LMFDB - Embedded newform 1134.2.k.d.971.6

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			971.6
Root			$0.500000 - 1.24626i$ of defining polynomial
Character	$\chi$	$=$	1134.971
Dual form			1134.2.k.d.647.6

$q$-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 $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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	−0.959822	−	0.280611i	$-0.909463\pi$
$5$	−0.529713	+	0.917490i	−0.236895	+	0.410314i	0.722927	+	0.690925i	$0.242796\pi$
$6$		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	−0.961868	−	0.273514i	$-0.911814\pi$
$11$	−3.99962	+	2.30918i	−1.20593	+	0.696245i	−0.244064	+	0.969759i	$0.578481\pi$
$12$		0			0
$13$			0.109947i			0.0304938i	0.999884	+	0.0152469i	$0.00485343\pi$
$13$			0.109947i			0.0304938i	−0.999884	+	0.0152469i	$0.995147\pi$
$14$	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	0.999990	+	0.00437840i	$0.00139369\pi$
$17$	2.07717	+	3.59776i	0.503787	+	0.872585i	−0.496203	+	0.868206i	$0.665273\pi$
$18$		0			0
$19$	6.05124	+	3.49369i	1.38825	+	0.801506i	0.993118	−	0.117118i	$-0.0373655\pi$
$19$	6.05124	+	3.49369i	1.38825	+	0.801506i	0.395132	+	0.918624i	$0.370699\pi$
$20$	−1.05943			−0.236895
$21$		0			0
$22$	−4.61837			−0.984639
$23$	5.36108	+	3.09522i	1.11786	+	0.645399i	0.940855	−	0.338811i	$-0.110025\pi$
$23$	5.36108	+	3.09522i	1.11786	+	0.645399i	0.177009	+	0.984209i	$0.443358\pi$
$24$		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	$0.0567169\pi$
$29$			1.90893i			0.354480i	−0.984168	+	0.177240i	$0.943283\pi$
$30$		0			0
$31$	−7.12988	+	4.11644i	−1.28056	+	0.739334i	−0.976952	−	0.213461i	$-0.931526\pi$
$31$	−7.12988	+	4.11644i	−1.28056	+	0.739334i	−0.303613	+	0.952795i	$0.598193\pi$
$32$	−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	−0.565817	−	0.824531i	$-0.691439\pi$
$37$	2.62262	−	4.54251i	0.431156	−	0.746784i	0.996973	+	0.0777470i	$0.0247726\pi$
$38$	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	−0.976926	−	0.213579i	$-0.931488\pi$
$47$	−2.08068	+	3.60384i	−0.303498	+	0.525674i	0.673428	+	0.739253i	$0.264821\pi$
$48$		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	−0.124599	−	0.992207i	$-0.539764\pi$
$53$	4.89499	−	2.82612i	0.672378	−	0.388198i	0.796977	+	0.604009i	$0.206431\pi$
$54$		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	−0.979645	−	0.200736i	$-0.935667\pi$
$59$	−5.09771	−	8.82949i	−0.663665	−	1.14950i	0.315981	−	0.948766i	$-0.397667\pi$
$60$		0			0
$61$	−7.17201	−	4.14076i	−0.918281	−	0.530170i	−0.0351949	−	0.999380i	$-0.511205\pi$
$61$	−7.17201	−	4.14076i	−0.918281	−	0.530170i	−0.883086	+	0.469211i	$0.844539\pi$
$62$	−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	0.870099	−	0.492877i	$-0.164055\pi$
$67$	0.0671680	+	0.116338i	0.00820587	+	0.0142130i	−0.861893	+	0.507090i	$0.830721\pi$
$68$	−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	$0.309314\pi$
$71$			13.9178i			1.65173i	−0.563865	+	0.825867i	$0.690686\pi$
$72$		0			0
$73$	12.4976	−	7.21551i	1.46274	−	0.844512i	0.463600	−	0.886044i	$-0.346557\pi$
$73$	12.4976	−	7.21551i	1.46274	−	0.844512i	0.999137	+	0.0415326i	$0.0132240\pi$
$74$	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	−0.805068	−	0.593183i	$-0.797871\pi$
