LMFDB - Embedded newform 354.6.c.a.353.13

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			353.13
Character	$\chi$	$=$	354.353
Dual form			354.6.c.a.353.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +(-11.5231 - 10.4984i) q^{3} +16.0000 q^{4} -67.9871i q^{5} +(46.0925 + 41.9938i) q^{6} -61.6810 q^{7} -64.0000 q^{8} +(22.5654 + 241.950i) q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +(-11.5231 - 10.4984i) q^{3} +16.0000 q^{4} -67.9871i q^{5} +(46.0925 + 41.9938i) q^{6} -61.6810 q^{7} -64.0000 q^{8} +(22.5654 + 241.950i) q^{9} +271.948i q^{10} -640.601 q^{11} +(-184.370 - 167.975i) q^{12} -578.165i q^{13} +246.724 q^{14} +(-713.759 + 783.425i) q^{15} +256.000 q^{16} +1376.50i q^{17} +(-90.2615 - 967.800i) q^{18} +2526.34 q^{19} -1087.79i q^{20} +(710.759 + 647.555i) q^{21} +2562.40 q^{22} -625.726 q^{23} +(737.481 + 671.900i) q^{24} -1497.25 q^{25} +2312.66i q^{26} +(2280.07 - 3024.92i) q^{27} -986.896 q^{28} +5938.65i q^{29} +(2855.04 - 3133.70i) q^{30} -491.012i q^{31} -1024.00 q^{32} +(7381.73 + 6725.31i) q^{33} -5505.99i q^{34} +4193.51i q^{35} +(361.046 + 3871.20i) q^{36} +13518.0i q^{37} -10105.4 q^{38} +(-6069.83 + 6662.27i) q^{39} +4351.17i q^{40} +780.794i q^{41} +(-2843.04 - 2590.22i) q^{42} -4535.21i q^{43} -10249.6 q^{44} +(16449.5 - 1534.15i) q^{45} +2502.90 q^{46} -18392.4 q^{47} +(-2949.92 - 2687.60i) q^{48} -13002.5 q^{49} +5988.99 q^{50} +(14451.1 - 15861.6i) q^{51} -9250.64i q^{52} -17224.9i q^{53} +(-9120.30 + 12099.7i) q^{54} +43552.6i q^{55} +3947.58 q^{56} +(-29111.3 - 26522.6i) q^{57} -23754.6i q^{58} +(26733.8 + 479.840i) q^{59} +(-11420.1 + 12534.8i) q^{60} +854.058i q^{61} +1964.05i q^{62} +(-1391.85 - 14923.7i) q^{63} +4096.00 q^{64} -39307.8 q^{65} +(-29526.9 - 26901.3i) q^{66} -28501.6i q^{67} +22024.0i q^{68} +(7210.33 + 6569.15i) q^{69} -16774.1i q^{70} +52928.0i q^{71} +(-1444.18 - 15484.8i) q^{72} +50734.2i q^{73} -54071.9i q^{74} +(17253.0 + 15718.8i) q^{75} +40421.4 q^{76} +39512.9 q^{77} +(24279.3 - 26649.1i) q^{78} +99496.1 q^{79} -17404.7i q^{80} +(-58030.6 + 10919.4i) q^{81} -3123.18i q^{82} +64946.2 q^{83} +(11372.1 + 10360.9i) q^{84} +93584.1 q^{85} +18140.8i q^{86} +(62346.6 - 68431.8i) q^{87} +40998.5 q^{88} -122151. q^{89} +(-65797.9 + 6136.62i) q^{90} +35661.8i q^{91} -10011.6 q^{92} +(-5154.86 + 5658.00i) q^{93} +73569.5 q^{94} -171758. i q^{95} +(11799.7 + 10750.4i) q^{96} -828.060i q^{97} +52009.8 q^{98} +(-14455.4 - 154993. i) 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
$3$	−11.5231	−	10.4984i	−0.739210	−	0.673475i
$3$	−11.5231	−	10.4984i	−0.739210	−	0.673475i
$4$	16.0000			0.500000
$5$		−	67.9871i		−	1.21619i	−0.793864	−	0.608095i	$-0.791934\pi$
$5$		−	67.9871i		−	1.21619i	0.793864	−	0.608095i	$-0.208066\pi$
$6$	46.0925	+	41.9938i	0.522700	+	0.476219i
$7$	−61.6810			−0.475780			−0.237890	−	0.971292i	$-0.576456\pi$
$7$	−61.6810			−0.475780			−0.237890	+	0.971292i	$0.576456\pi$
$8$	−64.0000			−0.353553
$9$	22.5654	+	241.950i	0.0928616	+	0.995679i
$10$			271.948i			0.859976i
$11$	−640.601			−1.59627			−0.798134	−	0.602480i	$-0.794179\pi$
$11$	−640.601			−1.59627			−0.798134	+	0.602480i	$0.794179\pi$
$12$	−184.370	−	167.975i	−0.369605	−	0.336738i
$13$		−	578.165i		−	0.948841i	−0.880298	−	0.474420i	$-0.842658\pi$
$13$		−	578.165i		−	0.948841i	0.880298	−	0.474420i	$-0.157342\pi$
$14$	246.724			0.336427
$15$	−713.759	+	783.425i	−0.819074	+	0.899020i
$16$	256.000			0.250000
$17$			1376.50i			1.15519i	0.816324	+	0.577595i	$0.196009\pi$
$17$			1376.50i			1.15519i	−0.816324	+	0.577595i	$0.803991\pi$
$18$	−90.2615	−	967.800i	−0.0656631	−	0.704051i
$19$	2526.34			1.60549			0.802745	−	0.596322i	$-0.203372\pi$
$19$	2526.34			1.60549			0.802745	+	0.596322i	$0.203372\pi$
$20$		−	1087.79i		−	0.608095i
$21$	710.759	+	647.555i	0.351701	+	0.320426i
$22$	2562.40			1.12873
$23$	−625.726			−0.246641			−0.123320	−	0.992367i	$-0.539354\pi$
$23$	−625.726			−0.246641			−0.123320	+	0.992367i	$0.539354\pi$
$24$	737.481	+	671.900i	0.261350	+	0.238110i
$25$	−1497.25			−0.479119
$26$			2312.66i			0.670932i
$27$	2280.07	−	3024.92i	0.601921	−	0.798555i
$28$	−986.896			−0.237890
$29$			5938.65i			1.31127i	0.755077	+	0.655636i	$0.227599\pi$
$29$			5938.65i			1.31127i	−0.755077	+	0.655636i	$0.772401\pi$
$30$	2855.04	−	3133.70i	0.579173	−	0.635703i
$31$		−	491.012i		−	0.0917673i	−0.998947	−	0.0458837i	$-0.985390\pi$
$31$		−	491.012i		−	0.0917673i	0.998947	−	0.0458837i	$-0.0146104\pi$
$32$	−1024.00			−0.176777
$33$	7381.73	+	6725.31i	1.17998	+	1.07505i
$34$		−	5505.99i		−	0.816842i
$35$			4193.51i			0.578639i
$36$	361.046	+	3871.20i	0.0464308	+	0.497840i
$37$			13518.0i			1.62333i	0.584123	+	0.811665i	$0.301439\pi$
$37$			13518.0i			1.62333i	−0.584123	+	0.811665i	$0.698561\pi$
$38$	−10105.4			−1.13525
$39$	−6069.83	+	6662.27i	−0.639021	+	0.701392i
$40$			4351.17i			0.429988i
$41$			780.794i			0.0725399i	0.999342	+	0.0362699i	$0.0115476\pi$
$41$			780.794i			0.0725399i	−0.999342	+	0.0362699i	$0.988452\pi$
$42$	−2843.04	−	2590.22i	−0.248690	−	0.226576i
$43$		−	4535.21i		−	0.374047i	−0.982355	−	0.187023i	$-0.940116\pi$
$43$		−	4535.21i		−	0.374047i	0.982355	−	0.187023i	$-0.0598840\pi$
$44$	−10249.6			−0.798134
$45$	16449.5	−	1534.15i	1.21094	−	0.112937i
$46$	2502.90			0.174401
$47$	−18392.4			−1.21449			−0.607244	−	0.794516i	$-0.707725\pi$
$47$	−18392.4			−1.21449			−0.607244	+	0.794516i	$0.707725\pi$
$48$	−2949.92	−	2687.60i	−0.184802	−	0.168369i
$49$	−13002.5			−0.773633
$50$	5988.99			0.338788
$51$	14451.1	−	15861.6i	0.777992	−	0.853927i
$52$		−	9250.64i		−	0.474420i
$53$		−	17224.9i		−	0.842299i	−0.906991	−	0.421150i	$-0.861627\pi$
$53$		−	17224.9i		−	0.842299i	0.906991	−	0.421150i	$-0.138373\pi$
$54$	−9120.30	+	12099.7i	−0.425623	+	0.564664i
$55$			43552.6i			1.94137i
$56$	3947.58			0.168214
$57$	−29111.3	−	26522.6i	−1.18679	−	1.08126i
$58$		−	23754.6i		−	0.927209i
$59$	26733.8	+	479.840i	0.999839	+	0.0179459i
$59$	26733.8	+	479.840i	0.999839	+	0.0179459i
$60$	−11420.1	+	12534.8i	−0.409537	+	0.449510i
$61$			854.058i			0.0293875i	0.999892	+	0.0146937i	$0.00467733\pi$
$61$			854.058i			0.0293875i	−0.999892	+	0.0146937i	$0.995323\pi$
$62$			1964.05i			0.0648893i
$63$	−1391.85	−	14923.7i	−0.0441817	−	0.473724i
$64$	4096.00			0.125000
$65$	−39307.8			−1.15397
$66$	−29526.9	−	26901.3i	−0.834370	−	0.760173i
$67$		−	28501.6i		−	0.775679i	−0.921727	−	0.387840i	$-0.873221\pi$
$67$		−	28501.6i		−	0.775679i	0.921727	−	0.387840i	$-0.126779\pi$
$68$			22024.0i			0.577595i
$69$	7210.33	+	6569.15i	0.182319	+	0.166106i
$70$		−	16774.1i		−	0.409160i
$71$			52928.0i			1.24606i	0.782198	+	0.623030i	$0.214099\pi$
$71$			52928.0i			1.24606i	−0.782198	+	0.623030i	$0.785901\pi$
$72$	−1444.18	−	15484.8i	−0.0328315	−	0.352026i
$73$			50734.2i			1.11428i	0.830419	+	0.557139i	$0.188101\pi$
$73$			50734.2i			1.11428i	−0.830419	+	0.557139i	$0.811899\pi$
$74$		−	54071.9i		−	1.14787i
$75$	17253.0	+	15718.8i	0.354169	+	0.322675i
$76$	40421.4			0.802745
$77$	39512.9			0.759473
$78$	24279.3	−	26649.1i	0.451856	−	0.495959i
$79$	99496.1			1.79365			0.896826	−	0.442382i	$-0.145867\pi$
$79$	99496.1			1.79365			0.896826	+	0.442382i	$0.145867\pi$
$80$		−	17404.7i		−	0.304048i
$81$	−58030.6	+	10919.4i	−0.982753	+	0.184921i
$82$		−	3123.18i		−	0.0512934i
$83$	64946.2			1.03480			0.517402	−	0.855742i	$-0.326899\pi$
