LMFDB - Embedded newform 882.2.m.b.293.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(293,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("882.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.m (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:	$7.04280545828$
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} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			293.3
Root			$0.765614 - 1.55365i$ of defining polynomial
Character	$\chi$	$=$	882.293
Dual form			882.2.m.b.587.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.0569233 + 1.73112i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.82207 + 3.15592i) q^{5} +(-0.816261 - 1.52765i) q^{6} +1.00000i q^{8} +(-2.99352 - 0.197082i) q^{9} -3.64414i q^{10} +(-4.38809 + 2.53346i) q^{11} +(1.47073 + 0.914855i) q^{12} +(2.94391 + 1.69967i) q^{13} +(-5.35954 - 3.33386i) q^{15} +(-0.500000 - 0.866025i) q^{16} +1.54939 q^{17} +(2.69100 - 1.32608i) q^{18} +0.816535i q^{19} +(1.82207 + 3.15592i) q^{20} +(2.53346 - 4.38809i) q^{22} +(-1.47275 - 0.850294i) q^{23} +(-1.73112 - 0.0569233i) q^{24} +(-4.13989 - 7.17050i) q^{25} -3.39934 q^{26} +(0.511572 - 5.17091i) q^{27} +(-3.60693 + 2.08246i) q^{29} +(6.30843 + 0.207437i) q^{30} +(-1.87924 - 1.08498i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.13593 - 7.74050i) q^{33} +(-1.34181 + 0.774696i) q^{34} +(-1.66744 + 2.49392i) q^{36} +6.79957 q^{37} +(-0.408267 - 0.707140i) q^{38} +(-3.10990 + 4.99950i) q^{39} +(-3.15592 - 1.82207i) q^{40} +(1.01681 - 1.76117i) q^{41} +(3.06189 + 5.30335i) q^{43} +5.06693i q^{44} +(6.07638 - 9.08821i) q^{45} +1.70059 q^{46} +(3.37127 + 5.83922i) q^{47} +(1.52765 - 0.816261i) q^{48} +(7.17050 + 4.13989i) q^{50} +(-0.0881966 + 2.68218i) q^{51} +(2.94391 - 1.69967i) q^{52} -13.2745i q^{53} +(2.14242 + 4.73392i) q^{54} -18.4646i q^{55} +(-1.41352 - 0.0464799i) q^{57} +(2.08246 - 3.60693i) q^{58} +(1.08816 - 1.88475i) q^{59} +(-5.56698 + 2.97457i) q^{60} +(-6.28199 + 3.62691i) q^{61} +2.16996 q^{62} -1.00000 q^{64} +(-10.7280 + 6.19384i) q^{65} +(7.45207 + 4.63550i) q^{66} +(-1.22820 + 2.12731i) q^{67} +(0.774696 - 1.34181i) q^{68} +(1.55579 - 2.50110i) q^{69} -6.74272i q^{71} +(0.197082 - 2.99352i) q^{72} +4.35220i q^{73} +(-5.88860 + 3.39979i) q^{74} +(12.6486 - 6.75846i) q^{75} +(0.707140 + 0.408267i) q^{76} +(0.193502 - 5.88465i) q^{78} +(-6.37651 - 11.0444i) q^{79} +3.64414 q^{80} +(8.92232 + 1.17994i) q^{81} +2.03363i q^{82} +(0.768040 + 1.33028i) q^{83} +(-2.82310 + 4.88976i) q^{85} +(-5.30335 - 3.06189i) q^{86} +(-3.39966 - 6.36254i) q^{87} +(-2.53346 - 4.38809i) q^{88} +12.0336 q^{89} +(-0.718194 + 10.9088i) q^{90} +(-1.47275 + 0.850294i) q^{92} +(1.98519 - 3.19142i) q^{93} +(-5.83922 - 3.37127i) q^{94} +(-2.57692 - 1.48778i) q^{95} +(-0.914855 + 1.47073i) q^{96} +(-5.59509 + 3.23033i) q^{97} +(13.6351 - 6.71916i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 6 q^{9} - 12 q^{11} + 6 q^{13} - 18 q^{15} - 8 q^{16} + 36 q^{17} + 6 q^{23} - 6 q^{24} - 8 q^{25} - 24 q^{26} + 36 q^{27} + 6 q^{29} + 18 q^{30} + 6 q^{31} + 18 q^{33} + 4 q^{37} + 42 q^{39}+ \cdots + 18 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 6 * q^9 - 12 * q^11 + 6 * q^13 - 18 * q^15 - 8 * q^16 + 36 * q^17 + 6 * q^23 - 6 * q^24 - 8 * q^25 - 24 * q^26 + 36 * q^27 + 6 * q^29 + 18 * q^30 + 6 * q^31 + 18 * q^33 + 4 * q^37 + 42 * q^39 - 6 * q^41 - 2 * q^43 + 42 * q^45 - 12 * q^46 + 18 * q^47 - 12 * q^50 - 6 * q^51 + 6 * q^52 + 6 * q^57 + 6 * q^58 - 30 * q^59 - 12 * q^60 - 60 * q^61 + 36 * q^62 - 16 * q^64 - 42 * q^65 + 24 * q^66 + 14 * q^67 + 18 * q^68 - 42 * q^69 - 12 * q^72 - 18 * q^74 - 30 * q^75 - 16 * q^79 - 18 * q^81 - 12 * q^85 - 24 * q^86 - 24 * q^87 + 48 * q^89 + 18 * q^90 + 6 * q^92 + 12 * q^93 + 66 * q^95 - 6 * q^96 + 6 * q^97 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.0569233	+	1.73112i	−0.0328647	+	0.999460i
$3$	−0.0569233	+	1.73112i	−0.0328647	+	0.999460i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.82207	+	3.15592i	−0.814855	+	1.41137i	0.0945763	+	0.995518i	$0.469850\pi$
$5$	−1.82207	+	3.15592i	−0.814855	+	1.41137i	−0.909432	+	0.415853i	$0.863483\pi$
$6$	−0.816261	−	1.52765i	−0.333237	−	0.623661i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−2.99352	−	0.197082i	−0.997840	−	0.0656939i
$10$		−	3.64414i		−	1.15238i
$11$	−4.38809	+	2.53346i	−1.32306	+	0.763868i	−0.984215	−	0.176975i	$-0.943369\pi$
$11$	−4.38809	+	2.53346i	−1.32306	+	0.763868i	−0.338843	+	0.940843i	$0.610035\pi$
$12$	1.47073	+	0.914855i	0.424563	+	0.264096i
$13$	2.94391	+	1.69967i	0.816495	+	0.471404i	0.849206	−	0.528061i	$-0.177081\pi$
$13$	2.94391	+	1.69967i	0.816495	+	0.471404i	−0.0327114	+	0.999465i	$0.510414\pi$
$14$		0			0
$15$	−5.35954	−	3.33386i	−1.38383	−	0.860799i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.54939			0.375783			0.187891	−	0.982190i	$-0.439835\pi$
$17$	1.54939			0.375783			0.187891	+	0.982190i	$0.439835\pi$
$18$	2.69100	−	1.32608i	0.634276	−	0.312561i
$19$			0.816535i			0.187326i	0.995604	+	0.0936629i	$0.0298576\pi$
$19$			0.816535i			0.187326i	−0.995604	+	0.0936629i	$0.970142\pi$
$20$	1.82207	+	3.15592i	0.407428	+	0.705685i
$21$		0			0
$22$	2.53346	−	4.38809i	0.540136	−	0.935543i
$23$	−1.47275	−	0.850294i	−0.307090	−	0.177299i	0.338533	−	0.940954i	$-0.390069\pi$
$23$	−1.47275	−	0.850294i	−0.307090	−	0.177299i	−0.645624	+	0.763656i	$0.723402\pi$
$24$	−1.73112	−	0.0569233i	−0.353362	−	0.0116194i
$25$	−4.13989	−	7.17050i	−0.827979	−	1.43410i
$26$	−3.39934			−0.666665
$27$	0.511572	−	5.17091i	0.0984521	−	0.995142i
$28$		0			0
$29$	−3.60693	+	2.08246i	−0.669789	+	0.386703i	−0.795997	−	0.605301i	$-0.793053\pi$
$29$	−3.60693	+	2.08246i	−0.669789	+	0.386703i	0.126208	+	0.992004i	$0.459719\pi$
$30$	6.30843	+	0.207437i	1.15176	+	0.0378726i
$31$	−1.87924	−	1.08498i	−0.337521	−	0.194868i	0.321654	−	0.946857i	$-0.395761\pi$
$31$	−1.87924	−	1.08498i	−0.337521	−	0.194868i	−0.659175	+	0.751989i	$0.729094\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−4.13593	−	7.74050i	−0.719973	−	1.34745i
$34$	−1.34181	+	0.774696i	−0.230119	+	0.132859i
$35$		0			0
$36$	−1.66744	+	2.49392i	−0.277906	+	0.415654i
$37$	6.79957			1.11784			0.558921	−	0.829221i	$-0.311215\pi$
$37$	6.79957			1.11784			0.558921	+	0.829221i	$0.311215\pi$
$38$	−0.408267	−	0.707140i	−0.0662297	−	0.114713i
$39$	−3.10990	+	4.99950i	−0.497983	+	0.800561i
$40$	−3.15592	−	1.82207i	−0.498995	−	0.288095i
$41$	1.01681	−	1.76117i	0.158799	−	0.275049i	−0.775637	−	0.631180i	$-0.782571\pi$
$41$	1.01681	−	1.76117i	0.158799	−	0.275049i	0.934436	+	0.356131i	$0.115904\pi$
$42$		0			0
$43$	3.06189	+	5.30335i	0.466934	+	0.808753i	0.999286	−	0.0377695i	$-0.0120253\pi$
$43$	3.06189	+	5.30335i	0.466934	+	0.808753i	−0.532353	+	0.846523i	$0.678692\pi$
$44$			5.06693i			0.763868i
$45$	6.07638	−	9.08821i	0.905814	−	1.35479i
$46$	1.70059			0.250738
$47$	3.37127	+	5.83922i	0.491751	+	0.851737i	0.999955	−	0.00949933i	$-0.00302378\pi$
$47$	3.37127	+	5.83922i	0.491751	+	0.851737i	−0.508204	+	0.861237i	$0.669690\pi$
$48$	1.52765	−	0.816261i	0.220497	−	0.117817i
$49$		0			0
$50$	7.17050	+	4.13989i	1.01406	+	0.585469i
$51$	−0.0881966	+	2.68218i	−0.0123500	+	0.375580i
$52$	2.94391	−	1.69967i	0.408247	−	0.235702i
$53$		−	13.2745i		−	1.82340i	−0.410862	−	0.911698i	$-0.634772\pi$
$53$		−	13.2745i		−	1.82340i	0.410862	−	0.911698i	$-0.365228\pi$
$54$	2.14242	+	4.73392i	0.291546	+	0.644205i
$55$		−	18.4646i		−	2.48977i
$56$		0			0
$57$	−1.41352	−	0.0464799i	−0.187225	−	0.00615641i
$58$	2.08246	−	3.60693i	0.273440	−	0.473612i
$59$	1.08816	−	1.88475i	0.141666	−	0.245373i	−0.786458	−	0.617644i	$-0.788087\pi$
$59$	1.08816	−	1.88475i	0.141666	−	0.245373i	0.928124	+	0.372271i	$0.121421\pi$
$60$	−5.56698	+	2.97457i	−0.718694	+	0.384015i
$61$	−6.28199	+	3.62691i	−0.804326	+	0.464378i	−0.844982	−	0.534795i	$-0.820389\pi$
$61$	−6.28199	+	3.62691i	−0.804326	+	0.464378i	0.0406555	+	0.999173i	$0.487055\pi$
$62$	2.16996			0.275585
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−10.7280	+	6.19384i	−1.33065	+	0.768251i
$66$	7.45207	+	4.63550i	0.917286	+	0.570591i
$67$	−1.22820	+	2.12731i	−0.150049	+	0.259892i	−0.931245	−	0.364393i	$-0.881276\pi$
$67$	−1.22820	+	2.12731i	−0.150049	+	0.259892i	0.781196	+	0.624285i	$0.214610\pi$
$68$	0.774696	−	1.34181i	0.0939457	−	0.162719i
$69$	1.55579	−	2.50110i	0.187295	−	0.301097i
$70$		0			0
$71$		−	6.74272i		−	0.800213i	−0.916469	−	0.400107i	$-0.868973\pi$
$71$		−	6.74272i		−	0.800213i	0.916469	−	0.400107i	$-0.131027\pi$
