LMFDB - Embedded newform 165.2.c.b.34.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(34,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("165.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.c (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:	$1.31753163335$
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			34.1
Root			$-0.854638 - 0.854638i$ of defining polynomial
Character	$\chi$	$=$	165.34
Dual form			165.2.c.b.34.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.17009i q^{2} +1.00000i q^{3} -2.70928 q^{4} +(2.17009 + 0.539189i) q^{5} +2.17009 q^{6} -3.70928i q^{7} +1.53919i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.17009i q^{2} +1.00000i q^{3} -2.70928 q^{4} +(2.17009 + 0.539189i) q^{5} +2.17009 q^{6} -3.70928i q^{7} +1.53919i q^{8} -1.00000 q^{9} +(1.17009 - 4.70928i) q^{10} +1.00000 q^{11} -2.70928i q^{12} -1.70928i q^{13} -8.04945 q^{14} +(-0.539189 + 2.17009i) q^{15} -2.07838 q^{16} +6.04945i q^{17} +2.17009i q^{18} +3.07838 q^{19} +(-5.87936 - 1.46081i) q^{20} +3.70928 q^{21} -2.17009i q^{22} +4.00000i q^{23} -1.53919 q^{24} +(4.41855 + 2.34017i) q^{25} -3.70928 q^{26} -1.00000i q^{27} +10.0494i q^{28} -5.26180 q^{29} +(4.70928 + 1.17009i) q^{30} -6.34017 q^{31} +7.58864i q^{32} +1.00000i q^{33} +13.1278 q^{34} +(2.00000 - 8.04945i) q^{35} +2.70928 q^{36} +3.41855i q^{37} -6.68035i q^{38} +1.70928 q^{39} +(-0.829914 + 3.34017i) q^{40} +9.57531 q^{41} -8.04945i q^{42} -3.12783i q^{43} -2.70928 q^{44} +(-2.17009 - 0.539189i) q^{45} +8.68035 q^{46} -2.73820i q^{47} -2.07838i q^{48} -6.75872 q^{49} +(5.07838 - 9.58864i) q^{50} -6.04945 q^{51} +4.63090i q^{52} +13.7587i q^{53} -2.17009 q^{54} +(2.17009 + 0.539189i) q^{55} +5.70928 q^{56} +3.07838i q^{57} +11.4186i q^{58} +3.60197 q^{59} +(1.46081 - 5.87936i) q^{60} -14.6803 q^{61} +13.7587i q^{62} +3.70928i q^{63} +12.3112 q^{64} +(0.921622 - 3.70928i) q^{65} +2.17009 q^{66} -1.84324i q^{67} -16.3896i q^{68} -4.00000 q^{69} +(-17.4680 - 4.34017i) q^{70} -7.23513 q^{71} -1.53919i q^{72} +6.38962i q^{73} +7.41855 q^{74} +(-2.34017 + 4.41855i) q^{75} -8.34017 q^{76} -3.70928i q^{77} -3.70928i q^{78} +7.44521 q^{79} +(-4.51026 - 1.12064i) q^{80} +1.00000 q^{81} -20.7792i q^{82} -7.86603i q^{83} -10.0494 q^{84} +(-3.26180 + 13.1278i) q^{85} -6.78765 q^{86} -5.26180i q^{87} +1.53919i q^{88} +5.02052 q^{89} +(-1.17009 + 4.70928i) q^{90} -6.34017 q^{91} -10.8371i q^{92} -6.34017i q^{93} -5.94214 q^{94} +(6.68035 + 1.65983i) q^{95} -7.58864 q^{96} -16.9939i q^{97} +14.6670i q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 2 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^9	$ 6 q - 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{9} - 4 q^{10} + 6 q^{11} - 12 q^{14} - 6 q^{16} + 12 q^{19} - 10 q^{20} + 8 q^{21} - 6 q^{24} - 2 q^{25} - 8 q^{26} - 16 q^{29} + 14 q^{30} - 16 q^{31} + 36 q^{34} + 12 q^{35} + 2 q^{36} - 4 q^{39} - 16 q^{40} + 16 q^{41} - 2 q^{44} - 2 q^{45} + 8 q^{46} + 10 q^{49} + 24 q^{50} - 2 q^{54} + 2 q^{55} + 20 q^{56} - 16 q^{59} + 12 q^{60} - 44 q^{61} + 22 q^{64} + 12 q^{65} + 2 q^{66} - 24 q^{69} - 40 q^{70} - 24 q^{71} + 16 q^{74} + 8 q^{75} - 28 q^{76} + 20 q^{79} + 6 q^{80} + 6 q^{81} - 24 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} + 4 q^{90} - 16 q^{91} + 24 q^{94} - 4 q^{95} - 6 q^{96} - 6 q^{99}+O(q^{100}) $ 6 * q - 2 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^9 - 4 * q^10 + 6 * q^11 - 12 * q^14 - 6 * q^16 + 12 * q^19 - 10 * q^20 + 8 * q^21 - 6 * q^24 - 2 * q^25 - 8 * q^26 - 16 * q^29 + 14 * q^30 - 16 * q^31 + 36 * q^34 + 12 * q^35 + 2 * q^36 - 4 * q^39 - 16 * q^40 + 16 * q^41 - 2 * q^44 - 2 * q^45 + 8 * q^46 + 10 * q^49 + 24 * q^50 - 2 * q^54 + 2 * q^55 + 20 * q^56 - 16 * q^59 + 12 * q^60 - 44 * q^61 + 22 * q^64 + 12 * q^65 + 2 * q^66 - 24 * q^69 - 40 * q^70 - 24 * q^71 + 16 * q^74 + 8 * q^75 - 28 * q^76 + 20 * q^79 + 6 * q^80 + 6 * q^81 - 24 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 + 4 * q^90 - 16 * q^91 + 24 * q^94 - 4 * q^95 - 6 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	2.17009i		−	1.53448i	−0.641358	−	0.767241i	$-0.721629\pi$
$2$		−	2.17009i		−	1.53448i	0.641358	−	0.767241i	$-0.278371\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−2.70928			−1.35464
$5$	2.17009	+	0.539189i	0.970492	+	0.241133i
$5$	2.17009	+	0.539189i	0.970492	+	0.241133i
$6$	2.17009			0.885934
$7$		−	3.70928i		−	1.40197i	−0.713174	−	0.700987i	$-0.752743\pi$
$7$		−	3.70928i		−	1.40197i	0.713174	−	0.700987i	$-0.247257\pi$
$8$			1.53919i			0.544185i
$9$	−1.00000			−0.333333
$10$	1.17009	−	4.70928i	0.370014	−	1.48920i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$		−	2.70928i		−	0.782100i
$13$		−	1.70928i		−	0.474068i	−0.971501	−	0.237034i	$-0.923825\pi$
$13$		−	1.70928i		−	0.474068i	0.971501	−	0.237034i	$-0.0761752\pi$
$14$	−8.04945			−2.15131
$15$	−0.539189	+	2.17009i	−0.139218	+	0.560314i
$16$	−2.07838			−0.519594
$17$			6.04945i			1.46721i	0.679578	+	0.733603i	$0.262163\pi$
$17$			6.04945i			1.46721i	−0.679578	+	0.733603i	$0.737837\pi$
$18$			2.17009i			0.511494i
$19$	3.07838			0.706228			0.353114	−	0.935580i	$-0.385123\pi$
$19$	3.07838			0.706228			0.353114	+	0.935580i	$0.385123\pi$
$20$	−5.87936	−	1.46081i	−1.31467	−	0.326647i
$21$	3.70928			0.809430
$22$		−	2.17009i		−	0.462664i
$23$			4.00000i			0.834058i	0.908893	+	0.417029i	$0.136929\pi$
$23$			4.00000i			0.834058i	−0.908893	+	0.417029i	$0.863071\pi$
$24$	−1.53919			−0.314186
$25$	4.41855	+	2.34017i	0.883710	+	0.468035i
$26$	−3.70928			−0.727449
$27$		−	1.00000i		−	0.192450i
$28$			10.0494i			1.89917i
$29$	−5.26180			−0.977091			−0.488545	−	0.872538i	$-0.662472\pi$
$29$	−5.26180			−0.977091			−0.488545	+	0.872538i	$0.662472\pi$
$30$	4.70928	+	1.17009i	0.859792	+	0.213628i
$31$	−6.34017			−1.13873			−0.569364	−	0.822085i	$-0.692811\pi$
$31$	−6.34017			−1.13873			−0.569364	+	0.822085i	$0.692811\pi$
$32$			7.58864i			1.34149i
$33$			1.00000i			0.174078i
$34$	13.1278			2.25140
$35$	2.00000	−	8.04945i	0.338062	−	1.36061i
$36$	2.70928			0.451546
$37$			3.41855i			0.562006i	0.959707	+	0.281003i	$0.0906671\pi$
$37$			3.41855i			0.562006i	−0.959707	+	0.281003i	$0.909333\pi$
$38$		−	6.68035i		−	1.08370i
$39$	1.70928			0.273703
$40$	−0.829914	+	3.34017i	−0.131221	+	0.528128i
$41$	9.57531			1.49541			0.747706	−	0.664030i	$-0.231155\pi$
$41$	9.57531			1.49541			0.747706	+	0.664030i	$0.231155\pi$
$42$		−	8.04945i		−	1.24206i
$43$		−	3.12783i		−	0.476989i	−0.971144	−	0.238495i	$-0.923346\pi$
$43$		−	3.12783i		−	0.476989i	0.971144	−	0.238495i	$-0.0766539\pi$
$44$	−2.70928			−0.408439
$45$	−2.17009	−	0.539189i	−0.323497	−	0.0803775i
$46$	8.68035			1.27985
$47$		−	2.73820i		−	0.399408i	−0.979856	−	0.199704i	$-0.936002\pi$
$47$		−	2.73820i		−	0.399408i	0.979856	−	0.199704i	$-0.0639981\pi$
$48$		−	2.07838i		−	0.299988i
$49$	−6.75872			−0.965532
$50$	5.07838	−	9.58864i	0.718191	−	1.35604i
$51$	−6.04945			−0.847092
$52$			4.63090i			0.642190i
$53$			13.7587i			1.88991i	0.327206	+	0.944953i	$0.393893\pi$
$53$			13.7587i			1.88991i	−0.327206	+	0.944953i	$0.606107\pi$
$54$	−2.17009			−0.295311
$55$	2.17009	+	0.539189i	0.292614	+	0.0727042i
$56$	5.70928			0.762934
$57$			3.07838i			0.407741i
