LMFDB - Embedded newform 1950.2.bc.h.901.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(751,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1950.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.bc (of order $6$, degree $2$, 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:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 87 x^{10} - 380 x^{9} + 2556 x^{8} - 8010 x^{7} + 29687 x^{6} - 62556 x^{5} + \cdots + 14089 $ x^12 - 6x^11 + 87x^10 - 380x^9 + 2556x^8 - 8010x^7 + 29687x^6 - 62556x^5 + 115386x^4 - 135130x^3 + 113253x^2 - 54888*x + 14089
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.2
Root			$0.500000 - 0.822735i$ of defining polynomial
Character	$\chi$	$=$	1950.901
Dual form			1950.2.bc.h.751.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(-2.32854 + 1.34438i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(-2.32854 + 1.34438i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(4.61081 + 2.66205i) q^{11} -1.00000 q^{12} +(3.42711 - 1.12022i) q^{13} +2.68876 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.18370 - 3.78228i) q^{17} +1.00000i q^{18} +(2.70388 - 1.56109i) q^{19} -2.68876i q^{21} +(-2.66205 - 4.61081i) q^{22} +(0.478355 - 0.828535i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-3.52808 - 0.743415i) q^{26} +1.00000 q^{27} +(-2.32854 - 1.34438i) q^{28} +(-1.59858 + 2.76882i) q^{29} -6.98118i q^{31} +(0.866025 - 0.500000i) q^{32} +(-4.61081 + 2.66205i) q^{33} +4.36740i q^{34} +(0.500000 - 0.866025i) q^{36} +(-4.20388 - 2.42711i) q^{37} -3.12217 q^{38} +(-0.743415 + 3.52808i) q^{39} +(3.78228 + 2.18370i) q^{41} +(-1.34438 + 2.32854i) q^{42} +(0.620223 + 1.07426i) q^{43} +5.32411i q^{44} +(-0.828535 + 0.478355i) q^{46} +2.61378i q^{47} +(-0.500000 - 0.866025i) q^{48} +(0.114717 - 0.198696i) q^{49} +4.36740 q^{51} +(2.68370 + 2.40786i) q^{52} +6.98118 q^{53} +(-0.866025 - 0.500000i) q^{54} +(1.34438 + 2.32854i) q^{56} +3.12217i q^{57} +(2.76882 - 1.59858i) q^{58} +(5.03242 - 2.90547i) q^{59} +(-1.42711 - 2.47183i) q^{61} +(-3.49059 + 6.04588i) q^{62} +(2.32854 + 1.34438i) q^{63} -1.00000 q^{64} +5.32411 q^{66} +(-1.34894 - 0.778812i) q^{67} +(2.18370 - 3.78228i) q^{68} +(0.478355 + 0.828535i) q^{69} +(8.89482 - 5.13543i) q^{71} +(-0.866025 + 0.500000i) q^{72} +0.569326i q^{73} +(2.42711 + 4.20388i) q^{74} +(2.70388 + 1.56109i) q^{76} -14.3152 q^{77} +(2.40786 - 2.68370i) q^{78} +17.1863 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-2.18370 - 3.78228i) q^{82} +13.3082i q^{83} +(2.32854 - 1.34438i) q^{84} -1.24045i q^{86} +(-1.59858 - 2.76882i) q^{87} +(2.66205 - 4.61081i) q^{88} +(-0.243193 - 0.140408i) q^{89} +(-6.47415 + 7.21582i) q^{91} +0.956710 q^{92} +(6.04588 + 3.49059i) q^{93} +(1.30689 - 2.26360i) q^{94} +1.00000i q^{96} +(10.4135 - 6.01223i) q^{97} +(-0.198696 + 0.114717i) q^{98} -5.32411i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 6 q^{4} - 6 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^7 - 6 * q^9	$ 12 q - 6 q^{3} + 6 q^{4} - 6 q^{7} - 6 q^{9} - 12 q^{11} - 12 q^{12} + 8 q^{14} - 6 q^{16} - 6 q^{19} - 4 q^{22} + 4 q^{23} - 4 q^{26} + 12 q^{27} - 6 q^{28} + 12 q^{33} + 6 q^{36} - 12 q^{37} + 24 q^{38} + 6 q^{39} - 4 q^{42} - 10 q^{43} + 12 q^{46} - 6 q^{48} + 32 q^{49} + 6 q^{52} - 16 q^{53} + 4 q^{56} + 24 q^{61} + 8 q^{62} + 6 q^{63} - 12 q^{64} + 8 q^{66} + 6 q^{67} + 4 q^{69} + 12 q^{71} - 12 q^{74} - 6 q^{76} - 48 q^{77} + 8 q^{78} + 52 q^{79} - 6 q^{81} + 6 q^{84} + 4 q^{88} + 24 q^{89} - 54 q^{91} + 8 q^{92} - 8 q^{94} + 12 q^{97} + 36 q^{98}+O(q^{100}) $ 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^7 - 6 * q^9 - 12 * q^11 - 12 * q^12 + 8 * q^14 - 6 * q^16 - 6 * q^19 - 4 * q^22 + 4 * q^23 - 4 * q^26 + 12 * q^27 - 6 * q^28 + 12 * q^33 + 6 * q^36 - 12 * q^37 + 24 * q^38 + 6 * q^39 - 4 * q^42 - 10 * q^43 + 12 * q^46 - 6 * q^48 + 32 * q^49 + 6 * q^52 - 16 * q^53 + 4 * q^56 + 24 * q^61 + 8 * q^62 + 6 * q^63 - 12 * q^64 + 8 * q^66 + 6 * q^67 + 4 * q^69 + 12 * q^71 - 12 * q^74 - 6 * q^76 - 48 * q^77 + 8 * q^78 + 52 * q^79 - 6 * q^81 + 6 * q^84 + 4 * q^88 + 24 * q^89 - 54 * q^91 + 8 * q^92 - 8 * q^94 + 12 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	−2.32854	+	1.34438i	−0.880104	+	0.508128i	−0.870693	−	0.491828i	$-0.836329\pi$
$7$	−2.32854	+	1.34438i	−0.880104	+	0.508128i	−0.00941100	+	0.999956i	$0.502996\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	4.61081	+	2.66205i	1.39021	+	0.802639i	0.993338	−	0.115234i	$-0.0367619\pi$
$11$	4.61081	+	2.66205i	1.39021	+	0.802639i	0.396873	+	0.917873i	$0.370095\pi$
$12$	−1.00000			−0.288675
$13$	3.42711	−	1.12022i	0.950510	−	0.310694i
$13$	3.42711	−	1.12022i	0.950510	−	0.310694i
$14$	2.68876			0.718602
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.18370	−	3.78228i	−0.529624	−	0.917336i	−0.999403	−	0.0345521i	$-0.989000\pi$
$17$	−2.18370	−	3.78228i	−0.529624	−	0.917336i	0.469778	−	0.882784i	$-0.344334\pi$
$18$			1.00000i			0.235702i
$19$	2.70388	−	1.56109i	0.620313	−	0.358138i	−0.156678	−	0.987650i	$-0.550078\pi$
$19$	2.70388	−	1.56109i	0.620313	−	0.358138i	0.776991	+	0.629512i	$0.216745\pi$
$20$		0			0
$21$		−	2.68876i		−	0.586736i
$22$	−2.66205	−	4.61081i	−0.567552	−	0.983028i
$23$	0.478355	−	0.828535i	0.0997439	−	0.172762i	−0.811835	−	0.583887i	$-0.801531\pi$
$23$	0.478355	−	0.828535i	0.0997439	−	0.172762i	0.911579	+	0.411126i	$0.134864\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$		0			0
$26$	−3.52808	−	0.743415i	−0.691913	−	0.145796i
$27$	1.00000			0.192450
$28$	−2.32854	−	1.34438i	−0.440052	−	0.254064i
$29$	−1.59858	+	2.76882i	−0.296848	+	0.514157i	−0.975413	−	0.220384i	$-0.929269\pi$
$29$	−1.59858	+	2.76882i	−0.296848	+	0.514157i	0.678565	+	0.734541i	$0.262602\pi$
$30$		0			0
$31$		−	6.98118i		−	1.25386i	−0.779077	−	0.626928i	$-0.784312\pi$
$31$		−	6.98118i		−	1.25386i	0.779077	−	0.626928i	$-0.215688\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−4.61081	+	2.66205i	−0.802639	+	0.463404i
$34$			4.36740i			0.749002i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−4.20388	−	2.42711i	−0.691114	−	0.399015i	0.112915	−	0.993605i	$-0.463981\pi$
$37$	−4.20388	−	2.42711i	−0.691114	−	0.399015i	−0.804029	+	0.594590i	$0.797314\pi$
$38$	−3.12217			−0.506484
$39$	−0.743415	+	3.52808i	−0.119042	+	0.564945i
$40$		0			0
$41$	3.78228	+	2.18370i	0.590692	+	0.341036i	0.765371	−	0.643589i	$-0.222555\pi$
$41$	3.78228	+	2.18370i	0.590692	+	0.341036i	−0.174679	+	0.984625i	$0.555889\pi$
$42$	−1.34438	+	2.32854i	−0.207442	+	0.359301i
$43$	0.620223	+	1.07426i	0.0945831	+	0.163823i	0.909435	−	0.415847i	$-0.136515\pi$
$43$	0.620223	+	1.07426i	0.0945831	+	0.163823i	−0.814851	+	0.579670i	$0.803182\pi$
$44$			5.32411i			0.802639i
$45$		0			0
$46$	−0.828535	+	0.478355i	−0.122161	+	0.0705296i
$47$			2.61378i			0.381259i	0.981662	+	0.190630i	$0.0610529\pi$
$47$			2.61378i			0.381259i	−0.981662	+	0.190630i	$0.938947\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	0.114717	−	0.198696i	0.0163882	−	0.0283852i
$50$		0			0
$51$	4.36740			0.611558
$52$	2.68370	+	2.40786i	0.372162	+	0.333909i
$53$	6.98118			0.958938			0.479469	−	0.877559i	$-0.340829\pi$
$53$	6.98118			0.958938			0.479469	+	0.877559i	$0.340829\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$		0			0
$56$	1.34438	+	2.32854i	0.179650	+	0.311164i
$57$			3.12217i			0.413542i
$58$	2.76882	−	1.59858i	0.363564	−	0.209904i
$59$	5.03242	−	2.90547i	0.655165	−	0.378260i	−0.135267	−	0.990809i	$-0.543189\pi$
$59$	5.03242	−	2.90547i	0.655165	−	0.378260i	0.790432	+	0.612549i	$0.209856\pi$
$60$		0			0
$61$	−1.42711	−	2.47183i	−0.182723	−	0.316486i	0.760084	−	0.649825i	$-0.225158\pi$
$61$	−1.42711	−	2.47183i	−0.182723	−	0.316486i	−0.942807	+	0.333339i	$0.891825\pi$
$62$	−3.49059	+	6.04588i	−0.443305	+	0.767827i
$63$	2.32854	+	1.34438i	0.293368	+	0.169376i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	5.32411			0.655352
