LMFDB - Embedded newform 675.2.r.a.46.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(46,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.46"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([20, 18])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			46.8
Character	$\chi$	$=$	675.46
Dual form			675.2.r.a.631.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.955162 - 1.06081i) q^{2} +(-0.00393676 + 0.0374558i) q^{4} +(-0.397449 + 2.20046i) q^{5} +(1.20474 - 2.08666i) q^{7} +(-2.26620 + 1.64649i) q^{8} +(2.71391 - 1.68018i) q^{10} +(0.0211445 + 0.0234833i) q^{11} +(-4.22250 + 4.68956i) q^{13} +(-3.36428 + 0.715100i) q^{14} +(3.98488 + 0.847013i) q^{16} +(-2.72065 + 1.97667i) q^{17} +(1.81267 - 1.31698i) q^{19} +(-0.0808554 - 0.0235495i) q^{20} +(0.00471506 - 0.0448608i) q^{22} +(1.88117 - 0.399856i) q^{23} +(-4.68407 - 1.74914i) q^{25} +9.00793 q^{26} +(0.0734149 + 0.0533391i) q^{28} +(-8.54224 + 3.80325i) q^{29} +(-3.43471 - 1.52923i) q^{31} +(-0.106511 - 0.184482i) q^{32} +(4.69554 + 0.998067i) q^{34} +(4.11281 + 3.48032i) q^{35} +(3.22975 + 9.94014i) q^{37} +(-3.12847 - 0.664976i) q^{38} +(-2.72234 - 5.64107i) q^{40} +(-1.08631 + 1.20647i) q^{41} +(-5.58816 + 9.67898i) q^{43} +(-0.000962828 + 0.000699535i) q^{44} +(-2.22100 - 1.61365i) q^{46} +(2.88640 - 1.28511i) q^{47} +(0.597221 + 1.03442i) q^{49} +(2.61853 + 6.63964i) q^{50} +(-0.159028 - 0.176619i) q^{52} +(-1.23376 - 0.896379i) q^{53} +(-0.0600780 + 0.0371942i) q^{55} +(0.705499 + 6.71237i) q^{56} +(12.1938 + 5.42901i) q^{58} +(8.58158 - 9.53081i) q^{59} +(7.10677 + 7.89287i) q^{61} +(1.65848 + 5.10426i) q^{62} +(2.42385 - 7.45983i) q^{64} +(-8.64097 - 11.1553i) q^{65} +(-2.07993 - 0.926044i) q^{67} +(-0.0633271 - 0.109686i) q^{68} +(-0.236421 - 7.68719i) q^{70} +(3.63556 + 2.64139i) q^{71} +(0.380414 - 1.17080i) q^{73} +(7.45971 - 12.9206i) q^{74} +(0.0421926 + 0.0730797i) q^{76} +(0.0744753 - 0.0158302i) q^{77} +(0.840545 - 0.374235i) q^{79} +(-3.44761 + 8.43194i) q^{80} +2.31745 q^{82} +(0.581163 + 5.52940i) q^{83} +(-3.26826 - 6.77231i) q^{85} +(15.6052 - 3.31699i) q^{86} +(-0.0865826 - 0.0184037i) q^{88} +(0.932477 - 2.86987i) q^{89} +(4.69854 + 14.4606i) q^{91} +(0.00757118 + 0.0720350i) q^{92} +(-4.12024 - 1.83445i) q^{94} +(2.17753 + 4.51214i) q^{95} +(-9.49506 + 4.22747i) q^{97} +(0.526882 - 1.62158i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.955162	−	1.06081i	−0.675401	−	0.750109i	0.303859	−	0.952717i	$-0.401725\pi$
$2$	−0.955162	−	1.06081i	−0.675401	−	0.750109i	−0.979260	+	0.202608i	$0.935058\pi$
$3$		0			0
$3$		0			0
$4$	−0.00393676	+	0.0374558i	−0.00196838	+	0.0187279i
$5$	−0.397449	+	2.20046i	−0.177745	+	0.984077i
$5$	−0.397449	+	2.20046i	−0.177745	+	0.984077i
$6$		0			0
$7$	1.20474	−	2.08666i	0.455348	−	0.788685i	−0.543361	−	0.839499i	$-0.682848\pi$
$7$	1.20474	−	2.08666i	0.455348	−	0.788685i	0.998708	+	0.0508144i	$0.0161817\pi$
$8$	−2.26620	+	1.64649i	−0.801221	+	0.582121i
$9$		0			0
$10$	2.71391	−	1.68018i	0.858214	−	0.531319i
$11$	0.0211445	+	0.0234833i	0.00637530	+	0.00708049i	0.746324	−	0.665583i	$-0.231817\pi$
$11$	0.0211445	+	0.0234833i	0.00637530	+	0.00708049i	−0.739949	+	0.672663i	$0.765150\pi$
$12$		0			0
$13$	−4.22250	+	4.68956i	−1.17111	+	1.30065i	−0.225914	+	0.974147i	$0.572537\pi$
$13$	−4.22250	+	4.68956i	−1.17111	+	1.30065i	−0.945196	+	0.326503i	$0.894130\pi$
$14$	−3.36428	+	0.715100i	−0.899142	+	0.191119i
$15$		0			0
$16$	3.98488	+	0.847013i	0.996220	+	0.211753i
$17$	−2.72065	+	1.97667i	−0.659854	+	0.479412i	−0.866614	−	0.498980i	$-0.833708\pi$
$17$	−2.72065	+	1.97667i	−0.659854	+	0.479412i	0.206760	+	0.978392i	$0.433708\pi$
$18$		0			0
$19$	1.81267	−	1.31698i	0.415855	−	0.302136i	−0.360113	−	0.932909i	$-0.617262\pi$
$19$	1.81267	−	1.31698i	0.415855	−	0.302136i	0.775968	+	0.630772i	$0.217262\pi$
$20$	−0.0808554	−	0.0235495i	−0.0180798	−	0.00526582i
$21$		0			0
$22$	0.00471506	−	0.0448608i	0.00100525	−	0.00956434i
$23$	1.88117	−	0.399856i	0.392252	−	0.0833756i	−0.00756369	−	0.999971i	$-0.502408\pi$
$23$	1.88117	−	0.399856i	0.392252	−	0.0833756i	0.399815	+	0.916596i	$0.369074\pi$
$24$		0			0
$25$	−4.68407	−	1.74914i	−0.936814	−	0.349829i
$26$	9.00793			1.76660
$27$		0			0
$28$	0.0734149	+	0.0533391i	0.0138741	+	0.0100801i
$29$	−8.54224	+	3.80325i	−1.58625	+	0.706246i	−0.994966	−	0.100215i	$-0.968047\pi$
$29$	−8.54224	+	3.80325i	−1.58625	+	0.706246i	−0.591288	+	0.806460i	$0.701380\pi$
$30$		0			0
$31$	−3.43471	−	1.52923i	−0.616893	−	0.274658i	0.0744052	−	0.997228i	$-0.476294\pi$
$31$	−3.43471	−	1.52923i	−0.616893	−	0.274658i	−0.691298	+	0.722570i	$0.742961\pi$
$32$	−0.106511	−	0.184482i	−0.0188286	−	0.0326121i
$33$		0			0
$34$	4.69554	+	0.998067i	0.805278	+	0.171167i
$35$	4.11281	+	3.48032i	0.695191	+	0.588281i
$36$		0			0
$37$	3.22975	+	9.94014i	0.530967	+	1.63415i	0.752205	+	0.658929i	$0.228990\pi$
$37$	3.22975	+	9.94014i	0.530967	+	1.63415i	−0.221238	+	0.975220i	$0.571010\pi$
$38$	−3.12847	−	0.664976i	−0.507504	−	0.107873i
$39$		0			0
$40$	−2.72234	−	5.64107i	−0.430439	−	0.891932i
$41$	−1.08631	+	1.20647i	−0.169654	+	0.188420i	−0.821976	−	0.569522i	$-0.807128\pi$
$41$	−1.08631	+	1.20647i	−0.169654	+	0.188420i	0.652322	+	0.757942i	$0.273795\pi$
$42$		0			0
$43$	−5.58816	+	9.67898i	−0.852186	+	1.47603i	0.0270444	+	0.999634i	$0.491390\pi$
$43$	−5.58816	+	9.67898i	−0.852186	+	1.47603i	−0.879231	+	0.476396i	$0.841943\pi$
$44$	−0.000962828	0	0.000699535i	−0.000145152	0	0.000105459i
$45$		0			0
$46$	−2.22100	−	1.61365i	−0.327468	−	0.237919i
$47$	2.88640	−	1.28511i	0.421025	−	0.187452i	−0.185278	−	0.982686i	$-0.559319\pi$
$47$	2.88640	−	1.28511i	0.421025	−	0.187452i	0.606303	+	0.795234i	$0.292652\pi$
$48$		0			0
$49$	0.597221	+	1.03442i	0.0853173	+	0.147774i
$50$	2.61853	+	6.63964i	0.370316	+	0.938987i
$51$		0			0
$52$	−0.159028	−	0.176619i	−0.0220533	−	0.0244926i
$53$	−1.23376	−	0.896379i	−0.169470	−	0.123127i	0.499817	−	0.866131i	$-0.333400\pi$
$53$	−1.23376	−	0.896379i	−0.169470	−	0.123127i	−0.669287	+	0.743004i	$0.733400\pi$
$54$		0			0
$55$	−0.0600780	+	0.0371942i	−0.00810092	+	0.00501527i
$56$	0.705499	+	6.71237i	0.0942763	+	0.896979i
$57$		0			0
$58$	12.1938	+	5.42901i	1.60112	+	0.712864i
$59$	8.58158	−	9.53081i	1.11723	−	1.24081i	0.149511	−	0.988760i	$-0.452230\pi$
$59$	8.58158	−	9.53081i	1.11723	−	1.24081i	0.967715	−	0.252046i	$-0.0811034\pi$
$60$		0			0
$61$	7.10677	+	7.89287i	0.909929	+	1.01058i	0.999893	+	0.0146335i	$0.00465815\pi$
$61$	7.10677	+	7.89287i	0.909929	+	1.01058i	−0.0899640	+	0.995945i	$0.528675\pi$
$62$	1.65848	+	5.10426i	0.210627	+	0.648242i
$63$		0			0
$64$	2.42385	−	7.45983i	0.302981	−	0.932479i
$65$	−8.64097	−	11.1553i	−1.07178	−	1.38365i
$66$		0			0
$67$	−2.07993	−	0.926044i	−0.254104	−	0.113134i	0.275732	−	0.961235i	$-0.411080\pi$
$67$	−2.07993	−	0.926044i	−0.254104	−	0.113134i	−0.529836	+	0.848100i	$0.677746\pi$
$68$	−0.0633271	−	0.109686i	−0.00767954	−	0.0133014i
$69$		0			0
$70$	−0.236421	−	7.68719i	−0.0282577	−	0.918795i
$71$	3.63556	+	2.64139i	0.431462	+	0.313475i	0.782233	−	0.622986i	$-0.214081\pi$
$71$	3.63556	+	2.64139i	0.431462	+	0.313475i	−0.350771	+	0.936461i	$0.614081\pi$
$72$		0			0
$73$	0.380414	−	1.17080i	0.0445241	−	0.137031i	−0.926323	−	0.376730i	$-0.877049\pi$
$73$	0.380414	−	1.17080i	0.0445241	−	0.137031i	0.970847	+	0.239698i	$0.0770486\pi$
$74$	7.45971	−	12.9206i	0.867174	−	1.50199i
$75$		0			0
$76$	0.0421926	+	0.0730797i	0.00483982	+	0.00838281i
$77$	0.0744753	−	0.0158302i	0.00848725	−	0.00180402i
$78$		0			0
$79$	0.840545	−	0.374235i	0.0945687	−	0.0421047i	−0.358907	−	0.933373i	$-0.616851\pi$
$79$	0.840545	−	0.374235i	0.0945687	−	0.0421047i	0.453476	+	0.891269i	$0.350184\pi$
