LMFDB - Embedded newform 354.6.c.a.353.8

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			353.8
Character	$\chi$	$=$	354.353
Dual form			354.6.c.a.353.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +(-13.3335 + 8.07581i) q^{3} +16.0000 q^{4} -83.4718i q^{5} +(53.3339 - 32.3032i) q^{6} -123.882 q^{7} -64.0000 q^{8} +(112.563 - 215.357i) q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +(-13.3335 + 8.07581i) q^{3} +16.0000 q^{4} -83.4718i q^{5} +(53.3339 - 32.3032i) q^{6} -123.882 q^{7} -64.0000 q^{8} +(112.563 - 215.357i) q^{9} +333.887i q^{10} -49.5960 q^{11} +(-213.335 + 129.213i) q^{12} +349.752i q^{13} +495.527 q^{14} +(674.102 + 1112.97i) q^{15} +256.000 q^{16} -992.945i q^{17} +(-450.251 + 861.428i) q^{18} +2082.59 q^{19} -1335.55i q^{20} +(1651.77 - 1000.45i) q^{21} +198.384 q^{22} +3919.24 q^{23} +(853.342 - 516.852i) q^{24} -3842.53 q^{25} -1399.01i q^{26} +(238.332 + 3780.49i) q^{27} -1982.11 q^{28} +1009.07i q^{29} +(-2696.41 - 4451.87i) q^{30} -1159.28i q^{31} -1024.00 q^{32} +(661.287 - 400.528i) q^{33} +3971.78i q^{34} +10340.6i q^{35} +(1801.00 - 3445.71i) q^{36} +2578.31i q^{37} -8330.36 q^{38} +(-2824.53 - 4663.40i) q^{39} +5342.19i q^{40} +12183.2i q^{41} +(-6607.10 + 4001.78i) q^{42} -437.653i q^{43} -793.537 q^{44} +(-17976.2 - 9395.80i) q^{45} -15677.0 q^{46} +24038.1 q^{47} +(-3413.37 + 2067.41i) q^{48} -1460.30 q^{49} +15370.1 q^{50} +(8018.83 + 13239.4i) q^{51} +5596.03i q^{52} -18010.8i q^{53} +(-953.328 - 15122.0i) q^{54} +4139.87i q^{55} +7928.44 q^{56} +(-27768.1 + 16818.6i) q^{57} -4036.28i q^{58} +(-17519.1 + 20199.1i) q^{59} +(10785.6 + 17807.5i) q^{60} +26801.7i q^{61} +4637.13i q^{62} +(-13944.5 + 26678.8i) q^{63} +4096.00 q^{64} +29194.4 q^{65} +(-2645.15 + 1602.11i) q^{66} -69317.7i q^{67} -15887.1i q^{68} +(-52257.1 + 31651.1i) q^{69} -41362.5i q^{70} -15132.9i q^{71} +(-7204.01 + 13782.9i) q^{72} -17212.0i q^{73} -10313.2i q^{74} +(51234.3 - 31031.6i) q^{75} +33321.4 q^{76} +6144.05 q^{77} +(11298.1 + 18653.6i) q^{78} -41543.6 q^{79} -21368.8i q^{80} +(-33708.3 - 48482.3i) q^{81} -48732.9i q^{82} +95126.3 q^{83} +(26428.4 - 16007.1i) q^{84} -82882.8 q^{85} +1750.61i q^{86} +(-8149.06 - 13454.4i) q^{87} +3174.15 q^{88} +121660. q^{89} +(71904.9 + 37583.2i) q^{90} -43327.9i q^{91} +62707.9 q^{92} +(9362.14 + 15457.2i) q^{93} -96152.6 q^{94} -173837. i q^{95} +(13653.5 - 8269.63i) q^{96} -49297.1i q^{97} +5841.18 q^{98} +(-5582.66 + 10680.9i) 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
$3$	−13.3335	+	8.07581i	−0.855342	+	0.518063i
$3$	−13.3335	+	8.07581i	−0.855342	+	0.518063i
$4$	16.0000			0.500000
$5$		−	83.4718i		−	1.49319i	−0.665280	−	0.746594i	$-0.731688\pi$
$5$		−	83.4718i		−	1.49319i	0.665280	−	0.746594i	$-0.268312\pi$
$6$	53.3339	−	32.3032i	0.604818	−	0.366326i
$7$	−123.882			−0.955570			−0.477785	−	0.878477i	$-0.658560\pi$
$7$	−123.882			−0.955570			−0.477785	+	0.878477i	$0.658560\pi$
$8$	−64.0000			−0.353553
$9$	112.563	−	215.357i	0.463221	−	0.886243i
$10$			333.887i			1.05584i
$11$	−49.5960			−0.123585			−0.0617924	−	0.998089i	$-0.519682\pi$
$11$	−49.5960			−0.123585			−0.0617924	+	0.998089i	$0.519682\pi$
$12$	−213.335	+	129.213i	−0.427671	+	0.259032i
$13$			349.752i			0.573986i	0.957933	+	0.286993i	$0.0926557\pi$
$13$			349.752i			0.573986i	−0.957933	+	0.286993i	$0.907344\pi$
$14$	495.527			0.675690
$15$	674.102	+	1112.97i	0.773566	+	1.27719i
$16$	256.000			0.250000
$17$		−	992.945i		−	0.833302i	−0.909066	−	0.416651i	$-0.863204\pi$
$17$		−	992.945i		−	0.833302i	0.909066	−	0.416651i	$-0.136796\pi$
$18$	−450.251	+	861.428i	−0.327547	+	0.626668i
$19$	2082.59			1.32349			0.661743	−	0.749730i	$-0.269817\pi$
$19$	2082.59			1.32349			0.661743	+	0.749730i	$0.269817\pi$
$20$		−	1335.55i		−	0.746594i
$21$	1651.77	−	1000.45i	0.817339	−	0.495046i
$22$	198.384			0.0873877
$23$	3919.24			1.54484			0.772418	−	0.635114i	$-0.219047\pi$
$23$	3919.24			1.54484			0.772418	+	0.635114i	$0.219047\pi$
$24$	853.342	−	516.852i	0.302409	−	0.183163i
$25$	−3842.53			−1.22961
$26$		−	1399.01i		−	0.405870i
$27$	238.332	+	3780.49i	0.0629177	+	0.998019i
$28$	−1982.11			−0.477785
$29$			1009.07i			0.222806i	0.993775	+	0.111403i	$0.0355344\pi$
$29$			1009.07i			0.222806i	−0.993775	+	0.111403i	$0.964466\pi$
$30$	−2696.41	−	4451.87i	−0.546994	−	0.903107i
$31$		−	1159.28i		−	0.216663i	−0.994115	−	0.108332i	$-0.965449\pi$
$31$		−	1159.28i		−	0.216663i	0.994115	−	0.108332i	$-0.0345508\pi$
$32$	−1024.00			−0.176777
$33$	661.287	−	400.528i	0.105707	−	0.0640248i
$34$			3971.78i			0.589234i
$35$			10340.6i			1.42685i
$36$	1801.00	−	3445.71i	0.231610	−	0.443121i
$37$			2578.31i			0.309621i	0.987944	+	0.154811i	$0.0494767\pi$
$37$			2578.31i			0.309621i	−0.987944	+	0.154811i	$0.950523\pi$
$38$	−8330.36			−0.935847
$39$	−2824.53	−	4663.40i	−0.297361	−	0.490955i
$40$			5342.19i			0.527922i
$41$			12183.2i			1.13189i	0.824445	+	0.565943i	$0.191488\pi$
$41$			12183.2i			1.13189i	−0.824445	+	0.565943i	$0.808512\pi$
$42$	−6607.10	+	4001.78i	−0.577946	+	0.350050i
$43$		−	437.653i		−	0.0360959i	−0.999837	−	0.0180480i	$-0.994255\pi$
$43$		−	437.653i		−	0.0360959i	0.999837	−	0.0180480i	$-0.00574516\pi$
$44$	−793.537			−0.0617924
$45$	−17976.2	−	9395.80i	−1.32333	−	0.691676i
$46$	−15677.0			−1.09236
$47$	24038.1			1.58729			0.793645	−	0.608381i	$-0.208181\pi$
$47$	24038.1			1.58729			0.793645	+	0.608381i	$0.208181\pi$
$48$	−3413.37	+	2067.41i	−0.213836	+	0.129516i
$49$	−1460.30			−0.0868861
$50$	15370.1			0.869466
$51$	8018.83	+	13239.4i	0.431703	+	0.712759i
$52$			5596.03i			0.286993i
$53$		−	18010.8i		−	0.880733i	−0.897818	−	0.440366i	$-0.854849\pi$
$53$		−	18010.8i		−	0.880733i	0.897818	−	0.440366i	$-0.145151\pi$
$54$	−953.328	−	15122.0i	−0.0444895	−	0.705706i
$55$			4139.87i			0.184535i
$56$	7928.44			0.337845
$57$	−27768.1	+	16818.6i	−1.13203	+	0.685650i
$58$		−	4036.28i		−	0.157547i
$59$	−17519.1	+	20199.1i	−0.655212	+	0.755445i
$59$	−17519.1	+	20199.1i	−0.655212	+	0.755445i
$60$	10785.6	+	17807.5i	0.386783	+	0.638593i
$61$			26801.7i			0.922228i	0.887341	+	0.461114i	$0.152550\pi$
$61$			26801.7i			0.922228i	−0.887341	+	0.461114i	$0.847450\pi$
$62$			4637.13i			0.153204i
$63$	−13944.5	+	26678.8i	−0.442640	+	0.846867i
$64$	4096.00			0.125000
$65$	29194.4			0.857070
$66$	−2645.15	+	1602.11i	−0.0747464	+	0.0452724i
$67$		−	69317.7i		−	1.88650i	−0.332082	−	0.943251i	$-0.607751\pi$
$67$		−	69317.7i		−	1.88650i	0.332082	−	0.943251i	$-0.392249\pi$
$68$		−	15887.1i		−	0.416651i
$69$	−52257.1	+	31651.1i	−1.32136	+	0.800323i
$70$		−	41362.5i		−	1.00893i
$71$		−	15132.9i		−	0.356267i	−0.984006	−	0.178134i	$-0.942994\pi$
$71$		−	15132.9i		−	0.356267i	0.984006	−	0.178134i	$-0.0570059\pi$
$72$	−7204.01	+	13782.9i	−0.163773	+	0.313334i
$73$		−	17212.0i		−	0.378029i	−0.981974	−	0.189015i	$-0.939471\pi$
$73$		−	17212.0i		−	0.378029i	0.981974	−	0.189015i	$-0.0605293\pi$
$74$		−	10313.2i		−	0.218935i
$75$	51234.3	−	31031.6i	1.05174	−	0.637016i
$76$	33321.4			0.661743
$77$	6144.05			0.118094
$78$	11298.1	+	18653.6i	0.210266	+	0.347157i
$79$	−41543.6			−0.748922			−0.374461	−	0.927243i	$-0.622172\pi$
$79$	−41543.6			−0.748922			−0.374461	+	0.927243i	$0.622172\pi$
$80$		−	21368.8i		−	0.373297i
$81$	−33708.3	−	48482.3i	−0.570853	−	0.821052i
$82$		−	48732.9i		−	0.800364i
$83$	95126.3			1.51567			0.757836	−	0.652445i	$-0.226256\pi$
