LMFDB - Embedded newform 164.2.k.a.45.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [164,2,Mod(25,164)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(164, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([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("164.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 164 = 2^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	164.k (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:	$1.30954659315$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 39x^{14} + 594x^{12} + 4428x^{10} + 16529x^{8} + 28236x^{6} + 17856x^{4} + 4032x^{2} + 256 $ x^16 + 39x^14 + 594x^12 + 4428x^10 + 16529x^8 + 28236x^6 + 17856x^4 + 4032*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			45.3
Root			$-0.770134i$ of defining polynomial
Character	$\chi$	$=$	164.45
Dual form			164.2.k.a.113.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.770134i q^{3} +(1.14437 - 3.52202i) q^{5} +(0.0442579 - 0.0609158i) q^{7} +2.40689 q^{9} +O(q^{10})$	\(q+0.770134i q^{3} +(1.14437 - 3.52202i) q^{5} +(0.0442579 - 0.0609158i) q^{7} +2.40689 q^{9} +(-0.480026 + 0.155970i) q^{11} +(1.14539 + 1.57649i) q^{13} +(2.71242 + 0.881320i) q^{15} +(0.0228224 - 0.00741543i) q^{17} +(-3.03645 + 4.17931i) q^{19} +(0.0469133 + 0.0340845i) q^{21} +(2.59141 - 1.88277i) q^{23} +(-7.04993 - 5.12207i) q^{25} +4.16403i q^{27} +(-7.19341 - 2.33728i) q^{29} +(-1.07598 - 3.31152i) q^{31} +(-0.120118 - 0.369684i) q^{33} +(-0.163899 - 0.225587i) q^{35} +(-0.706708 + 2.17502i) q^{37} +(-1.21411 + 0.882101i) q^{39} +(-5.98274 + 2.28185i) q^{41} +(-7.85127 + 5.70428i) q^{43} +(2.75438 - 8.47712i) q^{45} +(6.54746 + 9.01181i) q^{47} +(2.16137 + 6.65200i) q^{49} +(0.00571088 + 0.0175763i) q^{51} +(9.92007 + 3.22323i) q^{53} +1.86915i q^{55} +(-3.21863 - 2.33847i) q^{57} +(7.60346 - 5.52424i) q^{59} +(-7.03395 - 5.11046i) q^{61} +(0.106524 - 0.146618i) q^{63} +(6.86317 - 2.22998i) q^{65} +(-15.3288 - 4.98064i) q^{67} +(1.44998 + 1.99573i) q^{69} +(-2.44150 + 0.793292i) q^{71} +8.20048 q^{73} +(3.94468 - 5.42939i) q^{75} +(-0.0117439 + 0.0361441i) q^{77} -7.71060i q^{79} +4.01382 q^{81} +8.88973 q^{83} -0.0888668i q^{85} +(1.80002 - 5.53989i) q^{87} +(0.164845 - 0.226890i) q^{89} +0.146726 q^{91} +(2.55032 - 0.828648i) q^{93} +(11.2448 + 15.4771i) q^{95} +(3.21442 + 1.04443i) q^{97} +(-1.15537 + 0.375403i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{5} - 30 q^{9}+O(q^{10}) $ 16 * q + 4 * q^5 - 30 * q^9	$ 16 q + 4 q^{5} - 30 q^{9} - 5 q^{11} - 10 q^{15} + 5 q^{17} + 15 q^{19} + 19 q^{21} + 12 q^{23} - 2 q^{25} + 20 q^{29} + 3 q^{31} - 25 q^{33} + 5 q^{35} + 2 q^{37} - 28 q^{39} - 4 q^{41} - 22 q^{43} - 48 q^{45} + 15 q^{47} - 28 q^{49} + 17 q^{51} + 25 q^{53} - 8 q^{57} + 8 q^{59} - 46 q^{61} - 40 q^{63} - 10 q^{65} - 45 q^{67} + 10 q^{69} + 15 q^{71} + 34 q^{73} + 135 q^{75} + 23 q^{77} + 108 q^{81} + 12 q^{83} + 14 q^{87} + 60 q^{93} - 30 q^{95} - 40 q^{97} + 70 q^{99}+O(q^{100}) $ 16 * q + 4 * q^5 - 30 * q^9 - 5 * q^11 - 10 * q^15 + 5 * q^17 + 15 * q^19 + 19 * q^21 + 12 * q^23 - 2 * q^25 + 20 * q^29 + 3 * q^31 - 25 * q^33 + 5 * q^35 + 2 * q^37 - 28 * q^39 - 4 * q^41 - 22 * q^43 - 48 * q^45 + 15 * q^47 - 28 * q^49 + 17 * q^51 + 25 * q^53 - 8 * q^57 + 8 * q^59 - 46 * q^61 - 40 * q^63 - 10 * q^65 - 45 * q^67 + 10 * q^69 + 15 * q^71 + 34 * q^73 + 135 * q^75 + 23 * q^77 + 108 * q^81 + 12 * q^83 + 14 * q^87 + 60 * q^93 - 30 * q^95 - 40 * q^97 + 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/164\mathbb{Z}\right)^\times$.

$n$	$83$	$129$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$			0.770134i			0.444637i	0.974974	+	0.222319i	$0.0713625\pi$
$3$			0.770134i			0.444637i	−0.974974	+	0.222319i	$0.928638\pi$
$4$		0			0
$5$	1.14437	−	3.52202i	0.511779	−	1.57509i	−0.277288	−	0.960787i	$-0.589436\pi$
$5$	1.14437	−	3.52202i	0.511779	−	1.57509i	0.789067	−	0.614307i	$-0.210564\pi$
$6$		0			0
$7$	0.0442579	−	0.0609158i	0.0167279	−	0.0230240i	−0.800571	−	0.599238i	$-0.795470\pi$
$7$	0.0442579	−	0.0609158i	0.0167279	−	0.0230240i	0.817299	+	0.576214i	$0.195470\pi$
$8$		0			0
$9$	2.40689			0.802298
$10$		0			0
$11$	−0.480026	+	0.155970i	−0.144733	+	0.0470267i	−0.380488	−	0.924786i	$-0.624244\pi$
$11$	−0.480026	+	0.155970i	−0.144733	+	0.0470267i	0.235754	+	0.971813i	$0.424244\pi$
$12$		0			0
$13$	1.14539	+	1.57649i	0.317673	+	0.437240i	0.937755	−	0.347298i	$-0.112901\pi$
$13$	1.14539	+	1.57649i	0.317673	+	0.437240i	−0.620082	+	0.784537i	$0.712901\pi$
$14$		0			0
$15$	2.71242	+	0.881320i	0.700345	+	0.227556i
$16$		0			0
$17$	0.0228224	−	0.00741543i	0.00553524	−	0.00179851i	−0.306248	−	0.951952i	$-0.599074\pi$
$17$	0.0228224	−	0.00741543i	0.00553524	−	0.00179851i	0.311783	+	0.950153i	$0.399074\pi$
$18$		0			0
$19$	−3.03645	+	4.17931i	−0.696609	+	0.958801i	0.303373	+	0.952872i	$0.401887\pi$
$19$	−3.03645	+	4.17931i	−0.696609	+	0.958801i	−0.999982	+	0.00592871i	$0.998113\pi$
$20$		0			0
$21$	0.0469133	+	0.0340845i	0.0102373	+	0.00743785i
$22$		0			0
$23$	2.59141	−	1.88277i	0.540345	−	0.392584i	−0.283868	−	0.958863i	$-0.591618\pi$
$23$	2.59141	−	1.88277i	0.540345	−	0.392584i	0.824213	+	0.566280i	$0.191618\pi$
$24$		0			0
$25$	−7.04993	−	5.12207i	−1.40999	−	1.02441i
$26$		0			0
$27$			4.16403i			0.801368i
$28$		0			0
$29$	−7.19341	−	2.33728i	−1.33578	−	0.434022i	−0.447896	−	0.894086i	$-0.647827\pi$
$29$	−7.19341	−	2.33728i	−1.33578	−	0.434022i	−0.887886	+	0.460064i	$0.847827\pi$
$30$		0			0
$31$	−1.07598	−	3.31152i	−0.193252	−	0.594767i	−0.999993	−	0.00386196i	$-0.998771\pi$
$31$	−1.07598	−	3.31152i	−0.193252	−	0.594767i	0.806741	−	0.590905i	$-0.201229\pi$
$32$		0			0
$33$	−0.120118	−	0.369684i	−0.0209098	−	0.0643538i
$34$		0			0
$35$	−0.163899	−	0.225587i	−0.0277040	−	0.0381312i
$36$		0			0
$37$	−0.706708	+	2.17502i	−0.116182	+	0.357572i	−0.992192	−	0.124722i	$-0.960196\pi$
$37$	−0.706708	+	2.17502i	−0.116182	+	0.357572i	0.876010	+	0.482293i	$0.160196\pi$
$38$		0			0
$39$	−1.21411	+	0.882101i	−0.194413	+	0.141249i
$40$		0			0
$41$	−5.98274	+	2.28185i	−0.934347	+	0.356366i
$41$	−5.98274	+	2.28185i	−0.934347	+	0.356366i
$42$		0			0
$43$	−7.85127	+	5.70428i	−1.19731	+	0.869894i	−0.994017	−	0.109224i	$-0.965163\pi$
$43$	−7.85127	+	5.70428i	−1.19731	+	0.869894i	−0.203290	+	0.979119i	$0.565163\pi$
$44$		0			0
$45$	2.75438	−	8.47712i	0.410599	−	1.26369i
$46$		0			0
$47$	6.54746	+	9.01181i	0.955045	+	1.31451i	0.949250	+	0.314524i	$0.101845\pi$
$47$	6.54746	+	9.01181i	0.955045	+	1.31451i	0.00579557	+	0.999983i	$0.498155\pi$
$48$		0			0
$49$	2.16137	+	6.65200i	0.308767	+	0.950286i
$50$		0			0
$51$	0.00571088	+	0.0175763i	0.000799683	+	0.00246117i
$52$		0			0
$53$	9.92007	+	3.22323i	1.36263	+	0.442744i	0.896919	−	0.442195i	$-0.145800\pi$
$53$	9.92007	+	3.22323i	1.36263	+	0.442744i	0.465707	+	0.884939i	$0.345800\pi$
$54$		0			0
$55$			1.86915i			0.252036i
$56$		0			0
$57$	−3.21863	−	2.33847i	−0.426318	−	0.309738i
$58$		0			0