$79$	0.988165	−	1.71155i	0.111177	−	0.192565i	0.916245	+	0.400618i	$0.131205\pi$
$80$	−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	−0.846583	−	0.532256i	$-0.821344\pi$
$89$	0.355241	−	0.615296i	0.0376555	−	0.0652213i	0.884239	+	0.467035i	$0.154678\pi$
$90$		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	$-0.955817\pi$
$97$		−	2.72538i		−	0.276720i	0.990382	−	0.138360i	$-0.0441831\pi$
$98$	−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	0.534324	−	0.845280i	$-0.320566\pi$
$101$	−4.67191	−	8.09198i	−0.464872	−	0.805182i	−0.999196	+	0.0400980i	$0.987233\pi$
$102$		0			0
$103$	−5.07651	−	2.93092i	−0.500203	−	0.288792i	0.228594	−	0.973522i	$-0.426587\pi$
$103$	−5.07651	−	2.93092i	−0.500203	−	0.288792i	−0.728797	+	0.684729i	$0.759920\pi$
$104$	−0.109947			−0.0107812
$105$		0			0
$106$	5.65224			0.548994
$107$	13.6257	+	7.86678i	1.31724	+	0.760510i	0.983284	−	0.182078i	$-0.0582823\pi$
$107$	13.6257	+	7.86678i	1.31724	+	0.760510i	0.333958	+	0.942588i	$0.391616\pi$
$108$		0			0
$109$	4.38244	+	7.59060i	0.419761	+	0.727048i	0.995915	−	0.0902934i	$-0.0287805\pi$
$109$	4.38244	+	7.59060i	0.419761	+	0.727048i	−0.576154	+	0.817341i	$0.695447\pi$
$110$	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	$0.206154\pi$
$113$			12.8267i			1.20663i	−0.797502	+	0.603317i	$0.793846\pi$
$114$		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	−0.237615	−	0.971359i	$-0.576366\pi$
$131$	8.26841	−	14.3213i	0.722414	−	1.25126i	0.960030	−	0.279899i	$-0.0903009\pi$
$132$		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	−0.299049	−	0.954238i	$-0.596670\pi$
$137$	4.42227	−	2.55320i	0.377820	−	0.218134i	0.676869	+	0.736103i	$0.263336\pi$
$138$		0			0
$139$		−	12.2236i		−	1.03679i	−0.855140	−	0.518397i	$-0.826529\pi$
$139$		−	12.2236i		−	1.03679i	0.855140	−	0.518397i	$-0.173471\pi$
$140$	−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	−0.156496	−	0.987679i	$-0.550020\pi$
$149$	−13.3064	−	7.68243i	−1.09010	−	0.629369i	−0.933603	+	0.358310i	$0.883353\pi$
$150$		0			0
$151$	−2.21622	−	3.83861i	−0.180353	−	0.312381i	0.761648	−	0.647992i	$-0.224391\pi$
$151$	−2.21622	−	3.83861i	−0.180353	−	0.312381i	−0.942001	+	0.335610i	$0.891057\pi$
$152$	−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	−0.221833	−	0.975085i	$-0.571204\pi$
$157$	6.41157	−	3.70172i	0.511699	−	0.295430i	0.733532	+	0.679655i	$0.237871\pi$
$158$	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	−0.525299	−	0.850918i	$-0.676047\pi$
$163$	6.05503	−	10.4876i	0.474267	−	0.821454i	0.999566	+	0.0294636i	$0.00937992\pi$
$164$	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	−0.631680	−	0.775229i	$-0.717634\pi$
$173$	4.67625	−	8.09950i	0.355529	−	0.615793i	0.987208	+	0.159436i	$0.0509676\pi$
$174$		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	0.0271369	−	0.999632i	$-0.491361\pi$
$179$	12.1270	−	7.00151i	0.906412	−	0.523317i	0.879275	+	0.476315i	$0.158028\pi$
$180$		0			0
$181$		−	21.0404i		−	1.56392i	−0.623330	−	0.781959i	$-0.714221\pi$
$181$		−	21.0404i		−	1.56392i	0.623330	−	0.781959i	$-0.285779\pi$
$182$	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	0.694253	−	0.719731i	$-0.255735\pi$
$191$	5.77791	+	3.33588i	0.418075	+	0.241376i	−0.276178	+	0.961106i	$0.589068\pi$
