LMFDB - Embedded newform 387.2.y.c.100.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(10,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(42))

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("387.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.y (of order $21$, degree $12$, 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:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 43)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			100.1
Character	$\chi$	$=$	387.100
Dual form			387.2.y.c.298.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.993512 + 0.478450i) q^{2} +(-0.488828 + 0.612971i) q^{4} +(3.17479 - 0.979294i) q^{5} +(1.23273 - 2.13515i) q^{7} +(0.683135 - 2.99301i) q^{8} +O(q^{10})$	\(q+(-0.993512 + 0.478450i) q^{2} +(-0.488828 + 0.612971i) q^{4} +(3.17479 - 0.979294i) q^{5} +(1.23273 - 2.13515i) q^{7} +(0.683135 - 2.99301i) q^{8} +(-2.68565 + 2.49192i) q^{10} +(-0.748014 - 0.937980i) q^{11} +(-4.22417 - 3.91945i) q^{13} +(-0.203169 + 2.71110i) q^{14} +(0.404382 + 1.77171i) q^{16} +(-1.02040 - 0.314752i) q^{17} +(2.13226 + 0.321387i) q^{19} +(-0.951649 + 2.42476i) q^{20} +(1.19194 + 0.574007i) q^{22} +(2.16225 - 5.50933i) q^{23} +(4.98911 - 3.40152i) q^{25} +(6.07203 + 1.87297i) q^{26} +(0.706193 + 1.79935i) q^{28} +(-0.177883 + 2.37368i) q^{29} +(6.31519 + 4.30562i) q^{31} +(2.57877 + 3.23367i) q^{32} +(1.16437 - 0.175501i) q^{34} +(1.82273 - 7.98588i) q^{35} +(-2.83033 - 4.90228i) q^{37} +(-2.27220 + 0.700880i) q^{38} +(-0.762225 - 10.1712i) q^{40} +(8.77658 - 4.22658i) q^{41} +(-2.45449 + 6.08075i) q^{43} +0.940604 q^{44} +(0.487716 + 6.50812i) q^{46} +(-3.30437 + 4.14355i) q^{47} +(0.460743 + 0.798031i) q^{49} +(-3.32928 + 5.76649i) q^{50} +(4.46740 - 0.673352i) q^{52} +(-2.69519 + 2.50077i) q^{53} +(-3.29335 - 2.24537i) q^{55} +(-5.54842 - 5.14818i) q^{56} +(-0.958961 - 2.44339i) q^{58} +(-0.208748 - 0.914583i) q^{59} +(-2.31407 + 1.57771i) q^{61} +(-8.33425 - 1.25619i) q^{62} +(-7.38381 - 3.55585i) q^{64} +(-17.2492 - 8.30676i) q^{65} +(11.8546 + 1.78679i) q^{67} +(0.691734 - 0.471616i) q^{68} +(2.00995 + 8.80616i) q^{70} +(5.54884 + 14.1382i) q^{71} +(-4.99699 - 4.63653i) q^{73} +(5.15747 + 3.51630i) q^{74} +(-1.23931 + 1.14991i) q^{76} +(-2.92483 + 0.440848i) q^{77} +(-1.18802 + 2.05771i) q^{79} +(3.01886 + 5.22882i) q^{80} +(-6.69743 + 8.39832i) q^{82} +(0.533459 + 7.11852i) q^{83} -3.54780 q^{85} +(-0.470767 - 7.21565i) q^{86} +(-3.31838 + 1.59805i) q^{88} +(0.113343 + 1.51246i) q^{89} +(-13.5759 + 4.18761i) q^{91} +(2.32009 + 4.01851i) q^{92} +(1.30045 - 5.69764i) q^{94} +(7.08423 - 1.06778i) q^{95} +(-6.73777 - 8.44890i) q^{97} +(-0.839572 - 0.572410i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) $ 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8	$ 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) $ 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8 - 7 * q^10 + 4 * q^11 - 18 * q^14 - 10 * q^16 + 10 * q^17 + 10 * q^19 + 3 * q^20 - 3 * q^22 - 4 * q^23 - 2 * q^25 + 15 * q^26 + 20 * q^28 - 9 * q^29 + 40 * q^31 - 48 * q^32 - 42 * q^34 - 11 * q^35 - 19 * q^37 + 21 * q^38 - 97 * q^40 + 28 * q^41 - 8 * q^43 - 14 * q^44 - 61 * q^46 + 30 * q^47 + 6 * q^49 + 3 * q^50 - 8 * q^52 + 24 * q^53 + 14 * q^55 - 39 * q^56 + 64 * q^58 + q^59 - 14 * q^61 - 33 * q^62 + 48 * q^64 - 38 * q^65 + 66 * q^67 - 66 * q^68 + 47 * q^70 + 33 * q^71 + 29 * q^73 + 40 * q^74 - 39 * q^76 + 27 * q^77 - 17 * q^79 - 8 * q^80 - 54 * q^82 + 23 * q^83 - 56 * q^85 + 45 * q^86 - 17 * q^88 + 19 * q^89 - 13 * q^91 + 18 * q^92 + 44 * q^94 - q^95 - 31 * q^97 + 5 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{10}{21}\right)$	$1$

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 $

$2$	−0.993512	+	0.478450i	−0.702519	+	0.338315i	−0.750810	−	0.660518i	$-0.770337\pi$
$2$	−0.993512	+	0.478450i	−0.702519	+	0.338315i	0.0482911	+	0.998833i	$0.484622\pi$
$3$		0			0
$3$		0			0
$4$	−0.488828	+	0.612971i	−0.244414	+	0.306485i
$5$	3.17479	−	0.979294i	1.41981	−	0.437954i	0.512599	−	0.858628i	$-0.328683\pi$
$5$	3.17479	−	0.979294i	1.41981	−	0.437954i	0.907212	+	0.420674i	$0.138206\pi$
$6$		0			0
$7$	1.23273	−	2.13515i	0.465929	−	0.807013i	−0.533314	−	0.845917i	$-0.679054\pi$
$7$	1.23273	−	2.13515i	0.465929	−	0.807013i	0.999243	+	0.0389048i	$0.0123869\pi$
$8$	0.683135	−	2.99301i	0.241525	−	1.05819i
$9$		0			0
$10$	−2.68565	+	2.49192i	−0.849278	+	0.788015i
$11$	−0.748014	−	0.937980i	−0.225535	−	0.282812i	0.656170	−	0.754613i	$-0.272175\pi$
$11$	−0.748014	−	0.937980i	−0.225535	−	0.282812i	−0.881705	+	0.471801i	$0.843604\pi$
$12$		0			0
$13$	−4.22417	−	3.91945i	−1.17157	−	1.08706i	−0.994699	−	0.102828i	$-0.967211\pi$
$13$	−4.22417	−	3.91945i	−1.17157	−	1.08706i	−0.176874	−	0.984233i	$-0.556599\pi$
$14$	−0.203169	+	2.71110i	−0.0542992	+	0.724573i
$15$		0			0
$16$	0.404382	+	1.77171i	0.101096	+	0.442928i
$17$	−1.02040	−	0.314752i	−0.247483	−	0.0763385i	0.168532	−	0.985696i	$-0.446097\pi$
$17$	−1.02040	−	0.314752i	−0.247483	−	0.0763385i	−0.416015	+	0.909358i	$0.636574\pi$
$18$		0			0
$19$	2.13226	+	0.321387i	0.489175	+	0.0737312i	0.388998	−	0.921238i	$-0.372821\pi$
$19$	2.13226	+	0.321387i	0.489175	+	0.0737312i	0.100176	+	0.994970i	$0.468059\pi$
$20$	−0.951649	+	2.42476i	−0.212795	+	0.542193i
$21$		0			0
$22$	1.19194	+	0.574007i	0.254122	+	0.122379i
$23$	2.16225	−	5.50933i	0.450861	−	1.14877i	−0.507103	−	0.861886i	$-0.669284\pi$
$23$	2.16225	−	5.50933i	0.450861	−	1.14877i	0.957964	−	0.286889i	$-0.0926212\pi$
$24$		0			0
$25$	4.98911	−	3.40152i	0.997821	−	0.680303i
$26$	6.07203	+	1.87297i	1.19082	+	0.367320i
$27$		0			0
$28$	0.706193	+	1.79935i	0.133458	+	0.340045i
$29$	−0.177883	+	2.37368i	−0.0330320	+	0.440782i	0.956029	+	0.293273i	$0.0947445\pi$
$29$	−0.177883	+	2.37368i	−0.0330320	+	0.440782i	−0.989061	+	0.147509i	$0.952875\pi$
$30$		0			0
$31$	6.31519	+	4.30562i	1.13424	+	0.773313i	0.976787	−	0.214213i	$-0.0687188\pi$
$31$	6.31519	+	4.30562i	1.13424	+	0.773313i	0.157455	+	0.987526i	$0.449671\pi$
$32$	2.57877	+	3.23367i	0.455866	+	0.571638i
$33$		0			0
$34$	1.16437	−	0.175501i	0.199688	−	0.0300982i
$35$	1.82273	−	7.98588i	0.308097	−	1.34986i
$36$		0			0
$37$	−2.83033	−	4.90228i	−0.465304	−	0.805930i	0.533911	−	0.845541i	$-0.320722\pi$
$37$	−2.83033	−	4.90228i	−0.465304	−	0.805930i	−0.999215	+	0.0396104i	$0.987388\pi$
$38$	−2.27220	+	0.700880i	−0.368599	+	0.113698i
$39$		0			0
$40$	−0.762225	−	10.1712i	−0.120518	−	1.60820i
$41$	8.77658	−	4.22658i	1.37067	−	0.660081i	0.403683	−	0.914899i	$-0.367730\pi$
$41$	8.77658	−	4.22658i	1.37067	−	0.660081i	0.966989	+	0.254818i	$0.0820156\pi$
$42$		0			0
$43$	−2.45449	+	6.08075i	−0.374306	+	0.927305i
$43$	−2.45449	+	6.08075i	−0.374306	+	0.927305i
$44$	0.940604			0.141801
$45$		0			0
$46$	0.487716	+	6.50812i	0.0719098	+	0.959570i
$47$	−3.30437	+	4.14355i	−0.481992	+	0.604398i	−0.962062	−	0.272832i	$-0.912040\pi$
$47$	−3.30437	+	4.14355i	−0.481992	+	0.604398i	0.480070	+	0.877230i	$0.340611\pi$
$48$		0			0
$49$	0.460743	+	0.798031i	0.0658205	+	0.114004i
$50$	−3.32928	+	5.76649i	−0.470832	+	0.815504i
$51$		0			0
$52$	4.46740	−	0.673352i	0.619517	−	0.0933772i
$53$	−2.69519	+	2.50077i	−0.370212	+	0.343507i	−0.843237	−	0.537542i	$-0.819353\pi$
$53$	−2.69519	+	2.50077i	−0.370212	+	0.343507i	0.473024	+	0.881049i	$0.343162\pi$
$54$		0			0
$55$	−3.29335	−	2.24537i	−0.444075	−	0.302765i
$56$	−5.54842	−	5.14818i	−0.741438	−	0.687954i
$57$		0			0
$58$	−0.958961	−	2.44339i	−0.125918	−	0.320833i
$59$	−0.208748	−	0.914583i	−0.0271766	−	0.119069i	0.959520	−	0.281640i	$-0.0908784\pi$
$59$	−0.208748	−	0.914583i	−0.0271766	−	0.119069i	−0.986697	+	0.162571i	$0.948021\pi$
$60$		0			0
$61$	−2.31407	+	1.57771i	−0.296287	+	0.202005i	−0.702335	−	0.711847i	$-0.747859\pi$
$61$	−2.31407	+	1.57771i	−0.296287	+	0.202005i	0.406048	+	0.913852i	$0.366907\pi$
$62$	−8.33425	−	1.25619i	−1.05845	−	0.159536i
$63$		0			0
