LMFDB - Embedded newform 567.2.ba.a.143.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(143,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 3]))

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

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

chi := DirichletCharacter("567.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.ba (of order $18$, degree $6$, not 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			143.5
Character	$\chi$	$=$	567.143
Dual form			567.2.ba.a.341.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06515 + 1.26940i) q^{2} +(-0.129525 - 0.734574i) q^{4} +(2.93903 - 2.46614i) q^{5} +(2.02233 + 1.70592i) q^{7} +(-1.79971 - 1.03907i) q^{8} +O(q^{10})$	\(q+(-1.06515 + 1.26940i) q^{2} +(-0.129525 - 0.734574i) q^{4} +(2.93903 - 2.46614i) q^{5} +(2.02233 + 1.70592i) q^{7} +(-1.79971 - 1.03907i) q^{8} +6.35759i q^{10} +(-1.84743 + 2.20168i) q^{11} +(1.44158 - 3.96072i) q^{13} +(-4.31958 + 0.750072i) q^{14} +(4.63779 - 1.68802i) q^{16} +3.18833 q^{17} +2.26672i q^{19} +(-2.19224 - 1.83951i) q^{20} +(-0.827014 - 4.69023i) q^{22} +(0.782500 - 2.14990i) q^{23} +(1.68781 - 9.57204i) q^{25} +(3.49221 + 6.04869i) q^{26} +(0.991186 - 1.70651i) q^{28} +(-0.356349 - 0.979061i) q^{29} +(8.54472 - 1.50666i) q^{31} +(-1.37565 + 3.77958i) q^{32} +(-3.39605 + 4.04725i) q^{34} +(10.1507 + 0.0264162i) q^{35} +(-0.0122349 + 0.0211914i) q^{37} +(-2.87736 - 2.41439i) q^{38} +(-7.85188 + 1.38450i) q^{40} +(-2.99981 - 1.09184i) q^{41} +(-0.110557 + 0.627001i) q^{43} +(1.85658 + 1.07190i) q^{44} +(1.89560 + 3.28327i) q^{46} +(-1.86595 + 10.5823i) q^{47} +(1.17964 + 6.89989i) q^{49} +(10.3529 + 12.3382i) q^{50} +(-3.09616 - 0.545937i) q^{52} +(1.91685 + 1.10670i) q^{53} +11.0268i q^{55} +(-1.86705 - 5.17151i) q^{56} +(1.62238 + 0.590498i) q^{58} +(10.2914 + 3.74577i) q^{59} +(-7.50570 - 1.32346i) q^{61} +(-7.18884 + 12.4514i) q^{62} +(1.60294 + 2.77637i) q^{64} +(-5.53082 - 15.1958i) q^{65} +(-8.32749 + 6.98759i) q^{67} +(-0.412969 - 2.34207i) q^{68} +(-10.8456 + 12.8571i) q^{70} +(-3.88604 + 2.24361i) q^{71} +(1.92730 - 1.11273i) q^{73} +(-0.0138683 - 0.0381028i) q^{74} +(1.66507 - 0.293597i) q^{76} +(-7.49200 + 1.30095i) q^{77} +(-9.68949 - 8.13045i) q^{79} +(9.46771 - 16.3986i) q^{80} +(4.58122 - 2.64497i) q^{82} +(4.16888 - 1.51735i) q^{83} +(9.37059 - 7.86286i) q^{85} +(-0.678152 - 0.808190i) q^{86} +(5.61252 - 2.04279i) q^{88} -4.73160 q^{89} +(9.67205 - 5.55065i) q^{91} +(-1.68062 - 0.296338i) q^{92} +(-11.4457 - 13.6404i) q^{94} +(5.59003 + 6.66194i) q^{95} +(13.0174 + 2.29533i) q^{97} +(-10.0152 - 5.85198i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34} - 18 q^{35} + 3 q^{37} + 99 q^{38} - 54 q^{40} - 12 q^{43} + 9 q^{44} + 3 q^{46} - 45 q^{47} - 24 q^{49} + 9 q^{50} - 9 q^{52} + 45 q^{53} - 3 q^{56} - 3 q^{58} - 36 q^{59} - 9 q^{61} + 99 q^{62} + 18 q^{64} - 69 q^{65} - 3 q^{67} - 36 q^{68} + 66 q^{70} - 18 q^{71} - 9 q^{73} - 75 q^{74} + 36 q^{76} - 15 q^{77} - 21 q^{79} - 72 q^{80} - 18 q^{82} + 90 q^{83} + 9 q^{85} + 105 q^{86} - 63 q^{88} + 18 q^{89} + 6 q^{91} - 150 q^{92} - 9 q^{94} - 45 q^{95} - 27 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{18}\right)$

Coefficient data

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

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

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

$2$	−1.06515	+	1.26940i	−0.753174	+	0.897598i	−0.997396	−	0.0721215i	$-0.977023\pi$
$2$	−1.06515	+	1.26940i	−0.753174	+	0.897598i	0.244222	+	0.969719i	$0.421468\pi$
$3$		0			0
$3$		0			0
$4$	−0.129525	−	0.734574i	−0.0647626	−	0.367287i
$5$	2.93903	−	2.46614i	1.31437	−	1.10289i	0.326907	−	0.945057i	$-0.393994\pi$
$5$	2.93903	−	2.46614i	1.31437	−	1.10289i	0.987466	−	0.157833i	$-0.0504508\pi$
$6$		0			0
$7$	2.02233	+	1.70592i	0.764369	+	0.644779i
$7$	2.02233	+	1.70592i	0.764369	+	0.644779i
$8$	−1.79971	−	1.03907i	−0.636295	−	0.367365i
$9$		0			0
$10$			6.35759i			2.01045i
$11$	−1.84743	+	2.20168i	−0.557020	+	0.663830i	−0.968913	−	0.247402i	$-0.920423\pi$
$11$	−1.84743	+	2.20168i	−0.557020	+	0.663830i	0.411893	+	0.911232i	$0.364868\pi$
$12$		0			0
$13$	1.44158	−	3.96072i	0.399823	−	1.09851i	−0.562547	−	0.826765i	$-0.690179\pi$
$13$	1.44158	−	3.96072i	0.399823	−	1.09851i	0.962371	−	0.271740i	$-0.0875992\pi$
$14$	−4.31958	+	0.750072i	−1.15446	+	0.200465i
$15$		0			0
$16$	4.63779	−	1.68802i	1.15945	−	0.422005i
$17$	3.18833			0.773284			0.386642	−	0.922230i	$-0.373635\pi$
$17$	3.18833			0.773284			0.386642	+	0.922230i	$0.373635\pi$
$18$		0			0
$19$			2.26672i			0.520020i	0.965606	+	0.260010i	$0.0837259\pi$
$19$			2.26672i			0.520020i	−0.965606	+	0.260010i	$0.916274\pi$
$20$	−2.19224	−	1.83951i	−0.490200	−	0.411326i
$21$		0			0
$22$	−0.827014	−	4.69023i	−0.176320	−	0.999960i
$23$	0.782500	−	2.14990i	0.163163	−	0.448285i	−0.830988	−	0.556291i	$-0.812224\pi$
$23$	0.782500	−	2.14990i	0.163163	−	0.448285i	0.994150	+	0.108005i	$0.0344463\pi$
$24$		0			0
$25$	1.68781	−	9.57204i	0.337562	−	1.91441i
$26$	3.49221	+	6.04869i	0.684880	+	1.18625i
$27$		0			0
$28$	0.991186	−	1.70651i	0.187317	−	0.322501i
$29$	−0.356349	−	0.979061i	−0.0661723	−	0.181807i	0.902199	−	0.431320i	$-0.141952\pi$
$29$	−0.356349	−	0.979061i	−0.0661723	−	0.181807i	−0.968372	+	0.249513i	$0.919730\pi$
$30$		0			0
$31$	8.54472	−	1.50666i	1.53468	−	0.270605i	0.658495	−	0.752585i	$-0.271194\pi$
$31$	8.54472	−	1.50666i	1.53468	−	0.270605i	0.876182	+	0.481981i	$0.160082\pi$
$32$	−1.37565	+	3.77958i	−0.243183	+	0.668141i
$33$		0			0
$34$	−3.39605	+	4.04725i	−0.582417	+	0.694098i
$35$	10.1507	+	0.0264162i	1.71579	+	0.00446515i
$36$		0			0
$37$	−0.0122349	+	0.0211914i	−0.00201140	+	0.00348384i	−0.867029	−	0.498257i	$-0.833974\pi$
$37$	−0.0122349	+	0.0211914i	−0.00201140	+	0.00348384i	0.865018	+	0.501741i	$0.167307\pi$
$38$	−2.87736	−	2.41439i	−0.466769	−	0.391666i
$39$		0			0
$40$	−7.85188	+	1.38450i	−1.24149	+	0.218909i
$41$	−2.99981	−	1.09184i	−0.468492	−	0.170517i	0.0969772	−	0.995287i	$-0.469083\pi$
$41$	−2.99981	−	1.09184i	−0.468492	−	0.170517i	−0.565469	+	0.824770i	$0.691305\pi$
$42$		0			0
$43$	−0.110557	+	0.627001i	−0.0168598	+	0.0956167i	−0.992077	−	0.125635i	$-0.959903\pi$
$43$	−0.110557	+	0.627001i	−0.0168598	+	0.0956167i	0.975217	+	0.221252i	$0.0710143\pi$
$44$	1.85658	+	1.07190i	0.279890	+	0.161595i
$45$		0			0
$46$	1.89560	+	3.28327i	0.279490	+	0.484091i
$47$	−1.86595	+	10.5823i	−0.272177	+	1.54359i	0.475611	+	0.879656i	$0.342227\pi$
$47$	−1.86595	+	10.5823i	−0.272177	+	1.54359i	−0.747788	+	0.663937i	$0.768884\pi$
$48$		0			0
$49$	1.17964	+	6.89989i	0.168520	+	0.985698i
$50$	10.3529	+	12.3382i	1.46413	+	1.74488i
$51$		0			0
$52$	−3.09616	−	0.545937i	−0.429361	−	0.0757079i
$53$	1.91685	+	1.10670i	0.263300	+	0.152016i	0.625839	−	0.779952i	$-0.284757\pi$
$53$	1.91685	+	1.10670i	0.263300	+	0.152016i	−0.362539	+	0.931969i	$0.618090\pi$
$54$		0			0
$55$			11.0268i			1.48685i
$56$	−1.86705	−	5.17151i	−0.249495	−	0.691072i
$57$		0			0
$58$	1.62238	+	0.590498i	0.213029	+	0.0775362i
$59$	10.2914	+	3.74577i	1.33983	+	0.487658i	0.909759	−	0.415138i	$-0.136267\pi$
$59$	10.2914	+	3.74577i	1.33983	+	0.487658i	0.430070	+	0.902795i	$0.358489\pi$
$60$		0			0
$61$	−7.50570	−	1.32346i	−0.961006	−	0.169451i	−0.328927	−	0.944355i	$-0.606687\pi$
$61$	−7.50570	−	1.32346i	−0.961006	−	0.169451i	−0.632079	+	0.774904i	$0.717798\pi$
$62$	−7.18884	+	12.4514i	−0.912984	+	1.58133i
$63$		0			0
$64$	1.60294	+	2.77637i	0.200367	+	0.347046i
$65$	−5.53082	−	15.1958i	−0.686014	−	1.88481i
$66$		0			0
$67$	−8.32749	+	6.98759i	−1.01736	+	0.853670i	−0.989294	−	0.145936i	$-0.953381\pi$
$67$	−8.32749	+	6.98759i	−1.01736	+	0.853670i	−0.0280702	+	0.999606i	$0.508936\pi$