$192$		0			0
$193$	8.95874	+	15.5170i	0.644864	+	1.11694i	0.984333	+	0.176321i	$0.0564195\pi$
$193$	8.95874	+	15.5170i	0.644864	+	1.11694i	−0.339468	+	0.940617i	$0.610247\pi$
$194$	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	$-0.808770\pi$
$197$		−	15.8680i		−	1.13055i	0.824903	−	0.565274i	$-0.191230\pi$
$198$		0			0
$199$	−22.4402	+	12.9559i	−1.59074	+	0.918417i	−0.597566	+	0.801820i	$0.703865\pi$
$199$	−22.4402	+	12.9559i	−1.59074	+	0.918417i	−0.993179	+	0.116597i	$0.962801\pi$
$200$	−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	$0.286465\pi$
$223$			23.3943i			1.56660i	−0.621643	+	0.783301i	$0.713535\pi$
$224$	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	0.584226	−	0.811591i	$-0.301398\pi$
$227$	−6.18850	−	10.7188i	−0.410745	−	0.711432i	−0.994971	+	0.100159i	$0.968065\pi$
$228$		0			0
$229$	23.7156	+	13.6922i	1.56717	+	0.904806i	0.996497	+	0.0836293i	$0.0266512\pi$
$229$	23.7156	+	13.6922i	1.56717	+	0.904806i	0.570674	+	0.821177i	$0.306682\pi$
$230$	−6.55832			−0.432443
$231$		0			0
$232$	−1.90893			−0.125328
$233$	−24.2790	−	14.0175i	−1.59057	−	0.918316i	−0.993209	−	0.116343i	$-0.962883\pi$
$233$	−24.2790	−	14.0175i	−1.59057	−	0.918316i	−0.597361	−	0.801973i	$-0.703784\pi$
$234$		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	$-0.908381\pi$
$239$		−	8.77707i		−	0.567741i	0.958863	−	0.283871i	$-0.0916186\pi$
$240$		0			0
$241$	−10.3742	+	5.98957i	−0.668264	+	0.385822i	−0.795418	−	0.606061i	$-0.792749\pi$
$241$	−10.3742	+	5.98957i	−0.668264	+	0.385822i	0.127155	+	0.991883i	$0.459416\pi$
$242$	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	−0.141433	−	0.989948i	$-0.545171\pi$
$257$	12.6102	−	21.8415i	0.786604	−	1.36244i	0.928036	−	0.372489i	$-0.121496\pi$
$258$		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	−0.468593	−	0.883414i	$-0.655239\pi$
$263$	1.00821	−	0.582090i	0.0621689	−	0.0358932i	0.530762	+	0.847521i	$0.321906\pi$
$264$		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	0.983644	−	0.180121i	$-0.0576490\pi$
$269$	5.50806	+	9.54025i	0.335833	+	0.581679i	−0.647812	+	0.761800i	$0.724316\pi$
$270$		0			0
$271$	16.3994	+	9.46818i	0.996191	+	0.575151i	0.907119	−	0.420874i	$-0.138277\pi$
$271$	16.3994	+	9.46818i	0.996191	+	0.575151i	0.0890717	+	0.996025i	$0.471610\pi$
$272$	−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	0.669484	−	0.742826i	$-0.266515\pi$
$277$	−5.13554	−	8.89501i	−0.308564	−	0.534449i	−0.978049	+	0.208377i	$0.933182\pi$
$278$	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	$0.184148\pi$
$281$			18.3315i			1.09357i	−0.837274	+	0.546784i	$0.815852\pi$
$282$		0			0
$283$	−5.13375	+	2.96397i	−0.305170	+	0.176190i	−0.644763	−	0.764383i	$-0.723044\pi$
$283$	−5.13375	+	2.96397i	−0.305170	+	0.176190i	0.339593	+	0.940572i	$0.389711\pi$
$284$	−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	$-0.889509\pi$
$307$		−	11.9212i		−	0.680380i	0.940357	−	0.340190i	$-0.110491\pi$
$308$	−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	−0.959017	−	0.283349i	$-0.908555\pi$
$311$	−12.7837	−	22.1420i	−0.724896	−	1.25556i	0.234121	−	0.972207i	$-0.424779\pi$
$312$		0			0
$313$	25.0836	+	14.4820i	1.41781	+	0.818573i	0.996106	−	0.0881598i	$-0.0280986\pi$
