LMFDB - Embedded newform 1950.2.y.m.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(49,1950)]

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, 3, 5]))

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

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

chi := DirichletCharacter("1950.49");

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.y (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$15.5708283941$
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			199.2
Root			$0.500000 + 0.822735i$ of defining polynomial
Character	$\chi$	$=$	1950.199
Dual form			1950.2.y.m.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(1.34438 + 2.32854i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(1.34438 + 2.32854i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(4.61081 + 2.66205i) q^{11} +1.00000i q^{12} +(1.12022 + 3.42711i) q^{13} -2.68876 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.78228 + 2.18370i) q^{17} -1.00000 q^{18} +(-2.70388 + 1.56109i) q^{19} -2.68876i q^{21} +(-4.61081 + 2.66205i) q^{22} +(0.828535 + 0.478355i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-3.52808 - 0.743415i) q^{26} -1.00000i q^{27} +(1.34438 - 2.32854i) q^{28} +(1.59858 - 2.76882i) q^{29} -6.98118i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.66205 - 4.61081i) q^{33} -4.36740i q^{34} +(0.500000 - 0.866025i) q^{36} +(-2.42711 + 4.20388i) q^{37} -3.12217i q^{38} +(0.743415 - 3.52808i) q^{39} +(3.78228 + 2.18370i) q^{41} +(2.32854 + 1.34438i) q^{42} +(-1.07426 + 0.620223i) q^{43} -5.32411i q^{44} +(-0.828535 + 0.478355i) q^{46} +2.61378 q^{47} +(0.866025 - 0.500000i) q^{48} +(-0.114717 + 0.198696i) q^{49} +4.36740 q^{51} +(2.40786 - 2.68370i) q^{52} +6.98118i q^{53} +(0.866025 + 0.500000i) q^{54} +(1.34438 + 2.32854i) q^{56} +3.12217 q^{57} +(1.59858 + 2.76882i) q^{58} +(-5.03242 + 2.90547i) q^{59} +(-1.42711 - 2.47183i) q^{61} +(6.04588 + 3.49059i) q^{62} +(-1.34438 + 2.32854i) q^{63} +1.00000 q^{64} +5.32411 q^{66} +(-0.778812 + 1.34894i) q^{67} +(3.78228 + 2.18370i) q^{68} +(-0.478355 - 0.828535i) q^{69} +(8.89482 - 5.13543i) q^{71} +(0.500000 + 0.866025i) q^{72} -0.569326 q^{73} +(-2.42711 - 4.20388i) q^{74} +(2.70388 + 1.56109i) q^{76} +14.3152i q^{77} +(2.68370 + 2.40786i) q^{78} -17.1863 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-3.78228 + 2.18370i) q^{82} -13.3082 q^{83} +(-2.32854 + 1.34438i) q^{84} -1.24045i q^{86} +(-2.76882 + 1.59858i) q^{87} +(4.61081 + 2.66205i) q^{88} +(0.243193 + 0.140408i) q^{89} +(-6.47415 + 7.21582i) q^{91} -0.956710i q^{92} +(-3.49059 + 6.04588i) q^{93} +(-1.30689 + 2.26360i) q^{94} +1.00000i q^{96} +(-6.01223 - 10.4135i) q^{97} +(-0.114717 - 0.198696i) q^{98} +5.32411i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{4} + 4 q^{7} + 12 q^{8} + 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 - 6 * q^4 + 4 * q^7 + 12 * q^8 + 6 * q^9	$ 12 q - 6 q^{2} - 6 q^{4} + 4 q^{7} + 12 q^{8} + 6 q^{9} - 12 q^{11} - 4 q^{13} - 8 q^{14} - 6 q^{16} - 12 q^{18} + 6 q^{19} + 12 q^{22} - 12 q^{23} - 4 q^{26} + 4 q^{28} - 6 q^{32} - 4 q^{33} + 6 q^{36} + 12 q^{37} - 6 q^{39} + 6 q^{42} - 12 q^{43} + 12 q^{46} - 16 q^{47} - 32 q^{49} + 8 q^{52} + 4 q^{56} - 24 q^{57} + 24 q^{61} - 4 q^{63} + 12 q^{64} + 8 q^{66} - 24 q^{67} - 4 q^{69} + 12 q^{71} + 6 q^{72} + 40 q^{73} + 12 q^{74} - 6 q^{76} + 6 q^{78} - 52 q^{79} - 6 q^{81} - 32 q^{83} - 6 q^{84} - 12 q^{88} - 24 q^{89} - 54 q^{91} + 8 q^{93} + 8 q^{94} - 24 q^{97} - 32 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^4 + 4 * q^7 + 12 * q^8 + 6 * q^9 - 12 * q^11 - 4 * q^13 - 8 * q^14 - 6 * q^16 - 12 * q^18 + 6 * q^19 + 12 * q^22 - 12 * q^23 - 4 * q^26 + 4 * q^28 - 6 * q^32 - 4 * q^33 + 6 * q^36 + 12 * q^37 - 6 * q^39 + 6 * q^42 - 12 * q^43 + 12 * q^46 - 16 * q^47 - 32 * q^49 + 8 * q^52 + 4 * q^56 - 24 * q^57 + 24 * q^61 - 4 * q^63 + 12 * q^64 + 8 * q^66 - 24 * q^67 - 4 * q^69 + 12 * q^71 + 6 * q^72 + 40 * q^73 + 12 * q^74 - 6 * q^76 + 6 * q^78 - 52 * q^79 - 6 * q^81 - 32 * q^83 - 6 * q^84 - 12 * q^88 - 24 * q^89 - 54 * q^91 + 8 * q^93 + 8 * q^94 - 24 * q^97 - 32 * 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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	1.34438	+	2.32854i	0.508128	+	0.880104i	0.999956	+	0.00941100i	$0.00299566\pi$
$7$	1.34438	+	2.32854i	0.508128	+	0.880104i	−0.491828	+	0.870693i	$0.663671\pi$
$8$	1.00000			0.353553
$9$	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	$0.370095\pi$
$12$			1.00000i			0.288675i
$13$	1.12022	+	3.42711i	0.310694	+	0.950510i
$13$	1.12022	+	3.42711i	0.310694	+	0.950510i
$14$	−2.68876			−0.718602
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.78228	+	2.18370i	−0.917336	+	0.529624i	−0.882784	−	0.469778i	$-0.844334\pi$
$17$	−3.78228	+	2.18370i	−0.917336	+	0.529624i	−0.0345521	+	0.999403i	$0.511000\pi$
$18$	−1.00000			−0.235702
$19$	−2.70388	+	1.56109i	−0.620313	+	0.358138i	−0.776991	−	0.629512i	$-0.783255\pi$
$19$	−2.70388	+	1.56109i	−0.620313	+	0.358138i	0.156678	+	0.987650i	$0.449922\pi$
$20$		0			0
$21$		−	2.68876i		−	0.586736i
$22$	−4.61081	+	2.66205i	−0.983028	+	0.567552i
$23$	0.828535	+	0.478355i	0.172762	+	0.0997439i	0.583887	−	0.811835i	$-0.301531\pi$
$23$	0.828535	+	0.478355i	0.172762	+	0.0997439i	−0.411126	+	0.911579i	$0.634864\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$		0			0
$26$	−3.52808	−	0.743415i	−0.691913	−	0.145796i
$27$		−	1.00000i		−	0.192450i
$28$	1.34438	−	2.32854i	0.254064	−	0.440052i
$29$	1.59858	−	2.76882i	0.296848	−	0.514157i	−0.678565	−	0.734541i	$-0.737398\pi$
$29$	1.59858	−	2.76882i	0.296848	−	0.514157i	0.975413	+	0.220384i	$0.0707311\pi$
$30$		0			0
$31$		−	6.98118i		−	1.25386i	−0.779077	−	0.626928i	$-0.784312\pi$
$31$		−	6.98118i		−	1.25386i	0.779077	−	0.626928i	$-0.215688\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−2.66205	−	4.61081i	−0.463404	−	0.802639i
$34$		−	4.36740i		−	0.749002i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−2.42711	+	4.20388i	−0.399015	+	0.691114i	−0.993605	−	0.112915i	$-0.963981\pi$
$37$	−2.42711	+	4.20388i	−0.399015	+	0.691114i	0.594590	+	0.804029i	$0.297314\pi$
$38$		−	3.12217i		−	0.506484i
$39$	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	$0.555889\pi$
$42$	2.32854	+	1.34438i	0.359301	+	0.207442i
$43$	−1.07426	+	0.620223i	−0.163823	+	0.0945831i	−0.579670	−	0.814851i	$-0.696818\pi$
$43$	−1.07426	+	0.620223i	−0.163823	+	0.0945831i	0.415847	+	0.909435i	$0.363485\pi$
$44$		−	5.32411i		−	0.802639i
$45$		0			0
$46$	−0.828535	+	0.478355i	−0.122161	+	0.0705296i
$47$	2.61378			0.381259			0.190630	−	0.981662i	$-0.438947\pi$
$47$	2.61378			0.381259			0.190630	+	0.981662i	$0.438947\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	−0.114717	+	0.198696i	−0.0163882	+	0.0283852i
$50$		0			0
$51$	4.36740			0.611558
$52$	2.40786	−	2.68370i	0.333909	−	0.372162i
$53$			6.98118i			0.958938i	0.877559	+	0.479469i	$0.159171\pi$
$53$			6.98118i			0.958938i	−0.877559	+	0.479469i	$0.840829\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$		0			0
$56$	1.34438	+	2.32854i	0.179650	+	0.311164i
$57$	3.12217			0.413542
$58$	1.59858	+	2.76882i	0.209904	+	0.363564i
$59$	−5.03242	+	2.90547i	−0.655165	+	0.378260i	−0.790432	−	0.612549i	$-0.790144\pi$
$59$	−5.03242	+	2.90547i	−0.655165	+	0.378260i	0.135267	+	0.990809i	$0.456811\pi$
