LMFDB - Embedded newform 363.2.e.m.124.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(124,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("363.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.e (of order $5$, degree $4$, not 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:	$2.89856959337$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.324000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 $ x^8 + 3x^6 + 9x^4 + 27*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			124.1
Root			$0.535233 + 1.64728i$ of defining polynomial
Character	$\chi$	$=$	363.124
Dual form			363.2.e.m.202.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40126 + 1.01807i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.42705 + 1.76336i) q^{5} +(1.40126 + 1.01807i) q^{6} +(-1.07047 + 3.29456i) q^{7} +(-0.535233 - 1.64728i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.40126 + 1.01807i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.42705 + 1.76336i) q^{5} +(1.40126 + 1.01807i) q^{6} +(-1.07047 + 3.29456i) q^{7} +(-0.535233 - 1.64728i) q^{8} +(-0.809017 + 0.587785i) q^{9} -5.19615 q^{10} -1.00000 q^{12} +(1.40126 - 1.01807i) q^{13} +(-1.85410 - 5.70634i) q^{14} +(0.927051 - 2.85317i) q^{15} +(4.04508 + 2.93893i) q^{16} +(-1.40126 - 1.01807i) q^{17} +(0.535233 - 1.64728i) q^{18} +(2.14093 + 6.58911i) q^{19} +(2.42705 - 1.76336i) q^{20} +3.46410 q^{21} -6.00000 q^{23} +(-1.40126 + 1.01807i) q^{24} +(1.23607 + 3.80423i) q^{25} +(-0.927051 + 2.85317i) q^{26} +(0.809017 + 0.587785i) q^{27} +(2.80252 + 2.03615i) q^{28} +(-0.535233 + 1.64728i) q^{29} +(1.60570 + 4.94183i) q^{30} +(-3.23607 + 2.35114i) q^{31} -5.19615 q^{32} +3.00000 q^{34} +(-8.40755 + 6.10844i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-3.39919 + 10.4616i) q^{37} +(-9.70820 - 7.05342i) q^{38} +(-1.40126 - 1.01807i) q^{39} +(1.60570 - 4.94183i) q^{40} +(-0.535233 - 1.64728i) q^{41} +(-4.85410 + 3.52671i) q^{42} +3.46410 q^{43} -3.00000 q^{45} +(8.40755 - 6.10844i) q^{46} +(1.54508 - 4.75528i) q^{48} +(-4.04508 - 2.93893i) q^{49} +(-5.60503 - 4.07230i) q^{50} +(-0.535233 + 1.64728i) q^{51} +(-0.535233 - 1.64728i) q^{52} +(7.28115 - 5.29007i) q^{53} -1.73205 q^{54} +6.00000 q^{56} +(5.60503 - 4.07230i) q^{57} +(-0.927051 - 2.85317i) q^{58} +(-1.85410 + 5.70634i) q^{59} +(-2.42705 - 1.76336i) q^{60} +(2.14093 - 6.58911i) q^{62} +(-1.07047 - 3.29456i) q^{63} +(-0.809017 + 0.587785i) q^{64} +5.19615 q^{65} -2.00000 q^{67} +(-1.40126 + 1.01807i) q^{68} +(1.85410 + 5.70634i) q^{69} +(5.56231 - 17.1190i) q^{70} +(4.85410 + 3.52671i) q^{71} +(1.40126 + 1.01807i) q^{72} +(2.14093 - 6.58911i) q^{73} +(-5.88756 - 18.1201i) q^{74} +(3.23607 - 2.35114i) q^{75} +6.92820 q^{76} +3.00000 q^{78} +(4.63525 + 14.2658i) q^{80} +(0.309017 - 0.951057i) q^{81} +(2.42705 + 1.76336i) q^{82} +(1.07047 - 3.29456i) q^{84} +(-1.60570 - 4.94183i) q^{85} +(-4.85410 + 3.52671i) q^{86} +1.73205 q^{87} +9.00000 q^{89} +(4.20378 - 3.05422i) q^{90} +(1.85410 + 5.70634i) q^{91} +(-1.85410 + 5.70634i) q^{92} +(3.23607 + 2.35114i) q^{93} +(-6.42280 + 19.7673i) q^{95} +(1.60570 + 4.94183i) q^{96} +(5.66312 - 4.11450i) q^{97} +8.66025 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - 2 q^{4} + 6 q^{5} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 - 2 * q^4 + 6 * q^5 - 2 * q^9	$ 8 q + 2 q^{3} - 2 q^{4} + 6 q^{5} - 2 q^{9} - 8 q^{12} + 12 q^{14} - 6 q^{15} + 10 q^{16} + 6 q^{20} - 48 q^{23} - 8 q^{25} + 6 q^{26} + 2 q^{27} - 8 q^{31} + 24 q^{34} - 2 q^{36} + 22 q^{37} - 24 q^{38} - 12 q^{42} - 24 q^{45} - 10 q^{48} - 10 q^{49} + 18 q^{53} + 48 q^{56} + 6 q^{58} + 12 q^{59} - 6 q^{60} - 2 q^{64} - 16 q^{67} - 12 q^{69} - 36 q^{70} + 12 q^{71} + 8 q^{75} + 24 q^{78} - 30 q^{80} - 2 q^{81} + 6 q^{82} - 12 q^{86} + 72 q^{89} - 12 q^{91} + 12 q^{92} + 8 q^{93} + 14 q^{97}+O(q^{100}) $ 8 * q + 2 * q^3 - 2 * q^4 + 6 * q^5 - 2 * q^9 - 8 * q^12 + 12 * q^14 - 6 * q^15 + 10 * q^16 + 6 * q^20 - 48 * q^23 - 8 * q^25 + 6 * q^26 + 2 * q^27 - 8 * q^31 + 24 * q^34 - 2 * q^36 + 22 * q^37 - 24 * q^38 - 12 * q^42 - 24 * q^45 - 10 * q^48 - 10 * q^49 + 18 * q^53 + 48 * q^56 + 6 * q^58 + 12 * q^59 - 6 * q^60 - 2 * q^64 - 16 * q^67 - 12 * q^69 - 36 * q^70 + 12 * q^71 + 8 * q^75 + 24 * q^78 - 30 * q^80 - 2 * q^81 + 6 * q^82 - 12 * q^86 + 72 * q^89 - 12 * q^91 + 12 * q^92 + 8 * q^93 + 14 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.40126	+	1.01807i	−0.990839	+	0.719887i	−0.960105	−	0.279641i	$-0.909785\pi$
$2$	−1.40126	+	1.01807i	−0.990839	+	0.719887i	−0.0307347	+	0.999528i	$0.509785\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	2.42705	+	1.76336i	1.08541	+	0.788597i	0.978618	−	0.205685i	$-0.0659421\pi$
$5$	2.42705	+	1.76336i	1.08541	+	0.788597i	0.106792	+	0.994281i	$0.465942\pi$
$6$	1.40126	+	1.01807i	0.572061	+	0.415627i
$7$	−1.07047	+	3.29456i	−0.404598	+	1.24523i	0.516632	+	0.856208i	$0.327186\pi$
$7$	−1.07047	+	3.29456i	−0.404598	+	1.24523i	−0.921230	+	0.389018i	$0.872814\pi$
$8$	−0.535233	−	1.64728i	−0.189233	−	0.582401i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−5.19615			−1.64317
$11$		0			0
$11$		0			0
$12$	−1.00000			−0.288675
$13$	1.40126	−	1.01807i	0.388639	−	0.282363i	−0.376258	−	0.926515i	$-0.622790\pi$
$13$	1.40126	−	1.01807i	0.388639	−	0.282363i	0.764898	+	0.644152i	$0.222790\pi$
$14$	−1.85410	−	5.70634i	−0.495530	−	1.52508i
$15$	0.927051	−	2.85317i	0.239364	−	0.736685i
$16$	4.04508	+	2.93893i	1.01127	+	0.734732i
$17$	−1.40126	−	1.01807i	−0.339855	−	0.246919i	0.404746	−	0.914429i	$-0.367360\pi$
$17$	−1.40126	−	1.01807i	−0.339855	−	0.246919i	−0.744601	+	0.667510i	$0.767360\pi$
$18$	0.535233	−	1.64728i	0.126156	−	0.388267i
$19$	2.14093	+	6.58911i	0.491164	+	1.51165i	0.822851	+	0.568257i	$0.192382\pi$
$19$	2.14093	+	6.58911i	0.491164	+	1.51165i	−0.331688	+	0.943389i	$0.607618\pi$
$20$	2.42705	−	1.76336i	0.542705	−	0.394298i
$21$	3.46410			0.755929
$22$		0			0
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$	−1.40126	+	1.01807i	−0.286031	+	0.207813i
$25$	1.23607	+	3.80423i	0.247214	+	0.760845i
$26$	−0.927051	+	2.85317i	−0.181810	+	0.559553i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	2.80252	+	2.03615i	0.529626	+	0.384796i
$29$	−0.535233	+	1.64728i	−0.0993903	+	0.305892i	−0.988373	−	0.152049i	$-0.951413\pi$
$29$	−0.535233	+	1.64728i	−0.0993903	+	0.305892i	0.888983	+	0.457941i	$0.151413\pi$
$30$	1.60570	+	4.94183i	0.293159	+	0.902251i
$31$	−3.23607	+	2.35114i	−0.581215	+	0.422277i	−0.839162	−	0.543882i	$-0.816954\pi$
$31$	−3.23607	+	2.35114i	−0.581215	+	0.422277i	0.257947	+	0.966159i	$0.416954\pi$
$32$	−5.19615			−0.918559
$33$		0			0
$34$	3.00000			0.514496
