LMFDB - Embedded newform 825.2.bi.h.101.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(101,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 1]))

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

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

chi := DirichletCharacter("825.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.bi (of order $10$, degree $4$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			101.15
Character	$\chi$	$=$	825.101
Dual form			825.2.bi.h.776.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.428747 - 1.31955i) q^{2} +(-0.140712 + 1.72633i) q^{3} +(0.0606486 + 0.0440638i) q^{4} +(2.21764 + 0.925835i) q^{6} +(-0.527114 + 0.725510i) q^{7} +(2.32910 - 1.69219i) q^{8} +(-2.96040 - 0.485831i) q^{9} +O(q^{10})$	\(q+(0.428747 - 1.31955i) q^{2} +(-0.140712 + 1.72633i) q^{3} +(0.0606486 + 0.0440638i) q^{4} +(2.21764 + 0.925835i) q^{6} +(-0.527114 + 0.725510i) q^{7} +(2.32910 - 1.69219i) q^{8} +(-2.96040 - 0.485831i) q^{9} +(-2.46596 + 2.21790i) q^{11} +(-0.0846024 + 0.0984989i) q^{12} +(6.22748 + 2.02343i) q^{13} +(0.731347 + 1.00661i) q^{14} +(-1.18800 - 3.65629i) q^{16} +(0.994701 + 3.06137i) q^{17} +(-1.91034 + 3.69809i) q^{18} +(0.445440 + 0.613095i) q^{19} +(-1.17829 - 1.01206i) q^{21} +(1.86935 + 4.20487i) q^{22} +0.697650i q^{23} +(2.59354 + 4.25889i) q^{24} +(5.34003 - 7.34992i) q^{26} +(1.25527 - 5.04225i) q^{27} +(-0.0639374 + 0.0207745i) q^{28} +(-2.21328 - 1.60804i) q^{29} +(-2.39303 + 7.36499i) q^{31} +0.423844 q^{32} +(-3.48182 - 4.56913i) q^{33} +4.46611 q^{34} +(-0.158137 - 0.159911i) q^{36} +(3.98689 + 2.89665i) q^{37} +(0.999990 - 0.324916i) q^{38} +(-4.36938 + 10.4659i) q^{39} +(-2.66350 + 1.93515i) q^{41} +(-1.84065 + 1.12090i) q^{42} +7.94703i q^{43} +(-0.247286 + 0.0258529i) q^{44} +(0.920583 + 0.299116i) q^{46} +(-4.78514 - 6.58618i) q^{47} +(6.47911 - 1.53639i) q^{48} +(1.91460 + 5.89254i) q^{49} +(-5.42489 + 1.28640i) q^{51} +(0.288528 + 0.397124i) q^{52} +(6.58232 + 2.13872i) q^{53} +(-6.11531 - 3.81824i) q^{54} +2.58176i q^{56} +(-1.12108 + 0.682704i) q^{57} +(-3.07083 + 2.23109i) q^{58} +(7.04822 - 9.70104i) q^{59} +(1.65156 - 0.536624i) q^{61} +(8.69246 + 6.31544i) q^{62} +(1.91294 - 1.89171i) q^{63} +(2.55772 - 7.87186i) q^{64} +(-7.52201 + 2.63543i) q^{66} +1.90261 q^{67} +(-0.0745685 + 0.229498i) q^{68} +(-1.20437 - 0.0981680i) q^{69} +(0.354205 - 0.115088i) q^{71} +(-7.71718 + 3.87801i) q^{72} +(2.97667 - 4.09704i) q^{73} +(5.53164 - 4.01897i) q^{74} +0.0568111i q^{76} +(-0.309265 - 2.95816i) q^{77} +(11.9370 + 10.2529i) q^{78} +(-14.2056 - 4.61569i) q^{79} +(8.52794 + 2.87651i) q^{81} +(1.41155 + 4.34432i) q^{82} +(-0.265916 - 0.818406i) q^{83} +(-0.0268668 - 0.113300i) q^{84} +(10.4865 + 3.40727i) q^{86} +(3.08744 - 3.59457i) q^{87} +(-1.99036 + 9.33856i) q^{88} -5.24506i q^{89} +(-4.75061 + 3.45152i) q^{91} +(-0.0307411 + 0.0423115i) q^{92} +(-12.3776 - 5.16749i) q^{93} +(-10.7424 + 3.49042i) q^{94} +(-0.0596401 + 0.731693i) q^{96} +(3.83972 - 11.8174i) q^{97} +8.59638 q^{98} +(8.37774 - 5.36782i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{4} - 10 q^{6} + 10 q^{9}+O(q^{10}) $ 80 * q - 4 * q^4 - 10 * q^6 + 10 * q^9	$ 80 q - 4 q^{4} - 10 q^{6} + 10 q^{9} - 60 q^{16} + 20 q^{19} + 30 q^{24} - 20 q^{31} + 56 q^{34} + 2 q^{36} + 50 q^{39} - 40 q^{46} - 72 q^{49} + 30 q^{51} - 96 q^{64} - 42 q^{66} - 30 q^{69} - 66 q^{81} - 140 q^{84} + 48 q^{91} - 60 q^{94} - 70 q^{96} - 60 q^{99}+O(q^{100}) $ 80 * q - 4 * q^4 - 10 * q^6 + 10 * q^9 - 60 * q^16 + 20 * q^19 + 30 * q^24 - 20 * q^31 + 56 * q^34 + 2 * q^36 + 50 * q^39 - 40 * q^46 - 72 * q^49 + 30 * q^51 - 96 * q^64 - 42 * q^66 - 30 * q^69 - 66 * q^81 - 140 * q^84 + 48 * q^91 - 60 * q^94 - 70 * q^96 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$	$1$

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 $

$2$	0.428747	−	1.31955i	0.303170	−	0.933062i	−0.677183	−	0.735814i	$-0.736800\pi$
$2$	0.428747	−	1.31955i	0.303170	−	0.933062i	0.980354	−	0.197248i	$-0.0632004\pi$
$3$	−0.140712	+	1.72633i	−0.0812404	+	0.996695i
$3$	−0.140712	+	1.72633i	−0.0812404	+	0.996695i
$4$	0.0606486	+	0.0440638i	0.0303243	+	0.0220319i
$5$		0			0
$5$		0			0
$6$	2.21764	+	0.925835i	0.905348	+	0.377970i
$7$	−0.527114	+	0.725510i	−0.199230	+	0.274217i	−0.896929	−	0.442174i	$-0.854207\pi$
$7$	−0.527114	+	0.725510i	−0.199230	+	0.274217i	0.697699	+	0.716391i	$0.254207\pi$
$8$	2.32910	−	1.69219i	0.823461	−	0.598279i
$9$	−2.96040	−	0.485831i	−0.986800	−	0.161944i
$10$		0			0
$11$	−2.46596	+	2.21790i	−0.743514	+	0.668721i
$11$	−2.46596	+	2.21790i	−0.743514	+	0.668721i
$12$	−0.0846024	+	0.0984989i	−0.0244226	+	0.0284342i
$13$	6.22748	+	2.02343i	1.72719	+	0.561199i	0.993039	−	0.117785i	$-0.0375795\pi$
$13$	6.22748	+	2.02343i	1.72719	+	0.561199i	0.734153	+	0.678984i	$0.237579\pi$
$14$	0.731347	+	1.00661i	0.195461	+	0.269029i
$15$		0			0
$16$	−1.18800	−	3.65629i	−0.297000	−	0.914072i
$17$	0.994701	+	3.06137i	0.241250	+	0.742492i	0.996231	+	0.0867447i	$0.0276464\pi$
$17$	0.994701	+	3.06137i	0.241250	+	0.742492i	−0.754980	+	0.655748i	$0.772354\pi$
$18$	−1.91034	+	3.69809i	−0.450272	+	0.871649i
$19$	0.445440	+	0.613095i	0.102191	+	0.140654i	0.857050	−	0.515233i	$-0.172295\pi$
$19$	0.445440	+	0.613095i	0.102191	+	0.140654i	−0.754859	+	0.655887i	$0.772295\pi$
$20$		0			0
$21$	−1.17829	−	1.01206i	−0.257125	−	0.220849i
$22$	1.86935	+	4.20487i	0.398547	+	0.896481i
$23$			0.697650i			0.145470i	0.997351	+	0.0727350i	$0.0231727\pi$
$23$			0.697650i			0.145470i	−0.997351	+	0.0727350i	$0.976827\pi$
$24$	2.59354	+	4.25889i	0.529403	+	0.869343i
$25$		0			0
$26$	5.34003	−	7.34992i	1.04727	−	1.44144i
$27$	1.25527	−	5.04225i	0.241576	−	0.970382i
$28$	−0.0639374	+	0.0207745i	−0.0120830	+	0.00392602i
$29$	−2.21328	−	1.60804i	−0.410996	−	0.298606i	0.363009	−	0.931786i	$-0.381749\pi$
$29$	−2.21328	−	1.60804i	−0.410996	−	0.298606i	−0.774005	+	0.633180i	$0.781749\pi$
$30$		0			0
$31$	−2.39303	+	7.36499i	−0.429801	+	1.32279i	0.468521	+	0.883452i	$0.344787\pi$
$31$	−2.39303	+	7.36499i	−0.429801	+	1.32279i	−0.898322	+	0.439338i	$0.855213\pi$
$32$	0.423844			0.0749258
$33$	−3.48182	−	4.56913i	−0.606107	−	0.795383i
$34$	4.46611			0.765931
$35$		0			0
$36$	−0.158137	−	0.159911i	−0.0263561	−	0.0266519i
$37$	3.98689	+	2.89665i	0.655441	+	0.476206i	0.865120	−	0.501565i	$-0.167242\pi$
$37$	3.98689	+	2.89665i	0.655441	+	0.476206i	−0.209679	+	0.977770i	$0.567242\pi$
$38$	0.999990	−	0.324916i	0.162220	−	0.0527084i
$39$	−4.36938	+	10.4659i	−0.699661	+	1.67589i
$40$		0			0
$41$	−2.66350	+	1.93515i	−0.415970	+	0.302220i	−0.776014	−	0.630716i	$-0.782761\pi$
$41$	−2.66350	+	1.93515i	−0.415970	+	0.302220i	0.360045	+	0.932935i	$0.382761\pi$
$42$	−1.84065	+	1.12090i	−0.284019	+	0.172959i
$43$			7.94703i			1.21191i	0.795499	+	0.605955i	$0.207209\pi$
$43$			7.94703i			1.21191i	−0.795499	+	0.605955i	$0.792791\pi$
$44$	−0.247286	+	0.0258529i	−0.0372797	+	0.00389747i
$45$		0			0
$46$	0.920583	+	0.299116i	0.135733	+	0.0441022i
$47$	−4.78514	−	6.58618i	−0.697984	−	0.960693i	−0.999973	−	0.00738149i	$-0.997650\pi$
$47$	−4.78514	−	6.58618i	−0.697984	−	0.960693i	0.301988	−	0.953312i	$-0.402350\pi$
$48$	6.47911	−	1.53639i	0.935179	−	0.221759i
$49$	1.91460	+	5.89254i	0.273515	+	0.841792i
$50$		0			0
$51$	−5.42489	+	1.28640i	−0.759637	+	0.180133i
$52$	0.288528	+	0.397124i	0.0400116	+	0.0550713i
$53$	6.58232	+	2.13872i	0.904151	+	0.293776i	0.723949	−	0.689853i	$-0.242325\pi$
$53$	6.58232	+	2.13872i	0.904151	+	0.293776i	0.180202	+	0.983630i	$0.442325\pi$
$54$	−6.11531	−	3.81824i	−0.832188	−	0.519597i
$55$		0			0
$56$			2.58176i			0.345002i
$57$	−1.12108	+	0.682704i	−0.148491	+	0.0904263i
$58$	−3.07083	+	2.23109i	−0.403220	+	0.292956i
$59$	7.04822	−	9.70104i	0.917600	−	1.26297i	−0.0469036	−	0.998899i	$-0.514935\pi$
$59$	7.04822	−	9.70104i	0.917600	−	1.26297i	0.964504	−	0.264069i	$-0.0850646\pi$
$60$		0			0
$61$	1.65156	−	0.536624i	0.211460	−	0.0687076i	−0.201371	−	0.979515i	$-0.564540\pi$
$61$	1.65156	−	0.536624i	0.211460	−	0.0687076i	0.412832	+	0.910807i	$0.364540\pi$
$62$	8.69246	+	6.31544i	1.10394	+	0.802062i
$63$	1.91294	−	1.89171i	0.241008	−	0.238333i
$64$	2.55772	−	7.87186i	0.319715	−	0.983982i
$65$		0			0
$66$	−7.52201	+	2.63543i	−0.925896	+	0.324399i
$67$	1.90261			0.232441			0.116220	−	0.993223i	$-0.462922\pi$
$67$	1.90261			0.232441			0.116220	+	0.993223i	$0.462922\pi$
$68$	−0.0745685	+	0.229498i	−0.00904276	+	0.0278308i
