LMFDB - Embedded newform 585.2.bt.b.571.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

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

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

chi := DirichletCharacter("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (of order $6$, degree $2$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			571.2
Character	$\chi$	$=$	585.571
Dual form			585.2.bt.b.376.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.36351 + 1.36457i) q^{2} +(1.68089 - 0.417855i) q^{3} +(2.72413 - 4.71833i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-3.40262 + 3.28131i) q^{6} +(3.99906 - 2.30886i) q^{7} +9.41082i q^{8} +(2.65080 - 1.40474i) q^{9} +O(q^{10})$	\(q+(-2.36351 + 1.36457i) q^{2} +(1.68089 - 0.417855i) q^{3} +(2.72413 - 4.71833i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-3.40262 + 3.28131i) q^{6} +(3.99906 - 2.30886i) q^{7} +9.41082i q^{8} +(2.65080 - 1.40474i) q^{9} +2.72915 q^{10} +(3.27016 - 1.88803i) q^{11} +(2.60739 - 9.06929i) q^{12} +(-3.58605 + 0.374474i) q^{13} +(-6.30123 + 10.9140i) q^{14} +(-1.66462 - 0.478573i) q^{15} +(-7.39350 - 12.8059i) q^{16} +0.475463 q^{17} +(-4.34832 + 6.93732i) q^{18} -0.112571i q^{19} +(-4.71833 + 2.72413i) q^{20} +(5.75722 - 5.55197i) q^{21} +(-5.15272 + 8.92477i) q^{22} +(-1.58104 + 2.73845i) q^{23} +(3.93235 + 15.8186i) q^{24} +(0.500000 + 0.866025i) q^{25} +(7.96468 - 5.77851i) q^{26} +(3.86872 - 3.46886i) q^{27} -25.1585i q^{28} +(-3.16117 - 5.47531i) q^{29} +(4.58741 - 1.14039i) q^{30} +(-1.42093 - 0.820373i) q^{31} +(18.6493 + 10.7672i) q^{32} +(4.70787 - 4.54003i) q^{33} +(-1.12376 + 0.648805i) q^{34} -4.61772 q^{35} +(0.593096 - 16.3340i) q^{36} +5.54346i q^{37} +(0.153612 + 0.266064i) q^{38} +(-5.87129 + 2.12790i) q^{39} +(4.70541 - 8.15001i) q^{40} +(-10.4728 - 6.04647i) q^{41} +(-6.03120 + 20.9783i) q^{42} +(1.34138 + 2.32333i) q^{43} -20.5730i q^{44} +(-2.99802 - 0.108860i) q^{45} -8.62981i q^{46} +(5.28707 - 3.05249i) q^{47} +(-17.7787 - 18.4360i) q^{48} +(7.16167 - 12.4044i) q^{49} +(-2.36351 - 1.36457i) q^{50} +(0.799202 - 0.198674i) q^{51} +(-8.00198 + 17.9403i) q^{52} -2.21477 q^{53} +(-4.41026 + 13.4779i) q^{54} -3.77606 q^{55} +(21.7283 + 37.6344i) q^{56} +(-0.0470384 - 0.189220i) q^{57} +(14.9429 + 8.62731i) q^{58} +(7.78385 + 4.49401i) q^{59} +(-6.79271 + 6.55054i) q^{60} +(0.717381 + 1.24254i) q^{61} +4.47784 q^{62} +(7.35736 - 11.7379i) q^{63} -29.1964 q^{64} +(3.29285 + 1.46872i) q^{65} +(-4.93191 + 17.1547i) q^{66} +(10.8645 + 6.27264i) q^{67} +(1.29522 - 2.24339i) q^{68} +(-1.51329 + 5.26368i) q^{69} +(10.9140 - 6.30123i) q^{70} +9.75529i q^{71} +(13.2197 + 24.9461i) q^{72} -1.60702i q^{73} +(-7.56446 - 13.1020i) q^{74} +(1.20232 + 1.24677i) q^{75} +(-0.531149 - 0.306659i) q^{76} +(8.71840 - 15.1007i) q^{77} +(10.9732 - 13.0411i) q^{78} +(2.25865 + 3.91210i) q^{79} +14.7870i q^{80} +(5.05343 - 7.44734i) q^{81} +33.0035 q^{82} +(-1.12664 + 0.650468i) q^{83} +(-10.5126 - 42.2888i) q^{84} +(-0.411763 - 0.237732i) q^{85} +(-6.34072 - 3.66082i) q^{86} +(-7.60147 - 7.88249i) q^{87} +(17.7679 + 30.7749i) q^{88} +7.82871i q^{89} +(7.23442 - 3.83374i) q^{90} +(-13.4762 + 9.77724i) q^{91} +(8.61393 + 14.9198i) q^{92} +(-2.73122 - 0.785217i) q^{93} +(-8.33071 + 14.4292i) q^{94} +(-0.0562856 + 0.0974896i) q^{95} +(35.8465 + 10.3058i) q^{96} +(-4.83079 + 2.78906i) q^{97} +39.0905i q^{98} +(6.01635 - 9.59850i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

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 $

$2$	−2.36351	+	1.36457i	−1.67126	+	0.964900i	−0.704320	+	0.709883i	$0.748748\pi$
$2$	−2.36351	+	1.36457i	−1.67126	+	0.964900i	−0.966937	+	0.255017i	$0.917919\pi$
$3$	1.68089	−	0.417855i	0.970463	−	0.241248i
$3$	1.68089	−	0.417855i	0.970463	−	0.241248i
$4$	2.72413	−	4.71833i	1.36206	−	2.35917i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	−3.40262	+	3.28131i	−1.38911	+	1.33959i
$7$	3.99906	−	2.30886i	1.51150	−	0.872667i	0.511594	−	0.859227i	$-0.329055\pi$
$7$	3.99906	−	2.30886i	1.51150	−	0.872667i	0.999910	−	0.0134398i	$-0.00427816\pi$
$8$			9.41082i			3.32723i
$9$	2.65080	−	1.40474i	0.883598	−	0.468246i
$10$	2.72915			0.863033
$11$	3.27016	−	1.88803i	0.985992	−	0.569263i	0.0819179	−	0.996639i	$-0.473895\pi$
$11$	3.27016	−	1.88803i	0.985992	−	0.569263i	0.904074	+	0.427377i	$0.140562\pi$
$12$	2.60739	−	9.06929i	0.752689	−	2.61808i
$13$	−3.58605	+	0.374474i	−0.994592	+	0.103860i
$13$	−3.58605	+	0.374474i	−0.994592	+	0.103860i
$14$	−6.30123	+	10.9140i	−1.68407	+	2.91690i
$15$	−1.66462	−	0.478573i	−0.429804	−	0.123567i
$16$	−7.39350	−	12.8059i	−1.84838	−	3.20148i
$17$	0.475463			0.115317			0.0576584	−	0.998336i	$-0.481637\pi$
$17$	0.475463			0.115317			0.0576584	+	0.998336i	$0.481637\pi$
$18$	−4.34832	+	6.93732i	−1.02491	+	1.63514i
$19$		−	0.112571i		−	0.0258256i	−0.999917	−	0.0129128i	$-0.995890\pi$
$19$		−	0.112571i		−	0.0258256i	0.999917	−	0.0129128i	$-0.00411039\pi$
$20$	−4.71833	+	2.72413i	−1.05505	+	0.609134i
$21$	5.75722	−	5.55197i	1.25633	−	1.21154i
$22$	−5.15272	+	8.92477i	−1.09856	+	1.90277i
$23$	−1.58104	+	2.73845i	−0.329670	+	0.571006i	−0.982446	−	0.186545i	$-0.940271\pi$
$23$	−1.58104	+	2.73845i	−0.329670	+	0.571006i	0.652776	+	0.757551i	$0.273604\pi$
$24$	3.93235	+	15.8186i	0.802688	+	3.22895i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	7.96468	−	5.77851i	1.56200	−	1.13326i
$27$	3.86872	−	3.46886i	0.744536	−	0.667582i
$28$		−	25.1585i		−	4.75452i
$29$	−3.16117	−	5.47531i	−0.587014	−	1.01674i	−0.994621	−	0.103581i	$-0.966970\pi$
$29$	−3.16117	−	5.47531i	−0.587014	−	1.01674i	0.407607	−	0.913158i	$-0.366363\pi$
$30$	4.58741	−	1.14039i	0.837542	−	0.208205i
$31$	−1.42093	−	0.820373i	−0.255206	−	0.147343i	0.366940	−	0.930245i	$-0.380406\pi$
$31$	−1.42093	−	0.820373i	−0.255206	−	0.147343i	−0.622146	+	0.782901i	$0.713739\pi$
$32$	18.6493	+	10.7672i	3.29676	+	1.90338i
$33$	4.70787	−	4.54003i	0.819535	−	0.790317i
$34$	−1.12376	+	0.648805i	−0.192724	+	0.111269i
$35$	−4.61772			−0.780537
$36$	0.593096	−	16.3340i	0.0988493	−	2.72234i
$37$			5.54346i			0.911339i	0.890149	+	0.455669i	$0.150600\pi$
$37$			5.54346i			0.911339i	−0.890149	+	0.455669i	$0.849400\pi$
$38$	0.153612	+	0.266064i	0.0249192	+	0.0431612i
$39$	−5.87129	+	2.12790i	−0.940159	+	0.340736i
$40$	4.70541	−	8.15001i	0.743990	−	1.28863i
$41$	−10.4728	−	6.04647i	−1.63558	−	0.944301i	−0.982330	−	0.187155i	$-0.940073\pi$
$41$	−10.4728	−	6.04647i	−1.63558	−	0.944301i	−0.653246	−	0.757146i	$-0.726593\pi$
$42$	−6.03120	+	20.9783i	−0.930634	+	3.23703i
$43$	1.34138	+	2.32333i	0.204558	+	0.354305i	0.949992	−	0.312275i	$-0.101091\pi$
$43$	1.34138	+	2.32333i	0.204558	+	0.354305i	−0.745434	+	0.666580i	$0.767758\pi$
$44$		−	20.5730i		−	3.10149i
$45$	−2.99802	−	0.108860i	−0.446919	−	0.0162278i
$46$		−	8.62981i		−	1.27240i
$47$	5.28707	−	3.05249i	0.771198	−	0.445252i	−0.0621036	−	0.998070i	$-0.519781\pi$
$47$	5.28707	−	3.05249i	0.771198	−	0.445252i	0.833302	+	0.552818i	$0.186448\pi$
$48$	−17.7787	−	18.4360i	−2.56613	−	2.66100i
$49$	7.16167	−	12.4044i	1.02310	−	1.77205i
$50$	−2.36351	−	1.36457i	−0.334251	−	0.192980i
$51$	0.799202	−	0.198674i	0.111911	−	0.0278200i
$52$	−8.00198	+	17.9403i	−1.10967	+	2.48787i
$53$	−2.21477			−0.304222			−0.152111	−	0.988363i	$-0.548607\pi$
$53$	−2.21477			−0.304222			−0.152111	+	0.988363i	$0.548607\pi$
$54$	−4.41026	+	13.4779i	−0.600161	+	1.83410i
$55$	−3.77606			−0.509164
$56$	21.7283	+	37.6344i	2.90356	+	5.02911i
$57$	−0.0470384	−	0.189220i	−0.00623039	−	0.0250628i
$58$	14.9429	+	8.62731i	1.96210	+	1.13282i
$59$	7.78385	+	4.49401i	1.01337	+	0.585070i	0.912177	−	0.409796i	$-0.134400\pi$
$59$	7.78385	+	4.49401i	1.01337	+	0.585070i	0.101194	+	0.994867i	$0.467734\pi$
$60$	−6.79271	+	6.55054i	−0.876936	+	0.845672i
$61$	0.717381	+	1.24254i	0.0918513	+	0.159091i	0.908290	−	0.418341i	$-0.137388\pi$
$61$	0.717381	+	1.24254i	0.0918513	+	0.159091i	−0.816439	+	0.577432i	$0.804055\pi$
$62$	4.47784			0.568686
$63$	7.35736	−	11.7379i	0.926940	−	1.47884i
$64$	−29.1964			−3.64955
$65$	3.29285	+	1.46872i	0.408428	+	0.182173i
$66$	−4.93191	+	17.1547i	−0.607076	+	2.11159i
$67$	10.8645	+	6.27264i	1.32731	+	0.766325i	0.984884	−	0.173217i	$-0.0554164\pi$
$67$	10.8645	+	6.27264i	1.32731	+	0.766325i	0.342431	+	0.939543i	$0.388750\pi$
$68$	1.29522	−	2.24339i	0.157069	−	0.272051i
$69$	−1.51329	+	5.26368i	−0.182179	+	0.633673i
$70$	10.9140	−	6.30123i	1.30448	−	0.753140i
$71$			9.75529i			1.15774i	0.815420	+	0.578870i	$0.196506\pi$
$71$			9.75529i			1.15774i	−0.815420	+	0.578870i	$0.803494\pi$
$72$	13.2197	+	24.9461i	1.55796	+	2.93993i
$73$		−	1.60702i		−	0.188087i	−0.995568	−	0.0940435i	$-0.970021\pi$