$60$		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	$0.891825\pi$
$62$	6.04588	+	3.49059i	0.767827	+	0.443305i
$63$	−1.34438	+	2.32854i	−0.169376	+	0.293368i
$64$	1.00000			0.125000
$65$		0			0
$66$	5.32411			0.655352
$67$	−0.778812	+	1.34894i	−0.0951471	+	0.164800i	−0.909670	−	0.415332i	$-0.863665\pi$
$67$	−0.778812	+	1.34894i	−0.0951471	+	0.164800i	0.814523	+	0.580131i	$0.196999\pi$
$68$	3.78228	+	2.18370i	0.458668	+	0.264812i
$69$	−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	$0.124718\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−0.569326			−0.0666345			−0.0333173	−	0.999445i	$-0.510607\pi$
$73$	−0.569326			−0.0666345			−0.0333173	+	0.999445i	$0.510607\pi$
$74$	−2.42711	−	4.20388i	−0.282146	−	0.488691i
$75$		0			0
$76$	2.70388	+	1.56109i	0.310157	+	0.179069i
$77$			14.3152i			1.63137i
$78$	2.68370	+	2.40786i	0.303869	+	0.272636i
$79$	−17.1863			−1.93361			−0.966804	−	0.255518i	$-0.917754\pi$
$79$	−17.1863			−1.93361			−0.966804	+	0.255518i	$0.917754\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.78228	+	2.18370i	−0.417682	+	0.241149i
$83$	−13.3082			−1.46076			−0.730382	−	0.683038i	$-0.760658\pi$
$83$	−13.3082			−1.46076			−0.730382	+	0.683038i	$0.760658\pi$
$84$	−2.32854	+	1.34438i	−0.254064	+	0.146684i
$85$		0			0
$86$		−	1.24045i		−	0.133761i
$87$	−2.76882	+	1.59858i	−0.296848	+	0.171386i
$88$	4.61081	+	2.66205i	0.491514	+	0.283776i
$89$	0.243193	+	0.140408i	0.0257784	+	0.0148832i	0.512834	−	0.858488i	$-0.328596\pi$
$89$	0.243193	+	0.140408i	0.0257784	+	0.0148832i	−0.487055	+	0.873371i	$0.661929\pi$
$90$		0			0
$91$	−6.47415	+	7.21582i	−0.678675	+	0.756424i
$92$		−	0.956710i		−	0.0997439i
$93$	−3.49059	+	6.04588i	−0.361957	+	0.626928i
$94$	−1.30689	+	2.26360i	−0.134795	+	0.233473i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	−6.01223	−	10.4135i	−0.610450	−	1.05733i	−0.991165	−	0.132637i	$-0.957655\pi$
$97$	−6.01223	−	10.4135i	−0.610450	−	1.05733i	0.380715	−	0.924692i	$-0.375678\pi$
$98$	−0.114717	−	0.198696i	−0.0115882	−	0.0200713i
$99$			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	$0.924790\pi$
$102$	−2.18370	+	3.78228i	−0.216218	+	0.374501i
$103$			18.1600i			1.78935i	0.446715	+	0.894677i	$0.352594\pi$
$103$			18.1600i			1.78935i	−0.446715	+	0.894677i	$0.647406\pi$
$104$	1.12022	+	3.42711i	0.109847	+	0.336056i
$105$		0			0
$106$	−6.04588	−	3.49059i	−0.587227	−	0.339036i
$107$	17.7164	+	10.2286i	1.71271	+	0.988833i	0.930868	+	0.365356i	$0.119053\pi$
$107$	17.7164	+	10.2286i	1.71271	+	0.988833i	0.781841	+	0.623477i	$0.214281\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$		−	6.49435i		−	0.622045i	−0.950402	−	0.311023i	$-0.899328\pi$
$109$		−	6.49435i		−	0.622045i	0.950402	−	0.311023i	$-0.100672\pi$
$110$		0			0
$111$	4.20388	−	2.42711i	0.399015	−	0.230371i
$112$	−2.68876			−0.254064
$113$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$113$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$114$	−1.56109	+	2.70388i	−0.146209	+	0.253242i
$115$		0			0
$116$	−3.19716			−0.296848
$117$	−2.40786	+	2.68370i	−0.222606	+	0.248108i
$118$		−	5.81094i		−	0.534940i
$119$	−10.1696	−	5.87144i	−0.932249	−	0.538234i
$120$		0			0
$121$	8.67305	+	15.0222i	0.788459	+	1.36565i
$122$	2.85423			0.258409
$123$	−2.18370	−	3.78228i	−0.196897	−	0.341036i
$124$	−6.04588	+	3.49059i	−0.542936	+	0.313464i
$125$		0			0
$126$	−1.34438	−	2.32854i	−0.119767	−	0.207442i
$127$	−18.6803	−	10.7851i	−1.65761	−	0.957022i	−0.973813	−	0.227352i	$-0.926993\pi$
$127$	−18.6803	−	10.7851i	−1.65761	−	0.957022i	−0.683799	−	0.729671i	$-0.739673\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	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	$0.457095\pi$
$132$	−2.66205	+	4.61081i	−0.231702	+	0.401320i
$133$	−7.27009	−	4.19739i	−0.630397	−	0.363960i
$134$	−0.778812	−	1.34894i	−0.0672791	−	0.116531i
$135$		0			0
$136$	−3.78228	+	2.18370i	−0.324327	+	0.187251i
$137$	9.79473	+	16.9650i	0.836820	+	1.44942i	0.892540	+	0.450969i	$0.148921\pi$
$137$	9.79473	+	16.9650i	0.836820	+	1.44942i	−0.0557195	+	0.998446i	$0.517745\pi$
$138$	0.956710			0.0814406
$139$	7.77583	+	13.4681i	0.659538	+	1.14235i	0.980735	+	0.195340i	$0.0625812\pi$
$139$	7.77583	+	13.4681i	0.659538	+	1.14235i	−0.321198	+	0.947012i	$0.604085\pi$
$140$		0			0
$141$	−2.26360	−	1.30689i	−0.190630	−	0.110060i
$142$			10.2709i			0.861911i
$143$	−3.95802	+	18.7839i	−0.330986	+	1.57079i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	0.284663	−	0.493050i	0.0235589	−	0.0408051i
$147$	0.198696	−	0.114717i	0.0163882	−	0.00946172i
$148$	4.85423			0.399015
$149$	13.8328	−	7.98638i	1.13323	−	0.654270i	0.188484	−	0.982076i	$-0.439643\pi$
$149$	13.8328	−	7.98638i	1.13323	−	0.654270i	0.944745	+	0.327807i	$0.106309\pi$
$150$		0			0
$151$			10.0784i			0.820172i	0.912047	+	0.410086i	$0.134501\pi$
$151$			10.0784i			0.820172i	−0.912047	+	0.410086i	$0.865499\pi$
$152$	−2.70388	+	1.56109i	−0.219314	+	0.126621i
$153$	−3.78228	−	2.18370i	−0.305779	−	0.176541i
$154$	−12.3974	−	7.15762i	−0.999008	−	0.576778i
$155$		0			0
$156$	−3.42711	+	1.12022i	−0.274389	+	0.0896896i
$157$		−	20.3755i		−	1.62614i	−0.582165	−	0.813070i	$-0.697794\pi$
$157$		−	20.3755i		−	1.62614i	0.582165	−	0.813070i	$-0.302206\pi$
$158$	8.59314	−	14.8838i	0.683634	−	1.18409i
$159$	3.49059	−	6.04588i	0.276822	−	0.479469i
$160$		0			0
$161$			2.57236i			0.202731i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	−2.85959	−	4.95296i	−0.223981	−	0.387946i	0.732033	−	0.681270i	$-0.238572\pi$
$163$	−2.85959	−	4.95296i	−0.223981	−	0.387946i	−0.956013	+	0.293324i	$0.905239\pi$
$164$		−	4.36740i		−	0.341036i
$165$		0			0
$166$	6.65410	−	11.5252i	0.516458	−	0.894532i
$167$	0.478355	−	0.828535i	0.0370162	−	0.0641140i	−0.846924	−	0.531714i	$-0.821548\pi$
$167$	0.478355	−	0.828535i	0.0370162	−	0.0641140i	0.883940	+	0.467600i	$0.154881\pi$
$168$		−	2.68876i		−	0.207442i
$169$	−10.4902	+	7.67826i	−0.806939	+	0.590635i
$170$		0			0
$171$	−2.70388	−	1.56109i	−0.206771	−	0.119379i
$172$	1.07426	+	0.620223i	0.0819113	+	0.0472915i
$173$	−0.711327	+	0.410685i	−0.0540812	+	0.0312238i	−0.526797	−	0.849991i	$-0.676607\pi$
$173$	−0.711327	+	0.410685i	−0.0540812	+	0.0312238i	0.472716	+	0.881215i	$0.343274\pi$
$174$		−	3.19716i		−	0.242376i
$175$		0			0
$176$	−4.61081	+	2.66205i	−0.347553	+	0.200660i
$177$	5.81094			0.436777
$178$	−0.243193	+	0.140408i	−0.0182281	+	0.0105240i
$179$	−0.0905528	+	0.156842i	−0.00676823	+	0.0117229i	−0.869390	−	0.494127i	$-0.835488\pi$
$179$	−0.0905528	+	0.156842i	−0.00676823	+	0.0117229i	0.862621	+	0.505850i	$0.168821\pi$
$180$		0			0
$181$	5.28082			0.392520			0.196260	−	0.980552i	$-0.437120\pi$
$181$	5.28082			0.392520			0.196260	+	0.980552i	$0.437120\pi$
$182$	−3.01201	−	9.21469i	−0.223265	−	0.683038i
$183$			2.85423i			0.210990i
$184$	0.828535	+	0.478355i	0.0610804	+	0.0352648i
$185$		0			0
$186$	−3.49059	−	6.04588i	−0.255942	−	0.443305i
$187$	−23.2525			−1.70039
$188$	−1.30689	−	2.26360i	−0.0953148	−	0.165090i
$189$	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	$0.545807\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−7.03844	+	12.1909i	−0.506638	+	0.877523i	0.493333	+	0.869841i	$0.335779\pi$
$193$	−7.03844	+	12.1909i	−0.506638	+	0.877523i	−0.999970	+	0.00768190i	$0.997555\pi$
$194$	12.0245			0.863306
