LMFDB - Embedded newform 180.4.k.e.163.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [180,4,Mod(127,180)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("180.127"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(180, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	180.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,6,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.6203438010$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 44x^{8} - 156x^{6} + 704x^{4} - 1792x^{2} + 4096 $ x^12 - 7x^10 + 44x^8 - 156x^6 + 704x^4 - 1792*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			163.1
Root			$-1.76129 - 0.947553i$ of defining polynomial
Character	$\chi$	$=$	180.163
Dual form			180.4.k.e.127.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.70884 - 0.813737i) q^{2} +(6.67566 + 4.40857i) q^{4} +(0.435501 + 11.1719i) q^{5} +(-17.7783 - 17.7783i) q^{7} +(-14.4959 - 17.3744i) q^{8} +(7.91125 - 30.6172i) q^{10} -7.37590i q^{11} +(-2.68249 - 2.68249i) q^{13} +(33.6917 + 62.6254i) q^{14} +(25.1290 + 58.8603i) q^{16} +(20.2367 - 20.2367i) q^{17} +135.808 q^{19} +(-46.3447 + 76.4995i) q^{20} +(-6.00204 + 19.9802i) q^{22} +(71.0426 - 71.0426i) q^{23} +(-124.621 + 9.73070i) q^{25} +(5.08361 + 9.44930i) q^{26} +(-40.3050 - 197.059i) q^{28} -34.2890i q^{29} -187.974i q^{31} +(-20.1737 - 179.892i) q^{32} +(-71.2855 + 38.3507i) q^{34} +(190.874 - 206.359i) q^{35} +(250.679 - 250.679i) q^{37} +(-367.882 - 110.512i) q^{38} +(187.791 - 169.513i) q^{40} +211.105 q^{41} +(46.7326 - 46.7326i) q^{43} +(32.5172 - 49.2390i) q^{44} +(-250.253 + 134.633i) q^{46} +(-189.707 - 189.707i) q^{47} +289.134i q^{49} +(345.496 + 75.0495i) q^{50} +(-6.08147 - 29.7334i) q^{52} +(74.5742 + 74.5742i) q^{53} +(82.4025 - 3.21221i) q^{55} +(-51.1739 + 566.598i) q^{56} +(-27.9022 + 92.8835i) q^{58} -101.072 q^{59} +232.112 q^{61} +(-152.961 + 509.191i) q^{62} +(-91.7370 + 503.715i) q^{64} +(28.8002 - 31.1367i) q^{65} +(-34.7419 - 34.7419i) q^{67} +(224.309 - 45.8785i) q^{68} +(-684.969 + 403.672i) q^{70} -614.600i q^{71} +(-37.4378 - 37.4378i) q^{73} +(-883.036 + 475.063i) q^{74} +(906.607 + 598.718i) q^{76} +(-131.131 + 131.131i) q^{77} -1002.91 q^{79} +(-646.635 + 306.371i) q^{80} +(-571.850 - 171.784i) q^{82} +(423.190 - 423.190i) q^{83} +(234.895 + 217.269i) q^{85} +(-164.619 + 88.5632i) q^{86} +(-128.152 + 106.920i) q^{88} +1049.38i q^{89} +95.3802i q^{91} +(787.453 - 161.060i) q^{92} +(359.514 + 668.257i) q^{94} +(59.1444 + 1517.22i) q^{95} +(-536.526 + 536.526i) q^{97} +(235.279 - 783.218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 12 q^{8} - 110 q^{10} + 116 q^{13} + 312 q^{16} + 332 q^{17} - 140 q^{20} + 360 q^{22} + 340 q^{25} + 164 q^{26} - 880 q^{28} + 376 q^{32} + 508 q^{37} - 1600 q^{38} + 1420 q^{40} + 656 q^{41}+ \cdots - 1698 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 + 12 * q^8 - 110 * q^10 + 116 * q^13 + 312 * q^16 + 332 * q^17 - 140 * q^20 + 360 * q^22 + 340 * q^25 + 164 * q^26 - 880 * q^28 + 376 * q^32 + 508 * q^37 - 1600 * q^38 + 1420 * q^40 + 656 * q^41 - 1432 * q^46 + 1570 * q^50 - 932 * q^52 + 644 * q^53 - 2048 * q^56 + 1576 * q^58 - 896 * q^61 - 2440 * q^62 + 2740 * q^65 + 844 * q^68 - 3040 * q^70 + 1436 * q^73 + 800 * q^76 - 3120 * q^77 - 1840 * q^80 - 1352 * q^82 + 500 * q^85 + 2552 * q^86 - 2400 * q^88 + 1840 * q^92 - 4772 * q^97 - 1698 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−2.70884	−	0.813737i	−0.957721	−	0.287699i
$2$	−2.70884	−	0.813737i	−0.957721	−	0.287699i
$3$		0			0
$3$		0			0
$4$	6.67566	+	4.40857i	0.834458	+	0.551071i
$5$	0.435501	+	11.1719i	0.0389524	+	0.999241i
$5$	0.435501	+	11.1719i	0.0389524	+	0.999241i
$6$		0			0
$7$	−17.7783	−	17.7783i	−0.959936	−	0.959936i	0.0392914	−	0.999228i	$-0.487490\pi$
$7$	−17.7783	−	17.7783i	−0.959936	−	0.959936i	−0.999228	+	0.0392914i	$0.987490\pi$
$8$	−14.4959	−	17.3744i	−0.640635	−	0.767846i
$9$		0			0
$10$	7.91125	−	30.6172i	0.250176	−	0.968200i
$11$		−	7.37590i		−	0.202174i	−0.994878	−	0.101087i	$-0.967768\pi$
$11$		−	7.37590i		−	0.202174i	0.994878	−	0.101087i	$-0.0322321\pi$
$12$		0			0
$13$	−2.68249	−	2.68249i	−0.0572300	−	0.0572300i	0.677913	−	0.735143i	$-0.262885\pi$
$13$	−2.68249	−	2.68249i	−0.0572300	−	0.0572300i	−0.735143	+	0.677913i	$0.762885\pi$
$14$	33.6917	+	62.6254i	0.643178	+	1.19552i
$15$		0			0
$16$	25.1290	+	58.8603i	0.392641	+	0.919692i
$17$	20.2367	−	20.2367i	0.288713	−	0.288713i	−0.547858	−	0.836571i	$-0.684557\pi$
$17$	20.2367	−	20.2367i	0.288713	−	0.288713i	0.836571	+	0.547858i	$0.184557\pi$
$18$		0			0
$19$	135.808			1.63981			0.819906	−	0.572498i	$-0.194025\pi$
$19$	135.808			1.63981			0.819906	+	0.572498i	$0.194025\pi$
$20$	−46.3447	+	76.4995i	−0.518149	+	0.855290i
$21$		0			0
$22$	−6.00204	+	19.9802i	−0.0581654	+	0.193627i
$23$	71.0426	−	71.0426i	0.644061	−	0.644061i	−0.307490	−	0.951551i	$-0.599489\pi$
$23$	71.0426	−	71.0426i	0.644061	−	0.644061i	0.951551	+	0.307490i	$0.0994892\pi$
$24$		0			0
$25$	−124.621	+	9.73070i	−0.996965	+	0.0778456i
$26$	5.08361	+	9.44930i	0.0383453	+	0.0712754i
$27$		0			0
$28$	−40.3050	−	197.059i	−0.272033	−	1.33002i
$29$		−	34.2890i		−	0.219562i	−0.993956	−	0.109781i	$-0.964985\pi$
$29$		−	34.2890i		−	0.219562i	0.993956	−	0.109781i	$-0.0350150\pi$
$30$		0			0
$31$		−	187.974i		−	1.08907i	−0.838739	−	0.544533i	$-0.816707\pi$
$31$		−	187.974i		−	1.08907i	0.838739	−	0.544533i	$-0.183293\pi$
$32$	−20.1737	−	179.892i	−0.111445	−	0.993771i
$33$		0			0
$34$	−71.2855	+	38.3507i	−0.359569	+	0.193444i
$35$	190.874	−	206.359i	0.921816	−	0.996600i
$36$		0			0
$37$	250.679	−	250.679i	1.11382	−	1.11382i	0.121190	−	0.992629i	$-0.461329\pi$
$37$	250.679	−	250.679i	1.11382	−	1.11382i	0.992629	−	0.121190i	$-0.0386712\pi$
$38$	−367.882	−	110.512i	−1.57048	−	0.471773i
$39$		0			0
$40$	187.791	−	169.513i	0.742309	−	0.670058i
$41$	211.105			0.804122			0.402061	−	0.915613i	$-0.368294\pi$
$41$	211.105			0.804122			0.402061	+	0.915613i	$0.368294\pi$
$42$		0			0
$43$	46.7326	−	46.7326i	0.165736	−	0.165736i	−0.619366	−	0.785102i	$-0.712610\pi$
$43$	46.7326	−	46.7326i	0.165736	−	0.165736i	0.785102	+	0.619366i	$0.212610\pi$
$44$	32.5172	−	49.2390i	0.111412	−	0.168706i
$45$		0			0
$46$	−250.253	+	134.633i	−0.802126	+	0.431535i
$47$	−189.707	−	189.707i	−0.588757	−	0.588757i	0.348538	−	0.937295i	$-0.386678\pi$
$47$	−189.707	−	189.707i	−0.588757	−	0.588757i	−0.937295	+	0.348538i	$0.886678\pi$
$48$		0			0
$49$			289.134i			0.842956i
$50$	345.496	+	75.0495i	0.977211	+	0.212272i
$51$		0			0
$52$	−6.08147	−	29.7334i	−0.0162182	−	0.0792939i
$53$	74.5742	+	74.5742i	0.193275	+	0.193275i	0.797109	−	0.603835i	$-0.206361\pi$
$53$	74.5742	+	74.5742i	0.193275	+	0.193275i	−0.603835	+	0.797109i	$0.706361\pi$
$54$		0			0
$55$	82.4025	−	3.21221i	0.202021	−	0.00787517i
$56$	−51.1739	+	566.598i	−0.122114	+	1.35205i
$57$		0			0
$58$	−27.9022	+	92.8835i	−0.0631679	+	0.210279i
$59$	−101.072			−0.223024			−0.111512	−	0.993763i	$-0.535569\pi$
$59$	−101.072			−0.223024			−0.111512	+	0.993763i	$0.535569\pi$
$60$		0			0
$61$	232.112			0.487196			0.243598	−	0.969876i	$-0.421672\pi$
$61$	232.112			0.487196			0.243598	+	0.969876i	$0.421672\pi$
$62$	−152.961	+	509.191i	−0.313324	+	1.04302i
$63$		0			0
$64$	−91.7370	+	503.715i	−0.179174	+	0.983817i
$65$	28.8002	−	31.1367i	0.0549573	−	0.0594158i
$66$		0			0
$67$	−34.7419	−	34.7419i	−0.0633493	−	0.0633493i	0.674722	−	0.738072i	$-0.264263\pi$
