LMFDB - Embedded newform 354.6.c.a.353.4

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			353.4
Character	$\chi$	$=$	354.353
Dual form			354.6.c.a.353.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +(-15.5391 + 1.23947i) q^{3} +16.0000 q^{4} -14.2214i q^{5} +(62.1564 - 4.95787i) q^{6} +129.028 q^{7} -64.0000 q^{8} +(239.927 - 38.5204i) q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +(-15.5391 + 1.23947i) q^{3} +16.0000 q^{4} -14.2214i q^{5} +(62.1564 - 4.95787i) q^{6} +129.028 q^{7} -64.0000 q^{8} +(239.927 - 38.5204i) q^{9} +56.8857i q^{10} +605.594 q^{11} +(-248.626 + 19.8315i) q^{12} -1141.46i q^{13} -516.113 q^{14} +(17.6270 + 220.988i) q^{15} +256.000 q^{16} -1592.88i q^{17} +(-959.710 + 154.082i) q^{18} +1358.06 q^{19} -227.543i q^{20} +(-2004.98 + 159.926i) q^{21} -2422.37 q^{22} +2753.22 q^{23} +(994.503 - 79.3259i) q^{24} +2922.75 q^{25} +4565.84i q^{26} +(-3680.51 + 895.955i) q^{27} +2064.45 q^{28} +4296.59i q^{29} +(-70.5080 - 883.953i) q^{30} +4108.59i q^{31} -1024.00 q^{32} +(-9410.38 + 750.614i) q^{33} +6371.52i q^{34} -1834.97i q^{35} +(3838.84 - 616.327i) q^{36} -6125.80i q^{37} -5432.25 q^{38} +(1414.80 + 17737.2i) q^{39} +910.172i q^{40} -8518.43i q^{41} +(8019.94 - 639.706i) q^{42} -783.566i q^{43} +9689.50 q^{44} +(-547.816 - 3412.11i) q^{45} -11012.9 q^{46} -16365.7 q^{47} +(-3978.01 + 317.304i) q^{48} -158.695 q^{49} -11691.0 q^{50} +(1974.32 + 24751.9i) q^{51} -18263.3i q^{52} +32996.8i q^{53} +(14722.0 - 3583.82i) q^{54} -8612.41i q^{55} -8257.81 q^{56} +(-21103.1 + 1683.28i) q^{57} -17186.4i q^{58} +(9617.66 + 24948.4i) q^{59} +(282.032 + 3535.81i) q^{60} -44628.9i q^{61} -16434.4i q^{62} +(30957.4 - 4970.23i) q^{63} +4096.00 q^{64} -16233.2 q^{65} +(37641.5 - 3002.45i) q^{66} -6514.81i q^{67} -25486.1i q^{68} +(-42782.5 + 3412.52i) q^{69} +7339.87i q^{70} +70303.4i q^{71} +(-15355.4 + 2465.31i) q^{72} -37855.1i q^{73} +24503.2i q^{74} +(-45416.9 + 3622.65i) q^{75} +21729.0 q^{76} +78138.7 q^{77} +(-5659.20 - 70949.0i) q^{78} +88936.0 q^{79} -3640.69i q^{80} +(56081.4 - 18484.2i) q^{81} +34073.7i q^{82} +32348.9 q^{83} +(-32079.7 + 2558.82i) q^{84} -22653.0 q^{85} +3134.27i q^{86} +(-5325.48 - 66765.1i) q^{87} -38758.0 q^{88} -63430.2 q^{89} +(2191.26 + 13648.4i) q^{90} -147281. i q^{91} +44051.5 q^{92} +(-5092.47 - 63843.9i) q^{93} +65462.8 q^{94} -19313.6i q^{95} +(15912.0 - 1269.21i) q^{96} -174688. i q^{97} +634.780 q^{98} +(145299. - 23327.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 200 q^{2} - 13 q^{3} + 800 q^{4} + 52 q^{6} + 38 q^{7} - 3200 q^{8} + 51 q^{9}+O(q^{10}) $ 50 * q - 200 * q^2 - 13 * q^3 + 800 * q^4 + 52 * q^6 + 38 * q^7 - 3200 * q^8 + 51 * q^9	$ 50 q - 200 q^{2} - 13 q^{3} + 800 q^{4} + 52 q^{6} + 38 q^{7} - 3200 q^{8} + 51 q^{9} - 652 q^{11} - 208 q^{12} - 152 q^{14} - 2107 q^{15} + 12800 q^{16} - 204 q^{18} - 894 q^{19} - 3801 q^{21} + 2608 q^{22} + 2456 q^{23} + 832 q^{24} - 23956 q^{25} + 9890 q^{27} + 608 q^{28} + 8428 q^{30} - 51200 q^{32} - 9744 q^{33} + 816 q^{36} + 3576 q^{38} + 1388 q^{39} + 15204 q^{42} - 10432 q^{44} + 33067 q^{45} - 9824 q^{46} - 27144 q^{47} - 3328 q^{48} + 85768 q^{49} + 95824 q^{50} + 3338 q^{51} - 39560 q^{54} - 2432 q^{56} - 63969 q^{57} - 23840 q^{59} - 33712 q^{60} + 94781 q^{63} + 204800 q^{64} - 9400 q^{65} + 38976 q^{66} - 115930 q^{69} - 3264 q^{72} + 24248 q^{75} - 14304 q^{76} - 150240 q^{77} - 5552 q^{78} - 68658 q^{79} + 47095 q^{81} - 175140 q^{83} - 60816 q^{84} - 138524 q^{85} + 138261 q^{87} + 41728 q^{88} + 104908 q^{89} - 132268 q^{90} + 39296 q^{92} - 91204 q^{93} + 108576 q^{94} + 13312 q^{96} - 343072 q^{98} - 111406 q^{99}+O(q^{100}) $ 50 * q - 200 * q^2 - 13 * q^3 + 800 * q^4 + 52 * q^6 + 38 * q^7 - 3200 * q^8 + 51 * q^9 - 652 * q^11 - 208 * q^12 - 152 * q^14 - 2107 * q^15 + 12800 * q^16 - 204 * q^18 - 894 * q^19 - 3801 * q^21 + 2608 * q^22 + 2456 * q^23 + 832 * q^24 - 23956 * q^25 + 9890 * q^27 + 608 * q^28 + 8428 * q^30 - 51200 * q^32 - 9744 * q^33 + 816 * q^36 + 3576 * q^38 + 1388 * q^39 + 15204 * q^42 - 10432 * q^44 + 33067 * q^45 - 9824 * q^46 - 27144 * q^47 - 3328 * q^48 + 85768 * q^49 + 95824 * q^50 + 3338 * q^51 - 39560 * q^54 - 2432 * q^56 - 63969 * q^57 - 23840 * q^59 - 33712 * q^60 + 94781 * q^63 + 204800 * q^64 - 9400 * q^65 + 38976 * q^66 - 115930 * q^69 - 3264 * q^72 + 24248 * q^75 - 14304 * q^76 - 150240 * q^77 - 5552 * q^78 - 68658 * q^79 + 47095 * q^81 - 175140 * q^83 - 60816 * q^84 - 138524 * q^85 + 138261 * q^87 + 41728 * q^88 + 104908 * q^89 - 132268 * q^90 + 39296 * q^92 - 91204 * q^93 + 108576 * q^94 + 13312 * q^96 - 343072 * q^98 - 111406 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−4.00000			−0.707107
$2$	−4.00000			−0.707107
$3$	−15.5391	+	1.23947i	−0.996834	+	0.0795119i
$3$	−15.5391	+	1.23947i	−0.996834	+	0.0795119i
$4$	16.0000			0.500000
$5$		−	14.2214i		−	0.254401i	−0.991877	−	0.127200i	$-0.959401\pi$
$5$		−	14.2214i		−	0.254401i	0.991877	−	0.127200i	$-0.0405991\pi$
$6$	62.1564	−	4.95787i	0.704868	−	0.0562234i
$7$	129.028			0.995268			0.497634	−	0.867387i	$-0.334202\pi$
$7$	129.028			0.995268			0.497634	+	0.867387i	$0.334202\pi$
$8$	−64.0000			−0.353553
$9$	239.927	−	38.5204i	0.987356	−	0.158520i
$10$			56.8857i			0.179888i
$11$	605.594			1.50904			0.754518	−	0.656279i	$-0.227871\pi$
$11$	605.594			1.50904			0.754518	+	0.656279i	$0.227871\pi$
$12$	−248.626	+	19.8315i	−0.498417	+	0.0397559i
$13$		−	1141.46i		−	1.87328i	−0.350298	−	0.936638i	$-0.613920\pi$
$13$		−	1141.46i		−	1.87328i	0.350298	−	0.936638i	$-0.386080\pi$
$14$	−516.113			−0.703761
$15$	17.6270	+	220.988i	0.0202279	+	0.253595i
$16$	256.000			0.250000
$17$		−	1592.88i		−	1.33678i	−0.743810	−	0.668391i	$-0.766983\pi$
$17$		−	1592.88i		−	1.33678i	0.743810	−	0.668391i	$-0.233017\pi$
$18$	−959.710	+	154.082i	−0.698166	+	0.112091i
$19$	1358.06			0.863050			0.431525	−	0.902101i	$-0.357976\pi$
$19$	1358.06			0.863050			0.431525	+	0.902101i	$0.357976\pi$
$20$		−	227.543i		−	0.127200i
$21$	−2004.98	+	159.926i	−0.992117	+	0.0791356i
$22$	−2422.37			−1.06705
$23$	2753.22			1.08523			0.542614	−	0.839982i	$-0.317435\pi$
$23$	2753.22			1.08523			0.542614	+	0.839982i	$0.317435\pi$
$24$	994.503	−	79.3259i	0.352434	−	0.0281117i
$25$	2922.75			0.935280
$26$			4565.84i			1.32461i
$27$	−3680.51	+	895.955i	−0.971625	+	0.236525i
$28$	2064.45			0.497634
$29$			4296.59i			0.948700i	0.880336	+	0.474350i	$0.157317\pi$
$29$			4296.59i			0.948700i	−0.880336	+	0.474350i	$0.842683\pi$
$30$	−70.5080	−	883.953i	−0.0143033	−	0.179319i
$31$			4108.59i			0.767872i	0.923360	+	0.383936i	$0.125432\pi$
$31$			4108.59i			0.767872i	−0.923360	+	0.383936i	$0.874568\pi$
$32$	−1024.00			−0.176777
$33$	−9410.38	+	750.614i	−1.50426	+	0.119986i
$34$			6371.52i			0.945248i
$35$		−	1834.97i		−	0.253197i
$36$	3838.84	−	616.327i	0.493678	−	0.0792601i
$37$		−	6125.80i		−	0.735629i	−0.929899	−	0.367814i	$-0.880106\pi$
$37$		−	6125.80i		−	0.735629i	0.929899	−	0.367814i	$-0.119894\pi$
$38$	−5432.25			−0.610269
$39$	1414.80	+	17737.2i	0.148948	+	1.86735i
$40$			910.172i			0.0899442i
$41$		−	8518.43i		−	0.791407i	−0.918378	−	0.395703i	$-0.870501\pi$
$41$		−	8518.43i		−	0.791407i	0.918378	−	0.395703i	$-0.129499\pi$
$42$	8019.94	−	639.706i	0.701532	−	0.0559573i
$43$		−	783.566i		−	0.0646256i	−0.999478	−	0.0323128i	$-0.989713\pi$
$43$		−	783.566i		−	0.0646256i	0.999478	−	0.0323128i	$-0.0102873\pi$
$44$	9689.50			0.754518
$45$	−547.816	−	3412.11i	−0.0403277	−	0.251184i
$46$	−11012.9			−0.767372
$47$	−16365.7			−1.08066			−0.540331	−	0.841453i	$-0.681701\pi$
$47$	−16365.7			−1.08066			−0.540331	+	0.841453i	$0.681701\pi$
$48$	−3978.01	+	317.304i	−0.249208	+	0.0198780i