$35$	−8.40755	+	6.10844i	−1.42114	+	1.03252i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	−3.39919	+	10.4616i	−0.558823	+	1.71988i	0.126805	+	0.991928i	$0.459528\pi$
$37$	−3.39919	+	10.4616i	−0.558823	+	1.71988i	−0.685628	+	0.727952i	$0.740472\pi$
$38$	−9.70820	−	7.05342i	−1.57488	−	1.14422i
$39$	−1.40126	−	1.01807i	−0.224381	−	0.163022i
$40$	1.60570	−	4.94183i	0.253883	−	0.781373i
$41$	−0.535233	−	1.64728i	−0.0835894	−	0.257262i	0.900523	−	0.434808i	$-0.143184\pi$
$41$	−0.535233	−	1.64728i	−0.0835894	−	0.257262i	−0.984112	+	0.177547i	$0.943184\pi$
$42$	−4.85410	+	3.52671i	−0.749004	+	0.544183i
$43$	3.46410			0.528271			0.264135	−	0.964486i	$-0.414913\pi$
$43$	3.46410			0.528271			0.264135	+	0.964486i	$0.414913\pi$
$44$		0			0
$45$	−3.00000			−0.447214
$46$	8.40755	−	6.10844i	1.23963	−	0.900641i
$47$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$47$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$48$	1.54508	−	4.75528i	0.223014	−	0.686366i
$49$	−4.04508	−	2.93893i	−0.577869	−	0.419847i
$50$	−5.60503	−	4.07230i	−0.792672	−	0.575910i
$51$	−0.535233	+	1.64728i	−0.0749476	+	0.230665i
$52$	−0.535233	−	1.64728i	−0.0742235	−	0.228436i
$53$	7.28115	−	5.29007i	1.00014	−	0.726647i	0.0380244	−	0.999277i	$-0.487894\pi$
$53$	7.28115	−	5.29007i	1.00014	−	0.726647i	0.962119	+	0.272630i	$0.0878935\pi$
$54$	−1.73205			−0.235702
$55$		0			0
$56$	6.00000			0.801784
$57$	5.60503	−	4.07230i	0.742405	−	0.539389i
$58$	−0.927051	−	2.85317i	−0.121728	−	0.374640i
$59$	−1.85410	+	5.70634i	−0.241384	+	0.742902i	0.754827	+	0.655924i	$0.227721\pi$
$59$	−1.85410	+	5.70634i	−0.241384	+	0.742902i	−0.996210	+	0.0869778i	$0.972279\pi$
$60$	−2.42705	−	1.76336i	−0.313331	−	0.227648i
$61$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$61$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$62$	2.14093	−	6.58911i	0.271899	−	0.836818i
$63$	−1.07047	−	3.29456i	−0.134866	−	0.415075i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	5.19615			0.644503
$66$		0			0
$67$	−2.00000			−0.244339			−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000			−0.244339			−0.122169	+	0.992509i	$0.538985\pi$
$68$	−1.40126	+	1.01807i	−0.169928	+	0.123460i
$69$	1.85410	+	5.70634i	0.223208	+	0.686963i
$70$	5.56231	−	17.1190i	0.664823	−	2.04611i
$71$	4.85410	+	3.52671i	0.576076	+	0.418544i	0.837307	−	0.546733i	$-0.184129\pi$
$71$	4.85410	+	3.52671i	0.576076	+	0.418544i	−0.261231	+	0.965276i	$0.584129\pi$
$72$	1.40126	+	1.01807i	0.165140	+	0.119981i
$73$	2.14093	−	6.58911i	0.250577	−	0.771197i	−0.744092	−	0.668077i	$-0.767117\pi$
$73$	2.14093	−	6.58911i	0.250577	−	0.771197i	0.994669	−	0.103120i	$-0.0328825\pi$
$74$	−5.88756	−	18.1201i	−0.684415	−	2.10641i
$75$	3.23607	−	2.35114i	0.373669	−	0.271486i
$76$	6.92820			0.794719
$77$		0			0
$78$	3.00000			0.339683
$79$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$79$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$80$	4.63525	+	14.2658i	0.518237	+	1.59497i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	2.42705	+	1.76336i	0.268023	+	0.194730i
$83$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$83$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$84$	1.07047	−	3.29456i	0.116797	−	0.359466i
$85$	−1.60570	−	4.94183i	−0.174163	−	0.536017i
$86$	−4.85410	+	3.52671i	−0.523431	+	0.380295i
$87$	1.73205			0.185695
$88$		0			0
$89$	9.00000			0.953998			0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000			0.953998			0.476999	+	0.878904i	$0.341725\pi$
$90$	4.20378	−	3.05422i	0.443117	−	0.321943i
$91$	1.85410	+	5.70634i	0.194363	+	0.598187i
$92$	−1.85410	+	5.70634i	−0.193303	+	0.594927i
$93$	3.23607	+	2.35114i	0.335565	+	0.243802i
$94$		0			0
$95$	−6.42280	+	19.7673i	−0.658965	+	2.02809i
$96$	1.60570	+	4.94183i	0.163881	+	0.504374i
$97$	5.66312	−	4.11450i	0.575003	−	0.417764i	−0.261916	−	0.965091i	$-0.584354\pi$
$97$	5.66312	−	4.11450i	0.575003	−	0.417764i	0.836919	+	0.547327i	$0.184354\pi$
$98$	8.66025			0.874818
$99$		0			0
$100$	4.00000			0.400000
$101$	11.2101	−	8.14459i	1.11544	−	0.810417i	0.131931	−	0.991259i	$-0.457882\pi$
$101$	11.2101	−	8.14459i	1.11544	−	0.810417i	0.983512	+	0.180842i	$0.0578822\pi$
$102$	−0.927051	−	2.85317i	−0.0917917	−	0.282506i
$103$	4.32624	−	13.3148i	0.426277	−	1.31195i	−0.475489	−	0.879721i	$-0.657729\pi$
$103$	4.32624	−	13.3148i	0.426277	−	1.31195i	0.901766	−	0.432224i	$-0.142271\pi$
$104$	−2.42705	−	1.76336i	−0.237992	−	0.172911i
$105$	8.40755	+	6.10844i	0.820493	+	0.596123i
$106$	−4.81710	+	14.8255i	−0.467878	+	1.43998i
$107$	1.07047	+	3.29456i	0.103486	+	0.318497i	0.989372	−	0.145406i	$-0.0464488\pi$
$107$	1.07047	+	3.29456i	0.103486	+	0.318497i	−0.885886	+	0.463903i	$0.846449\pi$
$108$	0.809017	−	0.587785i	0.0778477	−	0.0565597i
$109$	15.5885			1.49310			0.746552	−	0.665327i	$-0.231708\pi$
$109$	15.5885			1.49310			0.746552	+	0.665327i	$0.231708\pi$
$110$		0			0
$111$	11.0000			1.04407
$112$	−14.0126	+	10.1807i	−1.32406	+	0.961989i
$113$	−6.48936	−	19.9722i	−0.610467	−	1.87883i	−0.453599	−	0.891206i	$-0.649860\pi$
$113$	−6.48936	−	19.9722i	−0.610467	−	1.87883i	−0.156868	−	0.987620i	$-0.550140\pi$
$114$	−3.70820	+	11.4127i	−0.347305	+	1.06890i
$115$	−14.5623	−	10.5801i	−1.35794	−	0.986603i
$116$	1.40126	+	1.01807i	0.130104	+	0.0945258i
$117$	−0.535233	+	1.64728i	−0.0494823	+	0.152291i
$118$	−3.21140	−	9.88367i	−0.295633	−	0.909866i
$119$	4.85410	−	3.52671i	0.444975	−	0.323293i
$120$	−5.19615			−0.474342
$121$		0			0
$122$		0			0
$123$	−1.40126	+	1.01807i	−0.126347	+	0.0917966i
$124$	1.23607	+	3.80423i	0.111002	+	0.341630i
$125$	0.927051	−	2.85317i	0.0829180	−	0.255195i
$126$	4.85410	+	3.52671i	0.432438	+	0.314184i
$127$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$127$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$128$	3.74663	−	11.5309i	0.331159	−	1.01920i
$129$	−1.07047	−	3.29456i	−0.0942493	−	0.290070i
$130$	−7.28115	+	5.29007i	−0.638599	+	0.463970i
$131$	−17.3205			−1.51330			−0.756650	−	0.653820i	$-0.773165\pi$
$131$	−17.3205			−1.51330			−0.756650	+	0.653820i	$0.773165\pi$
$132$		0			0
$133$	−24.0000			−2.08106
$134$	2.80252	−	2.03615i	0.242101	−	0.175896i
$135$	0.927051	+	2.85317i	0.0797878	+	0.245562i
$136$	−0.927051	+	2.85317i	−0.0794940	+	0.244657i
$137$	4.85410	+	3.52671i	0.414714	+	0.301307i	0.775507	−	0.631338i	$-0.217494\pi$
$137$	4.85410	+	3.52671i	0.414714	+	0.301307i	−0.360794	+	0.932646i	$0.617494\pi$
$138$	−8.40755	−	6.10844i	−0.715698	−	0.519985i
$139$	3.21140	−	9.88367i	0.272387	−	0.838322i	−0.717512	−	0.696547i	$-0.754719\pi$
$139$	3.21140	−	9.88367i	0.272387	−	0.838322i	0.989899	−	0.141775i	$-0.0452810\pi$
$140$	3.21140	+	9.88367i	0.271413	+	0.835323i
$141$		0			0
$142$	−10.3923			−0.872103
$143$		0			0
