LMFDB - Embedded newform 2646.2.m.a.881.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(881,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, 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("2646.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.m (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$21.1284163748$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.5
Root			$0.765614 - 1.55365i$ of defining polynomial
Character	$\chi$	$=$	2646.881
Dual form			2646.2.m.a.1763.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.82207 + 3.15592i) q^{5} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.82207 + 3.15592i) q^{5} -1.00000i q^{8} +3.64414i q^{10} +(4.38809 - 2.53346i) q^{11} +(-2.94391 - 1.69967i) q^{13} +(-0.500000 - 0.866025i) q^{16} +1.54939 q^{17} -0.816535i q^{19} +(1.82207 + 3.15592i) q^{20} +(2.53346 - 4.38809i) q^{22} +(1.47275 + 0.850294i) q^{23} +(-4.13989 - 7.17050i) q^{25} -3.39934 q^{26} +(3.60693 - 2.08246i) q^{29} +(1.87924 + 1.08498i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.34181 - 0.774696i) q^{34} +6.79957 q^{37} +(-0.408267 - 0.707140i) q^{38} +(3.15592 + 1.82207i) q^{40} +(1.01681 - 1.76117i) q^{41} +(3.06189 + 5.30335i) q^{43} -5.06693i q^{44} +1.70059 q^{46} +(3.37127 + 5.83922i) q^{47} +(-7.17050 - 4.13989i) q^{50} +(-2.94391 + 1.69967i) q^{52} +13.2745i q^{53} +18.4646i q^{55} +(2.08246 - 3.60693i) q^{58} +(1.08816 - 1.88475i) q^{59} +(6.28199 - 3.62691i) q^{61} +2.16996 q^{62} -1.00000 q^{64} +(10.7280 - 6.19384i) q^{65} +(-1.22820 + 2.12731i) q^{67} +(0.774696 - 1.34181i) q^{68} +6.74272i q^{71} -4.35220i q^{73} +(5.88860 - 3.39979i) q^{74} +(-0.707140 - 0.408267i) q^{76} +(-6.37651 - 11.0444i) q^{79} +3.64414 q^{80} -2.03363i q^{82} +(0.768040 + 1.33028i) q^{83} +(-2.82310 + 4.88976i) q^{85} +(5.30335 + 3.06189i) q^{86} +(-2.53346 - 4.38809i) q^{88} +12.0336 q^{89} +(1.47275 - 0.850294i) q^{92} +(5.83922 + 3.37127i) q^{94} +(2.57692 + 1.48778i) q^{95} +(5.59509 - 3.23033i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} + 12 q^{11} - 6 q^{13} - 8 q^{16} + 36 q^{17} - 6 q^{23} - 8 q^{25} - 24 q^{26} - 6 q^{29} - 6 q^{31} + 4 q^{37} - 6 q^{41} - 2 q^{43} - 12 q^{46} + 18 q^{47} + 12 q^{50} - 6 q^{52} + 6 q^{58} - 30 q^{59} + 60 q^{61} + 36 q^{62} - 16 q^{64} + 42 q^{65} + 14 q^{67} + 18 q^{68} + 18 q^{74} - 16 q^{79} - 12 q^{85} + 24 q^{86} + 48 q^{89} - 6 q^{92} - 66 q^{95} - 6 q^{97}+O(q^{100}) $ 16 * q + 8 * q^4 + 12 * q^11 - 6 * q^13 - 8 * q^16 + 36 * q^17 - 6 * q^23 - 8 * q^25 - 24 * q^26 - 6 * q^29 - 6 * q^31 + 4 * q^37 - 6 * q^41 - 2 * q^43 - 12 * q^46 + 18 * q^47 + 12 * q^50 - 6 * q^52 + 6 * q^58 - 30 * q^59 + 60 * q^61 + 36 * q^62 - 16 * q^64 + 42 * q^65 + 14 * q^67 + 18 * q^68 + 18 * q^74 - 16 * q^79 - 12 * q^85 + 24 * q^86 + 48 * q^89 - 6 * q^92 - 66 * q^95 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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
$5$	−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			0
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$			3.64414i			1.15238i
$11$	4.38809	−	2.53346i	1.32306	−	0.763868i	0.338843	−	0.940843i	$-0.389965\pi$
$11$	4.38809	−	2.53346i	1.32306	−	0.763868i	0.984215	+	0.176975i	$0.0566313\pi$
$12$		0			0
$13$	−2.94391	−	1.69967i	−0.816495	−	0.471404i	0.0327114	−	0.999465i	$-0.489586\pi$
$13$	−2.94391	−	1.69967i	−0.816495	−	0.471404i	−0.849206	+	0.528061i	$0.822919\pi$
$14$		0			0
$15$		0			0
$16$	−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	$0.439835\pi$
$18$		0			0
$19$		−	0.816535i		−	0.187326i	−0.995604	−	0.0936629i	$-0.970142\pi$
$19$		−	0.816535i		−	0.187326i	0.995604	−	0.0936629i	$-0.0298576\pi$
$20$	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	0.645624	−	0.763656i	$-0.276598\pi$
$23$	1.47275	+	0.850294i	0.307090	+	0.177299i	−0.338533	+	0.940954i	$0.609931\pi$
$24$		0			0
$25$	−4.13989	−	7.17050i	−0.827979	−	1.43410i
$26$	−3.39934			−0.666665
$27$		0			0
$28$		0			0
$29$	3.60693	−	2.08246i	0.669789	−	0.386703i	−0.126208	−	0.992004i	$-0.540281\pi$
$29$	3.60693	−	2.08246i	0.669789	−	0.386703i	0.795997	+	0.605301i	$0.206947\pi$
$30$		0			0
$31$	1.87924	+	1.08498i	0.337521	+	0.194868i	0.659175	−	0.751989i	$-0.270906\pi$
$31$	1.87924	+	1.08498i	0.337521	+	0.194868i	−0.321654	+	0.946857i	$0.604239\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	1.34181	−	0.774696i	0.230119	−	0.132859i
$35$		0			0
$36$		0			0
$37$	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
$39$		0			0
$40$	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
$45$		0			0
$46$	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	$0.669690\pi$
$48$		0			0
$49$		0			0
$50$	−7.17050	−	4.13989i	−1.01406	−	0.585469i
$51$		0			0
$52$	−2.94391	+	1.69967i	−0.408247	+	0.235702i
$53$			13.2745i			1.82340i	0.410862	+	0.911698i	$0.365228\pi$
$53$			13.2745i			1.82340i	−0.410862	+	0.911698i	$0.634772\pi$
$54$		0			0
$55$			18.4646i			2.48977i
$56$		0			0
$57$		0			0