$49$	−158.695			−0.00944220
$50$	−11691.0			−0.661343
$51$	1974.32	+	24751.9i	0.106290	+	1.33255i
$52$		−	18263.3i		−	0.936638i
$53$			32996.8i			1.61355i	0.590860	+	0.806774i	$0.298789\pi$
$53$			32996.8i			1.61355i	−0.590860	+	0.806774i	$0.701211\pi$
$54$	14722.0	−	3583.82i	0.687043	−	0.167248i
$55$		−	8612.41i		−	0.383900i
$56$	−8257.81			−0.351880
$57$	−21103.1	+	1683.28i	−0.860318	+	0.0686227i
$58$		−	17186.4i		−	0.670832i
$59$	9617.66	+	24948.4i	0.359699	+	0.933068i
$59$	9617.66	+	24948.4i	0.359699	+	0.933068i
$60$	282.032	+	3535.81i	0.0101139	+	0.126798i
$61$		−	44628.9i		−	1.53565i	−0.640662	−	0.767823i	$-0.721340\pi$
$61$		−	44628.9i		−	1.53565i	0.640662	−	0.767823i	$-0.278660\pi$
$62$		−	16434.4i		−	0.542968i
$63$	30957.4	−	4970.23i	0.982683	−	0.157770i
$64$	4096.00			0.125000
$65$	−16233.2			−0.476563
$66$	37641.5	−	3002.45i	1.06367	−	0.0848431i
$67$		−	6514.81i		−	0.177302i	−0.996063	−	0.0886512i	$-0.971744\pi$
$67$		−	6514.81i		−	0.177302i	0.996063	−	0.0886512i	$-0.0282557\pi$
$68$		−	25486.1i		−	0.668391i
$69$	−42782.5	+	3412.52i	−1.08179	+	0.0862885i
$70$			7339.87i			0.179037i
$71$			70303.4i			1.65512i	0.561375	+	0.827562i	$0.310273\pi$
$71$			70303.4i			1.65512i	−0.561375	+	0.827562i	$0.689727\pi$
$72$	−15355.4	+	2465.31i	−0.349083	+	0.0560454i
$73$		−	37855.1i		−	0.831413i	−0.909499	−	0.415707i	$-0.863534\pi$
$73$		−	37855.1i		−	0.831413i	0.909499	−	0.415707i	$-0.136466\pi$
$74$			24503.2i			0.520168i
$75$	−45416.9	+	3622.65i	−0.932319	+	0.0743659i
$76$	21729.0			0.431525
$77$	78138.7			1.50189
$78$	−5659.20	−	70949.0i	−0.105322	−	1.32041i
$79$	88936.0			1.60328			0.801641	−	0.597805i	$-0.203960\pi$
$79$	88936.0			1.60328			0.801641	+	0.597805i	$0.203960\pi$
$80$		−	3640.69i		−	0.0636002i
$81$	56081.4	−	18484.2i	0.949743	−	0.313032i
$82$			34073.7i			0.559609i
$83$	32348.9			0.515424			0.257712	−	0.966222i	$-0.417031\pi$
$83$	32348.9			0.515424			0.257712	+	0.966222i	$0.417031\pi$
$84$	−32079.7	+	2558.82i	−0.496058	+	0.0395678i
$85$	−22653.0			−0.340078
$86$			3134.27i			0.0456972i
$87$	−5325.48	−	66765.1i	−0.0754329	−	0.945696i
$88$	−38758.0			−0.533525
$89$	−63430.2			−0.848830			−0.424415	−	0.905468i	$-0.639520\pi$
$89$	−63430.2			−0.848830			−0.424415	+	0.905468i	$0.639520\pi$
$90$	2191.26	+	13648.4i	0.0285160	+	0.177614i
$91$		−	147281.i		−	1.86441i
$92$	44051.5			0.542614
$93$	−5092.47	−	63843.9i	−0.0610550	−	0.765441i
$94$	65462.8			0.764143
$95$		−	19313.6i		−	0.219561i
$96$	15912.0	−	1269.21i	0.176217	−	0.0140558i
$97$		−	174688.i		−	1.88510i	−0.334063	−	0.942551i	$-0.608420\pi$
$97$		−	174688.i		−	1.88510i	0.334063	−	0.942551i	$-0.391580\pi$
$98$	634.780			0.00667664
$99$	145299.	−	23327.7i	1.48996	−	0.239213i
$100$	46764.0			0.467640
$101$	−15232.9			−0.148586			−0.0742932	−	0.997236i	$-0.523670\pi$
$101$	−15232.9			−0.148586			−0.0742932	+	0.997236i	$0.523670\pi$
$102$	−7897.29	−	99007.7i	−0.0751584	−	0.942255i
$103$		−	22013.2i		−	0.204452i	−0.994761	−	0.102226i	$-0.967404\pi$
$103$		−	22013.2i		−	0.204452i	0.994761	−	0.102226i	$-0.0325965\pi$
$104$			73053.4i			0.662303i
$105$	2274.38	+	28513.7i	0.0201322	+	0.252395i
$106$		−	131987.i		−	1.14095i
$107$		−	75985.9i		−	0.641614i	−0.947145	−	0.320807i	$-0.896046\pi$
$107$		−	75985.9i		−	0.641614i	0.947145	−	0.320807i	$-0.103954\pi$
$108$	−58888.2	+	14335.3i	−0.485813	+	0.118262i
$109$			101895.i			0.821462i	0.911757	+	0.410731i	$0.134726\pi$
$109$			101895.i			0.821462i	−0.911757	+	0.410731i	$0.865274\pi$
$110$			34449.6i			0.271458i
$111$	7592.74	+	95189.5i	0.0584912	+	0.733300i
$112$	33031.2			0.248817
$113$	−57304.1			−0.422172			−0.211086	−	0.977467i	$-0.567700\pi$
$113$	−57304.1			−0.422172			−0.211086	+	0.977467i	$0.567700\pi$
$114$	84412.3	−	6733.10i	0.608336	−	0.0485236i
$115$		−	39154.7i		−	0.276083i
$116$			68745.4i			0.474350i
$117$	−43969.5	−	273867.i	−0.296952	−	1.84959i
$118$	−38470.7	−	99793.8i	−0.254346	−	0.659779i
$119$		−	205527.i		−	1.33046i
$120$	−1128.13	−	14143.3i	−0.00715164	−	0.0896595i
$121$	205693.			1.27719
$122$			178515.i			1.08587i
$123$	10558.3	+	132369.i	0.0629262	+	0.788901i
$124$			65737.5i			0.383936i
$125$		−	86007.7i		−	0.492337i
$126$	−123830.	+	19880.9i	−0.694862	+	0.111560i
$127$	45887.0			0.252453			0.126226	−	0.992001i	$-0.459713\pi$
$127$	45887.0			0.252453			0.126226	+	0.992001i	$0.459713\pi$
$128$	−16384.0			−0.0883883
$129$	971.205	+	12175.9i	0.00513850	+	0.0644210i
$130$	64932.7			0.336981
$131$	−101481.			−0.516661			−0.258330	−	0.966057i	$-0.583172\pi$
$131$	−101481.			−0.516661			−0.258330	+	0.966057i	$0.583172\pi$
$132$	−150566.	+	12009.8i	−0.752129	+	0.0599931i
$133$	175229.			0.858966
$134$			26059.2i			0.125372i
$135$	12741.8	+	52342.2i	0.0601721	+	0.247182i
$136$			101944.i			0.472624i
$137$			145700.i			0.663221i	0.943416	+	0.331610i	$0.107592\pi$
$137$			145700.i			0.663221i	−0.943416	+	0.331610i	$0.892408\pi$
$138$	171130.	−	13650.1i	0.764943	−	0.0610152i
$139$	−239234.			−1.05023			−0.525117	−	0.851030i	$-0.675978\pi$
$139$	−239234.			−1.05023			−0.525117	+	0.851030i	$0.675978\pi$
$140$		−	29359.5i		−	0.126598i
$141$	254308.	−	20284.7i	1.07724	−	0.0859255i
$142$		−	281214.i		−	1.17035i
$143$		−	691260.i		−	2.82684i
$144$	61421.4	−	9861.23i	0.246839	−	0.0396301i
$145$	61103.7			0.241350
$146$			151420.i			0.587898i
$147$	2465.98	−	196.697i	0.00941231	−	0.000750767i
$148$		−	98012.9i		−	0.367814i
$149$	404084.			1.49110			0.745549	−	0.666451i	$-0.232187\pi$
$149$	404084.			1.49110			0.745549	+	0.666451i	$0.232187\pi$
$150$	181668.	−	14490.6i	0.659249	−	0.0525846i
$151$		−	279557.i		−	0.997763i	−0.866670	−	0.498881i	$-0.833744\pi$
$151$		−	279557.i		−	0.997763i	0.866670	−	0.498881i	$-0.166256\pi$
$152$	−86916.1			−0.305134
$153$	−61358.4	−	382176.i	−0.211907	−	1.31988i
$154$	−312555.			−1.06200
$155$	58430.1			0.195347
$156$	22636.8	+	283796.i	0.0744739	+	0.933673i
$157$			493971.i			1.59938i	0.600412	+	0.799691i	$0.295003\pi$
$157$			493971.i			1.59938i	−0.600412	+	0.799691i	$0.704997\pi$
$158$	−355744.			−1.13369
$159$	−40898.5	−	512741.i	−0.128296	−	1.60844i
$160$			14562.7i			0.0449721i
$161$	355243.			1.08009
$162$	−224325.	+	73936.9i	−0.671569	+	0.221347i
$163$	−94184.9			−0.277659			−0.138830	−	0.990316i	$-0.544334\pi$
$163$	−94184.9			−0.277659			−0.138830	+	0.990316i	$0.544334\pi$
$164$		−	136295.i		−	0.395703i
$165$	10674.8	+	133829.i	0.0305246	+	0.382684i
$166$	−129396.			−0.364460
$167$			256795.i			0.712517i	0.934387	+	0.356259i	$0.115948\pi$
$167$			256795.i			0.712517i	−0.934387	+	0.356259i	$0.884052\pi$
$168$	128319.	−	10235.3i	0.350766	−	0.0279787i
$169$	−931635.			−2.50916
$170$	90612.1			0.240472
$171$	325837.	−	52313.2i	0.852138	−	0.136811i
$172$		−	12537.1i		−	0.0323128i
$173$	−69165.4			−0.175701			−0.0878503	−	0.996134i	$-0.528000\pi$
$173$	−69165.4			−0.175701			−0.0878503	+	0.996134i	$0.528000\pi$
$174$	21301.9	+	267061.i	0.0533391	+	0.668708i
$175$	377118.			0.930854
$176$	155032.			0.377259
$177$	−180373.	−	375756.i	−0.432750	−	0.901514i
$178$	253721.			0.600214
$179$	−513097.			−1.19693			−0.598463	−	0.801151i	$-0.704222\pi$
$179$	−513097.			−1.19693			−0.598463	+	0.801151i	$0.704222\pi$
$180$	−8765.05	−	54593.8i	−0.0201638	−	0.125592i
$181$	527570.			1.19697			0.598486	−	0.801134i	$-0.295769\pi$
$181$	527570.			1.19697			0.598486	+	0.801134i	$0.295769\pi$
$182$			589122.i			1.31834i
$183$	55316.0	+	693492.i	0.122102	+	1.53078i
$184$	−176206.			−0.383686
$185$	−87117.7			−0.187145
$186$	20369.9	+	255375.i	0.0431724	+	0.541249i
$187$		−	964638.i		−	2.01725i
$188$	−261851.			−0.540331
$189$	−474890.	+	115604.i	−0.967027	+	0.235406i