$69$	−1.20437	−	0.0981680i	−0.144989	−	0.0118180i
$70$		0			0
$71$	0.354205	−	0.115088i	0.0420364	−	0.0136585i	−0.287923	−	0.957653i	$-0.592965\pi$
$71$	0.354205	−	0.115088i	0.0420364	−	0.0136585i	0.329960	+	0.943995i	$0.392965\pi$
$72$	−7.71718	+	3.87801i	−0.909478	+	0.457028i
$73$	2.97667	−	4.09704i	0.348393	−	0.479522i	−0.598476	−	0.801141i	$-0.704227\pi$
$73$	2.97667	−	4.09704i	0.348393	−	0.479522i	0.946869	+	0.321618i	$0.104227\pi$
$74$	5.53164	−	4.01897i	0.643040	−	0.467196i
$75$		0			0
$76$			0.0568111i			0.00651668i
$77$	−0.309265	−	2.95816i	−0.0352441	−	0.337114i
$78$	11.9370	+	10.2529i	1.35159	+	1.16091i
$79$	−14.2056	−	4.61569i	−1.59826	−	0.519306i	−0.631583	−	0.775309i	$-0.717594\pi$
$79$	−14.2056	−	4.61569i	−1.59826	−	0.519306i	−0.966676	+	0.256003i	$0.917594\pi$
$80$		0			0
$81$	8.52794	+	2.87651i	0.947549	+	0.319612i
$82$	1.41155	+	4.34432i	0.155880	+	0.479749i
$83$	−0.265916	−	0.818406i	−0.0291881	−	0.0898317i	0.935401	−	0.353588i	$-0.115039\pi$
$83$	−0.265916	−	0.818406i	−0.0291881	−	0.0898317i	−0.964589	+	0.263756i	$0.915039\pi$
$84$	−0.0268668	−	0.113300i	−0.00293141	−	0.0123620i
$85$		0			0
$86$	10.4865	+	3.40727i	1.13079	+	0.367415i
$87$	3.08744	−	3.59457i	0.331008	−	0.385378i
$88$	−1.99036	+	9.33856i	−0.212173	+	0.995494i
$89$		−	5.24506i		−	0.555976i	−0.960585	−	0.277988i	$-0.910333\pi$
$89$		−	5.24506i		−	0.555976i	0.960585	−	0.277988i	$-0.0896675\pi$
$90$		0			0
$91$	−4.75061	+	3.45152i	−0.497999	+	0.361818i
$92$	−0.0307411	+	0.0423115i	−0.00320498	+	0.00441128i
$93$	−12.3776	−	5.16749i	−1.28350	−	0.535844i
$94$	−10.7424	+	3.49042i	−1.10799	+	0.360009i
$95$		0			0
$96$	−0.0596401	+	0.731693i	−0.00608700	+	0.0746781i
$97$	3.83972	−	11.8174i	0.389864	−	1.19988i	−0.543025	−	0.839716i	$-0.682721\pi$
$97$	3.83972	−	11.8174i	0.389864	−	1.19988i	0.932890	−	0.360163i	$-0.117279\pi$
$98$	8.59638			0.868366
$99$	8.37774	−	5.36782i	0.841994	−	0.539486i
$100$		0			0
$101$	4.08008	−	12.5572i	0.405983	−	1.24949i	−0.514089	−	0.857737i	$-0.671870\pi$
$101$	4.08008	−	12.5572i	0.405983	−	1.24949i	0.920072	−	0.391750i	$-0.128130\pi$
$102$	−0.628437	+	7.70996i	−0.0622245	+	0.763400i
$103$	−0.353627	−	0.256925i	−0.0348439	−	0.0253156i	0.570227	−	0.821487i	$-0.306855\pi$
$103$	−0.353627	−	0.256925i	−0.0348439	−	0.0253156i	−0.605071	+	0.796172i	$0.706855\pi$
$104$	17.9284	−	5.82530i	1.75803	−	0.571218i
$105$		0			0
$106$	5.64430	−	7.76872i	0.548223	−	0.754565i
$107$	0.509781	−	0.370378i	0.0492824	−	0.0358058i	−0.562871	−	0.826545i	$-0.690303\pi$
$107$	0.509781	−	0.370378i	0.0492824	−	0.0358058i	0.612154	+	0.790739i	$0.290303\pi$
$108$	0.298311	−	0.250494i	0.0287050	−	0.0241038i
$109$			2.55958i			0.245164i	0.992458	+	0.122582i	$0.0391174\pi$
$109$			2.55958i			0.245164i	−0.992458	+	0.122582i	$0.960883\pi$
$110$		0			0
$111$	−5.56156	+	6.47508i	−0.527880	+	0.614587i
$112$	3.27888	+	1.06537i	0.309825	+	0.100668i
$113$	−5.92260	−	8.15175i	−0.557151	−	0.766853i	0.433810	−	0.901004i	$-0.357169\pi$
$113$	−5.92260	−	8.15175i	−0.557151	−	0.766853i	−0.990961	+	0.134152i	$0.957169\pi$
$114$	0.420201	+	1.77203i	0.0393554	+	0.165966i
$115$		0			0
$116$	−0.0633759	−	0.195051i	−0.00588430	−	0.0181100i
$117$	−17.4528	−	9.01567i	−1.61351	−	0.833499i
$118$	−9.77910	−	13.4598i	−0.900239	−	1.23907i
$119$	−2.74538	−	0.892027i	−0.251668	−	0.0817720i
$120$		0			0
$121$	1.16188	−	10.9385i	0.105626	−	0.994406i
$122$		−	2.40939i		−	0.218136i
$123$	−2.96591	−	4.87038i	−0.267427	−	0.439147i
$124$	−0.469663	+	0.341230i	−0.0421770	+	0.0306434i
$125$		0			0
$126$	−1.67604	−	3.33529i	−0.149313	−	0.297131i
$127$	4.43732	−	1.44177i	0.393749	−	0.127937i	−0.105449	−	0.994425i	$-0.533628\pi$
$127$	4.43732	−	1.44177i	0.393749	−	0.127937i	0.499198	+	0.866488i	$0.333628\pi$
$128$	−8.60489	−	6.25182i	−0.760572	−	0.552588i
$129$	−13.7192	−	1.11825i	−1.20790	−	0.0984560i
$130$		0			0
$131$	−13.4283			−1.17324			−0.586618	−	0.809864i	$-0.699541\pi$
$131$	−13.4283			−1.17324			−0.586618	+	0.809864i	$0.699541\pi$
$132$	−0.00983430	−	0.430533i	−0.000855966	−	0.0374731i
$133$	−0.679604			−0.0589291
$134$	0.815740	−	2.51059i	0.0704692	−	0.216882i
$135$		0			0
$136$	7.49718	+	5.44702i	0.642878	+	0.467078i
$137$	−10.8493	+	3.52514i	−0.926915	+	0.301173i	−0.733300	−	0.679905i	$-0.762021\pi$
$137$	−10.8493	+	3.52514i	−0.926915	+	0.301173i	−0.193614	+	0.981078i	$0.562021\pi$
$138$	−0.645908	+	1.54714i	−0.0549834	+	0.131701i
$139$	9.81539	−	13.5097i	0.832531	−	1.14588i	−0.154916	−	0.987928i	$-0.549511\pi$
$139$	9.81539	−	13.5097i	0.832531	−	1.14588i	0.987447	−	0.157953i	$-0.0504894\pi$
$140$		0			0
$141$	12.0432	−	7.33395i	1.01422	−	0.617630i
$142$		−	0.516735i		−	0.0433634i
$143$	−19.8444	+	8.82221i	−1.65948	+	0.737750i
$144$	1.74062	+	11.4012i	0.145051	+	0.950103i
$145$		0			0
$146$	−4.13000	−	5.68446i	−0.341802	−	0.470450i
$147$	−10.4419	+	2.47607i	−0.861230	+	0.204223i
$148$	0.114162	+	0.351355i	0.00938407	+	0.0288812i
$149$	4.31014	+	13.2653i	0.353101	+	1.08673i	0.957103	+	0.289749i	$0.0935718\pi$
$149$	4.31014	+	13.2653i	0.353101	+	1.08673i	−0.604002	+	0.796983i	$0.706428\pi$
$150$		0			0
$151$	−8.48297	−	11.6758i	−0.690334	−	0.950164i	0.309666	−	0.950846i	$-0.399783\pi$
$151$	−8.48297	−	11.6758i	−0.690334	−	0.950164i	−1.00000		0.000681994i	$0.999783\pi$
$152$	2.07495	+	0.674191i	0.168300	+	0.0546841i
$153$	−1.45740	−	9.54615i	−0.117824	−	0.771760i
$154$	−4.03603	−	0.860212i	−0.325233	−	0.0693179i
$155$		0			0
$156$	−0.726166	+	0.442213i	−0.0581398	+	0.0354053i
$157$	0.278110	−	0.202058i	0.0221956	−	0.0161260i	−0.576632	−	0.817004i	$-0.695633\pi$
$157$	0.278110	−	0.202058i	0.0221956	−	0.0161260i	0.598828	+	0.800878i	$0.295633\pi$
$158$	−12.1813	+	16.7661i	−0.969089	+	1.33384i
$159$	−4.61835	+	11.0623i	−0.366259	+	0.877296i
$160$		0			0
$161$	−0.506152	−	0.367741i	−0.0398904	−	0.0289820i
$162$	7.45202	−	10.0197i	0.585486	−	0.787225i
$163$	3.29710	−	10.1474i	0.258249	−	0.794809i	−0.734923	−	0.678151i	$-0.762782\pi$
$163$	3.29710	−	10.1474i	0.258249	−	0.794809i	0.993172	−	0.116659i	$-0.0372183\pi$
$164$	−0.246808			−0.0192725
$165$		0			0
$166$	−1.19394			−0.0926675
$167$	−0.413471	+	1.27253i	−0.0319953	+	0.0984715i	−0.965779	−	0.259367i	$-0.916486\pi$
$167$	−0.413471	+	1.27253i	−0.0319953	+	0.0984715i	0.933784	+	0.357838i	$0.116486\pi$
$168$	−4.45696	−	0.363286i	−0.343862	−	0.0280281i
$169$	24.1700	+	17.5605i	1.85923	+	1.35081i
$170$		0			0
$171$	−1.02082	−	2.03141i	−0.0780640	−	0.155346i
$172$	−0.350176	+	0.481976i	−0.0267007	+	0.0367503i
$173$	9.22022	−	6.69889i	0.701001	−	0.509307i	−0.179257	−	0.983802i	$-0.557369\pi$
$173$	9.22022	−	6.69889i	0.701001	−	0.509307i	0.880258	+	0.474495i	$0.157369\pi$
$174$	−3.41948	−	5.61519i	−0.259230	−	0.425687i
$175$		0			0
$176$	11.0388	+	6.38139i	0.832082	+	0.481015i
$177$	15.7554	+	13.5326i	1.18425	+	1.01717i
$178$	−6.92112	−	2.24881i	−0.518760	−	0.168555i
$179$	−0.931229	−	1.28173i	−0.0696033	−	0.0958008i	0.772796	−	0.634654i	$-0.218858\pi$
$179$	−0.931229	−	1.28173i	−0.0696033	−	0.0958008i	−0.842399	+	0.538854i	$0.818858\pi$
$180$		0			0
$181$	4.63880	+	14.2768i	0.344799	+	1.06118i	0.961691	+	0.274135i	$0.0883915\pi$
$181$	4.63880	+	14.2768i	0.344799	+	1.06118i	−0.616892	+	0.787048i	$0.711609\pi$
$182$	2.51764	+	7.74849i	0.186620	+	0.574357i
$183$	0.693992	+	2.92664i	0.0513014	+	0.216343i
$184$	1.18056	+	1.62489i	0.0870317	+	0.119789i
$185$		0			0
$186$	−12.1256	+	14.1173i	−0.889095	+	1.03513i
$187$	−9.24270	−	5.34307i	−0.675893	−	0.390724i
$188$		−	0.610294i		−	0.0445103i
$189$	2.99654	+	3.56855i	0.217966	+	0.259574i
$190$		0			0
$191$	8.33023	−	11.4656i	0.602754	−	0.829620i	−0.393203	−	0.919452i	$-0.628633\pi$
$191$	8.33023	−	11.4656i	0.602754	−	0.829620i	0.995957	+	0.0898317i	$0.0286329\pi$
$192$	13.2295	+	5.52313i	0.954756	+	0.398598i
$193$	20.1414	−	6.54433i	1.44981	−	0.471072i	0.524869	−	0.851183i	$-0.324114\pi$
$193$	20.1414	−	6.54433i	1.44981	−	0.471072i	0.924941	+	0.380112i	$0.124114\pi$
$194$	−13.9474	−	10.1334i	−1.00137	−	0.727535i
$195$		0			0
$196$	−0.143530	+	0.441739i	−0.0102521	+	0.0315528i
$197$	−12.2325			−0.871530			−0.435765	−	0.900061i	$-0.643522\pi$
$197$	−12.2325			−0.871530			−0.435765	+	0.900061i	$0.643522\pi$
$198$	−3.49117	−	13.3563i	−0.248106	−	0.949189i
$199$	−9.12394			−0.646779			−0.323390	−	0.946266i	$-0.604822\pi$
$199$	−9.12394			−0.646779			−0.323390	+	0.946266i	$0.604822\pi$
$200$		0			0
$201$	−0.267721	+	3.28453i	−0.0188836	+	0.231673i
