LMFDB - Embedded newform 324.2.l.a.143.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [324,2,Mod(35,324)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(324, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("324.35"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.l (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			143.14
Character	$\chi$	$=$	324.143
Dual form			324.2.l.a.179.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.30706 + 0.540000i) q^{2} +(1.41680 + 1.41162i) q^{4} +(-0.137245 + 0.0242000i) q^{5} +(2.98823 - 3.56123i) q^{7} +(1.08956 + 2.61015i) q^{8} +(-0.192456 - 0.0424817i) q^{10} +(-0.182573 + 1.03542i) q^{11} +(-1.46220 - 0.532196i) q^{13} +(5.82886 - 3.04109i) q^{14} +(0.0146392 + 3.99997i) q^{16} +(-5.25631 + 3.03473i) q^{17} +(3.80088 + 2.19444i) q^{19} +(-0.228610 - 0.159452i) q^{20} +(-0.797761 + 1.25477i) q^{22} +(1.94128 - 1.62893i) q^{23} +(-4.68021 + 1.70346i) q^{25} +(-1.62379 - 1.48520i) q^{26} +(9.26084 - 0.827297i) q^{28} +(-0.210458 - 0.578229i) q^{29} +(-3.18818 - 3.79952i) q^{31} +(-2.14085 + 5.23610i) q^{32} +(-8.50906 + 1.12816i) q^{34} +(-0.323938 + 0.561078i) q^{35} +(-1.43991 - 2.49400i) q^{37} +(3.78297 + 4.92073i) q^{38} +(-0.212703 - 0.331863i) q^{40} +(2.25297 - 6.18999i) q^{41} +(-2.15530 - 0.380038i) q^{43} +(-1.72029 + 1.20926i) q^{44} +(3.41698 - 1.08081i) q^{46} +(-8.46639 - 7.10414i) q^{47} +(-2.53733 - 14.3899i) q^{49} +(-7.03718 - 0.300799i) q^{50} +(-1.32038 - 2.81809i) q^{52} +8.73360i q^{53} -0.146525i q^{55} +(12.5512 + 3.91953i) q^{56} +(0.0371630 - 0.869426i) q^{58} +(-1.42477 - 8.08025i) q^{59} +(8.56477 + 7.18670i) q^{61} +(-2.11539 - 6.68781i) q^{62} +(-5.62571 + 5.68782i) q^{64} +(0.213559 + 0.0376562i) q^{65} +(-1.93034 + 5.30357i) q^{67} +(-11.7310 - 3.12033i) q^{68} +(-0.726388 + 0.558434i) q^{70} +(2.33277 + 4.04048i) q^{71} +(-5.64518 + 9.77774i) q^{73} +(-0.535287 - 4.03736i) q^{74} +(2.28736 + 8.47449i) q^{76} +(3.14181 + 3.74426i) q^{77} +(-0.572755 - 1.57363i) q^{79} +(-0.0988087 - 0.548623i) q^{80} +(6.28736 - 6.87406i) q^{82} +(2.20553 - 0.802749i) q^{83} +(0.647964 - 0.543706i) q^{85} +(-2.61188 - 1.66060i) q^{86} +(-2.90152 + 0.651613i) q^{88} +(-7.63741 - 4.40946i) q^{89} +(-6.26466 + 3.61690i) q^{91} +(5.04983 + 0.432493i) q^{92} +(-7.22981 - 13.8574i) q^{94} +(-0.574758 - 0.209195i) q^{95} +(-0.978443 + 5.54902i) q^{97} +(4.45412 - 20.1786i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38}+ \cdots + 180 q^{98}+O(q^{100}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$

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 $

$2$	1.30706	+	0.540000i	0.924229	+	0.381838i
$2$	1.30706	+	0.540000i	0.924229	+	0.381838i
$3$		0			0
$3$		0			0
$4$	1.41680	+	1.41162i	0.708400	+	0.705812i
$5$	−0.137245	+	0.0242000i	−0.0613780	+	0.0108226i	−0.204253	−	0.978918i	$-0.565476\pi$
$5$	−0.137245	+	0.0242000i	−0.0613780	+	0.0108226i	0.142875	+	0.989741i	$0.454365\pi$
$6$		0			0
$7$	2.98823	−	3.56123i	1.12944	−	1.34602i	0.198824	−	0.980035i	$-0.436288\pi$
$7$	2.98823	−	3.56123i	1.12944	−	1.34602i	0.930621	−	0.365984i	$-0.119268\pi$
$8$	1.08956	+	2.61015i	0.385218	+	0.922826i
$9$		0			0
$10$	−0.192456	−	0.0424817i	−0.0608598	−	0.0134339i
$11$	−0.182573	+	1.03542i	−0.0550477	+	0.312191i	−0.999882	−	0.0153574i	$-0.995111\pi$
$11$	−0.182573	+	1.03542i	−0.0550477	+	0.312191i	0.944834	+	0.327549i	$0.106223\pi$
$12$		0			0
$13$	−1.46220	−	0.532196i	−0.405541	−	0.147605i	0.131192	−	0.991357i	$-0.458119\pi$
$13$	−1.46220	−	0.532196i	−0.405541	−	0.147605i	−0.536733	+	0.843752i	$0.680342\pi$
$14$	5.82886	−	3.04109i	1.55783	−	0.812766i
$15$		0			0
$16$	0.0146392	+	3.99997i	0.00365980	+	0.999993i
$17$	−5.25631	+	3.03473i	−1.27484	+	0.736031i	−0.975895	−	0.218238i	$-0.929969\pi$
$17$	−5.25631	+	3.03473i	−1.27484	+	0.736031i	−0.298948	+	0.954269i	$0.596636\pi$
$18$		0			0
$19$	3.80088	+	2.19444i	0.871981	+	0.503439i	0.868006	−	0.496553i	$-0.165401\pi$
$19$	3.80088	+	2.19444i	0.871981	+	0.503439i	0.00397518	+	0.999992i	$0.498735\pi$
$20$	−0.228610	−	0.159452i	−0.0511188	−	0.0356546i
$21$		0			0
$22$	−0.797761	+	1.25477i	−0.170083	+	0.267517i
$23$	1.94128	−	1.62893i	0.404785	−	0.339655i	−0.417555	−	0.908652i	$-0.637113\pi$
$23$	1.94128	−	1.62893i	0.404785	−	0.339655i	0.822340	+	0.568997i	$0.192668\pi$
$24$		0			0
$25$	−4.68021	+	1.70346i	−0.936042	+	0.340692i
$26$	−1.62379	−	1.48520i	−0.318451	−	0.291271i
$27$		0			0
$28$	9.26084	−	0.827297i	1.75013	−	0.156345i
$29$	−0.210458	−	0.578229i	−0.0390811	−	0.107374i	0.918617	−	0.395149i	$-0.129307\pi$
$29$	−0.210458	−	0.578229i	−0.0390811	−	0.107374i	−0.957698	+	0.287774i	$0.907085\pi$
$30$		0			0
$31$	−3.18818	−	3.79952i	−0.572613	−	0.682414i	0.399552	−	0.916711i	$-0.369166\pi$
$31$	−3.18818	−	3.79952i	−0.572613	−	0.682414i	−0.972165	+	0.234297i	$0.924721\pi$
$32$	−2.14085	+	5.23610i	−0.378453	+	0.925621i
$33$		0			0
$34$	−8.50906	+	1.12816i	−1.45929	+	0.193478i
$35$	−0.323938	+	0.561078i	−0.0547556	+	0.0948394i
$36$		0			0
$37$	−1.43991	−	2.49400i	−0.236720	−	0.410012i	0.723051	−	0.690795i	$-0.242739\pi$
$37$	−1.43991	−	2.49400i	−0.236720	−	0.410012i	−0.959771	+	0.280783i	$0.909406\pi$
$38$	3.78297	+	4.92073i	0.613679	+	0.798248i
$39$		0			0
$40$	−0.212703	−	0.331863i	−0.0336313	−	0.0524721i
$41$	2.25297	−	6.18999i	0.351855	−	0.966713i	−0.629919	−	0.776661i	$-0.716912\pi$
$41$	2.25297	−	6.18999i	0.351855	−	0.966713i	0.981774	−	0.190053i	$-0.0608658\pi$
$42$		0			0
$43$	−2.15530	−	0.380038i	−0.328681	−	0.0579553i	0.00687300	−	0.999976i	$-0.497812\pi$
$43$	−2.15530	−	0.380038i	−0.328681	−	0.0579553i	−0.335554	+	0.942021i	$0.608923\pi$
$44$	−1.72029	+	1.20926i	−0.259344	+	0.182303i
$45$		0			0
$46$	3.41698	−	1.08081i	0.503807	−	0.159357i
$47$	−8.46639	−	7.10414i	−1.23495	−	1.03625i	−0.997902	−	0.0647475i	$-0.979376\pi$
$47$	−8.46639	−	7.10414i	−1.23495	−	1.03625i	−0.237048	−	0.971498i	$-0.576180\pi$
$48$		0			0
$49$	−2.53733	−	14.3899i	−0.362476	−	2.05570i
$50$	−7.03718	−	0.300799i	−0.995207	−	0.0425394i
$51$		0			0
$52$	−1.32038	−	2.81809i	−0.183104	−	0.390798i
$53$			8.73360i			1.19965i	0.800130	+	0.599826i	$0.204764\pi$
$53$			8.73360i			1.19965i	−0.800130	+	0.599826i	$0.795236\pi$
$54$		0			0
$55$		−	0.146525i		−	0.0197574i
$56$	12.5512	+	3.91953i	1.67722	+	0.523770i
$57$		0			0
$58$	0.0371630	−	0.869426i	0.00487974	−	0.114161i
$59$	−1.42477	−	8.08025i	−0.185489	−	1.05196i	−0.925326	−	0.379173i	$-0.876208\pi$
$59$	−1.42477	−	8.08025i	−0.185489	−	1.05196i	0.739837	−	0.672786i	$-0.234903\pi$
$60$		0			0
$61$	8.56477	+	7.18670i	1.09661	+	0.920162i	0.997192	−	0.0748840i	$-0.0238587\pi$
$61$	8.56477	+	7.18670i	1.09661	+	0.920162i	0.0994142	+	0.995046i	$0.468303\pi$
$62$	−2.11539	−	6.68781i	−0.268654	−	0.849353i
$63$		0			0
$64$	−5.62571	+	5.68782i	−0.703214	+	0.710978i
$65$	0.213559	+	0.0376562i	0.0264887	+	0.00467068i
$66$		0			0
$67$	−1.93034	+	5.30357i	−0.235829	+	0.647934i	0.764167	+	0.645019i	$0.223150\pi$
$67$	−1.93034	+	5.30357i	−0.235829	+	0.647934i	−0.999996	+	0.00291580i	$0.999072\pi$
$68$	−11.7310	−	3.12033i	−1.42260	−	0.378395i
$69$		0			0
$70$	−0.726388	+	0.558434i	−0.0868200	+	0.0667456i
$71$	2.33277	+	4.04048i	0.276849	+	0.479517i	0.970600	−	0.240698i	$-0.0773764\pi$
$71$	2.33277	+	4.04048i	0.276849	+	0.479517i	−0.693751	+	0.720215i	$0.744043\pi$
$72$		0			0
$73$	−5.64518	+	9.77774i	−0.660718	+	1.14440i	0.319709	+	0.947516i	$0.396415\pi$
$73$	−5.64518	+	9.77774i	−0.660718	+	1.14440i	−0.980427	+	0.196882i	$0.936918\pi$
$74$	−0.535287	−	4.03736i	−0.0622258	−	0.469334i
$75$		0			0
$76$	2.28736	+	8.47449i	0.262378	+	0.972090i
$77$	3.14181	+	3.74426i	0.358042	+	0.426698i
$78$		0			0
$79$	−0.572755	−	1.57363i	−0.0644400	−	0.177047i	0.903294	−	0.429023i	$-0.141142\pi$
