LMFDB - Embedded newform 65.2.b.a.14.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(14,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("65.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.b (of order $2$, degree $1$, 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:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			14.2
Root			$-0.854638 + 0.854638i$ of defining polynomial
Character	$\chi$	$=$	65.14
Dual form			65.2.b.a.14.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.53919i q^{2} +3.17009i q^{3} -0.369102 q^{4} +(0.539189 - 2.17009i) q^{5} +4.87936 q^{6} +1.70928i q^{7} -2.51026i q^{8} -7.04945 q^{9} +O(q^{10})$	\(q-1.53919i q^{2} +3.17009i q^{3} -0.369102 q^{4} +(0.539189 - 2.17009i) q^{5} +4.87936 q^{6} +1.70928i q^{7} -2.51026i q^{8} -7.04945 q^{9} +(-3.34017 - 0.829914i) q^{10} -2.53919 q^{11} -1.17009i q^{12} -1.00000i q^{13} +2.63090 q^{14} +(6.87936 + 1.70928i) q^{15} -4.60197 q^{16} -0.921622i q^{17} +10.8504i q^{18} +0.539189 q^{19} +(-0.199016 + 0.800984i) q^{20} -5.41855 q^{21} +3.90829i q^{22} +2.82991i q^{23} +7.95774 q^{24} +(-4.41855 - 2.34017i) q^{25} -1.53919 q^{26} -12.8371i q^{27} -0.630898i q^{28} +5.12783 q^{29} +(2.63090 - 10.5886i) q^{30} +0.879362 q^{31} +2.06278i q^{32} -8.04945i q^{33} -1.41855 q^{34} +(3.70928 + 0.921622i) q^{35} +2.60197 q^{36} +6.04945i q^{37} -0.829914i q^{38} +3.17009 q^{39} +(-5.44748 - 1.35350i) q^{40} +1.26180 q^{41} +8.34017i q^{42} +6.43188i q^{43} +0.937221 q^{44} +(-3.80098 + 15.2979i) q^{45} +4.35577 q^{46} -5.70928i q^{47} -14.5886i q^{48} +4.07838 q^{49} +(-3.60197 + 6.80098i) q^{50} +2.92162 q^{51} +0.369102i q^{52} +8.49693i q^{53} -19.7587 q^{54} +(-1.36910 + 5.51026i) q^{55} +4.29072 q^{56} +1.70928i q^{57} -7.89269i q^{58} +4.72261 q^{59} +(-2.53919 - 0.630898i) q^{60} +8.04945 q^{61} -1.35350i q^{62} -12.0494i q^{63} -6.02893 q^{64} +(-2.17009 - 0.539189i) q^{65} -12.3896 q^{66} -7.86603i q^{67} +0.340173i q^{68} -8.97107 q^{69} +(1.41855 - 5.70928i) q^{70} -14.4813 q^{71} +17.6959i q^{72} -1.95055i q^{73} +9.31124 q^{74} +(7.41855 - 14.0072i) q^{75} -0.199016 q^{76} -4.34017i q^{77} -4.87936i q^{78} -0.496928 q^{79} +(-2.48133 + 9.98667i) q^{80} +19.5464 q^{81} -1.94214i q^{82} +8.63090i q^{83} +2.00000 q^{84} +(-2.00000 - 0.496928i) q^{85} +9.89988 q^{86} +16.2557i q^{87} +6.37402i q^{88} -12.8371 q^{89} +(23.5464 + 5.85043i) q^{90} +1.70928 q^{91} -1.04453i q^{92} +2.78765i q^{93} -8.78765 q^{94} +(0.290725 - 1.17009i) q^{95} -6.53919 q^{96} -5.91548i q^{97} -6.27739i q^{98} +17.8999 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{4} + 4 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 10 * q^4 + 4 * q^6 - 6 * q^9	$ 6 q - 10 q^{4} + 4 q^{6} - 6 q^{9} + 2 q^{10} - 12 q^{11} + 8 q^{14} + 16 q^{15} + 10 q^{16} - 20 q^{20} - 4 q^{21} + 16 q^{24} + 2 q^{25} - 6 q^{26} - 12 q^{29} + 8 q^{30} - 20 q^{31} + 20 q^{34} + 8 q^{35} - 22 q^{36} + 8 q^{39} - 34 q^{40} - 8 q^{41} + 40 q^{44} - 4 q^{45} + 32 q^{46} + 18 q^{49} + 16 q^{50} + 24 q^{51} - 68 q^{54} - 16 q^{55} + 40 q^{56} + 16 q^{59} - 12 q^{60} + 12 q^{61} - 66 q^{64} - 2 q^{65} - 16 q^{66} - 24 q^{69} - 20 q^{70} - 24 q^{71} + 4 q^{74} + 16 q^{75} - 20 q^{76} + 32 q^{79} + 48 q^{80} + 46 q^{81} + 12 q^{84} - 12 q^{85} - 32 q^{86} - 20 q^{89} + 70 q^{90} - 4 q^{91} - 32 q^{94} + 16 q^{95} - 36 q^{96} + 16 q^{99}+O(q^{100}) $ 6 * q - 10 * q^4 + 4 * q^6 - 6 * q^9 + 2 * q^10 - 12 * q^11 + 8 * q^14 + 16 * q^15 + 10 * q^16 - 20 * q^20 - 4 * q^21 + 16 * q^24 + 2 * q^25 - 6 * q^26 - 12 * q^29 + 8 * q^30 - 20 * q^31 + 20 * q^34 + 8 * q^35 - 22 * q^36 + 8 * q^39 - 34 * q^40 - 8 * q^41 + 40 * q^44 - 4 * q^45 + 32 * q^46 + 18 * q^49 + 16 * q^50 + 24 * q^51 - 68 * q^54 - 16 * q^55 + 40 * q^56 + 16 * q^59 - 12 * q^60 + 12 * q^61 - 66 * q^64 - 2 * q^65 - 16 * q^66 - 24 * q^69 - 20 * q^70 - 24 * q^71 + 4 * q^74 + 16 * q^75 - 20 * q^76 + 32 * q^79 + 48 * q^80 + 46 * q^81 + 12 * q^84 - 12 * q^85 - 32 * q^86 - 20 * q^89 + 70 * q^90 - 4 * q^91 - 32 * q^94 + 16 * q^95 - 36 * q^96 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.53919i		−	1.08837i	−0.838965	−	0.544185i	$-0.816839\pi$
$2$		−	1.53919i		−	1.08837i	0.838965	−	0.544185i	$-0.183161\pi$
$3$			3.17009i			1.83025i	0.403170	+	0.915125i	$0.367908\pi$
$3$			3.17009i			1.83025i	−0.403170	+	0.915125i	$0.632092\pi$
$4$	−0.369102			−0.184551
$5$	0.539189	−	2.17009i	0.241133	−	0.970492i
$5$	0.539189	−	2.17009i	0.241133	−	0.970492i
$6$	4.87936			1.99199
$7$			1.70928i			0.646045i	0.946391	+	0.323023i	$0.104699\pi$
$7$			1.70928i			0.646045i	−0.946391	+	0.323023i	$0.895301\pi$
$8$		−	2.51026i		−	0.887511i
$9$	−7.04945			−2.34982
$10$	−3.34017	−	0.829914i	−1.05626	−	0.262442i
$11$	−2.53919			−0.765594			−0.382797	−	0.923832i	$-0.625039\pi$
$11$	−2.53919			−0.765594			−0.382797	+	0.923832i	$0.625039\pi$
$12$		−	1.17009i		−	0.337775i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	2.63090			0.703137
$15$	6.87936	+	1.70928i	1.77624	+	0.441333i
$16$	−4.60197			−1.15049
$17$		−	0.921622i		−	0.223526i	−0.993735	−	0.111763i	$-0.964350\pi$
$17$		−	0.921622i		−	0.223526i	0.993735	−	0.111763i	$-0.0356498\pi$
$18$			10.8504i			2.55747i
$19$	0.539189			0.123698			0.0618492	−	0.998086i	$-0.480300\pi$
$19$	0.539189			0.123698			0.0618492	+	0.998086i	$0.480300\pi$
$20$	−0.199016	+	0.800984i	−0.0445013	+	0.179105i
$21$	−5.41855			−1.18242
$22$			3.90829i			0.833250i
$23$			2.82991i			0.590078i	0.955485	+	0.295039i	$0.0953326\pi$
$23$			2.82991i			0.590078i	−0.955485	+	0.295039i	$0.904667\pi$
$24$	7.95774			1.62437
$25$	−4.41855	−	2.34017i	−0.883710	−	0.468035i
$26$	−1.53919			−0.301860
$27$		−	12.8371i		−	2.47050i
$28$		−	0.630898i		−	0.119228i
$29$	5.12783			0.952213			0.476107	−	0.879388i	$-0.342048\pi$
$29$	5.12783			0.952213			0.476107	+	0.879388i	$0.342048\pi$
$30$	2.63090	−	10.5886i	0.480334	−	1.93321i
$31$	0.879362			0.157938			0.0789690	−	0.996877i	$-0.474837\pi$
$31$	0.879362			0.157938			0.0789690	+	0.996877i	$0.474837\pi$
$32$			2.06278i			0.364651i
$33$		−	8.04945i		−	1.40123i
$34$	−1.41855			−0.243279
$35$	3.70928	+	0.921622i	0.626982	+	0.155783i
$36$	2.60197			0.433661
$37$			6.04945i			0.994523i	0.867601	+	0.497262i	$0.165661\pi$
$37$			6.04945i			0.994523i	−0.867601	+	0.497262i	$0.834339\pi$
$38$		−	0.829914i		−	0.134630i
$39$	3.17009			0.507620
$40$	−5.44748	−	1.35350i	−0.861322	−	0.214008i
$41$	1.26180			0.197059			0.0985297	−	0.995134i	$-0.468586\pi$
$41$	1.26180			0.197059			0.0985297	+	0.995134i	$0.468586\pi$
$42$			8.34017i			1.28692i
$43$			6.43188i			0.980853i	0.871483	+	0.490426i	$0.163159\pi$
$43$			6.43188i			0.980853i	−0.871483	+	0.490426i	$0.836841\pi$
$44$	0.937221			0.141291
$45$	−3.80098	+	15.2979i	−0.566617	+	2.28048i
$46$	4.35577			0.642223
$47$		−	5.70928i		−	0.832783i	−0.909185	−	0.416392i	$-0.863295\pi$
$47$		−	5.70928i		−	0.832783i	0.909185	−	0.416392i	$-0.136705\pi$
$48$		−	14.5886i		−	2.10569i
$49$	4.07838			0.582625
$50$	−3.60197	+	6.80098i	−0.509395	+	0.961804i
$51$	2.92162			0.409109
$52$			0.369102i			0.0511853i
$53$			8.49693i			1.16714i	0.812062	+	0.583571i	$0.198345\pi$
$53$			8.49693i			1.16714i	−0.812062	+	0.583571i	$0.801655\pi$
$54$	−19.7587			−2.68882
$55$	−1.36910	+	5.51026i	−0.184610	+	0.743003i
$56$	4.29072			0.573372
$57$			1.70928i			0.226399i
$58$		−	7.89269i		−	1.03636i
$59$	4.72261			0.614831			0.307415	−	0.951575i	$-0.400536\pi$
