LMFDB - Embedded newform 207.2.i.d.190.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(55,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, 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("207.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 7 x^{19} + 24 x^{18} - 70 x^{17} + 209 x^{16} - 527 x^{15} + 1115 x^{14} - 2187 x^{13} + \cdots + 529 $ x^20 - 7x^19 + 24x^18 - 70x^17 + 209x^16 - 527x^15 + 1115x^14 - 2187x^13 + 4165x^12 - 7040x^11 + 10649x^10 - 13519x^9 + 15111x^8 - 12101x^7 + 8244x^6 - 2837x^5 + 1859x^4 - 1730x^3 + 1957x^2 - 1656*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 69)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			190.2
Root			$0.545935 - 0.160301i$ of defining polynomial
Character	$\chi$	$=$	207.190
Dual form			207.2.i.d.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.10489 - 2.41937i) q^{2} +(-3.32285 - 3.83478i) q^{4} +(2.44470 - 1.57111i) q^{5} +(-0.326826 + 2.27313i) q^{7} +(-7.84516 + 2.30355i) q^{8} +(-1.09998 - 7.65055i) q^{10} +(-0.0494206 - 0.108216i) q^{11} +(0.614381 + 4.27311i) q^{13} +(5.13843 + 3.30227i) q^{14} +(-1.65065 + 11.4805i) q^{16} +(1.68604 - 1.94579i) q^{17} +(-1.13103 - 1.30528i) q^{19} +(-14.1483 - 4.15430i) q^{20} -0.316419 q^{22} +(-4.00915 + 2.63187i) q^{23} +(1.43109 - 3.13366i) q^{25} +(11.0171 + 3.23490i) q^{26} +(9.80293 - 6.29996i) q^{28} +(0.933494 - 1.07731i) q^{29} +(5.49527 - 1.61356i) q^{31} +(12.1951 + 7.83731i) q^{32} +(-2.84470 - 6.22903i) q^{34} +(2.77235 + 6.07060i) q^{35} +(5.79948 + 3.72710i) q^{37} +(-4.40762 + 1.29419i) q^{38} +(-15.5599 + 17.9571i) q^{40} +(5.48180 - 3.52294i) q^{41} +(-8.28385 - 2.43236i) q^{43} +(-0.250767 + 0.549102i) q^{44} +(1.93781 + 12.6075i) q^{46} -5.91880 q^{47} +(1.65616 + 0.486293i) q^{49} +(-6.00028 - 6.92469i) q^{50} +(14.3449 - 16.5549i) q^{52} +(0.514895 - 3.58117i) q^{53} +(-0.290838 - 0.186910i) q^{55} +(-2.67225 - 18.5859i) q^{56} +(-1.57500 - 3.44878i) q^{58} +(-0.386194 - 2.68604i) q^{59} +(-12.0589 + 3.54081i) q^{61} +(2.16787 - 15.0779i) q^{62} +(12.9209 - 8.30375i) q^{64} +(8.21553 + 9.48123i) q^{65} +(-0.0349839 + 0.0766041i) q^{67} -13.0641 q^{68} +17.7502 q^{70} +(-6.43563 + 14.0921i) q^{71} +(0.455430 + 0.525595i) q^{73} +(15.4250 - 9.91306i) q^{74} +(-1.24721 + 8.67450i) q^{76} +(0.262140 - 0.0769714i) q^{77} +(1.05210 + 7.31752i) q^{79} +(14.0019 + 30.6598i) q^{80} +(-2.46651 - 17.1550i) q^{82} +(-2.33903 - 1.50321i) q^{83} +(1.06480 - 7.40583i) q^{85} +(-15.0375 + 17.3542i) q^{86} +(0.636992 + 0.735128i) q^{88} +(-12.7468 - 3.74281i) q^{89} -9.91413 q^{91} +(23.4144 + 6.62886i) q^{92} +(-6.53962 + 14.3198i) q^{94} +(-4.81578 - 1.41404i) q^{95} +(-7.16897 + 4.60722i) q^{97} +(3.00640 - 3.46957i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8} - 18 q^{10} + 16 q^{11} + 14 q^{13} + 22 q^{14} - 8 q^{16} - 11 q^{17} - 11 q^{19} - 57 q^{20} + 26 q^{22} - 4 q^{25} + 14 q^{26} - 14 q^{28} - 12 q^{29}+ \cdots - 85 q^{98}+O(q^{100}) $ 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 10 * q^8 - 18 * q^10 + 16 * q^11 + 14 * q^13 + 22 * q^14 - 8 * q^16 - 11 * q^17 - 11 * q^19 - 57 * q^20 + 26 * q^22 - 4 * q^25 + 14 * q^26 - 14 * q^28 - 12 * q^29 + 41 * q^31 + 46 * q^32 - 3 * q^34 + 26 * q^35 - 18 * q^37 - 70 * q^38 - 13 * q^40 - 10 * q^43 + 3 * q^44 - 24 * q^46 - 18 * q^47 - 10 * q^49 - 33 * q^50 + 61 * q^52 + 20 * q^53 - 17 * q^55 - 6 * q^56 - 37 * q^58 - 40 * q^59 - 12 * q^61 + 89 * q^62 - 2 * q^64 + 51 * q^65 - 47 * q^67 + 12 * q^68 + 32 * q^70 + 47 * q^71 + 39 * q^73 + 50 * q^74 - 39 * q^76 - 22 * q^77 - 2 * q^79 - 12 * q^80 + 26 * q^82 + 52 * q^83 + 35 * q^85 - 34 * q^86 + 30 * q^88 - 36 * q^89 + 8 * q^91 + 19 * q^92 + 21 * q^94 - 89 * q^95 - 85 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	1.10489	−	2.41937i	0.781275	−	1.71075i	0.0811848	−	0.996699i	$-0.474130\pi$
$2$	1.10489	−	2.41937i	0.781275	−	1.71075i	0.700090	−	0.714054i	$-0.253143\pi$
$3$		0			0
$3$		0			0
$4$	−3.32285	−	3.83478i	−1.66143	−	1.91739i
$5$	2.44470	−	1.57111i	1.09330	−	0.702624i	0.135711	−	0.990748i	$-0.456668\pi$
$5$	2.44470	−	1.57111i	1.09330	−	0.702624i	0.957593	+	0.288125i	$0.0930317\pi$
$6$		0			0
$7$	−0.326826	+	2.27313i	−0.123529	+	0.859161i	0.829979	+	0.557794i	$0.188352\pi$
$7$	−0.326826	+	2.27313i	−0.123529	+	0.859161i	−0.953508	+	0.301367i	$0.902557\pi$
$8$	−7.84516	+	2.30355i	−2.77368	+	0.814426i
$9$		0			0
$10$	−1.09998	−	7.65055i	−0.347845	−	2.41932i
$11$	−0.0494206	−	0.108216i	−0.0149009	−	0.0326283i	0.902035	−	0.431662i	$-0.142073\pi$
$11$	−0.0494206	−	0.108216i	−0.0149009	−	0.0326283i	−0.916936	+	0.399034i	$0.869346\pi$
$12$		0			0
$13$	0.614381	+	4.27311i	0.170399	+	1.18515i	0.878044	+	0.478580i	$0.158849\pi$
$13$	0.614381	+	4.27311i	0.170399	+	1.18515i	−0.707645	+	0.706568i	$0.750242\pi$
$14$	5.13843	+	3.30227i	1.37330	+	0.882568i
$15$		0			0
$16$	−1.65065	+	11.4805i	−0.412663	+	2.87013i
$17$	1.68604	−	1.94579i	0.408924	−	0.471923i	−0.513507	−	0.858085i	$-0.671654\pi$
$17$	1.68604	−	1.94579i	0.408924	−	0.471923i	0.922431	+	0.386162i	$0.126200\pi$
$18$		0			0
$19$	−1.13103	−	1.30528i	−0.259476	−	0.299452i	0.611031	−	0.791606i	$-0.290755\pi$
$19$	−1.13103	−	1.30528i	−0.259476	−	0.299452i	−0.870508	+	0.492155i	$0.836209\pi$
$20$	−14.1483	−	4.15430i	−3.16365	−	0.928931i
$21$		0			0
$22$	−0.316419			−0.0674607
$23$	−4.00915	+	2.63187i	−0.835965	+	0.548783i
$23$	−4.00915	+	2.63187i	−0.835965	+	0.548783i
$24$		0			0
$25$	1.43109	−	3.13366i	0.286219	−	0.626731i
$26$	11.0171	+	3.23490i	2.16063	+	0.634417i
$27$		0			0
$28$	9.80293	−	6.29996i	1.85258	−	1.19058i
$29$	0.933494	−	1.07731i	0.173345	−	0.200051i	−0.662428	−	0.749125i	$-0.730474\pi$
$29$	0.933494	−	1.07731i	0.173345	−	0.200051i	0.835774	+	0.549074i	$0.185020\pi$
$30$		0			0
$31$	5.49527	−	1.61356i	0.986980	−	0.289803i	0.251877	−	0.967759i	$-0.418952\pi$
$31$	5.49527	−	1.61356i	0.986980	−	0.289803i	0.735103	+	0.677956i	$0.237134\pi$
$32$	12.1951	+	7.83731i	2.15581	+	1.38545i
$33$		0			0
$34$	−2.84470	−	6.22903i	−0.487862	−	1.06827i
$35$	2.77235	+	6.07060i	0.468613	+	1.02612i
$36$		0			0
$37$	5.79948	+	3.72710i	0.953429	+	0.612731i	0.922172	−	0.386780i	$-0.126413\pi$
$37$	5.79948	+	3.72710i	0.953429	+	0.612731i	0.0312566	+	0.999511i	$0.490049\pi$
$38$	−4.40762	+	1.29419i	−0.715010	+	0.209946i
$39$		0			0
$40$	−15.5599	+	17.9571i	−2.46024	+	2.83927i
$41$	5.48180	−	3.52294i	0.856113	−	0.550190i	−0.0373628	−	0.999302i	$-0.511896\pi$
$41$	5.48180	−	3.52294i	0.856113	−	0.550190i	0.893476	+	0.449111i	$0.148259\pi$
$42$		0			0
$43$	−8.28385	−	2.43236i	−1.26327	−	0.370931i	−0.419562	−	0.907726i	$-0.637816\pi$
$43$	−8.28385	−	2.43236i	−1.26327	−	0.370931i	−0.843712	+	0.536796i	$0.819635\pi$
$44$	−0.250767	+	0.549102i	−0.0378045	+	0.0827803i
$45$		0			0
$46$	1.93781	+	12.6075i	0.285714	+	1.85888i
$47$	−5.91880			−0.863345			−0.431673	−	0.902030i	$-0.642076\pi$
$47$	−5.91880			−0.863345			−0.431673	+	0.902030i	$0.642076\pi$
$48$		0			0
$49$	1.65616	+	0.486293i	0.236595	+	0.0694704i
$50$	−6.00028	−	6.92469i	−0.848567	−	0.979299i
$51$		0			0
$52$	14.3449	−	16.5549i	1.98929	−	2.29576i
$53$	0.514895	−	3.58117i	0.0707263	−	0.491912i	−0.923413	−	0.383807i	$-0.874613\pi$
$53$	0.514895	−	3.58117i	0.0707263	−	0.491912i	0.994140	−	0.108105i	$-0.0344782\pi$
$54$		0			0
$55$	−0.290838	−	0.186910i	−0.0392166	−	0.0252030i
$56$	−2.67225	−	18.5859i	−0.357094	−	2.48364i
$57$		0			0
$58$	−1.57500	−	3.44878i	−0.206808	−	0.452846i
$59$	−0.386194	−	2.68604i	−0.0502782	−	0.349692i	−0.999395	−	0.0347692i	$-0.988930\pi$
$59$	−0.386194	−	2.68604i	−0.0502782	−	0.349692i	0.949117	−	0.314923i	$-0.101979\pi$
$60$		0			0
$61$	−12.0589	+	3.54081i	−1.54398	+	0.453354i	−0.939296	−	0.343109i	$-0.888520\pi$