$67$	−1.34894	−	0.778812i	−0.164800	−	0.0951471i	0.415332	−	0.909670i	$-0.363665\pi$
$67$	−1.34894	−	0.778812i	−0.164800	−	0.0951471i	−0.580131	+	0.814523i	$0.696999\pi$
$68$	2.18370	−	3.78228i	0.264812	−	0.458668i
$69$	0.478355	+	0.828535i	0.0575872	+	0.0997439i
$70$		0			0
$71$	8.89482	−	5.13543i	1.05562	−	0.609463i	0.131403	−	0.991329i	$-0.458052\pi$
$71$	8.89482	−	5.13543i	1.05562	−	0.609463i	0.924218	+	0.381866i	$0.124718\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$			0.569326i			0.0666345i	0.999445	+	0.0333173i	$0.0106072\pi$
$73$			0.569326i			0.0666345i	−0.999445	+	0.0333173i	$0.989393\pi$
$74$	2.42711	+	4.20388i	0.282146	+	0.488691i
$75$		0			0
$76$	2.70388	+	1.56109i	0.310157	+	0.179069i
$77$	−14.3152			−1.63137
$78$	2.40786	−	2.68370i	0.272636	−	0.303869i
$79$	17.1863			1.93361			0.966804	−	0.255518i	$-0.0822460\pi$
$79$	17.1863			1.93361			0.966804	+	0.255518i	$0.0822460\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.18370	−	3.78228i	−0.241149	−	0.417682i
$83$			13.3082i			1.46076i	0.683038	+	0.730382i	$0.260658\pi$
$83$			13.3082i			1.46076i	−0.683038	+	0.730382i	$0.739342\pi$
$84$	2.32854	−	1.34438i	0.254064	−	0.146684i
$85$		0			0
$86$		−	1.24045i		−	0.133761i
$87$	−1.59858	−	2.76882i	−0.171386	−	0.296848i
$88$	2.66205	−	4.61081i	0.283776	−	0.491514i
$89$	−0.243193	−	0.140408i	−0.0257784	−	0.0148832i	0.487055	−	0.873371i	$-0.338071\pi$
$89$	−0.243193	−	0.140408i	−0.0257784	−	0.0148832i	−0.512834	+	0.858488i	$0.671404\pi$
$90$		0			0
$91$	−6.47415	+	7.21582i	−0.678675	+	0.756424i
$92$	0.956710			0.0997439
$93$	6.04588	+	3.49059i	0.626928	+	0.361957i
$94$	1.30689	−	2.26360i	0.134795	−	0.233473i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	10.4135	−	6.01223i	1.05733	−	0.610450i	0.132637	−	0.991165i	$-0.457655\pi$
$97$	10.4135	−	6.01223i	1.05733	−	0.610450i	0.924692	+	0.380715i	$0.124322\pi$
$98$	−0.198696	+	0.114717i	−0.0200713	+	0.0115882i
$99$		−	5.32411i		−	0.535093i
$100$		0			0
$101$	−6.92268	+	11.9904i	−0.688833	+	1.19309i	0.283383	+	0.959007i	$0.408543\pi$
$101$	−6.92268	+	11.9904i	−0.688833	+	1.19309i	−0.972216	+	0.234086i	$0.924790\pi$
$102$	−3.78228	−	2.18370i	−0.374501	−	0.216218i
$103$	18.1600			1.78935			0.894677	−	0.446715i	$-0.147406\pi$
$103$	18.1600			1.78935			0.894677	+	0.446715i	$0.147406\pi$
$104$	−1.12022	−	3.42711i	−0.109847	−	0.336056i
$105$		0			0
$106$	−6.04588	−	3.49059i	−0.587227	−	0.339036i
$107$	−10.2286	+	17.7164i	−0.988833	+	1.71271i	−0.365356	+	0.930868i	$0.619053\pi$
$107$	−10.2286	+	17.7164i	−0.988833	+	1.71271i	−0.623477	+	0.781841i	$0.714281\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$			6.49435i			0.622045i	0.950402	+	0.311023i	$0.100672\pi$
$109$			6.49435i			0.622045i	−0.950402	+	0.311023i	$0.899328\pi$
$110$		0			0
$111$	4.20388	−	2.42711i	0.399015	−	0.230371i
$112$		−	2.68876i		−	0.254064i
$113$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$113$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$114$	1.56109	−	2.70388i	0.146209	−	0.253242i
$115$		0			0
$116$	−3.19716			−0.296848
$117$	−2.68370	−	2.40786i	−0.248108	−	0.222606i
$118$	−5.81094			−0.534940
$119$	10.1696	+	5.87144i	0.932249	+	0.538234i
$120$		0			0
$121$	8.67305	+	15.0222i	0.788459	+	1.36565i
$122$			2.85423i			0.258409i
$123$	−3.78228	+	2.18370i	−0.341036	+	0.196897i
$124$	6.04588	−	3.49059i	0.542936	−	0.313464i
$125$		0			0
$126$	−1.34438	−	2.32854i	−0.119767	−	0.207442i
$127$	10.7851	−	18.6803i	0.957022	−	1.65761i	0.227352	−	0.973813i	$-0.426993\pi$
$127$	10.7851	−	18.6803i	0.957022	−	1.65761i	0.729671	−	0.683799i	$-0.239673\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−1.24045			−0.109215
$130$		0			0
$131$	3.07615			0.268764			0.134382	−	0.990930i	$-0.457095\pi$
$131$	3.07615			0.268764			0.134382	+	0.990930i	$0.457095\pi$
$132$	−4.61081	−	2.66205i	−0.401320	−	0.231702i
$133$	−4.19739	+	7.27009i	−0.363960	+	0.630397i
$134$	0.778812	+	1.34894i	0.0672791	+	0.116531i
$135$		0			0
$136$	−3.78228	+	2.18370i	−0.324327	+	0.187251i
$137$	−16.9650	+	9.79473i	−1.44942	+	0.836820i	−0.998446	−	0.0557195i	$-0.982255\pi$
$137$	−16.9650	+	9.79473i	−1.44942	+	0.836820i	−0.450969	+	0.892540i	$0.648921\pi$
$138$		−	0.956710i		−	0.0814406i
$139$	−7.77583	−	13.4681i	−0.659538	−	1.14235i	−0.980735	−	0.195340i	$-0.937419\pi$
$139$	−7.77583	−	13.4681i	−0.659538	−	1.14235i	0.321198	−	0.947012i	$-0.395915\pi$
$140$		0			0
$141$	−2.26360	−	1.30689i	−0.190630	−	0.110060i
$142$	−10.2709			−0.861911
$143$	18.7839	+	3.95802i	1.57079	+	0.330986i
$144$	1.00000			0.0833333
$145$		0			0
$146$	0.284663	−	0.493050i	0.0235589	−	0.0408051i
$147$	0.114717	+	0.198696i	0.00946172	+	0.0163882i
$148$		−	4.85423i		−	0.399015i
$149$	−13.8328	+	7.98638i	−1.13323	+	0.654270i	−0.944745	−	0.327807i	$-0.893691\pi$
$149$	−13.8328	+	7.98638i	−1.13323	+	0.654270i	−0.188484	+	0.982076i	$0.560357\pi$
$150$		0			0
$151$			10.0784i			0.820172i	0.912047	+	0.410086i	$0.134501\pi$
$151$			10.0784i			0.820172i	−0.912047	+	0.410086i	$0.865499\pi$
$152$	−1.56109	−	2.70388i	−0.126621	−	0.219314i
$153$	−2.18370	+	3.78228i	−0.176541	+	0.305779i
$154$	12.3974	+	7.15762i	0.999008	+	0.576778i
$155$		0			0
$156$	−3.42711	+	1.12022i	−0.274389	+	0.0896896i
$157$	20.3755			1.62614			0.813070	−	0.582165i	$-0.197794\pi$
$157$	20.3755			1.62614			0.813070	+	0.582165i	$0.197794\pi$
$158$	−14.8838	−	8.59314i	−1.18409	−	0.683634i
$159$	−3.49059	+	6.04588i	−0.276822	+	0.479469i
$160$		0			0
$161$			2.57236i			0.202731i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	−4.95296	+	2.85959i	−0.387946	+	0.223981i	−0.681270	−	0.732033i	$-0.738572\pi$
$163$	−4.95296	+	2.85959i	−0.387946	+	0.223981i	0.293324	+	0.956013i	$0.405239\pi$
$164$			4.36740i			0.341036i
$165$		0			0
$166$	6.65410	−	11.5252i	0.516458	−	0.894532i
$167$	0.828535	+	0.478355i	0.0641140	+	0.0370162i	0.531714	−	0.846924i	$-0.321548\pi$
$167$	0.828535	+	0.478355i	0.0641140	+	0.0370162i	−0.467600	+	0.883940i	$0.654881\pi$
$168$	−2.68876			−0.207442
$169$	10.4902	−	7.67826i	0.806939	−	0.590635i
$170$		0			0
$171$	−2.70388	−	1.56109i	−0.206771	−	0.119379i
$172$	−0.620223	+	1.07426i	−0.0472915	+	0.0819113i
$173$	0.410685	+	0.711327i	0.0312238	+	0.0540812i	0.881215	−	0.472716i	$-0.156726\pi$
$173$	0.410685	+	0.711327i	0.0312238	+	0.0540812i	−0.849991	+	0.526797i	$0.823393\pi$
$174$			3.19716i			0.242376i
$175$		0			0
$176$	−4.61081	+	2.66205i	−0.347553	+	0.200660i
$177$			5.81094i			0.436777i
$178$	0.140408	+	0.243193i	0.0105240	+	0.0182281i
$179$	0.0905528	−	0.156842i	0.00676823	−	0.0117229i	−0.862621	−	0.505850i	$-0.831179\pi$
$179$	0.0905528	−	0.156842i	0.00676823	−	0.0117229i	0.869390	+	0.494127i	$0.164512\pi$
$180$		0			0
$181$	5.28082			0.392520			0.196260	−	0.980552i	$-0.437120\pi$
$181$	5.28082			0.392520			0.196260	+	0.980552i	$0.437120\pi$
$182$	9.21469	−	3.01201i	0.683038	−	0.223265i
$183$	2.85423			0.210990
$184$	−0.828535	−	0.478355i	−0.0610804	−	0.0352648i
$185$		0			0
$186$	−3.49059	−	6.04588i	−0.255942	−	0.443305i
$187$		−	23.2525i		−	1.70039i
$188$	−2.26360	+	1.30689i	−0.165090	+	0.0953148i
$189$	−2.32854	+	1.34438i	−0.169376	+	0.0977893i
$190$		0			0
$191$	10.8540	+	18.7997i	0.785368	+	1.36030i	0.928779	+	0.370634i	$0.120860\pi$
$191$	10.8540	+	18.7997i	0.785368	+	1.36030i	−0.143411	+	0.989663i	$0.545807\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	12.1909	+	7.03844i	0.877523	+	0.506638i	0.869841	−	0.493333i	$-0.164221\pi$
$193$	12.1909	+	7.03844i	0.877523	+	0.506638i	0.00768190	+	0.999970i	$0.497555\pi$
$194$	−12.0245			−0.863306
$195$		0			0
$196$	0.229435			0.0163882
$197$	11.0999	+	6.40851i	0.790833	+	0.456587i	0.840256	−	0.542190i	$-0.182405\pi$
$197$	11.0999	+	6.40851i	0.790833	+	0.456587i	−0.0494229	+	0.998778i	$0.515738\pi$
$198$	−2.66205	+	4.61081i	−0.189184	+	0.327676i
$199$	−5.88282	−	10.1893i	−0.417022	−	0.722303i	0.578616	−	0.815600i	$-0.303593\pi$
