LMFDB - Embedded newform 693.2.m.i.631.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			631.3
Root			$0.901622 + 0.655067i$ of defining polynomial
Character	$\chi$	$=$	693.631
Dual form			693.2.m.i.190.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.901622 + 0.655067i) q^{2} +(-0.234224 - 0.720867i) q^{4} +(2.79603 - 2.03143i) q^{5} +(0.309017 + 0.951057i) q^{7} +(0.949813 - 2.92322i) q^{8} +O(q^{10})$	\(q+(0.901622 + 0.655067i) q^{2} +(-0.234224 - 0.720867i) q^{4} +(2.79603 - 2.03143i) q^{5} +(0.309017 + 0.951057i) q^{7} +(0.949813 - 2.92322i) q^{8} +3.85168 q^{10} +(-3.31530 + 0.0938970i) q^{11} +(1.66629 + 1.21063i) q^{13} +(-0.344389 + 1.05992i) q^{14} +(1.54487 - 1.12241i) q^{16} +(1.56442 - 1.13662i) q^{17} +(0.501522 - 1.54353i) q^{19} +(-2.11929 - 1.53975i) q^{20} +(-3.05065 - 2.08708i) q^{22} +0.807136 q^{23} +(2.14596 - 6.60459i) q^{25} +(0.709322 + 2.18307i) q^{26} +(0.613206 - 0.445520i) q^{28} +(-2.46400 - 7.58342i) q^{29} +(-0.637845 - 0.463421i) q^{31} -4.01918 q^{32} +2.15508 q^{34} +(2.79603 + 2.03143i) q^{35} +(3.10926 + 9.56931i) q^{37} +(1.46330 - 1.06315i) q^{38} +(-3.28263 - 10.1029i) q^{40} +(0.657011 - 2.02207i) q^{41} +3.08043 q^{43} +(0.844208 + 2.36789i) q^{44} +(0.727732 + 0.528728i) q^{46} +(-2.33812 + 7.19600i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(6.26129 - 4.54910i) q^{50} +(0.482420 - 1.48474i) q^{52} +(8.75554 + 6.36127i) q^{53} +(-9.07891 + 6.99733i) q^{55} +3.07366 q^{56} +(2.74605 - 8.45147i) q^{58} +(1.01872 + 3.13529i) q^{59} +(0.871010 - 0.632826i) q^{61} +(-0.271523 - 0.835662i) q^{62} +(-6.71351 - 4.87765i) q^{64} +7.11832 q^{65} +2.40314 q^{67} +(-1.18577 - 0.861515i) q^{68} +(1.19024 + 3.66317i) q^{70} +(-2.57963 + 1.87421i) q^{71} +(0.378940 + 1.16626i) q^{73} +(-3.46516 + 10.6647i) q^{74} -1.23015 q^{76} +(-1.11378 - 3.12402i) q^{77} +(7.67096 + 5.57328i) q^{79} +(2.03939 - 6.27659i) q^{80} +(1.91697 - 1.39276i) q^{82} +(-13.0004 + 9.44536i) q^{83} +(2.06520 - 6.35602i) q^{85} +(2.77738 + 2.01789i) q^{86} +(-2.87443 + 9.78053i) q^{88} +4.43830 q^{89} +(-0.636468 + 1.95885i) q^{91} +(-0.189050 - 0.581837i) q^{92} +(-6.82196 + 4.95645i) q^{94} +(-1.73330 - 5.33455i) q^{95} +(-5.23278 - 3.80184i) q^{97} -1.11447 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8}+O(q^{10}) $ 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8	$ 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8} + 12 q^{10} + 3 q^{11} - 7 q^{13} - 2 q^{14} + 17 q^{16} + 5 q^{17} + 19 q^{19} - q^{20} - 33 q^{22} - 32 q^{23} + 7 q^{25} + 27 q^{26} + 4 q^{28} - 3 q^{29} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 4 q^{37} + 5 q^{38} - 10 q^{40} + 10 q^{41} - 8 q^{43} + 38 q^{44} - 42 q^{46} + 23 q^{47} - 4 q^{49} - 52 q^{50} + 33 q^{52} - 4 q^{53} - 12 q^{55} + 20 q^{58} - 17 q^{59} - 7 q^{61} - 79 q^{62} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} - 18 q^{70} + 14 q^{71} - 35 q^{73} + 29 q^{74} + 52 q^{76} + 3 q^{77} + 15 q^{79} + 87 q^{80} + 19 q^{82} - 5 q^{83} + 6 q^{85} + 52 q^{86} + 55 q^{88} - 74 q^{89} + 13 q^{91} + 55 q^{92} - 24 q^{94} - 32 q^{95} + 20 q^{97} - 2 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8 + 12 * q^10 + 3 * q^11 - 7 * q^13 - 2 * q^14 + 17 * q^16 + 5 * q^17 + 19 * q^19 - q^20 - 33 * q^22 - 32 * q^23 + 7 * q^25 + 27 * q^26 + 4 * q^28 - 3 * q^29 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 4 * q^37 + 5 * q^38 - 10 * q^40 + 10 * q^41 - 8 * q^43 + 38 * q^44 - 42 * q^46 + 23 * q^47 - 4 * q^49 - 52 * q^50 + 33 * q^52 - 4 * q^53 - 12 * q^55 + 20 * q^58 - 17 * q^59 - 7 * q^61 - 79 * q^62 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 - 18 * q^70 + 14 * q^71 - 35 * q^73 + 29 * q^74 + 52 * q^76 + 3 * q^77 + 15 * q^79 + 87 * q^80 + 19 * q^82 - 5 * q^83 + 6 * q^85 + 52 * q^86 + 55 * q^88 - 74 * q^89 + 13 * q^91 + 55 * q^92 - 24 * q^94 - 32 * q^95 + 20 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.901622	+	0.655067i	0.637543	+	0.463202i	0.859005	−	0.511967i	$-0.171083\pi$
$2$	0.901622	+	0.655067i	0.637543	+	0.463202i	−0.221462	+	0.975169i	$0.571083\pi$
$3$		0			0
$3$		0			0
$4$	−0.234224	−	0.720867i	−0.117112	−	0.360433i
$5$	2.79603	−	2.03143i	1.25042	−	0.908484i	0.252174	−	0.967682i	$-0.418854\pi$
$5$	2.79603	−	2.03143i	1.25042	−	0.908484i	0.998246	+	0.0591979i	$0.0188543\pi$
$6$		0			0
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$	0.949813	−	2.92322i	0.335810	−	1.03352i
$9$		0			0
$10$	3.85168			1.21801
$11$	−3.31530	+	0.0938970i	−0.999599	+	0.0283110i
$11$	−3.31530	+	0.0938970i	−0.999599	+	0.0283110i
$12$		0			0
$13$	1.66629	+	1.21063i	0.462147	+	0.335769i	0.794373	−	0.607430i	$-0.207800\pi$
$13$	1.66629	+	1.21063i	0.462147	+	0.335769i	−0.332226	+	0.943200i	$0.607800\pi$
$14$	−0.344389	+	1.05992i	−0.0920419	+	0.283276i
$15$		0			0
$16$	1.54487	−	1.12241i	0.386217	−	0.280603i
$17$	1.56442	−	1.13662i	0.379427	−	0.275670i	−0.381682	−	0.924294i	$-0.624655\pi$
$17$	1.56442	−	1.13662i	0.379427	−	0.275670i	0.761109	+	0.648624i	$0.224655\pi$
$18$		0			0
$19$	0.501522	−	1.54353i	0.115057	−	0.354109i	−0.876902	−	0.480669i	$-0.840394\pi$
$19$	0.501522	−	1.54353i	0.115057	−	0.354109i	0.991959	+	0.126560i	$0.0403937\pi$
$20$	−2.11929	−	1.53975i	−0.473887	−	0.344299i
$21$		0			0
$22$	−3.05065	−	2.08708i	−0.650401	−	0.444967i
$23$	0.807136			0.168299			0.0841497	−	0.996453i	$-0.473183\pi$
$23$	0.807136			0.168299			0.0841497	+	0.996453i	$0.473183\pi$
$24$		0			0
$25$	2.14596	−	6.60459i	0.429192	−	1.32092i
$26$	0.709322	+	2.18307i	0.139109	+	0.428135i
$27$		0			0
$28$	0.613206	−	0.445520i	0.115885	−	0.0841954i
$29$	−2.46400	−	7.58342i	−0.457554	−	1.40821i	−0.868111	−	0.496371i	$-0.834666\pi$
$29$	−2.46400	−	7.58342i	−0.457554	−	1.40821i	0.410557	−	0.911835i	$-0.365334\pi$
$30$		0			0
$31$	−0.637845	−	0.463421i	−0.114560	−	0.0832330i	0.529030	−	0.848603i	$-0.322556\pi$
$31$	−0.637845	−	0.463421i	−0.114560	−	0.0832330i	−0.643590	+	0.765370i	$0.722556\pi$
$32$	−4.01918			−0.710497
$33$		0			0
$34$	2.15508			0.369592
$35$	2.79603	+	2.03143i	0.472615	+	0.343375i
$36$		0			0
$37$	3.10926	+	9.56931i	0.511159	+	1.57318i	0.790164	+	0.612895i	$0.209995\pi$
$37$	3.10926	+	9.56931i	0.511159	+	1.57318i	−0.279005	+	0.960290i	$0.590005\pi$
$38$	1.46330	−	1.06315i	0.237378	−	0.172465i
$39$		0			0
$40$	−3.28263	−	10.1029i	−0.519029	−	1.59741i
$41$	0.657011	−	2.02207i	0.102608	−	0.315795i	−0.886554	−	0.462626i	$-0.846907\pi$
$41$	0.657011	−	2.02207i	0.102608	−	0.315795i	0.989162	+	0.146831i	$0.0469074\pi$
$42$		0			0
$43$	3.08043			0.469761			0.234880	−	0.972024i	$-0.424530\pi$
$43$	3.08043			0.469761			0.234880	+	0.972024i	$0.424530\pi$
$44$	0.844208	+	2.36789i	0.127269	+	0.356973i
$45$		0			0
$46$	0.727732	+	0.528728i	0.107298	+	0.0779567i
$47$	−2.33812	+	7.19600i	−0.341050	+	1.04964i	0.622615	+	0.782529i	$0.286070\pi$
$47$	−2.33812	+	7.19600i	−0.341050	+	1.04964i	−0.963665	+	0.267115i	$0.913930\pi$
$48$		0			0
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	6.26129	−	4.54910i	0.885481	−	0.643339i
$51$		0			0
$52$	0.482420	−	1.48474i	0.0668996	−	0.205896i
$53$	8.75554	+	6.36127i	1.20267	+	0.873788i	0.994544	−	0.104315i	$-0.0332649\pi$
$53$	8.75554	+	6.36127i	1.20267	+	0.873788i	0.208122	+	0.978103i	$0.433265\pi$
$54$		0			0
$55$	−9.07891	+	6.99733i	−1.22420	+	0.943520i
$56$	3.07366			0.410735
$57$		0			0
$58$	2.74605	−	8.45147i	0.360574	−	1.10973i
$59$	1.01872	+	3.13529i	0.132626	+	0.408180i	0.995213	−	0.0977281i	$-0.0311576\pi$
$59$	1.01872	+	3.13529i	0.132626	+	0.408180i	−0.862587	+	0.505908i	$0.831158\pi$
$60$		0			0
$61$	0.871010	−	0.632826i	0.111521	−	0.0810250i	−0.530627	−	0.847606i	$-0.678043\pi$
$61$	0.871010	−	0.632826i	0.111521	−	0.0810250i	0.642148	+	0.766581i	$0.278043\pi$
$62$	−0.271523	−	0.835662i	−0.0344835	−	0.106129i
$63$		0			0
$64$	−6.71351	−	4.87765i	−0.839189	−	0.609707i