$195$		0			0
$196$	0.229435			0.0163882
$197$	6.40851	−	11.0999i	0.456587	−	0.790833i	−0.542190	−	0.840256i	$-0.682405\pi$
$197$	6.40851	−	11.0999i	0.456587	−	0.790833i	0.998778	+	0.0494229i	$0.0157382\pi$
$198$	−4.61081	−	2.66205i	−0.327676	−	0.189184i
$199$	5.88282	+	10.1893i	0.417022	+	0.722303i	0.995638	−	0.0932965i	$-0.0297404\pi$
$199$	5.88282	+	10.1893i	0.417022	+	0.722303i	−0.578616	+	0.815600i	$0.696407\pi$
$200$		0			0
$201$	1.34894	−	0.778812i	0.0951471	−	0.0549332i
$202$	−6.92268	−	11.9904i	−0.487078	−	0.843644i
$203$	8.59639			0.603348
$204$	−2.18370	−	3.78228i	−0.152889	−	0.264812i
$205$		0			0
$206$	−15.7270	−	9.07998i	−1.09575	−	0.632632i
$207$			0.956710i			0.0664959i
$208$	−3.52808	−	0.743415i	−0.244628	−	0.0515466i
$209$	−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	$0.165445\pi$
$212$	6.04588	−	3.49059i	0.415232	−	0.239735i
$213$	−10.2709			−0.703747
$214$	−17.7164	+	10.2286i	−1.21107	+	0.699211i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	16.2559	−	9.38536i	1.10352	−	0.637119i
$218$	5.62427	+	3.24717i	0.380923	+	0.219926i
$219$	0.493050	+	0.284663i	0.0333173	+	0.0192357i
$220$		0			0
$221$	−11.7208	−	10.5161i	−0.788424	−	0.707386i
$222$			4.85423i			0.325794i
$223$	−4.31035	+	7.46575i	−0.288643	+	0.499944i	−0.973486	−	0.228747i	$-0.926537\pi$
$223$	−4.31035	+	7.46575i	−0.288643	+	0.499944i	0.684843	+	0.728690i	$0.259871\pi$
$224$	1.34438	−	2.32854i	0.0898252	−	0.155582i
$225$		0			0
$226$		0			0
$227$	−10.3191	−	17.8732i	−0.684904	−	1.18629i	−0.973467	−	0.228828i	$-0.926511\pi$
$227$	−10.3191	−	17.8732i	−0.684904	−	1.18629i	0.288563	−	0.957461i	$-0.406823\pi$
$228$	−1.56109	−	2.70388i	−0.103386	−	0.179069i
$229$			3.12928i			0.206789i	0.994640	+	0.103394i	$0.0329704\pi$
$229$			3.12928i			0.206789i	−0.994640	+	0.103394i	$0.967030\pi$
$230$		0			0
$231$	7.15762	−	12.3974i	0.470937	−	0.815687i
$232$	1.59858	−	2.76882i	0.104952	−	0.181782i
$233$			9.31414i			0.610190i	0.952322	+	0.305095i	$0.0986882\pi$
$233$			9.31414i			0.610190i	−0.952322	+	0.305095i	$0.901312\pi$
$234$	−1.12022	−	3.42711i	−0.0732312	−	0.224037i
$235$		0			0
$236$	5.03242	+	2.90547i	0.327582	+	0.189130i
$237$	14.8838	+	8.59314i	0.966804	+	0.558185i
$238$	10.1696	−	5.87144i	0.659199	−	0.380589i
$239$			18.4726i			1.19489i	0.801909	+	0.597447i	$0.203818\pi$
$239$			18.4726i			1.19489i	−0.801909	+	0.597447i	$0.796182\pi$
$240$		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	$0.309646\pi$
$242$	−17.3461			−1.11505
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−1.42711	+	2.47183i	−0.0913615	+	0.158243i
$245$		0			0
$246$	4.36740			0.278455
$247$	−8.37897	−	7.51774i	−0.533141	−	0.478343i
$248$		−	6.98118i		−	0.443305i
$249$	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	$0.597858\pi$
$252$	2.68876			0.169376
$253$	2.54681	+	4.41121i	0.160117	+	0.277330i
$254$	18.6803	−	10.7851i	1.17211	−	0.676717i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.46481	+	5.46451i	0.590399	+	0.340867i	0.765255	−	0.643727i	$-0.222613\pi$
$257$	9.46481	+	5.46451i	0.590399	+	0.340867i	−0.174856	+	0.984594i	$0.555946\pi$
$258$	−0.620223	+	1.07426i	−0.0386134	+	0.0668803i
$259$	−13.0519			−0.811003
$260$		0			0
$261$	3.19716			0.197899
$262$	−1.53807	+	2.66402i	−0.0950224	+	0.164584i
$263$	11.6825	+	6.74488i	0.720372	+	0.415907i	0.814889	−	0.579616i	$-0.196798\pi$
$263$	11.6825	+	6.74488i	0.720372	+	0.415907i	−0.0945177	+	0.995523i	$0.530131\pi$
$264$	−2.66205	−	4.61081i	−0.163838	−	0.283776i
$265$		0			0
$266$	7.27009	−	4.19739i	0.445758	−	0.257359i
$267$	−0.140408	−	0.243193i	−0.00859280	−	0.0148832i
$268$	1.55762			0.0951471
$269$	−4.25014	−	7.36146i	−0.259136	−	0.448836i	0.706875	−	0.707339i	$-0.250104\pi$
$269$	−4.25014	−	7.36146i	−0.259136	−	0.448836i	−0.966011	+	0.258502i	$0.916771\pi$
$270$		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	$0.904501\pi$
$272$		−	4.36740i		−	0.264812i
$273$	9.21469	−	3.01201i	0.557698	−	0.182295i
$274$	−19.5895			−1.18344
$275$		0			0
$276$	−0.478355	+	0.828535i	−0.0287936	+	0.0498720i
$277$	24.9904	−	14.4282i	1.50152	−	0.866906i	0.501526	−	0.865142i	$-0.332772\pi$
$277$	24.9904	−	14.4282i	1.50152	−	0.866906i	0.999998	−	0.00176347i	$-0.000561331\pi$
$278$	−15.5517			−0.932727
$279$	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	$-0.273752\pi$
$282$	2.26360	−	1.30689i	0.134795	−	0.0778242i
$283$	−9.94021	−	5.73899i	−0.590884	−	0.341147i	0.174563	−	0.984646i	$-0.444149\pi$
$283$	−9.94021	−	5.73899i	−0.590884	−	0.341147i	−0.765447	+	0.643499i	$0.777482\pi$
$284$	−8.89482	−	5.13543i	−0.527810	−	0.304731i
$285$		0			0
$286$	−14.2883	−	12.8197i	−0.844884	−	0.758043i
$287$			11.7429i			0.693160i
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	1.03707	−	1.79626i	0.0610041	−	0.105662i
$290$		0			0
$291$			12.0245i			0.704887i
$292$	0.284663	+	0.493050i	0.0166586	+	0.0288536i
$293$	1.68599	+	2.92023i	0.0984969	+	0.170602i	0.911063	−	0.412268i	$-0.135263\pi$
$293$	1.68599	+	2.92023i	0.0984969	+	0.170602i	−0.812566	+	0.582869i	$0.801930\pi$
$294$			0.229435i			0.0133809i
$295$		0			0
$296$	−2.42711	+	4.20388i	−0.141073	+	0.244346i
$297$	2.66205	−	4.61081i	0.154468	−	0.267546i
$298$			15.9728i			0.925277i
$299$	−0.711233	+	3.37535i	−0.0411316	+	0.195201i
$300$		0			0
$301$	−2.88842	−	1.66763i	−0.166486	−	0.0961206i
$302$	−8.72819	−	5.03922i	−0.502251	−	0.289975i
$303$	11.9904	−	6.92268i	0.688833	−	0.397698i
$304$		−	3.12217i		−	0.179069i
$305$		0			0
$306$	3.78228	−	2.18370i	0.216218	−	0.124834i
$307$	−12.5113			−0.714057			−0.357029	−	0.934093i	$-0.616210\pi$
$307$	−12.5113			−0.714057			−0.357029	+	0.934093i	$0.616210\pi$
$308$	12.3974	−	7.15762i	0.706405	−	0.407843i
$309$	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	$0.744090\pi$
$312$	0.743415	−	3.52808i	0.0420876	−	0.199738i
$313$		−	28.8758i		−	1.63216i	−0.577942	−	0.816078i	$-0.696144\pi$
$313$		−	28.8758i		−	1.63216i	0.577942	−	0.816078i	$-0.303856\pi$
$314$	17.6457	+	10.1877i	0.995804	+	0.574928i
$315$		0			0
$316$	8.59314	+	14.8838i	0.483402	+	0.837277i
$317$	−12.8139			−0.719698			−0.359849	−	0.933011i	$-0.617172\pi$
$317$	−12.8139			−0.719698			−0.359849	+	0.933011i	$0.617172\pi$
$318$	3.49059	+	6.04588i	0.195742	+	0.339036i
$319$	14.7415	−	8.51099i	0.825364	−	0.476524i
$320$		0			0
$321$	−10.2286	−	17.7164i	−0.570903	−	0.988833i
$322$	−2.22773	−	1.28618i	−0.124147	−	0.0716761i
$323$	6.81788	−	11.8089i	0.379357	−	0.657066i
$324$	1.00000			0.0555556
$325$		0			0
$326$	5.71918			0.316756
$327$	−3.24717	+	5.62427i	−0.179569	+	0.311023i
$328$	3.78228	+	2.18370i	0.208841	+	0.120575i
$329$	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	$0.930296\pi$
$332$	6.65410	+	11.5252i	0.365191	+	0.632530i
$333$	−4.85423			−0.266010
$334$	0.478355	+	0.828535i	0.0261744	+	0.0453354i
$335$		0			0
$336$	2.32854	+	1.34438i	0.127032	+	0.0733420i
$337$		−	27.2945i		−	1.48683i	−0.668831	−	0.743414i	$-0.733205\pi$
$337$		−	27.2945i		−	1.48683i	0.668831	−	0.743414i	$-0.266795\pi$
$338$	−1.40447	−	12.9239i	−0.0763928	−	0.702968i
$339$		0			0
$340$		0			0
$341$	18.5843	−	32.1889i	1.00639	−	1.74313i
$342$	2.70388	−	1.56109i	0.146209	−	0.0844139i
$343$	18.2044			0.982947
$344$	−1.07426	+	0.620223i	−0.0579201	+	0.0334402i
$345$		0			0
$346$		−	0.821370i		−	0.0441571i
