LMFDB - Embedded newform 196.4.d.b.195.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,4,Mod(195,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("196.195");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	196.d (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:	$11.5643743611$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} - 24 x^{17} + 28 x^{16} + 56 x^{15} - 192 x^{14} + 352 x^{13} - 448 x^{12} + \cdots + 1073741824 $ x^20 - 2x^18 - 24x^17 + 28x^16 + 56x^15 - 192x^14 + 352x^13 - 448x^12 + 5376x^11 - 41472x^10 + 43008x^9 - 28672x^8 + 180224x^7 - 786432x^6 + 1835008x^5 + 7340032x^4 - 50331648x^3 - 33554432*x^2 + 1073741824
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{34}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			195.7
Root			$2.82698 + 0.0903966i$ of defining polynomial
Character	$\chi$	$=$	196.195
Dual form			196.4.d.b.195.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33521 + 2.49344i) q^{2} -9.30691 q^{3} +(-4.43445 - 6.65850i) q^{4} -5.90673i q^{5} +(12.4266 - 23.2062i) q^{6} +(22.5235 - 2.16656i) q^{8} +59.6185 q^{9} +O(q^{10})$	\(q+(-1.33521 + 2.49344i) q^{2} -9.30691 q^{3} +(-4.43445 - 6.65850i) q^{4} -5.90673i q^{5} +(12.4266 - 23.2062i) q^{6} +(22.5235 - 2.16656i) q^{8} +59.6185 q^{9} +(14.7281 + 7.88670i) q^{10} +0.308914i q^{11} +(41.2710 + 61.9700i) q^{12} -43.7232i q^{13} +54.9734i q^{15} +(-24.6712 + 59.0536i) q^{16} -31.2679i q^{17} +(-79.6029 + 148.655i) q^{18} -79.4629 q^{19} +(-39.3300 + 26.1931i) q^{20} +(-0.770257 - 0.412464i) q^{22} -19.0596i q^{23} +(-209.624 + 20.1640i) q^{24} +90.1105 q^{25} +(109.021 + 58.3795i) q^{26} -303.577 q^{27} -40.1025 q^{29} +(-137.073 - 73.4008i) q^{30} -85.7007 q^{31} +(-114.305 - 140.365i) q^{32} -2.87503i q^{33} +(77.9645 + 41.7490i) q^{34} +(-264.375 - 396.970i) q^{36} -144.912 q^{37} +(106.099 - 198.136i) q^{38} +406.928i q^{39} +(-12.7973 - 133.040i) q^{40} +254.872i q^{41} +366.848i q^{43} +(2.05690 - 1.36986i) q^{44} -352.150i q^{45} +(47.5238 + 25.4484i) q^{46} +10.2478 q^{47} +(229.613 - 549.606i) q^{48} +(-120.316 + 224.685i) q^{50} +291.007i q^{51} +(-291.131 + 193.889i) q^{52} -630.491 q^{53} +(405.338 - 756.951i) q^{54} +1.82467 q^{55} +739.554 q^{57} +(53.5451 - 99.9930i) q^{58} +515.250 q^{59} +(366.040 - 243.777i) q^{60} +772.591i q^{61} +(114.428 - 213.689i) q^{62} +(502.612 - 97.5970i) q^{64} -258.261 q^{65} +(7.16871 + 3.83876i) q^{66} -519.982i q^{67} +(-208.197 + 138.656i) q^{68} +177.386i q^{69} +261.211i q^{71} +(1342.81 - 129.167i) q^{72} +679.260i q^{73} +(193.488 - 361.330i) q^{74} -838.650 q^{75} +(352.375 + 529.104i) q^{76} +(-1014.65 - 543.332i) q^{78} +345.908i q^{79} +(348.814 + 145.726i) q^{80} +1215.67 q^{81} +(-635.507 - 340.306i) q^{82} -805.619 q^{83} -184.691 q^{85} +(-914.712 - 489.817i) q^{86} +373.230 q^{87} +(0.669282 + 6.95781i) q^{88} +47.0003i q^{89} +(878.065 + 470.193i) q^{90} +(-126.908 + 84.5187i) q^{92} +797.609 q^{93} +(-13.6829 + 25.5521i) q^{94} +469.366i q^{95} +(1063.83 + 1306.36i) q^{96} +763.587i q^{97} +18.4170i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 8 q^{4} + 72 q^{8} + 112 q^{9}+O(q^{10}) $ 20 * q - 8 * q^4 + 72 * q^8 + 112 * q^9	$ 20 q - 8 q^{4} + 72 q^{8} + 112 q^{9} + 208 q^{16} - 136 q^{18} - 184 q^{22} + 72 q^{25} - 352 q^{29} - 1288 q^{30} + 80 q^{32} + 208 q^{36} - 516 q^{37} + 2496 q^{44} - 464 q^{46} - 864 q^{50} - 1140 q^{53} + 1452 q^{57} - 4488 q^{58} + 1472 q^{60} + 2560 q^{64} + 248 q^{65} + 9344 q^{72} - 1664 q^{74} - 4056 q^{78} + 2524 q^{81} - 2980 q^{85} - 11392 q^{86} + 2792 q^{88} + 3312 q^{92} + 612 q^{93}+O(q^{100}) $ 20 * q - 8 * q^4 + 72 * q^8 + 112 * q^9 + 208 * q^16 - 136 * q^18 - 184 * q^22 + 72 * q^25 - 352 * q^29 - 1288 * q^30 + 80 * q^32 + 208 * q^36 - 516 * q^37 + 2496 * q^44 - 464 * q^46 - 864 * q^50 - 1140 * q^53 + 1452 * q^57 - 4488 * q^58 + 1472 * q^60 + 2560 * q^64 + 248 * q^65 + 9344 * q^72 - 1664 * q^74 - 4056 * q^78 + 2524 * q^81 - 2980 * q^85 - 11392 * q^86 + 2792 * q^88 + 3312 * q^92 + 612 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.33521	+	2.49344i	−0.472066	+	0.881563i
$2$	−1.33521	+	2.49344i	−0.472066	+	0.881563i
$3$	−9.30691			−1.79111			−0.895557	−	0.444946i	$-0.853223\pi$
$3$	−9.30691			−1.79111			−0.895557	+	0.444946i	$0.853223\pi$
$4$	−4.43445	−	6.65850i	−0.554307	−	0.832313i
$5$		−	5.90673i		−	0.528314i	−0.964480	−	0.264157i	$-0.914906\pi$
$5$		−	5.90673i		−	0.528314i	0.964480	−	0.264157i	$-0.0850937\pi$
$6$	12.4266	−	23.2062i	0.845525	−	1.57898i
$7$		0			0
$7$		0			0
$8$	22.5235	−	2.16656i	0.995405	−	0.0957495i
$9$	59.6185			2.20809
$10$	14.7281	+	7.88670i	0.465742	+	0.249399i
$11$			0.308914i			0.00846737i	0.999991	+	0.00423368i	$0.00134763\pi$
$11$			0.308914i			0.00846737i	−0.999991	+	0.00423368i	$0.998652\pi$
$12$	41.2710	+	61.9700i	0.992827	+	1.49077i
$13$		−	43.7232i		−	0.932818i	−0.884569	−	0.466409i	$-0.845547\pi$
$13$		−	43.7232i		−	0.932818i	0.884569	−	0.466409i	$-0.154453\pi$
$14$		0			0
$15$			54.9734i			0.946271i
$16$	−24.6712	+	59.0536i	−0.385488	+	0.922713i
$17$		−	31.2679i		−	0.446093i	−0.974808	−	0.223046i	$-0.928400\pi$
$17$		−	31.2679i		−	0.446093i	0.974808	−	0.223046i	$-0.0716001\pi$
$18$	−79.6029	+	148.655i	−1.04237	+	1.94657i
$19$	−79.4629			−0.959476			−0.479738	−	0.877412i	$-0.659268\pi$
$19$	−79.4629			−0.959476			−0.479738	+	0.877412i	$0.659268\pi$
$20$	−39.3300	+	26.1931i	−0.439722	+	0.292848i
$21$		0			0
$22$	−0.770257	−	0.412464i	−0.00746452	−	0.00399716i
$23$		−	19.0596i		−	0.172791i	−0.996261	−	0.0863955i	$-0.972465\pi$
$23$		−	19.0596i		−	0.172791i	0.996261	−	0.0863955i	$-0.0275349\pi$
$24$	−209.624	+	20.1640i	−1.78289	+	0.171498i
$25$	90.1105			0.720884
$26$	109.021	+	58.3795i	0.822338	+	0.440352i
$27$	−303.577			−2.16383
$28$		0			0
$29$	−40.1025			−0.256788			−0.128394	−	0.991723i	$-0.540982\pi$
$29$	−40.1025			−0.256788			−0.128394	+	0.991723i	$0.540982\pi$
$30$	−137.073	−	73.4008i	−0.834198	−	0.446703i
$31$	−85.7007			−0.496526			−0.248263	−	0.968693i	$-0.579860\pi$
$31$	−85.7007			−0.496526			−0.248263	+	0.968693i	$0.579860\pi$
$32$	−114.305	−	140.365i	−0.631453	−	0.775414i
$33$		−	2.87503i		−	0.0151660i
$34$	77.9645	+	41.7490i	0.393259	+	0.210585i
$35$		0			0
$36$	−264.375	−	396.970i	−1.22396	−	1.83782i
$37$	−144.912			−0.643876			−0.321938	−	0.946761i	$-0.604334\pi$
$37$	−144.912			−0.643876			−0.321938	+	0.946761i	$0.604334\pi$
$38$	106.099	−	198.136i	0.452936	−	0.845838i
$39$			406.928i			1.67078i
$40$	−12.7973	−	133.040i	−0.0505858	−	0.525887i
$41$			254.872i			0.970837i	0.874282	+	0.485418i	$0.161333\pi$
$41$			254.872i			0.970837i	−0.874282	+	0.485418i	$0.838667\pi$
$42$		0			0
$43$			366.848i			1.30102i	0.759499	+	0.650509i	$0.225444\pi$
$43$			366.848i			1.30102i	−0.759499	+	0.650509i	$0.774556\pi$
$44$	2.05690	−	1.36986i	0.00704750	−	0.00469352i
$45$		−	352.150i		−	1.16657i
$46$	47.5238	+	25.4484i	0.152326	+	0.0815688i
$47$	10.2478			0.0318040			0.0159020	−	0.999874i	$-0.494938\pi$
$47$	10.2478			0.0318040			0.0159020	+	0.999874i	$0.494938\pi$
$48$	229.613	−	549.606i	0.690454	−	1.65268i
$49$		0			0
$50$	−120.316	+	224.685i	−0.340305	+	0.635505i
$51$			291.007i			0.799003i
$52$	−291.131	+	193.889i	−0.776396	+	0.517067i
$53$	−630.491			−1.63405			−0.817024	−	0.576604i	$-0.804378\pi$
$53$	−630.491			−1.63405			−0.817024	+	0.576604i	$0.804378\pi$
$54$	405.338	−	756.951i	1.02147	−	1.90755i
$55$	1.82467			0.00447343
$56$		0			0
$57$	739.554			1.71853
$58$	53.5451	−	99.9930i	0.121221	−	0.226375i
