LMFDB - Embedded newform 890.2.b.a.179.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [890,2,Mod(179,890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(890, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("890.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 890 = 2 \cdot 5 \cdot 89 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	890.b (of order $2$, degree $1$, 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:	$7.10668577989$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 24x^{14} + 218x^{12} + 948x^{10} + 2061x^{8} + 2076x^{6} + 748x^{4} + 96x^{2} + 4 $ x^16 + 24x^14 + 218x^12 + 948x^10 + 2061x^8 + 2076x^6 + 748x^4 + 96*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			179.1
Root			$-1.85072i$ of defining polynomial
Character	$\chi$	$=$	890.179
Dual form			890.2.b.a.179.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -2.85072i q^{3} -1.00000 q^{4} +(1.58682 - 1.57543i) q^{5} -2.85072 q^{6} -4.52360i q^{7} +1.00000i q^{8} -5.12662 q^{9} +(-1.57543 - 1.58682i) q^{10} -1.22864 q^{11} +2.85072i q^{12} +1.37273i q^{13} -4.52360 q^{14} +(-4.49113 - 4.52360i) q^{15} +1.00000 q^{16} +4.61484i q^{17} +5.12662i q^{18} +4.47801 q^{19} +(-1.58682 + 1.57543i) q^{20} -12.8955 q^{21} +1.22864i q^{22} -4.38002i q^{23} +2.85072 q^{24} +(0.0360184 - 4.99987i) q^{25} +1.37273 q^{26} +6.06241i q^{27} +4.52360i q^{28} +5.55434 q^{29} +(-4.52360 + 4.49113i) q^{30} +6.27071 q^{31} -1.00000i q^{32} +3.50252i q^{33} +4.61484 q^{34} +(-7.12662 - 7.17815i) q^{35} +5.12662 q^{36} +7.27164i q^{37} -4.47801i q^{38} +3.91327 q^{39} +(1.57543 + 1.58682i) q^{40} -3.98348 q^{41} +12.8955i q^{42} -6.25152i q^{43} +1.22864 q^{44} +(-8.13505 + 8.07665i) q^{45} -4.38002 q^{46} +10.6104i q^{47} -2.85072i q^{48} -13.4629 q^{49} +(-4.99987 - 0.0360184i) q^{50} +13.1556 q^{51} -1.37273i q^{52} -10.4611i q^{53} +6.06241 q^{54} +(-1.94964 + 1.93564i) q^{55} +4.52360 q^{56} -12.7656i q^{57} -5.55434i q^{58} +6.84371 q^{59} +(4.49113 + 4.52360i) q^{60} +13.9786 q^{61} -6.27071i q^{62} +23.1908i q^{63} -1.00000 q^{64} +(2.16264 + 2.17828i) q^{65} +3.50252 q^{66} -0.657004i q^{67} -4.61484i q^{68} -12.4862 q^{69} +(-7.17815 + 7.12662i) q^{70} -1.09617 q^{71} -5.12662i q^{72} +9.58493i q^{73} +7.27164 q^{74} +(-14.2532 - 0.102678i) q^{75} -4.47801 q^{76} +5.55787i q^{77} -3.91327i q^{78} -15.9984 q^{79} +(1.58682 - 1.57543i) q^{80} +1.90240 q^{81} +3.98348i q^{82} +11.4611i q^{83} +12.8955 q^{84} +(7.27038 + 7.32294i) q^{85} -6.25152 q^{86} -15.8339i q^{87} -1.22864i q^{88} +1.00000 q^{89} +(8.07665 + 8.13505i) q^{90} +6.20967 q^{91} +4.38002i q^{92} -17.8761i q^{93} +10.6104 q^{94} +(7.10582 - 7.05481i) q^{95} -2.85072 q^{96} +15.1680i q^{97} +13.4629i q^{98} +6.29878 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 2 q^{5} - 8 q^{6} - 2 q^{10} - 8 q^{11} + 4 q^{14} + 16 q^{16} + 16 q^{19} + 2 q^{20} - 20 q^{21} + 8 q^{24} - 4 q^{25} - 8 q^{26} + 20 q^{29} + 4 q^{30} + 28 q^{34} - 32 q^{35} + 20 q^{39}+ \cdots - 24 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 - 2 * q^5 - 8 * q^6 - 2 * q^10 - 8 * q^11 + 4 * q^14 + 16 * q^16 + 16 * q^19 + 2 * q^20 - 20 * q^21 + 8 * q^24 - 4 * q^25 - 8 * q^26 + 20 * q^29 + 4 * q^30 + 28 * q^34 - 32 * q^35 + 20 * q^39 + 2 * q^40 + 8 * q^44 - 26 * q^45 - 48 * q^46 + 8 * q^49 - 8 * q^50 + 8 * q^51 + 20 * q^54 - 8 * q^55 - 4 * q^56 + 8 * q^59 - 4 * q^61 - 16 * q^64 - 52 * q^65 - 20 * q^66 + 36 * q^69 - 8 * q^70 + 40 * q^71 + 28 * q^74 - 64 * q^75 - 16 * q^76 - 4 * q^79 - 2 * q^80 - 8 * q^81 + 20 * q^84 - 12 * q^85 - 8 * q^86 + 16 * q^89 + 6 * q^90 + 40 * q^91 + 56 * q^94 - 28 * q^95 - 8 * q^96 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/890\mathbb{Z}\right)^\times$.

$n$	$181$	$357$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	2.85072i		−	1.64587i	−0.568139	−	0.822933i	$-0.692336\pi$
$3$		−	2.85072i		−	1.64587i	0.568139	−	0.822933i	$-0.307664\pi$
$4$	−1.00000			−0.500000
$5$	1.58682	−	1.57543i	0.709649	−	0.704555i
$5$	1.58682	−	1.57543i	0.709649	−	0.704555i
$6$	−2.85072			−1.16380
$7$		−	4.52360i		−	1.70976i	−0.518827	−	0.854879i	$-0.673631\pi$
$7$		−	4.52360i		−	1.70976i	0.518827	−	0.854879i	$-0.326369\pi$
$8$			1.00000i			0.353553i
$9$	−5.12662			−1.70887
$10$	−1.57543	−	1.58682i	−0.498196	−	0.501798i
$11$	−1.22864			−0.370449			−0.185225	−	0.982696i	$-0.559301\pi$
$11$	−1.22864			−0.370449			−0.185225	+	0.982696i	$0.559301\pi$
$12$			2.85072i			0.822933i
$13$			1.37273i			0.380726i	0.981714	+	0.190363i	$0.0609665\pi$
$13$			1.37273i			0.380726i	−0.981714	+	0.190363i	$0.939033\pi$
$14$	−4.52360			−1.20898
$15$	−4.49113	−	4.52360i	−1.15960	−	1.16799i
$16$	1.00000			0.250000
$17$			4.61484i			1.11926i	0.828741	+	0.559632i	$0.189058\pi$
$17$			4.61484i			1.11926i	−0.828741	+	0.559632i	$0.810942\pi$
$18$			5.12662i			1.20836i
$19$	4.47801			1.02733			0.513664	−	0.857992i	$-0.328288\pi$
$19$	4.47801			1.02733			0.513664	+	0.857992i	$0.328288\pi$
$20$	−1.58682	+	1.57543i	−0.354825	+	0.352278i
$21$	−12.8955			−2.81403
$22$			1.22864i			0.261947i
$23$		−	4.38002i		−	0.913298i	−0.889647	−	0.456649i	$-0.849050\pi$
$23$		−	4.38002i		−	0.913298i	0.889647	−	0.456649i	$-0.150950\pi$
$24$	2.85072			0.581901
$25$	0.0360184	−	4.99987i	0.00720368	−	0.999974i
$26$	1.37273			0.269214
$27$			6.06241i			1.16671i
$28$			4.52360i			0.854879i
$29$	5.55434			1.03142			0.515708	−	0.856764i	$-0.327529\pi$
$29$	5.55434			1.03142			0.515708	+	0.856764i	$0.327529\pi$
$30$	−4.52360	+	4.49113i	−0.825892	+	0.819964i
$31$	6.27071			1.12625			0.563126	−	0.826371i	$-0.309598\pi$
$31$	6.27071			1.12625			0.563126	+	0.826371i	$0.309598\pi$
$32$		−	1.00000i		−	0.176777i
$33$			3.50252i			0.609710i
$34$	4.61484			0.791439
$35$	−7.12662	−	7.17815i	−1.20462	−	1.21333i
$36$	5.12662			0.854437
$37$			7.27164i			1.19545i	0.801701	+	0.597725i	$0.203929\pi$
$37$			7.27164i			1.19545i	−0.801701	+	0.597725i	$0.796071\pi$
$38$		−	4.47801i		−	0.726430i
$39$	3.91327			0.626624
$40$	1.57543	+	1.58682i	0.249098	+	0.250899i
$41$	−3.98348			−0.622114			−0.311057	−	0.950391i	$-0.600683\pi$
$41$	−3.98348			−0.622114			−0.311057	+	0.950391i	$0.600683\pi$
$42$			12.8955i			1.98982i
$43$		−	6.25152i		−	0.953348i	−0.879080	−	0.476674i	$-0.841842\pi$
$43$		−	6.25152i		−	0.953348i	0.879080	−	0.476674i	$-0.158158\pi$
$44$	1.22864			0.185225
$45$	−8.13505	+	8.07665i	−1.21270	+	1.20400i
$46$	−4.38002			−0.645799
$47$			10.6104i			1.54769i	0.633374	+	0.773845i	$0.281669\pi$
$47$			10.6104i			1.54769i	−0.633374	+	0.773845i	$0.718331\pi$
$48$		−	2.85072i		−	0.411466i
$49$	−13.4629			−1.92327
$50$	−4.99987	−	0.0360184i	−0.707088	−	0.00509377i
$51$	13.1556			1.84216
$52$		−	1.37273i		−	0.190363i
$53$		−	10.4611i		−	1.43694i	−0.695559	−	0.718469i	$-0.744843\pi$
$53$		−	10.4611i		−	1.43694i	0.695559	−	0.718469i	$-0.255157\pi$
$54$	6.06241			0.824990
$55$	−1.94964	+	1.93564i	−0.262889	+	0.261002i
$56$	4.52360			0.604491
$57$		−	12.7656i		−	1.69084i
$58$		−	5.55434i		−	0.729321i
$59$	6.84371			0.890976			0.445488	−	0.895288i	$-0.353030\pi$
