LMFDB - Embedded newform 690.2.w.a.373.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			373.4
Character	$\chi$	$=$	690.373
Dual form			690.2.w.a.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.877679 + 0.479249i) q^{2} +(-0.997452 + 0.0713392i) q^{3} +(0.540641 - 0.841254i) q^{4} +(0.565910 - 2.16327i) q^{5} +(0.841254 - 0.540641i) q^{6} +(1.25538 - 3.36582i) q^{7} +(-0.0713392 + 0.997452i) q^{8} +(0.989821 - 0.142315i) q^{9} +O(q^{10})$	\(q+(-0.877679 + 0.479249i) q^{2} +(-0.997452 + 0.0713392i) q^{3} +(0.540641 - 0.841254i) q^{4} +(0.565910 - 2.16327i) q^{5} +(0.841254 - 0.540641i) q^{6} +(1.25538 - 3.36582i) q^{7} +(-0.0713392 + 0.997452i) q^{8} +(0.989821 - 0.142315i) q^{9} +(0.540059 + 2.16987i) q^{10} +(0.643696 + 2.19223i) q^{11} +(-0.479249 + 0.877679i) q^{12} +(2.56028 - 0.954935i) q^{13} +(0.511239 + 3.55575i) q^{14} +(-0.410142 + 2.19813i) q^{15} +(-0.415415 - 0.909632i) q^{16} +(0.483874 + 0.105260i) q^{17} +(-0.800541 + 0.599278i) q^{18} +(-2.66297 - 1.71139i) q^{19} +(-1.51391 - 1.64563i) q^{20} +(-1.01207 + 3.44680i) q^{21} +(-1.61558 - 1.61558i) q^{22} +(-3.80423 - 2.92025i) q^{23} -1.00000i q^{24} +(-4.35949 - 2.44843i) q^{25} +(-1.78945 + 2.06514i) q^{26} +(-0.977147 + 0.212565i) q^{27} +(-2.15279 - 2.87579i) q^{28} +(1.40781 + 2.19060i) q^{29} +(-0.693479 - 2.12581i) q^{30} +(-2.17981 - 2.51564i) q^{31} +(0.800541 + 0.599278i) q^{32} +(-0.798447 - 2.14072i) q^{33} +(-0.475132 + 0.139511i) q^{34} +(-6.57074 - 4.62049i) q^{35} +(0.415415 - 0.909632i) q^{36} +(2.70205 - 3.60952i) q^{37} +(3.15741 + 0.225823i) q^{38} +(-2.48563 + 1.13515i) q^{39} +(2.11739 + 0.718794i) q^{40} +(-1.05283 + 7.32257i) q^{41} +(-0.763601 - 3.51022i) q^{42} +(-0.0953980 - 1.33384i) q^{43} +(2.19223 + 0.643696i) q^{44} +(0.252284 - 2.22179i) q^{45} +(4.73842 + 0.739870i) q^{46} +(6.96281 - 6.96281i) q^{47} +(0.479249 + 0.877679i) q^{48} +(-4.46248 - 3.86676i) q^{49} +(4.99964 + 0.0596573i) q^{50} +(-0.490151 - 0.0704730i) q^{51} +(0.580849 - 2.67012i) q^{52} +(-3.48357 - 1.29930i) q^{53} +(0.755750 - 0.654861i) q^{54} +(5.10666 - 0.151886i) q^{55} +(3.26768 + 1.49230i) q^{56} +(2.77827 + 1.51705i) q^{57} +(-2.28545 - 1.24795i) q^{58} +(1.75019 + 0.799287i) q^{59} +(1.62745 + 1.53343i) q^{60} +(6.99406 - 6.06038i) q^{61} +(3.11880 + 1.16325i) q^{62} +(0.763601 - 3.51022i) q^{63} +(-0.989821 - 0.142315i) q^{64} +(-0.616896 - 6.07899i) q^{65} +(1.72672 + 1.49621i) q^{66} +(-3.79946 - 6.95819i) q^{67} +(0.350153 - 0.350153i) q^{68} +(4.00286 + 2.64142i) q^{69} +(7.98137 + 0.906283i) q^{70} +(-8.39210 - 2.46414i) q^{71} +(0.0713392 + 0.997452i) q^{72} +(-2.60192 - 11.9608i) q^{73} +(-0.641676 + 4.46295i) q^{74} +(4.52305 + 2.13119i) q^{75} +(-2.87942 + 1.31499i) q^{76} +(8.18672 + 0.585526i) q^{77} +(1.63757 - 2.18753i) q^{78} +(-3.20130 + 7.00988i) q^{79} +(-2.20287 + 0.383886i) q^{80} +(0.959493 - 0.281733i) q^{81} +(-2.58529 - 6.93143i) q^{82} +(-2.35691 - 1.76436i) q^{83} +(2.35246 + 2.71489i) q^{84} +(0.501536 - 0.987184i) q^{85} +(0.722970 + 1.12496i) q^{86} +(-1.56050 - 2.08459i) q^{87} +(-2.23256 + 0.485664i) q^{88} +(-10.3008 + 11.8878i) q^{89} +(0.843366 + 2.07093i) q^{90} -9.81624i q^{91} +(-4.51339 + 1.62151i) q^{92} +(2.35372 + 2.35372i) q^{93} +(-2.77419 + 9.44804i) q^{94} +(-5.20920 + 4.79224i) q^{95} +(-0.841254 - 0.540641i) q^{96} +(12.4769 - 9.34012i) q^{97} +(5.76977 + 1.25514i) q^{98} +(0.949130 + 2.07830i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{6}+O(q^{10}) $ 240 * q - 24 * q^6	$ 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) $ 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{22}\right)$

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 $

$2$	−0.877679	+	0.479249i	−0.620613	+	0.338880i
$2$	−0.877679	+	0.479249i	−0.620613	+	0.338880i
$3$	−0.997452	+	0.0713392i	−0.575879	+	0.0411877i
$3$	−0.997452	+	0.0713392i	−0.575879	+	0.0411877i
$4$	0.540641	−	0.841254i	0.270320	−	0.420627i
$5$	0.565910	−	2.16327i	0.253083	−	0.967445i
$5$	0.565910	−	2.16327i	0.253083	−	0.967445i
$6$	0.841254	−	0.540641i	0.343440	−	0.220716i
$7$	1.25538	−	3.36582i	0.474491	−	1.27216i	−0.450706	−	0.892672i	$-0.648828\pi$
$7$	1.25538	−	3.36582i	0.474491	−	1.27216i	0.925197	−	0.379487i	$-0.123899\pi$
$8$	−0.0713392	+	0.997452i	−0.0252222	+	0.352653i
$9$	0.989821	−	0.142315i	0.329940	−	0.0474383i
$10$	0.540059	+	2.16987i	0.170782	+	0.686173i
$11$	0.643696	+	2.19223i	0.194082	+	0.660981i	0.997820	+	0.0659979i	$0.0210231\pi$
$11$	0.643696	+	2.19223i	0.194082	+	0.660981i	−0.803738	+	0.594983i	$0.797159\pi$
$12$	−0.479249	+	0.877679i	−0.138347	+	0.253364i
$13$	2.56028	−	0.954935i	0.710094	−	0.264851i	0.0316453	−	0.999499i	$-0.489925\pi$
$13$	2.56028	−	0.954935i	0.710094	−	0.264851i	0.678449	+	0.734648i	$0.262653\pi$
$14$	0.511239	+	3.55575i	0.136634	+	0.950314i
$15$	−0.410142	+	2.19813i	−0.105898	+	0.567555i
$16$	−0.415415	−	0.909632i	−0.103854	−	0.227408i
$17$	0.483874	+	0.105260i	0.117357	+	0.0255294i	0.270860	−	0.962619i	$-0.412692\pi$
$17$	0.483874	+	0.105260i	0.117357	+	0.0255294i	−0.153503	+	0.988148i	$0.549056\pi$
$18$	−0.800541	+	0.599278i	−0.188689	+	0.141251i
$19$	−2.66297	−	1.71139i	−0.610927	−	0.392619i	0.198278	−	0.980146i	$-0.436465\pi$
$19$	−2.66297	−	1.71139i	−0.610927	−	0.392619i	−0.809205	+	0.587527i	$0.800102\pi$
$20$	−1.51391	−	1.64563i	−0.338520	−	0.367973i
$21$	−1.01207	+	3.44680i	−0.220852	+	0.752153i
$22$	−1.61558	−	1.61558i	−0.344443	−	0.344443i
$23$	−3.80423	−	2.92025i	−0.793236	−	0.608914i
$23$	−3.80423	−	2.92025i	−0.793236	−	0.608914i
$24$		−	1.00000i		−	0.204124i
$25$	−4.35949	−	2.44843i	−0.871898	−	0.489687i
$26$	−1.78945	+	2.06514i	−0.350940	+	0.405007i
$27$	−0.977147	+	0.212565i	−0.188052	+	0.0409082i
$28$	−2.15279	−	2.87579i	−0.406840	−	0.543474i
$29$	1.40781	+	2.19060i	0.261425	+	0.406785i	0.947008	−	0.321209i	$-0.104089\pi$
$29$	1.40781	+	2.19060i	0.261425	+	0.406785i	−0.685584	+	0.727994i	$0.740453\pi$
$30$	−0.693479	−	2.12581i	−0.126611	−	0.388119i
$31$	−2.17981	−	2.51564i	−0.391506	−	0.451822i	0.525441	−	0.850830i	$-0.323900\pi$
$31$	−2.17981	−	2.51564i	−0.391506	−	0.451822i	−0.916948	+	0.399007i	$0.869355\pi$
$32$	0.800541	+	0.599278i	0.141517	+	0.105938i
$33$	−0.798447	−	2.14072i	−0.138992	−	0.372651i
$34$	−0.475132	+	0.139511i	−0.0814845	+	0.0239260i
$35$	−6.57074	−	4.62049i	−1.11066	−	0.781005i
$36$	0.415415	−	0.909632i	0.0692358	−	0.151605i
$37$	2.70205	−	3.60952i	0.444215	−	0.593401i	−0.521421	−	0.853299i	$-0.674598\pi$
$37$	2.70205	−	3.60952i	0.444215	−	0.593401i	0.965636	+	0.259898i	$0.0836890\pi$
$38$	3.15741	+	0.225823i	0.512200	+	0.0366333i
$39$	−2.48563	+	1.13515i	−0.398020	+	0.181770i
$40$	2.11739	+	0.718794i	0.334789	+	0.113651i
$41$	−1.05283	+	7.32257i	−0.164424	+	1.14359i	0.725746	+	0.687963i	$0.241495\pi$
$41$	−1.05283	+	7.32257i	−0.164424	+	1.14359i	−0.890169	+	0.455630i	$0.849414\pi$
$42$	−0.763601	−	3.51022i	−0.117826	−	0.541638i
$43$	−0.0953980	−	1.33384i	−0.0145481	−	0.203408i	−0.999528	−	0.0307369i	$-0.990215\pi$
$43$	−0.0953980	−	1.33384i	−0.0145481	−	0.203408i	0.984979	−	0.172672i	$-0.0552399\pi$
$44$	2.19223	+	0.643696i	0.330491	+	0.0970408i
$45$	0.252284	−	2.22179i	0.0376083	−	0.331205i
$46$	4.73842	+	0.739870i	0.698641	+	0.109088i
$47$	6.96281	−	6.96281i	1.01563	−	1.01563i	0.0157550	−	0.999876i	$-0.494985\pi$
$47$	6.96281	−	6.96281i	1.01563	−	1.01563i	0.999876	−	0.0157550i	$-0.00501518\pi$
$48$	0.479249	+	0.877679i	0.0691736	+	0.126682i
$49$	−4.46248	−	3.86676i	−0.637498	−	0.552395i
$50$	4.99964	+	0.0596573i	0.707056	+	0.00843681i
$51$	−0.490151	−	0.0704730i	−0.0686348	−	0.00986820i
$52$	0.580849	−	2.67012i	0.0805493	−	0.370279i
$53$	−3.48357	−	1.29930i	−0.478505	−	0.178473i	0.0986263	−	0.995125i	$-0.468555\pi$
$53$	−3.48357	−	1.29930i	−0.478505	−	0.178473i	−0.577131	+	0.816651i	$0.695828\pi$
$54$	0.755750	−	0.654861i	0.102844	−	0.0891153i
$55$	5.10666	−	0.151886i	0.688581	−	0.0204803i
$56$	3.26768	+	1.49230i	0.436662	+	0.199417i
$57$	2.77827	+	1.51705i	0.367991	+	0.200938i
$58$	−2.28545	−	1.24795i	−0.300095	−	0.163864i
$59$	1.75019	+	0.799287i	0.227856	+	0.104058i	0.526072	−	0.850440i	$-0.323664\pi$
$59$	1.75019	+	0.799287i	0.227856	+	0.104058i	−0.298216	+	0.954498i	$0.596392\pi$
$60$	1.62745	+	1.53343i	0.210102	+	0.197965i
$61$	6.99406	−	6.06038i	0.895497	−	0.775953i	−0.0798089	−	0.996810i	$-0.525431\pi$
$61$	6.99406	−	6.06038i	0.895497	−	0.775953i	0.975306	+	0.220857i	$0.0708856\pi$
$62$	3.11880	+	1.16325i	0.396087	+	0.147733i
$63$	0.763601	−	3.51022i	0.0962047	−	0.442246i
$64$	−0.989821	−	0.142315i	−0.123728	−	0.0177894i
$65$	−0.616896	−	6.07899i	−0.0765166	−	0.754006i
$66$	1.72672	+	1.49621i	0.212544	+	0.184171i
$67$	−3.79946	−	6.95819i	−0.464178	−	0.850079i	−0.999984	−	0.00573723i	$-0.998174\pi$
$67$	−3.79946	−	6.95819i	−0.464178	−	0.850079i	0.535805	−	0.844341i	$-0.320008\pi$
$68$	0.350153	−	0.350153i	0.0424623	−	0.0424623i
$69$	4.00286	+	2.64142i	0.481888	+	0.317989i
$70$	7.98137	+	0.906283i	0.953956	+	0.108322i
$71$	−8.39210	−	2.46414i	−0.995959	−	0.292440i	−0.257163	−	0.966368i	$-0.582788\pi$
$71$	−8.39210	−	2.46414i	−0.995959	−	0.292440i	−0.738797	+	0.673928i	$0.764606\pi$
$72$	0.0713392	+	0.997452i	0.00840740	+	0.117551i
$73$	−2.60192	−	11.9608i	−0.304532	−	1.39991i	−0.834087	−	0.551634i	$-0.814005\pi$
$73$	−2.60192	−	11.9608i	−0.304532	−	1.39991i	0.529555	−	0.848276i	$-0.322359\pi$
$74$	−0.641676	+	4.46295i	−0.0745933	+	0.518808i