$68$	−0.412969	−	2.34207i	−0.0500799	−	0.284017i
$69$		0			0
$70$	−10.8456	+	12.8571i	−1.29629	+	1.53672i
$71$	−3.88604	+	2.24361i	−0.461188	+	0.266267i	−0.712544	−	0.701628i	$-0.752457\pi$
$71$	−3.88604	+	2.24361i	−0.461188	+	0.266267i	0.251356	+	0.967895i	$0.419124\pi$
$72$		0			0
$73$	1.92730	−	1.11273i	0.225574	−	0.130235i	−0.382955	−	0.923767i	$-0.625093\pi$
$73$	1.92730	−	1.11273i	0.225574	−	0.130235i	0.608528	+	0.793532i	$0.291760\pi$
$74$	−0.0138683	−	0.0381028i	−0.00161216	−	0.00442937i
$75$		0			0
$76$	1.66507	−	0.293597i	0.190997	−	0.0336779i
$77$	−7.49200	+	1.30095i	−0.853793	+	0.148257i
$78$		0			0
$79$	−9.68949	−	8.13045i	−1.09015	−	0.914747i	−0.0934288	−	0.995626i	$-0.529783\pi$
$79$	−9.68949	−	8.13045i	−1.09015	−	0.914747i	−0.996724	+	0.0808793i	$0.974227\pi$
$80$	9.46771	−	16.3986i	1.05852	−	1.83342i
$81$		0			0
$82$	4.58122	−	2.64497i	0.505912	−	0.292088i
$83$	4.16888	−	1.51735i	0.457594	−	0.166550i	−0.102931	−	0.994689i	$-0.532822\pi$
$83$	4.16888	−	1.51735i	0.457594	−	0.166550i	0.560524	+	0.828138i	$0.310600\pi$
$84$		0			0
$85$	9.37059	−	7.86286i	1.01638	−	0.852846i
$86$	−0.678152	−	0.808190i	−0.0731270	−	0.0871494i
$87$		0			0
$88$	5.61252	−	2.04279i	0.598297	−	0.217762i
$89$	−4.73160			−0.501549			−0.250774	−	0.968046i	$-0.580685\pi$
$89$	−4.73160			−0.501549			−0.250774	+	0.968046i	$0.580685\pi$
$90$		0			0
$91$	9.67205	−	5.55065i	1.01391	−	0.581866i
$92$	−1.68062	−	0.296338i	−0.175216	−	0.0308954i
$93$		0			0
$94$	−11.4457	−	13.6404i	−1.18053	−	1.40690i
$95$	5.59003	+	6.66194i	0.573525	+	0.683500i
$96$		0			0
$97$	13.0174	+	2.29533i	1.32172	+	0.233055i	0.789605	−	0.613616i	$-0.210286\pi$
$97$	13.0174	+	2.29533i	1.32172	+	0.233055i	0.532117	+	0.846671i	$0.321397\pi$
$98$	−10.0152	−	5.85198i	−1.01169	−	0.591139i
$99$		0			0
$100$	−7.24999			−0.724999
$101$	−2.55038	+	0.928261i	−0.253772	+	0.0923654i	−0.465774	−	0.884904i	$-0.654224\pi$
$101$	−2.55038	+	0.928261i	−0.253772	+	0.0923654i	0.212002	+	0.977269i	$0.432002\pi$
$102$		0			0
$103$	−6.27600	−	7.47944i	−0.618393	−	0.736972i	0.362401	−	0.932022i	$-0.381957\pi$
$103$	−6.27600	−	7.47944i	−0.618393	−	0.736972i	−0.980793	+	0.195051i	$0.937513\pi$
$104$	−6.70988	+	5.63026i	−0.657958	+	0.552092i
$105$		0			0
$106$	−3.44657	+	1.25445i	−0.334761	+	0.121843i
$107$	12.2288	−	7.06029i	1.18220	−	0.682544i	0.225678	−	0.974202i	$-0.427540\pi$
$107$	12.2288	−	7.06029i	1.18220	−	0.682544i	0.956523	+	0.291658i	$0.0942070\pi$
$108$		0			0
$109$	2.48897	−	4.31103i	0.238400	−	0.412922i	−0.721855	−	0.692044i	$-0.756710\pi$
$109$	2.48897	−	4.31103i	0.238400	−	0.412922i	0.960255	+	0.279123i	$0.0900436\pi$
$110$	−13.9974	−	11.7452i	−1.33460	−	1.11986i
$111$		0			0
$112$	12.2588	+	4.49799i	1.15835	+	0.425021i
$113$	−7.89136	+	1.39146i	−0.742357	+	0.130898i	−0.532020	−	0.846732i	$-0.678567\pi$
$113$	−7.89136	+	1.39146i	−0.742357	+	0.130898i	−0.210336	+	0.977629i	$0.567456\pi$
$114$		0			0
$115$	−3.00216	−	8.24837i	−0.279953	−	0.769164i
$116$	−0.673037	+	0.388578i	−0.0624899	+	0.0360786i
$117$		0			0
$118$	−15.7168	+	9.07408i	−1.44684	+	0.835336i
$119$	6.44786	+	5.43905i	0.591074	+	0.498597i
$120$		0			0
$121$	0.475733	+	2.69802i	0.0432485	+	0.245274i
$122$	9.67468	−	8.11802i	0.875904	−	0.734971i
$123$		0			0
$124$	−2.21351	−	6.08158i	−0.198779	−	0.546142i
$125$	−9.05388	−	15.6818i	−0.809804	−	1.40262i
$126$		0			0
$127$	−3.39217	+	5.87541i	−0.301006	+	0.521358i	−0.976364	−	0.216132i	$-0.930656\pi$
$127$	−3.39217	+	5.87541i	−0.301006	+	0.521358i	0.675358	+	0.737490i	$0.263989\pi$
$128$	−13.1537	−	2.31936i	−1.16264	−	0.205004i
$129$		0			0
$130$	25.1806	+	9.16500i	2.20849	+	0.803823i
$131$	−18.8911	−	6.87581i	−1.65053	−	0.600742i	−0.661693	−	0.749775i	$-0.730162\pi$
$131$	−18.8911	−	6.87581i	−1.65053	−	0.600742i	−0.988832	+	0.149033i	$0.952384\pi$
$132$		0			0
$133$	−3.86685	+	4.58405i	−0.335298	+	0.397487i
$134$		−	18.0137i		−	1.55615i
$135$		0			0
$136$	−5.73808	−	3.31288i	−0.492036	−	0.284077i
$137$	18.4568	+	3.25444i	1.57687	+	0.278045i	0.892487	−	0.451073i	$-0.148959\pi$
$137$	18.4568	+	3.25444i	1.57687	+	0.278045i	0.684387	+	0.729119i	$0.260070\pi$
$138$		0			0
$139$	−8.49230	−	10.1207i	−0.720308	−	0.858429i	0.274353	−	0.961629i	$-0.411536\pi$
$139$	−8.49230	−	10.1207i	−0.720308	−	0.858429i	−0.994661	+	0.103200i	$0.967092\pi$
$140$	−1.29537	−	7.45989i	−0.109479	−	0.630475i
$141$		0			0
$142$	1.29119	−	7.32269i	0.108354	−	0.614507i
$143$	6.05700	+	10.4910i	0.506512	+	0.877304i
$144$		0			0
$145$	−3.46182	−	1.99868i	−0.287488	−	0.165981i
$146$	−0.640372	+	3.63173i	−0.0529976	+	0.300564i
$147$		0			0
$148$	0.0171514	+	0.00624259i	0.00140983	+	0.000513138i
$149$	−13.0187	+	2.29555i	−1.06654	+	0.188059i	−0.679255	−	0.733902i	$-0.737697\pi$
$149$	−13.0187	+	2.29555i	−1.06654	+	0.188059i	−0.387282	+	0.921962i	$0.626586\pi$
$150$		0			0
$151$	−9.62231	−	8.07407i	−0.783052	−	0.657059i	0.160963	−	0.986960i	$-0.448540\pi$
$151$	−9.62231	−	8.07407i	−0.783052	−	0.657059i	−0.944015	+	0.329902i	$0.892984\pi$
$152$	2.35527	−	4.07944i	0.191037	−	0.330886i
$153$		0			0
$154$	6.32868	−	10.8960i	0.509980	−	0.878026i
$155$	21.3975	−	25.5006i	1.71869	−	2.04825i
$156$		0			0
$157$	−6.20286	+	17.0422i	−0.495042	+	1.36012i	0.400971	+	0.916091i	$0.368673\pi$
$157$	−6.20286	+	17.0422i	−0.495042	+	1.36012i	−0.896013	+	0.444027i	$0.853549\pi$
$158$	20.6415	−	3.63965i	1.64215	−	0.289555i
$159$		0			0
$160$	5.27787	+	14.5008i	0.417252	+	1.14639i
$161$	5.25004	−	3.01292i	0.413761	−	0.237452i
$162$		0			0
$163$	2.93944	+	5.09126i	0.230235	+	0.398779i	0.957877	−	0.287178i	$-0.0927172\pi$
$163$	2.93944	+	5.09126i	0.230235	+	0.398779i	−0.727642	+	0.685957i	$0.759384\pi$
$164$	−0.413488	+	2.34501i	−0.0322880	+	0.183114i
$165$		0			0
$166$	−2.51436	+	6.90815i	−0.195152	+	0.536177i
$167$	−1.43991	−	8.16616i	−0.111424	−	0.631916i	−0.988459	−	0.151490i	$-0.951593\pi$
$167$	−1.43991	−	8.16616i	−0.111424	−	0.631916i	0.877035	−	0.480427i	$-0.159518\pi$
$168$		0			0
$169$	−3.65055	−	3.06317i	−0.280811	−	0.235629i
$170$			20.2701i			1.55464i
$171$		0			0
$172$	0.474899			0.0362107
$173$	18.3478	−	6.67804i	1.39495	−	0.507722i	0.468277	−	0.883582i	$-0.344875\pi$
$173$	18.3478	−	6.67804i	1.39495	−	0.507722i	0.926677	+	0.375860i	$0.122653\pi$
$174$		0			0
$175$	19.7425	−	16.4786i	1.49239	−	1.24566i
$176$	−4.85151	+	13.3294i	−0.365696	+	1.00474i
$177$		0			0
$178$	5.03986	−	6.00627i	0.377754	−	0.450189i
$179$			2.96390i			0.221532i	0.993846	+	0.110766i	$0.0353305\pi$
$179$			2.96390i			0.221532i	−0.993846	+	0.110766i	$0.964670\pi$
$180$		0			0
$181$	−22.0624	−	12.7377i	−1.63988	−	0.946787i	−0.980872	−	0.194653i	$-0.937642\pi$
$181$	−22.0624	−	12.7377i	−1.63988	−	0.946787i	−0.659011	−	0.752134i	$-0.729025\pi$
$182$	−3.25620	+	18.1899i	−0.241366	+	1.34833i
$183$		0			0
$184$	−3.64216	+	3.05614i	−0.268504	+	0.225302i
$185$	0.0163023	+	0.0924549i	0.00119857	+	0.00679742i
$186$		0			0
$187$	−5.89020	+	7.01967i	−0.430734	+	0.513329i
$188$	8.01521			0.584569
$189$		0			0
$190$	−14.4108			−1.04547
$191$	−14.5728	+	17.3672i	−1.05445	+	1.25665i	−0.0890120	+	0.996031i	$0.528371\pi$
$191$	−14.5728	+	17.3672i	−1.05445	+	1.25665i	−0.965442	+	0.260619i	$0.916073\pi$
$192$		0			0
$193$	−2.59185	−	14.6991i	−0.186566	−	1.05807i	−0.923927	−	0.382568i	$-0.875040\pi$
$193$	−2.59185	−	14.6991i	−0.186566	−	1.05807i	0.737361	−	0.675498i	$-0.236071\pi$
$194$	−16.7792	+	14.0794i	−1.20468	+	1.01084i
$195$		0			0
$196$	4.91569	−	1.76024i	0.351121	−	0.125732i
$197$	−16.5142	−	9.53447i	−1.17659	−	0.679303i	−0.221364	−	0.975191i	$-0.571051\pi$
$197$	−16.5142	−	9.53447i	−1.17659	−	0.679303i	−0.955222	+	0.295889i	$0.904384\pi$
$198$		0			0
$199$		−	5.80784i		−	0.411707i	−0.978583	−	0.205854i	$-0.934003\pi$
