LMFDB - Embedded newform 354.6.c.b.353.14

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

$q$-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	$0.208066\pi$
$5$			67.9871i			1.21619i	−0.793864	+	0.608095i	$0.791934\pi$
$6$	−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	$-0.205821\pi$
$11$	640.601			1.59627			0.798134	+	0.602480i	$0.205821\pi$
$12$	−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	$-0.803991\pi$
$17$		−	1376.50i		−	1.15519i	0.816324	−	0.577595i	$-0.196009\pi$
$18$	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	$-0.460646\pi$
$23$	625.726			0.246641			0.123320	+	0.992367i	$0.460646\pi$
$24$	−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	$-0.772401\pi$
$29$		−	5938.65i		−	1.31127i	0.755077	−	0.655636i	$-0.227599\pi$
$30$	−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	$-0.988452\pi$
$41$		−	780.794i		−	0.0725399i	0.999342	−	0.0362699i	$-0.0115476\pi$
$42$	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	$-0.292275\pi$
$47$	18392.4			1.21449			0.607244	+	0.794516i	$0.292275\pi$
$48$	−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	$0.138373\pi$
$53$			17224.9i			0.842299i	−0.906991	+	0.421150i	$0.861627\pi$
$54$	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	$-0.785901\pi$
$71$		−	52928.0i		−	1.24606i	0.782198	−	0.623030i	$-0.214099\pi$
$72$	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	$-0.673101\pi$
$83$	−64946.2			−1.03480			−0.517402	+	0.855742i	$0.673101\pi$
$84$	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	$-0.195461\pi$
$89$	122151.			1.63463			0.817317	+	0.576189i	$0.195461\pi$
$90$	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	$-0.480390\pi$
$101$	12623.5			0.123134			0.0615670	+	0.998103i	$0.480390\pi$
$102$	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	$0.216003\pi$
$107$			148676.i			1.25540i	−0.778456	+	0.627699i	$0.783997\pi$
$108$	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	$-0.367211\pi$
$113$	109993.			0.810345			0.405173	+	0.914240i	$0.367211\pi$
$114$	−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	$-0.551351\pi$
$131$	−63098.3			−0.321247			−0.160624	+	0.987016i	$0.551351\pi$
$132$	−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	$0.0758774\pi$
$137$			103746.i			0.472250i	−0.971723	+	0.236125i	$0.924123\pi$
$138$	−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	$-0.541554\pi$
$149$	−70555.1			−0.260353			−0.130177	+	0.991491i	$0.541554\pi$
$150$	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	$0.270096\pi$
$167$			540832.i			1.50062i	−0.661085	+	0.750311i	$0.729904\pi$
$168$	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	$-0.330843\pi$
$173$	398977.			1.01352			0.506760	+	0.862087i	$0.330843\pi$
$174$	249386.	+	273727.i	0.624452	+	0.685402i
$175$	92351.7			0.227955
$176$	163994.			0.399067
$177$	313094.	−	275134.i	0.751177	−	0.660101i
$178$	488602.			1.15586
$179$	−734947.			−1.71445			−0.857223	−	0.514946i	$-0.827812\pi$
$179$	−734947.			−1.71445			−0.857223	+	0.514946i	$0.827812\pi$
$180$	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	$-0.701446\pi$
$191$	−596396.			−1.18291			−0.591454	+	0.806339i	$0.701446\pi$
$192$	−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	$-0.741582\pi$
$197$		−	790437.i		−	1.45111i	0.688162	−	0.725557i	$-0.258418\pi$
$198$	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	$-0.437876\pi$
$227$	301122.			0.387862			0.193931	+	0.981015i	$0.437876\pi$
$228$	−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	$-0.286971\pi$
$233$	1.02823e6			1.24080			0.620399	+	0.784286i	$0.286971\pi$
$234$	−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	$-0.615116\pi$
$239$		−	1.65190e6i		−	1.87063i	0.353815	−	0.935316i	$-0.384884\pi$
$240$	−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	$0.0300252\pi$
$251$			188021.i			0.188374i	−0.995555	+	0.0941871i	$0.969975\pi$
$252$	−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	$0.0905351\pi$
$257$			594235.i			0.561210i	−0.959823	+	0.280605i	$0.909465\pi$
$258$	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	$0.151876\pi$
$263$			1.03027e6i			0.918465i	−0.888316	+	0.459233i	$0.848124\pi$
$264$	−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	$-0.748050\pi$
$269$	−1.66809e6			−1.40552			−0.702762	+	0.711425i	$0.748050\pi$
$270$	−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	$0.123474\pi$