$313$	25.0836	+	14.4820i	1.41781	+	0.818573i	0.421705	+	0.906733i	$0.361432\pi$
$314$	7.40344			0.417800
$315$		0			0
$316$	1.97633			0.111177
$317$	−5.06909	−	2.92664i	−0.284709	−	0.164377i	0.350844	−	0.936434i	$-0.385895\pi$
$317$	−5.06909	−	2.92664i	−0.284709	−	0.164377i	−0.635553	+	0.772057i	$0.719228\pi$
$318$		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	−0.797871	−	0.602828i	$-0.794041\pi$
$331$	2.24013	−	3.88002i	0.123129	−	0.213265i	0.921000	+	0.389563i	$0.127374\pi$
$332$	−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	−0.0511808	−	0.998689i	$-0.516298\pi$
$347$	14.6810	−	8.47610i	0.788119	−	0.455021i	0.839300	+	0.543669i	$0.182965\pi$
$348$		0			0
$349$			23.7573i			1.27170i	0.771813	+	0.635850i	$0.219350\pi$
$349$			23.7573i			1.27170i	−0.771813	+	0.635850i	$0.780650\pi$
$350$	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	0.797467	−	0.603363i	$-0.206173\pi$
$353$	−2.32588	−	4.02854i	−0.123794	−	0.214417i	−0.921261	+	0.388945i	$0.872840\pi$
$354$		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	0.118485	−	0.992956i	$-0.462196\pi$
$359$	−12.9258	−	7.46271i	−0.682197	−	0.393867i	−0.800682	+	0.599089i	$0.795530\pi$
$360$		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	−0.979211	−	0.202843i	$-0.934982\pi$
$367$	−24.7732	+	14.3028i	−1.29315	+	0.746600i	−0.313938	+	0.949443i	$0.601648\pi$
$368$	−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	−0.561769	−	0.827294i	$-0.689879\pi$
$373$	8.41233	−	14.5706i	0.435574	−	0.754436i	0.997342	+	0.0728586i	$0.0232122\pi$
$374$	−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	−0.490114	−	0.871658i	$-0.663045\pi$
$383$	9.97740	−	17.2814i	0.509821	−	0.883037i	0.999935	−	0.0113781i	$-0.00362185\pi$
$384$		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	0.0567415	−	0.998389i	$-0.481929\pi$
$389$	18.7318	−	10.8148i	0.949742	−	0.548334i	0.893001	+	0.450055i	$0.148596\pi$
$390$		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	0.995034	−	0.0995319i	$-0.0317345\pi$
$397$	28.0214	+	16.1782i	1.40635	+	0.811959i	0.411320	+	0.911491i	$0.365068\pi$
$398$	−25.9117			−1.29884
$399$		0			0
$400$	−3.87762			−0.193881
$401$	21.0976	+	12.1807i	1.05357	+	0.608276i	0.923645	−	0.383248i	$-0.125195\pi$
$401$	21.0976	+	12.1807i	1.05357	+	0.608276i	0.129920	+	0.991524i	$0.458528\pi$
$402$		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	−0.829025	−	0.559211i	$-0.811104\pi$
$409$	−15.3548	+	8.86511i	−0.759247	+	0.438351i	0.0697785	+	0.997563i	$0.477771\pi$
$410$	−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	−0.451227	−	0.892409i	$-0.649013\pi$
$431$	1.99320	−	1.15078i	0.0960092	−	0.0554310i	0.547236	+	0.836978i	$0.315680\pi$
$432$		0			0
$433$		−	20.3476i		−	0.977841i	−0.872328	−	0.488920i	$-0.837391\pi$
$433$		−	20.3476i		−	0.977841i	0.872328	−	0.488920i	$-0.162609\pi$
$434$	−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	0.127568	−	0.991830i	$-0.459283\pi$
$439$	−13.9877	−	8.07581i	−0.667597	−	0.385438i	−0.795166	+	0.606392i	$0.792616\pi$
$440$	4.89282			0.233256
$441$		0			0
$442$	−0.456756			−0.0217257
$443$	31.7511	+	18.3315i	1.50854	+	0.870955i	0.999951	+	0.00994511i	$0.00316568\pi$
$443$	31.7511	+	18.3315i	1.50854	+	0.870955i	0.508588	+	0.861010i	$0.330168\pi$