$144$	−5.00000			−0.416667
$145$	−4.20378	+	3.05422i	−0.349105	+	0.253639i
$146$	3.70820	+	11.4127i	0.306893	+	0.944520i
$147$	−1.54508	+	4.75528i	−0.127436	+	0.392209i
$148$	8.89919	+	6.46564i	0.731509	+	0.531472i
$149$	9.80881	+	7.12652i	0.803569	+	0.583827i	0.911959	−	0.410281i	$-0.134570\pi$
$149$	9.80881	+	7.12652i	0.803569	+	0.583827i	−0.108390	+	0.994108i	$0.534570\pi$
$150$	−2.14093	+	6.58911i	−0.174806	+	0.537999i
$151$	4.28187	+	13.1782i	0.348453	+	1.07243i	0.959709	+	0.280996i	$0.0906647\pi$
$151$	4.28187	+	13.1782i	0.348453	+	1.07243i	−0.611256	+	0.791433i	$0.709335\pi$
$152$	9.70820	−	7.05342i	0.787439	−	0.572108i
$153$	1.73205			0.140028
$154$		0			0
$155$	−12.0000			−0.963863
$156$	−1.40126	+	1.01807i	−0.112190	+	0.0815111i
$157$	−4.32624	−	13.3148i	−0.345271	−	1.06264i	−0.961438	−	0.275020i	$-0.911315\pi$
$157$	−4.32624	−	13.3148i	−0.345271	−	1.06264i	0.616167	−	0.787616i	$-0.288685\pi$
$158$		0			0
$159$	−7.28115	−	5.29007i	−0.577433	−	0.419530i
$160$	−12.6113	−	9.16267i	−0.997013	−	0.724372i
$161$	6.42280	−	19.7673i	0.506187	−	1.55788i
$162$	0.535233	+	1.64728i	0.0420519	+	0.129422i
$163$	−1.61803	+	1.17557i	−0.126734	+	0.0920778i	−0.649347	−	0.760493i	$-0.724958\pi$
$163$	−1.61803	+	1.17557i	−0.126734	+	0.0920778i	0.522612	+	0.852570i	$0.324958\pi$
$164$	−1.73205			−0.135250
$165$		0			0
$166$		0			0
$167$	2.80252	−	2.03615i	0.216865	−	0.157562i	−0.474049	−	0.880498i	$-0.657208\pi$
$167$	2.80252	−	2.03615i	0.216865	−	0.157562i	0.690914	+	0.722937i	$0.257208\pi$
$168$	−1.85410	−	5.70634i	−0.143047	−	0.440254i
$169$	−3.09017	+	9.51057i	−0.237705	+	0.731582i
$170$	7.28115	+	5.29007i	0.558439	+	0.405730i
$171$	−5.60503	−	4.07230i	−0.428628	−	0.311416i
$172$	1.07047	−	3.29456i	0.0816223	−	0.251208i
$173$	6.42280	+	19.7673i	0.488316	+	1.50288i	0.827120	+	0.562026i	$0.189978\pi$
$173$	6.42280	+	19.7673i	0.488316	+	1.50288i	−0.338803	+	0.940857i	$0.610022\pi$
$174$	−2.42705	+	1.76336i	−0.183994	+	0.133680i
$175$	−13.8564			−1.04745
$176$		0			0
$177$	6.00000			0.450988
$178$	−12.6113	+	9.16267i	−0.945259	+	0.686771i
$179$	3.70820	+	11.4127i	0.277164	+	0.853024i	0.988639	+	0.150312i	$0.0480277\pi$
$179$	3.70820	+	11.4127i	0.277164	+	0.853024i	−0.711474	+	0.702712i	$0.751972\pi$
$180$	−0.927051	+	2.85317i	−0.0690983	+	0.212663i
$181$	5.66312	+	4.11450i	0.420936	+	0.305828i	0.778014	−	0.628246i	$-0.216227\pi$
$181$	5.66312	+	4.11450i	0.420936	+	0.305828i	−0.357078	+	0.934075i	$0.616227\pi$
$182$	−8.40755	−	6.10844i	−0.623209	−	0.452788i
$183$		0			0
$184$	3.21140	+	9.88367i	0.236747	+	0.728634i
$185$	−26.6976	+	19.3969i	−1.96284	+	1.42609i
$186$	−6.92820			−0.508001
$187$		0			0
$188$		0			0
$189$	−2.80252	+	2.03615i	−0.203853	+	0.148108i
$190$	−11.1246	−	34.2380i	−0.807064	−	2.48389i
$191$	3.70820	−	11.4127i	0.268316	−	0.825792i	−0.722595	−	0.691272i	$-0.757051\pi$
$191$	3.70820	−	11.4127i	0.268316	−	0.825792i	0.990911	−	0.134520i	$-0.0429494\pi$
$192$	0.809017	+	0.587785i	0.0583858	+	0.0424197i
$193$	4.20378	+	3.05422i	0.302594	+	0.219848i	0.728712	−	0.684820i	$-0.240119\pi$
$193$	4.20378	+	3.05422i	0.302594	+	0.219848i	−0.426118	+	0.904668i	$0.640119\pi$
$194$	−3.74663	+	11.5309i	−0.268992	+	0.827874i
$195$	−1.60570	−	4.94183i	−0.114987	−	0.353892i
$196$	−4.04508	+	2.93893i	−0.288935	+	0.209923i
$197$	−19.0526			−1.35744			−0.678719	−	0.734398i	$-0.737465\pi$
$197$	−19.0526			−1.35744			−0.678719	+	0.734398i	$0.737465\pi$
$198$		0			0
$199$	10.0000			0.708881			0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000			0.708881			0.354441	+	0.935079i	$0.384671\pi$
$200$	5.60503	−	4.07230i	0.396336	−	0.287955i
$201$	0.618034	+	1.90211i	0.0435928	+	0.134165i
$202$	−7.41641	+	22.8254i	−0.521817	+	1.60599i
$203$	−4.85410	−	3.52671i	−0.340691	−	0.247527i
$204$	1.40126	+	1.01807i	0.0981077	+	0.0712794i
$205$	1.60570	−	4.94183i	0.112147	−	0.345153i
$206$	7.49326	+	23.0619i	0.522080	+	1.60680i
$207$	4.85410	−	3.52671i	0.337383	−	0.245123i
$208$	8.66025			0.600481
$209$		0			0
$210$	−18.0000			−1.24212
$211$	14.0126	−	10.1807i	0.964666	−	0.700871i	0.0104364	−	0.999946i	$-0.496678\pi$
$211$	14.0126	−	10.1807i	0.964666	−	0.700871i	0.954230	+	0.299075i	$0.0966779\pi$
$212$	−2.78115	−	8.55951i	−0.191010	−	0.587869i
$213$	1.85410	−	5.70634i	0.127041	−	0.390992i
$214$	−4.85410	−	3.52671i	−0.331820	−	0.241081i
$215$	8.40755	+	6.10844i	0.573390	+	0.416592i
$216$	0.535233	−	1.64728i	0.0364180	−	0.112083i
$217$	−4.28187	−	13.1782i	−0.290672	−	0.894596i
$218$	−21.8435	+	15.8702i	−1.47943	+	1.07487i
$219$	−6.92820			−0.468165
$220$		0			0
$221$	−3.00000			−0.201802
$222$	−15.4138	+	11.1988i	−1.03451	+	0.751615i
$223$	6.18034	+	19.0211i	0.413866	+	1.27375i	0.913261	+	0.407375i	$0.133556\pi$
$223$	6.18034	+	19.0211i	0.413866	+	1.27375i	−0.499395	+	0.866374i	$0.666444\pi$
$224$	5.56231	−	17.1190i	0.371647	−	1.14381i
$225$	−3.23607	−	2.35114i	−0.215738	−	0.156743i
$226$	29.4264	+	21.3796i	1.95742	+	1.42215i
$227$	−7.49326	+	23.0619i	−0.497345	+	1.53067i	0.315924	+	0.948784i	$0.397686\pi$
$227$	−7.49326	+	23.0619i	−0.497345	+	1.53067i	−0.813269	+	0.581887i	$0.802314\pi$
$228$	−2.14093	−	6.58911i	−0.141787	−	0.436375i
$229$	18.6074	−	13.5191i	1.22961	−	0.893365i	0.232750	−	0.972537i	$-0.425228\pi$
$229$	18.6074	−	13.5191i	1.22961	−	0.893365i	0.996861	+	0.0791719i	$0.0252276\pi$
$230$	31.1769			2.05574
$231$		0			0
$232$	3.00000			0.196960
$233$	−23.8214	+	17.3073i	−1.56059	+	1.13384i	−0.625069	+	0.780570i	$0.714929\pi$
$233$	−23.8214	+	17.3073i	−1.56059	+	1.13384i	−0.935523	+	0.353266i	$0.885071\pi$
$234$	−0.927051	−	2.85317i	−0.0606032	−	0.186518i
$235$		0			0
$236$	4.85410	+	3.52671i	0.315975	+	0.229569i
$237$		0			0
$238$	−3.21140	+	9.88367i	−0.208164	+	0.640663i
$239$	−2.14093	−	6.58911i	−0.138485	−	0.426214i	0.857630	−	0.514266i	$-0.171936\pi$
$239$	−2.14093	−	6.58911i	−0.138485	−	0.426214i	−0.996116	+	0.0880522i	$0.971936\pi$
$240$	12.1353	−	8.81678i	0.783327	−	0.569121i
$241$	−20.7846			−1.33885			−0.669427	−	0.742878i	$-0.733460\pi$
$241$	−20.7846			−1.33885			−0.669427	+	0.742878i	$0.733460\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−4.63525	−	14.2658i	−0.296136	−	0.911412i
$246$	0.927051	−	2.85317i	0.0591066	−	0.181911i
$247$	9.70820	+	7.05342i	0.617718	+	0.448799i
$248$	5.60503	+	4.07230i	0.355920	+	0.258591i
$249$		0			0
$250$	1.60570	+	4.94183i	0.101553	+	0.312549i
$251$	4.85410	−	3.52671i	0.306388	−	0.222604i	−0.423957	−	0.905682i	$-0.639359\pi$
$251$	4.85410	−	3.52671i	0.306388	−	0.222604i	0.730345	+	0.683078i	$0.239359\pi$
$252$	−3.46410			−0.218218
$253$		0			0
$254$		0			0
$255$	−4.20378	+	3.05422i	−0.263251	+	0.191263i
$256$	5.87132	+	18.0701i	0.366958	+	1.12938i