$64$	−7.38381	−	3.55585i	−0.922976	−	0.444482i
$65$	−17.2492	−	8.30676i	−2.13950	−	1.03033i
$66$		0			0
$67$	11.8546	+	1.78679i	1.44827	+	0.218291i	0.825628	−	0.564216i	$-0.190821\pi$
$67$	11.8546	+	1.78679i	1.44827	+	0.218291i	0.622642	+	0.782507i	$0.286059\pi$
$68$	0.691734	−	0.471616i	0.0838850	−	0.0571919i
$69$		0			0
$70$	2.00995	+	8.80616i	0.240235	+	1.05254i
$71$	5.54884	+	14.1382i	0.658527	+	1.67790i	0.732612	+	0.680647i	$0.238301\pi$
$71$	5.54884	+	14.1382i	0.658527	+	1.67790i	−0.0740851	+	0.997252i	$0.523604\pi$
$72$		0			0
$73$	−4.99699	−	4.63653i	−0.584853	−	0.542664i	0.331283	−	0.943531i	$-0.392518\pi$
$73$	−4.99699	−	4.63653i	−0.584853	−	0.542664i	−0.916136	+	0.400867i	$0.868709\pi$
$74$	5.15747	+	3.51630i	0.599544	+	0.408762i
$75$		0			0
$76$	−1.23931	+	1.14991i	−0.142159	+	0.131904i
$77$	−2.92483	+	0.440848i	−0.333316	+	0.0502393i
$78$		0			0
$79$	−1.18802	+	2.05771i	−0.133662	+	0.231510i	−0.925086	−	0.379759i	$-0.876007\pi$
$79$	−1.18802	+	2.05771i	−0.133662	+	0.231510i	0.791423	+	0.611268i	$0.209340\pi$
$80$	3.01886	+	5.22882i	0.337519	+	0.584599i
$81$		0			0
$82$	−6.69743	+	8.39832i	−0.739608	+	0.927439i
$83$	0.533459	+	7.11852i	0.0585548	+	0.781359i	0.946766	+	0.321923i	$0.104329\pi$
$83$	0.533459	+	7.11852i	0.0585548	+	0.781359i	−0.888211	+	0.459436i	$0.848052\pi$
$84$		0			0
$85$	−3.54780			−0.384813
$86$	−0.470767	−	7.21565i	−0.0507642	−	0.778083i
$87$		0			0
$88$	−3.31838	+	1.59805i	−0.353740	+	0.170352i
$89$	0.113343	+	1.51246i	0.0120143	+	0.160320i	0.999984	+	0.00567185i	$0.00180541\pi$
$89$	0.113343	+	1.51246i	0.0120143	+	0.160320i	−0.987970	+	0.154648i	$0.950576\pi$
$90$		0			0
$91$	−13.5759	+	4.18761i	−1.42314	+	0.438981i
$92$	2.32009	+	4.01851i	0.241886	+	0.418959i
$93$		0			0
$94$	1.30045	−	5.69764i	0.134131	−	0.587667i
$95$	7.08423	−	1.06778i	0.726827	−	0.109551i
$96$		0			0
$97$	−6.73777	−	8.44890i	−0.684117	−	0.857856i	0.311609	−	0.950210i	$-0.399132\pi$
$97$	−6.73777	−	8.44890i	−0.684117	−	0.857856i	−0.995726	+	0.0923546i	$0.970561\pi$
$98$	−0.839572	−	0.572410i	−0.0848096	−	0.0578222i
$99$		0			0
$100$	−0.353785	+	4.72093i	−0.0353785	+	0.472093i
$101$	−4.38155	−	11.1640i	−0.435981	−	1.11086i	−0.965000	−	0.262251i	$-0.915535\pi$
$101$	−4.38155	−	11.1640i	−0.435981	−	1.11086i	0.529019	−	0.848610i	$-0.322560\pi$
$102$		0			0
$103$	10.0219	+	3.09135i	0.987489	+	0.304600i	0.746104	−	0.665829i	$-0.231922\pi$
$103$	10.0219	+	3.09135i	0.987489	+	0.304600i	0.241385	+	0.970429i	$0.422398\pi$
$104$	−14.6166	+	9.96546i	−1.43328	+	0.977193i
$105$		0			0
$106$	1.48121	−	3.77406i	0.143868	−	0.366569i
$107$	−8.45359	−	4.07104i	−0.817240	−	0.393562i	−0.0219258	−	0.999760i	$-0.506980\pi$
$107$	−8.45359	−	4.07104i	−0.817240	−	0.393562i	−0.795314	+	0.606198i	$0.792694\pi$
$108$		0			0
$109$	−5.33036	+	13.5815i	−0.510556	+	1.30087i	0.410648	+	0.911794i	$0.365302\pi$
$109$	−5.33036	+	13.5815i	−0.510556	+	1.30087i	−0.921204	+	0.389080i	$0.872793\pi$
$110$	4.34628	+	0.655096i	0.414401	+	0.0624610i
$111$		0			0
$112$	4.28138	+	1.32063i	0.404552	+	0.124788i
$113$	−0.492626	−	2.15834i	−0.0463424	−	0.203039i	0.946457	−	0.322831i	$-0.104635\pi$
$113$	−0.492626	−	2.15834i	−0.0463424	−	0.203039i	−0.992799	+	0.119792i	$0.961777\pi$
$114$		0			0
$115$	1.46945	−	19.6085i	0.137027	−	1.82850i
$116$	−1.36804	−	1.26936i	−0.127020	−	0.117857i
$117$		0			0
$118$	0.644976	+	0.808774i	0.0593748	+	0.0744537i
$119$	−1.92992	+	1.79071i	−0.176916	+	0.164154i
$120$		0			0
$121$	2.12745	−	9.32096i	0.193404	−	0.847360i
$122$	1.54420	−	2.67464i	0.139806	−	0.242150i
$123$		0			0
$124$	−5.72626	+	1.76632i	−0.514234	+	0.158620i
$125$	2.15089	−	2.69713i	0.192382	−	0.241239i
$126$		0			0
$127$	−0.116462	+	0.0560852i	−0.0103343	+	0.00497676i	−0.439044	−	0.898466i	$-0.644683\pi$
$127$	−0.116462	+	0.0560852i	−0.0103343	+	0.00497676i	0.428709	+	0.903442i	$0.358968\pi$
$128$	0.765157			0.0676310
$129$		0			0
$130$	21.1116			1.85161
$131$	−1.92224	+	0.925700i	−0.167946	+	0.0808788i	−0.515968	−	0.856608i	$-0.672568\pi$
$131$	−1.92224	+	0.925700i	−0.167946	+	0.0808788i	0.348022	+	0.937486i	$0.386853\pi$
$132$		0			0
$133$	3.31472	−	4.15653i	0.287423	−	0.360417i
$134$	−12.6326	+	3.89663i	−1.09129	+	0.336618i
$135$		0			0
$136$	−1.63913	+	2.83905i	−0.140554	+	0.243447i
$137$	0.137699	−	0.603299i	0.0117644	−	0.0515433i	−0.968705	−	0.248215i	$-0.920156\pi$
$137$	0.137699	−	0.603299i	0.0117644	−	0.0515433i	0.980469	+	0.196672i	$0.0630133\pi$
$138$		0			0
$139$	−6.96371	+	6.46138i	−0.590654	+	0.548047i	−0.917859	−	0.396906i	$-0.870084\pi$
$139$	−6.96371	+	6.46138i	−0.590654	+	0.548047i	0.327205	+	0.944953i	$0.393893\pi$
$140$	4.00411	+	5.02100i	0.338409	+	0.424352i
$141$		0			0
$142$	−12.2773	−	11.3917i	−1.03029	−	0.955966i
$143$	−0.516633	+	6.89399i	−0.0432030	+	0.576505i
$144$		0			0
$145$	1.75979	+	7.71016i	0.146143	+	0.640294i
$146$	7.18292	+	2.21564i	0.594462	+	0.183367i
$147$		0			0
$148$	4.38850	+	0.661460i	0.360733	+	0.0543717i
$149$	1.57707	−	4.01830i	0.129198	−	0.329192i	−0.851607	−	0.524180i	$-0.824372\pi$
$149$	1.57707	−	4.01830i	0.129198	−	0.329192i	0.980806	+	0.194989i	$0.0624670\pi$
$150$		0			0
$151$	−4.00622	−	1.92929i	−0.326022	−	0.157004i	0.263712	−	0.964601i	$-0.415053\pi$
$151$	−4.00622	−	1.92929i	−0.326022	−	0.157004i	−0.589734	+	0.807598i	$0.700767\pi$
$152$	2.41854	−	6.16233i	0.196169	−	0.499831i
$153$		0			0
$154$	2.69493	−	1.83737i	0.217164	−	0.148060i
$155$	24.2659	+	7.48504i	1.94908	+	0.601213i
$156$		0			0
$157$	5.11902	+	13.0430i	0.408542	+	1.04095i	0.976043	+	0.217576i	$0.0698149\pi$
$157$	5.11902	+	13.0430i	0.408542	+	1.04095i	−0.567502	+	0.823372i	$0.692090\pi$
$158$	0.195799	−	2.61276i	0.0155770	−	0.207860i
$159$		0			0
$160$	11.3538	+	7.74087i	0.897595	+	0.611970i
$161$	−9.09779	−	11.4083i	−0.717007	−	0.899098i
$162$		0			0
$163$	1.88482	−	0.284091i	0.147630	−	0.0222517i	−0.0748113	−	0.997198i	$-0.523835\pi$
$163$	1.88482	−	0.284091i	0.147630	−	0.0222517i	0.222442	+	0.974946i	$0.428597\pi$
$164$	−1.69947	+	7.44586i	−0.132706	+	0.581424i
$165$		0			0
$166$	−3.93586	−	6.81710i	−0.305482	−	0.529110i
$167$	13.2910	−	4.09972i	1.02849	−	0.317246i	0.265809	−	0.964026i	$-0.414361\pi$
$167$	13.2910	−	4.09972i	1.02849	−	0.317246i	0.762677	+	0.646780i	$0.223885\pi$
$168$		0			0
$169$	1.50997	+	20.1492i	0.116152	+	1.54994i
$170$	3.52478	−	1.69744i	0.270338	−	0.130188i
$171$		0			0
$172$	−2.52750	−	4.47697i	−0.192720	−	0.341366i
$173$	9.52832			0.724424			0.362212	−	0.932096i	$-0.382022\pi$
$173$	9.52832			0.724424			0.362212	+	0.932096i	$0.382022\pi$
$174$		0			0
$175$	−1.11253	−	14.8457i	−0.0840993	−	1.12223i
$176$	1.35935	−	1.70457i	0.102465	−	0.128487i
$177$		0			0
$178$	−0.836244	−	1.44842i	−0.0626791	−	0.108563i
$179$	−3.21069	+	5.56108i	−0.239978	+	0.415655i	−0.960708	−	0.277562i	$-0.910474\pi$
$179$	−3.21069	+	5.56108i	−0.239978	+	0.415655i	0.720729	+	0.693216i	$0.243807\pi$
$180$		0			0
$181$	8.53898	−	1.28704i	0.634697	−	0.0956652i	0.176191	−	0.984356i	$-0.443623\pi$
$181$	8.53898	−	1.28704i	0.634697	−	0.0956652i	0.458507	+	0.888691i	$0.348384\pi$
$182$	11.4843	−	10.6558i	0.851270	−	0.789863i
$183$		0			0
$184$	−15.0124	−	10.2353i	−1.10673	−	0.754553i
$185$	−13.7865	−	12.7920i	−1.01360	−	0.940487i
$186$		0			0
$187$	0.468043	+	1.19255i	0.0342267	+	0.0872082i
$188$	−0.924605	−	4.05096i	−0.0674338	−	0.295447i
$189$		0			0
$190$	−6.52739	+	4.45030i	−0.473547	+	0.322859i
$191$	2.21966	+	0.334559i	0.160609	+	0.0242079i	0.228854	−	0.973461i	$-0.426502\pi$
$191$	2.21966	+	0.334559i	0.160609	+	0.0242079i	−0.0682457	+	0.997669i	$0.521740\pi$
$192$		0			0
$193$	−15.2825	−	7.35968i	−1.10006	−	0.529761i	−0.206383	−	0.978471i	$-0.566169\pi$
$193$	−15.2825	−	7.35968i	−1.10006	−	0.529761i	−0.893678	+	0.448710i	$0.851884\pi$
$194$	10.7364	+	5.17040i	0.770831	+	0.371213i
$195$		0			0
$196$	−0.714394	−	0.107677i	−0.0510281	−	0.00769125i
