LMFDB - Embedded newform 1755.2.i.f.586.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1755,2,Mod(586,1755)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1755, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1755.586");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1755 = 3^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1755.i (of order $3$, degree $2$, not 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:	$14.0137455547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 20 x^{14} - 44 x^{13} + 96 x^{12} - 107 x^{11} + 178 x^{10} - 19 x^{9} + 231 x^{8} + \cdots + 268 $ x^16 - 5x^15 + 20x^14 - 44x^13 + 96x^12 - 107x^11 + 178x^10 - 19x^9 + 231x^8 + 326x^7 + 551x^6 + 859x^5 + 1118x^4 + 1215x^3 + 1103x^2 + 770*x + 268
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 585)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			586.2
Root			$1.48460 - 1.66288i$ of defining polynomial
Character	$\chi$	$=$	1755.586
Dual form			1755.2.i.f.1171.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984603 + 1.70538i) q^{2} +(-0.938888 - 1.62620i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.51414 - 2.62256i) q^{7} -0.240686 q^{8} +O(q^{10})$	\(q+(-0.984603 + 1.70538i) q^{2} +(-0.938888 - 1.62620i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.51414 - 2.62256i) q^{7} -0.240686 q^{8} +1.96921 q^{10} +(-2.15197 + 3.72733i) q^{11} +(0.500000 + 0.866025i) q^{13} +(2.98165 + 5.16437i) q^{14} +(2.11476 - 3.66286i) q^{16} +0.303306 q^{17} -6.04909 q^{19} +(-0.938888 + 1.62620i) q^{20} +(-4.23768 - 7.33988i) q^{22} +(1.47524 + 2.55520i) q^{23} +(-0.500000 + 0.866025i) q^{25} -1.96921 q^{26} -5.68642 q^{28} +(4.44268 - 7.69494i) q^{29} +(-0.0319947 - 0.0554165i) q^{31} +(3.92370 + 6.79606i) q^{32} +(-0.298636 + 0.517253i) q^{34} -3.02828 q^{35} +11.1045 q^{37} +(5.95595 - 10.3160i) q^{38} +(0.120343 + 0.208440i) q^{40} +(4.09849 + 7.09879i) q^{41} +(-1.45536 + 2.52075i) q^{43} +8.08184 q^{44} -5.81012 q^{46} +(-3.44432 + 5.96573i) q^{47} +(-1.08523 - 1.87967i) q^{49} +(-0.984603 - 1.70538i) q^{50} +(0.938888 - 1.62620i) q^{52} -11.8296 q^{53} +4.30395 q^{55} +(-0.364432 + 0.631214i) q^{56} +(8.74855 + 15.1529i) q^{58} +(4.57534 + 7.92472i) q^{59} +(-0.657031 + 1.13801i) q^{61} +0.126009 q^{62} -6.99415 q^{64} +(0.500000 - 0.866025i) q^{65} +(7.91564 + 13.7103i) q^{67} +(-0.284770 - 0.493236i) q^{68} +(2.98165 - 5.16437i) q^{70} +2.85405 q^{71} -11.2819 q^{73} +(-10.9335 + 18.9374i) q^{74} +(5.67942 + 9.83704i) q^{76} +(6.51677 + 11.2874i) q^{77} +(-5.17979 + 8.97167i) q^{79} -4.22951 q^{80} -16.1415 q^{82} +(-3.53463 + 6.12217i) q^{83} +(-0.151653 - 0.262670i) q^{85} +(-2.86590 - 4.96389i) q^{86} +(0.517949 - 0.897115i) q^{88} -4.26865 q^{89} +3.02828 q^{91} +(2.77018 - 4.79809i) q^{92} +(-6.78257 - 11.7478i) q^{94} +(3.02455 + 5.23867i) q^{95} +(-2.91854 + 5.05505i) q^{97} +4.27408 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8}+O(q^{10}) $ 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8	$ 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8} - 6 q^{10} + 6 q^{11} + 8 q^{13} + 10 q^{14} - 11 q^{16} + 4 q^{17} - 20 q^{19} - 9 q^{20} - 3 q^{22} + 6 q^{23} - 8 q^{25} + 6 q^{26} - 68 q^{28} + 14 q^{29} + 31 q^{31} + q^{32} + 7 q^{34} - 22 q^{35} + 2 q^{37} + 9 q^{38} - 6 q^{40} - 12 q^{41} - 15 q^{43} - 32 q^{44} - 64 q^{46} - 18 q^{47} - 17 q^{49} + 3 q^{50} + 9 q^{52} - 4 q^{53} - 12 q^{55} + 16 q^{56} + 42 q^{58} + 24 q^{59} + 9 q^{61} + 40 q^{62} - 60 q^{64} + 8 q^{65} + 18 q^{67} - 14 q^{68} + 10 q^{70} - 20 q^{71} + 12 q^{73} - 37 q^{74} + 53 q^{76} - 34 q^{77} + 3 q^{79} + 22 q^{80} - 68 q^{82} - 10 q^{83} - 2 q^{85} + 60 q^{86} + 14 q^{88} + 26 q^{89} + 22 q^{91} + 5 q^{92} - 17 q^{94} + 10 q^{95} + 34 q^{97} + 60 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8 - 6 * q^10 + 6 * q^11 + 8 * q^13 + 10 * q^14 - 11 * q^16 + 4 * q^17 - 20 * q^19 - 9 * q^20 - 3 * q^22 + 6 * q^23 - 8 * q^25 + 6 * q^26 - 68 * q^28 + 14 * q^29 + 31 * q^31 + q^32 + 7 * q^34 - 22 * q^35 + 2 * q^37 + 9 * q^38 - 6 * q^40 - 12 * q^41 - 15 * q^43 - 32 * q^44 - 64 * q^46 - 18 * q^47 - 17 * q^49 + 3 * q^50 + 9 * q^52 - 4 * q^53 - 12 * q^55 + 16 * q^56 + 42 * q^58 + 24 * q^59 + 9 * q^61 + 40 * q^62 - 60 * q^64 + 8 * q^65 + 18 * q^67 - 14 * q^68 + 10 * q^70 - 20 * q^71 + 12 * q^73 - 37 * q^74 + 53 * q^76 - 34 * q^77 + 3 * q^79 + 22 * q^80 - 68 * q^82 - 10 * q^83 - 2 * q^85 + 60 * q^86 + 14 * q^88 + 26 * q^89 + 22 * q^91 + 5 * q^92 - 17 * q^94 + 10 * q^95 + 34 * q^97 + 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1755\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	−0.984603	+	1.70538i	−0.696220	+	1.20589i	0.273548	+	0.961858i	$0.411803\pi$
$2$	−0.984603	+	1.70538i	−0.696220	+	1.20589i	−0.969768	+	0.244030i	$0.921531\pi$
$3$		0			0
$3$		0			0
$4$	−0.938888	−	1.62620i	−0.469444	−	0.813101i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	1.51414	−	2.62256i	0.572290	−	0.991236i	−0.424040	−	0.905644i	$-0.639388\pi$
$7$	1.51414	−	2.62256i	0.572290	−	0.991236i	0.996330	−	0.0855926i	$-0.0272783\pi$
$8$	−0.240686			−0.0850953
$9$		0			0
$10$	1.96921			0.622718
$11$	−2.15197	+	3.72733i	−0.648844	+	1.12383i	0.334555	+	0.942376i	$0.391414\pi$
$11$	−2.15197	+	3.72733i	−0.648844	+	1.12383i	−0.983399	+	0.181455i	$0.941919\pi$
$12$		0			0
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	2.98165	+	5.16437i	0.796880	+	1.38024i
$15$		0			0
$16$	2.11476	−	3.66286i	0.528689	−	0.915716i
$17$	0.303306			0.0735625			0.0367812	−	0.999323i	$-0.488290\pi$
$17$	0.303306			0.0735625			0.0367812	+	0.999323i	$0.488290\pi$
$18$		0			0
$19$	−6.04909			−1.38776			−0.693878	−	0.720092i	$-0.744099\pi$
$19$	−6.04909			−1.38776			−0.693878	+	0.720092i	$0.744099\pi$
$20$	−0.938888	+	1.62620i	−0.209942	+	0.363630i
$21$		0			0
$22$	−4.23768	−	7.33988i	−0.903476	−	1.56487i
$23$	1.47524	+	2.55520i	0.307610	+	0.532796i	0.977839	−	0.209358i	$-0.0671375\pi$
$23$	1.47524	+	2.55520i	0.307610	+	0.532796i	−0.670229	+	0.742154i	$0.733804\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.96921			−0.386193
$27$		0			0
$28$	−5.68642			−1.07463
$29$	4.44268	−	7.69494i	0.824984	−	1.42891i	−0.0769469	−	0.997035i	$-0.524517\pi$
$29$	4.44268	−	7.69494i	0.824984	−	1.42891i	0.901931	−	0.431880i	$-0.142149\pi$
$30$		0			0
$31$	−0.0319947	−	0.0554165i	−0.00574643	−	0.00995310i	0.863138	−	0.504968i	$-0.168496\pi$
$31$	−0.0319947	−	0.0554165i	−0.00574643	−	0.00995310i	−0.868884	+	0.495015i	$0.835162\pi$
$32$	3.92370	+	6.79606i	0.693620	+	1.20138i
$33$		0			0
$34$	−0.298636	+	0.517253i	−0.0512156	+	0.0887081i
$35$	−3.02828			−0.511872
$36$		0			0
$37$	11.1045			1.82556			0.912781	−	0.408450i	$-0.133930\pi$
$37$	11.1045			1.82556			0.912781	+	0.408450i	$0.133930\pi$
$38$	5.95595	−	10.3160i	0.966183	−	1.67348i
$39$		0			0
$40$	0.120343	+	0.208440i	0.0190279	+	0.0329573i
$41$	4.09849	+	7.09879i	0.640076	+	1.10865i	0.985415	+	0.170167i	$0.0544307\pi$
$41$	4.09849	+	7.09879i	0.640076	+	1.10865i	−0.345339	+	0.938478i	$0.612236\pi$
$42$		0			0
$43$	−1.45536	+	2.52075i	−0.221940	+	0.384411i	−0.955397	−	0.295324i	$-0.904572\pi$
$43$	−1.45536	+	2.52075i	−0.221940	+	0.384411i	0.733457	+	0.679736i	$0.237906\pi$
$44$	8.08184			1.21838
$45$		0			0
$46$	−5.81012			−0.856656
$47$	−3.44432	+	5.96573i	−0.502405	+	0.870192i	0.497591	+	0.867412i	$0.334218\pi$
$47$	−3.44432	+	5.96573i	−0.502405	+	0.870192i	−0.999996	+	0.00277976i	$0.999115\pi$