$257$	2.78115	−	8.55951i	0.173484	−	0.533927i	−0.826077	−	0.563557i	$-0.809433\pi$
$257$	2.78115	−	8.55951i	0.173484	−	0.533927i	0.999561	+	0.0296292i	$0.00943265\pi$
$258$	4.85410	+	3.52671i	0.302203	+	0.219563i
$259$	−30.8277	−	22.3976i	−1.91554	−	1.39172i
$260$	1.60570	−	4.94183i	0.0995812	−	0.306480i
$261$	−0.535233	−	1.64728i	−0.0331301	−	0.101964i
$262$	24.2705	−	17.6336i	1.49944	−	1.08940i
$263$	13.8564			0.854423			0.427211	−	0.904152i	$-0.359496\pi$
$263$	13.8564			0.854423			0.427211	+	0.904152i	$0.359496\pi$
$264$		0			0
$265$	27.0000			1.65860
$266$	33.6302	−	24.4338i	2.06200	−	1.49813i
$267$	−2.78115	−	8.55951i	−0.170204	−	0.523833i
$268$	−0.618034	+	1.90211i	−0.0377524	+	0.116190i
$269$	16.9894	+	12.3435i	1.03586	+	0.752596i	0.969473	−	0.245198i	$-0.0788530\pi$
$269$	16.9894	+	12.3435i	1.03586	+	0.752596i	0.0663864	+	0.997794i	$0.478853\pi$
$270$	−4.20378	−	3.05422i	−0.255834	−	0.185874i
$271$	−1.07047	+	3.29456i	−0.0650262	+	0.200130i	−0.978291	−	0.207237i	$-0.933553\pi$
$271$	−1.07047	+	3.29456i	−0.0650262	+	0.200130i	0.913265	+	0.407367i	$0.133553\pi$
$272$	−2.67617	−	8.23639i	−0.162266	−	0.499405i
$273$	4.85410	−	3.52671i	0.293784	−	0.213446i
$274$	−10.3923			−0.627822
$275$		0			0
$276$	6.00000			0.361158
$277$	4.20378	−	3.05422i	0.252580	−	0.183510i	−0.454289	−	0.890854i	$-0.650107\pi$
$277$	4.20378	−	3.05422i	0.252580	−	0.183510i	0.706870	+	0.707344i	$0.250107\pi$
$278$	5.56231	+	17.1190i	0.333605	+	1.02673i
$279$	1.23607	−	3.80423i	0.0740015	−	0.227753i
$280$	14.5623	+	10.5801i	0.870264	+	0.632284i
$281$	5.60503	+	4.07230i	0.334368	+	0.242933i	0.742282	−	0.670088i	$-0.233744\pi$
$281$	5.60503	+	4.07230i	0.334368	+	0.242933i	−0.407914	+	0.913021i	$0.633744\pi$
$282$		0			0
$283$	−9.63420	−	29.6510i	−0.572694	−	1.76257i	−0.643902	−	0.765108i	$-0.722686\pi$
$283$	−9.63420	−	29.6510i	−0.572694	−	1.76257i	0.0712084	−	0.997461i	$-0.477314\pi$
$284$	4.85410	−	3.52671i	0.288038	−	0.209272i
$285$	20.7846			1.23117
$286$		0			0
$287$	6.00000			0.354169
$288$	4.20378	−	3.05422i	0.247710	−	0.179972i
$289$	−4.32624	−	13.3148i	−0.254485	−	0.783223i
$290$	2.78115	−	8.55951i	0.163315	−	0.502632i
$291$	−5.66312	−	4.11450i	−0.331978	−	0.241196i
$292$	−5.60503	−	4.07230i	−0.328010	−	0.238313i
$293$	5.88756	−	18.1201i	0.343955	−	1.05859i	−0.618186	−	0.786032i	$-0.712132\pi$
$293$	5.88756	−	18.1201i	0.343955	−	1.05859i	0.962141	−	0.272553i	$-0.0878680\pi$
$294$	−2.67617	−	8.23639i	−0.156077	−	0.480356i
$295$	−14.5623	+	10.5801i	−0.847850	+	0.615999i
$296$	19.0526			1.10741
$297$		0			0
$298$	−21.0000			−1.21650
$299$	−8.40755	+	6.10844i	−0.486221	+	0.353260i
$300$	−1.23607	−	3.80423i	−0.0713644	−	0.219637i
$301$	−3.70820	+	11.4127i	−0.213737	+	0.657816i
$302$	−19.4164	−	14.1068i	−1.11729	−	0.811758i
$303$	−11.2101	−	8.14459i	−0.644002	−	0.467895i
$304$	−10.7047	+	32.9456i	−0.613955	+	1.88956i
$305$		0			0
$306$	−2.42705	+	1.76336i	−0.138745	+	0.100804i
$307$	3.46410			0.197707			0.0988534	−	0.995102i	$-0.468483\pi$
$307$	3.46410			0.197707			0.0988534	+	0.995102i	$0.468483\pi$
$308$		0			0
$309$	−14.0000			−0.796432
$310$	16.8151	−	12.2169i	0.955034	−	0.693873i
$311$	3.70820	+	11.4127i	0.210273	+	0.647154i	0.999456	+	0.0329949i	$0.0105045\pi$
$311$	3.70820	+	11.4127i	0.210273	+	0.647154i	−0.789183	+	0.614159i	$0.789495\pi$
$312$	−0.927051	+	2.85317i	−0.0524839	+	0.161529i
$313$	−5.66312	−	4.11450i	−0.320098	−	0.232565i	0.416119	−	0.909310i	$-0.363390\pi$
$313$	−5.66312	−	4.11450i	−0.320098	−	0.232565i	−0.736217	+	0.676745i	$0.763390\pi$
$314$	19.6176	+	14.2530i	1.10709	+	0.804345i
$315$	3.21140	−	9.88367i	0.180942	−	0.556882i
$316$		0			0
$317$	−4.85410	+	3.52671i	−0.272634	+	0.198080i	−0.715698	−	0.698410i	$-0.753891\pi$
$317$	−4.85410	+	3.52671i	−0.272634	+	0.198080i	0.443064	+	0.896490i	$0.353891\pi$
$318$	15.5885			0.874157
$319$		0			0
$320$	−3.00000			−0.167705
$321$	2.80252	−	2.03615i	0.156421	−	0.113647i
$322$	11.1246	+	34.2380i	0.619950	+	1.90801i
$323$	3.70820	−	11.4127i	0.206330	−	0.635018i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	5.60503	+	4.07230i	0.310911	+	0.225890i
$326$	1.07047	−	3.29456i	0.0592876	−	0.182469i
$327$	−4.81710	−	14.8255i	−0.266386	−	0.819852i
$328$	−2.42705	+	1.76336i	−0.134011	+	0.0973650i
$329$		0			0
$330$		0			0
$331$	20.0000			1.09930			0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000			1.09930			0.549650	+	0.835395i	$0.314761\pi$
$332$		0			0
$333$	−3.39919	−	10.4616i	−0.186274	−	0.573293i
$334$	−1.85410	+	5.70634i	−0.101452	+	0.312237i
$335$	−4.85410	−	3.52671i	−0.265208	−	0.192685i
$336$	14.0126	+	10.1807i	0.764449	+	0.555405i
$337$	−3.74663	+	11.5309i	−0.204092	+	0.628131i	0.795657	+	0.605747i	$0.207126\pi$
$337$	−3.74663	+	11.5309i	−0.204092	+	0.628131i	−0.999749	+	0.0223838i	$0.992874\pi$
$338$	−5.35233	−	16.4728i	−0.291128	−	0.896001i
$339$	−16.9894	+	12.3435i	−0.922735	+	0.670406i
$340$	−5.19615			−0.281801
$341$		0			0
$342$	12.0000			0.648886
$343$	−5.60503	+	4.07230i	−0.302643	+	0.219883i
$344$	−1.85410	−	5.70634i	−0.0999665	−	0.307665i
$345$	−5.56231	+	17.1190i	−0.299464	+	0.921657i
$346$	−29.1246	−	21.1603i	−1.56575	−	1.13758i
$347$	−22.4201	−	16.2892i	−1.20358	−	0.874449i	−0.208944	−	0.977928i	$-0.567003\pi$
$347$	−22.4201	−	16.2892i	−1.20358	−	0.874449i	−0.994632	+	0.103478i	$0.967003\pi$
$348$	0.535233	−	1.64728i	0.0286915	−	0.0883034i
$349$	−0.535233	−	1.64728i	−0.0286504	−	0.0881768i	0.935709	−	0.352773i	$-0.114761\pi$
$349$	−0.535233	−	1.64728i	−0.0286504	−	0.0881768i	−0.964359	+	0.264596i	$0.914761\pi$
$350$	19.4164	−	14.1068i	1.03785	−	0.754043i
$351$	1.73205			0.0924500
$352$		0			0
$353$	21.0000			1.11772			0.558859	−	0.829263i	$-0.311239\pi$
$353$	21.0000			1.11772			0.558859	+	0.829263i	$0.311239\pi$
$354$	−8.40755	+	6.10844i	−0.446856	+	0.324660i
$355$	5.56231	+	17.1190i	0.295217	+	0.908583i
$356$	2.78115	−	8.55951i	0.147401	−	0.453653i
$357$	−4.85410	−	3.52671i	−0.256906	−	0.186653i
$358$	−16.8151	−	12.2169i	−0.888706	−	0.645683i
$359$	9.63420	−	29.6510i	0.508473	−	1.56492i	−0.286378	−	0.958117i	$-0.592451\pi$
$359$	9.63420	−	29.6510i	0.508473	−	1.56492i	0.794852	−	0.606804i	$-0.207549\pi$
$360$	1.60570	+	4.94183i	0.0846278	+	0.260458i
$361$	−23.4615	+	17.0458i	−1.23482	+	0.897146i
$362$	−12.1244			−0.637242
$363$		0			0
$364$	6.00000			0.314485
$365$	16.8151	−	12.2169i	0.880143	−	0.639461i
$366$		0			0
$367$	8.03444	−	24.7275i	0.419394	−	1.29076i	−0.488866	−	0.872359i	$-0.662589\pi$
$367$	8.03444	−	24.7275i	0.419394	−	1.29076i	0.908261	−	0.418405i	$-0.137411\pi$
$368$	−24.2705	−	17.6336i	−1.26519	−	0.919213i
$369$	1.40126	+	1.01807i	0.0729466	+	0.0529988i
$370$	17.6627	−	54.3602i	0.918240	−	2.82605i