$197$	4.64209	−	3.16493i	0.330736	−	0.225492i	−0.386554	−	0.922267i	$-0.626335\pi$
$197$	4.64209	−	3.16493i	0.330736	−	0.225492i	0.717290	+	0.696775i	$0.245382\pi$
$198$		0			0
$199$	4.08945	+	17.9170i	0.289893	+	1.27011i	0.884671	+	0.466216i	$0.154383\pi$
$199$	4.08945	+	17.9170i	0.289893	+	1.27011i	−0.594778	+	0.803890i	$0.702760\pi$
$200$	−6.77254	−	17.2561i	−0.478891	−	1.22019i
$201$		0			0
$202$	9.69455	+	8.99523i	0.682106	+	0.632902i
$203$	4.84890	+	3.30592i	0.340326	+	0.232030i
$204$		0			0
$205$	23.7248	−	22.0134i	1.65701	−	1.53748i
$206$	−11.4360	+	1.72369i	−0.796781	+	0.120095i
$207$		0			0
$208$	5.23597	−	9.06897i	0.363049	−	0.628820i
$209$	−1.29351	−	2.24042i	−0.0894738	−	0.154973i
$210$		0			0
$211$	16.5493	−	20.7522i	1.13930	−	1.42864i	0.251830	−	0.967771i	$-0.418968\pi$
$211$	16.5493	−	20.7522i	1.13930	−	1.42864i	0.887470	−	0.460865i	$-0.152461\pi$
$212$	−0.215415	−	2.87452i	−0.0147948	−	0.197423i
$213$		0			0
$214$	10.3465			0.707275
$215$	−1.83766	+	21.7088i	−0.125328	+	1.48053i
$216$		0			0
$217$	16.9781	−	8.17623i	1.15255	−	0.555038i
$218$	−1.20231	−	16.0437i	−0.0814308	−	1.08662i
$219$		0			0
$220$	2.98623	−	0.921128i	0.201331	−	0.0621025i
$221$	3.07669	+	5.32898i	0.206960	+	0.358466i
$222$		0			0
$223$	−4.19133	+	18.3634i	−0.280672	+	1.22970i	0.616262	+	0.787541i	$0.288646\pi$
$223$	−4.19133	+	18.3634i	−0.280672	+	1.22970i	−0.896934	+	0.442164i	$0.854211\pi$
$224$	10.0833	−	1.51982i	0.673720	−	0.101547i
$225$		0			0
$226$	1.52209	+	1.90864i	0.101248	+	0.126961i
$227$	2.52166	+	1.71924i	0.167369	+	0.114110i	0.644108	−	0.764935i	$-0.277229\pi$
$227$	2.52166	+	1.71924i	0.167369	+	0.114110i	−0.476739	+	0.879045i	$0.658181\pi$
$228$		0			0
$229$	−0.742392	+	9.90653i	−0.0490586	+	0.654642i	0.917424	+	0.397911i	$0.130265\pi$
$229$	−0.742392	+	9.90653i	−0.0490586	+	0.654642i	−0.966483	+	0.256731i	$0.917354\pi$
$230$	7.92176	+	20.1843i	0.522345	+	1.33091i
$231$		0			0
$232$	6.98294	+	2.15395i	0.458452	+	0.141414i
$233$	6.09982	−	4.15878i	0.399612	−	0.272451i	−0.346794	−	0.937941i	$-0.612730\pi$
$233$	6.09982	−	4.15878i	0.399612	−	0.272451i	0.746407	+	0.665490i	$0.231777\pi$
$234$		0			0
$235$	−6.43294	+	16.3909i	−0.419638	+	1.06922i
$236$	0.662654	+	0.319117i	0.0431351	+	0.0207728i
$237$		0			0
$238$	1.06064	−	2.70246i	0.0687510	−	0.175175i
$239$	−14.7596	−	2.22464i	−0.954716	−	0.143900i	−0.346833	−	0.937927i	$-0.612743\pi$
$239$	−14.7596	−	2.22464i	−0.954716	−	0.143900i	−0.607883	+	0.794027i	$0.707981\pi$
$240$		0			0
$241$	3.67789	+	1.13448i	0.236914	+	0.0730781i	0.410938	−	0.911663i	$-0.365201\pi$
$241$	3.67789	+	1.13448i	0.236914	+	0.0730781i	−0.174025	+	0.984741i	$0.555677\pi$
$242$	2.34597	+	10.2784i	0.150805	+	0.660719i
$243$		0			0
$244$	0.164094	−	2.18969i	0.0105051	−	0.140180i
$245$	2.24427	+	2.08238i	0.143381	+	0.133038i
$246$		0			0
$247$	−7.74737	−	9.71490i	−0.492954	−	0.618144i
$248$	17.2009	−	15.9601i	1.09226	−	1.01347i
$249$		0			0
$250$	−0.846494	+	3.70873i	−0.0535370	+	0.234561i
$251$	7.11768	−	12.3282i	0.449264	−	0.778148i	−0.549075	−	0.835773i	$-0.685020\pi$
$251$	7.11768	−	12.3282i	0.449264	−	0.778148i	0.998338	+	0.0576258i	$0.0183530\pi$
$252$		0			0
$253$	−6.78504	+	2.09291i	−0.426572	+	0.131580i
$254$	0.0888726	−	0.111443i	0.00557636	−	0.00699254i
$255$		0			0
$256$	14.0074	−	6.74562i	0.875464	−	0.421601i
$257$	6.95341			0.433742			0.216871	−	0.976200i	$-0.430415\pi$
$257$	6.95341			0.433742			0.216871	+	0.976200i	$0.430415\pi$
$258$		0			0
$259$	−13.9562			−0.867194
$260$	13.5237	−	6.51266i	0.838702	−	0.403898i
$261$		0			0
$262$	1.46686	−	1.83939i	0.0906231	−	0.113638i
$263$	−6.90646	+	2.13036i	−0.425871	+	0.131364i	−0.500279	−	0.865864i	$-0.666769\pi$
$263$	−6.90646	+	2.13036i	−0.425871	+	0.131364i	0.0744085	+	0.997228i	$0.476293\pi$
$264$		0			0
$265$	−6.10768	+	10.5788i	−0.375192	+	0.649851i
$266$	−1.30452	+	5.71549i	−0.0799854	+	0.350439i
$267$		0			0
$268$	−6.89011	+	6.39309i	−0.420880	+	0.390520i
$269$	2.32631	+	2.91711i	0.141838	+	0.177859i	0.847676	−	0.530514i	$-0.178001\pi$
$269$	2.32631	+	2.91711i	0.141838	+	0.177859i	−0.705838	+	0.708373i	$0.749430\pi$
$270$		0			0
$271$	−10.5145	−	9.75608i	−0.638713	−	0.592639i	0.292877	−	0.956150i	$-0.405387\pi$
$271$	−10.5145	−	9.75608i	−0.638713	−	0.592639i	−0.931590	+	0.363511i	$0.881578\pi$
$272$	0.145018	−	1.93514i	0.00879304	−	0.117335i
$273$		0			0
$274$	0.151843	+	0.665267i	0.00917317	+	0.0401903i
$275$	−6.92248	−	2.13530i	−0.417441	−	0.128763i
$276$		0			0
$277$	−25.3438	−	3.81996i	−1.52276	−	0.229519i	−0.666281	−	0.745701i	$-0.732115\pi$
$277$	−25.3438	−	3.81996i	−1.52276	−	0.229519i	−0.856479	+	0.516182i	$0.827353\pi$
$278$	3.82708	−	9.75125i	0.229533	−	0.584841i
$279$		0			0
$280$	−22.6567	−	10.9109i	−1.35399	−	0.652049i
$281$	−7.49491	+	19.0967i	−0.447109	+	1.13921i	0.512702	+	0.858567i	$0.328645\pi$
$281$	−7.49491	+	19.0967i	−0.447109	+	1.13921i	−0.959811	+	0.280648i	$0.909451\pi$
$282$		0			0
$283$	−0.291221	+	0.198551i	−0.0173113	+	0.0118027i	−0.571945	−	0.820292i	$-0.693811\pi$
$283$	−0.291221	+	0.198551i	−0.0173113	+	0.0118027i	0.554633	+	0.832095i	$0.312858\pi$
$284$	−11.3787	−	3.50988i	−0.675204	−	0.208273i
$285$		0			0
$286$	−2.78515	−	7.09645i	−0.164689	−	0.419622i
$287$	1.79477	−	23.9496i	0.105942	−	1.41370i
$288$		0			0
$289$	−13.1039	−	8.93410i	−0.770818	−	0.525535i
$290$	−5.43730	−	6.81816i	−0.319289	−	0.400376i
$291$		0			0
$292$	5.28472	−	0.796544i	0.309265	−	0.0466142i
$293$	−5.80931	+	25.4523i	−0.339384	+	1.48694i	0.460974	+	0.887414i	$0.347500\pi$
$293$	−5.80931	+	25.4523i	−0.339384	+	1.48694i	−0.800357	+	0.599523i	$0.795357\pi$
$294$		0			0
$295$	−1.55838	−	2.69919i	−0.0907322	−	0.157153i
$296$	−16.6061	+	5.12230i	−0.965209	+	0.297727i
$297$		0			0
$298$	0.355722	+	4.74678i	0.0206064	+	0.274973i
$299$	−30.7273	+	14.7975i	−1.77700	+	0.855760i
$300$		0			0
$301$	9.95760	+	12.7366i	0.573947	+	0.734128i
$302$	4.90330			0.282153
$303$		0			0
$304$	0.292843	+	3.90772i	0.0167957	+	0.224123i
$305$	−5.80166	+	7.27505i	−0.332202	+	0.416568i
$306$		0			0
$307$	7.67349	+	13.2909i	0.437949	+	0.758551i	0.997531	−	0.0702244i	$-0.0223715\pi$
$307$	7.67349	+	13.2909i	0.437949	+	0.758551i	−0.559582	+	0.828775i	$0.689038\pi$
$308$	1.15951	−	2.00834i	0.0660694	−	0.114436i
$309$		0			0
$310$	−27.6897	+	4.17355i	−1.57267	+	0.237042i
$311$	−23.6164	+	21.9128i	−1.33916	+	1.24256i	−0.392729	+	0.919654i	$0.628469\pi$
$311$	−23.6164	+	21.9128i	−1.33916	+	1.24256i	−0.946431	+	0.322905i	$0.895341\pi$
$312$		0			0
$313$	21.6774	+	14.7794i	1.22528	+	0.835380i	0.990613	−	0.136696i	$-0.0436484\pi$
$313$	21.6774	+	14.7794i	1.22528	+	0.835380i	0.234665	+	0.972076i	$0.424601\pi$
$314$	−11.3263	−	10.5092i	−0.639177	−	0.593070i
$315$		0			0
$316$	−0.680577	−	1.73408i	−0.0382855	−	0.0975498i
$317$	−0.463392	−	2.03025i	−0.0260267	−	0.114030i	0.960246	−	0.279155i	$-0.0900544\pi$
$317$	−0.463392	−	2.03025i	−0.0260267	−	0.114030i	−0.986273	+	0.165125i	$0.947197\pi$
$318$		0			0
$319$	2.35953	−	1.60870i	0.132108	−	0.0900698i
$320$	−26.9243	−	4.05818i	−1.50511	−	0.226859i
$321$		0			0
$322$	14.4971	+	6.98142i	0.807890	+	0.389059i
$323$	−2.07461	−	0.999077i	−0.115434	−	0.0555901i
$324$		0			0
$325$	−34.4069	−	5.18601i	−1.90855	−	0.287668i
$326$	−1.73667	+	1.18404i	−0.0961850	+	0.0655778i
$327$		0			0
$328$	−6.65460	−	29.1557i	−0.367439	−	1.60986i
$329$	4.77371	+	12.1632i	0.263183	+	0.670580i
$330$		0			0
$331$	−3.94165	−	3.65732i	−0.216653	−	0.201024i	0.564379	−	0.825516i	$-0.309116\pi$
$331$	−3.94165	−	3.65732i	−0.216653	−	0.201024i	−0.781032	+	0.624492i	$0.785306\pi$
$332$	−4.62421	−	3.15274i	−0.253787	−	0.173029i
$333$		0			0
$334$	−11.2432	+	10.4322i	−0.615202	+	0.570824i
$335$	39.3857	−	5.93644i	2.15187	−	0.324342i
$336$		0			0
$337$	6.11409	−	10.5899i	0.333055	−	0.576869i	−0.650054	−	0.759888i	$-0.725254\pi$
$337$	6.11409	−	10.5899i	0.333055	−	0.576869i	0.983109	+	0.183019i	$0.0585870\pi$