$347$	22.8324	−	13.1823i	1.22571	−	0.707663i	0.259580	−	0.965722i	$-0.416416\pi$
$347$	22.8324	−	13.1823i	1.22571	−	0.707663i	0.966129	+	0.258058i	$0.0830826\pi$
$348$	2.76882	+	1.59858i	0.148424	+	0.0856928i
$349$	24.7225	+	14.2735i	1.32336	+	0.764044i	0.984264	−	0.176707i	$-0.0565444\pi$
$349$	24.7225	+	14.2735i	1.32336	+	0.764044i	0.339099	+	0.940751i	$0.389878\pi$
$350$		0			0
$351$	3.42711	−	1.12022i	0.182926	−	0.0597931i
$352$		−	5.32411i		−	0.283776i
$353$	9.12551	−	15.8058i	0.485702	−	0.841260i	−0.514163	−	0.857692i	$-0.671897\pi$
$353$	9.12551	−	15.8058i	0.485702	−	0.841260i	0.999865	+	0.0164323i	$0.00523081\pi$
$354$	−2.90547	+	5.03242i	−0.154424	+	0.267470i
$355$		0			0
$356$		−	0.280815i		−	0.0148832i
$357$	5.87144	+	10.1696i	0.310750	+	0.538234i
$358$	−0.0905528	−	0.156842i	−0.00478586	−	0.00828936i
$359$			15.0243i			0.792954i	0.918045	+	0.396477i	$0.129767\pi$
$359$			15.0243i			0.792954i	−0.918045	+	0.396477i	$0.870233\pi$
$360$		0			0
$361$	−4.62601	+	8.01249i	−0.243474	+	0.421710i
$362$	−2.64041	+	4.57332i	−0.138777	+	0.240368i
$363$		−	17.3461i		−	0.910434i
$364$	9.48616	+	1.99887i	0.497210	+	0.104769i
$365$		0			0
$366$	−2.47183	−	1.42711i	−0.129205	−	0.0745964i
$367$	−4.11131	−	2.37367i	−0.214609	−	0.123904i	0.388843	−	0.921304i	$-0.372875\pi$
$367$	−4.11131	−	2.37367i	−0.214609	−	0.123904i	−0.603451	+	0.797400i	$0.706208\pi$
$368$	−0.828535	+	0.478355i	−0.0431904	+	0.0249360i
$369$			4.36740i			0.227358i
$370$		0			0
$371$	−16.2559	+	9.38536i	−0.843965	+	0.487263i
$372$	6.98118			0.361957
$373$	0.917697	−	0.529832i	0.0475165	−	0.0274337i	−0.476054	−	0.879416i	$-0.657933\pi$
$373$	0.917697	−	0.529832i	0.0475165	−	0.0274337i	0.523570	+	0.851983i	$0.324600\pi$
$374$	11.6262	−	20.1372i	0.601178	−	1.04127i
$375$		0			0
$376$	2.61378			0.134795
$377$	11.2798	+	2.37681i	0.580940	+	0.122412i
$378$			2.68876i			0.138295i
$379$	23.6727	+	13.6675i	1.21599	+	0.702051i	0.964057	−	0.265695i	$-0.0856013\pi$
$379$	23.6727	+	13.6675i	1.21599	+	0.702051i	0.251930	+	0.967745i	$0.418935\pi$
$380$		0			0
$381$	10.7851	+	18.6803i	0.552537	+	0.957022i
$382$	−21.7080			−1.11068
$383$	−5.93911	−	10.2868i	−0.303474	−	0.525633i	0.673446	−	0.739236i	$-0.264813\pi$
$383$	−5.93911	−	10.2868i	−0.303474	−	0.525633i	−0.976920	+	0.213603i	$0.931480\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$		0			0
$386$	−7.03844	−	12.1909i	−0.358247	−	0.620502i
$387$	−1.07426	−	0.620223i	−0.0546076	−	0.0315277i
$388$	−6.01223	+	10.4135i	−0.305225	+	0.528665i
$389$	−3.19716			−0.162102			−0.0810511	−	0.996710i	$-0.525828\pi$
$389$	−3.19716			−0.162102			−0.0810511	+	0.996710i	$0.525828\pi$
$390$		0			0
$391$	−4.17833			−0.211307
$392$	−0.114717	+	0.198696i	−0.00579410	+	0.0100357i
$393$	−2.66402	−	1.53807i	−0.134382	−	0.0775855i
$394$	6.40851	+	11.0999i	0.322856	+	0.559203i
$395$		0			0
$396$	4.61081	−	2.66205i	0.231702	−	0.133773i
$397$	6.15517	+	10.6611i	0.308919	+	0.535064i	0.978126	−	0.208012i	$-0.0666994\pi$
$397$	6.15517	+	10.6611i	0.308919	+	0.535064i	−0.669207	+	0.743076i	$0.733366\pi$
$398$	−11.7656			−0.589758
$399$	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	$0.731366\pi$
$402$			1.55762i			0.0776872i
$403$	23.9253	−	7.82047i	1.19180	−	0.389565i
$404$	13.8454			0.688833
$405$		0			0
$406$	−4.29819	+	7.44469i	−0.213316	+	0.369474i
$407$	−22.3819	+	12.9222i	−1.10943	+	0.640530i
$408$	4.36740			0.216218
$409$	28.4502	−	16.4257i	1.40677	−	0.812200i	0.411696	−	0.911321i	$-0.364937\pi$
$409$	28.4502	−	16.4257i	1.40677	−	0.812200i	0.995075	+	0.0991214i	$0.0316032\pi$
$410$		0			0
$411$		−	19.5895i		−	0.966277i
$412$	15.7270	−	9.07998i	0.774813	−	0.447338i
$413$	−13.5310	−	7.81211i	−0.665815	−	0.384409i
$414$	−0.828535	−	0.478355i	−0.0407203	−	0.0235099i
$415$		0			0
$416$	2.40786	−	2.68370i	0.118055	−	0.131579i
$417$		−	15.5517i		−	0.761568i
$418$	8.31139	−	14.3958i	0.406524	−	0.704119i
$419$	3.79887	−	6.57984i	0.185587	−	0.321446i	−0.758187	−	0.652037i	$-0.773915\pi$
$419$	3.79887	−	6.57984i	0.185587	−	0.321446i	0.943774	+	0.330591i	$0.107248\pi$
$420$		0			0
$421$			23.8487i			1.16231i	0.813792	+	0.581157i	$0.197400\pi$
$421$			23.8487i			1.16231i	−0.813792	+	0.581157i	$0.802600\pi$
$422$	0.0557449	+	0.0965530i	0.00271362	+	0.00470013i
$423$	1.30689	+	2.26360i	0.0635432	+	0.110060i
$424$			6.98118i			0.339036i
$425$		0			0
$426$	5.13543	−	8.89482i	0.248812	−	0.430955i
$427$	3.83716	−	6.64616i	0.185693	−	0.321630i
$428$		−	20.4571i		−	0.988833i
$429$	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	$0.299357\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	−3.26035	+	1.88236i	−0.156682	+	0.0904606i	−0.576291	−	0.817244i	$-0.695501\pi$
$433$	−3.26035	+	1.88236i	−0.156682	+	0.0904606i	0.419609	+	0.907705i	$0.362167\pi$
$434$			18.7707i			0.901023i
$435$		0			0
$436$	−5.62427	+	3.24717i	−0.269354	+	0.155511i
$437$	−2.98702			−0.142888
$438$	−0.493050	+	0.284663i	−0.0235589	+	0.0136017i
$439$	−5.63368	+	9.75782i	−0.268881	+	0.465715i	−0.968573	−	0.248729i	$-0.919987\pi$
$439$	−5.63368	+	9.75782i	−0.268881	+	0.465715i	0.699692	+	0.714444i	$0.253320\pi$
$440$		0			0
$441$	−0.229435			−0.0109255
$442$	14.9676	−	4.89245i	0.711934	−	0.232710i
$443$			13.6139i			0.646817i	0.946259	+	0.323409i	$0.104829\pi$
$443$			13.6139i			0.646817i	−0.946259	+	0.323409i	$0.895171\pi$
$444$	−4.20388	−	2.42711i	−0.199507	−	0.115186i
$445$		0			0
$446$	−4.31035	−	7.46575i	−0.204101	−	0.353514i
$447$	−15.9728			−0.755486
$448$	1.34438	+	2.32854i	0.0635160	+	0.110013i
$449$	26.1944	−	15.1233i	1.23619	−	0.713714i	0.267876	−	0.963453i	$-0.413678\pi$
$449$	26.1944	−	15.1233i	1.23619	−	0.713714i	0.968313	+	0.249739i	$0.0803449\pi$
$450$		0			0
$451$	11.6262	+	20.1372i	0.547458	+	0.948225i
$452$		0			0
$453$	5.03922	−	8.72819i	0.236763	−	0.410086i
$454$	20.6382			0.968601
$455$		0			0
$456$	3.12217			0.146209
$457$	−18.1752	+	31.4804i	−0.850201	+	1.47259i	0.0308251	+	0.999525i	$0.490187\pi$
$457$	−18.1752	+	31.4804i	−0.850201	+	1.47259i	−0.881026	+	0.473067i	$0.843147\pi$
$458$	−2.71004	−	1.56464i	−0.126632	−	0.0731109i
$459$	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	$0.151759\pi$
$462$	7.15762	+	12.3974i	0.333003	+	0.576778i
$463$	6.40156			0.297506			0.148753	−	0.988874i	$-0.452474\pi$
$463$	6.40156			0.297506			0.148753	+	0.988874i	$0.452474\pi$
$464$	1.59858	+	2.76882i	0.0742121	+	0.128539i
$465$		0			0
$466$	−8.06628	−	4.65707i	−0.373663	−	0.215735i
$467$		−	20.7210i		−	0.958854i	−0.877582	−	0.479427i	$-0.840845\pi$
$467$		−	20.7210i		−	0.958854i	0.877582	−	0.479427i	$-0.159155\pi$
$468$	3.52808	+	0.743415i	0.163085	+	0.0343644i
$469$	−4.18808			−0.193388
$470$		0			0
$471$	−10.1877	+	17.6457i	−0.469426	+	0.813070i
$472$	−5.03242	+	2.90547i	−0.231636	+	0.133735i
$473$	−6.60426			−0.303664
$474$	−14.8838	+	8.59314i	−0.683634	+	0.394696i
$475$		0			0
$476$			11.7429i			0.538234i
$477$	−6.04588	+	3.49059i	−0.276822	+	0.159823i
$478$	−15.9977	−	9.23630i	−0.731720	−	0.422459i
$479$	−24.9299	−	14.3933i	−1.13908	−	0.657647i	−0.192876	−	0.981223i	$-0.561781\pi$
$479$	−24.9299	−	14.3933i	−1.13908	−	0.657647i	−0.946202	+	0.323576i	$0.895115\pi$
$480$		0			0
$481$	−17.1261	−	3.60870i	−0.780882	−	0.164543i
$482$			2.30832i			0.105141i
$483$	1.28618	−	2.22773i	0.0585233	−	0.101365i