$65$	7.11832			0.882919
$66$		0			0
$67$	2.40314			0.293590			0.146795	−	0.989167i	$-0.453104\pi$
$67$	2.40314			0.293590			0.146795	+	0.989167i	$0.453104\pi$
$68$	−1.18577	−	0.861515i	−0.143796	−	0.104474i
$69$		0			0
$70$	1.19024	+	3.66317i	0.142260	+	0.437832i
$71$	−2.57963	+	1.87421i	−0.306145	+	0.222428i	−0.730241	−	0.683190i	$-0.760592\pi$
$71$	−2.57963	+	1.87421i	−0.306145	+	0.222428i	0.424095	+	0.905618i	$0.360592\pi$
$72$		0			0
$73$	0.378940	+	1.16626i	0.0443516	+	0.136500i	0.970780	−	0.239970i	$-0.0771377\pi$
$73$	0.378940	+	1.16626i	0.0443516	+	0.136500i	−0.926429	+	0.376470i	$0.877138\pi$
$74$	−3.46516	+	10.6647i	−0.402817	+	1.23974i
$75$		0			0
$76$	−1.23015			−0.141107
$77$	−1.11378	−	3.12402i	−0.126927	−	0.356015i
$78$		0			0
$79$	7.67096	+	5.57328i	0.863050	+	0.627043i	0.928713	−	0.370799i	$-0.120916\pi$
$79$	7.67096	+	5.57328i	0.863050	+	0.627043i	−0.0656630	+	0.997842i	$0.520916\pi$
$80$	2.03939	−	6.27659i	0.228010	−	0.701744i
$81$		0			0
$82$	1.91697	−	1.39276i	0.211694	−	0.153805i
$83$	−13.0004	+	9.44536i	−1.42698	+	1.03676i	−0.436412	+	0.899747i	$0.643751\pi$
$83$	−13.0004	+	9.44536i	−1.42698	+	1.03676i	−0.990569	+	0.137016i	$0.956249\pi$
$84$		0			0
$85$	2.06520	−	6.35602i	0.224002	−	0.689407i
$86$	2.77738	+	2.01789i	0.299493	+	0.217594i
$87$		0			0
$88$	−2.87443	+	9.78053i	−0.306415	+	1.04261i
$89$	4.43830			0.470459			0.235230	−	0.971940i	$-0.424416\pi$
$89$	4.43830			0.470459			0.235230	+	0.971940i	$0.424416\pi$
$90$		0			0
$91$	−0.636468	+	1.95885i	−0.0667199	+	0.205343i
$92$	−0.189050	−	0.581837i	−0.0197099	−	0.0606607i
$93$		0			0
$94$	−6.82196	+	4.95645i	−0.703632	+	0.511218i
$95$	−1.73330	−	5.33455i	−0.177833	−	0.547313i
$96$		0			0
$97$	−5.23278	−	3.80184i	−0.531308	−	0.386018i	0.289539	−	0.957166i	$-0.406498\pi$
$97$	−5.23278	−	3.80184i	−0.531308	−	0.386018i	−0.820847	+	0.571148i	$0.806498\pi$
$98$	−1.11447			−0.112578
$99$		0			0
$100$	−5.26366			−0.526366
$101$	−12.4952	−	9.07828i	−1.24332	−	0.903323i	−0.245503	−	0.969396i	$-0.578953\pi$
$101$	−12.4952	−	9.07828i	−1.24332	−	0.903323i	−0.997815	+	0.0660728i	$0.978953\pi$
$102$		0			0
$103$	2.75276	+	8.47213i	0.271238	+	0.834784i	0.990190	+	0.139725i	$0.0446218\pi$
$103$	2.75276	+	8.47213i	0.271238	+	0.834784i	−0.718953	+	0.695059i	$0.755378\pi$
$104$	5.12162	−	3.72107i	0.502216	−	0.364881i
$105$		0			0
$106$	3.72713	+	11.4709i	0.362011	+	1.11416i
$107$	−1.08533	+	3.34029i	−0.104922	+	0.322918i	−0.989712	−	0.143072i	$-0.954302\pi$
$107$	−1.08533	+	3.34029i	−0.104922	+	0.322918i	0.884790	+	0.465990i	$0.154302\pi$
$108$		0			0
$109$	3.87655			0.371306			0.185653	−	0.982615i	$-0.440560\pi$
$109$	3.87655			0.371306			0.185653	+	0.982615i	$0.440560\pi$
$110$	−12.7695	+	0.361662i	−1.21752	+	0.0344831i
$111$		0			0
$112$	1.54487	+	1.12241i	0.145976	+	0.106058i
$113$	−3.29224	+	10.1325i	−0.309708	+	0.953183i	0.668170	+	0.744008i	$0.267078\pi$
$113$	−3.29224	+	10.1325i	−0.309708	+	0.953183i	−0.977878	+	0.209175i	$0.932922\pi$
$114$		0			0
$115$	2.25677	−	1.63964i	0.210445	−	0.152897i
$116$	−4.88951	+	3.55243i	−0.453979	+	0.329835i
$117$		0			0
$118$	−1.13533	+	3.49417i	−0.104515	+	0.321665i
$119$	1.56442	+	1.13662i	0.143410	+	0.104194i
$120$		0			0
$121$	10.9824	−	0.622593i	0.998397	−	0.0565993i
$122$	1.19987			0.108631
$123$		0			0
$124$	−0.184667	+	0.568346i	−0.0165836	+	0.0510389i
$125$	−2.07667	−	6.39134i	−0.185743	−	0.571659i
$126$		0			0
$127$	−15.7361	+	11.4330i	−1.39635	+	1.01451i	−0.401220	+	0.915982i	$0.631414\pi$
$127$	−15.7361	+	11.4330i	−1.39635	+	1.01451i	−0.995134	+	0.0985289i	$0.968586\pi$
$128$	−0.373878	−	1.15068i	−0.0330464	−	0.101706i
$129$		0			0
$130$	6.41804	+	4.66298i	0.562899	+	0.408970i
$131$	−5.11284			−0.446711			−0.223355	−	0.974737i	$-0.571701\pi$
$131$	−5.11284			−0.446711			−0.223355	+	0.974737i	$0.571701\pi$
$132$		0			0
$133$	1.62296			0.140728
$134$	2.16672	+	1.57422i	0.187176	+	0.135992i
$135$		0			0
$136$	−1.83668	−	5.65272i	−0.157494	−	0.484717i
$137$	7.36247	−	5.34915i	0.629019	−	0.457009i	−0.227042	−	0.973885i	$-0.572905\pi$
$137$	7.36247	−	5.34915i	0.629019	−	0.457009i	0.856060	+	0.516876i	$0.172905\pi$
$138$		0			0
$139$	−4.02234	−	12.3795i	−0.341171	−	1.05002i	−0.963602	−	0.267341i	$-0.913855\pi$
$139$	−4.02234	−	12.3795i	−0.341171	−	1.05002i	0.622431	−	0.782675i	$-0.286145\pi$
$140$	0.809496	−	2.49137i	0.0684149	−	0.210559i
$141$		0			0
$142$	−3.55358			−0.298210
$143$	−5.63793	−	3.85715i	−0.471468	−	0.322551i
$144$		0			0
$145$	−22.2946	−	16.1980i	−1.85147	−	1.34517i
$146$	−0.422316	+	1.29975i	−0.0349511	+	0.107568i
$147$		0			0
$148$	6.16994	−	4.48272i	0.507166	−	0.368477i
$149$	−2.54557	+	1.84947i	−0.208541	+	0.151514i	−0.687153	−	0.726512i	$-0.741140\pi$
$149$	−2.54557	+	1.84947i	−0.208541	+	0.151514i	0.478612	+	0.878026i	$0.341140\pi$
$150$		0			0
$151$	0.885940	−	2.72664i	0.0720968	−	0.221891i	−0.908515	−	0.417853i	$-0.862783\pi$
$151$	0.885940	−	2.72664i	0.0720968	−	0.221891i	0.980612	+	0.195962i	$0.0627828\pi$
$152$	−4.03572	−	2.93212i	−0.327340	−	0.237827i
$153$		0			0
$154$	1.04223	−	3.54629i	0.0839851	−	0.285768i
$155$	−2.72484			−0.218864
$156$		0			0
$157$	−6.64062	+	20.4377i	−0.529979	+	1.63111i	0.224275	+	0.974526i	$0.427999\pi$
$157$	−6.64062	+	20.4377i	−0.529979	+	1.63111i	−0.754254	+	0.656582i	$0.772001\pi$
$158$	3.26544	+	10.0500i	0.259784	+	0.799534i
$159$		0			0
$160$	−11.2377	+	8.16468i	−0.888420	+	0.645475i
$161$	0.249419	+	0.767632i	0.0196569	+	0.0604978i
$162$		0			0
$163$	6.65210	+	4.83304i	0.521033	+	0.378553i	0.816993	−	0.576648i	$-0.195639\pi$
$163$	6.65210	+	4.83304i	0.521033	+	0.378553i	−0.295960	+	0.955200i	$0.595639\pi$
$164$	−1.61153			−0.125840
$165$		0			0
$166$	−17.9088			−1.38999
$167$	−17.5626	−	12.7600i	−1.35904	−	0.987397i	−0.998506	−	0.0546489i	$-0.982596\pi$
$167$	−17.5626	−	12.7600i	−1.35904	−	0.987397i	−0.360529	−	0.932748i	$-0.617404\pi$
$168$		0			0
$169$	−2.70632	−	8.32919i	−0.208178	−	0.640707i
$170$	6.02565	−	4.37789i	0.462146	−	0.335769i
$171$		0			0
$172$	−0.721509	−	2.22058i	−0.0550146	−	0.169317i
$173$	2.48624	−	7.65185i	0.189025	−	0.581760i	−0.810969	−	0.585089i	$-0.801060\pi$
$173$	2.48624	−	7.65185i	0.189025	−	0.581760i	0.999994	+	0.00332915i	$0.00105970\pi$
$174$		0			0
$175$	6.94447			0.524953
$176$	−5.01630	+	3.86619i	−0.378118	+	0.291425i
$177$		0			0
$178$	4.00167	+	2.90739i	0.299938	+	0.217918i
$179$	1.11892	−	3.44369i	0.0836322	−	0.257393i	−0.900493	−	0.434871i	$-0.856794\pi$
$179$	1.11892	−	3.44369i	0.0836322	−	0.257393i	0.984125	+	0.177478i	$0.0567938\pi$
$180$		0			0
$181$	−12.7970	+	9.29753i	−0.951190	+	0.691080i	−0.951088	−	0.308920i	$-0.900033\pi$
$181$	−12.7970	+	9.29753i	−0.951190	+	0.691080i	−0.000102207		1.00000i	$0.500033\pi$
$182$	−1.85703	+	1.34921i	−0.137652	+	0.100010i
$183$		0			0
$184$	0.766628	−	2.35944i	0.0565165	−	0.173940i
$185$	28.1330	+	20.4398i	2.06838	+	1.50276i
$186$		0			0
$187$	−5.07979	+	3.91512i	−0.371471	+	0.286302i
$188$	5.73500			0.418268
$189$		0			0
$190$	1.93170	−	5.94518i	0.140141	−	0.431308i
$191$	−0.132593	−	0.408080i	−0.00959411	−	0.0295276i	0.946145	−	0.323744i	$-0.104942\pi$
$191$	−0.132593	−	0.408080i	−0.00959411	−	0.0295276i	−0.955739	+	0.294216i	$0.904942\pi$
$192$		0			0
$193$	12.2767	−	8.91954i	0.883696	−	0.642042i	−0.0505310	−	0.998722i	$-0.516091\pi$
$193$	12.2767	−	8.91954i	0.883696	−	0.642042i	0.934227	+	0.356680i	$0.116091\pi$
$194$	−2.22753	−	6.85564i	−0.159927	−	0.492206i
$195$		0			0
$196$	0.613206	+	0.445520i	0.0438004	+	0.0318229i
$197$	20.8082			1.48252			0.741262	−	0.671216i	$-0.234228\pi$
$197$	20.8082			1.48252			0.741262	+	0.671216i	$0.234228\pi$
$198$		0			0
$199$	8.44567			0.598698			0.299349	−	0.954144i	$-0.403231\pi$
$199$	8.44567			0.598698			0.299349	+	0.954144i	$0.403231\pi$
$200$	−17.2684	−	12.5462i	−1.22106	−	0.887153i
