LMFDB - Embedded newform 198.2.f.d.181.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,2,Mod(37,198)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("198.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	198.f (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:	$1.58103796002$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ 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:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	198.181
Dual form			198.2.f.d.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(-1.11803 + 3.44095i) q^{5} +(3.11803 - 2.26538i) q^{7} +(0.809017 + 0.587785i) q^{8} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(-1.11803 + 3.44095i) q^{5} +(3.11803 - 2.26538i) q^{7} +(0.809017 + 0.587785i) q^{8} +3.61803 q^{10} +(3.23607 + 0.726543i) q^{11} +(2.00000 + 6.15537i) q^{13} +(-3.11803 - 2.26538i) q^{14} +(0.309017 - 0.951057i) q^{16} +(1.00000 - 3.07768i) q^{17} +(-1.61803 - 1.17557i) q^{19} +(-1.11803 - 3.44095i) q^{20} +(-0.309017 - 3.30220i) q^{22} -2.76393 q^{23} +(-6.54508 - 4.75528i) q^{25} +(5.23607 - 3.80423i) q^{26} +(-1.19098 + 3.66547i) q^{28} +(0.309017 - 0.224514i) q^{29} +(0.0450850 + 0.138757i) q^{31} -1.00000 q^{32} -3.23607 q^{34} +(4.30902 + 13.2618i) q^{35} +(-3.00000 + 2.17963i) q^{37} +(-0.618034 + 1.90211i) q^{38} +(-2.92705 + 2.12663i) q^{40} +(-5.47214 - 3.97574i) q^{41} +(-3.04508 + 1.31433i) q^{44} +(0.854102 + 2.62866i) q^{46} +(3.85410 + 2.80017i) q^{47} +(2.42705 - 7.46969i) q^{49} +(-2.50000 + 7.69421i) q^{50} +(-5.23607 - 3.80423i) q^{52} +(-2.89919 - 8.92278i) q^{53} +(-6.11803 + 10.3229i) q^{55} +3.85410 q^{56} +(-0.309017 - 0.224514i) q^{58} +(9.97214 - 7.24518i) q^{59} +(0.854102 - 2.62866i) q^{61} +(0.118034 - 0.0857567i) q^{62} +(0.309017 + 0.951057i) q^{64} -23.4164 q^{65} -10.9443 q^{67} +(1.00000 + 3.07768i) q^{68} +(11.2812 - 8.19624i) q^{70} +(0.236068 - 0.726543i) q^{71} +(1.92705 - 1.40008i) q^{73} +(3.00000 + 2.17963i) q^{74} +2.00000 q^{76} +(11.7361 - 5.06555i) q^{77} +(-2.20820 - 6.79615i) q^{79} +(2.92705 + 2.12663i) q^{80} +(-2.09017 + 6.43288i) q^{82} +(-2.40983 + 7.41669i) q^{83} +(9.47214 + 6.88191i) q^{85} +(2.19098 + 2.48990i) q^{88} +6.18034 q^{89} +(20.1803 + 14.6619i) q^{91} +(2.23607 - 1.62460i) q^{92} +(1.47214 - 4.53077i) q^{94} +(5.85410 - 4.25325i) q^{95} +(-2.20820 - 6.79615i) q^{97} -7.85410 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{4} + 8 q^{7} + q^{8}+O(q^{10}) $ 4 * q + q^2 - q^4 + 8 * q^7 + q^8	$ 4 q + q^{2} - q^{4} + 8 q^{7} + q^{8} + 10 q^{10} + 4 q^{11} + 8 q^{13} - 8 q^{14} - q^{16} + 4 q^{17} - 2 q^{19} + q^{22} - 20 q^{23} - 15 q^{25} + 12 q^{26} - 7 q^{28} - q^{29} - 11 q^{31} - 4 q^{32} - 4 q^{34} + 15 q^{35} - 12 q^{37} + 2 q^{38} - 5 q^{40} - 4 q^{41} - q^{44} - 10 q^{46} + 2 q^{47} + 3 q^{49} - 10 q^{50} - 12 q^{52} + 13 q^{53} - 20 q^{55} + 2 q^{56} + q^{58} + 22 q^{59} - 10 q^{61} - 4 q^{62} - q^{64} - 40 q^{65} - 8 q^{67} + 4 q^{68} + 25 q^{70} - 8 q^{71} + q^{73} + 12 q^{74} + 8 q^{76} + 38 q^{77} + 18 q^{79} + 5 q^{80} + 14 q^{82} - 32 q^{83} + 20 q^{85} + 11 q^{88} - 20 q^{89} + 36 q^{91} - 12 q^{94} + 10 q^{95} + 18 q^{97} - 18 q^{98}+O(q^{100}) $ 4 * q + q^2 - q^4 + 8 * q^7 + q^8 + 10 * q^10 + 4 * q^11 + 8 * q^13 - 8 * q^14 - q^16 + 4 * q^17 - 2 * q^19 + q^22 - 20 * q^23 - 15 * q^25 + 12 * q^26 - 7 * q^28 - q^29 - 11 * q^31 - 4 * q^32 - 4 * q^34 + 15 * q^35 - 12 * q^37 + 2 * q^38 - 5 * q^40 - 4 * q^41 - q^44 - 10 * q^46 + 2 * q^47 + 3 * q^49 - 10 * q^50 - 12 * q^52 + 13 * q^53 - 20 * q^55 + 2 * q^56 + q^58 + 22 * q^59 - 10 * q^61 - 4 * q^62 - q^64 - 40 * q^65 - 8 * q^67 + 4 * q^68 + 25 * q^70 - 8 * q^71 + q^73 + 12 * q^74 + 8 * q^76 + 38 * q^77 + 18 * q^79 + 5 * q^80 + 14 * q^82 - 32 * q^83 + 20 * q^85 + 11 * q^88 - 20 * q^89 + 36 * q^91 - 12 * q^94 + 10 * q^95 + 18 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−1.11803	+	3.44095i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$5$	−1.11803	+	3.44095i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$6$		0			0
$7$	3.11803	−	2.26538i	1.17851	−	0.856235i	0.186504	−	0.982454i	$-0.440284\pi$
$7$	3.11803	−	2.26538i	1.17851	−	0.856235i	0.992002	+	0.126219i	$0.0402844\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$		0			0
$10$	3.61803			1.14412
$11$	3.23607	+	0.726543i	0.975711	+	0.219061i
$11$	3.23607	+	0.726543i	0.975711	+	0.219061i
$12$		0			0
$13$	2.00000	+	6.15537i	0.554700	+	1.70719i	0.696734	+	0.717330i	$0.254636\pi$
$13$	2.00000	+	6.15537i	0.554700	+	1.70719i	−0.142034	+	0.989862i	$0.545364\pi$
$14$	−3.11803	−	2.26538i	−0.833330	−	0.605449i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	1.00000	−	3.07768i	0.242536	−	0.746448i	−0.753496	−	0.657452i	$-0.771634\pi$
$17$	1.00000	−	3.07768i	0.242536	−	0.746448i	0.996032	−	0.0889958i	$-0.0283658\pi$
$18$		0			0
$19$	−1.61803	−	1.17557i	−0.371202	−	0.269694i	0.386507	−	0.922287i	$-0.373682\pi$
$19$	−1.61803	−	1.17557i	−0.371202	−	0.269694i	−0.757709	+	0.652592i	$0.773682\pi$
$20$	−1.11803	−	3.44095i	−0.250000	−	0.769421i
$21$		0			0
$22$	−0.309017	−	3.30220i	−0.0658826	−	0.704031i
$23$	−2.76393			−0.576320			−0.288160	−	0.957582i	$-0.593043\pi$
$23$	−2.76393			−0.576320			−0.288160	+	0.957582i	$0.593043\pi$
$24$		0			0
$25$	−6.54508	−	4.75528i	−1.30902	−	0.951057i
$26$	5.23607	−	3.80423i	1.02688	−	0.746070i
$27$		0			0
$28$	−1.19098	+	3.66547i	−0.225075	+	0.692708i
$29$	0.309017	−	0.224514i	0.0573830	−	0.0416912i	−0.558724	−	0.829354i	$-0.688709\pi$
$29$	0.309017	−	0.224514i	0.0573830	−	0.0416912i	0.616107	+	0.787662i	$0.288709\pi$
$30$		0			0
$31$	0.0450850	+	0.138757i	0.00809750	+	0.0249215i	0.955024	−	0.296530i	$-0.0958294\pi$
$31$	0.0450850	+	0.138757i	0.00809750	+	0.0249215i	−0.946926	+	0.321451i	$0.895829\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−3.23607			−0.554981
$35$	4.30902	+	13.2618i	0.728357	+	2.24165i
$36$		0			0
$37$	−3.00000	+	2.17963i	−0.493197	+	0.358329i	−0.806412	−	0.591354i	$-0.798594\pi$
$37$	−3.00000	+	2.17963i	−0.493197	+	0.358329i	0.313215	+	0.949682i	$0.398594\pi$
$38$	−0.618034	+	1.90211i	−0.100258	+	0.308563i
$39$		0			0
$40$	−2.92705	+	2.12663i	−0.462807	+	0.336249i
$41$	−5.47214	−	3.97574i	−0.854604	−	0.620906i	0.0718076	−	0.997419i	$-0.477123\pi$
$41$	−5.47214	−	3.97574i	−0.854604	−	0.620906i	−0.926412	+	0.376512i	$0.877123\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	−3.04508	+	1.31433i	−0.459064	+	0.198142i
$45$		0			0
$46$	0.854102	+	2.62866i	0.125930	+	0.387574i
$47$	3.85410	+	2.80017i	0.562179	+	0.408447i	0.832256	−	0.554392i	$-0.187049\pi$
$47$	3.85410	+	2.80017i	0.562179	+	0.408447i	−0.270077	+	0.962839i	$0.587049\pi$
$48$		0			0
$49$	2.42705	−	7.46969i	0.346722	−	1.06710i
$50$	−2.50000	+	7.69421i	−0.353553	+	1.08813i
$51$		0			0
$52$	−5.23607	−	3.80423i	−0.726112	−	0.527551i
$53$	−2.89919	−	8.92278i	−0.398234	−	1.22564i	−0.926414	−	0.376506i	$-0.877125\pi$
$53$	−2.89919	−	8.92278i	−0.398234	−	1.22564i	0.528180	−	0.849132i	$-0.322875\pi$
$54$		0			0
$55$	−6.11803	+	10.3229i	−0.824956	+	1.39193i
$56$	3.85410			0.515026
$57$		0			0
$58$	−0.309017	−	0.224514i	−0.0405759	−	0.0294801i
$59$	9.97214	−	7.24518i	1.29826	−	0.943242i	0.298324	−	0.954465i	$-0.403572\pi$
$59$	9.97214	−	7.24518i	1.29826	−	0.943242i	0.999937	+	0.0112223i	$0.00357224\pi$
$60$		0			0
$61$	0.854102	−	2.62866i	0.109357	−	0.336565i	−0.881372	−	0.472423i	$-0.843379\pi$
$61$	0.854102	−	2.62866i	0.109357	−	0.336565i	0.990728	+	0.135859i	$0.0433793\pi$
$62$	0.118034	−	0.0857567i	0.0149903	−	0.0108911i
