LMFDB - Embedded newform 1242.2.e.b.415.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1242,2,Mod(415,1242)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1242, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1242.415");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1242 = 2 \cdot 3^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1242.e (of order $3$, degree $2$, 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:	$9.91741993104$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 414)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			415.3
Root			$0.827154 - 1.43267i$ of defining polynomial
Character	$\chi$	$=$	1242.415
Dual form			1242.2.e.b.829.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.217761 + 0.377174i) q^{5} +(2.31474 + 4.00925i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.217761 + 0.377174i) q^{5} +(2.31474 + 4.00925i) q^{7} +1.00000 q^{8} +0.435523 q^{10} +(-2.10068 - 3.63849i) q^{11} +(1.60224 - 2.77517i) q^{13} +(2.31474 - 4.00925i) q^{14} +(-0.500000 - 0.866025i) q^{16} +5.97604 q^{17} -6.45604 q^{19} +(-0.217761 - 0.377174i) q^{20} +(-2.10068 + 3.63849i) q^{22} +(0.500000 - 0.866025i) q^{23} +(2.40516 + 4.16586i) q^{25} -3.20449 q^{26} -4.62948 q^{28} +(1.77412 + 3.07286i) q^{29} +(2.03777 - 3.52952i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.98802 - 5.17540i) q^{34} -2.01624 q^{35} +7.64429 q^{37} +(3.22802 + 5.59110i) q^{38} +(-0.217761 + 0.377174i) q^{40} +(-1.97990 + 3.42928i) q^{41} +(6.28438 + 10.8849i) q^{43} +4.20136 q^{44} -1.00000 q^{46} +(4.71761 + 8.17113i) q^{47} +(-7.21604 + 12.4986i) q^{49} +(2.40516 - 4.16586i) q^{50} +(1.60224 + 2.77517i) q^{52} -0.713953 q^{53} +1.82979 q^{55} +(2.31474 + 4.00925i) q^{56} +(1.77412 - 3.07286i) q^{58} +(1.06162 - 1.83878i) q^{59} +(4.20052 + 7.27551i) q^{61} -4.07554 q^{62} +1.00000 q^{64} +(0.697814 + 1.20865i) q^{65} +(2.31474 - 4.00925i) q^{67} +(-2.98802 + 5.17540i) q^{68} +(1.00812 + 1.74612i) q^{70} -7.53311 q^{71} +11.5243 q^{73} +(-3.82214 - 6.62015i) q^{74} +(3.22802 - 5.59110i) q^{76} +(9.72506 - 16.8443i) q^{77} +(-3.42225 - 5.92751i) q^{79} +0.435523 q^{80} +3.95980 q^{82} +(-3.57688 - 6.19533i) q^{83} +(-1.30135 + 2.25401i) q^{85} +(6.28438 - 10.8849i) q^{86} +(-2.10068 - 3.63849i) q^{88} -10.8502 q^{89} +14.8351 q^{91} +(0.500000 + 0.866025i) q^{92} +(4.71761 - 8.17113i) q^{94} +(1.40588 - 2.43505i) q^{95} +(3.77412 + 6.53696i) q^{97} +14.4321 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - 5 q^{4} + q^{5} + 5 q^{7} + 10 q^{8}+O(q^{10}) $ 10 * q - 5 * q^2 - 5 * q^4 + q^5 + 5 * q^7 + 10 * q^8	$ 10 q - 5 q^{2} - 5 q^{4} + q^{5} + 5 q^{7} + 10 q^{8} - 2 q^{10} + 11 q^{11} + 6 q^{13} + 5 q^{14} - 5 q^{16} - 2 q^{17} - 6 q^{19} + q^{20} + 11 q^{22} + 5 q^{23} - 12 q^{26} - 10 q^{28} + 8 q^{29} + 4 q^{31} - 5 q^{32} + q^{34} - 46 q^{35} - 28 q^{37} + 3 q^{38} + q^{40} + 24 q^{41} + 27 q^{43} - 22 q^{44} - 10 q^{46} + 9 q^{47} - 12 q^{49} + 6 q^{52} + 26 q^{53} + 16 q^{55} + 5 q^{56} + 8 q^{58} + 9 q^{59} + 3 q^{61} - 8 q^{62} + 10 q^{64} - 5 q^{65} + 5 q^{67} + q^{68} + 23 q^{70} - 54 q^{71} + 34 q^{73} + 14 q^{74} + 3 q^{76} + 13 q^{77} - 11 q^{79} - 2 q^{80} - 48 q^{82} + 23 q^{83} + 23 q^{85} + 27 q^{86} + 11 q^{88} - 78 q^{89} - 30 q^{91} + 5 q^{92} + 9 q^{94} + 37 q^{95} + 28 q^{97} + 24 q^{98}+O(q^{100}) $ 10 * q - 5 * q^2 - 5 * q^4 + q^5 + 5 * q^7 + 10 * q^8 - 2 * q^10 + 11 * q^11 + 6 * q^13 + 5 * q^14 - 5 * q^16 - 2 * q^17 - 6 * q^19 + q^20 + 11 * q^22 + 5 * q^23 - 12 * q^26 - 10 * q^28 + 8 * q^29 + 4 * q^31 - 5 * q^32 + q^34 - 46 * q^35 - 28 * q^37 + 3 * q^38 + q^40 + 24 * q^41 + 27 * q^43 - 22 * q^44 - 10 * q^46 + 9 * q^47 - 12 * q^49 + 6 * q^52 + 26 * q^53 + 16 * q^55 + 5 * q^56 + 8 * q^58 + 9 * q^59 + 3 * q^61 - 8 * q^62 + 10 * q^64 - 5 * q^65 + 5 * q^67 + q^68 + 23 * q^70 - 54 * q^71 + 34 * q^73 + 14 * q^74 + 3 * q^76 + 13 * q^77 - 11 * q^79 - 2 * q^80 - 48 * q^82 + 23 * q^83 + 23 * q^85 + 27 * q^86 + 11 * q^88 - 78 * q^89 - 30 * q^91 + 5 * q^92 + 9 * q^94 + 37 * q^95 + 28 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1242\mathbb{Z}\right)^\times$.

$n$	$461$	$649$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.217761	+	0.377174i	−0.0973859	+	0.168677i	−0.910602	−	0.413285i	$-0.864381\pi$
$5$	−0.217761	+	0.377174i	−0.0973859	+	0.168677i	0.813216	+	0.581962i	$0.197715\pi$
$6$		0			0
$7$	2.31474	+	4.00925i	0.874889	+	1.51535i	0.856880	+	0.515515i	$0.172399\pi$
$7$	2.31474	+	4.00925i	0.874889	+	1.51535i	0.0180091	+	0.999838i	$0.494267\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	0.435523			0.137724
$11$	−2.10068	−	3.63849i	−0.633379	−	1.09704i	−0.986856	−	0.161602i	$-0.948334\pi$
$11$	−2.10068	−	3.63849i	−0.633379	−	1.09704i	0.353477	−	0.935443i	$-0.384999\pi$
$12$		0			0
$13$	1.60224	−	2.77517i	0.444383	−	0.769693i	−0.553626	−	0.832765i	$-0.686756\pi$
$13$	1.60224	−	2.77517i	0.444383	−	0.769693i	0.998009	+	0.0630718i	$0.0200897\pi$
$14$	2.31474	−	4.00925i	0.618640	−	1.07152i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	5.97604			1.44940			0.724701	−	0.689063i	$-0.241978\pi$
$17$	5.97604			1.44940			0.724701	+	0.689063i	$0.241978\pi$
$18$		0			0
$19$	−6.45604			−1.48112			−0.740559	−	0.671991i	$-0.765439\pi$
$19$	−6.45604			−1.48112			−0.740559	+	0.671991i	$0.765439\pi$
$20$	−0.217761	−	0.377174i	−0.0486930	−	0.0843387i
$21$		0			0
$22$	−2.10068	+	3.63849i	−0.447867	+	0.775728i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$24$		0			0
$25$	2.40516	+	4.16586i	0.481032	+	0.833172i
$26$	−3.20449			−0.628452
$27$		0			0
$28$	−4.62948			−0.874889
$29$	1.77412	+	3.07286i	0.329445	+	0.570616i	0.982402	−	0.186780i	$-0.0598050\pi$
$29$	1.77412	+	3.07286i	0.329445	+	0.570616i	−0.652957	+	0.757395i	$0.726472\pi$
$30$		0			0
$31$	2.03777	−	3.52952i	0.365994	−	0.633920i	−0.622941	−	0.782269i	$-0.714062\pi$
$31$	2.03777	−	3.52952i	0.365994	−	0.633920i	0.988935	+	0.148349i	$0.0473958\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−2.98802	−	5.17540i	−0.512441	−	0.887574i
$35$	−2.01624			−0.340808
$36$		0			0
$37$	7.64429			1.25671			0.628357	−	0.777925i	$-0.283728\pi$
$37$	7.64429			1.25671			0.628357	+	0.777925i	$0.283728\pi$
$38$	3.22802	+	5.59110i	0.523654	+	0.906996i
$39$		0			0
$40$	−0.217761	+	0.377174i	−0.0344311	+	0.0596364i
$41$	−1.97990	+	3.42928i	−0.309208	+	0.535564i	−0.978189	−	0.207715i	$-0.933397\pi$
$41$	−1.97990	+	3.42928i	−0.309208	+	0.535564i	0.668981	+	0.743279i	$0.266731\pi$
$42$		0			0
$43$	6.28438	+	10.8849i	0.958358	+	1.65993i	0.726488	+	0.687179i	$0.241151\pi$
$43$	6.28438	+	10.8849i	0.958358	+	1.65993i	0.231870	+	0.972747i	$0.425516\pi$
$44$	4.20136			0.633379
$45$		0			0
$46$	−1.00000			−0.147442
$47$	4.71761	+	8.17113i	0.688134	+	1.19188i	0.972441	+	0.233149i	$0.0749031\pi$
$47$	4.71761	+	8.17113i	0.688134	+	1.19188i	−0.284307	+	0.958733i	$0.591764\pi$
$48$		0			0
$49$	−7.21604	+	12.4986i	−1.03086	+	1.78551i
$50$	2.40516	−	4.16586i	0.340141	−	0.589141i
$51$		0			0
$52$	1.60224	+	2.77517i	0.222191	+	0.384847i
$53$	−0.713953			−0.0980690			−0.0490345	−	0.998797i	$-0.515614\pi$
$53$	−0.713953			−0.0980690			−0.0490345	+	0.998797i	$0.515614\pi$
$54$		0			0
$55$	1.82979			0.246729
$56$	2.31474	+	4.00925i	0.309320	+	0.535758i
$57$		0			0
$58$	1.77412	−	3.07286i	0.232953	−	0.403486i