$83$	95126.3			1.51567			0.757836	+	0.652445i	$0.226256\pi$
$84$	26428.4	−	16007.1i	0.408670	−	0.247523i
$85$	−82882.8			−1.24428
$86$			1750.61i			0.0255237i
$87$	−8149.06	−	13454.4i	−0.115427	−	0.190575i
$88$	3174.15			0.0436938
$89$	121660.			1.62807			0.814037	−	0.580813i	$-0.197265\pi$
$89$	121660.			1.62807			0.814037	+	0.580813i	$0.197265\pi$
$90$	71904.9	+	37583.2i	0.935734	+	0.489089i
$91$		−	43327.9i		−	0.548484i
$92$	62707.9			0.772418
$93$	9362.14	+	15457.2i	0.112245	+	0.185321i
$94$	−96152.6			−1.12238
$95$		−	173837.i		−	1.97621i
$96$	13653.5	−	8269.63i	0.151205	−	0.0915815i
$97$		−	49297.1i		−	0.531976i	−0.963976	−	0.265988i	$-0.914302\pi$
$97$		−	49297.1i		−	0.531976i	0.963976	−	0.265988i	$-0.0856981\pi$
$98$	5841.18			0.0614378
$99$	−5582.66	+	10680.9i	−0.0572471	+	0.109526i
$100$	−61480.5			−0.614805
$101$	20439.8			0.199376			0.0996882	−	0.995019i	$-0.468215\pi$
$101$	20439.8			0.199376			0.0996882	+	0.995019i	$0.468215\pi$
$102$	−32075.3	−	52957.6i	−0.305260	−	0.503997i
$103$		−	113953.i		−	1.05836i	−0.848510	−	0.529179i	$-0.822500\pi$
$103$		−	113953.i		−	1.05836i	0.848510	−	0.529179i	$-0.177500\pi$
$104$		−	22384.1i		−	0.202935i
$105$	−83509.0	−	137876.i	−0.739196	−	1.22044i
$106$			72043.3i			0.622772i
$107$		−	175340.i		−	1.48054i	−0.672309	−	0.740270i	$-0.734697\pi$
$107$		−	175340.i		−	1.48054i	0.672309	−	0.740270i	$-0.265303\pi$
$108$	3813.31	+	60487.8i	0.0314589	+	0.499009i
$109$			83381.3i			0.672206i	0.941825	+	0.336103i	$0.109109\pi$
$109$			83381.3i			0.672206i	−0.941825	+	0.336103i	$0.890891\pi$
$110$		−	16559.5i		−	0.130486i
$111$	−20821.9	−	34377.8i	−0.160403	−	0.264832i
$112$	−31713.7			−0.238892
$113$	72575.1			0.534677			0.267339	−	0.963603i	$-0.413856\pi$
$113$	72575.1			0.534677			0.267339	+	0.963603i	$0.413856\pi$
$114$	111073.	−	67274.4i	0.800469	−	0.484828i
$115$		−	327146.i		−	2.30673i
$116$			16145.1i			0.111403i
$117$	75321.5	+	39369.0i	0.508691	+	0.265882i
$118$	70076.4	−	80796.6i	0.463305	−	0.534180i
$119$			123008.i			0.796279i
$120$	−43142.5	−	71229.9i	−0.273497	−	0.451554i
$121$	−158591.			−0.984727
$122$		−	107207.i		−	0.652114i
$123$	−98389.3	−	162445.i	−0.586388	−	0.968149i
$124$		−	18548.5i		−	0.108332i
$125$			59893.7i			0.342852i
$126$	55777.9	−	106715.i	0.312994	−	0.598825i
$127$	−57264.1			−0.315046			−0.157523	−	0.987515i	$-0.550351\pi$
$127$	−57264.1			−0.315046			−0.157523	+	0.987515i	$0.550351\pi$
$128$	−16384.0			−0.0883883
$129$	3534.40	+	5835.43i	0.0187000	+	0.0308744i
$130$	−116778.			−0.606040
$131$	−339038.			−1.72611			−0.863057	−	0.505106i	$-0.831453\pi$
$131$	−339038.			−1.72611			−0.863057	+	0.505106i	$0.831453\pi$
$132$	10580.6	−	6408.45i	0.0528537	−	0.0320124i
$133$	−257995.			−1.26468
$134$			277271.i			1.33396i
$135$	315564.	−	19894.0i	1.49023	−	0.0939480i
$136$			63548.4i			0.294617i
$137$			225299.i			1.02555i	0.858522	+	0.512776i	$0.171383\pi$
$137$			225299.i			1.02555i	−0.858522	+	0.512776i	$0.828617\pi$
$138$	209028.	−	126604.i	0.934346	−	0.565914i
$139$	68116.2			0.299029			0.149515	−	0.988760i	$-0.452229\pi$
$139$	68116.2			0.299029			0.149515	+	0.988760i	$0.452229\pi$
$140$			165450.i			0.713423i
$141$	−320512.	+	194127.i	−1.35768	+	0.822317i
$142$			60531.5i			0.251919i
$143$		−	17346.3i		−	0.0709360i
$144$	28816.0	−	55131.4i	0.115805	−	0.221561i
$145$	84228.9			0.332691
$146$			68848.2i			0.267307i
$147$	19470.8	−	11793.1i	0.0743174	−	0.0450125i
$148$			41252.9i			0.154811i
$149$	−120297.			−0.443905			−0.221952	−	0.975057i	$-0.571243\pi$
$149$	−120297.			−0.443905			−0.221952	+	0.975057i	$0.571243\pi$
$150$	−204937.	+	124126.i	−0.743691	+	0.450438i
$151$		−	198371.i		−	0.708004i	−0.935245	−	0.354002i	$-0.884821\pi$
$151$		−	198371.i		−	0.708004i	0.935245	−	0.354002i	$-0.115179\pi$
$152$	−133286.			−0.467923
$153$	−213838.	−	111768.i	−0.738508	−	0.386003i
$154$	−24576.2			−0.0835050
$155$	−96767.3			−0.323519
$156$	−45192.5	−	74614.5i	−0.148681	−	0.245477i
$157$		−	600515.i		−	1.94435i	−0.234255	−	0.972175i	$-0.575265\pi$
$157$		−	600515.i		−	1.94435i	0.234255	−	0.972175i	$-0.424735\pi$
$158$	166175.			0.529568
$159$	145452.	+	240147.i	0.456275	+	0.753328i
$160$			85475.1i			0.263961i
$161$	−485523.			−1.47620
$162$	134833.	+	193929.i	0.403654	+	0.580572i
$163$	348306.			1.02682			0.513408	−	0.858145i	$-0.328383\pi$
$163$	348306.			1.02682			0.513408	+	0.858145i	$0.328383\pi$
$164$			194931.i			0.565943i
$165$	−33432.8	−	55198.8i	−0.0956010	−	0.157841i
$166$	−380505.			−1.07174
$167$		−	60096.0i		−	0.166746i	−0.996518	−	0.0833728i	$-0.973431\pi$
$167$		−	60096.0i		−	0.166746i	0.996518	−	0.0833728i	$-0.0265692\pi$
$168$	−105714.	+	64028.5i	−0.288973	+	0.175025i
$169$	248967.			0.670540
$170$	331531.			0.879837
$171$	234422.	−	448500.i	0.613067	−	1.17293i
$172$		−	7002.44i		−	0.0180480i
$173$	71391.0			0.181354			0.0906772	−	0.995880i	$-0.471097\pi$
$173$	71391.0			0.181354			0.0906772	+	0.995880i	$0.471097\pi$
$174$	32596.2	+	53817.6i	0.0816196	+	0.134757i
$175$	476020.			1.17498
$176$	−12696.6			−0.0308962
$177$	70465.9	−	410805.i	0.169062	−	0.985605i
$178$	−486642.			−1.15122
$179$	−360034.			−0.839867			−0.419933	−	0.907555i	$-0.637947\pi$
$179$	−360034.			−0.839867			−0.419933	+	0.907555i	$0.637947\pi$
$180$	−287620.	−	150333.i	−0.661664	−	0.345838i
$181$	24631.3			0.0558844			0.0279422	−	0.999610i	$-0.491105\pi$
$181$	24631.3			0.0558844			0.0279422	+	0.999610i	$0.491105\pi$
$182$			173312.i			0.387837i
$183$	−216446.	−	357360.i	−0.477773	−	0.788821i
$184$	−250832.			−0.546182
$185$	215216.			0.462323
$186$	−37448.5	−	61829.0i	−0.0793693	−	0.131042i
$187$			49246.1i			0.102984i
$188$	384610.			0.793645
$189$	−29525.0	−	468334.i	−0.0601223	−	0.953677i
$190$			695350.i			1.39739i
$191$	701461.			1.39130			0.695649	−	0.718382i	$-0.255117\pi$
$191$	701461.			1.39130			0.695649	+	0.718382i	$0.255117\pi$
$192$	−54613.9	+	33078.5i	−0.106918	+	0.0647579i
$193$	−310272.			−0.599583			−0.299791	−	0.954005i	$-0.596917\pi$
$193$	−310272.			−0.599583			−0.299791	+	0.954005i	$0.596917\pi$
$194$			197188.i			0.376164i
$195$	−389263.	+	235768.i	−0.733088	+	0.444016i
$196$	−23364.7			−0.0434431
$197$		−	229531.i		−	0.421381i	−0.977553	−	0.210691i	$-0.932429\pi$
$197$		−	229531.i		−	0.421381i	0.977553	−	0.210691i	$-0.0675713\pi$
$198$	22330.6	−	42723.4i	0.0404798	−	0.0774467i
$199$	874890.			1.56610			0.783052	−	0.621956i	$-0.213662\pi$
$199$	874890.			1.56610			0.783052	+	0.621956i	$0.213662\pi$
$200$	245922.			0.434733
$201$	559796.	+	924245.i	0.977327	+	1.61360i
$202$	−81759.3			−0.140980
$203$		−	125005.i		−	0.212906i
$204$	128301.	+	211830.i	0.215852	+	0.356379i
$205$	1.01695e6			1.69012
$206$			455812.i			0.748373i
$207$	441160.	−	844037.i	0.715600	−	1.36910i
$208$			89536.5i			0.143497i
$209$	−103288.			−0.163563
$210$	334036.	+	551506.i	0.522691	+	0.862982i
$211$			634.451i			0.000981051i	1.00000		0.000490526i	$0.000156139\pi$
$211$			634.451i			0.000981051i	−1.00000		0.000490526i	$0.999844\pi$
$212$		−	288173.i		−	0.440366i
$213$	122210.	+	201774.i	0.184569	+	0.304730i
$214$			701358.i			1.04690i
$215$	−36531.6			−0.0538980
$216$	−15253.2	−	241951.i	−0.0222448	−	0.352853i
$217$			143614.i			0.207037i
$218$		−	333525.i		−	0.475321i
$219$	139001.	+	229496.i	0.195843	+	0.323344i
$220$			66237.9i			0.0922677i
$221$	347284.			0.478304
$222$	83287.7	+	137511.i	0.113422	+	0.187265i