$63$		0			0
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−23.4164			−2.90445
$66$		0			0
$67$	−10.9443			−1.33706			−0.668528	−	0.743687i	$-0.733075\pi$
$67$	−10.9443			−1.33706			−0.668528	+	0.743687i	$0.733075\pi$
$68$	1.00000	+	3.07768i	0.121268	+	0.373224i
$69$		0			0
$70$	11.2812	−	8.19624i	1.34836	−	0.979638i
$71$	0.236068	−	0.726543i	0.0280161	−	0.0862247i	−0.936071	−	0.351812i	$-0.885566\pi$
$71$	0.236068	−	0.726543i	0.0280161	−	0.0862247i	0.964087	+	0.265587i	$0.0855657\pi$
$72$		0			0
$73$	1.92705	−	1.40008i	0.225544	−	0.163867i	−0.469275	−	0.883052i	$-0.655485\pi$
$73$	1.92705	−	1.40008i	0.225544	−	0.163867i	0.694819	+	0.719185i	$0.255485\pi$
$74$	3.00000	+	2.17963i	0.348743	+	0.253377i
$75$		0			0
$76$	2.00000			0.229416
$77$	11.7361	−	5.06555i	1.33745	−	0.577273i
$78$		0			0
$79$	−2.20820	−	6.79615i	−0.248442	−	0.764627i	−0.995051	−	0.0993636i	$-0.968319\pi$
$79$	−2.20820	−	6.79615i	−0.248442	−	0.764627i	0.746609	−	0.665263i	$-0.231681\pi$
$80$	2.92705	+	2.12663i	0.327254	+	0.237764i
$81$		0			0
$82$	−2.09017	+	6.43288i	−0.230821	+	0.710393i
$83$	−2.40983	+	7.41669i	−0.264513	+	0.814088i	0.727292	+	0.686328i	$0.240779\pi$
$83$	−2.40983	+	7.41669i	−0.264513	+	0.814088i	−0.991805	+	0.127760i	$0.959221\pi$
$84$		0			0
$85$	9.47214	+	6.88191i	1.02740	+	0.746448i
$86$		0			0
$87$		0			0
$88$	2.19098	+	2.48990i	0.233560	+	0.265424i
$89$	6.18034			0.655115			0.327557	−	0.944831i	$-0.393775\pi$
$89$	6.18034			0.655115			0.327557	+	0.944831i	$0.393775\pi$
$90$		0			0
$91$	20.1803	+	14.6619i	2.11547	+	1.53698i
$92$	2.23607	−	1.62460i	0.233126	−	0.169376i
$93$		0			0
$94$	1.47214	−	4.53077i	0.151839	−	0.467313i
$95$	5.85410	−	4.25325i	0.600618	−	0.436375i
$96$		0			0
$97$	−2.20820	−	6.79615i	−0.224209	−	0.690045i	−0.998371	−	0.0570570i	$-0.981828\pi$
$97$	−2.20820	−	6.79615i	−0.224209	−	0.690045i	0.774162	−	0.632988i	$-0.218172\pi$
$98$	−7.85410			−0.793384
$99$		0			0
$100$	8.09017			0.809017
$101$	−1.82624	−	5.62058i	−0.181717	−	0.559269i	0.818159	−	0.574992i	$-0.194995\pi$
$101$	−1.82624	−	5.62058i	−0.181717	−	0.559269i	−0.999876	+	0.0157233i	$0.994995\pi$
$102$		0			0
$103$	6.35410	−	4.61653i	0.626088	−	0.454880i	−0.228955	−	0.973437i	$-0.573531\pi$
$103$	6.35410	−	4.61653i	0.626088	−	0.454880i	0.855043	+	0.518557i	$0.173531\pi$
$104$	−2.00000	+	6.15537i	−0.196116	+	0.603583i
$105$		0			0
$106$	−7.59017	+	5.51458i	−0.737222	+	0.535623i
$107$	−11.2082	−	8.14324i	−1.08354	−	0.787236i	−0.105242	−	0.994447i	$-0.533562\pi$
$107$	−11.2082	−	8.14324i	−1.08354	−	0.787236i	−0.978296	+	0.207210i	$0.933562\pi$
$108$		0			0
$109$	4.76393			0.456302			0.228151	−	0.973626i	$-0.426732\pi$
$109$	4.76393			0.456302			0.228151	+	0.973626i	$0.426732\pi$
$110$	11.7082	+	2.62866i	1.11633	+	0.250632i
$111$		0			0
$112$	−1.19098	−	3.66547i	−0.112537	−	0.346354i
$113$	−7.85410	−	5.70634i	−0.738852	−	0.536807i	0.153500	−	0.988149i	$-0.450946\pi$
$113$	−7.85410	−	5.70634i	−0.738852	−	0.536807i	−0.892351	+	0.451341i	$0.850946\pi$
$114$		0			0
$115$	3.09017	−	9.51057i	0.288160	−	0.886865i
$116$	−0.118034	+	0.363271i	−0.0109592	+	0.0337289i
$117$		0			0
$118$	−9.97214	−	7.24518i	−0.918010	−	0.666973i
$119$	−3.85410	−	11.8617i	−0.353305	−	1.08736i
$120$		0			0
$121$	9.94427	+	4.70228i	0.904025	+	0.427480i
$122$	−2.76393			−0.250235
$123$		0			0
$124$	−0.118034	−	0.0857567i	−0.0105998	−	0.00770118i
$125$	9.04508	−	6.57164i	0.809017	−	0.587785i
$126$		0			0
$127$	0.291796	−	0.898056i	0.0258927	−	0.0796896i	−0.937275	−	0.348590i	$-0.886660\pi$
$127$	0.291796	−	0.898056i	0.0258927	−	0.0796896i	0.963168	+	0.268901i	$0.0866604\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$		0			0
$130$	7.23607	+	22.2703i	0.634645	+	1.95324i
$131$	11.0902			0.968953			0.484476	−	0.874804i	$-0.339010\pi$
$131$	11.0902			0.968953			0.484476	+	0.874804i	$0.339010\pi$
$132$		0			0
$133$	−7.70820			−0.668386
$134$	3.38197	+	10.4086i	0.292157	+	0.899168i
$135$		0			0
$136$	2.61803	−	1.90211i	0.224495	−	0.163105i
$137$	−5.09017	+	15.6659i	−0.434883	+	1.33843i	0.458324	+	0.888785i	$0.348450\pi$
$137$	−5.09017	+	15.6659i	−0.434883	+	1.33843i	−0.893207	+	0.449646i	$0.851550\pi$
$138$		0			0
$139$	−3.00000	+	2.17963i	−0.254457	+	0.184874i	−0.707700	−	0.706513i	$-0.750267\pi$
$139$	−3.00000	+	2.17963i	−0.254457	+	0.184874i	0.453243	+	0.891387i	$0.350267\pi$
$140$	−11.2812	−	8.19624i	−0.953431	−	0.692708i
$141$		0			0
$142$	−0.763932			−0.0641078
$143$	2.00000	+	21.3723i	0.167248	+	1.78724i
$144$		0			0
$145$	0.427051	+	1.31433i	0.0354647	+	0.109149i
$146$	−1.92705	−	1.40008i	−0.159484	−	0.115872i
$147$		0			0
$148$	1.14590	−	3.52671i	0.0941922	−	0.289894i
$149$	−3.28115	+	10.0984i	−0.268803	+	0.827289i	0.721990	+	0.691903i	$0.243227\pi$
$149$	−3.28115	+	10.0984i	−0.268803	+	0.827289i	−0.990793	+	0.135386i	$0.956773\pi$
$150$		0			0
$151$	10.3992	+	7.55545i	0.846274	+	0.614854i	0.924116	−	0.382112i	$-0.124803\pi$
$151$	10.3992	+	7.55545i	0.846274	+	0.614854i	−0.0778423	+	0.996966i	$0.524803\pi$
$152$	−0.618034	−	1.90211i	−0.0501292	−	0.154282i
$153$		0			0
$154$	−8.44427	−	9.59632i	−0.680459	−	0.773294i
$155$	−0.527864			−0.0423991
$156$		0			0
$157$	−12.7082	−	9.23305i	−1.01423	−	0.736878i	−0.0491340	−	0.998792i	$-0.515646\pi$
$157$	−12.7082	−	9.23305i	−1.01423	−	0.736878i	−0.965091	+	0.261915i	$0.915646\pi$
$158$	−5.78115	+	4.20025i	−0.459924	+	0.334154i
$159$		0			0
$160$	1.11803	−	3.44095i	0.0883883	−	0.272031i
$161$	−8.61803	+	6.26137i	−0.679196	+	0.493465i
$162$		0			0
$163$	−6.76393	−	20.8172i	−0.529792	−	1.63053i	−0.754640	−	0.656139i	$-0.772189\pi$
$163$	−6.76393	−	20.8172i	−0.529792	−	1.63053i	0.224848	−	0.974394i	$-0.427811\pi$
$164$	6.76393			0.528174
$165$		0			0
$166$	7.79837			0.605271
$167$	6.38197	+	19.6417i	0.493851	+	1.51992i	0.818739	+	0.574166i	$0.194673\pi$
$167$	6.38197	+	19.6417i	0.493851	+	1.51992i	−0.324888	+	0.945753i	$0.605327\pi$
$168$		0			0
$169$	−23.3713	+	16.9803i	−1.79779	+	1.30617i
$170$	3.61803	−	11.1352i	0.277491	−	0.854028i
$171$		0			0
$172$		0			0
$173$	13.8262	+	10.0453i	1.05119	+	0.763734i	0.972438	−	0.233160i	$-0.0749068\pi$
$173$	13.8262	+	10.0453i	1.05119	+	0.763734i	0.0787511	+	0.996894i	$0.474907\pi$
$174$		0			0
$175$	−31.1803			−2.35701
$176$	1.69098	−	2.85317i	0.127463	−	0.215066i
$177$		0			0
$178$	−1.90983	−	5.87785i	−0.143148	−	0.440564i
$179$	−16.0172	−	11.6372i	−1.19718	−	0.869805i	−0.203179	−	0.979142i	$-0.565127\pi$
$179$	−16.0172	−	11.6372i	−1.19718	−	0.869805i	−0.994005	+	0.109337i	$0.965127\pi$
$180$		0			0
$181$	−7.52786	+	23.1684i	−0.559542	+	1.72209i	0.124095	+	0.992270i	$0.460397\pi$
$181$	−7.52786	+	23.1684i	−0.559542	+	1.72209i	−0.683637	+	0.729822i	$0.739603\pi$
$182$	7.70820	−	23.7234i	0.571370	−	1.75850i
$183$		0			0
$184$	−2.23607	−	1.62460i	−0.164845	−	0.119767i
$185$	−4.14590	−	12.7598i	−0.304812	−	0.938116i
$186$		0			0
$187$	5.47214	−	9.23305i	0.400162	−	0.675188i
$188$	−4.76393			−0.347445
$189$		0			0
$190$	−5.85410	−	4.25325i	−0.424701	−	0.308563i
$191$	12.3262	−	8.95554i	0.891895	−	0.648000i	−0.0444762	−	0.999010i	$-0.514162\pi$
$191$	12.3262	−	8.95554i	0.891895	−	0.648000i	0.936371	+	0.351011i	$0.114162\pi$
$192$		0			0
$193$	−1.89919	+	5.84510i	−0.136706	+	0.420739i	−0.995852	−	0.0909928i	$-0.970996\pi$
$193$	−1.89919	+	5.84510i	−0.136706	+	0.420739i	0.859145	+	0.511732i	$0.170996\pi$
$194$	−5.78115	+	4.20025i	−0.415063	+	0.301561i
$195$		0			0
$196$	2.42705	+	7.46969i	0.173361	+	0.533550i
$197$	−0.381966			−0.0272140			−0.0136070	−	0.999907i	$-0.504331\pi$