$199$		−	5.80784i		−	0.411707i	0.978583	−	0.205854i	$-0.0659971\pi$
$200$	−12.9836	+	15.4732i	−0.918076	+	1.09412i
$201$		0			0
$202$	1.53820	−	4.22617i	0.108227	−	0.297352i
$203$	0.949549	−	2.58789i	0.0666453	−	0.181634i
$204$		0			0
$205$	−11.5092	+	4.18899i	−0.803834	+	0.292572i
$206$	16.1792			1.12726
$207$		0			0
$208$		−	20.8024i		−	1.44239i
$209$	−4.99057	−	4.18759i	−0.345205	−	0.289662i
$210$		0			0
$211$	0.180568	+	1.02405i	0.0124308	+	0.0704985i	0.990392	−	0.138288i	$-0.0441599\pi$
$211$	0.180568	+	1.02405i	0.0124308	+	0.0704985i	−0.977961	+	0.208786i	$0.933049\pi$
$212$	0.564670	−	1.55142i	0.0387817	−	0.106552i
$213$		0			0
$214$	−4.06317	+	23.0434i	−0.277753	+	1.57521i
$215$	1.22134	+	2.11542i	0.0832946	+	0.144271i
$216$		0			0
$217$	19.8505	+	11.5297i	1.34754	+	0.782685i
$218$	2.82127	+	7.75138i	0.191081	+	0.524990i
$219$		0			0
$220$	8.10000	−	1.42825i	0.546102	−	0.0962925i
$221$	4.59624	−	12.6281i	0.309177	−	0.849456i
$222$		0			0
$223$	−4.95104	+	5.90042i	−0.331546	+	0.395122i	−0.905904	−	0.423483i	$-0.860807\pi$
$223$	−4.95104	+	5.90042i	−0.331546	+	0.395122i	0.574358	+	0.818604i	$0.305252\pi$
$224$	−9.22970	+	5.29679i	−0.616685	+	0.353907i
$225$		0			0
$226$	6.63916	−	11.4994i	0.441630	−	0.764926i
$227$	−2.48407	−	2.08438i	−0.164873	−	0.138345i	0.556618	−	0.830768i	$-0.312099\pi$
$227$	−2.48407	−	2.08438i	−0.164873	−	0.138345i	−0.721491	+	0.692423i	$0.756543\pi$
$228$		0			0
$229$	−21.5273	+	3.79585i	−1.42257	+	0.250837i	−0.831382	−	0.555701i	$-0.812450\pi$
$229$	−21.5273	+	3.79585i	−1.42257	+	0.250837i	−0.591183	+	0.806537i	$0.701339\pi$
$230$	13.6682	+	4.97481i	0.901254	+	0.328030i
$231$		0			0
$232$	−0.375982	+	2.13230i	−0.0246844	+	0.139992i
$233$	−8.06698	−	4.65747i	−0.528486	−	0.305121i	0.211914	−	0.977288i	$-0.432030\pi$
$233$	−8.06698	−	4.65747i	−0.528486	−	0.305121i	−0.740400	+	0.672167i	$0.765364\pi$
$234$		0			0
$235$	20.6134	+	35.7035i	1.34467	+	2.32904i
$236$	1.41855	−	8.04499i	0.0923396	−	0.523684i
$237$		0			0
$238$	−13.7722	+	2.39148i	−0.892721	+	0.155016i
$239$	3.92573	+	4.67850i	0.253934	+	0.302627i	0.877919	−	0.478810i	$-0.158932\pi$
$239$	3.92573	+	4.67850i	0.253934	+	0.302627i	−0.623984	+	0.781437i	$0.714487\pi$
$240$		0			0
$241$	0.327723	+	0.0577863i	0.0211105	+	0.00372235i	0.184193	−	0.982890i	$-0.441033\pi$
$241$	0.327723	+	0.0577863i	0.0211105	+	0.00372235i	−0.163083	+	0.986612i	$0.552144\pi$
$242$	−3.93158	−	2.26990i	−0.252731	−	0.145915i
$243$		0			0
$244$			5.68492i			0.363939i
$245$	20.4831	+	17.3698i	1.30861	+	1.10972i
$246$		0			0
$247$	8.97782	+	3.26766i	0.571245	+	0.207916i
$248$	−16.9436	−	6.16695i	−1.07592	−	0.391602i
$249$		0			0
$250$	29.5501	+	5.21048i	1.86891	+	0.329540i
$251$	6.85299	−	11.8697i	0.432557	−	0.749210i	−0.564536	−	0.825409i	$-0.690945\pi$
$251$	6.85299	−	11.8697i	0.432557	−	0.749210i	0.997093	+	0.0761982i	$0.0242782\pi$
$252$		0			0
$253$	3.28778	+	5.69460i	0.206701	+	0.358016i
$254$	−3.84505	−	10.5642i	−0.241260	−	0.662856i
$255$		0			0
$256$	12.0432	−	10.1054i	0.752700	−	0.631590i
$257$	0.00716061	+	0.0406099i	0.000446667	+	0.00253317i	0.985030	−	0.172381i	$-0.0551462\pi$
$257$	0.00716061	+	0.0406099i	0.000446667	+	0.00253317i	−0.984584	+	0.174915i	$0.944035\pi$
$258$		0			0
$259$	−0.0608938	+	0.0219842i	−0.00378376	+	0.00136603i
$260$	−10.4461	+	6.03104i	−0.647837	+	0.374029i
$261$		0			0
$262$	28.8500	−	16.6565i	1.78236	−	1.02904i
$263$	4.77109	+	13.1085i	0.294198	+	0.808302i	0.995441	+	0.0953797i	$0.0304065\pi$
$263$	4.77109	+	13.1085i	0.294198	+	0.808302i	−0.701243	+	0.712922i	$0.747371\pi$
$264$		0			0
$265$	8.36295	−	1.47461i	0.513732	−	0.0905848i
$266$	−1.70020	−	9.79125i	−0.104246	−	0.600340i
$267$		0			0
$268$	6.21152	+	5.21209i	0.379429	+	0.318379i
$269$	−11.2526	+	19.4900i	−0.686081	+	1.18833i	0.287015	+	0.957926i	$0.407337\pi$
$269$	−11.2526	+	19.4900i	−0.686081	+	1.18833i	−0.973096	+	0.230401i	$0.925996\pi$
$270$		0			0
$271$	5.53035	−	3.19295i	0.335945	−	0.193958i	−0.322533	−	0.946558i	$-0.604534\pi$
$271$	5.53035	−	3.19295i	0.335945	−	0.193958i	0.658477	+	0.752601i	$0.271201\pi$
$272$	14.7868	−	5.38196i	0.896582	−	0.326329i
$273$		0			0
$274$	−23.7905	+	19.9626i	−1.43723	+	1.20598i
$275$	17.9564	+	21.3997i	1.08281	+	1.29045i
$276$		0			0
$277$	−5.89401	+	2.14524i	−0.354137	+	0.128895i	−0.512962	−	0.858412i	$-0.671452\pi$
$277$	−5.89401	+	2.14524i	−0.354137	+	0.128895i	0.158825	+	0.987307i	$0.449229\pi$
$278$	21.8928			1.31304
$279$		0			0
$280$	−18.2410	−	10.5948i	−1.09011	−	0.633161i
$281$	6.25888	+	1.10361i	0.373373	+	0.0658358i	0.357186	−	0.934033i	$-0.383736\pi$
$281$	6.25888	+	1.10361i	0.373373	+	0.0658358i	0.0161870	+	0.999869i	$0.494847\pi$
$282$		0			0
$283$	−0.373940	−	0.445644i	−0.0222284	−	0.0264908i	0.754816	−	0.655937i	$-0.227726\pi$
$283$	−0.373940	−	0.445644i	−0.0222284	−	0.0264908i	−0.777044	+	0.629446i	$0.783282\pi$
$284$	2.15144	+	2.56398i	0.127664	+	0.152144i
$285$		0			0
$286$	−19.7689	−	3.48579i	−1.16896	−	0.206119i
$287$	−4.20401	−	7.32552i	−0.248155	−	0.432412i
$288$		0			0
$289$	−6.83455			−0.402033
$290$	6.22447	−	2.26552i	0.365513	−	0.133036i
$291$		0			0
$292$	−1.06702	−	1.27162i	−0.0624424	−	0.0744160i
$293$	−7.63328	+	6.40508i	−0.445941	+	0.374189i	−0.837927	−	0.545782i	$-0.816233\pi$
$293$	−7.63328	+	6.40508i	−0.445941	+	0.374189i	0.391986	+	0.919971i	$0.371788\pi$
$294$		0			0
$295$	39.4843	−	14.3711i	2.29887	−	0.836719i
$296$	0.0440385	−	0.0254256i	0.00255968	−	0.00147783i
$297$		0			0
$298$	10.9529	−	18.9710i	0.634486	−	1.09896i
$299$	−7.38711	−	6.19852i	−0.427208	−	0.358470i
$300$		0			0
$301$	−1.29320	+	1.07940i	−0.0745388	+	0.0622156i
$302$	20.4984	−	3.61442i	1.17955	−	0.207986i
$303$		0			0
$304$	3.82626	+	10.5126i	0.219451	+	0.602937i
$305$	−25.3233	+	14.6204i	−1.45001	+	0.837162i
$306$		0			0
$307$	−1.93850	+	1.11920i	−0.110636	+	0.0638759i	−0.554297	−	0.832319i	$-0.687013\pi$
$307$	−1.93850	+	1.11920i	−0.110636	+	0.0638759i	0.443661	+	0.896195i	$0.353680\pi$
$308$	1.92605	+	5.33493i	0.109747	+	0.303986i
$309$		0			0
$310$	9.57875	+	54.3238i	0.544037	+	3.08538i
$311$	2.85296	−	2.39391i	0.161776	−	0.135746i	−0.558306	−	0.829635i	$-0.688548\pi$
$311$	2.85296	−	2.39391i	0.161776	−	0.135746i	0.720082	+	0.693889i	$0.244104\pi$
$312$		0			0
$313$	4.97702	+	13.6743i	0.281318	+	0.772915i	0.997206	+	0.0746997i	$0.0237998\pi$
$313$	4.97702	+	13.6743i	0.281318	+	0.772915i	−0.715888	+	0.698215i	$0.753978\pi$
$314$	−15.0263	−	26.0264i	−0.847986	−	1.46875i
$315$		0			0
$316$	−4.71738	+	8.17075i	−0.265374	+	0.459641i
$317$	−1.20663	−	0.212762i	−0.0677713	−	0.0119499i	0.139660	−	0.990200i	$-0.455399\pi$
$317$	−1.20663	−	0.212762i	−0.0677713	−	0.0119499i	−0.207431	+	0.978250i	$0.566510\pi$
$318$		0			0
$319$	2.81390	+	1.02418i	0.157548	+	0.0573429i
$320$	11.5580	+	4.20676i	0.646111	+	0.235165i
$321$		0			0
$322$	−1.76749	+	9.87359i	−0.0984982	+	0.550234i
$323$			7.22704i			0.402123i
$324$		0			0
$325$	−35.4790	−	20.4838i	−1.96802	−	1.13624i
$326$	−9.59377	−	1.69164i	−0.531350	−	0.0936913i
$327$		0			0
$328$	4.26431	+	5.08200i	0.235457	+	0.280607i
$329$	−21.8263	+	18.2178i	−1.20332	+	1.00438i
$330$		0			0
$331$	3.55819	−	20.1795i	0.195576	−	1.10917i	−0.716020	−	0.698080i	$-0.754038\pi$
$331$	3.55819	−	20.1795i	0.195576	−	1.10917i	0.911596	−	0.411087i	$-0.134851\pi$
$332$	−1.65458	−	2.86582i	−0.0908068	−	0.157282i
$333$		0			0
$334$	11.8998	+	6.87035i	0.651128	+	0.375929i
$335$	−7.24235	+	41.0734i	−0.395692	+	2.24408i
$336$		0			0
$337$	18.8694	+	6.86790i	1.02788	+	0.374119i	0.800274	−	0.599634i	$-0.204687\pi$
$337$	18.8694	+	6.86790i	1.02788	+	0.374119i	0.227608	+	0.973753i	$0.426909\pi$
$338$	7.77675	−	1.37125i	0.422999	−	0.0745862i