$59$	1.06162	−	1.83878i	0.138211	−	0.239389i	−0.788608	−	0.614896i	$-0.789198\pi$
$59$	1.06162	−	1.83878i	0.138211	−	0.239389i	0.926820	+	0.375507i	$0.122531\pi$
$60$		0			0
$61$	4.20052	+	7.27551i	0.537821	+	0.931533i	0.999021	+	0.0442370i	$0.0140857\pi$
$61$	4.20052	+	7.27551i	0.537821	+	0.931533i	−0.461200	+	0.887296i	$0.652581\pi$
$62$	−4.07554			−0.517593
$63$		0			0
$64$	1.00000			0.125000
$65$	0.697814	+	1.20865i	0.0865532	+	0.149915i
$66$		0			0
$67$	2.31474	−	4.00925i	0.282790	−	0.489808i	−0.689280	−	0.724495i	$-0.742073\pi$
$67$	2.31474	−	4.00925i	0.282790	−	0.489808i	0.972071	+	0.234687i	$0.0754065\pi$
$68$	−2.98802	+	5.17540i	−0.362351	+	0.627610i
$69$		0			0
$70$	1.00812	+	1.74612i	0.120494	+	0.208701i
$71$	−7.53311			−0.894016			−0.447008	−	0.894530i	$-0.647510\pi$
$71$	−7.53311			−0.894016			−0.447008	+	0.894530i	$0.647510\pi$
$72$		0			0
$73$	11.5243			1.34881			0.674407	−	0.738360i	$-0.264399\pi$
$73$	11.5243			1.34881			0.674407	+	0.738360i	$0.264399\pi$
$74$	−3.82214	−	6.62015i	−0.444315	−	0.769577i
$75$		0			0
$76$	3.22802	−	5.59110i	0.370280	−	0.641343i
$77$	9.72506	−	16.8443i	1.10827	−	1.91959i
$78$		0			0
$79$	−3.42225	−	5.92751i	−0.385033	−	0.666897i	0.606741	−	0.794900i	$-0.292477\pi$
$79$	−3.42225	−	5.92751i	−0.385033	−	0.666897i	−0.991774	+	0.128003i	$0.959143\pi$
$80$	0.435523			0.0486930
$81$		0			0
$82$	3.95980			0.437286
$83$	−3.57688	−	6.19533i	−0.392613	−	0.680026i	0.600180	−	0.799865i	$-0.295096\pi$
$83$	−3.57688	−	6.19533i	−0.392613	−	0.680026i	−0.992793	+	0.119839i	$0.961762\pi$
$84$		0			0
$85$	−1.30135	+	2.25401i	−0.141151	+	0.244481i
$86$	6.28438	−	10.8849i	0.677662	−	1.17374i
$87$		0			0
$88$	−2.10068	−	3.63849i	−0.223933	−	0.387864i
$89$	−10.8502			−1.15012			−0.575060	−	0.818111i	$-0.695021\pi$
$89$	−10.8502			−1.15012			−0.575060	+	0.818111i	$0.695021\pi$
$90$		0			0
$91$	14.8351			1.55514
$92$	0.500000	+	0.866025i	0.0521286	+	0.0902894i
$93$		0			0
$94$	4.71761	−	8.17113i	0.486584	−	0.842788i
$95$	1.40588	−	2.43505i	0.144240	−	0.249831i
$96$		0			0
$97$	3.77412	+	6.53696i	0.383203	+	0.663728i	0.991518	−	0.129968i	$-0.0414875\pi$
$97$	3.77412	+	6.53696i	0.383203	+	0.663728i	−0.608315	+	0.793696i	$0.708154\pi$
$98$	14.4321			1.45786
$99$		0			0
$100$	−4.81032			−0.481032
$101$	0.371813	+	0.643998i	0.0369967	+	0.0640802i	0.883931	−	0.467618i	$-0.154888\pi$
$101$	0.371813	+	0.643998i	0.0369967	+	0.0640802i	−0.846934	+	0.531698i	$0.821554\pi$
$102$		0			0
$103$	6.35827	−	11.0128i	0.626499	−	1.08513i	−0.361750	−	0.932275i	$-0.617821\pi$
$103$	6.35827	−	11.0128i	0.626499	−	1.08513i	0.988249	−	0.152853i	$-0.0488460\pi$
$104$	1.60224	−	2.77517i	0.157113	−	0.272128i
$105$		0			0
$106$	0.356976	+	0.618301i	0.0346726	+	0.0600547i
$107$	7.41469			0.716805			0.358403	−	0.933567i	$-0.383322\pi$
$107$	7.41469			0.716805			0.358403	+	0.933567i	$0.383322\pi$
$108$		0			0
$109$	−14.8914			−1.42633			−0.713167	−	0.700995i	$-0.752740\pi$
$109$	−14.8914			−1.42633			−0.713167	+	0.700995i	$0.752740\pi$
$110$	−0.914895	−	1.58464i	−0.0872318	−	0.151090i
$111$		0			0
$112$	2.31474	−	4.00925i	0.218722	−	0.378838i
$113$	−6.46792	+	11.2028i	−0.608451	+	1.05387i	0.383045	+	0.923730i	$0.374875\pi$
$113$	−6.46792	+	11.2028i	−0.608451	+	1.05387i	−0.991496	+	0.130138i	$0.958458\pi$
$114$		0			0
$115$	0.217761	+	0.377174i	0.0203064	+	0.0351717i
$116$	−3.54823			−0.329445
$117$		0			0
$118$	−2.12324			−0.195460
$119$	13.8330	+	23.9594i	1.26807	+	2.19636i
$120$		0			0
$121$	−3.32572	+	5.76031i	−0.302338	+	0.523665i
$122$	4.20052	−	7.27551i	0.380297	−	0.658693i
$123$		0			0
$124$	2.03777	+	3.52952i	0.182997	+	0.316960i
$125$	−4.27262			−0.382155
$126$		0			0
$127$	7.43240			0.659518			0.329759	−	0.944065i	$-0.393032\pi$
$127$	7.43240			0.659518			0.329759	+	0.944065i	$0.393032\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	0.697814	−	1.20865i	0.0612024	−	0.106006i
$131$	7.23302	−	12.5280i	0.631952	−	1.09457i	−0.355201	−	0.934790i	$-0.615587\pi$
$131$	7.23302	−	12.5280i	0.631952	−	1.09457i	0.987152	−	0.159782i	$-0.0510792\pi$
$132$		0			0
$133$	−14.9441	−	25.8839i	−1.29581	−	2.24442i
$134$	−4.62948			−0.399926
$135$		0			0
$136$	5.97604			0.512441
$137$	9.39974	+	16.2808i	0.803074	+	1.39096i	0.917584	+	0.397543i	$0.130137\pi$
$137$	9.39974	+	16.2808i	0.803074	+	1.39096i	−0.114510	+	0.993422i	$0.536530\pi$
$138$		0			0
$139$	2.03255	−	3.52048i	0.172399	−	0.298603i	−0.766859	−	0.641815i	$-0.778182\pi$
$139$	2.03255	−	3.52048i	0.172399	−	0.298603i	0.939258	+	0.343212i	$0.111515\pi$
$140$	1.00812	−	1.74612i	0.0852019	−	0.147574i
$141$		0			0
$142$	3.76656	+	6.52387i	0.316082	+	0.547471i
$143$	−13.4632			−1.12585
$144$		0			0
$145$	−1.54534			−0.128333
$146$	−5.76214	−	9.98031i	−0.476878	−	0.825977i
$147$		0			0
$148$	−3.82214	+	6.62015i	−0.314178	+	0.544173i
$149$	6.07929	−	10.5296i	0.498035	−	0.862621i	−0.501963	−	0.864889i	$-0.667389\pi$
$149$	6.07929	−	10.5296i	0.498035	−	0.862621i	0.999997	+	0.00226808i	$0.000721952\pi$
$150$		0			0
$151$	5.08214	+	8.80253i	0.413579	+	0.716340i	0.995278	−	0.0970643i	$-0.0309453\pi$
$151$	5.08214	+	8.80253i	0.413579	+	0.716340i	−0.581699	+	0.813404i	$0.697612\pi$
$152$	−6.45604			−0.523654
$153$		0			0
$154$	−19.4501			−1.56734
$155$	0.887495	+	1.53719i	0.0712853	+	0.123470i
$156$		0			0
$157$	4.78208	−	8.28281i	0.381652	−	0.661040i	−0.609647	−	0.792673i	$-0.708689\pi$
$157$	4.78208	−	8.28281i	0.381652	−	0.661040i	0.991299	+	0.131633i	$0.0420220\pi$
$158$	−3.42225	+	5.92751i	−0.272260	+	0.471568i
$159$		0			0
$160$	−0.217761	−	0.377174i	−0.0172156	−	0.0298182i
$161$	4.62948			0.364854
$162$		0			0
$163$	−8.54769			−0.669507			−0.334753	−	0.942306i	$-0.608653\pi$
$163$	−8.54769			−0.669507			−0.334753	+	0.942306i	$0.608653\pi$
$164$	−1.97990	−	3.42928i	−0.154604	−	0.267782i
$165$		0			0
$166$	−3.57688	+	6.19533i	−0.277619	+	0.480851i
$167$	−7.40786	+	12.8308i	−0.573238	+	0.992876i	0.422993	+	0.906133i	$0.360979\pi$
$167$	−7.40786	+	12.8308i	−0.573238	+	0.992876i	−0.996231	+	0.0867436i	$0.972354\pi$
$168$		0			0
$169$	1.36562	+	2.36533i	0.105048	+	0.181949i
$170$	2.60270			0.199618
$171$		0			0
$172$	−12.5688			−0.958358
$173$	4.45239	+	7.71177i	0.338509	+	0.586315i	0.984152	−	0.177324i	$-0.0567441\pi$
$173$	4.45239	+	7.71177i	0.338509	+	0.586315i	−0.645643	+	0.763639i	$0.723411\pi$
$174$		0			0
$175$	−11.1346	+	19.2858i	−0.841700	+	1.45787i
$176$	−2.10068	+	3.63849i	−0.158345	+	0.274261i
$177$		0			0
$178$	5.42511	+	9.39656i	0.406629	+	0.704302i
$179$	−0.543955			−0.0406571			−0.0203286	−	0.999793i	$-0.506471\pi$
$179$	−0.543955			−0.0406571			−0.0203286	+	0.999793i	$0.506471\pi$
$180$		0			0
$181$	1.79810			0.133651			0.0668257	−	0.997765i	$-0.478713\pi$
$181$	1.79810			0.133651			0.0668257	+	0.997765i	$0.478713\pi$
$182$	−7.41756	−	12.8476i	−0.549826	−	0.952327i
$183$		0			0
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	−1.66463	+	2.88323i	−0.122386	+	0.211979i
$186$		0			0
$187$	−12.5538	−	21.7437i	−0.918021	−	1.59006i
$188$	−9.43521			−0.688134
$189$		0			0
$190$	−2.81176			−0.203986
$191$	−11.8864	−	20.5878i	−0.860066	−	1.48968i	−0.871864	−	0.489748i	$-0.837089\pi$
$191$	−11.8864	−	20.5878i	−0.860066	−	1.48968i	0.0117980	−	0.999930i	$-0.496244\pi$
$192$		0			0
$193$	4.63979	−	8.03635i	0.333979	−	0.578469i	−0.649309	−	0.760525i	$-0.724942\pi$