$197$	−0.381966			−0.0272140			−0.0136070	+	0.999907i	$0.504331\pi$
$198$		0			0
$199$	9.79837			0.694588			0.347294	−	0.937756i	$-0.387101\pi$
$199$	9.79837			0.694588			0.347294	+	0.937756i	$0.387101\pi$
$200$	−2.50000	−	7.69421i	−0.176777	−	0.544063i
$201$		0			0
$202$	−4.78115	+	3.47371i	−0.336401	+	0.244409i
$203$	0.454915	−	1.40008i	0.0319288	−	0.0982667i
$204$		0			0
$205$	19.7984	−	14.3844i	1.38278	−	1.00465i
$206$	−6.35410	−	4.61653i	−0.442711	−	0.321649i
$207$		0			0
$208$	6.47214			0.448762
$209$	−4.38197	−	4.97980i	−0.303107	−	0.344460i
$210$		0			0
$211$	2.14590	+	6.60440i	0.147730	+	0.454665i	0.997352	−	0.0727265i	$-0.0231700\pi$
$211$	2.14590	+	6.60440i	0.147730	+	0.454665i	−0.849622	+	0.527392i	$0.823170\pi$
$212$	7.59017	+	5.51458i	0.521295	+	0.378743i
$213$		0			0
$214$	−4.28115	+	13.1760i	−0.292654	+	0.900695i
$215$		0			0
$216$		0			0
$217$	0.454915	+	0.330515i	0.0308816	+	0.0224368i
$218$	−1.47214	−	4.53077i	−0.0997056	−	0.306862i
$219$		0			0
$220$	−1.11803	−	11.9475i	−0.0753778	−	0.805498i
$221$	20.9443			1.40886
$222$		0			0
$223$	−7.16312	−	5.20431i	−0.479678	−	0.348506i	0.321523	−	0.946902i	$-0.395805\pi$
$223$	−7.16312	−	5.20431i	−0.479678	−	0.348506i	−0.801201	+	0.598395i	$0.795805\pi$
$224$	−3.11803	+	2.26538i	−0.208332	+	0.151362i
$225$		0			0
$226$	−3.00000	+	9.23305i	−0.199557	+	0.614173i
$227$	−8.16312	+	5.93085i	−0.541805	+	0.393645i	−0.824755	−	0.565490i	$-0.808687\pi$
$227$	−8.16312	+	5.93085i	−0.541805	+	0.393645i	0.282950	+	0.959135i	$0.408687\pi$
$228$		0			0
$229$	−5.47214	−	16.8415i	−0.361609	−	1.11292i	−0.952077	−	0.305857i	$-0.901057\pi$
$229$	−5.47214	−	16.8415i	−0.361609	−	1.11292i	0.590468	−	0.807061i	$-0.298943\pi$
$230$	−10.0000			−0.659380
$231$		0			0
$232$	0.381966			0.0250773
$233$	−4.29180	−	13.2088i	−0.281165	−	0.865337i	−0.987522	−	0.157481i	$-0.949663\pi$
$233$	−4.29180	−	13.2088i	−0.281165	−	0.865337i	0.706357	−	0.707856i	$-0.250337\pi$
$234$		0			0
$235$	−13.9443	+	10.1311i	−0.909624	+	0.660881i
$236$	−3.80902	+	11.7229i	−0.247946	+	0.763099i
$237$		0			0
$238$	−10.0902	+	7.33094i	−0.654049	+	0.475194i
$239$	10.8541	+	7.88597i	0.702093	+	0.510101i	0.880613	−	0.473836i	$-0.157131\pi$
$239$	10.8541	+	7.88597i	0.702093	+	0.510101i	−0.178520	+	0.983936i	$0.557131\pi$
$240$		0			0
$241$	10.5066			0.676788			0.338394	−	0.941004i	$-0.390116\pi$
$241$	10.5066			0.676788			0.338394	+	0.941004i	$0.390116\pi$
$242$	1.39919	−	10.9106i	0.0899431	−	0.701363i
$243$		0			0
$244$	0.854102	+	2.62866i	0.0546783	+	0.168282i
$245$	22.9894	+	16.7027i	1.46874	+	1.06710i
$246$		0			0
$247$	4.00000	−	12.3107i	0.254514	−	0.783313i
$248$	−0.0450850	+	0.138757i	−0.00286290	+	0.00881110i
$249$		0			0
$250$	−9.04508	−	6.57164i	−0.572061	−	0.415627i
$251$	6.11803	+	18.8294i	0.386167	+	1.18850i	0.935630	+	0.352982i	$0.114832\pi$
$251$	6.11803	+	18.8294i	0.386167	+	1.18850i	−0.549463	+	0.835518i	$0.685168\pi$
$252$		0			0
$253$	−8.94427	−	2.00811i	−0.562322	−	0.126249i
$254$	−0.944272			−0.0592489
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−12.0902	+	8.78402i	−0.754164	+	0.547932i	−0.897115	−	0.441798i	$-0.854341\pi$
$257$	−12.0902	+	8.78402i	−0.754164	+	0.547932i	0.142951	+	0.989730i	$0.454341\pi$
$258$		0			0
$259$	−4.41641	+	13.5923i	−0.274422	+	0.844585i
$260$	18.9443	−	13.7638i	1.17487	−	0.853596i
$261$		0			0
$262$	−3.42705	−	10.5474i	−0.211724	−	0.651619i
$263$	−14.9443			−0.921503			−0.460752	−	0.887529i	$-0.652420\pi$
$263$	−14.9443			−0.921503			−0.460752	+	0.887529i	$0.652420\pi$
$264$		0			0
$265$	33.9443			2.08518
$266$	2.38197	+	7.33094i	0.146048	+	0.449489i
$267$		0			0
$268$	8.85410	−	6.43288i	0.540850	−	0.392951i
$269$	−2.14590	+	6.60440i	−0.130838	+	0.402677i	−0.994919	−	0.100675i	$-0.967900\pi$
$269$	−2.14590	+	6.60440i	−0.130838	+	0.402677i	0.864082	+	0.503352i	$0.167900\pi$
$270$		0			0
$271$	18.9443	−	13.7638i	1.15078	−	0.836092i	0.162198	−	0.986758i	$-0.448142\pi$
$271$	18.9443	−	13.7638i	1.15078	−	0.836092i	0.988585	+	0.150666i	$0.0481417\pi$
$272$	−2.61803	−	1.90211i	−0.158742	−	0.115333i
$273$		0			0
$274$	16.4721			0.995118
$275$	−17.7254	−	20.1437i	−1.06888	−	1.21471i
$276$		0			0
$277$	−4.32624	−	13.3148i	−0.259938	−	0.800008i	−0.992816	−	0.119648i	$-0.961823\pi$
$277$	−4.32624	−	13.3148i	−0.259938	−	0.800008i	0.732878	−	0.680360i	$-0.238177\pi$
$278$	3.00000	+	2.17963i	0.179928	+	0.130725i
$279$		0			0
$280$	−4.30902	+	13.2618i	−0.257513	+	0.792544i
$281$	−2.76393	+	8.50651i	−0.164882	+	0.507456i	−0.999028	−	0.0440891i	$-0.985961\pi$
$281$	−2.76393	+	8.50651i	−0.164882	+	0.507456i	0.834145	+	0.551545i	$0.185961\pi$
$282$		0			0
$283$	22.4164	+	16.2865i	1.33252	+	0.968130i	0.999684	+	0.0251447i	$0.00800465\pi$
$283$	22.4164	+	16.2865i	1.33252	+	0.968130i	0.332833	+	0.942986i	$0.391995\pi$
$284$	0.236068	+	0.726543i	0.0140081	+	0.0431124i
$285$		0			0
$286$	19.7082	−	8.50651i	1.16537	−	0.503000i
$287$	−26.0689			−1.53880
$288$		0			0
$289$	5.28115	+	3.83698i	0.310656	+	0.225705i
$290$	1.11803	−	0.812299i	0.0656532	−	0.0476999i
$291$		0			0
$292$	−0.736068	+	2.26538i	−0.0430751	+	0.132572i
$293$	19.5902	−	14.2331i	1.14447	−	0.831506i	0.156734	−	0.987641i	$-0.449903\pi$
$293$	19.5902	−	14.2331i	1.14447	−	0.831506i	0.987736	+	0.156135i	$0.0499034\pi$
$294$		0			0
$295$	13.7812	+	42.4140i	0.802370	+	2.46944i
$296$	−3.70820			−0.215535
$297$		0			0
$298$	10.6180			0.615086
$299$	−5.52786	−	17.0130i	−0.319685	−	0.983888i
$300$		0			0
$301$		0			0
$302$	3.97214	−	12.2250i	0.228571	−	0.703468i
$303$		0			0
$304$	−1.61803	+	1.17557i	−0.0928006	+	0.0674236i
$305$	8.09017	+	5.87785i	0.463242	+	0.336565i
$306$		0			0
$307$	−20.3607			−1.16205			−0.581023	−	0.813887i	$-0.697347\pi$
$307$	−20.3607			−1.16205			−0.581023	+	0.813887i	$0.697347\pi$
$308$	−6.51722	+	10.9964i	−0.371353	+	0.626578i
$309$		0			0
$310$	0.163119	+	0.502029i	0.00926453	+	0.0285133i
$311$	−9.09017	−	6.60440i	−0.515456	−	0.374501i	0.299433	−	0.954117i	$-0.403202\pi$
$311$	−9.09017	−	6.60440i	−0.515456	−	0.374501i	−0.814889	+	0.579616i	$0.803202\pi$
$312$		0			0
$313$	−3.50000	+	10.7719i	−0.197832	+	0.608863i	0.802100	+	0.597190i	$0.203716\pi$
$313$	−3.50000	+	10.7719i	−0.197832	+	0.608863i	−0.999932	+	0.0116738i	$0.996284\pi$
$314$	−4.85410	+	14.9394i	−0.273933	+	0.843079i
$315$		0			0
$316$	5.78115	+	4.20025i	0.325215	+	0.236283i
$317$	10.1459	+	31.2259i	0.569850	+	1.75382i	0.653080	+	0.757289i	$0.273476\pi$
$317$	10.1459	+	31.2259i	0.569850	+	1.75382i	−0.0832297	+	0.996530i	$0.526524\pi$
$318$		0			0
$319$	1.16312	−	0.502029i	0.0651222	−	0.0281082i
$320$	−3.61803			−0.202254
$321$		0			0
$322$	8.61803	+	6.26137i	0.480264	+	0.348932i
$323$	−5.23607	+	3.80423i	−0.291343	+	0.211673i
$324$		0			0
$325$	16.1803	−	49.7980i	0.897524	−	2.76229i
$326$	−17.7082	+	12.8658i	−0.980767	+	0.712569i
$327$		0			0
$328$	−2.09017	−	6.43288i	−0.115410	−	0.355196i
$329$	18.3607			1.01226
$330$		0			0
$331$	−8.29180			−0.455758			−0.227879	−	0.973689i	$-0.573179\pi$
$331$	−8.29180			−0.455758			−0.227879	+	0.973689i	$0.573179\pi$
$332$	−2.40983	−	7.41669i	−0.132257	−	0.407044i
$333$		0			0
$334$	16.7082	−	12.1392i	0.914232	−	0.664229i
$335$	12.2361	−	37.6587i	0.668528	−	2.05752i
$336$		0			0
$337$	−18.5623	+	13.4863i	−1.01115	+	0.734646i	−0.964451	−	0.264263i	$-0.914871\pi$
$337$	−18.5623	+	13.4863i	−1.01115	+	0.734646i	−0.0467026	+	0.998909i	$0.514871\pi$
$338$	23.3713	+	16.9803i	1.27123	+	0.923604i
$339$		0			0
$340$	−11.7082			−0.634967
$341$	0.0450850	+	0.481784i	0.00244149	+	0.0260901i