$190$			77254.4i			0.155253i
$191$	−346312.			−0.686885			−0.343442	−	0.939174i	$-0.611593\pi$
$191$	−346312.			−0.686885			−0.343442	+	0.939174i	$0.611593\pi$
$192$	−63648.2	+	5076.86i	−0.124604	+	0.00993899i
$193$	262442.			0.507154			0.253577	−	0.967315i	$-0.418393\pi$
$193$	262442.			0.507154			0.253577	+	0.967315i	$0.418393\pi$
$194$			698753.i			1.33297i
$195$	252249.	−	20120.5i	0.475054	−	0.0378924i
$196$	−2539.12			−0.00472110
$197$			318442.i			0.584608i	0.956326	+	0.292304i	$0.0944218\pi$
$197$			318442.i			0.584608i	−0.956326	+	0.292304i	$0.905578\pi$
$198$	−581194.	+	93310.9i	−1.05356	+	0.169149i
$199$	889315.			1.59193			0.795963	−	0.605345i	$-0.206965\pi$
$199$	889315.			1.59193			0.795963	+	0.605345i	$0.206965\pi$
$200$	−187056.			−0.330672
$201$	8074.90	+	101234.i	0.0140977	+	0.176741i
$202$	60931.6			0.105066
$203$			554382.i			0.944210i
$204$	31589.2	+	396031.i	0.0531450	+	0.666275i
$205$	−121144.			−0.201334
$206$			88053.0i			0.144569i
$207$	660573.	−	106055.i	1.07151	−	0.172031i
$208$		−	292213.i		−	0.468319i
$209$	822435.			1.30237
$210$	−9097.53	−	114055.i	−0.0142356	−	0.178470i
$211$			803756.i			1.24285i	0.783474	+	0.621424i	$0.213446\pi$
$211$			803756.i			1.24285i	−0.783474	+	0.621424i	$0.786554\pi$
$212$			527949.i			0.806774i
$213$	−87138.8	−	1.09245e6i	−0.131602	−	1.64988i
$214$			303944.i			0.453690i
$215$	−11143.4			−0.0164408
$216$	235553.	−	57341.1i	0.343521	−	0.0836242i
$217$			530125.i			0.764238i
$218$		−	407581.i		−	0.580861i
$219$	46920.1	+	588234.i	0.0661072	+	0.828781i
$220$		−	137799.i		−	0.191950i
$221$	−1.81821e6			−2.50416
$222$	−30370.9	−	380758.i	−0.0413596	−	0.518521i
$223$	−478296.			−0.644072			−0.322036	−	0.946727i	$-0.604367\pi$
$223$	−478296.			−0.644072			−0.322036	+	0.946727i	$0.604367\pi$
$224$	−132125.			−0.175940
$225$	701248.	−	112586.i	0.923454	−	0.148261i
$226$	229217.			0.298521
$227$	1.11247e6			1.43292			0.716460	−	0.697628i	$-0.245761\pi$
$227$	1.11247e6			1.43292			0.716460	+	0.697628i	$0.245761\pi$
$228$	−337649.	+	26932.4i	−0.430159	+	0.0343114i
$229$		−	734722.i		−	0.925837i	−0.886401	−	0.462919i	$-0.846802\pi$
$229$		−	734722.i		−	0.925837i	0.886401	−	0.462919i	$-0.153198\pi$
$230$			156619.i			0.195220i
$231$	−1.21421e6	+	96850.4i	−1.49714	+	0.119418i
$232$		−	274982.i		−	0.335416i
$233$	842809.			1.01704			0.508522	−	0.861049i	$-0.330192\pi$
$233$	842809.			1.01704			0.508522	+	0.861049i	$0.330192\pi$
$234$	175878.	+	1.09547e6i	0.209977	+	1.30786i
$235$			232744.i			0.274921i
$236$	153883.	+	399175.i	0.179850	+	0.466534i
$237$	−1.38199e6	+	110233.i	−1.59821	+	0.127480i
$238$			822106.i			0.940775i
$239$		−	814744.i		−	0.922627i	−0.887237	−	0.461314i	$-0.847378\pi$
$239$		−	814744.i		−	0.922627i	0.887237	−	0.461314i	$-0.152622\pi$
$240$	4512.51	+	56573.0i	0.00505697	+	0.0633988i
$241$	−1.34891e6			−1.49603			−0.748013	−	0.663684i	$-0.768992\pi$
$241$	−1.34891e6			−1.49603			−0.748013	+	0.663684i	$0.768992\pi$
$242$	−822771.			−0.903109
$243$	−848543.	+	356739.i	−0.921846	+	0.387557i
$244$		−	714062.i		−	0.767823i
$245$			2256.87i			0.00240210i
$246$	−42233.3	−	529475.i	−0.0444956	−	0.557837i
$247$		−	1.55017e6i		−	1.61673i
$248$		−	262950.i		−	0.271484i
$249$	−502673.	+	40095.5i	−0.513792	+	0.0409823i
$250$			344031.i			0.348135i
$251$			79737.5i			0.0798874i	0.999202	+	0.0399437i	$0.0127179\pi$
$251$			79737.5i			0.0798874i	−0.999202	+	0.0399437i	$0.987282\pi$
$252$	495319.	−	79523.6i	0.491342	−	0.0788851i
$253$	1.66733e6			1.63765
$254$	−183548.			−0.178511
$255$	352008.	−	28077.7i	0.339002	−	0.0270403i
$256$	65536.0			0.0625000
$257$			783465.i			0.739923i	0.929047	+	0.369962i	$0.120629\pi$
$257$			783465.i			0.739923i	−0.929047	+	0.369962i	$0.879371\pi$
$258$	−3884.82	−	48703.7i	−0.00363347	−	0.0455525i
$259$		−	790402.i		−	0.732148i
$260$	−259731.			−0.238281
$261$	165506.	+	1.03087e6i	0.150388	+	0.936704i
$262$	405923.			0.365334
$263$		−	2.09474e6i		−	1.86742i	−0.358035	−	0.933708i	$-0.616553\pi$
$263$		−	2.09474e6i		−	1.86742i	0.358035	−	0.933708i	$-0.383447\pi$
$264$	602264.	−	48039.3i	0.531836	−	0.0424216i
$265$	469262.			0.410488
$266$	−700915.			−0.607381
$267$	985648.	−	78619.6i	0.846143	−	0.0674921i
$268$		−	104237.i		−	0.0886512i
$269$	−351268.			−0.295977			−0.147988	−	0.988989i	$-0.547280\pi$
$269$	−351268.			−0.295977			−0.147988	+	0.988989i	$0.547280\pi$
$270$	−50967.1	−	209369.i	−0.0425481	−	0.174784i
$271$	351700.			0.290903			0.145452	−	0.989365i	$-0.453536\pi$
$271$	351700.			0.290903			0.145452	+	0.989365i	$0.453536\pi$
$272$		−	407777.i		−	0.334196i
$273$	182549.	+	2.28861e6i	0.148243	+	1.85851i
$274$		−	582800.i		−	0.468968i
$275$	1.77000e6			1.41137
$276$	−684521.	+	54600.4i	−0.540896	+	0.0431443i
$277$	−668952.			−0.523836			−0.261918	−	0.965090i	$-0.584355\pi$
$277$	−668952.			−0.523836			−0.261918	+	0.965090i	$0.584355\pi$
$278$	956936.			0.742627
$279$	158265.	+	985764.i	0.121723	+	0.758163i
$280$			117438.i			0.0895186i
$281$			1.81360e6i			1.37017i	0.728462	+	0.685087i	$0.240236\pi$
$281$			1.81360e6i			1.37017i	−0.728462	+	0.685087i	$0.759764\pi$
$282$	−1.01723e6	+	81139.0i	−0.761724	+	0.0607585i
$283$			1.09259e6i			0.810946i	0.914107	+	0.405473i	$0.132893\pi$
$283$			1.09259e6i			0.810946i	−0.914107	+	0.405473i	$0.867107\pi$
$284$			1.12485e6i			0.827562i
$285$	23938.6	+	300116.i	0.0174577	+	0.218865i
$286$			2.76504e6i			1.99888i
$287$		−	1.09912e6i		−	0.787662i
$288$	−245686.	+	39444.9i	−0.174541	+	0.0280227i
$289$	−1.11741e6			−0.786988
$290$	−244415.			−0.170660
$291$	216521.	+	2.71450e6i	0.149888	+	1.87913i
$292$		−	605681.i		−	0.415707i
$293$			684238.i			0.465627i	0.972521	+	0.232813i	$0.0747931\pi$
$293$			684238.i			0.465627i	−0.972521	+	0.232813i	$0.925207\pi$
$294$	−9863.92	+	786.790i	−0.00665551	+	0.000530873i
$295$	354803.	−	136777.i	0.237373	−	0.0915078i
$296$			392052.i			0.260084i
$297$	−2.22889e6	+	542585.i	−1.46622	+	0.356925i
$298$	−1.61634e6			−1.05437
$299$		−	3.14269e6i		−	2.03293i
$300$	−726671.	+	57962.5i	−0.466160	+	0.0371829i
$301$		−	101102.i		−	0.0643198i
$302$			1.11823e6i			0.705525i
$303$	236706.	−	18880.7i	0.148116	−	0.0118144i
$304$	347664.			0.215763
$305$	−634686.			−0.390670
$306$	245434.	+	1.52870e6i	0.149841	+	0.933296i
$307$	−455938.			−0.276096			−0.138048	−	0.990426i	$-0.544083\pi$
$307$	−455938.			−0.276096			−0.138048	+	0.990426i	$0.544083\pi$
$308$	1.25022e6			0.750947
$309$	27284.7	+	342066.i	0.0162563	+	0.203805i
$310$	−233720.			−0.138131
$311$			146725.i			0.0860206i	0.999075	+	0.0430103i	$0.0136948\pi$
$311$			146725.i			0.0860206i	−0.999075	+	0.0430103i	$0.986305\pi$
$312$	−90547.3	−	1.13518e6i	−0.0526610	−	0.660206i
$313$			203464.i			0.117389i	0.998276	+	0.0586944i	$0.0186937\pi$
$313$			203464.i			0.117389i	−0.998276	+	0.0586944i	$0.981306\pi$
$314$		−	1.97588e6i		−	1.13093i
$315$	−70683.7	−	440259.i	−0.0401368	−	0.249995i
$316$	1.42298e6			0.801641
$317$		−	1.07360e6i		−	0.600058i	−0.953930	−	0.300029i	$-0.903004\pi$
$317$		−	1.07360e6i		−	0.600058i	0.953930	−	0.300029i	$-0.0969963\pi$
$318$	163594.	+	2.05096e6i	0.0907192	+	1.13734i
$319$			2.60199e6i			1.43162i
$320$		−	58251.0i		−	0.0318001i
$321$	94182.1	+	1.18075e6i	0.0510159	+	0.639583i
$322$	−1.42097e6			−0.763741
$323$		−	2.16323e6i		−	1.15371i
$324$	897302.	−	295747.i	0.474871	−	0.156516i
$325$		−	3.33620e6i		−	1.75204i
$326$	376739.			0.196335
$327$	−126296.	−	1.58336e6i	−0.0653160	−	0.818861i
$328$			545179.i			0.279805i
$329$	−2.11164e6			−1.07555
$330$	−42699.2	−	535316.i	−0.0215842	−	0.270599i
$331$	−2.65257e6			−1.33075			−0.665377	−	0.746508i	$-0.731729\pi$
$331$	−2.65257e6			−1.33075			−0.665377	+	0.746508i	$0.731729\pi$
