LMFDB - Embedded newform 138.2.e.c.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(13,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("138.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.e (of order $11$, degree $10$, 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:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			49.1
Root			$0.142315 + 0.989821i$ of defining polynomial
Character	$\chi$	$=$	138.49
Dual form			138.2.e.c.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.59283 - 1.83823i) q^{5} +(0.959493 + 0.281733i) q^{6} +(1.56130 - 1.00339i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.59283 - 1.83823i) q^{5} +(0.959493 + 0.281733i) q^{6} +(1.56130 - 1.00339i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(2.04620 + 1.31501i) q^{10} +(-0.790323 + 5.49682i) q^{11} +(-0.142315 + 0.989821i) q^{12} +(0.966031 + 0.620830i) q^{13} +(1.21537 + 1.40261i) q^{14} +(-1.01042 - 2.21252i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-7.20366 - 2.11519i) q^{17} +(0.654861 - 0.755750i) q^{18} +(4.29408 - 1.26086i) q^{19} +(-1.01042 + 2.21252i) q^{20} +(-0.264125 - 1.83703i) q^{21} -5.55334 q^{22} +(-2.45093 + 4.12225i) q^{23} -1.00000 q^{24} +(-0.130388 - 0.906870i) q^{25} +(-0.477031 + 1.04455i) q^{26} +(-0.959493 + 0.281733i) q^{27} +(-1.21537 + 1.40261i) q^{28} +(-2.81913 - 0.827771i) q^{29} +(2.04620 - 1.31501i) q^{30} +(-0.863019 - 1.88975i) q^{31} +(0.654861 + 0.755750i) q^{32} +(4.67177 + 3.00236i) q^{33} +(1.06847 - 7.43136i) q^{34} +(0.642438 - 4.46825i) q^{35} +(0.841254 + 0.540641i) q^{36} +(-5.06718 - 5.84784i) q^{37} +(1.85913 + 4.07093i) q^{38} +(0.966031 - 0.620830i) q^{39} +(-2.33380 - 0.685265i) q^{40} +(-0.450833 + 0.520289i) q^{41} +(1.78074 - 0.522874i) q^{42} +(-3.55862 + 7.79229i) q^{43} +(-0.790323 - 5.49682i) q^{44} -2.43232 q^{45} +(-4.42909 - 1.83933i) q^{46} +7.09992 q^{47} +(-0.142315 - 0.989821i) q^{48} +(-1.47703 + 3.23425i) q^{49} +(0.879083 - 0.258122i) q^{50} +(-4.91655 + 5.67400i) q^{51} +(-1.10181 - 0.323520i) q^{52} +(4.53311 - 2.91326i) q^{53} +(-0.415415 - 0.909632i) q^{54} +(8.84555 + 10.2083i) q^{55} +(-1.56130 - 1.00339i) q^{56} +(0.636911 - 4.42981i) q^{57} +(0.418141 - 2.90824i) q^{58} +(-3.39399 - 2.18119i) q^{59} +(1.59283 + 1.83823i) q^{60} +(-0.157543 - 0.344971i) q^{61} +(1.74769 - 1.12317i) q^{62} +(-1.78074 - 0.522874i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(2.67995 - 0.786905i) q^{65} +(-2.30694 + 5.05150i) q^{66} +(-0.420243 - 2.92285i) q^{67} +7.50778 q^{68} +(2.73158 + 3.94189i) q^{69} +4.51420 q^{70} +(2.14473 + 14.9169i) q^{71} +(-0.415415 + 0.909632i) q^{72} +(11.0242 - 3.23701i) q^{73} +(5.06718 - 5.84784i) q^{74} +(-0.879083 - 0.258122i) q^{75} +(-3.76492 + 2.41956i) q^{76} +(4.28150 + 9.37518i) q^{77} +(0.751992 + 0.867845i) q^{78} +(8.86394 + 5.69651i) q^{79} +(0.346156 - 2.40757i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-0.579153 - 0.372199i) q^{82} +(-6.84228 - 7.89641i) q^{83} +(0.770978 + 1.68821i) q^{84} +(-15.3624 + 9.87283i) q^{85} +(-8.21942 - 2.41344i) q^{86} +(-1.92408 + 2.22050i) q^{87} +(5.32839 - 1.56456i) q^{88} +(4.47642 - 9.80199i) q^{89} +(-0.346156 - 2.40757i) q^{90} +2.13120 q^{91} +(1.19028 - 4.64578i) q^{92} -2.07749 q^{93} +(1.01042 + 7.02765i) q^{94} +(4.52201 - 9.90183i) q^{95} +(0.959493 - 0.281733i) q^{96} +(6.51094 - 7.51402i) q^{97} +(-3.41153 - 1.00172i) q^{98} +(4.67177 - 3.00236i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9}+O(q^{10}) $ 10 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 + q^8 - q^9	$ 10 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9} + 11 q^{10} + 11 q^{11} - q^{12} - 13 q^{13} + 13 q^{14} - 11 q^{15} - q^{16} + q^{18} - 2 q^{19} - 11 q^{20} + 9 q^{21} - 22 q^{22} - 10 q^{23} - 10 q^{24} + 5 q^{25} - 9 q^{26} - q^{27} - 13 q^{28} - 27 q^{29} + 11 q^{30} - 18 q^{31} + q^{32} + 33 q^{34} + 44 q^{35} - q^{36} - q^{37} + 13 q^{38} - 13 q^{39} - 11 q^{40} - 16 q^{41} + 2 q^{42} + 20 q^{43} + 11 q^{44} + 22 q^{45} - q^{46} - q^{48} - 19 q^{49} - 27 q^{50} - 11 q^{51} - 2 q^{52} - q^{53} + q^{54} + 33 q^{55} + 2 q^{56} - 13 q^{57} - 17 q^{58} - q^{59} - 34 q^{61} - 4 q^{62} - 2 q^{63} - q^{64} + 11 q^{65} + 8 q^{67} + 22 q^{68} + 23 q^{69} + 22 q^{70} - 22 q^{71} + q^{72} + 31 q^{73} + q^{74} + 27 q^{75} - 2 q^{76} + 22 q^{77} + 2 q^{78} + 32 q^{79} - q^{81} - 28 q^{82} + 33 q^{83} + 9 q^{84} - 11 q^{85} - 20 q^{86} + 6 q^{87} + 22 q^{88} - 23 q^{89} + 18 q^{91} + 23 q^{92} + 4 q^{93} + 11 q^{94} - 22 q^{95} + q^{96} - q^{97} - 14 q^{98}+O(q^{100}) $ 10 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 + q^8 - q^9 + 11 * q^10 + 11 * q^11 - q^12 - 13 * q^13 + 13 * q^14 - 11 * q^15 - q^16 + q^18 - 2 * q^19 - 11 * q^20 + 9 * q^21 - 22 * q^22 - 10 * q^23 - 10 * q^24 + 5 * q^25 - 9 * q^26 - q^27 - 13 * q^28 - 27 * q^29 + 11 * q^30 - 18 * q^31 + q^32 + 33 * q^34 + 44 * q^35 - q^36 - q^37 + 13 * q^38 - 13 * q^39 - 11 * q^40 - 16 * q^41 + 2 * q^42 + 20 * q^43 + 11 * q^44 + 22 * q^45 - q^46 - q^48 - 19 * q^49 - 27 * q^50 - 11 * q^51 - 2 * q^52 - q^53 + q^54 + 33 * q^55 + 2 * q^56 - 13 * q^57 - 17 * q^58 - q^59 - 34 * q^61 - 4 * q^62 - 2 * q^63 - q^64 + 11 * q^65 + 8 * q^67 + 22 * q^68 + 23 * q^69 + 22 * q^70 - 22 * q^71 + q^72 + 31 * q^73 + q^74 + 27 * q^75 - 2 * q^76 + 22 * q^77 + 2 * q^78 + 32 * q^79 - q^81 - 28 * q^82 + 33 * q^83 + 9 * q^84 - 11 * q^85 - 20 * q^86 + 6 * q^87 + 22 * q^88 - 23 * q^89 + 18 * q^91 + 23 * q^92 + 4 * q^93 + 11 * q^94 - 22 * q^95 + q^96 - q^97 - 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$

Coefficient data

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

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

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

$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	1.59283	−	1.83823i	0.712337	−	0.822080i	−0.278027	−	0.960573i	$-0.589680\pi$
$5$	1.59283	−	1.83823i	0.712337	−	0.822080i	0.990363	+	0.138493i	$0.0442259\pi$
$6$	0.959493	+	0.281733i	0.391711	+	0.115017i
$7$	1.56130	−	1.00339i	0.590116	−	0.379245i	−0.211238	−	0.977435i	$-0.567750\pi$
$7$	1.56130	−	1.00339i	0.590116	−	0.379245i	0.801354	+	0.598190i	$0.204113\pi$
$8$	−0.415415	−	0.909632i	−0.146871	−	0.321603i
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$	2.04620	+	1.31501i	0.647065	+	0.415844i
$11$	−0.790323	+	5.49682i	−0.238291	+	1.65735i	0.422188	+	0.906508i	$0.361262\pi$
$11$	−0.790323	+	5.49682i	−0.238291	+	1.65735i	−0.660479	+	0.750844i	$0.729647\pi$
$12$	−0.142315	+	0.989821i	−0.0410828	+	0.285737i
$13$	0.966031	+	0.620830i	0.267929	+	0.172187i	0.667706	−	0.744425i	$-0.267276\pi$
$13$	0.966031	+	0.620830i	0.267929	+	0.172187i	−0.399777	+	0.916612i	$0.630913\pi$
$14$	1.21537	+	1.40261i	0.324821	+	0.374864i
$15$	−1.01042	−	2.21252i	−0.260890	−	0.571270i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−7.20366	−	2.11519i	−1.74714	−	0.513008i	−0.757043	−	0.653365i	$-0.773357\pi$
$17$	−7.20366	−	2.11519i	−1.74714	−	0.513008i	−0.990101	+	0.140357i	$0.955175\pi$
$18$	0.654861	−	0.755750i	0.154352	−	0.178132i
$19$	4.29408	−	1.26086i	0.985130	−	0.289260i	0.250789	−	0.968042i	$-0.419310\pi$
$19$	4.29408	−	1.26086i	0.985130	−	0.289260i	0.734340	+	0.678781i	$0.237492\pi$
$20$	−1.01042	+	2.21252i	−0.225938	+	0.494734i
$21$	−0.264125	−	1.83703i	−0.0576368	−	0.400873i
$22$	−5.55334			−1.18398
$23$	−2.45093	+	4.12225i	−0.511054	+	0.859548i
$23$	−2.45093	+	4.12225i	−0.511054	+	0.859548i
$24$	−1.00000			−0.204124
$25$	−0.130388	−	0.906870i	−0.0260776	−	0.181374i
$26$	−0.477031	+	1.04455i	−0.0935534	+	0.204853i
$27$	−0.959493	+	0.281733i	−0.184655	+	0.0542195i
$28$	−1.21537	+	1.40261i	−0.229683	+	0.265069i
$29$	−2.81913	−	0.827771i	−0.523499	−	0.153713i	0.00929715	−	0.999957i	$-0.497041\pi$
$29$	−2.81913	−	0.827771i	−0.523499	−	0.153713i	−0.532796	+	0.846244i	$0.678859\pi$
$30$	2.04620	−	1.31501i	0.373583	−	0.240087i
$31$	−0.863019	−	1.88975i	−0.155003	−	0.339409i	0.816160	−	0.577826i	$-0.196099\pi$
$31$	−0.863019	−	1.88975i	−0.155003	−	0.339409i	−0.971163	+	0.238417i	$0.923371\pi$
$32$	0.654861	+	0.755750i	0.115764	+	0.133599i
$33$	4.67177	+	3.00236i	0.813251	+	0.522644i
$34$	1.06847	−	7.43136i	0.183241	−	1.27447i
$35$	0.642438	−	4.46825i	0.108592	−	0.755273i
$36$	0.841254	+	0.540641i	0.140209	+	0.0901068i
$37$	−5.06718	−	5.84784i	−0.833039	−	0.961379i	0.166657	−	0.986015i	$-0.446703\pi$
$37$	−5.06718	−	5.84784i	−0.833039	−	0.961379i	−0.999696	+	0.0246361i	$0.992157\pi$
$38$	1.85913	+	4.07093i	0.301591	+	0.660393i
$39$	0.966031	−	0.620830i	0.154689	−	0.0994124i
$40$	−2.33380	−	0.685265i	−0.369006	−	0.108350i
$41$	−0.450833	+	0.520289i	−0.0704083	+	0.0812555i	−0.789861	−	0.613286i	$-0.789847\pi$
$41$	−0.450833	+	0.520289i	−0.0704083	+	0.0812555i	0.719453	+	0.694542i	$0.244393\pi$
$42$	1.78074	−	0.522874i	0.274775	−	0.0806811i
$43$	−3.55862	+	7.79229i	−0.542684	+	1.18831i	0.417431	+	0.908709i	$0.362931\pi$
$43$	−3.55862	+	7.79229i	−0.542684	+	1.18831i	−0.960115	+	0.279604i	$0.909797\pi$
$44$	−0.790323	−	5.49682i	−0.119146	−	0.828676i
$45$	−2.43232			−0.362589
$46$	−4.42909	−	1.83933i	−0.653034	−	0.271194i
$47$	7.09992			1.03563			0.517815	−	0.855493i	$-0.326746\pi$
$47$	7.09992			1.03563			0.517815	+	0.855493i	$0.326746\pi$
$48$	−0.142315	−	0.989821i	−0.0205414	−	0.142868i
$49$	−1.47703	+	3.23425i	−0.211004	+	0.462035i
$50$	0.879083	−	0.258122i	0.124321	−	0.0365040i
$51$	−4.91655	+	5.67400i	−0.688455	+	0.794519i
$52$	−1.10181	−	0.323520i	−0.152793	−	0.0448641i
$53$	4.53311	−	2.91326i	0.622671	−	0.400166i	−0.190919	−	0.981606i	$-0.561147\pi$
$53$	4.53311	−	2.91326i	0.622671	−	0.400166i	0.813590	+	0.581439i	$0.197510\pi$
$54$	−0.415415	−	0.909632i	−0.0565308	−	0.123785i