$59$	515.250			1.13695			0.568473	−	0.822702i	$-0.307534\pi$
$59$	515.250			1.13695			0.568473	+	0.822702i	$0.307534\pi$
$60$	366.040	−	243.777i	0.787593	−	0.524524i
$61$			772.591i			1.62164i	0.585295	+	0.810820i	$0.300979\pi$
$61$			772.591i			1.62164i	−0.585295	+	0.810820i	$0.699021\pi$
$62$	114.428	−	213.689i	0.234393	−	0.437719i
$63$		0			0
$64$	502.612	−	97.5970i	0.981664	−	0.190619i
$65$	−258.261			−0.492821
$66$	7.16871	+	3.83876i	0.0133698	+	0.00715937i
$67$		−	519.982i		−	0.948148i	−0.880485	−	0.474074i	$-0.842783\pi$
$67$		−	519.982i		−	0.948148i	0.880485	−	0.474074i	$-0.157217\pi$
$68$	−208.197	+	138.656i	−0.371289	+	0.247272i
$69$			177.386i			0.309489i
$70$		0			0
$71$			261.211i			0.436621i	0.975879	+	0.218310i	$0.0700545\pi$
$71$			261.211i			0.436621i	−0.975879	+	0.218310i	$0.929945\pi$
$72$	1342.81	−	129.167i	2.19795	−	0.211424i
$73$			679.260i			1.08906i	0.838741	+	0.544530i	$0.183292\pi$
$73$			679.260i			1.08906i	−0.838741	+	0.544530i	$0.816708\pi$
$74$	193.488	−	361.330i	0.303952	−	0.567618i
$75$	−838.650			−1.29119
$76$	352.375	+	529.104i	0.531844	+	0.798584i
$77$		0			0
$78$	−1014.65	−	543.332i	−1.47290	−	0.788721i
$79$			345.908i			0.492629i	0.969190	+	0.246314i	$0.0792196\pi$
$79$			345.908i			0.492629i	−0.969190	+	0.246314i	$0.920780\pi$
$80$	348.814	+	145.726i	0.487482	+	0.203659i
$81$	1215.67			1.66758
$82$	−635.507	−	340.306i	−0.855854	−	0.458299i
$83$	−805.619			−1.06540			−0.532700	−	0.846304i	$-0.678823\pi$
$83$	−805.619			−1.06540			−0.532700	+	0.846304i	$0.678823\pi$
$84$		0			0
$85$	−184.691			−0.235677
$86$	−914.712	−	489.817i	−1.14693	−	0.614167i
$87$	373.230			0.459936
$88$	0.669282	+	6.95781i	0.000810747	+	0.00842847i
$89$			47.0003i			0.0559778i	0.999608	+	0.0279889i	$0.00891030\pi$
$89$			47.0003i			0.0559778i	−0.999608	+	0.0279889i	$0.991090\pi$
$90$	878.065	+	470.193i	1.02840	+	0.550697i
$91$		0			0
$92$	−126.908	+	84.5187i	−0.143816	+	0.0957792i
$93$	797.609			0.889335
$94$	−13.6829	+	25.5521i	−0.0150136	+	0.0280372i
$95$			469.366i			0.506905i
$96$	1063.83	+	1306.36i	1.13101	+	1.38886i
$97$			763.587i			0.799283i	0.916671	+	0.399642i	$0.130865\pi$
$97$			763.587i			0.799283i	−0.916671	+	0.399642i	$0.869135\pi$
$98$		0			0
$99$			18.4170i			0.0186967i
$100$	−399.591	−	600.001i	−0.399591	−	0.600001i
$101$			773.385i			0.761928i	0.924590	+	0.380964i	$0.124408\pi$
$101$			773.385i			0.761928i	−0.924590	+	0.380964i	$0.875592\pi$
$102$	−725.608	−	388.554i	−0.704372	−	0.377183i
$103$	285.696			0.273306			0.136653	−	0.990619i	$-0.456366\pi$
$103$	285.696			0.273306			0.136653	+	0.990619i	$0.456366\pi$
$104$	−94.7292	−	984.798i	−0.0893169	−	0.928532i
$105$		0			0
$106$	841.834	−	1572.09i	0.771379	−	1.44052i
$107$		−	2120.28i		−	1.91565i	−0.287346	−	0.957827i	$-0.592773\pi$
$107$		−	2120.28i		−	1.91565i	0.287346	−	0.957827i	$-0.407227\pi$
$108$	1346.20	+	2021.37i	1.19943	+	1.80098i
$109$	841.498			0.739458			0.369729	−	0.929140i	$-0.379451\pi$
$109$	841.498			0.739458			0.369729	+	0.929140i	$0.379451\pi$
$110$	−2.43631	+	4.54970i	−0.00211176	+	0.00394361i
$111$	1348.68			1.15326
$112$		0			0
$113$	−777.276			−0.647079			−0.323540	−	0.946215i	$-0.604873\pi$
$113$	−777.276			−0.647079			−0.323540	+	0.946215i	$0.604873\pi$
$114$	−987.456	+	1844.03i	−0.811261	+	1.51499i
$115$	−112.580			−0.0912879
$116$	177.833	+	267.022i	0.142339	+	0.213728i
$117$		−	2606.71i		−	2.05975i
$118$	−687.964	+	1284.74i	−0.536714	+	1.00229i
$119$		0			0
$120$	119.103	+	1238.19i	0.0906050	+	0.941924i
$121$	1330.90			0.999928
$122$	−1926.41	−	1031.57i	−1.42958	−	0.765522i
$123$		−	2372.07i		−	1.73888i
$124$	380.036	+	570.638i	0.275228	+	0.413265i
$125$		−	1270.60i		−	0.909167i
$126$		0			0
$127$		−	430.270i		−	0.300633i	−0.988638	−	0.150316i	$-0.951971\pi$
$127$		−	430.270i		−	0.300633i	0.988638	−	0.150316i	$-0.0480292\pi$
$128$	−427.738	+	1383.54i	−0.295368	+	0.955384i
$129$		−	3414.22i		−	2.33027i
$130$	344.832	−	643.958i	0.232644	−	0.434453i
$131$	−1639.28			−1.09332			−0.546659	−	0.837355i	$-0.684101\pi$
$131$	−1639.28			−1.09332			−0.546659	+	0.837355i	$0.684101\pi$
$132$	−19.1434	+	12.7492i	−0.0126229	+	0.00840663i
$133$		0			0
$134$	1296.54	+	694.283i	0.835852	+	0.447589i
$135$			1793.15i			1.14318i
$136$	−67.7439	−	704.261i	−0.0427132	−	0.444043i
$137$	−1793.26			−1.11831			−0.559155	−	0.829063i	$-0.688874\pi$
$137$	−1793.26			−1.11831			−0.559155	+	0.829063i	$0.688874\pi$
$138$	−442.300	−	236.846i	−0.272834	−	0.146099i
$139$	678.322			0.413918			0.206959	−	0.978350i	$-0.433643\pi$
$139$	678.322			0.413918			0.206959	+	0.978350i	$0.433643\pi$
$140$		0			0
$141$	−95.3749			−0.0569646
$142$	−651.314	−	348.771i	−0.384909	−	0.206114i
$143$	13.5067			0.00789852
$144$	−1470.86	+	3520.69i	−0.851194	+	2.03743i
$145$			236.875i			0.135665i
$146$	−1693.69	−	906.952i	−0.960075	−	0.514109i
$147$		0			0
$148$	642.607	+	964.898i	0.356905	+	0.535906i
$149$	−1411.04			−0.775821			−0.387910	−	0.921697i	$-0.626803\pi$
$149$	−1411.04			−0.775821			−0.387910	+	0.921697i	$0.626803\pi$
$150$	1119.77	−	2091.12i	0.609526	−	1.13826i
$151$			2423.96i			1.30635i	0.757207	+	0.653176i	$0.226564\pi$
$151$			2423.96i			1.30635i	−0.757207	+	0.653176i	$0.773436\pi$
$152$	−1789.78	+	172.161i	−0.955067	+	0.0918693i
$153$		−	1864.14i		−	0.985014i
$154$		0			0
$155$			506.211i			0.262322i
$156$	2709.53	−	1804.50i	1.39061	−	0.926127i
$157$			3060.41i			1.55572i	0.628439	+	0.777859i	$0.283694\pi$
$157$			3060.41i			1.55572i	−0.628439	+	0.777859i	$0.716306\pi$
$158$	−862.499	−	461.858i	−0.434283	−	0.232553i
$159$	5867.92			2.92677
$160$	−829.098	+	675.171i	−0.409662	+	0.333606i
$161$		0			0
$162$	−1623.16	+	3031.18i	−0.787208	+	1.47008i
$163$		−	908.272i		−	0.436450i	−0.975898	−	0.218225i	$-0.929973\pi$
$163$		−	908.272i		−	0.436450i	0.975898	−	0.218225i	$-0.0700267\pi$
$164$	1697.06	−	1130.22i	0.808040	−	0.538141i
$165$	−16.9820			−0.00801243
$166$	1075.67	−	2008.76i	0.502939	−	0.939217i
$167$	−1203.87			−0.557832			−0.278916	−	0.960315i	$-0.589975\pi$
$167$	−1203.87			−0.557832			−0.278916	+	0.960315i	$0.589975\pi$
$168$		0			0
$169$	285.280			0.129850
$170$	246.600	−	460.515i	0.111255	−	0.207764i
$171$	−4737.46			−2.11861
$172$	2442.66	−	1626.77i	1.08285	−	0.721163i
$173$			1207.30i			0.530572i	0.964170	+	0.265286i	$0.0854664\pi$
$173$			1207.30i			0.530572i	−0.964170	+	0.265286i	$0.914534\pi$
$174$	−498.339	+	930.626i	−0.217121	+	0.405463i
$175$		0			0
$176$	−18.2425	−	7.62129i	−0.00781295	−	0.00326407i
$177$	−4795.38			−2.03640
$178$	−117.192	−	62.7550i	−0.0493479	−	0.0264252i
$179$			1526.68i			0.637484i	0.947841	+	0.318742i	$0.103260\pi$
$179$			1526.68i			0.637484i	−0.947841	+	0.318742i	$0.896740\pi$
$180$	−2344.79	+	1561.59i	−0.970948	+	0.646635i
$181$			987.406i			0.405488i	0.979232	+	0.202744i	$0.0649859\pi$
$181$			987.406i			0.405488i	−0.979232	+	0.202744i	$0.935014\pi$
$182$		0			0
$183$		−	7190.43i		−	2.90454i
$184$	−41.2938	−	429.287i	−0.0165447	−	0.171997i
$185$			855.958i			0.340169i
$186$	−1064.97	+	1988.79i	−0.419825	+	0.784005i
$187$	9.65909			0.00377723
$188$	−45.4432	−	68.2347i	−0.0176292	−	0.0264709i
$189$		0			0
$190$	−1170.33	−	626.700i	−0.446868	−	0.239293i
$191$			3924.48i			1.48673i	0.668885	+	0.743366i	$0.266772\pi$
$191$			3924.48i			1.48673i	−0.668885	+	0.743366i	$0.733228\pi$
$192$	−4677.76	+	908.326i	−1.75827	+	0.341421i
$193$	−3715.61			−1.38578			−0.692890	−	0.721043i	$-0.743663\pi$
$193$	−3715.61			−1.38578			−0.692890	+	0.721043i	$0.743663\pi$
