LMFDB - Embedded newform 1134.2.k.d.647.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(647,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("1134.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.k (of order $6$, degree $2$, 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:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 796 x^{12} - 2228 x^{11} + 5254 x^{10} - 10232 x^{9} + \cdots + 225 $ x^16 - 8x^15 + 52x^14 - 224x^13 + 796x^12 - 2228x^11 + 5254x^10 - 10232x^9 + 16903x^8 - 23292x^7 + 26994x^6 - 25716x^5 + 19962x^4 - 12096x^3 + 5454x^2 - 1620*x + 225
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			647.6
Root			$0.500000 + 1.24626i$ of defining polynomial
Character	$\chi$	$=$	1134.647
Dual form			1134.2.k.d.971.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.529713 - 0.917490i) q^{5} +(1.22963 + 2.34265i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.529713 - 0.917490i) q^{5} +(1.22963 + 2.34265i) q^{7} -1.00000i q^{8} +(-0.917490 - 0.529713i) q^{10} +(-3.99962 - 2.30918i) q^{11} -0.109947i q^{13} +(2.23621 + 1.41398i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.07717 - 3.59776i) q^{17} +(6.05124 - 3.49369i) q^{19} -1.05943 q^{20} -4.61837 q^{22} +(5.36108 - 3.09522i) q^{23} +(1.93881 - 3.35811i) q^{25} +(-0.0549735 - 0.0952168i) q^{26} +(2.64361 + 0.106438i) q^{28} -1.90893i q^{29} +(-7.12988 - 4.11644i) q^{31} +(-0.866025 - 0.500000i) q^{32} -4.15433i q^{34} +(1.49801 - 2.36910i) q^{35} +(2.62262 + 4.54251i) q^{37} +(3.49369 - 6.05124i) q^{38} +(-0.917490 + 0.529713i) q^{40} +0.183214 q^{41} +3.94198 q^{43} +(-3.99962 + 2.30918i) q^{44} +(3.09522 - 5.36108i) q^{46} +(-2.08068 - 3.60384i) q^{47} +(-3.97604 + 5.76117i) q^{49} -3.87762i q^{50} +(-0.0952168 - 0.0549735i) q^{52} +(4.89499 + 2.82612i) q^{53} +4.89282i q^{55} +(2.34265 - 1.22963i) q^{56} +(-0.954467 - 1.65318i) q^{58} +(-5.09771 + 8.82949i) q^{59} +(-7.17201 + 4.14076i) q^{61} -8.23288 q^{62} -1.00000 q^{64} +(-0.100875 + 0.0582404i) q^{65} +(0.0671680 - 0.116338i) q^{67} +(-2.07717 - 3.59776i) q^{68} +(0.112764 - 2.80071i) q^{70} -13.9178i q^{71} +(12.4976 + 7.21551i) q^{73} +(4.54251 + 2.62262i) q^{74} -6.98737i q^{76} +(0.491571 - 12.2092i) q^{77} +(0.988165 + 1.71155i) q^{79} +(-0.529713 + 0.917490i) q^{80} +(0.158668 - 0.0916071i) q^{82} -8.77457 q^{83} -4.40121 q^{85} +(3.41385 - 1.97099i) q^{86} +(-2.30918 + 3.99962i) q^{88} +(0.355241 + 0.615296i) q^{89} +(0.257567 - 0.135194i) q^{91} -6.19045i q^{92} +(-3.60384 - 2.08068i) q^{94} +(-6.41085 - 3.70130i) q^{95} +2.72538i q^{97} +(-0.562763 + 6.97734i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 + 8 * q^7	$ 16 q + 8 q^{4} + 8 q^{7} + 12 q^{11} + 12 q^{14} - 8 q^{16} + 12 q^{23} - 8 q^{25} + 4 q^{28} + 12 q^{31} + 60 q^{35} + 4 q^{37} - 12 q^{38} - 48 q^{41} - 32 q^{43} + 12 q^{44} + 4 q^{49} - 12 q^{52} + 12 q^{56} - 12 q^{58} - 24 q^{59} - 12 q^{61} - 48 q^{62} - 16 q^{64} + 48 q^{65} - 4 q^{67} - 24 q^{70} + 36 q^{73} + 36 q^{74} + 84 q^{77} + 8 q^{79} - 72 q^{83} + 24 q^{85} + 24 q^{86} + 24 q^{89} - 12 q^{91} - 36 q^{94} + 12 q^{95} + 36 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 + 8 * q^7 + 12 * q^11 + 12 * q^14 - 8 * q^16 + 12 * q^23 - 8 * q^25 + 4 * q^28 + 12 * q^31 + 60 * q^35 + 4 * q^37 - 12 * q^38 - 48 * q^41 - 32 * q^43 + 12 * q^44 + 4 * q^49 - 12 * q^52 + 12 * q^56 - 12 * q^58 - 24 * q^59 - 12 * q^61 - 48 * q^62 - 16 * q^64 + 48 * q^65 - 4 * q^67 - 24 * q^70 + 36 * q^73 + 36 * q^74 + 84 * q^77 + 8 * q^79 - 72 * q^83 + 24 * q^85 + 24 * q^86 + 24 * q^89 - 12 * q^91 - 36 * q^94 + 12 * q^95 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.529713	−	0.917490i	−0.236895	−	0.410314i	0.722927	−	0.690925i	$-0.242796\pi$
$5$	−0.529713	−	0.917490i	−0.236895	−	0.410314i	−0.959822	+	0.280611i	$0.909463\pi$
$6$		0			0
$7$	1.22963	+	2.34265i	0.464755	+	0.885439i
$7$	1.22963	+	2.34265i	0.464755	+	0.885439i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.917490	−	0.529713i	−0.290136	−	0.167510i
$11$	−3.99962	−	2.30918i	−1.20593	−	0.696245i	−0.244064	−	0.969759i	$-0.578481\pi$
$11$	−3.99962	−	2.30918i	−1.20593	−	0.696245i	−0.961868	+	0.273514i	$0.911814\pi$
$12$		0			0
$13$		−	0.109947i		−	0.0304938i	−0.999884	−	0.0152469i	$-0.995147\pi$
$13$		−	0.109947i		−	0.0304938i	0.999884	−	0.0152469i	$-0.00485343\pi$
$14$	2.23621	+	1.41398i	0.597653	+	0.377903i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.07717	−	3.59776i	0.503787	−	0.872585i	−0.496203	−	0.868206i	$-0.665273\pi$
$17$	2.07717	−	3.59776i	0.503787	−	0.872585i	0.999990	−	0.00437840i	$-0.00139369\pi$
$18$		0			0
$19$	6.05124	−	3.49369i	1.38825	−	0.801506i	0.395132	−	0.918624i	$-0.370699\pi$
$19$	6.05124	−	3.49369i	1.38825	−	0.801506i	0.993118	+	0.117118i	$0.0373655\pi$
$20$	−1.05943			−0.236895
$21$		0			0
$22$	−4.61837			−0.984639
$23$	5.36108	−	3.09522i	1.11786	−	0.645399i	0.177009	−	0.984209i	$-0.443358\pi$
$23$	5.36108	−	3.09522i	1.11786	−	0.645399i	0.940855	+	0.338811i	$0.110025\pi$
$24$		0			0
$25$	1.93881	−	3.35811i	0.387762	−	0.671623i
$26$	−0.0549735	−	0.0952168i	−0.0107812	−	0.0186736i
$27$		0			0
$28$	2.64361	+	0.106438i	0.499595	+	0.0201150i
$29$		−	1.90893i		−	0.354480i	−0.984168	−	0.177240i	$-0.943283\pi$
$29$		−	1.90893i		−	0.354480i	0.984168	−	0.177240i	$-0.0567169\pi$
$30$		0			0
$31$	−7.12988	−	4.11644i	−1.28056	−	0.739334i	−0.303613	−	0.952795i	$-0.598193\pi$
$31$	−7.12988	−	4.11644i	−1.28056	−	0.739334i	−0.976952	+	0.213461i	$0.931526\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$		−	4.15433i		−	0.712462i
$35$	1.49801	−	2.36910i	0.253210	−	0.400452i
$36$		0			0
$37$	2.62262	+	4.54251i	0.431156	+	0.746784i	0.996973	−	0.0777470i	$-0.0247726\pi$
$37$	2.62262	+	4.54251i	0.431156	+	0.746784i	−0.565817	+	0.824531i	$0.691439\pi$
$38$	3.49369	−	6.05124i	0.566751	−	0.981641i
$39$		0			0
$40$	−0.917490	+	0.529713i	−0.145068	+	0.0837550i
$41$	0.183214			0.0286132			0.0143066	−	0.999898i	$-0.495446\pi$
$41$	0.183214			0.0286132			0.0143066	+	0.999898i	$0.495446\pi$
$42$		0			0
$43$	3.94198			0.601146			0.300573	−	0.953759i	$-0.402822\pi$
$43$	3.94198			0.601146			0.300573	+	0.953759i	$0.402822\pi$
$44$	−3.99962	+	2.30918i	−0.602966	+	0.348123i
$45$		0			0
$46$	3.09522	−	5.36108i	0.456366	−	0.790449i
$47$	−2.08068	−	3.60384i	−0.303498	−	0.525674i	0.673428	−	0.739253i	$-0.264821\pi$
$47$	−2.08068	−	3.60384i	−0.303498	−	0.525674i	−0.976926	+	0.213579i	$0.931488\pi$
$48$		0			0
$49$	−3.97604	+	5.76117i	−0.568005	+	0.823025i
$50$		−	3.87762i		−	0.548378i
$51$		0			0
$52$	−0.0952168	−	0.0549735i	−0.0132042	−	0.00762345i
$53$	4.89499	+	2.82612i	0.672378	+	0.388198i	0.796977	−	0.604009i	$-0.206431\pi$
$53$	4.89499	+	2.82612i	0.672378	+	0.388198i	−0.124599	+	0.992207i	$0.539764\pi$
$54$		0			0
$55$			4.89282i			0.659748i
$56$	2.34265	−	1.22963i	0.313050	−	0.164316i
$57$		0			0
$58$	−0.954467	−	1.65318i	−0.125328	−	0.217074i
$59$	−5.09771	+	8.82949i	−0.663665	+	1.14950i	0.315981	+	0.948766i	$0.397667\pi$
$59$	−5.09771	+	8.82949i	−0.663665	+	1.14950i	−0.979645	+	0.200736i	$0.935667\pi$
$60$		0			0
$61$	−7.17201	+	4.14076i	−0.918281	+	0.530170i	−0.883086	−	0.469211i	$-0.844539\pi$
$61$	−7.17201	+	4.14076i	−0.918281	+	0.530170i	−0.0351949	+	0.999380i	$0.511205\pi$
$62$	−8.23288			−1.04558
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.100875	+	0.0582404i	−0.0125120	+	0.00722383i
$66$		0			0