$79$	−0.572755	−	1.57363i	−0.0644400	−	0.177047i	−0.967734	+	0.251975i	$0.918920\pi$
$80$	−0.0988087	−	0.548623i	−0.0110471	−	0.0613379i
$81$		0			0
$82$	6.28736	−	6.87406i	0.694322	−	0.759113i
$83$	2.20553	−	0.802749i	0.242089	−	0.0881131i	−0.218126	−	0.975921i	$-0.569994\pi$
$83$	2.20553	−	0.802749i	0.242089	−	0.0881131i	0.460215	+	0.887807i	$0.347772\pi$
$84$		0			0
$85$	0.647964	−	0.543706i	0.0702815	−	0.0589732i
$86$	−2.61188	−	1.66060i	−0.281647	−	0.179067i
$87$		0			0
$88$	−2.90152	+	0.651613i	−0.309303	+	0.0694622i
$89$	−7.63741	−	4.40946i	−0.809564	−	0.467402i	0.0372408	−	0.999306i	$-0.488143\pi$
$89$	−7.63741	−	4.40946i	−0.809564	−	0.467402i	−0.846804	+	0.531905i	$0.821476\pi$
$90$		0			0
$91$	−6.26466	+	3.61690i	−0.656715	+	0.379154i
$92$	5.04983	+	0.432493i	0.526481	+	0.0450905i
$93$		0			0
$94$	−7.22981	−	13.8574i	−0.745698	−	1.42928i
$95$	−0.574758	−	0.209195i	−0.0589689	−	0.0214629i
$96$		0			0
$97$	−0.978443	+	5.54902i	−0.0993458	+	0.563418i	0.893983	+	0.448101i	$0.147899\pi$
$97$	−0.978443	+	5.54902i	−0.0993458	+	0.563418i	−0.993329	+	0.115317i	$0.963212\pi$
$98$	4.45412	−	20.1786i	0.449934	−	2.03835i
$99$		0			0
$100$	−9.03556	−	4.19324i	−0.903556	−	0.419324i
$101$	6.72190	−	8.01085i	0.668854	−	0.797109i	−0.319773	−	0.947494i	$-0.603607\pi$
$101$	6.72190	−	8.01085i	0.668854	−	0.797109i	0.988628	+	0.150385i	$0.0480512\pi$
$102$		0			0
$103$	1.52148	−	0.268277i	0.149915	−	0.0264341i	−0.0981867	−	0.995168i	$-0.531304\pi$
$103$	1.52148	−	0.268277i	0.149915	−	0.0264341i	0.248102	+	0.968734i	$0.420193\pi$
$104$	−0.204043	−	4.39641i	−0.0200081	−	0.431103i
$105$		0			0
$106$	−4.71615	+	11.4153i	−0.458073	+	1.10875i
$107$	7.89051			0.762805			0.381402	−	0.924409i	$-0.375441\pi$
$107$	7.89051			0.762805			0.381402	+	0.924409i	$0.375441\pi$
$108$		0			0
$109$	1.78550			0.171020			0.0855098	−	0.996337i	$-0.472748\pi$
$109$	1.78550			0.171020			0.0855098	+	0.996337i	$0.472748\pi$
$110$	0.0791235	−	0.191516i	0.00754413	−	0.0182604i
$111$		0			0
$112$	14.2886	+	11.9007i	1.35014	+	1.12451i
$113$	10.4607	−	1.84450i	0.984057	−	0.173516i	0.341607	−	0.939843i	$-0.389029\pi$
$113$	10.4607	−	1.84450i	0.984057	−	0.173516i	0.642451	+	0.766327i	$0.277918\pi$
$114$		0			0
$115$	−0.227011	+	0.270542i	−0.0211689	+	0.0252281i
$116$	0.518064	−	1.11632i	0.0481011	−	0.103648i
$117$		0			0
$118$	2.50109	−	11.3307i	0.230244	−	1.04308i
$119$	−4.89968	+	27.7874i	−0.449152	+	2.54727i
$120$		0			0
$121$	9.29786	+	3.38414i	0.845260	+	0.307649i
$122$	7.31383	+	14.0184i	0.662163	+	1.26917i
$123$		0			0
$124$	0.846487	−	9.88366i	0.0760167	−	0.887579i
$125$	1.20457	−	0.695459i	0.107740	−	0.0622038i
$126$		0			0
$127$	2.89596	+	1.67198i	0.256975	+	0.148364i	0.622954	−	0.782259i	$-0.285933\pi$
$127$	2.89596	+	1.67198i	0.256975	+	0.148364i	−0.365979	+	0.930623i	$0.619266\pi$
$128$	−10.4246	+	4.39642i	−0.921410	+	0.388593i
$129$		0			0
$130$	0.258799	+	0.164541i	0.0226982	+	0.0144312i
$131$	2.00847	−	1.68531i	0.175481	−	0.147246i	−0.550817	−	0.834626i	$-0.685684\pi$
$131$	2.00847	−	1.68531i	0.175481	−	0.147246i	0.726298	+	0.687380i	$0.241239\pi$
$132$		0			0
$133$	19.1728	−	6.97833i	1.66249	−	0.605098i
$134$	−5.38700	+	5.88969i	−0.465366	+	0.508791i
$135$		0			0
$136$	−13.6482	−	10.4132i	−1.17032	−	0.892926i
$137$	−3.04906	−	8.37723i	−0.260499	−	0.715715i	−0.999134	−	0.0416094i	$-0.986752\pi$
$137$	−3.04906	−	8.37723i	−0.260499	−	0.715715i	0.738635	−	0.674106i	$-0.235471\pi$
$138$		0			0
$139$	−9.64531	−	11.4948i	−0.818105	−	0.974979i	0.181860	−	0.983324i	$-0.441788\pi$
$139$	−9.64531	−	11.4948i	−0.818105	−	0.974979i	−0.999965	+	0.00834505i	$0.997344\pi$
$140$	−1.25099	+	0.337655i	−0.105728	+	0.0285371i
$141$		0			0
$142$	0.867207	+	6.54084i	0.0727744	+	0.548895i
$143$	0.818005	−	1.41683i	0.0684050	−	0.118481i
$144$		0			0
$145$	0.0428775	+	0.0742661i	0.00356079	+	0.00616746i
$146$	−12.6586	+	9.73167i	−1.04763	+	0.805398i
$147$		0			0
$148$	1.48053	−	5.56612i	0.121698	−	0.457532i
$149$	−6.19266	+	17.0142i	−0.507323	+	1.39386i	0.376666	+	0.926349i	$0.377071\pi$
$149$	−6.19266	+	17.0142i	−0.507323	+	1.39386i	−0.883989	+	0.467509i	$0.845152\pi$
$150$		0			0
$151$	14.3804	+	2.53565i	1.17026	+	0.206348i	0.724803	−	0.688956i	$-0.241931\pi$
$151$	14.3804	+	2.53565i	1.17026	+	0.206348i	0.445456	+	0.895304i	$0.353042\pi$
$152$	−1.58651	+	12.3118i	−0.128683	+	0.998620i
$153$		0			0
$154$	2.08462	+	6.59054i	0.167983	+	0.531081i
$155$	0.529511	+	0.444312i	0.0425313	+	0.0356880i
$156$		0			0
$157$	0.0237965	+	0.134957i	0.00189917	+	0.0107707i	0.985743	−	0.168260i	$-0.0538149\pi$
$157$	0.0237965	+	0.134957i	0.00189917	+	0.0107707i	−0.983843	+	0.179031i	$0.942704\pi$
$158$	0.101138	−	2.36612i	0.00804610	−	0.188238i
$159$		0			0
$160$	0.167108	−	0.770439i	0.0132111	−	0.0609085i
$161$		−	11.7810i		−	0.928469i
$162$		0			0
$163$			12.0210i			0.941554i	0.882252	+	0.470777i	$0.156026\pi$
$163$			12.0210i			0.941554i	−0.882252	+	0.470777i	$0.843974\pi$
$164$	11.9299	−	5.58962i	0.931571	−	0.436476i
$165$		0			0
$166$	3.31624	+	0.141750i	0.257390	+	0.0110020i
$167$	1.95387	+	11.0810i	0.151195	+	0.857471i	0.962182	+	0.272407i	$0.0878196\pi$
$167$	1.95387	+	11.0810i	0.151195	+	0.857471i	−0.810987	+	0.585064i	$0.801069\pi$
$168$		0			0
$169$	−8.10379	−	6.79989i	−0.623368	−	0.523068i
$170$	1.14053	−	0.360754i	0.0874744	−	0.0276686i
$171$		0			0
$172$	−2.51716	−	3.58091i	−0.191932	−	0.273042i
$173$	−5.61630	−	0.990305i	−0.426999	−	0.0752915i	−0.0439813	−	0.999032i	$-0.514004\pi$
$173$	−5.61630	−	0.990305i	−0.426999	−	0.0752915i	−0.383018	+	0.923741i	$0.625115\pi$
$174$		0			0
$175$	−7.91914	+	21.7577i	−0.598631	+	1.64472i
$176$	−4.14433	−	0.715128i	−0.312391	−	0.0539048i
$177$		0			0
$178$	−7.60142	−	9.88762i	−0.569751	−	0.741108i
$179$	6.20187	+	10.7419i	0.463549	+	0.802891i	0.999135	−	0.0415901i	$-0.0132424\pi$
$179$	6.20187	+	10.7419i	0.463549	+	0.802891i	−0.535585	+	0.844481i	$0.679909\pi$
$180$		0			0
$181$	0.582122	−	1.00827i	0.0432688	−	0.0749437i	−0.843580	−	0.537004i	$-0.819556\pi$
$181$	0.582122	−	1.00827i	0.0432688	−	0.0749437i	0.886849	+	0.462060i	$0.152889\pi$
$182$	−10.1414	+	1.34458i	−0.751730	+	0.0996670i
$183$		0			0
$184$	6.36688	+	3.29221i	0.469372	+	0.242705i
$185$	0.257976	+	0.307444i	0.0189668	+	0.0226037i
$186$		0			0
$187$	−2.18257	−	5.99656i	−0.159605	−	0.438512i
$188$	−1.96680	−	22.0165i	−0.143443	−	1.60572i
$189$		0			0
$190$	−0.638277	−	0.583799i	−0.0463055	−	0.0423533i
$191$	13.5161	−	4.91947i	0.977993	−	0.355960i	0.196934	−	0.980417i	$-0.436902\pi$
$191$	13.5161	−	4.91947i	0.977993	−	0.355960i	0.781060	+	0.624456i	$0.214679\pi$
$192$		0			0
$193$	−14.0915	+	11.8242i	−1.01433	+	0.851125i	−0.988905	−	0.148551i	$-0.952539\pi$
$193$	−14.0915	+	11.8242i	−1.01433	+	0.851125i	−0.0254271	+	0.999677i	$0.508095\pi$
$194$	−4.27536	+	6.72453i	−0.306953	+	0.482793i
$195$		0			0
$196$	16.7182	−	23.9694i	1.19416	−	1.71210i
$197$	18.3471	+	10.5927i	1.30718	+	0.754699i	0.981624	−	0.190825i	$-0.0611163\pi$
$197$	18.3471	+	10.5927i	1.30718	+	0.754699i	0.325553	+	0.945524i	$0.394450\pi$
$198$		0			0
$199$	5.80763	−	3.35304i	0.411692	−	0.237691i	−0.279824	−	0.960051i	$-0.590276\pi$
$199$	5.80763	−	3.35304i	0.411692	−	0.237691i	0.691517	+	0.722361i	$0.256943\pi$
$200$	−9.54565	−	10.3600i	−0.674979	−	0.732564i
$201$		0			0
$202$	13.1118	−	6.84081i	0.922541	−	0.481318i
$203$	−2.68810	−	0.978390i	−0.188668	−	0.0686695i
$204$		0			0
$205$	−0.159412	+	0.904068i	−0.0111338	+	0.0631429i
$206$	2.13353	+	0.470944i	0.148650	+	0.0328122i
$207$		0			0
$208$	2.10737	−	5.85654i	0.146120	−	0.406078i
$209$	−2.96610	+	3.53486i	−0.205170	+	0.244512i
$210$		0			0
$211$	17.3303	−	3.05581i	1.19307	−	0.210370i	0.458369	−	0.888762i	$-0.348434\pi$
$211$	17.3303	−	3.05581i	1.19307	−	0.210370i	0.734701	+	0.678391i	$0.237323\pi$