$201$		0			0
$202$	−5.31906	−	16.3704i	−0.374247	−	1.15182i
$203$	6.45084	−	4.68681i	0.452760	−	0.328950i
$204$		0			0
$205$	−2.27068	−	6.98844i	−0.158591	−	0.488094i
$206$	−3.06786	+	9.44190i	−0.213748	+	0.657849i
$207$		0			0
$208$	3.93303			0.272707
$209$	−1.51776	+	5.16434i	−0.104986	+	0.357225i
$210$		0			0
$211$	7.97632	+	5.79513i	0.549112	+	0.398953i	0.827458	−	0.561528i	$-0.189786\pi$
$211$	7.97632	+	5.79513i	0.549112	+	0.398953i	−0.278346	+	0.960481i	$0.589786\pi$
$212$	2.53487	−	7.80154i	0.174096	−	0.535812i
$213$		0			0
$214$	−3.16667	+	2.30072i	−0.216469	+	0.157274i
$215$	8.61295	−	6.25768i	0.587399	−	0.426770i
$216$		0			0
$217$	0.243635	−	0.749832i	0.0165390	−	0.0509019i
$218$	3.49518	+	2.53940i	0.236724	+	0.171990i
$219$		0			0
$220$	7.17064	+	4.90574i	0.483445	+	0.330745i
$221$	3.98281			0.267913
$222$		0			0
$223$	5.37562	−	16.5445i	0.359978	−	1.10790i	−0.593088	−	0.805138i	$-0.702091\pi$
$223$	5.37562	−	16.5445i	0.359978	−	1.10790i	0.953066	−	0.302762i	$-0.0979087\pi$
$224$	−1.24199	−	3.82246i	−0.0829842	−	0.255399i
$225$		0			0
$226$	−9.60581	+	6.97903i	−0.638969	+	0.464238i
$227$	3.90334	+	12.0133i	0.259074	+	0.797348i	0.993000	+	0.118118i	$0.0376861\pi$
$227$	3.90334	+	12.0133i	0.259074	+	0.797348i	−0.733926	+	0.679230i	$0.762314\pi$
$228$		0			0
$229$	−3.69997	−	2.68819i	−0.244501	−	0.177640i	0.458785	−	0.888547i	$-0.348285\pi$
$229$	−3.69997	−	2.68819i	−0.244501	−	0.177640i	−0.703286	+	0.710907i	$0.748285\pi$
$230$	3.10883			0.204990
$231$		0			0
$232$	−24.5084			−1.60905
$233$	19.3006	+	14.0227i	1.26443	+	0.918659i	0.998966	−	0.0454624i	$-0.0144761\pi$
$233$	19.3006	+	14.0227i	1.26443	+	0.918659i	0.265460	+	0.964122i	$0.414476\pi$
$234$		0			0
$235$	8.08073	+	24.8699i	0.527129	+	1.62234i
$236$	2.02152	−	1.46872i	0.131590	−	0.0956054i
$237$		0			0
$238$	0.665955	+	2.04960i	0.0431675	+	0.132856i
$239$	−2.73114	+	8.40558i	−0.176663	+	0.543711i	−0.999705	−	0.0242677i	$-0.992275\pi$
$239$	−2.73114	+	8.40558i	−0.176663	+	0.543711i	0.823043	+	0.567979i	$0.192275\pi$
$240$		0			0
$241$	18.9464			1.22045			0.610224	−	0.792229i	$-0.291079\pi$
$241$	18.9464			1.22045			0.610224	+	0.792229i	$0.291079\pi$
$242$	10.3098	+	6.63284i	0.662738	+	0.426375i
$243$		0			0
$244$	−0.660194	−	0.479659i	−0.0422646	−	0.0307070i
$245$	−1.06799	+	3.28693i	−0.0682312	+	0.209994i
$246$		0			0
$247$	2.70433	−	1.96481i	0.172072	−	0.125018i
$248$	−1.96052	+	1.42440i	−0.124493	+	0.0904495i
$249$		0			0
$250$	2.31438	−	7.12294i	0.146374	−	0.450494i
$251$	−2.31938	−	1.68513i	−0.146398	−	0.106364i	0.512175	−	0.858881i	$-0.328840\pi$
$251$	−2.31938	−	1.68513i	−0.146398	−	0.106364i	−0.658573	+	0.752516i	$0.728840\pi$
$252$		0			0
$253$	−2.67589	+	0.0757876i	−0.168232	+	0.00476473i
$254$	−21.6774			−1.36016
$255$		0			0
$256$	−4.71199	+	14.5020i	−0.294500	+	0.906377i
$257$	−6.92689	−	21.3188i	−0.432087	−	1.32983i	−0.896042	−	0.443969i	$-0.853570\pi$
$257$	−6.92689	−	21.3188i	−0.432087	−	1.32983i	0.463955	−	0.885859i	$-0.346430\pi$
$258$		0			0
$259$	−8.14014	+	5.91416i	−0.505804	+	0.367488i
$260$	−1.66728	−	5.13136i	−0.103400	−	0.318234i
$261$		0			0
$262$	−4.60985	−	3.34925i	−0.284797	−	0.206917i
$263$	−0.990706			−0.0610895			−0.0305448	−	0.999533i	$-0.509724\pi$
$263$	−0.990706			−0.0610895			−0.0305448	+	0.999533i	$0.509724\pi$
$264$		0			0
$265$	37.4032			2.29766
$266$	1.46330	+	1.06315i	0.0897205	+	0.0651858i
$267$		0			0
$268$	−0.562873	−	1.73234i	−0.0343829	−	0.105820i
$269$	−5.81713	+	4.22639i	−0.354677	+	0.257688i	−0.750828	−	0.660497i	$-0.770345\pi$
$269$	−5.81713	+	4.22639i	−0.354677	+	0.257688i	0.396152	+	0.918185i	$0.370345\pi$
$270$		0			0
$271$	−8.39423	−	25.8348i	−0.509913	−	1.56935i	−0.792351	−	0.610065i	$-0.791143\pi$
$271$	−8.39423	−	25.8348i	−0.509913	−	1.56935i	0.282438	−	0.959285i	$-0.408857\pi$
$272$	1.14107	−	3.51185i	0.0691874	−	0.212937i
$273$		0			0
$274$	10.1422			0.612714
$275$	−6.49434	+	22.0977i	−0.391624	+	1.33254i
$276$		0			0
$277$	−16.9777	−	12.3350i	−1.02009	−	0.741140i	−0.0537900	−	0.998552i	$-0.517130\pi$
$277$	−16.9777	−	12.3350i	−1.02009	−	0.741140i	−0.966302	+	0.257412i	$0.917130\pi$
$278$	4.48277	−	13.7965i	0.268859	−	0.827462i
$279$		0			0
$280$	8.59403	−	6.24393i	0.513592	−	0.373146i
$281$	−22.7803	+	16.5509i	−1.35896	+	0.987341i	−0.360448	+	0.932779i	$0.617376\pi$
$281$	−22.7803	+	16.5509i	−1.35896	+	0.987341i	−0.998510	+	0.0545621i	$0.982624\pi$
$282$		0			0
$283$	−8.09369	+	24.9098i	−0.481120	+	1.48074i	0.356403	+	0.934332i	$0.384003\pi$
$283$	−8.09369	+	24.9098i	−0.481120	+	1.48074i	−0.837523	+	0.546403i	$0.815997\pi$
$284$	1.95527	+	1.42058i	0.116024	+	0.0842961i
$285$		0			0
$286$	−2.55660	−	7.17091i	−0.151175	−	0.424025i
$287$	2.12613			0.125502
$288$		0			0
$289$	−4.09778	+	12.6117i	−0.241046	+	0.741863i
$290$	−9.49056	−	29.2089i	−0.557305	−	1.71521i
$291$		0			0
$292$	0.751959	−	0.546331i	0.0440051	−	0.0319716i
$293$	1.37941	+	4.24538i	0.0805858	+	0.248017i	0.983230	−	0.182370i	$-0.0583769\pi$
$293$	1.37941	+	4.24538i	0.0805858	+	0.248017i	−0.902644	+	0.430388i	$0.858377\pi$
$294$		0			0
$295$	9.21748	+	6.69689i	0.536663	+	0.389908i
$296$	30.9264			1.79756
$297$		0			0
$298$	−3.50667			−0.203136
$299$	1.34493	+	0.977145i	0.0777790	+	0.0565098i
$300$		0			0
$301$	0.951904	+	2.92966i	0.0548669	+	0.168863i
$302$	2.58492	−	1.87805i	0.148745	−	0.108070i
$303$		0			0
$304$	−0.957688	−	2.94746i	−0.0549271	−	0.169048i
$305$	1.14982	−	3.53879i	0.0658387	−	0.202631i
$306$		0			0
$307$	12.8841			0.735334			0.367667	−	0.929957i	$-0.380157\pi$
$307$	12.8841			0.735334			0.367667	+	0.929957i	$0.380157\pi$
$308$	−1.99113	+	1.53461i	−0.113455	+	0.0874425i
$309$		0			0
$310$	−2.45678	−	1.78495i	−0.139536	−	0.101379i
$311$	−8.28779	+	25.5072i	−0.469957	+	1.44638i	0.382682	+	0.923880i	$0.375001\pi$
$311$	−8.28779	+	25.5072i	−0.469957	+	1.44638i	−0.852639	+	0.522500i	$0.824999\pi$
$312$		0			0
$313$	−2.90331	+	2.10938i	−0.164105	+	0.119229i	−0.666807	−	0.745231i	$-0.732339\pi$
$313$	−2.90331	+	2.10938i	−0.164105	+	0.119229i	0.502702	+	0.864460i	$0.332339\pi$
$314$	−19.3754	+	14.0771i	−1.09342	+	0.794415i
$315$		0			0
$316$	2.22087	−	6.83513i	0.124934	−	0.384506i
$317$	−13.6870	−	9.94418i	−0.768738	−	0.558521i	0.132840	−	0.991138i	$-0.457590\pi$
$317$	−13.6870	−	9.94418i	−0.768738	−	0.558521i	−0.901578	+	0.432617i	$0.857590\pi$
$318$		0			0
$319$	8.88095	+	24.9099i	0.497238	+	1.39469i
$320$	−28.6798			−1.60325
$321$		0			0
$322$	−0.277969	+	0.855500i	−0.0154906	+	0.0476751i
$323$	−0.969808	−	2.98476i	−0.0539616	−	0.166077i
$324$		0			0
$325$	11.5715	−	8.40721i	0.641873	−	0.466348i
$326$	2.83172	+	8.71515i	0.156835	+	0.482687i
$327$		0			0
$328$	−5.28693	−	3.84118i	−0.291922	−	0.212094i
$329$	−7.56632			−0.417145
$330$		0			0
$331$	−1.23826			−0.0680610			−0.0340305	−	0.999421i	$-0.510834\pi$
$331$	−1.23826			−0.0680610			−0.0340305	+	0.999421i	$0.510834\pi$
$332$	9.85385	+	7.15924i	0.540800	+	0.392914i
$333$		0			0
$334$	−7.47620	−	23.0094i	−0.409079	−	1.25902i
$335$	6.71924	−	4.88181i	0.367111	−	0.266722i
$336$		0			0
$337$	−6.32885	−	19.4782i	−0.344754	−	1.06104i	−0.961715	−	0.274051i	$-0.911636\pi$
$337$	−6.32885	−	19.4782i	−0.344754	−	1.06104i	0.616961	−	0.786994i	$-0.288364\pi$
$338$	3.01610	−	9.28261i	0.164054	−	0.504907i
$339$		0			0
$340$	−5.06556			−0.274719
$341$	2.15816	+	1.47649i	0.116871	+	0.0799563i
$342$		0			0
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$	2.92583	−	9.00478i	0.157750	−	0.485505i
$345$		0			0
$346$	7.25412	−	5.27043i	0.389984	−	0.283340i
$347$	22.0618	−	16.0288i	1.18434	−	0.860472i	0.191684	−	0.981457i	$-0.438605\pi$
$347$	22.0618	−	16.0288i	1.18434	−	0.860472i	0.992654	+	0.120985i	$0.0386052\pi$
$348$		0			0
$349$	2.46730	−	7.59356i	0.132071	−	0.406474i	−0.863052	−	0.505116i	$-0.831450\pi$