$59$	7.60346	−	5.52424i	0.989886	−	0.719195i	0.0299902	−	0.999550i	$-0.490452\pi$
$59$	7.60346	−	5.52424i	0.989886	−	0.719195i	0.959896	+	0.280356i	$0.0904524\pi$
$60$		0			0
$61$	−7.03395	−	5.11046i	−0.900605	−	0.654328i	0.0380165	−	0.999277i	$-0.487896\pi$
$61$	−7.03395	−	5.11046i	−0.900605	−	0.654328i	−0.938621	+	0.344949i	$0.887896\pi$
$62$		0			0
$63$	0.106524	−	0.146618i	0.0134208	−	0.0184721i
$64$		0			0
$65$	6.86317	−	2.22998i	0.851272	−	0.276595i
$66$		0			0
$67$	−15.3288	−	4.98064i	−1.87271	−	0.608481i	−0.990478	−	0.137673i	$-0.956038\pi$
$67$	−15.3288	−	4.98064i	−1.87271	−	0.608481i	−0.882236	−	0.470808i	$-0.843962\pi$
$68$		0			0
$69$	1.44998	+	1.99573i	0.174557	+	0.240258i
$70$		0			0
$71$	−2.44150	+	0.793292i	−0.289753	+	0.0941464i	−0.450287	−	0.892884i	$-0.648678\pi$
$71$	−2.44150	+	0.793292i	−0.289753	+	0.0941464i	0.160534	+	0.987030i	$0.448678\pi$
$72$		0			0
$73$	8.20048			0.959794			0.479897	−	0.877325i	$-0.340674\pi$
$73$	8.20048			0.959794			0.479897	+	0.877325i	$0.340674\pi$
$74$		0			0
$75$	3.94468	−	5.42939i	0.455493	−	0.626932i
$76$		0			0
$77$	−0.0117439	+	0.0361441i	−0.00133834	+	0.00411900i
$78$		0			0
$79$		−	7.71060i		−	0.867511i	−0.901031	−	0.433755i	$-0.857188\pi$
$79$		−	7.71060i		−	0.867511i	0.901031	−	0.433755i	$-0.142812\pi$
$80$		0			0
$81$	4.01382			0.445980
$82$		0			0
$83$	8.88973			0.975775			0.487887	−	0.872907i	$-0.337768\pi$
$83$	8.88973			0.975775			0.487887	+	0.872907i	$0.337768\pi$
$84$		0			0
$85$		−	0.0888668i		−	0.00963895i
$86$		0			0
$87$	1.80002	−	5.53989i	0.192982	−	0.593938i
$88$		0			0
$89$	0.164845	−	0.226890i	0.0174736	−	0.0240503i	−0.800191	−	0.599745i	$-0.795268\pi$
$89$	0.164845	−	0.226890i	0.0174736	−	0.0240503i	0.817664	+	0.575695i	$0.195268\pi$
$90$		0			0
$91$	0.146726			0.0153810
$92$		0			0
$93$	2.55032	−	0.828648i	0.264456	−	0.0859268i
$94$		0			0
$95$	11.2448	+	15.4771i	1.15369	+	1.58792i
$96$		0			0
$97$	3.21442	+	1.04443i	0.326375	+	0.106046i	0.467621	−	0.883929i	$-0.345111\pi$
$97$	3.21442	+	1.04443i	0.326375	+	0.106046i	−0.141247	+	0.989974i	$0.545111\pi$
$98$		0			0
$99$	−1.15537	+	0.375403i	−0.116119	+	0.0377294i
$100$		0			0
$101$	2.88352	−	3.96883i	0.286921	−	0.394913i	−0.641090	−	0.767466i	$-0.721517\pi$
$101$	2.88352	−	3.96883i	0.286921	−	0.394913i	0.928011	+	0.372553i	$0.121517\pi$
$102$		0			0
$103$	11.5886	+	8.41963i	1.14186	+	0.829610i	0.987377	−	0.158385i	$-0.0506287\pi$
$103$	11.5886	+	8.41963i	1.14186	+	0.829610i	0.154483	+	0.987995i	$0.450629\pi$
$104$		0			0
$105$	0.173733	−	0.126224i	0.0169546	−	0.0123182i
$106$		0			0
$107$	−14.6340	−	10.6322i	−1.41472	−	1.02786i	−0.992615	−	0.121310i	$-0.961291\pi$
$107$	−14.6340	−	10.6322i	−1.41472	−	1.02786i	−0.422107	−	0.906546i	$-0.638709\pi$
$108$		0			0
$109$			12.7134i			1.21772i	0.793278	+	0.608860i	$0.208373\pi$
$109$			12.7134i			1.21772i	−0.793278	+	0.608860i	$0.791627\pi$
$110$		0			0
$111$	−1.67506	−	0.544260i	−0.158990	−	0.0516588i
$112$		0			0
$113$	0.329737	+	1.01483i	0.0310190	+	0.0954668i	0.965367	−	0.260894i	$-0.0840174\pi$
$113$	0.329737	+	1.01483i	0.0310190	+	0.0954668i	−0.934348	+	0.356361i	$0.884017\pi$
$114$		0			0
$115$	−3.66560	−	11.2816i	−0.341819	−	1.05201i
$116$		0			0
$117$	2.75682	+	3.79444i	0.254869	+	0.350796i
$118$		0			0
$119$	0.000558353	−	0.00171843i	5.11841e−5	−	0.000157529i
$120$		0			0
$121$	−8.69309	+	6.31590i	−0.790281	+	0.574173i
$122$		0			0
$123$	−1.75733	−	4.60751i	−0.158453	−	0.415445i
$124$		0			0
$125$	−11.1277	+	8.08477i	−0.995295	+	0.723124i
$126$		0			0
$127$	0.214190	−	0.659208i	0.0190063	−	0.0584953i	−0.941104	−	0.338118i	$-0.890210\pi$
$127$	0.214190	−	0.659208i	0.0190063	−	0.0584953i	0.960110	+	0.279623i	$0.0902095\pi$
$128$		0			0
$129$	−4.39306	−	6.04653i	−0.386787	−	0.532367i
$130$		0			0
$131$	−5.83885	−	17.9701i	−0.510142	−	1.57006i	−0.791950	−	0.610586i	$-0.790934\pi$
$131$	−5.83885	−	17.9701i	−0.510142	−	1.57006i	0.281808	−	0.959471i	$-0.409066\pi$
$132$		0			0
$133$	0.120199	+	0.369935i	0.0104226	+	0.0320775i
$134$		0			0
$135$	14.6658	+	4.76520i	1.26223	+	0.410124i
$136$		0			0
$137$		−	6.95809i		−	0.594469i	−0.954804	−	0.297235i	$-0.903936\pi$
$137$		−	6.95809i		−	0.594469i	0.954804	−	0.297235i	$-0.0960644\pi$
$138$		0			0
$139$	0.241041	+	0.175127i	0.0204448	+	0.0148540i	0.597961	−	0.801525i	$-0.295978\pi$
$139$	0.241041	+	0.175127i	0.0204448	+	0.0148540i	−0.577516	+	0.816379i	$0.695978\pi$
$140$		0			0
$141$	−6.94030	+	5.04242i	−0.584478	+	0.424648i
$142$		0			0
$143$	−0.795701	−	0.578111i	−0.0665398	−	0.0483440i
$144$		0			0
$145$	−16.4639	+	22.6606i	−1.36725	+	1.88186i
$146$		0			0
$147$	−5.12293	+	1.66454i	−0.422532	+	0.137289i
$148$		0			0
$149$	8.84865	+	2.87510i	0.724909	+	0.235537i	0.648150	−	0.761512i	$-0.275543\pi$
$149$	8.84865	+	2.87510i	0.724909	+	0.235537i	0.0767589	+	0.997050i	$0.475543\pi$
$150$		0			0
$151$	−7.42007	−	10.2129i	−0.603837	−	0.831110i	0.392216	−	0.919873i	$-0.371709\pi$
$151$	−7.42007	−	10.2129i	−0.603837	−	0.831110i	−0.996053	+	0.0887632i	$0.971709\pi$
$152$		0			0
$153$	0.0549310	−	0.0178482i	0.00444091	−	0.00144294i
$154$		0			0
$155$	−12.8946			−1.03572
$156$		0			0
$157$	−2.18448	+	3.00667i	−0.174340	+	0.239959i	−0.887241	−	0.461306i	$-0.847381\pi$
$157$	−2.18448	+	3.00667i	−0.174340	+	0.239959i	0.712901	+	0.701265i	$0.247381\pi$
$158$		0			0
$159$	−2.48232	+	7.63978i	−0.196860	+	0.605874i
$160$		0			0
$161$		−	0.241185i		−	0.0190080i
$162$		0			0
$163$	17.7714			1.39196			0.695981	−	0.718060i	$-0.254970\pi$
$163$	17.7714			1.39196			0.695981	+	0.718060i	$0.254970\pi$
$164$		0			0
$165$	−1.43949			−0.112064
$166$		0			0
$167$			8.05952i			0.623664i	0.950137	+	0.311832i	$0.100943\pi$
$167$			8.05952i			0.623664i	−0.950137	+	0.311832i	$0.899057\pi$
$168$		0			0
$169$	2.84381	−	8.75235i	0.218755	−	0.673258i
$170$		0			0
$171$	−7.30841	+	10.0592i	−0.558888	+	0.769244i
$172$		0			0
$173$	−6.71735			−0.510711			−0.255355	−	0.966847i	$-0.582192\pi$
$173$	−6.71735			−0.510711			−0.255355	+	0.966847i	$0.582192\pi$
$174$		0			0
$175$	−0.624030	+	0.202760i	−0.0471722	+	0.0153272i
$176$		0			0
$177$	4.25440	+	5.85568i	0.319781	+	0.440140i
$178$		0			0
$179$	−20.4061	−	6.63035i	−1.52522	−	0.495575i	−0.577970	−	0.816058i	$-0.696155\pi$
$179$	−20.4061	−	6.63035i	−1.52522	−	0.495575i	−0.947254	+	0.320483i	$0.896155\pi$
$180$		0			0
$181$	2.95540	−	0.960267i	0.219673	−	0.0713761i	−0.197113	−	0.980381i	$-0.563157\pi$
$181$	2.95540	−	0.960267i	0.219673	−	0.0713761i	0.416786	+	0.909005i	$0.363157\pi$
$182$		0			0
$183$	3.93574	−	5.41708i	0.290938	−	0.400442i
$184$		0			0
$185$	6.85173	+	4.97807i	0.503749	+	0.365995i
$186$		0			0
$187$	−0.00979875	+	0.00711921i	−0.000716555	+	0.000520608i
$188$		0			0
$189$	0.253655	+	0.184291i	0.0184507	+	0.0134052i
$190$		0			0
$191$		−	8.66590i		−	0.627043i	−0.949581	−	0.313521i	$-0.898491\pi$
$191$		−	8.66590i		−	0.627043i	0.949581	−	0.313521i	$-0.101509\pi$
$192$		0			0