$67$	0.0671680	−	0.116338i	0.00820587	−	0.0142130i	−0.861893	−	0.507090i	$-0.830721\pi$
$67$	0.0671680	−	0.116338i	0.00820587	−	0.0142130i	0.870099	+	0.492877i	$0.164055\pi$
$68$	−2.07717	−	3.59776i	−0.251894	−	0.436292i
$69$		0			0
$70$	0.112764	−	2.80071i	0.0134778	−	0.334749i
$71$		−	13.9178i		−	1.65173i	−0.563865	−	0.825867i	$-0.690686\pi$
$71$		−	13.9178i		−	1.65173i	0.563865	−	0.825867i	$-0.309314\pi$
$72$		0			0
$73$	12.4976	+	7.21551i	1.46274	+	0.844512i	0.999137	−	0.0415326i	$-0.0132240\pi$
$73$	12.4976	+	7.21551i	1.46274	+	0.844512i	0.463600	+	0.886044i	$0.346557\pi$
$74$	4.54251	+	2.62262i	0.528056	+	0.304873i
$75$		0			0
$76$		−	6.98737i		−	0.801506i
$77$	0.491571	−	12.2092i	0.0560198	−	1.39136i
$78$		0			0
$79$	0.988165	+	1.71155i	0.111177	+	0.192565i	0.916245	−	0.400618i	$-0.131205\pi$
$79$	0.988165	+	1.71155i	0.111177	+	0.192565i	−0.805068	+	0.593183i	$0.797871\pi$
$80$	−0.529713	+	0.917490i	−0.0592237	+	0.102579i
$81$		0			0
$82$	0.158668	−	0.0916071i	0.0175220	−	0.0101163i
$83$	−8.77457			−0.963134			−0.481567	−	0.876409i	$-0.659932\pi$
$83$	−8.77457			−0.963134			−0.481567	+	0.876409i	$0.659932\pi$
$84$		0			0
$85$	−4.40121			−0.477378
$86$	3.41385	−	1.97099i	0.368125	−	0.212537i
$87$		0			0
$88$	−2.30918	+	3.99962i	−0.246160	+	0.426361i
$89$	0.355241	+	0.615296i	0.0376555	+	0.0652213i	0.884239	−	0.467035i	$-0.154678\pi$
$89$	0.355241	+	0.615296i	0.0376555	+	0.0652213i	−0.846583	+	0.532256i	$0.821344\pi$
$90$		0			0
$91$	0.257567	−	0.135194i	0.0270004	−	0.0141721i
$92$		−	6.19045i		−	0.645399i
$93$		0			0
$94$	−3.60384	−	2.08068i	−0.371707	−	0.214605i
$95$	−6.41085	−	3.70130i	−0.657739	−	0.379746i
$96$		0			0
$97$			2.72538i			0.276720i	0.990382	+	0.138360i	$0.0441831\pi$
$97$			2.72538i			0.276720i	−0.990382	+	0.138360i	$0.955817\pi$
$98$	−0.562763	+	6.97734i	−0.0568476	+	0.704818i
$99$		0			0
$100$	−1.93881	−	3.35811i	−0.193881	−	0.335811i
$101$	−4.67191	+	8.09198i	−0.464872	+	0.805182i	−0.999196	−	0.0400980i	$-0.987233\pi$
$101$	−4.67191	+	8.09198i	−0.464872	+	0.805182i	0.534324	+	0.845280i	$0.320566\pi$
$102$		0			0
$103$	−5.07651	+	2.93092i	−0.500203	+	0.288792i	−0.728797	−	0.684729i	$-0.759920\pi$
$103$	−5.07651	+	2.93092i	−0.500203	+	0.288792i	0.228594	+	0.973522i	$0.426587\pi$
$104$	−0.109947			−0.0107812
$105$		0			0
$106$	5.65224			0.548994
$107$	13.6257	−	7.86678i	1.31724	−	0.760510i	0.333958	−	0.942588i	$-0.391616\pi$
$107$	13.6257	−	7.86678i	1.31724	−	0.760510i	0.983284	+	0.182078i	$0.0582823\pi$
$108$		0			0
$109$	4.38244	−	7.59060i	0.419761	−	0.727048i	−0.576154	−	0.817341i	$-0.695447\pi$
$109$	4.38244	−	7.59060i	0.419761	−	0.727048i	0.995915	+	0.0902934i	$0.0287805\pi$
$110$	2.44641	+	4.23731i	0.233256	+	0.404011i
$111$		0			0
$112$	1.41398	−	2.23621i	0.133609	−	0.211302i
$113$		−	12.8267i		−	1.20663i	−0.797502	−	0.603317i	$-0.793846\pi$
$113$		−	12.8267i		−	1.20663i	0.797502	−	0.603317i	$-0.206154\pi$
$114$		0			0
$115$	−5.67967	−	3.27916i	−0.529632	−	0.305783i
$116$	−1.65318	−	0.954467i	−0.153494	−	0.0886200i
$117$		0			0
$118$			10.1954i			0.938564i
$119$	10.9824	+	0.442180i	1.00676	+	0.0405346i
$120$		0			0
$121$	5.16466	+	8.94546i	0.469515	+	0.813224i
$122$	−4.14076	+	7.17201i	−0.374887	+	0.649323i
$123$		0			0
$124$	−7.12988	+	4.11644i	−0.640282	+	0.369667i
$125$	−9.40518			−0.841225
$126$		0			0
$127$	−18.5491			−1.64597			−0.822985	−	0.568063i	$-0.807693\pi$
$127$	−18.5491			−1.64597			−0.822985	+	0.568063i	$0.807693\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−0.0582404	+	0.100875i	−0.00510802	+	0.00884734i
$131$	8.26841	+	14.3213i	0.722414	+	1.25126i	0.960030	+	0.279899i	$0.0903009\pi$
$131$	8.26841	+	14.3213i	0.722414	+	1.25126i	−0.237615	+	0.971359i	$0.576366\pi$
$132$		0			0
$133$	15.6253	+	9.88002i	1.35488	+	0.856707i
$134$		−	0.134336i		−	0.0116049i
$135$		0			0
$136$	−3.59776	−	2.07717i	−0.308505	−	0.178116i
$137$	4.42227	+	2.55320i	0.377820	+	0.218134i	0.676869	−	0.736103i	$-0.263336\pi$
$137$	4.42227	+	2.55320i	0.377820	+	0.218134i	−0.299049	+	0.954238i	$0.596670\pi$
$138$		0			0
$139$			12.2236i			1.03679i	0.855140	+	0.518397i	$0.173471\pi$
$139$			12.2236i			1.03679i	−0.855140	+	0.518397i	$0.826529\pi$
$140$	−1.30270	−	2.48187i	−0.110098	−	0.209756i
$141$		0			0
$142$	−6.95888	−	12.0531i	−0.583976	−	1.01148i
$143$	−0.253888	+	0.439746i	−0.0212312	+	0.0367734i
$144$		0			0
$145$	−1.75143	+	1.01119i	−0.145448	+	0.0839745i
$146$	14.4310			1.19432
$147$		0			0
$148$	5.24524			0.431156
$149$	−13.3064	+	7.68243i	−1.09010	+	0.629369i	−0.933603	−	0.358310i	$-0.883353\pi$
$149$	−13.3064	+	7.68243i	−1.09010	+	0.629369i	−0.156496	+	0.987679i	$0.550020\pi$
$150$		0			0
$151$	−2.21622	+	3.83861i	−0.180353	+	0.312381i	−0.942001	−	0.335610i	$-0.891057\pi$
$151$	−2.21622	+	3.83861i	−0.180353	+	0.312381i	0.761648	+	0.647992i	$0.224391\pi$
$152$	−3.49369	−	6.05124i	−0.283375	−	0.490820i
$153$		0			0
$154$	−5.67887	−	10.8192i	−0.457616	−	0.871838i
$155$			8.72213i			0.700578i
$156$		0			0
$157$	6.41157	+	3.70172i	0.511699	+	0.295430i	0.733532	−	0.679655i	$-0.237871\pi$
$157$	6.41157	+	3.70172i	0.511699	+	0.295430i	−0.221833	+	0.975085i	$0.571204\pi$
$158$	1.71155	+	0.988165i	0.136164	+	0.0786142i
$159$		0			0
$160$			1.05943i			0.0837550i
$161$	13.8432	+	8.75319i	1.09099	+	0.689848i
$162$		0			0
$163$	6.05503	+	10.4876i	0.474267	+	0.821454i	0.999566	−	0.0294636i	$-0.00937992\pi$
$163$	6.05503	+	10.4876i	0.474267	+	0.821454i	−0.525299	+	0.850918i	$0.676047\pi$
$164$	0.0916071	−	0.158668i	0.00715331	−	0.0123899i
$165$		0			0
$166$	−7.59900	+	4.38728i	−0.589797	+	0.340519i
$167$	0.306725			0.0237351			0.0118675	−	0.999930i	$-0.496222\pi$
$167$	0.306725			0.0237351			0.0118675	+	0.999930i	$0.496222\pi$
$168$		0			0
$169$	12.9879			0.999070
$170$	−3.81156	+	2.20061i	−0.292333	+	0.168779i
$171$		0			0
$172$	1.97099	−	3.41385i	0.150286	−	0.260304i
$173$	4.67625	+	8.09950i	0.355529	+	0.615793i	0.987208	−	0.159436i	$-0.0509676\pi$
$173$	4.67625	+	8.09950i	0.355529	+	0.615793i	−0.631680	+	0.775229i	$0.717634\pi$
$174$		0			0
$175$	10.2509	+	0.412727i	0.774895	+	0.0311992i
$176$			4.61837i			0.348123i
$177$		0			0
$178$	0.615296	+	0.355241i	0.0461184	+	0.0266265i
$179$	12.1270	+	7.00151i	0.906412	+	0.523317i	0.879275	−	0.476315i	$-0.158028\pi$
$179$	12.1270	+	7.00151i	0.906412	+	0.523317i	0.0271369	+	0.999632i	$0.491361\pi$
$180$		0			0
$181$			21.0404i			1.56392i	0.623330	+	0.781959i	$0.285779\pi$
$181$			21.0404i			1.56392i	−0.623330	+	0.781959i	$0.714221\pi$
$182$	0.155463	−	0.245865i	0.0115237	−	0.0182247i
$183$		0			0
$184$	−3.09522	−	5.36108i	−0.228183	−	0.395224i
$185$	2.77847	−	4.81245i	0.204277	−	0.353819i
$186$		0			0
$187$	−16.6158	+	9.59312i	−1.21507	+	0.701519i
$188$	−4.16135			−0.303498
$189$		0			0
$190$	−7.40261			−0.537042
$191$	5.77791	−	3.33588i	0.418075	−	0.241376i	−0.276178	−	0.961106i	$-0.589068\pi$
$191$	5.77791	−	3.33588i	0.418075	−	0.241376i	0.694253	+	0.719731i	$0.255735\pi$
$192$		0			0
$193$	8.95874	−	15.5170i	0.644864	−	1.11694i	−0.339468	−	0.940617i	$-0.610247\pi$
$193$	8.95874	−	15.5170i	0.644864	−	1.11694i	0.984333	−	0.176321i	$-0.0564195\pi$
$194$	1.36269	+	2.36025i	0.0978354	+	0.169456i
$195$		0			0
$196$	3.00130	+	6.32394i	0.214379	+	0.451710i
$197$			15.8680i			1.13055i	0.824903	+	0.565274i	$0.191230\pi$
$197$			15.8680i			1.13055i	−0.824903	+	0.565274i	$0.808770\pi$
$198$		0			0
