LMFDB - Embedded newform 105.4.b.a.41.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(41,105)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("105.41");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.b (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:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 96 x^{14} + 3618 x^{12} + 68560 x^{10} + 697017 x^{8} + 3791184 x^{6} + 10461796 x^{4} + \cdots + 5760000 $ x^16 + 96x^14 + 3618x^12 + 68560x^10 + 697017x^8 + 3791184x^6 + 10461796x^4 + 13209792*x^2 + 5760000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			41.5
Root			$-2.73921i$ of defining polynomial
Character	$\chi$	$=$	105.41
Dual form			105.4.b.a.41.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.73921i q^{2} +(4.32728 - 2.87658i) q^{3} +0.496728 q^{4} -5.00000 q^{5} +(-7.87955 - 11.8533i) q^{6} +(-18.4646 + 1.43529i) q^{7} -23.2743i q^{8} +(10.4506 - 24.8955i) q^{9} +O(q^{10})$	\(q-2.73921i q^{2} +(4.32728 - 2.87658i) q^{3} +0.496728 q^{4} -5.00000 q^{5} +(-7.87955 - 11.8533i) q^{6} +(-18.4646 + 1.43529i) q^{7} -23.2743i q^{8} +(10.4506 - 24.8955i) q^{9} +13.6961i q^{10} -41.8023i q^{11} +(2.14948 - 1.42888i) q^{12} +5.42185i q^{13} +(3.93155 + 50.5783i) q^{14} +(-21.6364 + 14.3829i) q^{15} -59.7794 q^{16} +108.136 q^{17} +(-68.1939 - 28.6264i) q^{18} +47.5577i q^{19} -2.48364 q^{20} +(-75.7725 + 59.3256i) q^{21} -114.505 q^{22} -60.5116i q^{23} +(-66.9504 - 100.714i) q^{24} +25.0000 q^{25} +14.8516 q^{26} +(-26.3910 - 137.792i) q^{27} +(-9.17187 + 0.712948i) q^{28} +170.922i q^{29} +(39.3977 + 59.2666i) q^{30} +296.753i q^{31} -22.4462i q^{32} +(-120.247 - 180.890i) q^{33} -296.208i q^{34} +(92.3228 - 7.17644i) q^{35} +(5.19112 - 12.3663i) q^{36} +395.184 q^{37} +130.271 q^{38} +(15.5964 + 23.4618i) q^{39} +116.372i q^{40} -146.142 q^{41} +(162.505 + 207.557i) q^{42} +53.7791 q^{43} -20.7644i q^{44} +(-52.2531 + 124.477i) q^{45} -165.754 q^{46} +450.800 q^{47} +(-258.682 + 171.960i) q^{48} +(338.880 - 53.0039i) q^{49} -68.4803i q^{50} +(467.936 - 311.063i) q^{51} +2.69318i q^{52} -37.5333i q^{53} +(-377.440 + 72.2906i) q^{54} +209.011i q^{55} +(33.4053 + 429.750i) q^{56} +(136.803 + 205.795i) q^{57} +468.192 q^{58} -240.063 q^{59} +(-10.7474 + 7.14438i) q^{60} -439.503i q^{61} +812.868 q^{62} +(-157.234 + 474.684i) q^{63} -539.720 q^{64} -27.1092i q^{65} +(-495.496 + 329.383i) q^{66} -341.296 q^{67} +53.7144 q^{68} +(-174.066 - 261.850i) q^{69} +(-19.6578 - 252.892i) q^{70} +518.133i q^{71} +(-579.425 - 243.231i) q^{72} -835.450i q^{73} -1082.49i q^{74} +(108.182 - 71.9144i) q^{75} +23.6233i q^{76} +(59.9983 + 771.861i) q^{77} +(64.2669 - 42.7217i) q^{78} +321.013 q^{79} +298.897 q^{80} +(-510.569 - 