$371$	9.63420	+	29.6510i	0.500183	+	1.53940i
$372$	3.23607	−	2.35114i	0.167782	−	0.121901i
$373$	20.7846			1.07619			0.538093	−	0.842885i	$-0.319145\pi$
$373$	20.7846			1.07619			0.538093	+	0.842885i	$0.319145\pi$
$374$		0			0
$375$	−3.00000			−0.154919
$376$		0			0
$377$	0.927051	+	2.85317i	0.0477456	+	0.146946i
$378$	1.85410	−	5.70634i	0.0953647	−	0.293502i
$379$	−11.3262	−	8.22899i	−0.581790	−	0.422695i	0.257579	−	0.966257i	$-0.417075\pi$
$379$	−11.3262	−	8.22899i	−0.581790	−	0.422695i	−0.839369	+	0.543562i	$0.817075\pi$
$380$	16.8151	+	12.2169i	0.862597	+	0.626713i
$381$		0			0
$382$	6.42280	+	19.7673i	0.328619	+	1.01139i
$383$	−4.85410	+	3.52671i	−0.248033	+	0.180207i	−0.704855	−	0.709352i	$-0.748988\pi$
$383$	−4.85410	+	3.52671i	−0.248033	+	0.180207i	0.456822	+	0.889558i	$0.348988\pi$
$384$	−12.1244			−0.618718
$385$		0			0
$386$	−9.00000			−0.458088
$387$	−2.80252	+	2.03615i	−0.142460	+	0.103503i
$388$	−2.16312	−	6.65740i	−0.109816	−	0.337978i
$389$	−8.34346	+	25.6785i	−0.423030	+	1.30195i	0.481838	+	0.876260i	$0.339969\pi$
$389$	−8.34346	+	25.6785i	−0.423030	+	1.30195i	−0.904868	+	0.425692i	$0.860031\pi$
$390$	7.28115	+	5.29007i	0.368696	+	0.267873i
$391$	8.40755	+	6.10844i	0.425188	+	0.308917i
$392$	−2.67617	+	8.23639i	−0.135167	+	0.416001i
$393$	5.35233	+	16.4728i	0.269989	+	0.830942i
$394$	26.6976	−	19.3969i	1.34500	−	0.977202i
$395$		0			0
$396$		0			0
$397$	11.0000			0.552074			0.276037	−	0.961147i	$-0.410979\pi$
$397$	11.0000			0.552074			0.276037	+	0.961147i	$0.410979\pi$
$398$	−14.0126	+	10.1807i	−0.702387	+	0.510314i
$399$	7.41641	+	22.8254i	0.371285	+	1.14270i
$400$	−6.18034	+	19.0211i	−0.309017	+	0.951057i
$401$	−2.42705	−	1.76336i	−0.121201	−	0.0880578i	0.525533	−	0.850773i	$-0.323866\pi$
$401$	−2.42705	−	1.76336i	−0.121201	−	0.0880578i	−0.646734	+	0.762715i	$0.723866\pi$
$402$	−2.80252	−	2.03615i	−0.139777	−	0.101554i
$403$	−2.14093	+	6.58911i	−0.106647	+	0.328227i
$404$	−4.28187	−	13.1782i	−0.213031	−	0.655641i
$405$	2.42705	−	1.76336i	0.120601	−	0.0876219i
$406$	10.3923			0.515761
$407$		0			0
$408$	3.00000			0.148522
$409$	−1.40126	+	1.01807i	−0.0692878	+	0.0503405i	−0.621890	−	0.783105i	$-0.713635\pi$
$409$	−1.40126	+	1.01807i	−0.0692878	+	0.0503405i	0.552602	+	0.833445i	$0.313635\pi$
$410$	2.78115	+	8.55951i	0.137351	+	0.422724i
$411$	1.85410	−	5.70634i	0.0914561	−	0.281473i
$412$	−11.3262	−	8.22899i	−0.558004	−	0.405413i
$413$	−16.8151	−	12.2169i	−0.827417	−	0.601154i
$414$	−3.21140	+	9.88367i	−0.157832	+	0.485756i
$415$		0			0
$416$	−7.28115	+	5.29007i	−0.356988	+	0.259367i
$417$	−10.3923			−0.508913
$418$		0			0
$419$	−30.0000			−1.46560			−0.732798	−	0.680446i	$-0.761786\pi$
$419$	−30.0000			−1.46560			−0.732798	+	0.680446i	$0.761786\pi$
$420$	8.40755	−	6.10844i	0.410246	−	0.298062i
$421$	2.16312	+	6.65740i	0.105424	+	0.324462i	0.989830	−	0.142257i	$-0.0454360\pi$
$421$	2.16312	+	6.65740i	0.105424	+	0.324462i	−0.884406	+	0.466719i	$0.845436\pi$
$422$	−9.27051	+	28.5317i	−0.451281	+	1.38890i
$423$		0			0
$424$	−12.6113	−	9.16267i	−0.612460	−	0.444978i
$425$	2.14093	−	6.58911i	0.103850	−	0.319619i
$426$	3.21140	+	9.88367i	0.155593	+	0.478865i
$427$		0			0
$428$	3.46410			0.167444
$429$		0			0
$430$	−18.0000			−0.868037
$431$	14.0126	−	10.1807i	0.674962	−	0.490389i	−0.196720	−	0.980460i	$-0.563029\pi$
$431$	14.0126	−	10.1807i	0.674962	−	0.490389i	0.871683	+	0.490071i	$0.163029\pi$
$432$	1.54508	+	4.75528i	0.0743379	+	0.228789i
$433$	−5.87132	+	18.0701i	−0.282158	+	0.868392i	0.705078	+	0.709129i	$0.250912\pi$
$433$	−5.87132	+	18.0701i	−0.282158	+	0.868392i	−0.987236	+	0.159263i	$0.949088\pi$
$434$	19.4164	+	14.1068i	0.932017	+	0.677150i
$435$	4.20378	+	3.05422i	0.201556	+	0.146439i
$436$	4.81710	−	14.8255i	0.230697	−	0.710013i
$437$	−12.8456	−	39.5347i	−0.614488	−	1.89120i
$438$	9.70820	−	7.05342i	0.463876	−	0.337026i
$439$	−6.92820			−0.330665			−0.165333	−	0.986238i	$-0.552870\pi$
$439$	−6.92820			−0.330665			−0.165333	+	0.986238i	$0.552870\pi$
$440$		0			0
$441$	5.00000			0.238095
$442$	4.20378	−	3.05422i	0.199953	−	0.145275i
$443$	−5.56231	−	17.1190i	−0.264273	−	0.813349i	−0.991860	−	0.127333i	$-0.959358\pi$
$443$	−5.56231	−	17.1190i	−0.264273	−	0.813349i	0.727587	−	0.686016i	$-0.240642\pi$
$444$	3.39919	−	10.4616i	0.161318	−	0.496487i
$445$	21.8435	+	15.8702i	1.03548	+	0.752320i
$446$	−28.0252	−	20.3615i	−1.32703	−	0.964144i
$447$	3.74663	−	11.5309i	0.177210	−	0.545395i
$448$	−1.07047	−	3.29456i	−0.0505748	−	0.155653i
$449$	−16.9894	+	12.3435i	−0.801777	+	0.582525i	−0.911435	−	0.411444i	$-0.865025\pi$
$449$	−16.9894	+	12.3435i	−0.801777	+	0.582525i	0.109658	+	0.993969i	$0.465025\pi$
$450$	6.92820			0.326599
$451$		0			0
$452$	−21.0000			−0.987757
$453$	11.2101	−	8.14459i	0.526695	−	0.382666i
$454$	−12.9787	−	39.9444i	−0.609121	−	1.87468i
$455$	−5.56231	+	17.1190i	−0.260765	+	0.802552i
$456$	−9.70820	−	7.05342i	−0.454628	−	0.330307i
$457$	23.8214	+	17.3073i	1.11432	+	0.809599i	0.983338	−	0.181786i	$-0.0581877\pi$
$457$	23.8214	+	17.3073i	1.11432	+	0.809599i	0.130980	+	0.991385i	$0.458188\pi$
$458$	−12.3104	+	37.8874i	−0.575225	+	1.77036i
$459$	−0.535233	−	1.64728i	−0.0249825	−	0.0768884i
$460$	−14.5623	+	10.5801i	−0.678971	+	0.493301i
$461$	−15.5885			−0.726027			−0.363013	−	0.931784i	$-0.618252\pi$
$461$	−15.5885			−0.726027			−0.363013	+	0.931784i	$0.618252\pi$
$462$		0			0
$463$	−34.0000			−1.58011			−0.790057	−	0.613033i	$-0.789949\pi$
$463$	−34.0000			−1.58011			−0.790057	+	0.613033i	$0.789949\pi$
$464$	−7.00629	+	5.09037i	−0.325259	+	0.236314i
$465$	3.70820	+	11.4127i	0.171964	+	0.529250i
$466$	15.7599	−	48.5039i	0.730062	−	2.24690i
$467$	14.5623	+	10.5801i	0.673863	+	0.489590i	0.871316	−	0.490722i	$-0.163267\pi$
$467$	14.5623	+	10.5801i	0.673863	+	0.489590i	−0.197453	+	0.980312i	$0.563267\pi$
$468$	1.40126	+	1.01807i	0.0647732	+	0.0470605i
$469$	2.14093	−	6.58911i	0.0988591	−	0.304257i
$470$		0			0
$471$	−11.3262	+	8.22899i	−0.521885	+	0.379172i
$472$	10.3923			0.478345
$473$		0			0
$474$		0			0
$475$	−22.4201	+	16.2892i	−1.02871	+	0.747399i
$476$	−1.85410	−	5.70634i	−0.0849826	−	0.261550i
$477$	−2.78115	+	8.55951i	−0.127340	+	0.391913i
$478$	9.70820	+	7.05342i	0.444043	+	0.322616i
$479$	−19.6176	−	14.2530i	−0.896352	−	0.651238i	0.0411745	−	0.999152i	$-0.486890\pi$
$479$	−19.6176	−	14.2530i	−0.896352	−	0.651238i	−0.937526	+	0.347914i	$0.886890\pi$
$480$	−4.81710	+	14.8255i	−0.219869	+	0.676689i
$481$	5.88756	+	18.1201i	0.268450	+	0.826204i
$482$	29.1246	−	21.1603i	1.32659	−	0.963824i
$483$	−20.7846			−0.945732
$484$		0			0
$485$	21.0000			0.953561
$486$	1.40126	−	1.01807i	0.0635624	−	0.0461808i
$487$	−11.7426	−	36.1401i	−0.532110	−	1.63767i	−0.749812	−	0.661651i	$-0.769856\pi$
