LMFDB - Embedded newform 342.2.bf.c.257.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(155,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([3, 13]))

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

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

chi := DirichletCharacter("342.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.bf (of order $18$, degree $6$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			257.5
Character	$\chi$	$=$	342.257
Dual form			342.2.bf.c.173.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(-0.115449 - 1.72820i) q^{3} +(0.173648 - 0.984808i) q^{4} +(1.78747 + 2.13022i) q^{5} +(1.19930 + 1.24967i) q^{6} +1.17514 q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.97334 + 0.399038i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.115449 - 1.72820i) q^{3} +(0.173648 - 0.984808i) q^{4} +(1.78747 + 2.13022i) q^{5} +(1.19930 + 1.24967i) q^{6} +1.17514 q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.97334 + 0.399038i) q^{9} +(-2.73856 - 0.482882i) q^{10} +(3.35969 + 1.93972i) q^{11} +(-1.72199 - 0.186403i) q^{12} +(0.457354 + 1.25657i) q^{13} +(-0.900213 + 0.755368i) q^{14} +(3.47508 - 3.33503i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-4.02985 + 0.710571i) q^{17} +(2.02122 - 2.21691i) q^{18} +(1.86865 - 3.93804i) q^{19} +(2.40825 - 1.39040i) q^{20} +(-0.135669 - 2.03088i) q^{21} +(-3.82049 + 0.673656i) q^{22} +(7.57361 + 1.33543i) q^{23} +(1.43894 - 0.964081i) q^{24} +(-0.474558 + 2.69135i) q^{25} +(-1.15806 - 0.668607i) q^{26} +(1.03289 + 5.09246i) q^{27} +(0.204062 - 1.15729i) q^{28} +(9.53825 - 3.47164i) q^{29} +(-0.518351 + 4.78852i) q^{30} +(-4.31744 + 2.49268i) q^{31} +(0.939693 - 0.342020i) q^{32} +(2.96434 - 6.03014i) q^{33} +(2.63030 - 3.13467i) q^{34} +(2.10053 + 2.50332i) q^{35} +(-0.123340 + 2.99746i) q^{36} -5.90890i q^{37} +(1.09985 + 4.21786i) q^{38} +(2.11880 - 0.935469i) q^{39} +(-0.951091 + 2.61310i) q^{40} +(-0.345350 - 1.95858i) q^{41} +(1.40936 + 1.46854i) q^{42} +(0.327752 + 1.85878i) q^{43} +(2.49365 - 2.97182i) q^{44} +(-6.16479 - 5.62061i) q^{45} +(-6.66012 + 3.84522i) q^{46} +(2.20531 + 6.05904i) q^{47} +(-0.482592 + 1.66346i) q^{48} -5.61904 q^{49} +(-1.36644 - 2.36674i) q^{50} +(1.69325 + 6.88235i) q^{51} +(1.31690 - 0.232205i) q^{52} +(-7.76367 + 2.82574i) q^{53} +(-4.06461 - 3.23712i) q^{54} +(1.87331 + 10.6240i) q^{55} +(0.587572 + 1.01770i) q^{56} +(-7.02145 - 2.77476i) q^{57} +(-5.07520 + 8.79050i) q^{58} +(-10.4488 - 3.80307i) q^{59} +(-2.68092 - 4.00141i) q^{60} +(-0.356510 - 0.299147i) q^{61} +(1.70509 - 4.68470i) q^{62} +(-3.49411 + 0.468927i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.85926 + 3.22034i) q^{65} +(1.60528 + 6.52480i) q^{66} +(6.30563 - 7.51475i) q^{67} +4.09202i q^{68} +(1.43353 - 13.2429i) q^{69} +(-3.21820 - 0.567456i) q^{70} +(-5.68527 - 2.06927i) q^{71} +(-1.83225 - 2.37547i) q^{72} +(-8.71361 + 7.31159i) q^{73} +(3.79817 + 4.52648i) q^{74} +(4.70598 + 0.509417i) q^{75} +(-3.55372 - 2.52410i) q^{76} +(3.94812 + 2.27945i) q^{77} +(-1.02179 + 2.07855i) q^{78} +(3.09332 - 8.49883i) q^{79} +(-0.951091 - 2.61310i) q^{80} +(8.68154 - 2.37295i) q^{81} +(1.52350 + 1.27837i) q^{82} +2.83959i q^{83} +(-2.02359 - 0.219051i) q^{84} +(-8.71690 - 7.31434i) q^{85} +(-1.44587 - 1.21323i) q^{86} +(-7.10087 - 16.0832i) q^{87} +3.87943i q^{88} +(2.01011 + 1.68668i) q^{89} +(8.33536 + 0.342984i) q^{90} +(0.537457 + 1.47665i) q^{91} +(2.63029 - 7.22665i) q^{92} +(4.80628 + 7.17362i) q^{93} +(-5.58404 - 3.22395i) q^{94} +(11.7290 - 3.05847i) q^{95} +(-0.699565 - 1.58449i) q^{96} +(-3.47997 - 4.14727i) q^{97} +(4.30443 - 3.61185i) q^{98} +(-10.7635 - 4.42680i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 3 q^{6} + 30 q^{8}+O(q^{10}) $ 60 * q + 3 * q^6 + 30 * q^8	$ 60 q + 3 q^{6} + 30 q^{8} + 3 q^{13} - 3 q^{14} - 6 q^{15} + 27 q^{17} + 18 q^{18} + 3 q^{19} - 9 q^{22} - 18 q^{25} + 24 q^{27} + 3 q^{28} - 27 q^{29} - 36 q^{33} - 3 q^{36} + 9 q^{38} - 30 q^{39} + 9 q^{41} + 6 q^{43} + 9 q^{44} - 3 q^{48} + 60 q^{49} - 66 q^{50} - 33 q^{51} - 3 q^{52} - 60 q^{57} - 81 q^{59} + 27 q^{60} - 78 q^{61} + 3 q^{62} - 33 q^{63} - 30 q^{64} + 18 q^{65} + 57 q^{66} + 15 q^{67} + 6 q^{69} + 18 q^{71} - 66 q^{73} - 3 q^{74} - 45 q^{78} + 48 q^{79} + 36 q^{81} + 3 q^{84} + 3 q^{86} - 72 q^{87} + 27 q^{89} + 6 q^{90} - 69 q^{91} - 18 q^{92} + 105 q^{93} - 18 q^{94} - 108 q^{97} - 60 q^{98} - 30 q^{99}+O(q^{100}) $ 60 * q + 3 * q^6 + 30 * q^8 + 3 * q^13 - 3 * q^14 - 6 * q^15 + 27 * q^17 + 18 * q^18 + 3 * q^19 - 9 * q^22 - 18 * q^25 + 24 * q^27 + 3 * q^28 - 27 * q^29 - 36 * q^33 - 3 * q^36 + 9 * q^38 - 30 * q^39 + 9 * q^41 + 6 * q^43 + 9 * q^44 - 3 * q^48 + 60 * q^49 - 66 * q^50 - 33 * q^51 - 3 * q^52 - 60 * q^57 - 81 * q^59 + 27 * q^60 - 78 * q^61 + 3 * q^62 - 33 * q^63 - 30 * q^64 + 18 * q^65 + 57 * q^66 + 15 * q^67 + 6 * q^69 + 18 * q^71 - 66 * q^73 - 3 * q^74 - 45 * q^78 + 48 * q^79 + 36 * q^81 + 3 * q^84 + 3 * q^86 - 72 * q^87 + 27 * q^89 + 6 * q^90 - 69 * q^91 - 18 * q^92 + 105 * q^93 - 18 * q^94 - 108 * q^97 - 60 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	−0.115449	−	1.72820i	−0.0666546	−	0.997776i
$3$	−0.115449	−	1.72820i	−0.0666546	−	0.997776i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	1.78747	+	2.13022i	0.799379	+	0.952663i	0.999633	−	0.0270808i	$-0.00862115\pi$
$5$	1.78747	+	2.13022i	0.799379	+	0.952663i	−0.200254	+	0.979744i	$0.564177\pi$
$6$	1.19930	+	1.24967i	0.489614	+	0.510175i
$7$	1.17514			0.444163			0.222081	−	0.975028i	$-0.428715\pi$
$7$	1.17514			0.444163			0.222081	+	0.975028i	$0.428715\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−2.97334	+	0.399038i	−0.991114	+	0.133013i
$10$	−2.73856	−	0.482882i	−0.866008	−	0.152701i
$11$	3.35969	+	1.93972i	1.01298	+	0.584846i	0.912064	−	0.410048i	$-0.134488\pi$
$11$	3.35969	+	1.93972i	1.01298	+	0.584846i	0.100919	+	0.994895i	$0.467822\pi$
$12$	−1.72199	−	0.186403i	−0.497096	−	0.0538100i
$13$	0.457354	+	1.25657i	0.126847	+	0.348510i	0.986818	−	0.161833i	$-0.0517407\pi$
$13$	0.457354	+	1.25657i	0.126847	+	0.348510i	−0.859971	+	0.510343i	$0.829518\pi$
$14$	−0.900213	+	0.755368i	−0.240592	+	0.201881i
$15$	3.47508	−	3.33503i	0.897262	−	0.861101i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−4.02985	+	0.710571i	−0.977382	+	0.172339i	−0.639451	−	0.768832i	$-0.720838\pi$
$17$	−4.02985	+	0.710571i	−0.977382	+	0.172339i	−0.337931	+	0.941171i	$0.609727\pi$
$18$	2.02122	−	2.21691i	0.476405	−	0.522530i
$19$	1.86865	−	3.93804i	0.428698	−	0.903448i
$19$	1.86865	−	3.93804i	0.428698	−	0.903448i
$20$	2.40825	−	1.39040i	0.538500	−	0.310903i
$21$	−0.135669	−	2.03088i	−0.0296055	−	0.443175i
$22$	−3.82049	+	0.673656i	−0.814532	+	0.143624i
$23$	7.57361	+	1.33543i	1.57921	+	0.278457i	0.893378	−	0.449306i	$-0.148329\pi$
$23$	7.57361	+	1.33543i	1.57921	+	0.278457i	0.685829	+	0.727763i	$0.259440\pi$
$24$	1.43894	−	0.964081i	0.293722	−	0.196792i
$25$	−0.474558	+	2.69135i	−0.0949117	+	0.538271i
$26$	−1.15806	−	0.668607i	−0.227114	−	0.131125i
$27$	1.03289	+	5.09246i	0.198779	+	0.980044i
$28$	0.204062	−	1.15729i	0.0385640	−	0.218707i
$29$	9.53825	−	3.47164i	1.77121	−	0.644667i	0.771242	−	0.636542i	$-0.219636\pi$
$29$	9.53825	−	3.47164i	1.77121	−	0.644667i	0.999967	−	0.00812567i	$-0.00258651\pi$
$30$	−0.518351	+	4.78852i	−0.0946376	+	0.874260i
$31$	−4.31744	+	2.49268i	−0.775435	+	0.447698i	−0.834810	−	0.550538i	$-0.814423\pi$
$31$	−4.31744	+	2.49268i	−0.775435	+	0.447698i	0.0593749	+	0.998236i	$0.481089\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	2.96434	−	6.03014i	0.516026	−	1.04971i
$34$	2.63030	−	3.13467i	0.451092	−	0.537591i
$35$	2.10053	+	2.50332i	0.355055	+	0.423138i
$36$	−0.123340	+	2.99746i	−0.0205567	+	0.499577i
$37$		−	5.90890i		−	0.971417i	−0.874121	−	0.485709i	$-0.838562\pi$
$37$		−	5.90890i		−	0.971417i	0.874121	−	0.485709i	$-0.161438\pi$
$38$	1.09985	+	4.21786i	0.178419	+	0.684227i
$39$	2.11880	−	0.935469i	0.339280	−	0.149795i
$40$	−0.951091	+	2.61310i	−0.150381	+	0.413168i
$41$	−0.345350	−	1.95858i	−0.0539346	−	0.305878i	0.945892	−	0.324481i	$-0.105190\pi$
$41$	−0.345350	−	1.95858i	−0.0539346	−	0.305878i	−0.999827	+	0.0186022i	$0.994078\pi$
$42$	1.40936	+	1.46854i	0.217468	+	0.226601i
$43$	0.327752	+	1.85878i	0.0499818	+	0.283461i	0.999547	−	0.0301101i	$-0.00958580\pi$
$43$	0.327752	+	1.85878i	0.0499818	+	0.283461i	−0.949565	+	0.313571i	$0.898475\pi$
$44$	2.49365	−	2.97182i	0.375932	−	0.448018i
$45$	−6.16479	−	5.62061i	−0.918993	−	0.837871i
$46$	−6.66012	+	3.84522i	−0.981981	+	0.566947i
$47$	2.20531	+	6.05904i	0.321677	+	0.883802i	0.990143	+	0.140059i	$0.0447291\pi$
$47$	2.20531	+	6.05904i	0.321677	+	0.883802i	−0.668466	+	0.743743i	$0.733049\pi$
$48$	−0.482592	+	1.66346i	−0.0696562	+	0.240100i
$49$	−5.61904			−0.802719
$50$	−1.36644	−	2.36674i	−0.193243	−	0.334707i
$51$	1.69325	+	6.88235i	0.237103	+	0.963722i
$52$	1.31690	−	0.232205i	0.182621	−	0.0322010i
$53$	−7.76367	+	2.82574i	−1.06642	+	0.388146i	−0.814838	−	0.579689i	$-0.803174\pi$
$53$	−7.76367	+	2.82574i	−1.06642	+	0.388146i	−0.251585	+	0.967835i	$0.580952\pi$
$54$	−4.06461	−	3.23712i	−0.553123	−	0.440517i
$55$	1.87331	+	10.6240i	0.252596	+	1.43255i
$56$	0.587572	+	1.01770i	0.0785176	+	0.135997i
$57$	−7.02145	−	2.77476i	−0.930013	−	0.367526i
$58$	−5.07520	+	8.79050i	−0.666406	+	1.15425i
$59$	−10.4488	−	3.80307i	−1.36032	−	0.495117i	−0.444169	−	0.895943i	$-0.646501\pi$
$59$	−10.4488	−	3.80307i	−1.36032	−	0.495117i	−0.916154	+	0.400825i	$0.868723\pi$
$60$	−2.68092	−	4.00141i	−0.346105	−	0.516580i