$67$	−34.7419	−	34.7419i	−0.0633493	−	0.0633493i	−0.738072	+	0.674722i	$0.764263\pi$
$68$	224.309	−	45.8785i	0.400021	−	0.0818175i
$69$		0			0
$70$	−684.969	+	403.672i	−1.16956	+	0.689258i
$71$		−	614.600i		−	1.02732i	−0.857994	−	0.513660i	$-0.828289\pi$
$71$		−	614.600i		−	1.02732i	0.857994	−	0.513660i	$-0.171711\pi$
$72$		0			0
$73$	−37.4378	−	37.4378i	−0.0600242	−	0.0600242i	0.676457	−	0.736482i	$-0.263514\pi$
$73$	−37.4378	−	37.4378i	−0.0600242	−	0.0600242i	−0.736482	+	0.676457i	$0.763514\pi$
$74$	−883.036	+	475.063i	−1.38717	+	0.746283i
$75$		0			0
$76$	906.607	+	598.718i	1.36836	+	0.903654i
$77$	−131.131	+	131.131i	−0.194074	+	0.194074i
$78$		0			0
$79$	−1002.91			−1.42831			−0.714153	−	0.699990i	$-0.753188\pi$
$79$	−1002.91			−1.42831			−0.714153	+	0.699990i	$0.753188\pi$
$80$	−646.635	+	306.371i	−0.903700	+	0.428167i
$81$		0			0
$82$	−571.850	−	171.784i	−0.770125	−	0.231346i
$83$	423.190	−	423.190i	0.559652	−	0.559652i	−0.369556	−	0.929208i	$-0.620490\pi$
$83$	423.190	−	423.190i	0.559652	−	0.559652i	0.929208	+	0.369556i	$0.120490\pi$
$84$		0			0
$85$	234.895	+	217.269i	0.299740	+	0.277248i
$86$	−164.619	+	88.5632i	−0.206411	+	0.111047i
$87$		0			0
$88$	−128.152	+	106.920i	−0.155239	+	0.129520i
$89$			1049.38i			1.24982i	0.780695	+	0.624912i	$0.214865\pi$
$89$			1049.38i			1.24982i	−0.780695	+	0.624912i	$0.785135\pi$
$90$		0			0
$91$			95.3802i			0.109874i
$92$	787.453	−	161.060i	0.892365	−	0.182518i
$93$		0			0
$94$	359.514	+	668.257i	0.394479	+	0.733249i
$95$	59.1444	+	1517.22i	0.0638746	+	1.63857i
$96$		0			0
$97$	−536.526	+	536.526i	−0.561608	+	0.561608i	−0.929764	−	0.368156i	$-0.879989\pi$
$97$	−536.526	+	536.526i	−0.561608	+	0.561608i	0.368156	+	0.929764i	$0.379989\pi$
$98$	235.279	−	783.218i	0.242518	−	0.807316i
$99$		0			0
$100$	−874.824	−	484.440i	−0.874824	−	0.484440i
$101$	1415.80			1.39483			0.697414	−	0.716668i	$-0.254334\pi$
$101$	1415.80			1.39483			0.697414	+	0.716668i	$0.254334\pi$
$102$		0			0
$103$	284.920	−	284.920i	0.272563	−	0.272563i	−0.557568	−	0.830131i	$-0.688265\pi$
$103$	284.920	−	284.920i	0.272563	−	0.272563i	0.830131	+	0.557568i	$0.188265\pi$
$104$	−7.72143	+	85.4919i	−0.00728027	+	0.0806074i
$105$		0			0
$106$	−141.326	−	262.694i	−0.129498	−	0.240708i
$107$	−464.315	−	464.315i	−0.419505	−	0.419505i	0.465528	−	0.885033i	$-0.345864\pi$
$107$	−464.315	−	464.315i	−0.419505	−	0.419505i	−0.885033	+	0.465528i	$0.845864\pi$
$108$		0			0
$109$			638.365i			0.560957i	0.959860	+	0.280478i	$0.0904931\pi$
$109$			638.365i			0.560957i	−0.959860	+	0.280478i	$0.909507\pi$
$110$	−225.829	−	58.3525i	−0.195745	−	0.0505791i
$111$		0			0
$112$	599.684	−	1493.18i	0.505936	−	1.25976i
$113$	−1001.84	−	1001.84i	−0.834027	−	0.834027i	0.154038	−	0.988065i	$-0.450772\pi$
$113$	−1001.84	−	1001.84i	−0.834027	−	0.834027i	−0.988065	+	0.154038i	$0.950772\pi$
$114$		0			0
$115$	824.616	+	762.738i	0.668660	+	0.618484i
$116$	151.165	−	228.902i	0.120994	−	0.183216i
$117$		0			0
$118$	273.787	+	82.2456i	0.213594	+	0.0641638i
$119$	−719.548			−0.554293
$120$		0			0
$121$	1276.60			0.959126
$122$	−628.756	−	188.878i	−0.466598	−	0.140166i
$123$		0			0
$124$	828.695	−	1254.85i	0.600153	−	0.908780i
$125$	−162.982	−	1388.01i	−0.116621	−	0.993177i
$126$		0			0
$127$	619.456	+	619.456i	0.432818	+	0.432818i	0.889586	−	0.456768i	$-0.150993\pi$
$127$	619.456	+	619.456i	0.432818	+	0.432818i	−0.456768	+	0.889586i	$0.650993\pi$
$128$	658.392	−	1289.83i	0.454642	−	0.890674i
$129$		0			0
$130$	−103.352	+	60.9086i	−0.0697277	+	0.0410926i
$131$			1620.12i			1.08054i	0.841491	+	0.540270i	$0.181678\pi$
$131$			1620.12i			1.08054i	−0.841491	+	0.540270i	$0.818322\pi$
$132$		0			0
$133$	−2414.43	−	2414.43i	−1.57412	−	1.57412i
$134$	65.8397	+	122.381i	0.0424454	+	0.0788965i
$135$		0			0
$136$	−644.950	−	58.2504i	−0.406647	−	0.0367274i
$137$	−825.076	+	825.076i	−0.514533	+	0.514533i	−0.915912	−	0.401379i	$-0.868531\pi$
$137$	−825.076	+	825.076i	−0.514533	+	0.514533i	0.401379	+	0.915912i	$0.368531\pi$
$138$		0			0
$139$	−1264.21			−0.771430			−0.385715	−	0.922618i	$-0.626045\pi$
$139$	−1264.21			−0.771430			−0.385715	+	0.922618i	$0.626045\pi$
$140$	2183.96	−	536.101i	1.31841	−	0.323634i
$141$		0			0
$142$	−500.123	+	1664.86i	−0.295559	+	0.983885i
$143$	−19.7858	+	19.7858i	−0.0115704	+	0.0115704i
$144$		0			0
$145$	383.072	−	14.9329i	0.219396	−	0.00855247i
$146$	70.9487	+	131.878i	0.0402175	+	0.0747553i
$147$		0			0
$148$	2778.58	−	568.312i	1.54323	−	0.315642i
$149$		−	1351.49i		−	0.743079i	−0.928417	−	0.371539i	$-0.878830\pi$
$149$		−	1351.49i		−	0.743079i	0.928417	−	0.371539i	$-0.121170\pi$
$150$		0			0
$151$		−	2325.64i		−	1.25336i	−0.779275	−	0.626682i	$-0.784412\pi$
$151$		−	2325.64i		−	1.25336i	0.779275	−	0.626682i	$-0.215588\pi$
$152$	−1968.66	−	2359.57i	−1.05052	−	1.25912i
$153$		0			0
$154$	461.918	−	248.507i	0.241704	−	0.130034i
$155$	2100.01	−	81.8626i	1.08824	−	0.0424217i
$156$		0			0
$157$	162.486	−	162.486i	0.0825976	−	0.0825976i	−0.664601	−	0.747199i	$-0.731398\pi$
$157$	162.486	−	162.486i	0.0825976	−	0.0825976i	0.747199	+	0.664601i	$0.231398\pi$
$158$	2716.73	+	816.105i	1.36792	+	0.410923i
$159$		0			0
$160$	2000.94	−	303.721i	0.988675	−	0.150070i
$161$	−2526.03			−1.23651
$162$		0			0
$163$	−932.441	+	932.441i	−0.448064	+	0.448064i	−0.894710	−	0.446647i	$-0.852618\pi$
$163$	−932.441	+	932.441i	−0.448064	+	0.448064i	0.446647	+	0.894710i	$0.352618\pi$
$164$	1409.26	+	930.670i	0.671006	+	0.443129i
$165$		0			0
$166$	−1490.72	+	801.990i	−0.697002	+	0.374979i
$167$	976.461	+	976.461i	0.452460	+	0.452460i	0.896170	−	0.443710i	$-0.146338\pi$
$167$	976.461	+	976.461i	0.452460	+	0.452460i	−0.443710	+	0.896170i	$0.646338\pi$
$168$		0			0
$169$		−	2182.61i		−	0.993449i
$170$	−459.494	−	779.689i	−0.207303	−	0.351761i
$171$		0			0
$172$	517.995	−	105.947i	0.229632	−	0.0469674i
$173$	−761.698	−	761.698i	−0.334745	−	0.334745i	0.519640	−	0.854385i	$-0.326066\pi$
$173$	−761.698	−	761.698i	−0.334745	−	0.334745i	−0.854385	+	0.519640i	$0.826066\pi$
$174$		0			0
$175$	2388.54	+	2042.54i	1.03175	+	0.882296i
$176$	434.148	−	185.349i	0.185938	−	0.0793818i
$177$		0			0
$178$	853.921	−	2842.61i	0.359574	−	1.19698i
$179$	−4003.32			−1.67163			−0.835816	−	0.549009i	$-0.815005\pi$
$179$	−4003.32			−1.67163			−0.835816	+	0.549009i	$0.815005\pi$
$180$		0			0
$181$	−1950.00			−0.800785			−0.400392	−	0.916344i	$-0.631126\pi$
$181$	−1950.00			−0.800785			−0.400392	+	0.916344i	$0.631126\pi$
$182$	77.6144	−	258.370i	0.0316108	−	0.105229i
$183$		0			0
$184$	−2264.15	−	204.493i	−0.907147	−	0.0819315i
$185$	2909.72	+	2691.38i	1.15636	+	1.06959i
$186$		0			0
$187$	−149.264	−	149.264i	−0.0583704	−	0.0583704i
$188$	−430.083	−	2102.75i	−0.166846	−	0.815740i
$189$		0			0
$190$	1074.41	−	4158.05i	0.410241	−	1.58767i
$191$			1458.80i			0.552644i	0.961065	+	0.276322i	$0.0891156\pi$
$191$			1458.80i			0.552644i	−0.961065	+	0.276322i	$0.910884\pi$
$192$		0			0
$193$	2264.70	+	2264.70i	0.844647	+	0.844647i	0.989459	−	0.144812i	$-0.0462577\pi$
$193$	2264.70	+	2264.70i	0.844647	+	0.844647i	−0.144812	+	0.989459i	$0.546258\pi$
$194$	1889.96	−	1016.77i	0.699438	−	0.376289i
$195$		0			0
$196$	−1274.67	+	1930.16i	−0.464529	+	0.703411i
$197$	−2092.70	+	2092.70i	−0.756845	+	0.756845i	−0.975747	−	0.218902i	$-0.929753\pi$
$197$	−2092.70	+	2092.70i	−0.756845	+	0.756845i	0.218902	+	0.975747i	$0.429753\pi$
$198$		0			0
$199$	2087.70			0.743683			0.371842	−	0.928296i	$-0.378726\pi$
