LMFDB - Embedded newform 378.2.l.a.143.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(143,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("378.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.l (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:	$3.01834519640$
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			143.4
Root			$0.765614 - 1.55365i$ of defining polynomial
Character	$\chi$	$=$	378.143
Dual form			378.2.l.a.341.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -1.00000 q^{4} +(1.82207 - 3.15592i) q^{5} +(-1.58246 - 2.12034i) q^{7} +1.00000i q^{8} +(-3.15592 - 1.82207i) q^{10} +(-4.38809 + 2.53346i) q^{11} +(2.94391 - 1.69967i) q^{13} +(-2.12034 + 1.58246i) q^{14} +1.00000 q^{16} +(0.774696 - 1.34181i) q^{17} +(-0.707140 + 0.408267i) q^{19} +(-1.82207 + 3.15592i) q^{20} +(2.53346 + 4.38809i) q^{22} +(-1.47275 - 0.850294i) q^{23} +(-4.13989 - 7.17050i) q^{25} +(-1.69967 - 2.94391i) q^{26} +(1.58246 + 2.12034i) q^{28} +(3.60693 + 2.08246i) q^{29} -2.16996i q^{31} -1.00000i q^{32} +(-1.34181 - 0.774696i) q^{34} +(-9.57497 + 1.13071i) q^{35} +(-3.39979 - 5.88860i) q^{37} +(0.408267 + 0.707140i) q^{38} +(3.15592 + 1.82207i) q^{40} +(-1.01681 - 1.76117i) q^{41} +(3.06189 - 5.30335i) q^{43} +(4.38809 - 2.53346i) q^{44} +(-0.850294 + 1.47275i) q^{46} +6.74255 q^{47} +(-1.99165 + 6.71069i) q^{49} +(-7.17050 + 4.13989i) q^{50} +(-2.94391 + 1.69967i) q^{52} +(11.4961 + 6.63726i) q^{53} +18.4646i q^{55} +(2.12034 - 1.58246i) q^{56} +(2.08246 - 3.60693i) q^{58} +2.17632 q^{59} +7.25382i q^{61} -2.16996 q^{62} -1.00000 q^{64} -12.3877i q^{65} +2.45641 q^{67} +(-0.774696 + 1.34181i) q^{68} +(1.13071 + 9.57497i) q^{70} -6.74272i q^{71} +(3.76912 + 2.17610i) q^{73} +(-5.88860 + 3.39979i) q^{74} +(0.707140 - 0.408267i) q^{76} +(12.3158 + 5.29511i) q^{77} +12.7530 q^{79} +(1.82207 - 3.15592i) q^{80} +(-1.76117 + 1.01681i) q^{82} +(-0.768040 + 1.33028i) q^{83} +(-2.82310 - 4.88976i) q^{85} +(-5.30335 - 3.06189i) q^{86} +(-2.53346 - 4.38809i) q^{88} +(6.01679 + 10.4214i) q^{89} +(-8.26249 - 3.55243i) q^{91} +(1.47275 + 0.850294i) q^{92} -6.74255i q^{94} +2.97557i q^{95} +(-5.59509 - 3.23033i) q^{97} +(6.71069 + 1.99165i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 2 q^{7} - 12 q^{11} + 6 q^{13} + 6 q^{14} + 16 q^{16} + 18 q^{17} + 6 q^{23} - 8 q^{25} - 12 q^{26} - 2 q^{28} - 6 q^{29} - 30 q^{35} - 2 q^{37} + 6 q^{41} - 2 q^{43} + 12 q^{44} + 6 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 16 * q - 16 * q^4 + 2 * q^7 - 12 * q^11 + 6 * q^13 + 6 * q^14 + 16 * q^16 + 18 * q^17 + 6 * q^23 - 8 * q^25 - 12 * q^26 - 2 * q^28 - 6 * q^29 - 30 * q^35 - 2 * q^37 + 6 * q^41 - 2 * q^43 + 12 * q^44 + 6 * q^46 + 36 * q^47 - 8 * q^49 + 12 * q^50 - 6 * q^52 + 36 * q^53 - 6 * q^56 + 6 * q^58 - 60 * q^59 - 36 * q^62 - 16 * q^64 - 28 * q^67 - 18 * q^68 - 18 * q^70 - 18 * q^74 + 42 * q^77 + 32 * q^79 - 12 * q^85 - 24 * q^86 + 24 * q^89 - 12 * q^91 - 6 * q^92 + 6 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	1.82207	−	3.15592i	0.814855	−	1.41137i	−0.0945763	−	0.995518i	$-0.530150\pi$
$5$	1.82207	−	3.15592i	0.814855	−	1.41137i	0.909432	−	0.415853i	$-0.136517\pi$
$6$		0			0
$7$	−1.58246	−	2.12034i	−0.598113	−	0.801412i
$7$	−1.58246	−	2.12034i	−0.598113	−	0.801412i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−3.15592	−	1.82207i	−0.997990	−	0.576190i
$11$	−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	$0.610035\pi$
$12$		0			0
$13$	2.94391	−	1.69967i	0.816495	−	0.471404i	−0.0327114	−	0.999465i	$-0.510414\pi$
$13$	2.94391	−	1.69967i	0.816495	−	0.471404i	0.849206	+	0.528061i	$0.177081\pi$
$14$	−2.12034	+	1.58246i	−0.566684	+	0.422930i
$15$		0			0
$16$	1.00000			0.250000
$17$	0.774696	−	1.34181i	0.187891	−	0.325438i	−0.756656	−	0.653814i	$-0.773168\pi$
$17$	0.774696	−	1.34181i	0.187891	−	0.325438i	0.944547	+	0.328376i	$0.106501\pi$
$18$		0			0
$19$	−0.707140	+	0.408267i	−0.162229	+	0.0936629i	−0.578916	−	0.815387i	$-0.696524\pi$
$19$	−0.707140	+	0.408267i	−0.162229	+	0.0936629i	0.416687	+	0.909050i	$0.363191\pi$
$20$	−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	$0.723402\pi$
$24$		0			0
$25$	−4.13989	−	7.17050i	−0.827979	−	1.43410i
$26$	−1.69967	−	2.94391i	−0.333333	−	0.577349i
$27$		0			0
$28$	1.58246	+	2.12034i	0.299057	+	0.400706i
$29$	3.60693	+	2.08246i	0.669789	+	0.386703i	0.795997	−	0.605301i	$-0.206947\pi$
$29$	3.60693	+	2.08246i	0.669789	+	0.386703i	−0.126208	+	0.992004i	$0.540281\pi$
$30$		0			0
$31$		−	2.16996i		−	0.389736i	−0.980830	−	0.194868i	$-0.937572\pi$
$31$		−	2.16996i		−	0.389736i	0.980830	−	0.194868i	$-0.0624278\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−1.34181	−	0.774696i	−0.230119	−	0.132859i
$35$	−9.57497	+	1.13071i	−1.61846	+	0.191125i
$36$		0			0
$37$	−3.39979	−	5.88860i	−0.558921	−	0.968080i	−0.997587	−	0.0694297i	$-0.977882\pi$
$37$	−3.39979	−	5.88860i	−0.558921	−	0.968080i	0.438666	−	0.898650i	$-0.355451\pi$
$38$	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	$-0.217429\pi$
$41$	−1.01681	−	1.76117i	−0.158799	−	0.275049i	−0.934436	+	0.356131i	$0.884096\pi$
$42$		0			0
$43$	3.06189	−	5.30335i	0.466934	−	0.808753i	−0.532353	−	0.846523i	$-0.678692\pi$
$43$	3.06189	−	5.30335i	0.466934	−	0.808753i	0.999286	+	0.0377695i	$0.0120253\pi$
$44$	4.38809	−	2.53346i	0.661529	−	0.381934i
$45$		0			0
$46$	−0.850294	+	1.47275i	−0.125369	+	0.217146i
$47$	6.74255			0.983502			0.491751	−	0.870736i	$-0.336357\pi$
$47$	6.74255			0.983502			0.491751	+	0.870736i	$0.336357\pi$
$48$		0			0
$49$	−1.99165	+	6.71069i	−0.284521	+	0.958670i
$50$	−7.17050	+	4.13989i	−1.01406	+	0.585469i
$51$		0			0
$52$	−2.94391	+	1.69967i	−0.408247	+	0.235702i
$53$	11.4961	+	6.63726i	1.57911	+	0.911698i	0.994984	+	0.100032i	$0.0318946\pi$
$53$	11.4961	+	6.63726i	1.57911	+	0.911698i	0.584123	+	0.811665i	$0.301439\pi$
$54$		0			0
$55$			18.4646i			2.48977i
$56$	2.12034	−	1.58246i	0.283342	−	0.211465i
$57$		0			0
$58$	2.08246	−	3.60693i	0.273440	−	0.473612i
$59$	2.17632			0.283333			0.141666	−	0.989914i	$-0.454754\pi$
$59$	2.17632			0.283333			0.141666	+	0.989914i	$0.454754\pi$
$60$		0			0
$61$			7.25382i			0.928756i	0.885637	+	0.464378i	$0.153722\pi$
$61$			7.25382i			0.928756i	−0.885637	+	0.464378i	$0.846278\pi$
$62$	−2.16996			−0.275585
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	12.3877i		−	1.53650i
$66$		0			0
$67$	2.45641			0.300098			0.150049	−	0.988679i	$-0.452057\pi$
$67$	2.45641			0.300098			0.150049	+	0.988679i	$0.452057\pi$
$68$	−0.774696	+	1.34181i	−0.0939457	+	0.162719i
$69$		0			0
$70$	1.13071	+	9.57497i	0.135146	+	1.14443i