$199$	−5.88282	−	10.1893i	−0.417022	−	0.722303i	−0.995638	+	0.0932965i	$0.970260\pi$
$200$		0			0
$201$	1.34894	−	0.778812i	0.0951471	−	0.0549332i
$202$	11.9904	−	6.92268i	0.843644	−	0.487078i
$203$		−	8.59639i		−	0.603348i
$204$	2.18370	+	3.78228i	0.152889	+	0.264812i
$205$		0			0
$206$	−15.7270	−	9.07998i	−1.09575	−	0.632632i
$207$	−0.956710			−0.0664959
$208$	−0.743415	+	3.52808i	−0.0515466	+	0.244628i
$209$	16.6228			1.14982
$210$		0			0
$211$	0.0557449	−	0.0965530i	0.00383764	−	0.00664698i	−0.864100	−	0.503320i	$-0.832112\pi$
$211$	0.0557449	−	0.0965530i	0.00383764	−	0.00664698i	0.867938	+	0.496673i	$0.165445\pi$
$212$	3.49059	+	6.04588i	0.239735	+	0.415232i
$213$			10.2709i			0.703747i
$214$	17.7164	−	10.2286i	1.21107	−	0.699211i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	9.38536	+	16.2559i	0.637119	+	1.10352i
$218$	3.24717	−	5.62427i	0.219926	−	0.380923i
$219$	−0.493050	−	0.284663i	−0.0333173	−	0.0192357i
$220$		0			0
$221$	−11.7208	−	10.5161i	−0.788424	−	0.707386i
$222$	−4.85423			−0.325794
$223$	7.46575	+	4.31035i	0.499944	+	0.288643i	0.728690	−	0.684843i	$-0.240129\pi$
$223$	7.46575	+	4.31035i	0.499944	+	0.288643i	−0.228747	+	0.973486i	$0.573463\pi$
$224$	−1.34438	+	2.32854i	−0.0898252	+	0.155582i
$225$		0			0
$226$		0			0
$227$	17.8732	−	10.3191i	1.18629	−	0.684904i	0.228828	−	0.973467i	$-0.426511\pi$
$227$	17.8732	−	10.3191i	1.18629	−	0.684904i	0.957461	+	0.288563i	$0.0931774\pi$
$228$	−2.70388	+	1.56109i	−0.179069	+	0.103386i
$229$		−	3.12928i		−	0.206789i	−0.994640	−	0.103394i	$-0.967030\pi$
$229$		−	3.12928i		−	0.206789i	0.994640	−	0.103394i	$-0.0329704\pi$
$230$		0			0
$231$	7.15762	−	12.3974i	0.470937	−	0.815687i
$232$	2.76882	+	1.59858i	0.181782	+	0.104952i
$233$	9.31414			0.610190			0.305095	−	0.952322i	$-0.401312\pi$
$233$	9.31414			0.610190			0.305095	+	0.952322i	$0.401312\pi$
$234$	1.12022	+	3.42711i	0.0732312	+	0.224037i
$235$		0			0
$236$	5.03242	+	2.90547i	0.327582	+	0.189130i
$237$	−8.59314	+	14.8838i	−0.558185	+	0.966804i
$238$	−5.87144	−	10.1696i	−0.380589	−	0.659199i
$239$		−	18.4726i		−	1.19489i	−0.801909	−	0.597447i	$-0.796182\pi$
$239$		−	18.4726i		−	1.19489i	0.801909	−	0.597447i	$-0.203818\pi$
$240$		0			0
$241$	1.99906	−	1.15416i	0.128771	−	0.0743460i	−0.434231	−	0.900802i	$-0.642980\pi$
$241$	1.99906	−	1.15416i	0.128771	−	0.0743460i	0.563002	+	0.826456i	$0.309646\pi$
$242$		−	17.3461i		−	1.11505i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	1.42711	−	2.47183i	0.0913615	−	0.158243i
$245$		0			0
$246$	4.36740			0.278455
$247$	7.51774	−	8.37897i	0.478343	−	0.533141i
$248$	−6.98118			−0.443305
$249$	−11.5252	−	6.65410i	−0.730382	−	0.421686i
$250$		0			0
$251$	10.6800	+	18.4983i	0.674116	+	1.16760i	0.976726	+	0.214489i	$0.0688087\pi$
$251$	10.6800	+	18.4983i	0.674116	+	1.16760i	−0.302610	+	0.953115i	$0.597858\pi$
$252$			2.68876i			0.169376i
$253$	4.41121	−	2.54681i	0.277330	−	0.160117i
$254$	−18.6803	+	10.7851i	−1.17211	+	0.676717i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.46451	+	9.46481i	−0.340867	+	0.590399i	−0.984594	−	0.174856i	$-0.944054\pi$
$257$	−5.46451	+	9.46481i	−0.340867	+	0.590399i	0.643727	+	0.765255i	$0.277387\pi$
$258$	1.07426	+	0.620223i	0.0668803	+	0.0386134i
$259$	13.0519			0.811003
$260$		0			0
$261$	3.19716			0.197899
$262$	−2.66402	−	1.53807i	−0.164584	−	0.0950224i
$263$	6.74488	−	11.6825i	0.415907	−	0.720372i	−0.579616	−	0.814889i	$-0.696798\pi$
$263$	6.74488	−	11.6825i	0.415907	−	0.720372i	0.995523	+	0.0945177i	$0.0301309\pi$
$264$	2.66205	+	4.61081i	0.163838	+	0.283776i
$265$		0			0
$266$	7.27009	−	4.19739i	0.445758	−	0.257359i
$267$	0.243193	−	0.140408i	0.0148832	−	0.00859280i
$268$		−	1.55762i		−	0.0951471i
$269$	4.25014	+	7.36146i	0.259136	+	0.448836i	0.966011	−	0.258502i	$-0.0832290\pi$
$269$	4.25014	+	7.36146i	0.259136	+	0.448836i	−0.706875	+	0.707339i	$0.749896\pi$
$270$		0			0
$271$	−19.3767	−	11.1872i	−1.17705	−	0.679572i	−0.221722	−	0.975110i	$-0.571168\pi$
$271$	−19.3767	−	11.1872i	−1.17705	−	0.679572i	−0.955331	+	0.295538i	$0.904501\pi$
$272$	4.36740			0.264812
$273$	−3.01201	−	9.21469i	−0.182295	−	0.557698i
$274$	19.5895			1.18344
$275$		0			0
$276$	−0.478355	+	0.828535i	−0.0287936	+	0.0498720i
$277$	14.4282	+	24.9904i	0.866906	+	1.50152i	0.865142	+	0.501526i	$0.167228\pi$
$277$	14.4282	+	24.9904i	0.866906	+	1.50152i	0.00176347	+	0.999998i	$0.499439\pi$
$278$			15.5517i			0.932727i
$279$	−6.04588	+	3.49059i	−0.361957	+	0.208976i
$280$		0			0
$281$		−	25.4079i		−	1.51571i	−0.652424	−	0.757854i	$-0.726248\pi$
$281$		−	25.4079i		−	1.51571i	0.652424	−	0.757854i	$-0.273752\pi$
$282$	1.30689	+	2.26360i	0.0778242	+	0.134795i
$283$	−5.73899	+	9.94021i	−0.341147	+	0.590884i	−0.984646	−	0.174563i	$-0.944149\pi$
$283$	−5.73899	+	9.94021i	−0.341147	+	0.590884i	0.643499	+	0.765447i	$0.277482\pi$
$284$	8.89482	+	5.13543i	0.527810	+	0.304731i
$285$		0			0
$286$	−14.2883	−	12.8197i	−0.844884	−	0.758043i
$287$	−11.7429			−0.693160
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	−1.03707	+	1.79626i	−0.0610041	+	0.105662i
$290$		0			0
$291$			12.0245i			0.704887i
$292$	−0.493050	+	0.284663i	−0.0288536	+	0.0166586i
$293$	2.92023	−	1.68599i	0.170602	−	0.0984969i	−0.412268	−	0.911063i	$-0.635263\pi$
$293$	2.92023	−	1.68599i	0.170602	−	0.0984969i	0.582869	+	0.812566i	$0.301930\pi$
$294$		−	0.229435i		−	0.0133809i
$295$		0			0
$296$	−2.42711	+	4.20388i	−0.141073	+	0.244346i
$297$	4.61081	+	2.66205i	0.267546	+	0.154468i
$298$	15.9728			0.925277
$299$	0.711233	−	3.37535i	0.0411316	−	0.195201i
$300$		0			0
$301$	−2.88842	−	1.66763i	−0.166486	−	0.0961206i
$302$	5.03922	−	8.72819i	0.289975	−	0.502251i
$303$	−6.92268	−	11.9904i	−0.397698	−	0.688833i
$304$			3.12217i			0.179069i
$305$		0			0
$306$	3.78228	−	2.18370i	0.216218	−	0.124834i
$307$		−	12.5113i		−	0.714057i	−0.934093	−	0.357029i	$-0.883790\pi$
$307$		−	12.5113i		−	0.714057i	0.934093	−	0.357029i	$-0.116210\pi$
$308$	−7.15762	−	12.3974i	−0.407843	−	0.706405i
$309$	−9.07998	+	15.7270i	−0.516542	+	0.894677i
$310$		0			0
$311$	−24.4726			−1.38771			−0.693857	−	0.720113i	$-0.744090\pi$
$311$	−24.4726			−1.38771			−0.693857	+	0.720113i	$0.744090\pi$
$312$	3.52808	+	0.743415i	0.199738	+	0.0420876i
$313$	−28.8758			−1.63216			−0.816078	−	0.577942i	$-0.803856\pi$
$313$	−28.8758			−1.63216			−0.816078	+	0.577942i	$0.803856\pi$
$314$	−17.6457	−	10.1877i	−0.995804	−	0.574928i
$315$		0			0
$316$	8.59314	+	14.8838i	0.483402	+	0.837277i
$317$		−	12.8139i		−	0.719698i	−0.933011	−	0.359849i	$-0.882828\pi$
$317$		−	12.8139i		−	0.719698i	0.933011	−	0.359849i	$-0.117172\pi$
$318$	6.04588	−	3.49059i	0.339036	−	0.195742i
$319$	−14.7415	+	8.51099i	−0.825364	+	0.476524i
$320$		0			0
$321$	−10.2286	−	17.7164i	−0.570903	−	0.988833i
$322$	1.28618	−	2.22773i	0.0716761	−	0.124147i
$323$	−11.8089	−	6.81788i	−0.657066	−	0.379357i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	5.71918			0.316756
$327$	−5.62427	−	3.24717i	−0.311023	−	0.179569i
$328$	2.18370	−	3.78228i	0.120575	−	0.208841i
$329$	−3.51391	−	6.08628i	−0.193728	−	0.335547i
$330$		0			0
$331$	−30.0612	+	17.3558i	−1.65231	+	0.953962i	−0.676192	+	0.736726i	$0.736371\pi$
$331$	−30.0612	+	17.3558i	−1.65231	+	0.953962i	−0.976119	+	0.217236i	$0.930296\pi$
$332$	−11.5252	+	6.65410i	−0.632530	+	0.365191i
$333$			4.85423i			0.266010i
$334$	−0.478355	−	0.828535i	−0.0261744	−	0.0453354i
$335$		0			0
$336$	2.32854	+	1.34438i	0.127032	+	0.0733420i
$337$	27.2945			1.48683			0.743414	−	0.668831i	$-0.233205\pi$
$337$	27.2945			1.48683			0.743414	+	0.668831i	$0.233205\pi$
$338$	−12.9239	+	1.40447i	−0.702968	+	0.0763928i
$339$		0			0
$340$		0			0
$341$	18.5843	−	32.1889i	1.00639	−	1.74313i
$342$	1.56109	+	2.70388i	0.0844139	+	0.146209i
$343$		−	18.2044i		−	0.982947i
$344$	1.07426	−	0.620223i	0.0579201	−	0.0334402i
$345$		0			0
$346$		−	0.821370i		−	0.0441571i
