LMFDB - Embedded newform 105.4.b.b.41.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(41,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("105.41");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.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:	$6.19520055060$
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} + 96 x^{14} + 3618 x^{12} + 68560 x^{10} + 697017 x^{8} + 3791184 x^{6} + 10461796 x^{4} + \cdots + 5760000 $ x^16 + 96x^14 + 3618x^12 + 68560x^10 + 697017x^8 + 3791184x^6 + 10461796x^4 + 13209792*x^2 + 5760000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			41.2
Root			$-4.61386i$ of defining polynomial
Character	$\chi$	$=$	105.41
Dual form			105.4.b.b.41.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.61386i q^{2} +(3.98691 + 3.33234i) q^{3} -13.2877 q^{4} +5.00000 q^{5} +(15.3750 - 18.3951i) q^{6} +(0.582685 - 18.5111i) q^{7} +24.3969i q^{8} +(4.79097 + 26.5715i) q^{9} +O(q^{10})$	\(q-4.61386i q^{2} +(3.98691 + 3.33234i) q^{3} -13.2877 q^{4} +5.00000 q^{5} +(15.3750 - 18.3951i) q^{6} +(0.582685 - 18.5111i) q^{7} +24.3969i q^{8} +(4.79097 + 26.5715i) q^{9} -23.0693i q^{10} -65.3963i q^{11} +(-52.9770 - 44.2793i) q^{12} -30.9388i q^{13} +(-85.4076 - 2.68843i) q^{14} +(19.9346 + 16.6617i) q^{15} +6.26191 q^{16} +85.8927 q^{17} +(122.597 - 22.1049i) q^{18} +6.24097i q^{19} -66.4386 q^{20} +(64.0084 - 71.8604i) q^{21} -301.730 q^{22} +193.142i q^{23} +(-81.2987 + 97.2682i) q^{24} +25.0000 q^{25} -142.747 q^{26} +(-69.4443 + 121.904i) q^{27} +(-7.74256 + 245.970i) q^{28} +30.7085i q^{29} +(76.8749 - 91.9754i) q^{30} +61.0950i q^{31} +166.283i q^{32} +(217.923 - 260.730i) q^{33} -396.297i q^{34} +(2.91342 - 92.5555i) q^{35} +(-63.6612 - 353.075i) q^{36} -8.71591 q^{37} +28.7950 q^{38} +(103.099 - 123.350i) q^{39} +121.984i q^{40} +387.588 q^{41} +(-331.554 - 295.326i) q^{42} -281.233 q^{43} +868.968i q^{44} +(23.9549 + 132.858i) q^{45} +891.130 q^{46} +208.528 q^{47} +(24.9657 + 20.8668i) q^{48} +(-342.321 - 21.5723i) q^{49} -115.347i q^{50} +(342.447 + 286.224i) q^{51} +411.106i q^{52} -211.802i q^{53} +(562.447 + 320.406i) q^{54} -326.982i q^{55} +(451.612 + 14.2157i) q^{56} +(-20.7971 + 24.8822i) q^{57} +141.685 q^{58} +213.993 q^{59} +(-264.885 - 221.396i) q^{60} +673.667i q^{61} +281.884 q^{62} +(494.660 - 73.2033i) q^{63} +817.303 q^{64} -154.694i q^{65} +(-1202.97 - 1005.47i) q^{66} -500.399 q^{67} -1141.32 q^{68} +(-643.615 + 770.040i) q^{69} +(-427.038 - 13.4421i) q^{70} -319.460i q^{71} +(-648.262 + 116.885i) q^{72} +555.337i q^{73} +40.2140i q^{74} +(99.6729 + 83.3086i) q^{75} -82.9283i q^{76} +(-1210.56 - 38.1054i) q^{77} +(-569.121 - 475.683i) q^{78} +842.582 q^{79} +31.3095 q^{80} +(-683.093 + 254.607i) q^{81} -1788.28i q^{82} -887.665 q^{83} +(-850.527 + 954.862i) q^{84} +429.463 q^{85} +1297.57i q^{86} +(-102.331 + 122.432i) q^{87} +1595.46 q^{88} +480.245 q^{89} +(612.987 - 110.524i) q^{90} +(-572.710 - 18.0275i) q^{91} -2566.42i q^{92} +(-203.589 + 243.580i) q^{93} -962.120i q^{94} +31.2048i q^{95} +(-554.113 + 662.957i) q^{96} +477.578i q^{97} +(-99.5315 + 1579.42i) q^{98} +(1737.68 - 313.312i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{3} - 64 q^{4} + 80 q^{5} + 28 q^{6} - 4 q^{7} - 22 q^{9}+O(q^{10}) $ 16 * q + 2 * q^3 - 64 * q^4 + 80 * q^5 + 28 * q^6 - 4 * q^7 - 22 * q^9	$ 16 q + 2 q^{3} - 64 q^{4} + 80 q^{5} + 28 q^{6} - 4 q^{7} - 22 q^{9} + 66 q^{12} + 90 q^{14} + 10 q^{15} + 376 q^{16} + 72 q^{17} - 182 q^{18} - 320 q^{20} - 70 q^{21} - 276 q^{22} - 526 q^{24} + 400 q^{25} - 696 q^{26} + 128 q^{27} + 10 q^{28} + 140 q^{30} + 502 q^{33} - 20 q^{35} + 996 q^{36} - 812 q^{37} + 1200 q^{38} - 594 q^{39} + 936 q^{41} - 974 q^{42} - 548 q^{43} - 110 q^{45} + 1224 q^{46} - 912 q^{47} - 1850 q^{48} + 328 q^{49} + 750 q^{51} + 2950 q^{54} - 1254 q^{56} + 432 q^{57} + 576 q^{58} + 552 q^{59} + 330 q^{60} + 1860 q^{62} + 362 q^{63} - 4000 q^{64} - 1378 q^{66} + 1004 q^{67} - 3828 q^{68} - 1988 q^{69} + 450 q^{70} + 1988 q^{72} + 50 q^{75} - 1152 q^{77} + 1446 q^{78} + 1292 q^{79} + 1880 q^{80} - 2950 q^{81} + 1752 q^{83} - 420 q^{84} + 360 q^{85} - 1910 q^{87} - 912 q^{88} - 6096 q^{89} - 910 q^{90} - 552 q^{91} - 1080 q^{93} + 9546 q^{96} + 4824 q^{98} + 2530 q^{99}+O(q^{100}) $ 16 * q + 2 * q^3 - 64 * q^4 + 80 * q^5 + 28 * q^6 - 4 * q^7 - 22 * q^9 + 66 * q^12 + 90 * q^14 + 10 * q^15 + 376 * q^16 + 72 * q^17 - 182 * q^18 - 320 * q^20 - 70 * q^21 - 276 * q^22 - 526 * q^24 + 400 * q^25 - 696 * q^26 + 128 * q^27 + 10 * q^28 + 140 * q^30 + 502 * q^33 - 20 * q^35 + 996 * q^36 - 812 * q^37 + 1200 * q^38 - 594 * q^39 + 936 * q^41 - 974 * q^42 - 548 * q^43 - 110 * q^45 + 1224 * q^46 - 912 * q^47 - 1850 * q^48 + 328 * q^49 + 750 * q^51 + 2950 * q^54 - 1254 * q^56 + 432 * q^57 + 576 * q^58 + 552 * q^59 + 330 * q^60 + 1860 * q^62 + 362 * q^63 - 4000 * q^64 - 1378 * q^66 + 1004 * q^67 - 3828 * q^68 - 1988 * q^69 + 450 * q^70 + 1988 * q^72 + 50 * q^75 - 1152 * q^77 + 1446 * q^78 + 1292 * q^79 + 1880 * q^80 - 2950 * q^81 + 1752 * q^83 - 420 * q^84 + 360 * q^85 - 1910 * q^87 - 912 * q^88 - 6096 * q^89 - 910 * q^90 - 552 * q^91 - 1080 * q^93 + 9546 * q^96 + 4824 * q^98 + 2530 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$		−	4.61386i		−	1.63125i	−0.578583	−	0.815623i	$-0.696394\pi$
$2$		−	4.61386i		−	1.63125i	0.578583	−	0.815623i	$-0.303606\pi$
$3$	3.98691	+	3.33234i	0.767282	+	0.641310i
$3$	3.98691	+	3.33234i	0.767282	+	0.641310i
$4$	−13.2877			−1.66097
$5$	5.00000			0.447214
$5$	5.00000			0.447214
$6$	15.3750	−	18.3951i	1.04613	−	1.25163i
$7$	0.582685	−	18.5111i	0.0314620	−	0.999505i
$7$	0.582685	−	18.5111i	0.0314620	−	0.999505i
$8$			24.3969i			1.07820i
$9$	4.79097	+	26.5715i	0.177444	+	0.984131i
$10$		−	23.0693i		−	0.729516i
$11$		−	65.3963i		−	1.79252i	−0.443528	−	0.896260i	$-0.646273\pi$
$11$		−	65.3963i		−	1.79252i	0.443528	−	0.896260i	$-0.353727\pi$
$12$	−52.9770	−	44.2793i	−1.27443	−	1.06519i
$13$		−	30.9388i		−	0.660067i	−0.943969	−	0.330033i	$-0.892940\pi$
$13$		−	30.9388i		−	0.660067i	0.943969	−	0.330033i	$-0.107060\pi$
$14$	−85.4076	−	2.68843i	−1.63044	−	0.0513223i
$15$	19.9346	+	16.6617i	0.343139	+	0.286802i
$16$	6.26191			0.0978423
$17$	85.8927			1.22541			0.612707	−	0.790310i	$-0.290081\pi$
$17$	85.8927			1.22541			0.612707	+	0.790310i	$0.290081\pi$
$18$	122.597	−	22.1049i	1.60536	−	0.289454i
$19$			6.24097i			0.0753567i	0.999290	+	0.0376783i	$0.0119962\pi$
$19$			6.24097i			0.0753567i	−0.999290	+	0.0376783i	$0.988004\pi$
$20$	−66.4386			−0.742807
$21$	64.0084	−	71.8604i	0.665133	−	0.746725i
$22$	−301.730			−2.92404
$23$			193.142i			1.75099i	0.483224	+	0.875497i	$0.339466\pi$
$23$			193.142i			1.75099i	−0.483224	+	0.875497i	$0.660534\pi$
$24$	−81.2987	+	97.2682i	−0.691459	+	0.827283i
$25$	25.0000			0.200000
$26$	−142.747			−1.07673
$27$	−69.4443	+	121.904i	−0.494984	+	0.868902i
$28$	−7.74256	+	245.970i	−0.0522574	+	1.66014i
$29$			30.7085i			0.196635i	0.995155	+	0.0983176i	$0.0313461\pi$
$29$			30.7085i			0.196635i	−0.995155	+	0.0983176i	$0.968654\pi$
$30$	76.8749	−	91.9754i	0.467846	−	0.559744i
$31$			61.0950i			0.353967i	0.984214	+	0.176984i	$0.0566339\pi$
$31$			61.0950i			0.353967i	−0.984214	+	0.176984i	$0.943366\pi$
$32$			166.283i			0.918594i
$33$	217.923	−	260.730i	1.14956	−	1.37537i
$34$		−	396.297i		−	1.99895i
$35$	2.91342	−	92.5555i	0.0140702	−	0.446992i
$36$	−63.6612	−	353.075i	−0.294728	−	1.63461i
$37$	−8.71591			−0.0387267			−0.0193633	−	0.999813i	$-0.506164\pi$
$37$	−8.71591			−0.0387267			−0.0193633	+	0.999813i	$0.506164\pi$
$38$	28.7950			0.122925
$39$	103.099	−	123.350i	0.423307	−	0.506457i
$40$			121.984i			0.482185i
$41$	387.588			1.47637			0.738183	−	0.674600i	$-0.235684\pi$
$41$	387.588			1.47637			0.738183	+	0.674600i	$0.235684\pi$
$42$	−331.554	−	295.326i	−1.21809	−	1.08500i
$43$	−281.233			−0.997388			−0.498694	−	0.866778i	$-0.666187\pi$
$43$	−281.233			−0.997388			−0.498694	+	0.866778i	$0.666187\pi$