$71$		−	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			0
$73$	3.76912	+	2.17610i	0.441142	+	0.254694i	0.704082	−	0.710119i	$-0.251359\pi$
$73$	3.76912	+	2.17610i	0.441142	+	0.254694i	−0.262940	+	0.964812i	$0.584692\pi$
$74$	−5.88860	+	3.39979i	−0.684536	+	0.395217i
$75$		0			0
$76$	0.707140	−	0.408267i	0.0811145	−	0.0468315i
$77$	12.3158	+	5.29511i	1.40351	+	0.603434i
$78$		0			0
$79$	12.7530			1.43483			0.717414	−	0.696647i	$-0.245326\pi$
$79$	12.7530			1.43483			0.717414	+	0.696647i	$0.245326\pi$
$80$	1.82207	−	3.15592i	0.203714	−	0.352843i
$81$		0			0
$82$	−1.76117	+	1.01681i	−0.194489	+	0.112288i
$83$	−0.768040	+	1.33028i	−0.0843034	+	0.146018i	−0.905094	−	0.425211i	$-0.860200\pi$
$83$	−0.768040	+	1.33028i	−0.0843034	+	0.146018i	0.820791	+	0.571229i	$0.193533\pi$
$84$		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
$89$	6.01679	+	10.4214i	0.637778	+	1.10466i	0.985919	+	0.167222i	$0.0534798\pi$
$89$	6.01679	+	10.4214i	0.637778	+	1.10466i	−0.348141	+	0.937442i	$0.613187\pi$
$90$		0			0
$91$	−8.26249	−	3.55243i	−0.866145	−	0.372396i
$92$	1.47275	+	0.850294i	0.153545	+	0.0886493i
$93$		0			0
$94$		−	6.74255i		−	0.695441i
$95$			2.97557i			0.305287i
$96$		0			0
$97$	−5.59509	−	3.23033i	−0.568095	−	0.327990i	0.188293	−	0.982113i	$-0.439705\pi$
$97$	−5.59509	−	3.23033i	−0.568095	−	0.327990i	−0.756388	+	0.654123i	$0.773038\pi$
$98$	6.71069	+	1.99165i	0.677882	+	0.201187i
$99$		0			0
$100$	4.13989	+	7.17050i	0.413989	+	0.717050i
$101$	−5.95045	−	10.3065i	−0.592092	−	1.02553i	−0.993950	−	0.109831i	$-0.964969\pi$
$101$	−5.95045	−	10.3065i	−0.592092	−	1.02553i	0.401858	−	0.915702i	$-0.368364\pi$
$102$		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
$107$	2.87453	−	1.65961i	0.277891	−	0.160440i	−0.354577	−	0.935027i	$-0.615375\pi$
$107$	2.87453	−	1.65961i	0.277891	−	0.160440i	0.632468	+	0.774586i	$0.282042\pi$
$108$		0			0
$109$	1.41837	−	2.45668i	0.135855	−	0.235308i	−0.790069	−	0.613018i	$-0.789955\pi$
$109$	1.41837	−	2.45668i	0.135855	−	0.235308i	0.925924	+	0.377711i	$0.123289\pi$
$110$	18.4646			1.76053
$111$		0			0
$112$	−1.58246	−	2.12034i	−0.149528	−	0.200353i
$113$	6.80465	−	3.92866i	0.640127	−	0.369578i	−0.144536	−	0.989500i	$-0.546169\pi$
$113$	6.80465	−	3.92866i	0.640127	−	0.369578i	0.784664	+	0.619922i	$0.212836\pi$
$114$		0			0
$115$	−5.36692	+	3.09859i	−0.500468	+	0.288945i
$116$	−3.60693	−	2.08246i	−0.334895	−	0.193351i
$117$		0			0
$118$		−	2.17632i		−	0.200346i
$119$	−4.07102	+	0.480749i	−0.373190	+	0.0440702i
$120$		0			0
$121$	7.33687	−	12.7078i	0.666988	−	1.15526i
$122$	7.25382			0.656730
$123$		0			0
$124$			2.16996i			0.194868i
$125$	−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	$0.781364\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	−12.3877			−1.08647
$131$	−1.61603	+	2.79904i	−0.141193	+	0.244554i	−0.927946	−	0.372714i	$-0.878427\pi$
$131$	−1.61603	+	2.79904i	−0.141193	+	0.244554i	0.786753	+	0.617268i	$0.211760\pi$
$132$		0			0
$133$	1.98468	+	0.853307i	0.172094	+	0.0739911i
$134$		−	2.45641i		−	0.212201i
$135$		0			0
$136$	1.34181	+	0.774696i	0.115060	+	0.0664297i
$137$	−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			0
$139$	−4.97814	+	2.87413i	−0.422240	+	0.243780i	−0.696035	−	0.718008i	$-0.745054\pi$
$139$	−4.97814	+	2.87413i	−0.422240	+	0.243780i	0.273795	+	0.961788i	$0.411721\pi$
$140$	9.57497	−	1.13071i	0.809232	−	0.0955626i
$141$		0			0
$142$	−6.74272			−0.565836
$143$	−8.61210	+	14.9166i	−0.720180	+	1.24739i
$144$		0			0
$145$	13.1442	−	7.58878i	1.09156	−	0.630214i
$146$	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	$0.742030\pi$
$150$		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	$0.659418\pi$
$152$	−0.408267	−	0.707140i	−0.0331148	−	0.0573566i
$153$		0			0
$154$	5.29511	−	12.3158i	0.426692	−	0.992432i
$155$	−6.84821	−	3.95382i	−0.550062	−	0.317578i
$156$		0			0
$157$			12.7707i			1.01921i	0.860407	+	0.509607i	$0.170209\pi$
$157$			12.7707i			1.01921i	−0.860407	+	0.509607i	$0.829791\pi$
$158$		−	12.7530i		−	1.01458i
$159$		0			0
$160$	−3.15592	−	1.82207i	−0.249497	−	0.144047i
$161$	0.527662	+	4.46829i	0.0415856	+	0.352150i
$162$		0			0
$163$	−1.51018	−	2.61570i	−0.118286	−	0.204878i	0.800802	−	0.598929i	$-0.204407\pi$
$163$	−1.51018	−	2.61570i	−0.118286	−	0.204878i	−0.919089	+	0.394051i	$0.871073\pi$
$164$	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	0.998048	+	0.0624443i	$0.0198896\pi$
$167$	7.14766	+	12.3801i	0.553103	+	0.958002i	−0.444946	+	0.895557i	$0.646777\pi$
$168$		0			0
$169$	−0.722247	+	1.25097i	−0.0555575	+	0.0962284i
$170$	−4.88976	+	2.82310i	−0.375028	+	0.216522i
$171$		0			0
$172$	−3.06189	+	5.30335i	−0.233467	+	0.404377i
$173$	−2.19905			−0.167191			−0.0835954	−	0.996500i	$-0.526640\pi$
$173$	−2.19905			−0.167191			−0.0835954	+	0.996500i	$0.526640\pi$
$174$		0			0
$175$	−8.65267	+	20.1250i	−0.654080	+	1.52131i
$176$	−4.38809	+	2.53346i	−0.330764	+	0.190967i
$177$		0			0
$178$	10.4214	−	6.01679i	0.781116	−	0.450977i
$179$	−9.30715	−	5.37349i	−0.695649	−	0.401633i	0.110076	−	0.993923i	$-0.464891\pi$
$179$	−9.30715	−	5.37349i	−0.695649	−	0.401633i	−0.805725	+	0.592290i	$0.798224\pi$
$180$		0			0
$181$		−	14.4710i		−	1.07562i	−0.843065	−	0.537811i	$-0.819251\pi$
$181$		−	14.4710i		−	1.07562i	0.843065	−	0.537811i	$-0.180749\pi$
$182$	−3.55243	+	8.26249i	−0.263323	+	0.612457i
$183$		0			0
$184$	0.850294	−	1.47275i	0.0626845	−	0.108573i
$185$	−24.7786			−1.82176
$186$		0			0
$187$			7.85066i			0.574097i
$188$	−6.74255			−0.491751
$189$		0			0
$190$	2.97557			0.215871
$191$		−	8.33194i		−	0.602878i	−0.953485	−	0.301439i	$-0.902533\pi$
$191$		−	8.33194i		−	0.602878i	0.953485	−	0.301439i	$-0.0974670\pi$
$192$		0			0
$193$	−9.56786			−0.688710			−0.344355	−	0.938840i	$-0.611902\pi$
$193$	−9.56786			−0.688710			−0.344355	+	0.938840i	$0.611902\pi$
$194$	−3.23033	+	5.59509i	−0.231924	+	0.401704i
$195$		0			0
$196$	1.99165	−	6.71069i	0.142260	−	0.479335i
$197$		−	2.37228i		−	0.169018i	−0.996423	−	0.0845089i	$-0.973068\pi$
$197$		−	2.37228i		−	0.169018i	0.996423	−	0.0845089i	$-0.0269322\pi$
$198$		0			0
$199$	19.4983	+	11.2573i	1.38220	+	0.798011i	0.992419	−	0.122898i	$-0.0392188\pi$
$199$	19.4983	+	11.2573i	1.38220	+	0.798011i	0.389777	+	0.920909i	$0.372552\pi$
$200$	7.17050	−	4.13989i	0.507031	−	0.292735i
$201$		0			0
$202$	−10.3065	+	5.95045i	−0.725161	+	0.418672i
$203$	−1.29230	−	10.9433i	−0.0907016	−	0.768069i
$204$		0			0
$205$	−7.41083			−0.517594
$206$	7.34240	−	12.7174i	0.511569	−	0.886064i
$207$		0			0
$208$	2.94391	−	1.69967i	0.204124	−	0.117851i
$209$	2.06866	−	3.58302i	0.143092	−	0.247843i
$210$		0			0
