LMFDB - Embedded newform 350.3.i.b.199.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [350,3,Mod(199,350)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(350, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("350.199"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	350.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$9.53680925261$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.11007531417600000000.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} + 48x^{8} - 7x^{4} + 1 $ x^16 - 7x^12 + 48x^8 - 7*x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{16} $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.8
Root			$1.56290 - 0.418778i$ of defining polynomial
Character	$\chi$	$=$	350.199
Dual form			350.3.i.b.299.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22474 - 0.707107i) q^{2} +(2.16226 - 3.74514i) q^{3} +(1.00000 - 1.73205i) q^{4} -6.11578i q^{6} +(-6.91361 - 1.09634i) q^{7} -2.82843i q^{8} +(-4.85071 - 8.40167i) q^{9} +(3.49028 - 6.04534i) q^{11} +(-4.32451 - 7.49028i) q^{12} -22.0427 q^{13} +(-9.24264 + 3.54593i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-0.410964 + 0.711810i) q^{17} +(-11.8818 - 6.85993i) q^{18} +(32.0456 - 18.5016i) q^{19} +(-19.0549 + 23.5219i) q^{21} -9.87199i q^{22} +(4.92302 - 2.84231i) q^{23} +(-10.5928 - 6.11578i) q^{24} +(-26.9967 + 15.5865i) q^{26} -3.03326 q^{27} +(-8.81253 + 10.8784i) q^{28} +23.1260 q^{29} +(-6.45601 - 3.72738i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-15.0937 - 26.1431i) q^{33} +1.16238i q^{34} -19.4028 q^{36} +(33.3397 - 19.2487i) q^{37} +(26.1651 - 45.3194i) q^{38} +(-47.6619 + 82.5529i) q^{39} +59.8867i q^{41} +(-6.70498 + 42.2822i) q^{42} -30.2482i q^{43} +(-6.98055 - 12.0907i) q^{44} +(4.01963 - 6.96220i) q^{46} +(31.8629 + 55.1881i) q^{47} -17.2981 q^{48} +(46.5961 + 15.1593i) q^{49} +(1.77722 + 3.07823i) q^{51} +(-22.0427 + 38.1790i) q^{52} +(-16.6595 - 9.61837i) q^{53} +(-3.71497 + 2.14484i) q^{54} +(-3.10092 + 19.5546i) q^{56} -160.020i q^{57} +(28.3235 - 16.3526i) q^{58} +(-67.4057 - 38.9167i) q^{59} +(-13.3160 + 7.68798i) q^{61} -10.5426 q^{62} +(24.3248 + 63.4039i) q^{63} -8.00000 q^{64} +(-36.9720 - 21.3458i) q^{66} +(-39.5693 - 22.8453i) q^{67} +(0.821928 + 1.42362i) q^{68} -24.5832i q^{69} +98.8553 q^{71} +(-23.7635 + 13.7199i) q^{72} +(9.42281 - 16.3208i) q^{73} +(27.2218 - 47.1495i) q^{74} -74.0062i q^{76} +(-30.7582 + 37.9686i) q^{77} +134.808i q^{78} +(25.2828 + 43.7911i) q^{79} +(37.0977 - 64.2550i) q^{81} +(42.3463 + 73.3460i) q^{82} +34.9833 q^{83} +(21.6861 + 56.5260i) q^{84} +(-21.3887 - 37.0463i) q^{86} +(50.0044 - 86.6101i) q^{87} +(-17.0988 - 9.87199i) q^{88} +(71.6107 - 41.3445i) q^{89} +(152.395 + 24.1663i) q^{91} -11.3692i q^{92} +(-27.9191 + 16.1191i) q^{93} +(78.0478 + 45.0609i) q^{94} +(-21.1857 + 12.2316i) q^{96} -177.301 q^{97} +(67.7876 - 14.3821i) q^{98} -67.7212 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4} - 24 q^{9} - 16 q^{11} - 80 q^{14} - 32 q^{16} + 8 q^{21} + 48 q^{24} - 192 q^{26} + 240 q^{29} - 144 q^{31} - 96 q^{36} - 48 q^{39} + 32 q^{44} + 40 q^{46} - 48 q^{49} + 112 q^{51} - 360 q^{54}+ \cdots - 192 q^{99}+O(q^{100}) $ 16 * q + 16 * q^4 - 24 * q^9 - 16 * q^11 - 80 * q^14 - 32 * q^16 + 8 * q^21 + 48 * q^24 - 192 * q^26 + 240 * q^29 - 144 * q^31 - 96 * q^36 - 48 * q^39 + 32 * q^44 + 40 * q^46 - 48 * q^49 + 112 * q^51 - 360 * q^54 - 80 * q^56 - 96 * q^59 + 144 * q^61 - 128 * q^64 - 384 * q^66 + 128 * q^71 + 160 * q^74 + 576 * q^79 + 608 * q^81 + 80 * q^84 + 8 * q^86 + 264 * q^89 + 1232 * q^91 + 672 * q^94 + 96 * q^96 - 192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$	2.16226	−	3.74514i	0.720752	−	1.24838i	−0.239947	−	0.970786i	$-0.577130\pi$
$3$	2.16226	−	3.74514i	0.720752	−	1.24838i	0.960699	−	0.277593i	$-0.0895367\pi$
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		−	6.11578i		−	1.01930i
$7$	−6.91361	−	1.09634i	−0.987659	−	0.156620i
$7$	−6.91361	−	1.09634i	−0.987659	−	0.156620i
$8$		−	2.82843i		−	0.353553i
$9$	−4.85071	−	8.40167i	−0.538967	−	0.933519i
$10$		0			0
$11$	3.49028	−	6.04534i	0.317298	−	0.549576i	−0.662625	−	0.748951i	$-0.730558\pi$
$11$	3.49028	−	6.04534i	0.317298	−	0.549576i	0.979923	+	0.199375i	$0.0638912\pi$
$12$	−4.32451	−	7.49028i	−0.360376	−	0.624190i
$13$	−22.0427			−1.69559			−0.847796	−	0.530323i	$-0.822071\pi$
$13$	−22.0427			−1.69559			−0.847796	+	0.530323i	$0.822071\pi$
$14$	−9.24264	+	3.54593i	−0.660189	+	0.253280i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−0.410964	+	0.711810i	−0.0241744	+	0.0418712i	−0.877859	−	0.478918i	$-0.841029\pi$
$17$	−0.410964	+	0.711810i	−0.0241744	+	0.0418712i	0.853685	+	0.520789i	$0.174362\pi$
$18$	−11.8818	−	6.85993i	−0.660097	−	0.381107i
$19$	32.0456	−	18.5016i	1.68661	−	0.973766i	0.729530	−	0.683948i	$-0.239739\pi$
$19$	32.0456	−	18.5016i	1.68661	−	0.973766i	0.957082	−	0.289818i	$-0.0935946\pi$
$20$		0			0
$21$	−19.0549	+	23.5219i	−0.907378	+	1.12009i
$22$		−	9.87199i		−	0.448727i
$23$	4.92302	−	2.84231i	0.214044	−	0.123579i	−0.389145	−	0.921176i	$-0.627230\pi$
$23$	4.92302	−	2.84231i	0.214044	−	0.123579i	0.603190	+	0.797598i	$0.293896\pi$
$24$	−10.5928	−	6.11578i	−0.441369	−	0.254824i
$25$		0			0
$26$	−26.9967	+	15.5865i	−1.03833	+	0.599482i
$27$	−3.03326			−0.112343
$28$	−8.81253	+	10.8784i	−0.314733	+	0.388514i
$29$	23.1260			0.797449			0.398725	−	0.917071i	$-0.369453\pi$
$29$	23.1260			0.797449			0.398725	+	0.917071i	$0.369453\pi$
$30$		0			0
$31$	−6.45601	−	3.72738i	−0.208259	−	0.120238i	0.392243	−	0.919862i	$-0.371699\pi$
$31$	−6.45601	−	3.72738i	−0.208259	−	0.120238i	−0.600502	+	0.799623i	$0.705032\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$	−15.0937	−	26.1431i	−0.457386	−	0.792216i
$34$			1.16238i			0.0341877i
$35$		0			0
$36$	−19.4028			−0.538967
$37$	33.3397	−	19.2487i	0.901074	−	0.520235i	0.0235257	−	0.999723i	$-0.492511\pi$
$37$	33.3397	−	19.2487i	0.901074	−	0.520235i	0.877549	+	0.479488i	$0.159178\pi$
$38$	26.1651	−	45.3194i	0.688557	−	1.19261i
$39$	−47.6619	+	82.5529i	−1.22210	+	2.11674i
$40$		0			0
$41$			59.8867i			1.46065i	0.683099	+	0.730326i	$0.260632\pi$
$41$			59.8867i			1.46065i	−0.683099	+	0.730326i	$0.739368\pi$
$42$	−6.70498	+	42.2822i	−0.159642	+	1.00672i
$43$		−	30.2482i		−	0.703446i	−0.936104	−	0.351723i	$-0.885596\pi$
$43$		−	30.2482i		−	0.703446i	0.936104	−	0.351723i	$-0.114404\pi$
$44$	−6.98055	−	12.0907i	−0.158649	−	0.274788i
$45$		0			0
$46$	4.01963	−	6.96220i	0.0873832	−	0.151352i
$47$	31.8629	+	55.1881i	0.677934	+	1.17422i	0.975602	+	0.219546i	$0.0704577\pi$
$47$	31.8629	+	55.1881i	0.677934	+	1.17422i	−0.297668	+	0.954669i	$0.596209\pi$
$48$	−17.2981			−0.360376
$49$	46.5961	+	15.1593i	0.950940	+	0.309374i
$50$		0			0
$51$	1.77722	+	3.07823i	0.0348474	+	0.0603575i
$52$	−22.0427	+	38.1790i	−0.423898	+	0.734212i
$53$	−16.6595	−	9.61837i	−0.314330	−	0.181479i	0.334532	−	0.942384i	$-0.391422\pi$
$53$	−16.6595	−	9.61837i	−0.314330	−	0.181479i	−0.648863	+	0.760906i	$0.724755\pi$
$54$	−3.71497	+	2.14484i	−0.0687957	+	0.0397192i
$55$		0			0
$56$	−3.10092	+	19.5546i	−0.0553735	+	0.349190i
$57$		−	160.020i		−	2.80738i
$58$	28.3235	−	16.3526i	0.488336	−	0.281941i
$59$	−67.4057	−	38.9167i	−1.14247	−	0.659605i	−0.195428	−	0.980718i	$-0.562610\pi$
$59$	−67.4057	−	38.9167i	−1.14247	−	0.659605i	−0.947041	+	0.321113i	$0.895943\pi$
$60$		0			0
$61$	−13.3160	+	7.68798i	−0.218295	+	0.126032i	−0.605160	−	0.796104i	$-0.706891\pi$
$61$	−13.3160	+	7.68798i	−0.218295	+	0.126032i	0.386866	+	0.922136i	$0.373558\pi$
$62$	−10.5426			−0.170042
$63$	24.3248	+	63.4039i	0.386108	+	1.00641i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	−36.9720	−	21.3458i	−0.560181	−	0.323421i
$67$	−39.5693	−	22.8453i	−0.590586	−	0.340975i	0.174743	−	0.984614i	$-0.444091\pi$
$67$	−39.5693	−	22.8453i	−0.590586	−	0.340975i	−0.765329	+	0.643639i	$0.777424\pi$