$223$	−550857.			−0.741783			−0.370891	−	0.928676i	$-0.620948\pi$
$223$	−550857.			−0.741783			−0.370891	+	0.928676i	$0.620948\pi$
$224$	126855.			0.168922
$225$	−432526.	+	827517.i	−0.569581	+	1.08973i
$226$	−290300.			−0.378074
$227$	291191.			0.375071			0.187535	−	0.982258i	$-0.439950\pi$
$227$	291191.			0.375071			0.187535	+	0.982258i	$0.439950\pi$
$228$	−444290.	+	269097.i	−0.566017	+	0.342825i
$229$			996785.i			1.25607i	0.778186	+	0.628033i	$0.216140\pi$
$229$			996785.i			1.25607i	−0.778186	+	0.628033i	$0.783860\pi$
$230$			1.30858e6i			1.63111i
$231$	−81921.4	+	49618.1i	−0.101011	+	0.0611802i
$232$		−	64580.5i		−	0.0787737i
$233$	−1.44079e6			−1.73865			−0.869325	−	0.494241i	$-0.835446\pi$
$233$	−1.44079e6			−1.73865			−0.869325	+	0.494241i	$0.835446\pi$
$234$	−301286.	−	157476.i	−0.359699	−	0.188007i
$235$		−	2.00651e6i		−	2.37012i
$236$	−280306.	+	323186.i	−0.327606	+	0.377723i
$237$	553921.	−	335498.i	0.640585	−	0.387989i
$238$		−	492031.i		−	0.563054i
$239$		−	223954.i		−	0.253609i	−0.991928	−	0.126805i	$-0.959528\pi$
$239$		−	223954.i		−	0.253609i	0.991928	−	0.126805i	$-0.0404721\pi$
$240$	172570.	+	284920.i	0.193391	+	0.319297i
$241$	−1.25588e6			−1.39285			−0.696426	−	0.717629i	$-0.745227\pi$
$241$	−1.25588e6			−1.39285			−0.696426	+	0.717629i	$0.745227\pi$
$242$	634365.			0.696307
$243$	840982.	+	374215.i	0.913632	+	0.406543i
$244$			428828.i			0.461114i
$245$			121893.i			0.129737i
$246$	393557.	+	649778.i	0.414639	+	0.684585i
$247$			728389.i			0.759663i
$248$			74194.0i			0.0766019i
$249$	−1.26836e6	+	768222.i	−1.29642	+	0.785215i
$250$		−	239575.i		−	0.242433i
$251$			359598.i			0.360274i	0.983641	+	0.180137i	$0.0576542\pi$
$251$			359598.i			0.360274i	−0.983641	+	0.180137i	$0.942346\pi$
$252$	−223111.	+	426861.i	−0.221320	+	0.423434i
$253$	−194379.			−0.190918
$254$	229057.			0.222771
$255$	1.10512e6	−	669346.i	1.06428	−	0.644614i
$256$	65536.0			0.0625000
$257$		−	1.51002e6i		−	1.42610i	−0.701113	−	0.713050i	$-0.747313\pi$
$257$		−	1.51002e6i		−	1.42610i	0.701113	−	0.713050i	$-0.252687\pi$
$258$	−14137.6	−	23341.7i	−0.0132229	−	0.0218315i
$259$		−	319406.i		−	0.295865i
$260$	467110.			0.428535
$261$	217310.	+	113584.i	0.197460	+	0.103208i
$262$	1.35615e6			1.22055
$263$			1.66472e6i			1.48406i	0.670367	+	0.742029i	$0.266137\pi$
$263$			1.66472e6i			1.48406i	−0.670367	+	0.742029i	$0.733863\pi$
$264$	−42322.4	+	25633.8i	−0.0373732	+	0.0226362i
$265$	−1.50340e6			−1.31510
$266$	1.03198e6			0.894267
$267$	−1.62215e6	+	982506.i	−1.39256	+	0.843446i
$268$		−	1.10908e6i		−	0.943251i
$269$	−1.00523e6			−0.847004			−0.423502	−	0.905895i	$-0.639199\pi$
$269$	−1.00523e6			−0.847004			−0.423502	+	0.905895i	$0.639199\pi$
$270$	−1.26226e6	+	79575.9i	−1.05375	+	0.0664312i
$271$	−1.29510e6			−1.07122			−0.535612	−	0.844464i	$-0.679919\pi$
$271$	−1.29510e6			−1.07122			−0.535612	+	0.844464i	$0.679919\pi$
$272$		−	254194.i		−	0.208326i
$273$	349908.	+	577711.i	0.284150	+	0.469142i
$274$		−	901196.i		−	0.725175i
$275$	190574.			0.151961
$276$	−836113.	+	506417.i	−0.660682	+	0.400162i
$277$	−371136.			−0.290625			−0.145313	−	0.989386i	$-0.546419\pi$
$277$	−371136.			−0.290625			−0.145313	+	0.989386i	$0.546419\pi$
$278$	−272465.			−0.211446
$279$	−249659.	−	130492.i	−0.192016	−	0.100363i
$280$		−	661800.i		−	0.504466i
$281$		−	1.20986e6i		−	0.914047i	−0.889455	−	0.457023i	$-0.848916\pi$
$281$		−	1.20986e6i		−	0.914047i	0.889455	−	0.457023i	$-0.151084\pi$
$282$	1.28205e6	−	776510.i	0.960022	−	0.581466i
$283$			704548.i			0.522931i	0.965213	+	0.261466i	$0.0842058\pi$
$283$			704548.i			0.522931i	−0.965213	+	0.261466i	$0.915794\pi$
$284$		−	242126.i		−	0.178134i
$285$	1.40388e6	+	2.31785e6i	1.02380	+	1.69034i
$286$			69385.2i			0.0501593i
$287$		−	1.50928e6i		−	1.08160i
$288$	−115264.	+	220526.i	−0.0818866	+	0.156667i
$289$	433918.			0.305607
$290$	−336915.			−0.235248
$291$	398114.	+	657301.i	0.275597	+	0.455021i
$292$		−	275393.i		−	0.189015i
$293$			209264.i			0.142405i	0.997462	+	0.0712026i	$0.0226837\pi$
$293$			209264.i			0.142405i	−0.997462	+	0.0712026i	$0.977316\pi$
$294$	−77883.2	+	47172.3i	−0.0525503	+	0.0318287i
$295$	1.68606e6	+	1.46235e6i	1.12802	+	0.978355i
$296$		−	165012.i		−	0.109468i
$297$	−11820.3	−	187497.i	−0.00777567	−	0.123340i
$298$	481189.			0.313888
$299$			1.37076e6i			0.886715i
$300$	819749.	−	496505.i	0.525869	−	0.318508i
$301$			54217.2i			0.0344922i
$302$			793484.i			0.500634i
$303$	−272534.	+	165068.i	−0.170535	+	0.103290i
$304$	533143.			0.330872
$305$	2.23719e6			1.37706
$306$	855350.	+	447074.i	0.522204	+	0.272945i
$307$	−2.53595e6			−1.53566			−0.767829	−	0.640655i	$-0.778663\pi$
$307$	−2.53595e6			−1.53566			−0.767829	+	0.640655i	$0.778663\pi$
$308$	98304.7			0.0590470
$309$	920263.	+	1.51939e6i	0.548297	+	0.905259i
$310$	387069.			0.228762
$311$		−	95828.3i		−	0.0561814i	−0.999605	−	0.0280907i	$-0.991057\pi$
$311$		−	95828.3i		−	0.0561814i	0.999605	−	0.0280907i	$-0.00894273\pi$
$312$	180770.	+	298458.i	0.105133	+	0.173579i
$313$		−	473579.i		−	0.273232i	−0.990624	−	0.136616i	$-0.956377\pi$
$313$		−	473579.i		−	0.273232i	0.990624	−	0.136616i	$-0.0436226\pi$
$314$			2.40206e6i			1.37486i
$315$	2.22693e6	+	1.16397e6i	1.26453	+	0.660944i
$316$	−664698.			−0.374461
$317$		−	855413.i		−	0.478110i	−0.971006	−	0.239055i	$-0.923162\pi$
$317$		−	855413.i		−	0.478110i	0.971006	−	0.239055i	$-0.0768376\pi$
$318$	−581808.	−	960587.i	−0.322635	−	0.532683i
$319$		−	50045.9i		−	0.0275354i
$320$		−	341900.i		−	0.186649i
$321$	1.41601e6	+	2.33788e6i	0.767014	+	1.26637i
$322$	1.94209e6			1.04383
$323$		−	2.06790e6i		−	1.10286i
$324$	−539333.	−	775717.i	−0.285427	−	0.410526i
$325$		−	1.34393e6i		−	0.705780i
$326$	−1.39323e6			−0.726068
$327$	−673371.	−	1.11176e6i	−0.348245	−	0.574966i
$328$		−	779726.i		−	0.400182i
$329$	−2.97789e6			−1.51677
$330$	133731.	+	220795.i	0.0676001	+	0.111610i
$331$	−1.41824e6			−0.711506			−0.355753	−	0.934580i	$-0.615776\pi$
$331$	−1.41824e6			−0.711506			−0.355753	+	0.934580i	$0.615776\pi$
$332$	1.52202e6			0.757836
$333$	555257.	+	290221.i	0.274400	+	0.143423i
$334$			240384.i			0.117907i
$335$	−5.78607e6			−2.81690
$336$	422854.	−	256114.i	0.204335	−	0.123761i
$337$			910389.i			0.436669i	0.975874	+	0.218335i	$0.0700624\pi$
$337$			910389.i			0.436669i	−0.975874	+	0.218335i	$0.929938\pi$
$338$	−995867.			−0.474143
$339$	−967678.	+	586103.i	−0.457332	+	0.276997i
$340$	−1.32613e6			−0.622139
$341$			57495.8i			0.0267763i
$342$	−937687.	+	1.79400e6i	−0.433504	+	0.829387i
$343$	2.26299e6			1.03860
$344$			28009.8i			0.0127618i
$345$	2.64197e6	+	4.36199e6i	1.19503	+	1.97305i
$346$	−285564.			−0.128237
$347$	2.74870e6			1.22547			0.612737	−	0.790287i	$-0.290069\pi$
$347$	2.74870e6			1.22547			0.612737	+	0.790287i	$0.290069\pi$
$348$	−130385.	−	215270.i	−0.0577137	−	0.0952876i
$349$		−	1.34806e6i		−	0.592440i	−0.955120	−	0.296220i	$-0.904274\pi$
$349$		−	1.34806e6i		−	0.592440i	0.955120	−	0.296220i	$-0.0957261\pi$
$350$	−1.90408e6			−0.830836
$351$	−1.32223e6	+	83357.0i	−0.572849	+	0.0361139i
$352$	50786.3			0.0218469
$353$	−1.00614e6			−0.429756			−0.214878	−	0.976641i	$-0.568935\pi$
$353$	−1.00614e6			−0.429756			−0.214878	+	0.976641i	$0.568935\pi$
$354$	−281864.	+	1.64322e6i	−0.119545	+	0.696928i
$355$	−1.26317e6			−0.531974
$356$	1.94657e6			0.814037
$357$	−993387.	−	1.64012e6i	−0.412523	−	0.681091i