$73$		−	1.60702i		−	0.188087i	0.995568	−	0.0940435i	$-0.0299793\pi$
$74$	−7.56446	−	13.1020i	−0.879351	−	1.52308i
$75$	1.20232	+	1.24677i	0.138832	+	0.143964i
$76$	−0.531149	−	0.306659i	−0.0609269	−	0.0351762i
$77$	8.71840	−	15.1007i	0.993553	−	1.72088i
$78$	10.9732	−	13.0411i	1.24247	−	1.47662i
$79$	2.25865	+	3.91210i	0.254118	+	0.440146i	0.964656	−	0.263514i	$-0.0848814\pi$
$79$	2.25865	+	3.91210i	0.254118	+	0.440146i	−0.710537	+	0.703660i	$0.751548\pi$
$80$			14.7870i			1.65324i
$81$	5.05343	−	7.44734i	0.561492	−	0.827482i
$82$	33.0035			3.64462
$83$	−1.12664	+	0.650468i	−0.123665	+	0.0713981i	−0.560557	−	0.828116i	$-0.689413\pi$
$83$	−1.12664	+	0.650468i	−0.123665	+	0.0713981i	0.436891	+	0.899514i	$0.356079\pi$
$84$	−10.5126	−	42.2888i	−1.14702	−	4.61408i
$85$	−0.411763	−	0.237732i	−0.0446620	−	0.0257856i
$86$	−6.34072	−	3.66082i	−0.683738	−	0.394756i
$87$	−7.60147	−	7.88249i	−0.814963	−	0.845091i
$88$	17.7679	+	30.7749i	1.89406	+	3.28062i
$89$			7.82871i			0.829842i	0.909857	+	0.414921i	$0.136191\pi$
$89$			7.82871i			0.829842i	−0.909857	+	0.414921i	$0.863809\pi$
$90$	7.23442	−	3.83374i	0.762575	−	0.404111i
$91$	−13.4762	+	9.77724i	−1.41269	+	1.02493i
$92$	8.61393	+	14.9198i	0.898065	+	1.55549i
$93$	−2.73122	−	0.785217i	−0.283215	−	0.0814232i
$94$	−8.33071	+	14.4292i	−0.859247	+	1.48826i
$95$	−0.0562856	+	0.0974896i	−0.00577479	+	0.0100022i
$96$	35.8465	+	10.3058i	3.65857	+	1.05183i
$97$	−4.83079	+	2.78906i	−0.490492	+	0.283186i	−0.724779	−	0.688982i	$-0.758058\pi$
$97$	−4.83079	+	2.78906i	−0.490492	+	0.283186i	0.234286	+	0.972168i	$0.424725\pi$
$98$			39.0905i			3.94874i
$99$	6.01635	−	9.59850i	0.604666	−	0.964686i
$100$	5.44826			0.544826
$101$	−4.18649	−	7.25121i	−0.416571	−	0.721523i	0.579021	−	0.815313i	$-0.303435\pi$
$101$	−4.18649	−	7.25121i	−0.416571	−	0.721523i	−0.995592	+	0.0937903i	$0.970102\pi$
$102$	−1.61782	+	1.56014i	−0.160188	+	0.154477i
$103$	−6.26887	+	10.8580i	−0.617690	+	1.06987i	0.372217	+	0.928146i	$0.378598\pi$
$103$	−6.26887	+	10.8580i	−0.617690	+	1.06987i	−0.989906	+	0.141724i	$0.954735\pi$
$104$	−3.52411	−	33.7477i	−0.345567	−	3.30923i
$105$	−7.76189	+	1.92954i	−0.757483	+	0.188303i
$106$	5.23464	−	3.02222i	0.508433	−	0.293544i
$107$	17.4030			1.68241			0.841206	−	0.540715i	$-0.181846\pi$
$107$	17.4030			1.68241			0.841206	+	0.540715i	$0.181846\pi$
$108$	−5.82831	−	27.7035i	−0.560830	−	2.66577i
$109$		−	14.5696i		−	1.39551i	−0.716335	−	0.697757i	$-0.754182\pi$
$109$		−	14.5696i		−	1.39551i	0.716335	−	0.697757i	$-0.245818\pi$
$110$	8.92477	−	5.15272i	0.850943	−	0.491292i
$111$	2.31636	+	9.31795i	0.219859	+	0.884421i
$112$	−59.1342	−	34.1411i	−5.58765	−	3.22603i
$113$	−0.225447	+	0.390485i	−0.0212082	+	0.0367338i	−0.876435	−	0.481521i	$-0.840085\pi$
$113$	−0.225447	+	0.390485i	−0.0212082	+	0.0367338i	0.855226	+	0.518254i	$0.173418\pi$
$114$	0.369381	+	0.383037i	0.0345957	+	0.0358747i
$115$	2.73845	−	1.58104i	0.255362	−	0.147433i
$116$	−34.4457			−3.19821
$117$	−8.97985	+	6.03011i	−0.830188	+	0.557484i
$118$	−24.5297			−2.25814
$119$	1.90141	−	1.09778i	0.174302	−	0.100633i
$120$	4.50376	−	15.6655i	0.411136	−	1.43005i
$121$	1.62932	−	2.82206i	0.148120	−	0.256551i
$122$	−3.39108	−	1.95784i	−0.307014	−	0.177255i
$123$	−20.1302	−	5.78736i	−1.81508	−	0.521829i
$124$	−7.74158	+	4.46960i	−0.695215	+	0.401382i
$125$		−	1.00000i		−	0.0894427i
$126$	−1.37190	+	37.7825i	−0.122219	+	3.36593i
$127$	−1.43741			−0.127549			−0.0637747	−	0.997964i	$-0.520314\pi$
$127$	−1.43741			−0.127549			−0.0637747	+	0.997964i	$0.520314\pi$
$128$	31.7075	−	18.3063i	2.80258	−	1.61807i
$129$	3.22552	+	3.34477i	0.283992	+	0.294491i
$130$	−9.78687	+	1.02200i	−0.858366	+	0.0896349i
$131$	6.21464	−	10.7641i	0.542976	−	0.940461i	−0.455756	−	0.890105i	$-0.650631\pi$
$131$	6.21464	−	10.7641i	0.542976	−	0.940461i	0.998731	−	0.0503564i	$-0.0160357\pi$
$132$	−8.59650	−	34.5809i	−0.748230	−	3.00988i
$133$	−0.259911	−	0.450180i	−0.0225372	−	0.0390355i
$134$	−34.2380			−2.95771
$135$	−5.08484	+	1.06976i	−0.437634	+	0.0920700i
$136$			4.47450i			0.383685i
$137$	−2.55126	+	1.47297i	−0.217969	+	0.125844i	−0.605009	−	0.796218i	$-0.706831\pi$
$137$	−2.55126	+	1.47297i	−0.217969	+	0.125844i	0.387041	+	0.922063i	$0.373497\pi$
$138$	−3.60601	−	14.5058i	−0.306964	−	1.23481i
$139$	0.180328	−	0.312337i	0.0152952	−	0.0264921i	−0.858276	−	0.513188i	$-0.828465\pi$
$139$	0.180328	−	0.312337i	0.0152952	−	0.0264921i	0.873572	+	0.486695i	$0.161798\pi$
$140$	−12.5793	+	21.7879i	−1.06314	+	1.84142i
$141$	7.61149	−	7.34013i	0.641003	−	0.618151i
$142$	−13.3118	−	23.0568i	−1.11710	−	1.93488i
$143$	−11.0200	+	7.99517i	−0.921535	+	0.668589i
$144$	−37.5876	−	23.5600i	−3.13230	−	1.96333i
$145$			6.32234i			0.525042i
$146$	2.19289	+	3.79820i	0.181485	+	0.314342i
$147$	6.85477	−	23.8430i	0.565372	−	1.96653i
$148$	26.1559	+	15.1011i	2.15000	+	1.24130i
$149$	3.04895	+	1.76031i	0.249780	+	0.144210i	0.619663	−	0.784868i	$-0.287269\pi$
$149$	3.04895	+	1.76031i	0.249780	+	0.144210i	−0.369884	+	0.929078i	$0.620602\pi$
$150$	−4.54300	−	1.30610i	−0.370935	−	0.106642i
$151$	8.56013	−	4.94220i	0.696614	−	0.402190i	−0.109471	−	0.993990i	$-0.534916\pi$
$151$	8.56013	−	4.94220i	0.696614	−	0.402190i	0.806085	+	0.591800i	$0.201582\pi$
$152$	1.05939			0.0859277
$153$	1.26036	−	0.667901i	0.101894	−	0.0539966i
$154$			47.5876i			3.83472i
$155$	0.820373	+	1.42093i	0.0658939	+	0.114132i
$156$	−5.95403	+	33.4994i	−0.476704	+	2.68210i
$157$	−6.57684	+	11.3914i	−0.524889	+	0.909134i	0.474691	+	0.880152i	$0.342560\pi$
$157$	−6.57684	+	11.3914i	−0.524889	+	0.909134i	−0.999580	+	0.0289814i	$0.990774\pi$
$158$	−10.6767	−	6.16420i	−0.849394	−	0.490398i
$159$	−3.72279	+	0.925453i	−0.295237	+	0.0733932i
$160$	−10.7672	−	18.6493i	−0.851219	−	1.47435i
$161$			14.6016i			1.15077i
$162$	−1.78139	+	24.4977i	−0.139959	+	1.92472i
$163$		−	10.6298i		−	0.832590i	−0.909230	−	0.416295i	$-0.863328\pi$
$163$		−	10.6298i		−	0.832590i	0.909230	−	0.416295i	$-0.136672\pi$
$164$	−57.0585	+	32.9428i	−4.45552	+	2.57240i
$165$	−6.34715	+	1.57784i	−0.494125	+	0.122835i
$166$	1.77522	−	3.07478i	0.137784	−	0.238649i
$167$	−15.8516	−	9.15192i	−1.22663	−	0.708197i	−0.260309	−	0.965525i	$-0.583824\pi$
$167$	−15.8516	−	9.15192i	−1.22663	−	0.708197i	−0.966324	+	0.257329i	$0.917158\pi$
$168$	52.2486	+	54.1802i	4.03107	+	4.18009i
$169$	12.7195	−	2.68577i	0.978426	−	0.206597i
$170$	1.29761			0.0995222
$171$	−0.158133	−	0.298403i	−0.0120927	−	0.0228195i
$172$	14.6163			1.11449
$173$	1.03253	+	1.78839i	0.0785018	+	0.135969i	0.902604	−	0.430472i	$-0.141653\pi$
$173$	1.03253	+	1.78839i	0.0785018	+	0.135969i	−0.824102	+	0.566442i	$0.808320\pi$
$174$	28.7224	+	8.25759i	2.17744	+	0.626007i
$175$	3.99906	+	2.30886i	0.302301	+	0.174533i
$176$	−48.3559	−	27.9183i	−3.64497	−	2.10442i
$177$	14.9617	+	4.30143i	1.12459	+	0.323315i
$178$	−10.6829	−	18.5033i	−0.800715	−	1.38688i
$179$	12.1238			0.906172			0.453086	−	0.891467i	$-0.350323\pi$
$179$	12.1238			0.906172			0.453086	+	0.891467i	$0.350323\pi$
$180$	−8.68064	+	13.8491i	−0.647017	+	1.03225i
$181$	−3.34386			−0.248547			−0.124274	−	0.992248i	$-0.539660\pi$
$181$	−3.34386			−0.248547			−0.124274	+	0.992248i	$0.539660\pi$
$182$	18.5095	−	41.4980i	1.37202	−	3.07603i
$183$	1.72504	+	1.78882i	0.127519	+	0.132233i
$184$	−25.7710	−	14.8789i	−1.89987	−	1.09689i
$185$	2.77173	−	4.80077i	0.203782	−	0.352960i
$186$	7.52677	−	1.87109i	0.551889	−	0.137195i
$187$	1.55484	−	0.897689i	0.113701	−	0.0656455i
$188$		−	33.2615i		−	2.42585i
$189$	7.46216	−	22.8045i	0.542793	−	1.65879i
$190$		−	0.307224i		−	0.0222884i
$191$	4.16937	+	7.22157i	0.301685	+	0.522534i	0.976518	−	0.215437i	$-0.0691175\pi$
$191$	4.16937	+	7.22157i	0.301685	+	0.522534i	−0.674833	+	0.737971i	$0.735784\pi$
$192$	−49.0760	+	12.1999i	−3.54175	+	0.880448i
$193$	−8.66903	−	5.00507i	−0.624011	−	0.360273i	0.154418	−	0.988006i	$-0.450650\pi$
$193$	−8.66903	−	5.00507i	−0.624011	−	0.360273i	−0.778429	+	0.627733i	$0.783983\pi$
$194$	7.61175	−	13.1839i	0.546492	−	0.946552i
$195$	6.14864	+	1.09283i	0.440313	+	0.0782592i
$196$	−39.0186	−	67.5823i	−2.78705	−	4.82730i
$197$			12.3180i			0.877622i	0.898579	+	0.438811i	$0.144600\pi$
$197$			12.3180i			0.877622i	−0.898579	+	0.438811i	$0.855400\pi$
$198$	−1.12185	+	30.8959i	−0.0797262	+	2.19568i
$199$	−1.32463			−0.0939008			−0.0469504	−	0.998897i	$-0.514950\pi$
$199$	−1.32463			−0.0939008			−0.0469504	+	0.998897i	$0.514950\pi$
$200$	−8.15001	+	4.70541i	−0.576292	+	0.332723i
$201$	20.8832	+	6.00384i	1.47299	+	0.423478i
$202$	19.7896	+	11.4256i	1.39239	+	0.803899i
$203$	−25.2834	−	14.5974i	−1.77455	−	1.02454i
$204$	1.23972	−	4.31212i	0.0867976	−	0.301908i
$205$	6.04647	+	10.4728i	0.422304	+	0.731452i