$199$	2087.70			0.743683			0.371842	+	0.928296i	$0.378726\pi$
$200$	1975.56	+	2024.15i	0.698464	+	0.715645i
$201$		0			0
$202$	−3835.19	−	1152.09i	−1.33586	−	0.401291i
$203$	−609.599	+	609.599i	−0.210766	+	0.210766i
$204$		0			0
$205$	91.9363	+	2358.43i	0.0313225	+	0.803512i
$206$	−1003.65	+	539.954i	−0.339456	+	0.182623i
$207$		0			0
$208$	90.4840	−	225.301i	0.0301632	−	0.0751048i
$209$		−	1001.70i		−	0.331528i
$210$		0			0
$211$			199.597i			0.0651223i	0.999470	+	0.0325611i	$0.0103664\pi$
$211$			199.597i			0.0651223i	−0.999470	+	0.0325611i	$0.989634\pi$
$212$	169.067	+	826.598i	0.0547714	+	0.267788i
$213$		0			0
$214$	879.926	+	1635.59i	0.281077	+	0.522460i
$215$	542.442	+	501.738i	0.172066	+	0.159155i
$216$		0			0
$217$	−3341.84	+	3341.84i	−1.04543	+	1.04543i
$218$	519.461	−	1729.23i	0.161387	−	0.537240i
$219$		0			0
$220$	564.252	+	341.834i	0.172918	+	0.104756i
$221$	−108.570			−0.0330461
$222$		0			0
$223$	−3340.24	+	3340.24i	−1.00304	+	1.00304i	−0.00304854	+	0.999995i	$0.500970\pi$
$223$	−3340.24	+	3340.24i	−1.00304	+	1.00304i	−0.999995	+	0.00304854i	$0.999030\pi$
$224$	−2839.51	+	3556.82i	−0.846976	+	1.06094i
$225$		0			0
$226$	1898.59	+	3529.06i	0.558816	+	1.03871i
$227$	824.316	+	824.316i	0.241021	+	0.241021i	0.817272	−	0.576251i	$-0.195485\pi$
$227$	824.316	+	824.316i	0.241021	+	0.241021i	−0.576251	+	0.817272i	$0.695485\pi$
$228$		0			0
$229$		−	4512.23i		−	1.30208i	−0.759043	−	0.651041i	$-0.774333\pi$
$229$		−	4512.23i		−	1.30208i	0.759043	−	0.651041i	$-0.225667\pi$
$230$	−1613.09	−	2737.16i	−0.462452	−	0.784708i
$231$		0			0
$232$	−595.749	+	497.050i	−0.168590	+	0.140659i
$233$	292.574	+	292.574i	0.0822625	+	0.0822625i	0.747041	−	0.664778i	$-0.231474\pi$
$233$	292.574	+	292.574i	0.0822625	+	0.0822625i	−0.664778	+	0.747041i	$0.731474\pi$
$234$		0			0
$235$	2036.76	−	2201.99i	0.565376	−	0.611243i
$236$	−674.720	−	445.581i	−0.186104	−	0.122902i
$237$		0			0
$238$	1949.14	+	585.522i	0.530858	+	0.159470i
$239$	2925.20			0.791696			0.395848	−	0.918316i	$-0.370451\pi$
$239$	2925.20			0.791696			0.395848	+	0.918316i	$0.370451\pi$
$240$		0			0
$241$	4259.40			1.13847			0.569236	−	0.822174i	$-0.307239\pi$
$241$	4259.40			1.13847			0.569236	+	0.822174i	$0.307239\pi$
$242$	−3458.10	−	1038.81i	−0.918574	−	0.275940i
$243$		0			0
$244$	1549.50	+	1023.28i	0.406544	+	0.268480i
$245$	−3230.16	+	125.918i	−0.842316	+	0.0328351i
$246$		0			0
$247$	−364.304	−	364.304i	−0.0938465	−	0.0938465i
$248$	−3265.92	+	2724.85i	−0.836235	+	0.697694i
$249$		0			0
$250$	−687.978	+	3892.52i	−0.174046	+	0.984737i
$251$		−	5268.72i		−	1.32493i	−0.749091	−	0.662467i	$-0.769509\pi$
$251$		−	5268.72i		−	1.32493i	0.749091	−	0.662467i	$-0.230491\pi$
$252$		0			0
$253$	−524.003	−	524.003i	−0.130213	−	0.130213i
$254$	−1173.94	−	2182.08i	−0.289997	−	0.539040i
$255$		0			0
$256$	−2833.07	+	2958.20i	−0.691667	+	0.722217i
$257$	5635.08	−	5635.08i	1.36773	−	1.36773i	0.504061	−	0.863668i	$-0.331839\pi$
$257$	5635.08	−	5635.08i	1.36773	−	1.36773i	0.863668	−	0.504061i	$-0.168161\pi$
$258$		0			0
$259$	−8913.27			−2.13839
$260$	329.529	−	80.8902i	0.0786020	−	0.0192946i
$261$		0			0
$262$	1318.35	−	4388.66i	0.310871	−	1.03486i
$263$	−2721.99	+	2721.99i	−0.638195	+	0.638195i	−0.950110	−	0.311915i	$-0.899030\pi$
$263$	−2721.99	+	2721.99i	−0.638195	+	0.638195i	0.311915	+	0.950110i	$0.399030\pi$
$264$		0			0
$265$	−800.655	+	865.609i	−0.185599	+	0.200656i
$266$	4575.60	+	8505.01i	1.05469	+	1.96044i
$267$		0			0
$268$	−78.7632	−	385.088i	−0.0179523	−	0.0877723i
$269$		−	603.964i		−	0.136893i	−0.997655	−	0.0684467i	$-0.978196\pi$
$269$		−	603.964i		−	0.136893i	0.997655	−	0.0684467i	$-0.0218043\pi$
$270$		0			0
$271$		−	4232.24i		−	0.948672i	−0.880344	−	0.474336i	$-0.842688\pi$
$271$		−	4232.24i		−	0.948672i	0.880344	−	0.474336i	$-0.157312\pi$
$272$	1699.67	+	682.611i	0.378888	+	0.152167i
$273$		0			0
$274$	2906.40	−	1563.61i	0.640810	−	0.344748i
$275$	71.7727	+	919.189i	0.0157384	+	0.201561i
$276$		0			0
$277$	3214.07	−	3214.07i	0.697165	−	0.697165i	−0.266633	−	0.963798i	$-0.585911\pi$
$277$	3214.07	−	3214.07i	0.697165	−	0.697165i	0.963798	+	0.266633i	$0.0859113\pi$
$278$	3424.54	+	1028.73i	0.738815	+	0.221940i
$279$		0			0
$280$	−6352.24	−	324.953i	−1.35578	−	0.0693559i
$281$	7574.78			1.60809			0.804046	−	0.594567i	$-0.202677\pi$
$281$	7574.78			1.60809			0.804046	+	0.594567i	$0.202677\pi$
$282$		0			0
$283$	504.094	−	504.094i	0.105884	−	0.105884i	−0.652180	−	0.758064i	$-0.726145\pi$
$283$	504.094	−	504.094i	0.105884	−	0.105884i	0.758064	+	0.652180i	$0.226145\pi$
$284$	2709.51	−	4102.87i	0.566126	−	0.857255i
$285$		0			0
$286$	69.6971	−	37.4962i	0.0144101	−	0.00775244i
$287$	−3753.08	−	3753.08i	−0.771906	−	0.771906i
$288$		0			0
$289$			4093.95i			0.833289i
$290$	−1049.83	−	271.269i	−0.212580	−	0.0549291i
$291$		0			0
$292$	−84.8750	−	414.970i	−0.0170101	−	0.0831653i
$293$	244.144	+	244.144i	0.0486793	+	0.0486793i	0.731027	−	0.682348i	$-0.239041\pi$
$293$	244.144	+	244.144i	0.0486793	+	0.0486793i	−0.682348	+	0.731027i	$0.739041\pi$
$294$		0			0
$295$	−44.0167	−	1129.16i	−0.00868730	−	0.222854i
$296$	−7989.20	−	721.566i	−1.56879	−	0.141690i
$297$		0			0
$298$	−1099.76	+	3660.99i	−0.213783	+	0.711662i
$299$	−381.143			−0.0737192
$300$		0			0
$301$	−1661.65			−0.318192
$302$	−1892.46	+	6299.80i	−0.360592	+	1.20037i
$303$		0			0
$304$	3412.71	+	7993.69i	0.643857	+	1.50812i
$305$	101.085	+	2593.13i	0.0189774	+	0.486826i
$306$		0			0
$307$	6853.22	+	6853.22i	1.27405	+	1.27405i	0.943942	+	0.330110i	$0.107086\pi$
$307$	6853.22	+	6853.22i	1.27405	+	1.27405i	0.330110	+	0.943942i	$0.392914\pi$
$308$	−1453.48	+	297.286i	−0.268896	+	0.0549981i
$309$		0			0
$310$	−5755.22	−	1487.11i	−1.05443	−	0.272458i
$311$		−	10802.7i		−	1.96966i	−0.173510	−	0.984832i	$-0.555511\pi$
$311$		−	10802.7i		−	1.96966i	0.173510	−	0.984832i	$-0.444489\pi$
$312$		0			0
$313$	2618.43	+	2618.43i	0.472851	+	0.472851i	0.902836	−	0.429985i	$-0.141481\pi$
$313$	2618.43	+	2618.43i	0.472851	+	0.472851i	−0.429985	+	0.902836i	$0.641481\pi$
$314$	−572.372	+	307.929i	−0.102869	+	0.0553422i
$315$		0			0
$316$	−6695.09	−	4421.40i	−1.19186	−	0.787098i
$317$	−3652.64	+	3652.64i	−0.647170	+	0.647170i	−0.952308	−	0.305138i	$-0.901297\pi$
$317$	−3652.64	+	3652.64i	−0.647170	+	0.647170i	0.305138	+	0.952308i	$0.401297\pi$
$318$		0			0
$319$	−252.912			−0.0443898
$320$	−5667.38	−	805.504i	−0.990050	−	0.140716i
$321$		0			0
$322$	6842.61	+	2055.52i	1.18424	+	0.355745i
$323$	2748.30	−	2748.30i	0.473436	−	0.473436i
$324$		0			0
$325$	360.397	+	308.192i	0.0615115	+	0.0526012i
$326$	3284.60	−	1767.07i	0.558028	−	0.300212i
$327$		0			0
$328$	−3060.16	−	3667.81i	−0.515149	−	0.617442i
$329$			6745.31i			1.13034i
$330$		0			0
$331$		−	7839.91i		−	1.30187i	−0.759131	−	0.650937i	$-0.774376\pi$
$331$		−	7839.91i		−	1.30187i	0.759131	−	0.650937i	$-0.225624\pi$
$332$	4690.74	−	959.411i	0.775415	−	0.158598i
$333$		0			0
$334$	−1850.50	−	3439.66i	−0.303158	−	0.563503i
$335$	373.002	−	403.262i	0.0608336	−	0.0657688i
$336$		0			0
$337$	−4503.23	+	4503.23i	−0.727912	+	0.727912i	−0.970204	−	0.242291i	$-0.922101\pi$
$337$	−4503.23	+	4503.23i	−0.727912	+	0.727912i	0.242291	+	0.970204i	$0.422101\pi$
$338$	−1776.07	+	5912.34i	−0.285815	+	0.951447i
$339$		0			0
$340$	610.235	+	2485.96i	0.0973371	+	0.396530i
$341$	−1386.47			−0.220181
$342$		0			0
$343$	−957.648	+	957.648i	−0.150753	+	0.150753i
$344$	−1489.38	−	134.517i	−0.233436	−	0.0210834i
