LMFDB - Embedded newform 354.6.c.a.353.3

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

$q$-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	$0.0405991\pi$
$5$			14.2214i			0.254401i	−0.991877	+	0.127200i	$0.959401\pi$
$6$	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	$0.386080\pi$
$13$			1141.46i			1.87328i	−0.350298	+	0.936638i	$0.613920\pi$
$14$	−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	$0.233017\pi$
$17$			1592.88i			1.33678i	−0.743810	+	0.668391i	$0.766983\pi$
$18$	−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	$-0.842683\pi$
$29$		−	4296.59i		−	0.948700i	0.880336	−	0.474350i	$-0.157317\pi$
$30$	−70.5080	+	883.953i	−0.0143033	+	0.179319i
$31$		−	4108.59i		−	0.767872i	−0.923360	−	0.383936i	$-0.874568\pi$
$31$		−	4108.59i		−	0.767872i	0.923360	−	0.383936i	$-0.125432\pi$
$32$	−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	$0.119894\pi$
$37$			6125.80i			0.735629i	−0.929899	+	0.367814i	$0.880106\pi$
$38$	−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	$0.129499\pi$
$41$			8518.43i			0.791407i	−0.918378	+	0.395703i	$0.870501\pi$
$42$	8019.94	+	639.706i	0.701532	+	0.0559573i
$43$			783.566i			0.0646256i	0.999478	+	0.0323128i	$0.0102873\pi$
$43$			783.566i			0.0646256i	−0.999478	+	0.0323128i	$0.989713\pi$
$44$	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	$-0.701211\pi$
$53$		−	32996.8i		−	1.61355i	0.590860	−	0.806774i	$-0.298789\pi$
$54$	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	$0.278660\pi$
$61$			44628.9i			1.53565i	−0.640662	+	0.767823i	$0.721340\pi$
$62$			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	$0.0282557\pi$
$67$			6514.81i			0.177302i	−0.996063	+	0.0886512i	$0.971744\pi$
$68$			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	$-0.689727\pi$
$71$		−	70303.4i		−	1.65512i	0.561375	−	0.827562i	$-0.310273\pi$
$72$	−15355.4	−	2465.31i	−0.349083	−	0.0560454i
$73$			37855.1i			0.831413i	0.909499	+	0.415707i	$0.136466\pi$
$73$			37855.1i			0.831413i	−0.909499	+	0.415707i	$0.863534\pi$
$74$		−	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	$0.391580\pi$
$97$			174688.i			1.88510i	−0.334063	+	0.942551i	$0.608420\pi$
$98$	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	$0.0325965\pi$
$103$			22013.2i			0.204452i	−0.994761	+	0.102226i	$0.967404\pi$
$104$		−	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	$0.103954\pi$
$107$			75985.9i			0.641614i	−0.947145	+	0.320807i	$0.896046\pi$
$108$	−58888.2	−	14335.3i	−0.485813	−	0.118262i
$109$		−	101895.i		−	0.821462i	−0.911757	−	0.410731i	$-0.865274\pi$
$109$		−	101895.i		−	0.821462i	0.911757	−	0.410731i	$-0.134726\pi$
$110$		−	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	$-0.892408\pi$
$137$		−	145700.i		−	0.663221i	0.943416	−	0.331610i	$-0.107592\pi$
$138$	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	$0.166256\pi$
$151$			279557.i			0.997763i	−0.866670	+	0.498881i	$0.833744\pi$
$152$	−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	$-0.704997\pi$
$157$		−	493971.i		−	1.59938i	0.600412	−	0.799691i	$-0.295003\pi$
$158$	−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	$-0.884052\pi$
$167$		−	256795.i		−	0.712517i	0.934387	−	0.356259i	$-0.115948\pi$
$168$	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	$-0.905578\pi$
$197$		−	318442.i		−	0.584608i	0.956326	−	0.292304i	$-0.0944218\pi$
$198$	−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	$-0.786554\pi$
$211$		−	803756.i		−	1.24285i	0.783474	−	0.621424i	$-0.213446\pi$
$212$		−	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	$0.153198\pi$
$229$			734722.i			0.925837i	−0.886401	+	0.462919i	$0.846802\pi$
$230$		−	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	$0.152622\pi$
$239$			814744.i			0.922627i	−0.887237	+	0.461314i	$0.847378\pi$
$240$	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	$-0.987282\pi$
$251$		−	79737.5i		−	0.0798874i	0.999202	−	0.0399437i	$-0.0127179\pi$
$252$	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	$-0.879371\pi$
$257$		−	783465.i		−	0.739923i	0.929047	−	0.369962i	$-0.120629\pi$
$258$	−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	$0.383447\pi$
$263$			2.09474e6i			1.86742i	−0.358035	+	0.933708i	$0.616553\pi$