$349$	2.46730	−	7.59356i	0.132071	−	0.406474i	0.995123	+	0.0986418i	$0.0314498\pi$
$350$	6.26129	+	4.54910i	0.334680	+	0.243159i
$351$		0			0
$352$	13.3248	−	0.377388i	0.710212	−	0.0201149i
$353$	−5.93472			−0.315873			−0.157937	−	0.987449i	$-0.550484\pi$
$353$	−5.93472			−0.315873			−0.157937	+	0.987449i	$0.550484\pi$
$354$		0			0
$355$	−3.40538	+	10.4807i	−0.180739	+	0.556256i
$356$	−1.03956	−	3.19942i	−0.0550964	−	0.169569i
$357$		0			0
$358$	3.26469	−	2.37194i	0.172544	−	0.125361i
$359$	−8.78235	−	27.0293i	−0.463515	−	1.42655i	−0.860841	−	0.508874i	$-0.830062\pi$
$359$	−8.78235	−	27.0293i	−0.463515	−	1.42655i	0.397326	−	0.917677i	$-0.369938\pi$
$360$		0			0
$361$	13.2404	+	9.61969i	0.696862	+	0.506300i
$362$	−17.6285			−0.926535
$363$		0			0
$364$	1.56114			0.0818261
$365$	3.42870	+	2.49109i	0.179466	+	0.130390i
$366$		0			0
$367$	−9.39456	−	28.9135i	−0.490392	−	1.50927i	−0.824017	−	0.566565i	$-0.808272\pi$
$367$	−9.39456	−	28.9135i	−0.490392	−	1.50927i	0.333625	−	0.942706i	$-0.391728\pi$
$368$	1.24692	−	0.905939i	0.0650001	−	0.0472253i
$369$		0			0
$370$	11.9759	+	36.8580i	0.622596	+	1.91615i
$371$	−3.34432	+	10.2928i	−0.173628	+	0.534373i
$372$		0			0
$373$	14.4226			0.746772			0.373386	−	0.927676i	$-0.378197\pi$
$373$	14.4226			0.746772			0.373386	+	0.927676i	$0.378197\pi$
$374$	−7.14471	+	0.202355i	−0.369444	+	0.0104635i
$375$		0			0
$376$	18.8147	+	13.6697i	0.970296	+	0.704961i
$377$	5.07499	−	15.6192i	0.261375	−	0.804430i
$378$		0			0
$379$	18.1278	−	13.1706i	0.931163	−	0.676529i	−0.0151144	−	0.999886i	$-0.504811\pi$
$379$	18.1278	−	13.1706i	0.931163	−	0.676529i	0.946277	+	0.323356i	$0.104811\pi$
$380$	−3.43952	+	2.49896i	−0.176444	+	0.128194i
$381$		0			0
$382$	0.147771	−	0.454792i	0.00756061	−	0.0232692i
$383$	27.2465	+	19.7957i	1.39223	+	1.01152i	0.995616	+	0.0935305i	$0.0298153\pi$
$383$	27.2465	+	19.7957i	1.39223	+	1.01152i	0.396615	+	0.917985i	$0.370185\pi$
$384$		0			0
$385$	−9.46040	−	6.47226i	−0.482146	−	0.329857i
$386$	16.9118			0.860790
$387$		0			0
$388$	−1.51498	+	4.66262i	−0.0769112	+	0.236708i
$389$	−0.750241	−	2.30900i	−0.0380387	−	0.117071i	0.930234	−	0.366967i	$-0.119604\pi$
$389$	−0.750241	−	2.30900i	−0.0380387	−	0.117071i	−0.968273	+	0.249896i	$0.919604\pi$
$390$		0			0
$391$	1.26270	−	0.917404i	0.0638574	−	0.0463951i
$392$	0.949813	+	2.92322i	0.0479728	+	0.147645i
$393$		0			0
$394$	18.7611	+	13.6308i	0.945173	+	0.686708i
$395$	32.7699			1.64883
$396$		0			0
$397$	−5.89696			−0.295960			−0.147980	−	0.988990i	$-0.547277\pi$
$397$	−5.89696			−0.295960			−0.147980	+	0.988990i	$0.547277\pi$
$398$	7.61481	+	5.53248i	0.381696	+	0.277318i
$399$		0			0
$400$	−4.09784	−	12.6119i	−0.204892	−	0.630593i
$401$	9.09302	−	6.60646i	0.454084	−	0.329911i	−0.337122	−	0.941461i	$-0.609454\pi$
$401$	9.09302	−	6.60646i	0.454084	−	0.329911i	0.791206	+	0.611550i	$0.209454\pi$
$402$		0			0
$403$	−0.501804	−	1.54439i	−0.0249966	−	0.0769317i
$404$	−3.61756	+	11.1337i	−0.179981	+	0.553923i
$405$		0			0
$406$	8.88640			0.441025
$407$	−11.2066	−	31.4331i	−0.555492	−	1.55808i
$408$		0			0
$409$	−23.7320	−	17.2423i	−1.17347	−	0.852578i	−0.182052	−	0.983289i	$-0.558274\pi$
$409$	−23.7320	−	17.2423i	−1.17347	−	0.852578i	−0.991421	+	0.130711i	$0.958274\pi$
$410$	2.53060	−	7.78839i	0.124977	−	0.384641i
$411$		0			0
$412$	5.46251	−	3.96875i	0.269119	−	0.195526i
$413$	−2.66704	+	1.93771i	−0.131236	+	0.0953487i
$414$		0			0
$415$	−17.1619	+	52.8189i	−0.842445	+	2.59278i
$416$	−6.69713	−	4.86575i	−0.328354	−	0.238563i
$417$		0			0
$418$	−4.75144	+	3.66205i	−0.232400	+	0.179117i
$419$	20.2858			0.991027			0.495514	−	0.868600i	$-0.334980\pi$
$419$	20.2858			0.991027			0.495514	+	0.868600i	$0.334980\pi$
$420$		0			0
$421$	−0.945600	+	2.91026i	−0.0460857	+	0.141837i	−0.971452	−	0.237238i	$-0.923758\pi$
$421$	−0.945600	+	2.91026i	−0.0460857	+	0.141837i	0.925366	+	0.379075i	$0.123758\pi$
$422$	3.39542	+	10.4500i	0.165287	+	0.508700i
$423$		0			0
$424$	26.9116	−	19.5524i	1.30694	−	0.949548i
$425$	−4.14971	−	12.7715i	−0.201290	−	0.619508i
$426$		0			0
$427$	0.871010	+	0.632826i	0.0421511	+	0.0306246i
$428$	2.66211			0.128678
$429$		0			0
$430$	11.8648			0.572173
$431$	6.10158	+	4.43306i	0.293903	+	0.213533i	0.724959	−	0.688792i	$-0.241859\pi$
$431$	6.10158	+	4.43306i	0.293903	+	0.213533i	−0.431056	+	0.902325i	$0.641859\pi$
$432$		0			0
$433$	−9.93848	−	30.5875i	−0.477613	−	1.46994i	−0.842401	−	0.538851i	$-0.818859\pi$
$433$	−9.93848	−	30.5875i	−0.477613	−	1.46994i	0.364788	−	0.931091i	$-0.381141\pi$
$434$	0.710857	−	0.516468i	0.0341222	−	0.0247912i
$435$		0			0
$436$	−0.907980	−	2.79447i	−0.0434844	−	0.133831i
$437$	0.404796	−	1.24584i	0.0193640	−	0.0595964i
$438$		0			0
$439$	−4.66725			−0.222756			−0.111378	−	0.993778i	$-0.535526\pi$
$439$	−4.66725			−0.222756			−0.111378	+	0.993778i	$0.535526\pi$
$440$	11.8315	+	33.1858i	0.564045	+	1.58207i
$441$		0			0
$442$	3.59099	+	2.60901i	0.170806	+	0.124098i
$443$	−5.33893	+	16.4315i	−0.253660	+	0.780686i	0.740430	+	0.672133i	$0.234622\pi$
$443$	−5.33893	+	16.4315i	−0.253660	+	0.780686i	−0.994091	+	0.108553i	$0.965378\pi$
$444$		0			0
$445$	12.4096	−	9.01611i	0.588272	−	0.427404i
$446$	15.6845	−	11.3955i	0.742684	−	0.539591i
$447$		0			0
$448$	2.56433	−	7.89221i	0.121153	−	0.372872i
$449$	−13.5430	−	9.83957i	−0.639134	−	0.464358i	0.220418	−	0.975405i	$-0.429258\pi$
$449$	−13.5430	−	9.83957i	−0.639134	−	0.464358i	−0.859553	+	0.511047i	$0.829258\pi$
$450$		0			0
$451$	−1.98832	+	6.76546i	−0.0936264	+	0.318573i
$452$	8.07529			0.379829
$453$		0			0
$454$	−4.35015	+	13.3884i	−0.204162	+	0.628347i
$455$	2.19968	+	6.76992i	0.103123	+	0.317379i
$456$		0			0
$457$	17.5536	−	12.7534i	0.821121	−	0.596580i	−0.0959121	−	0.995390i	$-0.530577\pi$
$457$	17.5536	−	12.7534i	0.821121	−	0.596580i	0.917033	+	0.398810i	$0.130577\pi$
$458$	−1.57503	−	4.84746i	−0.0735965	−	0.226507i
$459$		0			0
$460$	−1.71055	−	1.24279i	−0.0797549	−	0.0579453i
$461$	6.07778			0.283070			0.141535	−	0.989933i	$-0.454796\pi$
$461$	6.07778			0.283070			0.141535	+	0.989933i	$0.454796\pi$
$462$		0			0
$463$	−5.14719			−0.239210			−0.119605	−	0.992822i	$-0.538163\pi$
$463$	−5.14719			−0.239210			−0.119605	+	0.992822i	$0.538163\pi$
$464$	−12.3183	−	8.94975i	−0.571862	−	0.415482i
$465$		0			0
$466$	8.21605	+	25.2864i	0.380601	+	1.17137i
$467$	−3.17076	+	2.30369i	−0.146725	+	0.106602i	−0.658726	−	0.752383i	$-0.728904\pi$
$467$	−3.17076	+	2.30369i	−0.146725	+	0.106602i	0.512001	+	0.858985i	$0.328904\pi$
$468$		0			0
$469$	0.742611	+	2.28552i	0.0342906	+	0.105536i
$470$	−9.00570	+	27.7167i	−0.415402	+	1.27848i
$471$		0			0
$472$	10.1327			0.466397
$473$	−10.2125	+	0.289243i	−0.469572	+	0.0132994i
$474$		0			0
$475$	−9.11811	−	6.62469i	−0.418368	−	0.303962i
$476$	0.452925	−	1.39396i	0.0207598	−	0.0638921i
$477$		0			0
$478$	−7.96867	+	5.78958i	−0.364478	+	0.264809i
$479$	−12.2266	+	8.88315i	−0.558648	+	0.405882i	−0.830964	−	0.556326i	$-0.812210\pi$
$479$	−12.2266	+	8.88315i	−0.558648	+	0.405882i	0.272316	+	0.962208i	$0.412210\pi$
$480$		0			0
$481$	−6.40399	+	19.7095i	−0.291997	+	0.898674i
$482$	17.0825	+	12.4112i	0.778088	+	0.565314i
$483$		0			0
$484$	−3.02114	−	7.77100i	−0.137324	−	0.353227i
$485$	−22.3541			−1.01505
$486$		0			0
$487$	7.74916	−	23.8495i	0.351148	−	1.08072i	−0.607062	−	0.794655i	$-0.707652\pi$
$487$	7.74916	−	23.8495i	0.351148	−	1.08072i	0.958210	−	0.286067i	$-0.0923480\pi$
$488$	−1.02259	−	3.14722i	−0.0462907	−	0.142468i
$489$		0			0
$490$	−3.11608	+	2.26396i	−0.140770	+	0.102275i
$491$	−11.5019	−	35.3991i	−0.519071	−	1.59754i	−0.775750	−	0.631040i	$-0.782628\pi$
$491$	−11.5019	−	35.3991i	−0.519071	−	1.59754i	0.256679	−	0.966497i	$-0.417372\pi$
$492$		0			0
$493$	−12.4742	−	9.06302i	−0.561809	−	0.408178i
$494$	3.72536			0.167612
$495$		0			0
$496$	−1.50554			−0.0676006
$497$	−2.57963	−	1.87421i	−0.115712	−	0.0840698i