$202$	−14.8205	−	10.7677i	−1.04277	−	0.757614i
$203$	2.33330	−	0.758135i	0.163766	−	0.0532107i
$204$	−0.385696	−	0.161023i	−0.0270041	−	0.0112738i
$205$		0			0
$206$	−0.490642	+	0.356472i	−0.0341847	+	0.0248366i
$207$	0.338940	−	2.06532i	0.0235579	−	0.143550i
$208$		−	25.1733i		−	1.74545i
$209$	−2.45822	−	0.523927i	−0.170038	−	0.0362408i
$210$		0			0
$211$	5.93176	+	1.92735i	0.408359	+	0.132684i	0.505991	−	0.862539i	$-0.331127\pi$
$211$	5.93176	+	1.92735i	0.408359	+	0.132684i	−0.0976320	+	0.995223i	$0.531127\pi$
$212$	0.304968	+	0.419752i	0.0209453	+	0.0288287i
$213$	0.148839	+	0.627668i	0.0101983	+	0.0430071i
$214$	−0.270164	−	0.831480i	−0.0184680	−	0.0568388i
$215$		0			0
$216$	−5.60880	−	13.8680i	−0.381631	−	0.943601i
$217$	−4.08197	−	5.61835i	−0.277102	−	0.381399i
$218$	3.37750	+	1.09742i	0.228753	+	0.0743263i
$219$	6.65397	+	5.71521i	0.449634	+	0.386198i
$220$		0			0
$221$			21.0774i			1.41782i
$222$	6.15968	+	10.1149i	0.413411	+	0.678869i
$223$	−13.7966	+	10.0238i	−0.923891	+	0.671246i	−0.944489	−	0.328542i	$-0.893443\pi$
$223$	−13.7966	+	10.0238i	−0.923891	+	0.671246i	0.0205984	+	0.999788i	$0.493443\pi$
$224$	−0.223414	+	0.307503i	−0.0149275	+	0.0205459i
$225$		0			0
$226$	−13.2959	+	4.32011i	−0.884433	+	0.287370i
$227$	4.29548	+	3.12085i	0.285101	+	0.207138i	0.721139	−	0.692790i	$-0.243619\pi$
$227$	4.29548	+	3.12085i	0.285101	+	0.207138i	−0.436038	+	0.899928i	$0.643619\pi$
$228$	−0.0980744	−	0.00799403i	−0.00649514	−	0.000529417i
$229$	0.209053	−	0.643400i	0.0138146	−	0.0425171i	−0.943912	−	0.330198i	$-0.892884\pi$
$229$	0.209053	−	0.643400i	0.0138146	−	0.0425171i	0.957726	+	0.287681i	$0.0928844\pi$
$230$		0			0
$231$	5.15026	−	0.117643i	0.338862	−	0.00774035i
$232$	−7.87606			−0.517088
$233$	−0.653719	+	2.01194i	−0.0428265	+	0.131807i	−0.970184	−	0.242371i	$-0.922075\pi$
$233$	−0.653719	+	2.01194i	−0.0428265	+	0.131807i	0.927357	+	0.374177i	$0.122075\pi$
$234$	−19.3795	+	19.1644i	−1.26687	+	1.25281i
$235$		0			0
$236$	0.854929	−	0.277783i	0.0556511	−	0.0180822i
$237$	9.96709	−	23.8741i	0.647432	−	1.55079i
$238$	−2.35415	+	3.24021i	−0.152597	+	0.210031i
$239$	−6.90685	+	5.01812i	−0.446767	+	0.324595i	−0.788318	−	0.615268i	$-0.789048\pi$
$239$	−6.90685	+	5.01812i	−0.446767	+	0.324595i	0.341551	+	0.939863i	$0.389048\pi$
$240$		0			0
$241$			4.62484i			0.297912i	0.988844	+	0.148956i	$0.0475912\pi$
$241$			4.62484i			0.297912i	−0.988844	+	0.148956i	$0.952409\pi$
$242$	−13.9357	−	6.22300i	−0.895820	−	0.400030i
$243$	−6.16578	+	14.3172i	−0.395535	+	0.918451i
$244$	0.123810	+	0.0402284i	0.00792614	+	0.00257536i
$245$		0			0
$246$	−7.69833	+	1.82550i	−0.490827	+	0.116390i
$247$	1.53341	+	4.71935i	0.0975686	+	0.300285i
$248$	6.88935	+	21.2032i	0.437474	+	1.34641i
$249$	1.45025	−	0.343898i	0.0919060	−	0.0217937i
$250$		0			0
$251$	−21.8508	−	7.09975i	−1.37921	−	0.448132i	−0.476799	−	0.879012i	$-0.658203\pi$
$251$	−21.8508	−	7.09975i	−1.37921	−	0.448132i	−0.902409	+	0.430880i	$0.858203\pi$
$252$	0.199373	−	0.0304381i	0.0125593	−	0.00191742i
$253$	−1.54731	−	1.72037i	−0.0972788	−	0.108159i
$254$		−	6.47342i		−	0.406179i
$255$		0			0
$256$	1.45350	−	1.05603i	0.0908435	−	0.0660016i
$257$	10.2799	−	14.1491i	0.641243	−	0.882595i	−0.357439	−	0.933937i	$-0.616350\pi$
$257$	10.2799	−	14.1491i	0.641243	−	0.882595i	0.998681	+	0.0513419i	$0.0163498\pi$
$258$	−7.35763	+	17.6237i	−0.458066	+	1.09720i
$259$	−4.20309	+	1.36567i	−0.261167	+	0.0848584i
$260$		0			0
$261$	5.77096	+	5.83573i	0.357213	+	0.361222i
$262$	−5.75735	+	17.7193i	−0.355690	+	1.09470i
$263$	2.19449			0.135318			0.0676590	−	0.997709i	$-0.478447\pi$
$263$	2.19449			0.135318			0.0676590	+	0.997709i	$0.478447\pi$
$264$	−15.8413	−	4.75006i	−0.974966	−	0.292346i
$265$		0			0
$266$	−0.291378	+	0.896771i	−0.0178656	+	0.0549845i
$267$	9.05469	+	0.738046i	0.554138	+	0.0451677i
$268$	0.115391	+	0.0838362i	0.00704861	+	0.00512111i
$269$	−1.13650	+	0.369271i	−0.0692937	+	0.0225149i	−0.343459	−	0.939168i	$-0.611599\pi$
$269$	−1.13650	+	0.369271i	−0.0692937	+	0.0225149i	0.274165	+	0.961683i	$0.411599\pi$
$270$		0			0
$271$	1.08529	−	1.49377i	0.0659264	−	0.0907399i	−0.774781	−	0.632230i	$-0.782140\pi$
$271$	1.08529	−	1.49377i	0.0659264	−	0.0907399i	0.840707	+	0.541490i	$0.182140\pi$
$272$	10.0116	−	7.27382i	0.607040	−	0.441040i
$273$	−5.28998	−	8.68677i	−0.320164	−	0.525747i
$274$			15.8275i			0.956176i
$275$		0			0
$276$	−0.0687177	−	0.0590229i	−0.00413632	−	0.00355276i
$277$	−28.6337	−	9.30364i	−1.72043	−	0.559002i	−0.728417	−	0.685134i	$-0.759744\pi$
$277$	−28.6337	−	9.30364i	−1.72043	−	0.559002i	−0.992013	+	0.126132i	$0.959744\pi$
$278$	−13.6184	−	18.7442i	−0.816779	−	1.12420i
$279$	10.6625	−	20.6407i	0.638345	−	1.23573i
$280$		0			0
$281$	6.00625	+	18.4853i	0.358303	+	1.10274i	0.954070	+	0.299585i	$0.0968483\pi$
$281$	6.00625	+	18.4853i	0.358303	+	1.10274i	−0.595767	+	0.803158i	$0.703152\pi$
$282$	−4.51401	−	19.0360i	−0.268805	−	1.13358i
$283$	−12.5870	−	17.3245i	−0.748217	−	1.02983i	−0.998104	−	0.0615572i	$-0.980393\pi$
$283$	−12.5870	−	17.3245i	−0.748217	−	1.02983i	0.249887	−	0.968275i	$-0.419607\pi$
$284$	0.0265533	+	0.00862768i	0.00157565	+	0.000511958i
$285$		0			0
$286$	3.13308	+	29.9682i	0.185263	+	1.77206i
$287$		−	2.95244i		−	0.174277i
$288$	−1.25475	−	0.205917i	−0.0739367	−	0.0121338i
$289$	5.37071	−	3.90205i	0.315924	−	0.229532i
$290$		0			0
$291$	19.8605	+	8.29146i	1.16424	+	0.486054i
$292$	0.361062	−	0.117316i	0.0211296	−	0.00686541i
$293$	−15.8153	−	11.4905i	−0.923938	−	0.671280i	0.0205632	−	0.999789i	$-0.493454\pi$
$293$	−15.8153	−	11.4905i	−0.923938	−	0.671280i	−0.944501	+	0.328508i	$0.893454\pi$
$294$	−1.20962	+	14.8402i	−0.0705463	+	0.865495i
$295$		0			0
$296$	14.1875			0.824634
$297$	8.08775	+	15.2180i	0.469299	+	0.883039i
$298$	19.3521			1.12104
$299$	−1.41165	+	4.34460i	−0.0816376	+	0.251255i
$300$		0			0
$301$	−5.76565	−	4.18899i	−0.332326	−	0.241449i
$302$	−19.0438	+	6.18772i	−1.09585	+	0.356063i
$303$	21.1037	+	8.81049i	1.21237	+	0.506150i
$304$	1.71247	−	2.35701i	0.0982169	−	0.135184i
$305$		0			0
$306$	−13.2215	−	2.16977i	−0.755821	−	0.124038i
$307$			1.52564i			0.0870730i	0.999052	+	0.0435365i	$0.0138625\pi$
$307$			1.52564i			0.0870730i	−0.999052	+	0.0435365i	$0.986138\pi$
$308$	0.111591	−	0.193036i	0.00635850	−	0.0109992i
$309$	0.493296	−	0.574323i	0.0280626	−	0.0326721i
$310$		0			0
$311$	4.08414	+	5.62134i	0.231591	+	0.318757i	0.908958	−	0.416888i	$-0.136879\pi$
$311$	4.08414	+	5.62134i	0.231591	+	0.318757i	−0.677367	+	0.735645i	$0.736879\pi$
$312$	7.53362	+	31.7700i	0.426507	+	1.79862i
$313$	8.95555	+	27.5623i	0.506197	+	1.55792i	0.798748	+	0.601666i	$0.205496\pi$
$313$	8.95555	+	27.5623i	0.506197	+	1.55792i	−0.292551	+	0.956250i	$0.594504\pi$
$314$	−0.147387	−	0.453611i	−0.00831754	−	0.0255988i
$315$		0			0
$316$	−0.658167	−	0.905889i	−0.0370248	−	0.0509602i
$317$	12.1266	+	3.94019i	0.681100	+	0.221303i	0.629077	−	0.777343i	$-0.283433\pi$
$317$	12.1266	+	3.94019i	0.681100	+	0.221303i	0.0520233	+	0.998646i	$0.483433\pi$
$318$	12.6171	+	10.8371i	0.707533	+	0.607712i
$319$	9.02432	−	0.943462i	0.505265	−	0.0528237i
$320$		0			0
$321$	0.567660	+	0.932165i	0.0316837	+	0.0520284i
$322$	−0.702263	+	0.510224i	−0.0391356	+	0.0284337i
$323$	−1.43383	+	1.97350i	−0.0797807	+	0.109809i
$324$	0.390457	+	0.550229i	0.0216921	+	0.0305683i
$325$		0			0
$326$	−11.9764	−	8.70138i	−0.663313	−	0.481925i
$327$	−4.41868	−	0.360165i	−0.244353	−	0.0199172i
$328$	−2.92893	+	9.01431i	−0.161723	+	0.497732i
$329$	7.30065			0.402498
$330$		0			0
$331$	−2.04823			−0.112581			−0.0562903	−	0.998414i	$-0.517927\pi$
$331$	−2.04823			−0.112581			−0.0562903	+	0.998414i	$0.517927\pi$
$332$	0.0199346	−	0.0613524i	0.00109405	−	0.00336715i
$333$	−10.3955	−	10.5122i	−0.569671	−	0.576064i
$334$	1.50189	+	1.09119i	0.0821800	+	0.0597072i
$335$		0			0
$336$	−2.30056	+	5.51051i	−0.125506	+	0.300623i
$337$	1.14962	−	1.58232i	0.0626238	−	0.0861943i	−0.776556	−	0.630048i	$-0.783035\pi$
$337$	1.14962	−	1.58232i	0.0626238	−	0.0861943i	0.839180	+	0.543854i	$0.183035\pi$
$338$	33.5348	−	24.3645i	1.82405	−	1.32525i
$339$	14.9060	−	9.07728i	0.809581	−	0.493010i
$340$		0			0
$341$	−10.4337	−	23.4692i	−0.565015	−	1.27093i
$342$	−3.11823	+	0.476057i	−0.168614	+	0.0257422i
$343$	−11.2545	−	3.65682i	−0.607687	−	0.197450i
$344$	13.4479	+	18.5094i	0.725061	+	0.997960i
$345$		0			0
$346$	−4.88636	−	15.0387i	−0.262692	−	0.808484i
$347$	7.49213	+	23.0584i	0.402199	+	1.23784i	0.923212	+	0.384292i	$0.125554\pi$