$264$	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	$-0.759764\pi$
$281$		−	1.81360e6i		−	1.37017i	0.728462	−	0.685087i	$-0.240236\pi$
$282$	−1.01723e6	−	81139.0i	−0.761724	−	0.0607585i
$283$		−	1.09259e6i		−	0.810946i	−0.914107	−	0.405473i	$-0.867107\pi$
$283$		−	1.09259e6i		−	0.810946i	0.914107	−	0.405473i	$-0.132893\pi$
$284$		−	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	$-0.925207\pi$
$293$		−	684238.i		−	0.465627i	0.972521	−	0.232813i	$-0.0747931\pi$
$294$	−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	$-0.986305\pi$
$311$		−	146725.i		−	0.0860206i	0.999075	−	0.0430103i	$-0.0136948\pi$
$312$	−90547.3	+	1.13518e6i	−0.0526610	+	0.660206i
$313$		−	203464.i		−	0.117389i	−0.998276	−	0.0586944i	$-0.981306\pi$
$313$		−	203464.i		−	0.117389i	0.998276	−	0.0586944i	$-0.0186937\pi$
$314$			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	$0.0969963\pi$
$317$			1.07360e6i			0.600058i	−0.953930	+	0.300029i	$0.903004\pi$
$318$	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	$-0.631593\pi$
$337$		−	3.81843e6i		−	1.83151i	0.401735	−	0.915756i	$-0.368407\pi$
$338$	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	$0.0212865\pi$
$349$			304105.i			0.133647i	−0.997765	+	0.0668235i	$0.978714\pi$
$350$	−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	$0.106405\pi$
$359$			1.60236e6i			0.656182i	−0.944646	+	0.328091i	$0.893595\pi$
$360$	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	$-0.976792\pi$
$367$		−	375916.i		−	0.145689i	0.997343	−	0.0728443i	$-0.0232076\pi$
$368$	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	$0.304637\pi$
$383$			4.69365e6i			1.63499i	−0.575939	+	0.817493i	$0.695363\pi$
$384$	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	$0.0224874\pi$
$389$			421339.i			0.141175i	−0.997506	+	0.0705875i	$0.977513\pi$
$390$	−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	$0.137717\pi$
$397$			2.63335e6i			0.838557i	−0.907858	+	0.419279i	$0.862283\pi$
$398$	−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	$0.188401\pi$
$409$			3.77495e6i			1.11584i	−0.829894	+	0.557921i	$0.811599\pi$
$410$	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	$0.196853\pi$
$421$			4.21680e6i			1.15952i	−0.814788	+	0.579759i	$0.803147\pi$
$422$			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	$0.206657\pi$
$449$			5.16530e6i			1.20915i	−0.796549	+	0.604574i	$0.793343\pi$
$450$	−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	$0.0975296\pi$
$457$			2.69333e6i			0.603253i	−0.953426	+	0.301627i	$0.902470\pi$
$458$		−	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	$-0.849806\pi$
$461$		−	4.14808e6i		−	0.909065i	0.890730	−	0.454532i	$-0.150194\pi$
$462$	4.85682e6	+	387402.i	1.05864	+	0.0844416i
$463$			437497.i			0.0948469i	0.998875	+	0.0474234i	$0.0151010\pi$
$463$			437497.i			0.0948469i	−0.998875	+	0.0474234i	$0.984899\pi$
$464$		−	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	$-0.945820\pi$
$479$		−	1.70121e6i		−	0.338780i	0.985549	−	0.169390i	$-0.0541798\pi$
$480$	−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	$0.243606\pi$
$491$			7.40145e6i			1.38552i	−0.721168	+	0.692760i	$0.756394\pi$
$492$	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	$0.0966399\pi$
$521$			3.70457e6i			0.597921i	−0.954265	+	0.298961i	$0.903360\pi$
$522$	−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	$-0.879397\pi$
$541$		−	5.03604e6i		−	0.739768i	0.929078	−	0.369884i	$-0.120603\pi$
$542$	−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	$-0.598719\pi$
$557$		−	1.39456e7i		−	1.90459i	0.305186	−	0.952293i	$-0.401281\pi$
$558$	−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	$-0.824180\pi$
$571$		−	8.17573e6i		−	1.04939i	0.851291	−	0.524694i	$-0.175820\pi$
$572$			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	$0.0119114\pi$
$593$			640732.i			0.0748238i	−0.999300	+	0.0374119i	$0.988089\pi$
$594$	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	$0.0684827\pi$
$599$			3.74949e6i			0.426978i	−0.976946	+	0.213489i	$0.931517\pi$
$600$	2.90668e6	+	231850.i	0.329625	+	0.0262923i
$601$			3.68646e6i			0.416316i	0.978095	+	0.208158i	$0.0667469\pi$
