LMFDB - Embedded newform 273.2.bl.c.88.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(88,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 5]))

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

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

chi := DirichletCharacter("273.88");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bl (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			88.4
Root			$-1.38488 - 0.286553i$ of defining polynomial
Character	$\chi$	$=$	273.88
Dual form			273.2.bl.c.121.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.496325 + 0.286553i) q^{2} +1.00000 q^{3} +(-0.835774 - 1.44760i) q^{4} +(2.74304 - 1.58369i) q^{5} +(0.496325 + 0.286553i) q^{6} +(-2.25549 + 1.38302i) q^{7} -2.10419i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.496325 + 0.286553i) q^{2} +1.00000 q^{3} +(-0.835774 - 1.44760i) q^{4} +(2.74304 - 1.58369i) q^{5} +(0.496325 + 0.286553i) q^{6} +(-2.25549 + 1.38302i) q^{7} -2.10419i q^{8} +1.00000 q^{9} +1.81525 q^{10} +0.352996i q^{11} +(-0.835774 - 1.44760i) q^{12} +(1.81339 - 3.11635i) q^{13} +(-1.51577 + 0.0401100i) q^{14} +(2.74304 - 1.58369i) q^{15} +(-1.06859 + 1.85085i) q^{16} +(0.444277 + 0.769510i) q^{17} +(0.496325 + 0.286553i) q^{18} +1.53108i q^{19} +(-4.58512 - 2.64722i) q^{20} +(-2.25549 + 1.38302i) q^{21} +(-0.101152 + 0.175201i) q^{22} +(-2.26579 + 3.92446i) q^{23} -2.10419i q^{24} +(2.51618 - 4.35815i) q^{25} +(1.79303 - 1.02709i) q^{26} +1.00000 q^{27} +(3.88715 + 2.10916i) q^{28} +(0.213739 + 0.370207i) q^{29} +1.81525 q^{30} +(7.47692 + 4.31680i) q^{31} +(-4.70529 + 2.71660i) q^{32} +0.352996i q^{33} +0.509236i q^{34} +(-3.99662 + 7.36570i) q^{35} +(-0.835774 - 1.44760i) q^{36} +(2.88399 + 1.66507i) q^{37} +(-0.438737 + 0.759914i) q^{38} +(1.81339 - 3.11635i) q^{39} +(-3.33239 - 5.77187i) q^{40} +(-4.73839 + 2.73571i) q^{41} +(-1.51577 + 0.0401100i) q^{42} +(-0.380909 + 0.659754i) q^{43} +(0.510998 - 0.295025i) q^{44} +(2.74304 - 1.58369i) q^{45} +(-2.24913 + 1.29854i) q^{46} +(-8.53765 + 4.92921i) q^{47} +(-1.06859 + 1.85085i) q^{48} +(3.17449 - 6.23880i) q^{49} +(2.49768 - 1.44204i) q^{50} +(0.444277 + 0.769510i) q^{51} +(-6.02682 - 0.0205021i) q^{52} +(2.06487 - 3.57646i) q^{53} +(0.496325 + 0.286553i) q^{54} +(0.559038 + 0.968281i) q^{55} +(2.91014 + 4.74598i) q^{56} +1.53108i q^{57} +0.244990i q^{58} +(-9.96812 + 5.75510i) q^{59} +(-4.58512 - 2.64722i) q^{60} -15.1561 q^{61} +(2.47399 + 4.28507i) q^{62} +(-2.25549 + 1.38302i) q^{63} +1.16054 q^{64} +(0.0388491 - 11.4201i) q^{65} +(-0.101152 + 0.175201i) q^{66} -9.35501i q^{67} +(0.742630 - 1.28627i) q^{68} +(-2.26579 + 3.92446i) q^{69} +(-4.09429 + 2.51054i) q^{70} +(10.7783 + 6.22283i) q^{71} -2.10419i q^{72} +(5.88903 + 3.40003i) q^{73} +(0.954265 + 1.65284i) q^{74} +(2.51618 - 4.35815i) q^{75} +(2.21640 - 1.27964i) q^{76} +(-0.488201 - 0.796179i) q^{77} +(1.79303 - 1.02709i) q^{78} +(-3.48680 - 6.03932i) q^{79} +6.76926i q^{80} +1.00000 q^{81} -3.13571 q^{82} -14.9864i q^{83} +(3.88715 + 2.10916i) q^{84} +(2.43734 + 1.40720i) q^{85} +(-0.378110 + 0.218302i) q^{86} +(0.213739 + 0.370207i) q^{87} +0.742770 q^{88} +(-5.29223 - 3.05547i) q^{89} +1.81525 q^{90} +(0.219900 + 9.53686i) q^{91} +7.57475 q^{92} +(7.47692 + 4.31680i) q^{93} -5.64993 q^{94} +(2.42477 + 4.19982i) q^{95} +(-4.70529 + 2.71660i) q^{96} +(11.3769 + 6.56845i) q^{97} +(3.36333 - 2.18681i) q^{98} +0.352996i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 12 q^{3} + 5 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} + 12 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 + 12 * q^3 + 5 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 + 12 * q^9	$ 12 q - 3 q^{2} + 12 q^{3} + 5 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} + 12 q^{9} + 14 q^{10} + 5 q^{12} - q^{13} - 16 q^{14} + 6 q^{15} + 3 q^{16} - 3 q^{18} - 27 q^{20} + 3 q^{21} + 7 q^{22} - 16 q^{23} + 10 q^{25} - q^{26} + 12 q^{27} + 24 q^{28} - 5 q^{29} + 14 q^{30} + 15 q^{31} - 6 q^{32} - 2 q^{35} + 5 q^{36} + 6 q^{37} + 24 q^{38} - q^{39} + 21 q^{40} - 15 q^{41} - 16 q^{42} - 13 q^{43} - 30 q^{44} + 6 q^{45} - 9 q^{46} - 9 q^{47} + 3 q^{48} + 9 q^{49} - 63 q^{50} - 55 q^{52} + 18 q^{53} - 3 q^{54} + 13 q^{55} - 21 q^{56} - 33 q^{59} - 27 q^{60} - 52 q^{61} - 13 q^{62} + 3 q^{63} - 4 q^{64} - 41 q^{65} + 7 q^{66} - 16 q^{69} - 42 q^{70} - 15 q^{71} - 18 q^{73} + 38 q^{74} + 10 q^{75} - 30 q^{76} + 20 q^{77} - q^{78} - 4 q^{79} + 12 q^{81} + 28 q^{82} + 24 q^{84} - 12 q^{85} - 15 q^{86} - 5 q^{87} - 32 q^{88} + 12 q^{89} + 14 q^{90} + 49 q^{91} - 40 q^{92} + 15 q^{93} + 6 q^{94} - 28 q^{95} - 6 q^{96} + 45 q^{97} + 48 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 + 12 * q^3 + 5 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 + 12 * q^9 + 14 * q^10 + 5 * q^12 - q^13 - 16 * q^14 + 6 * q^15 + 3 * q^16 - 3 * q^18 - 27 * q^20 + 3 * q^21 + 7 * q^22 - 16 * q^23 + 10 * q^25 - q^26 + 12 * q^27 + 24 * q^28 - 5 * q^29 + 14 * q^30 + 15 * q^31 - 6 * q^32 - 2 * q^35 + 5 * q^36 + 6 * q^37 + 24 * q^38 - q^39 + 21 * q^40 - 15 * q^41 - 16 * q^42 - 13 * q^43 - 30 * q^44 + 6 * q^45 - 9 * q^46 - 9 * q^47 + 3 * q^48 + 9 * q^49 - 63 * q^50 - 55 * q^52 + 18 * q^53 - 3 * q^54 + 13 * q^55 - 21 * q^56 - 33 * q^59 - 27 * q^60 - 52 * q^61 - 13 * q^62 + 3 * q^63 - 4 * q^64 - 41 * q^65 + 7 * q^66 - 16 * q^69 - 42 * q^70 - 15 * q^71 - 18 * q^73 + 38 * q^74 + 10 * q^75 - 30 * q^76 + 20 * q^77 - q^78 - 4 * q^79 + 12 * q^81 + 28 * q^82 + 24 * q^84 - 12 * q^85 - 15 * q^86 - 5 * q^87 - 32 * q^88 + 12 * q^89 + 14 * q^90 + 49 * q^91 - 40 * q^92 + 15 * q^93 + 6 * q^94 - 28 * q^95 - 6 * q^96 + 45 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.496325	+	0.286553i	0.350955	+	0.202624i	0.665106	−	0.746749i	$-0.268386\pi$
$2$	0.496325	+	0.286553i	0.350955	+	0.202624i	−0.314151	+	0.949373i	$0.601720\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−0.835774	−	1.44760i	−0.417887	−	0.723802i
$5$	2.74304	−	1.58369i	1.22672	−	0.708250i	0.260381	−	0.965506i	$-0.416152\pi$
$5$	2.74304	−	1.58369i	1.22672	−	0.708250i	0.966343	+	0.257256i	$0.0828184\pi$
$6$	0.496325	+	0.286553i	0.202624	+	0.116985i
$7$	−2.25549	+	1.38302i	−0.852496	+	0.522734i
$7$	−2.25549	+	1.38302i	−0.852496	+	0.522734i
$8$		−	2.10419i		−	0.743943i
$9$	1.00000			0.333333
$10$	1.81525			0.574033
$11$			0.352996i			0.106432i	0.998583	+	0.0532161i	$0.0169472\pi$
$11$			0.352996i			0.106432i	−0.998583	+	0.0532161i	$0.983053\pi$
$12$	−0.835774	−	1.44760i	−0.241267	−	0.417887i
$13$	1.81339	−	3.11635i	0.502943	−	0.864319i
$13$	1.81339	−	3.11635i	0.502943	−	0.864319i
$14$	−1.51577	+	0.0401100i	−0.405106	+	0.0107198i
$15$	2.74304	−	1.58369i	0.708250	−	0.408908i
$16$	−1.06859	+	1.85085i	−0.267147	+	0.462711i
$17$	0.444277	+	0.769510i	0.107753	+	0.186633i	0.914860	−	0.403772i	$-0.132301\pi$
$17$	0.444277	+	0.769510i	0.107753	+	0.186633i	−0.807107	+	0.590406i	$0.798968\pi$
$18$	0.496325	+	0.286553i	0.116985	+	0.0675413i
$19$			1.53108i			0.351254i	0.984457	+	0.175627i	$0.0561953\pi$
$19$			1.53108i			0.351254i	−0.984457	+	0.175627i	$0.943805\pi$
$20$	−4.58512	−	2.64722i	−1.02526	−	0.591937i
$21$	−2.25549	+	1.38302i	−0.492189	+	0.301800i
$22$	−0.101152	+	0.175201i	−0.0215657	+	0.0373529i
$23$	−2.26579	+	3.92446i	−0.472449	+	0.818306i	−0.999503	−	0.0315258i	$-0.989963\pi$
$23$	−2.26579	+	3.92446i	−0.472449	+	0.818306i	0.527054	+	0.849832i	$0.323297\pi$
$24$		−	2.10419i		−	0.429516i
$25$	2.51618	−	4.35815i	0.503235	−	0.871629i
$26$	1.79303	−	1.02709i	0.351642	−	0.201429i
$27$	1.00000			0.192450
$28$	3.88715	+	2.10916i	0.734603	+	0.398595i
$29$	0.213739	+	0.370207i	0.0396903	+	0.0687457i	0.885188	−	0.465233i	$-0.154030\pi$
$29$	0.213739	+	0.370207i	0.0396903	+	0.0687457i	−0.845498	+	0.533979i	$0.820696\pi$
$30$	1.81525			0.331418
$31$	7.47692	+	4.31680i	1.34289	+	0.775320i	0.987231	−	0.159294i	$-0.0509219\pi$
$31$	7.47692	+	4.31680i	1.34289	+	0.775320i	0.355663	+	0.934614i	$0.384255\pi$
$32$	−4.70529	+	2.71660i	−0.831786	+	0.480232i
$33$			0.352996i			0.0614487i
$34$			0.509236i			0.0873332i
$35$	−3.99662	+	7.36570i	−0.675552	+	1.24503i
$36$	−0.835774	−	1.44760i	−0.139296	−	0.241267i
$37$	2.88399	+	1.66507i	0.474125	+	0.273736i	0.717965	−	0.696079i	$-0.245074\pi$
$37$	2.88399	+	1.66507i	0.474125	+	0.273736i	−0.243840	+	0.969816i	$0.578407\pi$
$38$	−0.438737	+	0.759914i	−0.0711725	+	0.123274i
$39$	1.81339	−	3.11635i	0.290374	−	0.499015i
$40$	−3.33239	−	5.77187i	−0.526898	−	0.912613i
$41$	−4.73839	+	2.73571i	−0.740012	+	0.427246i	−0.822074	−	0.569381i	$-0.807183\pi$
$41$	−4.73839	+	2.73571i	−0.740012	+	0.427246i	0.0820619	+	0.996627i	$0.473849\pi$
$42$	−1.51577	+	0.0401100i	−0.233888	+	0.00618911i
$43$	−0.380909	+	0.659754i	−0.0580881	+	0.100612i	−0.893607	−	0.448850i	$-0.851834\pi$
$43$	−0.380909	+	0.659754i	−0.0580881	+	0.100612i	0.835519	+	0.549462i	$0.185167\pi$
$44$	0.510998	−	0.295025i	0.0770359	−	0.0444767i
$45$	2.74304	−	1.58369i	0.408908	−	0.236083i
$46$	−2.24913	+	1.29854i	−0.331617	+	0.191459i
$47$	−8.53765	+	4.92921i	−1.24534	+	0.719000i	−0.970177	−	0.242397i	$-0.922066\pi$
$47$	−8.53765	+	4.92921i	−1.24534	+	0.719000i	−0.275167	+	0.961397i	$0.588733\pi$
$48$	−1.06859	+	1.85085i	−0.154237	+	0.267147i