$347$	7.49213	+	23.0584i	0.402199	+	1.23784i	−0.521013	+	0.853549i	$0.674446\pi$
$348$	0.345639	−	0.0819613i	0.0185282	−	0.00439359i
$349$	−16.3915	−	22.5610i	−0.877417	−	1.20766i	−0.977130	−	0.212645i	$-0.931792\pi$
$349$	−16.3915	−	22.5610i	−0.877417	−	1.20766i	0.0997123	−	0.995016i	$-0.468208\pi$
$350$		0			0
$351$	18.0198	−	28.8606i	0.961826	−	1.54046i
$352$	−1.04518	+	0.940042i	−0.0557083	+	0.0501044i
$353$			2.24413i			0.119443i	0.998215	+	0.0597215i	$0.0190213\pi$
$353$			2.24413i			0.119443i	−0.998215	+	0.0597215i	$0.980979\pi$
$354$	24.6120	−	14.9879i	1.30811	−	0.796600i
$355$		0			0
$356$	0.231117	−	0.318106i	0.0122492	−	0.0168596i
$357$	1.92624	−	4.61390i	0.101947	−	0.244193i
$358$	−2.09056	+	0.679265i	−0.110490	+	0.0359003i
$359$	−5.48619	−	3.98595i	−0.289550	−	0.210370i	0.433522	−	0.901143i	$-0.357271\pi$
$359$	−5.48619	−	3.98595i	−0.289550	−	0.210370i	−0.723072	+	0.690773i	$0.757271\pi$
$360$		0			0
$361$	5.69385	−	17.5239i	0.299677	−	0.922309i
$362$	20.8277			1.09468
$363$	18.7199	+	3.54496i	0.982538	+	0.186062i
$364$	−0.440205			−0.0230730
$365$		0			0
$366$	4.15939	+	0.339031i	0.217415	+	0.0177214i
$367$	23.9070	+	17.3694i	1.24793	+	0.906677i	0.998100	−	0.0616119i	$-0.0196241\pi$
$367$	23.9070	+	17.3694i	1.24793	+	0.906677i	0.249834	+	0.968289i	$0.419624\pi$
$368$	2.55081	−	0.828808i	0.132970	−	0.0432046i
$369$	8.82520	−	4.43480i	0.459421	−	0.230867i
$370$		0			0
$371$	−5.02130	+	3.64819i	−0.260693	+	0.189404i
$372$	−0.522987	−	0.858806i	−0.0271156	−	0.0445270i
$373$		−	8.05921i		−	0.417290i	−0.977991	−	0.208645i	$-0.933095\pi$
$373$		−	8.05921i		−	0.417290i	0.977991	−	0.208645i	$-0.0669053\pi$
$374$	−11.0132	+	9.90536i	−0.569480	+	0.512194i
$375$		0			0
$376$	−22.2901	−	7.24250i	−1.14953	−	0.373503i
$377$	−10.5294	−	14.4925i	−0.542291	−	0.746400i
$378$	5.99363	−	2.42407i	0.308279	−	0.124681i
$379$	−7.73325	−	23.8005i	−0.397230	−	1.22255i	−0.927211	−	0.374540i	$-0.877801\pi$
$379$	−7.73325	−	23.8005i	−0.397230	−	1.22255i	0.529981	−	0.848010i	$-0.322199\pi$
$380$		0			0
$381$	1.86458	+	7.86314i	0.0955256	+	0.402841i
$382$	−11.5578	−	15.9080i	−0.591350	−	0.813923i
$383$	23.6246	+	7.67611i	1.20716	+	0.392231i	0.842391	−	0.538867i	$-0.181147\pi$
$383$	23.6246	+	7.67611i	1.20716	+	0.392231i	0.364771	+	0.931097i	$0.381147\pi$
$384$	12.0035	−	13.9751i	0.612551	−	0.713166i
$385$		0			0
$386$		−	29.3834i		−	1.49558i
$387$	3.86091	−	23.5264i	0.196261	−	1.19591i
$388$	0.753594	−	0.547518i	0.0382580	−	0.0277960i
$389$	10.0232	−	13.7958i	0.508198	−	0.699475i	−0.475416	−	0.879761i	$-0.657702\pi$
$389$	10.0232	−	13.7958i	0.508198	−	0.699475i	0.983614	+	0.180286i	$0.0577024\pi$
$390$		0			0
$391$	−2.13577	+	0.693953i	−0.108010	+	0.0350947i
$392$	14.4306	+	10.4844i	0.728855	+	0.529544i
$393$	1.88953	−	23.1816i	0.0953141	−	1.16936i
$394$	−5.24465	+	16.1414i	−0.264222	+	0.813191i
$395$		0			0
$396$	0.744624	+	0.0436042i	0.0374188	+	0.00219119i
$397$	8.32149			0.417643			0.208822	−	0.977954i	$-0.433037\pi$
$397$	8.32149			0.417643			0.208822	+	0.977954i	$0.433037\pi$
$398$	−3.91187	+	12.0395i	−0.196084	+	0.603485i
$399$	0.0956287	−	1.17322i	0.00478742	−	0.0587343i
$400$		0			0
$401$	13.0428	−	4.23786i	0.651327	−	0.211629i	0.0353277	−	0.999376i	$-0.488753\pi$
$401$	13.0428	−	4.23786i	0.651327	−	0.211629i	0.615999	+	0.787747i	$0.288753\pi$
$402$	4.21931	+	1.76150i	0.210440	+	0.0878558i
$403$	−29.8051	+	41.0232i	−1.48470	+	2.04351i
$404$	0.800768	−	0.581792i	0.0398397	−	0.0289452i
$405$		0			0
$406$		−	3.40395i		−	0.168935i
$407$	−16.2560	+	1.69950i	−0.805778	+	0.0842413i
$408$	−10.4583	+	12.1761i	−0.517762	+	0.602807i
$409$	−21.6718	−	7.04159i	−1.07160	−	0.348184i	−0.280490	−	0.959857i	$-0.590497\pi$
$409$	−21.6718	−	7.04159i	−1.07160	−	0.348184i	−0.791111	+	0.611673i	$0.790497\pi$
$410$		0			0
$411$	−4.55891	−	19.2254i	−0.224874	−	0.948318i
$412$	−0.0101259	−	0.0311643i	−0.000498867	−	0.00153535i
$413$	3.32299	+	10.2271i	0.163514	+	0.503243i
$414$	−2.57997	−	1.33275i	−0.126799	−	0.0655011i
$415$		0			0
$416$	2.63948	+	0.857619i	0.129411	+	0.0420482i
$417$	21.9410	+	18.8456i	1.07446	+	0.922871i
$418$	−1.74530	+	3.01910i	−0.0853655	+	0.147669i
$419$			30.6229i			1.49603i	0.663685	+	0.748013i	$0.268992\pi$
$419$			30.6229i			1.49603i	−0.663685	+	0.748013i	$0.731008\pi$
$420$		0			0
$421$	25.6246	−	18.6173i	1.24886	−	0.907353i	0.250709	−	0.968063i	$-0.419336\pi$
$421$	25.6246	−	18.6173i	1.24886	−	0.907353i	0.998155	+	0.0607095i	$0.0193363\pi$
$422$	5.08645	−	7.00090i	0.247605	−	0.340799i
$423$	10.9662	+	21.8225i	0.533193	+	1.06105i
$424$	18.9500	−	6.15723i	0.920293	−	0.299021i
$425$		0			0
$426$	0.892052	+	0.0727110i	0.0432201	+	0.00352286i
$427$	−0.481233	+	1.48108i	−0.0232885	+	0.0716746i
$428$	0.0472377			0.00228332
$429$	−12.4376	−	35.4994i	−0.600495	−	1.71393i
$430$		0			0
$431$	−6.62702	+	20.3959i	−0.319212	+	0.982434i	0.654774	+	0.755825i	$0.272764\pi$
$431$	−6.62702	+	20.3959i	−0.319212	+	0.982434i	−0.973986	+	0.226609i	$0.927236\pi$
$432$	−19.9272	+	1.40058i	−0.958747	+	0.0673852i
$433$	18.1221	+	13.1665i	0.870892	+	0.632740i	0.930826	−	0.365462i	$-0.119089\pi$
$433$	18.1221	+	13.1665i	0.870892	+	0.632740i	−0.0599343	+	0.998202i	$0.519089\pi$
$434$	−9.16383	+	2.97751i	−0.439878	+	0.142925i
$435$		0			0
$436$	−0.112785	+	0.155235i	−0.00540142	+	0.00743442i
$437$	−0.427726	+	0.310761i	−0.0204609	+	0.0148657i
$438$	10.3944	−	6.32986i	0.496663	−	0.302452i
$439$			19.2175i			0.917200i	0.888643	+	0.458600i	$0.151649\pi$
$439$			19.2175i			0.917200i	−0.888643	+	0.458600i	$0.848351\pi$
$440$		0			0
$441$	−2.80521	−	18.3745i	−0.133582	−	0.874974i
$442$	27.8126	+	9.03686i	1.32291	+	0.429840i
$443$	14.3128	+	19.6998i	0.680019	+	0.935966i	0.999934	−	0.0114800i	$-0.00365427\pi$
$443$	14.3128	+	19.6998i	0.680019	+	0.935966i	−0.319915	+	0.947446i	$0.603654\pi$
$444$	−0.622617	+	0.147641i	−0.0295481	+	0.00700673i
$445$		0			0
$446$	7.31168	+	22.5030i	0.346218	+	1.06555i
$447$	−23.5066	+	5.57412i	−1.11183	+	0.263647i
$448$	4.36290	+	6.00502i	0.206128	+	0.283710i
$449$	7.10410	+	2.30826i	0.335263	+	0.108934i	0.471811	−	0.881700i	$-0.343601\pi$
$449$	7.10410	+	2.30826i	0.335263	+	0.108934i	−0.136547	+	0.990634i	$0.543601\pi$
$450$		0			0
$451$	2.27613	−	10.6794i	0.107179	−	0.502872i
$452$		−	0.755364i		−	0.0355293i
$453$	21.3499	−	13.0014i	1.00311	−	0.610861i
$454$	5.95979	−	4.33004i	0.279707	−	0.203219i
$455$		0			0
$456$	−1.45584	+	3.48716i	−0.0681761	+	0.163301i
$457$	12.8323	−	4.16948i	0.600272	−	0.195040i	0.00691008	−	0.999976i	$-0.497800\pi$
$457$	12.8323	−	4.16948i	0.600272	−	0.195040i	0.593362	+	0.804936i	$0.297800\pi$
$458$	−0.759367	−	0.551712i	−0.0354829	−	0.0257798i
$459$	16.6848	−	1.17269i	0.778781	−	0.0547364i
$460$		0			0
$461$	−15.5766			−0.725475			−0.362737	−	0.931891i	$-0.618158\pi$
$461$	−15.5766			−0.725475			−0.362737	+	0.931891i	$0.618158\pi$
$462$	2.05293	−	6.84646i	0.0955108	−	0.318526i
$463$	31.2181			1.45083			0.725414	−	0.688313i	$-0.241649\pi$
$463$	31.2181			1.45083			0.725414	+	0.688313i	$0.241649\pi$
$464$	−3.25009	+	10.0027i	−0.150882	+	0.464366i
$465$		0			0
$466$	2.37457	+	1.72523i	0.110000	+	0.0799197i
$467$	6.71752	−	2.18266i	0.310850	−	0.101001i	−0.149438	−	0.988771i	$-0.547746\pi$
$467$	6.71752	−	2.18266i	0.310850	−	0.101001i	0.460288	+	0.887770i	$0.347746\pi$
$468$	−0.661222	−	1.31582i	−0.0305650	−	0.0608239i
$469$	−1.00289	+	1.38036i	−0.0463093	+	0.0637392i
$470$		0			0
$471$	0.309685	+	0.508540i	0.0142695	+	0.0234323i
$472$		−	34.5216i		−	1.58899i
$473$	−17.6257	−	19.5970i	−0.810429	−	0.901072i
$474$	−27.2296	−	23.3880i	−1.25070	−	1.07425i
$475$		0			0
$476$	−0.127197	−	0.175072i	−0.00583007	−	0.00802441i
$477$	−18.4472	−	9.52937i	−0.844641	−	0.436320i
$478$	3.66036	+	11.2654i	0.167421	+	0.515269i
$479$	−8.42706	−	25.9358i	−0.385042	−	1.18504i	−0.936450	−	0.350802i	$-0.885909\pi$
$479$	−8.42706	−	25.9358i	−0.385042	−	1.18504i	0.551407	−	0.834236i	$-0.314091\pi$
$480$		0			0
$481$	18.9671	+	26.1060i	0.864826	+	1.19033i
$482$	6.10270	+	1.98289i	0.277970	+	0.0903180i
$483$	0.706062	−	0.822037i	0.0321269	−	0.0374040i
$484$	0.552457	−	0.612206i	0.0251117	−	0.0278275i
$485$		0			0
$486$	16.2487	+	14.2745i	0.737058	+	0.647505i
$487$	−17.2161	+	12.5083i	−0.780137	+	0.566803i	−0.905020	−	0.425368i	$-0.860145\pi$
$487$	−17.2161	+	12.5083i	−0.780137	+	0.566803i	0.124883	+	0.992172i	$0.460145\pi$
$488$	2.93857	−	4.04460i	0.133023	−	0.183090i