$498$		0			0
$499$	−9.83087	−	30.2563i	−0.440090	−	1.35446i	−0.887780	−	0.460269i	$-0.847753\pi$
$499$	−9.83087	−	30.2563i	−0.440090	−	1.35446i	0.447689	−	0.894189i	$-0.352247\pi$
$500$	−4.12090	+	2.99401i	−0.184292	+	0.133896i
$501$		0			0
$502$	−0.987334	−	3.03870i	−0.0440669	−	0.135624i
$503$	5.93493	−	18.2658i	0.264626	−	0.814434i	−0.727154	−	0.686474i	$-0.759157\pi$
$503$	5.93493	−	18.2658i	0.264626	−	0.814434i	0.991779	−	0.127959i	$-0.0408426\pi$
$504$		0			0
$505$	−53.3788			−2.37532
$506$	−2.46229	−	1.68456i	−0.109462	−	0.0748877i
$507$		0			0
$508$	11.9274	+	8.66577i	0.529193	+	0.384481i
$509$	−0.777328	+	2.39237i	−0.0344545	+	0.106040i	−0.966805	−	0.255516i	$-0.917754\pi$
$509$	−0.777328	+	2.39237i	−0.0344545	+	0.106040i	0.932350	+	0.361556i	$0.117754\pi$
$510$		0			0
$511$	−0.992078	+	0.720787i	−0.0438869	+	0.0318857i
$512$	−15.7059	+	11.4110i	−0.694109	+	0.504300i
$513$		0			0
$514$	7.71978	−	23.7590i	0.340505	−	1.04797i
$515$	24.9073	+	18.0962i	1.09755	+	0.797416i
$516$		0			0
$517$	7.07588	−	24.0764i	0.311197	−	1.05888i
$518$	−11.2135			−0.492693
$519$		0			0
$520$	6.76107	−	20.8084i	0.296493	−	0.912510i
$521$	−4.60335	−	14.1677i	−0.201677	−	0.620697i	−0.999834	−	0.0182471i	$-0.994191\pi$
$521$	−4.60335	−	14.1677i	−0.201677	−	0.620697i	0.798157	−	0.602450i	$-0.205809\pi$
$522$		0			0
$523$	8.01333	−	5.82203i	0.350399	−	0.254579i	−0.398638	−	0.917109i	$-0.630517\pi$
$523$	8.01333	−	5.82203i	0.350399	−	0.254579i	0.749036	+	0.662529i	$0.230517\pi$
$524$	1.19755	+	3.68567i	0.0523151	+	0.161009i
$525$		0			0
$526$	−0.893242	−	0.648979i	−0.0389472	−	0.0282968i
$527$	−1.52459			−0.0664122
$528$		0			0
$529$	−22.3485			−0.971675
$530$	33.7236	+	24.5016i	1.46486	+	1.06428i
$531$		0			0
$532$	−0.380136	−	1.16994i	−0.0164810	−	0.0507232i
$533$	3.54276	−	2.57397i	0.153454	−	0.111491i
$534$		0			0
$535$	3.75097	+	11.5443i	0.162169	+	0.499104i
$536$	2.28253	−	7.02491i	0.0985904	−	0.303430i
$537$		0			0
$538$	−8.01342			−0.345483
$539$	2.62694	−	2.02465i	0.113150	−	0.0872077i
$540$		0			0
$541$	17.8052	+	12.9362i	0.765503	+	0.556171i	0.900593	−	0.434663i	$-0.143132\pi$
$541$	17.8052	+	12.9362i	0.765503	+	0.556171i	−0.135090	+	0.990833i	$0.543132\pi$
$542$	9.35508	−	28.7920i	0.401835	−	1.23672i
$543$		0			0
$544$	−6.28768	+	4.56826i	−0.269582	+	0.195863i
$545$	10.8389	−	7.87494i	0.464289	−	0.337325i
$546$		0			0
$547$	−3.35724	+	10.3325i	−0.143545	+	0.441787i	−0.996821	−	0.0796728i	$-0.974612\pi$
$547$	−3.35724	+	10.3325i	−0.143545	+	0.441787i	0.853276	+	0.521460i	$0.174612\pi$
$548$	−5.58049	−	4.05446i	−0.238387	−	0.173198i
$549$		0			0
$550$	−20.3309	+	15.6695i	−0.866912	+	0.668150i
$551$	−12.9410			−0.551303
$552$		0			0
$553$	−2.93004	+	9.01775i	−0.124598	+	0.383474i
$554$	−7.22721	−	22.2431i	−0.307055	−	0.945018i
$555$		0			0
$556$	−7.98184	+	5.79915i	−0.338506	+	0.245939i
$557$	−10.3869	−	31.9675i	−0.440105	−	1.35451i	−0.887763	−	0.460300i	$-0.847742\pi$
$557$	−10.3869	−	31.9675i	−0.440105	−	1.35451i	0.447658	−	0.894205i	$-0.352258\pi$
$558$		0			0
$559$	5.13290	+	3.72927i	0.217098	+	0.157731i
$560$	6.59959			0.278884
$561$		0			0
$562$	−31.3811			−1.32373
$563$	−1.66130	−	1.20701i	−0.0700155	−	0.0508693i	0.552227	−	0.833694i	$-0.313778\pi$
$563$	−1.66130	−	1.20701i	−0.0700155	−	0.0508693i	−0.622242	+	0.782825i	$0.713778\pi$
$564$		0			0
$565$	11.3782	+	35.0186i	0.478686	+	1.47324i
$566$	−23.6151	+	17.1573i	−0.992615	+	0.721177i
$567$		0			0
$568$	3.02857	+	9.32098i	0.127076	+	0.391099i
$569$	−1.01177	+	3.11391i	−0.0424156	+	0.130542i	−0.970022	−	0.243017i	$-0.921863\pi$
$569$	−1.01177	+	3.11391i	−0.0424156	+	0.130542i	0.927606	+	0.373559i	$0.121863\pi$
$570$		0			0
$571$	−43.8897			−1.83673			−0.918363	−	0.395738i	$-0.870489\pi$
$571$	−43.8897			−1.83673			−0.918363	+	0.395738i	$0.870489\pi$
$572$	−1.45995	+	4.96763i	−0.0610437	+	0.207707i
$573$		0			0
$574$	1.91697	+	1.39276i	0.0800128	+	0.0581327i
$575$	1.73208	−	5.33080i	0.0722328	−	0.222310i
$576$		0			0
$577$	35.5081	−	25.7981i	1.47822	−	1.07399i	0.500096	−	0.865970i	$-0.333298\pi$
$577$	35.5081	−	25.7981i	1.47822	−	1.07399i	0.978125	−	0.208020i	$-0.0667019\pi$
$578$	−11.9561	+	8.68664i	−0.497310	+	0.361317i
$579$		0			0
$580$	−6.45466	+	19.8654i	−0.268015	+	0.824866i
$581$	−13.0004	−	9.44536i	−0.539348	−	0.391859i
$582$		0			0
$583$	−29.6245	−	20.2674i	−1.22692	−	0.839389i
$584$	3.76915			0.155969
$585$		0			0
$586$	−1.53730	+	4.73133i	−0.0635054	+	0.195449i
$587$	−0.862670	−	2.65503i	−0.0356062	−	0.109585i	0.931674	−	0.363296i	$-0.118349\pi$
$587$	−0.862670	−	2.65503i	−0.0356062	−	0.109585i	−0.967280	+	0.253711i	$0.918349\pi$
$588$		0			0
$589$	−1.03520	+	0.752114i	−0.0426545	+	0.0309903i
$590$	3.92378	+	12.0761i	0.161539	+	0.497167i
$591$		0			0
$592$	15.5441	+	11.2935i	0.638859	+	0.464158i
$593$	−23.2526			−0.954871			−0.477435	−	0.878667i	$-0.658434\pi$
$593$	−23.2526			−0.954871			−0.477435	+	0.878667i	$0.658434\pi$
$594$		0			0
$595$	6.68312			0.273981
$596$	1.92945	+	1.40183i	0.0790334	+	0.0574211i
$597$		0			0
$598$	0.572519	+	1.76203i	0.0234120	+	0.0720549i
$599$	8.46187	−	6.14791i	0.345743	−	0.251197i	−0.401338	−	0.915930i	$-0.631455\pi$
$599$	8.46187	−	6.14791i	0.345743	−	0.251197i	0.747081	+	0.664733i	$0.231455\pi$
$600$		0			0
$601$	6.89406	+	21.2177i	0.281215	+	0.865489i	0.987508	+	0.157570i	$0.0503660\pi$
$601$	6.89406	+	21.2177i	0.281215	+	0.865489i	−0.706293	+	0.707919i	$0.749634\pi$
$602$	−1.06087	+	3.26501i	−0.0432376	+	0.133072i
$603$		0			0
$604$	−2.17306			−0.0884204
$605$	29.4422	−	24.0507i	1.19700	−	0.977800i
$606$		0			0
$607$	−15.3619	−	11.1611i	−0.623522	−	0.453015i	0.230628	−	0.973042i	$-0.425922\pi$
$607$	−15.3619	−	11.1611i	−0.623522	−	0.453015i	−0.854150	+	0.520027i	$0.825922\pi$
$608$	−2.01571	+	6.20370i	−0.0817477	+	0.251593i
$609$		0			0
$610$	3.35485	−	2.43744i	0.135834	−	0.0986892i
$611$	−12.6077	+	9.16004i	−0.510053	+	0.370576i
$612$		0			0
$613$	6.23030	−	19.1749i	0.251639	−	0.774467i	−0.742834	−	0.669476i	$-0.766519\pi$
$613$	6.23030	−	19.1749i	0.251639	−	0.774467i	0.994473	−	0.104991i	$-0.0334813\pi$
$614$	11.6166	+	8.43995i	0.468807	+	0.340608i
$615$		0			0
$616$	−10.1901	+	0.288607i	−0.410570	+	0.0116283i
$617$	−7.03919			−0.283387			−0.141694	−	0.989911i	$-0.545255\pi$
$617$	−7.03919			−0.283387			−0.141694	+	0.989911i	$0.545255\pi$
$618$		0			0
$619$	−9.60520	+	29.5618i	−0.386066	+	1.18819i	0.549639	+	0.835402i	$0.314765\pi$
$619$	−9.60520	+	29.5618i	−0.386066	+	1.18819i	−0.935704	+	0.352785i	$0.885235\pi$
$620$	0.638222	+	1.96425i	0.0256316	+	0.0788860i
$621$		0			0
$622$	−24.1814	+	17.5688i	−0.969585	+	0.704445i
$623$	1.37151	+	4.22108i	0.0549484	+	0.169114i
$624$		0			0
$625$	9.30098	+	6.75756i	0.372039	+	0.270302i
$626$	−3.99947			−0.159851
$627$		0			0
$628$	16.2883			0.649973
$629$	15.7408	+	11.4364i	0.627628	+	0.455998i
$630$		0			0
$631$	6.78971	+	20.8966i	0.270294	+	0.831880i	0.990426	+	0.138043i	$0.0440812\pi$
$631$	6.78971	+	20.8966i	0.270294	+	0.831880i	−0.720132	+	0.693837i	$0.755919\pi$
$632$	23.5779	−	17.1303i	0.937879	−	0.681409i
$633$		0			0
$634$	−5.82639	−	17.9318i	−0.231396	−	0.712163i
$635$	−20.7733	+	63.9337i	−0.824364	+	2.53713i
$636$		0			0
$637$	−2.05965			−0.0816064
$638$	−8.31039	+	28.2770i	−0.329012	+	1.11950i
$639$		0			0
$640$	−3.38290	−	2.45782i	−0.133721	−	0.0971538i
$641$	4.10713	−	12.6404i	0.162222	−	0.499267i	−0.836599	−	0.547816i	$-0.815460\pi$
$641$	4.10713	−	12.6404i	0.162222	−	0.499267i	0.998821	+	0.0485485i	$0.0154595\pi$
$642$		0			0
$643$	−11.8848	+	8.63480i	−0.468690	+	0.340523i	−0.796930	−	0.604071i	$-0.793544\pi$
$643$	−11.8848	+	8.63480i	−0.468690	+	0.340523i	0.328241	+	0.944594i	$0.393544\pi$
$644$	0.494940	−	0.359595i	0.0195034	−	0.0141700i
$645$		0			0
$646$	1.08082	−	3.32642i	0.0425242	−	0.130876i