$601$			3.68646e6i			0.416316i	−0.978095	+	0.208158i	$0.933253\pi$
$602$		−	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	$-0.877777\pi$
$613$		−	6.97045e6i		−	0.749220i	0.927182	−	0.374610i	$-0.122223\pi$
$614$	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	$0.351805\pi$
$617$			1.68993e7i			1.78713i	−0.448931	+	0.893566i	$0.648195\pi$
$618$	−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	$-0.936523\pi$
$641$		−	4.12153e6i		−	0.396199i	0.980182	−	0.198100i	$-0.0634770\pi$
$642$	−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	$-0.688076\pi$
$647$		−	1.76853e7i		−	1.66093i	0.557073	−	0.830464i	$-0.311924\pi$
$648$	−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	$-0.920176\pi$
$653$		−	5.40800e6i		−	0.496311i	0.968720	−	0.248155i	$-0.0798244\pi$
$654$	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	$0.218372\pi$
$673$			1.48867e7i			1.26695i	−0.773763	+	0.633475i	$0.781628\pi$
$674$			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	$0.156455\pi$
$677$			1.12567e7i			0.943932i	−0.881617	+	0.471966i	$0.843545\pi$
$678$	−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	$-0.957565\pi$
$691$		−	3.33663e6i		−	0.265835i	0.991127	−	0.132918i	$-0.0424346\pi$
$692$	−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	$-0.726131\pi$
$739$		−	2.25094e7i		−	1.51619i	0.652145	−	0.758094i	$-0.273869\pi$
$740$	−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	$0.0720378\pi$
$743$			6.75303e6i			0.448773i	−0.974500	+	0.224386i	$0.927962\pi$
$744$	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	$-0.841066\pi$
$751$		−	1.48012e7i		−	0.957632i	0.877915	−	0.478816i	$-0.158934\pi$
$752$	−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	$-0.814029\pi$
$761$		−	1.76235e7i		−	1.10314i	0.834130	−	0.551569i	$-0.185971\pi$
$762$	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	$0.0435979\pi$
$769$			4.47820e6i			0.273078i	−0.990635	+	0.136539i	$0.956402\pi$
$770$		−	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	$-0.838686\pi$
$811$		−	1.81824e7i		−	0.970733i	0.874311	−	0.485367i	$-0.161314\pi$
$812$		−	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	$0.185337\pi$
$823$			2.13707e7i			1.09981i	−0.835226	+	0.549906i	$0.814663\pi$
$824$		−	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	$0.149727\pi$
$827$			1.78283e7i			0.906454i	−0.891395	+	0.453227i	$0.850273\pi$
$828$	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	$-0.973454\pi$
$859$		−	3.60296e6i		−	0.166601i	0.996524	−	0.0833004i	$-0.0265461\pi$
$860$	−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	$0.182479\pi$
$911$			2.71728e7i			1.08477i	−0.840130	+	0.542385i	$0.817521\pi$
$912$	−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	$0.139172\pi$
$919$			2.16817e7i			0.846846i	−0.905932	+	0.423423i	$0.860828\pi$
$920$		−	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	$-0.949657\pi$
$937$		−	8.46554e6i		−	0.314996i	0.987519	−	0.157498i	$-0.0503429\pi$
$938$		−	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	$0.0880538\pi$
$947$			1.50747e7i			0.546229i	−0.961982	+	0.273114i	$0.911946\pi$
$948$	−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	$0.0723202\pi$
$953$			1.26308e7i			0.450502i	−0.974301	+	0.225251i	$0.927680\pi$
$954$	−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	$0.328285\pi$
$967$			4.98973e7i			1.71597i	−0.513671	+	0.857987i	$0.671715\pi$
$968$	−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	$-0.775827\pi$
$971$		−	3.80450e7i		−	1.29494i	0.762091	−	0.647470i	$-0.224173\pi$
$972$	−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	$0.0341276\pi$
$991$			6.61663e6i			0.214019i	−0.994258	+	0.107010i	$0.965872\pi$
$992$			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.353.3	✓	50
3.2	odd	2		354.6.c.b.353.4	yes	50
59.58	odd	2		354.6.c.b.353.3	yes	50
177.176	even	2	inner	354.6.c.a.353.4	yes	50

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +(-15.5391 - 1.23947i) q^{3} +16.0000 q^{4} +14.2214i q^{5} +(62.1564 + 4.95787i) q^{6} +129.028 q^{7} -64.0000 q^{8} +(239.927 + 38.5204i) q^{9} +O(q^{10})\)	\(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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