$444$		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	$0.0380469\pi$
$449$			5.05345i			0.238487i	−0.992865	+	0.119243i	$0.961953\pi$
$450$		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	−0.441717	−	0.897154i	$-0.645631\pi$
$457$	11.8881	−	20.5907i	0.556100	−	0.963193i	0.997817	−	0.0660385i	$-0.0210360\pi$
$458$	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	−0.865792	−	0.500404i	$-0.833185\pi$
$467$	0.0100896	−	0.0174757i	0.000466891	−	0.000808679i	0.866259	+	0.499596i	$0.166518\pi$
$468$		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	0.651198	−	0.758908i	$-0.274267\pi$
$479$	−7.25817	−	12.5715i	−0.331634	−	0.574407i	−0.982832	+	0.184500i	$0.940933\pi$
$480$		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	0.999313	−	0.0370614i	$-0.0117997\pi$
$487$	10.3182	+	17.8716i	0.467560	+	0.809838i	−0.531753	+	0.846900i	$0.678466\pi$
$488$	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	$0.0857594\pi$
$491$			11.7960i			0.532347i	−0.963925	+	0.266174i	$0.914241\pi$
$492$		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	0.389970	+	0.920828i	$0.372485\pi$
$499$	−13.4583	+	23.3104i	−0.602475	+	1.04352i	−0.992445	+	0.122690i	$0.960848\pi$
$500$	−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	−0.996065	−	0.0886236i	$-0.971753\pi$
$509$	−9.50456	+	16.4624i	−0.421282	+	0.729682i	0.574783	+	0.818306i	$0.305087\pi$
$510$		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	−0.828861	−	0.559455i	$-0.811011\pi$
$521$	−20.5185	−	35.5391i	−0.898933	−	1.55700i	−0.0700717	−	0.997542i	$-0.522323\pi$
$522$		0			0
$523$	3.71694	+	2.14598i	0.162531	+	0.0938371i	0.579059	−	0.815286i	$-0.303420\pi$
$523$	3.71694	+	2.14598i	0.162531	+	0.0938371i	−0.416528	+	0.909123i	$0.636753\pi$
$524$	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	−0.694751	−	0.719251i	$-0.744485\pi$
$541$	6.40829	−	11.0995i	0.275514	−	0.477204i	0.970265	+	0.242047i	$0.0778187\pi$
$542$	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	−0.823494	−	0.567324i	$-0.807979\pi$
$557$	−17.5572	+	10.1367i	−0.743924	+	0.429505i	0.0795702	+	0.996829i	$0.474645\pi$
$558$		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	0.998950	+	0.0458223i	$0.0145908\pi$
$563$	12.7929	+	22.1580i	0.539158	+	0.933849i	−0.459791	+	0.888027i	$0.652076\pi$
$564$		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	0.683863	−	0.729611i	$-0.260299\pi$
$569$	9.39677	+	5.42523i	0.393933	+	0.227437i	−0.289930	+	0.957048i	$0.593632\pi$
$570$		0			0
$571$	−10.0578	−	17.4207i	−0.420908	−	0.729033i	0.575121	−	0.818068i	$-0.304955\pi$
$571$	−10.0578	−	17.4207i	−0.420908	−	0.729033i	−0.996028	+	0.0890351i	$0.971622\pi$
$572$	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	−0.289209	−	0.957266i	$-0.593392\pi$
$577$	9.49312	−	5.48085i	0.395204	−	0.228171i	0.684412	+	0.729095i	$0.260059\pi$
$578$	−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	−0.977728	−	0.209877i	$-0.932694\pi$
$593$	−7.47849	+	12.9531i	−0.307105	+	0.531921i	0.670623	+	0.741798i	$0.266027\pi$
$594$		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	0.157896	−	0.987456i	$-0.449529\pi$
$599$	26.7263	−	15.4304i	1.09201	−	0.630470i	0.934110	+	0.356986i	$0.116196\pi$
$600$		0			0
$601$			9.88311i			0.403140i	0.979474	+	0.201570i	$0.0646044\pi$