$80$	−3.44761	+	8.43194i	−0.385454	+	0.942719i
$81$		0			0
$82$	2.31745			0.255920
$83$	0.581163	+	5.52940i	0.0637909	+	0.606930i	0.978987	+	0.203922i	$0.0653688\pi$
$83$	0.581163	+	5.52940i	0.0637909	+	0.606930i	−0.915196	+	0.403008i	$0.867965\pi$
$84$		0			0
$85$	−3.26826	−	6.77231i	−0.354493	−	0.734560i
$86$	15.6052	−	3.31699i	1.68275	−	0.357680i
$87$		0			0
$88$	−0.0865826	−	0.0184037i	−0.00922973	−	0.00196184i
$89$	0.932477	−	2.86987i	0.0988424	−	0.304206i	−0.889394	−	0.457142i	$-0.848873\pi$
$89$	0.932477	−	2.86987i	0.0988424	−	0.304206i	0.988236	+	0.152937i	$0.0488730\pi$
$90$		0			0
$91$	4.69854	+	14.4606i	0.492541	+	1.51589i
$92$	0.00757118	+	0.0720350i	0.000789350	+	0.00751017i
$93$		0			0
$94$	−4.12024	−	1.83445i	−0.424971	−	0.189209i
$95$	2.17753	+	4.51214i	0.223409	+	0.462936i
$96$		0			0
$97$	−9.49506	+	4.22747i	−0.964077	+	0.429235i	−0.827544	−	0.561401i	$-0.810263\pi$
$97$	−9.49506	+	4.22747i	−0.964077	+	0.429235i	−0.136533	+	0.990636i	$0.543596\pi$
$98$	0.526882	−	1.62158i	0.0532232	−	0.163804i
$99$		0			0
$100$	0.0839556	−	0.168560i	0.00839556	−	0.0168560i
$101$	−2.74091	+	4.74740i	−0.272731	+	0.472384i	−0.969560	−	0.244853i	$-0.921260\pi$
$101$	−2.74091	+	4.74740i	−0.272731	+	0.472384i	0.696829	+	0.717237i	$0.254594\pi$
$102$		0			0
$103$	0.191572	−	1.82268i	0.0188761	−	0.179594i	−0.981022	−	0.193899i	$-0.937887\pi$
$103$	0.191572	−	1.82268i	0.0188761	−	0.179594i	0.999898	+	0.0143043i	$0.00455337\pi$
$104$	1.84771	−	17.5798i	0.181183	−	1.72384i
$105$		0			0
$106$	0.227548	+	2.16498i	0.0221014	+	0.210281i
$107$	−18.4750			−1.78604			−0.893021	−	0.450014i	$-0.851419\pi$
$107$	−18.4750			−1.78604			−0.893021	+	0.450014i	$0.851419\pi$
$108$		0			0
$109$	1.39665	+	4.29846i	0.133775	+	0.411718i	0.995397	−	0.0958324i	$-0.0305513\pi$
$109$	1.39665	+	4.29846i	0.133775	+	0.411718i	−0.861622	+	0.507550i	$0.830551\pi$
$110$	0.0968404	+	0.0282052i	0.00923337	+	0.00268926i
$111$		0			0
$112$	6.56816	−	7.29468i	0.620633	−	0.689283i
$113$	−2.49461	+	2.77055i	−0.234673	+	0.260631i	−0.848966	−	0.528447i	$-0.822775\pi$
$113$	−2.49461	+	2.77055i	−0.234673	+	0.260631i	0.614293	+	0.789078i	$0.289441\pi$
$114$		0			0
$115$	0.132197	+	4.29837i	0.0123274	+	0.400825i
$116$	−0.108825	−	0.334929i	−0.0101041	−	0.0310974i
$117$		0			0
$118$	−18.3072			−1.68532
$119$	0.846976	+	8.05844i	0.0776422	+	0.738716i
$120$		0			0
$121$	1.14971	−	10.9387i	0.104519	−	0.994432i
$122$	1.58476	−	15.0779i	0.143477	−	1.36509i
$123$		0			0
$124$	0.0708003	−	0.122630i	0.00635806	−	0.0110125i
$125$	5.71060	−	9.61192i	0.510772	−	0.859716i
$126$		0			0
$127$	3.06084	−	9.42031i	0.271606	−	0.835917i	−0.718492	−	0.695536i	$-0.755167\pi$
$127$	3.06084	−	9.42031i	0.271606	−	0.835917i	0.990098	−	0.140381i	$-0.0448329\pi$
$128$	−10.6179	+	4.72738i	−0.938496	+	0.417845i
$129$		0			0
$130$	−3.58019	+	19.8216i	−0.314003	+	1.73847i
$131$	−0.808980	−	0.360181i	−0.0706809	−	0.0314692i	0.371092	−	0.928596i	$-0.378984\pi$
$131$	−0.808980	−	0.360181i	−0.0706809	−	0.0314692i	−0.441773	+	0.897127i	$0.645650\pi$
$132$		0			0
$133$	−0.564310	−	5.36905i	−0.0489319	−	0.465556i
$134$	1.00431	+	3.09094i	0.0867590	+	0.267017i
$135$		0			0
$136$	2.91097	−	8.95903i	0.249613	−	0.768230i
$137$	−10.9483	−	2.32714i	−0.935378	−	0.198821i	−0.285083	−	0.958503i	$-0.592021\pi$
$137$	−10.9483	−	2.32714i	−0.935378	−	0.198821i	−0.650295	+	0.759682i	$0.725355\pi$
$138$		0			0
$139$	0.0394061	−	0.00837602i	0.00334238	−	0.000710445i	−0.206240	−	0.978501i	$-0.566123\pi$
$139$	0.0394061	−	0.00837602i	0.00334238	−	0.000710445i	0.209583	+	0.977791i	$0.432789\pi$
$140$	−0.146549	+	0.140347i	−0.0123857	+	0.0118615i
$141$		0			0
$142$	−0.670525	−	6.37962i	−0.0562692	−	0.535365i
$143$	−0.199409			−0.0166754
$144$		0			0
$145$	−4.97380	−	20.3085i	−0.413052	−	1.68653i
$146$	−1.60535	+	0.714750i	−0.132860	+	0.0591531i
$147$		0			0
$148$	−0.385031	+	0.0818408i	−0.0316493	+	0.00672727i
$149$	−4.04741	−	7.01032i	−0.331577	−	0.574308i	0.651245	−	0.758868i	$-0.274247\pi$
$149$	−4.04741	−	7.01032i	−0.331577	−	0.574308i	−0.982821	+	0.184560i	$0.940914\pi$
$150$		0			0
$151$	−4.63305	+	8.02468i	−0.377032	+	0.653039i	−0.990629	−	0.136580i	$-0.956389\pi$
$151$	−4.63305	+	8.02468i	−0.377032	+	0.653039i	0.613597	+	0.789620i	$0.289722\pi$
$152$	−1.93947	+	5.96908i	−0.157312	+	0.484156i
$153$		0			0
$154$	−0.0879289	−	0.0638841i	−0.00708552	−	0.00514793i
$155$	4.73014	−	6.95017i	0.379934	−	0.558251i
$156$		0			0
$157$	−5.80545	−	10.0553i	−0.463326	−	0.802503i	0.535799	−	0.844346i	$-0.320011\pi$
$157$	−5.80545	−	10.0553i	−0.463326	−	0.802503i	−0.999124	+	0.0418424i	$0.986677\pi$
$158$	−1.19985	−	0.534208i	−0.0954549	−	0.0424993i
$159$		0			0
$160$	0.448277	−	0.161050i	0.0354394	−	0.0127321i
$161$	1.43195	−	4.40710i	0.112854	−	0.347328i
$162$		0			0
$163$	−1.85642	−	5.71348i	−0.145406	−	0.447515i	0.851657	−	0.524100i	$-0.175598\pi$
$163$	−1.85642	−	5.71348i	−0.145406	−	0.447515i	−0.997063	+	0.0765854i	$0.975598\pi$
$164$	−0.0409129	−	0.0454384i	−0.00319476	−	0.00354814i
$165$		0			0
$166$	5.31056	−	5.89797i	0.412179	−	0.457772i
$167$	−12.3524	−	5.49964i	−0.955857	−	0.425575i	−0.131293	−	0.991344i	$-0.541913\pi$
$167$	−12.3524	−	5.49964i	−0.955857	−	0.425575i	−0.824564	+	0.565769i	$0.808580\pi$
$168$		0			0
$169$	−2.80361	−	26.6745i	−0.215662	−	2.05189i
$170$	−4.06245	+	9.93567i	−0.311575	+	0.762031i
$171$		0			0
$172$	−0.340535	−	0.247413i	−0.0259655	−	0.0188651i
$173$	4.52702	+	5.02776i	0.344183	+	0.382254i	0.890238	−	0.455495i	$-0.150538\pi$
$173$	4.52702	+	5.02776i	0.344183	+	0.382254i	−0.546055	+	0.837749i	$0.683871\pi$
$174$		0			0
$175$	−9.29294	+	7.66682i	−0.702480	+	0.579557i
$176$	0.0643676	+	0.111488i	0.00485189	+	0.00840372i
$177$		0			0
$178$	−3.93507	+	1.75200i	−0.294946	+	0.131318i
$179$	−5.82355	−	4.23106i	−0.435272	−	0.316244i	0.348481	−	0.937316i	$-0.386698\pi$
$179$	−5.82355	−	4.23106i	−0.435272	−	0.316244i	−0.783754	+	0.621072i	$0.786698\pi$
$180$		0			0
$181$	−5.56870	+	4.04590i	−0.413918	+	0.300729i	−0.775186	−	0.631733i	$-0.782344\pi$
$181$	−5.56870	+	4.04590i	−0.413918	+	0.300729i	0.361268	+	0.932462i	$0.382344\pi$
$182$	10.8522	−	18.7965i	0.804417	−	1.39329i
$183$		0			0
$184$	−3.60475	+	4.00348i	−0.265746	+	0.295140i
$185$	−23.1566	+	3.15624i	−1.70250	+	0.232051i
$186$		0			0
$187$	−0.103945	−	0.0220943i	−0.00760124	−	0.00161569i
$188$	0.0367717	+	0.113172i	0.00268185	+	0.00825389i
$189$		0			0
$190$	2.70666	−	6.61978i	0.196362	−	0.480249i
$191$	11.0464	+	2.34798i	0.799289	+	0.169894i	0.589411	−	0.807834i	$-0.299360\pi$
$191$	11.0464	+	2.34798i	0.799289	+	0.169894i	0.209878	+	0.977728i	$0.432693\pi$
$192$		0			0
$193$	11.1617	+	19.3326i	0.803434	+	1.39159i	0.917343	+	0.398098i	$0.130330\pi$
$193$	11.1617	+	19.3326i	0.803434	+	1.39159i	−0.113909	+	0.993491i	$0.536337\pi$
$194$	13.5539	+	6.03458i	0.973112	+	0.433257i
$195$		0			0
$196$	−0.0410961	+	0.0182971i	−0.00293543	+	0.00130694i
$197$	21.1964	+	15.4001i	1.51018	+	1.09721i	0.966097	+	0.258179i	$0.0831224\pi$
$197$	21.1964	+	15.4001i	1.51018	+	1.09721i	0.544083	+	0.839031i	$0.316878\pi$
$198$		0			0
$199$	−16.6094			−1.17741			−0.588703	−	0.808349i	$-0.700361\pi$
$199$	−16.6094			−1.17741			−0.588703	+	0.808349i	$0.700361\pi$
$200$	13.4950	−	3.74836i	0.954238	−	0.265049i
$201$		0			0
$202$	7.65412	−	1.62693i	0.538542	−	0.114471i
$203$	−2.35504	+	22.4067i	−0.165291	+	1.57264i
$204$		0			0
$205$	−2.22305	−	2.86991i	−0.155264	−	0.200443i
$206$	−2.11651	+	1.53774i	−0.147464	+	0.107139i
$207$		0			0
$208$	−20.7983	+	15.1108i	−1.44210	+	1.04775i
$209$	0.0692551	+	0.0147206i	0.00479047	+	0.00101825i
$210$		0			0