$49$	3.17449	−	6.23880i	0.453499	−	0.891257i
$50$	2.49768	−	1.44204i	0.353226	−	0.203935i
$51$	0.444277	+	0.769510i	0.0622112	+	0.107753i
$52$	−6.02682	−	0.0205021i	−0.835770	−	0.00284313i
$53$	2.06487	−	3.57646i	0.283632	−	0.491265i	−0.688645	−	0.725099i	$-0.741794\pi$
$53$	2.06487	−	3.57646i	0.283632	−	0.491265i	0.972276	+	0.233834i	$0.0751273\pi$
$54$	0.496325	+	0.286553i	0.0675413	+	0.0389950i
$55$	0.559038	+	0.968281i	0.0753806	+	0.130563i
$56$	2.91014	+	4.74598i	0.388884	+	0.634209i
$57$			1.53108i			0.202797i
$58$			0.244990i			0.0321688i
$59$	−9.96812	+	5.75510i	−1.29774	+	0.749250i	−0.980013	−	0.198932i	$-0.936253\pi$
$59$	−9.96812	+	5.75510i	−1.29774	+	0.749250i	−0.317726	+	0.948183i	$0.602919\pi$
$60$	−4.58512	−	2.64722i	−0.591937	−	0.341755i
$61$	−15.1561			−1.94053			−0.970267	−	0.242037i	$-0.922184\pi$
$61$	−15.1561			−1.94053			−0.970267	+	0.242037i	$0.922184\pi$
$62$	2.47399	+	4.28507i	0.314197	+	0.544204i
$63$	−2.25549	+	1.38302i	−0.284165	+	0.174245i
$64$	1.16054			0.145067
$65$	0.0388491	−	11.4201i	0.00481864	−	1.41649i
$66$	−0.101152	+	0.175201i	−0.0124510	+	0.0215657i
$67$		−	9.35501i		−	1.14290i	−0.820638	−	0.571448i	$-0.806382\pi$
$67$		−	9.35501i		−	1.14290i	0.820638	−	0.571448i	$-0.193618\pi$
$68$	0.742630	−	1.28627i	0.0900571	−	0.155983i
$69$	−2.26579	+	3.92446i	−0.272769	+	0.472449i
$70$	−4.09429	+	2.51054i	−0.489361	+	0.300066i
$71$	10.7783	+	6.22283i	1.27914	+	0.738514i	0.976691	−	0.214651i	$-0.0688613\pi$
$71$	10.7783	+	6.22283i	1.27914	+	0.738514i	0.302453	+	0.953164i	$0.402195\pi$
$72$		−	2.10419i		−	0.247981i
$73$	5.88903	+	3.40003i	0.689259	+	0.397944i	0.803334	−	0.595528i	$-0.203057\pi$
$73$	5.88903	+	3.40003i	0.689259	+	0.397944i	−0.114075	+	0.993472i	$0.536391\pi$
$74$	0.954265	+	1.65284i	0.110931	+	0.192138i
$75$	2.51618	−	4.35815i	0.290543	−	0.503235i
$76$	2.21640	−	1.27964i	0.254239	−	0.146785i
$77$	−0.488201	−	0.796179i	−0.0556357	−	0.0907331i
$78$	1.79303	−	1.02709i	0.203021	−	0.116295i
$79$	−3.48680	−	6.03932i	−0.392296	−	0.679476i	0.600456	−	0.799658i	$-0.294986\pi$
$79$	−3.48680	−	6.03932i	−0.392296	−	0.679476i	−0.992752	+	0.120182i	$0.961652\pi$
$80$			6.76926i			0.756826i
$81$	1.00000			0.111111
$82$	−3.13571			−0.346281
$83$		−	14.9864i		−	1.64498i	−0.568782	−	0.822488i	$-0.692585\pi$
$83$		−	14.9864i		−	1.64498i	0.568782	−	0.822488i	$-0.307415\pi$
$84$	3.88715	+	2.10916i	0.424123	+	0.230129i
$85$	2.43734	+	1.40720i	0.264366	+	0.152632i
$86$	−0.378110	+	0.218302i	−0.0407726	+	0.0235401i
$87$	0.213739	+	0.370207i	0.0229152	+	0.0396903i
$88$	0.742770			0.0791796
$89$	−5.29223	−	3.05547i	−0.560975	−	0.323879i	0.192561	−	0.981285i	$-0.438321\pi$
$89$	−5.29223	−	3.05547i	−0.560975	−	0.323879i	−0.753537	+	0.657406i	$0.771654\pi$
$90$	1.81525			0.191344
$91$	0.219900	+	9.53686i	0.0230518	+	0.999734i
$92$	7.57475			0.789722
$93$	7.47692	+	4.31680i	0.775320	+	0.447631i
$94$	−5.64993			−0.582746
$95$	2.42477	+	4.19982i	0.248776	+	0.430892i
$96$	−4.70529	+	2.71660i	−0.480232	+	0.277262i
$97$	11.3769	+	6.56845i	1.15515	+	0.666925i	0.950137	−	0.311834i	$-0.100943\pi$
$97$	11.3769	+	6.56845i	1.15515	+	0.666925i	0.205012	+	0.978759i	$0.434277\pi$
$98$	3.36333	−	2.18681i	0.339748	−	0.220901i
$99$			0.352996i			0.0354774i
$100$	−8.41182			−0.841182
$101$	−12.0469			−1.19871			−0.599355	−	0.800484i	$-0.704576\pi$
$101$	−12.0469			−1.19871			−0.599355	+	0.800484i	$0.704576\pi$
$102$			0.509236i			0.0504219i
$103$	6.84541	+	11.8566i	0.674498	+	1.16827i	0.976615	+	0.214995i	$0.0689734\pi$
$103$	6.84541	+	11.8566i	0.674498	+	1.16827i	−0.302117	+	0.953271i	$0.597693\pi$
$104$	−6.55739	−	3.81571i	−0.643005	−	0.374161i
$105$	−3.99662	+	7.36570i	−0.390030	+	0.718819i
$106$	2.04969	−	1.18339i	0.199084	−	0.114941i
$107$	2.56579	−	4.44409i	0.248045	−	0.429626i	−0.714938	−	0.699187i	$-0.753545\pi$
$107$	2.56579	−	4.44409i	0.248045	−	0.429626i	0.962983	+	0.269561i	$0.0868787\pi$
$108$	−0.835774	−	1.44760i	−0.0804224	−	0.139296i
$109$	−0.865142	−	0.499490i	−0.0828656	−	0.0478425i	0.457995	−	0.888955i	$-0.348568\pi$
$109$	−0.865142	−	0.499490i	−0.0828656	−	0.0478425i	−0.540860	+	0.841112i	$0.681901\pi$
$110$			0.640776i			0.0610956i
$111$	2.88399	+	1.66507i	0.273736	+	0.158042i
$112$	−0.149574	−	5.65245i	−0.0141334	−	0.534106i
$113$	−1.46152	+	2.53143i	−0.137488	+	0.238137i	−0.926545	−	0.376183i	$-0.877236\pi$
$113$	−1.46152	+	2.53143i	−0.137488	+	0.238137i	0.789057	+	0.614320i	$0.210570\pi$
$114$	−0.438737	+	0.759914i	−0.0410915	+	0.0711725i
$115$			14.3533i			1.33845i
$116$	0.357275	−	0.618818i	0.0331722	−	0.0574559i
$117$	1.81339	−	3.11635i	0.167648	−	0.288106i
$118$	−6.59657			−0.607264
$119$	−2.06631	−	1.12118i	−0.189419	−	0.102778i
$120$	−3.33239	−	5.77187i	−0.304204	−	0.526898i
$121$	10.8754			0.988672
$122$	−7.52233	−	4.34302i	−0.681040	−	0.393198i
$123$	−4.73839	+	2.73571i	−0.427246	+	0.246671i
$124$		−	14.4315i		−	1.29599i
$125$		−	0.102477i		−	0.00916579i
$126$	−1.51577	+	0.0401100i	−0.135035	+	0.00357328i
$127$	−7.80251	−	13.5143i	−0.692361	−	1.19920i	−0.971062	−	0.238826i	$-0.923237\pi$
$127$	−7.80251	−	13.5143i	−0.692361	−	1.19920i	0.278701	−	0.960378i	$-0.410096\pi$
$128$	9.98659	+	5.76576i	0.882698	+	0.509626i
$129$	−0.380909	+	0.659754i	−0.0335372	+	0.0580881i
$130$	3.29175	−	5.65696i	0.288706	−	0.496148i
$131$	−2.73134	−	4.73083i	−0.238639	−	0.413334i	0.721685	−	0.692221i	$-0.243368\pi$
$131$	−2.73134	−	4.73083i	−0.238639	−	0.413334i	−0.960324	+	0.278887i	$0.910034\pi$
$132$	0.510998	−	0.295025i	0.0444767	−	0.0256786i
$133$	−2.11752	−	3.45335i	−0.183613	−	0.299443i
$134$	2.68071	−	4.64312i	0.231578	−	0.401105i
$135$	2.74304	−	1.58369i	0.236083	−	0.136303i
$136$	1.61919	−	0.934842i	0.138845	−	0.0801620i
$137$	13.6631	−	7.88838i	1.16732	−	0.673950i	0.214270	−	0.976775i	$-0.431263\pi$
$137$	13.6631	−	7.88838i	1.16732	−	0.673950i	0.953046	+	0.302824i	$0.0979296\pi$
$138$	−2.24913	+	1.29854i	−0.191459	+	0.110539i
$139$	4.66230	−	8.07533i	0.395451	−	0.684941i	−0.597708	−	0.801714i	$-0.703922\pi$
$139$	4.66230	−	8.07533i	0.395451	−	0.684941i	0.993159	+	0.116773i	$0.0372550\pi$
$140$	14.0029	−	0.370542i	1.18346	−	0.0313165i
$141$	−8.53765	+	4.92921i	−0.719000	+	0.415115i
$142$	3.56634	+	6.17709i	0.299281	+	0.518370i
$143$	1.10006	+	0.640118i	0.0919915	+	0.0535294i
$144$	−1.06859	+	1.85085i	−0.0890488	+	0.154237i
$145$	1.17259	+	0.676994i	0.0973782	+	0.0562213i
$146$	1.94858	+	3.37504i	0.161266	+	0.279321i
$147$	3.17449	−	6.23880i	0.261828	−	0.514567i
$148$		−	5.56650i		−	0.457564i
$149$		−	2.80497i		−	0.229792i	−0.993378	−	0.114896i	$-0.963346\pi$
$149$		−	2.80497i		−	0.229792i	0.993378	−	0.114896i	$-0.0366535\pi$
$150$	2.49768	−	1.44204i	0.203935	−	0.117742i
$151$	17.5134	+	10.1114i	1.42522	+	0.822853i	0.996739	−	0.0806967i	$-0.0257145\pi$
$151$	17.5134	+	10.1114i	1.42522	+	0.822853i	0.428484	+	0.903549i	$0.359048\pi$
$152$	3.22169			0.261313
$153$	0.444277	+	0.769510i	0.0359176	+	0.0622112i
$154$	−0.0141587	−	0.535060i	−0.00114094	−	0.0431163i
$155$	27.3460			2.19648
$156$	−6.02682	−	0.0205021i	−0.482532	−	0.00164148i
$157$	2.32141	−	4.02080i	0.185269	−	0.320894i	−0.758398	−	0.651791i	$-0.774018\pi$
$157$	2.32141	−	4.02080i	0.185269	−	0.320894i	0.943667	+	0.330897i	$0.107351\pi$
$158$		−	3.99662i		−	0.317954i
$159$	2.06487	−	3.57646i	0.163755	−	0.283632i
$160$	−8.60454	+	14.9035i	−0.680249	+	1.17823i
$161$	−0.317151	−	11.9852i	−0.0249950	−	0.944568i
$162$	0.496325	+	0.286553i	0.0389950	+	0.0225138i
$163$			3.26327i			0.255599i	0.991800	+	0.127800i	$0.0407914\pi$
$163$			3.26327i			0.255599i	−0.991800	+	0.127800i	$0.959209\pi$
$164$	7.92044	+	4.57287i	0.618483	+	0.357081i
$165$	0.559038	+	0.968281i	0.0435210	+	0.0753806i
$166$	4.29442	−	7.43815i	0.333311	−	0.577312i
$167$	20.9079	−	12.0712i	1.61790	−	0.934096i	0.630441	−	0.776238i	$-0.282874\pi$
$167$	20.9079	−	12.0712i	1.61790	−	0.934096i	0.987462	−	0.157859i	$-0.0504591\pi$
$168$	2.91014	+	4.74598i	0.224522	+	0.366161i
$169$	−6.42325	−	11.3023i	−0.494096	−	0.869407i
$170$	0.806474	+	1.39685i	0.0618537	+	0.107134i
$171$			1.53108i			0.117085i
$172$	1.27342			0.0970971
$173$	−19.1914			−1.45909			−0.729547	−	0.683931i	$-0.760269\pi$
$173$	−19.1914			−1.45909			−0.729547	+	0.683931i	$0.760269\pi$
$174$			0.244990i			0.0185727i
$175$	0.352199	+	13.3097i	0.0266238	+	1.00612i
$176$	−0.653341	−	0.377206i	−0.0492474	−	0.0284330i
$177$	−9.96812	+	5.75510i	−0.749250	+	0.432580i
$178$	−1.75111	−	3.03301i	−0.131251	−	0.227334i
$179$	−22.7875			−1.70322			−0.851608	−	0.524179i	$-0.824372\pi$
$179$	−22.7875			−1.70322			−0.851608	+	0.524179i	$0.824372\pi$
$180$	−4.58512	−	2.64722i	−0.341755	−	0.197312i
$181$	1.32420			0.0984270			0.0492135	−	0.998788i	$-0.484329\pi$
$181$	1.32420			0.0984270			0.0492135	+	0.998788i	$0.484329\pi$
$182$	−2.62368	+	4.79639i	−0.194480	+	0.355532i
$183$	−15.1561			−1.12037
$184$	8.25780	+	4.76765i	0.608773	+	0.351475i
$185$	10.5479			0.775495
$186$	2.47399	+	4.28507i	0.181401	+	0.314197i
$187$	−0.271634	+	0.156828i	−0.0198638	+	0.0114684i
$188$	14.2711	+	8.23942i	1.04083	+	0.600921i
$189$	−2.25549	+	1.38302i	−0.164063	+	0.100600i
$190$			2.77930i			0.201632i
$191$	−7.77636			−0.562678			−0.281339	−	0.959608i	$-0.590778\pi$