$345$		0			0
$346$	1443.50	+	2683.14i	0.224286	+	0.416898i
$347$	8458.77	+	8458.77i	1.30862	+	1.30862i	0.922413	+	0.386205i	$0.126214\pi$
$347$	8458.77	+	8458.77i	1.30862	+	1.30862i	0.386205	+	0.922413i	$0.373786\pi$
$348$		0			0
$349$		−	5515.41i		−	0.845941i	−0.906144	−	0.422970i	$-0.860987\pi$
$349$		−	5515.41i		−	0.845941i	0.906144	−	0.422970i	$-0.139013\pi$
$350$	−4808.07	−	7476.57i	−0.734292	−	1.14183i
$351$		0			0
$352$	−1326.86	+	148.799i	−0.200915	+	0.0225314i
$353$	761.447	+	761.447i	0.114810	+	0.114810i	0.762178	−	0.647368i	$-0.224130\pi$
$353$	761.447	+	761.447i	0.114810	+	0.114810i	−0.647368	+	0.762178i	$0.724130\pi$
$354$		0			0
$355$	6866.23	−	267.659i	1.02654	−	0.0400165i
$356$	−4626.28	+	7005.33i	−0.688742	+	1.04293i
$357$		0			0
$358$	10844.4	+	3257.65i	1.60096	+	0.480928i
$359$	3564.71			0.524062			0.262031	−	0.965059i	$-0.415608\pi$
$359$	3564.71			0.524062			0.262031	+	0.965059i	$0.415608\pi$
$360$		0			0
$361$	11584.8			1.68899
$362$	5282.23	+	1586.78i	0.766928	+	0.230385i
$363$		0			0
$364$	−420.491	+	636.726i	−0.0605486	+	0.0916855i
$365$	401.946	−	434.554i	0.0576405	−	0.0623167i
$366$		0			0
$367$	−4407.82	−	4407.82i	−0.626939	−	0.626939i	0.320358	−	0.947297i	$-0.396197\pi$
$367$	−4407.82	−	4407.82i	−0.626939	−	0.626939i	−0.947297	+	0.320358i	$0.896197\pi$
$368$	5966.81	+	2396.36i	0.845222	+	0.339453i
$369$		0			0
$370$	−5691.90	−	9658.26i	−0.799750	−	1.35705i
$371$		−	2651.60i		−	0.371063i
$372$		0			0
$373$	−8371.19	−	8371.19i	−1.16205	−	1.16205i	−0.984027	−	0.178021i	$-0.943030\pi$
$373$	−8371.19	−	8371.19i	−1.16205	−	1.16205i	−0.178021	−	0.984027i	$-0.556970\pi$
$374$	282.871	+	525.794i	0.0391094	+	0.0726957i
$375$		0			0
$376$	−546.061	+	6046.00i	−0.0748962	+	0.829252i
$377$	−91.9800	+	91.9800i	−0.0125656	+	0.0125656i
$378$		0			0
$379$	11130.1			1.50848			0.754240	−	0.656599i	$-0.228006\pi$
$379$	11130.1			1.50848			0.754240	+	0.656599i	$0.228006\pi$
$380$	−6293.97	+	10389.2i	−0.849667	+	1.40252i
$381$		0			0
$382$	1187.08	−	3951.66i	0.158995	−	0.529279i
$383$	1006.62	−	1006.62i	0.134297	−	0.134297i	−0.636763	−	0.771060i	$-0.719727\pi$
$383$	1006.62	−	1006.62i	0.134297	−	0.134297i	0.771060	+	0.636763i	$0.219727\pi$
$384$		0			0
$385$	−1522.08	−	1407.87i	−0.201487	−	0.186367i
$386$	−4291.85	−	7977.60i	−0.565932	−	1.05194i
$387$		0			0
$388$	−5946.98	+	1216.35i	−0.778124	+	0.159152i
$389$		−	13548.4i		−	1.76589i	−0.469478	−	0.882944i	$-0.655558\pi$
$389$		−	13548.4i		−	1.76589i	0.469478	−	0.882944i	$-0.344442\pi$
$390$		0			0
$391$		−	2875.34i		−	0.371898i
$392$	5023.52	−	4191.26i	0.647260	−	0.540027i
$393$		0			0
$394$	7371.69	−	3965.88i	0.942590	−	0.507102i
$395$	−436.768	−	11204.4i	−0.0556359	−	1.42722i
$396$		0			0
$397$	1822.81	−	1822.81i	0.230439	−	0.230439i	−0.582437	−	0.812876i	$-0.697901\pi$
$397$	1822.81	−	1822.81i	0.230439	−	0.230439i	0.812876	+	0.582437i	$0.197901\pi$
$398$	−5655.25	−	1698.84i	−0.712241	−	0.213957i
$399$		0			0
$400$	−3704.34	−	7090.69i	−0.463043	−	0.886336i
$401$	−5922.04			−0.737488			−0.368744	−	0.929531i	$-0.620212\pi$
$401$	−5922.04			−0.737488			−0.368744	+	0.929531i	$0.620212\pi$
$402$		0			0
$403$	−504.238	+	504.238i	−0.0623273	+	0.0623273i
$404$	9451.43	+	6241.67i	1.16393	+	0.768650i
$405$		0			0
$406$	2147.36	−	1155.25i	0.262492	−	0.141218i
$407$	−1848.98	−	1848.98i	−0.225186	−	0.225186i
$408$		0			0
$409$			8533.05i			1.03162i	0.856703	+	0.515809i	$0.172509\pi$
$409$			8533.05i			1.03162i	−0.856703	+	0.515809i	$0.827491\pi$
$410$	1670.10	−	6463.43i	0.201172	−	0.778552i
$411$		0			0
$412$	3158.12	−	645.940i	0.377644	−	0.0772408i
$413$	1796.88	+	1796.88i	0.214088	+	0.214088i
$414$		0			0
$415$	4912.12	+	4543.52i	0.581027	+	0.537428i
$416$	−428.443	+	536.674i	−0.0504955	+	0.0632515i
$417$		0			0
$418$	−815.124	+	2713.46i	−0.0953804	+	0.317511i
$419$	−7128.02			−0.831089			−0.415545	−	0.909573i	$-0.636409\pi$
$419$	−7128.02			−0.831089			−0.415545	+	0.909573i	$0.636409\pi$
$420$		0			0
$421$	−611.239			−0.0707601			−0.0353800	−	0.999374i	$-0.511264\pi$
$421$	−611.239			−0.0707601			−0.0353800	+	0.999374i	$0.511264\pi$
$422$	162.419	−	540.676i	0.0187356	−	0.0623690i
$423$		0			0
$424$	214.658	−	2376.70i	0.0245866	−	0.272223i
$425$	−2325.00	+	2718.83i	−0.265362	+	0.310312i
$426$		0			0
$427$	−4126.56	−	4126.56i	−0.467677	−	0.467677i
$428$	−1052.65	−	5146.58i	−0.118882	−	0.581236i
$429$		0			0
$430$	−1061.11	−	1800.53i	−0.119003	−	0.201929i
$431$			9361.72i			1.04626i	0.852253	+	0.523130i	$0.175236\pi$
$431$			9361.72i			1.04626i	−0.852253	+	0.523130i	$0.824764\pi$
$432$		0			0
$433$	−1769.48	−	1769.48i	−0.196388	−	0.196388i	0.602062	−	0.798450i	$-0.294346\pi$
$433$	−1769.48	−	1769.48i	−0.196388	−	0.196388i	−0.798450	+	0.602062i	$0.794346\pi$
$434$	11771.9	−	6333.15i	1.30200	−	0.700463i
$435$		0			0
$436$	−2814.28	+	4261.51i	−0.309127	+	0.468095i
$437$	9648.13	−	9648.13i	1.05614	−	1.05614i
$438$		0			0
$439$	−7823.34			−0.850541			−0.425271	−	0.905066i	$-0.639821\pi$
$439$	−7823.34			−0.850541			−0.425271	+	0.905066i	$0.639821\pi$
$440$	−1250.31	−	1385.13i	−0.135469	−	0.150076i
$441$		0			0
$442$	294.099	+	88.3472i	0.0316490	+	0.00950735i
$443$	−9066.48	+	9066.48i	−0.972374	+	0.972374i	−0.999629	−	0.0272545i	$-0.991324\pi$
$443$	−9066.48	+	9066.48i	−0.972374	+	0.972374i	0.0272545	+	0.999629i	$0.491324\pi$
$444$		0			0
$445$	−11723.5	+	457.007i	−1.24888	+	0.0486836i
$446$	11766.3	−	6330.10i	1.24921	−	0.672061i
$447$		0			0
$448$	10586.1	−	7324.25i	1.11640	−	0.772407i
$449$			3381.93i			0.355464i	0.984079	+	0.177732i	$0.0568759\pi$
$449$			3381.93i			0.355464i	−0.984079	+	0.177732i	$0.943124\pi$
$450$		0			0
$451$		−	1557.09i		−	0.162573i
$452$	−2271.26	−	11104.6i	−0.236352	−	1.15557i
$453$		0			0
$454$	−1562.17	−	2903.72i	−0.161489	−	0.300173i
$455$	−1065.57	+	41.5382i	−0.109791	+	0.00427987i
$456$		0			0
$457$	10289.7	−	10289.7i	1.05324	−	1.05324i	0.0547399	−	0.998501i	$-0.482567\pi$
$457$	10289.7	−	10289.7i	1.05324	−	1.05324i	0.998501	−	0.0547399i	$-0.0174330\pi$
$458$	−3671.77	+	12222.9i	−0.374608	+	1.24703i
$459$		0			0
$460$	2142.28	+	8727.16i	0.217140	+	0.884579i
$461$	5310.20			0.536488			0.268244	−	0.963351i	$-0.413557\pi$
$461$	5310.20			0.536488			0.268244	+	0.963351i	$0.413557\pi$
$462$		0			0
$463$	−7686.78	+	7686.78i	−0.771566	+	0.771566i	−0.978380	−	0.206814i	$-0.933690\pi$
$463$	−7686.78	+	7686.78i	−0.771566	+	0.771566i	0.206814	+	0.978380i	$0.433690\pi$
$464$	2018.26	−	861.648i	0.201930	−	0.0862091i
$465$		0			0
$466$	−554.459	−	1030.62i	−0.0551176	−	0.102451i
$467$	4535.99	+	4535.99i	0.449466	+	0.449466i	0.895177	−	0.445711i	$-0.147049\pi$
$467$	4535.99	+	4535.99i	0.449466	+	0.449466i	−0.445711	+	0.895177i	$0.647049\pi$
$468$		0			0
$469$			1235.30i			0.121623i
$470$	−7309.10	+	4307.47i	−0.717327	+	0.422742i
$471$		0			0
$472$	1465.12	+	1756.05i	0.142877	+	0.171248i
$473$	−344.695	−	344.695i	−0.0335076	−	0.0335076i
$474$		0			0
$475$	−16924.5	+	1321.51i	−1.63484	+	0.127652i
$476$	−4803.46	−	3172.18i	−0.462534	−	0.305455i
$477$		0			0
$478$	−7923.91	−	2380.34i	−0.758224	−	0.227771i
$479$	10969.6			1.04638			0.523189	−	0.852217i	$-0.324742\pi$
$479$	10969.6			1.04638			0.523189	+	0.852217i	$0.324742\pi$
$480$		0			0
$481$	−1344.89			−0.127488
$482$	−11538.0	−	3466.03i	−1.09034	−	0.327538i
$483$		0			0
$484$	8522.13	+	5627.97i	0.800350	+	0.528547i
$485$	−6227.65	−	5760.33i	−0.583058	−	0.539306i
$486$		0			0