$193$	4.63979	−	8.03635i	0.333979	−	0.578469i	0.983288	+	0.182056i	$0.0582751\pi$
$194$	3.77412	−	6.53696i	0.270966	−	0.469326i
$195$		0			0
$196$	−7.21604	−	12.4986i	−0.515432	−	0.892754i
$197$	0.921570			0.0656591			0.0328296	−	0.999461i	$-0.489548\pi$
$197$	0.921570			0.0656591			0.0328296	+	0.999461i	$0.489548\pi$
$198$		0			0
$199$	−9.68718			−0.686706			−0.343353	−	0.939206i	$-0.611563\pi$
$199$	−9.68718			−0.686706			−0.343353	+	0.939206i	$0.611563\pi$
$200$	2.40516	+	4.16586i	0.170070	+	0.294571i
$201$		0			0
$202$	0.371813	−	0.643998i	0.0261606	−	0.0453116i
$203$	−8.21323	+	14.2257i	−0.576456	+	0.998451i
$204$		0			0
$205$	−0.862291	−	1.49353i	−0.0602250	−	0.104313i
$206$	−12.7165			−0.886003
$207$		0			0
$208$	−3.20449			−0.222191
$209$	13.5621	+	23.4902i	0.938109	+	1.62485i
$210$		0			0
$211$	0.902750	−	1.56361i	0.0621479	−	0.107643i	−0.833277	−	0.552855i	$-0.813538\pi$
$211$	0.902750	−	1.56361i	0.0621479	−	0.107643i	0.895425	+	0.445212i	$0.146872\pi$
$212$	0.356976	−	0.618301i	0.0245172	−	0.0424651i
$213$		0			0
$214$	−3.70735	−	6.42131i	−0.253429	−	0.438952i
$215$	−5.47398			−0.373322
$216$		0			0
$217$	18.8676			1.28082
$218$	7.44568	+	12.8963i	0.504285	+	0.873447i
$219$		0			0
$220$	−0.914895	+	1.58464i	−0.0616822	+	0.106837i
$221$	9.57508	−	16.5845i	0.644089	−	1.11560i
$222$		0			0
$223$	−3.03682	−	5.25992i	−0.203360	−	0.352230i	0.746249	−	0.665667i	$-0.231853\pi$
$223$	−3.03682	−	5.25992i	−0.203360	−	0.352230i	−0.949609	+	0.313437i	$0.898520\pi$
$224$	−4.62948			−0.309320
$225$		0			0
$226$	12.9358			0.860479
$227$	−2.17687	−	3.77044i	−0.144484	−	0.250253i	0.784697	−	0.619880i	$-0.212819\pi$
$227$	−2.17687	−	3.77044i	−0.144484	−	0.250253i	−0.929180	+	0.369627i	$0.879485\pi$
$228$		0			0
$229$	2.54308	−	4.40475i	0.168052	−	0.291074i	−0.769683	−	0.638426i	$-0.779586\pi$
$229$	2.54308	−	4.40475i	0.168052	−	0.291074i	0.937735	+	0.347352i	$0.112919\pi$
$230$	0.217761	−	0.377174i	0.0143588	−	0.0248701i
$231$		0			0
$232$	1.77412	+	3.07286i	0.116476	+	0.201743i
$233$	26.8186			1.75694			0.878471	−	0.477795i	$-0.158564\pi$
$233$	26.8186			1.75694			0.878471	+	0.477795i	$0.158564\pi$
$234$		0			0
$235$	−4.10925			−0.268058
$236$	1.06162	+	1.83878i	0.0691056	+	0.119694i
$237$		0			0
$238$	13.8330	−	23.9594i	0.896659	−	1.55306i
$239$	−7.40208	+	12.8208i	−0.478801	+	0.829307i	−0.999705	−	0.0243081i	$-0.992262\pi$
$239$	−7.40208	+	12.8208i	−0.478801	+	0.829307i	0.520904	+	0.853615i	$0.325595\pi$
$240$		0			0
$241$	−13.7842	−	23.8750i	−0.887921	−	1.53792i	−0.842329	−	0.538963i	$-0.818816\pi$
$241$	−13.7842	−	23.8750i	−0.887921	−	1.53792i	−0.0455913	−	0.998960i	$-0.514517\pi$
$242$	6.65144			0.427571
$243$		0			0
$244$	−8.40103			−0.537821
$245$	−3.14275	−	5.44341i	−0.200783	−	0.347767i
$246$		0			0
$247$	−10.3442	+	17.9166i	−0.658183	+	1.14001i
$248$	2.03777	−	3.52952i	0.129398	−	0.224125i
$249$		0			0
$250$	2.13631	+	3.70020i	0.135112	+	0.234021i
$251$	5.65292			0.356809			0.178404	−	0.983957i	$-0.442906\pi$
$251$	5.65292			0.356809			0.178404	+	0.983957i	$0.442906\pi$
$252$		0			0
$253$	−4.20136			−0.264137
$254$	−3.71620	−	6.43664i	−0.233175	−	0.403871i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.82050	+	4.88525i	−0.175938	+	0.304734i	−0.940486	−	0.339834i	$-0.889629\pi$
$257$	−2.82050	+	4.88525i	−0.175938	+	0.304734i	0.764547	+	0.644567i	$0.222963\pi$
$258$		0			0
$259$	17.6945	+	30.6478i	1.09949	+	1.90436i
$260$	−1.39563			−0.0865532
$261$		0			0
$262$	−14.4660			−0.893715
$263$	−7.20692	−	12.4828i	−0.444398	−	0.769719i	0.553612	−	0.832774i	$-0.313249\pi$
$263$	−7.20692	−	12.4828i	−0.444398	−	0.769719i	−0.998010	+	0.0630551i	$0.979916\pi$
$264$		0			0
$265$	0.155471	−	0.269284i	0.00955053	−	0.0165420i
$266$	−14.9441	+	25.8839i	−0.916279	+	1.58704i
$267$		0			0
$268$	2.31474	+	4.00925i	0.141395	+	0.244904i
$269$	−0.980220			−0.0597651			−0.0298825	−	0.999553i	$-0.509513\pi$
$269$	−0.980220			−0.0597651			−0.0298825	+	0.999553i	$0.509513\pi$
$270$		0			0
$271$	0.0900885			0.00547249			0.00273624	−	0.999996i	$-0.499129\pi$
$271$	0.0900885			0.00547249			0.00273624	+	0.999996i	$0.499129\pi$
$272$	−2.98802	−	5.17540i	−0.181175	−	0.313805i
$273$		0			0
$274$	9.39974	−	16.2808i	0.567859	−	0.983561i
$275$	10.1049	−	17.5023i	0.609351	−	1.05543i
$276$		0			0
$277$	1.54449	+	2.67514i	0.0927995	+	0.160733i	0.908688	−	0.417476i	$-0.137085\pi$
$277$	1.54449	+	2.67514i	0.0927995	+	0.160733i	−0.815889	+	0.578209i	$0.803752\pi$
$278$	−4.06510			−0.243809
$279$		0			0
$280$	−2.01624			−0.120494
$281$	−1.66280	−	2.88005i	−0.0991941	−	0.171809i	0.812157	−	0.583439i	$-0.198293\pi$
$281$	−1.66280	−	2.88005i	−0.0991941	−	0.171809i	−0.911351	+	0.411629i	$0.864960\pi$
$282$		0			0
$283$	−5.45975	+	9.45656i	−0.324548	+	0.562134i	−0.981421	−	0.191868i	$-0.938546\pi$
$283$	−5.45975	+	9.45656i	−0.324548	+	0.562134i	0.656873	+	0.754002i	$0.271879\pi$
$284$	3.76656	−	6.52387i	0.223504	−	0.387120i
$285$		0			0
$286$	6.73161	+	11.6595i	0.398048	+	0.689440i
$287$	−18.3318			−1.08209
$288$		0			0
$289$	18.7131			1.10077
$290$	0.772668	+	1.33830i	0.0453726	+	0.0785877i
$291$		0			0
$292$	−5.76214	+	9.98031i	−0.337204	+	0.584054i
$293$	1.94896	−	3.37570i	0.113859	−	0.197210i	−0.803464	−	0.595354i	$-0.797012\pi$
$293$	1.94896	−	3.37570i	0.113859	−	0.197210i	0.917323	+	0.398143i	$0.130345\pi$
$294$		0			0
$295$	0.462360	+	0.800831i	0.0269196	+	0.0466262i
$296$	7.64429			0.444315
$297$		0			0
$298$	−12.1586			−0.704327
$299$	−1.60224	−	2.77517i	−0.0926602	−	0.160492i
$300$		0			0
$301$	−29.0934	+	50.3912i	−1.67692	+	2.90450i
$302$	5.08214	−	8.80253i	0.292444	−	0.506529i
$303$		0			0
$304$	3.22802	+	5.59110i	0.185140	+	0.320672i
$305$	−3.65884			−0.209505
$306$		0			0
$307$	−32.6824			−1.86529			−0.932643	−	0.360802i	$-0.882503\pi$
$307$	−32.6824			−1.86529			−0.932643	+	0.360802i	$0.882503\pi$
$308$	9.72506	+	16.8443i	0.554137	+	0.959793i
$309$		0			0
$310$	0.887495	−	1.53719i	0.0504063	−	0.0873063i
$311$	−2.81771	+	4.88042i	−0.159778	+	0.276743i	−0.934788	−	0.355205i	$-0.884411\pi$
$311$	−2.81771	+	4.88042i	−0.159778	+	0.276743i	0.775011	+	0.631948i	$0.217744\pi$
$312$		0			0
$313$	−7.65418	−	13.2574i	−0.432640	−	0.749354i	0.564460	−	0.825460i	$-0.309084\pi$
$313$	−7.65418	−	13.2574i	−0.432640	−	0.749354i	−0.997100	+	0.0761064i	$0.975751\pi$
$314$	−9.56417			−0.539737
$315$		0			0
$316$	6.84450			0.385033
$317$	−15.5534	−	26.9394i	−0.873568	−	1.51306i	−0.858280	−	0.513182i	$-0.828467\pi$
$317$	−15.5534	−	26.9394i	−0.873568	−	1.51306i	−0.0152884	−	0.999883i	$-0.504867\pi$
$318$		0			0
$319$	7.45370	−	12.9102i	0.417327	−	0.722832i
$320$	−0.217761	+	0.377174i	−0.0121732	+	0.0210847i
$321$		0			0
$322$	−2.31474	−	4.00925i	−0.128995	−	0.223427i
$323$	−38.5816			−2.14674
$324$		0			0
$325$	15.4146			0.855049
$326$	4.27384	+	7.40252i	0.236706	+	0.409987i
$327$		0			0
$328$	−1.97990	+	3.42928i	−0.109322	+	0.189351i
$329$	−21.8401	+	37.8281i	−1.20408	+	2.08553i
$330$		0			0
$331$	−14.0945	−	24.4125i	−0.774706	−	1.34183i	−0.934960	−	0.354754i	$-0.884564\pi$
$331$	−14.0945	−	24.4125i	−0.774706	−	1.34183i	0.160253	−	0.987076i	$-0.448769\pi$
$332$	7.15375			0.392613
$333$		0			0
$334$	14.8157			0.810680
$335$	1.00812	+	1.74612i	0.0550796	+	0.0954007i
$336$		0			0
$337$	4.72176	−	8.17832i	0.257210	−	0.445501i	−0.708283	−	0.705928i	$-0.750530\pi$