$338$	−11.1406	−	19.2960i	−0.605967	−	1.04957i
$339$		0			0
$340$	1.73426	−	2.17470i	0.0940535	−	0.117939i
$341$	−0.685262	−	9.14419i	−0.0371090	−	0.495186i
$342$		0			0
$343$	19.5301			1.05453
$344$	16.5230	+	11.5003i	0.890859	+	0.620054i
$345$		0			0
$346$	−9.46650	+	4.55882i	−0.508922	+	0.245084i
$347$	−0.201738	−	2.69200i	−0.0108299	−	0.144514i	0.989168	−	0.146791i	$-0.0468944\pi$
$347$	−0.201738	−	2.69200i	−0.0108299	−	0.144514i	−0.999997	+	0.00227647i	$0.999275\pi$
$348$		0			0
$349$	−7.19519	+	2.21942i	−0.385150	+	0.118803i	−0.481283	−	0.876566i	$-0.659829\pi$
$349$	−7.19519	+	2.21942i	−0.385150	+	0.118803i	0.0961326	+	0.995369i	$0.469353\pi$
$350$	8.20823	+	14.2171i	0.438748	+	0.759934i
$351$		0			0
$352$	1.10417	−	4.83766i	0.0588522	−	0.257848i
$353$	−5.44003	+	0.819952i	−0.289543	+	0.0436416i	−0.292208	−	0.956355i	$-0.594390\pi$
$353$	−5.44003	+	0.819952i	−0.289543	+	0.0436416i	0.00266456	+	0.999996i	$0.499152\pi$
$354$		0			0
$355$	31.4619	+	39.4520i	1.66983	+	2.09389i
$356$	−0.982498	−	0.669855i	−0.0520723	−	0.0355023i
$357$		0			0
$358$	0.529161	−	7.06116i	0.0279670	−	0.373194i
$359$	7.75539	+	19.7604i	0.409314	+	1.04292i	0.975765	+	0.218820i	$0.0702207\pi$
$359$	7.75539	+	19.7604i	0.409314	+	1.04292i	−0.566451	+	0.824095i	$0.691684\pi$
$360$		0			0
$361$	−13.7126	−	4.22979i	−0.721717	−	0.222620i
$362$	−7.86779	+	5.36417i	−0.413522	+	0.281935i
$363$		0			0
$364$	4.06940	−	10.3687i	0.213294	−	0.543465i
$365$	−20.4049	−	9.82650i	−1.06804	−	0.514342i
$366$		0			0
$367$	4.40104	−	11.2137i	0.229733	−	0.585349i	−0.768801	−	0.639488i	$-0.779146\pi$
$367$	4.40104	−	11.2137i	0.229733	−	0.585349i	0.998533	+	0.0541392i	$0.0172415\pi$
$368$	10.6353	+	1.60302i	0.554405	+	0.0835631i
$369$		0			0
$370$	19.8174	+	6.11286i	1.03026	+	0.317792i
$371$	2.01708	+	8.83742i	0.104722	+	0.458816i
$372$		0			0
$373$	−0.440427	+	5.87708i	−0.0228044	+	0.304304i	0.974126	+	0.226007i	$0.0725672\pi$
$373$	−0.440427	+	5.87708i	−0.0228044	+	0.304304i	−0.996930	+	0.0782968i	$0.975052\pi$
$374$	−1.03558	−	0.960882i	−0.0535488	−	0.0496860i
$375$		0			0
$376$	10.1443	+	12.7206i	0.523155	+	0.656015i
$377$	10.0550	−	9.32963i	0.517856	−	0.480501i
$378$		0			0
$379$	−4.00235	+	17.5354i	−0.205587	+	0.900734i	0.761876	+	0.647722i	$0.224278\pi$
$379$	−4.00235	+	17.5354i	−0.205587	+	0.900734i	−0.967463	+	0.253012i	$0.918579\pi$
$380$	−2.80845	+	4.86438i	−0.144071	+	0.249538i
$381$		0			0
$382$	−2.36532	+	0.729606i	−0.121021	+	0.0373299i
$383$	22.5411	−	28.2656i	1.15180	−	1.44431i	0.276308	−	0.961069i	$-0.410889\pi$
$383$	22.5411	−	28.2656i	1.15180	−	1.44431i	0.875489	−	0.483238i	$-0.160539\pi$
$384$		0			0
$385$	−8.85402	+	4.26387i	−0.451243	+	0.217307i
$386$	18.7046			0.952040
$387$		0			0
$388$	8.47254			0.430128
$389$	−21.0115	+	10.1186i	−1.06532	+	0.513032i	−0.882596	−	0.470131i	$-0.844207\pi$
$389$	−21.0115	+	10.1186i	−1.06532	+	0.513032i	−0.182726	+	0.983164i	$0.558492\pi$
$390$		0			0
$391$	−3.94044	+	4.94115i	−0.199276	+	0.249885i
$392$	2.70326	−	0.833846i	0.136535	−	0.0421156i
$393$		0			0
$394$	−3.09772	+	5.36540i	−0.156061	+	0.270305i
$395$	−1.75661	+	7.69621i	−0.0883846	+	0.387238i
$396$		0			0
$397$	9.30669	−	8.63535i	0.467089	−	0.433396i	−0.411185	−	0.911552i	$-0.634885\pi$
$397$	9.30669	−	8.63535i	0.467089	−	0.433396i	0.878275	+	0.478156i	$0.158695\pi$
$398$	−12.6353	−	15.8442i	−0.633352	−	0.794198i
$399$		0			0
$400$	8.04402	+	7.46376i	0.402201	+	0.373188i
$401$	−0.288681	+	3.85218i	−0.0144160	+	0.192369i	0.985346	+	0.170566i	$0.0545596\pi$
$401$	−0.288681	+	3.85218i	−0.0144160	+	0.192369i	−0.999762	+	0.0218027i	$0.993059\pi$
$402$		0			0
$403$	−9.80072	−	42.9398i	−0.488209	−	2.13898i
$404$	8.98503	+	2.77152i	0.447022	+	0.137888i
$405$		0			0
$406$	−6.39916	−	0.964518i	−0.317585	−	0.0478682i
$407$	−2.48111	+	6.32177i	−0.122984	+	0.313359i
$408$		0			0
$409$	−11.8839	−	5.72298i	−0.587621	−	0.282983i	0.116355	−	0.993208i	$-0.462879\pi$
$409$	−11.8839	−	5.72298i	−0.587621	−	0.282983i	−0.703975	+	0.710225i	$0.748593\pi$
$410$	−13.0386	+	33.2217i	−0.643928	+	1.64070i
$411$		0			0
$412$	−6.79390	+	4.63201i	−0.334712	+	0.228203i
$413$	−2.21011	−	0.681727i	−0.108752	−	0.0335456i
$414$		0			0
$415$	8.66475	+	22.0774i	0.425336	+	1.08374i
$416$	1.78109	−	23.7669i	0.0873249	−	1.16527i
$417$		0			0
$418$	2.35705	+	1.60701i	0.115287	+	0.0786013i
$419$	−11.9422	−	14.9750i	−0.583414	−	0.731578i	0.399277	−	0.916830i	$-0.369261\pi$
$419$	−11.9422	−	14.9750i	−0.583414	−	0.731578i	−0.982691	+	0.185253i	$0.940690\pi$
$420$		0			0
$421$	30.1408	−	4.54299i	1.46897	−	0.221412i	0.634698	−	0.772761i	$-0.281125\pi$
$421$	30.1408	−	4.54299i	1.46897	−	0.221412i	0.834275	+	0.551348i	$0.185887\pi$
$422$	−6.51305	+	28.5355i	−0.317050	+	1.38909i
$423$		0			0
$424$	5.64365	+	9.77508i	0.274080	+	0.474720i
$425$	−6.16152	+	1.90058i	−0.298878	+	0.0921915i
$426$		0			0
$427$	0.516019	+	6.88579i	0.0249719	+	0.333227i
$428$	6.62778	−	3.19177i	0.320366	−	0.154280i
$429$		0			0
$430$	−8.56083	−	22.4472i	−0.412840	−	1.08250i
$431$	35.9315			1.73076			0.865380	−	0.501117i	$-0.167077\pi$
$431$	35.9315			1.73076			0.865380	+	0.501117i	$0.167077\pi$
$432$		0			0
$433$	−0.437619	−	5.83962i	−0.0210306	−	0.280634i	−0.997798	−	0.0663305i	$-0.978871\pi$
$433$	−0.437619	−	5.83962i	−0.0210306	−	0.280634i	0.976767	−	0.214304i	$-0.0687482\pi$
$434$	−12.9560	+	16.2464i	−0.621910	+	0.779850i
$435$		0			0
$436$	−5.71945	−	9.90638i	−0.273912	−	0.474430i
$437$	6.38112	−	11.0524i	0.305250	−	0.528709i
$438$		0			0
$439$	19.2178	−	2.89662i	0.917217	−	0.138248i	0.326565	−	0.945175i	$-0.394109\pi$
$439$	19.2178	−	2.89662i	0.917217	−	0.138248i	0.590652	+	0.806927i	$0.298871\pi$
$440$	−8.97021	+	8.32314i	−0.427638	+	0.396790i
$441$		0			0
$442$	−5.60638	−	3.82236i	−0.266668	−	0.181811i
$443$	7.50104	+	6.95994i	0.356385	+	0.330677i	0.837964	−	0.545726i	$-0.183746\pi$
$443$	7.50104	+	6.95994i	0.356385	+	0.330677i	−0.481579	+	0.876403i	$0.659936\pi$
$444$		0			0
$445$	1.84098	+	4.69075i	0.0872709	+	0.222363i
$446$	−4.62184	−	20.2496i	−0.218851	−	0.958847i
$447$		0			0
$448$	−16.6946	+	11.3822i	−0.788744	+	0.537756i
$449$	13.5432	+	2.04130i	0.639142	+	0.0963351i	0.460615	−	0.887600i	$-0.347629\pi$
$449$	13.5432	+	2.04130i	0.639142	+	0.0963351i	0.178527	+	0.983935i	$0.442867\pi$
$450$		0			0
$451$	−10.5295	−	5.07072i	−0.495813	−	0.238771i
$452$	1.56381	+	0.753090i	0.0735553	+	0.0354224i
$453$		0			0
$454$	−3.32787	−	0.501596i	−0.156185	−	0.0235411i
$455$	−38.9998	+	26.5896i	−1.82834	+	1.24654i
$456$		0			0
$457$	−2.14851	−	9.41322i	−0.100503	−	0.440332i	−0.999994	−	0.00339341i	$-0.998920\pi$
$457$	−2.14851	−	9.41322i	−0.100503	−	0.440332i	0.899491	−	0.436939i	$-0.143937\pi$
$458$	−4.00221	−	10.1975i	−0.187011	−	0.476496i
$459$		0			0
$460$	11.3011	+	10.4859i	0.526917	+	0.488908i
$461$	−5.55916	−	3.79017i	−0.258916	−	0.176526i	0.426904	−	0.904297i	$-0.359604\pi$
$461$	−5.55916	−	3.79017i	−0.258916	−	0.176526i	−0.685820	+	0.727771i	$0.740556\pi$
$462$		0			0
$463$	−4.14568	+	3.84663i	−0.192666	+	0.178768i	−0.770607	−	0.637311i	$-0.780047\pi$
$463$	−4.14568	+	3.84663i	−0.192666	+	0.178768i	0.577941	+	0.816079i	$0.303856\pi$
$464$	−4.27742	+	0.644717i	−0.198574	+	0.0299303i
$465$		0			0
$466$	−4.07047	+	7.05026i	−0.188561	+	0.326597i
$467$	−5.33101	−	9.23357i	−0.246690	−	0.427279i	0.715916	−	0.698187i	$-0.246009\pi$
$467$	−5.33101	−	9.23357i	−0.246690	−	0.427279i	−0.962605	+	0.270908i	$0.912676\pi$
$468$		0			0
$469$	18.4286	−	23.1088i	0.850955	−	1.06706i
$470$	−1.45101	−	19.3624i	−0.0669300	−	0.893119i
$471$		0			0
$472$	−2.87996			−0.132561
$473$	7.53961	−	2.24622i	0.346672	−	0.103281i
$474$		0			0
$475$	11.7313	−	5.64949i	0.538269	−	0.259216i
$476$	−0.154251	−	2.05833i	−0.00707008	−	0.0943436i
$477$		0			0
$478$	15.7282	−	4.85150i	0.719390	−	0.221902i
$479$	−5.41065	−	9.37152i	−0.247219	−	0.428196i	0.715534	−	0.698578i	$-0.246183\pi$