$487$	−11.7426	−	36.1401i	−0.532110	−	1.63767i	0.217702	−	0.976015i	$-0.430144\pi$
$488$		0			0
$489$	1.61803	+	1.17557i	0.0731700	+	0.0531611i
$490$	21.0189	+	15.2711i	0.949536	+	0.689878i
$491$	−6.42280	+	19.7673i	−0.289857	+	0.892087i	0.695044	+	0.718967i	$0.255385\pi$
$491$	−6.42280	+	19.7673i	−0.289857	+	0.892087i	−0.984901	+	0.173120i	$0.944615\pi$
$492$	0.535233	+	1.64728i	0.0241302	+	0.0742650i
$493$	2.42705	−	1.76336i	0.109309	−	0.0794175i
$494$	−20.7846			−0.935144
$495$		0			0
$496$	−20.0000			−0.898027
$497$	−16.8151	+	12.2169i	−0.754260	+	0.548002i
$498$		0			0
$499$	6.79837	−	20.9232i	0.304337	−	0.936653i	−0.675587	−	0.737280i	$-0.736110\pi$
$499$	6.79837	−	20.9232i	0.304337	−	0.936653i	0.979924	−	0.199373i	$-0.0638904\pi$
$500$	−2.42705	−	1.76336i	−0.108541	−	0.0788597i
$501$	−2.80252	−	2.03615i	−0.125207	−	0.0909684i
$502$	−3.21140	+	9.88367i	−0.143332	+	0.441130i
$503$	9.63420	+	29.6510i	0.429568	+	1.32207i	0.898552	+	0.438867i	$0.144620\pi$
$503$	9.63420	+	29.6510i	0.429568	+	1.32207i	−0.468985	+	0.883206i	$0.655380\pi$
$504$	−4.85410	+	3.52671i	−0.216219	+	0.157092i
$505$	41.5692			1.84981
$506$		0			0
$507$	10.0000			0.444116
$508$		0			0
$509$	5.56231	+	17.1190i	0.246545	+	0.758787i	0.995379	+	0.0960291i	$0.0306142\pi$
$509$	5.56231	+	17.1190i	0.246545	+	0.758787i	−0.748834	+	0.662758i	$0.769386\pi$
$510$	2.78115	−	8.55951i	0.123152	−	0.379021i
$511$	19.4164	+	14.1068i	0.858931	+	0.624050i
$512$	−7.00629	−	5.09037i	−0.309637	−	0.224965i
$513$	−2.14093	+	6.58911i	−0.0945245	+	0.290916i
$514$	4.81710	+	14.8255i	0.212473	+	0.653925i
$515$	33.9787	−	24.6870i	1.49728	−	1.08784i
$516$	−3.46410			−0.152499
$517$		0			0
$518$	66.0000			2.89987
$519$	16.8151	−	12.2169i	0.738101	−	0.536262i
$520$	−2.78115	−	8.55951i	−0.121962	−	0.375359i
$521$	1.85410	−	5.70634i	0.0812297	−	0.249999i	−0.902191	−	0.431336i	$-0.858042\pi$
$521$	1.85410	−	5.70634i	0.0812297	−	0.249999i	0.983421	+	0.181337i	$0.0580424\pi$
$522$	2.42705	+	1.76336i	0.106229	+	0.0771800i
$523$	33.6302	+	24.4338i	1.47055	+	1.06841i	0.980455	+	0.196743i	$0.0630365\pi$
$523$	33.6302	+	24.4338i	1.47055	+	1.06841i	0.490091	+	0.871671i	$0.336963\pi$
$524$	−5.35233	+	16.4728i	−0.233818	+	0.719617i
$525$	4.28187	+	13.1782i	0.186876	+	0.575145i
$526$	−19.4164	+	14.1068i	−0.846596	+	0.615088i
$527$	6.92820			0.301797
$528$		0			0
$529$	13.0000			0.565217
$530$	−37.8340	+	27.4880i	−1.64340	+	1.19400i
$531$	−1.85410	−	5.70634i	−0.0804612	−	0.247634i
$532$	−7.41641	+	22.8254i	−0.321542	+	0.989605i
$533$	−2.42705	−	1.76336i	−0.105127	−	0.0763794i
$534$	12.6113	+	9.16267i	0.545745	+	0.396507i
$535$	−3.21140	+	9.88367i	−0.138841	+	0.427308i
$536$	1.07047	+	3.29456i	0.0462371	+	0.142303i
$537$	9.70820	−	7.05342i	0.418940	−	0.304378i
$538$	−36.3731			−1.56815
$539$		0			0
$540$	3.00000			0.129099
$541$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$541$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$542$	−1.85410	−	5.70634i	−0.0796405	−	0.245108i
$543$	2.16312	−	6.65740i	0.0928283	−	0.285696i
$544$	7.28115	+	5.29007i	0.312177	+	0.226810i
$545$	37.8340	+	27.4880i	1.62063	+	1.17746i
$546$	−3.21140	+	9.88367i	−0.137435	+	0.422982i
$547$	−10.7047	−	32.9456i	−0.457698	−	1.40865i	−0.867938	−	0.496673i	$-0.834555\pi$
$547$	−10.7047	−	32.9456i	−0.457698	−	1.40865i	0.410240	−	0.911978i	$-0.365445\pi$
$548$	4.85410	−	3.52671i	0.207357	−	0.150654i
$549$		0			0
$550$		0			0
$551$	−12.0000			−0.511217
$552$	8.40755	−	6.10844i	0.357849	−	0.259993i
$553$		0			0
$554$	−2.78115	+	8.55951i	−0.118160	+	0.363659i
$555$	26.6976	+	19.3969i	1.13325	+	0.823353i
$556$	−8.40755	−	6.10844i	−0.356560	−	0.259056i
$557$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$557$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$558$	2.14093	+	6.58911i	0.0906329	+	0.278939i
$559$	4.85410	−	3.52671i	0.205307	−	0.149164i
$560$	−51.9615			−2.19578
$561$		0			0
$562$	−12.0000			−0.506189
$563$	−14.0126	+	10.1807i	−0.590560	+	0.429067i	−0.842516	−	0.538672i	$-0.818926\pi$
$563$	−14.0126	+	10.1807i	−0.590560	+	0.429067i	0.251956	+	0.967739i	$0.418926\pi$
$564$		0			0
$565$	19.4681	−	59.9166i	0.819028	−	2.52071i
$566$	43.6869	+	31.7404i	1.83630	+	1.33415i
$567$	2.80252	+	2.03615i	0.117695	+	0.0855102i
$568$	3.21140	−	9.88367i	0.134747	−	0.414710i
$569$	−8.56373	−	26.3565i	−0.359010	−	1.10492i	−0.953648	−	0.300926i	$-0.902704\pi$
$569$	−8.56373	−	26.3565i	−0.359010	−	1.10492i	0.594637	−	0.803994i	$-0.297296\pi$
$570$	−29.1246	+	21.1603i	−1.21990	+	0.886306i
$571$	3.46410			0.144968			0.0724841	−	0.997370i	$-0.476907\pi$
$571$	3.46410			0.144968			0.0724841	+	0.997370i	$0.476907\pi$
$572$		0			0
$573$	−12.0000			−0.501307
$574$	−8.40755	+	6.10844i	−0.350924	+	0.254962i
$575$	−7.41641	−	22.8254i	−0.309286	−	0.951883i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	−10.5172	−	7.64121i	−0.437838	−	0.318108i	0.346938	−	0.937888i	$-0.387222\pi$
$577$	−10.5172	−	7.64121i	−0.437838	−	0.318108i	−0.784775	+	0.619781i	$0.787222\pi$
$578$	19.6176	+	14.2530i	0.815985	+	0.592848i
$579$	1.60570	−	4.94183i	0.0667306	−	0.205376i
$580$	1.60570	+	4.94183i	0.0666730	+	0.205199i
$581$		0			0
$582$	12.1244			0.502571
$583$		0			0
$584$	−12.0000			−0.496564
$585$	−4.20378	+	3.05422i	−0.173805	+	0.126277i
$586$	10.1976	+	31.3849i	0.421257	+	1.29650i
$587$	−3.70820	+	11.4127i	−0.153054	+	0.471052i	−0.997959	−	0.0638654i	$-0.979657\pi$
$587$	−3.70820	+	11.4127i	−0.153054	+	0.471052i	0.844905	+	0.534917i	$0.179657\pi$
$588$	4.04508	+	2.93893i	0.166816	+	0.121199i
$589$	−22.4201	−	16.2892i	−0.923806	−	0.671184i
$590$	9.63420	−	29.6510i	0.396634	−	1.22071i
$591$	5.88756	+	18.1201i	0.242182	+	0.745360i
$592$	−44.4959	+	32.3282i	−1.82877	+	1.32868i
$593$	−22.5167			−0.924648			−0.462324	−	0.886711i	$-0.652984\pi$
$593$	−22.5167			−0.924648			−0.462324	+	0.886711i	$0.652984\pi$
$594$		0			0
$595$	18.0000			0.737928
$596$	9.80881	−	7.12652i	0.401785	−	0.291914i
$597$	−3.09017	−	9.51057i	−0.126472	−	0.389242i
$598$	5.56231	−	17.1190i	0.227460	−	0.700049i
$599$	−19.4164	−	14.1068i	−0.793333	−	0.576390i	0.115618	−	0.993294i	$-0.463115\pi$
$599$	−19.4164	−	14.1068i	−0.793333	−	0.576390i	−0.908951	+	0.416904i	$0.863115\pi$
$600$	−5.60503	−	4.07230i	−0.228825	−	0.166251i
$601$	−6.95803	+	21.4146i	−0.283824	+	0.873520i	0.702925	+	0.711264i	$0.251877\pi$
$601$	−6.95803	+	21.4146i	−0.283824	+	0.873520i	−0.986749	+	0.162256i	$0.948123\pi$
$602$	−6.42280	−	19.7673i	−0.261774	−	0.805657i
$603$	1.61803	−	1.17557i	0.0658914	−	0.0478729i
$604$	13.8564			0.563809
$605$		0			0
$606$	24.0000			0.974933
$607$	−16.8151	+	12.2169i	−0.682504	+	0.495868i	−0.874187	−	0.485589i	$-0.838605\pi$