$211$	9.41180	−	2.00054i	0.647935	−	0.137723i	0.127791	−	0.991801i	$-0.459211\pi$
$211$	9.41180	−	2.00054i	0.647935	−	0.137723i	0.520145	+	0.854078i	$0.325878\pi$
$212$	0.0384316	−	0.0426826i	0.00263949	−	0.00293146i
$213$		0			0
$214$	17.6466	+	19.5985i	1.20630	+	1.33973i
$215$	−19.0772	−	16.1434i	−1.30106	−	1.10097i
$216$		0			0
$217$	−7.32892	+	5.32477i	−0.497520	+	0.361469i
$218$	3.22584	−	5.58731i	0.218481	−	0.378421i
$219$		0			0
$220$	−0.00115663	−	0.00239670i	−7.79797e−5	−	0.000161585i
$221$	2.21824	−	21.1051i	0.149215	−	1.41968i
$222$		0			0
$223$	−17.3409	−	19.2591i	−1.16124	−	1.28968i	−0.950001	−	0.312248i	$-0.898918\pi$
$223$	−17.3409	−	19.2591i	−1.16124	−	1.28968i	−0.211235	−	0.977435i	$-0.567749\pi$
$224$	−0.513268			−0.0342942
$225$		0			0
$226$	5.32179			0.354000
$227$	−13.4978	−	14.9908i	−0.895881	−	0.994977i	−1.00000		0.000411914i	$-0.999869\pi$
$227$	−13.4978	−	14.9908i	−0.895881	−	0.994977i	0.104119	−	0.994565i	$-0.466798\pi$
$228$		0			0
$229$	0.727435	−	6.92109i	0.0480703	−	0.457358i	−0.943839	−	0.330407i	$-0.892814\pi$
$229$	0.727435	−	6.92109i	0.0480703	−	0.457358i	0.991909	−	0.126951i	$-0.0405193\pi$
$230$	4.43351	−	4.24588i	0.292337	−	0.279965i
$231$		0			0
$232$	13.0964	−	22.6836i	0.859820	−	1.48925i
$233$	22.8409	−	16.5949i	1.49636	−	1.08717i	0.524551	−	0.851379i	$-0.324233\pi$
$233$	22.8409	−	16.5949i	1.49636	−	1.08717i	0.971805	−	0.235787i	$-0.0757666\pi$
$234$		0			0
$235$	1.68064	+	6.86218i	0.109633	+	0.447639i
$236$	0.323201	+	0.358951i	0.0210386	+	0.0233657i
$237$		0			0
$238$	7.73951	−	8.59560i	0.501678	−	0.557170i
$239$	4.35020	−	0.924664i	0.281391	−	0.0598115i	−0.0650541	−	0.997882i	$-0.520722\pi$
$239$	4.35020	−	0.924664i	0.281391	−	0.0598115i	0.346445	+	0.938070i	$0.387389\pi$
$240$		0			0
$241$	−14.8371	−	3.15373i	−0.955743	−	0.203149i	−0.296461	−	0.955045i	$-0.595806\pi$
$241$	−14.8371	−	3.15373i	−0.955743	−	0.203149i	−0.659282	+	0.751895i	$0.729140\pi$
$242$	−12.7021	+	9.22865i	−0.816525	+	0.593240i
$243$		0			0
$244$	−0.323612	+	0.235118i	−0.0207171	+	0.0150519i
$245$	−2.51356	+	0.903035i	−0.160586	+	0.0576928i
$246$		0			0
$247$	−1.47793	+	14.0616i	−0.0940385	+	0.894717i
$248$	10.3016	−	2.18967i	0.654152	−	0.139044i
$249$		0			0
$250$	−15.6510	+	3.12305i	−0.989857	+	0.197519i
$251$	14.0348			0.885869			0.442935	−	0.896554i	$-0.353937\pi$
$251$	14.0348			0.885869			0.442935	+	0.896554i	$0.353937\pi$
$252$		0			0
$253$	0.0491663	+	0.0357214i	0.00309106	+	0.00224579i
$254$	−12.9168	+	5.75093i	−0.810472	+	0.360845i
$255$		0			0
$256$	0.825455	+	0.367516i	0.0515909	+	0.0229698i
$257$	4.76132	+	8.24684i	0.297003	+	0.514424i	0.975449	−	0.220226i	$-0.0706796\pi$
$257$	4.76132	+	8.24684i	0.297003	+	0.514424i	−0.678446	+	0.734650i	$0.737346\pi$
$258$		0			0
$259$	24.6327	+	5.23585i	1.53060	+	0.325340i
$260$	0.451849	−	0.279739i	0.0280225	−	0.0173487i
$261$		0			0
$262$	0.390622	+	1.20221i	0.0241327	+	0.0742728i
$263$	23.7423	+	5.04659i	1.46402	+	0.311186i	0.869914	−	0.493204i	$-0.164174\pi$
$263$	23.7423	+	5.04659i	1.46402	+	0.311186i	0.594101	+	0.804390i	$0.297508\pi$
$264$		0			0
$265$	2.46280	−	2.35858i	0.151289	−	0.144886i
$266$	−5.15656	+	5.72694i	−0.316169	+	0.351141i
$267$		0			0
$268$	0.0428739	−	0.0742598i	0.00261894	−	0.00453614i
$269$	12.9182	−	9.38564i	0.787638	−	0.572252i	−0.119624	−	0.992819i	$-0.538169\pi$
$269$	12.9182	−	9.38564i	0.787638	−	0.572252i	0.907262	+	0.420567i	$0.138169\pi$
$270$		0			0
$271$	11.6010	+	8.42860i	0.704709	+	0.512001i	0.881462	−	0.472254i	$-0.156560\pi$
$271$	11.6010	+	8.42860i	0.704709	+	0.512001i	−0.176754	+	0.984255i	$0.556560\pi$
$272$	−12.5157	+	5.57236i	−0.758877	+	0.337874i
$273$		0			0
$274$	7.98875	+	13.8369i	0.482618	+	0.835919i
$275$	−0.0579665	−	0.146982i	−0.00349551	−	0.00886336i
$276$		0			0
$277$	−10.5642	−	11.7327i	−0.634740	−	0.704950i	0.336867	−	0.941552i	$-0.390633\pi$
$277$	−10.5642	−	11.7327i	−0.634740	−	0.704950i	−0.971607	+	0.236602i	$0.923966\pi$
$278$	−0.0465246	−	0.0338021i	−0.00279036	−	0.00202732i
$279$		0			0
$280$	−15.0507	−	1.11540i	−0.899453	−	0.0666580i
$281$	−0.154395	−	1.46897i	−0.00921045	−	0.0876316i	0.988951	−	0.148243i	$-0.0473617\pi$
$281$	−0.154395	−	1.46897i	−0.00921045	−	0.0876316i	−0.998161	+	0.0606112i	$0.980695\pi$
$282$		0			0
$283$	−12.4438	−	5.54033i	−0.739706	−	0.329338i	0.00205936	−	0.999998i	$-0.499344\pi$
$283$	−12.4438	−	5.54033i	−0.739706	−	0.329338i	−0.741765	+	0.670660i	$0.766011\pi$
$284$	−0.113248	+	0.125774i	−0.00672002	+	0.00746334i
$285$		0			0
$286$	0.190468	+	0.211536i	0.0112626	+	0.0125084i
$287$	1.20879	+	3.72026i	0.0713523	+	0.219600i
$288$		0			0
$289$	−1.75857	+	5.41233i	−0.103445	+	0.318372i
$290$	−16.7927	+	24.6742i	−0.986104	+	1.44892i
$291$		0			0
$292$	0.0423555	+	0.0188579i	0.00247867	+	0.00110357i
$293$	8.13530	+	14.0908i	0.475270	+	0.823191i	0.999599	−	0.0283246i	$-0.00901721\pi$
$293$	8.13530	+	14.0908i	0.475270	+	0.823191i	−0.524329	+	0.851516i	$0.675684\pi$
$294$		0			0
$295$	17.5615	+	22.6715i	1.02247	+	1.31998i
$296$	−23.6856	−	17.2086i	−1.37669	−	1.00023i
$297$		0			0
$298$	−3.57072	+	10.9895i	−0.206846	+	0.636607i
$299$	−6.06810	+	10.5103i	−0.350927	+	0.607824i
$300$		0			0
$301$	13.4645	+	23.3212i	0.776082	+	1.34421i
$302$	12.9380	−	2.75006i	0.744499	−	0.158248i
$303$		0			0
$304$	8.33877	−	3.71266i	0.478262	−	0.212936i
$305$	−20.1925	+	12.5012i	−1.15622	+	0.715815i
$306$		0			0
$307$	14.3507			0.819040			0.409520	−	0.912301i	$-0.365696\pi$
$307$	14.3507			0.819040			0.409520	+	0.912301i	$0.365696\pi$
$308$	0.000299742		0.00285185i	1.70794e−5		0.000162499i
$309$		0			0
$310$	−11.8909	+	1.62073i	−0.675357	+	0.0920512i
$311$	−21.9008	+	4.65515i	−1.24188	+	0.263970i	−0.781586	−	0.623797i	$-0.785589\pi$
$311$	−21.9008	+	4.65515i	−1.24188	+	0.263970i	−0.460293	+	0.887767i	$0.652256\pi$
$312$		0			0
$313$	23.9037	+	5.08090i	1.35112	+	0.287189i	0.825919	−	0.563789i	$-0.190657\pi$
$313$	23.9037	+	5.08090i	1.35112	+	0.287189i	0.525200	+	0.850979i	$0.323990\pi$
$314$	−5.12170	+	15.7630i	−0.289035	+	0.889557i
$315$		0			0
$316$	0.0107082	+	0.0329566i	0.000602385	+	0.00185395i
$317$	1.80810	+	17.2029i	0.101553	+	0.966213i	0.920076	+	0.391740i	$0.128127\pi$
$317$	1.80810	+	17.2029i	0.101553	+	0.966213i	−0.818523	+	0.574474i	$0.805207\pi$
$318$		0			0
$319$	−0.269934	−	0.120182i	−0.0151134	−	0.00672892i
$320$	15.4517	+	8.29848i	0.863778	+	0.463899i
$321$		0			0
$322$	−6.04286	+	2.69045i	−0.336755	+	0.149933i
$323$	−2.32840	+	7.16609i	−0.129556	+	0.398732i
$324$		0			0
$325$	27.9812	−	14.5805i	1.55212	−	0.808779i
$326$	−4.28776	+	7.42662i	−0.237477	+	0.411323i
$327$		0			0
$328$	0.475356	−	4.52271i	0.0262472	−	0.249725i
$329$	0.795762	−	7.57117i	0.0438718	−	0.417412i
$330$		0			0
$331$	2.74019	+	26.0711i	0.150614	+	1.43300i	0.765019	+	0.644008i	$0.222730\pi$
$331$	2.74019	+	26.0711i	0.150614	+	1.43300i	−0.614404	+	0.788991i	$0.710604\pi$
$332$	−0.209396			−0.0114921
$333$		0			0
$334$	5.96444	+	18.3567i	0.326360	+	1.00443i
$335$	2.86439	−	4.20875i	0.156498	−	0.229949i
$336$		0			0
$337$	10.8044	−	11.9995i	0.588553	−	0.653654i	−0.373143	−	0.927774i	$-0.621720\pi$
$337$	10.8044	−	11.9995i	0.588553	−	0.653654i	0.961696	+	0.274120i	$0.0883864\pi$
$338$	−25.6189	+	28.4526i	−1.39348	+	1.54762i
$339$		0			0
$340$	0.266529	−	0.0957544i	0.0144545	−	0.00519301i
$341$	−0.0367138	−	0.112993i	−0.00198816	−	0.00611893i
$342$		0			0
$343$	19.7443			1.06609
$344$	−3.27245	−	31.1353i	−0.176439	−	1.67870i
$345$		0			0
$346$	1.00949	−	9.60465i	0.0542705	−	0.516349i
$347$	−1.95974	+	18.6457i	−0.105205	+	1.00095i	0.806814	+	0.590806i	$0.201190\pi$
$347$	−1.95974	+	18.6457i	−0.105205	+	1.00095i	−0.912019	+	0.410149i	$0.865477\pi$
$348$		0			0