$59$	4.72261			0.614831			0.307415	+	0.951575i	$0.400536\pi$
$60$	−2.53919	−	0.630898i	−0.327808	−	0.0814485i
$61$	8.04945			1.03063			0.515313	−	0.857002i	$-0.327676\pi$
$61$	8.04945			1.03063			0.515313	+	0.857002i	$0.327676\pi$
$62$		−	1.35350i		−	0.171895i
$63$		−	12.0494i		−	1.51809i
$64$	−6.02893			−0.753616
$65$	−2.17009	−	0.539189i	−0.269166	−	0.0668781i
$66$	−12.3896			−1.52506
$67$		−	7.86603i		−	0.960989i	−0.876998	−	0.480494i	$-0.840457\pi$
$67$		−	7.86603i		−	0.960989i	0.876998	−	0.480494i	$-0.159543\pi$
$68$			0.340173i			0.0412520i
$69$	−8.97107			−1.07999
$70$	1.41855	−	5.70928i	0.169549	−	0.682389i
$71$	−14.4813			−1.71862			−0.859309	−	0.511457i	$-0.829106\pi$
$71$	−14.4813			−1.71862			−0.859309	+	0.511457i	$0.829106\pi$
$72$			17.6959i			2.08549i
$73$		−	1.95055i		−	0.228295i	−0.993464	−	0.114147i	$-0.963586\pi$
$73$		−	1.95055i		−	0.228295i	0.993464	−	0.114147i	$-0.0364136\pi$
$74$	9.31124			1.08241
$75$	7.41855	−	14.0072i	0.856620	−	1.61741i
$76$	−0.199016			−0.0228287
$77$		−	4.34017i		−	0.494609i
$78$		−	4.87936i		−	0.552479i
$79$	−0.496928			−0.0559088			−0.0279544	−	0.999609i	$-0.508899\pi$
$79$	−0.496928			−0.0559088			−0.0279544	+	0.999609i	$0.508899\pi$
$80$	−2.48133	+	9.98667i	−0.277421	+	1.11654i
$81$	19.5464			2.17182
$82$		−	1.94214i		−	0.214474i
$83$			8.63090i			0.947364i	0.880696	+	0.473682i	$0.157075\pi$
$83$			8.63090i			0.947364i	−0.880696	+	0.473682i	$0.842925\pi$
$84$	2.00000			0.218218
$85$	−2.00000	−	0.496928i	−0.216930	−	0.0538995i
$86$	9.89988			1.06753
$87$			16.2557i			1.74279i
$88$			6.37402i			0.679473i
$89$	−12.8371			−1.36073			−0.680365	−	0.732873i	$-0.738179\pi$
$89$	−12.8371			−1.36073			−0.680365	+	0.732873i	$0.738179\pi$
$90$	23.5464	+	5.85043i	2.48201	+	0.616690i
$91$	1.70928			0.179181
$92$		−	1.04453i		−	0.108900i
$93$			2.78765i			0.289066i
$94$	−8.78765			−0.906377
$95$	0.290725	−	1.17009i	0.0298277	−	0.120048i
$96$	−6.53919			−0.667403
$97$		−	5.91548i		−	0.600626i	−0.953841	−	0.300313i	$-0.902909\pi$
$97$		−	5.91548i		−	0.600626i	0.953841	−	0.300313i	$-0.0970911\pi$
$98$		−	6.27739i		−	0.634113i
$99$	17.8999			1.79901
$100$	1.63090	+	0.863763i	0.163090	+	0.0863763i
$101$	−16.4391			−1.63575			−0.817874	−	0.575397i	$-0.804848\pi$
$101$	−16.4391			−1.63575			−0.817874	+	0.575397i	$0.804848\pi$
$102$		−	4.49693i		−	0.445262i
$103$		−	10.1906i		−	1.00411i	−0.864836	−	0.502055i	$-0.832577\pi$
$103$		−	10.1906i		−	1.00411i	0.864836	−	0.502055i	$-0.167423\pi$
$104$	−2.51026			−0.246151
$105$	−2.92162	+	11.7587i	−0.285121	+	1.14753i
$106$	13.0784			1.27028
$107$		−	9.75154i		−	0.942717i	−0.881942	−	0.471358i	$-0.843764\pi$
$107$		−	9.75154i		−	0.942717i	0.881942	−	0.471358i	$-0.156236\pi$
$108$			4.73820i			0.455934i
$109$	16.8638			1.61526			0.807628	−	0.589693i	$-0.200751\pi$
$109$	16.8638			1.61526			0.807628	+	0.589693i	$0.200751\pi$
$110$	8.48133	+	2.10731i	0.808663	+	0.200924i
$111$	−19.1773			−1.82023
$112$		−	7.86603i		−	0.743270i
$113$		−	11.7587i		−	1.10617i	−0.833126	−	0.553084i	$-0.813451\pi$
$113$		−	11.7587i		−	1.10617i	0.833126	−	0.553084i	$-0.186549\pi$
$114$	2.63090			0.246406
$115$	6.14116	+	1.52586i	0.572666	+	0.142287i
$116$	−1.89269			−0.175732
$117$			7.04945i			0.651722i
$118$		−	7.26898i		−	0.669164i
$119$	1.57531			0.144408
$120$	4.29072	−	17.2690i	0.391688	−	1.57644i
$121$	−4.55252			−0.413865
$122$		−	12.3896i		−	1.12170i
$123$			4.00000i			0.360668i
$124$	−0.324575			−0.0291477
$125$	−7.46081	+	8.32684i	−0.667315	+	0.744775i
$126$	−18.5464			−1.65224
$127$			18.0072i			1.59788i	0.601411	+	0.798940i	$0.294605\pi$
$127$			18.0072i			1.59788i	−0.601411	+	0.798940i	$0.705395\pi$
$128$			13.4052i			1.18487i
$129$	−20.3896			−1.79521
$130$	−0.829914	+	3.34017i	−0.0727882	+	0.292953i
$131$	14.2557			1.24552			0.622761	−	0.782412i	$-0.286011\pi$
$131$	14.2557			1.24552			0.622761	+	0.782412i	$0.286011\pi$
$132$			2.97107i			0.258599i
$133$			0.921622i			0.0799148i
$134$	−12.1073			−1.04591
$135$	−27.8576	−	6.92162i	−2.39760	−	0.595718i
$136$	−2.31351			−0.198382
$137$		−	13.7854i		−	1.17776i	−0.808219	−	0.588882i	$-0.799568\pi$
$137$		−	13.7854i		−	1.17776i	0.808219	−	0.588882i	$-0.200432\pi$
$138$			13.8082i			1.17543i
$139$	6.65368			0.564358			0.282179	−	0.959362i	$-0.408943\pi$
$139$	6.65368			0.564358			0.282179	+	0.959362i	$0.408943\pi$
$140$	−1.36910	−	0.340173i	−0.115710	−	0.0287499i
$141$	18.0989			1.52420
$142$			22.2895i			1.87049i
$143$			2.53919i			0.212338i
$144$	32.4413			2.70344
$145$	2.76487	−	11.1278i	0.229610	−	0.924116i
$146$	−3.00227			−0.248469
$147$			12.9288i			1.06635i
$148$		−	2.23287i		−	0.183540i
$149$	9.07838			0.743730			0.371865	−	0.928287i	$-0.378718\pi$
$149$	9.07838			0.743730			0.371865	+	0.928287i	$0.378718\pi$
$150$	−21.5597	−	11.4186i	−1.76034	−	0.932321i
$151$	3.27739			0.266711			0.133355	−	0.991068i	$-0.457425\pi$
$151$	3.27739			0.266711			0.133355	+	0.991068i	$0.457425\pi$
$152$		−	1.35350i		−	0.109784i
$153$			6.49693i			0.525246i
$154$	−6.68035			−0.538318
$155$	0.474142	−	1.90829i	0.0380840	−	0.153278i
$156$	−1.17009			−0.0936819
$157$		−	12.8371i		−	1.02451i	−0.858833	−	0.512256i	$-0.828810\pi$
$157$		−	12.8371i		−	1.02451i	0.858833	−	0.512256i	$-0.171190\pi$
$158$			0.764867i			0.0608495i
$159$	−26.9360			−2.13616
$160$	4.47641	+	1.11223i	0.353891	+	0.0879293i
$161$	−4.83710			−0.381217
$162$		−	30.0856i		−	2.36375i
$163$			12.0494i			0.943786i	0.881656	+	0.471893i	$0.156429\pi$
$163$			12.0494i			0.943786i	−0.881656	+	0.471893i	$0.843571\pi$
$164$	−0.465732			−0.0363675
$165$	−17.4680	−	4.34017i	−1.35988	−	0.337882i
$166$	13.2846			1.03108
$167$		−	8.72979i		−	0.675532i	−0.941230	−	0.337766i	$-0.890329\pi$
$167$		−	8.72979i		−	0.675532i	0.941230	−	0.337766i	$-0.109671\pi$
$168$			13.6020i			1.04941i
$169$	−1.00000			−0.0769231
$170$	−0.764867	+	3.07838i	−0.0586626	+	0.236101i
$171$	−3.80098			−0.290669
$172$		−	2.37402i		−	0.181018i
$173$			0.863763i			0.0656707i	0.999461	+	0.0328354i	$0.0104537\pi$
$173$			0.863763i			0.0656707i	−0.999461	+	0.0328354i	$0.989546\pi$
$174$	25.0205			1.89680
$175$	4.00000	−	7.55252i	0.302372	−	0.570917i
$176$	11.6853			0.880810
$177$			14.9711i			1.12529i
$178$			19.7587i			1.48098i
$179$	−19.9155			−1.48855			−0.744276	−	0.667872i	$-0.767205\pi$
$179$	−19.9155			−1.48855			−0.744276	+	0.667872i	$0.767205\pi$
$180$	1.40295	−	5.64650i	0.104570	−	0.420865i
$181$	14.3896			1.06957			0.534786	−	0.844987i	$-0.320392\pi$
$181$	14.3896			1.06957			0.534786	+	0.844987i	$0.320392\pi$
$182$		−	2.63090i		−	0.195015i
$183$			25.5174i			1.88630i
$184$	7.10382			0.523700
$185$	13.1278	+	3.26180i	0.965177	+	0.239812i
$186$	4.29072			0.314611
$187$			2.34017i			0.171130i
$188$			2.10731i			0.153691i
$189$	21.9421			1.59606
$190$	−1.80098	−	0.447480i	−0.130657	−	0.0324636i
$191$	1.47641			0.106829			0.0534146	−	0.998572i	$-0.482990\pi$
$191$	1.47641			0.106829			0.0534146	+	0.998572i	$0.482990\pi$
$192$		−	19.1122i		−	1.37931i
$193$		−	17.7321i		−	1.27638i	−0.769878	−	0.638191i	$-0.779683\pi$
$193$		−	17.7321i		−	1.27638i	0.769878	−	0.638191i	$-0.220317\pi$
$194$	−9.10504			−0.653704
$195$	1.70928	−	6.87936i	0.122404	−	0.492641i
$196$	−1.50534			−0.107524
$197$		−	2.00000i		−	0.142494i	−0.997459	−	0.0712470i	$-0.977302\pi$
$197$		−	2.00000i		−	0.142494i	0.997459	−	0.0712470i	$-0.0226979\pi$
$198$		−	27.5513i		−	1.95799i