$647$	−4.97160	−	3.61208i	−0.195454	−	0.142005i	0.485754	−	0.874095i	$-0.338545\pi$
$647$	−4.97160	−	3.61208i	−0.195454	−	0.142005i	−0.681208	+	0.732090i	$0.738545\pi$
$648$		0			0
$649$	−3.67174	−	10.2988i	−0.144128	−	0.404261i
$650$	15.9404			0.625236
$651$		0			0
$652$	1.92589	−	5.92729i	0.0754238	−	0.232131i
$653$	12.5674	+	38.6786i	0.491802	+	1.51361i	0.821882	+	0.569658i	$0.192924\pi$
$653$	12.5674	+	38.6786i	0.491802	+	1.51361i	−0.330079	+	0.943953i	$0.607076\pi$
$654$		0			0
$655$	−14.2956	+	10.3864i	−0.558576	+	0.405829i
$656$	−1.25460	−	3.86127i	−0.0489841	−	0.150757i
$657$		0			0
$658$	−6.82196	−	4.95645i	−0.265948	−	0.193222i
$659$	−18.0090			−0.701531			−0.350765	−	0.936463i	$-0.614079\pi$
$659$	−18.0090			−0.701531			−0.350765	+	0.936463i	$0.614079\pi$
$660$		0			0
$661$	−17.1420			−0.666745			−0.333373	−	0.942795i	$-0.608187\pi$
$661$	−17.1420			−0.666745			−0.333373	+	0.942795i	$0.608187\pi$
$662$	−1.11644	−	0.811145i	−0.0433919	−	0.0315260i
$663$		0			0
$664$	15.2629	+	46.9744i	0.592316	+	1.82296i
$665$	4.53784	−	3.29693i	0.175970	−	0.127850i
$666$		0			0
$667$	−1.98878	−	6.12085i	−0.0770060	−	0.237000i
$668$	−5.08466	+	15.6490i	−0.196732	+	0.605478i
$669$		0			0
$670$	9.25613			0.357596
$671$	−2.82823	+	2.17979i	−0.109183	+	0.0841498i
$672$		0			0
$673$	18.7632	+	13.6322i	0.723268	+	0.525485i	0.887426	−	0.460949i	$-0.152491\pi$
$673$	18.7632	+	13.6322i	0.723268	+	0.525485i	−0.164159	+	0.986434i	$0.552491\pi$
$674$	7.05329	−	21.7078i	0.271683	−	0.836153i
$675$		0			0
$676$	−5.37035	+	3.90179i	−0.206552	+	0.150069i
$677$	−22.3050	+	16.2056i	−0.857252	+	0.622830i	−0.927136	−	0.374725i	$-0.877737\pi$
$677$	−22.3050	+	16.2056i	−0.857252	+	0.622830i	0.0698841	+	0.997555i	$0.477737\pi$
$678$		0			0
$679$	1.99874	−	6.15150i	0.0767047	−	0.236073i
$680$	−16.6185	−	12.0741i	−0.637291	−	0.463019i
$681$		0			0
$682$	0.978646	+	2.74497i	0.0374743	+	0.105110i
$683$	−21.9351			−0.839322			−0.419661	−	0.907681i	$-0.637851\pi$
$683$	−21.9351			−0.839322			−0.419661	+	0.907681i	$0.637851\pi$
$684$		0			0
$685$	9.71923	−	29.9127i	0.371353	−	1.14291i
$686$	−0.344389	−	1.05992i	−0.0131488	−	0.0404680i
$687$		0			0
$688$	4.75885	−	3.45751i	0.181430	−	0.131816i
$689$	6.88814	+	21.1995i	0.262417	+	0.807637i
$690$		0			0
$691$	20.7647	+	15.0865i	0.789928	+	0.573916i	0.907942	−	0.419096i	$-0.137653\pi$
$691$	20.7647	+	15.0865i	0.789928	+	0.573916i	−0.118014	+	0.993012i	$0.537653\pi$
$692$	−6.09830			−0.231823
$693$		0			0
$694$	30.3913			1.15364
$695$	−36.3947	−	26.4423i	−1.38053	−	1.00301i
$696$		0			0
$697$	−1.27048	−	3.91014i	−0.0481229	−	0.148107i
$698$	7.19886	−	5.23028i	0.272481	−	0.197969i
$699$		0			0
$700$	−1.62656	−	5.00604i	−0.0614782	−	0.189211i
$701$	5.69007	−	17.5122i	0.214911	−	0.661428i	−0.784249	−	0.620446i	$-0.786951\pi$
$701$	5.69007	−	17.5122i	0.214911	−	0.661428i	0.999160	−	0.0409817i	$-0.0130485\pi$
$702$		0			0
$703$	16.3298			0.615892
$704$	22.7153	+	15.5405i	0.856114	+	0.585704i
$705$		0			0
$706$	−5.35087	−	3.88764i	−0.201383	−	0.146313i
$707$	4.77274	−	14.6890i	0.179497	−	0.552436i
$708$		0			0
$709$	−19.1430	+	13.9082i	−0.718930	+	0.522334i	−0.886042	−	0.463604i	$-0.846556\pi$
$709$	−19.1430	+	13.9082i	−0.718930	+	0.522334i	0.167112	+	0.985938i	$0.446556\pi$
$710$	−9.93591	+	7.21886i	−0.372888	+	0.270919i
$711$		0			0
$712$	4.21556	−	12.9741i	0.157985	−	0.486227i
$713$	−0.514827	−	0.374044i	−0.0192804	−	0.0140081i
$714$		0			0
$715$	−23.5993	+	0.668389i	−0.882565	+	0.0249963i
$716$	−2.74452			−0.102568
$717$		0			0
$718$	9.78763	−	30.1232i	0.365271	−	1.12419i
$719$	−3.43696	−	10.5779i	−0.128177	−	0.394488i	0.866289	−	0.499542i	$-0.166498\pi$
$719$	−3.43696	−	10.5779i	−0.128177	−	0.394488i	−0.994467	+	0.105054i	$0.966498\pi$
$720$		0			0
$721$	−7.20682	+	5.23606i	−0.268396	+	0.195001i
$722$	5.63627	+	17.3467i	0.209760	+	0.645576i
$723$		0			0
$724$	9.69964	+	7.04720i	0.360484	+	0.261907i
$725$	−55.3730			−2.05650
$726$		0			0
$727$	42.4803			1.57551			0.787753	−	0.615991i	$-0.211244\pi$
$727$	42.4803			1.57551			0.787753	+	0.615991i	$0.211244\pi$
$728$	5.12162	+	3.72107i	0.189820	+	0.137912i
$729$		0			0
$730$	1.45956	+	4.49205i	0.0540206	+	0.166258i
$731$	4.81908	−	3.50127i	0.178240	−	0.129499i
$732$		0			0
$733$	6.85660	+	21.1025i	0.253254	+	0.779437i	0.994169	+	0.107837i	$0.0343925\pi$
$733$	6.85660	+	21.1025i	0.253254	+	0.779437i	−0.740914	+	0.671600i	$0.765607\pi$
$734$	10.4699	−	32.2231i	0.386452	−	1.18938i
$735$		0			0
$736$	−3.24402			−0.119576
$737$	−7.96712	+	0.225648i	−0.293473	+	0.00831184i
$738$		0			0
$739$	−23.8240	−	17.3092i	−0.876381	−	0.636728i	0.0559106	−	0.998436i	$-0.482194\pi$
$739$	−23.8240	−	17.3092i	−0.876381	−	0.636728i	−0.932292	+	0.361708i	$0.882194\pi$
$740$	8.14496	−	25.0676i	0.299415	−	0.921504i
$741$		0			0
$742$	−9.75776	+	7.08943i	−0.358219	+	0.260261i
$743$	13.6772	−	9.93704i	0.501766	−	0.364555i	−0.307925	−	0.951411i	$-0.599635\pi$
$743$	13.6772	−	9.93704i	0.501766	−	0.364555i	0.809691	+	0.586856i	$0.199635\pi$
$744$		0			0
$745$	−3.36042	+	10.3423i	−0.123116	+	0.378913i
$746$	13.0037	+	9.44774i	0.476099	+	0.345906i
$747$		0			0
$748$	4.01208	+	2.74484i	0.146696	+	0.100361i
$749$	−3.51219			−0.128333
$750$		0			0
$751$	−0.479429	+	1.47553i	−0.0174946	+	0.0538429i	−0.959423	−	0.281972i	$-0.909012\pi$
$751$	−0.479429	+	1.47553i	−0.0174946	+	0.0538429i	0.941928	+	0.335815i	$0.109012\pi$
$752$	4.46479	+	13.7412i	0.162814	+	0.501090i
$753$		0			0
$754$	14.8074	−	10.7582i	0.539252	−	0.391789i
$755$	−3.06188	−	9.42349i	−0.111433	−	0.342956i
$756$		0			0
$757$	−10.1505	−	7.37474i	−0.368925	−	0.268040i	0.387840	−	0.921727i	$-0.373221\pi$
$757$	−10.1505	−	7.37474i	−0.368925	−	0.268040i	−0.756765	+	0.653687i	$0.773221\pi$
$758$	24.9721			0.907027
$759$		0			0
$760$	−17.2404			−0.625375
$761$	−7.30895	−	5.31026i	−0.264949	−	0.192497i	0.447377	−	0.894346i	$-0.352358\pi$
$761$	−7.30895	−	5.31026i	−0.264949	−	0.192497i	−0.712326	+	0.701849i	$0.752358\pi$
$762$		0			0
$763$	1.19792	+	3.68682i	0.0433676	+	0.133472i
$764$	−0.263115	+	0.191164i	−0.00951916	+	0.00691608i
$765$		0			0
$766$	11.5985	+	35.6966i	0.419072	+	1.28977i
$767$	−2.09820	+	6.45761i	−0.0757617	+	0.233171i
$768$		0			0
$769$	−16.1383			−0.581963			−0.290981	−	0.956729i	$-0.593982\pi$
$769$	−16.1383			−0.581963			−0.290981	+	0.956729i	$0.593982\pi$
$770$	−4.28994	−	12.0327i	−0.154599	−	0.433629i
$771$		0			0
$772$	−9.30529	−	6.76069i	−0.334905	−	0.243323i
$773$	5.69007	−	17.5122i	0.204657	−	0.629871i	−0.795070	−	0.606518i	$-0.792566\pi$
$773$	5.69007	−	17.5122i	0.204657	−	0.629871i	0.999727	−	0.0233530i	$-0.00743416\pi$
$774$		0			0
$775$	−4.42950	+	3.21822i	−0.159112	+	0.115602i
$776$	−16.0838	+	11.6855i	−0.577374	+	0.419487i
$777$		0			0
$778$	0.836118	−	2.57331i	0.0299763	−	0.0922575i
$779$	−2.79162	−	2.02823i	−0.100020	−	0.0726689i
$780$		0			0
$781$	8.37624	−	6.45578i	0.299726	−	0.231006i
$782$	1.73944			0.0622022
$783$		0			0
$784$	−0.590087	+	1.81610i	−0.0210745	+	0.0648608i
$785$	22.9505	+	70.6344i	0.819139	+	2.52105i
$786$		0			0
$787$	−38.0133	+	27.6183i	−1.35503	+	0.984486i	−0.356284	+	0.934378i	$0.615957\pi$
$787$	−38.0133	+	27.6183i	−1.35503	+	0.984486i	−0.998744	+	0.0501080i	$0.984043\pi$
$788$	−4.87378	−	14.9999i	−0.173621	−	0.534351i
$789$		0			0
$790$	29.5461	+	21.4665i	1.05120	+	0.763744i
$791$	−10.6539			−0.378810
$792$		0			0
$793$	2.21748			0.0787450
$794$	−5.31683	−	3.86291i	−0.188687	−	0.137089i
$795$		0			0
$796$	−1.97818	−	6.08821i	−0.0701147	−	0.215791i
$797$	−2.52781	+	1.83656i	−0.0895395	+	0.0650543i	−0.631654	−	0.775250i	$-0.717624\pi$
$797$	−2.52781	+	1.83656i	−0.0895395	+	0.0650543i	0.542115	+	0.840304i	$0.317624\pi$
$798$		0			0
$799$	4.52129	+	13.9151i	0.159952	+	0.492281i
$800$	−8.62499	+	26.5450i	−0.304940	+	0.938507i
$801$		0			0
$802$	12.5261			0.442314