$75$	4.52305	+	2.13119i	0.522277	+	0.246089i
$76$	−2.87942	+	1.31499i	−0.330292	+	0.150839i
$77$	8.18672	+	0.585526i	0.932963	+	0.0667268i
$78$	1.63757	−	2.18753i	0.185418	−	0.247690i
$79$	−3.20130	+	7.00988i	−0.360175	+	0.788673i	0.639625	+	0.768687i	$0.279090\pi$
$79$	−3.20130	+	7.00988i	−0.360175	+	0.788673i	−0.999800	+	0.0199862i	$0.993638\pi$
$80$	−2.20287	+	0.383886i	−0.246288	+	0.0429197i
$81$	0.959493	−	0.281733i	0.106610	−	0.0313036i
$82$	−2.58529	−	6.93143i	−0.285497	−	0.765448i
$83$	−2.35691	−	1.76436i	−0.258704	−	0.193663i	0.462051	−	0.886853i	$-0.347114\pi$
$83$	−2.35691	−	1.76436i	−0.258704	−	0.193663i	−0.720755	+	0.693190i	$0.756205\pi$
$84$	2.35246	+	2.71489i	0.256675	+	0.296219i
$85$	0.501536	−	0.987184i	0.0543993	−	0.107075i
$86$	0.722970	+	1.12496i	0.0779598	+	0.121308i
$87$	−1.56050	−	2.08459i	−0.167304	−	0.223491i
$88$	−2.23256	+	0.485664i	−0.237992	+	0.0517720i
$89$	−10.3008	+	11.8878i	−1.09188	+	1.26010i	−0.128574	+	0.991700i	$0.541040\pi$
$89$	−10.3008	+	11.8878i	−1.09188	+	1.26010i	−0.963308	+	0.268399i	$0.913505\pi$
$90$	0.843366	+	2.07093i	0.0888986	+	0.218295i
$91$		−	9.81624i		−	1.02902i
$92$	−4.51339	+	1.62151i	−0.470554	+	0.169054i
$93$	2.35372	+	2.35372i	0.244070	+	0.244070i
$94$	−2.77419	+	9.44804i	−0.286136	+	0.974491i
$95$	−5.20920	+	4.79224i	−0.534452	+	0.491673i
$96$	−0.841254	−	0.540641i	−0.0858601	−	0.0551789i
$97$	12.4769	−	9.34012i	1.26684	−	0.948345i	0.266959	−	0.963708i	$-0.413981\pi$
$97$	12.4769	−	9.34012i	1.26684	−	0.948345i	0.999882	+	0.0153629i	$0.00489036\pi$
$98$	5.76977	+	1.25514i	0.582835	+	0.126788i
$99$	0.949130	+	2.07830i	0.0953912	+	0.208878i
$100$	−4.41667	+	2.34371i	−0.441667	+	0.234371i
$101$	0.146100	+	1.01615i	0.0145375	+	0.101111i	0.995798	−	0.0915738i	$-0.0291898\pi$
$101$	0.146100	+	1.01615i	0.0145375	+	0.101111i	−0.981261	+	0.192684i	$0.938281\pi$
$102$	0.463969	−	0.173052i	0.0459398	−	0.0171347i
$103$	−5.89348	+	10.7931i	−0.580702	+	1.06348i	0.407915	+	0.913020i	$0.366256\pi$
$103$	−5.89348	+	10.7931i	−0.580702	+	1.06348i	−0.988617	+	0.150456i	$0.951926\pi$
$104$	0.769854	+	2.62188i	0.0754904	+	0.257097i
$105$	6.88362	+	4.13996i	0.671773	+	0.404019i
$106$	3.68014	−	0.529125i	0.357447	−	0.0513932i
$107$	−0.00344790	+	0.0482080i	−0.000333321	+	0.00466044i	−0.997616	−	0.0690088i	$-0.978016\pi$
$107$	−0.00344790	+	0.0482080i	−0.000333321	+	0.00466044i	0.997283	+	0.0736692i	$0.0234709\pi$
$108$	−0.349464	+	0.936950i	−0.0336272	+	0.0901580i
$109$	5.20839	−	3.34723i	0.498873	−	0.320606i	−0.266892	−	0.963726i	$-0.585997\pi$
$109$	5.20839	−	3.34723i	0.498873	−	0.320606i	0.765765	+	0.643120i	$0.222360\pi$
$110$	−4.40921	+	2.58067i	−0.420402	+	0.246057i
$111$	−2.43767	+	3.79308i	−0.231373	+	0.360024i
$112$	−3.58316	+	0.256273i	−0.338577	+	0.0242155i
$113$	−3.67817	+	2.00843i	−0.346013	+	0.188937i	−0.642852	−	0.765990i	$-0.722249\pi$
$113$	−3.67817	+	2.00843i	−0.346013	+	0.188937i	0.296840	+	0.954927i	$0.404067\pi$
$114$	−3.16548			−0.296474
$115$	−8.47014	+	6.57698i	−0.789845	+	0.613306i
$116$	2.60397			0.241773
$117$	2.39832	−	1.30958i	0.221725	−	0.121071i
$118$	−1.91917	+	0.137262i	−0.176674	+	0.0126359i
$119$	0.961736	−	1.49649i	0.0881622	−	0.137183i
$120$	−2.16327	−	0.565910i	−0.197479	−	0.0516603i
$121$	4.86228	−	3.12480i	0.442025	−	0.284072i
$122$	−3.23410	+	8.67097i	−0.292802	+	0.785032i
$123$	0.527758	−	7.37902i	0.0475863	−	0.665344i
$124$	−3.29479	+	0.473719i	−0.295881	+	0.0425412i
$125$	−7.76371	+	8.04517i	−0.694407	+	0.719582i
$126$	1.01207	+	3.44680i	0.0901625	+	0.307065i
$127$	−2.07191	+	3.79441i	−0.183852	+	0.336700i	−0.953308	−	0.302000i	$-0.902346\pi$
$127$	−2.07191	+	3.79441i	−0.183852	+	0.336700i	0.769456	+	0.638700i	$0.220527\pi$
$128$	0.936950	−	0.349464i	0.0828154	−	0.0308886i
$129$	0.190310	+	1.32363i	0.0167559	+	0.116540i
$130$	3.45479	+	5.03975i	0.303005	+	0.442016i
$131$	−6.59436	−	14.4396i	−0.576152	−	1.26160i	−0.943457	−	0.331496i	$-0.892447\pi$
$131$	−6.59436	−	14.4396i	−0.576152	−	1.26160i	0.367305	−	0.930101i	$-0.380280\pi$
$132$	−2.23256	−	0.485664i	−0.194320	−	0.0422716i
$133$	−9.10326	+	6.81462i	−0.789353	+	0.590902i
$134$	6.66941	+	4.28617i	0.576150	+	0.370269i
$135$	−0.0931406	+	2.23413i	−0.00801626	+	0.192283i
$136$	−0.139511	+	0.475132i	−0.0119630	+	0.0407423i
$137$	7.99322	+	7.99322i	0.682907	+	0.682907i	0.960654	−	0.277747i	$-0.0895878\pi$
$137$	7.99322	+	7.99322i	0.682907	+	0.682907i	−0.277747	+	0.960654i	$0.589588\pi$
$138$	−4.77913	−	0.399950i	−0.406826	−	0.0340460i
$139$			17.9085i			1.51898i	0.650519	+	0.759490i	$0.274551\pi$
$139$			17.9085i			1.51898i	−0.650519	+	0.759490i	$0.725449\pi$
$140$	−7.43941	+	3.02964i	−0.628745	+	0.256051i
$141$	−6.44835	+	7.44180i	−0.543049	+	0.626712i
$142$	8.54651	−	1.85918i	0.717207	−	0.156019i
$143$	3.74147	+	4.99803i	0.312878	+	0.417956i
$144$	−0.540641	−	0.841254i	−0.0450534	−	0.0701045i
$145$	5.53556	−	1.80580i	0.459704	−	0.149964i
$146$	8.01587	+	9.25080i	0.663398	+	0.765602i
$147$	4.72697	+	3.53856i	0.389874	+	0.291856i
$148$	−1.57568	−	4.22456i	−0.129520	−	0.347257i
$149$	21.5708	−	6.33375i	1.76715	−	0.518881i	0.773737	−	0.633507i	$-0.218385\pi$
$149$	21.5708	−	6.33375i	1.76715	−	0.518881i	0.993409	+	0.114626i	$0.0365671\pi$
$150$	−4.99116	+	0.297165i	−0.407527	+	0.0242634i
$151$	5.23075	−	11.4537i	0.425672	−	0.932093i	−0.568337	−	0.822796i	$-0.692413\pi$
$151$	5.23075	−	11.4537i	0.425672	−	0.932093i	0.994009	−	0.109297i	$-0.0348598\pi$
$152$	1.89700	−	2.53410i	0.153867	−	0.205542i
$153$	0.493929	+	0.0353265i	0.0399318	+	0.00285598i
$154$	−7.46592	+	3.40957i	−0.601621	+	0.274751i
$155$	−6.67559	+	3.29191i	−0.536197	+	0.264412i
$156$	−0.388885	+	2.70476i	−0.0311357	+	0.216554i
$157$	−0.423291	−	1.94584i	−0.0337823	−	0.155295i	0.957166	−	0.289541i	$-0.0935025\pi$
$157$	−0.423291	−	1.94584i	−0.0337823	−	0.155295i	−0.990948	+	0.134246i	$0.957139\pi$
$158$	−0.549760	−	7.68665i	−0.0437365	−	0.611517i
$159$	3.56738	+	1.04748i	0.282912	+	0.0830704i
$160$	1.74943	−	1.39265i	0.138305	−	0.110099i
$161$	−14.6048	+	9.13829i	−1.15102	+	0.720198i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	0.657305	+	1.20376i	0.0514841	+	0.0942861i	0.902154	−	0.431414i	$-0.141985\pi$
$163$	0.657305	+	1.20376i	0.0514841	+	0.0942861i	−0.850670	+	0.525700i	$0.823803\pi$
$164$	5.59093	+	4.84457i	0.436579	+	0.378298i
$165$	−5.08281	+	0.515804i	−0.395696	+	0.0401553i
$166$	2.91417	+	0.418995i	0.226184	+	0.0325203i
$167$	−0.920977	+	4.23366i	−0.0712673	+	0.327611i	−0.998953	−	0.0457520i	$-0.985432\pi$
$167$	−0.920977	+	4.23366i	−0.0712673	+	0.327611i	0.927686	+	0.373363i	$0.121795\pi$
$168$	−3.36582	−	1.25538i	−0.259678	−	0.0968550i
$169$	−4.18161	+	3.62339i	−0.321662	+	0.278722i
$170$	0.0329191	+	1.10679i	0.00252478	+	0.0848870i
$171$	−2.87942	−	1.31499i	−0.220195	−	0.100560i
$172$	−1.17367	−	0.640874i	−0.0894917	−	0.0488662i
$173$	13.0789	+	7.14162i	0.994370	+	0.542967i	0.892123	−	0.451792i	$-0.149215\pi$
$173$	13.0789	+	7.14162i	0.994370	+	0.542967i	0.102247	+	0.994759i	$0.467397\pi$
$174$	2.36866	+	1.08173i	0.179567	+	0.0820057i
$175$	−13.7138	+	11.5995i	−1.03667	+	0.876842i
$176$	1.72672	−	1.49621i	0.130156	−	0.112781i
$177$	−1.80276	−	0.672393i	−0.135503	−	0.0505402i
$178$	3.34360	−	15.3703i	0.250613	−	1.15205i
$179$	−13.7258	−	1.97347i	−1.02591	−	0.147504i	−0.391244	−	0.920287i	$-0.627955\pi$
$179$	−13.7258	−	1.97347i	−1.02591	−	0.147504i	−0.634670	+	0.772783i	$0.718864\pi$
$180$	−1.73269	−	1.41343i	−0.129147	−	0.105351i
$181$	14.8467	+	12.8647i	1.10355	+	0.956229i	0.999266	−	0.0383190i	$-0.0122003\pi$
$181$	14.8467	+	12.8647i	1.10355	+	0.956229i	0.104281	+	0.994548i	$0.466746\pi$
$182$	4.70443	+	8.61551i	0.348715	+	0.638624i
$183$	−6.54389	+	6.54389i	−0.483739	+	0.483739i
$184$	3.18420	−	3.58621i	0.234742	−	0.264379i
$185$	−6.27925	−	7.88794i	−0.461660	−	0.579933i
$186$	−3.19384	−	0.937795i	−0.234183	−	0.0687624i
$187$	0.0807132	+	1.12852i	0.00590233	+	0.0825254i
$188$	−2.09311	−	9.62187i	−0.152656	−	0.701747i
$189$	−0.511239	+	3.55575i	−0.0371872	+	0.258643i
$190$	2.27533	−	6.70255i	0.165070	−	0.486254i
$191$	18.7050	−	8.54228i	1.35345	−	0.618098i	0.399129	−	0.916895i	$-0.369313\pi$
$191$	18.7050	−	8.54228i	1.35345	−	0.618098i	0.954317	+	0.298797i	$0.0965853\pi$
$192$	0.997452	+	0.0713392i	0.0719849	+	0.00514846i
$193$	−9.48039	+	12.6643i	−0.682414	+	0.911598i	−0.999320	−	0.0368588i	$-0.988265\pi$
$193$	−9.48039	+	12.6643i	−0.682414	+	0.911598i	0.316907	+	0.948457i	$0.397356\pi$
$194$	−6.47450	+	14.1772i	−0.464842	+	1.01786i
$195$	1.04899	+	6.01949i	0.0751201	+	0.431065i
$196$	−5.66553	+	1.66355i	−0.404681	+	0.118825i
$197$	−3.26281	−	8.74793i	−0.232466	−	0.623264i	0.767374	−	0.641200i	$-0.221563\pi$
$197$	−3.26281	−	8.74793i	−0.232466	−	0.623264i	−0.999839	+	0.0179360i	$0.994290\pi$
$198$	−1.82906	−	1.36921i	−0.129985	−	0.0973059i
$199$	8.62482	+	9.95357i	0.611397	+	0.705590i	0.974050	−	0.226335i	$-0.0726743\pi$
$199$	8.62482	+	9.95357i	0.611397	+	0.705590i	−0.362653	+	0.931924i	$0.618129\pi$
$200$	2.75320	−	4.17372i	0.194681	−	0.295126i
$201$	4.28617	+	6.66941i	0.302323	+	0.470424i
$202$	−0.615217	−	0.821834i	−0.0432865	−	0.0578240i
$203$	9.14051	−	1.98840i	0.641538	−	0.139558i
$204$	−0.324281	+	0.374240i	−0.0227042	+	0.0262021i
$205$	15.2449	+	6.42146i	1.06475	+	0.448494i
$206$		−	12.2973i		−	0.856795i
$207$	−4.18110	−	2.34913i	−0.290607	−	0.163276i