$206$		−	34.2173i		−	2.38404i
$207$	−0.344224	+	9.48001i	−0.0239252	+	0.658906i
$208$	31.3090	+	43.1540i	2.17089	+	2.99219i
$209$	−0.212538	−	0.368127i	−0.0147016	−	0.0254638i
$210$	15.7123	−	15.1522i	1.08425	−	1.04560i
$211$	−3.88208	+	6.72396i	−0.267253	+	0.462896i	−0.968152	−	0.250365i	$-0.919449\pi$
$211$	−3.88208	+	6.72396i	−0.267253	+	0.462896i	0.700898	+	0.713261i	$0.252783\pi$
$212$	−6.03333	+	10.4500i	−0.414370	+	0.717711i
$213$	4.07629	+	16.3976i	0.279303	+	1.12354i
$214$	−41.1322	+	23.7477i	−2.81174	+	1.62336i
$215$		−	2.68275i		−	0.182962i
$216$	32.6448	+	36.4079i	2.22120	+	2.47724i
$217$	−7.57651			−0.514327
$218$	19.8813	+	34.4354i	1.34653	+	2.33226i
$219$	−0.671499	−	2.70122i	−0.0453757	−	0.182532i
$220$	−10.2865	+	17.8167i	−0.693514	+	1.20120i
$221$	−1.70504	+	0.178049i	−0.114693	+	0.0119768i
$222$	−18.1898	−	18.8623i	−1.22082	−	1.26595i
$223$	−12.9585	+	7.48161i	−0.867767	+	0.501006i	−0.866606	−	0.498994i	$-0.833703\pi$
$223$	−12.9585	+	7.48161i	−0.867767	+	0.501006i	−0.00116171	+	0.999999i	$0.500370\pi$
$224$	99.4395			6.64408
$225$	2.54194	+	1.59329i	0.169462	+	0.106219i
$226$		−	1.23056i		−	0.0818554i
$227$	−3.81516	+	2.20268i	−0.253221	+	0.146197i	−0.621238	−	0.783622i	$-0.713370\pi$
$227$	−3.81516	+	2.20268i	−0.253221	+	0.146197i	0.368017	+	0.929819i	$0.380037\pi$
$228$	−1.02094	−	0.293517i	−0.0676135	−	0.0194387i
$229$	18.5963	+	10.7366i	1.22888	+	0.709494i	0.966796	−	0.255551i	$-0.0822569\pi$
$229$	18.5963	+	10.7366i	1.22888	+	0.709494i	0.262084	+	0.965045i	$0.415590\pi$
$230$	−4.31490	+	7.47363i	−0.284516	+	0.492797i
$231$	8.34478	−	29.0257i	0.549046	−	1.90975i
$232$	51.5271	−	29.7492i	3.38292	−	1.95313i
$233$	−24.1867			−1.58453			−0.792263	−	0.610180i	$-0.791097\pi$
$233$	−24.1867			−1.58453			−0.792263	+	0.610180i	$0.791097\pi$
$234$	12.9955	−	26.5059i	0.849540	−	1.73275i
$235$	−6.10498			−0.398245
$236$	42.4084	−	24.4845i	2.76055	−	1.59381i
$237$	5.43124	+	5.63203i	0.352797	+	0.365840i
$238$	−2.99600	+	5.18923i	−0.194202	+	0.336367i
$239$	5.83846	+	3.37084i	0.377658	+	0.218041i	0.676799	−	0.736168i	$-0.263367\pi$
$239$	5.83846	+	3.37084i	0.377658	+	0.218041i	−0.299141	+	0.954209i	$0.596700\pi$
$240$	6.17882	+	24.8554i	0.398841	+	1.60441i
$241$	−7.59632	+	4.38574i	−0.489322	+	0.282510i	−0.724293	−	0.689492i	$-0.757834\pi$
$241$	−7.59632	+	4.38574i	−0.489322	+	0.282510i	0.234971	+	0.972002i	$0.424500\pi$
$242$			8.89329i			0.571683i
$243$	5.38236	−	14.6298i	0.345279	−	0.938500i
$244$	7.81696			0.500430
$245$	−12.4044	+	7.16167i	−0.792487	+	0.457542i
$246$	55.4753	−	13.7907i	3.53697	−	0.879260i
$247$	0.0421550	+	0.403686i	0.00268226	+	0.0256860i
$248$	7.72038	−	13.3721i	0.490245	−	0.849128i
$249$	−1.62196	+	1.56414i	−0.102788	+	0.0991233i
$250$	1.36457	+	2.36351i	0.0863033	+	0.149482i
$251$	−2.22703			−0.140569			−0.0702845	−	0.997527i	$-0.522391\pi$
$251$	−2.22703			−0.140569			−0.0702845	+	0.997527i	$0.522391\pi$
$252$	−35.3411	−	66.6901i	−2.22628	−	4.20108i
$253$			11.9402i			0.750676i
$254$	3.39734	−	1.96145i	0.213168	−	0.123072i
$255$	−0.791467	−	0.227544i	−0.0495636	−	0.0142494i
$256$	−20.7644	+	35.9649i	−1.29777	+	2.24781i
$257$	9.65981	−	16.7313i	0.602562	−	1.04367i	−0.389869	−	0.920870i	$-0.627480\pi$
$257$	9.65981	−	16.7313i	0.602562	−	1.04367i	0.992432	−	0.122798i	$-0.0391869\pi$
$258$	−12.1878	−	3.50394i	−0.758777	−	0.218146i
$259$	12.7991	+	22.1686i	0.795295	+	1.37749i
$260$	15.9001	−	11.5358i	0.986080	−	0.715418i
$261$	−16.0710	−	10.0733i	−0.994768	−	0.623522i
$262$			33.9214i			2.09567i
$263$	5.67702	+	9.83289i	0.350060	+	0.606322i	0.986260	−	0.165203i	$-0.0528279\pi$
$263$	5.67702	+	9.83289i	0.350060	+	0.606322i	−0.636200	+	0.771524i	$0.719495\pi$
$264$	42.7254	+	44.3049i	2.62956	+	2.72678i
$265$	1.91805	+	1.10739i	0.117825	+	0.0680262i
$266$	1.22861	+	0.709337i	0.0753308	+	0.0434922i
$267$	3.27126	+	13.1592i	0.200198	+	0.805331i
$268$	59.1928	−	34.1750i	3.61578	−	2.08757i
$269$	9.62823			0.587044			0.293522	−	0.955952i	$-0.405173\pi$
$269$	9.62823			0.587044			0.293522	+	0.955952i	$0.405173\pi$
$270$	10.5583	−	9.46703i	0.642559	−	0.576145i
$271$			21.0694i			1.27988i	0.768426	+	0.639938i	$0.221040\pi$
$271$			21.0694i			1.27988i	−0.768426	+	0.639938i	$0.778960\pi$
$272$	−3.51534	−	6.08875i	−0.213149	−	0.369184i
$273$	−18.5666	+	22.0656i	−1.12370	+	1.33547i
$274$	4.01995	−	6.96276i	0.242854	−	0.420636i
$275$	3.27016	+	1.88803i	0.197198	+	0.113853i
$276$	20.7134	+	21.4791i	1.24680	+	1.29289i
$277$	10.6042	+	18.3670i	0.637146	+	1.10357i	0.986056	+	0.166413i	$0.0532183\pi$
$277$	10.6042	+	18.3670i	0.637146	+	1.10357i	−0.348911	+	0.937156i	$0.613448\pi$
$278$			0.984284i			0.0590334i
$279$	−4.91900	−	0.178611i	−0.294493	−	0.0106932i
$280$		−	43.4565i		−	2.59702i
$281$	−24.1490	+	13.9425i	−1.44061	+	0.831737i	−0.997890	−	0.0649224i	$-0.979320\pi$
$281$	−24.1490	+	13.9425i	−1.44061	+	0.831737i	−0.442721	+	0.896660i	$0.645987\pi$
$282$	−7.97371	+	27.7350i	−0.474827	+	1.65159i
$283$	2.59505	−	4.49476i	0.154260	−	0.267186i	−0.778529	−	0.627608i	$-0.784034\pi$
$283$	2.59505	−	4.49476i	0.154260	−	0.267186i	0.932789	+	0.360422i	$0.117367\pi$
$284$	46.0287	+	26.5747i	2.73130	+	1.57692i
$285$	−0.0538736	+	0.187389i	−0.00319120	+	0.0110999i
$286$	15.1358	−	33.9342i	0.895000	−	2.00657i
$287$	−55.8418			−3.29624
$288$	64.5604	+	2.34422i	3.80426	+	0.138135i
$289$	−16.7739			−0.986702
$290$	−8.62731	−	14.9429i	−0.506613	−	0.877479i
$291$	−6.95461	+	6.70667i	−0.407687	+	0.393152i
$292$	−7.58243	−	4.37772i	−0.443728	−	0.256187i
$293$	9.03451	+	5.21608i	0.527802	+	0.304726i	0.740121	−	0.672474i	$-0.234768\pi$
$293$	9.03451	+	5.21608i	0.527802	+	0.304726i	−0.212319	+	0.977200i	$0.568102\pi$
$294$	16.3342	+	65.7070i	0.952628	+	3.83211i
$295$	−4.49401	−	7.78385i	−0.261651	−	0.453193i
$296$	−52.1685			−3.03223
$297$	6.10205	−	18.6480i	0.354077	−	1.08207i
$298$	−9.60831			−0.556594
$299$	4.64423	−	10.4123i	0.268583	−	0.602157i
$300$	9.15793	−	2.27658i	0.528734	−	0.131438i
$301$	10.7285	+	6.19410i	0.618380	+	0.357022i
$302$	−13.4880	+	23.3619i	−0.776147	+	1.34433i
$303$	−10.0670	−	10.4392i	−0.578333	−	0.599714i
$304$	−1.44158	+	0.832296i	−0.0826803	+	0.0477355i
$305$		−	1.43476i		−	0.0821543i
$306$	−2.06747	+	3.29844i	−0.118189	+	0.188559i
$307$			7.43423i			0.424294i	0.977238	+	0.212147i	$0.0680455\pi$
$307$			7.43423i			0.424294i	−0.977238	+	0.212147i	$0.931954\pi$
$308$	−47.5001	−	82.2725i	−2.70657	−	4.68791i
$309$	−6.00022	+	20.8706i	−0.341341	+	1.18729i
$310$	−3.87792	−	2.23892i	−0.220251	−	0.127162i
$311$	−13.2721	+	22.9880i	−0.752594	+	1.30353i	0.193968	+	0.981008i	$0.437864\pi$
$311$	−13.2721	+	22.9880i	−0.752594	+	1.30353i	−0.946562	+	0.322523i	$0.895469\pi$
$312$	−20.0253	−	55.2536i	−1.13371	−	3.12812i
$313$	6.89074	+	11.9351i	0.389488	+	0.674613i	0.992381	−	0.123209i	$-0.0393187\pi$
$313$	6.89074	+	11.9351i	0.389488	+	0.674613i	−0.602893	+	0.797822i	$0.705985\pi$
$314$		−	35.8983i		−	2.02586i
$315$	−12.2406	+	6.48668i	−0.689681	+	0.365483i
$316$	24.6115			1.38450
$317$	−1.99198	+	1.15007i	−0.111881	+	0.0645945i	−0.554896	−	0.831920i	$-0.687242\pi$
$317$	−1.99198	+	1.15007i	−0.111881	+	0.0645945i	0.443015	+	0.896514i	$0.353909\pi$
$318$	7.53602	−	7.26735i	0.422599	−	0.407533i
$319$	−20.6751	−	11.9368i	−1.15758	−	0.668331i
$320$	25.2848	+	14.5982i	1.41346	+	0.816064i
$321$	29.2526	−	7.27192i	1.63272	−	0.405879i
$322$	−19.9250	−	34.5111i	−1.11038	−	1.92323i
$323$		−	0.0535235i		−	0.00297813i
$324$	−21.3728	−	44.1313i	−1.18738	−	2.45174i
$325$	−2.11733	−	2.91838i	−0.117448	−	0.161882i
$326$	14.5051	+	25.1237i	0.803366	+	1.39147i
$327$	−6.08797	−	24.4899i	−0.336665	−	1.35429i
$328$	56.9022	−	98.5576i	3.14190	−	5.44193i
$329$	14.0955	−	24.4142i	0.777113	−	1.34600i
$330$	12.8485	−	12.3904i	0.707286	−	0.682070i
$331$	22.8603	−	13.1984i	1.25652	−	0.725451i	0.284122	−	0.958788i	$-0.408298\pi$
$331$	22.8603	−	13.1984i	1.25652	−	0.725451i	0.972396	+	0.233337i	$0.0749644\pi$
$332$			7.08783i			0.388995i
$333$	7.78710	+	14.6946i	0.426730	+	0.805257i
$334$	49.9539			2.73336
$335$	−6.27264	−	10.8645i	−0.342711	−	0.593593i
$336$	−113.664	−	32.6781i	−6.20089	−	1.78273i
$337$	−9.07033	+	15.7103i	−0.494092	+	0.855793i	−0.999977	−	0.00680836i	$-0.997833\pi$
$337$	−9.07033	+	15.7103i	−0.494092	+	0.855793i	0.505885	+	0.862601i	$0.331166\pi$
$338$	−26.3979	+	23.7046i	−1.43585	+	1.28936i
$339$	−0.215786	+	0.750567i	−0.0117199	+	0.0407652i
$340$	−2.24339	+	1.29522i	−0.121665	+	0.0702433i
$341$	−6.19556			−0.335508
$342$	0.780943	+	0.489496i	0.0422286	+	0.0264689i
$343$		−	33.8171i		−	1.82595i
$344$	−21.8645	+	12.6234i	−1.17885	+	0.680611i
$345$	3.94239	−	3.80184i	0.212251	−	0.204684i
$346$	−4.88079	−	2.81793i	−0.262393	−	0.151493i