$48$		0			0
$49$	−1.08523	−	1.87967i	−0.155033	−	0.268525i
$50$	−0.984603	−	1.70538i	−0.139244	−	0.241178i
$51$		0			0
$52$	0.938888	−	1.62620i	0.130200	−	0.225514i
$53$	−11.8296			−1.62493			−0.812463	−	0.583012i	$-0.801874\pi$
$53$	−11.8296			−1.62493			−0.812463	+	0.583012i	$0.801874\pi$
$54$		0			0
$55$	4.30395			0.580344
$56$	−0.364432	+	0.631214i	−0.0486992	+	0.0843495i
$57$		0			0
$58$	8.74855	+	15.1529i	1.14874	+	1.98968i
$59$	4.57534	+	7.92472i	0.595658	+	1.03171i	0.993454	+	0.114236i	$0.0364421\pi$
$59$	4.57534	+	7.92472i	0.595658	+	1.03171i	−0.397795	+	0.917474i	$0.630225\pi$
$60$		0			0
$61$	−0.657031	+	1.13801i	−0.0841241	+	0.145707i	−0.905018	−	0.425374i	$-0.860143\pi$
$61$	−0.657031	+	1.13801i	−0.0841241	+	0.145707i	0.820894	+	0.571081i	$0.193476\pi$
$62$	0.126009			0.0160031
$63$		0			0
$64$	−6.99415			−0.874269
$65$	0.500000	−	0.866025i	0.0620174	−	0.107417i
$66$		0			0
$67$	7.91564	+	13.7103i	0.967049	+	1.67498i	0.704006	+	0.710194i	$0.251393\pi$
$67$	7.91564	+	13.7103i	0.967049	+	1.67498i	0.263043	+	0.964784i	$0.415274\pi$
$68$	−0.284770	−	0.493236i	−0.0345334	−	0.0598137i
$69$		0			0
$70$	2.98165	−	5.16437i	0.356375	−	0.617260i
$71$	2.85405			0.338714			0.169357	−	0.985555i	$-0.445831\pi$
$71$	2.85405			0.338714			0.169357	+	0.985555i	$0.445831\pi$
$72$		0			0
$73$	−11.2819			−1.32045			−0.660223	−	0.751070i	$-0.729538\pi$
$73$	−11.2819			−1.32045			−0.660223	+	0.751070i	$0.729538\pi$
$74$	−10.9335	+	18.9374i	−1.27099	+	2.20142i
$75$		0			0
$76$	5.67942	+	9.83704i	0.651474	+	1.12839i
$77$	6.51677	+	11.2874i	0.742655	+	1.28632i
$78$		0			0
$79$	−5.17979	+	8.97167i	−0.582772	+	1.00939i	0.412377	+	0.911013i	$0.364699\pi$
$79$	−5.17979	+	8.97167i	−0.582772	+	1.00939i	−0.995149	+	0.0983781i	$0.968635\pi$
$80$	−4.22951			−0.472874
$81$		0			0
$82$	−16.1415			−1.78254
$83$	−3.53463	+	6.12217i	−0.387977	+	0.671995i	−0.992177	−	0.124837i	$-0.960159\pi$
$83$	−3.53463	+	6.12217i	−0.387977	+	0.671995i	0.604201	+	0.796832i	$0.293493\pi$
$84$		0			0
$85$	−0.151653	−	0.262670i	−0.0164491	−	0.0284906i
$86$	−2.86590	−	4.96389i	−0.309038	−	0.535270i
$87$		0			0
$88$	0.517949	−	0.897115i	0.0552136	−	0.0956328i
$89$	−4.26865			−0.452476			−0.226238	−	0.974072i	$-0.572643\pi$
$89$	−4.26865			−0.452476			−0.226238	+	0.974072i	$0.572643\pi$
$90$		0			0
$91$	3.02828			0.317450
$92$	2.77018	−	4.79809i	0.288811	−	0.500235i
$93$		0			0
$94$	−6.78257	−	11.7478i	−0.699569	−	1.21169i
$95$	3.02455	+	5.23867i	0.310312	+	0.537476i
$96$		0			0
$97$	−2.91854	+	5.05505i	−0.296333	+	0.513263i	−0.975294	−	0.220911i	$-0.929097\pi$
$97$	−2.91854	+	5.05505i	−0.296333	+	0.513263i	0.678961	+	0.734174i	$0.262430\pi$
$98$	4.27408			0.431747
$99$		0			0
$100$	1.87778			0.187778
$101$	5.32443	−	9.22219i	0.529801	−	0.917642i	−0.469595	−	0.882882i	$-0.655600\pi$
$101$	5.32443	−	9.22219i	0.529801	−	0.917642i	0.999396	−	0.0347599i	$-0.0110667\pi$
$102$		0			0
$103$	8.95821	+	15.5161i	0.882679	+	1.52885i	0.848351	+	0.529434i	$0.177596\pi$
$103$	8.95821	+	15.5161i	0.882679	+	1.52885i	0.0343282	+	0.999411i	$0.489071\pi$
$104$	−0.120343	−	0.208440i	−0.0118006	−	0.0204392i
$105$		0			0
$106$	11.6475	−	20.1741i	1.13131	−	1.95948i
$107$	1.12190			0.108458			0.0542288	−	0.998529i	$-0.482730\pi$
$107$	1.12190			0.108458			0.0542288	+	0.998529i	$0.482730\pi$
$108$		0			0
$109$	14.1268			1.35310			0.676552	−	0.736394i	$-0.263473\pi$
$109$	14.1268			1.35310			0.676552	+	0.736394i	$0.263473\pi$
$110$	−4.23768	+	7.33988i	−0.404047	+	0.699830i
$111$		0			0
$112$	−6.40406	−	11.0922i	−0.605127	−	1.04811i
$113$	−0.144808	−	0.250816i	−0.0136224	−	0.0235947i	0.859134	−	0.511751i	$-0.171003\pi$
$113$	−0.144808	−	0.250816i	−0.0136224	−	0.0235947i	−0.872756	+	0.488156i	$0.837670\pi$
$114$		0			0
$115$	1.47524	−	2.55520i	0.137567	−	0.238274i
$116$	−16.6847			−1.54914
$117$		0			0
$118$	−18.0196			−1.65884
$119$	0.459247	−	0.795439i	0.0420991	−	0.0729178i
$120$		0			0
$121$	−3.76198	−	6.51593i	−0.341998	−	0.592357i
$122$	−1.29383	−	2.24098i	−0.117138	−	0.202889i
$123$		0			0
$124$	−0.0600789	+	0.104060i	−0.00539525	+	0.00934484i
$125$	1.00000			0.0894427
$126$		0			0
$127$	4.70408			0.417419			0.208710	−	0.977978i	$-0.433074\pi$
$127$	4.70408			0.417419			0.208710	+	0.977978i	$0.433074\pi$
$128$	−0.960946	+	1.66441i	−0.0849364	+	0.147114i
$129$		0			0
$130$	0.984603	+	1.70538i	0.0863554	+	0.149572i
$131$	−11.0430	−	19.1271i	−0.964835	−	1.67114i	−0.710057	−	0.704145i	$-0.751331\pi$
$131$	−11.0430	−	19.1271i	−0.964835	−	1.67114i	−0.254779	−	0.966999i	$-0.582003\pi$
$132$		0			0
$133$	−9.15916	+	15.8641i	−0.794200	+	1.37559i
$134$	−31.1751			−2.69311
$135$		0			0
$136$	−0.0730014			−0.00625982
$137$	−1.08441	+	1.87825i	−0.0926473	+	0.160470i	−0.908624	−	0.417615i	$-0.862866\pi$
$137$	−1.08441	+	1.87825i	−0.0926473	+	0.160470i	0.815977	+	0.578084i	$0.196200\pi$
$138$		0			0
$139$	0.606433	+	1.05037i	0.0514370	+	0.0890914i	0.890597	−	0.454792i	$-0.150287\pi$
$139$	0.606433	+	1.05037i	0.0514370	+	0.0890914i	−0.839161	+	0.543884i	$0.816953\pi$
$140$	2.84321	+	4.92459i	0.240295	+	0.416203i
$141$		0			0
$142$	−2.81011	+	4.86726i	−0.235819	+	0.408451i
$143$	−4.30395			−0.359914
$144$		0			0
$145$	−8.88535			−0.737888
$146$	11.1082	−	19.2399i	0.919320	−	1.59231i
$147$		0			0
$148$	−10.4258	−	18.0581i	−0.856999	−	1.48437i
$149$	2.93510	+	5.08374i	0.240453	+	0.416476i	0.960843	−	0.277092i	$-0.0893707\pi$
$149$	2.93510	+	5.08374i	0.240453	+	0.416476i	−0.720391	+	0.693569i	$0.756037\pi$
$150$		0			0
$151$	4.65223	−	8.05789i	0.378593	−	0.655742i	−0.612265	−	0.790653i	$-0.709741\pi$
$151$	4.65223	−	8.05789i	0.378593	−	0.655742i	0.990858	+	0.134911i	$0.0430747\pi$
$152$	1.45593			0.118092
$153$		0			0
$154$	−25.6657			−2.06820
$155$	−0.0319947	+	0.0554165i	−0.00256988	+	0.00445116i
$156$		0			0
$157$	9.14727	+	15.8435i	0.730031	+	1.26445i	0.956869	+	0.290519i	$0.0938280\pi$
$157$	9.14727	+	15.8435i	0.730031	+	1.26445i	−0.226838	+	0.973933i	$0.572839\pi$
$158$	−10.2001	−	17.6671i	−0.811475	−	1.40552i
$159$		0			0
$160$	3.92370	−	6.79606i	0.310196	−	0.537275i
$161$	8.93490			0.704169
$162$		0			0
$163$	−11.9524			−0.936186			−0.468093	−	0.883679i	$-0.655059\pi$
$163$	−11.9524			−0.936186			−0.468093	+	0.883679i	$0.655059\pi$
$164$	7.69604	−	13.3299i	0.600960	−	1.04089i
$165$		0			0
$166$	−6.96043	−	12.0558i	−0.540234	−	0.935712i
$167$	6.66491	+	11.5440i	0.515746	+	0.893298i	0.999833	+	0.0182782i	$0.00581847\pi$
$167$	6.66491	+	11.5440i	0.515746	+	0.893298i	−0.484087	+	0.875020i	$0.660848\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	0.597272			0.0458087
$171$		0			0
$172$	5.46567			0.416753
$173$	−8.28672	+	14.3530i	−0.630028	+	1.09124i	0.357517	+	0.933906i	$0.383623\pi$
$173$	−8.28672	+	14.3530i	−0.630028	+	1.09124i	−0.987545	+	0.157334i	$0.949710\pi$
$174$		0			0
$175$	1.51414	+	2.62256i	0.114458	+	0.198247i
$176$	9.10179	+	15.7648i	0.686073	+	1.18831i
$177$		0			0
$178$	4.20293	−	7.27968i	0.315023	−	0.545635i
$179$	−13.5386			−1.01192			−0.505961	−	0.862556i	$-0.668862\pi$
$179$	−13.5386			−1.01192			−0.505961	+	0.862556i	$0.668862\pi$
$180$		0			0
$181$	−3.59303			−0.267068			−0.133534	−	0.991044i	$-0.542632\pi$
$181$	−3.59303			−0.267068			−0.133534	+	0.991044i	$0.542632\pi$
$182$	−2.98165	+	5.16437i	−0.221015	+	0.382809i
$183$		0			0
$184$	−0.355071	−	0.615000i	−0.0261762	−	0.0453384i
$185$	−5.55223	−	9.61674i	−0.408208	−	0.707037i