$347$	13.1823	+	22.8324i	0.707663	+	1.22571i	0.965722	+	0.259580i	$0.0835840\pi$
$347$	13.1823	+	22.8324i	0.707663	+	1.22571i	−0.258058	+	0.966129i	$0.583083\pi$
$348$	1.59858	−	2.76882i	0.0856928	−	0.148424i
$349$	−24.7225	−	14.2735i	−1.32336	−	0.764044i	−0.339099	−	0.940751i	$-0.610122\pi$
$349$	−24.7225	−	14.2735i	−1.32336	−	0.764044i	−0.984264	+	0.176707i	$0.943456\pi$
$350$		0			0
$351$	3.42711	−	1.12022i	0.182926	−	0.0597931i
$352$	5.32411			0.283776
$353$	−15.8058	−	9.12551i	−0.841260	−	0.485702i	0.0164323	−	0.999865i	$-0.494769\pi$
$353$	−15.8058	−	9.12551i	−0.841260	−	0.485702i	−0.857692	+	0.514163i	$0.828103\pi$
$354$	2.90547	−	5.03242i	0.154424	−	0.267470i
$355$		0			0
$356$		−	0.280815i		−	0.0148832i
$357$	−10.1696	+	5.87144i	−0.538234	+	0.310750i
$358$	−0.156842	+	0.0905528i	−0.00828936	+	0.00478586i
$359$		−	15.0243i		−	0.792954i	−0.918045	−	0.396477i	$-0.870233\pi$
$359$		−	15.0243i		−	0.792954i	0.918045	−	0.396477i	$-0.129767\pi$
$360$		0			0
$361$	−4.62601	+	8.01249i	−0.243474	+	0.421710i
$362$	−4.57332	−	2.64041i	−0.240368	−	0.138777i
$363$	−17.3461			−0.910434
$364$	−9.48616	−	1.99887i	−0.497210	−	0.104769i
$365$		0			0
$366$	−2.47183	−	1.42711i	−0.129205	−	0.0745964i
$367$	2.37367	−	4.11131i	0.123904	−	0.214609i	−0.797400	−	0.603451i	$-0.793792\pi$
$367$	2.37367	−	4.11131i	0.123904	−	0.214609i	0.921304	+	0.388843i	$0.127125\pi$
$368$	0.478355	+	0.828535i	0.0249360	+	0.0431904i
$369$		−	4.36740i		−	0.227358i
$370$		0			0
$371$	−16.2559	+	9.38536i	−0.843965	+	0.487263i
$372$			6.98118i			0.361957i
$373$	−0.529832	−	0.917697i	−0.0274337	−	0.0475165i	0.851983	−	0.523570i	$-0.175400\pi$
$373$	−0.529832	−	0.917697i	−0.0274337	−	0.0475165i	−0.879416	+	0.476054i	$0.842067\pi$
$374$	−11.6262	+	20.1372i	−0.601178	+	1.04127i
$375$		0			0
$376$	2.61378			0.134795
$377$	−2.37681	+	11.2798i	−0.122412	+	0.580940i
$378$	2.68876			0.138295
$379$	−23.6727	−	13.6675i	−1.21599	−	0.702051i	−0.251930	−	0.967745i	$-0.581065\pi$
$379$	−23.6727	−	13.6675i	−1.21599	−	0.702051i	−0.964057	+	0.265695i	$0.914399\pi$
$380$		0			0
$381$	10.7851	+	18.6803i	0.552537	+	0.957022i
$382$		−	21.7080i		−	1.11068i
$383$	−10.2868	+	5.93911i	−0.525633	+	0.303474i	−0.739236	−	0.673446i	$-0.764813\pi$
$383$	−10.2868	+	5.93911i	−0.525633	+	0.303474i	0.213603	+	0.976920i	$0.431480\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$		0			0
$386$	−7.03844	−	12.1909i	−0.358247	−	0.620502i
$387$	0.620223	−	1.07426i	0.0315277	−	0.0546076i
$388$	10.4135	+	6.01223i	0.528665	+	0.305225i
$389$	3.19716			0.162102			0.0810511	−	0.996710i	$-0.474172\pi$
$389$	3.19716			0.162102			0.0810511	+	0.996710i	$0.474172\pi$
$390$		0			0
$391$	−4.17833			−0.211307
$392$	−0.198696	−	0.114717i	−0.0100357	−	0.00579410i
$393$	−1.53807	+	2.66402i	−0.0775855	+	0.134382i
$394$	−6.40851	−	11.0999i	−0.322856	−	0.559203i
$395$		0			0
$396$	4.61081	−	2.66205i	0.231702	−	0.133773i
$397$	−10.6611	+	6.15517i	−0.535064	+	0.308919i	−0.743076	−	0.669207i	$-0.766634\pi$
$397$	−10.6611	+	6.15517i	−0.535064	+	0.308919i	0.208012	+	0.978126i	$0.433301\pi$
$398$			11.7656i			0.589758i
$399$	−4.19739	−	7.27009i	−0.210132	−	0.363960i
$400$		0			0
$401$	−7.00145	−	4.04229i	−0.349636	−	0.201862i	0.314889	−	0.949128i	$-0.398033\pi$
$401$	−7.00145	−	4.04229i	−0.349636	−	0.201862i	−0.664525	+	0.747266i	$0.731366\pi$
$402$	−1.55762			−0.0776872
$403$	−7.82047	−	23.9253i	−0.389565	−	1.19180i
$404$	−13.8454			−0.688833
$405$		0			0
$406$	−4.29819	+	7.44469i	−0.213316	+	0.369474i
$407$	−12.9222	−	22.3819i	−0.640530	−	1.10943i
$408$		−	4.36740i		−	0.216218i
$409$	−28.4502	+	16.4257i	−1.40677	+	0.812200i	−0.995075	−	0.0991214i	$-0.968397\pi$
$409$	−28.4502	+	16.4257i	−1.40677	+	0.812200i	−0.411696	+	0.911321i	$0.635063\pi$
$410$		0			0
$411$		−	19.5895i		−	0.966277i
$412$	9.07998	+	15.7270i	0.447338	+	0.774813i
$413$	−7.81211	+	13.5310i	−0.384409	+	0.665815i
$414$	0.828535	+	0.478355i	0.0407203	+	0.0235099i
$415$		0			0
$416$	2.40786	−	2.68370i	0.118055	−	0.131579i
$417$	15.5517			0.761568
$418$	−14.3958	−	8.31139i	−0.704119	−	0.406524i
$419$	−3.79887	+	6.57984i	−0.185587	+	0.321446i	−0.943774	−	0.330591i	$-0.892752\pi$
$419$	−3.79887	+	6.57984i	−0.185587	+	0.321446i	0.758187	+	0.652037i	$0.226085\pi$
$420$		0			0
$421$			23.8487i			1.16231i	0.813792	+	0.581157i	$0.197400\pi$
$421$			23.8487i			1.16231i	−0.813792	+	0.581157i	$0.802600\pi$
$422$	−0.0965530	+	0.0557449i	−0.00470013	+	0.00271362i
$423$	2.26360	−	1.30689i	0.110060	−	0.0635432i
$424$		−	6.98118i		−	0.339036i
$425$		0			0
$426$	5.13543	−	8.89482i	0.248812	−	0.430955i
$427$	6.64616	+	3.83716i	0.321630	+	0.185693i
$428$	−20.4571			−0.988833
$429$	−12.8197	+	14.2883i	−0.618940	+	0.689845i
$430$		0			0
$431$	32.8790	+	18.9827i	1.58373	+	0.914365i	0.994309	+	0.106536i	$0.0339761\pi$
$431$	32.8790	+	18.9827i	1.58373	+	0.914365i	0.589418	+	0.807829i	$0.299357\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	1.88236	+	3.26035i	0.0904606	+	0.156682i	0.907705	−	0.419609i	$-0.137833\pi$
$433$	1.88236	+	3.26035i	0.0904606	+	0.156682i	−0.817244	+	0.576291i	$0.804499\pi$
$434$		−	18.7707i		−	0.901023i
$435$		0			0
$436$	−5.62427	+	3.24717i	−0.269354	+	0.155511i
$437$		−	2.98702i		−	0.142888i
$438$	0.284663	+	0.493050i	0.0136017	+	0.0235589i
$439$	5.63368	−	9.75782i	0.268881	−	0.465715i	−0.699692	−	0.714444i	$-0.746680\pi$
$439$	5.63368	−	9.75782i	0.268881	−	0.465715i	0.968573	+	0.248729i	$0.0800129\pi$
$440$		0			0
$441$	−0.229435			−0.0109255
$442$	4.89245	+	14.9676i	0.232710	+	0.711934i
$443$	13.6139			0.646817			0.323409	−	0.946259i	$-0.395171\pi$
$443$	13.6139			0.646817			0.323409	+	0.946259i	$0.395171\pi$
$444$	4.20388	+	2.42711i	0.199507	+	0.115186i
$445$		0			0
$446$	−4.31035	−	7.46575i	−0.204101	−	0.353514i
$447$		−	15.9728i		−	0.755486i
$448$	2.32854	−	1.34438i	0.110013	−	0.0635160i
$449$	−26.1944	+	15.1233i	−1.23619	+	0.713714i	−0.968313	−	0.249739i	$-0.919655\pi$
$449$	−26.1944	+	15.1233i	−1.23619	+	0.713714i	−0.267876	+	0.963453i	$0.586322\pi$
$450$		0			0
$451$	11.6262	+	20.1372i	0.547458	+	0.948225i
$452$		0			0
$453$	−8.72819	−	5.03922i	−0.410086	−	0.236763i
$454$	−20.6382			−0.968601
$455$		0			0
$456$	3.12217			0.146209
$457$	−31.4804	−	18.1752i	−1.47259	−	0.850201i	−0.473067	−	0.881026i	$-0.656853\pi$
$457$	−31.4804	−	18.1752i	−1.47259	−	0.850201i	−0.999525	+	0.0308251i	$0.990187\pi$
$458$	−1.56464	+	2.71004i	−0.0731109	+	0.126632i
$459$	−2.18370	−	3.78228i	−0.101926	−	0.176541i
$460$		0			0
$461$	20.0818	−	11.5942i	0.935302	−	0.539997i	0.0468172	−	0.998903i	$-0.485092\pi$
$461$	20.0818	−	11.5942i	0.935302	−	0.539997i	0.888484	+	0.458907i	$0.151759\pi$
$462$	−12.3974	+	7.15762i	−0.576778	+	0.333003i
$463$		−	6.40156i		−	0.297506i	−0.988874	−	0.148753i	$-0.952474\pi$
$463$		−	6.40156i		−	0.297506i	0.988874	−	0.148753i	$-0.0475259\pi$
$464$	−1.59858	−	2.76882i	−0.0742121	−	0.128539i
$465$		0			0
$466$	−8.06628	−	4.65707i	−0.373663	−	0.215735i
$467$	20.7210			0.958854			0.479427	−	0.877582i	$-0.340845\pi$
$467$	20.7210			0.958854			0.479427	+	0.877582i	$0.340845\pi$
$468$	0.743415	−	3.52808i	0.0343644	−	0.163085i
$469$	4.18808			0.193388
$470$		0			0
$471$	−10.1877	+	17.6457i	−0.469426	+	0.813070i
$472$	−2.90547	−	5.03242i	−0.133735	−	0.231636i
$473$			6.60426i			0.303664i
$474$	14.8838	−	8.59314i	0.683634	−	0.394696i
$475$		0			0
$476$			11.7429i			0.538234i
$477$	−3.49059	−	6.04588i	−0.159823	−	0.276822i
$478$	−9.23630	+	15.9977i	−0.422459	+	0.731720i
$479$	24.9299	+	14.3933i	1.13908	+	0.657647i	0.946202	−	0.323576i	$-0.104885\pi$
$479$	24.9299	+	14.3933i	1.13908	+	0.657647i	0.192876	+	0.981223i	$0.438219\pi$
$480$		0			0
$481$	−17.1261	−	3.60870i	−0.780882	−	0.164543i
$482$	−2.30832			−0.105141
$483$	−2.22773	−	1.28618i	−0.101365	−	0.0585233i