$358$	1.44013e6			0.593875
$359$		−	3.81028e6i		−	1.56035i	−0.625563	−	0.780174i	$-0.715131\pi$
$359$		−	3.81028e6i		−	1.56035i	0.625563	−	0.780174i	$-0.284869\pi$
$360$	1.15048e6	+	601331.i	0.467867	+	0.244544i
$361$	1.86108e6			0.751618
$362$	−98525.2			−0.0395163
$363$	2.11457e6	−	1.28075e6i	0.842278	−	0.510151i
$364$		−	693246.i		−	0.274242i
$365$	−1.43672e6			−0.564469
$366$	865783.	+	1.42944e6i	0.337836	+	0.557781i
$367$			3.66548e6i			1.42058i	0.703909	+	0.710290i	$0.251436\pi$
$367$			3.66548e6i			1.42058i	−0.703909	+	0.710290i	$0.748564\pi$
$368$	1.00333e6			0.386209
$369$	2.62374e6	+	1.37138e6i	1.00313	+	0.524313i
$370$	−860864.			−0.326911
$371$			2.23121e6i			0.841602i
$372$	149794.	+	247316.i	0.0561226	+	0.0926605i
$373$	−2.73328e6			−1.01721			−0.508607	−	0.860999i	$-0.669839\pi$
$373$	−2.73328e6			−1.01721			−0.508607	+	0.860999i	$0.669839\pi$
$374$		−	196984.i		−	0.0728204i
$375$	−483690.	−	798591.i	−0.177619	−	0.293256i
$376$	−1.53844e6			−0.561192
$377$	−352924.			−0.127887
$378$	118100.	+	1.87334e6i	0.0425129	+	0.674351i
$379$	1.06476e6			0.380761			0.190380	−	0.981710i	$-0.439028\pi$
$379$	1.06476e6			0.380761			0.190380	+	0.981710i	$0.439028\pi$
$380$		−	2.78140e6i		−	0.988107i
$381$	763529.	−	462454.i	0.269472	−	0.163214i
$382$	−2.80585e6			−0.983797
$383$		−	4.45191e6i		−	1.55078i	−0.631485	−	0.775388i	$-0.717554\pi$
$383$		−	4.45191e6i		−	1.55078i	0.631485	−	0.775388i	$-0.282446\pi$
$384$	218456.	−	132314.i	0.0756023	−	0.0457908i
$385$		−	512854.i		−	0.176336i
$386$	1.24109e6			0.423969
$387$	−94251.5	−	49263.3i	−0.0319898	−	0.0167204i
$388$		−	788753.i		−	0.265988i
$389$			4.52828e6i			1.51726i	0.651523	+	0.758629i	$0.274130\pi$
$389$			4.52828e6i			1.51726i	−0.651523	+	0.758629i	$0.725870\pi$
$390$	1.55705e6	−	943073.i	0.518371	−	0.313967i
$391$		−	3.89159e6i		−	1.28732i
$392$	93458.9			0.0307189
$393$	4.52055e6	−	2.73800e6i	1.47642	−	0.894237i
$394$			918123.i			0.297962i
$395$			3.46772e6i			1.11828i
$396$	−89322.6	+	170894.i	−0.0286235	+	0.0547631i
$397$		−	2.82711e6i		−	0.900257i	−0.892964	−	0.450129i	$-0.851378\pi$
$397$		−	2.82711e6i		−	0.900257i	0.892964	−	0.450129i	$-0.148622\pi$
$398$	−3.49956e6			−1.10740
$399$	3.43997e6	−	2.08352e6i	1.08174	−	0.655187i
$400$	−983688.			−0.307403
$401$	282437.			0.0877123			0.0438562	−	0.999038i	$-0.486036\pi$
$401$	282437.			0.0877123			0.0438562	+	0.999038i	$0.486036\pi$
$402$	−2.23919e6	−	3.69698e6i	−0.691075	−	1.14099i
$403$	405461.			0.124362
$404$	327037.			0.0996882
$405$	−4.04690e6	+	2.81369e6i	−1.22599	+	0.852391i
$406$			500022.i			0.150548i
$407$		−	127874.i		−	0.0382645i
$408$	−513205.	−	847321.i	−0.152630	−	0.251998i
$409$		−	5.30731e6i		−	1.56879i	−0.620259	−	0.784397i	$-0.712972\pi$
$409$		−	5.30731e6i		−	1.56879i	0.620259	−	0.784397i	$-0.287028\pi$
$410$	−4.06782e6			−1.19509
$411$	−1.81947e6	−	3.00402e6i	−0.531301	−	0.877198i
$412$		−	1.82325e6i		−	0.529179i
$413$	2.17030e6	−	2.50231e6i	0.626101	−	0.721881i
$414$	−1.76464e6	+	3.37615e6i	−0.506006	+	0.968100i
$415$		−	7.94036e6i		−	2.26318i
$416$		−	358146.i		−	0.101467i
$417$	−908225.	+	550093.i	−0.255772	+	0.154916i
$418$	413153.			0.115656
$419$	1.01232e6			0.281697			0.140848	−	0.990031i	$-0.455017\pi$
$419$	1.01232e6			0.281697			0.140848	+	0.990031i	$0.455017\pi$
$420$	−1.33614e6	−	2.20602e6i	−0.369598	−	0.610221i
$421$			614149.i			0.168876i	0.996429	+	0.0844381i	$0.0269095\pi$
$421$			614149.i			0.168876i	−0.996429	+	0.0844381i	$0.973090\pi$
$422$		−	2537.80i		−	0.000693708i
$423$	2.70580e6	−	5.17678e6i	0.735266	−	1.40672i
$424$			1.15269e6i			0.311386i
$425$			3.81542e6i			1.02464i
$426$	−488841.	−	807095.i	−0.130510	−	0.215477i
$427$		−	3.32025e6i		−	0.881254i
$428$		−	2.80543e6i		−	0.740270i
$429$	140085.	+	231286.i	0.0367494	+	0.0606746i
$430$	146126.			0.0381117
$431$	−1.70105e6			−0.441086			−0.220543	−	0.975377i	$-0.570783\pi$
$431$	−1.70105e6			−0.441086			−0.220543	+	0.975377i	$0.570783\pi$
$432$	61013.0	+	967805.i	0.0157294	+	0.249505i
$433$	−3.76932e6			−0.966148			−0.483074	−	0.875580i	$-0.660480\pi$
$433$	−3.76932e6			−0.966148			−0.483074	+	0.875580i	$0.660480\pi$
$434$		−	574456.i		−	0.146397i
$435$	−1.12306e6	+	680216.i	−0.284565	+	0.172355i
$436$			1.33410e6i			0.336103i
$437$	8.16217e6			2.04457
$438$	−556005.	−	917985.i	−0.138482	−	0.228639i
$439$	−7.29868e6			−1.80752			−0.903760	−	0.428039i	$-0.859205\pi$
$439$	−7.29868e6			−1.80752			−0.903760	+	0.428039i	$0.859205\pi$
$440$		−	264952.i		−	0.0652431i
$441$	−164375.	+	314485.i	−0.0402475	+	0.0770022i
$442$	−1.38914e6			−0.338212
$443$	−1.67725e6			−0.406058			−0.203029	−	0.979173i	$-0.565079\pi$
$443$	−1.67725e6			−0.406058			−0.203029	+	0.979173i	$0.565079\pi$
$444$	−333151.	−	550045.i	−0.0802017	−	0.132416i
$445$		−	1.01552e7i		−	2.43102i
$446$	2.20343e6			0.524520
$447$	1.60398e6	−	971497.i	0.379691	−	0.229971i
$448$	−507420.			−0.119446
$449$		−	1.02996e6i		−	0.241103i	−0.992707	−	0.120552i	$-0.961534\pi$
$449$		−	1.02996e6i		−	0.241103i	0.992707	−	0.120552i	$-0.0384664\pi$
$450$	1.73010e6	−	3.31007e6i	0.402755	−	0.770558i
$451$		−	604239.i		−	0.139884i
$452$	1.16120e6			0.267339
$453$	1.60201e6	+	2.64497e6i	0.366791	+	0.605586i
$454$	−1.16476e6			−0.265215
$455$	−3.61666e6			−0.818990
$456$	1.77716e6	−	1.07639e6i	0.400235	−	0.242414i
$457$			6.68240e6i			1.49672i	0.663290	+	0.748362i	$0.269160\pi$
$457$			6.68240e6i			1.49672i	−0.663290	+	0.748362i	$0.730840\pi$
$458$		−	3.98714e6i		−	0.888173i
$459$	3.75382e6	−	236650.i	0.831651	−	0.0524295i
$460$		−	5.23434e6i		−	1.15337i
$461$		−	2.75947e6i		−	0.604746i	−0.953190	−	0.302373i	$-0.902221\pi$
$461$		−	2.75947e6i		−	0.604746i	0.953190	−	0.302373i	$-0.0977787\pi$
$462$	327686.	−	198473.i	0.0714254	−	0.0432609i
$463$			5.12622e6i			1.11133i	0.831405	+	0.555667i	$0.187537\pi$
$463$			5.12622e6i			1.11133i	−0.831405	+	0.555667i	$0.812463\pi$
$464$			258322.i			0.0557014i
$465$	1.29024e6	−	781474.i	0.276719	−	0.167603i
$466$	5.76318e6			1.22941
$467$	1.45600e6			0.308936			0.154468	−	0.987998i	$-0.450634\pi$
$467$	1.45600e6			0.308936			0.154468	+	0.987998i	$0.450634\pi$
$468$	1.20514e6	+	629904.i	0.254346	+	0.132941i
$469$			8.58720e6i			1.80268i
$470$			8.02602e6i			1.67593i
$471$	4.84964e6	+	8.00694e6i	1.00730	+	1.66308i
$472$	1.12122e6	−	1.29275e6i	0.231652	−	0.267090i
$473$			21705.8i			0.00446091i
$474$	−2.21568e6	+	1.34199e6i	−0.452962	+	0.274350i
$475$	−8.00242e6			−1.62737
$476$			1.96812e6i			0.398139i
$477$	−3.87876e6	−	2.02735e6i	−0.780543	−	0.407974i
$478$			895818.i			0.179329i
$479$		−	1.92485e6i		−	0.383317i	−0.981462	−	0.191658i	$-0.938613\pi$
$479$		−	1.92485e6i		−	0.383317i	0.981462	−	0.191658i	$-0.0613866\pi$
$480$	−690280.	−	1.13968e6i	−0.136748	−	0.225777i
$481$	−901768.			−0.177718
$482$	5.02351e6			0.984894
$483$	6.47370e6	−	3.92099e6i	1.26266	−	0.764765i
$484$	−2.53746e6			−0.492363
$485$	−4.11491e6			−0.794340
$486$	−3.36393e6	−	1.49686e6i	−0.646035	−	0.287469i
$487$	2.21716e6			0.423617			0.211809	−	0.977311i	$-0.432065\pi$
$487$	2.21716e6			0.423617			0.211809	+	0.977311i	$0.432065\pi$
$488$		−	1.71531e6i		−	0.326057i
$489$	−4.64413e6	+	2.81286e6i	−0.878279	+	0.531956i
$490$		−	487574.i		−	0.0917382i
$491$		−	8.44469e6i		−	1.58081i	−0.612584	−	0.790406i	$-0.709870\pi$
$491$		−	8.44469e6i		−	1.58081i	0.612584	−	0.790406i	$-0.290130\pi$