$489$	17.0538	+	7.11975i	0.771202	+	0.321966i
$490$		0			0
$491$	29.1024	+	21.1442i	1.31337	+	0.954223i	0.999989	+	0.00459659i	$0.00146314\pi$
$491$	29.1024	+	21.1442i	1.31337	+	0.954223i	0.313385	+	0.949626i	$0.398537\pi$
$492$	0.0347289	−	0.426071i	0.00156570	−	0.0192087i
$493$	2.72127	−	8.37520i	0.122560	−	0.377200i
$494$	6.88486			0.309765
$495$		0			0
$496$	29.7714			1.33678
$497$	−0.103209	+	0.317644i	−0.00462955	+	0.0142483i
$498$	0.168002	−	2.06112i	0.00752834	−	0.0923612i
$499$	4.98953	+	3.62511i	0.223362	+	0.162282i	0.693839	−	0.720130i	$-0.255918\pi$
$499$	4.98953	+	3.62511i	0.223362	+	0.162282i	−0.470477	+	0.882412i	$0.655918\pi$
$500$		0			0
$501$	−2.13862	−	0.892846i	−0.0955467	−	0.0398894i
$502$	−18.7369	+	25.7892i	−0.836270	+	1.15103i
$503$	24.7294	−	17.9669i	1.10263	−	0.801106i	0.121141	−	0.992635i	$-0.461345\pi$
$503$	24.7294	−	17.9669i	1.10263	−	0.801106i	0.981487	+	0.191529i	$0.0613447\pi$
$504$	1.25430	−	7.64304i	0.0558709	−	0.340448i
$505$		0			0
$506$	−2.93352	+	1.30415i	−0.130411	+	0.0579766i
$507$	−33.7162	+	39.2543i	−1.49739	+	1.74335i
$508$	0.332647	+	0.108084i	0.0147588	+	0.00479544i
$509$	0.464290	+	0.639040i	0.0205793	+	0.0283249i	0.819183	−	0.573533i	$-0.194427\pi$
$509$	0.464290	+	0.639040i	0.0205793	+	0.0283249i	−0.798603	+	0.601858i	$0.794427\pi$
$510$		0			0
$511$	1.40340	+	4.31921i	0.0620827	+	0.191071i
$512$	−7.34385	−	22.6020i	−0.324555	−	0.998879i
$513$	3.65053	−	1.47642i	0.161175	−	0.0651856i
$514$	−14.2629	−	19.6312i	−0.629110	−	0.865896i
$515$		0			0
$516$	−0.782773	−	0.672338i	−0.0344597	−	0.0295980i
$517$	26.4074	+	5.62829i	1.16140	+	0.247532i
$518$			6.13171i			0.269412i
$519$	10.2671	+	16.8597i	0.450674	+	0.740060i
$520$		0			0
$521$	−23.0782	+	31.7645i	−1.01108	+	1.39163i	−0.0928006	+	0.995685i	$0.529582\pi$
$521$	−23.0782	+	31.7645i	−1.01108	+	1.39163i	−0.918275	+	0.395942i	$0.870418\pi$
$522$	10.1748	−	5.11301i	0.445339	−	0.223790i
$523$	−17.8563	+	5.80188i	−0.780803	+	0.253698i	−0.672183	−	0.740385i	$-0.734643\pi$
$523$	−17.8563	+	5.80188i	−0.780803	+	0.253698i	−0.108620	+	0.994083i	$0.534643\pi$
$524$	−0.814408	−	0.591702i	−0.0355776	−	0.0258486i
$525$		0			0
$526$	0.940881	−	2.89574i	0.0410244	−	0.126260i
$527$	−24.9273			−1.08585
$528$	−12.5697	+	18.1587i	−0.547024	+	0.790254i
$529$	22.5133			0.978838
$530$		0			0
$531$	−25.5786	+	25.2947i	−1.11002	+	1.09770i
$532$	−0.0412170	−	0.0299459i	−0.00178698	−	0.00129832i
$533$	−20.5026	+	6.66169i	−0.888065	+	0.288550i
$534$	4.85606	−	11.6317i	0.210142	−	0.503352i
$535$		0			0
$536$	4.43137	−	3.21958i	0.191406	−	0.139065i
$537$	2.34371	−	1.42725i	0.101139	−	0.0615904i
$538$			1.65799i			0.0714811i
$539$	−17.7904	−	10.2844i	−0.766286	−	0.442979i
$540$		0			0
$541$	−28.2488	−	9.17858i	−1.21451	−	0.394618i	−0.369429	−	0.929259i	$-0.620447\pi$
$541$	−28.2488	−	9.17858i	−1.21451	−	0.394618i	−0.845079	+	0.534641i	$0.820447\pi$
$542$	−1.50579	−	2.07254i	−0.0646790	−	0.0890230i
$543$	−25.2991	+	5.99916i	−1.08569	+	0.257449i
$544$	0.421598	+	1.29755i	0.0180759	+	0.0556318i
$545$		0			0
$546$	−13.7307	+	3.25595i	−0.587619	+	0.139342i
$547$	9.51221	+	13.0924i	0.406713	+	0.559792i	0.962413	−	0.271591i	$-0.0875497\pi$
$547$	9.51221	+	13.0924i	0.406713	+	0.559792i	−0.555700	+	0.831383i	$0.687550\pi$
$548$	−0.813323	−	0.264265i	−0.0347434	−	0.0112888i
$549$	−5.14998	+	0.786243i	−0.219796	+	0.0335560i
$550$		0			0
$551$		−	2.07324i		−	0.0883228i
$552$	−2.97122	+	1.80938i	−0.126463	+	0.0770123i
$553$	10.8367	−	7.87333i	0.460824	−	0.334808i
$554$	−24.5532	+	33.7946i	−1.04317	+	1.43580i
$555$		0			0
$556$	1.19058	−	0.386843i	0.0504918	−	0.0164058i
$557$	20.8491	+	15.1478i	0.883406	+	0.641832i	0.934150	−	0.356880i	$-0.116159\pi$
$557$	20.8491	+	15.1478i	0.883406	+	0.641832i	−0.0507444	+	0.998712i	$0.516159\pi$
$558$	−22.6649	−	22.9193i	−0.959482	−	0.970251i
$559$	−16.0803	+	49.4900i	−0.680123	+	2.09320i
$560$		0			0
$561$	10.5244	−	15.2041i	0.444342	−	0.641916i
$562$	26.9675			1.13755
$563$	1.46581	−	4.51129i	0.0617764	−	0.190128i	−0.915405	−	0.402533i	$-0.868130\pi$
$563$	1.46581	−	4.51129i	0.0617764	−	0.190128i	0.977182	+	0.212405i	$0.0681297\pi$
$564$	1.05357	+	0.0858759i	0.0443631	+	0.00361603i
$565$		0			0
$566$	−28.2571	+	9.18129i	−1.18773	+	0.385918i
$567$	−6.58213	+	4.67086i	−0.276423	+	0.196158i
$568$	0.630227	−	0.867434i	0.0264438	−	0.0363967i
$569$	−31.8594	+	23.1472i	−1.33561	+	0.970380i	−0.336020	+	0.941855i	$0.609081\pi$
$569$	−31.8594	+	23.1472i	−1.33561	+	0.970380i	−0.999593	+	0.0285253i	$0.990919\pi$
$570$		0			0
$571$			5.45810i			0.228415i	0.993457	+	0.114207i	$0.0364328\pi$
$571$			5.45810i			0.228415i	−0.993457	+	0.114207i	$0.963567\pi$
$572$	−1.59228	−	0.339367i	−0.0665765	−	0.0141897i
$573$	18.6212	+	15.9940i	0.777910	+	0.668161i
$574$	−3.89589	−	1.26585i	−0.162611	−	0.0528357i
$575$		0			0
$576$	−11.3963	+	22.0612i	−0.474845	+	0.919218i
$577$	−5.16605	−	15.8995i	−0.215066	−	0.661904i	−0.999149	−	0.0412482i	$-0.986867\pi$
$577$	−5.16605	−	15.8995i	−0.215066	−	0.661904i	0.784083	−	0.620656i	$-0.213133\pi$
$578$	−2.84627	−	8.75991i	−0.118389	−	0.364364i
$579$	8.46351	+	35.6915i	0.351731	+	1.48329i
$580$		0			0
$581$	0.733930	+	0.238468i	0.0304485	+	0.00989333i
$582$	19.4561	−	22.6519i	0.806482	−	0.938951i
$583$	−20.9752	+	9.32489i	−0.868703	+	0.386197i
$584$		−	14.5795i		−	0.603304i
$585$		0			0
$586$	−21.9430	+	15.9425i	−0.906457	+	0.658579i
$587$	7.78966	−	10.7215i	0.321514	−	0.442525i	−0.617415	−	0.786638i	$-0.711820\pi$
$587$	7.78966	−	10.7215i	0.321514	−	0.442525i	0.938929	+	0.344112i	$0.111820\pi$
$588$	−0.742389	−	0.309937i	−0.0306156	−	0.0127816i
$589$	−5.58139	+	1.81350i	−0.229977	+	0.0747241i
$590$		0			0
$591$	1.72127	−	21.1173i	0.0708034	−	0.868649i
$592$	5.85454	−	18.0184i	0.240620	−	0.740553i
$593$	2.52752			0.103793			0.0518964	−	0.998652i	$-0.483473\pi$
$593$	2.52752			0.103793			0.0518964	+	0.998652i	$0.483473\pi$
$594$	23.5485	−	4.14750i	0.966208	−	0.170174i
$595$		0			0
$596$	−0.323113	+	0.994440i	−0.0132352	+	0.0407338i
$597$	1.28385	−	15.7509i	0.0525446	−	0.644641i
$598$	5.12767	+	3.72547i	0.209686	+	0.152346i
$599$	−39.2198	+	12.7433i	−1.60248	+	0.520677i	−0.967719	−	0.252033i	$-0.918901\pi$
$599$	−39.2198	+	12.7433i	−1.60248	+	0.520677i	−0.634759	+	0.772710i	$0.718901\pi$
$600$		0			0
$601$	−15.3992	+	21.1951i	−0.628145	+	0.864567i	−0.997914	−	0.0645567i	$-0.979437\pi$
$601$	−15.3992	+	21.1951i	−0.628145	+	0.864567i	0.369769	+	0.929124i	$0.379437\pi$
$602$	−7.99958	+	5.81204i	−0.326039	+	0.236881i
$603$	−5.63249	−	0.924347i	−0.229373	−	0.0376423i
$604$		−	1.08191i		−	0.0440224i
$605$		0			0
$606$	20.6740	−	24.0699i	0.839825	−	0.977771i
$607$	16.5155	+	5.36623i	0.670345	+	0.217808i	0.624364	−	0.781134i	$-0.285358\pi$
$607$	16.5155	+	5.36623i	0.670345	+	0.217808i	0.0459818	+	0.998942i	$0.485358\pi$
$608$	0.188797	+	0.259857i	0.00765673	+	0.0105386i
$609$	0.980464	+	4.13472i	0.0397304	+	0.167547i
$610$		0			0
$611$	−16.4727	−	50.6977i	−0.666413	−	2.05101i
$612$	0.332250	−	0.643179i	0.0134304	−	0.0259990i
$613$	3.70849	+	5.10430i	0.149784	+	0.206161i	0.877315	−	0.479914i	$-0.159332\pi$
$613$	3.70849	+	5.10430i	0.149784	+	0.206161i	−0.727531	+	0.686075i	$0.759332\pi$
$614$	2.01316	+	0.654115i	0.0812445	+	0.0263979i
$615$		0			0
$616$	−5.72607	−	6.36651i	−0.230710	−	0.256514i
$617$		−	33.6793i		−	1.35588i	−0.735117	−	0.677940i	$-0.762873\pi$
$617$		−	33.6793i		−	1.35588i	0.735117	−	0.677940i	$-0.237127\pi$
$618$	−0.546348	−	0.897168i	−0.0219773	−	0.0360894i
$619$	6.36477	−	4.62428i	0.255822	−	0.185865i	−0.452481	−	0.891774i	$-0.649461\pi$
$619$	6.36477	−	4.62428i	0.255822	−	0.185865i	0.708303	+	0.705909i	$0.249461\pi$
$620$		0			0
$621$	3.51773	+	0.875737i	0.141161	+	0.0351421i
$622$	9.16870	−	2.97909i	0.367631	−	0.119451i
$623$	3.80535	+	2.76475i	0.152458	+	0.110767i
$624$	43.4573	+	3.54220i	1.73968	+	0.141801i
$625$		0			0
$626$	40.2095			1.60710
$627$	1.25037	−	4.16996i	0.0499350	−	0.166532i
$628$	0.0257704			0.00102835
$629$	−4.90195	+	15.0867i	−0.195454	+	0.601544i
$630$		0			0
$631$	18.4492	+	13.4041i	0.734451	+	0.533610i	0.890968	−	0.454065i	$-0.150027\pi$
$631$	18.4492	+	13.4041i	0.734451	+	0.533610i	−0.156517	+	0.987675i	$0.550027\pi$
$632$	−40.8969	+	13.2882i	−1.62679	+	0.528577i
$633$	−4.16190	+	9.96895i	−0.165421	+	0.396230i
$634$	10.3985	−	14.3124i	0.412979	−	0.568416i
$635$		0			0
$636$	−0.767542	+	0.467410i	−0.0304350	+	0.0185340i