$194$	−1903.95	−	1019.54i	−0.704619	−	0.377315i
$195$	2403.61			0.882699
$196$		0			0
$197$	−4711.80			−1.70407			−0.852035	−	0.523485i	$-0.824632\pi$
$197$	−4711.80			−1.70407			−0.852035	+	0.523485i	$0.824632\pi$
$198$	−45.9216	−	24.5905i	−0.0164823	−	0.00882610i
$199$	−9.20740			−0.00327988			−0.00163994	−	0.999999i	$-0.500522\pi$
$199$	−9.20740			−0.00327988			−0.00163994	+	0.999999i	$0.500522\pi$
$200$	2029.60	−	195.230i	0.717572	−	0.0690243i
$201$			4839.43i			1.69824i
$202$	−1928.39	−	1032.63i	−0.671687	−	0.359680i
$203$		0			0
$204$	1937.67	−	1290.46i	0.665020	−	0.442893i
$205$	1505.46			0.512907
$206$	−381.463	+	712.366i	−0.129018	+	0.240936i
$207$		−	1136.30i		−	0.381538i
$208$	2582.01	+	1078.71i	0.860723	+	0.359590i
$209$		−	24.5472i		−	0.00812424i
$210$		0			0
$211$			682.060i			0.222535i	0.993790	+	0.111268i	$0.0354911\pi$
$211$			682.060i			0.222535i	−0.993790	+	0.111268i	$0.964509\pi$
$212$	2795.88	+	4198.12i	0.905764	+	1.36004i
$213$		−	2431.07i		−	0.782038i
$214$	5286.78	+	2831.01i	1.68877	+	0.904316i
$215$	2166.87			0.687346
$216$	−6837.61	+	657.719i	−2.15389	+	0.207186i
$217$		0			0
$218$	−1123.57	+	2098.22i	−0.349073	+	0.651879i
$219$		−	6321.81i		−	1.95063i
$220$	−8.09142	−	12.1496i	−0.00247965	−	0.00372329i
$221$	−1367.13			−0.416123
$222$	−1800.77	+	3362.86i	−0.544414	+	1.01667i
$223$	3872.62			1.16292			0.581458	−	0.813577i	$-0.302483\pi$
$223$	3872.62			1.16292			0.581458	+	0.813577i	$0.302483\pi$
$224$		0			0
$225$	5372.25			1.59178
$226$	1037.82	−	1938.09i	0.305464	−	0.570441i
$227$	3287.11			0.961115			0.480558	−	0.876963i	$-0.340434\pi$
$227$	3287.11			0.961115			0.480558	+	0.876963i	$0.340434\pi$
$228$	−3279.52	−	4924.32i	−0.952593	−	1.43036i
$229$		−	2818.66i		−	0.813374i	−0.913568	−	0.406687i	$-0.866684\pi$
$229$		−	2818.66i		−	0.813374i	0.913568	−	0.406687i	$-0.133316\pi$
$230$	150.317	−	280.710i	0.0430940	−	0.0804761i
$231$		0			0
$232$	−903.247	+	86.8846i	−0.255608	+	0.0245873i
$233$	5803.62			1.63179			0.815896	−	0.578199i	$-0.196244\pi$
$233$	5803.62			1.63179			0.815896	+	0.578199i	$0.196244\pi$
$234$	6499.67	+	3480.50i	1.81580	+	0.972338i
$235$		−	60.5307i		−	0.0168025i
$236$	−2284.85	−	3430.79i	−0.630217	−	0.946294i
$237$		−	3219.33i		−	0.882355i
$238$		0			0
$239$			5958.79i			1.61273i	0.591419	+	0.806364i	$0.298568\pi$
$239$			5958.79i			1.61273i	−0.591419	+	0.806364i	$0.701432\pi$
$240$	−3246.38	−	1356.26i	−0.873137	−	0.364776i
$241$			2117.71i			0.566031i	0.959115	+	0.283016i	$0.0913348\pi$
$241$			2117.71i			0.566031i	−0.959115	+	0.283016i	$0.908665\pi$
$242$	−1777.03	+	3318.53i	−0.472033	+	0.881500i
$243$	−3117.50			−0.822993
$244$	5144.29	−	3426.02i	1.34971	−	0.898886i
$245$		0			0
$246$	5914.60	+	3167.20i	1.53293	+	0.820867i
$247$			3474.37i			0.895017i
$248$	−1930.28	+	185.676i	−0.494245	+	0.0475421i
$249$	7497.82			1.90825
$250$	3168.16	+	1696.51i	0.801488	+	0.429187i
$251$	−1950.88			−0.490591			−0.245296	−	0.969448i	$-0.578885\pi$
$251$	−1950.88			−0.490591			−0.245296	+	0.969448i	$0.578885\pi$
$252$		0			0
$253$	5.88776			0.00146309
$254$	1072.85	+	574.499i	0.265027	+	0.141919i
$255$	1718.90			0.422125
$256$	−2878.66	−	2913.85i	−0.702798	−	0.711390i
$257$		−	6873.33i		−	1.66828i	−0.551556	−	0.834138i	$-0.685966\pi$
$257$		−	6873.33i		−	1.66828i	0.551556	−	0.834138i	$-0.314034\pi$
$258$	8513.13	+	4558.68i	2.05428	+	1.10004i
$259$		0			0
$260$	1145.25	+	1719.63i	0.273174	+	0.410181i
$261$	−2390.85			−0.567011
$262$	2188.78	−	4087.45i	0.516119	−	0.963829i
$263$		−	2240.35i		−	0.525270i	−0.964895	−	0.262635i	$-0.915408\pi$
$263$		−	2240.35i		−	0.525270i	0.964895	−	0.262635i	$-0.0845915\pi$
$264$	−6.22894	−	64.7557i	−0.00145214	−	0.0150963i
$265$			3724.14i			0.863290i
$266$		0			0
$267$		−	437.427i		−	0.100263i
$268$	−3462.30	+	2305.84i	−0.789156	+	0.525565i
$269$			282.383i			0.0640045i	0.999488	+	0.0320023i	$0.0101884\pi$
$269$			282.383i			0.0640045i	−0.999488	+	0.0320023i	$0.989812\pi$
$270$	−4471.10	−	2394.22i	−1.00779	−	0.539658i
$271$	−4208.99			−0.943461			−0.471730	−	0.881743i	$-0.656370\pi$
$271$	−4208.99			−0.943461			−0.471730	+	0.881743i	$0.656370\pi$
$272$	1846.48	+	771.418i	0.411615	+	0.171963i
$273$		0			0
$274$	2394.37	−	4471.38i	0.527917	−	0.985861i
$275$			27.8364i			0.00610399i
$276$	1181.12	−	786.608i	0.257591	−	0.171552i
$277$	2635.10			0.571581			0.285790	−	0.958292i	$-0.407744\pi$
$277$	2635.10			0.571581			0.285790	+	0.958292i	$0.407744\pi$
$278$	−905.699	+	1691.35i	−0.195397	+	0.364894i
$279$	−5109.35			−1.09638
$280$		0			0
$281$	−2512.44			−0.533380			−0.266690	−	0.963782i	$-0.585930\pi$
$281$	−2512.44			−0.533380			−0.266690	+	0.963782i	$0.585930\pi$
$282$	127.345	−	237.811i	0.0268911	−	0.0502179i
$283$	−2327.75			−0.488942			−0.244471	−	0.969657i	$-0.578614\pi$
$283$	−2327.75			−0.488942			−0.244471	+	0.969657i	$0.578614\pi$
$284$	1739.28	−	1158.33i	0.363405	−	0.242022i
$285$		−	4368.35i		−	0.907924i
$286$	−18.0342	+	33.6781i	−0.00372862	+	0.00696304i
$287$		0			0
$288$	−6814.71	−	8368.34i	−1.39431	−	1.71219i
$289$	3935.32			0.801001
$290$	−590.632	−	316.276i	−0.119597	−	0.0640427i
$291$		−	7106.63i		−	1.43161i
$292$	4522.85	−	3012.15i	0.906438	−	0.603673i
$293$		−	5654.92i		−	1.12752i	−0.825938	−	0.563761i	$-0.809354\pi$
$293$		−	5654.92i		−	1.12752i	0.825938	−	0.563761i	$-0.190646\pi$
$294$		0			0
$295$		−	3043.44i		−	0.600665i
$296$	−3263.92	+	313.962i	−0.640918	+	0.0616509i
$297$		−	93.7792i		−	0.0183220i
$298$	1884.03	−	3518.35i	0.366239	−	0.683935i
$299$	−833.345			−0.161183
$300$	3718.95	+	5584.15i	0.715713	+	1.07467i
$301$		0			0
$302$	−6043.99	−	3236.48i	−1.15163	−	0.616684i
$303$		−	7197.82i		−	1.36470i
$304$	1960.45	−	4692.57i	0.369867	−	0.885321i
$305$	4563.48			0.856736
$306$	4648.13	+	2489.02i	0.868352	+	0.464992i
$307$	3797.48			0.705972			0.352986	−	0.935629i	$-0.385166\pi$
$307$	3797.48			0.705972			0.352986	+	0.935629i	$0.385166\pi$
$308$		0			0
$309$	−2658.95			−0.489522
$310$	−1262.21	−	675.896i	−0.231253	−	0.123833i
$311$	5743.64			1.04724			0.523621	−	0.851951i	$-0.324581\pi$
$311$	5743.64			1.04724			0.523621	+	0.851951i	$0.324581\pi$
$312$	881.635	+	9165.42i	0.159977	+	1.66311i
$313$			6247.53i			1.12822i	0.825701	+	0.564108i	$0.190780\pi$
$313$			6247.53i			1.12822i	−0.825701	+	0.564108i	$0.809220\pi$
$314$	−7630.95	−	4086.28i	−1.37146	−	0.734402i
$315$		0			0
$316$	2303.23	−	1533.91i	0.410021	−	0.273067i
$317$	−4625.80			−0.819593			−0.409796	−	0.912177i	$-0.634400\pi$
$317$	−4625.80			−0.819593			−0.409796	+	0.912177i	$0.634400\pi$
$318$	−7834.87	+	14631.3i	−1.38163	+	2.58013i
$319$		−	12.3882i		−	0.00217432i
$320$	−576.479	−	2968.79i	−0.100707	−	0.518627i
$321$			19733.2i			3.43116i
$322$		0			0
$323$			2484.64i			0.428015i
$324$	−5390.81	−	8094.51i	−0.924350	−	1.38795i
$325$		−	3939.92i		−	0.672454i
$326$	2264.72	+	1212.73i	0.384758	+	0.206033i
$327$	−7831.74			−1.32445
$328$	552.196	+	5740.60i	0.0929572	+	0.966376i
$329$		0			0
$330$	22.6745	−	42.3437i	0.00378240	−	0.00706346i
$331$			6535.46i			1.08526i	0.839972	+	0.542630i	$0.182571\pi$
$331$			6535.46i			1.08526i	−0.839972	+	0.542630i	$0.817429\pi$
$332$	3572.48	+	5364.21i	0.590558	+	0.886746i
$333$	−8639.45			−1.42174
$334$	1607.41	−	3001.77i	0.263334	−	0.491764i
$335$	−3071.40			−0.500920
$336$		0			0
$337$	4777.67			0.772274			0.386137	−	0.922441i	$-0.373809\pi$
$337$	4777.67			0.772274			0.386137	+	0.922441i	$0.373809\pi$
$338$	−380.908	+	711.329i	−0.0612978	+	0.114471i
$339$	7234.03			1.15899