$347$	2.39311	−	4.14498i	0.128469	−	0.222514i	−0.794615	−	0.607114i	$-0.792327\pi$
$347$	2.39311	−	4.14498i	0.128469	−	0.222514i	0.923084	+	0.384600i	$0.125660\pi$
$348$	−57.8996	+	14.3933i	−3.10374	+	0.771562i
$349$	−16.4569	+	9.50141i	−0.880919	+	0.508599i	−0.870961	−	0.491352i	$-0.836503\pi$
$349$	−16.4569	+	9.50141i	−0.880919	+	0.508599i	−0.00995766	+	0.999950i	$0.503170\pi$
$350$	−12.6025			−0.673629
$351$	−12.5744	+	13.8882i	−0.671174	+	0.741299i
$352$	81.3149			4.33410
$353$	2.38986	−	1.37979i	0.127200	−	0.0734387i	−0.435050	−	0.900406i	$-0.643269\pi$
$353$	2.38986	−	1.37979i	0.127200	−	0.0734387i	0.562250	+	0.826968i	$0.309936\pi$
$354$	−41.2317	+	10.2498i	−2.19144	+	0.544772i
$355$	4.87765	−	8.44833i	0.258879	−	0.448391i
$356$	36.9385	+	21.3264i	1.95773	+	1.13030i
$357$	2.73735	−	2.63976i	0.144876	−	0.139711i
$358$	−28.6546	+	16.5438i	−1.51445	+	0.874365i
$359$			10.4831i			0.553279i	0.960974	+	0.276640i	$0.0892208\pi$
$359$			10.4831i			0.553279i	−0.960974	+	0.276640i	$0.910779\pi$
$360$	1.02446	−	28.2139i	0.0539937	−	1.48700i
$361$	18.9873			0.999333
$362$	7.90326	−	4.56295i	0.415386	−	0.239823i
$363$	1.55949	−	5.42439i	0.0818522	−	0.284707i
$364$	9.42122	+	90.2198i	0.493806	+	4.72880i
$365$	−0.803508	+	1.39172i	−0.0420575	+	0.0728458i
$366$	−6.51813	−	1.87394i	−0.340708	−	0.0979525i
$367$	−9.68919	−	16.7822i	−0.505771	−	0.876022i	−0.999978	−	0.00667714i	$-0.997875\pi$
$367$	−9.68919	−	16.7822i	−0.505771	−	0.876022i	0.494206	−	0.869345i	$-0.335459\pi$
$368$	46.7578			2.43742
$369$	−36.2549	−	1.31643i	−1.88736	−	0.0685309i
$370$			15.1289i			0.786515i
$371$	−8.85701	+	5.11360i	−0.459833	+	0.265485i
$372$	−11.1451	+	10.7478i	−0.577847	+	0.557246i
$373$	−14.8231	+	25.6744i	−0.767511	+	1.32937i	0.171397	+	0.985202i	$0.445172\pi$
$373$	−14.8231	+	25.6744i	−0.767511	+	1.32937i	−0.938909	+	0.344167i	$0.888162\pi$
$374$	−2.44993	+	4.24340i	−0.126683	+	0.219421i
$375$	−0.417855	−	1.68089i	−0.0215779	−	0.0868009i
$376$	28.7264	+	49.7556i	1.48145	+	2.56595i
$377$	13.3865	+	18.4510i	0.689439	+	0.950273i
$378$	13.4816	+	64.0815i	0.693417	+	3.29600i
$379$			22.8221i			1.17229i	0.810205	+	0.586147i	$0.199356\pi$
$379$			22.8221i			1.17229i	−0.810205	+	0.586147i	$0.800644\pi$
$380$	0.306659	+	0.531149i	0.0157313	+	0.0272473i
$381$	−2.41613	+	0.600628i	−0.123782	+	0.0307711i
$382$	−19.7087	−	11.3788i	−1.00839	−	0.582192i
$383$	−2.22332	−	1.28363i	−0.113606	−	0.0655907i	0.442120	−	0.896956i	$-0.354226\pi$
$383$	−2.22332	−	1.28363i	−0.113606	−	0.0655907i	−0.555726	+	0.831365i	$0.687560\pi$
$384$	45.6475	−	44.0201i	2.32944	−	2.24639i
$385$	−15.1007	+	8.71840i	−0.769603	+	0.444331i
$386$	27.3192			1.39051
$387$	6.81939	+	4.27440i	0.346649	+	0.217280i
$388$			30.3910i			1.54287i
$389$	−4.18812	−	7.25404i	−0.212346	−	0.367795i	0.740102	−	0.672495i	$-0.234777\pi$
$389$	−4.18812	−	7.25404i	−0.212346	−	0.367795i	−0.952448	+	0.304700i	$0.901444\pi$
$390$	−16.0236	+	5.80735i	−0.811388	+	0.294067i
$391$	−0.751728	+	1.30203i	−0.0380165	+	0.0658465i
$392$	116.735	+	67.3972i	5.89602	+	3.40407i
$393$	5.94832	−	20.6901i	0.300053	−	1.04368i
$394$	−16.8088	−	29.1138i	−0.846817	−	1.46673i
$395$		−	4.51731i		−	0.227290i
$396$	−28.8996	−	54.5347i	−1.45226	−	2.74047i
$397$		−	37.9166i		−	1.90298i	−0.307679	−	0.951490i	$-0.599552\pi$
$397$		−	37.9166i		−	1.90298i	0.307679	−	0.951490i	$-0.400448\pi$
$398$	3.13079	−	1.80756i	0.156932	−	0.0906049i
$399$	−0.624993	−	0.648098i	−0.0312888	−	0.0324455i
$400$	7.39350	−	12.8059i	0.369675	−	0.640296i
$401$	19.2557	+	11.1173i	0.961585	+	0.555172i	0.896661	−	0.442719i	$-0.145986\pi$
$401$	19.2557	+	11.1173i	0.961585	+	0.555172i	0.0649247	+	0.997890i	$0.479319\pi$
$402$	−57.5503	+	14.3065i	−2.87035	+	0.713543i
$403$	5.40273	+	2.40980i	0.269129	+	0.120041i
$404$	−45.6182			−2.26959
$405$	−8.10007	+	3.92287i	−0.402496	+	0.194929i
$406$	79.6770			3.95430
$407$	10.4662	+	18.1280i	0.518791	+	0.898572i
$408$	1.86969	+	7.52114i	0.0925634	+	0.372352i
$409$	18.0842	+	10.4409i	0.894204	+	0.516269i	0.875315	−	0.483553i	$-0.160654\pi$
$409$	18.0842	+	10.4409i	0.894204	+	0.516269i	0.0188889	+	0.999822i	$0.493987\pi$
$410$	−28.5818	−	16.5017i	−1.41156	−	0.814962i
$411$	−3.67290	+	3.54196i	−0.181171	+	0.174712i
$412$	34.1544	+	59.1572i	1.68267	+	2.91446i
$413$	41.5042			2.04229
$414$	−12.1226	−	22.8759i	−0.595794	−	1.12429i
$415$	1.30094			0.0638604
$416$	−70.9093	−	31.6279i	−3.47661	−	1.55069i
$417$	0.172600	−	0.600356i	0.00845227	−	0.0293996i
$418$	1.00467	+	0.580048i	0.0491401	+	0.0283711i
$419$	−5.01978	+	8.69451i	−0.245232	+	0.424754i	−0.962197	−	0.272355i	$-0.912197\pi$
$419$	−5.01978	+	8.69451i	−0.245232	+	0.424754i	0.716965	+	0.697109i	$0.245531\pi$
$420$	−12.0402	+	41.8795i	−0.587502	+	2.04351i
$421$	−4.67787	+	2.70077i	−0.227986	+	0.131628i	−0.609642	−	0.792677i	$-0.708687\pi$
$421$	−4.67787	+	2.70077i	−0.227986	+	0.131628i	0.381657	+	0.924304i	$0.375354\pi$
$422$		−	21.1896i		−	1.03149i
$423$	9.72699	−	15.5185i	0.472942	−	0.754534i
$424$		−	20.8428i		−	1.01222i
$425$	0.237732	+	0.411763i	0.0115317	+	0.0199734i
$426$	−32.0101	−	33.1935i	−1.55090	−	1.60823i
$427$	5.73771	+	3.31267i	0.277667	+	0.160311i
$428$	47.4080	−	82.1131i	2.29155	−	3.96909i
$429$	−15.1825	+	18.0438i	−0.733020	+	0.871160i
$430$	3.66082	+	6.34072i	0.176540	+	0.305777i
$431$			29.5975i			1.42566i	0.701335	+	0.712831i	$0.252588\pi$
$431$			29.5975i			1.42566i	−0.701335	+	0.712831i	$0.747412\pi$
$432$	−73.0254	−	23.8956i	−3.51343	−	1.14968i
$433$	−20.5685			−0.988458			−0.494229	−	0.869332i	$-0.664550\pi$
$433$	−20.5685			−0.988458			−0.494229	+	0.869332i	$0.664550\pi$
$434$	17.9072	−	10.3387i	0.859572	−	0.496274i
$435$	2.64182	+	10.6272i	0.126665	+	0.509534i
$436$	−68.7441	−	39.6894i	−3.29225	−	1.90078i
$437$	0.308271	+	0.177980i	0.0147466	+	0.00851394i
$438$	5.27311	+	5.46806i	0.251959	+	0.261274i
$439$	−17.9052	−	31.0128i	−0.854571	−	1.48016i	−0.877043	−	0.480412i	$-0.840487\pi$
$439$	−17.9052	−	31.0128i	−0.854571	−	1.48016i	0.0224719	−	0.999747i	$-0.492846\pi$
$440$		−	35.5358i		−	1.69410i
$441$	1.55923	−	42.9417i	0.0742493	−	2.04484i
$442$	3.78691	−	2.74747i	0.180125	−	0.130684i
$443$	16.4749	+	28.5353i	0.782745	+	1.35575i	0.930337	+	0.366706i	$0.119515\pi$
$443$	16.4749	+	28.5353i	0.782745	+	1.35575i	−0.147592	+	0.989048i	$0.547152\pi$
$444$	50.2752	+	14.4540i	2.38596	+	0.685955i
$445$	3.91436	−	6.77986i	0.185558	−	0.321396i
$446$	20.4184	−	35.3658i	0.966841	−	1.67462i
$447$	5.86051	+	1.68488i	0.277193	+	0.0796919i
$448$	−116.758	+	67.4104i	−5.51631	+	3.18484i
$449$			6.88768i			0.325050i	0.986704	+	0.162525i	$0.0519638\pi$
$449$			6.88768i			0.325050i	−0.986704	+	0.162525i	$0.948036\pi$
$450$	−8.18206	−	0.297094i	−0.385706	−	0.0140052i
$451$	−45.6637			−2.15022
$452$	1.22829	+	2.12746i	0.0577740	+	0.100068i
$453$	12.3235	−	11.8842i	0.579010	−	0.558368i
$454$	6.01146	−	10.4121i	0.282132	−	0.488666i
$455$	16.5594	−	1.72922i	0.776316	−	0.0810669i
$456$	1.78072	−	0.442670i	0.0833897	−	0.0207299i
$457$	−26.2730	+	15.1687i	−1.22900	+	0.709562i	−0.966820	−	0.255458i	$-0.917774\pi$
$457$	−26.2730	+	15.1687i	−1.22900	+	0.709562i	−0.262177	+	0.965020i	$0.584441\pi$
$458$	−58.6035			−2.73836
$459$	1.83944	−	1.64931i	0.0858575	−	0.0769834i
$460$		−	17.2279i		−	0.803253i
$461$	17.8514	−	10.3065i	0.831421	−	0.480021i	−0.0229182	−	0.999737i	$-0.507296\pi$
$461$	17.8514	−	10.3065i	0.831421	−	0.480021i	0.854339	+	0.519716i	$0.173962\pi$
$462$	19.8847	+	79.9896i	0.925120	+	3.72145i
$463$	−33.8281	−	19.5306i	−1.57212	−	0.907666i	−0.995908	−	0.0903681i	$-0.971196\pi$
$463$	−33.8281	−	19.5306i	−1.57212	−	0.907666i	−0.576215	−	0.817298i	$-0.695471\pi$
$464$	−46.7442	+	80.9634i	−2.17005	+	3.75863i
$465$	1.97270	+	2.04563i	0.0914817	+	0.0948638i
$466$	57.1657	−	33.0046i	2.64815	−	1.52891i
$467$	−11.6991			−0.541368			−0.270684	−	0.962668i	$-0.587250\pi$
$467$	−11.6991			−0.541368			−0.270684	+	0.962668i	$0.587250\pi$
$468$	3.98979	+	58.7967i	0.184428	+	2.71788i
$469$	57.9306			2.67499
$470$	14.4292	−	8.33071i	0.665570	−	0.384267i
$471$	−6.29499	+	21.8959i	−0.290058	+	1.00891i
$472$	−42.2923	+	73.2524i	−1.94666	+	3.37172i
$473$	8.77304	+	5.06512i	0.403385	+	0.232894i
$474$	−20.5221	−	5.90005i	−0.942613	−	0.270998i
$475$	0.0974896	−	0.0562856i	0.00447313	−	0.00258256i
$476$		−	11.9620i		−	0.548275i
$477$	−5.87091	+	3.11117i	−0.268810	+	0.142451i
$478$	−18.3990			−0.841552
$479$	4.62394	−	2.66964i	0.211273	−	0.121979i	−0.390630	−	0.920548i	$-0.627743\pi$
$479$	4.62394	−	2.66964i	0.211273	−	0.121979i	0.601903	+	0.798569i	$0.294409\pi$
$480$	−25.8911	−	26.8483i	−1.18176	−	1.22545i
$481$	−2.07588	−	19.8791i	−0.0946520	−	0.906410i
$482$	11.9693	−	20.7315i	0.545188	−	0.944293i