$55$	8.84555	+	10.2083i	1.19273	+	1.37649i
$56$	−1.56130	−	1.00339i	−0.208638	−	0.134083i
$57$	0.636911	−	4.42981i	0.0843609	−	0.586743i
$58$	0.418141	−	2.90824i	0.0549047	−	0.381870i
$59$	−3.39399	−	2.18119i	−0.441860	−	0.283966i	0.300734	−	0.953708i	$-0.402768\pi$
$59$	−3.39399	−	2.18119i	−0.441860	−	0.283966i	−0.742594	+	0.669742i	$0.766405\pi$
$60$	1.59283	+	1.83823i	0.205634	+	0.237314i
$61$	−0.157543	−	0.344971i	−0.0201713	−	0.0441690i	0.899278	−	0.437377i	$-0.144092\pi$
$61$	−0.157543	−	0.344971i	−0.0201713	−	0.0441690i	−0.919450	+	0.393208i	$0.871365\pi$
$62$	1.74769	−	1.12317i	0.221957	−	0.142643i
$63$	−1.78074	−	0.522874i	−0.224353	−	0.0658759i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	2.67995	−	0.786905i	0.332407	−	0.0976036i
$66$	−2.30694	+	5.05150i	−0.283965	+	0.621796i
$67$	−0.420243	−	2.92285i	−0.0513408	−	0.357083i	−0.999256	−	0.0385611i	$-0.987723\pi$
$67$	−0.420243	−	2.92285i	−0.0513408	−	0.357083i	0.947915	−	0.318522i	$-0.103187\pi$
$68$	7.50778			0.910452
$69$	2.73158	+	3.94189i	0.328843	+	0.474548i
$70$	4.51420			0.539550
$71$	2.14473	+	14.9169i	0.254532	+	1.77031i	0.570264	+	0.821462i	$0.306841\pi$
$71$	2.14473	+	14.9169i	0.254532	+	1.77031i	−0.315731	+	0.948849i	$0.602250\pi$
$72$	−0.415415	+	0.909632i	−0.0489571	+	0.107201i
$73$	11.0242	−	3.23701i	1.29029	−	0.378863i	0.436605	−	0.899653i	$-0.356181\pi$
$73$	11.0242	−	3.23701i	1.29029	−	0.378863i	0.853685	+	0.520790i	$0.174363\pi$
$74$	5.06718	−	5.84784i	0.589048	−	0.679797i
$75$	−0.879083	−	0.258122i	−0.101508	−	0.0298054i
$76$	−3.76492	+	2.41956i	−0.431866	+	0.277543i
$77$	4.28150	+	9.37518i	0.487923	+	1.06840i
$78$	0.751992	+	0.867845i	0.0851463	+	0.0982640i
$79$	8.86394	+	5.69651i	0.997272	+	0.640908i	0.934069	−	0.357093i	$-0.116232\pi$
$79$	8.86394	+	5.69651i	0.997272	+	0.640908i	0.0632029	+	0.998001i	$0.479868\pi$
$80$	0.346156	−	2.40757i	0.0387014	−	0.269174i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	−0.579153	−	0.372199i	−0.0639568	−	0.0411025i
$83$	−6.84228	−	7.89641i	−0.751037	−	0.866743i	0.243631	−	0.969868i	$-0.421661\pi$
$83$	−6.84228	−	7.89641i	−0.751037	−	0.866743i	−0.994668	+	0.103125i	$0.967116\pi$
$84$	0.770978	+	1.68821i	0.0841206	+	0.184198i
$85$	−15.3624	+	9.87283i	−1.66629	+	1.07086i
$86$	−8.21942	−	2.41344i	−0.886323	−	0.260248i
$87$	−1.92408	+	2.22050i	−0.206283	+	0.238063i
$88$	5.32839	−	1.56456i	0.568009	−	0.166782i
$89$	4.47642	−	9.80199i	0.474499	−	1.03901i	−0.509440	−	0.860506i	$-0.670147\pi$
$89$	4.47642	−	9.80199i	0.474499	−	1.03901i	0.983939	−	0.178502i	$-0.0571252\pi$
$90$	−0.346156	−	2.40757i	−0.0364880	−	0.253780i
$91$	2.13120			0.223410
$92$	1.19028	−	4.64578i	0.124095	−	0.484356i
$93$	−2.07749			−0.215425
$94$	1.01042	+	7.02765i	0.104217	+	0.724847i
$95$	4.52201	−	9.90183i	0.463949	−	1.01591i
$96$	0.959493	−	0.281733i	0.0979278	−	0.0287542i
$97$	6.51094	−	7.51402i	0.661085	−	0.762933i	−0.321869	−	0.946784i	$-0.604311\pi$
$97$	6.51094	−	7.51402i	0.661085	−	0.762933i	0.982954	+	0.183851i	$0.0588564\pi$
$98$	−3.41153	−	1.00172i	−0.344616	−	0.101189i
$99$	4.67177	−	3.00236i	0.469530	−	0.301749i
$100$	0.380601	+	0.833401i	0.0380601	+	0.0833401i
$101$	3.21670	+	3.71227i	0.320074	+	0.369385i	0.892871	−	0.450312i	$-0.148687\pi$
$101$	3.21670	+	3.71227i	0.320074	+	0.369385i	−0.572797	+	0.819697i	$0.694142\pi$
$102$	−6.31594	−	4.05901i	−0.625372	−	0.401902i
$103$	1.11616	−	7.76307i	0.109979	−	0.764918i	−0.857957	−	0.513721i	$-0.828267\pi$
$103$	1.11616	−	7.76307i	0.109979	−	0.764918i	0.967936	−	0.251197i	$-0.0808243\pi$
$104$	0.163423	−	1.13663i	0.0160250	−	0.111456i
$105$	−3.79759	−	2.44056i	−0.370607	−	0.238174i
$106$	3.52873	+	4.07237i	0.342741	+	0.395544i
$107$	−3.86497	−	8.46310i	−0.373641	−	0.818159i	−0.999276	−	0.0380435i	$-0.987887\pi$
$107$	−3.86497	−	8.46310i	−0.373641	−	0.818159i	0.625635	−	0.780116i	$-0.284840\pi$
$108$	0.841254	−	0.540641i	0.0809497	−	0.0520232i
$109$	−13.9016	−	4.08189i	−1.33153	−	0.390974i	−0.462893	−	0.886414i	$-0.653188\pi$
$109$	−13.9016	−	4.08189i	−1.33153	−	0.390974i	−0.868642	+	0.495441i	$0.835007\pi$
$110$	−8.84555	+	10.2083i	−0.843390	+	0.973324i
$111$	−7.42436	+	2.17999i	−0.704689	+	0.206916i
$112$	0.770978	−	1.68821i	0.0728506	−	0.159520i
$113$	−2.09266	−	14.5548i	−0.196861	−	1.36920i	−0.813322	−	0.581814i	$-0.802343\pi$
$113$	−2.09266	−	14.5548i	−0.196861	−	1.36920i	0.616461	−	0.787385i	$-0.288566\pi$
$114$	4.47536			0.419156
$115$	3.67371	+	11.0714i	0.342575	+	1.03242i
$116$	2.93814			0.272800
$117$	−0.163423	−	1.13663i	−0.0151085	−	0.105082i
$118$	1.67597	−	3.66986i	0.154285	−	0.337838i
$119$	−13.3694	+	3.92562i	−1.22557	+	0.359861i
$120$	−1.59283	+	1.83823i	−0.145405	+	0.167806i
$121$	−19.0360	−	5.58946i	−1.73054	−	0.508133i
$122$	0.319039	−	0.205034i	0.0288844	−	0.0185629i
$123$	0.285989	+	0.626228i	0.0257867	+	0.0564651i
$124$	1.36046	+	1.57006i	0.122173	+	0.140996i
$125$	8.35628	+	5.37026i	0.747409	+	0.480330i
$126$	0.264125	−	1.83703i	0.0235301	−	0.163656i
$127$	−0.987167	+	6.86590i	−0.0875969	+	0.609250i	0.897982	+	0.440033i	$0.145033\pi$
$127$	−0.987167	+	6.86590i	−0.0875969	+	0.609250i	−0.985579	+	0.169217i	$0.945876\pi$
$128$	−0.841254	−	0.540641i	−0.0743570	−	0.0477863i
$129$	5.60981	+	6.47407i	0.493916	+	0.570010i
$130$	1.16029	+	2.54069i	0.101764	+	0.222833i
$131$	2.85424	−	1.83431i	0.249376	−	0.160264i	−0.409981	−	0.912094i	$-0.634465\pi$
$131$	2.85424	−	1.83431i	0.249376	−	0.160264i	0.659357	+	0.751830i	$0.270828\pi$
$132$	−5.32839	−	1.56456i	−0.463777	−	0.136177i
$133$	5.43923	−	6.27720i	0.471641	−	0.544302i
$134$	2.83329	−	0.831930i	0.244759	−	0.0718678i
$135$	−1.01042	+	2.21252i	−0.0869634	+	0.190423i
$136$	1.06847	+	7.43136i	0.0916204	+	0.637234i
$137$	9.21973			0.787695			0.393847	−	0.919176i	$-0.371144\pi$
$137$	9.21973			0.787695			0.393847	+	0.919176i	$0.371144\pi$
$138$	−3.51302	+	3.26476i	−0.299048	+	0.277915i
$139$	−13.4691			−1.14244			−0.571218	−	0.820798i	$-0.693529\pi$
$139$	−13.4691			−1.14244			−0.571218	+	0.820798i	$0.693529\pi$
$140$	0.642438	+	4.46825i	0.0542959	+	0.377636i
$141$	2.94941	−	6.45831i	0.248385	−	0.543888i
$142$	−14.4598	+	4.24579i	−1.21344	+	0.356299i
$143$	−4.17607	+	4.81944i	−0.349220	+	0.403022i
$144$	−0.959493	−	0.281733i	−0.0799577	−	0.0234777i
$145$	−6.01203	+	3.86370i	−0.499272	+	0.320863i
$146$	4.77297	+	10.4514i	0.395014	+	0.864960i
$147$	2.32839	+	2.68711i	0.192043	+	0.221629i
$148$	6.50945	+	4.18337i	0.535074	+	0.343871i
$149$	1.58769	−	11.0426i	0.130068	−	0.904646i	−0.815392	−	0.578909i	$-0.803479\pi$
$149$	1.58769	−	11.0426i	0.130068	−	0.904646i	0.945461	−	0.325737i	$-0.105612\pi$
$150$	0.130388	−	0.906870i	0.0106462	−	0.0740456i
$151$	12.8717	+	8.27212i	1.04748	+	0.673176i	0.946826	−	0.321746i	$-0.104270\pi$
$151$	12.8717	+	8.27212i	1.04748	+	0.673176i	0.100656	+	0.994921i	$0.467906\pi$
$152$	−2.93074	−	3.38226i	−0.237714	−	0.274337i
$153$	3.11884	+	6.82931i	0.252144	+	0.552117i
$154$	−8.67044	+	5.57215i	−0.698684	+	0.449017i
$155$	−4.84843	−	1.42363i	−0.389436	−	0.114349i
$156$	−0.751992	+	0.867845i	−0.0602075	+	0.0694832i
$157$	−2.71881	+	0.798314i	−0.216984	+	0.0637124i	−0.388418	−	0.921483i	$-0.626978\pi$
$157$	−2.71881	+	0.798314i	−0.216984	+	0.0637124i	0.171434	+	0.985196i	$0.445160\pi$
$158$	−4.37706	+	9.58442i	−0.348220	+	0.762496i
$159$	−0.766867	−	5.33368i	−0.0608165	−	0.422988i
$160$	2.43232			0.192292
$161$	0.309572	+	8.89530i	0.0243977	+	0.701048i
$162$	−1.00000			−0.0785674
$163$	−3.55284	−	24.7105i	−0.278280	−	1.93548i	−0.347055	−	0.937845i	$-0.612818\pi$
$163$	−3.55284	−	24.7105i	−0.278280	−	1.93548i	0.0687756	−	0.997632i	$-0.478091\pi$
$164$	0.285989	−	0.626228i	0.0223320	−	0.0489002i
$165$	12.9604	−	3.80551i	1.00896	−	0.296258i
$166$	6.84228	−	7.89641i	0.531064	−	0.612880i
$167$	−8.32792	−	2.44530i	−0.644434	−	0.189223i	−0.0568457	−	0.998383i	$-0.518104\pi$
$167$	−8.32792	−	2.44530i	−0.644434	−	0.189223i	−0.587588	+	0.809160i	$0.699923\pi$
$168$	−1.56130	+	1.00339i	−0.120457	+	0.0774130i
$169$	−4.85261	−	10.6257i	−0.373278	−	0.817364i
$170$	−11.9586	−	13.8010i	−0.917185	−	1.05849i
$171$	−3.76492	−	2.41956i	−0.287910	−	0.185029i
$172$	1.21913	−	8.47922i	0.0929577	−	0.646535i
$173$	−2.19552	+	15.2702i	−0.166922	+	1.16097i	0.718277	+	0.695757i	$0.244931\pi$
$173$	−2.19552	+	15.2702i	−0.166922	+	1.16097i	−0.885199	+	0.465212i	$0.845978\pi$
$174$	−2.47172	−	1.58848i	−0.187381	−	0.120422i
$175$	−1.11352	−	1.28507i	−0.0841739	−	0.0971419i
$176$	2.30694	+	5.05150i	0.173892	+	0.380771i
$177$	−3.39399	+	2.18119i	−0.255108	+	0.163948i
$178$	10.3393	+	3.03589i	0.774962	+	0.227549i
$179$	3.96185	−	4.57222i	0.296123	−	0.341744i	−0.588118	−	0.808775i	$-0.700131\pi$
$179$	3.96185	−	4.57222i	0.296123	−	0.341744i	0.884241	+	0.467031i	$0.154676\pi$
$180$	2.33380	−	0.685265i	0.173951	−	0.0510766i
$181$	−2.60376	+	5.70144i	−0.193536	+	0.423784i	−0.981376	−	0.192095i	$-0.938472\pi$
$181$	−2.60376	+	5.70144i	−0.193536	+	0.423784i	0.787841	+	0.615879i	$0.211199\pi$
$182$	0.303301	+	2.10951i	0.0224822	+	0.156367i
$183$	−0.379242			−0.0280344
$184$	4.76788	+	0.517000i	0.351493	+	0.0381138i
$185$	−18.8208			−1.38373
$186$	−0.295657	−	2.05634i	−0.0216786	−	0.150778i
$187$	17.3200	−	37.9255i	1.26656	−	2.77339i
$188$	−6.81232	+	2.00028i	−0.496840	+	0.145885i
$189$	−1.21537	+	1.40261i	−0.0884052	+	0.102025i
$190$	10.4446	+	3.06681i	0.757730	+	0.222490i
$191$	16.2287	−	10.4295i	1.17427	−	0.754655i	0.199942	−	0.979808i	$-0.435924\pi$
$191$	16.2287	−	10.4295i	1.17427	−	0.754655i	0.974323	+	0.225153i	$0.0722881\pi$
$192$	0.415415	+	0.909632i	0.0299800	+	0.0656470i
$193$	16.9481	+	19.5591i	1.21995	+	1.40790i	0.884955	+	0.465677i	$0.154189\pi$