$61$	−0.356510	−	0.299147i	−0.0456464	−	0.0383019i	0.619679	−	0.784855i	$-0.287263\pi$
$61$	−0.356510	−	0.299147i	−0.0456464	−	0.0383019i	−0.665325	+	0.746553i	$0.731707\pi$
$62$	1.70509	−	4.68470i	0.216547	−	0.594957i
$63$	−3.49411	+	0.468927i	−0.440216	+	0.0590793i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−1.85926	+	3.22034i	−0.230613	+	0.399434i
$66$	1.60528	+	6.52480i	0.197597	+	0.803147i
$67$	6.30563	−	7.51475i	0.770355	−	0.918073i	−0.228100	−	0.973638i	$-0.573251\pi$
$67$	6.30563	−	7.51475i	0.770355	−	0.918073i	0.998455	+	0.0555645i	$0.0176958\pi$
$68$			4.09202i			0.496230i
$69$	1.43353	−	13.2429i	0.172576	−	1.59425i
$70$	−3.21820	−	0.567456i	−0.384649	−	0.0678239i
$71$	−5.68527	−	2.06927i	−0.674717	−	0.245577i	−0.0181395	−	0.999835i	$-0.505774\pi$
$71$	−5.68527	−	2.06927i	−0.674717	−	0.245577i	−0.656578	+	0.754259i	$0.727997\pi$
$72$	−1.83225	−	2.37547i	−0.215933	−	0.279952i
$73$	−8.71361	+	7.31159i	−1.01985	+	0.855757i	−0.989609	−	0.143786i	$-0.954072\pi$
$73$	−8.71361	+	7.31159i	−1.01985	+	0.855757i	−0.0302425	+	0.999543i	$0.509628\pi$
$74$	3.79817	+	4.52648i	0.441528	+	0.526193i
$75$	4.70598	+	0.509417i	0.543400	+	0.0588224i
$76$	−3.55372	−	2.52410i	−0.407640	−	0.289534i
$77$	3.94812	+	2.27945i	0.449929	+	0.259767i
$78$	−1.02179	+	2.07855i	−0.115695	+	0.235349i
$79$	3.09332	−	8.49883i	0.348026	−	0.956193i	−0.634965	−	0.772541i	$-0.718986\pi$
$79$	3.09332	−	8.49883i	0.348026	−	0.956193i	0.982991	−	0.183653i	$-0.0587922\pi$
$80$	−0.951091	−	2.61310i	−0.106335	−	0.292154i
$81$	8.68154	−	2.37295i	0.964615	−	0.263661i
$82$	1.52350	+	1.27837i	0.168243	+	0.141172i
$83$			2.83959i			0.311685i	0.987782	+	0.155843i	$0.0498093\pi$
$83$			2.83959i			0.311685i	−0.987782	+	0.155843i	$0.950191\pi$
$84$	−2.02359	−	0.219051i	−0.220792	−	0.0239004i
$85$	−8.71690	−	7.31434i	−0.945480	−	0.793352i
$86$	−1.44587	−	1.21323i	−0.155912	−	0.130826i
$87$	−7.10087	−	16.0832i	−0.761293	−	1.72430i
$88$			3.87943i			0.413549i
$89$	2.01011	+	1.68668i	0.213071	+	0.178788i	0.743077	−	0.669206i	$-0.233366\pi$
$89$	2.01011	+	1.68668i	0.213071	+	0.178788i	−0.530006	+	0.847994i	$0.677810\pi$
$90$	8.33536	+	0.342984i	0.878624	+	0.0361537i
$91$	0.537457	+	1.47665i	0.0563408	+	0.154795i
$92$	2.63029	−	7.22665i	0.274226	−	0.753431i
$93$	4.80628	+	7.17362i	0.498388	+	0.743870i
$94$	−5.58404	−	3.22395i	−0.575950	−	0.332525i
$95$	11.7290	−	3.05847i	1.20337	−	0.313792i
$96$	−0.699565	−	1.58449i	−0.0713991	−	0.161716i
$97$	−3.47997	−	4.14727i	−0.353338	−	0.421091i	0.559874	−	0.828578i	$-0.310850\pi$
$97$	−3.47997	−	4.14727i	−0.353338	−	0.421091i	−0.913211	+	0.407487i	$0.866405\pi$
$98$	4.30443	−	3.61185i	0.434813	−	0.364852i
$99$	−10.7635	−	4.42680i	−1.08177	−	0.444910i
$100$	2.56806	+	0.934698i	0.256806	+	0.0934698i
$101$	−12.3978	−	2.18607i	−1.23363	−	0.217523i	−0.481447	−	0.876475i	$-0.659889\pi$
$101$	−12.3978	−	2.18607i	−1.23363	−	0.217523i	−0.752184	+	0.658953i	$0.771000\pi$
$102$	−5.72099	−	4.18378i	−0.566463	−	0.414256i
$103$		−	4.99850i		−	0.492517i	−0.969204	−	0.246258i	$-0.920799\pi$
$103$		−	4.99850i		−	0.492517i	0.969204	−	0.246258i	$-0.0792012\pi$
$104$	−0.859544	+	1.02437i	−0.0842853	+	0.100447i
$105$	4.08372	−	3.91914i	0.398531	−	0.382469i
$106$	4.13096	−	7.15504i	0.401235	−	0.694959i
$107$	−8.82894	+	15.2922i	−0.853526	+	1.47835i	0.0244794	+	0.999700i	$0.492207\pi$
$107$	−8.82894	+	15.2922i	−0.853526	+	1.47835i	−0.878006	+	0.478650i	$0.841126\pi$
$108$	5.19445	−	0.132898i	0.499836	−	0.0127882i
$109$	−1.28445	+	3.52899i	−0.123028	+	0.338016i	−0.985883	−	0.167435i	$-0.946452\pi$
$109$	−1.28445	+	3.52899i	−0.123028	+	0.338016i	0.862855	+	0.505451i	$0.168674\pi$
$110$	−8.26404	−	6.93435i	−0.787945	−	0.661165i
$111$	−10.2118	+	0.682177i	−0.969257	+	0.0647494i
$112$	−1.10427	−	0.401923i	−0.104344	−	0.0379782i
$113$	1.79185	−	3.10358i	0.168563	−	0.291960i	−0.769352	−	0.638825i	$-0.779421\pi$
$113$	1.79185	−	3.10358i	0.168563	−	0.291960i	0.937915	+	0.346865i	$0.112754\pi$
$114$	7.16232	−	2.38771i	0.670813	−	0.223629i
$115$	10.6928	+	18.5205i	0.997110	+	1.72704i
$116$	−1.76260	−	9.99619i	−0.163653	−	0.928123i
$117$	−1.86129	−	3.55371i	−0.172076	−	0.328541i
$118$	10.4488	−	3.80307i	0.961894	−	0.350101i
$119$	−4.73566	+	0.835024i	−0.434117	+	0.0765465i
$120$	4.62576	+	1.34199i	0.422272	+	0.122507i
$121$	2.02499	+	3.50739i	0.184090	+	0.318853i
$122$	0.465390			0.0421345
$123$	−3.34494	+	0.822949i	−0.301603	+	0.0742029i
$124$	1.70509	+	4.68470i	0.153122	+	0.420698i
$125$	5.45980	−	3.15222i	0.488340	−	0.281943i
$126$	2.37522	−	2.60519i	0.211601	−	0.232089i
$127$	−7.01087	+	8.35523i	−0.622114	+	0.741407i	−0.981432	−	0.191808i	$-0.938565\pi$
$127$	−7.01087	+	8.35523i	−0.622114	+	0.741407i	0.359318	+	0.933215i	$0.383009\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	3.17450	−	0.781015i	0.279499	−	0.0687646i
$130$	−0.645716	−	3.66204i	−0.0566330	−	0.321182i
$131$	−3.88635	+	10.6776i	−0.339552	+	0.932911i	0.645970	+	0.763363i	$0.276453\pi$
$131$	−3.88635	+	10.6776i	−0.339552	+	0.932911i	−0.985522	+	0.169548i	$0.945769\pi$
$132$	−5.42378	−	3.96643i	−0.472079	−	0.345233i
$133$	2.19594	−	4.62776i	0.190412	−	0.401278i
$134$			9.80981i			0.847439i
$135$	−9.00181	+	11.3029i	−0.774752	+	0.972797i
$136$	−2.63030	−	3.13467i	−0.225546	−	0.268796i
$137$	−7.89203	+	9.40535i	−0.674262	+	0.803554i	−0.989357	−	0.145506i	$-0.953519\pi$
$137$	−7.89203	+	9.40535i	−0.674262	+	0.803554i	0.315096	+	0.949060i	$0.397963\pi$
$138$	7.41421	+	11.0661i	0.631140	+	0.942008i
$139$	16.5995	−	6.04173i	1.40795	−	0.512453i	0.477424	−	0.878673i	$-0.341571\pi$
$139$	16.5995	−	6.04173i	1.40795	−	0.512453i	0.930528	+	0.366220i	$0.119348\pi$
$140$	2.83004	−	1.63392i	0.239182	−	0.138092i
$141$	10.2166	−	4.51072i	0.860395	−	0.379872i
$142$	5.68527	−	2.06927i	0.477097	−	0.173649i
$143$	−0.900822	+	5.10882i	−0.0753305	+	0.427221i
$144$	2.93051	+	0.641970i	0.244209	+	0.0534975i
$145$	24.4447	+	14.1131i	2.03002	+	1.17203i
$146$	1.97522	−	11.2020i	0.163470	−	0.927085i
$147$	0.648713	+	9.71081i	0.0535049	+	0.800934i
$148$	−5.81913	−	1.02607i	−0.478330	−	0.0843424i
$149$	−17.9858	+	3.17138i	−1.47345	+	0.259809i	−0.851958	−	0.523610i	$-0.824585\pi$
$149$	−17.9858	+	3.17138i	−1.47345	+	0.259809i	−0.621494	+	0.783419i	$0.713474\pi$
$150$	−3.93244	+	2.63471i	−0.321082	+	0.215123i
$151$	4.55480	−	2.62972i	0.370665	−	0.214003i	−0.303084	−	0.952964i	$-0.598016\pi$
$151$	4.55480	−	2.62972i	0.370665	−	0.214003i	0.673749	+	0.738960i	$0.264683\pi$
$152$	4.34477	−	0.350717i	0.352407	−	0.0284469i
$153$	11.6986	−	3.72084i	0.945774	−	0.300812i
$154$	−4.48963	+	0.791643i	−0.361785	+	0.0637924i
$155$	−13.0272	−	4.74152i	−1.04637	−	0.380848i
$156$	−0.553331	−	2.24905i	−0.0443019	−	0.180068i
$157$	−5.95678	+	4.99833i	−0.475403	+	0.398910i	−0.848761	−	0.528777i	$-0.822651\pi$
$157$	−5.95678	+	4.99833i	−0.475403	+	0.398910i	0.373358	+	0.927687i	$0.378206\pi$
$158$	3.09332	+	8.49883i	0.246091	+	0.676131i
$159$	5.77976	+	13.0909i	0.458365	+	1.03818i
$160$	2.40825	+	1.39040i	0.190389	+	0.109921i
$161$	8.90008	+	1.56932i	0.701425	+	0.123680i
$162$	−5.12514	+	7.39817i	−0.402669	+	0.581255i
$163$	−1.27861	−	2.21461i	−0.100148	−	0.173462i	0.811597	−	0.584217i	$-0.198598\pi$
$163$	−1.27861	−	2.21461i	−0.100148	−	0.173462i	−0.911746	+	0.410755i	$0.865265\pi$
$164$	−1.98879			−0.155299
$165$	18.1442	−	4.46398i	1.41252	−	0.347520i
$166$	−1.82525	−	2.17525i	−0.141667	−	0.168832i
$167$	0.803568	−	4.55726i	0.0621819	−	0.352651i	−0.937803	−	0.347168i	$-0.887143\pi$
$167$	0.803568	−	4.55726i	0.0621819	−	0.352651i	0.999985	−	0.00548351i	$-0.00174546\pi$
$168$	1.69096	−	1.13293i	0.130461	−	0.0874078i
$169$	8.58878	−	7.20684i	0.660676	−	0.554373i
$170$	11.3791			0.872737
$171$	−3.98472	+	12.4548i	−0.304719	+	0.952442i
$172$	1.88745			0.143917
$173$	−7.43701	+	6.24039i	−0.565426	+	0.474448i	−0.880124	−	0.474743i	$-0.842541\pi$
$173$	−7.43701	+	6.24039i	−0.565426	+	0.474448i	0.314699	+	0.949192i	$0.398096\pi$
$174$	15.7777	+	7.75610i	1.19610	+	0.587988i
$175$	−0.557675	+	3.16273i	−0.0421562	+	0.239080i
$176$	−2.49365	−	2.97182i	−0.187966	−	0.224009i
$177$	−5.36615	+	18.4967i	−0.403345	+	1.39030i
$178$	−2.62401			−0.196678
$179$	−7.98627	−	13.8326i	−0.596922	−	1.03390i	−0.993273	−	0.115800i	$-0.963057\pi$
$179$	−7.98627	−	13.8326i	−0.596922	−	1.03390i	0.396350	−	0.918099i	$-0.370277\pi$
$180$	−6.60572	+	5.09512i	−0.492361	+	0.379768i
$181$	7.85770	+	1.38552i	0.584058	+	0.102985i	0.457867	−	0.889021i	$-0.348614\pi$
$181$	7.85770	+	1.38552i	0.584058	+	0.102985i	0.126191	+	0.992006i	$0.459725\pi$
$182$	−1.36089	−	0.785710i	−0.100876	−	0.0582407i
$183$	−0.475827	+	0.650656i	−0.0351742	+	0.0480979i
$184$	2.63029	+	7.22665i	0.193907	+	0.532756i
$185$	12.5873	−	10.5620i	0.925434	−	0.776531i
$186$	−8.29294	−	2.40589i	−0.608068	−	0.176409i
$187$	−14.9173	−	5.42947i	−1.09086	−	0.397042i
$188$	6.34994	−	1.11967i	0.463117	−	0.0816600i
$189$	1.21379	+	5.98438i	0.0882903	+	0.435299i
$190$	−7.01902	+	9.88220i	−0.509213	+	0.716930i
$191$	19.9692	−	11.5292i	1.44492	−	0.834227i	0.446751	−	0.894658i	$-0.352581\pi$
$191$	19.9692	−	11.5292i	1.44492	−	0.834227i	0.998172	+	0.0604313i	$0.0192476\pi$
$192$	1.55439	+	0.764118i	0.112178	+	0.0551454i
$193$	−8.96885	+	1.58145i	−0.645592	+	0.113835i	−0.486851	−	0.873485i	$-0.661855\pi$
$193$	−8.96885	+	1.58145i	−0.645592	+	0.113835i	−0.158741	+	0.987320i	$0.550743\pi$
$194$	5.33163	+	0.940110i	0.382788	+	0.0674959i
$195$	5.78004	+	2.84139i	0.413917	+	0.203476i
$196$	−0.975735	+	5.53367i	−0.0696954	+	0.395262i