$342$		0			0
$343$	−1.01722	−	3.13068i	−0.0549248	−	0.169041i
$344$		0			0
$345$		0			0
$346$	5.28115	−	16.2537i	0.283917	−	0.873805i
$347$	3.62868	−	11.1679i	0.194798	−	0.599525i	−0.805181	−	0.593029i	$-0.797932\pi$
$347$	3.62868	−	11.1679i	0.194798	−	0.599525i	0.999979	−	0.00649662i	$-0.00206795\pi$
$348$		0			0
$349$	8.61803	+	6.26137i	0.461313	+	0.335163i	0.794046	−	0.607858i	$-0.207971\pi$
$349$	8.61803	+	6.26137i	0.461313	+	0.335163i	−0.332733	+	0.943021i	$0.607971\pi$
$350$	9.63525	+	29.6543i	0.515026	+	1.58509i
$351$		0			0
$352$	−3.23607	−	0.726543i	−0.172483	−	0.0387248i
$353$	−24.6525			−1.31212			−0.656059	−	0.754709i	$-0.727778\pi$
$353$	−24.6525			−1.31212			−0.656059	+	0.754709i	$0.727778\pi$
$354$		0			0
$355$	2.23607	+	1.62460i	0.118678	+	0.0862247i
$356$	−5.00000	+	3.63271i	−0.264999	+	0.192533i
$357$		0			0
$358$	−6.11803	+	18.8294i	−0.323348	+	0.995163i
$359$	10.8541	−	7.88597i	0.572858	−	0.416205i	−0.263285	−	0.964718i	$-0.584806\pi$
$359$	10.8541	−	7.88597i	0.572858	−	0.416205i	0.836142	+	0.548513i	$0.184806\pi$
$360$		0			0
$361$	−4.63525	−	14.2658i	−0.243961	−	0.750834i
$362$	24.3607			1.28037
$363$		0			0
$364$	−24.9443			−1.30744
$365$	2.66312	+	8.19624i	0.139394	+	0.429011i
$366$		0			0
$367$	4.39919	−	3.19620i	0.229636	−	0.166840i	−0.467018	−	0.884248i	$-0.654672\pi$
$367$	4.39919	−	3.19620i	0.229636	−	0.166840i	0.696653	+	0.717408i	$0.254672\pi$
$368$	−0.854102	+	2.62866i	−0.0445231	+	0.137028i
$369$		0			0
$370$	−10.8541	+	7.88597i	−0.564278	+	0.409972i
$371$	−29.2533	−	21.2538i	−1.51876	−	1.10344i
$372$		0			0
$373$	1.70820			0.0884474			0.0442237	−	0.999022i	$-0.485919\pi$
$373$	1.70820			0.0884474			0.0442237	+	0.999022i	$0.485919\pi$
$374$	−10.4721	−	2.35114i	−0.541501	−	0.121575i
$375$		0			0
$376$	1.47214	+	4.53077i	0.0759196	+	0.233657i
$377$	2.00000	+	1.45309i	0.103005	+	0.0748377i
$378$		0			0
$379$	8.90983	−	27.4216i	0.457667	−	1.40855i	−0.410308	−	0.911947i	$-0.634579\pi$
$379$	8.90983	−	27.4216i	0.457667	−	1.40855i	0.867975	−	0.496608i	$-0.165421\pi$
$380$	−2.23607	+	6.88191i	−0.114708	+	0.353035i
$381$		0			0
$382$	−12.3262	−	8.95554i	−0.630665	−	0.458205i
$383$	−5.05573	−	15.5599i	−0.258336	−	0.795075i	−0.993154	−	0.116812i	$-0.962733\pi$
$383$	−5.05573	−	15.5599i	−0.258336	−	0.795075i	0.734818	−	0.678264i	$-0.237267\pi$
$384$		0			0
$385$	4.30902	+	46.0467i	0.219608	+	2.34676i
$386$	6.14590			0.312818
$387$		0			0
$388$	5.78115	+	4.20025i	0.293494	+	0.213236i
$389$	−6.85410	+	4.97980i	−0.347517	+	0.252486i	−0.747827	−	0.663894i	$-0.768903\pi$
$389$	−6.85410	+	4.97980i	−0.347517	+	0.252486i	0.400310	+	0.916380i	$0.368903\pi$
$390$		0			0
$391$	−2.76393	+	8.50651i	−0.139778	+	0.430193i
$392$	6.35410	−	4.61653i	0.320931	−	0.233170i
$393$		0			0
$394$	0.118034	+	0.363271i	0.00594647	+	0.0183013i
$395$	25.8541			1.30086
$396$		0			0
$397$	−31.4164			−1.57674			−0.788372	−	0.615199i	$-0.789076\pi$
$397$	−31.4164			−1.57674			−0.788372	+	0.615199i	$0.789076\pi$
$398$	−3.02786	−	9.31881i	−0.151773	−	0.467110i
$399$		0			0
$400$	−6.54508	+	4.75528i	−0.327254	+	0.237764i
$401$	4.03444	−	12.4167i	0.201470	−	0.620062i	−0.798369	−	0.602168i	$-0.794304\pi$
$401$	4.03444	−	12.4167i	0.201470	−	0.620062i	0.999840	−	0.0178943i	$-0.00569623\pi$
$402$		0			0
$403$	−0.763932	+	0.555029i	−0.0380542	+	0.0276480i
$404$	4.78115	+	3.47371i	0.237871	+	0.172824i
$405$		0			0
$406$	−1.47214			−0.0730609
$407$	−11.2918	+	4.87380i	−0.559714	+	0.241585i
$408$		0			0
$409$	−6.79180	−	20.9030i	−0.335833	−	1.03359i	−0.966310	−	0.257379i	$-0.917141\pi$
$409$	−6.79180	−	20.9030i	−0.335833	−	1.03359i	0.630478	−	0.776207i	$-0.282859\pi$
$410$	−19.7984	−	14.3844i	−0.977772	−	0.710393i
$411$		0			0
$412$	−2.42705	+	7.46969i	−0.119572	+	0.368005i
$413$	14.6803	−	45.1814i	0.722372	−	2.22323i
$414$		0			0
$415$	−22.8262	−	16.5842i	−1.12050	−	0.814088i
$416$	−2.00000	−	6.15537i	−0.0980581	−	0.301792i
$417$		0			0
$418$	−3.38197	+	5.70634i	−0.165417	+	0.279106i
$419$	13.1459			0.642219			0.321110	−	0.947042i	$-0.395944\pi$
$419$	13.1459			0.642219			0.321110	+	0.947042i	$0.395944\pi$
$420$		0			0
$421$	13.8541	+	10.0656i	0.675208	+	0.490567i	0.871764	−	0.489925i	$-0.162976\pi$
$421$	13.8541	+	10.0656i	0.675208	+	0.490567i	−0.196557	+	0.980492i	$0.562976\pi$
$422$	5.61803	−	4.08174i	0.273482	−	0.198696i
$423$		0			0
$424$	2.89919	−	8.92278i	0.140797	−	0.433328i
$425$	−21.1803	+	15.3884i	−1.02740	+	0.746448i
$426$		0			0
$427$	−3.29180	−	10.1311i	−0.159301	−	0.490279i
$428$	13.8541			0.669663
$429$		0			0
$430$		0			0
$431$	−12.5623	−	38.6628i	−0.605105	−	1.86232i	−0.496067	−	0.868284i	$-0.665223\pi$
$431$	−12.5623	−	38.6628i	−0.605105	−	1.86232i	−0.109038	−	0.994038i	$-0.534777\pi$
$432$		0			0
$433$	10.2082	−	7.41669i	0.490575	−	0.356424i	−0.314830	−	0.949148i	$-0.601948\pi$
$433$	10.2082	−	7.41669i	0.490575	−	0.356424i	0.805405	+	0.592724i	$0.201948\pi$
$434$	0.173762	−	0.534785i	0.00834085	−	0.0256705i
$435$		0			0
$436$	−3.85410	+	2.80017i	−0.184578	+	0.134104i
$437$	4.47214	+	3.24920i	0.213931	+	0.155430i
$438$		0			0
$439$	−15.8541			−0.756675			−0.378338	−	0.925668i	$-0.623504\pi$
$439$	−15.8541			−0.756675			−0.378338	+	0.925668i	$0.623504\pi$
$440$	−11.0172	+	4.75528i	−0.525225	+	0.226699i
$441$		0			0
$442$	−6.47214	−	19.9192i	−0.307848	−	0.947459i
$443$	26.2082	+	19.0414i	1.24519	+	0.904683i	0.997933	−	0.0642670i	$-0.0204709\pi$
$443$	26.2082	+	19.0414i	1.24519	+	0.904683i	0.247257	+	0.968950i	$0.420471\pi$
$444$		0			0
$445$	−6.90983	+	21.2663i	−0.327557	+	1.00812i
$446$	−2.73607	+	8.42075i	−0.129557	+	0.398734i
$447$		0			0
$448$	3.11803	+	2.26538i	0.147313	+	0.107029i
$449$	4.41641	+	13.5923i	0.208423	+	0.641461i	0.999555	+	0.0298154i	$0.00949196\pi$
$449$	4.41641	+	13.5923i	0.208423	+	0.641461i	−0.791132	+	0.611645i	$0.790508\pi$
$450$		0			0
$451$	−14.8197	−	16.8415i	−0.697831	−	0.793035i
$452$	9.70820			0.456636
$453$		0			0
$454$	8.16312	+	5.93085i	0.383114	+	0.278349i
$455$	−73.0132	+	53.0472i	−3.42291	+	2.48689i
$456$		0			0
$457$	−0.791796	+	2.43690i	−0.0370387	+	0.113993i	−0.967866	−	0.251465i	$-0.919088\pi$
$457$	−0.791796	+	2.43690i	−0.0370387	+	0.113993i	0.930828	+	0.365458i	$0.119088\pi$
$458$	−14.3262	+	10.4086i	−0.669421	+	0.486363i
$459$		0			0
$460$	3.09017	+	9.51057i	0.144080	+	0.443432i
$461$	32.4721			1.51238			0.756189	−	0.654353i	$-0.227059\pi$
$461$	32.4721			1.51238			0.756189	+	0.654353i	$0.227059\pi$
$462$		0			0
$463$	−15.2705			−0.709681			−0.354840	−	0.934927i	$-0.615465\pi$
$463$	−15.2705			−0.709681			−0.354840	+	0.934927i	$0.615465\pi$
$464$	−0.118034	−	0.363271i	−0.00547959	−	0.0168644i
$465$		0			0
$466$	−11.2361	+	8.16348i	−0.520501	+	0.378166i
$467$	−8.75329	+	26.9399i	−0.405054	+	1.24663i	0.515796	+	0.856711i	$0.327496\pi$
$467$	−8.75329	+	26.9399i	−0.405054	+	1.24663i	−0.920850	+	0.389916i	$0.872504\pi$
$468$		0			0
$469$	−34.1246	+	24.7930i	−1.57573	+	1.14483i
$470$	13.9443	+	10.1311i	0.643201	+	0.467313i
$471$		0			0
$472$	12.3262			0.567361
$473$		0			0
$474$		0			0
$475$	5.00000	+	15.3884i	0.229416	+	0.706069i
$476$	10.0902	+	7.33094i	0.462482	+	0.336013i
$477$		0			0
$478$	4.14590	−	12.7598i	0.189629	−	0.583618i
$479$	8.76393	−	26.9726i	0.400434	−	1.23241i	−0.524214	−	0.851587i	$-0.675641\pi$
$479$	8.76393	−	26.9726i	0.400434	−	1.23241i	0.924648	−	0.380823i	$-0.124359\pi$
$480$		0			0
$481$	−19.4164	−	14.1068i	−0.885312	−	0.643217i
$482$	−3.24671	−	9.99235i	−0.147884	−	0.455139i
$483$		0			0
$484$	−10.8090	+	2.04087i	−0.491319	+	0.0927668i