$193$	16.9481	+	19.5591i	1.21995	+	1.40790i	0.334995	+	0.942220i	$0.391265\pi$
$194$	8.36414	+	5.37531i	0.600510	+	0.385925i
$195$	0.397498	−	2.76466i	0.0284655	−	0.197982i
$196$	0.506008	−	3.51936i	0.0361434	−	0.251383i
$197$	15.4650	+	9.93876i	1.10184	+	0.708107i	0.959499	−	0.281711i	$-0.0909020\pi$
$197$	15.4650	+	9.93876i	1.10184	+	0.708107i	0.142337	+	0.989818i	$0.454538\pi$
$198$	3.63667	+	4.19694i	0.258447	+	0.298263i
$199$	3.59651	+	7.87525i	0.254949	+	0.558262i	0.993221	−	0.116242i	$-0.0370849\pi$
$199$	3.59651	+	7.87525i	0.254949	+	0.558262i	−0.738271	+	0.674504i	$0.764358\pi$
$200$	−0.770753	+	0.495333i	−0.0545004	+	0.0350253i
$201$	−2.83329	−	0.831930i	−0.199845	−	0.0586799i
$202$	−3.21670	+	3.71227i	−0.226326	+	0.261195i
$203$	−5.23208	+	1.53628i	−0.367220	+	0.107826i
$204$	3.11884	−	6.82931i	0.218363	−	0.478148i
$205$	0.238308	+	1.65747i	0.0166441	+	0.115762i
$206$	7.84290			0.546441
$207$	4.72041	−	0.847210i	0.328091	−	0.0588851i
$208$	1.14832			0.0796219
$209$	3.53698	+	24.6003i	0.244658	+	1.70164i
$210$	1.87527	−	4.10626i	0.129406	−	0.283359i
$211$	−13.3232	+	3.91206i	−0.917209	+	0.269317i	−0.706073	−	0.708140i	$-0.749535\pi$
$211$	−13.3232	+	3.91206i	−0.917209	+	0.269317i	−0.211137	+	0.977457i	$0.567717\pi$
$212$	−3.52873	+	4.07237i	−0.242354	+	0.279692i
$213$	14.4598	+	4.24579i	0.990772	+	0.290917i
$214$	7.82692	−	5.03006i	0.535037	−	0.343847i
$215$	8.65571	+	18.9534i	0.590315	+	1.29261i
$216$	0.654861	+	0.755750i	0.0445576	+	0.0514222i
$217$	−3.24358	−	2.08452i	−0.220189	−	0.141507i
$218$	2.06193	−	14.3410i	0.139652	−	0.971298i
$219$	1.63515	−	11.3727i	0.110493	−	0.768496i
$220$	−11.3633	−	7.30272i	−0.766110	−	0.492349i
$221$	−5.64579	−	6.51558i	−0.379777	−	0.438286i
$222$	−3.21440	−	7.03855i	−0.215736	−	0.472397i
$223$	3.18413	−	2.04631i	0.213225	−	0.137031i	−0.429669	−	0.902986i	$-0.641370\pi$
$223$	3.18413	−	2.04631i	0.213225	−	0.137031i	0.642894	+	0.765955i	$0.277733\pi$
$224$	1.78074	+	0.522874i	0.118981	+	0.0349360i
$225$	−0.599980	+	0.692414i	−0.0399987	+	0.0461610i
$226$	14.1088	−	4.14272i	0.938505	−	0.275570i
$227$	4.08445	−	8.94371i	0.271095	−	0.593615i	−0.724299	−	0.689486i	$-0.757836\pi$
$227$	4.08445	−	8.94371i	0.271095	−	0.593615i	0.995394	+	0.0958714i	$0.0305638\pi$
$228$	0.636911	+	4.42981i	0.0421804	+	0.293371i
$229$	−19.7726			−1.30661			−0.653307	−	0.757093i	$-0.726619\pi$
$229$	−19.7726			−1.30661			−0.653307	+	0.757093i	$0.726619\pi$
$230$	−10.4359	+	5.21194i	−0.688123	+	0.343665i
$231$	10.3066			0.678122
$232$	0.418141	+	2.90824i	0.0274523	+	0.190935i
$233$	−6.94406	+	15.2054i	−0.454921	+	0.996137i	0.533695	+	0.845677i	$0.320803\pi$
$233$	−6.94406	+	15.2054i	−0.454921	+	0.996137i	−0.988616	+	0.150460i	$0.951924\pi$
$234$	1.10181	−	0.323520i	0.0720274	−	0.0211492i
$235$	11.3090	−	13.0513i	0.737717	−	0.851370i
$236$	3.87102	+	1.13663i	0.251982	+	0.0739886i
$237$	8.86394	−	5.69651i	0.575775	−	0.370028i
$238$	−5.78833	−	12.6747i	−0.375202	−	0.821577i
$239$	5.60130	+	6.46424i	0.362318	+	0.418137i	0.907415	−	0.420236i	$-0.138053\pi$
$239$	5.60130	+	6.46424i	0.362318	+	0.418137i	−0.545097	+	0.838373i	$0.683507\pi$
$240$	−2.04620	−	1.31501i	−0.132082	−	0.0848837i
$241$	−3.00884	+	20.9269i	−0.193816	+	1.34802i	0.627975	+	0.778234i	$0.283884\pi$
$241$	−3.00884	+	20.9269i	−0.193816	+	1.34802i	−0.821791	+	0.569789i	$0.807025\pi$
$242$	2.82347	−	19.6377i	0.181500	−	1.26236i
$243$	0.841254	+	0.540641i	0.0539664	+	0.0346821i
$244$	0.248351	+	0.286612i	0.0158990	+	0.0183485i
$245$	3.59262	+	7.86673i	0.229524	+	0.502587i
$246$	−0.579153	+	0.372199i	−0.0369255	+	0.0237306i
$247$	4.93099	+	1.44787i	0.313751	+	0.0921258i
$248$	−1.36046	+	1.57006i	−0.0863896	+	0.0996989i
$249$	−10.0252	+	2.94367i	−0.635322	+	0.186547i
$250$	−4.12637	+	9.03549i	−0.260975	+	0.571455i
$251$	1.65048	+	11.4793i	0.104177	+	0.724569i	0.973227	+	0.229845i	$0.0738218\pi$
$251$	1.65048	+	11.4793i	0.104177	+	0.724569i	−0.869050	+	0.494724i	$0.835269\pi$
$252$	1.85592			0.116912
$253$	−20.7222	−	16.7302i	−1.30280	−	1.05182i
$254$	−6.93650			−0.435235
$255$	2.59886	+	18.0755i	0.162747	+	1.13193i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	8.10542	−	2.37997i	0.505602	−	0.148458i	−0.0189768	−	0.999820i	$-0.506041\pi$
$257$	8.10542	−	2.37997i	0.505602	−	0.148458i	0.524579	+	0.851362i	$0.324223\pi$
$258$	−5.60981	+	6.47407i	−0.349252	+	0.403058i
$259$	−13.7790	−	4.04589i	−0.856188	−	0.251399i
$260$	−2.34970	+	1.51006i	−0.145722	+	0.0936499i
$261$	1.22055	+	2.67263i	0.0755501	+	0.165432i
$262$	2.22184	+	2.56414i	0.137266	+	0.158413i
$263$	−26.3237	−	16.9172i	−1.62319	−	1.04316i	−0.953884	−	0.300175i	$-0.902955\pi$
$263$	−26.3237	−	16.9172i	−1.62319	−	1.04316i	−0.669307	−	0.742986i	$-0.733409\pi$
$264$	0.790323	−	5.49682i	0.0486410	−	0.338306i
$265$	1.86527	−	12.9732i	0.114582	−	0.796939i
$266$	6.98739	+	4.49052i	0.428424	+	0.275332i
$267$	−7.05663	−	8.14379i	−0.431859	−	0.498392i
$268$	1.22668	+	2.68606i	0.0749316	+	0.164077i
$269$	−7.78907	+	5.00573i	−0.474908	+	0.305205i	−0.756111	−	0.654443i	$-0.772903\pi$
$269$	−7.78907	+	5.00573i	−0.474908	+	0.305205i	0.281203	+	0.959648i	$0.409267\pi$
$270$	−2.33380	−	0.685265i	−0.142030	−	0.0417039i
$271$	−10.7864	+	12.4482i	−0.655228	+	0.756173i	−0.981990	−	0.188933i	$-0.939497\pi$
$271$	−10.7864	+	12.4482i	−0.655228	+	0.756173i	0.326762	+	0.945107i	$0.394042\pi$
$272$	−7.20366	+	2.11519i	−0.436786	+	0.128252i
$273$	0.885331	−	1.93861i	0.0535827	−	0.117330i
$274$	1.31210	+	9.12588i	0.0792671	+	0.551315i
$275$	5.08795			0.306815
$276$	−3.73149	−	3.01264i	−0.224609	−	0.181340i
$277$	29.2151			1.75537			0.877684	−	0.479240i	$-0.159088\pi$
$277$	29.2151			1.75537			0.877684	+	0.479240i	$0.159088\pi$
$278$	−1.91686	−	13.3320i	−0.114965	−	0.799602i
$279$	−0.863019	+	1.88975i	−0.0516676	+	0.113136i
$280$	−4.33134	+	1.27180i	−0.258847	+	0.0760044i
$281$	−7.87921	+	9.09310i	−0.470034	+	0.542449i	−0.940421	−	0.340012i	$-0.889569\pi$
$281$	−7.87921	+	9.09310i	−0.470034	+	0.542449i	0.470387	+	0.882460i	$0.344114\pi$
$282$	6.81232	+	2.00028i	0.405668	+	0.119115i
$283$	−8.64671	+	5.55691i	−0.513994	+	0.330324i	−0.771792	−	0.635875i	$-0.780639\pi$
$283$	−8.64671	+	5.55691i	−0.513994	+	0.330324i	0.257798	+	0.966199i	$0.417003\pi$
$284$	−6.26043	−	13.7084i	−0.371488	−	0.813445i
$285$	−7.12851	−	8.22674i	−0.422256	−	0.487310i
$286$	−5.36470	−	3.44768i	−0.317221	−	0.203866i
$287$	−0.181835	+	1.26469i	−0.0107334	+	0.0746521i
$288$	0.142315	−	0.989821i	0.00838598	−	0.0583258i
$289$	33.1174	+	21.2833i	1.94808	+	1.25196i
$290$	−4.67997	−	5.40098i	−0.274817	−	0.317156i
$291$	−4.13025	−	9.04399i	−0.242120	−	0.530168i
$292$	−9.66571	+	6.21177i	−0.565643	+	0.363517i
$293$	0.242114	+	0.0710912i	0.0141445	+	0.00415319i	0.288797	−	0.957390i	$-0.406745\pi$
$293$	0.242114	+	0.0710912i	0.0141445	+	0.00415319i	−0.274653	+	0.961544i	$0.588563\pi$
$294$	−2.32839	+	2.68711i	−0.135795	+	0.156715i
$295$	−9.41558	+	2.76466i	−0.548196	+	0.160965i
$296$	−3.21440	+	7.03855i	−0.186833	+	0.409107i
$297$	−0.790323	−	5.49682i	−0.0458592	−	0.318958i
$298$	11.1562			0.646259
$299$	−4.92689	+	2.46061i	−0.284929	+	0.142301i
$300$	0.916195			0.0528966
$301$	2.26261	+	15.7368i	0.130414	+	0.907053i
$302$	−6.35609	+	13.9179i	−0.365752	+	0.800885i
$303$	4.71307	−	1.38388i	0.270759	−	0.0795019i
$304$	2.93074	−	3.38226i	0.168090	−	0.193986i
$305$	−0.885075	−	0.259881i	−0.0506792	−	0.0148808i
$306$	−6.31594	+	4.05901i	−0.361059	+	0.232038i
$307$	−0.121406	−	0.265842i	−0.00692900	−	0.0151724i	0.906136	−	0.422987i	$-0.139018\pi$
$307$	−0.121406	−	0.265842i	−0.00692900	−	0.0151724i	−0.913065	+	0.407814i	$0.866291\pi$
$308$	−6.74937	−	7.78919i	−0.384581	−	0.443830i
$309$	−6.59787	−	4.24019i	−0.375340	−	0.241216i
$310$	0.719134	−	5.00169i	0.0408441	−	0.284077i
$311$	1.28912	−	8.96601i	0.0730991	−	0.508416i	−0.920072	−	0.391749i	$-0.871870\pi$
$311$	1.28912	−	8.96601i	0.0730991	−	0.508416i	0.993171	−	0.116666i	$-0.0372208\pi$
$312$	−0.966031	−	0.620830i	−0.0546907	−	0.0351476i
$313$	−3.74536	−	4.32238i	−0.211700	−	0.244315i	0.639961	−	0.768407i	$-0.278950\pi$
$313$	−3.74536	−	4.32238i	−0.211700	−	0.244315i	−0.851662	+	0.524092i	$0.824405\pi$
$314$	−1.17711	−	2.57752i	−0.0664284	−	0.145458i
$315$	−3.79759	+	2.44056i	−0.213970	+	0.137510i
$316$	−10.1098	−	2.96850i	−0.568720	−	0.166991i
$317$	11.9911	−	13.8385i	0.673487	−	0.777245i	−0.311431	−	0.950269i	$-0.600808\pi$
$317$	11.9911	−	13.8385i	0.673487	−	0.777245i	0.984918	+	0.173024i	$0.0553537\pi$
$318$	5.17025	−	1.51812i	0.289933	−	0.0851321i
$319$	6.77813	−	14.8420i	0.379502	−	0.830994i
$320$	0.346156	+	2.40757i	0.0193507	+	0.134587i
$321$	−9.30388			−0.519292
$322$	−8.76071	+	1.57236i	−0.488215	+	0.0876239i
$323$	−33.6000			−1.86956
$324$	−0.142315	−	0.989821i	−0.00790638	−	0.0549901i
$325$	0.437053	−	0.957013i	0.0242434	−	0.0530855i
$326$	23.9534	−	7.03335i	1.32665	−	0.389541i
$327$	−9.48796	+	10.9497i	−0.524685	+	0.605519i
$328$	0.660554	+	0.193956i	0.0364730	+	0.0107094i
$329$	11.0851	−	7.12396i	0.611142	−	0.392757i
$330$	5.61123	+	12.2869i	0.308888	+	0.676370i
$331$	0.756224	+	0.872729i	0.0415658	+	0.0479695i	0.776152	−	0.630546i	$-0.217169\pi$
$331$	0.756224	+	0.872729i	0.0415658	+	0.0479695i	−0.734586	+	0.678516i	$0.762624\pi$
$332$	8.78979	+	5.64886i	0.482402	+	0.310021i
$333$	−1.10120	+	7.65904i	−0.0603456	+	0.419713i
$334$	1.23522	−	8.59116i	0.0675883	−	0.470087i
$335$	−6.04224	−	3.88311i	−0.330123	−	0.212157i
$336$	−1.21537	−	1.40261i	−0.0663039	−	0.0765188i
$337$	−6.90165	−	15.1125i	−0.375957	−	0.823230i	−0.999152	−	0.0411644i	$-0.986893\pi$
$337$	−6.90165	−	15.1125i	−0.375957	−	0.823230i	0.623196	−	0.782066i	$-0.285834\pi$
$338$	9.82698	−	6.31542i	0.534517	−	0.343513i