$191$	−7.77636			−0.562678			−0.281339	+	0.959608i	$0.590778\pi$
$192$	1.16054			0.0837546
$193$			10.9731i			0.789858i	0.918712	+	0.394929i	$0.129231\pi$
$193$			10.9731i			0.789858i	−0.918712	+	0.394929i	$0.870769\pi$
$194$	3.76442	+	6.52017i	0.270270	+	0.468121i
$195$	0.0388491	−	11.4201i	0.00278204	−	0.817812i
$196$	−11.6845	+	0.618818i	−0.834605	+	0.0442013i
$197$	5.20917	−	3.00752i	0.371138	−	0.214277i	−0.302818	−	0.953049i	$-0.597927\pi$
$197$	5.20917	−	3.00752i	0.371138	−	0.214277i	0.673955	+	0.738772i	$0.264594\pi$
$198$	−0.101152	+	0.175201i	−0.00718857	+	0.0124510i
$199$	−7.41270	−	12.8392i	−0.525473	−	0.910145i	−0.999560	−	0.0296673i	$-0.990555\pi$
$199$	−7.41270	−	12.8392i	−0.525473	−	0.910145i	0.474087	−	0.880478i	$-0.342778\pi$
$200$	−9.17036	−	5.29451i	−0.648443	−	0.374379i
$201$		−	9.35501i		−	0.659851i
$202$	−5.97917	−	3.45207i	−0.420693	−	0.242887i
$203$	−0.994091	−	0.539392i	−0.0697715	−	0.0378579i
$204$	0.742630	−	1.28627i	0.0519945	−	0.0900571i
$205$	−8.66505	+	15.0083i	−0.605194	+	1.04823i
$206$			7.84630i			0.546678i
$207$	−2.26579	+	3.92446i	−0.157483	+	0.272769i
$208$	3.83012	+	6.68639i	0.265571	+	0.463617i
$209$	−0.540466			−0.0373848
$210$	−4.09429	+	2.51054i	−0.282533	+	0.173243i
$211$	−10.3820	−	17.9821i	−0.714725	−	1.23794i	−0.963065	−	0.269267i	$-0.913218\pi$
$211$	−10.3820	−	17.9821i	−0.714725	−	1.23794i	0.248340	−	0.968673i	$-0.420115\pi$
$212$	−6.90306			−0.474104
$213$	10.7783	+	6.22283i	0.738514	+	0.426381i
$214$	2.54694	−	1.47047i	0.174105	−	0.100520i
$215$			2.41298i			0.164564i
$216$		−	2.10419i		−	0.143172i
$217$	−22.8344	+	0.604239i	−1.55010	+	0.0410184i
$218$	−0.286261	−	0.495819i	−0.0193880	−	0.0335811i
$219$	5.88903	+	3.40003i	0.397944	+	0.229753i
$220$	0.934459	−	1.61853i	0.0630012	−	0.109121i
$221$	3.20371	+	0.0108984i	0.215505	+	0.000733106i
$222$	0.954265	+	1.65284i	0.0640461	+	0.110931i
$223$	−6.16220	+	3.55775i	−0.412652	+	0.238244i	−0.691928	−	0.721966i	$-0.743239\pi$
$223$	−6.16220	+	3.55775i	−0.412652	+	0.238244i	0.279277	+	0.960211i	$0.409905\pi$
$224$	6.85563	−	12.6348i	0.458061	−	0.844199i
$225$	2.51618	−	4.35815i	0.167745	−	0.290543i
$226$	−1.45078	+	0.837607i	−0.0965043	+	0.0557168i
$227$	−3.21292	+	1.85498i	−0.213249	+	0.123119i	−0.602820	−	0.797877i	$-0.705956\pi$
$227$	−3.21292	+	1.85498i	−0.213249	+	0.123119i	0.389572	+	0.920996i	$0.372623\pi$
$228$	2.21640	−	1.27964i	0.146785	−	0.0847462i
$229$	−11.3004	+	6.52429i	−0.746751	+	0.431137i	−0.824519	−	0.565834i	$-0.808554\pi$
$229$	−11.3004	+	6.52429i	−0.746751	+	0.431137i	0.0777675	+	0.996972i	$0.475221\pi$
$230$	−4.11297	+	7.12388i	−0.271202	+	0.469735i
$231$	−0.488201	−	0.796179i	−0.0321213	−	0.0523848i
$232$	0.778985	−	0.449747i	0.0511429	−	0.0295273i
$233$	−8.10047	−	14.0304i	−0.530679	−	0.919164i	−0.999359	−	0.0357956i	$-0.988603\pi$
$233$	−8.10047	−	14.0304i	−0.530679	−	0.919164i	0.468680	−	0.883368i	$-0.344730\pi$
$234$	1.79303	−	1.02709i	0.117214	−	0.0671429i
$235$	−15.6127	+	27.0421i	−1.01846	+	1.76403i
$236$	16.6622	+	9.61993i	1.08462	+	0.626204i
$237$	−3.48680	−	6.03932i	−0.226492	−	0.392296i
$238$	−0.704285	−	1.14858i	−0.0456520	−	0.0744512i
$239$			14.4871i			0.937093i	0.883439	+	0.468547i	$0.155222\pi$
$239$			14.4871i			0.937093i	−0.883439	+	0.468547i	$0.844778\pi$
$240$			6.76926i			0.436954i
$241$	17.8835	−	10.3251i	1.15198	−	0.665096i	0.202610	−	0.979259i	$-0.435057\pi$
$241$	17.8835	−	10.3251i	1.15198	−	0.665096i	0.949369	+	0.314164i	$0.101724\pi$
$242$	5.39773	+	3.11638i	0.346979	+	0.200329i
$243$	1.00000			0.0641500
$244$	12.6670	+	21.9400i	0.810924	+	1.40456i
$245$	−1.17259	−	22.1407i	−0.0749139	−	1.41452i
$246$	−3.13571			−0.199925
$247$	4.77139	+	2.77645i	0.303596	+	0.176661i
$248$	9.08336	−	15.7328i	0.576794	−	0.999037i
$249$		−	14.9864i		−	0.949728i
$250$	0.0293650	−	0.0508617i	0.00185721	−	0.00321678i
$251$	−12.9380	+	22.4093i	−0.816642	+	1.41447i	0.0915012	+	0.995805i	$0.470833\pi$
$251$	−12.9380	+	22.4093i	−0.816642	+	1.41447i	−0.908143	+	0.418660i	$0.862500\pi$
$252$	3.88715	+	2.10916i	0.244868	+	0.132865i
$253$	−1.38532	−	0.799814i	−0.0870942	−	0.0502838i
$254$		−	8.94334i		−	0.561155i
$255$	2.43734	+	1.40720i	0.152632	+	0.0881221i
$256$	2.14386	+	3.71327i	0.133991	+	0.232080i
$257$	0.945343	−	1.63738i	0.0589689	−	0.102137i	−0.835034	−	0.550198i	$-0.814552\pi$
$257$	0.945343	−	1.63738i	0.0589689	−	0.102137i	0.894003	+	0.448061i	$0.147885\pi$
$258$	−0.378110	+	0.218302i	−0.0235401	+	0.0135909i
$259$	−8.80766	+	0.233067i	−0.547281	+	0.0144821i
$260$	−16.5643	+	9.48840i	−1.02727	+	0.588446i
$261$	0.213739	+	0.370207i	0.0132301	+	0.0229152i
$262$		−	3.13070i		−	0.193415i
$263$	6.09316			0.375721			0.187860	−	0.982196i	$-0.439845\pi$
$263$	6.09316			0.375721			0.187860	+	0.982196i	$0.439845\pi$
$264$	0.742770			0.0457143
$265$		−	13.0805i		−	0.803529i
$266$	−0.0614117	−	2.32076i	−0.00376539	−	0.142295i
$267$	−5.29223	−	3.05547i	−0.323879	−	0.186992i
$268$	−13.5423	+	7.81868i	−0.827230	+	0.477602i
$269$	0.702043	+	1.21597i	0.0428043	+	0.0741393i	0.886634	−	0.462472i	$-0.153037\pi$
$269$	0.702043	+	1.21597i	0.0428043	+	0.0741393i	−0.843830	+	0.536611i	$0.819704\pi$
$270$	1.81525			0.110473
$271$	−11.4852	−	6.63099i	−0.697677	−	0.402804i	0.108805	−	0.994063i	$-0.465298\pi$
$271$	−11.4852	−	6.63099i	−0.697677	−	0.402804i	−0.806482	+	0.591259i	$0.798631\pi$
$272$	−1.89899			−0.115143
$273$	0.219900	+	9.53686i	0.0133090	+	0.577197i
$274$	9.04177			0.546233
$275$	1.53841	+	0.888200i	0.0927695	+	0.0535605i
$276$	7.57475			0.455946
$277$	−8.44494	−	14.6271i	−0.507407	−	0.878855i	−0.999963	−	0.00857458i	$-0.997271\pi$
$277$	−8.44494	−	14.6271i	−0.507407	−	0.878855i	0.492556	−	0.870281i	$-0.336063\pi$
$278$	4.62803	−	2.67199i	0.277571	−	0.160256i
$279$	7.47692	+	4.31680i	0.447631	+	0.258440i
$280$	15.4988	+	8.40964i	0.926232	+	0.502572i
$281$			22.5550i			1.34552i	0.739860	+	0.672761i	$0.234892\pi$
$281$			22.5550i			1.34552i	−0.739860	+	0.672761i	$0.765108\pi$
$282$	−5.64993			−0.336448
$283$	0.798257			0.0474514			0.0237257	−	0.999719i	$-0.492447\pi$
$283$	0.798257			0.0474514			0.0237257	+	0.999719i	$0.492447\pi$
$284$		−	20.8035i		−	1.23446i
$285$	2.42477	+	4.19982i	0.143631	+	0.248776i
$286$	0.362558	+	0.632932i	0.0214385	+	0.0374261i
$287$	6.90385	−	12.7237i	0.407521	−	0.751054i
$288$	−4.70529	+	2.71660i	−0.277262	+	0.160077i
$289$	8.10524	−	14.0387i	0.476779	−	0.825805i
$290$	0.387990	+	0.672018i	0.0227836	+	0.0394623i
$291$	11.3769	+	6.56845i	0.666925	+	0.385049i
$292$		−	11.3666i		−	0.665182i
$293$	−26.6711	−	15.3986i	−1.55814	−	0.899593i	−0.997435	−	0.0715779i	$-0.977197\pi$
$293$	−26.6711	−	15.3986i	−1.55814	−	0.899593i	−0.560706	−	0.828015i	$-0.689470\pi$
$294$	3.36333	−	2.18681i	0.196153	−	0.127537i
$295$	−18.2286	+	31.5729i	−1.06131	+	1.83825i
$296$	3.50363	−	6.06846i	0.203644	−	0.352722i
$297$			0.352996i			0.0204829i
$298$	0.803774	−	1.39218i	0.0465614	−	0.0806467i
$299$	8.12123	+	14.1775i	0.469663	+	0.819909i
$300$	−8.41182			−0.485657
$301$	−0.0533174	−	2.01488i	−0.00307316	−	0.116136i
$302$	5.79490	+	10.0371i	0.333459	+	0.577568i
$303$	−12.0469			−0.692075
$304$	−2.83380	−	1.63609i	−0.162529	−	0.0938364i
$305$	−41.5737	+	24.0026i	−2.38050	+	1.37438i
$306$			0.509236i			0.0291111i
$307$		−	21.4161i		−	1.22228i	−0.791522	−	0.611140i	$-0.790711\pi$
$307$		−	21.4161i		−	1.22228i	0.791522	−	0.611140i	$-0.209289\pi$
$308$	−0.744526	+	1.37215i	−0.0424233	+	0.0781854i
$309$	6.84541	+	11.8566i	0.389422	+	0.674498i
$310$	13.5725	+	7.83608i	0.770865	+	0.445059i
$311$	−9.69378	+	16.7901i	−0.549684	+	0.952081i	0.448612	+	0.893727i	$0.351919\pi$
$311$	−9.69378	+	16.7901i	−0.549684	+	0.952081i	−0.998296	+	0.0583541i	$0.981415\pi$
$312$	−6.55739	−	3.81571i	−0.371239	−	0.216022i
$313$	3.85148	+	6.67096i	0.217699	+	0.377065i	0.954104	−	0.299476i	$-0.0968117\pi$
$313$	3.85148	+	6.67096i	0.217699	+	0.377065i	−0.736405	+	0.676540i	$0.763478\pi$
$314$	2.30435	−	1.33041i	0.130042	−	0.0750796i
$315$	−3.99662	+	7.36570i	−0.225184	+	0.415010i
$316$	−5.82836	+	10.0950i	−0.327871	+	0.567889i
$317$	12.7818	−	7.37956i	0.717896	−	0.414477i	−0.0960819	−	0.995373i	$-0.530631\pi$
$317$	12.7818	−	7.37956i	0.717896	−	0.414477i	0.813978	+	0.580896i	$0.197298\pi$
$318$	2.04969	−	1.18339i	0.114941	−	0.0663613i
$319$	−0.130681	+	0.0754489i	−0.00731675	+	0.00422433i
$320$	3.18340	−	1.83794i	0.177958	−	0.102744i
$321$	2.56579	−	4.44409i	0.143209	−	0.248045i
$322$	3.27700	−	6.03945i	0.182620	−	0.336565i
$323$	−1.17818	+	0.680224i	−0.0655558	+	0.0378487i
$324$	−0.835774	−	1.44760i	−0.0464319	−	0.0804224i
$325$	−9.01870	−	15.7443i	−0.500267	−	0.873336i
$326$	−0.935102	+	1.61964i	−0.0517905	+	0.0897038i
$327$	−0.865142	−	0.499490i	−0.0478425	−	0.0276219i
$328$	5.75645	+	9.97046i	0.317847	+	0.550527i
$329$	12.4394	−	22.9256i	0.685805	−	1.26393i
$330$			0.640776i			0.0352736i
$331$			1.65551i			0.0909950i	0.998964	+	0.0454975i	$0.0144873\pi$
$331$			1.65551i			0.0909950i	−0.998964	+	0.0454975i	$0.985513\pi$
$332$	−21.6944	+	12.5253i	−1.19064	+	0.687415i
$333$	2.88399	+	1.66507i	0.158042	+	0.0912455i
$334$	13.8362			0.757081
$335$	−14.8155	−	25.6612i	−0.809456	−	1.40202i
$336$	−0.149574	−	5.65245i	−0.00815994	−	0.308366i