$58$			11.4186i			1.49933i
$59$	3.60197			0.468936			0.234468	−	0.972124i	$-0.424665\pi$
$59$	3.60197			0.468936			0.234468	+	0.972124i	$0.424665\pi$
$60$	1.46081	−	5.87936i	0.188590	−	0.759022i
$61$	−14.6803			−1.87963			−0.939813	−	0.341690i	$-0.889001\pi$
$61$	−14.6803			−1.87963			−0.939813	+	0.341690i	$0.889001\pi$
$62$			13.7587i			1.74736i
$63$			3.70928i			0.467325i
$64$	12.3112			1.53891
$65$	0.921622	−	3.70928i	0.114313	−	0.460079i
$66$	2.17009			0.267119
$67$		−	1.84324i		−	0.225188i	−0.993641	−	0.112594i	$-0.964084\pi$
$67$		−	1.84324i		−	0.225188i	0.993641	−	0.112594i	$-0.0359160\pi$
$68$		−	16.3896i		−	1.98753i
$69$	−4.00000			−0.481543
$70$	−17.4680	−	4.34017i	−2.08783	−	0.518750i
$71$	−7.23513			−0.858652			−0.429326	−	0.903150i	$-0.641249\pi$
$71$	−7.23513			−0.858652			−0.429326	+	0.903150i	$0.641249\pi$
$72$		−	1.53919i		−	0.181395i
$73$			6.38962i			0.747849i	0.927459	+	0.373924i	$0.121988\pi$
$73$			6.38962i			0.747849i	−0.927459	+	0.373924i	$0.878012\pi$
$74$	7.41855			0.862389
$75$	−2.34017	+	4.41855i	−0.270220	+	0.510210i
$76$	−8.34017			−0.956683
$77$		−	3.70928i		−	0.422711i
$78$		−	3.70928i		−	0.419993i
$79$	7.44521			0.837652			0.418826	−	0.908067i	$-0.362442\pi$
$79$	7.44521			0.837652			0.418826	+	0.908067i	$0.362442\pi$
$80$	−4.51026	−	1.12064i	−0.504262	−	0.125291i
$81$	1.00000			0.111111
$82$		−	20.7792i		−	2.29468i
$83$		−	7.86603i		−	0.863409i	−0.902015	−	0.431705i	$-0.857912\pi$
$83$		−	7.86603i		−	0.863409i	0.902015	−	0.431705i	$-0.142088\pi$
$84$	−10.0494			−1.09648
$85$	−3.26180	+	13.1278i	−0.353791	+	1.42391i
$86$	−6.78765			−0.731931
$87$		−	5.26180i		−	0.564124i
$88$			1.53919i			0.164078i
$89$	5.02052			0.532174			0.266087	−	0.963949i	$-0.414269\pi$
$89$	5.02052			0.532174			0.266087	+	0.963949i	$0.414269\pi$
$90$	−1.17009	+	4.70928i	−0.123338	+	0.496401i
$91$	−6.34017			−0.664631
$92$		−	10.8371i		−	1.12985i
$93$		−	6.34017i		−	0.657445i
$94$	−5.94214			−0.612885
$95$	6.68035	+	1.65983i	0.685389	+	0.170295i
$96$	−7.58864			−0.774512
$97$		−	16.9939i		−	1.72546i	−0.505661	−	0.862732i	$-0.668751\pi$
$97$		−	16.9939i		−	1.72546i	0.505661	−	0.862732i	$-0.331249\pi$
$98$			14.6670i			1.48159i
$99$	−1.00000			−0.100504
$100$	−11.9711	−	6.34017i	−1.19711	−	0.634017i
$101$	−18.9360			−1.88420			−0.942101	−	0.335329i	$-0.891153\pi$
$101$	−18.9360			−1.88420			−0.942101	+	0.335329i	$0.891153\pi$
$102$			13.1278i			1.29985i
$103$		−	11.7854i		−	1.16125i	−0.814172	−	0.580624i	$-0.802809\pi$
$103$		−	11.7854i		−	1.16125i	0.814172	−	0.580624i	$-0.197191\pi$
$104$	2.63090			0.257981
$105$	8.04945	+	2.00000i	0.785546	+	0.195180i
$106$	29.8576			2.90003
$107$		−	11.2846i		−	1.09092i	−0.838136	−	0.545461i	$-0.816355\pi$
$107$		−	11.2846i		−	1.09092i	0.838136	−	0.545461i	$-0.183645\pi$
$108$			2.70928i			0.260700i
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$	1.17009	−	4.70928i	0.111563	−	0.449012i
$111$	−3.41855			−0.324474
$112$			7.70928i			0.728458i
$113$		−	0.496928i		−	0.0467471i	−0.999727	−	0.0233735i	$-0.992559\pi$
$113$		−	0.496928i		−	0.0467471i	0.999727	−	0.0233735i	$-0.00744071\pi$
$114$	6.68035			0.625672
$115$	−2.15676	+	8.68035i	−0.201118	+	0.809446i
$116$	14.2557			1.32360
$117$			1.70928i			0.158023i
$118$		−	7.81658i		−	0.719575i
$119$	22.4391			2.05699
$120$	−3.34017	−	0.829914i	−0.304915	−	0.0757604i
$121$	1.00000			0.0909091
$122$			31.8576i			2.88425i
$123$			9.57531i			0.863376i
$124$	17.1773			1.54256
$125$	8.32684	+	7.46081i	0.744775	+	0.667315i
$126$	8.04945			0.717102
$127$		−	2.81432i		−	0.249730i	−0.992174	−	0.124865i	$-0.960150\pi$
$127$		−	2.81432i		−	0.249730i	0.992174	−	0.124865i	$-0.0398498\pi$
$128$		−	11.5392i		−	1.01993i
$129$	3.12783			0.275390
$130$	−8.04945	−	2.00000i	−0.705983	−	0.175412i
$131$	8.68035			0.758405			0.379203	−	0.925314i	$-0.376198\pi$
$131$	8.68035			0.758405			0.379203	+	0.925314i	$0.376198\pi$
$132$		−	2.70928i		−	0.235812i
$133$		−	11.4186i		−	0.990114i
$134$	−4.00000			−0.345547
$135$	0.539189	−	2.17009i	0.0464060	−	0.186771i
$136$	−9.31124			−0.798433
$137$		−	1.07838i		−	0.0921320i	−0.998938	−	0.0460660i	$-0.985332\pi$
$137$		−	1.07838i		−	0.0921320i	0.998938	−	0.0460660i	$-0.0146685\pi$
$138$			8.68035i			0.738920i
$139$	−10.2823			−0.872135			−0.436067	−	0.899914i	$-0.643629\pi$
$139$	−10.2823			−0.872135			−0.436067	+	0.899914i	$0.643629\pi$
$140$	−5.41855	+	21.8082i	−0.457951	+	1.84313i
$141$	2.73820			0.230598
$142$			15.7009i			1.31759i
$143$		−	1.70928i		−	0.142937i
$144$	2.07838			0.173198
$145$	−11.4186	−	2.83710i	−0.948259	−	0.235608i
$146$	13.8660			1.14756
$147$		−	6.75872i		−	0.557450i
$148$		−	9.26180i		−	0.761315i
$149$	−11.4186			−0.935444			−0.467722	−	0.883876i	$-0.654925\pi$
$149$	−11.4186			−0.935444			−0.467722	+	0.883876i	$0.654925\pi$
$150$	9.58864	+	5.07838i	0.782909	+	0.414648i
$151$	−4.92162			−0.400516			−0.200258	−	0.979743i	$-0.564178\pi$
$151$	−4.92162			−0.400516			−0.200258	+	0.979743i	$0.564178\pi$
$152$			4.73820i			0.384319i
$153$		−	6.04945i		−	0.489069i
$154$	−8.04945			−0.648643
$155$	−13.7587	−	3.41855i	−1.10513	−	0.274585i
$156$	−4.63090			−0.370769
$157$			3.41855i			0.272830i	0.990652	+	0.136415i	$0.0435581\pi$
$157$			3.41855i			0.272830i	−0.990652	+	0.136415i	$0.956442\pi$
$158$		−	16.1568i		−	1.28536i
$159$	−13.7587			−1.09114
$160$	−4.09171	+	16.4680i	−0.323478	+	1.30191i
$161$	14.8371			1.16933
$162$		−	2.17009i		−	0.170498i
$163$			9.26180i			0.725440i	0.931898	+	0.362720i	$0.118152\pi$
$163$			9.26180i			0.725440i	−0.931898	+	0.362720i	$0.881848\pi$
$164$	−25.9421			−2.02574
$165$	−0.539189	+	2.17009i	−0.0419758	+	0.168941i
$166$	−17.0700			−1.32489
$167$		−	7.55252i		−	0.584432i	−0.956352	−	0.292216i	$-0.905607\pi$
$167$		−	7.55252i		−	0.584432i	0.956352	−	0.292216i	$-0.0943925\pi$
$168$			5.70928i			0.440480i
$169$	10.0784			0.775260
$170$	28.4885	+	7.07838i	2.18497	+	0.542887i
$171$	−3.07838			−0.235409
$172$			8.47414i			0.646147i
$173$			6.14834i			0.467450i	0.972303	+	0.233725i	$0.0750915\pi$
$173$			6.14834i			0.467450i	−0.972303	+	0.233725i	$0.924908\pi$
$174$	−11.4186			−0.865638
$175$	8.68035	−	16.3896i	0.656172	−	1.23894i
$176$	−2.07838			−0.156664
$177$			3.60197i			0.270741i
$178$		−	10.8950i		−	0.816612i
$179$	6.15676			0.460178			0.230089	−	0.973170i	$-0.426098\pi$
$179$	6.15676			0.460178			0.230089	+	0.973170i	$0.426098\pi$
$180$	5.87936	+	1.46081i	0.438222	+	0.108882i
$181$	14.5958			1.08490			0.542450	−	0.840088i	$-0.317497\pi$
$181$	14.5958			1.08490			0.542450	+	0.840088i	$0.317497\pi$
$182$			13.7587i			1.01986i
$183$		−	14.6803i		−	1.08520i
$184$	−6.15676			−0.453882
$185$	−1.84324	+	7.41855i	−0.135518	+	0.545423i
$186$	−13.7587			−1.00884
$187$			6.04945i			0.442379i
$188$			7.41855i			0.541053i
$189$	−3.70928			−0.269810
$190$	3.60197	−	14.4969i	0.261314	−	1.05172i
$191$	5.84324			0.422802			0.211401	−	0.977399i	$-0.432197\pi$
$191$	5.84324			0.422802			0.211401	+	0.977399i	$0.432197\pi$
$192$			12.3112i			0.888487i
$193$			2.02279i			0.145603i	0.997346	+	0.0728017i	$0.0231940\pi$
$193$			2.02279i			0.145603i	−0.997346	+	0.0728017i	$0.976806\pi$
$194$	−36.8781			−2.64770
$195$	3.70928	+	0.921622i	0.265627	+	0.0659987i