$197$	−11.7780	−	6.80002i	−0.839146	−	0.484481i	0.0178278	−	0.999841i	$-0.494325\pi$
$197$	−11.7780	−	6.80002i	−0.839146	−	0.484481i	−0.856974	+	0.515360i	$0.827658\pi$
$198$	11.0908	−	3.52753i	0.788190	−	0.250691i
$199$	3.35965	−	19.0535i	0.238160	−	1.35067i	−0.597697	−	0.801722i	$-0.703917\pi$
$199$	3.35965	−	19.0535i	0.238160	−	1.35067i	0.835857	−	0.548948i	$-0.184971\pi$
$200$	−2.56806	+	0.934698i	−0.181589	+	0.0660931i
$201$	−13.7150	−	10.0298i	−0.967379	−	0.707448i
$202$	10.9025	−	6.29455i	0.767096	−	0.442883i
$203$	11.2088	−	4.07968i	0.786705	−	0.286337i
$204$	7.07182	−	0.472420i	0.495126	−	0.0330760i
$205$	3.55490	−	4.23656i	0.248285	−	0.295894i
$206$	3.21297	+	3.82907i	0.223858	+	0.266784i
$207$	−23.0518	−	0.948539i	−1.60221	−	0.0659280i
$208$		−	1.33721i		−	0.0927191i
$209$	13.9168	−	9.60591i	0.962642	−	0.664455i
$210$	−0.609138	+	5.62720i	−0.0420345	+	0.388314i
$211$	3.91195	−	10.7480i	0.269310	−	0.739922i	−0.729146	−	0.684359i	$-0.760082\pi$
$211$	3.91195	−	10.7480i	0.269310	−	0.739922i	0.998455	−	0.0555635i	$-0.0176955\pi$
$212$	1.43467	+	8.13641i	0.0985334	+	0.558811i
$213$	−2.91975	+	10.0642i	−0.200058	+	0.689585i
$214$	−3.06626	−	17.3896i	−0.209605	−	1.18873i
$215$	−3.37375	+	4.02068i	−0.230088	+	0.274208i
$216$	−3.89376	+	3.44074i	−0.264937	+	0.234112i
$217$	−5.07362	+	2.92925i	−0.344419	+	0.198851i
$218$	−1.28445	−	3.52899i	−0.0869937	−	0.239013i
$219$	13.6419	+	14.2147i	0.921832	+	0.960543i
$220$	10.7879			0.727323
$221$	−2.73595	−	4.73881i	−0.184040	−	0.318767i
$222$	7.38416	−	7.08657i	0.495593	−	0.475619i
$223$	7.17284	−	1.26477i	0.480329	−	0.0846950i	0.0717591	−	0.997422i	$-0.477139\pi$
$223$	7.17284	−	1.26477i	0.480329	−	0.0846950i	0.408570	+	0.912727i	$0.366028\pi$
$224$	1.10427	−	0.401923i	0.0737824	−	0.0268546i
$225$	0.337072	−	8.19169i	0.0224715	−	0.546112i
$226$	0.622303	+	3.52926i	0.0413950	+	0.234763i
$227$	12.6498	+	21.9101i	0.839597	+	1.45422i	0.890232	+	0.455507i	$0.150542\pi$
$227$	12.6498	+	21.9101i	0.839597	+	1.45422i	−0.0506357	+	0.998717i	$0.516125\pi$
$228$	−3.95187	+	6.43294i	−0.261719	+	0.426032i
$229$	−1.57138	+	2.72171i	−0.103840	+	0.179855i	−0.913264	−	0.407369i	$-0.866446\pi$
$229$	−1.57138	+	2.72171i	−0.103840	+	0.179855i	0.809424	+	0.587225i	$0.199780\pi$
$230$	−20.0959	−	7.31431i	−1.32508	−	0.482291i
$231$	3.48353	−	7.08629i	0.229199	−	0.466244i
$232$	7.77566	+	6.52455i	0.510497	+	0.428358i
$233$	7.30676	−	20.0752i	0.478682	−	1.31517i	−0.431931	−	0.901907i	$-0.642168\pi$
$233$	7.30676	−	20.0752i	0.478682	−	1.31517i	0.910613	−	0.413261i	$-0.135610\pi$
$234$	3.71011	+	1.52589i	0.242538	+	0.0997504i
$235$	−8.96517	+	15.5281i	−0.584823	+	1.01294i
$236$	−5.55972	+	9.62971i	−0.361907	+	0.626841i
$237$	−15.0448	−	4.36469i	−0.977264	−	0.283517i
$238$	3.09098	−	3.68369i	0.200358	−	0.238778i
$239$		−	17.4368i		−	1.12790i	−0.825811	−	0.563948i	$-0.809282\pi$
$239$		−	17.4368i		−	1.12790i	0.825811	−	0.563948i	$-0.190718\pi$
$240$	−4.40616	+	1.94535i	−0.284416	+	0.125572i
$241$	9.98977	+	1.76147i	0.643498	+	0.113466i	0.485868	−	0.874032i	$-0.338504\pi$
$241$	9.98977	+	1.76147i	0.643498	+	0.113466i	0.157630	+	0.987498i	$0.449615\pi$
$242$	−3.80574	−	1.38517i	−0.244642	−	0.0890424i
$243$	−5.10321	−	14.7295i	−0.327371	−	0.944896i
$244$	−0.356510	+	0.299147i	−0.0228232	+	0.0191509i
$245$	−10.0438	−	11.9698i	−0.641677	−	0.764721i
$246$	2.03339	−	2.78050i	0.129644	−	0.177278i
$247$	5.80305	+	0.547016i	0.369240	+	0.0348058i
$248$	−4.31744	−	2.49268i	−0.274158	−	0.158285i
$249$	4.90737	−	0.327828i	0.310992	−	0.0207752i
$250$	−2.15624	+	5.92423i	−0.136373	+	0.374681i
$251$	7.81288	+	21.4657i	0.493145	+	1.35490i	0.897788	+	0.440429i	$0.145174\pi$
$251$	7.81288	+	21.4657i	0.493145	+	1.35490i	−0.404643	+	0.914475i	$0.632604\pi$
$252$	−0.144942	+	3.52245i	−0.00913050	+	0.221894i
$253$	22.8546	+	19.1773i	1.43686	+	1.20566i
$254$		−	10.9070i		−	0.684365i
$255$	−11.6343	+	15.9090i	−0.728567	+	0.996258i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−13.8820	−	11.6484i	−0.865938	−	0.726608i	0.0973010	−	0.995255i	$-0.468979\pi$
$257$	−13.8820	−	11.6484i	−0.865938	−	0.726608i	−0.963239	+	0.268647i	$0.913423\pi$
$258$	−1.92978	+	2.63882i	−0.120143	+	0.164286i
$259$		−	6.94381i		−	0.431467i
$260$	2.84856	+	2.39022i	0.176660	+	0.148235i
$261$	−26.9752	+	14.1285i	−1.66972	+	0.874532i
$262$	−3.88635	−	10.6776i	−0.240099	−	0.659667i
$263$	−3.24253	+	8.90878i	−0.199943	+	0.549339i	−0.998625	−	0.0524139i	$-0.983308\pi$
$263$	−3.24253	+	8.90878i	−0.199943	+	0.549339i	0.798682	+	0.601753i	$0.205531\pi$
$264$	6.70443	−	0.447877i	0.412629	−	0.0275649i
$265$	−19.8968	−	11.4874i	−1.22225	−	0.705665i
$266$	1.29248	+	4.95659i	0.0792472	+	0.303908i
$267$	2.68286	−	3.66859i	0.164188	−	0.224514i
$268$	−6.30563	−	7.51475i	−0.385177	−	0.459037i
$269$	9.81767	−	8.23801i	0.598594	−	0.502280i	−0.292399	−	0.956296i	$-0.594454\pi$
$269$	9.81767	−	8.23801i	0.598594	−	0.502280i	0.890993	+	0.454016i	$0.150009\pi$
$270$	−0.369565	−	14.4448i	−0.0224910	−	0.879080i
$271$	−8.23256	−	2.99641i	−0.500092	−	0.182019i	0.0796432	−	0.996823i	$-0.474622\pi$
$271$	−8.23256	−	2.99641i	−0.500092	−	0.182019i	−0.579736	+	0.814805i	$0.696844\pi$
$272$	4.02985	+	0.710571i	0.244346	+	0.0430847i
$273$	2.48990	−	1.09931i	0.150695	−	0.0665333i
$274$		−	12.2778i		−	0.741730i
$275$	−6.81483	+	8.12160i	−0.410950	+	0.489751i
$276$	−12.7928	−	3.71135i	−0.770034	−	0.223397i
$277$	5.56893	−	9.64567i	0.334605	−	0.579552i	−0.648804	−	0.760955i	$-0.724731\pi$
$277$	5.56893	−	9.64567i	0.334605	−	0.579552i	0.983409	+	0.181403i	$0.0580639\pi$
$278$	−8.83242	+	15.2982i	−0.529733	+	0.917525i
$279$	11.8426	−	9.13440i	0.708996	−	0.546862i
$280$	−1.11767	+	3.07077i	−0.0667935	+	0.183514i
$281$	−9.65052	−	8.09775i	−0.575702	−	0.483071i	0.307831	−	0.951441i	$-0.400397\pi$
$281$	−9.65052	−	8.09775i	−0.575702	−	0.483071i	−0.883532	+	0.468370i	$0.844841\pi$
$282$	−4.92695	+	10.0225i	−0.293396	+	0.596833i
$283$	−18.6480	−	6.78731i	−1.10851	−	0.403464i	−0.278061	−	0.960563i	$-0.589692\pi$
$283$	−18.6480	−	6.78731i	−1.10851	−	0.403464i	−0.830446	+	0.557100i	$0.811914\pi$
$284$	−3.02507	+	5.23957i	−0.179505	+	0.310911i
$285$	−6.63975	−	19.9170i	−0.393305	−	1.17978i
$286$	−2.59381	−	4.49262i	−0.153375	−	0.265654i
$287$	−0.405836	−	2.30161i	−0.0239557	−	0.135860i
$288$	−2.65755	+	1.39192i	−0.156598	+	0.0820195i
$289$	−0.239989	+	0.0873490i	−0.0141170	+	0.00513818i
$290$	−27.7974	+	4.90144i	−1.63232	+	0.287822i
$291$	−6.76555	+	6.49288i	−0.396603	+	0.380620i
$292$	5.68741	+	9.85088i	0.332830	+	0.576479i
$293$	−22.1782			−1.29567			−0.647833	−	0.761783i	$-0.724324\pi$
$293$	−22.1782			−1.29567			−0.647833	+	0.761783i	$0.724324\pi$
$294$	−6.73893	−	7.02193i	−0.393022	−	0.409527i
$295$	−10.5756	−	29.0562i	−0.615735	−	1.69172i
$296$	5.11726	−	2.95445i	0.297435	−	0.171724i
$297$	−6.40775	+	19.1126i	−0.371815	+	1.10902i
$298$	11.7394	−	13.9904i	0.680044	−	0.810445i
$299$	1.78576	+	10.1275i	0.103273	+	0.585690i
$300$	1.31886	−	4.54603i	0.0761446	−	0.262465i
$301$	0.385156	+	2.18433i	0.0222000	+	0.125903i
$302$	−1.79883	+	4.94225i	−0.103511	+	0.284395i
$303$	−2.34665	+	21.6783i	−0.134812	+	1.24539i
$304$	−3.10285	+	3.06143i	−0.177961	+	0.175585i
$305$		−	1.29416i		−	0.0741034i
$306$	−6.56993	+	10.3700i	−0.375578	+	0.592815i
$307$	11.3681	+	13.5480i	0.648814	+	0.773227i	0.985735	−	0.168306i	$-0.0538298\pi$
$307$	11.3681	+	13.5480i	0.648814	+	0.773227i	−0.336920	+	0.941533i	$0.609385\pi$
$308$	2.93040	−	3.49231i	0.166975	−	0.198993i
$309$	−8.63840	+	0.577072i	−0.491421	+	0.0328285i
$310$	13.0272	−	4.74152i	0.739897	−	0.269300i
$311$	30.0801	−	17.3668i	1.70569	−	0.984780i	0.765940	−	0.642912i	$-0.222274\pi$
$311$	30.0801	−	17.3668i	1.70569	−	0.984780i	0.939748	−	0.341868i	$-0.111059\pi$
$312$	1.86954	+	1.36720i	0.105842	+	0.0774026i
$313$	21.2186	−	7.72294i	1.19935	−	0.436527i	0.336351	−	0.941737i	$-0.390807\pi$
$313$	21.2186	−	7.72294i	1.19935	−	0.436527i	0.862996	+	0.505210i	$0.168585\pi$
$314$	1.35029	−	7.65788i	0.0762014	−	0.432159i
$315$	−7.24452	−	6.60502i	−0.408182	−	0.372151i
$316$	−7.83257	−	4.52213i	−0.440616	−	0.254390i
$317$	1.55557	−	8.82209i	0.0873697	−	0.495498i	−0.909450	−	0.415812i	$-0.863497\pi$
$317$	1.55557	−	8.82209i	0.0873697	−	0.495498i	0.996820	−	0.0796855i	$-0.0253916\pi$
$318$	−12.8422	−	6.31308i	−0.720157	−	0.354020i
$319$	38.7795	+	6.83788i	2.17124	+	0.382848i
$320$	−2.73856	+	0.482882i	−0.153090	+	0.0269939i
$321$	27.4472	+	13.4927i	1.53195	+	0.753089i
$322$	−7.82660	+	4.51869i	−0.436159	+	0.251817i
$323$	−4.73214	+	17.1975i	−0.263303	+	0.956895i
$324$	−0.829370	−	8.96170i	−0.0460761	−	0.497872i
$325$	−3.59892	+	0.634586i	−0.199632	+	0.0352005i
$326$	2.40299	+	0.874618i	0.133089	+	0.0484406i
$327$	6.24708	+	1.81236i	0.345464	+	0.100224i
$328$	1.52350	−	1.27837i	0.0841214	−	0.0705862i
$329$	2.59156	+	7.12024i	0.142877	+	0.392552i
$330$	−11.0299	+	15.0825i	−0.607174	+	0.830263i
$331$	3.32308	+	1.91858i	0.182653	+	0.105455i	0.588539	−	0.808469i	$-0.299703\pi$
$331$	3.32308	+	1.91858i	0.182653	+	0.105455i	−0.405885	+	0.913924i	$0.633037\pi$
$332$	2.79645	+	0.493089i	0.153475	+	0.0270618i
$333$	2.35788	+	17.5692i	0.129211	+	0.962786i
$334$	2.31378	+	4.00759i	0.126604	+	0.219285i
$335$	27.2792			1.49042
$336$	−0.567115	+	1.95481i	−0.0309387	+	0.106643i
$337$	15.0950	+	17.9895i	0.822278	+	0.979952i	0.999991	−	0.00412974i	$-0.00131454\pi$
$337$	15.0950	+	17.9895i	0.822278	+	0.979952i	−0.177714	+	0.984082i	$0.556870\pi$
$338$	−1.94692	+	11.0415i	−0.105898	+	0.600580i
$339$	−5.57047	−	2.73837i	−0.302546	−	0.148728i