$199$	5.39189			0.382221			0.191110	−	0.981569i	$-0.438791\pi$
$199$	5.39189			0.382221			0.191110	+	0.981569i	$0.438791\pi$
$200$	−5.87444	+	11.0917i	−0.415386	+	0.784302i
$201$	24.9360			1.75885
$202$			25.3028i			1.78030i
$203$			8.76487i			0.615173i
$204$	−1.07838			−0.0755015
$205$	0.680346	−	2.73820i	0.0475174	−	0.191245i
$206$	−15.6853			−1.09284
$207$		−	19.9493i		−	1.38657i
$208$			4.60197i			0.319089i
$209$	−1.36910			−0.0947028
$210$	18.0989	+	4.49693i	1.24894	+	0.310318i
$211$	−22.7526			−1.56635			−0.783176	−	0.621800i	$-0.786402\pi$
$211$	−22.7526			−1.56635			−0.783176	+	0.621800i	$0.786402\pi$
$212$		−	3.13624i		−	0.215398i
$213$		−	45.9071i		−	3.14550i
$214$	−15.0095			−1.02603
$215$	13.9577	+	3.46800i	0.951910	+	0.236516i
$216$	−32.2245			−2.19260
$217$			1.50307i			0.102035i
$218$		−	25.9565i		−	1.75800i
$219$	6.18342			0.417837
$220$	0.505339	−	2.03385i	0.0340699	−	0.137122i
$221$	−0.921622			−0.0619950
$222$			29.5174i			1.98108i
$223$			8.76099i			0.586679i	0.956008	+	0.293340i	$0.0947667\pi$
$223$			8.76099i			0.586679i	−0.956008	+	0.293340i	$0.905233\pi$
$224$	−3.52586			−0.235581
$225$	31.1483	+	16.4969i	2.07656	+	1.09980i
$226$	−18.0989			−1.20392
$227$			17.2267i			1.14338i	0.820470	+	0.571689i	$0.193712\pi$
$227$			17.2267i			1.14338i	−0.820470	+	0.571689i	$0.806288\pi$
$228$		−	0.630898i		−	0.0417822i
$229$	−3.07838			−0.203425			−0.101712	−	0.994814i	$-0.532432\pi$
$229$	−3.07838			−0.203425			−0.101712	+	0.994814i	$0.532432\pi$
$230$	2.34858	−	9.45240i	0.154861	−	0.623273i
$231$	13.7587			0.905258
$232$		−	12.8722i		−	0.845100i
$233$			18.9360i			1.24054i	0.784389	+	0.620269i	$0.212977\pi$
$233$			18.9360i			1.24054i	−0.784389	+	0.620269i	$0.787023\pi$
$234$	10.8504			0.709315
$235$	−12.3896	−	3.07838i	−0.808210	−	0.200811i
$236$	−1.74313			−0.113468
$237$		−	1.57531i		−	0.102327i
$238$		−	2.42469i		−	0.157170i
$239$	−6.63809			−0.429382			−0.214691	−	0.976682i	$-0.568874\pi$
$239$	−6.63809			−0.429382			−0.214691	+	0.976682i	$0.568874\pi$
$240$	−31.6586	−	7.86603i	−2.04355	−	0.507750i
$241$	−9.47641			−0.610429			−0.305215	−	0.952284i	$-0.598728\pi$
$241$	−9.47641			−0.610429			−0.305215	+	0.952284i	$0.598728\pi$
$242$			7.00719i			0.450439i
$243$			23.4524i			1.50447i
$244$	−2.97107			−0.190203
$245$	2.19902	−	8.85043i	0.140490	−	0.565433i
$246$	6.15676			0.392540
$247$		−	0.539189i		−	0.0343078i
$248$		−	2.20743i		−	0.140172i
$249$	−27.3607			−1.73391
$250$	12.8166	+	11.4836i	0.810592	+	0.726286i
$251$	29.4596			1.85947			0.929736	−	0.368226i	$-0.120035\pi$
$251$	29.4596			1.85947			0.929736	+	0.368226i	$0.120035\pi$
$252$			4.44748i			0.280165i
$253$		−	7.18568i		−	0.451760i
$254$	27.7165			1.73909
$255$	1.57531	−	6.34017i	0.0986495	−	0.397037i
$256$	8.57531			0.535957
$257$			20.4657i			1.27662i	0.769781	+	0.638309i	$0.220366\pi$
$257$			20.4657i			1.27662i	−0.769781	+	0.638309i	$0.779634\pi$
$258$			31.3835i			1.95385i
$259$	−10.3402			−0.642507
$260$	0.800984	+	0.199016i	0.0496749	+	0.0123424i
$261$	−36.1483			−2.23753
$262$		−	21.9421i		−	1.35559i
$263$			9.14342i			0.563808i	0.959443	+	0.281904i	$0.0909659\pi$
$263$			9.14342i			0.563808i	−0.959443	+	0.281904i	$0.909034\pi$
$264$	−20.2062			−1.24361
$265$	18.4391	+	4.58145i	1.13270	+	0.281436i
$266$	1.41855			0.0869769
$267$		−	40.6947i		−	2.49048i
$268$			2.90337i			0.177352i
$269$	−11.3919			−0.694576			−0.347288	−	0.937759i	$-0.612897\pi$
$269$	−11.3919			−0.694576			−0.347288	+	0.937759i	$0.612897\pi$
$270$	−10.6537	+	42.8781i	−0.648363	+	2.60948i
$271$	−21.1350			−1.28386			−0.641930	−	0.766763i	$-0.721866\pi$
$271$	−21.1350			−1.28386			−0.641930	+	0.766763i	$0.721866\pi$
$272$			4.24128i			0.257165i
$273$			5.41855i			0.327946i
$274$	−21.2183			−1.28185
$275$	11.2195	+	5.94214i	0.676563	+	0.358325i
$276$	3.31124			0.199313
$277$			13.0784i			0.785804i	0.919580	+	0.392902i	$0.128529\pi$
$277$			13.0784i			0.785804i	−0.919580	+	0.392902i	$0.871471\pi$
$278$		−	10.2413i		−	0.614231i
$279$	−6.19902			−0.371125
$280$	2.31351	−	9.31124i	0.138259	−	0.556453i
$281$	−0.680346			−0.0405860			−0.0202930	−	0.999794i	$-0.506460\pi$
$281$	−0.680346			−0.0405860			−0.0202930	+	0.999794i	$0.506460\pi$
$282$		−	27.8576i		−	1.65890i
$283$		−	19.2956i		−	1.14701i	−0.819203	−	0.573504i	$-0.805584\pi$
$283$		−	19.2956i		−	1.14701i	0.819203	−	0.573504i	$-0.194416\pi$
$284$	5.34509			0.317173
$285$	3.70928	+	0.921622i	0.219719	+	0.0545922i
$286$	3.90829			0.231102
$287$			2.15676i			0.127309i
$288$		−	14.5415i		−	0.856864i
$289$	16.1506			0.950036
$290$	−17.1278	−	4.25565i	−1.00578	−	0.249900i
$291$	18.7526			1.09930
$292$			0.719953i			0.0421321i
$293$		−	9.46800i		−	0.553126i	−0.960996	−	0.276563i	$-0.910804\pi$
$293$		−	9.46800i		−	0.553126i	0.960996	−	0.276563i	$-0.0891955\pi$
$294$	19.8999			1.16058
$295$	2.54638	−	10.2485i	0.148256	−	0.596689i
$296$	15.1857			0.882650
$297$			32.5958i			1.89140i
$298$		−	13.9733i		−	0.809454i
$299$	2.82991			0.163658
$300$	−2.73820	+	5.17009i	−0.158090	+	0.298495i
$301$	−10.9939			−0.633675
$302$		−	5.04453i		−	0.290280i
$303$		−	52.1133i		−	2.99383i
$304$	−2.48133			−0.142314
$305$	4.34017	−	17.4680i	0.248518	−	1.00021i
$306$	10.0000			0.571662
$307$			0.264063i			0.0150709i	0.999972	+	0.00753543i	$0.00239862\pi$
$307$			0.264063i			0.0150709i	−0.999972	+	0.00753543i	$0.997601\pi$
$308$			1.60197i			0.0912806i
$309$	32.3051			1.83777
$310$	−2.93722	−	0.729794i	−0.166823	−	0.0414495i
$311$	13.0472			0.739838			0.369919	−	0.929064i	$-0.379385\pi$
$311$	13.0472			0.739838			0.369919	+	0.929064i	$0.379385\pi$
$312$		−	7.95774i		−	0.450518i
$313$		−	33.7009i		−	1.90489i	−0.304718	−	0.952443i	$-0.598562\pi$
$313$		−	33.7009i		−	1.90489i	0.304718	−	0.952443i	$-0.401438\pi$
$314$	−19.7587			−1.11505
$315$	−26.1483	−	6.49693i	−1.47329	−	0.366060i
$316$	0.183417			0.0103180
$317$			13.9506i			0.783541i	0.920063	+	0.391771i	$0.128137\pi$
$317$			13.9506i			0.783541i	−0.920063	+	0.391771i	$0.871863\pi$
$318$			41.4596i			2.32494i
$319$	−13.0205			−0.729009
$320$	−3.25073	+	13.0833i	−0.181721	+	0.731379i
$321$	30.9132			1.72541
$322$			7.44521i			0.414905i
$323$		−	0.496928i		−	0.0276498i
$324$	−7.21461			−0.400812
$325$	−2.34017	+	4.41855i	−0.129809	+	0.245097i
$326$	18.5464			1.02719
$327$			53.4596i			2.95632i
$328$		−	3.16743i		−	0.174892i
$329$	9.75872			0.538016
$330$	−6.68035	+	26.8865i	−0.367741	+	1.48006i
$331$	−18.4547			−1.01436			−0.507180	−	0.861840i	$-0.669312\pi$
$331$	−18.4547			−1.01436			−0.507180	+	0.861840i	$0.669312\pi$
$332$		−	3.18568i		−	0.174837i
$333$		−	42.6453i		−	2.33695i
$334$	−13.4368			−0.735229
$335$	−17.0700	−	4.24128i	−0.932632	−	0.231726i
$336$	24.9360			1.36037
$337$			15.8576i			0.863820i	0.901917	+	0.431910i	$0.142160\pi$
$337$			15.8576i			0.863820i	−0.901917	+	0.431910i	$0.857840\pi$
$338$			1.53919i			0.0837208i
$339$	37.2762			2.02456
$340$	0.738205	+	0.183417i	0.0400348	+	0.00994721i
$341$	−2.23287			−0.120916
$342$			5.85043i			0.316355i
$343$			18.9360i			1.02245i
$344$	16.1457			0.870517
$345$	−4.83710	+	19.4680i	−0.260421	+	1.04812i
$346$	1.32950			0.0714741
$347$		−	9.72487i		−	0.522059i	−0.965331	−	0.261029i	$-0.915938\pi$
$347$		−	9.72487i		−	0.522059i	0.965331	−	0.261029i	$-0.0840619\pi$
$348$		−	6.00000i		−	0.321634i
$349$	30.9093			1.65454			0.827269	−	0.561805i	$-0.189893\pi$
$349$	30.9093			1.65454			0.827269	+	0.561805i	$0.189893\pi$