$193$	12.5714	+	4.08469i	0.904909	+	0.294023i	0.724262	−	0.689525i	$-0.242181\pi$
$193$	12.5714	+	4.08469i	0.904909	+	0.294023i	0.180647	+	0.983548i	$0.442181\pi$
$194$		0			0
$195$	1.71738	+	5.28556i	0.122984	+	0.378507i
$196$		0			0
$197$	−6.45853	−	19.8773i	−0.460151	−	1.41620i	−0.864979	−	0.501807i	$-0.832669\pi$
$197$	−6.45853	−	19.8773i	−0.460151	−	1.41620i	0.404828	−	0.914393i	$-0.367331\pi$
$198$		0			0
$199$	−13.4729	−	18.5439i	−0.955069	−	1.31454i	−0.949239	−	0.314557i	$-0.898144\pi$
$199$	−13.4729	−	18.5439i	−0.955069	−	1.31454i	−0.00583070	−	0.999983i	$-0.501856\pi$
$200$		0			0
$201$	3.83576	−	11.8052i	0.270553	−	0.832678i
$202$		0			0
$203$	−0.460742	+	0.334749i	−0.0323378	+	0.0234948i
$204$		0			0
$205$	1.19025	+	23.6826i	0.0831305	+	1.65406i
$206$		0			0
$207$	6.23724	−	4.53162i	0.433518	−	0.314969i
$208$		0			0
$209$	0.805728	−	2.47978i	0.0557334	−	0.171530i
$210$		0			0
$211$	−4.25381	−	5.85486i	−0.292844	−	0.403065i	0.637091	−	0.770788i	$-0.280137\pi$
$211$	−4.25381	−	5.85486i	−0.292844	−	0.403065i	−0.929935	+	0.367723i	$0.880137\pi$
$212$		0			0
$213$	−0.610941	−	1.88028i	−0.0418610	−	0.128835i
$214$		0			0
$215$	11.1058	+	34.1801i	0.757409	+	2.33106i
$216$		0			0
$217$	−0.249345	−	0.0810170i	−0.0169266	−	0.00549979i
$218$		0			0
$219$			6.31547i			0.426760i
$220$		0			0
$221$	0.0378308	+	0.0274857i	0.00254477	+	0.00184889i
$222$		0			0
$223$	10.7964	−	7.84402i	0.722978	−	0.525274i	−0.164356	−	0.986401i	$-0.552555\pi$
$223$	10.7964	−	7.84402i	0.722978	−	0.525274i	0.887334	+	0.461127i	$0.152555\pi$
$224$		0			0
$225$	−16.9684	−	12.3283i	−1.13123	−	0.821886i
$226$		0			0
$227$	−7.54066	+	10.3788i	−0.500491	+	0.688867i	−0.982280	−	0.187421i	$-0.939987\pi$
$227$	−7.54066	+	10.3788i	−0.500491	+	0.688867i	0.481789	+	0.876287i	$0.339987\pi$
$228$		0			0
$229$	17.1150	−	5.56100i	1.13099	−	0.367481i	0.317038	−	0.948413i	$-0.397312\pi$
$229$	17.1150	−	5.56100i	1.13099	−	0.367481i	0.813952	+	0.580932i	$0.197312\pi$
$230$		0			0
$231$	−0.0278358	−	0.00904439i	−0.00183146	−	0.000595077i
$232$		0			0
$233$	−1.05088	−	1.44641i	−0.0688453	−	0.0947574i	0.773206	−	0.634155i	$-0.218652\pi$
$233$	−1.05088	−	1.44641i	−0.0688453	−	0.0947574i	−0.842051	+	0.539398i	$0.818652\pi$
$234$		0			0
$235$	39.2325	−	12.7474i	2.55924	−	0.831549i
$236$		0			0
$237$	5.93820			0.385727
$238$		0			0
$239$	15.8833	−	21.8615i	1.02740	−	1.41410i	0.120525	−	0.992710i	$-0.461542\pi$
$239$	15.8833	−	21.8615i	1.02740	−	1.41410i	0.906879	−	0.421391i	$-0.138458\pi$
$240$		0			0
$241$	−4.65006	+	14.3114i	−0.299537	+	0.921879i	0.682123	+	0.731238i	$0.261057\pi$
$241$	−4.65006	+	14.3114i	−0.299537	+	0.921879i	−0.981660	+	0.190642i	$0.938943\pi$
$242$		0			0
$243$			15.5833i			0.999668i
$244$		0			0
$245$	25.9019			1.65481
$246$		0			0
$247$	−10.0666			−0.640520
$248$		0			0
$249$			6.84628i			0.433866i
$250$		0			0
$251$	−6.50974	+	20.0349i	−0.410891	+	1.26459i	0.504984	+	0.863129i	$0.331498\pi$
$251$	−6.50974	+	20.0349i	−0.410891	+	1.26459i	−0.915875	+	0.401464i	$0.868502\pi$
$252$		0			0
$253$	−0.950288	+	1.30796i	−0.0597441	+	0.0822307i
$254$		0			0
$255$	0.0684393			0.00428584
$256$		0			0
$257$	17.9687	−	5.83839i	1.12086	−	0.364189i	0.310763	−	0.950487i	$-0.399416\pi$
$257$	17.9687	−	5.83839i	1.12086	−	0.364189i	0.810095	+	0.586299i	$0.199416\pi$
$258$		0			0
$259$	0.101216	+	0.139312i	0.00628924	+	0.00865640i
$260$		0			0
$261$	−17.3138	−	5.62558i	−1.07169	−	0.348215i
$262$		0			0
$263$	6.37231	−	2.07049i	0.392933	−	0.127672i	−0.105885	−	0.994378i	$-0.533767\pi$
$263$	6.37231	−	2.07049i	0.392933	−	0.127672i	0.498818	+	0.866707i	$0.333767\pi$
$264$		0			0
$265$	22.7045	−	31.2501i	1.39473	−	1.91968i
$266$		0			0
$267$	0.174736	+	0.126953i	0.0106937	+	0.00776940i
$268$		0			0
$269$	−16.4125	+	11.9244i	−1.00069	+	0.727041i	−0.962235	−	0.272219i	$-0.912242\pi$
$269$	−16.4125	+	11.9244i	−1.00069	+	0.727041i	−0.0384513	+	0.999260i	$0.512242\pi$
$270$		0			0
$271$	4.49009	+	3.26224i	0.272753	+	0.198167i	0.715750	−	0.698356i	$-0.246085\pi$
$271$	4.49009	+	3.26224i	0.272753	+	0.198167i	−0.442997	+	0.896523i	$0.646085\pi$
$272$		0			0
$273$			0.112998i			0.00683897i
$274$		0			0
$275$	4.18304	+	1.35915i	0.252247	+	0.0819600i
$276$		0			0
$277$	−7.96506	−	24.5139i	−0.478574	−	1.47290i	−0.841077	−	0.540916i	$-0.818078\pi$
$277$	−7.96506	−	24.5139i	−0.478574	−	1.47290i	0.362503	−	0.931983i	$-0.381922\pi$
$278$		0			0
$279$	−2.58977	−	7.97049i	−0.155045	−	0.477180i
$280$		0			0
$281$	−7.39746	−	10.1817i	−0.441295	−	0.607391i	0.529204	−	0.848495i	$-0.322491\pi$
$281$	−7.39746	−	10.1817i	−0.441295	−	0.607391i	−0.970499	+	0.241104i	$0.922491\pi$
$282$		0			0
$283$	1.58266	−	4.87093i	0.0940794	−	0.289547i	−0.892933	−	0.450189i	$-0.851357\pi$
$283$	1.58266	−	4.87093i	0.0940794	−	0.289547i	0.987013	+	0.160642i	$0.0513566\pi$
$284$		0			0
$285$	−11.9195	+	8.65999i	−0.706048	+	0.512974i
$286$		0			0
$287$	−0.125782	+	0.465433i	−0.00742470	+	0.0274736i
$288$		0			0
$289$	−13.7528	+	9.99201i	−0.808990	+	0.587765i
$290$		0			0
$291$	−0.804349	+	2.47553i	−0.0471518	+	0.145118i
$292$		0			0
$293$	−2.03116	−	2.79565i	−0.118662	−	0.163324i	0.745554	−	0.666445i	$-0.232185\pi$
$293$	−2.03116	−	2.79565i	−0.118662	−	0.163324i	−0.864216	+	0.503121i	$0.832185\pi$
$294$		0			0
$295$	−10.7553	−	33.1013i	−0.626196	−	1.92723i
$296$		0			0
$297$	−0.649464	−	1.99884i	−0.0376857	−	0.115985i
$298$		0			0
$299$	5.93632	+	1.92883i	0.343306	+	0.111547i
$300$		0			0
$301$			0.730725i			0.0421183i
$302$		0			0
$303$	3.05653	+	2.22070i	0.175593	+	0.127576i
$304$		0			0
$305$	−26.0486	+	18.9254i	−1.49154	+	1.08367i
$306$		0			0
$307$	18.9503	+	13.7682i	1.08155	+	0.785792i	0.977952	−	0.208828i	$-0.0669647\pi$
$307$	18.9503	+	13.7682i	1.08155	+	0.785792i	0.103597	+	0.994619i	$0.466965\pi$
$308$		0			0
$309$	−6.48424	+	8.92479i	−0.368876	+	0.507714i
$310$		0			0
$311$	−16.8607	+	5.47837i	−0.956082	+	0.310650i	−0.745185	−	0.666858i	$-0.767639\pi$
$311$	−16.8607	+	5.47837i	−0.956082	+	0.310650i	−0.210898	+	0.977508i	$0.567639\pi$
$312$		0			0
$313$	16.1567	+	5.24963i	0.913230	+	0.296726i	0.727687	−	0.685910i	$-0.240596\pi$
$313$	16.1567	+	5.24963i	0.913230	+	0.296726i	0.185543	+	0.982636i	$0.440596\pi$
$314$		0			0
$315$	−0.394487	−	0.542965i	−0.0222268	−	0.0305926i
$316$		0			0
$317$	19.7255	−	6.40920i	1.10789	−	0.359976i	0.302758	−	0.953067i	$-0.402093\pi$
$317$	19.7255	−	6.40920i	1.10789	−	0.359976i	0.805135	+	0.593091i	$0.202093\pi$
$318$		0			0
$319$	3.81757			0.213743
$320$		0			0
$321$	8.18824	−	11.2701i	0.457023	−	0.629038i
$322$		0			0
$323$	−0.0383075	+	0.117898i	−0.00213149	+	0.00656004i
$324$		0			0
$325$		−	16.9809i		−	0.941931i
$326$		0			0
$327$	−9.79099			−0.541443
$328$		0			0
$329$	0.838738			0.0462411
$330$		0			0
$331$			26.5088i			1.45705i	0.685017	+	0.728527i	$0.259795\pi$
$331$			26.5088i			1.45705i	−0.685017	+	0.728527i	$0.740205\pi$
$332$		0			0
$333$	−1.70097	+	5.23505i	−0.0932126	+	0.286879i