$199$	−22.4402	−	12.9559i	−1.59074	−	0.918417i	−0.993179	−	0.116597i	$-0.962801\pi$
$199$	−22.4402	−	12.9559i	−1.59074	−	0.918417i	−0.597566	−	0.801820i	$-0.703865\pi$
$200$	−3.35811	−	1.93881i	−0.237454	−	0.137094i
$201$		0			0
$202$			9.34381i			0.657428i
$203$	4.47197	−	2.34728i	0.313871	−	0.164746i
$204$		0			0
$205$	−0.0970510	−	0.168097i	−0.00677833	−	0.0117404i
$206$	−2.93092	+	5.07651i	−0.204207	+	0.353697i
$207$		0			0
$208$	−0.0952168	+	0.0549735i	−0.00660210	+	0.00381172i
$209$	−32.2703			−2.23218
$210$		0			0
$211$	8.79169			0.605245			0.302623	−	0.953110i	$-0.402138\pi$
$211$	8.79169			0.605245			0.302623	+	0.953110i	$0.402138\pi$
$212$	4.89499	−	2.82612i	0.336189	−	0.194099i
$213$		0			0
$214$	7.86678	−	13.6257i	0.537762	−	0.931431i
$215$	−2.08812	−	3.61673i	−0.142408	−	0.246659i
$216$		0			0
$217$	0.876294	−	21.7645i	0.0594867	−	1.47747i
$218$		−	8.76487i		−	0.593632i
$219$		0			0
$220$	4.23731	+	2.44641i	0.285679	+	0.164937i
$221$	−0.395563	−	0.228378i	−0.0266084	−	0.0153624i
$222$		0			0
$223$		−	23.3943i		−	1.56660i	−0.621643	−	0.783301i	$-0.713535\pi$
$223$		−	23.3943i		−	1.56660i	0.621643	−	0.783301i	$-0.286465\pi$
$224$	0.106438	−	2.64361i	0.00711171	−	0.176634i
$225$		0			0
$226$	−6.41334	−	11.1082i	−0.426609	−	0.738909i
$227$	−6.18850	+	10.7188i	−0.410745	+	0.711432i	−0.994971	−	0.100159i	$-0.968065\pi$
$227$	−6.18850	+	10.7188i	−0.410745	+	0.711432i	0.584226	+	0.811591i	$0.301398\pi$
$228$		0			0
$229$	23.7156	−	13.6922i	1.56717	−	0.904806i	0.570674	−	0.821177i	$-0.306682\pi$
$229$	23.7156	−	13.6922i	1.56717	−	0.904806i	0.996497	−	0.0836293i	$-0.0266512\pi$
$230$	−6.55832			−0.432443
$231$		0			0
$232$	−1.90893			−0.125328
$233$	−24.2790	+	14.0175i	−1.59057	+	0.918316i	−0.597361	+	0.801973i	$0.703784\pi$
$233$	−24.2790	+	14.0175i	−1.59057	+	0.918316i	−0.993209	+	0.116343i	$0.962883\pi$
$234$		0			0
$235$	−2.20432	+	3.81800i	−0.143794	+	0.249059i
$236$	5.09771	+	8.82949i	0.331832	+	0.574751i
$237$		0			0
$238$	9.73216	−	5.10828i	0.630842	−	0.331121i
$239$			8.77707i			0.567741i	0.958863	+	0.283871i	$0.0916186\pi$
$239$			8.77707i			0.567741i	−0.958863	+	0.283871i	$0.908381\pi$
$240$		0			0
$241$	−10.3742	−	5.98957i	−0.668264	−	0.385822i	0.127155	−	0.991883i	$-0.459416\pi$
$241$	−10.3742	−	5.98957i	−0.668264	−	0.385822i	−0.795418	+	0.606061i	$0.792749\pi$
$242$	8.94546	+	5.16466i	0.575036	+	0.331997i
$243$		0			0
$244$			8.28152i			0.530170i
$245$	7.39198	+	0.596206i	0.472256	+	0.0380902i
$246$		0			0
$247$	−0.384120	−	0.665315i	−0.0244410	−	0.0423330i
$248$	−4.11644	+	7.12988i	−0.261394	+	0.452748i
$249$		0			0
$250$	−8.14513	+	4.70259i	−0.515143	+	0.297418i
$251$	−21.4657			−1.35490			−0.677450	−	0.735568i	$-0.736915\pi$
$251$	−21.4657			−1.35490			−0.677450	+	0.735568i	$0.736915\pi$
$252$		0			0
$253$	−28.5898			−1.79742
$254$	−16.0640	+	9.27457i	−1.00795	+	0.581938i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	12.6102	+	21.8415i	0.786604	+	1.36244i	0.928036	+	0.372489i	$0.121496\pi$
$257$	12.6102	+	21.8415i	0.786604	+	1.36244i	−0.141433	+	0.989948i	$0.545171\pi$
$258$		0			0
$259$	−7.41667	+	11.7295i	−0.460850	+	0.728834i
$260$			0.116481i			0.00722383i
$261$		0			0
$262$	14.3213	+	8.26841i	0.884773	+	0.510824i
$263$	1.00821	+	0.582090i	0.0621689	+	0.0358932i	0.530762	−	0.847521i	$-0.321906\pi$
$263$	1.00821	+	0.582090i	0.0621689	+	0.0358932i	−0.468593	+	0.883414i	$0.655239\pi$
$264$		0			0
$265$		−	5.98814i		−	0.367848i
$266$	18.4719	+	0.743724i	1.13258	+	0.0456007i
$267$		0			0
$268$	−0.0671680	−	0.116338i	−0.00410294	−	0.00710650i
$269$	5.50806	−	9.54025i	0.335833	−	0.581679i	−0.647812	−	0.761800i	$-0.724316\pi$
$269$	5.50806	−	9.54025i	0.335833	−	0.581679i	0.983644	+	0.180121i	$0.0576490\pi$
$270$		0			0
$271$	16.3994	−	9.46818i	0.996191	−	0.575151i	0.0890717	−	0.996025i	$-0.471610\pi$
$271$	16.3994	−	9.46818i	0.996191	−	0.575151i	0.907119	+	0.420874i	$0.138277\pi$
$272$	−4.15433			−0.251894
$273$		0			0
$274$	5.10639			0.308489
$275$	−15.5090	+	8.95413i	−0.935228	+	0.539954i
$276$		0			0
$277$	−5.13554	+	8.89501i	−0.308564	+	0.534449i	−0.978049	−	0.208377i	$-0.933182\pi$
$277$	−5.13554	+	8.89501i	−0.308564	+	0.534449i	0.669484	+	0.742826i	$0.266515\pi$
$278$	6.11181	+	10.5860i	0.366562	+	0.634904i
$279$		0			0
$280$	−2.36910	−	1.49801i	−0.141581	−	0.0895233i
$281$		−	18.3315i		−	1.09357i	−0.837274	−	0.546784i	$-0.815852\pi$
$281$		−	18.3315i		−	1.09357i	0.837274	−	0.546784i	$-0.184148\pi$
$282$		0			0
$283$	−5.13375	−	2.96397i	−0.305170	−	0.176190i	0.339593	−	0.940572i	$-0.389711\pi$
$283$	−5.13375	−	2.96397i	−0.305170	−	0.176190i	−0.644763	+	0.764383i	$0.723044\pi$
$284$	−12.0531	−	6.95888i	−0.715222	−	0.412933i
$285$		0			0
$286$			0.507775i			0.0300254i
$287$	0.225285	+	0.429207i	0.0132982	+	0.0253353i
$288$		0			0
$289$	−0.129246	−	0.223861i	−0.00760272	−	0.0131683i
$290$	−1.01119	+	1.75143i	−0.0593790	+	0.102847i
$291$		0			0
$292$	12.4976	−	7.21551i	0.731369	−	0.422256i
$293$	4.21673			0.246344			0.123172	−	0.992385i	$-0.460693\pi$
$293$	4.21673			0.246344			0.123172	+	0.992385i	$0.460693\pi$
$294$		0			0
$295$	10.8013			0.628875
$296$	4.54251	−	2.62262i	0.264028	−	0.152437i
$297$		0			0
$298$	−7.68243	+	13.3064i	−0.445031	+	0.770816i
$299$	−0.340310	−	0.589435i	−0.0196807	−	0.0340879i
$300$		0			0
$301$	4.84716	+	9.23468i	0.279386	+	0.532278i
$302$			4.43244i			0.255058i
$303$		0			0
$304$	−6.05124	−	3.49369i	−0.347062	−	0.200377i
$305$	7.59821	+	4.38683i	0.435072	+	0.251189i
$306$		0			0
$307$			11.9212i			0.680380i	0.940357	+	0.340190i	$0.110491\pi$
$307$			11.9212i			0.680380i	−0.940357	+	0.340190i	$0.889509\pi$
$308$	−10.3277	−	6.53029i	−0.588473	−	0.372098i
$309$		0			0
$310$	4.36106	+	7.55359i	0.247692	+	0.429015i
$311$	−12.7837	+	22.1420i	−0.724896	+	1.25556i	0.234121	+	0.972207i	$0.424779\pi$
$311$	−12.7837	+	22.1420i	−0.724896	+	1.25556i	−0.959017	+	0.283349i	$0.908555\pi$
$312$		0			0
$313$	25.0836	−	14.4820i	1.41781	−	0.818573i	0.421705	−	0.906733i	$-0.361432\pi$
$313$	25.0836	−	14.4820i	1.41781	−	0.818573i	0.996106	+	0.0881598i	$0.0280986\pi$
$314$	7.40344			0.417800
$315$		0			0
$316$	1.97633			0.111177
$317$	−5.06909	+	2.92664i	−0.284709	+	0.164377i	−0.635553	−	0.772057i	$-0.719228\pi$
$317$	−5.06909	+	2.92664i	−0.284709	+	0.164377i	0.350844	+	0.936434i	$0.385895\pi$
$318$		0			0
$319$	−4.40808	+	7.63502i	−0.246805	+	0.427479i
$320$	0.529713	+	0.917490i	0.0296119	+	0.0512893i
$321$		0			0
$322$	16.3651	+	0.658901i	0.911993	+	0.0367191i
$323$		−	29.0279i		−	1.61515i
$324$		0			0
$325$	−0.369214	−	0.213166i	−0.0204803	−	0.0118243i
$326$	10.4876	+	6.05503i	0.580856	+	0.335357i
$327$		0			0
$328$		−	0.183214i		−	0.0101163i
$329$	5.88408	−	9.30567i	0.324400	−	0.513038i
$330$		0			0
$331$	2.24013	+	3.88002i	0.123129	+	0.213265i	0.921000	−	0.389563i	$-0.127374\pi$
$331$	2.24013	+	3.88002i	0.123129	+	0.213265i	−0.797871	+	0.602828i	$0.794041\pi$
$332$	−4.38728	+	7.59900i	−0.240783	+	0.417049i
$333$		0			0
$334$	0.265632	−	0.153363i	0.0145347	−	0.00839162i
$335$	−0.142319			−0.00777572
$336$		0			0
$337$	19.5461			1.06475			0.532373	−	0.846510i	$-0.321300\pi$
$337$	19.5461			1.06475			0.532373	+	0.846510i	$0.321300\pi$
$338$	11.2479	−	6.49396i	0.611803	−	0.353225i
$339$		0			0
$340$	−2.20061	+	3.81156i	−0.119345	+	0.206711i
$341$	19.0112	+	32.9284i	1.02952	+	1.78317i
$342$		0			0
$343$	−18.3855	−	2.23038i	−0.992722	−	0.120429i