$61$	−12.0589	+	3.54081i	−1.54398	+	0.453354i	−0.604687	+	0.796463i	$0.706702\pi$
$62$	2.16787	−	15.0779i	0.275320	−	1.91490i
$63$		0			0
$64$	12.9209	−	8.30375i	1.61511	−	1.03797i
$65$	8.21553	+	9.48123i	1.01901	+	1.17600i
$66$		0			0
$67$	−0.0349839	+	0.0766041i	−0.00427397	+	0.00935868i	−0.911757	−	0.410730i	$-0.865274\pi$
$67$	−0.0349839	+	0.0766041i	−0.00427397	+	0.00935868i	0.907483	+	0.420089i	$0.138001\pi$
$68$	−13.0641			−1.58426
$69$		0			0
$70$	17.7502			2.12155
$71$	−6.43563	+	14.0921i	−0.763769	+	1.67242i	−0.0238577	+	0.999715i	$0.507595\pi$
$71$	−6.43563	+	14.0921i	−0.763769	+	1.67242i	−0.739911	+	0.672705i	$0.765132\pi$
$72$		0			0
$73$	0.455430	+	0.525595i	0.0533041	+	0.0615162i	0.781775	−	0.623560i	$-0.214314\pi$
$73$	0.455430	+	0.525595i	0.0533041	+	0.0615162i	−0.728471	+	0.685076i	$0.759769\pi$
$74$	15.4250	−	9.91306i	1.79312	−	1.15237i
$75$		0			0
$76$	−1.24721	+	8.67450i	−0.143064	+	0.995034i
$77$	0.262140	−	0.0769714i	0.0298737	−	0.00877170i
$78$		0			0
$79$	1.05210	+	7.31752i	0.118371	+	0.823285i	0.959350	+	0.282218i	$0.0910702\pi$
$79$	1.05210	+	7.31752i	0.118371	+	0.823285i	−0.840980	+	0.541067i	$0.818021\pi$
$80$	14.0019	+	30.6598i	1.56546	+	3.42787i
$81$		0			0
$82$	−2.46651	−	17.1550i	−0.272381	−	1.89445i
$83$	−2.33903	−	1.50321i	−0.256742	−	0.164998i	0.405938	−	0.913901i	$-0.366945\pi$
$83$	−2.33903	−	1.50321i	−0.256742	−	0.164998i	−0.662680	+	0.748902i	$0.730581\pi$
$84$		0			0
$85$	1.06480	−	7.40583i	0.115493	−	0.803275i
$86$	−15.0375	+	17.3542i	−1.62154	+	1.87135i
$87$		0			0
$88$	0.636992	+	0.735128i	0.0679036	+	0.0783649i
$89$	−12.7468	−	3.74281i	−1.35116	−	0.396737i	−0.475522	−	0.879704i	$-0.657741\pi$
$89$	−12.7468	−	3.74281i	−1.35116	−	0.396737i	−0.875638	+	0.482967i	$0.839559\pi$
$90$		0			0
$91$	−9.91413			−1.03928
$92$	23.4144	+	6.62886i	2.44112	+	0.691107i
$93$		0			0
$94$	−6.53962	+	14.3198i	−0.674510	+	1.47697i
$95$	−4.81578	−	1.41404i	−0.494089	−	0.145077i
$96$		0			0
$97$	−7.16897	+	4.60722i	−0.727898	+	0.467792i	−0.851376	−	0.524555i	$-0.824232\pi$
$97$	−7.16897	+	4.60722i	−0.727898	+	0.467792i	0.123478	+	0.992347i	$0.460595\pi$
$98$	3.00640	−	3.46957i	0.303692	−	0.350479i
$99$		0			0
$100$	−16.7722	+	4.92476i	−1.67722	+	0.492476i
$101$	−5.88248	−	3.78044i	−0.585328	−	0.376168i	0.214206	−	0.976789i	$-0.431284\pi$
$101$	−5.88248	−	3.78044i	−0.585328	−	0.376168i	−0.799534	+	0.600621i	$0.794920\pi$
$102$		0			0
$103$	5.73944	+	12.5676i	0.565523	+	1.23832i	0.949147	+	0.314834i	$0.101949\pi$
$103$	5.73944	+	12.5676i	0.565523	+	1.23832i	−0.383623	+	0.923490i	$0.625324\pi$
$104$	−14.6632	−	32.1080i	−1.43785	−	3.14845i
$105$		0			0
$106$	−8.09528	−	5.20252i	−0.786283	−	0.505314i
$107$	7.88971	−	2.31663i	0.762727	−	0.223957i	0.122841	−	0.992426i	$-0.460800\pi$
$107$	7.88971	−	2.31663i	0.762727	−	0.223957i	0.639886	+	0.768469i	$0.278981\pi$
$108$		0			0
$109$	11.3104	−	13.0529i	1.08334	−	1.25024i	0.116958	−	0.993137i	$-0.462686\pi$
$109$	11.3104	−	13.0529i	1.08334	−	1.25024i	0.966383	−	0.257106i	$-0.0827688\pi$
$110$	−0.773550	+	0.497130i	−0.0737551	+	0.0473995i
$111$		0			0
$112$	−25.5572	−	7.50428i	−2.41493	−	0.709088i
$113$	−3.11467	+	6.82019i	−0.293004	+	0.641589i	−0.997690	−	0.0679300i	$-0.978361\pi$
$113$	−3.11467	+	6.82019i	−0.293004	+	0.641589i	0.704686	+	0.709519i	$0.251088\pi$
$114$		0			0
$115$	−5.66620	+	12.7330i	−0.528376	+	1.18736i
$116$	−7.23310			−0.671577
$117$		0			0
$118$	−6.92522	−	2.03343i	−0.637518	−	0.187192i
$119$	3.87198	+	4.46851i	0.354944	+	0.409627i
$120$		0			0
$121$	7.19420	−	8.30255i	0.654018	−	0.754777i
$122$	−4.75721	+	33.0871i	−0.430698	+	2.99557i
$123$		0			0
$124$	−24.4476	−	15.7115i	−2.19546	−	1.41094i
$125$	0.643114	+	4.47295i	0.0575218	+	0.400073i
$126$		0			0
$127$	−0.834395	−	1.82707i	−0.0740406	−	0.162126i	0.868992	−	0.494825i	$-0.164768\pi$
$127$	−0.834395	−	1.82707i	−0.0740406	−	0.162126i	−0.943033	+	0.332699i	$0.892041\pi$
$128$	−1.68761	−	11.7376i	−0.149165	−	1.03747i
$129$		0			0
$130$	32.0159	−	9.40071i	2.80798	−	0.824496i
$131$	−0.699047	+	4.86198i	−0.0610760	+	0.424793i	0.936227	+	0.351396i	$0.114293\pi$
$131$	−0.699047	+	4.86198i	−0.0610760	+	0.424793i	−0.997303	+	0.0733967i	$0.976616\pi$
$132$		0			0
$133$	3.33672	−	2.14438i	0.289330	−	0.185941i
$134$	0.146680	+	0.169278i	0.0126712	+	0.0146234i
$135$		0			0
$136$	−8.74500	+	19.1489i	−0.749877	+	1.64200i
$137$	−7.93152			−0.677636			−0.338818	−	0.940852i	$-0.610027\pi$
$137$	−7.93152			−0.677636			−0.338818	+	0.940852i	$0.610027\pi$
$138$		0			0
$139$	10.7987			0.915936			0.457968	−	0.888969i	$-0.348577\pi$
$139$	10.7987			0.915936			0.457968	+	0.888969i	$0.348577\pi$
$140$	14.0673	−	30.8030i	1.18890	−	2.60333i
$141$		0			0
$142$	26.9833	+	31.1403i	2.26439	+	2.61324i
$143$	0.432056	−	0.277665i	0.0361303	−	0.0232196i
$144$		0			0
$145$	0.589538	−	4.10033i	0.0489585	−	0.340514i
$146$	1.77481	−	0.521131i	0.146884	−	0.0431291i
$147$		0			0
$148$	−4.97822	−	34.6243i	−0.409207	−	2.84610i
$149$	−6.87613	−	15.0566i	−0.563315	−	1.23349i	−0.950281	−	0.311393i	$-0.899204\pi$
$149$	−6.87613	−	15.0566i	−0.563315	−	1.23349i	0.386967	−	0.922094i	$-0.373523\pi$
$150$		0			0
$151$	−2.68982	−	18.7081i	−0.218895	−	1.52245i	−0.742128	−	0.670258i	$-0.766184\pi$
$151$	−2.68982	−	18.7081i	−0.218895	−	1.52245i	0.523234	−	0.852189i	$-0.324726\pi$
$152$	11.8799	+	7.63474i	0.963586	+	0.619259i
$153$		0			0
$154$	0.103414	−	0.719260i	0.00833333	−	0.0579596i
$155$	10.8992	−	12.5784i	0.875446	−	1.01032i
$156$		0			0
$157$	−4.95301	−	5.71608i	−0.395293	−	0.456193i	0.522860	−	0.852419i	$-0.324865\pi$
$157$	−4.95301	−	5.71608i	−0.395293	−	0.456193i	−0.918153	+	0.396226i	$0.870320\pi$
$158$	18.8662	+	5.53963i	1.50092	+	0.440709i
$159$		0			0
$160$	42.1267			3.33041
$161$	−4.67228	−	9.97346i	−0.368227	−	0.786019i
$162$		0			0
$163$	0.693430	−	1.51840i	0.0543136	−	0.118930i	−0.880529	−	0.473992i	$-0.842813\pi$
$163$	0.693430	−	1.51840i	0.0543136	−	0.118930i	0.934843	+	0.355061i	$0.115540\pi$
$164$	−31.7249	−	9.31527i	−2.47730	−	0.727400i
$165$		0			0
$166$	−6.22119	+	3.99811i	−0.482858	+	0.310314i
$167$	14.0362	−	16.1987i	1.08615	−	1.25349i	0.120764	−	0.992681i	$-0.461465\pi$
$167$	14.0362	−	16.1987i	1.08615	−	1.25349i	0.965391	−	0.260808i	$-0.0839890\pi$
$168$		0			0
$169$	−5.40863	+	1.58812i	−0.416049	+	0.122163i
$170$	−16.7410	−	10.7588i	−1.28397	−	0.825159i
$171$		0			0
$172$	18.1985	+	39.8491i	1.38762	+	3.03846i
$173$	2.62976	+	5.75836i	0.199937	+	0.437800i	0.982869	−	0.184307i	$-0.0590041\pi$
$173$	2.62976	+	5.75836i	0.199937	+	0.437800i	−0.782932	+	0.622107i	$0.786277\pi$
$174$		0			0
$175$	6.65548	+	4.27722i	0.503107	+	0.323327i
$176$	1.32395	−	0.388747i	0.0997966	−	0.0293029i
$177$		0			0
$178$	−23.1391	+	26.7039i	−1.73435	+	2.00154i
$179$	−6.89203	+	4.42924i	−0.515134	+	0.331057i	−0.772245	−	0.635325i	$-0.780866\pi$
$179$	−6.89203	+	4.42924i	−0.515134	+	0.331057i	0.257110	+	0.966382i	$0.417230\pi$
$180$		0			0
$181$	−6.05668	−	1.77840i	−0.450189	−	0.132188i	0.0487755	−	0.998810i	$-0.484468\pi$
$181$	−6.05668	−	1.77840i	−0.450189	−	0.132188i	−0.498965	+	0.866622i	$0.666286\pi$
$182$	−10.9540	+	23.9859i	−0.811966	+	1.77796i
$183$		0			0
$184$	25.3897	−	29.8827i	1.87176	−	2.20298i
$185$	20.0337			1.47291
$186$		0			0
$187$	−0.293890	−	0.0862939i	−0.0214914	−	0.00631044i
$188$	19.6673	+	22.6973i	1.43438	+	1.65537i
$189$		0			0
$190$	−8.74199	+	10.0888i	−0.634211	+	0.731918i
$191$	1.84244	−	12.8144i	0.133314	−	0.927221i	−0.807878	−	0.589350i	$-0.799384\pi$
$191$	1.84244	−	12.8144i	0.133314	−	0.927221i	0.941192	−	0.337871i	$-0.109707\pi$
$192$		0			0
$193$	10.6093	+	6.81818i	0.763674	+	0.490784i	0.863579	−	0.504213i	$-0.168217\pi$
$193$	10.6093	+	6.81818i	0.763674	+	0.490784i	−0.0999048	+	0.994997i	$0.531854\pi$
$194$	3.22565	+	22.4349i	0.231588	+	1.61073i