$196$	18.3112			1.30795
$197$		−	17.8348i		−	1.27068i	−0.772233	−	0.635340i	$-0.780860\pi$
$197$		−	17.8348i		−	1.27068i	0.772233	−	0.635340i	$-0.219140\pi$
$198$			2.17009i			0.154221i
$199$	−25.6742			−1.82000			−0.909998	−	0.414613i	$-0.863917\pi$
$199$	−25.6742			−1.82000			−0.909998	+	0.414613i	$0.863917\pi$
$200$	−3.60197	+	6.80098i	−0.254698	+	0.480902i
$201$	1.84324			0.130012
$202$			41.0928i			2.89128i
$203$			19.5174i			1.36986i
$204$	16.3896			1.14750
$205$	20.7792	+	5.16290i	1.45129	+	0.360592i
$206$	−25.5753			−1.78192
$207$		−	4.00000i		−	0.278019i
$208$			3.55252i			0.246323i
$209$	3.07838			0.212936
$210$	4.34017	−	17.4680i	0.299500	−	1.20541i
$211$	8.43907			0.580970			0.290485	−	0.956880i	$-0.406183\pi$
$211$	8.43907			0.580970			0.290485	+	0.956880i	$0.406183\pi$
$212$		−	37.2762i		−	2.56014i
$213$		−	7.23513i		−	0.495743i
$214$	−24.4885			−1.67400
$215$	1.68649	−	6.78765i	0.115018	−	0.462914i
$216$	1.53919			0.104729
$217$			23.5174i			1.59647i
$218$		−	21.7009i		−	1.46977i
$219$	−6.38962			−0.431771
$220$	−5.87936	−	1.46081i	−0.396386	−	0.0984879i
$221$	10.3402			0.695555
$222$			7.41855i			0.497901i
$223$			12.5814i			0.842516i	0.906941	+	0.421258i	$0.138411\pi$
$223$			12.5814i			0.842516i	−0.906941	+	0.421258i	$0.861589\pi$
$224$	28.1483			1.88074
$225$	−4.41855	−	2.34017i	−0.294570	−	0.156012i
$226$	−1.07838			−0.0717326
$227$		−	4.23287i		−	0.280945i	−0.990085	−	0.140473i	$-0.955138\pi$
$227$		−	4.23287i		−	0.280945i	0.990085	−	0.140473i	$-0.0448622\pi$
$228$		−	8.34017i		−	0.552341i
$229$	26.1978			1.73120			0.865599	−	0.500737i	$-0.166938\pi$
$229$	26.1978			1.73120			0.865599	+	0.500737i	$0.166938\pi$
$230$	18.8371	+	4.68035i	1.24208	+	0.308613i
$231$	3.70928			0.244052
$232$		−	8.09890i		−	0.531719i
$233$		−	18.6309i		−	1.22055i	−0.792189	−	0.610275i	$-0.791059\pi$
$233$		−	18.6309i		−	1.22055i	0.792189	−	0.610275i	$-0.208941\pi$
$234$	3.70928			0.242483
$235$	1.47641	−	5.94214i	0.0963103	−	0.387623i
$236$	−9.75872			−0.635239
$237$			7.44521i			0.483619i
$238$		−	48.6947i		−	3.15641i
$239$	−22.3545			−1.44600			−0.722998	−	0.690850i	$-0.757236\pi$
$239$	−22.3545			−1.44600			−0.722998	+	0.690850i	$0.757236\pi$
$240$	1.12064	−	4.51026i	0.0723369	−	0.291136i
$241$	9.20394			0.592878			0.296439	−	0.955052i	$-0.404201\pi$
$241$	9.20394			0.592878			0.296439	+	0.955052i	$0.404201\pi$
$242$		−	2.17009i		−	0.139498i
$243$			1.00000i			0.0641500i
$244$	39.7731			2.54621
$245$	−14.6670	−	3.64423i	−0.937041	−	0.232821i
$246$	20.7792			1.32484
$247$		−	5.26180i		−	0.334800i
$248$		−	9.75872i		−	0.619680i
$249$	7.86603			0.498489
$250$	16.1906	−	18.0700i	1.02398	−	1.14285i
$251$	−22.1256			−1.39655			−0.698276	−	0.715828i	$-0.746049\pi$
$251$	−22.1256			−1.39655			−0.698276	+	0.715828i	$0.746049\pi$
$252$		−	10.0494i		−	0.633056i
$253$			4.00000i			0.251478i
$254$	−6.10731			−0.383207
$255$	−13.1278	−	3.26180i	−0.822096	−	0.204262i
$256$	−0.418551			−0.0261594
$257$		−	3.02052i		−	0.188415i	−0.995553	−	0.0942074i	$-0.969968\pi$
$257$		−	3.02052i		−	0.188415i	0.995553	−	0.0942074i	$-0.0300317\pi$
$258$		−	6.78765i		−	0.422581i
$259$	12.6803			0.787918
$260$	−2.49693	+	10.0494i	−0.154853	+	0.623240i
$261$	5.26180			0.325697
$262$		−	18.8371i		−	1.16376i
$263$			18.2907i			1.12785i	0.825825	+	0.563927i	$0.190710\pi$
$263$			18.2907i			1.12785i	−0.825825	+	0.563927i	$0.809290\pi$
$264$	−1.53919			−0.0947305
$265$	−7.41855	+	29.8576i	−0.455718	+	1.83414i
$266$	−24.7792			−1.51931
$267$			5.02052i			0.307251i
$268$			4.99386i			0.305048i
$269$	−30.5646			−1.86356			−0.931779	−	0.363026i	$-0.881744\pi$
$269$	−30.5646			−1.86356			−0.931779	+	0.363026i	$0.881744\pi$
$270$	−4.70928	−	1.17009i	−0.286597	−	0.0712092i
$271$	−20.0722			−1.21930			−0.609651	−	0.792670i	$-0.708690\pi$
$271$	−20.0722			−1.21930			−0.609651	+	0.792670i	$0.708690\pi$
$272$		−	12.5730i		−	0.762352i
$273$		−	6.34017i		−	0.383725i
$274$	−2.34017			−0.141375
$275$	4.41855	+	2.34017i	0.266449	+	0.141118i
$276$	10.8371			0.652317
$277$		−	0.760991i		−	0.0457235i	−0.999739	−	0.0228618i	$-0.992722\pi$
$277$		−	0.760991i		−	0.0457235i	0.999739	−	0.0228618i	$-0.00727776\pi$
$278$			22.3135i			1.33828i
$279$	6.34017			0.379576
$280$	12.3896	+	3.07838i	0.740421	+	0.183968i
$281$	0.581449			0.0346864			0.0173432	−	0.999850i	$-0.494479\pi$
$281$	0.581449			0.0346864			0.0173432	+	0.999850i	$0.494479\pi$
$282$		−	5.94214i		−	0.353849i
$283$		−	10.8143i		−	0.642844i	−0.946936	−	0.321422i	$-0.895839\pi$
$283$		−	10.8143i		−	0.642844i	0.946936	−	0.321422i	$-0.104161\pi$
$284$	19.6020			1.16316
$285$	−1.65983	+	6.68035i	−0.0983197	+	0.395710i
$286$	−3.70928			−0.219334
$287$		−	35.5174i		−	2.09653i
$288$		−	7.58864i		−	0.447165i
$289$	−19.5958			−1.15270
$290$	−6.15676	+	24.7792i	−0.361537	+	1.45509i
$291$	16.9939			0.996198
$292$		−	17.3112i		−	1.01306i
$293$			7.04331i			0.411474i	0.978607	+	0.205737i	$0.0659592\pi$
$293$			7.04331i			0.411474i	−0.978607	+	0.205737i	$0.934041\pi$
$294$	−14.6670			−0.855398
$295$	7.81658	+	1.94214i	0.455099	+	0.113076i
$296$	−5.26180			−0.305836
$297$		−	1.00000i		−	0.0580259i
$298$			24.7792i			1.43542i
$299$	6.83710			0.395400
$300$	6.34017	−	11.9711i	0.366050	−	0.691150i
$301$	−11.6020			−0.668726
$302$			10.6803i			0.614585i
$303$		−	18.9360i		−	1.08784i
$304$	−6.39803			−0.366952
$305$	−31.8576	−	7.91548i	−1.82416	−	0.453239i
$306$	−13.1278			−0.750468
$307$			20.1750i			1.15145i	0.817644	+	0.575724i	$0.195280\pi$
$307$			20.1750i			1.15145i	−0.817644	+	0.575724i	$0.804720\pi$
$308$			10.0494i			0.572620i
$309$	11.7854			0.670447
$310$	−7.41855	+	29.8576i	−0.421345	+	1.69580i
$311$	21.2762			1.20646			0.603230	−	0.797567i	$-0.293880\pi$
$311$	21.2762			1.20646			0.603230	+	0.797567i	$0.293880\pi$
$312$			2.63090i			0.148945i
$313$			16.4657i			0.930698i	0.885127	+	0.465349i	$0.154071\pi$
$313$			16.4657i			0.930698i	−0.885127	+	0.465349i	$0.845929\pi$
$314$	7.41855			0.418653
$315$	−2.00000	+	8.04945i	−0.112687	+	0.453535i
$316$	−20.1711			−1.13471
$317$			22.1711i			1.24525i	0.782518	+	0.622627i	$0.213935\pi$
$317$			22.1711i			1.24525i	−0.782518	+	0.622627i	$0.786065\pi$
$318$			29.8576i			1.67433i
$319$	−5.26180			−0.294604
$320$	26.7165	+	6.63809i	1.49350	+	0.371080i
$321$	11.2846			0.629844
$322$		−	32.1978i		−	1.79431i
$323$			18.6225i			1.03618i
$324$	−2.70928			−0.150515
$325$	4.00000	−	7.55252i	0.221880	−	0.418938i
$326$	20.0989			1.11317
$327$			10.0000i			0.553001i
$328$			14.7382i			0.813781i
$329$	−10.1568			−0.559960
$330$	4.70928	+	1.17009i	0.259237	+	0.0644111i
$331$	−6.34017			−0.348487			−0.174244	−	0.984703i	$-0.555748\pi$
$331$	−6.34017			−0.348487			−0.174244	+	0.984703i	$0.555748\pi$
$332$			21.3112i			1.16961i
$333$		−	3.41855i		−	0.187335i
$334$	−16.3896			−0.896800
$335$	0.993857	−	4.00000i	0.0543002	−	0.218543i
$336$	−7.70928			−0.420575
$337$		−	3.18568i		−	0.173535i	−0.996229	−	0.0867677i	$-0.972346\pi$
$337$		−	3.18568i		−	0.173535i	0.996229	−	0.0867677i	$-0.0276538\pi$
$338$		−	21.8710i		−	1.18962i
$339$	0.496928			0.0269894
$340$	8.83710	−	35.5669i	0.479259	−	1.92889i
$341$	−6.34017			−0.343340
$342$			6.68035i			0.361232i
$343$		−	0.894960i		−	0.0483233i
