LMFDB - Embedded newform 825.2.bi.h.101.6

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			101.6
Character	$\chi$	$=$	825.101
Dual form			825.2.bi.h.776.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.428747 + 1.31955i) q^{2} +(0.140712 - 1.72633i) q^{3} +(0.0606486 + 0.0440638i) q^{4} +(2.21764 + 0.925835i) q^{6} +(0.527114 - 0.725510i) q^{7} +(-2.32910 + 1.69219i) q^{8} +(-2.96040 - 0.485831i) q^{9} +O(q^{10})$	\(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	$0.263200\pi$
$2$	−0.428747	+	1.31955i	−0.303170	+	0.933062i	−0.980354	+	0.197248i	$0.936800\pi$
$3$	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	−0.697699	−	0.716391i	$-0.745793\pi$
$7$	0.527114	−	0.725510i	0.199230	−	0.274217i	0.896929	+	0.442174i	$0.145793\pi$
$8$	−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	−0.734153	−	0.678984i	$-0.762421\pi$
$13$	−6.22748	−	2.02343i	−1.72719	−	0.561199i	−0.993039	+	0.117785i	$0.962421\pi$
$14$	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	$-0.972354\pi$
$17$	−0.994701	−	3.06137i	−0.241250	−	0.742492i	0.754980	−	0.655748i	$-0.227646\pi$
$18$	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	$-0.976827\pi$
$23$		−	0.697650i		−	0.145470i	0.997351	−	0.0727350i	$-0.0231727\pi$
$24$	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	0.209679	−	0.977770i	$-0.432758\pi$
$37$	−3.98689	−	2.89665i	−0.655441	−	0.476206i	−0.865120	+	0.501565i	$0.832758\pi$
$38$	−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	$-0.792791\pi$
$43$		−	7.94703i		−	1.21191i	0.795499	−	0.605955i	$-0.207209\pi$
$44$	−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	$0.00234962\pi$
$47$	4.78514	+	6.58618i	0.697984	+	0.960693i	−0.301988	+	0.953312i	$0.597650\pi$
$48$	−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	−0.180202	−	0.983630i	$-0.557675\pi$
$53$	−6.58232	−	2.13872i	−0.904151	−	0.293776i	−0.723949	+	0.689853i	$0.757675\pi$
$54$	−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	$-0.537078\pi$
$67$	−1.90261			−0.232441			−0.116220	+	0.993223i	$0.537078\pi$
$68$	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	−0.946869	−	0.321618i	$-0.895773\pi$
$73$	−2.97667	+	4.09704i	−0.348393	+	0.479522i	0.598476	+	0.801141i	$0.295773\pi$
$74$	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	0.964589	−	0.263756i	$-0.0849615\pi$
$83$	0.265916	+	0.818406i	0.0291881	+	0.0898317i	−0.935401	+	0.353588i	$0.884961\pi$
$84$	−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	$0.317279\pi$
$97$	−3.83972	+	11.8174i	−0.389864	+	1.19988i	−0.932890	+	0.360163i	$0.882721\pi$
$98$	−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	0.605071	−	0.796172i	$-0.293145\pi$
$103$	0.353627	+	0.256925i	0.0348439	+	0.0253156i	−0.570227	+	0.821487i	$0.693145\pi$
$104$	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	−0.612154	−	0.790739i	$-0.709697\pi$
$107$	−0.509781	+	0.370378i	−0.0492824	+	0.0358058i	0.562871	+	0.826545i	$0.309697\pi$
$108$	−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	0.990961	−	0.134152i	$-0.0428310\pi$
$113$	5.92260	+	8.15175i	0.557151	+	0.766853i	−0.433810	+	0.901004i	$0.642831\pi$
$114$	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	−0.499198	−	0.866488i	$-0.666372\pi$
$127$	−4.43732	+	1.44177i	−0.393749	+	0.127937i	0.105449	+	0.994425i	$0.466372\pi$
$128$	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	0.193614	−	0.981078i	$-0.437979\pi$
$137$	10.8493	−	3.52514i	0.926915	−	0.301173i	0.733300	+	0.679905i	$0.237979\pi$
$138$	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	−0.598828	−	0.800878i	$-0.704367\pi$
$157$	−0.278110	+	0.202058i	−0.0221956	+	0.0161260i	0.576632	+	0.817004i	$0.304367\pi$
$158$	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	$0.237218\pi$
$163$	−3.29710	+	10.1474i	−0.258249	+	0.794809i	−0.993172	+	0.116659i	$0.962782\pi$
$164$	−0.246808			−0.0192725
$165$		0			0
$166$	−1.19394			−0.0926675
$167$	0.413471	−	1.27253i	0.0319953	−	0.0984715i	−0.933784	−	0.357838i	$-0.883514\pi$
$167$	0.413471	−	1.27253i	0.0319953	−	0.0984715i	0.965779	+	0.259367i	$0.0835139\pi$