520.346i) q^{81} +400.314i q^{82} -785.850 q^{83} +(-37.6383 + 29.4687i) q^{84} -540.682 q^{85} -147.312i q^{86} +(491.671 + 739.628i) q^{87} -972.920 q^{88} -615.123 q^{89} +(340.970 + 143.132i) q^{90} +(-7.78191 - 100.112i) q^{91} -30.0578i q^{92} +(853.632 + 1284.13i) q^{93} -1234.84i q^{94} -237.788i q^{95} +(-64.5681 - 97.1307i) q^{96} +1372.86i q^{97} +(-145.189 - 928.263i) q^{98} +(-1040.69 - 436.860i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} - 64 q^{4} - 80 q^{5} - 28 q^{6} - 4 q^{7} - 22 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 - 64 * q^4 - 80 * q^5 - 28 * q^6 - 4 * q^7 - 22 * q^9	$ 16 q - 2 q^{3} - 64 q^{4} - 80 q^{5} - 28 q^{6} - 4 q^{7} - 22 q^{9} - 66 q^{12} - 90 q^{14} + 10 q^{15} + 376 q^{16} - 72 q^{17} - 182 q^{18} + 320 q^{20} - 74 q^{21} - 276 q^{22} + 526 q^{24} + 400 q^{25} + 696 q^{26} - 128 q^{27} + 10 q^{28} + 140 q^{30} - 502 q^{33} + 20 q^{35} + 996 q^{36} - 812 q^{37} - 1200 q^{38} - 594 q^{39} - 936 q^{41} - 1834 q^{42} - 548 q^{43} + 110 q^{45} + 1224 q^{46} + 912 q^{47} + 1850 q^{48} + 328 q^{49} + 750 q^{51} - 2950 q^{54} + 1254 q^{56} + 432 q^{57} + 576 q^{58} - 552 q^{59} + 330 q^{60} - 1860 q^{62} - 898 q^{63} - 4000 q^{64} + 1378 q^{66} + 1004 q^{67} + 3828 q^{68} + 1988 q^{69} + 450 q^{70} + 1988 q^{72} - 50 q^{75} + 1152 q^{77} + 1446 q^{78} + 1292 q^{79} - 1880 q^{80} - 2950 q^{81} - 1752 q^{83} + 1068 q^{84} + 360 q^{85} + 1910 q^{87} - 912 q^{88} + 6096 q^{89} + 910 q^{90} - 552 q^{91} - 1080 q^{93} - 9546 q^{96} - 4824 q^{98} + 2530 q^{99}+O(q^{100}) $ 16 * q - 2 * q^3 - 64 * q^4 - 80 * q^5 - 28 * q^6 - 4 * q^7 - 22 * q^9 - 66 * q^12 - 90 * q^14 + 10 * q^15 + 376 * q^16 - 72 * q^17 - 182 * q^18 + 320 * q^20 - 74 * q^21 - 276 * q^22 + 526 * q^24 + 400 * q^25 + 696 * q^26 - 128 * q^27 + 10 * q^28 + 140 * q^30 - 502 * q^33 + 20 * q^35 + 996 * q^36 - 812 * q^37 - 1200 * q^38 - 594 * q^39 - 936 * q^41 - 1834 * q^42 - 548 * q^43 + 110 * q^45 + 1224 * q^46 + 912 * q^47 + 1850 * q^48 + 328 * q^49 + 750 * q^51 - 2950 * q^54 + 1254 * q^56 + 432 * q^57 + 576 * q^58 - 552 * q^59 + 330 * q^60 - 1860 * q^62 - 898 * q^63 - 4000 * q^64 + 1378 * q^66 + 1004 * q^67 + 3828 * q^68 + 1988 * q^69 + 450 * q^70 + 1988 * q^72 - 50 * q^75 + 1152 * q^77 + 1446 * q^78 + 1292 * q^79 - 1880 * q^80 - 2950 * q^81 - 1752 * q^83 + 1068 * q^84 + 360 * q^85 + 1910 * q^87 - 912 * q^88 + 6096 * q^89 + 910 * q^90 - 552 * q^91 - 1080 * q^93 - 9546 * q^96 - 4824 * q^98 + 2530 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$		−	2.73921i		−	0.968457i	−0.874942	−	0.484229i	$-0.839100\pi$
$2$		−	2.73921i		−	0.968457i	0.874942	−	0.484229i	$-0.160900\pi$
$3$	4.32728	−	2.87658i	0.832784	−	0.553597i
$3$	4.32728	−	2.87658i	0.832784	−	0.553597i