$44$			868.968i			2.97732i
$45$	23.9549	+	132.858i	0.0793551	+	0.440117i
$46$	891.130			2.85630
$47$	208.528			0.647169			0.323585	−	0.946199i	$-0.395112\pi$
$47$	208.528			0.647169			0.323585	+	0.946199i	$0.395112\pi$
$48$	24.9657	+	20.8668i	0.0750727	+	0.0627472i
$49$	−342.321	−	21.5723i	−0.998020	−	0.0628929i
$50$		−	115.347i		−	0.326249i
$51$	342.447	+	286.224i	0.940238	+	0.785870i
$52$			411.106i			1.09635i
$53$		−	211.802i		−	0.548929i	−0.961597	−	0.274464i	$-0.911499\pi$
$53$		−	211.802i		−	0.548929i	0.961597	−	0.274464i	$-0.0885005\pi$
$54$	562.447	+	320.406i	1.41739	+	0.807440i
$55$		−	326.982i		−	0.801640i
$56$	451.612	+	14.2157i	1.07767	+	0.0339223i
$57$	−20.7971	+	24.8822i	−0.0483270	+	0.0578198i
$58$	141.685			0.320760
$59$	213.993			0.472195			0.236097	−	0.971729i	$-0.424132\pi$
$59$	213.993			0.472195			0.236097	+	0.971729i	$0.424132\pi$
$60$	−264.885	−	221.396i	−0.569942	−	0.476369i
$61$			673.667i			1.41400i	0.707212	+	0.707001i	$0.249953\pi$
$61$			673.667i			1.41400i	−0.707212	+	0.707001i	$0.750047\pi$
$62$	281.884			0.577408
$63$	494.660	−	73.2033i	0.989227	−	0.146393i
$64$	817.303			1.59630
$65$		−	154.694i		−	0.295191i
$66$	−1202.97	−	1005.47i	−2.24357	−	1.87522i
$67$	−500.399			−0.912440			−0.456220	−	0.889867i	$-0.650797\pi$
$67$	−500.399			−0.912440			−0.456220	+	0.889867i	$0.650797\pi$
$68$	−1141.32			−2.03537
$69$	−643.615	+	770.040i	−1.12293	+	1.34351i
$70$	−427.038	−	13.4421i	−0.729155	−	0.0229520i
$71$		−	319.460i		−	0.533984i	−0.963699	−	0.266992i	$-0.913970\pi$
$71$		−	319.460i		−	0.533984i	0.963699	−	0.266992i	$-0.0860298\pi$
$72$	−648.262	+	116.885i	−1.06109	+	0.191319i
$73$			555.337i			0.890374i	0.895438	+	0.445187i	$0.146863\pi$
$73$			555.337i			0.890374i	−0.895438	+	0.445187i	$0.853137\pi$
$74$			40.2140i			0.0631728i
$75$	99.6729	+	83.3086i	0.153456	+	0.128262i
$76$		−	82.9283i		−	0.125165i
$77$	−1210.56	−	38.1054i	−1.79163	−	0.0563963i
$78$	−569.121	−	475.683i	−0.826157	−	0.690518i
$79$	842.582			1.19997			0.599987	−	0.800010i	$-0.295173\pi$
$79$	842.582			1.19997			0.599987	+	0.800010i	$0.295173\pi$
$80$	31.3095			0.0437564
$81$	−683.093	+	254.607i	−0.937028	+	0.349255i
$82$		−	1788.28i		−	2.40832i
$83$	−887.665			−1.17390			−0.586951	−	0.809622i	$-0.699672\pi$
$83$	−887.665			−1.17390			−0.586951	+	0.809622i	$0.699672\pi$
$84$	−850.527	+	954.862i	−1.10476	+	1.24029i
$85$	429.463			0.548022
$86$			1297.57i			1.62699i
$87$	−102.331	+	122.432i	−0.126104	+	0.150875i
$88$	1595.46			1.93269
$89$	480.245			0.571976			0.285988	−	0.958233i	$-0.407678\pi$
$89$	480.245			0.571976			0.285988	+	0.958233i	$0.407678\pi$
$90$	612.987	−	110.524i	0.717939	−	0.129448i
$91$	−572.710	−	18.0275i	−0.659740	−	0.0207670i
$92$		−	2566.42i		−	2.90834i
$93$	−203.589	+	243.580i	−0.227003	+	0.271593i
$94$		−	962.120i		−	1.05569i
$95$			31.2048i			0.0337005i
$96$	−554.113	+	662.957i	−0.589103	+	0.704821i
$97$			477.578i			0.499904i	0.968258	+	0.249952i	$0.0804149\pi$
$97$			477.578i			0.499904i	−0.968258	+	0.249952i	$0.919585\pi$
$98$	−99.5315	+	1579.42i	−0.102594	+	1.62802i
$99$	1737.68	−	313.312i	1.76408	−	0.318071i
$100$	−332.193			−0.332193
$101$	1177.46			1.16002			0.580009	−	0.814610i	$-0.303049\pi$
$101$	1177.46			1.16002			0.580009	+	0.814610i	$0.303049\pi$
$102$	1320.60	−	1580.00i	1.28195	−	1.53376i
$103$		−	236.191i		−	0.225948i	−0.993598	−	0.112974i	$-0.963962\pi$
$103$		−	236.191i		−	0.225948i	0.993598	−	0.112974i	$-0.0360376\pi$
$104$	754.808			0.711683
$105$	320.042	−	359.302i	0.297456	−	0.333946i
$106$	−977.225			−0.895438
$107$			381.844i			0.344993i	0.985010	+	0.172497i	$0.0551834\pi$
$107$			381.844i			0.344993i	−0.985010	+	0.172497i	$0.944817\pi$
$108$	922.757	−	1619.82i	0.822151	−	1.44322i
$109$	−66.2128			−0.0581838			−0.0290919	−	0.999577i	$-0.509262\pi$
$109$	−66.2128			−0.0581838			−0.0290919	+	0.999577i	$0.509262\pi$
$110$	−1508.65			−1.30767
$111$	−34.7496	−	29.0444i	−0.0297143	−	0.0248358i
$112$	3.64872	−	115.915i	0.00307832	−	0.0977939i
$113$			1640.52i			1.36573i	0.730545	+	0.682864i	$0.239266\pi$
$113$			1640.52i			1.36573i	−0.730545	+	0.682864i	$0.760734\pi$
$114$	114.803	+	95.9547i	0.0943184	+	0.0788332i
$115$			965.709i			0.783068i
$116$		−	408.046i		−	0.326604i
$117$	822.090	−	148.227i	0.649592	−	0.117125i
$118$		−	987.333i		−	0.770266i
$119$	50.0484	−	1589.97i	0.0385540	−	1.22481i
$120$	−406.494	+	486.341i	−0.309230	+	0.369972i
$121$	−2945.68			−2.21313
$122$	3108.20			2.30659
$123$	1545.28	+	1291.58i	1.13279	+	0.946809i
$124$		−	811.813i		−	0.587927i
$125$	125.000			0.0894427
$126$	−337.750	−	2282.29i	−0.238803	−	1.61367i
$127$	405.224			0.283133			0.141566	−	0.989929i	$-0.454786\pi$
$127$	405.224			0.283133			0.141566	+	0.989929i	$0.454786\pi$
$128$		−	2440.66i		−	1.68536i
$129$	−1121.25	−	937.166i	−0.765278	−	0.639635i
$130$	−713.736			−0.481529
$131$	−2002.74			−1.33573			−0.667865	−	0.744283i	$-0.732792\pi$
$131$	−2002.74			−1.33573			−0.667865	+	0.744283i	$0.732792\pi$
$132$	−2895.70	+	3464.50i	−1.90938	+	2.28444i
$133$	115.527	+	3.63652i	0.0753194	+	0.00237087i
$134$			2308.77i			1.48841i
$135$	−347.221	+	609.518i	−0.221363	+	0.388585i
$136$			2095.51i			1.32124i
$137$		−	2374.19i		−	1.48059i	−0.672281	−	0.740296i	$-0.734685\pi$
$137$		−	2374.19i		−	1.48059i	0.672281	−	0.740296i	$-0.265315\pi$
$138$	3552.86	+	2969.55i	2.19159	+	1.83178i
$139$		−	1018.72i		−	0.621631i	−0.950470	−	0.310815i	$-0.899398\pi$
$139$		−	1018.72i		−	0.621631i	0.950470	−	0.310815i	$-0.100602\pi$
$140$	−38.7128	+	1229.85i	−0.0233702	+	0.742439i
$141$	831.384	+	694.887i	0.496561	+	0.415036i
$142$	−1473.94			−0.871060
$143$	−2023.28			−1.18318
$144$	30.0006	+	166.389i	0.0173615	+	0.0962897i
$145$			153.542i			0.0879379i
$146$	2562.25			1.45242
$147$	−1292.92	−	1226.74i	−0.725429	−	0.688297i
$148$	115.815			0.0643237
$149$		−	1957.03i		−	1.07601i	−0.842941	−	0.538007i	$-0.819178\pi$
$149$		−	1957.03i		−	1.07601i	0.842941	−	0.538007i	$-0.180822\pi$
$150$	384.374	−	459.877i	0.209227	−	0.250325i
$151$	965.606			0.520397			0.260198	−	0.965555i	$-0.416212\pi$
$151$	965.606			0.520397			0.260198	+	0.965555i	$0.416212\pi$
$152$	−152.260			−0.0812495
$153$	411.510	+	2282.30i	0.217442	+	1.20597i
$154$	−175.813	+	5585.34i	−0.0919964	+	2.92260i
$155$			305.475i			0.158299i
$156$	−1369.95	+	1639.04i	−0.703099	+	0.841208i
$157$			1279.67i			0.650501i	0.945628	+	0.325250i	$0.105449\pi$
$157$			1279.67i			0.650501i	−0.945628	+	0.325250i	$0.894551\pi$
$158$		−	3887.56i		−	1.95745i
$159$	705.797	−	844.436i	0.352033	−	0.421183i
$160$			831.416i			0.410808i
$161$	3575.27	+	112.541i	1.75013	+	0.0550898i
$162$	1174.72	+	3151.70i	0.569722	+	1.52852i
$163$	−1558.78			−0.749039			−0.374520	−	0.927219i	$-0.622192\pi$
$163$	−1558.78			−0.749039			−0.374520	+	0.927219i	$0.622192\pi$
$164$	−5150.16			−2.45220
$165$	1089.61	−	1303.65i	0.514099	−	0.615084i
$166$			4095.57i			1.91492i
$167$	428.816			0.198699			0.0993495	−	0.995053i	$-0.468324\pi$
$167$	428.816			0.198699			0.0993495	+	0.995053i	$0.468324\pi$
$168$	1753.17	+	1561.60i	0.805118	+	0.717145i
$169$	1239.79			0.564312
$170$		−	1981.49i		−	0.893959i
$171$	−165.832	+	29.9003i	−0.0741608	+	0.0133716i
$172$	3736.95			1.65663
$173$	1708.89			0.751010			0.375505	−	0.926820i	$-0.377469\pi$
$173$	1708.89			0.751010			0.375505	+	0.926820i	$0.377469\pi$
$174$	564.885	+	472.142i	0.246114	+	0.205707i
$175$	14.5671	−	462.777i	0.00629241	−	0.199901i
$176$		−	409.506i		−	0.175384i
$177$	853.171	+	713.097i	0.362306	+	0.302823i
$178$		−	2215.78i		−	0.933034i
$179$		−	1129.27i		−	0.471541i	−0.971809	−	0.235770i	$-0.924239\pi$
$179$		−	1129.27i		−	0.471541i	0.971809	−	0.235770i	$-0.0757613\pi$
$180$	−318.306	−	1765.38i	−0.131806	−	0.731019i
$181$		−	3997.53i		−	1.64162i	−0.571198	−	0.820812i	$-0.693521\pi$
$181$		−	3997.53i		−	1.64162i	0.571198	−	0.820812i	$-0.306479\pi$
$182$	−83.1766	+	2642.41i	−0.0338762	+	1.07620i
$183$	−2244.89	+	2685.85i	−0.906814	+	1.08494i