$339$		0			0
$340$	−6.98958	−	5.86495i	−0.379063	−	0.318072i
$341$	−12.4685	+	21.5962i	−0.675209	+	1.16950i
$342$		0			0
$343$	−9.38507	+	15.9662i	−0.506746	+	0.862095i
$344$	0.850466	−	1.01355i	0.0458540	−	0.0546467i
$345$		0			0
$346$	−11.0660	+	30.4037i	−0.594913	+	1.63451i
$347$	−0.621132	+	0.109522i	−0.0333441	+	0.00587947i	−0.190295	−	0.981727i	$-0.560945\pi$
$347$	−0.621132	+	0.109522i	−0.0333441	+	0.00587947i	0.156951	+	0.987606i	$0.449833\pi$
$348$		0			0
$349$	0.582328	+	1.59993i	0.0311713	+	0.0856425i	0.954302	−	0.298844i	$-0.0966009\pi$
$349$	0.582328	+	1.59993i	0.0311713	+	0.0856425i	−0.923131	+	0.384486i	$0.874379\pi$
$350$	−0.110896	+	42.6132i	−0.00592765	+	2.27777i
$351$		0			0
$352$	−5.77999	−	10.0112i	−0.308074	−	0.533600i
$353$	4.15166	−	23.5452i	0.220971	−	1.25319i	−0.649269	−	0.760559i	$-0.724925\pi$
$353$	4.15166	−	23.5452i	0.220971	−	1.25319i	0.870240	−	0.492628i	$-0.163964\pi$
$354$		0			0
$355$	−5.88813	+	16.1775i	−0.312510	+	0.858613i
$356$	0.612862	+	3.47571i	0.0324816	+	0.184212i
$357$		0			0
$358$	−3.76236	−	3.15700i	−0.198847	−	0.166852i
$359$			12.5117i			0.660342i	0.943921	+	0.330171i	$0.107106\pi$
$359$			12.5117i			0.660342i	−0.943921	+	0.330171i	$0.892894\pi$
$360$		0			0
$361$	13.8620			0.729579
$362$	39.6689	−	14.4383i	2.08495	−	0.758860i
$363$		0			0
$364$	−5.33014	−	6.38589i	−0.279375	−	0.334711i
$365$	2.92025	−	8.02333i	0.152853	−	0.419960i
$366$		0			0
$367$	8.47365	−	10.0985i	0.442321	−	0.527138i	−0.498114	−	0.867112i	$-0.665974\pi$
$367$	8.47365	−	10.0985i	0.442321	−	0.527138i	0.940435	+	0.339974i	$0.110418\pi$
$368$		−	11.2917i		−	0.588619i
$369$		0			0
$370$	−0.134726	−	0.0777842i	−0.00700408	−	0.00404381i
$371$	1.98857	+	5.50812i	0.103242	+	0.285967i
$372$		0			0
$373$	−8.57998	+	7.19946i	−0.444255	+	0.372774i	−0.837299	−	0.546746i	$-0.815866\pi$
$373$	−8.57998	+	7.19946i	−0.444255	+	0.372774i	0.393044	+	0.919520i	$0.371422\pi$
$374$	−2.63679	−	14.9540i	−0.136345	−	0.773252i
$375$		0			0
$376$	14.3539	−	17.1063i	0.740247	−	0.882192i
$377$	−4.39149			−0.226173
$378$		0			0
$379$	−6.24758			−0.320917			−0.160458	−	0.987043i	$-0.551297\pi$
$379$	−6.24758			−0.320917			−0.160458	+	0.987043i	$0.551297\pi$
$380$	4.16964	−	4.96918i	0.213898	−	0.254914i
$381$		0			0
$382$	−6.52364	−	36.9974i	−0.333778	−	1.89295i
$383$	10.9842	−	9.21682i	0.561266	−	0.470958i	−0.317469	−	0.948269i	$-0.602833\pi$
$383$	10.9842	−	9.21682i	0.561266	−	0.470958i	0.878734	+	0.477311i	$0.158388\pi$
$384$		0			0
$385$	−18.8109	+	22.2998i	−0.958691	+	1.13650i
$386$	21.4197	+	12.3667i	1.09023	+	0.629447i
$387$		0			0
$388$		−	9.85959i		−	0.500545i
$389$	5.55007	−	6.61432i	0.281400	−	0.335359i	−0.606768	−	0.794879i	$-0.707534\pi$
$389$	5.55007	−	6.61432i	0.281400	−	0.335359i	0.888167	+	0.459520i	$0.151979\pi$
$390$		0			0
$391$	2.49487	−	6.85459i	0.126171	−	0.346652i
$392$	5.04642	−	13.6435i	0.254883	−	0.689103i
$393$		0			0
$394$	29.6931	−	10.8074i	1.49591	−	0.544469i
$395$	−48.5285			−2.44173
$396$		0			0
$397$		−	0.00726859i		−	0.000364800i	−1.00000		0.000182400i	$-0.999942\pi$
$397$		−	0.00726859i		−	0.000364800i	1.00000		0.000182400i	$-5.80597e-5\pi$
$398$	7.37245	+	6.18622i	0.369548	+	0.310087i
$399$		0			0
$400$	−8.33008	−	47.2422i	−0.416504	−	2.36211i
$401$	5.18167	−	14.2365i	0.258760	−	0.710939i	−0.740484	−	0.672074i	$-0.765404\pi$
$401$	5.18167	−	14.2365i	0.258760	−	0.710939i	0.999244	−	0.0388646i	$-0.0123741\pi$
$402$		0			0
$403$	6.35045	−	36.0152i	0.316338	−	1.79404i
$404$	1.01222	+	1.75321i	0.0503596	+	0.0872254i
$405$		0			0
$406$	2.27364	+	3.96184i	0.112839	+	0.196623i
$407$	−0.0240536	−	0.0660867i	−0.00119229	−	0.00327580i
$408$		0			0
$409$	10.0811	−	1.77758i	0.498480	−	0.0878955i	0.0812453	−	0.996694i	$-0.474110\pi$
$409$	10.0811	−	1.77758i	0.498480	−	0.0878955i	0.417235	+	0.908799i	$0.362999\pi$
$410$	6.94148	−	19.0716i	0.342815	−	0.941878i
$411$		0			0
$412$	−4.68131	+	5.57897i	−0.230631	+	0.274856i
$413$	14.4227	+	25.1316i	0.709692	+	1.23664i
$414$		0			0
$415$	8.51046	−	14.7405i	0.417762	−	0.723585i
$416$	12.9867	+	10.8971i	0.636726	+	0.534277i
$417$		0			0
$418$	10.6314	−	1.87460i	0.519999	−	0.0916899i
$419$	−37.4662	−	13.6366i	−1.83034	−	0.666190i	−0.992795	−	0.119827i	$-0.961766\pi$
$419$	−37.4662	−	13.6366i	−1.83034	−	0.666190i	−0.837548	−	0.546363i	$-0.816012\pi$
$420$		0			0
$421$	3.81518	−	21.6370i	0.185940	−	1.05452i	−0.738801	−	0.673924i	$-0.764608\pi$
$421$	3.81518	−	21.6370i	0.185940	−	1.05452i	0.924741	−	0.380597i	$-0.124281\pi$
$422$	−1.49225	−	0.861554i	−0.0726418	−	0.0419398i
$423$		0			0
$424$	−2.29986	−	3.98347i	−0.111691	−	0.193455i
$425$	5.38129	−	30.5188i	0.261031	−	1.48038i
$426$		0			0
$427$	−12.9213	−	15.4806i	−0.625305	−	0.749160i
$428$	−6.77024	−	8.06846i	−0.327252	−	0.390004i
$429$		0			0
$430$	−3.98621	−	0.702877i	−0.192232	−	0.0338957i
$431$	5.61933	+	3.24432i	0.270673	+	0.156273i	0.629194	−	0.777249i	$-0.283385\pi$
$431$	5.61933	+	3.24432i	0.270673	+	0.156273i	−0.358520	+	0.933522i	$0.616719\pi$
$432$		0			0
$433$			1.48559i			0.0713927i	0.999363	+	0.0356963i	$0.0113649\pi$
$433$			1.48559i			0.0713927i	−0.999363	+	0.0356963i	$0.988635\pi$
$434$	−35.7794	+	12.9173i	−1.71747	+	0.620051i
$435$		0			0
$436$	−3.48916	−	1.26995i	−0.167100	−	0.0608195i
$437$	4.87321	+	1.77371i	0.233117	+	0.0848478i
$438$		0			0
$439$	12.4170	+	2.18946i	0.592632	+	0.104497i	0.461917	−	0.886923i	$-0.347162\pi$
$439$	12.4170	+	2.18946i	0.592632	+	0.104497i	0.130715	+	0.991420i	$0.458273\pi$
$440$	11.4576	−	19.8451i	0.546217	−	0.946076i
$441$		0			0
$442$	11.1343	+	19.2852i	0.529606	+	0.917305i
$443$	0.531961	+	1.46155i	0.0252742	+	0.0694403i	0.951688	−	0.307066i	$-0.0993474\pi$
$443$	0.531961	+	1.46155i	0.0252742	+	0.0694403i	−0.926414	+	0.376507i	$0.877125\pi$
$444$		0			0
$445$	−13.9063	+	11.6688i	−0.659222	+	0.553153i
$446$	−2.21637	−	12.5697i	−0.104948	−	0.595191i
$447$		0			0
$448$	−1.49461	+	8.34922i	−0.0706136	+	0.394464i
$449$	3.71332	−	2.14388i	0.175242	−	0.101176i	−0.409813	−	0.912169i	$-0.634406\pi$
$449$	3.71332	−	2.14388i	0.175242	−	0.101176i	0.585055	+	0.810993i	$0.301073\pi$
$450$		0			0
$451$	7.94581	−	4.58752i	0.374154	−	0.216018i
$452$	2.04426	+	5.61656i	0.0961540	+	0.264181i
$453$		0			0
$454$	5.29180	−	0.933088i	0.248357	−	0.0437920i
$455$	14.7377	−	40.1661i	0.690916	−	1.88302i
$456$		0			0
$457$	11.5949	+	9.72925i	0.542385	+	0.455115i	0.872353	−	0.488877i	$-0.162593\pi$
$457$	11.5949	+	9.72925i	0.542385	+	0.455115i	−0.329968	+	0.943992i	$0.607038\pi$
$458$	18.1114	−	31.3698i	0.846289	−	1.46582i
$459$		0			0
$460$	−5.67019	+	3.27368i	−0.264374	+	0.152636i
$461$	−6.54769	+	2.38316i	−0.304956	+	0.110995i	−0.489966	−	0.871742i	$-0.662991\pi$
$461$	−6.54769	+	2.38316i	−0.304956	+	0.110995i	0.185009	+	0.982737i	$0.440768\pi$
$462$		0			0
$463$	−30.9400	+	25.9617i	−1.43790	+	1.20654i	−0.497051	+	0.867721i	$0.665584\pi$
$463$	−30.9400	+	25.9617i	−1.43790	+	1.20654i	−0.940851	+	0.338822i	$0.889972\pi$
$464$	−3.30535	−	3.93916i	−0.153447	−	0.182871i
$465$		0			0
$466$	14.5047	−	5.27928i	0.671918	−	0.244558i
$467$	−8.42978			−0.390084			−0.195042	−	0.980795i	$-0.562484\pi$
$467$	−8.42978			−0.390084			−0.195042	+	0.980795i	$0.562484\pi$
$468$		0			0
$469$	−28.7612	−	0.0748481i	−1.32807	−	0.00345616i
$470$	−67.2782	−	11.8630i	−3.10331	−	0.547197i
$471$		0			0
$472$	−14.6295	−	17.4348i	−0.673378	−	0.802500i
$473$	−1.17621	−	1.40175i	−0.0540820	−	0.0644525i
$474$		0			0
$475$	21.6971	+	3.82578i	0.995531	+	0.175539i
$476$	3.16023	−	5.44092i	0.144849	−	0.249384i
$477$		0			0
$478$	−10.1204			−0.462894
$479$	−21.6306	+	7.87291i	−0.988329	+	0.359722i	−0.785073	−	0.619403i	$-0.787375\pi$
$479$	−21.6306	+	7.87291i	−0.988329	+	0.359722i	−0.203256	+	0.979126i	$0.565152\pi$