$58$	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	$0.121421\pi$
$60$		0			0
$61$	6.28199	−	3.62691i	0.804326	−	0.464378i	−0.0406555	−	0.999173i	$-0.512945\pi$
$61$	6.28199	−	3.62691i	0.804326	−	0.464378i	0.844982	+	0.534795i	$0.179611\pi$
$62$	2.16996			0.275585
$63$		0			0
$64$	−1.00000			−0.125000
$65$	10.7280	−	6.19384i	1.33065	−	0.768251i
$66$		0			0
$67$	−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
$69$		0			0
$70$		0			0
$71$			6.74272i			0.800213i	0.916469	+	0.400107i	$0.131027\pi$
$71$			6.74272i			0.800213i	−0.916469	+	0.400107i	$0.868973\pi$
$72$		0			0
$73$		−	4.35220i		−	0.509387i	−0.967022	−	0.254694i	$-0.918025\pi$
$73$		−	4.35220i		−	0.509387i	0.967022	−	0.254694i	$-0.0819746\pi$
$74$	5.88860	−	3.39979i	0.684536	−	0.395217i
$75$		0			0
$76$	−0.707140	−	0.408267i	−0.0811145	−	0.0468315i
$77$		0			0
$78$		0			0
$79$	−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
$81$		0			0
$82$		−	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
$87$		0			0
$88$	−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			0
$91$		0			0
$92$	1.47275	−	0.850294i	0.153545	−	0.0886493i
$93$		0			0
$94$	5.83922	+	3.37127i	0.602269	+	0.347720i
$95$	2.57692	+	1.48778i	0.264386	+	0.152643i
$96$		0			0
$97$	5.59509	−	3.23033i	0.568095	−	0.327990i	−0.188293	−	0.982113i	$-0.560295\pi$
$97$	5.59509	−	3.23033i	0.568095	−	0.327990i	0.756388	+	0.654123i	$0.226962\pi$
$98$		0			0
$99$		0			0
$100$	−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	$0.631636\pi$
$102$		0			0
$103$	12.7174	+	7.34240i	1.25308	+	0.723468i	0.971721	−	0.236134i	$-0.0758803\pi$
$103$	12.7174	+	7.34240i	1.25308	+	0.723468i	0.281363	+	0.959601i	$0.409214\pi$
$104$	−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	$-0.948709\pi$
$107$		−	3.31922i		−	0.320881i	0.987046	−	0.160440i	$-0.0512915\pi$
$108$		0			0
$109$	−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			0
$112$		0			0
$113$	6.80465	+	3.92866i	0.640127	+	0.369578i	0.784664	−	0.619922i	$-0.212836\pi$
$113$	6.80465	+	3.92866i	0.640127	+	0.369578i	−0.144536	+	0.989500i	$0.546169\pi$
$114$		0			0
$115$	−5.36692	+	3.09859i	−0.500468	+	0.288945i
$116$		−	4.16492i		−	0.386703i
$117$		0			0
$118$		−	2.17632i		−	0.200346i
$119$		0			0
$120$		0			0
$121$	7.33687	−	12.7078i	0.666988	−	1.15526i
$122$	3.62691	−	6.28199i	0.328365	−	0.568744i
$123$		0			0
$124$	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
$129$		0			0
$130$	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	$0.121573\pi$
$132$		0			0
$133$		0			0
$134$			2.45641i			0.212201i
$135$		0			0
$136$		−	1.54939i		−	0.132859i
$137$	12.6284	−	7.29101i	1.07892	−	0.622913i	0.148313	−	0.988940i	$-0.452616\pi$
$137$	12.6284	−	7.29101i	1.07892	−	0.622913i	0.930604	+	0.366027i	$0.119282\pi$
$138$		0			0
$139$	4.97814	+	2.87413i	0.422240	+	0.243780i	0.696035	−	0.718008i	$-0.254946\pi$
$139$	4.97814	+	2.87413i	0.422240	+	0.243780i	−0.273795	+	0.961788i	$0.588279\pi$
$140$		0			0
$141$		0			0
$142$	3.37136	+	5.83936i	0.282918	+	0.490029i
$143$	−17.2242			−1.44036
$144$		0			0
$145$			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	0.689182	−	0.724589i	$-0.257970\pi$
$149$	4.95904	+	2.86310i	0.406261	+	0.234555i	−0.282921	+	0.959143i	$0.591303\pi$
$150$		0			0
$151$	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
$153$		0			0
$154$		0			0
$155$	−6.84821	+	3.95382i	−0.550062	+	0.317578i
$156$		0			0
$157$	−11.0598	−	6.38536i	−0.882666	−	0.509607i	−0.0111295	−	0.999938i	$-0.503543\pi$
$157$	−11.0598	−	6.38536i	−0.882666	−	0.509607i	−0.871537	+	0.490331i	$0.836876\pi$
$158$	−11.0444	−	6.37651i	−0.878649	−	0.507288i
$159$		0			0
$160$	3.15592	−	1.82207i	0.249497	−	0.144047i
$161$		0			0
$162$		0			0
$163$	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
$165$		0			0
$166$	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			0
$172$	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	$0.859974\pi$
$174$		0			0
$175$		0			0
$176$	−4.38809	−	2.53346i	−0.330764	−	0.190967i
$177$		0			0
$178$	10.4214	−	6.01679i	0.781116	−	0.450977i
$179$		−	10.7470i		−	0.803266i	−0.915801	−	0.401633i	$-0.868443\pi$
$179$		−	10.7470i		−	0.803266i	0.915801	−	0.401633i	$-0.131557\pi$
$180$		0			0
$181$		−	14.4710i		−	1.07562i	−0.843065	−	0.537811i	$-0.819251\pi$
$181$		−	14.4710i		−	1.07562i	0.843065	−	0.537811i	$-0.180749\pi$
$182$		0			0
$183$		0			0
$184$	0.850294	−	1.47275i	0.0626845	−	0.108573i
$185$	−12.3893	+	21.4589i	−0.910880	+	1.57769i
$186$		0			0
$187$	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	−0.215689	−	0.976462i	$-0.569200\pi$
$191$	7.21567	−	4.16597i	0.522108	−	0.301439i	0.737797	+	0.675023i	$0.235866\pi$
$192$		0			0
$193$	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
$195$		0			0
$196$		0			0
$197$			2.37228i			0.169018i	0.996423	+	0.0845089i	$0.0269322\pi$
$197$			2.37228i			0.169018i	−0.996423	+	0.0845089i	$0.973068\pi$
$198$		0			0
$199$		−	22.5147i		−	1.59602i	−0.602642	−	0.798011i	$-0.705885\pi$