$83$	64946.2			1.03480			0.517402	+	0.855742i	$0.326899\pi$
$84$	11372.1	+	10360.9i	0.175851	+	0.160213i
$85$	93584.1			1.40493
$86$			18140.8i			0.264491i
$87$	62346.6	−	68431.8i	0.883109	−	0.969304i
$88$	40998.5			0.564366
$89$	−122151.			−1.63463			−0.817317	−	0.576189i	$-0.804539\pi$
$89$	−122151.			−1.63463			−0.817317	+	0.576189i	$0.804539\pi$
$90$	−65797.9	+	6136.62i	−0.856260	+	0.0798588i
$91$			35661.8i			0.451440i
$92$	−10011.6			−0.123320
$93$	−5154.86	+	5658.00i	−0.0618030	+	0.0678353i
$94$	73569.5			0.858772
$95$		−	171758.i		−	1.95258i
$96$	11799.7	+	10750.4i	0.130675	+	0.119055i
$97$		−	828.060i		−	0.00893578i	−0.999990	−	0.00446789i	$-0.998578\pi$
$97$		−	828.060i		−	0.00893578i	0.999990	−	0.00446789i	$-0.00142218\pi$
$98$	52009.8			0.547041
$99$	−14455.4	−	154993.i	−0.148232	−	1.58937i
$100$	−23955.9			−0.239559
$101$	−12623.5			−0.123134			−0.0615670	−	0.998103i	$-0.519610\pi$
$101$	−12623.5			−0.123134			−0.0615670	+	0.998103i	$0.519610\pi$
$102$	−57804.3	+	63446.3i	−0.550123	+	0.603817i
$103$			5852.85i			0.0543593i	0.999631	+	0.0271797i	$0.00865262\pi$
$103$			5852.85i			0.0543593i	−0.999631	+	0.0271797i	$0.991347\pi$
$104$			37002.6i			0.335466i
$105$	44025.4	−	48322.4i	0.389699	−	0.427736i
$106$			68899.5i			0.595595i
$107$		−	148676.i		−	1.25540i	−0.778456	−	0.627699i	$-0.783997\pi$
$107$		−	148676.i		−	1.25540i	0.778456	−	0.627699i	$-0.216003\pi$
$108$	36481.2	−	48398.8i	0.300961	−	0.399278i
$109$		−	136292.i		−	1.09876i	−0.835573	−	0.549380i	$-0.814864\pi$
$109$		−	136292.i		−	1.09876i	0.835573	−	0.549380i	$-0.185136\pi$
$110$		−	174210.i		−	1.37275i
$111$	141918.	−	155769.i	1.09327	−	1.19998i
$112$	−15790.3			−0.118945
$113$	−109993.			−0.810345			−0.405173	−	0.914240i	$-0.632789\pi$
$113$	−109993.			−0.810345			−0.405173	+	0.914240i	$0.632789\pi$
$114$	116445.	+	106091.i	0.839190	+	0.764565i
$115$			42541.3i			0.299962i
$116$			95018.4i			0.655636i
$117$	139887.	−	13046.5i	0.944741	−	0.0881109i
$118$	−106935.	−	1919.36i	−0.706993	−	0.0126897i
$119$		−	84903.8i		−	0.549616i
$120$	45680.6	−	50139.2i	0.289587	−	0.317851i
$121$	249319.			1.54807
$122$		−	3416.23i		−	0.0207801i
$123$	8197.12	−	8997.19i	0.0488538	−	0.0536222i
$124$		−	7856.19i		−	0.0458837i
$125$		−	110666.i		−	0.633491i
$126$	5567.42	+	59694.9i	0.0312412	+	0.334974i
$127$	253692.			1.39572			0.697858	−	0.716236i	$-0.254137\pi$
$127$	253692.			1.39572			0.697858	+	0.716236i	$0.254137\pi$
$128$	−16384.0			−0.0883883
$129$	−47612.6	+	52259.8i	−0.251911	+	0.276499i
$130$	157231.			0.815981
$131$	63098.3			0.321247			0.160624	−	0.987016i	$-0.448649\pi$
$131$	63098.3			0.321247			0.160624	+	0.987016i	$0.448649\pi$
$132$	118108.	+	107605.i	0.589988	+	0.537524i
$133$	−155827.			−0.763860
$134$			114006.i			0.548488i
$135$	−205656.	−	155016.i	−0.971195	−	0.732051i
$136$		−	88095.8i		−	0.408421i
$137$		−	103746.i		−	0.472250i	−0.971723	−	0.236125i	$-0.924123\pi$
$137$		−	103746.i		−	0.472250i	0.971723	−	0.236125i	$-0.0758774\pi$
$138$	−28841.3	−	26276.6i	−0.128919	−	0.117455i
$139$	−26564.6			−0.116618			−0.0583091	−	0.998299i	$-0.518571\pi$
$139$	−26564.6			−0.116618			−0.0583091	+	0.998299i	$0.518571\pi$
$140$			67096.2i			0.289320i
$141$	211938.	+	193091.i	0.897761	+	0.817927i
$142$		−	211712.i		−	0.881098i
$143$			370373.i			1.51460i
$144$	5776.73	+	61939.2i	0.0232154	+	0.248920i
$145$	403751.			1.59476
$146$		−	202937.i		−	0.787914i
$147$	149829.	+	136506.i	0.571877	+	0.521023i
$148$			216287.i			0.811665i
$149$	70555.1			0.260353			0.130177	−	0.991491i	$-0.458446\pi$
$149$	70555.1			0.260353			0.130177	+	0.991491i	$0.458446\pi$
$150$	−69011.9	−	62875.0i	−0.250435	−	0.228166i
$151$		−	250380.i		−	0.893630i	−0.894626	−	0.446815i	$-0.852558\pi$
$151$		−	250380.i		−	0.893630i	0.894626	−	0.446815i	$-0.147442\pi$
$152$	−161686.			−0.567626
$153$	−333044.	+	31061.2i	−1.15020	+	0.107273i
$154$	−158052.			−0.537029
$155$	−33382.5			−0.111607
$156$	−97117.3	+	106596.i	−0.319511	+	0.350696i
$157$		−	227010.i		−	0.735013i	−0.930021	−	0.367507i	$-0.880212\pi$
$157$		−	227010.i		−	0.735013i	0.930021	−	0.367507i	$-0.119788\pi$
$158$	−397984.			−1.26830
$159$	−180834.	+	198485.i	−0.567268	+	0.622636i
$160$			69618.8i			0.214994i
$161$	38595.4			0.117347
$162$	232122.	−	43677.5i	0.694912	−	0.130759i
$163$	−116534.			−0.343544			−0.171772	−	0.985137i	$-0.554949\pi$
$163$	−116534.			−0.343544			−0.171772	+	0.985137i	$0.554949\pi$
$164$			12492.7i			0.0362699i
$165$	457235.	−	501863.i	1.30746	−	1.43508i
$166$	−259785.			−0.731717
$167$		−	540832.i		−	1.50062i	−0.661085	−	0.750311i	$-0.729904\pi$
$167$		−	540832.i		−	1.50062i	0.661085	−	0.750311i	$-0.270096\pi$
$168$	−45488.6	−	41443.5i	−0.124345	−	0.113288i
$169$	37018.3			0.0997010
$170$	−374336.			−0.993435
$171$	57007.8	+	611248.i	0.149088	+	1.59855i
$172$		−	72563.3i		−	0.187023i
$173$	−398977.			−1.01352			−0.506760	−	0.862087i	$-0.669157\pi$
$173$	−398977.			−1.01352			−0.506760	+	0.862087i	$0.669157\pi$
$174$	−249386.	+	273727.i	−0.624452	+	0.685402i
$175$	92351.7			0.227955
$176$	−163994.			−0.399067
$177$	−303019.	−	286192.i	−0.727004	−	0.686633i
$178$	488602.			1.15586
$179$	734947.			1.71445			0.857223	−	0.514946i	$-0.172188\pi$
$179$	734947.			1.71445			0.857223	+	0.514946i	$0.172188\pi$
$180$	263192.	−	24546.5i	0.605468	−	0.0564687i
$181$	−238526.			−0.541176			−0.270588	−	0.962695i	$-0.587218\pi$
$181$	−238526.			−0.541176			−0.270588	+	0.962695i	$0.587218\pi$
$182$		−	142647.i		−	0.319216i
$183$	8966.27	−	9841.42i	0.0197918	−	0.0217235i
$184$	40046.5			0.0872006
$185$	919047.			1.97428
$186$	20619.5	−	22632.0i	0.0437013	−	0.0479668i
$187$		−	881786.i		−	1.84399i
$188$	−294278.			−0.607244
$189$	−140637.	+	186580.i	−0.286382	+	0.379937i
$190$			687034.i			1.38068i
$191$	596396.			1.18291			0.591454	−	0.806339i	$-0.298554\pi$
$191$	596396.			1.18291			0.591454	+	0.806339i	$0.298554\pi$
$192$	−47198.8	−	43001.6i	−0.0924012	−	0.0841844i
$193$	779874.			1.50706			0.753531	−	0.657413i	$-0.228349\pi$
$193$	779874.			1.50706			0.753531	+	0.657413i	$0.228349\pi$
$194$			3312.24i			0.00631855i
$195$	452949.	+	412670.i	0.853026	+	0.777171i
$196$	−208039.			−0.386817
$197$			790437.i			1.45111i	0.688162	+	0.725557i	$0.258418\pi$
$197$			790437.i			1.45111i	−0.688162	+	0.725557i	$0.741582\pi$
$198$	57821.6	+	619974.i	0.104816	+	1.12386i
$199$	−1.06710e6			−1.91017			−0.955086	−	0.296327i	$-0.904238\pi$
$199$	−1.06710e6			−1.91017			−0.955086	+	0.296327i	$0.904238\pi$
$200$	95823.8			0.169394
$201$	−299222.	+	328428.i	−0.522401	+	0.573390i
$202$	50494.2			0.0870689
$203$		−	366302.i		−	0.623877i
$204$	231217.	−	253785.i	0.388996	−	0.426963i
$205$	53083.9			0.0882223
$206$		−	23411.4i		−	0.0384379i
$207$	−14119.7	−	151394.i	−0.0229034	−	0.245575i
$208$		−	148010.i		−	0.237210i
$209$	−1.61838e6			−2.56279
$210$	−176101.	+	193290.i	−0.275559	+	0.302455i
$211$			1.11368e6i			1.72208i	0.508535	+	0.861041i	$0.330187\pi$
$211$			1.11368e6i			1.72208i	−0.508535	+	0.861041i	$0.669813\pi$
$212$		−	275598.i		−	0.421150i
$213$	555661.	−	609896.i	0.839192	−	0.921100i
$214$			594704.i			0.887700i
$215$	−308335.			−0.454912
$216$	−145925.	+	193595.i	−0.212811	+	0.282332i
$217$			30286.1i			0.0436611i
$218$			545166.i			0.776940i
$219$	532630.	−	584617.i	0.750439	−	0.823685i
$220$			696842.i			0.970683i
$221$	795843.			1.09609
$222$	−567670.	+	623077.i	−0.773061	+	0.848515i