$480$		0			0
$481$	0.0662955	+	0.0790079i	0.00302282	+	0.00360245i
$482$	−0.422427	+	0.354458i	−0.0192410	+	0.0161451i
$483$		0			0
$484$	1.92028	−	0.698923i	0.0872852	−	0.0317692i
$485$	43.9192	−	25.3568i	1.99427	−	1.15139i
$486$		0			0
$487$	−13.2168	+	22.8922i	−0.598912	+	1.03735i	0.394070	+	0.919080i	$0.371067\pi$
$487$	−13.2168	+	22.8922i	−0.598912	+	1.03735i	−0.992982	+	0.118265i	$0.962267\pi$
$488$	12.1330	+	10.1808i	0.549233	+	0.460861i
$489$		0			0
$490$	−43.8667	+	7.49967i	−1.98169	+	0.338801i
$491$	12.8648	−	2.26841i	0.580580	−	0.102372i	0.124357	−	0.992238i	$-0.460313\pi$
$491$	12.8648	−	2.26841i	0.580580	−	0.102372i	0.456223	+	0.889866i	$0.349202\pi$
$492$		0			0
$493$	−1.13616	−	3.12157i	−0.0511700	−	0.140588i
$494$	−13.7107	+	7.91586i	−0.616872	+	0.356151i
$495$		0			0
$496$	37.0854	−	21.4112i	1.66518	−	0.961393i
$497$	−11.6863	−	2.09198i	−0.524201	−	0.0938380i
$498$		0			0
$499$	4.49105	+	25.4700i	0.201047	+	1.14019i	0.903540	+	0.428503i	$0.140959\pi$
$499$	4.49105	+	25.4700i	0.201047	+	1.14019i	−0.702494	+	0.711690i	$0.747930\pi$
$500$	−10.3467	+	8.68194i	−0.462720	+	0.388268i
$501$		0			0
$502$	7.76792	+	21.3422i	0.346699	+	0.952548i
$503$	11.7401	+	20.3345i	0.523467	+	0.906672i	0.999627	+	0.0273131i	$0.00869510\pi$
$503$	11.7401	+	20.3345i	0.523467	+	0.906672i	−0.476160	+	0.879359i	$0.657972\pi$
$504$		0			0
$505$	−5.20641	+	9.01776i	−0.231682	+	0.401285i
$506$	−10.7307	−	1.89211i	−0.477036	−	0.0841143i
$507$		0			0
$508$	4.75530	+	1.73079i	0.210982	+	0.0767912i
$509$	−26.6729	−	9.70814i	−1.18226	−	0.430306i	−0.325257	−	0.945626i	$-0.605451\pi$
$509$	−26.6729	−	9.70814i	−1.18226	−	0.430306i	−0.856998	+	0.515320i	$0.827673\pi$
$510$		0			0
$511$	5.79587	+	1.03753i	0.256394	+	0.0458975i
$512$		−	0.661943i		−	0.0292540i
$513$		0			0
$514$	−0.0591771	−	0.0341659i	−0.00261019	−	0.00150699i
$515$	−36.8907	−	6.50482i	−1.62560	−	0.286637i
$516$		0			0
$517$	−19.8517	−	23.6583i	−0.873076	−	1.04049i
$518$	0.0369543	−	0.100715i	0.00162368	−	0.00442515i
$519$		0			0
$520$	−5.83554	+	33.0950i	−0.255905	+	1.45131i
$521$	7.53866	+	13.0573i	0.330275	+	0.572053i	0.982566	−	0.185916i	$-0.0595253\pi$
$521$	7.53866	+	13.0573i	0.330275	+	0.572053i	−0.652291	+	0.757969i	$0.726192\pi$
$522$		0			0
$523$	−4.13584	−	2.38783i	−0.180848	−	0.104412i	0.406843	−	0.913498i	$-0.366630\pi$
$523$	−4.13584	−	2.38783i	−0.180848	−	0.104412i	−0.587691	+	0.809086i	$0.699963\pi$
$524$	−2.60391	+	14.7675i	−0.113752	+	0.645122i
$525$		0			0
$526$	−21.7217	−	7.90606i	−0.947112	−	0.344721i
$527$	27.2434	−	4.80374i	1.18674	−	0.209254i
$528$		0			0
$529$	13.6093	+	11.4195i	0.591707	+	0.496501i
$530$	−7.03592	+	12.1866i	−0.305621	+	0.529351i
$531$		0			0
$532$	3.86818	+	2.24674i	0.167707	+	0.0974084i
$533$	−8.64896	+	10.3074i	−0.374628	+	0.446464i
$534$		0			0
$535$	18.5291	−	50.9082i	0.801082	−	2.20095i
$536$	22.2477	−	3.92286i	0.960952	−	0.169442i
$537$		0			0
$538$	−12.7549	−	35.0437i	−0.549902	−	1.51084i
$539$	−17.3706	−	10.1498i	−0.748206	−	0.437185i
$540$		0			0
$541$	−10.3759	−	17.9716i	−0.446094	−	0.772657i	0.552034	−	0.833822i	$-0.313852\pi$
$541$	−10.3759	−	17.9716i	−0.446094	−	0.772657i	−0.998128	+	0.0611643i	$0.980519\pi$
$542$	−1.83753	+	10.4212i	−0.0789287	+	0.447627i
$543$		0			0
$544$	−4.38604	+	12.0505i	−0.188050	+	0.516662i
$545$	−3.31642	−	18.8084i	−0.142060	−	0.805662i
$546$		0			0
$547$	−9.38962	−	7.87883i	−0.401471	−	0.336874i	0.419591	−	0.907713i	$-0.362174\pi$
$547$	−9.38962	−	7.87883i	−0.401471	−	0.336874i	−0.821062	+	0.570839i	$0.806618\pi$
$548$		−	13.9795i		−	0.597173i
$549$		0			0
$550$	−46.2909			−1.97385
$551$	2.21925	−	0.807742i	0.0945433	−	0.0344110i
$552$		0			0
$553$	−5.72542	−	32.9720i	−0.243470	−	1.40211i
$554$	3.55484	−	9.76683i	0.151031	−	0.414953i
$555$		0			0
$556$	−6.33446	+	7.54912i	−0.268641	+	0.320154i
$557$		−	21.4809i		−	0.910173i	−0.890447	−	0.455086i	$-0.849608\pi$
$557$		−	21.4809i		−	0.910173i	0.890447	−	0.455086i	$-0.150392\pi$
$558$		0			0
$559$	2.32400	+	1.34176i	0.0982945	+	0.0567504i
$560$	47.1216	−	17.0121i	1.99125	−	0.718893i
$561$		0			0
$562$	−8.06755	+	6.76948i	−0.340309	+	0.285553i
$563$	2.80189	+	15.8903i	0.118085	+	0.669696i	0.985176	+	0.171546i	$0.0548761\pi$
$563$	2.80189	+	15.8903i	0.118085	+	0.669696i	−0.867091	+	0.498150i	$0.834013\pi$
$564$		0			0
$565$	−19.7614	+	23.5507i	−0.831368	+	0.990786i
$566$	0.964001			0.0405200
$567$		0			0
$568$	9.32501			0.391269
$569$	17.0772	−	20.3518i	0.715912	−	0.853191i	−0.278314	−	0.960490i	$-0.589776\pi$
$569$	17.0772	−	20.3518i	0.715912	−	0.853191i	0.994227	+	0.107299i	$0.0342202\pi$
$570$		0			0
$571$	5.14784	+	29.1948i	0.215430	+	1.22177i	0.880158	+	0.474680i	$0.157436\pi$
$571$	5.14784	+	29.1948i	0.215430	+	1.22177i	−0.664728	+	0.747085i	$0.731453\pi$
$572$	6.92191	−	5.80817i	0.289420	−	0.242852i
$573$		0			0
$574$	13.7769	+	2.46622i	0.575036	+	0.102938i
$575$	−19.2582	−	11.1187i	−0.803124	−	0.463684i
$576$		0			0
$577$			36.2985i			1.51113i	0.655075	+	0.755564i	$0.272637\pi$
$577$			36.2985i			1.51113i	−0.655075	+	0.755564i	$0.727363\pi$
$578$	7.27982	−	8.67575i	0.302801	−	0.360864i
$579$		0			0
$580$	−1.01979	+	2.80184i	−0.0423443	+	0.116340i
$581$	11.0193	+	4.04321i	0.457159	+	0.167741i
$582$		0			0
$583$	−5.97783	+	2.17575i	−0.247577	+	0.0901105i
$584$	−4.62479			−0.191375
$585$		0			0
$586$		−	16.5120i		−	0.682105i
$587$	27.4601	+	23.0418i	1.13340	+	0.951035i	0.999203	−	0.0399198i	$-0.0127102\pi$
$587$	27.4601	+	23.0418i	1.13340	+	0.951035i	0.134196	+	0.990955i	$0.457155\pi$
$588$		0			0
$589$	3.41518	+	19.3684i	0.140720	+	0.798063i
$590$	−23.8141	+	65.4286i	−0.980410	+	2.69365i
$591$		0			0
$592$	−0.0209713	+	0.118934i	−0.000861913	+	0.00488815i
$593$	9.90996	+	17.1646i	0.406953	+	0.704864i	0.994547	−	0.104293i	$-0.0332578\pi$
$593$	9.90996	+	17.1646i	0.406953	+	0.704864i	−0.587593	+	0.809156i	$0.699924\pi$
$594$		0			0
$595$	32.3639	+	0.0842236i	1.32679	+	0.00345283i
$596$	3.37251	+	9.26590i	0.138143	+	0.379546i
$597$		0			0
$598$	15.7368	−	2.77481i	0.643524	−	0.113471i
$599$	−6.33165	+	17.3961i	−0.258704	+	0.710783i	0.740544	+	0.672008i	$0.234568\pi$
$599$	−6.33165	+	17.3961i	−0.258704	+	0.710783i	−0.999248	+	0.0387755i	$0.987654\pi$
$600$		0			0
$601$	−27.1016	+	32.2984i	−1.10550	+	1.31748i	−0.161741	+	0.986833i	$0.551711\pi$
$601$	−27.1016	+	32.2984i	−1.10550	+	1.31748i	−0.943755	+	0.330646i	$0.892734\pi$
$602$	0.00726407	−	2.79130i	0.000296062	−	0.113765i
$603$		0			0
$604$	−4.68468	+	8.11410i	−0.190617	+	0.330158i
$605$	8.05187	+	6.75632i	0.327355	+	0.274684i
$606$		0			0
$607$	40.5770	−	7.15482i	1.64697	−	0.290405i	0.728249	−	0.685313i	$-0.240335\pi$
$607$	40.5770	−	7.15482i	1.64697	−	0.290405i	0.918721	+	0.394908i	$0.129223\pi$
$608$	−8.56722	−	3.11821i	−0.347447	−	0.126460i
$609$		0			0
$610$	8.41400	−	47.7182i	0.340673	−	1.93205i
$611$	39.2237	+	22.6458i	1.58682	+	0.916153i
$612$		0			0
$613$	16.8946	+	29.2623i	0.682366	+	1.18189i	0.974257	+	0.225441i	$0.0723823\pi$
$613$	16.8946	+	29.2623i	0.682366	+	1.18189i	−0.291891	+	0.956452i	$0.594284\pi$
$614$	0.644094	−	3.65284i	0.0259935	−	0.147417i
$615$		0			0
$616$	14.8352	+	5.44334i	0.597728	+	0.219319i
$617$	−12.0622	−	14.3752i	−0.485607	−	0.578724i	0.466487	−	0.884528i	$-0.345519\pi$
$617$	−12.0622	−	14.3752i	−0.485607	−	0.578724i	−0.952095	+	0.305803i	$0.901075\pi$
$618$		0			0
$619$	−14.2587	−	2.51420i	−0.573107	−	0.101054i	−0.120419	−	0.992723i	$-0.538424\pi$
$619$	−14.2587	−	2.51420i	−0.573107	−	0.101054i	−0.452688	+	0.891669i	$0.649535\pi$
$620$	−21.5036	−	12.4151i	−0.863605	−	0.498602i
$621$		0			0
$622$			6.17140i			0.247451i
$623$	−9.56886	−	8.07176i	−0.383368	−	0.323388i