$337$	−2.88666			−0.157246			−0.0786231	−	0.996904i	$-0.525052\pi$
$337$	−2.88666			−0.157246			−0.0786231	+	0.996904i	$0.525052\pi$
$338$	0.0506891	−	7.45021i	0.00275712	−	0.405238i
$339$	−1.46152	+	2.53143i	−0.0793789	+	0.137488i
$340$		−	4.70440i		−	0.255132i
$341$	−1.52381	+	2.63932i	−0.0825191	+	0.142927i
$342$	−0.438737	+	0.759914i	−0.0237242	+	0.0410915i
$343$	1.46836	+	18.4620i	0.0792837	+	0.996852i
$344$	1.38825	+	0.801505i	0.0748493	+	0.0432143i
$345$			14.3533i			0.772754i
$346$	−9.52517	−	5.49936i	−0.512076	−	0.295647i
$347$	14.5438	+	25.1906i	0.780753	+	1.35230i	0.931504	+	0.363732i	$0.118497\pi$
$347$	14.5438	+	25.1906i	0.780753	+	1.35230i	−0.150751	+	0.988572i	$0.548169\pi$
$348$	0.357275	−	0.618818i	0.0191520	−	0.0331722i
$349$	−15.8747	+	9.16529i	−0.849756	+	0.490607i	−0.860568	−	0.509335i	$-0.829891\pi$
$349$	−15.8747	+	9.16529i	−0.849756	+	0.490607i	0.0108128	+	0.999942i	$0.496558\pi$
$350$	−3.63913	+	6.70686i	−0.194520	+	0.358497i
$351$	1.81339	−	3.11635i	0.0967915	−	0.166338i
$352$	−0.958950	−	1.66095i	−0.0511122	−	0.0885289i
$353$		−	7.14831i		−	0.380466i	−0.981739	−	0.190233i	$-0.939076\pi$
$353$		−	7.14831i		−	0.380466i	0.981739	−	0.190233i	$-0.0609243\pi$
$354$	−6.59657			−0.350604
$355$	39.4202			2.09221
$356$			10.2147i			0.541380i
$357$	−2.06631	−	1.12118i	−0.109361	−	0.0593390i
$358$	−11.3100	−	6.52983i	−0.597752	−	0.345112i
$359$	−13.0092	+	7.51088i	−0.686601	+	0.396409i	−0.802337	−	0.596871i	$-0.796410\pi$
$359$	−13.0092	+	7.51088i	−0.686601	+	0.396409i	0.115737	+	0.993280i	$0.463077\pi$
$360$	−3.33239	−	5.77187i	−0.175633	−	0.304204i
$361$	16.6558			0.876620
$362$	0.657234	+	0.379454i	0.0345434	+	0.0199437i
$363$	10.8754			0.570810
$364$	13.6218	−	8.28899i	0.713976	−	0.434461i
$365$	21.5385			1.12737
$366$	−7.52233	−	4.34302i	−0.393198	−	0.227013i
$367$	−4.04901			−0.211357			−0.105678	−	0.994400i	$-0.533701\pi$
$367$	−4.04901			−0.211357			−0.105678	+	0.994400i	$0.533701\pi$
$368$	−4.84238	−	8.38725i	−0.252426	−	0.437215i
$369$	−4.73839	+	2.73571i	−0.246671	+	0.142415i
$370$	5.23517	+	3.02253i	0.272164	+	0.157134i
$371$	0.289028	+	10.9224i	0.0150056	+	0.567065i
$372$		−	14.4315i		−	0.748237i
$373$	19.0094			0.984271			0.492135	−	0.870519i	$-0.336217\pi$
$373$	19.0094			0.984271			0.492135	+	0.870519i	$0.336217\pi$
$374$	−0.179758			−0.00929507
$375$		−	0.102477i		−	0.00529187i
$376$	10.3720	+	17.9648i	0.534895	+	0.926465i
$377$	1.54128	+	0.00524316i	0.0793802	+	0.000270037i
$378$	−1.51577	+	0.0401100i	−0.0779627	+	0.00206304i
$379$	14.4405	−	8.33722i	0.741758	−	0.428254i	−0.0809502	−	0.996718i	$-0.525795\pi$
$379$	14.4405	−	8.33722i	0.741758	−	0.428254i	0.822708	+	0.568464i	$0.192462\pi$
$380$	4.05312	−	7.02020i	0.207920	−	0.360129i
$381$	−7.80251	−	13.5143i	−0.399735	−	0.692361i
$382$	−3.85960	−	2.22834i	−0.197474	−	0.114012i
$383$			8.64093i			0.441531i	0.975327	+	0.220765i	$0.0708555\pi$
$383$			8.64093i			0.441531i	−0.975327	+	0.220765i	$0.929145\pi$
$384$	9.98659	+	5.76576i	0.509626	+	0.294233i
$385$	−2.60006	−	1.41079i	−0.132511	−	0.0719005i
$386$	−3.14437	+	5.44620i	−0.160044	+	0.277204i
$387$	−0.380909	+	0.659754i	−0.0193627	+	0.0335372i
$388$		−	21.9590i		−	1.11480i
$389$	3.54047	−	6.13227i	0.179509	−	0.310918i	−0.762204	−	0.647337i	$-0.775883\pi$
$389$	3.54047	−	6.13227i	0.179509	−	0.310918i	0.941712	+	0.336419i	$0.109216\pi$
$390$	3.29175	−	5.65696i	0.166684	−	0.286451i
$391$	−4.02654			−0.203631
$392$	−13.1276	−	6.67973i	−0.663044	−	0.337378i
$393$	−2.73134	−	4.73083i	−0.137778	−	0.238639i
$394$	3.44725			0.173670
$395$	−19.1289	−	11.0441i	−0.962478	−	0.555687i
$396$	0.510998	−	0.295025i	0.0256786	−	0.0148256i
$397$		−	21.6490i		−	1.08653i	−0.839561	−	0.543266i	$-0.817188\pi$
$397$		−	21.6490i		−	1.08653i	0.839561	−	0.543266i	$-0.182812\pi$
$398$		−	8.49654i		−	0.425893i
$399$	−2.11752	−	3.45335i	−0.106009	−	0.172884i
$400$	5.37750	+	9.31411i	0.268875	+	0.465705i
$401$	12.7821	+	7.37974i	0.638307	+	0.368527i	0.783962	−	0.620809i	$-0.213196\pi$
$401$	12.7821	+	7.37974i	0.638307	+	0.368527i	−0.145655	+	0.989335i	$0.546529\pi$
$402$	2.68071	−	4.64312i	0.133702	−	0.231578i
$403$	27.0112	−	15.4726i	1.34552	−	0.770747i
$404$	10.0685	+	17.4391i	0.500925	+	0.867628i
$405$	2.74304	−	1.58369i	0.136303	−	0.0786944i
$406$	−0.338827	−	0.552574i	−0.0168157	−	0.0274238i
$407$	−0.587764	+	1.01804i	−0.0291344	+	0.0504622i
$408$	1.61919	−	0.934842i	0.0801620	−	0.0462816i
$409$	15.1665	−	8.75636i	0.749933	−	0.432974i	−0.0757365	−	0.997128i	$-0.524131\pi$
$409$	15.1665	−	8.75636i	0.749933	−	0.432974i	0.825670	+	0.564154i	$0.190797\pi$
$410$	−8.60136	+	4.96600i	−0.424791	+	0.245253i
$411$	13.6631	−	7.88838i	0.673950	−	0.389105i
$412$	11.4424	−	19.8189i	0.563729	−	0.976406i
$413$	14.5236	−	26.7667i	0.714659	−	1.31710i
$414$	−2.24913	+	1.29854i	−0.110539	+	0.0638197i
$415$	−23.7340	−	41.1084i	−1.16505	−	2.01793i
$416$	−0.0666401	+	19.5896i	−0.00326730	+	0.960459i
$417$	4.66230	−	8.07533i	0.228314	−	0.395451i
$418$	−0.268247	−	0.154872i	−0.0131204	−	0.00757505i
$419$	15.4087	+	26.6887i	0.752764	+	1.30383i	0.946478	+	0.322768i	$0.104613\pi$
$419$	15.4087	+	26.6887i	0.752764	+	1.30383i	−0.193714	+	0.981058i	$0.562053\pi$
$420$	14.0029	−	0.370542i	0.683271	−	0.0180806i
$421$			29.3681i			1.43131i	0.698452	+	0.715657i	$0.253873\pi$
$421$			29.3681i			1.43131i	−0.698452	+	0.715657i	$0.746127\pi$
$422$		−	11.9000i		−	0.579281i
$423$	−8.53765	+	4.92921i	−0.415115	+	0.239667i
$424$	−7.52555	−	4.34488i	−0.365473	−	0.211006i
$425$	4.47151			0.216900
$426$	3.56634	+	6.17709i	0.172790	+	0.299281i
$427$	34.1844	−	20.9612i	1.65430	−	1.01438i
$428$	−8.57770			−0.414619
$429$	1.10006	+	0.640118i	0.0531113	+	0.0309052i
$430$	−0.691446	+	1.19762i	−0.0333445	+	0.0577544i
$431$			21.2927i			1.02563i	0.858498	+	0.512816i	$0.171398\pi$
$431$			21.2927i			1.02563i	−0.858498	+	0.512816i	$0.828602\pi$
$432$	−1.06859	+	1.85085i	−0.0514124	+	0.0890488i
$433$	8.80166	−	15.2449i	0.422981	−	0.732624i	−0.573249	−	0.819381i	$-0.694317\pi$
$433$	8.80166	−	15.2449i	0.422981	−	0.732624i	0.996229	+	0.0867574i	$0.0276505\pi$
$434$	−11.5064	−	6.24336i	−0.552325	−	0.299691i
$435$	1.17259	+	0.676994i	0.0562213	+	0.0324594i
$436$			1.66984i			0.0799710i
$437$	−6.00867	−	3.46911i	−0.287434	−	0.165950i
$438$	1.94858	+	3.37504i	0.0931068	+	0.161266i
$439$	−11.4066	+	19.7569i	−0.544409	+	0.942944i	0.454235	+	0.890882i	$0.349913\pi$
$439$	−11.4066	+	19.7569i	−0.544409	+	0.942944i	−0.998644	+	0.0520618i	$0.983421\pi$
$440$	2.03745	−	1.17632i	0.0971315	−	0.0560789i
$441$	3.17449	−	6.23880i	0.151166	−	0.297086i
$442$	1.58696	+	0.923442i	0.0754838	+	0.0439236i
$443$	−19.5291	−	33.8254i	−0.927857	−	1.60709i	−0.786901	−	0.617079i	$-0.788316\pi$
$443$	−19.5291	−	33.8254i	−0.927857	−	1.60709i	−0.140955	−	0.990016i	$-0.545017\pi$
$444$		−	5.56650i		−	0.264175i
$445$	−19.3557			−0.917550
$446$	−4.07794			−0.193096
$447$		−	2.80497i		−	0.132671i
$448$	−2.61758	+	1.60505i	−0.123669	+	0.0758315i
$449$	−10.3848	−	5.99568i	−0.490090	−	0.282954i	0.234522	−	0.972111i	$-0.424648\pi$
$449$	−10.3848	−	5.99568i	−0.490090	−	0.282954i	−0.724612	+	0.689157i	$0.757981\pi$
$450$	2.49768	−	1.44204i	0.117742	−	0.0679783i
$451$	−0.965694	−	1.67263i	−0.0454727	−	0.0787611i
$452$	4.88601			0.229818
$453$	17.5134	+	10.1114i	0.822853	+	0.475074i
$454$	−2.12620			−0.0997876
$455$	15.7067	+	25.8117i	0.736340	+	1.21007i
$456$	3.22169			0.150869
$457$	−2.15752	−	1.24565i	−0.100925	−	0.0582689i	0.448688	−	0.893688i	$-0.351891\pi$
$457$	−2.15752	−	1.24565i	−0.100925	−	0.0582689i	−0.549613	+	0.835420i	$0.685225\pi$
$458$	−7.47823			−0.349435
$459$	0.444277	+	0.769510i	0.0207371	+	0.0359176i
$460$	20.7778	−	11.9961i	0.968771	−	0.559320i
$461$	−28.0132	−	16.1734i	−1.30471	−	0.753273i	−0.323499	−	0.946228i	$-0.604859\pi$
$461$	−28.0132	−	16.1734i	−1.30471	−	0.753273i	−0.981207	+	0.192956i	$0.938193\pi$
$462$	−0.0141587	−	0.535060i	−0.000658721	−	0.0248932i
$463$		−	23.4856i		−	1.09147i	−0.837958	−	0.545735i	$-0.816251\pi$
$463$		−	23.4856i		−	1.09147i	0.837958	−	0.545735i	$-0.183749\pi$
$464$	−0.913594			−0.0424125
$465$	27.3460			1.26814
$466$		−	9.28487i		−	0.430113i
$467$	−1.27155	−	2.20240i	−0.0588405	−	0.101915i	0.835105	−	0.550091i	$-0.185407\pi$
$467$	−1.27155	−	2.20240i	−0.0588405	−	0.101915i	−0.893945	+	0.448176i	$0.852074\pi$
$468$	−6.02682	−	0.0205021i	−0.278590	−	0.000947711i
$469$	12.9382	+	21.1002i	0.597430	+	0.974314i
$470$	−15.4980	+	8.94776i	−0.714869	+	0.412730i
$471$	2.32141	−	4.02080i	0.106965	−	0.185269i
$472$	12.1098	+	20.9748i	0.557400	+	0.965444i
$473$	−0.232891	−	0.134459i	−0.0107083	−	0.00618245i
$474$		−	3.99662i		−	0.183571i
$475$	6.67268	+	3.85247i	0.306164	+	0.176764i
$476$	0.103949	+	3.92825i	0.00476449	+	0.180051i
$477$	2.06487	−	3.57646i	0.0945439	−	0.163755i
$478$	−4.15133	+	7.19031i	−0.189877	+	0.328877i
$479$			19.6154i			0.896249i	0.893971	+	0.448124i	$0.147908\pi$
$479$			19.6154i			0.896249i	−0.893971	+	0.448124i	$0.852092\pi$
$480$	−8.60454	+	14.9035i	−0.392742	+	0.680249i
$481$	10.4187	−	5.96810i	0.475054	−	0.272122i
$482$	11.8347			0.539057
$483$	−0.317151	−	11.9852i	−0.0144309	−	0.545347i
$484$	−9.08938	−	15.7433i	−0.413153	−	0.715603i
$485$	41.6097			1.88940