$195$		0			0
$196$	−3.63836	−	7.96689i	−0.259883	−	0.569064i
$197$	−2.06820	−	14.3847i	−0.147353	−	1.02486i	−0.920530	−	0.390673i	$-0.872242\pi$
$197$	−2.06820	−	14.3847i	−0.147353	−	1.02486i	0.773176	−	0.634191i	$-0.218667\pi$
$198$		0			0
$199$	−19.3561	+	5.68347i	−1.37212	+	0.402890i	−0.883019	−	0.469337i	$-0.844493\pi$
$199$	−19.3561	+	5.68347i	−1.37212	+	0.402890i	−0.489100	+	0.872228i	$0.662675\pi$
$200$	−4.00863	+	27.8806i	−0.283453	+	1.97146i
$201$		0			0
$202$	−15.6458	+	10.0549i	−1.10083	+	0.707462i
$203$	2.14377	+	2.47404i	0.150463	+	0.173644i
$204$		0			0
$205$	7.86642	−	17.2251i	0.549415	−	1.20305i
$206$	36.7472			2.56030
$207$		0			0
$208$	−50.0717			−3.47185
$209$	−0.0853558	+	0.186903i	−0.00590419	+	0.0129284i
$210$		0			0
$211$	−4.88121	−	5.63321i	−0.336036	−	0.387806i	0.562433	−	0.826843i	$-0.309865\pi$
$211$	−4.88121	−	5.63321i	−0.336036	−	0.387806i	−0.898469	+	0.439036i	$0.855320\pi$
$212$	−15.4439	+	9.92520i	−1.06069	+	0.681666i
$213$		0			0
$214$	3.11248	−	21.6478i	0.212765	−	1.47981i
$215$	−24.0731	+	7.06849i	−1.64177	+	0.482067i
$216$		0			0
$217$	1.87182	+	13.0188i	0.127067	+	0.883774i
$218$	−19.0831	−	41.7861i	−1.29247	−	2.83011i
$219$		0			0
$220$	0.249653	+	1.73637i	0.0168316	+	0.117066i
$221$	9.35044	+	6.00917i	0.628979	+	0.404220i
$222$		0			0
$223$	−0.239369	+	1.66485i	−0.0160293	+	0.111486i	−0.996265	−	0.0863458i	$-0.972481\pi$
$223$	−0.239369	+	1.66485i	−0.0160293	+	0.111486i	0.980236	+	0.197832i	$0.0633901\pi$
$224$	−21.8009	+	25.1596i	−1.45663	+	1.68104i
$225$		0			0
$226$	13.0592	+	15.0711i	0.868684	+	1.00252i
$227$	10.3447	+	3.03747i	0.686601	+	0.201604i	0.606383	−	0.795173i	$-0.292620\pi$
$227$	10.3447	+	3.03747i	0.686601	+	0.201604i	0.0802184	+	0.996777i	$0.474438\pi$
$228$		0			0
$229$	21.9077			1.44770			0.723852	−	0.689955i	$-0.242370\pi$
$229$	21.9077			1.44770			0.723852	+	0.689955i	$0.242370\pi$
$230$	24.5453	+	27.7772i	1.61847	+	1.83157i
$231$		0			0
$232$	−4.84177	+	10.6020i	−0.317878	+	0.696056i
$233$	23.8637	+	7.00702i	1.56336	+	0.459045i	0.945061	−	0.326894i	$-0.106002\pi$
$233$	23.8637	+	7.00702i	1.56336	+	0.459045i	0.618304	+	0.785939i	$0.287820\pi$
$234$		0			0
$235$	−14.4697	+	9.29911i	−0.943899	+	0.606607i
$236$	−9.01709	+	10.4063i	−0.586962	+	0.677391i
$237$		0			0
$238$	15.0891	−	4.43056i	0.978080	−	0.287190i
$239$	−3.53060	−	2.26898i	−0.228375	−	0.146768i	0.421450	−	0.906852i	$-0.361521\pi$
$239$	−3.53060	−	2.26898i	−0.228375	−	0.146768i	−0.649825	+	0.760084i	$0.725158\pi$
$240$		0			0
$241$	−11.3946	−	24.9507i	−0.733991	−	1.60722i	−0.793193	−	0.608971i	$-0.791583\pi$
$241$	−11.3946	−	24.9507i	−0.733991	−	1.60722i	0.0592012	−	0.998246i	$-0.481145\pi$
$242$	−12.1381	−	26.5788i	−0.780270	−	1.70855i
$243$		0			0
$244$	53.6481	+	34.4776i	3.43447	+	2.20720i
$245$	4.81284	−	1.41318i	0.307481	−	0.0902847i
$246$		0			0
$247$	4.88272	−	5.63496i	0.310680	−	0.358544i
$248$	−39.3944	+	25.3172i	−2.50154	+	1.60764i
$249$		0			0
$250$	11.5323	+	3.38619i	0.729367	+	0.214161i
$251$	5.36870	−	11.7558i	0.338869	−	0.742020i	−0.661096	−	0.750301i	$-0.729909\pi$
$251$	5.36870	−	11.7558i	0.338869	−	0.742020i	0.999966	+	0.00828064i	$0.00263584\pi$
$252$		0			0
$253$	0.482945	+	0.303785i	0.0303625	+	0.0190988i
$254$	−5.34227			−0.335204
$255$		0			0
$256$	−0.788305	−	0.231467i	−0.0492691	−	0.0144667i
$257$	−0.940093	−	1.08493i	−0.0586414	−	0.0676758i	0.725671	−	0.688042i	$-0.241529\pi$
$257$	−0.940093	−	1.08493i	−0.0586414	−	0.0676758i	−0.784312	+	0.620366i	$0.786984\pi$
$258$		0			0
$259$	−10.3676	+	11.9648i	−0.644211	+	0.743459i
$260$	9.05939	−	63.0095i	0.561840	−	3.90768i
$261$		0			0
$262$	10.9906	+	7.06320i	0.678999	+	0.436366i
$263$	2.04437	+	14.2189i	0.126061	+	0.876774i	0.950478	+	0.310791i	$0.100594\pi$
$263$	2.04437	+	14.2189i	0.126061	+	0.876774i	−0.824417	+	0.565983i	$0.808497\pi$
$264$		0			0
$265$	−4.36767	−	9.56386i	−0.268304	−	0.587503i
$266$	−1.50134	−	10.4421i	−0.0920531	−	0.640244i
$267$		0			0
$268$	0.410006	−	0.120389i	0.0250451	−	0.00735390i
$269$	−2.75934	+	19.1916i	−0.168240	+	1.17013i	0.714281	+	0.699859i	$0.246754\pi$
$269$	−2.75934	+	19.1916i	−0.168240	+	1.17013i	−0.882520	+	0.470274i	$0.844155\pi$
$270$		0			0
$271$	13.7459	−	8.83395i	0.835004	−	0.536624i	−0.0518607	−	0.998654i	$-0.516515\pi$
$271$	13.7459	−	8.83395i	0.835004	−	0.536624i	0.886864	+	0.462030i	$0.152879\pi$
$272$	19.5556	+	22.5684i	1.18573	+	1.36841i
$273$		0			0
$274$	−8.76346	+	19.1893i	−0.529420	+	1.15927i
$275$	−0.409837			−0.0247141
$276$		0			0
$277$	20.1827			1.21266			0.606332	−	0.795212i	$-0.292640\pi$
$277$	20.1827			1.21266			0.606332	+	0.795212i	$0.292640\pi$
$278$	11.9314	−	26.1261i	0.715598	−	1.56694i
$279$		0			0
$280$	−35.7334	−	41.2386i	−2.13548	−	2.46448i
$281$	−7.16101	+	4.60210i	−0.427190	+	0.274538i	−0.736519	−	0.676417i	$-0.763532\pi$
$281$	−7.16101	+	4.60210i	−0.427190	+	0.274538i	0.309329	+	0.950955i	$0.399896\pi$
$282$		0			0
$283$	0.480803	−	3.34406i	0.0285808	−	0.198784i	−0.970528	−	0.240987i	$-0.922529\pi$
$283$	0.480803	−	3.34406i	0.0285808	−	0.198784i	0.999109	+	0.0422038i	$0.0134379\pi$
$284$	75.4246	−	22.1466i	4.47562	−	1.31416i
$285$		0			0
$286$	−0.194402	−	1.35209i	−0.0114952	−	0.0799509i
$287$	6.21649	+	13.6122i	0.366948	+	0.803503i
$288$		0			0
$289$	1.47597	+	10.2656i	0.0868220	+	0.603861i
$290$	−9.26883	−	5.95672i	−0.544285	−	0.349791i
$291$		0			0
$292$	0.502210	−	3.49295i	0.0293896	−	0.204409i
$293$	−2.70239	+	3.11873i	−0.157876	+	0.182198i	−0.829177	−	0.558987i	$-0.811190\pi$
$293$	−2.70239	+	3.11873i	−0.157876	+	0.182198i	0.671301	+	0.741185i	$0.265736\pi$
$294$		0			0
$295$	−5.16420	−	5.95981i	−0.300671	−	0.346993i
$296$	−54.0834	−	15.8803i	−3.14353	−	0.923024i
$297$		0			0
$298$	−44.0249			−2.55030
$299$	−13.7094	−	15.5146i	−0.792837	−	0.897231i
$300$		0			0
$301$	8.23643	−	18.0353i	0.474740	−	1.03954i
$302$	−48.2339	−	14.1627i	−2.77555	−	0.814975i
$303$		0			0
$304$	16.8522	−	10.8303i	0.966542	−	0.621159i
$305$	−23.9174	+	27.6021i	−1.36951	+	1.58049i
$306$		0			0
$307$	−9.98433	+	2.93166i	−0.569836	+	0.167319i	−0.553943	−	0.832555i	$-0.686877\pi$
$307$	−9.98433	+	2.93166i	−0.569836	+	0.167319i	−0.0158931	+	0.999874i	$0.505059\pi$
$308$	−1.16622	−	0.749485i	−0.0664517	−	0.0427059i
$309$		0			0
$310$	−18.3893	−	40.2670i	−1.04444	−	2.28701i
$311$	−5.48023	−	12.0000i	−0.310756	−	0.680460i	0.688230	−	0.725493i	$-0.258388\pi$
$311$	−5.48023	−	12.0000i	−0.310756	−	0.680460i	−0.998986	+	0.0450328i	$0.985661\pi$
$312$		0			0
$313$	−11.5760	−	7.43943i	−0.654313	−	0.420501i	0.170927	−	0.985284i	$-0.445324\pi$
$313$	−11.5760	−	7.43943i	−0.654313	−	0.420501i	−0.825240	+	0.564782i	$0.808960\pi$
$314$	−19.3018	+	5.66753i	−1.08927	+	0.319837i
$315$		0			0
$316$	24.5651	−	28.3496i	1.38189	−	1.59479i
$317$	12.0651	−	7.75378i	0.677645	−	0.435496i	−0.156029	−	0.987752i	$-0.549869\pi$
$317$	12.0651	−	7.75378i	0.677645	−	0.435496i	0.833674	+	0.552257i	$0.186233\pi$
$318$		0			0
$319$	−0.162716	−	0.0477777i	−0.00911033	−	0.00267504i
$320$	18.5416	−	40.6004i	1.03651	−	2.26963i
$321$		0			0
$322$	−29.2919	+	0.284406i	−1.63237	+	0.0158493i
$323$	−4.44676			−0.247424
$324$		0			0
$325$	14.2697	+	4.18996i	0.791541	+	0.232417i
$326$	−2.90741	−	3.35533i	−0.161026	−	0.185834i
$327$		0			0
$328$	−34.8903	+	40.2656i	−1.92650	+	2.22329i
$329$	1.93442	−	13.4542i	0.106648	−	0.741753i
$330$		0			0
$331$	−9.95577	−	6.39818i	−0.547219	−	0.351676i	0.237638	−	0.971354i	$-0.423627\pi$
$331$	−9.95577	−	6.39818i	−0.547219	−	0.351676i	−0.784856	+	0.619678i	$0.787263\pi$
$332$	2.00781	+	13.9646i	0.110193	+	0.766407i
$333$		0			0
$334$	−23.6821	−	51.8565i	−1.29583	−	2.83746i
$335$	0.0348286	+	0.242238i	0.00190289	+	0.0132349i
$336$		0			0