$72$	0.197082	−	2.99352i	0.0232263	−	0.352790i
$73$			4.35220i			0.509387i	0.967022	+	0.254694i	$0.0819746\pi$
$73$			4.35220i			0.509387i	−0.967022	+	0.254694i	$0.918025\pi$
$74$	−5.88860	+	3.39979i	−0.684536	+	0.395217i
$75$	12.6486	−	6.75846i	1.46054	−	0.780400i
$76$	0.707140	+	0.408267i	0.0811145	+	0.0468315i
$77$		0			0
$78$	0.193502	−	5.88465i	0.0219097	−	0.666305i
$79$	−6.37651	−	11.0444i	−0.717414	−	1.24260i	−0.962021	−	0.272975i	$-0.911992\pi$
$79$	−6.37651	−	11.0444i	−0.717414	−	1.24260i	0.244607	−	0.969622i	$-0.421341\pi$
$80$	3.64414			0.407428
$81$	8.92232	+	1.17994i	0.991369	+	0.131104i
$82$			2.03363i			0.224576i
$83$	0.768040	+	1.33028i	0.0843034	+	0.146018i	0.905094	−	0.425211i	$-0.139800\pi$
$83$	0.768040	+	1.33028i	0.0843034	+	0.146018i	−0.820791	+	0.571229i	$0.806467\pi$
$84$		0			0
$85$	−2.82310	+	4.88976i	−0.306209	+	0.530369i
$86$	−5.30335	−	3.06189i	−0.571875	−	0.330172i
$87$	−3.39966	−	6.36254i	−0.364482	−	0.682136i
$88$	−2.53346	−	4.38809i	−0.270068	−	0.467772i
$89$	12.0336			1.27556			0.637778	−	0.770220i	$-0.279854\pi$
$89$	12.0336			1.27556			0.637778	+	0.770220i	$0.279854\pi$
$90$	−0.718194	+	10.9088i	−0.0757043	+	1.14989i
$91$		0			0
$92$	−1.47275	+	0.850294i	−0.153545	+	0.0886493i
$93$	1.98519	−	3.19142i	0.205855	−	0.330934i
$94$	−5.83922	−	3.37127i	−0.602269	−	0.347720i
$95$	−2.57692	−	1.48778i	−0.264386	−	0.152643i
$96$	−0.914855	+	1.47073i	−0.0933720	+	0.150106i
$97$	−5.59509	+	3.23033i	−0.568095	+	0.327990i	−0.756388	−	0.654123i	$-0.773038\pi$
$97$	−5.59509	+	3.23033i	−0.568095	+	0.327990i	0.188293	+	0.982113i	$0.439705\pi$
$98$		0			0
$99$	13.6351	−	6.71916i	1.37038	−	0.675301i
$100$	−8.27979			−0.827979
$101$	5.95045	+	10.3065i	0.592092	+	1.02553i	0.993950	+	0.109831i	$0.0350311\pi$
$101$	5.95045	+	10.3065i	0.592092	+	1.02553i	−0.401858	+	0.915702i	$0.631636\pi$
$102$	−1.26471	−	2.36693i	−0.125225	−	0.234361i
$103$	−12.7174	−	7.34240i	−1.25308	−	0.723468i	−0.281363	−	0.959601i	$-0.590786\pi$
$103$	−12.7174	−	7.34240i	−1.25308	−	0.723468i	−0.971721	+	0.236134i	$0.924120\pi$
$104$	−1.69967	+	2.94391i	−0.166666	+	0.288675i
$105$		0			0
$106$	6.63726	+	11.4961i	0.644668	+	1.11660i
$107$			3.31922i			0.320881i	0.987046	+	0.160440i	$0.0512915\pi$
$107$			3.31922i			0.320881i	−0.987046	+	0.160440i	$0.948709\pi$
$108$	−4.22235	−	3.02849i	−0.406296	−	0.291416i
$109$	−2.83674			−0.271710			−0.135855	−	0.990729i	$-0.543378\pi$
$109$	−2.83674			−0.271710			−0.135855	+	0.990729i	$0.543378\pi$
$110$	9.23230	+	15.9908i	0.880266	+	1.52466i
$111$	−0.387054	+	11.7708i	−0.0367376	+	1.11724i
$112$		0			0
$113$	−6.80465	−	3.92866i	−0.640127	−	0.369578i	0.144536	−	0.989500i	$-0.453831\pi$
$113$	−6.80465	−	3.92866i	−0.640127	−	0.369578i	−0.784664	+	0.619922i	$0.787164\pi$
$114$	1.24738	−	0.666505i	0.116828	−	0.0624239i
$115$	5.36692	−	3.09859i	0.500468	−	0.288945i
$116$			4.16492i			0.386703i
$117$	−8.47769	−	5.66819i	−0.783763	−	0.524024i
$118$			2.17632i			0.200346i
$119$		0			0
$120$	3.33386	−	5.35954i	0.304339	−	0.489257i
$121$	7.33687	−	12.7078i	0.666988	−	1.15526i
$122$	3.62691	−	6.28199i	0.328365	−	0.568744i
$123$	2.99091	+	1.86047i	0.269681	+	0.167753i
$124$	−1.87924	+	1.08498i	−0.168761	+	0.0974339i
$125$	11.9520			1.06902
$126$		0			0
$127$	−17.4279			−1.54647			−0.773237	−	0.634117i	$-0.781364\pi$
$127$	−17.4279			−1.54647			−0.773237	+	0.634117i	$0.781364\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−9.35500	+	4.99860i	−0.823662	+	0.440102i
$130$	6.19384	−	10.7280i	0.543236	−	0.940912i
$131$	1.61603	−	2.79904i	0.141193	−	0.244554i	−0.786753	−	0.617268i	$-0.788240\pi$
$131$	1.61603	−	2.79904i	0.141193	−	0.244554i	0.927946	+	0.372714i	$0.121573\pi$
$132$	−8.77143	−	0.288426i	−0.763455	−	0.0251043i
$133$		0			0
$134$		−	2.45641i		−	0.212201i
$135$	15.3869	+	11.0362i	1.32429	+	0.949849i
$136$			1.54939i			0.132859i
$137$	−12.6284	+	7.29101i	−1.07892	+	0.622913i	−0.930604	−	0.366027i	$-0.880718\pi$
$137$	−12.6284	+	7.29101i	−1.07892	+	0.622913i	−0.148313	+	0.988940i	$0.547384\pi$
$138$	−0.0968031	+	2.94391i	−0.00824043	+	0.250603i
$139$	−4.97814	−	2.87413i	−0.422240	−	0.243780i	0.273795	−	0.961788i	$-0.411721\pi$
$139$	−4.97814	−	2.87413i	−0.422240	−	0.243780i	−0.696035	+	0.718008i	$0.745054\pi$
$140$		0			0
$141$	−10.3003	+	5.50368i	−0.867438	+	0.463493i
$142$	3.37136	+	5.83936i	0.282918	+	0.490029i
$143$	−17.2242			−1.44036
$144$	1.32608	+	2.69100i	0.110507	+	0.224250i
$145$		−	15.1776i		−	1.26043i
$146$	−2.17610	−	3.76912i	−0.180096	−	0.311935i
$147$		0			0
$148$	3.39979	−	5.88860i	0.279461	−	0.484040i
$149$	−4.95904	−	2.86310i	−0.406261	−	0.234555i	0.282921	−	0.959143i	$-0.408697\pi$
$149$	−4.95904	−	2.86310i	−0.406261	−	0.234555i	−0.689182	+	0.724589i	$0.742030\pi$
$150$	−7.57480	+	12.1773i	−0.618480	+	0.994273i
$151$	6.38483	+	11.0589i	0.519590	+	0.899957i	0.999741	+	0.0227705i	$0.00724870\pi$
$151$	6.38483	+	11.0589i	0.519590	+	0.899957i	−0.480151	+	0.877186i	$0.659418\pi$
$152$	−0.816535			−0.0662297
$153$	−4.63814	−	0.305357i	−0.374971	−	0.0246866i
$154$		0			0
$155$	6.84821	−	3.95382i	0.550062	−	0.317578i
$156$	2.77475	+	5.19300i	0.222158	+	0.415773i
$157$	11.0598	+	6.38536i	0.882666	+	0.509607i	0.871537	−	0.490331i	$-0.163124\pi$
$157$	11.0598	+	6.38536i	0.882666	+	0.509607i	0.0111295	+	0.999938i	$0.496457\pi$
$158$	11.0444	+	6.37651i	0.878649	+	0.507288i
$159$	22.9797	+	0.755630i	1.82241	+	0.0599253i
$160$	−3.15592	+	1.82207i	−0.249497	+	0.144047i
$161$		0			0
$162$	−8.31692	+	3.43930i	−0.653439	+	0.270217i
$163$	3.02035			0.236572			0.118286	−	0.992980i	$-0.462260\pi$
$163$	3.02035			0.236572			0.118286	+	0.992980i	$0.462260\pi$
$164$	−1.01681	−	1.76117i	−0.0793997	−	0.137524i
$165$	31.9644	+	1.05107i	2.48842	+	0.0818254i
$166$	−1.33028	−	0.768040i	−0.103250	−	0.0596115i
$167$	−7.14766	+	12.3801i	−0.553103	+	0.958002i	0.444946	+	0.895557i	$0.353223\pi$
$167$	−7.14766	+	12.3801i	−0.553103	+	0.958002i	−0.998048	+	0.0624443i	$0.980110\pi$
$168$		0			0
$169$	−0.722247	−	1.25097i	−0.0555575	−	0.0962284i
$170$		−	5.64621i		−	0.433045i
$171$	0.160924	−	2.44431i	0.0123062	−	0.186921i
$172$	6.12378			0.466934
$173$	−1.09953	−	1.90444i	−0.0835954	−	0.144792i	0.821196	−	0.570646i	$-0.193307\pi$
$173$	−1.09953	−	1.90444i	−0.0835954	−	0.144792i	−0.904792	+	0.425854i	$0.859974\pi$
$174$	6.12546	+	3.81029i	0.464370	+	0.288858i
$175$		0			0
$176$	4.38809	+	2.53346i	0.330764	+	0.190967i
$177$	3.20077	+	1.99102i	0.240585	+	0.149654i
$178$	−10.4214	+	6.01679i	−0.781116	+	0.450977i
$179$			10.7470i			0.803266i	0.915801	+	0.401633i	$0.131557\pi$
$179$			10.7470i			0.803266i	−0.915801	+	0.401633i	$0.868443\pi$
$180$	−4.83243	−	9.80641i	−0.360188	−	0.730927i
$181$			14.4710i			1.07562i	0.843065	+	0.537811i	$0.180749\pi$
$181$			14.4710i			1.07562i	−0.843065	+	0.537811i	$0.819251\pi$
$182$		0			0
$183$	−5.92100	−	11.0813i	−0.437693	−	0.819153i
$184$	0.850294	−	1.47275i	0.0626845	−	0.108573i
$185$	−12.3893	+	21.4589i	−0.910880	+	1.57769i
$186$	−0.123521	+	3.75644i	−0.00905701	+	0.275436i
$187$	−6.79887	+	3.92533i	−0.497183	+	0.287048i
$188$	6.74255			0.491751
$189$		0			0
$190$	2.97557			0.215871
$191$	−7.21567	+	4.16597i	−0.522108	+	0.301439i	−0.737797	−	0.675023i	$-0.764134\pi$
$191$	−7.21567	+	4.16597i	−0.522108	+	0.301439i	0.215689	+	0.976462i	$0.430800\pi$
$192$	0.0569233	−	1.73112i	0.00410809	−	0.124932i
$193$	4.78393	−	8.28601i	0.344355	−	0.596440i	−0.640881	−	0.767640i	$-0.721431\pi$
$193$	4.78393	−	8.28601i	0.344355	−	0.596440i	0.985236	+	0.171200i	$0.0547643\pi$
$194$	3.23033	−	5.59509i	0.231924	−	0.401704i
$195$	−10.1116	−	18.9241i	−0.724105	−	1.35518i
$196$		0			0
$197$		−	2.37228i		−	0.169018i	−0.996423	−	0.0845089i	$-0.973068\pi$
$197$		−	2.37228i		−	0.169018i	0.996423	−	0.0845089i	$-0.0269322\pi$
$198$	−8.44878	+	12.6365i	−0.600429	+	0.898039i
$199$			22.5147i			1.59602i	0.602642	+	0.798011i	$0.294115\pi$
$199$			22.5147i			1.59602i	−0.602642	+	0.798011i	$0.705885\pi$
$200$	7.17050	−	4.13989i	0.507031	−	0.292735i
$201$	−3.61271	−	2.24726i	−0.254821	−	0.158509i
$202$	−10.3065	−	5.95045i	−0.725161	−	0.418672i
$203$		0			0
$204$	2.27874	+	1.41747i	0.159543	+	0.0992427i
$205$	3.70541	+	6.41796i	0.258797	+	0.448250i
$206$	14.6848			1.02314
$207$	4.24114	+	2.83562i	0.294779	+	0.197090i
$208$		−	3.39934i		−	0.235702i
$209$	−2.06866	−	3.58302i	−0.143092	−	0.247843i
$210$		0			0
$211$	−7.27211	+	12.5957i	−0.500632	+	0.867121i	0.499367	+	0.866390i	$0.333566\pi$