$4$	0.496728			0.0620910
$5$	−5.00000			−0.447214
$5$	−5.00000			−0.447214
$6$	−7.87955	−	11.8533i	−0.536135	−	0.806516i
$7$	−18.4646	+	1.43529i	−0.996992	+	0.0774982i
$7$	−18.4646	+	1.43529i	−0.996992	+	0.0774982i
$8$		−	23.2743i		−	1.02859i
$9$	10.4506	−	24.8955i	0.387060	−	0.922055i
$10$			13.6961i			0.433107i
$11$		−	41.8023i		−	1.14581i	−0.819623	−	0.572903i	$-0.805817\pi$
$11$		−	41.8023i		−	1.14581i	0.819623	−	0.572903i	$-0.194183\pi$
$12$	2.14948	−	1.42888i	0.0517084	−	0.0343734i
$13$			5.42185i			0.115673i	0.998326	+	0.0578365i	$0.0184202\pi$
$13$			5.42185i			0.115673i	−0.998326	+	0.0578365i	$0.981580\pi$
$14$	3.93155	+	50.5783i	0.0750537	+	0.965544i
$15$	−21.6364	+	14.3829i	−0.372433	+	0.247576i
$16$	−59.7794			−0.934054
$17$	108.136			1.54276			0.771380	−	0.636375i	$-0.219567\pi$
$17$	108.136			1.54276			0.771380	+	0.636375i	$0.219567\pi$
$18$	−68.1939	−	28.6264i	−0.892970	−	0.374851i
$19$			47.5577i			0.574236i	0.957895	+	0.287118i	$0.0926972\pi$
$19$			47.5577i			0.574236i	−0.957895	+	0.287118i	$0.907303\pi$
$20$	−2.48364			−0.0277680
$21$	−75.7725	+	59.3256i	−0.787377	+	0.616472i
$22$	−114.505			−1.10966
$23$		−	60.5116i		−	0.548588i	−0.961646	−	0.274294i	$-0.911556\pi$
$23$		−	60.5116i		−	0.548588i	0.961646	−	0.274294i	$-0.0884442\pi$
$24$	−66.9504	−	100.714i	−0.569424	−	0.856593i
$25$	25.0000			0.200000
$26$	14.8516			0.112024
$27$	−26.3910	−	137.792i	−0.188109	−	0.982148i
$28$	−9.17187	+	0.712948i	−0.0619043	+	0.00481195i
$29$			170.922i			1.09447i	0.836981	+	0.547233i	$0.184319\pi$
$29$			170.922i			1.09447i	−0.836981	+	0.547233i	$0.815681\pi$
$30$	39.3977	+	59.2666i	0.239767	+	0.360685i
$31$			296.753i			1.71930i	0.510881	+	0.859651i	$0.329319\pi$
$31$			296.753i			1.71930i	−0.510881	+	0.859651i	$0.670681\pi$
$32$		−	22.4462i		−	0.123999i
$33$	−120.247	−	180.890i	−0.634315	−	0.954209i
$34$		−	296.208i		−	1.49410i
$35$	92.3228	−	7.17644i	0.445869	−	0.0346583i
$36$	5.19112	−	12.3663i	0.0240330	−	0.0572513i
$37$	395.184			1.75589			0.877945	−	0.478762i	$-0.158914\pi$
$37$	395.184			1.75589			0.877945	+	0.478762i	$0.158914\pi$
$38$	130.271			0.556123
$39$	15.5964	+	23.4618i	0.0640363	+	0.0963307i
$40$			116.372i			0.459999i
$41$	−146.142			−0.556673			−0.278336	−	0.960484i	$-0.589783\pi$
$41$	−146.142			−0.556673			−0.278336	+	0.960484i	$0.589783\pi$
$42$	162.505	+	207.557i	0.597026	+	0.762541i
$43$	53.7791			0.190726			0.0953632	−	0.995443i	$-0.469599\pi$
$43$	53.7791			0.190726			0.0953632	+	0.995443i	$0.469599\pi$
$44$		−	20.7644i		−	0.0711443i
$45$	−52.2531	+	124.477i	−0.173098	+	0.412355i
$46$	−165.754			−0.531284
$47$	450.800			1.39906			0.699531	−	0.714602i	$-0.253392\pi$
$47$	450.800			1.39906			0.699531	+	0.714602i	$0.253392\pi$