$212$	−12.3286	+	12.3738i	−0.846729	+	0.849833i
$213$		0			0
$214$	10.3134	+	4.26088i	0.705006	+	0.291268i
$215$	0.305002			0.0208010
$216$		0			0
$217$	−23.0580			−1.56528
$218$	2.33375	+	0.964170i	0.158061	+	0.0653018i
$219$		0			0
$220$	0.206838	−	0.207596i	0.0139450	−	0.0139961i
$221$	9.30084	−	1.63999i	0.625643	−	0.110318i
$222$		0			0
$223$	−5.95915	+	7.10184i	−0.399054	+	0.475574i	−0.927731	−	0.373249i	$-0.878244\pi$
$223$	−5.95915	+	7.10184i	−0.399054	+	0.475574i	0.528677	+	0.848823i	$0.322688\pi$
$224$	12.2496	+	23.2707i	0.818462	+	1.55484i
$225$		0			0
$226$	14.6687	+	3.23790i	0.975749	+	0.215382i
$227$	3.87558	−	21.9795i	0.257231	−	1.45883i	−0.533049	−	0.846085i	$-0.678954\pi$
$227$	3.87558	−	21.9795i	0.257231	−	1.45883i	0.790280	−	0.612746i	$-0.209935\pi$
$228$		0			0
$229$	24.7476	+	9.00740i	1.63537	+	0.595226i	0.986221	−	0.165435i	$-0.0529028\pi$
$229$	24.7476	+	9.00740i	1.63537	+	0.595226i	0.649149	+	0.760661i	$0.275125\pi$
$230$	−0.442809	+	0.231027i	−0.0291980	+	0.0152335i
$231$		0			0
$232$	1.27995	−	1.17934i	0.0840331	−	0.0774276i
$233$	6.49629	−	3.75063i	0.425586	−	0.245712i	−0.271878	−	0.962332i	$-0.587645\pi$
$233$	6.49629	−	3.75063i	0.425586	−	0.245712i	0.697464	+	0.716619i	$0.254312\pi$
$234$		0			0
$235$	1.33389	+	0.770123i	0.0870135	+	0.0502373i
$236$	9.38767	−	13.4593i	0.611085	−	0.876128i
$237$		0			0
$238$	−21.4094	+	33.6740i	−1.38776	+	2.18276i
$239$	2.63068	−	2.20740i	0.170165	−	0.142785i	−0.553728	−	0.832697i	$-0.686795\pi$
$239$	2.63068	−	2.20740i	0.170165	−	0.142785i	0.723893	+	0.689912i	$0.242351\pi$
$240$		0			0
$241$	1.59962	−	0.582213i	0.103040	−	0.0375036i	−0.289986	−	0.957031i	$-0.593650\pi$
$241$	1.59962	−	0.582213i	0.103040	−	0.0375036i	0.393026	+	0.919527i	$0.371428\pi$
$242$	10.3254	+	9.44411i	0.663741	+	0.607091i
$243$		0			0
$244$	1.98965	+	22.2723i	0.127374	+	1.42584i
$245$	0.696473	+	1.91354i	0.0444960	+	0.122252i
$246$		0			0
$247$	−4.38976	−	5.23152i	−0.279314	−	0.332873i
$248$	6.44359	−	12.4614i	0.409168	−	0.791300i
$249$		0			0
$250$	1.94999	−	0.258537i	0.123328	−	0.0163513i
$251$	−7.79783	+	13.5062i	−0.492195	+	0.852506i	−0.999960	−	0.00898943i	$-0.997139\pi$
$251$	−7.79783	+	13.5062i	−0.492195	+	0.852506i	0.507765	+	0.861496i	$0.330472\pi$
$252$		0			0
$253$	1.33220	+	2.30744i	0.0837547	+	0.145067i
$254$	2.88231	+	3.74919i	0.180852	+	0.235245i
$255$		0			0
$256$	−15.9996	+	0.117113i	−0.999973	+	0.00731954i
$257$	3.39598	−	9.33039i	0.211836	−	0.582014i	−0.787579	−	0.616213i	$-0.788666\pi$
$257$	3.39598	−	9.33039i	0.211836	−	0.582014i	0.999415	+	0.0341995i	$0.0108882\pi$
$258$		0			0
$259$	−13.1845	−	2.32479i	−0.819246	−	0.144455i
$260$	0.249414	+	0.354816i	0.0154680	+	0.0220048i
$261$		0			0
$262$	3.53526	−	1.11822i	0.218409	−	0.0690839i
$263$	−20.0312	−	16.8082i	−1.23518	−	1.03644i	−0.997885	−	0.0649985i	$-0.979296\pi$
$263$	−20.0312	−	16.8082i	−1.23518	−	1.03644i	−0.237292	−	0.971438i	$-0.576260\pi$
$264$		0			0
$265$	−0.211354	−	1.19865i	−0.0129833	−	0.0736322i
$266$	28.8283	+	1.23224i	1.76757	+	0.0755537i
$267$		0			0
$268$	−10.2216	+	4.78918i	−0.624381	+	0.292546i
$269$		−	0.465194i		−	0.0283634i	−0.999899	−	0.0141817i	$-0.995486\pi$
$269$		−	0.465194i		−	0.0283634i	0.999899	−	0.0141817i	$-0.00451432\pi$
$270$		0			0
$271$		−	15.6578i		−	0.951143i	−0.879677	−	0.475571i	$-0.842241\pi$
$271$		−	15.6578i		−	0.951143i	0.879677	−	0.475571i	$-0.157759\pi$
$272$	−12.2158	−	20.9807i	−0.740692	−	1.27214i
$273$		0			0
$274$	0.538408	−	12.5960i	0.0325264	−	0.760953i
$275$	−0.909317	−	5.15699i	−0.0548339	−	0.310978i
$276$		0			0
$277$	−7.55460	−	6.33906i	−0.453912	−	0.380877i	0.386973	−	0.922091i	$-0.373521\pi$
$277$	−7.55460	−	6.33906i	−0.453912	−	0.380877i	−0.840885	+	0.541214i	$0.817965\pi$
$278$	−6.39976	−	20.2329i	−0.383832	−	1.21349i
$279$		0			0
$280$	−1.81744	−	0.234198i	−0.108613	−	0.0139960i
$281$	−16.8051	−	2.96320i	−1.00251	−	0.176770i	−0.351783	−	0.936081i	$-0.614425\pi$
$281$	−16.8051	−	2.96320i	−1.00251	−	0.176770i	−0.650727	+	0.759312i	$0.725536\pi$
$282$		0			0
$283$	3.24599	−	8.91828i	0.192954	−	0.530137i	−0.805056	−	0.593199i	$-0.797865\pi$
$283$	3.24599	−	8.91828i	0.192954	−	0.530137i	0.998010	+	0.0630625i	$0.0200868\pi$
$284$	−2.39857	+	9.01754i	−0.142329	+	0.535093i
$285$		0			0
$286$	1.83427	−	1.41015i	0.108462	−	0.0833839i
$287$	−15.3116	−	26.5204i	−0.903814	−	1.56545i
$288$		0			0
$289$	9.91922	−	17.1806i	0.583484	−	1.01062i
$290$	0.0159397	+	0.120224i	0.000936011	+	0.00705979i
$291$		0			0
$292$	−21.8006	+	5.88422i	−1.27578	+	0.344348i
$293$	−1.45797	−	1.73754i	−0.0851753	−	0.101508i	0.721774	−	0.692129i	$-0.243327\pi$
$293$	−1.45797	−	1.73754i	−0.0851753	−	0.101508i	−0.806949	+	0.590621i	$0.798883\pi$
$294$		0			0
$295$	0.391085	+	1.07450i	0.0227699	+	0.0625597i
$296$	4.94084	−	6.47575i	0.287180	−	0.376395i
$297$		0			0
$298$	−17.2818	+	18.8945i	−1.00111	+	1.09453i
$299$	−3.70544	+	1.34867i	−0.214291	+	0.0779957i
$300$		0			0
$301$	−7.79394	+	6.53989i	−0.449235	+	0.376953i
$302$	17.4267	+	11.0797i	1.00280	+	0.637562i
$303$		0			0
$304$	−8.72205	+	15.2355i	−0.500244	+	0.873818i
$305$	−1.34939	−	0.779072i	−0.0772660	−	0.0446095i
$306$		0			0
$307$	10.5153	−	6.07100i	0.600138	−	0.346490i	−0.168958	−	0.985623i	$-0.554040\pi$
$307$	10.5153	−	6.07100i	0.600138	−	0.346490i	0.769096	+	0.639133i	$0.220707\pi$
$308$	−0.834175	+	9.73991i	−0.0475315	+	0.554983i
$309$		0			0
$310$	0.452172	+	0.866678i	0.0256817	+	0.0492240i
$311$	16.3253	+	5.94192i	0.925723	+	0.336936i	0.760513	−	0.649323i	$-0.224948\pi$
$311$	16.3253	+	5.94192i	0.925723	+	0.336936i	0.165210	+	0.986258i	$0.447170\pi$
$312$		0			0
$313$	2.82602	−	16.0272i	0.159736	−	0.905909i	−0.794591	−	0.607145i	$-0.792315\pi$
$313$	2.82602	−	16.0272i	0.159736	−	0.905909i	0.954327	−	0.298764i	$-0.0965743\pi$
$314$	−0.0417733	+	0.189246i	−0.00235740	+	0.0106798i
$315$		0			0
$316$	1.40990	−	3.03804i	0.0793129	−	0.170903i
$317$	−18.7298	+	22.3213i	−1.05197	+	1.25369i	−0.0856578	+	0.996325i	$0.527299\pi$
$317$	−18.7298	+	22.3213i	−1.05197	+	1.25369i	−0.966314	+	0.257366i	$0.917145\pi$
$318$		0			0
$319$	0.637134	−	0.112344i	0.0356727	−	0.00629005i
$320$	0.634457	−	0.916769i	0.0354672	−	0.0512490i
$321$		0			0
$322$	6.36172	−	15.3984i	0.354525	−	0.858118i
$323$	−26.6381			−1.48219
$324$		0			0
$325$	7.74997			0.429891
$326$	−6.49132	+	15.7121i	−0.359521	+	0.870212i
$327$		0			0
$328$	18.6115	−	0.863785i	1.02765	−	0.0476946i
$329$	−50.5990	+	8.92197i	−2.78961	+	0.491884i
$330$		0			0
$331$	1.75836	−	2.09553i	0.0966481	−	0.115181i	−0.715553	−	0.698559i	$-0.753825\pi$
$331$	1.75836	−	2.09553i	0.0966481	−	0.115181i	0.812201	+	0.583378i	$0.198269\pi$
$332$	4.25798	+	1.97605i	0.233687	+	0.108450i
$333$		0			0
$334$	−3.42990	+	15.5386i	−0.187676	+	0.850232i
$335$	0.136584	−	0.774604i	0.00746236	−	0.0423212i
$336$		0			0
$337$	−6.48096	−	2.35888i	−0.353040	−	0.128496i	0.159411	−	0.987212i	$-0.449040\pi$
$337$	−6.48096	−	2.35888i	−0.353040	−	0.128496i	−0.512452	+	0.858716i	$0.671263\pi$
$338$	−6.92018	−	13.2639i	−0.376408	−	0.721461i
$339$		0			0
$340$	1.68554	+	0.144358i	0.0914114	+	0.00782893i
$341$	4.51618	−	2.60742i	0.244565	−	0.141199i
$342$		0			0
$343$	−30.6457	−	17.6933i	−1.65471	−	0.955349i
$344$	−1.35638	−	6.03973i	−0.0731310	−	0.325640i
$345$		0			0
$346$	−6.80606	−	4.32719i	−0.365896	−	0.232631i
$347$	−17.5469	+	14.7236i	−0.941964	+	0.790402i	−0.977926	−	0.208951i	$-0.932995\pi$
$347$	−17.5469	+	14.7236i	−0.941964	+	0.790402i	0.0359618	+	0.999353i	$0.488551\pi$
$348$		0			0
$349$	−25.4917	+	9.27824i	−1.36454	+	0.496653i	−0.917456	−	0.397838i	$-0.869760\pi$
$349$	−25.4917	+	9.27824i	−1.36454	+	0.496653i	−0.447086	+	0.894491i	$0.647538\pi$
$350$	−22.0999	+	24.1622i	−1.18129	+	1.29152i
$351$		0			0