$337$	4.72176	−	8.17832i	0.257210	−	0.445501i	0.965494	+	0.260427i	$0.0838633\pi$
$338$	1.36562	−	2.36533i	0.0742802	−	0.128657i
$339$		0			0
$340$	−1.30135	−	2.25401i	−0.0705757	−	0.122241i
$341$	−17.1228			−0.927251
$342$		0			0
$343$	−34.4067			−1.85779
$344$	6.28438	+	10.8849i	0.338831	+	0.586872i
$345$		0			0
$346$	4.45239	−	7.71177i	0.239362	−	0.414587i
$347$	−12.2666	+	21.2464i	−0.658508	+	1.14057i	0.322495	+	0.946571i	$0.395479\pi$
$347$	−12.2666	+	21.2464i	−0.658508	+	1.14057i	−0.981002	+	0.193997i	$0.937855\pi$
$348$		0			0
$349$	−8.54208	−	14.7953i	−0.457247	−	0.791975i	0.541567	−	0.840657i	$-0.317831\pi$
$349$	−8.54208	−	14.7953i	−0.457247	−	0.791975i	−0.998814	+	0.0486822i	$0.984498\pi$
$350$	22.2693			1.19034
$351$		0			0
$352$	4.20136			0.223933
$353$	6.42640	+	11.1309i	0.342043	+	0.592435i	0.984812	−	0.173624i	$-0.0555479\pi$
$353$	6.42640	+	11.1309i	0.342043	+	0.592435i	−0.642769	+	0.766060i	$0.722215\pi$
$354$		0			0
$355$	1.64042	−	2.84129i	0.0870646	−	0.150800i
$356$	5.42511	−	9.39656i	0.287530	−	0.498017i
$357$		0			0
$358$	0.271978	+	0.471079i	0.0143745	+	0.0248973i
$359$	−35.5998			−1.87889			−0.939444	−	0.342704i	$-0.888657\pi$
$359$	−35.5998			−1.87889			−0.939444	+	0.342704i	$0.888657\pi$
$360$		0			0
$361$	22.6805			1.19371
$362$	−0.899048	−	1.55720i	−0.0472529	−	0.0818445i
$363$		0			0
$364$	−7.41756	+	12.8476i	−0.388786	+	0.673397i
$365$	−2.50954	+	4.34666i	−0.131355	+	0.227514i
$366$		0			0
$367$	−0.228597	−	0.395941i	−0.0119327	−	0.0206680i	0.859997	−	0.510298i	$-0.170465\pi$
$367$	−0.228597	−	0.395941i	−0.0119327	−	0.0206680i	−0.871930	+	0.489630i	$0.837132\pi$
$368$	−1.00000			−0.0521286
$369$		0			0
$370$	3.32926			0.173080
$371$	−1.65261	−	2.86241i	−0.0857995	−	0.148609i
$372$		0			0
$373$	1.06866	−	1.85097i	0.0553329	−	0.0958395i	−0.837032	−	0.547154i	$-0.815711\pi$
$373$	1.06866	−	1.85097i	0.0553329	−	0.0958395i	0.892365	+	0.451314i	$0.149045\pi$
$374$	−12.5538	+	21.7437i	−0.649139	+	1.12434i
$375$		0			0
$376$	4.71761	+	8.17113i	0.243292	+	0.421394i
$377$	11.3703			0.585599
$378$		0			0
$379$	0.0602809			0.00309642			0.00154821	−	0.999999i	$-0.499507\pi$
$379$	0.0602809			0.00309642			0.00154821	+	0.999999i	$0.499507\pi$
$380$	1.40588	+	2.43505i	0.0721200	+	0.124916i
$381$		0			0
$382$	−11.8864	+	20.5878i	−0.608159	+	1.05336i
$383$	6.41495	−	11.1110i	0.327788	−	0.567746i	−0.654284	−	0.756249i	$-0.727030\pi$
$383$	6.41495	−	11.1110i	0.327788	−	0.567746i	0.982073	+	0.188502i	$0.0603634\pi$
$384$		0			0
$385$	4.23549	+	7.33608i	0.215860	+	0.373881i
$386$	−9.27958			−0.472318
$387$		0			0
$388$	−7.54823			−0.383203
$389$	−4.00954	−	6.94473i	−0.203292	−	0.352112i	0.746295	−	0.665615i	$-0.231831\pi$
$389$	−4.00954	−	6.94473i	−0.203292	−	0.352112i	−0.949587	+	0.313503i	$0.898497\pi$
$390$		0			0
$391$	2.98802	−	5.17540i	0.151111	−	0.261731i
$392$	−7.21604	+	12.4986i	−0.364465	+	0.631272i
$393$		0			0
$394$	−0.460785	−	0.798103i	−0.0232140	−	0.0402078i
$395$	2.98094			0.149987
$396$		0			0
$397$	23.1224			1.16048			0.580240	−	0.814446i	$-0.302959\pi$
$397$	23.1224			1.16048			0.580240	+	0.814446i	$0.302959\pi$
$398$	4.84359	+	8.38934i	0.242787	+	0.420520i
$399$		0			0
$400$	2.40516	−	4.16586i	0.120258	−	0.208293i
$401$	6.31865	−	10.9442i	0.315538	−	0.546528i	−0.664014	−	0.747720i	$-0.731148\pi$
$401$	6.31865	−	10.9442i	0.315538	−	0.546528i	0.979552	+	0.201192i	$0.0644817\pi$
$402$		0			0
$403$	−6.53000	−	11.3103i	−0.325283	−	0.563406i
$404$	−0.743625			−0.0369967
$405$		0			0
$406$	16.4265			0.815232
$407$	−16.0582	−	27.8136i	−0.795976	−	1.37867i
$408$		0			0
$409$	−6.62673	+	11.4778i	−0.327671	+	0.567542i	−0.982049	−	0.188625i	$-0.939597\pi$
$409$	−6.62673	+	11.4778i	−0.327671	+	0.567542i	0.654379	+	0.756167i	$0.272930\pi$
$410$	−0.862291	+	1.49353i	−0.0425855	+	0.0737603i
$411$		0			0
$412$	6.35827	+	11.0128i	0.313249	+	0.542564i
$413$	9.82950			0.483678
$414$		0			0
$415$	3.11562			0.152940
$416$	1.60224	+	2.77517i	0.0785565	+	0.136064i
$417$		0			0
$418$	13.5621	−	23.4902i	0.663343	−	1.14894i
$419$	2.78746	−	4.82802i	0.136176	−	0.235864i	−0.789870	−	0.613274i	$-0.789852\pi$
$419$	2.78746	−	4.82802i	0.136176	−	0.235864i	0.926046	+	0.377410i	$0.123185\pi$
$420$		0			0
$421$	−12.0656	−	20.8983i	−0.588044	−	1.01852i	−0.994488	−	0.104846i	$-0.966565\pi$
$421$	−12.0656	−	20.8983i	−0.588044	−	1.01852i	0.406445	−	0.913675i	$-0.366768\pi$
$422$	−1.80550			−0.0878904
$423$		0			0
$424$	−0.713953			−0.0346726
$425$	14.3733	+	24.8953i	0.697209	+	1.20760i
$426$		0			0
$427$	−19.4462	+	33.6818i	−0.941068	+	1.62998i
$428$	−3.70735	+	6.42131i	−0.179201	+	0.310386i
$429$		0			0
$430$	2.73699	+	4.74061i	0.131989	+	0.228612i
$431$	−4.23209			−0.203852			−0.101926	−	0.994792i	$-0.532501\pi$
$431$	−4.23209			−0.203852			−0.101926	+	0.994792i	$0.532501\pi$
$432$		0			0
$433$	7.59737			0.365107			0.182553	−	0.983196i	$-0.441564\pi$
$433$	7.59737			0.365107			0.182553	+	0.983196i	$0.441564\pi$
$434$	−9.43380	−	16.3398i	−0.452837	−	0.784337i
$435$		0			0
$436$	7.44568	−	12.8963i	0.356583	−	0.617620i
$437$	−3.22802	+	5.59110i	−0.154417	+	0.267459i
$438$		0			0
$439$	5.03882	+	8.72749i	0.240490	+	0.416540i	0.960854	−	0.277056i	$-0.0893587\pi$
$439$	5.03882	+	8.72749i	0.240490	+	0.416540i	−0.720364	+	0.693596i	$0.756025\pi$
$440$	1.82979			0.0872318
$441$		0			0
$442$	−19.1502			−0.910880
$443$	−1.45152	−	2.51411i	−0.0689640	−	0.119449i	0.829482	−	0.558534i	$-0.188636\pi$
$443$	−1.45152	−	2.51411i	−0.0689640	−	0.119449i	−0.898446	+	0.439085i	$0.855303\pi$
$444$		0			0
$445$	2.36276	−	4.09242i	0.112006	−	0.193999i
$446$	−3.03682	+	5.25992i	−0.143797	+	0.249064i
$447$		0			0
$448$	2.31474	+	4.00925i	0.109361	+	0.189419i
$449$	24.3808			1.15060			0.575300	−	0.817943i	$-0.304885\pi$
$449$	24.3808			1.15060			0.575300	+	0.817943i	$0.304885\pi$
$450$		0			0
$451$	16.6365			0.783384
$452$	−6.46792	−	11.2028i	−0.304225	−	0.526934i
$453$		0			0
$454$	−2.17687	+	3.77044i	−0.102165	+	0.176956i
$455$	−3.23052	+	5.59542i	−0.151449	+	0.262317i
$456$		0			0
$457$	−4.79877	−	8.31171i	−0.224477	−	0.388805i	0.731686	−	0.681642i	$-0.238734\pi$
$457$	−4.79877	−	8.31171i	−0.224477	−	0.388805i	−0.956162	+	0.292837i	$0.905401\pi$
$458$	−5.08616			−0.237661
$459$		0			0
$460$	−0.435523			−0.0203064
$461$	8.31611	+	14.4039i	0.387320	+	0.670858i	0.992088	−	0.125544i	$-0.0400676\pi$
$461$	8.31611	+	14.4039i	0.387320	+	0.670858i	−0.604768	+	0.796402i	$0.706734\pi$
$462$		0			0
$463$	9.29582	−	16.1008i	0.432014	−	0.748269i	−0.565033	−	0.825068i	$-0.691137\pi$
$463$	9.29582	−	16.1008i	0.432014	−	0.748269i	0.997047	+	0.0767988i	$0.0244699\pi$
$464$	1.77412	−	3.07286i	0.0823613	−	0.142654i
$465$		0			0
$466$	−13.4093	−	23.2256i	−0.621173	−	1.07590i
$467$	0.707813			0.0327537			0.0163768	−	0.999866i	$-0.494787\pi$
$467$	0.707813			0.0327537			0.0163768	+	0.999866i	$0.494787\pi$
$468$		0			0
$469$	21.4321			0.989642
$470$	2.05463	+	3.55872i	0.0947728	+	0.164151i
$471$		0			0
$472$	1.06162	−	1.83878i	0.0488650	−	0.0846367i
$473$	26.4029	−	45.7312i	1.21401	−	2.10272i
$474$		0			0
$475$	−15.5278	−	26.8950i	−0.712465	−	1.23403i
$476$	−27.6660			−1.26807
$477$		0			0
$478$	14.8042			0.677127
$479$	20.8161	+	36.0546i	0.951113	+	1.64738i	0.743023	+	0.669266i	$0.233391\pi$