$340$	−8.71690	+	7.31434i	−0.472740	+	0.396676i
$341$	−19.3403			−1.04734
$342$	−4.95332	−	12.1023i	−0.267845	−	0.654415i
$343$	−14.8292			−0.800701
$344$	−1.44587	+	1.21323i	−0.0779561	+	0.0654130i
$345$	30.7726	−	20.6175i	1.65674	−	1.11001i
$346$	1.68583	−	9.56084i	0.0906310	−	0.513994i
$347$	−8.52661	−	10.1616i	−0.457733	−	0.545504i	0.486976	−	0.873415i	$-0.338100\pi$
$347$	−8.52661	−	10.1616i	−0.457733	−	0.545504i	−0.944709	+	0.327911i	$0.893655\pi$
$348$	−17.0719	+	4.20017i	−0.915151	+	0.225153i
$349$	−30.7450			−1.64574			−0.822871	−	0.568229i	$-0.807629\pi$
$349$	−30.7450			−1.64574			−0.822871	+	0.568229i	$0.807629\pi$
$350$	−1.60576	−	2.78126i	−0.0858315	−	0.148664i
$351$	−5.92664	+	3.62695i	−0.316340	+	0.193592i
$352$	3.82049	+	0.673656i	0.203633	+	0.0359060i
$353$	1.16376	+	0.671898i	0.0619408	+	0.0357615i	0.530651	−	0.847591i	$-0.321948\pi$
$353$	1.16376	+	0.671898i	0.0619408	+	0.0357615i	−0.468710	+	0.883352i	$0.655281\pi$
$354$	−7.77877	−	17.6186i	−0.413437	−	0.936419i
$355$	−5.75423	−	15.8096i	−0.305403	−	0.839087i
$356$	2.01011	−	1.68668i	0.106536	−	0.0893940i
$357$	1.98981	+	8.08775i	0.105312	+	0.428049i
$358$	15.0093	+	5.46293i	0.793265	+	0.288725i
$359$	−20.8762	+	3.68103i	−1.10180	+	0.194278i	−0.694838	−	0.719166i	$-0.744524\pi$
$359$	−20.8762	+	3.68103i	−1.10180	+	0.194278i	−0.406965	+	0.913444i	$0.633413\pi$
$360$	1.78519	−	8.14917i	0.0940880	−	0.429499i
$361$	−12.0163	−	14.7177i	−0.632435	−	0.774613i
$362$	−6.90994	+	3.98946i	−0.363179	+	0.209681i
$363$	5.82768	−	3.90451i	0.305874	−	0.204934i
$364$	1.54755	−	0.272874i	0.0811134	−	0.0143025i
$365$	−31.1506	−	5.49269i	−1.63050	−	0.287500i
$366$	−0.0537289	−	0.804287i	−0.00280845	−	0.0420408i
$367$	−2.07592	+	11.7731i	−0.108362	+	0.614552i	0.881462	+	0.472255i	$0.156560\pi$
$367$	−2.07592	+	11.7731i	−0.108362	+	0.614552i	−0.989824	+	0.142297i	$0.954551\pi$
$368$	−6.66012	−	3.84522i	−0.347183	−	0.200446i
$369$	1.80839	+	5.68571i	0.0941411	+	0.295986i
$370$	−2.85330	+	16.1819i	−0.148336	+	0.841255i
$371$	−9.12343	+	3.32066i	−0.473665	+	0.172400i
$372$	7.89924	−	3.48758i	0.409556	−	0.180823i
$373$	−8.25642	+	4.76685i	−0.427501	+	0.246818i	−0.698282	−	0.715823i	$-0.746052\pi$
$373$	−8.25642	+	4.76685i	−0.427501	+	0.246818i	0.270780	+	0.962641i	$0.412718\pi$
$374$	14.9173	−	5.42947i	0.771357	−	0.280751i
$375$	−6.07799	−	9.07170i	−0.313866	−	0.468461i
$376$	−4.14463	+	4.93937i	−0.213743	+	0.254729i
$377$	8.72472	+	10.3977i	0.449346	+	0.535509i
$378$	−4.77650	−	3.80409i	−0.245677	−	0.195661i
$379$		−	29.6107i		−	1.52100i	−0.649337	−	0.760500i	$-0.724954\pi$
$379$		−	29.6107i		−	1.52100i	0.649337	−	0.760500i	$-0.275046\pi$
$380$	−0.975277	−	12.0819i	−0.0500306	−	0.619791i
$381$	15.2489	+	11.1516i	0.781225	+	0.571313i
$382$	−7.88647	+	21.6679i	−0.403507	+	1.10863i
$383$	5.04403	+	28.6061i	0.257738	+	1.46171i	0.788945	+	0.614463i	$0.210627\pi$
$383$	5.04403	+	28.6061i	0.257738	+	1.46171i	−0.531207	+	0.847242i	$0.678261\pi$
$384$	−1.68190	+	0.413794i	−0.0858289	+	0.0211163i
$385$	2.20140	+	12.4848i	0.112194	+	0.636284i
$386$	5.85400	−	6.97653i	0.297961	−	0.355096i
$387$	−1.71624	−	5.39599i	−0.0872415	−	0.274294i
$388$	−4.68855	+	2.70694i	−0.238025	+	0.137424i
$389$	10.6105	+	29.1522i	0.537976	+	1.47808i	0.849371	+	0.527797i	$0.176982\pi$
$389$	10.6105	+	29.1522i	0.537976	+	1.47808i	−0.311395	+	0.950281i	$0.600796\pi$
$390$	−6.25418	+	1.53870i	−0.316693	+	0.0779153i
$391$	−31.4694			−1.59148
$392$	−2.80952	−	4.86623i	−0.141902	−	0.245782i
$393$	18.9018	+	5.48365i	0.953469	+	0.276614i
$394$	13.3934	−	2.36162i	0.674751	−	0.118977i
$395$	23.6336	−	8.60192i	1.18913	−	0.432810i
$396$	−6.22861	+	9.83129i	−0.312999	+	0.494041i
$397$	−1.32705	−	7.52606i	−0.0666026	−	0.377722i	−0.999830	−	0.0184360i	$-0.994131\pi$
$397$	−1.32705	−	7.52606i	−0.0666026	−	0.377722i	0.933227	−	0.359286i	$-0.116980\pi$
$398$	9.67374	+	16.7554i	0.484901	+	0.839872i
$399$	−8.25121	−	3.26075i	−0.413077	−	0.163241i
$400$	1.36644	−	2.36674i	0.0683218	−	0.118337i
$401$	8.64001	+	3.14471i	0.431461	+	0.157039i	0.548616	−	0.836075i	$-0.315155\pi$
$401$	8.64001	+	3.14471i	0.431461	+	0.157039i	−0.117154	+	0.993114i	$0.537377\pi$
$402$	16.9533	−	1.13253i	0.845554	−	0.0564857i
$403$	−5.10682	−	4.28513i	−0.254389	−	0.213458i
$404$	−4.30573	+	11.8299i	−0.214218	+	0.588559i
$405$	20.5729	+	14.2520i	1.02227	+	0.708188i
$406$	−5.96409	+	10.3301i	−0.295993	+	0.512675i
$407$	11.4616	−	19.8520i	0.568130	−	0.984029i
$408$	−5.11366	+	4.90757i	−0.253164	+	0.242961i
$409$	−7.79370	+	9.28817i	−0.385374	+	0.459271i	−0.923503	−	0.383592i	$-0.874687\pi$
$409$	−7.79370	+	9.28817i	−0.385374	+	0.459271i	0.538129	+	0.842863i	$0.319131\pi$
$410$			5.53044i			0.273129i
$411$	17.1654	+	12.5532i	0.846709	+	0.619202i
$412$	−4.92256	−	0.867980i	−0.242517	−	0.0427623i
$413$	−12.2789	−	4.46915i	−0.604205	−	0.219913i
$414$	18.2684	−	14.0908i	0.897844	−	0.692525i
$415$	−6.04895	+	5.07567i	−0.296931	+	0.249155i
$416$	0.859544	+	1.02437i	0.0421426	+	0.0502236i
$417$	−12.3577	−	27.9897i	−0.605160	−	1.37066i
$418$	−4.48629	+	16.3041i	−0.219432	+	0.797458i
$419$	20.7805	+	11.9976i	1.01520	+	0.586123i	0.912709	−	0.408611i	$-0.133987\pi$
$419$	20.7805	+	11.9976i	1.01520	+	0.586123i	0.102487	+	0.994734i	$0.467320\pi$
$420$	−3.15047	−	4.70223i	−0.153727	−	0.229446i
$421$	−10.2813	+	28.2477i	−0.501081	+	1.37671i	0.389140	+	0.921178i	$0.372772\pi$
$421$	−10.2813	+	28.2477i	−0.501081	+	1.37671i	−0.890221	+	0.455529i	$0.849450\pi$
$422$	3.91195	+	10.7480i	0.190431	+	0.523204i
$423$	−8.97493	−	17.1356i	−0.436376	−	0.833161i
$424$	−6.32900	−	5.31066i	−0.307363	−	0.257909i
$425$		−	11.1830i		−	0.542453i
$426$	−4.23247	−	9.58638i	−0.205064	−	0.464462i
$427$	−0.418950	−	0.351541i	−0.0202744	−	0.0170123i
$428$	13.5267	+	11.3503i	0.653839	+	0.548636i
$429$	8.93305	+	0.966992i	0.431292	+	0.0466868i
$430$		−	5.24863i		−	0.253111i
$431$	−1.80155	−	1.51168i	−0.0867774	−	0.0728149i	0.598367	−	0.801222i	$-0.295816\pi$
$431$	−1.80155	−	1.51168i	−0.0867774	−	0.0728149i	−0.685144	+	0.728407i	$0.740261\pi$
$432$	0.771128	−	5.13861i	0.0371009	−	0.247232i
$433$	−11.1783	−	30.7122i	−0.537196	−	1.47593i	−0.850343	−	0.526229i	$-0.823606\pi$
$433$	−11.1783	−	30.7122i	−0.537196	−	1.47593i	0.313147	−	0.949705i	$-0.398617\pi$
$434$	2.00373	−	5.50520i	0.0961820	−	0.264258i
$435$	21.5682	−	43.8746i	1.03412	−	2.10363i
$436$	3.25233	+	1.87773i	0.155758	+	0.0899272i
$437$	19.4114	−	27.3297i	0.928574	−	1.30736i
$438$	−19.5873	−	2.12030i	−0.935919	−	0.101312i
$439$	−20.7166	−	24.6890i	−0.988747	−	1.17834i	−0.983966	−	0.178355i	$-0.942923\pi$
$439$	−20.7166	−	24.6890i	−0.988747	−	1.17834i	−0.00478126	−	0.999989i	$-0.501522\pi$
$440$	−8.26404	+	6.93435i	−0.393973	+	0.330582i
$441$	16.7073	−	2.24221i	0.795587	−	0.106772i
$442$	5.14191	+	1.87150i	0.244576	+	0.0890182i
$443$	−0.778461	−	0.137264i	−0.0369858	−	0.00652159i	0.155125	−	0.987895i	$-0.450422\pi$
$443$	−0.778461	−	0.137264i	−0.0369858	−	0.00652159i	−0.192110	+	0.981373i	$0.561533\pi$
$444$	−1.10144	+	10.1751i	−0.0522720	+	0.482888i
$445$			7.29686i			0.345904i
$446$	−4.68174	+	5.57948i	−0.221687	+	0.264196i
$447$	7.55721	+	30.7169i	0.357444	+	1.45286i
$448$	−0.587572	+	1.01770i	−0.0277602	+	0.0480820i
$449$	15.5179	−	26.8778i	0.732336	−	1.26844i	−0.223546	−	0.974693i	$-0.571763\pi$
$449$	15.5179	−	26.8778i	0.732336	−	1.26844i	0.955882	−	0.293750i	$-0.0949032\pi$
$450$	5.00730	+	6.49186i	0.236046	+	0.306029i
$451$	2.63881	−	7.25008i	0.124257	−	0.341393i
$452$	−2.74528	−	2.30356i	−0.129127	−	0.108350i
$453$	−5.07052	−	7.56801i	−0.238234	−	0.355576i
$454$	−23.7738	−	8.65297i	−1.11576	−	0.406104i
$455$	−2.18490	+	3.78437i	−0.102430	+	0.177414i
$456$	−1.10771	−	7.46813i	−0.0518732	−	0.349727i
$457$	21.1132	+	36.5692i	0.987635	+	1.71063i	0.629586	+	0.776931i	$0.283225\pi$
$457$	21.1132	+	36.5692i	0.987635	+	1.71063i	0.358049	+	0.933703i	$0.383442\pi$
$458$	−0.545734	−	3.09501i	−0.0255005	−	0.144620i
$459$	−7.78094	−	19.7879i	−0.363183	−	0.923621i
$460$	20.0959	−	7.31431i	0.936977	−	0.341032i
$461$	−10.8985	+	1.92170i	−0.507593	+	0.0895023i	−0.421579	−	0.906792i	$-0.638524\pi$
$461$	−10.8985	+	1.92170i	−0.507593	+	0.0895023i	−0.0860137	+	0.996294i	$0.527413\pi$
$462$	1.88644	+	7.66758i	0.0877652	+	0.356728i
$463$	11.9159	+	20.6390i	0.553781	+	0.959176i	0.997997	+	0.0632567i	$0.0201487\pi$
$463$	11.9159	+	20.6390i	0.553781	+	0.959176i	−0.444217	+	0.895919i	$0.646518\pi$
$464$	−10.1504			−0.471220
$465$	−6.69031	+	23.0610i	−0.310256	+	1.06943i
$466$	7.30676	+	20.0752i	0.338479	+	0.929964i
$467$	12.1003	−	6.98612i	0.559936	−	0.323279i	−0.193184	−	0.981163i	$-0.561881\pi$
$467$	12.1003	−	6.98612i	0.559936	−	0.323279i	0.753120	+	0.657883i	$0.228548\pi$
$468$	−3.82293	+	1.21592i	−0.176715	+	0.0562058i
$469$	7.41002	−	8.83092i	0.342163	−	0.407774i
$470$	−3.11357	−	17.6579i	−0.143618	−	0.814500i
$471$	9.32581	+	9.71744i	0.429711	+	0.447756i
$472$	−1.93087	−	10.9505i	−0.0888754	−	0.504038i
$473$	−2.50435	+	6.88065i	−0.115150	+	0.316373i
$474$	14.3306	−	6.32706i	0.658224	−	0.290611i
$475$	9.71187	+	6.89804i	0.445611	+	0.316504i
$476$			4.80871i			0.220407i
$477$	21.9565	−	11.4999i	1.00532	−	0.526545i
$478$	11.2082	+	13.3574i	0.512650	+	0.610953i
$479$	4.26136	−	5.07850i	0.194707	−	0.232042i	−0.659854	−	0.751394i	$-0.729382\pi$
$479$	4.26136	−	5.07850i	0.194707	−	0.232042i	0.854561	+	0.519351i	$0.173826\pi$
$480$	2.12486	−	4.32245i	0.0969862	−	0.197292i
$481$	7.42495	−	2.70246i	0.338548	−	0.123222i
$482$	−8.78486	+	5.07194i	−0.400139	+	0.231021i
