LMFDB - Embedded newform 153.4.l.a.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,4,Mod(19,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("153.19");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	153.l (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.02729223088$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{8})$
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} + 54x^{10} + 1085x^{8} + 9836x^{6} + 38276x^{4} + 49664x^{2} + 16384 $ x^12 + 54x^10 + 1085x^8 + 9836x^6 + 38276x^4 + 49664*x^2 + 16384
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			145.2
Root			$-0.705468i$ of defining polynomial
Character	$\chi$	$=$	153.145
Dual form			153.4.l.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20595 - 1.20595i) q^{2} +5.09138i q^{4} +(-2.60601 + 6.29147i) q^{5} +(-5.31013 - 12.8198i) q^{7} +(15.7875 + 15.7875i) q^{8} +O(q^{10})$	\(q+(1.20595 - 1.20595i) q^{2} +5.09138i q^{4} +(-2.60601 + 6.29147i) q^{5} +(-5.31013 - 12.8198i) q^{7} +(15.7875 + 15.7875i) q^{8} +(4.44447 + 10.7299i) q^{10} +(-28.4888 + 11.8005i) q^{11} +66.0130i q^{13} +(-21.8637 - 9.05625i) q^{14} -2.65318 q^{16} +(-3.91802 + 69.9832i) q^{17} +(-56.3670 + 56.3670i) q^{19} +(-32.0322 - 13.2682i) q^{20} +(-20.1253 + 48.5868i) q^{22} +(26.6989 - 11.0590i) q^{23} +(55.5971 + 55.5971i) q^{25} +(79.6082 + 79.6082i) q^{26} +(65.2704 - 27.0359i) q^{28} +(101.871 - 245.938i) q^{29} +(-33.0662 - 13.6965i) q^{31} +(-129.500 + 129.500i) q^{32} +(79.6712 + 89.1210i) q^{34} +94.4935 q^{35} +(330.633 + 136.953i) q^{37} +135.951i q^{38} +(-140.469 + 58.1842i) q^{40} +(-12.5311 - 30.2527i) q^{41} +(-364.978 - 364.978i) q^{43} +(-60.0806 - 145.047i) q^{44} +(18.8608 - 45.5340i) q^{46} +210.602i q^{47} +(106.388 - 106.388i) q^{49} +134.094 q^{50} -336.097 q^{52} +(-61.6826 + 61.6826i) q^{53} -209.989i q^{55} +(118.559 - 286.226i) q^{56} +(-173.737 - 419.439i) q^{58} +(-219.718 - 219.718i) q^{59} +(139.774 + 337.444i) q^{61} +(-56.3933 + 23.3589i) q^{62} +291.115i q^{64} +(-415.318 - 172.030i) q^{65} +660.131 q^{67} +(-356.311 - 19.9481i) q^{68} +(113.954 - 113.954i) q^{70} +(367.732 + 152.319i) q^{71} +(246.235 - 594.463i) q^{73} +(563.884 - 233.568i) q^{74} +(-286.986 - 286.986i) q^{76} +(302.558 + 302.558i) q^{77} +(-355.241 + 147.146i) q^{79} +(6.91421 - 16.6924i) q^{80} +(-51.5949 - 21.3713i) q^{82} +(-108.533 + 108.533i) q^{83} +(-430.087 - 207.027i) q^{85} -880.289 q^{86} +(-636.068 - 263.468i) q^{88} -599.053i q^{89} +(846.272 - 350.537i) q^{91} +(56.3057 + 135.934i) q^{92} +(253.975 + 253.975i) q^{94} +(-207.738 - 501.524i) q^{95} +(-17.0560 + 41.1767i) q^{97} -256.598i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 20 q^{5} - 4 q^{7} - 28 q^{8}+O(q^{10}) $ 12 * q + 4 * q^2 + 20 * q^5 - 4 * q^7 - 28 * q^8	$ 12 q + 4 q^{2} + 20 q^{5} - 4 q^{7} - 28 q^{8} - 116 q^{10} - 40 q^{11} + 132 q^{14} + 184 q^{16} - 52 q^{17} - 12 q^{19} - 572 q^{20} - 620 q^{22} + 276 q^{23} - 464 q^{25} + 708 q^{26} + 452 q^{28} - 632 q^{29} + 188 q^{31} - 700 q^{32} + 764 q^{34} + 632 q^{35} + 940 q^{37} - 1864 q^{40} - 176 q^{41} - 1360 q^{43} + 1364 q^{44} + 452 q^{46} + 1044 q^{49} - 2856 q^{50} + 792 q^{52} + 360 q^{53} + 1788 q^{56} - 360 q^{58} + 584 q^{59} - 1052 q^{61} + 380 q^{62} - 404 q^{65} + 1080 q^{67} - 2532 q^{68} + 2072 q^{70} - 28 q^{71} + 824 q^{73} + 2292 q^{74} + 1328 q^{76} + 1252 q^{77} - 196 q^{79} + 904 q^{80} - 1528 q^{82} + 1008 q^{83} - 2824 q^{85} + 1200 q^{86} - 56 q^{88} + 2456 q^{91} - 396 q^{92} + 6360 q^{94} - 2172 q^{95} - 904 q^{97}+O(q^{100}) $ 12 * q + 4 * q^2 + 20 * q^5 - 4 * q^7 - 28 * q^8 - 116 * q^10 - 40 * q^11 + 132 * q^14 + 184 * q^16 - 52 * q^17 - 12 * q^19 - 572 * q^20 - 620 * q^22 + 276 * q^23 - 464 * q^25 + 708 * q^26 + 452 * q^28 - 632 * q^29 + 188 * q^31 - 700 * q^32 + 764 * q^34 + 632 * q^35 + 940 * q^37 - 1864 * q^40 - 176 * q^41 - 1360 * q^43 + 1364 * q^44 + 452 * q^46 + 1044 * q^49 - 2856 * q^50 + 792 * q^52 + 360 * q^53 + 1788 * q^56 - 360 * q^58 + 584 * q^59 - 1052 * q^61 + 380 * q^62 - 404 * q^65 + 1080 * q^67 - 2532 * q^68 + 2072 * q^70 - 28 * q^71 + 824 * q^73 + 2292 * q^74 + 1328 * q^76 + 1252 * q^77 - 196 * q^79 + 904 * q^80 - 1528 * q^82 + 1008 * q^83 - 2824 * q^85 + 1200 * q^86 - 56 * q^88 + 2456 * q^91 - 396 * q^92 + 6360 * q^94 - 2172 * q^95 - 904 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$

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 $

$2$	1.20595	−	1.20595i	0.426367	−	0.426367i	−0.461022	−	0.887389i	$-0.652517\pi$
$2$	1.20595	−	1.20595i	0.426367	−	0.426367i	0.887389	+	0.461022i	$0.152517\pi$
$3$		0			0
$3$		0			0
$4$			5.09138i			0.636422i
$5$	−2.60601	+	6.29147i	−0.233089	+	0.562726i	−0.996538	−	0.0831423i	$-0.973504\pi$
$5$	−2.60601	+	6.29147i	−0.233089	+	0.562726i	0.763449	+	0.645868i	$0.223504\pi$
$6$		0			0
$7$	−5.31013	−	12.8198i	−0.286720	−	0.692203i	0.713242	−	0.700918i	$-0.247226\pi$
$7$	−5.31013	−	12.8198i	−0.286720	−	0.692203i	−0.999962	+	0.00871466i	$0.997226\pi$
$8$	15.7875	+	15.7875i	0.697716	+	0.697716i
$9$		0			0
$10$	4.44447	+	10.7299i	0.140546	+	0.339309i
$11$	−28.4888	+	11.8005i	−0.780882	+	0.323452i	−0.737271	−	0.675597i	$-0.763886\pi$
$11$	−28.4888	+	11.8005i	−0.780882	+	0.323452i	−0.0436106	+	0.999049i	$0.513886\pi$
$12$		0			0
$13$			66.0130i			1.40836i	0.710021	+	0.704181i	$0.248686\pi$
$13$			66.0130i			1.40836i	−0.710021	+	0.704181i	$0.751314\pi$
$14$	−21.8637	−	9.05625i	−0.417380	−	0.172885i
$15$		0			0
$16$	−2.65318			−0.0414559
$17$	−3.91802	+	69.9832i	−0.0558976	+	0.998437i
$17$	−3.91802	+	69.9832i	−0.0558976	+	0.998437i
$18$		0			0
$19$	−56.3670	+	56.3670i	−0.680604	+	0.680604i	−0.960136	−	0.279532i	$-0.909821\pi$
$19$	−56.3670	+	56.3670i	−0.680604	+	0.680604i	0.279532	+	0.960136i	$0.409821\pi$
$20$	−32.0322	−	13.2682i	−0.358131	−	0.148343i
$21$		0			0
$22$	−20.1253	+	48.5868i	−0.195033	+	0.470852i
$23$	26.6989	−	11.0590i	0.242048	−	0.100259i	−0.258362	−	0.966048i	$-0.583183\pi$
$23$	26.6989	−	11.0590i	0.242048	−	0.100259i	0.500410	+	0.865789i	$0.333183\pi$
$24$		0			0
$25$	55.5971	+	55.5971i	0.444777	+	0.444777i
$26$	79.6082	+	79.6082i	0.600479	+	0.600479i
$27$		0			0
$28$	65.2704	−	27.0359i	0.440534	−	0.182475i
$29$	101.871	−	245.938i	0.652308	−	1.57481i	−0.157113	−	0.987581i	$-0.550219\pi$
$29$	101.871	−	245.938i	0.652308	−	1.57481i	0.809421	−	0.587229i	$-0.199781\pi$
$30$		0			0
$31$	−33.0662	−	13.6965i	−0.191576	−	0.0793534i	0.284833	−	0.958577i	$-0.408062\pi$
$31$	−33.0662	−	13.6965i	−0.191576	−	0.0793534i	−0.476409	+	0.879224i	$0.658062\pi$
$32$	−129.500	+	129.500i	−0.715392	+	0.715392i
$33$		0			0
$34$	79.6712	+	89.1210i	0.401867	+	0.449533i
$35$	94.4935			0.456352
$36$		0			0
$37$	330.633	+	136.953i	1.46907	+	0.608510i	0.966648	−	0.256110i	$-0.0824409\pi$
$37$	330.633	+	136.953i	1.46907	+	0.608510i	0.502426	+	0.864620i	$0.332441\pi$
$38$			135.951i			0.580374i
$39$		0			0
$40$	−140.469	+	58.1842i	−0.555253	+	0.229993i
$41$	−12.5311	−	30.2527i	−0.0477323	−	0.115236i	0.898215	−	0.439556i	$-0.144864\pi$
$41$	−12.5311	−	30.2527i	−0.0477323	−	0.115236i	−0.945947	+	0.324321i	$0.894864\pi$
$42$		0			0
$43$	−364.978	−	364.978i	−1.29439	−	1.29439i	−0.932045	−	0.362342i	$-0.881977\pi$
$43$	−364.978	−	364.978i	−1.29439	−	1.29439i	−0.362342	−	0.932045i	$-0.618023\pi$
$44$	−60.0806	−	145.047i	−0.205852	−	0.496971i
$45$		0			0
$46$	18.8608	−	45.5340i	0.0604538	−	0.145948i
$47$			210.602i			0.653606i	0.945093	+	0.326803i	$0.105971\pi$
$47$			210.602i			0.653606i	−0.945093	+	0.326803i	$0.894029\pi$
$48$		0			0
$49$	106.388	−	106.388i	0.310170	−	0.310170i
$50$	134.094			0.379276
$51$		0			0
$52$	−336.097			−0.896313