$484$	8.67305	−	15.0222i	0.394229	−	0.682825i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	−6.29515	−	10.9035i	−0.285260	−	0.494086i	0.687412	−	0.726268i	$-0.258747\pi$
$487$	−6.29515	−	10.9035i	−0.285260	−	0.494086i	−0.972672	+	0.232182i	$0.925413\pi$
$488$	−1.42711	−	2.47183i	−0.0646024	−	0.111895i
$489$			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	$0.00743969\pi$
$492$	−2.18370	+	3.78228i	−0.0984487	+	0.170518i
$493$			13.9632i			0.628873i
$494$	10.7000	−	3.49753i	0.481418	−	0.157361i
$495$		0			0
$496$	6.04588	+	3.49059i	0.271468	+	0.156732i
$497$	23.9160	+	13.8079i	1.07278	+	0.619370i
$498$	−11.5252	+	6.65410i	−0.516458	+	0.298177i
$499$			13.0237i			0.583022i	0.956568	+	0.291511i	$0.0941579\pi$
$499$			13.0237i			0.583022i	−0.956568	+	0.291511i	$0.905842\pi$
$500$		0			0
$501$	−0.828535	+	0.478355i	−0.0370162	+	0.0213713i
$502$	−21.3600			−0.953345
$503$	−17.0516	+	9.84475i	−0.760293	+	0.438956i	−0.829401	−	0.558654i	$-0.811318\pi$
$503$	−17.0516	+	9.84475i	−0.760293	+	0.438956i	0.0691077	+	0.997609i	$0.477985\pi$
$504$	−1.34438	+	2.32854i	−0.0598835	+	0.103721i
$505$		0			0
$506$	−5.09362			−0.226439
$507$	12.9239	−	1.40447i	0.573971	−	0.0623745i
$508$			21.5702i			0.957022i
$509$	17.0602	+	9.84972i	0.756181	+	0.436581i	0.827923	−	0.560842i	$-0.189522\pi$
$509$	17.0602	+	9.84972i	0.756181	+	0.436581i	−0.0717419	+	0.997423i	$0.522856\pi$
$510$		0			0
$511$	−0.765390	−	1.32569i	−0.0338589	−	0.0586453i
$512$	1.00000			0.0441942
$513$	1.56109	+	2.70388i	0.0689237	+	0.119379i
$514$	−9.46481	+	5.46451i	−0.417475	+	0.241029i
$515$		0			0
$516$	−0.620223	−	1.07426i	−0.0273038	−	0.0472915i
$517$	12.0516	+	6.95802i	0.530031	+	0.306013i
$518$	6.52593	−	11.3032i	0.286733	−	0.496636i
$519$	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	$0.400659\pi$
$522$	−1.59858	+	2.76882i	−0.0699678	+	0.121188i
$523$	30.4323	+	17.5701i	1.33071	+	0.768288i	0.985409	−	0.170203i	$-0.0544424\pi$
$523$	30.4323	+	17.5701i	1.33071	+	0.768288i	0.345304	+	0.938491i	$0.387776\pi$
$524$	−1.53807	−	2.66402i	−0.0671910	−	0.116378i
$525$		0			0
$526$	−11.6825	+	6.74488i	−0.509380	+	0.294091i
$527$	15.2448	+	26.4047i	0.664073	+	1.15021i
$528$	5.32411			0.231702
$529$	−11.0424	−	19.1259i	−0.480102	−	0.831562i
$530$		0			0
$531$	−5.03242	−	2.90547i	−0.218388	−	0.126087i
$532$			8.39478i			0.363960i
$533$	−3.24679	+	15.4085i	−0.140634	+	0.667417i
$534$	0.280815			0.0121521
$535$		0			0
$536$	−0.778812	+	1.34894i	−0.0336396	+	0.0582654i
$537$	0.156842	−	0.0905528i	0.00676823	−	0.00390764i
$538$	8.50029			0.366473
$539$	−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	$-0.175219\pi$
$542$	19.3767	−	11.1872i	0.832302	−	0.480530i
$543$	−4.57332	−	2.64041i	−0.196260	−	0.113311i
$544$	3.78228	+	2.18370i	0.162164	+	0.0936253i
$545$		0			0
$546$	−1.99887	+	9.48616i	−0.0855435	+	0.405970i
$547$			1.58059i			0.0675810i	0.999429	+	0.0337905i	$0.0107579\pi$
$547$			1.58059i			0.0675810i	−0.999429	+	0.0337905i	$0.989242\pi$
$548$	9.79473	−	16.9650i	0.418410	−	0.724708i
$549$	1.42711	−	2.47183i	0.0609077	−	0.105495i
$550$		0			0
$551$			9.98208i			0.425251i
$552$	−0.478355	−	0.828535i	−0.0203601	−	0.0352648i
$553$	−23.1049	−	40.0189i	−0.982521	−	1.70178i
$554$			28.8564i			1.22599i
$555$		0			0
$556$	7.77583	−	13.4681i	0.329769	−	0.571176i
$557$	3.74274	−	6.48261i	0.158585	−	0.274677i	−0.775774	−	0.631011i	$-0.782640\pi$
$557$	3.74274	−	6.48261i	0.158585	−	0.274677i	0.934359	+	0.356334i	$0.115974\pi$
$558$			6.98118i			0.295537i
$559$	−3.32898	−	2.98681i	−0.140801	−	0.126329i
$560$		0			0
$561$	20.1372	+	11.6262i	0.850195	+	0.490860i
$562$	22.0039	+	12.7040i	0.928178	+	0.535884i
$563$	26.6120	−	15.3644i	1.12156	−	0.647533i	0.179762	−	0.983710i	$-0.442467\pi$
$563$	26.6120	−	15.3644i	1.12156	−	0.647533i	0.941799	+	0.336177i	$0.109134\pi$
$564$			2.61378i			0.110060i
$565$		0			0
$566$	9.94021	−	5.73899i	0.417818	−	0.241228i
$567$	−2.68876			−0.112917
$568$	8.89482	−	5.13543i	0.373218	−	0.215478i
$569$	2.63200	−	4.55877i	0.110339	−	0.191113i	−0.805568	−	0.592504i	$-0.798140\pi$
$569$	2.63200	−	4.55877i	0.110339	−	0.191113i	0.915907	+	0.401390i	$0.131473\pi$
$570$		0			0
$571$	−28.2057			−1.18037			−0.590186	−	0.807267i	$-0.700946\pi$
$571$	−28.2057			−1.18037			−0.590186	+	0.807267i	$0.700946\pi$
$572$	18.2463	−	5.96418i	0.762916	−	0.249375i
$573$		−	21.7080i		−	0.906865i
$574$	−10.1696	−	5.87144i	−0.424472	−	0.245069i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−15.6557			−0.651754			−0.325877	−	0.945412i	$-0.605659\pi$
$577$	−15.6557			−0.651754			−0.325877	+	0.945412i	$0.605659\pi$
$578$	1.03707	+	1.79626i	0.0431364	+	0.0747145i
$579$	12.1909	−	7.03844i	0.506638	−	0.292508i
$580$		0			0
$581$	−17.8913	−	30.9886i	−0.742256	−	1.28562i
$582$	−10.4135	−	6.01223i	−0.431653	−	0.249215i
$583$	−18.5843	+	32.1889i	−0.769681	+	1.33313i
$584$	−0.569326			−0.0235589
$585$		0			0
$586$	−3.37199			−0.139296
$587$	−8.95173	+	15.5048i	−0.369477	+	0.639954i	−0.989484	−	0.144643i	$-0.953797\pi$
$587$	−8.95173	+	15.5048i	−0.369477	+	0.639954i	0.620007	+	0.784597i	$0.287130\pi$
$588$	−0.198696	−	0.114717i	−0.00819409	−	0.00473086i
$589$	10.8982	+	18.8763i	0.449054	+	0.777783i
$590$		0			0
$591$	−11.0999	+	6.40851i	−0.456587	+	0.263611i
$592$	−2.42711	−	4.20388i	−0.0997537	−	0.172779i
$593$	−26.0909			−1.07142			−0.535712	−	0.844401i	$-0.679957\pi$
$593$	−26.0909			−1.07142			−0.535712	+	0.844401i	$0.679957\pi$
$594$	2.66205	+	4.61081i	0.109225	+	0.189184i
$595$		0			0
$596$	−13.8328	−	7.98638i	−0.566614	−	0.327135i
$597$		−	11.7656i		−	0.481536i
$598$	−2.56752	−	2.30362i	−0.104994	−	0.0942020i
$599$	−2.85624			−0.116703			−0.0583515	−	0.998296i	$-0.518584\pi$
$599$	−2.85624			−0.116703			−0.0583515	+	0.998296i	$0.518584\pi$
$600$		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	$-0.0970450\pi$
$602$	2.88842	−	1.66763i	0.117723	−	0.0679675i
$603$	−1.55762			−0.0634314
$604$	8.72819	−	5.03922i	0.355145	−	0.205043i
$605$		0			0
$606$			13.8454i			0.562430i
$607$	19.2125	−	11.0924i	0.779813	−	0.450225i	−0.0565511	−	0.998400i	$-0.518010\pi$
$607$	19.2125	−	11.0924i	0.779813	−	0.450225i	0.836364	+	0.548175i	$0.184677\pi$
$608$	2.70388	+	1.56109i	0.109657	+	0.0633104i
$609$	−7.44469	−	4.29819i	−0.301674	−	0.174172i
$610$		0			0
$611$	2.92802	+	8.95772i	0.118455	+	0.362391i
$612$			4.36740i			0.176541i
$613$	10.3564	−	17.9378i	0.418291	−	0.724501i	−0.577477	−	0.816407i	$-0.695963\pi$
$613$	10.3564	−	17.9378i	0.418291	−	0.724501i	0.995768	+	0.0919062i	$0.0292960\pi$
$614$	6.25565	−	10.8351i	0.252457	−	0.437269i
$615$		0			0
$616$			14.3152i			0.576778i
$617$	5.27937	+	9.14413i	0.212539	+	0.368129i	0.952509	−	0.304512i	$-0.0984933\pi$
$617$	5.27937	+	9.14413i	0.212539	+	0.368129i	−0.739969	+	0.672641i	$0.765160\pi$
$618$	9.07998	+	15.7270i	0.365250	+	0.632632i
$619$			22.1430i			0.890002i	0.895530	+	0.445001i	$0.146797\pi$
$619$			22.1430i			0.890002i	−0.895530	+	0.445001i	$0.853203\pi$
$620$		0			0
$621$	0.478355	−	0.828535i	0.0191957	−	0.0332480i
$622$	12.2363	−	21.1939i	0.490631	−	0.849798i
$623$			0.755044i			0.0302502i
$624$	2.68370	+	2.40786i	0.107434	+	0.0963914i
$625$		0			0
$626$	25.0072	+	14.4379i	0.999487	+	0.577054i
$627$	14.3958	+	8.31139i	0.574911	+	0.331925i
$628$	−17.6457	+	10.1877i	−0.704140	+	0.406535i