$349$	−0.899591	+	1.55814i	−0.0481540	+	0.0834051i	−0.889098	−	0.457717i	$-0.848667\pi$
$349$	−0.899591	+	1.55814i	−0.0481540	+	0.0834051i	0.840944	+	0.541123i	$0.182000\pi$
$350$	17.0093	+	2.53503i	0.909188	+	0.135503i
$351$		0			0
$352$	0.00208013	−	0.00640199i	0.000110871	−	0.000341227i
$353$	1.67743	−	0.746839i	0.0892805	−	0.0397502i	−0.361610	−	0.932329i	$-0.617773\pi$
$353$	1.67743	−	0.746839i	0.0892805	−	0.0397502i	0.450891	+	0.892579i	$0.351106\pi$
$354$		0			0
$355$	−7.25723	+	6.95010i	−0.385174	+	0.368873i
$356$	0.103822	+	0.0462247i	0.00550257	+	0.00244990i
$357$		0			0
$358$	1.07407	+	10.2190i	0.0567661	+	0.540093i
$359$	10.8516	+	33.3977i	0.572724	+	1.76266i	0.643802	+	0.765192i	$0.277356\pi$
$359$	10.8516	+	33.3977i	0.572724	+	1.76266i	−0.0710775	+	0.997471i	$0.522644\pi$
$360$		0			0
$361$	−4.31999	+	13.2956i	−0.227368	+	0.699767i
$362$	9.61096	+	2.04287i	0.505141	+	0.107371i
$363$		0			0
$364$	−0.560131	+	0.119060i	−0.0293589	+	0.00624042i
$365$	2.42510	+	1.30242i	0.126935	+	0.0681717i
$366$		0			0
$367$	−2.51317	−	23.9112i	−0.131186	−	1.24815i	−0.839933	−	0.542690i	$-0.817406\pi$
$367$	−2.51317	−	23.9112i	−0.131186	−	1.24815i	0.708747	−	0.705463i	$-0.249261\pi$
$368$	7.83493			0.408424
$369$		0			0
$370$	25.4664	+	21.5501i	1.32394	+	1.12034i
$371$	−3.35680	+	1.49454i	−0.174276	+	0.0775928i
$372$		0			0
$373$	−1.97274	+	0.419319i	−0.102145	+	0.0217115i	−0.258700	−	0.965958i	$-0.583294\pi$
$373$	−1.97274	+	0.419319i	−0.102145	+	0.0217115i	0.156556	+	0.987669i	$0.449961\pi$
$374$	0.0758467	+	0.131370i	0.00392194	+	0.00679300i
$375$		0			0
$376$	−4.42524	+	7.66473i	−0.228214	+	0.395278i
$377$	18.2340	−	56.1186i	0.939100	−	2.89025i
$378$		0			0
$379$	−15.2526	−	11.0817i	−0.783474	−	0.569227i	0.122546	−	0.992463i	$-0.460894\pi$
$379$	−15.2526	−	11.0817i	−0.783474	−	0.569227i	−0.906020	+	0.423236i	$0.860894\pi$
$380$	−0.177578	+	0.0637977i	−0.00910958	+	0.00327275i
$381$		0			0
$382$	−8.06032	−	13.9609i	−0.412402	−	0.714301i
$383$	−10.1089	−	4.50077i	−0.516541	−	0.229979i	0.131873	−	0.991267i	$-0.457901\pi$
$383$	−10.1089	−	4.50077i	−0.516541	−	0.229979i	−0.648414	+	0.761288i	$0.724567\pi$
$384$		0			0
$385$	0.00523367	+	0.170172i	0.000266732	+	0.00867276i
$386$	9.84708	−	30.3062i	0.501203	−	1.54254i
$387$		0			0
$388$	−0.120964	−	0.372288i	−0.00614100	−	0.0189000i
$389$	14.4803	+	16.0820i	0.734181	+	0.815391i	0.988419	−	0.151751i	$-0.0484912\pi$
$389$	14.4803	+	16.0820i	0.734181	+	0.815391i	−0.254238	+	0.967142i	$0.581825\pi$
$390$		0			0
$391$	−4.32763	+	4.80632i	−0.218858	+	0.243066i
$392$	−3.05658	−	1.36088i	−0.154380	−	0.0687346i
$393$		0			0
$394$	−3.90935	−	37.1950i	−0.196950	−	1.87386i
$395$	0.489416	+	1.99833i	0.0246252	+	0.100547i
$396$		0			0
$397$	6.42510	+	4.66811i	0.322467	+	0.234286i	0.737227	−	0.675645i	$-0.236135\pi$
$397$	6.42510	+	4.66811i	0.322467	+	0.234286i	−0.414761	+	0.909931i	$0.636135\pi$
$398$	15.8646	+	17.6195i	0.795222	+	0.883184i
$399$		0			0
$400$	−17.1839	−	10.9376i	−0.859196	−	0.546880i
$401$	−6.27204	−	10.8635i	−0.313211	−	0.542497i	0.665845	−	0.746090i	$-0.268071\pi$
$401$	−6.27204	−	10.8635i	−0.313211	−	0.542497i	−0.979056	+	0.203593i	$0.934738\pi$
$402$		0			0
$403$	21.6745	−	9.65011i	1.07968	−	0.480706i
$404$	−0.167027	−	0.121352i	−0.00830992	−	0.00603751i
$405$		0			0
$406$	26.0188	−	18.9038i	1.29129	−	0.938178i
$407$	−0.165136	+	0.286024i	−0.00818549	+	0.0141777i
$408$		0			0
$409$	−2.96912	+	3.29754i	−0.146813	+	0.163053i	−0.812066	−	0.583565i	$-0.801657\pi$
$409$	−2.96912	+	3.29754i	−0.146813	+	0.163053i	0.665253	+	0.746618i	$0.268324\pi$
$410$	−0.921069	+	5.09947i	−0.0454884	+	0.251845i
$411$		0			0
$412$	0.0675159	+	0.0143510i	0.00332627	+	0.000707021i
$413$	−9.54906	−	29.3890i	−0.469879	−	1.44614i
$414$		0			0
$415$	−12.3982	−	0.918825i	−0.608604	−	0.0451034i
$416$	1.31488	+	0.279486i	0.0644672	+	0.0137029i
$417$		0			0
$418$	−0.0505340	−	0.0875274i	−0.00247170	−	0.00428110i
$419$	6.70380	+	2.98472i	0.327502	+	0.145813i	0.563900	−	0.825843i	$-0.309300\pi$
$419$	6.70380	+	2.98472i	0.327502	+	0.145813i	−0.236398	+	0.971656i	$0.575967\pi$
$420$		0			0
$421$	−7.15154	+	3.18407i	−0.348545	+	0.155182i	−0.573540	−	0.819178i	$-0.694430\pi$
$421$	−7.15154	+	3.18407i	−0.348545	+	0.155182i	0.224995	+	0.974360i	$0.427763\pi$
$422$	−11.1120	−	8.07334i	−0.540924	−	0.393004i
$423$		0			0
$424$	4.27182			0.207458
$425$	16.2012	−	4.50004i	0.785872	−	0.218284i
$426$		0			0
$427$	25.0316	−	5.32062i	1.21136	−	0.257483i
$428$	0.0727316	−	0.691995i	0.00351562	−	0.0334488i
$429$		0			0
$430$	1.09664	+	35.6570i	0.0528845	+	1.71953i
$431$	−10.2026	+	7.41261i	−0.491441	+	0.357053i	−0.805738	−	0.592272i	$-0.798231\pi$
$431$	−10.2026	+	7.41261i	−0.491441	+	0.357053i	0.314297	+	0.949325i	$0.398231\pi$
$432$		0			0
$433$	30.3440	−	22.0462i	1.45824	−	1.05947i	0.474425	−	0.880296i	$-0.342656\pi$
$433$	30.3440	−	22.0462i	1.45824	−	1.05947i	0.983817	−	0.179179i	$-0.0573441\pi$
$434$	12.6489	+	2.68861i	0.607167	+	0.129057i
$435$		0			0
$436$	−0.166501	+	0.0353908i	−0.00797393	+	0.00169491i
$437$	2.88334	−	3.20228i	0.137929	−	0.153186i
$438$		0			0
$439$	23.3463	+	25.9287i	1.11426	+	1.23751i	0.968721	+	0.248154i	$0.0798239\pi$
$439$	23.3463	+	25.9287i	1.11426	+	1.23751i	0.145536	+	0.989353i	$0.453509\pi$
$440$	0.0749088	−	0.183207i	0.00357114	−	0.00873406i
$441$		0			0
$442$	−24.5074	+	17.8057i	−1.16570	+	0.846929i
$443$	12.2771	−	21.2646i	0.583304	−	1.01031i	−0.411780	−	0.911283i	$-0.635093\pi$
$443$	12.2771	−	21.2646i	0.583304	−	1.01031i	0.995085	−	0.0990295i	$-0.0315738\pi$
$444$		0			0
$445$	5.94443	+	3.19251i	0.281793	+	0.151339i
$446$	−3.86690	+	36.7911i	−0.183103	+	1.74211i
$447$		0			0
$448$	−12.6461	−	14.0449i	−0.597471	−	0.663558i
$449$	−5.69752			−0.268882			−0.134441	−	0.990922i	$-0.542924\pi$
$449$	−5.69752			−0.268882			−0.134441	+	0.990922i	$0.542924\pi$
$450$		0			0
$451$	−0.0513016			−0.00241570
$452$	−0.0939523	−	0.104345i	−0.00441915	−	0.00490796i
$453$		0			0
$454$	−3.00991	+	28.6374i	−0.141262	+	1.34402i
$455$	−33.6875	+	4.59160i	−1.57929	+	0.215258i
$456$		0			0
$457$	−14.9907	+	25.9647i	−0.701238	+	1.21458i	0.266795	+	0.963753i	$0.414035\pi$
$457$	−14.9907	+	25.9647i	−0.701238	+	1.21458i	−0.968032	+	0.250826i	$0.919298\pi$
$458$	−8.03681	+	5.83908i	−0.375535	+	0.272842i
$459$		0			0
$460$	−0.161519	−	0.0119701i	−0.00753088	−	0.000558110i
$461$	3.32317	+	3.69076i	0.154776	+	0.171896i	0.815546	−	0.578693i	$-0.196437\pi$
$461$	3.32317	+	3.69076i	0.154776	+	0.171896i	−0.660770	+	0.750588i	$0.729770\pi$
$462$		0			0
$463$	7.65307	−	8.49959i	0.355668	−	0.395009i	−0.538585	−	0.842571i	$-0.681041\pi$
$463$	7.65307	−	8.49959i	0.355668	−	0.395009i	0.894253	+	0.447562i	$0.147708\pi$
$464$	−37.2612	+	7.92011i	−1.72981	+	0.367682i
$465$		0			0
$466$	−39.4208	−	8.37915i	−1.82613	−	0.388157i
$467$	−21.2823	+	15.4625i	−0.984827	+	0.715518i	−0.958782	−	0.284142i	$-0.908291\pi$
$467$	−21.2823	+	15.4625i	−0.984827	+	0.715518i	−0.0260445	+	0.999661i	$0.508291\pi$
$468$		0			0
$469$	−4.43811	+	3.22447i	−0.204933	+	0.148892i
$470$	5.67422	−	8.33734i	0.261732	−	0.384573i
$471$		0			0
$472$	−3.75518	+	35.7282i	−0.172846	+	1.64452i
$473$	−0.345453	+	0.0734284i	−0.0158840	+	0.00337624i
$474$		0			0
$475$	−10.7943	+	2.99821i	−0.495275	+	0.137568i
$476$	−0.305170			−0.0139874
$477$		0			0
$478$	−5.13604	−	3.73155i	−0.234917	−	0.170677i
$479$	−0.427614	+	0.190386i	−0.0195382	+	0.00869896i	−0.416482	−	0.909144i	$-0.636737\pi$
$479$	−0.427614	+	0.190386i	−0.0195382	+	0.00869896i	0.396944	+	0.917843i	$0.370071\pi$
$480$		0			0
$481$	−60.2525	−	26.8261i	−2.74728	−	1.22317i
$482$	10.8263	+	18.7518i	0.493126	+	0.854119i
$483$		0			0
