LMFDB - Embedded newform 354.6.c.a.353.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,6,Mod(353,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("354.353");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	354.c (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:	$56.7758722138$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			353.2
Character	$\chi$	$=$	354.353
Dual form			354.6.c.a.353.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +(-15.5824 + 0.434789i) q^{3} +16.0000 q^{4} +38.7472i q^{5} +(62.3296 - 1.73916i) q^{6} -41.9790 q^{7} -64.0000 q^{8} +(242.622 - 13.5501i) q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +(-15.5824 + 0.434789i) q^{3} +16.0000 q^{4} +38.7472i q^{5} +(62.3296 - 1.73916i) q^{6} -41.9790 q^{7} -64.0000 q^{8} +(242.622 - 13.5501i) q^{9} -154.989i q^{10} -166.287 q^{11} +(-249.318 + 6.95663i) q^{12} +75.0672i q^{13} +167.916 q^{14} +(-16.8469 - 603.774i) q^{15} +256.000 q^{16} +428.041i q^{17} +(-970.488 + 54.2005i) q^{18} -703.692 q^{19} +619.955i q^{20} +(654.133 - 18.2520i) q^{21} +665.149 q^{22} -2799.73 q^{23} +(997.273 - 27.8265i) q^{24} +1623.66 q^{25} -300.269i q^{26} +(-3774.74 + 316.633i) q^{27} -671.663 q^{28} +647.558i q^{29} +(67.3874 + 2415.10i) q^{30} +3883.69i q^{31} -1024.00 q^{32} +(2591.15 - 72.2999i) q^{33} -1712.17i q^{34} -1626.57i q^{35} +(3881.95 - 216.802i) q^{36} +10063.6i q^{37} +2814.77 q^{38} +(-32.6384 - 1169.73i) q^{39} -2479.82i q^{40} +18919.8i q^{41} +(-2616.53 + 73.0080i) q^{42} -13342.8i q^{43} -2660.60 q^{44} +(525.029 + 9400.92i) q^{45} +11198.9 q^{46} +19122.3 q^{47} +(-3989.09 + 111.306i) q^{48} -15044.8 q^{49} -6494.62 q^{50} +(-186.108 - 6669.91i) q^{51} +1201.08i q^{52} +25973.9i q^{53} +(15099.0 - 1266.53i) q^{54} -6443.16i q^{55} +2686.65 q^{56} +(10965.2 - 305.958i) q^{57} -2590.23i q^{58} +(-5728.51 + 26117.2i) q^{59} +(-269.550 - 9660.38i) q^{60} -10016.2i q^{61} -15534.8i q^{62} +(-10185.0 + 568.820i) q^{63} +4096.00 q^{64} -2908.64 q^{65} +(-10364.6 + 289.200i) q^{66} -11220.5i q^{67} +6848.66i q^{68} +(43626.5 - 1217.29i) q^{69} +6506.27i q^{70} -2995.96i q^{71} +(-15527.8 + 867.207i) q^{72} -49102.6i q^{73} -40254.4i q^{74} +(-25300.4 + 705.948i) q^{75} -11259.1 q^{76} +6980.57 q^{77} +(130.554 + 4678.91i) q^{78} -38832.8 q^{79} +9919.28i q^{80} +(58681.8 - 6575.11i) q^{81} -75679.1i q^{82} -46082.8 q^{83} +(10466.1 - 292.032i) q^{84} -16585.4 q^{85} +53371.3i q^{86} +(-281.551 - 10090.5i) q^{87} +10642.4 q^{88} -85295.8 q^{89} +(-2100.11 - 37603.7i) q^{90} -3151.24i q^{91} -44795.6 q^{92} +(-1688.59 - 60517.2i) q^{93} -76489.1 q^{94} -27266.1i q^{95} +(15956.4 - 445.224i) q^{96} -116154. i q^{97} +60179.1 q^{98} +(-40344.9 + 2253.21i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 200 q^{2} - 13 q^{3} + 800 q^{4} + 52 q^{6} + 38 q^{7} - 3200 q^{8} + 51 q^{9}+O(q^{10}) $ 50 * q - 200 * q^2 - 13 * q^3 + 800 * q^4 + 52 * q^6 + 38 * q^7 - 3200 * q^8 + 51 * q^9	$ 50 q - 200 q^{2} - 13 q^{3} + 800 q^{4} + 52 q^{6} + 38 q^{7} - 3200 q^{8} + 51 q^{9} - 652 q^{11} - 208 q^{12} - 152 q^{14} - 2107 q^{15} + 12800 q^{16} - 204 q^{18} - 894 q^{19} - 3801 q^{21} + 2608 q^{22} + 2456 q^{23} + 832 q^{24} - 23956 q^{25} + 9890 q^{27} + 608 q^{28} + 8428 q^{30} - 51200 q^{32} - 9744 q^{33} + 816 q^{36} + 3576 q^{38} + 1388 q^{39} + 15204 q^{42} - 10432 q^{44} + 33067 q^{45} - 9824 q^{46} - 27144 q^{47} - 3328 q^{48} + 85768 q^{49} + 95824 q^{50} + 3338 q^{51} - 39560 q^{54} - 2432 q^{56} - 63969 q^{57} - 23840 q^{59} - 33712 q^{60} + 94781 q^{63} + 204800 q^{64} - 9400 q^{65} + 38976 q^{66} - 115930 q^{69} - 3264 q^{72} + 24248 q^{75} - 14304 q^{76} - 150240 q^{77} - 5552 q^{78} - 68658 q^{79} + 47095 q^{81} - 175140 q^{83} - 60816 q^{84} - 138524 q^{85} + 138261 q^{87} + 41728 q^{88} + 104908 q^{89} - 132268 q^{90} + 39296 q^{92} - 91204 q^{93} + 108576 q^{94} + 13312 q^{96} - 343072 q^{98} - 111406 q^{99}+O(q^{100}) $ 50 * q - 200 * q^2 - 13 * q^3 + 800 * q^4 + 52 * q^6 + 38 * q^7 - 3200 * q^8 + 51 * q^9 - 652 * q^11 - 208 * q^12 - 152 * q^14 - 2107 * q^15 + 12800 * q^16 - 204 * q^18 - 894 * q^19 - 3801 * q^21 + 2608 * q^22 + 2456 * q^23 + 832 * q^24 - 23956 * q^25 + 9890 * q^27 + 608 * q^28 + 8428 * q^30 - 51200 * q^32 - 9744 * q^33 + 816 * q^36 + 3576 * q^38 + 1388 * q^39 + 15204 * q^42 - 10432 * q^44 + 33067 * q^45 - 9824 * q^46 - 27144 * q^47 - 3328 * q^48 + 85768 * q^49 + 95824 * q^50 + 3338 * q^51 - 39560 * q^54 - 2432 * q^56 - 63969 * q^57 - 23840 * q^59 - 33712 * q^60 + 94781 * q^63 + 204800 * q^64 - 9400 * q^65 + 38976 * q^66 - 115930 * q^69 - 3264 * q^72 + 24248 * q^75 - 14304 * q^76 - 150240 * q^77 - 5552 * q^78 - 68658 * q^79 + 47095 * q^81 - 175140 * q^83 - 60816 * q^84 - 138524 * q^85 + 138261 * q^87 + 41728 * q^88 + 104908 * q^89 - 132268 * q^90 + 39296 * q^92 - 91204 * q^93 + 108576 * q^94 + 13312 * q^96 - 343072 * q^98 - 111406 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−4.00000			−0.707107
$2$	−4.00000			−0.707107
$3$	−15.5824	+	0.434789i	−0.999611	+	0.0278917i
$3$	−15.5824	+	0.434789i	−0.999611	+	0.0278917i
$4$	16.0000			0.500000
$5$			38.7472i			0.693131i	0.938026	+	0.346565i	$0.112652\pi$
$5$			38.7472i			0.693131i	−0.938026	+	0.346565i	$0.887348\pi$
$6$	62.3296	−	1.73916i	0.706832	−	0.0197224i
$7$	−41.9790			−0.323807			−0.161904	−	0.986807i	$-0.551763\pi$
$7$	−41.9790			−0.323807			−0.161904	+	0.986807i	$0.551763\pi$
$8$	−64.0000			−0.353553
$9$	242.622	−	13.5501i	0.998444	−	0.0557618i
$10$		−	154.989i		−	0.490117i
$11$	−166.287			−0.414359			−0.207180	−	0.978303i	$-0.566428\pi$
$11$	−166.287			−0.414359			−0.207180	+	0.978303i	$0.566428\pi$
$12$	−249.318	+	6.95663i	−0.499805	+	0.0139459i
$13$			75.0672i			0.123195i	0.998101	+	0.0615973i	$0.0196195\pi$
$13$			75.0672i			0.123195i	−0.998101	+	0.0615973i	$0.980381\pi$
$14$	167.916			0.228966
$15$	−16.8469	−	603.774i	−0.0193326	−	0.692861i
$16$	256.000			0.250000
$17$			428.041i			0.359222i	0.983738	+	0.179611i	$0.0574840\pi$
$17$			428.041i			0.359222i	−0.983738	+	0.179611i	$0.942516\pi$
$18$	−970.488	+	54.2005i	−0.706007	+	0.0394295i
$19$	−703.692			−0.447196			−0.223598	−	0.974681i	$-0.571780\pi$
$19$	−703.692			−0.447196			−0.223598	+	0.974681i	$0.571780\pi$
$20$			619.955i			0.346565i
$21$	654.133	−	18.2520i	0.323681	−	0.00903155i
$22$	665.149			0.292996
$23$	−2799.73			−1.10356			−0.551780	−	0.833990i	$-0.686051\pi$
$23$	−2799.73			−1.10356			−0.551780	+	0.833990i	$0.686051\pi$
$24$	997.273	−	27.8265i	0.353416	−	0.00986122i
$25$	1623.66			0.519570
$26$		−	300.269i		−	0.0871118i
$27$	−3774.74	+	316.633i	−0.996500	+	0.0835884i
$28$	−671.663			−0.161904
$29$			647.558i			0.142983i	0.997441	+	0.0714914i	$0.0227759\pi$
$29$			647.558i			0.142983i	−0.997441	+	0.0714914i	$0.977224\pi$
$30$	67.3874	+	2415.10i	0.0136702	+	0.489927i
$31$			3883.69i			0.725839i	0.931820	+	0.362920i	$0.118220\pi$
$31$			3883.69i			0.725839i	−0.931820	+	0.362920i	$0.881780\pi$
$32$	−1024.00			−0.176777
$33$	2591.15	−	72.2999i	0.414198	−	0.0115572i
$34$		−	1712.17i		−	0.254009i
$35$		−	1626.57i		−	0.224441i
$36$	3881.95	−	216.802i	0.499222	−	0.0278809i
$37$			10063.6i			1.20851i	0.796792	+	0.604254i	$0.206529\pi$
$37$			10063.6i			1.20851i	−0.796792	+	0.604254i	$0.793471\pi$
$38$	2814.77			0.316216
$39$	−32.6384	−	1169.73i	−0.00343611	−	0.123147i
$40$		−	2479.82i		−	0.245059i
$41$			18919.8i			1.75775i	0.477055	+	0.878874i	$0.341704\pi$
$41$			18919.8i			1.75775i	−0.477055	+	0.878874i	$0.658296\pi$
$42$	−2616.53	+	73.0080i	−0.228877	+	0.00638627i
$43$		−	13342.8i		−	1.10047i	−0.835011	−	0.550233i	$-0.814539\pi$
$43$		−	13342.8i		−	1.10047i	0.835011	−	0.550233i	$-0.185461\pi$
$44$	−2660.60			−0.207180
$45$	525.029	+	9400.92i	0.0386502	+	0.692052i
$46$	11198.9			0.780335
$47$	19122.3			1.26268			0.631342	−	0.775505i	$-0.282504\pi$
$47$	19122.3			1.26268			0.631342	+	0.775505i	$0.282504\pi$
$48$	−3989.09	+	111.306i	−0.249903	+	0.00697294i
$49$	−15044.8			−0.895149