$68$	0.821928	+	1.42362i	0.0120872	+	0.0209356i
$69$		−	24.5832i		−	0.356278i
$70$		0			0
$71$	98.8553			1.39233			0.696164	−	0.717883i	$-0.254889\pi$
$71$	98.8553			1.39233			0.696164	+	0.717883i	$0.254889\pi$
$72$	−23.7635	+	13.7199i	−0.330049	+	0.190554i
$73$	9.42281	−	16.3208i	0.129080	−	0.223573i	−0.794241	−	0.607603i	$-0.792131\pi$
$73$	9.42281	−	16.3208i	0.129080	−	0.223573i	0.923320	+	0.384031i	$0.125464\pi$
$74$	27.2218	−	47.1495i	0.367862	−	0.637156i
$75$		0			0
$76$		−	74.0062i		−	0.973766i
$77$	−30.7582	+	37.9686i	−0.399457	+	0.493098i
$78$			134.808i			1.72831i
$79$	25.2828	+	43.7911i	0.320035	+	0.554317i	0.980495	−	0.196544i	$-0.0629719\pi$
$79$	25.2828	+	43.7911i	0.320035	+	0.554317i	−0.660460	+	0.750861i	$0.729639\pi$
$80$		0			0
$81$	37.0977	−	64.2550i	0.457996	−	0.793272i
$82$	42.3463	+	73.3460i	0.516419	+	0.894463i
$83$	34.9833			0.421486			0.210743	−	0.977542i	$-0.432412\pi$
$83$	34.9833			0.421486			0.210743	+	0.977542i	$0.432412\pi$
$84$	21.6861	+	56.5260i	0.258168	+	0.672929i
$85$		0			0
$86$	−21.3887	−	37.0463i	−0.248706	−	0.430771i
$87$	50.0044	−	86.6101i	0.574763	−	0.995519i
$88$	−17.0988	−	9.87199i	−0.194304	−	0.112182i
$89$	71.6107	−	41.3445i	0.804615	−	0.464545i	−0.0404675	−	0.999181i	$-0.512885\pi$
$89$	71.6107	−	41.3445i	0.804615	−	0.464545i	0.845082	+	0.534636i	$0.179551\pi$
$90$		0			0
$91$	152.395	+	24.1663i	1.67467	+	0.265563i
$92$		−	11.3692i		−	0.123579i
$93$	−27.9191	+	16.1191i	−0.300206	+	0.173324i
$94$	78.0478	+	45.0609i	0.830296	+	0.479372i
$95$		0			0
$96$	−21.1857	+	12.2316i	−0.220684	+	0.127412i
$97$	−177.301			−1.82785			−0.913923	−	0.405887i	$-0.866962\pi$
$97$	−177.301			−1.82785			−0.913923	+	0.405887i	$0.866962\pi$
$98$	67.7876	−	14.3821i	0.691710	−	0.146756i
$99$	−67.7212			−0.684052
$100$		0			0
$101$	−43.8387	−	25.3103i	−0.434046	−	0.250597i	0.267023	−	0.963690i	$-0.413960\pi$
$101$	−43.8387	−	25.3103i	−0.434046	−	0.250597i	−0.701069	+	0.713094i	$0.747293\pi$
$102$	4.35328	+	2.51337i	0.0426792	+	0.0246409i
$103$	64.9638	+	112.521i	0.630716	+	1.09243i	0.987406	+	0.158209i	$0.0505721\pi$
$103$	64.9638	+	112.521i	0.630716	+	1.09243i	−0.356690	+	0.934223i	$0.616095\pi$
$104$			62.3461i			0.599482i
$105$		0			0
$106$	−27.2049			−0.256650
$107$	106.156	−	61.2895i	0.992117	−	0.572799i	0.0862104	−	0.996277i	$-0.472524\pi$
$107$	106.156	−	61.2895i	0.992117	−	0.572799i	0.905906	+	0.423478i	$0.139191\pi$
$108$	−3.03326	+	5.25376i	−0.0280857	+	0.0486459i
$109$	3.48287	−	6.03251i	0.0319530	−	0.0553442i	−0.849607	−	0.527417i	$-0.823161\pi$
$109$	3.48287	−	6.03251i	0.0319530	−	0.0553442i	0.881560	+	0.472073i	$0.156494\pi$
$110$		0			0
$111$		−	166.483i		−	1.49984i
$112$	10.0294	+	26.1421i	0.0895482	+	0.233412i
$113$		−	118.975i		−	1.05287i	−0.850214	−	0.526437i	$-0.823528\pi$
$113$		−	118.975i		−	1.05287i	0.850214	−	0.526437i	$-0.176472\pi$
$114$	−113.152	−	195.984i	−0.992557	−	1.71916i
$115$		0			0
$116$	23.1260	−	40.0554i	0.199362	−	0.345306i
$117$	106.923	+	185.195i	0.913868	+	1.58287i
$118$	−110.073			−0.932822
$119$	3.62163	−	4.47063i	0.0304339	−	0.0375683i
$120$		0			0
$121$	36.1359	+	62.5893i	0.298644	+	0.517267i
$122$	−10.8724	+	18.8316i	−0.0891184	+	0.154358i
$123$	224.284	+	129.490i	1.82345	+	1.05277i
$124$	−12.9120	+	7.45476i	−0.104129	+	0.0601191i
$125$		0			0
$126$	74.6250	+	60.4534i	0.592262	+	0.479789i
$127$			201.068i			1.58321i	0.611031	+	0.791607i	$0.290755\pi$
$127$			201.068i			1.58321i	−0.611031	+	0.791607i	$0.709245\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$	−113.284	−	65.4044i	−0.878168	−	0.507010i
$130$		0			0
$131$	−130.427	+	75.3022i	−0.995628	+	0.574826i	−0.906952	−	0.421234i	$-0.861597\pi$
$131$	−130.427	+	75.3022i	−0.995628	+	0.574826i	−0.0886762	+	0.996061i	$0.528264\pi$
$132$	−60.3750			−0.457386
$133$	−241.835	+	92.7797i	−1.81831	+	0.697592i
$134$	−64.6164			−0.482212
$135$		0			0
$136$	2.01330	+	1.16238i	0.0148037	+	0.00854692i
$137$	163.221	+	94.2355i	1.19139	+	0.687851i	0.958622	−	0.284681i	$-0.0918877\pi$
$137$	163.221	+	94.2355i	1.19139	+	0.687851i	0.232770	+	0.972532i	$0.425221\pi$
$138$	−17.3829	−	30.1081i	−0.125963	−	0.218175i
$139$		−	54.0378i		−	0.388761i	−0.980926	−	0.194381i	$-0.937730\pi$
$139$		−	54.0378i		−	0.388761i	0.980926	−	0.194381i	$-0.0622697\pi$
$140$		0			0
$141$	275.583			1.95449
$142$	121.073	−	69.9013i	0.852623	−	0.492262i
$143$	−76.9350	+	133.255i	−0.538007	+	0.931856i
$144$	−19.4028	+	33.6067i	−0.134742	+	0.233380i
$145$		0			0
$146$		−	26.6517i		−	0.182546i
$147$	157.526	−	141.730i	1.07161	−	0.964152i
$148$		−	76.9948i		−	0.520235i
$149$	45.6402	+	79.0511i	0.306310	+	0.530545i	0.977552	−	0.210694i	$-0.0675722\pi$
$149$	45.6402	+	79.0511i	0.306310	+	0.530545i	−0.671242	+	0.741238i	$0.734239\pi$
$150$		0			0
$151$	−95.6003	+	165.584i	−0.633114	+	1.09659i	0.353797	+	0.935322i	$0.384890\pi$
$151$	−95.6003	+	165.584i	−0.633114	+	1.09659i	−0.986911	+	0.161264i	$0.948443\pi$
$152$	−52.3303	−	90.6387i	−0.344278	−	0.596307i
$153$	7.97386			0.0521167
$154$	−10.8231	+	68.2511i	−0.0702796	+	0.443189i
$155$		0			0
$156$	95.3239	+	165.106i	0.611050	+	1.05837i
$157$	−8.44893	+	14.6340i	−0.0538149	+	0.0932101i	−0.891678	−	0.452670i	$-0.850471\pi$
$157$	−8.44893	+	14.6340i	−0.0538149	+	0.0932101i	0.837863	+	0.545881i	$0.183805\pi$
$158$	61.9299	+	35.7553i	0.391962	+	0.226299i
$159$	−72.0442	+	41.5948i	−0.453108	+	0.261602i
$160$		0			0
$161$	−37.1520	+	14.2533i	−0.230758	+	0.0885298i
$162$		−	104.928i		−	0.647704i
$163$	105.470	−	60.8933i	0.647057	−	0.373579i	−0.140271	−	0.990113i	$-0.544797\pi$
$163$	105.470	−	60.8933i	0.647057	−	0.373579i	0.787328	+	0.616535i	$0.211464\pi$
$164$	103.727	+	59.8867i	0.632481	+	0.365163i
$165$		0			0
$166$	42.8457	−	24.7370i	0.258106	−	0.149018i
$167$	−201.448			−1.20627			−0.603137	−	0.797637i	$-0.706083\pi$
$167$	−201.448			−1.20627			−0.603137	+	0.797637i	$0.706083\pi$
$168$	66.5299	+	53.8955i	0.396011	+	0.320807i
$169$	316.880			1.87503
$170$		0			0
$171$	−310.888	−	179.491i	−1.81806	−	1.04966i
$172$	−52.3914	−	30.2482i	−0.304601	−	0.175862i
$173$	−92.1482	−	159.605i	−0.532648	−	0.922574i	−0.999273	−	0.0381186i	$-0.987864\pi$
$173$	−92.1482	−	159.605i	−0.532648	−	0.922574i	0.466625	−	0.884455i	$-0.345470\pi$
$174$		−	141.434i		−	0.812838i
$175$		0			0
$176$	−27.9222			−0.158649
$177$	−291.497	+	168.296i	−1.64687	+	0.950823i
$178$	58.4699	−	101.273i	0.328483	−	0.568949i
$179$	−83.4294	+	144.504i	−0.466086	+	0.807285i	−0.999250	−	0.0387275i	$-0.987670\pi$
$179$	−83.4294	+	144.504i	−0.466086	+	0.807285i	0.533164	+	0.846012i	$0.321003\pi$
$180$		0			0
$181$		−	154.927i		−	0.855953i	−0.903790	−	0.427976i	$-0.859227\pi$
$181$		−	154.927i		−	0.855953i	0.903790	−	0.427976i	$-0.140773\pi$
$182$	203.733	−	78.1617i	1.11941	−	0.429460i
$183$			66.4935i			0.363353i
$184$	−8.03926	−	13.9244i	−0.0436916	−	0.0756761i
$185$		0			0
$186$	−22.7959	+	39.4836i	−0.122558	+	0.212277i
$187$	2.86876	+	4.96883i	0.0153409	+	0.0265713i
$188$	127.452			0.677934
$189$	20.9708	+	3.32548i	0.110956	+	0.0175951i
$190$		0			0
$191$	−67.6393	−	117.155i	−0.354132	−	0.613375i	0.632837	−	0.774285i	$-0.281890\pi$
$191$	−67.6393	−	117.155i	−0.354132	−	0.613375i	−0.986969	+	0.160910i	$0.948557\pi$
$192$	−17.2981	+	29.9611i	−0.0900940	+	0.156047i
$193$	92.2060	+	53.2351i	0.477751	+	0.275830i	0.719479	−	0.694514i	$-0.244381\pi$
$193$	92.2060	+	53.2351i	0.477751	+	0.275830i	−0.241728	+	0.970344i	$0.577714\pi$
$194$	−217.149	+	125.371i	−1.11932	+	0.646241i
$195$		0			0
$196$	72.8528	−	65.5474i	0.371698	−	0.334426i
$197$		−	237.675i		−	1.20647i	−0.797563	−	0.603236i	$-0.793878\pi$
$197$		−	237.675i		−	1.20647i	0.797563	−	0.603236i	$-0.206122\pi$
$198$	−82.9412	+	47.8861i	−0.418895	+	0.241849i
$199$	165.715	+	95.6753i	0.832736	+	0.480780i	0.854789	−	0.518976i	$-0.173687\pi$
$199$	165.715	+	95.6753i	0.832736	+	0.480780i	−0.0220524	+	0.999757i	$0.507020\pi$