$223$	−225046.			−0.303046			−0.151523	−	0.988454i	$-0.548418\pi$
$223$	−225046.			−0.303046			−0.151523	+	0.988454i	$0.548418\pi$
$224$	63161.4			0.0841069
$225$	−33785.9	−	362259.i	−0.0444917	−	0.477049i
$226$	439973.			0.573001
$227$	−301122.			−0.387862			−0.193931	−	0.981015i	$-0.562124\pi$
$227$	−301122.			−0.387862			−0.193931	+	0.981015i	$0.562124\pi$
$228$	−465782.	−	424362.i	−0.593397	−	0.540629i
$229$			191794.i			0.241683i	0.992672	+	0.120842i	$0.0385594\pi$
$229$			191794.i			0.241683i	−0.992672	+	0.120842i	$0.961441\pi$
$230$		−	170165.i		−	0.212105i
$231$	−455313.	−	414824.i	−0.561410	−	0.511486i
$232$		−	380073.i		−	0.463604i
$233$	−1.02823e6			−1.24080			−0.620399	−	0.784286i	$-0.713029\pi$
$233$	−1.02823e6			−1.24080			−0.620399	+	0.784286i	$0.713029\pi$
$234$	−559548.	+	52186.0i	−0.668033	+	0.0623038i
$235$			1.25044e6i			1.47705i
$236$	427740.	+	7677.44i	0.499919	+	0.00897297i
$237$	−1.14651e6	−	1.04455e6i	−1.32589	−	1.20798i
$238$			339615.i			0.388637i
$239$			1.65190e6i			1.87063i	0.353815	+	0.935316i	$0.384884\pi$
$239$			1.65190e6i			1.87063i	−0.353815	+	0.935316i	$0.615116\pi$
$240$	−182722.	+	200557.i	−0.204769	+	0.224755i
$241$	537218.			0.595811			0.297905	−	0.954595i	$-0.403712\pi$
$241$	537218.			0.595811			0.297905	+	0.954595i	$0.403712\pi$
$242$	−997275.			−1.09465
$243$	783331.	+	483406.i	0.851000	+	0.525165i
$244$			13664.9i			0.0146937i
$245$			883999.i			0.940885i
$246$	−32788.5	+	35988.8i	−0.0345449	+	0.0379166i
$247$		−	1.46064e6i		−	1.52335i
$248$			31424.8i			0.0324446i
$249$	−748384.	−	681834.i	−0.764937	−	0.696915i
$250$			442665.i			0.447946i
$251$		−	188021.i		−	0.188374i	−0.995555	−	0.0941871i	$-0.969975\pi$
$251$		−	188021.i		−	0.188374i	0.995555	−	0.0941871i	$-0.0300252\pi$
$252$	−22269.7	−	238780.i	−0.0220909	−	0.236862i
$253$	400841.			0.393705
$254$	−1.01477e6			−0.986920
$255$	−1.07838e6	−	982487.i	−1.03854	−	0.946186i
$256$	65536.0			0.0625000
$257$		−	594235.i		−	0.561210i	−0.959823	−	0.280605i	$-0.909465\pi$
$257$		−	594235.i		−	0.561210i	0.959823	−	0.280605i	$-0.0905351\pi$
$258$	190450.	−	209039.i	0.178128	−	0.195514i
$259$		−	833802.i		−	0.772349i
$260$	−628924.			−0.576986
$261$	−1.43686e6	+	134008.i	−1.30561	+	0.121767i
$262$	−252393.			−0.227156
$263$		−	1.03027e6i		−	0.918465i	−0.888316	−	0.459233i	$-0.848124\pi$
$263$		−	1.03027e6i		−	0.918465i	0.888316	−	0.459233i	$-0.151876\pi$
$264$	−472431.	−	430420.i	−0.417185	−	0.380087i
$265$	−1.17107e6			−1.02440
$266$	623309.			0.540131
$267$	1.40756e6	+	1.28239e6i	1.20834	+	1.10089i
$268$		−	456026.i		−	0.387840i
$269$	1.66809e6			1.40552			0.702762	−	0.711425i	$-0.251950\pi$
$269$	1.66809e6			1.40552			0.702762	+	0.711425i	$0.251950\pi$
$270$	822623.	+	620063.i	0.686739	+	0.517638i
$271$	175207.			0.144920			0.0724599	−	0.997371i	$-0.476915\pi$
$271$	175207.			0.144920			0.0724599	+	0.997371i	$0.476915\pi$
$272$			352383.i			0.288797i
$273$	374393.	−	410936.i	0.304034	−	0.333709i
$274$			414986.i			0.333931i
$275$	959138.			0.764802
$276$	115365.	+	105106.i	0.0911595	+	0.0830532i
$277$	868840.			0.680363			0.340181	−	0.940360i	$-0.389512\pi$
$277$	868840.			0.680363			0.340181	+	0.940360i	$0.389512\pi$
$278$	106258.			0.0824615
$279$	118800.	−	11079.9i	0.0913708	−	0.00852166i
$280$		−	268385.i		−	0.204580i
$281$		−	1.00132e6i		−	0.756497i	−0.925704	−	0.378249i	$-0.876526\pi$
$281$		−	1.00132e6i		−	0.756497i	0.925704	−	0.378249i	$-0.123474\pi$
$282$	−847751.	−	772365.i	−0.634813	−	0.578362i
$283$		−	972862.i		−	0.722080i	−0.932550	−	0.361040i	$-0.882422\pi$
$283$		−	972862.i		−	0.722080i	0.932550	−	0.361040i	$-0.117578\pi$
$284$			846847.i			0.623030i
$285$	−1.80320e6	+	1.97920e6i	−1.31502	+	1.44337i
$286$		−	1.48149e6i		−	1.07099i
$287$		−	48160.2i		−	0.0345130i
$288$	−23106.9	−	247757.i	−0.0164158	−	0.176013i
$289$	−474888.			−0.334462
$290$	−1.61501e6			−1.12766
$291$	−8693.34	+	9541.84i	−0.00601803	+	0.00660541i
$292$			811747.i			0.557139i
$293$			968990.i			0.659402i	0.944085	+	0.329701i	$0.106948\pi$
$293$			968990.i			0.659402i	−0.944085	+	0.329701i	$0.893052\pi$
$294$	−599316.	−	546022.i	−0.404378	−	0.368419i
$295$	32622.9	−	1.81755e6i	0.0218257	−	1.21599i
$296$		−	865150.i		−	0.573934i
$297$	−1.46062e6	+	1.93777e6i	−0.960828	+	1.27471i
$298$	−282221.			−0.184098
$299$			361773.i			0.234023i
$300$	276048.	+	251500.i	0.177085	+	0.161337i
$301$			279736.i			0.177964i
$302$			1.00152e6i			0.631892i
$303$	145463.	+	132528.i	0.0910218	+	0.0829277i
$304$	646743.			0.401372
$305$	58064.9			0.0357408
$306$	1.33217e6	−	124245.i	0.813312	−	0.0758532i
$307$	−30538.1			−0.0184925			−0.00924626	−	0.999957i	$-0.502943\pi$
$307$	−30538.1			−0.0184925			−0.00924626	+	0.999957i	$0.502943\pi$
$308$	632207.			0.379737
$309$	61445.8	−	67443.2i	0.0366097	−	0.0401830i
$310$	133530.			0.0789177
$311$			1.90264e6i			1.11546i	0.830021	+	0.557732i	$0.188328\pi$
$311$			1.90264e6i			1.11546i	−0.830021	+	0.557732i	$0.811672\pi$
$312$	388469.	−	426386.i	0.225928	−	0.247980i
$313$			3.28821e6i			1.89713i	0.316576	+	0.948567i	$0.397467\pi$
$313$			3.28821e6i			1.89713i	−0.316576	+	0.948567i	$0.602533\pi$
$314$			908039.i			0.519733i
$315$	−1.01462e6	+	94628.2i	−0.576139	+	0.0537334i
$316$	1.59194e6			0.896826
$317$			1.06305e6i			0.594165i	0.954852	+	0.297082i	$0.0960136\pi$
$317$			1.06305e6i			0.594165i	−0.954852	+	0.297082i	$0.903986\pi$
$318$	723337.	−	793938.i	0.401119	−	0.440270i
$319$		−	3.80430e6i		−	2.09314i
$320$		−	278475.i		−	0.152024i
$321$	−1.56087e6	+	1.71321e6i	−0.845480	+	0.928002i
$322$	−154382.			−0.0829767
$323$			3.47750e6i			1.85464i
$324$	−928490.	+	174710.i	−0.491377	+	0.0924603i
$325$			865655.i			0.454608i
$326$	466134.			0.242922
$327$	−1.43085e6	+	1.57051e6i	−0.739988	+	0.812213i
$328$		−	49970.8i		−	0.0256467i
$329$	1.13446e6			0.577829
$330$	−1.82894e6	+	2.00745e6i	−0.924516	+	1.01475i
$331$	−928130.			−0.465627			−0.232814	−	0.972521i	$-0.574793\pi$
$331$	−928130.			−0.465627			−0.232814	+	0.972521i	$0.574793\pi$
$332$	1.03914e6			0.517402
$333$	−3.27067e6	+	305038.i	−1.61632	+	0.150745i
$334$			2.16333e6i			1.06110i
$335$	−1.93774e6			−0.943374
$336$	181954.	+	165774.i	0.0879253	+	0.0801066i
$337$		−	780581.i		−	0.374406i	−0.982321	−	0.187203i	$-0.940058\pi$
$337$		−	780581.i		−	0.374406i	0.982321	−	0.187203i	$-0.0599423\pi$
$338$	−148073.			−0.0704992
$339$	1.26747e6	+	1.15476e6i	0.599015	+	0.545748i
$340$	1.49735e6			0.702465
$341$			314543.i			0.146485i
$342$	−228031.	−	2.44499e6i	−0.105421	−	1.13035i
$343$	1.83868e6			0.843860
$344$			290253.i			0.132245i
$345$	446617.	−	490209.i	0.202017	−	0.221735i
$346$	1.59591e6			0.716667
$347$	4.03174e6			1.79750			0.898751	−	0.438460i	$-0.144476\pi$
$347$	4.03174e6			1.79750			0.898751	+	0.438460i	$0.144476\pi$
$348$	997545.	−	1.09491e6i	0.441555	−	0.484652i
$349$			434684.i			0.191034i	0.995428	+	0.0955170i	$0.0304504\pi$
$349$			434684.i			0.191034i	−0.995428	+	0.0955170i	$0.969550\pi$
$350$	−369407.			−0.161189
$351$	−1.74891e6	−	1.31826e6i	−0.757702	−	0.571127i
$352$	655975.			0.282183
$353$	1.05919e6			0.452415			0.226208	−	0.974079i	$-0.427367\pi$
$353$	1.05919e6			0.452415			0.226208	+	0.974079i	$0.427367\pi$
$354$	1.21208e6	+	1.14477e6i	0.514070	+	0.485523i
$355$	3.59842e6			1.51545
$356$	−1.95441e6			−0.817317
$357$	−891357.	+	978358.i	−0.370153	+	0.406282i