$350$	−11.6248	−	6.15676i	−0.621369	−	0.329092i
$351$	−12.8371			−0.685194
$352$		−	5.23779i		−	0.279175i
$353$			5.95055i			0.316716i	0.987382	+	0.158358i	$0.0506200\pi$
$353$			5.95055i			0.316716i	−0.987382	+	0.158358i	$0.949380\pi$
$354$	23.0433			1.22474
$355$	−7.80817	+	31.4257i	−0.414415	+	1.66791i
$356$	4.73820			0.251124
$357$			4.99386i			0.264303i
$358$			30.6537i			1.62010i
$359$	−10.9783			−0.579410			−0.289705	−	0.957116i	$-0.593557\pi$
$359$	−10.9783			−0.579410			−0.289705	+	0.957116i	$0.593557\pi$
$360$	38.4017	+	9.54146i	2.02395	+	0.502879i
$361$	−18.7093			−0.984699
$362$		−	22.1483i		−	1.16409i
$363$		−	14.4319i		−	0.757477i
$364$	−0.630898			−0.0330680
$365$	−4.23287	−	1.05172i	−0.221558	−	0.0550493i
$366$	39.2762			2.05300
$367$		−	10.3740i		−	0.541520i	−0.962647	−	0.270760i	$-0.912725\pi$
$367$		−	10.3740i		−	0.541520i	0.962647	−	0.270760i	$-0.0872749\pi$
$368$		−	13.0232i		−	0.678880i
$369$	−8.89496			−0.463053
$370$	5.02052	−	20.2062i	0.261004	−	1.05047i
$371$	−14.5236			−0.754027
$372$		−	1.02893i		−	0.0533475i
$373$			23.9877i			1.24204i	0.783796	+	0.621018i	$0.213281\pi$
$373$			23.9877i			1.24204i	−0.783796	+	0.621018i	$0.786719\pi$
$374$	3.60197			0.186253
$375$	−26.3968	−	23.6514i	−1.36313	−	1.22135i
$376$	−14.3318			−0.739104
$377$		−	5.12783i		−	0.264096i
$378$		−	33.7731i		−	1.73710i
$379$	−29.7575			−1.52854			−0.764270	−	0.644896i	$-0.776901\pi$
$379$	−29.7575			−1.52854			−0.764270	+	0.644896i	$0.776901\pi$
$380$	−0.107307	+	0.431882i	−0.00550474	+	0.0221551i
$381$	−57.0843			−2.92452
$382$		−	2.27247i		−	0.116270i
$383$			12.4163i			0.634442i	0.948352	+	0.317221i	$0.102750\pi$
$383$			12.4163i			0.634442i	−0.948352	+	0.317221i	$0.897250\pi$
$384$	−42.4957			−2.16860
$385$	−9.41855	−	2.34017i	−0.480014	−	0.119266i
$386$	−27.2930			−1.38918
$387$		−	45.3412i		−	2.30482i
$388$			2.18342i			0.110846i
$389$	16.8371			0.853675			0.426837	−	0.904328i	$-0.359628\pi$
$389$	16.8371			0.853675			0.426837	+	0.904328i	$0.359628\pi$
$390$	−10.5886	−	2.63090i	−0.536176	−	0.133221i
$391$	2.60811			0.131898
$392$		−	10.2378i		−	0.517086i
$393$			45.1917i			2.27962i
$394$	−3.07838			−0.155086
$395$	−0.267938	+	1.07838i	−0.0134814	+	0.0542591i
$396$	−6.60689			−0.332009
$397$			3.89269i			0.195369i	0.995217	+	0.0976843i	$0.0311436\pi$
$397$			3.89269i			0.195369i	−0.995217	+	0.0976843i	$0.968856\pi$
$398$		−	8.29914i		−	0.415998i
$399$	−2.92162			−0.146264
$400$	20.3340	+	10.7694i	1.01670	+	0.538470i
$401$	−9.10504			−0.454684			−0.227342	−	0.973815i	$-0.573004\pi$
$401$	−9.10504			−0.454684			−0.227342	+	0.973815i	$0.573004\pi$
$402$		−	38.3812i		−	1.91428i
$403$		−	0.879362i		−	0.0438041i
$404$	6.06770			0.301879
$405$	10.5392	−	42.4173i	0.523697	−	2.10773i
$406$	13.4908			0.669536
$407$		−	15.3607i		−	0.761401i
$408$		−	7.33403i		−	0.363089i
$409$	19.4186			0.960186			0.480093	−	0.877218i	$-0.340603\pi$
$409$	19.4186			0.960186			0.480093	+	0.877218i	$0.340603\pi$
$410$	−4.21461	−	1.04718i	−0.208145	−	0.0517166i
$411$	43.7009			2.15560
$412$			3.76138i			0.185310i
$413$			8.07223i			0.397209i
$414$	−30.7058			−1.50911
$415$	18.7298	+	4.65368i	0.919409	+	0.228440i
$416$	2.06278			0.101136
$417$			21.0928i			1.03292i
$418$			2.10731i			0.103072i
$419$	16.7792			0.819720			0.409860	−	0.912149i	$-0.365578\pi$
$419$	16.7792			0.819720			0.409860	+	0.912149i	$0.365578\pi$
$420$	1.07838	−	4.34017i	0.0526194	−	0.211779i
$421$	−19.0205			−0.927003			−0.463502	−	0.886096i	$-0.653407\pi$
$421$	−19.0205			−0.927003			−0.463502	+	0.886096i	$0.653407\pi$
$422$			35.0205i			1.70477i
$423$			40.2472i			1.95689i
$424$	21.3295			1.03585
$425$	−2.15676	+	4.07223i	−0.104618	+	0.197532i
$426$	−70.6596			−3.42347
$427$			13.7587i			0.665831i
$428$			3.59932i			0.173979i
$429$	−8.04945			−0.388631
$430$	5.33791	−	21.4836i	0.257417	−	1.03603i
$431$	8.02997			0.386790			0.193395	−	0.981121i	$-0.438050\pi$
$431$	8.02997			0.386790			0.193395	+	0.981121i	$0.438050\pi$
$432$			59.0759i			2.84229i
$433$			13.0472i			0.627008i	0.949587	+	0.313504i	$0.101503\pi$
$433$			13.0472i			0.627008i	−0.949587	+	0.313504i	$0.898497\pi$
$434$	2.31351			0.111052
$435$	35.2762	+	8.76487i	1.69136	+	0.420243i
$436$	−6.22446			−0.298097
$437$			1.52586i			0.0729917i
$438$		−	9.51745i		−	0.454761i
$439$	7.70086			0.367542			0.183771	−	0.982969i	$-0.441169\pi$
$439$	7.70086			0.367542			0.183771	+	0.982969i	$0.441169\pi$
$440$	13.8322	+	3.43680i	0.659423	+	0.163843i
$441$	−28.7503			−1.36906
$442$			1.41855i			0.0674736i
$443$			6.39084i			0.303638i	0.988408	+	0.151819i	$0.0485131\pi$
$443$			6.39084i			0.303638i	−0.988408	+	0.151819i	$0.951487\pi$
$444$	7.07838			0.335925
$445$	−6.92162	+	27.8576i	−0.328116	+	1.32058i
$446$	13.4848			0.638525
$447$			28.7792i			1.36121i
$448$		−	10.3051i		−	0.486870i
$449$	−31.6163			−1.49207			−0.746034	−	0.665908i	$-0.768044\pi$
$449$	−31.6163			−1.49207			−0.746034	+	0.665908i	$0.768044\pi$
$450$	25.3919	−	47.9432i	1.19699	−	2.26006i
$451$	−3.20394			−0.150867
$452$			4.34017i			0.204145i
$453$			10.3896i			0.488147i
$454$	26.5152			1.24442
$455$	0.921622	−	3.70928i	0.0432063	−	0.173894i
$456$	4.29072			0.200932
$457$		−	35.6430i		−	1.66731i	−0.552286	−	0.833655i	$-0.686244\pi$
$457$		−	35.6430i		−	1.66731i	0.552286	−	0.833655i	$-0.313756\pi$
$458$			4.73820i			0.221402i
$459$	−11.8310			−0.552222
$460$	−2.26672	−	0.563198i	−0.105686	−	0.0262592i
$461$	−14.9795			−0.697664			−0.348832	−	0.937185i	$-0.613422\pi$
$461$	−14.9795			−0.697664			−0.348832	+	0.937185i	$0.613422\pi$
$462$		−	21.1773i		−	0.985256i
$463$			9.09663i			0.422756i	0.977404	+	0.211378i	$0.0677951\pi$
$463$			9.09663i			0.422756i	−0.977404	+	0.211378i	$0.932205\pi$
$464$	−23.5981			−1.09551
$465$	6.04945	+	1.50307i	0.280536	+	0.0697033i
$466$	29.1461			1.35017
$467$			1.87709i			0.0868616i	0.999056	+	0.0434308i	$0.0138288\pi$
$467$			1.87709i			0.0868616i	−0.999056	+	0.0434308i	$0.986171\pi$
$468$		−	2.60197i		−	0.120276i
$469$	13.4452			0.620842
$470$	−4.73820	+	19.0700i	−0.218557	+	0.879632i
$471$	40.6947			1.87511
$472$		−	11.8550i		−	0.545669i
$473$		−	16.3318i		−	0.750935i
$474$	−2.42469			−0.111370
$475$	−2.38243	−	1.26180i	−0.109314	−	0.0578951i
$476$	−0.581449			−0.0266507
$477$		−	59.8987i		−	2.74257i
$478$			10.2173i			0.467327i
$479$	15.7431			0.719322			0.359661	−	0.933083i	$-0.382892\pi$
$479$	15.7431			0.719322			0.359661	+	0.933083i	$0.382892\pi$
$480$	−3.52586	+	14.1906i	−0.160933	+	0.647710i
$481$	6.04945			0.275831
$482$			14.5860i			0.664373i
$483$		−	15.3340i		−	0.697723i
$484$	1.68035			0.0763794
$485$	−12.8371	−	3.18956i	−0.582903	−	0.144830i
$486$	36.0977			1.63742
$487$			4.94441i			0.224053i	0.993705	+	0.112026i	$0.0357341\pi$
$487$			4.94441i			0.224053i	−0.993705	+	0.112026i	$0.964266\pi$
$488$		−	20.2062i		−	0.914692i
$489$	−38.1978			−1.72736
$490$	−13.6225	−	3.38470i	−0.615401	−	0.152905i
$491$	39.4863			1.78199			0.890995	−	0.454014i	$-0.150008\pi$
$491$	39.4863			1.78199			0.890995	+	0.454014i	$0.150008\pi$
$492$		−	1.47641i		−	0.0665617i
$493$		−	4.72592i		−	0.212845i
$494$	−0.829914			−0.0373396
$495$	9.65142	−	38.8443i	0.433799	−	1.74592i
$496$	−4.04680			−0.181706
$497$		−	24.7526i		−	1.11030i
$498$			42.1133i			1.88714i
$499$	−1.67089			−0.0747993			−0.0373997	−	0.999300i	$-0.511907\pi$
$499$	−1.67089			−0.0747993			−0.0373997	+	0.999300i	$0.511907\pi$
$500$	2.75380	−	3.07346i	0.123154	−	0.137449i