$53$	−61.6826	+	61.6826i	−0.159863	+	0.159863i	−0.782506	−	0.622643i	$-0.786059\pi$
$53$	−61.6826	+	61.6826i	−0.159863	+	0.159863i	0.622643	+	0.782506i	$0.286059\pi$
$54$		0			0
$55$		−	209.989i		−	0.514815i
$56$	118.559	−	286.226i	0.282912	−	0.683011i
$57$		0			0
$58$	−173.737	−	419.439i	−0.393324	−	0.949569i
$59$	−219.718	−	219.718i	−0.484828	−	0.484828i	0.421841	−	0.906670i	$-0.361384\pi$
$59$	−219.718	−	219.718i	−0.484828	−	0.484828i	−0.906670	+	0.421841i	$0.861384\pi$
$60$		0			0
$61$	139.774	+	337.444i	0.293381	+	0.708284i	1.00000		0.000689814i	$0.000219575\pi$
$61$	139.774	+	337.444i	0.293381	+	0.708284i	−0.706619	+	0.707594i	$0.749780\pi$
$62$	−56.3933	+	23.3589i	−0.115515	+	0.0478481i
$63$		0			0
$64$			291.115i			0.568583i
$65$	−415.318	−	172.030i	−0.792521	−	0.328273i
$66$		0			0
$67$	660.131			1.20370			0.601850	−	0.798609i	$-0.294431\pi$
$67$	660.131			1.20370			0.601850	+	0.798609i	$0.294431\pi$
$68$	−356.311	−	19.9481i	−0.635427	−	0.0355745i
$69$		0			0
$70$	113.954	−	113.954i	0.194573	−	0.194573i
$71$	367.732	+	152.319i	0.614672	+	0.254605i	0.668225	−	0.743960i	$-0.267054\pi$
$71$	367.732	+	152.319i	0.614672	+	0.254605i	−0.0535526	+	0.998565i	$0.517054\pi$
$72$		0			0
$73$	246.235	−	594.463i	0.394789	−	0.953105i	−0.594092	−	0.804397i	$-0.702489\pi$
$73$	246.235	−	594.463i	0.394789	−	0.953105i	0.988881	−	0.148708i	$-0.0475115\pi$
$74$	563.884	−	233.568i	0.885813	−	0.366916i
$75$		0			0
$76$	−286.986	−	286.986i	−0.433152	−	0.433152i
$77$	302.558	+	302.558i	0.447789	+	0.447789i
$78$		0			0
$79$	−355.241	+	147.146i	−0.505921	+	0.209559i	−0.621020	−	0.783795i	$-0.713282\pi$
$79$	−355.241	+	147.146i	−0.505921	+	0.209559i	0.115099	+	0.993354i	$0.463282\pi$
$80$	6.91421	−	16.6924i	0.00966290	−	0.0233283i
$81$		0			0
$82$	−51.5949	−	21.3713i	−0.0694842	−	0.0287813i
$83$	−108.533	+	108.533i	−0.143530	+	0.143530i	−0.775221	−	0.631690i	$-0.782361\pi$
$83$	−108.533	+	108.533i	−0.143530	+	0.143530i	0.631690	+	0.775221i	$0.282361\pi$
$84$		0			0
$85$	−430.087	−	207.027i	−0.548817	−	0.264179i
$86$	−880.289			−1.10377
$87$		0			0
$88$	−636.068	−	263.468i	−0.770512	−	0.319157i
$89$		−	599.053i		−	0.713477i	−0.934204	−	0.356738i	$-0.883889\pi$
$89$		−	599.053i		−	0.713477i	0.934204	−	0.356738i	$-0.116111\pi$
$90$		0			0
$91$	846.272	−	350.537i	0.974872	−	0.403805i
$92$	56.3057	+	135.934i	0.0638073	+	0.154045i
$93$		0			0
$94$	253.975	+	253.975i	0.278676	+	0.278676i
$95$	−207.738	−	501.524i	−0.224352	−	0.541635i
$96$		0			0
$97$	−17.0560	+	41.1767i	−0.0178533	+	0.0431017i	−0.932555	−	0.361028i	$-0.882426\pi$
$97$	−17.0560	+	41.1767i	−0.0178533	+	0.0431017i	0.914701	+	0.404130i	$0.132426\pi$
$98$		−	256.598i		−	0.264492i
$99$		0			0
$100$	−283.066	+	283.066i	−0.283066	+	0.283066i
$101$	1478.33			1.45643			0.728215	−	0.685348i	$-0.240350\pi$
$101$	1478.33			1.45643			0.728215	+	0.685348i	$0.240350\pi$
$102$		0			0
$103$	618.133			0.591325			0.295662	−	0.955293i	$-0.404460\pi$
$103$	618.133			0.591325			0.295662	+	0.955293i	$0.404460\pi$
$104$	−1042.18	+	1042.18i	−0.982637	+	0.982637i
$105$		0			0
$106$			148.772i			0.136321i
$107$	−53.1850	+	128.400i	−0.0480522	+	0.116008i	−0.946083	−	0.323924i	$-0.894998\pi$
$107$	−53.1850	+	128.400i	−0.0480522	+	0.116008i	0.898031	+	0.439933i	$0.144998\pi$
$108$		0			0
$109$	315.127	+	760.783i	0.276914	+	0.668531i	0.999747	−	0.0224926i	$-0.00716024\pi$
$109$	315.127	+	760.783i	0.276914	+	0.668531i	−0.722833	+	0.691023i	$0.757160\pi$
$110$	−253.235	−	253.235i	−0.219500	−	0.219500i
$111$		0			0
$112$	14.0887	+	34.0132i	0.0118862	+	0.0286959i
$113$	556.614	−	230.557i	0.463379	−	0.191938i	−0.138765	−	0.990325i	$-0.544313\pi$
$113$	556.614	−	230.557i	0.463379	−	0.191938i	0.602144	+	0.798387i	$0.294313\pi$
$114$		0			0
$115$			196.795i			0.159576i
$116$	1252.16	+	518.663i	1.00224	+	0.415143i
$117$		0			0
$118$	−529.937			−0.413430
$119$	917.975	−	321.392i	0.707148	−	0.247579i
$120$		0			0
$121$	−268.797	+	268.797i	−0.201951	+	0.201951i
$122$	575.501	+	238.380i	0.427077	+	0.176901i
$123$		0			0
$124$	69.7339	−	168.352i	0.0505023	−	0.121923i
$125$	−1281.11	+	530.652i	−0.916686	+	0.379704i
$126$		0			0
$127$	−1065.60	−	1065.60i	−0.744538	−	0.744538i	0.228909	−	0.973448i	$-0.426484\pi$
$127$	−1065.60	−	1065.60i	−0.744538	−	0.744538i	−0.973448	+	0.228909i	$0.926484\pi$
$128$	−684.929	−	684.929i	−0.472967	−	0.472967i
$129$		0			0
$130$	−708.312	+	293.392i	−0.477870	+	0.197940i
$131$	−1065.23	+	2571.69i	−0.710455	+	1.71519i	−0.0115939	+	0.999933i	$0.503691\pi$
$131$	−1065.23	+	2571.69i	−0.710455	+	1.71519i	−0.698861	+	0.715257i	$0.746309\pi$
$132$		0			0
$133$	1021.93	+	423.297i	0.666259	+	0.275974i
$134$	796.084	−	796.084i	0.513218	−	0.513218i
$135$		0			0
$136$	−1166.72	+	1043.01i	−0.735626	+	0.657625i
$137$	629.783			0.392744			0.196372	−	0.980529i	$-0.437084\pi$
$137$	629.783			0.392744			0.196372	+	0.980529i	$0.437084\pi$
$138$		0			0
$139$	2452.07	+	1015.68i	1.49627	+	0.619775i	0.972671	−	0.232190i	$-0.0745890\pi$
$139$	2452.07	+	1015.68i	1.49627	+	0.619775i	0.523599	+	0.851965i	$0.324589\pi$
$140$			481.102i			0.290432i
$141$		0			0
$142$	627.154	−	259.776i	0.370631	−	0.153520i
$143$	−778.983	−	1880.63i	−0.455537	−	1.09976i
$144$		0			0
$145$	1281.83	+	1281.83i	0.734141	+	0.734141i
$146$	−419.946	−	1013.84i	−0.238048	−	0.574698i
$147$		0			0
$148$	−697.278	+	1683.38i	−0.387270	+	0.934951i
$149$			2216.30i			1.21857i	0.792953	+	0.609283i	$0.208543\pi$
$149$			2216.30i			1.21857i	−0.792953	+	0.609283i	$0.791457\pi$
$150$		0			0
$151$	−1508.37	+	1508.37i	−0.812908	+	0.812908i	−0.985069	−	0.172161i	$-0.944925\pi$
$151$	−1508.37	+	1508.37i	−0.812908	+	0.812908i	0.172161	+	0.985069i	$0.444925\pi$
$152$	−1779.79			−0.949737
$153$		0			0
$154$	729.740			0.381845
$155$	172.342	−	172.342i	0.0893085	−	0.0893085i
$156$		0			0
$157$			345.107i			0.175430i	0.996146	+	0.0877152i	$0.0279565\pi$
$157$			345.107i			0.175430i	−0.996146	+	0.0877152i	$0.972043\pi$
$158$	−250.952	+	605.853i	−0.126359	+	0.305057i
$159$		0			0
$160$	−477.266	−	1152.22i	−0.235820	−	0.569319i
$161$	−283.549	−	283.549i	−0.138800	−	0.138800i
$162$		0			0
$163$	259.661	+	626.876i	0.124774	+	0.301231i	0.973907	−	0.226948i	$-0.0728748\pi$
$163$	259.661	+	626.876i	0.124774	+	0.301231i	−0.849133	+	0.528180i	$0.822875\pi$
$164$	154.028	−	63.8004i	0.0733387	−	0.0303779i
$165$		0			0
$166$			261.770i			0.122393i
$167$	738.909	+	306.066i	0.342386	+	0.141821i	0.547249	−	0.836970i	$-0.315675\pi$
$167$	738.909	+	306.066i	0.342386	+	0.141821i	−0.204863	+	0.978791i	$0.565675\pi$
$168$		0			0
$169$	−2160.71			−0.983483
$170$	−768.326	+	268.998i	−0.346635	+	0.121360i
$171$		0			0
$172$	1858.24	−	1858.24i	0.823777	−	0.823777i
$173$	1741.96	+	721.542i	0.765540	+	0.317097i	0.731064	−	0.682308i	$-0.239024\pi$
$173$	1741.96	+	721.542i	0.765540	+	0.317097i	0.0344756	+	0.999406i	$0.489024\pi$
$174$		0			0
$175$	417.515	−	1007.97i	0.180350	−	0.435402i
$176$	75.5859	−	31.3087i	0.0323722	−	0.0134090i
$177$		0			0
$178$	−722.426	−	722.426i	−0.304203	−	0.304203i
$179$	2537.71	+	2537.71i	1.05965	+	1.05965i	0.998104	+	0.0615460i	$0.0196031\pi$
$179$	2537.71	+	2537.71i	1.05965	+	1.05965i	0.0615460	+	0.998104i	$0.480397\pi$
$180$		0			0
$181$	−426.229	+	176.550i	−0.175035	+	0.0725020i	−0.468480	−	0.883474i	$-0.655198\pi$
$181$	−426.229	+	176.550i	−0.175035	+	0.0725020i	0.293445	+	0.955976i	$0.405198\pi$
$182$	597.830	−	1443.29i	0.243484	−	0.587823i
$183$		0			0
$184$	596.103	+	246.914i	0.238833	+	0.0989280i
$185$	−1723.27	+	1723.27i	−0.684849	+	0.684849i
$186$		0			0
$187$	−714.214	−	2039.97i	−0.279297	−	0.797741i
$188$	−1072.26			−0.415969
$189$		0			0
$190$	−855.333	−	354.291i	−0.326592	−	0.135279i