$340$	819.004	+	1229.77i	0.130637	+	0.196157i
$341$		−	26.4742i		−	0.00420427i
$342$	6325.48	−	11812.6i	1.00013	−	1.86769i
$343$		0			0
$344$	794.799	+	8262.68i	0.124572	+	1.29504i
$345$	1047.77			0.163507
$346$	−3010.32	−	1611.99i	−0.467733	−	0.250465i
$347$			9200.48i			1.42337i	0.702501	+	0.711683i	$0.252067\pi$
$347$			9200.48i			1.42337i	−0.702501	+	0.711683i	$0.747933\pi$
$348$	−1655.07	−	2485.15i	−0.254946	−	0.382811i
$349$		−	6940.92i		−	1.06458i	−0.846562	−	0.532290i	$-0.821331\pi$
$349$		−	6940.92i		−	1.06458i	0.846562	−	0.532290i	$-0.178669\pi$
$350$		0			0
$351$			13273.4i			2.01846i
$352$	43.3607	−	35.3105i	0.00656572	−	0.00534675i
$353$			1575.95i			0.237619i	0.992917	+	0.118809i	$0.0379077\pi$
$353$			1575.95i			0.237619i	−0.992917	+	0.118809i	$0.962092\pi$
$354$	6402.82	−	11957.0i	0.961316	−	1.79522i
$355$	1542.90			0.230673
$356$	312.951	−	208.421i	0.0465910	−	0.0310288i
$357$		0			0
$358$	−3806.69	−	2038.44i	−0.561983	−	0.300935i
$359$		−	7564.00i		−	1.11201i	−0.831178	−	0.556006i	$-0.812333\pi$
$359$		−	7564.00i		−	1.11201i	0.831178	−	0.556006i	$-0.187667\pi$
$360$	−762.956	−	7931.64i	−0.111698	−	1.16121i
$361$	−544.647			−0.0794062
$362$	−2462.03	−	1318.39i	−0.357463	−	0.191417i
$363$	−12386.6			−1.79099
$364$		0			0
$365$	4012.21			0.575366
$366$	17928.9	+	9600.70i	2.56054	+	1.37114i
$367$	−11820.3			−1.68124			−0.840618	−	0.541628i	$-0.817808\pi$
$367$	−11820.3			−1.68124			−0.840618	+	0.541628i	$0.817808\pi$
$368$	1125.54	+	470.223i	0.159436	+	0.0666089i
$369$			15195.1i			2.14370i
$370$	−2134.28	−	1142.88i	−0.299880	−	0.160582i
$371$		0			0
$372$	−3536.96	−	5310.88i	−0.492964	−	0.740205i
$373$	3451.18			0.479076			0.239538	−	0.970887i	$-0.423004\pi$
$373$	3451.18			0.479076			0.239538	+	0.970887i	$0.423004\pi$
$374$	−12.8969	+	24.0843i	−0.00178310	+	0.00332987i
$375$			11825.4i			1.62842i
$376$	230.815	−	22.2024i	0.0316579	−	0.00304522i
$377$			1753.41i			0.239536i
$378$		0			0
$379$		−	363.409i		−	0.0492535i	−0.999697	−	0.0246267i	$-0.992160\pi$
$379$		−	363.409i		−	0.0492535i	0.999697	−	0.0246267i	$-0.00783973\pi$
$380$	3125.27	−	2081.38i	0.421903	−	0.280981i
$381$			4004.49i			0.538467i
$382$	−9785.45	−	5239.99i	−1.31065	−	0.701836i
$383$	1510.57			0.201532			0.100766	−	0.994910i	$-0.467871\pi$
$383$	1510.57			0.201532			0.100766	+	0.994910i	$0.467871\pi$
$384$	3980.92	−	12876.5i	0.529038	−	1.71120i
$385$		0			0
$386$	4961.11	−	9264.64i	0.654180	−	1.22165i
$387$			21870.9i			2.87277i
$388$	5084.34	−	3386.09i	0.665253	−	0.443048i
$389$	−1911.58			−0.249154			−0.124577	−	0.992210i	$-0.539757\pi$
$389$	−1911.58			−0.249154			−0.124577	+	0.992210i	$0.539757\pi$
$390$	−3209.32	+	5993.26i	−0.416693	+	0.778155i
$391$	−595.952			−0.0770808
$392$		0			0
$393$	15256.6			1.95826
$394$	6291.22	−	11748.6i	0.804434	−	1.50225i
$395$	2043.18			0.260263
$396$	122.629	−	81.6693i	0.0155615	−	0.0103637i
$397$			10793.1i			1.36446i	0.731137	+	0.682230i	$0.238990\pi$
$397$			10793.1i			1.36446i	−0.731137	+	0.682230i	$0.761010\pi$
$398$	12.2938	−	22.9581i	0.00154832	−	0.00289142i
$399$		0			0
$400$	−2223.14	+	5321.35i	−0.277892	+	0.665169i
$401$	−8992.60			−1.11987			−0.559936	−	0.828536i	$-0.689174\pi$
$401$	−8992.60			−1.11987			−0.559936	+	0.828536i	$0.689174\pi$
$402$	−12066.8	−	6461.63i	−1.49711	−	0.801683i
$403$			3747.11i			0.463169i
$404$	5149.59	−	3429.54i	0.634162	−	0.422342i
$405$		−	7180.61i		−	0.881005i
$406$		0			0
$407$		−	44.7654i		−	0.00545194i
$408$	630.486	+	6554.49i	0.0765042	+	0.795332i
$409$		−	7176.82i		−	0.867655i	−0.900996	−	0.433828i	$-0.857163\pi$
$409$		−	7176.82i		−	0.867655i	0.900996	−	0.433828i	$-0.142837\pi$
$410$	−2010.10	+	3753.77i	−0.242126	+	0.452160i
$411$	16689.7			2.00302
$412$	−1266.91	−	1902.31i	−0.151495	−	0.227476i
$413$		0			0
$414$	2833.30	+	1517.20i	0.336350	+	0.180111i
$415$			4758.58i			0.562866i
$416$	−6137.20	+	4997.79i	−0.723320	+	0.589031i
$417$	−6313.08			−0.741374
$418$	61.2069	+	32.7756i	0.00716203	+	0.00383518i
$419$	−1863.89			−0.217320			−0.108660	−	0.994079i	$-0.534656\pi$
$419$	−1863.89			−0.217320			−0.108660	+	0.994079i	$0.534656\pi$
$420$		0			0
$421$	−4925.47			−0.570196			−0.285098	−	0.958498i	$-0.592026\pi$
$421$	−4925.47			−0.570196			−0.285098	+	0.958498i	$0.592026\pi$
$422$	−1700.67	−	910.690i	−0.196179	−	0.105051i
$423$	610.956			0.0702262
$424$	−14200.8	+	1366.00i	−1.62654	+	0.156459i
$425$		−	2817.57i		−	0.321581i
$426$	6061.72	+	3245.98i	0.689416	+	0.369174i
$427$		0			0
$428$	−14117.9	+	9402.27i	−1.59442	+	1.06186i
$429$	−125.706			−0.0141472
$430$	−2893.22	+	5402.96i	−0.324473	+	0.605939i
$431$		−	12814.8i		−	1.43217i	−0.698011	−	0.716087i	$-0.745931\pi$
$431$		−	12814.8i		−	1.43217i	0.698011	−	0.716087i	$-0.254069\pi$
$432$	7489.63	−	17927.3i	0.834132	−	1.99660i
$433$		−	12764.8i		−	1.41672i	−0.705854	−	0.708358i	$-0.749436\pi$
$433$		−	12764.8i		−	1.41672i	0.705854	−	0.708358i	$-0.250564\pi$
$434$		0			0
$435$		−	2204.57i		−	0.242991i
$436$	−3731.58	−	5603.11i	−0.409886	−	0.615460i
$437$			1514.53i			0.165789i
$438$	15763.0	+	8440.91i	1.71960	+	0.920827i
$439$	−15250.8			−1.65804			−0.829020	−	0.559218i	$-0.811101\pi$
$439$	−15250.8			−1.65804			−0.829020	+	0.559218i	$0.811101\pi$
$440$	41.0979	−	3.95327i	0.00445288	−	0.000428329i
$441$		0			0
$442$	1825.40	−	3408.86i	0.196438	−	0.366839i
$443$		−	7750.99i		−	0.831288i	−0.909527	−	0.415644i	$-0.863556\pi$
$443$		−	7750.99i		−	0.831288i	0.909527	−	0.415644i	$-0.136444\pi$
$444$	−5980.68	−	8980.22i	−0.639258	−	0.959870i
$445$	277.618			0.0295738
$446$	−5170.75	+	9656.14i	−0.548973	+	1.02518i
$447$	13132.5			1.38958
$448$		0			0
$449$	862.920			0.0906987			0.0453493	−	0.998971i	$-0.485560\pi$
$449$	862.920			0.0906987			0.0453493	+	0.998971i	$0.485560\pi$
$450$	−7173.06	+	13395.4i	−0.751425	+	1.40325i
$451$	−78.7335			−0.00822043
$452$	3446.79	+	5175.49i	0.358680	+	0.538572i
$453$		−	22559.6i		−	2.33982i
$454$	−4388.97	+	8196.20i	−0.453710	+	0.847283i
$455$		0			0
$456$	16657.3	−	1602.29i	1.71064	−	0.164549i
$457$	−5600.12			−0.573222			−0.286611	−	0.958047i	$-0.592529\pi$
$457$	−5600.12			−0.573222			−0.286611	+	0.958047i	$0.592529\pi$
$458$	7028.16	+	3763.49i	0.717040	+	0.383966i
$459$			9492.22i			0.965270i
$460$	499.229	+	749.612i	0.0506015	+	0.0759801i
$461$			13128.5i			1.32637i	0.748458	+	0.663183i	$0.230795\pi$
$461$			13128.5i			1.32637i	−0.748458	+	0.663183i	$0.769205\pi$
$462$		0			0
$463$			3349.52i			0.336210i	0.985769	+	0.168105i	$0.0537648\pi$
$463$			3349.52i			0.336210i	−0.985769	+	0.168105i	$0.946235\pi$
$464$	989.378	−	2368.20i	0.0989887	−	0.236941i
$465$		−	4711.26i		−	0.469848i
$466$	−7749.02	+	14471.0i	−0.770314	+	1.43853i
$467$	2122.09			0.210275			0.105138	−	0.994458i	$-0.466472\pi$
$467$	2122.09			0.210275			0.105138	+	0.994458i	$0.466472\pi$
$468$	−17356.8	+	11559.3i	−1.71435	+	1.14173i
$469$		0			0
$470$	150.930	+	80.8210i	0.0148125	+	0.00793190i
$471$		−	28483.0i		−	2.78647i
$472$	11605.2	−	1116.32i	1.13172	−	0.108862i
$473$	−113.324			−0.0110162
$474$	8027.20	+	4298.47i	0.777851	+	0.416530i
$475$	−7160.44			−0.691671
$476$		0			0
$477$	−37588.9			−3.60813
$478$	−14857.9	−	7956.21i	−1.42172	−	0.761315i
$479$	−7932.72			−0.756692			−0.378346	−	0.925664i	$-0.623507\pi$
$479$	−7932.72			−0.756692			−0.378346	+	0.925664i	$0.623507\pi$
$480$	7716.33	−	6283.75i	0.733752	−	0.597526i
$481$			6336.03i			0.600620i
$482$	−5280.37	−	2827.57i	−0.498992	−	0.267204i
$483$		0			0
$484$	−5901.83	−	8861.83i	−0.554267	−	0.832253i