$344$	4.81432			0.259570
$345$	−8.68035	−	2.15676i	−0.467334	−	0.116116i
$346$	13.3424			0.717294
$347$			5.39576i			0.289660i	0.989457	+	0.144830i	$0.0462635\pi$
$347$			5.39576i			0.289660i	−0.989457	+	0.144830i	$0.953737\pi$
$348$			14.2557i			0.764183i
$349$	15.6742			0.839021			0.419510	−	0.907751i	$-0.362202\pi$
$349$	15.6742			0.839021			0.419510	+	0.907751i	$0.362202\pi$
$350$	−35.5669	−	18.8371i	−1.90113	−	1.00689i
$351$	−1.70928			−0.0912344
$352$			7.58864i			0.404476i
$353$		−	5.75872i		−	0.306506i	−0.988187	−	0.153253i	$-0.951025\pi$
$353$		−	5.75872i		−	0.306506i	0.988187	−	0.153253i	$-0.0489749\pi$
$354$	7.81658			0.415447
$355$	−15.7009	−	3.90110i	−0.833315	−	0.207049i
$356$	−13.6020			−0.720903
$357$			22.4391i			1.18760i
$358$		−	13.3607i		−	0.706135i
$359$	10.5236			0.555414			0.277707	−	0.960666i	$-0.410426\pi$
$359$	10.5236			0.555414			0.277707	+	0.960666i	$0.410426\pi$
$360$	0.829914	−	3.34017i	0.0437403	−	0.176043i
$361$	−9.52359			−0.501242
$362$		−	31.6742i		−	1.66476i
$363$			1.00000i			0.0524864i
$364$	17.1773			0.900334
$365$	−3.44521	+	13.8660i	−0.180331	+	0.725781i
$366$	−31.8576			−1.66522
$367$		−	8.89496i		−	0.464313i	−0.972678	−	0.232157i	$-0.925422\pi$
$367$		−	8.89496i		−	0.464313i	0.972678	−	0.232157i	$-0.0745782\pi$
$368$		−	8.31351i		−	0.433372i
$369$	−9.57531			−0.498471
$370$	16.0989	+	4.00000i	0.836942	+	0.207950i
$371$	51.0349			2.64960
$372$			17.1773i			0.890600i
$373$		−	23.1689i		−	1.19964i	−0.800136	−	0.599819i	$-0.795239\pi$
$373$		−	23.1689i		−	1.19964i	0.800136	−	0.599819i	$-0.204761\pi$
$374$	13.1278			0.678824
$375$	−7.46081	+	8.32684i	−0.385275	+	0.429996i
$376$	4.21461			0.217352
$377$			8.99386i			0.463207i
$378$			8.04945i			0.414019i
$379$	11.8310			0.607716			0.303858	−	0.952717i	$-0.401725\pi$
$379$	11.8310			0.607716			0.303858	+	0.952717i	$0.401725\pi$
$380$	−18.0989	−	4.49693i	−0.928454	−	0.230688i
$381$	2.81432			0.144182
$382$		−	12.6803i		−	0.648783i
$383$			25.9421i			1.32558i	0.748805	+	0.662791i	$0.230628\pi$
$383$			25.9421i			1.32558i	−0.748805	+	0.662791i	$0.769372\pi$
$384$	11.5392			0.588857
$385$	2.00000	−	8.04945i	0.101929	−	0.410238i
$386$	4.38962			0.223426
$387$			3.12783i			0.158996i
$388$			46.0410i			2.33738i
$389$	−1.00614			−0.0510135			−0.0255067	−	0.999675i	$-0.508120\pi$
$389$	−1.00614			−0.0510135			−0.0255067	+	0.999675i	$0.508120\pi$
$390$	2.00000	−	8.04945i	0.101274	−	0.407600i
$391$	−24.1978			−1.22374
$392$		−	10.4030i		−	0.525428i
$393$			8.68035i			0.437866i
$394$	−38.7031			−1.94984
$395$	16.1568	+	4.01438i	0.812935	+	0.201985i
$396$	2.70928			0.136146
$397$		−	34.7214i		−	1.74262i	−0.490736	−	0.871308i	$-0.663272\pi$
$397$		−	34.7214i		−	1.74262i	0.490736	−	0.871308i	$-0.336728\pi$
$398$			55.7152i			2.79275i
$399$	11.4186			0.571643
$400$	−9.18342	−	4.86376i	−0.459171	−	0.243188i
$401$	−13.0205			−0.650214			−0.325107	−	0.945677i	$-0.605400\pi$
$401$	−13.0205			−0.650214			−0.325107	+	0.945677i	$0.605400\pi$
$402$		−	4.00000i		−	0.199502i
$403$			10.8371i			0.539834i
$404$	51.3028			2.55241
$405$	2.17009	+	0.539189i	0.107832	+	0.0267925i
$406$	42.3545			2.10202
$407$			3.41855i			0.169451i
$408$		−	9.31124i		−	0.460975i
$409$	29.5174			1.45954			0.729772	−	0.683691i	$-0.239626\pi$
$409$	29.5174			1.45954			0.729772	+	0.683691i	$0.239626\pi$
$410$	11.2039	−	45.0928i	0.553323	−	2.22697i
$411$	1.07838			0.0531925
$412$			31.9299i			1.57307i
$413$		−	13.3607i		−	0.657437i
$414$	−8.68035			−0.426616
$415$	4.24128	−	17.0700i	0.208196	−	0.837932i
$416$	12.9711			0.635959
$417$		−	10.2823i		−	0.503527i
$418$		−	6.68035i		−	0.326746i
$419$	6.15676			0.300777			0.150389	−	0.988627i	$-0.451948\pi$
$419$	6.15676			0.300777			0.150389	+	0.988627i	$0.451948\pi$
$420$	−21.8082	−	5.41855i	−1.06413	−	0.264398i
$421$	9.96880			0.485850			0.242925	−	0.970045i	$-0.421893\pi$
$421$	9.96880			0.485850			0.242925	+	0.970045i	$0.421893\pi$
$422$		−	18.3135i		−	0.891488i
$423$			2.73820i			0.133136i
$424$	−21.1773			−1.02846
$425$	−14.1568	+	26.7298i	−0.686704	+	1.29659i
$426$	−15.7009			−0.760709
$427$			54.4534i			2.63519i
$428$			30.5730i			1.47780i
$429$	1.70928			0.0825246
$430$	−14.7298	−	3.65983i	−0.710334	−	0.176493i
$431$	8.68035			0.418118			0.209059	−	0.977903i	$-0.432960\pi$
$431$	8.68035			0.418118			0.209059	+	0.977903i	$0.432960\pi$
$432$			2.07838i			0.0999960i
$433$		−	16.0000i		−	0.768911i	−0.923144	−	0.384455i	$-0.874389\pi$
$433$		−	16.0000i		−	0.768911i	0.923144	−	0.384455i	$-0.125611\pi$
$434$	51.0349			2.44975
$435$	2.83710	−	11.4186i	0.136029	−	0.547478i
$436$	−27.0928			−1.29751
$437$			12.3135i			0.589035i
$438$			13.8660i			0.662545i
$439$	−3.07838			−0.146923			−0.0734615	−	0.997298i	$-0.523405\pi$
$439$	−3.07838			−0.146923			−0.0734615	+	0.997298i	$0.523405\pi$
$440$	−0.829914	+	3.34017i	−0.0395646	+	0.159236i
$441$	6.75872			0.321844
$442$		−	22.4391i		−	1.06732i
$443$			29.2618i			1.39027i	0.718879	+	0.695135i	$0.244655\pi$
$443$			29.2618i			1.39027i	−0.718879	+	0.695135i	$0.755345\pi$
$444$	9.26180			0.439545
$445$	10.8950	+	2.70701i	0.516471	+	0.128324i
$446$	27.3028			1.29283
$447$		−	11.4186i		−	0.540079i
$448$		−	45.6658i		−	2.15751i
$449$	−10.6947			−0.504715			−0.252358	−	0.967634i	$-0.581206\pi$
$449$	−10.6947			−0.504715			−0.252358	+	0.967634i	$0.581206\pi$
$450$	−5.07838	+	9.58864i	−0.239397	+	0.452013i
$451$	9.57531			0.450884
$452$			1.34632i			0.0633254i
$453$		−	4.92162i		−	0.231238i
$454$	−9.18568			−0.431106
$455$	−13.7587	−	3.41855i	−0.645019	−	0.160264i
$456$	−4.73820			−0.221887
$457$		−	22.8554i		−	1.06913i	−0.845128	−	0.534564i	$-0.820476\pi$
$457$		−	22.8554i		−	1.06913i	0.845128	−	0.534564i	$-0.179524\pi$
$458$		−	56.8515i		−	2.65650i
$459$	6.04945			0.282364
$460$	5.84324	−	23.5174i	0.272443	−	1.09651i
$461$	−21.7731			−1.01407			−0.507037	−	0.861924i	$-0.669259\pi$
$461$	−21.7731			−1.01407			−0.507037	+	0.861924i	$0.669259\pi$
$462$		−	8.04945i		−	0.374494i
$463$			24.8950i			1.15697i	0.815694	+	0.578483i	$0.196355\pi$
$463$			24.8950i			1.15697i	−0.815694	+	0.578483i	$0.803645\pi$
$464$	10.9360			0.507691
$465$	3.41855	−	13.7587i	0.158531	−	0.638046i
$466$	−40.4307			−1.87291
$467$			19.2039i			0.888652i	0.895865	+	0.444326i	$0.146557\pi$
$467$			19.2039i			0.888652i	−0.895865	+	0.444326i	$0.853443\pi$
$468$		−	4.63090i		−	0.214063i
$469$	−6.83710			−0.315708
$470$	−12.8950	−	3.20394i	−0.594800	−	0.147787i
$471$	−3.41855			−0.157519
$472$			5.54411i			0.255188i
$473$		−	3.12783i		−	0.143818i
$474$	16.1568			0.742104
$475$	13.6020	+	7.20394i	0.624101	+	0.330539i
$476$	−60.7936			−2.78647
$477$		−	13.7587i		−	0.629969i
$478$			48.5113i			2.21886i
$479$	−9.47641			−0.432988			−0.216494	−	0.976284i	$-0.569462\pi$
$479$	−9.47641			−0.432988			−0.216494	+	0.976284i	$0.569462\pi$
$480$	−16.4680	−	4.09171i	−0.751658	−	0.186760i
$481$	5.84324			0.266429
$482$		−	19.9733i		−	0.909761i
$483$			14.8371i			0.675111i
$484$	−2.70928			−0.123149
$485$	9.16290	−	36.8781i	0.416066	−	1.67455i
$486$	2.17009			0.0984371
$487$		−	35.2039i		−	1.59524i	−0.603159	−	0.797621i	$-0.706091\pi$
$487$		−	35.2039i		−	1.59524i	0.603159	−	0.797621i	$-0.293909\pi$