$199$		−	22.5147i		−	1.59602i	0.602642	−	0.798011i	$-0.294115\pi$
$200$	−7.17050	+	4.13989i	−0.507031	+	0.292735i
$201$		0			0
$202$	10.3065	+	5.95045i	0.725161	+	0.418672i
$203$		0			0
$204$		0			0
$205$	3.70541	+	6.41796i	0.258797	+	0.448250i
$206$	14.6848			1.02314
$207$		0			0
$208$			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
$213$		0			0
$214$	−1.65961	−	2.87453i	−0.113449	−	0.196499i
$215$	−22.3159			−1.52193
$216$		0			0
$217$		0			0
$218$	−2.45668	+	1.41837i	−0.166388	+	0.0960640i
$219$		0			0
$220$	15.9908	+	9.23230i	1.07810	+	0.622442i
$221$	−4.56128	−	2.63346i	−0.306825	−	0.177145i
$222$		0			0
$223$	22.5221	−	13.0031i	1.50819	−	0.870753i	0.508235	−	0.861219i	$-0.330298\pi$
$223$	22.5221	−	13.0031i	1.50819	−	0.870753i	0.999955	−	0.00953489i	$-0.00303510\pi$
$224$		0			0
$225$		0			0
$226$	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			0
$229$	−23.3224	−	13.4652i	−1.54118	−	0.889803i	−0.998764	−	0.0496960i	$-0.984175\pi$
$229$	−23.3224	−	13.4652i	−1.54118	−	0.889803i	−0.542420	−	0.840107i	$-0.682492\pi$
$230$	−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	$-0.953847\pi$
$233$		−	4.41099i		−	0.288974i	0.989507	−	0.144487i	$-0.0461532\pi$
$234$		0			0
$235$	−24.5708			−1.60282
$236$	−1.08816	−	1.88475i	−0.0708331	−	0.122687i
$237$		0			0
$238$		0			0
$239$	−16.1660	−	9.33343i	−1.04569	−	0.603729i	−0.124250	−	0.992251i	$-0.539653\pi$
$239$	−16.1660	−	9.33343i	−1.04569	−	0.603729i	−0.921440	+	0.388522i	$0.872986\pi$
$240$		0			0
$241$	0.412458	−	0.238133i	0.0265688	−	0.0153395i	−0.486657	−	0.873593i	$-0.661784\pi$
$241$	0.412458	−	0.238133i	0.0265688	−	0.0153395i	0.513226	+	0.858254i	$0.328450\pi$
$242$		−	14.6737i		−	0.943263i
$243$		0			0
$244$		−	7.25382i		−	0.464378i
$245$		0			0
$246$		0			0
$247$	−1.38784	+	2.40381i	−0.0883061	+	0.152951i
$248$	1.08498	−	1.87924i	0.0688962	−	0.119332i
$249$		0			0
$250$	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
$255$		0			0
$256$	−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	$0.909243\pi$
$258$		0			0
$259$		0			0
$260$		−	12.3877i		−	0.768251i
$261$		0			0
$262$		−	3.23206i		−	0.199677i
$263$	2.98247	−	1.72193i	0.183907	−	0.106179i	−0.405220	−	0.914219i	$-0.632805\pi$
$263$	2.98247	−	1.72193i	0.183907	−	0.106179i	0.589127	+	0.808040i	$0.299472\pi$
$264$		0			0
$265$	−41.8933	−	24.1871i	−2.57349	−	1.48580i
$266$		0			0
$267$		0			0
$268$	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	$0.421440\pi$
$270$		0			0
$271$		−	1.79088i		−	0.108788i	−0.998520	−	0.0543942i	$-0.982677\pi$
$271$		−	1.79088i		−	0.108788i	0.998520	−	0.0543942i	$-0.0173228\pi$
$272$	−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
$276$		0			0
$277$	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
$279$		0			0
$280$		0			0
$281$	−18.6262	+	10.7539i	−1.11115	+	0.641521i	−0.939126	−	0.343572i	$-0.888363\pi$
$281$	−18.6262	+	10.7539i	−1.11115	+	0.641521i	−0.172021	+	0.985093i	$0.555030\pi$
$282$		0			0
$283$	17.2755	+	9.97402i	1.02692	+	0.592894i	0.916101	−	0.400947i	$-0.131319\pi$
$283$	17.2755	+	9.97402i	1.02692	+	0.592894i	0.110821	+	0.993840i	$0.464652\pi$
$284$	5.83936	+	3.37136i	0.346502	+	0.200053i
$285$		0			0
$286$	−14.9166	+	8.61210i	−0.882037	+	0.509244i
$287$		0			0
$288$		0			0
$289$	−14.5994			−0.858787
$290$	7.58878	+	13.1442i	0.445629	+	0.771851i
$291$		0			0
$292$	−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
$297$		0			0
$298$	5.72621			0.331710
$299$	−2.89044	−	5.00639i	−0.167158	−	0.289527i
$300$		0			0
$301$		0			0
$302$	11.0589	+	6.38483i	0.636365	+	0.367406i
$303$		0			0
$304$	−0.707140	+	0.408267i	−0.0405572	+	0.0234157i
$305$			26.4339i			1.51360i
$306$		0			0
$307$			9.23124i			0.526854i	0.964679	+	0.263427i	$0.0848529\pi$
$307$			9.23124i			0.526854i	−0.964679	+	0.263427i	$0.915147\pi$
$308$		0			0
$309$		0			0
$310$	−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	$0.940893\pi$
$312$		0			0
$313$	5.57145	−	3.21668i	0.314917	−	0.181818i	−0.334208	−	0.942500i	$-0.608469\pi$
$313$	5.57145	−	3.21668i	0.314917	−	0.181818i	0.649125	+	0.760682i	$0.275135\pi$
$314$	−12.7707			−0.720694
$315$		0			0
$316$	−12.7530			−0.717414
$317$	7.56502	−	4.36767i	0.424894	−	0.245313i	−0.272275	−	0.962219i	$-0.587776\pi$
$317$	7.56502	−	4.36767i	0.424894	−	0.245313i	0.697169	+	0.716907i	$0.254443\pi$
$318$		0			0
$319$	10.5517	−	18.2760i	0.590780	−	1.02326i
$320$	1.82207	−	3.15592i	0.101857	−	0.176421i
$321$		0			0
$322$		0			0
$323$		−	1.26513i		−	0.0703939i
$324$		0			0
$325$			28.1458i			1.56125i
$326$	2.61570	−	1.51018i	0.144870	−	0.0836410i
$327$		0			0
$328$	−1.76117	−	1.01681i	−0.0972444	−	0.0561441i
$329$		0			0
$330$		0			0
$331$	−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
$333$		0			0
$334$			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
$339$		0			0
$340$	2.82310	+	4.88976i	0.153104	+	0.265185i
$341$	10.9950			0.595413
$342$		0			0
$343$		0			0