$637$			40.5698i			1.60743i
$638$	2.62421	−	12.3125i	0.103893	−	0.487458i
$639$	−1.10450	+	0.168623i	−0.0436934	+	0.00667064i
$640$		0			0
$641$	−15.8714	−	21.8451i	−0.626881	−	0.862828i	0.370950	−	0.928653i	$-0.379032\pi$
$641$	−15.8714	−	21.8451i	−0.626881	−	0.862828i	−0.997831	+	0.0658247i	$0.979032\pi$
$642$	1.47342	−	0.349392i	0.0581512	−	0.0137894i
$643$	−10.5161	−	32.3653i	−0.414716	−	1.27636i	−0.912505	−	0.409065i	$-0.865855\pi$
$643$	−10.5161	−	32.3653i	−0.414716	−	1.27636i	0.497789	−	0.867298i	$-0.334145\pi$
$644$	−0.0144933	−	0.0446059i	−0.000571118	−	0.00175772i
$645$		0			0
$646$	1.98938	+	2.73815i	0.0782712	+	0.107731i
$647$	20.7519	+	6.74272i	0.815843	+	0.265084i	0.687071	−	0.726591i	$-0.258896\pi$
$647$	20.7519	+	6.74272i	0.815843	+	0.265084i	0.128773	+	0.991674i	$0.458896\pi$
$648$	24.7300	−	7.73121i	0.971486	−	0.303711i
$649$	4.13529	+	39.5546i	0.162325	+	1.55265i
$650$		0			0
$651$	10.2735	−	6.25624i	0.402650	−	0.245201i
$652$	0.647099	−	0.470145i	0.0253424	−	0.0184123i
$653$	11.2822	−	15.5286i	0.441506	−	0.607680i	−0.529040	−	0.848597i	$-0.677448\pi$
$653$	11.2822	−	15.5286i	0.441506	−	0.607680i	0.970546	+	0.240916i	$0.0774480\pi$
$654$	−2.36975	+	5.67624i	−0.0926646	+	0.221959i
$655$		0			0
$656$	10.2397	+	7.43958i	0.399793	+	0.290467i
$657$	−10.8026	+	10.6827i	−0.421450	+	0.416773i
$658$	3.13014	−	9.63357i	0.122025	−	0.375556i
$659$	−12.8998			−0.502507			−0.251253	−	0.967921i	$-0.580843\pi$
$659$	−12.8998			−0.502507			−0.251253	+	0.967921i	$0.580843\pi$
$660$		0			0
$661$	−33.7036			−1.31092			−0.655459	−	0.755231i	$-0.727525\pi$
$661$	−33.7036			−1.31092			−0.655459	+	0.755231i	$0.727525\pi$
$662$	−0.878172	+	2.70273i	−0.0341311	+	0.105045i
$663$	−36.3864	−	2.96585i	−1.41313	−	0.115184i
$664$	−2.00424	−	1.45617i	−0.0777797	−	0.0565102i
$665$		0			0
$666$	−18.3284	+	9.21031i	−0.710211	+	0.356892i
$667$	1.12185	−	1.54409i	0.0434382	−	0.0597876i
$668$	−0.0811490	+	0.0589582i	−0.00313975	+	0.00228116i
$669$	−15.3631	−	25.2280i	−0.593970	−	0.975369i
$670$		0			0
$671$	−2.88249	+	4.98627i	−0.111277	+	0.192493i
$672$	−0.499413	−	0.428955i	−0.0192653	−	0.0165473i
$673$	−17.5771	−	5.71116i	−0.677549	−	0.220149i	−0.0500268	−	0.998748i	$-0.515931\pi$
$673$	−17.5771	−	5.71116i	−0.677549	−	0.220149i	−0.627522	+	0.778599i	$0.715931\pi$
$674$	−1.59505	−	2.19539i	−0.0614389	−	0.0845634i
$675$		0			0
$676$	0.692093	+	2.13004i	0.0266190	+	0.0819248i
$677$	13.7407	+	42.2894i	0.528096	+	1.62531i	0.758110	+	0.652126i	$0.226123\pi$
$677$	13.7407	+	42.2894i	0.528096	+	1.62531i	−0.230014	+	0.973187i	$0.573877\pi$
$678$	−5.58702	−	23.5610i	−0.214568	−	0.904855i
$679$	6.54970	+	9.01489i	0.251354	+	0.345960i
$680$		0			0
$681$	−5.99203	+	6.97626i	−0.229615	+	0.267331i
$682$	−35.4422	+	3.70536i	−1.35715	+	0.141886i
$683$			33.7026i			1.28959i	0.764354	+	0.644797i	$0.223058\pi$
$683$			33.7026i			1.28959i	−0.764354	+	0.644797i	$0.776942\pi$
$684$	0.0276006	−	0.168184i	0.00105533	−	0.00643066i
$685$		0			0
$686$	−9.65070	+	13.2831i	−0.368466	+	0.507149i
$687$	1.08130	+	0.451428i	0.0412542	+	0.0172231i
$688$	29.0566	−	9.44107i	1.10777	−	0.359937i
$689$	36.6637	+	26.6377i	1.39678	+	1.01482i
$690$		0			0
$691$	−5.77678	+	17.7791i	−0.219759	+	0.676349i	0.779022	+	0.626996i	$0.215716\pi$
$691$	−5.77678	+	17.7791i	−0.219759	+	0.676349i	−0.998781	+	0.0493527i	$0.984284\pi$
$692$	0.854372			0.0324783
$693$	−0.521616	+	8.90759i	−0.0198145	+	0.338371i
$694$	33.6390			1.27692
$695$		0			0
$696$	1.10826	−	13.5966i	0.0420085	−	0.515379i
$697$	−8.57361	−	6.22909i	−0.324749	−	0.235944i
$698$	−36.7981	+	11.9564i	−1.39283	+	0.452558i
$699$	−3.38128	−	1.41164i	−0.127892	−	0.0533930i
$700$		0			0
$701$	1.42323	−	1.03404i	0.0537547	−	0.0390550i	−0.560583	−	0.828098i	$-0.689423\pi$
$701$	1.42323	−	1.03404i	0.0537547	−	0.0390550i	0.614338	+	0.789043i	$0.289423\pi$
$702$	−30.3570	−	36.1519i	−1.14575	−	1.36447i
$703$			3.73462i			0.140854i
$704$	11.1517	+	25.0844i	0.420297	+	0.945405i
$705$		0			0
$706$	2.96124	+	0.962166i	0.111448	+	0.0362116i
$707$	6.95970	+	9.57920i	0.261746	+	0.360263i
$708$	0.359245	+	1.51497i	0.0135013	+	0.0569362i
$709$	−5.03949	−	15.5100i	−0.189262	−	0.582489i	0.810734	−	0.585415i	$-0.199069\pi$
$709$	−5.03949	−	15.5100i	−0.189262	−	0.582489i	−0.999996	+	0.00292630i	$0.999069\pi$
$710$		0			0
$711$	39.8119	+	20.5658i	1.49306	+	0.771279i
$712$	−8.87564	−	12.2163i	−0.332629	−	0.457824i
$713$	−5.13818	−	1.66950i	−0.192426	−	0.0625231i
$714$	−5.26239	−	4.51996i	−0.196940	−	0.169155i
$715$		0			0
$716$		−	0.118768i		−	0.00443858i
$717$	−7.69103	−	12.6296i	−0.287227	−	0.471661i
$718$	−7.61184	+	5.53033i	−0.284072	+	0.206390i
$719$	−13.1663	+	18.1219i	−0.491020	+	0.675831i	−0.980576	−	0.196141i	$-0.937159\pi$
$719$	−13.1663	+	18.1219i	−0.491020	+	0.675831i	0.489556	+	0.871972i	$0.337159\pi$
$720$		0			0
$721$	0.372804	−	0.121131i	0.0138839	−	0.00451116i
$722$	−20.6824	−	15.0266i	−0.769719	−	0.559234i
$723$	−7.98397	−	0.650772i	−0.296927	−	0.0242025i
$724$	−0.347751	+	1.07027i	−0.0129241	+	0.0397762i
$725$		0			0
$726$	12.7038	−	23.1819i	0.471484	−	0.860360i
$727$	3.83594			0.142267			0.0711336	−	0.997467i	$-0.477338\pi$
$727$	3.83594			0.142267			0.0711336	+	0.997467i	$0.477338\pi$
$728$	−5.22401	+	16.0779i	−0.193615	+	0.595885i
$729$	−23.8486	−	12.6587i	−0.883282	−	0.468843i
$730$		0			0
$731$	−24.3288	+	7.90491i	−0.899834	+	0.292374i
$732$	−0.0868690	+	0.208076i	−0.00321077	+	0.00769072i
$733$	21.4067	−	29.4638i	0.790676	−	1.08827i	−0.203348	−	0.979107i	$-0.565182\pi$
$733$	21.4067	−	29.4638i	0.790676	−	1.08827i	0.994024	−	0.109165i	$-0.0348177\pi$
$734$	33.1699	−	24.0993i	1.22432	−	0.889522i
$735$		0			0
$736$			0.295695i			0.0108995i
$737$	−4.69176	+	4.21979i	−0.172823	+	0.155438i
$738$	−2.06816	−	13.5467i	−0.0761301	−	0.498661i
$739$	−5.34301	−	1.73605i	−0.196546	−	0.0638616i	0.209090	−	0.977896i	$-0.432950\pi$
$739$	−5.34301	−	1.73605i	−0.196546	−	0.0638616i	−0.405636	+	0.914035i	$0.632950\pi$
$740$		0			0
$741$	−8.36291	+	1.98309i	−0.307219	+	0.0728508i
$742$	2.66109	+	8.19000i	0.0976917	+	0.300664i
$743$	3.90188	+	12.0088i	0.143146	+	0.440558i	0.996768	−	0.0803349i	$-0.0255990\pi$
$743$	3.90188	+	12.0088i	0.143146	+	0.440558i	−0.853622	+	0.520893i	$0.825599\pi$
$744$	−37.5731	+	8.90970i	−1.37750	+	0.326645i
$745$		0			0
$746$	−10.6345	−	3.45537i	−0.389358	−	0.126510i
$747$	0.389611	+	2.55200i	0.0142551	+	0.0933728i
$748$	−0.325120	−	0.731318i	−0.0118876	−	0.0267396i
$749$			0.565082i			0.0206477i
$750$		0			0
$751$	24.0215	−	17.4526i	0.876556	−	0.636855i	−0.0557822	−	0.998443i	$-0.517765\pi$
$751$	24.0215	−	17.4526i	0.876556	−	0.636855i	0.932338	+	0.361588i	$0.117765\pi$
$752$	−18.3962	+	25.3202i	−0.670841	+	0.923334i
$753$	15.3311	−	36.7225i	0.558698	−	1.33824i
$754$	−23.6380	+	7.68044i	−0.860844	+	0.279705i
$755$		0			0
$756$	0.0244918	+	0.348466i	0.000890759	+	0.0126736i
$757$	−1.86354	+	5.73537i	−0.0677314	+	0.208456i	−0.979194	−	0.202928i	$-0.934954\pi$
$757$	−1.86354	+	5.73537i	−0.0677314	+	0.208456i	0.911462	+	0.411384i	$0.134954\pi$
$758$	−34.7215			−1.26114
$759$	3.18765	−	2.42909i	0.115704	−	0.0881704i
$760$		0			0
$761$	−11.0839	+	34.1128i	−0.401792	+	1.23659i	0.521752	+	0.853097i	$0.325279\pi$
$761$	−11.0839	+	34.1128i	−0.401792	+	1.23659i	−0.923544	+	0.383492i	$0.874721\pi$
$762$	11.1752	+	0.910891i	0.404836	+	0.0329981i
$763$	−1.85700	−	1.34919i	−0.0672281	−	0.0488440i
$764$	1.01043	−	0.328310i	0.0365562	−	0.0118778i
$765$		0			0
$766$	20.2580	−	27.8827i	0.731951	−	1.00744i
$767$	63.5220	−	46.1515i	2.29365	−	1.66643i
$768$	1.61852	+	2.65780i	0.0584033	+	0.0959052i
$769$		−	27.6384i		−	0.996666i	−0.866986	−	0.498333i	$-0.833946\pi$
$769$		−	27.6384i		−	0.996666i	0.866986	−	0.498333i	$-0.166054\pi$
$770$		0			0
$771$	22.9794	+	19.7374i	0.827583	+	0.710825i
$772$	1.50991	+	0.490601i	0.0543430	+	0.0176571i
$773$	−23.8655	−	32.8480i	−0.858382	−	1.18146i	−0.981953	−	0.189126i	$-0.939435\pi$
$773$	−23.8655	−	32.8480i	−0.858382	−	1.18146i	0.123571	−	0.992336i	$-0.460565\pi$
$774$	−29.3889	−	15.1815i	−1.05636	−	0.545689i
$775$		0			0
$776$	−11.0543	−	34.0215i	−0.396825	−	1.22130i
$777$	−1.76616	−	7.44807i	−0.0633606	−	0.267198i
$778$	−13.9068	−	19.1411i	−0.498583	−	0.686240i
$779$	−2.37286	−	0.770989i	−0.0850166	−	0.0276236i
$780$		0			0
$781$	−0.618201	+	1.06939i	−0.0221210	+	0.0382659i
$782$			3.11578i			0.111420i
$783$	−10.8864	+	9.14139i	−0.389049	+	0.326687i