$487$	12736.0	+	12736.0i	1.18506	+	1.18506i	0.978416	+	0.206646i	$0.0662547\pi$
$487$	12736.0	+	12736.0i	1.18506	+	1.18506i	0.206646	+	0.978416i	$0.433745\pi$
$488$	−3364.68	−	4032.80i	−0.312115	−	0.374091i
$489$		0			0
$490$	8852.46	+	2287.41i	0.816150	+	0.210887i
$491$			10518.6i			0.966796i	0.875401	+	0.483398i	$0.160598\pi$
$491$			10518.6i			0.966796i	−0.875401	+	0.483398i	$0.839402\pi$
$492$		0			0
$493$	−693.897	−	693.897i	−0.0633905	−	0.0633905i
$494$	690.394	+	1283.29i	0.0628792	+	0.116878i
$495$		0			0
$496$	11064.2	−	4723.59i	1.00161	−	0.427612i
$497$	−10926.5	+	10926.5i	−0.986161	+	0.986161i
$498$		0			0
$499$	2445.26			0.219368			0.109684	−	0.993966i	$-0.465016\pi$
$499$	2445.26			0.219368			0.109684	+	0.993966i	$0.465016\pi$
$500$	5031.11	−	9984.38i	0.449996	−	0.893031i
$501$		0			0
$502$	−4287.35	+	14272.1i	−0.381183	+	1.26892i
$503$	−12216.7	+	12216.7i	−1.08293	+	1.08293i	−0.0866986	+	0.996235i	$0.527632\pi$
$503$	−12216.7	+	12216.7i	−1.08293	+	1.08293i	−0.996235	+	0.0866986i	$0.972368\pi$
$504$		0			0
$505$	616.584	+	15817.1i	0.0543319	+	1.39377i
$506$	993.041	+	1845.84i	0.0872452	+	0.162169i
$507$		0			0
$508$	1404.37	+	6866.20i	0.122655	+	0.599682i
$509$			5615.75i			0.489025i	0.969646	+	0.244512i	$0.0786279\pi$
$509$			5615.75i			0.489025i	−0.969646	+	0.244512i	$0.921372\pi$
$510$		0			0
$511$			1331.16i			0.115239i
$512$	10081.5	−	5707.93i	0.870205	−	0.492690i
$513$		0			0
$514$	−19850.0	+	10679.1i	−1.70340	+	0.916408i
$515$	3307.17	+	3059.00i	0.282973	+	0.261739i
$516$		0			0
$517$	−1399.26	+	1399.26i	−0.119031	+	0.119031i
$518$	24144.6	+	7253.05i	2.04798	+	0.615214i
$519$		0			0
$520$	−958.465	−	49.0309i	−0.0808298	−	0.00413490i
$521$	−5287.10			−0.444591			−0.222296	−	0.974979i	$-0.571355\pi$
$521$	−5287.10			−0.444591			−0.222296	+	0.974979i	$0.571355\pi$
$522$		0			0
$523$	−4328.34	+	4328.34i	−0.361883	+	0.361883i	−0.864506	−	0.502623i	$-0.832369\pi$
$523$	−4328.34	+	4328.34i	−0.361883	+	0.361883i	0.502623	+	0.864506i	$0.332369\pi$
$524$	−7142.43	+	10815.4i	−0.595455	+	0.901666i
$525$		0			0
$526$	9588.45	−	5158.47i	0.794821	−	0.427605i
$527$	−3803.97	−	3803.97i	−0.314428	−	0.314428i
$528$		0			0
$529$			2072.91i			0.170371i
$530$	2873.23	−	1693.28i	0.235481	−	0.138776i
$531$		0			0
$532$	−5473.73	−	26762.1i	−0.446083	−	2.18098i
$533$	−566.287	−	566.287i	−0.0460199	−	0.0460199i
$534$		0			0
$535$	4985.05	−	5389.47i	0.402846	−	0.435527i
$536$	−100.003	+	1107.23i	−0.00805871	+	0.0892262i
$537$		0			0
$538$	−491.468	+	1636.04i	−0.0393841	+	0.131106i
$539$	2132.62			0.170424
$540$		0			0
$541$	−13608.6			−1.08148			−0.540739	−	0.841190i	$-0.681855\pi$
$541$	−13608.6			−1.08148			−0.540739	+	0.841190i	$0.681855\pi$
$542$	−3443.93	+	11464.5i	−0.272932	+	0.908563i
$543$		0			0
$544$	−4048.67	−	3232.17i	−0.319090	−	0.254739i
$545$	−7131.72	+	278.009i	−0.560531	+	0.0218506i
$546$		0			0
$547$	−2884.33	−	2884.33i	−0.225457	−	0.225457i	0.585335	−	0.810792i	$-0.300963\pi$
$547$	−2884.33	−	2884.33i	−0.225457	−	0.225457i	−0.810792	+	0.585335i	$0.800963\pi$
$548$	−9145.34	+	1870.52i	−0.712901	+	0.145812i
$549$		0			0
$550$	553.557	−	2548.34i	0.0429159	−	0.197567i
$551$		−	4656.71i		−	0.360041i
$552$		0			0
$553$	17830.0	+	17830.0i	1.37108	+	1.37108i
$554$	−11321.8	+	6091.00i	−0.868263	+	0.467115i
$555$		0			0
$556$	−8439.43	−	5573.35i	−0.643726	−	0.425113i
$557$	6538.87	−	6538.87i	0.497416	−	0.497416i	−0.413216	−	0.910633i	$-0.635595\pi$
$557$	6538.87	−	6538.87i	0.497416	−	0.497416i	0.910633	+	0.413216i	$0.135595\pi$
$558$		0			0
$559$	−250.720			−0.0189702
$560$	16942.8	+	6049.30i	1.27851	+	0.456481i
$561$		0			0
$562$	−20518.9	−	6163.88i	−1.54010	−	0.462647i
$563$	−6499.93	+	6499.93i	−0.486571	+	0.486571i	−0.907222	−	0.420651i	$-0.861802\pi$
$563$	−6499.93	+	6499.93i	−0.486571	+	0.486571i	0.420651	+	0.907222i	$0.361802\pi$
$564$		0			0
$565$	10756.1	−	11628.7i	0.800907	−	0.865882i
$566$	−1775.71	+	955.311i	−0.131870	+	0.0709447i
$567$		0			0
$568$	−10678.3	+	8909.19i	−0.788822	+	0.658136i
$569$		−	5264.67i		−	0.387885i	−0.981013	−	0.193942i	$-0.937872\pi$
$569$		−	5264.67i		−	0.387885i	0.981013	−	0.193942i	$-0.0621275\pi$
$570$		0			0
$571$			22034.0i			1.61488i	0.589952	+	0.807438i	$0.299147\pi$
$571$			22034.0i			1.61488i	−0.589952	+	0.807438i	$0.700853\pi$
$572$	−219.311	+	44.8563i	−0.0160312	+	0.00327891i
$573$		0			0
$574$	7112.48	+	13220.5i	0.517194	+	0.961348i
$575$	−8162.08	+	9544.67i	−0.591969	+	0.692244i
$576$		0			0
$577$	−9208.58	+	9208.58i	−0.664399	+	0.664399i	−0.956414	−	0.292015i	$-0.905674\pi$
$577$	−9208.58	+	9208.58i	−0.664399	+	0.664399i	0.292015	+	0.956414i	$0.405674\pi$
$578$	3331.40	−	11089.9i	0.239737	−	0.798059i
$579$		0			0
$580$	2623.09	+	1589.11i	0.187789	+	0.113766i
$581$	−15047.2			−1.07446
$582$		0			0
$583$	550.052	−	550.052i	0.0390751	−	0.0390751i
$584$	−107.763	+	1193.15i	−0.00763572	+	0.0845429i
$585$		0			0
$586$	−462.679	−	860.016i	−0.0326162	−	0.0606262i
$587$	−6536.20	−	6536.20i	−0.459587	−	0.459587i	0.438933	−	0.898520i	$-0.355357\pi$
$587$	−6536.20	−	6536.20i	−0.459587	−	0.459587i	−0.898520	+	0.438933i	$0.855357\pi$
$588$		0			0
$589$		−	25528.3i		−	1.78586i
$590$	−799.602	+	3094.53i	−0.0557951	+	0.215932i
$591$		0			0
$592$	21054.3	+	8455.72i	1.46170	+	0.587040i
$593$	11033.7	+	11033.7i	0.764079	+	0.764079i	0.977057	−	0.212978i	$-0.0683163\pi$
$593$	11033.7	+	11033.7i	0.764079	+	0.764079i	−0.212978	+	0.977057i	$0.568316\pi$
$594$		0			0
$595$	−313.364	−	8038.68i	−0.0215910	−	0.553872i
$596$	5958.16	−	9022.12i	0.409489	−	0.620068i
$597$		0			0
$598$	1032.46	+	310.150i	0.0706024	+	0.0212090i
$599$	−1861.62			−0.126985			−0.0634923	−	0.997982i	$-0.520224\pi$
$599$	−1861.62			−0.126985			−0.0634923	+	0.997982i	$0.520224\pi$
$600$		0			0
$601$	−21693.2			−1.47235			−0.736177	−	0.676789i	$-0.763371\pi$
$601$	−21693.2			−1.47235			−0.736177	+	0.676789i	$0.763371\pi$
$602$	4501.15	+	1352.15i	0.304739	+	0.0915437i
$603$		0			0
$604$	10252.8	−	15525.2i	0.690693	−	1.04588i
$605$	555.959	+	14261.9i	0.0373602	+	0.958398i
$606$		0			0
$607$	617.817	+	617.817i	0.0413121	+	0.0413121i	0.727461	−	0.686149i	$-0.240700\pi$
$607$	617.817	+	617.817i	0.0413121	+	0.0413121i	−0.686149	+	0.727461i	$0.740700\pi$
$608$	−2739.75	−	24430.7i	−0.182749	−	1.62960i
$609$		0			0
$610$	1836.30	−	7106.63i	0.121884	−	0.471703i
$611$			1017.77i			0.0673891i
$612$		0			0
$613$	5656.87	+	5656.87i	0.372722	+	0.372722i	0.868468	−	0.495745i	$-0.165105\pi$
$613$	5656.87	+	5656.87i	0.372722	+	0.372722i	−0.495745	+	0.868468i	$0.665105\pi$
$614$	−12987.6	−	24141.0i	−0.853642	−	1.58673i
$615$		0			0
$616$	4179.17	+	377.453i	0.273350	+	0.0246884i
$617$	−12811.8	+	12811.8i	−0.835953	+	0.835953i	−0.988323	−	0.152370i	$-0.951309\pi$
$617$	−12811.8	+	12811.8i	−0.835953	+	0.835953i	0.152370	+	0.988323i	$0.451309\pi$
$618$		0			0
$619$	−12163.2			−0.789788			−0.394894	−	0.918727i	$-0.629219\pi$
$619$	−12163.2			−0.789788			−0.394894	+	0.918727i	$0.629219\pi$
$620$	14379.9	+	8711.57i	0.931468	+	0.564299i
$621$		0			0
$622$	−8790.56	+	29262.9i	−0.566671	+	1.88639i
$623$	18656.2	−	18656.2i	1.19975	−	1.19975i
$624$		0			0
$625$	15435.6	−	2425.29i	0.987880	−	0.155219i
$626$	−4962.20	−	9223.62i	−0.316820	−	0.588898i
$627$		0			0
$628$	1801.04	−	368.372i	0.114441	−	0.0234071i
$629$		−	10145.8i		−	0.643149i
$630$		0			0
$631$			3347.17i			0.211171i	0.994410	+	0.105585i	$0.0336716\pi$