$332$	517583.			0.257712
$333$	−235969.	−	1.46975e6i	−0.116612	−	0.726327i
$334$		−	1.02718e6i		−	0.503826i
$335$	−92649.9			−0.0451059
$336$	−513276.	+	40941.2i	−0.248029	+	0.0197839i
$337$			3.81843e6i			1.83151i	0.401735	+	0.915756i	$0.368407\pi$
$337$			3.81843e6i			1.83151i	−0.401735	+	0.915756i	$0.631593\pi$
$338$	3.72654e6			1.77425
$339$	890455.	−	71026.6i	0.420836	−	0.0335677i
$340$	−362449.			−0.170039
$341$			2.48814e6i			1.15875i
$342$	−1.30335e6	+	209253.i	−0.602552	+	0.0967400i
$343$	−2.18905e6			−1.00467
$344$			50148.3i			0.0228486i
$345$	48531.0	+	608429.i	0.0219519	+	0.275209i
$346$	276661.			0.124239
$347$	671603.			0.299425			0.149713	−	0.988730i	$-0.452165\pi$
$347$	671603.			0.299425			0.149713	+	0.988730i	$0.452165\pi$
$348$	−85207.7	−	1.06824e6i	−0.0377165	−	0.472848i
$349$		−	304105.i		−	0.133647i	−0.997765	−	0.0668235i	$-0.978714\pi$
$349$		−	304105.i		−	0.133647i	0.997765	−	0.0668235i	$-0.0212865\pi$
$350$	−1.50847e6			−0.658213
$351$	1.02270e6	+	4.20115e6i	0.443077	+	1.82012i
$352$	−620128.			−0.266762
$353$	−1.44409e6			−0.616817			−0.308409	−	0.951254i	$-0.599796\pi$
$353$	−1.44409e6			−0.616817			−0.308409	+	0.951254i	$0.599796\pi$
$354$	721491.	+	1.50302e6i	0.306001	+	0.637466i
$355$	999815.			0.421065
$356$	−1.01488e6			−0.424415
$357$	254744.	+	3.19370e6i	0.105787	+	1.32624i
$358$	2.05239e6			0.846354
$359$		−	1.60236e6i		−	0.656182i	−0.944646	−	0.328091i	$-0.893595\pi$
$359$		−	1.60236e6i		−	0.656182i	0.944646	−	0.328091i	$-0.106405\pi$
$360$	35060.2	+	218375.i	0.0142580	+	0.0888070i
$361$	−631763.			−0.255144
$362$	−2.11028e6			−0.846386
$363$	−3.19628e6	+	254949.i	−1.27315	+	0.101552i
$364$		−	2.35649e6i		−	0.932206i
$365$	−538353.			−0.211512
$366$	−221264.	−	2.77397e6i	−0.0863392	−	1.08243i
$367$			375916.i			0.145689i	0.997343	+	0.0728443i	$0.0232076\pi$
$367$			375916.i			0.145689i	−0.997343	+	0.0728443i	$0.976792\pi$
$368$	704824.			0.271307
$369$	−328133.	−	2.04380e6i	−0.125454	−	0.781400i
$370$	348471.			0.132331
$371$			4.25752e6i			1.60591i
$372$	−81479.5	−	1.02150e6i	−0.0305275	−	0.382721i
$373$	4.61342e6			1.71692			0.858461	−	0.512878i	$-0.171421\pi$
$373$	4.61342e6			1.71692			0.858461	+	0.512878i	$0.171421\pi$
$374$			3.85855e6i			1.42641i
$375$	106604.	+	1.33648e6i	0.0391466	+	0.490778i
$376$	1.04740e6			0.382072
$377$	4.90438e6			1.77718
$378$	1.89956e6	−	462414.i	0.683792	−	0.166457i
$379$	5.39379e6			1.92884			0.964420	−	0.264373i	$-0.0851651\pi$
$379$	5.39379e6			1.92884			0.964420	+	0.264373i	$0.0851651\pi$
$380$		−	309018.i		−	0.109780i
$381$	−713042.	+	56875.4i	−0.251653	+	0.0200730i
$382$	1.38525e6			0.485701
$383$		−	4.69365e6i		−	1.63499i	−0.575939	−	0.817493i	$-0.695363\pi$
$383$		−	4.69365e6i		−	1.63499i	0.575939	−	0.817493i	$-0.304637\pi$
$384$	254593.	−	20307.4i	0.0881085	−	0.00702792i
$385$		−	1.11124e6i		−	0.382083i
$386$	−1.04977e6			−0.358612
$387$	−30183.3	−	187999.i	−0.0102445	−	0.0638085i
$388$		−	2.79501e6i		−	0.942551i
$389$		−	421339.i		−	0.141175i	−0.997506	−	0.0705875i	$-0.977513\pi$
$389$		−	421339.i		−	0.141175i	0.997506	−	0.0705875i	$-0.0224874\pi$
$390$	−1.00900e6	+	80482.0i	−0.335914	+	0.0267940i
$391$		−	4.38555e6i		−	1.45071i
$392$	10156.5			0.00333832
$393$	1.57692e6	−	125782.i	0.515025	−	0.0410807i
$394$		−	1.27377e6i		−	0.413380i
$395$		−	1.26480e6i		−	0.407876i
$396$	2.32478e6	−	373244.i	0.744978	−	0.119606i
$397$		−	2.63335e6i		−	0.838557i	−0.907858	−	0.419279i	$-0.862283\pi$
$397$		−	2.63335e6i		−	0.838557i	0.907858	−	0.419279i	$-0.137717\pi$
$398$	−3.55726e6			−1.12566
$399$	−2.72290e6	+	217190.i	−0.856246	+	0.0682980i
$400$	748224.			0.233820
$401$	−1.60285e6			−0.497772			−0.248886	−	0.968533i	$-0.580065\pi$
$401$	−1.60285e6			−0.497772			−0.248886	+	0.968533i	$0.580065\pi$
$402$	−32299.6	−	404937.i	−0.00996855	−	0.124975i
$403$	4.68979e6			1.43844
$404$	−243726.			−0.0742932
$405$	−262872.	−	797557.i	−0.0796355	−	0.241615i
$406$		−	2.21753e6i		−	0.667658i
$407$		−	3.70975e6i		−	1.11009i
$408$	−126357.	−	1.58412e6i	−0.0375792	−	0.471128i
$409$		−	3.77495e6i		−	1.11584i	−0.829894	−	0.557921i	$-0.811599\pi$
$409$		−	3.77495e6i		−	1.11584i	0.829894	−	0.557921i	$-0.188401\pi$
$410$	484577.			0.142365
$411$	−180590.	−	2.26405e6i	−0.0527339	−	0.661121i
$412$		−	352212.i		−	0.102226i
$413$	1.24095e6	+	3.21906e6i	0.357997	+	0.928653i
$414$	−2.64229e6	+	424221.i	−0.757669	+	0.121644i
$415$		−	460048.i		−	0.131124i
$416$			1.16885e6i			0.331152i
$417$	3.71748e6	−	296523.i	1.04691	−	0.0835060i
$418$	−3.28974e6			−0.920917
$419$	−2.59094e6			−0.720979			−0.360489	−	0.932763i	$-0.617390\pi$
$419$	−2.59094e6			−0.720979			−0.360489	+	0.932763i	$0.617390\pi$
$420$	36390.1	+	456220.i	0.0100661	+	0.126198i
$421$		−	4.21680e6i		−	1.15952i	−0.814788	−	0.579759i	$-0.803147\pi$
$421$		−	4.21680e6i		−	1.15952i	0.814788	−	0.579759i	$-0.196853\pi$
$422$		−	3.21502e6i		−	0.878826i
$423$	−3.92658e6	+	630414.i	−1.06700	+	0.171307i
$424$		−	2.11179e6i		−	0.570476i
$425$		−	4.65559e6i		−	1.25027i
$426$	348555.	+	4.36981e6i	0.0930567	+	1.16664i
$427$		−	5.75839e6i		−	1.52838i
$428$		−	1.21578e6i		−	0.320807i
$429$	856795.	+	1.07416e7i	0.224767	+	2.81789i
$430$	44573.7			0.0116254
$431$	4.06248e6			1.05341			0.526705	−	0.850048i	$-0.323427\pi$
$431$	4.06248e6			1.05341			0.526705	+	0.850048i	$0.323427\pi$
$432$	−942211.	+	229365.i	−0.242906	+	0.0591312i
$433$	−2.90356e6			−0.744237			−0.372118	−	0.928185i	$-0.621368\pi$
$433$	−2.90356e6			−0.744237			−0.372118	+	0.928185i	$0.621368\pi$
$434$		−	2.12050e6i		−	0.540398i
$435$	−949496.	+	75736.0i	−0.240586	+	0.0191902i
$436$			1.63032e6i			0.410731i
$437$	3.73904e6			0.936606
$438$	−187681.	−	2.35294e6i	−0.0467449	−	0.586037i
$439$	1.49706e6			0.370747			0.185374	−	0.982668i	$-0.440650\pi$
$439$	1.49706e6			0.370747			0.185374	+	0.982668i	$0.440650\pi$
$440$			551194.i			0.135729i
$441$	−38075.3	+	6113.00i	−0.00932281	+	0.00149678i
$442$	7.27283e6			1.77071
$443$	4.03523e6			0.976920			0.488460	−	0.872586i	$-0.337559\pi$
$443$	4.03523e6			0.976920			0.488460	+	0.872586i	$0.337559\pi$
$444$	121484.	+	1.52303e6i	0.0292456	+	0.366650i
$445$			902068.i			0.215943i
$446$	1.91318e6			0.455428
$447$	−6.27911e6	+	500849.i	−1.48638	+	0.118560i
$448$	528500.			0.124408
$449$		−	5.16530e6i		−	1.20915i	−0.796549	−	0.604574i	$-0.793343\pi$
$449$		−	5.16530e6i		−	1.20915i	0.796549	−	0.604574i	$-0.206657\pi$
$450$	−2.80499e6	+	450342.i	−0.652981	+	0.104836i
$451$		−	5.15870e6i		−	1.19426i
$452$	−916866.			−0.211086
$453$	346501.	+	4.34406e6i	0.0793340	+	0.994604i
$454$	−4.44987e6			−1.01323
$455$	−2.09454e6			−0.474308
$456$	1.35060e6	−	107730.i	0.304168	−	0.0242618i
$457$		−	2.69333e6i		−	0.603253i	−0.953426	−	0.301627i	$-0.902470\pi$
$457$		−	2.69333e6i		−	0.603253i	0.953426	−	0.301627i	$-0.0975296\pi$
$458$			2.93889e6i			0.654666i
$459$	1.42715e6	+	5.86261e6i	0.316182	+	1.29885i
$460$		−	626475.i		−	0.138041i
$461$			4.14808e6i			0.909065i	0.890730	+	0.454532i	$0.150194\pi$
$461$			4.14808e6i			0.909065i	−0.890730	+	0.454532i	$0.849806\pi$
$462$	4.85682e6	−	387402.i	1.05864	−	0.0844416i
$463$		−	437497.i		−	0.0948469i	−0.998875	−	0.0474234i	$-0.984899\pi$
$463$		−	437497.i		−	0.0948469i	0.998875	−	0.0474234i	$-0.0151010\pi$
$464$			1.09993e6i			0.237175i
$465$	−907951.	+	72422.2i	−0.194729	+	0.0155324i
$466$	−3.37124e6			−0.719158
$467$	855327.			0.181485			0.0907423	−	0.995874i	$-0.471076\pi$
$467$	855327.			0.181485			0.0907423	+	0.995874i	$0.471076\pi$
$468$	−703512.	−	4.38188e6i	−0.148476	−	0.924795i
$469$		−	840595.i		−	0.176463i
$470$		−	930975.i		−	0.194399i
$471$	−612261.	−	7.67586e6i	−0.127170	−	1.59432i