$191$		−	4519.91i		−	1.71230i	−0.516728	−	0.856149i	$-0.672850\pi$
$191$		−	4519.91i		−	1.71230i	0.516728	−	0.856149i	$-0.327150\pi$
$192$		0			0
$193$	−2705.97	+	1120.85i	−1.00922	+	0.418034i	−0.825171	−	0.564882i	$-0.808922\pi$
$193$	−2705.97	+	1120.85i	−1.00922	+	0.418034i	−0.184052	+	0.982916i	$0.558922\pi$
$194$	29.0884	+	70.2256i	0.0107651	+	0.0259892i
$195$		0			0
$196$	541.663	+	541.663i	0.197399	+	0.197399i
$197$	−737.100	−	1779.52i	−0.266580	−	0.643580i	0.732738	−	0.680511i	$-0.238242\pi$
$197$	−737.100	−	1779.52i	−0.266580	−	0.643580i	−0.999318	+	0.0369306i	$0.988242\pi$
$198$		0			0
$199$	1181.20	−	2851.66i	0.420767	−	1.01582i	−0.561354	−	0.827576i	$-0.689720\pi$
$199$	1181.20	−	2851.66i	0.420767	−	1.01582i	0.982122	−	0.188247i	$-0.0602805\pi$
$200$			1755.48i			0.620656i
$201$		0			0
$202$	1782.79	−	1782.79i	0.620974	−	0.620974i
$203$	−3693.81			−1.27712
$204$		0			0
$205$	222.990			0.0759721
$206$	745.436	−	745.436i	0.252121	−	0.252121i
$207$		0			0
$208$		−	175.144i		−	0.0583849i
$209$	940.673	−	2270.99i	0.311329	−	0.751614i
$210$		0			0
$211$	−1378.58	−	3328.18i	−0.449787	−	1.08588i	−0.972402	−	0.233314i	$-0.925043\pi$
$211$	−1378.58	−	3328.18i	−0.449787	−	1.08588i	0.522614	−	0.852569i	$-0.324957\pi$
$212$	−314.050	−	314.050i	−0.101741	−	0.101741i
$213$		0			0
$214$	90.7053	+	218.982i	0.0289742	+	0.0699500i
$215$	3247.38	−	1345.11i	1.03009	−	0.426678i
$216$		0			0
$217$			496.631i			0.155362i
$218$	1297.49	+	537.439i	0.403106	+	0.166972i
$219$		0			0
$220$	1069.13			0.327640
$221$	−4619.80	−	258.640i	−1.40616	−	0.0787241i
$222$		0			0
$223$	−1115.41	+	1115.41i	−0.334948	+	0.334948i	−0.854462	−	0.519514i	$-0.826113\pi$
$223$	−1115.41	+	1115.41i	−0.334948	+	0.334948i	0.519514	+	0.854462i	$0.326113\pi$
$224$	2347.82	+	972.498i	0.700314	+	0.290079i
$225$		0			0
$226$	393.208	−	949.287i	0.115734	−	0.279405i
$227$	3966.12	−	1642.82i	1.15965	−	0.480343i	0.281892	−	0.959446i	$-0.409038\pi$
$227$	3966.12	−	1642.82i	1.15965	−	0.480343i	0.877759	+	0.479103i	$0.159038\pi$
$228$		0			0
$229$	−410.753	−	410.753i	−0.118530	−	0.118530i	0.645354	−	0.763884i	$-0.276710\pi$
$229$	−410.753	−	410.753i	−0.118530	−	0.118530i	−0.763884	+	0.645354i	$0.776710\pi$
$230$	237.324	+	237.324i	0.0680378	+	0.0680378i
$231$		0			0
$232$	5491.03	−	2274.46i	1.55390	−	0.643645i
$233$	257.078	−	620.642i	0.0722823	−	0.174505i	−0.883609	−	0.468225i	$-0.844894\pi$
$233$	257.078	−	620.642i	0.0722823	−	0.174505i	0.955891	+	0.293721i	$0.0948935\pi$
$234$		0			0
$235$	−1325.00	−	548.831i	−0.367801	−	0.152348i
$236$	1118.67	−	1118.67i	0.308556	−	0.308556i
$237$		0			0
$238$	719.448	−	1494.61i	0.195945	−	0.407064i
$239$	273.635			0.0740584			0.0370292	−	0.999314i	$-0.488211\pi$
$239$	273.635			0.0740584			0.0370292	+	0.999314i	$0.488211\pi$
$240$		0			0
$241$	5992.80	+	2482.30i	1.60178	+	0.663481i	0.991667	−	0.128831i	$-0.0411223\pi$
$241$	5992.80	+	2482.30i	1.60178	+	0.663481i	0.610117	+	0.792311i	$0.291122\pi$
$242$			648.310i			0.172211i
$243$		0			0
$244$	−1718.06	+	711.643i	−0.450768	+	0.186714i
$245$	392.089	+	946.587i	0.102244	+	0.246838i
$246$		0			0
$247$	−3720.95	−	3720.95i	−0.958537	−	0.958537i
$248$	−305.800	−	738.266i	−0.0782996	−	0.189032i
$249$		0			0
$250$	−905.010	+	2184.89i	−0.228951	+	0.552738i
$251$			2527.58i			0.635615i	0.948155	+	0.317808i	$0.102947\pi$
$251$			2527.58i			0.635615i	−0.948155	+	0.317808i	$0.897053\pi$
$252$		0			0
$253$	−630.117	+	630.117i	−0.156582	+	0.156582i
$254$	−2570.11			−0.634893
$255$		0			0
$256$	−3980.89			−0.971898
$257$	−1203.81	+	1203.81i	−0.292184	+	0.292184i	−0.837943	−	0.545758i	$-0.816242\pi$
$257$	−1203.81	+	1203.81i	−0.292184	+	0.292184i	0.545758	+	0.837943i	$0.316242\pi$
$258$		0			0
$259$		−	4965.88i		−	1.19137i
$260$	875.872	−	2114.54i	0.208920	−	0.504378i
$261$		0			0
$262$	1816.72	+	4385.94i	0.428386	+	1.03421i
$263$	−3022.46	−	3022.46i	−0.708641	−	0.708641i	0.257608	−	0.966249i	$-0.417066\pi$
$263$	−3022.46	−	3022.46i	−0.708641	−	0.708641i	−0.966249	+	0.257608i	$0.917066\pi$
$264$		0			0
$265$	−227.328	−	548.819i	−0.0526969	−	0.127222i
$266$	1742.87	−	721.919i	0.401737	−	0.166405i
$267$		0			0
$268$			3360.98i			0.766061i
$269$	−7387.65	−	3060.07i	−1.67447	−	0.693589i	−0.675434	−	0.737420i	$-0.736044\pi$
$269$	−7387.65	−	3060.07i	−1.67447	−	0.693589i	−0.999039	+	0.0438311i	$0.986044\pi$
$270$		0			0
$271$	−474.268			−0.106309			−0.0531545	−	0.998586i	$-0.516928\pi$
$271$	−474.268			−0.106309			−0.0531545	+	0.998586i	$0.516928\pi$
$272$	10.3952	−	185.678i	0.00231729	−	0.0413911i
$273$		0			0
$274$	759.485	−	759.485i	0.167453	−	0.167453i
$275$	−2239.97	−	927.825i	−0.491182	−	0.203454i
$276$		0			0
$277$	−1081.56	+	2611.11i	−0.234601	+	0.566378i	−0.996708	−	0.0810736i	$-0.974165\pi$
$277$	−1081.56	+	2611.11i	−0.234601	+	0.566378i	0.762107	+	0.647451i	$0.224165\pi$
$278$	4181.92	−	1732.21i	0.902212	−	0.373708i
$279$		0			0
$280$	1491.82	+	1491.82i	0.318404	+	0.318404i
$281$	1766.46	+	1766.46i	0.375011	+	0.375011i	0.869299	−	0.494287i	$-0.164571\pi$
$281$	1766.46	+	1766.46i	0.375011	+	0.375011i	−0.494287	+	0.869299i	$0.664571\pi$
$282$		0			0
$283$	2233.09	−	924.974i	0.469057	−	0.194290i	−0.135619	−	0.990761i	$-0.543302\pi$
$283$	2233.09	−	924.974i	0.469057	−	0.194290i	0.604676	+	0.796471i	$0.293302\pi$
$284$	−775.516	+	1872.26i	−0.162037	+	0.391191i
$285$		0			0
$286$	−3207.36	−	1328.53i	−0.663129	−	0.274677i
$287$	−321.291	+	321.291i	−0.0660808	+	0.0660808i
$288$		0			0
$289$	−4882.30	−	548.391i	−0.993751	−	0.111620i
$290$	3091.65			0.626027
$291$		0			0
$292$	3026.64	+	1253.67i	0.606577	+	0.251253i
$293$			6652.17i			1.32636i	0.748459	+	0.663181i	$0.230794\pi$
$293$			6652.17i			1.32636i	−0.748459	+	0.663181i	$0.769206\pi$
$294$		0			0
$295$	1954.94	−	809.761i	0.385833	−	0.159817i
$296$	3057.73	+	7382.02i	0.600429	+	1.44956i
$297$		0			0
$298$	2672.74	+	2672.74i	0.519557	+	0.519557i
$299$	730.039	+	1762.47i	0.141202	+	0.340891i
$300$		0			0
$301$	−2740.86	+	6617.02i	−0.524852	+	1.26711i
$302$			3638.02i			0.693194i
$303$		0			0
$304$	149.552	−	149.552i	0.0282151	−	0.0282151i
$305$	−2487.27			−0.466954
$306$		0			0
$307$	−2511.18			−0.466842			−0.233421	−	0.972376i	$-0.574992\pi$
$307$	−2511.18			−0.466842			−0.233421	+	0.972376i	$0.574992\pi$
$308$	−1540.44	+	1540.44i	−0.284983	+	0.284983i
$309$		0			0
$310$		−	415.670i		−	0.0761563i
$311$	−1371.96	+	3312.20i	−0.250150	+	0.603916i	−0.998216	−	0.0597089i	$-0.980983\pi$
$311$	−1371.96	+	3312.20i	−0.250150	+	0.603916i	0.748066	+	0.663625i	$0.230983\pi$
$312$		0			0
$313$	−999.691	−	2413.47i	−0.180530	−	0.435838i	0.807546	−	0.589804i	$-0.200795\pi$
$313$	−999.691	−	2413.47i	−0.180530	−	0.435838i	−0.988076	+	0.153967i	$0.950795\pi$
$314$	416.182	+	416.182i	0.0747977	+	0.0747977i
$315$		0			0
$316$	−749.175	−	1808.67i	−0.133368	−	0.321980i
$317$	3606.64	−	1493.92i	0.639019	−	0.264690i	−0.0395609	−	0.999217i	$-0.512596\pi$
$317$	3606.64	−	1493.92i	0.639019	−	0.264690i	0.678579	+	0.734527i	$0.262596\pi$
$318$		0			0
$319$			8208.60i			1.44073i
$320$	−1831.54	−	758.647i	−0.319956	−	0.132530i
$321$		0			0
$322$	−683.890			−0.118359
$323$	−3723.90	−	4165.59i	−0.641496	−	0.717584i
$324$		0			0
$325$	−3670.13	+	3670.13i	−0.626407	+	0.626407i
$326$	1069.12	+	442.843i	0.181635	+	0.0752355i
$327$		0			0
$328$	279.780	−	675.449i	0.0470984	−	0.113706i
$329$	2699.87	−	1118.32i	0.452428	−	0.187402i
$330$		0			0
$331$	4409.54	+	4409.54i	0.732236	+	0.732236i	0.971062	−	0.238826i	$-0.0767626\pi$
$331$	4409.54	+	4409.54i	0.732236	+	0.732236i	−0.238826	+	0.971062i	$0.576763\pi$
$332$	−552.581	−	552.581i	−0.0913459	−	0.0913459i
$333$		0			0