$479$	−5.41065	−	9.37152i	−0.247219	−	0.428196i	−0.962753	+	0.270382i	$0.912850\pi$
$480$		0			0
$481$	−7.25847	+	31.8014i	−0.330958	+	1.45002i
$482$	−4.19682	+	0.632568i	−0.191160	+	0.0288127i
$483$		0			0
$484$	4.67352	+	5.86041i	0.212433	+	0.266382i
$485$	−29.6650	−	20.2253i	−1.34702	−	0.918382i
$486$		0			0
$487$	1.44501	−	19.2824i	0.0654799	−	0.873768i	−0.863668	−	0.504061i	$-0.831839\pi$
$487$	1.44501	−	19.2824i	0.0654799	−	0.873768i	0.929148	−	0.369708i	$-0.120542\pi$
$488$	3.14127	+	8.00383i	0.142199	+	0.362316i
$489$		0			0
$490$	−3.22603	−	0.995097i	−0.145737	−	0.0449539i
$491$	26.1499	−	17.8287i	1.18013	−	0.804599i	0.195750	−	0.980654i	$-0.437286\pi$
$491$	26.1499	−	17.8287i	1.18013	−	0.804599i	0.984380	+	0.176054i	$0.0563335\pi$
$492$		0			0
$493$	0.928633	−	2.36612i	0.0418235	−	0.106565i
$494$	12.3452	+	5.94514i	0.555437	+	0.267484i
$495$		0			0
$496$	−5.07458	+	12.9298i	−0.227855	+	0.580566i
$497$	37.0275	+	5.58100i	1.66091	+	0.250342i
$498$		0			0
$499$	−9.47408	−	2.92237i	−0.424118	−	0.130823i	0.0753466	−	0.997157i	$-0.475994\pi$
$499$	−9.47408	−	2.92237i	−0.424118	−	0.130823i	−0.499464	+	0.866334i	$0.666470\pi$
$500$	0.601848	+	2.63687i	0.0269155	+	0.117924i
$501$		0			0
$502$	−1.17308	+	15.6536i	−0.0523571	+	0.698656i
$503$	5.65458	+	5.24668i	0.252125	+	0.233938i	0.796102	−	0.605162i	$-0.206892\pi$
$503$	5.65458	+	5.24668i	0.252125	+	0.233938i	−0.543977	+	0.839100i	$0.683082\pi$
$504$		0			0
$505$	−24.8434	−	31.1526i	−1.10552	−	1.38627i
$506$	5.73967	−	5.32563i	0.255159	−	0.236753i
$507$		0			0
$508$	0.0225513	−	0.0988039i	0.00100055	−	0.00438371i
$509$	−18.6174	+	32.2464i	−0.825204	+	1.42929i	0.0765602	+	0.997065i	$0.475606\pi$
$509$	−18.6174	+	32.2464i	−0.825204	+	1.42929i	−0.901764	+	0.432229i	$0.857727\pi$
$510$		0			0
$511$	−16.0596	+	4.95375i	−0.710437	+	0.219141i
$512$	−11.6432	+	14.6002i	−0.514563	+	0.645242i
$513$		0			0
$514$	−6.90829	+	3.32686i	−0.304712	+	0.146741i
$515$	34.8449			1.53545
$516$		0			0
$517$	6.35828			0.279637
$518$	13.8656	−	6.67733i	0.609221	−	0.293385i
$519$		0			0
$520$	−36.6457	+	45.9523i	−1.60702	+	2.01514i
$521$	4.65069	−	1.43455i	0.203751	−	0.0628487i	−0.191200	−	0.981551i	$-0.561238\pi$
$521$	4.65069	−	1.43455i	0.203751	−	0.0628487i	0.394951	+	0.918702i	$0.370762\pi$
$522$		0			0
$523$	4.05474	−	7.02302i	0.177301	−	0.307095i	−0.763654	−	0.645626i	$-0.776597\pi$
$523$	4.05474	−	7.02302i	0.177301	−	0.307095i	0.940955	+	0.338531i	$0.109930\pi$
$524$	0.372215	−	1.63078i	0.0162603	−	0.0712410i
$525$		0			0
$526$	5.84238	−	5.42094i	0.254740	−	0.236364i
$527$	−5.08882	−	6.38118i	−0.221673	−	0.277969i
$528$		0			0
$529$	−8.81719	−	8.18116i	−0.383356	−	0.355703i
$530$	1.00662	−	13.4324i	0.0437247	−	0.583466i
$531$		0			0
$532$	0.927502	+	4.06365i	0.0402123	+	0.176182i
$533$	−53.6396	−	16.5456i	−2.32339	−	0.716671i
$534$		0			0
$535$	−30.8252	−	4.64615i	−1.33269	−	0.200870i
$536$	13.4462	−	34.2603i	0.580786	−	1.47982i
$537$		0			0
$538$	−3.70691	−	1.78515i	−0.159816	−	0.0769635i
$539$	0.403894	−	1.02911i	0.0173970	−	0.0443267i
$540$		0			0
$541$	13.4980	−	9.20276i	0.580323	−	0.395657i	−0.237279	−	0.971442i	$-0.576256\pi$
$541$	13.4980	−	9.20276i	0.580323	−	0.395657i	0.817602	+	0.575784i	$0.195303\pi$
$542$	15.1141	+	4.66209i	0.649207	+	0.200254i
$543$		0			0
$544$	−1.61357	−	4.11131i	−0.0691813	−	0.176271i
$545$	−3.62247	+	48.3385i	−0.155170	+	2.07060i
$546$		0			0
$547$	22.1302	+	15.0881i	0.946220	+	0.645122i	0.934937	−	0.354814i	$-0.115456\pi$
$547$	22.1302	+	15.0881i	0.946220	+	0.645122i	0.0112835	+	0.999936i	$0.496408\pi$
$548$	0.302494	+	0.379315i	0.0129219	+	0.0162035i
$549$		0			0
$550$	7.89920	−	1.19061i	0.336823	−	0.0507679i
$551$	−1.14216	+	5.00415i	−0.0486578	+	0.213184i
$552$		0			0
$553$	2.92901	+	5.07320i	0.124554	+	0.215734i
$554$	27.0070	−	8.33056i	1.14742	−	0.353932i
$555$		0			0
$556$	−0.556581	−	7.42705i	−0.0236043	−	0.314977i
$557$	14.4359	−	6.95199i	0.611671	−	0.294565i	−0.102286	−	0.994755i	$-0.532616\pi$
$557$	14.4359	−	6.95199i	0.611671	−	0.294565i	0.713957	+	0.700190i	$0.246901\pi$
$558$		0			0
$559$	34.2014	−	16.0658i	1.44656	−	0.679512i
$560$	14.8858			0.629039
$561$		0			0
$562$	−1.69055	−	22.5588i	−0.0713114	−	0.951584i
$563$	−3.02373	+	3.79164i	−0.127435	+	0.159799i	−0.841456	−	0.540326i	$-0.818301\pi$
$563$	−3.02373	+	3.79164i	−0.127435	+	0.159799i	0.714021	+	0.700125i	$0.246872\pi$
$564$		0			0
$565$	−3.67764	−	6.36985i	−0.154719	−	0.267982i
$566$	0.194335	−	0.336598i	0.00816851	−	0.0141483i
$567$		0			0
$568$	46.1065	−	6.94943i	1.93458	−	0.291592i
$569$	20.5386	−	19.0571i	0.861024	−	0.798913i	−0.120006	−	0.992773i	$-0.538291\pi$
$569$	20.5386	−	19.0571i	0.861024	−	0.798913i	0.981029	+	0.193860i	$0.0621008\pi$
$570$		0			0
$571$	4.39256	+	2.99480i	0.183823	+	0.125328i	0.651735	−	0.758447i	$-0.274041\pi$
$571$	4.39256	+	2.99480i	0.183823	+	0.125328i	−0.467912	+	0.883775i	$0.654994\pi$
$572$	−3.97327	−	3.68666i	−0.166131	−	0.154147i
$573$		0			0
$574$	9.67556	+	24.6529i	0.403850	+	1.02899i
$575$	−7.95236	−	34.8416i	−0.331636	−	1.45299i
$576$		0			0
$577$	0.478277	−	0.326083i	0.0199109	−	0.0135750i	−0.553324	−	0.832966i	$-0.686641\pi$
$577$	0.478277	−	0.326083i	0.0199109	−	0.0135750i	0.573235	+	0.819391i	$0.305688\pi$
$578$	17.2934	+	2.60656i	0.719311	+	0.108419i
$579$		0			0
$580$	−5.58634	−	2.69024i	−0.231960	−	0.111706i
$581$	15.8568	+	7.63621i	0.657849	+	0.316803i
$582$		0			0
$583$	4.36171	+	0.657422i	0.180644	+	0.0272276i
$584$	−17.2908	+	11.7887i	−0.715498	+	0.487818i
$585$		0			0
$586$	−6.40602	−	28.0666i	−0.264630	−	1.15942i
$587$	12.9290	+	32.9425i	0.533636	+	1.35968i	0.902697	+	0.430278i	$0.141584\pi$
$587$	12.9290	+	32.9425i	0.533636	+	1.35968i	−0.369060	+	0.929406i	$0.620320\pi$
$588$		0			0
$589$	12.0819	+	11.2103i	0.497825	+	0.461914i
$590$	2.83969	+	1.93607i	0.116908	+	0.0797067i
$591$		0			0
$592$	7.54090	−	6.99694i	0.309929	−	0.287572i
$593$	−13.8979	+	2.09477i	−0.570719	+	0.0860221i	−0.428061	−	0.903750i	$-0.640803\pi$
$593$	−13.8979	+	2.09477i	−0.570719	+	0.0860221i	−0.142658	+	0.989772i	$0.545565\pi$
$594$		0			0
$595$	−4.37348	+	7.57509i	−0.179295	+	0.310549i
$596$	1.69219	+	2.93095i	0.0693146	+	0.120056i
$597$		0			0
$598$	23.4481	−	29.4030i	0.958863	−	1.20238i
$599$	−0.831581	−	11.0967i	−0.0339775	−	0.453398i	−0.988082	−	0.153925i	$-0.950808\pi$
$599$	−0.831581	−	11.0967i	−0.0339775	−	0.453398i	0.954105	−	0.299472i	$-0.0968106\pi$
$600$		0			0
$601$	0.417393			0.0170258			0.00851291	−	0.999964i	$-0.497290\pi$
$601$	0.417393			0.0170258			0.00851291	+	0.999964i	$0.497290\pi$
$602$	−15.9869	−	7.88980i	−0.651575	−	0.321564i
$603$		0			0
$604$	3.14095	−	1.51260i	0.127804	−	0.0615469i
$605$	−2.37375	−	31.6755i	−0.0965068	−	1.28779i
$606$		0			0
$607$	−0.457176	+	0.141020i	−0.0185562	+	0.00572383i	−0.304019	−	0.952666i	$-0.598329\pi$
$607$	−0.457176	+	0.141020i	−0.0185562	+	0.00572383i	0.285463	+	0.958390i	$0.407853\pi$
$608$	4.45935	+	7.72382i	0.180851	+	0.313242i
$609$		0			0
$610$	2.28327	−	10.0037i	0.0924469	−	0.405036i
$611$	30.1986	−	4.55171i	1.22171	−	0.184143i
$612$		0			0
$613$	3.59411	+	4.50687i	0.145165	+	0.182031i	0.849098	−	0.528235i	$-0.177146\pi$
$613$	3.59411	+	4.50687i	0.145165	+	0.182031i	−0.703933	+	0.710266i	$0.748575\pi$
$614$	−13.9827	−	9.53327i	−0.564297	−	0.384731i
$615$		0			0
$616$	−0.678594	+	9.05521i	−0.0273413	+	0.364845i
$617$	5.05717	+	12.8854i	0.203594	+	0.518749i	0.995805	−	0.0914981i	$-0.0291655\pi$
$617$	5.05717	+	12.8854i	0.203594	+	0.518749i	−0.792211	+	0.610247i	$0.791070\pi$
$618$		0			0
$619$	−30.6878	−	9.46594i	−1.23345	−	0.380468i	−0.391576	−	0.920146i	$-0.628070\pi$
$619$	−30.6878	−	9.46594i	−1.23345	−	0.380468i	−0.841872	+	0.539678i	$0.818546\pi$
$620$	−16.4500	+	11.2154i	−0.660646	+	0.450421i
$621$		0			0
$622$	12.9790	−	33.0699i	0.520409	−	1.32598i
$623$	3.36905	+	1.62245i	0.134978	+	0.0650021i
$624$		0			0