$485$	25.8541			1.17397
$486$		0			0
$487$	10.3541	+	7.52270i	0.469189	+	0.340886i	0.797125	−	0.603814i	$-0.206353\pi$
$487$	10.3541	+	7.52270i	0.469189	+	0.340886i	−0.327936	+	0.944700i	$0.606353\pi$
$488$	2.23607	−	1.62460i	0.101222	−	0.0735421i
$489$		0			0
$490$	8.78115	−	27.0256i	0.396692	−	1.22089i
$491$	−19.4164	+	14.1068i	−0.876250	+	0.636633i	−0.932257	−	0.361797i	$-0.882163\pi$
$491$	−19.4164	+	14.1068i	−0.876250	+	0.636633i	0.0560065	+	0.998430i	$0.482163\pi$
$492$		0			0
$493$	−0.381966	−	1.17557i	−0.0172029	−	0.0529450i
$494$	−12.9443			−0.582390
$495$		0			0
$496$	0.145898			0.00655102
$497$	−0.909830	−	2.80017i	−0.0408115	−	0.125605i
$498$		0			0
$499$	17.3262	−	12.5882i	0.775629	−	0.563527i	−0.128035	−	0.991770i	$-0.540867\pi$
$499$	17.3262	−	12.5882i	0.775629	−	0.563527i	0.903664	+	0.428242i	$0.140867\pi$
$500$	−3.45492	+	10.6331i	−0.154508	+	0.475528i
$501$		0			0
$502$	16.0172	−	11.6372i	0.714884	−	0.519393i
$503$	28.2705	+	20.5397i	1.26052	+	0.915821i	0.998783	−	0.0493181i	$-0.0157048\pi$
$503$	28.2705	+	20.5397i	1.26052	+	0.915821i	0.261737	+	0.965139i	$0.415705\pi$
$504$		0			0
$505$	21.3820			0.951485
$506$	0.854102	+	9.12705i	0.0379695	+	0.405747i
$507$		0			0
$508$	0.291796	+	0.898056i	0.0129464	+	0.0398448i
$509$	−19.0623	−	13.8496i	−0.844922	−	0.613872i	0.0788193	−	0.996889i	$-0.474885\pi$
$509$	−19.0623	−	13.8496i	−0.844922	−	0.613872i	−0.923741	+	0.383017i	$0.874885\pi$
$510$		0			0
$511$	2.83688	−	8.73102i	0.125496	−	0.386238i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$		0			0
$514$	12.0902	+	8.78402i	0.533275	+	0.387447i
$515$	8.78115	+	27.0256i	0.386944	+	1.19089i
$516$		0			0
$517$	10.4377	+	11.8617i	0.459049	+	0.521677i
$518$	14.2918			0.627945
$519$		0			0
$520$	−18.9443	−	13.7638i	−0.830761	−	0.603583i
$521$	−24.3262	+	17.6740i	−1.06575	+	0.774314i	−0.975144	−	0.221573i	$-0.928881\pi$
$521$	−24.3262	+	17.6740i	−1.06575	+	0.774314i	−0.0906080	+	0.995887i	$0.528881\pi$
$522$		0			0
$523$	−9.76393	+	30.0503i	−0.426947	+	1.31401i	0.474171	+	0.880433i	$0.342748\pi$
$523$	−9.76393	+	30.0503i	−0.426947	+	1.31401i	−0.901118	+	0.433575i	$0.857252\pi$
$524$	−8.97214	+	6.51864i	−0.391950	+	0.284768i
$525$		0			0
$526$	4.61803	+	14.2128i	0.201356	+	0.619710i
$527$	0.472136			0.0205666
$528$		0			0
$529$	−15.3607			−0.667856
$530$	−10.4894	−	32.2829i	−0.455629	−	1.40228i
$531$		0			0
$532$	6.23607	−	4.53077i	0.270368	−	0.196434i
$533$	13.5279	−	41.6345i	0.585957	−	1.80339i
$534$		0			0
$535$	40.5517	−	29.4625i	1.75320	−	1.27378i
$536$	−8.85410	−	6.43288i	−0.382439	−	0.277858i
$537$		0			0
$538$	6.94427			0.299389
$539$	13.2812	−	22.4091i	0.572060	−	0.965228i
$540$		0			0
$541$	12.1803	+	37.4872i	0.523674	+	1.61170i	0.766924	+	0.641738i	$0.221786\pi$
$541$	12.1803	+	37.4872i	0.523674	+	1.61170i	−0.243250	+	0.969964i	$0.578214\pi$
$542$	−18.9443	−	13.7638i	−0.813726	−	0.591207i
$543$		0			0
$544$	−1.00000	+	3.07768i	−0.0428746	+	0.131955i
$545$	−5.32624	+	16.3925i	−0.228151	+	0.702176i
$546$		0			0
$547$	−5.14590	−	3.73871i	−0.220023	−	0.159856i	0.472314	−	0.881430i	$-0.343419\pi$
$547$	−5.14590	−	3.73871i	−0.220023	−	0.159856i	−0.692337	+	0.721574i	$0.743419\pi$
$548$	−5.09017	−	15.6659i	−0.217441	−	0.669215i
$549$		0			0
$550$	−13.6803	+	23.0826i	−0.583332	+	0.984247i
$551$	−0.763932			−0.0325446
$552$		0			0
$553$	−22.2812	−	16.1882i	−0.947491	−	0.688393i
$554$	−11.3262	+	8.22899i	−0.481206	+	0.349616i
$555$		0			0
$556$	1.14590	−	3.52671i	0.0485969	−	0.149566i
$557$	−7.59017	+	5.51458i	−0.321606	+	0.233660i	−0.736860	−	0.676045i	$-0.763693\pi$
$557$	−7.59017	+	5.51458i	−0.321606	+	0.233660i	0.415255	+	0.909705i	$0.363693\pi$
$558$		0			0
$559$		0			0
$560$	13.9443			0.589253
$561$		0			0
$562$	8.94427			0.377291
$563$	−1.81966	−	5.60034i	−0.0766895	−	0.236026i	0.905361	−	0.424642i	$-0.139600\pi$
$563$	−1.81966	−	5.60034i	−0.0766895	−	0.236026i	−0.982051	+	0.188616i	$0.939600\pi$
$564$		0			0
$565$	28.4164	−	20.6457i	1.19549	−	0.868572i
$566$	8.56231	−	26.3521i	0.359901	−	1.10766i
$567$		0			0
$568$	0.618034	−	0.449028i	0.0259321	−	0.0188408i
$569$	−13.4721	−	9.78808i	−0.564781	−	0.410338i	0.268424	−	0.963301i	$-0.413497\pi$
$569$	−13.4721	−	9.78808i	−0.564781	−	0.410338i	−0.833206	+	0.552963i	$0.813497\pi$
$570$		0			0
$571$	32.7639			1.37113			0.685564	−	0.728012i	$-0.259556\pi$
$571$	32.7639			1.37113			0.685564	+	0.728012i	$0.259556\pi$
$572$	−14.1803	−	16.1150i	−0.592910	−	0.673800i
$573$		0			0
$574$	8.05573	+	24.7930i	0.336240	+	1.03484i
$575$	18.0902	+	13.1433i	0.754412	+	0.548113i
$576$		0			0
$577$	10.8435	−	33.3727i	0.451419	−	1.38933i	−0.423869	−	0.905723i	$-0.639328\pi$
$577$	10.8435	−	33.3727i	0.451419	−	1.38933i	0.875288	−	0.483602i	$-0.160672\pi$
$578$	2.01722	−	6.20837i	0.0839053	−	0.258234i
$579$		0			0
$580$	−1.11803	−	0.812299i	−0.0464238	−	0.0337289i
$581$	9.28773	+	28.5847i	0.385320	+	1.18589i
$582$		0			0
$583$	−2.89919	−	30.9811i	−0.120072	−	1.28311i
$584$	2.38197			0.0985665
$585$		0			0
$586$	−19.5902	−	14.2331i	−0.809262	−	0.587964i
$587$	34.1976	−	24.8460i	1.41148	−	1.02550i	0.418380	−	0.908272i	$-0.362598\pi$
$587$	34.1976	−	24.8460i	1.41148	−	1.02550i	0.993105	−	0.117231i	$-0.0374019\pi$
$588$		0			0
$589$	0.0901699	−	0.277515i	0.00371539	−	0.0114348i
$590$	36.0795	−	26.2133i	1.48537	−	1.07918i
$591$		0			0
$592$	1.14590	+	3.52671i	0.0470961	+	0.144947i
$593$	9.70820			0.398668			0.199334	−	0.979932i	$-0.436122\pi$
$593$	9.70820			0.398668			0.199334	+	0.979932i	$0.436122\pi$
$594$		0			0
$595$	45.1246			1.84993
$596$	−3.28115	−	10.0984i	−0.134401	−	0.413645i
$597$		0			0
$598$	−14.4721	+	10.5146i	−0.591810	+	0.429975i
$599$	−2.72949	+	8.40051i	−0.111524	+	0.343235i	−0.991206	−	0.132327i	$-0.957755\pi$
$599$	−2.72949	+	8.40051i	−0.111524	+	0.343235i	0.879682	+	0.475562i	$0.157755\pi$
$600$		0			0
$601$	−5.44427	+	3.95550i	−0.222076	+	0.161348i	−0.693261	−	0.720687i	$-0.743827\pi$
$601$	−5.44427	+	3.95550i	−0.222076	+	0.161348i	0.471184	+	0.882035i	$0.343827\pi$
$602$		0			0
$603$		0			0
$604$	−12.8541			−0.523026
$605$	−27.2984	+	28.9605i	−1.10984	+	1.17741i
$606$		0			0
$607$	12.0000	+	36.9322i	0.487065	+	1.49903i	0.828968	+	0.559297i	$0.188929\pi$
$607$	12.0000	+	36.9322i	0.487065	+	1.49903i	−0.341903	+	0.939735i	$0.611071\pi$
$608$	1.61803	+	1.17557i	0.0656199	+	0.0476757i
$609$		0			0
$610$	3.09017	−	9.51057i	0.125117	−	0.385072i
$611$	−9.52786	+	29.3238i	−0.385456	+	1.18631i
$612$		0			0
$613$	27.9443	+	20.3027i	1.12866	+	0.820018i	0.985499	−	0.169681i	$-0.0542738\pi$
$613$	27.9443	+	20.3027i	1.12866	+	0.820018i	0.143160	+	0.989700i	$0.454274\pi$
$614$	6.29180	+	19.3642i	0.253916	+	0.781474i
$615$		0			0
$616$	12.4721	+	2.80017i	0.502517	+	0.112822i
$617$	−32.0689			−1.29104			−0.645522	−	0.763741i	$-0.723360\pi$
$617$	−32.0689			−1.29104			−0.645522	+	0.763741i	$0.723360\pi$
$618$		0			0
$619$	−2.61803	−	1.90211i	−0.105228	−	0.0764524i	0.533927	−	0.845531i	$-0.320716\pi$
$619$	−2.61803	−	1.90211i	−0.105228	−	0.0764524i	−0.639155	+	0.769078i	$0.720716\pi$
$620$	0.427051	−	0.310271i	0.0171508	−	0.0124608i
$621$		0			0
$622$	−3.47214	+	10.6861i	−0.139220	+	0.428475i
$623$	19.2705	−	14.0008i	0.772057	−	0.560932i
$624$		0			0
$625$		0			0
$626$	11.3262			0.452688
$627$		0			0
$628$	15.7082			0.626826
$629$	3.70820	+	11.4127i	0.147856	+	0.455053i
$630$		0			0
$631$	−37.6697	+	27.3686i	−1.49961	+	1.08953i	−0.529069	+	0.848579i	$0.677459\pi$
$631$	−37.6697	+	27.3686i	−1.49961	+	1.08953i	−0.970538	+	0.240950i	$0.922541\pi$