$344$		−	3.94198i		−	0.212537i
$345$		0			0
$346$	8.09950	+	4.67625i	0.435432	+	0.251397i
$347$	14.6810	+	8.47610i	0.788119	+	0.455021i	0.839300	−	0.543669i	$-0.182965\pi$
$347$	14.6810	+	8.47610i	0.788119	+	0.455021i	−0.0511808	+	0.998689i	$0.516298\pi$
$348$		0			0
$349$		−	23.7573i		−	1.27170i	−0.771813	−	0.635850i	$-0.780650\pi$
$349$		−	23.7573i		−	1.27170i	0.771813	−	0.635850i	$-0.219350\pi$
$350$	9.08390	−	4.76802i	0.485555	−	0.254861i
$351$		0			0
$352$	2.30918	+	3.99962i	0.123080	+	0.213181i
$353$	−2.32588	+	4.02854i	−0.123794	+	0.214417i	−0.921261	−	0.388945i	$-0.872840\pi$
$353$	−2.32588	+	4.02854i	−0.123794	+	0.214417i	0.797467	+	0.603363i	$0.206173\pi$
$354$		0			0
$355$	−12.7694	+	7.37242i	−0.677730	+	0.391287i
$356$	0.710483			0.0376555
$357$		0			0
$358$	14.0030			0.740082
$359$	−12.9258	+	7.46271i	−0.682197	+	0.393867i	−0.800682	−	0.599089i	$-0.795530\pi$
$359$	−12.9258	+	7.46271i	−0.682197	+	0.393867i	0.118485	+	0.992956i	$0.462196\pi$
$360$		0			0
$361$	14.9117	−	25.8278i	0.784825	−	1.35936i
$362$	10.5202	+	18.2215i	0.552928	+	0.957700i
$363$		0			0
$364$	0.0117026	−	0.290657i	0.000613381	−	0.0152346i
$365$		−	15.2886i		−	0.800242i
$366$		0			0
$367$	−24.7732	−	14.3028i	−1.29315	−	0.746600i	−0.313938	−	0.949443i	$-0.601648\pi$
$367$	−24.7732	−	14.3028i	−1.29315	−	0.746600i	−0.979211	+	0.202843i	$0.934982\pi$
$368$	−5.36108	−	3.09522i	−0.279466	−	0.161350i
$369$		0			0
$370$		−	5.55694i		−	0.288892i
$371$	−0.601616	+	14.9423i	−0.0312343	+	0.775767i
$372$		0			0
$373$	8.41233	+	14.5706i	0.435574	+	0.754436i	0.997342	−	0.0728586i	$-0.0232122\pi$
$373$	8.41233	+	14.5706i	0.435574	+	0.754436i	−0.561769	+	0.827294i	$0.689879\pi$
$374$	−9.59312	+	16.6158i	−0.496049	+	0.859181i
$375$		0			0
$376$	−3.60384	+	2.08068i	−0.185854	+	0.107303i
$377$	−0.209881			−0.0108094
$378$		0			0
$379$	−31.2010			−1.60269			−0.801345	−	0.598202i	$-0.795882\pi$
$379$	−31.2010			−1.60269			−0.801345	+	0.598202i	$0.795882\pi$
$380$	−6.41085	+	3.70130i	−0.328869	+	0.189873i
$381$		0			0
$382$	3.33588	−	5.77791i	0.170678	−	0.295624i
$383$	9.97740	+	17.2814i	0.509821	+	0.883037i	0.999935	+	0.0113781i	$0.00362185\pi$
$383$	9.97740	+	17.2814i	0.509821	+	0.883037i	−0.490114	+	0.871658i	$0.663045\pi$
$384$		0			0
$385$	−11.4622	+	6.01634i	−0.584167	+	0.306621i
$386$		−	17.9175i		−	0.911976i
$387$		0			0
$388$	2.36025	+	1.36269i	0.119823	+	0.0691801i
$389$	18.7318	+	10.8148i	0.949742	+	0.548334i	0.893001	−	0.450055i	$-0.148596\pi$
$389$	18.7318	+	10.8148i	0.949742	+	0.548334i	0.0567415	+	0.998389i	$0.481929\pi$
$390$		0			0
$391$		−	25.7172i		−	1.30057i
$392$	5.76117	+	3.97604i	0.290983	+	0.200820i
$393$		0			0
$394$	7.93400	+	13.7421i	0.399709	+	0.692316i
$395$	1.04689	−	1.81326i	0.0526747	−	0.0912352i
$396$		0			0
$397$	28.0214	−	16.1782i	1.40635	−	0.811959i	0.411320	−	0.911491i	$-0.365068\pi$
$397$	28.0214	−	16.1782i	1.40635	−	0.811959i	0.995034	+	0.0995319i	$0.0317345\pi$
$398$	−25.9117			−1.29884
$399$		0			0
$400$	−3.87762			−0.193881
$401$	21.0976	−	12.1807i	1.05357	−	0.608276i	0.129920	−	0.991524i	$-0.458528\pi$
$401$	21.0976	−	12.1807i	1.05357	−	0.608276i	0.923645	+	0.383248i	$0.125195\pi$
$402$		0			0
$403$	−0.452590	+	0.783909i	−0.0225451	+	0.0390493i
$404$	4.67191	+	8.09198i	0.232436	+	0.402591i
$405$		0			0
$406$	2.69920	−	4.26878i	0.133959	−	0.211856i
$407$		−	24.2244i		−	1.20076i
$408$		0			0
$409$	−15.3548	−	8.86511i	−0.759247	−	0.438351i	0.0697785	−	0.997563i	$-0.477771\pi$
$409$	−15.3548	−	8.86511i	−0.759247	−	0.438351i	−0.829025	+	0.559211i	$0.811104\pi$
$410$	−0.168097	−	0.0970510i	−0.00830173	−	0.00479301i
$411$		0			0
$412$			5.86185i			0.288792i
$413$	−26.9527	−	1.08518i	−1.32626	−	0.0533984i
$414$		0			0
$415$	4.64800	+	8.05058i	0.228162	+	0.395187i
$416$	−0.0549735	+	0.0952168i	−0.00269530	+	0.00466839i
$417$		0			0
$418$	−27.9469	+	16.1351i	−1.36693	+	0.789195i
$419$	−26.5850			−1.29876			−0.649382	−	0.760463i	$-0.724972\pi$
$419$	−26.5850			−1.29876			−0.649382	+	0.760463i	$0.724972\pi$
$420$		0			0
$421$	21.5180			1.04873			0.524363	−	0.851495i	$-0.324304\pi$
$421$	21.5180			1.04873			0.524363	+	0.851495i	$0.324304\pi$
$422$	7.61383	−	4.39585i	0.370635	−	0.213986i
$423$		0			0
$424$	2.82612	−	4.89499i	0.137249	−	0.237722i
$425$	−8.05446	−	13.9507i	−0.390698	−	0.676710i
$426$		0			0
$427$	−18.5192	−	11.7099i	−0.896209	−	0.566683i
$428$		−	15.7336i		−	0.760510i
$429$		0			0
$430$	−3.61673	−	2.08812i	−0.174414	−	0.100698i
$431$	1.99320	+	1.15078i	0.0960092	+	0.0554310i	0.547236	−	0.836978i	$-0.315680\pi$
$431$	1.99320	+	1.15078i	0.0960092	+	0.0554310i	−0.451227	+	0.892409i	$0.649013\pi$
$432$		0			0
$433$			20.3476i			0.977841i	0.872328	+	0.488920i	$0.162609\pi$
$433$			20.3476i			0.977841i	−0.872328	+	0.488920i	$0.837391\pi$
$434$	−10.1234	−	19.2868i	−0.485937	−	0.925794i
$435$		0			0
$436$	−4.38244	−	7.59060i	−0.209881	−	0.363524i
$437$	21.6275	−	37.4599i	1.03458	−	1.79195i
$438$		0			0
$439$	−13.9877	+	8.07581i	−0.667597	+	0.385438i	−0.795166	−	0.606392i	$-0.792616\pi$
$439$	−13.9877	+	8.07581i	−0.667597	+	0.385438i	0.127568	+	0.991830i	$0.459283\pi$
$440$	4.89282			0.233256
$441$		0			0
$442$	−0.456756			−0.0217257
$443$	31.7511	−	18.3315i	1.50854	−	0.870955i	0.508588	−	0.861010i	$-0.330168\pi$
$443$	31.7511	−	18.3315i	1.50854	−	0.870955i	0.999951	−	0.00994511i	$-0.00316568\pi$
$444$		0			0
$445$	0.376352	−	0.651861i	0.0178408	−	0.0309012i
$446$	−11.6972	−	20.2601i	−0.553877	−	0.959343i
$447$		0			0
$448$	−1.22963	−	2.34265i	−0.0580944	−	0.110680i
$449$		−	5.05345i		−	0.238487i	−0.992865	−	0.119243i	$-0.961953\pi$
$449$		−	5.05345i		−	0.238487i	0.992865	−	0.119243i	$-0.0380469\pi$
$450$		0			0
$451$	−0.732788	−	0.423075i	−0.0345056	−	0.0199218i
$452$	−11.1082	−	6.41334i	−0.522488	−	0.301658i
$453$		0			0
$454$			12.3770i			0.580882i
$455$	−0.260476	−	0.164702i	−0.0122113	−	0.00772134i
$456$		0			0
$457$	11.8881	+	20.5907i	0.556100	+	0.963193i	0.997817	+	0.0660385i	$0.0210360\pi$
$457$	11.8881	+	20.5907i	0.556100	+	0.963193i	−0.441717	+	0.897154i	$0.645631\pi$
$458$	13.6922	−	23.7156i	0.639795	−	1.10816i
$459$		0			0
$460$	−5.67967	+	3.27916i	−0.264816	+	0.152892i
$461$	30.7582			1.43255			0.716275	−	0.697818i	$-0.245846\pi$
$461$	30.7582			1.43255			0.716275	+	0.697818i	$0.245846\pi$
$462$		0			0
$463$	−6.71080			−0.311877			−0.155939	−	0.987767i	$-0.549840\pi$
$463$	−6.71080			−0.311877			−0.155939	+	0.987767i	$0.549840\pi$
$464$	−1.65318	+	0.954467i	−0.0767472	+	0.0443100i
$465$		0			0
$466$	−14.0175	+	24.2790i	−0.649347	+	1.12470i
$467$	0.0100896	+	0.0174757i	0.000466891	+	0.000808679i	0.866259	−	0.499596i	$-0.166518\pi$
$467$	0.0100896	+	0.0174757i	0.000466891	+	0.000808679i	−0.865792	+	0.500404i	$0.833185\pi$
$468$		0			0
$469$	0.355132	+	0.0142985i	0.0163985	+	0.000660243i
$470$			4.40865i			0.203356i
$471$		0			0
$472$	8.82949	+	5.09771i	0.406410	+	0.234641i
$473$	−15.7664	−	9.10275i	−0.724941	−	0.418545i
$474$		0			0
$475$		−	27.0943i		−	1.24317i
$476$	5.87416	−	9.28998i	0.269242	−	0.425805i
$477$		0			0
$478$	4.38853	+	7.60116i	0.200727	+	0.347669i
$479$	−7.25817	+	12.5715i	−0.331634	+	0.574407i	−0.982832	−	0.184500i	$-0.940933\pi$
$479$	−7.25817	+	12.5715i	−0.331634	+	0.574407i	0.651198	+	0.758908i	$0.274267\pi$
$480$		0			0
$481$	0.499435	−	0.288349i	0.0227723	−	0.0131476i
$482$	−11.9791			−0.545635
$483$		0			0
$484$	10.3293			0.469515