$184$	−4712.05			−1.88792
$185$	−43.5796			−0.0173191
$186$	1123.85	+	939.334i	0.443035	+	0.370297i
$187$		−	5617.06i		−	2.19658i
$188$	−2770.87			−1.07493
$189$	2216.10	+	1356.52i	0.852899	+	0.522076i
$190$	143.975			0.0549739
$191$		−	544.334i		−	0.206213i	−0.994670	−	0.103106i	$-0.967122\pi$
$191$		−	544.334i		−	0.206213i	0.994670	−	0.103106i	$-0.0328782\pi$
$192$	3258.52	+	2723.54i	1.22481	+	1.02372i
$193$	−4438.14			−1.65526			−0.827628	−	0.561276i	$-0.810310\pi$
$193$	−4438.14			−1.65526			−0.827628	+	0.561276i	$0.810310\pi$
$194$	2203.48			0.815467
$195$	515.493	−	616.751i	0.189309	−	0.226495i
$196$	4548.67	+	286.646i	1.65768	+	0.104463i
$197$			1163.82i			0.420906i	0.977604	+	0.210453i	$0.0674939\pi$
$197$			1163.82i			0.420906i	−0.977604	+	0.210453i	$0.932506\pi$
$198$	−1445.58	−	8017.42i	−0.518853	−	2.87764i
$199$		−	2295.86i		−	0.817837i	−0.912571	−	0.408918i	$-0.865906\pi$
$199$		−	2295.86i		−	0.817837i	0.912571	−	0.408918i	$-0.134094\pi$
$200$			609.921i			0.215640i
$201$	−1995.05	−	1667.50i	−0.700099	−	0.585156i
$202$		−	5432.65i		−	1.89228i
$203$	568.447	+	17.8934i	0.196538	+	0.00618654i
$204$	−4550.34	−	3803.27i	−1.56170	−	1.30530i
$205$	1937.94			0.660251
$206$	−1089.75			−0.368576
$207$	−5132.08	+	925.338i	−1.72321	+	0.310702i
$208$		−	193.736i		−	0.0645825i
$209$	408.136			0.135078
$210$	−1657.77	−	1476.63i	−0.544748	−	0.485225i
$211$	1364.52			0.445200			0.222600	−	0.974910i	$-0.428546\pi$
$211$	1364.52			0.445200			0.222600	+	0.974910i	$0.428546\pi$
$212$			2814.37i			0.911752i
$213$	1064.55	−	1273.66i	0.342449	−	0.409717i
$214$	1761.78			0.562769
$215$	−1406.17			−0.446046
$216$	−2974.06	−	1694.22i	−0.936849	−	0.533691i
$217$	1130.93	+	35.5991i	0.353792	+	0.0111365i
$218$			305.497i			0.0949121i
$219$	−1850.57	+	2214.08i	−0.571005	+	0.683168i
$220$			4344.84i			1.33150i
$221$		−	2657.41i		−	0.808855i
$222$	−134.007	+	160.330i	−0.0405133	+	0.0484713i
$223$		−	782.650i		−	0.235023i	−0.993072	−	0.117511i	$-0.962508\pi$
$223$		−	782.650i		−	0.235023i	0.993072	−	0.117511i	$-0.0374917\pi$
$224$	3078.08	+	96.8907i	0.918139	+	0.0289008i
$225$	119.774	+	664.288i	0.0354887	+	0.196826i
$226$	7569.14			2.22784
$227$	−431.312			−0.126111			−0.0630555	−	0.998010i	$-0.520085\pi$
$227$	−431.312			−0.126111			−0.0630555	+	0.998010i	$0.520085\pi$
$228$	276.346	−	330.628i	0.0802695	−	0.0960368i
$229$			5093.80i			1.46990i	0.678119	+	0.734952i	$0.262795\pi$
$229$			5093.80i			1.46990i	−0.678119	+	0.734952i	$0.737205\pi$
$230$	4455.65			1.27738
$231$	−4699.41	−	4185.92i	−1.33852	−	1.19226i
$232$	−749.190			−0.212012
$233$			3844.93i			1.08107i	0.841321	+	0.540536i	$0.181778\pi$
$233$			3844.93i			1.08107i	−0.841321	+	0.540536i	$0.818222\pi$
$234$	−683.898	−	3793.01i	−0.191059	−	1.05964i
$235$	1042.64			0.289423
$236$	−2843.48			−0.784299
$237$	3359.30	+	2807.77i	0.920718	+	0.769555i
$238$	−7335.89	−	230.916i	−1.99796	−	0.0628911i
$239$		−	1426.08i		−	0.385964i	−0.981202	−	0.192982i	$-0.938184\pi$
$239$		−	1426.08i		−	0.385964i	0.981202	−	0.192982i	$-0.0618159\pi$
$240$	124.828	+	104.334i	0.0335735	+	0.0280614i
$241$			5231.73i			1.39836i	0.714945	+	0.699181i	$0.246452\pi$
$241$			5231.73i			1.39836i	−0.714945	+	0.699181i	$0.753548\pi$
$242$			13591.0i			3.61016i
$243$	−3571.87	−	1261.20i	−0.942945	−	0.332948i
$244$		−	8951.50i		−	2.34861i
$245$	−1711.60	−	107.861i	−0.446328	−	0.0281266i
$246$	5959.15	−	7129.71i	1.54448	−	1.84786i
$247$	193.088			0.0497404
$248$	−1490.53			−0.381647
$249$	−3539.05	−	2958.01i	−0.900714	−	0.752835i
$250$		−	576.733i		−	0.145903i
$251$	−2122.49			−0.533746			−0.266873	−	0.963732i	$-0.585990\pi$
$251$	−2122.49			−0.533746			−0.266873	+	0.963732i	$0.585990\pi$
$252$	−6572.90	+	972.706i	−1.64307	+	0.243154i
$253$	12630.8			3.13869
$254$		−	1869.65i		−	0.461859i
$255$	1712.23	+	1431.12i	0.420487	+	0.351452i
$256$	−4722.44			−1.15294
$257$	−6347.65			−1.54068			−0.770341	−	0.637632i	$-0.779914\pi$
$257$	−6347.65			−1.54068			−0.770341	+	0.637632i	$0.779914\pi$
$258$	−4323.96	+	5173.31i	−1.04340	+	1.24836i
$259$	−5.07863	+	161.341i	−0.00121842	+	0.0387075i
$260$			2055.53i			0.490302i
$261$	−815.971	+	147.123i	−0.193515	+	0.0348916i
$262$			9240.39i			2.17890i
$263$			931.743i			0.218455i	0.994017	+	0.109228i	$0.0348378\pi$
$263$			931.743i			0.218455i	−0.994017	+	0.109228i	$0.965162\pi$
$264$	6360.98	+	5316.64i	1.48292	+	1.23946i
$265$		−	1059.01i		−	0.245488i
$266$	16.7784	−	533.026i	0.00386748	−	0.122864i
$267$	1914.70	+	1600.34i	0.438867	+	0.366814i
$268$	6649.16			1.51553
$269$	−3245.79			−0.735685			−0.367843	−	0.929888i	$-0.619903\pi$
$269$	−3245.79			−0.735685			−0.367843	+	0.929888i	$0.619903\pi$
$270$	2812.23	+	1602.03i	0.633878	+	0.361098i
$271$		−	2735.96i		−	0.613276i	−0.951826	−	0.306638i	$-0.900796\pi$
$271$		−	2735.96i		−	0.613276i	0.951826	−	0.306638i	$-0.0992041\pi$
$272$	537.852			0.119897
$273$	−2223.27	−	1980.34i	−0.492888	−	0.439032i
$274$	−10954.2			−2.41521
$275$		−	1634.91i		−	0.358504i
$276$	8552.18	−	10232.1i	1.86515	−	2.23152i
$277$	−2982.49			−0.646934			−0.323467	−	0.946239i	$-0.604848\pi$
$277$	−2982.49			−0.646934			−0.323467	+	0.946239i	$0.604848\pi$
$278$	−4700.23			−1.01403
$279$	−1623.39	+	292.704i	−0.348350	+	0.0628092i
$280$	2258.06	+	71.0784i	0.481946	+	0.0151705i
$281$		−	2595.38i		−	0.550987i	−0.961303	−	0.275494i	$-0.911159\pi$
$281$		−	2595.38i		−	0.550987i	0.961303	−	0.275494i	$-0.0888413\pi$
$282$	3206.12	−	3835.89i	0.677026	−	0.810014i
$283$		−	6717.96i		−	1.41110i	−0.708660	−	0.705550i	$-0.750700\pi$
$283$		−	6717.96i		−	1.41110i	0.708660	−	0.705550i	$-0.249300\pi$
$284$			4244.89i			0.886930i
$285$	−103.985	+	124.411i	−0.0216125	+	0.0258578i
$286$			9335.14i			1.93006i
$287$	225.842	−	7174.67i	0.0464495	−	1.47564i
$288$	−4418.40	+	796.659i	−0.904017	+	0.162999i
$289$	2464.55			0.501639
$290$	708.423			0.143448
$291$	−1591.45	+	1904.06i	−0.320594	+	0.383568i
$292$		−	7379.17i		−	1.47888i
$293$	7321.08			1.45973			0.729867	−	0.683589i	$-0.239582\pi$
$293$	7321.08			1.45973			0.729867	+	0.683589i	$0.239582\pi$
$294$	−5660.00	+	5965.35i	−1.12278	+	1.18335i
$295$	1069.96			0.211172
$296$		−	212.641i		−	0.0417551i
$297$	7972.05	+	4541.40i	1.55753	+	0.887269i
$298$	−9029.46			−1.75524
$299$	5975.57			1.15577
$300$	−1324.43	−	1106.98i	−0.254886	−	0.213039i
$301$	−163.870	+	5205.94i	−0.0313799	+	0.996894i
$302$		−	4455.17i		−	0.848895i
$303$	4694.44	+	3923.71i	0.890061	+	0.743931i
$304$			39.0804i			0.00737307i
$305$			3368.33i			0.632361i
$306$	10530.2	−	1898.65i	1.96723	−	0.354701i
$307$			7027.37i			1.30643i	0.757173	+	0.653214i	$0.226580\pi$
$307$			7027.37i			1.30643i	−0.757173	+	0.653214i	$0.773420\pi$
$308$	16085.6	+	506.335i	2.97584	+	0.0936724i
$309$	787.070	−	941.674i	0.144902	−	0.173365i
$310$	1409.42			0.258225
$311$	−8857.75			−1.61504			−0.807520	−	0.589841i	$-0.799191\pi$
$311$	−8857.75			−1.61504			−0.807520	+	0.589841i	$0.799191\pi$
$312$	3009.36	+	2515.28i	0.546062	+	0.456409i
$313$			8152.90i			1.47230i	0.676820	+	0.736148i	$0.263357\pi$
$313$			8152.90i			1.47230i	−0.676820	+	0.736148i	$0.736643\pi$
$314$	5904.21			1.06113
$315$	2473.30	−	366.017i	0.442396	−	0.0654689i
$316$	−11196.0			−1.99312
$317$			8636.70i			1.53024i	0.643889	+	0.765119i	$0.277320\pi$
$317$			8636.70i			1.53024i	−0.643889	+	0.765119i	$0.722680\pi$
$318$	−3896.11	−	3256.45i	−0.687054	−	0.574253i
$319$	2008.22			0.352473
$320$	4086.52			0.713885
$321$	−1272.44	+	1522.38i	−0.221247	+	0.264707i
$322$	519.248	−	16495.8i	0.0898651	−	2.85489i
$323$			536.054i			0.0923431i
$324$	9076.76	−	3383.15i	1.55637	−	0.580101i
$325$		−	773.469i		−	0.132013i
$326$			7192.02i			1.22187i
$327$	−263.985	−	220.644i	−0.0446434	−	0.0373138i
$328$			9455.92i			1.59182i
$329$	121.506	−	3860.08i	0.0203613	−	0.646849i
$330$	−6014.85	−	5027.33i	−1.00335	−	0.838623i
$331$	−8444.88			−1.40233			−0.701167	−	0.712997i	$-0.747337\pi$
$331$	−8444.88			−1.40233			−0.701167	+	0.712997i	$0.747337\pi$