$486$	0.496325	+	0.286553i	0.0225138	+	0.0129983i
$487$	−3.05279	+	1.76253i	−0.138335	+	0.0798678i	−0.567570	−	0.823325i	$-0.692116\pi$
$487$	−3.05279	+	1.76253i	−0.138335	+	0.0798678i	0.429235	+	0.903193i	$0.358783\pi$
$488$			31.8912i			1.44365i
$489$			3.26327i			0.147570i
$490$	5.76251	−	11.3250i	0.260323	−	0.511611i
$491$	−8.85905	−	15.3443i	−0.399803	−	0.692480i	0.593898	−	0.804540i	$-0.297588\pi$
$491$	−8.85905	−	15.3443i	−0.399803	−	0.692480i	−0.993701	+	0.112061i	$0.964255\pi$
$492$	7.92044	+	4.57287i	0.357081	+	0.206161i
$493$	−0.189918	+	0.328948i	−0.00855349	+	0.0148151i
$494$	1.57256	+	2.74528i	0.0707527	+	0.123516i
$495$	0.559038	+	0.968281i	0.0251269	+	0.0435210i
$496$	−15.9795	+	9.22574i	−0.717499	+	0.414248i
$497$	−32.9166	+	0.871034i	−1.47651	+	0.0390712i
$498$	4.29442	−	7.43815i	0.192437	−	0.333311i
$499$	−10.2757	+	5.93271i	−0.460006	+	0.265584i	−0.712047	−	0.702132i	$-0.752232\pi$
$499$	−10.2757	+	5.93271i	−0.460006	+	0.265584i	0.252041	+	0.967717i	$0.418898\pi$
$500$	−0.148346	+	0.0856473i	−0.00663421	+	0.00383026i
$501$	20.9079	−	12.0712i	0.934096	−	0.539301i
$502$	−12.8429	+	7.41488i	−0.573209	+	0.330942i
$503$	−12.6878	+	21.9759i	−0.565722	+	0.979858i	0.431261	+	0.902227i	$0.358069\pi$
$503$	−12.6878	+	21.9759i	−0.565722	+	0.979858i	−0.996982	+	0.0776311i	$0.975264\pi$
$504$	2.91014	+	4.74598i	0.129628	+	0.211403i
$505$	−33.0451	+	19.0786i	−1.47049	+	0.848985i
$506$	−0.458378	−	0.793935i	−0.0203774	−	0.0352947i
$507$	−6.42325	−	11.3023i	−0.285267	−	0.501952i
$508$	−13.0423	+	22.5899i	−0.578657	+	1.00226i
$509$	11.1989	+	6.46570i	0.496384	+	0.286587i	0.727219	−	0.686406i	$-0.240813\pi$
$509$	11.1989	+	6.46570i	0.496384	+	0.286587i	−0.230835	+	0.972993i	$0.574146\pi$
$510$	0.806474	+	1.39685i	0.0357113	+	0.0618537i
$511$	−17.9850	+	0.475916i	−0.795609	+	0.0210533i
$512$		−	20.6057i		−	0.910653i
$513$			1.53108i			0.0675989i
$514$	0.938395	−	0.541783i	0.0413908	−	0.0238970i
$515$	37.5545	+	21.6821i	1.65485	+	0.955427i
$516$	1.27342			0.0560591
$517$	−1.73999	−	3.01375i	−0.0765247	−	0.132545i
$518$	−4.43825	−	2.40819i	−0.195005	−	0.105810i
$519$	−19.1914			−0.842408
$520$	−24.0301	−	0.0817459i	−1.05379	−	0.00358479i
$521$	11.6491	−	20.1769i	0.510357	−	0.883964i	−0.489571	−	0.871963i	$-0.662847\pi$
$521$	11.6491	−	20.1769i	0.510357	−	0.883964i	0.999928	−	0.0120008i	$-0.00382005\pi$
$522$			0.244990i			0.0107229i
$523$	−7.67978	+	13.3018i	−0.335813	+	0.581646i	−0.983641	−	0.180141i	$-0.942345\pi$
$523$	−7.67978	+	13.3018i	−0.335813	+	0.581646i	0.647827	+	0.761787i	$0.275678\pi$
$524$	−4.56557	+	7.90781i	−0.199448	+	0.345454i
$525$	0.352199	+	13.3097i	0.0153712	+	0.580883i
$526$	3.02419	+	1.74602i	0.131861	+	0.0761299i
$527$			7.67141i			0.334172i
$528$	−0.653341	−	0.377206i	−0.0284330	−	0.0164158i
$529$	1.23242	+	2.13461i	0.0535833	+	0.0928089i
$530$	3.74826	−	6.49218i	0.162814	−	0.282002i
$531$	−9.96812	+	5.75510i	−0.432580	+	0.249750i
$532$	−3.22930	+	5.95155i	−0.140008	+	0.258032i
$533$	−0.0671088	+	19.7274i	−0.00290681	+	0.854487i
$534$	−1.75111	−	3.03301i	−0.0757780	−	0.131251i
$535$		−	16.2537i		−	0.702711i
$536$	−19.6847			−0.850250
$537$	−22.7875			−0.983352
$538$			0.804692i			0.0346927i
$539$	2.20227	+	1.12058i	0.0948585	+	0.0482669i
$540$	−4.58512	−	2.64722i	−0.197312	−	0.113918i
$541$	−27.6990	+	15.9920i	−1.19087	+	0.687551i	−0.958505	−	0.285077i	$-0.907981\pi$
$541$	−27.6990	+	15.9920i	−1.19087	+	0.687551i	−0.232368	+	0.972628i	$0.574647\pi$
$542$	−3.80026	−	6.58225i	−0.163235	−	0.282732i
$543$	1.32420			0.0568269
$544$	−4.18090	−	2.41385i	−0.179255	−	0.103493i
$545$	−3.16416			−0.135538
$546$	−2.62368	+	4.79639i	−0.112283	+	0.205267i
$547$	−3.77706			−0.161496			−0.0807478	−	0.996735i	$-0.525731\pi$
$547$	−3.77706			−0.161496			−0.0807478	+	0.996735i	$0.525731\pi$
$548$	−22.8385	−	13.1858i	−0.975613	−	0.563270i
$549$	−15.1561			−0.646845
$550$	0.509033	+	0.881672i	0.0217053	+	0.0375946i
$551$	−0.566817	+	0.327252i	−0.0241472	+	0.0139414i
$552$	8.25780	+	4.76765i	0.351475	+	0.202924i
$553$	16.2170	+	8.79931i	0.689616	+	0.374185i
$554$		−	9.67971i		−	0.411251i
$555$	10.5479			0.447732
$556$	−15.5865			−0.661015
$557$		−	5.51609i		−	0.233724i	−0.993148	−	0.116862i	$-0.962716\pi$
$557$		−	5.51609i		−	0.233724i	0.993148	−	0.116862i	$-0.0372835\pi$
$558$	2.47399	+	4.28507i	0.104732	+	0.181401i
$559$	1.36529	+	2.38344i	0.0577455	+	0.100809i
$560$	−9.36204	−	15.2680i	−0.395618	−	0.645191i
$561$	−0.271634	+	0.156828i	−0.0114684	+	0.00662127i
$562$	−6.46322	+	11.1946i	−0.272635	+	0.472217i
$563$	−1.32611	−	2.29689i	−0.0558888	−	0.0968022i	0.836727	−	0.547620i	$-0.184466\pi$
$563$	−1.32611	−	2.29689i	−0.0558888	−	0.0968022i	−0.892616	+	0.450817i	$0.851133\pi$
$564$	14.2711	+	8.23942i	0.600921	+	0.346942i
$565$			9.25841i			0.389504i
$566$	0.396195	+	0.228743i	0.0166533	+	0.00961479i
$567$	−2.25549	+	1.38302i	−0.0947218	+	0.0580815i
$568$	13.0940	−	22.6795i	0.549412	−	0.951610i
$569$	−14.8182	+	25.6658i	−0.621210	+	1.07597i	0.368051	+	0.929806i	$0.380025\pi$
$569$	−14.8182	+	25.6658i	−0.621210	+	1.07597i	−0.989261	+	0.146161i	$0.953308\pi$
$570$			2.77930i			0.116412i
$571$	13.1073	−	22.7025i	0.548522	−	0.950068i	−0.449854	−	0.893102i	$-0.648524\pi$
$571$	13.1073	−	22.7025i	0.548522	−	0.950068i	0.998376	−	0.0569662i	$-0.0181427\pi$
$572$	0.00723716	−	2.12744i	0.000302601	−	0.0889528i
$573$	−7.77636			−0.324862
$574$	7.07256	−	4.33675i	0.295203	−	0.181013i
$575$	11.4022	+	19.7493i	0.475506	+	0.823601i
$576$	1.16054			0.0483557
$577$	24.6222	+	14.2157i	1.02504	+	0.591806i	0.915559	−	0.402183i	$-0.131749\pi$
$577$	24.6222	+	14.2157i	1.02504	+	0.591806i	0.109478	+	0.993989i	$0.465082\pi$
$578$	8.04566	−	4.64517i	0.334655	−	0.193213i
$579$			10.9731i			0.456025i
$580$		−	2.26326i		−	0.0939767i
$581$	20.7266	+	33.8018i	0.859885	+	1.40234i
$582$	3.76442	+	6.52017i	0.156040	+	0.270270i
$583$	1.26248	+	0.728891i	0.0522864	+	0.0301876i
$584$	7.15431	−	12.3916i	0.296048	−	0.512769i
$585$	0.0388491	−	11.4201i	0.00160621	−	0.472164i
$586$	−8.82501	−	15.2854i	−0.364558	−	0.631433i
$587$	0.721765	−	0.416711i	0.0297904	−	0.0171995i	−0.485031	−	0.874497i	$-0.661192\pi$
$587$	0.721765	−	0.416711i	0.0297904	−	0.0171995i	0.514821	+	0.857298i	$0.327858\pi$
$588$	−11.6845	+	0.618818i	−0.481859	+	0.0255196i
$589$	−6.60938	+	11.4478i	−0.272335	+	0.471697i
$590$	−18.0947	+	10.4470i	−0.744945	+	0.430094i
$591$	5.20917	−	3.00752i	0.214277	−	0.123713i
$592$	−6.16359	+	3.55855i	−0.253322	+	0.146255i
$593$	23.9758	−	13.8424i	0.984566	−	0.568440i	0.0809207	−	0.996721i	$-0.474214\pi$
$593$	23.9758	−	13.8424i	0.984566	−	0.568440i	0.903646	+	0.428281i	$0.140881\pi$
$594$	−0.101152	+	0.175201i	−0.00415032	+	0.00718857i
$595$	−7.44358	+	0.196971i	−0.305157	+	0.00807502i
$596$	−4.06049	+	2.34432i	−0.166324	+	0.0960272i
$597$	−7.41270	−	12.8392i	−0.303382	−	0.525473i
$598$	−0.0318540	+	9.36384i	−0.00130261	+	0.382916i
$599$	12.4488	−	21.5620i	0.508645	−	0.881000i	−0.491304	−	0.870988i	$-0.663480\pi$
$599$	12.4488	−	21.5620i	0.508645	−	0.881000i	0.999950	−	0.0100118i	$-0.00318692\pi$
$600$	−9.17036	−	5.29451i	−0.374379	−	0.216148i
$601$	15.3339	+	26.5592i	0.625485	+	1.08337i	0.988447	+	0.151568i	$0.0484321\pi$
$601$	15.3339	+	26.5592i	0.625485	+	1.08337i	−0.362962	+	0.931804i	$0.618235\pi$
$602$	0.550907	−	1.01531i	0.0224533	−	0.0413810i
$603$		−	9.35501i		−	0.380965i
$604$		−	33.8033i		−	1.37544i
$605$	29.8316	−	17.2233i	1.21283	−	0.700227i
$606$	−5.97917	−	3.45207i	−0.242887	−	0.140231i
$607$	8.23275			0.334157			0.167079	−	0.985944i	$-0.446567\pi$
$607$	8.23275			0.334157			0.167079	+	0.985944i	$0.446567\pi$
$608$	−4.15934	−	7.20419i	−0.168684	−	0.292169i
$609$	−0.994091	−	0.539392i	−0.0402826	−	0.0218573i
$610$	−27.5121			−1.11393
$611$	−0.120917	+	35.5449i	−0.00489178	+	1.43799i
$612$	0.742630	−	1.28627i	0.0300190	−	0.0519945i
$613$			38.9795i			1.57437i	0.616718	+	0.787184i	$0.288462\pi$
$613$			38.9795i			1.57437i	−0.616718	+	0.787184i	$0.711538\pi$
$614$	6.13685	−	10.6293i	0.247663	−	0.428965i
$615$	−8.66505	+	15.0083i	−0.349409	+	0.605194i
$616$	−1.67531	+	1.02727i	−0.0675003	+	0.0413898i
$617$	−39.3193	−	22.7010i	−1.58293	−	0.913907i	−0.994428	−	0.105414i	$-0.966383\pi$
$617$	−39.3193	−	22.7010i	−1.58293	−	0.913907i	−0.588506	−	0.808493i	$-0.700284\pi$
$618$			7.84630i			0.315625i
$619$	20.2395	+	11.6853i	0.813495	+	0.469672i	0.848168	−	0.529727i	$-0.177706\pi$
$619$	20.2395	+	11.6853i	0.813495	+	0.469672i	−0.0346730	+	0.999399i	$0.511039\pi$
$620$	−22.8551	−	39.5861i	−0.917881	−	1.58982i
$621$	−2.26579	+	3.92446i	−0.0909229	+	0.157483i
$622$	−9.62253	+	5.55557i	−0.385828	+	0.222758i
$623$	16.1624	−	0.427686i	0.647532	−	0.0171349i
$624$	3.83012	+	6.68639i	0.153327	+	0.267670i
$625$	12.4186	+	21.5096i	0.496744	+	0.860385i
$626$			4.41462i			0.176444i
$627$	−0.540466			−0.0215841
$628$	−7.76069			−0.309685
$629$			2.95901i			0.117984i
$630$	−4.09429	+	2.51054i	−0.163120	+	0.100022i
$631$	27.7776	+	16.0374i	1.10581	+	0.638439i	0.937741	−	0.347336i	$-0.112914\pi$
$631$	27.7776	+	16.0374i	1.10581	+	0.638439i	0.168069	+	0.985775i	$0.446247\pi$
$632$	−12.7079	+	7.33689i	−0.505492	+	0.291846i
$633$	−10.3820	−	17.9821i	−0.412647	−	0.714725i