$337$	−25.6791	+	7.54006i	−1.39883	+	0.410733i	−0.892281	−	0.451480i	$-0.850896\pi$
$337$	−25.6791	+	7.54006i	−1.39883	+	0.410733i	−0.506547	+	0.862213i	$0.669078\pi$
$338$	−2.13370	+	14.8402i	−0.116058	+	0.807199i
$339$		0			0
$340$	−31.9379	+	20.5252i	−1.73207	+	1.11314i
$341$	−0.446192	−	0.514933i	−0.0241626	−	0.0278852i
$342$		0			0
$343$	−8.32469	+	18.2285i	−0.449491	+	0.984248i
$344$	70.5911			3.80602
$345$		0			0
$346$	16.8372			0.905174
$347$	3.67463	−	8.04631i	0.197264	−	0.431948i	−0.784989	−	0.619510i	$-0.787331\pi$
$347$	3.67463	−	8.04631i	0.197264	−	0.431948i	0.982253	+	0.187562i	$0.0600585\pi$
$348$		0			0
$349$	19.5011	+	22.5054i	1.04387	+	1.20469i	0.978376	+	0.206834i	$0.0663160\pi$
$349$	19.5011	+	22.5054i	1.04387	+	1.20469i	0.0654913	+	0.997853i	$0.479139\pi$
$350$	17.7017	−	11.3762i	0.946198	−	0.608084i
$351$		0			0
$352$	0.245433	−	1.70703i	0.0130816	−	0.0909849i
$353$	−16.5145	+	4.84909i	−0.878978	+	0.258091i	−0.689930	−	0.723877i	$-0.742359\pi$
$353$	−16.5145	+	4.84909i	−0.878978	+	0.258091i	−0.189048	+	0.981968i	$0.560540\pi$
$354$		0			0
$355$	6.40705	+	44.5620i	0.340051	+	2.36511i
$356$	28.0030	+	61.3180i	1.48416	+	3.24985i
$357$		0			0
$358$	3.10104	+	21.5682i	0.163895	+	1.13991i
$359$	5.99586	+	3.85331i	0.316449	+	0.203370i	0.689217	−	0.724555i	$-0.257955\pi$
$359$	5.99586	+	3.85331i	0.316449	+	0.203370i	−0.372767	+	0.927925i	$0.621591\pi$
$360$		0			0
$361$	2.27946	−	15.8540i	0.119972	−	0.834420i
$362$	−10.9946	+	12.6884i	−0.577862	+	0.666888i
$363$		0			0
$364$	32.9432	+	38.0185i	1.72669	+	1.99271i
$365$	1.93916	+	0.569389i	0.101500	+	0.0298032i
$366$		0			0
$367$	13.5836			0.709060			0.354530	−	0.935045i	$-0.384641\pi$
$367$	13.5836			0.709060			0.354530	+	0.935045i	$0.384641\pi$
$368$	−23.5976	−	50.3714i	−1.23011	−	2.62579i
$369$		0			0
$370$	22.1350	−	48.4690i	1.15075	−	2.51978i
$371$	7.97218	+	2.34084i	0.413895	+	0.121531i
$372$		0			0
$373$	15.7544	−	10.1247i	0.815733	−	0.524240i	−0.0649821	−	0.997886i	$-0.520699\pi$
$373$	15.7544	−	10.1247i	0.815733	−	0.524240i	0.880715	+	0.473647i	$0.157063\pi$
$374$	−0.533493	+	0.615684i	−0.0275863	+	0.0318363i
$375$		0			0
$376$	46.4339	−	13.6342i	2.39465	−	0.703131i
$377$	5.17699	+	3.32705i	0.266628	+	0.171352i
$378$		0			0
$379$	−4.16129	−	9.11196i	−0.213751	−	0.468050i	0.772137	−	0.635456i	$-0.219188\pi$
$379$	−4.16129	−	9.11196i	−0.213751	−	0.468050i	−0.985888	+	0.167406i	$0.946461\pi$
$380$	10.5796	+	23.1661i	0.542722	+	1.18839i
$381$		0			0
$382$	−28.9672	−	18.6161i	−1.48209	−	0.952482i
$383$	−27.9432	+	8.20488i	−1.42783	+	0.419250i	−0.902147	−	0.431429i	$-0.858010\pi$
$383$	−27.9432	+	8.20488i	−1.42783	+	0.419250i	−0.525686	+	0.850679i	$0.676191\pi$
$384$		0			0
$385$	0.519924	−	0.600025i	0.0264978	−	0.0305801i
$386$	28.2178	−	18.1345i	1.43625	−	0.923022i
$387$		0			0
$388$	41.4891	+	12.1823i	2.10629	+	0.618462i
$389$	−1.82086	+	3.98712i	−0.0923211	+	0.202155i	−0.950159	−	0.311765i	$-0.899080\pi$
$389$	−1.82086	+	3.98712i	−0.0923211	+	0.202155i	0.857838	+	0.513920i	$0.171807\pi$
$390$		0			0
$391$	−1.63850	+	12.2384i	−0.0828624	+	0.618921i
$392$	−14.1130			−0.712816
$393$		0			0
$394$	−37.0869	−	10.8897i	−1.86841	−	0.548616i
$395$	14.0687	+	16.2362i	0.707875	+	0.816931i
$396$		0			0
$397$	−0.0954283	+	0.110130i	−0.00478941	+	0.00552727i	−0.758139	−	0.652093i	$-0.773891\pi$
$397$	−0.0954283	+	0.110130i	−0.00478941	+	0.00552727i	0.753350	+	0.657620i	$0.228437\pi$
$398$	−7.63595	+	53.1092i	−0.382756	+	2.66213i
$399$		0			0
$400$	33.6138	+	21.6023i	1.68069	+	1.08011i
$401$	−4.79060	−	33.3194i	−0.239231	−	1.66389i	−0.655912	−	0.754837i	$-0.727716\pi$
$401$	−4.79060	−	33.3194i	−0.239231	−	1.66389i	0.416681	−	0.909053i	$-0.363193\pi$
$402$		0			0
$403$	10.2711	+	22.4906i	0.511640	+	1.12034i
$404$	5.04947	+	35.1198i	0.251220	+	1.74728i
$405$		0			0
$406$	8.35425	−	2.45303i	0.414615	−	0.121742i
$407$	0.116718	−	0.811791i	0.00578549	−	0.0402390i
$408$		0			0
$409$	−25.4633	+	16.3642i	−1.25908	+	0.809160i	−0.988158	−	0.153442i	$-0.950964\pi$
$409$	−25.4633	+	16.3642i	−1.25908	+	0.809160i	−0.270920	+	0.962602i	$0.587328\pi$
$410$	−32.9823	−	38.0636i	−1.62888	−	1.87983i
$411$		0			0
$412$	29.1227	−	63.7698i	1.43477	−	3.14171i
$413$	6.23192			0.306653
$414$		0			0
$415$	−8.07995			−0.396629
$416$	−25.9973	+	56.9261i	−1.27462	+	2.79103i
$417$		0			0
$418$	0.357879	+	0.413015i	0.0175045	+	0.0202012i
$419$	−15.7624	+	10.1299i	−0.770044	+	0.494877i	−0.865716	−	0.500536i	$-0.833136\pi$
$419$	−15.7624	+	10.1299i	−0.770044	+	0.494877i	0.0956719	+	0.995413i	$0.469500\pi$
$420$		0			0
$421$	−5.57819	+	38.7972i	−0.271864	+	1.89086i	0.157173	+	0.987571i	$0.449762\pi$
$421$	−5.57819	+	38.7972i	−0.271864	+	1.89086i	−0.429038	+	0.903287i	$0.641147\pi$
$422$	−19.0220	+	5.58537i	−0.925978	+	0.271892i
$423$		0			0
$424$	4.20996	+	29.2809i	0.204454	+	1.42201i
$425$	−3.68456	−	8.06806i	−0.178727	−	0.391358i
$426$		0			0
$427$	−4.10755	−	28.5686i	−0.198778	−	1.38253i
$428$	−35.1001	−	22.5575i	−1.69663	−	1.09036i
$429$		0			0
$430$	−9.49678	+	66.0515i	−0.457975	+	3.18529i
$431$	14.0594	−	16.2254i	0.677217	−	0.781550i	−0.308271	−	0.951299i	$-0.599750\pi$
$431$	14.0594	−	16.2254i	0.677217	−	0.781550i	0.985487	+	0.169749i	$0.0542957\pi$
$432$		0			0
$433$	0.496613	+	0.573122i	0.0238657	+	0.0275425i	0.767557	−	0.640981i	$-0.221472\pi$
$433$	0.496613	+	0.573122i	0.0238657	+	0.0275425i	−0.743691	+	0.668523i	$0.766927\pi$
$434$	33.5655	+	9.85571i	1.61119	+	0.473089i
$435$		0			0
$436$	−87.6378			−4.19709
$437$	7.96980	+	2.25633i	0.381247	+	0.107935i
$438$		0			0
$439$	5.44584	−	11.9247i	0.259916	−	0.569136i	−0.734016	−	0.679132i	$-0.762357\pi$
$439$	5.44584	−	11.9247i	0.259916	−	0.569136i	0.993932	+	0.109996i	$0.0350838\pi$
$440$	2.71223	+	0.796382i	0.129300	+	0.0379660i
$441$		0			0
$442$	24.8696	−	15.9827i	1.18293	−	0.760221i
$443$	−2.00368	+	2.31237i	−0.0951976	+	0.109864i	−0.801349	−	0.598197i	$-0.795884\pi$
$443$	−2.00368	+	2.31237i	−0.0951976	+	0.109864i	0.706152	+	0.708061i	$0.250430\pi$
$444$		0			0
$445$	−37.0426	+	10.8767i	−1.75599	+	0.515604i
$446$	3.76340	+	2.41859i	0.178202	+	0.114524i
$447$		0			0
$448$	14.6526	+	32.0847i	0.692270	+	1.51586i
$449$	3.18597	+	6.97630i	0.150355	+	0.329232i	0.969790	−	0.243940i	$-0.0784400\pi$
$449$	3.18597	+	6.97630i	0.150355	+	0.329232i	−0.819435	+	0.573172i	$0.805713\pi$
$450$		0			0
$451$	−0.652151	−	0.419112i	−0.0307086	−	0.0197352i
$452$	36.5035	−	10.7184i	1.71698	−	0.504151i
$453$		0			0
$454$	18.7785	−	21.6716i	0.881319	−	1.01710i
$455$	−24.2371	+	15.5762i	−1.13625	+	0.730225i
$456$		0			0
$457$	−8.60068	−	2.52539i	−0.402323	−	0.118133i	0.0743097	−	0.997235i	$-0.476325\pi$
$457$	−8.60068	−	2.52539i	−0.402323	−	0.118133i	−0.476633	+	0.879103i	$0.658143\pi$
$458$	24.2056	−	53.0030i	1.13106	−	2.47667i
$459$		0			0
$460$	67.6560	−	20.5812i	3.15448	−	0.959602i
$461$	7.53704			0.351035			0.175517	−	0.984476i	$-0.443840\pi$
$461$	7.53704			0.351035			0.175517	+	0.984476i	$0.443840\pi$
$462$		0			0
$463$	31.6291	+	9.28715i	1.46993	+	0.431610i	0.916076	−	0.401004i	$-0.131339\pi$
$463$	31.6291	+	9.28715i	1.46993	+	0.431610i	0.553853	+	0.832614i	$0.313157\pi$
$464$	10.8272	+	12.4953i	0.502640	+	0.580078i
$465$		0			0
$466$	43.3194	−	49.9932i	2.00673	−	2.31589i
$467$	−1.91901	+	13.3470i	−0.0888010	+	0.617624i	0.896015	+	0.444024i	$0.146449\pi$
$467$	−1.91901	+	13.3470i	−0.0888010	+	0.617624i	−0.984816	+	0.173601i	$0.944460\pi$
$468$		0			0
$469$	−0.162697	−	0.104559i	−0.00751265	−	0.00482809i
$470$	6.51058	+	45.2821i	0.300311	+	2.08871i
$471$		0			0
$472$	9.21716	+	20.1828i	0.424254	+	0.928987i
$473$	0.146173	+	1.01665i	0.00672102	+	0.0467457i
$474$		0			0
$475$	−5.70891	+	1.67629i	−0.261943	+	0.0769133i
$476$	4.26969	−	29.6964i	0.195701	−	1.36113i
$477$		0			0