$50$	−6494.62			−0.367391
$51$	−186.108	−	6669.91i	−0.0100193	−	0.359083i
$52$			1201.08i			0.0615973i
$53$			25973.9i			1.27013i	0.772460	+	0.635063i	$0.219026\pi$
$53$			25973.9i			1.27013i	−0.772460	+	0.635063i	$0.780974\pi$
$54$	15099.0	−	1266.53i	0.704632	−	0.0591059i
$55$		−	6443.16i		−	0.287205i
$56$	2686.65			0.114483
$57$	10965.2	−	305.958i	0.447022	−	0.0124731i
$58$		−	2590.23i		−	0.101104i
$59$	−5728.51	+	26117.2i	−0.214245	+	0.976780i
$59$	−5728.51	+	26117.2i	−0.214245	+	0.976780i
$60$	−269.550	−	9660.38i	−0.00966631	−	0.346430i
$61$		−	10016.2i		−	0.344650i	−0.985040	−	0.172325i	$-0.944872\pi$
$61$		−	10016.2i		−	0.344650i	0.985040	−	0.172325i	$-0.0551279\pi$
$62$		−	15534.8i		−	0.513246i
$63$	−10185.0	+	568.820i	−0.323303	+	0.0180561i
$64$	4096.00			0.125000
$65$	−2908.64			−0.0853900
$66$	−10364.6	+	289.200i	−0.292882	+	0.00817218i
$67$		−	11220.5i		−	0.305370i	−0.988275	−	0.152685i	$-0.951208\pi$
$67$		−	11220.5i		−	0.305370i	0.988275	−	0.152685i	$-0.0487920\pi$
$68$			6848.66i			0.179611i
$69$	43626.5	−	1217.29i	1.10313	−	0.0307802i
$70$			6506.27i			0.158704i
$71$		−	2995.96i		−	0.0705326i	−0.999378	−	0.0352663i	$-0.988772\pi$
$71$		−	2995.96i		−	0.0705326i	0.999378	−	0.0352663i	$-0.0112279\pi$
$72$	−15527.8	+	867.207i	−0.353003	+	0.0197148i
$73$		−	49102.6i		−	1.07844i	−0.842164	−	0.539222i	$-0.818718\pi$
$73$		−	49102.6i		−	1.07844i	0.842164	−	0.539222i	$-0.181282\pi$
$74$		−	40254.4i		−	0.854544i
$75$	−25300.4	+	705.948i	−0.519368	+	0.0144917i
$76$	−11259.1			−0.223598
$77$	6980.57			0.134173
$78$	130.554	+	4678.91i	0.00242970	+	0.0870779i
$79$	−38832.8			−0.700054			−0.350027	−	0.936740i	$-0.613828\pi$
$79$	−38832.8			−0.700054			−0.350027	+	0.936740i	$0.613828\pi$
$80$			9919.28i			0.173283i
$81$	58681.8	−	6575.11i	0.993781	−	0.111350i
$82$		−	75679.1i		−	1.24291i
$83$	−46082.8			−0.734250			−0.367125	−	0.930172i	$-0.619658\pi$
$83$	−46082.8			−0.734250			−0.367125	+	0.930172i	$0.619658\pi$
$84$	10466.1	−	292.032i	0.161841	−	0.00451577i
$85$	−16585.4			−0.248988
$86$			53371.3i			0.778147i
$87$	−281.551	−	10090.5i	−0.00398804	−	0.142927i
$88$	10642.4			0.146498
$89$	−85295.8			−1.14144			−0.570720	−	0.821145i	$-0.693336\pi$
$89$	−85295.8			−1.14144			−0.570720	+	0.821145i	$0.693336\pi$
$90$	−2100.11	−	37603.7i	−0.0273298	−	0.489355i
$91$		−	3151.24i		−	0.0398913i
$92$	−44795.6			−0.551780
$93$	−1688.59	−	60517.2i	−0.0202449	−	0.725557i
$94$	−76489.1			−0.892852
$95$		−	27266.1i		−	0.309966i
$96$	15956.4	−	445.224i	0.176708	−	0.00493061i
$97$		−	116154.i		−	1.25345i	−0.779242	−	0.626723i	$-0.784396\pi$
$97$		−	116154.i		−	1.25345i	0.779242	−	0.626723i	$-0.215604\pi$
$98$	60179.1			0.632966
$99$	−40344.9	+	2253.21i	−0.413715	+	0.0231054i
$100$	25978.5			0.259785
$101$	97370.3			0.949780			0.474890	−	0.880045i	$-0.342488\pi$
$101$	97370.3			0.949780			0.474890	+	0.880045i	$0.342488\pi$
$102$	744.431	+	26679.6i	0.00708474	+	0.253910i
$103$		−	180702.i		−	1.67830i	−0.543897	−	0.839152i	$-0.683052\pi$
$103$		−	180702.i		−	1.67830i	0.543897	−	0.839152i	$-0.316948\pi$
$104$		−	4804.30i		−	0.0435559i
$105$	707.214	+	25345.8i	0.00626004	+	0.224353i
$106$		−	103895.i		−	0.898115i
$107$		−	64241.8i		−	0.542448i	−0.962516	−	0.271224i	$-0.912572\pi$
$107$		−	64241.8i		−	0.542448i	0.962516	−	0.271224i	$-0.0874284\pi$
$108$	−60395.8	+	5066.12i	−0.498250	+	0.0417942i
$109$		−	191269.i		−	1.54198i	−0.636848	−	0.770990i	$-0.719762\pi$
$109$		−	191269.i		−	1.54198i	0.636848	−	0.770990i	$-0.280238\pi$
$110$			25772.7i			0.203085i
$111$	−4375.55	−	156815.i	−0.0337074	−	1.20804i
$112$	−10746.6			−0.0809518
$113$	9433.42			0.0694981			0.0347491	−	0.999396i	$-0.488937\pi$
$113$	9433.42			0.0694981			0.0347491	+	0.999396i	$0.488937\pi$
$114$	−43860.8	+	1223.83i	−0.316093	+	0.00881981i
$115$		−	108482.i		−	0.764912i
$116$			10360.9i			0.0714914i
$117$	1017.17	+	18213.0i	0.00686955	+	0.123003i
$118$	22914.0	−	104469.i	0.151494	−	0.690688i
$119$		−	17968.7i		−	0.116319i
$120$	1078.20	+	38641.5i	0.00683511	+	0.244963i
$121$	−133400.			−0.828306
$122$			40064.8i			0.243704i
$123$	−8226.12	−	294815.i	−0.0490266	−	1.75706i
$124$			62139.1i			0.362920i
$125$			183997.i			1.05326i
$126$	40740.1	−	2275.28i	0.228610	−	0.0127676i
$127$	−79947.0			−0.439838			−0.219919	−	0.975518i	$-0.570579\pi$
$127$	−79947.0			−0.439838			−0.219919	+	0.975518i	$0.570579\pi$
$128$	−16384.0			−0.0883883
$129$	5801.32	+	207913.i	0.0306939	+	1.10004i
$130$	11634.6			0.0603798
$131$	144246.			0.734388			0.367194	−	0.930144i	$-0.380318\pi$
$131$	144246.			0.734388			0.367194	+	0.930144i	$0.380318\pi$
$132$	41458.5	−	1156.80i	0.207099	−	0.00577860i
$133$	29540.2			0.144805
$134$			44882.2i			0.215929i
$135$	−12268.6	−	146260.i	−0.0579377	−	0.690705i
$136$		−	27394.6i		−	0.127004i
$137$		−	238777.i		−	1.08690i	−0.839440	−	0.543452i	$-0.817117\pi$
$137$		−	238777.i		−	1.08690i	0.839440	−	0.543452i	$-0.182883\pi$
$138$	−174506.	+	4869.17i	−0.780032	+	0.0217649i
$139$	219083.			0.961770			0.480885	−	0.876784i	$-0.340315\pi$
$139$	219083.			0.961770			0.480885	+	0.876784i	$0.340315\pi$
$140$		−	26025.1i		−	0.112220i
$141$	−297971.	+	8314.15i	−1.26219	+	0.0352185i
$142$			11983.8i			0.0498740i
$143$		−	12482.7i		−	0.0510469i
$144$	62111.2	−	3468.83i	0.249611	−	0.0139404i
$145$	−25091.1			−0.0991058
$146$			196411.i			0.762575i
$147$	234433.	−	6541.30i	0.894801	−	0.0249673i
$148$			161018.i			0.604254i
$149$	100312.			0.370159			0.185080	−	0.982724i	$-0.440746\pi$
$149$	100312.			0.370159			0.185080	+	0.982724i	$0.440746\pi$
$150$	101202.	−	2823.79i	0.367248	−	0.0102472i
$151$			362945.i			1.29538i	0.761903	+	0.647691i	$0.224265\pi$
$151$			362945.i			1.29538i	−0.761903	+	0.647691i	$0.775735\pi$
$152$	45036.3			0.158108
$153$	5800.01	+	103852.i	0.0200309	+	0.358663i
$154$	−27922.3			−0.0948744
$155$	−150482.			−0.503102
$156$	−522.215	−	18715.6i	−0.00171806	−	0.0615734i
$157$		−	164128.i		−	0.531415i	−0.964054	−	0.265708i	$-0.914394\pi$
$157$		−	164128.i		−	0.531415i	0.964054	−	0.265708i	$-0.0856056\pi$
$158$	155331.			0.495013
$159$	−11293.2	−	404735.i	−0.0354260	−	1.26963i
$160$		−	39677.1i		−	0.122529i
$161$	117530.			0.357341
$162$	−234727.	+	26300.4i	−0.702709	+	0.0787364i
$163$	−443415.			−1.30720			−0.653599	−	0.756841i	$-0.726742\pi$
$163$	−443415.			−1.30720			−0.653599	+	0.756841i	$0.726742\pi$
$164$			302716.i			0.878874i
$165$	2801.42	+	100400.i	0.00801066	+	0.287094i
$166$	184331.			0.519193
$167$		−	664817.i		−	1.84464i	−0.386430	−	0.922319i	$-0.626292\pi$
$167$		−	664817.i		−	1.84464i	0.386430	−	0.922319i	$-0.373708\pi$
$168$	−41864.5	+	1168.13i	−0.114439	+	0.00319313i
$169$	365658.			0.984823
$170$	66341.6			0.176061
$171$	−170731.	+	9535.10i	−0.446501	+	0.0249365i
$172$		−	213485.i		−	0.550233i
$173$	183621.			0.466453			0.233226	−	0.972422i	$-0.425072\pi$
$173$	183621.			0.466453			0.233226	+	0.972422i	$0.425072\pi$
$174$	1126.21	+	40362.0i	0.00281997	+	0.101065i
$175$	−68159.4			−0.168241
$176$	−42569.5			−0.103590
$177$	77908.4	−	409459.i	0.186918	−	0.982376i
$178$	341183.			0.807119
$179$	−284365.			−0.663351			−0.331675	−	0.943394i	$-0.607614\pi$
$179$	−284365.			−0.663351			−0.331675	+	0.943394i	$0.607614\pi$
$180$	8400.46	+	150415.i	0.0193251	+	0.346026i
$181$	−221445.			−0.502424			−0.251212	−	0.967932i	$-0.580829\pi$
$181$	−221445.			−0.502424			−0.251212	+	0.967932i	$0.580829\pi$
$182$			12605.0i			0.0282074i
$183$	4354.94	+	156076.i	0.00961289	+	0.344516i
$184$	179183.			0.390168
$185$	−389936.			−0.837654
$186$	6754.35	+	242069.i	0.0143153	+	0.513046i
$187$		−	71177.8i		−	0.148847i
$188$	305956.			0.631342
$189$	158460.	−	13291.9i	0.322674	−	0.0270665i
$190$			109064.i			0.219179i
$191$	−238946.			−0.473932			−0.236966	−	0.971518i	$-0.576153\pi$
$191$	−238946.			−0.473932			−0.236966	+	0.971518i	$0.576153\pi$
$192$	−63825.5	+	1780.90i	−0.124951	+	0.00348647i
$193$	550517.			1.06384			0.531921	−	0.846794i	$-0.321470\pi$
$193$	550517.			1.06384			0.531921	+	0.846794i	$0.321470\pi$