$634$	8.45855			0.335932
$635$	−42.8052	−	24.7136i	−1.69867	−	0.980729i
$636$	−6.90306			−0.273724
$637$	−13.6857	−	21.2062i	−0.542246	−	0.840220i
$638$	−0.0864806			−0.00342380
$639$	10.7783	+	6.22283i	0.426381	+	0.246171i
$640$	36.5248			1.44377
$641$	15.6071	+	27.0323i	0.616444	+	1.06771i	0.990129	+	0.140157i	$0.0447606\pi$
$641$	15.6071	+	27.0323i	0.616444	+	1.06771i	−0.373685	+	0.927555i	$0.621906\pi$
$642$	2.54694	−	1.47047i	0.100520	−	0.0580350i
$643$	−6.24367	−	3.60479i	−0.246226	−	0.142159i	0.371809	−	0.928309i	$-0.378738\pi$
$643$	−6.24367	−	3.60479i	−0.246226	−	0.142159i	−0.618035	+	0.786150i	$0.712071\pi$
$644$	−17.0848	+	10.4761i	−0.673235	+	0.412814i
$645$			2.41298i			0.0950108i
$646$	−0.779682			−0.0306762
$647$	−23.0552			−0.906393			−0.453196	−	0.891411i	$-0.649716\pi$
$647$	−23.0552			−0.906393			−0.453196	+	0.891411i	$0.649716\pi$
$648$		−	2.10419i		−	0.0826604i
$649$	−2.03153	−	3.51871i	−0.0797444	−	0.138121i
$650$	0.0353742	−	10.3986i	0.00138749	−	0.407868i
$651$	−22.8344	+	0.604239i	−0.894949	+	0.0236820i
$652$	4.72393	−	2.72736i	0.185003	−	0.106812i
$653$	8.74305	−	15.1434i	0.342142	−	0.592608i	−0.642688	−	0.766128i	$-0.722181\pi$
$653$	8.74305	−	15.1434i	0.342142	−	0.592608i	0.984830	+	0.173520i	$0.0555142\pi$
$654$	−0.286261	−	0.495819i	−0.0111937	−	0.0193880i
$655$	−14.9844	−	8.65123i	−0.585488	−	0.338031i
$656$		−	11.6934i		−	0.456549i
$657$	5.88903	+	3.40003i	0.229753	+	0.132648i
$658$	12.7434	−	7.81398i	0.496789	−	0.304621i
$659$	20.2279	−	35.0357i	0.787967	−	1.36480i	−0.139244	−	0.990258i	$-0.544467\pi$
$659$	20.2279	−	35.0357i	0.787967	−	1.36480i	0.927211	−	0.374540i	$-0.122199\pi$
$660$	0.934459	−	1.61853i	0.0363737	−	0.0630012i
$661$			44.6913i			1.73829i	0.494556	+	0.869146i	$0.335331\pi$
$661$			44.6913i			1.73829i	−0.494556	+	0.869146i	$0.664669\pi$
$662$	−0.474392	+	0.821670i	−0.0184378	+	0.0319351i
$663$	3.20371	+	0.0108984i	0.124422	+	0.000423259i
$664$	−31.5343			−1.22377
$665$	−11.2775	−	6.11915i	−0.437322	−	0.237291i
$666$	0.954265	+	1.65284i	0.0369770	+	0.0640461i
$667$	−1.93715			−0.0750067
$668$	−34.9486	−	20.1776i	−1.35220	−	0.780694i
$669$	−6.16220	+	3.55775i	−0.238244	+	0.137551i
$670$		−	16.9817i		−	0.656060i
$671$		−	5.35002i		−	0.206535i
$672$	6.85563	−	12.6348i	0.264462	−	0.487398i
$673$	6.76618	+	11.7194i	0.260817	+	0.451748i	0.966459	−	0.256820i	$-0.0826748\pi$
$673$	6.76618	+	11.7194i	0.260817	+	0.451748i	−0.705642	+	0.708568i	$0.749341\pi$
$674$	−1.43272	−	0.827181i	−0.0551863	−	0.0318618i
$675$	2.51618	−	4.35815i	0.0968477	−	0.167745i
$676$	−10.9928	+	18.7445i	−0.422802	+	0.720942i
$677$	16.7974	+	29.0939i	0.645575	+	1.11817i	0.984168	+	0.177237i	$0.0567158\pi$
$677$	16.7974	+	29.0939i	0.645575	+	1.11817i	−0.338593	+	0.940933i	$0.609951\pi$
$678$	−1.45078	+	0.837607i	−0.0557168	+	0.0321681i
$679$	−34.7448	+	0.919412i	−1.33338	+	0.0352838i
$680$	2.96101	−	5.12862i	0.113549	−	0.196673i
$681$	−3.21292	+	1.85498i	−0.123119	+	0.0710829i
$682$	−1.51261	+	0.873307i	−0.0579209	+	0.0334407i
$683$	35.6936	−	20.6077i	1.36578	−	0.788533i	0.375393	−	0.926866i	$-0.377508\pi$
$683$	35.6936	−	20.6077i	1.36578	−	0.788533i	0.990386	+	0.138332i	$0.0441743\pi$
$684$	2.21640	−	1.27964i	0.0847462	−	0.0489282i
$685$	24.9856	−	43.2763i	0.954650	−	1.65350i
$686$	−4.56156	+	9.58389i	−0.174161	+	0.365915i
$687$	−11.3004	+	6.52429i	−0.431137	+	0.248917i
$688$	−0.814069	−	1.41001i	−0.0310361	−	0.0537561i
$689$	−7.40109	−	12.9204i	−0.281959	−	0.492227i
$690$	−4.11297	+	7.12388i	−0.156578	+	0.271202i
$691$	3.78880	+	2.18747i	0.144133	+	0.0832152i	0.570332	−	0.821414i	$-0.306814\pi$
$691$	3.78880	+	2.18747i	0.144133	+	0.0832152i	−0.426199	+	0.904629i	$0.640148\pi$
$692$	16.0397	+	27.7815i	0.609737	+	1.05610i
$693$	−0.488201	−	0.796179i	−0.0185452	−	0.0302444i
$694$			16.6703i			0.632796i
$695$		−	29.5346i		−	1.12031i
$696$	0.778985	−	0.449747i	0.0295273	−	0.0170476i
$697$	−4.21031	−	2.43082i	−0.159477	−	0.0920740i
$698$	−10.5054			−0.397634
$699$	−8.10047	−	14.0304i	−0.306388	−	0.530679i
$700$	18.9728	−	11.6337i	0.717105	−	0.439714i
$701$	41.1220			1.55316			0.776579	−	0.630020i	$-0.216953\pi$
$701$	41.1220			1.55316			0.776579	+	0.630020i	$0.216953\pi$
$702$	1.79303	−	1.02709i	0.0676735	−	0.0387650i
$703$	−2.54936	+	4.41563i	−0.0961511	+	0.166539i
$704$			0.409665i			0.0154398i
$705$	−15.6127	+	27.0421i	−0.588010	+	1.01846i
$706$	2.04837	−	3.54788i	0.0770915	−	0.133526i
$707$	27.1716	−	16.6611i	1.02189	−	0.626606i
$708$	16.6622	+	9.61993i	0.626204	+	0.361539i
$709$			19.1185i			0.718010i	0.933336	+	0.359005i	$0.116884\pi$
$709$			19.1185i			0.718010i	−0.933336	+	0.359005i	$0.883116\pi$
$710$	19.5652	+	11.2960i	0.734271	+	0.423931i
$711$	−3.48680	−	6.03932i	−0.130765	−	0.226492i
$712$	−6.42929	+	11.1359i	−0.240948	+	0.417334i
$713$	−33.8822	+	19.5619i	−1.26890	+	0.732599i
$714$	−0.704285	−	1.14858i	−0.0263572	−	0.0429844i
$715$	4.03125	+	0.0137136i	0.150760	+	0.000512859i
$716$	19.0452	+	32.9872i	0.711752	+	1.23279i
$717$			14.4871i			0.541031i
$718$	−8.60907			−0.321288
$719$	−14.9938			−0.559174			−0.279587	−	0.960120i	$-0.590198\pi$
$719$	−14.9938			−0.559174			−0.279587	+	0.960120i	$0.590198\pi$
$720$			6.76926i			0.252275i
$721$	−31.8377	−	17.2751i	−1.18570	−	0.643359i
$722$	8.26668	+	4.77277i	0.307654	+	0.177624i
$723$	17.8835	−	10.3251i	0.665096	−	0.383993i
$724$	−1.10673	−	1.91692i	−0.0411314	−	0.0712417i
$725$	2.15122			0.0798943
$726$	5.39773	+	3.11638i	0.200329	+	0.115660i
$727$	18.8699			0.699847			0.349923	−	0.936778i	$-0.386208\pi$
$727$	18.8699			0.699847			0.349923	+	0.936778i	$0.386208\pi$
$728$	20.0674	−	0.462712i	0.743746	−	0.0171493i
$729$	1.00000			0.0370370
$730$	10.6901	+	6.17192i	0.395657	+	0.228433i
$731$	−0.676916			−0.0250367
$732$	12.6670	+	21.9400i	0.468187	+	0.810924i
$733$	−22.4233	+	12.9461i	−0.828225	+	0.478176i	−0.853244	−	0.521511i	$-0.825368\pi$
$733$	−22.4233	+	12.9461i	−0.828225	+	0.478176i	0.0250198	+	0.999687i	$0.492035\pi$
$734$	−2.00962	−	1.16026i	−0.0741766	−	0.0428259i
$735$	−1.17259	−	22.1407i	−0.0432516	−	0.816672i
$736$		−	24.6210i		−	0.907541i
$737$	3.30228			0.121641
$738$	−3.13571			−0.115427
$739$		−	39.9592i		−	1.46992i	−0.678108	−	0.734962i	$-0.737200\pi$
$739$		−	39.9592i		−	1.46992i	0.678108	−	0.734962i	$-0.262800\pi$
$740$	−8.81564	−	15.2691i	−0.324069	−	0.561305i
$741$	4.77139	+	2.77645i	0.175281	+	0.101995i
$742$	−2.98641	+	5.50391i	−0.109635	+	0.202055i
$743$	−10.9942	+	6.34749i	−0.403337	+	0.232867i	−0.687923	−	0.725784i	$-0.741477\pi$
$743$	−10.9942	+	6.34749i	−0.403337	+	0.232867i	0.284586	+	0.958651i	$0.408144\pi$
$744$	9.08336	−	15.7328i	0.333012	−	0.576794i
$745$	−4.44222	−	7.69415i	−0.162750	−	0.281892i
$746$	9.43485	+	5.44721i	0.345434	+	0.199437i
$747$		−	14.9864i		−	0.548325i
$748$	0.454049	+	0.262145i	0.0166017	+	0.00958498i
$749$	0.359144	+	13.5722i	0.0131229	+	0.495916i
$750$	0.0293650	−	0.0508617i	0.00107226	−	0.00185721i
$751$	18.6544	−	32.3104i	0.680709	−	1.17902i	−0.294056	−	0.955788i	$-0.595005\pi$
$751$	18.6544	−	32.3104i	0.680709	−	1.17902i	0.974765	−	0.223234i	$-0.0716614\pi$
$752$		−	21.0692i		−	0.768313i
$753$	−12.9380	+	22.4093i	−0.471488	+	0.816642i
$754$	0.763475	+	0.444263i	0.0278041	+	0.0161791i
$755$	64.0534			2.33114
$756$	3.88715	+	2.10916i	0.141374	+	0.0767095i
$757$	12.2949	+	21.2953i	0.446864	+	0.773992i	0.998180	−	0.0603051i	$-0.0192074\pi$
$757$	12.2949	+	21.2953i	0.446864	+	0.773992i	−0.551316	+	0.834297i	$0.685874\pi$
$758$	9.55623			0.347098
$759$	−1.38532	−	0.799814i	−0.0502838	−	0.0290314i
$760$	8.83722	−	5.10217i	0.320559	−	0.185075i
$761$			14.4088i			0.522318i	0.965296	+	0.261159i	$0.0841048\pi$
$761$			14.4088i			0.522318i	−0.965296	+	0.261159i	$0.915895\pi$
$762$		−	8.94334i		−	0.323983i
$763$	2.64213	−	0.0699156i	0.0956514	−	0.00253111i
$764$	6.49928	+	11.2571i	0.235136	+	0.407267i
$765$	2.43734	+	1.40720i	0.0881221	+	0.0508773i
$766$	−2.47609	+	4.28871i	−0.0894646	+	0.154957i
$767$	−0.141177	+	41.5004i	−0.00509759	+	1.49849i
$768$	2.14386	+	3.71327i	0.0773599	+	0.133991i
$769$	−22.7651	+	13.1435i	−0.820932	+	0.473965i	−0.850738	−	0.525590i	$-0.823845\pi$
$769$	−22.7651	+	13.1435i	−0.820932	+	0.473965i	0.0298056	+	0.999556i	$0.490511\pi$
$770$	−0.886209	−	1.44527i	−0.0319367	−	0.0520838i
$771$	0.945343	−	1.63738i	0.0340457	−	0.0589689i
$772$	15.8846	−	9.17100i	0.571701	−	0.330071i
$773$	37.8101	−	21.8297i	1.35993	−	0.785158i	0.370319	−	0.928905i	$-0.379248\pi$
$773$	37.8101	−	21.8297i	1.35993	−	0.785158i	0.989615	+	0.143746i	$0.0459150\pi$
$774$	−0.378110	+	0.218302i	−0.0135909	+	0.00784669i
$775$	37.6265	−	21.7237i	1.35158	−	0.780337i
$776$	13.8213	−	23.9391i	0.496155	−	0.859365i
$777$	−8.80766	+	0.233067i	−0.315973	+	0.00836123i
$778$	3.51444	−	2.02906i	0.125999	−	0.0727455i
$779$	−4.18860	−	7.25486i	−0.150072	−	0.259932i
$780$	−16.5643	+	9.48840i	−0.593096	+	0.339739i
$781$	−2.19663	+	3.80468i	−0.0786017	+	0.136142i
$782$	−1.99847	−	1.15382i	−0.0714653	−	0.0412605i
$783$	0.213739	+	0.370207i	0.00763841	+	0.0132301i
$784$	8.15483	+	12.5422i	0.291244	+	0.447935i
$785$		−	14.7056i		−	0.524866i
$786$		−	3.13070i		−	0.111668i
$787$	−13.7440	+	7.93508i	−0.489919	+	0.282855i	−0.724541	−	0.689232i	$-0.757948\pi$