$332$	11795.1			1.94981
$333$	−41.7577	−	231.595i	−0.00687180	−	0.0381121i
$334$		−	1978.50i		−	0.324127i
$335$	−2501.99			−0.408055
$336$	400.815	−	449.983i	0.0650781	−	0.0730613i
$337$	−2136.69			−0.345380			−0.172690	−	0.984976i	$-0.555246\pi$
$337$	−2136.69			−0.345380			−0.172690	+	0.984976i	$0.555246\pi$
$338$		−	5720.24i		−	0.920532i
$339$	−5466.78	+	6540.62i	−0.875855	+	1.04790i
$340$	−5706.59			−0.910245
$341$	3995.39			0.634493
$342$	137.956	+	765.127i	0.0218123	+	0.120975i
$343$	−598.791	+	6324.16i	−0.0942615	+	0.995547i
$344$		−	6861.21i		−	1.07538i
$345$	−3218.07	+	3850.20i	−0.502189	+	0.600834i
$346$		−	7884.60i		−	1.22508i
$347$		−	7751.53i		−	1.19920i	−0.800298	−	0.599602i	$-0.795326\pi$
$347$		−	7751.53i		−	1.19920i	0.800298	−	0.599602i	$-0.204674\pi$
$348$	1359.75	−	1626.84i	0.209455	−	0.250598i
$349$		−	8211.51i		−	1.25946i	−0.776814	−	0.629731i	$-0.783165\pi$
$349$		−	8211.51i		−	1.25946i	0.776814	−	0.629731i	$-0.216835\pi$
$350$	−2135.19	−	67.2107i	−0.326088	−	0.0102645i
$351$	3771.55	+	2148.52i	0.573533	+	0.326722i
$352$	10874.3			1.64660
$353$	5500.56			0.829364			0.414682	−	0.909966i	$-0.363893\pi$
$353$	5500.56			0.829364			0.414682	+	0.909966i	$0.363893\pi$
$354$	3290.13	−	3936.41i	0.493979	−	0.591011i
$355$		−	1597.30i		−	0.238805i
$356$	−6381.37			−0.950033
$357$	5497.86	−	6172.28i	0.815063	−	0.915047i
$358$	−5210.31			−0.769200
$359$			7487.50i			1.10077i	0.834912	+	0.550383i	$0.185518\pi$
$359$			7487.50i			1.10077i	−0.834912	+	0.550383i	$0.814482\pi$
$360$	−3241.31	+	584.424i	−0.474533	+	0.0855606i
$361$	6820.05			0.994321
$362$	−18444.1			−2.67790
$363$	−11744.2	−	9816.01i	−1.69810	−	1.41930i
$364$	7610.02	+	239.545i	1.09581	+	0.0344933i
$365$			2776.69i			0.398187i
$366$	12392.1	+	10357.6i	1.76980	+	1.47924i
$367$		−	2158.05i		−	0.306946i	−0.988153	−	0.153473i	$-0.950954\pi$
$367$		−	2158.05i		−	0.306946i	0.988153	−	0.153473i	$-0.0490458\pi$
$368$			1209.44i			0.171321i
$369$	1856.92	+	10298.8i	0.261972	+	1.45294i
$370$			201.070i			0.0282517i
$371$	−3920.68	−	123.414i	−0.548657	−	0.0172704i
$372$	2705.24	−	3236.63i	0.377044	−	0.451106i
$373$	3989.15			0.553755			0.276877	−	0.960905i	$-0.410700\pi$
$373$	3989.15			0.553755			0.276877	+	0.960905i	$0.410700\pi$
$374$	−25916.4			−3.58316
$375$	498.364	+	416.543i	0.0686278	+	0.0573605i
$376$			5087.43i			0.697777i
$377$	950.082			0.129792
$378$	6258.80	−	10224.8i	0.851635	−	1.39129i
$379$	−6120.41			−0.829510			−0.414755	−	0.909933i	$-0.636133\pi$
$379$	−6120.41			−0.829510			−0.414755	+	0.909933i	$0.636133\pi$
$380$		−	414.642i		−	0.0559754i
$381$	1615.60	+	1350.35i	0.217243	+	0.181576i
$382$	−2511.48			−0.336384
$383$	7418.34			0.989711			0.494856	−	0.868975i	$-0.335221\pi$
$383$	7418.34			0.989711			0.494856	+	0.868975i	$0.335221\pi$
$384$	8133.12	−	9730.70i	1.08084	−	1.29315i
$385$	−6052.79	−	190.527i	−0.801243	−	0.0252212i
$386$			20477.0i			2.70013i
$387$	−1347.38	−	7472.80i	−0.176980	−	0.981561i
$388$		−	6345.93i		−	0.830324i
$389$			10680.3i			1.39206i	0.718012	+	0.696031i	$0.245052\pi$
$389$			10680.3i			1.39206i	−0.718012	+	0.696031i	$0.754948\pi$
$390$	−2845.60	−	2378.41i	−0.369469	−	0.308809i
$391$			16589.5i			2.14569i
$392$	526.295	−	8351.55i	0.0678111	−	1.07606i
$393$	−7984.77	−	6673.83i	−1.02488	−	0.856616i
$394$	5369.69			0.686601
$395$	4212.91			0.536644
$396$	−23089.8	+	4163.21i	−2.93007	+	0.528305i
$397$			7169.57i			0.906374i	0.891415	+	0.453187i	$0.149713\pi$
$397$			7169.57i			0.906374i	−0.891415	+	0.453187i	$0.850287\pi$
$398$	−10592.8			−1.33409
$399$	448.479	+	399.475i	0.0562707	+	0.0501222i
$400$	156.548			0.0195685
$401$		−	3463.68i		−	0.431341i	−0.976466	−	0.215671i	$-0.930806\pi$
$401$		−	3463.68i		−	0.431341i	0.976466	−	0.215671i	$-0.0691938\pi$
$402$	−7693.62	+	9204.88i	−0.954535	+	1.14203i
$403$	1890.20			0.233642
$404$	−15645.8			−1.92675
$405$	−3415.47	+	1273.04i	−0.419051	+	0.156192i
$406$	82.5575	−	2622.74i	0.0100918	−	0.320602i
$407$			569.989i			0.0694184i
$408$	−6982.96	+	8354.62i	−0.847324	+	1.01376i
$409$		−	12770.9i		−	1.54396i	−0.635646	−	0.771980i	$-0.719266\pi$
$409$		−	12770.9i		−	1.54396i	0.635646	−	0.771980i	$-0.280734\pi$
$410$		−	8941.38i		−	1.07703i
$411$	7911.63	−	9465.71i	0.949518	−	1.13603i
$412$			3138.44i			0.375291i
$413$	124.690	−	3961.24i	0.0148562	−	0.471961i
$414$	4269.38	+	23678.7i	0.506832	+	2.81098i
$415$	−4438.33			−0.524985
$416$	5144.60			0.606333
$417$	3394.72	−	4061.55i	0.398658	−	0.476966i
$418$		−	1883.09i		−	0.220346i
$419$	15235.0			1.77632			0.888159	−	0.459536i	$-0.151984\pi$
$419$	15235.0			1.77632			0.888159	+	0.459536i	$0.151984\pi$
$420$	−4252.63	+	4774.31i	−0.494065	+	0.554673i
$421$	−7109.57			−0.823039			−0.411519	−	0.911401i	$-0.635002\pi$
$421$	−7109.57			−0.823039			−0.411519	+	0.911401i	$0.635002\pi$
$422$		−	6295.70i		−	0.726232i
$423$	999.053	+	5540.91i	0.114836	+	0.636899i
$424$	5167.30			0.591854
$425$	2147.32			0.245083
$426$	−5876.48	−	4911.68i	−0.668349	−	0.558619i
$427$	12470.3	+	392.535i	1.41330	+	0.0444874i
$428$		−	5073.84i		−	0.573022i
$429$	−8066.65	−	6742.27i	−0.907835	−	0.758787i
$430$			6487.86i			0.727610i
$431$		−	6091.94i		−	0.680832i	−0.940275	−	0.340416i	$-0.889432\pi$
$431$		−	6091.94i		−	0.680832i	0.940275	−	0.340416i	$-0.110568\pi$
$432$	−434.854	+	763.349i	−0.0484304	+	0.0850154i
$433$			1238.51i			0.137457i	0.997635	+	0.0687285i	$0.0218942\pi$
$433$			1238.51i			0.137457i	−0.997635	+	0.0687285i	$0.978106\pi$
$434$	164.249	−	5217.98i	0.0181664	−	0.577122i
$435$	−511.656	+	612.160i	−0.0563954	+	0.0674732i
$436$	879.817			0.0966413
$437$	−1205.39			−0.131949
$438$	10215.5	+	8538.29i	1.11442	+	0.931451i
$439$		−	2934.43i		−	0.319027i	−0.987196	−	0.159513i	$-0.949007\pi$
$439$		−	2934.43i		−	0.319027i	0.987196	−	0.159513i	$-0.0509925\pi$
$440$	7977.32			0.864327
$441$	−1066.84	−	9199.35i	−0.115197	−	0.993343i
$442$	−12260.9			−1.31944
$443$		−	1995.37i		−	0.214002i	−0.994259	−	0.107001i	$-0.965875\pi$
$443$		−	1995.37i		−	0.214002i	0.994259	−	0.107001i	$-0.0341247\pi$
$444$	461.743	+	385.934i	0.0493544	+	0.0412514i
$445$	2401.23			0.255795
$446$	−3611.04			−0.383380
$447$	6521.49	−	7802.50i	0.690058	−	0.825606i
$448$	476.230	−	15129.2i	0.0502227	−	1.59551i
$449$		−	8336.05i		−	0.876175i	−0.898932	−	0.438088i	$-0.855656\pi$
$449$		−	8336.05i		−	0.876175i	0.898932	−	0.438088i	$-0.144344\pi$
$450$	3064.94	−	552.622i	0.321072	−	0.0578908i
$451$		−	25346.8i		−	2.64642i
$452$		−	21798.8i		−	2.26843i
$453$	3849.79	+	3217.73i	0.399291	+	0.333735i
$454$			1990.02i			0.205718i
$455$	−2863.55	−	90.1377i	−0.295045	−	0.00928730i
$456$	−607.048	−	507.383i	−0.0623413	−	0.0521061i
$457$	−4202.63			−0.430177			−0.215088	−	0.976595i	$-0.569004\pi$
$457$	−4202.63			−0.430177			−0.215088	+	0.976595i	$0.569004\pi$
$458$	23502.1			2.39778
$459$	−5964.76	+	10470.6i	−0.606560	+	1.06476i
$460$		−	12832.1i		−	1.30065i
$461$	−2079.74			−0.210116			−0.105058	−	0.994466i	$-0.533503\pi$
$461$	−2079.74			−0.210116			−0.105058	+	0.994466i	$0.533503\pi$
$462$	−19313.2	+	21682.4i	−1.94488	+	2.18346i
$463$	18876.0			1.89469			0.947344	−	0.320219i	$-0.103757\pi$
$463$	18876.0			1.89469			0.947344	+	0.320219i	$0.103757\pi$
$464$			192.294i			0.0192392i
$465$	−1017.95	+	1217.90i	−0.101519	+	0.121460i
$466$	17740.0			1.76349
$467$	−13053.4			−1.29345			−0.646725	−	0.762723i	$-0.723862\pi$
$467$	−13053.4			−1.29345			−0.646725	+	0.762723i	$0.723862\pi$
$468$	−10923.7	+	1969.60i	−1.07895	+	0.194540i
$469$	−291.575	+	9262.93i	−0.0287072	+	0.911988i
$470$		−	4810.60i		−	0.472120i
$471$	−4264.29	+	5101.93i	−0.417172	+	0.499118i
$472$			5220.75i			0.509120i
$473$			18391.6i			1.78784i
$474$	12954.7	−	15499.4i	1.25533	−	1.50192i
$475$			156.024i			0.0150713i
$476$	−665.029	+	21127.1i	−0.0640369	+	2.03436i
$477$	5627.90	−	1014.74i	0.540218	−	0.0974039i
$478$	−6579.73			−0.629602
$479$	17589.1			1.67780			0.838898	−	0.544289i	$-0.183200\pi$