$478$	−9.39042	+	6.03486i	−0.429508	+	0.276028i
$479$	−13.6684	−	15.7742i	−0.624524	−	0.720740i	0.352035	−	0.935987i	$-0.385490\pi$
$479$	−13.6684	−	15.7742i	−0.624524	−	0.720740i	−0.976560	+	0.215247i	$0.930944\pi$
$480$		0			0
$481$	−12.3632	+	27.0717i	−0.563715	+	1.23436i
$482$	−72.9548			−3.32300
$483$		0			0
$484$	−55.7437			−2.53380
$485$	−10.2875	+	22.5265i	−0.467133	+	1.02288i
$486$		0			0
$487$	5.41275	+	6.24665i	0.245275	+	0.283063i	0.865016	−	0.501744i	$-0.167308\pi$
$487$	5.41275	+	6.24665i	0.245275	+	0.283063i	−0.619741	+	0.784806i	$0.712762\pi$
$488$	86.4475	−	55.5564i	3.91329	−	2.51492i
$489$		0			0
$490$	1.89866	−	13.2055i	0.0857727	−	0.596562i
$491$	−10.6572	+	3.12922i	−0.480951	+	0.141220i	−0.513216	−	0.858259i	$-0.671546\pi$
$491$	−10.6572	+	3.12922i	−0.480951	+	0.141220i	0.0322652	+	0.999479i	$0.489728\pi$
$492$		0			0
$493$	−0.522312	−	3.63276i	−0.0235238	−	0.163611i
$494$	−8.23820	−	18.0391i	−0.370654	−	0.811619i
$495$		0			0
$496$	9.45372	+	65.7520i	0.424484	+	2.95235i
$497$	−29.9297	−	19.2347i	−1.34253	−	0.862792i
$498$		0			0
$499$	0.865761	−	6.02150i	0.0387568	−	0.269559i	−0.961224	−	0.275769i	$-0.911067\pi$
$499$	0.865761	−	6.02150i	0.0387568	−	0.269559i	0.999981	+	0.00620960i	$0.00197659\pi$
$500$	15.0158	−	17.3292i	0.671527	−	0.774984i
$501$		0			0
$502$	−22.5099	−	25.9778i	−1.00466	−	1.15944i
$503$	−7.54921	−	2.21665i	−0.336602	−	0.0988354i	0.109063	−	0.994035i	$-0.465215\pi$
$503$	−7.54921	−	2.21665i	−0.336602	−	0.0988354i	−0.445666	+	0.895199i	$0.647033\pi$
$504$		0			0
$505$	−20.3204			−0.904246
$506$	1.26857	−	0.832773i	0.0563948	−	0.0370213i
$507$		0			0
$508$	−4.23383	+	9.27080i	−0.187846	+	0.411325i
$509$	28.5327	+	8.37797i	1.26469	+	0.371347i	0.844238	−	0.535968i	$-0.180053\pi$
$509$	28.5327	+	8.37797i	1.26469	+	0.371347i	0.420453	+	0.907315i	$0.361871\pi$
$510$		0			0
$511$	−1.34359	+	0.863473i	−0.0594369	+	0.0381978i
$512$	14.1000	−	16.2723i	0.623140	−	0.719142i
$513$		0			0
$514$	−3.66354	+	1.07571i	−0.161592	+	0.0474476i
$515$	33.7764	+	21.7068i	1.48836	+	0.956514i
$516$		0			0
$517$	0.292510	+	0.640508i	0.0128646	+	0.0281695i
$518$	17.4923	+	38.3029i	0.768569	+	1.68293i
$519$		0			0
$520$	−86.2926	−	55.4569i	−3.78418	−	2.43194i
$521$	−18.2067	+	5.34598i	−0.797651	+	0.234211i	−0.655066	−	0.755571i	$-0.727359\pi$
$521$	−18.2067	+	5.34598i	−0.797651	+	0.234211i	−0.142584	+	0.989783i	$0.545541\pi$
$522$		0			0
$523$	17.3500	−	20.0229i	0.758661	−	0.875542i	−0.236717	−	0.971579i	$-0.576071\pi$
$523$	17.3500	−	20.0229i	0.758661	−	0.875542i	0.995378	+	0.0960371i	$0.0306168\pi$
$524$	20.9674	−	13.4749i	0.915966	−	0.588656i
$525$		0			0
$526$	36.6595	+	10.7642i	1.59843	+	0.469342i
$527$	6.12558	−	13.4131i	0.266834	−	0.584286i
$528$		0			0
$529$	9.14651	−	21.1031i	0.397674	−	0.917527i
$530$	−27.9643			−1.21469
$531$		0			0
$532$	−19.3106	−	5.67011i	−0.837222	−	0.245831i
$533$	18.4218	+	21.2599i	0.797938	+	0.920869i
$534$		0			0
$535$	15.6483	−	18.0591i	0.676535	−	0.780763i
$536$	0.0979933	−	0.681558i	0.00423266	−	0.0294388i
$537$		0			0
$538$	43.3829	+	27.8805i	1.87037	+	1.20201i
$539$	−0.0292238	−	0.203256i	−0.00125876	−	0.00875485i
$540$		0			0
$541$	13.5708	+	29.7159i	0.583454	+	1.27759i	0.939318	+	0.343049i	$0.111460\pi$
$541$	13.5708	+	29.7159i	0.583454	+	1.27759i	−0.355863	+	0.934538i	$0.615813\pi$
$542$	−6.18490	−	43.0170i	−0.265664	−	1.84774i
$543$		0			0
$544$	35.8111	−	10.5151i	1.53539	−	0.450831i
$545$	7.14297	−	49.6805i	0.305971	−	2.12808i
$546$		0			0
$547$	38.2357	−	24.5726i	1.63484	−	1.05065i	0.689639	−	0.724153i	$-0.257769\pi$
$547$	38.2357	−	24.5726i	1.63484	−	1.05065i	0.945199	−	0.326494i	$-0.105867\pi$
$548$	26.3553	+	30.4156i	1.12584	+	1.29929i
$549$		0			0
$550$	−0.452824	+	0.991547i	−0.0193085	+	0.0422797i
$551$	−2.46200			−0.104885
$552$		0			0
$553$	−16.9775			−0.721957
$554$	22.2997	−	48.8295i	0.947424	−	2.07457i
$555$		0			0
$556$	−35.8826	−	41.4107i	−1.52176	−	1.75620i
$557$	−12.6601	+	8.13615i	−0.536425	+	0.344740i	−0.780639	−	0.624982i	$-0.785106\pi$
$557$	−12.6601	+	8.13615i	−0.536425	+	0.344740i	0.244214	+	0.969721i	$0.421470\pi$
$558$		0			0
$559$	5.30430	−	36.8922i	0.224348	−	1.56037i
$560$	−74.2699	+	21.8076i	−3.13848	+	0.921539i
$561$		0			0
$562$	3.22206	+	22.4099i	0.135915	+	0.945307i
$563$	14.1960	+	31.0849i	0.598290	+	1.31007i	0.930301	+	0.366796i	$0.119545\pi$
$563$	14.1960	+	31.0849i	0.598290	+	1.31007i	−0.332012	+	0.943275i	$0.607727\pi$
$564$		0			0
$565$	3.10084	+	21.5668i	0.130453	+	0.907324i
$566$	−7.55928	−	4.85805i	−0.317740	−	0.204199i
$567$		0			0
$568$	18.0268	−	125.379i	0.756388	−	5.26079i
$569$	−12.0761	+	13.9366i	−0.506257	+	0.584252i	−0.950136	−	0.311835i	$-0.899056\pi$
$569$	−12.0761	+	13.9366i	−0.506257	+	0.584252i	0.443879	+	0.896087i	$0.353602\pi$
$570$		0			0
$571$	−4.34404	−	5.01329i	−0.181792	−	0.209799i	0.657538	−	0.753422i	$-0.271598\pi$
$571$	−4.34404	−	5.01329i	−0.181792	−	0.209799i	−0.839330	+	0.543622i	$0.817053\pi$
$572$	−2.50044	−	0.734196i	−0.104549	−	0.0306983i
$573$		0			0
$574$	39.8015			1.66128
$575$	2.50992	+	16.3297i	0.104671	+	0.680997i
$576$		0			0
$577$	−5.22293	+	11.4366i	−0.217433	+	0.476112i	−0.986646	−	0.162881i	$-0.947921\pi$
$577$	−5.22293	+	11.4366i	−0.217433	+	0.476112i	0.769213	+	0.638993i	$0.220649\pi$
$578$	26.4672	+	7.77146i	1.10089	+	0.323250i
$579$		0			0
$580$	−17.6828	+	11.3640i	−0.734237	+	0.471866i
$581$	4.18144	−	4.82563i	0.173475	−	0.200201i
$582$		0			0
$583$	−0.412986	+	0.121264i	−0.0171041	+	0.00502223i
$584$	−4.78365	−	3.07427i	−0.197949	−	0.127214i
$585$		0			0
$586$	4.55952	+	9.98395i	0.188352	+	0.412433i
$587$	−0.454966	−	0.996237i	−0.0187785	−	0.0411191i	0.900010	−	0.435868i	$-0.143559\pi$
$587$	−0.454966	−	0.996237i	−0.0187785	−	0.0411191i	−0.918789	+	0.394749i	$0.870831\pi$
$588$		0			0
$589$	−8.32147	−	5.34788i	−0.342880	−	0.220356i
$590$	−20.1249	+	5.90919i	−0.828527	+	0.243278i
$591$		0			0
$592$	−52.3620	+	60.4290i	−2.15206	+	2.48361i
$593$	−1.95340	+	1.25538i	−0.0802167	+	0.0515521i	−0.580134	−	0.814521i	$-0.697000\pi$
$593$	−1.95340	+	1.25538i	−0.0802167	+	0.0515521i	0.499918	+	0.866073i	$0.333364\pi$
$594$		0			0
$595$	16.4864	+	4.84084i	0.675876	+	0.198455i
$596$	−34.8904	+	76.3994i	−1.42917	+	3.12944i
$597$		0			0
$598$	−52.6829	+	16.0263i	−2.15436	+	0.655364i
$599$	43.0508			1.75901			0.879504	−	0.475892i	$-0.157875\pi$
$599$	43.0508			1.75901			0.879504	+	0.475892i	$0.157875\pi$
$600$		0			0
$601$	−12.7347	−	3.73926i	−0.519461	−	0.152527i	0.0114837	−	0.999934i	$-0.496345\pi$
$601$	−12.7347	−	3.73926i	−0.519461	−	0.152527i	−0.530944	+	0.847407i	$0.678163\pi$
$602$	−34.5337	−	39.8540i	−1.40749	−	1.62433i
$603$		0			0
$604$	−62.8036	+	72.4793i	−2.55544	+	2.94914i
$605$	4.54342	−	31.6002i	0.184716	−	1.28473i
$606$		0			0
$607$	−27.6867	−	17.7932i	−1.12377	−	0.722203i	−0.159520	−	0.987195i	$-0.550995\pi$
$607$	−27.6867	−	17.7932i	−1.12377	−	0.722203i	−0.964251	+	0.264991i	$0.914631\pi$
$608$	−3.56315	−	24.7822i	−0.144505	−	1.00505i
$609$		0			0
$610$	40.3537	+	88.3623i	1.63387	+	3.57769i
$611$	−3.63640	−	25.2917i	−0.147113	−	1.02319i
$612$		0			0
$613$	38.7731	−	11.3848i	1.56603	−	0.459828i	0.620188	−	0.784454i	$-0.287057\pi$
$613$	38.7731	−	11.3848i	1.56603	−	0.459828i	0.945843	+	0.324626i	$0.105238\pi$
$614$	−3.93880	+	27.3950i	−0.158957	+	1.10557i
$615$		0			0
$616$	−1.87923	+	1.20770i	−0.0757162	+	0.0486598i
$617$	19.6464	+	22.6732i	0.790935	+	0.912788i	0.997848	−	0.0655717i	$-0.0208871\pi$
$617$	19.6464	+	22.6732i	0.790935	+	0.912788i	−0.206913	+	0.978359i	$0.566342\pi$
$618$		0			0
$619$	11.0046	−	24.0967i	0.442313	−	0.968530i	−0.548855	−	0.835918i	$-0.684936\pi$
$619$	11.0046	−	24.0967i	0.442313	−	0.968530i	0.991168	−	0.132613i	$-0.0423366\pi$
$620$	−84.4517			−3.39166