$803$	−1.36581	−	3.83091i	−0.0481982	−	0.135190i
$804$		0			0
$805$	2.25677	+	1.63964i	0.0795408	+	0.0577897i
$806$	0.559243	−	1.72117i	0.0196985	−	0.0606258i
$807$		0			0
$808$	−38.4059	+	27.9036i	−1.35112	+	0.981643i
$809$	−26.4756	+	19.2357i	−0.930833	+	0.676290i	−0.946197	−	0.323592i	$-0.895109\pi$
$809$	−26.4756	+	19.2357i	−0.930833	+	0.676290i	0.0153636	+	0.999882i	$0.495109\pi$
$810$		0			0
$811$	10.0929	−	31.0627i	0.354410	−	1.09076i	−0.601941	−	0.798540i	$-0.705606\pi$
$811$	10.0929	−	31.0627i	0.354410	−	1.09076i	0.956351	−	0.292220i	$-0.0943941\pi$
$812$	−4.88951	−	3.55243i	−0.171588	−	0.124666i
$813$		0			0
$814$	10.4867	−	35.6819i	0.367557	−	1.25065i
$815$	28.4174			0.995419
$816$		0			0
$817$	1.54490	−	4.75472i	0.0540493	−	0.166347i
$818$	−10.1024	−	31.0921i	−0.353224	−	1.08711i
$819$		0			0
$820$	−4.50589	+	3.27372i	−0.157352	+	0.114323i
$821$	2.29644	+	7.06770i	0.0801461	+	0.246664i	0.983099	−	0.183075i	$-0.0586053\pi$
$821$	2.29644	+	7.06770i	0.0801461	+	0.246664i	−0.902953	+	0.429740i	$0.858605\pi$
$822$		0			0
$823$	−5.30607	−	3.85509i	−0.184958	−	0.134380i	0.491453	−	0.870904i	$-0.336466\pi$
$823$	−5.30607	−	3.85509i	−0.184958	−	0.134380i	−0.676411	+	0.736524i	$0.736466\pi$
$824$	27.3805			0.953846
$825$		0			0
$826$	−3.67399			−0.127835
$827$	19.2982	+	14.0209i	0.671063	+	0.487556i	0.870381	−	0.492379i	$-0.163873\pi$
$827$	19.2982	+	14.0209i	0.671063	+	0.487556i	−0.199318	+	0.979935i	$0.563873\pi$
$828$		0			0
$829$	−8.07867	−	24.8636i	−0.280584	−	0.863549i	−0.987688	−	0.156439i	$-0.949999\pi$
$829$	−8.07867	−	24.8636i	−0.280584	−	0.863549i	0.707104	−	0.707110i	$-0.250001\pi$
$830$	−50.0735	+	36.3805i	−1.73808	+	1.26279i
$831$		0			0
$832$	−5.28164	−	16.2552i	−0.183108	−	0.563548i
$833$	−0.597555	+	1.83909i	−0.0207041	+	0.0637205i
$834$		0			0
$835$	−75.0265			−2.59640
$836$	4.07830	−	0.115507i	0.141051	−	0.00399489i
$837$		0			0
$838$	18.2901	+	13.2886i	0.631823	+	0.459046i
$839$	−10.5959	+	32.6107i	−0.365810	+	1.12585i	0.583662	+	0.811997i	$0.301619\pi$
$839$	−10.5959	+	32.6107i	−0.365810	+	1.12585i	−0.949472	+	0.313851i	$0.898381\pi$
$840$		0			0
$841$	−27.9754	+	20.3253i	−0.964670	+	0.700874i
$842$	−2.75899	+	2.00452i	−0.0950810	+	0.0690804i
$843$		0			0
$844$	2.30928	−	7.10722i	0.0794885	−	0.244641i
$845$	−24.4871	−	17.7909i	−0.842383	−	0.612027i
$846$		0			0
$847$	3.98586	+	10.2525i	0.136956	+	0.352279i
$848$	20.6661			0.709678
$849$		0			0
$850$	4.62471	−	14.2334i	0.158626	−	0.488201i
$851$	2.50959	+	7.72373i	0.0860277	+	0.264766i
$852$		0			0
$853$	−17.3002	+	12.5693i	−0.592347	+	0.430365i	−0.843154	−	0.537672i	$-0.819304\pi$
$853$	−17.3002	+	12.5693i	−0.592347	+	0.430365i	0.250807	+	0.968037i	$0.419304\pi$
$854$	0.370779	+	1.14114i	0.0126878	+	0.0390490i
$855$		0			0
$856$	8.73356	+	6.34530i	0.298507	+	0.216878i
$857$	−42.8697			−1.46440			−0.732200	−	0.681090i	$-0.761506\pi$
$857$	−42.8697			−1.46440			−0.732200	+	0.681090i	$0.761506\pi$
$858$		0			0
$859$	−30.3915			−1.03695			−0.518473	−	0.855094i	$-0.673499\pi$
$859$	−30.3915			−1.03695			−0.518473	+	0.855094i	$0.673499\pi$
$860$	−6.52831	−	4.74310i	−0.222614	−	0.161738i
$861$		0			0
$862$	2.59737	+	7.99389i	0.0884668	+	0.272273i
$863$	9.56130	−	6.94669i	0.325471	−	0.236468i	−0.413036	−	0.910715i	$-0.635532\pi$
$863$	9.56130	−	6.94669i	0.325471	−	0.236468i	0.738506	+	0.674247i	$0.235532\pi$
$864$		0			0
$865$	−8.59263	−	26.4454i	−0.292158	−	0.899170i
$866$	11.0761	−	34.0887i	0.376381	−	1.15838i
$867$		0			0
$868$	−0.597594			−0.0202837
$869$	−25.9548	−	17.7568i	−0.880456	−	0.602357i
$870$		0			0
$871$	4.00434	+	2.90932i	0.135682	+	0.0985786i
$872$	3.68200	−	11.3320i	0.124688	−	0.383750i
$873$		0			0
$874$	1.18108	−	0.858104i	0.0399506	−	0.0290258i
$875$	5.43680	−	3.95007i	0.183797	−	0.133537i
$876$		0			0
$877$	−2.84446	+	8.75436i	−0.0960507	+	0.295614i	−0.987526	−	0.157455i	$-0.949671\pi$
$877$	−2.84446	+	8.75436i	−0.0960507	+	0.295614i	0.891475	+	0.453069i	$0.149671\pi$
$878$	−4.20810	−	3.05736i	−0.142016	−	0.103181i
$879$		0			0
$880$	−6.17182	+	21.0002i	−0.208052	+	0.707918i
$881$	41.9030			1.41175			0.705874	−	0.708338i	$-0.250555\pi$
$881$	41.9030			1.41175			0.705874	+	0.708338i	$0.250555\pi$
$882$		0			0
$883$	−4.95906	+	15.2624i	−0.166886	+	0.513621i	−0.999170	−	0.0407275i	$-0.987032\pi$
$883$	−4.95906	+	15.2624i	−0.166886	+	0.513621i	0.832285	+	0.554348i	$0.187032\pi$
$884$	−0.932869	−	2.87108i	−0.0313758	−	0.0965647i
$885$		0			0
$886$	−15.5775	+	11.3177i	−0.523335	+	0.380225i
$887$	10.4597	+	32.1917i	0.351203	+	1.08089i	0.958179	+	0.286171i	$0.0923825\pi$
$887$	10.4597	+	32.1917i	0.351203	+	1.08089i	−0.606976	+	0.794720i	$0.707618\pi$
$888$		0			0
$889$	−15.7361	−	11.4330i	−0.527772	−	0.383449i
$890$	17.0949			0.573024
$891$		0			0
$892$	−13.1855			−0.441482
$893$	9.93459	+	7.21790i	0.332448	+	0.241538i
$894$		0			0
$895$	−3.86708	−	11.9017i	−0.129262	−	0.397829i
$896$	0.978825	−	0.711158i	0.0327002	−	0.0237581i
$897$		0			0
$898$	−5.76510	−	17.7432i	−0.192384	−	0.592097i
$899$	−1.94267	+	5.97892i	−0.0647916	+	0.199408i
$900$		0			0
$901$	20.9277			0.697202
$902$	−6.22455	+	4.79741i	−0.207255	+	0.159736i
$903$		0			0
$904$	26.4925	+	19.2479i	0.881127	+	0.640176i
$905$	−16.8933	+	51.9923i	−0.561553	+	1.72828i
$906$		0			0
$907$	35.6787	−	25.9221i	1.18469	−	0.860730i	0.192000	−	0.981395i	$-0.438503\pi$
$907$	35.6787	−	25.9221i	1.18469	−	0.860730i	0.992693	+	0.120665i	$0.0385027\pi$
$908$	7.74570	−	5.62758i	0.257050	−	0.186758i
$909$		0			0
$910$	−2.45147	+	7.54486i	−0.0812655	+	0.250110i
$911$	40.1075	+	29.1398i	1.32882	+	0.965446i	0.999777	+	0.0211316i	$0.00672689\pi$
$911$	40.1075	+	29.1398i	1.32882	+	0.965446i	0.329045	+	0.944314i	$0.393273\pi$
$912$		0			0
$913$	42.2133	−	32.5348i	1.39706	−	1.07675i
$914$	24.1810			0.799837
$915$		0			0
$916$	−1.07120	+	3.29682i	−0.0353935	+	0.108930i
$917$	−1.57995	−	4.86260i	−0.0521746	−	0.160577i
$918$		0			0
$919$	33.0019	−	23.9773i	1.08863	−	0.790939i	0.109466	−	0.993991i	$-0.465086\pi$
$919$	33.0019	−	23.9773i	1.08863	−	0.790939i	0.979168	+	0.203052i	$0.0650860\pi$
$920$	−2.64953	−	8.15440i	−0.0873523	−	0.268843i
$921$		0			0
$922$	5.47986	+	3.98135i	0.180470	+	0.131119i
$923$	−6.56740			−0.216169
$924$		0			0
$925$	69.8737			2.29743
$926$	−4.64082	−	3.37176i	−0.152507	−	0.110803i
$927$		0			0
$928$	9.90326	+	30.4791i	0.325090	+	1.00053i
$929$	33.4876	−	24.3301i	1.09869	−	0.798246i	0.117846	−	0.993032i	$-0.462401\pi$
$929$	33.4876	−	24.3301i	1.09869	−	0.798246i	0.980846	+	0.194786i	$0.0624012\pi$
$930$		0			0
$931$	0.501522	+	1.54353i	0.0164367	+	0.0505870i
$932$	5.58785	−	17.1976i	0.183036	−	0.563327i
$933$		0			0
$934$	−4.36790			−0.142922
$935$	−6.24993	+	21.2660i	−0.204394	+	0.695473i
$936$		0			0
$937$	−1.29155	−	0.938364i	−0.0421930	−	0.0306550i	0.566489	−	0.824069i	$-0.308301\pi$
$937$	−1.29155	−	0.938364i	−0.0421930	−	0.0306550i	−0.608682	+	0.793414i	$0.708301\pi$
$938$	−0.827615	+	2.54714i	−0.0270226	+	0.0831670i
$939$		0			0
$940$	16.0352	−	11.6503i	0.523011	−	0.379990i
$941$	5.75039	−	4.17790i	0.187457	−	0.136196i	−0.490099	−	0.871667i	$-0.663039\pi$
$941$	5.75039	−	4.17790i	0.187457	−	0.136196i	0.677556	+	0.735471i	$0.263039\pi$
$942$		0			0
$943$	0.530297	−	1.63209i	0.0172689	−	0.0531481i
$944$	5.09287	+	3.70019i	0.165759	+	0.120431i
$945$		0			0
$946$	−9.39731	−	6.42910i	−0.305533	−	0.209028i
$947$	2.45986			0.0799347			0.0399674	−	0.999201i	$-0.487275\pi$
$947$	2.45986			0.0799347			0.0399674	+	0.999201i	$0.487275\pi$
$948$		0			0
$949$	−0.780485	+	2.40209i	−0.0253356	+	0.0779750i
$950$	−3.88147	−	11.9459i	−0.125932	−	0.387578i
$951$		0			0
$952$	4.80849	−	3.49357i	0.155844	−	0.113227i
$953$	8.83790	+	27.2003i	0.286288	+	0.881103i	0.986010	+	0.166688i	$0.0533071\pi$
$953$	8.83790	+	27.2003i	0.286288	+	0.881103i	−0.699722	+	0.714415i	$0.746693\pi$