$492$	−1.57423e6	−	2.59911e6i	−0.293194	−	0.484075i
$493$	1.00195e6			0.185665
$494$		−	2.91356e6i		−	0.537163i
$495$	891550.	+	465994.i	0.163543	+	0.0854806i
$496$		−	296776.i		−	0.0541658i
$497$			1.87469e6i			0.340438i
$498$	5.07345e6	−	3.07289e6i	0.916707	−	0.555231i
$499$	−2.57302e6			−0.462584			−0.231292	−	0.972884i	$-0.574295\pi$
$499$	−2.57302e6			−0.462584			−0.231292	+	0.972884i	$0.574295\pi$
$500$			958300.i			0.171426i
$501$	485324.	+	801288.i	0.0863848	+	0.142625i
$502$		−	1.43839e6i		−	0.254753i
$503$	6.79019e6			1.19664			0.598318	−	0.801259i	$-0.295836\pi$
$503$	6.79019e6			1.19664			0.598318	+	0.801259i	$0.295836\pi$
$504$	892446.	−	1.70744e6i	0.156497	−	0.299413i
$505$		−	1.70615e6i		−	0.297706i
$506$	777516.			0.135000
$507$	−3.31959e6	+	2.01061e6i	−0.573541	+	0.347382i
$508$	−916226.			−0.157523
$509$	6.16337e6			1.05444			0.527222	−	0.849728i	$-0.323234\pi$
$509$	6.16337e6			1.05444			0.527222	+	0.849728i	$0.323234\pi$
$510$	−4.42046e6	+	2.67738e6i	−0.752562	+	0.455811i
$511$			2.13226e6i			0.361233i
$512$	−262144.			−0.0441942
$513$	496348.	+	7.87321e6i	0.0832708	+	1.32086i
$514$			6.04008e6i			1.00840i
$515$	−9.51186e6			−1.58033
$516$	56550.4	+	93366.8i	0.00934999	+	0.0154372i
$517$	−1.19220e6			−0.196165
$518$			1.27762e6i			0.209208i
$519$	−951889.	+	576540.i	−0.155120	+	0.0939531i
$520$	−1.86844e6			−0.303020
$521$			2.62880e6i			0.424291i	0.977238	+	0.212146i	$0.0680451\pi$
$521$			2.62880e6i			0.424291i	−0.977238	+	0.212146i	$0.931955\pi$
$522$	−869241.	−	454334.i	−0.139625	−	0.0729792i
$523$	2.50488e6			0.400436			0.200218	−	0.979751i	$-0.435835\pi$
$523$	2.50488e6			0.400436			0.200218	+	0.979751i	$0.435835\pi$
$524$	−5.42460e6			−0.863057
$525$	−6.34700e6	+	3.84425e6i	−1.00501	+	0.608713i
$526$		−	6.65887e6i		−	1.04939i
$527$	−1.15110e6			−0.180546
$528$	169289.	−	102535.i	0.0264268	−	0.0160062i
$529$	8.92412e6			1.38652
$530$	6.01358e6			0.929916
$531$	2.37803e6	+	6.04653e6i	0.366000	+	0.930615i
$532$	−4.12792e6			−0.632342
$533$	−4.26110e6			−0.649687
$534$	6.48862e6	−	3.93002e6i	0.984689	−	0.596406i
$535$	−1.46359e7			−2.21073
$536$			4.43633e6i			0.666979i
$537$	4.80050e6	−	2.90756e6i	0.718374	−	0.435104i
$538$	4.02093e6			0.598923
$539$	72424.9			0.0107378
$540$	5.04903e6	−	318304.i	0.745115	−	0.0469740i
$541$			1.17067e7i			1.71965i	0.510588	+	0.859825i	$0.329428\pi$
$541$			1.17067e7i			1.71965i	−0.510588	+	0.859825i	$0.670572\pi$
$542$	5.18040e6			0.757469
$543$	−328421.	+	198918.i	−0.0478003	+	0.0289517i
$544$			1.01678e6i			0.147308i
$545$	6.95998e6			1.00373
$546$	−1.39963e6	−	2.31084e6i	−0.200924	−	0.331733i
$547$	9.24318e6			1.32085			0.660424	−	0.750893i	$-0.270376\pi$
$547$	9.24318e6			1.32085			0.660424	+	0.750893i	$0.270376\pi$
$548$			3.60478e6i			0.512776i
$549$	5.77194e6	+	3.01688e6i	0.817318	+	0.427195i
$550$	−762298.			−0.107453
$551$			2.10148e6i			0.294880i
$552$	3.34445e6	−	2.02567e6i	0.467173	−	0.282957i
$553$	5.14650e6			0.715647
$554$	1.48454e6			0.205503
$555$	−2.86957e6	+	1.73804e6i	−0.395444	+	0.239512i
$556$	1.08986e6			0.149515
$557$		−	6.68503e6i		−	0.912989i	−0.889726	−	0.456494i	$-0.849105\pi$
$557$		−	6.68503e6i		−	0.912989i	0.889726	−	0.456494i	$-0.150895\pi$
$558$	998638.	+	521967.i	0.135776	+	0.0709672i
$559$	153070.			0.0207186
$560$			2.64720e6i			0.356711i
$561$	−397702.	−	656621.i	−0.0533520	−	0.0880862i
$562$			4.83943e6i			0.646329i
$563$	7.37241e6			0.980253			0.490127	−	0.871651i	$-0.336951\pi$
$563$	7.37241e6			0.980253			0.490127	+	0.871651i	$0.336951\pi$
$564$	−5.12819e6	+	3.10604e6i	−0.678838	+	0.411158i
$565$		−	6.05797e6i		−	0.798374i
$566$		−	2.81819e6i		−	0.369768i
$567$	4.17585e6	+	6.00608e6i	0.545490	+	0.784573i
$568$			968504.i			0.125959i
$569$	1.20608e7			1.56169			0.780844	−	0.624726i	$-0.214790\pi$
$569$	1.20608e7			1.56169			0.780844	+	0.624726i	$0.214790\pi$
$570$	−5.61551e6	−	9.27142e6i	−0.723939	−	1.19525i
$571$		−	5.25538e6i		−	0.674550i	−0.941406	−	0.337275i	$-0.890495\pi$
$571$		−	5.25538e6i		−	0.674550i	0.941406	−	0.337275i	$-0.109505\pi$
$572$		−	277541.i		−	0.0354680i
$573$	−9.35291e6	+	5.66487e6i	−1.19004	+	0.720781i
$574$			6.03712e6i			0.764803i
$575$	−1.50598e7			−1.89955
$576$	461057.	−	882102.i	0.0579026	−	0.110780i
$577$	−4.25031e6			−0.531473			−0.265737	−	0.964046i	$-0.585615\pi$
$577$	−4.25031e6			−0.531473			−0.265737	+	0.964046i	$0.585615\pi$
$578$	−1.73567e6			−0.216097
$579$	4.13700e6	−	2.50570e6i	0.512849	−	0.310622i
$580$	1.34766e6			0.166345
$581$	−1.17844e7			−1.44833
$582$	−1.59246e6	−	2.62920e6i	−0.194877	−	0.321749i
$583$			893266.i			0.108845i
$584$			1.10157e6i			0.133653i
$585$	3.28620e6	−	6.28722e6i	0.397012	−	0.759572i
$586$		−	837057.i		−	0.100696i
$587$	8.55612e6			1.02490			0.512450	−	0.858717i	$-0.328738\pi$
$587$	8.55612e6			1.02490			0.512450	+	0.858717i	$0.328738\pi$
$588$	311533.	−	188689.i	0.0371587	−	0.0225063i
$589$		−	2.41431e6i		−	0.286751i
$590$	−6.74423e6	−	5.84940e6i	−0.797632	−	0.691801i
$591$	1.85365e6	+	3.06044e6i	0.218302	+	0.360425i
$592$			660047.i			0.0774053i
$593$		−	5.09022e6i		−	0.594429i	−0.954811	−	0.297214i	$-0.903942\pi$
$593$		−	5.09022e6i		−	0.594429i	0.954811	−	0.297214i	$-0.0960576\pi$
$594$	47281.3	+	749989.i	0.00549823	+	0.0872145i
$595$	1.02677e7			1.18899
$596$	−1.92476e6			−0.221952
$597$	−1.16653e7	+	7.06544e6i	−1.33956	+	0.811341i
$598$		−	5.48305e6i		−	0.627002i
$599$		−	6.84215e6i		−	0.779159i	−0.920993	−	0.389579i	$-0.872620\pi$
$599$		−	6.84215e6i		−	0.779159i	0.920993	−	0.389579i	$-0.127380\pi$
$600$	−3.27899e6	+	1.98602e6i	−0.371845	+	0.225219i
$601$		−	8.05004e6i		−	0.909101i	−0.890721	−	0.454550i	$-0.849800\pi$
$601$		−	8.05004e6i		−	0.909101i	0.890721	−	0.454550i	$-0.150200\pi$
$602$		−	216869.i		−	0.0243897i
$603$	−1.49281e7	−	7.80258e6i	−1.67190	−	0.873866i
$604$		−	3.17393e6i		−	0.354002i
$605$			1.32379e7i			1.47038i
$606$	1.09013e6	−	660272.i	0.120587	−	0.0730368i
$607$	−2.39056e6			−0.263346			−0.131673	−	0.991293i	$-0.542035\pi$
$607$	−2.39056e6			−0.263346			−0.131673	+	0.991293i	$0.542035\pi$
$608$	−2.13257e6			−0.233962
$609$	1.00952e6	+	1.66676e6i	0.110299	+	0.182108i
$610$	−8.94875e6			−0.973729
$611$			8.40738e6i			0.911083i
$612$	−3.42140e6	−	1.78830e6i	−0.369254	−	0.193002i
$613$			589107.i			0.0633203i	0.999499	+	0.0316602i	$0.0100794\pi$
$613$			589107.i			0.0633203i	−0.999499	+	0.0316602i	$0.989921\pi$
$614$	1.01438e7			1.08587
$615$	−1.35595e7	+	8.21273e6i	−1.44563	+	0.875588i
$616$	−393219.			−0.0417525
$617$		−	689630.i		−	0.0729295i	−0.999335	−	0.0364647i	$-0.988390\pi$
$617$		−	689630.i		−	0.0729295i	0.999335	−	0.0364647i	$-0.0116097\pi$
$618$	−3.68105e6	−	6.07756e6i	−0.387705	−	0.640115i
$619$	1.26104e7			1.32282			0.661412	−	0.750023i	$-0.269958\pi$
$619$	1.26104e7			1.32282			0.661412	+	0.750023i	$0.269958\pi$
$620$	−1.54828e6			−0.161759
$621$	934081.	+	1.48167e7i	0.0971976	+	1.54178i
$622$			383313.i			0.0397263i
$623$	−1.50715e7			−1.55574
$624$	−723079.	−	1.19383e6i	−0.0743403	−	0.122739i
$625$	−7.00848e6			−0.717668
$626$			1.89431e6i			0.193204i
$627$	1.37719e6	−	834135.i	0.139902	−	0.0847360i
$628$		−	9.60823e6i		−	0.972175i
$629$	2.56012e6			0.258008
$630$	−8.90771e6	−	4.65588e6i	−0.894159	−	0.467358i
$631$	1.55072e6			0.155046			0.0775229	−	0.996991i	$-0.475299\pi$
$631$	1.55072e6			0.155046			0.0775229	+	0.996991i	$0.475299\pi$
$632$	2.65879e6			0.264784