$59$	6.84371			0.890976			0.445488	+	0.895288i	$0.353030\pi$
$60$	4.49113	+	4.52360i	0.579802	+	0.583994i
$61$	13.9786			1.78977			0.894887	−	0.446293i	$-0.147256\pi$
$61$	13.9786			1.78977			0.894887	+	0.446293i	$0.147256\pi$
$62$		−	6.27071i		−	0.796381i
$63$			23.1908i			2.92176i
$64$	−1.00000			−0.125000
$65$	2.16264	+	2.17828i	0.268243	+	0.270182i
$66$	3.50252			0.431130
$67$		−	0.657004i		−	0.0802658i	−0.999194	−	0.0401329i	$-0.987222\pi$
$67$		−	0.657004i		−	0.0802658i	0.999194	−	0.0401329i	$-0.0127781\pi$
$68$		−	4.61484i		−	0.559632i
$69$	−12.4862			−1.50317
$70$	−7.17815	+	7.12662i	−0.857953	+	0.851794i
$71$	−1.09617			−0.130092			−0.0650460	−	0.997882i	$-0.520719\pi$
$71$	−1.09617			−0.130092			−0.0650460	+	0.997882i	$0.520719\pi$
$72$		−	5.12662i		−	0.604178i
$73$			9.58493i			1.12183i	0.827873	+	0.560916i	$0.189551\pi$
$73$			9.58493i			1.12183i	−0.827873	+	0.560916i	$0.810449\pi$
$74$	7.27164			0.845311
$75$	−14.2532	−	0.102678i	−1.64582	−	0.0118563i
$76$	−4.47801			−0.513664
$77$			5.55787i			0.633378i
$78$		−	3.91327i		−	0.443090i
$79$	−15.9984			−1.79996			−0.899979	−	0.435934i	$-0.856418\pi$
$79$	−15.9984			−1.79996			−0.899979	+	0.435934i	$0.856418\pi$
$80$	1.58682	−	1.57543i	0.177412	−	0.176139i
$81$	1.90240			0.211377
$82$			3.98348i			0.439901i
$83$			11.4611i			1.25801i	0.777400	+	0.629007i	$0.216538\pi$
$83$			11.4611i			1.25801i	−0.777400	+	0.629007i	$0.783462\pi$
$84$	12.8955			1.40702
$85$	7.27038	+	7.32294i	0.788583	+	0.794285i
$86$	−6.25152			−0.674119
$87$		−	15.8339i		−	1.69757i
$88$		−	1.22864i		−	0.130974i
$89$	1.00000			0.106000
$89$	1.00000			0.106000
$90$	8.07665	+	8.13505i	0.851354	+	0.857509i
$91$	6.20967			0.650950
$92$			4.38002i			0.456649i
$93$		−	17.8761i		−	1.85366i
$94$	10.6104			1.09438
$95$	7.10582	−	7.05481i	0.729042	−	0.723809i
$96$	−2.85072			−0.290951
$97$			15.1680i			1.54007i	0.638000	+	0.770036i	$0.279762\pi$
$97$			15.1680i			1.54007i	−0.638000	+	0.770036i	$0.720238\pi$
$98$			13.4629i			1.35996i
$99$	6.29878			0.633051
$100$	−0.0360184	+	4.99987i	−0.00360184	+	0.499987i
$101$	−4.96914			−0.494448			−0.247224	−	0.968958i	$-0.579518\pi$
$101$	−4.96914			−0.494448			−0.247224	+	0.968958i	$0.579518\pi$
$102$		−	13.1556i		−	1.30260i
$103$		−	12.8655i		−	1.26767i	−0.773467	−	0.633837i	$-0.781479\pi$
$103$		−	12.8655i		−	1.26767i	0.773467	−	0.633837i	$-0.218521\pi$
$104$	−1.37273			−0.134607
$105$	−20.4629	+	20.3160i	−1.99698	+	1.98264i
$106$	−10.4611			−1.01607
$107$			13.6498i			1.31958i	0.751450	+	0.659790i	$0.229355\pi$
$107$			13.6498i			1.31958i	−0.751450	+	0.659790i	$0.770645\pi$
$108$		−	6.06241i		−	0.583356i
$109$	3.90012			0.373563			0.186782	−	0.982401i	$-0.440194\pi$
$109$	3.90012			0.373563			0.186782	+	0.982401i	$0.440194\pi$
$110$	1.93564	+	1.94964i	0.184556	+	0.185891i
$111$	20.7294			1.96755
$112$		−	4.52360i		−	0.427440i
$113$		−	1.60019i		−	0.150533i	−0.997163	−	0.0752665i	$-0.976019\pi$
$113$		−	1.60019i		−	0.150533i	0.997163	−	0.0752665i	$-0.0239808\pi$
$114$	−12.7656			−1.19561
$115$	−6.90043	−	6.95032i	−0.643469	−	0.648121i
$116$	−5.55434			−0.515708
$117$		−	7.03746i		−	0.650613i
$118$		−	6.84371i		−	0.630015i
$119$	20.8757			1.91367
$120$	4.52360	−	4.49113i	0.412946	−	0.409982i
$121$	−9.49044			−0.862767
$122$		−	13.9786i		−	1.26556i
$123$			11.3558i			1.02392i
$124$	−6.27071			−0.563126
$125$	−7.81981	−	7.99066i	−0.699425	−	0.714706i
$126$	23.1908			2.06600
$127$		−	8.82600i		−	0.783181i	−0.920140	−	0.391590i	$-0.871925\pi$
$127$		−	8.82600i		−	0.783181i	0.920140	−	0.391590i	$-0.128075\pi$
$128$			1.00000i			0.0883883i
$129$	−17.8214			−1.56908
$130$	2.17828	−	2.16264i	0.191048	−	0.189676i
$131$	5.31775			0.464614			0.232307	−	0.972642i	$-0.425373\pi$
$131$	5.31775			0.464614			0.232307	+	0.972642i	$0.425373\pi$
$132$		−	3.50252i		−	0.304855i
$133$		−	20.2567i		−	1.75648i
$134$	−0.657004			−0.0567565
$135$	9.55093	+	9.61998i	0.822013	+	0.827956i
$136$	−4.61484			−0.395720
$137$		−	0.978495i		−	0.0835985i	−0.999126	−	0.0417992i	$-0.986691\pi$
$137$		−	0.978495i		−	0.0835985i	0.999126	−	0.0417992i	$-0.0133090\pi$
$138$			12.4862i			1.06290i
$139$	−4.23577			−0.359273			−0.179637	−	0.983733i	$-0.557492\pi$
$139$	−4.23577			−0.359273			−0.179637	+	0.983733i	$0.557492\pi$
$140$	7.12662	+	7.17815i	0.602310	+	0.606664i
$141$	30.2474			2.54729
$142$			1.09617i			0.0919890i
$143$		−	1.68659i		−	0.141040i
$144$	−5.12662			−0.427219
$145$	8.81377	−	8.75050i	0.731943	−	0.726690i
$146$	9.58493			0.793255
$147$			38.3790i			3.16545i
$148$		−	7.27164i		−	0.597725i
$149$	−8.49351			−0.695815			−0.347908	−	0.937529i	$-0.613108\pi$
$149$	−8.49351			−0.695815			−0.347908	+	0.937529i	$0.613108\pi$
$150$	−0.102678	+	14.2532i	−0.00838366	+	1.16377i
$151$	9.09426			0.740080			0.370040	−	0.929016i	$-0.379344\pi$
$151$	9.09426			0.740080			0.370040	+	0.929016i	$0.379344\pi$
$152$			4.47801i			0.363215i
$153$		−	23.6586i		−	1.91268i
$154$	5.55787			0.447866
$155$	9.95051	−	9.87909i	0.799244	−	0.793507i
$156$	−3.91327			−0.313312
$157$		−	16.5202i		−	1.31845i	−0.751944	−	0.659227i	$-0.770884\pi$
$157$		−	16.5202i		−	1.31845i	0.751944	−	0.659227i	$-0.229116\pi$
$158$			15.9984i			1.27276i
$159$	−29.8216			−2.36501
$160$	−1.57543	−	1.58682i	−0.124549	−	0.125449i
$161$	−19.8134			−1.56152
$162$		−	1.90240i		−	0.149466i
$163$		−	17.0813i		−	1.33791i	−0.743304	−	0.668954i	$-0.766743\pi$
$163$		−	17.0813i		−	1.33791i	0.743304	−	0.668954i	$-0.233257\pi$
$164$	3.98348			0.311057
$165$	5.51798	+	5.55787i	0.429574	+	0.432680i
$166$	11.4611			0.889550
$167$			2.94829i			0.228146i	0.993472	+	0.114073i	$0.0363897\pi$
$167$			2.94829i			0.228146i	−0.993472	+	0.114073i	$0.963610\pi$
$168$		−	12.8955i		−	0.994911i
$169$	11.1156			0.855048
$170$	7.32294	−	7.27038i	0.561644	−	0.557613i
$171$	−22.9571			−1.75557
$172$			6.25152i			0.476674i
$173$		−	5.36147i		−	0.407625i	−0.979010	−	0.203813i	$-0.934667\pi$
$173$		−	5.36147i		−	0.407625i	0.979010	−	0.203813i	$-0.0653333\pi$
$174$	−15.8339			−1.20036
$175$	−22.6174	−	0.162933i	−1.70971	−	0.0123165i
$176$	−1.22864			−0.0926123
$177$		−	19.5095i		−	1.46643i
$178$		−	1.00000i		−	0.0749532i
$179$	−11.5470			−0.863067			−0.431533	−	0.902097i	$-0.642027\pi$
$179$	−11.5470			−0.863067			−0.431533	+	0.902097i	$0.642027\pi$
$180$	8.13505	−	8.07665i	0.606351	−	0.601998i
$181$	−25.3052			−1.88092			−0.940459	−	0.339907i	$-0.889604\pi$
$181$	−25.3052			−1.88092			−0.940459	+	0.339907i	$0.889604\pi$
$182$		−	6.20967i		−	0.460291i
$183$		−	39.8491i		−	2.94573i
$184$	4.38002			0.322900
$185$	11.4560	+	11.5388i	0.842261	+	0.848350i
$186$	−17.8761			−1.31074
$187$		−	5.66999i		−	0.414630i
$188$		−	10.6104i		−	0.773845i
$189$	27.4239			1.99480
$190$	−7.05481	−	7.10582i	−0.511810	−	0.515510i
$191$	15.7942			1.14283			0.571413	−	0.820662i	$-0.306395\pi$
$191$	15.7942			1.14283			0.571413	+	0.820662i	$0.306395\pi$
$192$			2.85072i			0.205733i
$193$		−	7.69294i		−	0.553750i	−0.960906	−	0.276875i	$-0.910701\pi$