$472$	−615530.	−	1.59670e6i	−0.127173	−	0.329889i
$473$		−	474523.i		−	0.0975224i
$474$	5.52795e6	−	440933.i	1.13010	−	0.0901420i
$475$	3.96928e6			0.807194
$476$		−	3.28843e6i		−	0.665228i
$477$	1.27105e6	+	7.91684e6i	0.255780	+	1.59315i
$478$			3.25898e6i			0.652396i
$479$			1.70121e6i			0.338780i	0.985549	+	0.169390i	$0.0541798\pi$
$479$			1.70121e6i			0.338780i	−0.985549	+	0.169390i	$0.945820\pi$
$480$	−18050.1	−	226292.i	−0.00357582	−	0.0448297i
$481$	−6.99235e6			−1.37804
$482$	5.39563e6			1.05785
$483$	−5.52016e6	+	440312.i	−1.07667	+	0.0858802i
$484$	3.29108e6			0.638595
$485$	−2.48432e6			−0.479571
$486$	3.39417e6	−	1.42696e6i	0.651844	−	0.274044i
$487$	3.61906e6			0.691470			0.345735	−	0.938332i	$-0.387630\pi$
$487$	3.61906e6			0.691470			0.345735	+	0.938332i	$0.387630\pi$
$488$			2.85625e6i			0.542933i
$489$	1.46355e6	−	116739.i	0.276780	−	0.0220772i
$490$		−	9027.49i		−	0.00169854i
$491$		−	7.40145e6i		−	1.38552i	−0.721168	−	0.692760i	$-0.756394\pi$
$491$		−	7.40145e6i		−	1.38552i	0.721168	−	0.692760i	$-0.243606\pi$
$492$	168933.	+	2.11790e6i	0.0314631	+	0.394451i
$493$	6.84395e6			1.26821
$494$			6.20069e6i			1.14320i
$495$	−331754.	−	2.06635e6i	−0.0608559	−	0.379046i
$496$			1.05180e6i			0.191968i
$497$			9.07113e6i			1.64729i
$498$	2.01069e6	−	160382.i	0.363306	−	0.0289789i
$499$	−2.68222e6			−0.482217			−0.241109	−	0.970498i	$-0.577511\pi$
$499$	−2.68222e6			−0.482217			−0.241109	+	0.970498i	$0.577511\pi$
$500$		−	1.37612e6i		−	0.246168i
$501$	−318289.	−	3.99036e6i	−0.0566536	−	0.710261i
$502$		−	318950.i		−	0.0564889i
$503$	8.16116e6			1.43824			0.719121	−	0.694885i	$-0.244545\pi$
$503$	8.16116e6			1.43824			0.719121	+	0.694885i	$0.244545\pi$
$504$	−1.98128e6	+	318094.i	−0.347431	+	0.0557802i
$505$			216634.i			0.0378005i
$506$	−6.66933e6			−1.15799
$507$	1.44768e7	−	1.15473e6i	2.50122	−	0.199508i
$508$	734191.			0.126226
$509$	−1.03197e7			−1.76552			−0.882758	−	0.469827i	$-0.844316\pi$
$509$	−1.03197e7			−1.76552			−0.882758	+	0.469827i	$0.844316\pi$
$510$	−1.40803e6	+	112311.i	−0.239710	+	0.0191204i
$511$		−	4.88438e6i		−	0.827479i
$512$	−262144.			−0.0441942
$513$	−4.99837e6	+	1.21676e6i	−0.838562	+	0.204133i
$514$		−	3.13386e6i		−	0.523205i
$515$	−313060.			−0.0520127
$516$	15539.3	+	194815.i	0.00256925	+	0.0322105i
$517$	−9.91096e6			−1.63076
$518$			3.16161e6i			0.517707i
$519$	1.07477e6	−	85728.2i	0.175144	−	0.0139703i
$520$	1.03892e6			0.168490
$521$		−	3.70457e6i		−	0.597921i	−0.954265	−	0.298961i	$-0.903360\pi$
$521$		−	3.70457e6i		−	0.597921i	0.954265	−	0.298961i	$-0.0966399\pi$
$522$	−662026.	−	4.12348e6i	−0.106340	−	0.662350i
$523$	−8.93017e6			−1.42760			−0.713798	−	0.700351i	$-0.753027\pi$
$523$	−8.93017e6			−1.42760			−0.713798	+	0.700351i	$0.753027\pi$
$524$	−1.62369e6			−0.258330
$525$	−5.86007e6	+	467425.i	−0.927907	+	0.0740140i
$526$			8.37897e6i			1.32046i
$527$	6.54450e6			1.02648
$528$	−2.40906e6	+	192157.i	−0.376065	+	0.0299966i
$529$	1.14387e6			0.177720
$530$	−1.87705e6			−0.290259
$531$	3.26857e6	+	5.61534e6i	0.503061	+	0.864251i
$532$	2.80366e6			0.429483
$533$	−9.72343e6			−1.48252
$534$	−3.94259e6	+	314479.i	−0.598313	+	0.0477241i
$535$	−1.08063e6			−0.163227
$536$			416948.i			0.0626859i
$537$	7.97307e6	−	635968.i	1.19314	−	0.0951698i
$538$	1.40507e6			0.209287
$539$	−96104.7			−0.0142486
$540$	203868.	+	837475.i	0.0300861	+	0.123591i
$541$			5.03604e6i			0.739768i	0.929078	+	0.369884i	$0.120603\pi$
$541$			5.03604e6i			0.739768i	−0.929078	+	0.369884i	$0.879397\pi$
$542$	−1.40680e6			−0.205700
$543$	−8.19796e6	+	653906.i	−1.19318	+	0.0951734i
$544$			1.63111e6i			0.236312i
$545$	1.44909e6			0.208980
$546$	−730198.	−	9.15443e6i	−0.104824	−	1.31416i
$547$	−3.30050e6			−0.471642			−0.235821	−	0.971797i	$-0.575778\pi$
$547$	−3.30050e6			−0.471642			−0.235821	+	0.971797i	$0.575778\pi$
$548$			2.33120e6i			0.331610i
$549$	−1.71912e6	−	1.07077e7i	−0.243431	−	1.51623i
$550$	−7.08000e6			−0.997990
$551$			5.83504e6i			0.818776i
$552$	2.73808e6	−	218402.i	0.382471	−	0.0305076i
$553$	1.14753e7			1.59570
$554$	2.67581e6			0.370408
$555$	1.35373e6	−	107980.i	0.186552	−	0.0148802i
$556$	−3.82774e6			−0.525117
$557$			1.39456e7i			1.90459i	0.305186	+	0.952293i	$0.401281\pi$
$557$			1.39456e7i			1.90459i	−0.305186	+	0.952293i	$0.598719\pi$
$558$	−633059.	−	3.94306e6i	−0.0860714	−	0.536102i
$559$	−894409.			−0.121062
$560$		−	469752.i		−	0.0632992i
$561$	1.19564e6	+	1.49896e7i	0.160396	+	2.01087i
$562$		−	7.25440e6i		−	0.968859i
$563$	−6.74035e6			−0.896213			−0.448107	−	0.893980i	$-0.647902\pi$
$563$	−6.74035e6			−0.896213			−0.448107	+	0.893980i	$0.647902\pi$
$564$	4.06893e6	−	324556.i	0.538620	−	0.0429627i
$565$			814947.i			0.107401i
$566$		−	4.37037e6i		−	0.573425i
$567$	7.23608e6	−	2.38499e6i	0.945248	−	0.311550i
$568$		−	4.49942e6i		−	0.585175i
$569$	−1.44019e6			−0.186483			−0.0932414	−	0.995644i	$-0.529723\pi$
$569$	−1.44019e6			−0.186483			−0.0932414	+	0.995644i	$0.529723\pi$
$570$	−95754.4	−	1.20046e6i	−0.0123444	−	0.154761i
$571$			8.17573e6i			1.04939i	0.851291	+	0.524694i	$0.175820\pi$
$571$			8.17573e6i			1.04939i	−0.851291	+	0.524694i	$0.824180\pi$
$572$		−	1.10602e7i		−	1.41342i
$573$	5.38137e6	−	429242.i	0.684710	−	0.0546155i
$574$			4.39647e6i			0.556961i
$575$	8.04697e6			1.01499
$576$	982743.	−	157780.i	0.123419	−	0.0198150i
$577$	1.22088e7			1.52663			0.763315	−	0.646027i	$-0.223570\pi$
$577$	1.22088e7			1.52663			0.763315	+	0.646027i	$0.223570\pi$
$578$	4.46964e6			0.556484
$579$	−4.07811e6	+	325288.i	−0.505548	+	0.0403248i
$580$	977658.			0.120675
$581$	4.17393e6			0.512985
$582$	−866082.	−	1.08580e7i	−0.105987	−	1.32875i
$583$			1.99827e7i			2.43490i
$584$			2.42272e6i			0.293949i
$585$	−3.89479e6	+	625309.i	−0.470537	+	0.0755449i
$586$		−	2.73695e6i		−	0.329248i
$587$	−5.59392e6			−0.670072			−0.335036	−	0.942205i	$-0.608748\pi$
$587$	−5.59392e6			−0.670072			−0.335036	+	0.942205i	$0.608748\pi$
$588$	39455.7	−	3147.16i	0.00470615	−	0.000375384i
$589$			5.57973e6i			0.662712i
$590$	−1.41921e6	+	547108.i	−0.167848	+	0.0647058i
$591$	−394698.	−	4.94830e6i	−0.0464832	−	0.582757i
$592$		−	1.56821e6i		−	0.183907i
$593$		−	640732.i		−	0.0748238i	−0.999300	−	0.0374119i	$-0.988089\pi$
$593$		−	640732.i		−	0.0748238i	0.999300	−	0.0374119i	$-0.0119114\pi$
$594$	8.91558e6	−	2.17034e6i	1.03677	−	0.252384i
$595$	−2.92288e6			−0.338469
$596$	6.46535e6			0.745549
$597$	−1.38192e7	+	1.10228e6i	−1.58689	+	0.126577i
$598$			1.25707e7i			1.43750i
$599$		−	3.74949e6i		−	0.426978i	−0.976946	−	0.213489i	$-0.931517\pi$
$599$		−	3.74949e6i		−	0.426978i	0.976946	−	0.213489i	$-0.0684827\pi$
$600$	2.90668e6	−	231850.i	0.329625	−	0.0262923i
$601$		−	3.68646e6i		−	0.416316i	−0.978095	−	0.208158i	$-0.933253\pi$
$601$		−	3.68646e6i		−	0.416316i	0.978095	−	0.208158i	$-0.0667469\pi$
$602$			404409.i			0.0454810i
$603$	−250953.	−	1.56308e6i	−0.0281060	−	0.175061i
$604$		−	4.47291e6i		−	0.498881i
$605$		−	2.92524e6i		−	0.324918i
$606$	−946822.	+	75522.7i	−0.104734	+	0.00835403i
$607$	−4.98028e6			−0.548633			−0.274316	−	0.961639i	$-0.588452\pi$
$607$	−4.98028e6			−0.548633			−0.274316	+	0.961639i	$0.588452\pi$
$608$	−1.39066e6			−0.152567
$609$	−687138.	−	8.61459e6i	−0.0750759	−	0.941221i
$610$	2.53875e6			0.276245
$611$			1.86808e7i			2.02438i
$612$	−981735.	−	6.11481e6i	−0.105954	−	0.659940i
$613$			6.97045e6i			0.749220i	0.927182	+	0.374610i	$0.122223\pi$
$613$			6.97045e6i			0.749220i	−0.927182	+	0.374610i	$0.877777\pi$
$614$	1.82375e6			0.195229
$615$	1.88247e6	−	150154.i	0.200697	−	0.0160085i
$616$	−5.00088e6			−0.531000
$617$		−	1.68993e7i		−	1.78713i	−0.448931	−	0.893566i	$-0.648195\pi$