$194$			464617.i			0.886321i
$195$	45323.6	−	1264.65i	0.0853568	−	0.00238168i
$196$	−240716.			−0.447574
$197$			15545.0i			0.0285381i	0.999898	+	0.0142691i	$0.00454214\pi$
$197$			15545.0i			0.0285381i	−0.999898	+	0.0142691i	$0.995458\pi$
$198$	161380.	−	9012.85i	0.292541	−	0.0163380i
$199$	−423063.			−0.757308			−0.378654	−	0.925538i	$-0.623613\pi$
$199$	−423063.			−0.757308			−0.378654	+	0.925538i	$0.623613\pi$
$200$	−103914.			−0.183696
$201$	4878.57	+	174843.i	0.00851731	+	0.305251i
$202$	−389481.			−0.671596
$203$		−	27183.8i		−	0.0462989i
$204$	−2977.72	−	106719.i	−0.00500967	−	0.179541i
$205$	−733088.			−1.21835
$206$			722809.i			1.18674i
$207$	−679275.	+	37936.6i	−1.10184	+	0.0615365i
$208$			19217.2i			0.0307987i
$209$	117015.			0.185300
$210$	−2828.85	−	101383.i	−0.00442652	−	0.158642i
$211$		−	456665.i		−	0.706141i	−0.935597	−	0.353070i	$-0.885138\pi$
$211$		−	456665.i		−	0.706141i	0.935597	−	0.353070i	$-0.114862\pi$
$212$			415582.i			0.635063i
$213$	1302.61	+	46684.2i	0.00196728	+	0.0705051i
$214$			256967.i			0.383569i
$215$	516997.			0.762767
$216$	241583.	−	20264.5i	0.352316	−	0.0295530i
$217$		−	163033.i		−	0.235032i
$218$			765076.i			1.09034i
$219$	21349.3	+	765137.i	0.0300797	+	1.07802i
$220$		−	103091.i		−	0.143603i
$221$	−32131.9			−0.0442543
$222$	17502.2	+	627260.i	0.0238347	+	0.854212i
$223$	450392.			0.606497			0.303248	−	0.952912i	$-0.401929\pi$
$223$	450392.			0.606497			0.303248	+	0.952912i	$0.401929\pi$
$224$	42986.5			0.0572416
$225$	393935.	−	22000.7i	0.518762	−	0.0289721i
$226$	−37733.7			−0.0491426
$227$	212488.			0.273697			0.136849	−	0.990592i	$-0.456303\pi$
$227$	212488.			0.273697			0.136849	+	0.990592i	$0.456303\pi$
$228$	175443.	−	4895.32i	0.223511	−	0.00623654i
$229$			27099.6i			0.0341487i	0.999854	+	0.0170744i	$0.00543520\pi$
$229$			27099.6i			0.0341487i	−0.999854	+	0.0170744i	$0.994565\pi$
$230$			433926.i			0.540874i
$231$	−108774.	+	3035.08i	−0.134120	+	0.00374231i
$232$		−	41443.7i		−	0.0505521i
$233$	−180735.			−0.218098			−0.109049	−	0.994036i	$-0.534781\pi$
$233$	−180735.			−0.218098			−0.109049	+	0.994036i	$0.534781\pi$
$234$	−4068.68	−	72851.8i	−0.00485751	−	0.0869762i
$235$			740934.i			0.875205i
$236$	−91656.1	+	417875.i	−0.107123	+	0.488390i
$237$	605108.	−	16884.1i	0.699781	−	0.0195257i
$238$			71874.9i			0.0822498i
$239$		−	485691.i		−	0.550003i	−0.961444	−	0.275002i	$-0.911322\pi$
$239$		−	485691.i		−	0.550003i	0.961444	−	0.275002i	$-0.0886784\pi$
$240$	−4312.80	−	154566.i	−0.00483316	−	0.173215i
$241$	259306.			0.287588			0.143794	−	0.989608i	$-0.454070\pi$
$241$	259306.			0.287588			0.143794	+	0.989608i	$0.454070\pi$
$242$	533598.			0.585701
$243$	−911544.	+	127970.i	−0.990289	+	0.139025i
$244$		−	160259.i		−	0.172325i
$245$		−	582942.i		−	0.620455i
$246$	32904.5	+	1.17926e6i	0.0346671	+	1.24243i
$247$		−	52824.2i		−	0.0550922i
$248$		−	248556.i		−	0.256623i
$249$	718081.	−	20036.3i	0.733964	−	0.0204795i
$250$		−	735988.i		−	0.744768i
$251$		−	700873.i		−	0.702190i	−0.936340	−	0.351095i	$-0.885809\pi$
$251$		−	700873.i		−	0.702190i	0.936340	−	0.351095i	$-0.114191\pi$
$252$	−162960.	+	9101.12i	−0.161652	+	0.00902804i
$253$	465559.			0.457271
$254$	319788.			0.311013
$255$	258440.	−	7211.15i	0.248891	−	0.00694471i
$256$	65536.0			0.0625000
$257$			1.27937e6i			1.20826i	0.796884	+	0.604132i	$0.206480\pi$
$257$			1.27937e6i			1.20826i	−0.796884	+	0.604132i	$0.793520\pi$
$258$	−23205.3	−	831653.i	−0.0217039	−	0.777844i
$259$		−	422460.i		−	0.391324i
$260$	−46538.3			−0.0426950
$261$	8774.49	+	157112.i	0.00797298	+	0.142760i
$262$	−576984.			−0.519291
$263$			527749.i			0.470477i	0.971938	+	0.235238i	$0.0755871\pi$
$263$			527749.i			0.470477i	−0.971938	+	0.235238i	$0.924413\pi$
$264$	−165834.	+	4627.19i	−0.146441	+	0.00408609i
$265$	−1.00641e6			−0.880363
$266$	−118161.			−0.102393
$267$	1.32911e6	−	37085.7i	1.14100	−	0.0318367i
$268$		−	179529.i		−	0.152685i
$269$	−1.05984e6			−0.893014			−0.446507	−	0.894780i	$-0.647332\pi$
$269$	−1.05984e6			−0.893014			−0.446507	+	0.894780i	$0.647332\pi$
$270$	49074.5	+	585042.i	0.0409681	+	0.488402i
$271$	1.41943e6			1.17406			0.587032	−	0.809564i	$-0.300296\pi$
$271$	1.41943e6			1.17406			0.587032	+	0.809564i	$0.300296\pi$
$272$			109579.i			0.0898056i
$273$	1370.13	+	49103.9i	0.00111264	+	0.0398758i
$274$			955108.i			0.768557i
$275$	−269993.			−0.215289
$276$	698023.	−	19476.7i	0.551566	−	0.0153901i
$277$	−111139.			−0.0870299			−0.0435149	−	0.999053i	$-0.513856\pi$
$277$	−111139.			−0.0870299			−0.0435149	+	0.999053i	$0.513856\pi$
$278$	−876331.			−0.680074
$279$	52624.5	+	942269.i	0.0404741	+	0.724710i
$280$			104100.i			0.0793518i
$281$		−	536816.i		−	0.405565i	−0.979224	−	0.202782i	$-0.935002\pi$
$281$		−	536816.i		−	0.405565i	0.979224	−	0.202782i	$-0.0649984\pi$
$282$	1.19188e6	−	33256.6i	0.892505	−	0.0249032i
$283$		−	338215.i		−	0.251031i	−0.992092	−	0.125515i	$-0.959942\pi$
$283$		−	338215.i		−	0.251031i	0.992092	−	0.125515i	$-0.0400584\pi$
$284$		−	47935.3i		−	0.0352663i
$285$	11855.0	+	424871.i	0.00864548	+	0.309845i
$286$			49930.9i			0.0360956i
$287$		−	794233.i		−	0.569171i
$288$	−248445.	+	13875.3i	−0.176502	+	0.00985738i
$289$	1.23664e6			0.870959
$290$	100364.			0.0700784
$291$	50502.6	+	1.80996e6i	0.0349608	+	1.25296i
$292$		−	785642.i		−	0.539222i
$293$		−	323406.i		−	0.220079i	−0.993927	−	0.110040i	$-0.964902\pi$
$293$		−	323406.i		−	0.220079i	0.993927	−	0.110040i	$-0.0350978\pi$
$294$	−937734.	+	26165.2i	−0.632720	+	0.0176545i
$295$	−1.01197e6	−	221964.i	−0.677036	−	0.148500i
$296$		−	644071.i		−	0.427272i
$297$	627691.	−	52652.0i	0.412909	−	0.0346357i
$298$	−401249.			−0.261742
$299$		−	210168.i		−	0.135953i
$300$	−404807.	+	11295.2i	−0.259684	+	0.00724586i
$301$			560118.i			0.356339i
$302$		−	1.45178e6i		−	0.915974i
$303$	−1.51726e6	+	42335.6i	−0.949411	+	0.0264910i
$304$	−180145.			−0.111799
$305$	388099.			0.238888
$306$	−23200.0	−	415409.i	−0.0141640	−	0.253613i
$307$	−866266.			−0.524573			−0.262286	−	0.964990i	$-0.584476\pi$
$307$	−866266.			−0.524573			−0.262286	+	0.964990i	$0.584476\pi$
$308$	111689.			0.0670863
$309$	78567.4	+	2.81577e6i	0.0468108	+	1.67765i
$310$	601929.			0.355747
$311$		−	1.38735e6i		−	0.813367i	−0.913569	−	0.406683i	$-0.866685\pi$
$311$		−	1.38735e6i		−	0.813367i	0.913569	−	0.406683i	$-0.133315\pi$
$312$	2088.86	+	74862.5i	0.00121485	+	0.0435389i
$313$			711564.i			0.410538i	0.978706	+	0.205269i	$0.0658069\pi$
$313$			711564.i			0.410538i	−0.978706	+	0.205269i	$0.934193\pi$
$314$			656513.i			0.375767i
$315$	−22040.2	−	394641.i	−0.0125152	−	0.224092i
$316$	−621325.			−0.350027
$317$			2.39954e6i			1.34116i	0.741839	+	0.670579i	$0.233954\pi$
$317$			2.39954e6i			1.34116i	−0.741839	+	0.670579i	$0.766046\pi$
$318$	45172.6	+	1.61894e6i	0.0250500	+	0.897765i
$319$		−	107681.i		−	0.0592463i
$320$			158708.i			0.0866413i
$321$	27931.6	+	1.00104e6i	0.0151298	+	0.542237i
$322$	−470119.			−0.252678
$323$		−	301209.i		−	0.160643i
$324$	938909.	−	105202.i	0.496891	−	0.0556750i
$325$			121883.i			0.0640082i
$326$	1.77366e6			0.924329
$327$	83161.7	+	2.98043e6i	0.0430085	+	1.54138i
$328$		−	1.21087e6i		−	0.621457i
$329$	−802733.			−0.408866
$330$	−11205.7	−	401600.i	−0.00566439	−	0.203006i
$331$	3.15985e6			1.58525			0.792623	−	0.609712i	$-0.208715\pi$
$331$	3.15985e6			1.58525			0.792623	+	0.609712i	$0.208715\pi$
$332$	−737325.			−0.367125
$333$	136363.	+	2.44165e6i	0.0673885	+	1.20663i
$334$			2.65927e6i			1.30436i
$335$	434764.			0.211661
$336$	167458.	−	4672.51i	0.0809203	−	0.00225789i
$337$		−	3.00078e6i		−	1.43933i	−0.694323	−	0.719664i	$-0.744296\pi$
$337$		−	3.00078e6i		−	1.43933i	0.694323	−	0.719664i	$-0.255704\pi$
$338$	−1.46263e6			−0.696375
$339$	−146995.	+	4101.55i	−0.0694711	+	0.00193842i
$340$	−265366.			−0.124494
$341$		−	645809.i		−	0.300758i
$342$	682924.	−	38140.4i	0.315724	−	0.0176327i
$343$	1.33710e6			0.613663
$344$			853941.i			0.389074i