$208$	−1.93222	−	1.93222i	−0.133975	−	0.133975i
$209$	2.03760	−	6.93944i	0.140944	−	0.480011i
$210$	−8.02568	−	0.334590i	−0.553825	−	0.0230889i
$211$	−12.1531	−	7.81033i	−0.836655	−	0.537686i	0.0507312	−	0.998712i	$-0.483845\pi$
$211$	−12.1531	−	7.81033i	−0.836655	−	0.537686i	−0.887386	+	0.461027i	$0.847481\pi$
$212$	−2.97640	+	2.22811i	−0.204420	+	0.153027i
$213$	8.54651	+	1.85918i	0.585597	+	0.127389i
$214$	−0.0200775	−	0.0439635i	−0.00137247	−	0.00300528i
$215$	−2.93944	−	0.548461i	−0.200468	−	0.0374047i
$216$	−0.142315	−	0.989821i	−0.00968330	−	0.0673488i
$217$	−11.2037	+	4.17876i	−0.760556	+	0.283673i
$218$	−2.96714	+	5.43391i	−0.200960	+	0.368031i
$219$	3.44857	+	11.7447i	0.233032	+	0.793636i
$220$	2.63309	−	4.37811i	0.177523	−	0.295172i
$221$	1.33937	−	0.192572i	0.0900958	−	0.0129538i
$222$	0.321658	−	4.49736i	0.0215882	−	0.301843i
$223$	−5.37891	+	14.4214i	−0.360199	+	0.965730i	0.622843	+	0.782347i	$0.285978\pi$
$223$	−5.37891	+	14.4214i	−0.360199	+	0.965730i	−0.983042	+	0.183383i	$0.941295\pi$
$224$	3.02205	−	1.94215i	0.201919	−	0.129765i
$225$	−4.66357	−	1.80309i	−0.310904	−	0.120206i
$226$	2.26571	−	3.52551i	0.150713	−	0.234514i
$227$	−18.0623	+	1.29184i	−1.19884	+	0.0857425i	−0.656439	−	0.754379i	$-0.727938\pi$
$227$	−18.0623	+	1.29184i	−1.19884	+	0.0857425i	−0.542398	+	0.840122i	$0.682484\pi$
$228$	2.77827	−	1.51705i	0.183996	−	0.100469i
$229$	21.1307			1.39635			0.698177	−	0.715925i	$-0.253995\pi$
$229$	21.1307			1.39635			0.698177	+	0.715925i	$0.253995\pi$
$230$	4.28206	−	9.83178i	0.282351	−	0.648289i
$231$	−8.20763			−0.540022
$232$	−2.28545	+	1.24795i	−0.150047	+	0.0819320i
$233$	8.89259	−	0.636010i	0.582573	−	0.0416664i	0.223057	−	0.974805i	$-0.428396\pi$
$233$	8.89259	−	0.636010i	0.582573	−	0.0416664i	0.359516	+	0.933139i	$0.382942\pi$
$234$	−1.47734	+	2.29878i	−0.0965766	+	0.150276i
$235$	−11.1221	−	19.0028i	−0.725528	−	1.23961i
$236$	1.61863	−	1.04023i	0.105364	−	0.0677132i
$237$	2.69307	−	7.22040i	0.174934	−	0.469015i
$238$	−0.126904	+	1.77435i	−0.00822596	+	0.115014i
$239$	−6.86359	+	0.986835i	−0.443969	+	0.0638331i	−0.360674	−	0.932692i	$-0.617453\pi$
$239$	−6.86359	+	0.986835i	−0.443969	+	0.0638331i	−0.0832947	+	0.996525i	$0.526544\pi$
$240$	2.16987	−	0.540059i	0.140065	−	0.0348606i
$241$	5.78554	+	19.7038i	0.372680	+	1.26923i	0.905986	+	0.423308i	$0.139131\pi$
$241$	5.78554	+	19.7038i	0.372680	+	1.26923i	−0.533306	+	0.845922i	$0.679051\pi$
$242$	−2.76996	+	5.07281i	−0.178060	+	0.326093i
$243$	−0.936950	+	0.349464i	−0.0601054	+	0.0224181i
$244$	−1.31705	−	9.16027i	−0.0843153	−	0.586426i
$245$	−10.8902	+	7.46533i	−0.695751	+	0.476942i
$246$	3.07318	+	6.72934i	0.195939	+	0.429047i
$247$	−8.45221	−	1.83867i	−0.537801	−	0.116992i
$248$	2.66474	−	1.99480i	0.169211	−	0.126670i
$249$	2.47677	+	1.59172i	0.156959	+	0.100871i
$250$	2.95840	−	10.7818i	0.187106	−	0.681903i
$251$	8.35690	−	28.4610i	0.527483	−	1.79644i	−0.0736408	−	0.997285i	$-0.523462\pi$
$251$	8.35690	−	28.4610i	0.527483	−	1.79644i	0.601123	−	0.799156i	$-0.294720\pi$
$252$	−2.54015	−	2.54015i	−0.160014	−	0.160014i
$253$	3.95308	−	10.2195i	0.248528	−	0.642493i
$254$		−	4.32323i		−	0.271264i
$255$	−0.429834	+	1.02045i	−0.0269172	+	0.0639029i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	2.90549	−	0.632050i	0.181239	−	0.0394262i	−0.121030	−	0.992649i	$-0.538620\pi$
$257$	2.90549	−	0.632050i	0.181239	−	0.0394262i	0.302269	+	0.953223i	$0.402256\pi$
$258$	−0.801382	−	1.07052i	−0.0498918	−	0.0666477i
$259$	−8.75686	−	13.6259i	−0.544125	−	0.846675i
$260$	−5.44749	−	2.76758i	−0.337839	−	0.171638i
$261$	1.70524	+	1.96795i	0.105552	+	0.121813i
$262$	12.7079	+	9.51302i	0.785097	+	0.587716i
$263$	7.26378	+	19.4750i	0.447904	+	1.20088i	0.943221	+	0.332165i	$0.107779\pi$
$263$	7.26378	+	19.4750i	0.447904	+	1.20088i	−0.495317	+	0.868712i	$0.664948\pi$
$264$	2.19223	−	0.643696i	0.134922	−	0.0396167i
$265$	−4.78213	+	6.80062i	−0.293764	+	0.417759i
$266$	4.72385	−	10.3438i	0.289638	−	0.634218i
$267$	9.42649	−	12.5923i	0.576892	−	0.770637i
$268$	−7.90775	−	0.565573i	−0.483043	−	0.0345479i
$269$	12.3089	−	5.62127i	0.750484	−	0.342735i	−0.00317946	−	0.999995i	$-0.501012\pi$
$269$	12.3089	−	5.62127i	0.750484	−	0.342735i	0.753664	+	0.657260i	$0.228285\pi$
$270$	−0.988956	−	2.00548i	−0.0601859	−	0.122050i
$271$	−1.77814	+	12.3672i	−0.108014	+	0.751254i	0.861772	+	0.507296i	$0.169355\pi$
$271$	−1.77814	+	12.3672i	−0.108014	+	0.751254i	−0.969786	+	0.243958i	$0.921554\pi$
$272$	−0.105260	−	0.483874i	−0.00638235	−	0.0293392i
$273$	0.700283	+	9.79123i	0.0423830	+	0.592592i
$274$	−10.8462	−	3.18474i	−0.655244	−	0.192397i
$275$	2.56134	−	11.1330i	0.154454	−	0.671347i
$276$	4.38621	−	1.93936i	0.264019	−	0.116736i
$277$	0.832642	−	0.832642i	0.0500286	−	0.0500286i	−0.681650	−	0.731679i	$-0.738737\pi$
$277$	0.832642	−	0.832642i	0.0500286	−	0.0500286i	0.731679	+	0.681650i	$0.238737\pi$
$278$	−8.58263	−	15.7179i	−0.514752	−	0.942698i
$279$	−2.51564	−	2.17981i	−0.150607	−	0.130502i
$280$	5.07747	−	6.22438i	0.303437	−	0.371978i
$281$	31.3060	+	4.50112i	1.86756	+	0.268514i	0.980986	−	0.194079i	$-0.0621719\pi$
$281$	31.3060	+	4.50112i	1.86756	+	0.268514i	0.886571	+	0.462593i	$0.153081\pi$
$282$	2.09311	−	9.62187i	0.124643	−	0.572974i
$283$	22.3580	+	8.33911i	1.32905	+	0.495709i	0.910884	−	0.412663i	$-0.135401\pi$
$283$	22.3580	+	8.33911i	1.32905	+	0.495709i	0.418163	+	0.908372i	$0.362674\pi$
$284$	−6.61008	+	5.72767i	−0.392236	+	0.339875i
$285$	4.85405	−	5.15165i	0.287529	−	0.305157i
$286$	−5.67911	−	2.59356i	−0.335813	−	0.153361i
$287$	23.3247	+	12.7363i	1.37681	+	0.751798i
$288$	0.877679	+	0.479249i	0.0517177	+	0.0282400i
$289$	−15.2407	−	6.96019i	−0.896511	−	0.409423i
$290$	−3.99302	+	4.23783i	−0.234478	+	0.248854i
$291$	−11.7788	+	10.2064i	−0.690487	+	0.598310i
$292$	−11.4688	−	4.27764i	−0.671160	−	0.250330i
$293$	0.703753	−	3.23510i	0.0411137	−	0.188997i	−0.952010	−	0.306067i	$-0.900987\pi$
$293$	0.703753	−	3.23510i	0.0411137	−	0.188997i	0.993124	+	0.117071i	$0.0373504\pi$
$294$	−5.84461	−	0.840328i	−0.340865	−	0.0490089i
$295$	2.71953	−	3.33382i	0.158337	−	0.194103i
$296$	3.40756	+	2.95267i	0.198060	+	0.171620i
$297$	−1.09498	−	2.00530i	−0.0635370	−	0.116359i
$298$	−15.8968	+	15.8968i	−0.920875	+	0.920875i
$299$	−12.5285	−	3.84387i	−0.724544	−	0.222297i
$300$	4.23822	−	2.65282i	0.244694	−	0.153161i
$301$	−4.60922	−	1.35339i	−0.265671	−	0.0780080i
$302$	0.898276	+	12.5595i	0.0516900	+	0.722721i
$303$	−0.218219	−	1.00314i	−0.0125364	−	0.0576287i
$304$	−0.450495	+	3.13326i	−0.0258376	+	0.179705i
$305$	−9.15225	−	18.5597i	−0.524057	−	1.06272i
$306$	−0.450442	+	0.205710i	−0.0257500	+	0.0117596i
$307$	30.4613	+	2.17863i	1.73852	+	0.124341i	0.904245	−	0.427014i	$-0.140435\pi$
$307$	30.4613	+	2.17863i	1.73852	+	0.124341i	0.834271	+	0.551355i	$0.185889\pi$
$308$	4.91865	−	6.57055i	0.280266	−	0.374392i
$309$	5.10849	−	11.1860i	0.290612	−	0.636351i
$310$	4.28139	−	6.08851i	0.243166	−	0.345804i
$311$	27.5193	−	8.08040i	1.56048	−	0.458198i	0.616267	−	0.787538i	$-0.288644\pi$
$311$	27.5193	−	8.08040i	1.56048	−	0.458198i	0.944211	+	0.329340i	$0.106826\pi$
$312$	−0.954935	−	2.56028i	−0.0540626	−	0.144947i
$313$	−4.71886	−	3.53249i	−0.266726	−	0.199668i	0.457541	−	0.889189i	$-0.348730\pi$
$313$	−4.71886	−	3.53249i	−0.266726	−	0.199668i	−0.724266	+	0.689520i	$0.757821\pi$
$314$	1.30405	+	1.50496i	0.0735921	+	0.0849298i
$315$	−7.16143	−	3.63834i	−0.403501	−	0.204997i
$316$	4.16633	+	6.48294i	0.234374	+	0.364694i
$317$	−7.92341	−	10.5844i	−0.445023	−	0.594481i	0.520802	−	0.853678i	$-0.325633\pi$
$317$	−7.92341	−	10.5844i	−0.445023	−	0.594481i	−0.965825	+	0.259197i	$0.916542\pi$
$318$	−3.63302	+	0.790315i	−0.203730	+	0.0443187i
$319$	−3.89609	+	4.49633i	−0.218139	+	0.251746i
$320$	−0.868016	+	2.06072i	−0.0485235	+	0.115198i
$321$		−	0.0483311i		−	0.00269758i
$322$	8.43880	−	15.0198i	0.470276	−	0.837022i
$323$	−1.10840	−	1.10840i	−0.0616731	−	0.0616731i
$324$	0.281733	−	0.959493i	0.0156518	−	0.0533052i
$325$	−13.4996	−	2.10565i	−0.748824	−	0.116800i
$326$	−1.15381	−	0.741506i	−0.0639034	−	0.0410682i
$327$	−4.95633	+	3.71026i	−0.274086	+	0.205178i
$328$	−7.22880	−	1.57253i	−0.399144	−	0.0868284i
$329$	−14.6945	−	32.1766i	−0.810137	−	1.77395i
$330$	4.21388	−	2.88864i	0.231966	−	0.159014i
$331$	0.661737	+	4.60248i	0.0363724	+	0.252975i	0.999893	−	0.0146603i	$-0.00466670\pi$
$331$	0.661737	+	4.60248i	0.0363724	+	0.252975i	−0.963520	+	0.267636i	$0.913758\pi$
$332$	−2.75851	+	1.02887i	−0.151393	+	0.0564667i
$333$	2.16086	−	3.95732i	0.118414	−	0.216860i
$334$	−1.22066	−	4.15717i	−0.0667913	−	0.227470i
$335$	−17.2026	+	4.28156i	−0.939880	+	0.233926i
$336$	3.55575	−	0.511239i	0.193982	−	0.0278904i
$337$	−1.57575	+	22.0319i	−0.0858366	+	1.20015i	0.753837	+	0.657061i	$0.228201\pi$
$337$	−1.57575	+	22.0319i	−0.0858366	+	1.20015i	−0.839674	+	0.543091i	$0.817254\pi$
$338$	1.93361	−	5.18420i	0.105174	−	0.281983i
$339$	3.52551	−	2.26571i	0.191480	−	0.123056i
$340$	−0.559321	−	0.955631i	−0.0303334	−	0.0518264i
$341$	4.11172	−	6.39795i	0.222662	−	0.346469i
$342$	3.15741	−	0.225823i	0.170733	−	0.0122111i
$343$	3.45333	−	1.88566i	0.186462	−	0.101816i
$344$	1.33725			0.0720995
$345$	7.97937	−	7.16447i	0.429595	−	0.385722i
$346$	−14.9017			−0.801119
$347$	2.25716	−	1.23250i	0.121171	−	0.0661642i	−0.417520	−	0.908668i	$-0.637101\pi$
$347$	2.25716	−	1.23250i	0.121171	−	0.0661642i	0.538691	+	0.842503i	$0.318919\pi$