$479$	17589.1			1.67780			0.838898	+	0.544289i	$0.183200\pi$
$480$	−2770.56	+	3314.79i	−0.263455	+	0.315205i
$481$			269.659i			0.0255622i
$482$	24138.5			2.28107
$483$	13879.3	+	12362.7i	1.30751	+	1.16464i
$484$	39141.4			3.67594
$485$			2387.89i			0.223564i
$486$	−5819.02	+	16480.1i	−0.543120	+	1.53818i
$487$	−13335.6			−1.24085			−0.620426	−	0.784265i	$-0.713040\pi$
$487$	−13335.6			−1.24085			−0.620426	+	0.784265i	$0.713040\pi$
$488$	−16435.3			−1.52458
$489$	−6214.74	−	5194.40i	−0.574724	−	0.480366i
$490$	−497.657	+	7897.11i	−0.0458814	+	0.728072i
$491$		−	5242.11i		−	0.481819i	−0.970548	−	0.240910i	$-0.922554\pi$
$491$		−	5242.11i		−	0.481819i	0.970548	−	0.240910i	$-0.0774457\pi$
$492$	−20533.3	−	17162.1i	−1.88153	−	1.57262i
$493$			2637.63i			0.240959i
$494$		−	890.881i		−	0.0811389i
$495$	8688.40	−	1566.56i	0.788919	−	0.142246i
$496$			382.571i			0.0346330i
$497$	−5913.55	−	186.144i	−0.533720	−	0.0168002i
$498$	−13647.8	+	16328.7i	−1.22806	+	1.46929i
$499$	−2586.43			−0.232033			−0.116017	−	0.993247i	$-0.537013\pi$
$499$	−2586.43			−0.232033			−0.116017	+	0.993247i	$0.537013\pi$
$500$	−1660.97			−0.148561
$501$	1709.65	+	1428.96i	0.152458	+	0.127428i
$502$			9792.87i			0.870671i
$503$	−11209.5			−0.993648			−0.496824	−	0.867851i	$-0.665501\pi$
$503$	−11209.5			−0.993648			−0.496824	+	0.867851i	$0.665501\pi$
$504$	1785.93	+	12068.1i	0.157841	+	1.06658i
$505$	5887.31			0.518776
$506$		−	58276.6i		−	5.11998i
$507$	4942.95	+	4131.42i	0.432987	+	0.361899i
$508$	−5384.51			−0.470274
$509$	−7789.54			−0.678321			−0.339160	−	0.940729i	$-0.610143\pi$
$509$	−7789.54			−0.678321			−0.339160	+	0.940729i	$0.610143\pi$
$510$	6602.99	−	7900.01i	0.573304	−	0.685918i
$511$	10279.9	+	323.587i	0.889933	+	0.0280130i
$512$			2263.42i			0.195371i
$513$	−760.797	−	433.400i	−0.0654776	−	0.0373003i
$514$			29287.2i			2.51323i
$515$		−	1180.96i		−	0.101047i
$516$	14898.9	+	12452.8i	1.27110	+	1.06241i
$517$		−	13637.0i		−	1.16006i
$518$	744.406	+	23.4321i	0.0631415	+	0.00198754i
$519$	6813.21	+	5694.62i	0.576236	+	0.481630i
$520$	3774.04			0.318274
$521$	11342.0			0.953749			0.476874	−	0.878971i	$-0.341770\pi$
$521$	11342.0			0.953749			0.476874	+	0.878971i	$0.341770\pi$
$522$	678.808	+	3764.78i	0.0569169	+	0.315670i
$523$			13306.6i			1.11254i	0.831003	+	0.556269i	$0.187767\pi$
$523$			13306.6i			1.11254i	−0.831003	+	0.556269i	$0.812233\pi$
$524$	26611.9			2.21860
$525$	1600.21	−	1796.51i	0.133027	−	0.149345i
$526$	4298.94			0.356355
$527$			5247.61i			0.433756i
$528$	1364.61	−	1632.66i	0.112476	−	0.134569i
$529$	−25136.8			−2.06598
$530$	−4886.12			−0.400452
$531$	1025.23	+	5686.12i	0.0837879	+	0.464701i
$532$	−1535.09	−	48.3211i	−0.125103	−	0.00393794i
$533$		−	11991.5i		−	0.974501i
$534$	7383.76	−	8834.14i	0.598364	−	0.715900i
$535$			1909.22i			0.154286i
$536$		−	12208.2i		−	0.983791i
$537$	3763.12	−	4502.31i	0.302404	−	0.361805i
$538$			14975.6i			1.20008i
$539$	−1410.75	+	22386.5i	−0.112737	+	1.78897i
$540$	4613.78	−	8099.11i	0.367677	−	0.645426i
$541$	−11369.5			−0.903533			−0.451767	−	0.892136i	$-0.649206\pi$
$541$	−11369.5			−0.903533			−0.451767	+	0.892136i	$0.649206\pi$
$542$	−12623.4			−1.00040
$543$	13321.1	−	15937.8i	1.05279	−	1.25959i
$544$			14282.5i			1.12566i
$545$	−331.064			−0.0260206
$546$	−9137.02	+	10257.9i	−0.716169	+	0.804023i
$547$	−15590.8			−1.21867			−0.609336	−	0.792912i	$-0.708564\pi$
$547$	−15590.8			−1.21867			−0.609336	+	0.792912i	$0.708564\pi$
$548$			31547.6i			2.45921i
$549$	−17900.4	+	3227.52i	−1.39156	+	0.250906i
$550$	−7543.24			−0.584809
$551$	−191.651			−0.0148178
$552$	−18786.6	−	15702.2i	−1.44857	−	1.21074i
$553$	490.960	−	15597.1i	0.0377536	−	1.19938i
$554$			13760.8i			1.05531i
$555$	−173.748	−	145.222i	−0.0132886	−	0.0111069i
$556$			13536.5i			1.03251i
$557$			6966.49i			0.529946i	0.964256	+	0.264973i	$0.0853630\pi$
$557$			6966.49i			0.529946i	−0.964256	+	0.264973i	$0.914637\pi$
$558$	1350.50	+	7490.09i	0.102457	+	0.568245i
$559$			8701.01i			0.658343i
$560$	18.2436	−	579.574i	0.00137667	−	0.0437348i
$561$	18718.0	−	22394.8i	1.40869	−	1.68540i
$562$	−11974.7			−0.898796
$563$	−13867.2			−1.03807			−0.519035	−	0.854753i	$-0.673709\pi$
$563$	−13867.2			−1.03807			−0.519035	+	0.854753i	$0.673709\pi$
$564$	−11047.2	−	9233.48i	−0.824772	−	0.689361i
$565$			8202.61i			0.610772i
$566$	−30995.8			−2.30185
$567$	4315.03	+	12793.2i	0.319602	+	0.947552i
$568$	7793.81			0.575741
$569$			14357.4i			1.05781i	0.848680	+	0.528906i	$0.177398\pi$
$569$			14357.4i			1.05781i	−0.848680	+	0.528906i	$0.822602\pi$
$570$	574.016	+	479.774i	0.0421805	+	0.0352553i
$571$	15732.7			1.15305			0.576526	−	0.817079i	$-0.304408\pi$
$571$	15732.7			1.15305			0.576526	+	0.817079i	$0.304408\pi$
$572$	26884.8			1.96523
$573$	1813.91	−	2170.21i	0.132246	−	0.158223i
$574$	−33103.0	−	1042.00i	−2.40713	−	0.0757706i
$575$			4828.55i			0.350199i
$576$	3915.68	+	21717.0i	0.283252	+	1.57096i
$577$		−	15847.2i		−	1.14337i	−0.820472	−	0.571686i	$-0.806290\pi$
$577$		−	15847.2i		−	1.14337i	0.820472	−	0.571686i	$-0.193710\pi$
$578$		−	11371.1i		−	0.818297i
$579$	−17694.5	−	14789.4i	−1.27005	−	1.06153i
$580$		−	2040.23i		−	0.146062i
$581$	−517.229	+	16431.7i	−0.0369334	+	1.17332i
$582$	8785.09	+	7342.75i	0.625694	+	0.522967i
$583$	−13851.1			−0.983966
$584$	−13548.5			−0.960000
$585$	4110.45	−	741.134i	0.290506	−	0.0523797i
$586$		−	33778.5i		−	2.38119i
$587$	−18831.4			−1.32411			−0.662055	−	0.749455i	$-0.730316\pi$
$587$	−18831.4			−1.32411			−0.662055	+	0.749455i	$0.730316\pi$
$588$	17179.9	+	16300.6i	1.20491	+	1.14324i
$589$	−381.292			−0.0266738
$590$		−	4936.66i		−	0.344473i
$591$	−3878.23	+	4640.03i	−0.269931	+	0.322953i
$592$	−54.5783			−0.00378911
$593$	1882.77			0.130381			0.0651905	−	0.997873i	$-0.479234\pi$
$593$	1882.77			0.130381			0.0651905	+	0.997873i	$0.479234\pi$
$594$	20953.4	−	36781.9i	1.44735	−	2.54071i
$595$	250.242	−	7949.84i	0.0172419	−	0.547750i
$596$			26004.5i			1.78722i
$597$	7650.61	−	9153.42i	0.524487	−	0.627511i
$598$		−	27570.4i		−	1.88535i
$599$		−	11287.0i		−	0.769906i	−0.922936	−	0.384953i	$-0.874218\pi$
$599$		−	11287.0i		−	0.769906i	0.922936	−	0.384953i	$-0.125782\pi$
$600$	−2032.47	+	2431.70i	−0.138292	+	0.165457i
$601$		−	1723.22i		−	0.116958i	−0.998289	−	0.0584789i	$-0.981375\pi$
$601$		−	1723.22i		−	0.116958i	0.998289	−	0.0584789i	$-0.0186250\pi$
$602$	24019.5	+	756.076i	1.62618	+	0.0511883i
$603$	−2397.40	−	13296.4i	−0.161906	−	0.897960i
$604$	−12830.7			−0.864361
$605$	−14728.4			−0.989742
$606$	18103.4	−	21659.5i	1.21353	−	1.45191i
$607$			12098.5i			0.808997i	0.914539	+	0.404498i	$0.132554\pi$
$607$			12098.5i			0.808997i	−0.914539	+	0.404498i	$0.867446\pi$
$608$	−1037.77			−0.0692222
$609$	2206.72	+	1965.60i	0.146832	+	0.130788i
$610$	15541.0			1.03154
$611$		−	6451.60i		−	0.427175i
$612$	−5468.03	−	30326.6i	−0.361163	−	2.00307i
$613$	5440.08			0.358438			0.179219	−	0.983809i	$-0.442643\pi$
$613$	5440.08			0.358438			0.179219	+	0.983809i	$0.442643\pi$
$614$	32423.3			2.13111
$615$	7726.40	+	6457.88i	0.506599	+	0.423426i
$616$	929.653	−	29533.8i	0.0608065	−	1.93174i
$617$			4755.92i			0.310318i	0.987890	+	0.155159i	$0.0495890\pi$
$617$			4755.92i			0.310318i	−0.987890	+	0.155159i	$0.950411\pi$
$618$	−4344.75	−	3631.43i	−0.282802	−	0.236372i
$619$		−	1077.63i		−	0.0699734i	−0.999388	−	0.0349867i	$-0.988861\pi$
$619$		−	1077.63i		−	0.0699734i	0.999388	−	0.0349867i	$-0.0111389\pi$
$620$		−	4059.07i		−	0.262929i
$621$	−23544.7	−	13412.6i	−1.52144	−	0.866713i
$622$			40868.5i			2.63453i
$623$	279.832	−	8889.86i	0.0179955	−	0.571693i
$624$	645.594	−	772.408i	0.0414174	−	0.0495530i
$625$	625.000			0.0400000
$626$	37616.3			2.40168
$627$	1627.20	+	1360.05i	0.103643	+	0.0866271i
$628$		−	17003.9i		−	1.08046i
$629$	−748.633			−0.0474562
$630$	−1688.75	−	11411.5i	−0.106796	−	0.721656i
$631$	−9647.56			−0.608658			−0.304329	−	0.952567i	$-0.598432\pi$
$631$	−9647.56			−0.608658			−0.304329	+	0.952567i	$0.598432\pi$