$483$	1.68460	−	15.5623i	0.0766519	−	0.708109i
$484$	3.80574	−	1.38517i	0.172988	−	0.0629625i
$485$	2.61426	−	14.8262i	0.118707	−	0.673224i
$486$	13.3772	+	8.00315i	0.606802	+	0.363030i
$487$	4.35504	+	2.51439i	0.197346	+	0.113938i	0.595417	−	0.803417i	$-0.296987\pi$
$487$	4.35504	+	2.51439i	0.197346	+	0.113938i	−0.398071	+	0.917355i	$0.630320\pi$
$488$	0.0808142	−	0.458320i	0.00365829	−	0.0207472i
$489$	−3.67967	+	2.46536i	−0.166401	+	0.111487i
$490$	15.3881	+	2.71333i	0.695161	+	0.122576i
$491$	−5.62663	+	0.992126i	−0.253926	+	0.0447740i	−0.299162	−	0.954202i	$-0.596707\pi$
$491$	−5.62663	+	0.992126i	−0.253926	+	0.0447740i	0.0452360	+	0.998976i	$0.485596\pi$
$492$	0.229604	+	3.43703i	0.0103514	+	0.154953i
$493$	−35.9709	+	20.7678i	−1.62005	+	0.935335i
$494$	−4.79701	+	3.31109i	−0.215828	+	0.148973i
$495$	−9.80938	−	30.8414i	−0.440899	−	1.38622i
$496$	4.90961	−	0.865697i	0.220448	−	0.0388709i
$497$	−6.68101	−	2.43169i	−0.299684	−	0.109076i
$498$	−3.54854	+	3.40553i	−0.159014	+	0.152605i
$499$	23.3041	−	19.5545i	1.04323	−	0.875378i	0.0508686	−	0.998705i	$-0.483801\pi$
$499$	23.3041	−	19.5545i	1.04323	−	0.875378i	0.992366	+	0.123328i	$0.0393566\pi$
$500$	−2.15624	−	5.92423i	−0.0964302	−	0.264940i
$501$	−7.96862	−	0.862594i	−0.356012	−	0.0385378i
$502$	−19.7829	−	11.4217i	−0.882954	−	0.509774i
$503$	5.72167	+	1.00888i	0.255116	+	0.0449839i	0.299744	−	0.954020i	$-0.403099\pi$
$503$	5.72167	+	1.00888i	0.255116	+	0.0449839i	−0.0446271	+	0.999004i	$0.514210\pi$
$504$	−2.15316	−	2.79152i	−0.0959092	−	0.124344i
$505$	−17.5039	−	30.3177i	−0.778914	−	1.34912i
$506$	−29.8345			−1.32631
$507$	−13.4464	−	14.0111i	−0.597177	−	0.622255i
$508$	7.01087	+	8.35523i	0.311057	+	0.370703i
$509$	−7.05873	+	40.0320i	−0.312873	+	1.77439i	0.271036	+	0.962569i	$0.412634\pi$
$509$	−7.05873	+	40.0320i	−0.312873	+	1.77439i	−0.583909	+	0.811819i	$0.698477\pi$
$510$	−1.31371	−	19.6653i	−0.0581719	−	0.870796i
$511$	−10.2398	+	8.59217i	−0.452980	+	0.380095i
$512$	−1.00000			−0.0441942
$513$	21.9844	+	5.44849i	0.970635	+	0.240557i
$514$	18.1217			0.799314
$515$	10.6479	−	8.93465i	0.469203	−	0.393708i
$516$	−0.217904	−	3.26189i	−0.00959271	−	0.143597i
$517$	−4.34366	+	24.6341i	−0.191034	+	1.08341i
$518$	4.46340	+	5.31927i	0.196110	+	0.233715i
$519$	11.6432	+	12.1322i	0.511081	+	0.532544i
$520$	−3.71853			−0.163068
$521$	13.9689	+	24.1949i	0.611989	+	1.06000i	0.990905	+	0.134565i	$0.0429637\pi$
$521$	13.9689	+	24.1949i	0.611989	+	1.06000i	−0.378916	+	0.925431i	$0.623703\pi$
$522$	11.5826	−	28.1624i	0.506955	−	1.23263i
$523$	−13.3111	−	2.34710i	−0.582053	−	0.102632i	−0.125134	−	0.992140i	$-0.539936\pi$
$523$	−13.3111	−	2.34710i	−0.582053	−	0.102632i	−0.456919	+	0.889508i	$0.651047\pi$
$524$	9.84057	+	5.68146i	0.429888	+	0.248196i
$525$	5.53021	+	0.598638i	0.241358	+	0.0261267i
$526$	−3.24253	−	8.90878i	−0.141381	−	0.388441i
$527$	15.6274	−	13.1130i	0.680741	−	0.571210i
$528$	−4.84800	+	4.65262i	−0.210982	+	0.202479i
$529$	33.9632	+	12.3616i	1.47666	+	0.537461i
$530$	22.6258	−	3.98953i	0.982800	−	0.173294i
$531$	32.5856	+	7.13834i	1.41409	+	0.309778i
$532$	−4.17614	−	2.96618i	−0.181058	−	0.128600i
$533$	2.30314	−	1.32972i	0.0997601	−	0.0575965i
$534$	0.302940	+	4.53481i	0.0131095	+	0.196241i
$535$	−48.3571	+	8.52667i	−2.09066	+	0.368640i
$536$	9.66078	+	1.70346i	0.417282	+	0.0735781i
$537$	−22.9835	+	15.3988i	−0.991813	+	0.664509i
$538$	−2.22549	+	12.6214i	−0.0959475	+	0.544145i
$539$	−18.8782	−	10.8993i	−0.813141	−	0.469467i
$540$	9.56801	+	10.8278i	0.411742	+	0.465953i
$541$	−4.40391	+	24.9758i	−0.189339	+	1.07380i	0.730913	+	0.682470i	$0.239094\pi$
$541$	−4.40391	+	24.9758i	−0.189339	+	1.07380i	−0.920252	+	0.391325i	$0.872017\pi$
$542$	8.23256	−	2.99641i	0.353619	−	0.128707i
$543$	1.48730	−	13.7396i	0.0638260	−	0.589624i
$544$	−3.54379	+	2.04601i	−0.151939	+	0.0877219i
$545$	−9.81342	+	3.57179i	−0.420361	+	0.152999i
$546$	−1.20075	+	2.44260i	−0.0513873	+	0.104533i
$547$	−6.85212	+	8.16604i	−0.292976	+	0.349155i	−0.892374	−	0.451296i	$-0.850962\pi$
$547$	−6.85212	+	8.16604i	−0.292976	+	0.349155i	0.599399	+	0.800451i	$0.295406\pi$
$548$	7.89203	+	9.40535i	0.337131	+	0.401777i
$549$	1.17940	+	0.747206i	0.0503354	+	0.0318900i
$550$		−	10.6020i		−	0.452070i
$551$	4.15224	−	44.0493i	0.176891	−	1.87656i
$552$	12.1854	−	5.37997i	0.518646	−	0.228987i
$553$	3.63510	−	9.98735i	0.154580	−	0.424706i
$554$	1.93407	+	10.9687i	0.0821707	+	0.466013i
$555$	−19.7064	−	20.5339i	−0.836488	−	0.871616i
$556$	−3.06747	−	17.3965i	−0.130090	−	0.737774i
$557$	8.58232	−	10.2280i	0.363644	−	0.433374i	−0.552937	−	0.833223i	$-0.686493\pi$
$557$	8.58232	−	10.2280i	0.363644	−	0.433374i	0.916581	+	0.399849i	$0.130937\pi$
$558$	−3.20045	+	14.6096i	−0.135486	+	0.618474i
$559$	−2.18578	+	1.26196i	−0.0924488	+	0.0533753i
$560$	−1.11767	−	3.07077i	−0.0472301	−	0.129764i
$561$	−7.66101	+	26.4070i	−0.323448	+	1.11490i
$562$	12.5979			0.531409
$563$	−4.73327	−	8.19826i	−0.199484	−	0.345516i	0.748878	−	0.662708i	$-0.230593\pi$
$563$	−4.73327	−	8.19826i	−0.199484	−	0.345516i	−0.948361	+	0.317193i	$0.897260\pi$
$564$	−2.66810	−	10.8447i	−0.112347	−	0.456644i
$565$	9.81418	−	1.73050i	0.412886	−	0.0728029i
$566$	18.6480	−	6.78731i	0.783833	−	0.285292i
$567$	10.2021	−	2.78856i	0.428446	−	0.117109i
$568$	−1.05059	−	5.95822i	−0.0440820	−	0.250001i
$569$	13.3321	+	23.0920i	0.558913	+	0.968065i	0.997588	+	0.0694192i	$0.0221146\pi$
$569$	13.3321	+	23.0920i	0.558913	+	0.968065i	−0.438675	+	0.898646i	$0.644552\pi$
$570$	17.8888	+	10.9894i	0.749277	+	0.460294i
$571$	−3.06682	+	5.31188i	−0.128342	+	0.222295i	−0.923034	−	0.384717i	$-0.874299\pi$
$571$	−3.06682	+	5.31188i	−0.128342	+	0.222295i	0.794692	+	0.607013i	$0.207632\pi$
$572$	4.87478	+	1.77427i	0.203825	+	0.0741861i
$573$	−22.2303	−	33.1798i	−0.928682	−	1.38611i
$574$	1.79034	+	1.50227i	0.0747272	+	0.0627035i
$575$	−7.18824	+	19.7495i	−0.299770	+	0.823612i
$576$	1.14109	−	2.77451i	0.0475456	−	0.115605i
$577$	−8.40032	+	14.5498i	−0.349710	+	0.605715i	−0.986198	−	0.165572i	$-0.947053\pi$
$577$	−8.40032	+	14.5498i	−0.349710	+	0.605715i	0.636488	+	0.771287i	$0.280386\pi$
$578$	0.127696	−	0.221175i	0.00531144	−	0.00919969i
$579$	3.76851	+	15.3174i	0.156614	+	0.636569i
$580$	18.1435	−	21.6226i	0.753368	−	0.897829i
$581$			3.33693i			0.138439i
$582$	1.00917	−	9.32265i	0.0418312	−	0.386436i
$583$	−31.5646	−	5.56570i	−1.30727	−	0.230508i
$584$	−10.6888	−	3.89042i	−0.442307	−	0.160987i
$585$	4.24319	−	10.3171i	0.175434	−	0.426559i
$586$	16.9895	−	14.2559i	0.701830	−	0.588905i
$587$	11.9263	+	14.2132i	0.492251	+	0.586642i	0.953788	−	0.300479i	$-0.0971466\pi$
$587$	11.9263	+	14.2132i	0.492251	+	0.586642i	−0.461538	+	0.887121i	$0.652702\pi$
$588$	9.67593	+	1.04741i	0.399029	+	0.0431944i
$589$	1.74845	+	21.6602i	0.0720436	+	0.892492i
$590$	26.7783	+	15.4605i	1.10245	+	0.636498i
$591$	−10.3920	+	21.1397i	−0.427471	+	0.869573i
$592$	−2.02096	+	5.55255i	−0.0830611	+	0.228208i
$593$	−5.68766	−	15.6267i	−0.233564	−	0.641713i	0.766435	−	0.642321i	$-0.222029\pi$
$593$	−5.68766	−	15.6267i	−0.233564	−	0.641713i	−1.00000		0.000608559i	$0.999806\pi$
$594$	−7.37670	−	18.7599i	−0.302670	−	0.769728i
$595$	−10.2436	−	8.59541i	−0.419947	−	0.352377i
$596$			18.2632i			0.748091i
$597$	−33.3162	−	3.60644i	−1.36354	−	0.147602i
$598$	−7.87782	−	6.61028i	−0.322148	−	0.270314i
$599$	20.7446	+	17.4068i	0.847600	+	0.711221i	0.959260	−	0.282526i	$-0.0911722\pi$
$599$	20.7446	+	17.4068i	0.847600	+	0.711221i	−0.111660	+	0.993746i	$0.535617\pi$
$600$	1.91182	+	4.33021i	0.0780499	+	0.176780i
$601$			42.4512i			1.73162i	0.500373	+	0.865810i	$0.333196\pi$
$601$			42.4512i			1.73162i	−0.500373	+	0.865810i	$0.666804\pi$
$602$	−1.69911	−	1.42572i	−0.0692504	−	0.0581080i
$603$	−15.7501	+	24.8601i	−0.641394	+	1.01238i
$604$	−1.79883	−	4.94225i	−0.0731934	−	0.201097i
$605$	−3.85190	+	10.5830i	−0.156602	+	0.430260i
$606$	−12.1369	−	18.1150i	−0.493028	−	0.735870i
$607$	28.1075	+	16.2279i	1.14085	+	0.658670i	0.946641	−	0.322290i	$-0.104453\pi$
$607$	28.1075	+	16.2279i	1.14085	+	0.658670i	0.194209	+	0.980960i	$0.437786\pi$
$608$	0.409072	−	4.33966i	0.0165900	−	0.175997i
$609$	−8.34454	−	18.9001i	−0.338138	−	0.765870i
$610$	0.831870	+	0.991384i	0.0336814	+	0.0401400i
$611$	−6.60500	+	5.54225i	−0.267210	+	0.224215i
$612$	−1.63287	−	12.1670i	−0.0660049	−	0.491821i
$613$	17.5455	+	6.38603i	0.708655	+	0.257929i	0.671102	−	0.741365i	$-0.265821\pi$
$613$	17.5455	+	6.38603i	0.708655	+	0.257929i	0.0375531	+	0.999295i	$0.488044\pi$
$614$	−17.4170	−	3.07109i	−0.702893	−	0.123939i
$615$	−7.73203	−	5.65446i	−0.311786	−	0.228010i
$616$			4.55889i			0.183683i
$617$	−2.61445	+	3.11579i	−0.105254	+	0.125437i	−0.816100	−	0.577911i	$-0.803868\pi$
$617$	−2.61445	+	3.11579i	−0.105254	+	0.125437i	0.710846	+	0.703348i	$0.248312\pi$
$618$	6.24646	−	5.99472i	0.251270	−	0.241143i
$619$	5.57046	−	9.64832i	0.223896	−	0.387799i	−0.732092	−	0.681206i	$-0.761456\pi$
$619$	5.57046	−	9.64832i	0.223896	−	0.387799i	0.955988	+	0.293407i	$0.0947892\pi$
$620$	−6.93164	+	12.0060i	−0.278381	+	0.482171i
$621$	1.02205	+	39.9476i	0.0410134	+	1.60304i
$622$	−11.8796	+	32.6389i	−0.476328	+	1.30870i
$623$	2.36217	+	1.98209i	0.0946383	+	0.0794109i
$624$	−2.31097	+	0.154380i	−0.0925129	+	0.00618015i
$625$	29.3144	+	10.6696i	1.17258	+	0.426783i
$626$	−11.2902	+	19.5552i	−0.451247	+	0.781582i
$627$	−18.2076	−	22.9419i	−0.727142	−	0.916212i
$628$	3.88801	+	6.73423i	0.155148	+	0.268725i
$629$	4.19870	+	23.8120i	0.167413	+	0.949446i
$630$	9.79525	+	0.403056i	0.390252	+	0.0160581i