$787$	−13.7440	+	7.93508i	−0.489919	+	0.282855i	0.234622	+	0.972087i	$0.424615\pi$
$788$	−8.70738	−	5.02721i	−0.310188	−	0.179087i
$789$	6.09316			0.216922
$790$	−6.32942	−	10.9629i	−0.225191	−	0.390042i
$791$	−0.204575	−	7.73093i	−0.00727384	−	0.274880i
$792$	0.742770			0.0263932
$793$	−27.4838	+	47.2315i	−0.975978	+	1.67724i
$794$	6.20359	−	10.7449i	0.220157	−	0.381324i
$795$		−	13.0805i		−	0.463918i
$796$	−12.3907	+	21.4613i	−0.439176	+	0.760676i
$797$	14.7381	−	25.5272i	0.522051	−	0.904219i	−0.477620	−	0.878567i	$-0.658500\pi$
$797$	14.7381	−	25.5272i	0.522051	−	0.904219i	0.999671	−	0.0256525i	$-0.00816634\pi$
$798$	−0.0614117	−	2.32076i	−0.00217395	−	0.0821542i
$799$	−7.58615	−	4.37987i	−0.268379	−	0.154949i
$800$			27.3418i			0.966679i
$801$	−5.29223	−	3.05547i	−0.186992	−	0.107960i
$802$	4.22938	+	7.32550i	0.149345	+	0.258672i
$803$	−1.20020	+	2.07880i	−0.0423541	+	0.0733594i
$804$	−13.5423	+	7.81868i	−0.477602	+	0.275743i
$805$	−19.8509	−	32.3737i	−0.699652	−	1.14102i
$806$	17.8401	+	0.0606886i	0.628390	+	0.00213766i
$807$	0.702043	+	1.21597i	0.0247131	+	0.0428043i
$808$			25.3489i			0.891771i
$809$	6.49707			0.228425			0.114212	−	0.993456i	$-0.463566\pi$
$809$	6.49707			0.228425			0.114212	+	0.993456i	$0.463566\pi$
$810$	1.81525			0.0637815
$811$		−	20.7305i		−	0.727945i	−0.931410	−	0.363972i	$-0.881420\pi$
$811$		−	20.7305i		−	0.727945i	0.931410	−	0.363972i	$-0.118580\pi$
$812$	0.0500092	+	1.88986i	0.00175498	+	0.0663211i
$813$	−11.4852	−	6.63099i	−0.402804	−	0.232559i
$814$	−0.583444	+	0.336851i	−0.0204497	+	0.0118066i
$815$	5.16803	+	8.95129i	0.181028	+	0.313550i
$816$	−1.89899			−0.0664780
$817$	−1.01014	−	0.583204i	−0.0353403	−	0.0204037i
$818$	10.0367			0.350924
$819$	0.219900	+	9.53686i	0.00768394	+	0.333245i
$820$	28.9681			1.01161
$821$	21.7478	+	12.5561i	0.759002	+	0.438210i	0.828937	−	0.559341i	$-0.188946\pi$
$821$	21.7478	+	12.5561i	0.759002	+	0.438210i	−0.0699352	+	0.997552i	$0.522279\pi$
$822$	9.04177			0.315368
$823$	−25.2707	−	43.7701i	−0.880880	−	1.52573i	−0.850364	−	0.526195i	$-0.823618\pi$
$823$	−25.2707	−	43.7701i	−0.880880	−	1.52573i	−0.0305162	−	0.999534i	$-0.509715\pi$
$824$	24.9485	−	14.4040i	0.869123	−	0.501789i
$825$	1.53841	+	0.888200i	0.0535605	+	0.0309232i
$826$	14.8785	−	9.12321i	0.517690	−	0.317437i
$827$		−	7.58852i		−	0.263879i	−0.991258	−	0.131939i	$-0.957880\pi$
$827$		−	7.58852i		−	0.263879i	0.991258	−	0.131939i	$-0.0421204\pi$
$828$	7.57475			0.263241
$829$	−38.8190			−1.34824			−0.674120	−	0.738622i	$-0.735477\pi$
$829$	−38.8190			−1.34824			−0.674120	+	0.738622i	$0.735477\pi$
$830$		−	27.2042i		−	0.944271i
$831$	−8.44494	−	14.6271i	−0.292952	−	0.507407i
$832$	2.10450	−	3.61664i	0.0729606	−	0.125384i
$833$	6.21117	−	0.328948i	0.215204	−	0.0113974i
$834$	4.62803	−	2.67199i	0.160256	−	0.0925236i
$835$	38.2341	−	66.2235i	1.32315	−	2.29176i
$836$	0.451707	+	0.782380i	0.0156226	+	0.0270592i
$837$	7.47692	+	4.31680i	0.258440	+	0.149210i
$838$			17.6617i			0.610112i
$839$	−0.124870	−	0.0720936i	−0.00431098	−	0.00248895i	0.497843	−	0.867267i	$-0.334126\pi$
$839$	−0.124870	−	0.0720936i	−0.00431098	−	0.00248895i	−0.502154	+	0.864778i	$0.667459\pi$
$840$	15.4988	+	8.40964i	0.534760	+	0.290160i
$841$	14.4086	−	24.9565i	0.496849	−	0.860568i
$842$	−8.41553	+	14.5761i	−0.290018	+	0.502326i
$843$			22.5550i			0.776837i
$844$	−17.3540	+	30.0580i	−0.597349	+	1.03464i
$845$	−35.5186	−	20.8302i	−1.22188	−	0.716579i
$846$	−5.64993			−0.194249
$847$	−24.5294	+	15.0409i	−0.842839	+	0.516812i
$848$	4.41299	+	7.64351i	0.151543	+	0.262479i
$849$	0.798257			0.0273961
$850$	2.21932	+	1.28133i	0.0761222	+	0.0439492i
$851$	−13.0690	+	7.54540i	−0.448000	+	0.258653i
$852$		−	20.8035i		−	0.712717i
$853$		−	2.84303i		−	0.0973435i	−0.998815	−	0.0486718i	$-0.984501\pi$
$853$		−	2.84303i		−	0.0973435i	0.998815	−	0.0486718i	$-0.0154988\pi$
$854$	22.9731	−	0.607909i	0.786122	−	0.0208022i
$855$	2.42477	+	4.19982i	0.0829253	+	0.143631i
$856$	−9.35120	−	5.39892i	−0.319617	−	0.184531i
$857$	−16.0653	+	27.8259i	−0.548779	+	0.950513i	0.449580	+	0.893240i	$0.351574\pi$
$857$	−16.0653	+	27.8259i	−0.548779	+	0.950513i	−0.998359	+	0.0572728i	$0.981760\pi$
$858$	0.362558	+	0.632932i	0.0123775	+	0.0216079i
$859$	−14.7024	−	25.4653i	−0.501640	−	0.868866i	−0.999998	−	0.00189479i	$-0.999397\pi$
$859$	−14.7024	−	25.4653i	−0.501640	−	0.868866i	0.498358	−	0.866971i	$-0.333936\pi$
$860$	3.49303	−	2.01670i	0.119111	−	0.0687690i
$861$	6.90385	−	12.7237i	0.235282	−	0.433621i
$862$	−6.10149	+	10.5681i	−0.207818	+	0.359951i
$863$	−36.9726	+	21.3461i	−1.25856	+	0.726631i	−0.972795	−	0.231669i	$-0.925582\pi$
$863$	−36.9726	+	21.3461i	−1.25856	+	0.726631i	−0.285767	+	0.958299i	$0.592248\pi$
$864$	−4.70529	+	2.71660i	−0.160077	+	0.0924207i
$865$	−52.6427	+	30.3933i	−1.78991	+	1.03340i
$866$	8.73696	−	5.04429i	0.296894	−	0.171412i
$867$	8.10524	−	14.0387i	0.275268	−	0.476779i
$868$	19.9591	+	32.5501i	0.677455	+	1.10482i
$869$	2.13185	−	1.23083i	0.0723182	−	0.0417529i
$870$	0.387990	+	0.672018i	0.0131541	+	0.0227836i
$871$	−29.1535	−	16.9643i	−0.987827	−	0.574812i
$872$	−1.05102	+	1.82042i	−0.0355921	+	0.0616473i
$873$	11.3769	+	6.56845i	0.385049	+	0.222308i
$874$	−1.98817	−	3.44361i	−0.0672508	−	0.116482i
$875$	0.141728	+	0.231135i	0.00479127	+	0.00781380i
$876$		−	11.3666i		−	0.384043i
$877$		−	13.1036i		−	0.442478i	−0.975220	−	0.221239i	$-0.928990\pi$
$877$		−	13.1036i		−	0.442478i	0.975220	−	0.221239i	$-0.0710101\pi$
$878$	−11.3228	+	6.53722i	−0.382126	+	0.220620i
$879$	−26.6711	−	15.3986i	−0.899593	−	0.519380i
$880$	−2.38952			−0.0805507
$881$	−18.9666	−	32.8512i	−0.639002	−	1.10678i	−0.985652	−	0.168790i	$-0.946014\pi$
$881$	−18.9666	−	32.8512i	−0.639002	−	1.10678i	0.346650	−	0.937995i	$-0.387319\pi$
$882$	3.36333	−	2.18681i	0.113249	−	0.0736337i
$883$	15.9034			0.535194			0.267597	−	0.963531i	$-0.413770\pi$
$883$	15.9034			0.535194			0.267597	+	0.963531i	$0.413770\pi$
$884$	−2.66180	−	4.64680i	−0.0895260	−	0.156289i
$885$	−18.2286	+	31.5729i	−0.612749	+	1.06131i
$886$		−	22.3845i		−	0.752023i
$887$	5.08202	−	8.80231i	0.170637	−	0.295553i	−0.768005	−	0.640443i	$-0.778751\pi$
$887$	5.08202	−	8.80231i	0.170637	−	0.295553i	0.938643	+	0.344891i	$0.112084\pi$
$888$	3.50363	−	6.06846i	0.117574	−	0.203644i
$889$	36.2892	+	19.6905i	1.21710	+	0.660397i
$890$	−9.60673	−	5.54645i	−0.322018	−	0.185917i
$891$			0.352996i			0.0118258i
$892$	10.3004	+	5.94695i	0.344884	+	0.199119i
$893$	−7.54703	−	13.0718i	−0.252552	−	0.437433i
$894$	0.803774	−	1.39218i	0.0268822	−	0.0465614i
$895$	−62.5070	+	36.0884i	−2.08938	+	1.20630i
$896$	−30.4989	+	0.807057i	−1.01890	+	0.0269619i
$897$	8.12123	+	14.1775i	0.271160	+	0.473374i
$898$	−3.43616	−	5.95161i	−0.114666	−	0.198608i
$899$			3.69067i			0.123091i
$900$	−8.41182			−0.280394
$901$	3.66949			0.122249
$902$		−	1.10689i		−	0.0368554i
$903$	−0.0533174	−	2.01488i	−0.00177429	−	0.0670509i
$904$	5.32660	+	3.07532i	0.177160	+	0.102283i
$905$	3.63233	−	2.09713i	0.120743	−	0.0697109i
$906$	5.79490	+	10.0371i	0.192523	+	0.333459i
$907$	28.9503			0.961279			0.480639	−	0.876918i	$-0.340405\pi$
$907$	28.9503			0.961279			0.480639	+	0.876918i	$0.340405\pi$
$908$	5.37055	+	3.10069i	0.178228	+	0.102900i
$909$	−12.0469			−0.399570
$910$	0.399175	+	17.3118i	0.0132325	+	0.573881i
$911$	2.42075			0.0802032			0.0401016	−	0.999196i	$-0.487232\pi$
$911$	2.42075			0.0802032			0.0401016	+	0.999196i	$0.487232\pi$
$912$	−2.83380	−	1.63609i	−0.0938364	−	0.0541765i
$913$	5.29015			0.175079
$914$	−0.713889	−	1.23649i	−0.0236133	−	0.0408995i
$915$	−41.5737	+	24.0026i	−1.37438	+	0.793500i
$916$	18.8892	+	10.9057i	0.624116	+	0.360333i
$917$	12.7034	+	6.89283i	0.419502	+	0.227621i
$918$			0.509236i			0.0168073i
$919$	3.10470			0.102415			0.0512074	−	0.998688i	$-0.483693\pi$
$919$	3.10470			0.102415			0.0512074	+	0.998688i	$0.483693\pi$
$920$	30.2020			0.995730
$921$		−	21.4161i		−	0.705684i
$922$	−9.26911	−	16.0546i	−0.305262	−	0.528729i
$923$	38.9377	−	22.3044i	1.28165	−	0.734158i
$924$	−0.744526	+	1.37215i	−0.0244931	+	0.0451404i
$925$	14.5133	−	8.37924i	0.477193	−	0.275508i
$926$	6.72989	−	11.6565i	0.221158	−	0.383057i
$927$	6.84541	+	11.8566i	0.224833	+	0.389422i
$928$	−2.01141	−	1.16129i	−0.0660277	−	0.0381211i
$929$			8.19533i			0.268880i	0.990922	+	0.134440i	$0.0429236\pi$
$929$			8.19533i			0.268880i	−0.990922	+	0.134440i	$0.957076\pi$
$930$	13.5725	+	7.83608i	0.445059	+	0.256955i
$931$	9.55211	+	4.86041i	0.313058	+	0.159294i
$932$	−13.5403	+	23.4525i	−0.443528	+	0.768214i
$933$	−9.69378	+	16.7901i	−0.317360	+	0.549684i
$934$		−	1.45747i		−	0.0476899i
$935$	−0.496735	+	0.860369i	−0.0162450	+	0.0281371i
$936$	−6.55739	−	3.81571i	−0.214335	−	0.124720i
$937$	53.8795			1.76017			0.880084	−	0.474819i	$-0.157486\pi$
$937$	53.8795			1.76017			0.880084	+	0.474819i	$0.157486\pi$
$938$	0.375229	+	14.1800i	0.0122517	+	0.462994i
$939$	3.85148	+	6.67096i	0.125688	+	0.217699i
$940$	52.1949			1.70241
$941$	2.93824	+	1.69639i	0.0957838	+	0.0553008i	0.547127	−	0.837050i	$-0.315722\pi$
$941$	2.93824	+	1.69639i	0.0957838	+	0.0553008i	−0.451343	+	0.892351i	$0.649055\pi$
$942$	2.30435	−	1.33041i	0.0750796	−	0.0433472i
$943$		−	24.7941i		−	0.807408i