$632$			20556.4i			1.29381i
$633$	5440.22	+	4547.04i	0.341594	+	0.285511i
$634$	39848.5			2.49619
$635$	2026.12			0.126621
$636$	−9378.43	+	11220.6i	−0.584716	+	0.699571i
$637$	−667.419	+	10591.0i	−0.0415135	+	0.658760i
$638$		−	9265.65i		−	0.574970i
$639$	8488.53	−	1530.52i	0.525510	−	0.0947520i
$640$		−	12203.3i		−	0.753715i
$641$			5927.19i			0.365226i	0.983185	+	0.182613i	$0.0584555\pi$
$641$			5927.19i			0.365226i	−0.983185	+	0.182613i	$0.941544\pi$
$642$	7024.05	+	5870.84i	0.431803	+	0.360909i
$643$			431.199i			0.0264460i	0.999913	+	0.0132230i	$0.00420914\pi$
$643$			431.199i			0.0264460i	−0.999913	+	0.0132230i	$0.995791\pi$
$644$	−47507.2	−	1495.41i	−2.90690	−	0.0915023i
$645$	−5606.27	−	4685.83i	−0.342243	−	0.286053i
$646$	2473.28			0.150634
$647$	−5165.60			−0.313881			−0.156940	−	0.987608i	$-0.550163\pi$
$647$	−5165.60			−0.313881			−0.156940	+	0.987608i	$0.550163\pi$
$648$	−6211.61	−	16665.3i	−0.376567	−	1.01030i
$649$		−	13994.3i		−	0.846419i
$650$	−3568.68			−0.215346
$651$	4390.31	+	3910.59i	0.264316	+	0.235435i
$652$	20712.7			1.24413
$653$		−	9518.46i		−	0.570423i	−0.958465	−	0.285211i	$-0.907936\pi$
$653$		−	9518.46i		−	0.570423i	0.958465	−	0.285211i	$-0.0920638\pi$
$654$	−1018.02	+	1217.99i	−0.0608681	+	0.0728244i
$655$	−10013.7			−0.597356
$656$	2427.04			0.144451
$657$	−14756.2	+	2660.61i	−0.876244	+	0.157991i
$658$	−17809.9	−	560.613i	−1.05517	−	0.0332142i
$659$		−	21188.2i		−	1.25247i	−0.779636	−	0.626233i	$-0.784596\pi$
$659$		−	21188.2i		−	1.25247i	0.779636	−	0.626233i	$-0.215404\pi$
$660$	−14478.5	+	17322.5i	−0.853902	+	1.02163i
$661$			9084.73i			0.534577i	0.963617	+	0.267288i	$0.0861276\pi$
$661$			9084.73i			0.534577i	−0.963617	+	0.267288i	$0.913872\pi$
$662$			38963.5i			2.28755i
$663$	8855.41	−	10594.9i	0.518726	−	0.620620i
$664$		−	21656.2i		−	1.26570i
$665$	577.636	+	18.1826i	0.0336838	+	0.00106029i
$666$	−1068.55	+	192.664i	−0.0621703	+	0.0112096i
$667$	−5931.09			−0.344307
$668$	−5697.99			−0.330032
$669$	2608.06	−	3120.36i	0.150723	−	0.180329i
$670$			11543.9i			0.665639i
$671$	44055.3			2.53463
$672$	11949.2	+	10643.5i	0.685937	+	0.610987i
$673$	−27912.6			−1.59874			−0.799369	−	0.600841i	$-0.794833\pi$
$673$	−27912.6			−1.59874			−0.799369	+	0.600841i	$0.794833\pi$
$674$			9858.41i			0.563400i
$675$	−1736.11	+	3047.59i	−0.0989967	+	0.173780i
$676$	−16474.0			−0.937303
$677$	−6051.62			−0.343549			−0.171774	−	0.985136i	$-0.554950\pi$
$677$	−6051.62			−0.343549			−0.171774	+	0.985136i	$0.554950\pi$
$678$	30177.5	+	25223.0i	1.70938	+	1.42874i
$679$	8840.50	+	278.278i	0.499657	+	0.0157280i
$680$			10477.6i			0.590876i
$681$	−1719.61	−	1437.28i	−0.0967627	−	0.0808762i
$682$		−	18434.2i		−	1.03502i
$683$			13395.7i			0.750470i	0.926930	+	0.375235i	$0.122438\pi$
$683$			13395.7i			0.750470i	−0.926930	+	0.375235i	$0.877562\pi$
$684$	2203.53	−	397.307i	0.123179	−	0.0222097i
$685$		−	11871.0i		−	0.662141i
$686$	29178.8	+	2762.74i	1.62398	+	0.153764i
$687$	−16974.3	+	20308.6i	−0.942664	+	1.12783i
$688$	−1761.06			−0.0975868
$689$	−6552.89			−0.362330
$690$	17764.3	+	14847.8i	0.980109	+	0.819195i
$691$			11208.4i			0.617057i	0.951215	+	0.308528i	$0.0998365\pi$
$691$			11208.4i			0.617057i	−0.951215	+	0.308528i	$0.900164\pi$
$692$	−22707.3			−1.24740
$693$	−4787.23	−	32348.9i	−0.262412	−	1.77321i
$694$	−35764.5			−1.95620
$695$		−	5093.60i		−	0.278002i
$696$	−2986.96	−	2496.56i	−0.162673	−	0.135965i
$697$	33291.0			1.80916
$698$	−37886.8			−2.05449
$699$	−12812.6	+	15329.4i	−0.693302	+	0.829487i
$700$	−193.564	+	6149.26i	−0.0104515	+	0.332029i
$701$			23842.7i			1.28463i	0.766440	+	0.642316i	$0.222026\pi$
$701$			23842.7i			1.28463i	−0.766440	+	0.642316i	$0.777974\pi$
$702$	9912.97	−	17401.4i	0.532964	−	0.935575i
$703$		−	54.3958i		−	0.00291831i
$704$		−	53448.6i		−	2.86139i
$705$	4156.92	+	3474.44i	0.222069	+	0.185610i
$706$		−	25378.8i		−	1.35290i
$707$	686.089	−	21796.1i	0.0364965	−	1.15944i
$708$	−11336.7	−	9475.44i	−0.601779	−	0.502979i
$709$	−18980.0			−1.00537			−0.502686	−	0.864469i	$-0.667655\pi$
$709$	−18980.0			−1.00537			−0.502686	+	0.864469i	$0.667655\pi$
$710$	−7369.71			−0.389550
$711$	4036.79	+	22388.7i	0.212928	+	1.18093i
$712$			11716.5i			0.616704i
$713$	−11800.0			−0.619794
$714$	−28478.1	−	25366.3i	−1.49267	−	1.32957i
$715$	−10116.4			−0.529136
$716$			15005.5i			0.783213i
$717$	4752.18	−	5685.65i	0.247522	−	0.296143i
$718$	34546.3			1.79562
$719$	−8691.86			−0.450837			−0.225419	−	0.974262i	$-0.572375\pi$
$719$	−8691.86			−0.450837			−0.225419	+	0.974262i	$0.572375\pi$
$720$	150.003	+	831.943i	0.00776429	+	0.0430620i
$721$	−4372.15	−	137.625i	−0.225836	−	0.00710877i
$722$		−	31466.8i		−	1.62198i
$723$	−17433.9	+	20858.4i	−0.896783	+	1.07294i
$724$			53118.1i			2.72668i
$725$			767.712i			0.0393270i
$726$	−45289.7	+	54186.0i	−2.31523	+	2.77001i
$727$		−	3749.84i		−	0.191298i	−0.995415	−	0.0956492i	$-0.969507\pi$
$727$		−	3749.84i		−	0.191298i	0.995415	−	0.0956492i	$-0.0304927\pi$
$728$	439.815	−	13972.3i	0.0223910	−	0.711331i
$729$	−10038.0	−	16931.0i	−0.509982	−	0.860185i
$730$	12811.2			0.649542
$731$	−24155.9			−1.22221
$732$	29829.5	−	35688.9i	1.50619	−	1.80205i
$733$			18593.5i			0.936924i	0.883484	+	0.468462i	$0.155192\pi$
$733$			18593.5i			0.936924i	−0.883484	+	0.468462i	$0.844808\pi$
$734$	−9956.93			−0.500704
$735$	−6464.59	−	6133.69i	−0.324422	−	0.307816i
$736$	−32116.3			−1.60845
$737$			32724.2i			1.63557i
$738$	47517.3	−	8567.59i	2.37010	−	0.427341i
$739$	33391.6			1.66215			0.831077	−	0.556158i	$-0.187725\pi$
$739$	33391.6			1.66215			0.831077	+	0.556158i	$0.187725\pi$
$740$	579.073			0.0287664
$741$	769.825	+	643.435i	0.0381649	+	0.0318990i
$742$	−569.414	+	18089.5i	−0.0281723	+	0.894995i
$743$			7117.50i			0.351434i	0.984441	+	0.175717i	$0.0562244\pi$
$743$			7117.50i			0.351434i	−0.984441	+	0.175717i	$0.943776\pi$
$744$	−5942.60	−	4966.94i	−0.292831	−	0.244754i
$745$		−	9785.14i		−	0.481208i
$746$		−	18405.4i		−	0.903311i
$747$	−4252.78	−	23586.6i	−0.208301	−	1.15527i
$748$			74638.0i			3.64844i
$749$	7068.35	+	222.495i	0.344822	+	0.0108542i
$750$	1921.87	−	2299.38i	0.0935691	−	0.111949i
$751$	17029.8			0.827465			0.413733	−	0.910398i	$-0.364225\pi$
$751$	17029.8			0.827465			0.413733	+	0.910398i	$0.364225\pi$
$752$	1305.78			0.0633206
$753$	−8462.18	−	7072.86i	−0.409534	−	0.342297i
$754$		−	4383.55i		−	0.211723i
$755$	4828.03			0.232728
$756$	−29447.0	−	18025.1i	−1.41664	−	0.867151i
$757$	27250.9			1.30839			0.654195	−	0.756326i	$-0.273008\pi$
$757$	27250.9			1.30839			0.654195	+	0.756326i	$0.273008\pi$
$758$			28238.7i			1.35313i
$759$	50357.8	+	42090.0i	2.40826	+	2.01287i
$760$	−761.300			−0.0363359
$761$	−13216.0			−0.629537			−0.314769	−	0.949168i	$-0.601927\pi$
$761$	−13216.0			−0.629537			−0.314769	+	0.949168i	$0.601927\pi$
$762$	6230.32	−	7454.14i	0.296195	−	0.354376i
$763$	−38.5812	+	1225.67i	−0.00183058	+	0.0581550i
$764$			7232.97i			0.342513i
$765$	2057.55	+	11411.5i	0.0972429	+	0.539325i
$766$		−	34227.2i		−	1.61446i
$767$		−	6620.67i		−	0.311680i
$768$	−18828.0	−	15736.8i	−0.884630	−	0.739392i
$769$		−	5595.39i		−	0.262386i	−0.991357	−	0.131193i	$-0.958119\pi$
$769$		−	5595.39i		−	0.262386i	0.991357	−	0.131193i	$-0.0418808\pi$
$770$	−879.066	+	27926.7i	−0.0411420	+	1.30702i
$771$	−25307.5	−	21152.5i	−1.18214	−	0.988055i
$772$	58972.8			2.74933
$773$	21363.7			0.994046			0.497023	−	0.867737i	$-0.334427\pi$
$773$	21363.7			0.994046			0.497023	+	0.867737i	$0.334427\pi$
$774$	−34478.5	+	6216.64i	−1.60117	+	0.288698i
$775$			1527.37i			0.0707934i
$776$	−11651.4			−0.538996
$777$	−557.892	+	626.329i	−0.0257584	+	0.0289182i
$778$	49277.4			2.27080
$779$			2418.92i			0.111254i
$780$	−6849.73	+	8195.22i	−0.314435	+	0.376200i
$781$	−20891.5			−0.957178
$782$	76541.5			3.50015
$783$	−3743.47	−	2132.53i	−0.170857	−	0.0973312i
$784$	−2143.58	−	135.084i	−0.0976486	−	0.00615359i
$785$			6398.34i			0.290913i
$786$	−30792.1	+	36840.6i	−1.39735	+	1.67183i