$334$	1260.19	−	521.986i	0.206450	−	0.0855144i
$335$	−1720.31	+	4153.19i	−0.280569	+	0.677353i
$336$		0			0
$337$	3549.62	+	1470.30i	0.573769	+	0.237663i	0.650650	−	0.759378i	$-0.274496\pi$
$337$	3549.62	+	1470.30i	0.573769	+	0.237663i	−0.0768818	+	0.997040i	$0.524496\pi$
$338$	−2605.71	+	2605.71i	−0.419325	+	0.419325i
$339$		0			0
$340$	1054.05	−	2189.73i	0.168130	−	0.349279i
$341$	1103.64			0.175265
$342$		0			0
$343$	−6325.99	−	2620.31i	−0.995836	−	0.412489i
$344$		−	11524.2i		−	1.80623i
$345$		0			0
$346$	2970.85	−	1230.57i	0.461601	−	0.191201i
$347$	−3176.99	−	7669.92i	−0.491497	−	1.18658i	−0.953958	−	0.299940i	$-0.903034\pi$
$347$	−3176.99	−	7669.92i	−0.491497	−	1.18658i	0.462461	−	0.886640i	$-0.346966\pi$
$348$		0			0
$349$	3485.45	+	3485.45i	0.534590	+	0.534590i	0.921935	−	0.387345i	$-0.126608\pi$
$349$	3485.45	+	3485.45i	0.534590	+	0.534590i	−0.387345	+	0.921935i	$0.626608\pi$
$350$	−712.058	−	1719.06i	−0.108746	−	0.262536i
$351$		0			0
$352$	2161.14	−	5217.45i	0.327242	−	0.790032i
$353$			9607.54i			1.44861i	0.689482	+	0.724303i	$0.257838\pi$
$353$			9607.54i			1.44861i	−0.689482	+	0.724303i	$0.742162\pi$
$354$		0			0
$355$	−1916.62	+	1916.62i	−0.286546	+	0.286546i
$356$	3050.00			0.454073
$357$		0			0
$358$	6120.69			0.903600
$359$	1387.88	−	1387.88i	0.204038	−	0.204038i	−0.597690	−	0.801728i	$-0.703915\pi$
$359$	1387.88	−	1387.88i	0.204038	−	0.204038i	0.801728	+	0.597690i	$0.203915\pi$
$360$		0			0
$361$			504.522i			0.0735561i
$362$	−301.100	+	726.921i	−0.0437168	+	0.105542i
$363$		0			0
$364$	1784.72	+	4308.69i	0.256991	+	0.620431i
$365$	3098.36	+	3098.36i	0.444316	+	0.444316i
$366$		0			0
$367$	−1323.43	−	3195.04i	−0.188235	−	0.454441i	0.801385	−	0.598149i	$-0.204097\pi$
$367$	−1323.43	−	3195.04i	−0.188235	−	0.454441i	−0.989620	+	0.143709i	$0.954097\pi$
$368$	−70.8368	+	29.3416i	−0.0100343	+	0.00415634i
$369$		0			0
$370$			4156.34i			0.583994i
$371$	1118.30	+	463.215i	0.156494	+	0.0648219i
$372$		0			0
$373$	−2661.22			−0.369418			−0.184709	−	0.982793i	$-0.559134\pi$
$373$	−2661.22			−0.369418			−0.184709	+	0.982793i	$0.559134\pi$
$374$	−3321.41	−	1598.80i	−0.459213	−	0.221048i
$375$		0			0
$376$	−3324.88	+	3324.88i	−0.456031	+	0.456031i
$377$	16235.1	+	6724.79i	2.21790	+	0.918685i
$378$		0			0
$379$	2136.53	−	5158.04i	0.289568	−	0.699079i	−0.710421	−	0.703777i	$-0.751495\pi$
$379$	2136.53	−	5158.04i	0.289568	−	0.699079i	0.999989	+	0.00469813i	$0.00149547\pi$
$380$	2553.45	−	1057.67i	0.344708	−	0.142783i
$381$		0			0
$382$	−5450.77	−	5450.77i	−0.730068	−	0.730068i
$383$	−5538.16	−	5538.16i	−0.738868	−	0.738868i	0.233491	−	0.972359i	$-0.424985\pi$
$383$	−5538.16	−	5538.16i	−0.738868	−	0.738868i	−0.972359	+	0.233491i	$0.924985\pi$
$384$		0			0
$385$	−2692.01	+	1115.07i	−0.356357	+	0.147608i
$386$	−1911.57	+	4614.95i	−0.252064	+	0.608535i
$387$		0			0
$388$	−209.646	−	86.8383i	−0.0274309	−	0.0113622i
$389$	5255.89	−	5255.89i	0.685050	−	0.685050i	−0.276084	−	0.961134i	$-0.589037\pi$
$389$	5255.89	−	5255.89i	0.685050	−	0.685050i	0.961134	+	0.276084i	$0.0890368\pi$
$390$		0			0
$391$	669.339	+	1911.80i	0.0865728	+	0.247273i
$392$	3359.22			0.432821
$393$		0			0
$394$	−3034.91	−	1257.10i	−0.388062	−	0.160741i
$395$		−	2618.45i		−	0.333541i
$396$		0			0
$397$	8814.05	−	3650.90i	1.11427	−	0.461545i	0.251863	−	0.967763i	$-0.418957\pi$
$397$	8814.05	−	3650.90i	1.11427	−	0.461545i	0.862406	+	0.506218i	$0.168957\pi$
$398$	−2014.49	−	4863.41i	−0.253712	−	0.612514i
$399$		0			0
$400$	−147.509	−	147.509i	−0.0184386	−	0.0184386i
$401$	−3315.30	−	8003.85i	−0.412863	−	0.996741i	−0.984365	−	0.176140i	$-0.943639\pi$
$401$	−3315.30	−	8003.85i	−0.412863	−	0.996741i	0.571502	−	0.820601i	$-0.306361\pi$
$402$		0			0
$403$	904.144	−	2182.80i	0.111758	−	0.269808i
$404$			7526.75i			0.926905i
$405$		0			0
$406$	−4454.55	+	4454.55i	−0.544521	+	0.544521i
$407$	−11035.4			−1.34400
$408$		0			0
$409$	5279.17			0.638235			0.319117	−	0.947715i	$-0.396614\pi$
$409$	5279.17			0.638235			0.319117	+	0.947715i	$0.396614\pi$
$410$	268.914	−	268.914i	0.0323920	−	0.0323920i
$411$		0			0
$412$			3147.15i			0.376332i
$413$	−1650.01	+	3983.47i	−0.196590	+	0.474610i
$414$		0			0
$415$	−399.993	−	965.668i	−0.0473129	−	0.114224i
$416$	−8548.66	−	8548.66i	−1.00753	−	1.00753i
$417$		0			0
$418$	−1604.29	−	3873.09i	−0.187723	−	0.453204i
$419$	8692.08	−	3600.38i	1.01345	−	0.419785i	0.186738	−	0.982410i	$-0.440208\pi$
$419$	8692.08	−	3600.38i	1.01345	−	0.419785i	0.826713	+	0.562624i	$0.190208\pi$
$420$		0			0
$421$		−	8191.97i		−	0.948343i	−0.880433	−	0.474171i	$-0.842748\pi$
$421$		−	8191.97i		−	0.948343i	0.880433	−	0.474171i	$-0.157252\pi$
$422$	−5676.10	−	2351.12i	−0.654759	−	0.271210i
$423$		0			0
$424$	−1947.63			−0.223079
$425$	−4108.69	+	3673.03i	−0.468943	+	0.419219i
$426$		0			0
$427$	3583.75	−	3583.75i	0.406158	−	0.406158i
$428$	−653.733	−	270.785i	−0.0738303	−	0.0305815i
$429$		0			0
$430$	2294.04	−	5538.31i	0.257276	−	0.621119i
$431$	−1801.84	+	746.345i	−0.201372	+	0.0834111i	−0.481090	−	0.876671i	$-0.659759\pi$
$431$	−1801.84	+	746.345i	−0.201372	+	0.0834111i	0.279718	+	0.960082i	$0.409759\pi$
$432$		0			0
$433$	−7885.88	−	7885.88i	−0.875223	−	0.875223i	0.117813	−	0.993036i	$-0.462412\pi$
$433$	−7885.88	−	7885.88i	−0.875223	−	0.875223i	−0.993036	+	0.117813i	$0.962412\pi$
$434$	598.911	+	598.911i	0.0662411	+	0.0662411i
$435$		0			0
$436$	−3873.44	+	1604.43i	−0.425468	+	0.176235i
$437$	−881.570	+	2128.30i	−0.0965016	+	0.232976i
$438$		0			0
$439$	−434.369	−	179.922i	−0.0472240	−	0.0195608i	0.358946	−	0.933358i	$-0.383136\pi$
$439$	−434.369	−	179.922i	−0.0472240	−	0.0195608i	−0.406170	+	0.913797i	$0.633136\pi$
$440$	3315.20	−	3315.20i	0.359195	−	0.359195i
$441$		0			0
$442$	−5883.14	+	5259.33i	−0.633105	+	0.565975i
$443$	13132.9			1.40849			0.704246	−	0.709956i	$-0.251285\pi$
$443$	13132.9			1.40849			0.704246	+	0.709956i	$0.251285\pi$
$444$		0			0
$445$	3768.92	+	1561.14i	0.401492	+	0.166303i
$446$			2690.25i			0.285621i
$447$		0			0
$448$	3732.02	−	1545.86i	0.393575	−	0.163024i
$449$	−3992.55	−	9638.87i	−0.419644	−	1.01311i	−0.982451	−	0.186522i	$-0.940279\pi$
$449$	−3992.55	−	9638.87i	−0.419644	−	1.01311i	0.562807	−	0.826588i	$-0.309721\pi$
$450$		0			0
$451$	713.990	+	713.990i	0.0745465	+	0.0745465i
$452$	1173.85	+	2833.93i	0.122154	+	0.294905i
$453$		0			0
$454$	2801.78	−	6764.09i	0.289634	−	0.699239i
$455$			6237.79i			0.642708i
$456$		0			0
$457$	179.170	−	179.170i	0.0183397	−	0.0183397i	−0.697877	−	0.716217i	$-0.745872\pi$
$457$	179.170	−	179.170i	0.0183397	−	0.0183397i	0.716217	+	0.697877i	$0.245872\pi$
$458$	−990.694			−0.101074
$459$		0			0
$460$	−1001.96			−0.101558
$461$	−11002.7	+	11002.7i	−1.11160	+	1.11160i	−0.118665	+	0.992934i	$0.537861\pi$
$461$	−11002.7	+	11002.7i	−1.11160	+	1.11160i	−0.992934	+	0.118665i	$0.962139\pi$
$462$		0			0
$463$		−	10727.9i		−	1.07682i	−0.842684	−	0.538409i	$-0.819026\pi$
$463$		−	10727.9i		−	1.07682i	0.842684	−	0.538409i	$-0.180974\pi$
$464$	−270.281	+	652.516i	−0.0270420	+	0.0652852i
$465$		0			0
$466$	−438.439	−	1058.49i	−0.0435843	−	0.105222i
$467$	−1386.27	−	1386.27i	−0.137364	−	0.137364i	0.635081	−	0.772445i	$-0.280967\pi$
$467$	−1386.27	−	1386.27i	−0.137364	−	0.137364i	−0.772445	+	0.635081i	$0.780967\pi$
$468$		0			0
$469$	−3505.38	−	8462.74i	−0.345125	−	0.833205i
$470$	−2259.74	+	936.014i	−0.221774	+	0.0918619i
$471$		0			0
$472$		−	6937.61i		−	0.676545i
$473$	14704.7	+	6090.89i	1.42944	+	0.592092i
$474$		0			0
$475$	−6267.68			−0.605434
$476$	1636.33	+	4673.76i	0.157565	+	0.450045i
$477$		0			0
$478$	329.989	−	329.989i	0.0315761	−	0.0315761i
$479$	3967.31	+	1643.31i	0.378436	+	0.156754i	0.563790	−	0.825918i	$-0.309343\pi$