$488$		−	22.5958i		−	1.02286i
$489$	−9.26180			−0.418833
$490$	−7.90829	+	31.8287i	−0.357260	+	1.43787i
$491$	−8.00000			−0.361035			−0.180517	−	0.983572i	$-0.557777\pi$
$491$	−8.00000			−0.361035			−0.180517	+	0.983572i	$0.557777\pi$
$492$		−	25.9421i		−	1.16956i
$493$		−	31.8310i		−	1.43359i
$494$	−11.4186			−0.513745
$495$	−2.17009	−	0.539189i	−0.0975381	−	0.0242347i
$496$	13.1773			0.591677
$497$			26.8371i			1.20381i
$498$		−	17.0700i		−	0.764924i
$499$	−26.1568			−1.17094			−0.585469	−	0.810695i	$-0.699089\pi$
$499$	−26.1568			−1.17094			−0.585469	+	0.810695i	$0.699089\pi$
$500$	−22.5597	−	20.2134i	−1.00890	−	0.903970i
$501$	7.55252			0.337422
$502$			48.0144i			2.14299i
$503$		−	28.2784i		−	1.26087i	−0.776241	−	0.630437i	$-0.782876\pi$
$503$		−	28.2784i		−	1.26087i	0.776241	−	0.630437i	$-0.217124\pi$
$504$	−5.70928			−0.254311
$505$	−41.0928	−	10.2101i	−1.82860	−	0.454343i
$506$	8.68035			0.385888
$507$			10.0784i			0.447596i
$508$			7.62475i			0.338294i
$509$	−8.47027			−0.375438			−0.187719	−	0.982223i	$-0.560109\pi$
$509$	−8.47027			−0.375438			−0.187719	+	0.982223i	$0.560109\pi$
$510$	−7.07838	+	28.4885i	−0.313436	+	1.26149i
$511$	23.7009			1.04846
$512$		−	22.1701i		−	0.979789i
$513$		−	3.07838i		−	0.135914i
$514$	−6.55479			−0.289119
$515$	6.35455	−	25.5753i	0.280015	−	1.12698i
$516$	−8.47414			−0.373053
$517$		−	2.73820i		−	0.120426i
$518$		−	27.5174i		−	1.20905i
$519$	−6.14834			−0.269882
$520$	5.70928	+	1.41855i	0.250368	+	0.0622076i
$521$	13.7009			0.600246			0.300123	−	0.953901i	$-0.402972\pi$
$521$	13.7009			0.600246			0.300123	+	0.953901i	$0.402972\pi$
$522$		−	11.4186i		−	0.499776i
$523$			24.4885i			1.07081i	0.844596	+	0.535404i	$0.179841\pi$
$523$			24.4885i			1.07081i	−0.844596	+	0.535404i	$0.820159\pi$
$524$	−23.5174			−1.02736
$525$	16.3896	+	8.68035i	0.715302	+	0.378841i
$526$	39.6925			1.73067
$527$		−	38.3545i		−	1.67075i
$528$		−	2.07838i		−	0.0904498i
$529$	7.00000			0.304348
$530$	64.7936	+	16.0989i	2.81445	+	0.699291i
$531$	−3.60197			−0.156312
$532$			30.9360i			1.34125i
$533$		−	16.3668i		−	0.708926i
$534$	10.8950			0.471471
$535$	6.08452	−	24.4885i	0.263057	−	1.05873i
$536$	2.83710			0.122544
$537$			6.15676i			0.265684i
$538$			66.3279i			2.85960i
$539$	−6.75872			−0.291119
$540$	−1.46081	+	5.87936i	−0.0628633	+	0.253007i
$541$	4.83710			0.207963			0.103982	−	0.994579i	$-0.466842\pi$
$541$	4.83710			0.207963			0.103982	+	0.994579i	$0.466842\pi$
$542$			43.5585i			1.87100i
$543$			14.5958i			0.626367i
$544$	−45.9071			−1.96825
$545$	21.7009	+	5.39189i	0.929563	+	0.230963i
$546$	−13.7587			−0.588819
$547$			30.5464i			1.30607i	0.757328	+	0.653034i	$0.226504\pi$
$547$			30.5464i			1.30607i	−0.757328	+	0.653034i	$0.773496\pi$
$548$			2.92162i			0.124806i
$549$	14.6803			0.626542
$550$	5.07838	−	9.58864i	0.216543	−	0.408861i
$551$	−16.1978			−0.690049
$552$		−	6.15676i		−	0.262049i
$553$		−	27.6163i		−	1.17437i
$554$	−1.65142			−0.0701620
$555$	−7.41855	−	1.84324i	−0.314900	−	0.0782414i
$556$	27.8576			1.18143
$557$			7.57918i			0.321140i	0.987024	+	0.160570i	$0.0513333\pi$
$557$			7.57918i			0.321140i	−0.987024	+	0.160570i	$0.948667\pi$
$558$		−	13.7587i		−	0.582453i
$559$	−5.34632			−0.226125
$560$	−4.15676	+	16.7298i	−0.175655	+	0.706963i
$561$	−6.04945			−0.255408
$562$		−	1.26180i		−	0.0532256i
$563$		−	14.1750i		−	0.597405i	−0.954346	−	0.298703i	$-0.903446\pi$
$563$		−	14.1750i		−	0.597405i	0.954346	−	0.298703i	$-0.0965539\pi$
$564$	−7.41855			−0.312377
$565$	0.267938	−	1.07838i	0.0112722	−	0.0453677i
$566$	−23.4680			−0.986434
$567$		−	3.70928i		−	0.155775i
$568$		−	11.1362i		−	0.467266i
$569$	14.7382			0.617858			0.308929	−	0.951085i	$-0.400030\pi$
$569$	14.7382			0.617858			0.308929	+	0.951085i	$0.400030\pi$
$570$	14.4969	+	3.60197i	0.607210	+	0.150870i
$571$	1.23513			0.0516887			0.0258444	−	0.999666i	$-0.491773\pi$
$571$	1.23513			0.0516887			0.0258444	+	0.999666i	$0.491773\pi$
$572$			4.63090i			0.193628i
$573$			5.84324i			0.244105i
$574$	−77.0759			−3.21709
$575$	−9.36069	+	17.6742i	−0.390368	+	0.737065i
$576$	−12.3112			−0.512968
$577$		−	28.9770i		−	1.20633i	−0.797617	−	0.603165i	$-0.793906\pi$
$577$		−	28.9770i		−	1.20633i	0.797617	−	0.603165i	$-0.206094\pi$
$578$			42.5246i			1.76879i
$579$	−2.02279			−0.0840641
$580$	30.9360	+	7.68649i	1.28455	+	0.319164i
$581$	−29.1773			−1.21048
$582$		−	36.8781i		−	1.52865i
$583$			13.7587i			0.569828i
$584$	−9.83483			−0.406968
$585$	−0.921622	+	3.70928i	−0.0381044	+	0.153360i
$586$	15.2846			0.631400
$587$			20.9939i			0.866509i	0.901272	+	0.433255i	$0.142635\pi$
$587$			20.9939i			0.866509i	−0.901272	+	0.433255i	$0.857365\pi$
$588$			18.3112i			0.755143i
$589$	−19.5174			−0.804202
$590$	4.21461	−	16.9627i	0.173513	−	0.698342i
$591$	17.8348			0.733627
$592$		−	7.10504i		−	0.292015i
$593$		−	23.8927i		−	0.981155i	−0.871397	−	0.490578i	$-0.836786\pi$
$593$		−	23.8927i		−	0.981155i	0.871397	−	0.490578i	$-0.163214\pi$
$594$	−2.17009			−0.0890397
$595$	48.6947	+	12.0989i	1.99629	+	0.496006i
$596$	30.9360			1.26719
$597$		−	25.6742i		−	1.05078i
$598$		−	14.8371i		−	0.606734i
$599$	45.6742			1.86620			0.933099	−	0.359620i	$-0.117094\pi$
$599$	45.6742			1.86620			0.933099	+	0.359620i	$0.117094\pi$
$600$	−6.80098	−	3.60197i	−0.277649	−	0.147050i
$601$	−16.2101			−0.661223			−0.330611	−	0.943767i	$-0.607255\pi$
$601$	−16.2101			−0.661223			−0.330611	+	0.943767i	$0.607255\pi$
$602$			25.1773i			1.02615i
$603$			1.84324i			0.0750627i
$604$	13.3340			0.542554
$605$	2.17009	+	0.539189i	0.0882266	+	0.0219211i
$606$	−41.0928			−1.66928
$607$		−	20.8020i		−	0.844328i	−0.906519	−	0.422164i	$-0.861271\pi$
$607$		−	20.8020i		−	0.844328i	0.906519	−	0.422164i	$-0.138729\pi$
$608$			23.3607i			0.947401i
$609$	−19.5174			−0.790887
$610$	−17.1773	+	69.1338i	−0.695488	+	2.79915i
$611$	−4.68035			−0.189347
$612$			16.3896i			0.662511i
$613$			15.3835i			0.621333i	0.950519	+	0.310666i	$0.100552\pi$
$613$			15.3835i			0.621333i	−0.950519	+	0.310666i	$0.899448\pi$
$614$	43.7815			1.76688
$615$	−5.16290	+	20.7792i	−0.208188	+	0.837900i
$616$	5.70928			0.230033
$617$		−	21.9733i		−	0.884613i	−0.896864	−	0.442307i	$-0.854160\pi$
$617$		−	21.9733i		−	0.884613i	0.896864	−	0.442307i	$-0.145840\pi$
$618$		−	25.5753i		−	1.02879i
$619$	−10.3935			−0.417750			−0.208875	−	0.977942i	$-0.566980\pi$
$619$	−10.3935			−0.417750			−0.208875	+	0.977942i	$0.566980\pi$
$620$	37.2762	+	9.26180i	1.49705	+	0.371963i
$621$	4.00000			0.160514
$622$		−	46.1711i		−	1.85129i
$623$		−	18.6225i		−	0.746094i
$624$	−3.55252			−0.142215
$625$	14.0472	+	20.6803i	0.561887	+	0.827214i
$626$	35.7321			1.42814
$627$			3.07838i			0.122939i
$628$		−	9.26180i		−	0.369586i
$629$	−20.6803			−0.824579
$630$	17.4680	+	4.34017i	0.695942	+	0.172917i
$631$	38.7214			1.54147			0.770737	−	0.637153i	$-0.219888\pi$
$631$	38.7214			1.54147			0.770737	+	0.637153i	$0.219888\pi$
$632$			11.4596i			0.455838i
$633$			8.43907i			0.335423i
$634$	48.1133			1.91082
$635$	1.51745	−	6.10731i	0.0602181	−	0.242361i
$636$	37.2762			1.47810
$637$			11.5525i			0.457728i
$638$			11.4186i			0.452065i
$639$	7.23513			0.286217
$640$	6.22180	−	25.0410i	0.245938	−	0.989834i
$641$	24.2245			0.956808			0.478404	−	0.878140i	$-0.341215\pi$