$632$	2.20820	−	6.79615i	0.0878376	−	0.270336i
$633$		0			0
$634$	26.5623	−	19.2986i	1.05492	−	0.766447i
$635$	2.76393	+	2.00811i	0.109683	+	0.0796896i
$636$		0			0
$637$	50.8328			2.01407
$638$	−0.836881	−	0.951057i	−0.0331324	−	0.0376527i
$639$		0			0
$640$	1.11803	+	3.44095i	0.0441942	+	0.136016i
$641$	17.2361	+	12.5227i	0.680784	+	0.494618i	0.873618	−	0.486613i	$-0.161768\pi$
$641$	17.2361	+	12.5227i	0.680784	+	0.494618i	−0.192834	+	0.981231i	$0.561768\pi$
$642$		0			0
$643$	−3.27051	+	10.0656i	−0.128976	+	0.396948i	−0.994605	−	0.103739i	$-0.966919\pi$
$643$	−3.27051	+	10.0656i	−0.128976	+	0.396948i	0.865628	+	0.500687i	$0.166919\pi$
$644$	3.29180	−	10.1311i	0.129715	−	0.399222i
$645$		0			0
$646$	5.23607	+	3.80423i	0.206010	+	0.149675i
$647$	1.20163	+	3.69822i	0.0472408	+	0.145392i	0.971895	−	0.235417i	$-0.0756455\pi$
$647$	1.20163	+	3.69822i	0.0472408	+	0.145392i	−0.924654	+	0.380809i	$0.875646\pi$
$648$		0			0
$649$	37.5344	−	16.2007i	1.47336	−	0.635934i
$650$	−52.3607			−2.05375
$651$		0			0
$652$	17.7082	+	12.8658i	0.693507	+	0.503862i
$653$	−3.54508	+	2.57565i	−0.138730	+	0.100793i	−0.654986	−	0.755641i	$-0.727325\pi$
$653$	−3.54508	+	2.57565i	−0.138730	+	0.100793i	0.516256	+	0.856434i	$0.327325\pi$
$654$		0			0
$655$	−12.3992	+	38.1608i	−0.484476	+	1.49106i
$656$	−5.47214	+	3.97574i	−0.213651	+	0.155227i
$657$		0			0
$658$	−5.67376	−	17.4620i	−0.221186	−	0.680741i
$659$	−4.20163			−0.163672			−0.0818361	−	0.996646i	$-0.526078\pi$
$659$	−4.20163			−0.163672			−0.0818361	+	0.996646i	$0.526078\pi$
$660$		0			0
$661$	−16.1803			−0.629342			−0.314671	−	0.949201i	$-0.601894\pi$
$661$	−16.1803			−0.629342			−0.314671	+	0.949201i	$0.601894\pi$
$662$	2.56231	+	7.88597i	0.0995868	+	0.306497i
$663$		0			0
$664$	−6.30902	+	4.58377i	−0.244837	+	0.177885i
$665$	8.61803	−	26.5236i	0.334193	−	1.02854i
$666$		0			0
$667$	−0.854102	+	0.620541i	−0.0330710	+	0.0240275i
$668$	−16.7082	−	12.1392i	−0.646460	−	0.469681i
$669$		0			0
$670$	−39.5967			−1.52976
$671$	4.67376	−	7.88597i	0.180429	−	0.304434i
$672$		0			0
$673$	−11.0279	−	33.9403i	−0.425093	−	1.30830i	−0.902905	−	0.429840i	$-0.858570\pi$
$673$	−11.0279	−	33.9403i	−0.425093	−	1.30830i	0.477812	−	0.878462i	$-0.341430\pi$
$674$	18.5623	+	13.4863i	0.714993	+	0.519473i
$675$		0			0
$676$	8.92705	−	27.4746i	0.343348	−	1.05672i
$677$	−6.51722	+	20.0579i	−0.250477	+	0.770889i	0.744210	+	0.667946i	$0.232826\pi$
$677$	−6.51722	+	20.0579i	−0.250477	+	0.770889i	−0.994687	+	0.102944i	$0.967174\pi$
$678$		0			0
$679$	−22.2812	−	16.1882i	−0.855072	−	0.621246i
$680$	3.61803	+	11.1352i	0.138745	+	0.427014i
$681$		0			0
$682$	0.444272	−	0.191758i	0.0170121	−	0.00734279i
$683$	16.3262			0.624706			0.312353	−	0.949966i	$-0.398883\pi$
$683$	16.3262			0.624706			0.312353	+	0.949966i	$0.398883\pi$
$684$		0			0
$685$	−48.2148	−	35.0301i	−1.84219	−	1.33843i
$686$	−2.66312	+	1.93487i	−0.101678	+	0.0738736i
$687$		0			0
$688$		0			0
$689$	49.1246	−	35.6911i	1.87150	−	1.35972i
$690$		0			0
$691$	−1.29180	−	3.97574i	−0.0491422	−	0.151244i	0.923474	−	0.383661i	$-0.125337\pi$
$691$	−1.29180	−	3.97574i	−0.0491422	−	0.151244i	−0.972616	+	0.232416i	$0.925337\pi$
$692$	−17.0902			−0.649671
$693$		0			0
$694$	−11.7426			−0.445745
$695$	−4.14590	−	12.7598i	−0.157263	−	0.484005i
$696$		0			0
$697$	−17.7082	+	12.8658i	−0.670746	+	0.487326i
$698$	3.29180	−	10.1311i	0.124596	−	0.383468i
$699$		0			0
$700$	25.2254	−	18.3273i	0.953431	−	0.692708i
$701$	−14.5623	−	10.5801i	−0.550011	−	0.399606i	0.277779	−	0.960645i	$-0.410402\pi$
$701$	−14.5623	−	10.5801i	−0.550011	−	0.399606i	−0.827789	+	0.561039i	$0.810402\pi$
$702$		0			0
$703$	7.41641			0.279715
$704$	0.309017	+	3.30220i	0.0116465	+	0.124456i
$705$		0			0
$706$	7.61803	+	23.4459i	0.286708	+	0.882398i
$707$	−18.4271	−	13.3880i	−0.693021	−	0.503509i
$708$		0			0
$709$	−7.90983	+	24.3440i	−0.297060	+	0.914256i	0.685462	+	0.728109i	$0.259600\pi$
$709$	−7.90983	+	24.3440i	−0.297060	+	0.914256i	−0.982522	+	0.186148i	$0.940400\pi$
$710$	0.854102	−	2.62866i	0.0320539	−	0.0986517i
$711$		0			0
$712$	5.00000	+	3.63271i	0.187383	+	0.136142i
$713$	−0.124612	−	0.383516i	−0.00466675	−	0.0143628i
$714$		0			0
$715$	−75.7771	−	17.0130i	−2.83390	−	0.636251i
$716$	19.7984			0.739900
$717$		0			0
$718$	−10.8541	−	7.88597i	−0.405071	−	0.294302i
$719$	−6.00000	+	4.35926i	−0.223762	+	0.162573i	−0.694019	−	0.719957i	$-0.744161\pi$
$719$	−6.00000	+	4.35926i	−0.223762	+	0.162573i	0.470256	+	0.882530i	$0.344161\pi$
$720$		0			0
$721$	9.35410	−	28.7890i	0.348365	−	1.07216i
$722$	−12.1353	+	8.81678i	−0.451627	+	0.328127i
$723$		0			0
$724$	−7.52786	−	23.1684i	−0.279771	−	0.861046i
$725$	−3.09017			−0.114766
$726$		0			0
$727$	−28.0000			−1.03846			−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000			−1.03846			−0.519231	+	0.854634i	$0.673782\pi$
$728$	7.70820	+	23.7234i	0.285685	+	0.879248i
$729$		0			0
$730$	6.97214	−	5.06555i	0.258050	−	0.187485i
$731$		0			0
$732$		0			0
$733$	−20.0902	+	14.5964i	−0.742047	+	0.539129i	−0.893352	−	0.449358i	$-0.851653\pi$
$733$	−20.0902	+	14.5964i	−0.742047	+	0.539129i	0.151304	+	0.988487i	$0.451653\pi$
$734$	−4.39919	−	3.19620i	−0.162377	−	0.117974i
$735$		0			0
$736$	2.76393			0.101880
$737$	−35.4164	−	7.95148i	−1.30458	−	0.292896i
$738$		0			0
$739$	11.6525	+	35.8626i	0.428643	+	1.31923i	0.899462	+	0.436998i	$0.143958\pi$
$739$	11.6525	+	35.8626i	0.428643	+	1.31923i	−0.470819	+	0.882230i	$0.656042\pi$
$740$	10.8541	+	7.88597i	0.399005	+	0.289894i
$741$		0			0
$742$	−11.1738	+	34.3893i	−0.410202	+	1.26247i
$743$	−6.32624	+	19.4702i	−0.232087	+	0.714291i	0.765407	+	0.643546i	$0.222538\pi$
$743$	−6.32624	+	19.4702i	−0.232087	+	0.714291i	−0.997494	+	0.0707447i	$0.977462\pi$
$744$		0			0
$745$	−31.0795	−	22.5806i	−1.13867	−	0.827289i
$746$	−0.527864	−	1.62460i	−0.0193265	−	0.0594808i
$747$		0			0
$748$	1.00000	+	10.6861i	0.0365636	+	0.390724i
$749$	−53.3951			−1.95102
$750$		0			0
$751$	23.7082	+	17.2250i	0.865125	+	0.628550i	0.929274	−	0.369390i	$-0.120433\pi$
$751$	23.7082	+	17.2250i	0.865125	+	0.628550i	−0.0641496	+	0.997940i	$0.520433\pi$
$752$	3.85410	−	2.80017i	0.140545	−	0.102112i
$753$		0			0
$754$	0.763932	−	2.35114i	0.0278208	−	0.0856235i
$755$	−37.6246	+	27.3359i	−1.36930	+	0.994855i
$756$		0			0
$757$	15.5623	+	47.8959i	0.565622	+	1.74080i	0.666097	+	0.745865i	$0.267964\pi$
$757$	15.5623	+	47.8959i	0.565622	+	1.74080i	−0.100476	+	0.994940i	$0.532036\pi$
$758$	−28.8328			−1.04726
$759$		0			0
$760$	7.23607			0.262480
$761$	2.96556	+	9.12705i	0.107501	+	0.330855i	0.990309	−	0.138879i	$-0.0443498\pi$
$761$	2.96556	+	9.12705i	0.107501	+	0.330855i	−0.882808	+	0.469734i	$0.844350\pi$
$762$		0			0
$763$	14.8541	−	10.7921i	0.537755	−	0.390702i
$764$	−4.70820	+	14.4904i	−0.170337	+	0.524243i
$765$		0			0
$766$	−13.2361	+	9.61657i	−0.478239	+	0.347461i
$767$	64.5410	+	46.8918i	2.33044	+	1.69316i
$768$		0			0
$769$	21.9787			0.792573			0.396286	−	0.918127i	$-0.370299\pi$
$769$	21.9787			0.792573			0.396286	+	0.918127i	$0.370299\pi$
$770$	42.4615	−	18.3273i	1.53021	−	0.660472i
$771$		0			0
$772$	−1.89919	−	5.84510i	−0.0683532	−	0.210370i
$773$	−7.69098	−	5.58783i	−0.276625	−	0.200980i	0.440819	−	0.897596i	$-0.354688\pi$
$773$	−7.69098	−	5.58783i	−0.276625	−	0.200980i	−0.717444	+	0.696616i	$0.754688\pi$
$774$		0			0
$775$	0.364745	−	1.12257i	0.0131020	−	0.0403239i
$776$	2.20820	−	6.79615i	0.0792699	−	0.243968i
$777$		0			0
$778$	6.85410	+	4.97980i	0.245731	+	0.178534i
$779$	4.18034	+	12.8658i	0.149776	+	0.460964i