$193$		−	7.69294i		−	0.553750i	0.960906	−	0.276875i	$-0.0892988\pi$
$194$	15.1680			1.08900
$195$	6.20967	−	6.16509i	0.444683	−	0.441491i
$196$	13.4629			0.961637
$197$		−	0.115358i		−	0.00821893i	−0.999992	−	0.00410946i	$-0.998692\pi$
$197$		−	0.115358i		−	0.00821893i	0.999992	−	0.00410946i	$-0.00130809\pi$
$198$		−	6.29878i		−	0.447635i
$199$	−0.584508			−0.0414347			−0.0207173	−	0.999785i	$-0.506595\pi$
$199$	−0.584508			−0.0414347			−0.0207173	+	0.999785i	$0.506595\pi$
$200$	4.99987	+	0.0360184i	0.353544	+	0.00254689i
$201$	−1.87294			−0.132107
$202$			4.96914i			0.349627i
$203$		−	25.1256i		−	1.76347i
$204$	−13.1556			−0.921079
$205$	−6.32107	+	6.27570i	−0.441483	+	0.438314i
$206$	−12.8655			−0.896381
$207$			22.4547i			1.56071i
$208$			1.37273i			0.0951816i
$209$	−5.50187			−0.380572
$210$	20.3160	+	20.4629i	1.40194	+	1.41208i
$211$	−15.0506			−1.03613			−0.518063	−	0.855343i	$-0.673347\pi$
$211$	−15.0506			−1.03613			−0.518063	+	0.855343i	$0.673347\pi$
$212$			10.4611i			0.718469i
$213$			3.12489i			0.214114i
$214$	13.6498			0.933083
$215$	−9.84885	−	9.92006i	−0.671686	−	0.676542i
$216$	−6.06241			−0.412495
$217$		−	28.3662i		−	1.92562i
$218$		−	3.90012i		−	0.264149i
$219$	27.3240			1.84638
$220$	1.94964	−	1.93564i	0.131444	−	0.130501i
$221$	−6.33493			−0.426133
$222$		−	20.7294i		−	1.39127i
$223$		−	11.2778i		−	0.755219i	−0.925965	−	0.377609i	$-0.876746\pi$
$223$		−	11.2778i		−	0.755219i	0.925965	−	0.377609i	$-0.123254\pi$
$224$	−4.52360			−0.302245
$225$	−0.184653	+	25.6325i	−0.0123102	+	1.70883i
$226$	−1.60019			−0.106443
$227$			19.6413i			1.30364i	0.758375	+	0.651818i	$0.225994\pi$
$227$			19.6413i			1.30364i	−0.758375	+	0.651818i	$0.774006\pi$
$228$			12.7656i			0.845421i
$229$	13.2889			0.878152			0.439076	−	0.898450i	$-0.355306\pi$
$229$	13.2889			0.878152			0.439076	+	0.898450i	$0.355306\pi$
$230$	−6.95032	+	6.90043i	−0.458291	+	0.455001i
$231$	15.8440			1.04246
$232$			5.55434i			0.364661i
$233$		−	19.0035i		−	1.24496i	−0.782636	−	0.622480i	$-0.786125\pi$
$233$		−	19.0035i		−	1.24496i	0.782636	−	0.622480i	$-0.213875\pi$
$234$	−7.03746			−0.460053
$235$	16.7160	+	16.8369i	1.09043	+	1.09832i
$236$	−6.84371			−0.445488
$237$			45.6069i			2.96249i
$238$		−	20.8757i		−	1.35317i
$239$	−1.66519			−0.107712			−0.0538561	−	0.998549i	$-0.517151\pi$
$239$	−1.66519			−0.107712			−0.0538561	+	0.998549i	$0.517151\pi$
$240$	−4.49113	−	4.52360i	−0.289901	−	0.291997i
$241$	5.69530			0.366867			0.183433	−	0.983032i	$-0.441279\pi$
$241$	5.69530			0.366867			0.183433	+	0.983032i	$0.441279\pi$
$242$			9.49044i			0.610069i
$243$			12.7640i			0.818813i
$244$	−13.9786			−0.894887
$245$	−21.3633	+	21.2099i	−1.36485	+	1.35505i
$246$	11.3558			0.724019
$247$			6.14710i			0.391130i
$248$			6.27071i			0.398191i
$249$	32.6723			2.07052
$250$	−7.99066	+	7.81981i	−0.505374	+	0.494568i
$251$	−5.89313			−0.371971			−0.185986	−	0.982552i	$-0.559548\pi$
$251$	−5.89313			−0.371971			−0.185986	+	0.982552i	$0.559548\pi$
$252$		−	23.1908i		−	1.46088i
$253$			5.38147i			0.338330i
$254$	−8.82600			−0.553792
$255$	20.8757	−	20.7258i	1.30729	−	1.29790i
$256$	1.00000			0.0625000
$257$		−	0.854848i		−	0.0533240i	−0.999645	−	0.0266620i	$-0.991512\pi$
$257$		−	0.854848i		−	0.0533240i	0.999645	−	0.0266620i	$-0.00848778\pi$
$258$			17.8214i			1.10951i
$259$	32.8940			2.04393
$260$	−2.16264	−	2.17828i	−0.134121	−	0.135091i
$261$	−28.4750			−1.76256
$262$		−	5.31775i		−	0.328532i
$263$			18.3357i			1.13063i	0.824875	+	0.565315i	$0.191245\pi$
$263$			18.3357i			1.13063i	−0.824875	+	0.565315i	$0.808755\pi$
$264$	−3.50252			−0.215565
$265$	−16.4807	−	16.5999i	−1.01240	−	1.01972i
$266$	−20.2567			−1.24202
$267$		−	2.85072i		−	0.174461i
$268$			0.657004i			0.0401329i
$269$	12.3327			0.751941			0.375970	−	0.926632i	$-0.377309\pi$
$269$	12.3327			0.751941			0.375970	+	0.926632i	$0.377309\pi$
$270$	9.61998	−	9.55093i	0.585454	−	0.581251i
$271$	21.1708			1.28603			0.643017	−	0.765852i	$-0.277683\pi$
$271$	21.1708			1.28603			0.643017	+	0.765852i	$0.277683\pi$
$272$			4.61484i			0.279816i
$273$		−	17.7020i		−	1.07138i
$274$	−0.978495			−0.0591131
$275$	−0.0442537	+	6.14304i	−0.00266860	+	0.370440i
$276$	12.4862			0.751583
$277$			19.7804i			1.18849i	0.804283	+	0.594246i	$0.202549\pi$
$277$			19.7804i			1.18849i	−0.804283	+	0.594246i	$0.797451\pi$
$278$			4.23577i			0.254044i
$279$	−32.1476			−1.92462
$280$	7.17815	−	7.12662i	0.428976	−	0.425897i
$281$	−12.0499			−0.718837			−0.359419	−	0.933176i	$-0.617025\pi$
$281$	−12.0499			−0.718837			−0.359419	+	0.933176i	$0.617025\pi$
$282$		−	30.2474i		−	1.80121i
$283$		−	14.5109i		−	0.862583i	−0.902213	−	0.431291i	$-0.858058\pi$
$283$		−	14.5109i		−	0.862583i	0.902213	−	0.431291i	$-0.141942\pi$
$284$	1.09617			0.0650460
$285$	−20.1113	−	20.2567i	−1.19129	−	1.19990i
$286$	−1.68659			−0.0997301
$287$			18.0196i			1.06367i
$288$			5.12662i			0.302089i
$289$	−4.29679			−0.252752
$290$	−8.75050	−	8.81377i	−0.513847	−	0.517562i
$291$	43.2396			2.53475
$292$		−	9.58493i		−	0.560916i
$293$			14.8147i			0.865485i	0.901518	+	0.432743i	$0.142454\pi$
$293$			14.8147i			0.865485i	−0.901518	+	0.432743i	$0.857546\pi$
$294$	38.3790			2.23831
$295$	10.8598	−	10.7818i	0.632280	−	0.627742i
$296$	−7.27164			−0.422655
$297$		−	7.44853i		−	0.432208i
$298$			8.49351i			0.492016i
$299$	6.01258			0.347716
$300$	14.2532	+	0.102678i	0.822912	+	0.00592814i
$301$	−28.2793			−1.62999
$302$		−	9.09426i		−	0.523316i
$303$			14.1656i			0.813795i
$304$	4.47801			0.256832
$305$	22.1815	−	22.0223i	1.27011	−	1.26099i
$306$	−23.6586			−1.35247
$307$		−	33.2294i		−	1.89650i	−0.317520	−	0.948252i	$-0.602850\pi$
$307$		−	33.2294i		−	1.89650i	0.317520	−	0.948252i	$-0.397150\pi$
$308$		−	5.55787i		−	0.316689i
$309$	−36.6759			−2.08642
$310$	−9.87909	−	9.95051i	−0.561094	−	0.565151i
$311$	13.6843			0.775966			0.387983	−	0.921667i	$-0.373172\pi$
$311$	13.6843			0.775966			0.387983	+	0.921667i	$0.373172\pi$
$312$			3.91327i			0.221545i
$313$			8.07789i			0.456589i	0.973592	+	0.228295i	$0.0733150\pi$
$313$			8.07789i			0.456589i	−0.973592	+	0.228295i	$0.926685\pi$
$314$	−16.5202			−0.932288
$315$	36.5355	+	36.7997i	2.05854	+	2.07343i
$316$	15.9984			0.899979
$317$			30.2354i			1.69819i	0.528239	+	0.849096i	$0.322853\pi$
$317$			30.2354i			1.69819i	−0.528239	+	0.849096i	$0.677147\pi$
$318$			29.8216i			1.67231i
$319$	−6.82430			−0.382087
$320$	−1.58682	+	1.57543i	−0.0887061	+	0.0880694i
$321$	38.9119			2.17185
$322$			19.8134i			1.10416i
$323$			20.6653i			1.14985i
$324$	−1.90240			−0.105689
$325$	6.86346	+	0.0494435i	0.380716	+	0.00274263i
$326$	−17.0813			−0.946043
$327$		−	11.1182i		−	0.614835i
$328$		−	3.98348i		−	0.219951i
$329$	47.9973			2.64618
$330$	5.55787	−	5.51798i	0.305951	−	0.303755i
$331$	−0.808833			−0.0444575			−0.0222287	−	0.999753i	$-0.507076\pi$
$331$	−0.808833			−0.0444575			−0.0222287	+	0.999753i	$0.507076\pi$
$332$		−	11.4611i		−	0.629007i
$333$		−	37.2790i		−	2.04287i
$334$	2.94829			0.161323
$335$	−1.03507	−	1.04255i	−0.0565517	−	0.0569605i