$484$	−8.67305	+	15.0222i	−0.394229	+	0.682825i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	10.9035	−	6.29515i	0.494086	−	0.285260i	−0.232182	−	0.972672i	$-0.574587\pi$
$487$	10.9035	−	6.29515i	0.494086	−	0.285260i	0.726268	+	0.687412i	$0.241253\pi$
$488$	−2.47183	+	1.42711i	−0.111895	+	0.0646024i
$489$		−	5.71918i		−	0.258630i
$490$		0			0
$491$	10.6278	−	18.4078i	0.479624	−	0.830733i	−0.520103	−	0.854104i	$-0.674106\pi$
$491$	10.6278	−	18.4078i	0.479624	−	0.830733i	0.999727	+	0.0233703i	$0.00743969\pi$
$492$	−3.78228	−	2.18370i	−0.170518	−	0.0984487i
$493$	13.9632			0.628873
$494$	−10.7000	+	3.49753i	−0.481418	+	0.157361i
$495$		0			0
$496$	6.04588	+	3.49059i	0.271468	+	0.156732i
$497$	−13.8079	+	23.9160i	−0.619370	+	1.07278i
$498$	6.65410	+	11.5252i	0.298177	+	0.516458i
$499$		−	13.0237i		−	0.583022i	−0.956568	−	0.291511i	$-0.905842\pi$
$499$		−	13.0237i		−	0.583022i	0.956568	−	0.291511i	$-0.0941579\pi$
$500$		0			0
$501$	−0.828535	+	0.478355i	−0.0370162	+	0.0213713i
$502$		−	21.3600i		−	0.953345i
$503$	9.84475	+	17.0516i	0.438956	+	0.760293i	0.997609	−	0.0691077i	$-0.0220152\pi$
$503$	9.84475	+	17.0516i	0.438956	+	0.760293i	−0.558654	+	0.829401i	$0.688682\pi$
$504$	1.34438	−	2.32854i	0.0598835	−	0.103721i
$505$		0			0
$506$	−5.09362			−0.226439
$507$	1.40447	+	12.9239i	0.0623745	+	0.573971i
$508$	21.5702			0.957022
$509$	−17.0602	−	9.84972i	−0.756181	−	0.436581i	0.0717419	−	0.997423i	$-0.477144\pi$
$509$	−17.0602	−	9.84972i	−0.756181	−	0.436581i	−0.827923	+	0.560842i	$0.810478\pi$
$510$		0			0
$511$	−0.765390	−	1.32569i	−0.0338589	−	0.0586453i
$512$			1.00000i			0.0441942i
$513$	2.70388	−	1.56109i	0.119379	−	0.0689237i
$514$	9.46481	−	5.46451i	0.417475	−	0.241029i
$515$		0			0
$516$	−0.620223	−	1.07426i	−0.0273038	−	0.0472915i
$517$	−6.95802	+	12.0516i	−0.306013	+	0.530031i
$518$	−11.3032	−	6.52593i	−0.496636	−	0.286733i
$519$	−0.821370			−0.0360542
$520$		0			0
$521$	14.0170			0.614097			0.307049	−	0.951694i	$-0.400659\pi$
$521$	14.0170			0.614097			0.307049	+	0.951694i	$0.400659\pi$
$522$	−2.76882	−	1.59858i	−0.121188	−	0.0699678i
$523$	17.5701	−	30.4323i	0.768288	−	1.33071i	−0.170203	−	0.985409i	$-0.554442\pi$
$523$	17.5701	−	30.4323i	0.768288	−	1.33071i	0.938491	−	0.345304i	$-0.112224\pi$
$524$	1.53807	+	2.66402i	0.0671910	+	0.116378i
$525$		0			0
$526$	−11.6825	+	6.74488i	−0.509380	+	0.294091i
$527$	−26.4047	+	15.2448i	−1.15021	+	0.664073i
$528$		−	5.32411i		−	0.231702i
$529$	11.0424	+	19.1259i	0.480102	+	0.831562i
$530$		0			0
$531$	−5.03242	−	2.90547i	−0.218388	−	0.126087i
$532$	−8.39478			−0.363960
$533$	15.4085	+	3.24679i	0.667417	+	0.140634i
$534$	−0.280815			−0.0121521
$535$		0			0
$536$	−0.778812	+	1.34894i	−0.0336396	+	0.0582654i
$537$	0.0905528	+	0.156842i	0.00390764	+	0.00676823i
$538$		−	8.50029i		−	0.366473i
$539$	1.05788	−	0.610767i	0.0455661	−	0.0263076i
$540$		0			0
$541$		−	24.3334i		−	1.04617i	−0.852280	−	0.523086i	$-0.824781\pi$
$541$		−	24.3334i		−	1.04617i	0.852280	−	0.523086i	$-0.175219\pi$
$542$	11.1872	+	19.3767i	0.480530	+	0.832302i
$543$	−2.64041	+	4.57332i	−0.113311	+	0.196260i
$544$	−3.78228	−	2.18370i	−0.162164	−	0.0936253i
$545$		0			0
$546$	−1.99887	+	9.48616i	−0.0855435	+	0.405970i
$547$	−1.58059			−0.0675810			−0.0337905	−	0.999429i	$-0.510758\pi$
$547$	−1.58059			−0.0675810			−0.0337905	+	0.999429i	$0.510758\pi$
$548$	−16.9650	−	9.79473i	−0.724708	−	0.418410i
$549$	−1.42711	+	2.47183i	−0.0609077	+	0.105495i
$550$		0			0
$551$			9.98208i			0.425251i
$552$	0.828535	−	0.478355i	0.0352648	−	0.0203601i
$553$	−40.0189	+	23.1049i	−1.70178	+	0.982521i
$554$		−	28.8564i		−	1.22599i
$555$		0			0
$556$	7.77583	−	13.4681i	0.329769	−	0.571176i
$557$	6.48261	+	3.74274i	0.274677	+	0.158585i	0.631011	−	0.775774i	$-0.282640\pi$
$557$	6.48261	+	3.74274i	0.274677	+	0.158585i	−0.356334	+	0.934359i	$0.615974\pi$
$558$	6.98118			0.295537
$559$	3.32898	+	2.98681i	0.140801	+	0.126329i
$560$		0			0
$561$	20.1372	+	11.6262i	0.850195	+	0.490860i
$562$	−12.7040	+	22.0039i	−0.535884	+	0.928178i
$563$	−15.3644	−	26.6120i	−0.647533	−	1.12156i	−0.983710	−	0.179762i	$-0.942467\pi$
$563$	−15.3644	−	26.6120i	−0.647533	−	1.12156i	0.336177	−	0.941799i	$-0.390866\pi$
$564$		−	2.61378i		−	0.110060i
$565$		0			0
$566$	9.94021	−	5.73899i	0.417818	−	0.241228i
$567$		−	2.68876i		−	0.112917i
$568$	−5.13543	−	8.89482i	−0.215478	−	0.373218i
$569$	−2.63200	+	4.55877i	−0.110339	+	0.191113i	−0.915907	−	0.401390i	$-0.868527\pi$
$569$	−2.63200	+	4.55877i	−0.110339	+	0.191113i	0.805568	+	0.592504i	$0.201860\pi$
$570$		0			0
$571$	−28.2057			−1.18037			−0.590186	−	0.807267i	$-0.700946\pi$
$571$	−28.2057			−1.18037			−0.590186	+	0.807267i	$0.700946\pi$
$572$	5.96418	+	18.2463i	0.249375	+	0.762916i
$573$	−21.7080			−0.906865
$574$	10.1696	+	5.87144i	0.424472	+	0.245069i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$		−	15.6557i		−	0.651754i	−0.945412	−	0.325877i	$-0.894341\pi$
$577$		−	15.6557i		−	0.651754i	0.945412	−	0.325877i	$-0.105659\pi$
$578$	1.79626	−	1.03707i	0.0747145	−	0.0431364i
$579$	−12.1909	+	7.03844i	−0.506638	+	0.292508i
$580$		0			0
$581$	−17.8913	−	30.9886i	−0.742256	−	1.28562i
$582$	6.01223	−	10.4135i	0.249215	−	0.431653i
$583$	32.1889	+	18.5843i	1.33313	+	0.769681i
$584$	0.569326			0.0235589
$585$		0			0
$586$	−3.37199			−0.139296
$587$	−15.5048	−	8.95173i	−0.639954	−	0.369477i	0.144643	−	0.989484i	$-0.453797\pi$
$587$	−15.5048	−	8.95173i	−0.639954	−	0.369477i	−0.784597	+	0.620007i	$0.787130\pi$
$588$	−0.114717	+	0.198696i	−0.00473086	+	0.00819409i
$589$	−10.8982	−	18.8763i	−0.449054	−	0.777783i
$590$		0			0
$591$	−11.0999	+	6.40851i	−0.456587	+	0.263611i
$592$	4.20388	−	2.42711i	0.172779	−	0.0997537i
$593$			26.0909i			1.07142i	0.844401	+	0.535712i	$0.179957\pi$
$593$			26.0909i			1.07142i	−0.844401	+	0.535712i	$0.820043\pi$
$594$	−2.66205	−	4.61081i	−0.109225	−	0.189184i
$595$		0			0
$596$	−13.8328	−	7.98638i	−0.566614	−	0.327135i
$597$	11.7656			0.481536
$598$	−2.30362	+	2.56752i	−0.0942020	+	0.104994i
$599$	2.85624			0.116703			0.0583515	−	0.998296i	$-0.481416\pi$
$599$	2.85624			0.116703			0.0583515	+	0.998296i	$0.481416\pi$
$600$		0			0
$601$	18.0654	−	31.2901i	0.736901	−	1.27635i	−0.216983	−	0.976175i	$-0.569622\pi$
$601$	18.0654	−	31.2901i	0.736901	−	1.27635i	0.953884	−	0.300175i	$-0.0970450\pi$
$602$	1.66763	+	2.88842i	0.0679675	+	0.117723i
$603$			1.55762i			0.0634314i
$604$	−8.72819	+	5.03922i	−0.355145	+	0.205043i
$605$		0			0
$606$			13.8454i			0.562430i
$607$	11.0924	+	19.2125i	0.450225	+	0.779813i	0.998400	−	0.0565511i	$-0.0180104\pi$
$607$	11.0924	+	19.2125i	0.450225	+	0.779813i	−0.548175	+	0.836364i	$0.684677\pi$
$608$	1.56109	−	2.70388i	0.0633104	−	0.109657i
$609$	7.44469	+	4.29819i	0.301674	+	0.174172i
$610$		0			0
$611$	2.92802	+	8.95772i	0.118455	+	0.362391i
$612$	−4.36740			−0.176541
$613$	−17.9378	−	10.3564i	−0.724501	−	0.418291i	0.0919062	−	0.995768i	$-0.470704\pi$
$613$	−17.9378	−	10.3564i	−0.724501	−	0.418291i	−0.816407	+	0.577477i	$0.804037\pi$
$614$	−6.25565	+	10.8351i	−0.252457	+	0.437269i
$615$		0			0
$616$			14.3152i			0.576778i
$617$	−9.14413	+	5.27937i	−0.368129	+	0.212539i	−0.672641	−	0.739969i	$-0.734840\pi$
$617$	−9.14413	+	5.27937i	−0.368129	+	0.212539i	0.304512	+	0.952509i	$0.401507\pi$
$618$	15.7270	−	9.07998i	0.632632	−	0.365250i
$619$		−	22.1430i		−	0.890002i	−0.895530	−	0.445001i	$-0.853203\pi$
$619$		−	22.1430i		−	0.890002i	0.895530	−	0.445001i	$-0.146797\pi$
$620$		0			0
$621$	0.478355	−	0.828535i	0.0191957	−	0.0332480i
$622$	21.1939	+	12.2363i	0.849798	+	0.490631i
$623$	0.755044			0.0302502
$624$	−2.68370	−	2.40786i	−0.107434	−	0.0963914i
$625$		0			0
$626$	25.0072	+	14.4379i	0.999487	+	0.577054i
$627$	−8.31139	+	14.3958i	−0.331925	+	0.574911i
$628$	10.1877	+	17.6457i	0.406535	+	0.704140i
$629$			21.2003i			0.845312i
$630$		0			0
$631$	7.77715	−	4.49014i	0.309603	−	0.178750i	−0.337146	−	0.941453i	$-0.609461\pi$