$352$	−5.03071	−	3.17265i	−0.268138	−	0.169103i
$353$	2.30370	+	6.32935i	0.122613	+	0.336877i	0.985780	−	0.168042i	$-0.0537444\pi$
$353$	2.30370	+	6.32935i	0.122613	+	0.336877i	−0.863166	+	0.504919i	$0.831522\pi$
$354$		0			0
$355$	−0.417942	−	0.498084i	−0.0221820	−	0.0264355i
$356$	−4.59618	−	17.0285i	−0.243597	−	0.902507i
$357$		0			0
$358$	2.30554	+	17.3894i	0.121852	+	0.919056i
$359$	14.3604	−	24.8729i	0.757913	−	1.31274i	−0.186000	−	0.982550i	$-0.559552\pi$
$359$	14.3604	−	24.8729i	0.757913	−	1.31274i	0.943913	−	0.330194i	$-0.107114\pi$
$360$		0			0
$361$	0.131118	+	0.227104i	0.00690097	+	0.0119528i
$362$	1.30533	−	1.00351i	0.0686067	−	0.0527435i
$363$		0			0
$364$	−13.9815	−	3.71891i	−0.732828	−	0.194924i
$365$	0.538153	−	1.47856i	0.0281682	−	0.0773915i
$366$		0			0
$367$	3.84637	+	0.678219i	0.200779	+	0.0354027i	0.273133	−	0.961976i	$-0.411940\pi$
$367$	3.84637	+	0.678219i	0.200779	+	0.0354027i	−0.0723541	+	0.997379i	$0.523051\pi$
$368$	6.54408	+	7.74122i	0.341134	+	0.403539i
$369$		0			0
$370$	0.171170	+	0.541155i	0.00889870	+	0.0281333i
$371$	31.1024	+	26.0980i	1.61476	+	1.35494i
$372$		0			0
$373$	−1.89369	−	10.7397i	−0.0980518	−	0.556079i	−0.993769	−	0.111456i	$-0.964449\pi$
$373$	−1.89369	−	10.7397i	−0.0980518	−	0.556079i	0.895718	−	0.444623i	$-0.146662\pi$
$374$	0.385401	−	9.01643i	0.0199286	−	0.466229i
$375$		0			0
$376$	9.31820	−	29.8389i	0.480549	−	1.53882i
$377$			0.957490i			0.0493132i
$378$		0			0
$379$			5.95264i			0.305766i	0.988244	+	0.152883i	$0.0488558\pi$
$379$			5.95264i			0.305766i	−0.988244	+	0.152883i	$0.951144\pi$
$380$	−0.519012	−	1.10773i	−0.0266248	−	0.0568253i
$381$		0			0
$382$	20.3229	+	0.868687i	1.03981	+	0.0444459i
$383$	−1.15926	−	6.57451i	−0.0592356	−	0.335942i	0.940759	−	0.339075i	$-0.110114\pi$
$383$	−1.15926	−	6.57451i	−0.0592356	−	0.335942i	−0.999995	+	0.00313275i	$0.999003\pi$
$384$		0			0
$385$	−0.521809	−	0.437850i	−0.0265939	−	0.0223149i
$386$	−24.8035	+	7.84548i	−1.26247	+	0.399325i
$387$		0			0
$388$	−9.21939	+	6.48066i	−0.468043	+	0.329006i
$389$	30.0164	+	5.29270i	1.52189	+	0.268351i	0.871176	−	0.490970i	$-0.163358\pi$
$389$	30.0164	+	5.29270i	1.52189	+	0.268351i	0.650716	+	0.759321i	$0.274469\pi$
$390$		0			0
$391$	−5.26061	+	14.4534i	−0.266041	+	0.730941i
$392$	34.7952	−	22.3015i	1.75742	−	1.12639i
$393$		0			0
$394$	18.2607	+	23.7527i	0.919958	+	1.19664i
$395$	0.116690	+	0.202113i	0.00587131	+	0.0101694i
$396$		0			0
$397$	7.87633	−	13.6422i	0.395302	−	0.684683i	−0.597838	−	0.801617i	$-0.703973\pi$
$397$	7.87633	−	13.6422i	0.395302	−	0.684683i	0.993140	+	0.116934i	$0.0373067\pi$
$398$	9.40155	−	1.24649i	0.471257	−	0.0624809i
$399$		0			0
$400$	−6.88230	−	18.6958i	−0.344115	−	0.934789i
$401$	1.99200	+	2.37398i	0.0994758	+	0.118551i	0.813486	−	0.581585i	$-0.197567\pi$
$401$	1.99200	+	2.37398i	0.0994758	+	0.118551i	−0.714010	+	0.700136i	$0.753123\pi$
$402$		0			0
$403$	2.63965	+	7.25239i	0.131490	+	0.361267i
$404$	20.8319	−	1.86097i	1.03643	−	0.0925868i
$405$		0			0
$406$	−2.98518	−	2.73039i	−0.148152	−	0.135507i
$407$	2.84523	−	1.03558i	0.141033	−	0.0513318i
$408$		0			0
$409$	−20.1116	+	16.8756i	−0.994454	+	0.834446i	−0.986206	−	0.165520i	$-0.947070\pi$
$409$	−20.1116	+	16.8756i	−0.994454	+	0.834446i	−0.00824757	+	0.999966i	$0.502625\pi$
$410$	−0.696557	+	1.09559i	−0.0344005	+	0.0541072i
$411$		0			0
$412$	2.53433	+	1.76766i	0.124858	+	0.0870862i
$413$	−33.0332	−	19.0717i	−1.62546	−	0.938458i
$414$		0			0
$415$	−0.283273	+	0.163547i	−0.0139053	+	0.00802823i
$416$	5.91698	−	6.51686i	0.290104	−	0.319515i
$417$		0			0
$418$	−5.78570	+	3.01857i	−0.282988	+	0.147643i
$419$	−33.9869	−	12.3702i	−1.66037	−	0.604325i	−0.669949	−	0.742407i	$-0.733684\pi$
$419$	−33.9869	−	12.3702i	−1.66037	−	0.604325i	−0.990421	+	0.138082i	$0.955906\pi$
$420$		0			0
$421$	2.20155	−	12.4856i	0.107297	−	0.608511i	−0.882981	−	0.469409i	$-0.844467\pi$
$421$	2.20155	−	12.4856i	0.107297	−	0.608511i	0.990278	−	0.139103i	$-0.0444218\pi$
$422$	24.3019	+	5.36428i	1.18300	+	0.261129i
$423$		0			0
$424$	−22.7960	+	9.51579i	−1.10707	+	0.462128i
$425$	19.4311	−	23.1571i	0.942548	−	1.12328i
$426$		0			0
$427$	51.1870	−	9.02565i	2.47711	−	0.436782i
$428$	11.1793	+	11.1384i	0.540370	+	0.538396i
$429$		0			0
$430$	0.398655	+	0.164701i	0.0192249	+	0.00794260i
$431$	11.3033			0.544463			0.272231	−	0.962232i	$-0.412238\pi$
$431$	11.3033			0.544463			0.272231	+	0.962232i	$0.412238\pi$
$432$		0			0
$433$	18.1058			0.870111			0.435056	−	0.900404i	$-0.356729\pi$
$433$	18.1058			0.870111			0.435056	+	0.900404i	$0.356729\pi$
$434$	−30.1381	−	12.4513i	−1.44668	−	0.597682i
$435$		0			0
$436$	2.52969	+	2.52045i	0.121150	+	0.120708i
$437$	10.9531	−	1.93133i	0.523960	−	0.0923883i
$438$		0			0
$439$	8.79038	−	10.4760i	0.419542	−	0.499991i	−0.514333	−	0.857591i	$-0.671960\pi$
$439$	8.79038	−	10.4760i	0.419542	−	0.499991i	0.933875	+	0.357600i	$0.116405\pi$
$440$	0.382451	−	0.159648i	0.0182326	−	0.00761091i
$441$		0			0
$442$	13.0423	+	2.87890i	0.620361	+	0.136935i
$443$	1.88953	−	10.7160i	0.0897742	−	0.509135i	−0.906450	−	0.422314i	$-0.861218\pi$
$443$	1.88953	−	10.7160i	0.0897742	−	0.509135i	0.996224	−	0.0868210i	$-0.0276708\pi$
$444$		0			0
$445$	1.15491	+	0.420352i	0.0547479	+	0.0199266i
$446$	−11.6239	+	6.06457i	−0.550410	+	0.287166i
$447$		0			0
$448$	3.44474	+	37.0310i	0.162749	+	1.74955i
$449$	6.10203	−	3.52301i	0.287973	−	0.166261i	−0.349055	−	0.937102i	$-0.613497\pi$
$449$	6.10203	−	3.52301i	0.287973	−	0.166261i	0.637027	+	0.770841i	$0.280164\pi$
$450$		0			0
$451$	5.99791	+	3.46289i	0.282431	+	0.163061i
$452$	17.4244	+	12.1532i	0.819575	+	0.571641i
$453$		0			0
$454$	16.9345	−	26.6357i	0.794778	−	1.25007i
$455$	0.772266	−	0.648008i	0.0362044	−	0.0303791i
$456$		0			0
$457$	−23.9184	+	8.70557i	−1.11885	+	0.407229i	−0.834234	−	0.551411i	$-0.814090\pi$
$457$	−23.9184	+	8.70557i	−1.11885	+	0.407229i	−0.284620	+	0.958641i	$0.591867\pi$
$458$	27.4826	+	25.1369i	1.28418	+	1.17457i
$459$		0			0
$460$	−0.703532	+	0.0628485i	−0.0328024	+	0.00293033i
$461$	13.4094	+	36.8420i	0.624538	+	1.71590i	0.695597	+	0.718432i	$0.255140\pi$
$461$	13.4094	+	36.8420i	0.624538	+	1.71590i	−0.0710586	+	0.997472i	$0.522638\pi$
$462$		0			0
$463$	−4.80801	−	5.72997i	−0.223447	−	0.266294i	0.642661	−	0.766151i	$-0.277830\pi$
$463$	−4.80801	−	5.72997i	−0.223447	−	0.266294i	−0.866108	+	0.499857i	$0.833386\pi$
$464$	2.30982	−	0.850291i	0.107231	−	0.0394738i
$465$		0			0
$466$	10.5164	−	1.39430i	0.487161	−	0.0645895i
$467$	0.689932	−	1.19500i	0.0319262	−	0.0552979i	−0.849621	−	0.527394i	$-0.823169\pi$
$467$	0.689932	−	1.19500i	0.0319262	−	0.0552979i	0.881547	+	0.472096i	$0.156502\pi$
$468$		0			0
$469$	13.1189	+	22.7227i	0.605777	+	1.04924i
$470$	1.32761	+	1.72690i	0.0612379	+	0.0796558i
$471$		0			0
$472$	19.5383	−	12.5228i	0.899322	−	0.576408i
$473$	0.786999	−	2.16226i	0.0361862	−	0.0994209i
$474$		0			0
$475$	−21.5271	−	3.79580i	−0.987729	−	0.174163i
$476$	−46.1673	+	32.4527i	−2.11607	+	1.48747i
$477$		0			0
$478$	4.63045	−	1.46463i	0.211792	−	0.0669908i
$479$	9.74905	+	8.18042i	0.445445	+	0.373773i	0.837742	−	0.546066i	$-0.183875\pi$
$479$	9.74905	+	8.18042i	0.445445	+	0.373773i	−0.392297	+	0.919839i	$0.628319\pi$
$480$		0			0
$481$	0.778139	+	4.41304i	0.0354801	+	0.201217i
$482$	2.40519	+	0.102808i	0.109553	+	0.00468277i
$483$		0			0
$484$	8.39606	+	17.9197i	0.381639	+	0.814533i
$485$		−	0.785256i		−	0.0356566i
$486$		0			0
$487$		−	12.3932i		−	0.561588i	−0.959768	−	0.280794i	$-0.909402\pi$
$487$		−	12.3932i		−	0.561588i	0.959768	−	0.280794i	$-0.0905979\pi$
$488$	−9.42648	+	30.1856i	−0.426717	+	1.36644i
$489$		0			0
$490$	−0.122984	+	2.87721i	−0.00555586	+	0.129979i
$491$	4.61221	+	26.1572i	0.208146	+	1.18046i	0.892411	+	0.451223i	$0.149012\pi$