$631$			3347.17i			0.211171i	−0.994410	+	0.105585i	$0.966328\pi$
$632$	14538.1	+	17424.9i	0.915023	+	1.09672i
$633$		0			0
$634$	12866.7	−	6922.14i	0.805998	−	0.433617i
$635$	−6650.70	+	7190.25i	−0.415630	+	0.449349i
$636$		0			0
$637$	775.600	−	775.600i	0.0482424	−	0.0482424i
$638$	685.099	+	205.804i	0.0425131	+	0.0127709i
$639$		0			0
$640$	14696.6	+	6793.74i	0.907708	+	0.419603i
$641$	24791.3			1.52761			0.763803	−	0.645449i	$-0.223330\pi$
$641$	24791.3			1.52761			0.763803	+	0.645449i	$0.223330\pi$
$642$		0			0
$643$	12922.9	−	12922.9i	0.792583	−	0.792583i	−0.189330	−	0.981913i	$-0.560632\pi$
$643$	12922.9	−	12922.9i	0.792583	−	0.792583i	0.981913	+	0.189330i	$0.0606316\pi$
$644$	−16862.9	−	11136.2i	−1.03182	−	0.681408i
$645$		0			0
$646$	−9681.12	+	5208.33i	−0.589626	+	0.317212i
$647$	16924.5	+	16924.5i	1.02840	+	1.02840i	0.999585	+	0.0288113i	$0.00917218\pi$
$647$	16924.5	+	16924.5i	1.02840	+	1.02840i	0.0288113	+	0.999585i	$0.490828\pi$
$648$		0			0
$649$			745.493i			0.0450896i
$650$	−725.472	−	1128.11i	−0.0437774	−	0.0680741i
$651$		0			0
$652$	−10335.4	+	2113.93i	−0.620806	+	0.126975i
$653$	−10391.0	−	10391.0i	−0.622715	−	0.622715i	0.323510	−	0.946225i	$-0.395137\pi$
$653$	−10391.0	−	10391.0i	−0.622715	−	0.622715i	−0.946225	+	0.323510i	$0.895137\pi$
$654$		0			0
$655$	−18099.8	+	705.565i	−1.07972	+	0.0420896i
$656$	5304.85	+	12425.7i	0.315731	+	0.739545i
$657$		0			0
$658$	5488.91	−	18272.0i	0.325197	−	1.08255i
$659$	−773.045			−0.0456958			−0.0228479	−	0.999739i	$-0.507273\pi$
$659$	−773.045			−0.0456958			−0.0228479	+	0.999739i	$0.507273\pi$
$660$		0			0
$661$	17856.3			1.05073			0.525364	−	0.850878i	$-0.323929\pi$
$661$	17856.3			1.05073			0.525364	+	0.850878i	$0.323929\pi$
$662$	−6379.62	+	21237.1i	−0.374549	+	1.24683i
$663$		0			0
$664$	−13487.2	−	1218.13i	−0.788259	−	0.0711938i
$665$	25922.1	−	28025.1i	1.51161	−	1.63424i
$666$		0			0
$667$	−2435.98	−	2435.98i	−0.141411	−	0.141411i
$668$	2213.73	+	10823.3i	0.128221	+	0.626896i
$669$		0			0
$670$	−1338.55	+	788.848i	−0.0771833	+	0.0454864i
$671$		−	1712.04i		−	0.0984985i
$672$		0			0
$673$	−19931.6	−	19931.6i	−1.14161	−	1.14161i	−0.988155	−	0.153459i	$-0.950959\pi$
$673$	−19931.6	−	19931.6i	−1.14161	−	1.14161i	−0.153459	−	0.988155i	$-0.549041\pi$
$674$	15863.0	−	8534.10i	0.906557	−	0.487717i
$675$		0			0
$676$	9622.18	−	14570.4i	0.547462	−	0.828992i
$677$	5515.73	−	5515.73i	0.313126	−	0.313126i	−0.532993	−	0.846120i	$-0.678933\pi$
$677$	5515.73	−	5515.73i	0.313126	−	0.313126i	0.846120	+	0.532993i	$0.178933\pi$
$678$		0			0
$679$	19077.0			1.07822
$680$	369.889	−	7230.65i	0.0208597	−	0.407769i
$681$		0			0
$682$	3755.74	+	1128.22i	0.210872	+	0.0633460i
$683$	19946.1	−	19946.1i	1.11745	−	1.11745i	0.125331	−	0.992115i	$-0.460001\pi$
$683$	19946.1	−	19946.1i	1.11745	−	1.11745i	0.992115	−	0.125331i	$-0.0399992\pi$
$684$		0			0
$685$	−9576.95	−	8858.31i	−0.534185	−	0.494100i
$686$	3373.39	−	1814.85i	0.187750	−	0.101007i
$687$		0			0
$688$	3925.04	+	1576.35i	0.217501	+	0.0873515i
$689$		−	400.090i		−	0.0221222i
$690$		0			0
$691$		−	356.654i		−	0.0196350i	−0.999952	−	0.00981748i	$-0.996875\pi$
$691$		−	356.654i		−	0.0196350i	0.999952	−	0.00981748i	$-0.00312505\pi$
$692$	−1726.84	−	8442.84i	−0.0948621	−	0.463798i
$693$		0			0
$694$	−16030.3	−	29796.7i	−0.876802	−	1.62978i
$695$	−550.564	−	14123.6i	−0.0300490	−	0.770845i
$696$		0			0
$697$	4272.07	−	4272.07i	0.232161	−	0.232161i
$698$	−4488.09	+	14940.4i	−0.243377	+	0.810175i
$699$		0			0
$700$	6940.35	+	24165.4i	0.374744	+	1.30481i
$701$	−17230.0			−0.928343			−0.464172	−	0.885745i	$-0.653648\pi$
$701$	−17230.0			−0.928343			−0.464172	+	0.885745i	$0.653648\pi$
$702$		0			0
$703$	34044.1	−	34044.1i	1.82646	−	1.82646i
$704$	3715.35	+	676.643i	0.198903	+	0.0362243i
$705$		0			0
$706$	−1443.02	−	2682.26i	−0.0769248	−	0.142986i
$707$	−25170.5	−	25170.5i	−1.33895	−	1.33895i
$708$		0			0
$709$			8153.11i			0.431871i	0.976408	+	0.215935i	$0.0692801\pi$
$709$			8153.11i			0.431871i	−0.976408	+	0.215935i	$0.930720\pi$
$710$	−18817.3	−	4862.26i	−0.994651	−	0.257010i
$711$		0			0
$712$	18232.4	−	15211.8i	0.959672	−	0.800681i
$713$	−13354.1	−	13354.1i	−0.701425	−	0.701425i
$714$		0			0
$715$	−229.661	−	212.427i	−0.0120124	−	0.0111110i
$716$	−26724.8	−	17648.9i	−1.39491	−	0.921189i
$717$		0			0
$718$	−9656.25	−	2900.74i	−0.501905	−	0.150772i
$719$	−17219.3			−0.893147			−0.446573	−	0.894747i	$-0.647356\pi$
$719$	−17219.3			−0.893147			−0.446573	+	0.894747i	$0.647356\pi$
$720$		0			0
$721$	−10130.8			−0.523287
$722$	−31381.3	−	9426.94i	−1.61758	−	0.485920i
$723$		0			0
$724$	−13017.5	−	8596.70i	−0.668221	−	0.441290i
$725$	333.656	+	4273.12i	0.0170920	+	0.218896i
$726$		0			0
$727$	−8881.73	−	8881.73i	−0.453102	−	0.453102i	0.443281	−	0.896383i	$-0.353814\pi$
$727$	−8881.73	−	8881.73i	−0.453102	−	0.453102i	−0.896383	+	0.443281i	$0.853814\pi$
$728$	1657.17	−	1382.62i	0.0843665	−	0.0703893i
$729$		0			0
$730$	−1442.42	+	850.061i	−0.0731320	+	0.0430989i
$731$		−	1891.43i		−	0.0957004i
$732$		0			0
$733$	4401.20	+	4401.20i	0.221776	+	0.221776i	0.809246	−	0.587470i	$-0.199876\pi$
$733$	4401.20	+	4401.20i	0.221776	+	0.221776i	−0.587470	+	0.809246i	$0.699876\pi$
$734$	8353.30	+	15526.9i	0.420062	+	0.780802i
$735$		0			0
$736$	−14213.2	−	11346.8i	−0.711826	−	0.568271i
$737$	−256.253	+	256.253i	−0.0128076	+	0.0128076i
$738$		0			0
$739$	23097.8			1.14975			0.574875	−	0.818241i	$-0.305051\pi$
$739$	23097.8			1.14975			0.574875	+	0.818241i	$0.305051\pi$
$740$	7559.18	+	30794.4i	0.375515	+	1.52976i
$741$		0			0
$742$	−2157.70	+	7182.77i	−0.106754	+	0.355374i
$743$	17404.1	−	17404.1i	0.859348	−	0.859348i	−0.131913	−	0.991261i	$-0.542112\pi$
$743$	17404.1	−	17404.1i	0.859348	−	0.859348i	0.991261	+	0.131913i	$0.0421119\pi$
$744$		0			0
$745$	15098.7	−	588.577i	0.742515	−	0.0289447i
$746$	15864.3	+	29488.2i	0.778597	+	1.44724i
$747$		0			0
$748$	−338.395	−	1654.48i	−0.0165414	−	0.0808739i
$749$			16509.4i			0.805396i
$750$		0			0
$751$			2347.75i			0.114075i	0.998372	+	0.0570377i	$0.0181655\pi$
$751$			2347.75i			0.114075i	−0.998372	+	0.0570377i	$0.981834\pi$
$752$	6399.05	−	15933.3i	0.310305	−	0.772644i
$753$		0			0
$754$	324.007	−	174.312i	0.0156494	−	0.00841919i
$755$	25981.7	−	1012.82i	1.25241	−	0.0488215i
$756$		0			0
$757$	−7078.12	+	7078.12i	−0.339840	+	0.339840i	−0.856307	−	0.516467i	$-0.827247\pi$
$757$	−7078.12	+	7078.12i	−0.339840	+	0.339840i	0.516467	+	0.856307i	$0.327247\pi$
$758$	−30149.6	−	9056.95i	−1.44470	−	0.433989i
$759$		0			0
$760$	25503.5	−	23021.2i	1.21725	−	1.09877i
$761$	27017.6			1.28697			0.643486	−	0.765458i	$-0.277487\pi$
$761$	27017.6			1.28697			0.643486	+	0.765458i	$0.277487\pi$
$762$		0			0
$763$	11349.0	−	11349.0i	0.538483	−	0.538483i
$764$	−6431.22	+	9738.45i	−0.304546	+	0.461158i
$765$		0			0
$766$	−3545.90	+	1907.65i	−0.167257	+	0.0899821i
$767$	271.124	+	271.124i	0.0127636	+	0.0127636i
$768$		0			0
$769$			41584.0i			1.95001i	0.222183	+	0.975005i	$0.428682\pi$
$769$			41584.0i			1.95001i	−0.222183	+	0.975005i	$0.571318\pi$
$770$	2977.45	+	5052.26i	0.139350	+	0.236456i
$771$		0			0
$772$	5134.29	+	25102.5i	0.239362	+	1.17028i
$773$	19799.8	+	19799.8i	0.921280	+	0.921280i	0.997120	−	0.0758404i	$-0.0241639\pi$
$773$	19799.8	+	19799.8i	0.921280	+	0.921280i	−0.0758404	+	0.997120i	$0.524164\pi$
$774$		0			0
$775$	1829.12	+	23425.4i	0.0847790	+	1.08576i
$776$	17099.2	+	1544.36i	0.791014	+	0.0714426i
$777$		0			0