$358$	−2.93979e6			−1.21230
$359$			1.83912e6i			0.753136i	0.926389	+	0.376568i	$0.122896\pi$
$359$			1.83912e6i			0.753136i	−0.926389	+	0.376568i	$0.877104\pi$
$360$	−1.05277e6	+	98185.8i	−0.428130	+	0.0399294i
$361$	3.90629e6			1.57760
$362$	954102.			0.382669
$363$	−2.87293e6	−	2.61746e6i	−1.14435	−	1.04259i
$364$			570589.i			0.225720i
$365$	3.44927e6			1.35517
$366$	−35865.1	+	39365.7i	−0.0139949	+	0.0153608i
$367$		−	732025.i		−	0.283701i	−0.989888	−	0.141850i	$-0.954695\pi$
$367$		−	732025.i		−	0.283701i	0.989888	−	0.141850i	$-0.0453052\pi$
$368$	−160186.			−0.0616601
$369$	−188913.	+	17618.9i	−0.0722264	+	0.00673617i
$370$	−3.67619e6			−1.39603
$371$			1.06245e6i			0.400749i
$372$	−82477.8	+	90528.0i	−0.0309015	+	0.0339176i
$373$	232610.			0.0865677			0.0432839	−	0.999063i	$-0.486218\pi$
$373$	232610.			0.0865677			0.0432839	+	0.999063i	$0.486218\pi$
$374$			3.52714e6i			1.30390i
$375$	−1.16182e6	+	1.27522e6i	−0.426640	+	0.468282i
$376$	1.17711e6			0.429386
$377$	3.43352e6			1.24419
$378$	562549.	−	746322.i	0.202503	−	0.268656i
$379$	4.39352e6			1.57114			0.785569	−	0.618774i	$-0.212370\pi$
$379$	4.39352e6			1.57114			0.785569	+	0.618774i	$0.212370\pi$
$380$		−	2.74814e6i		−	0.976291i
$381$	−2.92333e6	−	2.66337e6i	−1.03173	−	0.939981i
$382$	−2.38558e6			−0.836442
$383$		−	3.62193e6i		−	1.26166i	−0.775920	−	0.630832i	$-0.782714\pi$
$383$		−	3.62193e6i		−	1.26166i	0.775920	−	0.630832i	$-0.217286\pi$
$384$	188795.	+	172006.i	0.0653375	+	0.0595274i
$385$		−	2.68637e6i		−	0.923664i
$386$	−3.11949e6			−1.06565
$387$	1.09729e6	−	102339.i	0.372430	−	0.0347346i
$388$		−	13249.0i		−	0.00446789i
$389$			294561.i			0.0986964i	0.998782	+	0.0493482i	$0.0157144\pi$
$389$			294561.i			0.0986964i	−0.998782	+	0.0493482i	$0.984286\pi$
$390$	−1.81179e6	−	1.65068e6i	−0.603181	−	0.549543i
$391$		−	861310.i		−	0.284917i
$392$	832157.			0.273521
$393$	−727090.	−	662434.i	−0.237469	−	0.216352i
$394$		−	3.16175e6i		−	1.02609i
$395$		−	6.76445e6i		−	2.18142i
$396$	−231286.	−	2.47989e6i	−0.0741160	−	0.794686i
$397$			3.03361e6i			0.966013i	0.875617	+	0.483006i	$0.160455\pi$
$397$			3.03361e6i			0.966013i	−0.875617	+	0.483006i	$0.839545\pi$
$398$	4.26840e6			1.35070
$399$	1.79562e6	+	1.63594e6i	0.564653	+	0.514441i
$400$	−383295.			−0.119780
$401$	3.46092e6			1.07481			0.537403	−	0.843326i	$-0.319405\pi$
$401$	3.46092e6			1.07481			0.537403	+	0.843326i	$0.319405\pi$
$402$	1.19689e6	−	1.31371e6i	0.369393	−	0.405448i
$403$	−283886.			−0.0870726
$404$	−201977.			−0.0615670
$405$	742377.	+	3.94533e6i	0.224899	+	1.19522i
$406$			1.46521e6i			0.441148i
$407$		−	8.65962e6i		−	2.59127i
$408$	−924869.	+	1.01514e6i	−0.275062	+	0.301909i
$409$			3.99942e6i			1.18220i	0.806600	+	0.591098i	$0.201305\pi$
$409$			3.99942e6i			1.18220i	−0.806600	+	0.591098i	$0.798695\pi$
$410$	−212336.			−0.0623826
$411$	−1.08918e6	+	1.19548e6i	−0.318049	+	0.349091i
$412$			93645.6i			0.0271797i
$413$	−1.64897e6	−	29597.0i	−0.475704	−	0.00853833i
$414$	56478.9	+	605578.i	0.0161952	+	0.173648i
$415$		−	4.41550e6i		−	1.25852i
$416$			592041.i			0.167733i
$417$	306108.	+	278887.i	0.0862053	+	0.0785395i
$418$	6.47350e6			1.81217
$419$	−6.69823e6			−1.86391			−0.931954	−	0.362575i	$-0.881898\pi$
$419$	−6.69823e6			−1.86391			−0.931954	+	0.362575i	$0.881898\pi$
$420$	704406.	−	773159.i	0.194850	−	0.213868i
$421$			1.61879e6i			0.445129i	0.974918	+	0.222564i	$0.0714428\pi$
$421$			1.61879e6i			0.445129i	−0.974918	+	0.222564i	$0.928557\pi$
$422$		−	4.45472e6i		−	1.21770i
$423$	−415030.	−	4.45003e6i	−0.112779	−	1.20924i
$424$			1.10239e6i			0.297798i
$425$		−	2.06096e6i		−	0.553473i
$426$	−2.22264e6	+	2.43958e6i	−0.593398	+	0.651316i
$427$		−	52679.1i		−	0.0139820i
$428$		−	2.37882e6i		−	0.627699i
$429$	3.88834e6	−	4.26786e6i	1.02005	−	1.11961i
$430$	1.23334e6			0.321671
$431$	457254.			0.118567			0.0592836	−	0.998241i	$-0.481118\pi$
$431$	457254.			0.118567			0.0592836	+	0.998241i	$0.481118\pi$
$432$	583699.	−	774381.i	0.150480	−	0.199639i
$433$	4.65440e6			1.19301			0.596505	−	0.802609i	$-0.296556\pi$
$433$	4.65440e6			1.19301			0.596505	+	0.802609i	$0.296556\pi$
$434$		−	121145.i		−	0.0308730i
$435$	−4.65248e6	−	4.23876e6i	−1.17886	−	1.07403i
$436$		−	2.18066e6i		−	0.549380i
$437$	−1.58080e6			−0.395979
$438$	−2.13052e6	+	2.33847e6i	−0.530641	+	0.582434i
$439$	530913.			0.131481			0.0657404	−	0.997837i	$-0.479059\pi$
$439$	530913.			0.131481			0.0657404	+	0.997837i	$0.479059\pi$
$440$		−	2.78737e6i		−	0.686377i
$441$	−293405.	−	3.14594e6i	−0.0718408	−	0.770290i
$442$	−3.18337e6			−0.775053
$443$	−1.49378e6			−0.361641			−0.180820	−	0.983516i	$-0.557875\pi$
$443$	−1.49378e6			−0.361641			−0.180820	+	0.983516i	$0.557875\pi$
$444$	2.27068e6	−	2.49231e6i	0.546637	−	0.599991i
$445$			8.30466e6i			1.98803i
$446$	900184.			0.214286
$447$	−813016.	−	740719.i	−0.192456	−	0.175342i
$448$	−252645.			−0.0594725
$449$		−	5.02089e6i		−	1.17534i	−0.809100	−	0.587671i	$-0.800045\pi$
$449$		−	5.02089e6i		−	1.17534i	0.809100	−	0.587671i	$-0.199955\pi$
$450$	135144.	+	1.44904e6i	0.0314604	+	0.337324i
$451$		−	500177.i		−	0.115793i
$452$	−1.75989e6			−0.405173
$453$	−2.62860e6	+	2.88517e6i	−0.601838	+	0.660580i
$454$	1.20449e6			0.274260
$455$	2.42454e6			0.549037
$456$	1.86313e6	+	1.69745e6i	0.419595	+	0.382282i
$457$			5.76591e6i			1.29145i	0.763571	+	0.645724i	$0.223445\pi$
$457$			5.76591e6i			1.29145i	−0.763571	+	0.645724i	$0.776555\pi$
$458$		−	767177.i		−	0.170896i
$459$	4.16380e6	+	3.13852e6i	0.922483	+	0.695333i
$460$			680661.i			0.149981i
$461$		−	4.59818e6i		−	1.00771i	−0.863790	−	0.503853i	$-0.831915\pi$
$461$		−	4.59818e6i		−	1.00771i	0.863790	−	0.503853i	$-0.168085\pi$
$462$	1.82125e6	+	1.65930e6i	0.396977	+	0.361676i
$463$		−	8.56666e6i		−	1.85720i	−0.371080	−	0.928601i	$-0.621012\pi$
$463$		−	8.56666e6i		−	1.85720i	0.371080	−	0.928601i	$-0.378988\pi$
$464$			1.52029e6i			0.327818i
$465$	384671.	+	350464.i	0.0825006	+	0.0751642i
$466$	4.11293e6			0.877377
$467$	−4.79502e6			−1.01742			−0.508708	−	0.860939i	$-0.669877\pi$
$467$	−4.79502e6			−1.01742			−0.508708	+	0.860939i	$0.669877\pi$
$468$	2.23819e6	−	208744.i	0.472370	−	0.0440554i
$469$			1.75801e6i			0.369053i
$470$		−	5.00178e6i		−	1.04443i
$471$	−2.38325e6	+	2.61586e6i	−0.495013	+	0.543329i
$472$	−1.71096e6	−	30709.8i	−0.353496	−	0.00634485i
$473$			2.90526e6i			0.597079i
$474$	4.58603e6	+	4.17822e6i	0.937543	+	0.854172i
$475$	−3.78255e6			−0.769220
$476$		−	1.35846e6i		−	0.274808i
$477$	4.16756e6	−	388685.i	0.838659	−	0.0782172i
$478$		−	6.60759e6i		−	1.32274i
$479$		−	1.94773e6i		−	0.387874i	−0.981014	−	0.193937i	$-0.937874\pi$
$479$		−	1.94773e6i		−	0.387874i	0.981014	−	0.193937i	$-0.0621258\pi$
$480$	730889.	−	802227.i	0.144793	−	0.158926i
$481$	7.81561e6			1.54028
$482$	−2.14887e6			−0.421302
$483$	−444740.	−	405192.i	−0.0867438	−	0.0790301i
$484$	3.98910e6			0.774036
$485$	−56297.4			−0.0108676
$486$	−3.13332e6	−	1.93362e6i	−0.601748	−	0.371348i
$487$	1.89207e6			0.361506			0.180753	−	0.983529i	$-0.442147\pi$
$487$	1.89207e6			0.361506			0.180753	+	0.983529i	$0.442147\pi$
$488$		−	54659.7i		−	0.0103900i
$489$	1.34283e6	+	1.22342e6i	0.253951	+	0.231368i
$490$		−	3.53600e6i		−	0.665306i
$491$			9.66735e6i			1.80969i	0.425743	+	0.904844i	$0.360013\pi$
$491$			9.66735e6i			1.80969i	−0.425743	+	0.904844i	$0.639987\pi$
$492$	131154.	−	143955.i	0.0244269	−	0.0268111i