$780$		0			0
$781$	1.29180	−	2.17963i	0.0462241	−	0.0779932i
$782$	8.94427			0.319847
$783$		0			0
$784$	−6.35410	−	4.61653i	−0.226932	−	0.164876i
$785$	45.9787	−	33.4055i	1.64105	−	1.19229i
$786$		0			0
$787$	−0.291796	+	0.898056i	−0.0104014	+	0.0320122i	−0.956123	−	0.292967i	$-0.905357\pi$
$787$	−0.291796	+	0.898056i	−0.0104014	+	0.0320122i	0.945721	+	0.324979i	$0.105357\pi$
$788$	0.309017	−	0.224514i	0.0110083	−	0.00799798i
$789$		0			0
$790$	−7.98936	−	24.5887i	−0.284249	−	0.874827i
$791$	−37.4164			−1.33037
$792$		0			0
$793$	17.8885			0.635241
$794$	9.70820	+	29.8788i	0.344531	+	1.06036i
$795$		0			0
$796$	−7.92705	+	5.75934i	−0.280967	+	0.204134i
$797$	−10.5172	+	32.3687i	−0.372539	+	1.14656i	0.572585	+	0.819845i	$0.305941\pi$
$797$	−10.5172	+	32.3687i	−0.372539	+	1.14656i	−0.945124	+	0.326712i	$0.894059\pi$
$798$		0			0
$799$	12.4721	−	9.06154i	0.441232	−	0.320574i
$800$	6.54508	+	4.75528i	0.231404	+	0.168125i
$801$		0			0
$802$	−13.0557			−0.461014
$803$	7.25329	−	3.13068i	0.255963	−	0.110479i
$804$		0			0
$805$	−11.9098	−	36.6547i	−0.419766	−	1.29191i
$806$	0.763932	+	0.555029i	0.0269084	+	0.0195501i
$807$		0			0
$808$	1.82624	−	5.62058i	0.0642468	−	0.197731i
$809$	8.09017	−	24.8990i	0.284435	−	0.875402i	−0.702132	−	0.712047i	$-0.747768\pi$
$809$	8.09017	−	24.8990i	0.284435	−	0.875402i	0.986567	−	0.163355i	$-0.0522316\pi$
$810$		0			0
$811$	−36.2148	−	26.3116i	−1.27167	−	0.923925i	−0.272405	−	0.962183i	$-0.587819\pi$
$811$	−36.2148	−	26.3116i	−1.27167	−	0.923925i	−0.999268	+	0.0382582i	$0.987819\pi$
$812$	0.454915	+	1.40008i	0.0159644	+	0.0491333i
$813$		0			0
$814$	8.12461	+	9.23305i	0.284767	+	0.323618i
$815$	79.1935			2.77403
$816$		0			0
$817$		0			0
$818$	−17.7812	+	12.9188i	−0.621703	+	0.451694i
$819$		0			0
$820$	−7.56231	+	23.2744i	−0.264087	+	0.812777i
$821$	−21.3541	+	15.5147i	−0.745263	+	0.541465i	−0.894355	−	0.447358i	$-0.852365\pi$
$821$	−21.3541	+	15.5147i	−0.745263	+	0.541465i	0.149092	+	0.988823i	$0.452365\pi$
$822$		0			0
$823$	6.73607	+	20.7315i	0.234805	+	0.722654i	0.997147	+	0.0754806i	$0.0240491\pi$
$823$	6.73607	+	20.7315i	0.234805	+	0.722654i	−0.762343	+	0.647174i	$0.775951\pi$
$824$	7.85410			0.273611
$825$		0			0
$826$	−47.5066			−1.65297
$827$	−8.66312	−	26.6623i	−0.301246	−	0.927140i	−0.981051	−	0.193748i	$-0.937936\pi$
$827$	−8.66312	−	26.6623i	−0.301246	−	0.927140i	0.679805	−	0.733393i	$-0.262064\pi$
$828$		0			0
$829$	−2.61803	+	1.90211i	−0.0909281	+	0.0660631i	−0.632320	−	0.774707i	$-0.717897\pi$
$829$	−2.61803	+	1.90211i	−0.0909281	+	0.0660631i	0.541392	+	0.840770i	$0.317897\pi$
$830$	−8.71885	+	26.8339i	−0.302636	+	0.931417i
$831$		0			0
$832$	−5.23607	+	3.80423i	−0.181528	+	0.131888i
$833$	−20.5623	−	14.9394i	−0.712442	−	0.517619i
$834$		0			0
$835$	−74.7214			−2.58584
$836$	6.47214	+	1.45309i	0.223844	+	0.0502560i
$837$		0			0
$838$	−4.06231	−	12.5025i	−0.140330	−	0.431891i
$839$	1.32624	+	0.963568i	0.0457868	+	0.0332661i	0.610443	−	0.792060i	$-0.290991\pi$
$839$	1.32624	+	0.963568i	0.0457868	+	0.0332661i	−0.564656	+	0.825326i	$0.690991\pi$
$840$		0			0
$841$	−8.91641	+	27.4419i	−0.307462	+	0.946272i
$842$	5.29180	−	16.2865i	0.182367	−	0.561269i
$843$		0			0
$844$	−5.61803	−	4.08174i	−0.193381	−	0.140499i
$845$	−32.2984	−	99.4042i	−1.11110	−	3.41961i
$846$		0			0
$847$	41.6591	−	7.86572i	1.43142	−	0.270269i
$848$	−9.38197			−0.322178
$849$		0			0
$850$	21.1803	+	15.3884i	0.726480	+	0.527818i
$851$	8.29180	−	6.02434i	0.284239	−	0.206512i
$852$		0			0
$853$	8.88854	−	27.3561i	0.304338	−	0.936656i	−0.675585	−	0.737282i	$-0.736109\pi$
$853$	8.88854	−	27.3561i	0.304338	−	0.936656i	0.979923	−	0.199374i	$-0.0638909\pi$
$854$	−8.61803	+	6.26137i	−0.294903	+	0.214260i
$855$		0			0
$856$	−4.28115	−	13.1760i	−0.146327	−	0.450348i
$857$	3.81966			0.130477			0.0652386	−	0.997870i	$-0.479219\pi$
$857$	3.81966			0.130477			0.0652386	+	0.997870i	$0.479219\pi$
$858$		0			0
$859$	40.7214			1.38939			0.694697	−	0.719302i	$-0.255538\pi$
$859$	40.7214			1.38939			0.694697	+	0.719302i	$0.255538\pi$
$860$		0			0
$861$		0			0
$862$	−32.8885	+	23.8949i	−1.12019	+	0.813864i
$863$	−13.7984	+	42.4670i	−0.469702	+	1.44559i	0.383269	+	0.923637i	$0.374798\pi$
$863$	−13.7984	+	42.4670i	−0.469702	+	1.44559i	−0.852971	+	0.521958i	$0.825202\pi$
$864$		0			0
$865$	−50.0238	+	36.3444i	−1.70086	+	1.23575i
$866$	−10.2082	−	7.41669i	−0.346889	−	0.252030i
$867$		0			0
$868$	−0.562306			−0.0190859
$869$	−2.20820	−	23.5972i	−0.0749082	−	0.800479i
$870$		0			0
$871$	−21.8885	−	67.3660i	−0.741665	−	2.28261i
$872$	3.85410	+	2.80017i	0.130516	+	0.0948257i
$873$		0			0
$874$	1.70820	−	5.25731i	0.0577809	−	0.177831i
$875$	13.3156	−	40.9812i	0.450149	−	1.38542i
$876$		0			0
$877$	10.7082	+	7.77997i	0.361590	+	0.262711i	0.753715	−	0.657201i	$-0.228260\pi$
$877$	10.7082	+	7.77997i	0.361590	+	0.262711i	−0.392125	+	0.919912i	$0.628260\pi$
$878$	4.89919	+	15.0781i	0.165340	+	0.508863i
$879$		0			0
$880$	7.92705	+	9.00854i	0.267221	+	0.303678i
$881$	13.8885			0.467917			0.233958	−	0.972247i	$-0.424832\pi$
$881$	13.8885			0.467917			0.233958	+	0.972247i	$0.424832\pi$
$882$		0			0
$883$	36.2705	+	26.3521i	1.22060	+	0.886818i	0.996150	−	0.0876679i	$-0.0279414\pi$
$883$	36.2705	+	26.3521i	1.22060	+	0.886818i	0.224450	+	0.974486i	$0.427941\pi$
$884$	−16.9443	+	12.3107i	−0.569898	+	0.414055i
$885$		0			0
$886$	10.0106	−	30.8096i	0.336314	−	1.03507i
$887$	24.3262	−	17.6740i	0.816795	−	0.593436i	−0.0989976	−	0.995088i	$-0.531564\pi$
$887$	24.3262	−	17.6740i	0.816795	−	0.593436i	0.915793	+	0.401651i	$0.131564\pi$
$888$		0			0
$889$	−1.12461	−	3.46120i	−0.0377183	−	0.116085i
$890$	22.3607			0.749532
$891$		0			0
$892$	8.85410			0.296457
$893$	−2.94427	−	9.06154i	−0.0985263	−	0.303233i
$894$		0			0
$895$	57.9508	−	42.1038i	1.93708	−	1.40737i
$896$	1.19098	−	3.66547i	0.0397879	−	0.122455i
$897$		0			0
$898$	11.5623	−	8.40051i	0.385839	−	0.280329i
$899$	0.0450850	+	0.0327561i	0.00150367	+	0.00109248i
$900$		0			0
$901$	−30.3607			−1.01146
$902$	−11.4377	+	19.2986i	−0.380834	+	0.642575i
$903$		0			0
$904$	−3.00000	−	9.23305i	−0.0997785	−	0.307087i
$905$	−71.3050	−	51.8061i	−2.37026	−	1.72209i
$906$		0			0
$907$	5.81966	−	17.9111i	0.193239	−	0.594727i	−0.806754	−	0.590887i	$-0.798778\pi$
$907$	5.81966	−	17.9111i	0.193239	−	0.594727i	0.999993	−	0.00383991i	$-0.00122229\pi$
$908$	3.11803	−	9.59632i	0.103476	−	0.318465i
$909$		0			0
$910$	73.0132	+	53.0472i	2.42036	+	1.75850i
$911$	−17.4164	−	53.6022i	−0.577031	−	1.77592i	−0.629156	−	0.777279i	$-0.716599\pi$
$911$	−17.4164	−	53.6022i	−0.577031	−	1.77592i	0.0521244	−	0.998641i	$-0.483401\pi$
$912$		0			0
$913$	−13.1869	+	22.2501i	−0.436423	+	0.736370i
$914$	2.56231			0.0847535
$915$		0			0
$916$	14.3262	+	10.4086i	0.473352	+	0.343911i
$917$	34.5795	−	25.1235i	1.14192	−	0.829651i
$918$		0			0
$919$	−2.91641	+	8.97578i	−0.0962034	+	0.296084i	−0.987565	−	0.157208i	$-0.949751\pi$
$919$	−2.91641	+	8.97578i	−0.0962034	+	0.296084i	0.891362	+	0.453292i	$0.149751\pi$
$920$	8.09017	−	5.87785i	0.266725	−	0.193787i
$921$		0			0
$922$	−10.0344	−	30.8828i	−0.330467	−	1.01707i
$923$	4.94427			0.162743
$924$		0			0
$925$	30.0000			0.986394
$926$	4.71885	+	14.5231i	0.155071	+	0.477259i
$927$		0			0
$928$	−0.309017	+	0.224514i	−0.0101440	+	0.00737003i
$929$	−0.742646	+	2.28563i	−0.0243654	+	0.0749890i	−0.962500	−	0.271282i	$-0.912552\pi$
$929$	−0.742646	+	2.28563i	−0.0243654	+	0.0749890i	0.938134	+	0.346271i	$0.112552\pi$
$930$		0			0
$931$	−12.7082	+	9.23305i	−0.416495	+	0.302601i