$345$	47166.6	+	1.69040e6i	0.0213347	+	0.764614i
$346$	−734485.			−0.329832
$347$	−4.17314e6			−1.86054			−0.930271	−	0.366874i	$-0.880428\pi$
$347$	−4.17314e6			−1.86054			−0.930271	+	0.366874i	$0.880428\pi$
$348$	−4504.82	−	161448.i	−0.00199402	−	0.0714636i
$349$			2.65064e6i			1.16490i	0.812868	+	0.582448i	$0.197905\pi$
$349$			2.65064e6i			1.16490i	−0.812868	+	0.582448i	$0.802095\pi$
$350$	272638.			0.118964
$351$	−23768.7	−	283359.i	−0.0102976	−	0.122764i
$352$	170278.			0.0732491
$353$	1.44753e6			0.618290			0.309145	−	0.951015i	$-0.399957\pi$
$353$	1.44753e6			0.618290			0.309145	+	0.951015i	$0.399957\pi$
$354$	−311633.	+	1.63784e6i	−0.132171	+	0.694644i
$355$	116085.			0.0488883
$356$	−1.36473e6			−0.570720
$357$	7812.61	+	279996.i	0.00324433	+	0.116274i
$358$	1.13746e6			0.469060
$359$		−	787279.i		−	0.322398i	−0.986922	−	0.161199i	$-0.948464\pi$
$359$		−	787279.i		−	0.322398i	0.986922	−	0.161199i	$-0.0515361\pi$
$360$	−33601.8	−	601659.i	−0.0136649	−	0.244677i
$361$	−1.98092e6			−0.800015
$362$	885781.			0.355267
$363$	2.07868e6	−	58000.7i	0.827984	−	0.0231029i
$364$		−	50419.9i		−	0.0199457i
$365$	1.90259e6			0.747503
$366$	−17419.7	−	624305.i	−0.00679734	−	0.243610i
$367$		−	3.84735e6i		−	1.49107i	−0.666469	−	0.745533i	$-0.732195\pi$
$367$		−	3.84735e6i		−	1.49107i	0.666469	−	0.745533i	$-0.267805\pi$
$368$	−716730.			−0.275890
$369$	256365.	+	4.59035e6i	0.0980151	+	1.75501i
$370$	1.55975e6			0.592311
$371$		−	1.09036e6i		−	0.411276i
$372$	−27017.4	−	968276.i	−0.0101225	−	0.362779i
$373$	−3.04456e6			−1.13306			−0.566529	−	0.824042i	$-0.691714\pi$
$373$	−3.04456e6			−1.13306			−0.566529	+	0.824042i	$0.691714\pi$
$374$			284711.i			0.105251i
$375$	−79999.9	−	2.86711e6i	−0.0293773	−	1.05285i
$376$	−1.22382e6			−0.446426
$377$	−48610.4			−0.0176147
$378$	−633838.	+	53167.6i	−0.228165	+	0.0191389i
$379$	−3.35683e6			−1.20042			−0.600208	−	0.799844i	$-0.704915\pi$
$379$	−3.35683e6			−1.20042			−0.600208	+	0.799844i	$0.704915\pi$
$380$		−	436257.i		−	0.154983i
$381$	1.24577e6	−	34760.1i	0.439667	−	0.0122679i
$382$	955784.			0.335121
$383$		−	4.56073e6i		−	1.58868i	−0.607471	−	0.794342i	$-0.707816\pi$
$383$		−	4.56073e6i		−	1.58868i	0.607471	−	0.794342i	$-0.292184\pi$
$384$	255302.	−	7123.59i	0.0883540	−	0.00246531i
$385$			270477.i			0.0929992i
$386$	−2.20207e6			−0.752250
$387$	−180797.	−	3.23726e6i	−0.0613640	−	1.09875i
$388$		−	1.85847e6i		−	0.626723i
$389$		−	3.04699e6i		−	1.02093i	−0.859898	−	0.510466i	$-0.829473\pi$
$389$		−	3.04699e6i		−	1.02093i	0.859898	−	0.510466i	$-0.170527\pi$
$390$	−181294.	+	5058.59i	−0.0603564	+	0.00168410i
$391$		−	1.19840e6i		−	0.396424i
$392$	962865.			0.316483
$393$	−2.24770e6	+	62716.7i	−0.734103	+	0.0204834i
$394$		−	62180.1i		−	0.0201795i
$395$		−	1.50466e6i		−	0.485229i
$396$	−645519.	+	36051.4i	−0.206857	+	0.0115527i
$397$		−	4.90310e6i		−	1.56133i	−0.624950	−	0.780665i	$-0.714881\pi$
$397$		−	4.90310e6i		−	1.56133i	0.624950	−	0.780665i	$-0.285119\pi$
$398$	1.69225e6			0.535497
$399$	−460308.	+	12843.8i	−0.144749	+	0.00403888i
$400$	415656.			0.129892
$401$	−1.05620e6			−0.328009			−0.164005	−	0.986460i	$-0.552441\pi$
$401$	−1.05620e6			−0.328009			−0.164005	+	0.986460i	$0.552441\pi$
$402$	−19514.3	−	699371.i	−0.00602265	−	0.215845i
$403$	−291538.			−0.0894196
$404$	1.55792e6			0.474890
$405$	254767.	+	2.27375e6i	0.0771801	+	0.688820i
$406$			108735.i			0.0327383i
$407$		−	1.67345e6i		−	0.500757i
$408$	11910.9	+	426874.i	0.00354237	+	0.126955i
$409$		−	3.92820e6i		−	1.16114i	−0.814209	−	0.580572i	$-0.802829\pi$
$409$		−	3.92820e6i		−	1.16114i	0.814209	−	0.580572i	$-0.197171\pi$
$410$	2.93235e6			0.861502
$411$	103818.	+	3.72072e6i	0.0303157	+	1.08648i
$412$		−	2.89124e6i		−	0.839152i
$413$	240477.	−	1.09637e6i	0.0693742	−	0.316288i
$414$	2.71710e6	−	151747.i	0.779121	−	0.0435129i
$415$		−	1.78558e6i		−	0.508931i
$416$		−	76868.8i		−	0.0217779i
$417$	−3.41383e6	+	95254.8i	−0.961396	+	0.0268254i
$418$	−468060.			−0.131027
$419$	4.02300e6			1.11948			0.559738	−	0.828669i	$-0.310902\pi$
$419$	4.02300e6			1.11948			0.559738	+	0.828669i	$0.310902\pi$
$420$	11315.4	+	405533.i	0.00313002	+	0.112177i
$421$			510067.i			0.140256i	0.997538	+	0.0701281i	$0.0223408\pi$
$421$			510067.i			0.140256i	−0.997538	+	0.0701281i	$0.977659\pi$
$422$			1.82666e6i			0.499317i
$423$	4.63948e6	−	259109.i	1.26072	−	0.0704095i
$424$		−	1.66233e6i		−	0.449057i
$425$			694992.i			0.186641i
$426$	−5210.44	−	186737.i	−0.00139107	−	0.0498546i
$427$			420470.i			0.111600i
$428$		−	1.02787e6i		−	0.271224i
$429$	5427.35	+	194511.i	0.00142379	+	0.0510270i
$430$	−2.06799e6			−0.539358
$431$	−809863.			−0.210000			−0.105000	−	0.994472i	$-0.533484\pi$
$431$	−809863.			−0.210000			−0.105000	+	0.994472i	$0.533484\pi$
$432$	−966333.	+	81057.9i	−0.249125	+	0.0208971i
$433$	−2.58437e6			−0.662423			−0.331211	−	0.943557i	$-0.607457\pi$
$433$	−2.58437e6			−0.662423			−0.331211	+	0.943557i	$0.607457\pi$
$434$			652134.i			0.166193i
$435$	390979.	−	10909.3i	0.0990672	−	0.00276423i
$436$		−	3.06031e6i		−	0.770990i
$437$	1.97014e6			0.493508
$438$	−85397.2	−	3.06055e6i	−0.0212696	−	0.762279i
$439$	1.71289e6			0.424199			0.212099	−	0.977248i	$-0.431970\pi$
$439$	1.71289e6			0.424199			0.212099	+	0.977248i	$0.431970\pi$
$440$			412362.i			0.101542i
$441$	−3.65019e6	+	203858.i	−0.893756	+	0.0499151i
$442$	128527.			0.0312925
$443$	−428626.			−0.103769			−0.0518847	−	0.998653i	$-0.516523\pi$
$443$	−428626.			−0.103769			−0.0518847	+	0.998653i	$0.516523\pi$
$444$	−70008.8	−	2.50904e6i	−0.0168537	−	0.604019i
$445$		−	3.30497e6i		−	0.791167i
$446$	−1.80157e6			−0.428858
$447$	−1.56310e6	+	43614.7i	−0.370015	+	0.0103244i
$448$	−171946.			−0.0404759
$449$			3.89386e6i			0.911516i	0.890104	+	0.455758i	$0.150632\pi$
$449$			3.89386e6i			0.911516i	−0.890104	+	0.455758i	$0.849368\pi$
$450$	−1.57574e6	+	88002.9i	−0.366820	+	0.0204864i
$451$		−	3.14612e6i		−	0.728339i
$452$	150935.			0.0347491
$453$	−157804.	−	5.65555e6i	−0.0361305	−	1.29488i
$454$	−849954.			−0.193533
$455$	122102.			0.0276499
$456$	−701773.	+	19581.3i	−0.158046	+	0.00440990i
$457$		−	5.94641e6i		−	1.33188i	−0.746006	−	0.665939i	$-0.768031\pi$
$457$		−	5.94641e6i		−	1.33188i	0.746006	−	0.665939i	$-0.231969\pi$
$458$		−	108398.i		−	0.0241468i
$459$	−135532.	−	1.61574e6i	−0.0300268	−	0.357965i
$460$		−	1.73570e6i		−	0.382456i
$461$			5.30111e6i			1.16175i	0.813991	+	0.580877i	$0.197290\pi$
$461$			5.30111e6i			1.16175i	−0.813991	+	0.580877i	$0.802710\pi$
$462$	435096.	−	12140.3i	0.0948375	−	0.00264621i
$463$		−	4.37774e6i		−	0.949068i	−0.880237	−	0.474534i	$-0.842617\pi$
$463$		−	4.37774e6i		−	0.949068i	0.880237	−	0.474534i	$-0.157383\pi$
$464$			165775.i			0.0357457i
$465$	2.34487e6	−	65428.0i	0.502906	−	0.0140324i
$466$	722940.			0.154219
$467$	−3.59111e6			−0.761967			−0.380984	−	0.924582i	$-0.624415\pi$
$467$	−3.59111e6			−0.761967			−0.380984	+	0.924582i	$0.624415\pi$
$468$	16274.7	+	291407.i	0.00343478	+	0.0615015i
$469$			471027.i			0.0988811i
$470$		−	2.96374e6i		−	0.618863i
$471$	71361.2	+	2.55751e6i	0.0148221	+	0.531209i
$472$	366624.	−	1.67150e6i	0.0757472	−	0.345344i
$473$			2.21874e6i			0.455989i
$474$	−2.42043e6	+	67536.4i	−0.494820	+	0.0138068i
$475$	−1.14255e6			−0.232350
$476$		−	287500.i		−	0.0581594i
$477$	351949.	+	6.30183e6i	0.0708245	+	1.26815i
$478$			1.94276e6i			0.388911i
$479$		−	4.40542e6i		−	0.877301i	−0.898658	−	0.438651i	$-0.855457\pi$
$479$		−	4.40542e6i		−	0.877301i	0.898658	−	0.438651i	$-0.144543\pi$
$480$	17251.2	+	618264.i	0.00341756	+	0.122482i
$481$	−755447.			−0.148882
$482$	−1.03722e6			−0.203355
$483$	−1.83139e6	+	51100.6i	−0.357202	+	0.00996686i
$484$	−2.13439e6			−0.414153
$485$	4.50065e6			0.868802
$486$	3.64618e6	−	511881.i	0.700240	−	0.0983055i
$487$	3.38142e6			0.646066			0.323033	−	0.946388i	$-0.395298\pi$
$487$	3.38142e6			0.646066			0.323033	+	0.946388i	$0.395298\pi$
$488$			641037.i			0.121852i
$489$	6.90947e6	−	192792.i	1.30669	−	0.0364600i