$479$	20.8161	+	36.0546i	0.951113	+	1.64738i	0.208090	+	0.978110i	$0.433275\pi$
$480$		0			0
$481$	12.2480	−	21.2142i	0.558462	−	0.967284i
$482$	−13.7842	+	23.8750i	−0.627855	+	1.08748i
$483$		0			0
$484$	−3.32572	−	5.76031i	−0.151169	−	0.261832i
$485$	−3.28743			−0.149274
$486$		0			0
$487$	−16.1155			−0.730265			−0.365133	−	0.930956i	$-0.618976\pi$
$487$	−16.1155			−0.730265			−0.365133	+	0.930956i	$0.618976\pi$
$488$	4.20052	+	7.27551i	0.190148	+	0.329347i
$489$		0			0
$490$	−3.14275	+	5.44341i	−0.141975	+	0.245908i
$491$	4.99631	−	8.65386i	0.225480	−	0.390543i	−0.730983	−	0.682396i	$-0.760938\pi$
$491$	4.99631	−	8.65386i	0.225480	−	0.390543i	0.956463	+	0.291852i	$0.0942715\pi$
$492$		0			0
$493$	10.6022	+	18.3635i	0.477499	+	0.827052i
$494$	20.6883			0.930812
$495$		0			0
$496$	−4.07554			−0.182997
$497$	−17.4372	−	30.2021i	−0.782165	−	1.35475i
$498$		0			0
$499$	−2.48566	+	4.30529i	−0.111273	+	0.192731i	−0.916284	−	0.400529i	$-0.868826\pi$
$499$	−2.48566	+	4.30529i	−0.111273	+	0.192731i	0.805011	+	0.593260i	$0.202160\pi$
$500$	2.13631	−	3.70020i	0.0955387	−	0.165478i
$501$		0			0
$502$	−2.82646	−	4.89557i	−0.126151	−	0.218500i
$503$	5.41695			0.241530			0.120765	−	0.992681i	$-0.461465\pi$
$503$	5.41695			0.241530			0.120765	+	0.992681i	$0.461465\pi$
$504$		0			0
$505$	−0.323866			−0.0144118
$506$	2.10068	+	3.63849i	0.0933866	+	0.161750i
$507$		0			0
$508$	−3.71620	+	6.43664i	−0.164880	+	0.285580i
$509$	8.96080	−	15.5206i	0.397180	−	0.687936i	−0.596197	−	0.802839i	$-0.703322\pi$
$509$	8.96080	−	15.5206i	0.397180	−	0.687936i	0.993377	+	0.114902i	$0.0366554\pi$
$510$		0			0
$511$	26.6757	+	46.2037i	1.18006	+	2.04393i
$512$	1.00000			0.0441942
$513$		0			0
$514$	5.64100			0.248814
$515$	2.76917	+	4.79635i	0.122024	+	0.211352i
$516$		0			0
$517$	19.8204	−	34.3299i	0.871699	−	1.50983i
$518$	17.6945	−	30.6478i	0.777454	−	1.34659i
$519$		0			0
$520$	0.697814	+	1.20865i	0.0306012	+	0.0530028i
$521$	−44.4983			−1.94951			−0.974753	−	0.223286i	$-0.928322\pi$
$521$	−44.4983			−1.94951			−0.974753	+	0.223286i	$0.928322\pi$
$522$		0			0
$523$	−1.42361			−0.0622501			−0.0311251	−	0.999515i	$-0.509909\pi$
$523$	−1.42361			−0.0622501			−0.0311251	+	0.999515i	$0.509909\pi$
$524$	7.23302	+	12.5280i	0.315976	+	0.547286i
$525$		0			0
$526$	−7.20692	+	12.4828i	−0.314237	+	0.544274i
$527$	12.1778	−	21.0925i	0.530472	−	0.918805i
$528$		0			0
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−0.310943			−0.0135065
$531$		0			0
$532$	29.8881			1.29581
$533$	6.34456	+	10.9891i	0.274813	+	0.475991i
$534$		0			0
$535$	−1.61463	+	2.79663i	−0.0698067	+	0.120909i
$536$	2.31474	−	4.00925i	0.0999815	−	0.173173i
$537$		0			0
$538$	0.490110	+	0.848895i	0.0211301	+	0.0365985i
$539$	60.6344			2.61171
$540$		0			0
$541$	9.66320			0.415453			0.207727	−	0.978187i	$-0.433394\pi$
$541$	9.66320			0.415453			0.207727	+	0.978187i	$0.433394\pi$
$542$	−0.0450442	−	0.0780189i	−0.00193482	−	0.00335120i
$543$		0			0
$544$	−2.98802	+	5.17540i	−0.128110	+	0.221894i
$545$	3.24276	−	5.61663i	0.138905	−	0.240590i
$546$		0			0
$547$	0.592206	+	1.02573i	0.0253209	+	0.0438571i	0.878408	−	0.477911i	$-0.158606\pi$
$547$	0.592206	+	1.02573i	0.0253209	+	0.0438571i	−0.853087	+	0.521768i	$0.825273\pi$
$548$	−18.7995			−0.803074
$549$		0			0
$550$	−20.2099			−0.861753
$551$	−11.4538	−	19.8385i	−0.487947	−	0.845149i
$552$		0			0
$553$	15.8432	−	27.4413i	0.673723	−	1.16692i
$554$	1.54449	−	2.67514i	0.0656191	−	0.113656i
$555$		0			0
$556$	2.03255	+	3.52048i	0.0861993	+	0.149302i
$557$	−9.20364			−0.389971			−0.194985	−	0.980806i	$-0.562466\pi$
$557$	−9.20364			−0.389971			−0.194985	+	0.980806i	$0.562466\pi$
$558$		0			0
$559$	40.2764			1.70351
$560$	1.00812	+	1.74612i	0.0426010	+	0.0737870i
$561$		0			0
$562$	−1.66280	+	2.88005i	−0.0701408	+	0.121488i
$563$	5.76234	−	9.98067i	0.242854	−	0.420635i	−0.718672	−	0.695349i	$-0.755250\pi$
$563$	5.76234	−	9.98067i	0.242854	−	0.420635i	0.961526	+	0.274714i	$0.0885832\pi$
$564$		0			0
$565$	−2.81693	−	4.87906i	−0.118509	−	0.205264i
$566$	10.9195			0.458981
$567$		0			0
$568$	−7.53311			−0.316082
$569$	7.41744	+	12.8474i	0.310955	+	0.538591i	0.978569	−	0.205917i	$-0.0660177\pi$
$569$	7.41744	+	12.8474i	0.310955	+	0.538591i	−0.667614	+	0.744508i	$0.732684\pi$
$570$		0			0
$571$	2.87907	−	4.98670i	0.120485	−	0.208687i	−0.799474	−	0.600701i	$-0.794888\pi$
$571$	2.87907	−	4.98670i	0.120485	−	0.208687i	0.919959	+	0.392014i	$0.128222\pi$
$572$	6.73161	−	11.6595i	0.281463	−	0.487508i
$573$		0			0
$574$	9.16590	+	15.8758i	0.382577	+	0.662643i
$575$	4.81032			0.200604
$576$		0			0
$577$	−23.0209			−0.958371			−0.479186	−	0.877714i	$-0.659068\pi$
$577$	−23.0209			−0.958371			−0.479186	+	0.877714i	$0.659068\pi$
$578$	−9.35653	−	16.2060i	−0.389180	−	0.674080i
$579$		0			0
$580$	0.772668	−	1.33830i	0.0320833	−	0.0555699i
$581$	16.5591	−	28.6812i	0.686986	−	1.18990i
$582$		0			0
$583$	1.49979	+	2.59771i	0.0621148	+	0.107586i
$584$	11.5243			0.476878
$585$		0			0
$586$	−3.89792			−0.161022
$587$	−0.975904	−	1.69031i	−0.0402799	−	0.0697668i	0.845183	−	0.534478i	$-0.179492\pi$
$587$	−0.975904	−	1.69031i	−0.0402799	−	0.0697668i	−0.885462	+	0.464711i	$0.846158\pi$
$588$		0			0
$589$	−13.1559	+	22.7867i	−0.542080	+	0.938910i
$590$	0.462360	−	0.800831i	0.0190351	−	0.0329697i
$591$		0			0
$592$	−3.82214	−	6.62015i	−0.157089	−	0.272086i
$593$	24.3221			0.998787			0.499394	−	0.866375i	$-0.333556\pi$
$593$	24.3221			0.998787			0.499394	+	0.866375i	$0.333556\pi$
$594$		0			0
$595$	−12.0492			−0.493967
$596$	6.07929	+	10.5296i	0.249017	+	0.431311i
$597$		0			0
$598$	−1.60224	+	2.77517i	−0.0655207	+	0.113485i
$599$	16.7619	−	29.0325i	0.684874	−	1.18624i	−0.288602	−	0.957449i	$-0.593190\pi$
$599$	16.7619	−	29.0325i	0.684874	−	1.18624i	0.973476	−	0.228788i	$-0.0734763\pi$
$600$		0			0
$601$	−6.29502	−	10.9033i	−0.256779	−	0.444754i	0.708598	−	0.705612i	$-0.249328\pi$
$601$	−6.29502	−	10.9033i	−0.256779	−	0.444754i	−0.965377	+	0.260858i	$0.915995\pi$
$602$	58.1868			2.37152
$603$		0			0
$604$	−10.1643			−0.413579
$605$	−1.44843	−	2.50875i	−0.0588869	−	0.101995i
$606$		0			0
$607$	2.25445	−	3.90482i	0.0915053	−	0.158492i	−0.816639	−	0.577148i	$-0.804166\pi$
$607$	2.25445	−	3.90482i	0.0915053	−	0.158492i	0.908145	+	0.418656i	$0.137499\pi$
$608$	3.22802	−	5.59110i	0.130914	−	0.226749i
$609$		0			0
$610$	1.82942	+	3.16865i	0.0740711	+	0.128295i
$611$	30.2350			1.22318
$612$		0			0
$613$	−25.5888			−1.03352			−0.516760	−	0.856130i	$-0.672862\pi$
$613$	−25.5888			−1.03352			−0.516760	+	0.856130i	$0.672862\pi$
$614$	16.3412	+	28.3038i	0.659478	+	1.14225i
$615$		0			0
$616$	9.72506	−	16.8443i	0.391834	−	0.678676i
$617$	−20.5875	+	35.6586i	−0.828821	+	1.43556i	0.0701425	+	0.997537i	$0.477655\pi$
$617$	−20.5875	+	35.6586i	−0.828821	+	1.43556i	−0.898964	+	0.438023i	$0.855679\pi$
$618$		0			0
$619$	14.0068	+	24.2605i	0.562982	+	0.975113i	0.997234	+	0.0743218i	$0.0236792\pi$
$619$	14.0068	+	24.2605i	0.562982	+	0.975113i	−0.434253	+	0.900791i	$0.642987\pi$
$620$	−1.77499			−0.0712853
$621$		0			0
$622$	5.63543			0.225960
$623$	−25.1154	−	43.5012i	−1.00623	−	1.74284i
$624$		0			0
$625$	−11.0954	+	19.2178i	−0.443815	+	0.768711i
$626$	−7.65418	+	13.2574i	−0.305923	+	0.529873i
$627$		0			0
$628$	4.78208	+	8.28281i	0.190826	+	0.330520i
$629$	45.6826			1.82148