$631$	7.77715	−	4.49014i	0.309603	−	0.178750i	0.646749	+	0.762703i	$0.276128\pi$
$632$		−	17.1863i		−	0.683634i
$633$	0.0557449	+	0.0965530i	0.00221566	+	0.00383764i
$634$	−6.40693	+	11.0971i	−0.254452	+	0.440723i
$635$		0			0
$636$	−6.98118			−0.276822
$637$	0.170565	−	0.809463i	0.00675804	−	0.0320721i
$638$	17.0220			0.673907
$639$	−8.89482	−	5.13543i	−0.351874	−	0.203154i
$640$		0			0
$641$	−21.1339	−	36.6049i	−0.834738	−	1.44581i	−0.894244	−	0.447580i	$-0.852286\pi$
$641$	−21.1339	−	36.6049i	−0.834738	−	1.44581i	0.0595063	−	0.998228i	$-0.481047\pi$
$642$			20.4571i			0.807379i
$643$	−29.2786	+	16.9040i	−1.15463	+	0.666628i	−0.950012	−	0.312213i	$-0.898930\pi$
$643$	−29.2786	+	16.9040i	−1.15463	+	0.666628i	−0.204622	+	0.978841i	$0.565596\pi$
$644$	−2.22773	+	1.28618i	−0.0877850	+	0.0506827i
$645$		0			0
$646$	6.81788	+	11.8089i	0.268246	+	0.464616i
$647$	9.52598	−	16.4995i	0.374505	−	0.648661i	−0.615748	−	0.787943i	$-0.711146\pi$
$647$	9.52598	−	16.4995i	0.374505	−	0.648661i	0.990253	+	0.139282i	$0.0444794\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	30.9380			1.21442
$650$		0			0
$651$	−18.7707			−0.735682
$652$	−4.95296	−	2.85959i	−0.193973	−	0.111990i
$653$	−10.4526	+	18.1045i	−0.409043	+	0.708484i	−0.994783	−	0.102016i	$-0.967471\pi$
$653$	−10.4526	+	18.1045i	−0.409043	+	0.708484i	0.585739	+	0.810499i	$0.300804\pi$
$654$	3.24717	+	5.62427i	0.126974	+	0.219926i
$655$		0			0
$656$	−3.78228	+	2.18370i	−0.147673	+	0.0852591i
$657$	0.493050	−	0.284663i	0.0192357	−	0.0111058i
$658$			7.02783i			0.273973i
$659$	1.99703	+	3.45896i	0.0777932	+	0.134742i	0.902298	−	0.431114i	$-0.141879\pi$
$659$	1.99703	+	3.45896i	0.0777932	+	0.134742i	−0.824504	+	0.565856i	$0.808546\pi$
$660$		0			0
$661$	−10.6480	−	6.14765i	−0.414161	−	0.239116i	0.278415	−	0.960461i	$-0.410191\pi$
$661$	−10.6480	−	6.14765i	−0.414161	−	0.239116i	−0.692576	+	0.721345i	$0.743524\pi$
$662$	34.7116			1.34911
$663$	14.9676	−	4.89245i	0.581292	−	0.190007i
$664$	13.3082			0.516458
$665$		0			0
$666$	2.42711	−	4.20388i	0.0940487	−	0.162897i
$667$	1.52938	+	2.64896i	0.0592176	+	0.102568i
$668$			0.956710i			0.0370162i
$669$	−7.46575	+	4.31035i	−0.288643	+	0.166648i
$670$		0			0
$671$		−	15.1962i		−	0.586643i
$672$	−1.34438	−	2.32854i	−0.0518606	−	0.0898252i
$673$	4.11435	−	7.12626i	0.158596	−	0.274697i	−0.775766	−	0.631020i	$-0.782636\pi$
$673$	4.11435	−	7.12626i	0.158596	−	0.274697i	0.934363	+	0.356323i	$0.115970\pi$
$674$	−23.6378	−	13.6473i	−0.910493	−	0.525673i
$675$		0			0
$676$	11.8947	+	5.24565i	0.457487	+	0.201756i
$677$	30.7000			1.17990			0.589949	−	0.807440i	$-0.299148\pi$
$677$	30.7000			1.17990			0.589949	+	0.807440i	$0.299148\pi$
$678$		0			0
$679$	−16.1655	+	27.9994i	−0.620373	+	1.07452i
$680$		0			0
$681$			20.6382i			0.790859i
$682$	−32.1889	+	18.5843i	−1.23258	+	0.711628i
$683$	−15.4446	+	8.91696i	−0.590972	+	0.341198i	−0.765482	−	0.643457i	$-0.777499\pi$
$683$	−15.4446	+	8.91696i	−0.590972	+	0.341198i	0.174510	+	0.984655i	$0.444166\pi$
$684$		−	3.12217i		−	0.119379i
$685$		0			0
$686$	−9.10222	+	15.7655i	−0.347524	+	0.601930i
$687$	2.71004	+	1.56464i	0.103394	+	0.0596948i
$688$	−1.24045			−0.0472915
$689$	23.9253	−	7.82047i	0.911480	−	0.297936i
$690$		0			0
$691$	38.1620	+	22.0329i	1.45175	+	0.838169i	0.998581	−	0.0532542i	$-0.0169594\pi$
$691$	38.1620	+	22.0329i	1.45175	+	0.838169i	0.453171	+	0.891424i	$0.350293\pi$
$692$	−0.410685	+	0.711327i	−0.0156119	+	0.0270406i
$693$	7.15762	+	12.3974i	0.271896	+	0.470937i
$694$		−	26.3646i		−	1.00079i
$695$		0			0
$696$	−2.76882	+	1.59858i	−0.104952	+	0.0605939i
$697$		−	19.0741i		−	0.722485i
$698$	14.2735	+	24.7225i	0.540261	+	0.935759i
$699$	−4.65707	+	8.06628i	−0.176147	+	0.305095i
$700$		0			0
$701$	14.3983			0.543817			0.271909	−	0.962323i	$-0.412345\pi$
$701$	14.3983			0.543817			0.271909	+	0.962323i	$0.412345\pi$
$702$	−3.52808	−	0.743415i	−0.133159	−	0.0280584i
$703$	−15.1557			−0.571610
$704$	−4.61081	−	2.66205i	−0.173776	−	0.100330i
$705$		0			0
$706$	9.12551	+	15.8058i	0.343443	+	0.594861i
$707$		−	37.2269i		−	1.40006i
$708$	−5.03242	+	2.90547i	−0.189130	+	0.109194i
$709$	−19.0873	+	11.0200i	−0.716838	+	0.413866i	−0.813588	−	0.581442i	$-0.802489\pi$
$709$	−19.0873	+	11.0200i	−0.716838	+	0.413866i	0.0967499	+	0.995309i	$0.469155\pi$
$710$		0			0
$711$	−8.59314	−	14.8838i	−0.322268	−	0.558185i
$712$	−0.140408	+	0.243193i	−0.00526199	+	0.00911404i
$713$	−5.78415	−	3.33948i	−0.216618	−	0.125065i
$714$	11.7429			0.439466
$715$		0			0
$716$	0.181106			0.00676823
$717$	15.9977	+	9.23630i	0.597447	+	0.344936i
$718$	−7.51217	+	13.0115i	−0.280352	+	0.485583i
$719$	−21.9534	−	38.0245i	−0.818725	−	1.41807i	−0.906622	−	0.421944i	$-0.861348\pi$
$719$	−21.9534	−	38.0245i	−0.818725	−	1.41807i	0.0878962	−	0.996130i	$-0.471986\pi$
$720$		0			0
$721$	−42.2861	+	24.4139i	−1.57482	+	0.909220i
$722$	8.01249	−	4.62601i	0.298194	−	0.172162i
$723$			2.30832i			0.0858473i
$724$	2.64041	+	4.57332i	0.0981300	+	0.169966i
$725$		0			0
$726$	15.0222	+	8.67305i	0.557525	+	0.321887i
$727$	2.66659			0.0988984			0.0494492	−	0.998777i	$-0.484253\pi$
$727$	2.66659			0.0988984			0.0494492	+	0.998777i	$0.484253\pi$
$728$	7.21582	+	6.47415i	0.267436	+	0.239948i
$729$	1.00000			0.0370370
$730$		0			0
$731$	2.70876	−	4.69170i	0.100187	−	0.173529i
$732$	1.42711	+	2.47183i	0.0527476	+	0.0913615i
$733$		−	21.1035i		−	0.779476i	−0.920926	−	0.389738i	$-0.872566\pi$
$733$		−	21.1035i		−	0.779476i	0.920926	−	0.389738i	$-0.127434\pi$
$734$	−4.11131	+	2.37367i	−0.151751	+	0.0876136i
$735$		0			0
$736$		−	0.956710i		−	0.0352648i
$737$	−4.14648	−	7.18191i	−0.152737	−	0.264549i
$738$	−2.18370	+	3.78228i	−0.0803830	+	0.139227i
$739$	21.4664	+	12.3936i	0.789653	+	0.455906i	0.839840	−	0.542834i	$-0.182649\pi$
$739$	21.4664	+	12.3936i	0.789653	+	0.455906i	−0.0501875	+	0.998740i	$0.515982\pi$
$740$		0			0
$741$	3.49753	+	10.7000i	0.128485	+	0.393076i
$742$	18.7707			0.689094
$743$	−22.5866	−	13.0404i	−0.828621	−	0.478405i	0.0247590	−	0.999693i	$-0.492118\pi$
$743$	−22.5866	−	13.0404i	−0.828621	−	0.478405i	−0.853380	+	0.521289i	$0.825451\pi$
$744$	3.49059	−	6.04588i	0.127971	−	0.221653i
$745$		0			0
$746$			1.05966i			0.0387971i
$747$	11.5252	−	6.65410i	0.421686	−	0.243461i
$748$	20.1372	−	11.6262i	0.736290	−	0.425097i
$749$		−	55.0044i		−	2.00982i
$750$		0			0
$751$	8.11074	−	14.0482i	0.295965	−	0.512627i	−0.679244	−	0.733913i	$-0.737692\pi$
$751$	8.11074	−	14.0482i	0.295965	−	0.512627i	0.975209	+	0.221286i	$0.0710254\pi$
$752$	−2.26360	−	1.30689i	−0.0825450	−	0.0476574i
$753$	−21.3600			−0.778403
$754$	7.69829	−	8.58020i	0.280355	−	0.312472i
$755$		0			0
$756$	−2.32854	−	1.34438i	−0.0846880	−	0.0488946i
$757$	−22.5166	+	38.9998i	−0.818379	+	1.41747i	0.0884976	+	0.996076i	$0.471793\pi$
$757$	−22.5166	+	38.9998i	−0.818379	+	1.41747i	−0.906876	+	0.421397i	$0.861540\pi$
$758$	13.6675	+	23.6727i	0.496425	+	0.859833i
$759$			5.09362i			0.184887i
$760$		0			0
$761$	−23.4606	+	13.5450i	−0.850447	+	0.491006i	−0.860802	−	0.508941i	$-0.830037\pi$
$761$	−23.4606	+	13.5450i	−0.850447	+	0.491006i	0.0103548	+	0.999946i	$0.496704\pi$
$762$		−	21.5702i		−	0.781406i
$763$	−8.73087	−	15.1223i	−0.316079	−	0.547464i
$764$	−10.8540	+	18.7997i	−0.392684	+	0.680149i
$765$		0			0
$766$	11.8782			0.429178
$767$	13.9919	−	15.5948i	0.505218	−	0.563095i
$768$	1.00000			0.0360844
$769$	24.9201	+	14.3876i	0.898643	+	0.518832i	0.876760	−	0.480929i	$-0.159700\pi$
$769$	24.9201	+	14.3876i	0.898643	+	0.518832i	0.0218832	+	0.999761i	$0.493034\pi$
$770$		0			0
$771$	−5.46451	−	9.46481i	−0.196800	−	0.340867i
$772$			14.0769i			0.506638i
$773$	40.5101	−	23.3885i	1.45705	−	0.841226i	0.458182	−	0.888858i	$-0.348501\pi$
$773$	40.5101	−	23.3885i	1.45705	−	0.841226i	0.998865	+	0.0476321i	$0.0151675\pi$
$774$	−1.07426	+	0.620223i	−0.0386134	+	0.0222934i
$775$		0			0
$776$	−6.01223	−	10.4135i	−0.215827	−	0.373823i