$617$		−	1.68993e7i		−	1.78713i	0.448931	−	0.893566i	$-0.351805\pi$
$618$	−109139.	−	1.36826e6i	−0.0114950	−	0.144112i
$619$	1.13654e7			1.19222			0.596110	−	0.802902i	$-0.296712\pi$
$619$	1.13654e7			1.19222			0.596110	+	0.802902i	$0.296712\pi$
$620$	934881.			0.0976736
$621$	−1.01333e7	+	2.46676e6i	−1.05444	+	0.256683i
$622$		−	586899.i		−	0.0608257i
$623$	−8.18429e6			−0.844813
$624$	362189.	+	4.54074e6i	0.0372369	+	0.466836i
$625$	7.91044e6			0.810029
$626$		−	813856.i		−	0.0830064i
$627$	−1.27799e7	+	1.01938e6i	−1.29825	+	0.103554i
$628$			7.90353e6i			0.799691i
$629$	−9.75767e6			−0.983376
$630$	282735.	+	1.76104e6i	0.0283810	+	0.176773i
$631$	−1.71244e7			−1.71215			−0.856075	−	0.516852i	$-0.827104\pi$
$631$	−1.71244e7			−1.71215			−0.856075	+	0.516852i	$0.827104\pi$
$632$	−5.69191e6			−0.566846
$633$	−996229.	−	1.24896e7i	−0.0988212	−	1.23891i
$634$			4.29439e6i			0.424305i
$635$		−	652578.i		−	0.0642241i
$636$	−654375.	−	8.20385e6i	−0.0641482	−	0.804220i
$637$			181144.i			0.0176879i
$638$		−	1.04079e7i		−	1.01231i
$639$	2.70812e6	+	1.68677e7i	0.262371	+	1.63420i
$640$			233004.i			0.0224861i
$641$			4.12153e6i			0.396199i	0.980182	+	0.198100i	$0.0634770\pi$
$641$			4.12153e6i			0.396199i	−0.980182	+	0.198100i	$0.936523\pi$
$642$	−376728.	−	4.72301e6i	−0.0360737	−	0.452253i
$643$	−1.00290e7			−0.956597			−0.478298	−	0.878197i	$-0.658746\pi$
$643$	−1.00290e7			−0.956597			−0.478298	+	0.878197i	$0.658746\pi$
$644$	5.68389e6			0.540046
$645$	173159.	−	13811.9i	0.0163888	−	0.00130724i
$646$			8.65293e6i			0.815796i
$647$			1.76853e7i			1.66093i	0.557073	+	0.830464i	$0.311924\pi$
$647$			1.76853e7i			1.66093i	−0.557073	+	0.830464i	$0.688076\pi$
$648$	−3.58921e6	+	1.18299e6i	−0.335785	+	0.110673i
$649$	5.82440e6	+	1.51086e7i	0.542799	+	1.40803i
$650$			1.33448e7i			1.23888i
$651$	−657073.	−	8.23766e6i	−0.0607660	−	0.761819i
$652$	−1.50696e6			−0.138830
$653$			5.40800e6i			0.496311i	0.968720	+	0.248155i	$0.0798244\pi$
$653$			5.40800e6i			0.496311i	−0.968720	+	0.248155i	$0.920176\pi$
$654$	505183.	+	6.33344e6i	0.0461854	+	0.579022i
$655$			1.44320e6i			0.131439i
$656$		−	2.18072e6i		−	0.197852i
$657$	−1.45819e6	−	9.08247e6i	−0.131796	−	0.820901i
$658$	8.44655e6			0.760527
$659$	9.77834e6			0.877105			0.438552	−	0.898706i	$-0.355491\pi$
$659$	9.77834e6			0.877105			0.438552	+	0.898706i	$0.355491\pi$
$660$	170797.	+	2.14127e6i	0.0152623	+	0.191342i
$661$	−4.89119e6			−0.435422			−0.217711	−	0.976013i	$-0.569859\pi$
$661$	−4.89119e6			−0.435422			−0.217711	+	0.976013i	$0.569859\pi$
$662$	1.06103e7			0.940985
$663$	2.82533e7	−	2.25361e6i	2.49623	−	0.199111i
$664$	−2.07033e6			−0.182230
$665$		−	2.49200e6i		−	0.218522i
$666$	943874.	+	5.87899e6i	0.0824572	+	0.513591i
$667$			1.18294e7i			1.02956i
$668$			4.10872e6i			0.356259i
$669$	7.43229e6	−	592832.i	0.642033	−	0.0512114i
$670$	370600.			0.0318947
$671$		−	2.70270e7i		−	2.31735i
$672$	2.05310e6	−	163765.i	0.175383	−	0.0139893i
$673$		−	1.48867e7i		−	1.26695i	−0.773763	−	0.633475i	$-0.781628\pi$
$673$		−	1.48867e7i		−	1.26695i	0.773763	−	0.633475i	$-0.218372\pi$
$674$		−	1.52737e7i		−	1.29507i
$675$	−1.07572e7	+	2.61865e6i	−0.908742	+	0.221217i
$676$	−1.49062e7			−1.25458
$677$		−	1.12567e7i		−	0.943932i	−0.881617	−	0.471966i	$-0.843545\pi$
$677$		−	1.12567e7i		−	0.943932i	0.881617	−	0.471966i	$-0.156455\pi$
$678$	−3.56182e6	+	284106.i	−0.297576	+	0.0237360i
$679$		−	2.25397e7i		−	1.87618i
$680$	1.44979e6			0.120236
$681$	−1.72867e7	+	1.37887e6i	−1.42838	+	0.113934i
$682$		−	9.95255e6i		−	0.819358i
$683$	−1.45678e7			−1.19493			−0.597464	−	0.801895i	$-0.703825\pi$
$683$	−1.45678e7			−1.19493			−0.597464	+	0.801895i	$0.703825\pi$
$684$	5.21339e6	−	837011.i	0.426069	−	0.0684055i
$685$	2.07206e6			0.168724
$686$	8.75622e6			0.710406
$687$	910665.	+	1.14169e7i	0.0736151	+	0.922906i
$688$		−	200593.i		−	0.0161564i
$689$	3.76645e7			3.02262
$690$	−194124.	−	2.43372e6i	−0.0155223	−	0.194602i
$691$			3.33663e6i			0.265835i	0.991127	+	0.132918i	$0.0424346\pi$
$691$			3.33663e6i			0.265835i	−0.991127	+	0.132918i	$0.957565\pi$
$692$	−1.10665e6			−0.0878503
$693$	1.87476e7	−	3.00994e6i	1.48290	−	0.238081i
$694$	−2.68641e6			−0.211726
$695$			3.40225e6i			0.267180i
$696$	340831.	+	4.27297e6i	0.0266696	+	0.334354i
$697$	−1.35688e7			−1.05794
$698$			1.21642e6i			0.0945027i
$699$	−1.30965e7	+	1.04463e6i	−1.01382	+	0.0808670i
$700$	6.03388e6			0.465427
$701$	−2.06107e7			−1.58416			−0.792079	−	0.610418i	$-0.791001\pi$
$701$	−2.06107e7			−1.58416			−0.792079	+	0.610418i	$0.791001\pi$
$702$	−4.09078e6	−	1.68046e7i	−0.313302	−	1.28702i
$703$		−	8.31923e6i		−	0.634885i
$704$	2.48051e6			0.188629
$705$	−288478.	−	3.61663e6i	−0.0218595	−	0.274051i
$706$	5.77635e6			0.436156
$707$	−1.96547e6			−0.147883
$708$	−2.88596e6	−	6.01209e6i	−0.216375	−	0.450757i
$709$	−9.10814e6			−0.680478			−0.340239	−	0.940339i	$-0.610508\pi$
$709$	−9.10814e6			−0.680478			−0.340239	+	0.940339i	$0.610508\pi$
$710$	−3.99926e6			−0.297738
$711$	2.13382e7	−	3.42585e6i	1.58301	−	0.254153i
$712$	4.05953e6			0.300107
$713$			1.13119e7i			0.833316i
$714$	−1.01897e6	−	1.27748e7i	−0.0748028	−	0.937796i
$715$	−9.83071e6			−0.719151
$716$	−8.20956e6			−0.598463
$717$	1.00985e6	+	1.26604e7i	0.0733598	+	0.919706i
$718$			6.40944e6i			0.463991i
$719$	1.11712e6			0.0805891			0.0402945	−	0.999188i	$-0.487170\pi$
$719$	1.11712e6			0.0805891			0.0402945	+	0.999188i	$0.487170\pi$
$720$	−140241.	−	873501.i	−0.0100819	−	0.0627960i
$721$		−	2.84033e6i		−	0.203484i
$722$	2.52705e6			0.180414
$723$	2.09608e7	−	1.67193e6i	1.49129	−	0.118952i
$724$	8.44112e6			0.598486
$725$			1.25579e7i			0.887300i
$726$	1.27851e7	−	1.01980e6i	0.900250	−	0.0718079i
$727$	1.94397e6			0.136412			0.0682060	−	0.997671i	$-0.478272\pi$
$727$	1.94397e6			0.136412			0.0682060	+	0.997671i	$0.478272\pi$
$728$			9.42595e6i			0.659169i
$729$	1.27434e7	−	6.59515e6i	0.888112	−	0.459627i
$730$	2.15341e6			0.149562
$731$	−1.24813e6			−0.0863904
$732$	885056.	+	1.10959e7i	0.0610511	+	0.765392i
$733$	2.58122e7			1.77446			0.887229	−	0.461329i	$-0.152627\pi$
$733$	2.58122e7			1.77446			0.887229	+	0.461329i	$0.152627\pi$
$734$		−	1.50366e6i		−	0.103017i
$735$	−2797.32	−	35069.8i	−0.000190996	−	0.00239450i
$736$	−2.81930e6			−0.191843
$737$		−	3.94533e6i		−	0.267556i
$738$	1.31253e6	+	8.17522e6i	0.0887094	+	0.552533i
$739$			2.25094e7i			1.51619i	0.652145	+	0.758094i	$0.273869\pi$
$739$			2.25094e7i			1.51619i	−0.652145	+	0.758094i	$0.726131\pi$
$740$	−1.39388e6			−0.0935723
$741$	1.92139e6	+	2.40883e7i	0.128549	+	1.61161i
$742$		−	1.70301e7i		−	1.13555i
$743$		−	6.75303e6i		−	0.448773i	−0.974500	−	0.224386i	$-0.927962\pi$
$743$		−	6.75303e6i		−	0.448773i	0.974500	−	0.224386i	$-0.0720378\pi$
$744$	325918.	+	4.08601e6i	0.0215862	+	0.270624i
$745$		−	5.74666e6i		−	0.379336i
$746$	−1.84537e7			−1.21405
$747$	7.76140e6	−	1.24609e6i	0.508907	−	0.0817052i
$748$		−	1.54342e7i		−	1.00863i
$749$		−	9.80434e6i		−	0.638578i
$750$	−426415.	−	5.34593e6i	−0.0276808	−	0.347032i
$751$			1.48012e7i			0.957632i	0.877915	+	0.478816i	$0.158934\pi$
$751$			1.48012e7i			0.957632i	−0.877915	+	0.478816i	$0.841066\pi$
$752$	−4.18962e6			−0.270165
$753$	−98832.0	−	1.23905e6i	−0.00635200	−	0.0796344i
$754$	−1.96175e7			−1.25665
$755$	−3.97570e6			−0.253832
$756$	−7.59824e6	+	1.84966e6i	−0.483514	+	0.117703i
$757$	−1.66906e7			−1.05860			−0.529301	−	0.848434i	$-0.677546\pi$
$757$	−1.66906e7			−1.05860			−0.529301	+	0.848434i	$0.677546\pi$
$758$	−2.15752e7			−1.36390
$759$	−2.59088e7	+	2.06660e6i	−1.63246	+	0.130212i
$760$			1.23607e6i			0.0776264i
$761$			1.76235e7i			1.10314i	0.834130	+	0.551569i	$0.185971\pi$