$211$	−7.27211	+	12.5957i	−0.500632	+	0.867121i	−1.00000		0.000730453i	$0.999767\pi$
$212$	−11.4961	−	6.63726i	−0.789553	−	0.455849i
$213$	11.6724	+	0.383818i	0.799781	+	0.0262988i
$214$	−1.65961	−	2.87453i	−0.113449	−	0.196499i
$215$	−22.3159			−1.52193
$216$	5.17091	+	0.511572i	0.351836	+	0.0348081i
$217$		0			0
$218$	2.45668	−	1.41837i	0.166388	−	0.0960640i
$219$	−7.53417	−	0.247742i	−0.509112	−	0.0167408i
$220$	−15.9908	−	9.23230i	−1.07810	−	0.622442i
$221$	4.56128	+	2.63346i	0.306825	+	0.177145i
$222$	−5.55022	−	10.3874i	−0.372506	−	0.697155i
$223$	−22.5221	+	13.0031i	−1.50819	+	0.870753i	−0.508235	+	0.861219i	$0.669702\pi$
$223$	−22.5221	+	13.0031i	−1.50819	+	0.870753i	−0.999955	+	0.00953489i	$0.996965\pi$
$224$		0			0
$225$	10.9797	+	22.2809i	0.731978	+	1.48540i
$226$	7.85733			0.522662
$227$	−11.4390	−	19.8129i	−0.759231	−	1.31503i	−0.943243	−	0.332103i	$-0.892242\pi$
$227$	−11.4390	−	19.8129i	−0.759231	−	1.31503i	0.184012	−	0.982924i	$-0.441091\pi$
$228$	−0.747010	+	1.20090i	−0.0494720	+	0.0795316i
$229$	23.3224	+	13.4652i	1.54118	+	0.889803i	0.998764	+	0.0496960i	$0.0158252\pi$
$229$	23.3224	+	13.4652i	1.54118	+	0.889803i	0.542420	+	0.840107i	$0.317508\pi$
$230$	−3.09859	+	5.36692i	−0.204315	+	0.353884i
$231$		0			0
$232$	−2.08246	−	3.60693i	−0.136720	−	0.236806i
$233$			4.41099i			0.288974i	0.989507	+	0.144487i	$0.0461532\pi$
$233$			4.41099i			0.288974i	−0.989507	+	0.144487i	$0.953847\pi$
$234$	10.1760	+	0.669947i	0.665225	+	0.0437958i
$235$	−24.5708			−1.60282
$236$	−1.08816	−	1.88475i	−0.0708331	−	0.122687i
$237$	19.4822	−	10.4098i	1.26550	−	0.676189i
$238$		0			0
$239$	16.1660	+	9.33343i	1.04569	+	0.603729i	0.921440	−	0.388522i	$-0.127014\pi$
$239$	16.1660	+	9.33343i	1.04569	+	0.603729i	0.124250	+	0.992251i	$0.460347\pi$
$240$	−0.207437	+	6.30843i	−0.0133900	+	0.407208i
$241$	−0.412458	+	0.238133i	−0.0265688	+	0.0153395i	−0.513226	−	0.858254i	$-0.671550\pi$
$241$	−0.412458	+	0.238133i	−0.0265688	+	0.0153395i	0.486657	+	0.873593i	$0.338216\pi$
$242$			14.6737i			0.943263i
$243$	−2.55049	+	15.3784i	−0.163614	+	0.986524i
$244$			7.25382i			0.464378i
$245$		0			0
$246$	−3.52044	−	0.115761i	−0.224455	−	0.00738063i
$247$	−1.38784	+	2.40381i	−0.0883061	+	0.152951i
$248$	1.08498	−	1.87924i	0.0688962	−	0.119332i
$249$	−2.34660	+	1.25384i	−0.148709	+	0.0794590i
$250$	−10.3507	+	5.97601i	−0.654639	+	0.377956i
$251$	−17.6939			−1.11683			−0.558415	−	0.829562i	$-0.688590\pi$
$251$	−17.6939			−1.11683			−0.558415	+	0.829562i	$0.688590\pi$
$252$		0			0
$253$	8.61675			0.541731
$254$	15.0930	−	8.71394i	0.947018	−	0.546761i
$255$	−8.30404	−	5.16546i	−0.520019	−	0.323474i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−11.5971	+	20.0867i	−0.723405	+	1.25297i	0.236222	+	0.971699i	$0.424091\pi$
$257$	−11.5971	+	20.0867i	−0.723405	+	1.25297i	−0.959627	+	0.281275i	$0.909243\pi$
$258$	5.60237	−	9.00642i	0.348788	−	0.560715i
$259$		0			0
$260$			12.3877i			0.768251i
$261$	11.2078	−	5.52302i	0.693746	−	0.341867i
$262$			3.23206i			0.199677i
$263$	−2.98247	+	1.72193i	−0.183907	+	0.106179i	−0.589127	−	0.808040i	$-0.700528\pi$
$263$	−2.98247	+	1.72193i	−0.183907	+	0.106179i	0.405220	+	0.914219i	$0.367195\pi$
$264$	7.74050	−	4.13593i	0.476395	−	0.254549i
$265$	41.8933	+	24.1871i	2.57349	+	1.48580i
$266$		0			0
$267$	−0.684991	+	20.8315i	−0.0419208	+	1.27487i
$268$	1.22820	+	2.12731i	0.0750245	+	0.129946i
$269$	8.01379			0.488610			0.244305	−	0.969698i	$-0.421440\pi$
$269$	8.01379			0.488610			0.244305	+	0.969698i	$0.421440\pi$
$270$	−18.8435	−	1.86424i	−1.14678	−	0.113454i
$271$			1.79088i			0.108788i	0.998520	+	0.0543942i	$0.0173228\pi$
$271$			1.79088i			0.108788i	−0.998520	+	0.0543942i	$0.982677\pi$
$272$	−0.774696	−	1.34181i	−0.0469729	−	0.0813594i
$273$		0			0
$274$	7.29101	−	12.6284i	0.440466	−	0.762910i
$275$	36.3324	+	20.9765i	2.19093	+	1.26493i
$276$	−1.38812	−	2.59791i	−0.0835552	−	0.156376i
$277$	12.2968	+	21.2986i	0.738841	+	1.27971i	0.953017	+	0.302915i	$0.0979599\pi$
$277$	12.2968	+	21.2986i	0.738841	+	1.27971i	−0.214176	+	0.976795i	$0.568707\pi$
$278$	5.74826			0.344757
$279$	5.41170	+	3.61827i	0.323990	+	0.216620i
$280$		0			0
$281$	18.6262	−	10.7539i	1.11115	−	0.641521i	0.172021	−	0.985093i	$-0.444970\pi$
$281$	18.6262	−	10.7539i	1.11115	−	0.641521i	0.939126	+	0.343572i	$0.111637\pi$
$282$	6.16845	−	9.91645i	0.367326	−	0.590516i
$283$	−17.2755	−	9.97402i	−1.02692	−	0.592894i	−0.110821	−	0.993840i	$-0.535348\pi$
$283$	−17.2755	−	9.97402i	−1.02692	−	0.592894i	−0.916101	+	0.400947i	$0.868681\pi$
$284$	−5.83936	−	3.37136i	−0.346502	−	0.200053i
$285$	2.72221	−	4.37625i	0.161250	−	0.259227i
$286$	14.9166	−	8.61210i	0.882037	−	0.509244i
$287$		0			0
$288$	−2.49392	−	1.66744i	−0.146956	−	0.0982547i
$289$	−14.5994			−0.858787
$290$	7.58878	+	13.1442i	0.445629	+	0.771851i
$291$	−5.27358	−	9.86963i	−0.309143	−	0.578568i
$292$	3.76912	+	2.17610i	0.220571	+	0.127347i
$293$	−1.24656	+	2.15911i	−0.0728251	+	0.126137i	−0.900138	−	0.435604i	$-0.856535\pi$
$293$	−1.24656	+	2.15911i	−0.0728251	+	0.126137i	0.827313	+	0.561741i	$0.189868\pi$
$294$		0			0
$295$	3.96541	+	6.86829i	0.230875	+	0.399887i
$296$			6.79957i			0.395217i
$297$	10.8555	+	23.9864i	0.629899	+	1.39183i
$298$	5.72621			0.331710
$299$	−2.89044	−	5.00639i	−0.167158	−	0.289527i
$300$	0.471313	−	14.3333i	0.0272113	−	0.827531i
$301$		0			0
$302$	−11.0589	−	6.38483i	−0.636365	−	0.367406i
$303$	−18.1804	+	9.71423i	−1.04444	+	0.558068i
$304$	0.707140	−	0.408267i	0.0405572	−	0.0234157i
$305$		−	26.4339i		−	1.51360i
$306$	4.16942	−	2.05462i	0.238350	−	0.117455i
$307$		−	9.23124i		−	0.526854i	−0.964679	−	0.263427i	$-0.915147\pi$
$307$		−	9.23124i		−	0.526854i	0.964679	−	0.263427i	$-0.0848529\pi$
$308$		0			0
$309$	13.4345	−	21.5973i	0.764259	−	1.22863i
$310$	−3.95382	+	6.84821i	−0.224562	+	0.388952i
$311$	−11.4857	+	19.8938i	−0.651294	+	1.12807i	0.331515	+	0.943450i	$0.392440\pi$
$311$	−11.4857	+	19.8938i	−0.651294	+	1.12807i	−0.982809	+	0.184624i	$0.940893\pi$
$312$	−4.99950	−	3.10990i	−0.283041	−	0.176063i
$313$	−5.57145	+	3.21668i	−0.314917	+	0.181818i	−0.649125	−	0.760682i	$-0.724865\pi$
$313$	−5.57145	+	3.21668i	−0.314917	+	0.181818i	0.334208	+	0.942500i	$0.391531\pi$
$314$	−12.7707			−0.720694
$315$		0			0
$316$	−12.7530			−0.717414
$317$	−7.56502	+	4.36767i	−0.424894	+	0.245313i	−0.697169	−	0.716907i	$-0.745557\pi$
$317$	−7.56502	+	4.36767i	−0.424894	+	0.245313i	0.272275	+	0.962219i	$0.412224\pi$
$318$	−20.2788	+	10.8355i	−1.13718	+	0.607623i
$319$	10.5517	−	18.2760i	0.590780	−	1.02326i
$320$	1.82207	−	3.15592i	0.101857	−	0.176421i
$321$	−5.74595	−	0.188941i	−0.320708	−	0.0105457i
$322$		0			0
$323$			1.26513i			0.0703939i
$324$	5.48301	−	7.13699i	0.304612	−	0.396499i
$325$		−	28.1458i		−	1.56125i
$326$	−2.61570	+	1.51018i	−0.144870	+	0.0836410i
$327$	0.161476	−	4.91072i	0.00892966	−	0.271563i
$328$	1.76117	+	1.01681i	0.0972444	+	0.0561441i
$329$		0			0
$330$	−28.2075	+	15.0719i	−1.55277	+	0.829682i
$331$	−15.8504	−	27.4537i	−0.871215	−	1.50899i	−0.860740	−	0.509044i	$-0.829999\pi$
$331$	−15.8504	−	27.4537i	−0.871215	−	1.50899i	−0.0104748	−	0.999945i	$-0.503334\pi$
$332$	1.53608			0.0843034
$333$	−20.3546	−	1.34007i	−1.11543	−	0.0734354i
$334$		−	14.2953i		−	0.782205i
$335$	−4.47575	−	7.75223i	−0.244536	−	0.423549i
$336$		0			0
$337$	16.1308	−	27.9393i	0.878700	−	1.52195i	0.0259314	−	0.999664i	$-0.491745\pi$
$337$	16.1308	−	27.9393i	0.878700	−	1.52195i	0.852768	−	0.522289i	$-0.174922\pi$
$338$	1.25097	+	0.722247i	0.0680437	+	0.0392851i
$339$	7.18831	−	11.5560i	0.390416	−	0.627636i
$340$	2.82310	+	4.88976i	0.153104	+	0.265185i
$341$	10.9950			0.595413
$342$	1.08279	+	2.19730i	0.0585507	+	0.118816i
$343$		0			0
$344$	−5.30335	+	3.06189i	−0.285937	+	0.165086i
$345$	5.05852	+	9.46714i	0.272342	+	0.509694i
$346$	1.90444	+	1.09953i	0.102383	+	0.0591109i
$347$	−5.90994	−	3.41210i	−0.317262	−	0.183171i	0.332909	−	0.942959i	$-0.391970\pi$
$347$	−5.90994	−	3.41210i	−0.317262	−	0.183171i	−0.650172	+	0.759787i	$0.725303\pi$
$348$	−7.20995	−	0.237081i	−0.386494	−	0.0127089i
$349$	−4.18379	+	2.41551i	−0.223953	+	0.129299i	−0.607779	−	0.794106i	$-0.707939\pi$
$349$	−4.18379	+	2.41551i	−0.223953	+	0.129299i	0.383826	+	0.923405i	$0.374606\pi$
$350$		0			0
$351$	10.2949	−	14.3532i	0.549499	−	0.766117i
$352$	−5.06693			−0.270068
$353$	−17.2922	−	29.9510i	−0.920371	−	1.59413i	−0.798842	−	0.601541i	$-0.794554\pi$
$353$	−17.2922	−	29.9510i	−0.920371	−	1.59413i	−0.121529	−	0.992588i	$-0.538780\pi$