$485$	2.50051	−	1.44367i	0.113542	−	0.0655536i
$486$		0			0
$487$	10.3182	−	17.8716i	0.467560	−	0.809838i	−0.531753	−	0.846900i	$-0.678466\pi$
$487$	10.3182	−	17.8716i	0.467560	−	0.809838i	0.999313	+	0.0370614i	$0.0117997\pi$
$488$	4.14076	+	7.17201i	0.187443	+	0.324661i
$489$		0			0
$490$	6.69975	−	3.17966i	0.302664	−	0.143642i
$491$		−	11.7960i		−	0.532347i	−0.963925	−	0.266174i	$-0.914241\pi$
$491$		−	11.7960i		−	0.532347i	0.963925	−	0.266174i	$-0.0857594\pi$
$492$		0			0
$493$	−6.86788	−	3.96517i	−0.309314	−	0.178582i
$494$	−0.665315	−	0.384120i	−0.0299340	−	0.0172824i
$495$		0			0
$496$			8.23288i			0.369667i
$497$	32.6045	−	17.1136i	1.46251	−	0.767652i
$498$		0			0
$499$	−13.4583	−	23.3104i	−0.602475	−	1.04352i	−0.992445	−	0.122690i	$-0.960848\pi$
$499$	−13.4583	−	23.3104i	−0.602475	−	1.04352i	0.389970	−	0.920828i	$-0.372485\pi$
$500$	−4.70259	+	8.14513i	−0.210306	+	0.364261i
$501$		0			0
$502$	−18.5898	+	10.7328i	−0.829704	+	0.479030i
$503$	−30.5315			−1.36133			−0.680666	−	0.732594i	$-0.738309\pi$
$503$	−30.5315			−1.36133			−0.680666	+	0.732594i	$0.738309\pi$
$504$		0			0
$505$	9.89908			0.440503
$506$	−24.7595	+	14.2949i	−1.10069	+	0.635485i
$507$		0			0
$508$	−9.27457	+	16.0640i	−0.411492	+	0.712726i
$509$	−9.50456	−	16.4624i	−0.421282	−	0.729682i	0.574783	−	0.818306i	$-0.305087\pi$
$509$	−9.50456	−	16.4624i	−0.421282	−	0.729682i	−0.996065	+	0.0886236i	$0.971753\pi$
$510$		0			0
$511$	−1.53601	+	38.1500i	−0.0679493	+	1.68766i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	21.8415	+	12.6102i	0.963389	+	0.556213i
$515$	5.37819	+	3.10510i	0.236991	+	0.136827i
$516$		0			0
$517$			19.2187i			0.845235i
$518$	−0.558294	+	13.8664i	−0.0245300	+	0.609253i
$519$		0			0
$520$	0.0582404	+	0.100875i	0.00255401	+	0.00442367i
$521$	−20.5185	+	35.5391i	−0.898933	+	1.55700i	−0.0700717	+	0.997542i	$0.522323\pi$
$521$	−20.5185	+	35.5391i	−0.898933	+	1.55700i	−0.828861	+	0.559455i	$0.811011\pi$
$522$		0			0
$523$	3.71694	−	2.14598i	0.162531	−	0.0938371i	−0.416528	−	0.909123i	$-0.636753\pi$
$523$	3.71694	−	2.14598i	0.162531	−	0.0938371i	0.579059	+	0.815286i	$0.303420\pi$
$524$	16.5368			0.722414
$525$		0			0
$526$	1.16418			0.0507607
$527$	−29.6199	+	17.1011i	−1.29026	+	0.744934i
$528$		0			0
$529$	7.66081	−	13.2689i	0.333079	−	0.576910i
$530$	−2.99407	−	5.18588i	−0.130054	−	0.225260i
$531$		0			0
$532$	16.3690	−	8.59186i	0.709685	−	0.372504i
$533$		−	0.0201438i		−	0.000872526i
$534$		0			0
$535$	−14.4354	−	8.33427i	−0.624096	−	0.360322i
$536$	−0.116338	−	0.0671680i	−0.00502505	−	0.00290121i
$537$		0			0
$538$		−	11.0161i		−	0.474939i
$539$	29.2063	−	13.8611i	1.25800	−	0.597041i
$540$		0			0
$541$	6.40829	+	11.0995i	0.275514	+	0.477204i	0.970265	−	0.242047i	$-0.0778187\pi$
$541$	6.40829	+	11.0995i	0.275514	+	0.477204i	−0.694751	+	0.719251i	$0.744485\pi$
$542$	9.46818	−	16.3994i	0.406693	−	0.704413i
$543$		0			0
$544$	−3.59776	+	2.07717i	−0.154253	+	0.0890578i
$545$	−9.28574			−0.397757
$546$		0			0
$547$	−3.30179			−0.141174			−0.0705871	−	0.997506i	$-0.522487\pi$
$547$	−3.30179			−0.141174			−0.0705871	+	0.997506i	$0.522487\pi$
$548$	4.42227	−	2.55320i	0.188910	−	0.109067i
$549$		0			0
$550$	−8.95413	+	15.5090i	−0.381805	+	0.661306i
$551$	−6.66921	−	11.5514i	−0.284118	−	0.492107i
$552$		0			0
$553$	−2.79450	+	4.41950i	−0.118834	+	0.187936i
$554$			10.2711i			0.436376i
$555$		0			0
$556$	10.5860	+	6.11181i	0.448945	+	0.259199i
$557$	−17.5572	−	10.1367i	−0.743924	−	0.429505i	0.0795702	−	0.996829i	$-0.474645\pi$
$557$	−17.5572	−	10.1367i	−0.743924	−	0.429505i	−0.823494	+	0.567324i	$0.807979\pi$
$558$		0			0
$559$		−	0.433408i		−	0.0183312i
$560$	−2.80071	−	0.112764i	−0.118352	−	0.00476513i
$561$		0			0
$562$	−9.16577	−	15.8756i	−0.386634	−	0.669671i
$563$	12.7929	−	22.1580i	0.539158	−	0.933849i	−0.459791	−	0.888027i	$-0.652076\pi$
$563$	12.7929	−	22.1580i	0.539158	−	0.933849i	0.998950	−	0.0458223i	$-0.0145908\pi$
$564$		0			0
$565$	−11.7684	+	6.79447i	−0.495099	+	0.285845i
$566$	−5.92795			−0.249170
$567$		0			0
$568$	−13.9178			−0.583976
$569$	9.39677	−	5.42523i	0.393933	−	0.227437i	−0.289930	−	0.957048i	$-0.593632\pi$
$569$	9.39677	−	5.42523i	0.393933	−	0.227437i	0.683863	+	0.729611i	$0.260299\pi$
$570$		0			0
$571$	−10.0578	+	17.4207i	−0.420908	+	0.729033i	−0.996028	−	0.0890351i	$-0.971622\pi$
$571$	−10.0578	+	17.4207i	−0.420908	+	0.729033i	0.575121	+	0.818068i	$0.304955\pi$
$572$	0.253888	+	0.439746i	0.0106156	+	0.0183867i
$573$		0			0
$574$	0.409706	+	0.259062i	0.0171008	+	0.0108130i
$575$		−	24.0042i		−	1.00104i
$576$		0			0
$577$	9.49312	+	5.48085i	0.395204	+	0.228171i	0.684412	−	0.729095i	$-0.260059\pi$
$577$	9.49312	+	5.48085i	0.395204	+	0.228171i	−0.289209	+	0.957266i	$0.593392\pi$
$578$	−0.223861	−	0.129246i	−0.00931139	−	0.00537593i
$579$		0			0
$580$			2.02237i			0.0839745i
$581$	−10.7894	−	20.5558i	−0.447621	−	0.852797i
$582$		0			0
$583$	−13.0521	−	22.6069i	−0.540562	−	0.936280i
$584$	7.21551	−	12.4976i	0.298580	−	0.517156i
$585$		0			0
$586$	3.65180	−	2.10837i	0.150854	−	0.0870958i
$587$	−3.99027			−0.164696			−0.0823481	−	0.996604i	$-0.526242\pi$
$587$	−3.99027			−0.164696			−0.0823481	+	0.996604i	$0.526242\pi$
$588$		0			0
$589$	−57.5262			−2.37032
$590$	9.35419	−	5.40065i	0.385106	−	0.222341i
$591$		0			0
$592$	2.62262	−	4.54251i	0.107789	−	0.186696i
$593$	−7.47849	−	12.9531i	−0.307105	−	0.531921i	0.670623	−	0.741798i	$-0.266027\pi$
$593$	−7.47849	−	12.9531i	−0.307105	−	0.531921i	−0.977728	+	0.209877i	$0.932694\pi$
$594$		0			0
$595$	−5.41185	−	10.3105i	−0.221864	−	0.422690i
$596$			15.3649i			0.629369i
$597$		0			0
$598$	−0.589435	−	0.340310i	−0.0241038	−	0.0139163i
$599$	26.7263	+	15.4304i	1.09201	+	0.630470i	0.934110	−	0.356986i	$-0.116196\pi$
$599$	26.7263	+	15.4304i	1.09201	+	0.630470i	0.157896	+	0.987456i	$0.449529\pi$
$600$		0			0
$601$		−	9.88311i		−	0.403140i	−0.979474	−	0.201570i	$-0.935396\pi$
$601$		−	9.88311i		−	0.403140i	0.979474	−	0.201570i	$-0.0646044\pi$
$602$	8.81510	+	5.57389i	0.359277	+	0.227175i
$603$		0			0
$604$	2.21622	+	3.83861i	0.0901767	+	0.156191i
$605$	5.47158	−	9.47706i	0.222451	−	0.385297i
$606$		0			0
$607$	−16.4036	+	9.47063i	−0.665802	+	0.384401i	−0.794484	−	0.607285i	$-0.792259\pi$
$607$	−16.4036	+	9.47063i	−0.665802	+	0.384401i	0.128682	+	0.991686i	$0.458925\pi$
$608$	−6.98737			−0.283375
$609$		0			0
$610$	8.77366			0.355235
$611$	−0.396231	+	0.228764i	−0.0160298	+	0.00925480i
$612$		0			0
$613$	−19.8499	+	34.3810i	−0.801730	+	1.38864i	0.116747	+	0.993162i	$0.462753\pi$
$613$	−19.8499	+	34.3810i	−0.801730	+	1.38864i	−0.918477	+	0.395475i	$0.870580\pi$
$614$	5.96061	+	10.3241i	0.240551	+	0.416646i
$615$		0			0
$616$	−12.2092	−	0.491571i	−0.491921	−	0.0198060i
$617$		−	40.3125i		−	1.62292i	−0.584409	−	0.811460i	$-0.698673\pi$
$617$		−	40.3125i		−	1.62292i	0.584409	−	0.811460i	$-0.301327\pi$
$618$		0			0
$619$	−3.41119	−	1.96945i	−0.137107	−	0.0791589i	0.429877	−	0.902887i	$-0.358557\pi$
$619$	−3.41119	−	1.96945i	−0.137107	−	0.0791589i	−0.566985	+	0.823728i	$0.691890\pi$
$620$	7.55359	+	4.36106i	0.303359	+	0.175145i
$621$		0			0
$622$			25.5673i			1.02516i
$623$	−1.00461	+	1.58879i	−0.0402489	+	0.0636536i
$624$		0			0
$625$	−4.71199	−	8.16141i	−0.188480	−	0.326456i
$626$	14.4820	−	25.0836i	0.578819	−	1.00254i
$627$		0			0
$628$	6.41157	−	3.70172i	0.255849	−	0.147715i
$629$	21.7905			0.868843
$630$		0			0