$778$	−11024.8	+	36700.5i	−0.508045	+	1.69123i
$779$	28669.7			1.31861
$780$		0			0
$781$	−4533.23			−0.207697
$782$	−2339.77	+	7788.84i	−0.106995	+	0.356174i
$783$		0			0
$784$	−17018.5	+	7265.64i	−0.775260	+	0.330979i
$785$	1886.04	+	1744.51i	0.0857523	+	0.0793176i
$786$		0			0
$787$	−23772.7	−	23772.7i	−1.07675	−	1.07675i	−0.996799	−	0.0799542i	$-0.974523\pi$
$787$	−23772.7	−	23772.7i	−1.07675	−	1.07675i	−0.0799542	−	0.996799i	$-0.525477\pi$
$788$	−23195.9	+	4744.34i	−1.04863	+	0.214480i
$789$		0			0
$790$	−7934.27	+	30706.3i	−0.357327	+	1.38289i
$791$			35621.9i			1.60123i
$792$		0			0
$793$	−622.640	−	622.640i	−0.0278822	−	0.0278822i
$794$	−6420.99	+	3454.42i	−0.286993	+	0.154399i
$795$		0			0
$796$	13936.8	+	9203.77i	0.620573	+	0.409823i
$797$	−8760.69	+	8760.69i	−0.389359	+	0.389359i	−0.874459	−	0.485100i	$-0.838783\pi$
$797$	−8760.69	+	8760.69i	−0.389359	+	0.389359i	0.485100	+	0.874459i	$0.338783\pi$
$798$		0			0
$799$	−7678.08			−0.339964
$800$	4264.54	+	22221.9i	0.188468	+	0.982079i
$801$		0			0
$802$	16041.9	+	4818.98i	0.706308	+	0.212175i
$803$	−276.138	+	276.138i	−0.0121353	+	0.0121353i
$804$		0			0
$805$	−1100.09	−	28220.4i	−0.0481652	−	1.23558i
$806$	1776.22	−	955.585i	0.0776236	−	0.0417606i
$807$		0			0
$808$	−20523.4	−	24598.7i	−0.893576	−	1.07101i
$809$			27571.0i			1.19820i	0.800673	+	0.599102i	$0.204475\pi$
$809$			27571.0i			1.19820i	−0.800673	+	0.599102i	$0.795525\pi$
$810$		0			0
$811$			20085.4i			0.869661i	0.900512	+	0.434831i	$0.143192\pi$
$811$			20085.4i			0.869661i	−0.900512	+	0.434831i	$0.856808\pi$
$812$	−6756.94	+	1382.02i	−0.292022	+	0.0597282i
$813$		0			0
$814$	3504.02	+	6513.18i	0.150879	+	0.280451i
$815$	−10823.2	−	10011.0i	−0.465177	−	0.430271i
$816$		0			0
$817$	6346.65	−	6346.65i	0.271776	−	0.271776i
$818$	6943.65	−	23114.7i	0.296796	−	0.988002i
$819$		0			0
$820$	−9783.57	+	16149.4i	−0.416655	+	0.687758i
$821$	−14867.5			−0.632008			−0.316004	−	0.948758i	$-0.602341\pi$
$821$	−14867.5			−0.632008			−0.316004	+	0.948758i	$0.602341\pi$
$822$		0			0
$823$	−23345.7	+	23345.7i	−0.988797	+	0.988797i	−0.999938	−	0.0111410i	$-0.996454\pi$
$823$	−23345.7	+	23345.7i	−0.988797	+	0.988797i	0.0111410	+	0.999938i	$0.496454\pi$
$824$	−9080.48	−	820.128i	−0.383900	−	0.0346730i
$825$		0			0
$826$	−3405.27	−	6329.64i	−0.143444	−	0.266630i
$827$	−3330.46	−	3330.46i	−0.140038	−	0.140038i	0.633613	−	0.773651i	$-0.281571\pi$
$827$	−3330.46	−	3330.46i	−0.140038	−	0.140038i	−0.773651	+	0.633613i	$0.781571\pi$
$828$		0			0
$829$			11521.6i			0.482703i	0.970438	+	0.241351i	$0.0775906\pi$
$829$			11521.6i			0.482703i	−0.970438	+	0.241351i	$0.922409\pi$
$830$	−9608.93	−	16304.8i	−0.401844	−	0.681867i
$831$		0			0
$832$	1597.30	−	1105.13i	0.0665580	−	0.0460498i
$833$	5851.12	+	5851.12i	0.243372	+	0.243372i
$834$		0			0
$835$	−10483.6	+	11334.1i	−0.434492	+	0.469741i
$836$	4416.09	−	6687.04i	0.182696	−	0.276646i
$837$		0			0
$838$	19308.7	+	5800.33i	0.795951	+	0.239104i
$839$	−33130.1			−1.36326			−0.681631	−	0.731696i	$-0.738729\pi$
$839$	−33130.1			−1.36326			−0.681631	+	0.731696i	$0.738729\pi$
$840$		0			0
$841$	23213.3			0.951792
$842$	1655.75	+	497.388i	0.0677684	+	0.0203576i
$843$		0			0
$844$	−879.936	+	1332.44i	−0.0358870	+	0.0543418i
$845$	24383.8	−	950.528i	0.992695	−	0.0386972i
$846$		0			0
$847$	−22695.7	−	22695.7i	−0.920699	−	0.920699i
$848$	−2515.48	+	6263.43i	−0.101866	+	0.253641i
$849$		0			0
$850$	8510.46	−	5472.95i	0.343419	−	0.220848i
$851$		−	35617.7i		−	1.43474i
$852$		0			0
$853$	12007.8	+	12007.8i	0.481994	+	0.481994i	0.905768	−	0.423774i	$-0.139295\pi$
$853$	12007.8	+	12007.8i	0.481994	+	0.481994i	−0.423774	+	0.905768i	$0.639295\pi$
$854$	7820.26	+	14536.1i	0.313354	+	0.582454i
$855$		0			0
$856$	−1336.51	+	14797.8i	−0.0533655	+	0.590864i
$857$	9369.48	−	9369.48i	0.373460	−	0.373460i	−0.495276	−	0.868736i	$-0.664933\pi$
$857$	9369.48	−	9369.48i	0.373460	−	0.373460i	0.868736	+	0.495276i	$0.164933\pi$
$858$		0			0
$859$	17337.1			0.688630			0.344315	−	0.938854i	$-0.388111\pi$
$859$	17337.1			0.688630			0.344315	+	0.938854i	$0.388111\pi$
$860$	1409.21	+	5740.83i	0.0558765	+	0.227629i
$861$		0			0
$862$	7617.98	−	25359.4i	0.301009	−	1.00203i
$863$	17345.8	−	17345.8i	0.684191	−	0.684191i	−0.276751	−	0.960942i	$-0.589258\pi$
$863$	17345.8	−	17345.8i	0.684191	−	0.684191i	0.960942	+	0.276751i	$0.0892576\pi$
$864$		0			0
$865$	8177.86	−	8841.30i	0.321451	−	0.347530i
$866$	3353.36	+	6233.15i	0.131584	+	0.244586i
$867$		0			0
$868$	−37041.8	+	7576.27i	−1.44848	+	0.296262i
$869$			7397.36i			0.288767i
$870$		0			0
$871$			186.390i			0.00725096i
$872$	11091.2	−	9253.69i	0.430728	−	0.359368i
$873$		0			0
$874$	−33986.3	+	18284.2i	−1.31534	+	0.707636i
$875$	−21778.8	+	27573.9i	−0.841438	+	1.06533i
$876$		0			0
$877$	−18857.4	+	18857.4i	−0.726075	+	0.726075i	−0.969836	−	0.243760i	$-0.921619\pi$
$877$	−18857.4	+	18857.4i	−0.726075	+	0.726075i	0.243760	+	0.969836i	$0.421619\pi$
$878$	21192.2	+	6366.14i	0.814581	+	0.244700i
$879$		0			0
$880$	2259.76	+	4769.51i	0.0865643	+	0.182705i
$881$	−27095.7			−1.03618			−0.518092	−	0.855325i	$-0.673357\pi$
$881$	−27095.7			−1.03618			−0.518092	+	0.855325i	$0.673357\pi$
$882$		0			0
$883$	−2484.93	+	2484.93i	−0.0947049	+	0.0947049i	−0.752872	−	0.658167i	$-0.771332\pi$
$883$	−2484.93	+	2484.93i	−0.0947049	+	0.0947049i	0.658167	+	0.752872i	$0.271332\pi$
$884$	−724.775	−	478.638i	−0.0275756	−	0.0182108i
$885$		0			0
$886$	31937.4	−	17182.0i	1.21101	−	0.651511i
$887$	−26609.3	−	26609.3i	−1.00727	−	1.00727i	−0.999973	−	0.00730049i	$-0.997676\pi$
$887$	−26609.3	−	26609.3i	−1.00727	−	1.00727i	−0.00730049	−	0.999973i	$-0.502324\pi$
$888$		0			0
$889$		−	22025.7i		−	0.830955i
$890$	32129.1	+	8301.92i	1.21008	+	0.312675i
$891$		0			0
$892$	−37024.0	+	7572.63i	−1.38975	+	0.284249i
$893$	−25763.6	−	25763.6i	−0.965451	−	0.965451i
$894$		0			0
$895$	−1743.45	−	44724.5i	−0.0651141	−	1.67036i
$896$	−34636.1	+	11225.9i	−1.29142	+	0.418563i
$897$		0			0
$898$	2752.00	−	9161.12i	0.102267	−	0.340435i
$899$	−6445.42			−0.239118
$900$		0			0
$901$	3018.27			0.111602
$902$	−1267.06	+	4217.90i	−0.0467721	+	0.155699i
$903$		0			0
$904$	−2883.74	+	31928.9i	−0.106097	+	1.17471i
$905$	−849.225	−	21785.1i	−0.0311925	−	0.800177i
$906$		0			0
$907$	23802.0	+	23802.0i	0.871369	+	0.871369i	0.992622	−	0.121252i	$-0.0386910\pi$
$907$	23802.0	+	23802.0i	0.871369	+	0.871369i	−0.121252	+	0.992622i	$0.538691\pi$
$908$	1868.80	+	9136.92i	0.0683022	+	0.333942i
$909$		0			0
$910$	2920.27	+	754.577i	0.106380	+	0.0274879i
$911$			36580.4i			1.33036i	0.746681	+	0.665182i	$0.231646\pi$
$911$			36580.4i			1.33036i	−0.746681	+	0.665182i	$0.768354\pi$
$912$		0			0
$913$	−3121.41	−	3121.41i	−0.113147	−	0.113147i
$914$	−36246.2	+	19500.0i	−1.31173	+	0.705694i
$915$		0			0
$916$	19892.5	−	30122.2i	0.717540	−	1.08653i
$917$	28803.0	−	28803.0i	1.03725	−	1.03725i
$918$		0			0
$919$	−32910.8			−1.18131			−0.590657	−	0.806923i	$-0.701131\pi$
$919$	−32910.8			−1.18131			−0.590657	+	0.806923i	$0.701131\pi$
$920$	1298.52	−	25383.8i	0.0465337	−	0.909650i
$921$		0			0
$922$	−14384.5	−	4321.11i	−0.513806	−	0.154347i
$923$	−1648.66	+	1648.66i	−0.0587935	+	0.0587935i
$924$		0			0
$925$	−28800.5	+	33679.0i	−1.02373	+	1.19715i
$926$	27077.3	−	14567.3i	0.960924	−	0.516966i
$927$		0			0
$928$	−6168.30	+	691.737i	−0.218195	+	0.0244692i
$929$			2662.19i			0.0940190i	0.998894	+	0.0470095i	$0.0149691\pi$