$186$		0			0
$187$	−0.652706	+	1.13052i	−0.0477306	+	0.0826718i
$188$	12.9353			0.943404
$189$		0			0
$190$	−11.9119			−0.864181
$191$	10.2707	−	17.7894i	0.743161	−	1.28719i	−0.207888	−	0.978153i	$-0.566659\pi$
$191$	10.2707	−	17.7894i	0.743161	−	1.28719i	0.951049	−	0.309040i	$-0.100008\pi$
$192$		0			0
$193$	0.763135	+	1.32179i	0.0549316	+	0.0951444i	0.892184	−	0.451673i	$-0.149173\pi$
$193$	0.763135	+	1.32179i	0.0549316	+	0.0951444i	−0.837252	+	0.546817i	$0.815839\pi$
$194$	−5.74720	−	9.95445i	−0.412625	−	0.714688i
$195$		0			0
$196$	−2.03782	+	3.52960i	−0.145558	+	0.252114i
$197$	1.07799			0.0768033			0.0384016	−	0.999262i	$-0.487773\pi$
$197$	1.07799			0.0768033			0.0384016	+	0.999262i	$0.487773\pi$
$198$		0			0
$199$	2.00263			0.141963			0.0709813	−	0.997478i	$-0.477387\pi$
$199$	2.00263			0.141963			0.0709813	+	0.997478i	$0.477387\pi$
$200$	0.120343	−	0.208440i	0.00850953	−	0.0147389i
$201$		0			0
$202$	10.4849	+	18.1604i	0.737716	+	1.27776i
$203$	−13.4537	−	23.3024i	−0.944261	−	1.63551i
$204$		0			0
$205$	4.09849	−	7.09879i	0.286251	−	0.495801i
$206$	−35.2812			−2.45815
$207$		0			0
$208$	4.22951			0.293264
$209$	13.0175	−	22.5469i	0.900438	−	1.55960i
$210$		0			0
$211$	0.117610	+	0.203707i	0.00809663	+	0.0140238i	0.870045	−	0.492972i	$-0.164089\pi$
$211$	0.117610	+	0.203707i	0.00809663	+	0.0140238i	−0.861949	+	0.506996i	$0.830756\pi$
$212$	11.1067	+	19.2374i	0.762812	+	1.32123i
$213$		0			0
$214$	−1.10462	+	1.91326i	−0.0755104	+	0.130788i
$215$	2.91072			0.198509
$216$		0			0
$217$	−0.193778			−0.0131545
$218$	−13.9093	+	24.0917i	−0.942058	+	1.63169i
$219$		0			0
$220$	−4.04092	−	6.99908i	−0.272439	−	0.471878i
$221$	0.151653	+	0.262670i	0.0102013	+	0.0176691i
$222$		0			0
$223$	−0.224073	+	0.388107i	−0.0150051	+	0.0259895i	−0.873430	−	0.486949i	$-0.838110\pi$
$223$	−0.224073	+	0.388107i	−0.0150051	+	0.0259895i	0.858425	+	0.512938i	$0.171443\pi$
$224$	23.7641			1.58781
$225$		0			0
$226$	0.570315			0.0379368
$227$	−4.89779	+	8.48323i	−0.325078	+	0.563052i	−0.981528	−	0.191318i	$-0.938724\pi$
$227$	−4.89779	+	8.48323i	−0.325078	+	0.563052i	0.656450	+	0.754369i	$0.272057\pi$
$228$		0			0
$229$	−1.43116	−	2.47884i	−0.0945735	−	0.163806i	0.814857	−	0.579662i	$-0.196815\pi$
$229$	−1.43116	−	2.47884i	−0.0945735	−	0.163806i	−0.909431	+	0.415856i	$0.863482\pi$
$230$	2.90506	+	5.03172i	0.191554	+	0.331782i
$231$		0			0
$232$	−1.06929	+	1.85206i	−0.0702023	+	0.121594i
$233$	15.5072			1.01591			0.507955	−	0.861384i	$-0.330402\pi$
$233$	15.5072			1.01591			0.507955	+	0.861384i	$0.330402\pi$
$234$		0			0
$235$	6.88864			0.449365
$236$	8.59146	−	14.8808i	0.559256	−	0.968660i
$237$		0			0
$238$	0.904352	+	1.56638i	0.0586204	+	0.101534i
$239$	−3.64054	−	6.30561i	−0.235487	−	0.407876i	0.723927	−	0.689877i	$-0.242335\pi$
$239$	−3.64054	−	6.30561i	−0.235487	−	0.407876i	−0.959414	+	0.282001i	$0.909002\pi$
$240$		0			0
$241$	−5.49432	+	9.51644i	−0.353920	+	0.613008i	−0.986933	−	0.161134i	$-0.948485\pi$
$241$	−5.49432	+	9.51644i	−0.353920	+	0.613008i	0.633012	+	0.774142i	$0.281818\pi$
$242$	14.8162			0.952422
$243$		0			0
$244$	2.46751			0.157966
$245$	−1.08523	+	1.87967i	−0.0693327	+	0.120088i
$246$		0			0
$247$	−3.02455	−	5.23867i	−0.192447	−	0.333328i
$248$	0.00770068	+	0.0133380i	0.000488994	+	0.000846962i
$249$		0			0
$250$	−0.984603	+	1.70538i	−0.0622718	+	0.107858i
$251$	−9.53838			−0.602057			−0.301029	−	0.953615i	$-0.597330\pi$
$251$	−9.53838			−0.602057			−0.301029	+	0.953615i	$0.597330\pi$
$252$		0			0
$253$	−12.6987			−0.798364
$254$	−4.63165	+	8.02225i	−0.290616	+	0.503361i
$255$		0			0
$256$	−8.88645	−	15.3918i	−0.555403	−	0.961986i
$257$	0.375550	+	0.650471i	0.0234261	+	0.0405753i	0.877501	−	0.479575i	$-0.159209\pi$
$257$	0.375550	+	0.650471i	0.0234261	+	0.0405753i	−0.854075	+	0.520150i	$0.825876\pi$
$258$		0			0
$259$	16.8137	−	29.1222i	1.04475	−	1.80956i
$260$	−1.87778			−0.116455
$261$		0			0
$262$	43.4921			2.68695
$263$	10.4188	−	18.0458i	0.642449	−	1.11275i	−0.342436	−	0.939541i	$-0.611252\pi$
$263$	10.4188	−	18.0458i	0.642449	−	1.11275i	0.984884	−	0.173212i	$-0.0554147\pi$
$264$		0			0
$265$	5.91482	+	10.2448i	0.363345	+	0.629331i
$266$	−18.0363	−	31.2397i	−1.10588	−	1.91543i
$267$		0			0
$268$	14.8638	−	25.7448i	0.907950	−	1.57262i
$269$	15.5184			0.946176			0.473088	−	0.881015i	$-0.343139\pi$
$269$	15.5184			0.946176			0.473088	+	0.881015i	$0.343139\pi$
$270$		0			0
$271$	0.983023			0.0597144			0.0298572	−	0.999554i	$-0.490495\pi$
$271$	0.983023			0.0597144			0.0298572	+	0.999554i	$0.490495\pi$
$272$	0.641417	−	1.11097i	0.0388916	−	0.0673623i
$273$		0			0
$274$	−2.13543	−	3.69867i	−0.129006	−	0.223445i
$275$	−2.15197	−	3.72733i	−0.129769	−	0.224766i
$276$		0			0
$277$	−12.1412	+	21.0291i	−0.729492	+	1.26352i	0.227606	+	0.973753i	$0.426910\pi$
$277$	−12.1412	+	21.0291i	−0.729492	+	1.26352i	−0.957098	+	0.289764i	$0.906423\pi$
$278$	−2.38838			−0.143246
$279$		0			0
$280$	0.728863			0.0435579
$281$	−1.52022	+	2.63310i	−0.0906888	+	0.157078i	−0.907801	−	0.419401i	$-0.862240\pi$
$281$	−1.52022	+	2.63310i	−0.0906888	+	0.157078i	0.817112	+	0.576478i	$0.195574\pi$
$282$		0			0
$283$	12.6309	+	21.8774i	0.750829	+	1.30047i	0.947421	+	0.319988i	$0.103679\pi$
$283$	12.6309	+	21.8774i	0.750829	+	1.30047i	−0.196593	+	0.980485i	$0.562988\pi$
$284$	−2.67964	−	4.64127i	−0.159007	−	0.275409i
$285$		0			0
$286$	4.23768	−	7.33988i	0.250579	−	0.434016i
$287$	24.8227			1.46524
$288$		0			0
$289$	−16.9080			−0.994589
$290$	8.74855	−	15.1529i	0.513732	−	0.889811i
$291$		0			0
$292$	10.5924	+	18.3466i	0.619875	+	1.07366i
$293$	−13.2059	−	22.8732i	−0.771495	−	1.33627i	−0.936744	−	0.350016i	$-0.886176\pi$
$293$	−13.2059	−	22.8732i	−0.771495	−	1.33627i	0.165249	−	0.986252i	$-0.447157\pi$
$294$		0			0
$295$	4.57534	−	7.92472i	0.266387	−	0.461395i
$296$	−2.67269			−0.155347
$297$		0			0
$298$	−11.5596			−0.669632
$299$	−1.47524	+	2.55520i	−0.0853156	+	0.147771i
$300$		0			0
$301$	4.40723	+	7.63354i	0.254028	+	0.439990i
$302$	9.16120	+	15.8677i	0.527168	+	0.913081i
$303$		0			0
$304$	−12.7923	+	22.1570i	−0.733691	+	1.27079i
$305$	1.31406			0.0752429
$306$		0			0
$307$	−15.3240			−0.874586			−0.437293	−	0.899319i	$-0.644063\pi$
$307$	−15.3240			−0.874586			−0.437293	+	0.899319i	$0.644063\pi$
$308$	12.2370	−	21.1952i	0.697269	−	1.20771i
$309$		0			0
$310$	−0.0630043	−	0.109127i	−0.00357840	−	0.00619797i
$311$	1.45646	+	2.52267i	0.0825884	+	0.143047i	0.904361	−	0.426768i	$-0.140348\pi$
$311$	1.45646	+	2.52267i	0.0825884	+	0.143047i	−0.821773	+	0.569816i	$0.807015\pi$
$312$		0			0
$313$	5.44556	−	9.43198i	0.307801	−	0.533127i	−0.670080	−	0.742289i	$-0.733740\pi$
$313$	5.44556	−	9.43198i	0.307801	−	0.533127i	0.977881	+	0.209162i	$0.0670735\pi$
$314$	−36.0257			−2.03305
$315$		0			0
$316$	19.4530			1.09432
$317$	−4.11235	+	7.12280i	−0.230973	+	0.400057i	−0.958095	−	0.286452i	$-0.907524\pi$
$317$	−4.11235	+	7.12280i	−0.230973	+	0.400057i	0.727122	+	0.686508i	$0.240857\pi$
$318$		0			0
$319$	19.1210	+	33.1186i	1.07057	+	1.85429i
$320$	3.49707	+	6.05711i	0.195492	+	0.338603i
$321$		0			0
$322$	−8.79733	+	15.2374i	−0.490256	+	0.849149i
$323$	−1.83472			−0.102087
$324$		0			0
$325$	−1.00000			−0.0554700
$326$	11.7684	−	20.3835i	0.651791	−	1.12894i
$327$		0			0
$328$	−0.986448	−	1.70858i	−0.0544675	−	0.0943405i
$329$	10.4303	+	18.0659i	0.575044	+	0.996005i
$330$		0			0