$336$	−12.8955			−0.703508
$337$		−	24.0398i		−	1.30953i	−0.755832	−	0.654766i	$-0.772767\pi$
$337$		−	24.0398i		−	1.30953i	0.755832	−	0.654766i	$-0.227233\pi$
$338$		−	11.1156i		−	0.604610i
$339$	−4.56169			−0.247757
$340$	−7.27038	−	7.32294i	−0.394292	−	0.397142i
$341$	−7.70445			−0.417219
$342$			22.9571i			1.24138i
$343$			29.2356i			1.57857i
$344$	6.25152			0.337059
$345$	−19.8134	+	19.6712i	−1.06672	+	1.05906i
$346$	−5.36147			−0.288235
$347$			21.4905i			1.15367i	0.816860	+	0.576835i	$0.195713\pi$
$347$			21.4905i			1.15367i	−0.816860	+	0.576835i	$0.804287\pi$
$348$			15.8339i			0.848786i
$349$	30.2476			1.61912			0.809558	−	0.587040i	$-0.199707\pi$
$349$	30.2476			1.61912			0.809558	+	0.587040i	$0.199707\pi$
$350$	−0.162933	+	22.6174i	−0.00870912	+	1.20895i
$351$	−8.32205			−0.444198
$352$			1.22864i			0.0654868i
$353$			24.0131i			1.27809i	0.769171	+	0.639043i	$0.220669\pi$
$353$			24.0131i			1.27809i	−0.769171	+	0.639043i	$0.779331\pi$
$354$	−19.5095			−1.03692
$355$	−1.73944	+	1.72695i	−0.0923197	+	0.0916570i
$356$	−1.00000			−0.0529999
$357$		−	59.5108i		−	3.14965i
$358$			11.5470i			0.610281i
$359$	6.63025			0.349931			0.174966	−	0.984575i	$-0.444019\pi$
$359$	6.63025			0.349931			0.174966	+	0.984575i	$0.444019\pi$
$360$	−8.07665	−	8.13505i	−0.425677	−	0.428755i
$361$	1.05262			0.0554009
$362$			25.3052i			1.33001i
$363$			27.0546i			1.42000i
$364$	−6.20967			−0.325475
$365$	15.1004	+	15.2096i	0.790392	+	0.796107i
$366$	−39.8491			−2.08294
$367$		−	9.60858i		−	0.501564i	−0.968044	−	0.250782i	$-0.919312\pi$
$367$		−	9.60858i		−	0.501564i	0.968044	−	0.250782i	$-0.0806877\pi$
$368$		−	4.38002i		−	0.228324i
$369$	20.4218			1.06312
$370$	11.5388	−	11.4560i	0.599874	−	0.595568i
$371$	−47.3216			−2.45682
$372$			17.8761i			0.926831i
$373$			23.0875i			1.19543i	0.801710	+	0.597714i	$0.203924\pi$
$373$			23.0875i			1.19543i	−0.801710	+	0.597714i	$0.796076\pi$
$374$	−5.66999			−0.293188
$375$	−22.7792	+	22.2921i	−1.17631	+	1.15116i
$376$	−10.6104			−0.547191
$377$			7.62460i			0.392687i
$378$		−	27.4239i		−	1.41053i
$379$	30.1248			1.54741			0.773704	−	0.633547i	$-0.218402\pi$
$379$	30.1248			1.54741			0.773704	+	0.633547i	$0.218402\pi$
$380$	−7.10582	+	7.05481i	−0.364521	+	0.361904i
$381$	−25.1605			−1.28901
$382$		−	15.7942i		−	0.808100i
$383$			4.58478i			0.234271i	0.993116	+	0.117136i	$0.0373712\pi$
$383$			4.58478i			0.234271i	−0.993116	+	0.117136i	$0.962629\pi$
$384$	2.85072			0.145475
$385$	8.75606	+	8.81937i	0.446250	+	0.449476i
$386$	−7.69294			−0.391560
$387$			32.0492i			1.62915i
$388$		−	15.1680i		−	0.770036i
$389$	1.43129			0.0725691			0.0362846	−	0.999341i	$-0.488448\pi$
$389$	1.43129			0.0725691			0.0362846	+	0.999341i	$0.488448\pi$
$390$	−6.16509	−	6.20967i	−0.312182	−	0.314439i
$391$	20.2131			1.02222
$392$		−	13.4629i		−	0.679980i
$393$		−	15.1594i		−	0.764693i
$394$	−0.115358			−0.00581166
$395$	−25.3866	+	25.2044i	−1.27734	+	1.26817i
$396$	−6.29878			−0.316526
$397$		−	8.96970i		−	0.450176i	−0.974338	−	0.225088i	$-0.927733\pi$
$397$		−	8.96970i		−	0.450176i	0.974338	−	0.225088i	$-0.0722670\pi$
$398$			0.584508i			0.0292987i
$399$	−57.7463			−2.89093
$400$	0.0360184	−	4.99987i	0.00180092	−	0.249994i
$401$	6.18849			0.309039			0.154519	−	0.987990i	$-0.450617\pi$
$401$	6.18849			0.309039			0.154519	+	0.987990i	$0.450617\pi$
$402$			1.87294i			0.0934136i
$403$			8.60798i			0.428794i
$404$	4.96914			0.247224
$405$	3.01877	−	2.99710i	0.150004	−	0.148927i
$406$	−25.1256			−1.24696
$407$		−	8.93423i		−	0.442854i
$408$			13.1556i			0.651301i
$409$	15.5684			0.769807			0.384904	−	0.922957i	$-0.374235\pi$
$409$	15.5684			0.769807			0.384904	+	0.922957i	$0.374235\pi$
$410$	6.27570	+	6.32107i	0.309935	+	0.312176i
$411$	−2.78942			−0.137592
$412$			12.8655i			0.633837i
$413$		−	30.9582i		−	1.52335i
$414$	22.4547			1.10359
$415$	18.0561	+	18.1867i	0.886341	+	0.892749i
$416$	1.37273			0.0673035
$417$			12.0750i			0.591315i
$418$			5.50187i			0.269105i
$419$	−26.7703			−1.30782			−0.653908	−	0.756574i	$-0.726872\pi$
$419$	−26.7703			−1.30782			−0.653908	+	0.756574i	$0.726872\pi$
$420$	20.4629	−	20.3160i	0.998488	−	0.991321i
$421$	−30.2450			−1.47405			−0.737025	−	0.675865i	$-0.763770\pi$
$421$	−30.2450			−1.47405			−0.737025	+	0.675865i	$0.763770\pi$
$422$			15.0506i			0.732651i
$423$		−	54.3957i		−	2.64481i
$424$	10.4611			0.508034
$425$	23.0736	+	0.166219i	1.11924	+	0.00806282i
$426$	3.12489			0.151401
$427$		−	63.2334i		−	3.06008i
$428$		−	13.6498i		−	0.659790i
$429$	−4.80800			−0.232132
$430$	−9.92006	+	9.84885i	−0.478388	+	0.474954i
$431$	32.0590			1.54423			0.772114	−	0.635484i	$-0.219199\pi$
$431$	32.0590			1.54423			0.772114	+	0.635484i	$0.219199\pi$
$432$			6.06241i			0.291678i
$433$		−	8.68039i		−	0.417153i	−0.978006	−	0.208576i	$-0.933117\pi$
$433$		−	8.68039i		−	0.417153i	0.978006	−	0.208576i	$-0.0668830\pi$
$434$	−28.3662			−1.36162
$435$	−24.9453	−	25.1256i	−1.19603	−	1.20468i
$436$	−3.90012			−0.186782
$437$		−	19.6138i		−	0.938256i
$438$		−	27.3240i		−	1.30559i
$439$	−11.4514			−0.546547			−0.273273	−	0.961936i	$-0.588106\pi$
$439$	−11.4514			−0.546547			−0.273273	+	0.961936i	$0.588106\pi$
$440$	−1.93564	−	1.94964i	−0.0922781	−	0.0929453i
$441$	69.0193			3.28663
$442$			6.33493i			0.301322i
$443$			0.605849i			0.0287848i	0.999896	+	0.0143924i	$0.00458140\pi$
$443$			0.605849i			0.0287848i	−0.999896	+	0.0143924i	$0.995419\pi$
$444$	−20.7294			−0.983775
$445$	1.58682	−	1.57543i	0.0752227	−	0.0746827i
$446$	−11.2778			−0.534020
$447$			24.2126i			1.14522i
$448$			4.52360i			0.213720i
$449$	−7.76655			−0.366526			−0.183263	−	0.983064i	$-0.558666\pi$
$449$	−7.76655			−0.366526			−0.183263	+	0.983064i	$0.558666\pi$
$450$	25.6325	+	0.184653i	1.20833	+	0.00870461i
$451$	4.89426			0.230462
$452$			1.60019i			0.0752665i
$453$		−	25.9252i		−	1.21807i
$454$	19.6413			0.921810
$455$	9.85364	−	9.78292i	0.461946	−	0.458630i
$456$	12.7656			0.597803
$457$			24.3876i			1.14080i	0.821366	+	0.570402i	$0.193213\pi$
$457$			24.3876i			1.14080i	−0.821366	+	0.570402i	$0.806787\pi$
$458$		−	13.2889i		−	0.620948i
$459$	−27.9771			−1.30586
$460$	6.90043	+	6.95032i	0.321734	+	0.324060i
$461$	7.95362			0.370437			0.185218	−	0.982697i	$-0.440701\pi$
$461$	7.95362			0.370437			0.185218	+	0.982697i	$0.440701\pi$
$462$		−	15.8440i		−	0.737128i
$463$			15.0594i			0.699868i	0.936774	+	0.349934i	$0.113796\pi$
$463$			15.0594i			0.699868i	−0.936774	+	0.349934i	$0.886204\pi$
$464$	5.55434			0.257854
$465$	−28.1625	−	28.3662i	−1.30601	−	1.31545i
$466$	−19.0035			−0.880319
$467$		−	39.4937i		−	1.82755i	−0.406222	−	0.913775i	$-0.633154\pi$
$467$		−	39.4937i		−	1.82755i	0.406222	−	0.913775i	$-0.366846\pi$
$468$			7.03746i			0.325307i
$469$	−2.97202			−0.137235
$470$	16.8369	−	16.7160i	0.776628	−	0.771053i
$471$	−47.0945			−2.17000
$472$			6.84371i			0.315007i
$473$			7.68087i			0.353167i
$474$	45.6069			2.09480
$475$	0.161291	−	22.3895i	0.00740053	−	1.02730i
$476$	−20.8757			−0.956835
$477$			53.6299i			2.45555i