$334$		0			0
$335$	−35.0838	+	48.2887i	−1.91683	+	2.63829i
$336$		0			0
$337$	−16.7188			−0.910730			−0.455365	−	0.890305i	$-0.650491\pi$
$337$	−16.7188			−0.910730			−0.455365	+	0.890305i	$0.650491\pi$
$338$		0			0
$339$	−0.781552	+	0.253942i	−0.0424481	+	0.0137922i
$340$		0			0
$341$	1.03300	+	1.42180i	0.0559399	+	0.0769947i
$342$		0			0
$343$	1.00214	+	0.325617i	0.0541107	+	0.0175816i
$344$		0			0
$345$	8.68831	−	2.82300i	0.467763	−	0.151985i
$346$		0			0
$347$	3.04590	−	4.19233i	0.163513	−	0.225056i	−0.719397	−	0.694600i	$-0.755582\pi$
$347$	3.04590	−	4.19233i	0.163513	−	0.225056i	0.882909	+	0.469544i	$0.155582\pi$
$348$		0			0
$349$	14.4396	+	10.4910i	0.772932	+	0.561568i	0.902849	−	0.429957i	$-0.141471\pi$
$349$	14.4396	+	10.4910i	0.772932	+	0.561568i	−0.129917	+	0.991525i	$0.541471\pi$
$350$		0			0
$351$	−6.56455	+	4.76943i	−0.350390	+	0.254573i
$352$		0			0
$353$	−1.91586	−	1.39196i	−0.101971	−	0.0740863i	0.535631	−	0.844452i	$-0.320074\pi$
$353$	−1.91586	−	1.39196i	−0.101971	−	0.0740863i	−0.637602	+	0.770366i	$0.720074\pi$
$354$		0			0
$355$			9.50683i			0.504570i
$356$		0			0
$357$	0.00132342		0.000430006i	7.00430e−5		2.27584e-5i
$358$		0			0
$359$	0.827243	+	2.54599i	0.0436602	+	0.134372i	0.970511	−	0.241059i	$-0.0774947\pi$
$359$	0.827243	+	2.54599i	0.0436602	+	0.134372i	−0.926850	+	0.375431i	$0.877495\pi$
$360$		0			0
$361$	−2.37532	−	7.31049i	−0.125017	−	0.384762i
$362$		0			0
$363$	−4.86409	−	6.69484i	−0.255298	−	0.351388i
$364$		0			0
$365$	9.38441	−	28.8822i	0.491202	−	1.51177i
$366$		0			0
$367$	−15.7263	+	11.4258i	−0.820907	+	0.596424i	−0.916972	−	0.398951i	$-0.869374\pi$
$367$	−15.7263	+	11.4258i	−0.820907	+	0.596424i	0.0960649	+	0.995375i	$0.469374\pi$
$368$		0			0
$369$	−14.3998	+	5.49218i	−0.749624	+	0.285911i
$370$		0			0
$371$	0.635387	−	0.461636i	0.0329876	−	0.0239669i
$372$		0			0
$373$	−7.01765	+	21.5981i	−0.363360	+	1.11831i	0.587641	+	0.809122i	$0.300057\pi$
$373$	−7.01765	+	21.5981i	−0.363360	+	1.11831i	−0.951002	+	0.309186i	$0.899943\pi$
$374$		0			0
$375$	−6.22636	−	8.56985i	−0.321528	−	0.442545i
$376$		0			0
$377$	−4.55454	−	14.0174i	−0.234571	−	0.721934i
$378$		0			0
$379$	2.22404	+	6.84490i	0.114241	+	0.351599i	0.991788	−	0.127892i	$-0.0408212\pi$
$379$	2.22404	+	6.84490i	0.114241	+	0.351599i	−0.877547	+	0.479491i	$0.840821\pi$
$380$		0			0
$381$	0.507679	+	0.164955i	0.0260092	+	0.00845089i
$382$		0			0
$383$			2.86290i			0.146287i	0.997321	+	0.0731436i	$0.0233031\pi$
$383$			2.86290i			0.146287i	−0.997321	+	0.0731436i	$0.976697\pi$
$384$		0			0
$385$	0.113861	+	0.0827246i	0.00580287	+	0.00421603i
$386$		0			0
$387$	−18.8972	+	13.7296i	−0.960597	+	0.697915i
$388$		0			0
$389$	−21.7191	−	15.7798i	−1.10120	−	0.800070i	−0.119946	−	0.992780i	$-0.538272\pi$
$389$	−21.7191	−	15.7798i	−1.10120	−	0.800070i	−0.981256	+	0.192711i	$0.938272\pi$
$390$		0			0
$391$	0.0451805	−	0.0621856i	0.00228487	−	0.00314486i
$392$		0			0
$393$	13.8394	−	4.49669i	0.698105	−	0.226828i
$394$		0			0
$395$	−27.1569	−	8.82380i	−1.36641	−	0.443974i
$396$		0			0
$397$	−13.5763	−	18.6862i	−0.681375	−	0.937832i	0.318575	−	0.947898i	$-0.396796\pi$
$397$	−13.5763	−	18.6862i	−0.681375	−	0.937832i	−0.999949	+	0.0100661i	$0.996796\pi$
$398$		0			0
$399$	−0.284900	+	0.0925696i	−0.0142628	+	0.00463427i
$400$		0			0
$401$	−10.2055			−0.509636			−0.254818	−	0.966989i	$-0.582016\pi$
$401$	−10.2055			−0.509636			−0.254818	+	0.966989i	$0.582016\pi$
$402$		0			0
$403$	3.98817	−	5.48925i	0.198665	−	0.273439i
$404$		0			0
$405$	4.59330	−	14.1367i	0.228243	−	0.702460i
$406$		0			0
$407$		−	1.15429i		−	0.0572162i
$408$		0			0
$409$	27.3511			1.35243			0.676213	−	0.736707i	$-0.263620\pi$
$409$	27.3511			1.35243			0.676213	+	0.736707i	$0.263620\pi$
$410$		0			0
$411$	5.35866			0.264323
$412$		0			0
$413$		−	0.707662i		−	0.0348218i
$414$		0			0
$415$	10.1732	−	31.3098i	0.499381	−	1.53694i
$416$		0			0
$417$	−0.134871	+	0.185634i	−0.00660466	+	0.00909053i
$418$		0			0
$419$	10.8648			0.530780			0.265390	−	0.964141i	$-0.414499\pi$
$419$	10.8648			0.530780			0.265390	+	0.964141i	$0.414499\pi$
$420$		0			0
$421$	20.1454	−	6.54563i	0.981825	−	0.319014i	0.226245	−	0.974070i	$-0.427355\pi$
$421$	20.1454	−	6.54563i	0.981825	−	0.319014i	0.755580	+	0.655056i	$0.227355\pi$
$422$		0			0
$423$	15.7590	+	21.6905i	0.766231	+	1.05463i
$424$		0			0
$425$	−0.198878	−	0.0646195i	−0.00964702	−	0.00313451i
$426$		0			0
$427$	−0.622616	+	0.202300i	−0.0301305	+	0.00978999i
$428$		0			0
$429$	0.445223	−	0.612796i	0.0214955	−	0.0295861i
$430$		0			0
$431$	−4.89412	−	3.55579i	−0.235742	−	0.171276i	0.463642	−	0.886022i	$-0.346542\pi$
$431$	−4.89412	−	3.55579i	−0.235742	−	0.171276i	−0.699384	+	0.714746i	$0.746542\pi$
$432$		0			0
$433$	−22.8286	+	16.5860i	−1.09707	+	0.797070i	−0.980580	−	0.196121i	$-0.937165\pi$
$433$	−22.8286	+	16.5860i	−1.09707	+	0.797070i	−0.116493	+	0.993191i	$0.537165\pi$
$434$		0			0
$435$	−17.4517	−	12.6794i	−0.836744	−	0.607930i
$436$		0			0
$437$			16.5472i			0.791561i
$438$		0			0
$439$	34.4942	+	11.2078i	1.64632	+	0.534921i	0.977937	−	0.208900i	$-0.0669882\pi$
$439$	34.4942	+	11.2078i	1.64632	+	0.534921i	0.668380	+	0.743820i	$0.266988\pi$
$440$		0			0
$441$	5.20218	+	16.0107i	0.247723	+	0.762413i
$442$		0			0
$443$	−0.288875	−	0.889065i	−0.0137249	−	0.0422408i	0.943960	−	0.330061i	$-0.107069\pi$
$443$	−0.288875	−	0.889065i	−0.0137249	−	0.0422408i	−0.957684	+	0.287820i	$0.907069\pi$
$444$		0			0
$445$	−0.610467	−	0.840236i	−0.0289389	−	0.0398310i
$446$		0			0
$447$	−2.21421	+	6.81464i	−0.104729	+	0.322321i
$448$		0			0
$449$	3.71710	−	2.70063i	0.175421	−	0.127451i	−0.496610	−	0.867974i	$-0.665422\pi$
$449$	3.71710	−	2.70063i	0.175421	−	0.127451i	0.672031	+	0.740523i	$0.265422\pi$
$450$		0			0
$451$	2.51597	−	2.02848i	0.118472	−	0.0955173i
$452$		0			0
$453$	7.86526	−	5.71445i	0.369542	−	0.268488i
$454$		0			0
$455$	0.167909	−	0.516770i	0.00787168	−	0.0242265i
$456$		0			0
$457$	16.9856	+	23.3787i	0.794554	+	1.09361i	0.993526	+	0.113605i	$0.0362397\pi$
$457$	16.9856	+	23.3787i	0.794554	+	1.09361i	−0.198972	+	0.980005i	$0.563760\pi$
$458$		0			0
$459$	0.0308781	+	0.0950330i	0.00144127	+	0.00443576i
$460$		0			0
$461$	3.30885	+	10.1836i	0.154109	+	0.474297i	0.998069	−	0.0621073i	$-0.0197821\pi$
$461$	3.30885	+	10.1836i	0.154109	+	0.474297i	−0.843961	+	0.536405i	$0.819782\pi$
$462$		0			0
$463$	−1.55971	−	0.506781i	−0.0724859	−	0.0235521i	0.272550	−	0.962142i	$-0.412133\pi$
$463$	−1.55971	−	0.506781i	−0.0724859	−	0.0235521i	−0.345035	+	0.938590i	$0.612133\pi$
$464$		0			0
$465$		−	9.93054i		−	0.460518i
$466$		0			0
$467$	5.98179	+	4.34603i	0.276804	+	0.201110i	0.717522	−	0.696535i	$-0.245276\pi$
$467$	5.98179	+	4.34603i	0.276804	+	0.201110i	−0.440718	+	0.897646i	$0.645276\pi$
$468$		0			0
$469$	−0.981821	+	0.713334i	−0.0453363	+	0.0329387i
$470$		0			0
$471$	−2.31554	−	1.68234i	−0.106695	−	0.0775181i
$472$		0			0
$473$	2.87912	−	3.96277i	0.132382	−	0.182208i