$331$	−9.02510	+	15.6319i	−0.496064	+	0.859209i	−0.999990	−	0.00453859i	$-0.998555\pi$
$331$	−9.02510	+	15.6319i	−0.496064	+	0.859209i	0.503925	+	0.863747i	$0.331889\pi$
$332$	13.2745			0.728533
$333$		0			0
$334$	−26.2492			−1.43629
$335$	7.91564	−	13.7103i	0.432478	−	0.749073i
$336$		0			0
$337$	−18.3022	−	31.7004i	−0.996985	−	1.72683i	−0.565690	−	0.824618i	$-0.691390\pi$
$337$	−18.3022	−	31.7004i	−0.996985	−	1.72683i	−0.431295	−	0.902211i	$-0.641943\pi$
$338$	−0.984603	−	1.70538i	−0.0535554	−	0.0927606i
$339$		0			0
$340$	−0.284770	+	0.493236i	−0.0154438	+	0.0267495i
$341$	0.275407			0.0149141
$342$		0			0
$343$	14.6252			0.789686
$344$	0.350284	−	0.606710i	0.0188861	−	0.0327116i
$345$		0			0
$346$	−16.3183	−	28.2641i	−0.877276	−	1.51949i
$347$	2.91466	+	5.04835i	0.156467	+	0.271009i	0.933592	−	0.358337i	$-0.116656\pi$
$347$	2.91466	+	5.04835i	0.156467	+	0.271009i	−0.777125	+	0.629346i	$0.783323\pi$
$348$		0			0
$349$	−1.50856	+	2.61290i	−0.0807513	+	0.139865i	−0.903573	−	0.428434i	$-0.859065\pi$
$349$	−1.50856	+	2.61290i	−0.0807513	+	0.139865i	0.822822	+	0.568300i	$0.192399\pi$
$350$	−5.96330			−0.318752
$351$		0			0
$352$	−33.7748			−1.80020
$353$	−4.68092	+	8.10759i	−0.249140	+	0.431524i	−0.963288	−	0.268472i	$-0.913481\pi$
$353$	−4.68092	+	8.10759i	−0.249140	+	0.431524i	0.714147	+	0.699995i	$0.246815\pi$
$354$		0			0
$355$	−1.42703	−	2.47168i	−0.0757388	−	0.131183i
$356$	4.00778	+	6.94168i	0.212412	+	0.367908i
$357$		0			0
$358$	13.3302	−	23.0885i	0.704521	−	1.22027i
$359$	−5.22577			−0.275806			−0.137903	−	0.990446i	$-0.544036\pi$
$359$	−5.22577			−0.275806			−0.137903	+	0.990446i	$0.544036\pi$
$360$		0			0
$361$	17.5915			0.925868
$362$	3.53771	−	6.12749i	0.185938	−	0.322054i
$363$		0			0
$364$	−2.84321	−	4.92459i	−0.149025	−	0.258118i
$365$	5.64095	+	9.77041i	0.295261	+	0.511406i
$366$		0			0
$367$	2.15082	−	3.72532i	0.112272	−	0.194460i	−0.804414	−	0.594069i	$-0.797521\pi$
$367$	2.15082	−	3.72532i	0.112272	−	0.194460i	0.916686	+	0.399609i	$0.130854\pi$
$368$	12.4791			0.650520
$369$		0			0
$370$	21.8670			1.13681
$371$	−17.9117	+	31.0240i	−0.929930	+	1.61069i
$372$		0			0
$373$	−13.2650	−	22.9757i	−0.686836	−	1.18964i	−0.972856	−	0.231412i	$-0.925666\pi$
$373$	−13.2650	−	22.9757i	−0.686836	−	1.18964i	0.286019	−	0.958224i	$-0.407668\pi$
$374$	−1.28531	−	2.22623i	−0.0664619	−	0.115115i
$375$		0			0
$376$	0.828999	−	1.43587i	0.0427523	−	0.0740492i
$377$	8.88535			0.457619
$378$		0			0
$379$	−3.48090			−0.178802			−0.0894008	−	0.995996i	$-0.528495\pi$
$379$	−3.48090			−0.178802			−0.0894008	+	0.995996i	$0.528495\pi$
$380$	5.67942	−	9.83704i	0.291348	−	0.504629i
$381$		0			0
$382$	20.2251	+	35.0309i	1.03481	+	1.79234i
$383$	12.3188	+	21.3368i	0.629461	+	1.09026i	0.987660	+	0.156614i	$0.0500577\pi$
$383$	12.3188	+	21.3368i	0.629461	+	1.09026i	−0.358199	+	0.933645i	$0.616609\pi$
$384$		0			0
$385$	6.51677	−	11.2874i	0.332125	−	0.575258i
$386$	−3.00554			−0.152978
$387$		0			0
$388$	10.9607			0.556446
$389$	−9.20953	+	15.9514i	−0.466942	+	0.808767i	−0.999287	−	0.0377606i	$-0.987978\pi$
$389$	−9.20953	+	15.9514i	−0.466942	+	0.808767i	0.532345	+	0.846527i	$0.321311\pi$
$390$		0			0
$391$	0.447450	+	0.775007i	0.0226285	+	0.0391938i
$392$	0.261199	+	0.452410i	0.0131926	+	0.0228502i
$393$		0			0
$394$	−1.06139	+	1.83838i	−0.0534720	+	0.0926162i
$395$	10.3596			0.521248
$396$		0			0
$397$	15.1217			0.758934			0.379467	−	0.925205i	$-0.376107\pi$
$397$	15.1217			0.758934			0.379467	+	0.925205i	$0.376107\pi$
$398$	−1.97180	+	3.41525i	−0.0988372	+	0.171191i
$399$		0			0
$400$	2.11476	+	3.66286i	0.105738	+	0.183143i
$401$	0.137657	+	0.238429i	0.00687426	+	0.0119066i	0.869442	−	0.494035i	$-0.164479\pi$
$401$	0.137657	+	0.238429i	0.00687426	+	0.0119066i	−0.862568	+	0.505941i	$0.831145\pi$
$402$		0			0
$403$	0.0319947	−	0.0554165i	0.00159377	−	0.00276049i
$404$	−19.9962			−0.994847
$405$		0			0
$406$	52.9860			2.62965
$407$	−23.8965	+	41.3899i	−1.18451	+	2.05162i
$408$		0			0
$409$	6.27626	+	10.8708i	0.310341	+	0.537527i	0.978436	−	0.206549i	$-0.0662234\pi$
$409$	6.27626	+	10.8708i	0.310341	+	0.537527i	−0.668095	+	0.744076i	$0.732890\pi$
$410$	8.07077	+	13.9790i	0.398587	+	0.690373i
$411$		0			0
$412$	16.8215	−	29.1357i	0.828736	−	1.43541i
$413$	27.7108			1.36356
$414$		0			0
$415$	7.06927			0.347017
$416$	−3.92370	+	6.79606i	−0.192375	+	0.333204i
$417$		0			0
$418$	25.6341	+	44.3996i	1.25381	+	2.17165i
$419$	11.4351	+	19.8062i	0.558641	+	0.967595i	0.997610	+	0.0690927i	$0.0220104\pi$
$419$	11.4351	+	19.8062i	0.558641	+	0.967595i	−0.438969	+	0.898502i	$0.644656\pi$
$420$		0			0
$421$	12.4879	−	21.6296i	0.608622	−	1.05416i	−0.382846	−	0.923812i	$-0.625056\pi$
$421$	12.4879	−	21.6296i	0.608622	−	1.05416i	0.991468	−	0.130352i	$-0.0416106\pi$
$422$	−0.463198			−0.0225481
$423$		0			0
$424$	2.84723			0.138274
$425$	−0.151653	+	0.262670i	−0.00735625	+	0.0127414i
$426$		0			0
$427$	1.98967	+	3.44621i	0.0962869	+	0.166774i
$428$	−1.05333	−	1.82443i	−0.0509148	−	0.0881870i
$429$		0			0
$430$	−2.86590	+	4.96389i	−0.138206	+	0.239380i
$431$	34.4612			1.65994			0.829969	−	0.557809i	$-0.188358\pi$
$431$	34.4612			1.65994			0.829969	+	0.557809i	$0.188358\pi$
$432$		0			0
$433$	15.6584			0.752495			0.376247	−	0.926519i	$-0.377214\pi$
$433$	15.6584			0.752495			0.376247	+	0.926519i	$0.377214\pi$
$434$	0.190794	−	0.330466i	0.00915842	−	0.0158629i
$435$		0			0
$436$	−13.2635	−	22.9731i	−0.635207	−	1.10021i
$437$	−8.92389	−	15.4566i	−0.426888	−	0.739391i
$438$		0			0
$439$	14.4634	−	25.0513i	0.690299	−	1.19563i	−0.281441	−	0.959578i	$-0.590812\pi$
$439$	14.4634	−	25.0513i	0.690299	−	1.19563i	0.971740	−	0.236054i	$-0.0758542\pi$
$440$	−1.03590			−0.0493845
$441$		0			0
$442$	−0.597272			−0.0284093
$443$	−12.6006	+	21.8249i	−0.598673	+	1.03693i	0.394344	+	0.918963i	$0.370972\pi$
$443$	−12.6006	+	21.8249i	−0.598673	+	1.03693i	−0.993017	+	0.117969i	$0.962362\pi$
$444$		0			0
$445$	2.13433	+	3.69676i	0.101177	+	0.175243i
$446$	−0.441247	−	0.764262i	−0.0208936	−	0.0361889i
$447$		0			0
$448$	−10.5901	+	18.3426i	−0.500336	+	0.866607i
$449$	21.5777			1.01832			0.509158	−	0.860673i	$-0.329957\pi$
$449$	21.5777			1.01832			0.509158	+	0.860673i	$0.329957\pi$
$450$		0			0
$451$	−35.2794			−1.66124
$452$	−0.271918	+	0.470975i	−0.0127899	+	0.0221528i
$453$		0			0
$454$	−9.64477	−	16.7052i	−0.452651	−	0.784015i
$455$	−1.51414	−	2.62256i	−0.0709839	−	0.122948i
$456$		0			0
$457$	−0.247288	+	0.428315i	−0.0115676	+	0.0200357i	−0.871751	−	0.489949i	$-0.837016\pi$
$457$	−0.247288	+	0.428315i	−0.0115676	+	0.0200357i	0.860184	+	0.509984i	$0.170349\pi$
$458$	5.63649			0.263376
$459$		0			0
$460$	−5.54036			−0.258320
$461$	6.81679	−	11.8070i	0.317490	−	0.549908i	−0.662474	−	0.749085i	$-0.730493\pi$
$461$	6.81679	−	11.8070i	0.317490	−	0.549908i	0.979964	+	0.199177i	$0.0638267\pi$
$462$		0			0
$463$	−10.3778	−	17.9749i	−0.482297	−	0.835363i	0.517496	−	0.855686i	$-0.326864\pi$
$463$	−10.3778	−	17.9749i	−0.482297	−	0.835363i	−0.999793	+	0.0203221i	$0.993531\pi$
$464$	−18.7903	−	32.5458i	−0.872320	−	1.51090i
$465$		0			0
$466$	−15.2684	+	26.4457i	−0.707296	+	1.22507i
$467$	34.9625			1.61787			0.808935	−	0.587898i	$-0.200044\pi$
$467$	34.9625			1.61787			0.808935	+	0.587898i	$0.200044\pi$
$468$		0			0
$469$	47.9415			2.21373
$470$	−6.78257	+	11.7478i	−0.312857	+	0.541884i
$471$		0			0
$472$	−1.10122	−	1.90737i	−0.0506877	−	0.0877937i
$473$	−6.26378	−	10.8492i	−0.288009	−	0.498846i