$601$			9.88311i			0.403140i	−0.979474	+	0.201570i	$0.935396\pi$
$602$	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	0.128682	−	0.991686i	$-0.458925\pi$
$607$	−16.4036	−	9.47063i	−0.665802	−	0.384401i	−0.794484	+	0.607285i	$0.792259\pi$
$608$	−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	−0.918477	−	0.395475i	$-0.870580\pi$
$613$	−19.8499	−	34.3810i	−0.801730	−	1.38864i	0.116747	−	0.993162i	$-0.462753\pi$
$614$	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	$0.301327\pi$
$617$			40.3125i			1.62292i	−0.584409	+	0.811460i	$0.698673\pi$
$618$		0			0
$619$	−3.41119	+	1.96945i	−0.137107	+	0.0791589i	−0.566985	−	0.823728i	$-0.691890\pi$
$619$	−3.41119	+	1.96945i	−0.137107	+	0.0791589i	0.429877	+	0.902887i	$0.358557\pi$
$620$	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	−0.961666	−	0.274223i	$-0.911579\pi$
$641$	−30.5086	+	17.6141i	−1.20502	+	0.695716i	−0.243349	+	0.969939i	$0.578246\pi$
$642$		0			0
$643$			12.5707i			0.495738i	0.968794	+	0.247869i	$0.0797303\pi$
$643$			12.5707i			0.495738i	−0.968794	+	0.247869i	$0.920270\pi$
$644$	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	0.841278	−	0.540603i	$-0.181804\pi$
$647$	−1.20915	−	2.09431i	−0.0475366	−	0.0823359i	−0.888815	+	0.458267i	$0.848470\pi$
$648$		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	−0.997246	−	0.0741631i	$-0.976371\pi$
$653$	−39.8665	−	23.0169i	−1.56010	−	0.900722i	−0.562850	−	0.826559i	$-0.690295\pi$
$654$		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	$0.0164488\pi$
$659$			2.65193i			0.103305i	−0.998665	+	0.0516523i	$0.983551\pi$
$660$		0			0
$661$	−2.21722	+	1.28011i	−0.0862399	+	0.0497906i	−0.542500	−	0.840056i	$-0.682522\pi$
$661$	−2.21722	+	1.28011i	−0.0862399	+	0.0497906i	0.456260	+	0.889847i	$0.349189\pi$
$662$	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	−0.303693	−	0.952770i	$-0.598220\pi$
$677$	17.5181	−	30.3423i	0.673277	−	1.16615i	0.976969	−	0.213380i	$-0.0684471\pi$
$678$		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	−0.998814	−	0.0486825i	$-0.984498\pi$
$683$	−38.0531	+	21.9700i	−1.45606	+	0.840657i	−0.457247	+	0.889340i	$0.651164\pi$
$684$		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	0.624985	−	0.780637i	$-0.285105\pi$
$691$	6.87208	+	3.96760i	0.261426	+	0.150935i	−0.363559	+	0.931571i	$0.618438\pi$
$692$	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	$-0.891443\pi$
$701$		−	17.7111i		−	0.668940i	0.942406	−	0.334470i	$-0.108557\pi$
$702$		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	−0.882999	−	0.469376i	$-0.844479\pi$
$709$	−0.932165	+	1.61456i	−0.0350082	+	0.0606359i	0.847990	+	0.530011i	$0.177812\pi$
$710$	−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	−0.781602	−	0.623778i	$-0.785597\pi$
$719$	4.00621	−	6.93896i	0.149406	−	0.258779i	0.931008	+	0.364998i	$0.118930\pi$
$720$		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	$-0.990985\pi$
$727$		−	1.52705i		−	0.0566350i	0.999599	−	0.0283175i	$-0.00901494\pi$
$728$	−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	0.593375	−	0.804926i	$-0.297795\pi$
$733$	5.22464	+	3.01645i	0.192977	+	0.111415i	−0.400399	+	0.916341i	$0.631128\pi$
$734$	−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	0.807257	−	0.590200i	$-0.200951\pi$