$777$	−6.52593	+	11.3032i	−0.234116	+	0.405501i
$778$	−2.76882	−	1.59858i	−0.0992669	−	0.0573118i
$779$	13.6358			0.488552
$780$		0			0
$781$	54.6831			1.95671
$782$	3.61854	+	2.08917i	0.129399	+	0.0747084i
$783$	−1.59858	+	2.76882i	−0.0571285	+	0.0989495i
$784$	0.114717	+	0.198696i	0.00409705	+	0.00709629i
$785$		0			0
$786$	2.66402	−	1.53807i	0.0950224	−	0.0548612i
$787$	21.4254	−	12.3700i	0.763735	−	0.440942i	−0.0669004	−	0.997760i	$-0.521311\pi$
$787$	21.4254	−	12.3700i	0.763735	−	0.440942i	0.830635	+	0.556817i	$0.187978\pi$
$788$			12.8170i			0.456587i
$789$	6.74488	+	11.6825i	0.240124	+	0.415907i
$790$		0			0
$791$		0			0
$792$	−5.32411			−0.189184
$793$	−7.65988	−	6.87256i	−0.272010	−	0.244052i
$794$	12.3103			0.436878
$795$		0			0
$796$	5.88282	−	10.1893i	0.208511	−	0.361152i
$797$	−24.2274	−	41.9631i	−0.858179	−	1.48641i	−0.873664	−	0.486529i	$-0.838263\pi$
$797$	−24.2274	−	41.9631i	−0.858179	−	1.48641i	0.0154857	−	0.999880i	$-0.495071\pi$
$798$			8.39478i			0.297172i
$799$	9.88604	−	5.70771i	0.349743	−	0.201924i
$800$		0			0
$801$			0.280815i			0.00992211i
$802$	4.04229	+	7.00145i	0.142738	+	0.247230i
$803$	−1.51557	+	2.62505i	−0.0534835	+	0.0926361i
$804$	1.34894	+	0.778812i	0.0475735	+	0.0274666i
$805$		0			0
$806$	−5.18991	+	24.6301i	−0.182807	+	0.867559i
$807$	−8.50029			−0.299224
$808$	11.9904	+	6.92268i	0.421822	+	0.243539i
$809$	2.41226	−	4.17816i	0.0848106	−	0.146896i	−0.820500	−	0.571647i	$-0.806305\pi$
$809$	2.41226	−	4.17816i	0.0848106	−	0.146896i	0.905310	+	0.424750i	$0.139638\pi$
$810$		0			0
$811$		−	45.0952i		−	1.58351i	−0.610841	−	0.791754i	$-0.709168\pi$
$811$		−	45.0952i		−	1.58351i	0.610841	−	0.791754i	$-0.290832\pi$
$812$	7.44469	−	4.29819i	0.261257	−	0.150837i
$813$	19.3767	−	11.1872i	0.679572	−	0.392351i
$814$			25.8444i			0.905846i
$815$		0			0
$816$	−2.18370	+	3.78228i	−0.0764447	+	0.132406i
$817$	3.35402	+	1.93644i	0.117342	+	0.0677476i
$818$	32.8515			1.14862
$819$	9.48616	+	1.99887i	0.331473	+	0.0698460i
$820$		0			0
$821$	21.8528	+	12.6167i	0.762667	+	0.440326i	0.830252	−	0.557388i	$-0.188196\pi$
$821$	21.8528	+	12.6167i	0.762667	+	0.440326i	−0.0675856	+	0.997713i	$0.521530\pi$
$822$	−9.79473	+	16.9650i	−0.341630	+	0.591721i
$823$	−9.96940	−	17.2675i	−0.347511	−	0.601907i	0.638295	−	0.769792i	$-0.279640\pi$
$823$	−9.96940	−	17.2675i	−0.347511	−	0.601907i	−0.985807	+	0.167884i	$0.946307\pi$
$824$		−	18.1600i		−	0.632632i
$825$		0			0
$826$	13.5310	−	7.81211i	0.470803	−	0.271818i
$827$		−	18.2598i		−	0.634957i	−0.948265	−	0.317478i	$-0.897164\pi$
$827$		−	18.2598i		−	0.634957i	0.948265	−	0.317478i	$-0.102836\pi$
$828$	−0.478355	−	0.828535i	−0.0166240	−	0.0287936i
$829$	8.50136	−	14.7248i	0.295264	−	0.511413i	−0.679782	−	0.733414i	$-0.737926\pi$
$829$	8.50136	−	14.7248i	0.295264	−	0.511413i	0.975046	+	0.222001i	$0.0712589\pi$
$830$		0			0
$831$	−28.8564			−1.00102
$832$	−3.42711	+	1.12022i	−0.118814	+	0.0388367i
$833$	−1.00203			−0.0347183
$834$	−13.4681	−	7.77583i	−0.466363	−	0.269255i
$835$		0			0
$836$	8.31139	+	14.3958i	0.287456	+	0.497888i
$837$		−	6.98118i		−	0.241305i
$838$	6.57984	−	3.79887i	0.227297	−	0.131230i
$839$	45.9435	−	26.5255i	1.58615	−	0.915762i	0.592213	−	0.805781i	$-0.298254\pi$
$839$	45.9435	−	26.5255i	1.58615	−	0.915762i	0.993934	−	0.109981i	$-0.0350791\pi$
$840$		0			0
$841$	9.38910	+	16.2624i	0.323762	+	0.560772i
$842$	11.9243	−	20.6536i	0.410940	−	0.711769i
$843$	22.0039	+	12.7040i	0.757854	+	0.437547i
$844$	0.111490			0.00383764
$845$		0			0
$846$	−2.61378			−0.0898636
$847$	−40.3910	−	23.3197i	−1.38785	−	0.801276i
$848$	−3.49059	+	6.04588i	−0.119867	+	0.207616i
$849$	−5.73899	−	9.94021i	−0.196961	−	0.341147i
$850$		0			0
$851$	−4.02190	+	2.32204i	−0.137869	+	0.0795986i
$852$	−8.89482	+	5.13543i	−0.304731	+	0.175937i
$853$		−	38.5399i		−	1.31958i	−0.751450	−	0.659791i	$-0.770645\pi$
$853$		−	38.5399i		−	1.31958i	0.751450	−	0.659791i	$-0.229355\pi$
$854$	−3.83716	−	6.64616i	−0.131305	−	0.227427i
$855$		0			0
$856$	17.7164	+	10.2286i	0.605534	+	0.349605i
$857$	−38.8969			−1.32869			−0.664346	−	0.747425i	$-0.731290\pi$
$857$	−38.8969			−1.32869			−0.664346	+	0.747425i	$0.731290\pi$
$858$	18.2463	−	5.96418i	0.622919	−	0.203614i
$859$	−6.04530			−0.206263			−0.103131	−	0.994668i	$-0.532886\pi$
$859$	−6.04530			−0.206263			−0.103131	+	0.994668i	$0.532886\pi$
$860$		0			0
$861$	5.87144	−	10.1696i	0.200098	−	0.346580i
$862$	−18.9827	−	32.8790i	−0.646554	−	1.11986i
$863$		−	17.7572i		−	0.604462i	−0.953235	−	0.302231i	$-0.902269\pi$
$863$		−	17.7572i		−	0.604462i	0.953235	−	0.302231i	$-0.0977315\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$		0			0
$866$		−	3.76473i		−	0.127931i
$867$	−1.03707	−	1.79626i	−0.0352207	−	0.0610041i
$868$	−9.38536	+	16.2559i	−0.318560	+	0.551762i
$869$	79.2427	+	45.7508i	2.68813	+	1.55199i
$870$		0			0
$871$	−5.49542	−	1.15796i	−0.186205	−	0.0392360i
$872$	6.49435			0.219926
$873$	−10.4135	−	6.01223i	−0.352443	−	0.203483i
$874$	−1.49351	+	2.58683i	−0.0505187	+	0.0875009i
$875$		0			0
$876$		−	0.569326i		−	0.0192357i
$877$	−12.3802	+	7.14773i	−0.418051	+	0.241362i	−0.694243	−	0.719741i	$-0.744261\pi$
$877$	−12.3802	+	7.14773i	−0.418051	+	0.241362i	0.276192	+	0.961102i	$0.410927\pi$
$878$	−9.75782	+	5.63368i	−0.329310	+	0.190127i
$879$			3.37199i			0.113734i
$880$		0			0
$881$	22.2820	−	38.5935i	0.750698	−	1.30025i	−0.196786	−	0.980446i	$-0.563051\pi$
$881$	22.2820	−	38.5935i	0.750698	−	1.30025i	0.947485	−	0.319801i	$-0.103616\pi$
$882$	0.198696	+	0.114717i	0.00669045	+	0.00386273i
$883$	25.0584			0.843284			0.421642	−	0.906762i	$-0.361454\pi$
$883$	25.0584			0.843284			0.421642	+	0.906762i	$0.361454\pi$
$884$	3.24679	−	15.4085i	0.109201	−	0.518244i
$885$		0			0
$886$	−11.7900	−	6.80696i	−0.396093	−	0.228684i
$887$	−11.2041	+	19.4061i	−0.376197	+	0.651593i	−0.990505	−	0.137473i	$-0.956102\pi$
$887$	−11.2041	+	19.4061i	−0.376197	+	0.651593i	0.614308	+	0.789066i	$0.289435\pi$
$888$	−2.42711	−	4.20388i	−0.0814486	−	0.141073i
$889$			57.9971i			1.94516i
$890$		0			0
$891$	−4.61081	+	2.66205i	−0.154468	+	0.0891821i
$892$			8.62071i			0.288643i
$893$	4.08034	+	7.06735i	0.136543	+	0.236500i
$894$	−7.98638	+	13.8328i	−0.267104	+	0.462639i
$895$		0			0
$896$	−2.68876			−0.0898252
$897$	2.56752	+	2.30362i	0.0857270	+	0.0769156i
$898$	30.2467			1.00934
$899$	19.3296	+	11.1600i	0.644678	+	0.372205i
$900$		0			0
$901$	−15.2448	−	26.4047i	−0.507877	−	0.879669i
$902$		−	23.2525i		−	0.774223i
$903$	2.88842	−	1.66763i	0.0961206	−	0.0554953i
$904$		0			0
$905$		0			0
$906$	5.03922	+	8.72819i	0.167417	+	0.289975i
$907$	−14.8368	+	25.6982i	−0.492649	+	0.853294i	−0.999964	−	0.00846710i	$-0.997305\pi$
$907$	−14.8368	+	25.6982i	−0.492649	+	0.853294i	0.507315	+	0.861761i	$0.330638\pi$
$908$	17.8732	+	10.3191i	0.593144	+	0.342452i
$909$	13.8454			0.459222
$910$		0			0
$911$	−51.3944			−1.70277			−0.851386	−	0.524539i	$-0.824238\pi$
$911$	−51.3944			−1.70277			−0.851386	+	0.524539i	$0.824238\pi$
$912$	−2.70388	−	1.56109i	−0.0895345	−	0.0516928i
$913$	−35.4271	+	61.3616i	−1.17247	+	2.03077i
$914$	18.1752	+	31.4804i	0.601183	+	1.04128i
$915$		0			0
$916$	2.71004	−	1.56464i	0.0895421	−	0.0516972i
$917$	−7.16291	+	4.13551i	−0.236540	+	0.136567i
$918$			4.36740i			0.144146i
$919$	26.6932	+	46.2339i	0.880526	+	1.52512i	0.850757	+	0.525559i	$0.176144\pi$
$919$	26.6932	+	46.2339i	0.880526	+	1.52512i	0.0297687	+	0.999557i	$0.490523\pi$
$920$		0			0
$921$	10.8351	+	6.25565i	0.357029	+	0.206131i
$922$	−23.1884			−0.763671
$923$	24.7307	−	27.5639i	0.814022	−	0.907275i
$924$	14.3152			0.470937
$925$		0			0
$926$	−3.20078	+	5.54391i	−0.105184	+	0.182184i
$927$	−9.07998	−	15.7270i	−0.298226	−	0.516542i
$928$			3.19716i			0.104952i
$929$	10.5234	−	6.07570i	0.345262	−	0.199337i	−0.317334	−	0.948314i	$-0.602788\pi$
$929$	10.5234	−	6.07570i	0.345262	−	0.199337i	0.662597	+	0.748976i	$0.269454\pi$