$490$			2.33177e6i			0.438728i
$491$			2.64422e6i			0.494987i	0.968890	+	0.247494i	$0.0796069\pi$
$491$			2.64422e6i			0.494987i	−0.968890	+	0.247494i	$0.920393\pi$
$492$	−131618.	−	4.71705e6i	−0.0245133	−	0.878532i
$493$	−277182.			−0.0513626
$494$			211297.i			0.0389561i
$495$	−87305.6	−	1.56325e6i	−0.0160151	−	0.286758i
$496$			994225.i			0.181460i
$497$			125767.i			0.0228390i
$498$	−2.87232e6	+	80145.2i	−0.518991	+	0.0144812i
$499$	3.53350e6			0.635264			0.317632	−	0.948214i	$-0.397112\pi$
$499$	3.53350e6			0.635264			0.317632	+	0.948214i	$0.397112\pi$
$500$			2.94395e6i			0.526630i
$501$	289055.	+	1.03594e7i	0.0514502	+	1.84392i
$502$			2.80349e6i			0.496524i
$503$	−2.10626e6			−0.371187			−0.185593	−	0.982627i	$-0.559421\pi$
$503$	−2.10626e6			−0.371187			−0.185593	+	0.982627i	$0.559421\pi$
$504$	651841.	−	36404.5i	0.114305	−	0.00638379i
$505$			3.77282e6i			0.658322i
$506$	−1.86224e6			−0.323339
$507$	−5.69783e6	+	158984.i	−0.984440	+	0.0274684i
$508$	−1.27915e6			−0.219919
$509$	−6.61209e6			−1.13121			−0.565606	−	0.824675i	$-0.691358\pi$
$509$	−6.61209e6			−1.13121			−0.565606	+	0.824675i	$0.691358\pi$
$510$	−1.03376e6	+	28844.6i	−0.175993	+	0.00491065i
$511$			2.06128e6i			0.349208i
$512$	−262144.			−0.0441942
$513$	2.65625e6	−	222812.i	0.445631	−	0.0373805i
$514$		−	5.11746e6i		−	0.854372i
$515$	7.00170e6			1.16328
$516$	92821.1	+	3.32661e6i	0.0153470	+	0.550019i
$517$	−3.17979e6			−0.523205
$518$			1.68984e6i			0.276708i
$519$	−2.86126e6	+	79836.6i	−0.466271	+	0.0130102i
$520$	186153.			0.0301899
$521$			1.07711e6i			0.173846i	0.996215	+	0.0869230i	$0.0277034\pi$
$521$			1.07711e6i			0.173846i	−0.996215	+	0.0869230i	$0.972297\pi$
$522$	−35098.0	−	628447.i	−0.00563775	−	0.100947i
$523$	−5.91391e6			−0.945411			−0.472706	−	0.881220i	$-0.656723\pi$
$523$	−5.91391e6			−0.945411			−0.472706	+	0.881220i	$0.656723\pi$
$524$	2.30794e6			0.367194
$525$	1.06209e6	−	29635.0i	0.168175	−	0.00469252i
$526$		−	2.11100e6i		−	0.332677i
$527$	−1.66238e6			−0.260738
$528$	663335.	−	18508.8i	0.103550	−	0.00288930i
$529$	1.40213e6			0.217846
$530$	4.02566e6			0.622511
$531$	−1.03597e6	+	6.41423e6i	−0.159445	+	0.987207i
$532$	472644.			0.0724027
$533$	−1.42025e6			−0.216545
$534$	−5.31645e6	+	148343.i	−0.806805	+	0.0225120i
$535$	2.48919e6			0.375987
$536$			718114.i			0.107965i
$537$	4.43109e6	−	123639.i	0.663093	−	0.0185020i
$538$	4.23935e6			0.631457
$539$	2.50175e6			0.370913
$540$	−196298.	−	2.34017e6i	−0.0289689	−	0.345352i
$541$			3.30916e6i			0.486099i	0.970014	+	0.243050i	$0.0781478\pi$
$541$			3.30916e6i			0.486099i	−0.970014	+	0.243050i	$0.921852\pi$
$542$	−5.67774e6			−0.830189
$543$	3.45065e6	−	96282.1i	0.502228	−	0.0140135i
$544$		−	438314.i		−	0.0635021i
$545$	7.41114e6			1.06879
$546$	−5480.51	−	196416.i	−0.000786754	−	0.0281965i
$547$	1.11368e6			0.159144			0.0795720	−	0.996829i	$-0.474645\pi$
$547$	1.11368e6			0.159144			0.0795720	+	0.996829i	$0.474645\pi$
$548$		−	3.82043e6i		−	0.543452i
$549$	−135721.	−	2.43015e6i	−0.0192183	−	0.344114i
$550$	1.07997e6			0.152232
$551$		−	455681.i		−	0.0639414i
$552$	−2.79209e6	+	77906.7i	−0.390016	+	0.0108825i
$553$	1.63016e6			0.226682
$554$	444557.			0.0615394
$555$	6.07614e6	−	169540.i	0.837328	−	0.0233636i
$556$	3.50532e6			0.480885
$557$		−	1.62594e6i		−	0.222058i	−0.993817	−	0.111029i	$-0.964585\pi$
$557$		−	1.62594e6i		−	0.222058i	0.993817	−	0.111029i	$-0.0354146\pi$
$558$	−210498.	−	3.76908e6i	−0.0286195	−	0.512447i
$559$	1.00161e6			0.135572
$560$		−	416401.i		−	0.0561102i
$561$	30947.3	+	1.10912e6i	0.00415161	+	0.148789i
$562$			2.14727e6i			0.286777i
$563$	−1.34602e7			−1.78970			−0.894851	−	0.446365i	$-0.852718\pi$
$563$	−1.34602e7			−1.78970			−0.894851	+	0.446365i	$0.852718\pi$
$564$	−4.76753e6	+	133026.i	−0.631096	+	0.0176092i
$565$			365518.i			0.0481713i
$566$			1.35286e6i			0.177505i
$567$	−2.46340e6	+	276016.i	−0.321794	+	0.0360560i
$568$			191741.i			0.0249370i
$569$	−9.26475e6			−1.19965			−0.599823	−	0.800133i	$-0.704762\pi$
$569$	−9.26475e6			−1.19965			−0.599823	+	0.800133i	$0.704762\pi$
$570$	−47420.0	−	1.69948e6i	−0.00611328	−	0.219093i
$571$			1.08390e7i			1.39123i	0.718414	+	0.695616i	$0.244869\pi$
$571$			1.08390e7i			1.39123i	−0.718414	+	0.695616i	$0.755131\pi$
$572$		−	199724.i		−	0.0255234i
$573$	3.72335e6	−	103891.i	0.473748	−	0.0132188i
$574$			3.17693e6i			0.402465i
$575$	−4.54579e6			−0.573377
$576$	993779.	−	55501.3i	0.124806	−	0.00697022i
$577$	−6.04404e6			−0.755767			−0.377884	−	0.925853i	$-0.623348\pi$
$577$	−6.04404e6			−0.755767			−0.377884	+	0.925853i	$0.623348\pi$
$578$	−4.94655e6			−0.615861
$579$	−8.57837e6	+	239359.i	−1.06343	+	0.0296724i
$580$	−401457.			−0.0495529
$581$	1.93451e6			0.237755
$582$	−202010.	−	7.23985e6i	−0.0247210	−	0.885976i
$583$		−	4.31912e6i		−	0.526289i
$584$			3.14257e6i			0.381288i
$585$	−705700.	+	39412.4i	−0.0852571	+	0.00476150i
$586$			1.29362e6i			0.155620i
$587$	1.08758e7			1.30277			0.651383	−	0.758749i	$-0.274189\pi$
$587$	1.08758e7			1.30277			0.651383	+	0.758749i	$0.274189\pi$
$588$	3.75094e6	−	104661.i	0.447400	−	0.0124836i
$589$		−	2.73292e6i		−	0.324593i
$590$	4.04787e6	+	887854.i	0.478737	+	0.105005i
$591$	−6758.81	−	242229.i	−0.000795979	−	0.0285270i
$592$			2.57628e6i			0.302127i
$593$		−	1.80779e6i		−	0.211111i	−0.994413	−	0.105555i	$-0.966338\pi$
$593$		−	1.80779e6i		−	0.211111i	0.994413	−	0.105555i	$-0.0336620\pi$
$594$	−2.51076e6	+	210608.i	−0.291971	+	0.0244911i
$595$	696238.			0.0806241
$596$	1.60500e6			0.185080
$597$	6.59233e6	−	183943.i	0.757013	−	0.0211226i
$598$			840671.i			0.0961331i
$599$			6.76335e6i			0.770185i	0.922878	+	0.385093i	$0.125830\pi$
$599$			6.76335e6i			0.770185i	−0.922878	+	0.385093i	$0.874170\pi$
$600$	1.61923e6	−	45180.7i	0.183624	−	0.00512359i
$601$			1.28566e7i			1.45191i	0.687743	+	0.725954i	$0.258602\pi$
$601$			1.28566e7i			1.45191i	−0.687743	+	0.725954i	$0.741398\pi$
$602$		−	2.24047e6i		−	0.251970i
$603$	−152040.	−	2.72235e6i	−0.0170280	−	0.304895i
$604$			5.80712e6i			0.647691i
$605$		−	5.16886e6i		−	0.574124i
$606$	6.06905e6	−	169342.i	0.671335	−	0.0187320i
$607$	8.27006e6			0.911039			0.455520	−	0.890226i	$-0.349454\pi$
$607$	8.27006e6			0.911039			0.455520	+	0.890226i	$0.349454\pi$
$608$	720580.			0.0790539
$609$	11819.2	+	423589.i	0.00129136	+	0.0462809i
$610$	−1.55240e6			−0.168919
$611$			1.43546e6i			0.155556i
$612$	92800.1	+	1.66164e6i	0.0100154	+	0.179332i
$613$			6.57376e6i			0.706582i	0.935513	+	0.353291i	$0.114937\pi$
$613$			6.57376e6i			0.706582i	−0.935513	+	0.353291i	$0.885063\pi$
$614$	3.46507e6			0.370929
$615$	1.14233e7	−	318739.i	1.21787	−	0.0339819i
$616$	−446756.			−0.0474372
$617$		−	958721.i		−	0.101386i	−0.998714	−	0.0506931i	$-0.983857\pi$
$617$		−	958721.i		−	0.101386i	0.998714	−	0.0506931i	$-0.0161430\pi$
$618$	−314270.	−	1.12631e7i	−0.0331002	−	1.18628i
$619$	−1.12144e7			−1.17638			−0.588190	−	0.808723i	$-0.700159\pi$
$619$	−1.12144e7			−1.17638			−0.588190	+	0.808723i	$0.700159\pi$
$620$	−2.40771e6			−0.251551
$621$	1.05682e7	−	886485.i	1.09970	−	0.0922449i
$622$			5.54942e6i			0.575137i
$623$	3.58063e6			0.369606
$624$	−8355.43	−	299450.i	−0.000859028	−	0.0307867i
$625$	−2.05544e6			−0.210477
$626$		−	2.84626e6i		−	0.290294i
$627$	−1.82337e6	+	50876.8i	−0.185228	+	0.00516834i
$628$		−	2.62605e6i		−	0.265708i
$629$	−4.30764e6			−0.434123
$630$	88160.6	+	1.57856e6i	0.00884959	+	0.158457i
$631$	4.27214e6			0.427142			0.213571	−	0.976928i	$-0.431491\pi$
$631$	4.27214e6			0.427142			0.213571	+	0.976928i	$0.431491\pi$
$632$	2.48530e6			0.247506
$633$	198553.	+	7.11593e6i	0.0196955	+	0.705866i
$634$		−	9.59816e6i		−	0.948341i
$635$		−	3.09772e6i		−	0.304865i
$636$	−180690.	−	6.47576e6i	−0.0177130	−	0.634816i
$637$		−	1.12937e6i		−	0.110278i
$638$			430723.i			0.0418935i
$639$	−40595.5	−	726885.i	−0.00393302	−	0.0704228i
$640$		−	634834.i		−	0.0612647i
$641$		−	7.46254e6i		−	0.717367i	−0.933459	−	0.358684i	$-0.883226\pi$