$479$	3967.31	+	1643.31i	0.378436	+	0.156754i	−0.185353	+	0.982672i	$0.559343\pi$
$480$		0			0
$481$	−9040.65	+	21826.1i	−0.857002	+	2.06899i
$482$	10220.5	−	4233.48i	0.965834	−	0.400062i
$483$		0			0
$484$	−1368.55	−	1368.55i	−0.128526	−	0.128526i
$485$	−214.614	−	214.614i	−0.0200930	−	0.0200930i
$486$		0			0
$487$	16642.3	−	6893.47i	1.54853	−	0.641423i	0.565483	−	0.824760i	$-0.308690\pi$
$487$	16642.3	−	6893.47i	1.54853	−	0.641423i	0.983050	+	0.183337i	$0.0586899\pi$
$488$	−3120.73	+	7534.10i	−0.289485	+	0.698878i
$489$		0			0
$490$	1614.37	+	668.696i	0.148837	+	0.0616502i
$491$	9710.80	−	9710.80i	0.892551	−	0.892551i	−0.102212	−	0.994763i	$-0.532592\pi$
$491$	9710.80	−	9710.80i	0.892551	−	0.892551i	0.994763	+	0.102212i	$0.0325920\pi$
$492$		0			0
$493$	16812.4	+	8092.83i	1.53589	+	0.739316i
$494$	−8974.55			−0.817377
$495$		0			0
$496$	87.7304	+	36.3391i	0.00794196	+	0.00328967i
$497$		−	5523.07i		−	0.498478i
$498$		0			0
$499$	7157.95	−	2964.92i	0.642152	−	0.265988i	−0.0377542	−	0.999287i	$-0.512020\pi$
$499$	7157.95	−	2964.92i	0.642152	−	0.265988i	0.679906	+	0.733299i	$0.262020\pi$
$500$	−2701.75	−	6522.60i	−0.241652	−	0.583399i
$501$		0			0
$502$	3048.13	+	3048.13i	0.271005	+	0.271005i
$503$	−7348.93	−	17741.9i	−0.651436	−	1.57271i	−0.810694	−	0.585470i	$-0.800910\pi$
$503$	−7348.93	−	17741.9i	−0.651436	−	1.57271i	0.159258	−	0.987237i	$-0.449090\pi$
$504$		0			0
$505$	−3852.55	+	9300.87i	−0.339478	+	0.819571i
$506$			1519.78i			0.133522i
$507$		0			0
$508$	5425.35	−	5425.35i	0.473841	−	0.473841i
$509$	151.325			0.0131775			0.00658876	−	0.999978i	$-0.497903\pi$
$509$	151.325			0.0131775			0.00658876	+	0.999978i	$0.497903\pi$
$510$		0			0
$511$	−8928.43			−0.772936
$512$	678.683	−	678.683i	0.0585817	−	0.0585817i
$513$		0			0
$514$			2903.45i			0.249155i
$515$	−1610.86	+	3888.96i	−0.137831	+	0.332754i
$516$		0			0
$517$	−2485.20	−	5999.80i	−0.211410	−	0.510389i
$518$	−5988.59	−	5988.59i	−0.507961	−	0.507961i
$519$		0			0
$520$	−3840.91	−	9272.78i	−0.323914	−	0.781997i
$521$	−7897.89	+	3271.41i	−0.664133	+	0.275093i	−0.689176	−	0.724594i	$-0.742027\pi$
$521$	−7897.89	+	3271.41i	−0.664133	+	0.275093i	0.0250438	+	0.999686i	$0.492027\pi$
$522$		0			0
$523$			17874.0i			1.49441i	0.664593	+	0.747205i	$0.268605\pi$
$523$			17874.0i			1.49441i	−0.664593	+	0.747205i	$0.731395\pi$
$524$	−13093.5	−	5423.49i	−1.09159	−	0.452150i
$525$		0			0
$526$	−7289.85			−0.604283
$527$	1088.08	−	2260.41i	0.0899380	−	0.186841i
$528$		0			0
$529$	−8012.84	+	8012.84i	−0.658572	+	0.658572i
$530$	−935.994	−	387.701i	−0.0767113	−	0.0317749i
$531$		0			0
$532$	−2155.16	+	5203.03i	−0.175636	+	0.424022i
$533$	1997.07	−	827.212i	0.162294	−	0.0672243i
$534$		0			0
$535$	−669.223	−	669.223i	−0.0540805	−	0.0540805i
$536$	10421.8	+	10421.8i	0.839841	+	0.839841i
$537$		0			0
$538$	−12599.4	+	5218.85i	−1.00966	+	0.418216i
$539$	−1775.45	+	4286.31i	−0.141881	+	0.342531i
$540$		0			0
$541$	−1960.69	−	812.146i	−0.155817	−	0.0645414i	0.303412	−	0.952859i	$-0.401874\pi$
$541$	−1960.69	−	812.146i	−0.155817	−	0.0645414i	−0.459229	+	0.888318i	$0.651874\pi$
$542$	−571.942	+	571.942i	−0.0453266	+	0.0453266i
$543$		0			0
$544$	−8555.43	−	9570.19i	−0.674285	−	0.754262i
$545$	−5607.67			−0.440745
$546$		0			0
$547$	262.443	+	108.707i	0.0205141	+	0.00849724i	0.392917	−	0.919574i	$-0.371466\pi$
$547$	262.443	+	108.707i	0.0205141	+	0.00849724i	−0.372403	+	0.928071i	$0.621466\pi$
$548$			3206.46i			0.249951i
$549$		0			0
$550$	−3820.19	+	1582.38i	−0.296170	+	0.122678i
$551$	8120.62	+	19604.9i	0.627859	+	1.51579i
$552$		0			0
$553$	3772.75	+	3772.75i	0.290115	+	0.290115i
$554$	1844.56	+	4453.17i	0.141459	+	0.341511i
$555$		0			0
$556$	−5171.21	+	12484.4i	−0.394439	+	0.952260i
$557$		−	9915.36i		−	0.754268i	−0.926159	−	0.377134i	$-0.876910\pi$
$557$		−	9915.36i		−	0.754268i	0.926159	−	0.377134i	$-0.123090\pi$
$558$		0			0
$559$	24093.3	−	24093.3i	1.82297	−	1.82297i
$560$	−250.708			−0.0189185
$561$		0			0
$562$	4260.52			0.319785
$563$	3569.84	−	3569.84i	0.267231	−	0.267231i	−0.560753	−	0.827983i	$-0.689488\pi$
$563$	3569.84	−	3569.84i	0.267231	−	0.267231i	0.827983	+	0.560753i	$0.189488\pi$
$564$		0			0
$565$			4102.75i			0.305494i
$566$	1577.51	−	3808.46i	0.117152	−	0.282829i
$567$		0			0
$568$	3400.82	+	8210.32i	0.251224	+	0.606509i
$569$	7753.04	+	7753.04i	0.571220	+	0.571220i	0.932469	−	0.361249i	$-0.117650\pi$
$569$	7753.04	+	7753.04i	0.571220	+	0.571220i	−0.361249	+	0.932469i	$0.617650\pi$
$570$		0			0
$571$	2586.01	+	6243.18i	0.189529	+	0.457564i	0.989869	−	0.141983i	$-0.0453477\pi$
$571$	2586.01	+	6243.18i	0.189529	+	0.457564i	−0.800340	+	0.599546i	$0.795348\pi$
$572$	9575.01	−	3966.10i	0.699915	−	0.289914i
$573$		0			0
$574$			774.920i			0.0563494i
$575$	2099.23	+	869.529i	0.152250	+	0.0630641i
$576$		0			0
$577$	18050.9			1.30237			0.651187	−	0.758917i	$-0.274271\pi$
$577$	18050.9			1.30237			0.651187	+	0.758917i	$0.274271\pi$
$578$	−6549.13	+	5226.47i	−0.471294	+	0.376111i
$579$		0			0
$580$	−6526.29	+	6526.29i	−0.467224	+	0.467224i
$581$	1967.69	+	815.043i	0.140505	+	0.0581991i
$582$		0			0
$583$	1029.38	−	2485.15i	0.0731263	−	0.176543i
$584$	13272.5	−	5497.67i	0.940448	−	0.389546i
$585$		0			0
$586$	8022.17	+	8022.17i	0.565517	+	0.565517i
$587$	5265.87	+	5265.87i	0.370265	+	0.370265i	0.867574	−	0.497309i	$-0.165678\pi$
$587$	5265.87	+	5265.87i	0.370265	+	0.370265i	−0.497309	+	0.867574i	$0.665678\pi$
$588$		0			0
$589$	2635.87	−	1091.81i	0.184396	−	0.0763792i
$590$	1381.02	−	3334.08i	0.0963657	−	0.232647i
$591$		0			0
$592$	−877.228	−	363.360i	−0.0609018	−	0.0252263i
$593$	−869.258	+	869.258i	−0.0601958	+	0.0601958i	−0.736564	−	0.676368i	$-0.763553\pi$
$593$	−869.258	+	869.258i	−0.0601958	+	0.0601958i	0.676368	+	0.736564i	$0.263553\pi$
$594$		0			0
$595$	−370.227	+	6612.95i	−0.0255090	+	0.455638i
$596$	−11284.0			−0.775523
$597$		0			0
$598$	3005.84	+	1245.06i	0.205548	+	0.0851408i
$599$			10655.6i			0.726840i	0.931625	+	0.363420i	$0.118391\pi$
$599$			10655.6i			0.726840i	−0.931625	+	0.363420i	$0.881609\pi$
$600$		0			0
$601$	1972.01	−	816.833i	0.133843	−	0.0554398i	−0.314756	−	0.949172i	$-0.601923\pi$
$601$	1972.01	−	816.833i	0.133843	−	0.0554398i	0.448600	+	0.893733i	$0.351923\pi$
$602$	4674.45	+	11285.1i	0.316472	+	0.764032i
$603$		0			0
$604$	−7679.66	−	7679.66i	−0.517353	−	0.517353i
$605$	−990.639	−	2391.62i	−0.0665706	−	0.160716i
$606$		0			0
$607$	−4731.84	+	11423.7i	−0.316407	+	0.763875i	0.683032	+	0.730389i	$0.260661\pi$
$607$	−4731.84	+	11423.7i	−0.316407	+	0.763875i	−0.999439	+	0.0334863i	$0.989339\pi$
$608$		−	14599.0i		−	0.973797i
$609$		0			0
$610$	−2999.52	+	2999.52i	−0.199094	+	0.199094i
$611$	−13902.5			−0.920513
$612$		0			0
$613$	4888.87			0.322120			0.161060	−	0.986945i	$-0.448509\pi$
$613$	4888.87			0.322120			0.161060	+	0.986945i	$0.448509\pi$
$614$	−3028.35	+	3028.35i	−0.199046	+	0.199046i
$615$		0			0
$616$			9553.30i			0.624859i
$617$	9471.41	−	22866.0i	0.617998	−	1.49198i	−0.236027	−	0.971747i	$-0.575845\pi$
$617$	9471.41	−	22866.0i	0.617998	−	1.49198i	0.854025	−	0.520232i	$-0.174155\pi$
$618$		0			0
$619$	−4131.00	−	9973.11i	−0.268237	−	0.647582i	0.731163	−	0.682202i	$-0.238978\pi$
$619$	−4131.00	−	9973.11i	−0.268237	−	0.647582i	−0.999401	+	0.0346207i	$0.988978\pi$
$620$	877.456	+	877.456i	0.0568379	+	0.0568379i
$621$		0			0
$622$	2339.83	+	5648.86i	0.150834	+	0.364145i
$623$	−7679.72	+	3181.05i	−0.493871	+	0.204568i
$624$		0			0
$625$			385.346i			0.0246621i
$626$	−4116.09	−	1704.94i	−0.262799	−	0.108855i
$627$		0			0
$628$	−1757.07			−0.111648
$629$	−10879.8	+	22602.2i	−0.689677	+	1.43276i
$630$		0			0