$624$		0			0
$625$	−19.6153	−	7.13939i	−0.784613	−	0.285576i
$626$	−22.6593	−	8.24731i	−0.905648	−	0.329629i
$627$		0			0
$628$	13.3222	+	2.34907i	0.531614	+	0.0937379i
$629$	−0.0390087	+	0.0675651i	−0.00155538	+	0.00269400i
$630$		0			0
$631$	3.09835	+	5.36650i	0.123343	+	0.213637i	0.921084	−	0.389363i	$-0.127305\pi$
$631$	3.09835	+	5.36650i	0.123343	+	0.213637i	−0.797741	+	0.603001i	$0.793972\pi$
$632$	8.99024	+	24.7005i	0.357613	+	0.982533i
$633$		0			0
$634$	1.55532	−	1.30507i	0.0617698	−	0.0518310i
$635$	4.51988	+	25.6335i	0.179366	+	1.01724i
$636$		0			0
$637$	29.0291	+	5.27454i	1.15017	+	0.208985i
$638$	−4.29731	+	2.48105i	−0.170132	+	0.0982259i
$639$		0			0
$640$	−44.3791	+	25.6223i	−1.75424	+	1.01281i
$641$	−2.87706	−	7.90466i	−0.113637	−	0.312215i	0.869817	−	0.493375i	$-0.164237\pi$
$641$	−2.87706	−	7.90466i	−0.113637	−	0.312215i	−0.983454	+	0.181160i	$0.942015\pi$
$642$		0			0
$643$	12.6614	−	2.23255i	0.499317	−	0.0880430i	0.0816827	−	0.996658i	$-0.473971\pi$
$643$	12.6614	−	2.23255i	0.499317	−	0.0880430i	0.417634	+	0.908615i	$0.362859\pi$
$644$	−2.89323	−	3.46630i	−0.114009	−	0.136591i
$645$		0			0
$646$	−9.17397	−	7.69787i	−0.360945	−	0.302869i
$647$	−3.45841	+	5.99014i	−0.135964	+	0.235497i	−0.925965	−	0.377609i	$-0.876747\pi$
$647$	−3.45841	+	5.99014i	−0.135964	+	0.235497i	0.790001	+	0.613105i	$0.210080\pi$
$648$		0			0
$649$	−27.2596	+	15.7383i	−1.07003	+	0.617784i
$650$	63.7926	−	23.2186i	2.50215	−	0.910708i
$651$		0			0
$652$	3.35918	−	2.81869i	0.131556	−	0.110388i
$653$	−4.91550	−	5.85806i	−0.192358	−	0.229244i	0.661241	−	0.750173i	$-0.270030\pi$
$653$	−4.91550	−	5.85806i	−0.192358	−	0.229244i	−0.853600	+	0.520930i	$0.825585\pi$
$654$		0			0
$655$	−72.4782	+	26.3799i	−2.83196	+	1.03075i
$656$	−15.7556			−0.615151
$657$		0			0
$658$	0.122601	−	47.1108i	0.00477948	−	1.83657i
$659$	5.58789	+	0.985295i	0.217673	+	0.0383817i	0.281421	−	0.959584i	$-0.409194\pi$
$659$	5.58789	+	0.985295i	0.217673	+	0.0383817i	−0.0637479	+	0.997966i	$0.520305\pi$
$660$		0			0
$661$	30.7788	+	36.6808i	1.19716	+	1.42672i	0.877763	+	0.479094i	$0.159035\pi$
$661$	30.7788	+	36.6808i	1.19716	+	1.42672i	0.319394	+	0.947622i	$0.396521\pi$
$662$	21.8258	+	26.0110i	0.848283	+	1.01094i
$663$		0			0
$664$	−9.07941	−	1.60094i	−0.352349	−	0.0621287i
$665$	−0.0598780	+	23.0088i	−0.00232197	+	0.892243i
$666$		0			0
$667$	−2.38373			−0.0922983
$668$	−5.81214	+	2.11545i	−0.224879	+	0.0818491i
$669$		0			0
$670$	−44.4242	−	52.9427i	−1.71626	−	2.04536i
$671$	16.7800	−	14.0801i	0.647787	−	0.543557i
$672$		0			0
$673$	−17.7107	+	6.44618i	−0.682699	+	0.248482i	−0.660006	−	0.751260i	$-0.729446\pi$
$673$	−17.7107	+	6.44618i	−0.682699	+	0.248482i	−0.0226931	+	0.999742i	$0.507224\pi$
$674$	−28.8168	+	16.6374i	−1.10998	+	0.640849i
$675$		0			0
$676$	−1.77729	+	3.07836i	−0.0683573	+	0.118398i
$677$	−9.98143	−	8.37542i	−0.383618	−	0.321893i	0.430503	−	0.902589i	$-0.358336\pi$
$677$	−9.98143	−	8.37542i	−0.383618	−	0.321893i	−0.814121	+	0.580696i	$0.802781\pi$
$678$		0			0
$679$	22.4099	+	26.8487i	0.860014	+	1.03036i
$680$	−25.0344	+	4.41424i	−0.960025	+	0.169278i
$681$		0			0
$682$	−14.1332	−	38.8306i	−0.541188	−	1.48690i
$683$	35.9360	−	20.7476i	1.37505	−	0.793886i	0.383493	−	0.923544i	$-0.374721\pi$
$683$	35.9360	−	20.7476i	1.37505	−	0.793886i	0.991559	+	0.129658i	$0.0413878\pi$
$684$		0			0
$685$	62.2710	−	35.9522i	2.37925	−	1.37366i
$686$	−10.2710	−	28.9198i	−0.392147	−	1.10416i
$687$		0			0
$688$	0.545648	+	3.09452i	0.0208026	+	0.117978i
$689$	7.14662	−	5.99672i	0.272264	−	0.228457i
$690$		0			0
$691$	2.20345	+	6.05394i	0.0838234	+	0.230303i	0.974522	−	0.224291i	$-0.0720066\pi$
$691$	2.20345	+	6.05394i	0.0838234	+	0.230303i	−0.890699	+	0.454594i	$0.849784\pi$
$692$	−7.28201	−	12.6128i	−0.276821	−	0.479467i
$693$		0			0
$694$	0.522571	−	0.905120i	0.0198365	−	0.0343579i
$695$	−49.9182	−	8.80193i	−1.89351	−	0.333876i
$696$		0			0
$697$	−9.56439	−	3.48115i	−0.362277	−	0.131858i
$698$	−2.65121	−	0.964963i	−0.100350	−	0.0365244i
$699$		0			0
$700$	−14.6619	−	12.3679i	−0.554167	−	0.467464i
$701$			10.7905i			0.407550i	0.979018	+	0.203775i	$0.0653211\pi$
$701$			10.7905i			0.407550i	−0.979018	+	0.203775i	$0.934679\pi$
$702$		0			0
$703$	−0.0480348	−	0.0277329i	−0.00181167	−	0.00104597i
$704$	−9.07397	−	1.59999i	−0.341988	−	0.0603017i
$705$		0			0
$706$	25.4661	+	30.3493i	0.958428	+	1.14221i
$707$	−6.74125	−	2.47350i	−0.253531	−	0.0930255i
$708$		0			0
$709$	8.07759	−	45.8103i	0.303360	−	1.72044i	−0.327765	−	0.944759i	$-0.606295\pi$
$709$	8.07759	−	45.8103i	0.303360	−	1.72044i	0.631125	−	0.775681i	$-0.282594\pi$
$710$	−14.2639	−	24.7058i	−0.535315	−	0.927194i
$711$		0			0
$712$	8.51553	+	4.91644i	0.319133	+	0.184252i
$713$	3.44706	−	19.5493i	0.129093	−	0.732126i
$714$		0			0
$715$	43.6740	+	15.8960i	1.63332	+	0.594478i
$716$	2.17721	−	0.383900i	0.0813660	−	0.0143470i
$717$		0			0
$718$	−15.8823	−	13.3268i	−0.592722	−	0.497353i
$719$	7.91160	−	13.7033i	0.295053	−	0.511047i	−0.679944	−	0.733264i	$-0.737996\pi$
$719$	7.91160	−	13.7033i	0.295053	−	0.511047i	0.974997	+	0.222217i	$0.0713294\pi$
$720$		0			0
$721$	0.0672258	−	25.8323i	0.00250362	−	0.962045i
$722$	−14.7651	+	17.5964i	−0.549500	+	0.654869i
$723$		0			0
$724$	−6.49916	+	17.8563i	−0.241540	+	0.663624i
$725$	−9.97306	+	1.75852i	−0.370390	+	0.0653098i
$726$		0			0
$727$	11.4600	+	31.4861i	0.425028	+	1.16775i	0.948795	+	0.315893i	$0.102304\pi$
$727$	11.4600	+	31.4861i	0.425028	+	1.16775i	−0.523767	+	0.851862i	$0.675474\pi$
$728$	−23.1744	−	0.0603089i	−0.858900	−	0.00223520i
$729$		0			0
$730$	7.07427	+	12.2530i	0.261831	+	0.453504i
$731$	−0.352493	+	1.99909i	−0.0130374	+	0.0739388i
$732$		0			0
$733$	1.99386	−	5.47809i	0.0736449	−	0.202338i	−0.897408	−	0.441201i	$-0.854553\pi$
$733$	1.99386	−	5.47809i	0.0736449	−	0.202338i	0.971053	+	0.238863i	$0.0767748\pi$
$734$	3.79329	+	21.5128i	0.140013	+	0.794053i
$735$		0			0
$736$	7.04927	+	5.91504i	0.259839	+	0.218031i
$737$		−	31.2435i		−	1.15087i
$738$		0			0
$739$	−45.4032			−1.67019			−0.835093	−	0.550109i	$-0.814586\pi$
$739$	−45.4032			−1.67019			−0.835093	+	0.550109i	$0.814586\pi$
$740$	0.0658034	−	0.0239505i	0.00241898	−	0.000880437i
$741$		0			0
$742$	−9.11010	−	3.34268i	−0.334442	−	0.122714i
$743$	−8.03623	+	22.0794i	−0.294821	+	0.810013i	0.700524	+	0.713629i	$0.252950\pi$
$743$	−8.03623	+	22.0794i	−0.294821	+	0.810013i	−0.995344	+	0.0963839i	$0.969272\pi$
$744$		0			0
$745$	−32.6013	+	38.8527i	−1.19442	+	1.42345i
$746$		−	18.5599i		−	0.679526i
$747$		0			0
$748$	5.91940	+	3.41757i	0.216435	+	0.124959i
$749$	36.7749	+	6.58314i	1.34373	+	0.240543i
$750$		0			0
$751$	17.6288	−	14.7923i	0.643283	−	0.539779i	−0.261741	−	0.965138i	$-0.584297\pi$
$751$	17.6288	−	14.7923i	0.643283	−	0.539779i	0.905024	+	0.425359i	$0.139852\pi$
$752$	9.20929	+	52.2285i	0.335828	+	1.90458i
$753$		0			0
$754$	4.67759	−	5.57454i	0.170348	−	0.203013i
$755$	−48.1920			−1.75389
$756$		0			0
$757$	−0.0748603			−0.00272084			−0.00136042	−	0.999999i	$-0.500433\pi$
$757$	−0.0748603			−0.00272084			−0.00136042	+	0.999999i	$0.500433\pi$
$758$	6.65460	−	7.93065i	0.241706	−	0.288054i
$759$		0			0
$760$	−3.13827	−	17.7980i	−0.113837	−	0.645601i
$761$	−2.28947	+	1.92109i	−0.0829931	+	0.0696395i	−0.683340	−	0.730100i	$-0.739473\pi$
$761$	−2.28947	+	1.92109i	−0.0829931	+	0.0696395i	0.600347	+	0.799739i	$0.295029\pi$
$762$		0			0
$763$	12.3878	−	4.47232i	0.448469	−	0.161909i
$764$	14.6451	+	8.45534i	0.529840	+	0.305903i
$765$		0			0
$766$			23.7606i			0.858504i
$767$	29.6719	−	35.3616i	1.07139	−	1.27683i
$768$		0			0
$769$	−5.62460	+	15.4535i	−0.202828	+	0.557266i	−0.998847	−	0.0480060i	$-0.984713\pi$