$631$	6.32288	−	2.30134i	0.251710	−	0.0916150i	−0.213084	−	0.977034i	$-0.568351\pi$
$631$	6.32288	−	2.30134i	0.251710	−	0.0916150i	0.464794	+	0.885419i	$0.346128\pi$
$632$	8.90687	−	1.57052i	0.354296	−	0.0624720i
$633$	−19.0263	−	5.51978i	−0.756227	−	0.219392i
$634$	4.47909	+	7.75802i	0.177887	+	0.308110i
$635$	−30.3302			−1.20362
$636$	13.8957	−	3.41873i	0.551000	−	0.135562i
$637$	−2.56989	−	7.06071i	−0.101823	−	0.279756i
$638$	−34.1021	+	19.6889i	−1.35012	+	0.779490i
$639$	17.7300	+	3.88401i	0.701387	+	0.153649i
$640$	1.78747	−	2.13022i	0.0706558	−	0.0842043i
$641$	−0.286809	−	1.62658i	−0.0113283	−	0.0642459i	0.978620	−	0.205679i	$-0.0659402\pi$
$641$	−0.286809	−	1.62658i	−0.0113283	−	0.0642459i	−0.989948	+	0.141433i	$0.954829\pi$
$642$	−29.6987	+	7.30672i	−1.17212	+	0.288373i
$643$	−1.82136	−	10.3294i	−0.0718273	−	0.407353i	−0.999429	−	0.0337828i	$-0.989245\pi$
$643$	−1.82136	−	10.3294i	−0.0718273	−	0.407353i	0.927602	−	0.373570i	$-0.121867\pi$
$644$	3.09097	−	8.49236i	0.121801	−	0.334646i
$645$	7.33804	+	5.36633i	0.288935	+	0.211299i
$646$	−7.42932	−	16.2158i	−0.292303	−	0.638003i
$647$			12.7516i			0.501319i	0.968075	+	0.250659i	$0.0806475\pi$
$647$			12.7516i			0.501319i	−0.968075	+	0.250659i	$0.919353\pi$
$648$	6.39581	+	6.33196i	0.251251	+	0.248743i
$649$	−27.7280	−	33.0449i	−1.08842	−	1.29713i
$650$	2.34903	−	2.79946i	0.0921364	−	0.109804i
$651$	5.64808	+	8.43004i	0.221366	+	0.330399i
$652$	−2.40299	+	0.874618i	−0.0941085	+	0.0342527i
$653$	36.3606	−	20.9928i	1.42290	−	0.821511i	0.426353	−	0.904557i	$-0.359798\pi$
$653$	36.3606	−	20.9928i	1.42290	−	0.821511i	0.996546	+	0.0830458i	$0.0264648\pi$
$654$	−5.95050	+	2.62720i	−0.232683	+	0.102732i
$655$	−29.6925	+	10.8072i	−1.16018	+	0.422271i
$656$	−0.345350	+	1.95858i	−0.0134837	+	0.0764696i
$657$	22.9910	−	25.2169i	0.896963	−	0.983806i
$658$	−6.56205	−	3.78860i	−0.255815	−	0.147695i
$659$	−1.30578	+	7.40547i	−0.0508662	+	0.288476i	−0.999621	−	0.0275374i	$-0.991233\pi$
$659$	−1.30578	+	7.40547i	−0.0508662	+	0.288476i	0.948755	+	0.316014i	$0.102345\pi$
$660$	−1.24546	−	18.6437i	−0.0484794	−	0.725705i
$661$	−39.5505	−	6.97382i	−1.53834	−	0.271250i	−0.660726	−	0.750627i	$-0.729752\pi$
$661$	−39.5505	−	6.97382i	−1.53834	−	0.271250i	−0.877609	+	0.479377i	$0.840863\pi$
$662$	−3.77887	+	0.666317i	−0.146870	+	0.0258971i
$663$	−7.87374	+	5.27536i	−0.305791	+	0.204878i
$664$	−2.45916	+	1.41979i	−0.0954337	+	0.0550987i
$665$	13.7833	−	3.59414i	0.534494	−	0.139375i
$666$	−13.0995	−	11.9432i	−0.507595	−	0.462788i
$667$	76.8751	−	13.5552i	2.97662	−	0.524858i
$668$	−4.34849	−	1.58272i	−0.168248	−	0.0612373i
$669$	−3.01386	−	12.2501i	−0.116523	−	0.473616i
$670$	−20.8971	+	17.5347i	−0.807324	+	0.677425i
$671$	−0.617500	−	1.69657i	−0.0238383	−	0.0654953i
$672$	−0.822090	−	1.86200i	−0.0317128	−	0.0718284i
$673$	−3.64878	−	2.10662i	−0.140650	−	0.0812044i	0.428024	−	0.903768i	$-0.359210\pi$
$673$	−3.64878	−	2.10662i	−0.140650	−	0.0812044i	−0.568674	+	0.822563i	$0.692543\pi$
$674$	−23.1269	−	4.07790i	−0.890815	−	0.157075i
$675$	−14.1958	+	0.363195i	−0.546396	+	0.0139794i
$676$	−5.60593	−	9.70976i	−0.215613	−	0.373452i
$677$	24.9752			0.959873			0.479937	−	0.877303i	$-0.340660\pi$
$677$	24.9752			0.959873			0.479937	+	0.877303i	$0.340660\pi$
$678$	6.02742	−	1.48291i	0.231482	−	0.0569510i
$679$	−4.08947	−	4.87364i	−0.156939	−	0.187033i
$680$	1.97596	−	11.2062i	0.0757746	−	0.429739i
$681$	36.4046	−	24.3909i	1.39503	−	0.934660i
$682$	14.8155	−	12.4317i	0.567317	−	0.476035i
$683$	−25.3206			−0.968865			−0.484432	−	0.874829i	$-0.660974\pi$
$683$	−25.3206			−0.968865			−0.484432	+	0.874829i	$0.660974\pi$
$684$	11.5736	+	6.08694i	0.442529	+	0.232740i
$685$	−34.1422			−1.30451
$686$	11.3598	−	9.53202i	0.433720	−	0.363934i
$687$	4.88506	+	2.40143i	0.186377	+	0.0916205i
$688$	0.327752	−	1.85878i	0.0124954	−	0.0708652i
$689$	−7.10149	−	8.46323i	−0.270545	−	0.322423i
$690$	−10.3205	+	35.5742i	−0.392896	+	1.35429i
$691$	33.1171			1.25983			0.629917	−	0.776663i	$-0.283089\pi$
$691$	33.1171			1.25983			0.629917	+	0.776663i	$0.283089\pi$
$692$	4.85417	+	8.40766i	0.184528	+	0.319611i
$693$	−12.6487	−	5.20212i	−0.480484	−	0.197612i
$694$	13.0635	+	2.30345i	0.495885	+	0.0874379i
$695$	42.5413	+	24.5612i	1.61368	+	0.931660i
$696$	10.3780	−	14.1911i	0.393378	−	0.537913i
$697$	2.78342	+	7.64738i	0.105429	+	0.289665i
$698$	23.5520	−	19.7625i	0.891457	−	0.748022i
$699$	−35.5374	−	10.3099i	−1.34415	−	0.389955i
$700$	3.01784	+	1.09840i	0.114064	+	0.0415158i
$701$	14.6862	−	2.58958i	0.554692	−	0.0978071i	0.110726	−	0.993851i	$-0.464682\pi$
$701$	14.6862	−	2.58958i	0.554692	−	0.0978071i	0.443966	+	0.896044i	$0.353571\pi$
$702$	2.20871	−	6.58797i	0.0833623	−	0.248647i
$703$	−23.2695	−	11.0417i	−0.877625	−	0.416445i
$704$	−3.35969	+	1.93972i	−0.126623	+	0.0731058i
$705$	27.8707	+	13.7009i	1.04967	+	0.516005i
$706$	−1.32338	+	0.233348i	−0.0498061	+	0.00878216i
$707$	−14.5693	−	2.56895i	−0.547933	−	0.0966154i
$708$	17.2839	+	8.49655i	0.649569	+	0.319320i
$709$	5.64381	−	32.0076i	0.211958	−	1.20207i	−0.674151	−	0.738594i	$-0.735490\pi$
$709$	5.64381	−	32.0076i	0.211958	−	1.20207i	0.886108	−	0.463478i	$-0.153399\pi$
$710$	14.5702	+	8.41212i	0.546811	+	0.315701i
$711$	−5.80615	+	26.5043i	−0.217748	+	0.993989i
$712$	−0.455655	+	2.58415i	−0.0170764	+	0.0968450i
$713$	−36.0274	+	13.1129i	−1.34924	+	0.491082i
$714$	−6.72299	−	4.91655i	−0.251602	−	0.183997i
$715$	−12.4931	+	7.21289i	−0.467215	+	0.269747i
$716$	−15.0093	+	5.46293i	−0.560923	+	0.204159i
$717$	−30.1343	+	2.01307i	−1.12539	+	0.0751794i
$718$	13.6260	−	16.2388i	0.508516	−	0.606026i
$719$	−25.7038	−	30.6326i	−0.958591	−	1.14240i	−0.989739	−	0.142890i	$-0.954361\pi$
$719$	−25.7038	−	30.6326i	−0.958591	−	1.14240i	0.0311472	−	0.999515i	$-0.490084\pi$
$720$	3.87065	+	7.39013i	0.144250	+	0.275414i
$721$		−	5.87396i		−	0.218758i
$722$	18.6653	+	3.55046i	0.694651	+	0.132135i
$723$	1.89085	−	17.4677i	0.0703216	−	0.649630i
$724$	2.72895	−	7.49773i	0.101421	−	0.278651i
$725$	4.81696	+	27.3183i	0.178897	+	1.01458i
$726$	−1.95449	+	6.73699i	−0.0725379	+	0.250033i
$727$	3.01147	+	17.0789i	0.111689	+	0.633422i	0.988336	+	0.152288i	$0.0486640\pi$
$727$	3.01147	+	17.0789i	0.111689	+	0.633422i	−0.876647	+	0.481134i	$0.840225\pi$
$728$	−1.01009	+	1.20378i	−0.0374364	+	0.0446149i
$729$	−24.8663	+	10.5199i	−0.920974	+	0.389625i
$730$	27.3934	−	15.8156i	1.01387	−	0.585360i
$731$	−2.64159	−	7.25770i	−0.0977026	−	0.268436i
$732$	0.558145	+	0.581583i	0.0206296	+	0.0214959i
$733$	3.59652			0.132840			0.0664202	−	0.997792i	$-0.478842\pi$
$733$	3.59652			0.132840			0.0664202	+	0.997792i	$0.478842\pi$
$734$	−5.97737	−	10.3531i	−0.220629	−	0.382140i
$735$	−19.5266	+	18.7397i	−0.720250	+	0.691222i
$736$	7.57361	−	1.33543i	0.279167	−	0.0492247i
$737$	35.7614	−	13.0161i	1.31729	−	0.479454i
$738$	−5.04001	−	3.19310i	−0.185525	−	0.117540i
$739$	−1.38654	−	7.86348i	−0.0510048	−	0.289263i	0.948627	−	0.316397i	$-0.102473\pi$
$739$	−1.38654	−	7.86348i	−0.0510048	−	0.289263i	−0.999632	+	0.0271339i	$0.991362\pi$
$740$	−8.21575	−	14.2301i	−0.302017	−	0.523109i
$741$	0.275395	−	10.0920i	0.0101169	−	0.370738i
$742$	4.85448	−	8.40820i	0.178213	−	0.308675i
$743$	−29.9361	−	10.8959i	−1.09825	−	0.399731i	−0.271580	−	0.962416i	$-0.587546\pi$
$743$	−29.9361	−	10.8959i	−1.09825	−	0.399731i	−0.826671	+	0.562685i	$0.809768\pi$
$744$	−3.80939	+	7.74917i	−0.139659	+	0.284098i
$745$	−38.9047	−	32.6449i	−1.42536	−	1.19602i
$746$	3.26072	−	8.95874i	0.119383	−	0.328003i
$747$	−1.13310	−	8.44307i	−0.0414581	−	0.308916i
$748$	−7.93735	+	13.7479i	−0.290218	+	0.502673i
$749$	−10.3753	+	17.9705i	−0.379105	+	0.656628i
$750$	10.4872	+	3.04247i	0.382938	+	0.111095i
$751$	8.03425	−	9.57485i	0.293174	−	0.349391i	−0.599272	−	0.800546i	$-0.704543\pi$
$751$	8.03425	−	9.57485i	0.293174	−	0.349391i	0.892446	+	0.451154i	$0.148988\pi$
$752$		−	6.44789i		−	0.235131i
$753$	36.1950	−	15.9804i	1.31902	−	0.582358i
$754$	−13.3670	−	2.35697i	−0.486799	−	0.0858358i
$755$	13.7434	+	5.00220i	0.500175	+	0.182049i
$756$	6.10423	−	0.156175i	0.222009	−	0.00568003i
$757$	−33.0370	+	27.7213i	−1.20075	+	1.00755i	−0.201140	+	0.979562i	$0.564465\pi$
$757$	−33.0370	+	27.7213i	−1.20075	+	1.00755i	−0.999608	+	0.0279852i	$0.991091\pi$
$758$	19.0334	+	22.6831i	0.691325	+	0.823888i
$759$	30.5036	−	41.7113i	1.10721	−	1.51402i
$760$	8.51323	+	8.62841i	0.308807	+	0.312985i
$761$	−3.58301	−	2.06865i	−0.129884	−	0.0749886i	0.433650	−	0.901081i	$-0.357225\pi$
$761$	−3.58301	−	2.06865i	−0.129884	−	0.0749886i	−0.563534	+	0.826093i	$0.690559\pi$
$762$	−18.8494	+	1.25920i	−0.682843	+	0.0456160i
$763$	−1.50941	+	4.14707i	−0.0546443	+	0.150134i
$764$	−7.88647	−	21.6679i	−0.285322	−	0.783917i
$765$	28.8370	+	18.2697i	1.04260	+	0.660542i
$766$	−22.2516	−	18.6713i	−0.803984	−	0.674623i
$767$		−	14.8691i		−	0.536890i
$768$	1.02243	−	1.39809i	0.0368936	−	0.0504491i
$769$	19.5205	+	16.3797i	0.703928	+	0.590666i	0.922888	−	0.385068i	$-0.125822\pi$
$769$	19.5205	+	16.3797i	0.703928	+	0.590666i	−0.218960	+	0.975734i	$0.570266\pi$
$770$	−9.71144	−	8.14886i	−0.349976	−	0.293665i
$771$	−18.5281	+	25.3357i	−0.667273	+	0.912444i
$772$			9.10721i			0.327776i
$773$	−16.4113	−	13.7707i	−0.590273	−	0.495298i	0.298030	−	0.954557i	$-0.403671\pi$
$773$	−16.4113	−	13.7707i	−0.590273	−	0.495298i	−0.888303	+	0.459259i	$0.848115\pi$
$774$	4.78319	+	3.03039i	0.171928	+	0.108925i
$775$	−4.65980	−	12.8027i	−0.167385	−	0.459886i
$776$	1.85165	−	5.08738i	0.0664705	−	0.182626i
$777$	−12.0003	+	0.801657i	−0.430508	+	0.0287593i