$485$	4510.30			0.422273
$486$	4162.50	−	7773.28i	0.388508	−	0.725521i
$487$		−	11564.6i		−	1.07607i	−0.842924	−	0.538033i	$-0.819168\pi$
$487$		−	11564.6i		−	1.07607i	0.842924	−	0.538033i	$-0.180832\pi$
$488$	1673.87	+	17401.4i	0.155271	+	1.61419i
$489$			8453.20i			0.781732i
$490$		0			0
$491$		−	17001.3i		−	1.56264i	−0.624129	−	0.781322i	$-0.714546\pi$
$491$		−	17001.3i		−	1.56264i	0.624129	−	0.781322i	$-0.285454\pi$
$492$	−15794.4	+	10518.8i	−1.44729	+	0.963873i
$493$			1253.92i			0.114551i
$494$	−8663.13	−	4639.00i	−0.789014	−	0.422507i
$495$	108.784			0.00987775
$496$	2114.34	−	5060.94i	0.191405	−	0.458151i
$497$		0			0
$498$	−10011.1	+	18695.3i	−0.900822	+	1.68225i
$499$			13108.0i			1.17594i	0.808881	+	0.587972i	$0.200074\pi$
$499$			13108.0i			1.17594i	−0.808881	+	0.587972i	$0.799926\pi$
$500$	−8460.29	+	5634.42i	−0.756711	+	0.503958i
$501$	11204.3			0.999142
$502$	2604.83	−	4864.40i	0.231592	−	0.432487i
$503$	−16393.8			−1.45321			−0.726605	−	0.687055i	$-0.758903\pi$
$503$	−16393.8			−1.45321			−0.726605	+	0.687055i	$0.758903\pi$
$504$		0			0
$505$	4568.18			0.402537
$506$	−7.86137	+	14.6808i	−0.000690673	+	0.00128980i
$507$	−2655.08			−0.232576
$508$	−2864.96	+	1908.01i	−0.250220	+	0.166643i
$509$		−	19891.4i		−	1.73217i	−0.499900	−	0.866083i	$-0.666630\pi$
$509$		−	19891.4i		−	1.73217i	0.499900	−	0.866083i	$-0.333370\pi$
$510$	−2295.09	+	4285.97i	−0.199271	+	0.372130i
$511$		0			0
$512$	11109.1	−	3287.16i	0.958902	−	0.283737i
$513$	24123.1			2.07614
$514$	17138.2	+	9177.31i	1.47069	+	0.787537i
$515$		−	1687.53i		−	0.144391i
$516$	−22733.6	+	15140.2i	−1.93951	+	1.29169i
$517$			3.16567i			0.000269296i
$518$		0			0
$519$		−	11236.2i		−	0.950316i
$520$	−5816.94	+	559.540i	−0.490557	+	0.0471874i
$521$		−	21874.5i		−	1.83942i	−0.392593	−	0.919712i	$-0.628422\pi$
$521$		−	21874.5i		−	1.83942i	0.392593	−	0.919712i	$-0.371578\pi$
$522$	3192.28	−	5961.43i	0.267667	−	0.499856i
$523$	−5241.21			−0.438206			−0.219103	−	0.975702i	$-0.570313\pi$
$523$	−5241.21			−0.438206			−0.219103	+	0.975702i	$0.570313\pi$
$524$	7269.32	+	10915.2i	0.606034	+	0.909983i
$525$		0			0
$526$	5586.18	+	2991.33i	0.463059	+	0.247962i
$527$			2679.68i			0.221497i
$528$	169.781	+	70.9306i	0.0139939	+	0.00584633i
$529$	11803.7			0.970143
$530$	−9285.90	−	4972.49i	−0.761045	−	0.407530i
$531$	30718.4			2.51048
$532$		0			0
$533$	11143.8			0.905614
$534$	1090.70	+	584.055i	0.0883878	+	0.0473306i
$535$	−12523.9			−1.01207
$536$	−1126.57	−	11711.8i	−0.0907847	−	0.943792i
$537$		−	14208.7i		−	1.14181i
$538$	−704.105	−	377.040i	−0.0564240	−	0.0302144i
$539$		0			0
$540$	11939.7	−	7951.64i	0.951485	−	0.633674i
$541$	−7430.35			−0.590491			−0.295246	−	0.955421i	$-0.595402\pi$
$541$	−7430.35			−0.590491			−0.295246	+	0.955421i	$0.595402\pi$
$542$	5619.86	−	10494.8i	0.445376	−	0.831720i
$543$		−	9189.70i		−	0.726275i
$544$	−4388.91	+	3574.08i	−0.345906	+	0.281687i
$545$		−	4970.50i		−	0.390666i
$546$		0			0
$547$			16115.5i			1.25969i	0.776722	+	0.629843i	$0.216881\pi$
$547$			16115.5i			1.25969i	−0.776722	+	0.629843i	$0.783119\pi$
$548$	7952.12	+	11940.4i	0.619887	+	0.930783i
$549$			46060.7i			3.58073i
$550$	−69.4083	−	37.1673i	−0.00538105	−	0.00288149i
$551$	3186.66			0.246382
$552$	384.317	+	3995.33i	0.0296334	+	0.308067i
$553$		0			0
$554$	−3518.40	+	6570.46i	−0.269824	+	0.503884i
$555$		−	7966.32i		−	0.609282i
$556$	−3007.99	−	4516.61i	−0.229437	−	0.344509i
$557$	2425.22			0.184488			0.0922442	−	0.995736i	$-0.470596\pi$
$557$	2425.22			0.184488			0.0922442	+	0.995736i	$0.470596\pi$
$558$	6822.03	−	12739.8i	0.517562	−	0.966524i
$559$	16039.8			1.21361
$560$		0			0
$561$	−89.8962			−0.00676546
$562$	3354.63	−	6264.62i	0.251791	−	0.470208i
$563$	11706.1			0.876292			0.438146	−	0.898904i	$-0.355635\pi$
$563$	11706.1			0.876292			0.438146	+	0.898904i	$0.355635\pi$
$564$	422.935	+	635.054i	0.0315759	+	0.0474124i
$565$			4591.16i			0.341861i
$566$	3108.03	−	5804.11i	0.230813	−	0.431033i
$567$		0			0
$568$	565.931	+	5883.38i	0.0418062	+	0.434615i
$569$	−5646.05			−0.415984			−0.207992	−	0.978131i	$-0.566693\pi$
$569$	−5646.05			−0.415984			−0.207992	+	0.978131i	$0.566693\pi$
$570$	10892.2	+	5832.64i	0.800393	+	0.428601i
$571$		−	4284.63i		−	0.314021i	−0.987597	−	0.157011i	$-0.949814\pi$
$571$		−	4284.63i		−	0.314021i	0.987597	−	0.157011i	$-0.0501857\pi$
$572$	−59.8949	−	89.9344i	−0.00437820	−	0.00657403i
$573$		−	36524.8i		−	2.66291i
$574$		0			0
$575$		−	1717.47i		−	0.124562i
$576$	29965.0	−	5818.59i	2.16760	−	0.420905i
$577$			4363.85i			0.314852i	0.987531	+	0.157426i	$0.0503196\pi$
$577$			4363.85i			0.314852i	−0.987531	+	0.157426i	$0.949680\pi$
$578$	−5254.46	+	9812.47i	−0.378126	+	0.706133i
$579$	34580.9			2.48209
$580$	1577.23	−	1050.41i	0.112915	−	0.0751998i
$581$		0			0
$582$	17719.9	+	9488.81i	1.26205	+	0.675814i
$583$		−	194.767i		−	0.0138361i
$584$	1471.66	+	15299.3i	0.104277	+	1.08406i
$585$	−15397.1			−1.08819
$586$	14100.2	+	7550.48i	0.993982	+	0.532266i
$587$	23904.0			1.68079			0.840395	−	0.541974i	$-0.182323\pi$
$587$	23904.0			1.68079			0.840395	+	0.541974i	$0.182323\pi$
$588$		0			0
$589$	6810.03			0.476405
$590$	7588.63	+	4063.62i	0.529524	+	0.283554i
$591$	43852.3			3.05219
$592$	3575.17	−	8557.59i	0.248207	−	0.594113i
$593$			25855.3i			1.79047i	0.445595	+	0.895235i	$0.352992\pi$
$593$			25855.3i			1.79047i	−0.445595	+	0.895235i	$0.647008\pi$
$594$	233.833	+	125.215i	0.0161520	+	0.00864918i
$595$		0			0
$596$	6257.21	+	9395.44i	0.430043	+	0.645725i
$597$	85.6924			0.00587464
$598$	1112.69	−	2077.89i	0.0760889	−	0.142093i
$599$		−	13196.5i		−	0.900159i	−0.892989	−	0.450079i	$-0.851396\pi$
$599$		−	13196.5i		−	0.900159i	0.892989	−	0.450079i	$-0.148604\pi$
$600$	−18889.3	+	1816.99i	−1.28525	+	0.123630i
$601$			1378.53i			0.0935630i	0.998905	+	0.0467815i	$0.0148964\pi$
$601$			1378.53i			0.0935630i	−0.998905	+	0.0467815i	$0.985104\pi$
$602$		0			0
$603$		−	31000.6i		−	2.09360i
$604$	16139.9	−	10748.9i	1.08729	−	0.724119i
$605$		−	7861.30i		−	0.528276i
$606$	17947.3	+	9610.57i	1.20307	+	0.644229i
$607$	−15406.9			−1.03022			−0.515111	−	0.857123i	$-0.672249\pi$
$607$	−15406.9			−1.03022			−0.515111	+	0.857123i	$0.672249\pi$
$608$	9083.03	+	11153.8i	0.605864	+	0.743991i
$609$		0			0
$610$	−6093.19	+	11378.8i	−0.404436	+	0.755266i
$611$		−	448.065i		−	0.0296674i
$612$	−12412.4	+	8266.46i	−0.819839	+	0.546000i
$613$	−7151.26			−0.471186			−0.235593	−	0.971852i	$-0.575703\pi$
$613$	−7151.26			−0.471186			−0.235593	+	0.971852i	$0.575703\pi$
$614$	−5070.41	+	9468.77i	−0.333266	+	0.622359i
$615$	−14011.2			−0.918675
$616$		0			0
$617$	3499.63			0.228347			0.114173	−	0.993461i	$-0.463578\pi$
$617$	3499.63			0.228347			0.114173	+	0.993461i	$0.463578\pi$
$618$	3550.24	−	6629.92i	0.231087	−	0.431544i
$619$	−14339.3			−0.931094			−0.465547	−	0.885023i	$-0.654142\pi$
$619$	−14339.3			−0.931094			−0.465547	+	0.885023i	$0.654142\pi$
$620$	3370.61	−	2244.77i	0.218334	−	0.145407i
$621$			5786.05i			0.373891i
$622$	−7668.94	+	14321.4i	−0.494368	+	0.923209i
$623$		0			0
$624$	−24030.6	−	10039.4i	−1.54165	−	0.644068i
$625$	3758.72			0.240558
$626$	−15577.8	−	8341.74i	−0.994593	−	0.532592i
$627$			228.458i			0.0145514i
$628$	20377.8	−	13571.3i	1.29484	−	0.862344i
$629$			4531.10i			0.287229i
$630$		0			0
$631$		−	8745.97i		−	0.551778i	−0.961190	−	0.275889i	$-0.911028\pi$
$631$		−	8745.97i		−	0.551778i	0.961190	−	0.275889i	$-0.0889722\pi$
$632$	749.432	+	7791.04i	0.0471690	+	0.490365i
$633$		−	6347.87i		−	0.398586i