$629$		−	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	$0.276128\pi$
$632$	−17.1863			−0.683634
$633$	−0.0965530	+	0.0557449i	−0.00383764	+	0.00221566i
$634$	6.40693	−	11.0971i	0.254452	−	0.440723i
$635$		0			0
$636$	−6.98118			−0.276822
$637$	−0.809463	−	0.170565i	−0.0320721	−	0.00675804i
$638$			17.0220i			0.673907i
$639$	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	$-0.481047\pi$
$642$	20.4571			0.807379
$643$	−16.9040	−	29.2786i	−0.666628	−	1.15463i	−0.978841	−	0.204622i	$-0.934404\pi$
$643$	−16.9040	−	29.2786i	−0.666628	−	1.15463i	0.312213	−	0.950012i	$-0.398930\pi$
$644$	2.22773	−	1.28618i	0.0877850	−	0.0506827i
$645$		0			0
$646$	6.81788	+	11.8089i	0.268246	+	0.464616i
$647$	−16.4995	−	9.52598i	−0.648661	−	0.374505i	0.139282	−	0.990253i	$-0.455521\pi$
$647$	−16.4995	−	9.52598i	−0.648661	−	0.374505i	−0.787943	+	0.615748i	$0.788854\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−30.9380			−1.21442
$650$		0			0
$651$	−18.7707			−0.735682
$652$	−2.85959	+	4.95296i	−0.111990	+	0.193973i
$653$	−18.1045	−	10.4526i	−0.708484	−	0.409043i	0.102016	−	0.994783i	$-0.467471\pi$
$653$	−18.1045	−	10.4526i	−0.708484	−	0.409043i	−0.810499	+	0.585739i	$0.800804\pi$
$654$	−3.24717	−	5.62427i	−0.126974	−	0.219926i
$655$		0			0
$656$	−3.78228	+	2.18370i	−0.147673	+	0.0852591i
$657$	−0.284663	−	0.493050i	−0.0111058	−	0.0192357i
$658$	−7.02783			−0.273973
$659$	−1.99703	−	3.45896i	−0.0777932	−	0.134742i	0.824504	−	0.565856i	$-0.191454\pi$
$659$	−1.99703	−	3.45896i	−0.0777932	−	0.134742i	−0.902298	+	0.431114i	$0.858121\pi$
$660$		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	$0.743524\pi$
$662$		−	34.7116i		−	1.34911i
$663$	4.89245	+	14.9676i	0.190007	+	0.581292i
$664$	−13.3082			−0.516458
$665$		0			0
$666$	2.42711	−	4.20388i	0.0940487	−	0.162897i
$667$	2.64896	−	1.52938i	0.102568	−	0.0592176i
$668$	−0.956710			−0.0370162
$669$	7.46575	−	4.31035i	0.288643	−	0.166648i
$670$		0			0
$671$		−	15.1962i		−	0.586643i
$672$	−2.32854	+	1.34438i	−0.0898252	+	0.0518606i
$673$	7.12626	+	4.11435i	0.274697	+	0.158596i	0.631020	−	0.775766i	$-0.282636\pi$
$673$	7.12626	+	4.11435i	0.274697	+	0.158596i	−0.356323	+	0.934363i	$0.615970\pi$
$674$	23.6378	+	13.6473i	0.910493	+	0.525673i
$675$		0			0
$676$	11.8947	+	5.24565i	0.457487	+	0.201756i
$677$		−	30.7000i		−	1.17990i	−0.807440	−	0.589949i	$-0.799148\pi$
$677$		−	30.7000i		−	1.17990i	0.807440	−	0.589949i	$-0.200852\pi$
$678$		0			0
$679$	16.1655	−	27.9994i	0.620373	−	1.07452i
$680$		0			0
$681$			20.6382i			0.790859i
$682$	18.5843	+	32.1889i	0.711628	+	1.23258i
$683$	−8.91696	−	15.4446i	−0.341198	−	0.590972i	0.643457	−	0.765482i	$-0.277499\pi$
$683$	−8.91696	−	15.4446i	−0.341198	−	0.590972i	−0.984655	+	0.174510i	$0.944166\pi$
$684$			3.12217i			0.119379i
$685$		0			0
$686$	−9.10222	+	15.7655i	−0.347524	+	0.601930i
$687$	1.56464	−	2.71004i	0.0596948	−	0.103394i
$688$		−	1.24045i		−	0.0472915i
$689$	−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	$0.350293\pi$
$692$	0.711327	+	0.410685i	0.0270406	+	0.0156119i
$693$	−12.3974	+	7.15762i	−0.470937	+	0.271896i
$694$			26.3646i			1.00079i
$695$		0			0
$696$	−2.76882	+	1.59858i	−0.104952	+	0.0605939i
$697$	−19.0741			−0.722485
$698$	−24.7225	+	14.2735i	−0.935759	+	0.540261i
$699$	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	$0.412345\pi$
$702$	−0.743415	+	3.52808i	−0.0280584	+	0.133159i
$703$		−	15.1557i		−	0.571610i
$704$	4.61081	+	2.66205i	0.173776	+	0.100330i
$705$		0			0
$706$	9.12551	+	15.8058i	0.343443	+	0.594861i
$707$	−37.2269			−1.40006
$708$	−2.90547	−	5.03242i	−0.109194	−	0.189130i
$709$	19.0873	−	11.0200i	0.716838	−	0.413866i	−0.0967499	−	0.995309i	$-0.530845\pi$
$709$	19.0873	−	11.0200i	0.716838	−	0.413866i	0.813588	+	0.581442i	$0.197511\pi$
$710$		0			0
$711$	−8.59314	−	14.8838i	−0.322268	−	0.558185i
$712$	0.243193	+	0.140408i	0.00911404	+	0.00526199i
$713$	3.33948	−	5.78415i	0.125065	−	0.216618i
$714$	−11.7429			−0.439466
$715$		0			0
$716$	0.181106			0.00676823
$717$	9.23630	−	15.9977i	0.344936	−	0.597447i
$718$	−13.0115	−	7.51217i	−0.485583	−	0.280352i
$719$	21.9534	+	38.0245i	0.818725	+	1.41807i	0.906622	+	0.421944i	$0.138652\pi$
$719$	21.9534	+	38.0245i	0.818725	+	1.41807i	−0.0878962	+	0.996130i	$0.528014\pi$
$720$		0			0
$721$	−42.2861	+	24.4139i	−1.57482	+	0.909220i
$722$	−4.62601	−	8.01249i	−0.172162	−	0.298194i
$723$	−2.30832			−0.0858473
$724$	−2.64041	−	4.57332i	−0.0981300	−	0.169966i
$725$		0			0
$726$	15.0222	+	8.67305i	0.557525	+	0.321887i
$727$		−	2.66659i		−	0.0988984i	−0.998777	−	0.0494492i	$-0.984253\pi$
$727$		−	2.66659i		−	0.0988984i	0.998777	−	0.0494492i	$-0.0157466\pi$
$728$	−6.47415	+	7.21582i	−0.239948	+	0.267436i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	2.70876	−	4.69170i	0.100187	−	0.173529i
$732$	2.47183	−	1.42711i	0.0913615	−	0.0527476i
$733$	21.1035			0.779476			0.389738	−	0.920926i	$-0.372566\pi$
$733$	21.1035			0.779476			0.389738	+	0.920926i	$0.372566\pi$
$734$	4.11131	−	2.37367i	0.151751	−	0.0876136i
$735$		0			0
$736$		−	0.956710i		−	0.0352648i
$737$	−7.18191	+	4.14648i	−0.264549	+	0.152737i
$738$	−3.78228	−	2.18370i	−0.139227	−	0.0803830i
$739$	−21.4664	−	12.3936i	−0.789653	−	0.455906i	0.0501875	−	0.998740i	$-0.484018\pi$
$739$	−21.4664	−	12.3936i	−0.789653	−	0.455906i	−0.839840	+	0.542834i	$0.817351\pi$
$740$		0			0
$741$	3.49753	+	10.7000i	0.128485	+	0.393076i
$742$		−	18.7707i		−	0.689094i
$743$	13.0404	−	22.5866i	0.478405	−	0.828621i	−0.521289	−	0.853380i	$-0.674549\pi$
$743$	13.0404	−	22.5866i	0.478405	−	0.828621i	0.999693	+	0.0247590i	$0.00788185\pi$
$744$	−3.49059	+	6.04588i	−0.127971	+	0.221653i
$745$		0			0
$746$			1.05966i			0.0387971i
$747$	−6.65410	−	11.5252i	−0.243461	−	0.421686i
$748$	11.6262	+	20.1372i	0.425097	+	0.736290i
$749$			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	$0.0710254\pi$
$752$	−1.30689	+	2.26360i	−0.0476574	+	0.0825450i
$753$		−	21.3600i		−	0.778403i
$754$	−7.69829	+	8.58020i	−0.280355	+	0.312472i
$755$		0			0
$756$	−2.32854	−	1.34438i	−0.0846880	−	0.0488946i
$757$	38.9998	+	22.5166i	1.41747	+	0.818379i	0.996076	−	0.0884976i	$-0.0282066\pi$
$757$	38.9998	+	22.5166i	1.41747	+	0.818379i	0.421397	+	0.906876i	$0.361540\pi$
$758$	−23.6727	+	13.6675i	−0.859833	+	0.496425i
$759$		−	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	$0.496704\pi$
$762$	−21.5702			−0.781406
$763$	15.1223	−	8.73087i	0.547464	−	0.316079i
$764$	10.8540	−	18.7997i	0.392684	−	0.680149i
$765$		0			0
$766$	11.8782			0.429178
$767$	−15.5948	−	13.9919i	−0.563095	−	0.505218i
$768$			1.00000i			0.0360844i
$769$	−24.9201	−	14.3876i	−0.898643	−	0.518832i	−0.0218832	−	0.999761i	$-0.506966\pi$
$769$	−24.9201	−	14.3876i	−0.898643	−	0.518832i	−0.876760	+	0.480929i	$0.840300\pi$
$770$		0			0
$771$	−5.46451	−	9.46481i	−0.196800	−	0.340867i
$772$	14.0769			0.506638
$773$	23.3885	+	40.5101i	0.841226	+	1.45705i	0.888858	+	0.458182i	$0.151499\pi$
$773$	23.3885	+	40.5101i	0.841226	+	1.45705i	−0.0476321	+	0.998865i	$0.515168\pi$
$774$	1.07426	−	0.620223i	0.0386134	−	0.0222934i
$775$		0			0
$776$	−6.01223	−	10.4135i	−0.215827	−	0.373823i
$777$	11.3032	+	6.52593i	0.405501	+	0.234116i
$778$	1.59858	−	2.76882i	0.0573118	−	0.0992669i
$779$	−13.6358			−0.488552
$780$		0			0
$781$	54.6831			1.95671