$48$	−258.682	+	171.960i	−0.777865	+	0.517090i
$49$	338.880	−	53.0039i	0.987988	−	0.154530i
$50$		−	68.4803i		−	0.193691i
$51$	467.936	−	311.063i	1.28479	−	0.854068i
$52$			2.69318i			0.00718226i
$53$		−	37.5333i		−	0.0972753i	−0.998816	−	0.0486376i	$-0.984512\pi$
$53$		−	37.5333i		−	0.0972753i	0.998816	−	0.0486376i	$-0.0154879\pi$
$54$	−377.440	+	72.2906i	−0.951168	+	0.182176i
$55$			209.011i			0.512420i
$56$	33.4053	+	429.750i	0.0797139	+	1.02550i
$57$	136.803	+	205.795i	0.317896	+	0.478215i
$58$	468.192			1.05994
$59$	−240.063			−0.529721			−0.264861	−	0.964287i	$-0.585326\pi$
$59$	−240.063			−0.529721			−0.264861	+	0.964287i	$0.585326\pi$
$60$	−10.7474	+	7.14438i	−0.0231247	+	0.0153723i
$61$		−	439.503i		−	0.922501i	−0.887270	−	0.461251i	$-0.847401\pi$
$61$		−	439.503i		−	0.922501i	0.887270	−	0.461251i	$-0.152599\pi$
$62$	812.868			1.66507
$63$	−157.234	+	474.684i	−0.314438	+	0.949278i
$64$	−539.720			−1.05414
$65$		−	27.1092i		−	0.0517306i
$66$	−495.496	+	329.383i	−0.924111	+	0.614307i
$67$	−341.296			−0.622328			−0.311164	−	0.950356i	$-0.600719\pi$
$67$	−341.296			−0.622328			−0.311164	+	0.950356i	$0.600719\pi$
$68$	53.7144			0.0957916
$69$	−174.066	−	261.850i	−0.303697	−	0.456856i
$70$	−19.6578	−	252.892i	−0.0335650	−	0.431805i
$71$			518.133i			0.866071i	0.901377	+	0.433035i	$0.142557\pi$
$71$			518.133i			0.866071i	−0.901377	+	0.433035i	$0.857443\pi$
$72$	−579.425	−	243.231i	−0.948416	−	0.398126i
$73$		−	835.450i		−	1.33948i	−0.742596	−	0.669740i	$-0.766406\pi$
$73$		−	835.450i		−	1.33948i	0.742596	−	0.669740i	$-0.233594\pi$
$74$		−	1082.49i		−	1.70050i
$75$	108.182	−	71.9144i	0.166557	−	0.110719i
$76$			23.6233i			0.0356549i
$77$	59.9983	+	771.861i	0.0887979	+	1.14236i
$78$	64.2669	−	42.7217i	0.0932922	−	0.0620164i
$79$	321.013			0.457174			0.228587	−	0.973523i	$-0.426589\pi$
$79$	321.013			0.457174			0.228587	+	0.973523i	$0.426589\pi$
$80$	298.897			0.417722
$81$	−510.569	−	520.346i	−0.700369	−	0.713781i
$82$			400.314i			0.539113i
$83$	−785.850			−1.03926			−0.519628	−	0.854393i	$-0.673929\pi$
$83$	−785.850			−1.03926			−0.519628	+	0.854393i	$0.673929\pi$
$84$	−37.6383	+	29.4687i	−0.0488891	+	0.0382774i
$85$	−540.682			−0.689943
$86$		−	147.312i		−	0.184710i
$87$	491.671	+	739.628i	0.605893	+	0.911454i
$88$	−972.920			−1.17856
$89$	−615.123			−0.732617			−0.366308	−	0.930493i	$-0.619379\pi$
$89$	−615.123			−0.732617			−0.366308	+	0.930493i	$0.619379\pi$
$90$	340.970	+	143.132i	0.399348	+	0.167638i
$91$	−7.78191	−	100.112i	−0.00896446	−	0.115325i
$92$		−	30.0578i		−	0.0340624i
$93$	853.632	+	1284.13i	0.951801	+	1.43181i
$94$		−	1234.84i		−	1.35493i
$95$		−	237.788i		−	0.256806i
$96$	−64.5681	−	97.1307i	−0.0686453	−	0.103264i