$739$	−2.92233	−	5.06162i	−0.107500	−	0.186195i	−0.914757	+	0.404005i	$0.867618\pi$
$740$	−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	$0.0734789\pi$
$743$			12.4731i			0.457592i	−0.973474	+	0.228796i	$0.926521\pi$
$744$		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	−0.603857	−	0.797093i	$-0.706370\pi$
$751$	10.6432	−	18.4345i	0.388375	−	0.672684i	0.992231	+	0.124409i	$0.0397034\pi$
$752$	−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	−0.0571413	−	0.998366i	$-0.518199\pi$
$761$	23.0632	−	39.9466i	0.836040	−	1.44806i	0.893181	−	0.449697i	$-0.148468\pi$
$762$		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	$0.330316\pi$
$769$			47.7662i			1.72249i	−0.508188	+	0.861246i	$0.669684\pi$
$770$	−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	0.771371	−	0.636385i	$-0.219571\pi$
$773$	−4.59971	−	7.96693i	−0.165440	−	0.286551i	−0.936811	+	0.349835i	$0.886238\pi$
$774$		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	−0.364513	−	0.931198i	$-0.618764\pi$
$787$	7.28472	−	4.20584i	0.259672	−	0.149922i	0.624185	+	0.781277i	$0.285431\pi$
$788$	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	−0.427240	−	0.904138i	$-0.640514\pi$
$809$	4.04309	−	2.33428i	0.142147	−	0.0820688i	0.569387	+	0.822070i	$0.307181\pi$
$810$		0			0
$811$			54.0704i			1.89867i	0.314266	+	0.949335i	$0.398242\pi$
$811$			54.0704i			1.89867i	−0.314266	+	0.949335i	$0.601758\pi$
$812$	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	0.800881	−	0.598824i	$-0.204365\pi$
$821$	19.5622	+	11.2942i	0.682725	+	0.394171i	−0.118156	+	0.992995i	$0.537698\pi$
$822$		0			0
$823$	1.30824	+	2.26594i	0.0456023	+	0.0789856i	0.887926	−	0.459987i	$-0.152146\pi$
$823$	1.30824	+	2.26594i	0.0456023	+	0.0789856i	−0.842323	+	0.538973i	$0.818813\pi$
$824$	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	$0.000397267\pi$
$827$			0.0717819i			0.00249610i	−0.999999	+	0.00124805i	$0.999603\pi$
$828$		0			0
$829$	4.80202	−	2.77245i	0.166781	−	0.0962910i	−0.414286	−	0.910147i	$-0.635969\pi$
$829$	4.80202	−	2.77245i	0.166781	−	0.0962910i	0.581067	+	0.813856i	$0.302635\pi$
$830$	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	$-0.906906\pi$
$853$		−	16.8409i		−	0.576622i	0.957537	−	0.288311i	$-0.0930937\pi$
$854$	−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	−0.929226	−	0.369512i	$-0.879525\pi$
$857$	−22.9694	−	39.7842i	−0.784620	−	1.35900i	0.144606	−	0.989489i	$-0.453809\pi$
$858$		0			0
$859$	38.0554	+	21.9713i	1.29843	+	0.749650i	0.980133	−	0.198340i	$-0.0635552\pi$
$859$	38.0554	+	21.9713i	1.29843	+	0.749650i	0.318299	+	0.947990i	$0.396888\pi$
$860$	−4.17623			−0.142408
$861$		0			0
$862$	2.30155			0.0783912
$863$	11.1793	+	6.45435i	0.380547	+	0.219709i	0.678056	−	0.735010i	$-0.262823\pi$
$863$	11.1793	+	6.45435i	0.380547	+	0.219709i	−0.297509	+	0.954719i	$0.596156\pi$
$864$		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	−0.776203	−	0.630483i	$-0.782857\pi$
$877$	4.67644	−	8.09984i	0.157912	−	0.273512i	0.934116	+	0.356971i	$0.116190\pi$
$878$	−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	−0.968244	−	0.250005i	$-0.919568\pi$
$887$	−7.97015	+	13.8047i	−0.267611	+	0.463516i	0.700633	+	0.713522i	$0.252901\pi$