$625$	−6.84290	+	17.4354i	−0.273716	+	0.697417i
$626$	−28.6079	−	4.31195i	−1.14340	−	0.172340i
$627$		0			0
$628$	−10.4973	−	3.23799i	−0.418889	−	0.129210i
$629$	1.34507	+	5.89314i	0.0536315	+	0.234975i
$630$		0			0
$631$	−3.64187	+	48.5974i	−0.144981	+	1.93463i	0.169824	+	0.985474i	$0.445680\pi$
$631$	−3.64187	+	48.5974i	−0.144981	+	1.93463i	−0.314804	+	0.949157i	$0.601939\pi$
$632$	5.34716	+	4.96143i	0.212698	+	0.197355i
$633$		0			0
$634$	1.43176	+	1.79537i	0.0568624	+	0.0713032i
$635$	−0.314819	+	0.292110i	−0.0124932	+	0.0115920i
$636$		0			0
$637$	1.18159	−	5.17688i	0.0468162	−	0.205115i
$638$	−1.57454	+	2.72718i	−0.0623365	+	0.107970i
$639$		0			0
$640$	2.42922	−	0.749314i	0.0960232	−	0.0296192i
$641$	24.6012	−	30.8490i	0.971690	−	1.21846i	−0.00415371	−	0.999991i	$-0.501322\pi$
$641$	24.6012	−	30.8490i	0.971690	−	1.21846i	0.975844	−	0.218469i	$-0.0701064\pi$
$642$		0			0
$643$	−28.5864	+	13.7665i	−1.12734	+	0.542897i	−0.902152	−	0.431418i	$-0.858013\pi$
$643$	−28.5864	+	13.7665i	−1.12734	+	0.542897i	−0.225186	+	0.974316i	$0.572299\pi$
$644$	11.4402			0.450807
$645$		0			0
$646$	2.53915			0.0999017
$647$	−30.3021	+	14.5927i	−1.19130	+	0.573699i	−0.921183	−	0.389130i	$-0.872776\pi$
$647$	−30.3021	+	14.5927i	−1.19130	+	0.573699i	−0.270114	+	0.962828i	$0.587061\pi$
$648$		0			0
$649$	−0.701714	+	0.879922i	−0.0275447	+	0.0345400i
$650$	36.6649	−	11.3096i	1.43812	−	0.443600i
$651$		0			0
$652$	−0.747212	+	1.29421i	−0.0292631	+	0.0506851i
$653$	7.70936	−	33.7769i	0.301691	−	1.32179i	−0.565884	−	0.824485i	$-0.691465\pi$
$653$	7.70936	−	33.7769i	0.301691	−	1.32179i	0.867574	−	0.497308i	$-0.165678\pi$
$654$		0			0
$655$	−5.19617	+	4.82134i	−0.203031	+	0.188385i
$656$	11.0374	+	13.8404i	0.430937	+	0.540378i
$657$		0			0
$658$	−10.5622	−	9.80032i	−0.411759	−	0.382056i
$659$	−1.66762	+	22.2529i	−0.0649613	+	0.866849i	0.865605	+	0.500727i	$0.166934\pi$
$659$	−1.66762	+	22.2529i	−0.0649613	+	0.866849i	−0.930567	+	0.366122i	$0.880685\pi$
$660$		0			0
$661$	4.38980	+	19.2330i	0.170744	+	0.748077i	0.985694	+	0.168546i	$0.0539071\pi$
$661$	4.38980	+	19.2330i	0.170744	+	0.748077i	−0.814950	+	0.579531i	$0.803236\pi$
$662$	5.66592	+	1.74771i	0.220212	+	0.0679265i
$663$		0			0
$664$	21.6702	+	3.26626i	0.840968	+	0.126755i
$665$	6.45309	−	16.4422i	0.250240	−	0.637601i
$666$		0			0
$667$	12.6928	+	6.11252i	0.491466	+	0.236678i
$668$	−3.98399	+	10.1510i	−0.154145	+	0.392755i
$669$		0			0
$670$	−36.2899	+	24.7420i	−1.40200	+	0.955868i
$671$	3.21082	+	0.990406i	0.123952	+	0.0382342i
$672$		0			0
$673$	6.29767	+	16.0462i	0.242757	+	0.618535i	0.999376	−	0.0353210i	$-0.0112454\pi$
$673$	6.29767	+	16.0462i	0.242757	+	0.618535i	−0.756619	+	0.653856i	$0.773150\pi$
$674$	−1.00767	+	13.4465i	−0.0388142	+	0.517939i
$675$		0			0
$676$	−13.0890	−	8.92393i	−0.503423	−	0.343228i
$677$	−25.8174	−	32.3740i	−0.992242	−	1.24423i	−0.969652	−	0.244488i	$-0.921380\pi$
$677$	−25.8174	−	32.3740i	−0.992242	−	1.24423i	−0.0225900	−	0.999745i	$-0.507191\pi$
$678$		0			0
$679$	−26.3456	+	3.97096i	−1.01105	+	0.152391i
$680$	−2.42362	+	10.6186i	−0.0929417	+	0.407204i
$681$		0			0
$682$	5.05586	+	8.75700i	0.193599	+	0.335323i
$683$	−3.52745	+	1.08807i	−0.134974	+	0.0416339i	−0.361506	−	0.932370i	$-0.617737\pi$
$683$	−3.52745	+	1.08807i	−0.134974	+	0.0416339i	0.226532	+	0.974004i	$0.427261\pi$
$684$		0			0
$685$	−0.153641	−	2.05020i	−0.00587033	−	0.0783341i
$686$	−19.4034	+	9.34420i	−0.740827	+	0.356763i
$687$		0			0
$688$	−11.7659	−	1.88971i	−0.448570	−	0.0720446i
$689$	21.1866			0.807144
$690$		0			0
$691$	−3.62927	−	48.4292i	−0.138064	−	1.84233i	−0.450958	−	0.892545i	$-0.648918\pi$
$691$	−3.62927	−	48.4292i	−0.138064	−	1.84233i	0.312894	−	0.949788i	$-0.398702\pi$
$692$	−4.65771	+	5.84058i	−0.177059	+	0.222025i
$693$		0			0
$694$	1.48842	+	2.57802i	0.0564996	+	0.0978602i
$695$	−15.7808	+	27.3331i	−0.598598	+	1.03680i
$696$		0			0
$697$	−10.2860	+	1.55036i	−0.389608	+	0.0587240i
$698$	6.08663	−	5.64757i	0.230382	−	0.213764i
$699$		0			0
$700$	9.64380	+	6.57503i	0.364501	+	0.248513i
$701$	−30.4753	−	28.2769i	−1.15104	−	1.06801i	−0.996797	−	0.0799718i	$-0.974517\pi$
$701$	−30.4753	−	28.2769i	−1.15104	−	1.06801i	−0.154239	−	0.988034i	$-0.549293\pi$
$702$		0			0
$703$	−4.45949	−	11.3626i	−0.168193	−	0.428548i
$704$	2.18787	+	9.58569i	0.0824585	+	0.361274i
$705$		0			0
$706$	5.01243	−	3.41741i	0.188645	−	0.128616i
$707$	−29.2382	−	4.40694i	−1.09961	−	0.165740i
$708$		0			0
$709$	20.0646	+	9.66260i	0.753542	+	0.362887i	0.770895	−	0.636963i	$-0.219810\pi$
$709$	20.0646	+	9.66260i	0.753542	+	0.362887i	−0.0173527	+	0.999849i	$0.505524\pi$
$710$	−50.1336	−	24.1431i	−1.88148	−	0.906074i
$711$		0			0
$712$	4.60423	+	0.693976i	0.172551	+	0.0260078i
$713$	37.3761	−	25.4826i	1.39975	−	0.954332i
$714$		0			0
$715$	5.11104	+	22.3929i	0.191142	+	0.837449i
$716$	−1.83930	−	4.68647i	−0.0687380	−	0.175142i
$717$		0			0
$718$	−17.1595	−	15.9216i	−0.640385	−	0.594191i
$719$	11.2918	+	7.69860i	0.421112	+	0.287109i	0.755278	−	0.655405i	$-0.227502\pi$
$719$	11.2918	+	7.69860i	0.421112	+	0.287109i	−0.334166	+	0.942514i	$0.608454\pi$
$720$		0			0
$721$	18.9549	−	17.5875i	0.705916	−	0.654994i
$722$	15.6474	−	2.35847i	0.582336	−	0.0877730i
$723$		0			0
$724$	−3.38517	+	5.86329i	−0.125809	+	0.217907i
$725$	7.18665	+	12.4476i	0.266905	+	0.462294i
$726$		0			0
$727$	−17.9410	+	22.4973i	−0.665393	+	0.834377i	−0.993918	−	0.110118i	$-0.964877\pi$
$727$	−17.9410	+	22.4973i	−0.665393	+	0.834377i	0.328525	+	0.944495i	$0.393448\pi$
$728$	3.25939	+	43.4935i	0.120801	+	1.61198i
$729$		0			0
$730$	24.9740			0.924331
$731$	4.41849	−	5.43224i	0.163424	−	0.200919i
$732$		0			0
$733$	−37.8550	+	18.2300i	−1.39821	+	0.673342i	−0.972797	−	0.231659i	$-0.925585\pi$
$733$	−37.8550	+	18.2300i	−1.39821	+	0.673342i	−0.425411	+	0.905000i	$0.639870\pi$
$734$	0.992696	+	13.2466i	0.0366411	+	0.488941i
$735$		0			0
$736$	23.3913	−	7.21527i	0.862215	−	0.265958i
$737$	−7.19143	−	12.4559i	−0.264900	−	0.458820i
$738$		0			0
$739$	10.5095	−	46.0449i	0.386597	−	1.69379i	−0.289665	−	0.957128i	$-0.593544\pi$
$739$	10.5095	−	46.0449i	0.386597	−	1.69379i	0.676261	−	0.736662i	$-0.263599\pi$
$740$	14.5804	−	2.19763i	0.535984	−	0.0807867i
$741$		0			0
$742$	−6.23226	−	7.81501i	−0.228794	−	0.286898i
$743$	34.5776	+	23.5746i	1.26853	+	0.864870i	0.995277	−	0.0970725i	$-0.0309479\pi$
$743$	34.5776	+	23.5746i	1.26853	+	0.864870i	0.273253	+	0.961942i	$0.411900\pi$
$744$		0			0
$745$	1.07176	−	14.3017i	0.0392664	−	0.523973i
$746$	−2.37432	−	6.04968i	−0.0869302	−	0.221494i
$747$		0			0
$748$	−0.959793	−	0.296057i	−0.0350935	−	0.0108249i
$749$	−19.1133	+	13.0312i	−0.698385	+	0.476151i
$750$		0			0
$751$	0.465270	−	1.18549i	0.0169779	−	0.0432591i	−0.922133	−	0.386872i	$-0.873556\pi$
$751$	0.465270	−	1.18549i	0.0169779	−	0.0432591i	0.939111	+	0.343613i	$0.111651\pi$
$752$	−8.67740	−	4.17882i	−0.316432	−	0.152386i
$753$		0			0
$754$	−5.52595	+	14.0799i	−0.201243	+	0.512760i
$755$	−14.6083	−	2.20184i	−0.531649	−	0.0801333i
$756$		0			0
$757$	−27.2359	−	8.40115i	−0.989905	−	0.305345i	−0.242818	−	0.970072i	$-0.578072\pi$
$757$	−27.2359	−	8.40115i	−0.989905	−	0.305345i	−0.747087	+	0.664727i	$0.768548\pi$
$758$	−4.41345	−	19.3366i	−0.160304	−	0.702336i
$759$		0			0
$760$	1.64362	−	21.9326i	0.0596204	−	0.795579i
$761$	−17.4707	−	16.2105i	−0.633313	−	0.587629i	0.296783	−	0.954945i	$-0.404086\pi$
$761$	−17.4707	−	16.2105i	−0.633313	−	0.587629i	−0.930096	+	0.367316i	$0.880277\pi$
$762$		0			0
$763$	22.4278	+	28.1235i	0.811939	+	1.01814i
$764$	−1.29010	+	1.19704i	−0.0466743	+	0.0433075i
$765$		0			0
$766$	−8.87115	+	38.8671i	−0.320528	+	1.40432i
$767$	−2.70288	+	4.68153i	−0.0975954	+	0.169040i
$768$		0			0
$769$	43.8886	−	13.5379i	1.58266	−	0.488187i	0.626109	−	0.779736i	$-0.284647\pi$
$769$	43.8886	−	13.5379i	1.58266	−	0.488187i	0.956556	+	0.291548i	$0.0941705\pi$
$770$	6.75653	−	8.47242i	0.243488	−	0.305325i