$493$	−8.17453e6			−1.51477
$494$			5.84256e6i			1.07717i
$495$	−1.05376e7	+	982780.i	−1.93298	+	0.180278i
$496$		−	125699.i		−	0.0229418i
$497$		−	3.26465e6i		−	0.592851i
$498$	2.99353e6	+	2.72733e6i	0.540892	+	0.492794i
$499$	4.01375e6			0.721605			0.360802	−	0.932642i	$-0.382503\pi$
$499$	4.01375e6			0.721605			0.360802	+	0.932642i	$0.382503\pi$
$500$		−	1.77066e6i		−	0.316745i
$501$	−5.67789e6	+	6.23208e6i	−1.01063	+	1.10927i
$502$			752083.i			0.133201i
$503$	7.59071e6			1.33771			0.668856	−	0.743392i	$-0.266784\pi$
$503$	7.59071e6			1.33771			0.668856	+	0.743392i	$0.266784\pi$
$504$	89078.7	+	955118.i	0.0156206	+	0.167487i
$505$			858238.i			0.149754i
$506$	−1.60336e6			−0.278391
$507$	−426567.	−	388634.i	−0.0736999	−	0.0671462i
$508$	4.05907e6			0.697858
$509$	−7.49704e6			−1.28261			−0.641306	−	0.767285i	$-0.721607\pi$
$509$	−7.49704e6			−1.28261			−0.641306	+	0.767285i	$0.721607\pi$
$510$	4.31353e6	+	3.92995e6i	0.734357	+	0.669054i
$511$		−	3.12934e6i		−	0.530152i
$512$	−262144.			−0.0441942
$513$	5.76024e6	−	7.64198e6i	0.966379	−	1.28207i
$514$			2.37694e6i			0.396835i
$515$	397918.			0.0661113
$516$	−761802.	+	836157.i	−0.125956	+	0.138249i
$517$	1.17822e7			1.93865
$518$			3.33521e6i			0.546133i
$519$	4.59747e6	+	4.18864e6i	0.749204	+	0.682581i
$520$	2.51570e6			0.407990
$521$			4.75897e6i			0.768101i	0.923312	+	0.384051i	$0.125471\pi$
$521$			4.75897e6i			0.768101i	−0.923312	+	0.384051i	$0.874529\pi$
$522$	5.74742e6	−	536031.i	0.923202	−	0.0861021i
$523$	2.65362e6			0.424214			0.212107	−	0.977246i	$-0.431968\pi$
$523$	2.65362e6			0.424214			0.212107	+	0.977246i	$0.431968\pi$
$524$	1.00957e6			0.160624
$525$	−1.06418e6	−	969549.i	−0.168507	−	0.153522i
$526$			4.12109e6i			0.649453i
$527$	675877.			0.106009
$528$	1.88972e6	+	1.72168e6i	0.294994	+	0.268762i
$529$	−6.04481e6			−0.939168
$530$	4.68428e6			0.724357
$531$	487160.	+	6.47906e6i	0.0749782	+	0.997185i
$532$	−2.49323e6			−0.381930
$533$	451428.			0.0688288
$534$	−5.63023e6	−	5.12956e6i	−0.854423	−	0.778444i
$535$	−1.01081e7			−1.52680
$536$			1.82410e6i			0.274244i
$537$	−8.46890e6	−	7.71580e6i	−1.26733	−	1.15464i
$538$	−6.67236e6			−0.993856
$539$	8.32938e6			1.23493
$540$	−3.29049e6	−	2.48025e6i	−0.485598	−	0.366025i
$541$			422963.i			0.0621312i	0.999517	+	0.0310656i	$0.00989008\pi$
$541$			422963.i			0.0621312i	−0.999517	+	0.0310656i	$0.990110\pi$
$542$	−700827.			−0.102474
$543$	2.74856e6	+	2.50415e6i	0.400043	+	0.364469i
$544$		−	1.40953e6i		−	0.204211i
$545$	−9.26607e6			−1.33630
$546$	−1.49757e6	+	1.64374e6i	−0.214984	+	0.235968i
$547$	4.63365e6			0.662148			0.331074	−	0.943605i	$-0.392589\pi$
$547$	4.63365e6			0.662148			0.331074	+	0.943605i	$0.392589\pi$
$548$		−	1.65994e6i		−	0.236125i
$549$	−206639.	+	19272.1i	−0.0292605	+	0.00272897i
$550$	−3.83655e6			−0.540797
$551$			1.50030e7i			2.10523i
$552$	−461461.	−	420425.i	−0.0644595	−	0.0587275i
$553$	−6.13702e6			−0.853385
$554$	−3.47536e6			−0.481089
$555$	−1.05903e7	−	9.64856e6i	−1.45941	−	1.32963i
$556$	−425034.			−0.0583091
$557$		−	879897.i		−	0.120169i	−0.998193	−	0.0600847i	$-0.980863\pi$
$557$		−	879897.i		−	0.120169i	0.998193	−	0.0600847i	$-0.0191371\pi$
$558$	−475202.	+	44319.5i	−0.0646089	+	0.00602572i
$559$	−2.62210e6			−0.354911
$560$			1.07354e6i			0.144660i
$561$	−9.25738e6	+	1.01609e7i	−1.24188	+	1.36310i
$562$			4.00528e6i			0.534924i
$563$	1.03948e7			1.38212			0.691062	−	0.722795i	$-0.257143\pi$
$563$	1.03948e7			1.38212			0.691062	+	0.722795i	$0.257143\pi$
$564$	3.39100e6	+	3.08946e6i	0.448880	+	0.408964i
$565$			7.47813e6i			0.985534i
$566$			3.89145e6i			0.510588i
$567$	3.57939e6	−	673518.i	0.467575	−	0.0879816i
$568$		−	3.38739e6i		−	0.440549i
$569$	1.26199e6			0.163409			0.0817046	−	0.996657i	$-0.473964\pi$
$569$	1.26199e6			0.163409			0.0817046	+	0.996657i	$0.473964\pi$
$570$	7.21279e6	−	7.91679e6i	0.929856	−	1.02061i
$571$			547847.i			0.0703184i	0.999382	+	0.0351592i	$0.0111938\pi$
$571$			547847.i			0.0703184i	−0.999382	+	0.0351592i	$0.988806\pi$
$572$			5.92597e6i			0.757302i
$573$	−6.87235e6	−	6.26122e6i	−0.874417	−	0.796659i
$574$			192641.i			0.0244044i
$575$	936866.			0.118170
$576$	92427.7	+	991027.i	0.0116077	+	0.124460i
$577$	4.23898e6			0.530056			0.265028	−	0.964241i	$-0.414619\pi$
$577$	4.23898e6			0.530056			0.265028	+	0.964241i	$0.414619\pi$
$578$	1.89955e6			0.236500
$579$	−8.98659e6	−	8.18746e6i	−1.11403	−	1.01497i
$580$	6.46002e6			0.797378
$581$	−4.00595e6			−0.492340
$582$	34773.3	−	38167.4i	0.00425539	−	0.00467073i
$583$			1.10343e7i			1.34454i
$584$		−	3.24699e6i		−	0.393957i
$585$	−886994.	−	9.51051e6i	−0.107160	−	1.14898i
$586$		−	3.87596e6i		−	0.466268i
$587$	2.05122e6			0.245707			0.122854	−	0.992425i	$-0.460795\pi$
$587$	2.05122e6			0.245707			0.122854	+	0.992425i	$0.460795\pi$
$588$	2.39726e6	+	2.18409e6i	0.285939	+	0.260511i
$589$		−	1.24046e6i		−	0.147331i
$590$	−130492.	+	7.27020e6i	−0.0154331	+	0.859838i
$591$	8.29836e6	−	9.10831e6i	0.977290	−	1.07268i
$592$			3.46060e6i			0.405833i
$593$			6.62729e6i			0.773926i	0.922095	+	0.386963i	$0.126476\pi$
$593$			6.62729e6i			0.773926i	−0.922095	+	0.386963i	$0.873524\pi$
$594$	5.84247e6	−	7.75108e6i	0.679408	−	0.901355i
$595$	−5.77236e6			−0.668438
$596$	1.12888e6			0.130177
$597$	1.22963e7	+	1.12029e7i	1.41202	+	1.28645i
$598$		−	1.44709e6i		−	0.165479i
$599$			132382.i			0.0150751i	0.999972	+	0.00753756i	$0.00239930\pi$
$599$			132382.i			0.0150751i	−0.999972	+	0.00753756i	$0.997601\pi$
$600$	−1.10419e6	−	1.00600e6i	−0.125218	−	0.114083i
$601$			8.41412e6i			0.950217i	0.879927	+	0.475108i	$0.157591\pi$
$601$			8.41412e6i			0.950217i	−0.879927	+	0.475108i	$0.842409\pi$
$602$		−	1.11894e6i		−	0.125840i
$603$	6.89596e6	−	643149.i	0.772328	−	0.0720308i
$604$		−	4.00608e6i		−	0.446815i
$605$		−	1.69505e7i		−	1.88275i
$606$	−581851.	−	530110.i	−0.0643622	−	0.0586388i
$607$	1.20438e7			1.32675			0.663377	−	0.748285i	$-0.269122\pi$
$607$	1.20438e7			1.32675			0.663377	+	0.748285i	$0.269122\pi$
$608$	−2.58697e6			−0.283813
$609$	−3.84560e6	+	4.22095e6i	−0.420166	+	0.461176i
$610$	−232260.			−0.0252726
$611$			1.06338e7i			1.15236i
$612$	−5.32870e6	+	496979.i	−0.575099	+	0.0536363i
$613$		−	1.33948e7i		−	1.43974i	−0.694107	−	0.719872i	$-0.744200\pi$
$613$		−	1.33948e7i		−	1.43974i	0.694107	−	0.719872i	$-0.255800\pi$
$614$	122152.			0.0130762
$615$	−611693.	−	557298.i	−0.0652147	−	0.0594155i
$616$	−2.52883e6			−0.268514
$617$		−	7.75587e6i		−	0.820196i	−0.912041	−	0.410098i	$-0.865494\pi$
$617$		−	7.75587e6i		−	0.820196i	0.912041	−	0.410098i	$-0.134506\pi$
$618$	−245783.	+	269773.i	−0.0258870	+	0.0284136i
$619$	−8.24990e6			−0.865410			−0.432705	−	0.901536i	$-0.642441\pi$
$619$	−8.24990e6			−0.865410			−0.432705	+	0.901536i	$0.642441\pi$
$620$	−534120.			−0.0558033
$621$	−1.42670e6	+	1.89277e6i	−0.148458	+	0.196956i
$622$		−	7.61055e6i		−	0.788752i
$623$	7.53437e6			0.777726
$624$	−1.55388e6	+	1.70554e6i	−0.159755	+	0.175348i
$625$	−1.22028e7			−1.24956
$626$		−	1.31528e7i		−	1.34148i
$627$	1.86488e7	+	1.69904e7i	1.89444	+	1.72598i
$628$		−	3.63215e6i		−	0.367507i
$629$	−1.86074e7			−1.87525
$630$	4.05848e6	−	378513.i	0.407392	−	0.0379952i
$631$	−1.71699e6			−0.171670			−0.0858350	−	0.996309i	$-0.527356\pi$
$631$	−1.71699e6			−0.171670			−0.0858350	+	0.996309i	$0.527356\pi$
$632$	−6.36775e6			−0.634152