$630$		0			0
$631$	−40.1274			−1.59745			−0.798723	−	0.601698i	$-0.794491\pi$
$631$	−40.1274			−1.59745			−0.798723	+	0.601698i	$0.794491\pi$
$632$	−3.42225	−	5.92751i	−0.136130	−	0.235784i
$633$		0			0
$634$	−15.5534	+	26.9394i	−0.617706	+	1.06990i
$635$	−1.61849	+	2.80331i	−0.0642278	+	0.111246i
$636$		0			0
$637$	23.1237	+	40.0515i	0.916196	+	1.58690i
$638$	−14.9074			−0.590190
$639$		0			0
$640$	0.435523			0.0172156
$641$	−14.1763	−	24.5540i	−0.559929	−	0.969826i	−0.997502	−	0.0706426i	$-0.977495\pi$
$641$	−14.1763	−	24.5540i	−0.559929	−	0.969826i	0.437573	−	0.899183i	$-0.355838\pi$
$642$		0			0
$643$	2.19080	−	3.79457i	0.0863966	−	0.149643i	−0.819589	−	0.572952i	$-0.805798\pi$
$643$	2.19080	−	3.79457i	0.0863966	−	0.149643i	0.905985	+	0.423309i	$0.139131\pi$
$644$	−2.31474	+	4.00925i	−0.0912135	+	0.157986i
$645$		0			0
$646$	19.2908	+	33.4126i	0.758986	+	1.31460i
$647$	−20.3298			−0.799247			−0.399624	−	0.916679i	$-0.630859\pi$
$647$	−20.3298			−0.799247			−0.399624	+	0.916679i	$0.630859\pi$
$648$		0			0
$649$	−8.92050			−0.350160
$650$	−7.70731	−	13.3494i	−0.302306	−	0.523609i
$651$		0			0
$652$	4.27384	−	7.40252i	0.167377	−	0.289905i
$653$	−22.1343	+	38.3377i	−0.866182	+	1.50027i	−0.000312861		1.00000i	$0.500100\pi$
$653$	−22.1343	+	38.3377i	−0.866182	+	1.50027i	−0.865869	+	0.500271i	$0.833234\pi$
$654$		0			0
$655$	3.15015	+	5.45621i	0.123086	+	0.213192i
$656$	3.95980			0.154604
$657$		0			0
$658$	43.6801			1.70283
$659$	−13.6768	−	23.6890i	−0.532774	−	0.922791i	−0.999268	−	0.0382665i	$-0.987816\pi$
$659$	−13.6768	−	23.6890i	−0.532774	−	0.922791i	0.466494	−	0.884524i	$-0.345517\pi$
$660$		0			0
$661$	−6.86841	+	11.8964i	−0.267150	+	0.462718i	−0.968125	−	0.250468i	$-0.919415\pi$
$661$	−6.86841	+	11.8964i	−0.267150	+	0.462718i	0.700974	+	0.713186i	$0.252749\pi$
$662$	−14.0945	+	24.4125i	−0.547800	+	0.948817i
$663$		0			0
$664$	−3.57688	−	6.19533i	−0.138810	−	0.240425i
$665$	13.0170			0.504776
$666$		0			0
$667$	3.54823			0.137388
$668$	−7.40786	−	12.8308i	−0.286619	−	0.496438i
$669$		0			0
$670$	1.00812	−	1.74612i	0.0389472	−	0.0674585i
$671$	17.6479	−	30.5670i	0.681289	−	1.18003i
$672$		0			0
$673$	−23.8044	−	41.2305i	−0.917593	−	1.58932i	−0.803059	−	0.595899i	$-0.796796\pi$
$673$	−23.8044	−	41.2305i	−0.917593	−	1.58932i	−0.114534	−	0.993419i	$-0.536538\pi$
$674$	−9.44351			−0.363750
$675$		0			0
$676$	−2.73125			−0.105048
$677$	−0.266420	−	0.461453i	−0.0102393	−	0.0177351i	0.860860	−	0.508841i	$-0.169926\pi$
$677$	−0.266420	−	0.461453i	−0.0102393	−	0.0177351i	−0.871100	+	0.491106i	$0.836593\pi$
$678$		0			0
$679$	−17.4722	+	30.2627i	−0.670521	+	1.16138i
$680$	−1.30135	+	2.25401i	−0.0499046	+	0.0864372i
$681$		0			0
$682$	8.56140	+	14.8288i	0.327833	+	0.567823i
$683$	38.7409			1.48238			0.741190	−	0.671295i	$-0.234262\pi$
$683$	38.7409			1.48238			0.741190	+	0.671295i	$0.234262\pi$
$684$		0			0
$685$	−8.18760			−0.312832
$686$	17.2033	+	29.7971i	0.656827	+	1.13766i
$687$		0			0
$688$	6.28438	−	10.8849i	0.239590	−	0.414981i
$689$	−1.14393	+	1.98134i	−0.0435801	+	0.0754830i
$690$		0			0
$691$	−15.4566	−	26.7717i	−0.587998	−	1.01844i	−0.994494	−	0.104790i	$-0.966583\pi$
$691$	−15.4566	−	26.7717i	−0.587998	−	1.01844i	0.406497	−	0.913652i	$-0.366750\pi$
$692$	−8.90478			−0.338509
$693$		0			0
$694$	24.5333			0.931270
$695$	0.885222	+	1.53325i	0.0335784	+	0.0581595i
$696$		0			0
$697$	−11.8319	+	20.4935i	−0.448167	+	0.776248i
$698$	−8.54208	+	14.7953i	−0.323323	+	0.560011i
$699$		0			0
$700$	−11.1346	−	19.2858i	−0.420850	−	0.728933i
$701$	46.7636			1.76624			0.883119	−	0.469150i	$-0.155440\pi$
$701$	46.7636			1.76624			0.883119	+	0.469150i	$0.155440\pi$
$702$		0			0
$703$	−49.3519			−1.86134
$704$	−2.10068	−	3.63849i	−0.0791724	−	0.137131i
$705$		0			0
$706$	6.42640	−	11.1309i	0.241861	−	0.418915i
$707$	−1.72130	+	2.98138i	−0.0647361	+	0.112126i
$708$		0			0
$709$	13.1841	+	22.8355i	0.495138	+	0.857604i	0.999984	−	0.00560505i	$-0.00178415\pi$
$709$	13.1841	+	22.8355i	0.495138	+	0.857604i	−0.504846	+	0.863209i	$0.668451\pi$
$710$	−3.28084			−0.123128
$711$		0			0
$712$	−10.8502			−0.406629
$713$	−2.03777	−	3.52952i	−0.0763150	−	0.132181i
$714$		0			0
$715$	2.93177	−	5.07797i	0.109642	−	0.189905i
$716$	0.271978	−	0.471079i	0.0101643	−	0.0176051i
$717$		0			0
$718$	17.7999	+	30.8304i	0.664287	+	1.15058i
$719$	46.8541			1.74736			0.873682	−	0.486498i	$-0.161726\pi$
$719$	46.8541			1.74736			0.873682	+	0.486498i	$0.161726\pi$
$720$		0			0
$721$	58.8710			2.19247
$722$	−11.3403	−	19.6419i	−0.422041	−	0.730996i
$723$		0			0
$724$	−0.899048	+	1.55720i	−0.0334129	+	0.0578728i
$725$	−8.53407	+	14.7814i	−0.316947	+	0.548969i
$726$		0			0
$727$	−5.23445	−	9.06634i	−0.194135	−	0.336252i	0.752482	−	0.658613i	$-0.228857\pi$
$727$	−5.23445	−	9.06634i	−0.194135	−	0.336252i	−0.946617	+	0.322361i	$0.895523\pi$
$728$	14.8351			0.549826
$729$		0			0
$730$	5.01909			0.185765
$731$	37.5557	+	65.0484i	1.38905	+	2.40590i
$732$		0			0
$733$	1.16327	−	2.01485i	0.0429664	−	0.0744200i	−0.843742	−	0.536748i	$-0.819652\pi$
$733$	1.16327	−	2.01485i	0.0429664	−	0.0744200i	0.886709	+	0.462328i	$0.152986\pi$
$734$	−0.228597	+	0.395941i	−0.00843766	+	0.0146145i
$735$		0			0
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	−19.4501			−0.716454
$738$		0			0
$739$	11.2490			0.413802			0.206901	−	0.978362i	$-0.433662\pi$
$739$	11.2490			0.413802			0.206901	+	0.978362i	$0.433662\pi$
$740$	−1.66463	−	2.88323i	−0.0611931	−	0.105990i
$741$		0			0
$742$	−1.65261	+	2.86241i	−0.0606694	+	0.105082i
$743$	−0.148648	+	0.257467i	−0.00545338	+	0.00944554i	−0.868739	−	0.495270i	$-0.835069\pi$
$743$	−0.148648	+	0.257467i	−0.00545338	+	0.00944554i	0.863286	+	0.504715i	$0.168403\pi$
$744$		0			0
$745$	2.64767	+	4.58590i	0.0970031	+	0.168014i
$746$	−2.13731			−0.0782526
$747$		0			0
$748$	25.1075			0.918021
$749$	17.1631	+	29.7273i	0.627125	+	1.08621i
$750$		0			0
$751$	4.22109	−	7.31115i	0.154030	−	0.266788i	−0.778675	−	0.627427i	$-0.784108\pi$
$751$	4.22109	−	7.31115i	0.154030	−	0.266788i	0.932705	+	0.360639i	$0.117441\pi$
$752$	4.71761	−	8.17113i	0.172033	−	0.297971i
$753$		0			0
$754$	−5.68514	−	9.84694i	−0.207040	−	0.358605i
$755$	−4.42678			−0.161107
$756$		0			0
$757$	5.44738			0.197988			0.0989942	−	0.995088i	$-0.468437\pi$
$757$	5.44738			0.197988			0.0989942	+	0.995088i	$0.468437\pi$
$758$	−0.0301405	−	0.0522048i	−0.00109475	−	0.00189616i
$759$		0			0
$760$	1.40588	−	2.43505i	0.0509966	−	0.0883286i
$761$	0.866614	−	1.50102i	0.0314147	−	0.0544119i	−0.849891	−	0.526959i	$-0.823332\pi$
$761$	0.866614	−	1.50102i	0.0314147	−	0.0544119i	0.881305	+	0.472547i	$0.156665\pi$
$762$		0			0
$763$	−34.4696	−	59.7031i	−1.24788	−	2.16140i
$764$	23.7727			0.860066
$765$		0			0
$766$	−12.8299			−0.463563
$767$	−3.40195	−	5.89235i	−0.122837	−	0.212761i
$768$		0			0
$769$	21.3192	−	36.9260i	0.768791	−	1.33158i	−0.169429	−	0.985542i	$-0.554192\pi$
$769$	21.3192	−	36.9260i	0.768791	−	1.33158i	0.938219	−	0.346042i	$-0.112474\pi$
$770$	4.23549	−	7.33608i	0.152636	−	0.264374i
$771$		0			0
$772$	4.63979	+	8.03635i	0.166990	+	0.289235i
$773$	−14.1875			−0.510288			−0.255144	−	0.966903i	$-0.582123\pi$
$773$	−14.1875			−0.510288			−0.255144	+	0.966903i	$0.582123\pi$
$774$		0			0
$775$	19.6046			0.704219
$776$	3.77412	+	6.53696i	0.135483	+	0.234663i
$777$		0			0