$771$		0			0
$772$	11.9818	−	5.77013i	0.431234	−	0.207671i
$773$	−18.2262			−0.655551			−0.327776	−	0.944756i	$-0.606299\pi$
$773$	−18.2262			−0.655551			−0.327776	+	0.944756i	$0.606299\pi$
$774$		0			0
$775$	46.1528			1.65786
$776$	−29.8904	+	14.3945i	−1.07300	+	0.516732i
$777$		0			0
$778$	16.0339	−	20.1059i	0.574843	−	0.720830i
$779$	20.0724	−	6.19150i	0.719167	−	0.221834i
$780$		0			0
$781$	9.11076	−	15.7803i	0.326009	−	0.564663i
$782$	1.55078	−	6.79440i	0.0554557	−	0.242967i
$783$		0			0
$784$	−1.22757	+	1.13901i	−0.0438416	+	0.0406791i
$785$	29.0248	+	36.3959i	1.03594	+	1.29903i
$786$		0			0
$787$	13.8717	+	12.8710i	0.494472	+	0.458803i	0.887556	−	0.460700i	$-0.152402\pi$
$787$	13.8717	+	12.8710i	0.494472	+	0.458803i	−0.393084	+	0.919502i	$0.628592\pi$
$788$	−0.329178	+	4.39257i	−0.0117265	+	0.156479i
$789$		0			0
$790$	−1.93704	−	8.48673i	−0.0689168	−	0.301944i
$791$	−5.21566	−	1.60882i	−0.185448	−	0.0572030i
$792$		0			0
$793$	15.9588	+	2.40540i	0.566713	+	0.0854182i
$794$	−5.11473	+	13.0321i	−0.181515	+	0.462492i
$795$		0			0
$796$	−12.9817	−	6.25164i	−0.460123	−	0.221583i
$797$	−8.31314	+	21.1815i	−0.294466	+	0.750288i	0.704702	+	0.709504i	$0.251081\pi$
$797$	−8.31314	+	21.1815i	−0.294466	+	0.750288i	−0.999168	+	0.0407843i	$0.987014\pi$
$798$		0			0
$799$	4.67597	−	3.18802i	0.165424	−	0.112784i
$800$	23.8651	+	7.36142i	0.843760	+	0.260265i
$801$		0			0
$802$	−1.55627	−	3.96531i	−0.0549538	−	0.140020i
$803$	−0.611152	+	8.15526i	−0.0215671	+	0.287793i
$804$		0			0
$805$	−40.0557	−	27.3095i	−1.41178	−	0.962533i
$806$	30.2817	+	37.9720i	1.06663	+	1.33751i
$807$		0			0
$808$	−36.4072	+	5.48750i	−1.28080	+	0.193050i
$809$	4.00438	−	17.5443i	0.140787	−	0.616826i	−0.854467	−	0.519506i	$-0.826116\pi$
$809$	4.00438	−	17.5443i	0.140787	−	0.616826i	0.995253	−	0.0973198i	$-0.0310270\pi$
$810$		0			0
$811$	5.49259	+	9.51345i	0.192871	+	0.334062i	0.946201	−	0.323581i	$-0.104887\pi$
$811$	5.49259	+	9.51345i	0.192871	+	0.334062i	−0.753329	+	0.657643i	$0.771553\pi$
$812$	−4.39671	+	1.35621i	−0.154294	+	0.0475935i
$813$		0			0
$814$	−0.559638	−	7.46785i	−0.0196153	−	0.261748i
$815$	5.70570	−	2.74772i	0.199862	−	0.0962484i
$816$		0			0
$817$	−7.18789	+	12.1769i	−0.251473	+	0.426016i
$818$	14.5450			0.508552
$819$		0			0
$820$	1.89622	+	25.3033i	0.0662190	+	0.883631i
$821$	−25.8105	+	32.3653i	−0.900791	+	1.12956i	0.0902396	+	0.995920i	$0.471237\pi$
$821$	−25.8105	+	32.3653i	−0.900791	+	1.12956i	−0.991030	+	0.133636i	$0.957335\pi$
$822$		0			0
$823$	14.9966	+	25.9748i	0.522748	+	0.905426i	0.999650	+	0.0264695i	$0.00842650\pi$
$823$	14.9966	+	25.9748i	0.522748	+	0.905426i	−0.476902	+	0.878957i	$0.658240\pi$
$824$	16.0988	−	27.8839i	0.560827	−	0.971382i
$825$		0			0
$826$	2.52194	−	0.380121i	0.0877495	−	0.0132261i
$827$	5.08513	−	4.71831i	0.176827	−	0.164072i	−0.586794	−	0.809736i	$-0.699610\pi$
$827$	5.08513	−	4.71831i	0.176827	−	0.164072i	0.763621	+	0.645665i	$0.223420\pi$
$828$		0			0
$829$	−23.9390	−	16.3213i	−0.831436	−	0.566863i	0.0711043	−	0.997469i	$-0.477348\pi$
$829$	−23.9390	−	16.3213i	−0.831436	−	0.566863i	−0.902540	+	0.430605i	$0.858300\pi$
$830$	−19.1715	−	17.7885i	−0.665452	−	0.617449i
$831$		0			0
$832$	17.2534	+	43.9610i	0.598155	+	1.52407i
$833$	−0.218961	−	0.959331i	−0.00758655	−	0.0332388i
$834$		0			0
$835$	38.1813	−	26.0315i	1.32132	−	0.900859i
$836$	2.00562	+	0.302298i	0.0693657	+	0.0104552i
$837$		0			0
$838$	19.0295	+	9.16413i	0.657363	+	0.316569i
$839$	−45.4757	−	21.8999i	−1.56999	−	0.756070i	−0.572054	−	0.820216i	$-0.693853\pi$
$839$	−45.4757	−	21.8999i	−1.56999	−	0.756070i	−0.997940	+	0.0641464i	$0.979568\pi$
$840$		0			0
$841$	23.0734	+	3.47775i	0.795633	+	0.119922i
$842$	−27.7717	+	18.9344i	−0.957074	+	0.652522i
$843$		0			0
$844$	4.63071	+	20.2885i	0.159396	+	0.698357i
$845$	24.5259	+	62.4909i	0.843716	+	2.14975i
$846$		0			0
$847$	−17.2791	−	16.0327i	−0.593718	−	0.550889i
$848$	−5.52053	−	3.76383i	−0.189576	−	0.129251i
$849$		0			0
$850$	5.21221	−	4.83623i	0.178777	−	0.165881i
$851$	−33.1282	+	4.99327i	−1.13562	+	0.171167i
$852$		0			0
$853$	−11.4176	+	19.7759i	−0.390933	+	0.677115i	−0.992573	−	0.121652i	$-0.961181\pi$
$853$	−11.4176	+	19.7759i	−0.390933	+	0.677115i	0.601640	+	0.798767i	$0.294514\pi$
$854$	−3.80718	−	6.59423i	−0.130279	−	0.225650i
$855$		0			0
$856$	−17.9596	+	22.5206i	−0.613846	+	0.769739i
$857$	−2.82440	−	37.6890i	−0.0964796	−	1.28743i	−0.809847	−	0.586641i	$-0.800450\pi$
$857$	−2.82440	−	37.6890i	−0.0964796	−	1.28743i	0.713368	−	0.700790i	$-0.247169\pi$
$858$		0			0
$859$	−33.4445			−1.14111			−0.570556	−	0.821258i	$-0.693272\pi$
$859$	−33.4445			−1.14111			−0.570556	+	0.821258i	$0.693272\pi$
$860$	−12.4085	−	11.7383i	−0.423128	−	0.400272i
$861$		0			0
$862$	−35.6984	+	17.1914i	−1.21589	+	0.585542i
$863$	−2.89858	−	38.6788i	−0.0986687	−	1.31664i	−0.798353	−	0.602190i	$-0.794295\pi$
$863$	−2.89858	−	38.6788i	−0.0986687	−	1.31664i	0.699684	−	0.714452i	$-0.253324\pi$
$864$		0			0
$865$	30.2504	−	9.33103i	1.02855	−	0.317264i
$866$	3.22875	+	5.59235i	0.109717	+	0.190036i
$867$		0			0
$868$	−3.28759	+	14.4039i	−0.111588	+	0.488899i
$869$	2.81874	−	0.424857i	0.0956192	−	0.0144123i
$870$		0			0
$871$	−43.0725	−	54.0113i	−1.45946	−	1.83010i
$872$	37.0083	+	25.2318i	1.25326	+	0.854457i
$873$		0			0
$874$	−1.05169	+	14.0338i	−0.0355738	+	0.474699i
$875$	−3.10732	−	7.91733i	−0.105047	−	0.267655i
$876$		0			0
$877$	−32.7657	−	10.1069i	−1.10642	−	0.341285i	−0.312873	−	0.949795i	$-0.601291\pi$
$877$	−32.7657	−	10.1069i	−1.10642	−	0.341285i	−0.793546	+	0.608510i	$0.791767\pi$
$878$	−17.7073	+	12.0726i	−0.597591	+	0.407431i
$879$		0			0
$880$	2.64638	−	6.74286i	0.0892093	−	0.227302i
$881$	8.04747	+	3.87546i	0.271126	+	0.130567i	0.564507	−	0.825428i	$-0.309066\pi$
$881$	8.04747	+	3.87546i	0.271126	+	0.130567i	−0.293381	+	0.955996i	$0.594780\pi$
$882$		0			0
$883$	−1.33505	+	3.40166i	−0.0449281	+	0.114475i	−0.951576	−	0.307412i	$-0.900537\pi$
$883$	−1.33505	+	3.40166i	−0.0449281	+	0.114475i	0.906648	+	0.421887i	$0.138632\pi$
$884$	−4.77048	−	0.719034i	−0.160449	−	0.0241837i
$885$		0			0
$886$	−10.7824	−	3.32592i	−0.362240	−	0.111736i
$887$	−6.91531	−	30.2979i	−0.232193	−	1.01731i	−0.947816	−	0.318818i	$-0.896714\pi$
$887$	−6.91531	−	30.2979i	−0.232193	−	1.01731i	0.715623	−	0.698487i	$-0.246143\pi$
$888$		0			0
$889$	−0.0238160	+	0.317803i	−0.000798764	+	0.0106588i
$890$	−4.07333	−	3.77950i	−0.136538	−	0.126689i
$891$		0			0
$892$	−9.20739	−	11.5457i	−0.308286	−	0.386579i
$893$	−8.37746	+	7.77315i	−0.280341	+	0.260119i
$894$		0			0
$895$	−4.74735	+	20.7995i	−0.158686	+	0.695251i
$896$	0.943234	−	1.63373i	0.0315112	−	0.0545791i
$897$		0			0
$898$	−14.4320	+	4.45167i	−0.481601	+	0.148554i
$899$	−11.3436	+	14.2244i	−0.378329	+	0.474409i
$900$		0			0
$901$	3.53729	−	1.70347i	0.117844	−	0.0567508i
$902$	12.8872			0.429098
$903$		0			0
$904$	−6.79645			−0.226047
$905$	25.8491	−	12.4483i	0.859254	−	0.413795i
$906$		0			0
$907$	−36.4324	+	45.6848i	−1.20972	+	1.51694i	−0.415166	+	0.909746i	$0.636276\pi$
$907$	−36.4324	+	45.6848i	−1.20972	+	1.51694i	−0.794553	+	0.607194i	$0.792295\pi$
$908$	−2.28650	+	0.705293i	−0.0758803	+	0.0234060i
$909$		0			0
$910$	26.0250	−	45.0766i	0.862719	−	1.49427i
$911$	−11.7728	+	51.5800i	−0.390050	+	1.70892i	0.274422	+	0.961609i	$0.411513\pi$
$911$	−11.7728	+	51.5800i	−0.390050	+	1.70892i	−0.664473	+	0.747313i	$0.731344\pi$
$912$		0			0
$913$	6.27799	−	5.82513i	0.207771	−	0.192784i
$914$	6.63833	+	8.32420i	0.219576	+	0.275340i
$915$		0			0
$916$	−5.70951	−	5.29765i	−0.188648	−	0.175039i
$917$	−0.393089	+	5.24541i	−0.0129809	+	0.173219i
$918$		0			0
$919$	2.01670	+	8.83573i	0.0665247	+	0.291464i	0.997237	−	0.0742890i	$-0.0236687\pi$
$919$	2.01670	+	8.83573i	0.0665247	+	0.291464i	−0.930712	+	0.365753i	$0.880812\pi$
$920$	−57.6845	−	17.7933i	−1.90180	−	0.586628i
$921$		0			0
$922$	7.33650	+	1.10580i	0.241615	+	0.0364176i