$633$	−5123.70	−	8459.43i	−0.000508247	−	0.000839135i
$634$			3.42165e6i			0.338075i
$635$			4.77994e6i			0.470422i
$636$	2.32723e6	+	3.84235e6i	0.228138	+	0.376664i
$637$		−	510741.i		−	0.0498715i
$638$			200184.i			0.0194705i
$639$	−3.25897e6	−	1.70340e6i	−0.315739	−	0.165030i
$640$			1.36760e6i			0.131980i
$641$			7.63268e6i			0.733723i	0.930276	+	0.366861i	$0.119568\pi$
$641$			7.63268e6i			0.733723i	−0.930276	+	0.366861i	$0.880432\pi$
$642$	−5.66403e6	−	9.35153e6i	−0.542361	−	0.895458i
$643$	−1.06287e7			−1.01380			−0.506901	−	0.862004i	$-0.669209\pi$
$643$	−1.06287e7			−1.01380			−0.506901	+	0.862004i	$0.669209\pi$
$644$	−7.76837e6			−0.738100
$645$	487093.	−	295022.i	0.0461013	−	0.0279226i
$646$			8.27158e6i			0.779843i
$647$		−	2.08270e7i		−	1.95598i	−0.208645	−	0.977991i	$-0.566905\pi$
$647$		−	2.08270e7i		−	1.95598i	0.208645	−	0.977991i	$-0.433095\pi$
$648$	2.15733e6	+	3.10287e6i	0.201827	+	0.290286i
$649$	868878.	−	1.00180e6i	0.0809743	−	0.0933616i
$650$			5.37573e6i			0.499062i
$651$	−1.15980e6	−	1.91487e6i	−0.107258	−	0.177087i
$652$	5.57290e6			0.513408
$653$		−	1.23990e7i		−	1.13790i	−0.822371	−	0.568951i	$-0.807349\pi$
$653$		−	1.23990e7i		−	1.13790i	0.822371	−	0.568951i	$-0.192651\pi$
$654$	2.69349e6	+	4.44705e6i	0.246247	+	0.406562i
$655$			2.83001e7i			2.57741i
$656$			3.11890e6i			0.282971i
$657$	−3.70673e6	−	1.93743e6i	−0.335026	−	0.175111i
$658$	1.19116e7			1.07252
$659$	−4.83123e6			−0.433355			−0.216678	−	0.976243i	$-0.569522\pi$
$659$	−4.83123e6			−0.433355			−0.216678	+	0.976243i	$0.569522\pi$
$660$	−534924.	−	883181.i	−0.0478005	−	0.0789205i
$661$	3.32713e6			0.296187			0.148094	−	0.988973i	$-0.452686\pi$
$661$	3.32713e6			0.296187			0.148094	+	0.988973i	$0.452686\pi$
$662$	5.67295e6			0.503111
$663$	−4.63050e6	+	2.80460e6i	−0.409114	+	0.247792i
$664$	−6.08808e6			−0.535871
$665$			2.15353e7i			1.88841i
$666$	−2.22103e6	−	1.16089e6i	−0.194030	−	0.101415i
$667$			3.95479e6i			0.344198i
$668$		−	961536.i		−	0.0833728i
$669$	7.34483e6	−	4.44861e6i	0.634478	−	0.384290i
$670$	2.31443e7			1.99185
$671$		−	1.32926e6i		−	0.113973i
$672$	−1.69142e6	+	1.02446e6i	−0.144487	+	0.0875126i
$673$		−	1.21794e7i		−	1.03655i	−0.855215	−	0.518273i	$-0.826575\pi$
$673$		−	1.21794e7i		−	1.03655i	0.855215	−	0.518273i	$-0.173425\pi$
$674$		−	3.64156e6i		−	0.308772i
$675$	−915798.	−	1.45267e7i	−0.0773643	−	1.22717i
$676$	3.98347e6			0.335270
$677$		−	3.53619e6i		−	0.296527i	−0.988948	−	0.148263i	$-0.952632\pi$
$677$		−	3.53619e6i		−	0.296527i	0.988948	−	0.148263i	$-0.0473684\pi$
$678$	3.87071e6	−	2.34441e6i	0.323383	−	0.195866i
$679$			6.10701e6i			0.508340i
$680$	5.30450e6			0.439918
$681$	−3.88259e6	+	2.35160e6i	−0.320814	+	0.194311i
$682$		−	229983.i		−	0.0189337i
$683$	2.15655e7			1.76891			0.884457	−	0.466621i	$-0.154529\pi$
$683$	2.15655e7			1.76891			0.884457	+	0.466621i	$0.154529\pi$
$684$	3.75075e6	−	7.17600e6i	0.306533	−	0.586465i
$685$	1.88061e7			1.53134
$686$	−9.05194e6			−0.734398
$687$	−8.04984e6	−	1.32906e7i	−0.650722	−	1.07437i
$688$		−	112039.i		−	0.00902398i
$689$	6.29932e6			0.505529
$690$	−1.05679e7	−	1.74480e7i	−0.845016	−	1.39515i
$691$			457878.i			0.0364800i	0.999834	+	0.0182400i	$0.00580629\pi$
$691$			457878.i			0.0364800i	−0.999834	+	0.0182400i	$0.994194\pi$
$692$	1.14226e6			0.0906772
$693$	691590.	−	1.32316e6i	0.0547036	−	0.104660i
$694$	−1.09948e7			−0.866541
$695$		−	5.68578e6i		−	0.446507i
$696$	521540.	+	861082.i	0.0408098	+	0.0673785i
$697$	1.20973e7			0.943203
$698$			5.39222e6i			0.418918i
$699$	1.92108e7	−	1.16356e7i	1.48714	−	0.900731i
$700$	7.61632e6			0.587489
$701$	4.99643e6			0.384030			0.192015	−	0.981392i	$-0.438498\pi$
$701$	4.99643e6			0.384030			0.192015	+	0.981392i	$0.438498\pi$
$702$	5.28893e6	−	333428.i	0.405066	−	0.0255364i
$703$			5.36956e6i			0.409780i
$704$	−203145.			−0.0154481
$705$	1.62042e7	+	2.67537e7i	1.22787	+	2.02727i
$706$	4.02456e6			0.303883
$707$	−2.53212e6			−0.190518
$708$	1.12746e6	−	6.57289e6i	0.0845310	−	0.492803i
$709$	2.37778e7			1.77646			0.888230	−	0.459400i	$-0.151935\pi$
$709$	2.37778e7			1.77646			0.888230	+	0.459400i	$0.151935\pi$
$710$	5.05267e6			0.376162
$711$	−4.67626e6	+	8.94671e6i	−0.346916	+	0.663727i
$712$	−7.78627e6			−0.575611
$713$		−	4.54351e6i		−	0.334709i
$714$	3.97355e6	+	6.56048e6i	0.291698	+	0.481604i
$715$	−1.44793e6			−0.105921
$716$	−5.76054e6			−0.419933
$717$	1.80861e6	+	2.98609e6i	0.131386	+	0.216923i
$718$			1.52411e7i			1.10333i
$719$	9.74378e6			0.702919			0.351459	−	0.936203i	$-0.385686\pi$
$719$	9.74378e6			0.702919			0.351459	+	0.936203i	$0.385686\pi$
$720$	−4.60191e6	−	2.40532e6i	−0.330832	−	0.172919i
$721$			1.41167e7i			1.01134i
$722$	−7.44432e6			−0.531474
$723$	1.67452e7	−	1.01422e7i	1.19136	−	0.721585i
$724$	394101.			0.0279422
$725$		−	3.87739e6i		−	0.273964i
$726$	−8.45828e6	+	5.12301e6i	−0.595581	+	0.360731i
$727$	−5.47745e6			−0.384364			−0.192182	−	0.981359i	$-0.561556\pi$
$727$	−5.47745e6			−0.384364			−0.192182	+	0.981359i	$0.561556\pi$
$728$			2.77299e6i			0.193918i
$729$	−1.42353e7	+	1.80202e6i	−0.992083	+	0.125586i
$730$	5.74688e6			0.399140
$731$	−434565.			−0.0300788
$732$	−3.46313e6	−	5.71776e6i	−0.238886	−	0.394410i
$733$	1.42873e6			0.0982177			0.0491088	−	0.998793i	$-0.484362\pi$
$733$	1.42873e6			0.0982177			0.0491088	+	0.998793i	$0.484362\pi$
$734$		−	1.46619e7i		−	1.00450i
$735$	−984388.	−	1.62526e6i	−0.0672122	−	0.110970i
$736$	−4.01330e6			−0.273091
$737$			3.43788e6i			0.233143i
$738$	−1.04950e7	−	5.48550e6i	−0.709317	−	0.370745i
$739$			2.68142e7i			1.80615i	0.429482	+	0.903075i	$0.358696\pi$
$739$			2.68142e7i			1.80615i	−0.429482	+	0.903075i	$0.641304\pi$
$740$	3.44346e6			0.231161
$741$	−5.88233e6	−	9.71196e6i	−0.393554	−	0.649772i
$742$		−	8.92486e6i		−	0.595102i
$743$			2.27633e7i			1.51274i	0.654145	+	0.756369i	$0.273029\pi$
$743$			2.27633e7i			1.51274i	−0.654145	+	0.756369i	$0.726971\pi$
$744$	−599177.	−	989264.i	−0.0396847	−	0.0655209i
$745$			1.00414e7i			0.662834i
$746$	1.09331e7			0.719278
$747$	1.07077e7	−	2.04861e7i	0.702091	−	1.34325i
$748$			787938.i			0.0514918i
$749$			2.17214e7i			1.41476i
$750$	1.93476e6	+	3.19436e6i	0.125596	+	0.207363i
$751$			7.86433e6i			0.508817i	0.967097	+	0.254409i	$0.0818808\pi$
$751$			7.86433e6i			0.508817i	−0.967097	+	0.254409i	$0.918119\pi$
$752$	6.15376e6			0.396822
$753$	−2.90405e6	−	4.79469e6i	−0.186645	−	0.308158i
$754$	1.41170e6			0.0904301
$755$	−1.65584e7			−1.05718
$756$	−472400.	−	7.49334e6i	−0.0300611	−	0.476838i
$757$	−1.43744e7			−0.911693			−0.455847	−	0.890058i	$-0.650663\pi$
$757$	−1.43744e7			−0.911693			−0.455847	+	0.890058i	$0.650663\pi$
$758$	−4.25902e6			−0.269238
$759$	2.59174e6	−	1.56977e6i	0.163301	−	0.0989078i
$760$			1.11256e7i			0.698697i
$761$		−	1.95393e7i		−	1.22306i	−0.791222	−	0.611529i	$-0.790555\pi$
$761$		−	1.95393e7i		−	1.22306i	0.791222	−	0.611529i	$-0.209445\pi$
$762$	−3.05412e6	+	1.84982e6i	−0.190545	+	0.115409i
$763$		−	1.03294e7i		−	0.642340i
$764$	1.12234e7			0.695649
$765$	−9.32951e6	+	1.78494e7i	−0.576375	+	1.10273i
$766$			1.78076e7i			1.09656i
$767$	−7.06469e6	−	6.12734e6i	−0.433615	−	0.376083i
$768$	−873822.	+	529256.i	−0.0534589	+	0.0323790i
$769$			8.68770e6i			0.529772i	0.964280	+	0.264886i	$0.0853343\pi$
$769$			8.68770e6i			0.529772i	−0.964280	+	0.264886i	$0.914666\pi$
$770$			2.05142e6i			0.124689i