$483$	6.10136	+	24.5438i	0.277621	+	1.11678i
$484$	−8.87693	−	15.3753i	−0.403497	−	0.698877i
$485$	5.57811			0.253289
$486$	7.24213	+	41.9223i	0.328510	+	1.90163i
$487$		−	24.5506i		−	1.11249i	−0.831017	−	0.556247i	$-0.812241\pi$
$487$		−	24.5506i		−	1.11249i	0.831017	−	0.556247i	$-0.187759\pi$
$488$	−11.6933	+	6.75114i	−0.529332	+	0.305610i
$489$	−4.44171	−	17.8675i	−0.200861	−	0.807998i
$490$	19.5453	−	33.8534i	0.882965	−	1.52934i
$491$	20.2214	−	35.0245i	0.912580	−	1.58063i	0.102173	−	0.994767i	$-0.467420\pi$
$491$	20.2214	−	35.0245i	0.912580	−	1.58063i	0.810407	−	0.585868i	$-0.199246\pi$
$492$	−82.1439	+	79.2154i	−3.70333	+	3.57130i
$493$	−1.50302	−	2.60331i	−0.0676926	−	0.117247i
$494$	−0.650494	−	0.896595i	−0.0292671	−	0.0403397i
$495$	−10.0096	+	5.30437i	−0.449896	+	0.238414i
$496$			24.2617i			1.08938i
$497$	22.5236	+	39.0120i	1.01032	+	1.74993i
$498$	1.69915	−	5.91016i	0.0761407	−	0.264840i
$499$	6.71322	+	3.87588i	0.300525	+	0.173508i	0.642679	−	0.766136i	$-0.277823\pi$
$499$	6.71322	+	3.87588i	0.300525	+	0.173508i	−0.342154	+	0.939644i	$0.611156\pi$
$500$	−4.71833	−	2.72413i	−0.211010	−	0.121827i
$501$	−30.4690	−	8.75972i	−1.36125	−	0.391356i
$502$	5.26362	−	3.03895i	0.234927	−	0.135635i
$503$	35.2135			1.57009			0.785046	−	0.619437i	$-0.212639\pi$
$503$	35.2135			1.57009			0.785046	+	0.619437i	$0.212639\pi$
$504$	110.464	+	69.2387i	4.92044	+	3.08414i
$505$			8.37298i			0.372593i
$506$	−16.2933	−	28.2209i	−0.724327	−	1.25457i
$507$	20.2579	−	9.82940i	0.899685	−	0.436539i
$508$	−3.91569	+	6.78217i	−0.173731	+	0.300910i
$509$	−25.7902	−	14.8900i	−1.14313	−	0.659986i	−0.195925	−	0.980619i	$-0.562771\pi$
$509$	−25.7902	−	14.8900i	−1.14313	−	0.659986i	−0.947203	+	0.320633i	$0.896104\pi$
$510$	2.18114	−	0.542212i	0.0965826	−	0.0240096i
$511$	−3.71038	−	6.42656i	−0.164137	−	0.284294i
$512$		−	40.1127i		−	1.77275i
$513$	−0.390494	−	0.435507i	−0.0172407	−	0.0192281i
$514$			52.7261i			2.32565i
$515$	10.8580	−	6.26887i	0.478460	−	0.276239i
$516$	24.5685	−	6.10750i	1.08157	−	0.268868i
$517$	11.5264	−	19.9643i	0.506930	−	0.878029i
$518$	−60.5015	−	34.9306i	−2.65828	−	1.53476i
$519$	2.48286	+	2.57465i	0.108985	+	0.113015i
$520$	−13.8219	+	30.9884i	−0.606129	+	1.35893i
$521$	37.3604			1.63679			0.818394	−	0.574658i	$-0.194865\pi$
$521$	37.3604			1.63679			0.818394	+	0.574658i	$0.194865\pi$
$522$	51.7297	+	1.87833i	2.26415	+	0.0822124i
$523$	−15.6389			−0.683843			−0.341922	−	0.939728i	$-0.611078\pi$
$523$	−15.6389			−0.683843			−0.341922	+	0.939728i	$0.611078\pi$
$524$	−33.8590	−	58.6455i	−1.47914	−	2.56194i
$525$	7.68676	+	2.20992i	0.335478	+	0.0964487i
$526$	−26.8354	−	15.4934i	−1.17008	−	0.675546i
$527$	−0.675599	−	0.390057i	−0.0294295	−	0.0169912i
$528$	−92.9469	−	26.7219i	−4.04500	−	1.16292i
$529$	6.50060	+	11.2594i	0.282635	+	0.489538i
$530$	−6.04444			−0.262554
$531$	26.9463	+	0.978433i	1.16937	+	0.0424604i
$532$	−2.83213			−0.122788
$533$	39.8203	+	17.7612i	1.72481	+	0.769322i
$534$	−25.6884	−	26.6381i	−1.11165	−	1.15274i
$535$	−15.0714	−	8.70150i	−0.651595	−	0.376199i
$536$	−59.0307	+	102.244i	−2.54974	+	4.41628i
$537$	20.3787	−	5.06597i	0.879406	−	0.218613i
$538$	−22.7565	+	13.1384i	−0.981100	+	0.566439i
$539$		−	54.0858i		−	2.32964i
$540$	−8.80430	+	26.9061i	−0.378877	+	1.15786i
$541$		−	0.563222i		−	0.0242148i	−0.999927	−	0.0121074i	$-0.996146\pi$
$541$		−	0.563222i		−	0.0242148i	0.999927	−	0.0121074i	$-0.00385400\pi$
$542$	−28.7508	−	49.7979i	−1.23495	−	2.13900i
$543$	−5.62067	+	1.39725i	−0.241206	+	0.0599617i
$544$	8.86704	+	5.11939i	0.380171	+	0.219492i
$545$	−7.28479	+	12.6176i	−0.312046	+	0.540480i
$546$	13.7723	−	77.4879i	0.589402	−	3.31618i
$547$	−10.7895	−	18.6880i	−0.461326	−	0.799040i	0.537702	−	0.843135i	$-0.319293\pi$
$547$	−10.7895	−	18.6880i	−0.461326	−	0.799040i	−0.999027	+	0.0440956i	$0.985959\pi$
$548$			16.0502i			0.685632i
$549$	3.64707	+	2.28599i	0.155653	+	0.0975637i
$550$	−10.3054			−0.439425
$551$	−0.616362	+	0.355857i	−0.0262579	+	0.0151600i
$552$	−49.5355	−	14.2413i	−2.10837	−	0.606150i
$553$	18.0650	+	10.4298i	0.768202	+	0.443521i
$554$	−50.1264	−	28.9405i	−2.12967	−	1.22956i
$555$	2.65295	−	9.22776i	0.112611	−	0.391697i
$556$	−0.982474	−	1.70169i	−0.0416662	−	0.0721679i
$557$		−	4.64485i		−	0.196809i	−0.995147	−	0.0984043i	$-0.968626\pi$
$557$		−	4.64485i		−	0.196809i	0.995147	−	0.0984043i	$-0.0313738\pi$
$558$	11.8698	−	6.29019i	0.502490	−	0.266285i
$559$	−5.68027	−	7.82928i	−0.240250	−	0.331143i
$560$	34.1411	+	59.1342i	1.44273	+	2.49888i
$561$	2.23842	−	2.15862i	0.0945061	−	0.0911368i
$562$	38.0511	−	65.9064i	1.60509	−	2.78009i
$563$	−6.32849	+	10.9613i	−0.266714	+	0.461963i	−0.968011	−	0.250907i	$-0.919271\pi$
$563$	−6.32849	+	10.9613i	−0.266714	+	0.461963i	0.701297	+	0.712869i	$0.252605\pi$
$564$	−13.8985	−	55.9090i	−0.585232	−	2.35419i
$565$	0.390485	−	0.225447i	0.0164278	−	0.00948462i
$566$			14.1646i			0.595381i
$567$	3.01412	−	41.4500i	0.126581	−	1.74074i
$568$	−91.8053			−3.85206
$569$	−12.8814	−	22.3113i	−0.540017	−	0.935337i	−0.998902	−	0.0468414i	$-0.985084\pi$
$569$	−12.8814	−	22.3113i	−0.540017	−	0.935337i	0.458885	−	0.888496i	$-0.348249\pi$
$570$	−0.128375	−	0.516410i	−0.00537703	−	0.0216300i
$571$	−4.30979	+	7.46477i	−0.180359	+	0.312391i	−0.942003	−	0.335605i	$-0.891059\pi$
$571$	−4.30979	+	7.46477i	−0.180359	+	0.312391i	0.761644	+	0.647996i	$0.224393\pi$
$572$	7.70404	+	73.7757i	0.322122	+	3.08472i
$573$	10.0258	+	10.3965i	0.418835	+	0.434319i
$574$	131.983	−	76.2004i	5.50886	−	3.18054i
$575$	−3.16209			−0.131868
$576$	−77.3937	+	41.0133i	−3.22474	+	1.70889i
$577$		−	9.19409i		−	0.382755i	−0.981517	−	0.191377i	$-0.938705\pi$
$577$		−	9.19409i		−	0.382755i	0.981517	−	0.191377i	$-0.0612955\pi$
$578$	39.6454	−	22.8893i	1.64903	−	0.952069i
$579$	−16.6631	−	4.79058i	−0.692495	−	0.199090i
$580$	29.8309	+	17.2229i	1.23866	+	0.715141i
$581$	−3.00368	+	5.20252i	−0.124614	+	0.215837i
$582$	7.28556	−	25.3414i	0.301996	−	1.05043i
$583$	−7.24267	+	4.18156i	−0.299961	+	0.173182i
$584$	15.1233			0.625808
$585$	10.7918	−	0.732305i	0.446188	−	0.0302771i
$586$	−28.4709			−1.17612
$587$	23.2824	−	13.4421i	0.960966	−	0.554814i	0.0644959	−	0.997918i	$-0.479456\pi$
$587$	23.2824	−	13.4421i	0.960966	−	0.554814i	0.896470	+	0.443104i	$0.146123\pi$
$588$	−93.8257	−	97.2944i	−3.86931	−	4.01235i
$589$	−0.0923504	+	0.159956i	−0.00380523	+	0.00659086i
$590$	21.2433	+	12.2648i	0.874573	+	0.504935i
$591$	5.14714	+	20.7052i	0.211725	+	0.851700i
$592$	70.9891	−	40.9856i	2.91763	−	1.68450i
$593$			8.64729i			0.355102i	0.984112	+	0.177551i	$0.0568174\pi$
$593$			8.64729i			0.355102i	−0.984112	+	0.177551i	$0.943183\pi$
$594$	11.0243	+	52.4015i	0.452333	+	2.15006i
$595$	−2.19556			−0.0900090
$596$	16.6115	−	9.59063i	0.680432	−	0.392848i
$597$	−2.22657	+	0.553504i	−0.0911273	+	0.0226534i
$598$	3.23164	+	30.9469i	0.132152	+	1.26551i
$599$	−13.1393	+	22.7580i	−0.536859	+	0.929867i	0.462212	+	0.886770i	$0.347056\pi$
$599$	−13.1393	+	22.7580i	−0.536859	+	0.929867i	−0.999071	+	0.0430977i	$0.986277\pi$
$600$	−11.7331	+	11.3148i	−0.479002	+	0.461925i
$601$	22.3720	+	38.7494i	0.912571	+	1.58062i	0.810418	+	0.585851i	$0.199240\pi$
$601$	22.3720	+	38.7494i	0.912571	+	1.58062i	0.102153	+	0.994769i	$0.467427\pi$
$602$	−33.8093			−1.37796
$603$	37.6111	+	1.36568i	1.53164	+	0.0556147i
$604$		−	53.8527i		−	2.19124i
$605$	−2.82206	+	1.62932i	−0.114733	+	0.0662411i
$606$	38.0385	+	10.9359i	1.54521	+	0.444242i
$607$	20.7581	−	35.9541i	0.842545	−	1.45933i	−0.0451906	−	0.998978i	$-0.514390\pi$
$607$	20.7581	−	35.9541i	0.842545	−	1.45933i	0.887736	−	0.460353i	$-0.152277\pi$
$608$	1.21207	−	2.09937i	0.0491561	−	0.0851408i
$609$	−48.5983	−	13.9718i	−1.96930	−	0.566168i
$610$	1.95784	+	3.39108i	0.0792707	+	0.137301i
$611$	−17.8166	+	12.9263i	−0.720784	+	0.522941i
$612$	0.281995	−	7.76622i	0.0113990	−	0.313931i
$613$		−	30.1598i		−	1.21814i	−0.793116	−	0.609070i	$-0.791543\pi$
$613$		−	30.1598i		−	1.21814i	0.793116	−	0.609070i	$-0.208457\pi$
$614$	−10.1446	−	17.5709i	−0.409401	−	0.709104i
$615$	14.5396	+	15.0771i	0.586292	+	0.607967i
$616$	142.110	+	82.0472i	5.72577	+	3.30578i
$617$	5.17977	+	2.99054i	0.208530	+	0.120395i	0.600628	−	0.799529i	$-0.294917\pi$
$617$	5.17977	+	2.99054i	0.208530	+	0.120395i	−0.392098	+	0.919923i	$0.628251\pi$
$618$	−14.2979	−	57.5157i	−0.575145	−	2.31362i
$619$	10.1403	−	5.85448i	0.407571	−	0.235311i	−0.282174	−	0.959363i	$-0.591056\pi$
$619$	10.1403	−	5.85448i	0.407571	−	0.235311i	0.689746	+	0.724052i	$0.257722\pi$
$620$	8.93921			0.359007
$621$	3.38266	+	16.0787i	0.135742	+	0.645216i
$622$		−	72.4433i		−	2.90471i
$623$	18.0754	+	31.3075i	0.724176	+	1.25431i