$168$	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	−0.880258	−	0.474495i	$-0.842631\pi$
$173$	−9.22022	+	6.69889i	−0.701001	+	0.509307i	0.179257	+	0.983802i	$0.442631\pi$
$174$	−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	−0.924941	−	0.380112i	$-0.875886\pi$
$193$	−20.1414	+	6.54433i	−1.44981	+	0.471072i	−0.524869	+	0.851183i	$0.675886\pi$
$194$	−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	$-0.356478\pi$
$197$	12.2325			0.871530			0.435765	+	0.900061i	$0.356478\pi$
$198$	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	−0.0205984	−	0.999788i	$-0.506557\pi$
$223$	13.7966	−	10.0238i	0.923891	−	0.671246i	0.944489	+	0.328542i	$0.106557\pi$
$224$	−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	0.436038	−	0.899928i	$-0.356381\pi$
$227$	−4.29548	−	3.12085i	−0.285101	−	0.207138i	−0.721139	+	0.692790i	$0.756381\pi$
$228$	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	−0.927357	−	0.374177i	$-0.877925\pi$
$233$	0.653719	−	2.01194i	0.0428265	−	0.131807i	0.970184	+	0.242371i	$0.0779251\pi$
$234$	−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	−0.998681	−	0.0513419i	$-0.983650\pi$
$257$	−10.2799	+	14.1491i	−0.641243	+	0.882595i	0.357439	+	0.933937i	$0.383650\pi$
$258$	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	$-0.521553\pi$
$263$	−2.19449			−0.135318			−0.0676590	+	0.997709i	$0.521553\pi$
$264$	−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	0.992013	−	0.126132i	$-0.0402564\pi$
$277$	28.6337	+	9.30364i	1.72043	+	0.559002i	0.728417	+	0.685134i	$0.240256\pi$
$278$	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	$0.0196066\pi$
$283$	12.5870	+	17.3245i	0.748217	+	1.02983i	−0.249887	+	0.968275i	$0.580393\pi$
$284$	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	0.944501	−	0.328508i	$-0.106546\pi$
$293$	15.8153	+	11.4905i	0.923938	+	0.671280i	−0.0205632	+	0.999789i	$0.506546\pi$
$294$	−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	$-0.986138\pi$
$307$		−	1.52564i		−	0.0870730i	0.999052	−	0.0435365i	$-0.0138625\pi$
$308$	−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	$-0.794504\pi$
$313$	−8.95555	−	27.5623i	−0.506197	−	1.55792i	0.292551	−	0.956250i	$-0.405496\pi$
$314$	−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	−0.0520233	−	0.998646i	$-0.516567\pi$
$317$	−12.1266	−	3.94019i	−0.681100	−	0.221303i	−0.629077	+	0.777343i	$0.716567\pi$
$318$	−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	−0.839180	−	0.543854i	$-0.816965\pi$
$337$	−1.14962	+	1.58232i	−0.0626238	+	0.0861943i	0.776556	+	0.630048i	$0.216965\pi$
$338$	−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	$-0.874446\pi$
$347$	−7.49213	−	23.0584i	−0.402199	−	1.23784i	0.521013	−	0.853549i	$-0.325554\pi$
$348$	−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	$-0.980979\pi$
$353$		−	2.24413i		−	0.119443i	0.998215	−	0.0597215i	$-0.0190213\pi$
$354$	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	−0.249834	−	0.968289i	$-0.580376\pi$
$367$	−23.9070	−	17.3694i	−1.24793	−	0.906677i	−0.998100	+	0.0616119i	$0.980376\pi$
$368$	−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	$0.0669053\pi$
$373$			8.05921i			0.417290i	−0.977991	+	0.208645i	$0.933095\pi$
$374$	−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	−0.364771	−	0.931097i	$-0.618853\pi$
$383$	−23.6246	−	7.67611i	−1.20716	−	0.392231i	−0.842391	+	0.538867i	$0.818853\pi$
$384$	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	$-0.566963\pi$
$397$	−8.32149			−0.417643			−0.208822	+	0.977954i	$0.566963\pi$
$398$	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	0.0599343	−	0.998202i	$-0.480911\pi$
$433$	−18.1221	−	13.1665i	−0.870892	−	0.632740i	−0.930826	+	0.365462i	$0.880911\pi$
$434$	−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	0.319915	−	0.947446i	$-0.396346\pi$
$443$	−14.3128	−	19.6998i	−0.680019	−	0.935966i	−0.999934	+	0.0114800i	$0.996346\pi$
$444$	−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	−0.593362	−	0.804936i	$-0.702200\pi$