$641$	24.2245			0.956808			0.478404	+	0.878140i	$0.341215\pi$
$642$		−	24.4885i		−	0.966485i
$643$		−	25.8888i		−	1.02096i	−0.859891	−	0.510478i	$-0.829469\pi$
$643$		−	25.8888i		−	1.02096i	0.859891	−	0.510478i	$-0.170531\pi$
$644$	−40.1978			−1.58401
$645$	6.78765	+	1.68649i	0.267264	+	0.0664054i
$646$	40.4124			1.59000
$647$			0.581449i			0.0228591i	0.999935	+	0.0114296i	$0.00363822\pi$
$647$			0.581449i			0.0228591i	−0.999935	+	0.0114296i	$0.996362\pi$
$648$			1.53919i			0.0604650i
$649$	3.60197			0.141390
$650$	−16.3896	−	8.68035i	−0.642854	−	0.340471i
$651$	−23.5174			−0.921721
$652$		−	25.0928i		−	0.982708i
$653$			37.0082i			1.44824i	0.689672	+	0.724122i	$0.257755\pi$
$653$			37.0082i			1.44824i	−0.689672	+	0.724122i	$0.742245\pi$
$654$	21.7009			0.848571
$655$	18.8371	+	4.68035i	0.736026	+	0.182876i
$656$	−19.9011			−0.777008
$657$		−	6.38962i		−	0.249283i
$658$			22.0410i			0.859249i
$659$	−30.5236			−1.18903			−0.594515	−	0.804084i	$-0.702656\pi$
$659$	−30.5236			−1.18903			−0.594515	+	0.804084i	$0.702656\pi$
$660$	1.46081	−	5.87936i	0.0568620	−	0.228854i
$661$	5.88428			0.228872			0.114436	−	0.993431i	$-0.463494\pi$
$661$	5.88428			0.228872			0.114436	+	0.993431i	$0.463494\pi$
$662$			13.7587i			0.534748i
$663$			10.3402i			0.401579i
$664$	12.1073			0.469855
$665$	6.15676	−	24.7792i	0.238749	−	0.960898i
$666$	−7.41855			−0.287463
$667$		−	21.0472i		−	0.814950i
$668$			20.4619i			0.791693i
$669$	−12.5814			−0.486427
$670$	−8.68035	−	2.15676i	−0.335351	−	0.0833227i
$671$	−14.6803			−0.566728
$672$			28.1483i			1.08585i
$673$		−	26.9711i		−	1.03966i	−0.854270	−	0.519829i	$-0.825996\pi$
$673$		−	26.9711i		−	1.03966i	0.854270	−	0.519829i	$-0.174004\pi$
$674$	−6.91321			−0.266287
$675$	2.34017	−	4.41855i	0.0900733	−	0.170070i
$676$	−27.3051			−1.05020
$677$			17.9506i			0.689896i	0.938622	+	0.344948i	$0.112103\pi$
$677$			17.9506i			0.689896i	−0.938622	+	0.344948i	$0.887897\pi$
$678$		−	1.07838i		−	0.0414148i
$679$	−63.0349			−2.41906
$680$	−20.2062	−	5.02052i	−0.774873	−	0.192528i
$681$	4.23287			0.162204
$682$			13.7587i			0.526849i
$683$			8.77924i			0.335928i	0.985793	+	0.167964i	$0.0537193\pi$
$683$			8.77924i			0.335928i	−0.985793	+	0.167964i	$0.946281\pi$
$684$	8.34017			0.318894
$685$	0.581449	−	2.34017i	0.0222160	−	0.0894134i
$686$	−1.94214			−0.0741513
$687$			26.1978i			0.999508i
$688$			6.50080i			0.247841i
$689$	23.5174			0.895943
$690$	−4.68035	+	18.8371i	−0.178178	+	0.717116i
$691$	−14.7214			−0.560028			−0.280014	−	0.959996i	$-0.590339\pi$
$691$	−14.7214			−0.560028			−0.280014	+	0.959996i	$0.590339\pi$
$692$		−	16.6576i		−	0.633225i
$693$			3.70928i			0.140904i
$694$	11.7093			0.444478
$695$	−22.3135	−	5.54411i	−0.846400	−	0.210300i
$696$	8.09890			0.306988
$697$			57.9253i			2.19408i
$698$		−	34.0144i		−	1.28746i
$699$	18.6309			0.704685
$700$	−23.5174	+	44.4040i	−0.888876	+	1.67831i
$701$	−7.10504			−0.268354			−0.134177	−	0.990957i	$-0.542839\pi$
$701$	−7.10504			−0.268354			−0.134177	+	0.990957i	$0.542839\pi$
$702$			3.70928i			0.139998i
$703$			10.5236i			0.396905i
$704$	12.3112			0.463997
$705$	5.94214	+	1.47641i	0.223794	+	0.0556048i
$706$	−12.4969			−0.470328
$707$			70.2388i			2.64160i
$708$		−	9.75872i		−	0.366755i
$709$	34.1666			1.28315			0.641577	−	0.767059i	$-0.278281\pi$
$709$	34.1666			1.28315			0.641577	+	0.767059i	$0.278281\pi$
$710$	−8.46573	+	34.0722i	−0.317713	+	1.27871i
$711$	−7.44521			−0.279217
$712$			7.72753i			0.289601i
$713$		−	25.3607i		−	0.949765i
$714$	48.6947			1.82235
$715$	0.921622	−	3.70928i	0.0344667	−	0.138719i
$716$	−16.6803			−0.623374
$717$		−	22.3545i		−	0.834846i
$718$		−	22.8371i		−	0.852273i
$719$	−31.8310			−1.18709			−0.593547	−	0.804799i	$-0.702273\pi$
$719$	−31.8310			−1.18709			−0.593547	+	0.804799i	$0.702273\pi$
$720$	4.51026	+	1.12064i	0.168087	+	0.0417637i
$721$	−43.7152			−1.62804
$722$			20.6670i			0.769147i
$723$			9.20394i			0.342298i
$724$	−39.5441			−1.46965
$725$	−23.2495	−	12.3135i	−0.863465	−	0.457312i
$726$	2.17009			0.0805395
$727$		−	5.16290i		−	0.191481i	−0.995406	−	0.0957407i	$-0.969478\pi$
$727$		−	5.16290i		−	0.191481i	0.995406	−	0.0957407i	$-0.0305219\pi$
$728$		−	9.75872i		−	0.361682i
$729$	−1.00000			−0.0370370
$730$	30.0905	+	7.47641i	1.11370	+	0.276714i
$731$	18.9216			0.699841
$732$			39.7731i			1.47006i
$733$		−	36.4475i		−	1.34622i	−0.739543	−	0.673109i	$-0.764958\pi$
$733$		−	36.4475i		−	1.34622i	0.739543	−	0.673109i	$-0.235042\pi$
$734$	−19.3028			−0.712481
$735$	3.64423	−	14.6670i	0.134419	−	0.541001i
$736$	−30.3545			−1.11888
$737$		−	1.84324i		−	0.0678968i
$738$			20.7792i			0.764894i
$739$	−25.4329			−0.935565			−0.467783	−	0.883844i	$-0.654947\pi$
$739$	−25.4329			−0.935565			−0.467783	+	0.883844i	$0.654947\pi$
$740$	4.99386	−	20.0989i	0.183578	−	0.738850i
$741$	5.26180			0.193297
$742$		−	110.750i		−	4.06577i
$743$			10.1217i			0.371329i	0.982613	+	0.185664i	$0.0594437\pi$
$743$			10.1217i			0.371329i	−0.982613	+	0.185664i	$0.940556\pi$
$744$	9.75872			0.357772
$745$	−24.7792	−	6.15676i	−0.907841	−	0.225566i
$746$	−50.2784			−1.84082
$747$			7.86603i			0.287803i
$748$		−	16.3896i		−	0.599264i
$749$	−41.8576			−1.52944
$750$	18.0700	+	16.1906i	0.659822	+	0.591197i
$751$	10.4703			0.382065			0.191033	−	0.981584i	$-0.438816\pi$
$751$	10.4703			0.382065			0.191033	+	0.981584i	$0.438816\pi$
$752$			5.69102i			0.207530i
$753$		−	22.1256i		−	0.806300i
$754$	19.5174			0.710784
$755$	−10.6803	−	2.65368i	−0.388698	−	0.0965774i
$756$	10.0494			0.365495
$757$			6.73820i			0.244904i	0.992474	+	0.122452i	$0.0390758\pi$
$757$			6.73820i			0.244904i	−0.992474	+	0.122452i	$0.960924\pi$
$758$		−	25.6742i		−	0.932529i
$759$	−4.00000			−0.145191
$760$	−2.55479	+	10.2823i	−0.0926719	+	0.372979i
$761$	−5.57531			−0.202105			−0.101052	−	0.994881i	$-0.532221\pi$
$761$	−5.57531			−0.202105			−0.101052	+	0.994881i	$0.532221\pi$
$762$		−	6.10731i		−	0.221244i
$763$		−	37.0928i		−	1.34285i
$764$	−15.8310			−0.572744
$765$	3.26180	−	13.1278i	0.117930	−	0.474638i
$766$	56.2967			2.03408
$767$		−	6.15676i		−	0.222308i
$768$		−	0.418551i		−	0.0151031i
$769$	11.5297			0.415773			0.207886	−	0.978153i	$-0.433342\pi$
$769$	11.5297			0.415773			0.207886	+	0.978153i	$0.433342\pi$
$770$	−17.4680	−	4.34017i	−0.629503	−	0.156409i
$771$	3.02052			0.108781
$772$		−	5.48029i		−	0.197240i
$773$		−	28.7480i		−	1.03400i	−0.855987	−	0.516998i	$-0.827050\pi$
$773$		−	28.7480i		−	1.03400i	0.855987	−	0.516998i	$-0.172950\pi$
$774$	6.78765			0.243977
$775$	−28.0144	−	14.8371i	−1.00631	−	0.532964i
$776$	26.1568			0.938973
$777$			12.6803i			0.454905i
$778$			2.18342i			0.0782793i
$779$	29.4764			1.05610
$780$	−10.0494	−	2.49693i	−0.359828	−	0.0894044i
$781$	−7.23513			−0.258893
$782$			52.5113i			1.87780i
$783$			5.26180i			0.188041i
$784$	14.0472			0.501685
$785$	−1.84324	+	7.41855i	−0.0657882	+	0.264779i
$786$	18.8371			0.671897
$787$			13.4536i			0.479570i	0.970826	+	0.239785i	$0.0770769\pi$
$787$			13.4536i			0.479570i	−0.970826	+	0.239785i	$0.922923\pi$
$788$			48.3195i			1.72131i
$789$	−18.2907			−0.651167
$790$	8.71154	−	35.0616i	0.309943	−	1.24743i
$791$	−1.84324			−0.0655382
$792$		−	1.53919i		−	0.0546927i