$354$	−3.76746	−	0.123883i	−0.200238	−	0.00658432i
$355$	21.2795	+	12.2857i	1.12940	+	0.652058i
$356$	6.01679	−	10.4214i	0.318889	−	0.552332i
$357$		0			0
$358$	−5.37349	−	9.30715i	−0.283998	−	0.491898i
$359$		−	27.1483i		−	1.43283i	−0.697672	−	0.716417i	$-0.745781\pi$
$359$		−	27.1483i		−	1.43283i	0.697672	−	0.716417i	$-0.254219\pi$
$360$	9.08821	+	6.07638i	0.478991	+	0.320253i
$361$	18.3333			0.964909
$362$	−7.23551	−	12.5323i	−0.380290	−	0.658682i
$363$	21.5811	+	13.4243i	1.13271	+	0.704595i
$364$		0			0
$365$	−13.7352	−	7.93003i	−0.718934	−	0.415077i
$366$	10.6684	+	6.63619i	0.557646	+	0.346879i
$367$	10.3307	−	5.96444i	0.539259	−	0.311341i	−0.205520	−	0.978653i	$-0.565888\pi$
$367$	10.3307	−	5.96444i	0.539259	−	0.311341i	0.744778	+	0.667312i	$0.232555\pi$
$368$			1.70059i			0.0886493i
$369$	−3.39094	+	5.07171i	−0.176525	+	0.264022i
$370$		−	24.7786i		−	1.28818i
$371$		0			0
$372$	−1.77125	−	3.31494i	−0.0918350	−	0.171871i
$373$	−4.81925	+	8.34718i	−0.249531	+	0.432201i	−0.963396	−	0.268083i	$-0.913610\pi$
$373$	−4.81925	+	8.34718i	−0.249531	+	0.432201i	0.713865	+	0.700284i	$0.246943\pi$
$374$	3.92533	−	6.79887i	0.202974	−	0.351561i
$375$	−0.680348	+	20.6903i	−0.0351330	+	1.06844i
$376$	−5.83922	+	3.37127i	−0.301135	+	0.173860i
$377$	−14.1580			−0.729173
$378$		0			0
$379$	−16.0145			−0.822612			−0.411306	−	0.911497i	$-0.634927\pi$
$379$	−16.0145			−0.822612			−0.411306	+	0.911497i	$0.634927\pi$
$380$	−2.57692	+	1.48778i	−0.132193	+	0.0763217i
$381$	0.992053	−	30.1697i	0.0508244	−	1.54564i
$382$	4.16597	−	7.21567i	0.213150	−	0.369186i
$383$	−3.18472	+	5.51610i	−0.162732	+	0.281860i	−0.935847	−	0.352405i	$-0.885364\pi$
$383$	−3.18472	+	5.51610i	−0.162732	+	0.281860i	0.773116	+	0.634265i	$0.218697\pi$
$384$	0.816261	+	1.52765i	0.0416546	+	0.0779576i
$385$		0			0
$386$			9.56786i			0.486991i
$387$	−8.12063	−	16.4791i	−0.412795	−	0.837681i
$388$			6.46065i			0.327990i
$389$	15.2013	−	8.77645i	0.770735	−	0.444984i	−0.0624020	−	0.998051i	$-0.519876\pi$
$389$	15.2013	−	8.77645i	0.770735	−	0.444984i	0.833137	+	0.553067i	$0.186543\pi$
$390$	18.2189	+	11.3329i	0.922550	+	0.573865i
$391$	−2.28187	−	1.31744i	−0.115399	−	0.0666258i
$392$		0			0
$393$	4.75348	+	2.95686i	0.239781	+	0.149154i
$394$	1.18614	+	2.05445i	0.0597568	+	0.103502i
$395$	46.4739			2.33835
$396$	0.998598	−	15.1679i	0.0501814	−	0.762218i
$397$		−	13.3591i		−	0.670474i	−0.942134	−	0.335237i	$-0.891184\pi$
$397$		−	13.3591i		−	0.670474i	0.942134	−	0.335237i	$-0.108816\pi$
$398$	−11.2573	−	19.4983i	−0.564279	−	0.977360i
$399$		0			0
$400$	−4.13989	+	7.17050i	−0.206995	+	0.358525i
$401$	−3.66182	−	2.11415i	−0.182863	−	0.105576i	0.405774	−	0.913973i	$-0.367002\pi$
$401$	−3.66182	−	2.11415i	−0.182863	−	0.105576i	−0.588637	+	0.808398i	$0.700335\pi$
$402$	4.25232	+	0.139827i	0.212087	+	0.00697393i
$403$	−3.68821	−	6.38817i	−0.183723	−	0.318217i
$404$	11.9009			0.592092
$405$	−19.9809	+	26.0082i	−0.992858	+	1.29236i
$406$		0			0
$407$	−29.8371	+	17.2265i	−1.47897	+	0.853884i
$408$	−2.68218	−	0.0881966i	−0.132788	−	0.00436638i
$409$	33.2687	+	19.2077i	1.64503	+	0.949759i	0.979006	+	0.203829i	$0.0653387\pi$
$409$	33.2687	+	19.2077i	1.64503	+	0.949759i	0.666025	+	0.745930i	$0.267995\pi$
$410$	−6.41796	−	3.70541i	−0.316961	−	0.182997i
$411$	−11.9027	−	22.2762i	−0.587118	−	1.09881i
$412$	−12.7174	+	7.34240i	−0.626542	+	0.361734i
$413$		0			0
$414$	−5.09074	−	0.335155i	−0.250196	−	0.0164720i
$415$	−5.59770			−0.274780
$416$	1.69967	+	2.94391i	0.0833332	+	0.144337i
$417$	5.25882	−	8.45412i	0.257525	−	0.414000i
$418$	3.58302	+	2.06866i	0.175251	+	0.101181i
$419$	7.03301	−	12.1815i	0.343585	−	0.595107i	−0.641511	−	0.767114i	$-0.721692\pi$
$419$	7.03301	−	12.1815i	0.343585	−	0.595107i	0.985096	+	0.172007i	$0.0550253\pi$
$420$		0			0
$421$	10.5504	+	18.2738i	0.514195	+	0.890612i	0.999864	+	0.0164691i	$0.00524252\pi$
$421$	10.5504	+	18.2738i	0.514195	+	0.890612i	−0.485670	+	0.874143i	$0.661424\pi$
$422$		−	14.5442i		−	0.708001i
$423$	−8.94117	−	18.1442i	−0.434735	−	0.882202i
$424$	13.2745			0.644668
$425$	−6.41432	−	11.1099i	−0.311140	−	0.538911i
$426$	−10.3005	+	5.50381i	−0.499062	+	0.266661i
$427$		0			0
$428$	2.87453	+	1.65961i	0.138946	+	0.0802202i
$429$	0.980459	−	29.8171i	0.0473370	−	1.43958i
$430$	19.3262	−	11.1580i	0.931991	−	0.538085i
$431$			11.6542i			0.561362i	0.959801	+	0.280681i	$0.0905602\pi$
$431$			11.6542i			0.561362i	−0.959801	+	0.280681i	$0.909440\pi$
$432$	−4.73392	+	2.14242i	−0.227761	+	0.103077i
$433$		−	17.9149i		−	0.860936i	−0.902606	−	0.430468i	$-0.858348\pi$
$433$		−	17.9149i		−	0.860936i	0.902606	−	0.430468i	$-0.141652\pi$
$434$		0			0
$435$	26.2741	+	0.863957i	1.25975	+	0.0414236i
$436$	−1.41837	+	2.45668i	−0.0679275	+	0.117654i
$437$	0.694295	−	1.20255i	0.0332126	−	0.0575259i
$438$	6.64865	−	3.55253i	0.317685	−	0.169747i
$439$	−16.4783	+	9.51377i	−0.786468	+	0.454068i	−0.838718	−	0.544566i	$-0.816694\pi$
$439$	−16.4783	+	9.51377i	−0.786468	+	0.454068i	0.0522494	+	0.998634i	$0.483361\pi$
$440$	18.4646			0.880266
$441$		0			0
$442$	−5.26691			−0.250521
$443$	6.64877	−	3.83867i	0.315893	−	0.182381i	−0.333668	−	0.942691i	$-0.608286\pi$
$443$	6.64877	−	3.83867i	0.315893	−	0.182381i	0.649560	+	0.760310i	$0.274953\pi$
$444$	10.0003	+	6.22062i	0.474594	+	0.295217i
$445$	−21.9260	+	37.9770i	−1.03939	+	1.80028i
$446$	13.0031	−	22.5221i	0.615716	−	1.06645i
$447$	5.23865	−	8.42170i	0.247780	−	0.398333i
$448$		0			0
$449$		−	30.1018i		−	1.42059i	−0.703903	−	0.710296i	$-0.748561\pi$
$449$		−	30.1018i		−	1.42059i	0.703903	−	0.710296i	$-0.251439\pi$
$450$	−20.6491	−	13.8060i	−0.973410	−	0.650822i
$451$			10.3042i			0.485207i
$452$	−6.80465	+	3.92866i	−0.320064	+	0.184789i
$453$	−19.5076	+	10.4234i	−0.916547	+	0.489733i
$454$	19.8129	+	11.4390i	0.929864	+	0.536857i
$455$		0			0
$456$	0.0464799	−	1.41352i	0.00217662	−	0.0661939i
$457$	19.7438	+	34.1973i	0.923576	+	1.59968i	0.793835	+	0.608133i	$0.208081\pi$
$457$	19.7438	+	34.1973i	0.923576	+	1.59968i	0.129741	+	0.991548i	$0.458586\pi$
$458$	−26.9303			−1.25837
$459$	0.792626	−	8.01177i	0.0369966	−	0.373957i
$460$		−	6.19719i		−	0.288945i
$461$	11.3776	+	19.7066i	0.529909	+	0.917830i	0.999391	+	0.0348879i	$0.0111074\pi$
$461$	11.3776	+	19.7066i	0.529909	+	0.917830i	−0.469482	+	0.882942i	$0.655559\pi$
$462$		0			0
$463$	6.63866	−	11.4985i	0.308525	−	0.534381i	−0.669515	−	0.742798i	$-0.733498\pi$
$463$	6.63866	−	11.4985i	0.308525	−	0.534381i	0.978040	+	0.208418i	$0.0668314\pi$
$464$	3.60693	+	2.08246i	0.167447	+	0.0966757i
$465$	6.45469	+	12.0801i	0.299329	+	0.560202i
$466$	−2.20550	−	3.82003i	−0.102168	−	0.176960i
$467$	23.1746			1.07239			0.536195	−	0.844094i	$-0.319861\pi$
$467$	23.1746			1.07239			0.536195	+	0.844094i	$0.319861\pi$
$468$	−9.14764	+	4.50780i	−0.422850	+	0.208373i
$469$		0			0
$470$	21.2789	−	12.2854i	0.981525	−	0.566684i
$471$	−11.6834	+	18.7823i	−0.538341	+	0.865441i
$472$	1.88475	+	1.08816i	0.0867525	+	0.0500866i
$473$	−26.8717	−	15.5144i	−1.23556	−	0.713351i
$474$	−11.6672	+	18.7562i	−0.535891	+	0.861502i
$475$	5.85497	−	3.38037i	0.268644	−	0.155102i
$476$		0			0
$477$	−2.61616	+	39.7375i	−0.119786	+	1.81946i
$478$	−18.6669			−0.853802
$479$	−12.3567	−	21.4025i	−0.564594	−	0.977905i	−0.997087	−	0.0762684i	$-0.975699\pi$
$479$	−12.3567	−	21.4025i	−0.564594	−	0.977905i	0.432493	−	0.901637i	$-0.357634\pi$
$480$	−2.97457	−	5.56698i	−0.135770	−	0.254097i
$481$	20.0174	+	11.5570i	0.912713	+	0.526955i
$482$	0.238133	−	0.412458i	0.0108467	−	0.0187870i
$483$		0			0
$484$	−7.33687	−	12.7078i	−0.333494	−	0.577629i
$485$		−	23.5436i		−	1.06906i
$486$	−5.48041	−	14.5933i	−0.248596	−	0.661967i
$487$	−33.9755			−1.53958			−0.769788	−	0.638299i	$-0.779638\pi$
$487$	−33.9755			−1.53958			−0.769788	+	0.638299i	$0.779638\pi$
$488$	−3.62691	−	6.28199i	−0.164182	−	0.284372i
$489$	−0.171929	+	5.22858i	−0.00777488	+	0.236445i
$490$		0			0
$491$	−25.5933	−	14.7763i	−1.15501	−	0.666845i	−0.204906	−	0.978782i	$-0.565689\pi$
$491$	−25.5933	−	14.7763i	−1.15501	−	0.666845i	−0.950103	+	0.311937i	$0.899022\pi$
$492$	3.10667	−	1.65997i	0.140060	−	0.0748372i
$493$	−5.58854	+	3.22655i	−0.251695	+	0.145316i
$494$		−	2.77568i		−	0.124884i
$495$	−3.63904	+	55.2742i	−0.163562	+	2.48439i
$496$			2.16996i			0.0974339i
$497$		0			0
$498$	1.40529	−	2.25916i	0.0629726	−	0.101235i
$499$	5.38644	−	9.32959i	0.241130	−	0.417650i	−0.719906	−	0.694071i	$-0.755815\pi$