$491$	4.61221	+	26.1572i	0.208146	+	1.18046i	−0.684265	+	0.729233i	$0.739877\pi$
$492$		0			0
$493$	2.86100	+	2.40067i	0.128853	+	0.108121i
$494$	−2.91265	−	9.20837i	−0.131046	−	0.414304i
$495$		0			0
$496$	15.1513	−	12.8082i	0.680314	−	0.575107i
$497$	21.3599	+	3.76634i	0.958125	+	0.168943i
$498$		0			0
$499$	3.29755	−	9.05994i	0.147619	−	0.405579i	−0.843741	−	0.536750i	$-0.819652\pi$
$499$	3.29755	−	9.05994i	0.147619	−	0.405579i	0.991360	+	0.131172i	$0.0418739\pi$
$500$	2.68836	+	0.715074i	0.120227	+	0.0319791i
$501$		0			0
$502$	−17.4856	+	13.4426i	−0.780420	+	0.599973i
$503$	−4.28642	−	7.42429i	−0.191122	−	0.331033i	0.754500	−	0.656300i	$-0.227879\pi$
$503$	−4.28642	−	7.42429i	−0.191122	−	0.331033i	−0.945622	+	0.325267i	$0.894546\pi$
$504$		0			0
$505$	−0.728686	+	1.26212i	−0.0324261	+	0.0561637i
$506$	0.495245	+	3.73534i	0.0220163	+	0.166056i
$507$		0			0
$508$	1.74278	+	6.45686i	0.0773234	+	0.286477i
$509$	−19.9295	−	23.7511i	−0.883360	−	1.05275i	−0.998236	−	0.0593674i	$-0.981092\pi$
$509$	−19.9295	−	23.7511i	−0.883360	−	1.05275i	0.114876	−	0.993380i	$-0.463353\pi$
$510$		0			0
$511$	17.9517	+	49.3219i	0.794137	+	2.18187i
$512$	−20.9756	−	8.48670i	−0.926999	−	0.375063i
$513$		0			0
$514$	9.47716	−	10.3615i	0.418020	−	0.457027i
$515$	−0.202323	+	0.0736396i	−0.00891542	+	0.00324495i
$516$		0			0
$517$	8.90151	−	7.46925i	0.391488	−	0.328497i
$518$	−15.9775	−	10.1583i	−0.702013	−	0.446329i
$519$		0			0
$520$	0.134397	+	0.598448i	0.00589371	+	0.0262437i
$521$	25.2374	+	14.5708i	1.10567	+	0.638359i	0.937705	−	0.347433i	$-0.112947\pi$
$521$	25.2374	+	14.5708i	1.10567	+	0.638359i	0.167966	+	0.985793i	$0.446280\pi$
$522$		0			0
$523$	4.50959	−	2.60361i	0.197190	−	0.113848i	−0.398154	−	0.917319i	$-0.630349\pi$
$523$	4.50959	−	2.60361i	0.197190	−	0.113848i	0.595344	+	0.803471i	$0.297016\pi$
$524$	5.22463	+	0.447464i	0.228239	+	0.0195475i
$525$		0			0
$526$	−17.1055	−	32.7861i	−0.745836	−	1.42954i
$527$	28.2886	+	10.2962i	1.23227	+	0.448510i
$528$		0			0
$529$	−2.87875	+	16.3262i	−0.125163	+	0.709834i
$530$	0.371018	−	1.68083i	0.0161160	−	0.0730106i
$531$		0			0
$532$	37.0148	+	17.1779i	1.60479	+	0.744756i
$533$	−6.58858	+	7.85196i	−0.285383	+	0.340106i
$534$		0			0
$535$	−1.08294	+	0.190951i	−0.0468194	+	0.00825552i
$536$	−15.9463	+	0.740090i	−0.688776	+	0.0319670i
$537$		0			0
$538$	0.251205	−	0.608035i	0.0108302	−	0.0262143i
$539$	15.3629			0.661725
$540$		0			0
$541$	24.3664			1.04759			0.523797	−	0.851843i	$-0.324515\pi$
$541$	24.3664			1.04759			0.523797	+	0.851843i	$0.324515\pi$
$542$	8.45521	−	20.4656i	0.363182	−	0.879074i
$543$		0			0
$544$	−4.63718	−	34.0195i	−0.198817	−	1.45857i
$545$	−0.245051	+	0.0432091i	−0.0104968	+	0.00185088i
$546$		0			0
$547$	−22.9927	+	27.4016i	−0.983097	+	1.17161i	0.00206780	+	0.999998i	$0.499342\pi$
$547$	−22.9927	+	27.4016i	−0.983097	+	1.17161i	−0.985165	+	0.171611i	$0.945103\pi$
$548$	7.50558	−	16.1730i	0.320623	−	0.690875i
$549$		0			0
$550$	1.59625	−	7.23152i	0.0680643	−	0.308353i
$551$	0.468962	−	2.65961i	0.0199784	−	0.113303i
$552$		0			0
$553$	−7.31560	−	2.66266i	−0.311091	−	0.113228i
$554$	−6.45120	−	12.3650i	−0.274085	−	0.525339i
$555$		0			0
$556$	2.56091	−	29.9014i	0.108607	−	1.26810i
$557$	−10.4040	+	6.00674i	−0.440831	+	0.254514i	−0.703950	−	0.710250i	$-0.748582\pi$
$557$	−10.4040	+	6.00674i	−0.440831	+	0.254514i	0.263119	+	0.964763i	$0.415249\pi$
$558$		0			0
$559$	2.94922	+	1.70274i	0.124739	+	0.0720180i
$560$	−2.24904	−	1.28753i	−0.0950392	−	0.0544081i
$561$		0			0
$562$	−20.3651	−	12.9478i	−0.859052	−	0.546172i
$563$	3.65854	−	3.06988i	0.154189	−	0.129380i	−0.562430	−	0.826845i	$-0.690133\pi$
$563$	3.65854	−	3.06988i	0.154189	−	0.129380i	0.716619	+	0.697465i	$0.245689\pi$
$564$		0			0
$565$	−1.39104	+	0.506297i	−0.0585215	+	0.0213001i
$566$	9.05857	−	9.90387i	0.380760	−	0.416291i
$567$		0			0
$568$	−8.00454	+	10.4912i	−0.335863	+	0.440202i
$569$	−2.71384	−	7.45620i	−0.113770	−	0.312580i	0.869719	−	0.493547i	$-0.164300\pi$
$569$	−2.71384	−	7.45620i	−0.113770	−	0.312580i	−0.983489	+	0.180966i	$0.942078\pi$
$570$		0			0
$571$	10.4105	+	12.4067i	0.435666	+	0.519206i	0.938548	−	0.345149i	$-0.112172\pi$
$571$	10.4105	+	12.4067i	0.435666	+	0.519206i	−0.502882	+	0.864355i	$0.667727\pi$
$572$	3.15897	−	0.852643i	0.132083	−	0.0356508i
$573$		0			0
$574$	−5.69207	−	42.9320i	−0.237583	−	1.79195i
$575$	−6.31079	+	10.9306i	−0.263178	+	0.455838i
$576$		0			0
$577$	−8.09164	−	14.0151i	−0.336859	−	0.583458i	0.646981	−	0.762506i	$-0.276031\pi$
$577$	−8.09164	−	14.0151i	−0.336859	−	0.583458i	−0.983840	+	0.179049i	$0.942698\pi$
$578$	22.2425	−	17.0996i	0.925167	−	0.711251i
$579$		0			0
$580$	−0.0440869	+	0.165747i	−0.00183061	+	0.00688227i
$581$	3.73187	−	10.2532i	0.154824	−	0.425375i
$582$		0			0
$583$	−9.04295	−	1.59452i	−0.374521	−	0.0660381i
$584$	−31.6721	−	4.08130i	−1.31060	−	0.168885i
$585$		0			0
$586$	−0.967376	−	3.05836i	−0.0399619	−	0.126340i
$587$	19.9180	+	16.7132i	0.822103	+	0.689826i	0.953464	−	0.301508i	$-0.0974901\pi$
$587$	19.9180	+	16.7132i	0.822103	+	0.689826i	−0.131361	+	0.991335i	$0.541935\pi$
$588$		0			0
$589$	−3.78006	−	21.4378i	−0.155755	−	0.883328i
$590$	−0.0690583	+	1.61562i	−0.00284309	+	0.0665139i
$591$		0			0
$592$	9.95487	−	5.79613i	0.409143	−	0.238219i
$593$		−	7.68968i		−	0.315778i	−0.987457	−	0.157889i	$-0.949531\pi$
$593$		−	7.68968i		−	0.315778i	0.987457	−	0.157889i	$-0.0504687\pi$
$594$		0			0
$595$		−	3.93227i		−	0.161207i
$596$	−32.7914	+	15.3640i	−1.34319	+	0.629334i
$597$		0			0
$598$	−5.57151	−	0.238150i	−0.227836	−	0.00973869i
$599$	5.26567	+	29.8631i	0.215150	+	1.22017i	0.880647	+	0.473773i	$0.157108\pi$
$599$	5.26567	+	29.8631i	0.215150	+	1.22017i	−0.665497	+	0.746400i	$0.731780\pi$
$600$		0			0
$601$	14.0780	+	11.8129i	0.574254	+	0.481857i	0.883055	−	0.469270i	$-0.155483\pi$
$601$	14.0780	+	11.8129i	0.574254	+	0.481857i	−0.308800	+	0.951127i	$0.599927\pi$
$602$	−13.7187	+	4.33929i	−0.559132	+	0.176856i
$603$		0			0
$604$	16.7947	+	23.8922i	0.683368	+	0.972159i
$605$	−1.35798	−	0.239449i	−0.0552099	−	0.00973499i
$606$		0			0
$607$	−1.94501	+	5.34387i	−0.0789455	+	0.216901i	−0.972886	−	0.231284i	$-0.925707\pi$
$607$	−1.94501	+	5.34387i	−0.0789455	+	0.216901i	0.893941	+	0.448185i	$0.147930\pi$
$608$	−19.6274	+	15.2038i	−0.795997	+	0.616596i
$609$		0			0
$610$	−1.34303	−	1.74696i	−0.0543779	−	0.0707325i
$611$	8.59873	+	14.8934i	0.347867	+	0.602524i
$612$		0			0
$613$	−4.98728	+	8.63823i	−0.201434	+	0.348895i	−0.948991	−	0.315304i	$-0.897894\pi$
$613$	−4.98728	+	8.63823i	−0.201434	+	0.348895i	0.747556	+	0.664198i	$0.231227\pi$
$614$	17.0224	−	2.25689i	0.686969	−	0.0910806i
$615$		0			0
$616$	−6.34987	+	12.2802i	−0.255844	+	0.494782i
$617$	−12.6243	−	15.0451i	−0.508236	−	0.605692i	0.449521	−	0.893270i	$-0.351595\pi$
$617$	−12.6243	−	15.0451i	−0.508236	−	0.605692i	−0.957757	+	0.287577i	$0.907150\pi$
$618$		0			0
$619$	−11.9916	−	32.9466i	−0.481983	−	1.32424i	−0.907791	−	0.419423i	$-0.862232\pi$
$619$	−11.9916	−	32.9466i	−0.481983	−	1.32424i	0.425808	−	0.904814i	$-0.359990\pi$
$620$	0.123009	+	1.37697i	0.00494015	+	0.0553005i
$621$		0			0
$622$	18.1295	+	16.5821i	0.726926	+	0.664882i
$623$	−38.5254	+	14.0221i	−1.54349	+	0.561784i
$624$		0			0
$625$	18.9282	−	15.8827i	0.757129	−	0.635307i
$626$	12.3485	−	19.4224i	0.493543	−	0.776274i
$627$		0			0
$628$	−0.156793	+	0.224798i	−0.00625673	+	0.00897043i
$629$	15.1373	+	8.73951i	0.603563	+	0.348467i
$630$		0			0
$631$	−20.6478	+	11.9210i	−0.821976	+	0.474568i	−0.851097	−	0.525008i	$-0.824062\pi$
$631$	−20.6478	+	11.9210i	−0.821976	+	0.474568i	0.0291214	+	0.999576i	$0.490729\pi$
$632$	3.48336	−	3.20954i	0.138561	−	0.127669i
$633$		0			0
$634$	−36.5345	+	19.0612i	−1.45097	+	0.757015i
$635$	−0.437918	−	0.159389i	−0.0173783	−	0.00632517i