$631$	43.9338			1.74898			0.874489	−	0.485046i	$-0.161197\pi$
$631$	43.9338			1.74898			0.874489	+	0.485046i	$0.161197\pi$
$632$	1.71155	−	0.988165i	0.0680819	−	0.0393071i
$633$		0			0
$634$	−2.92664	+	5.06909i	−0.116232	+	0.201319i
$635$	9.82573	+	17.0187i	0.389922	+	0.675365i
$636$		0			0
$637$	0.633423	+	0.437153i	0.0250972	+	0.0173206i
$638$			8.81616i			0.349035i
$639$		0			0
$640$	0.917490	+	0.529713i	0.0362670	+	0.0209388i
$641$	−30.5086	−	17.6141i	−1.20502	−	0.695716i	−0.243349	−	0.969939i	$-0.578246\pi$
$641$	−30.5086	−	17.6141i	−1.20502	−	0.695716i	−0.961666	+	0.274223i	$0.911579\pi$
$642$		0			0
$643$		−	12.5707i		−	0.495738i	−0.968794	−	0.247869i	$-0.920270\pi$
$643$		−	12.5707i		−	0.495738i	0.968794	−	0.247869i	$-0.0797303\pi$
$644$	14.5021	−	7.61194i	0.571461	−	0.299952i
$645$		0			0
$646$	−14.5139	−	25.1389i	−0.571043	−	0.989076i
$647$	−1.20915	+	2.09431i	−0.0475366	+	0.0823359i	−0.888815	−	0.458267i	$-0.848470\pi$
$647$	−1.20915	+	2.09431i	−0.0475366	+	0.0823359i	0.841278	+	0.540603i	$0.181804\pi$
$648$		0			0
$649$	40.7778	−	23.5431i	1.60067	−	0.924147i
$650$	−0.426332			−0.0167221
$651$		0			0
$652$	12.1101			0.474267
$653$	−39.8665	+	23.0169i	−1.56010	+	0.900722i	−0.562850	+	0.826559i	$0.690295\pi$
$653$	−39.8665	+	23.0169i	−1.56010	+	0.900722i	−0.997246	+	0.0741631i	$0.976371\pi$
$654$		0			0
$655$	8.75977	−	15.1724i	0.342273	−	0.592833i
$656$	−0.0916071	−	0.158668i	−0.00357666	−	0.00619495i
$657$		0			0
$658$	0.442927	−	11.0010i	0.0172671	−	0.428863i
$659$		−	2.65193i		−	0.103305i	−0.998665	−	0.0516523i	$-0.983551\pi$
$659$		−	2.65193i		−	0.103305i	0.998665	−	0.0516523i	$-0.0164488\pi$
$660$		0			0
$661$	−2.21722	−	1.28011i	−0.0862399	−	0.0497906i	0.456260	−	0.889847i	$-0.349189\pi$
$661$	−2.21722	−	1.28011i	−0.0862399	−	0.0497906i	−0.542500	+	0.840056i	$0.682522\pi$
$662$	3.88002	+	2.24013i	0.150801	+	0.0870651i
$663$		0			0
$664$			8.77457i			0.340519i
$665$	0.787921	−	19.5696i	0.0305543	−	0.758877i
$666$		0			0
$667$	−5.90858	−	10.2340i	−0.228781	−	0.396260i
$668$	0.153363	−	0.265632i	0.00593377	−	0.0102776i
$669$		0			0
$670$	−0.123252	+	0.0711595i	−0.00476164	+	0.00274913i
$671$	38.2471			1.47651
$672$		0			0
$673$	−0.663559			−0.0255783			−0.0127892	−	0.999918i	$-0.504071\pi$
$673$	−0.663559			−0.0255783			−0.0127892	+	0.999918i	$0.504071\pi$
$674$	16.9274	−	9.77306i	0.652021	−	0.376444i
$675$		0			0
$676$	6.49396	−	11.2479i	0.249768	−	0.432610i
$677$	17.5181	+	30.3423i	0.673277	+	1.16615i	0.976969	+	0.213380i	$0.0684471\pi$
$677$	17.5181	+	30.3423i	0.673277	+	1.16615i	−0.303693	+	0.952770i	$0.598220\pi$
$678$		0			0
$679$	−6.38461	+	3.35120i	−0.245019	+	0.128607i
$680$			4.40121i			0.168779i
$681$		0			0
$682$	32.9284	+	19.0112i	1.26089	+	0.727978i
$683$	−38.0531	−	21.9700i	−1.45606	−	0.840657i	−0.457247	−	0.889340i	$-0.651164\pi$
$683$	−38.0531	−	21.9700i	−1.45606	−	0.840657i	−0.998814	+	0.0486825i	$0.984498\pi$
$684$		0			0
$685$		−	5.40985i		−	0.206700i
$686$	−17.0375	+	7.26117i	−0.650494	+	0.277233i
$687$		0			0
$688$	−1.97099	−	3.41385i	−0.0751432	−	0.130152i
$689$	0.310723	−	0.538189i	0.0118376	−	0.0205034i
$690$		0			0
$691$	6.87208	−	3.96760i	0.261426	−	0.150935i	−0.363559	−	0.931571i	$-0.618438\pi$
$691$	6.87208	−	3.96760i	0.261426	−	0.150935i	0.624985	+	0.780637i	$0.285105\pi$
$692$	9.35250			0.355529
$693$		0			0
$694$	16.9522			0.643497
$695$	11.2151	−	6.47502i	0.425411	−	0.245611i
$696$		0			0
$697$	0.380566	−	0.659160i	0.0144150	−	0.0249675i
$698$	−11.8787	−	20.5744i	−0.449614	−	0.778754i
$699$		0			0
$700$	5.48288	−	8.67118i	0.207233	−	0.327740i
$701$			17.7111i			0.668940i	0.942406	+	0.334470i	$0.108557\pi$
$701$			17.7111i			0.668940i	−0.942406	+	0.334470i	$0.891443\pi$
$702$		0			0
$703$	31.7402	+	18.3252i	1.19710	+	0.691148i
$704$	3.99962	+	2.30918i	0.150742	+	0.0870307i
$705$		0			0
$706$			4.65176i			0.175071i
$707$	−24.7014	−	0.994540i	−0.928991	−	0.0374035i
$708$		0			0
$709$	−0.932165	−	1.61456i	−0.0350082	−	0.0606359i	0.847990	−	0.530011i	$-0.177812\pi$
$709$	−0.932165	−	1.61456i	−0.0350082	−	0.0606359i	−0.882999	+	0.469376i	$0.844479\pi$
$710$	−7.37242	+	12.7694i	−0.276682	+	0.479227i
$711$		0			0
$712$	0.615296	−	0.355241i	0.0230592	−	0.0133132i
$713$	−50.9652			−1.90866
$714$		0			0
$715$	0.537951			0.0201182
$716$	12.1270	−	7.00151i	0.453206	−	0.261659i
$717$		0			0
$718$	−7.46271	+	12.9258i	−0.278506	+	0.482386i
$719$	4.00621	+	6.93896i	0.149406	+	0.258779i	0.931008	−	0.364998i	$-0.118930\pi$
$719$	4.00621	+	6.93896i	0.149406	+	0.258779i	−0.781602	+	0.623778i	$0.785597\pi$
$720$		0			0
$721$	−13.1083	−	8.28855i	−0.488180	−	0.308682i
$722$		−	29.8234i		−	1.10991i
$723$		0			0
$724$	18.2215	+	10.5202i	0.677196	+	0.390979i
$725$	−6.41042	−	3.70106i	−0.238077	−	0.137454i
$726$		0			0
$727$			1.52705i			0.0566350i	0.999599	+	0.0283175i	$0.00901494\pi$
$727$			1.52705i			0.0566350i	−0.999599	+	0.0283175i	$0.990985\pi$
$728$	−0.135194	−	0.257567i	−0.00501061	−	0.00954608i
$729$		0			0
$730$	−7.64431	−	13.2403i	−0.282928	−	0.490046i
$731$	8.18814	−	14.1823i	0.302849	−	0.524551i
$732$		0			0
$733$	5.22464	−	3.01645i	0.192977	−	0.111415i	−0.400399	−	0.916341i	$-0.631128\pi$
$733$	5.22464	−	3.01645i	0.192977	−	0.111415i	0.593375	+	0.804926i	$0.297795\pi$
$734$	−28.6056			−1.05585
$735$		0			0
$736$	−6.19045			−0.228183
$737$	−0.537293	+	0.310206i	−0.0197915	+	0.0114266i
$738$		0			0
$739$	−2.92233	+	5.06162i	−0.107500	+	0.186195i	−0.914757	−	0.404005i	$-0.867618\pi$
$739$	−2.92233	+	5.06162i	−0.107500	+	0.186195i	0.807257	+	0.590200i	$0.200951\pi$
$740$	−2.77847	−	4.81245i	−0.102139	−	0.176909i
$741$		0			0
$742$	6.95015	+	13.2412i	0.255148	+	0.486101i
$743$		−	12.4731i		−	0.457592i	−0.973474	−	0.228796i	$-0.926521\pi$
$743$		−	12.4731i		−	0.457592i	0.973474	−	0.228796i	$-0.0734789\pi$
$744$		0			0
$745$	14.0971	+	8.13897i	0.516478	+	0.298189i
$746$	14.5706	+	8.41233i	0.533467	+	0.307997i
$747$		0			0
$748$			19.1862i			0.701519i
$749$	35.1836	+	22.2470i	1.28558	+	0.812887i
$750$		0			0
$751$	10.6432	+	18.4345i	0.388375	+	0.672684i	0.992231	−	0.124409i	$-0.0397034\pi$
$751$	10.6432	+	18.4345i	0.388375	+	0.672684i	−0.603857	+	0.797093i	$0.706370\pi$
$752$	−2.08068	+	3.60384i	−0.0758744	+	0.131418i
$753$		0			0
$754$	−0.181763	+	0.104941i	−0.00661940	+	0.00382172i
$755$	4.69584			0.170899
$756$		0			0
$757$	−21.1527			−0.768808			−0.384404	−	0.923165i	$-0.625593\pi$
$757$	−21.1527			−0.768808			−0.384404	+	0.923165i	$0.625593\pi$
$758$	−27.0209	+	15.6005i	−0.981443	+	0.566637i
$759$		0			0
$760$	−3.70130	+	6.41085i	−0.134260	+	0.232546i
$761$	23.0632	+	39.9466i	0.836040	+	1.44806i	0.893181	+	0.449697i	$0.148468\pi$
$761$	23.0632	+	39.9466i	0.836040	+	1.44806i	−0.0571413	+	0.998366i	$0.518199\pi$
$762$		0			0
$763$	23.1709	+	0.932918i	0.838843	+	0.0337739i
$764$		−	6.67175i		−	0.241376i
$765$		0			0
$766$	17.2814	+	9.97740i	0.624401	+	0.360498i
$767$	0.970775	+	0.560477i	0.0350527	+	0.0202377i
$768$		0			0
$769$		−	47.7662i		−	1.72249i	−0.508188	−	0.861246i	$-0.669684\pi$
$769$		−	47.7662i		−	1.72249i	0.508188	−	0.861246i	$-0.330316\pi$
$770$	−6.91837	+	10.9414i	−0.249321	+	0.394301i
$771$		0			0
$772$	−8.95874	−	15.5170i	−0.322432	−	0.558469i
$773$	−4.59971	+	7.96693i	−0.165440	+	0.286551i	−0.936811	−	0.349835i	$-0.886238\pi$
$773$	−4.59971	+	7.96693i	−0.165440	+	0.286551i	0.771371	+	0.636385i	$0.219571\pi$
$774$		0			0
$775$	−27.6469	+	15.9620i	−0.993107	+	0.573371i