$641$		−	7.46254e6i		−	0.717367i	0.933459	−	0.358684i	$-0.116774\pi$
$642$	−111727.	−	4.00416e6i	−0.0106984	−	0.383419i
$643$	1.82096e6			0.173690			0.0868448	−	0.996222i	$-0.472322\pi$
$643$	1.82096e6			0.173690			0.0868448	+	0.996222i	$0.472322\pi$
$644$	1.88047e6			0.178670
$645$	−8.05605e6	+	224785.i	−0.762470	+	0.0212749i
$646$			1.20484e6i			0.113592i
$647$		−	3.46423e6i		−	0.325347i	−0.986680	−	0.162673i	$-0.947988\pi$
$647$		−	3.46423e6i		−	0.325347i	0.986680	−	0.162673i	$-0.0520117\pi$
$648$	−3.75563e6	+	420807.i	−0.351355	+	0.0393682i
$649$	952578.	−	4.34296e6i	0.0887746	−	0.404738i
$650$		−	487533.i		−	0.0452607i
$651$	70885.2	+	2.54045e6i	0.00655546	+	0.234941i
$652$	−7.09464e6			−0.653599
$653$			7.27715e6i			0.667849i	0.942600	+	0.333924i	$0.108373\pi$
$653$			7.27715e6i			0.667849i	−0.942600	+	0.333924i	$0.891627\pi$
$654$	−332647.	−	1.19217e7i	−0.0304116	−	1.08992i
$655$			5.58913e6i			0.509027i
$656$			4.84346e6i			0.439437i
$657$	−665346.	−	1.19134e7i	−0.0601360	−	1.07677i
$658$	3.21093e6			0.289112
$659$	1.99900e7			1.79308			0.896540	−	0.442962i	$-0.146073\pi$
$659$	1.99900e7			1.79308			0.896540	+	0.442962i	$0.146073\pi$
$660$	44822.7	+	1.60640e6i	0.00400533	+	0.143547i
$661$	696282.			0.0619842			0.0309921	−	0.999520i	$-0.490133\pi$
$661$	696282.			0.0619842			0.0309921	+	0.999520i	$0.490133\pi$
$662$	−1.26394e7			−1.12094
$663$	500691.	−	13970.6i	0.0442371	−	0.00123433i
$664$	2.94930e6			0.259596
$665$			1.14460e6i			0.100369i
$666$	−545452.	−	9.76661e6i	−0.0476509	−	0.853214i
$667$		−	1.81299e6i		−	0.157790i
$668$		−	1.06371e7i		−	0.922319i
$669$	−7.01819e6	+	195826.i	−0.606261	+	0.0169163i
$670$	−1.73906e6			−0.149667
$671$			1.66557e6i			0.142809i
$672$	−669832.	+	18690.0i	−0.0572193	+	0.00159657i
$673$			1.67712e7i			1.42734i	0.700484	+	0.713668i	$0.252968\pi$
$673$			1.67712e7i			1.42734i	−0.700484	+	0.713668i	$0.747032\pi$
$674$			1.20031e7i			1.01776i
$675$	−6.12888e6	+	514102.i	−0.517752	+	0.0434300i
$676$	5.85053e6			0.492412
$677$			1.86809e7i			1.56648i	0.621718	+	0.783241i	$0.286435\pi$
$677$			1.86809e7i			1.56648i	−0.621718	+	0.783241i	$0.713565\pi$
$678$	587981.	−	16406.2i	0.0491235	−	0.00137067i
$679$			4.87604e6i			0.405875i
$680$	1.06147e6			0.0880306
$681$	−3.31108e6	+	92387.7i	−0.273591	+	0.00763390i
$682$			2.58323e6i			0.212668i
$683$	−1.53915e7			−1.26249			−0.631246	−	0.775583i	$-0.717456\pi$
$683$	−1.53915e7			−1.26249			−0.631246	+	0.775583i	$0.717456\pi$
$684$	−2.73170e6	+	152562.i	−0.223250	+	0.0124682i
$685$	9.25194e6			0.753367
$686$	−5.34842e6			−0.433925
$687$	−11782.6	−	422277.i	−0.000952467	−	0.0341354i
$688$		−	3.41576e6i		−	0.275117i
$689$	−1.94979e6			−0.156473
$690$	−188666.	−	6.76161e6i	−0.0150859	−	0.540664i
$691$			1.22261e7i			0.974074i	0.873381	+	0.487037i	$0.161922\pi$
$691$			1.22261e7i			0.974074i	−0.873381	+	0.487037i	$0.838078\pi$
$692$	2.93794e6			0.233226
$693$	1.69364e6	−	94587.5i	0.133964	−	0.00748170i
$694$	1.66926e7			1.31560
$695$			8.48884e6i			0.666632i
$696$	18019.3	+	645793.i	0.00140999	+	0.0505324i
$697$	−8.09845e6			−0.631422
$698$		−	1.06026e7i		−	0.823706i
$699$	2.81628e6	−	78581.6i	0.218013	−	0.00608314i
$700$	−1.09055e6			−0.0841203
$701$	424402.			0.0326198			0.0163099	−	0.999867i	$-0.494808\pi$
$701$	424402.			0.0326198			0.0163099	+	0.999867i	$0.494808\pi$
$702$	95074.9	+	1.13344e6i	0.00728154	+	0.0868069i
$703$		−	7.08168e6i		−	0.540440i
$704$	−681113.			−0.0517949
$705$	−322150.	−	1.15455e7i	−0.0244110	−	0.874864i
$706$	−5.79014e6			−0.437197
$707$	−4.08750e6			−0.307546
$708$	1.24653e6	−	6.55135e6i	0.0934590	−	0.491188i
$709$	−4.54949e6			−0.339897			−0.169948	−	0.985453i	$-0.554360\pi$
$709$	−4.54949e6			−0.339897			−0.169948	+	0.985453i	$0.554360\pi$
$710$	−464339.			−0.0345692
$711$	−9.42169e6	+	526189.i	−0.698964	+	0.0390362i
$712$	5.45893e6			0.403560
$713$		−	1.08733e7i		−	0.801008i
$714$	−31250.4	−	1.11998e6i	−0.00229409	−	0.0822178i
$715$	483670.			0.0353822
$716$	−4.54984e6			−0.331675
$717$	211173.	+	7.56823e6i	0.0153406	+	0.549790i
$718$			3.14912e6i			0.227970i
$719$	−3.37342e6			−0.243359			−0.121680	−	0.992569i	$-0.538828\pi$
$719$	−3.37342e6			−0.243359			−0.121680	+	0.992569i	$0.538828\pi$
$720$	134407.	+	2.40663e6i	0.00966255	+	0.173013i
$721$			7.58569e6i			0.543447i
$722$	7.92367e6			0.565696
$723$	−4.04061e6	+	112744.i	−0.287476	+	0.00802132i
$724$	−3.54313e6			−0.251212
$725$			1.05141e6i			0.0742896i
$726$	−8.31474e6	+	232003.i	−0.585473	+	0.0163362i
$727$	−1.29643e7			−0.909734			−0.454867	−	0.890560i	$-0.650313\pi$
$727$	−1.29643e7			−0.909734			−0.454867	+	0.890560i	$0.650313\pi$
$728$			201680.i			0.0141037i
$729$	1.41484e7	−	2.39041e6i	0.986026	−	0.166592i
$730$	−7.61035e6			−0.528564
$731$	5.71128e6			0.395312
$732$	69679.0	+	2.49722e6i	0.00480645	+	0.172258i
$733$	6.01595e6			0.413565			0.206783	−	0.978387i	$-0.433701\pi$
$733$	6.01595e6			0.413565			0.206783	+	0.978387i	$0.433701\pi$
$734$			1.53894e7i			1.05434i
$735$	253457.	+	9.08364e6i	0.0173056	+	0.620214i
$736$	2.86692e6			0.195084
$737$			1.86583e6i			0.126533i
$738$	−1.02546e6	−	1.83614e7i	−0.0693071	−	1.24098i
$739$		−	1.23591e7i		−	0.832481i	−0.909255	−	0.416240i	$-0.863348\pi$
$739$		−	1.23591e7i		−	0.832481i	0.909255	−	0.416240i	$-0.136652\pi$
$740$	−6.23898e6			−0.418827
$741$	22967.4	+	823127.i	0.00153662	+	0.0550708i
$742$			4.36142e6i			0.290816i
$743$		−	1.15052e7i		−	0.764578i	−0.924043	−	0.382289i	$-0.875136\pi$
$743$		−	1.15052e7i		−	0.764578i	0.924043	−	0.382289i	$-0.124864\pi$
$744$	108070.	+	3.87310e6i	0.00715766	+	0.256523i
$745$			3.88682e6i			0.256569i
$746$	1.21782e7			0.801193
$747$	−1.11807e7	+	624427.i	−0.733107	+	0.0409431i
$748$		−	1.13885e6i		−	0.0744236i
$749$			2.69680e6i			0.175649i
$750$	320000.	+	1.14685e7i	0.0207729	+	0.744478i
$751$			1.68066e7i			1.08738i	0.839287	+	0.543688i	$0.182973\pi$
$751$			1.68066e7i			1.08738i	−0.839287	+	0.543688i	$0.817027\pi$
$752$	4.89530e6			0.315671
$753$	304732.	+	1.09213e7i	0.0195853	+	0.701917i
$754$	194442.			0.0124555
$755$	−1.40631e7			−0.897869
$756$	2.53535e6	−	212671.i	0.161337	−	0.0135333i
$757$	1.97078e7			1.24997			0.624984	−	0.780638i	$-0.285105\pi$
$757$	1.97078e7			1.24997			0.624984	+	0.780638i	$0.285105\pi$
$758$	1.34273e7			0.848822
$759$	−7.25452e6	+	202420.i	−0.457093	+	0.0127541i
$760$			1.74503e6i			0.109589i
$761$		−	3.81411e6i		−	0.238744i	−0.992850	−	0.119372i	$-0.961912\pi$
$761$		−	3.81411e6i		−	0.238744i	0.992850	−	0.119372i	$-0.0380881\pi$
$762$	−4.98306e6	+	139040.i	−0.310892	+	0.00867468i
$763$			8.02928e6i			0.499304i
$764$	−3.82314e6			−0.236966
$765$	−4.02398e6	+	224734.i	−0.248601	+	0.0138840i
$766$			1.82429e7i			1.12337i
$767$	−1.96055e6	−	430023.i	−0.120334	−	0.0263939i
$768$	−1.02121e6	+	28494.3i	−0.0624757	+	0.00174323i
$769$			6.75823e6i			0.412114i	0.978540	+	0.206057i	$0.0660632\pi$
$769$			6.75823e6i			0.412114i	−0.978540	+	0.206057i	$0.933937\pi$
$770$		−	1.08191e6i		−	0.0657603i
$771$	−556254.	−	1.99356e7i	−0.0337006	−	1.20779i
$772$	8.80827e6			0.531921
$773$	2.44929e7			1.47432			0.737161	−	0.675717i	$-0.236166\pi$
$773$	2.44929e7			1.47432			0.737161	+	0.675717i	$0.236166\pi$
$774$	723187.	+	1.29490e7i	0.0433909	+	0.776936i
$775$			6.30578e6i			0.377124i
$776$			7.43387e6i			0.443160i
$777$	183681.	+	6.58294e6i	0.0109147	+	0.391171i
$778$			1.21879e7i			0.721907i
$779$		−	1.33137e7i		−	0.786058i
$780$	725178.	−	20234.3i	0.0426784	−	0.00119084i
$781$			498189.i			0.0292258i
$782$			4.79360e6i			0.280314i
$783$	−205038.	−	2.44436e6i	−0.0119517	−	0.142482i
$784$	−3.85146e6			−0.223787
$785$	6.35951e6			0.368340
$786$	8.99080e6	−	250867.i	0.519089	−	0.0144839i
$787$	1.52116e7			0.875461			0.437730	−	0.899106i	$-0.355782\pi$
$787$	1.52116e7			0.875461			0.437730	+	0.899106i	$0.355782\pi$
$788$			248720.i			0.0142691i
$789$	−229460.	−	8.22360e6i	−0.0131224	−	0.470294i
$790$			6.01865e6i			0.343108i
$791$	−396005.			−0.0225040