$474$		0			0
$475$	42.8135	−	13.9110i	1.96442	−	0.638278i
$476$		0			0
$477$	23.8766	+	7.75796i	1.09323	+	0.355213i
$478$		0			0
$479$	−8.43803	−	11.6140i	−0.385544	−	0.530655i	0.571499	−	0.820603i	$-0.306362\pi$
$479$	−8.43803	−	11.6140i	−0.385544	−	0.530655i	−0.957043	+	0.289948i	$0.906362\pi$
$480$		0			0
$481$	−4.23835	+	1.37712i	−0.193252	+	0.0627915i
$482$		0			0
$483$	0.185745			0.00845167
$484$		0			0
$485$	7.35698	−	10.1260i	0.334063	−	0.459799i
$486$		0			0
$487$	−1.47996	+	4.55484i	−0.0670632	+	0.206399i	−0.978972	−	0.203993i	$-0.934608\pi$
$487$	−1.47996	+	4.55484i	−0.0670632	+	0.206399i	0.911909	+	0.410392i	$0.134608\pi$
$488$		0			0
$489$			13.6863i			0.618918i
$490$		0			0
$491$	30.1299			1.35974			0.679872	−	0.733331i	$-0.262036\pi$
$491$	30.1299			1.35974			0.679872	+	0.733331i	$0.262036\pi$
$492$		0			0
$493$	−0.181502			−0.00817446
$494$		0			0
$495$			4.49884i			0.202208i
$496$		0			0
$497$	−0.0597317	+	0.183835i	−0.00267933	+	0.00824614i
$498$		0			0
$499$	11.8267	−	16.2781i	0.529437	−	0.728707i	−0.457608	−	0.889154i	$-0.651294\pi$
$499$	11.8267	−	16.2781i	0.529437	−	0.728707i	0.987044	+	0.160447i	$0.0512936\pi$
$500$		0			0
$501$	−6.20691			−0.277304
$502$		0			0
$503$	−1.76177	+	0.572433i	−0.0785533	+	0.0255235i	−0.348030	−	0.937483i	$-0.613149\pi$
$503$	−1.76177	+	0.572433i	−0.0785533	+	0.0255235i	0.269477	+	0.963007i	$0.413149\pi$
$504$		0			0
$505$	−10.6785	−	14.6976i	−0.475185	−	0.654036i
$506$		0			0
$507$	6.74048	+	2.19012i	0.299355	+	0.0972665i
$508$		0			0
$509$	−20.1332	+	6.54166i	−0.892387	+	0.289954i	−0.719091	−	0.694916i	$-0.755442\pi$
$509$	−20.1332	+	6.54166i	−0.892387	+	0.289954i	−0.173296	+	0.984870i	$0.555442\pi$
$510$		0			0
$511$	0.362936	−	0.499539i	0.0160554	−	0.0220983i
$512$		0			0
$513$	−17.4028	−	12.6439i	−0.768352	−	0.558241i
$514$		0			0
$515$	42.9158	−	31.1801i	1.89109	−	1.37396i
$516$		0			0
$517$	−4.54852	−	3.30470i	−0.200044	−	0.145340i
$518$		0			0
$519$		−	5.17326i		−	0.227081i
$520$		0			0
$521$	−18.0824	−	5.87533i	−0.792204	−	0.257403i	−0.115162	−	0.993347i	$-0.536739\pi$
$521$	−18.0824	−	5.87533i	−0.792204	−	0.257403i	−0.677042	+	0.735944i	$0.736739\pi$
$522$		0			0
$523$	−9.18213	−	28.2597i	−0.401506	−	1.23571i	−0.923777	−	0.382930i	$-0.874915\pi$
$523$	−9.18213	−	28.2597i	−0.401506	−	1.23571i	0.522271	−	0.852780i	$-0.325085\pi$
$524$		0			0
$525$	−0.156152	−	0.480587i	−0.00681504	−	0.0209745i
$526$		0			0
$527$	−0.0491128	−	0.0675979i	−0.00213939	−	0.00294461i
$528$		0			0
$529$	−3.93682	+	12.1163i	−0.171166	+	0.526795i
$530$		0			0
$531$	18.3007	−	13.2963i	0.794184	−	0.577008i
$532$		0			0
$533$	−10.4499	−	6.81812i	−0.452634	−	0.295325i
$534$		0			0
$535$	−54.1936	+	39.3740i	−2.34299	+	1.70228i
$536$		0			0
$537$	5.10625	−	15.7154i	0.220351	−	0.678171i
$538$		0			0
$539$	−2.07503	−	2.85603i	−0.0893777	−	0.123018i
$540$		0			0
$541$	10.5633	+	32.5105i	0.454152	+	1.39774i	0.872127	+	0.489279i	$0.162740\pi$
$541$	10.5633	+	32.5105i	0.454152	+	1.39774i	−0.417975	+	0.908458i	$0.637260\pi$
$542$		0			0
$543$	0.739534	+	2.27605i	0.0317365	+	0.0976748i
$544$		0			0
$545$	44.7767	+	14.5488i	1.91802	+	0.623203i
$546$		0			0
$547$			22.5783i			0.965377i	0.875792	+	0.482689i	$0.160340\pi$
$547$			22.5783i			0.965377i	−0.875792	+	0.482689i	$0.839660\pi$
$548$		0			0
$549$	−16.9300	−	12.3003i	−0.722553	−	0.524966i
$550$		0			0
$551$	31.6106	−	22.9665i	1.34666	−	0.978405i
$552$		0			0
$553$	−0.469697	−	0.341255i	−0.0199736	−	0.0145116i
$554$		0			0
$555$	−3.83378	+	5.27675i	−0.162735	+	0.223986i
$556$		0			0
$557$	−31.3110	+	10.1736i	−1.32669	+	0.431068i	−0.884787	−	0.465995i	$-0.845697\pi$
$557$	−31.3110	+	10.1736i	−1.32669	+	0.431068i	−0.441903	+	0.897063i	$0.645697\pi$
$558$		0			0
$559$	−17.9855	−	5.84384i	−0.760705	−	0.247168i
$560$		0			0
$561$	−0.00548274	−	0.00754635i	−0.000231482	−	0.000318607i
$562$		0			0
$563$	16.7290	−	5.43558i	0.705044	−	0.229083i	0.0655169	−	0.997851i	$-0.479130\pi$
$563$	16.7290	−	5.43558i	0.705044	−	0.229083i	0.639527	+	0.768769i	$0.279130\pi$
$564$		0			0
$565$	3.95158			0.166244
$566$		0			0
$567$	0.177643	−	0.244505i	0.00746031	−	0.0102682i
$568$		0			0
$569$	−3.39129	+	10.4373i	−0.142170	+	0.437555i	−0.996636	−	0.0819521i	$-0.973885\pi$
$569$	−3.39129	+	10.4373i	−0.142170	+	0.437555i	0.854466	+	0.519507i	$0.173885\pi$
$570$		0			0
$571$		−	11.6749i		−	0.488580i	−0.969702	−	0.244290i	$-0.921445\pi$
$571$		−	11.6749i		−	0.488580i	0.969702	−	0.244290i	$-0.0785549\pi$
$572$		0			0
$573$	6.67391			0.278806
$574$		0			0
$575$	−27.9129			−1.16405
$576$		0			0
$577$		−	28.1427i		−	1.17159i	−0.810458	−	0.585797i	$-0.800782\pi$
$577$		−	28.1427i		−	1.17159i	0.810458	−	0.585797i	$-0.199218\pi$
$578$		0			0
$579$	−3.14576	+	9.68166i	−0.130733	+	0.402356i
$580$		0			0
$581$	0.393441	−	0.541525i	0.0163227	−	0.0224662i
$582$		0			0
$583$	−5.26462			−0.218038
$584$		0			0
$585$	16.5189	−	5.36732i	0.682974	−	0.221912i
$586$		0			0
$587$	7.99648	+	11.0062i	0.330050	+	0.454275i	0.941502	−	0.337006i	$-0.109414\pi$
$587$	7.99648	+	11.0062i	0.330050	+	0.454275i	−0.611452	+	0.791281i	$0.709414\pi$
$588$		0			0
$589$	17.1071	+	5.55842i	0.704884	+	0.229031i
$590$		0			0
$591$	15.3082	−	4.97393i	0.629695	−	0.204600i
$592$		0			0
$593$	−28.2522	+	38.8858i	−1.16018	+	1.59685i	−0.449605	+	0.893228i	$0.648435\pi$
$593$	−28.2522	+	38.8858i	−1.16018	+	1.59685i	−0.710575	+	0.703622i	$0.751565\pi$
$594$		0			0
$595$	−0.00541339	−	0.00393306i	−0.000221927	−	0.000161240i
$596$		0			0
$597$	14.2813	−	10.3759i	0.584493	−	0.424659i
$598$		0			0
$599$	−3.29307	−	2.39256i	−0.134551	−	0.0977571i	0.518474	−	0.855093i	$-0.326500\pi$
$599$	−3.29307	−	2.39256i	−0.134551	−	0.0977571i	−0.653025	+	0.757336i	$0.726500\pi$
$600$		0			0
$601$			34.8497i			1.42155i	0.703419	+	0.710775i	$0.251656\pi$
$601$			34.8497i			1.42155i	−0.703419	+	0.710775i	$0.748344\pi$
$602$		0			0
$603$	−36.8948	−	11.9879i	−1.50247	−	0.488183i
$604$		0			0
$605$	12.2966	+	37.8449i	0.499927	+	1.53862i
$606$		0			0
$607$	−10.5485	−	32.4648i	−0.428149	−	1.31771i	−0.899947	−	0.436000i	$-0.856395\pi$
$607$	−10.5485	−	32.4648i	−0.428149	−	1.31771i	0.471798	−	0.881707i	$-0.343605\pi$
$608$		0			0
$609$	−0.257801	−	0.354833i	−0.0104466	−	0.0143786i
$610$		0			0
$611$	−6.70764	+	20.6440i	−0.271362	+	0.835167i
$612$		0			0
$613$	−3.71731	+	2.70078i	−0.150141	+	0.109083i	−0.660320	−	0.750985i	$-0.729579\pi$
$613$	−3.71731	+	2.70078i	−0.150141	+	0.109083i	0.510179	+	0.860068i	$0.329579\pi$
$614$		0			0
$615$	−18.2388	+	0.916650i	−0.735458	+	0.0369629i
$616$		0			0
$617$	10.3437	−	7.51514i	0.416422	−	0.302548i	−0.359775	−	0.933039i	$-0.617146\pi$
$617$	10.3437	−	7.51514i	0.416422	−	0.302548i	0.776197	+	0.630491i	$0.217146\pi$
$618$		0			0
$619$	−4.16186	+	12.8089i	−0.167279	+	0.514832i	−0.999197	−	0.0400666i	$-0.987243\pi$
$619$	−4.16186	+	12.8089i	−0.167279	+	0.514832i	0.831918	+	0.554899i	$0.187243\pi$