$474$		0			0
$475$	3.02455	−	5.23867i	0.138776	−	0.240366i
$476$	−1.72472			−0.0790526
$477$		0			0
$478$	14.3380			0.655803
$479$	15.2877	−	26.4791i	0.698512	−	1.20986i	−0.270470	−	0.962728i	$-0.587179\pi$
$479$	15.2877	−	26.4791i	0.698512	−	1.20986i	0.968982	−	0.247131i	$-0.0794877\pi$
$480$		0			0
$481$	5.55223	+	9.61674i	0.253160	+	0.438486i
$482$	−10.8195	−	18.7398i	−0.492812	−	0.853576i
$483$		0			0
$484$	−7.06414	+	12.2355i	−0.321097	+	0.556157i
$485$	5.83707			0.265048
$486$		0			0
$487$	38.2764			1.73447			0.867235	−	0.497899i	$-0.165895\pi$
$487$	38.2764			1.73447			0.867235	+	0.497899i	$0.165895\pi$
$488$	0.158138	−	0.273903i	0.00715857	−	0.0123990i
$489$		0			0
$490$	−2.13704	−	3.70146i	−0.0965416	−	0.167215i
$491$	3.30374	+	5.72225i	0.149096	+	0.258241i	0.930894	−	0.365291i	$-0.119030\pi$
$491$	3.30374	+	5.72225i	0.149096	+	0.258241i	−0.781798	+	0.623532i	$0.785697\pi$
$492$		0			0
$493$	1.34749	−	2.33392i	0.0606879	−	0.105114i
$494$	11.9119			0.535942
$495$		0			0
$496$	−0.270644			−0.0121523
$497$	4.32143	−	7.48494i	0.193843	−	0.335746i
$498$		0			0
$499$	11.0238	+	19.0937i	0.493491	+	0.854752i	0.999972	−	0.00749916i	$-0.00238708\pi$
$499$	11.0238	+	19.0937i	0.493491	+	0.854752i	−0.506480	+	0.862251i	$0.669054\pi$
$500$	−0.938888	−	1.62620i	−0.0419883	−	0.0727259i
$501$		0			0
$502$	9.39153	−	16.2666i	0.419164	−	0.726014i
$503$	16.8779			0.752550			0.376275	−	0.926508i	$-0.377205\pi$
$503$	16.8779			0.752550			0.376275	+	0.926508i	$0.377205\pi$
$504$		0			0
$505$	−10.6489			−0.473868
$506$	12.5032	−	21.6562i	0.555836	−	0.962737i
$507$		0			0
$508$	−4.41660	−	7.64977i	−0.195955	−	0.339404i
$509$	−11.4775	−	19.8797i	−0.508732	−	0.881150i	−0.999949	−	0.0101129i	$-0.996781\pi$
$509$	−11.4775	−	19.8797i	−0.508732	−	0.881150i	0.491216	−	0.871038i	$-0.336552\pi$
$510$		0			0
$511$	−17.0823	+	29.5875i	−0.755678	+	1.30887i
$512$	31.1547			1.37686
$513$		0			0
$514$	−1.47907			−0.0652390
$515$	8.95821	−	15.5161i	0.394746	−	0.683720i
$516$		0			0
$517$	−14.8242	−	25.6762i	−0.651966	−	1.12924i
$518$	33.1096	+	57.3475i	1.45475	+	2.51971i
$519$		0			0
$520$	−0.120343	+	0.208440i	−0.00527739	+	0.00914070i
$521$	−10.6723			−0.467562			−0.233781	−	0.972289i	$-0.575110\pi$
$521$	−10.6723			−0.467562			−0.233781	+	0.972289i	$0.575110\pi$
$522$		0			0
$523$	−2.51360			−0.109912			−0.0549559	−	0.998489i	$-0.517502\pi$
$523$	−2.51360			−0.109912			−0.0549559	+	0.998489i	$0.517502\pi$
$524$	−20.7364	+	35.9164i	−0.905872	+	1.56902i
$525$		0			0
$526$	20.5167	+	35.5360i	0.894571	+	1.54944i
$527$	−0.00970419	−	0.0168082i	−0.000422721	−	0.000732175i
$528$		0			0
$529$	7.14730	−	12.3795i	0.310752	−	0.538239i
$530$	−23.2950			−1.01187
$531$		0			0
$532$	34.3977			1.49133
$533$	−4.09849	+	7.09879i	−0.177525	+	0.307483i
$534$		0			0
$535$	−0.560948	−	0.971590i	−0.0242519	−	0.0420055i
$536$	−1.90518	−	3.29987i	−0.0822913	−	0.142533i
$537$		0			0
$538$	−15.2795	+	26.4649i	−0.658747	+	1.14098i
$539$	9.34153			0.402368
$540$		0			0
$541$	−10.6855			−0.459404			−0.229702	−	0.973261i	$-0.573775\pi$
$541$	−10.6855			−0.459404			−0.229702	+	0.973261i	$0.573775\pi$
$542$	−0.967888	+	1.67643i	−0.0415744	+	0.0720089i
$543$		0			0
$544$	1.19008	+	2.06128i	0.0510244	+	0.0883768i
$545$	−7.06341	−	12.2342i	−0.302563	−	0.524055i
$546$		0			0
$547$	6.06138	−	10.4986i	0.259166	−	0.448889i	−0.706853	−	0.707361i	$-0.749886\pi$
$547$	6.06138	−	10.4986i	0.259166	−	0.448889i	0.966019	+	0.258472i	$0.0832190\pi$
$548$	4.07255			0.173971
$549$		0			0
$550$	8.47536			0.361391
$551$	−26.8742	+	46.5474i	−1.14488	+	1.98299i
$552$		0			0
$553$	15.6859	+	27.1687i	0.667030	+	1.15533i
$554$	−23.9085	−	41.4107i	−1.01577	−	1.75937i
$555$		0			0
$556$	1.13874	−	1.97236i	0.0482935	−	0.0836468i
$557$	−13.7918			−0.584377			−0.292189	−	0.956361i	$-0.594383\pi$
$557$	−13.7918			−0.584377			−0.292189	+	0.956361i	$0.594383\pi$
$558$		0			0
$559$	−2.91072			−0.123110
$560$	−6.40406	+	11.0922i	−0.270621	+	0.468729i
$561$		0			0
$562$	−2.99363	−	5.18512i	−0.126279	−	0.218721i
$563$	−5.37453	−	9.30896i	−0.226509	−	0.392326i	0.730262	−	0.683167i	$-0.239398\pi$
$563$	−5.37453	−	9.30896i	−0.226509	−	0.392326i	−0.956771	+	0.290842i	$0.906065\pi$
$564$		0			0
$565$	−0.144808	+	0.250816i	−0.00609214	+	0.0105519i
$566$	−49.7457			−2.09097
$567$		0			0
$568$	−0.686931			−0.0288230
$569$	5.63062	−	9.75252i	0.236048	−	0.408847i	−0.723529	−	0.690294i	$-0.757481\pi$
$569$	5.63062	−	9.75252i	0.236048	−	0.408847i	0.959577	+	0.281447i	$0.0908145\pi$
$570$		0			0
$571$	−12.9908	−	22.5007i	−0.543648	−	0.941627i	−0.998691	−	0.0511568i	$-0.983709\pi$
$571$	−12.9908	−	22.5007i	−0.543648	−	0.941627i	0.455042	−	0.890470i	$-0.349624\pi$
$572$	4.04092	+	6.99908i	0.168959	+	0.292646i
$573$		0			0
$574$	−24.4405	+	42.3322i	−1.02013	+	1.76691i
$575$	−2.95049			−0.123044
$576$		0			0
$577$	5.83579			0.242947			0.121474	−	0.992595i	$-0.461238\pi$
$577$	5.83579			0.242947			0.121474	+	0.992595i	$0.461238\pi$
$578$	16.6477	−	28.8346i	0.692452	−	1.19936i
$579$		0			0
$580$	8.34235	+	14.4494i	0.346397	+	0.599977i
$581$	10.7039	+	18.5396i	0.444071	+	0.769153i
$582$		0			0
$583$	25.4571	−	44.0929i	1.05432	−	1.82614i
$584$	2.71539			0.112364
$585$		0			0
$586$	52.0101			2.14852
$587$	−5.70440	+	9.88032i	−0.235446	+	0.407804i	−0.959402	−	0.282042i	$-0.908988\pi$
$587$	−5.70440	+	9.88032i	−0.235446	+	0.407804i	0.723956	+	0.689846i	$0.242322\pi$
$588$		0			0
$589$	0.193539	+	0.335220i	0.00797464	+	0.0138125i
$590$	9.00979	+	15.6054i	0.370927	+	0.642465i
$591$		0			0
$592$	23.4832	−	40.6741i	0.965154	−	1.67170i
$593$	21.1795			0.869737			0.434869	−	0.900494i	$-0.356795\pi$
$593$	21.1795			0.869737			0.434869	+	0.900494i	$0.356795\pi$
$594$		0			0
$595$	−0.918494			−0.0376546
$596$	5.51146	−	9.54613i	0.225758	−	0.391025i
$597$		0			0
$598$	−2.90506	−	5.03172i	−0.118797	−	0.205762i
$599$	−7.41622	−	12.8453i	−0.303019	−	0.524844i	0.673800	−	0.738914i	$-0.264661\pi$
$599$	−7.41622	−	12.8453i	−0.303019	−	0.524844i	−0.976818	+	0.214071i	$0.931328\pi$
$600$		0			0
$601$	−6.60333	+	11.4373i	−0.269355	+	0.466537i	−0.968695	−	0.248252i	$-0.920144\pi$
$601$	−6.60333	+	11.4373i	−0.269355	+	0.466537i	0.699340	+	0.714789i	$0.253477\pi$
$602$	−17.3575			−0.707438
$603$		0			0
$604$	−17.4717			−0.710912
$605$	−3.76198	+	6.51593i	−0.152946	+	0.264910i
$606$		0			0
$607$	16.7152	+	28.9516i	0.678451	+	1.17511i	0.975447	+	0.220233i	$0.0706816\pi$
$607$	16.7152	+	28.9516i	0.678451	+	1.17511i	−0.296997	+	0.954879i	$0.595985\pi$
$608$	−23.7348	−	41.1100i	−0.962575	−	1.66723i
$609$		0			0
$610$	−1.29383	+	2.24098i	−0.0523856	+	0.0907345i
$611$	−6.88864			−0.278684
$612$		0			0
$613$	−33.4817			−1.35231			−0.676157	−	0.736758i	$-0.736356\pi$
$613$	−33.4817			−1.35231			−0.676157	+	0.736758i	$0.736356\pi$
$614$	15.0881	−	26.1333i	0.608904	−	1.05465i
$615$		0			0
$616$	−1.56849	−	2.71671i	−0.0631964	−	0.109459i
$617$	−19.0566	−	33.0071i	−0.767191	−	1.32881i	−0.939080	−	0.343698i	$-0.888320\pi$
$617$	−19.0566	−	33.0071i	−0.767191	−	1.32881i	0.171889	−	0.985116i	$-0.445013\pi$
$618$		0			0
$619$	−21.3997	+	37.0653i	−0.860126	+	1.48978i	0.0116814	+	0.999932i	$0.496282\pi$
$619$	−21.3997	+	37.0653i	−0.860126	+	1.48978i	−0.871807	+	0.489849i	$0.837052\pi$
$620$	0.120158			0.00482566
$621$		0			0
$622$	−5.73615			−0.229999
$623$	−6.46333	+	11.1948i	−0.258948	+	0.448511i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	10.7234	+	18.5735i	0.428594	+	0.742347i