$633$	1.16919e7	−	1.28331e7i	1.15978	−	1.27298i
$634$		−	4.25221e6i		−	0.420138i
$635$		−	1.72478e7i		−	1.69746i
$636$	−2.89335e6	+	3.17575e6i	−0.283634	+	0.311318i
$637$			7.51756e6i			0.734055i
$638$			1.52172e7i			1.48007i
$639$	−1.28059e7	+	1.19434e6i	−1.24068	+	0.115711i
$640$			1.11390e6i			0.107497i
$641$			1.25723e7i			1.20856i	0.796771	+	0.604281i	$0.206540\pi$
$641$			1.25723e7i			1.20856i	−0.796771	+	0.604281i	$0.793460\pi$
$642$	6.24347e6	−	6.85286e6i	0.597844	−	0.656197i
$643$	8.15838e6			0.778173			0.389087	−	0.921201i	$-0.372791\pi$
$643$	8.15838e6			0.778173			0.389087	+	0.921201i	$0.372791\pi$
$644$	617527.			0.0586734
$645$	3.55299e6	+	3.23704e6i	0.336275	+	0.306372i
$646$		−	1.39100e7i		−	1.31143i
$647$			3.71468e6i			0.348868i	0.984669	+	0.174434i	$0.0558095\pi$
$647$			3.71468e6i			0.348868i	−0.984669	+	0.174434i	$0.944190\pi$
$648$	3.71396e6	−	698840.i	0.347456	−	0.0653793i
$649$	−1.71257e7	−	307386.i	−1.59601	−	0.0286465i
$650$		−	3.46262e6i		−	0.321456i
$651$	317957.	−	348991.i	0.0294047	−	0.0322747i
$652$	−1.86454e6			−0.171772
$653$			1.26167e7i			1.15788i	0.815370	+	0.578940i	$0.196533\pi$
$653$			1.26167e7i			1.15788i	−0.815370	+	0.578940i	$0.803467\pi$
$654$	5.72340e6	−	6.28202e6i	0.523250	−	0.574322i
$655$		−	4.28987e6i		−	0.390698i
$656$			199883.i			0.0181350i
$657$	−1.22751e7	+	1.14484e6i	−1.10946	+	0.103474i
$658$	−4.53784e6			−0.408587
$659$	4.65119e6			0.417206			0.208603	−	0.978000i	$-0.433108\pi$
$659$	4.65119e6			0.417206			0.208603	+	0.978000i	$0.433108\pi$
$660$	7.31575e6	−	8.02980e6i	0.653731	−	0.717538i
$661$	−2.16104e7			−1.92379			−0.961896	−	0.273415i	$-0.911847\pi$
$661$	−2.16104e7			−1.92379			−0.961896	+	0.273415i	$0.911847\pi$
$662$	3.71252e6			0.329248
$663$	−9.17060e6	−	8.35511e6i	−0.810241	−	0.738190i
$664$	−4.15655e6			−0.365859
$665$			1.05942e7i			0.929000i
$666$	1.30827e7	−	1.22015e6i	1.14291	−	0.106593i
$667$		−	3.71597e6i		−	0.323413i
$668$		−	8.65331e6i		−	0.750311i
$669$	2.59324e6	+	2.36263e6i	0.224015	+	0.204094i
$670$	7.75096e6			0.667066
$671$		−	547110.i		−	0.0469103i
$672$	−727817.	−	663096.i	−0.0621726	−	0.0566439i
$673$		−	1.33969e6i		−	0.114017i	−0.998374	−	0.0570083i	$-0.981844\pi$
$673$		−	1.33969e6i		−	0.114017i	0.998374	−	0.0570083i	$-0.0181562\pi$
$674$			3.12232e6i			0.264745i
$675$	−3.41383e6	+	4.52906e6i	−0.288392	+	0.382603i
$676$	592292.			0.0498505
$677$		−	1.77907e7i		−	1.49183i	−0.666040	−	0.745916i	$-0.732012\pi$
$677$		−	1.77907e7i		−	1.49183i	0.666040	−	0.745916i	$-0.267988\pi$
$678$	−5.06987e6	−	4.61903e6i	−0.423568	−	0.385902i
$679$			51075.6i			0.00425147i
$680$	−5.98938e6			−0.496718
$681$	3.46987e6	+	3.16131e6i	0.286712	+	0.261216i
$682$		−	1.25817e6i		−	0.103581i
$683$	1.56033e7			1.27986			0.639931	−	0.768432i	$-0.278963\pi$
$683$	1.56033e7			1.27986			0.639931	+	0.768432i	$0.278963\pi$
$684$	912124.	+	9.77996e6i	0.0745442	+	0.799276i
$685$	−7.05342e6			−0.574345
$686$	−7.35471e6			−0.596699
$687$	2.01354e6	−	2.21007e6i	0.162768	−	0.178655i
$688$		−	1.16101e6i		−	0.0935117i
$689$	−9.95882e6			−0.799208
$690$	−1.78647e6	+	1.96084e6i	−0.142848	+	0.156790i
$691$			2.04272e7i			1.62747i	0.581237	+	0.813734i	$0.302569\pi$
$691$			2.04272e7i			1.62747i	−0.581237	+	0.813734i	$0.697431\pi$
$692$	−6.38363e6			−0.506760
$693$	891623.	+	9.56015e6i	0.0705259	+	0.756191i
$694$	−1.61270e7			−1.27103
$695$			1.80605e6i			0.141830i
$696$	−3.99018e6	+	4.37964e6i	−0.312226	+	0.342701i
$697$	−1.07476e6			−0.0837973
$698$		−	1.73874e6i		−	0.135081i
$699$	1.18485e7	+	1.07948e7i	0.917210	+	0.835647i
$700$	1.47763e6			0.113978
$701$	2.07471e7			1.59464			0.797318	−	0.603560i	$-0.206252\pi$
$701$	2.07471e7			1.59464			0.797318	+	0.603560i	$0.206252\pi$
$702$	6.99562e6	+	5.27304e6i	0.535776	+	0.403848i
$703$			3.41510e7i			2.60624i
$704$	−2.62390e6			−0.199534
$705$	1.31277e7	−	1.44090e7i	0.994755	−	1.09185i
$706$	−4.23676e6			−0.319906
$707$	778633.			0.0585847
$708$	−4.84831e6	−	4.57907e6i	−0.363502	−	0.343316i
$709$	6.43455e6			0.480731			0.240366	−	0.970682i	$-0.422733\pi$
$709$	6.43455e6			0.480731			0.240366	+	0.970682i	$0.422733\pi$
$710$	−1.43937e7			−1.07158
$711$	2.24517e6	+	2.40731e7i	0.166561	+	1.78590i
$712$	7.81763e6			0.577930
$713$			307239.i			0.0226335i
$714$	3.56543e6	−	3.91343e6i	0.261738	−	0.287284i
$715$	2.51806e7			1.84205
$716$	1.17592e7			0.857223
$717$	1.73423e7	−	1.90350e7i	1.25982	−	1.38279i
$718$		−	7.35647e6i		−	0.532548i
$719$	−2.35870e7			−1.70157			−0.850786	−	0.525513i	$-0.823873\pi$
$719$	−2.35870e7			−1.70157			−0.850786	+	0.525513i	$0.823873\pi$
$720$	4.21107e6	−	392743.i	0.302734	−	0.0282343i
$721$		−	361010.i		−	0.0258631i
$722$	−1.56252e7			−1.11553
$723$	−6.19044e6	−	5.63996e6i	−0.440429	−	0.401264i
$724$	−3.81641e6			−0.270588
$725$		−	8.89162e6i		−	0.628255i
$726$	1.14917e7	+	1.04698e7i	0.809178	+	0.737222i
$727$	−2.16353e7			−1.51820			−0.759098	−	0.650976i	$-0.774360\pi$
$727$	−2.16353e7			−1.51820			−0.759098	+	0.650976i	$0.774360\pi$
$728$		−	2.28236e6i		−	0.159608i
$729$	−3.95143e6	−	1.37941e7i	−0.275382	−	0.961335i
$730$	−1.37971e7			−0.958253
$731$	6.24270e6			0.432095
$732$	143460.	−	157463.i	0.00989588	−	0.0108618i
$733$	−4.66859e6			−0.320941			−0.160471	−	0.987041i	$-0.551301\pi$
$733$	−4.66859e6			−0.320941			−0.160471	+	0.987041i	$0.551301\pi$
$734$			2.92810e6i			0.200607i
$735$	9.28061e6	−	1.01864e7i	0.633663	−	0.695511i
$736$	640743.			0.0436003
$737$			1.82582e7i			1.23819i
$738$	755652.	−	70475.6i	0.0510718	−	0.00476319i
$739$		−	1.63535e7i		−	1.10154i	−0.834658	−	0.550768i	$-0.814335\pi$
$739$		−	1.63535e7i		−	1.10154i	0.834658	−	0.550768i	$-0.185665\pi$
$740$	1.47048e7			0.987139
$741$	−1.53345e7	+	1.68312e7i	−1.02594	+	1.12608i
$742$		−	4.24979e6i		−	0.283373i
$743$			1.01064e7i			0.671621i	0.941930	+	0.335810i	$0.109010\pi$
$743$			1.01064e7i			0.671621i	−0.941930	+	0.335810i	$0.890990\pi$
$744$	329911.	−	362112.i	0.0218507	−	0.0239834i
$745$		−	4.79684e6i		−	0.316639i
$746$	−930439.			−0.0612126
$747$	1.46553e6	+	1.57137e7i	0.0960936	+	1.03033i
$748$		−	1.41086e7i		−	0.921996i
$749$			9.17049e6i			0.597294i
$750$	4.64729e6	−	5.10089e6i	0.301680	−	0.331126i
$751$		−	2.43944e7i		−	1.57831i	−0.614197	−	0.789153i	$-0.710520\pi$
$751$		−	2.43944e7i		−	1.57831i	0.614197	−	0.789153i	$-0.289480\pi$
$752$	−4.70845e6			−0.303622
$753$	−1.97392e6	+	2.16659e6i	−0.126865	+	0.139248i
$754$	−1.37341e7			−0.879774
$755$	−1.70226e7			−1.08682
$756$	−2.25020e6	+	2.98529e6i	−0.143191	+	0.189968i
$757$	−6.14979e6			−0.390050			−0.195025	−	0.980798i	$-0.562479\pi$
$757$	−6.14979e6			−0.390050			−0.195025	+	0.980798i	$0.562479\pi$
$758$	−1.75741e7			−1.11096
$759$	−4.61894e6	−	4.20820e6i	−0.291030	−	0.265150i
$760$			1.09925e7i			0.690342i
$761$			2.77313e7i			1.73584i	0.496705	+	0.867919i	$0.334543\pi$
$761$			2.77313e7i			1.73584i	−0.496705	+	0.867919i	$0.665457\pi$
$762$	1.16933e7	+	1.06535e7i	0.729541	+	0.664667i
$763$			8.40660e6i			0.522768i
$764$	9.54233e6			0.591454
$765$	2.11176e6	+	2.26427e7i	0.130464	+	1.39886i
$766$			1.44877e7i			0.892131i
$767$	277427.	−	1.54565e7i	0.0170278	−	0.948688i
$768$	−755180.	−	688026.i	−0.0462006	−	0.0420922i
$769$			8.11778e6i			0.495018i	0.968886	+	0.247509i	$0.0796120\pi$
$769$			8.11778e6i			0.495018i	−0.968886	+	0.247509i	$0.920388\pi$
$770$			1.07455e7i			0.653129i
$771$	−6.23854e6	+	6.84745e6i	−0.377961	+	0.414852i