$200$		0			0
$201$	−171.118	+	98.7949i	−0.851332	+	0.491517i
$202$	−71.5882			−0.354397
$203$	−159.884	−	25.3540i	−0.787608	−	0.124896i
$204$	7.10888			0.0348474
$205$		0			0
$206$	159.128	+	91.8726i	0.772466	+	0.445984i
$207$	−47.7602	−	27.5744i	−0.230726	−	0.133210i
$208$	44.0854	+	76.3581i	0.211949	+	0.367106i
$209$		−	258.302i		−	1.23590i
$210$		0			0
$211$	31.2440			0.148076			0.0740379	−	0.997255i	$-0.476411\pi$
$211$	31.2440			0.148076			0.0740379	+	0.997255i	$0.476411\pi$
$212$	−33.3190	+	19.2367i	−0.157165	+	0.0907393i
$213$	213.751	−	370.227i	1.00352	−	1.73815i
$214$	86.6764	−	150.128i	0.405030	−	0.701532i
$215$		0			0
$216$			8.57935i			0.0397192i
$217$	40.5479	+	32.8477i	0.186857	+	0.151372i
$218$		−	9.85105i		−	0.0451883i
$219$	−40.7491	−	70.5795i	−0.186069	−	0.322281i
$220$		0			0
$221$	9.05875	−	15.6902i	0.0409898	−	0.0709964i
$222$	−117.721	−	203.899i	−0.530275	−	0.918463i
$223$	109.738			0.492099			0.246049	−	0.969257i	$-0.420867\pi$
$223$	109.738			0.492099			0.246049	+	0.969257i	$0.420867\pi$
$224$	30.7687	+	24.9256i	0.137360	+	0.111275i
$225$		0			0
$226$	−84.1279	−	145.714i	−0.372247	−	0.644751i
$227$	−15.6299	+	27.0718i	−0.0688543	+	0.119259i	−0.898397	−	0.439184i	$-0.855268\pi$
$227$	−15.6299	+	27.0718i	−0.0688543	+	0.119259i	0.829543	+	0.558443i	$0.188601\pi$
$228$	−277.163	−	160.020i	−1.21563	−	0.701844i
$229$	−157.300	+	90.8171i	−0.686899	+	0.396581i	−0.802449	−	0.596720i	$-0.796470\pi$
$229$	−157.300	+	90.8171i	−0.686899	+	0.396581i	0.115550	+	0.993302i	$0.463137\pi$
$230$		0			0
$231$	75.6905	+	197.291i	0.327665	+	0.854075i
$232$		−	65.4103i		−	0.281941i
$233$	−184.132	+	106.309i	−0.790266	+	0.456260i	−0.840056	−	0.542499i	$-0.817478\pi$
$233$	−184.132	+	106.309i	−0.790266	+	0.456260i	0.0497903	+	0.998760i	$0.484145\pi$
$234$	261.906	+	151.211i	1.11926	+	0.646202i
$235$		0			0
$236$	−134.811	+	77.8334i	−0.571234	+	0.329802i
$237$	218.671			0.922664
$238$	1.27436	−	8.03626i	0.00535447	−	0.0337658i
$239$	−173.604			−0.726378			−0.363189	−	0.931715i	$-0.618312\pi$
$239$	−173.604			−0.726378			−0.363189	+	0.931715i	$0.618312\pi$
$240$		0			0
$241$	−64.1746	−	37.0512i	−0.266285	−	0.153739i	0.360913	−	0.932599i	$-0.382465\pi$
$241$	−64.1746	−	37.0512i	−0.266285	−	0.153739i	−0.627198	+	0.778860i	$0.715798\pi$
$242$	88.5146	+	51.1040i	0.365763	+	0.211173i
$243$	−174.079	−	301.514i	−0.716374	−	1.24080i
$244$			30.7519i			0.126032i
$245$		0			0
$246$	366.254			1.48884
$247$	−706.372	+	407.824i	−2.85980	+	1.65111i
$248$	−10.5426	+	18.2604i	−0.0425106	+	0.0736305i
$249$	75.6429	−	131.017i	0.303787	−	0.526174i
$250$		0			0
$251$		−	28.7841i		−	0.114678i	−0.998355	−	0.0573389i	$-0.981738\pi$
$251$		−	28.7841i		−	0.114678i	0.998355	−	0.0573389i	$-0.0182616\pi$
$252$	134.144	+	21.2721i	0.532316	+	0.0844130i
$253$		−	39.6817i		−	0.156845i
$254$	142.177	+	246.257i	0.559750	+	0.969516i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	44.2773	+	76.6906i	0.172285	+	0.298407i	0.939218	−	0.343320i	$-0.111552\pi$
$257$	44.2773	+	76.6906i	0.172285	+	0.298407i	−0.766933	+	0.641727i	$0.778218\pi$
$258$	−184.991			−0.717021
$259$	−251.601	+	96.5265i	−0.971433	+	0.372689i
$260$		0			0
$261$	−112.178	−	194.297i	−0.429799	−	0.744434i
$262$	−106.493	+	184.452i	−0.406463	+	0.704015i
$263$	−127.172	−	73.4230i	−0.483545	−	0.279175i	0.238347	−	0.971180i	$-0.423394\pi$
$263$	−127.172	−	73.4230i	−0.483545	−	0.279175i	−0.721893	+	0.692005i	$0.756728\pi$
$264$	−73.9439	+	42.6915i	−0.280091	+	0.161710i
$265$		0			0
$266$	−230.581	+	284.635i	−0.866846	+	1.07006i
$267$		−	357.589i		−	1.33929i
$268$	−79.1385	+	45.6907i	−0.295293	+	0.170488i
$269$	−401.264	−	231.670i	−1.49169	−	0.861226i	−0.491732	−	0.870747i	$-0.663636\pi$
$269$	−401.264	−	231.670i	−1.49169	−	0.861226i	−0.999955	+	0.00952123i	$0.996969\pi$
$270$		0			0
$271$	−219.843	+	126.927i	−0.811230	+	0.468364i	−0.847383	−	0.530982i	$-0.821823\pi$
$271$	−219.843	+	126.927i	−0.811230	+	0.468364i	0.0361526	+	0.999346i	$0.488490\pi$
$272$	3.28771			0.0120872
$273$	420.022	−	518.485i	1.53854	−	1.89921i
$274$	266.538			0.972768
$275$		0			0
$276$	−42.5793	−	24.5832i	−0.154273	−	0.0890695i
$277$	93.4084	+	53.9294i	0.337215	+	0.194691i	0.659040	−	0.752108i	$-0.270963\pi$
$277$	93.4084	+	53.9294i	0.337215	+	0.194691i	−0.321825	+	0.946799i	$0.604296\pi$
$278$	−38.2105	−	66.1825i	−0.137448	−	0.238067i
$279$			72.3217i			0.259218i
$280$		0			0
$281$	27.1043			0.0964566			0.0482283	−	0.998836i	$-0.484642\pi$
$281$	27.1043			0.0964566			0.0482283	+	0.998836i	$0.484642\pi$
$282$	337.519	−	194.867i	1.19688	−	0.691016i
$283$	−169.726	+	293.974i	−0.599738	+	1.03878i	0.393122	+	0.919486i	$0.371395\pi$
$283$	−169.726	+	293.974i	−0.599738	+	1.03878i	−0.992859	+	0.119290i	$0.961938\pi$
$284$	98.8553	−	171.222i	0.348082	−	0.602896i
$285$		0			0
$286$			217.605i			0.760857i
$287$	65.6562	−	414.034i	0.228767	−	1.44263i
$288$			54.8795i			0.190554i
$289$	144.162	+	249.696i	0.498831	+	0.864001i
$290$		0			0
$291$	−383.370	+	664.017i	−1.31742	+	2.28185i
$292$	−18.8456	−	32.6416i	−0.0645398	−	0.111786i
$293$	−99.0920			−0.338198			−0.169099	−	0.985599i	$-0.554086\pi$
$293$	−99.0920			−0.338198			−0.169099	+	0.985599i	$0.554086\pi$
$294$	92.7112	−	284.972i	0.315344	−	0.969291i
$295$		0			0
$296$	−54.4436	−	94.2990i	−0.183931	−	0.318578i
$297$	−10.5869	+	18.3371i	−0.0356462	+	0.0617410i
$298$	111.795	+	64.5450i	0.375152	+	0.216594i
$299$	−108.517	+	62.6521i	−0.362932	+	0.209539i
$300$		0			0
$301$	−33.1623	+	209.124i	−0.110174	+	0.694765i
$302$			270.398i			0.895359i
$303$	−189.581	+	109.455i	−0.625679	+	0.361236i
$304$	−128.183	−	74.0062i	−0.421653	−	0.243442i
$305$		0			0
$306$	9.76594	−	5.63837i	0.0319149	−	0.0184260i
$307$	335.904			1.09415			0.547075	−	0.837083i	$-0.315741\pi$
$307$	335.904			1.09415			0.547075	+	0.837083i	$0.315741\pi$
$308$	35.0054	+	91.2433i	0.113654	+	0.296244i
$309$	561.873			1.81836
$310$		0			0
$311$	−32.6670	−	18.8603i	−0.105039	−	0.0606441i	0.446560	−	0.894753i	$-0.352649\pi$
$311$	−32.6670	−	18.8603i	−0.105039	−	0.0606441i	−0.551599	+	0.834109i	$0.685982\pi$
$312$	233.495	+	134.808i	0.748381	+	0.432078i
$313$	146.482	+	253.714i	0.467993	+	0.810588i	0.999331	−	0.0365723i	$-0.0116439\pi$
$313$	146.482	+	253.714i	0.467993	+	0.810588i	−0.531338	+	0.847160i	$0.678311\pi$
$314$			23.8972i			0.0761057i
$315$		0			0
$316$	101.131			0.320035
$317$	235.294	−	135.847i	0.742253	−	0.428540i	−0.0806350	−	0.996744i	$-0.525695\pi$
$317$	235.294	−	135.847i	0.742253	−	0.428540i	0.822888	+	0.568204i	$0.192361\pi$
$318$	−58.8239	+	101.886i	−0.184981	+	0.320396i
$319$	80.7162	−	139.805i	0.253029	−	0.438259i
$320$		0			0
$321$		−	530.094i		−	1.65138i
$322$	−35.4231	+	43.7271i	−0.110010	+	0.135798i
$323$			30.4139i			0.0941606i
$324$	−74.1953	−	128.510i	−0.228998	−	0.396636i
$325$		0			0
$326$	86.1161	−	149.158i	0.264160	−	0.457538i
$327$	−15.0617	−	26.0877i	−0.0460603	−	0.0797789i
$328$	169.385			0.516419
$329$	−159.783	−	416.482i	−0.485662	−	1.26590i
$330$		0			0
$331$	−119.742	−	207.400i	−0.361760	−	0.626586i	0.626491	−	0.779429i	$-0.284491\pi$
$331$	−119.742	−	207.400i	−0.361760	−	0.626586i	−0.988251	+	0.152843i	$0.951157\pi$
$332$	34.9833	−	60.5929i	0.105371	−	0.182509i
$333$	−323.443	−	186.740i	−0.971299	−	0.560780i
$334$	−246.722	+	142.445i	−0.738689	+	0.426482i
$335$		0			0
$336$	119.592	+	18.9645i	0.355929	+	0.0564421i
$337$		−	143.003i		−	0.424342i	−0.977233	−	0.212171i	$-0.931947\pi$
$337$		−	143.003i		−	0.424342i	0.977233	−	0.212171i	$-0.0680533\pi$
$338$	388.097	−	224.068i	1.14822	−	0.662923i
$339$	−445.577	−	257.254i	−1.31439	−	0.758861i
$340$		0			0
$341$	−45.0665	+	26.0192i	−0.132160	+	0.0763026i
$342$	−507.678			−1.48444
$343$	−305.527	−	155.891i	−0.890751	−	0.454492i
$344$	−85.5548			−0.248706
$345$		0			0
$346$	−225.716	−	130.317i	−0.652358	−	0.376639i