$348$	−2.59734	+	0.185765i	−0.139232	+	0.00995807i
$349$	−3.11855	+	4.85256i	−0.166932	+	0.259751i	−0.914634	−	0.404283i	$-0.867521\pi$
$349$	−3.11855	+	4.85256i	−0.166932	+	0.259751i	0.747702	+	0.664035i	$0.231157\pi$
$350$	6.47727	−	16.7530i	0.346225	−	0.895485i
$351$	−2.29878	+	1.47734i	−0.122700	+	0.0788545i
$352$	−0.798447	+	2.14072i	−0.0425574	+	0.114101i
$353$	−0.0567029	+	0.792810i	−0.00301799	+	0.0421970i	−0.998738	−	0.0502247i	$-0.984006\pi$
$353$	−0.0567029	+	0.792810i	−0.00301799	+	0.0421970i	0.995720	+	0.0924217i	$0.0294608\pi$
$354$	1.90448	−	0.273824i	0.101222	−	0.0145536i
$355$	−10.0798	+	16.7599i	−0.534980	+	0.889524i
$356$	4.43158	+	15.0926i	0.234873	+	0.799905i
$357$	−0.852527	+	1.56129i	−0.0451205	+	0.0826321i
$358$	12.9926	−	4.84600i	0.686681	−	0.256119i
$359$	−2.80497	−	19.5090i	−0.148041	−	1.02965i	−0.919422	−	0.393272i	$-0.871343\pi$
$359$	−2.80497	−	19.5090i	−0.148041	−	1.02965i	0.771381	−	0.636373i	$-0.219566\pi$
$360$	2.19813	+	0.410142i	0.115852	+	0.0216164i
$361$	−3.73032	−	8.16827i	−0.196333	−	0.429909i
$362$	−19.1961	−	4.17585i	−1.00892	−	0.219478i
$363$	−4.62697	+	3.46371i	−0.242853	+	0.181797i
$364$	−8.25795	−	5.30706i	−0.432834	−	0.278166i
$365$	−27.3470	−	1.14009i	−1.43141	−	0.0596752i
$366$	2.60728	−	8.87959i	0.136285	−	0.464144i
$367$	11.2742	+	11.2742i	0.588511	+	0.588511i	0.937228	−	0.348717i	$-0.113383\pi$
$367$	11.2742	+	11.2742i	0.588511	+	0.588511i	−0.348717	+	0.937228i	$0.613383\pi$
$368$	−1.07602	+	4.67356i	−0.0560914	+	0.243626i
$369$			7.39787i			0.385118i
$370$	9.29145	+	3.91375i	0.483040	+	0.203466i
$371$	−8.74644	+	10.0939i	−0.454092	+	0.524050i
$372$	3.25260	−	0.707560i	0.168639	−	0.0366853i
$373$	6.77994	+	9.05693i	0.351052	+	0.468950i	0.940959	−	0.338521i	$-0.109927\pi$
$373$	6.77994	+	9.05693i	0.351052	+	0.468950i	−0.589907	+	0.807471i	$0.700836\pi$
$374$	−0.611681	−	0.951795i	−0.0316293	−	0.0492161i
$375$	7.16999	−	8.57853i	0.370257	−	0.442993i
$376$	6.44835	+	7.44180i	0.332548	+	0.383781i
$377$	5.69628	+	4.26418i	0.293373	+	0.219617i
$378$	−1.25538	−	3.36582i	−0.0645700	−	0.173119i
$379$	28.9637	−	8.50452i	1.48777	−	0.436848i	0.565939	−	0.824447i	$-0.308514\pi$
$379$	28.9637	−	8.50452i	1.48777	−	0.436848i	0.921828	+	0.387599i	$0.126696\pi$
$380$	1.21518	+	6.97313i	0.0623375	+	0.357714i
$381$	1.79594	−	3.93255i	0.0920086	−	0.201471i
$382$	−12.3231	+	16.4617i	−0.630505	+	0.842256i
$383$	−30.5319	−	2.18368i	−1.56011	−	0.111581i	−0.735593	−	0.677423i	$-0.763097\pi$
$383$	−30.5319	−	2.18368i	−1.56011	−	0.111581i	−0.824514	+	0.565842i	$0.808551\pi$
$384$	−0.909632	+	0.415415i	−0.0464195	+	0.0211991i
$385$	5.89960	−	17.3787i	0.300671	−	0.885703i
$386$	2.25138	−	15.6587i	0.114592	−	0.797006i
$387$	−0.284252	−	1.30669i	−0.0144493	−	0.0664226i
$388$	−1.11187	−	15.5459i	−0.0564464	−	0.789224i
$389$	−24.0331	−	7.05676i	−1.21853	−	0.357792i	−0.391618	−	0.920128i	$-0.628085\pi$
$389$	−24.0331	−	7.05676i	−1.21853	−	0.357792i	−0.826909	+	0.562336i	$0.809903\pi$
$390$	−3.80552	−	4.78045i	−0.192700	−	0.242068i
$391$	−1.53338	−	1.81347i	−0.0775464	−	0.0917111i
$392$	4.17526	−	4.17526i	0.210883	−	0.210883i
$393$	7.60767	+	13.9324i	0.383756	+	0.702797i
$394$	7.05614	+	6.11418i	0.355483	+	0.308028i
$395$	13.3526	+	10.8923i	0.671844	+	0.548049i
$396$	2.26152	+	0.325157i	0.113646	+	0.0163398i
$397$	7.27853	−	33.4589i	0.365299	−	1.67925i	−0.317195	−	0.948360i	$-0.602741\pi$
$397$	7.27853	−	33.4589i	0.365299	−	1.67925i	0.682494	−	0.730891i	$-0.260895\pi$
$398$	−12.3401	−	4.60260i	−0.618551	−	0.230708i
$399$	8.59392	−	7.44668i	0.430234	−	0.372800i
$400$	−0.416176	+	4.98265i	−0.0208088	+	0.249132i
$401$	5.51453	+	2.51840i	0.275382	+	0.125763i	0.548319	−	0.836269i	$-0.315268\pi$
$401$	5.51453	+	2.51840i	0.275382	+	0.125763i	−0.272937	+	0.962032i	$0.587995\pi$
$402$	−6.95819	−	3.79946i	−0.347043	−	0.189500i
$403$	−7.98321	−	4.35916i	−0.397672	−	0.217145i
$404$	0.933826	+	0.426464i	0.0464596	+	0.0212174i
$405$	−0.0664776	−	2.23508i	−0.00330330	−	0.111062i
$406$	−7.06950	+	6.12576i	−0.350853	+	0.304016i
$407$	9.65218	+	3.60008i	0.478441	+	0.178449i
$408$	0.105260	−	0.483874i	0.00521117	−	0.0239554i
$409$	34.1575	+	4.91111i	1.68898	+	0.242839i	0.918725	−	0.394897i	$-0.129220\pi$
$409$	34.1575	+	4.91111i	1.68898	+	0.242839i	0.770255	+	0.637736i	$0.220129\pi$
$410$	−16.4576	+	1.67012i	−0.812783	+	0.0824813i
$411$	−8.54309	−	7.40263i	−0.421399	−	0.365145i
$412$	5.89348	+	10.7931i	0.290351	+	0.531738i
$413$	4.88742	−	4.88742i	0.240494	−	0.240494i
$414$	4.79548	+	0.0579925i	0.235685	+	0.00285017i
$415$	−5.15058	+	4.10016i	−0.252832	+	0.201269i
$416$	2.62188	+	0.769854i	0.128548	+	0.0377452i
$417$	−1.27758	−	17.8629i	−0.0625633	−	0.874749i
$418$	1.53736	+	7.06712i	0.0751947	+	0.345664i
$419$	−4.37719	+	30.4440i	−0.213840	+	1.48729i	0.546333	+	0.837568i	$0.316023\pi$
$419$	−4.37719	+	30.4440i	−0.213840	+	1.48729i	−0.760173	+	0.649721i	$0.774886\pi$
$420$	7.20433	−	3.55264i	0.351535	−	0.173351i
$421$	28.3405	−	12.9427i	1.38123	−	0.630788i	0.420254	−	0.907407i	$-0.361941\pi$
$421$	28.3405	−	12.9427i	1.38123	−	0.630788i	0.960980	+	0.276619i	$0.0892138\pi$
$422$	14.4096	+	1.03060i	0.701450	+	0.0501687i
$423$	5.90103	−	7.88285i	0.286918	−	0.383278i
$424$	1.54451	−	3.38200i	0.0750079	−	0.164244i
$425$	−1.85172	−	1.64362i	−0.0898218	−	0.0797271i
$426$	−8.39210	+	2.46414i	−0.406599	+	0.119388i
$427$	−11.6179	−	31.1488i	−0.562230	−	1.50740i
$428$	0.0386910	+	0.0289638i	0.00187020	+	0.00140002i
$429$	−4.08850	−	4.71838i	−0.197395	−	0.227805i
$430$	2.84274	−	0.927352i	0.137089	−	0.0447209i
$431$	5.24188	+	8.15652i	0.252492	+	0.392886i	0.944242	−	0.329251i	$-0.106796\pi$
$431$	5.24188	+	8.15652i	0.252492	+	0.392886i	−0.691750	+	0.722137i	$0.743160\pi$
$432$	0.599278	+	0.800541i	0.0288328	+	0.0385161i
$433$	3.81680	−	0.830294i	0.183424	−	0.0399014i	−0.119915	−	0.992784i	$-0.538262\pi$
$433$	3.81680	−	0.830294i	0.183424	−	0.0399014i	0.303339	+	0.952883i	$0.401899\pi$
$434$	7.83058	−	9.03697i	0.375880	−	0.433788i
$435$	−5.39264	+	2.19610i	−0.258557	+	0.105295i
$436$		−	6.19122i		−	0.296506i
$437$	5.13286	+	14.2870i	0.245538	+	0.683442i
$438$	−8.65539	−	8.65539i	−0.413570	−	0.413570i
$439$	−7.36099	+	25.0692i	−0.351321	+	1.19649i	0.574493	+	0.818510i	$0.305199\pi$
$439$	−7.36099	+	25.0692i	−0.351321	+	1.19649i	−0.925814	+	0.377980i	$0.876619\pi$
$440$	−0.212805	+	5.10448i	−0.0101451	+	0.243347i
$441$	−4.96736	−	3.19233i	−0.236541	−	0.152016i
$442$	−1.08325	+	0.810909i	−0.0515248	+	0.0385710i
$443$	38.9885	+	8.48143i	1.85240	+	0.402965i	0.993941	−	0.109916i	$-0.0350582\pi$
$443$	38.9885	+	8.48143i	1.85240	+	0.402965i	0.858460	+	0.512881i	$0.171422\pi$
$444$	1.87304	+	4.10139i	0.0888907	+	0.194643i
$445$	19.8871	+	29.0108i	0.942740	+	1.37524i
$446$	−2.19049	−	15.2352i	−0.103723	−	0.721409i
$447$	−21.0640	+	7.85645i	−0.996291	+	0.371597i
$448$	−1.72161	+	3.15290i	−0.0813385	+	0.148960i
$449$	−7.02416	−	23.9221i	−0.331491	−	1.12895i	−0.941627	−	0.336657i	$-0.890704\pi$
$449$	−7.02416	−	23.9221i	−0.331491	−	1.12895i	0.610137	−	0.792296i	$-0.291114\pi$
$450$	4.95725	−	0.652473i	0.233687	−	0.0307579i
$451$	−16.7304	+	2.40547i	−0.787805	+	0.113269i
$452$	−0.298967	+	4.18011i	−0.0140622	+	0.196616i
$453$	−4.40032	+	11.7977i	−0.206745	+	0.554305i
$454$	15.2338	−	9.79016i	0.714957	−	0.459475i
$455$	−21.2352	−	5.55511i	−0.995522	−	0.260428i
$456$	−1.71139	+	2.66297i	−0.0801430	+	0.124705i
$457$	0.556939	−	0.0398331i	0.0260525	−	0.00186331i	−0.0583068	−	0.998299i	$-0.518570\pi$
$457$	0.556939	−	0.0398331i	0.0260525	−	0.00186331i	0.0843594	+	0.996435i	$0.473116\pi$
$458$	−18.5460	+	10.1269i	−0.866595	+	0.473197i
$459$	−0.495191			−0.0231135
$460$	0.953601	+	10.6813i	0.0444619	+	0.498019i
$461$	−22.5051			−1.04817			−0.524083	−	0.851667i	$-0.675592\pi$
$461$	−22.5051			−1.04817			−0.524083	+	0.851667i	$0.675592\pi$
$462$	7.20366	−	3.93350i	0.335145	−	0.183003i
$463$	−22.4893	+	1.60847i	−1.04517	+	0.0747518i	−0.583348	−	0.812222i	$-0.698258\pi$
$463$	−22.4893	+	1.60847i	−1.04517	+	0.0747518i	−0.461819	+	0.886974i	$0.652803\pi$
$464$	1.40781	−	2.19060i	0.0653561	−	0.101696i
$465$	6.42374	−	3.75975i	0.297894	−	0.174354i
$466$	−7.50003	+	4.81998i	−0.347432	+	0.223281i
$467$	−3.16895	+	8.49627i	−0.146641	+	0.393161i	−0.989416	−	0.145106i	$-0.953648\pi$
$467$	−3.16895	+	8.49627i	−0.146641	+	0.393161i	0.842775	+	0.538266i	$0.180921\pi$
$468$	0.194939	−	2.72561i	0.00901107	−	0.125991i
$469$	−28.1898	+	4.05308i	−1.30168	+	0.187154i
$470$	18.8687	+	11.3481i	0.870350	+	0.523448i
$471$	0.561027	+	1.91068i	0.0258508	+	0.0880396i
$472$	−0.922108	+	1.68871i	−0.0424435	+	0.0777294i
$473$	2.86267	−	1.06772i	0.131626	−	0.0490938i
$474$	1.09672	+	7.62784i	0.0503739	+	0.350358i
$475$	7.41898	+	13.9809i	0.340406	+	0.641487i
$476$	−0.738974	−	1.61813i	−0.0338708	−	0.0741668i
$477$	−3.63302	−	0.790315i	−0.166345	−	0.0361860i
$478$	5.55109	−	4.15549i	0.253901	−	0.190068i
$479$	3.76994	+	2.42279i	0.172253	+	0.110700i	0.623926	−	0.781483i	$-0.285536\pi$
$479$	3.76994	+	2.42279i	0.172253	+	0.110700i	−0.451674	+	0.892183i	$0.649173\pi$
$480$	−1.64563	+	1.51391i	−0.0751122	+	0.0691000i
$481$	3.47115	−	11.8217i	0.158271	−	0.539021i
$482$	−14.5209	−	14.5209i	−0.661407	−	0.661407i
$483$	13.9157	−	10.1569i	0.633185	−	0.462155i
$484$		−	5.77980i		−	0.262718i
$485$	−13.1444	−	32.2767i	−0.596856	−	1.46561i
$486$	0.654861	−	0.755750i	0.0297051	−	0.0342815i