$211$	−7.27211	−	12.5957i	−0.500632	−	0.867121i	−1.00000		0.000730453i	$-0.999767\pi$
$211$	−7.27211	−	12.5957i	−0.500632	−	0.867121i	0.499367	−	0.866390i	$-0.333566\pi$
$212$	−11.4961	−	6.63726i	−0.789553	−	0.455849i
$213$		0			0
$214$	−1.65961	−	2.87453i	−0.113449	−	0.196499i
$215$	−11.1580	−	19.3262i	−0.760967	−	1.31803i
$216$		0			0
$217$	−4.60104	+	3.43387i	−0.312339	+	0.233106i
$218$	−2.45668	−	1.41837i	−0.166388	−	0.0960640i
$219$		0			0
$220$		−	18.4646i		−	1.24488i
$221$		−	5.26691i		−	0.354291i
$222$		0			0
$223$	−22.5221	−	13.0031i	−1.50819	−	0.870753i	−0.999955	−	0.00953489i	$-0.996965\pi$
$223$	−22.5221	−	13.0031i	−1.50819	−	0.870753i	−0.508235	−	0.861219i	$-0.669702\pi$
$224$	−2.12034	+	1.58246i	−0.141671	+	0.105732i
$225$		0			0
$226$	−3.92866	−	6.80465i	−0.261331	−	0.452638i
$227$	11.4390	+	19.8129i	0.759231	+	1.31503i	0.943243	+	0.332103i	$0.107758\pi$
$227$	11.4390	+	19.8129i	0.759231	+	1.31503i	−0.184012	+	0.982924i	$0.558909\pi$
$228$		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
$233$	3.82003	−	2.20550i	0.250259	−	0.144487i	−0.369624	−	0.929181i	$-0.620514\pi$
$233$	3.82003	−	2.20550i	0.250259	−	0.144487i	0.619883	+	0.784694i	$0.287180\pi$
$234$		0			0
$235$	12.2854	−	21.2789i	0.801412	−	1.38809i
$236$	−2.17632			−0.141666
$237$		0			0
$238$	0.480749	+	4.07102i	0.0311623	+	0.263885i
$239$	−16.1660	+	9.33343i	−1.04569	+	0.603729i	−0.921440	−	0.388522i	$-0.872986\pi$
$239$	−16.1660	+	9.33343i	−1.04569	+	0.603729i	−0.124250	+	0.992251i	$0.539653\pi$
$240$		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	$0.328450\pi$
$242$	−12.7078	−	7.33687i	−0.816890	−	0.471632i
$243$		0			0
$244$		−	7.25382i		−	0.464378i
$245$	17.5495	+	18.5128i	1.12120	+	1.18274i
$246$		0			0
$247$	−1.38784	+	2.40381i	−0.0883061	+	0.152951i
$248$	2.16996			0.137792
$249$		0			0
$250$			11.9520i			0.755912i
$251$	17.6939			1.11683			0.558415	−	0.829562i	$-0.311410\pi$
$251$	17.6939			1.11683			0.558415	+	0.829562i	$0.311410\pi$
$252$		0			0
$253$	8.61675			0.541731
$254$			17.4279i			1.09352i
$255$		0			0
$256$	1.00000			0.0625000
$257$	11.5971	−	20.0867i	0.723405	−	1.25297i	−0.236222	−	0.971699i	$-0.575909\pi$
$257$	11.5971	−	20.0867i	0.723405	−	1.25297i	0.959627	−	0.281275i	$-0.0907573\pi$
$258$		0			0
$259$	−7.10579	+	16.5272i	−0.441532	+	1.02695i
$260$			12.3877i			0.768251i
$261$		0			0
$262$	2.79904	+	1.61603i	0.172925	+	0.0998386i
$263$	−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	$0.367195\pi$
$264$		0			0
$265$	41.8933	−	24.1871i	2.57349	−	1.48580i
$266$	0.853307	−	1.98468i	0.0523196	−	0.121689i
$267$		0			0
$268$	−2.45641			−0.150049
$269$	4.00690	−	6.94015i	0.244305	−	0.423148i	−0.717631	−	0.696423i	$-0.754774\pi$
$269$	4.00690	−	6.94015i	0.244305	−	0.423148i	0.961936	+	0.273275i	$0.0881069\pi$
$270$		0			0
$271$	−1.55095	+	0.895442i	−0.0942136	+	0.0543942i	−0.546367	−	0.837546i	$-0.683989\pi$
$271$	−1.55095	+	0.895442i	−0.0942136	+	0.0543942i	0.452153	+	0.891940i	$0.350656\pi$
$272$	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	$0.568707\pi$
$278$	2.87413	+	4.97814i	0.172379	+	0.298569i
$279$		0			0
$280$	−1.13071	−	9.57497i	−0.0675730	−	0.572214i
$281$	−18.6262	−	10.7539i	−1.11115	−	0.641521i	−0.172021	−	0.985093i	$-0.555030\pi$
$281$	−18.6262	−	10.7539i	−1.11115	−	0.641521i	−0.939126	+	0.343572i	$0.888363\pi$
$282$		0			0
$283$		−	19.9480i		−	1.18579i	−0.805281	−	0.592894i	$-0.797985\pi$
$283$		−	19.9480i		−	1.18579i	0.805281	−	0.592894i	$-0.202015\pi$
$284$			6.74272i			0.400107i
$285$		0			0
$286$	14.9166	+	8.61210i	0.882037	+	0.509244i
$287$	−2.12521	+	4.94297i	−0.125447	+	0.291774i
$288$		0			0
$289$	7.29969	+	12.6434i	0.429394	+	0.743732i
$290$	−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	$-0.143465\pi$
$293$	1.24656	+	2.15911i	0.0728251	+	0.126137i	−0.827313	+	0.561741i	$0.810132\pi$
$294$		0			0
$295$	3.96541	−	6.86829i	0.230875	−	0.399887i
$296$	5.88860	−	3.39979i	0.342268	−	0.197609i
$297$		0			0
$298$	−2.86310	+	4.95904i	−0.165855	+	0.287270i
$299$	−5.78088			−0.334317
$300$		0			0
$301$	−16.0902	+	1.90010i	−0.927423	+	0.109520i
$302$	11.0589	−	6.38483i	0.636365	−	0.367406i
$303$		0			0
$304$	−0.707140	+	0.408267i	−0.0405572	+	0.0234157i
$305$	22.8925	+	13.2170i	1.31082	+	0.756802i
$306$		0			0
$307$			9.23124i			0.526854i	0.964679	+	0.263427i	$0.0848529\pi$
$307$			9.23124i			0.526854i	−0.964679	+	0.263427i	$0.915147\pi$
$308$	−12.3158	−	5.29511i	−0.701755	−	0.301717i
$309$		0			0
$310$	−3.95382	+	6.84821i	−0.224562	+	0.388952i
$311$	−22.9714			−1.30259			−0.651294	−	0.758826i	$-0.725773\pi$
$311$	−22.9714			−1.30259			−0.651294	+	0.758826i	$0.725773\pi$
$312$		0			0
$313$			6.43336i			0.363635i	0.983332	+	0.181818i	$0.0581980\pi$
$313$			6.43336i			0.363635i	−0.983332	+	0.181818i	$0.941802\pi$
$314$	12.7707			0.720694
$315$		0			0
$316$	−12.7530			−0.717414
$317$		−	8.73533i		−	0.490625i	−0.969444	−	0.245313i	$-0.921109\pi$
$317$		−	8.73533i		−	0.490625i	0.969444	−	0.245313i	$-0.0788906\pi$
$318$		0			0
$319$	−21.1033			−1.18156
$320$	−1.82207	+	3.15592i	−0.101857	+	0.176421i
$321$		0			0
$322$	4.46829	−	0.527662i	0.249008	−	0.0294054i
$323$			1.26513i			0.0703939i
$324$		0			0
$325$	−24.3750	−	14.0729i	−1.35208	−	0.780624i
$326$	−2.61570	+	1.51018i	−0.144870	+	0.0836410i
$327$		0			0
$328$	1.76117	−	1.01681i	0.0972444	−	0.0561441i
$329$	−10.6698	−	14.2965i	−0.588245	−	0.788189i
$330$		0			0
$331$	31.7007			1.74243			0.871215	−	0.490901i	$-0.163332\pi$
$331$	31.7007			1.74243			0.871215	+	0.490901i	$0.163332\pi$
$332$	0.768040	−	1.33028i	0.0421517	−	0.0730088i
$333$		0			0
$334$	12.3801	−	7.14766i	0.677410	−	0.391103i
$335$	4.47575	−	7.75223i	0.244536	−	0.423549i
$336$		0			0
$337$	16.1308	+	27.9393i	0.878700	+	1.52195i	0.852768	+	0.522289i	$0.174922\pi$
$337$	16.1308	+	27.9393i	0.878700	+	1.52195i	0.0259314	+	0.999664i	$0.491745\pi$
$338$	1.25097	+	0.722247i	0.0680437	+	0.0392851i
$339$		0			0
$340$	2.82310	+	4.88976i	0.153104	+	0.265185i
$341$	5.49750	+	9.52196i	0.297707	+	0.515643i
$342$		0			0
$343$	17.3806	−	6.39643i	0.938465	−	0.345375i
$344$	5.30335	+	3.06189i	0.285937	+	0.165086i
$345$		0			0
$346$			2.19905i			0.118222i
$347$			6.82421i			0.366343i	0.983081	+	0.183171i	$0.0586363\pi$
$347$			6.82421i			0.366343i	−0.983081	+	0.183171i	$0.941364\pi$
$348$		0			0
$349$	−4.18379	−	2.41551i	−0.223953	−	0.129299i	0.383826	−	0.923405i	$-0.374606\pi$
$349$	−4.18379	−	2.41551i	−0.223953	−	0.129299i	−0.607779	+	0.794106i	$0.707939\pi$
$350$	20.1250	+	8.65267i	1.07573	+	0.462504i
$351$		0			0
$352$	2.53346	+	4.38809i	0.135034	+	0.233886i