$636$		0			0
$637$	−3.94818	+	22.3913i	−0.156433	+	0.887174i
$638$	0.893437	+	0.197213i	0.0353715	+	0.00780772i
$639$		0			0
$640$	1.32433	−	0.855663i	0.0523487	−	0.0338231i
$641$	−11.9138	+	14.1983i	−0.470568	+	0.560801i	−0.948165	−	0.317778i	$-0.897063\pi$
$641$	−11.9138	+	14.1983i	−0.470568	+	0.560801i	0.477598	+	0.878579i	$0.341508\pi$
$642$		0			0
$643$	−35.2470	+	6.21500i	−1.39001	+	0.245096i	−0.818031	−	0.575175i	$-0.804934\pi$
$643$	−35.2470	+	6.21500i	−1.39001	+	0.245096i	−0.571976	+	0.820270i	$0.693823\pi$
$644$	16.6303	−	16.6912i	0.655324	−	0.657727i
$645$		0			0
$646$	−34.8176	−	14.3846i	−1.36988	−	0.565955i
$647$	−31.4863			−1.23785			−0.618926	−	0.785449i	$-0.712432\pi$
$647$	−31.4863			−1.23785			−0.618926	+	0.785449i	$0.712432\pi$
$648$		0			0
$649$	8.62659			0.338623
$650$	10.1297	+	4.18499i	0.397318	+	0.164149i
$651$		0			0
$652$	−16.9691	+	17.0313i	−0.664560	+	0.666996i
$653$	26.5025	−	4.67310i	1.03712	−	0.182873i	0.370936	−	0.928658i	$-0.379037\pi$
$653$	26.5025	−	4.67310i	1.03712	−	0.182873i	0.666186	+	0.745786i	$0.267926\pi$
$654$		0			0
$655$	−0.234869	+	0.279906i	−0.00917709	+	0.0109368i
$656$	24.7928	+	8.92121i	0.967995	+	0.348315i
$657$		0			0
$658$	−70.9537	−	15.6620i	−2.76606	−	0.610567i
$659$	7.78431	−	44.1470i	0.303234	−	1.71972i	−0.328471	−	0.944514i	$-0.606533\pi$
$659$	7.78431	−	44.1470i	0.303234	−	1.71972i	0.631705	−	0.775209i	$-0.282355\pi$
$660$		0			0
$661$	19.0048	+	6.91718i	0.739201	+	0.269047i	0.684054	−	0.729431i	$-0.260215\pi$
$661$	19.0048	+	6.91718i	0.739201	+	0.269047i	0.0551465	+	0.998478i	$0.482437\pi$
$662$	3.42986	−	1.78946i	0.133305	−	0.0695495i
$663$		0			0
$664$	4.49835	+	4.88212i	0.174570	+	0.189463i
$665$	−2.46250	+	1.42173i	−0.0954917	+	0.0551322i
$666$		0			0
$667$	−1.35045	−	0.779683i	−0.0522896	−	0.0301894i
$668$	−12.8739	+	18.4576i	−0.498106	+	0.714147i
$669$		0			0
$670$	0.596809	−	0.938697i	0.0230568	−	0.0362650i
$671$	−9.00495	+	7.55605i	−0.347632	+	0.291698i
$672$		0			0
$673$	40.4201	−	14.7117i	1.55808	−	0.567094i	0.587784	−	0.809018i	$-0.300001\pi$
$673$	40.4201	−	14.7117i	1.55808	−	0.567094i	0.970295	+	0.241924i	$0.0777784\pi$
$674$	−7.19720	−	6.58291i	−0.277226	−	0.253564i
$675$		0			0
$676$	−1.88256	−	21.0736i	−0.0724062	−	0.810522i
$677$	−6.79083	−	18.6577i	−0.260993	−	0.717072i	−0.999101	−	0.0423898i	$-0.986503\pi$
$677$	−6.79083	−	18.6577i	−0.260993	−	0.717072i	0.738108	−	0.674682i	$-0.235719\pi$
$678$		0			0
$679$	16.8376	+	20.0662i	0.646166	+	0.770071i
$680$	2.12515	+	1.09888i	0.0814957	+	0.0421401i
$681$		0			0
$682$	7.31091	−	0.969305i	0.279949	−	0.0371166i
$683$	−16.6637	+	28.8624i	−0.637618	+	1.10439i	0.348336	+	0.937370i	$0.386747\pi$
$683$	−16.6637	+	28.8624i	−0.637618	+	1.10439i	−0.985954	+	0.167017i	$0.946586\pi$
$684$		0			0
$685$	0.621199	+	1.07595i	0.0237348	+	0.0411098i
$686$	−30.5013	−	39.6749i	−1.16455	−	1.51479i
$687$		0			0
$688$	1.48859	−	8.62672i	0.0567520	−	0.328890i
$689$	4.64799	−	12.7703i	0.177074	−	0.486508i
$690$		0			0
$691$	1.92394	+	0.339243i	0.0731902	+	0.0129054i	0.210123	−	0.977675i	$-0.432613\pi$
$691$	1.92394	+	0.339243i	0.0731902	+	0.0129054i	−0.136933	+	0.990580i	$0.543725\pi$
$692$	−6.55923	−	9.33116i	−0.249345	−	0.354718i
$693$		0			0
$694$	−30.8855	+	9.76923i	−1.17240	+	0.370835i
$695$	1.60195	+	1.34420i	0.0607654	+	0.0509882i
$696$		0			0
$697$	6.94264	+	39.3737i	0.262971	+	1.49138i
$698$	−38.3294	−	1.63836i	−1.45079	−	0.0620130i
$699$		0			0
$700$	−41.9334	+	19.6474i	−1.58493	+	0.742601i
$701$		−	15.9132i		−	0.601032i	−0.953777	−	0.300516i	$-0.902841\pi$
$701$		−	15.9132i		−	0.601032i	0.953777	−	0.300516i	$-0.0971588\pi$
$702$		0			0
$703$		−	12.6392i		−	0.476697i
$704$	−4.86219	−	6.86342i	−0.183251	−	0.258675i
$705$		0			0
$706$	−0.406790	+	9.51682i	−0.0153097	+	0.358170i
$707$	−8.44192	−	47.8765i	−0.317491	−	1.80058i
$708$		0			0
$709$	−25.2965	−	21.2262i	−0.950028	−	0.797169i	0.0292739	−	0.999571i	$-0.490681\pi$
$709$	−25.2965	−	21.2262i	−0.950028	−	0.797169i	−0.979302	+	0.202403i	$0.935125\pi$
$710$	−0.277309	−	0.876713i	−0.0104072	−	0.0329024i
$711$		0			0
$712$	3.18791	−	24.7391i	0.119472	−	0.927137i
$713$	−12.3783	−	2.18262i	−0.463570	−	0.0817399i
$714$		0			0
$715$	−0.0779800	+	0.214248i	−0.00291629	+	0.00801244i
$716$	−6.37679	+	23.9739i	−0.238312	+	0.895946i
$717$		0			0
$718$	32.2013	−	24.7558i	1.20174	−	0.923876i
$719$	4.06158	+	7.03487i	0.151471	+	0.262356i	0.931769	−	0.363053i	$-0.118266\pi$
$719$	4.06158	+	7.03487i	0.151471	+	0.262356i	−0.780297	+	0.625409i	$0.784932\pi$
$720$		0			0
$721$	3.59112	−	6.22000i	0.133740	−	0.231645i
$722$	0.0487432	+	0.367642i	0.00181403	+	0.0136822i
$723$		0			0
$724$	2.24804	−	0.606772i	0.0835478	−	0.0225505i
$725$	1.96998	+	2.34773i	0.0731631	+	0.0871924i
$726$		0			0
$727$	−12.8952	−	35.4294i	−0.478258	−	1.31400i	−0.910971	−	0.412470i	$-0.864666\pi$
$727$	−12.8952	−	35.4294i	−0.478258	−	1.31400i	0.432713	−	0.901532i	$-0.357556\pi$
$728$	−16.2664	−	12.4108i	−0.602872	−	0.459976i
$729$		0			0
$730$	1.50182	−	1.64196i	0.0555849	−	0.0607718i
$731$	12.4823	−	4.54317i	0.461673	−	0.168035i
$732$		0			0
$733$	−22.3955	+	18.7921i	−0.827198	+	0.694101i	−0.954646	−	0.297744i	$-0.903766\pi$
$733$	−22.3955	+	18.7921i	−0.827198	+	0.694101i	0.127448	+	0.991845i	$0.459321\pi$
$734$	4.66119	+	2.96351i	0.172048	+	0.109385i
$735$		0			0
$736$	4.37323	+	13.6520i	0.161199	+	0.503220i
$737$	−5.13900	−	2.96700i	−0.189298	−	0.109291i
$738$		0			0
$739$	−34.0829	+	19.6778i	−1.25376	+	0.723858i	−0.971854	−	0.235584i	$-0.924300\pi$
$739$	−34.0829	+	19.6778i	−1.25376	+	0.723858i	−0.281905	+	0.959442i	$0.590966\pi$
$740$	−0.0684948	+	0.799752i	−0.00251792	+	0.0293995i
$741$		0			0
$742$	26.5597	+	50.9069i	0.975036	+	1.86885i
$743$	10.4717	+	3.81140i	0.384171	+	0.139827i	0.526884	−	0.849937i	$-0.323360\pi$
$743$	10.4717	+	3.81140i	0.384171	+	0.139827i	−0.142713	+	0.989764i	$0.545583\pi$
$744$		0			0
$745$	0.438169	−	2.48498i	0.0160533	−	0.0910427i
$746$	3.32426	−	15.0600i	0.121710	−	0.551385i
$747$		0			0
$748$	5.37262	−	11.5769i	0.196442	−	0.423293i
$749$	23.5787	−	28.0999i	0.861545	−	1.02675i
$750$		0			0
$751$	−28.7902	+	5.07650i	−1.05057	+	0.185244i	−0.672169	−	0.740397i	$-0.734637\pi$
$751$	−28.7902	+	5.07650i	−1.05057	+	0.185244i	−0.378402	+	0.925641i	$0.623526\pi$
$752$	28.2924	−	33.9693i	1.03172	−	1.23873i
$753$		0			0
$754$	−0.517045	+	1.25149i	−0.0188297	+	0.0455767i
$755$	−2.03500			−0.0740613
$756$		0			0
$757$	−8.57552			−0.311682			−0.155841	−	0.987782i	$-0.549809\pi$
$757$	−8.57552			−0.311682			−0.155841	+	0.987782i	$0.549809\pi$
$758$	−3.21443	+	7.78044i	−0.116753	+	0.282598i
$759$		0			0
$760$	−0.0802050	−	1.72813i	−0.00290934	−	0.0626860i
$761$	5.54033	−	0.976910i	0.200837	−	0.0354130i	−0.0723247	−	0.997381i	$-0.523042\pi$
$761$	5.54033	−	0.976910i	0.200837	−	0.0354130i	0.273161	+	0.961968i	$0.411931\pi$
$762$		0			0
$763$	5.33548	−	6.35857i	0.193157	−	0.230196i
$764$	26.0941	+	12.1098i	0.944051	+	0.438117i
$765$		0			0
$766$	2.03501	−	9.21927i	0.0735281	−	0.333106i
$767$	−2.21699	+	12.5732i	−0.0800509	+	0.453991i
$768$		0			0
$769$	−2.35854	−	0.858439i	−0.0850512	−	0.0309561i	0.299144	−	0.954208i	$-0.403299\pi$
$769$	−2.35854	−	0.858439i	−0.0850512	−	0.0309561i	−0.384195	+	0.923252i	$0.625521\pi$
$770$	−0.445596	−	0.854072i	−0.0160582	−	0.0307786i
$771$		0			0
$772$	−36.6562	−	3.13942i	−1.31929	−	0.112990i
$773$	−0.0355587	+	0.0205298i	−0.00127896	+	0.000738407i	−0.500639	−	0.865656i	$-0.666902\pi$
$773$	−0.0355587	+	0.0205298i	−0.00127896	+	0.000738407i	0.499360	+	0.866394i	$0.333568\pi$
$774$		0			0
$775$	21.3937	+	12.3516i	0.768483	+	0.443684i
$776$	−15.5498	+	3.49212i	−0.558206	+	0.125360i
$777$		0			0
$778$	36.3751	+	23.1267i	1.30411	+	0.829134i