$772$	1.24780e7			0.753531
$773$	2.19116e7			1.31894			0.659469	−	0.751732i	$-0.270781\pi$
$773$	2.19116e7			1.31894			0.659469	+	0.751732i	$0.270781\pi$
$774$	−4.38917e6	+	409354.i	−0.263348	+	0.0245610i
$775$			735166.i			0.0439674i
$776$			52995.8i			0.00315927i
$777$	−8.75362e6	+	9.60801e6i	−0.520158	+	0.570927i
$778$		−	1.17824e6i		−	0.0697889i
$779$			1.97255e6i			0.116462i
$780$	7.24718e6	+	6.60273e6i	0.426513	+	0.388586i
$781$		−	3.39057e7i		−	1.98905i
$782$			3.44524e6i			0.201466i
$783$	1.79640e7	+	1.35406e7i	1.04712	+	0.789282i
$784$	−3.32863e6			−0.193408
$785$	−1.54337e7			−0.893916
$786$	2.90836e6	+	2.64973e6i	0.167916	+	0.152984i
$787$	−2.13860e7			−1.23082			−0.615408	−	0.788209i	$-0.711009\pi$
$787$	−2.13860e7			−1.23082			−0.615408	+	0.788209i	$0.711009\pi$
$788$			1.26470e7i			0.725557i
$789$	−1.08163e7	+	1.18720e7i	−0.618564	+	0.678938i
$790$			2.70578e7i			1.54250i
$791$	6.78450e6			0.385546
$792$	925145.	+	9.91958e6i	0.0524079	+	0.561928i
$793$	493786.			0.0278841
$794$		−	1.21344e7i		−	0.683074i
$795$	1.34944e7	+	1.22944e7i	0.757243	+	0.689906i
$796$	−1.70736e7			−0.955086
$797$	1.17905e7			0.657484			0.328742	−	0.944420i	$-0.393375\pi$
$797$	1.17905e7			0.657484			0.328742	+	0.944420i	$0.393375\pi$
$798$	−7.18247e6	−	6.54377e6i	−0.399270	−	0.363765i
$799$		−	2.53170e7i		−	1.40296i
$800$	1.53318e6			0.0846970
$801$	−2.75637e6	−	2.95543e7i	−0.151795	−	1.62757i
$802$	−1.38437e7			−0.760003
$803$		−	3.25004e7i		−	1.77869i
$804$	−4.78756e6	+	5.25484e6i	−0.261200	+	0.286695i
$805$		−	2.62399e6i		−	0.142716i
$806$	1.13554e6			0.0615696
$807$	−1.92216e7	−	1.75123e7i	−1.03898	−	0.946587i
$808$	807907.			0.0435344
$809$	−1.40910e7			−0.756954			−0.378477	−	0.925611i	$-0.623552\pi$
$809$	−1.40910e7			−0.756954			−0.378477	+	0.925611i	$0.623552\pi$
$810$	−2.96951e6	−	1.57813e7i	−0.159027	−	0.845145i
$811$		−	9.74526e6i		−	0.520285i	−0.965570	−	0.260142i	$-0.916230\pi$
$811$		−	9.74526e6i		−	0.520285i	0.965570	−	0.260142i	$-0.0837695\pi$
$812$		−	5.86083e6i		−	0.311938i
$813$	−2.01893e6	−	1.83940e6i	−0.107126	−	0.0976000i
$814$			3.46385e7i			1.83231i
$815$			7.92278e6i			0.417815i
$816$	3.69948e6	−	4.06056e6i	0.194498	−	0.213482i
$817$		−	1.14575e7i		−	0.600528i
$818$		−	1.59977e7i		−	0.835938i
$819$	−8.62837e6	+	804722.i	−0.449489	+	0.0419214i
$820$	849343.			0.0441111
$821$	1.67831e7			0.868989			0.434495	−	0.900674i	$-0.356927\pi$
$821$	1.67831e7			0.868989			0.434495	+	0.900674i	$0.356927\pi$
$822$	4.35670e6	−	4.78194e6i	0.224894	−	0.246845i
$823$		−	1.16730e7i		−	0.600735i	−0.953824	−	0.300368i	$-0.902891\pi$
$823$		−	1.16730e7i		−	0.600735i	0.953824	−	0.300368i	$-0.0971094\pi$
$824$		−	374582.i		−	0.0192189i
$825$	−1.10523e7	−	1.00695e7i	−0.565349	−	0.515076i
$826$	6.59586e6	+	118388.i	0.336373	+	0.00603751i
$827$		−	1.76854e7i		−	0.899192i	−0.893232	−	0.449596i	$-0.851568\pi$
$827$		−	1.76854e7i		−	0.899192i	0.893232	−	0.449596i	$-0.148432\pi$
$828$	−225916.	−	2.42231e6i	−0.0114517	−	0.122787i
$829$	2.51376e7			1.27039			0.635195	−	0.772351i	$-0.280920\pi$
$829$	2.51376e7			1.27039			0.635195	+	0.772351i	$0.280920\pi$
$830$			1.76620e7i			0.889907i
$831$	−1.00118e7	−	9.12147e6i	−0.502931	−	0.458208i
$832$		−	2.36816e6i		−	0.118605i
$833$		−	1.78978e7i		−	0.893693i
$834$	−1.22443e6	−	1.11555e6i	−0.0609564	−	0.0555358i
$835$	−3.67696e7			−1.82504
$836$	−2.58940e7			−1.28140
$837$	−1.48527e6	−	1.11954e6i	−0.0732813	−	0.0552367i
$838$	2.67929e7			1.31798
$839$	3.01541e7			1.47891			0.739455	−	0.673206i	$-0.235083\pi$
$839$	3.01541e7			1.47891			0.739455	+	0.673206i	$0.235083\pi$
$840$	−2.81762e6	+	3.09264e6i	−0.137780	+	0.151227i
$841$	−1.47564e7			−0.719432
$842$		−	6.47517e6i		−	0.314754i
$843$	−1.05123e7	+	1.15384e7i	−0.509482	+	0.559210i
$844$			1.78189e7i			0.861041i
$845$		−	2.51677e6i		−	0.121255i
$846$	1.66012e6	+	1.78001e7i	0.0797469	+	0.855062i
$847$	−1.53782e7			−0.736543
$848$		−	4.40957e6i		−	0.210575i
$849$	−1.02135e7	+	1.12104e7i	−0.486303	+	0.533768i
$850$			8.24382e6i			0.391364i
$851$		−	8.45854e6i		−	0.400379i
$852$	8.89058e6	−	9.75834e6i	0.419596	−	0.460550i
$853$	1.77743e7			0.836409			0.418205	−	0.908353i	$-0.362660\pi$
$853$	1.77743e7			0.836409			0.418205	+	0.908353i	$0.362660\pi$
$854$			210717.i			0.00988676i
$855$	4.15570e7	−	3.87579e6i	1.94414	−	0.181320i
$856$			9.51526e6i			0.443850i
$857$	8.71413e6			0.405296			0.202648	−	0.979252i	$-0.435045\pi$
$857$	8.71413e6			0.405296			0.202648	+	0.979252i	$0.435045\pi$
$858$	−1.55534e7	+	1.70714e7i	−0.721284	+	0.791684i
$859$			3.37258e7i			1.55948i	0.626105	+	0.779739i	$0.284648\pi$
$859$			3.37258e7i			1.55948i	−0.626105	+	0.779739i	$0.715352\pi$
$860$	−4.93337e6			−0.227456
$861$	−505607.	+	554956.i	−0.0232437	+	0.0255124i
$862$	−1.82902e6			−0.0838397
$863$	4.10905e7			1.87808			0.939041	−	0.343805i	$-0.111716\pi$
$863$	4.10905e7			1.87808			0.939041	+	0.343805i	$0.111716\pi$
$864$	−2.33480e6	+	3.09752e6i	−0.106406	+	0.141166i
$865$			2.71253e7i			1.23263i
$866$	−1.86176e7			−0.843586
$867$	5.47220e6	+	4.98558e6i	0.247237	+	0.225252i
$868$			484578.i			0.0218305i
$869$	−6.37373e7			−2.86315
$870$	1.86099e7	+	1.69550e7i	0.833579	+	0.759453i
$871$	−1.64786e7			−0.735996
$872$			8.72266e6i			0.388470i
$873$	200349.	−	18685.5i	0.00889716	−	0.000829790i
$874$	6.32318e6			0.279999
$875$			6.82601e6i			0.301402i
$876$	8.52208e6	−	9.35388e6i	0.375220	−	0.411843i
$877$	−9.02214e6			−0.396105			−0.198053	−	0.980191i	$-0.563462\pi$
$877$	−9.02214e6			−0.396105			−0.198053	+	0.980191i	$0.563462\pi$
$878$	−2.12365e6			−0.0929710
$879$	1.01729e7	−	1.11658e7i	0.444091	−	0.487436i
$880$			1.11495e7i			0.485342i
$881$	7.03034e6			0.305166			0.152583	−	0.988291i	$-0.451241\pi$
$881$	7.03034e6			0.305166			0.152583	+	0.988291i	$0.451241\pi$
$882$	1.17362e6	+	1.25838e7i	0.0507991	+	0.544677i
$883$	−8.57539e6			−0.370128			−0.185064	−	0.982726i	$-0.559249\pi$
$883$	−8.57539e6			−0.370128			−0.185064	+	0.982726i	$0.559249\pi$
$884$	1.27335e7			0.548045
$885$	−1.94574e7	+	2.06014e7i	−0.835076	+	0.884176i
$886$	5.97512e6			0.255719
$887$	4.11142e7			1.75462			0.877309	−	0.479925i	$-0.159336\pi$
$887$	4.11142e7			1.75462			0.877309	+	0.479925i	$0.159336\pi$
$888$	−9.08272e6	+	9.96924e6i	−0.386530	+	0.424257i
$889$	−1.56480e7			−0.664054
$890$		−	3.32186e7i		−	1.40575i
$891$	3.71745e7	−	6.99497e6i	1.56874	−	0.295183i
$892$	−3.60074e6			−0.151523
$893$	−4.64654e7			−1.94985
$894$	3.25207e6	+	2.96288e6i	0.136087	+	0.123985i
$895$		−	4.99669e7i		−	2.08509i
$896$	1.01058e6			0.0420534
$897$	3.79805e6	−	4.16876e6i	0.157609	−	0.172992i
$898$			2.00835e7i			0.831093i
$899$	2.91595e6			0.120332
$900$	−540575.	−	5.79614e6i	−0.0222459	−	0.238524i
$901$	2.37100e7			0.973015
$902$			2.00071e6i			0.0818781i
$903$	2.93679e6	−	3.22344e6i	0.119854	−	0.131553i
$904$	7.03957e6			0.286500
$905$			1.62167e7i			0.658173i
$906$	1.05144e7	−	1.15407e7i	0.425564	−	0.467101i
$907$	2.66769e7			1.07676			0.538378	−	0.842703i	$-0.319037\pi$
$907$	2.66769e7			1.07676			0.538378	+	0.842703i	$0.319037\pi$
$908$	−4.81795e6			−0.193931
$909$	−284855.	−	3.05427e6i	−0.0114344	−	0.122602i
$910$	−9.69817e6			−0.388228
$911$			3.14595e7i			1.25590i	0.778252	+	0.627952i	$0.216107\pi$
$911$			3.14595e7i			1.25590i	−0.778252	+	0.627952i	$0.783893\pi$
$912$	−7.45251e6	−	6.78979e6i	−0.296698	−	0.270315i