$944$		−	24.5993i		−	0.800638i
$945$	−3.99662	+	7.36570i	−0.130010	+	0.239606i
$946$	−0.0770596	−	0.133471i	−0.00250542	−	0.00433952i
$947$	38.2371	+	22.0762i	1.24254	+	0.717381i	0.969611	−	0.244653i	$-0.0786741\pi$
$947$	38.2371	+	22.0762i	1.24254	+	0.717381i	0.272929	+	0.962034i	$0.412007\pi$
$948$	−5.82836	+	10.0950i	−0.189296	+	0.327871i
$949$	21.2748	−	12.1867i	0.690609	−	0.395597i
$950$	2.20788	+	3.82416i	0.0716331	+	0.124072i
$951$	12.7818	−	7.37956i	0.414477	−	0.239299i
$952$	−2.35917	+	4.34791i	−0.0764612	+	0.140917i
$953$	8.43489	−	14.6097i	0.273233	−	0.473253i	−0.696455	−	0.717601i	$-0.745240\pi$
$953$	8.43489	−	14.6097i	0.273233	−	0.473253i	0.969688	+	0.244347i	$0.0785737\pi$
$954$	2.04969	−	1.18339i	0.0663613	−	0.0383137i
$955$	−21.3309	+	12.3154i	−0.690251	+	0.398516i
$956$	20.9716	−	12.1080i	0.678270	−	0.391599i
$957$	−0.130681	+	0.0754489i	−0.00422433	+	0.00243892i
$958$	−5.62085	+	9.73559i	−0.181601	+	0.314543i
$959$	−19.9072	+	36.6886i	−0.642836	+	1.18474i
$960$	3.18340	−	1.83794i	0.102744	−	0.0593192i
$961$	21.7695	+	37.7059i	0.702242	+	1.21632i
$962$	6.88126	+	0.0234088i	0.221861	+	0.000754729i
$963$	2.56579	−	4.44409i	0.0826816	−	0.143209i
$964$	−29.8932	−	17.2588i	−0.962795	−	0.555870i
$965$	17.3780	+	30.0995i	0.559417	+	0.968938i
$966$	3.27700	−	6.03945i	0.105436	−	0.194316i
$967$			21.6217i			0.695308i	0.937623	+	0.347654i	$0.113022\pi$
$967$			21.6217i			0.695308i	−0.937623	+	0.347654i	$0.886978\pi$
$968$		−	22.8839i		−	0.735516i
$969$	−1.17818	+	0.680224i	−0.0378487	+	0.0218519i
$970$	20.6519	+	11.9234i	0.663093	+	0.382837i
$971$	36.3657			1.16703			0.583515	−	0.812103i	$-0.301677\pi$
$971$	36.3657			1.16703			0.583515	+	0.812103i	$0.301677\pi$
$972$	−0.835774	−	1.44760i	−0.0268075	−	0.0464319i
$973$	0.652600	+	24.6619i	0.0209214	+	0.790625i
$974$	−2.02023			−0.0647325
$975$	−9.01870	−	15.7443i	−0.288829	−	0.504221i
$976$	16.1956	−	28.0515i	0.518407	−	0.897907i
$977$		−	12.0723i		−	0.386227i	−0.981176	−	0.193113i	$-0.938141\pi$
$977$		−	12.0723i		−	0.386227i	0.981176	−	0.193113i	$-0.0618585\pi$
$978$	−0.935102	+	1.61964i	−0.0299013	+	0.0517905i
$979$	1.07857	−	1.86814i	0.0344712	−	0.0597059i
$980$	−31.0709	+	20.2021i	−0.992524	+	0.645331i
$981$	−0.865142	−	0.499490i	−0.0276219	−	0.0159475i
$982$		−	10.1544i		−	0.324039i
$983$	−10.8771	−	6.27988i	−0.346925	−	0.200297i	0.316405	−	0.948624i	$-0.397524\pi$
$983$	−10.8771	−	6.27988i	−0.346925	−	0.200297i	−0.663330	+	0.748327i	$0.730857\pi$
$984$	5.75645	+	9.97046i	0.183509	+	0.317847i
$985$	9.52597	−	16.4995i	0.303523	−	0.525717i
$986$	−0.188522	+	0.108843i	−0.00600378	+	0.00346628i
$987$	12.4394	−	22.9256i	0.395950	−	0.729729i
$988$	0.0313904	−	9.22756i	0.000998663	−	0.293568i
$989$	−1.72612	−	2.98973i	−0.0548874	−	0.0950678i
$990$			0.640776i			0.0203652i
$991$	−9.13447			−0.290166			−0.145083	−	0.989419i	$-0.546345\pi$
$991$	−9.13447			−0.290166			−0.145083	+	0.989419i	$0.546345\pi$
$992$	−46.9081			−1.48933
$993$			1.65551i			0.0525360i
$994$	−16.5869	−	9.00004i	−0.526105	−	0.285464i
$995$	−40.6667	−	23.4789i	−1.28922	−	0.744332i
$996$	−21.6944	+	12.5253i	−0.687415	+	0.396879i
$997$	7.49594	+	12.9833i	0.237399	+	0.411187i	0.959967	−	0.280113i	$-0.0903719\pi$
$997$	7.49594	+	12.9833i	0.237399	+	0.411187i	−0.722568	+	0.691300i	$0.757039\pi$
$998$	−6.80015			−0.215255
$999$	2.88399	+	1.66507i	0.0912455	+	0.0526806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bl.c.88.4	yes	12
3.2	odd	2		819.2.do.f.361.3		12
7.2	even	3		273.2.t.c.205.3	yes	12
13.4	even	6		273.2.t.c.4.4	✓	12
21.2	odd	6		819.2.bm.e.478.4		12
39.17	odd	6		819.2.bm.e.550.3		12
91.30	even	6	inner	273.2.bl.c.121.4	yes	12
273.212	odd	6		819.2.do.f.667.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.c.4.4	✓	12	13.4	even	6
273.2.t.c.205.3	yes	12	7.2	even	3
273.2.bl.c.88.4	yes	12	1.1	even	1	trivial
273.2.bl.c.121.4	yes	12	91.30	even	6	inner
819.2.bm.e.478.4		12	21.2	odd	6
819.2.bm.e.550.3		12	39.17	odd	6
819.2.do.f.361.3		12	3.2	odd	2
819.2.do.f.667.3		12	273.212	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.496325 + 0.286553i) q^{2} +1.00000 q^{3} +(-0.835774 - 1.44760i) q^{4} +(2.74304 - 1.58369i) q^{5} +(0.496325 + 0.286553i) q^{6} +(-2.25549 + 1.38302i) q^{7} -2.10419i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.496325 + 0.286553i) q^{2} +1.00000 q^{3} +(-0.835774 - 1.44760i) q^{4} +(2.74304 - 1.58369i) q^{5} +(0.496325 + 0.286553i) q^{6} +(-2.25549 + 1.38302i) q^{7} -2.10419i q^{8} +1.00000 q^{9} +1.81525 q^{10} +0.352996i q^{11} +(-0.835774 - 1.44760i) q^{12} +(1.81339 - 3.11635i) q^{13} +(-1.51577 + 0.0401100i) q^{14} +(2.74304 - 1.58369i) q^{15} +(-1.06859 + 1.85085i) q^{16} +(0.444277 + 0.769510i) q^{17} +(0.496325 + 0.286553i) q^{18} +1.53108i q^{19} +(-4.58512 - 2.64722i) q^{20} +(-2.25549 + 1.38302i) q^{21} +(-0.101152 + 0.175201i) q^{22} +(-2.26579 + 3.92446i) q^{23} -2.10419i q^{24} +(2.51618 - 4.35815i) q^{25} +(1.79303 - 1.02709i) q^{26} +1.00000 q^{27} +(3.88715 + 2.10916i) q^{28} +(0.213739 + 0.370207i) q^{29} +1.81525 q^{30} +(7.47692 + 4.31680i) q^{31} +(-4.70529 + 2.71660i) q^{32} +0.352996i q^{33} +0.509236i q^{34} +(-3.99662 + 7.36570i) q^{35} +(-0.835774 - 1.44760i) q^{36} +(2.88399 + 1.66507i) q^{37} +(-0.438737 + 0.759914i) q^{38} +(1.81339 - 3.11635i) q^{39} +(-3.33239 - 5.77187i) q^{40} +(-4.73839 + 2.73571i) q^{41} +(-1.51577 + 0.0401100i) q^{42} +(-0.380909 + 0.659754i) q^{43} +(0.510998 - 0.295025i) q^{44} +(2.74304 - 1.58369i) q^{45} +(-2.24913 + 1.29854i) q^{46} +(-8.53765 + 4.92921i) q^{47} +(-1.06859 + 1.85085i) q^{48} +(3.17449 - 6.23880i) q^{49} +(2.49768 - 1.44204i) q^{50} +(0.444277 + 0.769510i) q^{51} +(-6.02682 - 0.0205021i) q^{52} +(2.06487 - 3.57646i) q^{53} +(0.496325 + 0.286553i) q^{54} +(0.559038 + 0.968281i) q^{55} +(2.91014 + 4.74598i) q^{56} +1.53108i q^{57} +0.244990i q^{58} +(-9.96812 + 5.75510i) q^{59} +(-4.58512 - 2.64722i) q^{60} -15.1561 q^{61} +(2.47399 + 4.28507i) q^{62} +(-2.25549 + 1.38302i) q^{63} +1.16054 q^{64} +(0.0388491 - 11.4201i) q^{65} +(-0.101152 + 0.175201i) q^{66} -9.35501i q^{67} +(0.742630 - 1.28627i) q^{68} +(-2.26579 + 3.92446i) q^{69} +(-4.09429 + 2.51054i) q^{70} +(10.7783 + 6.22283i) q^{71} -2.10419i q^{72} +(5.88903 + 3.40003i) q^{73} +(0.954265 + 1.65284i) q^{74} +(2.51618 - 4.35815i) q^{75} +(2.21640 - 1.27964i) q^{76} +(-0.488201 - 0.796179i) q^{77} +(1.79303 - 1.02709i) q^{78} +(-3.48680 - 6.03932i) q^{79} +6.76926i q^{80} +1.00000 q^{81} -3.13571 q^{82} -14.9864i q^{83} +(3.88715 + 2.10916i) q^{84} +(2.43734 + 1.40720i) q^{85} +(-0.378110 + 0.218302i) q^{86} +(0.213739 + 0.370207i) q^{87} +0.742770 q^{88} +(-5.29223 - 3.05547i) q^{89} +1.81525 q^{90} +(0.219900 + 9.53686i) q^{91} +7.57475 q^{92} +(7.47692 + 4.31680i) q^{93} -5.64993 q^{94} +(2.42477 + 4.19982i) q^{95} +(-4.70529 + 2.71660i) q^{96} +(11.3769 + 6.56845i) q^{97} +(3.36333 - 2.18681i) q^{98} +0.352996i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 12 q^{3} + 5 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} + 12 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 + 12 * q^3 + 5 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 + 12 * q^9	\( 12 q - 3 q^{2} + 12 q^{3} + 5 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} + 12 q^{9} + 14 q^{10} + 5 q^{12} - q^{13} - 16 q^{14} + 6 q^{15} + 3 q^{16} - 3 q^{18} - 27 q^{20} + 3 q^{21} + 7 q^{22} - 16 q^{23} + 10 q^{25} - q^{26} + 12 q^{27} + 24 q^{28} - 5 q^{29} + 14 q^{30} + 15 q^{31} - 6 q^{32} - 2 q^{35} + 5 q^{36} + 6 q^{37} + 24 q^{38} - q^{39} + 21 q^{40} - 15 q^{41} - 16 q^{42} - 13 q^{43} - 30 q^{44} + 6 q^{45} - 9 q^{46} - 9 q^{47} + 3 q^{48} + 9 q^{49} - 63 q^{50} - 55 q^{52} + 18 q^{53} - 3 q^{54} + 13 q^{55} - 21 q^{56} - 33 q^{59} - 27 q^{60} - 52 q^{61} - 13 q^{62} + 3 q^{63} - 4 q^{64} - 41 q^{65} + 7 q^{66} - 16 q^{69} - 42 q^{70} - 15 q^{71} - 18 q^{73} + 38 q^{74} + 10 q^{75} - 30 q^{76} + 20 q^{77} - q^{78} - 4 q^{79} + 12 q^{81} + 28 q^{82} + 24 q^{84} - 12 q^{85} - 15 q^{86} - 5 q^{87} - 32 q^{88} + 12 q^{89} + 14 q^{90} + 49 q^{91} - 40 q^{92} + 15 q^{93} + 6 q^{94} - 28 q^{95} - 6 q^{96} + 45 q^{97} + 48 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 + 12 * q^3 + 5 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 + 12 * q^9 + 14 * q^10 + 5 * q^12 - q^13 - 16 * q^14 + 6 * q^15 + 3 * q^16 - 3 * q^18 - 27 * q^20 + 3 * q^21 + 7 * q^22 - 16 * q^23 + 10 * q^25 - q^26 + 12 * q^27 + 24 * q^28 - 5 * q^29 + 14 * q^30 + 15 * q^31 - 6 * q^32 - 2 * q^35 + 5 * q^36 + 6 * q^37 + 24 * q^38 - q^39 + 21 * q^40 - 15 * q^41 - 16 * q^42 - 13 * q^43 - 30 * q^44 + 6 * q^45 - 9 * q^46 - 9 * q^47 + 3 * q^48 + 9 * q^49 - 63 * q^50 - 55 * q^52 + 18 * q^53 - 3 * q^54 + 13 * q^55 - 21 * q^56 - 33 * q^59 - 27 * q^60 - 52 * q^61 - 13 * q^62 + 3 * q^63 - 4 * q^64 - 41 * q^65 + 7 * q^66 - 16 * q^69 - 42 * q^70 - 15 * q^71 - 18 * q^73 + 38 * q^74 + 10 * q^75 - 30 * q^76 + 20 * q^77 - q^78 - 4 * q^79 + 12 * q^81 + 28 * q^82 + 24 * q^84 - 12 * q^85 - 15 * q^86 - 5 * q^87 - 32 * q^88 + 12 * q^89 + 14 * q^90 + 49 * q^91 - 40 * q^92 + 15 * q^93 + 6 * q^94 - 28 * q^95 - 6 * q^96 + 45 * q^97 + 48 * q^98

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