$487$	15.4624	−	3.36364i	0.700668	−	0.152421i	0.151900	−	0.988396i	$-0.451461\pi$
$487$	15.4624	−	3.36364i	0.700668	−	0.152421i	0.548768	+	0.835975i	$0.315097\pi$
$488$	5.54599	+	7.40858i	0.251055	+	0.335371i
$489$	−0.741506	−	1.15381i	−0.0335321	−	0.0521769i
$490$	5.98037	−	11.7713i	0.270166	−	0.531773i
$491$	0.398271	+	0.459629i	0.0179737	+	0.0207428i	0.764665	−	0.644428i	$-0.222904\pi$
$491$	0.398271	+	0.459629i	0.0179737	+	0.0207428i	−0.746692	+	0.665170i	$0.768359\pi$
$492$	−5.92230	−	4.43338i	−0.266998	−	0.199872i
$493$	0.450622	+	1.20816i	0.0202950	+	0.0544129i
$494$	8.29951	−	2.43696i	0.373412	−	0.109644i
$495$	5.03306	−	0.877093i	0.226219	−	0.0394224i
$496$	−1.38278	+	3.02786i	−0.0620886	+	0.135955i
$497$	−18.8292	+	25.1528i	−0.844604	+	1.12826i
$498$	−2.93664	−	0.210033i	−0.131594	−	0.00941178i
$499$	22.2689	−	10.1698i	0.996891	−	0.455265i	0.150950	−	0.988541i	$-0.451767\pi$
$499$	22.2689	−	10.1698i	0.996891	−	0.455265i	0.845941	+	0.533277i	$0.179040\pi$
$500$	2.57065	+	10.8808i	0.114963	+	0.486604i
$501$	0.616604	−	4.28858i	0.0275478	−	0.191599i
$502$	6.30522	+	28.9846i	0.281416	+	1.29365i
$503$	−1.83382	−	25.6402i	−0.0817660	−	1.14324i	−0.858295	−	0.513157i	$-0.828476\pi$
$503$	−1.83382	−	25.6402i	−0.0817660	−	1.14324i	0.776529	−	0.630082i	$-0.216979\pi$
$504$	3.44680	+	1.01207i	0.153533	+	0.0450812i
$505$	2.28088	+	0.258994i	0.101498	+	0.0115251i
$506$	1.42814	+	10.8639i	0.0634884	+	0.482961i
$507$	3.91247	−	3.91247i	0.173759	−	0.173759i
$508$	2.07191	+	3.79441i	0.0919259	+	0.168350i
$509$	0.310247	+	0.268831i	0.0137515	+	0.0119157i	0.661709	−	0.749760i	$-0.269831\pi$
$509$	0.310247	+	0.268831i	0.0137515	+	0.0119157i	−0.647958	+	0.761676i	$0.724377\pi$
$510$	−0.111793	−	1.10162i	−0.00495027	−	0.0487807i
$511$	−43.5244	−	6.25786i	−1.92540	−	0.276831i
$512$	0.212565	−	0.977147i	0.00939415	−	0.0431842i
$513$	2.96589	+	1.10622i	0.130947	+	0.0488409i
$514$	−2.24718	+	1.94719i	−0.0991187	+	0.0858868i
$515$	20.0132	+	18.8571i	0.881888	+	0.830944i
$516$	1.21640	+	0.555512i	0.0535491	+	0.0244551i
$517$	19.7460	+	10.7821i	0.868428	+	0.474198i
$518$	14.2159	+	7.76249i	0.624612	+	0.341064i
$519$	−13.5550	−	6.19038i	−0.595001	−	0.271728i
$520$	6.10751	−	0.181655i	0.267832	−	0.00796608i
$521$	−29.0454	+	25.1680i	−1.27250	+	1.10263i	−0.282846	+	0.959165i	$0.591279\pi$
$521$	−29.0454	+	25.1680i	−1.27250	+	1.10263i	−0.989656	+	0.143464i	$0.954176\pi$
$522$	−2.43979	−	0.909996i	−0.106787	−	0.0398294i
$523$	4.94763	−	22.7439i	0.216345	−	0.994520i	−0.732987	−	0.680243i	$-0.761874\pi$
$523$	4.94763	−	22.7439i	0.216345	−	0.994520i	0.949331	−	0.314277i	$-0.101762\pi$
$524$	−15.7126	−	2.25913i	−0.686407	−	0.0986904i
$525$	12.8514	−	12.5483i	0.560880	−	0.547653i
$526$	−15.7086	−	13.6116i	−0.684928	−	0.593494i
$527$	−0.789959	−	1.44670i	−0.0344112	−	0.0630194i
$528$	−1.61558	+	1.61558i	−0.0703091	+	0.0703091i
$529$	5.94428	+	22.2186i	0.258447	+	0.966025i
$530$	0.937989	−	8.26059i	0.0407437	−	0.358817i
$531$	1.84613	+	0.542073i	0.0801152	+	0.0235240i
$532$	0.811226	+	11.3424i	0.0351711	+	0.491756i
$533$	4.29705	+	19.7532i	0.186126	+	0.855606i
$534$	−2.23858	+	15.5696i	−0.0968727	+	0.673764i
$535$	0.102336	+	0.0347401i	0.00442436	+	0.00150195i
$536$	7.21152	−	3.29339i	0.311490	−	0.142253i
$537$	13.8316	+	0.989256i	0.596878	+	0.0426895i
$538$	−8.10924	+	10.8327i	−0.349614	+	0.467030i
$539$	5.60434	−	12.2718i	0.241396	−	0.528583i
$540$	1.82911	+	1.28622i	0.0787124	+	0.0553499i
$541$	9.69543	−	2.84683i	0.416839	−	0.122395i	−0.0665862	−	0.997781i	$-0.521211\pi$
$541$	9.69543	−	2.84683i	0.416839	−	0.122395i	0.483425	+	0.875386i	$0.339393\pi$
$542$	−4.36634	−	11.7066i	−0.187550	−	0.502842i
$543$	−15.7266	−	11.7728i	−0.674895	−	0.505220i
$544$	0.324281	+	0.374240i	0.0139034	+	0.0160454i
$545$	−4.29349	−	13.1614i	−0.183913	−	0.563772i
$546$	−5.30706	−	8.25795i	−0.227121	−	0.353408i
$547$	−10.4406	−	13.9470i	−0.446407	−	0.596330i	0.519739	−	0.854325i	$-0.326029\pi$
$547$	−10.4406	−	13.9470i	−0.446407	−	0.596330i	−0.966146	+	0.257995i	$0.916938\pi$
$548$	11.0458	−	2.40286i	0.471853	−	0.102645i
$549$	6.06038	−	6.99406i	0.258651	−	0.298499i
$550$	3.08747	+	10.9988i	0.131650	+	0.468988i
$551$		−	8.24282i		−	0.351156i
$552$	−2.92025	+	3.80423i	−0.124294	+	0.161919i
$553$	19.5751	+	19.5751i	0.832418	+	0.832418i
$554$	−0.331750	+	1.12984i	−0.0140947	+	0.0480021i
$555$	6.82597	+	7.41988i	0.289746	+	0.314956i
$556$	15.0656	+	9.68207i	0.638923	+	0.410611i
$557$	−14.0832	+	10.5425i	−0.596723	+	0.446702i	−0.854463	−	0.519513i	$-0.826113\pi$
$557$	−14.0832	+	10.5425i	−0.596723	+	0.446702i	0.257739	+	0.966215i	$0.417022\pi$
$558$	3.25260	+	0.707560i	0.137693	+	0.0299534i
$559$	−1.51797	−	3.32390i	−0.0642035	−	0.140586i
$560$	−1.47336	+	7.89638i	−0.0622608	+	0.333683i
$561$	−0.161015	−	1.11988i	−0.00679806	−	0.0472816i
$562$	−29.6337	+	11.0528i	−1.25002	+	0.466235i
$563$	16.0705	−	29.4310i	0.677292	−	1.24037i	−0.282396	−	0.959298i	$-0.591129\pi$
$563$	16.0705	−	29.4310i	0.677292	−	1.24037i	0.959687	−	0.281069i	$-0.0906891\pi$
$564$	2.77419	+	9.44804i	0.116815	+	0.397834i
$565$	2.26327	+	9.09346i	0.0952165	+	0.382565i
$566$	−23.6197	+	3.39600i	−0.992809	+	0.142744i
$567$	0.256273	−	3.58316i	0.0107624	−	0.150479i
$568$	3.05655	−	8.19493i	0.128250	−	0.343852i
$569$	4.11379	−	2.64377i	0.172459	−	0.110833i	−0.451564	−	0.892239i	$-0.649134\pi$
$569$	4.11379	−	2.64377i	0.172459	−	0.110833i	0.624023	+	0.781406i	$0.285497\pi$
$570$	−1.79138	+	6.84779i	−0.0750325	+	0.286822i
$571$	−15.2669	+	23.7558i	−0.638901	+	0.994149i	0.359243	+	0.933244i	$0.383035\pi$
$571$	−15.2669	+	23.7558i	−0.638901	+	0.994149i	−0.998144	+	0.0609050i	$0.980601\pi$
$572$	6.22740	−	0.445392i	0.260381	−	0.0186228i
$573$	−18.0479	+	9.85492i	−0.753963	+	0.411695i
$574$	−26.5755			−1.10924
$575$	9.43445	+	22.0452i	0.393444	+	0.919349i
$576$	−1.00000			−0.0416667
$577$	−37.8125	+	20.6472i	−1.57415	+	0.859554i	−0.575012	+	0.818145i	$0.695003\pi$
$577$	−37.8125	+	20.6472i	−1.57415	+	0.859554i	−0.999142	+	0.0414089i	$0.986815\pi$
$578$	16.7121	−	1.19527i	0.695132	−	0.0497168i
$579$	8.55278	−	13.3084i	0.355441	−	0.553077i
$580$	1.47361	−	5.63310i	0.0611885	−	0.233902i
$581$	−8.89732	+	5.71796i	−0.369123	+	0.237221i
$582$	5.44662	−	14.6029i	0.225770	−	0.605312i
$583$	0.606010	−	8.47312i	0.0250984	−	0.350921i
$584$	12.1160	−	1.74201i	0.501363	−	0.0720851i
$585$	−1.47575	−	5.92932i	−0.0610147	−	0.245147i
$586$	0.932750	+	3.17665i	0.0385315	+	0.131226i
$587$	−10.6555	+	19.5141i	−0.439800	+	0.805434i	−0.999733	−	0.0231043i	$-0.992645\pi$
$587$	−10.6555	+	19.5141i	−0.439800	+	0.805434i	0.559933	+	0.828538i	$0.310827\pi$
$588$	5.53242	−	2.06349i	0.228153	−	0.0850967i
$589$	1.49955	+	10.4296i	0.0617878	+	0.429743i
$590$	−0.789142	+	4.22936i	−0.0324884	+	0.174120i
$591$	3.87857	+	8.49288i	0.159543	+	0.349350i
$592$	−4.40581	−	0.958425i	−0.181078	−	0.0393910i
$593$	37.0770	−	27.7555i	1.52257	−	1.13978i	0.575924	−	0.817503i	$-0.304642\pi$
$593$	37.0770	−	27.7555i	1.52257	−	1.13978i	0.946645	−	0.322278i	$-0.104449\pi$
$594$	1.92208	+	1.23524i	0.0788637	+	0.0506826i
$595$	−2.69306	−	2.92738i	−0.110405	−	0.120011i
$596$	6.33375	−	21.5708i	0.259440	−	0.883573i
$597$	−9.31292	−	9.31292i	−0.381152	−	0.381152i
$598$	12.8382	−	2.63061i	0.524993	−	0.107573i
$599$			20.0505i			0.819242i	0.912256	+	0.409621i	$0.134339\pi$
$599$			20.0505i			0.819242i	−0.912256	+	0.409621i	$0.865661\pi$
$600$	−2.44843	+	4.35949i	−0.0999569	+	0.177976i
$601$	−23.3465	+	26.9433i	−0.952325	+	1.09904i	0.0426670	+	0.999089i	$0.486415\pi$
$601$	−23.3465	+	26.9433i	−0.952325	+	1.09904i	−0.994992	+	0.0999526i	$0.968131\pi$
$602$	4.69402	−	1.02112i	0.191314	−	0.0416178i
$603$	−4.75104	−	6.34665i	−0.193477	−	0.258456i
$604$	−6.80755	−	10.5928i	−0.276995	−	0.431013i
$605$	−4.00817	−	12.2868i	−0.162955	−	0.499529i
$606$	0.672278	+	0.775851i	0.0273094	+	0.0315168i
$607$	12.1907	+	9.12584i	0.494805	+	0.370406i	0.817344	−	0.576150i	$-0.195446\pi$
$607$	12.1907	+	9.12584i	0.494805	+	0.370406i	−0.322539	+	0.946556i	$0.604536\pi$
$608$	−1.10622	−	2.96589i	−0.0448632	−	0.120283i
$609$	−8.97537	+	2.63541i	−0.363700	+	0.106792i
$610$	16.9274	+	11.9032i	0.685372	+	0.481948i
$611$	11.1777	−	24.4758i	0.452202	−	0.990185i
$612$	0.296757	−	0.396421i	0.0119957	−	0.0160244i
$613$	−30.9991	−	2.21710i	−1.25204	−	0.0895478i	−0.570482	−	0.821310i	$-0.693244\pi$
$613$	−30.9991	−	2.21710i	−1.25204	−	0.0895478i	−0.681560	+	0.731762i	$0.738698\pi$
$614$	−27.7793	+	12.6864i	−1.12108	+	0.511981i
$615$	−15.6642	−	5.31754i	−0.631640	−	0.214424i
$616$	−1.16807	+	8.12409i	−0.0470628	+	0.327329i
$617$	4.73027	+	21.7447i	0.190433	+	0.875408i	0.968848	+	0.247657i	$0.0796607\pi$
$617$	4.73027	+	21.7447i	0.190433	+	0.875408i	−0.778414	+	0.627751i	$0.783976\pi$
$618$	0.877281	+	12.2660i	0.0352894	+	0.493410i
$619$	7.60644	+	2.23345i	0.305729	+	0.0897700i	0.430998	−	0.902353i	$-0.358161\pi$
$619$	7.60644	+	2.23345i	0.305729	+	0.0897700i	−0.125270	+	0.992123i	$0.539980\pi$
$620$	−0.839770	+	7.39561i	−0.0337260	+	0.297015i
$621$	4.33803	+	2.04487i	0.174079	+	0.0820577i
$622$	−20.2806	+	20.2806i	−0.813178	+	0.813178i
$623$	27.0805	+	49.5943i	1.08496	+	1.98695i
$624$	2.06514	+	1.78945i	0.0826717	+	0.0716354i
$625$	13.0103	+	21.3479i	0.520414	+	0.853914i
$626$	5.83459	+	0.838887i	0.233197	+	0.0335287i
$627$	−1.53736	+	7.06712i	−0.0613962	+	0.282234i