$339$	−14.1088	−	4.14272i	−0.766286	−	0.225002i
$340$	11.9586	−	13.8010i	0.648548	−	0.748464i
$341$	11.0697	−	3.25035i	0.599456	−	0.176016i
$342$	1.85913	−	4.07093i	0.100530	−	0.220131i
$343$	2.78799	+	19.3909i	0.150537	+	1.04701i
$344$	8.56642			0.461870
$345$	11.5970	+	1.25751i	0.624363	+	0.0677022i
$346$	−15.4272			−0.829371
$347$	0.0186228	+	0.129524i	0.000999725	+	0.00695324i	0.990315	−	0.138837i	$-0.0443365\pi$
$347$	0.0186228	+	0.129524i	0.000999725	+	0.00695324i	−0.989315	+	0.145791i	$0.953427\pi$
$348$	1.22055	−	2.67263i	0.0654283	−	0.143268i
$349$	−17.9308	+	5.26496i	−0.959815	+	0.281827i	−0.723868	−	0.689939i	$-0.757637\pi$
$349$	−17.9308	+	5.26496i	−0.959815	+	0.281827i	−0.235947	+	0.971766i	$0.575819\pi$
$350$	1.11352	−	1.28507i	0.0595200	−	0.0686897i
$351$	−1.10181	−	0.323520i	−0.0588102	−	0.0172682i
$352$	−4.67177	+	3.00236i	−0.249006	+	0.160027i
$353$	−13.6597	−	29.9105i	−0.727031	−	1.59198i	−0.803781	−	0.594925i	$-0.797182\pi$
$353$	−13.6597	−	29.9105i	−0.727031	−	1.59198i	0.0767505	−	0.997050i	$-0.475546\pi$
$354$	−2.64200	−	3.04903i	−0.140421	−	0.162054i
$355$	30.8368	+	19.8176i	1.63665	+	1.05181i
$356$	−1.53355	+	10.6661i	−0.0812781	+	0.565302i
$357$	−1.98299	+	13.7920i	−0.104951	+	0.729951i
$358$	5.08951	+	3.27083i	0.268989	+	0.172869i
$359$	−4.29811	−	4.96028i	−0.226845	−	0.261793i	0.630905	−	0.775860i	$-0.282684\pi$
$359$	−4.29811	−	4.96028i	−0.226845	−	0.261793i	−0.857750	+	0.514067i	$0.828138\pi$
$360$	1.01042	+	2.21252i	0.0532540	+	0.116610i
$361$	0.865557	−	0.556260i	0.0455556	−	0.0292768i
$362$	−6.01396	−	1.76586i	−0.316087	−	0.0928114i
$363$	−12.9922	+	14.9938i	−0.681913	+	0.786969i
$364$	−2.04487	+	0.600428i	−0.107180	+	0.0314710i
$365$	11.6094	−	25.4211i	0.607664	−	1.33060i
$366$	−0.0539718	−	0.375382i	−0.00282115	−	0.0196215i
$367$	−15.7482			−0.822052			−0.411026	−	0.911624i	$-0.634829\pi$
$367$	−15.7482			−0.822052			−0.411026	+	0.911624i	$0.634829\pi$
$368$	0.166803	+	4.79293i	0.00869518	+	0.249849i
$369$	0.688441			0.0358388
$370$	−2.67848	−	18.6293i	−0.139248	−	0.968489i
$371$	4.15443	−	9.09694i	0.215687	−	0.472289i
$372$	1.99333	−	0.585296i	0.103350	−	0.0303462i
$373$	−10.5690	+	12.1973i	−0.547243	+	0.631552i	−0.960238	−	0.279181i	$-0.909937\pi$
$373$	−10.5690	+	12.1973i	−0.547243	+	0.631552i	0.412996	+	0.910733i	$0.364482\pi$
$374$	40.0044	+	11.7463i	2.06858	+	0.607389i
$375$	8.35628	−	5.37026i	0.431517	−	0.277319i
$376$	−2.94941	−	6.45831i	−0.152104	−	0.333062i
$377$	−2.20946	−	2.54985i	−0.113793	−	0.131324i
$378$	−1.56130	−	1.00339i	−0.0803046	−	0.0516087i
$379$	−3.02940	+	21.0699i	−0.155610	+	1.08229i	0.750995	+	0.660308i	$0.229574\pi$
$379$	−3.02940	+	21.0699i	−0.155610	+	1.08229i	−0.906605	+	0.421981i	$0.861335\pi$
$380$	−1.54917	+	10.7747i	−0.0794709	+	0.552732i
$381$	5.83536	+	3.75016i	0.298954	+	0.192126i
$382$	12.6330	+	14.5792i	0.646359	+	0.745938i
$383$	11.1739	+	24.4675i	0.570961	+	1.25023i	0.946284	+	0.323336i	$0.104804\pi$
$383$	11.1739	+	24.4675i	0.570961	+	1.25023i	−0.375323	+	0.926894i	$0.622468\pi$
$384$	−0.841254	+	0.540641i	−0.0429300	+	0.0275895i
$385$	24.0534	+	7.06273i	1.22588	+	0.359950i
$386$	−16.9481	+	19.5591i	−0.862635	+	0.995534i
$387$	8.21942	−	2.41344i	0.417816	−	0.122682i
$388$	−4.13025	+	9.04399i	−0.209682	+	0.459139i
$389$	−4.15477	−	28.8971i	−0.210655	−	1.46514i	−0.770977	−	0.636864i	$-0.780231\pi$
$389$	−4.15477	−	28.8971i	−0.210655	−	1.46514i	0.560321	−	0.828275i	$-0.310678\pi$
$390$	2.79309			0.141434
$391$	26.3750	−	24.5111i	1.33384	−	1.23958i
$392$	3.55555			0.179583
$393$	−0.482852	−	3.35831i	−0.0243566	−	0.169404i
$394$	−7.63669	+	16.7220i	−0.384731	+	0.842444i
$395$	24.5903	−	7.22035i	1.23727	−	0.363295i
$396$	−3.63667	+	4.19694i	−0.182749	+	0.210904i
$397$	2.07632	+	0.609661i	0.104207	+	0.0305980i	0.333421	−	0.942778i	$-0.391797\pi$
$397$	2.07632	+	0.609661i	0.104207	+	0.0305980i	−0.229213	+	0.973376i	$0.573615\pi$
$398$	−7.28325	+	4.68066i	−0.365076	+	0.234620i
$399$	−3.45041	−	7.55534i	−0.172736	−	0.378240i
$400$	−0.599980	−	0.692414i	−0.0299990	−	0.0346207i
$401$	−5.73614	−	3.68639i	−0.286449	−	0.184090i	0.389523	−	0.921017i	$-0.372640\pi$
$401$	−5.73614	−	3.68639i	−0.286449	−	0.184090i	−0.675972	+	0.736927i	$0.736276\pi$
$402$	0.420243	−	2.92285i	0.0209598	−	0.145779i
$403$	0.339510	−	2.36134i	0.0169122	−	0.117627i
$404$	−4.13227	−	2.65565i	−0.205588	−	0.132123i
$405$	1.59283	+	1.83823i	0.0791485	+	0.0913422i
$406$	−2.26524	−	4.96019i	−0.112422	−	0.246170i
$407$	36.1492	−	23.2317i	1.79185	−	1.15155i
$408$	7.20366	+	2.11519i	0.356634	+	0.104717i
$409$	8.43702	−	9.73684i	0.417184	−	0.481456i	−0.507793	−	0.861479i	$-0.669539\pi$
$409$	8.43702	−	9.73684i	0.417184	−	0.481456i	0.924977	+	0.380023i	$0.124084\pi$
$410$	−1.60668	+	0.471764i	−0.0793483	+	0.0232988i
$411$	3.83001	−	8.38656i	0.188921	−	0.413678i
$412$	1.11616	+	7.76307i	0.0549893	+	0.382459i
$413$	−7.48762			−0.368441
$414$	1.51037	+	4.55179i	0.0742306	+	0.223708i
$415$	−25.4140			−1.24752
$416$	0.163423	+	1.13663i	0.00801249	+	0.0557281i
$417$	−5.59527	+	12.2519i	−0.274002	+	0.599980i
$418$	−23.8465	+	7.00196i	−1.16637	+	0.342477i
$419$	−4.88423	+	5.63670i	−0.238610	+	0.275371i	−0.862407	−	0.506216i	$-0.831044\pi$
$419$	−4.88423	+	5.63670i	−0.238610	+	0.275371i	0.623797	+	0.781587i	$0.285589\pi$
$420$	4.33134	+	1.27180i	0.211348	+	0.0620574i
$421$	0.720254	−	0.462879i	0.0351030	−	0.0225594i	−0.522972	−	0.852350i	$-0.675177\pi$
$421$	0.720254	−	0.462879i	0.0351030	−	0.0225594i	0.558075	+	0.829791i	$0.311540\pi$
$422$	−5.76833	−	12.6309i	−0.280798	−	0.614862i
$423$	−4.64946	−	5.36576i	−0.226064	−	0.260892i
$424$	−4.53311	−	2.91326i	−0.220147	−	0.141480i
$425$	−0.978926	+	6.80858i	−0.0474849	+	0.330264i
$426$	−2.14473	+	14.9169i	−0.103912	+	0.722726i
$427$	−0.592111	−	0.380527i	−0.0286543	−	0.0184150i
$428$	6.09274	+	7.03140i	0.294504	+	0.339876i
$429$	2.64911	+	5.80075i	0.127900	+	0.280063i
$430$	−17.5286	+	11.2650i	−0.845304	+	0.543244i
$431$	25.9406	+	7.61686i	1.24952	+	0.366891i	0.838583	−	0.544774i	$-0.183385\pi$
$431$	25.9406	+	7.61686i	1.24952	+	0.366891i	0.410934	+	0.911665i	$0.365203\pi$
$432$	−0.654861	+	0.755750i	−0.0315070	+	0.0363610i
$433$	20.9024	−	6.13751i	1.00451	−	0.294950i	0.262203	−	0.965013i	$-0.415551\pi$
$433$	20.9024	−	6.13751i	1.00451	−	0.294950i	0.742304	+	0.670063i	$0.233733\pi$
$434$	1.60170	−	3.50723i	0.0768839	−	0.168352i
$435$	1.01706	+	7.07377i	0.0487641	+	0.339162i
$436$	14.4885			0.693874
$437$	−5.32693	+	20.7915i	−0.254822	+	0.994594i
$438$	11.4896			0.548997
$439$	−2.15413	−	14.9823i	−0.102811	−	0.715067i	−0.974399	−	0.224827i	$-0.927818\pi$
$439$	−2.15413	−	14.9823i	−0.102811	−	0.715067i	0.871588	−	0.490240i	$-0.163091\pi$
$440$	5.61123	−	12.2869i	0.267505	−	0.585754i
$441$	3.41153	−	1.00172i	0.162454	−	0.0477007i
$442$	5.64579	−	6.51558i	0.268543	−	0.309915i
$443$	14.6455	+	4.30031i	0.695829	+	0.204314i	0.610474	−	0.792037i	$-0.290979\pi$
$443$	14.6455	+	4.30031i	0.695829	+	0.204314i	0.0853558	+	0.996351i	$0.472797\pi$
$444$	6.50945	−	4.18337i	0.308925	−	0.198534i
$445$	−10.8881	−	23.8416i	−0.516145	−	1.13020i
$446$	2.47863	+	2.86050i	0.117367	+	0.135448i
$447$	−9.38516	−	6.03148i	−0.443903	−	0.285279i
$448$	−0.264125	+	1.83703i	−0.0124787	+	0.0867916i
$449$	−4.03517	+	28.0652i	−0.190432	+	1.32448i	0.640436	+	0.768011i	$0.278753\pi$
$449$	−4.03517	+	28.0652i	−0.190432	+	1.32448i	−0.830868	+	0.556470i	$0.812156\pi$
$450$	−0.770753	−	0.495333i	−0.0363336	−	0.0233502i
$451$	−2.50363	−	2.88934i	−0.117891	−	0.136054i
$452$	6.10845	+	13.3756i	0.287317	+	0.629137i
$453$	12.8717	−	8.27212i	0.604764	−	0.388658i
$454$	9.43395	+	2.77006i	0.442757	+	0.130005i
$455$	3.39464	−	3.91763i	0.159143	−	0.183661i
$456$	−4.29408	+	1.26086i	−0.201089	+	0.0590450i
$457$	−8.21817	+	17.9953i	−0.384430	+	0.841784i	0.614185	+	0.789162i	$0.289485\pi$
$457$	−8.21817	+	17.9953i	−0.384430	+	0.841784i	−0.998615	+	0.0526214i	$0.983242\pi$
$458$	−2.81394	−	19.5714i	−0.131487	−	0.914511i
$459$	7.50778			0.350433
$460$	−6.64408	−	9.58795i	−0.309782	−	0.447040i
$461$	10.9505			0.510014			0.255007	−	0.966939i	$-0.417922\pi$
$461$	10.9505			0.510014			0.255007	+	0.966939i	$0.417922\pi$
$462$	1.46678	+	10.2017i	0.0682407	+	0.474624i
$463$	−3.99367	+	8.74491i	−0.185601	+	0.406410i	−0.979445	−	0.201712i	$-0.935350\pi$
$463$	−3.99367	+	8.74491i	−0.185601	+	0.406410i	0.793844	+	0.608122i	$0.208077\pi$
$464$	−2.81913	+	0.827771i	−0.130875	+	0.0384283i
$465$	−3.30909	+	3.81889i	−0.153455	+	0.177097i
$466$	−16.0388	−	4.70943i	−0.742985	−	0.218160i
$467$	−13.3427	+	8.57486i	−0.617428	+	0.396797i	−0.811636	−	0.584163i	$-0.801423\pi$
$467$	−13.3427	+	8.57486i	−0.617428	+	0.396797i	0.194208	+	0.980960i	$0.437786\pi$
$468$	0.477031	+	1.04455i	0.0220507	+	0.0482844i
$469$	−3.58888	−	4.14179i	−0.165719	−	0.191250i
$470$	14.5279	+	9.33648i	0.670120	+	0.430660i
$471$	−0.403262	+	2.80475i	−0.0185813	+	0.129236i
$472$	−0.574161	+	3.99338i	−0.0264279	+	0.183810i
$473$	−40.0203	−	25.7195i	−1.84014	−	1.18258i
$474$	6.90000	+	7.96302i	0.316927	+	0.365754i
$475$	−1.70333	−	3.72977i	−0.0781541	−	0.171134i
$476$	11.7219	−	7.53321i	0.537272	−	0.345284i
$477$	−5.17025	−	1.51812i	−0.236730	−	0.0695101i
$478$	−5.60130	+	6.46424i	−0.256197	+	0.295667i
$479$	−27.1063	+	7.95912i	−1.23852	+	0.363662i	−0.834458	−	0.551071i	$-0.814219\pi$
$479$	−27.1063	+	7.95912i	−1.23852	+	0.363662i	−0.404059	+	0.914733i	$0.632401\pi$
$480$	1.01042	−	2.21252i	0.0461193	−	0.100987i
$481$	−1.26454	−	8.79505i	−0.0576579	−	0.401020i
$482$	−21.1421			−0.962998
$483$	8.22005	+	3.41365i	0.374025	+	0.155326i
$484$	19.8396			0.901800
$485$	−3.44164	−	23.9372i	−0.156277	−	1.08693i
$486$	−0.415415	+	0.909632i	−0.0188436	+	0.0412617i