$499$	5.38644	−	9.32959i	0.241130	−	0.417650i	0.961037	+	0.276421i	$0.0891486\pi$
$500$	5.97601	−	10.3507i	0.267255	−	0.462899i
$501$	−21.0245	−	13.0781i	−0.939307	−	0.584288i
$502$	15.3234	−	8.84695i	0.683916	−	0.394859i
$503$	20.2016			0.900743			0.450372	−	0.892841i	$-0.351292\pi$
$503$	20.2016			0.900743			0.450372	+	0.892841i	$0.351292\pi$
$504$		0			0
$505$	−43.3686			−1.92988
$506$	−7.46233	+	4.30838i	−0.331741	+	0.191531i
$507$	2.20668	−	1.17908i	0.0980023	−	0.0523649i
$508$	−8.71394	+	15.0930i	−0.386619	+	0.669643i
$509$	−0.529272	+	0.916725i	−0.0234595	+	0.0406331i	−0.877517	−	0.479546i	$-0.840801\pi$
$509$	−0.529272	+	0.916725i	−0.0234595	+	0.0406331i	0.854057	+	0.520179i	$0.174135\pi$
$510$	9.77424	+	0.321401i	0.432811	+	0.0142319i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	4.22223	+	0.417716i	0.186416	+	0.0184426i
$514$		−	23.1941i		−	1.02305i
$515$	46.3441	−	26.7568i	2.04216	−	1.17904i
$516$	−0.348586	+	10.6010i	−0.0153456	+	0.466682i
$517$	−29.5869	−	17.0820i	−1.30123	−	0.751265i
$518$		0			0
$519$	3.35939	−	1.79500i	0.147461	−	0.0787918i
$520$	−6.19384	−	10.7280i	−0.271618	−	0.470456i
$521$	−10.1014			−0.442549			−0.221275	−	0.975212i	$-0.571022\pi$
$521$	−10.1014			−0.442549			−0.221275	+	0.975212i	$0.571022\pi$
$522$	−6.94474	+	10.3870i	−0.303963	+	0.454626i
$523$			9.27216i			0.405443i	0.979236	+	0.202722i	$0.0649786\pi$
$523$			9.27216i			0.405443i	−0.979236	+	0.202722i	$0.935021\pi$
$524$	−1.61603	−	2.79904i	−0.0705965	−	0.122277i
$525$		0			0
$526$	1.72193	−	2.98247i	0.0750797	−	0.130042i
$527$	−2.91168	−	1.68106i	−0.126835	−	0.0732280i
$528$	−4.63550	+	7.45207i	−0.201734	+	0.324310i
$529$	−10.0540	−	17.4140i	−0.437130	−	0.757132i
$530$	−48.3743			−2.10124
$531$	−3.62888	+	5.42757i	−0.157480	+	0.235537i
$532$		0			0
$533$	5.98682	−	3.45649i	0.259318	−	0.149717i
$534$	−9.82254	−	18.3831i	−0.425063	−	0.795515i
$535$	−10.4752	−	6.04786i	−0.452882	−	0.261472i
$536$	−2.12731	−	1.22820i	−0.0918858	−	0.0530503i
$537$	−18.6042	−	0.611753i	−0.802832	−	0.0263991i
$538$	−6.94015	+	4.00690i	−0.299211	+	0.172750i
$539$		0			0
$540$	17.2511	−	7.80729i	0.742369	−	0.335972i
$541$	5.74995			0.247210			0.123605	−	0.992332i	$-0.460554\pi$
$541$	5.74995			0.247210			0.123605	+	0.992332i	$0.460554\pi$
$542$	−0.895442	−	1.55095i	−0.0384625	−	0.0666191i
$543$	−25.0510	−	0.823739i	−1.07504	−	0.0353500i
$544$	1.34181	+	0.774696i	0.0575298	+	0.0332148i
$545$	5.16874	−	8.95251i	0.221404	−	0.383484i
$546$		0			0
$547$	18.3094	+	31.7128i	0.782853	+	1.35594i	0.930273	+	0.366867i	$0.119570\pi$
$547$	18.3094	+	31.7128i	0.782853	+	1.35594i	−0.147421	+	0.989074i	$0.547097\pi$
$548$			14.5820i			0.622913i
$549$	19.5201	−	9.61915i	0.833095	−	0.410535i
$550$	−41.9531			−1.78888
$551$	−1.70040	−	2.94518i	−0.0724395	−	0.125469i
$552$	2.50110	+	1.55579i	0.106454	+	0.0662189i
$553$		0			0
$554$	−21.2986	−	12.2968i	−0.904892	−	0.522440i
$555$	−36.4426	−	22.6688i	−1.54690	−	0.962238i
$556$	−4.97814	+	2.87413i	−0.211120	+	0.121890i
$557$		−	0.374010i		−	0.0158473i	−0.999969	−	0.00792365i	$-0.997478\pi$
$557$		−	0.374010i		−	0.0158473i	0.999969	−	0.00792365i	$-0.00252220\pi$
$558$	−6.49581	−	0.427659i	−0.274989	−	0.0181042i
$559$			20.8168i			0.880457i
$560$		0			0
$561$	−6.40818	−	11.9931i	−0.270554	−	0.506348i
$562$	−10.7539	+	18.6262i	−0.453624	+	0.785700i
$563$	2.18961	−	3.79252i	0.0922812	−	0.159836i	−0.816189	−	0.577784i	$-0.803917\pi$
$563$	2.18961	−	3.79252i	0.0922812	−	0.159836i	0.908471	+	0.417949i	$0.137251\pi$
$564$	−0.383808	+	11.6721i	−0.0161612	+	0.491485i
$565$	24.7971	−	14.3166i	1.04322	−	0.602305i
$566$	19.9480			0.838478
$567$		0			0
$568$	6.74272			0.282918
$569$	31.9253	−	18.4321i	1.33838	−	0.772712i	0.351810	−	0.936072i	$-0.385566\pi$
$569$	31.9253	−	18.4321i	1.33838	−	0.772712i	0.986567	+	0.163360i	$0.0522331\pi$
$570$	−0.169379	+	5.15105i	−0.00709452	+	0.215754i
$571$	−15.8297	+	27.4179i	−0.662454	+	1.14740i	0.317515	+	0.948253i	$0.397152\pi$
$571$	−15.8297	+	27.4179i	−0.662454	+	1.14740i	−0.979969	+	0.199150i	$0.936182\pi$
$572$	−8.61210	+	14.9166i	−0.360090	+	0.623694i
$573$	−6.80104	−	12.7283i	−0.284117	−	0.531732i
$574$		0			0
$575$			14.0805i			0.587198i
$576$	2.99352	+	0.197082i	0.124730	+	0.00821174i
$577$			14.1940i			0.590903i	0.955358	+	0.295452i	$0.0954701\pi$
$577$			14.1940i			0.590903i	−0.955358	+	0.295452i	$0.904530\pi$
$578$	12.6434	−	7.29969i	0.525898	−	0.303627i
$579$	14.0717	+	8.75320i	0.584801	+	0.363771i
$580$	−13.1442	−	7.58878i	−0.545781	−	0.315107i
$581$		0			0
$582$	9.50186	+	5.91056i	0.393865	+	0.245001i
$583$	33.6305	+	58.2497i	1.39283	+	2.41246i
$584$	−4.35220			−0.180096
$585$	33.3353	−	16.4271i	1.37825	−	0.679176i
$586$		−	2.49313i		−	0.102990i
$587$	−2.32227	−	4.02230i	−0.0958505	−	0.166018i	0.814113	−	0.580707i	$-0.197224\pi$
$587$	−2.32227	−	4.02230i	−0.0958505	−	0.166018i	−0.909963	+	0.414689i	$0.863890\pi$
$588$		0			0
$589$	0.885922	−	1.53446i	0.0365038	−	0.0632264i
$590$	−6.86829	−	3.96541i	−0.282763	−	0.163253i
$591$	4.10669	+	0.135038i	0.168927	+	0.00555472i
$592$	−3.39979	−	5.88860i	−0.139730	−	0.242020i
$593$	−23.0430			−0.946263			−0.473132	−	0.880992i	$-0.656877\pi$
$593$	−23.0430			−0.946263			−0.473132	+	0.880992i	$0.656877\pi$
$594$	−21.3943	−	15.3451i	−0.877821	−	0.629618i
$595$		0			0
$596$	−4.95904	+	2.86310i	−0.203130	+	0.117277i
$597$	−38.9755	−	1.28161i	−1.59516	−	0.0524528i
$598$	5.00639	+	2.89044i	0.204726	+	0.118199i
$599$	25.0820	+	14.4811i	1.02482	+	0.591682i	0.915497	−	0.402324i	$-0.131797\pi$
$599$	25.0820	+	14.4811i	1.02482	+	0.591682i	0.109326	+	0.994006i	$0.465131\pi$
$600$	6.75846	+	12.6486i	0.275913	+	0.516378i
$601$	5.04993	−	2.91558i	0.205991	−	0.118929i	−0.393456	−	0.919344i	$-0.628721\pi$
$601$	5.04993	−	2.91558i	0.205991	−	0.118929i	0.599447	+	0.800414i	$0.295387\pi$
$602$		0			0
$603$	4.09591	−	6.12609i	0.166798	−	0.249474i
$604$	12.7697			0.519590
$605$	26.7366	+	46.3092i	1.08700	+	1.88273i
$606$	10.8876	−	17.5030i	0.442278	−	0.711010i
$607$	−16.3750	−	9.45411i	−0.664641	−	0.383731i	0.129402	−	0.991592i	$-0.458694\pi$
$607$	−16.3750	−	9.45411i	−0.664641	−	0.383731i	−0.794043	+	0.607862i	$0.792028\pi$
$608$	−0.408267	+	0.707140i	−0.0165574	+	0.0286783i
$609$		0			0
$610$	13.2170	+	22.8925i	0.535140	+	0.926889i
$611$			22.9202i			0.927252i
$612$	−2.58352	+	3.86407i	−0.104432	+	0.156196i
$613$	33.1761			1.33997			0.669984	−	0.742375i	$-0.266301\pi$
$613$	33.1761			1.33997			0.669984	+	0.742375i	$0.266301\pi$
$614$	4.61562	+	7.99448i	0.186271	+	0.322631i
$615$	−11.3212	+	6.04916i	−0.456513	+	0.243926i
$616$		0			0
$617$	34.0222	+	19.6427i	1.36968	+	0.790786i	0.990887	−	0.134695i	$-0.0430054\pi$
$617$	34.0222	+	19.6427i	1.36968	+	0.790786i	0.378794	+	0.925481i	$0.376339\pi$
$618$	−0.835907	+	25.4211i	−0.0336251	+	1.02259i
$619$	8.46727	−	4.88858i	0.340329	−	0.196489i	−0.320089	−	0.947388i	$-0.603713\pi$
$619$	8.46727	−	4.88858i	0.340329	−	0.196489i	0.660417	+	0.750899i	$0.270379\pi$
$620$		−	7.90763i		−	0.317578i
$621$	−5.15021	+	7.18048i	−0.206671	+	0.288143i
$622$		−	22.9714i		−	0.921069i
$623$		0			0
$624$	5.88465	+	0.193502i	0.235574	+	0.00774627i
$625$	−1.07796	+	1.86708i	−0.0431185	+	0.0746834i
$626$	3.21668	−	5.57145i	0.128564	−	0.222680i
$627$	6.32038	−	3.37713i	0.252412	−	0.134870i
$628$	11.0598	−	6.38536i	0.441333	−	0.254804i
$629$	10.5352			0.420066
$630$		0			0
$631$	11.6364			0.463237			0.231618	−	0.972807i	$-0.425598\pi$
$631$	11.6364			0.463237			0.231618	+	0.972807i	$0.425598\pi$
$632$	11.0444	−	6.37651i	0.439325	−	0.253644i
$633$	−21.3906	−	13.3058i	−0.850199	−	0.528860i
$634$	4.36767	−	7.56502i	0.173462	−	0.300445i
$635$	31.7549	−	55.0010i	1.26015	−	2.18265i
$636$	12.1443	−	19.5232i	0.481551	−	0.774146i
$637$		0			0
$638$			21.1033i			0.835489i
$639$	−1.32887	+	20.1845i	−0.0525691	+	0.798485i
$640$			3.64414i			0.144047i
$641$	−25.2233	+	14.5627i	−0.996262	+	0.575192i	−0.907140	−	0.420828i	$-0.861739\pi$
$641$	−25.2233	+	14.5627i	−0.996262	+	0.575192i	−0.0891220	+	0.996021i	$0.528406\pi$
$642$	5.07061	−	2.70935i	0.200121	−	0.106929i
$643$	33.9410	+	19.5959i	1.33850	+	0.772785i	0.986585	−	0.163245i	$-0.0521962\pi$
$643$	33.9410	+	19.5959i	1.33850	+	0.772785i	0.351918	+	0.936031i	$0.385530\pi$
$644$		0			0
$645$	1.27030	−	38.6315i	0.0500179	−	1.52111i
$646$	−0.632566	−	1.09564i	−0.0248880	−	0.0431073i
$647$	−20.3601			−0.800437			−0.400218	−	0.916420i	$-0.631066\pi$
$647$	−20.3601			−0.800437			−0.400218	+	0.916420i	$0.631066\pi$