$457$	−12.8323	+	4.16948i	−0.600272	+	0.195040i	−0.00691008	+	0.999976i	$0.502200\pi$
$458$	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	$-0.758351\pi$
$463$	−31.2181			−1.45083			−0.725414	+	0.688313i	$0.758351\pi$
$464$	−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	−0.460288	−	0.887770i	$-0.652254\pi$
$467$	−6.71752	+	2.18266i	−0.310850	+	0.101001i	0.149438	+	0.988771i	$0.452254\pi$
$468$	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	−0.124883	−	0.992172i	$-0.539855\pi$
$487$	17.2161	−	12.5083i	0.780137	−	0.566803i	0.905020	+	0.425368i	$0.139855\pi$
$488$	−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	−0.981487	−	0.191529i	$-0.938655\pi$
$503$	−24.7294	+	17.9669i	−1.10263	+	0.801106i	−0.121141	+	0.992635i	$0.538655\pi$
$504$	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	0.108620	−	0.994083i	$-0.465357\pi$
$523$	17.8563	−	5.80188i	0.780803	−	0.253698i	0.672183	+	0.740385i	$0.265357\pi$
$524$	−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	0.555700	−	0.831383i	$-0.312450\pi$
$547$	−9.51221	−	13.0924i	−0.406713	−	0.559792i	−0.962413	+	0.271591i	$0.912450\pi$
$548$	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	0.0507444	−	0.998712i	$-0.483841\pi$
$557$	−20.8491	−	15.1478i	−0.883406	−	0.641832i	−0.934150	+	0.356880i	$0.883841\pi$
$558$	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	−0.977182	−	0.212405i	$-0.931870\pi$
$563$	−1.46581	+	4.51129i	−0.0617764	+	0.190128i	0.915405	+	0.402533i	$0.131870\pi$
$564$	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	$0.0131334\pi$
$577$	5.16605	+	15.8995i	0.215066	+	0.661904i	−0.784083	+	0.620656i	$0.786867\pi$
$578$	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	−0.938929	−	0.344112i	$-0.888180\pi$
$587$	−7.78966	+	10.7215i	−0.321514	+	0.442525i	0.617415	+	0.786638i	$0.288180\pi$
$588$	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	$-0.516527\pi$
$593$	−2.52752			−0.103793			−0.0518964	+	0.998652i	$0.516527\pi$
$594$	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	−0.0459818	−	0.998942i	$-0.514642\pi$
$607$	−16.5155	−	5.36623i	−0.670345	−	0.217808i	−0.624364	+	0.781134i	$0.714642\pi$
$608$	−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	0.727531	−	0.686075i	$-0.240668\pi$
$613$	−3.70849	−	5.10430i	−0.149784	−	0.206161i	−0.877315	+	0.479914i	$0.840668\pi$
$614$	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	$0.237127\pi$
$617$			33.6793i			1.35588i	−0.735117	+	0.677940i	$0.762873\pi$
$618$	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	$0.134145\pi$
$643$	10.5161	+	32.3653i	0.414716	+	1.27636i	−0.497789	+	0.867298i	$0.665855\pi$
$644$	−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	−0.128773	−	0.991674i	$-0.541104\pi$
$647$	−20.7519	−	6.74272i	−0.815843	−	0.265084i	−0.687071	+	0.726591i	$0.741104\pi$
$648$	−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	−0.970546	−	0.240916i	$-0.922552\pi$
$653$	−11.2822	+	15.5286i	−0.441506	+	0.607680i	0.529040	+	0.848597i	$0.322552\pi$
$654$	−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	0.627522	−	0.778599i	$-0.284069\pi$
$673$	17.5771	+	5.71116i	0.677549	+	0.220149i	0.0500268	+	0.998748i	$0.484069\pi$
$674$	−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	$-0.773877\pi$
$677$	−13.7407	−	42.2894i	−0.528096	−	1.62531i	0.230014	−	0.973187i	$-0.426123\pi$
$678$	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	$-0.776942\pi$
$683$		−	33.7026i		−	1.28959i	0.764354	−	0.644797i	$-0.223058\pi$
$684$	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	$-0.522662\pi$
$727$	−3.83594			−0.142267			−0.0711336	+	0.997467i	$0.522662\pi$
$728$	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	$0.434818\pi$
$733$	−21.4067	+	29.4638i	−0.790676	+	1.08827i	−0.994024	+	0.109165i	$0.965182\pi$
$734$	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	0.853622	−	0.520893i	$-0.174401\pi$
$743$	−3.90188	−	12.0088i	−0.143146	−	0.440558i	−0.996768	+	0.0803349i	$0.974401\pi$
$744$	−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	−0.911462	−	0.411384i	$-0.865046\pi$