$487$	1.94021	−	0.569697i	0.0879192	−	0.0258154i	−0.237477	−	0.971393i	$-0.576320\pi$
$487$	1.94021	−	0.569697i	0.0879192	−	0.0258154i	0.325396	+	0.945578i	$0.394502\pi$
$488$	−0.248351	+	0.286612i	−0.0112423	+	0.0129743i
$489$	−23.9534	−	7.03335i	−1.08321	−	0.318059i
$490$	−7.27538	+	4.67560i	−0.328668	+	0.211222i
$491$	7.65343	+	16.7587i	0.345394	+	0.756308i	1.00000		0.000337539i	$0.000107442\pi$
$491$	7.65343	+	16.7587i	0.345394	+	0.756308i	−0.654606	+	0.755971i	$0.727165\pi$
$492$	−0.450833	−	0.520289i	−0.0203251	−	0.0234564i
$493$	18.5572	+	11.9260i	0.835772	+	0.537118i
$494$	−0.731379	+	5.08685i	−0.0329063	+	0.228868i
$495$	1.92232	−	13.3700i	0.0864019	−	0.600938i
$496$	−1.74769	−	1.12317i	−0.0784738	−	0.0504320i
$497$	18.3160	+	21.1378i	0.821584	+	0.948159i
$498$	−4.34044	−	9.50424i	−0.194500	−	0.425895i
$499$	−10.6246	+	6.82800i	−0.475621	+	0.305663i	−0.756400	−	0.654109i	$-0.773044\pi$
$499$	−10.6246	+	6.82800i	−0.475621	+	0.305663i	0.280779	+	0.959772i	$0.409407\pi$
$500$	−9.53077	−	2.79849i	−0.426229	−	0.125152i
$501$	−5.68387	+	6.55953i	−0.253936	+	0.293058i
$502$	−11.1276	+	3.26736i	−0.496649	+	0.145829i
$503$	−0.161210	+	0.353000i	−0.00718798	+	0.0157395i	−0.913192	−	0.407530i	$-0.866390\pi$
$503$	−0.161210	+	0.353000i	−0.00718798	+	0.0157395i	0.906004	+	0.423269i	$0.139118\pi$
$504$	0.264125	+	1.83703i	0.0117651	+	0.0818279i
$505$	11.9477			0.531664
$506$	13.6109	−	22.8923i	0.605076	−	1.01769i
$507$	−11.6814			−0.518787
$508$	−0.987167	−	6.86590i	−0.0437985	−	0.304625i
$509$	13.9512	−	30.5489i	0.618376	−	1.35405i	−0.298319	−	0.954466i	$-0.596426\pi$
$509$	13.9512	−	30.5489i	0.618376	−	1.35405i	0.916695	−	0.399588i	$-0.130847\pi$
$510$	−17.5216	+	5.14481i	−0.775871	+	0.227816i
$511$	13.9642	−	16.1155i	0.617739	−	0.712909i
$512$	0.959493	+	0.281733i	0.0424040	+	0.0124509i
$513$	−3.76492	+	2.41956i	−0.166225	+	0.106826i
$514$	3.50926	+	7.68422i	0.154787	+	0.338936i
$515$	−12.4924	−	14.4170i	−0.550482	−	0.635290i
$516$	−7.20653	−	4.63136i	−0.317250	−	0.203884i
$517$	−5.61123	+	39.0269i	−0.246782	+	1.71640i
$518$	2.04375	−	14.2146i	0.0897971	−	0.624553i
$519$	12.9782	+	8.34057i	0.569679	+	0.366110i
$520$	−1.82909	−	2.11088i	−0.0802108	−	0.0925681i
$521$	0.362903	+	0.794646i	0.0158991	+	0.0348141i	0.917415	−	0.397932i	$-0.130272\pi$
$521$	0.362903	+	0.794646i	0.0158991	+	0.0348141i	−0.901516	+	0.432746i	$0.857545\pi$
$522$	−2.47172	+	1.58848i	−0.108184	+	0.0695259i
$523$	19.4906	+	5.72296i	0.852265	+	0.250248i	0.678555	−	0.734549i	$-0.262606\pi$
$523$	19.4906	+	5.72296i	0.852265	+	0.250248i	0.173710	+	0.984797i	$0.444425\pi$
$524$	−2.22184	+	2.56414i	−0.0970615	+	0.112015i
$525$	−1.63151	+	0.479054i	−0.0712049	+	0.0209076i
$526$	12.9988	−	28.4634i	0.566774	−	1.24106i
$527$	2.21973	+	15.4386i	0.0966929	+	0.672514i
$528$	5.55334			0.241678
$529$	−10.9859	−	20.2067i	−0.477647	−	0.878552i
$530$	13.1066			0.569316
$531$	0.574161	+	3.99338i	0.0249165	+	0.173298i
$532$	−3.45041	+	7.55534i	−0.149594	+	0.327565i
$533$	−0.758529	+	0.222724i	−0.0328556	+	0.00964726i
$534$	7.05663	−	8.14379i	0.305370	−	0.352416i
$535$	−21.7134	−	6.37562i	−0.938750	−	0.275642i
$536$	−2.48414	+	1.59646i	−0.107299	+	0.0689567i
$537$	−2.51322	−	5.50319i	−0.108454	−	0.237480i
$538$	−6.06328	−	6.99740i	−0.261407	−	0.301679i
$539$	−16.6107	−	10.6751i	−0.715475	−	0.459808i
$540$	0.346156	−	2.40757i	0.0148962	−	0.103605i
$541$	0.948836	−	6.59930i	0.0407936	−	0.283726i	−0.959206	−	0.282709i	$-0.908767\pi$
$541$	0.948836	−	6.59930i	0.0407936	−	0.283726i	0.999999	−	0.00101737i	$-0.000323839\pi$
$542$	−13.8565	−	8.90506i	−0.595189	−	0.382505i
$543$	4.10457	+	4.73692i	0.176144	+	0.203281i
$544$	−3.11884	−	6.82931i	−0.133719	−	0.292804i
$545$	−29.6464	+	19.0526i	−1.26991	+	0.816123i
$546$	2.04487	+	0.600428i	0.0875123	+	0.0256959i
$547$	8.89250	−	10.2625i	0.380216	−	0.438793i	−0.533095	−	0.846055i	$-0.678971\pi$
$547$	8.89250	−	10.2625i	0.380216	−	0.438793i	0.913311	+	0.407263i	$0.133517\pi$
$548$	−8.84626	+	2.59750i	−0.377894	+	0.110960i
$549$	−0.157543	+	0.344971i	−0.00672377	+	0.0147230i
$550$	0.724090	+	5.03616i	0.0308753	+	0.214743i
$551$	−13.1493			−0.560178
$552$	2.45093	−	4.12225i	0.104319	−	0.175455i
$553$	19.5551			0.831567
$554$	4.15775	+	28.9178i	0.176646	+	1.22860i
$555$	−7.81845	+	17.1200i	−0.331875	+	0.726705i
$556$	12.9235	−	3.79469i	0.548080	−	0.160931i
$557$	−10.5821	+	12.2124i	−0.448377	+	0.517454i	−0.934271	−	0.356563i	$-0.883948\pi$
$557$	−10.5821	+	12.2124i	−0.448377	+	0.517454i	0.485895	+	0.874017i	$0.338494\pi$
$558$	−1.99333	−	0.585296i	−0.0843846	−	0.0247775i
$559$	−8.27542	+	5.31829i	−0.350013	+	0.224940i
$560$	−1.87527	−	4.10626i	−0.0792445	−	0.173521i
$561$	−27.3033	−	31.5097i	−1.15275	−	1.33034i
$562$	−10.1219	−	6.50493i	−0.426965	−	0.274394i
$563$	0.467924	−	3.25448i	0.0197206	−	0.137160i	−0.977582	−	0.210553i	$-0.932474\pi$
$563$	0.467924	−	3.25448i	0.0197206	−	0.137160i	0.997303	+	0.0733928i	$0.0233827\pi$
$564$	−1.01042	+	7.02765i	−0.0425465	+	0.295917i
$565$	−30.0883	−	19.3366i	−1.26582	−	0.813495i
$566$	−6.73090	−	7.76787i	−0.282921	−	0.326508i
$567$	0.770978	+	1.68821i	0.0323780	+	0.0708980i
$568$	12.6779	−	8.14762i	0.531954	−	0.341866i
$569$	25.1220	+	7.37647i	1.05317	+	0.309238i	0.762096	−	0.647464i	$-0.224170\pi$
$569$	25.1220	+	7.37647i	1.05317	+	0.309238i	0.291071	+	0.956701i	$0.405988\pi$
$570$	7.12851	−	8.22674i	0.298580	−	0.344580i
$571$	−12.5762	+	3.69271i	−0.526299	+	0.154535i	−0.534079	−	0.845434i	$-0.679342\pi$
$571$	−12.5762	+	3.69271i	−0.526299	+	0.154535i	0.00778034	+	0.999970i	$0.497523\pi$
$572$	2.64911	−	5.80075i	0.110765	−	0.242542i
$573$	−2.74540	−	19.0947i	−0.114691	−	0.797693i
$574$	−1.27769			−0.0533298
$575$	4.05792	+	1.68518i	0.169227	+	0.0702769i
$576$	1.00000			0.0416667
$577$	−5.40643	−	37.6025i	−0.225073	−	1.56541i	−0.718437	−	0.695592i	$-0.755142\pi$
$577$	−5.40643	−	37.6025i	−0.225073	−	1.56541i	0.493365	−	0.869823i	$-0.335767\pi$
$578$	−16.3535	+	35.8092i	−0.680217	+	1.48947i
$579$	24.8321	−	7.29136i	1.03199	−	0.303019i
$580$	4.67997	−	5.40098i	0.194325	−	0.224263i
$581$	−18.6060	−	5.46322i	−0.771907	−	0.226652i
$582$	8.36414	−	5.37531i	0.346705	−	0.222814i
$583$	12.4310	+	27.2201i	0.514840	+	1.12734i
$584$	−7.52412	−	8.68330i	−0.311350	−	0.359317i
$585$	−2.34970	−	1.51006i	−0.0971481	−	0.0624333i
$586$	−0.0359111	+	0.249767i	−0.00148347	+	0.0103178i
$587$	−3.73817	+	25.9995i	−0.154291	+	1.07312i	0.754631	+	0.656149i	$0.227816\pi$
$587$	−3.73817	+	25.9995i	−0.154291	+	1.07312i	−0.908922	+	0.416966i	$0.863093\pi$
$588$	−2.99112	−	1.92228i	−0.123352	−	0.0792734i
$589$	−6.08858	−	7.02659i	−0.250875	−	0.289526i
$590$	−4.07650	−	8.92629i	−0.167827	−	0.367489i
$591$	15.4650	−	9.93876i	0.636145	−	0.408826i
$592$	−7.42436	−	2.17999i	−0.305140	−	0.0895970i
$593$	1.09857	−	1.26782i	0.0451130	−	0.0520632i	−0.732745	−	0.680504i	$-0.761761\pi$
$593$	1.09857	−	1.26782i	0.0451130	−	0.0520632i	0.777858	+	0.628441i	$0.216306\pi$
$594$	5.32839	−	1.56456i	0.218627	−	0.0641946i
$595$	−14.0791	+	30.8289i	−0.577186	+	1.26386i
$596$	1.58769	+	11.0426i	0.0650342	+	0.452323i
$597$	8.65762			0.354333
$598$	−3.13673	−	4.52656i	−0.128271	−	0.185105i
$599$	10.8835			0.444689			0.222344	−	0.974968i	$-0.428629\pi$
$599$	10.8835			0.444689			0.222344	+	0.974968i	$0.428629\pi$
$600$	0.130388	+	0.906870i	0.00532308	+	0.0370228i
$601$	−11.4599	+	25.0936i	−0.467458	+	1.02359i	0.518266	+	0.855220i	$0.326578\pi$
$601$	−11.4599	+	25.0936i	−0.467458	+	1.02359i	−0.985724	+	0.168370i	$0.946150\pi$
$602$	−15.2546	+	4.47915i	−0.621731	+	0.182557i
$603$	−1.93374	+	2.23166i	−0.0787481	+	0.0908802i
$604$	−14.6808	−	4.31067i	−0.597353	−	0.175399i
$605$	−40.5958	+	26.0893i	−1.65045	+	1.06068i
$606$	2.04053	+	4.46815i	0.0828911	+	0.181506i
$607$	24.2330	+	27.9663i	0.983586	+	1.13512i	0.990826	+	0.135145i	$0.0431501\pi$
$607$	24.2330	+	27.9663i	0.983586	+	1.13512i	−0.00723963	+	0.999974i	$0.502304\pi$
$608$	3.76492	+	2.41956i	0.152688	+	0.0981263i
$609$	−0.776038	+	5.39746i	−0.0314466	+	0.218716i
$610$	0.131277	−	0.913051i	0.00531525	−	0.0369683i
$611$	6.85874	+	4.40784i	0.277475	+	0.178322i
$612$	−4.91655	−	5.67400i	−0.198740	−	0.229358i
$613$	4.26350	+	9.33575i	0.172201	+	0.377068i	0.975980	−	0.217861i	$-0.0699078\pi$
$613$	4.26350	+	9.33575i	0.172201	+	0.377068i	−0.803779	+	0.594928i	$0.797181\pi$
$614$	0.245858	−	0.158003i	0.00992203	−	0.00637650i
$615$	1.60668	+	0.471764i	0.0647876	+	0.0190234i
$616$	6.74937	−	7.78919i	0.271940	−	0.313835i
$617$	6.74760	−	1.98128i	0.271648	−	0.0797631i	−0.143071	−	0.989712i	$-0.545698\pi$
$617$	6.74760	−	1.98128i	0.271648	−	0.0797631i	0.414720	+	0.909949i	$0.363880\pi$
$618$	3.25806	−	7.13415i	0.131058	−	0.286978i
$619$	5.21995	+	36.3055i	0.209808	+	1.45924i	0.773782	+	0.633451i	$0.218362\pi$
$619$	5.21995	+	36.3055i	0.209808	+	1.45924i	−0.563975	+	0.825792i	$0.690729\pi$
$620$	5.05312			0.202938
$621$	1.19028	−	4.64578i	0.0477642	−	0.186429i
$622$	9.05821			0.363201
$623$	−2.84615	−	19.7954i	−0.114029	−	0.793087i
$624$	0.477031	−	1.04455i	0.0190965	−	0.0418155i
$625$	27.5773	−	8.09743i	1.10309	−	0.323897i
$626$	3.74536	−	4.32238i	0.149695	−	0.172757i
$627$	23.8465	+	7.00196i	0.952338	+	0.279632i
$628$	2.38377	−	1.53195i	0.0951226	−	0.0611316i
$629$	24.1330	+	52.8439i	0.962245	+	2.10702i
$630$	−2.95617	−	3.41161i	−0.117777	−	0.135922i
$631$	−15.3141	−	9.84180i	−0.609646	−	0.391796i	0.199078	−	0.979984i	$-0.436205\pi$
$631$	−15.3141	−	9.84180i	−0.609646	−	0.391796i	−0.808724	+	0.588188i	$0.799842\pi$
$632$	1.49951	−	10.4293i	0.0596474	−	0.414857i
$633$	−1.97614	+	13.7444i	−0.0785446	+	0.546290i
$634$	15.4041	+	9.89962i	0.611775	+	0.393164i