$478$			1.66519i			0.0761641i
$479$	−15.7045			−0.717556			−0.358778	−	0.933423i	$-0.616807\pi$
$479$	−15.7045			−0.717556			−0.358778	+	0.933423i	$0.616807\pi$
$480$	−4.52360	+	4.49113i	−0.206473	+	0.204991i
$481$	−9.98198			−0.455139
$482$		−	5.69530i		−	0.259414i
$483$			56.4827i			2.57005i
$484$	9.49044			0.431384
$485$	23.8961	+	24.0689i	1.08507	+	1.09291i
$486$	12.7640			0.578988
$487$			40.3721i			1.82943i	0.404096	+	0.914717i	$0.367586\pi$
$487$			40.3721i			1.82943i	−0.404096	+	0.914717i	$0.632414\pi$
$488$			13.9786i			0.632781i
$489$	−48.6939			−2.20202
$490$	21.2099	+	21.3633i	0.958167	+	0.965094i
$491$	−17.2348			−0.777795			−0.388898	−	0.921281i	$-0.627144\pi$
$491$	−17.2348			−0.777795			−0.388898	+	0.921281i	$0.627144\pi$
$492$		−	11.3558i		−	0.511958i
$493$			25.6324i			1.15443i
$494$	6.14710			0.276571
$495$	9.99505	−	9.92331i	0.449244	−	0.446020i
$496$	6.27071			0.281563
$497$			4.95865i			0.222426i
$498$		−	32.6723i		−	1.46408i
$499$	−37.6760			−1.68661			−0.843305	−	0.537435i	$-0.819393\pi$
$499$	−37.6760			−1.68661			−0.843305	+	0.537435i	$0.819393\pi$
$500$	7.81981	+	7.99066i	0.349712	+	0.357353i
$501$	8.40476			0.375497
$502$			5.89313i			0.263023i
$503$		−	19.5597i		−	0.872126i	−0.899916	−	0.436063i	$-0.856373\pi$
$503$		−	19.5597i		−	0.872126i	0.899916	−	0.436063i	$-0.143627\pi$
$504$	−23.1908			−1.03300
$505$	−7.88515	+	7.82855i	−0.350885	+	0.348366i
$506$	5.38147			0.239236
$507$		−	31.6876i		−	1.40729i
$508$			8.82600i			0.391590i
$509$	−34.9703			−1.55003			−0.775015	−	0.631943i	$-0.782258\pi$
$509$	−34.9703			−1.55003			−0.775015	+	0.631943i	$0.782258\pi$
$510$	−20.7258	−	20.8757i	−0.917756	−	0.924391i
$511$	43.3583			1.91806
$512$		−	1.00000i		−	0.0441942i
$513$			27.1476i			1.19860i
$514$	−0.854848			−0.0377057
$515$	−20.2687	−	20.4153i	−0.893146	−	0.899604i
$516$	17.8214			0.784541
$517$		−	13.0364i		−	0.573341i
$518$		−	32.8940i		−	1.44528i
$519$	−15.2841			−0.670896
$520$	−2.17828	+	2.16264i	−0.0955238	+	0.0948381i
$521$	20.0609			0.878885			0.439443	−	0.898271i	$-0.355176\pi$
$521$	20.0609			0.878885			0.439443	+	0.898271i	$0.355176\pi$
$522$			28.4750i			1.24632i
$523$			10.1567i			0.444124i	0.975033	+	0.222062i	$0.0712787\pi$
$523$			10.1567i			0.444124i	−0.975033	+	0.222062i	$0.928721\pi$
$524$	−5.31775			−0.232307
$525$	−0.464476	+	64.4759i	−0.0202714	+	2.81396i
$526$	18.3357			0.799476
$527$			28.9384i			1.26057i
$528$			3.50252i			0.152427i
$529$	3.81541			0.165887
$530$	−16.5999	+	16.4807i	−0.721052	+	0.715876i
$531$	−35.0851			−1.52257
$532$			20.2567i			0.878240i
$533$		−	5.46823i		−	0.236855i
$534$	−2.85072			−0.123363
$535$	21.5044	+	21.6599i	0.929717	+	0.936438i
$536$	0.657004			0.0283782
$537$			32.9174i			1.42049i
$538$		−	12.3327i		−	0.531702i
$539$	16.5411			0.712475
$540$	−9.55093	−	9.61998i	−0.411007	−	0.413978i
$541$	9.93773			0.427256			0.213628	−	0.976915i	$-0.431472\pi$
$541$	9.93773			0.427256			0.213628	+	0.976915i	$0.431472\pi$
$542$		−	21.1708i		−	0.909363i
$543$			72.1380i			3.09574i
$544$	4.61484			0.197860
$545$	6.18880	−	6.14437i	0.265099	−	0.263196i
$546$	−17.7020			−0.757577
$547$		−	2.50925i		−	0.107288i	−0.998560	−	0.0536438i	$-0.982916\pi$
$547$		−	2.50925i		−	0.107288i	0.998560	−	0.0536438i	$-0.0170836\pi$
$548$			0.978495i			0.0417992i
$549$	−71.6629			−3.05850
$550$	6.14304	+	0.0442537i	0.261940	+	0.00188698i
$551$	24.8724			1.05960
$552$		−	12.4862i		−	0.531449i
$553$			72.3702i			3.07749i
$554$	19.7804			0.840391
$555$	32.8940	−	32.6578i	1.39627	−	1.38625i
$556$	4.23577			0.179637
$557$			22.8456i			0.967999i	0.875068	+	0.484000i	$0.160816\pi$
$557$			22.8456i			0.967999i	−0.875068	+	0.484000i	$0.839184\pi$
$558$			32.1476i			1.36092i
$559$	8.58164			0.362965
$560$	−7.12662	−	7.17815i	−0.301155	−	0.303332i
$561$	−16.1636			−0.682426
$562$			12.0499i			0.508295i
$563$			46.4571i			1.95793i	0.204020	+	0.978967i	$0.434599\pi$
$563$			46.4571i			1.95793i	−0.204020	+	0.978967i	$0.565401\pi$
$564$	−30.2474			−1.27365
$565$	−2.52099	−	2.53922i	−0.106059	−	0.106826i
$566$	−14.5109			−0.609938
$567$		−	8.60567i		−	0.361404i
$568$		−	1.09617i		−	0.0459945i
$569$	18.3145			0.767782			0.383891	−	0.923378i	$-0.374584\pi$
$569$	18.3145			0.767782			0.383891	+	0.923378i	$0.374584\pi$
$570$	−20.2567	+	20.1113i	−0.848461	+	0.842371i
$571$	0.758516			0.0317429			0.0158715	−	0.999874i	$-0.494948\pi$
$571$	0.758516			0.0317429			0.0158715	+	0.999874i	$0.494948\pi$
$572$			1.68659i			0.0705199i
$573$		−	45.0248i		−	1.88094i
$574$	18.0196			0.752125
$575$	−21.8995	−	0.157761i	−0.913274	−	0.00657910i
$576$	5.12662			0.213609
$577$		−	41.3238i		−	1.72033i	−0.510013	−	0.860167i	$-0.670359\pi$
$577$		−	41.3238i		−	1.72033i	0.510013	−	0.860167i	$-0.329641\pi$
$578$			4.29679i			0.178723i
$579$	−21.9304			−0.911398
$580$	−8.81377	+	8.75050i	−0.365972	+	0.363345i
$581$	51.8452			2.15090
$582$		−	43.2396i		−	1.79234i
$583$			12.8529i			0.532312i
$584$	−9.58493			−0.396627
$585$	−11.0870	−	11.1672i	−0.458393	−	0.461707i
$586$	14.8147			0.611990
$587$		−	8.87893i		−	0.366473i	−0.983069	−	0.183236i	$-0.941343\pi$
$587$		−	8.87893i		−	0.366473i	0.983069	−	0.183236i	$-0.0586573\pi$
$588$		−	38.3790i		−	1.58272i
$589$	28.0803			1.15703
$590$	−10.7818	−	10.8598i	−0.443880	−	0.447089i
$591$	−0.328854			−0.0135272
$592$			7.27164i			0.298863i
$593$		−	46.1189i		−	1.89387i	−0.321419	−	0.946937i	$-0.604160\pi$
$593$		−	46.1189i		−	1.89387i	0.321419	−	0.946937i	$-0.395840\pi$
$594$	−7.44853			−0.305617
$595$	33.1260	−	32.8883i	1.35803	−	1.34829i
$596$	8.49351			0.347908
$597$			1.66627i			0.0681959i
$598$		−	6.01258i		−	0.245873i
$599$	0.242231			0.00989730			0.00494865	−	0.999988i	$-0.498425\pi$
$599$	0.242231			0.00989730			0.00494865	+	0.999988i	$0.498425\pi$
$600$	0.102678	−	14.2532i	0.00419183	−	0.581886i
$601$	13.3805			0.545803			0.272902	−	0.962042i	$-0.412017\pi$
$601$	13.3805			0.545803			0.272902	+	0.962042i	$0.412017\pi$
$602$			28.2793i			1.15258i
$603$			3.36821i			0.137164i
$604$	−9.09426			−0.370040
$605$	−15.0597	+	14.9516i	−0.612262	+	0.607867i
$606$	14.1656			0.575440
$607$			8.09568i			0.328593i	0.986411	+	0.164297i	$0.0525355\pi$
$607$			8.09568i			0.328593i	−0.986411	+	0.164297i	$0.947465\pi$
$608$		−	4.47801i		−	0.181607i
$609$	−71.6262			−2.90244
$610$	−22.0223	−	22.1815i	−0.891658	−	0.898105i
$611$	−14.5652			−0.589247
$612$			23.6586i			0.956341i
$613$		−	38.8721i		−	1.57003i	−0.619477	−	0.785015i	$-0.712655\pi$
$613$		−	38.8721i		−	1.57003i	0.619477	−	0.785015i	$-0.287345\pi$
$614$	−33.2294			−1.34103
$615$	17.8903	+	18.0196i	0.721406	+	0.726622i
$616$	−5.55787			−0.223933
$617$		−	22.6884i		−	0.913401i	−0.889621	−	0.456700i	$-0.849031\pi$
$617$		−	22.6884i		−	0.913401i	0.889621	−	0.456700i	$-0.150969\pi$
$618$			36.6759i			1.47532i
$619$	7.03326			0.282691			0.141345	−	0.989960i	$-0.454857\pi$
$619$	7.03326			0.282691			0.141345	+	0.989960i	$0.454857\pi$
$620$	−9.95051	+	9.87909i	−0.399622	+	0.396754i
$621$	26.5535			1.06556
$622$		−	13.6843i		−	0.548691i