$923$	31.9749	−	81.4707i	1.05247	−	2.68164i
$924$		0			0
$925$	−30.7960	−	14.8306i	−1.01257	−	0.487627i
$926$	2.27836	−	5.80517i	0.0748716	−	0.190770i
$927$		0			0
$928$	−8.13443	+	5.54596i	−0.267026	+	0.182055i
$929$	15.6428	+	4.82516i	0.513223	+	0.158308i	0.540540	−	0.841318i	$-0.318220\pi$
$929$	15.6428	+	4.82516i	0.513223	+	0.158308i	−0.0273167	+	0.999627i	$0.508696\pi$
$930$		0			0
$931$	0.725949	+	1.84969i	0.0237920	+	0.0606211i
$932$	−0.432547	+	5.77194i	−0.0141685	+	0.189066i
$933$		0			0
$934$	9.71423	+	6.62305i	0.317859	+	0.216713i
$935$	2.65380	+	3.32776i	0.0867886	+	0.108829i
$936$		0			0
$937$	−4.93971	+	0.744541i	−0.161373	+	0.0243231i	−0.229232	−	0.973372i	$-0.573621\pi$
$937$	−4.93971	+	0.744541i	−0.161373	+	0.0243231i	0.0678587	+	0.997695i	$0.478383\pi$
$938$	−7.25267	+	31.7760i	−0.236808	+	1.03752i
$939$		0			0
$940$	−6.90252	−	11.9555i	−0.225135	−	0.389946i
$941$	1.96260	−	0.605383i	0.0639790	−	0.0197349i	−0.262600	−	0.964905i	$-0.584580\pi$
$941$	1.96260	−	0.605383i	0.0639790	−	0.0197349i	0.326579	+	0.945170i	$0.394104\pi$
$942$		0			0
$943$	−4.30843	−	57.4920i	−0.140302	−	1.87220i
$944$	1.53596	−	0.739682i	0.0499914	−	0.0240746i
$945$		0			0
$946$	−6.41599	+	5.83898i	−0.208602	+	0.189841i
$947$	−44.9310			−1.46006			−0.730031	−	0.683414i	$-0.760495\pi$
$947$	−44.9310			−1.46006			−0.730031	+	0.683414i	$0.760495\pi$
$948$		0			0
$949$	2.93546	+	39.1709i	0.0952889	+	1.27154i
$950$	−8.95218	+	11.2257i	−0.290447	+	0.364209i
$951$		0			0
$952$	4.04121	+	6.99958i	0.130976	+	0.226858i
$953$	−30.1466	+	52.2155i	−0.976545	+	1.69143i	−0.301805	+	0.953370i	$0.597589\pi$
$953$	−30.1466	+	52.2155i	−0.976545	+	1.69143i	−0.674740	+	0.738056i	$0.735744\pi$
$954$		0			0
$955$	7.37458	−	1.11154i	0.238636	−	0.0359686i
$956$	8.57852	−	7.95970i	0.277449	−	0.257435i
$957$		0			0
$958$	9.85935	+	6.72199i	0.318541	+	0.217178i
$959$	−1.11839	−	1.03772i	−0.0361147	−	0.0335096i
$960$		0			0
$961$	10.0177	+	25.5246i	0.323150	+	0.823374i
$962$	−8.00402	−	35.0679i	−0.258060	−	1.13064i
$963$		0			0
$964$	−2.49326	+	1.69987i	−0.0803023	+	0.0547492i
$965$	−55.7262	−	8.39937i	−1.79389	−	0.270385i
$966$		0			0
$967$	−38.2384	−	18.4147i	−1.22966	−	0.592175i	−0.297677	−	0.954667i	$-0.596212\pi$
$967$	−38.2384	−	18.4147i	−1.22966	−	0.592175i	−0.931987	+	0.362491i	$0.881926\pi$
$968$	−26.4444	−	12.7349i	−0.849955	−	0.409317i
$969$		0			0
$970$	39.1493	+	5.90081i	1.25701	+	0.189464i
$971$	2.07167	−	1.41244i	0.0664832	−	0.0453275i	−0.529622	−	0.848234i	$-0.677666\pi$
$971$	2.07167	−	1.41244i	0.0664832	−	0.0453275i	0.596106	+	0.802906i	$0.296714\pi$
$972$		0			0
$973$	5.21166	+	22.8338i	0.167078	+	0.732017i
$974$	7.79002	+	19.8487i	0.249608	+	0.635992i
$975$		0			0
$976$	−3.73101	−	3.46188i	−0.119427	−	0.110812i
$977$	−13.1561	−	8.96965i	−0.420900	−	0.286965i	0.334291	−	0.942470i	$-0.391503\pi$
$977$	−13.1561	−	8.96965i	−0.420900	−	0.286965i	−0.755190	+	0.655505i	$0.772456\pi$
$978$		0			0
$979$	1.33387	−	1.23765i	0.0426308	−	0.0395556i
$980$	−2.37350	+	0.357748i	−0.0758187	+	0.0114278i
$981$		0			0
$982$	−17.4501	+	30.2245i	−0.556856	+	0.964503i
$983$	−18.2286	−	31.5728i	−0.581402	−	1.00702i	−0.995314	−	0.0967001i	$-0.969171\pi$
$983$	−18.2286	−	31.5728i	−0.581402	−	1.00702i	0.413912	−	0.910317i	$-0.364162\pi$
$984$		0			0
$985$	11.6383	−	14.5940i	0.370827	−	0.465002i
$986$	0.209462	+	2.79507i	0.00667062	+	0.0890133i
$987$		0			0
$988$	9.74208			0.309937
$989$	28.1936	+	26.6707i	0.896505	+	0.848079i
$990$		0			0
$991$	45.1912	−	21.7629i	1.43555	−	0.691322i	0.455526	−	0.890222i	$-0.349451\pi$
$991$	45.1912	−	21.7629i	1.43555	−	0.691322i	0.980020	+	0.198900i	$0.0637369\pi$
$992$	2.36243	+	31.5245i	0.0750073	+	1.00090i
$993$		0			0
$994$	−39.4575	+	12.1710i	−1.25152	+	0.386042i
$995$	30.5292	+	52.8782i	0.967841	+	1.67635i
$996$		0			0
$997$	−8.53399	+	37.3899i	−0.270274	+	1.18415i	0.639416	+	0.768861i	$0.279176\pi$
$997$	−8.53399	+	37.3899i	−0.270274	+	1.18415i	−0.909690	+	0.415288i	$0.863681\pi$
$998$	10.8108	−	1.62947i	0.342210	−	0.0515799i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.y.c.100.1		36
3.2	odd	2		43.2.g.a.14.3	✓	36
12.11	even	2		688.2.bg.c.401.2		36
43.40	even	21	inner	387.2.y.c.298.1		36
129.56	odd	42		1849.2.a.n.1.7		18
129.83	odd	42		43.2.g.a.40.3	yes	36
129.116	even	42		1849.2.a.o.1.12		18
516.83	even	42		688.2.bg.c.513.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.14.3	✓	36	3.2	odd	2
43.2.g.a.40.3	yes	36	129.83	odd	42
387.2.y.c.100.1		36	1.1	even	1	trivial
387.2.y.c.298.1		36	43.40	even	21	inner
688.2.bg.c.401.2		36	12.11	even	2
688.2.bg.c.513.2		36	516.83	even	42
1849.2.a.n.1.7		18	129.56	odd	42
1849.2.a.o.1.12		18	129.116	even	42

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.y (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.993512 + 0.478450i) q^{2} +(-0.488828 + 0.612971i) q^{4} +(3.17479 - 0.979294i) q^{5} +(1.23273 - 2.13515i) q^{7} +(0.683135 - 2.99301i) q^{8} +O(q^{10})\)	\(q+(-0.993512 + 0.478450i) q^{2} +(-0.488828 + 0.612971i) q^{4} +(3.17479 - 0.979294i) q^{5} +(1.23273 - 2.13515i) q^{7} +(0.683135 - 2.99301i) q^{8} +(-2.68565 + 2.49192i) q^{10} +(-0.748014 - 0.937980i) q^{11} +(-4.22417 - 3.91945i) q^{13} +(-0.203169 + 2.71110i) q^{14} +(0.404382 + 1.77171i) q^{16} +(-1.02040 - 0.314752i) q^{17} +(2.13226 + 0.321387i) q^{19} +(-0.951649 + 2.42476i) q^{20} +(1.19194 + 0.574007i) q^{22} +(2.16225 - 5.50933i) q^{23} +(4.98911 - 3.40152i) q^{25} +(6.07203 + 1.87297i) q^{26} +(0.706193 + 1.79935i) q^{28} +(-0.177883 + 2.37368i) q^{29} +(6.31519 + 4.30562i) q^{31} +(2.57877 + 3.23367i) q^{32} +(1.16437 - 0.175501i) q^{34} +(1.82273 - 7.98588i) q^{35} +(-2.83033 - 4.90228i) q^{37} +(-2.27220 + 0.700880i) q^{38} +(-0.762225 - 10.1712i) q^{40} +(8.77658 - 4.22658i) q^{41} +(-2.45449 + 6.08075i) q^{43} +0.940604 q^{44} +(0.487716 + 6.50812i) q^{46} +(-3.30437 + 4.14355i) q^{47} +(0.460743 + 0.798031i) q^{49} +(-3.32928 + 5.76649i) q^{50} +(4.46740 - 0.673352i) q^{52} +(-2.69519 + 2.50077i) q^{53} +(-3.29335 - 2.24537i) q^{55} +(-5.54842 - 5.14818i) q^{56} +(-0.958961 - 2.44339i) q^{58} +(-0.208748 - 0.914583i) q^{59} +(-2.31407 + 1.57771i) q^{61} +(-8.33425 - 1.25619i) q^{62} +(-7.38381 - 3.55585i) q^{64} +(-17.2492 - 8.30676i) q^{65} +(11.8546 + 1.78679i) q^{67} +(0.691734 - 0.471616i) q^{68} +(2.00995 + 8.80616i) q^{70} +(5.54884 + 14.1382i) q^{71} +(-4.99699 - 4.63653i) q^{73} +(5.15747 + 3.51630i) q^{74} +(-1.23931 + 1.14991i) q^{76} +(-2.92483 + 0.440848i) q^{77} +(-1.18802 + 2.05771i) q^{79} +(3.01886 + 5.22882i) q^{80} +(-6.69743 + 8.39832i) q^{82} +(0.533459 + 7.11852i) q^{83} -3.54780 q^{85} +(-0.470767 - 7.21565i) q^{86} +(-3.31838 + 1.59805i) q^{88} +(0.113343 + 1.51246i) q^{89} +(-13.5759 + 4.18761i) q^{91} +(2.32009 + 4.01851i) q^{92} +(1.30045 - 5.69764i) q^{94} +(7.08423 - 1.06778i) q^{95} +(-6.73777 - 8.44890i) q^{97} +(-0.839572 - 0.572410i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) \) 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8	\( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) \) 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8 - 7 * q^10 + 4 * q^11 - 18 * q^14 - 10 * q^16 + 10 * q^17 + 10 * q^19 + 3 * q^20 - 3 * q^22 - 4 * q^23 - 2 * q^25 + 15 * q^26 + 20 * q^28 - 9 * q^29 + 40 * q^31 - 48 * q^32 - 42 * q^34 - 11 * q^35 - 19 * q^37 + 21 * q^38 - 97 * q^40 + 28 * q^41 - 8 * q^43 - 14 * q^44 - 61 * q^46 + 30 * q^47 + 6 * q^49 + 3 * q^50 - 8 * q^52 + 24 * q^53 + 14 * q^55 - 39 * q^56 + 64 * q^58 + q^59 - 14 * q^61 - 33 * q^62 + 48 * q^64 - 38 * q^65 + 66 * q^67 - 66 * q^68 + 47 * q^70 + 33 * q^71 + 29 * q^73 + 40 * q^74 - 39 * q^76 + 27 * q^77 - 17 * q^79 - 8 * q^80 - 54 * q^82 + 23 * q^83 - 56 * q^85 + 45 * q^86 - 17 * q^88 + 19 * q^89 - 13 * q^91 + 18 * q^92 + 44 * q^94 - q^95 - 31 * q^97 + 5 * q^98

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