$635$	11.0487	+	12.7509i	0.438454	+	0.506003i
$636$	2.23847	+	4.90157i	0.0887613	+	0.194360i
$637$	−3.43477	+	2.20740i	−0.136091	+	0.0874602i
$638$	15.6556	+	4.59689i	0.619811	+	0.181993i
$639$	9.86894	−	11.3894i	0.390409	−	0.450556i
$640$	−2.33380	+	0.685265i	−0.0922514	+	0.0270875i
$641$	2.11700	−	4.63559i	0.0836166	−	0.183095i	−0.863205	−	0.504853i	$-0.831547\pi$
$641$	2.11700	−	4.63559i	0.0836166	−	0.183095i	0.946822	+	0.321758i	$0.104274\pi$
$642$	−1.32408	−	9.20918i	−0.0522573	−	0.363457i
$643$	−5.24644			−0.206899			−0.103450	−	0.994635i	$-0.532988\pi$
$643$	−5.24644			−0.206899			−0.103450	+	0.994635i	$0.532988\pi$
$644$	−2.80313	−	8.44776i	−0.110459	−	0.332889i
$645$	20.8363			0.820428
$646$	−4.78178	−	33.2580i	−0.188137	−	1.30852i
$647$	−16.7895	+	36.7638i	−0.660062	+	1.44533i	0.222403	+	0.974955i	$0.428610\pi$
$647$	−16.7895	+	36.7638i	−0.660062	+	1.44533i	−0.882465	+	0.470379i	$0.844117\pi$
$648$	0.959493	−	0.281733i	0.0376924	−	0.0110675i
$649$	14.6719	−	16.9323i	0.575924	−	0.664651i
$650$	1.00947	+	0.296407i	0.0395947	+	0.0116261i
$651$	−3.24358	+	2.08452i	−0.127126	+	0.0816989i
$652$	10.3707	+	22.7086i	0.406147	+	0.889338i
$653$	−9.73558	−	11.2355i	−0.380982	−	0.439677i	0.532577	−	0.846381i	$-0.321223\pi$
$653$	−9.73558	−	11.2355i	−0.380982	−	0.439677i	−0.913560	+	0.406704i	$0.866678\pi$
$654$	−12.1885	−	7.83308i	−0.476609	−	0.306298i
$655$	1.17445	−	8.16849i	0.0458896	−	0.319169i
$656$	−0.0979753	+	0.681433i	−0.00382529	+	0.0266055i
$657$	−9.66571	−	6.21177i	−0.377095	−	0.242344i
$658$	8.62903	+	9.95843i	0.336395	+	0.388220i
$659$	−10.7801	−	23.6051i	−0.419932	−	0.919523i	−0.994854	−	0.101315i	$-0.967695\pi$
$659$	−10.7801	−	23.6051i	−0.419932	−	0.919523i	0.574922	−	0.818208i	$-0.305032\pi$
$660$	−11.3633	+	7.30272i	−0.442314	+	0.284258i
$661$	46.2443	+	13.5786i	1.79870	+	0.528145i	0.997526	−	0.0702937i	$-0.0223936\pi$
$661$	46.2443	+	13.5786i	1.79870	+	0.528145i	0.801169	+	0.598438i	$0.204212\pi$
$662$	−0.756224	+	0.872729i	−0.0293915	+	0.0339196i
$663$	−8.27213	+	2.42892i	−0.321263	+	0.0943313i
$664$	−4.34044	+	9.50424i	−0.168442	+	0.368836i
$665$	−2.87514	−	19.9971i	−0.111493	−	0.775453i
$666$	−7.73780			−0.299834
$667$	10.3218	−	9.59234i	0.399660	−	0.371417i
$668$	8.67950			0.335820
$669$	−0.538659	−	3.74645i	−0.0208258	−	0.144846i
$670$	2.98369	−	6.53337i	0.115270	−	0.252406i
$671$	2.02075	−	0.593346i	0.0780103	−	0.0229059i
$672$	1.21537	−	1.40261i	0.0468839	−	0.0541069i
$673$	14.9182	+	4.38039i	0.575056	+	0.168852i	0.556313	−	0.830973i	$-0.312216\pi$
$673$	14.9182	+	4.38039i	0.575056	+	0.168852i	0.0187425	+	0.999824i	$0.494034\pi$
$674$	13.9765	−	8.98213i	0.538354	−	0.345979i
$675$	0.380601	+	0.833401i	0.0146494	+	0.0320776i
$676$	7.64966	+	8.82818i	0.294218	+	0.339545i
$677$	−1.76046	−	1.13138i	−0.0676601	−	0.0434825i	0.506373	−	0.862314i	$-0.330986\pi$
$677$	−1.76046	−	1.13138i	−0.0676601	−	0.0434825i	−0.574034	+	0.818832i	$0.694622\pi$
$678$	2.09266	−	14.5548i	0.0803682	−	0.558973i
$679$	2.62606	−	18.2646i	0.100779	−	0.700932i
$680$	15.3624	+	9.87283i	0.589122	+	0.378606i
$681$	−6.43874	−	7.43070i	−0.246733	−	0.284745i
$682$	4.79264	+	10.4944i	0.183520	+	0.401852i
$683$	−11.4861	+	7.38168i	−0.439504	+	0.282452i	−0.741622	−	0.670818i	$-0.765943\pi$
$683$	−11.4861	+	7.38168i	−0.439504	+	0.282452i	0.302117	+	0.953271i	$0.402307\pi$
$684$	4.29408	+	1.26086i	0.164188	+	0.0482100i
$685$	14.6855	−	16.9480i	0.561104	−	0.647548i
$686$	−18.7967	+	5.51922i	−0.717663	+	0.210725i
$687$	−8.21385	+	17.9858i	−0.313378	+	0.686202i
$688$	1.21913	+	8.47922i	0.0464788	+	0.323267i
$689$	6.18777			0.235735
$690$	0.405718	+	11.6580i	0.0154454	+	0.443811i
$691$	−19.2615			−0.732744			−0.366372	−	0.930469i	$-0.619400\pi$
$691$	−19.2615			−0.732744			−0.366372	+	0.930469i	$0.619400\pi$
$692$	−2.19552	−	15.2702i	−0.0834611	−	0.580485i
$693$	4.28150	−	9.37518i	0.162641	−	0.356134i
$694$	−0.125556	+	0.0368665i	−0.00476603	+	0.00139943i
$695$	−21.4541	+	24.7593i	−0.813799	+	0.939174i
$696$	2.81913	+	0.827771i	0.106859	+	0.0313766i
$697$	4.34815	−	2.79439i	0.164698	−	0.105845i
$698$	−7.76320	−	16.9990i	−0.293841	−	0.643423i
$699$	10.9466	+	12.6331i	0.414039	+	0.477827i
$700$	1.43046	+	0.919299i	0.0540662	+	0.0347462i
$701$	0.843289	−	5.86520i	0.0318506	−	0.221526i	−0.967679	−	0.252184i	$-0.918851\pi$
$701$	0.843289	−	5.86520i	0.0318506	−	0.221526i	0.999530	+	0.0306582i	$0.00976033\pi$
$702$	0.163423	−	1.13663i	0.00616802	−	0.0428995i
$703$	−29.1322	−	18.7221i	−1.09874	−	0.706118i
$704$	−3.63667	−	4.19694i	−0.137062	−	0.158178i
$705$	−7.17392	−	15.7087i	−0.270186	−	0.591624i
$706$	27.6621	−	17.7773i	1.04108	−	0.669059i
$707$	8.74708	+	2.56838i	0.328968	+	0.0965937i
$708$	2.64200	−	3.04903i	0.0992924	−	0.114590i
$709$	6.20193	−	1.82105i	0.232918	−	0.0683910i	−0.163190	−	0.986595i	$-0.552179\pi$
$709$	6.20193	−	1.82105i	0.232918	−	0.0683910i	0.396109	+	0.918204i	$0.370360\pi$
$710$	−15.2274	+	33.3433i	−0.571473	+	1.25135i
$711$	−1.49951	−	10.4293i	−0.0562361	−	0.391131i
$712$	−10.7758			−0.403839
$713$	9.90522	+	1.07406i	0.370953	+	0.0402239i
$714$	−13.9338			−0.521461
$715$	2.20745	+	15.3531i	0.0825538	+	0.574174i
$716$	−2.51322	+	5.50319i	−0.0939236	+	0.205664i
$717$	8.20694	−	2.40978i	0.306494	−	0.0899947i
$718$	4.29811	−	4.96028i	0.160404	−	0.185116i
$719$	47.9418	+	14.0770i	1.78793	+	0.524983i	0.996294	−	0.0860135i	$-0.0274128\pi$
$719$	47.9418	+	14.0770i	1.78793	+	0.524983i	0.791633	+	0.610996i	$0.209231\pi$
$720$	−2.04620	+	1.31501i	−0.0762574	+	0.0490076i
$721$	−6.04670	−	13.2404i	−0.225191	−	0.493099i
$722$	0.673779	+	0.777583i	0.0250755	+	0.0289386i
$723$	17.7859	+	11.4303i	0.661465	+	0.425098i
$724$	0.892008	−	6.20405i	0.0331512	−	0.230572i
$725$	−0.383099	+	2.66451i	−0.0142280	+	0.0989576i
$726$	−16.6901	−	10.7261i	−0.619429	−	0.398083i
$727$	−14.5447	−	16.7855i	−0.539434	−	0.622540i	0.418955	−	0.908007i	$-0.362397\pi$
$727$	−14.5447	−	16.7855i	−0.539434	−	0.622540i	−0.958388	+	0.285467i	$0.907851\pi$
$728$	−0.885331	−	1.93861i	−0.0328126	−	0.0718495i
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$	26.8145	+	7.87345i	0.992449	+	0.291409i
$731$	42.1172	−	48.6059i	1.55776	−	1.79775i
$732$	0.363880	−	0.106845i	0.0134494	−	0.00394910i
$733$	16.0918	−	35.2361i	0.594364	−	1.30148i	−0.338405	−	0.941001i	$-0.609887\pi$
$733$	16.0918	−	35.2361i	0.594364	−	1.30148i	0.932769	−	0.360475i	$-0.117385\pi$
$734$	−2.24121	−	15.5880i	−0.0827245	−	0.575362i
$735$	8.64826			0.318996
$736$	−4.72041	+	0.847210i	−0.173996	+	0.0312286i
$737$	16.3985			0.604047
$738$	0.0979753	+	0.681433i	0.00360652	+	0.0250839i
$739$	−3.39732	+	7.43909i	−0.124972	+	0.273651i	−0.961769	−	0.273863i	$-0.911699\pi$
$739$	−3.39732	+	7.43909i	−0.124972	+	0.273651i	0.836796	+	0.547514i	$0.184426\pi$
$740$	18.0585	−	5.30244i	0.663842	−	0.194922i
$741$	3.36544	−	3.88392i	0.123632	−	0.142679i
$742$	9.59558	+	2.81752i	0.352265	+	0.103434i
$743$	5.79535	−	3.72445i	0.212611	−	0.136637i	−0.430001	−	0.902828i	$-0.641487\pi$
$743$	5.79535	−	3.72445i	0.212611	−	0.136637i	0.642612	+	0.766191i	$0.277851\pi$
$744$	0.863019	+	1.88975i	0.0316398	+	0.0692816i
$745$	−17.7699	−	20.5076i	−0.651039	−	0.751339i
$746$	−13.5773	−	8.72558i	−0.497099	−	0.319466i
$747$	−1.48697	+	10.3421i	−0.0544053	+	0.378397i
$748$	−5.93357	+	41.2689i	−0.216953	+	1.50894i
$749$	−14.5261	−	9.33539i	−0.530774	−	0.341108i
$750$	6.50482	+	7.50696i	0.237522	+	0.274115i
$751$	−6.35324	−	13.9117i	−0.231833	−	0.507643i	0.757585	−	0.652736i	$-0.226379\pi$
$751$	−6.35324	−	13.9117i	−0.231833	−	0.507643i	−0.989418	+	0.145093i	$0.953652\pi$
$752$	5.97283	−	3.83850i	0.217807	−	0.139976i
$753$	11.1276	+	3.26736i	0.405512	+	0.119069i
$754$	2.20946	−	2.54985i	0.0804638	−	0.0928601i
$755$	35.7085	−	10.4849i	1.29956	−	0.381586i
$756$	0.770978	−	1.68821i	0.0280402	−	0.0613995i
$757$	1.52276	+	10.5910i	0.0553456	+	0.384937i	0.998601	+	0.0528700i	$0.0168369\pi$
$757$	1.52276	+	10.5910i	0.0553456	+	0.384937i	−0.943256	+	0.332067i	$0.892254\pi$
$758$	−21.2866			−0.773163
$759$	−23.8267	+	11.8996i	−0.864853	+	0.431929i
$760$	−10.8855			−0.394860
$761$	−0.756832	−	5.26388i	−0.0274351	−	0.190816i	0.971495	−	0.237060i	$-0.0761838\pi$
$761$	−0.756832	−	5.26388i	−0.0274351	−	0.190816i	−0.998930	+	0.0462444i	$0.985275\pi$
$762$	−2.88153	+	6.30966i	−0.104387	+	0.228575i
$763$	−25.8003	+	7.57566i	−0.934035	+	0.274257i
$764$	−12.6330	+	14.5792i	−0.457045	+	0.527457i
$765$	17.5216	+	5.14481i	0.633496	+	0.186011i
$766$	−22.6282	+	14.5423i	−0.817591	+	0.525434i
$767$	−1.92455	−	4.21419i	−0.0694916	−	0.152165i
$768$	−0.654861	−	0.755750i	−0.0236303	−	0.0272708i
$769$	17.4129	+	11.1906i	0.627924	+	0.403542i	0.815540	−	0.578700i	$-0.196440\pi$
$769$	17.4129	+	11.1906i	0.627924	+	0.403542i	−0.187616	+	0.982242i	$0.560076\pi$
$770$	−3.56768	+	24.8137i	−0.128570	+	0.894225i
$771$	1.20222	−	8.36163i	0.0432969	−	0.301137i
$772$	−21.7720	−	13.9920i	−0.783592	−	0.503584i
$773$	17.5087	+	20.2061i	0.629743	+	0.726762i	0.977526	−	0.210813i	$-0.0676110\pi$
$773$	17.5087	+	20.2061i	0.629743	+	0.726762i	−0.347784	+	0.937575i	$0.613066\pi$
$774$	3.55862	+	7.79229i	0.127912	+	0.280088i
$775$	−1.60123	+	1.02905i	−0.0575178	+	0.0369645i
$776$	−9.53973	−	2.80112i	−0.342457	−	0.100554i
$777$	−9.40429	+	10.8531i	−0.337377	+	0.389354i
$778$	28.0116	−	8.22496i	1.00427	−	0.294879i
$779$	−1.27990	+	2.80260i	−0.0458573	+	0.100413i
$780$	0.397498	+	2.76466i	0.0142327	+	0.0989908i
$781$	−83.6905			−2.99468
$782$	28.0152	+	22.6182i	1.00182	+	0.808826i
$783$	2.93814			0.105001
$784$	0.506008	+	3.51936i	0.0180717	+	0.125692i
$785$	−2.86312	+	6.26937i	−0.102189	+	0.223763i
$786$	3.25541	−	0.955874i	0.116117	−	0.0340949i