$776$	2.72538			0.0978354
$777$		0			0
$778$	21.6297			0.775461
$779$	1.10867	−	0.640093i	0.0397223	−	0.0229337i
$780$		0			0
$781$	−32.1387	+	55.6658i	−1.15001	+	1.99188i
$782$	−12.8586	−	22.2717i	−0.459822	−	0.796436i
$783$		0			0
$784$	6.97734	+	0.562763i	0.249191	+	0.0200987i
$785$		−	7.84340i		−	0.279943i
$786$		0			0
$787$	7.28472	+	4.20584i	0.259672	+	0.149922i	0.624185	−	0.781277i	$-0.285431\pi$
$787$	7.28472	+	4.20584i	0.259672	+	0.149922i	−0.364513	+	0.931198i	$0.618764\pi$
$788$	13.7421	+	7.93400i	0.489542	+	0.282637i
$789$		0			0
$790$		−	2.09378i		−	0.0744933i
$791$	30.0485	−	15.7720i	1.06840	−	0.560789i
$792$		0			0
$793$	0.455264	+	0.788540i	0.0161669	+	0.0280019i
$794$	16.1782	−	28.0214i	0.574142	−	0.994443i
$795$		0			0
$796$	−22.4402	+	12.9559i	−0.795372	+	0.459209i
$797$	−6.13696			−0.217382			−0.108691	−	0.994076i	$-0.534666\pi$
$797$	−6.13696			−0.217382			−0.108691	+	0.994076i	$0.534666\pi$
$798$		0			0
$799$	−17.2876			−0.611593
$800$	−3.35811	+	1.93881i	−0.118727	+	0.0685472i
$801$		0			0
$802$	12.1807	−	21.0976i	0.430116	−	0.744983i
$803$	−33.3239	−	57.7187i	−1.17597	−	2.03685i
$804$		0			0
$805$	0.698057	−	17.3376i	0.0246033	−	0.611072i
$806$			0.905180i			0.0318836i
$807$		0			0
$808$	8.09198	+	4.67191i	0.284675	+	0.164357i
$809$	4.04309	+	2.33428i	0.142147	+	0.0820688i	0.569387	−	0.822070i	$-0.307181\pi$
$809$	4.04309	+	2.33428i	0.142147	+	0.0820688i	−0.427240	+	0.904138i	$0.640514\pi$
$810$		0			0
$811$		−	54.0704i		−	1.89867i	−0.314266	−	0.949335i	$-0.601758\pi$
$811$		−	54.0704i		−	1.89867i	0.314266	−	0.949335i	$-0.398242\pi$
$812$	0.203184	−	5.04647i	0.00713035	−	0.177097i
$813$		0			0
$814$	−12.1122	−	20.9790i	−0.424533	−	0.735313i
$815$	6.41486	−	11.1109i	0.224703	−	0.389197i
$816$		0			0
$817$	23.8539	−	13.7720i	0.834541	−	0.481822i
$818$	−17.7302			−0.619922
$819$		0			0
$820$	−0.194102			−0.00677833
$821$	19.5622	−	11.2942i	0.682725	−	0.394171i	−0.118156	−	0.992995i	$-0.537698\pi$
$821$	19.5622	−	11.2942i	0.682725	−	0.394171i	0.800881	+	0.598824i	$0.204365\pi$
$822$		0			0
$823$	1.30824	−	2.26594i	0.0456023	−	0.0789856i	−0.842323	−	0.538973i	$-0.818813\pi$
$823$	1.30824	−	2.26594i	0.0456023	−	0.0789856i	0.887926	+	0.459987i	$0.152146\pi$
$824$	2.93092	+	5.07651i	0.102104	+	0.176849i
$825$		0			0
$826$	−23.8843	+	12.5365i	−0.831041	+	0.436202i
$827$		−	0.0717819i		−	0.00249610i	−0.999999	−	0.00124805i	$-0.999603\pi$
$827$		−	0.0717819i		−	0.00249610i	0.999999	−	0.00124805i	$-0.000397267\pi$
$828$		0			0
$829$	4.80202	+	2.77245i	0.166781	+	0.0962910i	0.581067	−	0.813856i	$-0.302635\pi$
$829$	4.80202	+	2.77245i	0.166781	+	0.0962910i	−0.414286	+	0.910147i	$0.635969\pi$
$830$	8.05058	+	4.64800i	0.279440	+	0.161335i
$831$		0			0
$832$			0.109947i			0.00381172i
$833$	12.4684	+	26.2717i	0.432005	+	0.910262i
$834$		0			0
$835$	−0.162476	−	0.281417i	−0.00562272	−	0.00973884i
$836$	−16.1351	+	27.9469i	−0.558045	+	0.966562i
$837$		0			0
$838$	−23.0233	+	13.2925i	−0.795327	+	0.459182i
$839$	7.40563			0.255671			0.127835	−	0.991795i	$-0.459197\pi$
$839$	7.40563			0.255671			0.127835	+	0.991795i	$0.459197\pi$
$840$		0			0
$841$	25.3560			0.874344
$842$	18.6352	−	10.7590i	0.642210	−	0.370780i
$843$		0			0
$844$	4.39585	−	7.61383i	0.151311	−	0.262079i
$845$	−6.87987	−	11.9163i	−0.236675	−	0.409933i
$846$		0			0
$847$	−14.6055	+	23.0986i	−0.501851	+	0.793677i
$848$		−	5.65224i		−	0.194099i
$849$		0			0
$850$	−13.9507	−	8.05446i	−0.478506	−	0.276266i
$851$	28.1201	+	16.2352i	0.963946	+	0.556535i
$852$		0			0
$853$			16.8409i			0.576622i	0.957537	+	0.288311i	$0.0930937\pi$
$853$			16.8409i			0.576622i	−0.957537	+	0.288311i	$0.906906\pi$
$854$	−21.8931	−	0.881471i	−0.749167	−	0.0301633i
$855$		0			0
$856$	−7.86678	−	13.6257i	−0.268881	−	0.465715i
$857$	−22.9694	+	39.7842i	−0.784620	+	1.35900i	0.144606	+	0.989489i	$0.453809\pi$
$857$	−22.9694	+	39.7842i	−0.784620	+	1.35900i	−0.929226	+	0.369512i	$0.879525\pi$
$858$		0			0
$859$	38.0554	−	21.9713i	1.29843	−	0.749650i	0.318299	−	0.947990i	$-0.396888\pi$
$859$	38.0554	−	21.9713i	1.29843	−	0.749650i	0.980133	+	0.198340i	$0.0635552\pi$
$860$	−4.17623			−0.142408
$861$		0			0
$862$	2.30155			0.0783912
$863$	11.1793	−	6.45435i	0.380547	−	0.219709i	−0.297509	−	0.954719i	$-0.596156\pi$
$863$	11.1793	−	6.45435i	0.380547	−	0.219709i	0.678056	+	0.735010i	$0.262823\pi$
$864$		0			0
$865$	4.95414	−	8.58082i	0.168446	−	0.291757i
$866$	10.1738	+	17.6215i	0.345719	+	0.598803i
$867$		0			0
$868$	−18.4105	−	11.6411i	−0.624892	−	0.395126i
$869$		−	9.12742i		−	0.309627i
$870$		0			0
$871$	−0.0127910	−	0.00738491i	−0.000433408	−	0.000250228i
$872$	−7.59060	−	4.38244i	−0.257050	−	0.148408i
$873$		0			0
$874$		−	43.2549i		−	1.46312i
$875$	−11.5649	−	22.0331i	−0.390964	−	0.744854i
$876$		0			0
$877$	4.67644	+	8.09984i	0.157912	+	0.273512i	0.934116	−	0.356971i	$-0.116190\pi$
$877$	4.67644	+	8.09984i	0.157912	+	0.273512i	−0.776203	+	0.630483i	$0.782857\pi$
$878$	−8.07581	+	13.9877i	−0.272546	+	0.472063i
$879$		0			0
$880$	4.23731	−	2.44641i	0.142840	−	0.0824685i
$881$	26.9919			0.909380			0.454690	−	0.890650i	$-0.349750\pi$
$881$	26.9919			0.909380			0.454690	+	0.890650i	$0.349750\pi$
$882$		0			0
$883$	−35.4467			−1.19288			−0.596438	−	0.802659i	$-0.703418\pi$
$883$	−35.4467			−1.19288			−0.596438	+	0.802659i	$0.703418\pi$
$884$	−0.395563	+	0.228378i	−0.0133042	+	0.00768119i
$885$		0			0
$886$	18.3315	−	31.7511i	0.615858	−	1.06670i
$887$	−7.97015	−	13.8047i	−0.267611	−	0.463516i	0.700633	−	0.713522i	$-0.252901\pi$
$887$	−7.97015	−	13.8047i	−0.267611	−	0.463516i	−0.968244	+	0.250005i	$0.919568\pi$
$888$		0			0
$889$	−22.8085	−	43.4542i	−0.764973	−	1.45741i
$890$		−	0.752704i		−	0.0252307i
$891$		0			0
$892$	−20.2601	−	11.6972i	−0.678358	−	0.391650i
$893$	−25.1813	−	14.5385i	−0.842661	−	0.486511i
$894$		0			0
$895$		−	14.8352i		−	0.495885i
$896$	−2.23621	−	1.41398i	−0.0747067	−	0.0472379i
$897$		0			0
$898$	−2.52672	−	4.37641i	−0.0843178	−	0.146043i
$899$	−7.85801	+	13.6105i	−0.262079	+	0.453935i
$900$		0			0
$901$	20.3354	−	11.7407i	0.677471	−	0.391138i
$902$	−0.846151			−0.0281737
$903$		0			0
$904$	−12.8267			−0.426609
$905$	19.3043	−	11.1454i	0.641698	−	0.370484i
$906$		0			0
$907$	7.76961	−	13.4574i	0.257986	−	0.446844i	−0.707717	−	0.706496i	$-0.750275\pi$
$907$	7.76961	−	13.4574i	0.257986	−	0.446844i	0.965702	+	0.259652i	$0.0836079\pi$
$908$	6.18850	+	10.7188i	0.205373	+	0.355716i
$909$		0			0
$910$	−0.307929	−	0.0123980i	−0.0102078	−	0.000410990i
$911$			49.9833i			1.65602i	0.560714	+	0.828010i	$0.310527\pi$
$911$			49.9833i			1.65602i	−0.560714	+	0.828010i	$0.689473\pi$
$912$		0			0
$913$	35.0950	+	20.2621i	1.16147	+	0.670577i
$914$	20.5907	+	11.8881i	0.681080	+	0.393222i
$915$		0			0
$916$		−	27.3844i		−	0.904806i
$917$	−23.3828	+	36.9799i	−0.772167	+	1.22118i
$918$		0			0
$919$	−2.85795	−	4.95011i	−0.0942749	−	0.163289i	0.815031	−	0.579418i	$-0.196720\pi$
$919$	−2.85795	−	4.95011i	−0.0942749	−	0.163289i	−0.909306	+	0.416129i	$0.863387\pi$
$920$	−3.27916	+	5.67967i	−0.108111	+	0.187253i
$921$		0			0
$922$	26.6374	−	15.3791i	0.877254	−	0.506483i
$923$	−1.53021			−0.0503676
$924$		0			0
$925$	20.3390			0.668742
$926$	−5.81172	+	3.35540i	−0.190985	+	0.110265i
$927$		0			0
$928$	−0.954467	+	1.65318i	−0.0313319	+	0.0542685i
$929$	3.94662	+	6.83575i	0.129485	+	0.224274i	0.923477	−	0.383654i	$-0.125334\pi$