$620$		0			0
$621$	7.83990	+	10.7907i	0.314604	+	0.433016i
$622$		0			0
$623$	−0.00652548	−	0.0200834i	−0.000261438	−	0.000804623i
$624$		0			0
$625$	2.27627	+	7.00564i	0.0910508	+	0.280225i
$626$		0			0
$627$	1.90976	+	0.620518i	0.0762684	+	0.0247811i
$628$		0			0
$629$			0.0548797i			0.00218820i
$630$		0			0
$631$	−35.5805	−	25.8507i	−1.41644	−	1.02910i	−0.992347	−	0.123482i	$-0.960594\pi$
$631$	−35.5805	−	25.8507i	−1.41644	−	1.02910i	−0.424090	−	0.905620i	$-0.639406\pi$
$632$		0			0
$633$	4.50903	−	3.27600i	0.179218	−	0.130209i
$634$		0			0
$635$	−2.07663	−	1.50876i	−0.0824085	−	0.0598733i
$636$		0			0
$637$	−8.01121	+	11.0265i	−0.317416	+	0.436885i
$638$		0			0
$639$	−5.87644	+	1.90937i	−0.232468	+	0.0755335i
$640$		0			0
$641$	−20.4345	−	6.63958i	−0.807115	−	0.262248i	−0.123740	−	0.992315i	$-0.539489\pi$
$641$	−20.4345	−	6.63958i	−0.807115	−	0.262248i	−0.683376	+	0.730067i	$0.739489\pi$
$642$		0			0
$643$	−11.2779	−	15.5227i	−0.444758	−	0.612157i	0.526503	−	0.850173i	$-0.323503\pi$
$643$	−11.2779	−	15.5227i	−0.444758	−	0.612157i	−0.971261	+	0.238016i	$0.923503\pi$
$644$		0			0
$645$	−26.3233	+	8.55295i	−1.03648	+	0.336772i
$646$		0			0
$647$	16.9272			0.665477			0.332738	−	0.943019i	$-0.392027\pi$
$647$	16.9272			0.665477			0.332738	+	0.943019i	$0.392027\pi$
$648$		0			0
$649$	−2.78825	+	3.83769i	−0.109448	+	0.150643i
$650$		0			0
$651$	0.0623939	−	0.192029i	0.00244541	−	0.00752620i
$652$		0			0
$653$		−	17.8709i		−	0.699343i	−0.936872	−	0.349671i	$-0.886293\pi$
$653$		−	17.8709i		−	0.699343i	0.936872	−	0.349671i	$-0.113707\pi$
$654$		0			0
$655$	−69.9729			−2.73407
$656$		0			0
$657$	19.7377			0.770041
$658$		0			0
$659$		−	2.35140i		−	0.0915976i	−0.998951	−	0.0457988i	$-0.985417\pi$
$659$		−	2.35140i		−	0.0915976i	0.998951	−	0.0457988i	$-0.0145833\pi$
$660$		0			0
$661$	11.7335	−	36.1119i	0.456379	−	1.40459i	−0.413130	−	0.910672i	$-0.635564\pi$
$661$	11.7335	−	36.1119i	0.456379	−	1.40459i	0.869509	−	0.493917i	$-0.164436\pi$
$662$		0			0
$663$	−0.0211677	+	0.0291348i	−0.000822083	+	0.00113150i
$664$		0			0
$665$	1.44047			0.0558591
$666$		0			0
$667$	−23.0416	+	7.48666i	−0.892173	+	0.289885i
$668$		0			0
$669$	6.04095	+	8.31465i	0.233556	+	0.321463i
$670$		0			0
$671$	4.17356	+	1.35607i	0.161118	+	0.0523506i
$672$		0			0
$673$	−28.5923	+	9.29019i	−1.10215	+	0.358110i	−0.802930	−	0.596074i	$-0.796727\pi$
$673$	−28.5923	+	9.29019i	−1.10215	+	0.358110i	−0.299221	+	0.954184i	$0.596727\pi$
$674$		0			0
$675$	21.3285	−	29.3561i	0.820933	−	1.12992i
$676$		0			0
$677$	12.6096	+	9.16142i	0.484627	+	0.352102i	0.803114	−	0.595825i	$-0.203175\pi$
$677$	12.6096	+	9.16142i	0.484627	+	0.352102i	−0.318488	+	0.947927i	$0.603175\pi$
$678$		0			0
$679$	0.205886	−	0.149585i	0.00790116	−	0.00574053i
$680$		0			0
$681$	−7.99309	−	5.80732i	−0.306296	−	0.222537i
$682$		0			0
$683$			34.1216i			1.30563i	0.757519	+	0.652813i	$0.226411\pi$
$683$			34.1216i			1.30563i	−0.757519	+	0.652813i	$0.773589\pi$
$684$		0			0
$685$	−24.5065	−	7.96264i	−0.936345	−	0.304237i
$686$		0			0
$687$	4.28271	+	13.1808i	0.163396	+	0.502880i
$688$		0			0
$689$	6.28093	+	19.3307i	0.239285	+	0.736442i
$690$		0			0
$691$	28.1884	+	38.7981i	1.07234	+	1.47595i	0.867686	+	0.497113i	$0.165607\pi$
$691$	28.1884	+	38.7981i	1.07234	+	1.47595i	0.204653	+	0.978835i	$0.434393\pi$
$692$		0			0
$693$	−0.0282664	+	0.0869949i	−0.00107375	+	0.00330466i
$694$		0			0
$695$	0.892640	−	0.648541i	0.0338598	−	0.0246006i
$696$		0			0
$697$	−0.119619	+	0.0964419i	−0.00453090	+	0.00365300i
$698$		0			0
$699$	1.11393	−	0.809317i	0.0421327	−	0.0306112i
$700$		0			0
$701$	10.6809	−	32.8724i	0.403412	−	1.24157i	−0.518802	−	0.854895i	$-0.673622\pi$
$701$	10.6809	−	32.8724i	0.403412	−	1.24157i	0.922214	−	0.386680i	$-0.126378\pi$
$702$		0			0
$703$	−6.94422	−	9.55790i	−0.261906	−	0.360483i
$704$		0			0
$705$	9.81721	+	30.2143i	0.369737	+	1.13793i
$706$		0			0
$707$	−0.114146	−	0.351304i	−0.00429288	−	0.0132121i
$708$		0			0
$709$	−20.1735	−	6.55476i	−0.757630	−	0.246169i	−0.0953690	−	0.995442i	$-0.530403\pi$
$709$	−20.1735	−	6.55476i	−0.757630	−	0.246169i	−0.662261	+	0.749273i	$0.730403\pi$
$710$		0			0
$711$		−	18.5586i		−	0.696002i
$712$		0			0
$713$	−9.02312	−	6.55568i	−0.337919	−	0.245512i
$714$		0			0
$715$	−2.94669	+	2.14090i	−0.110200	+	0.0800650i
$716$		0			0
$717$	16.8363	+	12.2323i	0.628762	+	0.456822i
$718$		0			0
$719$	28.6854	−	39.4820i	1.06978	−	1.47243i	0.199488	−	0.979900i	$-0.436072\pi$
$719$	28.6854	−	39.4820i	1.06978	−	1.47243i	0.870295	−	0.492531i	$-0.163928\pi$
$720$		0			0
$721$	1.02578	−	0.333295i	0.0382019	−	0.0124125i
$722$		0			0
$723$	−11.0217	−	3.58117i	−0.409902	−	0.133185i
$724$		0			0
$725$	38.7413	+	53.3228i	1.43881	+	1.98036i
$726$		0			0
$727$	−8.79895	+	2.85895i	−0.326335	+	0.106033i	−0.467603	−	0.883939i	$-0.654882\pi$
$727$	−8.79895	+	2.85895i	−0.326335	+	0.106033i	0.141268	+	0.989971i	$0.454882\pi$
$728$		0			0
$729$	0.0402475			0.00149065
$730$		0			0
$731$	−0.136885	+	0.188406i	−0.00506286	+	0.00696844i
$732$		0			0
$733$	−6.15002	+	18.9278i	−0.227156	+	0.699115i	0.770909	+	0.636945i	$0.219802\pi$
$733$	−6.15002	+	18.9278i	−0.227156	+	0.699115i	−0.998066	+	0.0621700i	$0.980198\pi$
$734$		0			0
$735$			19.9479i			0.735790i
$736$		0			0
$737$	8.13506			0.299659
$738$		0			0
$739$	40.2669			1.48124			0.740622	−	0.671922i	$-0.234531\pi$
$739$	40.2669			1.48124			0.740622	+	0.671922i	$0.234531\pi$
$740$		0			0
$741$		−	7.75260i		−	0.284799i
$742$		0			0
$743$	12.6051	−	38.7945i	0.462436	−	1.42323i	−0.399743	−	0.916627i	$-0.630901\pi$
$743$	12.6051	−	38.7945i	0.462436	−	1.42323i	0.862179	−	0.506604i	$-0.169099\pi$
$744$		0			0
$745$	20.2523	−	27.8749i	0.741987	−	1.02126i
$746$		0			0
$747$	21.3966			0.782862
$748$		0			0
$749$	−1.29534	+	0.420882i	−0.0473307	+	0.0153787i
$750$		0			0
$751$	7.69705	+	10.5941i	0.280869	+	0.386584i	0.926022	−	0.377471i	$-0.123206\pi$
$751$	7.69705	+	10.5941i	0.280869	+	0.386584i	−0.645152	+	0.764054i	$0.723206\pi$
$752$		0			0
$753$	−15.4296	−	5.01337i	−0.562285	−	0.182697i
$754$		0			0
$755$	−44.4612	+	14.4463i	−1.61811	+	0.525755i
$756$		0			0
$757$	−12.1747	+	16.7571i	−0.442497	+	0.609046i	−0.970765	−	0.240033i	$-0.922842\pi$
$757$	−12.1747	+	16.7571i	−0.442497	+	0.609046i	0.528267	+	0.849078i	$0.322842\pi$
$758$		0			0
$759$	−1.00730	−	0.731849i	−0.0365628	−	0.0265644i
$760$		0			0
$761$	20.4580	−	14.8636i	0.741602	−	0.538805i	−0.151611	−	0.988440i	$-0.548446\pi$
$761$	20.4580	−	14.8636i	0.741602	−	0.538805i	0.893212	+	0.449635i	$0.148446\pi$
$762$		0			0
$763$	0.774444	+	0.562667i	0.0280368	+	0.0203699i
$764$		0			0
$765$		−	0.213893i		−	0.00773331i
$766$		0			0
$767$	17.4178	+	5.65939i	0.628921	+	0.204349i
$768$		0			0
$769$	−8.35117	−	25.7023i	−0.301151	−	0.926847i	−0.981086	−	0.193574i	$-0.937992\pi$
$769$	−8.35117	−	25.7023i	−0.301151	−	0.926847i	0.679935	−	0.733273i	$-0.262008\pi$
$770$		0			0
$771$	4.49634	+	13.8383i	0.161932	+	0.498375i