$769$	−5.62460	+	15.4535i	−0.202828	+	0.557266i	0.796019	+	0.605272i	$0.206936\pi$
$770$	−8.27089	−	47.6311i	−0.298062	−	1.71650i
$771$		0			0
$772$	−10.4619	+	3.80782i	−0.376532	+	0.137046i
$773$	39.0394			1.40415			0.702074	−	0.712104i	$-0.252257\pi$
$773$	39.0394			1.40415			0.702074	+	0.712104i	$0.252257\pi$
$774$		0			0
$775$		−	84.3334i		−	3.02934i
$776$	−21.0427	−	17.6569i	−0.755388	−	0.633846i
$777$		0			0
$778$	2.48453	+	14.0905i	0.0890747	+	0.505168i
$779$	2.47490	−	6.79972i	0.0886723	−	0.243625i
$780$		0			0
$781$	2.23947	−	12.7007i	0.0801347	−	0.454467i
$782$	6.04378	+	10.4681i	0.216125	+	0.374340i
$783$		0			0
$784$	17.1181	+	30.0090i	0.611360	+	1.07175i
$785$	23.7981	+	65.3847i	0.849390	+	2.33368i
$786$		0			0
$787$	4.74409	−	0.836511i	0.169108	−	0.0298184i	−0.0884527	−	0.996080i	$-0.528192\pi$
$787$	4.74409	−	0.836511i	0.169108	−	0.0298184i	0.257561	+	0.966262i	$0.417081\pi$
$788$	−4.86477	+	13.3658i	−0.173300	+	0.476139i
$789$		0			0
$790$	51.6900	−	61.6018i	1.83905	−	2.19169i
$791$	−18.3327	−	10.6481i	−0.651834	−	0.378602i
$792$		0			0
$793$	−16.0619	+	27.8201i	−0.570376	+	0.987920i
$794$	0.00922671	+	0.00774213i	0.000327444	+	0.000274758i
$795$		0			0
$796$	−4.26629	+	0.752263i	−0.151215	+	0.0266632i
$797$	16.1079	+	5.86280i	0.570572	+	0.207671i	0.611163	−	0.791505i	$-0.290702\pi$
$797$	16.1079	+	5.86280i	0.570572	+	0.207671i	−0.0405913	+	0.999176i	$0.512924\pi$
$798$		0			0
$799$	−5.94927	+	33.7400i	−0.210470	+	1.19364i
$800$	33.8564	+	19.5470i	1.19701	+	0.691091i
$801$		0			0
$802$	12.5525	+	21.7416i	0.443245	+	0.767723i
$803$	−1.11068	+	6.29898i	−0.0391950	+	0.222286i
$804$		0			0
$805$	7.99974	−	21.8024i	0.281954	−	0.768433i
$806$	38.9533	+	46.4228i	1.37207	+	1.63517i
$807$		0			0
$808$	5.55447	+	0.979403i	0.195406	+	0.0344553i
$809$	−1.45376	−	0.839326i	−0.0511113	−	0.0295091i	0.474227	−	0.880403i	$-0.342728\pi$
$809$	−1.45376	−	0.839326i	−0.0511113	−	0.0295091i	−0.525338	+	0.850894i	$0.676061\pi$
$810$		0			0
$811$			24.2899i			0.852933i	0.904503	+	0.426467i	$0.140242\pi$
$811$			24.2899i			0.852933i	−0.904503	+	0.426467i	$0.859758\pi$
$812$	−2.02399	−	0.362317i	−0.0710280	−	0.0127148i
$813$		0			0
$814$	0.109511	+	0.0398587i	0.00383835	+	0.00139705i
$815$	21.1949	+	7.71430i	0.742423	+	0.270220i
$816$		0			0
$817$	−1.42123	−	0.250602i	−0.0497226	−	0.00876744i
$818$	−8.48147	+	14.6903i	−0.296548	+	0.513636i
$819$		0			0
$820$	4.56785	+	7.91175i	0.159516	+	0.276290i
$821$	−0.666808	−	1.83204i	−0.0232718	−	0.0639386i	0.927513	−	0.373791i	$-0.121942\pi$
$821$	−0.666808	−	1.83204i	−0.0232718	−	0.0639386i	−0.950785	+	0.309853i	$0.899720\pi$
$822$		0			0
$823$	21.0262	−	17.6431i	0.732928	−	0.615000i	−0.198000	−	0.980202i	$-0.563445\pi$
$823$	21.0262	−	17.6431i	0.732928	−	0.615000i	0.930928	+	0.365202i	$0.119000\pi$
$824$	3.52337	+	19.9820i	0.122742	+	0.696107i
$825$		0			0
$826$	−47.2642	−	8.46083i	−1.64453	−	0.294390i
$827$	39.0581	−	22.5502i	1.35818	−	0.784147i	0.368804	−	0.929507i	$-0.379767\pi$
$827$	39.0581	−	22.5502i	1.35818	−	0.784147i	0.989379	+	0.145360i	$0.0464340\pi$
$828$		0			0
$829$	31.0293	−	17.9148i	1.07769	−	0.622207i	0.147420	−	0.989074i	$-0.452903\pi$
$829$	31.0293	−	17.9148i	1.07769	−	0.622207i	0.930273	+	0.366867i	$0.119570\pi$
$830$	9.64667	+	26.5040i	0.334841	+	0.919967i
$831$		0			0
$832$	13.3072	−	2.34641i	0.461343	−	0.0813473i
$833$	3.76108	+	21.9991i	0.130314	+	0.762224i
$834$		0			0
$835$	−24.3708	−	20.4495i	−0.843386	−	0.707685i
$836$	−2.42969	+	4.20835i	−0.0840326	+	0.145549i
$837$		0			0
$838$	57.2173	−	33.0344i	1.97654	−	1.14115i
$839$	−30.2589	+	11.0133i	−1.04465	+	0.380222i	−0.806642	−	0.591040i	$-0.798717\pi$
$839$	−30.2589	+	11.0133i	−1.04465	+	0.380222i	−0.238010	+	0.971263i	$0.576495\pi$
$840$		0			0
$841$	21.3837	−	17.9431i	0.737369	−	0.618726i
$842$	23.4021	+	27.8895i	0.806490	+	0.961137i
$843$		0			0
$844$	0.728852	−	0.265281i	0.0250881	−	0.00913133i
$845$	−18.2833			−0.628963
$846$		0			0
$847$	−3.64053	+	6.26785i	−0.125090	+	0.215366i
$848$	10.7581	+	1.89694i	0.369435	+	0.0651413i
$849$		0			0
$850$	33.0086	+	39.3381i	1.13218	+	1.34929i
$851$	0.0359856	+	0.0428860i	0.00123357	+	0.00147011i
$852$		0			0
$853$	−29.8196	−	5.25801i	−1.02100	−	0.180031i	−0.362007	−	0.932175i	$-0.617908\pi$
$853$	−29.8196	−	5.25801i	−1.02100	−	0.180031i	−0.658998	+	0.752145i	$0.729019\pi$
$854$	33.4141	+	0.0869568i	1.14341	+	0.00297560i
$855$		0			0
$856$	−29.3444			−1.00297
$857$	−43.6527	+	15.8883i	−1.49115	+	0.542734i	−0.953752	−	0.300596i	$-0.902814\pi$
$857$	−43.6527	+	15.8883i	−1.49115	+	0.542734i	−0.537397	+	0.843329i	$0.680592\pi$
$858$		0			0
$859$	29.6335	+	35.3158i	1.01108	+	1.20496i	0.978660	+	0.205487i	$0.0658778\pi$
$859$	29.6335	+	35.3158i	1.01108	+	1.20496i	0.0324227	+	0.999474i	$0.489678\pi$
$860$	1.39574	−	1.17116i	0.0475943	−	0.0399364i
$861$		0			0
$862$	−10.1037	+	3.67746i	−0.344135	+	0.125255i
$863$	2.45633	−	1.41816i	0.0836143	−	0.0482748i	−0.457610	−	0.889153i	$-0.651294\pi$
$863$	2.45633	−	1.41816i	0.0836143	−	0.0482748i	0.541224	+	0.840878i	$0.317961\pi$
$864$		0			0
$865$	37.4556	−	64.8750i	1.27353	−	2.20582i
$866$	−1.88580	−	1.58237i	−0.0640819	−	0.0537711i
$867$		0			0
$868$	5.89826	−	16.0751i	0.200200	−	0.545623i
$869$	35.8012	−	6.31272i	1.21447	−	0.214144i
$870$		0			0
$871$	15.6711	+	43.0560i	0.530995	+	1.45890i
$872$	−8.95888	+	5.17241i	−0.303386	+	0.175160i
$873$		0			0
$874$	−7.44223	+	4.29678i	−0.251737	+	0.145341i
$875$	8.44200	−	47.1590i	0.285392	−	1.59426i
$876$		0			0
$877$	−8.55341	−	48.5088i	−0.288828	−	1.63803i	−0.691282	−	0.722585i	$-0.742954\pi$
$877$	−8.55341	−	48.5088i	−0.288828	−	1.63803i	0.402454	−	0.915440i	$-0.368157\pi$
$878$	−16.0053	+	13.4300i	−0.540151	+	0.453241i
$879$		0			0
$880$	18.6134	+	51.1400i	0.627459	+	1.72393i
$881$	13.9157	+	24.1027i	0.468833	+	0.812042i	0.999365	−	0.0356225i	$-0.0113414\pi$
$881$	13.9157	+	24.1027i	0.468833	+	0.812042i	−0.530533	+	0.847664i	$0.678008\pi$
$882$		0			0
$883$	20.7815	−	35.9946i	0.699354	−	1.21132i	−0.269337	−	0.963046i	$-0.586805\pi$
$883$	20.7815	−	35.9946i	0.699354	−	1.21132i	0.968691	−	0.248270i	$-0.0798621\pi$
$884$	−9.87159	−	1.74063i	−0.332017	−	0.0585436i
$885$		0			0
$886$	−2.42190	−	0.881500i	−0.0813654	−	0.0296146i
$887$	−24.9185	−	9.06959i	−0.836681	−	0.304527i	−0.112083	−	0.993699i	$-0.535752\pi$
$887$	−24.9185	−	9.06959i	−0.836681	−	0.304527i	−0.724598	+	0.689172i	$0.757974\pi$
$888$		0			0
$889$	−16.8831	+	6.09523i	−0.566241	+	0.204427i
$890$		−	30.0816i		−	1.00834i
$891$		0			0
$892$	4.97559	+	2.87266i	0.166595	+	0.0961836i
$893$	−23.9872	−	4.22958i	−0.802700	−	0.141538i
$894$		0			0
$895$	7.30939	+	8.71099i	0.244326	+	0.291176i
$896$	−22.6446	−	27.1298i	−0.756502	−	0.906343i
$897$		0			0
$898$	−1.23380	+	6.99722i	−0.0411724	+	0.233500i
$899$	−4.52002	−	7.82890i	−0.150751	−	0.261108i
$900$		0			0
$901$	6.11156	+	3.52851i	0.203606	+	0.117552i
$902$	−2.64010	+	14.9728i	−0.0879058	+	0.498538i
$903$		0			0
$904$	15.6480	+	5.69541i	0.520445	+	0.189426i
$905$	−96.2548	+	16.9723i	−3.19962	+	0.564179i
$906$		0			0
$907$	−9.86503	−	8.27774i	−0.327563	−	0.274858i	0.464143	−	0.885760i	$-0.346362\pi$
$907$	−9.86503	−	8.27774i	−0.327563	−	0.274858i	−0.791706	+	0.610902i	$0.790807\pi$
$908$	−1.20938	+	2.09471i	−0.0401348	+	0.0695155i
$909$		0			0
$910$	35.2887	+	61.4909i	1.16981	+	2.03840i
$911$	1.43534	−	1.71057i	0.0475550	−	0.0566738i	−0.741743	−	0.670685i	$-0.766000\pi$
$911$	1.43534	−	1.71057i	0.0475550	−	0.0566738i	0.789298	+	0.614011i	$0.210445\pi$
$912$		0			0
$913$	−4.36098	+	11.9817i	−0.144327	+	0.396536i
$914$	−24.7005	+	4.35537i	−0.817020	+	0.144063i
$915$		0			0
$916$	5.57667	+	15.3218i	0.184258	+	0.506245i
$917$	−26.4745	−	46.1320i	−0.874265	−	1.52341i