$792$	2.58208e6	−	144206.i	0.146270	−	0.00816900i
$793$	751888.			0.0424591
$794$			1.96124e7i			1.10403i
$795$	1.56823e7	−	437578.i	0.880021	−	0.0245549i
$796$	−6.76901e6			−0.378654
$797$	−2.28925e6			−0.127658			−0.0638289	−	0.997961i	$-0.520331\pi$
$797$	−2.28925e6			−0.127658			−0.0638289	+	0.997961i	$0.520331\pi$
$798$	1.84123e6	−	51375.1i	0.102353	−	0.00285592i
$799$			8.18512e6i			0.453584i
$800$	−1.66262e6			−0.0918479
$801$	−2.06946e7	+	1.15577e6i	−1.13966	+	0.0636487i
$802$	4.22481e6			0.231937
$803$			8.16514e6i			0.446864i
$804$	78057.1	+	2.79749e6i	0.00425865	+	0.152626i
$805$			4.55394e6i			0.247684i
$806$	1.16615e6			0.0632292
$807$	1.65148e7	−	460806.i	0.892667	−	0.0249077i
$808$	−6.23170e6			−0.335798
$809$	6.82774e6			0.366780			0.183390	−	0.983040i	$-0.441293\pi$
$809$	6.82774e6			0.366780			0.183390	+	0.983040i	$0.441293\pi$
$810$	−1.01907e6	−	9.09502e6i	−0.0545746	−	0.487069i
$811$			1.53148e7i			0.817634i	0.912616	+	0.408817i	$0.134059\pi$
$811$			1.53148e7i			0.817634i	−0.912616	+	0.408817i	$0.865941\pi$
$812$		−	434941.i		−	0.0231494i
$813$	−2.21182e7	+	617155.i	−1.17361	+	0.0327467i
$814$			6.69380e6i			0.354088i
$815$		−	1.71811e7i		−	0.906059i
$816$	−47643.6	−	1.70750e6i	−0.00250483	−	0.0897706i
$817$			9.38924e6i			0.492125i
$818$			1.57128e7i			0.821052i
$819$	−42699.7	−	764561.i	−0.00222441	−	0.0398293i
$820$	−1.17294e7			−0.609174
$821$	−2.50169e7			−1.29532			−0.647658	−	0.761931i	$-0.724251\pi$
$821$	−2.50169e7			−1.29532			−0.647658	+	0.761931i	$0.724251\pi$
$822$	−415271.	−	1.48829e7i	−0.0214364	−	0.768258i
$823$			4.64963e6i			0.239287i	0.992817	+	0.119643i	$0.0381751\pi$
$823$			4.64963e6i			0.239287i	−0.992817	+	0.119643i	$0.961825\pi$
$824$			1.15649e7i			0.593370i
$825$	4.20714e6	−	117390.i	0.215205	−	0.00600478i
$826$	−961907.	+	4.38549e6i	−0.0490550	+	0.223650i
$827$		−	1.65370e7i		−	0.840800i	−0.907339	−	0.420400i	$-0.861890\pi$
$827$		−	1.65370e7i		−	0.840800i	0.907339	−	0.420400i	$-0.138110\pi$
$828$	−1.08684e7	+	606986.i	−0.550922	+	0.0307683i
$829$	−2.15245e6			−0.108779			−0.0543897	−	0.998520i	$-0.517321\pi$
$829$	−2.15245e6			−0.108779			−0.0543897	+	0.998520i	$0.517321\pi$
$830$			7.14232e6i			0.359869i
$831$	1.73182e6	−	48322.2i	0.0869960	−	0.00242741i
$832$			307475.i			0.0153993i
$833$		−	6.43978e6i		−	0.321557i
$834$	1.36553e7	−	381019.i	0.679809	−	0.0189684i
$835$	2.57598e7			1.27857
$836$	1.87224e6			0.0926501
$837$	−1.22970e6	−	1.46599e7i	−0.0606718	−	0.723299i
$838$	−1.60920e7			−0.791589
$839$	−1.85802e7			−0.911267			−0.455633	−	0.890168i	$-0.650587\pi$
$839$	−1.85802e7			−0.911267			−0.455633	+	0.890168i	$0.650587\pi$
$840$	−45261.7	−	1.62213e6i	−0.00221326	−	0.0793209i
$841$	2.00918e7			0.979556
$842$		−	2.04027e6i		−	0.0991762i
$843$	233402.	+	8.36488e6i	0.0113119	+	0.405407i
$844$		−	7.30664e6i		−	0.353070i
$845$			1.41682e7i			0.682611i
$846$	−1.85579e7	+	1.03644e6i	−0.891463	+	0.0497870i
$847$	5.59997e6			0.268212
$848$			6.64931e6i			0.317532i
$849$	147052.	+	5.27020e6i	0.00700168	+	0.250933i
$850$		−	2.77997e6i		−	0.131975i
$851$		−	2.81754e7i		−	1.33366i
$852$	20841.8	+	746947.i	0.000983638	+	0.0352526i
$853$	2.43055e7			1.14375			0.571876	−	0.820340i	$-0.306216\pi$
$853$	2.43055e7			1.14375			0.571876	+	0.820340i	$0.306216\pi$
$854$		−	1.68188e6i		−	0.0789133i
$855$	−369458.	−	6.61535e6i	−0.0172842	−	0.309483i
$856$			4.11147e6i			0.191784i
$857$	3.42121e7			1.59121			0.795606	−	0.605815i	$-0.207153\pi$
$857$	3.42121e7			1.59121			0.795606	+	0.605815i	$0.207153\pi$
$858$	−21709.4	−	778043.i	−0.00100677	−	0.0360816i
$859$		−	2.36643e7i		−	1.09423i	−0.837056	−	0.547117i	$-0.815725\pi$
$859$		−	2.36643e7i		−	1.09423i	0.837056	−	0.547117i	$-0.184275\pi$
$860$	8.27195e6			0.381383
$861$	345324.	+	1.23760e7i	0.0158752	+	0.568950i
$862$	3.23945e6			0.148492
$863$	4.21822e7			1.92798			0.963989	−	0.265942i	$-0.0856829\pi$
$863$	4.21822e7			1.92798			0.963989	+	0.265942i	$0.0856829\pi$
$864$	3.86533e6	−	324232.i	0.176158	−	0.0147765i
$865$			7.11481e6i			0.323313i
$866$	1.03375e7			0.468404
$867$	−1.92698e7	+	537677.i	−0.870620	+	0.0242926i
$868$		−	2.60853e6i		−	0.117516i
$869$	6.45740e6			0.290074
$870$	−1.56391e6	+	43637.3i	−0.0700511	+	0.00195461i
$871$	842295.			0.0376200
$872$			1.22412e7i			0.545172i
$873$	−1.57390e6	−	2.81816e7i	−0.0698944	−	1.25150i
$874$	−7.88058e6			−0.348963
$875$		−	7.72400e6i		−	0.341053i
$876$	341589.	+	1.22422e7i	0.0150398	+	0.539012i
$877$	−3.26201e7			−1.43214			−0.716071	−	0.698028i	$-0.754061\pi$
$877$	−3.26201e7			−1.43214			−0.716071	+	0.698028i	$0.754061\pi$
$878$	−6.85158e6			−0.299954
$879$	140613.	+	5.03944e6i	0.00613839	+	0.219994i
$880$		−	1.64945e6i		−	0.0718013i
$881$	−1.54894e7			−0.672348			−0.336174	−	0.941800i	$-0.609133\pi$
$881$	−1.54894e7			−0.672348			−0.336174	+	0.941800i	$0.609133\pi$
$882$	1.46008e7	−	815433.i	0.631981	−	0.0352953i
$883$	−2.50379e7			−1.08068			−0.540339	−	0.841448i	$-0.681704\pi$
$883$	−2.50379e7			−1.08068			−0.540339	+	0.841448i	$0.681704\pi$
$884$	−514110.			−0.0221271
$885$	1.58654e7	+	3.01873e6i	0.680915	+	0.129559i
$886$	1.71450e6			0.0733760
$887$	−2.45180e7			−1.04635			−0.523174	−	0.852226i	$-0.675252\pi$
$887$	−2.45180e7			−1.04635			−0.523174	+	0.852226i	$0.675252\pi$
$888$	280035.	+	1.00362e7i	0.0119174	+	0.427106i
$889$	3.35609e6			0.142423
$890$			1.32199e7i			0.559439i
$891$	−9.75803e6	+	1.09336e6i	−0.411783	+	0.0461389i
$892$	7.20627e6			0.303248
$893$	−1.34562e7			−0.564668
$894$	6.25242e6	−	174459.i	0.261640	−	0.00730044i
$895$		−	1.10183e7i		−	0.459789i
$896$	687783.			0.0286208
$897$	91378.7	+	3.27492e6i	0.00379196	+	0.135900i
$898$		−	1.55754e7i		−	0.644539i
$899$	−2.51492e6			−0.103783
$900$	6.30295e6	−	352012.i	0.259381	−	0.0144861i
$901$	−1.11179e7			−0.456258
$902$			1.25845e7i			0.515014i
$903$	−243533.	−	8.72798e6i	−0.00993891	−	0.356200i
$904$	−603739.			−0.0245713
$905$		−	8.58038e6i		−	0.348245i
$906$	631218.	+	2.26222e7i	0.0255481	+	0.915618i
$907$	−3.85574e7			−1.55629			−0.778144	−	0.628086i	$-0.783839\pi$
$907$	−3.85574e7			−1.55629			−0.778144	+	0.628086i	$0.783839\pi$
$908$	3.39981e6			0.136849
$909$	2.36242e7	−	1.31938e6i	0.948302	−	0.0529614i
$910$	−488407.			−0.0195514
$911$		−	1.61965e7i		−	0.646585i	−0.946299	−	0.323293i	$-0.895210\pi$
$911$		−	1.61965e7i		−	0.646585i	0.946299	−	0.323293i	$-0.104790\pi$
$912$	2.80709e6	−	78325.1i	0.111756	−	0.00311827i
$913$	7.66299e6			0.304243
$914$			2.37856e7i			0.941780i
$915$	−6.04752e6	+	168741.i	−0.238795	+	0.00666299i
$916$			433594.i			0.0170744i
$917$	−6.05530e6			−0.237800
$918$	542127.	+	6.46298e6i	0.0212322	+	0.253120i
$919$			3.55693e7i			1.38927i	0.719362	+	0.694636i	$0.244434\pi$
$919$			3.55693e7i			1.38927i	−0.719362	+	0.694636i	$0.755566\pi$
$920$			6.94282e6i			0.270437i
$921$	1.34985e7	−	376643.i	0.524368	−	0.0146312i
$922$		−	2.12044e7i		−	0.821484i
$923$	224898.			0.00868923
$924$	−1.74038e6	+	48561.2i	−0.0670602	+	0.00187115i
$925$			1.63398e7i			0.627904i
$926$			1.75110e7i			0.671093i
$927$	−2.44854e6	−	4.38423e7i	−0.0935852	−	1.67569i
$928$		−	663100.i		−	0.0252760i
$929$	−1.60484e7			−0.610089			−0.305045	−	0.952338i	$-0.598671\pi$
$929$	−1.60484e7			−0.610089			−0.305045	+	0.952338i	$0.598671\pi$
$930$	−9.37949e6	+	261712.i	−0.355608	+	0.00992239i
$931$	1.05869e7			0.400307
$932$	−2.89176e6			−0.109049
$933$	603207.	+	2.16183e7i	0.0226862	+	0.813050i
$934$	1.43644e7			0.538792
$935$	2.75794e6			0.103171
$936$	−65098.8	−	1.16563e6i	−0.00242875	−	0.0434881i
$937$		−	1.78410e7i		−	0.663849i	−0.943306	−	0.331924i	$-0.892302\pi$
$937$		−	1.78410e7i		−	0.663849i	0.943306	−	0.331924i	$-0.107698\pi$
$938$		−	1.88411e6i		−	0.0699195i
$939$	−309380.	−	1.10879e7i	−0.0114506	−	0.410378i
$940$			1.18549e7i			0.437602i
$941$	2.23757e7			0.823764			0.411882	−	0.911237i	$-0.364872\pi$
$941$	2.23757e7			0.823764			0.411882	+	0.911237i	$0.364872\pi$
$942$	−285445.	−	1.02300e7i	−0.0104808	−	0.375621i
$943$		−	5.29702e7i		−	1.93978i