$353$	17.2922	+	29.9510i	0.920371	+	1.59413i	0.798842	+	0.601541i	$0.205446\pi$
$353$	17.2922	+	29.9510i	0.920371	+	1.59413i	0.121529	+	0.992588i	$0.461220\pi$
$354$		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
$359$	−23.5112	+	13.5742i	−1.24087	+	0.716417i	−0.969272	−	0.245993i	$-0.920886\pi$
$359$	−23.5112	+	13.5742i	−1.24087	+	0.716417i	−0.271600	+	0.962410i	$0.587553\pi$
$360$		0			0
$361$	−9.16664	+	15.8771i	−0.482455	+	0.835636i
$362$	−14.4710			−0.760580
$363$		0			0
$364$	8.26249	+	3.55243i	0.433072	+	0.186198i
$365$	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	$0.434112\pi$
$368$	−1.47275	−	0.850294i	−0.0767725	−	0.0443246i
$369$		0			0
$370$			24.7786i			1.28818i
$371$	−4.11884	−	34.8787i	−0.213840	−	1.81081i
$372$		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	$0.246943\pi$
$374$	7.85066			0.405948
$375$		0			0
$376$			6.74255i			0.347720i
$377$	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	$0.634927\pi$
$380$		−	2.97557i		−	0.152643i
$381$		0			0
$382$	−8.33194			−0.426299
$383$	3.18472	−	5.51610i	0.162732	−	0.281860i	−0.773116	−	0.634265i	$-0.781303\pi$
$383$	3.18472	−	5.51610i	0.162732	−	0.281860i	0.935847	+	0.352405i	$0.114636\pi$
$384$		0			0
$385$	39.1512	−	29.2195i	1.99533	−	1.48916i
$386$			9.56786i			0.486991i
$387$		0			0
$388$	5.59509	+	3.23033i	0.284048	+	0.163995i
$389$	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	$0.186543\pi$
$390$		0			0
$391$	−2.28187	+	1.31744i	−0.115399	+	0.0666258i
$392$	−6.71069	−	1.99165i	−0.338941	−	0.100593i
$393$		0			0
$394$	−2.37228			−0.119514
$395$	23.2369	−	40.2476i	1.16918	−	2.02507i
$396$		0			0
$397$	11.5693	−	6.67955i	0.580647	−	0.335237i	−0.180743	−	0.983530i	$-0.557850\pi$
$397$	11.5693	−	6.67955i	0.580647	−	0.335237i	0.761391	+	0.648293i	$0.224517\pi$
$398$	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	$0.700335\pi$
$402$		0			0
$403$	−3.68821	−	6.38817i	−0.183723	−	0.318217i
$404$	5.95045	+	10.3065i	0.296046	+	0.512767i
$405$		0			0
$406$	−10.9433	+	1.29230i	−0.543107	+	0.0641357i
$407$	29.8371	+	17.2265i	1.47897	+	0.853884i
$408$		0			0
$409$			38.4154i			1.89952i	0.312982	+	0.949759i	$0.398672\pi$
$409$			38.4154i			1.89952i	−0.312982	+	0.949759i	$0.601328\pi$
$410$			7.41083i			0.365995i
$411$		0			0
$412$	−12.7174	−	7.34240i	−0.626542	−	0.361734i
$413$	−3.44394	−	4.61453i	−0.169465	−	0.227066i
$414$		0			0
$415$	2.79885	+	4.84775i	0.137390	+	0.237967i
$416$	−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	$-0.278308\pi$
$419$	−7.03301	−	12.1815i	−0.343585	−	0.595107i	−0.985096	+	0.172007i	$0.944975\pi$
$420$		0			0
$421$	10.5504	−	18.2738i	0.514195	−	0.890612i	−0.485670	−	0.874143i	$-0.661424\pi$
$421$	10.5504	−	18.2738i	0.514195	−	0.890612i	0.999864	−	0.0164691i	$-0.00524252\pi$
$422$	−12.5957	+	7.27211i	−0.613147	+	0.354001i
$423$		0			0
$424$	−6.63726	+	11.4961i	−0.322334	+	0.558299i
$425$	−12.8286			−0.622280
$426$		0			0
$427$	15.3805	−	11.4789i	0.744316	−	0.555501i
$428$	−2.87453	+	1.65961i	−0.138946	+	0.0802202i
$429$		0			0
$430$	−19.3262	+	11.1580i	−0.931991	+	0.538085i
$431$	−10.0928	−	5.82709i	−0.486154	−	0.280681i	0.236824	−	0.971553i	$-0.423894\pi$
$431$	−10.0928	−	5.82709i	−0.486154	−	0.280681i	−0.722977	+	0.690872i	$0.757227\pi$
$432$		0			0
$433$			17.9149i			0.860936i	0.902606	+	0.430468i	$0.141652\pi$
$433$			17.9149i			0.860936i	−0.902606	+	0.430468i	$0.858348\pi$
$434$	3.43387	+	4.60104i	0.164831	+	0.220857i
$435$		0			0
$436$	−1.41837	+	2.45668i	−0.0679275	+	0.117654i
$437$	1.38859			0.0664252
$438$		0			0
$439$			19.0275i			0.908135i	0.890967	+	0.454068i	$0.150028\pi$
$439$			19.0275i			0.908135i	−0.890967	+	0.454068i	$0.849972\pi$
$440$	−18.4646			−0.880266
$441$		0			0
$442$	−5.26691			−0.250521
$443$			7.67734i			0.364761i	0.983228	+	0.182381i	$0.0583803\pi$
$443$			7.67734i			0.364761i	−0.983228	+	0.182381i	$0.941620\pi$
$444$		0			0
$445$	43.8521			2.07879
$446$	−13.0031	+	22.5221i	−0.615716	+	1.06645i
$447$		0			0
$448$	1.58246	+	2.12034i	0.0747642	+	0.100176i
$449$		−	30.1018i		−	1.42059i	−0.703903	−	0.710296i	$-0.748561\pi$
$449$		−	30.1018i		−	1.42059i	0.703903	−	0.710296i	$-0.251439\pi$
$450$		0			0
$451$	8.92373	+	5.15212i	0.420202	+	0.242604i
$452$	−6.80465	+	3.92866i	−0.320064	+	0.184789i
$453$		0			0
$454$	19.8129	−	11.4390i	0.929864	−	0.536857i
$455$	−26.2660	+	19.6030i	−1.23137	+	0.919003i
$456$		0			0
$457$	−39.4876			−1.84715			−0.923576	−	0.383415i	$-0.874748\pi$
$457$	−39.4876			−1.84715			−0.923576	+	0.383415i	$0.874748\pi$
$458$	−13.4652	+	23.3224i	−0.629186	+	1.08978i
$459$		0			0
$460$	5.36692	−	3.09859i	0.250234	−	0.144473i
$461$	−11.3776	+	19.7066i	−0.529909	+	0.917830i	0.469482	+	0.882942i	$0.344441\pi$
$461$	−11.3776	+	19.7066i	−0.529909	+	0.917830i	−0.999391	+	0.0348879i	$0.988893\pi$
$462$		0			0
$463$	6.63866	+	11.4985i	0.308525	+	0.534381i	0.978040	−	0.208418i	$-0.0668314\pi$
$463$	6.63866	+	11.4985i	0.308525	+	0.534381i	−0.669515	+	0.742798i	$0.733498\pi$
$464$	3.60693	+	2.08246i	0.167447	+	0.0966757i
$465$		0			0
$466$	−2.20550	−	3.82003i	−0.102168	−	0.176960i
$467$	11.5873	+	20.0698i	0.536195	+	0.928717i	0.999104	+	0.0423116i	$0.0134722\pi$
$467$	11.5873	+	20.0698i	0.536195	+	0.928717i	−0.462909	+	0.886406i	$0.653194\pi$
$468$		0			0
$469$	−3.88716	−	5.20841i	−0.179493	−	0.240502i
$470$	−21.2789	−	12.2854i	−0.981525	−	0.566684i
$471$		0			0
$472$			2.17632i			0.100173i
$473$			31.0287i			1.42670i
$474$		0			0
$475$	5.85497	+	3.38037i	0.268644	+	0.155102i
$476$	4.07102	−	0.480749i	0.186595	−	0.0220351i
$477$		0			0
$478$	9.33343	+	16.1660i	0.426901	+	0.739414i
$479$	12.3567	+	21.4025i	0.564594	+	0.977905i	0.997087	+	0.0762684i	$0.0243006\pi$
$479$	12.3567	+	21.4025i	0.564594	+	0.977905i	−0.432493	+	0.901637i	$0.642366\pi$
$480$		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
$485$	−20.3893	+	11.7718i	−0.925831	+	0.534529i
$486$		0			0
$487$	16.9877	−	29.4236i	0.769788	−	1.33331i	−0.167889	−	0.985806i	$-0.553695\pi$
$487$	16.9877	−	29.4236i	0.769788	−	1.33331i	0.937678	−	0.347506i	$-0.112971\pi$
$488$	−7.25382			−0.328365
$489$		0			0
$490$	18.5128	−	17.5495i	0.836325	−	0.792805i
$491$	25.5933	−	14.7763i	1.15501	−	0.666845i	0.204906	−	0.978782i	$-0.434311\pi$
$491$	25.5933	−	14.7763i	1.15501	−	0.666845i	0.950103	+	0.311937i	$0.100978\pi$
$492$		0			0
$493$	5.58854	−	3.22655i	0.251695	−	0.145316i
$494$	2.40381	+	1.38784i	0.108152	+	0.0624418i
$495$		0			0
$496$		−	2.16996i		−	0.0974339i
$497$	−14.2968	+	10.6701i	−0.641300	+	0.478618i
$498$		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	$0.0891486\pi$