$772$		0			0
$773$	−23.2271	−	31.9694i	−0.835421	−	1.14986i	−0.986890	−	0.161396i	$-0.948400\pi$
$773$	−23.2271	−	31.9694i	−0.835421	−	1.14986i	0.151469	−	0.988462i	$-0.451600\pi$
$774$		0			0
$775$	−9.37629	+	28.8572i	−0.336806	+	1.03658i
$776$		0			0
$777$	−0.107289	+	0.0779497i	−0.00384896	+	0.00279643i
$778$		0			0
$779$	8.62970	−	31.9325i	0.309191	−	1.14410i
$780$		0			0
$781$	1.04826	−	0.761602i	0.0375095	−	0.0272523i
$782$		0			0
$783$	9.73251	−	29.9536i	0.347811	−	1.07045i
$784$		0			0
$785$	8.08970	+	11.1345i	0.288734	+	0.397408i
$786$		0			0
$787$	4.85503	+	14.9422i	0.173063	+	0.532633i	0.999540	−	0.0303377i	$-0.00965828\pi$
$787$	4.85503	+	14.9422i	0.173063	+	0.532633i	−0.826477	+	0.562971i	$0.809658\pi$
$788$		0			0
$789$	1.59455	+	4.90753i	0.0567676	+	0.174713i
$790$		0			0
$791$	0.0764124	+	0.0248279i	0.00271691	+	0.000882778i
$792$		0			0
$793$		−	16.9424i		−	0.601642i
$794$		0			0
$795$	24.0667	+	17.4855i	0.853560	+	0.620147i
$796$		0			0
$797$	6.41825	−	4.66313i	0.227346	−	0.165177i	−0.468281	−	0.883580i	$-0.655127\pi$
$797$	6.41825	−	4.66313i	0.227346	−	0.165177i	0.695627	+	0.718403i	$0.255127\pi$
$798$		0			0
$799$	0.216255	+	0.157118i	0.00765055	+	0.00555845i
$800$		0			0
$801$	0.396765	−	0.546101i	0.0140190	−	0.0192955i
$802$		0			0
$803$	−3.93645	+	1.27903i	−0.138914	+	0.0451360i
$804$		0			0
$805$	−0.849457	−	0.276005i	−0.0299394	−	0.00972790i
$806$		0			0
$807$	−9.18336	−	12.6398i	−0.323269	−	0.444942i
$808$		0			0
$809$	−26.1480	+	8.49600i	−0.919314	+	0.298703i	−0.730185	−	0.683249i	$-0.760566\pi$
$809$	−26.1480	+	8.49600i	−0.919314	+	0.298703i	−0.189129	+	0.981952i	$0.560566\pi$
$810$		0			0
$811$	29.8159			1.04698			0.523489	−	0.852032i	$-0.324630\pi$
$811$	29.8159			1.04698			0.523489	+	0.852032i	$0.324630\pi$
$812$		0			0
$813$	−2.51236	+	3.45797i	−0.0881124	+	0.121276i
$814$		0			0
$815$	20.3371	−	62.5911i	0.712377	−	2.19247i
$816$		0			0
$817$		−	50.1337i		−	1.75396i
$818$		0			0
$819$	0.353153			0.0123402
$820$		0			0
$821$	23.5182			0.820791			0.410396	−	0.911908i	$-0.365391\pi$
$821$	23.5182			0.820791			0.410396	+	0.911908i	$0.365391\pi$
$822$		0			0
$823$		−	1.36016i		−	0.0474122i	−0.999719	−	0.0237061i	$-0.992453\pi$
$823$		−	1.36016i		−	0.0474122i	0.999719	−	0.0237061i	$-0.00754660\pi$
$824$		0			0
$825$	−1.04673	+	3.22150i	−0.0364424	+	0.112158i
$826$		0			0
$827$	−5.36037	+	7.37792i	−0.186398	+	0.256555i	−0.891982	−	0.452072i	$-0.850685\pi$
$827$	−5.36037	+	7.37792i	−0.186398	+	0.256555i	0.705583	+	0.708627i	$0.250685\pi$
$828$		0			0
$829$	−37.4508			−1.30072			−0.650360	−	0.759626i	$-0.725382\pi$
$829$	−37.4508			−1.30072			−0.650360	+	0.759626i	$0.725382\pi$
$830$		0			0
$831$	18.8790	−	6.13416i	0.654905	−	0.212792i
$832$		0			0
$833$	0.0986550	+	0.135787i	0.00341819	+	0.00470474i
$834$		0			0
$835$	28.3858	+	9.22309i	0.982330	+	0.319178i
$836$		0			0
$837$	13.7893	−	4.48041i	0.476628	−	0.154866i
$838$		0			0
$839$	−11.8541	+	16.3157i	−0.409248	+	0.563281i	−0.963035	−	0.269377i	$-0.913182\pi$
$839$	−11.8541	+	16.3157i	−0.409248	+	0.563281i	0.553787	+	0.832658i	$0.313182\pi$
$840$		0			0
$841$	22.8207	+	16.5802i	0.786921	+	0.571732i
$842$		0			0
$843$	7.84129	−	5.69703i	0.270068	−	0.196216i
$844$		0			0
$845$	−27.5716	−	20.0319i	−0.948490	−	0.689119i
$846$		0			0
$847$			0.809075i			0.0278001i
$848$		0			0
$849$	3.75127	+	1.21886i	0.128743	+	0.0418312i
$850$		0			0
$851$	2.26369	+	6.96693i	0.0775984	+	0.238823i
$852$		0			0
$853$	8.84403	+	27.2191i	0.302814	+	0.931965i	0.980484	+	0.196599i	$0.0629897\pi$
$853$	8.84403	+	27.2191i	0.302814	+	0.931965i	−0.677670	+	0.735366i	$0.737010\pi$
$854$		0			0
$855$	27.0650	+	37.2518i	0.925604	+	1.27398i
$856$		0			0
$857$	6.44471	−	19.8348i	0.220147	−	0.677543i	−0.778601	−	0.627519i	$-0.784070\pi$
$857$	6.44471	−	19.8348i	0.220147	−	0.677543i	0.998748	−	0.0500237i	$-0.0159297\pi$
$858$		0			0
$859$	7.50445	−	5.45230i	0.256049	−	0.186030i	−0.452355	−	0.891838i	$-0.649416\pi$
$859$	7.50445	−	5.45230i	0.256049	−	0.186030i	0.708403	+	0.705808i	$0.249416\pi$
$860$		0			0
$861$	−0.358446	−	0.0968693i	−0.0122158	−	0.00330130i
$862$		0			0
$863$	7.62510	−	5.53996i	0.259562	−	0.188582i	−0.450392	−	0.892831i	$-0.648716\pi$
$863$	7.62510	−	5.53996i	0.259562	−	0.188582i	0.709954	+	0.704248i	$0.248716\pi$
$864$		0			0
$865$	−7.68715	+	23.6586i	−0.261371	+	0.804417i
$866$		0			0
$867$	−7.69519	−	10.5915i	−0.261342	−	0.359707i
$868$		0			0
$869$	1.20262	+	3.70129i	0.0407962	+	0.125558i
$870$		0			0
$871$	−9.70551	−	29.8705i	−0.328859	−	1.01212i
$872$		0			0
$873$	7.73676	+	2.51383i	0.261850	+	0.0850801i
$874$		0			0
$875$			1.03567i			0.0350120i
$876$		0			0
$877$	13.6721	+	9.93337i	0.461674	+	0.335426i	0.794188	−	0.607673i	$-0.207897\pi$
$877$	13.6721	+	9.93337i	0.461674	+	0.335426i	−0.332513	+	0.943098i	$0.607897\pi$
$878$		0			0
$879$	2.15302	−	1.56426i	0.0726197	−	0.0527613i
$880$		0			0
$881$	23.6754	+	17.2012i	0.797644	+	0.579522i	0.910222	−	0.414121i	$-0.135911\pi$
$881$	23.6754	+	17.2012i	0.797644	+	0.579522i	−0.112578	+	0.993643i	$0.535911\pi$
$882$		0			0
$883$	−8.96271	+	12.3361i	−0.301619	+	0.415143i	−0.932745	−	0.360538i	$-0.882593\pi$
$883$	−8.96271	+	12.3361i	−0.301619	+	0.415143i	0.631126	+	0.775681i	$0.282593\pi$
$884$		0			0
$885$	25.4924	−	8.28300i	0.856919	−	0.278430i
$886$		0			0
$887$	15.1008	+	4.90654i	0.507034	+	0.164745i	0.551353	−	0.834272i	$-0.314112\pi$
$887$	15.1008	+	4.90654i	0.507034	+	0.164745i	−0.0443189	+	0.999017i	$0.514112\pi$
$888$		0			0
$889$	−0.0306766	−	0.0422227i	−0.00102886	−	0.00141610i
$890$		0			0
$891$	−1.92674	+	0.626035i	−0.0645482	+	0.0209730i
$892$		0			0
$893$	−57.5442			−1.92564
$894$		0			0
$895$	−46.7044	+	64.2831i	−1.56116	+	2.14875i
$896$		0			0
$897$	−1.48546	+	4.57176i	−0.0495979	+	0.152647i
$898$		0			0
$899$			26.3360i			0.878355i
$900$		0			0
$901$	0.250301			0.00833874
$902$		0			0
$903$	−0.562756			−0.0187274
$904$		0			0
$905$		−	11.5079i		−	0.382534i
$906$		0			0
$907$	−16.3015	+	50.1707i	−0.541281	+	1.66589i	0.188391	+	0.982094i	$0.439673\pi$
$907$	−16.3015	+	50.1707i	−0.541281	+	1.66589i	−0.729672	+	0.683797i	$0.760327\pi$
$908$		0			0
$909$	6.94033	−	9.55254i	0.230196	−	0.316838i
$910$		0			0
$911$	16.2557			0.538574			0.269287	−	0.963060i	$-0.413212\pi$
$911$	16.2557			0.538574			0.269287	+	0.963060i	$0.413212\pi$
$912$		0			0
$913$	−4.26730	+	1.38653i	−0.141227	+	0.0458875i
$914$		0			0
$915$	−14.5751	−	20.0609i	−0.481838	−	0.663193i
$916$		0			0
$917$	−1.35308	−	0.439642i	−0.0446826	−	0.0145183i
$918$		0			0
$919$	47.9944	−	15.5943i	1.58319	−	0.514410i	0.620314	−	0.784354i	$-0.287005\pi$
$919$	47.9944	−	15.5943i	1.58319	−	0.514410i	0.962876	+	0.269944i	$0.0870051\pi$
$920$		0			0
$921$	−10.6033	+	14.5943i	−0.349392	+	0.480897i
$922$		0			0
$923$	−4.04708	−	2.94038i	−0.133211	−	0.0967837i
$924$		0			0
$925$	16.1229	−	11.7139i	0.530116	−	0.385152i
$926$		0			0