$624$	70.6591	+	59.4547i	2.82863	+	2.38009i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−32.5727	−	18.8059i	−1.30187	−	0.751634i
$627$	−0.511077	−	0.529971i	−0.0204104	−	0.0211650i
$628$	35.8323	+	62.0634i	1.42986	+	2.47660i
$629$			2.63571i			0.105093i
$630$	20.0793	−	32.0346i	0.799980	−	1.27629i
$631$		−	46.3399i		−	1.84476i	−0.386280	−	0.922382i	$-0.626240\pi$
$631$		−	46.3399i		−	1.84476i	0.386280	−	0.922382i	$-0.373760\pi$
$632$	−36.8161	+	21.2558i	−1.46446	+	0.845509i
$633$	−3.71572	+	12.9244i	−0.147687	+	0.513698i
$634$	3.13872	−	5.43643i	0.124655	−	0.215908i
$635$	1.24483	+	0.718705i	0.0493997	+	0.0285209i
$636$	−5.77478	+	20.0864i	−0.228985	+	0.796478i
$637$	−21.0370	+	47.1646i	−0.833517	+	1.86873i
$638$	65.1544			2.57949
$639$	13.7036	+	25.8593i	0.542107	+	1.02298i
$640$	−36.6127			−1.44724
$641$	5.31211	+	9.20085i	0.209816	+	0.363412i	0.951656	−	0.307165i	$-0.0993802\pi$
$641$	5.31211	+	9.20085i	0.209816	+	0.363412i	−0.741841	+	0.670576i	$0.766047\pi$
$642$	−59.2157	+	57.1046i	−2.33706	+	2.25374i
$643$	−28.5448	−	16.4803i	−1.12570	−	0.649921i	−0.182847	−	0.983141i	$-0.558531\pi$
$643$	−28.5448	−	16.4803i	−1.12570	−	0.649921i	−0.942849	+	0.333220i	$0.891865\pi$
$644$	68.8953	+	39.7767i	2.71486	+	1.56742i
$645$	−1.12100	−	4.50942i	−0.0441394	−	0.177558i
$646$	0.0730368	+	0.126503i	0.00287360	+	0.00497721i
$647$	0.532069			0.0209178			0.0104589	−	0.999945i	$-0.496671\pi$
$647$	0.532069			0.0209178			0.0104589	+	0.999945i	$0.496671\pi$
$648$	70.0855	+	47.5569i	2.75322	+	1.86821i
$649$	33.9393			1.33223
$650$	8.98668	+	4.00836i	0.352487	+	0.157221i
$651$	−12.7353	+	3.16588i	−0.499135	+	0.124081i
$652$	−50.1549	−	28.9569i	−1.96422	−	1.13404i
$653$	−16.3267	+	28.2786i	−0.638912	+	1.10663i	0.346760	+	0.937954i	$0.387282\pi$
$653$	−16.3267	+	28.2786i	−0.638912	+	1.10663i	−0.985672	+	0.168674i	$0.946052\pi$
$654$	47.8073	+	49.5747i	1.86941	+	1.93852i
$655$	−10.7641	+	6.21464i	−0.420587	+	0.242826i
$656$			178.819i			6.98169i
$657$	−2.25743	−	4.25987i	−0.0880709	−	0.166193i
$658$			76.9377i			2.99935i
$659$	−1.52693	−	2.64472i	−0.0594808	−	0.103024i	0.834752	−	0.550627i	$-0.185611\pi$
$659$	−1.52693	−	2.64472i	−0.0594808	−	0.103024i	−0.894232	+	0.447603i	$0.852278\pi$
$660$	−9.84567	+	34.2462i	−0.383242	+	1.33303i
$661$	−14.5034	−	8.37353i	−0.564116	−	0.325692i	0.190680	−	0.981652i	$-0.438931\pi$
$661$	−14.5034	−	8.37353i	−0.564116	−	0.325692i	−0.754796	+	0.655960i	$0.772264\pi$
$662$	−36.0205	+	62.3893i	−1.39998	+	2.42483i
$663$	−2.79158	+	1.01174i	−0.108416	+	0.0392926i
$664$	−6.12143	−	10.6026i	−0.237558	−	0.411462i
$665$			0.519823i			0.0201579i
$666$	−38.4567	−	24.1047i	−1.49017	−	0.934039i
$667$	19.9918			0.774085
$668$	−86.3635	+	49.8620i	−3.34151	+	1.92922i
$669$	−18.6557	+	17.9906i	−0.721270	+	0.695555i
$670$	29.6510	+	17.1190i	1.14552	+	0.661364i
$671$	4.69191	+	2.70888i	0.181129	+	0.104575i
$672$	167.147	−	41.5513i	6.44784	−	1.60287i
$673$	−4.75179	−	8.23034i	−0.183168	−	0.317256i	0.759790	−	0.650169i	$-0.225302\pi$
$673$	−4.75179	−	8.23034i	−0.183168	−	0.317256i	−0.942958	+	0.332913i	$0.891969\pi$
$674$		−	49.5086i		−	1.90700i
$675$	4.93848	+	1.61598i	0.190082	+	0.0621993i
$676$	21.9773	−	67.3314i	0.845282	−	2.58967i
$677$	0.888100	+	1.53823i	0.0341325	+	0.0591192i	0.882587	−	0.470149i	$-0.155800\pi$
$677$	0.888100	+	1.53823i	0.0341325	+	0.0591192i	−0.848455	+	0.529268i	$0.822467\pi$
$678$	−0.514193	−	2.06843i	−0.0197475	−	0.0794376i
$679$	−12.8791	+	22.3072i	−0.494254	+	0.856073i
$680$	2.23725	−	3.87503i	0.0857945	−	0.148601i
$681$	−5.49247	+	5.29666i	−0.210472	+	0.202968i
$682$	14.6433	−	8.45430i	0.560720	−	0.323732i
$683$		−	45.0955i		−	1.72553i	−0.505605	−	0.862765i	$-0.668731\pi$
$683$		−	45.0955i		−	1.72553i	0.505605	−	0.862765i	$-0.331269\pi$
$684$	−1.83874	−	0.0667656i	−0.0703060	−	0.00255285i
$685$	2.94594			0.112558
$686$	46.1460	+	79.9273i	1.76186	+	3.05164i
$687$	35.7447	+	10.2765i	1.36375	+	0.392073i
$688$	19.8349	−	34.3551i	0.756200	−	1.30978i
$689$	7.94229	−	0.829374i	0.302577	−	0.0315966i
$690$	−4.13000	+	14.3654i	−0.157226	+	0.546880i
$691$	4.61829	−	2.66637i	0.175688	−	0.101434i	−0.409577	−	0.912275i	$-0.634324\pi$
$691$	4.61829	−	2.66637i	0.175688	−	0.101434i	0.585265	+	0.810842i	$0.300990\pi$
$692$	11.2510			0.427698
$693$	1.89816	−	52.2759i	0.0721053	−	1.98580i
$694$			13.0623i			0.495838i
$695$	−0.312337	+	0.180328i	−0.0118476	+	0.00684023i
$696$	74.1806	−	71.5360i	2.81181	−	2.71156i
$697$	−4.97943	−	2.87488i	−0.188609	−	0.108894i
$698$	25.9308	−	44.9134i	0.981494	−	1.70000i
$699$	−40.6553	+	10.1065i	−1.53772	+	0.382265i
$700$	21.7879	−	12.5793i	0.823506	−	0.475452i
$701$	−18.7366			−0.707673			−0.353837	−	0.935307i	$-0.615123\pi$
$701$	−18.7366			−0.707673			−0.353837	+	0.935307i	$0.615123\pi$
$702$	10.7683	−	49.9838i	0.406424	−	1.88652i
$703$	0.624034			0.0235359
$704$	−95.4770	+	55.1237i	−3.59843	+	2.07755i
$705$	−10.2618	+	2.55099i	−0.386482	+	0.0960760i
$706$	−3.76565	+	6.52230i	−0.141722	+	0.245470i
$707$	−33.4841	−	19.3320i	−1.25930	−	0.727056i
$708$	61.0530	−	58.8764i	2.29451	−	2.21271i
$709$	−33.3321	+	19.2443i	−1.25181	+	0.722736i	−0.971470	−	0.237164i	$-0.923782\pi$
$709$	−33.3321	+	19.2443i	−1.25181	+	0.722736i	−0.280345	+	0.959899i	$0.590449\pi$
$710$			26.6237i			0.999168i
$711$	11.4827	+	7.19737i	0.430635	+	0.269922i
$712$	−73.6746			−2.76107
$713$	4.49310	−	2.59409i	0.168268	−	0.0971494i
$714$	−2.86761	+	9.97442i	−0.107318	+	0.373283i
$715$	13.5411	−	1.41404i	0.506410	−	0.0528820i
$716$	33.0267	−	57.2039i	1.23426	−	2.13781i
$717$	11.2223	+	3.22638i	0.419106	+	0.120491i
$718$	−14.3050	−	24.7770i	−0.533859	−	0.924671i
$719$	−30.4253			−1.13467			−0.567336	−	0.823486i	$-0.692026\pi$
$719$	−30.4253			−1.13467			−0.567336	+	0.823486i	$0.692026\pi$
$720$	20.7719	+	39.1973i	0.774121	+	1.46080i
$721$			57.8957i			2.15615i
$722$	−44.8768	+	25.9096i	−1.67014	+	0.964257i
$723$	−10.9360	+	10.5461i	−0.406714	+	0.392214i
$724$	−9.10911	+	15.7774i	−0.338538	+	0.586364i
$725$	3.16117	−	5.47531i	0.117403	−	0.203348i
$726$	3.71610	+	14.9487i	0.137918	+	0.554797i
$727$	26.2966	+	45.5470i	0.975286	+	1.68925i	0.678988	+	0.734150i	$0.262419\pi$
$727$	26.2966	+	45.5470i	0.975286	+	1.68925i	0.296298	+	0.955095i	$0.404248\pi$
$728$	−92.0118	−	126.822i	−3.41018	−	4.70035i
$729$	2.93405	−	26.8401i	0.108669	−	0.994078i
$730$		−	4.38579i		−	0.162325i
$731$	0.637775	+	1.10466i	0.0235890	+	0.0408573i
$732$	13.1395	−	3.26635i	0.485649	−	0.120728i
$733$	−8.95840	−	5.17214i	−0.330886	−	0.191037i	0.325348	−	0.945594i	$-0.394518\pi$
$733$	−8.95840	−	5.17214i	−0.330886	−	0.191037i	−0.656234	+	0.754557i	$0.727852\pi$
$734$	45.8010	+	26.4432i	1.69055	+	0.976038i
$735$	−17.8579	+	17.2212i	−0.658698	+	0.635214i
$736$	−58.9706	+	34.0467i	−2.17369	+	1.25498i
$737$	47.3718			1.74496
$738$	87.4854	−	46.3612i	3.22038	−	1.70658i
$739$			12.1858i			0.448261i	0.974559	+	0.224130i	$0.0719541\pi$
$739$			12.1858i			0.448261i	−0.974559	+	0.224130i	$0.928046\pi$
$740$	−15.1011	−	26.1559i	−0.555127	−	0.961509i
$741$	0.239540	+	0.660939i	0.00879973	+	0.0242802i
$742$	13.9558	−	24.1721i	0.512333	−	0.887386i
$743$	−35.8410	−	20.6928i	−1.31488	−	0.759146i	−0.331980	−	0.943286i	$-0.607717\pi$
$743$	−35.8410	−	20.6928i	−1.31488	−	0.759146i	−0.982900	+	0.184140i	$0.941050\pi$
$744$	7.38953	−	25.7030i	0.270913	−	0.942319i
$745$	−1.76031	−	3.04895i	−0.0644928	−	0.111705i
$746$		−	80.9089i		−	2.96229i
$747$	−2.07276	+	3.30689i	−0.0758385	+	0.120993i
$748$		−	9.78168i		−	0.357654i
$749$	69.5957	−	40.1811i	2.54297	−	1.46819i
$750$	3.28131	+	3.40262i	0.119816	+	0.124246i
$751$	−10.8042	+	18.7134i	−0.394250	+	0.682862i	−0.993005	−	0.118071i	$-0.962329\pi$
$751$	−10.8042	+	18.7134i	−0.394250	+	0.682862i	0.598755	+	0.800932i	$0.295662\pi$
$752$	−78.1799	−	45.1372i	−2.85093	−	1.64598i
$753$	−3.74340	+	0.930575i	−0.136417	+	0.0339121i
$754$	−56.8168	−	25.3422i	−2.06915	−	0.922909i
$755$	−9.88439			−0.359730
$756$	−87.2714	−	97.3314i	−3.17403	−	3.53991i
$757$	−21.1040			−0.767036			−0.383518	−	0.923533i	$-0.625288\pi$
$757$	−21.1040			−0.767036			−0.383518	+	0.923533i	$0.625288\pi$
$758$	−31.1425	−	53.9404i	−1.13115	−	1.95920i
$759$	4.98928	+	20.0702i	0.181099	+	0.728503i
$760$	−0.917457	−	0.529694i	−0.0332796	−	0.0192140i
$761$	1.79140	+	1.03427i	0.0649382	+	0.0374921i	0.532118	−	0.846670i	$-0.321396\pi$
$761$	1.79140	+	1.03427i	0.0649382	+	0.0374921i	−0.467179	+	0.884163i	$0.654730\pi$
$762$	4.89095	−	4.71658i	0.177180	−	0.170864i
$763$	−33.6391	−	58.2647i	−1.21782	−	2.10932i
$764$	45.4316			1.64366
$765$	−1.42545	−	0.0517588i	−0.0515373	−	0.00187134i
$766$	7.00646			0.253154
$767$	−29.5962	−	13.2009i	−1.06866	−	0.476657i