$628$	−1.86579	−	0.695904i	−0.0744532	−	0.0277696i
$629$	1.68739	−	1.46213i	0.0672808	−	0.0582991i
$630$	8.02911	−	0.238808i	0.319887	−	0.00951435i
$631$	−16.6491	−	7.60338i	−0.662790	−	0.302686i	0.0554708	−	0.998460i	$-0.482334\pi$
$631$	−16.6491	−	7.60338i	−0.662790	−	0.302686i	−0.718260	+	0.695774i	$0.755061\pi$
$632$	−6.76364	−	3.69323i	−0.269043	−	0.146909i
$633$	12.6793	+	6.92344i	0.503958	+	0.275182i
$634$	12.0268	+	5.49245i	0.477645	+	0.218133i
$635$	7.03583	+	6.62939i	0.279208	+	0.263079i
$636$	2.80987	−	2.43476i	0.111419	−	0.0965447i
$637$	−15.1177	−	5.63862i	−0.598986	−	0.223410i
$638$	1.26466	−	5.81353i	0.0500682	−	0.230160i
$639$	−8.65737	−	1.24474i	−0.342480	−	0.0492412i
$640$	−0.225757	−	2.22464i	−0.00892383	−	0.0879367i
$641$	2.01536	+	1.74632i	0.0796019	+	0.0689754i	0.693753	−	0.720213i	$-0.255956\pi$
$641$	2.01536	+	1.74632i	0.0796019	+	0.0689754i	−0.614151	+	0.789189i	$0.710501\pi$
$642$	0.0231626	+	0.0424192i	0.000914156	+	0.00167415i
$643$	−9.10016	+	9.10016i	−0.358875	+	0.358875i	−0.863398	−	0.504523i	$-0.831668\pi$
$643$	−9.10016	+	9.10016i	−0.358875	+	0.358875i	0.504523	+	0.863398i	$0.331668\pi$
$644$	−0.208327	+	17.2269i	−0.00820924	+	0.678834i
$645$	2.97108	+	0.337366i	0.116986	+	0.0132838i
$646$	1.50402	+	0.441620i	0.0591749	+	0.0173753i
$647$	1.69924	+	23.7584i	0.0668039	+	0.934041i	0.914766	+	0.403984i	$0.132375\pi$
$647$	1.69924	+	23.7584i	0.0668039	+	0.934041i	−0.847962	+	0.530057i	$0.822171\pi$
$648$	0.212565	+	0.977147i	0.00835035	+	0.0383860i
$649$	−0.625625	+	4.35132i	−0.0245579	+	0.170804i
$650$	12.8575	−	4.62160i	0.504311	−	0.181274i
$651$	10.8770	−	4.96738i	0.426305	−	0.194687i
$652$	1.36804	+	0.0978439i	0.0535765	+	0.00383186i
$653$	−20.8276	+	27.8224i	−0.815047	+	1.08877i	0.179425	+	0.983772i	$0.442576\pi$
$653$	−20.8276	+	27.8224i	−0.815047	+	1.08877i	−0.994472	+	0.105003i	$0.966515\pi$
$654$	2.57193	−	5.63174i	0.100570	−	0.220218i
$655$	−34.9687	+	6.09386i	−1.36634	+	0.238107i
$656$	7.09820	−	2.08422i	0.277138	−	0.0813751i
$657$	−4.27764	−	11.4688i	−0.166887	−	0.447440i
$658$	28.3177	+	21.1984i	1.10394	+	0.826398i
$659$	−7.71362	−	8.90199i	−0.300480	−	0.346772i	0.585351	−	0.810780i	$-0.300957\pi$
$659$	−7.71362	−	8.90199i	−0.300480	−	0.346772i	−0.885831	+	0.464007i	$0.846411\pi$
$660$	−2.31405	+	4.55480i	−0.0900743	+	0.177295i
$661$	14.0045	+	21.7914i	0.544711	+	0.847587i	0.999065	−	0.0432344i	$-0.0137662\pi$
$661$	14.0045	+	21.7914i	0.544711	+	0.847587i	−0.454354	+	0.890821i	$0.650130\pi$
$662$	−2.78653	−	3.72237i	−0.108302	−	0.144674i
$663$	−1.32222	+	0.287631i	−0.0513508	+	0.0111707i
$664$	1.92800	−	2.22503i	0.0748210	−	0.0863480i
$665$	9.59025	+	23.5493i	0.371894	+	0.913203i
$666$			4.50885i			0.174714i
$667$	1.04146	−	12.4447i	0.0403255	−	0.481861i
$668$	3.06366	+	3.06366i	0.118537	+	0.118537i
$669$	4.33640	−	14.7684i	0.167655	−	0.570980i
$670$	13.0464	−	12.0022i	0.504028	−	0.463684i
$671$	17.7878	+	11.4315i	0.686690	+	0.441309i
$672$	−2.87579	+	2.15279i	−0.110936	+	0.0830458i
$673$	−25.9720	−	5.64985i	−1.00115	−	0.217786i	−0.318018	−	0.948085i	$-0.603017\pi$
$673$	−25.9720	−	5.64985i	−1.00115	−	0.217786i	−0.683128	+	0.730299i	$0.739381\pi$
$674$	−9.17575	−	20.0921i	−0.353437	−	0.773918i
$675$	4.78032	+	1.46580i	0.183994	+	0.0564188i
$676$	0.787437	+	5.47675i	0.0302860	+	0.210644i
$677$	−40.3352	+	15.0443i	−1.55021	+	0.578198i	−0.971438	−	0.237292i	$-0.923740\pi$
$677$	−40.3352	+	15.0443i	−1.55021	+	0.578198i	−0.578771	+	0.815490i	$0.696467\pi$
$678$	−2.00843	+	3.67817i	−0.0771333	+	0.141259i
$679$	−15.7738	−	53.7205i	−0.605342	−	2.06160i
$680$	0.948890	+	0.570683i	0.0363883	+	0.0218847i
$681$	17.9241	−	2.57710i	0.686854	−	0.0987547i
$682$	−0.542553	+	7.58589i	−0.0207754	+	0.290479i
$683$	11.6262	−	31.1712i	0.444866	−	1.19273i	−0.500217	−	0.865900i	$-0.666746\pi$
$683$	11.6262	−	31.1712i	0.444866	−	1.19273i	0.945083	−	0.326831i	$-0.105981\pi$
$684$	−2.66297	+	1.71139i	−0.101821	+	0.0654365i
$685$	21.8150	−	12.7681i	0.833507	−	0.487843i
$686$	−2.12722	+	3.31001i	−0.0812175	+	0.126377i
$687$	−21.0768	+	1.50745i	−0.804132	+	0.0575126i
$688$	−1.17367	+	0.640874i	−0.0447458	+	0.0244331i
$689$	−10.1597			−0.387052
$690$	−3.56976	+	10.1122i	−0.135898	+	0.384965i
$691$	−40.0433			−1.52332			−0.761659	−	0.647978i	$-0.775615\pi$
$691$	−40.0433			−1.52332			−0.761659	+	0.647978i	$0.775615\pi$
$692$	13.0789	−	7.14162i	0.497185	−	0.271484i
$693$	8.18672	−	0.585526i	0.310988	−	0.0222423i
$694$	−1.39039	+	2.16348i	−0.0527783	+	0.0821247i
$695$	38.7410	+	10.1346i	1.46953	+	0.384427i
$696$	2.19060	−	1.40781i	0.0830346	−	0.0533631i
$697$	−1.28021	+	3.43238i	−0.0484915	+	0.130011i
$698$	0.411502	−	5.75355i	0.0155756	−	0.217775i
$699$	−8.82456	+	1.26878i	−0.333775	+	0.0479897i
$700$	2.34389	+	17.8080i	0.0885907	+	0.673078i
$701$	0.995671	+	3.39094i	0.0376060	+	0.128074i	0.976157	−	0.217067i	$-0.0696491\pi$
$701$	0.995671	+	3.39094i	0.0376060	+	0.128074i	−0.938551	+	0.345142i	$0.887831\pi$
$702$	1.30958	−	2.39832i	0.0494270	−	0.0905187i
$703$	−13.3728	+	4.98778i	−0.504363	+	0.188118i
$704$	−0.325157	−	2.26152i	−0.0122548	−	0.0852342i
$705$	12.4494	+	18.1609i	0.468873	+	0.683980i
$706$	−0.330186	−	0.723007i	−0.0124267	−	0.0272107i
$707$	3.60358	+	0.783911i	0.135527	+	0.0294820i
$708$	−1.54030	+	1.15305i	−0.0578879	+	0.0433343i
$709$	6.96510	+	4.47620i	0.261580	+	0.168107i	0.664857	−	0.746971i	$-0.268493\pi$
$709$	6.96510	+	4.47620i	0.261580	+	0.168107i	−0.403277	+	0.915078i	$0.632129\pi$
$710$	0.814644	−	19.5406i	0.0305731	−	0.733344i
$711$	−2.17111	+	7.39412i	−0.0814230	+	0.277301i
$712$	−11.1226	−	11.1226i	−0.416838	−	0.416838i
$713$	0.946211	+	15.9357i	0.0354359	+	0.596796i
$714$		−	1.77888i		−	0.0665730i
$715$	12.9294	−	5.26540i	0.483533	−	0.196915i
$716$	−9.08091	+	10.4799i	−0.339370	+	0.391653i
$717$	6.77570	−	1.47396i	0.253043	−	0.0550462i
$718$	11.8115	+	15.7784i	0.440802	+	0.588843i
$719$	−8.09344	−	12.5936i	−0.301834	−	0.469664i	0.656896	−	0.753982i	$-0.271869\pi$
$719$	−8.09344	−	12.5936i	−0.301834	−	0.469664i	−0.958730	+	0.284318i	$0.908233\pi$
$720$	−2.12581	+	0.693479i	−0.0792244	+	0.0258445i
$721$	28.9290	+	33.3859i	1.07737	+	1.24335i
$722$	7.18866	+	5.38136i	0.267534	+	0.200274i
$723$	−7.17645	−	19.2408i	−0.266895	−	0.715574i
$724$	18.8492	−	5.53464i	0.700527	−	0.205693i
$725$	−0.773810	−	12.9969i	−0.0287386	−	0.482691i
$726$	2.40102	−	5.25749i	0.0891101	−	0.195124i
$727$	−1.66468	+	2.22375i	−0.0617395	+	0.0824744i	−0.830348	−	0.557245i	$-0.811858\pi$
$727$	−1.66468	+	2.22375i	−0.0617395	+	0.0824744i	0.768609	+	0.639719i	$0.220949\pi$
$728$	9.79123	+	0.700283i	0.362887	+	0.0259542i
$729$	0.909632	−	0.415415i	0.0336901	−	0.0153857i
$730$	24.5483	−	12.1054i	0.908572	−	0.448040i
$731$	0.0942398	−	0.655452i	0.00348558	−	0.0242428i
$732$	1.96718	+	9.04297i	0.0727090	+	0.334238i
$733$	0.754236	+	10.5456i	0.0278584	+	0.389511i	0.992183	+	0.124789i	$0.0398255\pi$
$733$	0.754236	+	10.5456i	0.0278584	+	0.389511i	−0.964325	+	0.264721i	$0.914720\pi$
$734$	−15.2983	−	4.49200i	−0.564672	−	0.165803i
$735$	10.3299	−	8.22320i	0.381024	−	0.303317i
$736$	−1.29540	−	4.61757i	−0.0477491	−	0.170206i
$737$	12.8082	−	12.8082i	0.471797	−	0.471797i
$738$	−3.54542	−	6.49295i	−0.130509	−	0.239009i
$739$	31.7877	+	27.5442i	1.16933	+	1.01323i	0.999615	+	0.0277350i	$0.00882947\pi$
$739$	31.7877	+	27.5442i	1.16933	+	1.01323i	0.169713	+	0.985494i	$0.445716\pi$
$740$	−10.0306	+	1.01790i	−0.368731	+	0.0374189i
$741$	8.56185	+	1.23101i	0.314527	+	0.0452222i
$742$	2.83906	−	13.0509i	0.104225	−	0.479115i
$743$	17.3115	+	6.45685i	0.635097	+	0.236879i	0.646330	−	0.763058i	$-0.276303\pi$
$743$	17.3115	+	6.45685i	0.635097	+	0.236879i	−0.0112330	+	0.999937i	$0.503576\pi$
$744$	−2.51564	+	2.17981i	−0.0922279	+	0.0799159i
$745$	−1.49451	−	50.2478i	−0.0547546	−	1.84094i
$746$	−10.2911	−	4.69980i	−0.376785	−	0.172072i
$747$	−2.58401	−	1.41098i	−0.0945440	−	0.0516249i
$748$	0.993006	+	0.542223i	0.0363079	+	0.0198256i
$749$	0.157931	+	0.0721246i	0.00577066	+	0.00263537i
$750$	−2.18170	+	10.9654i	−0.0796644	+	0.400400i
$751$	32.3120	−	27.9985i	1.17908	−	1.02168i	0.179802	−	0.983703i	$-0.442454\pi$
$751$	32.3120	−	27.9985i	1.17908	−	1.02168i	0.999279	−	0.0379761i	$-0.0120911\pi$
$752$	−9.22606	−	3.44114i	−0.336440	−	0.125486i
$753$	−6.30522	+	28.9846i	−0.229775	+	1.05626i
$754$	−7.04311	−	1.01265i	−0.256495	−	0.0368784i
$755$	−21.8174	−	17.7973i	−0.794018	−	0.647711i
$756$	2.71489	+	2.35246i	0.0987396	+	0.0855583i
$757$	−5.70119	−	10.4409i	−0.207213	−	0.379483i	0.753317	−	0.657657i	$-0.228452\pi$
$757$	−5.70119	−	10.4409i	−0.207213	−	0.379483i	−0.960531	+	0.278174i	$0.910271\pi$
$758$	−21.3451	+	21.3451i	−0.775288	+	0.775288i
$759$	−3.21396	+	10.4754i	−0.116659	+	0.380235i
$760$	−4.40841	−	5.53780i	−0.159910	−	0.200877i
$761$	−14.1076	−	4.14238i	−0.511402	−	0.150161i	0.0158431	−	0.999874i	$-0.494957\pi$
$761$	−14.1076	−	4.14238i	−0.511402	−	0.150161i	−0.527245	+	0.849713i	$0.676775\pi$
$762$	0.308416	+	4.31222i	0.0111727	+	0.156215i
$763$	−4.72763	−	21.7325i	−0.171152	−	0.786771i
$764$	2.92646	−	20.3539i	0.105875	−	0.736380i
$765$	0.355940	−	1.04851i	0.0128691	−	0.0379090i
$766$	27.8437	−	12.7158i	1.00603	−	0.459441i
$767$	5.24426	+	0.375077i	0.189359	+	0.0135432i
$768$	0.599278	−	0.800541i	0.0216246	−	0.0288870i
$769$	2.94494	−	6.44852i	0.106197	−	0.232540i	−0.849072	−	0.528277i	$-0.822838\pi$
$769$	2.94494	−	6.44852i	0.106197	−	0.232540i	0.955269	+	0.295738i	$0.0955654\pi$