$97$			1372.86i			1.43704i	0.695509	+	0.718518i	$0.255179\pi$
$97$			1372.86i			1.43704i	−0.695509	+	0.718518i	$0.744821\pi$
$98$	−145.189	−	928.263i	−0.149656	−	0.956824i
$99$	−1040.69	−	436.860i	−1.05650	−	0.443496i
$100$	12.4182			0.0124182
$101$	514.856			0.507228			0.253614	−	0.967305i	$-0.418381\pi$
$101$	514.856			0.507228			0.253614	+	0.967305i	$0.418381\pi$
$102$	−852.066	−	1281.77i	−0.827128	−	1.24426i
$103$			632.545i			0.605112i	0.953132	+	0.302556i	$0.0978399\pi$
$103$			632.545i			0.605112i	−0.953132	+	0.302556i	$0.902160\pi$
$104$	126.190			0.118980
$105$	378.863	−	296.628i	0.352126	−	0.275695i
$106$	−102.811			−0.0942069
$107$			28.2498i			0.0255235i	0.999919	+	0.0127618i	$0.00406230\pi$
$107$			28.2498i			0.0255235i	−0.999919	+	0.0127618i	$0.995938\pi$
$108$	−13.1092	−	68.4450i	−0.0116799	−	0.0609826i
$109$	−87.4817			−0.0768736			−0.0384368	−	0.999261i	$-0.512238\pi$
$109$	−87.4817			−0.0768736			−0.0384368	+	0.999261i	$0.512238\pi$
$110$	572.526			0.496257
$111$	1710.07	−	1136.78i	1.46228	−	0.972056i
$112$	1103.80	−	85.8007i	0.931244	−	0.0723875i
$113$		−	2015.29i		−	1.67773i	−0.544343	−	0.838863i	$-0.683221\pi$
$113$		−	2015.29i		−	1.67773i	0.544343	−	0.838863i	$-0.316779\pi$
$114$	563.716	−	374.733i	0.463130	−	0.307868i
$115$			302.558i			0.245336i
$116$			84.9020i			0.0679565i
$117$	134.979	+	56.6616i	0.106657	+	0.0447724i
$118$			657.583i			0.513012i
$119$	−1996.69	+	155.207i	−1.53812	+	0.119561i
$120$	334.752	+	503.572i	0.254654	+	0.383080i
$121$	−416.431			−0.312871
$122$	−1203.89			−0.893403
$123$	−632.397	+	420.389i	−0.463588	+	0.308172i
$124$			147.406i			0.106753i
$125$	−125.000			−0.0894427
$126$	1300.26	+	430.697i	0.919335	+	0.304520i
$127$	627.270			0.438277			0.219139	−	0.975694i	$-0.429675\pi$
$127$	627.270			0.438277			0.219139	+	0.975694i	$0.429675\pi$
$128$			1298.84i			0.896892i
$129$	232.717	−	154.700i	0.158834	−	0.105586i
$130$	−74.2579			−0.0500988
$131$	365.701			0.243904			0.121952	−	0.992536i	$-0.461085\pi$
$131$	365.701			0.243904			0.121952	+	0.992536i	$0.461085\pi$
$132$	−59.7303	−	89.8532i	−0.0393853	−	0.0592478i
$133$	−68.2590	−	878.132i	−0.0445023	−	0.572509i
$134$			934.882i			0.602698i
$135$	131.955	+	688.958i	0.0841251	+	0.439230i
$136$		−	2516.80i		−	1.58687i
$137$			759.066i			0.473368i	0.971587	+	0.236684i	$0.0760606\pi$
$137$			759.066i			0.473368i	−0.971587	+	0.236684i	$0.923939\pi$
$138$	−717.263	+	476.804i	−0.442445	+	0.294118i
$139$			2973.78i			1.81462i	0.420458	+	0.907312i	$0.361869\pi$
$139$			2973.78i			1.81462i	−0.420458	+	0.907312i	$0.638131\pi$
$140$	45.8593	−	3.56474i	0.0276844	−	0.00215197i
$141$	1950.73	−	1296.76i	1.16512	−	0.774517i
$142$	1419.27			0.838752
$143$	226.646			0.132539