$779$	22.1468	−	18.5834i	0.793492	−	0.665819i
$780$		0			0
$781$	−4.60950	+	1.67772i	−0.164941	+	0.0600335i
$782$	−14.6808	+	16.0507i	−0.524983	+	0.573972i
$783$		0			0
$784$	57.5221	−	10.3599i	2.05436	−	0.369997i
$785$	−0.00653192	−	0.0179463i	−0.000233134	−	0.000640531i
$786$		0			0
$787$	−27.9726	−	33.3365i	−0.997116	−	1.18832i	−0.982087	−	0.188429i	$-0.939660\pi$
$787$	−27.9726	−	33.3365i	−0.997116	−	1.18832i	−0.0150289	−	0.999887i	$-0.504784\pi$
$788$	11.0412	+	40.9069i	0.393328	+	1.45725i
$789$		0			0
$790$	0.0433794	+	0.327186i	0.00154337	+	0.0116407i
$791$	24.6902	−	42.7647i	0.877882	−	1.52054i
$792$		0			0
$793$	−8.69865	−	15.0665i	−0.308898	−	0.535028i
$794$	17.6616	−	13.5779i	0.626787	−	0.481863i
$795$		0			0
$796$	12.9615	+	3.44761i	0.459407	+	0.122197i
$797$	−15.3705	+	42.2300i	−0.544450	+	1.49586i	0.296652	+	0.954986i	$0.404130\pi$
$797$	−15.3705	+	42.2300i	−0.544450	+	1.49586i	−0.841102	+	0.540877i	$0.818092\pi$
$798$		0			0
$799$	66.0612	+	11.6484i	2.33708	+	0.412090i
$800$	1.10017	−	28.1529i	0.0388969	−	0.995356i
$801$		0			0
$802$	1.32171	+	4.17860i	0.0466713	+	0.147552i
$803$	−9.09342	−	7.63028i	−0.320900	−	0.269267i
$804$		0			0
$805$	0.285100	+	1.61688i	0.0100484	+	0.0569875i
$806$	−0.466114	+	10.9047i	−0.0164182	+	0.384102i
$807$		0			0
$808$	28.2334	+	8.81683i	0.993248	+	0.310175i
$809$			39.4534i			1.38711i	0.720405	+	0.693553i	$0.243956\pi$
$809$			39.4534i			1.38711i	−0.720405	+	0.693553i	$0.756044\pi$
$810$		0			0
$811$			49.4348i			1.73589i	0.496659	+	0.867946i	$0.334560\pi$
$811$			49.4348i			1.73589i	−0.496659	+	0.867946i	$0.665440\pi$
$812$	−2.42739	−	5.18077i	−0.0851845	−	0.181809i
$813$		0			0
$814$	4.27810	+	0.182864i	0.149947	+	0.00640938i
$815$	−0.290908	−	1.64982i	−0.0101900	−	0.0577906i
$816$		0			0
$817$	−7.35807	−	6.17416i	−0.257426	−	0.216006i
$818$	−35.3998	+	11.1971i	−1.23773	+	0.391499i
$819$		0			0
$820$	−1.50206	+	1.05585i	−0.0524541	+	0.0368720i
$821$	−21.7656	−	3.83786i	−0.759624	−	0.133942i	−0.219598	−	0.975590i	$-0.570475\pi$
$821$	−21.7656	−	3.83786i	−0.759624	−	0.133942i	−0.540026	+	0.841648i	$0.681586\pi$
$822$		0			0
$823$	−6.69131	+	18.3842i	−0.233244	+	0.640833i	−0.999999	−	0.00110635i	$-0.999648\pi$
$823$	−6.69131	+	18.3842i	−0.233244	+	0.640833i	0.766755	+	0.641940i	$0.221870\pi$
$824$	2.35798	+	3.67897i	0.0821442	+	0.128163i
$825$		0			0
$826$	−32.8776	−	42.7658i	−1.14396	−	1.48801i
$827$	−8.39197	−	14.5353i	−0.291817	−	0.505442i	0.682422	−	0.730958i	$-0.260927\pi$
$827$	−8.39197	−	14.5353i	−0.291817	−	0.505442i	−0.974239	+	0.225516i	$0.927593\pi$
$828$		0			0
$829$	−18.8116	+	32.5827i	−0.653355	+	1.13164i	0.328949	+	0.944348i	$0.393306\pi$
$829$	−18.8116	+	32.5827i	−0.653355	+	1.13164i	−0.982304	+	0.187296i	$0.940028\pi$
$830$	−0.458569	+	0.0607987i	−0.0159172	+	0.00211035i
$831$		0			0
$832$	11.2529	−	5.32274i	0.390126	−	0.184533i
$833$	57.0065	+	67.9377i	1.97516	+	2.35390i
$834$		0			0
$835$	−0.536320	−	1.47353i	−0.0185601	−	0.0509935i
$836$	−9.19227	+	0.821172i	−0.317921	+	0.0284008i
$837$		0			0
$838$	−37.7429	−	34.5215i	−1.30381	−	1.19253i
$839$	−51.7302	+	18.8283i	−1.78592	+	0.650024i	−0.786449	+	0.617655i	$0.788083\pi$
$839$	−51.7302	+	18.8283i	−1.78592	+	0.650024i	−0.999476	+	0.0323683i	$0.989695\pi$
$840$		0			0
$841$	21.9252	−	18.3975i	0.756043	−	0.634395i
$842$	9.61979	−	15.1306i	0.331520	−	0.521434i
$843$		0			0
$844$	28.8673	+	20.1345i	0.993652	+	0.693057i
$845$	1.27676	+	0.737140i	0.0439220	+	0.0253584i
$846$		0			0
$847$	39.8358	−	22.9992i	1.36878	−	0.790263i
$848$	−34.9342	+	0.127853i	−1.19964	+	0.00439048i
$849$		0			0
$850$	37.9024	−	19.7749i	1.30004	−	0.678272i
$851$	−6.85782	−	2.49604i	−0.235083	−	0.0855633i
$852$		0			0
$853$	1.97889	−	11.2229i	0.0677560	−	0.384263i	−0.932006	−	0.362443i	$-0.881943\pi$
$853$	1.97889	−	11.2229i	0.0677560	−	0.384263i	0.999762	−	0.0218204i	$-0.00694619\pi$
$854$	71.7782	+	15.8440i	2.45620	+	0.542169i
$855$		0			0
$856$	8.59719	+	20.5954i	0.293846	+	0.703936i
$857$	−17.0466	+	20.3153i	−0.582300	+	0.693958i	−0.974106	−	0.226090i	$-0.927406\pi$
$857$	−17.0466	+	20.3153i	−0.582300	+	0.693958i	0.391807	+	0.920048i	$0.371850\pi$
$858$		0			0
$859$	−7.71712	+	1.36074i	−0.263305	+	0.0464277i	−0.303742	−	0.952754i	$-0.598236\pi$
$859$	−7.71712	+	1.36074i	−0.263305	+	0.0464277i	0.0404372	+	0.999182i	$0.487125\pi$
$860$	0.432127	+	0.430548i	0.0147354	+	0.0146816i
$861$		0			0
$862$	14.7741	+	6.10381i	0.503208	+	0.207896i
$863$	32.9090			1.12023			0.560117	−	0.828413i	$-0.310756\pi$
$863$	32.9090			1.12023			0.560117	+	0.828413i	$0.310756\pi$
$864$		0			0
$865$	0.794776			0.0270232
$866$	23.6654	+	9.77716i	0.804182	+	0.332242i
$867$		0			0
$868$	−32.6685	−	32.5492i	−1.10884	−	1.10479i
$869$	1.73394	−	0.305741i	0.0588199	−	0.0103715i
$870$		0			0
$871$	5.64508	−	6.72755i	0.191276	−	0.227954i
$872$	1.94541	+	4.66041i	0.0658798	+	0.157821i
$873$		0			0
$874$	15.3593	+	3.39034i	0.519536	+	0.114680i
$875$	1.12284	−	6.36795i	0.0379590	−	0.215276i
$876$		0			0
$877$	−37.2032	−	13.5408i	−1.25626	−	0.457242i	−0.373748	−	0.927530i	$-0.621928\pi$
$877$	−37.2032	−	13.5408i	−1.25626	−	0.457242i	−0.882513	+	0.470288i	$0.844150\pi$
$878$	17.1466	−	8.94588i	0.578668	−	0.301909i
$879$		0			0
$880$	0.586096	−	0.00214500i	0.0197573	−	7.23081e-5i
$881$	20.1797	−	11.6507i	0.679870	−	0.392523i	−0.119936	−	0.992782i	$-0.538269\pi$
$881$	20.1797	−	11.6507i	0.679870	−	0.392523i	0.799806	+	0.600259i	$0.204936\pi$
$882$		0			0
$883$	44.2753	+	25.5624i	1.48998	+	0.860242i	0.999934	−	0.0114524i	$-0.00364550\pi$
$883$	44.2753	+	25.5624i	1.48998	+	0.860242i	0.490049	+	0.871695i	$0.336979\pi$
$884$	15.4925	+	10.8058i	0.521068	+	0.363437i
$885$		0			0
$886$	8.25639	−	12.9861i	0.277379	−	0.436278i
$887$	−5.23482	+	4.39254i	−0.175768	+	0.147487i	−0.726428	−	0.687243i	$-0.758821\pi$
$887$	−5.23482	+	4.39254i	−0.175768	+	0.147487i	0.550659	+	0.834730i	$0.314376\pi$
$888$		0			0
$889$	14.6081	−	5.31691i	0.489940	−	0.178324i
$890$	1.28254	+	1.17307i	0.0429908	+	0.0393215i
$891$		0			0
$892$	−18.4680	+	1.64980i	−0.618356	+	0.0552395i
$893$	−16.5901	−	45.5809i	−0.555167	−	1.52531i
$894$		0			0
$895$	−1.11113	−	1.32420i	−0.0371411	−	0.0442630i
$896$	−15.4943	+	50.2618i	−0.517628	+	1.67913i
$897$		0			0
$898$	9.87813	−	1.30968i	0.329638	−	0.0437045i
$899$	−1.52601	+	2.64313i	−0.0508954	+	0.0881535i
$900$		0			0
$901$	−26.5042	−	45.9065i	−0.882981	−	1.52937i
$902$	5.96965	+	7.76508i	0.198768	+	0.258549i
$903$		0			0
$904$	16.2119	+	25.2942i	0.539201	+	0.841272i
$905$	−0.0554934	+	0.152467i	−0.00184466	+	0.00506817i
$906$		0			0
$907$	−7.37773	−	1.30089i	−0.244974	−	0.0431955i	0.0498130	−	0.998759i	$-0.484137\pi$
$907$	−7.37773	−	1.30089i	−0.244974	−	0.0431955i	−0.294787	+	0.955563i	$0.595249\pi$
$908$	36.5177	−	25.6697i	1.21188	−	0.851878i
$909$		0			0
$910$	1.35932	−	0.429960i	0.0450610	−	0.0142530i
$911$	19.8453	+	16.6521i	0.657503	+	0.551710i	0.909337	−	0.416060i	$-0.136589\pi$
$911$	19.8453	+	16.6521i	0.657503	+	0.551710i	−0.251835	+	0.967770i	$0.581034\pi$
$912$		0			0
$913$	0.428513	+	2.43022i	0.0141817	+	0.0804284i
$914$	−35.9637	−	1.53724i	−1.18957	−	0.0508474i
$915$		0			0
$916$	22.3474	+	47.6960i	0.738378	+	1.57592i
$917$		−	12.1887i		−	0.402508i
$918$		0			0
$919$		−	37.4197i		−	1.23436i	−0.786821	−	0.617182i	$-0.788274\pi$
$919$		−	37.4197i		−	1.23436i	0.786821	−	0.617182i	$-0.211726\pi$
$920$	−0.953495	−	0.297761i	−0.0314358	−	0.00981689i
$921$		0			0
$922$	−2.36785	+	55.3957i	−0.0779810	+	1.82436i
$923$	−1.26065	−	7.14947i	−0.0414946	−	0.235328i
$924$		0			0
$925$	10.9875	+	9.21963i	0.361268	+	0.303140i
$926$	−3.19017	−	10.0857i	−0.104835	−	0.331438i
$927$		0			0
$928$	3.47822	+	0.135923i	0.114178	+	0.00446190i
$929$	12.0979	+	2.13318i	0.396919	+	0.0699875i	0.368545	−	0.929610i	$-0.379856\pi$