$607$	−16.8151	+	12.2169i	−0.682504	+	0.495868i	0.191683	+	0.981457i	$0.438605\pi$
$608$	−11.1246	−	34.2380i	−0.451163	−	1.38854i
$609$	−1.85410	+	5.70634i	−0.0751320	+	0.231233i
$610$		0			0
$611$		0			0
$612$	0.535233	−	1.64728i	0.0216355	−	0.0665873i
$613$	5.88756	+	18.1201i	0.237796	+	0.731862i	0.996738	+	0.0807037i	$0.0257168\pi$
$613$	5.88756	+	18.1201i	0.237796	+	0.731862i	−0.758942	+	0.651159i	$0.774283\pi$
$614$	−4.85410	+	3.52671i	−0.195896	+	0.142326i
$615$	−5.19615			−0.209529
$616$		0			0
$617$	−9.00000			−0.362326			−0.181163	−	0.983453i	$-0.557986\pi$
$617$	−9.00000			−0.362326			−0.181163	+	0.983453i	$0.557986\pi$
$618$	19.6176	−	14.2530i	0.789136	−	0.573341i
$619$	−3.09017	−	9.51057i	−0.124204	−	0.382262i	0.869551	−	0.493843i	$-0.164408\pi$
$619$	−3.09017	−	9.51057i	−0.124204	−	0.382262i	−0.993755	+	0.111581i	$0.964408\pi$
$620$	−3.70820	+	11.4127i	−0.148925	+	0.458344i
$621$	−4.85410	−	3.52671i	−0.194788	−	0.141522i
$622$	−16.8151	−	12.2169i	−0.674224	−	0.489853i
$623$	−9.63420	+	29.6510i	−0.385986	+	1.18794i
$624$	−2.67617	−	8.23639i	−0.107132	−	0.329720i
$625$	23.4615	−	17.0458i	0.938460	−	0.681831i
$626$	12.1244			0.484587
$627$		0			0
$628$	−14.0000			−0.558661
$629$	15.4138	−	11.1988i	0.614590	−	0.446526i
$630$	5.56231	+	17.1190i	0.221608	+	0.682038i
$631$	−4.32624	+	13.3148i	−0.172225	+	0.530053i	−0.999496	−	0.0317495i	$-0.989892\pi$
$631$	−4.32624	+	13.3148i	−0.172225	+	0.530053i	0.827271	+	0.561803i	$0.189892\pi$
$632$		0			0
$633$	−14.0126	−	10.1807i	−0.556950	−	0.404648i
$634$	3.21140	−	9.88367i	0.127541	−	0.392531i
$635$		0			0
$636$	−7.28115	+	5.29007i	−0.288716	+	0.209765i
$637$	−8.66025			−0.343132
$638$		0			0
$639$	−6.00000			−0.237356
$640$	29.4264	−	21.3796i	1.16318	−	0.845101i
$641$	−4.63525	−	14.2658i	−0.183082	−	0.563467i	0.816828	−	0.576881i	$-0.195730\pi$
$641$	−4.63525	−	14.2658i	−0.183082	−	0.563467i	−0.999910	+	0.0134135i	$0.995730\pi$
$642$	−1.85410	+	5.70634i	−0.0731756	+	0.225211i
$643$	12.9443	+	9.40456i	0.510472	+	0.370880i	0.813003	−	0.582260i	$-0.197831\pi$
$643$	12.9443	+	9.40456i	0.510472	+	0.370880i	−0.302530	+	0.953140i	$0.597831\pi$
$644$	−16.8151	−	12.2169i	−0.662608	−	0.481413i
$645$	3.21140	−	9.88367i	0.126449	−	0.389169i
$646$	6.42280	+	19.7673i	0.252702	+	0.777736i
$647$	9.70820	−	7.05342i	0.381669	−	0.277299i	−0.380364	−	0.924837i	$-0.624201\pi$
$647$	9.70820	−	7.05342i	0.381669	−	0.277299i	0.762033	+	0.647538i	$0.224201\pi$
$648$	−1.73205			−0.0680414
$649$		0			0
$650$	−12.0000			−0.470679
$651$	−11.2101	+	8.14459i	−0.439357	+	0.319212i
$652$	0.618034	+	1.90211i	0.0242041	+	0.0744925i
$653$	−9.27051	+	28.5317i	−0.362783	+	1.11653i	0.588575	+	0.808443i	$0.299689\pi$
$653$	−9.27051	+	28.5317i	−0.362783	+	1.11653i	−0.951358	+	0.308089i	$0.900311\pi$
$654$	21.8435	+	15.8702i	0.854147	+	0.620574i
$655$	−42.0378	−	30.5422i	−1.64255	−	1.19338i
$656$	2.67617	−	8.23639i	0.104487	−	0.321577i
$657$	2.14093	+	6.58911i	0.0835257	+	0.257066i
$658$		0			0
$659$	13.8564			0.539769			0.269884	−	0.962893i	$-0.413014\pi$
$659$	13.8564			0.539769			0.269884	+	0.962893i	$0.413014\pi$
$660$		0			0
$661$	−41.0000			−1.59472			−0.797358	−	0.603507i	$-0.793769\pi$
$661$	−41.0000			−1.59472			−0.797358	+	0.603507i	$0.793769\pi$
$662$	−28.0252	+	20.3615i	−1.08923	+	0.791371i
$663$	0.927051	+	2.85317i	0.0360037	+	0.110808i
$664$		0			0
$665$	−58.2492	−	42.3205i	−2.25881	−	1.64112i
$666$	15.4138	+	11.1988i	0.597274	+	0.433945i
$667$	3.21140	−	9.88367i	0.124346	−	0.382697i
$668$	−1.07047	−	3.29456i	−0.0414176	−	0.127470i
$669$	16.1803	−	11.7557i	0.625568	−	0.454502i
$670$	10.3923			0.401490
$671$		0			0
$672$	−18.0000			−0.694365
$673$	16.8151	−	12.2169i	0.648175	−	0.470926i	−0.214474	−	0.976730i	$-0.568804\pi$
$673$	16.8151	−	12.2169i	0.648175	−	0.470926i	0.862649	+	0.505803i	$0.168804\pi$
$674$	−6.48936	−	19.9722i	−0.249961	−	0.769300i
$675$	−1.23607	+	3.80423i	−0.0475763	+	0.146425i
$676$	8.09017	+	5.87785i	0.311160	+	0.226071i
$677$	−26.6239	−	19.3434i	−1.02324	−	0.743427i	−0.0562955	−	0.998414i	$-0.517929\pi$
$677$	−26.6239	−	19.3434i	−1.02324	−	0.743427i	−0.966945	+	0.254987i	$0.917929\pi$
$678$	11.2399	−	34.5928i	0.431666	−	1.32853i
$679$	7.49326	+	23.0619i	0.287565	+	0.885034i
$680$	−7.28115	+	5.29007i	−0.279219	+	0.202865i
$681$	24.2487			0.929213
$682$		0			0
$683$	−6.00000			−0.229584			−0.114792	−	0.993390i	$-0.536620\pi$
$683$	−6.00000			−0.229584			−0.114792	+	0.993390i	$0.536620\pi$
$684$	−5.60503	+	4.07230i	−0.214314	+	0.155708i
$685$	5.56231	+	17.1190i	0.212525	+	0.654084i
$686$	3.70820	−	11.4127i	0.141580	−	0.435738i
$687$	−18.6074	−	13.5191i	−0.709916	−	0.515784i
$688$	14.0126	+	10.1807i	0.534225	+	0.388137i
$689$	4.81710	−	14.8255i	0.183517	−	0.564807i
$690$	−9.63420	−	29.6510i	−0.366768	−	1.12879i
$691$	8.09017	−	5.87785i	0.307765	−	0.223604i	−0.423172	−	0.906049i	$-0.639083\pi$
$691$	8.09017	−	5.87785i	0.307765	−	0.223604i	0.730937	+	0.682445i	$0.239083\pi$
$692$	20.7846			0.790112
$693$		0			0
$694$	48.0000			1.82206
$695$	25.2227	−	18.3253i	0.956750	−	0.695119i
$696$	−0.927051	−	2.85317i	−0.0351398	−	0.108149i
$697$	−0.927051	+	2.85317i	−0.0351146	+	0.108072i
$698$	2.42705	+	1.76336i	0.0918652	+	0.0667440i
$699$	23.8214	+	17.3073i	0.901008	+	0.654621i
$700$	−4.28187	+	13.1782i	−0.161839	+	0.498090i
$701$	−12.3104	−	37.8874i	−0.464956	−	1.43099i	−0.859038	−	0.511912i	$-0.828937\pi$
$701$	−12.3104	−	37.8874i	−0.464956	−	1.43099i	0.394082	−	0.919075i	$-0.371063\pi$
$702$	−2.42705	+	1.76336i	−0.0916031	+	0.0665536i
$703$	−76.2102			−2.87432
$704$		0			0
$705$		0			0
$706$	−29.4264	+	21.3796i	−1.10748	+	0.804630i
$707$	14.8328	+	45.6507i	0.557845	+	1.71687i
$708$	1.85410	−	5.70634i	0.0696814	−	0.214457i
$709$	−17.7984	−	12.9313i	−0.668432	−	0.485644i	0.201068	−	0.979577i	$-0.435559\pi$
$709$	−17.7984	−	12.9313i	−0.668432	−	0.485644i	−0.869500	+	0.493933i	$0.835559\pi$
$710$	−25.2227	−	18.3253i	−0.946589	−	0.687737i
$711$		0			0
$712$	−4.81710	−	14.8255i	−0.180528	−	0.555609i
$713$	19.4164	−	14.1068i	0.727150	−	0.528306i
$714$	10.3923			0.388922
$715$		0			0
$716$	12.0000			0.448461
$717$	−5.60503	+	4.07230i	−0.209324	+	0.152083i
$718$	16.6869	+	51.3571i	0.622750	+	1.91663i
$719$	−9.27051	+	28.5317i	−0.345732	+	1.06405i	0.615459	+	0.788169i	$0.288971\pi$
$719$	−9.27051	+	28.5317i	−0.345732	+	1.06405i	−0.961191	+	0.275884i	$0.911029\pi$
$720$	−12.1353	−	8.81678i	−0.452254	−	0.328582i
$721$	39.2352	+	28.5061i	1.46120	+	1.06162i
$722$	15.5218	−	47.7711i	0.577660	−	1.77786i
$723$	6.42280	+	19.7673i	0.238866	+	0.735155i
$724$	5.66312	−	4.11450i	0.210468	−	0.152914i
$725$	−6.92820			−0.257307
$726$		0			0