$787$	28.3878	−	32.7612i	1.01191	−	1.16781i	0.0261540	−	0.999658i	$-0.491674\pi$
$787$	28.3878	−	32.7612i	1.01191	−	1.16781i	0.985761	−	0.168154i	$-0.0537806\pi$
$788$	−17.6386	−	5.17917i	−0.628350	−	0.184500i
$789$	−26.3237	+	16.9172i	−0.937150	+	0.602270i
$790$	10.6464	+	23.3124i	0.378783	+	0.829418i
$791$	−17.8714	−	20.6246i	−0.635432	−	0.733328i
$792$	−4.67177	−	3.00236i	−0.166004	−	0.106684i
$793$	0.0619771	−	0.431060i	0.00220087	−	0.0153074i
$794$	−0.307965	+	2.14195i	−0.0109293	+	0.0760148i
$795$	−11.0260	−	7.08598i	−0.391052	−	0.251314i
$796$	−5.66954	−	6.54299i	−0.200951	−	0.231910i
$797$	−15.9326	−	34.8875i	−0.564361	−	1.23578i	−0.949746	−	0.313022i	$-0.898659\pi$
$797$	−15.9326	−	34.8875i	−0.564361	−	1.23578i	0.385385	−	0.922756i	$-0.374069\pi$
$798$	6.98739	−	4.49052i	0.247351	−	0.158963i
$799$	−51.1454	−	15.0176i	−1.80939	−	0.531286i
$800$	0.599980	−	0.692414i	0.0212125	−	0.0244805i
$801$	−10.3393	+	3.03589i	−0.365320	+	0.107268i
$802$	2.83253	−	6.20238i	0.100020	−	0.219014i
$803$	9.08053	+	63.1565i	0.320445	+	2.22874i
$804$	2.95291			0.104141
$805$	16.8447	+	13.5997i	0.593697	+	0.479325i
$806$	2.38563			0.0840301
$807$	1.31768	+	9.16465i	0.0463844	+	0.322611i
$808$	2.04053	−	4.46815i	0.0717858	−	0.157189i
$809$	−6.58065	+	1.93225i	−0.231363	+	0.0679344i	−0.395359	−	0.918527i	$-0.629380\pi$
$809$	−6.58065	+	1.93225i	−0.231363	+	0.0679344i	0.163996	+	0.986461i	$0.447562\pi$
$810$	−1.59283	+	1.83823i	−0.0559664	+	0.0645887i
$811$	2.26053	+	0.663751i	0.0793779	+	0.0233075i	0.321180	−	0.947018i	$-0.395920\pi$
$811$	2.26053	+	0.663751i	0.0793779	+	0.0233075i	−0.241802	+	0.970325i	$0.577739\pi$
$812$	4.58733	−	2.94810i	0.160984	−	0.103458i
$813$	6.84243	+	14.9828i	0.239974	+	0.525471i
$814$	28.1398	+	32.4751i	0.986299	+	1.13825i
$815$	−51.0826	−	32.8288i	−1.78935	−	1.14994i
$816$	−1.06847	+	7.43136i	−0.0374039	+	0.260150i
$817$	−5.45604	+	37.9476i	−0.190883	+	1.32762i
$818$	10.8384	+	6.96545i	0.378957	+	0.243541i
$819$	−1.39564	−	1.61065i	−0.0487675	−	0.0562807i
$820$	−0.695617	−	1.52319i	−0.0242920	−	0.0531920i
$821$	13.3148	−	8.55691i	0.464690	−	0.298638i	−0.287267	−	0.957851i	$-0.592747\pi$
$821$	13.3148	−	8.55691i	0.464690	−	0.298638i	0.751957	+	0.659212i	$0.229110\pi$
$822$	8.84626	+	2.59750i	0.308549	+	0.0905981i
$823$	−2.96189	+	3.41821i	−0.103245	+	0.119151i	−0.805020	−	0.593247i	$-0.797846\pi$
$823$	−2.96189	+	3.41821i	−0.103245	+	0.119151i	0.701775	+	0.712398i	$0.252391\pi$
$824$	−7.52521	+	2.20960i	−0.262153	+	0.0769751i
$825$	2.11361	−	4.62816i	0.0735864	−	0.161132i
$826$	−1.06560	−	7.41140i	−0.0370769	−	0.257876i
$827$	−6.29678			−0.218961			−0.109480	−	0.993989i	$-0.534919\pi$
$827$	−6.29678			−0.218961			−0.109480	+	0.993989i	$0.534919\pi$
$828$	−4.29051	+	2.14278i	−0.149106	+	0.0744669i
$829$	6.30959			0.219141			0.109570	−	0.993979i	$-0.465052\pi$
$829$	6.30959			0.219141			0.109570	+	0.993979i	$0.465052\pi$
$830$	−3.61679	−	25.1553i	−0.125541	−	0.873154i
$831$	12.1364	−	26.5750i	0.421007	−	0.921877i
$832$	−1.10181	+	0.323520i	−0.0381983	+	0.0112160i
$833$	17.4811	−	20.1742i	0.605683	−	0.698995i
$834$	−12.9235	−	3.79469i	−0.447505	−	0.131399i
$835$	−17.7600	+	11.4137i	−0.614610	+	0.394986i
$836$	−10.3244	−	22.6073i	−0.357077	−	0.781890i
$837$	1.36046	+	1.57006i	0.0470245	+	0.0542692i
$838$	−6.27442	−	4.03233i	−0.216746	−	0.139294i
$839$	0.626028	−	4.35412i	0.0216129	−	0.150321i	−0.976157	−	0.217064i	$-0.930352\pi$
$839$	0.626028	−	4.35412i	0.0216129	−	0.150321i	0.997770	+	0.0667435i	$0.0212609\pi$
$840$	−0.642438	+	4.46825i	−0.0221662	+	0.154169i
$841$	−17.1341	−	11.0114i	−0.590830	−	0.379703i
$842$	0.560671	+	0.647048i	0.0193220	+	0.0222988i
$843$	4.99823	+	10.9446i	0.172148	+	0.376952i
$844$	11.6814	−	7.50718i	0.402090	−	0.258408i
$845$	−27.2619	−	8.00482i	−0.937838	−	0.275374i
$846$	4.64946	−	5.36576i	0.159852	−	0.184479i
$847$	−35.3293	+	10.3736i	−1.21393	+	0.356441i
$848$	2.23847	−	4.90157i	0.0768695	−	0.168321i
$849$	1.46276	+	10.1737i	0.0502019	+	0.349162i
$850$	−6.87859			−0.235934
$851$	36.5256	−	6.55554i	1.25208	−	0.224721i
$852$	−15.0703			−0.516300
$853$	−0.505055	−	3.51274i	−0.0172928	−	0.120274i	0.979347	−	0.202189i	$-0.0648055\pi$
$853$	−0.505055	−	3.51274i	−0.0172928	−	0.120274i	−0.996639	+	0.0819151i	$0.973896\pi$
$854$	0.292387	−	0.640239i	0.0100053	−	0.0219085i
$855$	−10.4446	+	3.06681i	−0.357198	+	0.104883i
$856$	−6.09274	+	7.03140i	−0.208246	+	0.240328i
$857$	−45.7825	−	13.4430i	−1.56390	−	0.459203i	−0.618683	−	0.785641i	$-0.712334\pi$
$857$	−45.7825	−	13.4430i	−1.56390	−	0.459203i	−0.945219	+	0.326437i	$0.894152\pi$
$858$	−5.36470	+	3.44768i	−0.183148	+	0.117702i
$859$	−14.0609	−	30.7891i	−0.479752	−	1.05051i	−0.982532	−	0.186096i	$-0.940416\pi$
$859$	−14.0609	−	30.7891i	−0.479752	−	1.05051i	0.502779	−	0.864415i	$-0.332311\pi$
$860$	−13.6449	−	15.7470i	−0.465286	−	0.536969i
$861$	1.07486	+	0.690773i	0.0366312	+	0.0235415i
$862$	−3.84759	+	26.7606i	−0.131049	+	0.911469i
$863$	1.82291	−	12.6786i	0.0620525	−	0.431585i	−0.934986	−	0.354684i	$-0.884588\pi$
$863$	1.82291	−	12.6786i	0.0620525	−	0.431585i	0.997039	−	0.0769006i	$-0.0245024\pi$
$864$	−0.841254	−	0.540641i	−0.0286200	−	0.0183930i
$865$	24.5729	+	28.3587i	0.835505	+	0.964224i
$866$	9.04977	+	19.8162i	0.307524	+	0.673383i
$867$	33.1174	−	21.2833i	1.12473	−	0.722817i
$868$	3.69947	+	1.08626i	0.125568	+	0.0368702i
$869$	−38.3181	+	44.2214i	−1.29985	+	1.50011i
$870$	−6.85703	+	2.01341i	−0.232475	+	0.0682609i
$871$	1.40863	−	3.08446i	0.0477295	−	0.104513i
$872$	2.06193	+	14.3410i	0.0698258	+	0.485649i
$873$	−9.94247			−0.336502
$874$	−21.3380	−	2.31376i	−0.721769	−	0.0782643i
$875$	18.4351			0.623221
$876$	1.63515	+	11.3727i	0.0552465	+	0.384248i
$877$	−17.5440	+	38.4159i	−0.592417	+	1.29721i	0.341553	+	0.939862i	$0.389047\pi$
$877$	−17.5440	+	38.4159i	−0.592417	+	1.29721i	−0.933970	+	0.357350i	$0.883680\pi$
$878$	14.5232	−	4.26441i	0.490136	−	0.143917i
$879$	0.165245	−	0.190703i	0.00557357	−	0.00643224i
$880$	12.9604	+	3.80551i	0.436894	+	0.128284i
$881$	34.4876	−	22.1638i	1.16192	−	0.746718i	0.189939	−	0.981796i	$-0.439171\pi$
$881$	34.4876	−	22.1638i	1.16192	−	0.746718i	0.971976	+	0.235078i	$0.0755347\pi$
$882$	1.47703	+	3.23425i	0.0497342	+	0.108903i
$883$	−36.2725	−	41.8607i	−1.22067	−	1.40873i	−0.884250	−	0.467013i	$-0.845330\pi$
$883$	−36.2725	−	41.8607i	−1.22067	−	1.40873i	−0.336418	−	0.941713i	$-0.609215\pi$
$884$	7.25274	+	4.66106i	0.243936	+	0.156768i
$885$	−1.39655	+	9.71319i	−0.0469444	+	0.326505i
$886$	−2.17227	+	15.1084i	−0.0729787	+	0.507578i
$887$	24.3710	+	15.6623i	0.818299	+	0.525889i	0.881540	−	0.472109i	$-0.156507\pi$
$887$	24.3710	+	15.6623i	0.818299	+	0.525889i	−0.0632409	+	0.997998i	$0.520144\pi$
$888$	5.06718	+	5.84784i	0.170043	+	0.196241i
$889$	5.34789	+	11.7102i	0.179362	+	0.392749i
$890$	22.0494	−	14.1703i	0.739097	−	0.474989i
$891$	−5.32839	−	1.56456i	−0.178508	−	0.0524146i
$892$	−2.47863	+	2.86050i	−0.0829908	+	0.0957765i
$893$	30.4876	−	8.95197i	1.02023	−	0.299566i
$894$	4.63444	−	10.1480i	0.154999	−	0.339400i
$895$	−2.09421	−	14.5656i	−0.0700018	−	0.486873i
$896$	−1.85592			−0.0620020
$897$	0.191543	+	5.50383i	0.00639544	+	0.183768i
$898$	−28.3538			−0.946180
$899$	0.868684	+	6.04183i	0.0289722	+	0.201506i
$900$	0.380601	−	0.833401i	0.0126867	−	0.0277800i
$901$	−38.8171	+	11.3977i	−1.29318	+	0.379713i
$902$	2.50363	−	2.88934i	0.0833617	−	0.0962046i
$903$	15.2546	+	4.47915i	0.507641	+	0.149057i
$904$	−12.3702	+	7.94983i	−0.411426	+	0.264407i
$905$	6.33318	+	13.8677i	0.210522	+	0.460979i
$906$	10.0198	+	11.5634i	0.332884	+	0.384169i
$907$	−18.8032	−	12.0841i	−0.624348	−	0.401244i	0.189865	−	0.981810i	$-0.439195\pi$
$907$	−18.8032	−	12.0841i	−0.624348	−	0.401244i	−0.814213	+	0.580566i	$0.802831\pi$
$908$	−1.39927	+	9.73215i	−0.0464365	+	0.322973i
$909$	0.699056	−	4.86204i	0.0231862	−	0.161264i
$910$	4.36086	+	2.80255i	0.144561	+	0.0929037i
$911$	22.0772	+	25.4785i	0.731451	+	0.844139i	0.992634	−	0.121150i	$-0.0386583\pi$
$911$	22.0772	+	25.4785i	0.731451	+	0.844139i	−0.261184	+	0.965289i	$0.584113\pi$
$912$	−1.85913	−	4.07093i	−0.0615621	−	0.134802i
$913$	48.8127	−	31.3700i	1.61547	−	1.03820i
$914$	−18.9817	−	5.57352i	−0.627858	−	0.184356i
$915$	−0.604070	+	0.697134i	−0.0199699	+	0.0230465i
$916$	18.9717	−	5.57060i	0.626843	−	0.184058i
$917$	2.61581	−	5.72781i	0.0863815	−	0.189149i
$918$	1.06847	+	7.43136i	0.0352647	+	0.245271i
$919$	41.0403			1.35380			0.676898	−	0.736077i	$-0.263324\pi$
$919$	41.0403			1.35380			0.676898	+	0.736077i	$0.263324\pi$
$920$	8.54481	−	7.94096i	0.281714	−	0.261806i
$921$	−0.292252			−0.00963004
$922$	1.55841	+	10.8390i	0.0513237	+	0.356964i
$923$	−7.18899	+	15.7417i	−0.236629	+	0.518144i
$924$	−9.88908	+	2.90370i	−0.325327	+	0.0955246i
$925$	−4.64253	+	5.35776i	−0.152645	+	0.176162i
$926$	−9.22426	−	2.70849i	−0.303128	−	0.0890064i
$927$	−6.59787	+	4.24019i	−0.216702	+	0.139266i
$928$	−1.22055	−	2.67263i	−0.0400665	−	0.0877334i
$929$	22.4388	+	25.8958i	0.736194	+	0.849613i	0.993154	−	0.116809i	$-0.0372665\pi$
$929$	22.4388	+	25.8958i	0.736194	+	0.849613i	−0.256960	+	0.966422i	$0.582721\pi$
$930$	−4.25096	−	2.73192i	−0.139394	−	0.0895833i
$931$	−2.26457	+	15.7504i	−0.0742183	+	0.516200i
$932$	2.37893	−	16.5458i	0.0779244	−	0.541976i
$933$	−7.62025	−	4.89724i	−0.249476	−	0.160328i
$934$	−10.3864	−	11.9866i	−0.339855	−	0.392213i
$935$	−42.1278	−	92.2471i	−1.37773	−	3.01680i
$936$	−0.966031	+	0.620830i	−0.0315757	+	0.0202925i
$937$	−9.52597	−	2.79708i	−0.311200	−	0.0913766i	0.122403	−	0.992480i	$-0.460940\pi$
$937$	−9.52597	−	2.79708i	−0.311200	−	0.0913766i	−0.433603	+	0.901104i	$0.642758\pi$
$938$	3.58888	−	4.14179i	0.117181	−	0.135234i
$939$	−5.48765	+	1.61132i	−0.179083	+	0.0525835i