$631$	−5359.80	+	5359.80i	−0.338146	+	0.338146i	−0.855669	−	0.517523i	$-0.826854\pi$
$631$	−5359.80	+	5359.80i	−0.338146	+	0.338146i	0.517523	+	0.855669i	$0.326854\pi$
$632$	−7931.45	−	3285.31i	−0.499203	−	0.206777i
$633$		0			0
$634$	2547.83	−	6151.00i	0.159601	−	0.385312i
$635$	9481.12	−	3927.21i	0.592514	−	0.245427i
$636$		0			0
$637$	7023.01	+	7023.01i	0.436832	+	0.436832i
$638$	9899.14	+	9899.14i	0.614280	+	0.614280i
$639$		0			0
$640$	6094.14	−	2524.28i	0.376394	−	0.155907i
$641$	1217.52	−	2939.35i	0.0750219	−	0.181119i	−0.881920	−	0.471400i	$-0.843749\pi$
$641$	1217.52	−	2939.35i	0.0750219	−	0.181119i	0.956941	+	0.290281i	$0.0937488\pi$
$642$		0			0
$643$	−9749.51	−	4038.38i	−0.597952	−	0.247680i	0.0631154	−	0.998006i	$-0.479896\pi$
$643$	−9749.51	−	4038.38i	−0.597952	−	0.247680i	−0.661068	+	0.750326i	$0.729896\pi$
$644$	1443.65	−	1443.65i	0.0883353	−	0.0883353i
$645$		0			0
$646$	−9514.31	−	532.660i	−0.579467	−	0.0324415i
$647$	10952.0			0.665483			0.332742	−	0.943018i	$-0.392026\pi$
$647$	10952.0			0.665483			0.332742	+	0.943018i	$0.392026\pi$
$648$		0			0
$649$	8852.29	+	3666.74i	0.535412	+	0.221775i
$650$			8851.97i			0.534158i
$651$		0			0
$652$	−3191.66	+	1322.03i	−0.191710	+	0.0794090i
$653$	−2497.68	−	6029.94i	−0.149681	−	0.361362i	0.831199	−	0.555975i	$-0.187655\pi$
$653$	−2497.68	−	6029.94i	−0.149681	−	0.361362i	−0.980880	+	0.194613i	$0.937655\pi$
$654$		0			0
$655$	−13403.7	−	13403.7i	−0.799583	−	0.799583i
$656$	33.2471	+	80.2657i	0.00197878	+	0.00477721i
$657$		0			0
$658$	1907.27	−	4604.55i	0.112998	−	0.272802i
$659$			25717.9i			1.52022i	0.649793	+	0.760111i	$0.274855\pi$
$659$			25717.9i			1.52022i	−0.649793	+	0.760111i	$0.725145\pi$
$660$		0			0
$661$	−8350.18	+	8350.18i	−0.491353	+	0.491353i	−0.908732	−	0.417379i	$-0.862949\pi$
$661$	−8350.18	+	8350.18i	−0.491353	+	0.491353i	0.417379	+	0.908732i	$0.362949\pi$
$662$	10635.3			0.624403
$663$		0			0
$664$	−3426.93			−0.200287
$665$	−5326.31	+	5326.31i	−0.310595	+	0.310595i
$666$		0			0
$667$		−	7692.85i		−	0.446579i
$668$	−1558.30	+	3762.07i	−0.0902581	+	0.217902i
$669$		0			0
$670$	2933.93	+	7083.14i	0.169176	+	0.408426i
$671$	−7964.00	−	7964.00i	−0.458192	−	0.458192i
$672$		0			0
$673$	−2404.34	−	5804.60i	−0.137713	−	0.332468i	0.839945	−	0.542672i	$-0.182587\pi$
$673$	−2404.34	−	5804.60i	−0.137713	−	0.332468i	−0.977658	+	0.210204i	$0.932587\pi$
$674$	6053.76	−	2507.55i	0.345967	−	0.143304i
$675$		0			0
$676$		−	11001.0i		−	0.625910i
$677$	−17094.4	−	7080.72i	−0.970443	−	0.401970i	−0.159566	−	0.987187i	$-0.551009\pi$
$677$	−17094.4	−	7080.72i	−0.970443	−	0.401970i	−0.810877	+	0.585217i	$0.801009\pi$
$678$		0			0
$679$	618.446			0.0349540
$680$	−3521.56	−	10058.4i	−0.198596	−	0.567241i
$681$		0			0
$682$	1330.93	−	1330.93i	0.0747274	−	0.0747274i
$683$	−127.050	−	52.6260i	−0.00711779	−	0.00294828i	0.379122	−	0.925347i	$-0.376226\pi$
$683$	−127.050	−	52.6260i	−0.00711779	−	0.00294828i	−0.386239	+	0.922399i	$0.626226\pi$
$684$		0			0
$685$	−1641.22	+	3962.26i	−0.0915442	+	0.221007i
$686$	−10788.8	+	4468.86i	−0.600463	+	0.248720i
$687$		0			0
$688$	968.352	+	968.352i	0.0536600	+	0.0536600i
$689$	−4071.85	−	4071.85i	−0.225145	−	0.225145i
$690$		0			0
$691$	−280.152	+	116.043i	−0.0154233	+	0.00638854i	−0.390382	−	0.920653i	$-0.627657\pi$
$691$	−280.152	+	116.043i	−0.0154233	+	0.00638854i	0.374958	+	0.927042i	$0.377657\pi$
$692$	−3673.64	+	8868.96i	−0.201808	+	0.487207i
$693$		0			0
$694$	−13080.8	−	5418.25i	−0.715476	−	0.296360i
$695$	−12780.2	+	12780.2i	−0.697527	+	0.697527i
$696$		0			0
$697$	2166.27	−	758.433i	0.117724	−	0.0412162i
$698$	8406.54			0.455863
$699$		0			0
$700$	5131.96	+	2125.73i	0.277100	+	0.114778i
$701$		−	23434.3i		−	1.26263i	−0.775528	−	0.631313i	$-0.782516\pi$
$701$		−	23434.3i		−	1.26263i	0.775528	−	0.631313i	$-0.217484\pi$
$702$		0			0
$703$	−26356.4	+	10917.2i	−1.41401	+	0.585703i
$704$	−3435.28	−	8293.51i	−0.183909	−	0.443996i
$705$		0			0
$706$	11586.2	+	11586.2i	0.617638	+	0.617638i
$707$	−7850.13	−	18951.9i	−0.417588	−	1.00815i
$708$		0			0
$709$	19.9707	−	48.2136i	0.00105785	−	0.00255388i	−0.923350	−	0.383960i	$-0.874560\pi$
$709$	19.9707	−	48.2136i	0.00105785	−	0.00255388i	0.924408	+	0.381406i	$0.124560\pi$
$710$			4622.70i			0.244348i
$711$		0			0
$712$	9457.56	−	9457.56i	0.497805	−	0.497805i
$713$	−1034.30			−0.0543265
$714$		0			0
$715$	13862.0			0.725046
$716$	−12920.4	+	12920.4i	−0.674385	+	0.674385i
$717$		0			0
$718$		−	3347.43i		−	0.173990i
$719$	859.046	−	2073.92i	0.0445577	−	0.107572i	−0.900034	−	0.435820i	$-0.856458\pi$
$719$	859.046	−	2073.92i	0.0445577	−	0.107572i	0.944591	+	0.328248i	$0.106458\pi$
$720$		0			0
$721$	−3282.36	−	7924.33i	−0.169545	−	0.409317i
$722$	608.427	+	608.427i	0.0313619	+	0.0313619i
$723$		0			0
$724$	−898.883	−	2170.10i	−0.0461419	−	0.111396i
$725$	19337.1	−	8009.71i	0.990570	−	0.410308i
$726$		0			0
$727$		−	2971.90i		−	0.151612i	−0.997123	−	0.0758059i	$-0.975847\pi$
$727$		−	2971.90i		−	0.151612i	0.997123	−	0.0758059i	$-0.0241529\pi$
$728$	18894.6	+	7826.42i	0.961926	+	0.398443i
$729$		0			0
$730$	7472.91			0.378883
$731$	26972.3	−	24112.4i	1.36472	−	1.22001i
$732$		0			0
$733$	22418.7	−	22418.7i	1.12968	−	1.12968i	0.139447	−	0.990230i	$-0.455468\pi$
$733$	22418.7	−	22418.7i	1.12968	−	1.12968i	0.990230	−	0.139447i	$-0.0445324\pi$
$734$	−5449.04	−	2257.07i	−0.274016	−	0.113501i
$735$		0			0
$736$	−2025.35	+	4889.64i	−0.101434	+	0.244884i
$737$	−18806.4	+	7789.85i	−0.939947	+	0.389339i
$738$		0			0
$739$	26152.8	+	26152.8i	1.30182	+	1.30182i	0.927163	+	0.374657i	$0.122240\pi$
$739$	26152.8	+	26152.8i	1.30182	+	1.30182i	0.374657	+	0.927163i	$0.377760\pi$
$740$	−8773.80	−	8773.80i	−0.435853	−	0.435853i
$741$		0			0
$742$	1907.22	−	789.998i	0.0943617	−	0.0390859i
$743$	4057.18	−	9794.89i	0.200328	−	0.483633i	−0.791508	−	0.611159i	$-0.790704\pi$
$743$	4057.18	−	9794.89i	0.200328	−	0.483633i	0.991835	+	0.127526i	$0.0407035\pi$
$744$		0			0
$745$	−13943.8	−	5775.70i	−0.685719	−	0.284034i
$746$	−3209.30	+	3209.30i	−0.157508	+	0.157508i
$747$		0			0
$748$	10386.3	−	3636.33i	0.507700	−	0.177751i
$749$	1928.48			0.0940789
$750$		0			0
$751$	−26941.7	−	11159.6i	−1.30908	−	0.542238i	−0.384463	−	0.923141i	$-0.625613\pi$
$751$	−26941.7	−	11159.6i	−1.30908	−	0.542238i	−0.924615	+	0.380903i	$0.875613\pi$
$752$		−	558.765i		−	0.0270958i
$753$		0			0
$754$	27688.4	−	11468.9i	1.33734	−	0.553943i
$755$	−5559.01	−	13420.6i	−0.267965	−	0.646924i
$756$		0			0
$757$	−24358.4	−	24358.4i	−1.16951	−	1.16951i	−0.982325	−	0.187186i	$-0.940063\pi$
$757$	−24358.4	−	24358.4i	−1.16951	−	1.16951i	−0.187186	−	0.982325i	$-0.559937\pi$
$758$	−3643.79	−	8796.88i	−0.174602	−	0.421526i
$759$		0			0
$760$	4638.15	−	11197.5i	0.221373	−	0.534442i
$761$			14414.5i			0.686632i	0.939220	+	0.343316i	$0.111550\pi$
$761$			14414.5i			0.686632i	−0.939220	+	0.343316i	$0.888450\pi$
$762$		0			0
$763$	8079.71	−	8079.71i	0.383362	−	0.383362i
$764$	23012.6			1.08975
$765$		0			0
$766$	−13357.5			−0.630058
$767$	14504.2	−	14504.2i	0.682814	−	0.682814i
$768$		0			0
$769$			7049.33i			0.330566i	0.986246	+	0.165283i	$0.0528537\pi$
$769$			7049.33i			0.330566i	−0.986246	+	0.165283i	$0.947146\pi$
$770$	−1901.71	+	4591.13i	−0.0890037	+	0.214874i
$771$		0			0
$772$	−5706.67	−	13777.1i	−0.266046	−	0.642292i
$773$	18928.0	+	18928.0i	0.880716	+	0.880716i	0.993607	−	0.112891i	$-0.0360111\pi$
$773$	18928.0	+	18928.0i	0.880716	+	0.880716i	−0.112891	+	0.993607i	$0.536011\pi$
$774$		0			0
$775$	−1076.90	−	2599.87i	−0.0499141	−	0.120503i
$776$	−919.349	+	380.807i	−0.0425293	+	0.0176162i
$777$		0			0
$778$		−	12676.7i		−	0.584165i
$779$	2411.59	+	998.913i	0.110917	+	0.0459432i
$780$		0			0