$929$	3.94662	+	6.83575i	0.129485	+	0.224274i	−0.793992	+	0.607928i	$0.792001\pi$
$930$		0			0
$931$	−3.93223	+	48.7533i	−0.128874	+	1.59782i
$932$			28.0350i			0.918316i
$933$		0			0
$934$	0.0174757	+	0.0100896i	0.000571823	+	0.000330142i
$935$	17.6032	+	10.1632i	0.575686	+	0.332372i
$936$		0			0
$937$		−	0.209649i		−	0.00684893i	−0.999994	−	0.00342446i	$-0.998910\pi$
$937$		−	0.209649i		−	0.00684893i	0.999994	−	0.00342446i	$-0.00109004\pi$
$938$	0.314702	−	0.165183i	0.0102754	−	0.00539342i
$939$		0			0
$940$	2.20432	+	3.81800i	0.0718971	+	0.124529i
$941$	−10.1231	+	17.5338i	−0.330005	+	0.571585i	−0.982512	−	0.186197i	$-0.940384\pi$
$941$	−10.1231	+	17.5338i	−0.330005	+	0.571585i	0.652508	+	0.757782i	$0.273717\pi$
$942$		0			0
$943$	0.982227	−	0.567089i	0.0319857	−	0.0184670i
$944$	10.1954			0.331832
$945$		0			0
$946$	−18.2055			−0.591912
$947$	−20.5561	+	11.8681i	−0.667985	+	0.385661i	−0.795313	−	0.606200i	$-0.792693\pi$
$947$	−20.5561	+	11.8681i	−0.667985	+	0.385661i	0.127328	+	0.991861i	$0.459360\pi$
$948$		0			0
$949$	0.793324	−	1.37408i	0.0257524	−	0.0446044i
$950$	−13.5472	−	23.4644i	−0.439528	−	0.761285i
$951$		0			0
$952$	0.442180	−	10.9824i	0.0143312	−	0.355943i
$953$			30.4348i			0.985881i	0.870063	+	0.492940i	$0.164078\pi$
$953$			30.4348i			0.985881i	−0.870063	+	0.492940i	$0.835922\pi$
$954$		0			0
$955$	−6.12127	−	3.53412i	−0.198080	−	0.114361i
$956$	7.60116	+	4.38853i	0.245839	+	0.141935i
$957$		0			0
$958$			14.5163i			0.469002i
$959$	−0.543516	+	13.4993i	−0.0175511	+	0.435916i
$960$		0			0
$961$	18.3901	+	31.8527i	0.593230	+	1.02750i
$962$	0.288349	−	0.499435i	0.00929674	−	0.0161024i
$963$		0			0
$964$	−10.3742	+	5.98957i	−0.334132	+	0.192911i
$965$	−18.9823			−0.611061
$966$		0			0
$967$	−11.4541			−0.368339			−0.184169	−	0.982895i	$-0.558960\pi$
$967$	−11.4541			−0.368339			−0.184169	+	0.982895i	$0.558960\pi$
$968$	8.94546	−	5.16466i	0.287518	−	0.165999i
$969$		0			0
$970$	1.44367	−	2.50051i	0.0463534	−	0.0802865i
$971$	17.5086	+	30.3258i	0.561878	+	0.973202i	0.997333	+	0.0729909i	$0.0232544\pi$
$971$	17.5086	+	30.3258i	0.561878	+	0.973202i	−0.435454	+	0.900211i	$0.643412\pi$
$972$		0			0
$973$	−28.6357	+	15.0305i	−0.918019	+	0.481856i
$974$		−	20.6363i		−	0.661230i
$975$		0			0
$976$	7.17201	+	4.14076i	0.229570	+	0.132542i
$977$	49.3848	+	28.5123i	1.57996	+	0.912190i	0.994863	+	0.101227i	$0.0322769\pi$
$977$	49.3848	+	28.5123i	1.57996	+	0.912190i	0.585097	+	0.810963i	$0.301056\pi$
$978$		0			0
$979$		−	3.28127i		−	0.104870i
$980$	4.21232	−	6.10354i	0.134558	−	0.194970i
$981$		0			0
$982$	−5.89801	−	10.2157i	−0.188213	−	0.325995i
$983$	−17.1577	+	29.7181i	−0.547246	+	0.947859i	0.451215	+	0.892415i	$0.350991\pi$
$983$	−17.1577	+	29.7181i	−0.547246	+	0.947859i	−0.998462	+	0.0554435i	$0.982343\pi$
$984$		0			0
$985$	14.5587	−	8.40549i	0.463880	−	0.267821i
$986$	−7.93035			−0.252554
$987$		0			0
$988$	−0.768240			−0.0244410
$989$	21.1333	−	12.2013i	0.671999	−	0.387979i
$990$		0			0
$991$	2.38452	−	4.13011i	0.0757468	−	0.131197i	−0.825664	−	0.564162i	$-0.809199\pi$
$991$	2.38452	−	4.13011i	0.0757468	−	0.131197i	0.901411	+	0.432965i	$0.142533\pi$
$992$	4.11644	+	7.12988i	0.130697	+	0.226374i
$993$		0			0
$994$	19.6795	−	31.1231i	0.624195	−	0.987164i
$995$			27.4516i			0.870273i
$996$		0			0
$997$	−14.2714	−	8.23960i	−0.451980	−	0.260951i	0.256686	−	0.966495i	$-0.417369\pi$
$997$	−14.2714	−	8.23960i	−0.451980	−	0.260951i	−0.708666	+	0.705544i	$0.750703\pi$
$998$	−23.3104	−	13.4583i	−0.737878	−	0.426014i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.k.d.647.6	yes	16
3.2	odd	2		1134.2.k.c.647.3	✓	16
7.5	odd	6		1134.2.k.c.971.3	yes	16
9.2	odd	6		1134.2.t.h.1025.6		16
9.4	even	3		1134.2.l.g.269.6		16
9.5	odd	6		1134.2.l.h.269.3		16
9.7	even	3		1134.2.t.g.1025.3		16
21.5	even	6	inner	1134.2.k.d.971.6	yes	16
63.5	even	6		1134.2.t.g.593.3		16
63.40	odd	6		1134.2.t.h.593.6		16
63.47	even	6		1134.2.l.g.215.2		16
63.61	odd	6		1134.2.l.h.215.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.k.c.647.3	✓	16	3.2	odd	2
1134.2.k.c.971.3	yes	16	7.5	odd	6
1134.2.k.d.647.6	yes	16	1.1	even	1	trivial
1134.2.k.d.971.6	yes	16	21.5	even	6	inner
1134.2.l.g.215.2		16	63.47	even	6
1134.2.l.g.269.6		16	9.4	even	3
1134.2.l.h.215.7		16	63.61	odd	6
1134.2.l.h.269.3		16	9.5	odd	6
1134.2.t.g.593.3		16	63.5	even	6
1134.2.t.g.1025.3		16	9.7	even	3
1134.2.t.h.593.6		16	63.40	odd	6
1134.2.t.h.1025.6		16	9.2	odd	6

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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.529713 - 0.917490i) q^{5} +(1.22963 + 2.34265i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.529713 - 0.917490i) q^{5} +(1.22963 + 2.34265i) q^{7} -1.00000i q^{8} +(-0.917490 - 0.529713i) q^{10} +(-3.99962 - 2.30918i) q^{11} -0.109947i q^{13} +(2.23621 + 1.41398i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.07717 - 3.59776i) q^{17} +(6.05124 - 3.49369i) q^{19} -1.05943 q^{20} -4.61837 q^{22} +(5.36108 - 3.09522i) q^{23} +(1.93881 - 3.35811i) q^{25} +(-0.0549735 - 0.0952168i) q^{26} +(2.64361 + 0.106438i) q^{28} -1.90893i q^{29} +(-7.12988 - 4.11644i) q^{31} +(-0.866025 - 0.500000i) q^{32} -4.15433i q^{34} +(1.49801 - 2.36910i) q^{35} +(2.62262 + 4.54251i) q^{37} +(3.49369 - 6.05124i) q^{38} +(-0.917490 + 0.529713i) q^{40} +0.183214 q^{41} +3.94198 q^{43} +(-3.99962 + 2.30918i) q^{44} +(3.09522 - 5.36108i) q^{46} +(-2.08068 - 3.60384i) q^{47} +(-3.97604 + 5.76117i) q^{49} -3.87762i q^{50} +(-0.0952168 - 0.0549735i) q^{52} +(4.89499 + 2.82612i) q^{53} +4.89282i q^{55} +(2.34265 - 1.22963i) q^{56} +(-0.954467 - 1.65318i) q^{58} +(-5.09771 + 8.82949i) q^{59} +(-7.17201 + 4.14076i) q^{61} -8.23288 q^{62} -1.00000 q^{64} +(-0.100875 + 0.0582404i) q^{65} +(0.0671680 - 0.116338i) q^{67} +(-2.07717 - 3.59776i) q^{68} +(0.112764 - 2.80071i) q^{70} -13.9178i q^{71} +(12.4976 + 7.21551i) q^{73} +(4.54251 + 2.62262i) q^{74} -6.98737i q^{76} +(0.491571 - 12.2092i) q^{77} +(0.988165 + 1.71155i) q^{79} +(-0.529713 + 0.917490i) q^{80} +(0.158668 - 0.0916071i) q^{82} -8.77457 q^{83} -4.40121 q^{85} +(3.41385 - 1.97099i) q^{86} +(-2.30918 + 3.99962i) q^{88} +(0.355241 + 0.615296i) q^{89} +(0.257567 - 0.135194i) q^{91} -6.19045i q^{92} +(-3.60384 - 2.08068i) q^{94} +(-6.41085 - 3.70130i) q^{95} +2.72538i q^{97} +(-0.562763 + 6.97734i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 + 8 * q^7	\( 16 q + 8 q^{4} + 8 q^{7} + 12 q^{11} + 12 q^{14} - 8 q^{16} + 12 q^{23} - 8 q^{25} + 4 q^{28} + 12 q^{31} + 60 q^{35} + 4 q^{37} - 12 q^{38} - 48 q^{41} - 32 q^{43} + 12 q^{44} + 4 q^{49} - 12 q^{52} + 12 q^{56} - 12 q^{58} - 24 q^{59} - 12 q^{61} - 48 q^{62} - 16 q^{64} + 48 q^{65} - 4 q^{67} - 24 q^{70} + 36 q^{73} + 36 q^{74} + 84 q^{77} + 8 q^{79} - 72 q^{83} + 24 q^{85} + 24 q^{86} + 24 q^{89} - 12 q^{91} - 36 q^{94} + 12 q^{95} + 36 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 + 8 * q^7 + 12 * q^11 + 12 * q^14 - 8 * q^16 + 12 * q^23 - 8 * q^25 + 4 * q^28 + 12 * q^31 + 60 * q^35 + 4 * q^37 - 12 * q^38 - 48 * q^41 - 32 * q^43 + 12 * q^44 + 4 * q^49 - 12 * q^52 + 12 * q^56 - 12 * q^58 - 24 * q^59 - 12 * q^61 - 48 * q^62 - 16 * q^64 + 48 * q^65 - 4 * q^67 - 24 * q^70 + 36 * q^73 + 36 * q^74 + 84 * q^77 + 8 * q^79 - 72 * q^83 + 24 * q^85 + 24 * q^86 + 24 * q^89 - 12 * q^91 - 36 * q^94 + 12 * q^95 + 36 * q^98

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