$727$	−2.00000			−0.0741759			−0.0370879	−	0.999312i	$-0.511808\pi$
$727$	−2.00000			−0.0741759			−0.0370879	+	0.999312i	$0.511808\pi$
$728$	8.40755	−	6.10844i	0.311605	−	0.226394i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−11.1246	+	34.2380i	−0.411740	+	1.26721i
$731$	−4.85410	−	3.52671i	−0.179535	−	0.130440i
$732$		0			0
$733$	2.67617	−	8.23639i	0.0988464	−	0.304218i	−0.889391	−	0.457148i	$-0.848871\pi$
$733$	2.67617	−	8.23639i	0.0988464	−	0.304218i	0.988237	+	0.152930i	$0.0488709\pi$
$734$	13.9161	+	42.8292i	0.513651	+	1.58086i
$735$	−12.1353	+	8.81678i	−0.447616	+	0.325212i
$736$	31.1769			1.14920
$737$		0			0
$738$	−3.00000			−0.110432
$739$	22.4201	−	16.2892i	0.824738	−	0.599207i	−0.0933277	−	0.995635i	$-0.529750\pi$
$739$	22.4201	−	16.2892i	0.824738	−	0.599207i	0.918066	+	0.396428i	$0.129750\pi$
$740$	10.1976	+	31.3849i	0.374870	+	1.15373i
$741$	3.70820	−	11.4127i	0.136224	−	0.419255i
$742$	−43.6869	−	31.7404i	−1.60380	−	1.16523i
$743$	42.0378	+	30.5422i	1.54222	+	1.12049i	0.948927	+	0.315495i	$0.102171\pi$
$743$	42.0378	+	30.5422i	1.54222	+	1.12049i	0.593289	+	0.804990i	$0.297829\pi$
$744$	2.14093	−	6.58911i	0.0784904	−	0.241569i
$745$	11.2399	+	34.5928i	0.411798	+	1.26738i
$746$	−29.1246	+	21.1603i	−1.06633	+	0.774732i
$747$		0			0
$748$		0			0
$749$	−12.0000			−0.438470
$750$	4.20378	−	3.05422i	0.153500	−	0.111524i
$751$	−0.618034	−	1.90211i	−0.0225524	−	0.0694091i	0.939147	−	0.343516i	$-0.111618\pi$
$751$	−0.618034	−	1.90211i	−0.0225524	−	0.0694091i	−0.961699	+	0.274107i	$0.911618\pi$
$752$		0			0
$753$	−4.85410	−	3.52671i	−0.176893	−	0.128521i
$754$	−4.20378	−	3.05422i	−0.153092	−	0.111228i
$755$	−12.8456	+	39.5347i	−0.467499	+	1.43881i
$756$	1.07047	+	3.29456i	0.0389325	+	0.119822i
$757$	13.7533	−	9.99235i	0.499872	−	0.363178i	−0.309096	−	0.951031i	$-0.600027\pi$
$757$	13.7533	−	9.99235i	0.499872	−	0.363178i	0.808968	+	0.587853i	$0.200027\pi$
$758$	24.2487			0.880753
$759$		0			0
$760$	36.0000			1.30586
$761$	−26.6239	+	19.3434i	−0.965116	+	0.701198i	−0.954333	−	0.298744i	$-0.903432\pi$
$761$	−26.6239	+	19.3434i	−0.965116	+	0.701198i	−0.0107828	+	0.999942i	$0.503432\pi$
$762$		0			0
$763$	−16.6869	+	51.3571i	−0.604107	+	1.85925i
$764$	−9.70820	−	7.05342i	−0.351230	−	0.255184i
$765$	4.20378	+	3.05422i	0.151988	+	0.110426i
$766$	3.21140	−	9.88367i	0.116033	−	0.357111i
$767$	3.21140	+	9.88367i	0.115957	+	0.356879i
$768$	15.3713	−	11.1679i	0.554665	−	0.402988i
$769$	25.9808			0.936890			0.468445	−	0.883493i	$-0.344814\pi$
$769$	25.9808			0.936890			0.468445	+	0.883493i	$0.344814\pi$
$770$		0			0
$771$	−9.00000			−0.324127
$772$	4.20378	−	3.05422i	0.151297	−	0.109924i
$773$	5.56231	+	17.1190i	0.200062	+	0.615728i	0.999880	+	0.0154855i	$0.00492938\pi$
$773$	5.56231	+	17.1190i	0.200062	+	0.615728i	−0.799818	+	0.600243i	$0.795071\pi$
$774$	1.85410	−	5.70634i	0.0666443	−	0.205110i
$775$	−12.9443	−	9.40456i

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.40126 + 1.01807i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.42705 + 1.76336i) q^{5} +(1.40126 + 1.01807i) q^{6} +(-1.07047 + 3.29456i) q^{7} +(-0.535233 - 1.64728i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.40126 + 1.01807i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.42705 + 1.76336i) q^{5} +(1.40126 + 1.01807i) q^{6} +(-1.07047 + 3.29456i) q^{7} +(-0.535233 - 1.64728i) q^{8} +(-0.809017 + 0.587785i) q^{9} -5.19615 q^{10} -1.00000 q^{12} +(1.40126 - 1.01807i) q^{13} +(-1.85410 - 5.70634i) q^{14} +(0.927051 - 2.85317i) q^{15} +(4.04508 + 2.93893i) q^{16} +(-1.40126 - 1.01807i) q^{17} +(0.535233 - 1.64728i) q^{18} +(2.14093 + 6.58911i) q^{19} +(2.42705 - 1.76336i) q^{20} +3.46410 q^{21} -6.00000 q^{23} +(-1.40126 + 1.01807i) q^{24} +(1.23607 + 3.80423i) q^{25} +(-0.927051 + 2.85317i) q^{26} +(0.809017 + 0.587785i) q^{27} +(2.80252 + 2.03615i) q^{28} +(-0.535233 + 1.64728i) q^{29} +(1.60570 + 4.94183i) q^{30} +(-3.23607 + 2.35114i) q^{31} -5.19615 q^{32} +3.00000 q^{34} +(-8.40755 + 6.10844i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-3.39919 + 10.4616i) q^{37} +(-9.70820 - 7.05342i) q^{38} +(-1.40126 - 1.01807i) q^{39} +(1.60570 - 4.94183i) q^{40} +(-0.535233 - 1.64728i) q^{41} +(-4.85410 + 3.52671i) q^{42} +3.46410 q^{43} -3.00000 q^{45} +(8.40755 - 6.10844i) q^{46} +(1.54508 - 4.75528i) q^{48} +(-4.04508 - 2.93893i) q^{49} +(-5.60503 - 4.07230i) q^{50} +(-0.535233 + 1.64728i) q^{51} +(-0.535233 - 1.64728i) q^{52} +(7.28115 - 5.29007i) q^{53} -1.73205 q^{54} +6.00000 q^{56} +(5.60503 - 4.07230i) q^{57} +(-0.927051 - 2.85317i) q^{58} +(-1.85410 + 5.70634i) q^{59} +(-2.42705 - 1.76336i) q^{60} +(2.14093 - 6.58911i) q^{62} +(-1.07047 - 3.29456i) q^{63} +(-0.809017 + 0.587785i) q^{64} +5.19615 q^{65} -2.00000 q^{67} +(-1.40126 + 1.01807i) q^{68} +(1.85410 + 5.70634i) q^{69} +(5.56231 - 17.1190i) q^{70} +(4.85410 + 3.52671i) q^{71} +(1.40126 + 1.01807i) q^{72} +(2.14093 - 6.58911i) q^{73} +(-5.88756 - 18.1201i) q^{74} +(3.23607 - 2.35114i) q^{75} +6.92820 q^{76} +3.00000 q^{78} +(4.63525 + 14.2658i) q^{80} +(0.309017 - 0.951057i) q^{81} +(2.42705 + 1.76336i) q^{82} +(1.07047 - 3.29456i) q^{84} +(-1.60570 - 4.94183i) q^{85} +(-4.85410 + 3.52671i) q^{86} +1.73205 q^{87} +9.00000 q^{89} +(4.20378 - 3.05422i) q^{90} +(1.85410 + 5.70634i) q^{91} +(-1.85410 + 5.70634i) q^{92} +(3.23607 + 2.35114i) q^{93} +(-6.42280 + 19.7673i) q^{95} +(1.60570 + 4.94183i) q^{96} +(5.66312 - 4.11450i) q^{97} +8.66025 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 2 q^{4} + 6 q^{5} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 - 2 * q^4 + 6 * q^5 - 2 * q^9	\( 8 q + 2 q^{3} - 2 q^{4} + 6 q^{5} - 2 q^{9} - 8 q^{12} + 12 q^{14} - 6 q^{15} + 10 q^{16} + 6 q^{20} - 48 q^{23} - 8 q^{25} + 6 q^{26} + 2 q^{27} - 8 q^{31} + 24 q^{34} - 2 q^{36} + 22 q^{37} - 24 q^{38} - 12 q^{42} - 24 q^{45} - 10 q^{48} - 10 q^{49} + 18 q^{53} + 48 q^{56} + 6 q^{58} + 12 q^{59} - 6 q^{60} - 2 q^{64} - 16 q^{67} - 12 q^{69} - 36 q^{70} + 12 q^{71} + 8 q^{75} + 24 q^{78} - 30 q^{80} - 2 q^{81} + 6 q^{82} - 12 q^{86} + 72 q^{89} - 12 q^{91} + 12 q^{92} + 8 q^{93} + 14 q^{97}+O(q^{100}) \) 8 * q + 2 * q^3 - 2 * q^4 + 6 * q^5 - 2 * q^9 - 8 * q^12 + 12 * q^14 - 6 * q^15 + 10 * q^16 + 6 * q^20 - 48 * q^23 - 8 * q^25 + 6 * q^26 + 2 * q^27 - 8 * q^31 + 24 * q^34 - 2 * q^36 + 22 * q^37 - 24 * q^38 - 12 * q^42 - 24 * q^45 - 10 * q^48 - 10 * q^49 + 18 * q^53 + 48 * q^56 + 6 * q^58 + 12 * q^59 - 6 * q^60 - 2 * q^64 - 16 * q^67 - 12 * q^69 - 36 * q^70 + 12 * q^71 + 8 * q^75 + 24 * q^78 - 30 * q^80 - 2 * q^81 + 6 * q^82 - 12 * q^86 + 72 * q^89 - 12 * q^91 + 12 * q^92 + 8 * q^93 + 14 * q^97

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