$347$	410.006	+	236.717i	1.18157	+	0.682183i	0.956378	−	0.292131i	$-0.0943643\pi$
$347$	410.006	+	236.717i	1.18157	+	0.682183i	0.225197	+	0.974313i	$0.427698\pi$
$348$	−100.009	−	173.220i	−0.287382	−	0.497759i
$349$			359.028i			1.02873i	0.857570	+	0.514366i	$0.171973\pi$
$349$			359.028i			1.02873i	−0.857570	+	0.514366i	$0.828027\pi$
$350$		0			0
$351$	66.8612			0.190488
$352$	−34.1976	+	19.7440i	−0.0971522	+	0.0560909i
$353$	−134.895	+	233.644i	−0.382138	+	0.661882i	−0.991368	−	0.131112i	$-0.958145\pi$
$353$	−134.895	+	233.644i	−0.382138	+	0.661882i	0.609230	+	0.792994i	$0.291479\pi$
$354$	−238.006	+	412.238i	−0.672333	+	1.16452i
$355$		0			0
$356$		−	165.378i		−	0.464545i
$357$	−8.91221	−	23.2301i	−0.0249642	−	0.0650704i
$358$			235.974i			0.659145i
$359$	67.6777	+	117.221i	0.188517	+	0.326522i	0.944756	−	0.327774i	$-0.106298\pi$
$359$	67.6777	+	117.221i	0.188517	+	0.326522i	−0.756239	+	0.654296i	$0.772965\pi$
$360$		0			0
$361$	504.115	−	873.153i	1.39644	−	2.41871i
$362$	−109.550	−	189.747i	−0.302625	−	0.524162i
$363$	312.541			0.860994
$364$	194.252	−	239.789i	0.533659	−	0.658761i
$365$		0			0
$366$	47.0180	+	81.4376i	0.128465	+	0.222507i
$367$	−319.093	+	552.685i	−0.869463	+	1.50595i	−0.00691734	+	0.999976i	$0.502202\pi$
$367$	−319.093	+	552.685i	−0.869463	+	1.50595i	−0.862546	+	0.505979i	$0.831131\pi$
$368$	−19.6921	−	11.3692i	−0.0535111	−	0.0308946i
$369$	503.149	−	290.493i	1.36355	−	0.787244i
$370$		0			0
$371$	104.632	+	84.7621i	0.282028	+	0.228469i
$372$			64.4764i			0.173324i
$373$	61.0189	−	35.2293i	0.163590	−	0.0944485i	−0.415970	−	0.909378i	$-0.636558\pi$
$373$	61.0189	−	35.2293i	0.163590	−	0.0944485i	0.579560	+	0.814930i	$0.303225\pi$
$374$	7.02699	+	4.05703i	0.0187887	+	0.0108477i
$375$		0			0
$376$	156.096	−	90.1219i	0.415148	−	0.239686i
$377$	−509.760			−1.35215
$378$	28.0353	−	10.7557i	0.0741675	−	0.0284543i
$379$	81.1658			0.214158			0.107079	−	0.994251i	$-0.465850\pi$
$379$	81.1658			0.214158			0.107079	+	0.994251i	$0.465850\pi$
$380$		0			0
$381$	753.028	+	434.761i	1.97645	+	1.14110i
$382$	−165.682	−	95.6563i	−0.433722	−	0.250409i
$383$	274.336	+	475.164i	0.716281	+	1.24064i	0.962463	+	0.271412i	$0.0874907\pi$
$383$	274.336	+	475.164i	0.716281	+	1.24064i	−0.246182	+	0.969224i	$0.579176\pi$
$384$			48.9263i			0.127412i
$385$		0			0
$386$	150.572			0.390082
$387$	−254.135	+	146.725i	−0.656680	+	0.379135i
$388$	−177.301	+	307.094i	−0.456962	+	0.791481i
$389$	148.460	−	257.140i	0.381646	−	0.661030i	−0.609652	−	0.792669i	$-0.708691\pi$
$389$	148.460	−	257.140i	0.381646	−	0.661030i	0.991298	+	0.131640i	$0.0420242\pi$
$390$		0			0
$391$			4.67234i			0.0119497i
$392$	42.8771	−	131.794i	0.109380	−	0.336208i
$393$			651.291i			1.65723i
$394$	−168.062	−	291.091i	−0.426552	−	0.738810i
$395$		0			0
$396$	−67.7212	+	117.297i	−0.171013	+	0.296203i
$397$	249.148	+	431.537i	0.627576	+	1.08699i	0.988037	+	0.154220i	$0.0492863\pi$
$397$	249.148	+	431.537i	0.627576	+	1.08699i	−0.360460	+	0.932775i	$0.617380\pi$
$398$	270.611			0.679926
$399$	−175.437	+	1106.32i	−0.439691	+	2.77273i
$400$		0			0
$401$	199.855	+	346.159i	0.498392	+	0.863240i	0.999998	−	0.00185592i	$-0.000590757\pi$
$401$	199.855	+	346.159i	0.498392	+	0.863240i	−0.501606	+	0.865096i	$0.667257\pi$
$402$	−139.717	+	241.997i	−0.347555	+	0.601983i
$403$	142.308	+	82.1615i	0.353121	+	0.203875i
$404$	−87.6773	+	50.6205i	−0.217023	+	0.125298i
$405$		0			0
$406$	−213.746	+	82.0032i	−0.526467	+	0.201978i
$407$		−	268.733i		−	0.660278i
$408$	8.70656	−	5.02673i	0.0213396	−	0.0123204i
$409$	253.322	+	146.255i	0.619369	+	0.357593i	0.776623	−	0.629965i	$-0.216931\pi$
$409$	253.322	+	146.255i	0.619369	+	0.357593i	−0.157254	+	0.987558i	$0.550264\pi$
$410$		0			0
$411$	705.850	−	407.523i	1.71740	−	0.991540i
$412$	259.855			0.630716
$413$	423.351	+	342.954i	1.02506	+	0.830398i
$414$	−77.9921			−0.188387
$415$		0			0
$416$	107.987	+	62.3461i	0.259583	+	0.149870i
$417$	−202.379	−	116.844i	−0.485321	−	0.280200i
$418$	−182.647	−	316.354i	−0.436955	−	0.756828i
$419$		−	608.631i		−	1.45258i	−0.687388	−	0.726291i	$-0.741243\pi$
$419$		−	608.631i		−	1.45258i	0.687388	−	0.726291i	$-0.258757\pi$
$420$		0			0
$421$	−224.488			−0.533226			−0.266613	−	0.963804i	$-0.585905\pi$
$421$	−224.488			−0.533226			−0.266613	+	0.963804i	$0.585905\pi$
$422$	38.2659	−	22.0928i	0.0906775	−	0.0523527i
$423$	309.115	−	535.403i	0.730768	−	1.26573i
$424$	−27.2049	+	47.1202i	−0.0641624	+	0.111133i
$425$		0			0
$426$		−	604.578i		−	1.41920i
$427$	100.490	−	38.5529i	0.235340	−	0.0902878i
$428$		−	245.158i		−	0.572799i
$429$	332.707	+	576.265i	0.775540	+	1.34327i
$430$		0			0
$431$	14.5102	−	25.1325i	0.0336664	−	0.0583120i	−0.848701	−	0.528873i	$-0.822615\pi$
$431$	14.5102	−	25.1325i	0.0336664	−	0.0583120i	0.882368	+	0.470561i	$0.155948\pi$
$432$	6.06652	+	10.5075i	0.0140429	+	0.0243230i
$433$	−144.736			−0.334264			−0.167132	−	0.985935i	$-0.553451\pi$
$433$	−144.736			−0.334264			−0.167132	+	0.985935i	$0.553451\pi$
$434$	72.8876	+	11.5583i	0.167944	+	0.0266320i
$435$		0			0
$436$	−6.96575	−	12.0650i	−0.0159765	−	0.0276721i
$437$	105.174	−	182.167i	0.240673	−	0.416858i
$438$	−99.8145	−	57.6279i	−0.227887	−	0.131571i
$439$	63.5971	−	36.7178i	0.144868	−	0.0836396i	−0.425814	−	0.904811i	$-0.640012\pi$
$439$	63.5971	−	36.7178i	0.144868	−	0.0836396i	0.570682	+	0.821171i	$0.306679\pi$
$440$		0			0
$441$	−98.6602	−	465.018i	−0.223719	−	1.05446i
$442$		−	25.6220i		−	0.0579683i
$443$	403.063	−	232.708i	0.909848	−	0.525301i	0.0294659	−	0.999566i	$-0.490619\pi$
$443$	403.063	−	232.708i	0.909848	−	0.525301i	0.880382	+	0.474265i	$0.157286\pi$
$444$	−288.356	−	166.483i	−0.649451	−	0.374961i
$445$		0			0
$446$	134.401	−	77.5965i	0.301348	−	0.173983i
$447$	394.743			0.883094
$448$	55.3089	+	8.77072i	0.123457	+	0.0195775i
$449$	−763.116			−1.69959			−0.849795	−	0.527114i	$-0.823274\pi$
$449$	−763.116			−1.69959			−0.849795	+	0.527114i	$0.823274\pi$
$450$		0			0
$451$	362.035	+	209.021i	0.802739	+	0.463462i
$452$	−206.070	−	118.975i	−0.455908	−	0.263219i
$453$	413.424	+	716.072i	0.912637	+	1.58073i
$454$			44.2081i			0.0973747i
$455$		0			0
$456$	−452.606			−0.992557
$457$	243.288	−	140.463i	0.532360	−	0.307358i	−0.209617	−	0.977784i	$-0.567222\pi$
$457$	243.288	−	140.463i	0.532360	−	0.307358i	0.741977	+	0.670426i	$0.233888\pi$
$458$	−128.435	+	222.456i	−0.280425	+	0.485711i
$459$	1.24656	−	2.15911i	0.00271582	−	0.00470393i
$460$		0			0
$461$		−	269.455i		−	0.584500i	−0.956342	−	0.292250i	$-0.905596\pi$
$461$		−	269.455i		−	0.584500i	0.956342	−	0.292250i	$-0.0944039\pi$
$462$	232.208	+	188.110i	0.502614	+	0.407165i
$463$			369.738i			0.798570i	0.916827	+	0.399285i	$0.130742\pi$
$463$			369.738i			0.798570i	−0.916827	+	0.399285i	$0.869258\pi$
$464$	−46.2520	−	80.1109i	−0.0996811	−	0.172653i
$465$		0			0
$466$	−150.343	+	260.402i	−0.322625	+	0.558802i
$467$	145.295	+	251.659i	0.311125	+	0.538884i	0.978606	−	0.205742i	$-0.0659609\pi$
$467$	145.295	+	251.659i	0.311125	+	0.538884i	−0.667481	+	0.744627i	$0.732628\pi$
$468$	427.690			0.913868
$469$	248.520	+	201.325i	0.529894	+	0.429265i
$470$		0			0
$471$	36.5375	+	63.2848i	0.0775744	+	0.134363i
$472$	−110.073	+	190.652i	−0.233205	+	0.403924i
$473$	−182.860	−	105.575i	−0.386597	−	0.223202i
$474$	267.817	−	154.624i	0.565014	−	0.326211i
$475$		0			0
$476$	−4.12172	−	10.7435i	−0.00865907	−	0.0225703i
$477$			186.623i			0.391244i
$478$	−212.621	+	122.757i	−0.444814	+	0.256813i
$479$	520.829	+	300.701i	1.08733	+	0.627768i	0.932863	−	0.360231i	$-0.117302\pi$
$479$	520.829	+	300.701i	1.08733	+	0.627768i	0.154462	+	0.987999i	$0.450635\pi$
$480$		0			0
$481$	−734.897	+	424.293i	−1.52785	+	0.882107i
$482$	−104.797			−0.217420
$483$	−26.9515	+	169.959i	−0.0558002	+	0.351881i
$484$	144.544			0.298644
$485$		0			0
$486$	−426.405	−	246.185i	−0.877376	−	0.506553i
$487$	−38.6662	−	22.3240i	−0.0793968	−	0.0458397i	0.459776	−	0.888035i	$-0.347930\pi$