$648$	−1.17994	+	8.92232i	−0.0463522	+	0.350502i
$649$			11.0272i			0.432857i
$650$	14.0729	+	24.3750i	0.551985	+	0.956065i
$651$		0			0
$652$	1.51018	−	2.61570i	0.0591431	−	0.102439i
$653$	13.1105	+	7.56933i	0.513052	+	0.296211i	0.734087	−	0.679055i	$-0.237610\pi$
$653$	13.1105	+	7.56933i	0.513052	+	0.296211i	−0.221035	+	0.975266i	$0.570944\pi$
$654$	2.31552	+	4.33354i	0.0905438	+	0.169455i
$655$	5.88904	+	10.2001i	0.230104	+	0.398552i
$656$	−2.03363			−0.0793997
$657$	0.857740	−	13.0284i	0.0334636	−	0.508287i
$658$		0			0
$659$	−9.17413	+	5.29668i	−0.357373	+	0.206330i	−0.667928	−	0.744226i	$-0.732819\pi$
$659$	−9.17413	+	5.29668i	−0.357373	+	0.206330i	0.310555	+	0.950556i	$0.399485\pi$
$660$	16.8924	−	27.1564i	0.657537	−	1.05706i
$661$	−14.7583	−	8.52074i	−0.574033	−	0.331418i	0.184725	−	0.982790i	$-0.440860\pi$
$661$	−14.7583	−	8.52074i	−0.574033	−	0.331418i	−0.758759	+	0.651372i	$0.774194\pi$
$662$	27.4537	+	15.8504i	1.06702	+	0.616042i
$663$	−4.81846	+	7.74619i	−0.187133	+	0.300837i
$664$	−1.33028	+	0.768040i	−0.0516251	+	0.0298057i
$665$		0			0
$666$	18.2977	−	9.01679i	0.709021	−	0.349393i
$667$	7.08281			0.274248
$668$	7.14766	+	12.3801i	0.276551	+	0.479001i
$669$	−21.2279	−	39.7285i	−0.820717	−	1.53599i
$670$	7.75223	+	4.47575i	0.299495	+	0.172913i
$671$	18.3773	−	31.8304i	0.709447	−	1.22880i
$672$		0			0
$673$	−12.5048	−	21.6590i	−0.482025	−	0.834891i	0.517762	−	0.855524i	$-0.326765\pi$
$673$	−12.5048	−	21.6590i	−0.482025	−	0.834891i	−0.999787	+	0.0206331i	$0.993432\pi$
$674$			32.2616i			1.24267i
$675$	−39.1959	+	17.7388i	−1.50865	+	0.682766i
$676$	−1.44449			−0.0555575
$677$	−19.8534	−	34.3871i	−0.763028	−	1.32160i	−0.941283	−	0.337619i	$-0.890378\pi$
$677$	−19.8534	−	34.3871i	−0.763028	−	1.32160i	0.178255	−	0.983984i	$-0.442955\pi$
$678$	−0.447265	+	13.6019i	−0.0171771	+	0.522379i
$679$		0			0
$680$	−4.88976	−	2.82310i	−0.187514	−	0.108261i
$681$	34.9495	−	18.6744i	1.33927	−	0.715603i
$682$	−9.52196	+	5.49750i	−0.364615	+	0.210510i
$683$			2.67738i			0.102447i	0.998687	+	0.0512236i	$0.0163121\pi$
$683$			2.67738i			0.102447i	−0.998687	+	0.0512236i	$0.983688\pi$
$684$	−2.03637	−	1.36152i	−0.0778627	−	0.0520590i
$685$		−	53.1390i		−	2.03034i
$686$		0			0
$687$	−24.6373	+	39.6072i	−0.939973	+	1.51111i
$688$	3.06189	−	5.30335i	0.116733	−	0.202188i
$689$	22.5623	−	39.0790i	0.859555	−	1.48879i
$690$	−9.11438	−	5.66953i	−0.346978	−	0.215835i
$691$	16.6346	−	9.60399i	0.632810	−	0.365353i	−0.149030	−	0.988833i	$-0.547615\pi$
$691$	16.6346	−	9.60399i	0.632810	−	0.365353i	0.781839	+	0.623480i	$0.214282\pi$
$692$	−2.19905			−0.0835954
$693$		0			0
$694$	6.82421			0.259043
$695$	18.1410	−	10.4737i	0.688129	−	0.397291i
$696$	6.36254	−	3.39966i	0.241172	−	0.128864i
$697$	1.57544	−	2.72875i	0.0596741	−	0.103359i
$698$	2.41551	−	4.18379i	0.0914284	−	0.158359i
$699$	−7.63594	−	0.251088i	−0.288818	−	0.00949704i
$700$		0			0
$701$			34.1916i			1.29140i	0.763591	+	0.645700i	$0.223434\pi$
$701$			34.1916i			1.29140i	−0.763591	+	0.645700i	$0.776566\pi$
$702$	−1.73901	+	17.5777i	−0.0656346	+	0.663426i
$703$			5.55208i			0.209401i
$704$	4.38809	−	2.53346i	0.165382	−	0.0954835i
$705$	1.39865	−	42.5349i	0.0526763	−	1.60196i
$706$	29.9510	+	17.2922i	1.12722	+	0.650800i
$707$		0			0
$708$	3.32466	−	1.77644i	0.124948	−	0.0667628i
$709$	11.7284	+	20.3141i	0.440468	+	0.762914i	0.997724	−	0.0674271i	$-0.0214790\pi$
$709$	11.7284	+	20.3141i	0.440468	+	0.762914i	−0.557256	+	0.830341i	$0.688146\pi$
$710$	−24.5714			−0.922149
$711$	16.9116	+	34.3185i	0.634233	+	1.28704i
$712$			12.0336i			0.450977i
$713$	1.84510	+	3.19581i	0.0690996	+	0.119684i
$714$		0			0
$715$	31.3837	−	54.3582i	1.17368	−	2.03288i
$716$	9.30715	+	5.37349i	0.347825	+	0.200817i
$717$	−17.0775	+	27.4539i	−0.637769	+	1.02528i
$718$	13.5742	+	23.5112i	0.506584	+	0.877429i
$719$	15.9760			0.595805			0.297902	−	0.954596i	$-0.403713\pi$
$719$	15.9760			0.595805			0.297902	+	0.954596i	$0.403713\pi$
$720$	−10.9088	−	0.718194i	−0.406548	−	0.0267655i
$721$		0			0
$722$	−15.8771	+	9.16664i	−0.590884	+	0.341147i
$723$	−0.388757	−	0.727568i	−0.0144580	−	0.0270585i
$724$	12.5323	+	7.23551i	0.465758	+	0.268906i
$725$	29.8646	+	17.2423i	1.10914	+	0.640364i
$726$	−25.4019	−	0.835278i	−0.942754	−	0.0310001i
$727$	21.6787	−	12.5162i	0.804019	−	0.464201i	−0.0408555	−	0.999165i	$-0.513008\pi$
$727$	21.6787	−	12.5162i	0.804019	−	0.464201i	0.844875	+	0.534964i	$0.179675\pi$
$728$		0			0
$729$	−26.4766	−	5.29058i	−0.980614	−	0.195948i
$730$	15.8601			0.587007
$731$	4.74407	+	8.21697i	0.175466	+	0.303916i
$732$	−12.5572	−	0.412911i	−0.464127	−	0.0152616i
$733$	−10.1433	−	5.85625i	−0.374652	−	0.216305i	0.300837	−	0.953676i	$-0.402734\pi$
$733$	−10.1433	−	5.85625i	−0.374652	−	0.216305i	−0.675489	+	0.737370i	$0.736067\pi$
$734$	−5.96444	+	10.3307i	−0.220151	+	0.381313i
$735$		0			0
$736$	−0.850294	−	1.47275i	−0.0313423	−	0.0542864i
$737$		−	12.4464i		−	0.458470i
$738$	0.400790	−	6.08770i	0.0147533	−	0.224091i
$739$	16.4051			0.603472			0.301736	−	0.953392i	$-0.402434\pi$
$739$	16.4051			0.603472			0.301736	+	0.953392i	$0.402434\pi$
$740$	12.3893	+	21.4589i	0.455440	+	0.788845i
$741$	−4.08227	−	2.53934i	−0.149966	−	0.0932850i
$742$		0			0
$743$	8.02860	+	4.63532i	0.294541	+	0.170053i	0.639988	−	0.768385i	$-0.278939\pi$
$743$	8.02860	+	4.63532i	0.294541	+	0.170053i	−0.345447	+	0.938438i	$0.612273\pi$
$744$	3.19142	+	1.98519i	0.117003	+	0.0727808i
$745$	18.0715	−	10.4336i	0.662087	−	0.382256i
$746$		−	9.63850i		−	0.352890i
$747$	−2.03697	−	4.13360i	−0.0745288	−	0.151240i
$748$			7.85066i			0.287048i
$749$		0			0
$750$	−9.75596	−	18.2585i	−0.356237	−	0.666706i
$751$	−10.0756	+	17.4515i	−0.367665	+	0.636815i	−0.989200	−	0.146572i	$-0.953176\pi$
$751$	−10.0756	+	17.4515i	−0.367665	+	0.636815i	0.621535	+	0.783386i	$0.286509\pi$
$752$	3.37127	−	5.83922i	0.122938	−	0.212934i
$753$	1.00720	−	30.6302i	0.0367043	−	1.11623i
$754$	12.2612	−	7.07898i	0.446525	−	0.257801i
$755$	−46.5345			−1.69356
$756$		0			0
$757$	47.4297			1.72386			0.861932	−	0.507024i	$-0.169255\pi$
$757$	47.4297			1.72386			0.861932	+	0.507024i	$0.169255\pi$
$758$	13.8690	−	8.00727i	0.503745	−	0.290837i
$759$	−0.490494	+	14.9166i	−0.0178038	+	0.541438i
$760$	1.48778	−	2.57692i	0.0539676	−	0.0934747i
$761$	−24.0809	+	41.7094i	−0.872933	+	1.51196i	−0.0139853	+	0.999902i	$0.504452\pi$
$761$	−24.0809	+	41.7094i	−0.872933	+	1.51196i	−0.858948	+	0.512063i	$0.828882\pi$
$762$	14.2257	+	26.6237i	0.515342	+	0.964476i
$763$		0			0
$764$			8.33194i			0.301439i
$765$	9.41470	−	14.0812i	0.340389	−	0.509107i
$766$		−	6.36945i		−	0.230137i
$767$	6.40690	−	3.69902i	0.231340	−	0.133564i
$768$	−1.47073	−	0.914855i	−0.0530703	−	0.0330120i
$769$	9.84984	+	5.68681i	0.355194	+	0.205071i	0.666971	−	0.745084i	$-0.267591\pi$
$769$	9.84984	+	5.68681i	0.355194	+	0.205071i	−0.311776	+	0.950155i	$0.600924\pi$
$770$		0			0
$771$	−34.1123	−	21.2193i	−1.22852	−	0.764193i
$772$	−4.78393	−	8.28601i	−0.172177	−	0.298220i
$773$	−4.27556			−0.153781			−0.0768906	−	0.997040i	$-0.524499\pi$
$773$	−4.27556			−0.153781			−0.0768906	+	0.997040i	$0.524499\pi$
$774$	15.2722	+	10.2110i	0.548949	+	0.367028i
$775$			17.9668i			0.645386i
$776$	−3.23033	−	5.59509i	−0.115962	−	0.200852i
$777$		0			0
$778$	−8.77645	+	15.2013i	−0.314651	+	0.544992i
$779$	1.43806	+	0.830263i	0.0515238	+	0.0297473i
$780$	−21.4445	−	0.705148i	−0.767836	−	0.0252483i
$781$	17.0824	+	29.5876i	0.611257	+	1.05873i
$782$	2.63488			0.0942231
$783$	8.92300	+	19.7164i	0.318882	+	0.704607i
$784$		0			0
$785$	−40.3034	+	23.2692i	−1.43849	+	0.830513i
$786$	−5.59506	−	0.183979i	−0.199569	−	0.00656233i
$787$	−22.8644	−	13.2008i	−0.815029	−	0.470557i	0.0336701	−	0.999433i	$-0.489280\pi$
$787$	−22.8644	−	13.2008i	−0.815029	−	0.470557i	−0.848699	+	0.528876i	$0.822614\pi$
$788$	−2.05445	−	1.18614i	−0.0731869	−	0.0422545i
$789$	−2.81109	−	5.26102i	−0.100077	−	0.187297i
$790$	−40.2476	+	23.2369i	−1.43194	+	0.826733i
$791$		0			0
$792$	6.71916	+	13.6351i	0.238755	+	0.484503i
$793$	−24.6582			−0.875638
$794$	6.67955	+	11.5693i	0.237048	+	0.410580i
$795$	−44.2554	+	71.1454i	−1.56958	+	2.52327i
$796$	19.4983	+	11.2573i	0.691098	+	0.399006i
$797$	−26.7253	+	46.2896i	−0.946660	+	1.63966i	−0.194267	+	0.980949i	$0.562233\pi$
$797$	−26.7253	+	46.2896i	−0.946660	+	1.63966i	−0.752393	+	0.658715i	$0.771100\pi$
$798$		0			0
$799$	5.22343	+	9.04724i	0.184792	+	0.320068i
$800$		−	8.27979i		−	0.292735i
$801$	−36.0228	−	2.37160i	−1.27280	−	0.0837963i