$627$		0			0
$628$	17.1765	−	29.7506i	0.685418	−	1.18718i
$629$	3.36805			0.134293
$630$		0			0
$631$	−34.5751			−1.37641			−0.688206	−	0.725516i	$-0.741601\pi$
$631$	−34.5751			−1.37641			−0.688206	+	0.725516i	$0.741601\pi$
$632$	1.24670	−	2.15935i	0.0495912	−	0.0858945i
$633$		0			0
$634$	−8.09807	−	14.0263i	−0.321616	−	0.557054i
$635$	−2.35204	−	4.07385i	−0.0933378	−	0.161666i
$636$		0			0
$637$	1.08523	−	1.87967i	0.0429983	−	0.0744753i
$638$	−75.3066			−2.98142
$639$		0			0
$640$	1.92189			0.0759694
$641$	−10.5943	+	18.3499i	−0.418452	+	0.724779i	−0.995784	−	0.0917298i	$-0.970760\pi$
$641$	−10.5943	+	18.3499i	−0.418452	+	0.724779i	0.577332	+	0.816509i	$0.304094\pi$
$642$		0			0
$643$	−12.9509	−	22.4316i	−0.510732	−	0.884614i	−0.999923	−	0.0124372i	$-0.996041\pi$
$643$	−12.9509	−	22.4316i	−0.510732	−	0.884614i	0.489190	−	0.872177i	$-0.337292\pi$
$644$	−8.38887	−	14.5299i	−0.330568	−	0.572560i
$645$		0			0
$646$	1.80648	−	3.12891i	0.0710748	−	0.123105i
$647$	31.6341			1.24366			0.621832	−	0.783151i	$-0.286389\pi$
$647$	31.6341			1.24366			0.621832	+	0.783151i	$0.286389\pi$
$648$		0			0
$649$	−39.3840			−1.54596
$650$	0.984603	−	1.70538i	0.0386193	−	0.0668906i
$651$		0			0
$652$	11.2220	+	19.4370i	0.439487	+	0.761213i
$653$	−8.56340	−	14.8322i	−0.335112	−	0.580430i	0.648395	−	0.761304i	$-0.275441\pi$
$653$	−8.56340	−	14.8322i	−0.335112	−	0.580430i	−0.983506	+	0.180874i	$0.942107\pi$
$654$		0			0
$655$	−11.0430	+	19.1271i	−0.431488	+	0.747358i
$656$	34.6692			1.35361
$657$		0			0
$658$	−41.0790			−1.60143
$659$	19.3254	−	33.4726i	0.752812	−	1.30391i	−0.193643	−	0.981072i	$-0.562030\pi$
$659$	19.3254	−	33.4726i	0.752812	−	1.30391i	0.946455	−	0.322836i	$-0.104636\pi$
$660$		0			0
$661$	22.1320	+	38.3338i	0.860836	+	1.49101i	0.871123	+	0.491064i	$0.163392\pi$
$661$	22.1320	+	38.3338i	0.860836	+	1.49101i	−0.0102873	+	0.999947i	$0.503275\pi$
$662$	−17.7723	−	30.7825i	−0.690740	−	1.19640i
$663$		0			0
$664$	0.850737	−	1.47352i	0.0330150	−	0.0571836i
$665$	18.3183			0.710354
$666$		0			0
$667$	26.2161			1.01509
$668$	12.5152	−	21.6770i	0.484227	−	0.838707i
$669$		0			0
$670$	15.5875	+	26.9984i	0.602199	+	1.04304i
$671$	−2.82782	−	4.89793i	−0.109167	−	0.189083i
$672$		0			0
$673$	14.2308	−	24.6485i	0.548557	−	0.950129i	−0.449817	−	0.893121i	$-0.648511\pi$
$673$	14.2308	−	24.6485i	0.548557	−	0.950129i	0.998374	−	0.0570078i	$-0.0181560\pi$
$674$	72.0817			2.77648
$675$		0			0
$676$	1.87778			0.0722221
$677$	−6.81855	+	11.8101i	−0.262058	+	0.453898i	−0.966789	−	0.255577i	$-0.917735\pi$
$677$	−6.81855	+	11.8101i	−0.262058	+	0.453898i	0.704730	+	0.709475i	$0.251068\pi$
$678$		0			0
$679$	8.83814	+	15.3081i	0.339177	+	0.587471i
$680$	0.0365007	+	0.0632211i	0.00139974	+	0.00242442i
$681$		0			0
$682$	−0.271167	+	0.469675i	−0.0103835	+	0.0179848i
$683$	−47.3362			−1.81127			−0.905636	−	0.424057i	$-0.860606\pi$
$683$	−47.3362			−1.81127			−0.905636	+	0.424057i	$0.860606\pi$
$684$		0			0
$685$	2.16882			0.0828663
$686$	−14.4000	+	24.9415i	−0.549795	+	0.952273i
$687$		0			0
$688$	6.15545	+	10.6616i	0.234674	+	0.406468i
$689$	−5.91482	−	10.2448i	−0.225337	−	0.390295i
$690$		0			0
$691$	−8.31169	+	14.3963i	−0.316191	+	0.547660i	−0.979690	−	0.200518i	$-0.935738\pi$
$691$	−8.31169	+	14.3963i	−0.316191	+	0.547660i	0.663499	+	0.748178i	$0.269071\pi$
$692$	31.1212			1.18305
$693$		0			0
$694$	−11.4791			−0.435743
$695$	0.606433	−	1.05037i	0.0230033	−	0.0398429i
$696$		0			0
$697$	1.24310	+	2.15310i	0.0470856	+	0.0815546i
$698$	−2.97067	−	5.14534i	−0.112441	−	0.194754i
$699$		0			0
$700$	2.84321	−	4.92459i	0.107463	−	0.186132i
$701$	−21.7166			−0.820223			−0.410111	−	0.912035i	$-0.634510\pi$
$701$	−21.7166			−0.820223			−0.410111	+	0.912035i	$0.634510\pi$
$702$		0			0
$703$	−67.1719			−2.53343
$704$	15.0512	−	26.0695i	0.567264	−	0.982530i
$705$		0			0
$706$	−9.21770	−	15.9655i	−0.346913	−	0.600870i
$707$	−16.1239	−	27.9273i	−0.606400	−	1.05032i
$708$		0			0
$709$	20.1493	−	34.8996i	0.756723	−	1.31068i	−0.187790	−	0.982209i	$-0.560132\pi$
$709$	20.1493	−	34.8996i	0.756723	−	1.31068i	0.944513	−	0.328474i	$-0.106534\pi$
$710$	5.62022			0.210923
$711$		0			0
$712$	1.02740			0.0385036
$713$	0.0944002	−	0.163506i	0.00353531	−	0.00612334i
$714$		0			0
$715$	2.15197	+	3.72733i	0.0804792	+	0.139394i
$716$	12.7112	+	22.0165i	0.475041	+	0.822795i
$717$		0			0
$718$	5.14531	−	8.91194i	0.192021	−	0.332591i
$719$	−42.5521			−1.58693			−0.793463	−	0.608619i	$-0.791724\pi$
$719$	−42.5521			−1.58693			−0.793463	+	0.608619i	$0.791724\pi$
$720$		0			0
$721$	54.2559			2.02060
$722$	−17.3206	+	30.0002i	−0.644608	+	1.11649i
$723$		0			0
$724$	3.37345	+	5.84299i	0.125373	+	0.217153i
$725$	4.44268	+	7.69494i	0.164997	+	0.285783i
$726$		0			0
$727$	11.3584	−	19.6733i	0.421259	−	0.729641i	−0.574804	−	0.818291i	$-0.694922\pi$
$727$	11.3584	−	19.6733i	0.421259	−	0.729641i	0.996063	+	0.0886497i	$0.0282552\pi$
$728$	−0.728863			−0.0270135
$729$		0			0
$730$	−22.2164			−0.822265
$731$	−0.441419	+	0.764559i	−0.0163265	+	0.0282782i
$732$		0			0
$733$	14.2542	+	24.6889i	0.526490	+	0.911907i	0.999524	+	0.0308627i	$0.00982547\pi$
$733$	14.2542	+	24.6889i	0.526490	+	0.911907i	−0.473034	+	0.881044i	$0.656841\pi$
$734$	4.23540	+	7.33593i	0.156332	+	0.270774i
$735$		0			0
$736$	−11.5769	+	20.0517i	−0.426728	+	0.739115i
$737$	−68.1370			−2.50986
$738$		0			0
$739$	−10.2174			−0.375852			−0.187926	−	0.982183i	$-0.560177\pi$
$739$	−10.2174			−0.375852			−0.187926	+	0.982183i	$0.560177\pi$
$740$	−10.4258	+	18.0581i	−0.383261	+	0.663828i
$741$		0			0
$742$	−35.2719	−	61.0927i	−1.29487	−	2.24278i
$743$	26.3337	+	45.6113i	0.966090	+	1.67332i	0.706657	+	0.707556i	$0.250202\pi$
$743$	26.3337	+	45.6113i	0.966090	+	1.67332i	0.259433	+	0.965761i	$0.416464\pi$
$744$		0			0
$745$	2.93510	−	5.08374i	0.107534	−	0.186254i
$746$	52.2431			1.91276
$747$		0			0
$748$	2.45127			0.0896273
$749$	1.69870	−	2.94224i	0.0620693	−	0.107507i
$750$		0			0
$751$	−0.0215941	−	0.0374020i	−0.000787978	−	0.00136482i	0.865631	−	0.500682i	$-0.166917\pi$
$751$	−0.0215941	−	0.0374020i	−0.000787978	−	0.00136482i	−0.866419	+	0.499317i	$0.833584\pi$
$752$	14.5678	+	25.2321i	0.531232	+	0.920121i
$753$		0			0
$754$	−8.74855	+	15.1529i	−0.318603	+	0.551837i
$755$	−9.30445			−0.338624
$756$		0			0
$757$	−20.9410			−0.761113			−0.380557	−	0.924758i	$-0.624268\pi$
$757$	−20.9410			−0.761113			−0.380557	+	0.924758i	$0.624268\pi$
$758$	3.42730	−	5.93626i	0.124485	−	0.215615i
$759$		0			0
$760$	−0.727965	−	1.26087i	−0.0264061	−	0.0457367i
$761$	7.61100	+	13.1826i	0.275899	+	0.477870i	0.970361	−	0.241658i	$-0.0776913\pi$
$761$	7.61100	+	13.1826i	0.275899	+	0.477870i	−0.694463	+	0.719529i	$0.744358\pi$
$762$		0			0
$763$	21.3900	−	37.0485i	0.774369	−	1.34125i
$764$	−38.5721			−1.39549
$765$		0			0
$766$	−48.5165			−1.75297
$767$	−4.57534	+	7.92472i	−0.165206	+	0.286145i
$768$		0			0
$769$	8.12917	+	14.0801i	0.293145	+	0.507743i	0.974552	−	0.224163i	$-0.0719647\pi$
$769$	8.12917	+	14.0801i	0.293145	+	0.507743i	−0.681406	+	0.731905i	$0.738631\pi$
$770$	12.8329	+	22.2272i	0.462464	+	0.801012i
$771$		0			0
$772$	1.43300	−	2.48202i	0.0515746	−	0.0893299i
$773$	−14.6825			−0.528093			−0.264047	−	0.964510i	$-0.585057\pi$
$773$	−14.6825			−0.528093			−0.264047	+	0.964510i	$0.585057\pi$
$774$		0			0
$775$	0.0639895			0.00229857
$776$	0.702451	−	1.21668i	0.0252165	−	0.0436763i