$761$			1.76235e7i			1.10314i	−0.834130	+	0.551569i	$0.814029\pi$
$762$	2.85217e6	−	227502.i	0.177946	−	0.0141937i
$763$			1.31474e7i			0.817574i
$764$	−5.54099e6			−0.343442
$765$	−5.43509e6	+	872605.i	−0.335778	+	0.0539093i
$766$			1.87746e7i			1.15611i
$767$	2.84776e7	−	1.09782e7i	1.74789	−	0.673816i
$768$	−1.01837e6	+	81229.7i	−0.0623021	+	0.00496949i
$769$		−	4.47820e6i		−	0.273078i	−0.990635	−	0.136539i	$-0.956402\pi$
$769$		−	4.47820e6i		−	0.273078i	0.990635	−	0.136539i	$-0.0435979\pi$
$770$			4.44498e6i			0.270174i
$771$	−971079.	−	1.21743e7i	−0.0588327	−	0.737581i
$772$	4.19907e6			0.253577
$773$	3.89974e6			0.234740			0.117370	−	0.993088i	$-0.462554\pi$
$773$	3.89974e6			0.234740			0.117370	+	0.993088i	$0.462554\pi$
$774$	120733.	+	751996.i	0.00724393	+	0.0451194i
$775$			1.20084e7i			0.718176i
$776$			1.11801e7i			0.666484i
$777$	979678.	+	1.22821e7i	0.0582144	+	0.729830i
$778$			1.68536e6i			0.0998257i
$779$		−	1.15686e7i		−	0.683024i
$780$	4.03599e6	−	321928.i	0.237527	−	0.0189462i
$781$			4.25753e7i			2.49764i
$782$			1.75422e7i			1.02581i
$783$	−3.84955e6	−	1.58136e7i	−0.224391	−	0.921781i
$784$	−40625.9			−0.00236055
$785$	7.02497e6			0.406884
$786$	−6.30768e6	+	503129.i	−0.364178	+	0.0290484i
$787$	9.67164e6			0.556626			0.278313	−	0.960490i	$-0.410225\pi$
$787$	9.67164e6			0.556626			0.278313	+	0.960490i	$0.410225\pi$
$788$			5.09507e6i			0.292304i
$789$	2.59636e6	+	3.25504e7i	0.148482	+	1.86150i
$790$			5.05919e6i			0.288412i
$791$	−7.39385e6			−0.420175
$792$	−9.29911e6	+	1.49297e6i	−0.526779	+	0.0845745i
$793$	−5.09420e7			−2.87669
$794$			1.05334e7i			0.592950i
$795$	−7.29191e6	+	581635.i	−0.409188	+	0.0326387i
$796$	1.42290e7			0.795963
$797$	−3.19502e7			−1.78167			−0.890837	−	0.454324i	$-0.849881\pi$
$797$	−3.19502e7			−1.78167			−0.890837	+	0.454324i	$0.849881\pi$
$798$	1.08916e7	−	868761.i	0.605458	−	0.0482940i
$799$			2.60686e7i			1.44461i
$800$	−2.99290e6			−0.165336
$801$	−1.52186e7	+	2.44336e6i	−0.838097	+	0.134557i
$802$	6.41138e6			0.351978
$803$		−	2.29248e7i		−	1.25463i
$804$	129198.	+	1.61975e6i	0.00704883	+	0.0883706i
$805$		−	5.05207e6i		−	0.274776i
$806$	−1.87592e7			−1.01713
$807$	5.45839e6	−	435385.i	0.295040	−	0.0235337i
$808$	974905.			0.0525332
$809$	5.30475e6			0.284966			0.142483	−	0.989797i	$-0.454491\pi$
$809$	5.30475e6			0.284966			0.142483	+	0.989797i	$0.454491\pi$
$810$	1.05149e6	+	3.19023e6i	0.0563108	+	0.170848i
$811$			1.81824e7i			0.970733i	0.874311	+	0.485367i	$0.161314\pi$
$811$			1.81824e7i			0.970733i	−0.874311	+	0.485367i	$0.838686\pi$
$812$			8.87011e6i			0.472105i
$813$	−5.46510e6	+	435920.i	−0.289982	+	0.0231303i
$814$			1.48390e7i			0.784953i
$815$			1.33944e6i			0.0706367i
$816$	505427.	+	6.33649e6i	0.0265725	+	0.333138i
$817$		−	1.06413e6i		−	0.0557751i
$818$			1.50998e7i			0.789019i
$819$	−5.67331e6	−	3.53366e7i	−0.295547	−	1.84084i
$820$	−1.93831e6			−0.100667
$821$	3.60465e7			1.86640			0.933200	−	0.359357i	$-0.117004\pi$
$821$	3.60465e7			1.86640			0.933200	+	0.359357i	$0.117004\pi$
$822$	722362.	+	9.05619e6i	0.0372885	+	0.467483i
$823$		−	2.13707e7i		−	1.09981i	−0.835226	−	0.549906i	$-0.814663\pi$
$823$		−	2.13707e7i		−	1.09981i	0.835226	−	0.549906i	$-0.185337\pi$
$824$			1.40885e6i			0.0722846i
$825$	−2.75042e7	+	2.19386e6i	−1.40690	+	0.112221i
$826$	−4.96380e6	−	1.28762e7i	−0.253142	−	0.656657i
$827$		−	1.78283e7i		−	0.906454i	−0.891395	−	0.453227i	$-0.850273\pi$
$827$		−	1.78283e7i		−	0.906454i	0.891395	−	0.453227i	$-0.149727\pi$
$828$	1.05692e7	−	1.69688e6i	0.535753	−	0.0860153i
$829$	−1.32774e7			−0.671005			−0.335503	−	0.942039i	$-0.608906\pi$
$829$	−1.32774e7			−0.671005			−0.335503	+	0.942039i	$0.608906\pi$
$830$			1.84019e6i			0.0927189i
$831$	1.03949e7	−	829144.i	0.522178	−	0.0416512i
$832$		−	4.67542e6i		−	0.234160i
$833$			252782.i			0.0126222i
$834$	−1.48699e7	+	1.18609e6i	−0.740276	+	0.0590477i
$835$	3.65199e6			0.181265
$836$	1.31590e7			0.651187
$837$	−3.68112e6	−	1.51217e7i	−0.181621	−	0.746084i
$838$	1.03638e7			0.509809
$839$	8.61114e6			0.422334			0.211167	−	0.977450i	$-0.432274\pi$
$839$	8.61114e6			0.422334			0.211167	+	0.977450i	$0.432274\pi$
$840$	−145560.	−	1.82488e6i	−0.00711779	−	0.0892352i
$841$	2.05047e6			0.0999686
$842$			1.68672e7i			0.819904i
$843$	−2.24790e6	−	2.81817e7i	−0.108945	−	1.36584i
$844$			1.28601e7i			0.621424i
$845$			1.32492e7i			0.638333i
$846$	1.57063e7	−	2.52165e6i	0.754481	−	0.121132i
$847$	2.65402e7			1.27115
$848$			8.44718e6i			0.403387i
$849$	−1.35423e6	−	1.69779e7i	−0.0644798	−	0.808378i
$850$			1.86224e7i			0.884072i
$851$		−	1.68657e7i		−	0.798325i
$852$	−1.39422e6	−	1.74792e7i	−0.0658010	−	0.824942i
$853$	−1.44729e7			−0.681058			−0.340529	−	0.940234i	$-0.610606\pi$
$853$	−1.44729e7			−0.681058			−0.340529	+	0.940234i	$0.610606\pi$
$854$			2.30335e7i			1.08073i
$855$	−743968.	−	4.63386e6i	−0.0348048	−	0.216784i
$856$			4.86310e6i			0.226845i
$857$	−1.18909e7			−0.553047			−0.276524	−	0.961007i	$-0.589182\pi$
$857$	−1.18909e7			−0.553047			−0.276524	+	0.961007i	$0.589182\pi$
$858$	−3.42718e6	−	4.29663e7i	−0.158935	−	1.99255i
$859$			3.60296e6i			0.166601i	0.996524	+	0.0833004i	$0.0265461\pi$
$859$			3.60296e6i			0.166601i	−0.996524	+	0.0833004i	$0.973454\pi$
$860$	−178295.			−0.00822040
$861$	1.36232e6	+	1.70793e7i	0.0626285	+	0.785168i
$862$	−1.62499e7			−0.744874
$863$	−3.93352e7			−1.79785			−0.898927	−	0.438097i	$-0.855652\pi$
$863$	−3.93352e7			−1.79785			−0.898927	+	0.438097i	$0.855652\pi$
$864$	3.76884e6	−	917458.i	0.171761	−	0.0418121i
$865$			983631.i			0.0446984i
$866$	1.16142e7			0.526255
$867$	1.73635e7	−	1.38499e6i	0.784496	−	0.0625749i
$868$			8.48200e6i			0.382119i
$869$	5.38591e7			2.41941
$870$	3.79798e6	−	302944.i	0.170120	−	0.0135695i
$871$	−7.43639e6			−0.332137
$872$		−	6.52129e6i		−	0.290431i
$873$	−6.72907e6	−	4.19125e7i	−0.298827	−	1.86127i
$874$	−1.49562e7			−0.662281
$875$		−	1.10974e7i		−	0.490007i
$876$	750722.	+	9.41174e6i	0.0330536	+	0.414390i
$877$	1.34387e7			0.590010			0.295005	−	0.955496i	$-0.404679\pi$
$877$	1.34387e7			0.590010			0.295005	+	0.955496i	$0.404679\pi$
$878$	−5.98824e6			−0.262158
$879$	−848090.	−	1.06324e7i	−0.0370229	−	0.464152i
$880$		−	2.20478e6i		−	0.0959750i
$881$	2.98396e7			1.29525			0.647624	−	0.761960i	$-0.275763\pi$
$881$	2.98396e7			1.29525			0.647624	+	0.761960i	$0.275763\pi$
$882$	152301.	−	24452.0i	0.00659222	−	0.00105838i
$883$	3.11687e7			1.34529			0.672646	−	0.739965i	$-0.265158\pi$
$883$	3.11687e7			1.34529			0.672646	+	0.739965i	$0.265158\pi$
$884$	−2.90913e7			−1.25208
$885$	−5.34378e6	+	2.56516e6i	−0.229346	+	0.110092i
$886$	−1.61409e7			−0.690787
$887$	−3.74851e7			−1.59974			−0.799870	−	0.600174i	$-0.795098\pi$
$887$	−3.74851e7			−1.59974			−0.799870	+	0.600174i	$0.795098\pi$
$888$	−485935.	−	6.09213e6i	−0.0206798	−	0.259261i
$889$	5.92072e6			0.251258
$890$		−	3.60827e6i		−	0.152695i
$891$	3.39625e7	−	1.11939e7i	1.43320	−	0.472376i
$892$	−7.65273e6			−0.322036
$893$	−2.22257e7			−0.932665
$894$	2.51164e7	−	2.00340e6i	1.05103	−	0.0838346i
$895$			7.29698e6i			0.304499i
$896$	−2.11400e6			−0.0879701
$897$	3.89526e6	+	4.88345e7i	0.161642	+	2.02650i
$898$			2.06612e7i			0.854997i
$899$	−1.76529e7			−0.728480
$900$	1.12200e7	−	1.80137e6i	0.461727	−	0.0741304i
$901$	5.25599e7			2.15696
$902$			2.06348e7i			0.844470i
$903$	125313.	+	1.57104e6i	0.00511419	+	0.0641161i
$904$	3.66746e6			0.149260
$905$		−	7.50280e6i		−	0.304510i
$906$	−1.38601e6	−	1.73762e7i	−0.0560976	−	0.703291i
$907$	−3.19046e7			−1.28776			−0.643881	−	0.765126i	$-0.722677\pi$
$907$	−3.19046e7			−1.28776			−0.643881	+	0.765126i	$0.722677\pi$