$782$	2.08917	−	3.61854i	0.0747084	−	0.129399i
$783$	−2.76882	−	1.59858i	−0.0989495	−	0.0571285i
$784$	−0.114717	−	0.198696i	−0.00409705	−	0.00709629i
$785$		0			0
$786$	2.66402	−	1.53807i	0.0950224	−	0.0548612i
$787$	−12.3700	−	21.4254i	−0.440942	−	0.763735i	0.556817	−	0.830635i	$-0.312022\pi$
$787$	−12.3700	−	21.4254i	−0.440942	−	0.763735i	−0.997760	+	0.0669004i	$0.978689\pi$
$788$	−12.8170			−0.456587
$789$	−6.74488	−	11.6825i	−0.240124	−	0.415907i
$790$		0			0
$791$		0			0
$792$			5.32411i			0.189184i
$793$	6.87256	−	7.65988i	0.244052	−	0.272010i
$794$	−12.3103			−0.436878
$795$		0			0
$796$	5.88282	−	10.1893i	0.208511	−	0.361152i
$797$	−41.9631	+	24.2274i	−1.48641	+	0.858179i	−0.999880	−	0.0154857i	$-0.995071\pi$
$797$	−41.9631	+	24.2274i	−1.48641	+	0.858179i	−0.486529	+	0.873664i	$0.661737\pi$
$798$	−8.39478			−0.297172
$799$	−9.88604	+	5.70771i	−0.349743	+	0.201924i
$800$		0			0
$801$			0.280815i			0.00992211i
$802$	7.00145	−	4.04229i	0.247230	−	0.142738i
$803$	−2.62505	−	1.51557i	−0.0926361	−	0.0534835i
$804$	−1.34894	−	0.778812i	−0.0475735	−	0.0274666i
$805$		0			0
$806$	−5.18991	+	24.6301i	−0.182807	+	0.867559i
$807$			8.50029i			0.299224i
$808$	−6.92268	+	11.9904i	−0.243539	+	0.421822i
$809$	−2.41226	+	4.17816i	−0.0848106	+	0.146896i	−0.905310	−	0.424750i	$-0.860362\pi$
$809$	−2.41226	+	4.17816i	−0.0848106	+	0.146896i	0.820500	+	0.571647i	$0.193695\pi$
$810$		0			0
$811$		−	45.0952i		−	1.58351i	−0.610841	−	0.791754i	$-0.709168\pi$
$811$		−	45.0952i		−	1.58351i	0.610841	−	0.791754i	$-0.290832\pi$
$812$	−4.29819	−	7.44469i	−0.150837	−	0.261257i
$813$	11.1872	+	19.3767i	0.392351	+	0.679572i
$814$		−	25.8444i		−	0.905846i
$815$		0			0
$816$	−2.18370	+	3.78228i	−0.0764447	+	0.132406i
$817$	1.93644	−	3.35402i	0.0677476	−	0.117342i
$818$			32.8515i			1.14862i
$819$	−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	$0.521530\pi$
$822$	16.9650	+	9.79473i	0.591721	+	0.341630i
$823$	17.2675	−	9.96940i	0.601907	−	0.347511i	−0.167884	−	0.985807i	$-0.553693\pi$
$823$	17.2675	−	9.96940i	0.601907	−	0.347511i	0.769792	+	0.638295i	$0.220360\pi$
$824$			18.1600i			0.632632i
$825$		0			0
$826$	13.5310	−	7.81211i	0.470803	−	0.271818i
$827$	−18.2598			−0.634957			−0.317478	−	0.948265i	$-0.602836\pi$
$827$	−18.2598			−0.634957			−0.317478	+	0.948265i	$0.602836\pi$
$828$	0.828535	−	0.478355i	0.0287936	−	0.0166240i
$829$	−8.50136	+	14.7248i	−0.295264	+	0.511413i	−0.975046	−	0.222001i	$-0.928741\pi$
$829$	−8.50136	+	14.7248i	−0.295264	+	0.511413i	0.679782	+	0.733414i	$0.262074\pi$
$830$		0			0
$831$	−28.8564			−1.00102
$832$	1.12022	+	3.42711i	0.0388367	+	0.118814i
$833$		−	1.00203i		−	0.0347183i
$834$	13.4681	+	7.77583i	0.466363	+	0.269255i
$835$		0			0
$836$	8.31139	+	14.3958i	0.287456	+	0.497888i
$837$	−6.98118			−0.241305
$838$	3.79887	+	6.57984i	0.131230	+	0.227297i
$839$	−45.9435	+	26.5255i	−1.58615	+	0.915762i	−0.592213	+	0.805781i	$0.701746\pi$
$839$	−45.9435	+	26.5255i	−1.58615	+	0.915762i	−0.993934	+	0.109981i	$0.964921\pi$
$840$		0			0
$841$	9.38910	+	16.2624i	0.323762	+	0.560772i
$842$	−20.6536	−	11.9243i	−0.711769	−	0.410940i
$843$	−12.7040	+	22.0039i	−0.437547	+	0.757854i
$844$	−0.111490			−0.00383764
$845$		0			0
$846$	−2.61378			−0.0898636
$847$	−23.3197	+	40.3910i	−0.801276	+	1.38785i
$848$	−6.04588	−	3.49059i	−0.207616	−	0.119867i
$849$	5.73899	+	9.94021i	0.196961	+	0.341147i
$850$		0			0
$851$	−4.02190	+	2.32204i	−0.137869	+	0.0795986i
$852$	5.13543	+	8.89482i	0.175937	+	0.304731i
$853$	38.5399			1.31958			0.659791	−	0.751450i	$-0.270645\pi$
$853$	38.5399			1.31958			0.659791	+	0.751450i	$0.270645\pi$
$854$	3.83716	+	6.64616i	0.131305	+	0.227427i
$855$		0			0
$856$	17.7164	+	10.2286i	0.605534	+	0.349605i
$857$			38.8969i			1.32869i	0.747425	+	0.664346i	$0.231290\pi$
$857$			38.8969i			1.32869i	−0.747425	+	0.664346i	$0.768710\pi$
$858$	5.96418	+	18.2463i	0.203614	+	0.622919i
$859$	6.04530			0.206263			0.103131	−	0.994668i	$-0.467114\pi$
$859$	6.04530			0.206263			0.103131	+	0.994668i	$0.467114\pi$
$860$		0			0
$861$	5.87144	−	10.1696i	0.200098	−	0.346580i
$862$	−32.8790	+	18.9827i	−1.11986	+	0.646554i
$863$	17.7572			0.604462			0.302231	−	0.953235i	$-0.402269\pi$
$863$	17.7572			0.604462			0.302231	+	0.953235i	$0.402269\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$		0			0
$866$		−	3.76473i		−	0.127931i
$867$	−1.79626	+	1.03707i	−0.0610041	+	0.0352207i
$868$	−16.2559	−	9.38536i	−0.551762	−	0.318560i
$869$	−79.2427	−	45.7508i	−2.68813	−	1.55199i
$870$		0			0
$871$	−5.49542	−	1.15796i	−0.186205	−	0.0392360i
$872$		−	6.49435i		−	0.219926i
$873$	6.01223	−	10.4135i	0.203483	−	0.352443i
$874$	1.49351	−	2.58683i	0.0505187	−	0.0875009i
$875$		0			0
$876$		−	0.569326i		−	0.0192357i
$877$	7.14773	+	12.3802i	0.241362	+	0.418051i	0.961102	−	0.276192i	$-0.0890726\pi$
$877$	7.14773	+	12.3802i	0.241362	+	0.418051i	−0.719741	+	0.694243i	$0.755739\pi$
$878$	−5.63368	−	9.75782i	−0.190127	−	0.329310i
$879$		−	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	$-0.103616\pi$
$882$	0.114717	−	0.198696i	0.00386273	−	0.00669045i
$883$			25.0584i			0.843284i	0.906762	+	0.421642i	$0.138546\pi$
$883$			25.0584i			0.843284i	−0.906762	+	0.421642i	$0.861454\pi$
$884$	−3.24679	+	15.4085i	−0.109201	+	0.518244i
$885$		0			0
$886$	−11.7900	−	6.80696i	−0.396093	−	0.228684i
$887$	19.4061	+	11.2041i	0.651593	+	0.376197i	0.789066	−	0.614308i	$-0.210565\pi$
$887$	19.4061	+	11.2041i	0.651593	+	0.376197i	−0.137473	+	0.990505i	$0.543898\pi$
$888$	4.20388	−	2.42711i	0.141073	−	0.0814486i
$889$		−	57.9971i		−	1.94516i
$890$		0			0
$891$	−4.61081	+	2.66205i	−0.154468	+	0.0891821i
$892$	8.62071			0.288643
$893$	−7.06735	+	4.08034i	−0.236500	+	0.136543i
$894$	7.98638	−	13.8328i	0.267104	−	0.462639i
$895$		0			0
$896$	−2.68876			−0.0898252
$897$	2.30362	−	2.56752i	0.0769156	−	0.0857270i
$898$			30.2467i			1.00934i
$899$	−19.3296	−	11.1600i	−0.644678	−	0.372205i
$900$		0			0
$901$	−15.2448	−	26.4047i	−0.507877	−	0.879669i
$902$	−23.2525			−0.774223
$903$	1.66763	+	2.88842i	0.0554953	+	0.0961206i
$904$		0			0
$905$		0			0
$906$	5.03922	+	8.72819i	0.167417	+	0.289975i
$907$	25.6982	+	14.8368i	0.853294	+	0.492649i	0.861761	−	0.507315i	$-0.169362\pi$
$907$	25.6982	+	14.8368i	0.853294	+	0.492649i	−0.00846710	+	0.999964i	$0.502695\pi$
$908$	−10.3191	+	17.8732i	−0.342452	+	0.593144i
$909$	−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	$0.824238\pi$
$912$	−1.56109	+	2.70388i	−0.0516928	+	0.0895345i
$913$	−61.3616	−	35.4271i	−2.03077	−	1.17247i
$914$	−18.1752	−	31.4804i	−0.601183	−	1.04128i
$915$		0			0
$916$	2.71004	−	1.56464i	0.0895421	−	0.0516972i
$917$	4.13551	+	7.16291i	0.136567	+	0.236540i
$918$	−4.36740			−0.144146
$919$	−26.6932	−	46.2339i	−0.880526	−	1.52512i	−0.850757	−	0.525559i	$-0.823856\pi$
$919$	−26.6932	−	46.2339i	−0.880526	−	1.52512i	−0.0297687	−	0.999557i	$-0.509477\pi$
$920$		0			0
$921$	10.8351	+	6.25565i	0.357029	+	0.206131i
$922$			23.1884i			0.763671i
$923$	27.5639	+	24.7307i	0.907275	+	0.814022i
$924$	−14.3152			−0.470937
$925$		0			0
$926$	−3.20078	+	5.54391i	−0.105184	+	0.182184i
$927$	−15.7270	+	9.07998i	−0.516542	+	0.298226i
$928$	−3.19716			−0.104952
$929$	−10.5234	+	6.07570i	−0.345262	+	0.199337i	−0.662597	−	0.748976i	$-0.730546\pi$
$929$	−10.5234	+	6.07570i	−0.345262	+	0.199337i	0.317334	+	0.948314i	$0.397212\pi$