$623$		−	4.52360i		−	0.181234i
$624$	3.91327			0.156656
$625$	−24.9974	−	0.360175i	−0.999896	−	0.0144070i
$626$	8.07789			0.322857
$627$			15.6843i			0.626371i
$628$			16.5202i			0.659227i
$629$	−33.5575			−1.33802
$630$	36.7997	−	36.5355i	1.46613	−	1.45561i
$631$	16.9874			0.676256			0.338128	−	0.941100i	$-0.390206\pi$
$631$	16.9874			0.676256			0.338128	+	0.941100i	$0.390206\pi$
$632$		−	15.9984i		−	0.636381i
$633$			42.9051i			1.70532i
$634$	30.2354			1.20080
$635$	−13.9048	−	14.0053i	−0.551794	−	0.555783i
$636$	29.8216			1.18250
$637$		−	18.4809i		−	0.732241i
$638$			6.82430i			0.270176i
$639$	5.61968			0.222311
$640$	1.57543	+	1.58682i	0.0622745	+	0.0627247i
$641$	37.5611			1.48357			0.741787	−	0.670635i	$-0.233978\pi$
$641$	37.5611			1.48357			0.741787	+	0.670635i	$0.233978\pi$
$642$		−	38.9119i		−	1.53573i
$643$		−	18.0731i		−	0.712732i	−0.934347	−	0.356366i	$-0.884016\pi$
$643$		−	18.0731i		−	0.712732i	0.934347	−	0.356366i	$-0.115984\pi$
$644$	19.8134			0.780759
$645$	−28.2793	+	28.0764i	−1.11350	+	1.10551i
$646$	20.6653			0.813067
$647$			43.8207i			1.72277i	0.507952	+	0.861386i	$0.330403\pi$
$647$			43.8207i			1.72277i	−0.507952	+	0.861386i	$0.669597\pi$
$648$			1.90240i			0.0747332i
$649$	−8.40847			−0.330061
$650$	0.0494435	−	6.86346i	0.00193933	−	0.269207i
$651$	−80.8641			−3.16931
$652$			17.0813i			0.668954i
$653$			12.0487i			0.471504i	0.971813	+	0.235752i	$0.0757553\pi$
$653$			12.0487i			0.471504i	−0.971813	+	0.235752i	$0.924245\pi$
$654$	−11.1182			−0.434754
$655$	8.43834	−	8.37777i	0.329713	−	0.327346i
$656$	−3.98348			−0.155529
$657$		−	49.1383i		−	1.91707i
$658$		−	47.9973i		−	1.87113i
$659$	40.0336			1.55949			0.779744	−	0.626098i	$-0.215349\pi$
$659$	40.0336			1.55949			0.779744	+	0.626098i	$0.215349\pi$
$660$	−5.51798	−	5.55787i	−0.214787	−	0.216340i
$661$	−24.2278			−0.942351			−0.471175	−	0.882040i	$-0.656170\pi$
$661$	−24.2278			−0.942351			−0.471175	+	0.882040i	$0.656170\pi$
$662$			0.808833i			0.0314362i
$663$			18.0591i			0.701358i
$664$	−11.4611			−0.444775
$665$	−31.9131	−	32.1439i	−1.23754	−	1.24649i
$666$	−37.2790			−1.44453
$667$		−	24.3282i		−	0.941990i
$668$		−	2.94829i		−	0.114073i
$669$	−32.1499			−1.24299
$670$	−1.04255	+	1.03507i	−0.0402772	+	0.0399881i
$671$	−17.1747			−0.663020
$672$			12.8955i			0.497455i
$673$		−	33.6487i		−	1.29706i	−0.761188	−	0.648532i	$-0.775383\pi$
$673$		−	33.6487i		−	1.29706i	0.761188	−	0.648532i	$-0.224617\pi$
$674$	−24.0398			−0.925979
$675$	30.3113	+	0.218358i	1.16668	+	0.00840462i
$676$	−11.1156			−0.427524
$677$			36.8340i			1.41565i	0.706389	+	0.707823i	$0.250323\pi$
$677$			36.8340i			1.41565i	−0.706389	+	0.707823i	$0.749677\pi$
$678$			4.56169i			0.175191i
$679$	68.6137			2.63315
$680$	−7.32294	+	7.27038i	−0.280822	+	0.278806i
$681$	55.9918			2.14561
$682$			7.70445i			0.295019i
$683$			44.2202i			1.69204i	0.533151	+	0.846020i	$0.321008\pi$
$683$			44.2202i			1.69204i	−0.533151	+	0.846020i	$0.678992\pi$
$684$	22.9571			0.877786
$685$	−1.54155	−	1.55270i	−0.0588998	−	0.0593256i
$686$	29.2356			1.11622
$687$		−	37.8829i		−	1.44532i
$688$		−	6.25152i		−	0.238337i
$689$	14.3602			0.547080
$690$	19.6712	+	19.8134i	0.748871	+	0.754285i
$691$	15.6482			0.595286			0.297643	−	0.954677i	$-0.403800\pi$
$691$	15.6482			0.595286			0.297643	+	0.954677i	$0.403800\pi$
$692$			5.36147i			0.203813i
$693$		−	28.4931i		−	1.08236i
$694$	21.4905			0.815768
$695$	−6.72141	+	6.67317i	−0.254958	+	0.253128i
$696$	15.8339			0.600182
$697$		−	18.3831i		−	0.696310i
$698$		−	30.2476i		−	1.14489i
$699$	−54.1737			−2.04904
$700$	22.6174	+	0.162933i	0.854857	+	0.00615827i
$701$	−24.8434			−0.938324			−0.469162	−	0.883112i	$-0.655444\pi$
$701$	−24.8434			−0.938324			−0.469162	+	0.883112i	$0.655444\pi$
$702$			8.32205i			0.314095i
$703$			32.5625i			1.22812i
$704$	1.22864			0.0463061
$705$	47.9973	−	47.6528i	1.80768	−	1.79471i
$706$	24.0131			0.903743
$707$			22.4784i			0.845386i
$708$			19.5095i			0.733213i
$709$	25.7323			0.966397			0.483198	−	0.875511i	$-0.339475\pi$
$709$	25.7323			0.966397			0.483198	+	0.875511i	$0.339475\pi$
$710$	1.72695	+	1.73944i	0.0648113	+	0.0652799i
$711$	82.0176			3.07590
$712$			1.00000i			0.0374766i
$713$		−	27.4659i		−	1.02860i
$714$	−59.5108			−2.22714
$715$	−2.65711	−	2.67632i	−0.0993703	−	0.100089i
$716$	11.5470			0.431533
$717$			4.74700i			0.177280i
$718$		−	6.63025i		−	0.247439i
$719$	30.9572			1.15451			0.577254	−	0.816564i	$-0.304124\pi$
$719$	30.9572			1.15451			0.577254	+	0.816564i	$0.304124\pi$
$720$	−8.13505	+	8.07665i	−0.303175	+	0.300999i
$721$	−58.1982			−2.16742
$722$		−	1.05262i		−	0.0391744i
$723$		−	16.2357i		−	0.603813i
$724$	25.3052			0.940459
$725$	0.200059	−	27.7710i	0.00742999	−	1.03139i
$726$	27.0546			1.00409
$727$		−	0.0138657i		−	0.000514250i	−1.00000		0.000257125i	$-0.999918\pi$
$727$		−	0.0138657i		−	0.000514250i	1.00000		0.000257125i	$-8.18454e-5\pi$
$728$			6.20967i			0.230146i
$729$	42.0939			1.55903
$730$	15.2096	−	15.1004i	0.562932	−	0.558892i
$731$	28.8498			1.06705
$732$			39.8491i			1.47286i
$733$			11.7817i			0.435168i	0.976042	+	0.217584i	$0.0698176\pi$
$733$			11.7817i			0.435168i	−0.976042	+	0.217584i	$0.930182\pi$
$734$	−9.60858			−0.354659
$735$	60.4636	+	60.9008i	2.23023	+	2.24636i
$736$	−4.38002			−0.161450
$737$			0.807222i			0.0297344i
$738$		−	20.4218i		−	0.751736i
$739$	−12.7734			−0.469877			−0.234939	−	0.972010i	$-0.575489\pi$
$739$	−12.7734			−0.469877			−0.234939	+	0.972010i	$0.575489\pi$
$740$	−11.4560	−	11.5388i	−0.421130	−	0.424175i
$741$	17.5237			0.643748
$742$			47.3216i			1.73723i
$743$		−	34.0456i		−	1.24901i	−0.781019	−	0.624507i	$-0.785300\pi$
$743$		−	34.0456i		−	1.24901i	0.781019	−	0.624507i	$-0.214700\pi$
$744$	17.8761			0.655368
$745$	−13.4777	+	13.3810i	−0.493785	+	0.490240i
$746$	23.0875			0.845295
$747$		−	58.7565i		−	2.14979i
$748$			5.66999i			0.207315i
$749$	61.7463			2.25616
$750$	22.2921	+	22.7792i	0.813993	+	0.831777i
$751$	−18.0609			−0.659053			−0.329526	−	0.944146i	$-0.606889\pi$
$751$	−18.0609			−0.659053			−0.329526	+	0.944146i	$0.606889\pi$
$752$			10.6104i			0.386923i
$753$			16.7997i			0.612215i
$754$	7.62460			0.277672
$755$	14.4310	−	14.3274i	0.525197	−	0.521428i
$756$	−27.4239			−0.997398
$757$			28.5767i			1.03864i	0.854581	+	0.519319i	$0.173814\pi$
$757$			28.5767i			1.03864i	−0.854581	+	0.519319i	$0.826186\pi$
$758$		−	30.1248i		−	1.09418i
$759$	15.3411			0.556846
$760$	7.05481	+	7.10582i	0.255905	+	0.257755i
$761$	11.0520			0.400636			0.200318	−	0.979731i	$-0.435802\pi$
$761$	11.0520			0.400636			0.200318	+	0.979731i	$0.435802\pi$
$762$			25.1605i			0.911468i
$763$		−	17.6425i		−	0.638703i
$764$	−15.7942			−0.571413
$765$	−37.2725	−	37.5420i	−1.34759	−	1.35733i
$766$	4.58478			0.165655
$767$			9.39456i			0.339218i
$768$		−	2.85072i		−	0.102867i
$769$	10.9106			0.393445			0.196722	−	0.980459i	$-0.436970\pi$
$769$	10.9106			0.393445			0.196722	+	0.980459i	$0.436970\pi$
$770$	8.81937	−	8.75606i	0.317828	−	0.315547i
$771$	−2.43694			−0.0877641