$913$	−4.16046e7			−1.65183
$914$		−	2.30636e7i		−	0.913192i
$915$	−669090.	−	609591.i	−0.0264199	−	0.0240705i
$916$			3.06871e6i			0.120842i
$917$	−3.89197e6			−0.152843
$918$	−1.66552e7	−	1.25541e7i	−0.652294	−	0.491675i
$919$			2.61935e7i			1.02307i	0.859263	+	0.511534i	$0.170922\pi$
$919$			2.61935e7i			1.02307i	−0.859263	+	0.511534i	$0.829078\pi$
$920$		−	2.72264e6i		−	0.106053i
$921$	351895.	+	320603.i	0.0136699	+	0.0124543i
$922$			1.83927e7i			0.712556i
$923$	3.06011e7			1.18231
$924$	−7.28501e6	−	6.63719e6i	−0.280705	−	0.255743i
$925$		−	2.02397e7i		−	0.777768i
$926$			3.42666e7i			1.31324i
$927$	−1.41610e6	+	132072.i	−0.0541245	+	0.00504790i
$928$		−	6.08117e6i		−	0.231802i
$929$	8.27490e6			0.314574			0.157287	−	0.987553i	$-0.449725\pi$
$929$	8.27490e6			0.314574			0.157287	+	0.987553i	$0.449725\pi$
$930$	−1.53868e6	−	1.40186e6i	−0.0583367	−	0.0531491i
$931$	−3.28486e7			−1.24206
$932$	−1.64517e7			−0.620399
$933$	1.99747e7	−	2.19244e7i	0.751237	−	0.824561i
$934$	1.91801e7			0.719421
$935$	−5.99501e7			−2.24265
$936$	−8.95277e6	+	834976.i	−0.334016	+	0.0311519i
$937$			1.43587e7i			0.534277i	0.963658	+	0.267139i	$0.0860782\pi$
$937$			1.43587e7i			0.534277i	−0.963658	+	0.267139i	$0.913922\pi$
$938$		−	7.03203e6i		−	0.260960i
$939$	3.45210e7	−	3.78904e7i	1.27767	−	1.40238i
$940$			2.00071e7i			0.738524i
$941$	3.90698e7			1.43836			0.719179	−	0.694825i	$-0.244518\pi$
$941$	3.90698e7			1.43836			0.719179	+	0.694825i	$0.244518\pi$
$942$	9.53299e6	−	1.04635e7i	0.350027	−	0.384192i
$943$		−	488563.i		−	0.0178913i
$944$	6.84384e6	+	122839.i	0.249960	+	0.00448649i
$945$	1.26851e7	+	9.56152e6i	0.462076	+	0.348295i
$946$		−	1.16210e7i		−	0.422199i
$947$			2.84871e6i			0.103222i	0.998667	+	0.0516112i	$0.0164357\pi$
$947$			2.84871e6i			0.103222i	−0.998667	+	0.0516112i	$0.983564\pi$
$948$	−1.83441e7	−	1.67129e7i	−0.662943	−	0.603991i
$949$	2.93327e7			1.05727
$950$	1.51302e7			0.543921
$951$	1.11604e7	−	1.22497e7i	0.400155	−	0.439212i
$952$			5.43384e6i			0.194319i
$953$		−	5.80083e6i		−	0.206899i	−0.994635	−	0.103449i	$-0.967012\pi$
$953$		−	5.80083e6i		−	0.206899i	0.994635	−	0.103449i	$-0.0329880\pi$
$954$	−1.66702e7	+	1.55474e6i	−0.593022	+	0.0553079i
$955$		−	4.05472e7i		−	1.43864i
$956$			2.64303e7i			0.935316i
$957$	−3.99393e7	+	4.38375e7i	−1.40968	+	1.54727i
$958$			7.79093e6i			0.274268i
$959$			6.39918e6i			0.224687i
$960$	−2.92356e6	+	3.20891e6i	−0.102384	+	0.112377i
$961$	2.83881e7			0.991579
$962$	−3.12624e7			−1.08914
$963$	3.59722e7	−	3.35493e6i	1.24997	−	0.116578i
$964$	8.59550e6			0.297905
$965$		−	5.30213e7i		−	1.83287i
$966$	1.77896e6	+	1.62077e6i	0.0613371	+	0.0558827i
$967$		−	4.38765e7i		−	1.50892i	−0.656346	−	0.754460i	$-0.727899\pi$
$967$		−	4.38765e7i		−	1.50892i	0.656346	−	0.754460i	$-0.272101\pi$
$968$	−1.59564e7			−0.547326
$969$	3.65083e7	−	4.00717e7i	1.24906	−	1.37097i
$970$	225189.			0.00768456
$971$		−	1.00747e7i		−	0.342912i	−0.985192	−	0.171456i	$-0.945153\pi$
$971$		−	1.00747e7i		−	0.342912i	0.985192	−	0.171456i	$-0.0548471\pi$
$972$	1.25333e7	+	7.73449e6i	0.425500	+	0.262583i
$973$	1.63853e6			0.0554846
$974$	−7.56829e6			−0.255623
$975$	9.08803e6	−	9.97507e6i	0.306167	−	0.336050i
$976$			218639.i			0.00734687i
$977$	4.29086e7			1.43816			0.719080	−	0.694927i	$-0.244563\pi$
$977$	4.29086e7			1.43816			0.719080	+	0.694927i	$0.244563\pi$
$978$	−5.37133e6	−	4.89369e6i	−0.179570	−	0.163602i
$979$	7.82498e7			2.60931
$980$			1.41440e7i			0.470443i
$981$	3.29757e7	−	3.07547e6i	1.09401	−	0.102033i
$982$		−	3.86694e7i		−	1.27964i
$983$	−1.42845e7			−0.471499			−0.235750	−	0.971814i	$-0.575754\pi$
$983$	−1.42845e7			−0.471499			−0.235750	+	0.971814i	$0.575754\pi$
$984$	−524616.	+	575820.i	−0.0172724	+	0.0189583i
$985$	5.37395e7			1.76483
$986$	3.26981e7			1.07110
$987$	−1.30725e7	−	1.19101e7i	−0.427137	−	0.389154i
$988$		−	2.33702e7i		−	0.761677i
$989$			2.83780e6i			0.0922551i
$990$	4.21502e7	−	3.93112e6i	1.36682	−	0.127476i
$991$		−	2.30338e7i		−	0.745042i	−0.928024	−	0.372521i	$-0.878493\pi$
$991$		−	2.30338e7i		−	0.745042i	0.928024	−	0.372521i	$-0.121507\pi$
$992$			502796.i			0.0162223i
$993$	1.06950e7	+	9.74392e6i	0.344196	+	0.313589i
$994$			1.30586e7i			0.419209i
$995$			7.25491e7i			2.32313i
$996$	−1.19741e7	−	1.09093e7i	−0.382469	−	0.348458i
$997$	−2.36719e7			−0.754214			−0.377107	−	0.926170i	$-0.623081\pi$
$997$	−2.36719e7			−0.754214			−0.377107	+	0.926170i	$0.623081\pi$
$998$	−1.60550e7			−0.510252
$999$	4.08908e7	+	3.08220e7i	1.29632	+	0.977117i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.c.a.353.13	✓	50
3.2	odd	2		354.6.c.b.353.14	yes	50
59.58	odd	2		354.6.c.b.353.13	yes	50
177.176	even	2	inner	354.6.c.a.353.14	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.c.a.353.13	✓	50	1.1	even	1	trivial
354.6.c.a.353.14	yes	50	177.176	even	2	inner
354.6.c.b.353.13	yes	50	59.58	odd	2
354.6.c.b.353.14	yes	50	3.2	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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +(-11.5231 - 10.4984i) q^{3} +16.0000 q^{4} -67.9871i q^{5} +(46.0925 + 41.9938i) q^{6} -61.6810 q^{7} -64.0000 q^{8} +(22.5654 + 241.950i) q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +(-11.5231 - 10.4984i) q^{3} +16.0000 q^{4} -67.9871i q^{5} +(46.0925 + 41.9938i) q^{6} -61.6810 q^{7} -64.0000 q^{8} +(22.5654 + 241.950i) q^{9} +271.948i q^{10} -640.601 q^{11} +(-184.370 - 167.975i) q^{12} -578.165i q^{13} +246.724 q^{14} +(-713.759 + 783.425i) q^{15} +256.000 q^{16} +1376.50i q^{17} +(-90.2615 - 967.800i) q^{18} +2526.34 q^{19} -1087.79i q^{20} +(710.759 + 647.555i) q^{21} +2562.40 q^{22} -625.726 q^{23} +(737.481 + 671.900i) q^{24} -1497.25 q^{25} +2312.66i q^{26} +(2280.07 - 3024.92i) q^{27} -986.896 q^{28} +5938.65i q^{29} +(2855.04 - 3133.70i) q^{30} -491.012i q^{31} -1024.00 q^{32} +(7381.73 + 6725.31i) q^{33} -5505.99i q^{34} +4193.51i q^{35} +(361.046 + 3871.20i) q^{36} +13518.0i q^{37} -10105.4 q^{38} +(-6069.83 + 6662.27i) q^{39} +4351.17i q^{40} +780.794i q^{41} +(-2843.04 - 2590.22i) q^{42} -4535.21i q^{43} -10249.6 q^{44} +(16449.5 - 1534.15i) q^{45} +2502.90 q^{46} -18392.4 q^{47} +(-2949.92 - 2687.60i) q^{48} -13002.5 q^{49} +5988.99 q^{50} +(14451.1 - 15861.6i) q^{51} -9250.64i q^{52} -17224.9i q^{53} +(-9120.30 + 12099.7i) q^{54} +43552.6i q^{55} +3947.58 q^{56} +(-29111.3 - 26522.6i) q^{57} -23754.6i q^{58} +(26733.8 + 479.840i) q^{59} +(-11420.1 + 12534.8i) q^{60} +854.058i q^{61} +1964.05i q^{62} +(-1391.85 - 14923.7i) q^{63} +4096.00 q^{64} -39307.8 q^{65} +(-29526.9 - 26901.3i) q^{66} -28501.6i q^{67} +22024.0i q^{68} +(7210.33 + 6569.15i) q^{69} -16774.1i q^{70} +52928.0i q^{71} +(-1444.18 - 15484.8i) q^{72} +50734.2i q^{73} -54071.9i q^{74} +(17253.0 + 15718.8i) q^{75} +40421.4 q^{76} +39512.9 q^{77} +(24279.3 - 26649.1i) q^{78} +99496.1 q^{79} -17404.7i q^{80} +(-58030.6 + 10919.4i) q^{81} -3123.18i q^{82} +64946.2 q^{83} +(11372.1 + 10360.9i) q^{84} +93584.1 q^{85} +18140.8i q^{86} +(62346.6 - 68431.8i) q^{87} +40998.5 q^{88} -122151. q^{89} +(-65797.9 + 6136.62i) q^{90} +35661.8i q^{91} -10011.6 q^{92} +(-5154.86 + 5658.00i) q^{93} +73569.5 q^{94} -171758. i q^{95} +(11799.7 + 10750.4i) q^{96} -828.060i q^{97} +52009.8 q^{98} +(-14455.4 - 154993. i) 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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