$344$	5.30335	−	3.06189i	0.285937	−	0.165086i
$345$		0			0
$346$	−1.90444	−	1.09953i	−0.102383	−	0.0591109i
$347$	5.90994	+	3.41210i	0.317262	+	0.183171i	0.650172	−	0.759787i	$-0.274697\pi$
$347$	5.90994	+	3.41210i	0.317262	+	0.183171i	−0.332909	+	0.942959i	$0.608030\pi$
$348$		0			0
$349$	4.18379	−	2.41551i	0.223953	−	0.129299i	−0.383826	−	0.923405i	$-0.625394\pi$
$349$	4.18379	−	2.41551i	0.223953	−	0.129299i	0.607779	+	0.794106i	$0.292061\pi$
$350$		0			0
$351$		0			0
$352$	−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	$-0.538780\pi$
$354$		0			0
$355$	−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	$0.254219\pi$
$359$			27.1483i			1.43283i	−0.697672	+	0.716417i	$0.745781\pi$
$360$		0			0
$361$	18.3333			0.964909
$362$	−7.23551	−	12.5323i	−0.380290	−	0.658682i
$363$		0			0
$364$		0			0
$365$	13.7352	+	7.93003i	0.718934	+	0.415077i
$366$		0			0
$367$	−10.3307	+	5.96444i	−0.539259	+	0.311341i	−0.744778	−	0.667312i	$-0.767445\pi$
$367$	−10.3307	+	5.96444i	−0.539259	+	0.311341i	0.205520	+	0.978653i	$0.434112\pi$
$368$		−	1.70059i		−	0.0886493i
$369$		0			0
$370$			24.7786i			1.28818i
$371$		0			0
$372$		0			0
$373$	−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			0
$376$	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			0
$382$	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			0
$385$		0			0
$386$		−	9.56786i		−	0.486991i
$387$		0			0
$388$		−	6.46065i		−	0.327990i
$389$	−15.2013	+	8.77645i	−0.770735	+	0.444984i	−0.833137	−	0.553067i	$-0.813457\pi$
$389$	−15.2013	+	8.77645i	−0.770735	+	0.444984i	0.0624020	+	0.998051i	$0.480124\pi$
$390$		0			0
$391$	2.28187	+	1.31744i	0.115399	+	0.0666258i
$392$		0			0
$393$		0			0
$394$	1.18614	+	2.05445i	0.0597568	+	0.103502i
$395$	46.4739			2.33835
$396$		0			0
$397$			13.3591i			0.670474i	0.942134	+	0.335237i	$0.108816\pi$
$397$			13.3591i			0.670474i	−0.942134	+	0.335237i	$0.891184\pi$
$398$	−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	0.588637	−	0.808398i	$-0.299665\pi$
$401$	3.66182	+	2.11415i	0.182863	+	0.105576i	−0.405774	+	0.913973i	$0.632998\pi$
$402$		0			0
$403$	−3.68821	−	6.38817i	−0.183723	−	0.318217i
$404$	11.9009			0.592092
$405$		0			0
$406$		0			0
$407$	29.8371	−	17.2265i	1.47897	−	0.853884i
$408$		0			0
$409$	−33.2687	−	19.2077i	−1.64503	−	0.949759i	−0.979006	−	0.203829i	$-0.934661\pi$
$409$	−33.2687	−	19.2077i	−1.64503	−	0.949759i	−0.666025	−	0.745930i	$-0.732005\pi$
$410$	6.41796	+	3.70541i	0.316961	+	0.182997i
$411$		0			0
$412$	12.7174	−	7.34240i	0.626542	−	0.361734i
$413$		0			0
$414$		0			0
$415$	−5.59770			−0.274780
$416$	1.69967	+	2.94391i	0.0833332	+	0.144337i
$417$		0			0
$418$	−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
$423$		0			0
$424$	13.2745			0.644668
$425$	−6.41432	−	11.1099i	−0.311140	−	0.538911i
$426$		0			0
$427$		0			0
$428$	−2.87453	−	1.65961i	−0.138946	−	0.0802202i
$429$		0			0
$430$	−19.3262	+	11.1580i	−0.931991	+	0.538085i
$431$		−	11.6542i		−	0.561362i	−0.959801	−	0.280681i	$-0.909440\pi$
$431$		−	11.6542i		−	0.561362i	0.959801	−	0.280681i	$-0.0905602\pi$
$432$		0			0
$433$			17.9149i			0.860936i	0.902606	+	0.430468i	$0.141652\pi$
$433$			17.9149i			0.860936i	−0.902606	+	0.430468i	$0.858348\pi$
$434$		0			0
$435$		0			0
$436$	−1.41837	+	2.45668i	−0.0679275	+	0.117654i
$437$	0.694295	−	1.20255i	0.0332126	−	0.0575259i
$438$		0			0
$439$	16.4783	−	9.51377i	0.786468	−	0.454068i	−0.0522494	−	0.998634i	$-0.516639\pi$
$439$	16.4783	−	9.51377i	0.786468	−	0.454068i	0.838718	+	0.544566i	$0.183306\pi$
$440$	18.4646			0.880266
$441$		0			0
$442$	−5.26691			−0.250521
$443$	−6.64877	+	3.83867i	−0.315893	+	0.182381i	−0.649560	−	0.760310i	$-0.725047\pi$
$443$	−6.64877	+	3.83867i	−0.315893	+	0.182381i	0.333668	+	0.942691i	$0.391714\pi$
$444$		0			0
$445$	−21.9260	+	37.9770i	−1.03939	+	1.80028i
$446$	13.0031	−	22.5221i	0.615716	−	1.06645i
$447$		0			0
$448$		0			0
$449$			30.1018i			1.42059i	0.703903	+	0.710296i	$0.251439\pi$
$449$			30.1018i			1.42059i	−0.703903	+	0.710296i	$0.748561\pi$
$450$		0			0
$451$		−	10.3042i		−	0.485207i
$452$	6.80465	−	3.92866i	0.320064	−	0.184789i
$453$		0			0
$454$	−19.8129	−	11.4390i	−0.929864	−	0.536857i
$455$		0			0
$456$		0			0
$457$	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			0
$460$			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
$465$		0			0
$466$	−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	$0.319861\pi$
$468$		0			0
$469$		0			0
$470$	−21.2789	+	12.2854i	−0.981525	+	0.566684i
$471$		0			0
$472$	−1.88475	−	1.08816i	−0.0867525	−	0.0500866i
$473$	26.8717	+	15.5144i	1.23556	+	0.713351i
$474$		0			0
$475$	−5.85497	+	3.38037i	−0.268644	+	0.155102i
$476$		0			0
$477$		0			0
$478$	−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	$-0.357634\pi$
$480$		0			0
$481$	−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
$486$		0			0
$487$	−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			0
$490$		0			0