$787$		−	9648.50i		−	0.437017i	−0.975835	−	0.218508i	$-0.929881\pi$
$787$		−	9648.50i		−	0.437017i	0.975835	−	0.218508i	$-0.0701191\pi$
$788$		−	15464.5i		−	0.699110i
$789$	−3104.89	+	3714.78i	−0.140098	+	0.167617i
$790$		−	19437.8i		−	0.875400i
$791$	30367.8	+	955.907i	1.36505	+	0.0429686i
$792$	7643.83	+	42393.9i	0.342944	+	1.90202i
$793$	20842.4			0.933336
$794$	33079.4			1.47852
$795$	3528.98	−	4222.18i	0.157434	−	0.188359i
$796$			30506.8i			1.35840i
$797$	37706.0			1.67580			0.837901	−	0.545822i	$-0.183783\pi$
$797$	37706.0			1.67580			0.837901	+	0.545822i	$0.183783\pi$
$798$	1843.12	−	2069.22i	0.0817616	−	0.0917914i
$799$	17911.0			0.793050
$800$			4157.08i			0.183719i
$801$	2300.84	+	12760.8i	0.101493	+	0.562899i
$802$	−15980.9			−0.703624
$803$	36317.0			1.59601
$804$	26509.7	+	22157.3i	1.16284	+	0.971925i
$805$	17876.3	+	562.704i	0.782681	+	0.0246369i
$806$		−	8721.13i		−	0.381128i
$807$	−12940.7	−	10816.1i	−0.564478	−	0.471802i
$808$			28726.4i			1.25073i
$809$			31780.0i			1.38112i	0.723275	+	0.690560i	$0.242636\pi$
$809$			31780.0i			1.38112i	−0.723275	+	0.690560i	$0.757364\pi$
$810$	5873.61	+	15758.5i	0.254787	+	0.683576i
$811$			16076.8i			0.696096i	0.937477	+	0.348048i	$0.113155\pi$
$811$			16076.8i			0.696096i	−0.937477	+	0.348048i	$0.886845\pi$
$812$	−7553.37	−	237.762i	−0.326443	−	0.0102756i
$813$	9117.16	−	10908.0i	0.393300	−	0.470556i
$814$	2629.85			0.113239
$815$	−7793.92			−0.334981
$816$	2144.37	+	1792.31i	0.0919951	+	0.0768913i
$817$		−	1755.17i		−	0.0751599i
$818$	−58923.1			−2.51858
$819$	−2264.82	−	15304.2i	−0.0966291	−	0.652955i
$820$	−25750.8			−1.09666
$821$		−	2584.08i		−	0.109848i	−0.998491	−	0.0549239i	$-0.982508\pi$
$821$		−	2584.08i		−	0.109848i	0.998491	−	0.0549239i	$-0.0174916\pi$
$822$	−43673.5	−	36503.2i	−1.85315	−	1.54890i
$823$	−28772.6			−1.21865			−0.609326	−	0.792920i	$-0.708560\pi$
$823$	−28772.6			−1.21865			−0.609326	+	0.792920i	$0.708560\pi$
$824$	5762.32			0.243616
$825$	5448.07	−	6518.24i	0.229912	−	0.275074i
$826$	−18276.6	−	575.304i	−0.769884	−	0.0242341i
$827$		−	37901.7i		−	1.59368i	−0.604192	−	0.796839i	$-0.706504\pi$
$827$		−	37901.7i		−	1.59368i	0.604192	−	0.796839i	$-0.293496\pi$
$828$	68193.6	−	12295.6i	2.86219	−	0.516066i
$829$		−	28711.1i		−	1.20287i	−0.798922	−	0.601435i	$-0.794596\pi$
$829$		−	28711.1i		−	1.20287i	0.798922	−	0.601435i	$-0.205404\pi$
$830$			20477.8i			0.856380i
$831$	−11890.9	−	9938.69i	−0.496381	−	0.414885i
$832$		−	25286.3i		−	1.05366i
$833$	−29402.9	−	1852.90i	−1.22299	−	0.0770698i
$834$	−18739.4	−	15662.8i	−0.778049	−	0.650309i
$835$	2144.08			0.0888609
$836$	−5423.21			−0.224361
$837$	−7447.70	−	4242.70i	−0.307563	−	0.175208i
$838$		−	70292.1i		−	2.89761i
$839$	15203.4			0.625602			0.312801	−	0.949819i	$-0.398733\pi$
$839$	15203.4			0.625602			0.312801	+	0.949819i	$0.398733\pi$
$840$	8765.84	+	7808.02i	0.360060	+	0.320717i
$841$	23446.0			0.961335
$842$			32802.6i			1.34258i
$843$	8648.70	−	10347.6i	0.353354	−	0.422763i
$844$	−18131.3			−0.739463
$845$	6198.97			0.252368
$846$	25565.0	−	4609.49i	1.03894	−	0.187326i
$847$	−1716.40	+	54527.7i	−0.0696296	+	2.21204i
$848$		−	1326.28i		−	0.0537085i
$849$	22386.6	−	26783.9i	0.904952	−	1.08271i
$850$		−	9907.43i		−	0.399790i
$851$		−	1683.41i		−	0.0678102i
$852$	−14145.4	+	16924.0i	−0.568797	+	0.680525i
$853$		−	33912.6i		−	1.36125i	−0.732633	−	0.680624i	$-0.761709\pi$
$853$		−	33912.6i		−	1.36125i	0.732633	−	0.680624i	$-0.238291\pi$
$854$	1811.10	−	57536.3i	0.0725699	−	2.30545i
$855$	−829.161	+	149.502i	−0.0331657	+	0.00597994i
$856$	−9315.80			−0.371971
$857$	−39113.6			−1.55904			−0.779519	−	0.626379i	$-0.784536\pi$
$857$	−39113.6			−1.55904			−0.779519	+	0.626379i	$0.784536\pi$
$858$	−31107.9	+	37218.4i	−1.23777	+	1.48090i
$859$		−	40537.5i		−	1.61015i	−0.593171	−	0.805076i	$-0.702124\pi$
$859$		−	40537.5i		−	1.61015i	0.593171	−	0.805076i	$-0.297876\pi$
$860$	18684.8			0.740867
$861$	24808.9	−	27852.2i	0.981980	−	1.10244i
$862$	−28107.4			−1.11060
$863$		−	11206.6i		−	0.442034i	−0.975270	−	0.221017i	$-0.929062\pi$
$863$		−	11206.6i		−	0.442034i	0.975270	−	0.221017i	$-0.0709377\pi$
$864$	−20270.5	−	11547.4i	−0.798168	−	0.454689i
$865$	8544.46			0.335862
$866$	5714.31			0.224226
$867$	9825.96	+	8212.73i	0.384899	+	0.321706i
$868$	−15027.6	−	473.031i	−0.587636	−	0.0184974i
$869$		−	55101.8i		−	2.15098i
$870$	2824.42	+	2360.71i	0.110065	+	0.0919949i
$871$			15481.7i			0.602271i
$872$		−	1615.38i		−	0.0627337i
$873$	−12690.0	+	2288.07i	−0.491971	+	0.0887048i
$874$			5561.51i			0.215241i
$875$	72.8356	−	2313.89i	0.00281405	−	0.0893984i
$876$	24589.9	−	29420.1i	0.948421	−	1.13472i
$877$	13067.0			0.503124			0.251562	−	0.967841i	$-0.419056\pi$
$877$	13067.0			0.503124			0.251562	+	0.967841i	$0.419056\pi$
$878$	−13539.1			−0.520412
$879$	29188.5	+	24396.4i	1.12003	+	0.936142i
$880$		−	2047.53i		−	0.0784343i
$881$	12147.0			0.464521			0.232261	−	0.972654i	$-0.425388\pi$
$881$	12147.0			0.464521			0.232261	+	0.972654i	$0.425388\pi$
$882$	−42444.5	+	4922.27i	−1.62039	+	0.187915i
$883$	−30946.6			−1.17943			−0.589715	−	0.807611i	$-0.700760\pi$
$883$	−30946.6			−1.17943			−0.589715	+	0.807611i	$0.700760\pi$
$884$			35311.0i			1.34348i
$885$	4265.85	+	3565.49i	0.162028	+	0.135427i
$886$	−9206.35			−0.349089
$887$	46378.4			1.75562			0.877810	−	0.479009i	$-0.159004\pi$
$887$	46378.4			1.75562			0.877810	+	0.479009i	$0.159004\pi$
$888$	708.592	−	847.781i	0.0267779	−	0.0320379i
$889$	236.118	−	7501.15i	0.00890793	−	0.282993i
$890$		−	11078.9i		−	0.417266i
$891$	16650.4	+	44671.8i	0.626047	+	1.67964i
$892$			10399.6i			0.390365i
$893$			1301.42i			0.0487685i
$894$	−35999.7	−	30089.3i	−1.34677	−	1.12565i
$895$		−	5646.36i		−	0.210879i
$896$	−45179.3	−	1422.14i	−1.68452	−	0.0530248i
$897$	23824.1	+	19912.6i	0.886804	+	0.741208i
$898$	−38461.4			−1.42926
$899$	−1876.13			−0.0696024
$900$	−1591.53	−	8826.88i	−0.0589455	−	0.326922i
$901$		−	18192.2i		−	0.672665i
$902$	−116947.			−4.31696
$903$	−18001.3	+	20209.6i	−0.663395	+	0.744775i
$904$	−40023.6			−1.47253
$905$		−	19987.7i		−	0.734157i
$906$	14846.2	−	17762.4i	0.544405	−	0.651342i
$907$	6560.02			0.240157			0.120078	−	0.992764i	$-0.461685\pi$
$907$	6560.02			0.240157			0.120078	+	0.992764i	$0.461685\pi$
$908$	5731.16			0.209466
$909$	5641.19	+	31287.0i	0.205838	+	1.14161i
$910$	−415.883	+	13212.0i	−0.0151499	+	0.481291i
$911$			26129.2i			0.950274i	0.879912	+	0.475137i	$0.157601\pi$
$911$			26129.2i			0.950274i	−0.879912	+	0.475137i	$0.842399\pi$
$912$	−130.229	+	155.810i	−0.00472842	+	0.00565723i
$913$			58050.0i			2.10424i
$914$			19390.4i			0.701724i
$915$	−11224.4	+	13429.3i	−0.405539	+	0.485199i
$916$		−	67685.1i		−	2.44146i
$917$	−1166.97	+	37073.0i	−0.0420248	+	1.33507i
$918$	48310.0	+	27520.6i	1.73689	+	0.989449i
$919$	−7234.60			−0.259682			−0.129841	−	0.991535i	$-0.541447\pi$
$919$	−7234.60			−0.259682			−0.129841	+	0.991535i	$0.541447\pi$
$920$	−23560.3			−0.844303
$921$	−23417.6	+	28017.5i	−0.837825	+	1.00240i
$922$			9595.65i			0.342751i
$923$	−9883.68			−0.352465
$924$	62444.4	+	55621.3i	2.22324	+	1.98031i
$925$	−217.898			−0.00774534
$926$		−	87091.1i		−	3.09070i
$927$	6275.96	−	1131.59i	0.222362	−	0.0400929i
$928$	−5106.30			−0.180628
$929$	26897.8			0.949934			0.474967	−	0.880004i	$-0.342460\pi$
$929$	26897.8			0.949934			0.474967	+	0.880004i	$0.342460\pi$
$930$	5619.23	+	4696.67i	0.198131	+	0.165602i
$931$	134.632	−	2136.41i	0.00473940	−	0.0752075i
$932$		−	51090.4i		−	1.79562i
$933$	−35315.1	−	29517.1i	−1.23919	−	1.03574i
$934$			60226.8i			2.10994i
$935$		−	28085.3i		−	0.982340i
$936$	3616.27	+	20056.4i	0.126284	+	0.700389i
$937$			29633.3i			1.03317i	0.856237	+	0.516583i	$0.172796\pi$
$937$			29633.3i			1.03317i	−0.856237	+	0.516583i	$0.827204\pi$
$938$	42737.9	+	1345.29i	1.48768	+	0.0468285i
$939$	−27168.2	+	32504.9i	−0.944198	+	1.12967i
$940$	−13854.3			−0.480722
$941$	−52426.3			−1.81621			−0.908103	−	0.418747i	$-0.862469\pi$