$621$		0			0
$622$	−35.0876			−1.40688
$623$	12.6739	−	27.7519i	0.507768	−	1.11186i
$624$		0			0
$625$	19.8796	+	22.9423i	0.795185	+	0.917692i
$626$	−30.7889	+	19.7868i	−1.23057	+	0.790841i
$627$		0			0
$628$	−5.46176	+	37.9874i	−0.217948	+	1.51586i
$629$	17.0303	−	5.00054i	0.679041	−	0.199385i
$630$		0			0
$631$	−2.28418	−	15.8868i	−0.0909316	−	0.632443i	−0.983416	−	0.181365i	$-0.941948\pi$
$631$	−2.28418	−	15.8868i	−0.0909316	−	0.632443i	0.892484	−	0.451079i	$-0.148961\pi$
$632$	−25.1101	−	54.9835i	−0.998827	−	2.18713i
$633$		0			0
$634$	−5.42865	−	37.7571i	−0.215599	−	1.49953i
$635$	−4.91038	−	3.15571i	−0.194863	−	0.125231i
$636$		0			0
$637$	−1.06047	+	7.37574i	−0.0420174	+	0.292237i
$638$	−0.295375	+	0.340881i	−0.0116940	+	0.0134956i
$639$		0			0
$640$	−22.5668	−	26.0435i	−0.892031	−	1.02946i
$641$	−44.9585	−	13.2010i	−1.77575	−	0.521408i	−0.781074	−	0.624438i	$-0.785328\pi$
$641$	−44.9585	−	13.2010i	−1.77575	−	0.521408i	−0.994678	+	0.103030i	$0.967146\pi$
$642$		0			0
$643$	−27.2328			−1.07396			−0.536979	−	0.843596i	$-0.680435\pi$
$643$	−27.2328			−1.07396			−0.536979	+	0.843596i	$0.680435\pi$
$644$	−22.7207	+	51.0575i	−0.895321	+	2.01195i
$645$		0			0
$646$	−4.91317	+	10.7584i	−0.193306	+	0.423282i
$647$	23.7997	+	6.98823i	0.935664	+	0.274736i	0.713806	−	0.700343i	$-0.246970\pi$
$647$	23.7997	+	6.98823i	0.935664	+	0.274736i	0.221858	+	0.975079i	$0.428788\pi$
$648$		0			0
$649$	−0.271586	+	0.174538i	−0.0106607	+	0.00685121i
$650$	25.9035	−	29.8943i	1.01602	−	1.17255i
$651$		0			0
$652$	−8.12689	+	2.38627i	−0.318274	+	0.0934535i
$653$	24.7733	+	15.9208i	0.969455	+	0.623031i	0.926599	−	0.376050i	$-0.122718\pi$
$653$	24.7733	+	15.9208i	0.969455	+	0.623031i	0.0428558	+	0.999081i	$0.486354\pi$
$654$		0			0
$655$	5.92976	+	12.9844i	0.231695	+	0.507341i
$656$	31.3967	+	68.7491i	1.22583	+	2.68420i
$657$		0			0
$658$	−30.4133	−	19.5455i	−1.18563	−	0.761961i
$659$	13.4131	−	3.93844i	0.522500	−	0.153420i	−0.00983813	−	0.999952i	$-0.503132\pi$
$659$	13.4131	−	3.93844i	0.522500	−	0.153420i	0.532338	+	0.846532i	$0.321313\pi$
$660$		0			0
$661$	16.2537	−	18.7578i	0.632196	−	0.729593i	−0.345779	−	0.938316i	$-0.612385\pi$
$661$	16.2537	−	18.7578i	0.632196	−	0.729593i	0.977975	+	0.208723i	$0.0669308\pi$
$662$	−26.4796	+	17.0174i	−1.02916	+	0.661400i
$663$		0			0
$664$	21.8128	+	6.40481i	0.846501	+	0.248555i
$665$	4.78822	−	10.4847i	0.185679	−	0.406580i
$666$		0			0
$667$	−0.907174	+	6.77593i	−0.0351259	+	0.262365i
$668$	−108.758			−4.20799
$669$		0			0
$670$	0.624545	+	0.183383i	0.0241283	+	0.00708470i
$671$	0.979129	+	1.12998i	0.0377989	+	0.0436222i
$672$		0			0
$673$	−5.82979	+	6.72793i	−0.224722	+	0.259343i	−0.856903	−	0.515478i	$-0.827614\pi$
$673$	−5.82979	+	6.72793i	−0.224722	+	0.259343i	0.632181	+	0.774821i	$0.282160\pi$
$674$	−10.1303	+	70.4581i	−0.390206	+	2.71395i
$675$		0			0
$676$	24.0622	+	15.4638i	0.925468	+	0.594762i
$677$	0.401463	+	2.79223i	0.0154295	+	0.107314i	0.996081	−	0.0884485i	$-0.0281909\pi$
$677$	0.401463	+	2.79223i	0.0154295	+	0.107314i	−0.980651	+	0.195763i	$0.937282\pi$
$678$		0			0
$679$	−8.12978	−	17.8017i	−0.311992	−	0.683168i
$680$	8.70616	+	60.5527i	0.333866	+	2.32209i
$681$		0			0
$682$	−1.73881	+	0.510560i	−0.0665823	+	0.0195503i
$683$	2.95100	−	20.5247i	0.112917	−	0.785355i	−0.852140	−	0.523314i	$-0.824695\pi$
$683$	2.95100	−	20.5247i	0.112917	−	0.785355i	0.965057	−	0.262041i	$-0.0843956\pi$
$684$		0			0
$685$	−19.3902	+	12.4613i	−0.740862	+	0.476123i
$686$	34.9037	+	40.2810i	1.33263	+	1.53794i
$687$		0			0
$688$	41.5985	−	91.0880i	1.58593	−	3.47270i
$689$	15.6191			0.595040
$690$		0			0
$691$	1.36601			0.0519655			0.0259827	−	0.999662i	$-0.491729\pi$
$691$	1.36601			0.0519655			0.0259827	+	0.999662i	$0.491729\pi$
$692$	13.3437	−	29.2187i	0.507253	−	1.11073i
$693$		0			0
$694$	−15.4069	−	17.7806i	−0.584840	−	0.674941i
$695$	26.3997	−	16.9660i	1.00140	−	0.643558i
$696$		0			0
$697$	2.38761	−	16.6062i	0.0904373	−	0.629005i
$698$	75.9955	−	22.3143i	2.87647	−	0.844608i
$699$		0			0
$700$	−5.71301	−	39.7348i	−0.215931	−	1.50184i
$701$	−12.5045	−	27.3810i	−0.472288	−	1.03417i	−0.984512	−	0.175315i	$-0.943906\pi$
$701$	−12.5045	−	27.3810i	−0.472288	−	1.03417i	0.512224	−	0.858852i	$-0.328822\pi$
$702$		0			0
$703$	−1.69449	−	11.7854i	−0.0639087	−	0.444495i
$704$	−1.53716	−	0.987870i	−0.0579337	−	0.0372317i
$705$		0			0
$706$	−6.51494	+	45.3124i	−0.245193	+	1.70535i
$707$	10.5160	−	12.1361i	0.395493	−	0.456424i
$708$		0			0
$709$	25.9980	+	30.0033i	0.976375	+	1.12680i	0.991913	+	0.126918i	$0.0405085\pi$
$709$	25.9980	+	30.0033i	0.976375	+	1.12680i	−0.0155379	+	0.999879i	$0.504946\pi$
$710$	114.891	+	33.7351i	4.31179	+	1.26605i
$711$		0			0
$712$	108.623			4.07080
$713$	−17.7847	+	20.9318i	−0.666041	+	0.783903i
$714$		0			0
$715$	0.620004	−	1.35762i	0.0231868	−	0.0507721i
$716$	39.8863	+	11.7117i	1.49062	+	0.437686i
$717$		0			0
$718$	15.9473	−	10.2487i	0.595149	−	0.382479i
$719$	−6.00668	+	6.93208i	−0.224011	+	0.258523i	−0.856619	−	0.515950i	$-0.827439\pi$
$719$	−6.00668	+	6.93208i	−0.224011	+	0.258523i	0.632608	+	0.774473i	$0.281985\pi$
$720$		0			0
$721$	−30.4436	+	8.93904i	−1.13378	+	0.332907i
$722$	−35.8381	−	23.0318i	−1.33376	−	0.857153i
$723$		0			0
$724$	13.3057	+	29.1354i	0.494502	+	1.08281i
$725$	−2.04000	−	4.46698i	−0.0757637	−	0.165899i
$726$		0			0
$727$	−3.19987	−	2.05643i	−0.118676	−	0.0762687i	0.479956	−	0.877293i	$-0.340653\pi$
$727$	−3.19987	−	2.05643i	−0.118676	−	0.0762687i	−0.598632	+	0.801024i	$0.704289\pi$
$728$	77.7779	−	22.8376i	2.88264	−	0.846419i
$729$		0			0
$730$	3.52012	−	4.06244i	0.130286	−	0.150358i
$731$	−18.6997	+	12.0176i	−0.691634	+	0.444486i
$732$		0			0
$733$	−39.2138	−	11.5142i	−1.44839	−	0.425287i	−0.539384	−	0.842060i	$-0.681343\pi$
$733$	−39.2138	−	11.5142i	−1.44839	−	0.425287i	−0.909011	+	0.416773i	$0.863161\pi$
$734$	15.0084	−	32.8638i	0.553971	−	1.21303i
$735$		0			0
$736$	−69.5187	+	0.674985i	−2.56249	+	0.0248803i
$737$	0.0100187			0.000369044
$738$		0			0
$739$	28.0767	+	8.24407i	1.03282	+	0.303263i	0.753856	−	0.657039i	$-0.228191\pi$
$739$	28.0767	+	8.24407i	1.03282	+	0.303263i	0.278962	+	0.960302i	$0.410010\pi$
$740$	−66.5690	−	76.8248i	−2.44713	−	2.82413i
$741$		0			0
$742$	14.4717	−	16.7013i	0.531274	−	0.613123i
$743$	−1.23262	+	8.57306i	−0.0452204	+	0.314515i	0.954639	+	0.297765i	$0.0962411\pi$
$743$	−1.23262	+	8.57306i	−0.0452204	+	0.314515i	−0.999860	+	0.0167502i	$0.994668\pi$
$744$		0			0
$745$	−40.4658	−	26.0058i	−1.48255	−	0.952778i
$746$	−7.08863	−	49.3025i	−0.259533	−	1.80509i
$747$		0			0
$748$	0.645636	+	1.41374i	0.0236068	+	0.0516916i
$749$	2.68742	+	18.6914i	0.0981964	+	0.682971i
$750$		0			0
$751$	−6.59622	+	1.93683i	−0.240700	+	0.0706758i	−0.399857	−	0.916577i	$-0.630940\pi$
$751$	−6.59622	+	1.93683i	−0.240700	+	0.0706758i	0.159158	+	0.987253i	$0.449122\pi$
$752$	9.76987	−	67.9509i	0.356270	−	2.47792i
$753$		0			0
$754$	13.7694	−	8.84903i	0.501450	−	0.322263i
$755$	−35.9685	−	41.5098i	−1.30903	−	1.51070i
$756$		0			0
$757$	−1.31155	+	2.87190i	−0.0476692	+	0.104381i	−0.931968	−	0.362540i	$-0.881910\pi$
$757$	−1.31155	+	2.87190i	−0.0476692	+	0.104381i	0.884299	+	0.466921i	$0.154637\pi$
$758$	−26.6430			−0.967717
$759$		0			0
$760$	41.0378			1.48860
$761$	−7.11532	+	15.5804i	−0.257930	+	0.564788i	−0.993652	−	0.112495i	$-0.964116\pi$
$761$	−7.11532	+	15.5804i	−0.257930	+	0.564788i	0.735722	+	0.677284i	$0.236843\pi$
$762$		0			0
$763$	25.9744	+	29.9760i	0.940336	+	1.08521i
$764$	−55.2627	+	35.5152i	−1.99933	+	1.28489i
$765$		0			0
$766$	−11.0236	+	76.6706i	−0.398298	+	2.77022i
$767$	11.2405	−	3.30050i	0.405870	−	0.119174i
$768$		0			0
$769$	3.01514	+	20.9707i	0.108729	+	0.756224i	0.969120	+	0.246590i	$0.0793101\pi$