$484$	0.405194	+	0.0861265i	0.0184179	+	0.00391484i
$485$	−5.52859	−	22.5737i	−0.251041	−	1.02502i
$486$		0			0
$487$	1.55836	+	4.79614i	0.0706160	+	0.217334i	0.980136	−	0.198326i	$-0.0635506\pi$
$487$	1.55836	+	4.79614i	0.0706160	+	0.217334i	−0.909520	+	0.415660i	$0.863551\pi$
$488$	−29.1009	−	6.18558i	−1.31733	−	0.280008i
$489$		0			0
$490$	3.35881	+	1.80388i	0.151736	+	0.0814909i
$491$	5.02924	−	5.58554i	0.226966	−	0.252072i	−0.618896	−	0.785473i	$-0.712420\pi$
$491$	5.02924	−	5.58554i	0.226966	−	0.252072i	0.845862	+	0.533401i	$0.179086\pi$
$492$		0			0
$493$	15.7227	−	27.2325i	0.708113	−	1.22649i
$494$	16.3284	−	11.8633i	0.734649	−	0.533754i
$495$		0			0
$496$	−12.3916	−	9.00306i	−0.556401	−	0.404249i
$497$	9.89159	−	4.40402i	0.443699	−	0.197547i
$498$		0			0
$499$	4.05527	+	7.02394i	0.181539	+	0.314435i	0.942405	−	0.334474i	$-0.108559\pi$
$499$	4.05527	+	7.02394i	0.181539	+	0.314435i	−0.760866	+	0.648909i	$0.775225\pi$
$500$	0.337541	+	0.251735i	0.0150953	+	0.0112579i
$501$		0			0
$502$	−13.4055	−	14.8883i	−0.598317	−	0.664499i
$503$	16.3455	+	11.8757i	0.728812	+	0.529513i	0.889187	−	0.457543i	$-0.151271\pi$
$503$	16.3455	+	11.8757i	0.728812	+	0.529513i	−0.160376	+	0.987056i	$0.551271\pi$
$504$		0			0
$505$	−9.35710	−	7.91812i	−0.416385	−	0.352352i
$506$	−0.00906799	−	0.0862761i	−0.000403121	−	0.00383544i
$507$		0			0
$508$	0.340795	+	0.151732i	0.0151204	+	0.00673201i
$509$	−14.0043	+	15.5533i	−0.620728	+	0.689389i	−0.968733	−	0.248104i	$-0.920193\pi$
$509$	−14.0043	+	15.5533i	−0.620728	+	0.689389i	0.348005	+	0.937493i	$0.386859\pi$
$510$		0			0
$511$	−1.98476	−	2.20430i	−0.0878005	−	0.0975124i
$512$	6.78465	+	20.8810i	0.299842	+	0.922819i
$513$		0			0
$514$	4.20054	−	12.9279i	0.185278	−	0.570227i
$515$	3.93461	+	1.14597i	0.173379	+	0.0504975i
$516$		0			0
$517$	0.0912101	+	0.0406093i	0.00401141	+	0.00178600i
$518$	−17.9740	−	31.1318i	−0.789731	−	1.36785i
$519$		0			0
$520$	37.9492	+	11.0529i	1.66418	+	0.484700i
$521$	−5.09658	−	3.70289i	−0.223285	−	0.162226i	0.470519	−	0.882390i	$-0.344067\pi$
$521$	−5.09658	−	3.70289i	−0.223285	−	0.162226i	−0.693804	+	0.720164i	$0.744067\pi$
$522$		0			0
$523$	−6.61794	+	20.3679i	−0.289382	+	0.890628i	0.695668	+	0.718363i	$0.255108\pi$
$523$	−6.61794	+	20.3679i	−0.289382	+	0.890628i	−0.985051	+	0.172264i	$0.944892\pi$
$524$	0.0166756	−	0.0288831i	0.000728479	−	0.00126176i
$525$		0			0
$526$	−17.3243	−	30.0065i	−0.755374	−	1.30835i
$527$	12.3674	−	2.62878i	0.538734	−	0.114511i
$528$		0			0
$529$	−17.6326	+	7.85055i	−0.766636	+	0.341328i
$530$	−4.85439	−	0.359756i	−0.210861	−	0.0156268i
$531$		0			0
$532$	0.203324			0.00881520
$533$	−1.07087	−	10.1887i	−0.0463847	−	0.441321i
$534$		0			0
$535$	7.34286	−	40.6535i	0.317459	−	1.75760i
$536$	6.23825	−	1.32598i	0.269451	−	0.0572736i
$537$		0			0
$538$	−22.2954	−	4.73904i	−0.961224	−	0.204314i
$539$	−0.0116636	+	0.0358970i	−0.000502388	+	0.00154619i
$540$		0			0
$541$	2.06074	+	6.34232i	0.0885983	+	0.272678i	0.985533	−	0.169486i	$-0.0542109\pi$
$541$	2.06074	+	6.34232i	0.0885983	+	0.272678i	−0.896934	+	0.442164i	$0.854211\pi$
$542$	−2.13962	−	20.3572i	−0.0919047	−	0.874415i
$543$		0			0
$544$	0.654436	+	0.291374i	0.0280587	+	0.0124925i
$545$	−10.0137	+	1.36487i	−0.428939	+	0.0584644i
$546$		0			0
$547$	−28.9519	+	12.8902i	−1.23790	+	0.551147i	−0.918103	−	0.396341i	$-0.870280\pi$
$547$	−28.9519	+	12.8902i	−1.23790	+	0.551147i	−0.319792	+	0.947488i	$0.603613\pi$
$548$	0.130266	−	0.400917i	0.00556467	−	0.0171263i
$549$		0			0
$550$	−0.100553	+	0.201884i	−0.00428762	+	0.00860834i
$551$	−10.4754	+	18.1440i	−0.446269	+	0.772961i
$552$		0			0
$553$	0.231733	−	2.20479i	0.00985427	−	0.0937571i
$554$	−2.35573	+	22.4133i	−0.100085	+	0.952248i
$555$		0			0
$556$	0.000158598		0.00150896i	6.72606e−6		6.39942e-5i
$557$	23.0896			0.978337			0.489168	−	0.872189i	$-0.337300\pi$
$557$	23.0896			0.978337			0.489168	+	0.872189i	$0.337300\pi$
$558$		0			0
$559$	−21.7941	−	67.0755i	−0.921794	−	2.83699i
$560$	13.4412	+	17.3523i	0.567993	+	0.733267i
$561$		0			0
$562$	−1.41084	+	1.56689i	−0.0595125	+	0.0660953i
$563$	24.5755	−	27.2938i	1.03573	−	1.15030i	0.0472616	−	0.998883i	$-0.484951\pi$
$563$	24.5755	−	27.2938i	1.03573	−	1.15030i	0.988470	−	0.151414i	$-0.0483828\pi$
$564$		0			0
$565$	−5.10500	−	6.59045i	−0.214769	−	0.277262i
$566$	6.00856	+	18.4925i	0.252559	+	0.777296i
$567$		0			0
$568$	−12.5879			−0.528177
$569$	1.66757	+	15.8659i	0.0699083	+	0.665133i	0.972223	+	0.234055i	$0.0751997\pi$
$569$	1.66757	+	15.8659i	0.0699083	+	0.665133i	−0.902315	+	0.431077i	$0.858134\pi$
$570$		0			0
$571$	−0.299358	+	2.84820i	−0.0125277	+	0.119193i	−0.998998	−	0.0447439i	$-0.985753\pi$
$571$	−0.299358	+	2.84820i	−0.0125277	+	0.119193i	0.986471	+	0.163937i	$0.0524195\pi$
$572$	0.000785026	−	0.00746903i	3.28236e−5	−	0.000312296i
$573$		0			0
$574$	2.79192	−	4.83575i	0.116532	−	0.201840i
$575$	−9.51094	−	1.41749i	−0.396634	−	0.0591133i
$576$		0			0
$577$	2.14710	−	6.60811i	0.0893851	−	0.275099i	−0.896365	−	0.443318i	$-0.853801\pi$
$577$	2.14710	−	6.60811i	0.0893851	−	0.275099i	0.985750	+	0.168218i	$0.0538014\pi$
$578$	7.42120	−	3.30413i	0.308681	−	0.137434i
$579$		0			0
$580$	0.780251	−	0.106348i	0.0323982	−	0.00441587i
$581$	12.2381	+	5.44877i	0.507724	+	0.226053i
$582$		0			0
$583$	−0.00503725	−	0.0479262i	−0.000208622	−	0.00198490i
$584$	1.06561	+	3.27960i	0.0440951	+	0.135711i
$585$		0			0
$586$	7.17715	−	22.0890i	0.296485	−	0.912489i
$587$	0.784085	+	0.166662i	0.0323626	+	0.00687889i	0.224065	−	0.974574i	$-0.428067\pi$
$587$	0.784085	+	0.166662i	0.0323626	+	0.00687889i	−0.191702	+	0.981453i	$0.561401\pi$
$588$		0			0
$589$	−8.23998	+	1.75146i	−0.339522	+	0.0721677i
$590$	7.27619	−	40.2844i	0.299556	−	1.65848i
$591$		0			0
$592$	4.45073	+	42.3459i	0.182924	+	1.74041i
$593$	−19.9879			−0.820804			−0.410402	−	0.911905i	$-0.634612\pi$
$593$	−19.9879			−0.820804			−0.410402	+	0.911905i	$0.634612\pi$
$594$		0			0
$595$	−18.0689	−	1.33908i	−0.740754	−	0.0548969i
$596$	0.278511	−	0.124001i	0.0114082	−	0.00507928i
$597$		0			0
$598$	16.9455	−	3.60187i	0.692951	−	0.147291i
$599$	−1.80743	−	3.13056i	−0.0738495	−	0.127911i	0.826736	−	0.562590i	$-0.190195\pi$
$599$	−1.80743	−	3.13056i	−0.0738495	−	0.127911i	−0.900585	+	0.434679i	$0.856862\pi$
$600$		0			0
$601$	18.5936	−	32.2050i	0.758449	−	1.31367i	−0.185193	−	0.982702i	$-0.559291\pi$
$601$	18.5936	−	32.2050i	0.758449	−	1.31367i	0.943642	−	0.330969i	$-0.107376\pi$
$602$	11.8787	−	36.5589i	0.484140	−	1.49003i
$603$		0			0
$604$	−0.282332	−	0.205126i	−0.0114879	−	0.00834646i
$605$	23.6134	+	6.87748i	0.960019	+	0.279609i
$606$		0			0
$607$	−16.6597	−	28.8555i	−0.676197	−	1.17121i	−0.976117	−	0.217244i	$-0.930293\pi$
$607$	−16.6597	−	28.8555i	−0.676197	−	1.17121i	0.299920	−	0.953964i	$-0.403040\pi$
$608$	−0.436027	−	0.194132i	−0.0176832	−	0.00787309i
$609$		0			0
$610$	32.5486	+	9.47990i	1.31785	+	0.383830i
$611$	−6.16123	+	18.9623i	−0.249257	+	0.767134i
$612$		0			0
$613$	1.94595	+	5.98902i	0.0785962	+	0.241894i	0.982633	−	0.185561i	$-0.0594102\pi$
$613$	1.94595	+	5.98902i	0.0785962	+	0.241894i	−0.904037	+	0.427455i	$0.859410\pi$
$614$	−13.7073	−	15.2235i	−0.553181	−	0.614370i
$615$		0			0
$616$	−0.142711	+	0.158497i	−0.00575001	+	0.00638603i
$617$	−24.1693	−	10.7608i	−0.973018	−	0.433215i	−0.142248	−	0.989831i	$-0.545433\pi$
$617$	−24.1693	−	10.7608i	−0.973018	−	0.433215i	−0.830770	+	0.556616i	$0.812100\pi$
$618$		0			0
$619$	1.63835	+	15.5879i	0.0658508	+	0.626529i	0.976821	+	0.214057i	$0.0686678\pi$
$619$	1.63835	+	15.5879i	0.0658508	+	0.626529i	−0.910970	+	0.412472i	$0.864666\pi$
$620$	0.241703	+	0.204533i	0.00970701	+	0.00821423i