$802$	4.22830			0.149307
$803$	−11.0261	−	19.0978i	−0.389104	−	0.673948i
$804$	−3.75253	+	2.00507i	−0.132342	+	0.0707133i
$805$		0			0
$806$	6.38817	+	3.68821i	0.225014	+	0.129912i
$807$	−0.456172	+	13.8728i	−0.0160580	+	0.488346i
$808$	−10.3065	+	5.95045i	−0.362581	+	0.209336i
$809$			10.1215i			0.355854i	0.984044	+	0.177927i	$0.0569391\pi$
$809$			10.1215i			0.355854i	−0.984044	+	0.177927i	$0.943061\pi$
$810$	4.29985	−	32.5142i	0.151081	−	1.14243i
$811$			44.8854i			1.57614i	0.615586	+	0.788070i	$0.288920\pi$
$811$			44.8854i			1.57614i	−0.615586	+	0.788070i	$0.711080\pi$
$812$		0			0
$813$	−3.10023	−	0.101943i	−0.108730	−	0.00357530i
$814$	17.2265	−	29.8371i	0.603787	−	1.04579i
$815$	−5.50330	+	9.53200i	−0.192772	+	0.333891i
$816$	2.36693	−	1.26471i	0.0828592	−	0.0442736i
$817$	−4.33037	+	2.50014i	−0.151500	+	0.0874688i
$818$	−38.4154			−1.34316
$819$		0			0
$820$	7.41083			0.258797
$821$	−29.8527	+	17.2354i	−1.04187	+	0.601521i	−0.920361	−	0.391070i	$-0.872105\pi$
$821$	−29.8527	+	17.2354i	−1.04187	+	0.601521i	−0.121504	+	0.992591i	$0.538772\pi$
$822$	21.4462	+	13.3404i	0.748022	+	0.465301i
$823$	14.4561	−	25.0386i	0.503906	−	0.872792i	−0.496083	−	0.868275i	$-0.665229\pi$
$823$	14.4561	−	25.0386i	0.503906	−	0.872792i	0.999990	−	0.00451663i	$-0.00143769\pi$
$824$	7.34240	−	12.7174i	0.255785	−	0.443032i
$825$	−38.3810	+	61.7015i	−1.33625	+	2.14817i
$826$		0			0
$827$		−	18.8795i		−	0.656506i	−0.944590	−	0.328253i	$-0.893540\pi$
$827$		−	18.8795i		−	0.656506i	0.944590	−	0.328253i	$-0.106460\pi$
$828$	4.57629	−	2.25512i	0.159037	−	0.0783708i
$829$			18.0899i			0.628288i	0.949375	+	0.314144i	$0.101717\pi$
$829$			18.0899i			0.628288i	−0.949375	+	0.314144i	$0.898283\pi$
$830$	4.84775	−	2.79885i	0.168268	−	0.0971495i
$831$	−37.5703	+	20.0747i	−1.30330	+	0.696385i
$832$	−2.94391	−	1.69967i	−0.102062	−	0.0589254i
$833$		0			0
$834$	−0.327210	+	9.95089i	−0.0113303	+	0.344571i
$835$	−26.0471	−	45.1149i	−0.901397	−	1.56127i
$836$	−4.13732			−0.143092
$837$	−6.57169	+	9.16232i	−0.227151	+	0.316696i
$838$			14.0660i			0.485903i
$839$	2.53049	+	4.38294i	0.0873623	+	0.151316i	0.906395	−	0.422430i	$-0.138823\pi$
$839$	2.53049	+	4.38294i	0.0873623	+	0.151316i	−0.819033	+	0.573746i	$0.805490\pi$
$840$		0			0
$841$	−5.82673	+	10.0922i	−0.200922	+	0.348007i
$842$	−18.2738	−	10.5504i	−0.629758	−	0.363591i
$843$	17.5559	+	32.8563i	0.604657	+	1.13163i
$844$	7.27211	+	12.5957i	0.250316	+	0.433560i
$845$	5.26395			0.181085
$846$	16.8154	+	11.2428i	0.578125	+	0.386535i
$847$		0			0
$848$	−11.4961	+	6.63726i	−0.394777	+	0.227924i
$849$	18.2496	−	29.3381i	0.626323	−	1.00688i
$850$	11.1099	+	6.41432i	0.381067	+	0.220009i
$851$	−10.0141	−	5.78163i	−0.343278	−	0.198192i
$852$	6.16861	−	9.91670i	0.211333	−	0.339741i
$853$	37.0163	−	21.3714i	1.26741	−	0.731742i	0.292916	−	0.956138i	$-0.405374\pi$
$853$	37.0163	−	21.3714i	1.26741	−	0.731742i	0.974498	+	0.224397i	$0.0720412\pi$
$854$		0			0
$855$	7.42084	+	4.96158i	0.253787	+	0.169682i
$856$	−3.31922			−0.113449
$857$	0.537523	+	0.931017i	0.0183614	+	0.0318030i	0.875060	−	0.484014i	$-0.160822\pi$
$857$	0.537523	+	0.931017i	0.0183614	+	0.0318030i	−0.856699	+	0.515817i	$0.827488\pi$
$858$	14.0594	+	26.3126i	0.479981	+	0.898296i
$859$	20.9983	+	12.1234i	0.716452	+	0.413644i	0.813446	−	0.581641i	$-0.197589\pi$
$859$	20.9983	+	12.1234i	0.716452	+	0.413644i	−0.0969931	+	0.995285i	$0.530922\pi$
$860$	−11.1580	+	19.3262i	−0.380484	+	0.659017i
$861$		0			0
$862$	−5.82709	−	10.0928i	−0.198471	−	0.343762i
$863$			44.7112i			1.52199i	0.648759	+	0.760994i	$0.275288\pi$
$863$			44.7112i			1.52199i	−0.648759	+	0.760994i	$0.724712\pi$
$864$	3.02849	−	4.22235i	0.103031	−	0.143647i
$865$	8.01367			0.272473
$866$	8.95746	+	15.5148i	0.304387	+	0.527214i
$867$	0.831045	−	25.2732i	0.0282238	−	0.858323i
$868$		0			0
$869$	55.9614	+	32.3093i	1.89836	+	1.09602i
$870$	−23.1860	+	12.3888i	−0.786080	+	0.420021i
$871$	−7.23145	+	4.17508i	−0.245028	+	0.141467i
$872$		−	2.83674i		−	0.0960640i
$873$	17.3856	−	8.56736i	0.588415	−	0.289961i
$874$			1.38859i			0.0469697i
$875$		0			0
$876$	−3.98163	+	6.40091i	−0.134527	+	0.216267i
$877$	2.08435	−	3.61020i	0.0703835	−	0.121908i	−0.828686	−	0.559714i	$-0.810911\pi$
$877$	2.08435	−	3.61020i	0.0703835	−	0.121908i	0.899069	+	0.437806i	$0.144244\pi$
$878$	9.51377	−	16.4783i	0.321074	−	0.556117i
$879$	−3.66671	−	2.28085i	−0.123675	−	0.0769312i
$880$	−15.9908	+	9.23230i	−0.539050	+	0.311221i
$881$	−32.0880			−1.08107			−0.540536	−	0.841321i	$-0.681779\pi$
$881$	−32.0880			−1.08107			−0.540536	+	0.841321i	$0.681779\pi$
$882$		0			0
$883$	−29.5080			−0.993022			−0.496511	−	0.868031i	$-0.665386\pi$
$883$	−29.5080			−0.993022			−0.496511	+	0.868031i	$0.665386\pi$
$884$	4.56128	−	2.63346i	0.153412	−	0.0885727i
$885$	−12.1155	+	6.47362i	−0.407259	+	0.217608i
$886$	−3.83867	+	6.64877i	−0.128963	+	0.223370i
$887$	12.4214	−	21.5145i	0.417071	−	0.722387i	−0.578573	−	0.815631i	$-0.696390\pi$
$887$	12.4214	−	21.5145i	0.417071	−	0.722387i	0.995643	+	0.0932433i	$0.0297234\pi$
$888$	−11.7708	−	0.387054i	−0.395004	−	0.0129887i
$889$		0			0
$890$		−	43.8521i		−	1.46993i
$891$	−42.1412	+	17.4267i	−1.41178	+	0.583816i
$892$			26.0062i			0.870753i
$893$	−4.76792	+	2.75276i	−0.159552	+	0.0921176i
$894$	−0.325955	+	9.91273i	−0.0109016	+	0.331531i
$895$	−33.9166	−	19.5818i	−1.13371	−	0.654546i
$896$		0			0
$897$	8.83116	−	4.71870i	0.294864	−	0.157553i
$898$	15.0509	+	26.0689i	0.502255	+	0.869932i
$899$	9.03769			0.301424
$900$	24.7857	+	1.63179i	0.826190	+	0.0543931i
$901$		−	20.5674i		−	0.685201i
$902$	−5.15212	−	8.92373i	−0.171547	−	0.297128i
$903$		0			0
$904$	3.92866	−	6.80465i	0.130665	−	0.226319i
$905$	−45.6694	−	26.3673i	−1.51810	−	0.876477i
$906$	11.6824	−	18.7807i	0.388121	−	0.623947i
$907$	−20.4561	−	35.4311i	−0.679235	−	1.17647i	−0.975212	−	0.221274i	$-0.928979\pi$
$907$	−20.4561	−	35.4311i	−0.679235	−	1.17647i	0.295977	−	0.955195i	$-0.404355\pi$
$908$	−22.8779			−0.759231
$909$	−15.7816	−	32.0254i	−0.523442	−	1.06221i
$910$		0			0
$911$	2.21678	−	1.27986i	0.0734452	−	0.0424036i	−0.462828	−	0.886448i	$-0.653165\pi$
$911$	2.21678	−	1.27986i	0.0734452	−	0.0424036i	0.536273	+	0.844045i	$0.319832\pi$
$912$	0.666505	+	1.24738i	0.0220702	+	0.0413049i
$913$	−6.74045	−	3.89160i	−0.223076	−	0.128793i
$914$	−34.1973	−	19.7438i	−1.13115	−	0.653067i
$915$	45.7602	+	1.50471i	1.51279	+	0.0497441i
$916$	23.3224	−	13.4652i	0.770592	−	0.444902i
$917$		0			0
$918$	3.31945	+	7.33471i	0.109558	+	0.242081i
$919$	−10.2449			−0.337949			−0.168974	−	0.985620i	$-0.554046\pi$
$919$	−10.2449			−0.337949			−0.168974	+	0.985620i	$0.554046\pi$
$920$	3.09859	+	5.36692i	0.102158	+	0.176942i
$921$	15.9803	+	0.525473i	0.526570	+	0.0173149i
$922$	−19.7066	−	11.3776i	−0.649004	−	0.374703i
$923$	11.4604	−	19.8500i	0.377223	−	0.653370i
$924$		0			0
$925$	−28.1495	−	48.7564i	−0.925550	−	1.60310i
$926$			13.2773i			0.436320i
$927$	36.6228	+	24.4860i	1.20285	+	0.804225i
$928$	−4.16492			−0.136720
$929$	14.7852	+	25.6087i	0.485087	+	0.840195i	0.999853	−	0.0171358i	$-0.00545475\pi$
$929$	14.7852	+	25.6087i	0.485087	+	0.840195i	−0.514767	+	0.857330i	$0.672121\pi$
$930$	−11.6300	−	7.23434i	−0.381362	−	0.237223i
$931$		0			0
$932$	3.82003	+	2.20550i	0.125129	+	0.0722435i
$933$	−33.7847	−	21.0155i	−1.10606	−	0.688016i
$934$	−20.0698	+	11.5873i	−0.656702	+	0.379147i
$935$		−	28.6089i		−	0.935612i
$936$	5.66819	−	8.47769i	0.185270	−	0.277102i
$937$			17.9991i			0.588005i	0.955805	+	0.294002i	$0.0949874\pi$
$937$			17.9991i			0.588005i	−0.955805	+	0.294002i	$0.905013\pi$
$938$		0			0
$939$	−5.25130	−	9.82793i	−0.171370	−	0.320722i
$940$	−12.2854	+	21.2789i	−0.400706	+	0.694043i
$941$	−14.8619	+	25.7415i	−0.484483	+	0.839148i	−0.999841	−	0.0178263i	$-0.994325\pi$
$941$	−14.8619	+	25.7415i	−0.484483	+	0.839148i	0.515359	+	0.856975i	$0.327659\pi$
$942$	0.726952	−	22.1076i	0.0236854	−	0.720304i
$943$	−2.99503	+	1.72918i	−0.0975315	+	0.0563098i
$944$	−2.17632			−0.0708331
$945$		0			0
$946$	31.0287			1.00883
$947$	−19.2222	+	11.0980i	−0.624639	+	0.360635i	−0.778673	−	0.627430i	$-0.784107\pi$
$947$	−19.2222	+	11.0980i	−0.624639	+	0.360635i	0.154034	+	0.988066i	$0.450773\pi$
$948$	0.725945	−	22.0770i	0.0235776	−	0.717026i
$949$	−7.39731	+	12.8125i	−0.240127	+	0.415912i
$950$	−3.38037	+	5.85497i	−0.109674	+	0.189960i
$951$	−7.13031	−	13.3445i	−0.231216	−	0.432726i
$952$		0			0
$953$		−	2.12319i		−	0.0687769i	−0.999409	−	0.0343884i	$-0.989052\pi$