$757$	1.86354	−	5.73537i	0.0677314	−	0.208456i	0.979194	+	0.202928i	$0.0650457\pi$
$758$	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	$0.0605654\pi$
$773$	23.8655	+	32.8480i	0.858382	+	1.18146i	−0.123571	+	0.992336i	$0.539435\pi$
$774$	−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	0.367249	−	0.930123i	$-0.380300\pi$
$787$	33.9748	−	11.0391i	1.21107	−	0.393501i	0.843823	+	0.536622i	$0.180300\pi$
$788$	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	−0.467999	−	0.883729i	$-0.655025\pi$
$797$	−9.23655	+	3.00114i	−0.327175	+	0.106306i	0.140824	+	0.990035i	$0.455025\pi$
$798$	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	$0.263100\pi$
$823$	−8.69247	+	26.7527i	−0.303001	+	0.932540i	−0.980416	+	0.196939i	$0.936900\pi$
$824$	−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	$-0.556612\pi$
$827$	15.6650	−	48.2119i	0.544726	−	1.67649i	0.721641	−	0.692267i	$-0.243388\pi$
$828$	−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	−0.454137	−	0.890932i	$-0.650052\pi$
$853$	−8.69949	+	2.82664i	−0.297865	+	0.0967822i	0.156272	+	0.987714i	$0.450052\pi$
$854$	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	$-0.0873847\pi$
$857$	56.3567			1.92511			0.962554	+	0.271092i	$0.0873847\pi$
$858$	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	−0.407913	−	0.913021i	$-0.633743\pi$
$863$	−5.91241	+	1.92106i	−0.201261	+	0.0653936i	0.206652	+	0.978415i	$0.433743\pi$
$864$	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	0.961107	−	0.276178i	$-0.0890679\pi$
$877$	11.8885	+	16.3632i	0.401447	+	0.552545i	−0.559659	+	0.828723i	$0.689068\pi$
$878$	−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	0.132450	−	0.991190i	$-0.457716\pi$
$883$	33.1640	−	24.0950i	1.11606	−	0.810863i	0.983607	+	0.180327i	$0.0577156\pi$
$884$	−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	0.737229	−	0.675643i	$-0.236134\pi$
$887$	9.60397	+	6.97769i	0.322470	+	0.234288i	−0.414759	+	0.909931i	$0.636134\pi$
$888$	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	0.898869	−	0.438217i	$-0.144390\pi$
$907$	−2.58726	−	7.96276i	−0.0859085	−	0.264399i	−0.984778	+	0.173818i	$0.944390\pi$
$908$	−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	0.586997	−	0.809589i	$-0.300310\pi$
$937$	17.9384	+	5.82855i	0.586023	+	0.190410i	−0.000973916		1.00000i	$0.500310\pi$
$938$	−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	$0.0118509\pi$
$947$			2.29089i			0.0744441i	−0.999307	+	0.0372220i	$0.988149\pi$
$948$	−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	0.415215	−	0.909723i	$-0.363706\pi$
$953$	−9.93032	−	7.21480i	−0.321675	−	0.233710i	−0.736890	+	0.676013i	$0.763706\pi$
$954$	−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	$-0.896933\pi$
$967$		−	19.7879i		−	0.636335i	0.948035	−	0.318167i	$-0.103067\pi$
$968$	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	0.177394	−	0.984140i	$-0.443233\pi$
$977$	−8.05036	−	2.61572i	−0.257554	−	0.0836843i	−0.434948	+	0.900456i	$0.643233\pi$
$978$	−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	$0.403691\pi$
$983$	−22.0086	+	30.2923i	−0.701966	+	0.966173i	−0.999933	+	0.0115969i	$0.996309\pi$
$984$	−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	−0.799223	−	0.601034i	$-0.794756\pi$
$997$	0.611544	−	0.841718i	0.0193678	−	0.0266575i	0.818591	+	0.574377i	$0.194756\pi$
$998$	−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.101.6		80
3.2	odd	2	inner	825.2.bi.h.101.16		80
5.2	odd	4		165.2.r.a.134.5	✓	80
5.3	odd	4		165.2.r.a.134.16	yes	80
5.4	even	2	inner	825.2.bi.h.101.15		80
11.6	odd	10	inner	825.2.bi.h.776.16		80
15.2	even	4		165.2.r.a.134.15	yes	80
15.8	even	4		165.2.r.a.134.6	yes	80
15.14	odd	2	inner	825.2.bi.h.101.5		80
33.17	even	10	inner	825.2.bi.h.776.6		80
55.17	even	20		165.2.r.a.149.6	yes	80
55.28	even	20		165.2.r.a.149.15	yes	80
55.39	odd	10	inner	825.2.bi.h.776.5		80
165.17	odd	20		165.2.r.a.149.16	yes	80
165.83	odd	20		165.2.r.a.149.5	yes	80
165.149	even	10	inner	825.2.bi.h.776.15		80

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