$770$	3.15079	+	18.0803i	0.113547	+	0.651570i
$771$	−2.85299	+	0.837715i	−0.102748	+	0.0301696i
$772$	5.52842	+	14.8223i	0.198972	+	0.533465i
$773$	18.9635	+	14.1959i	0.682071	+	0.510592i	0.883214	−	0.468970i	$-0.155375\pi$
$773$	18.9635	+	14.1959i	0.682071	+	0.510592i	−0.201143	+	0.979562i	$0.564466\pi$
$774$	0.875710	+	1.01062i	0.0314767	+	0.0363261i
$775$	3.34350	+	16.3040i	0.120102	+	0.585659i
$776$	8.42622	+	13.1115i	0.302484	+	0.470674i
$777$	9.70662	+	12.9665i	0.348223	+	0.465171i
$778$	24.4753	−	5.32428i	0.877482	−	0.190885i
$779$	15.3354	−	17.6980i	0.549447	−	0.634096i
$780$	5.63105	+	2.37191i	0.201624	+	0.0849281i
$781$		−	19.9835i		−	0.715068i
$782$	2.21492	+	0.856772i	0.0792054	+	0.0306381i
$783$	−1.84129	−	1.84129i	−0.0658022	−	0.0658022i
$784$	−1.66355	+	5.66553i	−0.0594125	+	0.202340i
$785$	−4.44892	−	0.185475i	−0.158789	−	0.00661989i
$786$	−13.3542	−	8.58221i	−0.476328	−	0.306117i
$787$	8.04479	−	6.02226i	0.286766	−	0.214670i	−0.446204	−	0.894931i	$-0.647224\pi$
$787$	8.04479	−	6.02226i	0.286766	−	0.214670i	0.732970	+	0.680261i	$0.238134\pi$
$788$	−9.12324	−	1.98464i	−0.325002	−	0.0706998i
$789$	−8.63460	−	18.9071i	−0.307400	−	0.673112i
$790$	−16.9394	−	3.16067i	−0.602678	−	0.112452i
$791$	2.14250	+	14.9014i	0.0761784	+	0.529832i
$792$	−2.14072	+	0.798447i	−0.0760672	+	0.0283716i
$793$	12.1195	−	22.1952i	0.430375	−	0.788173i
$794$	9.64691	+	32.8544i	0.342356	+	1.16596i
$795$	4.28480	−	7.12444i	0.151966	−	0.252678i
$796$	13.0364	−	1.87435i	0.462063	−	0.0664346i
$797$	−1.62117	+	22.6669i	−0.0574248	+	0.802903i	0.884385	+	0.466758i	$0.154578\pi$
$797$	−1.62117	+	22.6669i	−0.0574248	+	0.802903i	−0.941810	+	0.336146i	$0.890877\pi$
$798$	−3.97389	+	10.6544i	−0.140674	+	0.377162i
$799$	4.10204	−	2.63622i	0.145120	−	0.0932627i
$800$	−2.02266	−	4.57262i	−0.0715119	−	0.161666i
$801$	−8.50415	+	13.2327i	−0.300479	+	0.467555i
$802$	−6.04693	+	0.432485i	−0.213524	+	0.0152716i
$803$	24.5460	−	13.4031i	0.866209	−	0.472986i
$804$	7.92795			0.279597
$805$	11.5036	+	36.7656i	0.405449	+	1.29582i
$806$	9.09582			0.320387
$807$	−11.8765	+	6.48505i	−0.418072	+	0.228284i
$808$	−1.02398	+	0.0732366i	−0.0360236	+	0.00257646i
$809$	17.1774	−	26.7286i	0.603925	−	0.939726i	−0.395846	−	0.918317i	$-0.629548\pi$
$809$	17.1774	−	26.7286i	0.603925	−	0.939726i	0.999771	−	0.0214088i	$-0.00681514\pi$
$810$	1.12951	+	1.92982i	0.0396868	+	0.0678071i
$811$	10.9744	−	7.05281i	0.385363	−	0.247658i	−0.333587	−	0.942719i	$-0.608259\pi$
$811$	10.9744	−	7.05281i	0.385363	−	0.247658i	0.718950	+	0.695061i	$0.244623\pi$
$812$	3.26899	−	8.76450i	0.114719	−	0.307574i
$813$	0.891339	−	12.4625i	0.0312606	−	0.437080i
$814$	−10.1968	+	1.46609i	−0.357399	+	0.0513863i
$815$	2.97605	−	0.740708i	0.104246	−	0.0259459i
$816$	0.139511	+	0.475132i	0.00488388	+	0.0166330i
$817$	−2.02867	+	3.71523i	−0.0709742	+	0.129980i
$818$	−32.3330	+	12.0596i	−1.13050	+	0.421653i
$819$	−1.39700	−	9.71633i	−0.0488150	−	0.339516i
$820$	13.6441	−	9.35312i	0.476472	−	0.326625i
$821$	−18.6971	−	40.9410i	−0.652534	−	1.42885i	−0.889319	−	0.457287i	$-0.848821\pi$
$821$	−18.6971	−	40.9410i	−0.652534	−	1.42885i	0.236786	−	0.971562i	$-0.423906\pi$
$822$	11.0458	+	2.40286i	0.385266	+	0.0838095i
$823$	−29.2726	+	21.9132i	−1.02038	+	0.763846i	−0.971999	−	0.234983i	$-0.924496\pi$
$823$	−29.2726	+	21.9132i	−1.02038	+	0.763846i	−0.0483790	+	0.998829i	$0.515406\pi$
$824$	−10.3452	−	6.64843i	−0.360391	−	0.231609i
$825$	−1.76059	+	11.2874i	−0.0612958	+	0.392977i
$826$	−1.94730	+	6.63188i	−0.0677551	+	0.230753i
$827$	−11.8291	−	11.8291i	−0.411337	−	0.411337i	0.470867	−	0.882204i	$-0.343941\pi$
$827$	−11.8291	−	11.8291i	−0.411337	−	0.411337i	−0.882204	+	0.470867i	$0.843941\pi$
$828$	−4.23669	+	2.24733i	−0.147235	+	0.0781001i
$829$		−	20.7192i		−	0.719606i	−0.933028	−	0.359803i	$-0.882844\pi$
$829$		−	20.7192i		−	0.719606i	0.933028	−	0.359803i	$-0.117156\pi$
$830$	2.55556	−	6.06703i	0.0887047	−	0.210590i
$831$	−0.771121	+	0.889921i	−0.0267499	+	0.0308710i
$832$	−2.67012	+	0.580849i	−0.0925698	+	0.0201373i
$833$	−1.75226	−	2.34075i	−0.0607124	−	0.0811022i
$834$	9.68207	+	15.0656i	0.335263	+	0.521679i
$835$	8.63737	+	4.38819i	0.298909	+	0.151860i
$836$	−4.73622	−	5.46589i	−0.163806	−	0.189042i
$837$	2.66474	+	1.99480i	0.0921068	+	0.0689503i
$838$	−10.7485	−	28.8179i	−0.371301	−	0.995496i
$839$	−15.7465	+	4.62359i	−0.543630	+	0.159624i	−0.542006	−	0.840375i	$-0.682335\pi$
$839$	−15.7465	+	4.62359i	−0.543630	+	0.159624i	−0.00162382	+	0.999999i	$0.500517\pi$
$840$	−4.62049	+	6.57074i	−0.159422	+	0.226712i
$841$	9.23024	−	20.2114i	0.318284	−	0.696945i
$842$	−18.6711	+	24.9417i	−0.643449	+	0.859548i
$843$	−31.5473	−	2.25631i	−1.08655	−	0.0777113i
$844$	−13.1409	+	6.00127i	−0.452330	+	0.206572i
$845$	5.47196	+	11.0965i	0.188241	+	0.381730i
$846$	−1.40136	+	9.74668i	−0.0481798	+	0.335098i
$847$	−4.41346	−	20.2884i	−0.151648	−	0.697116i
$848$	0.265238	+	3.70852i	0.00910832	+	0.127351i
$849$	−22.8960	−	6.72286i	−0.785788	−	0.230728i
$850$	2.41292	+	0.555131i	0.0827625	+	0.0190408i
$851$	−20.8199	+	5.84076i	−0.713697	+	0.200219i
$852$	6.18463	−	6.18463i	0.211882	−	0.211882i
$853$	−16.3552	−	29.9524i	−0.559993	−	1.02555i	−0.992304	−	0.123826i	$-0.960484\pi$
$853$	−16.3552	−	29.9524i	−0.559993	−	1.02555i	0.432311	−	0.901725i	$-0.357698\pi$
$854$	25.1248	+	21.7708i	0.859754	+	0.744981i
$855$	−4.47417	+	5.48480i	−0.153013	+	0.187576i
$856$	−0.0478392	−	0.00687823i	−0.00163511	−	0.000235093i
$857$	−1.48045	+	6.80551i	−0.0505711	+	0.232472i	−0.995494	−	0.0948201i	$-0.969772\pi$
$857$	−1.48045	+	6.80551i	−0.0505711	+	0.232472i	0.944923	+	0.327292i	$0.106136\pi$
$858$	5.84967	+	2.18181i	0.199704	+	0.0744858i
$859$	33.8660	−	29.3451i	1.15549	−	1.00124i	0.155583	−	0.987823i	$-0.450274\pi$
$859$	33.8660	−	29.3451i	1.15549	−	1.00124i	0.999910	−	0.0134180i	$-0.00427121\pi$
$860$	−2.05058	+	2.17630i	−0.0699241	+	0.0742111i
$861$	−24.1739	−	11.0398i	−0.823844	−	0.376237i
$862$	−8.50969	−	4.64664i	−0.289841	−	0.158265i
$863$	5.82695	+	3.18176i	0.198352	+	0.108308i	0.575355	−	0.817904i	$-0.304864\pi$
$863$	5.82695	+	3.18176i	0.198352	+	0.108308i	−0.377004	+	0.926212i	$0.623046\pi$
$864$	−0.909632	−	0.415415i	−0.0309463	−	0.0141327i
$865$	22.8507	−	24.2517i	0.776948	−	0.824582i
$866$	−2.95201	+	2.55793i	−0.100313	+	0.0869219i
$867$	15.6984	+	5.85520i	0.533145	+	0.198853i
$868$	−2.54178	+	11.6844i	−0.0862735	+	0.396593i
$869$	−17.4279	−	2.50575i	−0.591201	−	0.0850019i
$870$	3.68052	−	4.51189i	0.124781	−	0.152967i
$871$	−16.3723	−	14.1867i	−0.554755	−	0.480698i
$872$	2.96714	+	5.43391i	0.100480	+	0.184015i
$873$	11.0207	−	11.0207i	0.372994	−	0.372994i
$874$	−11.3521	−	10.0795i	−0.383989	−	0.340945i
$875$	17.3321	+	36.2310i	0.585933	+	1.22483i
$876$	11.7447	+	3.44857i	0.396818	+	0.116516i
$877$	−2.71494	−	37.9598i	−0.0916770	−	1.28181i	−0.810136	−	0.586243i	$-0.800607\pi$
$877$	−2.71494	−	37.9598i	−0.0916770	−	1.28181i	0.718458	−	0.695570i	$-0.244848\pi$
$878$	−5.55382	−	25.5305i	−0.187432	−	0.861612i
$879$	−0.471171	+	3.27706i	−0.0158922	+	0.110533i
$880$	−2.25954	−	4.58208i	−0.0761691	−	0.154462i
$881$	−48.4532	+	22.1279i	−1.63243	+	0.745506i	−0.999586	−	0.0287724i	$-0.990840\pi$
$881$	−48.4532	+	22.1279i	−1.63243	+	0.745506i	−0.632845	+	0.774279i	$0.718113\pi$
$882$	5.88967	+	0.421237i	0.198315	+	0.0141838i
$883$	−22.9204	+	30.6181i	−0.771334	+	1.03038i	0.227069	+	0.973879i	$0.427086\pi$
$883$	−22.9204	+	30.6181i	−0.771334	+	1.03038i	−0.998402	+	0.0565025i	$0.982005\pi$
$884$	0.562116	−	1.23086i	0.0189060	−	0.0413984i
$885$	−2.47477	+	3.51934i	−0.0831884	+	0.118301i
$886$	−38.2841	+	11.2412i	−1.28618	+	0.377657i
$887$	−16.3099	−	43.7285i	−0.547633	−	1.46826i	−0.855991	−	0.516990i	$-0.827052\pi$
$887$	−16.3099	−	43.7285i	−0.547633	−	1.46826i	0.308358	−	0.951270i	$-0.400220\pi$
$888$	−3.60952	−	2.70205i	−0.121128	−	0.0906749i
$889$	10.1703	+	11.7371i	0.341099	+	0.393650i
$890$	−31.3579	−	15.9313i	−1.05112	−	0.534019i
$891$	1.23524	+	1.92208i	0.0413822	+	0.0643920i
$892$	9.22402	+	12.3218i	0.308843	+	0.412566i
$893$	−30.4578	+	6.62570i	−1.01923	+	0.221720i
$894$	14.7222	−	16.9903i	0.492384	−	0.568241i
$895$	−12.0367	+	28.5758i	−0.402343	+	0.955184i
$896$		−	3.59231i		−	0.120011i
$897$	12.7708	+	2.94030i	0.426406	+	0.0981737i
$898$	17.6296	+	17.6296i	0.588307	+	0.588307i
$899$	2.44199	−	8.31666i	0.0814450	−	0.277376i
$900$	−4.03817	+	2.94842i	−0.134606	+	0.0982806i
$901$	−1.54884	−	0.995382i	−0.0515995	−	0.0331610i
$902$	13.5311	−	10.1293i	0.450537	−	0.337268i
$903$	4.69402	+	1.02112i	0.156207	+	0.0339808i
$904$	−1.74092	−	3.81207i	−0.0579020	−	0.126788i
$905$	36.2318	−	24.8372i	1.20439	−	0.825616i
$906$	−1.79198	−	12.4635i	−0.0595344	−	0.414071i
$907$	4.49534	−	1.67667i	0.149265	−	0.0556731i	−0.273721	−	0.961809i	$-0.588255\pi$
$907$	4.49534	−	1.67667i	0.149265	−	0.0556731i	0.422986	+	0.906136i	$0.360982\pi$
$908$	−8.67845	+	15.8934i	−0.288005	+	0.527441i
$909$	0.289226	+	0.985013i	0.00959302	+	0.0326708i
$910$	21.3000	−	5.30135i	0.706087	−	0.175738i
$911$	−36.2820	+	5.21657i	−1.20208	+	0.172833i	−0.714112	−	0.700031i	$-0.753169\pi$
$911$	−36.2820	+	5.21657i	−1.20208	+	0.172833i	−0.487964	+	0.872864i	$0.662260\pi$
$912$	0.225823	−	3.15741i	0.00747773	−	0.104552i
$913$	2.35074	−	6.30258i	0.0777981	−	0.208585i
$914$	−0.469724	+	0.301873i	−0.0155371	+	0.00998508i