$953$		−	2.12319i		−	0.0687769i	0.999409	−	0.0343884i	$-0.0109483\pi$
$954$	−17.6031	−	35.7218i	−0.569921	−	1.15654i
$955$		−	30.3628i		−	0.982517i
$956$	16.1660	−	9.33343i	0.522845	−	0.301865i
$957$	31.0373	+	19.3065i	1.00329	+	0.624090i
$958$	21.4025	+	12.3567i	0.691484	+	0.399228i
$959$		0			0
$960$	5.35954	+	3.33386i	0.172979	+	0.107600i
$961$	−13.1456	−	22.7689i	−0.424053	−	0.734481i
$962$	−23.1140			−0.745227
$963$	0.654157	−	9.93615i	0.0210799	−	0.320188i
$964$			0.476266i			0.0153395i
$965$	17.4333	+	30.1954i	0.561199	+	0.972025i
$966$		0			0
$967$	−2.23409	+	3.86955i	−0.0718434	+	0.124436i	−0.899709	−	0.436490i	$-0.856222\pi$
$967$	−2.23409	+	3.86955i	−0.0718434	+	0.124436i	0.827866	+	0.560926i	$0.189555\pi$
$968$	12.7078	+	7.33687i	0.408445	+	0.235816i
$969$	−2.19009	−	0.0720155i	−0.0703558	−	0.00231347i
$970$	11.7718	+	20.3893i	0.377969	+	0.654661i
$971$	1.83205			0.0587933			0.0293967	−	0.999568i	$-0.490641\pi$
$971$	1.83205			0.0587933			0.0293967	+	0.999568i	$0.490641\pi$
$972$	12.0428	+	9.89799i	0.386274	+	0.317478i
$973$		0			0
$974$	29.4236	−	16.9877i	0.942794	−	0.544322i
$975$	48.7236	+	1.60215i	1.56040	+	0.0513099i
$976$	6.28199	+	3.62691i	0.201082	+	0.116094i
$977$	26.8034	+	15.4749i	0.857515	+	0.495087i	0.863179	−	0.504897i	$-0.168470\pi$
$977$	26.8034	+	15.4749i	0.857515	+	0.495087i	−0.00566423	+	0.999984i	$0.501803\pi$
$978$	−2.46540	−	4.61405i	−0.0788347	−	0.147541i
$979$	−52.8044	+	30.4866i	−1.68764	+	0.974357i
$980$		0			0
$981$	8.49182	+	0.559068i	0.271123	+	0.0178497i
$982$	29.5526			0.943061
$983$	16.2825	+	28.2020i	0.519330	+	0.899505i	0.999748	+	0.0224656i	$0.00715163\pi$
$983$	16.2825	+	28.2020i	0.519330	+	0.899505i	−0.480418	+	0.877040i	$0.659515\pi$
$984$	−1.86047	+	2.99091i	−0.0593097	+	0.0953467i
$985$	7.48673	+	4.32246i	0.238547	+	0.137725i
$986$	3.22655	−	5.58854i	0.102754	−	0.177975i
$987$		0			0
$988$	1.38784	+	2.40381i	0.0441530	+	0.0764753i
$989$		−	10.4140i		−	0.331147i
$990$	−24.4856	−	49.6883i	−0.778203	−	1.57920i
$991$	−2.91460			−0.0925852			−0.0462926	−	0.998928i	$-0.514741\pi$
$991$	−2.91460			−0.0925852			−0.0462926	+	0.998928i	$0.514741\pi$
$992$	−1.08498	−	1.87924i	−0.0344481	−	0.0596659i
$993$	48.4277	−	25.8761i	1.53681	−	0.821152i
$994$		0			0
$995$	−71.0545	−	41.0234i	−2.25258	−	1.30053i
$996$	−0.0874388	+	2.65913i	−0.00277060	+	0.0842578i
$997$	−39.9943	+	23.0907i	−1.26663	+	0.731290i	−0.974349	−	0.225042i	$-0.927748\pi$
$997$	−39.9943	+	23.0907i	−1.26663	+	0.731290i	−0.292282	+	0.956332i	$0.594415\pi$
$998$			10.7729i			0.341010i
$999$	3.47847	−	35.1600i	0.110054	−	1.11241i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.m.b.293.3		16
3.2	odd	2		2646.2.m.b.881.8		16
7.2	even	3		882.2.t.a.815.5		16
7.3	odd	6		882.2.l.b.509.1		16
7.4	even	3		126.2.l.a.5.4	✓	16
7.5	odd	6		126.2.t.a.59.8	yes	16
7.6	odd	2		882.2.m.a.293.2		16
9.2	odd	6		882.2.m.a.587.2		16
9.7	even	3		2646.2.m.a.1763.5		16
21.2	odd	6		2646.2.t.b.2285.1		16
21.5	even	6		378.2.t.a.17.4		16
21.11	odd	6		378.2.l.a.341.8		16
21.17	even	6		2646.2.l.a.1097.5		16
21.20	even	2		2646.2.m.a.881.5		16
28.11	odd	6		1008.2.ca.c.257.2		16
28.19	even	6		1008.2.df.c.689.1		16
63.2	odd	6		882.2.l.b.227.5		16
63.4	even	3		1134.2.k.a.971.5		16
63.5	even	6		1134.2.k.a.647.5		16
63.11	odd	6		126.2.t.a.47.8	yes	16
63.16	even	3		2646.2.l.a.521.1		16
63.20	even	6	inner	882.2.m.b.587.3		16
63.25	even	3		378.2.t.a.89.4		16
63.32	odd	6		1134.2.k.b.971.4		16
63.34	odd	6		2646.2.m.b.1763.8		16
63.38	even	6		882.2.t.a.803.5		16
63.40	odd	6		1134.2.k.b.647.4		16
63.47	even	6		126.2.l.a.101.8	yes	16
63.52	odd	6		2646.2.t.b.1979.1		16
63.61	odd	6		378.2.l.a.143.4		16
84.11	even	6		3024.2.ca.c.2609.8		16
84.47	odd	6		3024.2.df.c.17.8		16
252.11	even	6		1008.2.df.c.929.1		16
252.47	odd	6		1008.2.ca.c.353.2		16
252.151	odd	6		3024.2.df.c.1601.8		16
252.187	even	6		3024.2.ca.c.2033.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.4	✓	16	7.4	even	3
126.2.l.a.101.8	yes	16	63.47	even	6
126.2.t.a.47.8	yes	16	63.11	odd	6
126.2.t.a.59.8	yes	16	7.5	odd	6
378.2.l.a.143.4		16	63.61	odd	6
378.2.l.a.341.8		16	21.11	odd	6
378.2.t.a.17.4		16	21.5	even	6
378.2.t.a.89.4		16	63.25	even	3
882.2.l.b.227.5		16	63.2	odd	6
882.2.l.b.509.1		16	7.3	odd	6
882.2.m.a.293.2		16	7.6	odd	2
882.2.m.a.587.2		16	9.2	odd	6
882.2.m.b.293.3		16	1.1	even	1	trivial
882.2.m.b.587.3		16	63.20	even	6	inner
882.2.t.a.803.5		16	63.38	even	6
882.2.t.a.815.5		16	7.2	even	3
1008.2.ca.c.257.2		16	28.11	odd	6
1008.2.ca.c.353.2		16	252.47	odd	6
1008.2.df.c.689.1		16	28.19	even	6
1008.2.df.c.929.1		16	252.11	even	6
1134.2.k.a.647.5		16	63.5	even	6
1134.2.k.a.971.5		16	63.4	even	3
1134.2.k.b.647.4		16	63.40	odd	6
1134.2.k.b.971.4		16	63.32	odd	6
2646.2.l.a.521.1		16	63.16	even	3
2646.2.l.a.1097.5		16	21.17	even	6
2646.2.m.a.881.5		16	21.20	even	2
2646.2.m.a.1763.5		16	9.7	even	3
2646.2.m.b.881.8		16	3.2	odd	2
2646.2.m.b.1763.8		16	63.34	odd	6
2646.2.t.b.1979.1		16	63.52	odd	6
2646.2.t.b.2285.1		16	21.2	odd	6
3024.2.ca.c.2033.8		16	252.187	even	6
3024.2.ca.c.2609.8		16	84.11	even	6
3024.2.df.c.17.8		16	84.47	odd	6
3024.2.df.c.1601.8		16	252.151	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.0569233 + 1.73112i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.82207 + 3.15592i) q^{5} +(-0.816261 - 1.52765i) q^{6} +1.00000i q^{8} +(-2.99352 - 0.197082i) q^{9} -3.64414i q^{10} +(-4.38809 + 2.53346i) q^{11} +(1.47073 + 0.914855i) q^{12} +(2.94391 + 1.69967i) q^{13} +(-5.35954 - 3.33386i) q^{15} +(-0.500000 - 0.866025i) q^{16} +1.54939 q^{17} +(2.69100 - 1.32608i) q^{18} +0.816535i q^{19} +(1.82207 + 3.15592i) q^{20} +(2.53346 - 4.38809i) q^{22} +(-1.47275 - 0.850294i) q^{23} +(-1.73112 - 0.0569233i) q^{24} +(-4.13989 - 7.17050i) q^{25} -3.39934 q^{26} +(0.511572 - 5.17091i) q^{27} +(-3.60693 + 2.08246i) q^{29} +(6.30843 + 0.207437i) q^{30} +(-1.87924 - 1.08498i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.13593 - 7.74050i) q^{33} +(-1.34181 + 0.774696i) q^{34} +(-1.66744 + 2.49392i) q^{36} +6.79957 q^{37} +(-0.408267 - 0.707140i) q^{38} +(-3.10990 + 4.99950i) q^{39} +(-3.15592 - 1.82207i) q^{40} +(1.01681 - 1.76117i) q^{41} +(3.06189 + 5.30335i) q^{43} +5.06693i q^{44} +(6.07638 - 9.08821i) q^{45} +1.70059 q^{46} +(3.37127 + 5.83922i) q^{47} +(1.52765 - 0.816261i) q^{48} +(7.17050 + 4.13989i) q^{50} +(-0.0881966 + 2.68218i) q^{51} +(2.94391 - 1.69967i) q^{52} -13.2745i q^{53} +(2.14242 + 4.73392i) q^{54} -18.4646i q^{55} +(-1.41352 - 0.0464799i) q^{57} +(2.08246 - 3.60693i) q^{58} +(1.08816 - 1.88475i) q^{59} +(-5.56698 + 2.97457i) q^{60} +(-6.28199 + 3.62691i) q^{61} +2.16996 q^{62} -1.00000 q^{64} +(-10.7280 + 6.19384i) q^{65} +(7.45207 + 4.63550i) q^{66} +(-1.22820 + 2.12731i) q^{67} +(0.774696 - 1.34181i) q^{68} +(1.55579 - 2.50110i) q^{69} -6.74272i q^{71} +(0.197082 - 2.99352i) q^{72} +4.35220i q^{73} +(-5.88860 + 3.39979i) q^{74} +(12.6486 - 6.75846i) q^{75} +(0.707140 + 0.408267i) q^{76} +(0.193502 - 5.88465i) q^{78} +(-6.37651 - 11.0444i) q^{79} +3.64414 q^{80} +(8.92232 + 1.17994i) q^{81} +2.03363i q^{82} +(0.768040 + 1.33028i) q^{83} +(-2.82310 + 4.88976i) q^{85} +(-5.30335 - 3.06189i) q^{86} +(-3.39966 - 6.36254i) q^{87} +(-2.53346 - 4.38809i) q^{88} +12.0336 q^{89} +(-0.718194 + 10.9088i) q^{90} +(-1.47275 + 0.850294i) q^{92} +(1.98519 - 3.19142i) q^{93} +(-5.83922 - 3.37127i) q^{94} +(-2.57692 - 1.48778i) q^{95} +(-0.914855 + 1.47073i) q^{96} +(-5.59509 + 3.23033i) q^{97} +(13.6351 - 6.71916i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 6 q^{9} - 12 q^{11} + 6 q^{13} - 18 q^{15} - 8 q^{16} + 36 q^{17} + 6 q^{23} - 6 q^{24} - 8 q^{25} - 24 q^{26} + 36 q^{27} + 6 q^{29} + 18 q^{30} + 6 q^{31} + 18 q^{33} + 4 q^{37} + 42 q^{39}+ \cdots + 18 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 6 * q^9 - 12 * q^11 + 6 * q^13 - 18 * q^15 - 8 * q^16 + 36 * q^17 + 6 * q^23 - 6 * q^24 - 8 * q^25 - 24 * q^26 + 36 * q^27 + 6 * q^29 + 18 * q^30 + 6 * q^31 + 18 * q^33 + 4 * q^37 + 42 * q^39 - 6 * q^41 - 2 * q^43 + 42 * q^45 - 12 * q^46 + 18 * q^47 - 12 * q^50 - 6 * q^51 + 6 * q^52 + 6 * q^57 + 6 * q^58 - 30 * q^59 - 12 * q^60 - 60 * q^61 + 36 * q^62 - 16 * q^64 - 42 * q^65 + 24 * q^66 + 14 * q^67 + 18 * q^68 - 42 * q^69 - 12 * q^72 - 18 * q^74 - 30 * q^75 - 16 * q^79 - 18 * q^81 - 12 * q^85 - 24 * q^86 - 24 * q^87 + 48 * q^89 + 18 * q^90 + 6 * q^92 + 12 * q^93 + 66 * q^95 - 6 * q^96 + 6 * q^97 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more