$621$		0			0
$622$	25.8570	+	18.7862i	1.03677	+	0.753260i
$623$	−4.86507	−	5.40320i	−0.194915	−	0.216475i
$624$		0			0
$625$	18.8810	+	16.3862i	0.755240	+	0.655448i
$626$	−17.4420	−	30.2105i	−0.697124	−	1.20745i
$627$		0			0
$628$	0.399486	−	0.177862i	0.0159412	−	0.00709748i
$629$	−28.4353	−	20.6595i	−1.13379	−	0.823748i
$630$		0			0
$631$	1.57126	−	1.14159i	0.0625508	−	0.0454458i	−0.556070	−	0.831135i	$-0.687692\pi$
$631$	1.57126	−	1.14159i	0.0625508	−	0.0454458i	0.618621	+	0.785689i	$0.287692\pi$
$632$	−1.28867	+	2.23204i	−0.0512604	+	0.0887856i
$633$		0			0
$634$	16.5221	−	18.3497i	0.656176	−	0.728758i
$635$	19.5125	+	10.4794i	0.774330	+	0.415861i
$636$		0			0
$637$	−7.37273	−	1.56712i	−0.292118	−	0.0620916i
$638$	0.130340	+	0.401144i	0.00516019	+	0.0158814i
$639$		0			0
$640$	−6.18236	−	25.2431i	−0.244379	−	0.997822i
$641$	16.3424	+	3.47368i	0.645484	+	0.137202i	0.519010	−	0.854768i	$-0.326301\pi$
$641$	16.3424	+	3.47368i	0.645484	+	0.137202i	0.126474	+	0.991970i	$0.459634\pi$
$642$		0			0
$643$	15.9436	+	27.6151i	0.628753	+	1.08903i	0.987802	+	0.155713i	$0.0497676\pi$
$643$	15.9436	+	27.6151i	0.628753	+	1.08903i	−0.359050	+	0.933319i	$0.616899\pi$
$644$	0.159434	+	0.0709846i	0.00628258	+	0.00279719i
$645$		0			0
$646$	9.82589	−	4.37477i	0.386595	−	0.172123i
$647$	−16.4808	−	11.9740i	−0.647928	−	0.470747i	0.214637	−	0.976694i	$-0.431143\pi$
$647$	−16.4808	−	11.9740i	−0.647928	−	0.470747i	−0.862565	+	0.505947i	$0.831143\pi$
$648$		0			0
$649$	0.405268			0.0159082
$650$	−42.1937	−	15.7561i	−1.65497	−	0.618007i
$651$		0			0
$652$	0.221312	−	0.0470412i	0.00866723	−	0.00184228i
$653$	3.91951	−	37.2917i	0.153382	−	1.45934i	−0.599074	−	0.800694i	$-0.704464\pi$
$653$	3.91951	−	37.2917i	0.153382	−	1.45934i	0.752456	−	0.658642i	$-0.228869\pi$
$654$		0			0
$655$	1.11409	−	1.63698i	0.0435312	−	0.0639620i
$656$	−5.35073	+	3.88754i	−0.208911	+	0.151783i
$657$		0			0
$658$	−8.79169	+	6.38754i	−0.342736	+	0.249012i
$659$	24.0150	+	5.10455i	0.935492	+	0.198845i	0.650345	−	0.759639i	$-0.274624\pi$
$659$	24.0150	+	5.10455i	0.935492	+	0.198845i	0.285147	+	0.958484i	$0.407958\pi$
$660$		0			0
$661$	6.52118	−	1.38612i	0.253645	−	0.0539138i	−0.0793344	−	0.996848i	$-0.525279\pi$
$661$	6.52118	−	1.38612i	0.253645	−	0.0539138i	0.332979	+	0.942934i	$0.391946\pi$
$662$	25.0393	−	27.8090i	0.973181	−	1.08083i
$663$		0			0
$664$	−10.4211	−	11.5738i	−0.404418	−	0.449151i
$665$	12.0387	+	0.892180i	0.466840	+	0.0345973i
$666$		0			0
$667$	−14.5487	+	10.5702i	−0.563327	+	0.409281i
$668$	0.254622	−	0.441018i	0.00985162	−	0.0170635i
$669$		0			0
$670$	−7.20066	+	0.981450i	−0.278186	+	0.0379167i
$671$	−0.0350818	+	0.333781i	−0.00135432	+	0.0128855i
$672$		0			0
$673$	8.06200	+	8.95376i	0.310767	+	0.345142i	0.878214	−	0.478268i	$-0.158735\pi$
$673$	8.06200	+	8.95376i	0.310767	+	0.345142i	−0.567446	+	0.823410i	$0.692069\pi$
$674$	−23.0492			−0.887822
$675$		0			0
$676$	1.01015			0.0388521
$677$	16.8244	+	18.6854i	0.646613	+	0.718137i	0.973948	−	0.226772i	$-0.0728172\pi$
$677$	16.8244	+	18.6854i	0.646613	+	0.718137i	−0.327335	+	0.944908i	$0.606151\pi$
$678$		0			0
$679$	−2.61773	+	24.9060i	−0.100459	+	0.955804i
$680$	18.5570	+	9.96623i	0.711630	+	0.382187i
$681$		0			0
$682$	−0.0847974	+	0.146873i	−0.00324706	+	0.00562408i
$683$	−29.2073	+	21.2203i	−1.11758	+	0.811973i	−0.983841	−	0.179043i	$-0.942700\pi$
$683$	−29.2073	+	21.2203i	−1.11758	+	0.811973i	−0.133743	+	0.991016i	$0.542700\pi$
$684$		0			0
$685$	9.47217	−	23.1664i	0.361913	−	0.885144i
$686$	−18.8590	−	20.9450i	−0.720039	−	0.799685i
$687$		0			0
$688$	−30.4664	+	33.8363i	−1.16152	+	1.29000i
$689$	9.41317	−	2.00083i	0.358613	−	0.0762256i
$690$		0			0
$691$	−7.37700	−	1.56803i	−0.280634	−	0.0596506i	0.0654442	−	0.997856i	$-0.479154\pi$
$691$	−7.37700	−	1.56803i	−0.280634	−	0.0596506i	−0.346078	+	0.938206i	$0.612487\pi$
$692$	−0.206141	+	0.149770i	−0.00783629	+	0.00569340i
$693$		0			0
$694$	21.6515	−	15.7308i	0.821881	−	0.597131i
$695$	0.00276922	+	0.0900406i	0.000105042	+	0.00341544i
$696$		0			0
$697$	0.570682	−	5.42968i	0.0216161	−	0.205664i
$698$	2.51215	−	0.533974i	0.0950862	−	0.0202112i
$699$		0			0
$700$	−0.250583	−	0.378257i	−0.00947115	−	0.0142968i
$701$	41.9293			1.58365			0.791824	−	0.610749i	$-0.209132\pi$
$701$	41.9293			1.58365			0.791824	+	0.610749i	$0.209132\pi$
$702$		0			0
$703$	18.9454	+	13.7647i	0.714541	+	0.519144i
$704$	0.226433	−	0.100814i	0.00853400	−	0.00379958i
$705$		0			0
$706$	−2.39447	−	1.06609i	−0.0901172	−	0.0401228i
$707$	6.60415	+	11.4387i	0.248375	+	0.430197i
$708$		0			0
$709$	0.535037	+	0.113726i	0.0200937	+	0.00427105i	0.217948	−	0.975960i	$-0.430064\pi$
$709$	0.535037	+	0.113726i	0.0200937	+	0.00427105i	−0.197854	+	0.980232i	$0.563397\pi$
$710$	14.3046	+	1.06011i	0.536842	+	0.0397851i
$711$		0			0
$712$	2.61203	+	8.03900i	0.0978899	+	0.301274i
$713$	−7.07276	−	1.50336i	−0.264877	−	0.0563014i
$714$		0			0
$715$	0.0792549	−	0.438792i	0.00296397	−	0.0164099i
$716$	0.181404	−	0.201469i	0.00677937	−	0.00752925i
$717$		0			0
$718$	25.0638	−	43.4117i	0.935371	−	1.62011i
$719$	23.1267	−	16.8026i	0.862482	−	0.626630i	−0.0660771	−	0.997815i	$-0.521048\pi$
$719$	23.1267	−	16.8026i	0.862482	−	0.626630i	0.928559	+	0.371185i	$0.121048\pi$
$720$		0			0
$721$	−3.57254	−	2.59560i	−0.133048	−	0.0966651i
$722$	18.2304	−	8.11671i	0.678466	−	0.302073i
$723$		0			0
$724$	−0.129620	−	0.224508i	−0.00481728	−	0.00834378i
$725$	46.6649	−	2.87309i	1.73309	−	0.106704i
$726$		0			0
$727$	26.0768	+	28.9613i	0.967136	+	1.07411i	0.997216	+	0.0745661i	$0.0237572\pi$
$727$	26.0768	+	28.9613i	0.967136	+	1.07411i	−0.0300799	+	0.999547i	$0.509576\pi$
$728$	−34.4571	−	25.0345i	−1.27706	−	0.927841i
$729$		0			0
$730$	−0.934734	−	3.81660i	−0.0345960	−	0.141259i
$731$	−3.92869	−	37.3790i	−0.145308	−	1.38251i
$732$		0			0
$733$	9.18772	+	4.09063i	0.339356	+	0.151091i	0.569337	−	0.822104i	$-0.307200\pi$
$733$	9.18772	+	4.09063i	0.339356	+	0.151091i	−0.229981	+	0.973195i	$0.573867\pi$
$734$	−22.9649	+	25.5051i	−0.847648	+	0.941409i
$735$		0			0
$736$	−0.274131	−	0.304453i	−0.0101046	−	0.0112223i
$737$	−0.0222324	−	0.0684244i	−0.000818942	−	0.00252044i
$738$		0			0
$739$	−12.4137	+	38.2054i	−0.456645	+	1.40541i	0.412548	+	0.910936i	$0.364639\pi$
$739$	−12.4137	+	38.2054i	−0.456645	+	1.40541i	−0.869193	+	0.494473i	$0.835361\pi$
$740$	−0.0270576	−	0.879773i	−0.000994656	−	0.0323411i
$741$		0			0
$742$	4.79172	+	2.13341i	0.175909	+	0.0783199i
$743$	−6.57831	−	11.3940i	−0.241335	−	0.418004i	0.719760	−	0.694223i	$-0.244252\pi$
$743$	−6.57831	−	11.3940i	−0.241335	−	0.418004i	−0.961095	+	0.276219i	$0.910919\pi$
$744$		0			0
$745$	17.0346	−	6.11993i	0.624099	−	0.224217i
$746$	2.32911	+	1.69220i	0.0852747	+	0.0619557i
$747$		0			0
$748$	0.00123677	−	0.00380638i	4.52207e−5	−	0.000139175i
$749$	−22.2575	+	38.5511i	−0.813270	+	1.40863i
$750$		0			0
$751$	6.07148	+	10.5161i	0.221552	+	0.383738i	0.955279	−	0.295705i	$-0.0955546\pi$
$751$	6.07148	+	10.5161i	0.221552	+	0.383738i	−0.733728	+	0.679444i	$0.762221\pi$
$752$	12.5905	−	2.67619i	0.459127	−	0.0975905i
$753$		0			0
$754$	−76.9478	+	34.2594i	−2.80228	+	1.24765i
$755$	−15.8166	−	13.3843i	−0.575625	−	0.487103i
$756$		0			0
$757$	−10.4368			−0.379330			−0.189665	−	0.981849i	$-0.560740\pi$
$757$	−10.4368			−0.379330			−0.189665	+	0.981849i	$0.560740\pi$
$758$	2.81311	+	26.7650i	0.102177	+	0.972148i
$759$		0			0
$760$	−12.3639	−	6.64014i	−0.448485	−	0.240863i
$761$	−3.64738	+	0.775275i	−0.132218	+	0.0281037i	−0.273545	−	0.961859i	$-0.588196\pi$
$761$	−3.64738	+	0.775275i	−0.132218	+	0.0281037i	0.141328	+	0.989963i	$0.454863\pi$
$762$		0			0
$763$	10.6520	+	2.26416i	0.385630	+	0.0819681i