$501$	27.6742			1.23639
$502$		−	45.3439i		−	2.02380i
$503$		−	9.08557i		−	0.405105i	−0.979271	−	0.202553i	$-0.935076\pi$
$503$		−	9.08557i		−	0.405105i	0.979271	−	0.202553i	$-0.0649237\pi$
$504$	−30.2472			−1.34732
$505$	−8.86376	+	35.6742i	−0.394432	+	1.58748i
$506$	−11.0601			−0.491683
$507$		−	3.17009i		−	0.140788i
$508$		−	6.64650i		−	0.294891i
$509$	19.5441			0.866277			0.433139	−	0.901327i	$-0.357406\pi$
$509$	19.5441			0.866277			0.433139	+	0.901327i	$0.357406\pi$
$510$	−9.75872	−	2.42469i	−0.432124	−	0.107367i
$511$	3.33403			0.147489
$512$			13.6114i			0.601546i
$513$		−	6.92162i		−	0.305597i
$514$	31.5006			1.38943
$515$	−22.1145	−	5.49466i	−0.974481	−	0.242124i
$516$	7.52586			0.331307
$517$			14.4969i			0.637574i
$518$			15.9155i			0.699286i
$519$	−2.73820			−0.120194
$520$	−1.35350	+	5.44748i	−0.0593551	+	0.238888i
$521$	6.50534			0.285004			0.142502	−	0.989795i	$-0.454485\pi$
$521$	6.50534			0.285004			0.142502	+	0.989795i	$0.454485\pi$
$522$			55.6391i			2.43526i
$523$		−	36.5452i		−	1.59801i	−0.601326	−	0.799004i	$-0.705361\pi$
$523$		−	36.5452i		−	1.59801i	0.601326	−	0.799004i	$-0.294639\pi$
$524$	−5.26180			−0.229863
$525$	23.9421	+	12.6803i	1.04492	+	0.553416i
$526$	14.0735			0.613632
$527$		−	0.810439i		−	0.0353033i
$528$			37.0433i			1.61210i
$529$	14.9916			0.651808
$530$	7.05172	−	28.3812i	0.306307	−	1.23280i
$531$	−33.2918			−1.44474
$532$		−	0.340173i		−	0.0147484i
$533$		−	1.26180i		−	0.0546544i
$534$	−62.6369			−2.71056
$535$	−21.1617	−	5.25792i	−0.914899	−	0.227320i
$536$	−19.7458			−0.852888
$537$		−	63.1338i		−	2.72442i
$538$			17.5343i			0.755956i
$539$	−10.3558			−0.446055
$540$	10.2823	+	2.55479i	0.442480	+	0.109941i
$541$	20.3402			0.874492			0.437246	−	0.899342i	$-0.355954\pi$
$541$	20.3402			0.874492			0.437246	+	0.899342i	$0.355954\pi$
$542$			32.5308i			1.39732i
$543$			45.6163i			1.95758i
$544$	1.90110			0.0815091
$545$	9.09275	−	36.5958i	0.389491	−	1.56759i
$546$	8.34017			0.356926
$547$		−	11.5948i		−	0.495757i	−0.968791	−	0.247879i	$-0.920267\pi$
$547$		−	11.5948i		−	0.495757i	0.968791	−	0.247879i	$-0.0797334\pi$
$548$			5.08822i			0.217358i
$549$	−56.7442			−2.42178
$550$	9.14608	−	17.2690i	0.389990	−	0.736352i
$551$	2.76487			0.117787
$552$			22.5197i			0.958503i
$553$		−	0.849388i		−	0.0361196i
$554$	20.1301			0.855246
$555$	−10.3402	+	41.6163i	−0.438916	+	1.76652i
$556$	−2.45589			−0.104153
$557$			10.7298i			0.454636i	0.973821	+	0.227318i	$0.0729957\pi$
$557$			10.7298i			0.454636i	−0.973821	+	0.227318i	$0.927004\pi$
$558$			9.54146i			0.403922i
$559$	6.43188			0.272040
$560$	−17.0700	−	4.24128i	−0.721338	−	0.179227i
$561$	−7.41855			−0.313211
$562$			1.04718i			0.0441727i
$563$		−	10.2485i		−	0.431921i	−0.976402	−	0.215961i	$-0.930712\pi$
$563$		−	10.2485i		−	0.431921i	0.976402	−	0.215961i	$-0.0692883\pi$
$564$	−6.68035			−0.281293
$565$	−25.5174	−	6.34017i	−1.07353	−	0.266733i
$566$	−29.6996			−1.24837
$567$			33.4101i			1.40309i
$568$			36.3519i			1.52529i
$569$	8.84551			0.370823			0.185412	−	0.982661i	$-0.440638\pi$
$569$	8.84551			0.370823			0.185412	+	0.982661i	$0.440638\pi$
$570$	1.41855	−	5.70928i	0.0594166	−	0.239135i
$571$	9.29299			0.388900			0.194450	−	0.980912i	$-0.437708\pi$
$571$	9.29299			0.388900			0.194450	+	0.980912i	$0.437708\pi$
$572$		−	0.937221i		−	0.0391872i
$573$			4.68035i			0.195524i
$574$	3.31965			0.138560
$575$	6.62249	−	12.5041i	0.276177	−	0.521458i
$576$	42.5006			1.77086
$577$		−	19.5259i		−	0.812872i	−0.913679	−	0.406436i	$-0.866771\pi$
$577$		−	19.5259i		−	0.812872i	0.913679	−	0.406436i	$-0.133229\pi$
$578$		−	24.8588i		−	1.03399i
$579$	56.2122			2.33610
$580$	−1.02052	+	4.10731i	−0.0423747	+	0.170547i
$581$	−14.7526			−0.612040
$582$		−	28.8638i		−	1.19644i
$583$		−	21.5753i		−	0.893558i
$584$	−4.89639			−0.202614
$585$	15.2979	+	3.80098i	0.632491	+	0.157151i
$586$	−14.5730			−0.602007
$587$			22.5029i			0.928794i	0.885627	+	0.464397i	$0.153729\pi$
$587$			22.5029i			0.928794i	−0.885627	+	0.464397i	$0.846271\pi$
$588$		−	4.77205i		−	0.196796i
$589$	0.474142			0.0195367
$590$	−15.7743	−	3.91935i	−0.649419	−	0.161357i
$591$	6.34017			0.260800
$592$		−	27.8394i		−	1.14419i
$593$		−	4.43907i		−	0.182291i	−0.995838	−	0.0911454i	$-0.970947\pi$
$593$		−	4.43907i		−	0.182291i	0.995838	−	0.0911454i	$-0.0290528\pi$
$594$	50.1711			2.05855
$595$	0.849388	−	3.41855i	0.0348215	−	0.140147i
$596$	−3.35085			−0.137256
$597$			17.0928i			0.699560i
$598$		−	4.35577i		−	0.178121i
$599$	−33.3607			−1.36308			−0.681540	−	0.731780i	$-0.738690\pi$
$599$	−33.3607			−1.36308			−0.681540	+	0.731780i	$0.738690\pi$
$600$	−35.1617	−	18.6225i	−1.43547	−	0.760260i
$601$	13.3197			0.543320			0.271660	−	0.962393i	$-0.412427\pi$
$601$	13.3197			0.543320			0.271660	+	0.962393i	$0.412427\pi$
$602$			16.9216i			0.689674i
$603$			55.4512i			2.25815i
$604$	−1.20969			−0.0492217
$605$	−2.45467	+	9.87936i	−0.0997964	+	0.401653i
$606$	−80.2122			−3.25840
$607$			14.1184i			0.573047i	0.958073	+	0.286523i	$0.0924996\pi$
$607$			14.1184i			0.573047i	−0.958073	+	0.286523i	$0.907500\pi$
$608$			1.11223i			0.0451068i
$609$	−27.7854			−1.12592
$610$	−26.8865	−	6.68035i	−1.08860	−	0.270479i
$611$	−5.70928			−0.230973
$612$		−	2.39803i		−	0.0969347i
$613$			26.8104i			1.08286i	0.840745	+	0.541432i	$0.182118\pi$
$613$			26.8104i			1.08286i	−0.840745	+	0.541432i	$0.817882\pi$
$614$	0.406442			0.0164027
$615$	8.68035	+	2.15676i	0.350025	+	0.0869688i
$616$	−10.8950			−0.438970
$617$			14.8950i			0.599649i	0.953994	+	0.299824i	$0.0969280\pi$
$617$			14.8950i			0.599649i	−0.953994	+	0.299824i	$0.903072\pi$
$618$		−	49.7237i		−	2.00018i
$619$	−45.3184			−1.82150			−0.910751	−	0.412956i	$-0.864496\pi$
$619$	−45.3184			−1.82150			−0.910751	+	0.412956i	$0.864496\pi$
$620$	−0.175007	+	0.704355i	−0.00702845	+	0.0282876i
$621$	36.3279			1.45779
$622$		−	20.0821i		−	0.805218i
$623$		−	21.9421i		−	0.879093i
$624$	−14.5886			−0.584013
$625$	14.0472	+	20.6803i	0.561887	+	0.827214i
$626$	−51.8720			−2.07322
$627$		−	4.34017i		−	0.173330i
$628$			4.73820i			0.189075i
$629$	5.57531			0.222302
$630$	−10.0000	+	40.2472i	−0.398410	+	1.60349i
$631$	37.8876			1.50828			0.754141	−	0.656713i	$-0.228054\pi$
$631$	37.8876			1.50828			0.754141	+	0.656713i	$0.228054\pi$
$632$			1.24742i			0.0496197i
$633$		−	72.1276i		−	2.86682i
$634$	21.4725			0.852783
$635$	39.0772	+	9.70928i	1.55073	+	0.385301i
$636$	9.94214			0.394232
$637$		−	4.07838i		−	0.161591i
$638$			20.0410i			0.793432i
$639$	102.085			4.03844
$640$	29.0905	+	7.22795i	1.14990	+	0.285710i
$641$	−8.47027			−0.334555			−0.167278	−	0.985910i	$-0.553498\pi$
$641$	−8.47027			−0.334555			−0.167278	+	0.985910i	$0.553498\pi$
$642$		−	47.5813i		−	1.87788i
$643$		−	34.1750i		−	1.34773i	−0.738854	−	0.673865i	$-0.764633\pi$
$643$		−	34.1750i		−	1.34773i	0.738854	−	0.673865i	$-0.235367\pi$
$644$	1.78539			0.0703541
$645$	−10.9939	+	44.2472i	−0.432883	+	1.74223i
$646$	−0.764867			−0.0300933
$647$		−	13.8238i		−	0.543468i	−0.962372	−	0.271734i	$-0.912403\pi$
$647$		−	13.8238i		−	0.543468i	0.962372	−	0.271734i	$-0.0875972\pi$
$648$		−	49.0665i		−	1.92751i
$649$	−11.9916			−0.470711
$650$	6.80098	+	3.60197i	0.266757	+	0.141281i
$651$	−4.76487			−0.186750
$652$		−	4.44748i		−	0.174177i
$653$			42.8781i			1.67795i	0.544169	+	0.838976i	$0.316845\pi$
$653$			42.8781i			1.67795i	−0.544169	+	0.838976i	$0.683155\pi$