$634$	6176.39	−	11534.1i	0.386902	−	0.722523i
$635$	−2541.49			−0.158828
$636$	−26021.0	−	39071.5i	−1.62233	−	2.43598i
$637$		0			0
$638$	30.8892	+	16.5408i	0.00191680	+	0.00102642i
$639$			15573.0i			0.964099i
$640$	8172.22	+	2526.53i	0.504743	+	0.156047i
$641$	15556.6			0.958576			0.479288	−	0.877658i	$-0.340895\pi$
$641$	15556.6			0.958576			0.479288	+	0.877658i	$0.340895\pi$
$642$	−49203.5	−	26347.9i	−3.02478	−	1.61973i
$643$	15506.4			0.951029			0.475514	−	0.879708i	$-0.342262\pi$
$643$	15506.4			0.951029			0.475514	+	0.879708i	$0.342262\pi$
$644$		0			0
$645$	−20166.9			−1.23112
$646$	−6195.29	−	3317.50i	−0.377322	−	0.202052i
$647$	−23477.7			−1.42659			−0.713296	−	0.700863i	$-0.752798\pi$
$647$	−23477.7			−1.42659			−0.713296	+	0.700863i	$0.752798\pi$
$648$	27381.0	−	2633.82i	1.65992	−	0.159670i
$649$			159.168i			0.00962694i
$650$	9823.95	+	5260.60i	0.592811	+	0.317443i
$651$		0			0
$652$	−6047.73	+	4027.69i	−0.363263	+	0.241927i
$653$	−17633.2			−1.05673			−0.528363	−	0.849018i	$-0.677194\pi$
$653$	−17633.2			−1.05673			−0.528363	+	0.849018i	$0.677194\pi$
$654$	10457.0	−	19528.0i	0.625230	−	1.16759i
$655$			9682.80i			0.577616i
$656$	−15051.1	−	6288.01i	−0.895803	−	0.374246i
$657$			40496.5i			2.40474i
$658$		0			0
$659$			398.945i			0.0235822i	0.999930	+	0.0117911i	$0.00375331\pi$
$659$			398.945i			0.0235822i	−0.999930	+	0.0117911i	$0.996247\pi$
$660$	75.3061	+	113.075i	0.00444134	+	0.00666884i
$661$			5967.11i			0.351125i	0.984468	+	0.175563i	$0.0561744\pi$
$661$			5967.11i			0.351125i	−0.984468	+	0.175563i	$0.943826\pi$
$662$	−16295.7	−	8726.17i	−0.956725	−	0.512315i
$663$	12723.8			0.745325
$664$	−18145.3	+	1745.43i	−1.06050	+	0.102012i
$665$		0			0
$666$	11535.4	−	21541.9i	0.671155	−	1.25335i
$667$			764.336i			0.0443706i
$668$	5338.49	+	8015.95i	0.309210	+	0.464291i
$669$	−36042.1			−2.08291
$670$	4100.94	−	7658.33i	0.236468	−	0.441593i
$671$	−238.664			−0.0137310
$672$		0			0
$673$	19669.6			1.12661			0.563304	−	0.826250i	$-0.309530\pi$
$673$	19669.6			1.12661			0.563304	+	0.826250i	$0.309530\pi$
$674$	−6379.17	+	11912.8i	−0.364565	+	0.680808i
$675$	−27355.5			−1.55987
$676$	−1265.06	−	1899.54i	−0.0719767	−	0.108076i
$677$			9551.68i			0.542246i	0.962545	+	0.271123i	$0.0873951\pi$
$677$			9551.68i			0.542246i	−0.962545	+	0.271123i	$0.912605\pi$
$678$	−9658.92	+	18037.6i	−0.547122	+	1.02173i
$679$		0			0
$680$	−4159.88	+	400.145i	−0.234594	+	0.0225660i
$681$	−30592.8			−1.72147
$682$	66.0116	+	35.3484i	0.00370633	+	0.00198469i
$683$			21307.0i			1.19369i	0.802358	+	0.596843i	$0.203579\pi$
$683$			21307.0i			1.19369i	−0.802358	+	0.596843i	$0.796421\pi$
$684$	21008.0	+	31544.4i	1.17436	+	1.76335i
$685$			10592.3i			0.590819i
$686$		0			0
$687$			26233.0i			1.45685i
$688$	−21663.7	−	9050.59i	−1.20047	−	0.501527i
$689$			27567.1i			1.52427i
$690$	−1398.99	+	2612.54i	−0.0771862	+	0.144142i
$691$	−8093.85			−0.445593			−0.222796	−	0.974865i	$-0.571518\pi$
$691$	−8093.85			−0.445593			−0.222796	+	0.974865i	$0.571518\pi$
$692$	8038.78	−	5353.70i	0.441602	−	0.294100i
$693$		0			0
$694$	−22940.8	−	12284.5i	−1.25479	−	0.671923i
$695$		−	4006.67i		−	0.218678i
$696$	8406.43	−	808.627i	0.457823	−	0.0440387i
$697$	7969.31			0.433083
$698$	17306.7	+	9267.55i	0.938495	+	0.502553i
$699$	−54013.7			−2.92273
$700$		0			0
$701$	−15840.9			−0.853498			−0.426749	−	0.904370i	$-0.640341\pi$
$701$	−15840.9			−0.853498			−0.426749	+	0.904370i	$0.640341\pi$
$702$	−33096.3	−	17722.7i	−1.77940	−	0.952848i
$703$	11515.1			0.617784
$704$	30.1491	+	155.264i	0.00161404	+	0.00831211i
$705$			563.354i			0.0300952i
$706$	−3929.53	−	2104.22i	−0.209476	−	0.112172i
$707$		0			0
$708$	21264.9	+	31930.0i	1.12879	+	1.69492i
$709$	24291.1			1.28670			0.643351	−	0.765572i	$-0.277544\pi$
$709$	24291.1			1.28670			0.643351	+	0.765572i	$0.277544\pi$
$710$	−2060.09	+	3847.14i	−0.108893	+	0.203353i
$711$			20622.5i			1.08777i
$712$	101.829	+	1058.61i	0.00535984	+	0.0557206i
$713$			1633.42i			0.0857952i
$714$		0			0
$715$		−	79.7805i		−	0.00417290i
$716$	10165.4	−	6770.01i	0.530586	−	0.353362i
$717$		−	55457.9i		−	2.88858i
$718$	18860.4	+	10099.5i	0.980309	+	0.524944i
$719$	30123.6			1.56248			0.781239	−	0.624232i	$-0.214588\pi$
$719$	30123.6			1.56248			0.781239	+	0.624232i	$0.214588\pi$
$720$	20795.8	+	8687.99i	1.07641	+	0.449698i
$721$		0			0
$722$	727.215	−	1358.04i	0.0374850	−	0.0700015i
$723$		−	19709.3i		−	1.01383i
$724$	6574.64	−	4378.61i	0.337493	−	0.224765i
$725$	−3613.66			−0.185114
$726$	16538.7	−	30885.2i	0.845464	−	1.57887i
$727$	−14109.8			−0.719810			−0.359905	−	0.932989i	$-0.617191\pi$
$727$	−14109.8			−0.719810			−0.359905	+	0.932989i	$0.617191\pi$
$728$		0			0
$729$	−3808.72			−0.193503
$730$	−5357.12	+	10004.2i	−0.271611	+	0.507221i
$731$	11470.6			0.580374
$732$	−47877.5	+	31885.6i	−2.41749	+	1.61001i
$733$		−	29870.0i		−	1.50515i	−0.658506	−	0.752575i	$-0.728811\pi$
$733$		−	29870.0i		−	1.50515i	0.658506	−	0.752575i	$-0.271189\pi$
$734$	15782.5	−	29473.1i	0.793655	−	1.48212i
$735$		0			0
$736$	−2675.29	+	2178.61i	−0.133985	+	0.109109i
$737$	160.630			0.00802832
$738$	−37888.0	−	20288.6i	−1.88980	−	1.01197i
$739$			4486.46i			0.223325i	0.993746	+	0.111662i	$0.0356175\pi$
$739$			4486.46i			0.223325i	−0.993746	+	0.111662i	$0.964382\pi$
$740$	5699.39	−	3795.70i	0.283127	−	0.188558i
$741$		−	32335.7i		−	1.60308i
$742$		0			0
$743$		−	21574.3i		−	1.06525i	−0.846350	−	0.532627i	$-0.821205\pi$
$743$		−	21574.3i		−	1.06525i	0.846350	−	0.532627i	$-0.178795\pi$
$744$	17964.9	−	1728.07i	0.885249	−	0.0851534i
$745$			8334.66i			0.409877i
$746$	−4608.04	+	8605.31i	−0.226156	+	0.422336i
$747$	−48029.8			−2.35250
$748$	−42.8328	−	64.3150i	−0.00209374	−	0.00314384i
$749$		0			0
$750$	−29485.8	−	15789.3i	−1.43556	−	0.768724i
$751$			38694.9i			1.88016i	0.340959	+	0.940078i	$0.389248\pi$
$751$			38694.9i			1.88016i	−0.340959	+	0.940078i	$0.610752\pi$
$752$	−252.825	+	605.167i	−0.0122601	+	0.0293460i
$753$	18156.7			0.878705
$754$	−4372.02	−	2341.16i	−0.211166	−	0.113077i
$755$	14317.7			0.690164
$756$		0			0
$757$	−4171.12			−0.200267			−0.100133	−	0.994974i	$-0.531927\pi$
$757$	−4171.12			−0.200267			−0.100133	+	0.994974i	$0.531927\pi$
$758$	906.138	+	485.226i	0.0434201	+	0.0232509i
$759$	−54.7969			−0.00262055
$760$	1016.91	+	10571.7i	0.0485359	+	0.504576i
$761$		−	3843.38i		−	0.183078i	−0.995801	−	0.0915390i	$-0.970821\pi$
$761$		−	3843.38i		−	0.183078i	0.995801	−	0.0915390i	$-0.0291786\pi$
$762$	−9984.93	−	5346.81i	−0.474693	−	0.254192i
$763$		0			0
$764$	26131.2	−	17402.9i	1.23743	−	0.824105i
$765$	−11011.0			−0.520397
$766$	−2016.93	+	3766.52i	−0.0951365	+	0.177663i
$767$		−	22528.4i		−	1.06056i
$768$	26791.4	+	27119.0i	1.25879	+	1.27418i
$769$		−	11022.0i		−	0.516857i	−0.966030	−	0.258428i	$-0.916795\pi$
$769$		−	11022.0i		−	0.516857i	0.966030	−	0.258428i	$-0.0832046\pi$
$770$		0			0
$771$			63969.5i			2.98807i
$772$	16476.7	+	24740.4i	0.768147	+	1.15340i
$773$		−	35214.6i		−	1.63853i	−0.573416	−	0.819264i	$-0.694382\pi$
$773$		−	35214.6i		−	1.63853i	0.573416	−	0.819264i	$-0.305618\pi$
$774$	−54533.7	−	29202.2i	−2.53252	−	1.35614i
$775$	−7722.54			−0.357938
$776$	1654.36	+	17198.6i	0.0765310	+	0.795611i
$777$		0			0
$778$	2552.35	−	4766.40i	0.117617	−	0.219645i
$779$		−	20252.9i		−	0.931494i
$780$	−10658.7	−	16004.5i	−0.489286	−	0.734682i
$781$	−80.6918			−0.00369703
$782$	795.719	−	1485.97i	0.0363873	−	0.0679516i
$783$	12174.2			0.555646
$784$		0			0
$785$	18077.0			0.821907