$778$	−26.8669	−	15.5116i	−0.963223	−	0.556117i
$779$	−8.35829	−	2.29990i	−0.299467	−	0.0824025i
$780$	3.80192	−	5.19883i	0.136131	−	0.186148i
$781$	−15.0869	−	17.9799i	−0.539852	−	0.643371i
$782$	24.1070	−	20.2282i	0.862064	−	0.723358i
$783$	27.5311	+	44.9874i	0.983882	+	1.60772i
$784$	5.28017	+	1.92182i	0.188577	+	0.0686366i
$785$	−21.2951	−	3.75490i	−0.760054	−	0.134018i
$786$	−18.0044	+	7.94910i	−0.642197	+	0.283535i
$787$		−	35.3212i		−	1.25907i	−0.776974	−	0.629533i	$-0.783246\pi$
$787$		−	35.3212i		−	1.25907i	0.776974	−	0.629533i	$-0.216754\pi$
$788$	−8.74193	+	10.4182i	−0.311419	+	0.371134i
$789$	15.7705	+	4.57523i	0.561444	+	0.162882i
$790$	−12.5752	+	21.7808i	−0.447404	+	0.774927i
$791$	2.10568	−	3.64715i	0.0748695	−	0.129678i
$792$	−1.54804	−	11.5349i	−0.0550072	−	0.409874i
$793$	0.212848	−	0.584796i	0.00755846	−	0.0207667i
$794$	5.85423	+	4.91229i	0.207759	+	0.174331i
$795$	−17.5554	+	35.7118i	−0.622628	+	1.26657i
$796$	−18.1807	−	6.61723i	−0.644397	−	0.234541i
$797$	−19.4955	+	33.7673i	−0.690567	+	1.19610i	0.281085	+	0.959683i	$0.409306\pi$
$797$	−19.4955	+	33.7673i	−0.690567	+	1.19610i	−0.971652	+	0.236415i	$0.924028\pi$
$798$	8.41676	−	2.80590i	0.297950	−	0.0993278i
$799$	−13.1924	−	22.8500i	−0.466715	−	0.808375i
$800$	0.474558	+	2.69135i	0.0167782	+	0.0951537i
$801$	−6.64979	−	4.21297i	−0.234959	−	0.148858i
$802$	−8.64001	+	3.14471i	−0.305089	+	0.111043i
$803$	−43.4574	+	7.66271i	−1.53358	+	0.270411i
$804$	−12.2590	+	11.7649i	−0.432342	+	0.414918i
$805$	12.5656	+	21.7642i	0.442879	+	0.767089i
$806$	6.66648			0.234817
$807$	−15.3704	−	16.0158i	−0.541062	−	0.563784i
$808$	−4.30573	−	11.8299i	−0.151475	−	0.416174i
$809$	−33.1413	+	19.1342i	−1.16519	+	0.672721i	−0.952542	−	0.304408i	$-0.901541\pi$
$809$	−33.1413	+	19.1342i	−1.16519	+	0.672721i	−0.212646	+	0.977129i	$0.568208\pi$
$810$	−24.9207	+	2.30632i	−0.875626	+	0.0810357i
$811$	−19.6262	+	23.3896i	−0.689169	+	0.821320i	−0.991255	−	0.131961i	$-0.957873\pi$
$811$	−19.6262	+	23.3896i	−0.689169	+	0.821320i	0.302085	+	0.953281i	$0.402317\pi$
$812$	−2.07131	−	11.7470i	−0.0726886	−	0.412238i
$813$	−4.22795	+	14.5734i	−0.148281	+	0.511113i
$814$	3.98057	+	22.5749i	0.139519	+	0.791250i
$815$	2.43214	−	6.68225i	0.0851942	−	0.234069i
$816$	0.762766	−	7.04642i	0.0267022	−	0.246674i
$817$	7.93238	+	2.18271i	0.277519	+	0.0763632i
$818$		−	12.1248i		−	0.423935i
$819$	−2.18728	−	4.17612i	−0.0764299	−	0.145926i
$820$	−3.55490	−	4.23656i	−0.124142	−	0.147947i
$821$	3.87375	−	4.61655i	0.135195	−	0.161119i	−0.694199	−	0.719783i	$-0.744241\pi$
$821$	3.87375	−	4.61655i	0.135195	−	0.161119i	0.829394	+	0.558664i	$0.188686\pi$
$822$	−21.2185	+	1.41746i	−0.740081	+	0.0494397i
$823$	30.6795	−	11.1664i	1.06942	−	0.389237i	0.253460	−	0.967346i	$-0.418431\pi$
$823$	30.6795	−	11.1664i	1.06942	−	0.389237i	0.815960	+	0.578109i	$0.196209\pi$
$824$	4.32883	−	2.49925i	0.150802	−	0.0870655i
$825$	14.8225	+	10.8397i	0.516053	+	0.377392i
$826$	12.2789	−	4.46915i	0.427238	−	0.155502i
$827$	4.62196	−	26.2124i	0.160721	−	0.911496i	−0.792646	−	0.609683i	$-0.791297\pi$
$827$	4.62196	−	26.2124i	0.160721	−	0.911496i	0.953367	−	0.301813i	$-0.0975919\pi$
$828$	−4.93704	+	22.5369i	−0.171574	+	0.783211i
$829$	−24.9175	−	14.3861i	−0.865421	−	0.499651i	0.000402818	−	1.00000i	$-0.499872\pi$
$829$	−24.9175	−	14.3861i	−0.865421	−	0.499651i	−0.865824	+	0.500349i	$0.833205\pi$
$830$	1.37118	−	7.77638i	0.0475945	−	0.269922i
$831$	−17.3126	−	8.51064i	−0.600566	−	0.295231i
$832$	−1.31690	−	0.232205i	−0.0456552	−	0.00805025i
$833$	22.6439	−	3.99273i	0.784564	−	0.138340i
$834$	27.4580	+	13.4980i	0.950793	+	0.467398i
$835$	11.1443	−	6.43417i	0.385665	−	0.222664i
$836$	−7.04336	−	15.3734i	−0.243600	−	0.531699i
$837$	−17.1533	−	19.4117i	−0.592904	−	0.670968i
$838$	−23.6307	+	4.16674i	−0.816310	+	0.143938i
$839$	14.9595	+	5.44480i	0.516458	+	0.187975i	0.587082	−	0.809528i	$-0.300277\pi$
$839$	14.9595	+	5.44480i	0.516458	+	0.187975i	−0.0706237	+	0.997503i	$0.522499\pi$
$840$	5.43594	+	1.57704i	0.187558	+	0.0544130i
$841$	56.7107	−	47.5859i	1.95554	−	1.64089i
$842$	−10.2813	−	28.2477i	−0.354317	−	0.973479i
$843$	−12.8804	+	17.6129i	−0.443624	+	0.606620i
$844$	−9.90540	−	5.71889i	−0.340958	−	0.196852i
$845$	30.7043	+	5.41400i	1.05626	+	0.186247i
$846$	17.8897	+	7.35766i	0.615062	+	0.252961i
$847$	2.37966	+	4.12168i	0.0817659	+	0.141623i
$848$	8.26193			0.283716
$849$	−9.57693	+	33.0110i	−0.328679	+	1.13293i
$850$	7.18827	+	8.56665i	0.246556	+	0.293834i
$851$	7.89093	−	44.7517i	0.270498	−	1.53407i
$852$	9.40426	+	4.62301i	0.322185	+	0.158382i
$853$	−12.0572	+	10.1172i	−0.412829	+	0.346405i	−0.825427	−	0.564508i	$-0.809066\pi$
$853$	−12.0572	+	10.1172i	−0.412829	+	0.346405i	0.412598	+	0.910913i	$0.364621\pi$
$854$	0.546901			0.0187146
$855$	−33.6540	+	13.7742i	−1.15094	+	0.471068i
$856$	−17.6579			−0.603534
$857$	−43.1823	+	36.2342i	−1.47508	+	1.23774i	−0.563823	+	0.825895i	$0.690670\pi$
$857$	−43.1823	+	36.2342i	−1.47508	+	1.23774i	−0.911255	+	0.411842i	$0.864885\pi$
$858$	−7.46468	+	5.00129i	−0.254840	+	0.170741i
$859$	−8.70454	+	49.3659i	−0.296995	+	1.68434i	0.361986	+	0.932183i	$0.382099\pi$
$859$	−8.70454	+	49.3659i	−0.296995	+	1.68434i	−0.658981	+	0.752159i	$0.729012\pi$
$860$	3.37375	+	4.02068i	0.115044	+	0.137104i
$861$	−3.93079	+	0.967084i	−0.133961	+	0.0329581i
$862$	2.35175			0.0801009
$863$	−6.88125	−	11.9187i	−0.234240	−	0.405716i	0.724811	−	0.688947i	$-0.241927\pi$
$863$	−6.88125	−	11.9187i	−0.234240	−	0.405716i	−0.959052	+	0.283231i	$0.908594\pi$
$864$	2.71232	+	4.43208i	0.0922750	+	0.150782i
$865$	−26.5868	−	4.68797i	−0.903979	−	0.159396i
$866$	28.3045	+	16.3416i	0.961826	+	0.555310i
$867$	0.178663	+	0.404665i	0.00606772	+	0.0137431i
$868$	2.00373	+	5.50520i	0.0680109	+	0.186859i
$869$	26.8779	−	22.5532i	0.911770	−	0.765066i
$870$	11.6799	+	47.4737i	0.395984	+	1.60951i
$871$	12.3267	+	4.48656i	0.417675	+	0.152021i
$872$	−3.69842	+	0.652130i	−0.125244	+	0.0220839i
$873$	12.0021	+	10.9426i	0.406208	+	0.370351i
$874$	2.69717	+	33.4132i	0.0912332	+	1.13022i
$875$	6.41606	−	3.70431i	0.216902	−	0.125229i
$876$	16.3677	−	10.9662i	0.553012	−	0.370515i
$877$	20.8813	−	3.68193i	0.705111	−	0.124330i	0.190416	−	0.981704i	$-0.439016\pi$
$877$	20.8813	−	3.68193i	0.705111	−	0.124330i	0.514695	+	0.857373i	$0.327905\pi$
$878$	31.7396	+	5.59655i	1.07116	+	0.188874i
$879$	2.56045	+	38.3284i	0.0863620	+	1.29278i
$880$	1.87331	−	10.6240i	0.0631491	−	0.358136i
$881$	−28.2708	−	16.3221i	−0.952466	−	0.549907i	−0.0586200	−	0.998280i	$-0.518670\pi$
$881$	−28.2708	−	16.3221i	−0.952466	−	0.549907i	−0.893846	+	0.448374i	$0.852003\pi$
$882$	−11.3573	+	12.4569i	−0.382420	+	0.419445i
$883$	4.30220	−	24.3990i	0.144781	−	0.821092i	−0.822762	−	0.568385i	$-0.807568\pi$
$883$	4.30220	−	24.3990i	0.144781	−	0.821092i	0.967543	−	0.252706i	$-0.0813206\pi$
$884$	−5.14191	+	1.87150i	−0.172941	+	0.0629454i
$885$	−48.9939	+	21.6312i	−1.64691	+	0.727126i
$886$	0.684567	−	0.395235i	0.0229985	−	0.0132782i
$887$	−0.294656	+	0.107246i	−0.00989359	+	0.00360097i	−0.346962	−	0.937879i	$-0.612787\pi$
$887$	−0.294656	+	0.107246i	−0.00989359	+	0.00360097i	0.337069	+	0.941480i	$0.390565\pi$
$888$	−5.69666	−	8.50255i	−0.191167	−	0.285327i
$889$	−8.23879	+	9.81860i	−0.276320	+	0.329305i
$890$	−4.69033	−	5.58972i	−0.157220	−	0.187368i
$891$	33.7701	+	8.86733i	1.13134	+	0.297067i
$892$		−	7.28350i		−	0.243869i
$893$	27.9817	+	2.63765i	0.936371	+	0.0882656i
$894$	−25.5336	−	18.6728i	−0.853971	−	0.624512i
$895$	15.1913	−	41.7379i	0.507791	−	1.39514i
$896$	−0.204062	−	1.15729i	−0.00681722	−	0.0386624i
$897$	17.2962	−	4.25536i	0.577504	−	0.142082i
$898$	5.38932	+	30.5643i	0.179844	+	1.01995i
$899$	−32.5272	+	38.7644i	−1.08484	+	1.29286i
$900$	−8.00870	−	1.75442i	−0.266957	−	0.0584808i
$901$	29.2785	−	16.9040i	0.975410	−	0.563153i
$902$	2.63881	+	7.25008i	0.0878629	+	0.241401i
$903$	3.73049	−	0.917806i	0.124143	−	0.0305427i
$904$	3.58370			0.119192
$905$	11.0939	+	19.2152i	0.368774	+	0.638735i
$906$	8.74887	+	2.53816i	0.290662	+	0.0843248i
$907$	−21.2789	+	3.75205i	−0.706556	+	0.124585i	−0.515368	−	0.856969i	$-0.672345\pi$
$907$	−21.2789	+	3.75205i	−0.706556	+	0.124585i	−0.191187	+	0.981554i	$0.561234\pi$
$908$	23.7738	−	8.65297i	0.788963	−	0.287159i
$909$	37.7354	+	1.55274i	1.25160	+	0.0515011i
$910$	−0.758809	−	4.30342i	−0.0251543	−	0.142657i
$911$	8.31668	+	14.4049i	0.275544	+	0.477256i	0.970272	−	0.242016i	$-0.0778087\pi$
$911$	8.31668	+	14.4049i	0.275544	+	0.477256i	−0.694728	+	0.719272i	$0.744475\pi$
$912$	5.64898	+	5.00890i	0.187056	+	0.165861i
$913$	−5.50799	+	9.54012i	−0.182288	+	0.315732i
$914$	−39.6799	−	14.4423i	−1.31249	−	0.477709i
$915$	−2.23657	+	0.149410i	−0.0739386	+	0.00493933i
$916$	2.40749	+	2.02012i	0.0795457	+	0.0667468i
$917$	−4.56702	+	12.5478i	−0.150816	+	0.414364i
$918$	18.6800	+	10.1569i	0.616531	+	0.335229i
$919$	18.3530	−	31.7884i	0.605410	−	1.04860i	−0.386576	−	0.922258i	$-0.626342\pi$
$919$	18.3530	−	31.7884i	0.605410	−	1.04860i	0.991986	−	0.126344i	$-0.0403243\pi$
$920$	−10.6928	+	18.5205i	−0.352531	+	0.610602i
$921$	22.1012	−	21.2105i	0.728261	−	0.698911i
$922$	7.11348	−	8.47751i	0.234270	−	0.279192i
$923$		−	8.09032i		−	0.266296i
$924$	−6.37372	−	4.66113i	−0.209680	−	0.153340i
$925$	15.9029	+	2.80412i	0.522886	+	0.0921988i
$926$	−22.3946	−	8.15098i	−0.735933	−	0.267858i
$927$	1.99459	+	14.8623i	0.0655110	+	0.488140i
$928$	7.77566	−	6.52455i	0.255248	−	0.214179i
$929$	−22.3365	−	26.6196i	−0.732838	−	0.873362i	0.262973	−	0.964803i	$-0.415297\pi$