$793$			25.0928i			0.891070i
$794$	−75.3484			−2.67401
$795$	−29.8576	−	7.41855i	−1.05894	−	0.263109i
$796$	69.5585			2.46544
$797$			48.3279i			1.71186i	0.517090	+	0.855931i	$0.327015\pi$
$797$			48.3279i			1.71186i	−0.517090	+	0.855931i	$0.672985\pi$
$798$		−	24.7792i		−	0.877176i
$799$	16.5646			0.586014
$800$	−17.7587	+	33.5308i	−0.627866	+	1.18549i
$801$	−5.02052			−0.177391
$802$			28.2557i			0.997742i
$803$			6.38962i			0.225485i
$804$	−4.99386			−0.176120
$805$	32.1978	+	8.00000i	1.13482	+	0.281963i
$806$	23.5174			0.828367
$807$		−	30.5646i		−	1.07593i
$808$		−	29.1461i		−	1.02536i
$809$	43.8141			1.54042			0.770212	−	0.637789i	$-0.220151\pi$
$809$	43.8141			1.54042			0.770212	+	0.637789i	$0.220151\pi$
$810$	1.17009	−	4.70928i	0.0411126	−	0.165467i
$811$	−47.2762			−1.66009			−0.830045	−	0.557696i	$-0.811686\pi$
$811$	−47.2762			−1.66009			−0.830045	+	0.557696i	$0.811686\pi$
$812$		−	52.8781i		−	1.85566i
$813$		−	20.0722i		−	0.703964i
$814$	7.41855			0.260020
$815$	−4.99386	+	20.0989i	−0.174927	+	0.704034i
$816$	12.5730			0.440144
$817$		−	9.62863i		−	0.336863i
$818$		−	64.0554i		−	2.23965i
$819$	6.34017			0.221544
$820$	−56.2967	−	13.9877i	−1.96597	−	0.488472i
$821$	−3.30283			−0.115270			−0.0576348	−	0.998338i	$-0.518356\pi$
$821$	−3.30283			−0.115270			−0.0576348	+	0.998338i	$0.518356\pi$
$822$		−	2.34017i		−	0.0816229i
$823$			11.0517i			0.385239i	0.981274	+	0.192619i	$0.0616982\pi$
$823$			11.0517i			0.385239i	−0.981274	+	0.192619i	$0.938302\pi$
$824$	18.1399			0.631935
$825$	−2.34017	+	4.41855i	−0.0814744	+	0.153834i
$826$	−28.9939			−1.00883
$827$		−	5.12783i		−	0.178312i	−0.996018	−	0.0891560i	$-0.971583\pi$
$827$		−	5.12783i		−	0.178312i	0.996018	−	0.0891560i	$-0.0284170\pi$
$828$			10.8371i			0.376615i
$829$	6.39803			0.222213			0.111106	−	0.993809i	$-0.464561\pi$
$829$	6.39803			0.222213			0.111106	+	0.993809i	$0.464561\pi$
$830$	−37.0433	−	9.20394i	−1.28579	−	0.319473i
$831$	0.760991			0.0263985
$832$		−	21.0433i		−	0.729545i
$833$		−	40.8865i		−	1.41663i
$834$	−22.3135			−0.772654
$835$	4.07223	−	16.3896i	0.140925	−	0.567186i
$836$	−8.34017			−0.288451
$837$			6.34017i			0.219148i
$838$		−	13.3607i		−	0.461537i
$839$	22.0722			0.762018			0.381009	−	0.924571i	$-0.375577\pi$
$839$	22.0722			0.762018			0.381009	+	0.924571i	$0.375577\pi$
$840$	−3.07838	+	12.3896i	−0.106214	+	0.427483i
$841$	−1.31351			−0.0452935
$842$		−	21.6332i		−	0.745528i
$843$			0.581449i			0.0200262i
$844$	−22.8638			−0.787003
$845$	21.8710	+	5.43415i	0.752384	+	0.186940i
$846$	5.94214			0.204295
$847$		−	3.70928i		−	0.127452i
$848$		−	28.5958i		−	0.981985i
$849$	10.8143			0.371146
$850$	58.0060	+	30.7214i	1.98959	+	1.05373i
$851$	−13.6742			−0.468746
$852$			19.6020i			0.671552i
$853$		−	8.76099i		−	0.299971i	−0.988688	−	0.149985i	$-0.952077\pi$
$853$		−	8.76099i		−	0.299971i	0.988688	−	0.149985i	$-0.0479226\pi$
$854$	118.169			4.04365
$855$	−6.68035	−	1.65983i	−0.228463	−	0.0567649i
$856$	17.3691			0.593664
$857$			36.5730i			1.24931i	0.780900	+	0.624656i	$0.214761\pi$
$857$			36.5730i			1.24931i	−0.780900	+	0.624656i	$0.785239\pi$
$858$		−	3.70928i		−	0.126633i
$859$	49.6886			1.69535			0.847676	−	0.530514i	$-0.178001\pi$
$859$	49.6886			1.69535			0.847676	+	0.530514i	$0.178001\pi$
$860$	−4.56916	+	18.3896i	−0.155807	+	0.627081i
$861$	35.5174			1.21043
$862$		−	18.8371i		−	0.641594i
$863$		−	34.1399i		−	1.16214i	−0.813855	−	0.581068i	$-0.802635\pi$
$863$		−	34.1399i		−	1.16214i	0.813855	−	0.581068i	$-0.197365\pi$
$864$	7.58864			0.258171
$865$	−3.31512	+	13.3424i	−0.112717	+	0.453657i
$866$	−34.7214			−1.17988
$867$		−	19.5958i		−	0.665509i
$868$		−	63.7152i		−	2.16264i
$869$	7.44521			0.252562
$870$	−24.7792	−	6.15676i	−0.840095	−	0.208734i
$871$	−3.15061			−0.106754
$872$			15.3919i			0.521235i
$873$			16.9939i			0.575155i
$874$	26.7214			0.903864
$875$	27.6742	−	30.8865i	0.935559	−	1.04416i
$876$	17.3112			0.584893
$877$			43.5357i			1.47010i	0.678015	+	0.735048i	$0.262840\pi$
$877$			43.5357i			1.47010i	−0.678015	+	0.735048i	$0.737160\pi$
$878$			6.68035i			0.225451i
$879$	−7.04331			−0.237565
$880$	−4.51026	−	1.12064i	−0.152041	−	0.0377767i
$881$	−8.52359			−0.287167			−0.143584	−	0.989638i	$-0.545863\pi$
$881$	−8.52359			−0.287167			−0.143584	+	0.989638i	$0.545863\pi$
$882$		−	14.6670i		−	0.493864i
$883$			43.0349i			1.44824i	0.689674	+	0.724120i	$0.257754\pi$
$883$			43.0349i			1.44824i	−0.689674	+	0.724120i	$0.742246\pi$
$884$	−28.0144			−0.942225
$885$	−1.94214	+	7.81658i	−0.0652844	+	0.262752i
$886$	63.5006			2.13335
$887$		−	17.0289i		−	0.571775i	−0.958263	−	0.285888i	$-0.907712\pi$
$887$		−	17.0289i		−	0.571775i	0.958263	−	0.285888i	$-0.0922884\pi$
$888$		−	5.26180i		−	0.176574i
$889$	−10.4391			−0.350115
$890$	5.87444	−	23.6430i	0.196912	−	0.792515i
$891$	1.00000			0.0335013
$892$		−	34.0866i		−	1.14130i
$893$		−	8.42923i		−	0.282073i
$894$	−24.7792			−0.828742
$895$	13.3607	+	3.31965i	0.446599	+	0.110964i
$896$	−42.8020			−1.42992
$897$			6.83710i			0.228284i
$898$			23.2085i			0.774477i
$899$	33.3607			1.11264
$900$	11.9711	+	6.34017i	0.399036	+	0.211339i
$901$	−83.2327			−2.77288
$902$		−	20.7792i		−	0.691873i
$903$		−	11.6020i		−	0.386089i
$904$	0.764867			0.0254391
$905$	31.6742	+	7.86991i	1.05289	+	0.261605i
$906$	−10.6803			−0.354831
$907$		−	6.13993i		−	0.203873i	−0.994791	−	0.101937i	$-0.967496\pi$
$907$		−	6.13993i		−	0.203873i	0.994791	−	0.101937i	$-0.0325039\pi$
$908$			11.4680i			0.380579i
$909$	18.9360			0.628067
$910$	−7.41855	+	29.8576i	−0.245923	+	0.989770i
$911$	53.8720			1.78486			0.892429	−	0.451187i	$-0.148999\pi$
$911$	53.8720			1.78486			0.892429	+	0.451187i	$0.148999\pi$
$912$		−	6.39803i		−	0.211860i
$913$		−	7.86603i		−	0.260328i
$914$	−49.5981			−1.64056
$915$	7.91548	−	31.8576i	0.261678	−	1.05318i
$916$	−70.9770			−2.34515
$917$		−	32.1978i		−	1.06326i
$918$		−	13.1278i		−	0.433283i
$919$	48.2700			1.59228			0.796141	−	0.605112i	$-0.206872\pi$
$919$	48.2700			1.59228			0.796141	+	0.605112i	$0.206872\pi$
$920$	−13.3607	−	3.31965i	−0.440489	−	0.109446i
$921$	−20.1750			−0.664789
$922$			47.2495i			1.55608i
$923$			12.3668i			0.407059i
$924$	−10.0494			−0.330603
$925$	−8.00000	+	15.1050i	−0.263038	+	0.496651i
$926$	54.0242			1.77535
$927$			11.7854i			0.387083i
$928$		−	39.9299i		−	1.31076i
$929$	−4.10343			−0.134629			−0.0673146	−	0.997732i	$-0.521443\pi$
$929$	−4.10343			−0.134629			−0.0673146	+	0.997732i	$0.521443\pi$
$930$	−29.8576	−	7.41855i	−0.979070	−	0.243264i
$931$	−20.8059			−0.681886
$932$			50.4762i			1.65340i
$933$			21.2762i			0.696551i
$934$	41.6742			1.36362
$935$	−3.26180	+	13.1278i	−0.106672	+	0.429326i
$936$	−2.63090			−0.0859936
$937$			38.5341i			1.25885i	0.777060	+	0.629427i	$0.216710\pi$
$937$			38.5341i			1.25885i	−0.777060	+	0.629427i	$0.783290\pi$
$938$			14.8371i			0.484449i
$939$	−16.4657			−0.537339
$940$	−4.00000	+	16.0989i	−0.130466	+	0.525088i
$941$	14.6849			0.478713			0.239357	−	0.970932i	$-0.423063\pi$
$941$	14.6849			0.478713			0.239357	+	0.970932i	$0.423063\pi$
$942$			7.41855i			0.241709i
$943$			38.3012i			1.24726i
$944$	−7.48625			−0.243657
$945$	−8.04945	−	2.00000i	−0.261849	−	0.0650600i
$946$	−6.78765			−0.220686