$784$	19.2703	−	14.0007i	0.688224	−	0.500024i
$785$		0			0
$786$	−29.7792	−	12.4324i	−1.06219	−	0.443449i
$787$	−33.9748	+	11.0391i	−1.21107	+	0.393501i	−0.843823	−	0.536622i	$-0.819700\pi$
$787$	−33.9748	+	11.0391i	−1.21107	+	0.393501i	−0.367249	+	0.930123i	$0.619700\pi$
$788$	−0.741884	−	0.539010i	−0.0264285	−	0.0192014i
$789$	−0.308792	+	3.78840i	−0.0109933	+	0.134871i
$790$		0			0
$791$	9.03606			0.321285
$792$	10.4292	−	26.6789i	0.370586	−	0.947993i
$793$	11.3709			0.403791
$794$	3.56782	−	10.9806i	0.126617	−	0.389687i
$795$		0			0
$796$	−0.553354	−	0.402035i	−0.0196131	−	0.0142498i
$797$	9.23655	−	3.00114i	0.327175	−	0.106306i	−0.140824	−	0.990035i	$-0.544975\pi$
$797$	9.23655	−	3.00114i	0.327175	−	0.106306i	0.467999	+	0.883729i	$0.344975\pi$
$798$	−1.50712	−	0.629201i	−0.0533514	−	0.0222735i
$799$	15.4030	−	21.2004i	0.544918	−	0.750016i
$800$		0			0
$801$	−2.54821	+	15.5275i	−0.0900367	+	0.548637i
$802$		−	19.0276i		−	0.671888i
$803$	1.74646	+	16.7051i	0.0616312	+	0.589509i
$804$	−0.160966	+	0.187405i	−0.00567682	+	0.00660927i
$805$		0			0
$806$	41.3532	+	56.9178i	1.45661	+	2.00485i
$807$	−0.477563	−	2.01393i	−0.0168110	−	0.0708937i
$808$	−11.7462	−	36.1512i	−0.413231	−	1.27179i
$809$	0.455901	+	1.40312i	0.0160286	+	0.0493310i	0.958751	−	0.284248i	$-0.0917437\pi$
$809$	0.455901	+	1.40312i	0.0160286	+	0.0493310i	−0.942722	+	0.333579i	$0.891744\pi$
$810$		0			0
$811$	−18.8256	−	25.9112i	−0.661056	−	0.909865i	0.338460	−	0.940981i	$-0.390094\pi$
$811$	−18.8256	−	25.9112i	−0.661056	−	0.909865i	−0.999516	+	0.0311156i	$0.990094\pi$
$812$	0.174918	+	0.0568342i	0.00613841	+	0.00199449i
$813$	2.42602	+	2.08375i	0.0850841	+	0.0730802i
$814$	−4.72712	+	22.1792i	−0.165685	+	0.777380i
$815$		0			0
$816$	11.1482	+	18.3067i	0.390266	+	0.640864i
$817$	−4.87228	+	3.53992i	−0.170460	+	0.123846i
$818$	−18.5834	+	25.5779i	−0.649755	+	0.894311i
$819$	15.7406	−	7.90989i	0.550020	−	0.276394i
$820$		0			0
$821$	−10.5911	−	7.69491i	−0.369633	−	0.268554i	0.387426	−	0.921901i	$-0.373364\pi$
$821$	−10.5911	−	7.69491i	−0.369633	−	0.268554i	−0.757059	+	0.653347i	$0.773364\pi$
$822$	−27.3235	−	2.22713i	−0.953015	−	0.0776801i
$823$	8.69247	−	26.7527i	0.303001	−	0.932540i	−0.677415	−	0.735601i	$-0.736900\pi$
$823$	8.69247	−	26.7527i	0.303001	−	0.932540i	0.980416	−	0.196939i	$-0.0631001\pi$
$824$	−1.25840			−0.0438384
$825$		0			0
$826$	14.9199			0.519130
$827$	−15.6650	+	48.2119i	−0.544726	+	1.67649i	0.176916	+	0.984226i	$0.443388\pi$
$827$	−15.6650	+	48.2119i	−0.544726	+	1.67649i	−0.721641	+	0.692267i	$0.756612\pi$
$828$	0.111562	−	0.110324i	0.00387705	−	0.00383402i
$829$	−42.3470	−	30.7669i	−1.47077	−	1.06858i	−0.980390	−	0.197069i	$-0.936858\pi$
$829$	−42.3470	−	30.7669i	−1.47077	−	1.06858i	−0.490381	−	0.871508i	$-0.663142\pi$
$830$		0			0
$831$	20.0902	−	48.1219i	0.696922	−	1.66933i
$832$	31.8563	−	43.8465i	1.10442	−	1.52010i
$833$	−16.1348	+	11.7226i	−0.559038	+	0.406165i
$834$	34.2748	−	20.8723i	1.18684	−	0.722749i
$835$		0			0
$836$	−0.126001	−	0.140094i	−0.00435784	−	0.00484524i
$837$	34.1322	+	21.3113i	1.17978	+	0.736626i
$838$	40.4084	+	13.1295i	1.39588	+	0.453550i
$839$	−27.2838	−	37.5530i	−0.941943	−	1.29647i	−0.955015	−	0.296559i	$-0.904161\pi$
$839$	−27.2838	−	37.5530i	−0.941943	−	1.29647i	0.0130716	−	0.999915i	$-0.495839\pi$
$840$		0			0
$841$	−6.64868	−	20.4625i	−0.229265	−	0.705605i
$842$	−13.5800	−	41.7950i	−0.467998	−	1.44035i
$843$	−32.7569	+	7.76763i	−1.12821	+	0.267531i
$844$	0.274827	+	0.378267i	0.00945993	+	0.0130205i
$845$		0			0
$846$	33.4976	−	5.11404i	1.15167	−	0.175824i
$847$	7.32352	+	6.60877i	0.251639	+	0.227080i
$848$		−	26.6077i		−	0.913711i
$849$	31.6788	−	19.2914i	1.08721	−	0.662080i
$850$		0			0
$851$	−2.02084	+	2.78145i	−0.0692736	+	0.0953470i
$852$	−0.0186306	+	0.0446255i	−0.000638272	+	0.00152885i
$853$	8.69949	−	2.82664i	0.297865	−	0.0967822i	−0.156272	−	0.987714i	$-0.549948\pi$
$853$	8.69949	−	2.82664i	0.297865	−	0.0967822i	0.454137	+	0.890932i	$0.349948\pi$
$854$	1.74803	+	1.27002i	0.0598165	+	0.0434592i
$855$		0			0
$856$	0.560581	−	1.72529i	0.0191603	−	0.0589693i
$857$	−56.3567			−1.92511			−0.962554	−	0.271092i	$-0.912615\pi$
$857$	−56.3567			−1.92511			−0.962554	+	0.271092i	$0.912615\pi$
$858$	−52.1758	+	1.19181i	−1.78125	+	0.0406876i
$859$	−8.91219			−0.304080			−0.152040	−	0.988374i	$-0.548584\pi$
$859$	−8.91219			−0.304080			−0.152040	+	0.988374i	$0.548584\pi$
$860$		0			0
$861$	5.09688	+	0.415445i	0.173701	+	0.0141583i
$862$	24.0720	+	17.4893i	0.819896	+	0.595689i
$863$	5.91241	−	1.92106i	0.201261	−	0.0653936i	−0.206652	−	0.978415i	$-0.566257\pi$
$863$	5.91241	−	1.92106i	0.201261	−	0.0653936i	0.407913	+	0.913021i	$0.366257\pi$
$864$	0.532038	−	2.13713i	0.0181003	−	0.0727066i
$865$		0			0
$866$	25.1436	−	18.2679i	0.854414	−	0.620768i
$867$	5.98048	+	9.82066i	0.203108	+	0.333527i
$868$		−	0.520612i		−	0.0176707i
$869$	45.2676	−	20.1245i	1.53560	−	0.682677i
$870$		0			0
$871$	11.8485	+	3.84980i	0.401470	+	0.130446i
$872$	4.33130	+	5.96152i	0.146676	+	0.201883i
$873$	−17.1084	+	33.1189i	−0.579031	+	1.12090i
$874$	0.226678	+	0.697643i	0.00766749	+	0.0235981i
$875$		0			0
$876$	0.151720	+	0.639819i	0.00512614	+	0.0216175i
$877$	−11.8885	−	16.3632i	−0.401447	−	0.552545i	0.559659	−	0.828723i	$-0.310932\pi$
$877$	−11.8885	−	16.3632i	−0.401447	−	0.552545i	−0.961107	+	0.276178i	$0.910932\pi$
$878$	25.3584	+	8.23945i	0.855805	+	0.278068i
$879$	22.0617	−	25.6855i	0.744122	−	0.866349i
$880$		0			0
$881$		−	27.2385i		−	0.917689i	−0.888516	−	0.458845i	$-0.848263\pi$
$881$		−	27.2385i		−	0.917689i	0.888516	−	0.458845i	$-0.151737\pi$
$882$	−25.4487	−	4.17639i	−0.856903	−	0.140626i
$883$	−33.1640	+	24.0950i	−1.11606	+	0.810863i	−0.983607	−	0.180327i	$-0.942284\pi$
$883$	−33.1640	+	24.0950i	−1.11606	+	0.810863i	−0.132450	+	0.991190i	$0.542284\pi$
$884$	−0.928748	+	1.27831i	−0.0312372	+	0.0429943i
$885$		0			0
$886$	32.1314	−	10.4401i	1.07948	−	0.350743i
$887$	−9.60397	−	6.97769i	−0.322470	−	0.234288i	0.414759	−	0.909931i	$-0.363866\pi$
$887$	−9.60397	−	6.97769i	−0.322470	−	0.234288i	−0.737229	+	0.675643i	$0.763866\pi$
$888$	−1.99636	+	24.4923i	−0.0669935	+	0.821908i
$889$	−1.29295	+	3.97930i	−0.0433643	+	0.133462i
$890$		0			0
$891$	−27.4093	+	11.8207i	−0.918247	+	0.396009i
$892$	−1.27843			−0.0428052
$893$	1.90646	−	5.86749i	0.0637974	−	0.196348i
$894$	−2.72308	+	33.4080i	−0.0910735	+	1.11733i
$895$		0			0
$896$	9.07152	−	2.94751i	0.303058	−	0.0984695i
$897$	−7.30156	−	3.04830i	−0.243792	−	0.101780i
$898$	6.09173	−	8.38455i	0.203284	−	0.279796i
$899$	17.1397	−	12.4527i	0.571639	−	0.415320i
$900$		0			0
$901$			22.2783i			0.742199i
$902$	−13.1161	−	7.58222i	−0.436717	−	0.252460i
$903$	8.04286	−	9.36394i	0.267649	−	0.311612i
$904$	−27.5886	−	8.96409i	−0.917584	−	0.298141i
$905$		0			0
$906$	−8.00232	−	33.7466i	−0.265859	−	1.12115i
$907$	2.58726	+	7.96276i	0.0859085	+	0.264399i	0.984778	−	0.173818i	$-0.0556103\pi$
$907$	2.58726	+	7.96276i	0.0859085	+	0.264399i	−0.898869	+	0.438217i	$0.855610\pi$
$908$	0.122998	+	0.378550i	0.00408185	+	0.0125626i
$909$	−18.1793	+	35.1921i	−0.602970	+	1.16725i
$910$		0			0
$911$	15.6294	+	5.07829i	0.517824	+	0.168251i	0.556258	−	0.831010i	$-0.312237\pi$
$911$	15.6294	+	5.07829i	0.517824	+	0.168251i	−0.0384333	+	0.999261i	$0.512237\pi$
$912$	3.82800	+	3.28794i	0.126758	+	0.108875i
$913$	2.47088	+	1.42838i	0.0817741	+	0.0472724i
$914$		−	18.7206i		−	0.619221i
$915$		0			0
$916$	0.0410294	−	0.0298096i	0.00135565	−	0.000984937i
$917$	7.07824	−	9.74237i	0.233744	−	0.321721i
$918$	5.60616	−	22.5192i	0.185031	−	0.743246i
$919$	29.7484	−	9.66583i	0.981308	−	0.318846i	0.225936	−	0.974142i	$-0.427456\pi$
$919$	29.7484	−	9.66583i	0.981308	−	0.318846i	0.755372	+	0.655296i	$0.227456\pi$
$920$		0			0
$921$	−2.63375	−	0.214677i	−0.0867851	−	0.00707384i
$922$	−6.67843	+	20.5541i	−0.219942	+	0.676913i
$923$	2.43868			0.0802701
$924$	0.317540	+	0.219805i	0.0104463	+	0.00723106i
$925$		0			0
$926$	13.3847	−	41.1938i	0.439848	−	1.35371i
$927$	0.922056	+	0.932404i	0.0302843	+	0.0306242i
$928$	−0.938086	−	0.681559i	−0.0307942	−	0.0223733i
$929$	30.5407	−	9.92327i	1.00201	−	0.325572i	0.238340	−	0.971182i	$-0.423397\pi$
$929$	30.5407	−	9.92327i	1.00201	−	0.325572i	0.763667	+	0.645610i	$0.223397\pi$
$930$		0			0
$931$	−2.75985	+	3.79861i	−0.0904504	+	0.124494i
$932$	−0.128301	+	0.0932160i	−0.00420263	+	0.00305339i
$933$	−10.2790	+	6.25957i	−0.336518	+	0.204929i