$930$		0			0
$931$		−	0.716335i		−	0.0234769i
$932$	8.06628	−	4.65707i	0.264220	−	0.152547i
$933$	21.1939	+	12.2363i	0.693857	+	0.400598i
$934$	17.9449	+	10.3605i	0.587176	+	0.339006i
$935$		0			0
$936$	−2.40786	+	2.68370i	−0.0787032	+	0.0877194i
$937$		−	10.4882i		−	0.342634i	−0.985216	−	0.171317i	$-0.945198\pi$
$937$		−	10.4882i		−	0.342634i	0.985216	−	0.171317i	$-0.0548023\pi$
$938$	2.09404	−	3.62698i	0.0683728	−	0.118425i
$939$	−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	$0.946628\pi$
$942$	−10.1877	−	17.6457i	−0.331935	−	0.574928i
$943$	2.08917	+	3.61854i	0.0680326	+	0.117836i
$944$		−	5.81094i		−	0.189130i
$945$		0			0
$946$	3.30213	−	5.71946i	0.107362	−	0.185956i
$947$	−7.49645	+	12.9842i	−0.243602	+	0.421931i	−0.961738	−	0.273972i	$-0.911662\pi$
$947$	−7.49645	+	12.9842i	−0.243602	+	0.421931i	0.718136	+	0.695903i	$0.244996\pi$
$948$		−	17.1863i		−	0.558185i
$949$	−0.637771	−	1.95114i	−0.0207029	−	0.0633368i
$950$		0			0
$951$	11.0971	+	6.40693i	0.359849	+	0.207759i
$952$	−10.1696	−	5.87144i	−0.329600	−	0.190294i
$953$	39.4097	−	22.7532i	1.27660	−	0.737048i	0.300382	−	0.953819i	$-0.402886\pi$
$953$	39.4097	−	22.7532i	1.27660	−	0.737048i	0.976222	+	0.216771i	$0.0695525\pi$
$954$		−	6.98118i		−	0.226024i
$955$		0			0
$956$	15.9977	−	9.23630i	0.517404	−	0.298723i
$957$	−17.0220			−0.550243
$958$	24.9299	−	14.3933i	0.805450	−	0.465027i
$959$	−26.3357	+	45.6147i	−0.850424	+	1.47298i
$960$		0			0
$961$	−17.7368			−0.572155
$962$	11.6883	−	13.0273i	0.376845	−	0.420016i
$963$			20.4571i			0.659222i
$964$	−1.99906	−	1.15416i	−0.0643855	−	0.0371730i
$965$		0			0
$966$	1.28618	+	2.22773i	0.0413822	+	0.0716761i
$967$	−11.4832			−0.369275			−0.184637	−	0.982807i	$-0.559111\pi$
$967$	−11.4832			−0.369275			−0.184637	+	0.982807i	$0.559111\pi$
$968$	8.67305	+	15.0222i	0.278762	+	0.482830i
$969$	−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	$0.564929\pi$
$972$	−0.866025	−	0.500000i	−0.0277778	−	0.0160375i
$973$	−20.9074	+	36.2126i	−0.670259	+	1.16092i
$974$	12.5903			0.403419
$975$		0			0
$976$	2.85423			0.0913615
$977$	−14.3077	+	24.7817i	−0.457745	+	0.792837i	−0.998841	−	0.0481231i	$-0.984676\pi$
$977$	−14.3077	+	24.7817i	−0.457745	+	0.792837i	0.541097	+	0.840960i	$0.318009\pi$
$978$	−4.95296	−	2.85959i	−0.158378	−	0.0914397i
$979$	0.747544	+	1.29478i	0.0238916	+	0.0413815i
$980$		0			0
$981$	5.62427	−	3.24717i	0.179569	−	0.103674i
$982$	10.6278	+	18.4078i	0.339145	+	0.587417i
$983$	−32.6951			−1.04281			−0.521406	−	0.853308i	$-0.674592\pi$
$983$	−32.6951			−1.04281			−0.521406	+	0.853308i	$0.674592\pi$
$984$	−2.18370	−	3.78228i	−0.0696137	−	0.120575i
$985$		0			0
$986$	−12.0925	−	6.98162i	−0.385104	−	0.222340i
$987$		−	7.02783i		−	0.223698i
$988$	−2.32107	+	11.0153i	−0.0738431	+	0.350443i
$989$	−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	$-0.0832987\pi$
$992$	−6.04588	+	3.49059i	−0.191957	+	0.110826i
$993$	34.7116			1.10154
$994$	−23.9160	+	13.8079i	−0.758571	+	0.437961i
$995$		0			0
$996$		−	13.3082i		−	0.421686i
$997$	44.2732	−	25.5611i	1.40215	−	0.809530i	0.407534	−	0.913190i	$-0.366389\pi$
$997$	44.2732	−	25.5611i	1.40215	−	0.809530i	0.994613	+	0.103661i	$0.0330556\pi$
$998$	−11.2789	−	6.51186i	−0.357026	−	0.206129i
$999$	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.y.m.199.2		12
5.2	odd	4		1950.2.bc.h.901.2	yes	12
5.3	odd	4		1950.2.bc.k.901.5	yes	12
5.4	even	2		1950.2.y.n.199.5		12
13.10	even	6		1950.2.y.n.49.5		12
65.23	odd	12		1950.2.bc.k.751.5	yes	12
65.49	even	6	inner	1950.2.y.m.49.2		12
65.62	odd	12		1950.2.bc.h.751.2	✓	12

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

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.y (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(1.34438 + 2.32854i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(1.34438 + 2.32854i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(4.61081 + 2.66205i) q^{11} +1.00000i q^{12} +(1.12022 + 3.42711i) q^{13} -2.68876 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.78228 + 2.18370i) q^{17} -1.00000 q^{18} +(-2.70388 + 1.56109i) q^{19} -2.68876i q^{21} +(-4.61081 + 2.66205i) q^{22} +(0.828535 + 0.478355i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-3.52808 - 0.743415i) q^{26} -1.00000i q^{27} +(1.34438 - 2.32854i) q^{28} +(1.59858 - 2.76882i) q^{29} -6.98118i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.66205 - 4.61081i) q^{33} -4.36740i q^{34} +(0.500000 - 0.866025i) q^{36} +(-2.42711 + 4.20388i) q^{37} -3.12217i q^{38} +(0.743415 - 3.52808i) q^{39} +(3.78228 + 2.18370i) q^{41} +(2.32854 + 1.34438i) q^{42} +(-1.07426 + 0.620223i) q^{43} -5.32411i q^{44} +(-0.828535 + 0.478355i) q^{46} +2.61378 q^{47} +(0.866025 - 0.500000i) q^{48} +(-0.114717 + 0.198696i) q^{49} +4.36740 q^{51} +(2.40786 - 2.68370i) q^{52} +6.98118i q^{53} +(0.866025 + 0.500000i) q^{54} +(1.34438 + 2.32854i) q^{56} +3.12217 q^{57} +(1.59858 + 2.76882i) q^{58} +(-5.03242 + 2.90547i) q^{59} +(-1.42711 - 2.47183i) q^{61} +(6.04588 + 3.49059i) q^{62} +(-1.34438 + 2.32854i) q^{63} +1.00000 q^{64} +5.32411 q^{66} +(-0.778812 + 1.34894i) q^{67} +(3.78228 + 2.18370i) q^{68} +(-0.478355 - 0.828535i) q^{69} +(8.89482 - 5.13543i) q^{71} +(0.500000 + 0.866025i) q^{72} -0.569326 q^{73} +(-2.42711 - 4.20388i) q^{74} +(2.70388 + 1.56109i) q^{76} +14.3152i q^{77} +(2.68370 + 2.40786i) q^{78} -17.1863 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-3.78228 + 2.18370i) q^{82} -13.3082 q^{83} +(-2.32854 + 1.34438i) q^{84} -1.24045i q^{86} +(-2.76882 + 1.59858i) q^{87} +(4.61081 + 2.66205i) q^{88} +(0.243193 + 0.140408i) q^{89} +(-6.47415 + 7.21582i) q^{91} -0.956710i q^{92} +(-3.49059 + 6.04588i) q^{93} +(-1.30689 + 2.26360i) q^{94} +1.00000i q^{96} +(-6.01223 - 10.4135i) q^{97} +(-0.114717 - 0.198696i) q^{98} +5.32411i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{4} + 4 q^{7} + 12 q^{8} + 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 - 6 * q^4 + 4 * q^7 + 12 * q^8 + 6 * q^9	\( 12 q - 6 q^{2} - 6 q^{4} + 4 q^{7} + 12 q^{8} + 6 q^{9} - 12 q^{11} - 4 q^{13} - 8 q^{14} - 6 q^{16} - 12 q^{18} + 6 q^{19} + 12 q^{22} - 12 q^{23} - 4 q^{26} + 4 q^{28} - 6 q^{32} - 4 q^{33} + 6 q^{36} + 12 q^{37} - 6 q^{39} + 6 q^{42} - 12 q^{43} + 12 q^{46} - 16 q^{47} - 32 q^{49} + 8 q^{52} + 4 q^{56} - 24 q^{57} + 24 q^{61} - 4 q^{63} + 12 q^{64} + 8 q^{66} - 24 q^{67} - 4 q^{69} + 12 q^{71} + 6 q^{72} + 40 q^{73} + 12 q^{74} - 6 q^{76} + 6 q^{78} - 52 q^{79} - 6 q^{81} - 32 q^{83} - 6 q^{84} - 12 q^{88} - 24 q^{89} - 54 q^{91} + 8 q^{93} + 8 q^{94} - 24 q^{97} - 32 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^4 + 4 * q^7 + 12 * q^8 + 6 * q^9 - 12 * q^11 - 4 * q^13 - 8 * q^14 - 6 * q^16 - 12 * q^18 + 6 * q^19 + 12 * q^22 - 12 * q^23 - 4 * q^26 + 4 * q^28 - 6 * q^32 - 4 * q^33 + 6 * q^36 + 12 * q^37 - 6 * q^39 + 6 * q^42 - 12 * q^43 + 12 * q^46 - 16 * q^47 - 32 * q^49 + 8 * q^52 + 4 * q^56 - 24 * q^57 + 24 * q^61 - 4 * q^63 + 12 * q^64 + 8 * q^66 - 24 * q^67 - 4 * q^69 + 12 * q^71 + 6 * q^72 + 40 * q^73 + 12 * q^74 - 6 * q^76 + 6 * q^78 - 52 * q^79 - 6 * q^81 - 32 * q^83 - 6 * q^84 - 12 * q^88 - 24 * q^89 - 54 * q^91 + 8 * q^93 + 8 * q^94 - 24 * q^97 - 32 * q^98

Introduction

L-functions

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