$781$	−12273.7			−0.562339
$782$	3112.72	+	1498.34i	0.142341	+	0.0685175i
$783$		0			0
$784$	−282.267	+	282.267i	−0.0128584	+	0.0128584i
$785$	−2171.23	−	899.353i	−0.0987192	−	0.0408908i
$786$		0			0
$787$	9982.50	−	24099.9i	0.452144	−	1.09157i	−0.519361	−	0.854555i	$-0.673830\pi$
$787$	9982.50	−	24099.9i	0.452144	−	1.09157i	0.971505	−	0.237018i	$-0.0761700\pi$
$788$	9060.19	−	3752.85i	0.409589	−	0.169657i
$789$		0			0
$790$	−3157.72	−	3157.72i	−0.142211	−	0.142211i
$791$	−5911.38	−	5911.38i	−0.265720	−	0.265720i
$792$		0			0
$793$	−22275.7	+	9226.90i	−0.997520	+	0.413186i
$794$	6226.49	−	15032.1i	0.278300	−	0.671875i
$795$		0			0
$796$	14518.9	+	6013.91i	0.646492	+	0.267786i
$797$	12804.7	−	12804.7i	0.569092	−	0.569092i	−0.362782	−	0.931874i	$-0.618173\pi$
$797$	12804.7	−	12804.7i	0.569092	−	0.569092i	0.931874	+	0.362782i	$0.118173\pi$
$798$		0			0
$799$	−14738.6	−	825.143i	−0.652584	−	0.0365350i
$800$	−14399.6			−0.636379
$801$		0			0
$802$	−13650.3	−	5654.14i	−0.601009	−	0.248946i
$803$			19841.2i			0.871958i
$804$		0			0
$805$	2522.87	−	1045.01i	0.110459	−	0.0457536i
$806$	−1541.99	−	3722.69i	−0.0673874	−	0.162687i
$807$		0			0
$808$	23339.2	+	23339.2i	1.01618	+	1.01618i
$809$	−2795.36	−	6748.59i	−0.121483	−	0.293285i	0.851426	−	0.524475i	$-0.175738\pi$
$809$	−2795.36	−	6748.59i	−0.121483	−	0.293285i	−0.972909	+	0.231189i	$0.925738\pi$
$810$		0			0
$811$	7466.79	−	18026.4i	0.323298	−	0.780510i	−0.675761	−	0.737121i	$-0.736185\pi$
$811$	7466.79	−	18026.4i	0.323298	−	0.780510i	0.999058	−	0.0433884i	$-0.0138153\pi$
$812$		−	18806.6i		−	0.812786i
$813$		0			0
$814$	−13308.2	+	13308.2i	−0.573036	+	0.573036i
$815$	−4620.65			−0.198594
$816$		0			0
$817$	41145.5			1.76193
$818$	6366.40	−	6366.40i	0.272122	−	0.272122i
$819$		0			0
$820$			1135.32i			0.0483503i
$821$	−11237.2	+	27129.1i	−0.477689	+	1.15324i	0.483001	+	0.875620i	$0.339547\pi$
$821$	−11237.2	+	27129.1i	−0.477689	+	1.15324i	−0.960690	+	0.277623i	$0.910453\pi$
$822$		0			0
$823$	10758.2	+	25972.5i	0.455657	+	1.10005i	0.970138	+	0.242552i	$0.0779846\pi$
$823$	10758.2	+	25972.5i	0.455657	+	1.10005i	−0.514481	+	0.857502i	$0.672015\pi$
$824$	9758.78	+	9758.78i	0.412577	+	0.412577i
$825$		0			0
$826$	2814.03	+	6793.68i	0.118538	+	0.286177i
$827$	−36364.4	+	15062.6i	−1.52904	+	0.633348i	−0.979377	−	0.202041i	$-0.935243\pi$
$827$	−36364.4	+	15062.6i	−1.52904	+	0.633348i	−0.549659	+	0.835389i	$0.685243\pi$
$828$		0			0
$829$			15525.3i			0.650443i	0.945638	+	0.325221i	$0.105439\pi$
$829$			15525.3i			0.650443i	−0.945638	+	0.325221i	$0.894561\pi$
$830$	−1646.92	−	682.175i	−0.0688738	−	0.0285285i
$831$		0			0
$832$	−19217.3			−0.800771
$833$	7028.56	+	7862.23i	0.292347	+	0.327023i
$834$		0			0
$835$	−3851.21	+	3851.21i	−0.159613	+	0.159613i
$836$	11562.4	+	4789.32i	0.478344	+	0.198137i
$837$		0			0
$838$	6140.33	−	14824.1i	0.253120	−	0.611085i
$839$	−27723.7	+	11483.5i	−1.14079	+	0.472533i	−0.871437	−	0.490508i	$-0.836811\pi$
$839$	−27723.7	+	11483.5i	−1.14079	+	0.472533i	−0.269358	+	0.963040i	$0.586811\pi$
$840$		0			0
$841$	−32862.1	−	32862.1i	−1.34741	−	1.34741i
$842$	−9879.09	−	9879.09i	−0.404342	−	0.404342i
$843$		0			0
$844$	16945.0	−	7018.86i	0.691080	−	0.286255i
$845$	5630.84	−	13594.0i	0.229239	−	0.553431i
$846$		0			0
$847$	4873.27	+	2018.57i	0.197695	+	0.0818878i
$848$	163.655	−	163.655i	0.00662728	−	0.00662728i
$849$		0			0
$850$	−525.385	+	9384.36i	−0.0212006	+	0.378683i
$851$	10342.1			0.416595
$852$		0			0
$853$	−4020.20	−	1665.22i	−0.161371	−	0.0668419i	0.300536	−	0.953770i	$-0.402834\pi$
$853$	−4020.20	−	1665.22i	−0.161371	−	0.0668419i	−0.461907	+	0.886929i	$0.652834\pi$
$854$		−	8643.62i		−	0.346345i
$855$		0			0
$856$	−2866.78	+	1187.46i	−0.114468	+	0.0474141i
$857$	9896.77	+	23892.9i	0.394478	+	0.952353i	0.988952	+	0.148238i	$0.0473603\pi$
$857$	9896.77	+	23892.9i	0.394478	+	0.952353i	−0.594474	+	0.804115i	$0.702640\pi$
$858$		0			0
$859$	13494.4	+	13494.4i	0.535999	+	0.535999i	0.922351	−	0.386352i	$-0.126265\pi$
$859$	13494.4	+	13494.4i	0.535999	+	0.535999i	−0.386352	+	0.922351i	$0.626265\pi$
$860$	6848.47	+	16533.7i	0.271548	+	0.655574i
$861$		0			0
$862$	−1272.87	+	3072.97i	−0.0502947	+	0.121422i
$863$		−	24790.2i		−	0.977831i	−0.872331	−	0.488916i	$-0.837393\pi$
$863$		−	24790.2i		−	0.977831i	0.872331	−	0.488916i	$-0.162607\pi$
$864$		0			0
$865$	−9079.11	+	9079.11i	−0.356877	+	0.356877i
$866$	−19019.9			−0.746332
$867$		0			0
$868$	−2528.54			−0.0988757
$869$	8384.02	−	8384.02i	0.327282	−	0.327282i
$870$		0			0
$871$			43577.2i			1.69524i
$872$	−7035.81	+	16986.0i	−0.273237	+	0.659653i
$873$		0			0
$874$	1503.49	+	3629.74i	0.0581880	+	0.140478i
$875$	13605.7	+	13605.7i	0.525664	+	0.525664i
$876$		0			0
$877$	−5508.33	−	13298.3i	−0.212090	−	0.512031i	0.781654	−	0.623713i	$-0.214376\pi$
$877$	−5508.33	−	13298.3i	−0.212090	−	0.512031i	−0.993744	+	0.111681i	$0.964376\pi$
$878$	−740.803	+	306.851i	−0.0284748	+	0.0117947i
$879$		0			0
$880$			557.137i			0.0213421i
$881$	−14161.8	−	5866.00i	−0.541569	−	0.224325i	0.0950925	−	0.995468i	$-0.469685\pi$
$881$	−14161.8	−	5866.00i	−0.541569	−	0.224325i	−0.636662	+	0.771143i	$0.719685\pi$
$882$		0			0
$883$	−8385.90			−0.319602			−0.159801	−	0.987149i	$-0.551085\pi$
$883$	−8385.90			−0.319602			−0.159801	+	0.987149i	$0.551085\pi$
$884$	1316.84	−	23521.1i	0.0501018	−	0.894912i
$885$		0			0
$886$	15837.6	−	15837.6i	0.600534	−	0.600534i
$887$	−8514.38	−	3526.77i	−0.322305	−	0.133503i	0.215664	−	0.976468i	$-0.430808\pi$
$887$	−8514.38	−	3526.77i	−0.322305	−	0.133503i	−0.537969	+	0.842964i	$0.680808\pi$
$888$		0			0
$889$	−8002.26	+	19319.2i	−0.301898	+	0.728846i
$890$	6427.77	−	2662.47i	0.242089	−	0.100277i
$891$		0			0
$892$	−5678.97	−	5678.97i	−0.213168	−	0.213168i
$893$	−11871.0	−	11871.0i	−0.444847	−	0.444847i
$894$		0			0
$895$	−22579.2	+	9352.62i	−0.843285	+	0.349300i
$896$	−5143.58	+	12417.7i	−0.191780	+	0.462998i
$897$		0			0
$898$	−16438.8	−	6809.17i	−0.610879	−	0.253034i
$899$	−6736.95	+	6736.95i	−0.249933	+	0.249933i
$900$		0			0
$901$	−4075.07	−	4558.42i	−0.150677	−	0.168549i
$902$	1722.07			0.0635684
$903$		0			0
$904$	12427.5	+	5147.63i	0.457225	+	0.189389i
$905$		−	3141.70i		−	0.115396i
$906$		0			0
$907$	−6900.44	+	2858.25i	−0.252619	+	0.104638i	−0.505400	−	0.862885i	$-0.668655\pi$
$907$	−6900.44	+	2858.25i	−0.252619	+	0.104638i	0.252781	+	0.967524i	$0.418655\pi$
$908$	8364.23	+	20193.0i	0.305701	+	0.738028i
$909$		0			0
$910$	7522.45	+	7522.45i	0.274030	+	0.274030i
$911$	11747.7	+	28361.5i	0.427244	+	1.03146i	0.980157	+	0.198220i	$0.0635161\pi$
$911$	11747.7	+	28361.5i	0.427244	+	1.03146i	−0.552913	+	0.833239i	$0.686484\pi$
$912$		0			0
$913$	1811.23	−	4372.71i	0.0656551	−	0.158505i
$914$		−	432.140i		−	0.0156389i
$915$		0			0
$916$	2091.30	−	2091.30i	0.0754351	−	0.0754351i
$917$	38625.1			1.39096
$918$		0			0
$919$	−24550.8			−0.881237			−0.440619	−	0.897694i	$-0.645241\pi$
$919$	−24550.8			−0.881237			−0.440619	+	0.897694i	$0.645241\pi$
$920$	−3106.90	+	3106.90i	−0.111339	+	0.111339i
$921$		0			0
$922$			26537.4i			0.947898i
$923$	−10055.1	+	24275.1i	−0.358577	+	0.865681i
$924$		0			0
$925$	10768.1	+	25996.4i	0.382759	+	0.924061i
$926$	−12937.3	−	12937.3i	−0.459119	−	0.459119i
$927$		0			0
$928$	18656.6	+	45041.1i	0.659951	+	1.59326i
$929$	38484.2	−	15940.7i	1.35912	−	0.562967i	0.420306	−	0.907383i	$-0.361923\pi$
$929$	38484.2	−	15940.7i	1.35912	−	0.562967i	0.938817	+	0.344415i	$0.111923\pi$
$930$		0			0
$931$			11993.6i			0.422206i
$932$	3159.93	+	1308.88i	0.111059	+	0.0460021i
$933$		0			0
$934$	−3343.54			−0.117135
$935$	14695.7	+	822.739i	0.514011	+	0.0287770i
$936$		0			0