$144$	−624.732	+	1488.24i	−0.361535	+	0.861248i
$145$		−	854.612i		−	0.489460i
$146$	−2288.47			−1.29723
$147$	1313.96	−	1204.18i	0.737234	−	0.675638i
$148$	196.299			0.109025
$149$			2793.34i			1.53583i	0.640550	+	0.767916i	$0.278706\pi$
$149$			2793.34i			1.53583i	−0.640550	+	0.767916i	$0.721294\pi$
$150$	−196.989	−	296.333i	−0.107227	−	0.161303i
$151$	−3266.74			−1.76055			−0.880277	−	0.474460i	$-0.842643\pi$
$151$	−3266.74			−1.76055			−0.880277	+	0.474460i	$0.842643\pi$
$152$	1106.87			0.590653
$153$	1130.09	−	2692.11i	0.597141	−	1.42251i
$154$	2114.29	−	164.348i	1.10633	−	0.0859970i
$155$		−	1483.76i		−	0.768896i
$156$	7.74715	+	11.6541i	0.00397608	+	0.00598127i
$157$			3058.86i			1.55493i	0.628928	+	0.777463i	$0.283494\pi$
$157$			3058.86i			1.55493i	−0.628928	+	0.777463i	$0.716506\pi$
$158$		−	879.322i		−	0.442754i
$159$	−107.967	−	162.417i	−0.0538513	−	0.0810093i
$160$			112.231i			0.0554539i
$161$	86.8515	+	1117.32i	0.0425146	+	0.546938i
$162$	−1425.34	+	1398.56i	−0.691266	+	0.678277i
$163$	1080.46			0.519193			0.259596	−	0.965717i	$-0.416411\pi$
$163$	1080.46			0.519193			0.259596	+	0.965717i	$0.416411\pi$
$164$	−72.5930			−0.0345644
$165$	601.237	+	904.450i	0.283674	+	0.426735i
$166$			2152.61i			1.00647i
$167$	−2870.57			−1.33013			−0.665064	−	0.746786i	$-0.731596\pi$
$167$	−2870.57			−1.33013			−0.665064	+	0.746786i	$0.731596\pi$
$168$	1380.76	+	1763.55i	0.634096	+	0.809888i
$169$	2167.60			0.986620
$170$			1481.04i			0.668181i
$171$	1183.97	+	497.007i	0.529477	+	0.222264i
$172$	26.7136			0.0118424
$173$	−925.329			−0.406656			−0.203328	−	0.979111i	$-0.565176\pi$
$173$	−925.329			−0.406656			−0.203328	+	0.979111i	$0.565176\pi$
$174$	2026.00	−	1346.79i	0.882704	−	0.586781i
$175$	−461.614	+	35.8822i	−0.199398	+	0.0154996i
$176$			2498.92i			1.07024i
$177$	−1038.82	+	690.560i	−0.441144	+	0.293252i
$178$			1684.95i			0.709508i
$179$		−	1906.10i		−	0.795915i	−0.917404	−	0.397957i	$-0.869719\pi$
$179$		−	1906.10i		−	0.795915i	0.917404	−	0.397957i	$-0.130281\pi$
$180$	−25.9556	+	61.8314i	−0.0107479	+	0.0256036i
$181$			870.134i			0.357329i	0.983910	+	0.178664i	$0.0571777\pi$
$181$			870.134i			0.357329i	−0.983910	+	0.178664i	$0.942822\pi$
$182$	−274.228	+	21.3163i	−0.111687	+	0.00868169i
$183$	−1264.26	−	1901.85i	−0.510694	−	0.768245i
$184$	−1408.37			−0.564272
$185$	−1975.92			−0.785258
$186$	3517.51	−	2338.28i	1.38665	−	0.921779i
$187$		−	4520.35i		−	1.76770i
$188$	223.925			0.0868692
$189$	685.069	+	2506.38i	0.263658	+	0.964616i
$190$	−651.353			−0.248706
$191$		−	2668.06i		−	1.01075i	−0.862899	−	0.505377i	$-0.831353\pi$
$191$		−	2668.06i		−	1.01075i	0.862899	−	0.505377i	$-0.168647\pi$
$192$	−2335.52	+	1552.55i	−0.877872	+	0.583570i