$654$	82.2844			3.21757
$655$	7.68649	−	30.9360i	0.300336	−	1.20877i
$656$	−5.80674			−0.226715
$657$			13.7503i			0.536451i
$658$		−	15.0205i		−	0.585561i
$659$	23.2495			0.905672			0.452836	−	0.891594i	$-0.350412\pi$
$659$	23.2495			0.905672			0.452836	+	0.891594i	$0.350412\pi$
$660$	6.44748	+	1.60197i	0.250968	+	0.0623565i
$661$	27.0661			1.05275			0.526374	−	0.850253i	$-0.323551\pi$
$661$	27.0661			1.05275			0.526374	+	0.850253i	$0.323551\pi$
$662$			28.4052i			1.10400i
$663$		−	2.92162i		−	0.113466i
$664$	21.6658			0.840796
$665$	2.00000	+	0.496928i	0.0775567	+	0.0192701i
$666$	−65.6391			−2.54346
$667$			14.5113i			0.561880i
$668$			3.22219i			0.124670i
$669$	−27.7731			−1.07377
$670$	−6.52813	+	26.2739i	−0.252203	+	1.01505i
$671$	−20.4391			−0.789042
$672$		−	11.1773i		−	0.431173i
$673$		−	16.1711i		−	0.623351i	−0.950189	−	0.311676i	$-0.899110\pi$
$673$		−	16.1711i		−	0.623351i	0.950189	−	0.311676i	$-0.100890\pi$
$674$	24.4079			0.940156
$675$	−30.0410	+	56.7214i	−1.15628	+	2.18321i
$676$	0.369102			0.0141962
$677$			43.1194i			1.65721i	0.559831	+	0.828607i	$0.310866\pi$
$677$			43.1194i			1.65721i	−0.559831	+	0.828607i	$0.689134\pi$
$678$		−	57.3751i		−	2.20348i
$679$	10.1112			0.388032
$680$	−1.24742	+	5.02052i	−0.0478363	+	0.192528i
$681$	−54.6102			−2.09267
$682$			3.43680i			0.131602i
$683$			17.7093i			0.677627i	0.940854	+	0.338813i	$0.110026\pi$
$683$			17.7093i			0.677627i	−0.940854	+	0.338813i	$0.889974\pi$
$684$	1.40295			0.0536432
$685$	−29.9155	−	7.43293i	−1.14301	−	0.283998i
$686$	29.1461			1.11280
$687$		−	9.75872i		−	0.372319i
$688$		−	29.5993i		−	1.12846i
$689$	8.49693			0.323707
$690$	29.9649	+	7.44521i	1.14075	+	0.283434i
$691$	−24.8794			−0.946456			−0.473228	−	0.880940i	$-0.656911\pi$
$691$	−24.8794			−0.946456			−0.473228	+	0.880940i	$0.656911\pi$
$692$		−	0.318817i		−	0.0121196i
$693$			30.5958i			1.16224i
$694$	−14.9684			−0.568193
$695$	3.58759	−	14.4391i	0.136085	−	0.547705i
$696$	40.8059			1.54674
$697$		−	1.16290i		−	0.0440479i
$698$		−	47.5753i		−	1.80075i
$699$	−60.0288			−2.27050
$700$	−1.47641	+	2.78765i	−0.0558030	+	0.105363i
$701$	33.0661			1.24889			0.624445	−	0.781069i	$-0.285325\pi$
$701$	33.0661			1.24889			0.624445	+	0.781069i	$0.285325\pi$
$702$			19.7587i			0.745745i
$703$			3.26180i			0.123021i
$704$	15.3086			0.576964
$705$	9.75872	−	39.2762i	0.367535	−	1.47923i
$706$	9.15902			0.344704
$707$		−	28.0989i		−	1.05677i
$708$		−	5.52586i		−	0.207674i
$709$	−2.18342			−0.0820000			−0.0410000	−	0.999159i	$-0.513054\pi$
$709$	−2.18342			−0.0820000			−0.0410000	+	0.999159i	$0.513054\pi$
$710$	48.3701	+	12.0183i	1.81530	+	0.451037i
$711$	3.50307			0.131375
$712$			32.2245i			1.20766i
$713$			2.48852i			0.0931957i
$714$	7.68649			0.287660
$715$	5.51026	+	1.36910i	0.206072	+	0.0512015i
$716$	7.35085			0.274714
$717$		−	21.0433i		−	0.785877i
$718$			16.8976i			0.630613i
$719$	−5.20847			−0.194243			−0.0971216	−	0.995273i	$-0.530964\pi$
$719$	−5.20847			−0.194243			−0.0971216	+	0.995273i	$0.530964\pi$
$720$	17.4920	−	70.4005i	0.651889	−	2.62367i
$721$	17.4186			0.648701
$722$			28.7971i			1.07172i
$723$		−	30.0410i		−	1.11724i
$724$	−5.31124			−0.197391
$725$	−22.6576	−	12.0000i	−0.841481	−	0.445669i
$726$	−22.2134			−0.824416
$727$		−	3.52464i		−	0.130721i	−0.997862	−	0.0653607i	$-0.979180\pi$
$727$		−	3.52464i		−	0.130721i	0.997862	−	0.0653607i	$-0.0208198\pi$
$728$		−	4.29072i		−	0.159025i
$729$	−15.7070			−0.581741
$730$	−1.61879	+	6.51518i	−0.0599141	+	0.241138i
$731$	5.92777			0.219246
$732$		−	9.41855i		−	0.348120i
$733$			21.8310i			0.806345i	0.915124	+	0.403172i	$0.132093\pi$
$733$			21.8310i			0.806345i	−0.915124	+	0.403172i	$0.867907\pi$
$734$	−15.9676			−0.589374
$735$	28.0566	+	6.97107i	1.03488	+	0.257132i
$736$	−5.83749			−0.215173
$737$			19.9733i			0.735727i
$738$			13.6910i			0.503974i
$739$	−50.3533			−1.85228			−0.926139	−	0.377184i	$-0.876893\pi$
$739$	−50.3533			−1.85228			−0.926139	+	0.377184i	$0.876893\pi$
$740$	−4.84551	−	1.20394i	−0.178125	−	0.0442576i
$741$	1.70928			0.0627918
$742$			22.3545i			0.820661i
$743$		−	30.7877i		−	1.12949i	−0.825266	−	0.564745i	$-0.808975\pi$
$743$		−	30.7877i		−	1.12949i	0.825266	−	0.564745i	$-0.191025\pi$
$744$	6.99773			0.256549
$745$	4.89496	−	19.7009i	0.179337	−	0.721784i
$746$	36.9216			1.35180
$747$		−	60.8431i		−	2.22613i
$748$		−	0.863763i		−	0.0315823i
$749$	16.6681			0.609038
$750$	−36.4040	+	40.6297i	−1.32929	+	1.48359i
$751$	−10.6225			−0.387620			−0.193810	−	0.981039i	$-0.562085\pi$
$751$	−10.6225			−0.387620			−0.193810	+	0.981039i	$0.562085\pi$
$752$			26.2739i			0.958111i
$753$			93.3894i			3.40330i
$754$	−7.89269			−0.287435
$755$	1.76713	−	7.11223i	0.0643126	−	0.258840i
$756$	−8.09890			−0.294554
$757$		−	7.98562i		−	0.290242i	−0.989414	−	0.145121i	$-0.953643\pi$
$757$		−	7.98562i		−	0.290242i	0.989414	−	0.145121i	$-0.0463572\pi$
$758$			45.8024i			1.66362i
$759$	22.7792			0.826834
$760$	−2.93722	−	0.729794i	−0.106544	−	0.0264724i
$761$	−48.9360			−1.77393			−0.886964	−	0.461838i	$-0.847190\pi$
$761$	−48.9360			−1.77393			−0.886964	+	0.461838i	$0.847190\pi$
$762$			87.8636i			3.18296i
$763$			28.8248i			1.04353i
$764$	−0.544946			−0.0197155
$765$	14.0989	+	3.50307i	0.509747	+	0.126654i
$766$	19.1110			0.690509
$767$		−	4.72261i		−	0.170523i
$768$			27.1845i			0.980935i
$769$	7.99547			0.288324			0.144162	−	0.989554i	$-0.453951\pi$
$769$	7.99547			0.288324			0.144162	+	0.989554i	$0.453951\pi$
$770$	−3.60197	+	14.4969i	−0.129806	+	0.522433i
$771$	−64.8781			−2.33653
$772$			6.54495i			0.235558i
$773$		−	26.6141i		−	0.957242i	−0.878022	−	0.478621i	$-0.841137\pi$
$773$		−	26.6141i		−	0.957242i	0.878022	−	0.478621i	$-0.158863\pi$
$774$	−69.7887			−2.50850
$775$	−3.88550	−	2.05786i	−0.139571	−	0.0739205i
$776$	−14.8494			−0.533062
$777$		−	32.7792i		−	1.17595i
$778$		−	25.9155i		−	0.929115i
$779$	0.680346			0.0243759
$780$	−0.630898	+	2.53919i	−0.0225898	+	0.0909175i
$781$	36.7708			1.31576
$782$		−	4.01438i		−	0.143554i
$783$		−	65.8264i		−	2.35244i
$784$	−18.7686			−0.670306
$785$	−27.8576	−	6.92162i	−0.994281	−	0.247043i
$786$	69.5585			2.48107
$787$			9.25792i			0.330009i	0.986293	+	0.165005i	$0.0527639\pi$
$787$			9.25792i			0.330009i	−0.986293	+	0.165005i	$0.947236\pi$
$788$			0.738205i			0.0262975i
$789$	−28.9854			−1.03191
$790$	1.65983	+	0.412408i	0.0590540	+	0.0146728i
$791$	20.0989			0.714634
$792$		−	44.9333i		−	1.59664i
$793$		−	8.04945i		−	0.285844i
$794$	5.99159			0.212634
$795$	−14.5236	+	58.4534i	−0.515099	+	2.07313i
$796$	−1.99016			−0.0705393
$797$			15.9421i			0.564700i	0.959312	+	0.282350i	$0.0911139\pi$
$797$			15.9421i			0.564700i	−0.959312	+	0.282350i	$0.908886\pi$
$798$			4.49693i			0.159190i
$799$	−5.26180			−0.186149
$800$	4.82726	−	9.11450i	0.170669	−	0.322246i
$801$	90.4945			3.19747
$802$			14.0144i			0.494865i
$803$			4.95282i			0.174781i
$804$	−9.20394			−0.324598
$805$	−2.60811	+	10.4969i	−0.0919238	+	0.369968i
$806$	−1.35350			−0.0476751
$807$		−	36.1133i		−	1.27125i
$808$			41.2663i			1.45174i
$809$	−17.9239			−0.630170			−0.315085	−	0.949063i	$-0.602033\pi$
$809$	−17.9239			−0.630170			−0.315085	+	0.949063i	$0.602033\pi$
$810$	−65.2883	−	16.2218i	−2.29400	−	0.569976i
$811$	7.43415			0.261048			0.130524	−	0.991445i	$-0.458334\pi$
$811$	7.43415			0.261048			0.130524	+	0.991445i	$0.458334\pi$
$812$		−	3.23513i		−	0.113531i
$813$		−	66.9998i		−	2.34979i