$768$	−19.8745	+	69.1296i	−0.717160	+	2.49450i
$769$	−0.922793	−	0.532774i	−0.0332767	−	0.0192123i	0.483269	−	0.875472i	$-0.339449\pi$
$769$	−0.922793	−	0.532774i	−0.0332767	−	0.0192123i	−0.516546	+	0.856259i	$0.672783\pi$
$770$	23.7938	−	41.2121i	0.857469	−	1.48518i
$771$	9.24585	−	32.1599i	0.332981	−	1.15821i
$772$	−47.2311	+	27.2689i	−1.69989	+	0.981430i
$773$			43.1846i			1.55324i	0.629969	+	0.776620i	$0.283068\pi$
$773$			43.1846i			1.55324i	−0.629969	+	0.776620i	$0.716932\pi$
$774$	−21.9504	−	0.797031i	−0.788992	−	0.0286487i
$775$		−	1.64075i		−	0.0589373i
$776$	−26.2473	−	45.4617i	−0.942223	−	1.63198i
$777$	30.7771	+	31.9149i	1.10412	+	1.14494i
$778$	19.7974	+	11.4300i	0.709770	+	0.409786i
$779$	−0.680659	+	1.17894i	−0.0243872	+	0.0422398i
$780$	21.9060	−	26.0343i	0.784361	−	0.932177i
$781$	18.4183	+	31.9014i	0.659058	+	1.14152i
$782$		−	4.10316i		−	0.146729i
$783$	−31.2227	−	10.2168i	−1.11581	−	0.365119i
$784$	−211.799			−7.56426
$785$	11.3914	−	6.57684i	0.406577	−	0.234737i
$786$	14.1742	+	57.0181i	0.505577	+	2.03377i
$787$	36.8085	+	21.2514i	1.31208	+	0.757530i	0.982440	−	0.186577i	$-0.0597392\pi$
$787$	36.8085	+	21.2514i	1.31208	+	0.757530i	0.329640	+	0.944107i	$0.393073\pi$
$788$	58.1204	+	33.5559i	2.07046	+	1.19538i
$789$	13.6512	+	14.1558i	0.485995	+	0.503962i
$790$	6.16420	+	10.6767i	0.219313	+	0.379860i
$791$			2.08210i			0.0740310i
$792$	90.3297	+	56.6188i	3.20973	+	2.01186i
$793$	−3.03787	−	4.18718i	−0.107878	−	0.148691i
$794$	51.7401	+	89.6164i	1.83619	+	3.18037i
$795$	3.68676	+	1.05993i	0.130756	+	0.0375919i
$796$	−3.60847	+	6.25006i	−0.127899	+	0.221527i
$797$	24.7683	−	42.8999i	0.877337	−	1.51959i	0.0230851	−	0.999734i	$-0.492651\pi$
$797$	24.7683	−	42.8999i	0.877337	−	1.51959i	0.854252	−	0.519859i	$-0.174016\pi$
$798$	2.36156	+	0.678939i	0.0835982	+	0.0240342i
$799$	2.51381	−	1.45135i	0.0889321	−	0.0513450i
$800$			21.5343i			0.761354i
$801$	10.9973	+	20.7523i	0.388570	+	0.733247i
$802$	−60.6816			−2.14274
$803$	−3.03409	−	5.25521i	−0.107071	−	0.185452i
$804$	85.2166	−	82.1785i	3.00536	−	2.89821i
$805$	7.30082	−	12.6454i	0.257320	−	0.445691i
$806$	−16.0578	+	1.67683i	−0.565611	+	0.0590640i
$807$	16.1840	−	4.02320i	0.569704	−	0.141623i
$808$	68.2398	−	39.3983i	2.40067	−	1.38603i
$809$	15.3582			0.539965			0.269983	−	0.962865i	$-0.412982\pi$
$809$	15.3582			0.539965			0.269983	+	0.962865i	$0.412982\pi$
$810$	13.7916	−	20.3249i	0.484586	−	0.714144i
$811$		−	15.5024i		−	0.544364i	−0.962246	−	0.272182i	$-0.912255\pi$
$811$		−	15.5024i		−	0.544364i	0.962246	−	0.272182i	$-0.0877453\pi$
$812$	−137.751	+	79.5304i	−4.83410	+	2.79097i
$813$	8.80396	+	35.4154i	0.308768	+	1.24207i
$814$	−49.4741	−	28.5639i	−1.73407	−	1.00116i
$815$	−5.31490	+	9.20567i	−0.186173	+	0.322461i
$816$	−8.45312	−	8.76562i	−0.295918	−	0.306858i
$817$	0.261541	−	0.151001i	0.00915015	−	0.00528284i
$818$	−56.9895			−1.99259
$819$	−21.9883	+	44.8480i	−0.768334	+	1.56712i
$820$	65.8855			2.30082
$821$	18.7990	−	10.8536i	0.656088	−	0.378793i	−0.134697	−	0.990887i	$-0.543006\pi$
$821$	18.7990	−	10.8536i	0.656088	−	0.378793i	0.790785	+	0.612094i	$0.209673\pi$
$822$	3.84768	−	13.3834i	0.134203	−	0.466800i
$823$	21.4761	−	37.1977i	0.748611	−	1.29663i	−0.199878	−	0.979821i	$-0.564055\pi$
$823$	21.4761	−	37.1977i	0.748611	−	1.29663i	0.948489	−	0.316811i	$-0.102612\pi$
$824$	−102.183	−	58.9951i	−3.55970	−	2.05519i
$825$	6.28571	+	1.80712i	0.218840	+	0.0629159i
$826$	−98.0956	+	56.6355i	−3.41318	+	1.97060i
$827$			6.95047i			0.241692i	0.992671	+	0.120846i	$0.0385607\pi$
$827$			6.95047i			0.241692i	−0.992671	+	0.120846i	$0.961439\pi$
$828$	43.7921	+	27.4489i	1.52188	+	0.953917i
$829$	17.6505			0.613027			0.306514	−	0.951866i	$-0.400838\pi$
$829$	17.6505			0.613027			0.306514	+	0.951866i	$0.400838\pi$
$830$	−3.07478	+	1.77522i	−0.106727	+	0.0616189i
$831$	25.4993	+	26.4420i	0.884561	+	0.917262i
$832$	104.700	−	10.9333i	3.62981	−	0.379044i
$833$	3.40511	−	5.89782i	0.117980	−	0.204347i
$834$	0.411288	+	1.65448i	0.0142417	+	0.0572898i
$835$	9.15192	+	15.8516i	0.316715	+	0.548567i
$836$	−2.31592			−0.0800979
$837$	−8.34293	+	1.75520i	−0.288374	+	0.0606686i
$838$		−	27.3994i		−	0.946498i
$839$	16.8431	−	9.72436i	0.581488	−	0.335722i	−0.180237	−	0.983623i	$-0.557686\pi$
$839$	16.8431	−	9.72436i	0.581488	−	0.335722i	0.761724	+	0.647901i	$0.224353\pi$
$840$	−18.1585	−	73.0457i	−0.626528	−	2.52032i
$841$	−5.48598	+	9.50200i	−0.189172	+	0.327655i
$842$	7.37081	−	12.7666i	0.254015	−	0.439967i
$843$	−34.7660	+	33.5265i	−1.19740	+	1.15472i
$844$	21.1506	+	36.6339i	0.728033	+	1.26099i
$845$	−12.3583	−	4.03383i	−0.425139	−	0.138768i
$846$	−1.81376	+	49.9513i	−0.0623582	+	1.71736i
$847$		−	15.0474i		−	0.517036i
$848$	16.3749	+	28.3622i	0.562317	+	0.973962i
$849$	2.48384	−	8.63956i	0.0852453	−	0.296509i
$850$	−1.12376	−	0.648805i	−0.0385448	−	0.0222538i
$851$	−15.1805	−	8.76445i	−0.520380	−	0.300441i
$852$	88.4736	+	25.4359i	3.03106	+	0.871418i
$853$	−40.8634	+	23.5925i	−1.39913	+	0.807791i	−0.994302	−	0.106600i	$-0.966004\pi$
$853$	−40.8634	+	23.5925i	−1.39913	+	0.807791i	−0.404833	+	0.914391i	$0.632670\pi$
$854$	−18.0815			−0.618737
$855$	−0.0122545	+	0.337491i	−0.000419094	+	0.0115420i
$856$			163.776i			5.59776i
$857$	−12.2627	−	21.2396i	−0.418885	−	0.725531i	0.576942	−	0.816785i	$-0.304246\pi$
$857$	−12.2627	−	21.2396i	−0.418885	−	0.725531i	−0.995828	+	0.0912542i	$0.970912\pi$
$858$	11.2621	−	63.3644i	0.384482	−	2.16322i
$859$	25.0585	−	43.4026i	0.854984	−	1.48088i	−0.0216754	−	0.999765i	$-0.506900\pi$
$859$	25.0585	−	43.4026i	0.854984	−	1.48088i	0.876660	−	0.481111i	$-0.159767\pi$
$860$	−12.6581	−	7.30817i	−0.431638	−	0.249206i
$861$	−93.8641	+	23.3338i	−3.19888	+	0.795213i
$862$	−40.3880	−	69.9542i	−1.37562	−	2.38265i
$863$			8.13933i			0.277066i	0.990358	+	0.138533i	$0.0442387\pi$
$863$			8.13933i			0.277066i	−0.990358	+	0.138533i	$0.955761\pi$
$864$	109.499	−	23.0365i	3.72522	−	0.783718i
$865$		−	2.06506i		−	0.0702141i
$866$	48.6139	−	28.0672i	1.65197	−	0.953764i
$867$	−28.1952	+	7.00907i	−0.957558	+	0.238040i
$868$	−20.6394	+	35.7485i	−0.700546	+	1.21338i
$869$	14.7723	+	8.52881i	0.501117	+	0.289320i
$870$	−20.7455	−	21.5125i	−0.703340	−	0.729342i
$871$	−41.3097	−	18.4255i	−1.39973	−	0.624326i
$872$	137.112			4.64319
$873$	−8.88754	+	14.1792i	−0.300798	+	0.479893i
$874$	−0.971469			−0.0328604
$875$	−2.30886	−	3.99906i	−0.0780537	−	0.135193i
$876$	−14.5745	−	4.19012i	−0.492427	−	0.141571i
$877$	6.28510	+	3.62870i	0.212233	+	0.122533i	0.602349	−	0.798233i	$-0.294232\pi$
$877$	6.28510	+	3.62870i	0.212233	+	0.122533i	−0.390116	+	0.920766i	$0.627565\pi$
$878$	84.6386	+	48.8661i	2.85641	+	1.64915i
$879$	17.3656	+	4.99255i	0.585727	+	0.168394i
$880$	27.9183	+	48.3559i	0.941126	+	1.63008i
$881$	−12.0209			−0.404993			−0.202496	−	0.979283i	$-0.564905\pi$
$881$	−12.0209			−0.404993			−0.202496	+	0.979283i	$0.564905\pi$
$882$	54.9119	+	103.621i	1.84898	+	3.48910i
$883$	−25.4194			−0.855430			−0.427715	−	0.903914i	$-0.640681\pi$
$883$	−25.4194			−0.855430			−0.427715	+	0.903914i	$0.640681\pi$
$884$	−3.80465	+	8.52995i	−0.127964	+	0.286893i
$885$	−10.8065	−	11.2060i	−0.363255	−	0.376685i
$886$	−77.8772	−	44.9624i	−2.61634	−	1.51054i
$887$	−27.1443	+	47.0153i	−0.911417	+	1.57862i	−0.0993528	+	0.995052i	$0.531677\pi$
$887$	−27.1443	+	47.0153i	−0.911417	+	1.57862i	−0.812064	+	0.583568i	$0.801656\pi$
$888$	−87.6895	+	21.7988i	−2.94267	+	0.731521i
$889$	−5.74829	+	3.31878i	−0.192791	+	0.111308i
$890$			21.3657i			0.716181i
$891$	2.46474	−	33.8950i	0.0825719	−	1.13553i
$892$			81.5235i			2.72961i
$893$	−0.343623	−	0.595172i	−0.0114989	−	0.0199167i
$894$	−16.1505	+	4.01488i	−0.540154	+	0.134278i
$895$	−10.4995	−	6.06188i	−0.350959	−	0.202626i
$896$	84.5336	−	146.416i	2.82407	−	4.89143i
$897$	3.45563	−	19.4425i	0.115380	−	0.649167i
$898$	−9.39876	−	16.2791i	−0.313641	−	0.543241i
$899$			10.3734i			0.345971i
$900$	14.4422	−	7.65337i	0.481407	−	0.255112i
$901$	−1.05304			−0.0350819
$902$	107.927	−	62.3115i	3.59357	−	2.07475i
$903$	20.6217	+	5.92866i	0.686247	+	0.197294i
$904$	−3.67478	−	2.12164i	−0.122222	−	0.0705646i
$905$	2.89587	+	1.67193i	0.0962620	+	0.0555769i
$906$	−12.9100	+	44.9048i	−0.428906	+	1.49186i
$907$	6.53507	+	11.3191i	0.216993	+	0.375844i	0.953887	−	0.300165i	$-0.0970417\pi$
$907$	6.53507	+	11.3191i	0.216993	+	0.375844i	−0.736894	+	0.676008i	$0.763708\pi$
$908$			24.0016i			0.796521i
$909$	−21.2836	−	13.3406i	−0.705931	−	0.442478i
$910$	−36.7787	+	26.6835i	−1.21920	+	0.884551i
$911$	−29.0511	−	50.3180i	−0.962506	−	1.66711i	−0.716172	−	0.697924i	$-0.754107\pi$
$911$	−29.0511	−	50.3180i	−0.962506	−	1.66711i	−0.246334	−	0.969185i	$-0.579226\pi$