$934$		−	9.79991i		−	0.320663i
$935$		0			0
$936$	−55.9055	+	8.53504i	−1.82733	+	0.278976i
$937$	−17.9384	−	5.82855i	−0.586023	−	0.190410i	0.000973916	−	1.00000i	$-0.499690\pi$
$937$	−17.9384	−	5.82855i	−0.586023	−	0.190410i	−0.586997	+	0.809589i	$0.699690\pi$
$938$	1.39147	+	1.91519i	0.0454331	+	0.0625333i
$939$	−48.8417	+	11.5818i	−1.59389	+	0.377959i
$940$		0			0
$941$	10.7722	+	33.1533i	0.351162	+	1.08077i	0.958201	+	0.286094i	$0.0923570\pi$
$941$	10.7722	+	33.1533i	0.351162	+	1.08077i	−0.607039	+	0.794672i	$0.707643\pi$
$942$	0.803820	−	0.190610i	0.0261899	−	0.00621040i
$943$	−1.35006	−	1.85819i	−0.0439639	−	0.0605111i
$944$	−43.8431	−	14.2455i	−1.42697	−	0.463651i
$945$		0			0
$946$	−33.4162	+	14.8558i	−1.08645	+	0.483003i
$947$		−	2.29089i		−	0.0744441i	−0.999307	−	0.0372220i	$-0.988149\pi$
$947$		−	2.29089i		−	0.0744441i	0.999307	−	0.0372220i	$-0.0118509\pi$
$948$	1.65647	−	1.00874i	0.0537997	−	0.0327624i
$949$	26.8273	−	19.4911i	0.870850	−	0.632709i
$950$		0			0
$951$	−8.50841	+	20.3801i	−0.275904	+	0.660870i
$952$	−7.90373	+	2.56808i	−0.256161	+	0.0832319i
$953$	9.93032	+	7.21480i	0.321675	+	0.233710i	0.736890	−	0.676013i	$-0.236294\pi$
$953$	9.93032	+	7.21480i	0.321675	+	0.233710i	−0.415215	+	0.909723i	$0.636294\pi$
$954$	−20.4837	+	20.2563i	−0.663184	+	0.655823i
$955$		0			0
$956$	−0.640008			−0.0206993
$957$	0.358888	+	15.7117i	0.0116012	+	0.507886i
$958$	−37.8367			−1.22245
$959$	3.16127	−	9.72939i	0.102083	−	0.314179i
$960$		0			0
$961$	−23.4369	−	17.0279i	−0.756029	−	0.549287i
$962$	42.5803	−	13.8352i	1.37284	−	0.446064i
$963$	−1.68910	+	0.848799i	−0.0544304	+	0.0273522i
$964$	−0.203788	+	0.280490i	−0.00656356	+	0.00903396i
$965$		0			0
$966$	−0.781996	−	1.28413i	−0.0251603	−	0.0413162i
$967$			19.7879i			0.636335i	0.948035	+	0.318167i	$0.103067\pi$
$967$			19.7879i			0.636335i	−0.948035	+	0.318167i	$0.896933\pi$
$968$	−15.8038	−	27.4429i	−0.507954	−	0.882048i
$969$	−3.20515	−	2.75296i	−0.102964	−	0.0884378i
$970$		0			0
$971$	−10.0957	−	13.8955i	−0.323986	−	0.445928i	0.615693	−	0.787986i	$-0.288876\pi$
$971$	−10.0957	−	13.8955i	−0.323986	−	0.445928i	−0.939679	+	0.342058i	$0.888876\pi$
$972$	−1.00482	+	0.596633i	−0.0322295	+	0.0191370i
$973$	4.62761	+	14.2423i	0.148355	+	0.456588i
$974$	9.12388	+	28.0804i	0.292348	+	0.899755i
$975$		0			0
$976$	−3.92410	−	5.40106i	−0.125607	−	0.172884i
$977$	8.05036	+	2.61572i	0.257554	+	0.0836843i	0.434948	−	0.900456i	$-0.356767\pi$
$977$	8.05036	+	2.61572i	0.257554	+	0.0836843i	−0.177394	+	0.984140i	$0.556767\pi$
$978$	16.7067	−	19.4508i	0.534220	−	0.621969i
$979$	11.6330	+	12.9341i	0.371792	+	0.413376i
$980$		0			0
$981$	1.24353	−	7.57739i	0.0397027	−	0.241928i
$982$	40.3784	−	29.3366i	1.28853	−	0.936168i
$983$	22.0086	−	30.2923i	0.701966	−	0.966173i	−0.297967	−	0.954576i	$-0.596309\pi$
$983$	22.0086	−	30.2923i	0.701966	−	0.966173i	0.999933	−	0.0115969i	$-0.00369149\pi$
$984$	−15.1495	−	6.32470i	−0.482948	−	0.201624i
$985$		0			0
$986$	−9.88475	−	7.18169i	−0.314795	−	0.228712i
$987$	−1.02729	+	12.6033i	−0.0326991	+	0.401168i
$988$	−0.114953	+	0.353790i	−0.00365715	+	0.0112556i
$989$	−5.54424			−0.176297
$990$		0			0
$991$	−5.33052			−0.169329			−0.0846647	−	0.996409i	$-0.526982\pi$
$991$	−5.33052			−0.169329			−0.0846647	+	0.996409i	$0.526982\pi$
$992$	−1.01427	+	3.12161i	−0.0322031	+	0.0991111i
$993$	0.288211	−	3.53591i	0.00914610	−	0.112209i
$994$	0.374896	+	0.272378i	0.0118910	+	0.00863931i
$995$		0			0
$996$	0.103109	+	0.0430467i	0.00326714	+	0.00136399i
$997$	−0.611544	+	0.841718i	−0.0193678	+	0.0266575i	−0.818591	−	0.574377i	$-0.805244\pi$
$997$	−0.611544	+	0.841718i	−0.0193678	+	0.0266575i	0.799223	+	0.601034i	$0.205244\pi$
$998$	6.92275	−	5.02968i	0.219136	−	0.159212i
$999$	19.6102	−	16.4668i	0.620440	−	0.520988i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.bi.h.101.15		80
3.2	odd	2	inner	825.2.bi.h.101.5		80
5.2	odd	4		165.2.r.a.134.16	yes	80
5.3	odd	4		165.2.r.a.134.5	✓	80
5.4	even	2	inner	825.2.bi.h.101.6		80
11.6	odd	10	inner	825.2.bi.h.776.5		80
15.2	even	4		165.2.r.a.134.6	yes	80
15.8	even	4		165.2.r.a.134.15	yes	80
15.14	odd	2	inner	825.2.bi.h.101.16		80
33.17	even	10	inner	825.2.bi.h.776.15		80
55.17	even	20		165.2.r.a.149.15	yes	80
55.28	even	20		165.2.r.a.149.6	yes	80
55.39	odd	10	inner	825.2.bi.h.776.16		80
165.17	odd	20		165.2.r.a.149.5	yes	80
165.83	odd	20		165.2.r.a.149.16	yes	80
165.149	even	10	inner	825.2.bi.h.776.6		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.r.a.134.5	✓	80	5.3	odd	4
165.2.r.a.134.6	yes	80	15.2	even	4
165.2.r.a.134.15	yes	80	15.8	even	4
165.2.r.a.134.16	yes	80	5.2	odd	4
165.2.r.a.149.5	yes	80	165.17	odd	20
165.2.r.a.149.6	yes	80	55.28	even	20
165.2.r.a.149.15	yes	80	55.17	even	20
165.2.r.a.149.16	yes	80	165.83	odd	20
825.2.bi.h.101.5		80	3.2	odd	2	inner
825.2.bi.h.101.6		80	5.4	even	2	inner
825.2.bi.h.101.15		80	1.1	even	1	trivial
825.2.bi.h.101.16		80	15.14	odd	2	inner
825.2.bi.h.776.5		80	11.6	odd	10	inner
825.2.bi.h.776.6		80	165.149	even	10	inner
825.2.bi.h.776.15		80	33.17	even	10	inner
825.2.bi.h.776.16		80	55.39	odd	10	inner

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.428747 - 1.31955i) q^{2} +(-0.140712 + 1.72633i) q^{3} +(0.0606486 + 0.0440638i) q^{4} +(2.21764 + 0.925835i) q^{6} +(-0.527114 + 0.725510i) q^{7} +(2.32910 - 1.69219i) q^{8} +(-2.96040 - 0.485831i) q^{9} +O(q^{10})\)	\(q+(0.428747 - 1.31955i) q^{2} +(-0.140712 + 1.72633i) q^{3} +(0.0606486 + 0.0440638i) q^{4} +(2.21764 + 0.925835i) q^{6} +(-0.527114 + 0.725510i) q^{7} +(2.32910 - 1.69219i) q^{8} +(-2.96040 - 0.485831i) q^{9} +(-2.46596 + 2.21790i) q^{11} +(-0.0846024 + 0.0984989i) q^{12} +(6.22748 + 2.02343i) q^{13} +(0.731347 + 1.00661i) q^{14} +(-1.18800 - 3.65629i) q^{16} +(0.994701 + 3.06137i) q^{17} +(-1.91034 + 3.69809i) q^{18} +(0.445440 + 0.613095i) q^{19} +(-1.17829 - 1.01206i) q^{21} +(1.86935 + 4.20487i) q^{22} +0.697650i q^{23} +(2.59354 + 4.25889i) q^{24} +(5.34003 - 7.34992i) q^{26} +(1.25527 - 5.04225i) q^{27} +(-0.0639374 + 0.0207745i) q^{28} +(-2.21328 - 1.60804i) q^{29} +(-2.39303 + 7.36499i) q^{31} +0.423844 q^{32} +(-3.48182 - 4.56913i) q^{33} +4.46611 q^{34} +(-0.158137 - 0.159911i) q^{36} +(3.98689 + 2.89665i) q^{37} +(0.999990 - 0.324916i) q^{38} +(-4.36938 + 10.4659i) q^{39} +(-2.66350 + 1.93515i) q^{41} +(-1.84065 + 1.12090i) q^{42} +7.94703i q^{43} +(-0.247286 + 0.0258529i) q^{44} +(0.920583 + 0.299116i) q^{46} +(-4.78514 - 6.58618i) q^{47} +(6.47911 - 1.53639i) q^{48} +(1.91460 + 5.89254i) q^{49} +(-5.42489 + 1.28640i) q^{51} +(0.288528 + 0.397124i) q^{52} +(6.58232 + 2.13872i) q^{53} +(-6.11531 - 3.81824i) q^{54} +2.58176i q^{56} +(-1.12108 + 0.682704i) q^{57} +(-3.07083 + 2.23109i) q^{58} +(7.04822 - 9.70104i) q^{59} +(1.65156 - 0.536624i) q^{61} +(8.69246 + 6.31544i) q^{62} +(1.91294 - 1.89171i) q^{63} +(2.55772 - 7.87186i) q^{64} +(-7.52201 + 2.63543i) q^{66} +1.90261 q^{67} +(-0.0745685 + 0.229498i) q^{68} +(-1.20437 - 0.0981680i) q^{69} +(0.354205 - 0.115088i) q^{71} +(-7.71718 + 3.87801i) q^{72} +(2.97667 - 4.09704i) q^{73} +(5.53164 - 4.01897i) q^{74} +0.0568111i q^{76} +(-0.309265 - 2.95816i) q^{77} +(11.9370 + 10.2529i) q^{78} +(-14.2056 - 4.61569i) q^{79} +(8.52794 + 2.87651i) q^{81} +(1.41155 + 4.34432i) q^{82} +(-0.265916 - 0.818406i) q^{83} +(-0.0268668 - 0.113300i) q^{84} +(10.4865 + 3.40727i) q^{86} +(3.08744 - 3.59457i) q^{87} +(-1.99036 + 9.33856i) q^{88} -5.24506i q^{89} +(-4.75061 + 3.45152i) q^{91} +(-0.0307411 + 0.0423115i) q^{92} +(-12.3776 - 5.16749i) q^{93} +(-10.7424 + 3.49042i) q^{94} +(-0.0596401 + 0.731693i) q^{96} +(3.83972 - 11.8174i) q^{97} +8.59638 q^{98} +(8.37774 - 5.36782i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{4} - 10 q^{6} + 10 q^{9}+O(q^{10}) \) 80 * q - 4 * q^4 - 10 * q^6 + 10 * q^9	\( 80 q - 4 q^{4} - 10 q^{6} + 10 q^{9} - 60 q^{16} + 20 q^{19} + 30 q^{24} - 20 q^{31} + 56 q^{34} + 2 q^{36} + 50 q^{39} - 40 q^{46} - 72 q^{49} + 30 q^{51} - 96 q^{64} - 42 q^{66} - 30 q^{69} - 66 q^{81} - 140 q^{84} + 48 q^{91} - 60 q^{94} - 70 q^{96} - 60 q^{99}+O(q^{100}) \) 80 * q - 4 * q^4 - 10 * q^6 + 10 * q^9 - 60 * q^16 + 20 * q^19 + 30 * q^24 - 20 * q^31 + 56 * q^34 + 2 * q^36 + 50 * q^39 - 40 * q^46 - 72 * q^49 + 30 * q^51 - 96 * q^64 - 42 * q^66 - 30 * q^69 - 66 * q^81 - 140 * q^84 + 48 * q^91 - 60 * q^94 - 70 * q^96 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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