$487$	−38.6662	−	22.3240i	−0.0793968	−	0.0458397i	−0.539173	+	0.842195i	$0.681263\pi$
$488$	21.7449	+	37.6632i	0.0445592	+	0.0771788i
$489$		−	526.668i		−	1.07703i
$490$		0			0
$491$	471.503			0.960291			0.480146	−	0.877189i	$-0.340584\pi$
$491$	471.503			0.960291			0.480146	+	0.877189i	$0.340584\pi$
$492$	448.568	−	258.981i	0.911724	−	0.526384i
$493$	−9.50396	+	16.4613i	−0.0192778	+	0.0333902i
$494$	−576.750	+	998.960i	−1.16751	+	2.02219i
$495$		0			0
$496$			29.8191i			0.0601191i
$497$	−683.447	−	108.379i	−1.37515	−	0.218066i
$498$		−	213.951i		−	0.429620i
$499$	−187.457	−	324.686i	−0.375666	−	0.650673i	0.614760	−	0.788714i	$-0.289253\pi$
$499$	−187.457	−	324.686i	−0.375666	−	0.650673i	−0.990426	+	0.138041i	$0.955919\pi$
$500$		0			0
$501$	−435.582	+	754.450i	−0.869425	+	1.50589i
$502$	−20.3535	−	35.2532i	−0.0405447	−	0.0702255i
$503$	68.1151			0.135418			0.0677089	−	0.997705i	$-0.478431\pi$
$503$	68.1151			0.135418			0.0677089	+	0.997705i	$0.478431\pi$
$504$	179.333	−	68.8010i	0.355820	−	0.136510i
$505$		0			0
$506$	−28.0592	−	48.6000i	−0.0554530	−	0.0960474i
$507$	685.176	−	1186.76i	1.35143	−	2.34075i
$508$	348.260	+	201.068i	0.685552	+	0.395803i
$509$	290.425	−	167.677i	0.570580	−	0.329424i	−0.186801	−	0.982398i	$-0.559812\pi$
$509$	290.425	−	167.677i	0.570580	−	0.329424i	0.757381	+	0.652973i	$0.226479\pi$
$510$		0			0
$511$	−83.0388	+	102.505i	−0.162503	+	0.200597i
$512$			22.6274i			0.0441942i
$513$	−97.2027	+	56.1200i	−0.189479	+	0.109396i
$514$	108.457	+	62.6176i	0.211006	+	0.121824i
$515$		0			0
$516$	−226.567	+	130.809i	−0.439084	+	0.253505i
$517$	444.841			0.860428
$518$	−239.893	+	296.129i	−0.463113	+	0.571678i
$519$	−796.992			−1.53563
$520$		0			0
$521$	170.918	+	98.6797i	0.328058	+	0.189405i	0.654979	−	0.755647i	$-0.272678\pi$
$521$	170.918	+	98.6797i	0.328058	+	0.189405i	−0.326920	+	0.945052i	$0.606011\pi$
$522$	−274.778	−	158.643i	−0.526394	−	0.303914i
$523$	−100.434	−	173.956i	−0.192034	−	0.332612i	0.753890	−	0.657000i	$-0.228175\pi$
$523$	−100.434	−	173.956i	−0.192034	−	0.332612i	−0.945924	+	0.324388i	$0.894842\pi$
$524$			301.209i			0.574826i
$525$		0			0
$526$	−207.672			−0.394813
$527$	5.30638	−	3.06364i	0.0100690	−	0.00581336i
$528$	−60.3750	+	104.573i	−0.114347	+	0.198054i
$529$	−248.343	+	430.142i	−0.469457	+	0.813123i
$530$		0			0
$531$			755.093i			1.42202i
$532$	−81.1359	+	511.650i	−0.152511	+	0.961749i
$533$		−	1320.06i		−	2.47667i
$534$	−252.854	−	437.956i	−0.473509	−	0.820142i
$535$		0			0
$536$	−64.6164	+	111.919i	−0.120553	+	0.208804i
$537$	360.791	+	624.909i	0.671865	+	1.16370i
$538$	−655.261			−1.21796
$539$	254.276	−	228.779i	0.471756	−	0.424450i
$540$		0			0
$541$	504.286	+	873.448i	0.932136	+	1.61451i	0.779663	+	0.626199i	$0.215390\pi$
$541$	504.286	+	873.448i	0.932136	+	1.61451i	0.152473	+	0.988308i	$0.451276\pi$
$542$	−179.501	+	310.906i	−0.331183	+	0.573626i
$543$	−580.225	−	334.993i	−1.06855	−	0.616930i
$544$	4.02661	−	2.32476i	0.00740185	−	0.00427346i
$545$		0			0
$546$	147.796	−	932.012i	0.270688	−	1.70698i
$547$			476.537i			0.871184i	0.900144	+	0.435592i	$0.143461\pi$
$547$			476.537i			0.871184i	−0.900144	+	0.435592i	$0.856539\pi$
$548$	326.441	−	188.471i	0.595696	−	0.343925i
$549$	129.184	+	74.5842i	0.235307	+	0.135855i
$550$		0			0
$551$	741.088	−	427.867i	1.34499	−	0.776529i
$552$	−69.5317			−0.125963
$553$	−126.786	−	330.473i	−0.229269	−	0.597600i
$554$	152.535			0.275335
$555$		0			0
$556$	−93.5962	−	54.0378i	−0.168338	−	0.0971903i
$557$	−477.207	−	275.515i	−0.856745	−	0.494642i	0.00617608	−	0.999981i	$-0.498034\pi$
$557$	−477.207	−	275.515i	−0.856745	−	0.494642i	−0.862921	+	0.505339i	$0.831367\pi$
$558$	51.1392	+	88.5757i	0.0916473	+	0.158738i
$559$			666.751i			1.19276i
$560$		0			0
$561$	24.8119			0.0442281
$562$	33.1959	−	19.1656i	0.0590674	−	0.0341026i
$563$	−181.277	+	313.980i	−0.321984	+	0.557692i	−0.980897	−	0.194527i	$-0.937683\pi$
$563$	−181.277	+	313.980i	−0.321984	+	0.557692i	0.658914	+	0.752219i	$0.271016\pi$
$564$	275.583	−	477.324i	0.488622	−	0.846319i
$565$		0			0
$566$			480.057i			0.848157i
$567$	−326.924	+	403.563i	−0.576586	+	0.711751i
$568$		−	279.605i		−	0.492262i
$569$	−137.129	−	237.514i	−0.241000	−	0.417424i	0.719999	−	0.693975i	$-0.244142\pi$
$569$	−137.129	−	237.514i	−0.241000	−	0.417424i	−0.960999	+	0.276550i	$0.910809\pi$
$570$		0			0
$571$	−68.1841	+	118.098i	−0.119412	+	0.206827i	−0.919535	−	0.393009i	$-0.871434\pi$
$571$	−68.1841	+	118.098i	−0.119412	+	0.206827i	0.800123	+	0.599836i	$0.204768\pi$
$572$	153.870	+	266.511i	0.269004	+	0.465928i
$573$	−585.014			−1.02097
$574$	−212.354	−	553.512i	−0.369955	−	0.964306i
$575$		0			0
$576$	38.8056	+	67.2133i	0.0673709	+	0.116690i
$577$	282.342	−	489.031i	0.489328	−	0.847541i	−0.510596	−	0.859821i	$-0.670575\pi$
$577$	282.342	−	489.031i	0.489328	−	0.847541i	0.999925	+	0.0122791i	$0.00390867\pi$
$578$	353.124	+	203.876i	0.610941	+	0.352727i
$579$	398.746	−	230.216i	0.688680	−	0.397610i
$580$		0			0
$581$	−241.861	−	38.3536i	−0.416284	−	0.0660131i
$582$			1084.34i			1.86312i
$583$	−116.293	+	67.1415i	−0.199473	+	0.115166i
$584$	−46.1622	−	26.6517i	−0.0790448	−	0.0456365i
$585$		0			0
$586$	−121.362	+	70.0686i	−0.207103	+	0.119571i
$587$	−282.316			−0.480947			−0.240473	−	0.970656i	$-0.577303\pi$
$587$	−282.316			−0.480947			−0.240473	+	0.970656i	$0.577303\pi$
$588$	−87.9578	−	414.574i	−0.149588	−	0.705058i
$589$	−275.849			−0.468335
$590$		0			0
$591$	−890.126	−	513.914i	−1.50613	−	0.869567i
$592$	−133.359	−	76.9948i	−0.225269	−	0.130059i
$593$	−522.130	−	904.355i	−0.880489	−	1.52505i	−0.850798	−	0.525492i	$-0.823881\pi$
$593$	−522.130	−	904.355i	−0.880489	−	1.52505i	−0.0296904	−	0.999559i	$-0.509452\pi$
$594$			29.9443i			0.0504113i
$595$		0			0
$596$	182.561			0.306310
$597$	716.635	−	413.749i	1.20039	−	0.693047i
$598$	−88.6034	+	153.466i	−0.148166	+	0.256631i
$599$	446.783	−	773.850i	0.745881	−	1.29190i	−0.203901	−	0.978992i	$-0.565362\pi$
$599$	446.783	−	773.850i	0.745881	−	1.29190i	0.949782	−	0.312912i	$-0.101305\pi$
$600$		0			0
$601$		−	158.211i		−	0.263246i	−0.991300	−	0.131623i	$-0.957981\pi$
$601$		−	158.211i		−	0.263246i	0.991300	−	0.131623i	$-0.0420188\pi$
$602$	107.258	+	279.573i	0.178169	+	0.464407i
$603$			443.264i			0.735098i
$604$	191.201	+	331.169i	0.316557	+	0.548293i
$605$		0			0
$606$	−154.792	+	268.108i	−0.255433	+	0.442422i
$607$	−329.285	−	570.339i	−0.542480	−	0.939602i	−0.998761	−	0.0497666i	$-0.984152\pi$
$607$	−329.285	−	570.339i	−0.542480	−	0.939602i	0.456281	−	0.889836i	$-0.349181\pi$
$608$	−209.321			−0.344278
$609$	−440.665	+	543.967i	−0.723588	+	0.893214i
$610$		0			0
$611$	−702.344	−	1216.49i	−1.14950	−	1.99099i
$612$	7.97386	−	13.8111i	0.0130292	−	0.0225672i
$613$	−233.226	−	134.653i	−0.380467	−	0.219663i	0.297555	−	0.954705i	$-0.403829\pi$
$613$	−233.226	−	134.653i	−0.380467	−	0.219663i	−0.678021	+	0.735042i	$0.737162\pi$
$614$	411.397	−	237.520i	0.670028	−	0.386841i
$615$		0			0
$616$	107.391	+	86.9972i	0.174337	+	0.141229i
$617$		−	595.352i		−	0.964914i	−0.875920	−	0.482457i	$-0.839744\pi$
$617$		−	595.352i		−	0.964914i	0.875920	−	0.482457i	$-0.160256\pi$
$618$	688.151	−	397.304i	1.11351	−	0.642887i
$619$	−138.279	−	79.8352i	−0.223390	−	0.128975i	0.384129	−	0.923280i	$-0.374502\pi$
$619$	−138.279	−	79.8352i	−0.223390	−	0.128975i	−0.607519	+	0.794305i	$0.707835\pi$
$620$		0			0
$621$	−14.9328	+	8.62145i	−0.0240464	+	0.0138832i
$622$	−53.3450			−0.0857637
$623$	−540.416	+	207.330i	−0.867442	+	0.332793i
$624$	381.295			0.611050
$625$		0			0
$626$	358.806	+	207.157i	0.573172	+	0.330921i
$627$	−967.377	−	558.515i	−1.54287	−	0.890774i
$628$	16.8979	+	29.2680i	0.0269074	+	0.0466050i
$629$			31.6421i			0.0503054i
$630$		0			0
$631$	−671.814			−1.06468			−0.532341	−	0.846530i	$-0.678688\pi$
$631$	−671.814			−1.06468			−0.532341	+	0.846530i	$0.678688\pi$