$930$		0			0
$931$		−	0.716335i		−	0.0234769i
$932$	4.65707	+	8.06628i	0.152547	+	0.264220i
$933$	12.2363	−	21.1939i	0.400598	−	0.693857i
$934$	−17.9449	−	10.3605i	−0.587176	−	0.339006i
$935$		0			0
$936$	−2.40786	+	2.68370i	−0.0787032	+	0.0877194i
$937$	10.4882			0.342634			0.171317	−	0.985216i	$-0.445198\pi$
$937$	10.4882			0.342634			0.171317	+	0.985216i	$0.445198\pi$
$938$	−3.62698	−	2.09404i	−0.118425	−	0.0683728i
$939$	14.4379	−	25.0072i	0.471163	−	0.816078i
$940$		0			0
$941$			10.2389i			0.333778i	0.985976	+	0.166889i	$0.0533721\pi$
$941$			10.2389i			0.333778i	−0.985976	+	0.166889i	$0.946628\pi$
$942$	17.6457	−	10.1877i	0.574928	−	0.331935i
$943$	3.61854	−	2.08917i	0.117836	−	0.0680326i
$944$			5.81094i			0.189130i
$945$		0			0
$946$	3.30213	−	5.71946i	0.107362	−	0.185956i
$947$	−12.9842	−	7.49645i	−0.421931	−	0.243602i	0.273972	−	0.961738i	$-0.411662\pi$
$947$	−12.9842	−	7.49645i	−0.421931	−	0.243602i	−0.695903	+	0.718136i	$0.744996\pi$
$948$	−17.1863			−0.558185
$949$	0.637771	+	1.95114i	0.0207029	+	0.0633368i
$950$		0			0
$951$	11.0971	+	6.40693i	0.359849	+	0.207759i
$952$	5.87144	−	10.1696i	0.190294	−	0.329600i
$953$	−22.7532	−	39.4097i	−0.737048	−	1.27660i	−0.953819	−	0.300382i	$-0.902886\pi$
$953$	−22.7532	−	39.4097i	−0.737048	−	1.27660i	0.216771	−	0.976222i	$-0.430448\pi$
$954$			6.98118i			0.226024i
$955$		0			0
$956$	15.9977	−	9.23630i	0.517404	−	0.298723i
$957$		−	17.0220i		−	0.550243i
$958$	−14.3933	−	24.9299i	−0.465027	−	0.805450i
$959$	26.3357	−	45.6147i	0.850424	−	1.47298i
$960$		0			0
$961$	−17.7368			−0.572155
$962$	13.0273	+	11.6883i	0.420016	+	0.376845i
$963$	20.4571			0.659222
$964$	1.99906	+	1.15416i	0.0643855	+	0.0371730i
$965$		0			0
$966$	1.28618	+	2.22773i	0.0413822	+	0.0716761i
$967$		−	11.4832i		−	0.369275i	−0.982807	−	0.184637i	$-0.940889\pi$
$967$		−	11.4832i		−	0.369275i	0.982807	−	0.184637i	$-0.0591111\pi$
$968$	15.0222	−	8.67305i	0.482830	−	0.278762i
$969$	11.8089	−	6.81788i	0.379357	−	0.219022i
$970$		0			0
$971$	23.2705	+	40.3058i	0.746787	+	1.29347i	0.949355	+	0.314205i	$0.101738\pi$
$971$	23.2705	+	40.3058i	0.746787	+	1.29347i	−0.202568	+	0.979268i	$0.564929\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	36.2126	+	20.9074i	1.16092	+	0.670259i
$974$	−12.5903			−0.403419
$975$		0			0
$976$	2.85423			0.0913615
$977$	−24.7817	−	14.3077i	−0.792837	−	0.457745i	0.0481231	−	0.998841i	$-0.484676\pi$
$977$	−24.7817	−	14.3077i	−0.792837	−	0.457745i	−0.840960	+	0.541097i	$0.818009\pi$
$978$	−2.85959	+	4.95296i	−0.0914397	+	0.158378i
$979$	−0.747544	−	1.29478i	−0.0238916	−	0.0413815i
$980$		0			0
$981$	5.62427	−	3.24717i	0.179569	−	0.103674i
$982$	−18.4078	+	10.6278i	−0.587417	+	0.339145i
$983$			32.6951i			1.04281i	0.853308	+	0.521406i	$0.174592\pi$
$983$			32.6951i			1.04281i	−0.853308	+	0.521406i	$0.825408\pi$
$984$	2.18370	+	3.78228i	0.0696137	+	0.120575i
$985$		0			0
$986$	−12.0925	−	6.98162i	−0.385104	−	0.222340i
$987$	7.02783			0.223698
$988$	11.0153	+	2.32107i	0.350443	+	0.0738431i
$989$	1.18675			0.0377363
$990$		0			0
$991$	22.2574	−	38.5510i	0.707030	−	1.22461i	−0.258924	−	0.965898i	$-0.583368\pi$
$991$	22.2574	−	38.5510i	0.707030	−	1.22461i	0.965954	−	0.258714i	$-0.0832987\pi$
$992$	−3.49059	−	6.04588i	−0.110826	−	0.191957i
$993$		−	34.7116i		−	1.10154i
$994$	23.9160	−	13.8079i	0.758571	−	0.437961i
$995$		0			0
$996$		−	13.3082i		−	0.421686i
$997$	25.5611	+	44.2732i	0.809530	+	1.40215i	0.913190	+	0.407534i	$0.133611\pi$
$997$	25.5611	+	44.2732i	0.809530	+	1.40215i	−0.103661	+	0.994613i	$0.533056\pi$
$998$	−6.51186	+	11.2789i	−0.206129	+	0.357026i
$999$	−4.20388	−	2.42711i	−0.133005	−	0.0767904i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.bc.h.901.2	yes	12
5.2	odd	4		1950.2.y.n.199.5		12
5.3	odd	4		1950.2.y.m.199.2		12
5.4	even	2		1950.2.bc.k.901.5	yes	12
13.10	even	6	inner	1950.2.bc.h.751.2	✓	12
65.23	odd	12		1950.2.y.n.49.5		12
65.49	even	6		1950.2.bc.k.751.5	yes	12
65.62	odd	12		1950.2.y.m.49.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.y.m.49.2		12	65.62	odd	12
1950.2.y.m.199.2		12	5.3	odd	4
1950.2.y.n.49.5		12	65.23	odd	12
1950.2.y.n.199.5		12	5.2	odd	4
1950.2.bc.h.751.2	✓	12	13.10	even	6	inner
1950.2.bc.h.901.2	yes	12	1.1	even	1	trivial
1950.2.bc.k.751.5	yes	12	65.49	even	6
1950.2.bc.k.901.5	yes	12	5.4	even	2

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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(-2.32854 + 1.34438i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(-2.32854 + 1.34438i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(4.61081 + 2.66205i) q^{11} -1.00000 q^{12} +(3.42711 - 1.12022i) q^{13} +2.68876 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.18370 - 3.78228i) q^{17} +1.00000i q^{18} +(2.70388 - 1.56109i) q^{19} -2.68876i q^{21} +(-2.66205 - 4.61081i) q^{22} +(0.478355 - 0.828535i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-3.52808 - 0.743415i) q^{26} +1.00000 q^{27} +(-2.32854 - 1.34438i) q^{28} +(-1.59858 + 2.76882i) q^{29} -6.98118i q^{31} +(0.866025 - 0.500000i) q^{32} +(-4.61081 + 2.66205i) q^{33} +4.36740i q^{34} +(0.500000 - 0.866025i) q^{36} +(-4.20388 - 2.42711i) q^{37} -3.12217 q^{38} +(-0.743415 + 3.52808i) q^{39} +(3.78228 + 2.18370i) q^{41} +(-1.34438 + 2.32854i) q^{42} +(0.620223 + 1.07426i) q^{43} +5.32411i q^{44} +(-0.828535 + 0.478355i) q^{46} +2.61378i q^{47} +(-0.500000 - 0.866025i) q^{48} +(0.114717 - 0.198696i) q^{49} +4.36740 q^{51} +(2.68370 + 2.40786i) q^{52} +6.98118 q^{53} +(-0.866025 - 0.500000i) q^{54} +(1.34438 + 2.32854i) q^{56} +3.12217i q^{57} +(2.76882 - 1.59858i) q^{58} +(5.03242 - 2.90547i) q^{59} +(-1.42711 - 2.47183i) q^{61} +(-3.49059 + 6.04588i) q^{62} +(2.32854 + 1.34438i) q^{63} -1.00000 q^{64} +5.32411 q^{66} +(-1.34894 - 0.778812i) q^{67} +(2.18370 - 3.78228i) q^{68} +(0.478355 + 0.828535i) q^{69} +(8.89482 - 5.13543i) q^{71} +(-0.866025 + 0.500000i) q^{72} +0.569326i q^{73} +(2.42711 + 4.20388i) q^{74} +(2.70388 + 1.56109i) q^{76} -14.3152 q^{77} +(2.40786 - 2.68370i) q^{78} +17.1863 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-2.18370 - 3.78228i) q^{82} +13.3082i q^{83} +(2.32854 - 1.34438i) q^{84} -1.24045i q^{86} +(-1.59858 - 2.76882i) q^{87} +(2.66205 - 4.61081i) q^{88} +(-0.243193 - 0.140408i) q^{89} +(-6.47415 + 7.21582i) q^{91} +0.956710 q^{92} +(6.04588 + 3.49059i) q^{93} +(1.30689 - 2.26360i) q^{94} +1.00000i q^{96} +(10.4135 - 6.01223i) q^{97} +(-0.198696 + 0.114717i) q^{98} -5.32411i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 6 q^{4} - 6 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^7 - 6 * q^9	\( 12 q - 6 q^{3} + 6 q^{4} - 6 q^{7} - 6 q^{9} - 12 q^{11} - 12 q^{12} + 8 q^{14} - 6 q^{16} - 6 q^{19} - 4 q^{22} + 4 q^{23} - 4 q^{26} + 12 q^{27} - 6 q^{28} + 12 q^{33} + 6 q^{36} - 12 q^{37} + 24 q^{38} + 6 q^{39} - 4 q^{42} - 10 q^{43} + 12 q^{46} - 6 q^{48} + 32 q^{49} + 6 q^{52} - 16 q^{53} + 4 q^{56} + 24 q^{61} + 8 q^{62} + 6 q^{63} - 12 q^{64} + 8 q^{66} + 6 q^{67} + 4 q^{69} + 12 q^{71} - 12 q^{74} - 6 q^{76} - 48 q^{77} + 8 q^{78} + 52 q^{79} - 6 q^{81} + 6 q^{84} + 4 q^{88} + 24 q^{89} - 54 q^{91} + 8 q^{92} - 8 q^{94} + 12 q^{97} + 36 q^{98}+O(q^{100}) \) 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^7 - 6 * q^9 - 12 * q^11 - 12 * q^12 + 8 * q^14 - 6 * q^16 - 6 * q^19 - 4 * q^22 + 4 * q^23 - 4 * q^26 + 12 * q^27 - 6 * q^28 + 12 * q^33 + 6 * q^36 - 12 * q^37 + 24 * q^38 + 6 * q^39 - 4 * q^42 - 10 * q^43 + 12 * q^46 - 6 * q^48 + 32 * q^49 + 6 * q^52 - 16 * q^53 + 4 * q^56 + 24 * q^61 + 8 * q^62 + 6 * q^63 - 12 * q^64 + 8 * q^66 + 6 * q^67 + 4 * q^69 + 12 * q^71 - 12 * q^74 - 6 * q^76 - 48 * q^77 + 8 * q^78 + 52 * q^79 - 6 * q^81 + 6 * q^84 + 4 * q^88 + 24 * q^89 - 54 * q^91 + 8 * q^92 - 8 * q^94 + 12 * q^97 + 36 * q^98

Introduction

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