$769$	3.01514	+	20.9707i	0.108729	+	0.756224i	−0.860391	+	0.509634i	$0.829781\pi$
$770$	−0.877223	−	1.92085i	−0.0316129	−	0.0692227i
$771$		0			0
$772$	−9.10694	−	63.3401i	−0.327766	−	2.27966i
$773$	−4.49268	−	2.88727i	−0.161590	−	0.103848i	0.457346	−	0.889289i	$-0.348800\pi$
$773$	−4.49268	−	2.88727i	−0.161590	−	0.103848i	−0.618937	+	0.785441i	$0.712436\pi$
$774$		0			0
$775$	2.80791	−	19.5294i	0.100863	−	0.701518i
$776$	45.6287	−	52.6584i	1.63798	−	1.89033i
$777$		0			0
$778$	7.63448	+	8.81066i	0.273709	+	0.315877i
$779$	−10.7985	−	3.17073i	−0.386897	−	0.113603i
$780$		0			0
$781$	1.84304			0.0659491
$782$	27.7988	+	17.4862i	0.994084	+	0.625305i
$783$		0			0
$784$	−8.31664	+	18.2109i	−0.297023	+	0.650390i
$785$	−21.0893	−	6.19236i	−0.752708	−	0.221015i
$786$		0			0
$787$	36.6862	−	23.5768i	1.30772	−	0.840423i	0.313693	−	0.949525i	$-0.398434\pi$
$787$	36.6862	−	23.5768i	1.30772	−	0.840423i	0.994031	+	0.109102i	$0.0347975\pi$
$788$	−48.2896	+	55.7292i	−1.72025	+	1.98527i
$789$		0			0
$790$	54.8257	−	16.0983i	1.95061	−	0.572751i
$791$	−14.4852	−	9.30907i	−0.515034	−	0.330992i
$792$		0			0
$793$	−22.5390	−	49.3536i	−0.800385	−	1.75260i
$794$	0.161008	+	0.352558i	0.00571396	+	0.0125118i
$795$		0			0
$796$	86.1124	+	55.3410i	3.05217	+	1.96151i
$797$	−11.1289	+	3.26774i	−0.394205	+	0.115749i	−0.472827	−	0.881155i	$-0.656766\pi$
$797$	−11.1289	+	3.26774i	−0.394205	+	0.115749i	0.0786214	+	0.996905i	$0.474948\pi$
$798$		0			0
$799$	−9.97930	+	11.5167i	−0.353042	+	0.407432i
$800$	42.0117	−	26.9993i	1.48534	−	0.954570i
$801$		0			0
$802$	−85.9050	−	25.2240i	−3.03341	−	0.890690i
$803$	0.0343701	−	0.0752600i	0.00121289	−	0.00265587i
$804$		0			0
$805$	−27.0918	−	17.0415i	−0.954860	−	0.600632i
$806$	65.7615			2.31635
$807$		0			0
$808$	54.8574	+	16.1076i	1.92988	+	0.566663i
$809$	−5.11925	−	5.90793i	−0.179983	−	0.207712i	0.658588	−	0.752504i	$-0.271154\pi$
$809$	−5.11925	−	5.90793i	−0.179983	−	0.207712i	−0.838571	+	0.544792i	$0.816609\pi$
$810$		0			0
$811$	−7.54232	+	8.70430i	−0.264847	+	0.305649i	−0.872560	−	0.488507i	$-0.837542\pi$
$811$	−7.54232	+	8.70430i	−0.264847	+	0.305649i	0.607713	+	0.794157i	$0.292087\pi$
$812$	2.36397	−	16.4418i	0.0829590	−	0.576993i
$813$		0			0
$814$	−1.83506	−	1.17932i	−0.0643189	−	0.0413353i
$815$	−0.690351	−	4.80149i	−0.0241819	−	0.168189i
$816$		0			0
$817$	6.19438	+	13.5638i	0.216714	+	0.474538i
$818$	11.4571	+	79.6858i	0.400588	+	2.78615i
$819$		0			0
$820$	−92.1932	+	27.0704i	−3.21953	+	0.945339i
$821$	−0.0743036	+	0.516793i	−0.00259321	+	0.0180362i	−0.991077	−	0.133291i	$-0.957446\pi$
$821$	−0.0743036	+	0.516793i	−0.00259321	+	0.0180362i	0.988484	+	0.151327i	$0.0483547\pi$
$822$		0			0
$823$	−28.0088	+	18.0002i	−0.976327	+	0.627447i	−0.928470	−	0.371407i	$-0.878876\pi$
$823$	−28.0088	+	18.0002i	−0.976327	+	0.627447i	−0.0478569	+	0.998854i	$0.515239\pi$
$824$	−73.9768	−	85.3738i	−2.57711	−	2.97414i
$825$		0			0
$826$	6.88558	−	15.0773i	0.239580	−	0.524607i
$827$	−24.2079			−0.841791			−0.420895	−	0.907109i	$-0.638284\pi$
$827$	−24.2079			−0.841791			−0.420895	+	0.907109i	$0.638284\pi$
$828$		0			0
$829$	26.4851			0.919866			0.459933	−	0.887954i	$-0.347873\pi$
$829$	26.4851			0.919866			0.459933	+	0.887954i	$0.347873\pi$
$830$	−8.92746	+	19.5484i	−0.309876	+	0.678535i
$831$		0			0
$832$	43.4212	+	50.1108i	1.50536	+	1.73728i
$833$	3.73857	−	2.40263i	0.129534	−	0.0832463i
$834$		0			0
$835$	8.86442	−	61.6534i	0.306766	−	2.13360i
$836$	1.00036	−	0.293731i	0.0345981	−	0.0101589i
$837$		0			0
$838$	7.09223	+	49.3275i	0.244997	+	1.70399i
$839$	16.0962	+	35.2458i	0.555703	+	1.21682i	0.954067	+	0.299593i	$0.0968510\pi$
$839$	16.0962	+	35.2458i	0.555703	+	1.21682i	−0.398364	+	0.917228i	$0.630422\pi$
$840$		0			0
$841$	3.83795	+	26.6935i	0.132343	+	0.920465i
$842$	87.7014	+	56.3623i	3.02239	+	1.94237i
$843$		0			0
$844$	−5.38258	+	37.4367i	−0.185276	+	1.28862i
$845$	−10.7274	+	12.3801i	−0.369033	+	0.425887i
$846$		0			0
$847$	16.5215	+	19.0668i	0.567685	+	0.655144i
$848$	40.2638	+	11.8225i	1.38267	+	0.405987i
$849$		0			0
$850$	−23.5907			−0.809153
$851$	−33.0602	+	0.320995i	−1.13329	+	0.0110036i
$852$		0			0
$853$	3.66776	−	8.03127i	0.125582	−	0.274985i	−0.836390	−	0.548135i	$-0.815338\pi$
$853$	3.66776	−	8.03127i	0.125582	−	0.274985i	0.961972	+	0.273149i	$0.0880654\pi$
$854$	−73.6565	−	21.6275i	−2.52047	−	0.740078i
$855$		0			0
$856$	−56.5596	+	36.3486i	−1.93317	+	1.24237i
$857$	−0.448206	+	0.517257i	−0.0153104	+	0.0176692i	−0.763353	−	0.645981i	$-0.776448\pi$
$857$	−0.448206	+	0.517257i	−0.0153104	+	0.0176692i	0.748043	+	0.663651i	$0.230994\pi$
$858$		0			0
$859$	−12.1210	+	3.55905i	−0.413563	+	0.121433i	−0.481894	−	0.876230i	$-0.660051\pi$
$859$	−12.1210	+	3.55905i	−0.413563	+	0.121433i	0.0683306	+	0.997663i	$0.478233\pi$
$860$	107.097	+	68.8272i	3.65199	+	2.34699i
$861$		0			0
$862$	−23.7212	−	51.9421i	−0.807946	−	1.76916i
$863$	2.36065	+	5.16909i	0.0803573	+	0.175958i	0.945546	−	0.325488i	$-0.105529\pi$
$863$	2.36065	+	5.16909i	0.0803573	+	0.175958i	−0.865189	+	0.501446i	$0.832801\pi$
$864$		0			0
$865$	15.4760	+	9.94583i	0.526200	+	0.338168i
$866$	1.93530	−	0.568255i	0.0657641	−	0.0193101i
$867$		0			0
$868$	43.7044	−	50.4376i	1.48342	−	1.71196i
$869$	0.739876	−	0.475490i	0.0250986	−	0.0161299i
$870$		0			0
$871$	−0.348831	−	0.102426i	−0.0118197	−	0.00347058i
$872$	−58.6640	+	128.456i	−1.98661	+	4.35008i
$873$		0			0
$874$	14.2646	−	16.7889i	0.482509	−	0.567893i
$875$	−10.3778			−0.350833
$876$		0			0
$877$	21.7361	+	6.38228i	0.733974	+	0.215514i	0.627298	−	0.778779i	$-0.284161\pi$
$877$	21.7361	+	6.38228i	0.733974	+	0.215514i	0.106677	+	0.994294i	$0.465979\pi$
$878$	−22.8333	−	26.3510i	−0.770585	−	0.889303i
$879$		0			0
$880$	2.62590	−	3.03045i	0.0885191	−	0.102157i
$881$	−3.21562	+	22.3652i	−0.108337	+	0.753501i	0.861149	+	0.508353i	$0.169746\pi$
$881$	−3.21562	+	22.3652i	−0.108337	+	0.753501i	−0.969486	+	0.245148i	$0.921164\pi$
$882$		0			0
$883$	34.5835	+	22.2255i	1.16383	+	0.747947i	0.972345	−	0.233549i	$-0.0750341\pi$
$883$	34.5835	+	22.2255i	1.16383	+	0.747947i	0.191483	+	0.981496i	$0.438670\pi$
$884$	−8.02634	−	55.8244i	−0.269955	−	1.87758i
$885$		0			0
$886$	3.38063	+	7.40255i	0.113575	+	0.248693i
$887$	−0.776455	−	5.40036i	−0.0260708	−	0.181326i	0.972625	−	0.232380i	$-0.0746512\pi$
$887$	−0.776455	−	5.40036i	−0.0260708	−	0.181326i	−0.998696	+	0.0510534i	$0.983742\pi$
$888$		0			0
$889$	4.42586	−	1.29955i	0.148439	−	0.0435855i
$890$	−14.6132	+	101.637i	−0.489837	+	3.40689i
$891$		0			0
$892$	7.17970	−	4.61411i	0.240394	−	0.154492i
$893$	6.69434	+	7.72569i	0.224018	+	0.258530i
$894$		0			0
$895$	−9.89011	+	21.6563i	−0.330590	+	0.723891i
$896$	27.2326			0.909776
$897$		0			0
$898$	20.3984			0.680703
$899$	3.39150	−	7.42635i	0.113113	−	0.247683i
$900$		0			0
$901$	−6.10007	−	7.03986i	−0.203223	−	0.234532i
$902$	−1.73454	+	1.11472i	−0.0577540	+	0.0371162i
$903$		0			0
$904$	8.72450	−	60.6802i	0.290173	−	2.01819i
$905$	−17.6008	+	5.16807i	−0.585072	+	0.171793i
$906$		0			0
$907$	−4.00188	−	27.8337i	−0.132880	−	0.924202i	−0.941774	−	0.336247i	$-0.890842\pi$
$907$	−4.00188	−	27.8337i	−0.132880	−	0.924202i	0.808894	−	0.587955i	$-0.200067\pi$
$908$	−22.7258	−	49.7626i	−0.754183	−	1.65143i
$909$		0			0
$910$	10.9054	+	75.8485i	0.361509	+	2.51435i
$911$	48.0980	+	30.9107i	1.59356	+	1.02412i	0.970239	+	0.242151i	$0.0778530\pi$
$911$	48.0980	+	30.9107i	1.59356	+	1.02412i	0.623320	+	0.781967i	$0.285783\pi$
$912$		0			0
$913$	−0.0470745	+	0.327410i	−0.00155794	+	0.0108357i
$914$	−15.6127	+	18.0180i	−0.516421	+	0.595981i
$915$		0			0
$916$	−72.7962	−	84.0113i	−2.40525	−	2.77581i
$917$	−10.8234	−	3.17804i	−0.357421	−	0.104948i
$918$		0			0
$919$	16.3674			0.539909			0.269955	−	0.962873i	$-0.412991\pi$