$281$			1.00132e6i			0.756497i	−0.925704	+	0.378249i	$0.876526\pi$
$282$	−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	$-0.893052\pi$
$293$		−	968990.i		−	0.659402i	0.944085	−	0.329701i	$-0.106948\pi$
$294$	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	$-0.811672\pi$
$311$		−	1.90264e6i		−	1.11546i	0.830021	−	0.557732i	$-0.188328\pi$
$312$	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	$-0.903986\pi$
$317$		−	1.06305e6i		−	0.594165i	0.954852	−	0.297082i	$-0.0960136\pi$
$318$	−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	$-0.855524\pi$
$347$	−4.03174e6			−1.79750			−0.898751	+	0.438460i	$0.855524\pi$
$348$	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	$-0.572633\pi$
$353$	−1.05919e6			−0.452415			−0.226208	+	0.974079i	$0.572633\pi$
$354$	1.25238e6	−	1.10053e6i	0.531162	−	0.466762i
$355$	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	$-0.877104\pi$
$359$		−	1.83912e6i		−	0.753136i	0.926389	−	0.376568i	$-0.122896\pi$
$360$	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	$0.217286\pi$
$383$			3.62193e6i			1.26166i	−0.775920	+	0.630832i	$0.782714\pi$
$384$	−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	$-0.984286\pi$
$389$		−	294561.i		−	0.0986964i	0.998782	−	0.0493482i	$-0.0157144\pi$
$390$	−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	$-0.680595\pi$
$401$	−3.46092e6			−1.07481			−0.537403	+	0.843326i	$0.680595\pi$
$402$	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	$-0.118102\pi$
$419$	6.69823e6			1.86391			0.931954	+	0.362575i	$0.118102\pi$
$420$	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	$-0.518882\pi$
$431$	−457254.			−0.118567			−0.0592836	+	0.998241i	$0.518882\pi$
$432$	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	$-0.442125\pi$
$443$	1.49378e6			0.361641			0.180820	+	0.983516i	$0.442125\pi$
$444$	−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	$0.199955\pi$
$449$			5.02089e6i			1.17534i	−0.809100	+	0.587671i	$0.800045\pi$
$450$	−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	$0.168085\pi$
$461$			4.59818e6i			1.00771i	−0.863790	+	0.503853i	$0.831915\pi$
$462$	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	$-0.330123\pi$
$467$	4.79502e6			1.01742			0.508708	+	0.860939i	$0.330123\pi$
$468$	−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	$0.0621258\pi$
$479$			1.94773e6i			0.387874i	−0.981014	+	0.193937i	$0.937874\pi$
$480$	−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	$-0.639987\pi$
$491$		−	9.66735e6i		−	1.80969i	0.425743	−	0.904844i	$-0.360013\pi$
$492$	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	$-0.733216\pi$
$503$	−7.59071e6			−1.33771			−0.668856	+	0.743392i	$0.733216\pi$
$504$	−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	$-0.278393\pi$
$509$	7.49704e6			1.28261			0.641306	+	0.767285i	$0.278393\pi$
$510$	−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	$-0.874529\pi$
$521$		−	4.75897e6i		−	0.768101i	0.923312	−	0.384051i	$-0.125471\pi$
$522$	−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
$531$	−719354.	+	6.45741e6i	−0.110715	+	0.993852i
$532$	−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	$0.0191371\pi$
$557$			879897.i			0.120169i	−0.998193	+	0.0600847i	$0.980863\pi$
$558$	−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	$-0.742857\pi$
$563$	−1.03948e7			−1.38212			−0.691062	+	0.722795i	$0.742857\pi$
$564$	−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	$-0.526036\pi$
$569$	−1.26199e6			−0.163409			−0.0817046	+	0.996657i	$0.526036\pi$
$570$	−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	$-0.539205\pi$
$587$	−2.05122e6			−0.245707			−0.122854	+	0.992425i	$0.539205\pi$
$588$	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	$-0.873524\pi$
$593$		−	6.62729e6i		−	0.773926i	0.922095	−	0.386963i	$-0.126476\pi$
$594$	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	$-0.997601\pi$
$599$		−	132382.i		−	0.0150751i	0.999972	−	0.00753756i	$-0.00239930\pi$
$600$	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	$0.134506\pi$
$617$			7.75587e6i			0.820196i	−0.912041	+	0.410098i	$0.865494\pi$
$618$	−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	$-0.793460\pi$
$641$		−	1.25723e7i		−	1.20856i	0.796771	−	0.604281i	$-0.206540\pi$
$642$	−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	$-0.944190\pi$