$786$	−20370.8	+	38041.5i	−0.924428	+	1.72633i
$787$	4036.59			0.182832			0.0914162	−	0.995813i	$-0.470861\pi$
$787$	4036.59			0.182832			0.0914162	+	0.995813i	$0.470861\pi$
$788$	20894.3	+	31373.5i	0.944577	+	1.41832i
$789$			20850.8i			0.940819i
$790$	−2728.07	+	5094.55i	−0.122861	+	0.229438i
$791$		0			0
$792$	39.9016	+	414.814i	0.00179020	+	0.0186108i
$793$	33780.1			1.51270
$794$	−26911.9	−	14411.0i	−1.20286	−	0.644116i
$795$		−	34660.2i		−	1.54625i
$796$	40.8298	+	61.3075i	0.00181806	+	0.00272988i
$797$		−	26004.8i		−	1.15575i	−0.816124	−	0.577877i	$-0.803881\pi$
$797$		−	26004.8i		−	1.15575i	0.816124	−	0.577877i	$-0.196119\pi$
$798$		0			0
$799$		−	320.426i		−	0.0141875i
$800$	−10300.1	−	12648.4i	−0.455205	−	0.558984i
$801$			2802.09i			0.123604i
$802$	12007.0	−	22422.5i	0.528654	−	0.987238i
$803$	−209.833			−0.00922147
$804$	32223.3	−	21460.2i	1.41347	−	0.941347i
$805$		0			0
$806$	−9343.19	−	5003.16i	−0.408312	−	0.218646i
$807$		−	2628.12i		−	0.114639i
$808$	1675.59	+	17419.3i	0.0729542	+	0.758427i
$809$	238.527			0.0103661			0.00518305	−	0.999987i	$-0.498350\pi$
$809$	238.527			0.0103661			0.00518305	+	0.999987i	$0.498350\pi$
$810$	17904.4	+	9587.58i	0.776662	+	0.415893i
$811$	−25463.7			−1.10253			−0.551264	−	0.834331i	$-0.685854\pi$
$811$	−25463.7			−1.10253			−0.551264	+	0.834331i	$0.685854\pi$
$812$		0			0
$813$	39172.7			1.68985
$814$	111.620	+	59.7710i	0.00480623	+	0.00257368i
$815$	−5364.92			−0.230583
$816$	−17185.0	−	7179.51i	−0.737251	−	0.308006i
$817$		−	29150.8i		−	1.24829i
$818$	17894.9	+	9582.53i	0.764893	+	0.409591i
$819$		0			0
$820$	−6675.89	−	10024.1i	−0.284308	−	0.426899i
$821$	24012.6			1.02076			0.510381	−	0.859948i	$-0.329504\pi$
$821$	24012.6			1.02076			0.510381	+	0.859948i	$0.329504\pi$
$822$	−22284.2	+	41614.7i	−0.945559	+	1.76579i
$823$			29367.6i			1.24385i	0.783076	+	0.621925i	$0.213649\pi$
$823$			29367.6i			1.24385i	−0.783076	+	0.621925i	$0.786351\pi$
$824$	6434.87	−	618.979i	0.272050	−	0.0261689i
$825$		−	259.071i		−	0.0109330i
$826$		0			0
$827$			2757.80i			0.115959i	0.998318	+	0.0579796i	$0.0184658\pi$
$827$			2757.80i			0.115959i	−0.998318	+	0.0579796i	$0.981534\pi$
$828$	−7566.07	+	5038.88i	−0.317559	+	0.211489i
$829$			28508.2i			1.19437i	0.802104	+	0.597184i	$0.203714\pi$
$829$			28508.2i			1.19437i	−0.802104	+	0.597184i	$0.796286\pi$
$830$	−11865.2	−	6353.68i	−0.496202	−	0.265710i
$831$	−24524.6			−1.02377
$832$	−4267.26	−	21975.8i	−0.177813	−	0.915714i
$833$		0			0
$834$	8429.26	−	15741.3i	0.349978	−	0.653568i
$835$			7110.92i			0.294711i
$836$	−163.448	+	108.853i	−0.00676190	+	0.00450332i
$837$	26016.8			1.07440
$838$	2488.68	−	4647.50i	0.102590	−	0.191581i
$839$	−22706.3			−0.934337			−0.467169	−	0.884168i	$-0.654726\pi$
$839$	−22706.3			−0.934337			−0.467169	+	0.884168i	$0.654726\pi$
$840$		0			0
$841$	−22780.8			−0.934060
$842$	6576.51	−	12281.3i	0.269170	−	0.502664i
$843$	23383.1			0.955345
$844$	4541.50	−	3024.56i	0.185219	−	0.123353i
$845$		−	1685.07i		−	0.0686016i
$846$	−815.751	+	1523.38i	−0.0331514	+	0.0619088i
$847$		0			0
$848$	15555.0	−	37232.7i	0.629906	−	1.50776i
$849$	21664.2			0.875751
$850$	7025.42	+	3762.03i	0.283494	+	0.151808i
$851$			2761.96i			0.111256i
$852$	−16187.3	+	10780.5i	−0.650900	+	0.433489i
$853$			31316.1i			1.25703i	0.777799	+	0.628513i	$0.216336\pi$
$853$			31316.1i			1.25703i	−0.777799	+	0.628513i	$0.783664\pi$
$854$		0			0
$855$			27982.9i			1.11929i
$856$	−4593.72	−	47756.0i	−0.183423	−	1.90685i
$857$		−	20122.3i		−	0.802060i	−0.916065	−	0.401030i	$-0.868652\pi$
$857$		−	20122.3i		−	0.802060i	0.916065	−	0.401030i	$-0.131348\pi$
$858$	167.843	−	313.439i	0.00667839	−	0.0124716i
$859$	−12041.8			−0.478301			−0.239151	−	0.970982i	$-0.576869\pi$
$859$	−12041.8			−0.478301			−0.239151	+	0.970982i	$0.576869\pi$
$860$	−9608.89	−	14428.1i	−0.381000	−	0.572087i
$861$		0			0
$862$	31952.9	+	17110.4i	1.26255	+	0.676082i
$863$		−	2872.09i		−	0.113287i	−0.998394	−	0.0566437i	$-0.981960\pi$
$863$		−	2872.09i		−	0.113287i	0.998394	−	0.0566437i	$-0.0180399\pi$
$864$	34700.5	+	42611.6i	1.36636	+	1.67787i
$865$	7131.17			0.280309
$866$	31828.2	+	17043.6i	1.24892	+	0.668784i
$867$	−36625.6			−1.43469
$868$		0			0
$869$	−106.856			−0.00417127
$870$	5496.96	+	2943.55i	0.214212	+	0.114708i
$871$	−22735.3			−0.884450
$872$	18953.4	−	1823.16i	0.736060	−	0.0708027i
$873$			45523.9i			1.76489i
$874$	−3776.38	−	2022.21i	−0.146153	−	0.0782633i
$875$		0			0
$876$	−42093.8	+	28033.8i	−1.62353	+	1.08125i
$877$	−12626.4			−0.486163			−0.243081	−	0.970006i	$-0.578158\pi$
$877$	−12626.4			−0.486163			−0.243081	+	0.970006i	$0.578158\pi$
$878$	20362.9	−	38026.8i	0.782705	−	1.46167i
$879$			52629.8i			2.01952i
$880$	−45.0169	+	107.753i	−0.00172445	+	0.00412769i
$881$			38693.9i			1.47972i	0.672762	+	0.739859i	$0.265108\pi$
$881$			38693.9i			1.47972i	−0.672762	+	0.739859i	$0.734892\pi$
$882$		0			0
$883$			33659.7i			1.28283i	0.767193	+	0.641416i	$0.221653\pi$
$883$			33659.7i			1.28283i	−0.767193	+	0.641416i	$0.778347\pi$
$884$	6062.49	+	9103.05i	0.230660	+	0.346345i
$885$			28325.0i			1.07586i
$886$	19326.6	+	10349.2i	0.732833	+	0.392423i
$887$	33241.6			1.25834			0.629168	−	0.777269i	$-0.283396\pi$
$887$	33241.6			1.25834			0.629168	+	0.777269i	$0.283396\pi$
$888$	30377.0	−	2922.01i	1.14796	−	0.110424i
$889$		0			0
$890$	−370.677	+	692.223i	−0.0139608	+	0.0260712i
$891$			375.536i			0.0141200i
$892$	−17173.0	−	25785.9i	−0.644612	−	0.967909i
$893$	−814.316			−0.0305152
$894$	−17534.5	+	32745.0i	−0.655976	+	1.22501i
$895$	9017.71			0.336792
$896$		0			0
$897$	7755.87			0.288697
$898$	−1152.18	+	2151.64i	−0.0428158	+	0.0799566i
$899$	3436.81			0.127502
$900$	−23823.0	−	35771.1i	−0.882334	−	1.32486i
$901$			19714.1i			0.728937i
$902$	105.125	−	196.317i	0.00388059	−	0.00724683i
$903$		0			0
$904$	−17506.9	+	1684.02i	−0.644106	+	0.0619575i
$905$	5832.34			0.214225
$906$	56250.8	+	30121.6i	2.06270	+	1.10455i
$907$			9276.61i			0.339608i	0.985478	+	0.169804i	$0.0543135\pi$
$907$			9276.61i			0.339608i	−0.985478	+	0.169804i	$0.945686\pi$
$908$	−14576.5	−	21887.2i	−0.532753	−	0.799948i
$909$			46108.1i			1.68241i
$910$		0			0
$911$		−	30720.4i		−	1.11725i	−0.829422	−	0.558623i	$-0.811330\pi$
$911$		−	30720.4i		−	1.11725i	0.829422	−	0.558623i	$-0.188670\pi$
$912$	−18245.7	+	43673.3i	−0.662474	+	1.58571i
$913$		−	248.867i		−	0.00902113i
$914$	7477.30	−	13963.5i	0.270599	−	0.505331i
$915$	−42471.9			−1.53451
$916$	−18768.1	+	12499.2i	−0.676981	+	0.450858i
$917$		0			0
$918$	−23668.2	−	12674.1i	−0.850946	−	0.455671i
$919$		−	14684.9i		−	0.527104i	−0.964645	−	0.263552i	$-0.915106\pi$
$919$		−	14684.9i		−	0.527104i	0.964645	−	0.263552i	$-0.0848941\pi$
$920$	−2535.68	+	243.911i	−0.0908685	+	0.00874078i
$921$	−35342.7			−1.26448
$922$	−32735.0	−	17529.2i	−1.16927	−	0.626132i
$923$	11421.0			0.407288
$924$		0			0
$925$	−13058.1			−0.464160
$926$	−8351.82	−	4472.30i	−0.296391	−	0.158714i
$927$	17032.8			0.603484
$928$	4583.93	+	5628.98i	0.162150	+	0.199117i
$929$			3743.03i			0.132190i	0.997813	+	0.0660951i	$0.0210541\pi$
$929$			3743.03i			0.132190i	−0.997813	+	0.0660951i	$0.978946\pi$
$930$	11747.2	+	6290.50i	0.414201	+	0.221800i
$931$		0			0
$932$	−25735.9	−	38643.4i	−0.904513	−	1.35816i
$933$	−53455.5			−1.87573
$934$	−2833.43	+	5291.30i	−0.0992639	+	0.185371i
$935$		−	57.0536i		−	0.00199556i
$936$	−5647.61	−	58712.2i	−0.197220	−	2.05029i
$937$		−	16171.0i		−	0.563803i	−0.959443	−	0.281901i	$-0.909035\pi$