$500$	11.9520			0.534510
$501$		0			0
$502$		−	17.6939i		−	0.789718i
$503$	−20.2016			−0.900743			−0.450372	−	0.892841i	$-0.648708\pi$
$503$	−20.2016			−0.900743			−0.450372	+	0.892841i	$0.648708\pi$
$504$		0			0
$505$	−43.3686			−1.92988
$506$		−	8.61675i		−	0.383061i
$507$		0			0
$508$	17.4279			0.773237
$509$	0.529272	−	0.916725i	0.0234595	−	0.0406331i	−0.854057	−	0.520179i	$-0.825865\pi$
$509$	0.529272	−	0.916725i	0.0234595	−	0.0406331i	0.877517	+	0.479546i	$0.159199\pi$
$510$		0			0
$511$	−1.35041	−	11.4354i	−0.0597387	−	0.505872i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−20.0867	−	11.5971i	−0.885987	−	0.511525i
$515$	46.3441	−	26.7568i	2.04216	−	1.17904i
$516$		0			0
$517$	−29.5869	+	17.0820i	−1.30123	+	0.751265i
$518$	16.5272	+	7.10579i	0.726162	+	0.312210i
$519$		0			0
$520$	12.3877			0.543236
$521$	−5.05068	+	8.74804i	−0.221275	+	0.383259i	−0.955195	−	0.295976i	$-0.904355\pi$
$521$	−5.05068	+	8.74804i	−0.221275	+	0.383259i	0.733921	+	0.679235i	$0.237688\pi$
$522$		0			0
$523$	−8.02992	+	4.63608i	−0.351124	+	0.202722i	−0.665180	−	0.746683i	$-0.731645\pi$
$523$	−8.02992	+	4.63608i	−0.351124	+	0.202722i	0.314056	+	0.949404i	$0.398312\pi$
$524$	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
$530$	−24.1871	−	41.8933i	−1.05062	−	1.81973i
$531$		0			0
$532$	−1.98468	−	0.853307i	−0.0860469	−	0.0369956i
$533$	−5.98682	−	3.45649i	−0.259318	−	0.149717i
$534$		0			0
$535$		−	12.0957i		−	0.522943i
$536$			2.45641i			0.106101i
$537$		0			0
$538$	−6.94015	−	4.00690i	−0.299211	−	0.172750i
$539$	−8.26177	−	34.4928i	−0.355859	−	1.48571i
$540$		0			0
$541$	−2.87498	−	4.97960i	−0.123605	−	0.214090i	0.797582	−	0.603211i	$-0.206112\pi$
$541$	−2.87498	−	4.97960i	−0.123605	−	0.214090i	−0.921187	+	0.389121i	$0.872779\pi$
$542$	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	−0.147421	−	0.989074i	$-0.547097\pi$
$547$	18.3094	−	31.7128i	0.782853	−	1.35594i	0.930273	−	0.366867i	$-0.119570\pi$
$548$	12.6284	−	7.29101i	0.539459	−	0.311457i
$549$		0			0
$550$	20.9765	−	36.3324i	0.894442	−	1.54922i
$551$	−3.40080			−0.144879
$552$		0			0
$553$	−20.1811	−	27.0407i	−0.858190	−	1.14989i
$554$	21.2986	−	12.2968i	0.904892	−	0.522440i
$555$		0			0
$556$	4.97814	−	2.87413i	0.211120	−	0.121890i
$557$	0.323902	+	0.187005i	0.0137242	+	0.00792365i	0.506846	−	0.862036i	$-0.330811\pi$
$557$	0.323902	+	0.187005i	0.0137242	+	0.00792365i	−0.493122	+	0.869960i	$0.664144\pi$
$558$		0			0
$559$		−	20.8168i		−	0.880457i
$560$	−9.57497	+	1.13071i	−0.404616	+	0.0477813i
$561$		0			0
$562$	−10.7539	+	18.6262i	−0.453624	+	0.785700i
$563$	4.37923			0.184562			0.0922812	−	0.995733i	$-0.470584\pi$
$563$	4.37923			0.184562			0.0922812	+	0.995733i	$0.470584\pi$
$564$		0			0
$565$		−	28.6332i		−	1.20461i
$566$	−19.9480			−0.838478
$567$		0			0
$568$	6.74272			0.282918
$569$			36.8641i			1.54542i	0.634757	+	0.772712i	$0.281100\pi$
$569$			36.8641i			1.54542i	−0.634757	+	0.772712i	$0.718900\pi$
$570$		0			0
$571$	31.6595			1.32491			0.662454	−	0.749103i	$-0.269515\pi$
$571$	31.6595			1.32491			0.662454	+	0.749103i	$0.269515\pi$
$572$	8.61210	−	14.9166i	0.360090	−	0.623694i
$573$		0			0
$574$	4.94297	+	2.12521i	0.206315	+	0.0887045i
$575$			14.0805i			0.587198i
$576$		0			0
$577$	12.2923	+	7.09699i	0.511737	+	0.295452i	0.733547	−	0.679638i	$-0.237863\pi$
$577$	12.2923	+	7.09699i	0.511737	+	0.295452i	−0.221810	+	0.975090i	$0.571197\pi$
$578$	12.6434	−	7.29969i	0.525898	−	0.303627i
$579$		0			0
$580$	−13.1442	+	7.58878i	−0.545781	+	0.315107i
$581$	4.03604	−	0.476618i	0.167443	−	0.0197734i
$582$		0			0
$583$	−67.2610			−2.78567
$584$	−2.17610	+	3.76912i	−0.0900478	+	0.155967i
$585$		0			0
$586$	2.15911	−	1.24656i	0.0891921	−	0.0514951i
$587$	2.32227	−	4.02230i	0.0958505	−	0.166018i	−0.814113	−	0.580707i	$-0.802776\pi$
$587$	2.32227	−	4.02230i	0.0958505	−	0.166018i	0.909963	+	0.414689i	$0.136110\pi$
$588$		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
$593$	−11.5215	−	19.9558i	−0.473132	−	0.819488i	0.526395	−	0.850240i	$-0.323543\pi$
$593$	−11.5215	−	19.9558i	−0.473132	−	0.819488i	−0.999527	+	0.0307518i	$0.990210\pi$
$594$		0			0
$595$	−5.90049	+	13.7238i	−0.241896	+	0.562620i
$596$	4.95904	+	2.86310i	0.203130	+	0.117277i
$597$		0			0
$598$			5.78088i			0.236398i
$599$		−	28.9622i		−	1.18336i	−0.806171	−	0.591682i	$-0.798464\pi$
$599$		−	28.9622i		−	1.18336i	0.806171	−	0.591682i	$-0.201536\pi$
$600$		0			0
$601$	5.04993	+	2.91558i	0.205991	+	0.118929i	0.599447	−	0.800414i	$-0.295387\pi$
$601$	5.04993	+	2.91558i	0.205991	+	0.118929i	−0.393456	+	0.919344i	$0.628721\pi$
$602$	1.90010	+	16.0902i	0.0774422	+	0.655787i
$603$		0			0
$604$	−6.38483	−	11.0589i	−0.259795	−	0.449978i
$605$	−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
$611$	19.8495	−	11.4601i	0.803024	−	0.463626i
$612$		0			0
$613$	−16.5880	+	28.7313i	−0.669984	+	1.16045i	0.307924	+	0.951411i	$0.400366\pi$
$613$	−16.5880	+	28.7313i	−0.669984	+	1.16045i	−0.977908	+	0.209036i	$0.932967\pi$
$614$	9.23124			0.372542
$615$		0			0
$616$	−5.29511	+	12.3158i	−0.213346	+	0.496216i
$617$	−34.0222	+	19.6427i	−1.36968	+	0.790786i	−0.990887	−	0.134695i	$-0.956995\pi$
$617$	−34.0222	+	19.6427i	−1.36968	+	0.790786i	−0.378794	+	0.925481i	$0.623661\pi$
$618$		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	$0.396287\pi$
$620$	6.84821	+	3.95382i	0.275031	+	0.158789i
$621$		0			0
$622$			22.9714i			0.921069i
$623$	12.5755	−	29.2490i	0.503827	−	1.17184i
$624$		0			0
$625$	−1.07796	+	1.86708i	−0.0431185	+	0.0746834i
$626$	6.43336			0.257129
$627$		0			0
$628$		−	12.7707i		−	0.509607i
$629$	−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	$0.425598\pi$
$632$			12.7530i			0.507288i
$633$		0			0
$634$	−8.73533			−0.346924
$635$	−31.7549	+	55.0010i	−1.26015	+	2.18265i
$636$		0			0
$637$	5.54272	+	23.1408i	0.219610	+	0.916873i
$638$			21.1033i			0.835489i
$639$		0			0
$640$	3.15592	+	1.82207i	0.124749	+	0.0720237i
$641$	−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	$0.528406\pi$
$642$		0			0
$643$	33.9410	−	19.5959i	1.33850	−	0.772785i	0.351918	−	0.936031i	$-0.385530\pi$
$643$	33.9410	−	19.5959i	1.33850	−	0.772785i	0.986585	+	0.163245i	$0.0521962\pi$
$644$	−0.527662	−	4.46829i	−0.0207928	−	0.176075i
$645$		0			0
$646$	1.26513			0.0497760
$647$	−10.1800	+	17.6323i	−0.400218	+	0.693199i	−0.993752	−	0.111610i	$-0.964399\pi$
$647$	−10.1800	+	17.6323i	−0.400218	+	0.693199i	0.593534	+	0.804809i	$0.297732\pi$
$648$		0			0
$649$	−9.54988	+	5.51362i	−0.374865	+	0.216429i
$650$	−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	$0.570944\pi$
$654$		0			0