$937$	59.2109	−	59.2109i	0.00206439	−	0.00206439i	−0.706074	−	0.708138i	$-0.749535\pi$
$937$	59.2109	−	59.2109i	0.00206439	−	0.00206439i	0.708138	+	0.706074i	$0.249535\pi$
$938$	−14432.9	−	5978.31i	−0.502401	−	0.208101i
$939$		0			0
$940$	2794.31	−	6746.06i	0.0969577	−	0.234077i
$941$	−45541.8	+	18864.0i	−1.57770	+	0.653507i	−0.988048	−	0.154147i	$-0.950737\pi$
$941$	−45541.8	+	18864.0i	−1.57770	+	0.653507i	−0.589657	+	0.807654i	$0.700737\pi$
$942$		0			0
$943$	−669.130	−	669.130i	−0.0231070	−	0.0231070i
$944$	582.951	+	582.951i	0.0200990	+	0.0200990i
$945$		0			0
$946$	25078.4	−	10387.8i	0.861913	−	0.357016i
$947$	−3614.55	+	8726.29i	−0.124031	+	0.299436i	−0.973683	−	0.227907i	$-0.926812\pi$
$947$	−3614.55	+	8726.29i	−0.124031	+	0.299436i	0.849652	+	0.527343i	$0.176812\pi$
$948$		0			0
$949$	39242.3	+	16254.7i	1.34232	+	0.556006i
$950$	−7558.50	+	7558.50i	−0.258137	+	0.258137i
$951$		0			0
$952$	19566.5	+	9418.57i	0.666129	+	0.320649i
$953$	−41693.4			−1.41719			−0.708595	−	0.705616i	$-0.750671\pi$
$953$	−41693.4			−1.41719			−0.708595	+	0.705616i	$0.750671\pi$
$954$		0			0
$955$	28436.8	+	11778.9i	0.963555	+	0.399117i
$956$			1393.18i			0.0471324i
$957$		0			0
$958$	6766.12	−	2802.62i	0.228187	−	0.0945183i
$959$	−3344.23	−	8073.68i	−0.112608	−	0.271859i
$960$		0			0
$961$	−20159.6	−	20159.6i	−0.676702	−	0.676702i
$962$	15418.5	+	37223.6i	0.516750	+	1.24755i
$963$		0			0
$964$	−12638.3	+	30511.6i	−0.422254	+	1.01941i
$965$		−	19945.5i		−	0.665355i
$966$		0			0
$967$	−22896.1	+	22896.1i	−0.761416	+	0.761416i	−0.976578	−	0.215162i	$-0.930972\pi$
$967$	−22896.1	+	22896.1i	−0.761416	+	0.761416i	0.215162	+	0.976578i	$0.430972\pi$
$968$	−8487.28			−0.281809
$969$		0			0
$970$	−517.626			−0.0171340
$971$	−3819.26	+	3819.26i	−0.126226	+	0.126226i	−0.767398	−	0.641171i	$-0.778449\pi$
$971$	−3819.26	+	3819.26i	−0.126226	+	0.126226i	0.641171	+	0.767398i	$0.278449\pi$
$972$		0			0
$973$		−	36828.3i		−	1.21342i
$974$	11756.6	−	28382.9i	0.386762	−	0.933725i
$975$		0			0
$976$	−370.845	−	895.300i	−0.0121624	−	0.0293626i
$977$	−17738.6	−	17738.6i	−0.580869	−	0.580869i	0.354273	−	0.935142i	$-0.384728\pi$
$977$	−17738.6	−	17738.6i	−0.580869	−	0.580869i	−0.935142	+	0.354273i	$0.884728\pi$
$978$		0			0
$979$	7069.09	+	17066.3i	0.230775	+	0.557141i
$980$	−4819.44	+	1996.28i	−0.157093	+	0.0650701i
$981$		0			0
$982$		−	23421.4i		−	0.761108i
$983$	55092.4	+	22820.0i	1.78756	+	0.740433i	0.990665	+	0.136322i	$0.0435280\pi$
$983$	55092.4	+	22820.0i	1.78756	+	0.740433i	0.796900	+	0.604112i	$0.206472\pi$
$984$		0			0
$985$	13116.7			0.424296
$986$	30034.4	−	10515.3i	0.970071	−	0.339631i
$987$		0			0
$988$	18944.8	−	18944.8i	0.610034	−	0.610034i
$989$	−13780.8	−	5708.20i	−0.443078	−	0.183529i
$990$		0			0
$991$	−15331.8	+	37014.1i	−0.491452	+	1.18647i	0.462529	+	0.886604i	$0.346942\pi$
$991$	−15331.8	+	37014.1i	−0.491452	+	1.18647i	−0.953981	+	0.299867i	$0.903058\pi$
$992$	6055.75	−	2508.37i	0.193821	−	0.0802832i
$993$		0			0
$994$	−6660.54	−	6660.54i	−0.212535	−	0.212535i
$995$	14862.9	+	14862.9i	0.473553	+	0.473553i
$996$		0			0
$997$	−9994.87	+	4140.01i	−0.317493	+	0.131510i	−0.535738	−	0.844384i	$-0.679967\pi$
$997$	−9994.87	+	4140.01i	−0.317493	+	0.131510i	0.218245	+	0.975894i	$0.429967\pi$
$998$	5056.58	−	12207.7i	0.160384	−	0.387201i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.4.l.a.145.2		12
3.2	odd	2		17.4.d.a.9.2	yes	12
17.2	even	8	inner	153.4.l.a.19.2		12
51.2	odd	8		17.4.d.a.2.2	✓	12
51.11	even	16		289.4.a.g.1.5		12
51.23	even	16		289.4.a.g.1.6		12
51.41	even	16		289.4.b.e.288.7		12
51.44	even	16		289.4.b.e.288.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.d.a.2.2	✓	12	51.2	odd	8
17.4.d.a.9.2	yes	12	3.2	odd	2
153.4.l.a.19.2		12	17.2	even	8	inner
153.4.l.a.145.2		12	1.1	even	1	trivial
289.4.a.g.1.5		12	51.11	even	16
289.4.a.g.1.6		12	51.23	even	16
289.4.b.e.288.7		12	51.41	even	16
289.4.b.e.288.8		12	51.44	even	16

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	153.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20595 - 1.20595i) q^{2} +5.09138i q^{4} +(-2.60601 + 6.29147i) q^{5} +(-5.31013 - 12.8198i) q^{7} +(15.7875 + 15.7875i) q^{8} +O(q^{10})\)	\(q+(1.20595 - 1.20595i) q^{2} +5.09138i q^{4} +(-2.60601 + 6.29147i) q^{5} +(-5.31013 - 12.8198i) q^{7} +(15.7875 + 15.7875i) q^{8} +(4.44447 + 10.7299i) q^{10} +(-28.4888 + 11.8005i) q^{11} +66.0130i q^{13} +(-21.8637 - 9.05625i) q^{14} -2.65318 q^{16} +(-3.91802 + 69.9832i) q^{17} +(-56.3670 + 56.3670i) q^{19} +(-32.0322 - 13.2682i) q^{20} +(-20.1253 + 48.5868i) q^{22} +(26.6989 - 11.0590i) q^{23} +(55.5971 + 55.5971i) q^{25} +(79.6082 + 79.6082i) q^{26} +(65.2704 - 27.0359i) q^{28} +(101.871 - 245.938i) q^{29} +(-33.0662 - 13.6965i) q^{31} +(-129.500 + 129.500i) q^{32} +(79.6712 + 89.1210i) q^{34} +94.4935 q^{35} +(330.633 + 136.953i) q^{37} +135.951i q^{38} +(-140.469 + 58.1842i) q^{40} +(-12.5311 - 30.2527i) q^{41} +(-364.978 - 364.978i) q^{43} +(-60.0806 - 145.047i) q^{44} +(18.8608 - 45.5340i) q^{46} +210.602i q^{47} +(106.388 - 106.388i) q^{49} +134.094 q^{50} -336.097 q^{52} +(-61.6826 + 61.6826i) q^{53} -209.989i q^{55} +(118.559 - 286.226i) q^{56} +(-173.737 - 419.439i) q^{58} +(-219.718 - 219.718i) q^{59} +(139.774 + 337.444i) q^{61} +(-56.3933 + 23.3589i) q^{62} +291.115i q^{64} +(-415.318 - 172.030i) q^{65} +660.131 q^{67} +(-356.311 - 19.9481i) q^{68} +(113.954 - 113.954i) q^{70} +(367.732 + 152.319i) q^{71} +(246.235 - 594.463i) q^{73} +(563.884 - 233.568i) q^{74} +(-286.986 - 286.986i) q^{76} +(302.558 + 302.558i) q^{77} +(-355.241 + 147.146i) q^{79} +(6.91421 - 16.6924i) q^{80} +(-51.5949 - 21.3713i) q^{82} +(-108.533 + 108.533i) q^{83} +(-430.087 - 207.027i) q^{85} -880.289 q^{86} +(-636.068 - 263.468i) q^{88} -599.053i q^{89} +(846.272 - 350.537i) q^{91} +(56.3057 + 135.934i) q^{92} +(253.975 + 253.975i) q^{94} +(-207.738 - 501.524i) q^{95} +(-17.0560 + 41.1767i) q^{97} -256.598i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 20 q^{5} - 4 q^{7} - 28 q^{8}+O(q^{10}) \) 12 * q + 4 * q^2 + 20 * q^5 - 4 * q^7 - 28 * q^8	\( 12 q + 4 q^{2} + 20 q^{5} - 4 q^{7} - 28 q^{8} - 116 q^{10} - 40 q^{11} + 132 q^{14} + 184 q^{16} - 52 q^{17} - 12 q^{19} - 572 q^{20} - 620 q^{22} + 276 q^{23} - 464 q^{25} + 708 q^{26} + 452 q^{28} - 632 q^{29} + 188 q^{31} - 700 q^{32} + 764 q^{34} + 632 q^{35} + 940 q^{37} - 1864 q^{40} - 176 q^{41} - 1360 q^{43} + 1364 q^{44} + 452 q^{46} + 1044 q^{49} - 2856 q^{50} + 792 q^{52} + 360 q^{53} + 1788 q^{56} - 360 q^{58} + 584 q^{59} - 1052 q^{61} + 380 q^{62} - 404 q^{65} + 1080 q^{67} - 2532 q^{68} + 2072 q^{70} - 28 q^{71} + 824 q^{73} + 2292 q^{74} + 1328 q^{76} + 1252 q^{77} - 196 q^{79} + 904 q^{80} - 1528 q^{82} + 1008 q^{83} - 2824 q^{85} + 1200 q^{86} - 56 q^{88} + 2456 q^{91} - 396 q^{92} + 6360 q^{94} - 2172 q^{95} - 904 q^{97}+O(q^{100}) \) 12 * q + 4 * q^2 + 20 * q^5 - 4 * q^7 - 28 * q^8 - 116 * q^10 - 40 * q^11 + 132 * q^14 + 184 * q^16 - 52 * q^17 - 12 * q^19 - 572 * q^20 - 620 * q^22 + 276 * q^23 - 464 * q^25 + 708 * q^26 + 452 * q^28 - 632 * q^29 + 188 * q^31 - 700 * q^32 + 764 * q^34 + 632 * q^35 + 940 * q^37 - 1864 * q^40 - 176 * q^41 - 1360 * q^43 + 1364 * q^44 + 452 * q^46 + 1044 * q^49 - 2856 * q^50 + 792 * q^52 + 360 * q^53 + 1788 * q^56 - 360 * q^58 + 584 * q^59 - 1052 * q^61 + 380 * q^62 - 404 * q^65 + 1080 * q^67 - 2532 * q^68 + 2072 * q^70 - 28 * q^71 + 824 * q^73 + 2292 * q^74 + 1328 * q^76 + 1252 * q^77 - 196 * q^79 + 904 * q^80 - 1528 * q^82 + 1008 * q^83 - 2824 * q^85 + 1200 * q^86 - 56 * q^88 + 2456 * q^91 - 396 * q^92 + 6360 * q^94 - 2172 * q^95 - 904 * q^97

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