$814$	−23.6430			−0.828687
$815$	26.1483	+	6.49693i	0.915937	+	0.227577i
$816$	−13.4452			−0.470677
$817$			3.46800i			0.121330i
$818$		−	29.8888i		−	1.04504i
$819$	−12.0494			−0.421042
$820$	−0.251117	+	1.01068i	−0.00876940	+	0.0352944i
$821$	20.4801			0.714761			0.357380	−	0.933959i	$-0.383670\pi$
$821$	20.4801			0.714761			0.357380	+	0.933959i	$0.383670\pi$
$822$		−	67.2639i		−	2.34610i
$823$			3.75154i			0.130770i	0.997860	+	0.0653852i	$0.0208276\pi$
$823$			3.75154i			0.130770i	−0.997860	+	0.0653852i	$0.979172\pi$
$824$	−25.5811			−0.891159
$825$	−18.8371	+	35.5669i	−0.655824	+	1.23828i
$826$	12.4247			0.432310
$827$		−	48.1483i		−	1.67428i	−0.546987	−	0.837141i	$-0.684225\pi$
$827$		−	48.1483i		−	1.67428i	0.546987	−	0.837141i	$-0.315775\pi$
$828$			7.36334i			0.255894i
$829$	−36.5608			−1.26981			−0.634904	−	0.772591i	$-0.718960\pi$
$829$	−36.5608			−1.26981			−0.634904	+	0.772591i	$0.718960\pi$
$830$	7.16290	−	28.8287i	0.248628	−	1.00066i
$831$	−41.4596			−1.43822
$832$			6.02893i			0.209016i
$833$		−	3.75872i		−	0.130232i
$834$	32.4657			1.12420
$835$	−18.9444	−	4.70701i	−0.655598	−	0.162893i
$836$	0.505339			0.0174775
$837$		−	11.2885i		−	0.390186i
$838$		−	25.8264i		−	0.892159i
$839$	−45.2294			−1.56149			−0.780746	−	0.624849i	$-0.785161\pi$
$839$	−45.2294			−1.56149			−0.780746	+	0.624849i	$0.785161\pi$
$840$	29.5174	+	7.33403i	1.01845	+	0.253048i
$841$	−2.70540			−0.0932896
$842$			29.2762i			1.00892i
$843$		−	2.15676i		−	0.0742826i
$844$	8.39803			0.289072
$845$	−0.539189	+	2.17009i	−0.0185487	+	0.0746532i
$846$	61.9481			2.12982
$847$		−	7.78151i		−	0.267376i
$848$		−	39.1026i		−	1.34279i
$849$	61.1689			2.09931
$850$	6.26794	+	3.31965i	0.214989	+	0.113863i
$851$	−17.1194			−0.586846
$852$			16.9444i			0.580506i
$853$			37.2534i			1.27553i	0.770230	+	0.637766i	$0.220141\pi$
$853$			37.2534i			1.27553i	−0.770230	+	0.637766i	$0.779859\pi$
$854$	21.1773			0.724671
$855$	−2.04945	+	8.24846i	−0.0700897	+	0.282092i
$856$	−24.4789			−0.836671
$857$			10.8371i			0.370188i	0.982721	+	0.185094i	$0.0592590\pi$
$857$			10.8371i			0.370188i	−0.982721	+	0.185094i	$0.940741\pi$
$858$			12.3896i			0.422975i
$859$	−14.6081			−0.498422			−0.249211	−	0.968449i	$-0.580171\pi$
$859$	−14.6081			−0.498422			−0.249211	+	0.968449i	$0.580171\pi$
$860$	−5.15183	−	1.28005i	−0.175676	−	0.0436492i
$861$	−6.83710			−0.233008
$862$		−	12.3596i		−	0.420971i
$863$			10.3440i			0.352116i	0.984380	+	0.176058i	$0.0563345\pi$
$863$			10.3440i			0.352116i	−0.984380	+	0.176058i	$0.943665\pi$
$864$	26.4801			0.900872
$865$	1.87444	+	0.465732i	0.0637329	+	0.0158354i
$866$	20.0821			0.682417
$867$			51.1988i			1.73880i
$868$		−	0.554787i		−	0.0188307i
$869$	1.26180			0.0428035
$870$	13.4908	−	54.2967i	0.457380	−	1.84083i
$871$	−7.86603			−0.266530
$872$		−	42.3324i		−	1.43356i
$873$			41.7009i			1.41136i
$874$	2.34858			0.0794420
$875$	−14.2329	−	12.7526i	−0.481159	−	0.431116i
$876$	−2.28231			−0.0771122
$877$			38.0677i			1.28545i	0.766095	+	0.642727i	$0.222197\pi$
$877$			38.0677i			1.28545i	−0.766095	+	0.642727i	$0.777803\pi$
$878$		−	11.8531i		−	0.400022i
$879$	30.0144			1.01236
$880$	6.30057	−	25.3580i	0.212392	−	0.854819i
$881$	12.0494			0.405956			0.202978	−	0.979183i	$-0.434938\pi$
$881$	12.0494			0.405956			0.202978	+	0.979183i	$0.434938\pi$
$882$			44.2522i			1.49005i
$883$			0.320699i			0.0107924i	0.999985	+	0.00539619i	$0.00171767\pi$
$883$			0.320699i			0.0107924i	−0.999985	+	0.00539619i	$0.998282\pi$
$884$	0.340173			0.0114413
$885$	32.4885	+	8.07223i	1.09209	+	0.271345i
$886$	9.83672			0.330471
$887$			3.62144i			0.121596i	0.998150	+	0.0607981i	$0.0193646\pi$
$887$			3.62144i			0.121596i	−0.998150	+	0.0607981i	$0.980635\pi$
$888$			48.1399i			1.61547i
$889$	−30.7792			−1.03230
$890$	42.8781	+	10.6537i	1.43728	+	0.357112i
$891$	−49.6319			−1.66273
$892$		−	3.23370i		−	0.108272i
$893$		−	3.07838i		−	0.103014i
$894$	44.2967			1.48150
$895$	−10.7382	+	43.2183i	−0.358939	+	1.44463i
$896$	−22.9132			−0.765477
$897$			8.97107i			0.299535i
$898$			48.6635i			1.62392i
$899$	4.50921			0.150391
$900$	−11.4969	−	6.08906i	−0.383231	−	0.202969i
$901$	7.83096			0.260887
$902$			4.93146i			0.164200i
$903$		−	34.8515i		−	1.15978i
$904$	−29.5174			−0.981736
$905$	7.75872	−	31.2267i	0.257909	−	1.03801i
$906$	15.9916			0.531285
$907$			10.9333i			0.363036i	0.983388	+	0.181518i	$0.0581010\pi$
$907$			10.9333i			0.363036i	−0.983388	+	0.181518i	$0.941899\pi$
$908$		−	6.35842i		−	0.211012i
$909$	115.886			3.84371
$910$	−5.70928	−	1.41855i	−0.189261	−	0.0470245i
$911$	−37.5897			−1.24540			−0.622701	−	0.782460i	$-0.713965\pi$
$911$	−37.5897			−1.24540			−0.622701	+	0.782460i	$0.713965\pi$
$912$		−	7.86603i		−	0.260470i
$913$		−	21.9155i		−	0.725297i
$914$	−54.8613			−1.81465
$915$	55.3751	+	13.7587i	1.83064	+	0.454849i
$916$	1.13624			0.0375423
$917$			24.3668i			0.804664i
$918$			18.2101i			0.601022i
$919$	−33.6742			−1.11081			−0.555405	−	0.831580i	$-0.687437\pi$
$919$	−33.6742			−1.11081			−0.555405	+	0.831580i	$0.687437\pi$
$920$	3.83030	−	15.4159i	0.126281	−	0.508247i
$921$	−0.837101			−0.0275834
$922$			23.0563i			0.759317i
$923$			14.4813i			0.476659i
$924$	−5.07838			−0.167066
$925$	14.1568	−	26.7298i	0.465471	−	0.878870i
$926$	14.0014			0.460116
$927$			71.8381i			2.35947i
$928$			10.5776i			0.347226i
$929$	43.2039			1.41748			0.708738	−	0.705472i	$-0.249265\pi$
$929$	43.2039			1.41748			0.708738	+	0.705472i	$0.249265\pi$
$930$	2.31351	−	9.31124i	0.0758630	−	0.305328i
$931$	2.19902			0.0720698
$932$		−	6.98932i		−	0.228943i
$933$			41.3607i			1.35409i
$934$	2.88920			0.0945376
$935$	5.07838	+	1.26180i	0.166081	+	0.0412651i
$936$	17.6959			0.578410
$937$		−	27.5630i		−	0.900445i	−0.892916	−	0.450222i	$-0.851345\pi$
$937$		−	27.5630i		−	0.900445i	0.892916	−	0.450222i	$-0.148655\pi$
$938$		−	20.6947i		−	0.675707i
$939$	106.835			3.48642
$940$	4.57304	+	1.13624i	0.149156	+	0.0370600i
$941$	58.1666			1.89618			0.948088	−	0.318007i	$-0.103013\pi$
$941$	58.1666			1.89618			0.948088	+	0.318007i	$0.103013\pi$
$942$		−	62.6369i		−	2.04082i
$943$			3.57077i			0.116280i
$944$	−21.7333			−0.707358
$945$	11.8310	−	47.6163i	0.384861	−	1.54896i
$946$	−25.1377			−0.817296
$947$		−	48.5152i		−	1.57653i	−0.615335	−	0.788266i	$-0.710979\pi$
$947$		−	48.5152i		−	1.57653i	0.615335	−	0.788266i	$-0.289021\pi$
$948$			0.581449i			0.0188846i
$949$	−1.95055			−0.0633176
$950$	−1.94214	+	3.66701i	−0.0630114	+	0.118974i
$951$	−44.2245			−1.43408
$952$		−	3.95443i		−	0.128164i
$953$		−	23.0349i		−	0.746173i	−0.927796	−	0.373087i	$-0.878299\pi$
$953$		−	23.0349i		−	0.746173i	0.927796	−	0.373087i	$-0.121701\pi$
$954$	−92.1953			−2.98493
$955$	0.796064	−	3.20394i	0.0257600	−	0.103677i
$956$	2.45013			0.0792430
$957$		−	41.2762i		−	1.33427i
$958$		−	24.2316i		−	0.782889i
$959$	23.5630			0.760890
$960$	−41.4752	−	10.3051i	−1.33861	−	0.332596i
$961$	−30.2267			−0.975056
$962$		−	9.31124i		−	0.300207i
$963$			68.7429i			2.21521i
$964$	3.49777			0.112655
$965$	−38.4801	−	9.56093i	−1.23872	−	0.307777i
$966$	−23.6020			−0.759381
$967$		−	54.9998i		−	1.76868i	−0.466848	−	0.884338i	$-0.654611\pi$
$967$		−	54.9998i		−	1.76868i	0.466848	−	0.884338i	$-0.345389\pi$
$968$			11.4280i			0.367310i
$969$	1.57531			0.0506061
$970$	−4.90934	+	19.7587i	−0.157629	+	0.634414i
$971$	9.70540			0.311461			0.155731	−	0.987800i	$-0.450227\pi$