$632$	123.860	−	71.5105i	0.195981	−	0.113150i
$633$	67.5575	−	117.013i	0.106726	−	0.184855i
$634$	192.117	−	332.756i	0.303023	−	0.524852i
$635$		0			0
$636$			166.379i			0.261602i
$637$	−1027.10	−	334.152i	−1.61241	−	0.524572i
$638$		−	228.300i		−	0.357837i
$639$	−479.518	−	830.549i	−0.750419	−	1.29976i
$640$		0			0
$641$	349.371	−	605.129i	0.545041	−	0.944039i	−0.453563	−	0.891224i	$-0.649847\pi$
$641$	349.371	−	605.129i	0.545041	−	0.944039i	0.998604	−	0.0528149i	$-0.0168193\pi$
$642$	−374.833	−	649.230i	−0.583852	−	1.01126i
$643$	965.126			1.50097			0.750486	−	0.660886i	$-0.229819\pi$
$643$	965.126			1.50097			0.750486	+	0.660886i	$0.229819\pi$
$644$	−12.4645	+	78.6024i	−0.0193549	+	0.122053i
$645$		0			0
$646$	21.5059	+	37.2493i	0.0332908	+	0.0576614i
$647$	448.968	−	777.635i	0.693922	−	1.20191i	−0.276620	−	0.960979i	$-0.589214\pi$
$647$	448.968	−	777.635i	0.693922	−	1.20191i	0.970543	−	0.240929i	$-0.0774522\pi$
$648$	−181.741	−	104.928i	−0.280464	−	0.161926i
$649$	−470.529	+	271.660i	−0.725006	+	0.418582i
$650$		0			0
$651$	210.694	−	80.8325i	0.323647	−	0.124167i
$652$		−	243.573i		−	0.373579i
$653$	−627.141	+	362.080i	−0.960399	+	0.554487i	−0.896296	−	0.443456i	$-0.853752\pi$
$653$	−627.141	+	362.080i	−0.960399	+	0.554487i	−0.0641035	+	0.997943i	$0.520419\pi$
$654$	−36.8936	−	21.3005i	−0.0564122	−	0.0325696i
$655$		0			0
$656$	207.454	−	119.773i	0.316240	−	0.182582i
$657$	−182.829			−0.278279
$658$	−490.190	−	397.101i	−0.744970	−	0.603497i
$659$	−29.5936			−0.0449069			−0.0224534	−	0.999748i	$-0.507148\pi$
$659$	−29.5936			−0.0449069			−0.0224534	+	0.999748i	$0.507148\pi$
$660$		0			0
$661$	435.031	+	251.166i	0.658141	+	0.379978i	0.791568	−	0.611080i	$-0.209265\pi$
$661$	435.031	+	251.166i	0.658141	+	0.379978i	−0.133427	+	0.991059i	$0.542598\pi$
$662$	−293.308	−	169.341i	−0.443063	−	0.255803i
$663$	−39.1747	−	67.8525i	−0.0590870	−	0.102342i
$664$		−	98.9478i		−	0.149018i
$665$		0			0
$666$	−528.179			−0.793062
$667$	113.850	−	65.7312i	0.170689	−	0.0985476i
$668$	−201.448	+	348.918i	−0.301569	+	0.522332i
$669$	237.282	−	410.984i	0.354681	−	0.614326i
$670$		0			0
$671$			107.333i			0.159959i
$672$	159.880	−	61.3376i	0.237916	−	0.0912762i
$673$		−	454.895i		−	0.675921i	−0.941160	−	0.337960i	$-0.890263\pi$
$673$		−	454.895i		−	0.675921i	0.941160	−	0.337960i	$-0.109737\pi$
$674$	−101.118	−	175.142i	−0.150027	−	0.259855i
$675$		0			0
$676$	316.880	−	548.852i	0.468757	−	0.811911i
$677$	353.064	+	611.526i	0.521513	+	0.903287i	0.999687	+	0.0250221i	$0.00796563\pi$
$677$	353.064	+	611.526i	0.521513	+	0.903287i	−0.478174	+	0.878265i	$0.658701\pi$
$678$	−727.624			−1.07319
$679$	1225.79	+	194.382i	1.80529	+	0.286277i
$680$		0			0
$681$	67.5918	+	117.073i	0.0992538	+	0.171913i
$682$	−36.7967	+	63.7337i	−0.0539541	+	0.0934512i
$683$	429.889	+	248.196i	0.629413	+	0.363392i	0.780525	−	0.625125i	$-0.214952\pi$
$683$	429.889	+	248.196i	0.629413	+	0.363392i	−0.151112	+	0.988517i	$0.548285\pi$
$684$	−621.776	+	358.982i	−0.909029	+	0.524828i
$685$		0			0
$686$	−484.425	+	25.1140i	−0.706158	+	0.0366093i
$687$			785.479i			1.14335i
$688$	−104.783	+	60.4964i	−0.152301	+	0.0879308i
$689$	367.220	+	212.015i	0.532976	+	0.307714i
$690$		0			0
$691$	−229.329	+	132.403i	−0.331879	+	0.191611i	−0.656675	−	0.754173i	$-0.728038\pi$
$691$	−229.329	+	132.403i	−0.331879	+	0.191611i	0.324796	+	0.945784i	$0.394704\pi$
$692$	−368.593			−0.532648
$693$	468.198	+	74.2454i	0.675611	+	0.107136i
$694$	669.538			0.964752
$695$		0			0
$696$	−244.970	−	141.434i	−0.351969	−	0.203209i
$697$	−42.6280	−	24.6113i	−0.0611593	−	0.0353103i
$698$	253.871	+	439.717i	0.363712	+	0.629968i
$699$			919.466i			1.31540i
$700$		0			0
$701$	−1349.57			−1.92521			−0.962603	−	0.270915i	$-0.912674\pi$
$701$	−1349.57			−1.92521			−0.962603	+	0.270915i	$0.912674\pi$
$702$	81.8879	−	47.2780i	0.116649	−	0.0673475i
$703$	712.262	−	1233.67i	1.01318	−	1.75487i
$704$	−27.9222	+	48.3627i	−0.0396622	+	0.0686970i
$705$		0			0
$706$			381.540i			0.540425i
$707$	275.335	+	223.047i	0.389441	+	0.315484i
$708$			673.183i			0.950823i
$709$	−426.332	−	738.429i	−0.601315	−	1.04151i	−0.992622	−	0.121248i	$-0.961310\pi$
$709$	−426.332	−	738.429i	−0.601315	−	1.04151i	0.391308	−	0.920260i	$-0.372023\pi$
$710$		0			0
$711$	245.279	−	424.835i	0.344977	−	0.597518i
$712$	−116.940	−	202.546i	−0.164241	−	0.284474i
$713$	−42.3774			−0.0594354
$714$	−27.3414	−	22.1491i	−0.0382933	−	0.0310212i
$715$		0			0
$716$	166.859	+	289.008i	0.233043	+	0.403642i
$717$	−375.377	+	650.172i	−0.523539	+	0.906795i
$718$	165.776	+	95.7108i	0.230886	+	0.133302i
$719$	1161.76	−	670.740i	1.61579	−	0.932879i	0.627802	−	0.778373i	$-0.283955\pi$
$719$	1161.76	−	670.740i	1.61579	−	0.932879i	0.987992	−	0.154506i	$-0.0493786\pi$
$720$		0			0
$721$	−325.774	−	849.146i	−0.451836	−	1.17773i
$722$		−	1425.85i		−	1.97487i
$723$	−277.524	+	160.228i	−0.383850	+	0.221616i
$724$	−268.342	−	154.927i	−0.370638	−	0.213988i
$725$		0			0
$726$	382.783	−	221.000i	0.527249	−	0.304407i
$727$	729.033			1.00280			0.501398	−	0.865217i	$-0.332819\pi$
$727$	729.033			1.00280			0.501398	+	0.865217i	$0.332819\pi$
$728$	68.3525	−	431.037i	0.0938908	−	0.592084i
$729$	−837.856			−1.14932
$730$		0			0
$731$	21.5310	+	12.4309i	0.0294541	+	0.0170054i
$732$	115.170	+	66.4935i	0.157336	+	0.0908381i
$733$	237.568	+	411.479i	0.324103	+	0.561363i	0.981330	−	0.192329i	$-0.0616042\pi$
$733$	237.568	+	411.479i	0.324103	+	0.561363i	−0.657227	+	0.753692i	$0.728271\pi$
$734$			902.531i			1.22961i
$735$		0			0
$736$	−32.1570			−0.0436916
$737$	−276.215	+	159.473i	−0.374783	+	0.216381i
$738$	410.819	−	711.559i	0.556665	−	0.964173i
$739$	−258.051	+	446.958i	−0.349190	+	0.604815i	−0.986106	−	0.166119i	$-0.946877\pi$
$739$	−258.051	+	446.958i	−0.349190	+	0.604815i	0.636916	+	0.770933i	$0.280210\pi$
$740$		0			0
$741$			3527.28i			4.76016i
$742$	188.084	+	29.8258i	0.253482	+	0.0401964i
$743$		−	292.423i		−	0.393570i	−0.980447	−	0.196785i	$-0.936950\pi$
$743$		−	292.423i		−	0.393570i	0.980447	−	0.196785i	$-0.0630501\pi$
$744$	45.5917	+	78.9672i	0.0612792	+	0.106139i
$745$		0			0
$746$	49.8218	−	86.2938i	0.0667852	−	0.115675i
$747$	−169.694	−	293.918i	−0.227167	−	0.393465i
$748$	11.4750			0.0153409
$749$	−801.119	+	307.348i	−1.06958	+	0.410345i
$750$		0			0
$751$	7.11394	+	12.3217i	0.00947262	+	0.0164071i	0.870723	−	0.491774i	$-0.163651\pi$
$751$	7.11394	+	12.3217i	0.00947262	+	0.0164071i	−0.861250	+	0.508181i	$0.830318\pi$
$752$	127.452	−	220.753i	0.169483	−	0.293554i
$753$	−107.801	−	62.2387i	−0.143161	−	0.0826543i
$754$	−624.325	+	360.454i	−0.828018	+	0.478056i
$755$		0			0
$756$	26.7307	−	32.9970i	0.0353580	−	0.0436468i
$757$			26.6276i			0.0351751i	0.999845	+	0.0175876i	$0.00559858\pi$
$757$			26.6276i			0.0351751i	−0.999845	+	0.0175876i	$0.994401\pi$
$758$	99.4075	−	57.3929i	0.131144	−	0.0757163i
$759$	−148.614	−	85.8021i	−0.195802	−	0.113046i
$760$		0			0
$761$	300.850	−	173.696i	0.395336	−	0.228247i	−0.289134	−	0.957289i	$-0.593367\pi$
$761$	300.850	−	173.696i	0.395336	−	0.228247i	0.684469	+	0.729042i	$0.260034\pi$
$762$	1229.69			1.61377
$763$	−30.6929	+	37.8881i	−0.0402266	+	0.0496567i
$764$	−270.557			−0.354132
$765$		0			0
$766$	671.983	+	387.969i	0.877262	+	0.506488i
$767$	1485.80	+	857.828i	1.93716	+	1.11842i
$768$	34.5961	+	59.9222i	0.0450470	+	0.0780237i
$769$		−	641.651i		−	0.834396i	−0.908816	−	0.417198i	$-0.863012\pi$
$769$		−	641.651i		−	0.834396i	0.908816	−	0.417198i	$-0.136988\pi$
$770$		0			0
$771$	382.956			0.496700
$772$	184.412	−	106.470i	0.238876	−	0.137915i
$773$	−214.517	+	371.554i	−0.277512	+	0.480665i	−0.970766	−	0.240029i	$-0.922843\pi$
$773$	−214.517	+	371.554i	−0.277512	+	0.480665i	0.693254	+	0.720693i	$0.256176\pi$
$774$	−207.501	+	359.402i	−0.268089	+	0.464343i
$775$		0			0
$776$			501.483i			0.646241i
$777$	−182.521	+	1151.00i	−0.234905	+	1.48133i
$778$		−	419.909i		−	0.539728i