$764$	−0.131433	+	0.404508i	−0.00475507	+	0.0146346i
$765$		0			0
$766$	4.88115	+	15.0226i	0.176363	+	0.542790i
$767$	8.45960	+	80.4877i	0.305458	+	2.90624i
$768$		0			0
$769$	−28.2623	−	12.5832i	−1.01916	−	0.453761i	−0.172003	−	0.985097i	$-0.555024\pi$
$769$	−28.2623	−	12.5832i	−1.01916	−	0.453761i	−0.847162	+	0.531335i	$0.821690\pi$
$770$	0.175522	−	0.168094i	0.00632537	−	0.00605767i
$771$		0			0
$772$	−0.768058	+	0.341961i	−0.0276430	+	0.0123075i
$773$	1.07567	−	3.31057i	0.0386891	−	0.119073i	−0.929847	−	0.367947i	$-0.880061\pi$
$773$	1.07567	−	3.31057i	0.0386891	−	0.119073i	0.968536	+	0.248874i	$0.0800607\pi$
$774$		0			0
$775$	13.4136	+	13.1708i	0.481830	+	0.473111i
$776$	14.5572	−	25.2138i	0.522572	−	0.905122i
$777$		0			0
$778$	3.22900	−	30.7219i	0.115765	−	1.10143i
$779$	−0.380225	+	3.61760i	−0.0136230	+	0.129614i
$780$		0			0
$781$	0.0148434	+	0.141226i	0.000531140	+	0.00505346i
$782$	9.23220			0.330143
$783$		0			0
$784$	1.50369	+	4.62788i	0.0537032	+	0.165282i
$785$	24.4338	−	8.77820i	0.872078	−	0.313307i
$786$		0			0
$787$	31.5111	−	34.9966i	1.12325	−	1.24749i	0.157640	−	0.987497i	$-0.449612\pi$
$787$	31.5111	−	34.9966i	1.12325	−	1.24749i	0.965609	−	0.259998i	$-0.0837218\pi$
$788$	−0.660268	+	0.733301i	−0.0235211	+	0.0261228i
$789$		0			0
$790$	1.65238	−	2.42790i	0.0587891	−	0.0863810i
$791$	2.77585	+	8.54319i	0.0986979	+	0.303761i
$792$		0			0
$793$	−67.0224			−2.38004
$794$	−1.18501	−	11.2746i	−0.0420545	−	0.400122i
$795$		0			0
$796$	0.0653872	−	0.622117i	0.00231759	−	0.0220504i
$797$	−3.29146	+	31.3161i	−0.116589	+	1.10927i	0.767206	+	0.641401i	$0.221646\pi$
$797$	−3.29146	+	31.3161i	−0.116589	+	1.10927i	−0.883795	+	0.467873i	$0.845020\pi$
$798$		0			0
$799$	−5.31265	+	9.20178i	−0.187948	+	0.325536i
$800$	0.176218	+	1.05043i	0.00623024	+	0.0371382i
$801$		0			0
$802$	−5.53334	+	17.0299i	−0.195389	+	0.601345i
$803$	0.0355378	−	0.0158225i	0.00125410	−	0.000558363i
$804$		0			0
$805$	9.12852	+	4.90255i	0.321738	+	0.172792i
$806$	−30.9397	−	13.7752i	−1.08980	−	0.485211i
$807$		0			0
$808$	−1.60509	−	15.2714i	−0.0564669	−	0.537246i
$809$	8.49171	+	26.1348i	0.298553	+	0.918851i	0.982005	+	0.188856i	$0.0604778\pi$
$809$	8.49171	+	26.1348i	0.298553	+	0.918851i	−0.683452	+	0.729995i	$0.739522\pi$
$810$		0			0
$811$	−2.41545	+	7.43400i	−0.0848180	+	0.261043i	−0.984467	−	0.175572i	$-0.943823\pi$
$811$	−2.41545	+	7.43400i	−0.0848180	+	0.261043i	0.899649	+	0.436615i	$0.143823\pi$
$812$	−0.829990	−	0.176420i	−0.0291269	−	0.00619112i
$813$		0			0
$814$	0.461150	−	0.0980206i	0.0161633	−	0.00343562i
$815$	13.3101	−	1.81417i	0.466234	−	0.0635477i
$816$		0			0
$817$	2.61755	+	24.9043i	0.0915764	+	0.871291i
$818$	6.33407			0.221466
$819$		0			0
$820$	0.116246	−	0.0719679i	0.00405950	−	0.00251323i
$821$	19.5212	−	8.69141i	0.681295	−	0.303332i	−0.0367542	−	0.999324i	$-0.511702\pi$
$821$	19.5212	−	8.69141i	0.681295	−	0.303332i	0.718049	+	0.695992i	$0.245035\pi$
$822$		0			0
$823$	30.8456	−	6.55643i	1.07521	−	0.228543i	0.363911	−	0.931434i	$-0.381441\pi$
$823$	30.8456	−	6.55643i	1.07521	−	0.228543i	0.711298	+	0.702891i	$0.248108\pi$
$824$	2.56689	+	4.44598i	0.0894217	+	0.154883i
$825$		0			0
$826$	−22.0554	+	38.2010i	−0.767405	+	1.32918i
$827$	−0.0456076	+	0.140366i	−0.00158593	+	0.00488099i	−0.951846	−	0.306575i	$-0.900817\pi$
$827$	−0.0456076	+	0.140366i	−0.00158593	+	0.00488099i	0.950260	+	0.311456i	$0.100817\pi$
$828$		0			0
$829$	−31.5635	−	22.9322i	−1.09625	−	0.796469i	−0.115802	−	0.993272i	$-0.536944\pi$
$829$	−31.5635	−	22.9322i	−1.09625	−	0.796469i	−0.980443	+	0.196803i	$0.936944\pi$
$830$	10.8676	+	14.0298i	0.377220	+	0.486982i
$831$		0			0
$832$	24.7486	+	42.8659i	0.858005	+	1.48611i
$833$	−3.66953	−	1.63378i	−0.127142	−	0.0566071i
$834$		0			0
$835$	17.0112	−	24.9952i	0.588697	−	0.864993i
$836$	−0.000824014		0.00253605i	−2.84991e−5		8.77112e-5i
$837$		0			0
$838$	−3.23698	−	9.96239i	−0.111819	−	0.344145i
$839$	−25.7166	−	28.5612i	−0.887836	−	0.986042i	0.112135	−	0.993693i	$-0.464231\pi$
$839$	−25.7166	−	28.5612i	−0.887836	−	0.986042i	−0.999971	+	0.00765121i	$0.997565\pi$
$840$		0			0
$841$	39.1003	−	43.4253i	1.34829	−	1.49743i
$842$	10.2086	+	4.54515i	0.351811	+	0.156636i
$843$		0			0
$844$	0.0378798	+	0.360402i	0.00130388	+	0.0124056i
$845$	59.8106	+	4.43254i	2.05755	+	0.152484i
$846$		0			0
$847$	−21.4404	−	15.5774i	−0.736701	−	0.535244i
$848$	−4.15714	−	4.61697i	−0.142757	−	0.158547i
$849$		0			0
$850$	−20.2485	−	12.8882i	−0.694516	−	0.442061i
$851$	10.0503	+	17.4077i	0.344521	+	0.596728i
$852$		0			0
$853$	−27.6057	+	12.2909i	−0.945202	+	0.420831i	−0.820681	−	0.571386i	$-0.806406\pi$
$853$	−27.6057	+	12.2909i	−0.945202	+	0.420831i	−0.124520	+	0.992217i	$0.539739\pi$
$854$	−29.5534	−	21.4718i	−1.01130	−	0.734750i
$855$		0			0
$856$	41.8679	−	30.4188i	1.43102	−	1.03969i
$857$	3.63200	−	6.29081i	0.124067	−	0.214890i	−0.797301	−	0.603582i	$-0.793740\pi$
$857$	3.63200	−	6.29081i	0.124067	−	0.214890i	0.921368	+	0.388692i	$0.127073\pi$
$858$		0			0
$859$	−21.0773	+	23.4088i	−0.719149	+	0.798696i	−0.986301	−	0.164958i	$-0.947251\pi$
$859$	−21.0773	+	23.4088i	−0.719149	+	0.798696i	0.267151	+	0.963655i	$0.413918\pi$
$860$	0.679768	−	0.651000i	0.0231799	−	0.0221989i
$861$		0			0
$862$	17.6085	+	3.74281i	0.599749	+	0.127481i
$863$	14.1918	+	43.6780i	0.483096	+	1.48682i	0.834719	+	0.550675i	$0.185630\pi$
$863$	14.1918	+	43.6780i	0.483096	+	1.48682i	−0.351623	+	0.936142i	$0.614370\pi$
$864$		0			0
$865$	−12.8627	+	7.96325i	−0.437344	+	0.270759i
$866$	−52.3705	−	11.1317i	−1.77962	−	0.378270i
$867$		0			0
$868$	−0.170591	−	0.295473i	−0.00579025	−	0.0100290i
$869$	0.0265612	+	0.0118258i	0.000901025	+	0.000401162i
$870$		0			0
$871$	13.1252	−	5.84373i	0.444732	−	0.198007i
$872$	−10.2424	−	7.44158i	−0.346853	−	0.252004i
$873$		0			0
$874$	−6.15108			−0.208063
$875$	−13.1771	−	23.4959i	−0.445467	−	0.794308i
$876$		0			0
$877$	−15.3320	+	3.25891i	−0.517724	+	0.110046i	−0.459361	−	0.888250i	$-0.651922\pi$
$877$	−15.3320	+	3.25891i	−0.517724	+	0.110046i	−0.0583633	+	0.998295i	$0.518588\pi$
$878$	5.20604	−	49.5321i	0.175695	−	1.67163i
$879$		0			0
$880$	−0.270908	+	0.0973277i	−0.00913230	+	0.00328091i
$881$	−36.7061	+	26.6685i	−1.23666	+	0.898486i	−0.997371	−	0.0724624i	$-0.976914\pi$
$881$	−36.7061	+	26.6685i	−1.23666	+	0.898486i	−0.239289	+	0.970948i	$0.576914\pi$
$882$		0			0
$883$	2.12115	−	1.54110i	0.0713823	−	0.0518623i	−0.551522	−	0.834160i	$-0.685953\pi$
$883$	2.12115	−	1.54110i	0.0713823	−	0.0518623i	0.622904	+	0.782298i	$0.285953\pi$
$884$	0.781777	+	0.166172i	0.0262940	+	0.00558896i
$885$		0			0
$886$	−34.2845	+	7.28739i	−1.15181	+	0.244825i
$887$	−21.0513	+	23.3798i	−0.706833	+	0.785017i	−0.984448	−	0.175675i	$-0.943789\pi$
$887$	−21.0513	+	23.3798i	−0.706833	+	0.785017i	0.277615	+	0.960692i	$0.410456\pi$
$888$		0			0
$889$	−15.9695	−	17.7359i	−0.535600	−	0.594844i
$890$	−2.29123	−	9.35530i	−0.0768023	−	0.313590i
$891$		0			0
$892$	0.789632	−	0.573701i	0.0264388	−	0.0192089i
$893$	3.53963	−	6.13082i	0.118449	−	0.205160i
$894$		0			0
$895$	11.6248	−	11.1329i	0.388576	−	0.372131i
$896$	−2.92728	+	27.8512i	−0.0977935	+	0.930443i
$897$		0			0
$898$	5.44205	+	6.04401i	0.181604	+	0.201691i
$899$	35.1562			1.17253
$900$		0			0
$901$	5.12847			0.170854
$902$	0.0490013	+	0.0544215i	0.00163157	+	0.00181204i
$903$		0			0
$904$	1.09161	−	10.3859i	0.0363063	−	0.345431i
$905$	−6.68957	−	13.8618i	−0.222369	−	0.460780i
$906$		0			0
$907$	19.4248	−	33.6448i	0.644991	−	1.11716i	−0.339312	−	0.940674i	$-0.610194\pi$
$907$	19.4248	−	33.6448i	0.644991	−	1.11716i	0.984304	−	0.176484i	$-0.0564724\pi$
$908$	0.614632	−	0.446556i	0.0203973	−	0.0148195i