$918$		0			0
$919$	−9.06589	−	15.7026i	−0.299056	−	0.517980i	0.676864	−	0.736108i	$-0.263338\pi$
$919$	−9.06589	−	15.7026i	−0.299056	−	0.517980i	−0.975920	+	0.218128i	$0.930005\pi$
$920$	−3.16756	+	17.9641i	−0.104431	+	0.592260i
$921$		0			0
$922$	3.94909	−	10.8500i	0.130056	−	0.357327i
$923$	3.28424	+	18.6258i	0.108102	+	0.613077i
$924$		0			0
$925$	0.182195	+	0.152880i	0.00599053	+	0.00502665i
$926$		−	66.9281i		−	2.19939i
$927$		0			0
$928$	4.19065			0.137565
$929$	−18.1050	+	6.58967i	−0.594005	+	0.216200i	−0.621490	−	0.783422i	$-0.713472\pi$
$929$	−18.1050	+	6.58967i	−0.594005	+	0.216200i	0.0274852	+	0.999622i	$0.491250\pi$
$930$		0			0
$931$	−15.6401	+	2.67391i	−0.512583	+	0.0876339i
$932$	−2.37638	+	6.52906i	−0.0778410	+	0.213866i
$933$		0			0
$934$	8.97897	−	10.7007i	0.293801	−	0.350138i
$935$			35.1570i			1.14976i
$936$		0			0
$937$	−26.1439	−	15.0942i	−0.854085	−	0.493106i	0.00794190	−	0.999968i	$-0.497472\pi$
$937$	−26.1439	−	15.0942i	−0.854085	−	0.493106i	−0.862027	+	0.506862i	$0.830805\pi$
$938$	30.7300	−	36.4296i	1.00337	−	1.18947i
$939$		0			0
$940$	23.5569	−	19.7666i	0.768341	−	0.644715i
$941$	−0.539980	−	3.06238i	−0.0176028	−	0.0998306i	0.974741	−	0.223340i	$-0.0716961\pi$
$941$	−0.539980	−	3.06238i	−0.0176028	−	0.0998306i	−0.992343	+	0.123510i	$0.960585\pi$
$942$		0			0
$943$	−4.69470	+	5.59493i	−0.152881	+	0.182196i
$944$	54.0524			1.75926
$945$		0			0
$946$	3.03221			0.0985856
$947$	32.0105	−	38.1487i	1.04020	−	1.23967i	0.0699551	−	0.997550i	$-0.477714\pi$
$947$	32.0105	−	38.1487i	1.04020	−	1.23967i	0.970248	−	0.242115i	$-0.0778412\pi$
$948$		0			0
$949$	−1.62884	−	9.23759i	−0.0528743	−	0.299865i
$950$	−27.9671	+	23.4672i	−0.907372	+	0.761375i
$951$		0			0
$952$	−5.95277	−	16.4885i	−0.192930	−	0.534395i
$953$	24.6725	+	14.2447i	0.799222	+	0.461431i	0.843199	−	0.537602i	$-0.180670\pi$
$953$	24.6725	+	14.2447i	0.799222	+	0.461431i	−0.0439773	+	0.999033i	$0.514003\pi$
$954$		0			0
$955$			86.9814i			2.81465i
$956$	2.92823	−	3.48972i	0.0947056	−	0.112866i
$957$		0			0
$958$	13.0460	−	35.8436i	0.421498	−	1.15806i
$959$	31.7740	+	38.0675i	1.02604	+	1.22926i
$960$		0			0
$961$	41.6117	−	15.1454i	1.34231	−	0.488562i
$962$	−0.170907			−0.00551026
$963$		0			0
$964$		−	0.248221i		−	0.00799467i
$965$	−43.8676	−	36.8093i	−1.41215	−	1.18493i
$966$		0			0
$967$	0.546444	+	3.09904i	0.0175725	+	0.0996584i	0.992333	−	0.123597i	$-0.0394429\pi$
$967$	0.546444	+	3.09904i	0.0175725	+	0.0996584i	−0.974760	+	0.223255i	$0.928332\pi$
$968$	1.94723	−	5.34998i	0.0625864	−	0.171955i
$969$		0			0
$970$	−14.5927	+	82.7596i	−0.468545	+	2.65725i
$971$	11.2478	+	19.4817i	0.360958	+	0.625197i	0.988119	−	0.153693i	$-0.0491165\pi$
$971$	11.2478	+	19.4817i	0.360958	+	0.625197i	−0.627161	+	0.778890i	$0.715783\pi$
$972$		0			0
$973$	0.0909659	−	34.9547i	0.00291623	−	1.12060i
$974$	−14.9814	−	41.1610i	−0.480034	−	1.31888i
$975$		0			0
$976$	−37.0439	+	6.53184i	−1.18575	+	0.209079i
$977$	15.2909	−	42.0113i	0.489198	−	1.34406i	−0.412209	−	0.911089i	$-0.635243\pi$
$977$	15.2909	−	42.0113i	0.489198	−	1.34406i	0.901407	−	0.432972i	$-0.142535\pi$
$978$		0			0
$979$	8.74128	−	10.4175i	0.279373	−	0.332943i
$980$	10.1063	−	17.2962i	0.322835	−	0.552506i
$981$		0			0
$982$	−10.8234	+	18.7467i	−0.345389	+	0.598231i
$983$	0.625742	+	0.525060i	0.0199581	+	0.0167468i	0.652712	−	0.757606i	$-0.273631\pi$
$983$	0.625742	+	0.525060i	0.0199581	+	0.0167468i	−0.632754	+	0.774353i	$0.718076\pi$
$984$		0			0
$985$	−72.0489	+	12.7042i	−2.29567	+	0.404788i
$986$	5.17268	+	1.88270i	0.164732	+	0.0599574i
$987$		0			0
$988$	1.23748	−	7.01812i	0.0393696	−	0.223276i
$989$	1.26148	+	0.728315i	0.0401127	+	0.0231591i
$990$		0			0
$991$	5.41879	+	9.38562i	0.172134	+	0.298144i	0.939166	−	0.343465i	$-0.111601\pi$
$991$	5.41879	+	9.38562i	0.172134	+	0.298144i	−0.767032	+	0.641609i	$0.778267\pi$
$992$	−6.06001	+	34.3681i	−0.192406	+	1.09119i
$993$		0			0
$994$	15.1032	−	12.6062i	0.479044	−	0.399845i
$995$	−14.3229	−	17.0694i	−0.454068	−	0.541137i
$996$		0			0
$997$	50.1411	+	8.84122i	1.58798	+	0.280004i	0.896720	−	0.442598i	$-0.145943\pi$
$997$	50.1411	+	8.84122i	1.58798	+	0.280004i	0.691264	+	0.722603i	$0.257054\pi$
$998$	−37.1151	−	21.4284i	−1.17486	−	0.678305i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.ba.a.143.5		132
3.2	odd	2		189.2.ba.a.101.18	✓	132
7.5	odd	6		567.2.bd.a.467.18		132
21.5	even	6		189.2.bd.a.47.5	yes	132
27.4	even	9		189.2.bd.a.185.5	yes	132
27.23	odd	18		567.2.bd.a.17.18		132
189.131	even	18	inner	567.2.ba.a.341.5		132
189.166	odd	18		189.2.ba.a.131.18	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.18	✓	132	3.2	odd	2
189.2.ba.a.131.18	yes	132	189.166	odd	18
189.2.bd.a.47.5	yes	132	21.5	even	6
189.2.bd.a.185.5	yes	132	27.4	even	9
567.2.ba.a.143.5		132	1.1	even	1	trivial
567.2.ba.a.341.5		132	189.131	even	18	inner
567.2.bd.a.17.18		132	27.23	odd	18
567.2.bd.a.467.18		132	7.5	odd	6

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.ba (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.06515 + 1.26940i) q^{2} +(-0.129525 - 0.734574i) q^{4} +(2.93903 - 2.46614i) q^{5} +(2.02233 + 1.70592i) q^{7} +(-1.79971 - 1.03907i) q^{8} +O(q^{10})\)	\(q+(-1.06515 + 1.26940i) q^{2} +(-0.129525 - 0.734574i) q^{4} +(2.93903 - 2.46614i) q^{5} +(2.02233 + 1.70592i) q^{7} +(-1.79971 - 1.03907i) q^{8} +6.35759i q^{10} +(-1.84743 + 2.20168i) q^{11} +(1.44158 - 3.96072i) q^{13} +(-4.31958 + 0.750072i) q^{14} +(4.63779 - 1.68802i) q^{16} +3.18833 q^{17} +2.26672i q^{19} +(-2.19224 - 1.83951i) q^{20} +(-0.827014 - 4.69023i) q^{22} +(0.782500 - 2.14990i) q^{23} +(1.68781 - 9.57204i) q^{25} +(3.49221 + 6.04869i) q^{26} +(0.991186 - 1.70651i) q^{28} +(-0.356349 - 0.979061i) q^{29} +(8.54472 - 1.50666i) q^{31} +(-1.37565 + 3.77958i) q^{32} +(-3.39605 + 4.04725i) q^{34} +(10.1507 + 0.0264162i) q^{35} +(-0.0122349 + 0.0211914i) q^{37} +(-2.87736 - 2.41439i) q^{38} +(-7.85188 + 1.38450i) q^{40} +(-2.99981 - 1.09184i) q^{41} +(-0.110557 + 0.627001i) q^{43} +(1.85658 + 1.07190i) q^{44} +(1.89560 + 3.28327i) q^{46} +(-1.86595 + 10.5823i) q^{47} +(1.17964 + 6.89989i) q^{49} +(10.3529 + 12.3382i) q^{50} +(-3.09616 - 0.545937i) q^{52} +(1.91685 + 1.10670i) q^{53} +11.0268i q^{55} +(-1.86705 - 5.17151i) q^{56} +(1.62238 + 0.590498i) q^{58} +(10.2914 + 3.74577i) q^{59} +(-7.50570 - 1.32346i) q^{61} +(-7.18884 + 12.4514i) q^{62} +(1.60294 + 2.77637i) q^{64} +(-5.53082 - 15.1958i) q^{65} +(-8.32749 + 6.98759i) q^{67} +(-0.412969 - 2.34207i) q^{68} +(-10.8456 + 12.8571i) q^{70} +(-3.88604 + 2.24361i) q^{71} +(1.92730 - 1.11273i) q^{73} +(-0.0138683 - 0.0381028i) q^{74} +(1.66507 - 0.293597i) q^{76} +(-7.49200 + 1.30095i) q^{77} +(-9.68949 - 8.13045i) q^{79} +(9.46771 - 16.3986i) q^{80} +(4.58122 - 2.64497i) q^{82} +(4.16888 - 1.51735i) q^{83} +(9.37059 - 7.86286i) q^{85} +(-0.678152 - 0.808190i) q^{86} +(5.61252 - 2.04279i) q^{88} -4.73160 q^{89} +(9.67205 - 5.55065i) q^{91} +(-1.68062 - 0.296338i) q^{92} +(-11.4457 - 13.6404i) q^{94} +(5.59003 + 6.66194i) q^{95} +(13.0174 + 2.29533i) q^{97} +(-10.0152 - 5.85198i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34} - 18 q^{35} + 3 q^{37} + 99 q^{38} - 54 q^{40} - 12 q^{43} + 9 q^{44} + 3 q^{46} - 45 q^{47} - 24 q^{49} + 9 q^{50} - 9 q^{52} + 45 q^{53} - 3 q^{56} - 3 q^{58} - 36 q^{59} - 9 q^{61} + 99 q^{62} + 18 q^{64} - 69 q^{65} - 3 q^{67} - 36 q^{68} + 66 q^{70} - 18 q^{71} - 9 q^{73} - 75 q^{74} + 36 q^{76} - 15 q^{77} - 21 q^{79} - 72 q^{80} - 18 q^{82} + 90 q^{83} + 9 q^{85} + 105 q^{86} - 63 q^{88} + 18 q^{89} + 6 q^{91} - 150 q^{92} - 9 q^{94} - 45 q^{95} - 27 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

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