$772$			7.69294i			0.276875i
$773$			27.6095i			0.993046i	0.868024	+	0.496523i	$0.165390\pi$
$773$			27.6095i			0.993046i	−0.868024	+	0.496523i	$0.834610\pi$
$774$	32.0492			1.15198
$775$	0.225861	−	31.3527i	0.00811316	−	1.12622i
$776$	−15.1680			−0.544498
$777$		−	93.7716i		−	3.36404i
$778$		−	1.43129i		−	0.0513141i
$779$	−17.8381			−0.639115
$780$	−6.20967	+	6.16509i	−0.222342	+	0.220746i
$781$	1.34681			0.0481925
$782$		−	20.2131i		−	0.722820i
$783$			33.6727i			1.20337i
$784$	−13.4629			−0.480818
$785$	−26.0265	−	26.2146i	−0.928924	−	0.935640i
$786$	−15.1594			−0.540720
$787$		−	54.2969i		−	1.93547i	−0.251962	−	0.967737i	$-0.581076\pi$
$787$		−	54.2969i		−	1.93547i	0.251962	−	0.967737i	$-0.418924\pi$
$788$			0.115358i			0.00410946i
$789$	52.2701			1.86086
$790$	25.2044	+	25.3866i	0.896731	+	0.903215i
$791$	−7.23860			−0.257375
$792$			6.29878i			0.223817i
$793$			19.1888i			0.681414i
$794$	−8.96970			−0.318323
$795$	−47.3216	+	46.9820i	−1.67833	+	1.66628i
$796$	0.584508			0.0207173
$797$		−	31.7349i		−	1.12411i	−0.827101	−	0.562053i	$-0.810012\pi$
$797$		−	31.7349i		−	1.12411i	0.827101	−	0.562053i	$-0.189988\pi$
$798$			57.7463i			2.04420i
$799$	−48.9655			−1.73227
$800$	−4.99987	−	0.0360184i	−0.176772	−	0.00127344i
$801$	−5.12662			−0.181140
$802$		−	6.18849i		−	0.218523i
$803$		−	11.7764i		−	0.415581i
$804$	1.87294			0.0660534
$805$	−31.4404	+	31.2148i	−1.10813	+	1.10018i
$806$	8.60798			0.303203
$807$		−	35.1572i		−	1.23759i
$808$		−	4.96914i		−	0.174814i
$809$	−0.435169			−0.0152997			−0.00764986	−	0.999971i	$-0.502435\pi$
$809$	−0.435169			−0.0152997			−0.00764986	+	0.999971i	$0.502435\pi$
$810$	−2.99710	−	3.01877i	−0.105307	−	0.106069i
$811$	8.86615			0.311333			0.155666	−	0.987810i	$-0.450248\pi$
$811$	8.86615			0.311333			0.155666	+	0.987810i	$0.450248\pi$
$812$			25.1256i			0.881736i
$813$		−	60.3520i		−	2.11664i
$814$	−8.93423			−0.313145
$815$	−26.9104	−	27.1049i	−0.942629	−	0.949445i
$816$	13.1556			0.460540
$817$		−	27.9944i		−	0.979400i
$818$		−	15.5684i		−	0.544336i
$819$	−31.8346			−1.11239
$820$	6.32107	−	6.27570i	0.220741	−	0.219157i
$821$	−6.17004			−0.215336			−0.107668	−	0.994187i	$-0.534338\pi$
$821$	−6.17004			−0.215336			−0.107668	+	0.994187i	$0.534338\pi$
$822$			2.78942i			0.0972922i
$823$			12.4662i			0.434544i	0.976111	+	0.217272i	$0.0697158\pi$
$823$			12.4662i			0.434544i	−0.976111	+	0.217272i	$0.930284\pi$
$824$	12.8655			0.448190
$825$	17.5121	+	0.126155i	0.609694	+	0.00439215i
$826$	−30.9582			−1.07717
$827$			35.5408i			1.23587i	0.786228	+	0.617937i	$0.212031\pi$
$827$			35.5408i			1.23587i	−0.786228	+	0.617937i	$0.787969\pi$
$828$		−	22.4547i		−	0.780356i
$829$	−38.5645			−1.33940			−0.669700	−	0.742632i	$-0.733577\pi$
$829$	−38.5645			−1.33940			−0.669700	+	0.742632i	$0.733577\pi$
$830$	18.1867	−	18.0561i	0.631269	−	0.626737i
$831$	56.3886			1.95610
$832$		−	1.37273i		−	0.0475908i
$833$		−	62.1292i		−	2.15265i
$834$	12.0750			0.418123
$835$	4.64484	+	4.67842i	0.160741	+	0.161903i
$836$	5.50187			0.190286
$837$			38.0156i			1.31401i
$838$			26.7703i			0.924765i
$839$	−10.5761			−0.365128			−0.182564	−	0.983194i	$-0.558440\pi$
$839$	−10.5761			−0.365128			−0.182564	+	0.983194i	$0.558440\pi$
$840$	−20.3160	−	20.4629i	−0.700970	−	0.706038i
$841$	1.85075			0.0638189
$842$			30.2450i			1.04231i
$843$			34.3509i			1.18311i
$844$	15.0506			0.518063
$845$	17.6385	−	17.5119i	0.606784	−	0.602428i
$846$	−54.3957			−1.87016
$847$			42.9309i			1.47512i
$848$		−	10.4611i		−	0.359234i
$849$	−41.3665			−1.41970
$850$	0.166219	−	23.0736i	0.00570127	−	0.791419i
$851$	31.8499			1.09180
$852$		−	3.12489i		−	0.107057i
$853$		−	0.122918i		−	0.00420863i	−0.999998	−	0.00210431i	$-0.999330\pi$
$853$		−	0.122918i		−	0.00420863i	0.999998	−	0.00210431i	$-0.000669824\pi$
$854$	−63.2334			−2.16380
$855$	−36.4289	+	36.1674i	−1.24584	+	1.23690i
$856$	−13.6498			−0.466542
$857$			34.3154i			1.17219i	0.810242	+	0.586096i	$0.199336\pi$
$857$			34.3154i			1.17219i	−0.810242	+	0.586096i	$0.800664\pi$
$858$			4.80800i			0.164142i
$859$	−12.4774			−0.425725			−0.212863	−	0.977082i	$-0.568279\pi$
$859$	−12.4774			−0.425725			−0.212863	+	0.977082i	$0.568279\pi$
$860$	9.84885	+	9.92006i	0.335843	+	0.338271i
$861$	51.3690			1.75065
$862$		−	32.0590i		−	1.09193i
$863$		−	23.0720i		−	0.785381i	−0.919671	−	0.392691i	$-0.871544\pi$
$863$		−	23.0720i		−	0.785381i	0.919671	−	0.392691i	$-0.128456\pi$
$864$	6.06241			0.206248
$865$	−8.44664	−	8.50771i	−0.287194	−	0.289271i
$866$	−8.68039			−0.294972
$867$			12.2489i			0.415996i
$868$			28.3662i			0.962810i
$869$	19.6563			0.666793
$870$	−25.1256	+	24.9453i	−0.851838	+	0.845723i
$871$	0.901888			0.0305593
$872$			3.90012i			0.132075i
$873$		−	77.7604i		−	2.63179i
$874$	−19.6138			−0.663447
$875$	−36.1465	+	35.3736i	−1.22197	+	1.19585i
$876$	−27.3240			−0.923192
$877$			29.9035i			1.00977i	0.863186	+	0.504885i	$0.168465\pi$
$877$			29.9035i			1.00977i	−0.863186	+	0.504885i	$0.831535\pi$
$878$			11.4514i			0.386467i
$879$	42.2327			1.42447
$880$	−1.94964	+	1.93564i	−0.0657222	+	0.0652505i
$881$	19.5416			0.658373			0.329186	−	0.944265i	$-0.393226\pi$
$881$	19.5416			0.658373			0.329186	+	0.944265i	$0.393226\pi$
$882$		−	69.0193i		−	2.32400i
$883$		−	47.3292i		−	1.59276i	−0.604799	−	0.796378i	$-0.706747\pi$
$883$		−	47.3292i		−	1.59276i	0.604799	−	0.796378i	$-0.293253\pi$
$884$	6.33493			0.213067
$885$	−30.7360	−	30.9582i	−1.03318	−	1.04065i
$886$	0.605849			0.0203539
$887$		−	49.1245i		−	1.64944i	−0.565543	−	0.824719i	$-0.691333\pi$
$887$		−	49.1245i		−	1.64944i	0.565543	−	0.824719i	$-0.308667\pi$
$888$			20.7294i			0.695634i
$889$	−39.9252			−1.33905
$890$	−1.57543	−	1.58682i	−0.0528087	−	0.0531904i
$891$	−2.33736			−0.0783046
$892$			11.2778i			0.377609i
$893$			47.5137i			1.58998i
$894$	24.2126			0.809792
$895$	−18.3231	+	18.1916i	−0.612475	+	0.608078i
$896$	4.52360			0.151123
$897$		−	17.1402i		−	0.572295i
$898$			7.76655i			0.259173i
$899$	34.8297			1.16164
$900$	0.184653	−	25.6325i	0.00615509	−	0.854415i
$901$	48.2762			1.60831
$902$		−	4.89426i		−	0.162961i
$903$			80.6166i			2.68275i
$904$	1.60019			0.0532215
$905$	−40.1548	+	39.8666i	−1.33479	+	1.32521i
$906$	−25.9252			−0.861308
$907$		−	5.68576i		−	0.188793i	−0.995535	−	0.0943963i	$-0.969908\pi$
$907$		−	5.68576i		−	0.188793i	0.995535	−	0.0943963i	$-0.0300921\pi$
$908$		−	19.6413i		−	0.651818i
$909$	25.4749			0.844949
$910$	−9.78292	−	9.85364i	−0.324300	−	0.326645i
$911$	2.89022			0.0957572			0.0478786	−	0.998853i	$-0.484754\pi$
$911$	2.89022			0.0957572			0.0478786	+	0.998853i	$0.484754\pi$
$912$		−	12.7656i		−	0.422711i
$913$		−	14.0815i		−	0.466030i
$914$	24.3876			0.806670
$915$	−62.7796	−	63.2334i	−2.07543	−	2.09043i
$916$	−13.2889			−0.439076
$917$		−	24.0554i		−	0.794378i
$918$			27.9771i			0.923382i
$919$	41.2095			1.35938			0.679688	−	0.733501i	$-0.262115\pi$
$919$	41.2095			1.35938			0.679688	+	0.733501i	$0.262115\pi$
$920$	6.95032	−	6.90043i	0.229145	−	0.227501i
$921$	−94.7279			−3.12139