$491$	25.5933	+	14.7763i	1.15501	+	0.666845i	0.950103	−	0.311937i	$-0.100978\pi$
$491$	25.5933	+	14.7763i	1.15501	+	0.666845i	0.204906	+	0.978782i	$0.434311\pi$
$492$		0			0
$493$	5.58854	−	3.22655i	0.251695	−	0.145316i
$494$			2.77568i			0.124884i
$495$		0			0
$496$		−	2.16996i		−	0.0974339i
$497$		0			0
$498$		0			0
$499$	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
$501$		0			0
$502$	−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
$507$		0			0
$508$	−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	$0.174135\pi$
$510$		0			0
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		0			0
$514$			23.1941i			1.02305i
$515$	−46.3441	+	26.7568i	−2.04216	+	1.17904i
$516$		0			0
$517$	29.5869	+	17.0820i	1.30123	+	0.751265i
$518$		0			0
$519$		0			0
$520$	−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	$0.571022\pi$
$522$		0			0
$523$		−	9.27216i		−	0.405443i	−0.979236	−	0.202722i	$-0.935021\pi$
$523$		−	9.27216i		−	0.405443i	0.979236	−	0.202722i	$-0.0649786\pi$
$524$	−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
$528$		0			0
$529$	−10.0540	−	17.4140i	−0.437130	−	0.757132i
$530$	−48.3743			−2.10124
$531$		0			0
$532$		0			0
$533$	−5.98682	+	3.45649i	−0.259318	+	0.149717i
$534$		0			0
$535$	10.4752	+	6.04786i	0.452882	+	0.261472i
$536$	2.12731	+	1.22820i	0.0918858	+	0.0530503i
$537$		0			0
$538$	6.94015	−	4.00690i	0.299211	−	0.172750i
$539$		0			0
$540$		0			0
$541$	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
$543$		0			0
$544$	−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
$549$		0			0
$550$	−41.9531			−1.78888
$551$	−1.70040	−	2.94518i	−0.0724395	−	0.125469i
$552$		0			0
$553$		0			0
$554$	21.2986	+	12.2968i	0.904892	+	0.522440i
$555$		0			0
$556$	4.97814	−	2.87413i	0.211120	−	0.121890i
$557$			0.374010i			0.0158473i	0.999969	+	0.00792365i	$0.00252220\pi$
$557$			0.374010i			0.0158473i	−0.999969	+	0.00792365i	$0.997478\pi$
$558$		0			0
$559$		−	20.8168i		−	0.880457i
$560$		0			0
$561$		0			0
$562$	−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			0
$565$	−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	−0.986567	−	0.163360i	$-0.947767\pi$
$569$	−31.9253	+	18.4321i	−1.33838	+	0.772712i	−0.351810	+	0.936072i	$0.614434\pi$
$570$		0			0
$571$	−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
$573$		0			0
$574$		0			0
$575$		−	14.0805i		−	0.587198i
$576$		0			0
$577$		−	14.1940i		−	0.590903i	−0.955358	−	0.295452i	$-0.904530\pi$
$577$		−	14.1940i		−	0.590903i	0.955358	−	0.295452i	$-0.0954701\pi$
$578$	−12.6434	+	7.29969i	−0.525898	+	0.303627i
$579$		0			0
$580$	13.1442	+	7.58878i	0.545781	+	0.315107i
$581$		0			0
$582$		0			0
$583$	33.6305	+	58.2497i	1.39283	+	2.41246i
$584$	−4.35220			−0.180096
$585$		0			0
$586$			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
$591$		0			0
$592$	−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	$0.656877\pi$
$594$		0			0
$595$		0			0
$596$	4.95904	−	2.86310i	0.203130	−	0.117277i
$597$		0			0
$598$	−5.00639	−	2.89044i	−0.204726	−	0.118199i
$599$	−25.0820	−	14.4811i	−1.02482	−	0.591682i	−0.109326	−	0.994006i	$-0.534869\pi$
$599$	−25.0820	−	14.4811i	−1.02482	−	0.591682i	−0.915497	+	0.402324i	$0.868203\pi$
$600$		0			0
$601$	−5.04993	+	2.91558i	−0.205991	+	0.118929i	−0.599447	−	0.800414i	$-0.704613\pi$
$601$	−5.04993	+	2.91558i	−0.205991	+	0.118929i	0.393456	+	0.919344i	$0.371279\pi$
$602$		0			0
$603$		0			0
$604$	12.7697			0.519590
$605$	26.7366	+	46.3092i	1.08700	+	1.88273i
$606$		0			0
$607$	16.3750	+	9.45411i	0.664641	+	0.383731i	0.794043	−	0.607862i	$-0.207972\pi$
$607$	16.3750	+	9.45411i	0.664641	+	0.383731i	−0.129402	+	0.991592i	$0.541306\pi$
$608$	−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
$612$		0			0
$613$	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
$615$		0			0
$616$		0			0
$617$	−34.0222	−	19.6427i	−1.36968	−	0.790786i	−0.378794	−	0.925481i	$-0.623661\pi$
$617$	−34.0222	−	19.6427i	−1.36968	−	0.790786i	−0.990887	+	0.134695i	$0.956995\pi$
$618$		0			0
$619$	−8.46727	+	4.88858i	−0.340329	+	0.196489i	−0.660417	−	0.750899i	$-0.729621\pi$
$619$	−8.46727	+	4.88858i	−0.340329	+	0.196489i	0.320089	+	0.947388i	$0.396287\pi$
$620$			7.90763i			0.317578i
$621$		0			0
$622$			22.9714i			0.921069i
$623$		0			0
$624$		0			0
$625$	−1.07796	+	1.86708i	−0.0431185	+	0.0746834i
$626$	3.21668	−	5.57145i	0.128564	−	0.222680i
$627$		0			0
$628$	−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
$633$		0			0
$634$	4.36767	−	7.56502i	0.173462	−	0.300445i
$635$	31.7549	−	55.0010i	1.26015	−	2.18265i
$636$		0			0
$637$		0			0
$638$		−	21.1033i		−	0.835489i
$639$		0			0
$640$		−	3.64414i		−	0.144047i
$641$	25.2233	−	14.5627i	0.996262	−	0.575192i	0.0891220	−	0.996021i	$-0.471594\pi$
$641$	25.2233	−	14.5627i	0.996262	−	0.575192i	0.907140	+	0.420828i	$0.138261\pi$
$642$		0			0
$643$	−33.9410	−	19.5959i	−1.33850	−	0.772785i	−0.351918	−	0.936031i	$-0.614470\pi$
$643$	−33.9410	−	19.5959i	−1.33850	−	0.772785i	−0.986585	+	0.163245i	$0.947804\pi$