$944$	−1.46650e6	+	6.68600e6i	−0.0535613	+	0.244195i
$945$	515024.	+	6.13986e6i	0.0187606	+	0.223655i
$946$		−	8.87497e6i		−	0.322433i
$947$		−	7.50347e6i		−	0.271886i	−0.990717	−	0.135943i	$-0.956594\pi$
$947$		−	7.50347e6i		−	0.271886i	0.990717	−	0.135943i	$-0.0434064\pi$
$948$	9.68173e6	−	270146.i	0.349891	−	0.00976286i
$949$	3.68600e6			0.132859
$950$	4.57021e6			0.164296
$951$	−1.04329e6	−	3.73906e7i	−0.0374072	−	1.34064i
$952$			1.15000e6i			0.0411249i
$953$		−	3.51975e7i		−	1.25539i	−0.778458	−	0.627696i	$-0.783998\pi$
$953$		−	3.51975e7i		−	1.25539i	0.778458	−	0.627696i	$-0.216002\pi$
$954$	−1.40780e6	−	2.52073e7i	−0.0500805	−	0.896717i
$955$		−	9.25848e6i		−	0.328497i
$956$		−	7.77106e6i		−	0.275002i
$957$	46818.4	+	1.67792e6i	0.00165248	+	0.0592232i
$958$			1.76217e7i			0.620346i
$959$			1.00236e7i			0.351947i
$960$	−69004.7	−	2.47306e6i	−0.00241658	−	0.0866076i
$961$	1.35461e7			0.473157
$962$	3.02179e6			0.105275
$963$	−870483.	−	1.55865e7i	−0.0302479	−	0.541604i
$964$	4.14890e6			0.143794
$965$			2.13310e7i			0.737382i
$966$	7.32557e6	−	204403.i	0.252580	−	0.00704764i
$967$			1.59141e7i			0.547287i	0.961831	+	0.273643i	$0.0882288\pi$
$967$			1.59141e7i			0.547287i	−0.961831	+	0.273643i	$0.911771\pi$
$968$	8.53757e6			0.292850
$969$	130962.	+	4.69356e6i	0.00448061	+	0.160580i
$970$	−1.80026e7			−0.614336
$971$		−	2.92552e7i		−	0.995761i	−0.867246	−	0.497881i	$-0.834112\pi$
$971$		−	2.92552e7i		−	0.995761i	0.867246	−	0.497881i	$-0.165888\pi$
$972$	−1.45847e7	+	2.04752e6i	−0.495144	+	0.0695125i
$973$	−9.19687e6			−0.311428
$974$	−1.35257e7			−0.456837
$975$	−52993.6	−	1.89923e6i	−0.00178530	−	0.0639833i
$976$		−	2.56415e6i		−	0.0861625i
$977$	−4.12285e7			−1.38185			−0.690926	−	0.722926i	$-0.742797\pi$
$977$	−4.12285e7			−1.38185			−0.690926	+	0.722926i	$0.742797\pi$
$978$	−2.76379e7	+	771169.i	−0.923969	+	0.0257811i
$979$	1.41836e7			0.472966
$980$		−	9.32708e6i		−	0.310228i
$981$	−2.59172e6	−	4.64061e7i	−0.0859835	−	1.53958i
$982$		−	1.05769e7i		−	0.350009i
$983$	−3.62217e7			−1.19560			−0.597799	−	0.801646i	$-0.703958\pi$
$983$	−3.62217e7			−1.19560			−0.597799	+	0.801646i	$0.703958\pi$
$984$	526471.	+	1.88682e7i	0.0173335	+	0.621216i
$985$	−602326.			−0.0197807
$986$	1.10873e6			0.0363189
$987$	1.25085e7	−	349020.i	0.408707	−	0.0114040i
$988$		−	845187.i		−	0.0275461i
$989$			3.73563e7i			1.21443i
$990$	349222.	+	6.25301e6i	0.0113244	+	0.202769i
$991$			3.46914e7i			1.12212i	0.827776	+	0.561058i	$0.189606\pi$
$991$			3.46914e7i			1.12212i	−0.827776	+	0.561058i	$0.810394\pi$
$992$		−	3.97690e6i		−	0.128312i
$993$	−4.92380e7	+	1.37387e6i	−1.58463	+	0.0442153i
$994$		−	503069.i		−	0.0161496i
$995$		−	1.63925e7i		−	0.524913i
$996$	1.14893e7	−	320581.i	0.366982	−	0.0102398i
$997$	−5.97624e6			−0.190410			−0.0952051	−	0.995458i	$-0.530351\pi$
$997$	−5.97624e6			−0.190410			−0.0952051	+	0.995458i	$0.530351\pi$
$998$	−1.41340e7			−0.449200
$999$	−3.18647e6	−	3.79875e7i	−0.101017	−	1.20428i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.c.a.353.2	yes	50
3.2	odd	2		354.6.c.b.353.1	yes	50
59.58	odd	2		354.6.c.b.353.2	yes	50
177.176	even	2	inner	354.6.c.a.353.1	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.c.a.353.1	✓	50	177.176	even	2	inner
354.6.c.a.353.2	yes	50	1.1	even	1	trivial
354.6.c.b.353.1	yes	50	3.2	odd	2
354.6.c.b.353.2	yes	50	59.58	odd	2

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	354.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +(-15.5824 + 0.434789i) q^{3} +16.0000 q^{4} +38.7472i q^{5} +(62.3296 - 1.73916i) q^{6} -41.9790 q^{7} -64.0000 q^{8} +(242.622 - 13.5501i) q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +(-15.5824 + 0.434789i) q^{3} +16.0000 q^{4} +38.7472i q^{5} +(62.3296 - 1.73916i) q^{6} -41.9790 q^{7} -64.0000 q^{8} +(242.622 - 13.5501i) q^{9} -154.989i q^{10} -166.287 q^{11} +(-249.318 + 6.95663i) q^{12} +75.0672i q^{13} +167.916 q^{14} +(-16.8469 - 603.774i) q^{15} +256.000 q^{16} +428.041i q^{17} +(-970.488 + 54.2005i) q^{18} -703.692 q^{19} +619.955i q^{20} +(654.133 - 18.2520i) q^{21} +665.149 q^{22} -2799.73 q^{23} +(997.273 - 27.8265i) q^{24} +1623.66 q^{25} -300.269i q^{26} +(-3774.74 + 316.633i) q^{27} -671.663 q^{28} +647.558i q^{29} +(67.3874 + 2415.10i) q^{30} +3883.69i q^{31} -1024.00 q^{32} +(2591.15 - 72.2999i) q^{33} -1712.17i q^{34} -1626.57i q^{35} +(3881.95 - 216.802i) q^{36} +10063.6i q^{37} +2814.77 q^{38} +(-32.6384 - 1169.73i) q^{39} -2479.82i q^{40} +18919.8i q^{41} +(-2616.53 + 73.0080i) q^{42} -13342.8i q^{43} -2660.60 q^{44} +(525.029 + 9400.92i) q^{45} +11198.9 q^{46} +19122.3 q^{47} +(-3989.09 + 111.306i) q^{48} -15044.8 q^{49} -6494.62 q^{50} +(-186.108 - 6669.91i) q^{51} +1201.08i q^{52} +25973.9i q^{53} +(15099.0 - 1266.53i) q^{54} -6443.16i q^{55} +2686.65 q^{56} +(10965.2 - 305.958i) q^{57} -2590.23i q^{58} +(-5728.51 + 26117.2i) q^{59} +(-269.550 - 9660.38i) q^{60} -10016.2i q^{61} -15534.8i q^{62} +(-10185.0 + 568.820i) q^{63} +4096.00 q^{64} -2908.64 q^{65} +(-10364.6 + 289.200i) q^{66} -11220.5i q^{67} +6848.66i q^{68} +(43626.5 - 1217.29i) q^{69} +6506.27i q^{70} -2995.96i q^{71} +(-15527.8 + 867.207i) q^{72} -49102.6i q^{73} -40254.4i q^{74} +(-25300.4 + 705.948i) q^{75} -11259.1 q^{76} +6980.57 q^{77} +(130.554 + 4678.91i) q^{78} -38832.8 q^{79} +9919.28i q^{80} +(58681.8 - 6575.11i) q^{81} -75679.1i q^{82} -46082.8 q^{83} +(10466.1 - 292.032i) q^{84} -16585.4 q^{85} +53371.3i q^{86} +(-281.551 - 10090.5i) q^{87} +10642.4 q^{88} -85295.8 q^{89} +(-2100.11 - 37603.7i) q^{90} -3151.24i q^{91} -44795.6 q^{92} +(-1688.59 - 60517.2i) q^{93} -76489.1 q^{94} -27266.1i q^{95} +(15956.4 - 445.224i) q^{96} -116154. i q^{97} +60179.1 q^{98} +(-40344.9 + 2253.21i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 200 q^{2} - 13 q^{3} + 800 q^{4} + 52 q^{6} + 38 q^{7} - 3200 q^{8} + 51 q^{9}+O(q^{10}) \) 50 * q - 200 * q^2 - 13 * q^3 + 800 * q^4 + 52 * q^6 + 38 * q^7 - 3200 * q^8 + 51 * q^9	\( 50 q - 200 q^{2} - 13 q^{3} + 800 q^{4} + 52 q^{6} + 38 q^{7} - 3200 q^{8} + 51 q^{9} - 652 q^{11} - 208 q^{12} - 152 q^{14} - 2107 q^{15} + 12800 q^{16} - 204 q^{18} - 894 q^{19} - 3801 q^{21} + 2608 q^{22} + 2456 q^{23} + 832 q^{24} - 23956 q^{25} + 9890 q^{27} + 608 q^{28} + 8428 q^{30} - 51200 q^{32} - 9744 q^{33} + 816 q^{36} + 3576 q^{38} + 1388 q^{39} + 15204 q^{42} - 10432 q^{44} + 33067 q^{45} - 9824 q^{46} - 27144 q^{47} - 3328 q^{48} + 85768 q^{49} + 95824 q^{50} + 3338 q^{51} - 39560 q^{54} - 2432 q^{56} - 63969 q^{57} - 23840 q^{59} - 33712 q^{60} + 94781 q^{63} + 204800 q^{64} - 9400 q^{65} + 38976 q^{66} - 115930 q^{69} - 3264 q^{72} + 24248 q^{75} - 14304 q^{76} - 150240 q^{77} - 5552 q^{78} - 68658 q^{79} + 47095 q^{81} - 175140 q^{83} - 60816 q^{84} - 138524 q^{85} + 138261 q^{87} + 41728 q^{88} + 104908 q^{89} - 132268 q^{90} + 39296 q^{92} - 91204 q^{93} + 108576 q^{94} + 13312 q^{96} - 343072 q^{98} - 111406 q^{99}+O(q^{100}) \) 50 * q - 200 * q^2 - 13 * q^3 + 800 * q^4 + 52 * q^6 + 38 * q^7 - 3200 * q^8 + 51 * q^9 - 652 * q^11 - 208 * q^12 - 152 * q^14 - 2107 * q^15 + 12800 * q^16 - 204 * q^18 - 894 * q^19 - 3801 * q^21 + 2608 * q^22 + 2456 * q^23 + 832 * q^24 - 23956 * q^25 + 9890 * q^27 + 608 * q^28 + 8428 * q^30 - 51200 * q^32 - 9744 * q^33 + 816 * q^36 + 3576 * q^38 + 1388 * q^39 + 15204 * q^42 - 10432 * q^44 + 33067 * q^45 - 9824 * q^46 - 27144 * q^47 - 3328 * q^48 + 85768 * q^49 + 95824 * q^50 + 3338 * q^51 - 39560 * q^54 - 2432 * q^56 - 63969 * q^57 - 23840 * q^59 - 33712 * q^60 + 94781 * q^63 + 204800 * q^64 - 9400 * q^65 + 38976 * q^66 - 115930 * q^69 - 3264 * q^72 + 24248 * q^75 - 14304 * q^76 - 150240 * q^77 - 5552 * q^78 - 68658 * q^79 + 47095 * q^81 - 175140 * q^83 - 60816 * q^84 - 138524 * q^85 + 138261 * q^87 + 41728 * q^88 + 104908 * q^89 - 132268 * q^90 + 39296 * q^92 - 91204 * q^93 + 108576 * q^94 + 13312 * q^96 - 343072 * q^98 - 111406 * q^99

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