$655$	5.88904	+	10.2001i	0.230104	+	0.398552i
$656$	−1.01681	−	1.76117i	−0.0396999	−	0.0687622i
$657$		0			0
$658$	−14.2965	+	10.6698i	−0.557334	+	0.415952i
$659$	9.17413	+	5.29668i	0.357373	+	0.206330i	0.667928	−	0.744226i	$-0.267181\pi$
$659$	9.17413	+	5.29668i	0.357373	+	0.206330i	−0.310555	+	0.950556i	$0.600515\pi$
$660$		0			0
$661$		−	17.0415i		−	0.662836i	−0.943484	−	0.331418i	$-0.892473\pi$
$661$		−	17.0415i		−	0.662836i	0.943484	−	0.331418i	$-0.107527\pi$
$662$		−	31.7007i		−	1.23208i
$663$		0			0
$664$	−1.33028	−	0.768040i	−0.0516251	−	0.0298057i
$665$	6.30921	−	4.70872i	0.244661	−	0.182596i
$666$		0			0
$667$	−3.54141	−	6.13389i	−0.137124	−	0.237505i
$668$	−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	−0.999787	−	0.0206331i	$-0.993432\pi$
$673$	−12.5048	+	21.6590i	−0.482025	+	0.834891i	0.517762	+	0.855524i	$0.326765\pi$
$674$	27.9393	−	16.1308i	1.07618	−	0.621335i
$675$		0			0
$676$	0.722247	−	1.25097i	0.0277787	−	0.0481142i
$677$	−39.7068			−1.52606			−0.763028	−	0.646365i	$-0.776288\pi$
$677$	−39.7068			−1.52606			−0.763028	+	0.646365i	$0.776288\pi$
$678$		0			0
$679$	2.00462	+	16.9753i	0.0769304	+	0.651453i
$680$	4.88976	−	2.82310i	0.187514	−	0.108261i
$681$		0			0
$682$	9.52196	−	5.49750i	0.364615	−	0.210510i
$683$	−2.31868	−	1.33869i	−0.0887218	−	0.0512236i	0.454983	−	0.890500i	$-0.349645\pi$
$683$	−2.31868	−	1.33869i	−0.0887218	−	0.0512236i	−0.543705	+	0.839277i	$0.682979\pi$
$684$		0			0
$685$			53.1390i			2.03034i
$686$	−6.39643	−	17.3806i	−0.244217	−	0.663595i
$687$		0			0
$688$	3.06189	−	5.30335i	0.116733	−	0.202188i
$689$	45.1246			1.71911
$690$		0			0
$691$		−	19.2080i		−	0.730706i	−0.930869	−	0.365353i	$-0.880948\pi$
$691$		−	19.2080i		−	0.730706i	0.930869	−	0.365353i	$-0.119052\pi$
$692$	2.19905			0.0835954
$693$		0			0
$694$	6.82421			0.259043
$695$			20.9475i			0.794583i
$696$		0			0
$697$	−3.15088			−0.119348
$698$	−2.41551	+	4.18379i	−0.0914284	+	0.158359i
$699$		0			0
$700$	8.65267	−	20.1250i	0.327040	−	0.760653i
$701$			34.1916i			1.29140i	0.763591	+	0.645700i	$0.223434\pi$
$701$			34.1916i			1.29140i	−0.763591	+	0.645700i	$0.776566\pi$
$702$		0			0
$703$	4.80825	+	2.77604i	0.181346	+	0.104700i
$704$	4.38809	−	2.53346i	0.165382	−	0.0954835i
$705$		0			0
$706$	29.9510	−	17.2922i	1.12722	−	0.650800i
$707$	−12.4369	+	28.9265i	−0.467736	+	1.08789i
$708$		0			0
$709$	−23.4568			−0.880937			−0.440468	−	0.897768i	$-0.645188\pi$
$709$	−23.4568			−0.880937			−0.440468	+	0.897768i	$0.645188\pi$
$710$	−12.2857	+	21.2795i	−0.461075	+	0.798605i
$711$		0			0
$712$	−10.4214	+	6.01679i	−0.390558	+	0.225489i
$713$	−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
$719$	7.98801	+	13.8356i	0.297902	+	0.515982i	0.975656	−	0.219307i	$-0.0703796\pi$
$719$	7.98801	+	13.8356i	0.297902	+	0.515982i	−0.677753	+	0.735289i	$0.737046\pi$
$720$		0			0
$721$	−4.55643	−	38.5842i	−0.169690	−	1.43695i
$722$	15.8771	+	9.16664i	0.590884	+	0.341147i
$723$		0			0
$724$			14.4710i			0.537811i
$725$		−	34.4846i		−	1.28073i
$726$		0			0
$727$	21.6787	+	12.5162i	0.804019	+	0.464201i	0.844875	−	0.534964i	$-0.179675\pi$
$727$	21.6787	+	12.5162i	0.804019	+	0.464201i	−0.0408555	+	0.999165i	$0.513008\pi$
$728$	3.55243	−	8.26249i	0.131662	−	0.306228i
$729$		0			0
$730$	−7.93003	−	13.7352i	−0.293504	−	0.508363i
$731$	−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
$737$	−10.7789	+	6.22322i	−0.397047	+	0.229235i
$738$		0			0
$739$	−8.20255	+	14.2072i	−0.301736	+	0.522622i	−0.976529	−	0.215385i	$-0.930899\pi$
$739$	−8.20255	+	14.2072i	−0.301736	+	0.522622i	0.674793	+	0.738007i	$0.264233\pi$
$740$	24.7786			0.910880
$741$		0			0
$742$	−34.8787	+	4.11884i	−1.28044	+	0.151208i
$743$	−8.02860	+	4.63532i	−0.294541	+	0.170053i	−0.639988	−	0.768385i	$-0.721061\pi$
$743$	−8.02860	+	4.63532i	−0.294541	+	0.170053i	0.345447	+	0.938438i	$0.387727\pi$
$744$		0			0
$745$	−18.0715	+	10.4336i	−0.662087	+	0.382256i
$746$	8.34718	+	4.81925i	0.305612	+	0.176445i
$747$		0			0
$748$		−	7.85066i		−	0.287048i
$749$	−8.06775	−	3.46870i	−0.294789	−	0.126744i
$750$		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	$0.286509\pi$
$752$	6.74255			0.245875
$753$		0			0
$754$		−	14.1580i		−	0.515603i
$755$	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	$0.169255\pi$
$758$			16.0145i			0.581675i
$759$		0			0
$760$	−2.97557			−0.107935
$761$	24.0809	−	41.7094i	0.872933	−	1.51196i	0.0139853	−	0.999902i	$-0.495548\pi$
$761$	24.0809	−	41.7094i	0.872933	−	1.51196i	0.858948	−	0.512063i	$-0.171118\pi$
$762$		0			0
$763$	−7.45350	+	0.880188i	−0.269835	+	0.0318649i
$764$			8.33194i			0.301439i
$765$		0			0
$766$	−5.51610	−	3.18472i	−0.199305	−	0.115069i
$767$	6.40690	−	3.69902i	0.231340	−	0.133564i
$768$		0			0
$769$	9.84984	−	5.68681i	0.355194	−	0.205071i	−0.311776	−	0.950155i	$-0.600924\pi$
$769$	9.84984	−	5.68681i	0.355194	−	0.205071i	0.666971	+	0.745084i	$0.267591\pi$
$770$	−29.2195	−	39.1512i	−1.05300	−	1.41091i
$771$		0			0
$772$	9.56786			0.344355
$773$	−2.13778	+	3.70275i	−0.0768906	+	0.133179i	−0.901907	−	0.431931i	$-0.857833\pi$
$773$	−2.13778	+	3.70275i	−0.0768906	+	0.133179i	0.825016	+	0.565109i	$0.191166\pi$
$774$		0			0
$775$	−15.5597	+	8.98339i	−0.558920	+	0.322693i
$776$	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
$782$	1.31744	+	2.28187i	0.0471115	+	0.0815996i
$783$		0			0
$784$	−1.99165	+	6.71069i	−0.0711302	+	0.239667i
$785$	40.3034	+	23.2692i	1.43849	+	0.830513i
$786$		0			0
$787$		−	26.4016i		−	0.941115i	−0.882369	−	0.470557i	$-0.844053\pi$
$787$		−	26.4016i		−	0.941115i	0.882369	−	0.470557i	$-0.155947\pi$
$788$			2.37228i			0.0845089i
$789$		0			0
$790$	−40.2476	−	23.2369i	−1.43194	−	0.826733i
$791$	−19.0982	−	8.21118i	−0.679053	−	0.291956i
$792$		0			0
$793$	12.3291	+	21.3546i	0.437819	+	0.758324i
$794$	−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	0.752393	+	0.658715i	$0.228900\pi$
$797$	26.7253	+	46.2896i	0.946660	+	1.63966i	0.194267	+	0.980949i	$0.437767\pi$
$798$		0			0
$799$	5.22343	−	9.04724i	0.184792	−	0.320068i
$800$	−7.17050	+	4.13989i	−0.253516	+	0.146367i
$801$		0			0
$802$	−2.11415	+	3.66182i	−0.0746533	+	0.129303i
$803$	−22.0523			−0.778209
$804$		0			0
$805$	15.0630	+	6.47628i	0.530901	+	0.228259i
$806$	−6.38817	+	3.68821i	−0.225014	+	0.129912i
$807$		0			0
$808$	10.3065	−	5.95045i	0.362581	−	0.209336i
$809$	−8.76550	−	5.06076i	−0.308179	−	0.177927i	0.337933	−	0.941170i	$-0.390272\pi$
$809$	−8.76550	−	5.06076i	−0.308179	−	0.177927i	−0.646111	+	0.763243i	$0.723606\pi$
$810$		0			0
$811$		−	44.8854i		−	1.57614i	−0.615586	−	0.788070i	$-0.711080\pi$
$811$		−	44.8854i		−	1.57614i	0.615586	−	0.788070i	$-0.288920\pi$