$644$		0			0
$645$		0			0
$646$	−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	$0.631066\pi$
$648$		0			0
$649$		−	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	0.221035	−	0.975266i	$-0.429056\pi$
$653$	−13.1105	−	7.56933i	−0.513052	−	0.296211i	−0.734087	+	0.679055i	$0.762390\pi$
$654$		0			0
$655$	5.88904	+	10.2001i	0.230104	+	0.398552i
$656$	−2.03363			−0.0793997
$657$		0			0
$658$		0			0
$659$	9.17413	−	5.29668i	0.357373	−	0.206330i	−0.310555	−	0.950556i	$-0.600515\pi$
$659$	9.17413	−	5.29668i	0.357373	−	0.206330i	0.667928	+	0.744226i	$0.267181\pi$
$660$		0			0
$661$	14.7583	+	8.52074i	0.574033	+	0.331418i	0.758759	−	0.651372i	$-0.225806\pi$
$661$	14.7583	+	8.52074i	0.574033	+	0.331418i	−0.184725	+	0.982790i	$0.559140\pi$
$662$	−27.4537	−	15.8504i	−1.06702	−	0.616042i
$663$		0			0
$664$	1.33028	−	0.768040i	0.0516251	−	0.0298057i
$665$		0			0
$666$		0			0
$667$	7.08281			0.274248
$668$	7.14766	+	12.3801i	0.276551	+	0.479001i
$669$		0			0
$670$	−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
$675$		0			0
$676$	−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			0
$679$		0			0
$680$	4.88976	+	2.82310i	0.187514	+	0.108261i
$681$		0			0
$682$	9.52196	−	5.49750i	0.364615	−	0.210510i
$683$		−	2.67738i		−	0.102447i	−0.998687	−	0.0512236i	$-0.983688\pi$
$683$		−	2.67738i		−	0.102447i	0.998687	−	0.0512236i	$-0.0163121\pi$
$684$		0			0
$685$			53.1390i			2.03034i
$686$		0			0
$687$		0			0
$688$	3.06189	−	5.30335i	0.116733	−	0.202188i
$689$	22.5623	−	39.0790i	0.859555	−	1.48879i
$690$		0			0
$691$	−16.6346	+	9.60399i	−0.632810	+	0.365353i	−0.781839	−	0.623480i	$-0.785718\pi$
$691$	−16.6346	+	9.60399i	−0.632810	+	0.365353i	0.149030	+	0.988833i	$0.452385\pi$
$692$	−2.19905			−0.0835954
$693$		0			0
$694$	6.82421			0.259043
$695$	−18.1410	+	10.4737i	−0.688129	+	0.397291i
$696$		0			0
$697$	1.57544	−	2.72875i	0.0596741	−	0.103359i
$698$	2.41551	−	4.18379i	0.0914284	−	0.158359i
$699$		0			0
$700$		0			0
$701$		−	34.1916i		−	1.29140i	−0.763591	−	0.645700i	$-0.776566\pi$
$701$		−	34.1916i		−	1.29140i	0.763591	−	0.645700i	$-0.223434\pi$
$702$		0			0
$703$		−	5.55208i		−	0.209401i
$704$	−4.38809	+	2.53346i	−0.165382	+	0.0954835i
$705$		0			0
$706$	−29.9510	−	17.2922i	−1.12722	−	0.650800i
$707$		0			0
$708$		0			0
$709$	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
$711$		0			0
$712$		−	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
$717$		0			0
$718$	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	$0.403713\pi$
$720$		0			0
$721$		0			0
$722$	15.8771	−	9.16664i	0.590884	−	0.341147i
$723$		0			0
$724$	−12.5323	−	7.23551i	−0.465758	−	0.268906i
$725$	−29.8646	−	17.2423i	−1.10914	−	0.640364i
$726$		0			0
$727$	−21.6787	+	12.5162i	−0.804019	+	0.464201i	−0.844875	−	0.534964i	$-0.820325\pi$
$727$	−21.6787	+	12.5162i	−0.804019	+	0.464201i	0.0408555	+	0.999165i	$0.486992\pi$
$728$		0			0
$729$		0			0
$730$	15.8601			0.587007
$731$	4.74407	+	8.21697i	0.175466	+	0.303916i
$732$		0			0
$733$	10.1433	+	5.85625i	0.374652	+	0.216305i	0.675489	−	0.737370i	$-0.263933\pi$
$733$	10.1433	+	5.85625i	0.374652	+	0.216305i	−0.300837	+	0.953676i	$0.597266\pi$
$734$	−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			0
$739$	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
$741$		0			0
$742$		0			0
$743$	−8.02860	−	4.63532i	−0.294541	−	0.170053i	0.345447	−	0.938438i	$-0.387727\pi$
$743$	−8.02860	−	4.63532i	−0.294541	−	0.170053i	−0.639988	+	0.768385i	$0.721061\pi$
$744$		0			0
$745$	−18.0715	+	10.4336i	−0.662087	+	0.382256i
$746$			9.63850i			0.352890i
$747$		0			0
$748$		−	7.85066i		−	0.287048i
$749$		0			0
$750$		0			0
$751$	−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
$753$		0			0
$754$	−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			0
$760$	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	$0.828882\pi$
$762$		0			0
$763$		0			0
$764$		−	8.33194i		−	0.301439i
$765$		0			0
$766$			6.36945i			0.230137i
$767$	−6.40690	+	3.69902i	−0.231340	+	0.133564i
$768$		0			0
$769$	−9.84984	−	5.68681i	−0.355194	−	0.205071i	0.311776	−	0.950155i	$-0.399076\pi$
$769$	−9.84984	−	5.68681i	−0.355194	−	0.205071i	−0.666971	+	0.745084i	$0.732409\pi$
$770$		0			0
$771$		0			0
$772$	−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	$0.524499\pi$
$774$		0			0
$775$		−	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
$780$		0			0
$781$	17.0824	+	29.5876i	0.611257	+	1.05873i
$782$	2.63488			0.0942231
$783$		0			0
$784$		0			0
$785$	40.3034	−	23.2692i	1.43849	−	0.830513i
$786$		0			0
$787$	22.8644	+	13.2008i	0.815029	+	0.470557i	0.848699	−	0.528876i	$-0.177386\pi$
$787$	22.8644	+	13.2008i	0.815029	+	0.470557i	−0.0336701	+	0.999433i	$0.510720\pi$
$788$	2.05445	+	1.18614i	0.0731869	+	0.0422545i
$789$		0			0
$790$	40.2476	−	23.2369i	1.43194	−	0.826733i
$791$		0			0
$792$		0			0
$793$	−24.6582			−0.875638
$794$	6.67955	+	11.5693i	0.237048	+	0.410580i
$795$		0			0