$771$	1.21946e7	+	2.01338e7i	0.738810	+	1.21980i
$772$	−4.96435e6			−0.299791
$773$	1.62208e7			0.976388			0.488194	−	0.872735i	$-0.337656\pi$
$773$	1.62208e7			0.976388			0.488194	+	0.872735i	$0.337656\pi$
$774$	377006.	+	197053.i	0.0226202	+	0.0118231i
$775$			4.45458e6i			0.266411i
$776$			3.15501e6i			0.188082i
$777$	2.57946e6	+	4.25878e6i	0.153277	+	0.253066i
$778$		−	1.81131e7i		−	1.07286i
$779$			2.53726e7i			1.49803i
$780$	−6.22820e6	+	3.77229e6i	−0.366544	+	0.222008i
$781$			750531.i			0.0440292i
$782$			1.55664e7i			0.910270i
$783$	−3.81478e6	+	240494.i	−0.222364	+	0.0140184i
$784$	−373836.			−0.0217215
$785$	−5.01260e7			−2.90328
$786$	−1.80822e7	+	1.09520e7i	−1.04399	+	0.632321i
$787$	1.87855e7			1.08115			0.540575	−	0.841296i	$-0.318207\pi$
$787$	1.87855e7			1.08115			0.540575	+	0.841296i	$0.318207\pi$
$788$		−	3.67249e6i		−	0.210691i
$789$	−1.34439e7	−	2.21964e7i	−0.768836	−	1.26938i
$790$		−	1.38709e7i		−	0.790745i
$791$	−8.99074e6			−0.510921
$792$	357290.	−	683575.i	0.0202399	−	0.0387234i
$793$	−9.37396e6			−0.529347
$794$			1.13084e7i			0.636578i
$795$	2.00455e7	−	1.21411e7i	1.12486	−	0.681305i
$796$	1.39982e7			0.783052
$797$	−2.55464e7			−1.42457			−0.712284	−	0.701891i	$-0.752339\pi$
$797$	−2.55464e7			−1.42457			−0.712284	+	0.701891i	$0.752339\pi$
$798$	−1.37599e7	+	8.33407e6i	−0.764904	+	0.463287i
$799$		−	2.38685e7i		−	1.32269i
$800$	3.93475e6			0.217366
$801$	1.36944e7	−	2.62004e7i	0.754158	−	1.44287i
$802$	−1.12975e6			−0.0620220
$803$			853649.i			0.0467187i
$804$	8.95674e6	+	1.47879e7i	0.488664	+	0.806802i
$805$			4.05274e7i			2.20424i
$806$	−1.62184e6			−0.0879369
$807$	1.34032e7	−	8.11806e6i	0.724479	−	0.438802i
$808$	−1.30815e6			−0.0704902
$809$	773799.			0.0415678			0.0207839	−	0.999784i	$-0.493384\pi$
$809$	773799.			0.0415678			0.0207839	+	0.999784i	$0.493384\pi$
$810$	1.61876e7	−	1.12548e7i	0.866903	−	0.602731i
$811$		−	1.09693e7i		−	0.585634i	−0.956168	−	0.292817i	$-0.905407\pi$
$811$		−	1.09693e7i		−	0.585634i	0.956168	−	0.292817i	$-0.0945927\pi$
$812$		−	2.00009e6i		−	0.106453i
$813$	1.72682e7	−	1.04590e7i	0.916263	−	0.554962i
$814$			511496.i			0.0270571i
$815$		−	2.90737e7i		−	1.53323i
$816$	2.05282e6	+	3.38928e6i	0.107926	+	0.178190i
$817$		−	911450.i		−	0.0477725i
$818$			2.12292e7i			1.10931i
$819$	−9.33097e6	−	4.87710e6i	−0.486090	−	0.254069i
$820$	1.62713e7			0.845059
$821$	−3.07510e7			−1.59222			−0.796108	−	0.605155i	$-0.793111\pi$
$821$	−3.07510e7			−1.59222			−0.796108	+	0.605155i	$0.793111\pi$
$822$	7.27789e6	+	1.20161e7i	0.375687	+	0.620273i
$823$			2.14291e7i			1.10282i	0.834235	+	0.551410i	$0.185910\pi$
$823$			2.14291e7i			1.10282i	−0.834235	+	0.551410i	$0.814090\pi$
$824$			7.29300e6i			0.374186i
$825$	−2.54102e6	+	1.53904e6i	−0.129979	+	0.0787255i
$826$	−8.68119e6	+	1.00092e7i	−0.442720	+	0.510447i
$827$			9.58039e6i			0.487101i	0.969888	+	0.243551i	$0.0783122\pi$
$827$			9.58039e6i			0.487101i	−0.969888	+	0.243551i	$0.921688\pi$
$828$	7.05857e6	−	1.35046e7i	0.357800	−	0.684550i
$829$	−1.67745e7			−0.847740			−0.423870	−	0.905723i	$-0.639329\pi$
$829$	−1.67745e7			−0.847740			−0.423870	+	0.905723i	$0.639329\pi$
$830$			3.17614e7i			1.60031i
$831$	4.94853e6	−	2.99722e6i	0.248584	−	0.150562i
$832$			1.43258e6i			0.0717483i
$833$			1.44999e6i			0.0724024i
$834$	3.63290e6	−	2.20037e6i	0.180858	−	0.109542i
$835$	−5.01632e6			−0.248982
$836$	−1.65261e6			−0.0817815
$837$	4.38265e6	−	276294.i	0.216234	−	0.0136319i
$838$	−4.04927e6			−0.199190
$839$	8.64706e6			0.424095			0.212048	−	0.977259i	$-0.431987\pi$
$839$	8.64706e6			0.424095			0.212048	+	0.977259i	$0.431987\pi$
$840$	5.34457e6	+	8.82409e6i	0.261345	+	0.431491i
$841$	1.94929e7			0.950358
$842$		−	2.45660e6i		−	0.119414i
$843$	9.77058e6	+	1.61316e7i	0.473534	+	0.781823i
$844$			10151.2i			0.000490526i
$845$		−	2.07817e7i		−	1.00124i
$846$	−1.08232e7	+	2.07071e7i	−0.519911	+	0.994704i
$847$	1.96466e7			0.940975
$848$		−	4.61077e6i		−	0.220183i
$849$	−5.68980e6	−	9.39407e6i	−0.270912	−	0.447285i
$850$		−	1.52617e7i		−	0.724528i
$851$			1.01050e7i			0.478314i
$852$	1.95536e6	+	3.22838e6i	0.0922845	+	0.152365i
$853$	−1.06549e7			−0.501393			−0.250697	−	0.968066i	$-0.580660\pi$
$853$	−1.06549e7			−0.501393			−0.250697	+	0.968066i	$0.580660\pi$
$854$			1.32810e7i			0.623140i
$855$	−3.74371e7	−	1.95676e7i	−1.75141	−	0.915424i
$856$			1.12217e7i			0.523450i
$857$	−1.84893e6			−0.0859939			−0.0429970	−	0.999075i	$-0.513691\pi$
$857$	−1.84893e6			−0.0859939			−0.0429970	+	0.999075i	$0.513691\pi$
$858$	−560342.	−	925145.i	−0.0259857	−	0.0429034i
$859$		−	2.65428e7i		−	1.22734i	−0.789563	−	0.613670i	$-0.789693\pi$
$859$		−	2.65428e7i		−	1.22734i	0.789563	−	0.613670i	$-0.210307\pi$
$860$	−584506.			−0.0269490
$861$	1.21886e7	+	2.01239e7i	0.560335	+	0.925134i
$862$	6.80420e6			0.311895
$863$	−3.13667e7			−1.43365			−0.716823	−	0.697255i	$-0.754405\pi$
$863$	−3.13667e7			−1.43365			−0.716823	+	0.697255i	$0.754405\pi$
$864$	−244052.	−	3.87122e6i	−0.0111224	−	0.176426i
$865$		−	5.95913e6i		−	0.270796i
$866$	1.50773e7			0.683170
$867$	−5.78563e6	+	3.50424e6i	−0.261399	+	0.158324i
$868$			2.29782e6i			0.103518i
$869$	2.06040e6			0.0925554
$870$	4.49225e6	−	2.72086e6i	0.201218	−	0.121873i
$871$	2.42440e7			1.08283
$872$		−	5.33640e6i		−	0.237661i
$873$	−1.06165e7	−	5.54901e6i	−0.471460	−	0.246422i
$874$	−3.26487e7			−1.44573
$875$		−	7.41975e6i		−	0.327619i
$876$	2.22402e6	+	3.67194e6i	0.0979215	+	0.161672i
$877$	−4.31339e7			−1.89374			−0.946869	−	0.321620i	$-0.895773\pi$
$877$	−4.31339e7			−1.89374			−0.946869	+	0.321620i	$0.895773\pi$
$878$	2.91947e7			1.27811
$879$	−1.68998e6	−	2.79022e6i	−0.0737749	−	0.121805i
$880$			1.05981e6i			0.0461339i
$881$	−3.88841e7			−1.68784			−0.843922	−	0.536465i	$-0.819759\pi$
$881$	−3.88841e7			−1.68784			−0.843922	+	0.536465i	$0.819759\pi$
$882$	657499.	−	1.25794e6i	0.0284593	−	0.0544488i
$883$	4.17333e6			0.180128			0.0900640	−	0.995936i	$-0.471293\pi$
$883$	4.17333e6			0.180128			0.0900640	+	0.995936i	$0.471293\pi$
$884$	5.55655e6			0.239152
$885$	−3.42907e7	−	5.88192e6i	−1.47169	−	0.252441i
$886$	6.70900e6			0.287127
$887$	9.75649e6			0.416375			0.208187	−	0.978089i	$-0.433244\pi$
$887$	9.75649e6			0.416375			0.208187	+	0.978089i	$0.433244\pi$
$888$	1.33260e6	+	2.20018e6i	0.0567112	+	0.0936323i
$889$	7.09398e6			0.301048
$890$			4.06208e7i			1.71899i
$891$	1.67180e6	+	2.40453e6i	0.0705488	+	0.101470i
$892$	−8.81371e6			−0.370891
$893$	5.00616e7			2.10076
$894$	−6.41592e6	+	3.88599e6i	−0.268482	+	0.162614i
$895$			3.00526e7i			1.25408i
$896$	2.02968e6			0.0844612
$897$	−1.10700e7	−	1.82770e7i	−0.459375	−	0.758445i
$898$			4.11983e6i			0.170486i
$899$	1.16980e6			0.0482738
$900$	−6.92041e6	+	1.32403e7i	−0.284791	+	0.544867i
$901$	−1.78838e7			−0.733917
$902$			2.41696e6i			0.0989128i
$903$	−437848.	−	722903.i	−0.0178691	−	0.0295026i
$904$	−4.64481e6			−0.189037
$905$		−	2.05602e6i		−	0.0834460i
$906$	−6.40802e6	−	1.05799e7i	−0.259360	−	0.428214i
$907$	3.95317e7			1.59561			0.797807	−	0.602913i	$-0.205993\pi$
$907$	3.95317e7			1.59561			0.797807	+	0.602913i	$0.205993\pi$
$908$	4.65906e6			0.187535
$909$	2.30076e6	−	4.40186e6i	0.0923553	−	0.176696i
$910$	1.44666e7			0.579113
$911$		−	1.44338e7i		−	0.576213i	−0.957598	−	0.288107i	$-0.906974\pi$
$911$		−	1.44338e7i		−	0.576213i	0.957598	−	0.288107i	$-0.0930258\pi$