$778$	−4.00954	+	6.94473i	−0.143749	+	0.248981i
$779$	12.7823	−	22.1396i	0.457974	−	0.793234i
$780$		0			0
$781$	15.8247	+	27.4091i	0.566251	+	0.980776i
$782$	−5.97604			−0.213703
$783$		0			0
$784$	14.4321			0.515432
$785$	2.08271	+	3.60735i	0.0743350	+	0.128752i
$786$		0			0
$787$	−13.6683	+	23.6742i	−0.487222	+	0.843893i	−0.999892	−	0.0146925i	$-0.995323\pi$
$787$	−13.6683	+	23.6742i	−0.487222	+	0.843893i	0.512670	+	0.858586i	$0.328656\pi$
$788$	−0.460785	+	0.798103i	−0.0164148	+	0.0284312i
$789$		0			0
$790$	−1.49047	−	2.58157i	−0.0530285	−	0.0918481i
$791$	−59.8862			−2.12931
$792$		0			0
$793$	26.9210			0.955993
$794$	−11.5612	−	20.0246i	−0.410291	−	0.710646i
$795$		0			0
$796$	4.84359	−	8.38934i	0.171676	−	0.297352i
$797$	−9.64903	+	16.7126i	−0.341786	+	0.591991i	−0.984764	−	0.173893i	$-0.944365\pi$
$797$	−9.64903	+	16.7126i	−0.341786	+	0.591991i	0.642978	+	0.765884i	$0.277699\pi$
$798$		0			0
$799$	28.1926	+	48.8310i	0.997383	+	1.72752i
$800$	−4.81032			−0.170070
$801$		0			0
$802$	−12.6373			−0.446238
$803$	−24.2088	−	41.9309i	−0.854311	−	1.47971i
$804$		0			0
$805$	−1.00812	+	1.74612i	−0.0355316	+	0.0615426i
$806$	−6.53000	+	11.3103i	−0.230010	+	0.398388i
$807$		0			0
$808$	0.371813	+	0.643998i	0.0130803	+	0.0226558i
$809$	29.9263			1.05215			0.526076	−	0.850438i	$-0.323663\pi$
$809$	29.9263			1.05215			0.526076	+	0.850438i	$0.323663\pi$
$810$		0			0
$811$	21.4708			0.753941			0.376971	−	0.926225i	$-0.376966\pi$
$811$	21.4708			0.753941			0.376971	+	0.926225i	$0.376966\pi$
$812$	−8.21323	−	14.2257i	−0.288228	−	0.499226i
$813$		0			0
$814$	−16.0582	+	27.8136i	−0.562840	+	0.974867i
$815$	1.86136	−	3.22397i	0.0652005	−	0.112931i
$816$		0			0
$817$	−40.5722	−	70.2731i	−1.41944	−	2.45855i
$818$	13.2535			0.463396
$819$		0			0
$820$	1.72458			0.0602250
$821$	−21.4212	−	37.1025i	−0.747604	−	1.29489i	−0.948968	−	0.315371i	$-0.897871\pi$
$821$	−21.4212	−	37.1025i	−0.747604	−	1.29489i	0.201364	−	0.979516i	$-0.435462\pi$
$822$		0			0
$823$	−17.6598	+	30.5878i	−0.615584	+	1.06622i	0.374698	+	0.927147i	$0.377746\pi$
$823$	−17.6598	+	30.5878i	−0.615584	+	1.06622i	−0.990282	+	0.139075i	$0.955587\pi$
$824$	6.35827	−	11.0128i	0.221501	−	0.383651i
$825$		0			0
$826$	−4.91475	−	8.51260i	−0.171006	−	0.296191i
$827$	−6.71444			−0.233484			−0.116742	−	0.993162i	$-0.537245\pi$
$827$	−6.71444			−0.233484			−0.116742	+	0.993162i	$0.537245\pi$
$828$		0			0
$829$	−40.2072			−1.39645			−0.698227	−	0.715876i	$-0.746027\pi$
$829$	−40.2072			−1.39645			−0.698227	+	0.715876i	$0.746027\pi$
$830$	−1.55781	−	2.69821i	−0.0540724	−	0.0936562i
$831$		0			0
$832$	1.60224	−	2.77517i	0.0555478	−	0.0962117i
$833$	−43.1234	+	74.6919i	−1.49414	+	2.58792i
$834$		0			0
$835$	−3.22629	−	5.58810i	−0.111651	−	0.193384i
$836$	−27.1242			−0.938109
$837$		0			0
$838$	−5.57491			−0.192582
$839$	−12.4982	−	21.6475i	−0.431486	−	0.747356i	0.565516	−	0.824738i	$-0.308677\pi$
$839$	−12.4982	−	21.6475i	−0.431486	−	0.747356i	−0.997002	+	0.0773820i	$0.975344\pi$
$840$		0			0
$841$	8.20502	−	14.2115i	0.282932	−	0.490052i
$842$	−12.0656	+	20.8983i	−0.415810	+	0.720203i
$843$		0			0
$844$	0.902750	+	1.56361i	0.0310739	+	0.0538217i
$845$	−1.18952			−0.0409208
$846$		0			0
$847$	−30.7927			−1.05805
$848$	0.356976	+	0.618301i	0.0122586	+	0.0212326i
$849$		0			0
$850$	14.3733	−	24.8953i	0.493001	−	0.853903i
$851$	3.82214	−	6.62015i	0.131021	−	0.226936i
$852$		0			0
$853$	21.7021	+	37.5891i	0.743064	+	1.28702i	0.951094	+	0.308902i	$0.0999616\pi$
$853$	21.7021	+	37.5891i	0.743064	+	1.28702i	−0.208030	+	0.978123i	$0.566705\pi$
$854$	38.8924			1.33087
$855$		0			0
$856$	7.41469			0.253429
$857$	1.37403	+	2.37989i	0.0469360	+	0.0812955i	0.888539	−	0.458801i	$-0.151721\pi$
$857$	1.37403	+	2.37989i	0.0469360	+	0.0812955i	−0.841603	+	0.540097i	$0.818388\pi$
$858$		0			0
$859$	14.8783	−	25.7700i	0.507642	−	0.879262i	−0.492319	−	0.870415i	$-0.663851\pi$
$859$	14.8783	−	25.7700i	0.507642	−	0.879262i	0.999961	−	0.00884669i	$-0.00281603\pi$
$860$	2.73699	−	4.74061i	0.0933306	−	0.161653i
$861$		0			0
$862$	2.11604	+	3.66509i	0.0720727	+	0.124834i
$863$	15.4133			0.524675			0.262338	−	0.964976i	$-0.415507\pi$
$863$	15.4133			0.524675			0.262338	+	0.964976i	$0.415507\pi$
$864$		0			0
$865$	−3.87824			−0.131864
$866$	−3.79869	−	6.57952i	−0.129085	−	0.223581i
$867$		0			0
$868$	−9.43380	+	16.3398i	−0.320204	+	0.554610i
$869$	−14.3781	+	24.9036i	−0.487744	+	0.844797i
$870$		0			0
$871$	−7.41756	−	12.8476i	−0.251334	−	0.435324i
$872$	−14.8914			−0.504285
$873$		0			0
$874$	6.45604			0.218379
$875$	−9.89000	−	17.1300i	−0.334343	−	0.579099i
$876$		0			0
$877$	7.86522	−	13.6230i	0.265590	−	0.460015i	−0.702128	−	0.712050i	$-0.747767\pi$
$877$	7.86522	−	13.6230i	0.265590	−	0.460015i	0.967718	+	0.252036i	$0.0811001\pi$
$878$	5.03882	−	8.72749i	0.170052	−	0.294538i
$879$		0			0
$880$	−0.914895	−	1.58464i	−0.0308411	−	0.0534183i
$881$	−17.2562			−0.581377			−0.290689	−	0.956818i	$-0.593884\pi$
$881$	−17.2562			−0.581377			−0.290689	+	0.956818i	$0.593884\pi$
$882$		0			0
$883$	33.0703			1.11290			0.556452	−	0.830880i	$-0.312162\pi$
$883$	33.0703			1.11290			0.556452	+	0.830880i	$0.312162\pi$
$884$	9.57508	+	16.5845i	0.322045	+	0.557798i
$885$		0			0
$886$	−1.45152	+	2.51411i	−0.0487649	+	0.0844633i
$887$	−15.3024	+	26.5046i	−0.513806	+	0.889938i	0.486066	+	0.873922i	$0.338431\pi$
$887$	−15.3024	+	26.5046i	−0.513806	+	0.889938i	−0.999872	+	0.0160155i	$0.994902\pi$
$888$		0			0
$889$	17.2041	+	29.7983i	0.577006	+	0.999403i
$890$	−4.72552			−0.158400
$891$		0			0
$892$	6.07363			0.203360
$893$	−30.4571	−	52.7532i	−1.01921	−	1.76532i
$894$		0			0
$895$	0.118453	−	0.205166i	0.00395943	−	0.00685794i
$896$	2.31474	−	4.00925i	0.0773300	−	0.133940i
$897$		0			0
$898$	−12.1904	−	21.1144i	−0.406798	−	0.704595i
$899$	14.4609			0.482299
$900$		0			0
$901$	−4.26661			−0.142141
$902$	−8.31827	−	14.4077i	−0.276968	−	0.479723i
$903$		0			0
$904$	−6.46792	+	11.2028i	−0.215120	+	0.372598i
$905$	−0.391556	+	0.678195i	−0.0130158	+	0.0225440i
$906$		0			0
$907$	−8.93204	−	15.4708i	−0.296584	−	0.513698i	0.678768	−	0.734352i	$-0.262514\pi$
$907$	−8.93204	−	15.4708i	−0.296584	−	0.513698i	−0.975352	+	0.220654i	$0.929181\pi$
$908$	4.35373			0.144484
$909$		0			0
$910$	6.46103			0.214181
$911$	15.8558	+	27.4630i	0.525325	+	0.909890i	0.999565	+	0.0294942i	$0.00938965\pi$
$911$	15.8558	+	27.4630i	0.525325	+	0.909890i	−0.474240	+	0.880396i	$0.657277\pi$
$912$		0			0
$913$	−15.0277	+	26.0288i	−0.497346	+	0.861428i
$914$	−4.79877	+	8.31171i	−0.158729	+	0.274927i
$915$		0			0
$916$	2.54308	+	4.40475i	0.0840258	+	0.145537i
$917$	66.9702			2.21155
$918$		0			0
$919$	−40.6594			−1.34123			−0.670616	−	0.741805i	$-0.733970\pi$
$919$	−40.6594			−1.34123			−0.670616	+	0.741805i	$0.733970\pi$
$920$	0.217761	+	0.377174i	0.00717938	+	0.0124351i
$921$		0			0
$922$	8.31611	−	14.4039i	0.273877	−	0.474368i
$923$	−12.0699	+	20.9057i	−0.397285	+	0.688118i
$924$		0			0
$925$	18.3857	+	31.8450i	0.604519	+	1.04706i
$926$	−18.5916			−0.610959
$927$		0			0
$928$	−3.54823			−0.116476
$929$	−0.178966	−	0.309978i	−0.00587167	−	0.0101700i	0.863075	−	0.505076i	$-0.168536\pi$
$929$	−0.178966	−	0.309978i	−0.00587167	−	0.0101700i	−0.868946	+	0.494906i	$0.835202\pi$
$930$		0			0
$931$	46.5871	−	80.6912i	1.52683	−	2.64455i