$954$		0			0
$955$	−1.19972	−	0.871648i	−0.0388221	−	0.0282059i
$956$	6.69900			0.216661
$957$		0			0
$958$	−16.8428			−0.544168
$959$	7.36247	+	5.34915i	0.237747	+	0.172733i
$960$		0			0
$961$	−9.38744	−	28.8916i	−0.302821	−	0.931986i
$962$	−18.6850	+	13.5754i	−0.602428	+	0.437690i
$963$		0			0
$964$	−4.43771	−	13.6579i	−0.142929	−	0.439890i
$965$	16.2065	−	49.8785i	0.521706	−	1.60565i
$966$		0			0
$967$	−0.213338			−0.00686047			−0.00343024	−	0.999994i	$-0.501092\pi$
$967$	−0.213338			−0.00686047			−0.00343024	+	0.999994i	$0.501092\pi$
$968$	8.61122	−	32.6953i	0.276775	−	1.05087i
$969$		0			0
$970$	−20.1550	−	14.6435i	−0.647138	−	0.470173i
$971$	0.255927	−	0.787664i	0.00821310	−	0.0252773i	−0.946866	−	0.321628i	$-0.895770\pi$
$971$	0.255927	−	0.787664i	0.00821310	−	0.0252773i	0.955079	+	0.296351i	$0.0957698\pi$
$972$		0			0
$973$	10.5306	−	7.65095i	0.337597	−	0.245278i
$974$	22.6098	−	16.4270i	0.724465	−	0.526354i
$975$		0			0
$976$	0.635304	−	1.95526i	0.0203356	−	0.0625865i
$977$	7.89369	+	5.73510i	0.252542	+	0.183482i	0.706852	−	0.707361i	$-0.250114\pi$
$977$	7.89369	+	5.73510i	0.252542	+	0.183482i	−0.454311	+	0.890843i	$0.650114\pi$
$978$		0			0
$979$	−14.7143	+	0.416743i	−0.470271	+	0.0133192i
$980$	2.61958			0.0836795
$981$		0			0
$982$	12.8184	−	39.4511i	0.409052	−	1.25893i
$983$	−13.9428	−	42.9114i	−0.444705	−	1.36866i	−0.882807	−	0.469737i	$-0.844349\pi$
$983$	−13.9428	−	42.9114i	−0.444705	−	1.36866i	0.438101	−	0.898926i	$-0.355651\pi$
$984$		0			0
$985$	58.1803	−	42.2704i	1.85378	−	1.34685i
$986$	−5.31011	−	16.3428i	−0.169108	−	0.520462i
$987$		0			0
$988$	−2.04978	−	1.48926i	−0.0652123	−	0.0473795i
$989$	2.48632			0.0790604
$990$		0			0
$991$	53.5405			1.70077			0.850384	−	0.526162i	$-0.176369\pi$
$991$	53.5405			1.70077			0.850384	+	0.526162i	$0.176369\pi$
$992$	2.56361	+	1.86257i	0.0813947	+	0.0591367i
$993$		0			0
$994$	−1.09812	−	3.37966i	−0.0348302	−	0.107196i
$995$	23.6143	−	17.1568i	0.748624	−	0.543907i
$996$		0			0
$997$	−9.62918	−	29.6356i	−0.304959	−	0.938568i	−0.979692	−	0.200506i	$-0.935741\pi$
$997$	−9.62918	−	29.6356i	−0.304959	−	0.938568i	0.674733	−	0.738062i	$-0.264259\pi$
$998$	10.9562	−	33.7196i	0.346812	−	1.06738i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.i.631.3		16
3.2	odd	2		77.2.f.b.15.2	✓	16
11.3	even	5	inner	693.2.m.i.190.3		16
11.5	even	5		7623.2.a.ct.1.3		8
11.6	odd	10		7623.2.a.cw.1.6		8
21.2	odd	6		539.2.q.g.312.2		32
21.5	even	6		539.2.q.f.312.2		32
21.11	odd	6		539.2.q.g.422.3		32
21.17	even	6		539.2.q.f.422.3		32
21.20	even	2		539.2.f.e.246.2		16
33.2	even	10		847.2.f.v.148.2		16
33.5	odd	10		847.2.a.p.1.6		8
33.8	even	10		847.2.f.x.729.3		16
33.14	odd	10		77.2.f.b.36.2	yes	16
33.17	even	10		847.2.a.o.1.3		8
33.20	odd	10		847.2.f.w.148.3		16
33.26	odd	10		847.2.f.w.372.3		16
33.29	even	10		847.2.f.v.372.2		16
33.32	even	2		847.2.f.x.323.3		16
231.47	even	30		539.2.q.f.410.3		32
231.80	even	30		539.2.q.f.520.2		32
231.83	odd	10		5929.2.a.bs.1.3		8
231.104	even	10		5929.2.a.bt.1.6		8
231.146	even	10		539.2.f.e.344.2		16
231.179	odd	30		539.2.q.g.520.2		32
231.212	odd	30		539.2.q.g.410.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.15.2	✓	16	3.2	odd	2
77.2.f.b.36.2	yes	16	33.14	odd	10
539.2.f.e.246.2		16	21.20	even	2
539.2.f.e.344.2		16	231.146	even	10
539.2.q.f.312.2		32	21.5	even	6
539.2.q.f.410.3		32	231.47	even	30
539.2.q.f.422.3		32	21.17	even	6
539.2.q.f.520.2		32	231.80	even	30
539.2.q.g.312.2		32	21.2	odd	6
539.2.q.g.410.3		32	231.212	odd	30
539.2.q.g.422.3		32	21.11	odd	6
539.2.q.g.520.2		32	231.179	odd	30
693.2.m.i.190.3		16	11.3	even	5	inner
693.2.m.i.631.3		16	1.1	even	1	trivial
847.2.a.o.1.3		8	33.17	even	10
847.2.a.p.1.6		8	33.5	odd	10
847.2.f.v.148.2		16	33.2	even	10
847.2.f.v.372.2		16	33.29	even	10
847.2.f.w.148.3		16	33.20	odd	10
847.2.f.w.372.3		16	33.26	odd	10
847.2.f.x.323.3		16	33.32	even	2
847.2.f.x.729.3		16	33.8	even	10
5929.2.a.bs.1.3		8	231.83	odd	10
5929.2.a.bt.1.6		8	231.104	even	10
7623.2.a.ct.1.3		8	11.5	even	5
7623.2.a.cw.1.6		8	11.6	odd	10

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.901622 + 0.655067i) q^{2} +(-0.234224 - 0.720867i) q^{4} +(2.79603 - 2.03143i) q^{5} +(0.309017 + 0.951057i) q^{7} +(0.949813 - 2.92322i) q^{8} +O(q^{10})\)	\(q+(0.901622 + 0.655067i) q^{2} +(-0.234224 - 0.720867i) q^{4} +(2.79603 - 2.03143i) q^{5} +(0.309017 + 0.951057i) q^{7} +(0.949813 - 2.92322i) q^{8} +3.85168 q^{10} +(-3.31530 + 0.0938970i) q^{11} +(1.66629 + 1.21063i) q^{13} +(-0.344389 + 1.05992i) q^{14} +(1.54487 - 1.12241i) q^{16} +(1.56442 - 1.13662i) q^{17} +(0.501522 - 1.54353i) q^{19} +(-2.11929 - 1.53975i) q^{20} +(-3.05065 - 2.08708i) q^{22} +0.807136 q^{23} +(2.14596 - 6.60459i) q^{25} +(0.709322 + 2.18307i) q^{26} +(0.613206 - 0.445520i) q^{28} +(-2.46400 - 7.58342i) q^{29} +(-0.637845 - 0.463421i) q^{31} -4.01918 q^{32} +2.15508 q^{34} +(2.79603 + 2.03143i) q^{35} +(3.10926 + 9.56931i) q^{37} +(1.46330 - 1.06315i) q^{38} +(-3.28263 - 10.1029i) q^{40} +(0.657011 - 2.02207i) q^{41} +3.08043 q^{43} +(0.844208 + 2.36789i) q^{44} +(0.727732 + 0.528728i) q^{46} +(-2.33812 + 7.19600i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(6.26129 - 4.54910i) q^{50} +(0.482420 - 1.48474i) q^{52} +(8.75554 + 6.36127i) q^{53} +(-9.07891 + 6.99733i) q^{55} +3.07366 q^{56} +(2.74605 - 8.45147i) q^{58} +(1.01872 + 3.13529i) q^{59} +(0.871010 - 0.632826i) q^{61} +(-0.271523 - 0.835662i) q^{62} +(-6.71351 - 4.87765i) q^{64} +7.11832 q^{65} +2.40314 q^{67} +(-1.18577 - 0.861515i) q^{68} +(1.19024 + 3.66317i) q^{70} +(-2.57963 + 1.87421i) q^{71} +(0.378940 + 1.16626i) q^{73} +(-3.46516 + 10.6647i) q^{74} -1.23015 q^{76} +(-1.11378 - 3.12402i) q^{77} +(7.67096 + 5.57328i) q^{79} +(2.03939 - 6.27659i) q^{80} +(1.91697 - 1.39276i) q^{82} +(-13.0004 + 9.44536i) q^{83} +(2.06520 - 6.35602i) q^{85} +(2.77738 + 2.01789i) q^{86} +(-2.87443 + 9.78053i) q^{88} +4.43830 q^{89} +(-0.636468 + 1.95885i) q^{91} +(-0.189050 - 0.581837i) q^{92} +(-6.82196 + 4.95645i) q^{94} +(-1.73330 - 5.33455i) q^{95} +(-5.23278 - 3.80184i) q^{97} -1.11447 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8}+O(q^{10}) \) 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8	\( 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8} + 12 q^{10} + 3 q^{11} - 7 q^{13} - 2 q^{14} + 17 q^{16} + 5 q^{17} + 19 q^{19} - q^{20} - 33 q^{22} - 32 q^{23} + 7 q^{25} + 27 q^{26} + 4 q^{28} - 3 q^{29} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 4 q^{37} + 5 q^{38} - 10 q^{40} + 10 q^{41} - 8 q^{43} + 38 q^{44} - 42 q^{46} + 23 q^{47} - 4 q^{49} - 52 q^{50} + 33 q^{52} - 4 q^{53} - 12 q^{55} + 20 q^{58} - 17 q^{59} - 7 q^{61} - 79 q^{62} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} - 18 q^{70} + 14 q^{71} - 35 q^{73} + 29 q^{74} + 52 q^{76} + 3 q^{77} + 15 q^{79} + 87 q^{80} + 19 q^{82} - 5 q^{83} + 6 q^{85} + 52 q^{86} + 55 q^{88} - 74 q^{89} + 13 q^{91} + 55 q^{92} - 24 q^{94} - 32 q^{95} + 20 q^{97} - 2 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8 + 12 * q^10 + 3 * q^11 - 7 * q^13 - 2 * q^14 + 17 * q^16 + 5 * q^17 + 19 * q^19 - q^20 - 33 * q^22 - 32 * q^23 + 7 * q^25 + 27 * q^26 + 4 * q^28 - 3 * q^29 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 4 * q^37 + 5 * q^38 - 10 * q^40 + 10 * q^41 - 8 * q^43 + 38 * q^44 - 42 * q^46 + 23 * q^47 - 4 * q^49 - 52 * q^50 + 33 * q^52 - 4 * q^53 - 12 * q^55 + 20 * q^58 - 17 * q^59 - 7 * q^61 - 79 * q^62 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 - 18 * q^70 + 14 * q^71 - 35 * q^73 + 29 * q^74 + 52 * q^76 + 3 * q^77 + 15 * q^79 + 87 * q^80 + 19 * q^82 - 5 * q^83 + 6 * q^85 + 52 * q^86 + 55 * q^88 - 74 * q^89 + 13 * q^91 + 55 * q^92 - 24 * q^94 - 32 * q^95 + 20 * q^97 - 2 * q^98

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