$932$	11.2361	+	8.16348i	0.368050	+	0.267404i
$933$		0			0
$934$	28.3262			0.926863
$935$	25.6525	+	29.1522i	0.838926	+	0.953380i
$936$		0			0
$937$	10.5517	+	32.4747i	0.344708	+	1.06090i	0.961740	+	0.273964i	$0.0883348\pi$
$937$	10.5517	+	32.4747i	0.344708	+	1.06090i	−0.617032	+	0.786938i	$0.711665\pi$
$938$	34.1246	+	24.7930i	1.11421	+	0.809520i
$939$		0			0
$940$	5.32624	−	16.3925i	0.173723	−	0.534664i
$941$	−11.8541	+	36.4832i	−0.386433	+	1.18932i	0.549003	+	0.835820i	$0.315008\pi$
$941$	−11.8541	+	36.4832i	−0.386433	+	1.18932i	−0.935436	+	0.353497i	$0.884992\pi$
$942$		0			0
$943$	15.1246	+	10.9887i	0.492525	+	0.357840i
$944$	−3.80902	−	11.7229i	−0.123973	−	0.381549i
$945$		0			0
$946$		0			0
$947$	−4.25735			−0.138345			−0.0691727	−	0.997605i	$-0.522036\pi$
$947$	−4.25735			−0.138345			−0.0691727	+	0.997605i	$0.522036\pi$
$948$		0			0
$949$	12.4721	+	9.06154i	0.404863	+	0.294150i
$950$	13.0902	−	9.51057i	0.424701	−	0.308563i
$951$		0			0
$952$	3.85410	−	11.8617i	0.124912	−	0.384440i
$953$	−21.5623	+	15.6659i	−0.698472	+	0.507469i	−0.879434	−	0.476021i	$-0.842079\pi$
$953$	−21.5623	+	15.6659i	−0.698472	+	0.507469i	0.180962	+	0.983490i	$0.442079\pi$
$954$		0			0
$955$	17.0344	+	52.4266i	0.551222	+	1.69649i
$956$	−13.4164			−0.433918
$957$		0			0
$958$	−28.3607			−0.916292
$959$	19.6180	+	60.3781i	0.633499	+	1.94971i
$960$		0			0
$961$	25.0623	−	18.2088i	0.808461	−	0.587382i
$962$	−7.41641	+	22.8254i	−0.239115	+	0.735919i
$963$		0			0
$964$	−8.50000	+	6.17561i	−0.273767	+	0.198903i
$965$	−17.9894	−	13.0700i	−0.579098	−	0.420739i
$966$		0			0
$967$	10.5623			0.339661			0.169830	−	0.985473i	$-0.445678\pi$
$967$	10.5623			0.339661			0.169830	+	0.985473i	$0.445678\pi$
$968$	5.28115	+	9.64932i	0.169743	+	0.310141i
$969$		0			0
$970$	−7.98936	−	24.5887i	−0.256523	−	0.789496i
$971$	10.0000	+	7.26543i	0.320915	+	0.233159i	0.736566	−	0.676366i	$-0.236446\pi$
$971$	10.0000	+	7.26543i	0.320915	+	0.233159i	−0.415651	+	0.909524i	$0.636446\pi$
$972$		0			0
$973$	−4.41641	+	13.5923i	−0.141584	+	0.435749i
$974$	3.95492	−	12.1720i	0.126724	−	0.390015i
$975$		0			0
$976$	−2.23607	−	1.62460i	−0.0715748	−	0.0520021i
$977$	3.90983	+	12.0332i	0.125087	+	0.384977i	0.993917	−	0.110133i	$-0.0351277\pi$
$977$	3.90983	+	12.0332i	0.125087	+	0.384977i	−0.868830	+	0.495110i	$0.835128\pi$
$978$		0			0
$979$	20.0000	+	4.49028i	0.639203	+	0.143510i
$980$	−28.4164			−0.907729
$981$		0			0
$982$	19.4164	+	14.1068i	0.619602	+	0.450168i
$983$	22.4164	−	16.2865i	0.714972	−	0.519458i	−0.169802	−	0.985478i	$-0.554313\pi$
$983$	22.4164	−	16.2865i	0.714972	−	0.519458i	0.884774	+	0.466020i	$0.154313\pi$
$984$		0			0
$985$	0.427051	−	1.31433i	0.0136070	−	0.0418780i
$986$	−1.00000	+	0.726543i	−0.0318465	+	0.0231378i
$987$		0			0
$988$	4.00000	+	12.3107i	0.127257	+	0.391657i
$989$		0			0
$990$		0			0
$991$	−38.5623			−1.22497			−0.612486	−	0.790481i	$-0.709830\pi$
$991$	−38.5623			−1.22497			−0.612486	+	0.790481i	$0.709830\pi$
$992$	−0.0450850	−	0.138757i	−0.00143145	−	0.00440555i
$993$		0			0
$994$	−2.38197	+	1.73060i	−0.0755514	+	0.0548913i
$995$	−10.9549	+	33.7158i	−0.347294	+	1.06886i
$996$		0			0
$997$	−8.94427	+	6.49839i	−0.283268	+	0.205806i	−0.720342	−	0.693620i	$-0.756015\pi$
$997$	−8.94427	+	6.49839i	−0.283268	+	0.205806i	0.437074	+	0.899426i	$0.356015\pi$
$998$	−17.3262	−	12.5882i	−0.548452	−	0.398474i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.2.f.d.181.1	yes	4
3.2	odd	2		198.2.f.b.181.1	yes	4
11.3	even	5		2178.2.a.n.1.1		2
11.8	odd	10		2178.2.a.w.1.1		2
11.9	even	5	inner	198.2.f.d.163.1	yes	4
33.8	even	10		2178.2.a.u.1.2		2
33.14	odd	10		2178.2.a.bc.1.2		2
33.20	odd	10		198.2.f.b.163.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.2.f.b.163.1	✓	4	33.20	odd	10
198.2.f.b.181.1	yes	4	3.2	odd	2
198.2.f.d.163.1	yes	4	11.9	even	5	inner
198.2.f.d.181.1	yes	4	1.1	even	1	trivial
2178.2.a.n.1.1		2	11.3	even	5
2178.2.a.u.1.2		2	33.8	even	10
2178.2.a.w.1.1		2	11.8	odd	10
2178.2.a.bc.1.2		2	33.14	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:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	198.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(-1.11803 + 3.44095i) q^{5} +(3.11803 - 2.26538i) q^{7} +(0.809017 + 0.587785i) q^{8} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(-1.11803 + 3.44095i) q^{5} +(3.11803 - 2.26538i) q^{7} +(0.809017 + 0.587785i) q^{8} +3.61803 q^{10} +(3.23607 + 0.726543i) q^{11} +(2.00000 + 6.15537i) q^{13} +(-3.11803 - 2.26538i) q^{14} +(0.309017 - 0.951057i) q^{16} +(1.00000 - 3.07768i) q^{17} +(-1.61803 - 1.17557i) q^{19} +(-1.11803 - 3.44095i) q^{20} +(-0.309017 - 3.30220i) q^{22} -2.76393 q^{23} +(-6.54508 - 4.75528i) q^{25} +(5.23607 - 3.80423i) q^{26} +(-1.19098 + 3.66547i) q^{28} +(0.309017 - 0.224514i) q^{29} +(0.0450850 + 0.138757i) q^{31} -1.00000 q^{32} -3.23607 q^{34} +(4.30902 + 13.2618i) q^{35} +(-3.00000 + 2.17963i) q^{37} +(-0.618034 + 1.90211i) q^{38} +(-2.92705 + 2.12663i) q^{40} +(-5.47214 - 3.97574i) q^{41} +(-3.04508 + 1.31433i) q^{44} +(0.854102 + 2.62866i) q^{46} +(3.85410 + 2.80017i) q^{47} +(2.42705 - 7.46969i) q^{49} +(-2.50000 + 7.69421i) q^{50} +(-5.23607 - 3.80423i) q^{52} +(-2.89919 - 8.92278i) q^{53} +(-6.11803 + 10.3229i) q^{55} +3.85410 q^{56} +(-0.309017 - 0.224514i) q^{58} +(9.97214 - 7.24518i) q^{59} +(0.854102 - 2.62866i) q^{61} +(0.118034 - 0.0857567i) q^{62} +(0.309017 + 0.951057i) q^{64} -23.4164 q^{65} -10.9443 q^{67} +(1.00000 + 3.07768i) q^{68} +(11.2812 - 8.19624i) q^{70} +(0.236068 - 0.726543i) q^{71} +(1.92705 - 1.40008i) q^{73} +(3.00000 + 2.17963i) q^{74} +2.00000 q^{76} +(11.7361 - 5.06555i) q^{77} +(-2.20820 - 6.79615i) q^{79} +(2.92705 + 2.12663i) q^{80} +(-2.09017 + 6.43288i) q^{82} +(-2.40983 + 7.41669i) q^{83} +(9.47214 + 6.88191i) q^{85} +(2.19098 + 2.48990i) q^{88} +6.18034 q^{89} +(20.1803 + 14.6619i) q^{91} +(2.23607 - 1.62460i) q^{92} +(1.47214 - 4.53077i) q^{94} +(5.85410 - 4.25325i) q^{95} +(-2.20820 - 6.79615i) q^{97} -7.85410 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{4} + 8 q^{7} + q^{8}+O(q^{10}) \) 4 * q + q^2 - q^4 + 8 * q^7 + q^8	\( 4 q + q^{2} - q^{4} + 8 q^{7} + q^{8} + 10 q^{10} + 4 q^{11} + 8 q^{13} - 8 q^{14} - q^{16} + 4 q^{17} - 2 q^{19} + q^{22} - 20 q^{23} - 15 q^{25} + 12 q^{26} - 7 q^{28} - q^{29} - 11 q^{31} - 4 q^{32} - 4 q^{34} + 15 q^{35} - 12 q^{37} + 2 q^{38} - 5 q^{40} - 4 q^{41} - q^{44} - 10 q^{46} + 2 q^{47} + 3 q^{49} - 10 q^{50} - 12 q^{52} + 13 q^{53} - 20 q^{55} + 2 q^{56} + q^{58} + 22 q^{59} - 10 q^{61} - 4 q^{62} - q^{64} - 40 q^{65} - 8 q^{67} + 4 q^{68} + 25 q^{70} - 8 q^{71} + q^{73} + 12 q^{74} + 8 q^{76} + 38 q^{77} + 18 q^{79} + 5 q^{80} + 14 q^{82} - 32 q^{83} + 20 q^{85} + 11 q^{88} - 20 q^{89} + 36 q^{91} - 12 q^{94} + 10 q^{95} + 18 q^{97} - 18 q^{98}+O(q^{100}) \) 4 * q + q^2 - q^4 + 8 * q^7 + q^8 + 10 * q^10 + 4 * q^11 + 8 * q^13 - 8 * q^14 - q^16 + 4 * q^17 - 2 * q^19 + q^22 - 20 * q^23 - 15 * q^25 + 12 * q^26 - 7 * q^28 - q^29 - 11 * q^31 - 4 * q^32 - 4 * q^34 + 15 * q^35 - 12 * q^37 + 2 * q^38 - 5 * q^40 - 4 * q^41 - q^44 - 10 * q^46 + 2 * q^47 + 3 * q^49 - 10 * q^50 - 12 * q^52 + 13 * q^53 - 20 * q^55 + 2 * q^56 + q^58 + 22 * q^59 - 10 * q^61 - 4 * q^62 - q^64 - 40 * q^65 - 8 * q^67 + 4 * q^68 + 25 * q^70 - 8 * q^71 + q^73 + 12 * q^74 + 8 * q^76 + 38 * q^77 + 18 * q^79 + 5 * q^80 + 14 * q^82 - 32 * q^83 + 20 * q^85 + 11 * q^88 - 20 * q^89 + 36 * q^91 - 12 * q^94 + 10 * q^95 + 18 * q^97 - 18 * q^98

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