$941$	−52426.3			−1.81621			−0.908103	+	0.418747i	$0.862469\pi$
$942$	23539.6	+	19674.9i	0.814184	+	0.680511i
$943$			74859.4i			2.58511i
$944$	1340.00			0.0462006
$945$	11080.5	+	6782.60i	0.381428	+	0.233479i
$946$	84856.5			2.91641
$947$			5941.91i			0.203893i	0.994790	+	0.101946i	$0.0325070\pi$
$947$			5941.91i			0.203893i	−0.994790	+	0.101946i	$0.967493\pi$
$948$	−44637.5	−	37308.9i	−1.52928	−	1.27820i
$949$	17181.4			0.587706
$950$	719.874			0.0245851
$951$	−28780.4	+	34433.8i	−0.981356	+	1.17412i
$952$	38790.2	+	1221.02i	1.32059	+	0.0415689i
$953$		−	15418.4i		−	0.524082i	−0.965057	−	0.262041i	$-0.915604\pi$
$953$		−	15418.4i		−	0.524082i	0.965057	−	0.262041i	$-0.0843956\pi$
$954$	−4681.86	−	25966.4i	−0.158890	−	0.881229i
$955$		−	2721.67i		−	0.0922212i
$956$			18949.3i			0.641073i
$957$	8006.60	+	6692.08i	0.270446	+	0.226044i
$958$		−	81153.5i		−	2.73690i
$959$	−43948.9	−	1383.41i	−1.47986	−	0.0465824i
$960$	16292.6	+	13617.7i	0.547751	+	0.457822i
$961$	26058.4			0.874707
$962$	1244.17			0.0416982
$963$	−10146.2	+	1829.41i	−0.339518	+	0.0612168i
$964$		−	69517.7i		−	2.32263i
$965$	−22190.7			−0.740253
$966$	57039.8	−	64037.0i	1.89982	−	2.13287i
$967$	−25966.2			−0.863512			−0.431756	−	0.901991i	$-0.642106\pi$
$967$	−25966.2			−0.863512			−0.431756	+	0.901991i	$0.642106\pi$
$968$		−	71865.3i		−	2.38620i
$969$	−1786.31	+	2137.20i	−0.0592205	+	0.0708532i
$970$	11017.4			0.364688
$971$	−9776.28			−0.323106			−0.161553	−	0.986864i	$-0.551650\pi$
$971$	−9776.28			−0.323106			−0.161553	+	0.986864i	$0.551650\pi$
$972$	47462.1	+	16758.5i	1.56620	+	0.553015i
$973$	−18857.6	−	593.592i	−0.621323	−	0.0195578i
$974$			61528.7i			2.02414i
$975$	2577.46	−	3083.75i	0.0846614	−	0.101291i
$976$			4218.44i			0.138349i
$977$			11309.1i			0.370328i	0.982708	+	0.185164i	$0.0592817\pi$
$977$			11309.1i			0.370328i	−0.982708	+	0.185164i	$0.940718\pi$
$978$	−23966.3	+	28674.0i	−0.783596	+	0.937517i
$979$		−	31406.3i		−	1.02528i
$980$	22743.3	+	1433.23i	0.741336	+	0.0467173i
$981$	−317.224	−	1759.37i	−0.0103243	−	0.0572605i
$982$	−24186.4			−0.785966
$983$	42744.9			1.38693			0.693464	−	0.720492i	$-0.256084\pi$
$983$	42744.9			1.38693			0.693464	+	0.720492i	$0.256084\pi$
$984$	−31510.4	+	37700.0i	−1.02085	+	1.22137i
$985$			5819.08i			0.188235i
$986$	12169.7			0.393064
$987$	13347.6	−	14984.9i	0.430453	−	0.483258i
$988$	−2565.70			−0.0826171
$989$		−	54317.9i		−	1.74642i
$990$	−7227.89	−	40087.1i	−0.232038	−	1.28692i
$991$	−1645.30			−0.0527392			−0.0263696	−	0.999652i	$-0.508395\pi$
$991$	−1645.30			−0.0527392			−0.0263696	+	0.999652i	$0.508395\pi$
$992$	−10159.1			−0.325152
$993$	−33669.0	−	28141.2i	−1.07599	−	0.899331i
$994$	−858.844	+	27284.3i	−0.0274053	+	0.870629i
$995$		−	11479.3i		−	0.365748i
$996$	47025.9	+	39305.2i	1.49606	+	1.25043i
$997$		−	37031.8i		−	1.17634i	−0.808738	−	0.588169i	$-0.799849\pi$
$997$		−	37031.8i		−	1.17634i	0.808738	−	0.588169i	$-0.200151\pi$
$998$			11933.5i			0.378504i
$999$	605.270	−	1062.50i	0.0191691	−	0.0336497i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.b.b.41.2	yes	16
3.2	odd	2		105.4.b.a.41.15	yes	16
7.6	odd	2		105.4.b.a.41.2	✓	16
21.20	even	2	inner	105.4.b.b.41.15	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.b.a.41.2	✓	16	7.6	odd	2
105.4.b.a.41.15	yes	16	3.2	odd	2
105.4.b.b.41.2	yes	16	1.1	even	1	trivial
105.4.b.b.41.15	yes	16	21.20	even	2	inner

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.61386i q^{2} +(3.98691 + 3.33234i) q^{3} -13.2877 q^{4} +5.00000 q^{5} +(15.3750 - 18.3951i) q^{6} +(0.582685 - 18.5111i) q^{7} +24.3969i q^{8} +(4.79097 + 26.5715i) q^{9} +O(q^{10})\)	\(q-4.61386i q^{2} +(3.98691 + 3.33234i) q^{3} -13.2877 q^{4} +5.00000 q^{5} +(15.3750 - 18.3951i) q^{6} +(0.582685 - 18.5111i) q^{7} +24.3969i q^{8} +(4.79097 + 26.5715i) q^{9} -23.0693i q^{10} -65.3963i q^{11} +(-52.9770 - 44.2793i) q^{12} -30.9388i q^{13} +(-85.4076 - 2.68843i) q^{14} +(19.9346 + 16.6617i) q^{15} +6.26191 q^{16} +85.8927 q^{17} +(122.597 - 22.1049i) q^{18} +6.24097i q^{19} -66.4386 q^{20} +(64.0084 - 71.8604i) q^{21} -301.730 q^{22} +193.142i q^{23} +(-81.2987 + 97.2682i) q^{24} +25.0000 q^{25} -142.747 q^{26} +(-69.4443 + 121.904i) q^{27} +(-7.74256 + 245.970i) q^{28} +30.7085i q^{29} +(76.8749 - 91.9754i) q^{30} +61.0950i q^{31} +166.283i q^{32} +(217.923 - 260.730i) q^{33} -396.297i q^{34} +(2.91342 - 92.5555i) q^{35} +(-63.6612 - 353.075i) q^{36} -8.71591 q^{37} +28.7950 q^{38} +(103.099 - 123.350i) q^{39} +121.984i q^{40} +387.588 q^{41} +(-331.554 - 295.326i) q^{42} -281.233 q^{43} +868.968i q^{44} +(23.9549 + 132.858i) q^{45} +891.130 q^{46} +208.528 q^{47} +(24.9657 + 20.8668i) q^{48} +(-342.321 - 21.5723i) q^{49} -115.347i q^{50} +(342.447 + 286.224i) q^{51} +411.106i q^{52} -211.802i q^{53} +(562.447 + 320.406i) q^{54} -326.982i q^{55} +(451.612 + 14.2157i) q^{56} +(-20.7971 + 24.8822i) q^{57} +141.685 q^{58} +213.993 q^{59} +(-264.885 - 221.396i) q^{60} +673.667i q^{61} +281.884 q^{62} +(494.660 - 73.2033i) q^{63} +817.303 q^{64} -154.694i q^{65} +(-1202.97 - 1005.47i) q^{66} -500.399 q^{67} -1141.32 q^{68} +(-643.615 + 770.040i) q^{69} +(-427.038 - 13.4421i) q^{70} -319.460i q^{71} +(-648.262 + 116.885i) q^{72} +555.337i q^{73} +40.2140i q^{74} +(99.6729 + 83.3086i) q^{75} -82.9283i q^{76} +(-1210.56 - 38.1054i) q^{77} +(-569.121 - 475.683i) q^{78} +842.582 q^{79} +31.3095 q^{80} +(-683.093 + 254.607i) q^{81} -1788.28i q^{82} -887.665 q^{83} +(-850.527 + 954.862i) q^{84} +429.463 q^{85} +1297.57i q^{86} +(-102.331 + 122.432i) q^{87} +1595.46 q^{88} +480.245 q^{89} +(612.987 - 110.524i) q^{90} +(-572.710 - 18.0275i) q^{91} -2566.42i q^{92} +(-203.589 + 243.580i) q^{93} -962.120i q^{94} +31.2048i q^{95} +(-554.113 + 662.957i) q^{96} +477.578i q^{97} +(-99.5315 + 1579.42i) q^{98} +(1737.68 - 313.312i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{3} - 64 q^{4} + 80 q^{5} + 28 q^{6} - 4 q^{7} - 22 q^{9}+O(q^{10}) \) 16 * q + 2 * q^3 - 64 * q^4 + 80 * q^5 + 28 * q^6 - 4 * q^7 - 22 * q^9	\( 16 q + 2 q^{3} - 64 q^{4} + 80 q^{5} + 28 q^{6} - 4 q^{7} - 22 q^{9} + 66 q^{12} + 90 q^{14} + 10 q^{15} + 376 q^{16} + 72 q^{17} - 182 q^{18} - 320 q^{20} - 70 q^{21} - 276 q^{22} - 526 q^{24} + 400 q^{25} - 696 q^{26} + 128 q^{27} + 10 q^{28} + 140 q^{30} + 502 q^{33} - 20 q^{35} + 996 q^{36} - 812 q^{37} + 1200 q^{38} - 594 q^{39} + 936 q^{41} - 974 q^{42} - 548 q^{43} - 110 q^{45} + 1224 q^{46} - 912 q^{47} - 1850 q^{48} + 328 q^{49} + 750 q^{51} + 2950 q^{54} - 1254 q^{56} + 432 q^{57} + 576 q^{58} + 552 q^{59} + 330 q^{60} + 1860 q^{62} + 362 q^{63} - 4000 q^{64} - 1378 q^{66} + 1004 q^{67} - 3828 q^{68} - 1988 q^{69} + 450 q^{70} + 1988 q^{72} + 50 q^{75} - 1152 q^{77} + 1446 q^{78} + 1292 q^{79} + 1880 q^{80} - 2950 q^{81} + 1752 q^{83} - 420 q^{84} + 360 q^{85} - 1910 q^{87} - 912 q^{88} - 6096 q^{89} - 910 q^{90} - 552 q^{91} - 1080 q^{93} + 9546 q^{96} + 4824 q^{98} + 2530 q^{99}+O(q^{100}) \) 16 * q + 2 * q^3 - 64 * q^4 + 80 * q^5 + 28 * q^6 - 4 * q^7 - 22 * q^9 + 66 * q^12 + 90 * q^14 + 10 * q^15 + 376 * q^16 + 72 * q^17 - 182 * q^18 - 320 * q^20 - 70 * q^21 - 276 * q^22 - 526 * q^24 + 400 * q^25 - 696 * q^26 + 128 * q^27 + 10 * q^28 + 140 * q^30 + 502 * q^33 - 20 * q^35 + 996 * q^36 - 812 * q^37 + 1200 * q^38 - 594 * q^39 + 936 * q^41 - 974 * q^42 - 548 * q^43 - 110 * q^45 + 1224 * q^46 - 912 * q^47 - 1850 * q^48 + 328 * q^49 + 750 * q^51 + 2950 * q^54 - 1254 * q^56 + 432 * q^57 + 576 * q^58 + 552 * q^59 + 330 * q^60 + 1860 * q^62 + 362 * q^63 - 4000 * q^64 - 1378 * q^66 + 1004 * q^67 - 3828 * q^68 - 1988 * q^69 + 450 * q^70 + 1988 * q^72 + 50 * q^75 - 1152 * q^77 + 1446 * q^78 + 1292 * q^79 + 1880 * q^80 - 2950 * q^81 + 1752 * q^83 - 420 * q^84 + 360 * q^85 - 1910 * q^87 - 912 * q^88 - 6096 * q^89 - 910 * q^90 - 552 * q^91 - 1080 * q^93 + 9546 * q^96 + 4824 * q^98 + 2530 * q^99

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