$909$		0			0
$910$	37.0478	+	31.3505i	1.22812	+	1.03926i
$911$	16.0647	+	17.8417i	0.532248	+	0.591121i	0.947966	−	0.318373i	$-0.103136\pi$
$911$	16.0647	+	17.8417i	0.532248	+	0.591121i	−0.415718	+	0.909494i	$0.636470\pi$
$912$		0			0
$913$	−0.117560	+	0.130564i	−0.00389067	+	0.00432103i
$914$	41.8624	−	8.89812i	1.38468	−	0.294324i
$915$		0			0
$916$	0.256371	+	0.0544934i	0.00847074	+	0.00180051i
$917$	−1.72619	+	1.25415i	−0.0570037	+	0.0414156i
$918$		0			0
$919$	34.1266	−	24.7944i	1.12573	−	0.817892i	0.140664	−	0.990057i	$-0.455076\pi$
$919$	34.1266	−	24.7944i	1.12573	−	0.817892i	0.985068	+	0.172165i	$0.0550762\pi$
$920$	−7.37680	−	9.52329i	−0.243206	−	0.313974i
$921$		0			0
$922$	0.741042	−	7.05054i	0.0244049	−	0.232197i
$923$	−27.7381	+	5.89592i	−0.913012	+	0.194067i
$924$		0			0
$925$	2.25836	−	52.2096i	0.0742545	−	1.71664i
$926$	−16.3264			−0.536519
$927$		0			0
$928$	1.61147	+	1.17080i	0.0528990	+	0.0384334i
$929$	−3.60542	+	1.60523i	−0.118290	+	0.0526660i	−0.465028	−	0.885296i	$-0.653956\pi$
$929$	−3.60542	+	1.60523i	−0.118290	+	0.0526660i	0.346738	+	0.937962i	$0.387289\pi$
$930$		0			0
$931$	2.44487	+	1.08853i	0.0801275	+	0.0356751i
$932$	0.531655	+	0.920854i	0.0174149	+	0.0301636i
$933$		0			0
$934$	36.7309	+	7.80738i	1.20187	+	0.255465i
$935$	0.0899306	−	0.219947i	0.00294105	−	0.00719302i
$936$		0			0
$937$	9.87834	+	30.4024i	0.322711	+	0.993204i	0.972463	+	0.233057i	$0.0748729\pi$
$937$	9.87834	+	30.4024i	0.322711	+	0.993204i	−0.649752	+	0.760147i	$0.725127\pi$
$938$	7.65968	+	1.62812i	0.250097	+	0.0531599i
$939$		0			0
$940$	−0.263645	+	0.0359348i	−0.00859915	+	0.00117206i
$941$	−9.66246	+	10.7313i	−0.314987	+	0.349829i	−0.879760	−	0.475417i	$-0.842297\pi$
$941$	−9.66246	+	10.7313i	−0.314987	+	0.349829i	0.564773	+	0.825246i	$0.308964\pi$
$942$		0			0
$943$	−1.56113	+	2.70396i	−0.0508374	+	0.0880529i
$944$	42.2693	−	30.7104i	1.37575	−	0.999540i
$945$		0			0
$946$	0.407858	+	0.296326i	0.0132606	+	0.00963439i
$947$	−43.6238	+	19.4226i	−1.41758	+	0.631149i	−0.965399	−	0.260776i	$-0.916022\pi$
$947$	−43.6238	+	19.4226i	−1.41758	+	0.631149i	−0.452184	+	0.891925i	$0.649355\pi$
$948$		0			0
$949$	3.88422	+	6.72766i	0.126087	+	0.218389i
$950$	13.4908	+	8.58693i	0.437700	+	0.278597i
$951$		0			0
$952$	−15.1875	−	16.8675i	−0.492231	−	0.546678i
$953$	14.1198	+	10.2587i	0.457387	+	0.332311i	0.792505	−	0.609865i	$-0.208776\pi$
$953$	14.1198	+	10.2587i	0.457387	+	0.332311i	−0.335119	+	0.942176i	$0.608776\pi$
$954$		0			0
$955$	−9.55702	+	23.3740i	−0.309258	+	0.756364i
$956$	0.0175083	+	0.166580i	0.000566259	+	0.00538760i
$957$		0			0
$958$	0.610405	+	0.271770i	0.0197213	+	0.00878048i
$959$	−18.0458	+	20.0419i	−0.582729	+	0.647186i
$960$		0			0
$961$	−11.2843	−	12.5325i	−0.364011	−	0.404275i
$962$	29.0933	+	89.5400i	0.938006	+	2.88689i
$963$		0			0
$964$	0.176536	−	0.543321i	0.00568583	−	0.0174992i
$965$	−46.9768	+	16.8771i	−1.51224	+	0.543294i
$966$		0			0
$967$	23.4521	+	10.4416i	0.754170	+	0.335778i	0.747555	−	0.664200i	$-0.231228\pi$
$967$	23.4521	+	10.4416i	0.754170	+	0.335778i	0.00661483	+	0.999978i	$0.497894\pi$
$968$	15.4051	+	26.6823i	0.495137	+	0.857603i
$969$		0			0
$970$	−18.6658	+	27.4264i	−0.599324	+	0.880608i
$971$	0.505556	+	0.367308i	0.0162241	+	0.0117875i	0.595868	−	0.803083i	$-0.296808\pi$
$971$	0.505556	+	0.367308i	0.0162241	+	0.0117875i	−0.579644	+	0.814870i	$0.696808\pi$
$972$		0			0
$973$	0.0299960	−	0.0923182i	0.000961627	−	0.00295958i
$974$	3.59933	−	6.23422i	0.115330	−	0.199757i
$975$		0			0
$976$	21.6343	+	37.4717i	0.692497	+	1.19944i
$977$	−36.0526	+	7.66322i	−1.15342	+	0.245168i	−0.744642	−	0.667464i	$-0.767380\pi$
$977$	−36.0526	+	7.66322i	−1.15342	+	0.245168i	−0.408783	+	0.912632i	$0.634047\pi$
$978$		0			0
$979$	0.0871108	−	0.0387842i	0.00278407	−	0.00123955i
$980$	−0.0239286	−	0.0977025i	−0.000764371	−	0.00312099i
$981$		0			0
$982$	−10.7290			−0.342375
$983$	−2.98616	−	28.4114i	−0.0952436	−	0.906182i	−0.932937	−	0.360041i	$-0.882763\pi$
$983$	−2.98616	−	28.4114i	−0.0952436	−	0.906182i	0.837693	−	0.546141i	$-0.183904\pi$
$984$		0			0
$985$	−42.3118	+	40.5211i	−1.34817	+	1.29111i
$986$	−43.9063	+	9.33257i	−1.39826	+	0.297210i
$987$		0			0
$988$	−0.520870	−	0.110714i	−0.0165711	−	0.00352229i
$989$	−6.64210	+	20.4423i	−0.211206	+	0.650027i
$990$		0			0
$991$	18.1246	+	55.7817i	0.575746	+	1.77196i	0.633626	+	0.773639i	$0.281566\pi$
$991$	18.1246	+	55.7817i	0.575746	+	1.77196i	−0.0578809	+	0.998323i	$0.518434\pi$
$992$	0.0837177	+	0.796521i	0.00265804	+	0.0252896i
$993$		0			0
$994$	−14.1199	−	6.28659i	−0.447857	−	0.199399i
$995$	6.60137	−	36.5483i	0.209278	−	1.15866i
$996$		0			0
$997$	−45.5343	+	20.2732i	−1.44209	+	0.642058i	−0.970793	−	0.239919i	$-0.922879\pi$
$997$	−45.5343	+	20.2732i	−1.44209	+	0.642058i	−0.471293	+	0.881977i	$0.656213\pi$
$998$	3.57766	−	11.0109i	0.113249	−	0.348544i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.46.8		224
3.2	odd	2		225.2.q.a.196.21	yes	224
9.4	even	3	inner	675.2.r.a.496.21		224
9.5	odd	6		225.2.q.a.121.8	yes	224
25.6	even	5	inner	675.2.r.a.181.21		224
75.56	odd	10		225.2.q.a.106.8	yes	224
225.31	even	15	inner	675.2.r.a.631.8		224
225.131	odd	30		225.2.q.a.31.21	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.21	✓	224	225.131	odd	30
225.2.q.a.106.8	yes	224	75.56	odd	10
225.2.q.a.121.8	yes	224	9.5	odd	6
225.2.q.a.196.21	yes	224	3.2	odd	2
675.2.r.a.46.8		224	1.1	even	1	trivial
675.2.r.a.181.21		224	25.6	even	5	inner
675.2.r.a.496.21		224	9.4	even	3	inner
675.2.r.a.631.8		224	225.31	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.955162 - 1.06081i) q^{2} +(-0.00393676 + 0.0374558i) q^{4} +(-0.397449 + 2.20046i) q^{5} +(1.20474 - 2.08666i) q^{7} +(-2.26620 + 1.64649i) q^{8} +(2.71391 - 1.68018i) q^{10} +(0.0211445 + 0.0234833i) q^{11} +(-4.22250 + 4.68956i) q^{13} +(-3.36428 + 0.715100i) q^{14} +(3.98488 + 0.847013i) q^{16} +(-2.72065 + 1.97667i) q^{17} +(1.81267 - 1.31698i) q^{19} +(-0.0808554 - 0.0235495i) q^{20} +(0.00471506 - 0.0448608i) q^{22} +(1.88117 - 0.399856i) q^{23} +(-4.68407 - 1.74914i) q^{25} +9.00793 q^{26} +(0.0734149 + 0.0533391i) q^{28} +(-8.54224 + 3.80325i) q^{29} +(-3.43471 - 1.52923i) q^{31} +(-0.106511 - 0.184482i) q^{32} +(4.69554 + 0.998067i) q^{34} +(4.11281 + 3.48032i) q^{35} +(3.22975 + 9.94014i) q^{37} +(-3.12847 - 0.664976i) q^{38} +(-2.72234 - 5.64107i) q^{40} +(-1.08631 + 1.20647i) q^{41} +(-5.58816 + 9.67898i) q^{43} +(-0.000962828 + 0.000699535i) q^{44} +(-2.22100 - 1.61365i) q^{46} +(2.88640 - 1.28511i) q^{47} +(0.597221 + 1.03442i) q^{49} +(2.61853 + 6.63964i) q^{50} +(-0.159028 - 0.176619i) q^{52} +(-1.23376 - 0.896379i) q^{53} +(-0.0600780 + 0.0371942i) q^{55} +(0.705499 + 6.71237i) q^{56} +(12.1938 + 5.42901i) q^{58} +(8.58158 - 9.53081i) q^{59} +(7.10677 + 7.89287i) q^{61} +(1.65848 + 5.10426i) q^{62} +(2.42385 - 7.45983i) q^{64} +(-8.64097 - 11.1553i) q^{65} +(-2.07993 - 0.926044i) q^{67} +(-0.0633271 - 0.109686i) q^{68} +(-0.236421 - 7.68719i) q^{70} +(3.63556 + 2.64139i) q^{71} +(0.380414 - 1.17080i) q^{73} +(7.45971 - 12.9206i) q^{74} +(0.0421926 + 0.0730797i) q^{76} +(0.0744753 - 0.0158302i) q^{77} +(0.840545 - 0.374235i) q^{79} +(-3.44761 + 8.43194i) q^{80} +2.31745 q^{82} +(0.581163 + 5.52940i) q^{83} +(-3.26826 - 6.77231i) q^{85} +(15.6052 - 3.31699i) q^{86} +(-0.0865826 - 0.0184037i) q^{88} +(0.932477 - 2.86987i) q^{89} +(4.69854 + 14.4606i) q^{91} +(0.00757118 + 0.0720350i) q^{92} +(-4.12024 - 1.83445i) q^{94} +(2.17753 + 4.51214i) q^{95} +(-9.49506 + 4.22747i) q^{97} +(0.526882 - 1.62158i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

L-functions

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