$888$		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	0.965702	−	0.259652i	$-0.0836079\pi$
$907$	7.76961	+	13.4574i	0.257986	+	0.446844i	−0.707717	+	0.706496i	$0.750275\pi$
$908$	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	$-0.689473\pi$
$911$		−	49.9833i		−	1.65602i	0.560714	−	0.828010i	$-0.310527\pi$
$912$		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	−0.909306	−	0.416129i	$-0.863387\pi$
$919$	−2.85795	+	4.95011i	−0.0942749	+	0.163289i	0.815031	+	0.579418i	$0.196720\pi$
$920$	−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	−0.793992	−	0.607928i	$-0.792001\pi$
$929$	3.94662	−	6.83575i	0.129485	−	0.224274i	0.923477	+	0.383654i	$0.125334\pi$
$930$		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	$0.00109004\pi$
$937$			0.209649i			0.00684893i	−0.999994	+	0.00342446i	$0.998910\pi$
$938$	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	0.652508	−	0.757782i	$-0.273717\pi$
$941$	−10.1231	−	17.5338i	−0.330005	−	0.571585i	−0.982512	+	0.186197i	$0.940384\pi$
$942$		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	0.127328	−	0.991861i	$-0.459360\pi$
$947$	−20.5561	−	11.8681i	−0.667985	−	0.385661i	−0.795313	+	0.606200i	$0.792693\pi$
$948$		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	$-0.835922\pi$
$953$		−	30.4348i		−	0.985881i	0.870063	−	0.492940i	$-0.164078\pi$
$954$		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	−0.435454	−	0.900211i	$-0.643412\pi$
$971$	17.5086	−	30.3258i	0.561878	−	0.973202i	0.997333	−	0.0729909i	$-0.0232544\pi$
$972$		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	0.585097	−	0.810963i	$-0.301056\pi$
$977$	49.3848	−	28.5123i	1.57996	−	0.912190i	0.994863	−	0.101227i	$-0.0322769\pi$
$978$		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	−0.998462	−	0.0554435i	$-0.982343\pi$
$983$	−17.1577	−	29.7181i	−0.547246	−	0.947859i	0.451215	−	0.892415i	$-0.350991\pi$
$984$		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	0.901411	−	0.432965i	$-0.142533\pi$
$991$	2.38452	+	4.13011i	0.0757468	+	0.131197i	−0.825664	+	0.564162i	$0.809199\pi$
$992$	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	−0.708666	−	0.705544i	$-0.750703\pi$
$997$	−14.2714	+	8.23960i	−0.451980	+	0.260951i	0.256686	+	0.966495i	$0.417369\pi$
$998$	−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.971.6	yes	16
3.2	odd	2		1134.2.k.c.971.3	yes	16
7.3	odd	6		1134.2.k.c.647.3	✓	16
9.2	odd	6		1134.2.l.h.215.7		16
9.4	even	3		1134.2.t.g.593.3		16
9.5	odd	6		1134.2.t.h.593.6		16
9.7	even	3		1134.2.l.g.215.2		16
21.17	even	6	inner	1134.2.k.d.647.6	yes	16
63.31	odd	6		1134.2.l.h.269.3		16
63.38	even	6		1134.2.t.g.1025.3		16
63.52	odd	6		1134.2.t.h.1025.6		16
63.59	even	6		1134.2.l.g.269.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.k.c.647.3	✓	16	7.3	odd	6
1134.2.k.c.971.3	yes	16	3.2	odd	2
1134.2.k.d.647.6	yes	16	21.17	even	6	inner
1134.2.k.d.971.6	yes	16	1.1	even	1	trivial
1134.2.l.g.215.2		16	9.7	even	3
1134.2.l.g.269.6		16	63.59	even	6
1134.2.l.h.215.7		16	9.2	odd	6
1134.2.l.h.269.3		16	63.31	odd	6
1134.2.t.g.593.3		16	9.4	even	3
1134.2.t.g.1025.3		16	63.38	even	6
1134.2.t.h.593.6		16	9.5	odd	6
1134.2.t.h.1025.6		16	63.52	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more