.00027	−	6.56968i	−0.0980146	−	0.214622i	0.854273	−	0.519825i	$-0.174003\pi$
$937$	−3.00027	−	6.56968i	−0.0980146	−	0.214622i	−0.952287	+	0.305203i	$0.901276\pi$
$938$	13.2842	−	3.90058i	0.433743	−	0.127359i
$939$		0			0
$940$	−0.204919	+	1.42524i	−0.00668372	+	0.0464863i
$941$	−11.1082	+	7.13881i	−0.362117	+	0.232718i	−0.709029	−	0.705179i	$-0.750867\pi$
$941$	−11.1082	+	7.13881i	−0.362117	+	0.232718i	0.346912	+	0.937898i	$0.387230\pi$
$942$		0			0
$943$	4.08258	+	2.25012i	0.132947	+	0.0732739i
$944$	8.60221			0.279978
$945$		0			0
$946$	4.61239	−	32.0799i	0.149962	−	1.04301i
$947$	−14.0374	+	30.7376i	−0.456154	+	0.998837i	0.532194	+	0.846623i	$0.321368\pi$
$947$	−14.0374	+	30.7376i	−0.456154	+	0.998837i	−0.988347	+	0.152215i	$0.951360\pi$
$948$		0			0
$949$	−26.3632	−	57.7274i	−0.855786	−	1.87391i
$950$	−2.79286	−	3.22313i	−0.0906122	−	0.104572i
$951$		0			0
$952$	6.00763	+	1.76400i	0.194709	+	0.0571716i
$953$	−14.7742	+	17.0503i	−0.478582	+	0.552313i	−0.942779	−	0.333419i	$-0.891798\pi$
$953$	−14.7742	+	17.0503i	−0.478582	+	0.552313i	0.464197	+	0.885732i	$0.346343\pi$
$954$		0			0
$955$	3.73482	+	2.40022i	0.120856	+	0.0776693i
$956$	−6.42877	+	7.41920i	−0.207921	+	0.239954i
$957$		0			0
$958$	−0.258315	−	1.79662i	−0.00834576	−	0.0580461i
$959$	23.2081	+	26.7836i	0.749428	+	0.864886i
$960$		0			0
$961$	28.7583	−	8.44420i	0.927687	−	0.272394i
$962$	−13.7762	+	30.1657i	−0.444163	+	0.972581i
$963$		0			0
$964$	−12.5379	+	8.05765i	−0.403820	+	0.259519i
$965$	−3.29107			−0.105943
$966$		0			0
$967$	−15.9309			−0.512303			−0.256152	−	0.966637i	$-0.582455\pi$
$967$	−15.9309			−0.512303			−0.256152	+	0.966637i	$0.582455\pi$
$968$	−24.1562	+	15.5243i	−0.776411	+	0.498969i
$969$		0			0
$970$	0.0904593	−	0.198078i	0.00290447	−	0.00635991i
$971$	40.4422	−	11.8749i	1.29785	−	0.381084i	0.441400	−	0.897310i	$-0.354482\pi$
$971$	40.4422	−	11.8749i	1.29785	−	0.381084i	0.856452	+	0.516227i	$0.172664\pi$
$972$		0			0
$973$	9.41665	+	10.8674i	0.301884	+	0.348392i
$974$	−2.30369	−	16.0225i	−0.0738149	−	0.513394i
$975$		0			0
$976$	−7.93700	+	9.15979i	−0.254057	+	0.293198i
$977$	26.7606	+	17.1980i	0.856147	+	0.550212i	0.893486	−	0.449090i	$-0.148252\pi$
$977$	26.7606	+	17.1980i	0.856147	+	0.550212i	−0.0373392	+	0.999303i	$0.511888\pi$
$978$		0			0
$979$	39.4184	−	45.4913i	1.25982	−	1.45391i
$980$	0.594646	+	0.174604i	0.0189953	+	0.00557752i
$981$		0			0
$982$	0.930916	+	1.07433i	0.0297067	+	0.0342834i
$983$	−8.23740	−	18.0374i	−0.262732	−	0.575303i	0.731586	−	0.681749i	$-0.238780\pi$
$983$	−8.23740	−	18.0374i	−0.262732	−	0.575303i	−0.994319	+	0.106446i	$0.966053\pi$
$984$		0			0
$985$	−0.101262	+	0.221732i	−0.00322646	+	0.00706497i
$986$	−2.47319	+	17.2014i	−0.0787624	+	0.547804i
$987$		0			0
$988$	4.13642			0.131597
$989$	−19.8025	+	14.7030i	−0.629683	+	0.467528i
$990$		0			0
$991$	5.30776	−	3.41109i	0.168606	−	0.108357i	−0.453616	−	0.891197i	$-0.649866\pi$
$991$	5.30776	−	3.41109i	0.168606	−	0.108357i	0.622223	+	0.782840i	$0.286230\pi$
$992$	−0.144265	+	1.00339i	−0.00458043	+	0.0318576i
$993$		0			0
$994$	−2.07763	+	0.610046i	−0.0658983	+	0.0193495i
$995$	2.00247	+	4.38480i	0.0634826	+	0.139008i
$996$		0			0
$997$	6.33856	+	44.0856i	0.200744	+	1.39621i	0.802083	+	0.597212i	$0.203725\pi$
$997$	6.33856	+	44.0856i	0.200744	+	1.39621i	−0.601339	+	0.798994i	$0.705366\pi$
$998$	19.7415	+	5.79663i	0.624907	+	0.183489i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.e.127.1		10
3.2	odd	2		138.2.e.b.127.1	yes	10
23.2	even	11	inner	414.2.i.e.163.1		10
23.5	odd	22		9522.2.a.br.1.3		5
23.18	even	11		9522.2.a.bs.1.3		5
69.2	odd	22		138.2.e.b.25.1	✓	10
69.5	even	22		3174.2.a.bb.1.3		5
69.41	odd	22		3174.2.a.ba.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.b.25.1	✓	10	69.2	odd	22
138.2.e.b.127.1	yes	10	3.2	odd	2
414.2.i.e.127.1		10	1.1	even	1	trivial
414.2.i.e.163.1		10	23.2	even	11	inner
3174.2.a.ba.1.3		5	69.41	odd	22
3174.2.a.bb.1.3		5	69.5	even	22
9522.2.a.br.1.3		5	23.5	odd	22
9522.2.a.bs.1.3		5	23.18	even	11

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.i (of order \(11\), degree \(10\), minimal)

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

Introduction

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