$929$	12.0979	+	2.13318i	0.396919	+	0.0699875i	0.0283738	+	0.999597i	$0.490967\pi$
$930$		0			0
$931$	21.9337	−	60.2623i	0.718848	−	1.97502i
$932$	14.4984	+	3.85642i	0.474911	+	0.126321i
$933$		0			0
$934$	1.54708	−	1.18937i	0.0506220	−	0.0389173i
$935$	0.444664	+	0.770181i	0.0145421	+	0.0251876i
$936$		0			0
$937$	−20.8028	+	36.0316i	−0.679599	+	1.17710i	0.295503	+	0.955342i	$0.404513\pi$
$937$	−20.8028	+	36.0316i	−0.679599	+	1.17710i	−0.975102	+	0.221758i	$0.928821\pi$
$938$	4.87696	+	36.7841i	0.159238	+	1.20104i
$939$		0			0
$940$	0.802734	+	2.97406i	0.0261823	+	0.0970032i
$941$	−33.5803	−	40.0194i	−1.09469	−	1.30460i	−0.949004	−	0.315265i	$-0.897907\pi$
$941$	−33.5803	−	40.0194i	−1.09469	−	1.30460i	−0.145682	−	0.989331i	$-0.546538\pi$
$942$		0			0
$943$	−5.70939	−	15.6864i	−0.185923	−	0.510820i
$944$	32.2999	−	5.81732i	1.05127	−	0.189338i
$945$		0			0
$946$	2.19627	−	2.40122i	0.0714070	−	0.0780704i
$947$	16.5986	−	6.04138i	0.539380	−	0.196318i	−0.0579415	−	0.998320i	$-0.518454\pi$
$947$	16.5986	−	6.04138i	0.539380	−	0.196318i	0.597322	+	0.802002i	$0.296231\pi$
$948$		0			0
$949$	13.4580	−	11.2926i	0.436867	−	0.366575i
$950$	−26.0874	−	16.5859i	−0.846386	−	0.538119i
$951$		0			0
$952$	−77.8677	+	17.4872i	−2.52371	+	0.566765i
$953$	−47.6750	−	27.5252i	−1.54435	−	0.891628i	−0.998557	−	0.0537052i	$-0.982897\pi$
$953$	−47.6750	−	27.5252i	−1.54435	−	0.891628i	−0.545788	−	0.837923i	$-0.683770\pi$
$954$		0			0
$955$	−1.73597	+	1.00227i	−0.0561748	+	0.0324325i
$956$	6.84317	+	0.586084i	0.221324	+	0.0189553i
$957$		0			0
$958$	8.32514	+	15.9568i	0.268973	+	0.515540i
$959$	−38.9446	−	14.1747i	−1.25759	−	0.457724i
$960$		0			0
$961$	1.11121	−	6.30196i	0.0358453	−	0.203289i
$962$	−1.36597	+	6.18830i	−0.0440407	+	0.199519i
$963$		0			0
$964$	3.08820	+	1.43318i	0.0994642	+	0.0461595i
$965$	1.64785	−	1.96383i	0.0530462	−	0.0632180i
$966$		0			0
$967$	−16.5590	+	2.91980i	−0.532502	+	0.0938945i	−0.433433	−	0.901186i	$-0.642698\pi$
$967$	−16.5590	+	2.91980i	−0.532502	+	0.0938945i	−0.0990696	+	0.995081i	$0.531587\pi$
$968$	1.29748	+	27.9560i	0.0417024	+	0.898539i
$969$		0			0
$970$	0.424038	−	1.02637i	0.0136151	−	0.0329549i
$971$	22.4986			0.722013			0.361007	−	0.932563i	$-0.382433\pi$
$971$	22.4986			0.722013			0.361007	+	0.932563i	$0.382433\pi$
$972$		0			0
$973$	−69.7582			−2.23635
$974$	6.69232	−	16.1986i	0.214436	−	0.519037i
$975$		0			0
$976$	−28.6212	+	34.3641i	−0.916143	+	1.09997i
$977$	−8.62912	+	1.52155i	−0.276070	+	0.0486786i	−0.309969	−	0.950747i	$-0.600319\pi$
$977$	−8.62912	+	1.52155i	−0.276070	+	0.0486786i	0.0338989	+	0.999425i	$0.489208\pi$
$978$		0			0
$979$	5.96003	−	7.10288i	0.190483	−	0.227009i
$980$	−1.71444	+	3.69426i	−0.0547658	+	0.118009i
$981$		0			0
$982$	−8.09645	+	36.6795i	−0.258368	+	1.17049i
$983$	1.90169	−	10.7850i	0.0606544	−	0.343988i	−0.939345	−	0.342973i	$-0.888566\pi$
$983$	1.90169	−	10.7850i	0.0606544	−	0.343988i	0.999999	−	0.00101465i	$-0.000322973\pi$
$984$		0			0
$985$	−2.77440	−	1.00980i	−0.0883996	−	0.0321748i
$986$	2.44314	+	4.68275i	0.0778053	+	0.149129i
$987$		0			0
$988$	1.16552	−	13.6087i	0.0370801	−	0.432950i
$989$	−4.80310	+	2.77307i	−0.152730	+	0.0881785i
$990$		0			0
$991$	−31.9842	−	18.4661i	−1.01601	−	0.586594i	−0.103065	−	0.994675i	$-0.532865\pi$
$991$	−31.9842	−	18.4661i	−1.01601	−	0.586594i	−0.912946	+	0.408081i	$0.866198\pi$
$992$	26.7201	−	8.55940i	0.848364	−	0.271761i
$993$		0			0
$994$	25.8849	+	16.4572i	0.821018	+	0.521991i
$995$	−0.715926	+	0.600734i	−0.0226964	+	0.0190445i
$996$		0			0
$997$	35.4190	−	12.8915i	1.12173	−	0.408276i	0.286447	−	0.958096i	$-0.407526\pi$
$997$	35.4190	−	12.8915i	1.12173	−	0.408276i	0.835283	+	0.549820i	$0.185304\pi$
$998$	9.20246	−	10.0612i	0.291299	−	0.318481i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.l.a.143.14		96
3.2	odd	2		108.2.l.a.47.3	yes	96
4.3	odd	2	inner	324.2.l.a.143.6		96
9.2	odd	6		972.2.l.d.107.9		96
9.4	even	3		972.2.l.b.755.4		96
9.5	odd	6		972.2.l.c.755.13		96
9.7	even	3		972.2.l.a.107.8		96
12.11	even	2		108.2.l.a.47.11	yes	96
27.4	even	9		108.2.l.a.23.11	yes	96
27.5	odd	18		972.2.l.b.215.6		96
27.13	even	9		972.2.l.d.863.1		96
27.14	odd	18		972.2.l.a.863.16		96
27.22	even	9		972.2.l.c.215.11		96
27.23	odd	18	inner	324.2.l.a.179.6		96
36.7	odd	6		972.2.l.a.107.16		96
36.11	even	6		972.2.l.d.107.1		96
36.23	even	6		972.2.l.c.755.11		96
36.31	odd	6		972.2.l.b.755.6		96
108.23	even	18	inner	324.2.l.a.179.14		96
108.31	odd	18		108.2.l.a.23.3	✓	96
108.59	even	18		972.2.l.b.215.4		96
108.67	odd	18		972.2.l.d.863.9		96
108.95	even	18		972.2.l.a.863.8		96
108.103	odd	18		972.2.l.c.215.13		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.3	✓	96	108.31	odd	18
108.2.l.a.23.11	yes	96	27.4	even	9
108.2.l.a.47.3	yes	96	3.2	odd	2
108.2.l.a.47.11	yes	96	12.11	even	2
324.2.l.a.143.6		96	4.3	odd	2	inner
324.2.l.a.143.14		96	1.1	even	1	trivial
324.2.l.a.179.6		96	27.23	odd	18	inner
324.2.l.a.179.14		96	108.23	even	18	inner
972.2.l.a.107.8		96	9.7	even	3
972.2.l.a.107.16		96	36.7	odd	6
972.2.l.a.863.8		96	108.95	even	18
972.2.l.a.863.16		96	27.14	odd	18
972.2.l.b.215.4		96	108.59	even	18
972.2.l.b.215.6		96	27.5	odd	18
972.2.l.b.755.4		96	9.4	even	3
972.2.l.b.755.6		96	36.31	odd	6
972.2.l.c.215.11		96	27.22	even	9
972.2.l.c.215.13		96	108.103	odd	18
972.2.l.c.755.11		96	36.23	even	6
972.2.l.c.755.13		96	9.5	odd	6
972.2.l.d.107.1		96	36.11	even	6
972.2.l.d.107.9		96	9.2	odd	6
972.2.l.d.863.1		96	27.13	even	9
972.2.l.d.863.9		96	108.67	odd	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.30706 + 0.540000i) q^{2} +(1.41680 + 1.41162i) q^{4} +(-0.137245 + 0.0242000i) q^{5} +(2.98823 - 3.56123i) q^{7} +(1.08956 + 2.61015i) q^{8} +(-0.192456 - 0.0424817i) q^{10} +(-0.182573 + 1.03542i) q^{11} +(-1.46220 - 0.532196i) q^{13} +(5.82886 - 3.04109i) q^{14} +(0.0146392 + 3.99997i) q^{16} +(-5.25631 + 3.03473i) q^{17} +(3.80088 + 2.19444i) q^{19} +(-0.228610 - 0.159452i) q^{20} +(-0.797761 + 1.25477i) q^{22} +(1.94128 - 1.62893i) q^{23} +(-4.68021 + 1.70346i) q^{25} +(-1.62379 - 1.48520i) q^{26} +(9.26084 - 0.827297i) q^{28} +(-0.210458 - 0.578229i) q^{29} +(-3.18818 - 3.79952i) q^{31} +(-2.14085 + 5.23610i) q^{32} +(-8.50906 + 1.12816i) q^{34} +(-0.323938 + 0.561078i) q^{35} +(-1.43991 - 2.49400i) q^{37} +(3.78297 + 4.92073i) q^{38} +(-0.212703 - 0.331863i) q^{40} +(2.25297 - 6.18999i) q^{41} +(-2.15530 - 0.380038i) q^{43} +(-1.72029 + 1.20926i) q^{44} +(3.41698 - 1.08081i) q^{46} +(-8.46639 - 7.10414i) q^{47} +(-2.53733 - 14.3899i) q^{49} +(-7.03718 - 0.300799i) q^{50} +(-1.32038 - 2.81809i) q^{52} +8.73360i q^{53} -0.146525i q^{55} +(12.5512 + 3.91953i) q^{56} +(0.0371630 - 0.869426i) q^{58} +(-1.42477 - 8.08025i) q^{59} +(8.56477 + 7.18670i) q^{61} +(-2.11539 - 6.68781i) q^{62} +(-5.62571 + 5.68782i) q^{64} +(0.213559 + 0.0376562i) q^{65} +(-1.93034 + 5.30357i) q^{67} +(-11.7310 - 3.12033i) q^{68} +(-0.726388 + 0.558434i) q^{70} +(2.33277 + 4.04048i) q^{71} +(-5.64518 + 9.77774i) q^{73} +(-0.535287 - 4.03736i) q^{74} +(2.28736 + 8.47449i) q^{76} +(3.14181 + 3.74426i) q^{77} +(-0.572755 - 1.57363i) q^{79} +(-0.0988087 - 0.548623i) q^{80} +(6.28736 - 6.87406i) q^{82} +(2.20553 - 0.802749i) q^{83} +(0.647964 - 0.543706i) q^{85} +(-2.61188 - 1.66060i) q^{86} +(-2.90152 + 0.651613i) q^{88} +(-7.63741 - 4.40946i) q^{89} +(-6.26466 + 3.61690i) q^{91} +(5.04983 + 0.432493i) q^{92} +(-7.22981 - 13.8574i) q^{94} +(-0.574758 - 0.209195i) q^{95} +(-0.978443 + 5.54902i) q^{97} +(4.45412 - 20.1786i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38}+ \cdots + 180 q^{98}+O(q^{100}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Introduction

L-functions

Modular forms

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