$927$	27.8926	+	20.2651i	0.916113	+	0.665595i
$928$		0			0
$929$		−	45.8803i		−	1.50528i	−0.658431	−	0.752641i	$-0.728780\pi$
$929$		−	45.8803i		−	1.50528i	0.658431	−	0.752641i	$-0.271220\pi$
$930$		0			0
$931$	−34.3637	−	11.1654i	−1.12622	−	0.365933i
$932$		0			0
$933$	−4.21908	−	12.9850i	−0.138126	−	0.425110i
$934$		0			0
$935$	0.0138605	+	0.0426584i	0.000453288	+	0.00139508i
$936$		0			0
$937$	−13.0324	−	17.9375i	−0.425749	−	0.585993i	0.541222	−	0.840880i	$-0.317962\pi$
$937$	−13.0324	−	17.9375i	−0.425749	−	0.585993i	−0.966971	+	0.254887i	$0.917962\pi$
$938$		0			0
$939$	−4.04292	+	12.4428i	−0.131936	+	0.406056i
$940$		0			0
$941$	1.42877	−	1.03806i	0.0465764	−	0.0338398i	−0.564253	−	0.825602i	$-0.690836\pi$
$941$	1.42877	−	1.03806i	0.0465764	−	0.0338398i	0.610830	+	0.791762i	$0.290836\pi$
$942$		0			0
$943$	−11.2075	+	17.1773i	−0.364966	+	0.559370i
$944$		0			0
$945$	0.939353	−	0.682480i	0.0305572	−	0.0222011i
$946$		0			0
$947$	−4.37140	+	13.4538i	−0.142052	+	0.437190i	−0.996620	−	0.0821490i	$-0.973822\pi$
$947$	−4.37140	+	13.4538i	−0.142052	+	0.437190i	0.854569	+	0.519339i	$0.173822\pi$
$948$		0			0
$949$	9.39273	+	12.9280i	0.304901	+	0.419660i
$950$		0			0
$951$	4.93594	+	15.1913i	0.160059	+	0.492610i
$952$		0			0
$953$	−5.68835	−	17.5069i	−0.184264	−	0.567105i	0.815671	−	0.578516i	$-0.196368\pi$
$953$	−5.68835	−	17.5069i	−0.184264	−	0.567105i	−0.999935	+	0.0114106i	$0.996368\pi$
$954$		0			0
$955$	−30.5215	−	9.91702i	−0.987651	−	0.320907i
$956$		0			0
$957$			2.94004i			0.0950380i
$958$		0			0
$959$	−0.423857	−	0.307950i	−0.0136871	−	0.00994423i
$960$		0			0
$961$	15.2711	−	11.0951i	0.492615	−	0.357906i
$962$		0			0
$963$	−35.2225	−	25.5906i	−1.13503	−	0.824647i
$964$		0			0
$965$	28.7727	−	39.6022i	0.926227	−	1.27484i
$966$		0			0
$967$	−18.9845	+	6.16844i	−0.610500	+	0.198364i	−0.597918	−	0.801557i	$-0.704005\pi$
$967$	−18.9845	+	6.16844i	−0.610500	+	0.198364i	−0.0125823	+	0.999921i	$0.504005\pi$
$968$		0			0
$969$	−0.0907976	−	0.0295019i	−0.00291684	−	0.000947738i
$970$		0			0
$971$	−11.6830	−	16.0802i	−0.374924	−	0.516039i	0.579307	−	0.815110i	$-0.303323\pi$
$971$	−11.6830	−	16.0802i	−0.374924	−	0.516039i	−0.954231	+	0.299071i	$0.903323\pi$
$972$		0			0
$973$	0.0213360	−	0.00693247i	0.000683999	−	0.000222245i
$974$		0			0
$975$	13.0776			0.418817
$976$		0			0
$977$	20.0185	−	27.5531i	0.640448	−	0.881501i	−0.358191	−	0.933648i	$-0.616606\pi$
$977$	20.0185	−	27.5531i	0.640448	−	0.881501i	0.998639	+	0.0521470i	$0.0166064\pi$
$978$		0			0
$979$	−0.0437421	+	0.134624i	−0.00139800	+	0.00430261i
$980$		0			0
$981$			30.5997i			0.976974i
$982$		0			0
$983$	−40.1776			−1.28147			−0.640734	−	0.767763i	$-0.721370\pi$
$983$	−40.1776			−1.28147			−0.640734	+	0.767763i	$0.721370\pi$
$984$		0			0
$985$	−77.3992			−2.46614
$986$		0			0
$987$			0.645941i			0.0205605i
$988$		0			0
$989$	−9.60599	+	29.5642i	−0.305453	+	0.940087i
$990$		0			0
$991$	11.3454	−	15.6155i	0.360397	−	0.496044i	−0.589862	−	0.807504i	$-0.700818\pi$
$991$	11.3454	−	15.6155i	0.360397	−	0.496044i	0.950259	+	0.311460i	$0.100818\pi$
$992$		0			0
$993$	−20.4153			−0.647860
$994$		0			0
$995$	−80.7298	+	26.2307i	−2.55931	+	0.831570i
$996$		0			0
$997$	−26.7546	−	36.8245i	−0.847326	−	1.16624i	−0.984446	−	0.175690i	$-0.943784\pi$
$997$	−26.7546	−	36.8245i	−0.847326	−	1.16624i	0.137119	−	0.990555i	$-0.456216\pi$
$998$		0			0
$999$	−9.05686	−	2.94275i	−0.286547	−	0.0931046i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	164.2.k.a.45.3	✓	16
3.2	odd	2		1476.2.bb.b.865.1		16
4.3	odd	2		656.2.be.e.209.2		16
41.20	even	20		6724.2.a.j.1.11		16
41.21	even	20		6724.2.a.j.1.6		16
41.31	even	10	inner	164.2.k.a.113.2	yes	16
123.113	odd	10		1476.2.bb.b.1261.1		16
164.31	odd	10		656.2.be.e.113.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
164.2.k.a.45.3	✓	16	1.1	even	1	trivial
164.2.k.a.113.2	yes	16	41.31	even	10	inner
656.2.be.e.113.3		16	164.31	odd	10
656.2.be.e.209.2		16	4.3	odd	2
1476.2.bb.b.865.1		16	3.2	odd	2
1476.2.bb.b.1261.1		16	123.113	odd	10
6724.2.a.j.1.6		16	41.21	even	20
6724.2.a.j.1.11		16	41.20	even	20

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:	\( N \)	\(=\)	\( 164 = 2^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	164.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+0.770134i q^{3} +(1.14437 - 3.52202i) q^{5} +(0.0442579 - 0.0609158i) q^{7} +2.40689 q^{9} +O(q^{10})\)	\(q+0.770134i q^{3} +(1.14437 - 3.52202i) q^{5} +(0.0442579 - 0.0609158i) q^{7} +2.40689 q^{9} +(-0.480026 + 0.155970i) q^{11} +(1.14539 + 1.57649i) q^{13} +(2.71242 + 0.881320i) q^{15} +(0.0228224 - 0.00741543i) q^{17} +(-3.03645 + 4.17931i) q^{19} +(0.0469133 + 0.0340845i) q^{21} +(2.59141 - 1.88277i) q^{23} +(-7.04993 - 5.12207i) q^{25} +4.16403i q^{27} +(-7.19341 - 2.33728i) q^{29} +(-1.07598 - 3.31152i) q^{31} +(-0.120118 - 0.369684i) q^{33} +(-0.163899 - 0.225587i) q^{35} +(-0.706708 + 2.17502i) q^{37} +(-1.21411 + 0.882101i) q^{39} +(-5.98274 + 2.28185i) q^{41} +(-7.85127 + 5.70428i) q^{43} +(2.75438 - 8.47712i) q^{45} +(6.54746 + 9.01181i) q^{47} +(2.16137 + 6.65200i) q^{49} +(0.00571088 + 0.0175763i) q^{51} +(9.92007 + 3.22323i) q^{53} +1.86915i q^{55} +(-3.21863 - 2.33847i) q^{57} +(7.60346 - 5.52424i) q^{59} +(-7.03395 - 5.11046i) q^{61} +(0.106524 - 0.146618i) q^{63} +(6.86317 - 2.22998i) q^{65} +(-15.3288 - 4.98064i) q^{67} +(1.44998 + 1.99573i) q^{69} +(-2.44150 + 0.793292i) q^{71} +8.20048 q^{73} +(3.94468 - 5.42939i) q^{75} +(-0.0117439 + 0.0361441i) q^{77} -7.71060i q^{79} +4.01382 q^{81} +8.88973 q^{83} -0.0888668i q^{85} +(1.80002 - 5.53989i) q^{87} +(0.164845 - 0.226890i) q^{89} +0.146726 q^{91} +(2.55032 - 0.828648i) q^{93} +(11.2448 + 15.4771i) q^{95} +(3.21442 + 1.04443i) q^{97} +(-1.15537 + 0.375403i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{5} - 30 q^{9}+O(q^{10}) \) 16 * q + 4 * q^5 - 30 * q^9	\( 16 q + 4 q^{5} - 30 q^{9} - 5 q^{11} - 10 q^{15} + 5 q^{17} + 15 q^{19} + 19 q^{21} + 12 q^{23} - 2 q^{25} + 20 q^{29} + 3 q^{31} - 25 q^{33} + 5 q^{35} + 2 q^{37} - 28 q^{39} - 4 q^{41} - 22 q^{43} - 48 q^{45} + 15 q^{47} - 28 q^{49} + 17 q^{51} + 25 q^{53} - 8 q^{57} + 8 q^{59} - 46 q^{61} - 40 q^{63} - 10 q^{65} - 45 q^{67} + 10 q^{69} + 15 q^{71} + 34 q^{73} + 135 q^{75} + 23 q^{77} + 108 q^{81} + 12 q^{83} + 14 q^{87} + 60 q^{93} - 30 q^{95} - 40 q^{97} + 70 q^{99}+O(q^{100}) \) 16 * q + 4 * q^5 - 30 * q^9 - 5 * q^11 - 10 * q^15 + 5 * q^17 + 15 * q^19 + 19 * q^21 + 12 * q^23 - 2 * q^25 + 20 * q^29 + 3 * q^31 - 25 * q^33 + 5 * q^35 + 2 * q^37 - 28 * q^39 - 4 * q^41 - 22 * q^43 - 48 * q^45 + 15 * q^47 - 28 * q^49 + 17 * q^51 + 25 * q^53 - 8 * q^57 + 8 * q^59 - 46 * q^61 - 40 * q^63 - 10 * q^65 - 45 * q^67 + 10 * q^69 + 15 * q^71 + 34 * q^73 + 135 * q^75 + 23 * q^77 + 108 * q^81 + 12 * q^83 + 14 * q^87 + 60 * q^93 - 30 * q^95 - 40 * q^97 + 70 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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