$812$	1.29230	+	10.9433i	0.0453508	+	0.384034i
$813$		0			0
$814$	17.2265	−	29.8371i	0.603787	−	1.04579i
$815$	−11.0066			−0.385544
$816$		0			0
$817$			5.00028i			0.174938i
$818$	38.4154			1.34316
$819$		0			0
$820$	7.41083			0.258797
$821$		−	34.4709i		−	1.20304i	−0.798857	−	0.601521i	$-0.794562\pi$
$821$		−	34.4709i		−	1.20304i	0.798857	−	0.601521i	$-0.205438\pi$
$822$		0			0
$823$	−28.9121			−1.00781			−0.503906	−	0.863758i	$-0.668104\pi$
$823$	−28.9121			−1.00781			−0.503906	+	0.863758i	$0.668104\pi$
$824$	−7.34240	+	12.7174i	−0.255785	+	0.443032i
$825$		0			0
$826$	−4.61453	+	3.44394i	−0.160560	+	0.119830i
$827$		−	18.8795i		−	0.656506i	−0.944590	−	0.328253i	$-0.893540\pi$
$827$		−	18.8795i		−	0.656506i	0.944590	−	0.328253i	$-0.106460\pi$
$828$		0			0
$829$	15.6663	+	9.04494i	0.544113	+	0.314144i	0.746744	−	0.665111i	$-0.231616\pi$
$829$	15.6663	+	9.04494i	0.544113	+	0.314144i	−0.202631	+	0.979255i	$0.564949\pi$
$830$	4.84775	−	2.79885i	0.168268	−	0.0971495i
$831$		0			0
$832$	−2.94391	+	1.69967i	−0.102062	+	0.0589254i
$833$	7.46157	+	7.87116i	0.258528	+	0.272720i
$834$		0			0
$835$	52.0942			1.80279
$836$	−2.06866	+	3.58302i	−0.0715461	+	0.123921i
$837$		0			0
$838$	−12.1815	+	7.03301i	−0.420804	+	0.242951i
$839$	−2.53049	+	4.38294i	−0.0873623	+	0.151316i	−0.906395	−	0.422430i	$-0.861177\pi$
$839$	−2.53049	+	4.38294i	−0.0873623	+	0.151316i	0.819033	+	0.573746i	$0.194510\pi$
$840$		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
$845$	2.63197	+	4.55871i	0.0905426	+	0.156824i
$846$		0			0
$847$	−38.5552	+	4.55300i	−1.32477	+	0.156443i
$848$	11.4961	+	6.63726i	0.394777	+	0.227924i
$849$		0			0
$850$			12.8286i			0.440019i
$851$			11.5633i			0.396384i
$852$		0			0
$853$	37.0163	+	21.3714i	1.26741	+	0.731742i	0.974498	−	0.224397i	$-0.0720412\pi$
$853$	37.0163	+	21.3714i	1.26741	+	0.731742i	0.292916	+	0.956138i	$0.405374\pi$
$854$	−11.4789	−	15.3805i	−0.392799	−	0.526311i
$855$		0			0
$856$	1.65961	+	2.87453i	0.0567243	+	0.0982493i
$857$	−0.537523	−	0.931017i	−0.0183614	−	0.0318030i	0.856699	−	0.515817i	$-0.172512\pi$
$857$	−0.537523	−	0.931017i	−0.0183614	−	0.0318030i	−0.875060	+	0.484014i	$0.839178\pi$
$858$		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
$863$	38.7211	−	22.3556i	1.31808	−	0.760994i	0.334661	−	0.942339i	$-0.391378\pi$
$863$	38.7211	−	22.3556i	1.31808	−	0.760994i	0.983420	+	0.181344i	$0.0580449\pi$
$864$		0			0
$865$	−4.00683	+	6.94004i	−0.136236	+	0.235968i
$866$	17.9149			0.608774
$867$		0			0
$868$	4.60104	−	3.43387i	0.156169	−	0.116553i
$869$	−55.9614	+	32.3093i	−1.89836	+	1.09602i
$870$		0			0
$871$	7.23145	−	4.17508i	0.245028	−	0.141467i
$872$	2.45668	+	1.41837i	0.0831938	+	0.0480320i
$873$		0			0
$874$		−	1.38859i		−	0.0469697i
$875$	18.9136	+	25.3423i	0.639395	+	0.856725i
$876$		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	$0.144244\pi$
$878$	19.0275			0.642149
$879$		0			0
$880$			18.4646i			0.622442i
$881$	32.0880			1.08107			0.540536	−	0.841321i	$-0.318221\pi$
$881$	32.0880			1.08107			0.540536	+	0.841321i	$0.318221\pi$
$882$		0			0
$883$	−29.5080			−0.993022			−0.496511	−	0.868031i	$-0.665386\pi$
$883$	−29.5080			−0.993022			−0.496511	+	0.868031i	$0.665386\pi$
$884$			5.26691i			0.177145i
$885$		0			0
$886$	7.67734			0.257925
$887$	−12.4214	+	21.5145i	−0.417071	+	0.722387i	−0.995643	−	0.0932433i	$-0.970277\pi$
$887$	−12.4214	+	21.5145i	−0.417071	+	0.722387i	0.578573	+	0.815631i	$0.303610\pi$
$888$		0			0
$889$	27.5789	+	36.9530i	0.924967	+	1.23936i
$890$		−	43.8521i		−	1.46993i
$891$		0			0
$892$	22.5221	+	13.0031i	0.754095	+	0.435377i
$893$	−4.76792	+	2.75276i	−0.159552	+	0.0921176i
$894$		0			0
$895$	−33.9166	+	19.5818i	−1.13371	+	0.654546i
$896$	2.12034	−	1.58246i	0.0708354	−	0.0528662i
$897$		0			0
$898$	−30.1018			−1.00451
$899$	4.51885	−	7.82687i	0.150712	−	0.261041i
$900$		0			0
$901$	17.8119	−	10.2837i	0.593401	−	0.342600i
$902$	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	$-0.404355\pi$
$908$	−11.4390	−	19.8129i	−0.379616	−	0.657513i
$909$		0			0
$910$	19.6030	+	26.2660i	0.649833	+	0.870711i
$911$	−2.21678	−	1.27986i	−0.0734452	−	0.0424036i	0.462828	−	0.886448i	$-0.346835\pi$
$911$	−2.21678	−	1.27986i	−0.0734452	−	0.0424036i	−0.536273	+	0.844045i	$0.680168\pi$
$912$		0			0
$913$		−	7.78320i		−	0.257586i
$914$			39.4876i			1.30613i
$915$		0			0
$916$	23.3224	+	13.4652i	0.770592	+	0.444902i
$917$	8.49221	−	1.00285i	0.280438	−	0.0331170i
$918$		0			0
$919$	5.12246	+	8.87236i	0.168974	+	0.292672i	0.938060	−	0.346474i	$-0.112621\pi$
$919$	5.12246	+	8.87236i	0.168974	+	0.292672i	−0.769085	+	0.639146i	$0.779288\pi$
$920$	−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
$926$	11.4985	−	6.63866i	0.377864	−	0.218160i
$927$		0			0
$928$	2.08246	−	3.60693i	0.0683601	−	0.118403i
$929$	29.5704			0.970173			0.485087	−	0.874466i	$-0.338788\pi$
$929$	29.5704			0.970173			0.485087	+	0.874466i	$0.338788\pi$
$930$		0			0
$931$	−1.33138	−	5.55852i	−0.0436343	−	0.182173i
$932$	−3.82003	+	2.20550i	−0.125129	+	0.0722435i
$933$		0			0
$934$	20.0698	−	11.5873i	0.656702	−	0.379147i
$935$	24.7761	+	14.3045i	0.810264	+	0.467806i
$936$		0			0
$937$		−	17.9991i		−	0.588005i	−0.955805	−	0.294002i	$-0.905013\pi$
$937$		−	17.9991i		−	0.588005i	0.955805	−	0.294002i	$-0.0949874\pi$
$938$	−5.20841	+	3.88716i	−0.170061	+	0.126920i
$939$		0			0
$940$	−12.2854	+	21.2789i	−0.400706	+	0.694043i
$941$	−29.7237			−0.968965			−0.484483	−	0.874801i	$-0.660992\pi$
$941$	−29.7237			−0.968965			−0.484483	+	0.874801i	$0.660992\pi$
$942$		0			0
$943$			3.45836i			0.112620i
$944$	2.17632			0.0708331
$945$		0			0
$946$	31.0287			1.00883
$947$		−	22.1959i		−	0.721270i	−0.932707	−	0.360635i	$-0.882560\pi$
$947$		−	22.1959i		−	0.721270i	0.932707	−	0.360635i	$-0.117440\pi$
$948$		0			0
$949$	14.7946			0.480254
$950$	3.38037	−	5.85497i	0.109674	−	0.189960i
$951$		0			0
$952$	−0.480749	−	4.07102i	−0.0155812	−	0.131943i
$953$		−	2.12319i		−	0.0687769i	−0.999409	−	0.0343884i	$-0.989052\pi$
$953$		−	2.12319i		−	0.0687769i	0.999409	−	0.0343884i	$-0.0109483\pi$
$954$		0			0
$955$	−26.2950	−	15.1814i	−0.850885	−	0.491258i
$956$	16.1660	−	9.33343i	0.522845	−	0.301865i
$957$		0			0
$958$	21.4025	−	12.3567i	0.691484	−	0.399228i
$959$	35.4433	+	15.2387i	1.14452	+	0.492084i
$960$		0			0
$961$	26.2913			0.848106
$962$	−11.5570	+	20.0174i	−0.372613	+	0.645385i
$963$		0			0
$964$	−0.412458	+	0.238133i	−0.0132844	+	0.00766974i
$965$	−17.4333	+	30.1954i	−0.561199	+	0.972025i
$966$		0			0
$967$	−2.23409	−	3.86955i	−0.0718434	−	0.124436i	0.827866	−	0.560926i	$-0.189555\pi$