$929$	−22.3365	−	26.6196i	−0.732838	−	0.873362i	−0.995810	+	0.0914412i	$0.970853\pi$
$930$	−9.69828	−	21.9662i	−0.318019	−	0.720301i
$931$	−10.5000	+	22.1280i	−0.344125	+	0.725215i
$932$	−18.5014	−	10.6818i	−0.606032	−	0.349893i
$933$	−33.4860	−	49.9795i	−1.09628	−	1.63625i
$934$	−4.77879	+	13.1296i	−0.156367	+	0.429614i
$935$	−15.0983	−	41.4822i	−0.493767	−	1.35661i
$936$	2.14696	−	3.38878i	0.0701756	−	0.110766i
$937$	36.3375	+	30.4908i	1.18710	+	0.996091i	0.999905	+	0.0137672i	$0.00438238\pi$
$937$	36.3375	+	30.4908i	1.18710	+	0.996091i	0.187190	+	0.982324i	$0.440062\pi$
$938$			11.5279i			0.376401i
$939$	−15.7965	−	35.7784i	−0.515498	−	1.16758i
$940$	13.7354	+	11.5254i	0.448000	+	0.375917i
$941$	−10.4242	−	8.74694i	−0.339819	−	0.285142i	0.456867	−	0.889535i	$-0.348971\pi$
$941$	−10.4242	−	8.74694i	−0.339819	−	0.285142i	−0.796687	+	0.604393i	$0.793416\pi$
$942$	−13.3902	−	1.44948i	−0.436278	−	0.0472265i
$943$		−	15.2947i		−	0.498064i
$944$	8.51798	+	7.14743i	0.277237	+	0.232629i
$945$	−10.5784	+	13.2825i	−0.344116	+	0.432080i
$946$	−2.50435	−	6.88065i	−0.0814235	−	0.223709i
$947$	6.66414	−	18.3096i	0.216556	−	0.594981i	−0.783082	−	0.621919i	$-0.786353\pi$
$947$	6.66414	−	18.3096i	0.216556	−	0.594981i	0.999637	+	0.0269376i	$0.00857553\pi$
$948$	−6.91088	+	14.0583i	−0.224455	+	0.456593i
$949$	−13.1727	−	7.60528i	−0.427605	−	0.246878i
$950$	−11.8737	+	0.958466i	−0.385234	+	0.0310967i
$951$	−15.4259	−	1.66984i	−0.500220	−	0.0541482i
$952$	−3.09098	−	3.68369i	−0.100179	−	0.119389i
$953$	−21.1702	+	17.7639i	−0.685770	+	0.575429i	−0.917686	−	0.397307i	$-0.869945\pi$
$953$	−21.1702	+	17.7639i	−0.685770	+	0.575429i	0.231916	+	0.972736i	$0.425500\pi$
$954$	−9.42764	+	22.9228i	−0.305231	+	0.742153i
$955$	60.2542	+	21.9307i	1.94978	+	0.709662i
$956$	−17.1719	−	3.02787i	−0.555380	−	0.0979285i
$957$	7.34015	−	67.8082i	0.237273	−	2.19193i
$958$			6.62951i			0.214190i
$959$	−9.27427	+	11.0526i	−0.299482	+	0.356909i
$960$	1.15068	+	4.67702i	0.0371380	+	0.150950i
$961$	−3.07314	+	5.32283i	−0.0991335	+	0.171704i
$962$	−3.95073	+	6.84287i	−0.127377	+	0.220623i
$963$	20.1493	−	48.9920i	0.649303	−	1.57874i
$964$	3.46941	−	9.53213i	0.111742	−	0.307009i
$965$	−19.4004	−	16.2788i	−0.624520	−	0.524034i
$966$	8.71277	+	13.0042i	0.280329	+	0.418405i
$967$	47.6062	+	17.3272i	1.53091	+	0.557206i	0.963845	−	0.266465i	$-0.0858557\pi$
$967$	47.6062	+	17.3272i	1.53091	+	0.557206i	0.567067	+	0.823671i	$0.308078\pi$
$968$	−2.02499	+	3.50739i	−0.0650856	+	0.112732i
$969$	30.2670	+	6.19264i	0.972318	+	0.198936i
$970$	7.52746	+	13.0380i	0.241692	+	0.418623i
$971$	10.4322	+	59.1638i	0.334784	+	1.89866i	0.429350	+	0.903138i	$0.358743\pi$
$971$	10.4322	+	59.1638i	0.334784	+	1.89866i	−0.0945655	+	0.995519i	$0.530146\pi$
$972$	−15.3919	+	2.46794i	−0.493694	+	0.0791591i
$973$	19.5068	−	7.09990i	0.625360	−	0.227612i
$974$	−4.95237	+	0.873237i	−0.158684	+	0.0279803i
$975$	1.51218	+	6.14638i	0.0484286	+	0.196842i
$976$	0.232695	+	0.403040i	0.00744839	+	0.0129010i
$977$	52.8067			1.68944			0.844718	−	0.535212i	$-0.179768\pi$
$977$	52.8067			1.68944			0.844718	+	0.535212i	$0.179768\pi$
$978$	1.23409	−	4.25382i	0.0394619	−	0.136022i
$979$	3.48165	+	9.56576i	0.111274	+	0.305723i
$980$	−13.5320	+	7.81272i	−0.432265	+	0.249568i
$981$	2.41090	−	11.0054i	0.0769741	−	0.351376i
$982$	3.67252	−	4.37674i	0.117195	−	0.139667i
$983$	3.83710	+	21.7613i	0.122384	+	0.694077i	0.982827	+	0.184529i	$0.0590761\pi$
$983$	3.83710	+	21.7613i	0.122384	+	0.694077i	−0.860443	+	0.509547i	$0.829813\pi$
$984$	−2.38517	−	2.48533i	−0.0760363	−	0.0792294i
$985$	−6.56721	−	37.2445i	−0.209249	−	1.18671i
$986$	14.2060	−	39.0307i	0.452412	−	1.24299i
$987$	12.0060	−	5.30075i	0.382155	−	0.168725i
$988$	1.54640	−	5.61990i	0.0491974	−	0.178793i
$989$			14.5153i			0.461561i
$990$	27.3389	+	17.3205i	0.868887	+	0.550483i
$991$	30.0656	+	35.8308i	0.955066	+	1.13820i	0.990317	+	0.138825i	$0.0443325\pi$
$991$	30.0656	+	35.8308i	0.955066	+	1.13820i	−0.0352509	+	0.999378i	$0.511223\pi$
$992$	−3.20452	+	3.81900i	−0.101744	+	0.121253i
$993$	2.93205	−	5.96445i	0.0930457	−	0.189276i
$994$	6.68101	−	2.43169i	0.211909	−	0.0771285i
$995$	46.5935	−	26.9008i	1.47711	−	0.852812i
$996$	0.529309	−	4.88975i	0.0167718	−	0.154938i
$997$	34.6675	−	12.6179i	1.09793	−	0.399614i	0.271377	−	0.962473i	$-0.412521\pi$
$997$	34.6675	−	12.6179i	1.09793	−	0.399614i	0.826553	+	0.562859i	$0.190299\pi$
$998$	−5.28261	+	29.9592i	−0.167218	+	0.948341i
$999$	30.0908	−	6.10323i	0.952032	−	0.193097i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.bf.c.257.5	yes	60
9.2	odd	6		342.2.x.c.29.2	✓	60
19.2	odd	18		342.2.x.c.59.2	yes	60
171.2	even	18	inner	342.2.bf.c.173.5	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.x.c.29.2	✓	60	9.2	odd	6
342.2.x.c.59.2	yes	60	19.2	odd	18
342.2.bf.c.173.5	yes	60	171.2	even	18	inner
342.2.bf.c.257.5	yes	60	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.115449 - 1.72820i) q^{3} +(0.173648 - 0.984808i) q^{4} +(1.78747 + 2.13022i) q^{5} +(1.19930 + 1.24967i) q^{6} +1.17514 q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.97334 + 0.399038i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.115449 - 1.72820i) q^{3} +(0.173648 - 0.984808i) q^{4} +(1.78747 + 2.13022i) q^{5} +(1.19930 + 1.24967i) q^{6} +1.17514 q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.97334 + 0.399038i) q^{9} +(-2.73856 - 0.482882i) q^{10} +(3.35969 + 1.93972i) q^{11} +(-1.72199 - 0.186403i) q^{12} +(0.457354 + 1.25657i) q^{13} +(-0.900213 + 0.755368i) q^{14} +(3.47508 - 3.33503i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-4.02985 + 0.710571i) q^{17} +(2.02122 - 2.21691i) q^{18} +(1.86865 - 3.93804i) q^{19} +(2.40825 - 1.39040i) q^{20} +(-0.135669 - 2.03088i) q^{21} +(-3.82049 + 0.673656i) q^{22} +(7.57361 + 1.33543i) q^{23} +(1.43894 - 0.964081i) q^{24} +(-0.474558 + 2.69135i) q^{25} +(-1.15806 - 0.668607i) q^{26} +(1.03289 + 5.09246i) q^{27} +(0.204062 - 1.15729i) q^{28} +(9.53825 - 3.47164i) q^{29} +(-0.518351 + 4.78852i) q^{30} +(-4.31744 + 2.49268i) q^{31} +(0.939693 - 0.342020i) q^{32} +(2.96434 - 6.03014i) q^{33} +(2.63030 - 3.13467i) q^{34} +(2.10053 + 2.50332i) q^{35} +(-0.123340 + 2.99746i) q^{36} -5.90890i q^{37} +(1.09985 + 4.21786i) q^{38} +(2.11880 - 0.935469i) q^{39} +(-0.951091 + 2.61310i) q^{40} +(-0.345350 - 1.95858i) q^{41} +(1.40936 + 1.46854i) q^{42} +(0.327752 + 1.85878i) q^{43} +(2.49365 - 2.97182i) q^{44} +(-6.16479 - 5.62061i) q^{45} +(-6.66012 + 3.84522i) q^{46} +(2.20531 + 6.05904i) q^{47} +(-0.482592 + 1.66346i) q^{48} -5.61904 q^{49} +(-1.36644 - 2.36674i) q^{50} +(1.69325 + 6.88235i) q^{51} +(1.31690 - 0.232205i) q^{52} +(-7.76367 + 2.82574i) q^{53} +(-4.06461 - 3.23712i) q^{54} +(1.87331 + 10.6240i) q^{55} +(0.587572 + 1.01770i) q^{56} +(-7.02145 - 2.77476i) q^{57} +(-5.07520 + 8.79050i) q^{58} +(-10.4488 - 3.80307i) q^{59} +(-2.68092 - 4.00141i) q^{60} +(-0.356510 - 0.299147i) q^{61} +(1.70509 - 4.68470i) q^{62} +(-3.49411 + 0.468927i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.85926 + 3.22034i) q^{65} +(1.60528 + 6.52480i) q^{66} +(6.30563 - 7.51475i) q^{67} +4.09202i q^{68} +(1.43353 - 13.2429i) q^{69} +(-3.21820 - 0.567456i) q^{70} +(-5.68527 - 2.06927i) q^{71} +(-1.83225 - 2.37547i) q^{72} +(-8.71361 + 7.31159i) q^{73} +(3.79817 + 4.52648i) q^{74} +(4.70598 + 0.509417i) q^{75} +(-3.55372 - 2.52410i) q^{76} +(3.94812 + 2.27945i) q^{77} +(-1.02179 + 2.07855i) q^{78} +(3.09332 - 8.49883i) q^{79} +(-0.951091 - 2.61310i) q^{80} +(8.68154 - 2.37295i) q^{81} +(1.52350 + 1.27837i) q^{82} +2.83959i q^{83} +(-2.02359 - 0.219051i) q^{84} +(-8.71690 - 7.31434i) q^{85} +(-1.44587 - 1.21323i) q^{86} +(-7.10087 - 16.0832i) q^{87} +3.87943i q^{88} +(2.01011 + 1.68668i) q^{89} +(8.33536 + 0.342984i) q^{90} +(0.537457 + 1.47665i) q^{91} +(2.63029 - 7.22665i) q^{92} +(4.80628 + 7.17362i) q^{93} +(-5.58404 - 3.22395i) q^{94} +(11.7290 - 3.05847i) q^{95} +(-0.699565 - 1.58449i) q^{96} +(-3.47997 - 4.14727i) q^{97} +(4.30443 - 3.61185i) q^{98} +(-10.7635 - 4.42680i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 3 q^{6} + 30 q^{8}+O(q^{10}) \) 60 * q + 3 * q^6 + 30 * q^8	\( 60 q + 3 q^{6} + 30 q^{8} + 3 q^{13} - 3 q^{14} - 6 q^{15} + 27 q^{17} + 18 q^{18} + 3 q^{19} - 9 q^{22} - 18 q^{25} + 24 q^{27} + 3 q^{28} - 27 q^{29} - 36 q^{33} - 3 q^{36} + 9 q^{38} - 30 q^{39} + 9 q^{41} + 6 q^{43} + 9 q^{44} - 3 q^{48} + 60 q^{49} - 66 q^{50} - 33 q^{51} - 3 q^{52} - 60 q^{57} - 81 q^{59} + 27 q^{60} - 78 q^{61} + 3 q^{62} - 33 q^{63} - 30 q^{64} + 18 q^{65} + 57 q^{66} + 15 q^{67} + 6 q^{69} + 18 q^{71} - 66 q^{73} - 3 q^{74} - 45 q^{78} + 48 q^{79} + 36 q^{81} + 3 q^{84} + 3 q^{86} - 72 q^{87} + 27 q^{89} + 6 q^{90} - 69 q^{91} - 18 q^{92} + 105 q^{93} - 18 q^{94} - 108 q^{97} - 60 q^{98} - 30 q^{99}+O(q^{100}) \) 60 * q + 3 * q^6 + 30 * q^8 + 3 * q^13 - 3 * q^14 - 6 * q^15 + 27 * q^17 + 18 * q^18 + 3 * q^19 - 9 * q^22 - 18 * q^25 + 24 * q^27 + 3 * q^28 - 27 * q^29 - 36 * q^33 - 3 * q^36 + 9 * q^38 - 30 * q^39 + 9 * q^41 + 6 * q^43 + 9 * q^44 - 3 * q^48 + 60 * q^49 - 66 * q^50 - 33 * q^51 - 3 * q^52 - 60 * q^57 - 81 * q^59 + 27 * q^60 - 78 * q^61 + 3 * q^62 - 33 * q^63 - 30 * q^64 + 18 * q^65 + 57 * q^66 + 15 * q^67 + 6 * q^69 + 18 * q^71 - 66 * q^73 - 3 * q^74 - 45 * q^78 + 48 * q^79 + 36 * q^81 + 3 * q^84 + 3 * q^86 - 72 * q^87 + 27 * q^89 + 6 * q^90 - 69 * q^91 - 18 * q^92 + 105 * q^93 - 18 * q^94 - 108 * q^97 - 60 * q^98 - 30 * q^99

Introduction

L-functions

Modular forms

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