$912$	−7.10864e6	+	4.30556e6i	−0.283009	+	0.171413i
$913$	−4.71789e6			−0.187314
$914$		−	2.67296e7i		−	1.05834i
$915$	−2.98295e7	+	1.80671e7i	−1.17786	+	0.713404i
$916$			1.59486e7i			0.628033i
$917$	4.20006e7			1.64942
$918$	−1.50153e7	+	946602.i	−0.588066	+	0.0370732i
$919$		−	4.52299e7i		−	1.76660i	−0.468813	−	0.883298i	$-0.655318\pi$
$919$		−	4.52299e7i		−	1.76660i	0.468813	−	0.883298i	$-0.344682\pi$
$920$			2.09373e7i			0.815553i
$921$	3.38130e7	−	2.04798e7i	1.31351	−	0.795568i
$922$			1.10379e7i			0.427620i
$923$	5.29275e6			0.204492
$924$	−1.31074e6	+	793890.i	−0.0505054	+	0.0305901i
$925$		−	9.90724e6i		−	0.380713i
$926$		−	2.05049e7i		−	0.785832i
$927$	−2.45406e7	−	1.28269e7i	−0.937963	−	0.490254i
$928$		−	1.03329e6i		−	0.0393869i
$929$	4.79295e7			1.82206			0.911031	−	0.412337i	$-0.135287\pi$
$929$	4.79295e7			1.82206			0.911031	+	0.412337i	$0.135287\pi$
$930$	−5.16097e6	+	3.12590e6i	−0.195670	+	0.118513i
$931$	−3.04120e6			−0.114993
$932$	−2.30527e7			−0.869325
$933$	773891.	+	1.27772e6i	0.0291055	+	0.0480543i
$934$	−5.82399e6			−0.218451
$935$	4.11066e6			0.153774
$936$	−4.82058e6	−	2.51962e6i	−0.179850	−	0.0940036i
$937$			3.05138e7i			1.13540i	0.823236	+	0.567699i	$0.192166\pi$
$937$			3.05138e7i			1.13540i	−0.823236	+	0.567699i	$0.807834\pi$
$938$		−	3.43488e7i		−	1.27469i
$939$	3.82453e6	+	6.31445e6i	0.141551	+	0.233707i
$940$		−	3.21041e7i		−	1.18506i
$941$	−1.07276e7			−0.394938			−0.197469	−	0.980309i	$-0.563272\pi$
$941$	−1.07276e7			−0.394938			−0.197469	+	0.980309i	$0.563272\pi$
$942$	−1.93986e7	−	3.20278e7i	−0.712266	−	1.17598i
$943$			4.77490e7i			1.74858i
$944$	−4.48489e6	+	5.17098e6i	−0.163803	+	0.188861i
$945$	−3.90927e7	+	2.46450e6i	−1.42402	+	0.0897738i
$946$		−	86823.3i		−	0.00315434i
$947$		−	6.86303e6i		−	0.248680i	−0.992240	−	0.124340i	$-0.960319\pi$
$947$		−	6.86303e6i		−	0.248680i	0.992240	−	0.124340i	$-0.0396814\pi$
$948$	8.86273e6	−	5.36797e6i	0.320292	−	0.193995i
$949$	6.01994e6			0.216984
$950$	3.20097e7			1.15073
$951$	6.90815e6	+	1.14056e7i	0.247691	+	0.408947i
$952$		−	7.87250e6i		−	0.281527i
$953$			1.48827e7i			0.530823i	0.964135	+	0.265412i	$0.0855079\pi$
$953$			1.48827e7i			0.530823i	−0.964135	+	0.265412i	$0.914492\pi$
$954$	1.55150e7	+	8.10939e6i	0.551927	+	0.288481i
$955$		−	5.85522e7i		−	2.07747i
$956$		−	3.58327e6i		−	0.126805i
$957$	404161.	+	667285.i	0.0142651	+	0.0235522i
$958$			7.69939e6i			0.271046i
$959$		−	2.79105e7i		−	0.979987i
$960$	2.76112e6	+	4.55872e6i	0.0966957	+	0.159648i
$961$	2.72852e7			0.953057
$962$	3.60707e6			0.125666
$963$	−3.77606e7	−	1.97367e7i	−1.31212	−	0.685817i
$964$	−2.00940e7			−0.696426
$965$			2.58989e7i			0.895290i
$966$	−2.58948e7	+	1.56840e7i	−0.892832	+	0.540770i
$967$		−	4.84371e7i		−	1.66576i	−0.553454	−	0.832879i	$-0.686691\pi$
$967$		−	4.84371e7i		−	1.66576i	0.553454	−	0.832879i	$-0.313309\pi$
$968$	1.01498e7			0.348153
$969$	1.66999e7	+	2.75722e7i	0.571354	+	0.943327i
$970$	1.64597e7			0.561683
$971$		−	3.74047e7i		−	1.27315i	−0.771217	−	0.636573i	$-0.780352\pi$
$971$		−	3.74047e7i		−	1.27315i	0.771217	−	0.636573i	$-0.219648\pi$
$972$	1.34557e7	+	5.98745e6i	0.456816	+	0.203271i
$973$	−8.43836e6			−0.285743
$974$	−8.86862e6			−0.299543
$975$	1.08533e7	+	1.79193e7i	0.365639	+	0.603683i
$976$			6.86125e6i			0.230557i
$977$	1.05786e7			0.354561			0.177280	−	0.984160i	$-0.443270\pi$
$977$	1.05786e7			0.354561			0.177280	+	0.984160i	$0.443270\pi$
$978$	1.85765e7	−	1.12514e7i	0.621037	−	0.376149i
$979$	−6.03387e6			−0.201205
$980$			1.95029e6i			0.0648687i
$981$	1.79567e7	+	9.38562e6i	0.595738	+	0.311380i
$982$			3.37788e7i			1.11780i
$983$	−5.59992e7			−1.84841			−0.924205	−	0.381897i	$-0.875271\pi$
$983$	−5.59992e7			−1.84841			−0.924205	+	0.381897i	$0.875271\pi$
$984$	6.29692e6	+	1.03964e7i	0.207320	+	0.342292i
$985$	−1.91593e7			−0.629201
$986$	−4.00780e6			−0.131285
$987$	3.97056e7	−	2.40489e7i	1.29735	−	0.785781i
$988$			1.16542e7i			0.379832i
$989$		−	1.71527e6i		−	0.0557623i
$990$	−3.56620e6	−	1.86398e6i	−0.115643	−	0.0604439i
$991$		−	5.03869e7i		−	1.62980i	−0.579604	−	0.814899i	$-0.696793\pi$
$991$		−	5.03869e7i		−	1.62980i	0.579604	−	0.814899i	$-0.303207\pi$
$992$			1.18710e6i			0.0383010i
$993$	1.89100e7	−	1.14534e7i	0.608581	−	0.368605i
$994$		−	7.49876e6i		−	0.240726i
$995$		−	7.30286e7i		−	2.33849i
$996$	−2.02938e7	+	1.22916e7i	−0.648210	+	0.392607i
$997$	−1.08973e7			−0.347202			−0.173601	−	0.984816i	$-0.555540\pi$
$997$	−1.08973e7			−0.347202			−0.173601	+	0.984816i	$0.555540\pi$
$998$	1.02921e7			0.327097
$999$	−9.74727e6	+	614493.i	−0.309008	+	0.0194807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.c.a.353.8	yes	50
3.2	odd	2		354.6.c.b.353.7	yes	50
59.58	odd	2		354.6.c.b.353.8	yes	50
177.176	even	2	inner	354.6.c.a.353.7	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.c.a.353.7	✓	50	177.176	even	2	inner
354.6.c.a.353.8	yes	50	1.1	even	1	trivial
354.6.c.b.353.7	yes	50	3.2	odd	2
354.6.c.b.353.8	yes	50	59.58	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +(-13.3335 + 8.07581i) q^{3} +16.0000 q^{4} -83.4718i q^{5} +(53.3339 - 32.3032i) q^{6} -123.882 q^{7} -64.0000 q^{8} +(112.563 - 215.357i) q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +(-13.3335 + 8.07581i) q^{3} +16.0000 q^{4} -83.4718i q^{5} +(53.3339 - 32.3032i) q^{6} -123.882 q^{7} -64.0000 q^{8} +(112.563 - 215.357i) q^{9} +333.887i q^{10} -49.5960 q^{11} +(-213.335 + 129.213i) q^{12} +349.752i q^{13} +495.527 q^{14} +(674.102 + 1112.97i) q^{15} +256.000 q^{16} -992.945i q^{17} +(-450.251 + 861.428i) q^{18} +2082.59 q^{19} -1335.55i q^{20} +(1651.77 - 1000.45i) q^{21} +198.384 q^{22} +3919.24 q^{23} +(853.342 - 516.852i) q^{24} -3842.53 q^{25} -1399.01i q^{26} +(238.332 + 3780.49i) q^{27} -1982.11 q^{28} +1009.07i q^{29} +(-2696.41 - 4451.87i) q^{30} -1159.28i q^{31} -1024.00 q^{32} +(661.287 - 400.528i) q^{33} +3971.78i q^{34} +10340.6i q^{35} +(1801.00 - 3445.71i) q^{36} +2578.31i q^{37} -8330.36 q^{38} +(-2824.53 - 4663.40i) q^{39} +5342.19i q^{40} +12183.2i q^{41} +(-6607.10 + 4001.78i) q^{42} -437.653i q^{43} -793.537 q^{44} +(-17976.2 - 9395.80i) q^{45} -15677.0 q^{46} +24038.1 q^{47} +(-3413.37 + 2067.41i) q^{48} -1460.30 q^{49} +15370.1 q^{50} +(8018.83 + 13239.4i) q^{51} +5596.03i q^{52} -18010.8i q^{53} +(-953.328 - 15122.0i) q^{54} +4139.87i q^{55} +7928.44 q^{56} +(-27768.1 + 16818.6i) q^{57} -4036.28i q^{58} +(-17519.1 + 20199.1i) q^{59} +(10785.6 + 17807.5i) q^{60} +26801.7i q^{61} +4637.13i q^{62} +(-13944.5 + 26678.8i) q^{63} +4096.00 q^{64} +29194.4 q^{65} +(-2645.15 + 1602.11i) q^{66} -69317.7i q^{67} -15887.1i q^{68} +(-52257.1 + 31651.1i) q^{69} -41362.5i q^{70} -15132.9i q^{71} +(-7204.01 + 13782.9i) q^{72} -17212.0i q^{73} -10313.2i q^{74} +(51234.3 - 31031.6i) q^{75} +33321.4 q^{76} +6144.05 q^{77} +(11298.1 + 18653.6i) q^{78} -41543.6 q^{79} -21368.8i q^{80} +(-33708.3 - 48482.3i) q^{81} -48732.9i q^{82} +95126.3 q^{83} +(26428.4 - 16007.1i) q^{84} -82882.8 q^{85} +1750.61i q^{86} +(-8149.06 - 13454.4i) q^{87} +3174.15 q^{88} +121660. q^{89} +(71904.9 + 37583.2i) q^{90} -43327.9i q^{91} +62707.9 q^{92} +(9362.14 + 15457.2i) q^{93} -96152.6 q^{94} -173837. i q^{95} +(13653.5 - 8269.63i) q^{96} -49297.1i q^{97} +5841.18 q^{98} +(-5582.66 + 10680.9i) 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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