$967$	−2.23409	−	3.86955i	−0.0718434	−	0.124436i	−0.899709	+	0.436490i	$0.856222\pi$
$968$	12.7078	+	7.33687i	0.408445	+	0.235816i
$969$		0			0
$970$	11.7718	+	20.3893i	0.377969	+	0.654661i
$971$	0.916026	+	1.58660i	0.0293967	+	0.0509165i	0.880349	−	0.474326i	$-0.157308\pi$
$971$	0.916026	+	1.58660i	0.0293967	+	0.0509165i	−0.850953	+	0.525242i	$0.823975\pi$
$972$		0			0
$973$	13.9718	+	6.00713i	0.447916	+	0.192580i
$974$	−29.4236	−	16.9877i	−0.942794	−	0.544322i
$975$		0			0
$976$			7.25382i			0.232189i
$977$		−	30.9498i		−	0.990173i	−0.868844	−	0.495087i	$-0.835136\pi$
$977$		−	30.9498i		−	0.990173i	0.868844	−	0.495087i	$-0.164864\pi$
$978$		0			0
$979$	−52.8044	−	30.4866i	−1.68764	−	0.974357i
$980$	−17.5495	−	18.5128i	−0.560598	−	0.591371i
$981$		0			0
$982$	−14.7763	−	25.5933i	−0.471531	−	0.816715i
$983$	−16.2825	−	28.2020i	−0.519330	−	0.899505i	−0.999748	−	0.0224656i	$-0.992848\pi$
$983$	−16.2825	−	28.2020i	−0.519330	−	0.899505i	0.480418	−	0.877040i	$-0.340485\pi$
$984$		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
$989$	−9.01881	+	5.20701i	−0.286782	+	0.165573i
$990$		0			0
$991$	1.45730	−	2.52411i	0.0462926	−	0.0801811i	−0.841951	−	0.539555i	$-0.818593\pi$
$991$	1.45730	−	2.52411i	0.0462926	−	0.0801811i	0.888243	+	0.459373i	$0.151926\pi$
$992$	−2.16996			−0.0688962
$993$		0			0
$994$	10.6701	+	14.2968i	0.338434	+	0.453468i
$995$	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	$0.0722520\pi$
$998$	−9.32959	−	5.38644i	−0.295323	−	0.170505i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.l.a.143.4		16
3.2	odd	2		126.2.l.a.101.8	yes	16
4.3	odd	2		3024.2.ca.c.2033.8		16
7.2	even	3		2646.2.t.b.1979.1		16
7.3	odd	6		2646.2.m.a.1763.5		16
7.4	even	3		2646.2.m.b.1763.8		16
7.5	odd	6		378.2.t.a.89.4		16
7.6	odd	2		2646.2.l.a.521.1		16
9.2	odd	6		1134.2.k.a.647.5		16
9.4	even	3		126.2.t.a.59.8	yes	16
9.5	odd	6		378.2.t.a.17.4		16
9.7	even	3		1134.2.k.b.647.4		16
12.11	even	2		1008.2.ca.c.353.2		16
21.2	odd	6		882.2.t.a.803.5		16
21.5	even	6		126.2.t.a.47.8	yes	16
21.11	odd	6		882.2.m.b.587.3		16
21.17	even	6		882.2.m.a.587.2		16
21.20	even	2		882.2.l.b.227.5		16
28.19	even	6		3024.2.df.c.1601.8		16
36.23	even	6		3024.2.df.c.17.8		16
36.31	odd	6		1008.2.df.c.689.1		16
63.4	even	3		882.2.m.a.293.2		16
63.5	even	6	inner	378.2.l.a.341.8		16
63.13	odd	6		882.2.t.a.815.5		16
63.23	odd	6		2646.2.l.a.1097.5		16
63.31	odd	6		882.2.m.b.293.3		16
63.32	odd	6		2646.2.m.a.881.5		16
63.40	odd	6		126.2.l.a.5.4	✓	16
63.41	even	6		2646.2.t.b.2285.1		16
63.47	even	6		1134.2.k.b.971.4		16
63.58	even	3		882.2.l.b.509.1		16
63.59	even	6		2646.2.m.b.881.8		16
63.61	odd	6		1134.2.k.a.971.5		16
84.47	odd	6		1008.2.df.c.929.1		16
252.103	even	6		1008.2.ca.c.257.2		16
252.131	odd	6		3024.2.ca.c.2609.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.4	✓	16	63.40	odd	6
126.2.l.a.101.8	yes	16	3.2	odd	2
126.2.t.a.47.8	yes	16	21.5	even	6
126.2.t.a.59.8	yes	16	9.4	even	3
378.2.l.a.143.4		16	1.1	even	1	trivial
378.2.l.a.341.8		16	63.5	even	6	inner
378.2.t.a.17.4		16	9.5	odd	6
378.2.t.a.89.4		16	7.5	odd	6
882.2.l.b.227.5		16	21.20	even	2
882.2.l.b.509.1		16	63.58	even	3
882.2.m.a.293.2		16	63.4	even	3
882.2.m.a.587.2		16	21.17	even	6
882.2.m.b.293.3		16	63.31	odd	6
882.2.m.b.587.3		16	21.11	odd	6
882.2.t.a.803.5		16	21.2	odd	6
882.2.t.a.815.5		16	63.13	odd	6
1008.2.ca.c.257.2		16	252.103	even	6
1008.2.ca.c.353.2		16	12.11	even	2
1008.2.df.c.689.1		16	36.31	odd	6
1008.2.df.c.929.1		16	84.47	odd	6
1134.2.k.a.647.5		16	9.2	odd	6
1134.2.k.a.971.5		16	63.61	odd	6
1134.2.k.b.647.4		16	9.7	even	3
1134.2.k.b.971.4		16	63.47	even	6
2646.2.l.a.521.1		16	7.6	odd	2
2646.2.l.a.1097.5		16	63.23	odd	6
2646.2.m.a.881.5		16	63.32	odd	6
2646.2.m.a.1763.5		16	7.3	odd	6
2646.2.m.b.881.8		16	63.59	even	6
2646.2.m.b.1763.8		16	7.4	even	3
2646.2.t.b.1979.1		16	7.2	even	3
2646.2.t.b.2285.1		16	63.41	even	6
3024.2.ca.c.2033.8		16	4.3	odd	2
3024.2.ca.c.2609.8		16	252.131	odd	6
3024.2.df.c.17.8		16	36.23	even	6
3024.2.df.c.1601.8		16	28.19	even	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(1.82207 - 3.15592i) q^{5} +(-1.58246 - 2.12034i) q^{7} +1.00000i q^{8} +(-3.15592 - 1.82207i) q^{10} +(-4.38809 + 2.53346i) q^{11} +(2.94391 - 1.69967i) q^{13} +(-2.12034 + 1.58246i) q^{14} +1.00000 q^{16} +(0.774696 - 1.34181i) q^{17} +(-0.707140 + 0.408267i) q^{19} +(-1.82207 + 3.15592i) q^{20} +(2.53346 + 4.38809i) q^{22} +(-1.47275 - 0.850294i) q^{23} +(-4.13989 - 7.17050i) q^{25} +(-1.69967 - 2.94391i) q^{26} +(1.58246 + 2.12034i) q^{28} +(3.60693 + 2.08246i) q^{29} -2.16996i q^{31} -1.00000i q^{32} +(-1.34181 - 0.774696i) q^{34} +(-9.57497 + 1.13071i) q^{35} +(-3.39979 - 5.88860i) q^{37} +(0.408267 + 0.707140i) q^{38} +(3.15592 + 1.82207i) q^{40} +(-1.01681 - 1.76117i) q^{41} +(3.06189 - 5.30335i) q^{43} +(4.38809 - 2.53346i) q^{44} +(-0.850294 + 1.47275i) q^{46} +6.74255 q^{47} +(-1.99165 + 6.71069i) q^{49} +(-7.17050 + 4.13989i) q^{50} +(-2.94391 + 1.69967i) q^{52} +(11.4961 + 6.63726i) q^{53} +18.4646i q^{55} +(2.12034 - 1.58246i) q^{56} +(2.08246 - 3.60693i) q^{58} +2.17632 q^{59} +7.25382i q^{61} -2.16996 q^{62} -1.00000 q^{64} -12.3877i q^{65} +2.45641 q^{67} +(-0.774696 + 1.34181i) q^{68} +(1.13071 + 9.57497i) q^{70} -6.74272i q^{71} +(3.76912 + 2.17610i) q^{73} +(-5.88860 + 3.39979i) q^{74} +(0.707140 - 0.408267i) q^{76} +(12.3158 + 5.29511i) q^{77} +12.7530 q^{79} +(1.82207 - 3.15592i) q^{80} +(-1.76117 + 1.01681i) q^{82} +(-0.768040 + 1.33028i) q^{83} +(-2.82310 - 4.88976i) q^{85} +(-5.30335 - 3.06189i) q^{86} +(-2.53346 - 4.38809i) q^{88} +(6.01679 + 10.4214i) q^{89} +(-8.26249 - 3.55243i) q^{91} +(1.47275 + 0.850294i) q^{92} -6.74255i q^{94} +2.97557i q^{95} +(-5.59509 - 3.23033i) q^{97} +(6.71069 + 1.99165i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 2 q^{7} - 12 q^{11} + 6 q^{13} + 6 q^{14} + 16 q^{16} + 18 q^{17} + 6 q^{23} - 8 q^{25} - 12 q^{26} - 2 q^{28} - 6 q^{29} - 30 q^{35} - 2 q^{37} + 6 q^{41} - 2 q^{43} + 12 q^{44} + 6 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 16 * q - 16 * q^4 + 2 * q^7 - 12 * q^11 + 6 * q^13 + 6 * q^14 + 16 * q^16 + 18 * q^17 + 6 * q^23 - 8 * q^25 - 12 * q^26 - 2 * q^28 - 6 * q^29 - 30 * q^35 - 2 * q^37 + 6 * q^41 - 2 * q^43 + 12 * q^44 + 6 * q^46 + 36 * q^47 - 8 * q^49 + 12 * q^50 - 6 * q^52 + 36 * q^53 - 6 * q^56 + 6 * q^58 - 60 * q^59 - 36 * q^62 - 16 * q^64 - 28 * q^67 - 18 * q^68 - 18 * q^70 - 18 * q^74 + 42 * q^77 + 32 * q^79 - 12 * q^85 - 24 * q^86 + 24 * q^89 - 12 * q^91 - 6 * q^92 + 6 * q^97 + 24 * q^98

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