$647$		−	3.71468e6i		−	0.348868i	0.984669	−	0.174434i	$-0.0558095\pi$
$648$	−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	$-0.803467\pi$
$653$		−	1.26167e7i		−	1.15788i	0.815370	−	0.578940i	$-0.196533\pi$
$654$	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	$-0.566892\pi$
$659$	−4.65119e6			−0.417206			−0.208603	+	0.978000i	$0.566892\pi$
$660$	−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	$0.267988\pi$
$677$			1.77907e7i			1.49183i	−0.666040	+	0.745916i	$0.732012\pi$
$678$	−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	$-0.721037\pi$
$683$	−1.56033e7			−1.27986			−0.639931	+	0.768432i	$0.721037\pi$
$684$	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	$-0.793748\pi$
$701$	−2.07471e7			−1.59464			−0.797318	+	0.603560i	$0.793748\pi$
$702$	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
$708$	5.00951e6	−	4.40214e6i	0.375588	−	0.330051i
$709$	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	$-0.176127\pi$
$719$	2.35870e7			1.70157			0.850786	+	0.525513i	$0.176127\pi$
$720$	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	$-0.890990\pi$
$743$		−	1.01064e7i		−	0.671621i	0.941930	−	0.335810i	$-0.109010\pi$
$744$	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	$-0.665457\pi$
$761$		−	2.77313e7i		−	1.73584i	0.496705	−	0.867919i	$-0.334543\pi$
$762$	−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	$-0.729219\pi$
$773$	−2.19116e7			−1.31894			−0.659469	+	0.751732i	$0.729219\pi$
$774$	−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	$-0.606625\pi$
$797$	−1.17905e7			−0.657484			−0.328742	+	0.944420i	$0.606625\pi$
$798$	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	$-0.376448\pi$
$809$	1.40910e7			0.756954			0.378477	+	0.925611i	$0.376448\pi$
$810$	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	$-0.643073\pi$
$821$	−1.67831e7			−0.868989			−0.434495	+	0.900674i	$0.643073\pi$
$822$	−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	$0.148432\pi$
$827$			1.76854e7i			0.899192i	−0.893232	+	0.449596i	$0.851568\pi$
$828$	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	$-0.764917\pi$
$839$	−3.01541e7			−1.47891			−0.739455	+	0.673206i	$0.764917\pi$
$840$	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	$-0.564955\pi$
$857$	−8.71413e6			−0.405296			−0.202648	+	0.979252i	$0.564955\pi$
$858$	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	$-0.888284\pi$
$863$	−4.10905e7			−1.87808			−0.939041	+	0.343805i	$0.888284\pi$
$864$	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	$-0.548759\pi$
$881$	−7.03034e6			−0.305166			−0.152583	+	0.988291i	$0.548759\pi$
$882$	−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
$885$	1.87055e7	+	2.12864e7i	0.802809	+	0.913574i
$886$	5.97512e6			0.255719
$887$	−4.11142e7			−1.75462			−0.877309	−	0.479925i	$-0.840664\pi$
$887$	−4.11142e7			−1.75462			−0.877309	+	0.479925i	$0.840664\pi$
$888$	−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	$-0.783893\pi$
$911$		−	3.14595e7i		−	1.25590i	0.778252	−	0.627952i	$-0.216107\pi$
$912$	−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	$-0.550275\pi$
$929$	−8.27490e6			−0.314574			−0.157287	+	0.987553i	$0.550275\pi$
$930$	−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	$-0.755482\pi$
$941$	−3.90698e7			−1.43836			−0.719179	+	0.694825i	$0.755482\pi$
$942$	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	$-0.983564\pi$
$947$		−	2.84871e6i		−	0.103222i	0.998667	−	0.0516112i	$-0.0164357\pi$
$948$	−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	$0.0329880\pi$
$953$			5.80083e6i			0.206899i	−0.994635	+	0.103449i	$0.967012\pi$
$954$	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	$0.0548471\pi$
$971$			1.00747e7i			0.342912i	−0.985192	+	0.171456i	$0.945153\pi$
$972$	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	$-0.755437\pi$
$977$	−4.29086e7			−1.43816			−0.719080	+	0.694927i	$0.755437\pi$
$978$	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	$-0.424246\pi$
$983$	1.42845e7			0.471499			0.235750	+	0.971814i	$0.424246\pi$
$984$	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.b.353.14	yes	50
3.2	odd	2		354.6.c.a.353.13	✓	50
59.58	odd	2		354.6.c.a.353.14	yes	50
177.176	even	2	inner	354.6.c.b.353.13	yes	50

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

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

Introduction

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