$922$		−	7.95362i		−	0.261938i
$923$		−	1.50475i		−	0.0495295i
$924$	−15.8440			−0.521228
$925$	36.3573	+	0.261913i	1.19542	+	0.00861164i
$926$	15.0594			0.494882
$927$			65.9565i			2.16630i
$928$		−	5.55434i		−	0.182330i
$929$	7.26885			0.238483			0.119242	−	0.992865i	$-0.461954\pi$
$929$	7.26885			0.238483			0.119242	+	0.992865i	$0.461954\pi$
$930$	−28.3662	+	28.1625i	−0.930163	+	0.923486i
$931$	−60.2871			−1.97583
$932$			19.0035i			0.622480i
$933$		−	39.0102i		−	1.27714i
$934$	−39.4937			−1.29227
$935$	−8.93269	−	8.99727i	−0.292130	−	0.294242i
$936$	7.03746			0.230027
$937$		−	2.12881i		−	0.0695453i	−0.999395	−	0.0347726i	$-0.988929\pi$
$937$		−	2.12881i		−	0.0695453i	0.999395	−	0.0347726i	$-0.0110707\pi$
$938$			2.97202i			0.0970399i
$939$	23.0278			0.751485
$940$	−16.7160	−	16.8369i	−0.545217	−	0.549159i
$941$	−4.37139			−0.142503			−0.0712517	−	0.997458i	$-0.522699\pi$
$941$	−4.37139			−0.142503			−0.0712517	+	0.997458i	$0.522699\pi$
$942$			47.0945i			1.53442i
$943$			17.4477i			0.568176i
$944$	6.84371			0.222744
$945$	43.5169	−	43.2045i	1.41561	−	1.40544i
$946$	7.68087			0.249727
$947$		−	8.73145i		−	0.283734i	−0.989886	−	0.141867i	$-0.954689\pi$
$947$		−	8.73145i		−	0.283734i	0.989886	−	0.141867i	$-0.0453105\pi$
$948$		−	45.6069i		−	1.48124i
$949$	−13.1575			−0.427111
$950$	−22.3895	−	0.161291i	−0.726411	−	0.00523297i
$951$	86.1929			2.79500
$952$			20.8757i			0.676585i
$953$			10.6958i			0.346470i	0.984881	+	0.173235i	$0.0554220\pi$
$953$			10.6958i			0.346470i	−0.984881	+	0.173235i	$0.944578\pi$
$954$	53.6299			1.73633
$955$	25.0626	−	24.8827i	0.811006	−	0.805185i
$956$	1.66519			0.0538561
$957$			19.4542i			0.628864i
$958$			15.7045i			0.507389i
$959$	−4.42632			−0.142933
$960$	4.49113	+	4.52360i	0.144950	+	0.145998i
$961$	8.32181			0.268445
$962$			9.98198i			0.321832i
$963$		−	69.9776i		−	2.25500i
$964$	−5.69530			−0.183433
$965$	−12.1197	−	12.2073i	−0.390147	−	0.392968i
$966$	56.4827			1.81730
$967$		−	25.2596i		−	0.812293i	−0.913808	−	0.406146i	$-0.866872\pi$
$967$		−	25.2596i		−	0.812293i	0.913808	−	0.406146i	$-0.133128\pi$
$968$		−	9.49044i		−	0.305034i
$969$	58.9112			1.89250
$970$	24.0689	−	23.8961i	0.772805	−	0.767258i
$971$	−46.0863			−1.47898			−0.739490	−	0.673167i	$-0.764933\pi$
$971$	−46.0863			−1.47898			−0.739490	+	0.673167i	$0.764933\pi$
$972$		−	12.7640i		−	0.409407i
$973$			19.1609i			0.614270i
$974$	40.3721			1.29360
$975$	0.140950	−	19.5658i	0.00451400	−	0.626608i
$976$	13.9786			0.447444
$977$			10.3767i			0.331980i	0.986127	+	0.165990i	$0.0530820\pi$
$977$			10.3767i			0.331980i	−0.986127	+	0.165990i	$0.946918\pi$
$978$			48.6939i			1.55706i
$979$	−1.22864			−0.0392675
$980$	21.3633	−	21.2099i	0.682425	−	0.677526i
$981$	−19.9944			−0.638373
$982$			17.2348i			0.549984i
$983$			0.254970i			0.00813227i	0.999992	+	0.00406614i	$0.00129430\pi$
$983$			0.254970i			0.00813227i	−0.999992	+	0.00406614i	$0.998706\pi$
$984$	−11.3558			−0.362009
$985$	−0.181739	−	0.183053i	−0.00579069	−	0.00583255i
$986$	25.6324			0.816303
$987$		−	136.827i		−	4.35525i
$988$		−	6.14710i		−	0.195565i
$989$	−27.3818			−0.870690
$990$	−9.92331	−	9.99505i	−0.315383	−	0.317664i
$991$	−16.0684			−0.510428			−0.255214	−	0.966885i	$-0.582146\pi$
$991$	−16.0684			−0.510428			−0.255214	+	0.966885i	$0.582146\pi$
$992$		−	6.27071i		−	0.199095i
$993$			2.30576i			0.0731710i
$994$	4.95865			0.157279
$995$	−0.927511	+	0.920854i	−0.0294041	+	0.0291930i
$996$	−32.6723			−1.03526
$997$			50.0379i			1.58472i	0.610057	+	0.792358i	$0.291147\pi$
$997$			50.0379i			1.58472i	−0.610057	+	0.792358i	$0.708853\pi$
$998$			37.6760i			1.19261i
$999$	−44.0837			−1.39475

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	890.2.b.a.179.1	✓	16
5.2	odd	4		4450.2.a.bj.1.1		8
5.3	odd	4		4450.2.a.bi.1.8		8
5.4	even	2	inner	890.2.b.a.179.16	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
890.2.b.a.179.1	✓	16	1.1	even	1	trivial
890.2.b.a.179.16	yes	16	5.4	even	2	inner
4450.2.a.bi.1.8		8	5.3	odd	4
4450.2.a.bj.1.1		8	5.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 890 = 2 \cdot 5 \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	890.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -2.85072i q^{3} -1.00000 q^{4} +(1.58682 - 1.57543i) q^{5} -2.85072 q^{6} -4.52360i q^{7} +1.00000i q^{8} -5.12662 q^{9} +(-1.57543 - 1.58682i) q^{10} -1.22864 q^{11} +2.85072i q^{12} +1.37273i q^{13} -4.52360 q^{14} +(-4.49113 - 4.52360i) q^{15} +1.00000 q^{16} +4.61484i q^{17} +5.12662i q^{18} +4.47801 q^{19} +(-1.58682 + 1.57543i) q^{20} -12.8955 q^{21} +1.22864i q^{22} -4.38002i q^{23} +2.85072 q^{24} +(0.0360184 - 4.99987i) q^{25} +1.37273 q^{26} +6.06241i q^{27} +4.52360i q^{28} +5.55434 q^{29} +(-4.52360 + 4.49113i) q^{30} +6.27071 q^{31} -1.00000i q^{32} +3.50252i q^{33} +4.61484 q^{34} +(-7.12662 - 7.17815i) q^{35} +5.12662 q^{36} +7.27164i q^{37} -4.47801i q^{38} +3.91327 q^{39} +(1.57543 + 1.58682i) q^{40} -3.98348 q^{41} +12.8955i q^{42} -6.25152i q^{43} +1.22864 q^{44} +(-8.13505 + 8.07665i) q^{45} -4.38002 q^{46} +10.6104i q^{47} -2.85072i q^{48} -13.4629 q^{49} +(-4.99987 - 0.0360184i) q^{50} +13.1556 q^{51} -1.37273i q^{52} -10.4611i q^{53} +6.06241 q^{54} +(-1.94964 + 1.93564i) q^{55} +4.52360 q^{56} -12.7656i q^{57} -5.55434i q^{58} +6.84371 q^{59} +(4.49113 + 4.52360i) q^{60} +13.9786 q^{61} -6.27071i q^{62} +23.1908i q^{63} -1.00000 q^{64} +(2.16264 + 2.17828i) q^{65} +3.50252 q^{66} -0.657004i q^{67} -4.61484i q^{68} -12.4862 q^{69} +(-7.17815 + 7.12662i) q^{70} -1.09617 q^{71} -5.12662i q^{72} +9.58493i q^{73} +7.27164 q^{74} +(-14.2532 - 0.102678i) q^{75} -4.47801 q^{76} +5.55787i q^{77} -3.91327i q^{78} -15.9984 q^{79} +(1.58682 - 1.57543i) q^{80} +1.90240 q^{81} +3.98348i q^{82} +11.4611i q^{83} +12.8955 q^{84} +(7.27038 + 7.32294i) q^{85} -6.25152 q^{86} -15.8339i q^{87} -1.22864i q^{88} +1.00000 q^{89} +(8.07665 + 8.13505i) q^{90} +6.20967 q^{91} +4.38002i q^{92} -17.8761i q^{93} +10.6104 q^{94} +(7.10582 - 7.05481i) q^{95} -2.85072 q^{96} +15.1680i q^{97} +13.4629i q^{98} +6.29878 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 2 q^{5} - 8 q^{6} - 2 q^{10} - 8 q^{11} + 4 q^{14} + 16 q^{16} + 16 q^{19} + 2 q^{20} - 20 q^{21} + 8 q^{24} - 4 q^{25} - 8 q^{26} + 20 q^{29} + 4 q^{30} + 28 q^{34} - 32 q^{35} + 20 q^{39}+ \cdots - 24 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 - 2 * q^5 - 8 * q^6 - 2 * q^10 - 8 * q^11 + 4 * q^14 + 16 * q^16 + 16 * q^19 + 2 * q^20 - 20 * q^21 + 8 * q^24 - 4 * q^25 - 8 * q^26 + 20 * q^29 + 4 * q^30 + 28 * q^34 - 32 * q^35 + 20 * q^39 + 2 * q^40 + 8 * q^44 - 26 * q^45 - 48 * q^46 + 8 * q^49 - 8 * q^50 + 8 * q^51 + 20 * q^54 - 8 * q^55 - 4 * q^56 + 8 * q^59 - 4 * q^61 - 16 * q^64 - 52 * q^65 - 20 * q^66 + 36 * q^69 - 8 * q^70 + 40 * q^71 + 28 * q^74 - 64 * q^75 - 16 * q^76 - 4 * q^79 - 2 * q^80 - 8 * q^81 + 20 * q^84 - 12 * q^85 - 8 * q^86 + 16 * q^89 + 6 * q^90 + 40 * q^91 + 56 * q^94 - 28 * q^95 - 8 * q^96 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more