$915$	10.4530	+	17.8595i	0.345564	+	0.590416i
$916$	11.4241	−	17.7763i	0.377463	−	0.587344i
$917$	−56.8796	+	4.06811i	−1.87833	+	0.134341i
$918$	0.434619	−	0.237320i	0.0143446	−	0.00783272i
$919$	2.53848			0.0837367			0.0418684	−	0.999123i	$-0.486669\pi$
$919$	2.53848			0.0837367			0.0418684	+	0.999123i	$0.486669\pi$
$920$	−5.95597	−	8.91776i	−0.196362	−	0.294010i
$921$	−30.5391			−1.00630
$922$	19.7522	−	10.7855i	0.650505	−	0.355203i
$923$	−23.8392	+	1.70502i	−0.784678	+	0.0561213i
$924$	−4.43738	+	6.90470i	−0.145979	+	0.227148i
$925$	−20.6172	+	9.11987i	−0.677891	+	0.299859i
$926$	18.9675	−	12.1897i	0.623312	−	0.400578i
$927$	−4.29747	+	11.5220i	−0.141148	+	0.378431i
$928$	−0.185765	+	2.59734i	−0.00609805	+	0.0852618i
$929$	17.7049	−	2.54559i	0.580880	−	0.0835179i	0.154390	−	0.988010i	$-0.450659\pi$
$929$	17.7049	−	2.54559i	0.580880	−	0.0835179i	0.426490	+	0.904492i	$0.359750\pi$
$930$	−3.83613	+	6.37843i	−0.125792	+	0.209157i
$931$	5.26593	+	17.9341i	0.172584	+	0.587767i
$932$	4.27265	−	7.82477i	0.139955	−	0.256309i
$933$	−26.8728	+	10.0230i	−0.879775	+	0.328139i
$934$	−1.29051	−	8.97571i	−0.0422269	−	0.293694i
$935$	2.48697	+	0.464035i	0.0813325	+	0.0151756i
$936$	1.13515	+	2.48563i	0.0371036	+	0.0812454i
$937$	−15.5900	−	3.39139i	−0.509302	−	0.110792i	−0.0494308	−	0.998778i	$-0.515741\pi$
$937$	−15.5900	−	3.39139i	−0.509302	−	0.110792i	−0.459871	+	0.887986i	$0.652104\pi$
$938$	22.7992	−	17.0672i	0.744419	−	0.557265i
$939$	4.95884	+	3.18685i	0.161826	+	0.103999i
$940$	−21.9992	−	0.917147i	−0.717536	−	0.0299140i
$941$	14.3728	−	48.9491i	0.468538	−	1.59569i	−0.298709	−	0.954344i	$-0.596556\pi$
$941$	14.3728	−	48.9491i	0.468538	−	1.59569i	0.767248	−	0.641351i	$-0.221626\pi$
$942$	−1.40809	−	1.40809i	−0.0458782	−	0.0458782i
$943$	25.3889	−	24.7822i	0.826777	−	0.807019i
$944$		−	1.92407i		−	0.0626231i
$945$	7.40274	+	3.11818i	0.240811	+	0.101435i
$946$	−2.00080	+	2.30905i	−0.0650516	+	0.0750736i
$947$	56.0750	−	12.1984i	1.82219	−	0.396394i	0.834271	−	0.551355i	$-0.185889\pi$
$947$	56.0750	−	12.1984i	1.82219	−	0.396394i	0.987921	+	0.154961i	$0.0495252\pi$
$948$	−4.61820	−	6.16920i	−0.149992	−	0.200366i
$949$	−18.0835	−	28.1384i	−0.587014	−	0.913411i
$950$	−13.2118	−	8.71519i	−0.428648	−	0.282758i
$951$	8.65831	+	9.99222i	0.280765	+	0.324020i
$952$	1.42407	+	1.06604i	0.0461543	+	0.0345507i
$953$	−15.7759	−	42.2968i	−0.511032	−	1.37013i	−0.894704	−	0.446660i	$-0.852613\pi$
$953$	−15.7759	−	42.2968i	−0.511032	−	1.37013i	0.383672	−	0.923469i	$-0.374659\pi$
$954$	3.56738	−	1.04748i	0.115498	−	0.0339134i
$955$	−7.89394	−	45.2982i	−0.255442	−	1.46581i
$956$	−2.88056	+	6.30754i	−0.0931639	+	0.204001i
$957$	3.56540	−	4.76282i	0.115253	−	0.153960i
$958$	−4.46992	−	0.319695i	−0.144416	−	0.0103289i
$959$	36.9383	−	16.8691i	1.19280	−	0.544733i
$960$	0.718794	−	2.11739i	0.0231990	−	0.0683384i
$961$	2.83491	−	19.7172i	0.0914486	−	0.636039i
$962$	2.61896	+	12.0392i	0.0844387	+	0.388158i
$963$	0.00344790	+	0.0482080i	0.000111107	+	0.00155348i
$964$	19.7038	+	5.78554i	0.634615	+	0.186340i
$965$	22.0313	+	27.6755i	0.709213	+	0.890907i
$966$	−7.34580	+	15.5836i	−0.236347	+	0.501393i
$967$	32.8122	−	32.8122i	1.05517	−	1.05517i	0.0567836	−	0.998387i	$-0.481915\pi$
$967$	32.8122	−	32.8122i	1.05517	−	1.05517i	0.998387	−	0.0567836i	$-0.0180845\pi$
$968$	2.76996	+	5.07281i	0.0890300	+	0.163046i
$969$	1.18465	+	1.02651i	0.0380564	+	0.0329761i
$970$	27.0051	+	22.0291i	0.867082	+	0.707312i
$971$	−16.7050	−	2.40181i	−0.536088	−	0.0770778i	−0.131047	−	0.991376i	$-0.541834\pi$
$971$	−16.7050	−	2.40181i	−0.536088	−	0.0770778i	−0.405041	+	0.914298i	$0.632743\pi$
$972$	−0.212565	+	0.977147i	−0.00681803	+	0.0313420i
$973$	60.2767	+	22.4821i	1.93238	+	0.720742i
$974$	−11.9590	+	10.3625i	−0.383191	+	0.332037i
$975$	13.6154	+	1.13723i	0.436043	+	0.0364205i
$976$	−8.41816	−	3.84444i	−0.269459	−	0.123058i
$977$	45.4800	+	24.8340i	1.45503	+	0.794509i	0.995600	−	0.0937030i	$-0.0298704\pi$
$977$	45.4800	+	24.8340i	1.45503	+	0.794509i	0.459434	+	0.888212i	$0.348052\pi$
$978$	1.20376	+	0.657305i	0.0384921	+	0.0210183i
$979$	−32.6912	−	14.9296i	−1.04482	−	0.477151i
$980$	0.392531	+	13.1975i	0.0125389	+	0.421579i
$981$	4.67902	−	4.05439i	0.149389	−	0.129447i
$982$	−0.569831	−	0.212536i	−0.0181840	−	0.00678229i
$983$	−7.59248	+	34.9021i	−0.242162	+	1.11320i	0.682044	+	0.731311i	$0.261091\pi$
$983$	−7.59248	+	34.9021i	−0.242162	+	1.11320i	−0.924207	+	0.381892i	$0.875273\pi$
$984$	7.32257	+	1.05283i	0.233435	+	0.0335629i
$985$	−20.7706	+	2.10780i	−0.661807	+	0.0671602i
$986$	−0.974512	−	0.844420i	−0.0310348	−	0.0268918i
$987$	16.9526	+	31.0463i	0.539606	+	0.988214i
$988$	−6.11640	+	6.11640i	−0.194588	+	0.194588i
$989$	−3.53223	+	5.35281i	−0.112318	+	0.170209i
$990$	−3.99707	+	3.18190i	−0.127035	+	0.101127i
$991$	−5.66343	−	1.66293i	−0.179905	−	0.0528248i	0.190539	−	0.981680i	$-0.438976\pi$
$991$	−5.66343	−	1.66293i	−0.179905	−	0.0528248i	−0.370444	+	0.928855i	$0.620794\pi$
$992$	−0.237465	−	3.32019i	−0.00753951	−	0.105416i
$993$	−0.988389	−	4.54355i	−0.0313656	−	0.144185i
$994$	4.47150	−	31.1000i	0.141827	−	0.986431i
$995$	26.4131	−	13.0250i	0.837353	−	0.412920i
$996$	2.67808	−	1.22304i	0.0848583	−	0.0387535i
$997$	−2.03639	−	0.145645i	−0.0644931	−	0.00461263i	0.0390554	−	0.999237i	$-0.487565\pi$
$997$	−2.03639	−	0.145645i	−0.0644931	−	0.00461263i	−0.103548	+	0.994624i	$0.533020\pi$
$998$	−14.6710	+	19.5982i	−0.464403	+	0.620370i
$999$	−1.87304	+	4.10139i	−0.0592605	+	0.129762i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.373.4	yes	240
5.2	odd	4	inner	690.2.w.a.97.4	yes	240
23.14	odd	22	inner	690.2.w.a.313.4	yes	240
115.37	even	44	inner	690.2.w.a.37.4	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.37.4	✓	240	115.37	even	44	inner
690.2.w.a.97.4	yes	240	5.2	odd	4	inner
690.2.w.a.313.4	yes	240	23.14	odd	22	inner
690.2.w.a.373.4	yes	240	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.877679 + 0.479249i) q^{2} +(-0.997452 + 0.0713392i) q^{3} +(0.540641 - 0.841254i) q^{4} +(0.565910 - 2.16327i) q^{5} +(0.841254 - 0.540641i) q^{6} +(1.25538 - 3.36582i) q^{7} +(-0.0713392 + 0.997452i) q^{8} +(0.989821 - 0.142315i) q^{9} +O(q^{10})\)	\(q+(-0.877679 + 0.479249i) q^{2} +(-0.997452 + 0.0713392i) q^{3} +(0.540641 - 0.841254i) q^{4} +(0.565910 - 2.16327i) q^{5} +(0.841254 - 0.540641i) q^{6} +(1.25538 - 3.36582i) q^{7} +(-0.0713392 + 0.997452i) q^{8} +(0.989821 - 0.142315i) q^{9} +(0.540059 + 2.16987i) q^{10} +(0.643696 + 2.19223i) q^{11} +(-0.479249 + 0.877679i) q^{12} +(2.56028 - 0.954935i) q^{13} +(0.511239 + 3.55575i) q^{14} +(-0.410142 + 2.19813i) q^{15} +(-0.415415 - 0.909632i) q^{16} +(0.483874 + 0.105260i) q^{17} +(-0.800541 + 0.599278i) q^{18} +(-2.66297 - 1.71139i) q^{19} +(-1.51391 - 1.64563i) q^{20} +(-1.01207 + 3.44680i) q^{21} +(-1.61558 - 1.61558i) q^{22} +(-3.80423 - 2.92025i) q^{23} -1.00000i q^{24} +(-4.35949 - 2.44843i) q^{25} +(-1.78945 + 2.06514i) q^{26} +(-0.977147 + 0.212565i) q^{27} +(-2.15279 - 2.87579i) q^{28} +(1.40781 + 2.19060i) q^{29} +(-0.693479 - 2.12581i) q^{30} +(-2.17981 - 2.51564i) q^{31} +(0.800541 + 0.599278i) q^{32} +(-0.798447 - 2.14072i) q^{33} +(-0.475132 + 0.139511i) q^{34} +(-6.57074 - 4.62049i) q^{35} +(0.415415 - 0.909632i) q^{36} +(2.70205 - 3.60952i) q^{37} +(3.15741 + 0.225823i) q^{38} +(-2.48563 + 1.13515i) q^{39} +(2.11739 + 0.718794i) q^{40} +(-1.05283 + 7.32257i) q^{41} +(-0.763601 - 3.51022i) q^{42} +(-0.0953980 - 1.33384i) q^{43} +(2.19223 + 0.643696i) q^{44} +(0.252284 - 2.22179i) q^{45} +(4.73842 + 0.739870i) q^{46} +(6.96281 - 6.96281i) q^{47} +(0.479249 + 0.877679i) q^{48} +(-4.46248 - 3.86676i) q^{49} +(4.99964 + 0.0596573i) q^{50} +(-0.490151 - 0.0704730i) q^{51} +(0.580849 - 2.67012i) q^{52} +(-3.48357 - 1.29930i) q^{53} +(0.755750 - 0.654861i) q^{54} +(5.10666 - 0.151886i) q^{55} +(3.26768 + 1.49230i) q^{56} +(2.77827 + 1.51705i) q^{57} +(-2.28545 - 1.24795i) q^{58} +(1.75019 + 0.799287i) q^{59} +(1.62745 + 1.53343i) q^{60} +(6.99406 - 6.06038i) q^{61} +(3.11880 + 1.16325i) q^{62} +(0.763601 - 3.51022i) q^{63} +(-0.989821 - 0.142315i) q^{64} +(-0.616896 - 6.07899i) q^{65} +(1.72672 + 1.49621i) q^{66} +(-3.79946 - 6.95819i) q^{67} +(0.350153 - 0.350153i) q^{68} +(4.00286 + 2.64142i) q^{69} +(7.98137 + 0.906283i) q^{70} +(-8.39210 - 2.46414i) q^{71} +(0.0713392 + 0.997452i) q^{72} +(-2.60192 - 11.9608i) q^{73} +(-0.641676 + 4.46295i) q^{74} +(4.52305 + 2.13119i) q^{75} +(-2.87942 + 1.31499i) q^{76} +(8.18672 + 0.585526i) q^{77} +(1.63757 - 2.18753i) q^{78} +(-3.20130 + 7.00988i) q^{79} +(-2.20287 + 0.383886i) q^{80} +(0.959493 - 0.281733i) q^{81} +(-2.58529 - 6.93143i) q^{82} +(-2.35691 - 1.76436i) q^{83} +(2.35246 + 2.71489i) q^{84} +(0.501536 - 0.987184i) q^{85} +(0.722970 + 1.12496i) q^{86} +(-1.56050 - 2.08459i) q^{87} +(-2.23256 + 0.485664i) q^{88} +(-10.3008 + 11.8878i) q^{89} +(0.843366 + 2.07093i) q^{90} -9.81624i q^{91} +(-4.51339 + 1.62151i) q^{92} +(2.35372 + 2.35372i) q^{93} +(-2.77419 + 9.44804i) q^{94} +(-5.20920 + 4.79224i) q^{95} +(-0.841254 - 0.540641i) q^{96} +(12.4769 - 9.34012i) q^{97} +(5.76977 + 1.25514i) q^{98} +(0.949130 + 2.07830i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{6}+O(q^{10}) \) 240 * q - 24 * q^6	\( 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) \) 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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