$779$	1108.00	+	1919.11i	1.42233	+	2.46355i
$780$		0			0
$781$	345.032	−	597.613i	0.441783	−	0.765190i
$782$	3.30384	+	5.72243i	0.00422486	+	0.00731768i
$783$	−70.1472			−0.0895878
$784$	−40.6787	−	191.732i	−0.0518861	−	0.244556i
$785$		0			0
$786$	460.532	+	797.665i	0.585919	+	1.01484i
$787$	−430.010	+	744.799i	−0.546392	+	0.946378i	0.452126	+	0.891954i	$0.350666\pi$
$787$	−430.010	+	744.799i	−0.546392	+	0.946378i	−0.998518	+	0.0544240i	$0.982668\pi$
$788$	−411.665	−	237.675i	−0.522418	−	0.301618i
$789$	−549.959	+	317.519i	−0.697033	+	0.402432i
$790$		0			0
$791$	−130.437	+	822.546i	−0.164901	+	1.03988i
$792$			191.544i			0.241849i
$793$	293.520	−	169.464i	0.370138	−	0.213699i
$794$	610.285	+	352.348i	0.768621	+	0.443764i
$795$		0			0
$796$	331.429	−	191.351i	0.416368	−	0.240390i
$797$	428.249			0.537326			0.268663	−	0.963234i	$-0.413418\pi$
$797$	428.249			0.537326			0.268663	+	0.963234i	$0.413418\pi$
$798$	567.421	+	1479.01i	0.711053	+	1.85340i
$799$	−52.3780			−0.0655544
$800$		0			0
$801$	−694.725	−	401.100i	−0.867322	−	0.500749i
$802$	489.543	+	282.638i	0.610403	+	0.352416i
$803$	−65.7764	−	113.928i	−0.0819134	−	0.141878i
$804$			395.180i			0.491517i
$805$		0			0
$806$	232.388			0.288322
$807$	−1735.27	+	1001.86i	−2.15027	+	1.24146i
$808$	−71.5882	+	123.994i	−0.0885993	+	0.153459i
$809$	−260.622	+	451.410i	−0.322153	+	0.557986i	−0.980932	−	0.194351i	$-0.937740\pi$
$809$	−260.622	+	451.410i	−0.322153	+	0.557986i	0.658779	+	0.752337i	$0.271073\pi$
$810$		0			0
$811$		−	466.461i		−	0.575168i	−0.957755	−	0.287584i	$-0.907148\pi$
$811$		−	466.461i		−	0.575168i	0.957755	−	0.287584i	$-0.0928520\pi$
$812$	−203.799	+	251.574i	−0.250984	+	0.309820i
$813$			1097.79i			1.35030i
$814$	−190.023	−	329.130i	−0.233444	−	0.404336i
$815$		0			0
$816$	7.10888	−	12.3129i	0.00871186	−	0.0150894i
$817$	−559.639	−	969.323i	−0.684992	−	1.18644i
$818$	413.673			0.505713
$819$	−536.184	−	1397.59i	−0.654682	−	1.70646i
$820$		0			0
$821$	−69.8347	−	120.957i	−0.0850605	−	0.147329i	0.820356	−	0.571852i	$-0.193775\pi$
$821$	−69.8347	−	120.957i	−0.0850605	−	0.147329i	−0.905417	+	0.424523i	$0.860442\pi$
$822$	576.324	−	998.223i	0.701124	−	1.21438i
$823$	290.590	+	167.772i	0.353087	+	0.203855i	0.666044	−	0.745913i	$-0.267986\pi$
$823$	290.590	+	167.772i	0.353087	+	0.203855i	−0.312957	+	0.949767i	$0.601320\pi$
$824$	318.256	−	183.745i	0.386233	−	0.222992i
$825$		0			0
$826$	761.002	+	120.677i	0.921310	+	0.146098i
$827$			1444.99i			1.74727i	0.486583	+	0.873634i	$0.338243\pi$
$827$			1444.99i			1.74727i	−0.486583	+	0.873634i	$0.661757\pi$
$828$	−95.5204	+	55.1488i	−0.115363	+	0.0666048i
$829$	−137.763	−	79.5378i	−0.166180	−	0.0959442i	0.414603	−	0.910002i	$-0.363920\pi$
$829$	−137.763	−	79.5378i	−0.166180	−	0.0959442i	−0.580783	+	0.814058i	$0.697254\pi$
$830$		0			0
$831$	403.946	−	233.218i	0.486096	−	0.280648i
$832$	176.341			0.211949
$833$	−29.9399	+	26.9376i	−0.0359422	+	0.0323381i
$834$	−330.484			−0.396263
$835$		0			0
$836$	−447.392	−	258.302i	−0.535158	−	0.308974i
$837$	19.5828	+	11.3061i	0.0233964	+	0.0135079i
$838$	−430.367	−	745.418i	−0.513565	−	0.889521i
$839$		−	529.134i		−	0.630672i	−0.948980	−	0.315336i	$-0.897883\pi$
$839$		−	529.134i		−	0.630672i	0.948980	−	0.315336i	$-0.102117\pi$
$840$		0			0
$841$	−306.187			−0.364075
$842$	−274.941	+	158.737i	−0.326533	+	0.188524i
$843$	58.6065	−	101.509i	0.0695213	−	0.120414i
$844$	31.2440	−	54.1162i	0.0370189	−	0.0641187i
$845$		0			0
$846$		−	874.309i		−	1.03346i
$847$	−181.211	−	472.335i	−0.213944	−	0.557657i
$848$			76.9469i			0.0907393i
$849$	733.981	+	1271.29i	0.864524	+	1.49740i
$850$		0			0
$851$	109.421	−	189.524i	0.128580	−	0.222707i
$852$	−427.501	−	740.454i	−0.501762	−	0.869077i
$853$	465.605			0.545844			0.272922	−	0.962036i	$-0.412010\pi$
$853$	465.605			0.545844			0.272922	+	0.962036i	$0.412010\pi$
$854$	95.8137	−	118.275i	0.112194	−	0.138495i
$855$		0			0
$856$	−173.353	−	300.256i	−0.202515	−	0.350766i
$857$	−728.046	+	1261.01i	−0.849528	+	1.47143i	0.0321012	+	0.999485i	$0.489780\pi$
$857$	−728.046	+	1261.01i	−0.849528	+	1.47143i	−0.881630	+	0.471942i	$0.843553\pi$
$858$	814.961	+	470.518i	0.949838	+	0.548389i
$859$	251.769	−	145.359i	0.293095	−	0.169219i	−0.346242	−	0.938145i	$-0.612542\pi$
$859$	251.769	−	145.359i	0.293095	−	0.169219i	0.639337	+	0.768927i	$0.279209\pi$
$860$		0			0
$861$	−1408.65	−	1141.14i	−1.63606	−	1.32536i
$862$		−	41.0411i		−	0.0476115i
$863$	−625.465	+	361.112i	−0.724756	+	0.418438i	−0.816501	−	0.577344i	$-0.804089\pi$
$863$	−625.465	+	361.112i	−0.724756	+	0.418438i	0.0917446	+	0.995783i	$0.470756\pi$
$864$	14.8599	+	8.57935i	0.0171989	+	0.00992980i
$865$		0			0
$866$	−177.265	+	102.344i	−0.204694	+	0.118180i
$867$	1246.86			1.43813
$868$	97.4417	−	37.3834i	0.112260	−	0.0430684i
$869$	352.976			0.406186
$870$		0			0
$871$	872.213	+	503.572i	1.00139	+	0.578154i
$872$	−17.0625	−	9.85105i	−0.0195671	−	0.0112971i
$873$	860.035	+	1489.62i	0.985149	+	1.70633i
$874$		−	297.477i		−	0.340363i
$875$		0			0
$876$	−162.996			−0.186069
$877$	767.986	−	443.397i	0.875697	−	0.505584i	0.00645970	−	0.999979i	$-0.497944\pi$
$877$	767.986	−	443.397i	0.875697	−	0.505584i	0.869237	+	0.494395i	$0.164610\pi$
$878$	51.9268	−	89.9399i	0.0591422	−	0.102437i
$879$	−214.262	+	371.113i	−0.243757	+	0.422199i
$880$		0			0
$881$		−	387.945i		−	0.440346i	−0.975461	−	0.220173i	$-0.929338\pi$
$881$		−	387.945i		−	0.440346i	0.975461	−	0.220173i	$-0.0706622\pi$
$882$	−449.651	−	499.765i	−0.509808	−	0.566627i
$883$		−	840.331i		−	0.951677i	−0.879533	−	0.475839i	$-0.842145\pi$
$883$		−	840.331i		−	0.951677i	0.879533	−	0.475839i	$-0.157855\pi$
$884$	−18.1175	−	31.3804i	−0.0204949	−	0.0354982i
$885$		0			0
$886$	329.099	−	570.017i	0.371444	−	0.643360i
$887$	−543.709	−	941.731i	−0.612975	−	1.06170i	−0.990736	−	0.135801i	$-0.956639\pi$
$887$	−543.709	−	941.731i	−0.612975	−	1.06170i	0.377761	−	0.925903i	$-0.376694\pi$
$888$	−470.884			−0.530275
$889$	220.439	−	1390.11i	0.247963	−	1.56367i
$890$		0			0
$891$	−258.962	−	448.536i	−0.290642	−	0.503407i
$892$	109.738	−	190.072i	0.123025	−	0.213085i
$893$	2042.13	+	1179.03i	2.28682	+	1.32030i
$894$	483.460	−	279.126i	0.540783	−	0.312221i
$895$		0			0
$896$	73.9411	−	28.3674i	0.0825236	−	0.0316601i
$897$			541.879i			0.604102i
$898$	−934.622	+	539.604i	−1.04078	+	0.600896i
$899$	−149.302	−	86.1995i	−0.166076	−	0.0958838i
$900$		0			0
$901$	13.6929	−	7.90561i	0.0151975	−	0.00877426i
$902$	591.201			0.655434
$903$	711.494	+	576.378i	0.787922	+	0.638292i
$904$	−336.512			−0.372247
$905$		0			0
$906$	1012.68	+	584.671i	1.11775	+	0.645332i
$907$	538.448	+	310.873i	0.593659	+	0.342749i	0.766543	−	0.642193i	$-0.221975\pi$
$907$	538.448	+	310.873i	0.593659	+	0.342749i	−0.172884	+	0.984942i	$0.555309\pi$
$908$	31.2599	+	54.1437i	0.0344272	+	0.0596296i
$909$			491.091i			0.540254i
$910$		0			0
$911$	−389.751			−0.427828			−0.213914	−	0.976853i	$-0.568621\pi$
$911$	−389.751			−0.427828			−0.213914	+	0.976853i	$0.568621\pi$
$912$	−554.327	+	320.041i	−0.607815	+	0.350922i
$913$	122.101	−	211.486i	0.133737	−	0.231639i
$914$	198.644	−	344.062i	0.217335	−	0.376435i
$915$		0			0
$916$			363.268i			0.396581i
$917$	984.280	−	377.618i	1.07337	−	0.411797i
$918$		−	3.52580i		−	0.00384075i
$919$	−496.225	−	859.486i	−0.539962	−	0.935241i	−0.998905	−	0.0467756i	$-0.985105\pi$
$919$	−496.225	−	859.486i	−0.539962	−	0.935241i	0.458944	−	0.888465i	$-0.348228\pi$
$920$		0			0
$921$	726.311	−	1258.01i	0.788611	−	1.36591i
$922$	−190.533	−	330.013i	−0.206652	−	0.357932i
$923$	−2179.04			−2.36082
$924$	417.409	+	66.1915i	0.451741	+	0.0716358i
$925$		0			0
$926$	261.444	+	452.835i	0.282337	+	0.489022i
$927$	630.240	−	1091.61i	0.679871	−	1.17757i
$928$	−113.294	−	65.4103i	−0.122084	−	0.0704852i
$929$	−466.320	+	269.230i	−0.501959	+	0.289806i	−0.729522	−	0.683957i	$-0.760258\pi$