$932$	−13.4093	+	23.2256i	−0.439236	+	0.760778i
$933$		0			0
$934$	−0.353907	−	0.612984i	−0.0115802	−	0.0200575i
$935$	10.9349			0.357609
$936$		0			0
$937$	47.0619			1.53744			0.768722	−	0.639583i	$-0.220893\pi$
$937$	47.0619			1.53744			0.768722	+	0.639583i	$0.220893\pi$
$938$	−10.7160	−	18.5607i	−0.349891	−	0.606029i
$939$		0			0
$940$	2.05463	−	3.55872i	0.0670145	−	0.116073i
$941$	9.59941	−	16.6267i	0.312932	−	0.542014i	−0.666064	−	0.745895i	$-0.732022\pi$
$941$	9.59941	−	16.6267i	0.312932	−	0.542014i	0.978996	+	0.203881i	$0.0653555\pi$
$942$		0			0
$943$	1.97990	+	3.42928i	0.0644743	+	0.111673i
$944$	−2.12324			−0.0691056
$945$		0			0
$946$	−52.8059			−1.71687
$947$	−27.6131	−	47.8272i	−0.897304	−	1.55418i	−0.830927	−	0.556381i	$-0.812190\pi$
$947$	−27.6131	−	47.8272i	−0.897304	−	1.55418i	−0.0663762	−	0.997795i	$-0.521144\pi$
$948$		0			0
$949$	18.4647	−	31.9818i	0.599390	−	1.03817i
$950$	−15.5278	+	26.8950i	−0.503789	+	0.872588i
$951$		0			0
$952$	13.8330	+	23.9594i	0.448329	+	0.776529i
$953$	−49.6992			−1.60991			−0.804957	−	0.593333i	$-0.797812\pi$
$953$	−49.6992			−1.60991			−0.804957	+	0.593333i	$0.797812\pi$
$954$		0			0
$955$	10.3536			0.335033
$956$	−7.40208	−	12.8208i	−0.239400	−	0.414654i
$957$		0			0
$958$	20.8161	−	36.0546i	0.672538	−	1.16487i
$959$	−43.5159	+	75.3718i	−1.40520	+	2.43388i
$960$		0			0
$961$	7.19501	+	12.4621i	0.232097	+	0.402004i
$962$	−24.4960			−0.789784
$963$		0			0
$964$	27.5685			0.887921
$965$	2.02073	+	3.50002i	0.0650498	+	0.112669i
$966$		0			0
$967$	−8.54366	+	14.7980i	−0.274745	+	0.475873i	−0.970071	−	0.242822i	$-0.921927\pi$
$967$	−8.54366	+	14.7980i	−0.274745	+	0.475873i	0.695325	+	0.718695i	$0.255260\pi$
$968$	−3.32572	+	5.76031i	−0.106893	+	0.185144i
$969$		0			0
$970$	1.64371	+	2.84700i	0.0527765	+	0.0914116i
$971$	−42.9555			−1.37851			−0.689254	−	0.724520i	$-0.742062\pi$
$971$	−42.9555			−1.37851			−0.689254	+	0.724520i	$0.742062\pi$
$972$		0			0
$973$	18.8193			0.603319
$974$	8.05777	+	13.9565i	0.258188	+	0.447194i
$975$		0			0
$976$	4.20052	−	7.27551i	0.134455	−	0.232883i
$977$	−14.4870	+	25.0923i	−0.463481	+	0.802773i	−0.999132	−	0.0416666i	$-0.986733\pi$
$977$	−14.4870	+	25.0923i	−0.463481	+	0.802773i	0.535650	+	0.844440i	$0.320067\pi$
$978$		0			0
$979$	22.7928	+	39.4783i	0.728462	+	1.26173i
$980$	6.28550			0.200783
$981$		0			0
$982$	−9.99262			−0.318877
$983$	24.8332	+	43.0124i	0.792056	+	1.37188i	0.924692	+	0.380717i	$0.124323\pi$
$983$	24.8332	+	43.0124i	0.792056	+	1.37188i	−0.132635	+	0.991165i	$0.542344\pi$
$984$		0			0
$985$	−0.200682	+	0.347592i	−0.00639427	+	0.0110752i
$986$	10.6022	−	18.3635i	0.337642	−	0.584814i
$987$		0			0
$988$	−10.3442	−	17.9166i	−0.329092	−	0.570003i
$989$	12.5688			0.399663
$990$		0			0
$991$	−21.8471			−0.693997			−0.346998	−	0.937866i	$-0.612799\pi$
$991$	−21.8471			−0.693997			−0.346998	+	0.937866i	$0.612799\pi$
$992$	2.03777	+	3.52952i	0.0646992	+	0.112062i
$993$		0			0
$994$	−17.4372	+	30.2021i	−0.553074	+	0.957953i
$995$	2.10949	−	3.65375i	0.0668755	−	0.115832i
$996$		0			0
$997$	−16.2651	−	28.1719i	−0.515120	−	0.892215i	−0.999846	−	0.0175483i	$-0.994414\pi$
$997$	−16.2651	−	28.1719i	−0.515120	−	0.892215i	0.484726	−	0.874666i	$-0.338919\pi$
$998$	4.97132			0.157364
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1242.2.e.b.415.3		10
3.2	odd	2		414.2.e.d.139.2	✓	10
9.2	odd	6		414.2.e.d.277.2	yes	10
9.4	even	3		3726.2.a.u.1.3		5
9.5	odd	6		3726.2.a.r.1.3		5
9.7	even	3	inner	1242.2.e.b.829.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.e.d.139.2	✓	10	3.2	odd	2
414.2.e.d.277.2	yes	10	9.2	odd	6
1242.2.e.b.415.3		10	1.1	even	1	trivial
1242.2.e.b.829.3		10	9.7	even	3	inner
3726.2.a.r.1.3		5	9.5	odd	6
3726.2.a.u.1.3		5	9.4	even	3

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:	\( N \)	\(=\)	\( 1242 = 2 \cdot 3^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1242.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.217761 + 0.377174i) q^{5} +(2.31474 + 4.00925i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.217761 + 0.377174i) q^{5} +(2.31474 + 4.00925i) q^{7} +1.00000 q^{8} +0.435523 q^{10} +(-2.10068 - 3.63849i) q^{11} +(1.60224 - 2.77517i) q^{13} +(2.31474 - 4.00925i) q^{14} +(-0.500000 - 0.866025i) q^{16} +5.97604 q^{17} -6.45604 q^{19} +(-0.217761 - 0.377174i) q^{20} +(-2.10068 + 3.63849i) q^{22} +(0.500000 - 0.866025i) q^{23} +(2.40516 + 4.16586i) q^{25} -3.20449 q^{26} -4.62948 q^{28} +(1.77412 + 3.07286i) q^{29} +(2.03777 - 3.52952i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.98802 - 5.17540i) q^{34} -2.01624 q^{35} +7.64429 q^{37} +(3.22802 + 5.59110i) q^{38} +(-0.217761 + 0.377174i) q^{40} +(-1.97990 + 3.42928i) q^{41} +(6.28438 + 10.8849i) q^{43} +4.20136 q^{44} -1.00000 q^{46} +(4.71761 + 8.17113i) q^{47} +(-7.21604 + 12.4986i) q^{49} +(2.40516 - 4.16586i) q^{50} +(1.60224 + 2.77517i) q^{52} -0.713953 q^{53} +1.82979 q^{55} +(2.31474 + 4.00925i) q^{56} +(1.77412 - 3.07286i) q^{58} +(1.06162 - 1.83878i) q^{59} +(4.20052 + 7.27551i) q^{61} -4.07554 q^{62} +1.00000 q^{64} +(0.697814 + 1.20865i) q^{65} +(2.31474 - 4.00925i) q^{67} +(-2.98802 + 5.17540i) q^{68} +(1.00812 + 1.74612i) q^{70} -7.53311 q^{71} +11.5243 q^{73} +(-3.82214 - 6.62015i) q^{74} +(3.22802 - 5.59110i) q^{76} +(9.72506 - 16.8443i) q^{77} +(-3.42225 - 5.92751i) q^{79} +0.435523 q^{80} +3.95980 q^{82} +(-3.57688 - 6.19533i) q^{83} +(-1.30135 + 2.25401i) q^{85} +(6.28438 - 10.8849i) q^{86} +(-2.10068 - 3.63849i) q^{88} -10.8502 q^{89} +14.8351 q^{91} +(0.500000 + 0.866025i) q^{92} +(4.71761 - 8.17113i) q^{94} +(1.40588 - 2.43505i) q^{95} +(3.77412 + 6.53696i) q^{97} +14.4321 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - 5 q^{4} + q^{5} + 5 q^{7} + 10 q^{8}+O(q^{10}) \) 10 * q - 5 * q^2 - 5 * q^4 + q^5 + 5 * q^7 + 10 * q^8	\( 10 q - 5 q^{2} - 5 q^{4} + q^{5} + 5 q^{7} + 10 q^{8} - 2 q^{10} + 11 q^{11} + 6 q^{13} + 5 q^{14} - 5 q^{16} - 2 q^{17} - 6 q^{19} + q^{20} + 11 q^{22} + 5 q^{23} - 12 q^{26} - 10 q^{28} + 8 q^{29} + 4 q^{31} - 5 q^{32} + q^{34} - 46 q^{35} - 28 q^{37} + 3 q^{38} + q^{40} + 24 q^{41} + 27 q^{43} - 22 q^{44} - 10 q^{46} + 9 q^{47} - 12 q^{49} + 6 q^{52} + 26 q^{53} + 16 q^{55} + 5 q^{56} + 8 q^{58} + 9 q^{59} + 3 q^{61} - 8 q^{62} + 10 q^{64} - 5 q^{65} + 5 q^{67} + q^{68} + 23 q^{70} - 54 q^{71} + 34 q^{73} + 14 q^{74} + 3 q^{76} + 13 q^{77} - 11 q^{79} - 2 q^{80} - 48 q^{82} + 23 q^{83} + 23 q^{85} + 27 q^{86} + 11 q^{88} - 78 q^{89} - 30 q^{91} + 5 q^{92} + 9 q^{94} + 37 q^{95} + 28 q^{97} + 24 q^{98}+O(q^{100}) \) 10 * q - 5 * q^2 - 5 * q^4 + q^5 + 5 * q^7 + 10 * q^8 - 2 * q^10 + 11 * q^11 + 6 * q^13 + 5 * q^14 - 5 * q^16 - 2 * q^17 - 6 * q^19 + q^20 + 11 * q^22 + 5 * q^23 - 12 * q^26 - 10 * q^28 + 8 * q^29 + 4 * q^31 - 5 * q^32 + q^34 - 46 * q^35 - 28 * q^37 + 3 * q^38 + q^40 + 24 * q^41 + 27 * q^43 - 22 * q^44 - 10 * q^46 + 9 * q^47 - 12 * q^49 + 6 * q^52 + 26 * q^53 + 16 * q^55 + 5 * q^56 + 8 * q^58 + 9 * q^59 + 3 * q^61 - 8 * q^62 + 10 * q^64 - 5 * q^65 + 5 * q^67 + q^68 + 23 * q^70 - 54 * q^71 + 34 * q^73 + 14 * q^74 + 3 * q^76 + 13 * q^77 - 11 * q^79 - 2 * q^80 - 48 * q^82 + 23 * q^83 + 23 * q^85 + 27 * q^86 + 11 * q^88 - 78 * q^89 - 30 * q^91 + 5 * q^92 + 9 * q^94 + 37 * q^95 + 28 * q^97 + 24 * q^98

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