$929$			2662.19i			0.0940190i	−0.998894	+	0.0470095i	$0.985031\pi$
$930$		0			0
$931$			39266.6i			1.38229i
$932$	663.293	+	3242.96i	0.0233121	+	0.113977i
$933$		0			0
$934$	−8596.18	−	15978.4i	−0.301152	−	0.559774i
$935$	1602.55	−	1732.56i	0.0560524	−	0.0605998i
$936$		0			0
$937$	37885.5	−	37885.5i	1.32088	−	1.32088i	0.407818	−	0.913063i	$-0.366290\pi$
$937$	37885.5	−	37885.5i	1.32088	−	1.32088i	0.913063	−	0.407818i	$-0.133710\pi$
$938$	1005.21	−	3346.24i	0.0349907	−	0.116480i
$939$		0			0
$940$	23304.4	−	5720.57i	0.808621	−	0.198494i
$941$	6516.65			0.225756			0.112878	−	0.993609i	$-0.463993\pi$
$941$	6516.65			0.225756			0.112878	+	0.993609i	$0.463993\pi$
$942$		0			0
$943$	14997.4	−	14997.4i	0.517904	−	0.517904i
$944$	−2539.83	−	5949.10i	−0.0875681	−	0.205113i
$945$		0			0
$946$	653.234	+	1214.22i	0.0224508	+	0.0417310i
$947$	10250.1	+	10250.1i	0.351724	+	0.351724i	0.860751	−	0.509026i	$-0.169994\pi$
$947$	10250.1	+	10250.1i	0.351724	+	0.351724i	−0.509026	+	0.860751i	$0.669994\pi$
$948$		0			0
$949$			200.854i			0.00687037i
$950$	46921.1	+	10192.3i	1.60244	+	0.348086i
$951$		0			0
$952$	10430.5	+	12501.7i	0.355099	+	0.425611i
$953$	−19249.8	−	19249.8i	−0.654314	−	0.654314i	0.299715	−	0.954029i	$-0.403109\pi$
$953$	−19249.8	−	19249.8i	−0.654314	−	0.654314i	−0.954029	+	0.299715i	$0.903109\pi$
$954$		0			0
$955$	−16297.5	+	635.308i	−0.552225	+	0.0215268i
$956$	19527.7	+	12896.0i	0.660637	+	0.436281i
$957$		0			0
$958$	−29715.0	−	8926.38i	−1.00214	−	0.301042i
$959$	29336.9			0.987838
$960$		0			0
$961$	−5543.06			−0.186065
$962$	3643.09	+	1094.39i	0.122098	+	0.0366782i
$963$		0			0
$964$	28434.3	+	18777.8i	0.950007	+	0.627379i
$965$	−24314.7	+	26287.2i	−0.811105	+	0.876907i
$966$		0			0
$967$	3744.56	+	3744.56i	0.124526	+	0.124526i	0.766623	−	0.642097i	$-0.221935\pi$
$967$	3744.56	+	3744.56i	0.124526	+	0.124526i	−0.642097	+	0.766623i	$0.721935\pi$
$968$	−18505.4	−	22180.0i	−0.614449	−	0.736460i
$969$		0			0
$970$	12182.3	+	20671.5i	0.403248	+	0.684250i
$971$			29491.0i			0.974677i	0.873213	+	0.487338i	$0.162032\pi$
$971$			29491.0i			0.974677i	−0.873213	+	0.487338i	$0.837968\pi$
$972$		0			0
$973$	22475.4	+	22475.4i	0.740524	+	0.740524i
$974$	−24136.1	−	44863.7i	−0.794016	−	1.47590i
$975$		0			0
$976$	5832.75	+	13662.2i	0.191293	+	0.448070i
$977$	−13592.2	+	13592.2i	−0.445092	+	0.445092i	−0.893719	−	0.448627i	$-0.851913\pi$
$977$	−13592.2	+	13592.2i	−0.445092	+	0.445092i	0.448627	+	0.893719i	$0.351913\pi$
$978$		0			0
$979$	7740.14			0.252682
$980$	−22118.6	−	13399.8i	−0.720972	−	0.436777i
$981$		0			0
$982$	8559.36	−	28493.2i	0.278147	−	0.925921i
$983$	−12087.1	+	12087.1i	−0.392185	+	0.392185i	−0.875466	−	0.483280i	$-0.839445\pi$
$983$	−12087.1	+	12087.1i	−0.392185	+	0.392185i	0.483280	+	0.875466i	$0.339445\pi$
$984$		0			0
$985$	−24290.7	−	22467.9i	−0.785752	−	0.726790i
$986$	1315.01	+	2444.31i	0.0424730	+	0.0789478i
$987$		0			0
$988$	−825.910	−	4038.03i	−0.0265949	−	0.130027i
$989$		−	6640.01i		−	0.213488i
$990$		0			0
$991$			52539.6i			1.68413i	0.539374	+	0.842066i	$0.318661\pi$
$991$			52539.6i			1.68413i	−0.539374	+	0.842066i	$0.681339\pi$
$992$	−33814.9	+	3792.13i	−1.08228	+	0.121371i
$993$		0			0
$994$	38489.6	−	20706.9i	1.22818	−	0.660749i
$995$	909.194	+	23323.5i	0.0289682	+	0.743119i
$996$		0			0
$997$	12067.7	−	12067.7i	0.383337	−	0.383337i	−0.488966	−	0.872303i	$-0.662626\pi$
$997$	12067.7	−	12067.7i	0.383337	−	0.383337i	0.872303	+	0.488966i	$0.162626\pi$
$998$	−6623.82	−	1989.80i	−0.210094	−	0.0631121i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.4.k.e.163.1		12
3.2	odd	2		20.4.e.b.3.6	yes	12
4.3	odd	2	inner	180.4.k.e.163.4		12
5.2	odd	4	inner	180.4.k.e.127.4		12
12.11	even	2		20.4.e.b.3.3	✓	12
15.2	even	4		20.4.e.b.7.3	yes	12
15.8	even	4		100.4.e.e.7.4		12
15.14	odd	2		100.4.e.e.43.1		12
20.7	even	4	inner	180.4.k.e.127.1		12
24.5	odd	2		320.4.n.k.63.4		12
24.11	even	2		320.4.n.k.63.3		12
60.23	odd	4		100.4.e.e.7.1		12
60.47	odd	4		20.4.e.b.7.6	yes	12
60.59	even	2		100.4.e.e.43.4		12
120.77	even	4		320.4.n.k.127.3		12
120.107	odd	4		320.4.n.k.127.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.4.e.b.3.3	✓	12	12.11	even	2
20.4.e.b.3.6	yes	12	3.2	odd	2
20.4.e.b.7.3	yes	12	15.2	even	4
20.4.e.b.7.6	yes	12	60.47	odd	4
100.4.e.e.7.1		12	60.23	odd	4
100.4.e.e.7.4		12	15.8	even	4
100.4.e.e.43.1		12	15.14	odd	2
100.4.e.e.43.4		12	60.59	even	2
180.4.k.e.127.1		12	20.7	even	4	inner
180.4.k.e.127.4		12	5.2	odd	4	inner
180.4.k.e.163.1		12	1.1	even	1	trivial
180.4.k.e.163.4		12	4.3	odd	2	inner
320.4.n.k.63.3		12	24.11	even	2
320.4.n.k.63.4		12	24.5	odd	2
320.4.n.k.127.3		12	120.77	even	4
320.4.n.k.127.4		12	120.107	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	180.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.70884 - 0.813737i) q^{2} +(6.67566 + 4.40857i) q^{4} +(0.435501 + 11.1719i) q^{5} +(-17.7783 - 17.7783i) q^{7} +(-14.4959 - 17.3744i) q^{8} +(7.91125 - 30.6172i) q^{10} -7.37590i q^{11} +(-2.68249 - 2.68249i) q^{13} +(33.6917 + 62.6254i) q^{14} +(25.1290 + 58.8603i) q^{16} +(20.2367 - 20.2367i) q^{17} +135.808 q^{19} +(-46.3447 + 76.4995i) q^{20} +(-6.00204 + 19.9802i) q^{22} +(71.0426 - 71.0426i) q^{23} +(-124.621 + 9.73070i) q^{25} +(5.08361 + 9.44930i) q^{26} +(-40.3050 - 197.059i) q^{28} -34.2890i q^{29} -187.974i q^{31} +(-20.1737 - 179.892i) q^{32} +(-71.2855 + 38.3507i) q^{34} +(190.874 - 206.359i) q^{35} +(250.679 - 250.679i) q^{37} +(-367.882 - 110.512i) q^{38} +(187.791 - 169.513i) q^{40} +211.105 q^{41} +(46.7326 - 46.7326i) q^{43} +(32.5172 - 49.2390i) q^{44} +(-250.253 + 134.633i) q^{46} +(-189.707 - 189.707i) q^{47} +289.134i q^{49} +(345.496 + 75.0495i) q^{50} +(-6.08147 - 29.7334i) q^{52} +(74.5742 + 74.5742i) q^{53} +(82.4025 - 3.21221i) q^{55} +(-51.1739 + 566.598i) q^{56} +(-27.9022 + 92.8835i) q^{58} -101.072 q^{59} +232.112 q^{61} +(-152.961 + 509.191i) q^{62} +(-91.7370 + 503.715i) q^{64} +(28.8002 - 31.1367i) q^{65} +(-34.7419 - 34.7419i) q^{67} +(224.309 - 45.8785i) q^{68} +(-684.969 + 403.672i) q^{70} -614.600i q^{71} +(-37.4378 - 37.4378i) q^{73} +(-883.036 + 475.063i) q^{74} +(906.607 + 598.718i) q^{76} +(-131.131 + 131.131i) q^{77} -1002.91 q^{79} +(-646.635 + 306.371i) q^{80} +(-571.850 - 171.784i) q^{82} +(423.190 - 423.190i) q^{83} +(234.895 + 217.269i) q^{85} +(-164.619 + 88.5632i) q^{86} +(-128.152 + 106.920i) q^{88} +1049.38i q^{89} +95.3802i q^{91} +(787.453 - 161.060i) q^{92} +(359.514 + 668.257i) q^{94} +(59.1444 + 1517.22i) q^{95} +(-536.526 + 536.526i) q^{97} +(235.279 - 783.218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 12 q^{8} - 110 q^{10} + 116 q^{13} + 312 q^{16} + 332 q^{17} - 140 q^{20} + 360 q^{22} + 340 q^{25} + 164 q^{26} - 880 q^{28} + 376 q^{32} + 508 q^{37} - 1600 q^{38} + 1420 q^{40} + 656 q^{41}+ \cdots - 1698 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 + 12 * q^8 - 110 * q^10 + 116 * q^13 + 312 * q^16 + 332 * q^17 - 140 * q^20 + 360 * q^22 + 340 * q^25 + 164 * q^26 - 880 * q^28 + 376 * q^32 + 508 * q^37 - 1600 * q^38 + 1420 * q^40 + 656 * q^41 - 1432 * q^46 + 1570 * q^50 - 932 * q^52 + 644 * q^53 - 2048 * q^56 + 1576 * q^58 - 896 * q^61 - 2440 * q^62 + 2740 * q^65 + 844 * q^68 - 3040 * q^70 + 1436 * q^73 + 800 * q^76 - 3120 * q^77 - 1840 * q^80 - 1352 * q^82 + 500 * q^85 + 2552 * q^86 - 2400 * q^88 + 1840 * q^92 - 4772 * q^97 - 1698 * q^98

Introduction

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