$971$	9.70540			0.311461			0.155731	+	0.987800i	$0.450227\pi$
$972$		−	8.65634i		−	0.277652i
$973$			11.3730i			0.364601i
$974$	7.61038			0.243852
$975$	−14.0072	−	7.41855i	−0.448589	−	0.237584i
$976$	−37.0433			−1.18573
$977$		−	32.2062i		−	1.03037i	−0.857080	−	0.515184i	$-0.827724\pi$
$977$		−	32.2062i		−	1.03037i	0.857080	−	0.515184i	$-0.172276\pi$
$978$			58.7936i			1.88001i
$979$	32.5958			1.04177
$980$	−0.811662	+	3.26672i	−0.0259276	+	0.104351i
$981$	−118.880			−3.79555
$982$		−	60.7768i		−	1.93947i
$983$			44.0782i			1.40588i	0.711251	+	0.702938i	$0.248129\pi$
$983$			44.0782i			1.40588i	−0.711251	+	0.702938i	$0.751871\pi$
$984$	10.0410			0.320097
$985$	−4.34017	−	1.07838i	−0.138289	−	0.0343600i
$986$	−7.27408			−0.231654
$987$			30.9360i			0.984704i
$988$			0.199016i			0.00633154i
$989$	−18.2017			−0.578779
$990$	−59.7887	−	14.8554i	−1.90021	−	0.472134i
$991$	12.0677			0.383343			0.191672	−	0.981459i	$-0.438609\pi$
$991$	12.0677			0.383343			0.191672	+	0.981459i	$0.438609\pi$
$992$			1.81393i			0.0575923i
$993$		−	58.5029i		−	1.85653i
$994$	−38.0989			−1.20842
$995$	2.90725	−	11.7009i	0.0921659	−	0.370942i
$996$	10.0989			0.319996
$997$		−	45.7587i		−	1.44919i	−0.689173	−	0.724597i	$-0.742026\pi$
$997$		−	45.7587i		−	1.44919i	0.689173	−	0.724597i	$-0.257974\pi$
$998$			2.57182i			0.0814094i
$999$	77.6574			2.45697

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.b.a.14.2	✓	6
3.2	odd	2		585.2.c.b.469.5		6
4.3	odd	2		1040.2.d.c.209.1		6
5.2	odd	4		325.2.a.k.1.2		3
5.3	odd	4		325.2.a.j.1.2		3
5.4	even	2	inner	65.2.b.a.14.5	yes	6
13.2	odd	12		845.2.l.e.654.3		12
13.3	even	3		845.2.n.f.529.5		12
13.4	even	6		845.2.n.g.484.5		12
13.5	odd	4		845.2.d.a.844.4		6
13.6	odd	12		845.2.l.e.699.4		12
13.7	odd	12		845.2.l.d.699.4		12
13.8	odd	4		845.2.d.b.844.4		6
13.9	even	3		845.2.n.f.484.2		12
13.10	even	6		845.2.n.g.529.2		12
13.11	odd	12		845.2.l.d.654.3		12
13.12	even	2		845.2.b.c.339.5		6
15.2	even	4		2925.2.a.bf.1.2		3
15.8	even	4		2925.2.a.bj.1.2		3
15.14	odd	2		585.2.c.b.469.2		6
20.3	even	4		5200.2.a.cj.1.3		3
20.7	even	4		5200.2.a.cb.1.1		3
20.19	odd	2		1040.2.d.c.209.6		6
65.4	even	6		845.2.n.g.484.2		12
65.9	even	6		845.2.n.f.484.5		12
65.12	odd	4		4225.2.a.ba.1.2		3
65.19	odd	12		845.2.l.d.699.3		12
65.24	odd	12		845.2.l.e.654.4		12
65.29	even	6		845.2.n.f.529.2		12
65.34	odd	4		845.2.d.a.844.3		6
65.38	odd	4		4225.2.a.bh.1.2		3
65.44	odd	4		845.2.d.b.844.3		6
65.49	even	6		845.2.n.g.529.5		12
65.54	odd	12		845.2.l.d.654.4		12
65.59	odd	12		845.2.l.e.699.3		12
65.64	even	2		845.2.b.c.339.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.b.a.14.2	✓	6	1.1	even	1	trivial
65.2.b.a.14.5	yes	6	5.4	even	2	inner
325.2.a.j.1.2		3	5.3	odd	4
325.2.a.k.1.2		3	5.2	odd	4
585.2.c.b.469.2		6	15.14	odd	2
585.2.c.b.469.5		6	3.2	odd	2
845.2.b.c.339.2		6	65.64	even	2
845.2.b.c.339.5		6	13.12	even	2
845.2.d.a.844.3		6	65.34	odd	4
845.2.d.a.844.4		6	13.5	odd	4
845.2.d.b.844.3		6	65.44	odd	4
845.2.d.b.844.4		6	13.8	odd	4
845.2.l.d.654.3		12	13.11	odd	12
845.2.l.d.654.4		12	65.54	odd	12
845.2.l.d.699.3		12	65.19	odd	12
845.2.l.d.699.4		12	13.7	odd	12
845.2.l.e.654.3		12	13.2	odd	12
845.2.l.e.654.4		12	65.24	odd	12
845.2.l.e.699.3		12	65.59	odd	12
845.2.l.e.699.4		12	13.6	odd	12
845.2.n.f.484.2		12	13.9	even	3
845.2.n.f.484.5		12	65.9	even	6
845.2.n.f.529.2		12	65.29	even	6
845.2.n.f.529.5		12	13.3	even	3
845.2.n.g.484.2		12	65.4	even	6
845.2.n.g.484.5		12	13.4	even	6
845.2.n.g.529.2		12	13.10	even	6
845.2.n.g.529.5		12	65.49	even	6
1040.2.d.c.209.1		6	4.3	odd	2
1040.2.d.c.209.6		6	20.19	odd	2
2925.2.a.bf.1.2		3	15.2	even	4
2925.2.a.bj.1.2		3	15.8	even	4
4225.2.a.ba.1.2		3	65.12	odd	4
4225.2.a.bh.1.2		3	65.38	odd	4
5200.2.a.cb.1.1		3	20.7	even	4
5200.2.a.cj.1.3		3	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.53919i q^{2} +3.17009i q^{3} -0.369102 q^{4} +(0.539189 - 2.17009i) q^{5} +4.87936 q^{6} +1.70928i q^{7} -2.51026i q^{8} -7.04945 q^{9} +O(q^{10})\)	\(q-1.53919i q^{2} +3.17009i q^{3} -0.369102 q^{4} +(0.539189 - 2.17009i) q^{5} +4.87936 q^{6} +1.70928i q^{7} -2.51026i q^{8} -7.04945 q^{9} +(-3.34017 - 0.829914i) q^{10} -2.53919 q^{11} -1.17009i q^{12} -1.00000i q^{13} +2.63090 q^{14} +(6.87936 + 1.70928i) q^{15} -4.60197 q^{16} -0.921622i q^{17} +10.8504i q^{18} +0.539189 q^{19} +(-0.199016 + 0.800984i) q^{20} -5.41855 q^{21} +3.90829i q^{22} +2.82991i q^{23} +7.95774 q^{24} +(-4.41855 - 2.34017i) q^{25} -1.53919 q^{26} -12.8371i q^{27} -0.630898i q^{28} +5.12783 q^{29} +(2.63090 - 10.5886i) q^{30} +0.879362 q^{31} +2.06278i q^{32} -8.04945i q^{33} -1.41855 q^{34} +(3.70928 + 0.921622i) q^{35} +2.60197 q^{36} +6.04945i q^{37} -0.829914i q^{38} +3.17009 q^{39} +(-5.44748 - 1.35350i) q^{40} +1.26180 q^{41} +8.34017i q^{42} +6.43188i q^{43} +0.937221 q^{44} +(-3.80098 + 15.2979i) q^{45} +4.35577 q^{46} -5.70928i q^{47} -14.5886i q^{48} +4.07838 q^{49} +(-3.60197 + 6.80098i) q^{50} +2.92162 q^{51} +0.369102i q^{52} +8.49693i q^{53} -19.7587 q^{54} +(-1.36910 + 5.51026i) q^{55} +4.29072 q^{56} +1.70928i q^{57} -7.89269i q^{58} +4.72261 q^{59} +(-2.53919 - 0.630898i) q^{60} +8.04945 q^{61} -1.35350i q^{62} -12.0494i q^{63} -6.02893 q^{64} +(-2.17009 - 0.539189i) q^{65} -12.3896 q^{66} -7.86603i q^{67} +0.340173i q^{68} -8.97107 q^{69} +(1.41855 - 5.70928i) q^{70} -14.4813 q^{71} +17.6959i q^{72} -1.95055i q^{73} +9.31124 q^{74} +(7.41855 - 14.0072i) q^{75} -0.199016 q^{76} -4.34017i q^{77} -4.87936i q^{78} -0.496928 q^{79} +(-2.48133 + 9.98667i) q^{80} +19.5464 q^{81} -1.94214i q^{82} +8.63090i q^{83} +2.00000 q^{84} +(-2.00000 - 0.496928i) q^{85} +9.89988 q^{86} +16.2557i q^{87} +6.37402i q^{88} -12.8371 q^{89} +(23.5464 + 5.85043i) q^{90} +1.70928 q^{91} -1.04453i q^{92} +2.78765i q^{93} -8.78765 q^{94} +(0.290725 - 1.17009i) q^{95} -6.53919 q^{96} -5.91548i q^{97} -6.27739i q^{98} +17.8999 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{4} + 4 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 10 * q^4 + 4 * q^6 - 6 * q^9	\( 6 q - 10 q^{4} + 4 q^{6} - 6 q^{9} + 2 q^{10} - 12 q^{11} + 8 q^{14} + 16 q^{15} + 10 q^{16} - 20 q^{20} - 4 q^{21} + 16 q^{24} + 2 q^{25} - 6 q^{26} - 12 q^{29} + 8 q^{30} - 20 q^{31} + 20 q^{34} + 8 q^{35} - 22 q^{36} + 8 q^{39} - 34 q^{40} - 8 q^{41} + 40 q^{44} - 4 q^{45} + 32 q^{46} + 18 q^{49} + 16 q^{50} + 24 q^{51} - 68 q^{54} - 16 q^{55} + 40 q^{56} + 16 q^{59} - 12 q^{60} + 12 q^{61} - 66 q^{64} - 2 q^{65} - 16 q^{66} - 24 q^{69} - 20 q^{70} - 24 q^{71} + 4 q^{74} + 16 q^{75} - 20 q^{76} + 32 q^{79} + 48 q^{80} + 46 q^{81} + 12 q^{84} - 12 q^{85} - 32 q^{86} - 20 q^{89} + 70 q^{90} - 4 q^{91} - 32 q^{94} + 16 q^{95} - 36 q^{96} + 16 q^{99}+O(q^{100}) \) 6 * q - 10 * q^4 + 4 * q^6 - 6 * q^9 + 2 * q^10 - 12 * q^11 + 8 * q^14 + 16 * q^15 + 10 * q^16 - 20 * q^20 - 4 * q^21 + 16 * q^24 + 2 * q^25 - 6 * q^26 - 12 * q^29 + 8 * q^30 - 20 * q^31 + 20 * q^34 + 8 * q^35 - 22 * q^36 + 8 * q^39 - 34 * q^40 - 8 * q^41 + 40 * q^44 - 4 * q^45 + 32 * q^46 + 18 * q^49 + 16 * q^50 + 24 * q^51 - 68 * q^54 - 16 * q^55 + 40 * q^56 + 16 * q^59 - 12 * q^60 + 12 * q^61 - 66 * q^64 - 2 * q^65 - 16 * q^66 - 24 * q^69 - 20 * q^70 - 24 * q^71 + 4 * q^74 + 16 * q^75 - 20 * q^76 + 32 * q^79 + 48 * q^80 + 46 * q^81 + 12 * q^84 - 12 * q^85 - 32 * q^86 - 20 * q^89 + 70 * q^90 - 4 * q^91 - 32 * q^94 + 16 * q^95 - 36 * q^96 + 16 * q^99

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