$193$	1088.43			0.405944			0.202972	−	0.979185i	$-0.434940\pi$
$193$	1088.43			0.405944			0.202972	+	0.979185i	$0.434940\pi$
$194$	3760.54			1.39171
$195$	−77.9818	−	117.309i	−0.0286379	−	0.0430804i
$196$	168.331	−	26.3285i	0.0613452	−	0.00959495i
$197$		−	3370.41i		−	1.21894i	−0.792809	−	0.609471i	$-0.791382\pi$
$197$		−	3370.41i		−	1.21894i	0.792809	−	0.609471i	$-0.208618\pi$
$198$	−1196.65	+	2850.66i	−0.429506	+	1.02317i
$199$		−	3629.56i		−	1.29293i	−0.762945	−	0.646464i	$-0.776247\pi$
$199$		−	3629.56i		−	1.29293i	0.762945	−	0.646464i	$-0.223753\pi$
$200$		−	581.858i		−	0.205718i
$201$	−1476.88	+	981.764i	−0.518265	+	0.344519i
$202$		−	1410.30i		−	0.491229i
$203$	−245.323	−	3156.01i	−0.0848191	−	1.09117i
$204$	232.437	−	154.514i	0.0797737	−	0.0530300i
$205$	730.711			0.248952
$206$	1732.67			0.586025
$207$	−1506.46	−	632.383i	−0.505828	−	0.212337i
$208$		−	324.115i		−	0.108045i
$209$	1988.02			0.657963
$210$	−812.526	−	1037.78i	−0.266998	−	0.341019i
$211$	−2504.71			−0.817209			−0.408605	−	0.912711i	$-0.633985\pi$
$211$	−2504.71			−0.817209			−0.408605	+	0.912711i	$0.633985\pi$
$212$		−	18.6438i		−	0.00603992i
$213$	1490.45	+	2242.10i	0.479454	+	0.721250i
$214$	77.3823			0.0247184
$215$	−268.895			−0.0852954
$216$	−3207.01	+	614.233i	−1.01023	+	0.193487i
$217$	−425.926	−	5479.41i	−0.133243	−	1.71413i
$218$			239.631i			0.0744488i
$219$	−2403.23	−	3615.22i	−0.741532	−	1.11550i
$220$			103.822i			0.0318167i
$221$			586.299i			0.178456i
$222$	−3113.87	−	4684.24i	−0.941394	−	1.41615i
$223$		−	4243.83i		−	1.27439i	−0.770705	−	0.637193i	$-0.780096\pi$
$223$		−	4243.83i		−	1.27439i	0.770705	−	0.637193i	$-0.219904\pi$
$224$	32.2167	+	414.458i	0.00960968	+	0.123626i
$225$	261.265	−	622.387i	0.0774120	−	0.184411i
$226$	−5520.32			−1.62481
$227$	−1912.74			−0.559263			−0.279632	−	0.960107i	$-0.590212\pi$
$227$	−1912.74			−0.559263			−0.279632	+	0.960107i	$0.590212\pi$
$228$	67.9541	+	102.224i	0.0197385	+	0.0296928i
$229$			4655.49i			1.34342i	0.740814	+	0.671710i	$0.234440\pi$
$229$			4655.49i			1.34342i	−0.740814	+	0.671710i	$0.765560\pi$
$230$	828.769			0.237598
$231$	2479.95	+	3167.46i	0.706357	+	0.902181i
$232$	3978.10			1.12576
$233$			2916.89i			0.820136i	0.912055	+	0.410068i	$0.134495\pi$
$233$			2916.89i			0.820136i	−0.912055	+	0.410068i	$0.865505\pi$
$234$	155.208	−	369.737i	0.0433601	−	0.103293i
$235$	−2254.00			−0.625679
$236$	−119.246			−0.0328909
$237$	1389.11	−	923.418i	0.380728	−	0.253091i
$238$	425.144	+	5469.36i	0.115790	+	1.48960i
$239$		−	2348.27i		−	0.635551i	−0.948166	−	0.317776i	$-0.897064\pi$
$239$		−	2348.27i		−	0.635551i	0.948166	−	0.317776i	$-0.102936\pi$
$240$	1293.41	−	859.801i	0.347872	−	0.231250i