$796$	−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
$801$		0			0
$802$	4.22830			0.149307
$803$	−11.0261	−	19.0978i	−0.389104	−	0.673948i
$804$		0			0
$805$		0			0
$806$	−6.38817	−	3.68821i	−0.225014	−	0.129912i
$807$		0			0
$808$	10.3065	−	5.95045i	0.362581	−	0.209336i
$809$		−	10.1215i		−	0.355854i	−0.984044	−	0.177927i	$-0.943061\pi$
$809$		−	10.1215i		−	0.355854i	0.984044	−	0.177927i	$-0.0569391\pi$
$810$		0			0
$811$		−	44.8854i		−	1.57614i	−0.615586	−	0.788070i	$-0.711080\pi$
$811$		−	44.8854i		−	1.57614i	0.615586	−	0.788070i	$-0.288920\pi$
$812$		0			0
$813$		0			0
$814$	17.2265	−	29.8371i	0.603787	−	1.04579i
$815$	−5.50330	+	9.53200i	−0.192772	+	0.333891i
$816$		0			0
$817$	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	0.121504	−	0.992591i	$-0.461228\pi$
$821$	29.8527	−	17.2354i	1.04187	−	0.601521i	0.920361	+	0.391070i	$0.127895\pi$
$822$		0			0
$823$	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
$825$		0			0
$826$		0			0
$827$			18.8795i			0.656506i	0.944590	+	0.328253i	$0.106460\pi$
$827$			18.8795i			0.656506i	−0.944590	+	0.328253i	$0.893540\pi$
$828$		0			0
$829$		−	18.0899i		−	0.628288i	−0.949375	−	0.314144i	$-0.898283\pi$
$829$		−	18.0899i		−	0.628288i	0.949375	−	0.314144i	$-0.101717\pi$
$830$	−4.84775	+	2.79885i	−0.168268	+	0.0971495i
$831$		0			0
$832$	2.94391	+	1.69967i	0.102062	+	0.0589254i
$833$		0			0
$834$		0			0
$835$	−26.0471	−	45.1149i	−0.901397	−	1.56127i
$836$	−4.13732			−0.143092
$837$		0			0
$838$		−	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
$843$		0			0
$844$	7.27211	+	12.5957i	0.250316	+	0.433560i
$845$	5.26395			0.181085
$846$		0			0
$847$		0			0
$848$	11.4961	−	6.63726i	0.394777	−	0.227924i
$849$		0			0
$850$	−11.1099	−	6.41432i	−0.381067	−	0.220009i
$851$	10.0141	+	5.78163i	0.343278	+	0.198192i
$852$		0			0
$853$	−37.0163	+	21.3714i	−1.26741	+	0.731742i	−0.974498	−	0.224397i	$-0.927959\pi$
$853$	−37.0163	+	21.3714i	−1.26741	+	0.731742i	−0.292916	+	0.956138i	$0.594626\pi$
$854$		0			0
$855$		0			0
$856$	−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	$0.827488\pi$
$858$		0			0
$859$	−20.9983	−	12.1234i	−0.716452	−	0.413644i	0.0969931	−	0.995285i	$-0.469078\pi$
$859$	−20.9983	−	12.1234i	−0.716452	−	0.413644i	−0.813446	+	0.581641i	$0.802411\pi$
$860$	−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	$-0.724712\pi$
$863$		−	44.7112i		−	1.52199i	0.648759	−	0.760994i	$-0.275288\pi$
$864$		0			0
$865$	8.01367			0.272473
$866$	8.95746	+	15.5148i	0.304387	+	0.527214i
$867$		0			0
$868$		0			0
$869$	−55.9614	−	32.3093i	−1.89836	−	1.09602i
$870$		0			0
$871$	7.23145	−	4.17508i	0.245028	−	0.141467i
$872$			2.83674i			0.0960640i
$873$		0			0
$874$		−	1.38859i		−	0.0469697i
$875$		0			0
$876$		0			0
$877$	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
$879$		0			0
$880$	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
$885$		0			0
$886$	−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	$0.0297234\pi$
$888$		0			0
$889$		0			0
$890$			43.8521i			1.46993i
$891$		0			0
$892$		−	26.0062i		−	0.870753i
$893$	4.76792	−	2.75276i	0.159552	−	0.0921176i
$894$		0			0
$895$	33.9166	+	19.5818i	1.13371	+	0.654546i
$896$		0			0
$897$		0			0
$898$	15.0509	+	26.0689i	0.502255	+	0.869932i
$899$	9.03769			0.301424
$900$		0			0
$901$			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
$906$		0			0
$907$	−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
$909$		0			0
$910$		0			0
$911$	−2.21678	+	1.27986i	−0.0734452	+	0.0424036i	−0.536273	−	0.844045i	$-0.680168\pi$
$911$	−2.21678	+	1.27986i	−0.0734452	+	0.0424036i	0.462828	+	0.886448i	$0.346835\pi$
$912$		0			0
$913$	6.74045	+	3.89160i	0.223076	+	0.128793i
$914$	34.1973	+	19.7438i	1.13115	+	0.653067i
$915$		0			0
$916$	−23.3224	+	13.4652i	−0.770592	+	0.444902i
$917$		0			0
$918$		0			0
$919$	−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
$921$		0			0
$922$	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
$927$		0			0
$928$	−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	$0.672121\pi$
$930$		0			0
$931$		0			0
$932$	−3.82003	−	2.20550i	−0.125129	−	0.0722435i
$933$		0			0
$934$	20.0698	−	11.5873i	0.656702	−	0.379147i
$935$			28.6089i			0.935612i
$936$		0			0
$937$		−	17.9991i		−	0.588005i	−0.955805	−	0.294002i	$-0.905013\pi$
$937$		−	17.9991i		−	0.588005i	0.955805	−	0.294002i	$-0.0949874\pi$
$938$		0			0
$939$		0			0
$940$	−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			0
$943$	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	−0.154034	−	0.988066i	$-0.549227\pi$
$947$	19.2222	−	11.0980i	0.624639	−	0.360635i	0.778673	+	0.627430i	$0.215893\pi$
$948$		0			0
$949$	−7.39731	+	12.8125i	−0.240127	+	0.415912i
$950$	−3.38037	+	5.85497i	−0.109674	+	0.189960i
$951$		0			0
$952$		0			0
$953$			2.12319i			0.0687769i	0.999409	+	0.0343884i	$0.0109483\pi$
$953$			2.12319i			0.0687769i	−0.999409	+	0.0343884i	$0.989052\pi$
$954$		0			0
$955$			30.3628i			0.982517i
$956$	−16.1660	+	9.33343i	−0.522845	+	0.301865i