$929$	−466.320	+	269.230i	−0.501959	+	0.289806i	0.227563	+	0.973763i	$0.426924\pi$
$930$		0			0
$931$	1773.67	−	376.310i	1.90513	−	0.404199i
$932$			425.235i			0.456260i
$933$	−141.269	+	81.5617i	−0.151414	+	0.0874187i
$934$	355.900	+	205.479i	0.381049	+	0.219999i
$935$		0			0
$936$	523.811	−	302.423i	0.559628	−	0.323101i
$937$	−309.686			−0.330508			−0.165254	−	0.986251i	$-0.552844\pi$
$937$	−309.686			−0.330508			−0.165254	+	0.986251i	$0.552844\pi$
$938$	446.732	+	70.8415i	0.476261	+	0.0755239i
$939$	1266.92			1.34923
$940$		0			0
$941$	139.993	+	80.8250i	0.148770	+	0.0858927i	0.572537	−	0.819879i	$-0.305959\pi$
$941$	139.993	+	80.8250i	0.148770	+	0.0858927i	−0.423767	+	0.905771i	$0.639292\pi$
$942$	89.4983	+	51.6719i	0.0950088	+	0.0548533i
$943$	170.216	+	294.824i	0.180505	+	0.312644i
$944$			311.333i			0.329802i
$945$		0			0
$946$	−298.610			−0.315655
$947$	−4.36722	+	2.52141i	−0.00461163	+	0.00266253i	−0.502304	−	0.864691i	$-0.667514\pi$
$947$	−4.36722	+	2.52141i	−0.00461163	+	0.00266253i	0.497692	+	0.867354i	$0.334181\pi$
$948$	218.671	−	378.750i	0.230666	−	0.399525i
$949$	−207.704	+	359.754i	−0.218866	+	0.379088i
$950$		0			0
$951$		−	1174.95i		−	1.23548i
$952$	−12.6448	−	10.2435i	−0.0132824	−	0.0107600i
$953$			531.467i			0.557678i	0.960338	+	0.278839i	$0.0899495\pi$
$953$			531.467i			0.557678i	−0.960338	+	0.278839i	$0.910050\pi$
$954$	131.963	+	228.566i	0.138326	+	0.239587i
$955$		0			0
$956$	−173.604	+	300.692i	−0.181595	+	0.314531i
$957$	−349.058	−	604.587i	−0.364742	−	0.631752i
$958$	850.510			0.887797
$959$	−1025.13	−	830.453i	−1.06896	−	0.865958i
$960$		0			0
$961$	−452.713	−	784.122i	−0.471086	−	0.815944i
$962$	−600.041	+	1039.30i	−0.623744	+	1.08036i
$963$	−1029.87	−	594.594i	−1.06944	−	0.617440i
$964$	−128.349	+	74.1024i	−0.133142	+	0.0768697i
$965$		0			0
$966$	87.1701	+	227.213i	0.0902382	+	0.235211i
$967$			666.012i			0.688740i	0.938834	+	0.344370i	$0.111907\pi$
$967$			666.012i			0.688740i	−0.938834	+	0.344370i	$0.888093\pi$
$968$	177.029	−	102.208i	0.182881	−	0.105587i
$969$	113.904	+	65.7626i	0.117548	+	0.0678665i
$970$		0			0
$971$	12.6436	−	7.29978i	0.0130212	−	0.00751780i	−0.493475	−	0.869760i	$-0.664274\pi$
$971$	12.6436	−	7.29978i	0.0130212	−	0.00751780i	0.506496	+	0.862242i	$0.330940\pi$
$972$	−696.316			−0.716374
$973$	−59.2438	+	373.596i	−0.0608877	+	0.383963i
$974$	−63.1417			−0.0648272
$975$		0			0
$976$	53.2639	+	30.7519i	0.0545736	+	0.0315081i
$977$	−391.731	−	226.166i	−0.400953	−	0.231490i	0.285942	−	0.958247i	$-0.407693\pi$
$977$	−391.731	−	226.166i	−0.400953	−	0.231490i	−0.686895	+	0.726757i	$0.741027\pi$
$978$	−372.410	−	645.034i	−0.380788	−	0.659544i
$979$		−	577.214i		−	0.589596i
$980$		0			0
$981$	−67.5776			−0.0688864
$982$	577.471	−	333.403i	0.588056	−	0.339514i
$983$	466.290	−	807.639i	0.474354	−	0.821606i	−0.525214	−	0.850970i	$-0.676015\pi$
$983$	466.290	−	807.639i	0.474354	−	0.821606i	0.999569	+	0.0293640i	$0.00934819\pi$
$984$	366.254	−	634.371i	0.372210	−	0.644686i
$985$		0			0
$986$			26.8813i			0.0272629i
$987$	−1905.27	−	302.132i	−1.93037	−	0.306112i
$988$			1631.30i			1.65111i
$989$	−85.9746	−	148.912i	−0.0869309	−	0.150569i
$990$		0			0
$991$	−105.284	+	182.356i	−0.106240	+	0.184013i	−0.914244	−	0.405164i	$-0.867214\pi$
$991$	−105.284	+	182.356i	−0.106240	+	0.184013i	0.808004	+	0.589177i	$0.200548\pi$
$992$	21.0853	+	36.5207i	0.0212553	+	0.0368153i
$993$	−1035.66			−1.04296
$994$	−913.684	+	350.534i	−0.919199	+	0.352650i
$995$		0			0
$996$	−151.286	−	262.035i	−0.151893	−	0.263087i
$997$	853.836	−	1478.89i	0.856405	−	1.48334i	−0.0189301	−	0.999821i	$-0.506026\pi$
$997$	853.836	−	1478.89i	0.856405	−	1.48334i	0.875335	−	0.483516i	$-0.160641\pi$
$998$	−459.175	−	265.105i	−0.460095	−	0.265636i
$999$	−101.128	+	58.3863i	−0.101229	+	0.0584448i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.3.i.b.199.8		16
5.2	odd	4		350.3.k.b.101.3		8
5.3	odd	4		70.3.j.a.31.2	✓	8
5.4	even	2	inner	350.3.i.b.199.1		16
7.5	odd	6	inner	350.3.i.b.299.1		16
15.8	even	4		630.3.v.a.451.3		8
20.3	even	4		560.3.bx.a.241.1		8
35.3	even	12		490.3.b.b.391.8		8
35.12	even	12		350.3.k.b.201.3		8
35.13	even	4		490.3.j.a.31.1		8
35.18	odd	12		490.3.b.b.391.5		8
35.19	odd	6	inner	350.3.i.b.299.8		16
35.23	odd	12		490.3.j.a.411.1		8
35.33	even	12		70.3.j.a.61.2	yes	8
105.68	odd	12		630.3.v.a.271.3		8
140.103	odd	12		560.3.bx.a.481.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.j.a.31.2	✓	8	5.3	odd	4
70.3.j.a.61.2	yes	8	35.33	even	12
350.3.i.b.199.1		16	5.4	even	2	inner
350.3.i.b.199.8		16	1.1	even	1	trivial
350.3.i.b.299.1		16	7.5	odd	6	inner
350.3.i.b.299.8		16	35.19	odd	6	inner
350.3.k.b.101.3		8	5.2	odd	4
350.3.k.b.201.3		8	35.12	even	12
490.3.b.b.391.5		8	35.18	odd	12
490.3.b.b.391.8		8	35.3	even	12
490.3.j.a.31.1		8	35.13	even	4
490.3.j.a.411.1		8	35.23	odd	12
560.3.bx.a.241.1		8	20.3	even	4
560.3.bx.a.481.1		8	140.103	odd	12
630.3.v.a.271.3		8	105.68	odd	12
630.3.v.a.451.3		8	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	350.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(2.16226 - 3.74514i) q^{3} +(1.00000 - 1.73205i) q^{4} -6.11578i q^{6} +(-6.91361 - 1.09634i) q^{7} -2.82843i q^{8} +(-4.85071 - 8.40167i) q^{9} +(3.49028 - 6.04534i) q^{11} +(-4.32451 - 7.49028i) q^{12} -22.0427 q^{13} +(-9.24264 + 3.54593i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-0.410964 + 0.711810i) q^{17} +(-11.8818 - 6.85993i) q^{18} +(32.0456 - 18.5016i) q^{19} +(-19.0549 + 23.5219i) q^{21} -9.87199i q^{22} +(4.92302 - 2.84231i) q^{23} +(-10.5928 - 6.11578i) q^{24} +(-26.9967 + 15.5865i) q^{26} -3.03326 q^{27} +(-8.81253 + 10.8784i) q^{28} +23.1260 q^{29} +(-6.45601 - 3.72738i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-15.0937 - 26.1431i) q^{33} +1.16238i q^{34} -19.4028 q^{36} +(33.3397 - 19.2487i) q^{37} +(26.1651 - 45.3194i) q^{38} +(-47.6619 + 82.5529i) q^{39} +59.8867i q^{41} +(-6.70498 + 42.2822i) q^{42} -30.2482i q^{43} +(-6.98055 - 12.0907i) q^{44} +(4.01963 - 6.96220i) q^{46} +(31.8629 + 55.1881i) q^{47} -17.2981 q^{48} +(46.5961 + 15.1593i) q^{49} +(1.77722 + 3.07823i) q^{51} +(-22.0427 + 38.1790i) q^{52} +(-16.6595 - 9.61837i) q^{53} +(-3.71497 + 2.14484i) q^{54} +(-3.10092 + 19.5546i) q^{56} -160.020i q^{57} +(28.3235 - 16.3526i) q^{58} +(-67.4057 - 38.9167i) q^{59} +(-13.3160 + 7.68798i) q^{61} -10.5426 q^{62} +(24.3248 + 63.4039i) q^{63} -8.00000 q^{64} +(-36.9720 - 21.3458i) q^{66} +(-39.5693 - 22.8453i) q^{67} +(0.821928 + 1.42362i) q^{68} -24.5832i q^{69} +98.8553 q^{71} +(-23.7635 + 13.7199i) q^{72} +(9.42281 - 16.3208i) q^{73} +(27.2218 - 47.1495i) q^{74} -74.0062i q^{76} +(-30.7582 + 37.9686i) q^{77} +134.808i q^{78} +(25.2828 + 43.7911i) q^{79} +(37.0977 - 64.2550i) q^{81} +(42.3463 + 73.3460i) q^{82} +34.9833 q^{83} +(21.6861 + 56.5260i) q^{84} +(-21.3887 - 37.0463i) q^{86} +(50.0044 - 86.6101i) q^{87} +(-17.0988 - 9.87199i) q^{88} +(71.6107 - 41.3445i) q^{89} +(152.395 + 24.1663i) q^{91} -11.3692i q^{92} +(-27.9191 + 16.1191i) q^{93} +(78.0478 + 45.0609i) q^{94} +(-21.1857 + 12.2316i) q^{96} -177.301 q^{97} +(67.7876 - 14.3821i) q^{98} -67.7212 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} - 24 q^{9} - 16 q^{11} - 80 q^{14} - 32 q^{16} + 8 q^{21} + 48 q^{24} - 192 q^{26} + 240 q^{29} - 144 q^{31} - 96 q^{36} - 48 q^{39} + 32 q^{44} + 40 q^{46} - 48 q^{49} + 112 q^{51} - 360 q^{54}+ \cdots - 192 q^{99}+O(q^{100}) \) 16 * q + 16 * q^4 - 24 * q^9 - 16 * q^11 - 80 * q^14 - 32 * q^16 + 8 * q^21 + 48 * q^24 - 192 * q^26 + 240 * q^29 - 144 * q^31 - 96 * q^36 - 48 * q^39 + 32 * q^44 + 40 * q^46 - 48 * q^49 + 112 * q^51 - 360 * q^54 - 80 * q^56 - 96 * q^59 + 144 * q^61 - 128 * q^64 - 384 * q^66 + 128 * q^71 + 160 * q^74 + 576 * q^79 + 608 * q^81 + 80 * q^84 + 8 * q^86 + 264 * q^89 + 1232 * q^91 + 672 * q^94 + 96 * q^96 - 192 * q^99

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