$912$	−2.07536	+	2.00137i	−0.0687221	+	0.0662720i
$913$	−2.45621	+	4.25427i	−0.0812885	+	0.140796i
$914$	41.3977	−	71.7029i	1.36931	−	2.37172i
$915$	−0.599522	−	2.41168i	−0.0198196	−	0.0797277i
$916$	101.318	−	58.4957i	3.34763	−	1.93275i
$917$		−	57.3949i		−	1.89535i
$918$	−2.09692	+	6.40822i	−0.0692086	+	0.211503i
$919$	52.4703			1.73084			0.865418	−	0.501051i	$-0.167053\pi$
$919$	52.4703			1.73084			0.865418	+	0.501051i	$0.167053\pi$
$920$	14.8789	+	25.7710i	0.490543	+	0.849646i
$921$	3.10643	+	12.4961i	0.102360	+	0.411762i
$922$	−28.1279	+	48.7190i	−0.926345	+	1.60448i
$923$	−3.65310	−	34.9830i	−0.120243	−	1.15148i
$924$	−114.220	−	118.443i	−3.75758	−	3.89649i
$925$	−4.80077	+	2.77173i	−0.157848	+	0.0911339i
$926$	106.604			3.50323
$927$	−1.36485	+	37.5884i	−0.0448277	+	1.23457i
$928$		−	136.147i		−	4.46926i
$929$	−16.8605	+	9.73442i	−0.553176	+	0.319376i	−0.750402	−	0.660982i	$-0.770140\pi$
$929$	−16.8605	+	9.73442i	−0.553176	+	0.319376i	0.197226	+	0.980358i	$0.436807\pi$
$930$	−7.45392	−	2.14298i	−0.244424	−	0.0702709i
$931$	−1.39638	−	0.806198i	−0.0457644	−	0.0264221i
$932$	−65.8878	+	114.121i	−2.15823	+	3.73816i
$933$	−12.7034	+	44.1862i	−0.415890	+	1.44659i
$934$	27.6509	−	15.9642i	0.904764	−	0.522366i
$935$	−1.79538			−0.0587151
$936$	−56.7483	−	84.5077i	−1.85488	−	2.76222i
$937$	−46.2692			−1.51155			−0.755775	−	0.654831i	$-0.772740\pi$
$937$	−46.2692			−1.51155			−0.755775	+	0.654831i	$0.772740\pi$
$938$	−136.920	+	79.0507i	−4.47059	+	2.58110i
$939$	16.5697	+	17.1823i	0.540733	+	0.560724i
$940$	−16.6308	+	28.8053i	−0.542436	+	0.939526i
$941$	−32.8208	−	18.9491i	−1.06993	−	0.617723i	−0.141766	−	0.989900i	$-0.545278\pi$
$941$	−32.8208	−	18.9491i	−1.06993	−	0.617723i	−0.928162	+	0.372177i	$0.878612\pi$
$942$	−15.0003	−	60.3412i	−0.488736	−	1.96602i
$943$	33.1159	−	19.1195i	1.07840	−	0.622616i
$944$		−	132.906i		−	4.32572i
$945$	−17.8647	+	16.0182i	−0.581138	+	0.521073i
$946$	−27.6469			−0.898880
$947$	−13.3754	+	7.72231i	−0.434643	+	0.250941i	−0.701323	−	0.712844i	$-0.747407\pi$
$947$	−13.3754	+	7.72231i	−0.434643	+	0.250941i	0.266679	+	0.963785i	$0.414073\pi$
$948$	41.3692	−	10.2840i	1.34361	−	0.334009i
$949$	0.601786	+	5.76284i	0.0195348	+	0.187070i
$950$	−0.153612	+	0.266064i	−0.00498383	+	0.00863225i
$951$	−2.86775	+	2.76551i	−0.0929931	+	0.0896778i
$952$	10.3310	+	17.8938i	0.334829	+	0.579941i
$953$	13.1318			0.425381			0.212690	−	0.977120i	$-0.431777\pi$
$953$	13.1318			0.425381			0.212690	+	0.977120i	$0.431777\pi$
$954$	9.63054	−	15.3646i	0.311800	−	0.497447i
$955$		−	8.33875i		−	0.269835i
$956$	31.8094	−	18.3652i	1.02879	−	0.593973i
$957$	−39.7404	−	11.4252i	−1.28463	−	0.369325i
$958$	−7.28584	+	12.6194i	−0.235395	+	0.407716i
$959$	−6.80176	+	11.7810i	−0.219640	+	0.380428i
$960$	48.6010	+	13.9726i	1.56859	+	0.450964i
$961$	−14.1540	−	24.5154i	−0.456580	−	0.790820i
$962$	32.0329	+	44.1519i	1.03278	+	1.42351i
$963$	46.1318	−	24.4466i	1.48658	−	0.787782i
$964$			47.7892i			1.53919i
$965$	5.00507	+	8.66903i	0.161119	+	0.279066i
$966$	−47.9124	−	49.6837i	−1.54156	−	1.59855i
$967$	5.62128	+	3.24545i	0.180768	+	0.104367i	0.587653	−	0.809113i	$-0.300052\pi$
$967$	5.62128	+	3.24545i	0.180768	+	0.104367i	−0.406885	+	0.913479i	$0.633385\pi$
$968$	26.5579	+	15.3332i	0.853602	+	0.492827i
$969$	−0.0223650	−	0.0899672i	−0.000718469	−	0.00289016i
$970$	−13.1839	+	7.61175i	−0.423311	+	0.244399i
$971$	13.5504			0.434853			0.217427	−	0.976077i	$-0.430234\pi$
$971$	13.5504			0.434853			0.217427	+	0.976077i	$0.430234\pi$
$972$	−54.3658	−	65.2492i	−1.74379	−	2.09287i
$973$		−	1.66541i		−	0.0533905i
$974$	33.5011	+	58.0257i	1.07345	+	1.85926i
$975$	−4.77846	−	4.02074i	−0.153033	−	0.128767i
$976$	10.6079	−	18.3735i	0.339551	−	0.588120i
$977$	40.1497	+	23.1805i	1.28450	+	0.741609i	0.977668	−	0.210154i	$-0.0673965\pi$
$977$	40.1497	+	23.1805i	1.28450	+	0.741609i	0.306835	+	0.951763i	$0.400730\pi$
$978$	34.8796	+	36.1691i	1.11533	+	1.15656i
$979$	14.7808	+	25.6012i	0.472398	+	0.818217i
$980$			78.0373i			2.49281i
$981$	−20.4664	−	38.6210i	−0.653443	−	1.23307i
$982$			110.375i			3.52219i
$983$	−14.8310	+	8.56269i	−0.473036	+	0.273107i	−0.717510	−	0.696549i	$-0.754718\pi$
$983$	−14.8310	+	8.56269i	−0.473036	+	0.273107i	0.244474	+	0.969656i	$0.421385\pi$
$984$	54.4638	−	189.442i	1.73624	−	6.03917i
$985$	6.15900	−	10.6677i	0.196242	−	0.339901i
$986$	7.10481	+	4.10197i	0.226263	+	0.130633i
$987$	13.4915	−	46.9275i	0.429439	−	1.49372i
$988$	2.01956	+	0.900793i	0.0642508	+	0.0286580i
$989$	−8.48310			−0.269747
$990$	16.4195	−	26.1957i	0.521847	−	0.832556i
$991$	−43.9561			−1.39631			−0.698155	−	0.715946i	$-0.745995\pi$
$991$	−43.9561			−1.39631			−0.698155	+	0.715946i	$0.745995\pi$
$992$	−17.6662	−	30.5987i	−0.560902	−	0.971511i
$993$	32.9108	−	31.7374i	1.04439	−	1.00716i
$994$	−106.470	−	61.4703i	−3.37701	−	1.94972i
$995$	1.14717	+	0.662317i	0.0363676	+	0.0209969i
$996$	2.96168	+	11.9139i	0.0938446	+	0.377506i
$997$	−6.77470	−	11.7341i	−0.214557	−	0.371623i	0.738579	−	0.674167i	$-0.235497\pi$
$997$	−6.77470	−	11.7341i	−0.214557	−	0.371623i	−0.953135	+	0.302544i	$0.902164\pi$
$998$	−21.1557			−0.669673
$999$	19.2295	+	21.4461i	0.608393	+	0.678525i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.571.2	yes	108
9.7	even	3	inner	585.2.bt.b.376.53	yes	108
13.12	even	2	inner	585.2.bt.b.571.53	yes	108
117.25	even	6	inner	585.2.bt.b.376.2	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.2	✓	108	117.25	even	6	inner
585.2.bt.b.376.53	yes	108	9.7	even	3	inner
585.2.bt.b.571.2	yes	108	1.1	even	1	trivial
585.2.bt.b.571.53	yes	108	13.12	even	2	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.36351 + 1.36457i) q^{2} +(1.68089 - 0.417855i) q^{3} +(2.72413 - 4.71833i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-3.40262 + 3.28131i) q^{6} +(3.99906 - 2.30886i) q^{7} +9.41082i q^{8} +(2.65080 - 1.40474i) q^{9} +O(q^{10})\)	\(q+(-2.36351 + 1.36457i) q^{2} +(1.68089 - 0.417855i) q^{3} +(2.72413 - 4.71833i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-3.40262 + 3.28131i) q^{6} +(3.99906 - 2.30886i) q^{7} +9.41082i q^{8} +(2.65080 - 1.40474i) q^{9} +2.72915 q^{10} +(3.27016 - 1.88803i) q^{11} +(2.60739 - 9.06929i) q^{12} +(-3.58605 + 0.374474i) q^{13} +(-6.30123 + 10.9140i) q^{14} +(-1.66462 - 0.478573i) q^{15} +(-7.39350 - 12.8059i) q^{16} +0.475463 q^{17} +(-4.34832 + 6.93732i) q^{18} -0.112571i q^{19} +(-4.71833 + 2.72413i) q^{20} +(5.75722 - 5.55197i) q^{21} +(-5.15272 + 8.92477i) q^{22} +(-1.58104 + 2.73845i) q^{23} +(3.93235 + 15.8186i) q^{24} +(0.500000 + 0.866025i) q^{25} +(7.96468 - 5.77851i) q^{26} +(3.86872 - 3.46886i) q^{27} -25.1585i q^{28} +(-3.16117 - 5.47531i) q^{29} +(4.58741 - 1.14039i) q^{30} +(-1.42093 - 0.820373i) q^{31} +(18.6493 + 10.7672i) q^{32} +(4.70787 - 4.54003i) q^{33} +(-1.12376 + 0.648805i) q^{34} -4.61772 q^{35} +(0.593096 - 16.3340i) q^{36} +5.54346i q^{37} +(0.153612 + 0.266064i) q^{38} +(-5.87129 + 2.12790i) q^{39} +(4.70541 - 8.15001i) q^{40} +(-10.4728 - 6.04647i) q^{41} +(-6.03120 + 20.9783i) q^{42} +(1.34138 + 2.32333i) q^{43} -20.5730i q^{44} +(-2.99802 - 0.108860i) q^{45} -8.62981i q^{46} +(5.28707 - 3.05249i) q^{47} +(-17.7787 - 18.4360i) q^{48} +(7.16167 - 12.4044i) q^{49} +(-2.36351 - 1.36457i) q^{50} +(0.799202 - 0.198674i) q^{51} +(-8.00198 + 17.9403i) q^{52} -2.21477 q^{53} +(-4.41026 + 13.4779i) q^{54} -3.77606 q^{55} +(21.7283 + 37.6344i) q^{56} +(-0.0470384 - 0.189220i) q^{57} +(14.9429 + 8.62731i) q^{58} +(7.78385 + 4.49401i) q^{59} +(-6.79271 + 6.55054i) q^{60} +(0.717381 + 1.24254i) q^{61} +4.47784 q^{62} +(7.35736 - 11.7379i) q^{63} -29.1964 q^{64} +(3.29285 + 1.46872i) q^{65} +(-4.93191 + 17.1547i) q^{66} +(10.8645 + 6.27264i) q^{67} +(1.29522 - 2.24339i) q^{68} +(-1.51329 + 5.26368i) q^{69} +(10.9140 - 6.30123i) q^{70} +9.75529i q^{71} +(13.2197 + 24.9461i) q^{72} -1.60702i q^{73} +(-7.56446 - 13.1020i) q^{74} +(1.20232 + 1.24677i) q^{75} +(-0.531149 - 0.306659i) q^{76} +(8.71840 - 15.1007i) q^{77} +(10.9732 - 13.0411i) q^{78} +(2.25865 + 3.91210i) q^{79} +14.7870i q^{80} +(5.05343 - 7.44734i) q^{81} +33.0035 q^{82} +(-1.12664 + 0.650468i) q^{83} +(-10.5126 - 42.2888i) q^{84} +(-0.411763 - 0.237732i) q^{85} +(-6.34072 - 3.66082i) q^{86} +(-7.60147 - 7.88249i) q^{87} +(17.7679 + 30.7749i) q^{88} +7.82871i q^{89} +(7.23442 - 3.83374i) q^{90} +(-13.4762 + 9.77724i) q^{91} +(8.61393 + 14.9198i) q^{92} +(-2.73122 - 0.785217i) q^{93} +(-8.33071 + 14.4292i) q^{94} +(-0.0562856 + 0.0974896i) q^{95} +(35.8465 + 10.3058i) q^{96} +(-4.83079 + 2.78906i) q^{97} +39.0905i q^{98} +(6.01635 - 9.59850i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

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