$940$	−7.17392	+	15.7087i	−0.233988	+	0.512361i
$941$	−2.54908	−	17.7293i	−0.0830977	−	0.577957i	−0.988247	−	0.152864i	$-0.951150\pi$
$941$	−2.54908	−	17.7293i	−0.0830977	−	0.577957i	0.905150	−	0.425093i	$-0.139759\pi$
$942$	−2.83359			−0.0923233
$943$	−1.03980	−	3.13364i	−0.0338606	−	0.102045i
$944$	−4.03445			−0.131310
$945$	0.642438	+	4.46825i	0.0208985	+	0.145352i
$946$	19.7622	−	43.2732i	0.642525	−	1.40693i
$947$	−34.9446	+	10.2607i	−1.13555	+	0.333427i	−0.794886	−	0.606759i	$-0.792469\pi$
$947$	−34.9446	+	10.2607i	−1.13555	+	0.333427i	−0.340662	+	0.940186i	$0.610651\pi$
$948$	−6.90000	+	7.96302i	−0.224102	+	0.258627i
$949$	12.6594	+	3.71713i	0.410941	+	0.120663i
$950$	3.44940	−	2.21679i	0.111913	−	0.0719223i
$951$	−7.60662	−	16.6562i	−0.246662	−	0.540114i
$952$	9.12473	+	10.5305i	0.295734	+	0.341295i
$953$	−37.7109	−	24.2353i	−1.22157	−	0.785058i	−0.239016	−	0.971016i	$-0.576825\pi$
$953$	−37.7109	−	24.2353i	−1.22157	−	0.785058i	−0.982558	+	0.185957i	$0.940461\pi$
$954$	0.766867	−	5.33368i	0.0248282	−	0.172684i
$955$	6.67771	−	46.4445i	0.216086	−	1.50291i
$956$	−7.19559	−	4.62433i	−0.232722	−	0.149561i
$957$	−10.6850	−	12.3312i	−0.345399	−	0.398611i
$958$	−11.7357	−	25.6977i	−0.379164	−	0.830254i
$959$	14.3948	−	9.25096i	0.464831	−	0.298729i
$960$	2.33380	+	0.685265i	0.0753230	+	0.0221168i
$961$	17.4743	−	20.1665i	0.563688	−	0.650531i
$962$	8.52557	−	2.50333i	0.274875	−	0.0807107i
$963$	−3.86497	+	8.46310i	−0.124547	+	0.272720i
$964$	−3.00884	−	20.9269i	−0.0969082	−	0.674011i
$965$	62.9496			2.02642
$966$	−2.20906	+	8.62220i	−0.0710755	+	0.277415i
$967$	−15.8234			−0.508846			−0.254423	−	0.967093i	$-0.581885\pi$
$967$	−15.8234			−0.508846			−0.254423	+	0.967093i	$0.581885\pi$
$968$	2.82347	+	19.6377i	0.0907498	+	0.631179i
$969$	−13.9580	+	30.5637i	−0.448394	+	0.981847i
$970$	23.2037	−	6.81323i	0.745026	−	0.218759i
$971$	15.9576	−	18.4161i	0.512105	−	0.591001i	−0.439531	−	0.898227i	$-0.644856\pi$
$971$	15.9576	−	18.4161i	0.512105	−	0.591001i	0.951636	+	0.307227i	$0.0994010\pi$
$972$	−0.959493	−	0.281733i	−0.0307758	−	0.00903658i
$973$	−21.0293	+	13.5147i	−0.674170	+	0.433263i
$974$	0.840018	+	1.83938i	0.0269159	+	0.0589377i
$975$	−0.688971	−	0.795115i	−0.0220647	−	0.0254641i
$976$	−0.319039	−	0.205034i	−0.0102122	−	0.00656298i
$977$	0.300639	−	2.09099i	0.00961831	−	0.0668968i	−0.984447	−	0.175682i	$-0.943787\pi$
$977$	0.300639	−	2.09099i	0.00961831	−	0.0668968i	0.994065	+	0.108785i	$0.0346961\pi$
$978$	3.55284	−	24.7105i	0.113607	−	0.790155i
$979$	50.3419	+	32.3528i	1.60893	+	1.03400i
$980$	−5.66340	−	6.53592i	−0.180911	−	0.208782i
$981$	6.01875	+	13.1792i	0.192164	+	0.420780i
$982$	−15.4989	+	9.96053i	−0.494590	+	0.317853i
$983$	5.63251	+	1.65385i	0.179649	+	0.0527497i	0.370320	−	0.928904i	$-0.379248\pi$
$983$	5.63251	+	1.65385i	0.179649	+	0.0527497i	−0.190671	+	0.981654i	$0.561066\pi$
$984$	0.450833	−	0.520289i	0.0143720	−	0.0165862i
$985$	42.9029	−	12.5974i	1.36700	−	0.401387i
$986$	−9.16361	+	20.0655i	−0.291829	+	0.639016i
$987$	−1.87527	−	13.0428i	−0.0596904	−	0.415156i
$988$	−5.13916			−0.163499
$989$	−23.3998	−	33.7679i	−0.744071	−	1.07376i
$990$	13.5075			0.429297
$991$	7.05110	+	49.0415i	0.223985	+	1.55785i	0.722746	+	0.691114i	$0.242880\pi$
$991$	7.05110	+	49.0415i	0.223985	+	1.55785i	−0.498761	+	0.866740i	$0.666211\pi$
$992$	0.863019	−	1.88975i	0.0274009	−	0.0599996i
$993$	1.10801	−	0.325341i	0.0351616	−	0.0103244i
$994$	−18.3160	+	21.1378i	−0.580948	+	0.670450i
$995$	20.2051	+	5.93276i	0.640546	+	0.188081i
$996$	8.78979	−	5.64886i	0.278515	−	0.178991i
$997$	−0.732045	−	1.60296i	−0.0231841	−	0.0507661i	0.897686	−	0.440636i	$-0.145247\pi$
$997$	−0.732045	−	1.60296i	−0.0231841	−	0.0507661i	−0.920870	+	0.389870i	$0.872520\pi$
$998$	−8.27053	−	9.54470i	−0.261799	−	0.302132i
$999$	6.50945	+	4.18337i	0.205950	+	0.132356i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.e.c.49.1	yes	10
3.2	odd	2		414.2.i.b.325.1		10
23.8	even	11	inner	138.2.e.c.31.1	✓	10
23.10	odd	22		3174.2.a.y.1.5		5
23.13	even	11		3174.2.a.z.1.1		5
69.8	odd	22		414.2.i.b.307.1		10
69.56	even	22		9522.2.a.ca.1.1		5
69.59	odd	22		9522.2.a.bv.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.c.31.1	✓	10	23.8	even	11	inner
138.2.e.c.49.1	yes	10	1.1	even	1	trivial
414.2.i.b.307.1		10	69.8	odd	22
414.2.i.b.325.1		10	3.2	odd	2
3174.2.a.y.1.5		5	23.10	odd	22
3174.2.a.z.1.1		5	23.13	even	11
9522.2.a.bv.1.5		5	69.59	odd	22
9522.2.a.ca.1.1		5	69.56	even	22

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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.59283 - 1.83823i) q^{5} +(0.959493 + 0.281733i) q^{6} +(1.56130 - 1.00339i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.59283 - 1.83823i) q^{5} +(0.959493 + 0.281733i) q^{6} +(1.56130 - 1.00339i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(2.04620 + 1.31501i) q^{10} +(-0.790323 + 5.49682i) q^{11} +(-0.142315 + 0.989821i) q^{12} +(0.966031 + 0.620830i) q^{13} +(1.21537 + 1.40261i) q^{14} +(-1.01042 - 2.21252i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-7.20366 - 2.11519i) q^{17} +(0.654861 - 0.755750i) q^{18} +(4.29408 - 1.26086i) q^{19} +(-1.01042 + 2.21252i) q^{20} +(-0.264125 - 1.83703i) q^{21} -5.55334 q^{22} +(-2.45093 + 4.12225i) q^{23} -1.00000 q^{24} +(-0.130388 - 0.906870i) q^{25} +(-0.477031 + 1.04455i) q^{26} +(-0.959493 + 0.281733i) q^{27} +(-1.21537 + 1.40261i) q^{28} +(-2.81913 - 0.827771i) q^{29} +(2.04620 - 1.31501i) q^{30} +(-0.863019 - 1.88975i) q^{31} +(0.654861 + 0.755750i) q^{32} +(4.67177 + 3.00236i) q^{33} +(1.06847 - 7.43136i) q^{34} +(0.642438 - 4.46825i) q^{35} +(0.841254 + 0.540641i) q^{36} +(-5.06718 - 5.84784i) q^{37} +(1.85913 + 4.07093i) q^{38} +(0.966031 - 0.620830i) q^{39} +(-2.33380 - 0.685265i) q^{40} +(-0.450833 + 0.520289i) q^{41} +(1.78074 - 0.522874i) q^{42} +(-3.55862 + 7.79229i) q^{43} +(-0.790323 - 5.49682i) q^{44} -2.43232 q^{45} +(-4.42909 - 1.83933i) q^{46} +7.09992 q^{47} +(-0.142315 - 0.989821i) q^{48} +(-1.47703 + 3.23425i) q^{49} +(0.879083 - 0.258122i) q^{50} +(-4.91655 + 5.67400i) q^{51} +(-1.10181 - 0.323520i) q^{52} +(4.53311 - 2.91326i) q^{53} +(-0.415415 - 0.909632i) q^{54} +(8.84555 + 10.2083i) q^{55} +(-1.56130 - 1.00339i) q^{56} +(0.636911 - 4.42981i) q^{57} +(0.418141 - 2.90824i) q^{58} +(-3.39399 - 2.18119i) q^{59} +(1.59283 + 1.83823i) q^{60} +(-0.157543 - 0.344971i) q^{61} +(1.74769 - 1.12317i) q^{62} +(-1.78074 - 0.522874i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(2.67995 - 0.786905i) q^{65} +(-2.30694 + 5.05150i) q^{66} +(-0.420243 - 2.92285i) q^{67} +7.50778 q^{68} +(2.73158 + 3.94189i) q^{69} +4.51420 q^{70} +(2.14473 + 14.9169i) q^{71} +(-0.415415 + 0.909632i) q^{72} +(11.0242 - 3.23701i) q^{73} +(5.06718 - 5.84784i) q^{74} +(-0.879083 - 0.258122i) q^{75} +(-3.76492 + 2.41956i) q^{76} +(4.28150 + 9.37518i) q^{77} +(0.751992 + 0.867845i) q^{78} +(8.86394 + 5.69651i) q^{79} +(0.346156 - 2.40757i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-0.579153 - 0.372199i) q^{82} +(-6.84228 - 7.89641i) q^{83} +(0.770978 + 1.68821i) q^{84} +(-15.3624 + 9.87283i) q^{85} +(-8.21942 - 2.41344i) q^{86} +(-1.92408 + 2.22050i) q^{87} +(5.32839 - 1.56456i) q^{88} +(4.47642 - 9.80199i) q^{89} +(-0.346156 - 2.40757i) q^{90} +2.13120 q^{91} +(1.19028 - 4.64578i) q^{92} -2.07749 q^{93} +(1.01042 + 7.02765i) q^{94} +(4.52201 - 9.90183i) q^{95} +(0.959493 - 0.281733i) q^{96} +(6.51094 - 7.51402i) q^{97} +(-3.41153 - 1.00172i) q^{98} +(4.67177 - 3.00236i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9}+O(q^{10}) \) 10 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 + q^8 - q^9	\( 10 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9} + 11 q^{10} + 11 q^{11} - q^{12} - 13 q^{13} + 13 q^{14} - 11 q^{15} - q^{16} + q^{18} - 2 q^{19} - 11 q^{20} + 9 q^{21} - 22 q^{22} - 10 q^{23} - 10 q^{24} + 5 q^{25} - 9 q^{26} - q^{27} - 13 q^{28} - 27 q^{29} + 11 q^{30} - 18 q^{31} + q^{32} + 33 q^{34} + 44 q^{35} - q^{36} - q^{37} + 13 q^{38} - 13 q^{39} - 11 q^{40} - 16 q^{41} + 2 q^{42} + 20 q^{43} + 11 q^{44} + 22 q^{45} - q^{46} - q^{48} - 19 q^{49} - 27 q^{50} - 11 q^{51} - 2 q^{52} - q^{53} + q^{54} + 33 q^{55} + 2 q^{56} - 13 q^{57} - 17 q^{58} - q^{59} - 34 q^{61} - 4 q^{62} - 2 q^{63} - q^{64} + 11 q^{65} + 8 q^{67} + 22 q^{68} + 23 q^{69} + 22 q^{70} - 22 q^{71} + q^{72} + 31 q^{73} + q^{74} + 27 q^{75} - 2 q^{76} + 22 q^{77} + 2 q^{78} + 32 q^{79} - q^{81} - 28 q^{82} + 33 q^{83} + 9 q^{84} - 11 q^{85} - 20 q^{86} + 6 q^{87} + 22 q^{88} - 23 q^{89} + 18 q^{91} + 23 q^{92} + 4 q^{93} + 11 q^{94} - 22 q^{95} + q^{96} - q^{97} - 14 q^{98}+O(q^{100}) \) 10 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 + q^8 - q^9 + 11 * q^10 + 11 * q^11 - q^12 - 13 * q^13 + 13 * q^14 - 11 * q^15 - q^16 + q^18 - 2 * q^19 - 11 * q^20 + 9 * q^21 - 22 * q^22 - 10 * q^23 - 10 * q^24 + 5 * q^25 - 9 * q^26 - q^27 - 13 * q^28 - 27 * q^29 + 11 * q^30 - 18 * q^31 + q^32 + 33 * q^34 + 44 * q^35 - q^36 - q^37 + 13 * q^38 - 13 * q^39 - 11 * q^40 - 16 * q^41 + 2 * q^42 + 20 * q^43 + 11 * q^44 + 22 * q^45 - q^46 - q^48 - 19 * q^49 - 27 * q^50 - 11 * q^51 - 2 * q^52 - q^53 + q^54 + 33 * q^55 + 2 * q^56 - 13 * q^57 - 17 * q^58 - q^59 - 34 * q^61 - 4 * q^62 - 2 * q^63 - q^64 + 11 * q^65 + 8 * q^67 + 22 * q^68 + 23 * q^69 + 22 * q^70 - 22 * q^71 + q^72 + 31 * q^73 + q^74 + 27 * q^75 - 2 * q^76 + 22 * q^77 + 2 * q^78 + 32 * q^79 - q^81 - 28 * q^82 + 33 * q^83 + 9 * q^84 - 11 * q^85 - 20 * q^86 + 6 * q^87 + 22 * q^88 - 23 * q^89 + 18 * q^91 + 23 * q^92 + 4 * q^93 + 11 * q^94 - 22 * q^95 + q^96 - q^97 - 14 * q^98

Introduction

L-functions

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