$919$	16.3674			0.539909			0.269955	+	0.962873i	$0.412991\pi$
$920$	15.1212	−	112.944i	0.498532	−	3.72367i
$921$		0			0
$922$	8.32759	−	18.2349i	0.274255	−	0.600534i
$923$	−64.1709	−	18.8423i	−2.11221	−	0.620201i
$924$		0			0
$925$	19.9790	−	12.8397i	0.656907	−	0.422168i
$926$	57.4157	−	66.2613i	1.88680	−	2.17748i
$927$		0			0
$928$	19.8272	−	5.82181i	0.650861	−	0.191110i
$929$	−32.1390	−	20.6545i	−1.05445	−	0.677651i	−0.105928	−	0.994374i	$-0.533781\pi$
$929$	−32.1390	−	20.6545i	−1.05445	−	0.677651i	−0.948518	+	0.316723i	$0.897418\pi$
$930$		0			0
$931$	−1.23842	−	2.71177i	−0.0405877	−	0.0888746i
$932$	−52.4253	−	114.795i	−1.71725	−	3.76025i
$933$		0			0
$934$	30.1710	+	19.3897i	0.987225	+	0.634451i
$935$	−0.854051	+	0.250772i	−0.0279305	+	0.00820112i
$936$		0			0
$937$	−9.21800	+	10.6381i	−0.301139	+	0.347533i	−0.886071	−	0.463549i	$-0.846576\pi$
$937$	−9.21800	+	10.6381i	−0.301139	+	0.347533i	0.584932	+	0.811082i	$0.301121\pi$
$938$	−0.432730	+	0.278098i	−0.0141291	+	0.00908023i
$939$		0			0
$940$	83.7407	+	24.5885i	2.73132	+	0.801988i
$941$	18.0891	−	39.6097i	0.589689	−	1.29124i	−0.345940	−	0.938256i	$-0.612440\pi$
$941$	18.0891	−	39.6097i	0.589689	−	1.29124i	0.935630	−	0.352983i	$-0.114833\pi$
$942$		0			0
$943$	−12.7054	+	28.5514i	−0.413745	+	0.929760i
$944$	31.4746			1.02441
$945$		0			0
$946$	2.62116	+	0.769643i	0.0852214	+	0.0250233i
$947$	20.1689	+	23.2762i	0.655403	+	0.756375i	0.982019	−	0.188782i	$-0.0604540\pi$
$947$	20.1689	+	23.2762i	0.655403	+	0.756375i	−0.326616	+	0.945157i	$0.605908\pi$
$948$		0			0
$949$	−1.96612	+	2.26902i	−0.0638229	+	0.0736556i
$950$	−2.25215	+	15.6641i	−0.0730695	+	0.508210i
$951$		0			0
$952$	−40.6697	−	26.1368i	−1.31811	−	0.847100i
$953$	7.63117	+	53.0760i	0.247198	+	1.71930i	0.614261	+	0.789103i	$0.289454\pi$
$953$	7.63117	+	53.0760i	0.247198	+	1.71930i	−0.367063	+	0.930196i	$0.619637\pi$
$954$		0			0
$955$	−15.6288	−	34.2222i	−0.505734	−	1.10740i
$956$	3.03063	+	21.0785i	0.0980177	+	0.681728i
$957$		0			0
$958$	−53.2656	+	15.6402i	−1.72093	+	0.505312i
$959$	2.59223	−	18.0294i	0.0837075	−	0.582198i
$960$		0			0
$961$	1.51558	−	0.974001i	0.0488895	−	0.0314194i
$962$	51.8365	+	59.8225i	1.67127	+	1.92875i
$963$		0			0
$964$	−57.8178	+	126.603i	−1.86219	+	4.07762i
$965$	36.6487			1.17976
$966$		0			0
$967$	−35.8006			−1.15127			−0.575635	−	0.817707i	$-0.695245\pi$
$967$	−35.8006			−1.15127			−0.575635	+	0.817707i	$0.695245\pi$
$968$	−37.3143	+	81.7070i	−1.19933	+	2.62616i
$969$		0			0
$970$	43.1335	+	49.7787i	1.38493	+	1.59830i
$971$	17.7167	−	11.3859i	0.568557	−	0.365390i	−0.224558	−	0.974461i	$-0.572094\pi$
$971$	17.7167	−	11.3859i	0.568557	−	0.365390i	0.793116	+	0.609071i	$0.208458\pi$
$972$		0			0
$973$	−3.52931	+	24.5469i	−0.113144	+	0.786937i
$974$	21.0934	−	6.19359i	0.675878	−	0.198456i
$975$		0			0
$976$	−20.7454	−	144.287i	−0.664043	−	4.61852i
$977$	17.6014	+	38.5417i	0.563119	+	1.23306i	0.950381	+	0.311088i	$0.100693\pi$
$977$	17.6014	+	38.5417i	0.563119	+	1.23306i	−0.387262	+	0.921970i	$0.626579\pi$
$978$		0			0
$979$	0.224924	+	1.56438i	0.00718860	+	0.0499978i
$980$	−21.4116	−	13.7604i	−0.683968	−	0.439560i
$981$		0			0
$982$	−4.20423	+	29.2411i	−0.134162	+	0.933120i
$983$	18.1016	−	20.8903i	0.577351	−	0.666299i	−0.389682	−	0.920949i	$-0.627415\pi$
$983$	18.1016	−	20.8903i	0.577351	−	0.666299i	0.967033	+	0.254651i	$0.0819605\pi$
$984$		0			0
$985$	−27.6561	−	31.9168i	−0.881196	−	1.01695i
$986$	−9.36610	−	2.75013i	−0.298277	−	0.0875821i
$987$		0			0
$988$	−37.8334			−1.20364
$989$	39.6128	−	12.0503i	1.25961	−	0.383179i
$990$		0			0
$991$	−18.8737	+	41.3276i	−0.599543	+	1.31282i	0.329958	+	0.943996i	$0.392966\pi$
$991$	−18.8737	+	41.3276i	−0.599543	+	1.31282i	−0.929501	+	0.368820i	$0.879762\pi$
$992$	79.6613	+	23.3907i	2.52925	+	0.742654i
$993$		0			0
$994$	−79.6048	+	51.1589i	−2.52491	+	1.62266i
$995$	−38.3906	+	44.3051i	−1.21706	+	1.40457i
$996$		0			0
$997$	12.5546	−	3.68635i	0.397607	−	0.116748i	−0.0768154	−	0.997045i	$-0.524475\pi$
$997$	12.5546	−	3.68635i	0.397607	−	0.116748i	0.474422	+	0.880297i	$0.342657\pi$
$998$	−13.6117	−	8.74769i	−0.430870	−	0.276903i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.i.d.190.2		20
3.2	odd	2		69.2.e.c.52.1	yes	20
23.2	even	11		4761.2.a.bt.1.10		10
23.4	even	11	inner	207.2.i.d.73.2		20
23.21	odd	22		4761.2.a.bu.1.10		10
69.2	odd	22		1587.2.a.u.1.1		10
69.44	even	22		1587.2.a.t.1.1		10
69.50	odd	22		69.2.e.c.4.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.c.4.1	✓	20	69.50	odd	22
69.2.e.c.52.1	yes	20	3.2	odd	2
207.2.i.d.73.2		20	23.4	even	11	inner
207.2.i.d.190.2		20	1.1	even	1	trivial
1587.2.a.t.1.1		10	69.44	even	22
1587.2.a.u.1.1		10	69.2	odd	22
4761.2.a.bt.1.10		10	23.2	even	11
4761.2.a.bu.1.10		10	23.21	odd	22

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.10489 - 2.41937i) q^{2} +(-3.32285 - 3.83478i) q^{4} +(2.44470 - 1.57111i) q^{5} +(-0.326826 + 2.27313i) q^{7} +(-7.84516 + 2.30355i) q^{8} +(-1.09998 - 7.65055i) q^{10} +(-0.0494206 - 0.108216i) q^{11} +(0.614381 + 4.27311i) q^{13} +(5.13843 + 3.30227i) q^{14} +(-1.65065 + 11.4805i) q^{16} +(1.68604 - 1.94579i) q^{17} +(-1.13103 - 1.30528i) q^{19} +(-14.1483 - 4.15430i) q^{20} -0.316419 q^{22} +(-4.00915 + 2.63187i) q^{23} +(1.43109 - 3.13366i) q^{25} +(11.0171 + 3.23490i) q^{26} +(9.80293 - 6.29996i) q^{28} +(0.933494 - 1.07731i) q^{29} +(5.49527 - 1.61356i) q^{31} +(12.1951 + 7.83731i) q^{32} +(-2.84470 - 6.22903i) q^{34} +(2.77235 + 6.07060i) q^{35} +(5.79948 + 3.72710i) q^{37} +(-4.40762 + 1.29419i) q^{38} +(-15.5599 + 17.9571i) q^{40} +(5.48180 - 3.52294i) q^{41} +(-8.28385 - 2.43236i) q^{43} +(-0.250767 + 0.549102i) q^{44} +(1.93781 + 12.6075i) q^{46} -5.91880 q^{47} +(1.65616 + 0.486293i) q^{49} +(-6.00028 - 6.92469i) q^{50} +(14.3449 - 16.5549i) q^{52} +(0.514895 - 3.58117i) q^{53} +(-0.290838 - 0.186910i) q^{55} +(-2.67225 - 18.5859i) q^{56} +(-1.57500 - 3.44878i) q^{58} +(-0.386194 - 2.68604i) q^{59} +(-12.0589 + 3.54081i) q^{61} +(2.16787 - 15.0779i) q^{62} +(12.9209 - 8.30375i) q^{64} +(8.21553 + 9.48123i) q^{65} +(-0.0349839 + 0.0766041i) q^{67} -13.0641 q^{68} +17.7502 q^{70} +(-6.43563 + 14.0921i) q^{71} +(0.455430 + 0.525595i) q^{73} +(15.4250 - 9.91306i) q^{74} +(-1.24721 + 8.67450i) q^{76} +(0.262140 - 0.0769714i) q^{77} +(1.05210 + 7.31752i) q^{79} +(14.0019 + 30.6598i) q^{80} +(-2.46651 - 17.1550i) q^{82} +(-2.33903 - 1.50321i) q^{83} +(1.06480 - 7.40583i) q^{85} +(-15.0375 + 17.3542i) q^{86} +(0.636992 + 0.735128i) q^{88} +(-12.7468 - 3.74281i) q^{89} -9.91413 q^{91} +(23.4144 + 6.62886i) q^{92} +(-6.53962 + 14.3198i) q^{94} +(-4.81578 - 1.41404i) q^{95} +(-7.16897 + 4.60722i) q^{97} +(3.00640 - 3.46957i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8} - 18 q^{10} + 16 q^{11} + 14 q^{13} + 22 q^{14} - 8 q^{16} - 11 q^{17} - 11 q^{19} - 57 q^{20} + 26 q^{22} - 4 q^{25} + 14 q^{26} - 14 q^{28} - 12 q^{29}+ \cdots - 85 q^{98}+O(q^{100}) \) 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 10 * q^8 - 18 * q^10 + 16 * q^11 + 14 * q^13 + 22 * q^14 - 8 * q^16 - 11 * q^17 - 11 * q^19 - 57 * q^20 + 26 * q^22 - 4 * q^25 + 14 * q^26 - 14 * q^28 - 12 * q^29 + 41 * q^31 + 46 * q^32 - 3 * q^34 + 26 * q^35 - 18 * q^37 - 70 * q^38 - 13 * q^40 - 10 * q^43 + 3 * q^44 - 24 * q^46 - 18 * q^47 - 10 * q^49 - 33 * q^50 + 61 * q^52 + 20 * q^53 - 17 * q^55 - 6 * q^56 - 37 * q^58 - 40 * q^59 - 12 * q^61 + 89 * q^62 - 2 * q^64 + 51 * q^65 - 47 * q^67 + 12 * q^68 + 32 * q^70 + 47 * q^71 + 39 * q^73 + 50 * q^74 - 39 * q^76 - 22 * q^77 - 2 * q^79 - 12 * q^80 + 26 * q^82 + 52 * q^83 + 35 * q^85 - 34 * q^86 + 30 * q^88 - 36 * q^89 + 8 * q^91 + 19 * q^92 + 21 * q^94 - 89 * q^95 - 85 * q^98

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