$947$		−	6.05786i		−	0.196854i	−0.995144	−	0.0984270i	$-0.968619\pi$
$947$		−	6.05786i		−	0.196854i	0.995144	−	0.0984270i	$-0.0313811\pi$
$948$		−	20.1711i		−	0.655128i
$949$	10.9216			0.354531
$950$	15.6332	−	29.5174i	0.507207	−	0.957672i
$951$	−22.1711			−0.718948
$952$			34.5380i			1.11938i
$953$			40.1438i			1.30039i	0.759769	+	0.650193i	$0.225312\pi$
$953$			40.1438i			1.30039i	−0.759769	+	0.650193i	$0.774688\pi$
$954$	−29.8576			−0.966676
$955$	12.6803	+	3.15061i	0.410326	+	0.101951i
$956$	60.5646			1.95880
$957$		−	5.26180i		−	0.170090i
$958$			20.5646i			0.664413i
$959$	−4.00000			−0.129167
$960$	−6.63809	+	26.7165i	−0.214243	+	0.862270i
$961$	9.19779			0.296703
$962$		−	12.6803i		−	0.408831i
$963$			11.2846i			0.363641i
$964$	−24.9360			−0.803134
$965$	−1.09066	+	4.38962i	−0.0351097	+	0.141307i
$966$	32.1978			1.03595
$967$			50.6285i			1.62810i	0.580794	+	0.814051i	$0.302742\pi$
$967$			50.6285i			1.62810i	−0.580794	+	0.814051i	$0.697258\pi$
$968$			1.53919i			0.0494714i
$969$	−18.6225			−0.598240
$970$	−80.0288	−	19.8843i	−2.56957	−	0.638446i
$971$	−6.69263			−0.214777			−0.107388	−	0.994217i	$-0.534249\pi$
$971$	−6.69263			−0.214777			−0.107388	+	0.994217i	$0.534249\pi$
$972$		−	2.70928i		−	0.0869000i
$973$			38.1399i			1.22271i
$974$	−76.3956			−2.44787
$975$	7.55252	+	4.00000i	0.241874	+	0.128103i
$976$	30.5113			0.976643
$977$		−	38.5835i		−	1.23440i	−0.786808	−	0.617198i	$-0.788268\pi$
$977$		−	38.5835i		−	1.23440i	0.786808	−	0.617198i	$-0.211732\pi$
$978$			20.0989i			0.642692i
$979$	5.02052			0.160456
$980$	39.7370	+	9.87322i	1.26935	+	0.315388i
$981$	−10.0000			−0.319275
$982$			17.3607i			0.554002i
$983$		−	28.4657i		−	0.907916i	−0.891023	−	0.453958i	$-0.850012\pi$
$983$		−	28.4657i		−	0.907916i	0.891023	−	0.453958i	$-0.149988\pi$
$984$	−14.7382			−0.469837
$985$	9.61634	−	38.7031i	0.306402	−	1.23318i
$986$	−69.0759			−2.19983
$987$		−	10.1568i		−	0.323293i
$988$			14.2557i			0.453533i
$989$	12.5113			0.397836
$990$	−1.17009	+	4.70928i	−0.0371878	+	0.149671i
$991$	2.65368			0.0842970			0.0421485	−	0.999111i	$-0.486580\pi$
$991$	2.65368			0.0842970			0.0421485	+	0.999111i	$0.486580\pi$
$992$		−	48.1133i		−	1.52760i
$993$		−	6.34017i		−	0.201199i
$994$	58.2388			1.84722
$995$	−55.7152	−	13.8432i	−1.76629	−	0.438860i
$996$	−21.3112			−0.675273
$997$			8.08065i			0.255917i	0.991780	+	0.127958i	$0.0408424\pi$
$997$			8.08065i			0.255917i	−0.991780	+	0.127958i	$0.959158\pi$
$998$			56.7624i			1.79678i
$999$	3.41855			0.108158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.c.b.34.1	✓	6
3.2	odd	2		495.2.c.e.199.6		6
4.3	odd	2		2640.2.d.h.529.3		6
5.2	odd	4		825.2.a.l.1.3		3
5.3	odd	4		825.2.a.j.1.1		3
5.4	even	2	inner	165.2.c.b.34.6	yes	6
11.10	odd	2		1815.2.c.e.364.6		6
15.2	even	4		2475.2.a.ba.1.1		3
15.8	even	4		2475.2.a.bc.1.3		3
15.14	odd	2		495.2.c.e.199.1		6
20.19	odd	2		2640.2.d.h.529.6		6
55.32	even	4		9075.2.a.cg.1.1		3
55.43	even	4		9075.2.a.ch.1.3		3
55.54	odd	2		1815.2.c.e.364.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.c.b.34.1	✓	6	1.1	even	1	trivial
165.2.c.b.34.6	yes	6	5.4	even	2	inner
495.2.c.e.199.1		6	15.14	odd	2
495.2.c.e.199.6		6	3.2	odd	2
825.2.a.j.1.1		3	5.3	odd	4
825.2.a.l.1.3		3	5.2	odd	4
1815.2.c.e.364.1		6	55.54	odd	2
1815.2.c.e.364.6		6	11.10	odd	2
2475.2.a.ba.1.1		3	15.2	even	4
2475.2.a.bc.1.3		3	15.8	even	4
2640.2.d.h.529.3		6	4.3	odd	2
2640.2.d.h.529.6		6	20.19	odd	2
9075.2.a.cg.1.1		3	55.32	even	4
9075.2.a.ch.1.3		3	55.43	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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.17009i q^{2} +1.00000i q^{3} -2.70928 q^{4} +(2.17009 + 0.539189i) q^{5} +2.17009 q^{6} -3.70928i q^{7} +1.53919i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.17009i q^{2} +1.00000i q^{3} -2.70928 q^{4} +(2.17009 + 0.539189i) q^{5} +2.17009 q^{6} -3.70928i q^{7} +1.53919i q^{8} -1.00000 q^{9} +(1.17009 - 4.70928i) q^{10} +1.00000 q^{11} -2.70928i q^{12} -1.70928i q^{13} -8.04945 q^{14} +(-0.539189 + 2.17009i) q^{15} -2.07838 q^{16} +6.04945i q^{17} +2.17009i q^{18} +3.07838 q^{19} +(-5.87936 - 1.46081i) q^{20} +3.70928 q^{21} -2.17009i q^{22} +4.00000i q^{23} -1.53919 q^{24} +(4.41855 + 2.34017i) q^{25} -3.70928 q^{26} -1.00000i q^{27} +10.0494i q^{28} -5.26180 q^{29} +(4.70928 + 1.17009i) q^{30} -6.34017 q^{31} +7.58864i q^{32} +1.00000i q^{33} +13.1278 q^{34} +(2.00000 - 8.04945i) q^{35} +2.70928 q^{36} +3.41855i q^{37} -6.68035i q^{38} +1.70928 q^{39} +(-0.829914 + 3.34017i) q^{40} +9.57531 q^{41} -8.04945i q^{42} -3.12783i q^{43} -2.70928 q^{44} +(-2.17009 - 0.539189i) q^{45} +8.68035 q^{46} -2.73820i q^{47} -2.07838i q^{48} -6.75872 q^{49} +(5.07838 - 9.58864i) q^{50} -6.04945 q^{51} +4.63090i q^{52} +13.7587i q^{53} -2.17009 q^{54} +(2.17009 + 0.539189i) q^{55} +5.70928 q^{56} +3.07838i q^{57} +11.4186i q^{58} +3.60197 q^{59} +(1.46081 - 5.87936i) q^{60} -14.6803 q^{61} +13.7587i q^{62} +3.70928i q^{63} +12.3112 q^{64} +(0.921622 - 3.70928i) q^{65} +2.17009 q^{66} -1.84324i q^{67} -16.3896i q^{68} -4.00000 q^{69} +(-17.4680 - 4.34017i) q^{70} -7.23513 q^{71} -1.53919i q^{72} +6.38962i q^{73} +7.41855 q^{74} +(-2.34017 + 4.41855i) q^{75} -8.34017 q^{76} -3.70928i q^{77} -3.70928i q^{78} +7.44521 q^{79} +(-4.51026 - 1.12064i) q^{80} +1.00000 q^{81} -20.7792i q^{82} -7.86603i q^{83} -10.0494 q^{84} +(-3.26180 + 13.1278i) q^{85} -6.78765 q^{86} -5.26180i q^{87} +1.53919i q^{88} +5.02052 q^{89} +(-1.17009 + 4.70928i) q^{90} -6.34017 q^{91} -10.8371i q^{92} -6.34017i q^{93} -5.94214 q^{94} +(6.68035 + 1.65983i) q^{95} -7.58864 q^{96} -16.9939i q^{97} +14.6670i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 2 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^9	\( 6 q - 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{9} - 4 q^{10} + 6 q^{11} - 12 q^{14} - 6 q^{16} + 12 q^{19} - 10 q^{20} + 8 q^{21} - 6 q^{24} - 2 q^{25} - 8 q^{26} - 16 q^{29} + 14 q^{30} - 16 q^{31} + 36 q^{34} + 12 q^{35} + 2 q^{36} - 4 q^{39} - 16 q^{40} + 16 q^{41} - 2 q^{44} - 2 q^{45} + 8 q^{46} + 10 q^{49} + 24 q^{50} - 2 q^{54} + 2 q^{55} + 20 q^{56} - 16 q^{59} + 12 q^{60} - 44 q^{61} + 22 q^{64} + 12 q^{65} + 2 q^{66} - 24 q^{69} - 40 q^{70} - 24 q^{71} + 16 q^{74} + 8 q^{75} - 28 q^{76} + 20 q^{79} + 6 q^{80} + 6 q^{81} - 24 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} + 4 q^{90} - 16 q^{91} + 24 q^{94} - 4 q^{95} - 6 q^{96} - 6 q^{99}+O(q^{100}) \) 6 * q - 2 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^9 - 4 * q^10 + 6 * q^11 - 12 * q^14 - 6 * q^16 + 12 * q^19 - 10 * q^20 + 8 * q^21 - 6 * q^24 - 2 * q^25 - 8 * q^26 - 16 * q^29 + 14 * q^30 - 16 * q^31 + 36 * q^34 + 12 * q^35 + 2 * q^36 - 4 * q^39 - 16 * q^40 + 16 * q^41 - 2 * q^44 - 2 * q^45 + 8 * q^46 + 10 * q^49 + 24 * q^50 - 2 * q^54 + 2 * q^55 + 20 * q^56 - 16 * q^59 + 12 * q^60 - 44 * q^61 + 22 * q^64 + 12 * q^65 + 2 * q^66 - 24 * q^69 - 40 * q^70 - 24 * q^71 + 16 * q^74 + 8 * q^75 - 28 * q^76 + 20 * q^79 + 6 * q^80 + 6 * q^81 - 24 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 + 4 * q^90 - 16 * q^91 + 24 * q^94 - 4 * q^95 - 6 * q^96 - 6 * q^99

Introduction

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