$908$	1.77995e7			0.716460
$909$	−3.65479e6	+	586778.i	−0.146708	+	0.0235540i
$910$	8.37816e6			0.335386
$911$		−	2.71728e7i		−	1.08477i	−0.840130	−	0.542385i	$-0.817521\pi$
$911$		−	2.71728e7i		−	1.08477i	0.840130	−	0.542385i	$-0.182479\pi$
$912$	−5.40239e6	+	430919.i	−0.215079	+	0.0171557i
$913$	1.95903e7			0.777794
$914$			1.07733e7i			0.426564i
$915$	9.86246e6	−	786673.i	0.389433	−	0.0310629i
$916$		−	1.17556e7i		−	0.462919i
$917$	−1.30939e7			−0.514216
$918$	−5.70860e6	−	2.34505e7i	−0.223575	−	0.918427i
$919$		−	2.16817e7i		−	0.846846i	−0.905932	−	0.423423i	$-0.860828\pi$
$919$		−	2.16817e7i		−	0.846846i	0.905932	−	0.423423i	$-0.139172\pi$
$920$			2.50590e6i			0.0976100i
$921$	7.08486e6	−	565120.i	0.275221	−	0.0219529i
$922$		−	1.65923e7i		−	0.642806i
$923$	8.02484e7			3.10050
$924$	−1.94273e7	+	1.54961e6i	−0.748570	+	0.0597092i
$925$		−	1.79042e7i		−	0.688019i
$926$			1.74999e6i			0.0670669i
$927$	−847960.	−	5.28158e6i	−0.0324098	−	0.201867i
$928$		−	4.39971e6i		−	0.167708i
$929$	−3.05378e7			−1.16091			−0.580455	−	0.814292i	$-0.697125\pi$
$929$	−3.05378e7			−1.16091			−0.580455	+	0.814292i	$0.697125\pi$
$930$	3.63180e6	−	289689.i	0.137694	−	0.0109831i
$931$	−215518.			−0.00814909
$932$	1.34849e7			0.508522
$933$	−181860.	−	2.27997e6i	−0.00683966	−	0.0857482i
$934$	−3.42131e6			−0.128329
$935$	−1.37185e7			−0.513191
$936$	2.81405e6	+	1.75275e7i	0.104988	+	0.653929i
$937$			8.46554e6i			0.314996i	0.987519	+	0.157498i	$0.0503429\pi$
$937$			8.46554e6i			0.314996i	−0.987519	+	0.157498i	$0.949657\pi$
$938$			3.36238e6i			0.124778i
$939$	−252187.	−	3.16165e6i	−0.00933380	−	0.117017i
$940$			3.72390e6i			0.137461i
$941$	−6.25372e6			−0.230231			−0.115116	−	0.993352i	$-0.536724\pi$
$941$	−6.25372e6			−0.230231			−0.115116	+	0.993352i	$0.536724\pi$
$942$	2.44904e6	+	3.07034e7i	0.0899227	+	1.12735i
$943$		−	2.34531e7i		−	0.858857i
$944$	2.46212e6	+	6.38680e6i	0.0899248	+	0.233267i
$945$	1.64405e6	+	6.75362e6i	0.0598874	+	0.246012i
$946$			1.89809e6i			0.0689587i
$947$		−	1.50747e7i		−	0.546229i	−0.961982	−	0.273114i	$-0.911946\pi$
$947$		−	1.50747e7i		−	0.546229i	0.961982	−	0.273114i	$-0.0880538\pi$
$948$	−2.21118e7	+	1.76373e6i	−0.799103	+	0.0637400i
$949$	−4.32100e7			−1.55747
$950$	−1.58771e7			−0.570772
$951$	1.33069e6	+	1.66827e7i	0.0477117	+	0.598158i
$952$			1.31537e7i			0.470387i
$953$		−	1.26308e7i		−	0.450502i	−0.974301	−	0.225251i	$-0.927680\pi$
$953$		−	1.26308e7i		−	0.450502i	0.974301	−	0.225251i	$-0.0723202\pi$
$954$	−5.08420e6	−	3.16673e7i	−0.180864	−	1.12652i
$955$			4.92505e6i			0.174744i
$956$		−	1.30359e7i		−	0.461314i
$957$	−3.22508e6	−	4.04325e7i	−0.113831	−	1.42709i
$958$		−	6.80482e6i		−	0.239554i
$959$			1.87994e7i			0.660082i
$960$	72200.2	+	905168.i	0.00252849	+	0.0316994i
$961$	1.17486e7			0.410372
$962$	2.79694e7			0.974419
$963$	−2.92701e6	−	1.82311e7i	−0.101709	−	0.633501i
$964$	−2.15825e7			−0.748013
$965$		−	3.73230e6i		−	0.129020i
$966$	2.20806e7	−	1.76125e6i	0.761323	−	0.0607265i
$967$		−	4.98973e7i		−	1.71597i	−0.513671	−	0.857987i	$-0.671715\pi$
$967$		−	4.98973e7i		−	1.71597i	0.513671	−	0.857987i	$-0.328285\pi$
$968$	−1.31643e7			−0.451555
$969$	2.68126e6	+	3.36147e7i	0.0917337	+	1.15006i
$970$	9.93728e6			0.339108
$971$			3.80450e7i			1.29494i	0.762091	+	0.647470i	$0.224173\pi$
$971$			3.80450e7i			1.29494i	−0.762091	+	0.647470i	$0.775827\pi$
$972$	−1.35767e7	+	5.70783e6i	−0.460923	+	0.193778i
$973$	−3.08679e7			−1.04526
$974$	−1.44762e7			−0.488943
$975$	4.13511e6	+	5.18416e7i	0.139308	+	1.74649i
$976$		−	1.14250e7i		−	0.383912i
$977$	4.20985e7			1.41101			0.705505	−	0.708705i	$-0.250720\pi$
$977$	4.20985e7			1.41101			0.705505	+	0.708705i	$0.250720\pi$
$978$	−5.85419e6	+	466956.i	−0.195713	+	0.0156109i
$979$	−3.84129e7			−1.28092
$980$			36109.9i			0.00120105i
$981$	3.92504e6	+	2.44474e7i	0.130218	+	0.811075i
$982$			2.96058e7i			0.979711i
$983$	4.07536e7			1.34518			0.672592	−	0.740013i	$-0.265181\pi$
$983$	4.07536e7			1.34518			0.672592	+	0.740013i	$0.265181\pi$
$984$	−675732.	−	8.47160e6i	−0.0222478	−	0.278919i
$985$	4.52870e6			0.148725
$986$	−2.73758e7			−0.896757
$987$	3.28130e7	−	2.61731e6i	1.07214	−	0.0855188i
$988$		−	2.48028e7i		−	0.808366i
$989$		−	2.15733e6i		−	0.0701335i
$990$	1.32701e6	+	8.26541e6i	0.0430316	+	0.268026i
$991$		−	6.61663e6i		−	0.214019i	−0.994258	−	0.107010i	$-0.965872\pi$
$991$		−	6.61663e6i		−	0.214019i	0.994258	−	0.107010i	$-0.0341276\pi$
$992$		−	4.20720e6i		−	0.135742i
$993$	4.12186e7	−	3.28778e6i	1.32654	−	0.105811i
$994$		−	3.62845e7i		−	1.16481i
$995$		−	1.26473e7i		−	0.404987i
$996$	−8.04277e6	+	641527.i	−0.256896	+	0.0204912i
$997$	−1.84668e7			−0.588375			−0.294188	−	0.955748i	$-0.595049\pi$
$997$	−1.84668e7			−0.588375			−0.294188	+	0.955748i	$0.595049\pi$
$998$	1.07289e7			0.340979
$999$	5.48845e6	+	2.25461e7i	0.173995	+	0.714756i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.c.a.353.4	yes	50
3.2	odd	2		354.6.c.b.353.3	yes	50
59.58	odd	2		354.6.c.b.353.4	yes	50
177.176	even	2	inner	354.6.c.a.353.3	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.c.a.353.3	✓	50	177.176	even	2	inner
354.6.c.a.353.4	yes	50	1.1	even	1	trivial
354.6.c.b.353.3	yes	50	3.2	odd	2
354.6.c.b.353.4	yes	50	59.58	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +(-15.5391 + 1.23947i) q^{3} +16.0000 q^{4} -14.2214i q^{5} +(62.1564 - 4.95787i) q^{6} +129.028 q^{7} -64.0000 q^{8} +(239.927 - 38.5204i) q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +(-15.5391 + 1.23947i) q^{3} +16.0000 q^{4} -14.2214i q^{5} +(62.1564 - 4.95787i) q^{6} +129.028 q^{7} -64.0000 q^{8} +(239.927 - 38.5204i) q^{9} +56.8857i q^{10} +605.594 q^{11} +(-248.626 + 19.8315i) q^{12} -1141.46i q^{13} -516.113 q^{14} +(17.6270 + 220.988i) q^{15} +256.000 q^{16} -1592.88i q^{17} +(-959.710 + 154.082i) q^{18} +1358.06 q^{19} -227.543i q^{20} +(-2004.98 + 159.926i) q^{21} -2422.37 q^{22} +2753.22 q^{23} +(994.503 - 79.3259i) q^{24} +2922.75 q^{25} +4565.84i q^{26} +(-3680.51 + 895.955i) q^{27} +2064.45 q^{28} +4296.59i q^{29} +(-70.5080 - 883.953i) q^{30} +4108.59i q^{31} -1024.00 q^{32} +(-9410.38 + 750.614i) q^{33} +6371.52i q^{34} -1834.97i q^{35} +(3838.84 - 616.327i) q^{36} -6125.80i q^{37} -5432.25 q^{38} +(1414.80 + 17737.2i) q^{39} +910.172i q^{40} -8518.43i q^{41} +(8019.94 - 639.706i) q^{42} -783.566i q^{43} +9689.50 q^{44} +(-547.816 - 3412.11i) q^{45} -11012.9 q^{46} -16365.7 q^{47} +(-3978.01 + 317.304i) q^{48} -158.695 q^{49} -11691.0 q^{50} +(1974.32 + 24751.9i) q^{51} -18263.3i q^{52} +32996.8i q^{53} +(14722.0 - 3583.82i) q^{54} -8612.41i q^{55} -8257.81 q^{56} +(-21103.1 + 1683.28i) q^{57} -17186.4i q^{58} +(9617.66 + 24948.4i) q^{59} +(282.032 + 3535.81i) q^{60} -44628.9i q^{61} -16434.4i q^{62} +(30957.4 - 4970.23i) q^{63} +4096.00 q^{64} -16233.2 q^{65} +(37641.5 - 3002.45i) q^{66} -6514.81i q^{67} -25486.1i q^{68} +(-42782.5 + 3412.52i) q^{69} +7339.87i q^{70} +70303.4i q^{71} +(-15355.4 + 2465.31i) q^{72} -37855.1i q^{73} +24503.2i q^{74} +(-45416.9 + 3622.65i) q^{75} +21729.0 q^{76} +78138.7 q^{77} +(-5659.20 - 70949.0i) q^{78} +88936.0 q^{79} -3640.69i q^{80} +(56081.4 - 18484.2i) q^{81} +34073.7i q^{82} +32348.9 q^{83} +(-32079.7 + 2558.82i) q^{84} -22653.0 q^{85} +3134.27i q^{86} +(-5325.48 - 66765.1i) q^{87} -38758.0 q^{88} -63430.2 q^{89} +(2191.26 + 13648.4i) q^{90} -147281. i q^{91} +44051.5 q^{92} +(-5092.47 - 63843.9i) q^{93} +65462.8 q^{94} -19313.6i q^{95} +(15912.0 - 1269.21i) q^{96} -174688. i q^{97} +634.780 q^{98} +(145299. - 23327.7i) 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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