$777$		0			0
$778$	−18.1355	−	31.4116i	−0.650188	−	1.12616i
$779$	−24.7921	−	42.9412i	−0.888270	−	1.53853i
$780$		0			0
$781$	−6.14185	+	10.6380i	−0.219773	+	0.380657i
$782$	−1.76224			−0.0630177
$783$		0			0
$784$	−9.17997			−0.327856
$785$	9.14727	−	15.8435i	0.326480	−	0.565480i
$786$		0			0
$787$	9.34140	+	16.1798i	0.332985	+	0.576747i	0.983096	−	0.183093i	$-0.0586108\pi$
$787$	9.34140	+	16.1798i	0.332985	+	0.576747i	−0.650111	+	0.759840i	$0.725277\pi$
$788$	−1.01211	−	1.75302i	−0.0360548	−	0.0624488i
$789$		0			0
$790$	−10.2001	+	17.6671i	−0.362903	+	0.628566i
$791$	−0.877040			−0.0311839
$792$		0			0
$793$	−1.31406			−0.0466637
$794$	−14.8888	+	25.7882i	−0.528385	+	0.915190i
$795$		0			0
$796$	−1.88024	−	3.25668i	−0.0666435	−	0.115430i
$797$	−11.1340	−	19.2846i	−0.394385	−	0.683095i	0.598637	−	0.801020i	$-0.295709\pi$
$797$	−11.1340	−	19.2846i	−0.394385	−	0.683095i	−0.993022	+	0.117925i	$0.962376\pi$
$798$		0			0
$799$	−1.04468	+	1.80944i	−0.0369582	+	0.0640134i
$800$	−7.84741			−0.277448
$801$		0			0
$802$	−0.542150			−0.0191440
$803$	24.2783	−	42.0513i	0.856764	−	1.48396i
$804$		0			0
$805$	−4.46745	−	7.73785i	−0.157457	−	0.272723i
$806$	0.0630043	+	0.109127i	0.00221923	+	0.00384382i
$807$		0			0
$808$	−1.28152	+	2.21965i	−0.0450836	+	0.0780870i
$809$	10.6028			0.372776			0.186388	−	0.982476i	$-0.440322\pi$
$809$	10.6028			0.372776			0.186388	+	0.982476i	$0.440322\pi$
$810$		0			0
$811$	−29.8215			−1.04718			−0.523588	−	0.851972i	$-0.675407\pi$
$811$	−29.8215			−1.04718			−0.523588	+	0.851972i	$0.675407\pi$
$812$	−25.2629	+	43.7567i	−0.886555	+	1.53556i
$813$		0			0
$814$	−47.0571	−	81.5053i	−1.64935	−	2.85676i
$815$	5.97621	+	10.3511i	0.209338	+	0.362583i
$816$		0			0
$817$	8.80359	−	15.2483i	0.307999	−	0.533469i
$818$	−24.7185			−0.864262
$819$		0			0
$820$	−15.3921			−0.537515
$821$	9.61358	−	16.6512i	0.335516	−	0.581131i	−0.648067	−	0.761583i	$-0.724423\pi$
$821$	9.61358	−	16.6512i	0.335516	−	0.581131i	0.983584	+	0.180451i	$0.0577559\pi$
$822$		0			0
$823$	−6.02944	−	10.4433i	−0.210173	−	0.364030i	0.741595	−	0.670847i	$-0.234069\pi$
$823$	−6.02944	−	10.4433i	−0.210173	−	0.364030i	−0.951769	+	0.306817i	$0.900736\pi$
$824$	−2.15612	−	3.73450i	−0.0751118	−	0.130098i
$825$		0			0
$826$	−27.2841	+	47.2575i	−0.949336	+	1.64430i
$827$	−12.5315			−0.435765			−0.217882	−	0.975975i	$-0.569915\pi$
$827$	−12.5315			−0.435765			−0.217882	+	0.975975i	$0.569915\pi$
$828$		0			0
$829$	−44.7564			−1.55445			−0.777227	−	0.629220i	$-0.783374\pi$
$829$	−44.7564			−1.55445			−0.777227	+	0.629220i	$0.783374\pi$
$830$	−6.96043	+	12.0558i	−0.241600	+	0.418463i
$831$		0			0
$832$	−3.49707	−	6.05711i	−0.121239	−	0.209993i
$833$	−0.329156	−	0.570115i	−0.0114046	−	0.0197533i
$834$		0			0
$835$	6.66491	−	11.5440i	0.230649	−	0.399495i
$836$	−48.8878			−1.69082
$837$		0			0
$838$	−45.0361			−1.55575
$839$	−9.95639	+	17.2450i	−0.343733	+	0.595363i	−0.985123	−	0.171852i	$-0.945025\pi$
$839$	−9.95639	+	17.2450i	−0.343733	+	0.595363i	0.641390	+	0.767215i	$0.278358\pi$
$840$		0			0
$841$	−24.9748	−	43.2575i	−0.861198	−	1.49164i
$842$	24.5912	+	42.5932i	0.847469	+	1.46786i
$843$		0			0
$844$	0.220846	−	0.382516i	0.00760183	−	0.0131668i
$845$	1.00000			0.0344010
$846$		0			0
$847$	−22.7846			−0.782888
$848$	−25.0168	+	43.3304i	−0.859081	+	1.48797i
$849$		0			0
$850$	−0.298636	−	0.517253i	−0.0102431	−	0.0177416i
$851$	16.3818	+	28.3741i	0.561561	+	0.972652i
$852$		0			0
$853$	1.60989	−	2.78841i	0.0551215	−	0.0954732i	−0.837148	−	0.546976i	$-0.815779\pi$
$853$	1.60989	−	2.78841i	0.0551215	−	0.0954732i	0.892269	+	0.451503i	$0.149112\pi$
$854$	−7.83614			−0.268147
$855$		0			0
$856$	−0.270024			−0.00922924
$857$	−1.58737	+	2.74941i	−0.0542236	+	0.0939180i	−0.891863	−	0.452305i	$-0.850602\pi$
$857$	−1.58737	+	2.74941i	−0.0542236	+	0.0939180i	0.837640	+	0.546223i	$0.183935\pi$
$858$		0			0
$859$	−12.8326	−	22.2268i	−0.437844	−	0.758368i	0.559679	−	0.828709i	$-0.310924\pi$
$859$	−12.8326	−	22.2268i	−0.437844	−	0.758368i	−0.997523	+	0.0703416i	$0.977591\pi$
$860$	−2.73284	−	4.73341i	−0.0931889	−	0.161408i
$861$		0			0
$862$	−33.9306	+	58.7696i	−1.15568	+	2.00170i
$863$	40.8808			1.39160			0.695799	−	0.718236i	$-0.255050\pi$
$863$	40.8808			1.39160			0.695799	+	0.718236i	$0.255050\pi$
$864$		0			0
$865$	16.5734			0.563514
$866$	−15.4173	+	26.7036i	−0.523902	+	0.907424i
$867$		0			0
$868$	0.181936	+	0.315122i	0.00617530	+	0.0106959i
$869$	−22.2936	−	38.6136i	−0.756257	−	1.30988i
$870$		0			0
$871$	−7.91564	+	13.7103i	−0.268211	+	0.464555i
$872$	−3.40013			−0.115143
$873$		0			0
$874$	35.1460			1.18883
$875$	1.51414	−	2.62256i	0.0511872	−	0.0886589i
$876$		0			0
$877$	−24.7475	−	42.8639i	−0.835663	−	1.44741i	−0.893489	−	0.449084i	$-0.851750\pi$
$877$	−24.7475	−	42.8639i	−0.835663	−	1.44741i	0.0578261	−	0.998327i	$-0.481583\pi$
$878$	28.4814	+	49.3311i	0.961199	+	1.66485i
$879$		0			0
$880$	9.10179	−	15.7648i	0.306821	−	0.531430i
$881$	46.0194			1.55043			0.775216	−	0.631696i	$-0.217641\pi$
$881$	46.0194			1.55043			0.775216	+	0.631696i	$0.217641\pi$
$882$		0			0
$883$	−23.7208			−0.798267			−0.399134	−	0.916893i	$-0.630689\pi$
$883$	−23.7208			−0.798267			−0.399134	+	0.916893i	$0.630689\pi$
$884$	0.284770	−	0.493236i	0.00957785	−	0.0165893i
$885$		0			0
$886$	−24.8132	−	42.9777i	−0.833616	−	1.44387i
$887$	27.1668	+	47.0542i	0.912170	+	1.57993i	0.810992	+	0.585057i	$0.198928\pi$
$887$	27.1668	+	47.0542i	0.912170	+	1.57993i	0.101178	+	0.994868i	$0.467739\pi$
$888$		0			0
$889$	7.12262	−	12.3367i	0.238885	−	0.413761i
$890$	−8.40586			−0.281765
$891$		0			0
$892$	0.841519			0.0281761
$893$	20.8350	−	36.0873i	0.697216	−	1.20761i
$894$		0			0
$895$	6.76930	+	11.7248i	0.226273	+	0.391916i
$896$	2.91001	+	5.04028i	0.0972166	+	0.168384i
$897$		0			0
$898$	−21.2455	+	36.7983i	−0.708972	+	1.22798i
$899$	−0.568569			−0.0189628
$900$		0			0
$901$	−3.58800			−0.119534
$902$	34.7362	−	60.1648i	1.15659	−	2.00327i
$903$		0			0
$904$	0.0348533	+	0.0603678i	0.00115920	+	0.00200780i
$905$	1.79651	+	3.11165i	0.0597182	+	0.103435i
$906$		0			0
$907$	−21.4464	+	37.1462i	−0.712116	+	1.23342i	0.251946	+	0.967741i	$0.418930\pi$
$907$	−21.4464	+	37.1462i	−0.712116	+	1.23342i	−0.964061	+	0.265679i	$0.914404\pi$
$908$	18.3939			0.610423
$909$		0			0
$910$	5.96330			0.197682
$911$	13.5606	−	23.4877i	0.449284	−	0.778183i	−0.549056	−	0.835786i	$-0.685012\pi$
$911$	13.5606	−	23.4877i	0.449284	−	0.778183i	0.998340	+	0.0576032i	$0.0183458\pi$
$912$		0			0
$913$	−15.2129	−	26.3495i	−0.503473	−	0.872040i
$914$	−0.486961	−	0.843441i	−0.0161072	−	0.0278986i
$915$		0			0
$916$	−2.68739	+	4.65470i	−0.0887939	+	0.153796i
$917$	−66.8828			−2.20866
$918$		0			0
$919$	2.27072			0.0749043			0.0374522	−	0.999298i	$-0.488076\pi$
$919$	2.27072			0.0749043			0.0374522	+	0.999298i	$0.488076\pi$
$920$	−0.355071	+	0.615000i	−0.0117063	+	0.0202760i
$921$		0			0
$922$	13.4237	+	23.2505i	0.442085	+	0.765714i
$923$	1.42703	+	2.47168i	0.0469712	+	0.0813565i
$924$		0			0
$925$	−5.55223	+	9.61674i	−0.182556	+	0.316197i
$926$	40.8721			1.34314
$927$		0			0
$928$	69.7270			2.28890
$929$	0.235938	−	0.408657i	0.00774088	−	0.0134076i	−0.862129	−	0.506689i	$-0.830869\pi$
$929$	0.235938	−	0.408657i	0.00774088	−	0.0134076i	0.869870	+	0.493281i	$0.164203\pi$
$930$		0			0
$931$	6.56465	+	11.3703i	0.215148	+	0.372647i
$932$	−14.5595	−	25.2178i	−0.476912	−	0.826036i
$933$		0			0