$937$		−	16171.0i		−	0.563803i	0.959443	−	0.281901i	$-0.0909651\pi$
$938$		0			0
$939$		−	58145.2i		−	2.02076i
$940$	−403.044	+	268.421i	−0.0139849	+	0.00931374i
$941$			21397.3i			0.741268i	0.928779	+	0.370634i	$0.120860\pi$
$941$			21397.3i			0.741268i	−0.928779	+	0.370634i	$0.879140\pi$
$942$	71020.5	+	38030.6i	2.45645	+	1.31540i
$943$	4857.75			0.167752
$944$	−12711.9	+	30427.4i	−0.438279	+	1.04907i
$945$		0			0
$946$	151.311	−	282.567i	0.00520038	−	0.00971147i
$947$			5852.40i			0.200821i	0.994946	+	0.100410i	$0.0320156\pi$
$947$			5852.40i			0.200821i	−0.994946	+	0.100410i	$0.967984\pi$
$948$	−21435.9	+	14276.0i	−0.734395	+	0.489095i
$949$	29699.4			1.01590
$950$	9560.66	−	17854.1i	0.326515	−	0.609752i
$951$	43051.9			1.46798
$952$		0			0
$953$	−14470.9			−0.491875			−0.245938	−	0.969286i	$-0.579096\pi$
$953$	−14470.9			−0.491875			−0.245938	+	0.969286i	$0.579096\pi$
$954$	50188.9	−	93725.5i	1.70328	−	3.18079i
$955$	23180.9			0.785461
$956$	39676.6	−	26424.0i	1.34229	−	0.893946i
$957$			115.296i			0.00389445i
$958$	10591.8	−	19779.7i	0.357209	−	0.667071i
$959$		0			0
$960$	5365.24	+	27630.3i	0.180377	+	0.928920i
$961$	−22446.4			−0.753462
$962$	−15798.5	−	8459.90i	−0.529484	−	0.283532i
$963$		−	126408.i		−	4.22994i
$964$	14100.8	−	9390.88i	0.471115	−	0.313755i
$965$			21947.1i			0.732127i
$966$		0			0
$967$		−	6344.28i		−	0.210981i	−0.994420	−	0.105490i	$-0.966359\pi$
$967$		−	6344.28i		−	0.210981i	0.994420	−	0.105490i	$-0.0336412\pi$
$968$	29976.6	−	2883.49i	0.995334	−	0.0957427i
$969$		−	23124.3i		−	0.766624i
$970$	−6022.18	+	11246.2i	−0.199341	+	0.372260i
$971$	2546.66			0.0841672			0.0420836	−	0.999114i	$-0.486600\pi$
$971$	2546.66			0.0841672			0.0420836	+	0.999114i	$0.486600\pi$
$972$	13824.4	+	20757.8i	0.456191	+	0.684988i
$973$		0			0
$974$	28835.7	+	15441.2i	0.948619	+	0.507974i
$975$			36668.5i			1.20444i
$976$	−45624.3	−	19060.8i	−1.49631	−	0.625123i
$977$	−43391.1			−1.42088			−0.710442	−	0.703755i	$-0.751505\pi$
$977$	−43391.1			−1.42088			−0.710442	+	0.703755i	$0.751505\pi$
$978$	−21077.5	−	11286.8i	−0.689146	−	0.369030i
$979$	−14.5190			−0.000473984
$980$		0			0
$981$	50168.8			1.63279
$982$	42391.7	+	22700.2i	1.37757	+	0.737671i
$983$	46755.9			1.51707			0.758536	−	0.651632i	$-0.225915\pi$
$983$	46755.9			1.51707			0.758536	+	0.651632i	$0.225915\pi$
$984$	−5139.24	−	53427.2i	−0.166497	−	1.73089i
$985$			27831.3i			0.900284i
$986$	−3126.57	−	1674.24i	−0.100984	−	0.0540758i
$987$		0			0
$988$	23134.1	−	15406.9i	0.744934	−	0.496114i
$989$	6991.96			0.224804
$990$	−145.249	+	271.246i	−0.00466295	+	0.00870786i
$991$		−	26027.1i		−	0.834287i	−0.908841	−	0.417144i	$-0.863031\pi$
$991$		−	26027.1i		−	0.834287i	0.908841	−	0.417144i	$-0.136969\pi$
$992$	9796.05	+	12029.4i	0.313533	+	0.385013i
$993$		−	60824.9i		−	1.94383i
$994$		0			0
$995$			54.3857i			0.00173281i
$996$	−33248.7	−	49924.2i	−1.05776	−	1.58826i
$997$			26367.4i			0.837576i	0.908084	+	0.418788i	$0.137545\pi$
$997$			26367.4i			0.837576i	−0.908084	+	0.418788i	$0.862455\pi$
$998$	−32684.1	−	17501.9i	−1.03667	−	0.555124i
$999$	43992.1			1.39324

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.4.d.b.195.7		20
4.3	odd	2	inner	196.4.d.b.195.6		20
7.2	even	3		196.4.f.d.31.10		20
7.3	odd	6		196.4.f.d.19.4		20
7.4	even	3		28.4.f.a.19.4	yes	20
7.5	odd	6		28.4.f.a.3.10	yes	20
7.6	odd	2	inner	196.4.d.b.195.8		20
28.3	even	6		196.4.f.d.19.10		20
28.11	odd	6		28.4.f.a.19.10	yes	20
28.19	even	6		28.4.f.a.3.4	✓	20
28.23	odd	6		196.4.f.d.31.4		20
28.27	even	2	inner	196.4.d.b.195.5		20
56.5	odd	6		448.4.p.h.255.10		20
56.11	odd	6		448.4.p.h.383.10		20
56.19	even	6		448.4.p.h.255.1		20
56.53	even	6		448.4.p.h.383.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.4.f.a.3.4	✓	20	28.19	even	6
28.4.f.a.3.10	yes	20	7.5	odd	6
28.4.f.a.19.4	yes	20	7.4	even	3
28.4.f.a.19.10	yes	20	28.11	odd	6
196.4.d.b.195.5		20	28.27	even	2	inner
196.4.d.b.195.6		20	4.3	odd	2	inner
196.4.d.b.195.7		20	1.1	even	1	trivial
196.4.d.b.195.8		20	7.6	odd	2	inner
196.4.f.d.19.4		20	7.3	odd	6
196.4.f.d.19.10		20	28.3	even	6
196.4.f.d.31.4		20	28.23	odd	6
196.4.f.d.31.10		20	7.2	even	3
448.4.p.h.255.1		20	56.19	even	6
448.4.p.h.255.10		20	56.5	odd	6
448.4.p.h.383.1		20	56.53	even	6
448.4.p.h.383.10		20	56.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	196.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33521 + 2.49344i) q^{2} -9.30691 q^{3} +(-4.43445 - 6.65850i) q^{4} -5.90673i q^{5} +(12.4266 - 23.2062i) q^{6} +(22.5235 - 2.16656i) q^{8} +59.6185 q^{9} +O(q^{10})\)	\(q+(-1.33521 + 2.49344i) q^{2} -9.30691 q^{3} +(-4.43445 - 6.65850i) q^{4} -5.90673i q^{5} +(12.4266 - 23.2062i) q^{6} +(22.5235 - 2.16656i) q^{8} +59.6185 q^{9} +(14.7281 + 7.88670i) q^{10} +0.308914i q^{11} +(41.2710 + 61.9700i) q^{12} -43.7232i q^{13} +54.9734i q^{15} +(-24.6712 + 59.0536i) q^{16} -31.2679i q^{17} +(-79.6029 + 148.655i) q^{18} -79.4629 q^{19} +(-39.3300 + 26.1931i) q^{20} +(-0.770257 - 0.412464i) q^{22} -19.0596i q^{23} +(-209.624 + 20.1640i) q^{24} +90.1105 q^{25} +(109.021 + 58.3795i) q^{26} -303.577 q^{27} -40.1025 q^{29} +(-137.073 - 73.4008i) q^{30} -85.7007 q^{31} +(-114.305 - 140.365i) q^{32} -2.87503i q^{33} +(77.9645 + 41.7490i) q^{34} +(-264.375 - 396.970i) q^{36} -144.912 q^{37} +(106.099 - 198.136i) q^{38} +406.928i q^{39} +(-12.7973 - 133.040i) q^{40} +254.872i q^{41} +366.848i q^{43} +(2.05690 - 1.36986i) q^{44} -352.150i q^{45} +(47.5238 + 25.4484i) q^{46} +10.2478 q^{47} +(229.613 - 549.606i) q^{48} +(-120.316 + 224.685i) q^{50} +291.007i q^{51} +(-291.131 + 193.889i) q^{52} -630.491 q^{53} +(405.338 - 756.951i) q^{54} +1.82467 q^{55} +739.554 q^{57} +(53.5451 - 99.9930i) q^{58} +515.250 q^{59} +(366.040 - 243.777i) q^{60} +772.591i q^{61} +(114.428 - 213.689i) q^{62} +(502.612 - 97.5970i) q^{64} -258.261 q^{65} +(7.16871 + 3.83876i) q^{66} -519.982i q^{67} +(-208.197 + 138.656i) q^{68} +177.386i q^{69} +261.211i q^{71} +(1342.81 - 129.167i) q^{72} +679.260i q^{73} +(193.488 - 361.330i) q^{74} -838.650 q^{75} +(352.375 + 529.104i) q^{76} +(-1014.65 - 543.332i) q^{78} +345.908i q^{79} +(348.814 + 145.726i) q^{80} +1215.67 q^{81} +(-635.507 - 340.306i) q^{82} -805.619 q^{83} -184.691 q^{85} +(-914.712 - 489.817i) q^{86} +373.230 q^{87} +(0.669282 + 6.95781i) q^{88} +47.0003i q^{89} +(878.065 + 470.193i) q^{90} +(-126.908 + 84.5187i) q^{92} +797.609 q^{93} +(-13.6829 + 25.5521i) q^{94} +469.366i q^{95} +(1063.83 + 1306.36i) q^{96} +763.587i q^{97} +18.4170i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 8 q^{4} + 72 q^{8} + 112 q^{9}+O(q^{10}) \) 20 * q - 8 * q^4 + 72 * q^8 + 112 * q^9	\( 20 q - 8 q^{4} + 72 q^{8} + 112 q^{9} + 208 q^{16} - 136 q^{18} - 184 q^{22} + 72 q^{25} - 352 q^{29} - 1288 q^{30} + 80 q^{32} + 208 q^{36} - 516 q^{37} + 2496 q^{44} - 464 q^{46} - 864 q^{50} - 1140 q^{53} + 1452 q^{57} - 4488 q^{58} + 1472 q^{60} + 2560 q^{64} + 248 q^{65} + 9344 q^{72} - 1664 q^{74} - 4056 q^{78} + 2524 q^{81} - 2980 q^{85} - 11392 q^{86} + 2792 q^{88} + 3312 q^{92} + 612 q^{93}+O(q^{100}) \) 20 * q - 8 * q^4 + 72 * q^8 + 112 * q^9 + 208 * q^16 - 136 * q^18 - 184 * q^22 + 72 * q^25 - 352 * q^29 - 1288 * q^30 + 80 * q^32 + 208 * q^36 - 516 * q^37 + 2496 * q^44 - 464 * q^46 - 864 * q^50 - 1140 * q^53 + 1452 * q^57 - 4488 * q^58 + 1472 * q^60 + 2560 * q^64 + 248 * q^65 + 9344 * q^72 - 1664 * q^74 - 4056 * q^78 + 2524 * q^81 - 2980 * q^85 - 11392 * q^86 + 2792 * q^88 + 3312 * q^92 + 612 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more