$957$		0			0
$958$	−21.4025	−	12.3567i	−0.691484	−	0.399228i
$959$		0			0
$960$		0			0
$961$	−13.1456	−	22.7689i	−0.424053	−	0.734481i
$962$	−23.1140			−0.745227
$963$		0			0
$964$		−	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
$969$		0			0
$970$	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	$0.490641\pi$
$972$		0			0
$973$		0			0
$974$	−29.4236	+	16.9877i	−0.942794	+	0.544322i
$975$		0			0
$976$	−6.28199	−	3.62691i	−0.201082	−	0.116094i
$977$	−26.8034	−	15.4749i	−0.857515	−	0.495087i	0.00566423	−	0.999984i	$-0.498197\pi$
$977$	−26.8034	−	15.4749i	−0.857515	−	0.495087i	−0.863179	+	0.504897i	$0.831530\pi$
$978$		0			0
$979$	52.8044	−	30.4866i	1.68764	−	0.974357i
$980$		0			0
$981$		0			0
$982$	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	$0.659515\pi$
$984$		0			0
$985$	−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
$990$		0			0
$991$	−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
$993$		0			0
$994$		0			0
$995$	71.0545	+	41.0234i	2.25258	+	1.30053i
$996$		0			0
$997$	39.9943	−	23.0907i	1.26663	−	0.731290i	0.292282	−	0.956332i	$-0.405585\pi$
$997$	39.9943	−	23.0907i	1.26663	−	0.731290i	0.974349	+	0.225042i	$0.0722520\pi$
$998$		−	10.7729i		−	0.341010i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.4	✓	16	21.17	even	6
126.2.l.a.101.8	yes	16	63.16	even	3
126.2.t.a.47.8	yes	16	63.52	odd	6
126.2.t.a.59.8	yes	16	21.2	odd	6
378.2.l.a.143.4		16	63.2	odd	6
378.2.l.a.341.8		16	7.3	odd	6
378.2.t.a.17.4		16	7.2	even	3
378.2.t.a.89.4		16	63.38	even	6
882.2.l.b.227.5		16	63.61	odd	6
882.2.l.b.509.1		16	21.11	odd	6
882.2.m.a.293.2		16	3.2	odd	2
882.2.m.a.587.2		16	63.34	odd	6
882.2.m.b.293.3		16	21.20	even	2
882.2.m.b.587.3		16	9.7	even	3
882.2.t.a.803.5		16	63.25	even	3
882.2.t.a.815.5		16	21.5	even	6
1008.2.ca.c.257.2		16	84.59	odd	6
1008.2.ca.c.353.2		16	252.79	odd	6
1008.2.df.c.689.1		16	84.23	even	6
1008.2.df.c.929.1		16	252.115	even	6
1134.2.k.a.647.5		16	63.58	even	3
1134.2.k.a.971.5		16	63.59	even	6
1134.2.k.b.647.4		16	63.23	odd	6
1134.2.k.b.971.4		16	63.31	odd	6
2646.2.l.a.521.1		16	63.47	even	6
2646.2.l.a.1097.5		16	7.4	even	3
2646.2.m.a.881.5		16	1.1	even	1	trivial
2646.2.m.a.1763.5		16	63.20	even	6	inner
2646.2.m.b.881.8		16	7.6	odd	2
2646.2.m.b.1763.8		16	9.2	odd	6
2646.2.t.b.1979.1		16	63.11	odd	6
2646.2.t.b.2285.1		16	7.5	odd	6
3024.2.ca.c.2033.8		16	252.191	even	6
3024.2.ca.c.2609.8		16	28.3	even	6
3024.2.df.c.17.8		16	28.23	odd	6
3024.2.df.c.1601.8		16	252.227	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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.82207 + 3.15592i) q^{5} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.82207 + 3.15592i) q^{5} -1.00000i q^{8} +3.64414i q^{10} +(4.38809 - 2.53346i) q^{11} +(-2.94391 - 1.69967i) q^{13} +(-0.500000 - 0.866025i) q^{16} +1.54939 q^{17} -0.816535i q^{19} +(1.82207 + 3.15592i) q^{20} +(2.53346 - 4.38809i) q^{22} +(1.47275 + 0.850294i) q^{23} +(-4.13989 - 7.17050i) q^{25} -3.39934 q^{26} +(3.60693 - 2.08246i) q^{29} +(1.87924 + 1.08498i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.34181 - 0.774696i) q^{34} +6.79957 q^{37} +(-0.408267 - 0.707140i) q^{38} +(3.15592 + 1.82207i) q^{40} +(1.01681 - 1.76117i) q^{41} +(3.06189 + 5.30335i) q^{43} -5.06693i q^{44} +1.70059 q^{46} +(3.37127 + 5.83922i) q^{47} +(-7.17050 - 4.13989i) q^{50} +(-2.94391 + 1.69967i) q^{52} +13.2745i q^{53} +18.4646i q^{55} +(2.08246 - 3.60693i) q^{58} +(1.08816 - 1.88475i) q^{59} +(6.28199 - 3.62691i) q^{61} +2.16996 q^{62} -1.00000 q^{64} +(10.7280 - 6.19384i) q^{65} +(-1.22820 + 2.12731i) q^{67} +(0.774696 - 1.34181i) q^{68} +6.74272i q^{71} -4.35220i q^{73} +(5.88860 - 3.39979i) q^{74} +(-0.707140 - 0.408267i) q^{76} +(-6.37651 - 11.0444i) q^{79} +3.64414 q^{80} -2.03363i q^{82} +(0.768040 + 1.33028i) q^{83} +(-2.82310 + 4.88976i) q^{85} +(5.30335 + 3.06189i) q^{86} +(-2.53346 - 4.38809i) q^{88} +12.0336 q^{89} +(1.47275 - 0.850294i) q^{92} +(5.83922 + 3.37127i) q^{94} +(2.57692 + 1.48778i) q^{95} +(5.59509 - 3.23033i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} + 12 q^{11} - 6 q^{13} - 8 q^{16} + 36 q^{17} - 6 q^{23} - 8 q^{25} - 24 q^{26} - 6 q^{29} - 6 q^{31} + 4 q^{37} - 6 q^{41} - 2 q^{43} - 12 q^{46} + 18 q^{47} + 12 q^{50} - 6 q^{52} + 6 q^{58} - 30 q^{59} + 60 q^{61} + 36 q^{62} - 16 q^{64} + 42 q^{65} + 14 q^{67} + 18 q^{68} + 18 q^{74} - 16 q^{79} - 12 q^{85} + 24 q^{86} + 48 q^{89} - 6 q^{92} - 66 q^{95} - 6 q^{97}+O(q^{100}) \) 16 * q + 8 * q^4 + 12 * q^11 - 6 * q^13 - 8 * q^16 + 36 * q^17 - 6 * q^23 - 8 * q^25 - 24 * q^26 - 6 * q^29 - 6 * q^31 + 4 * q^37 - 6 * q^41 - 2 * q^43 - 12 * q^46 + 18 * q^47 + 12 * q^50 - 6 * q^52 + 6 * q^58 - 30 * q^59 + 60 * q^61 + 36 * q^62 - 16 * q^64 + 42 * q^65 + 14 * q^67 + 18 * q^68 + 18 * q^74 - 16 * q^79 - 12 * q^85 + 24 * q^86 + 48 * q^89 - 6 * q^92 - 66 * q^95 - 6 * q^97

Introduction

L-functions

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