$934$	−34.4242	+	59.6244i	−1.12639	+	1.95097i
$935$	1.30541			0.0426915
$936$		0			0
$937$	44.6044			1.45716			0.728581	−	0.684960i	$-0.240180\pi$
$937$	44.6044			1.45716			0.728581	+	0.684960i	$0.240180\pi$
$938$	−47.2033	+	81.7586i	−1.54124	+	2.66951i
$939$		0			0
$940$	−6.46765	−	11.2023i	−0.210952	−	0.365379i
$941$	11.2513	+	19.4878i	0.366781	+	0.635283i	0.989060	−	0.147512i	$-0.0471265\pi$
$941$	11.2513	+	19.4878i	0.366781	+	0.635283i	−0.622279	+	0.782795i	$0.713793\pi$
$942$		0			0
$943$	−12.0926	+	20.9449i	−0.393788	+	0.682060i
$944$	38.7029			1.25967
$945$		0			0
$946$	24.6694			0.802070
$947$	−7.13395	+	12.3564i	−0.231822	+	0.401528i	−0.958344	−	0.285615i	$-0.907802\pi$
$947$	−7.13395	+	12.3564i	−0.231822	+	0.401528i	0.726522	+	0.687143i	$0.241135\pi$
$948$		0			0
$949$	−5.64095	−	9.77041i	−0.183113	−	0.317161i
$950$	5.95595	+	10.3160i	0.193237	+	0.334696i
$951$		0			0
$952$	−0.110534	+	0.191451i	−0.00358243	+	0.00620496i
$953$	49.4934			1.60325			0.801624	−	0.597829i	$-0.203970\pi$
$953$	49.4934			1.60325			0.801624	+	0.597829i	$0.203970\pi$
$954$		0			0
$955$	−20.5414			−0.664704
$956$	−6.83612	+	11.8405i	−0.221096	+	0.382950i
$957$		0			0
$958$	30.1046	+	52.1427i	0.972636	+	1.68466i
$959$	3.28389	+	5.68786i	0.106042	+	0.183671i
$960$		0			0
$961$	15.4980	−	26.8432i	0.499934	−	0.865911i
$962$	−21.8670			−0.705020
$963$		0			0
$964$	20.6342			0.664583
$965$	0.763135	−	1.32179i	0.0245662	−	0.0425499i
$966$		0			0
$967$	−14.6823	−	25.4305i	−0.472151	−	0.817789i	0.527342	−	0.849653i	$-0.323189\pi$
$967$	−14.6823	−	25.4305i	−0.472151	−	0.817789i	−0.999492	+	0.0318645i	$0.989855\pi$
$968$	0.905454	+	1.56829i	0.0291024	+	0.0504068i
$969$		0			0
$970$	−5.74720	+	9.95445i	−0.184532	+	0.319618i
$971$	7.22467			0.231851			0.115925	−	0.993258i	$-0.463017\pi$
$971$	7.22467			0.231851			0.115925	+	0.993258i	$0.463017\pi$
$972$		0			0
$973$	3.67289			0.117748
$974$	−37.6871	+	65.2760i	−1.20757	+	2.09158i
$975$		0			0
$976$	2.77892	+	4.81323i	0.0889510	+	0.154068i
$977$	−20.3574	−	35.2601i	−0.651292	−	1.12807i	−0.982810	−	0.184622i	$-0.940894\pi$
$977$	−20.3574	−	35.2601i	−0.651292	−	1.12807i	0.331518	−	0.943449i	$-0.392439\pi$
$978$		0			0
$979$	9.18602	−	15.9107i	0.293586	−	0.508507i
$980$	4.07563			0.130191
$981$		0			0
$982$	−13.0115			−0.415214
$983$	−17.2643	+	29.9027i	−0.550646	+	0.953747i	0.447582	+	0.894243i	$0.352285\pi$
$983$	−17.2643	+	29.9027i	−0.550646	+	0.953747i	−0.998228	+	0.0595044i	$0.981048\pi$
$984$		0			0
$985$	−0.538993	−	0.933563i	−0.0171737	−	0.0297458i
$986$	2.65349	+	4.59597i	0.0845042	+	0.146366i
$987$		0			0
$988$	−5.67942	+	9.83704i	−0.180686	+	0.312958i
$989$	−8.58804			−0.273084
$990$		0			0
$991$	−14.9325			−0.474346			−0.237173	−	0.971467i	$-0.576221\pi$
$991$	−14.9325			−0.474346			−0.237173	+	0.971467i	$0.576221\pi$
$992$	0.251076	−	0.434876i	0.00797167	−	0.0138073i
$993$		0			0
$994$	8.50980	+	14.7394i	0.269914	+	0.467505i
$995$	−1.00131	−	1.73433i	−0.0317438	−	0.0549819i
$996$		0			0
$997$	−9.74539	+	16.8795i	−0.308640	+	0.534580i	−0.978065	−	0.208300i	$-0.933207\pi$
$997$	−9.74539	+	16.8795i	−0.308640	+	0.534580i	0.669425	+	0.742879i	$0.266540\pi$
$998$	−43.4161			−1.37431
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1755.2.i.f.586.2		16
3.2	odd	2		585.2.i.e.196.7	✓	16
9.2	odd	6		5265.2.a.bf.1.2		8
9.4	even	3	inner	1755.2.i.f.1171.2		16
9.5	odd	6		585.2.i.e.391.7	yes	16
9.7	even	3		5265.2.a.ba.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.e.196.7	✓	16	3.2	odd	2
585.2.i.e.391.7	yes	16	9.5	odd	6
1755.2.i.f.586.2		16	1.1	even	1	trivial
1755.2.i.f.1171.2		16	9.4	even	3	inner
5265.2.a.ba.1.7		8	9.7	even	3
5265.2.a.bf.1.2		8	9.2	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:	\( N \)	\(=\)	\( 1755 = 3^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1755.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.984603 + 1.70538i) q^{2} +(-0.938888 - 1.62620i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.51414 - 2.62256i) q^{7} -0.240686 q^{8} +O(q^{10})\)	\(q+(-0.984603 + 1.70538i) q^{2} +(-0.938888 - 1.62620i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.51414 - 2.62256i) q^{7} -0.240686 q^{8} +1.96921 q^{10} +(-2.15197 + 3.72733i) q^{11} +(0.500000 + 0.866025i) q^{13} +(2.98165 + 5.16437i) q^{14} +(2.11476 - 3.66286i) q^{16} +0.303306 q^{17} -6.04909 q^{19} +(-0.938888 + 1.62620i) q^{20} +(-4.23768 - 7.33988i) q^{22} +(1.47524 + 2.55520i) q^{23} +(-0.500000 + 0.866025i) q^{25} -1.96921 q^{26} -5.68642 q^{28} +(4.44268 - 7.69494i) q^{29} +(-0.0319947 - 0.0554165i) q^{31} +(3.92370 + 6.79606i) q^{32} +(-0.298636 + 0.517253i) q^{34} -3.02828 q^{35} +11.1045 q^{37} +(5.95595 - 10.3160i) q^{38} +(0.120343 + 0.208440i) q^{40} +(4.09849 + 7.09879i) q^{41} +(-1.45536 + 2.52075i) q^{43} +8.08184 q^{44} -5.81012 q^{46} +(-3.44432 + 5.96573i) q^{47} +(-1.08523 - 1.87967i) q^{49} +(-0.984603 - 1.70538i) q^{50} +(0.938888 - 1.62620i) q^{52} -11.8296 q^{53} +4.30395 q^{55} +(-0.364432 + 0.631214i) q^{56} +(8.74855 + 15.1529i) q^{58} +(4.57534 + 7.92472i) q^{59} +(-0.657031 + 1.13801i) q^{61} +0.126009 q^{62} -6.99415 q^{64} +(0.500000 - 0.866025i) q^{65} +(7.91564 + 13.7103i) q^{67} +(-0.284770 - 0.493236i) q^{68} +(2.98165 - 5.16437i) q^{70} +2.85405 q^{71} -11.2819 q^{73} +(-10.9335 + 18.9374i) q^{74} +(5.67942 + 9.83704i) q^{76} +(6.51677 + 11.2874i) q^{77} +(-5.17979 + 8.97167i) q^{79} -4.22951 q^{80} -16.1415 q^{82} +(-3.53463 + 6.12217i) q^{83} +(-0.151653 - 0.262670i) q^{85} +(-2.86590 - 4.96389i) q^{86} +(0.517949 - 0.897115i) q^{88} -4.26865 q^{89} +3.02828 q^{91} +(2.77018 - 4.79809i) q^{92} +(-6.78257 - 11.7478i) q^{94} +(3.02455 + 5.23867i) q^{95} +(-2.91854 + 5.05505i) q^{97} +4.27408 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8}+O(q^{10}) \) 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8	\( 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8} - 6 q^{10} + 6 q^{11} + 8 q^{13} + 10 q^{14} - 11 q^{16} + 4 q^{17} - 20 q^{19} - 9 q^{20} - 3 q^{22} + 6 q^{23} - 8 q^{25} + 6 q^{26} - 68 q^{28} + 14 q^{29} + 31 q^{31} + q^{32} + 7 q^{34} - 22 q^{35} + 2 q^{37} + 9 q^{38} - 6 q^{40} - 12 q^{41} - 15 q^{43} - 32 q^{44} - 64 q^{46} - 18 q^{47} - 17 q^{49} + 3 q^{50} + 9 q^{52} - 4 q^{53} - 12 q^{55} + 16 q^{56} + 42 q^{58} + 24 q^{59} + 9 q^{61} + 40 q^{62} - 60 q^{64} + 8 q^{65} + 18 q^{67} - 14 q^{68} + 10 q^{70} - 20 q^{71} + 12 q^{73} - 37 q^{74} + 53 q^{76} - 34 q^{77} + 3 q^{79} + 22 q^{80} - 68 q^{82} - 10 q^{83} - 2 q^{85} + 60 q^{86} + 14 q^{88} + 26 q^{89} + 22 q^{91} + 5 q^{92} - 17 q^{94} + 10 q^{95} + 34 q^{97} + 60 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8 - 6 * q^10 + 6 * q^11 + 8 * q^13 + 10 * q^14 - 11 * q^16 + 4 * q^17 - 20 * q^19 - 9 * q^20 - 3 * q^22 + 6 * q^23 - 8 * q^25 + 6 * q^26 - 68 * q^28 + 14 * q^29 + 31 * q^31 + q^32 + 7 * q^34 - 22 * q^35 + 2 * q^37 + 9 * q^38 - 6 * q^40 - 12 * q^41 - 15 * q^43 - 32 * q^44 - 64 * q^46 - 18 * q^47 - 17 * q^49 + 3 * q^50 + 9 * q^52 - 4 * q^53 - 12 * q^55 + 16 * q^56 + 42 * q^58 + 24 * q^59 + 9 * q^61 + 40 * q^62 - 60 * q^64 + 8 * q^65 + 18 * q^67 - 14 * q^68 + 10 * q^70 - 20 * q^71 + 12 * q^73 - 37 * q^74 + 53 * q^76 - 34 * q^77 + 3 * q^79 + 22 * q^80 - 68 * q^82 - 10 * q^83 - 2 * q^85 + 60 * q^86 + 14 * q^88 + 26 * q^89 + 22 * q^91 + 5 * q^92 - 17 * q^94 + 10 * q^95 + 34 * q^97 + 60 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more