$241$			1635.59i			0.437168i	0.975818	+	0.218584i	$0.0701437\pi$
$241$			1635.59i			0.437168i	−0.975818	+	0.218584i	$0.929856\pi$
$242$			1140.69i			0.303002i
$243$	−3706.19	−	782.990i	−0.978404	−	0.206703i
$244$		−	218.313i		−	0.0572791i
$245$	−1694.40	+	265.020i	−0.441842	+	0.0691081i
$246$	1151.53	+	1732.27i	0.298452	+	0.448965i
$247$	−257.851			−0.0664236
$248$	6906.72			1.76846
$249$	−3400.59	+	2260.56i	−0.865476	+	0.575329i
$250$			342.401i			0.0866214i
$251$	182.821			0.0459743			0.0229871	−	0.999736i	$-0.492682\pi$
$251$	182.821			0.0459743			0.0229871	+	0.999736i	$0.492682\pi$
$252$	−78.1025	+	235.789i	−0.0195238	+	0.0589416i
$253$	−2529.52			−0.628576
$254$		−	1718.23i		−	0.424453i
$255$	−2339.68	+	1555.31i	−0.574574	+	0.381951i
$256$	−759.972			−0.185540
$257$	3140.95			0.762363			0.381181	−	0.924500i	$-0.375517\pi$
$257$	3140.95			0.762363			0.381181	+	0.924500i	$0.375517\pi$
$258$	−423.755	−	637.461i	−0.102255	−	0.153824i
$259$	−7296.90	+	567.203i	−1.75061	+	0.136078i
$260$		−	13.4659i		−	0.00321200i
$261$	4255.19	+	1786.24i	1.00916	+	0.423624i
$262$		−	1001.73i		−	0.236210i
$263$			6614.80i			1.55090i	0.631411	+	0.775449i	$0.282476\pi$
$263$			6614.80i			1.55090i	−0.631411	+	0.775449i	$0.717524\pi$
$264$	−4210.09	+	2798.68i	−0.981490	+	0.652450i
$265$			187.666i			0.0435028i
$266$	−2405.39	+	186.976i	−0.554450	+	0.0430985i
$267$	−2661.81	+	1769.45i	−0.610112	+	0.405575i
$268$	−169.531			−0.0386410
$269$	6813.86			1.54442			0.772209	−	0.635369i	$-0.219152\pi$
$269$	6813.86			1.54442			0.772209	+	0.635369i	$0.219152\pi$
$270$	1887.20	−	361.453i	0.425375	−	0.0814715i
$271$			616.810i			0.138260i	0.997608	+	0.0691302i	$0.0220224\pi$
$271$			616.810i			0.138260i	−0.997608	+	0.0691302i	$0.977978\pi$
$272$	−6464.33			−1.44102
$273$	−321.654	−	410.827i	−0.0713092	−	0.0910783i
$274$	2079.24			0.458436
$275$		−	1045.06i		−	0.229161i
$276$	−86.4636	−	130.068i	−0.0188569	−	0.0283667i
$277$	7991.94			1.73354			0.866768	−	0.498712i	$-0.166193\pi$
$277$	7991.94			1.73354			0.866768	+	0.498712i	$0.166193\pi$
$278$	8145.81			1.75738
$279$	7387.80	+	3101.25i	1.58529	+	0.665473i
$280$	−167.027	−	2148.75i	−0.0356491	−	0.458616i
$281$			2969.98i			0.630512i	0.949007	+	0.315256i	$0.102090\pi$
$281$			2969.98i			0.630512i	−0.949007	+	0.315256i	$0.897910\pi$
$282$	−3552.10	−	5343.47i	−0.750086	−	1.12837i
$283$		−	3548.79i		−	0.745420i	−0.927948	−	0.372710i	$-0.878429\pi$
$283$		−	3548.79i		−	0.745420i	0.927948	−	0.372710i	$-0.121571\pi$
$284$			257.371i			0.0537752i
$285$	−684.017	−	1028.98i	−0.142167	−	0.213864i
$286$		−	620.830i		−	0.128358i
$287$	2698.45	−	209.756i	0.554998	−	0.0431411i
$288$	−558.808	−	234.576i	−0.114334	−	0.0479949i
$289$	6780.48			1.38011
$290$	−2340.96			−0.474021
$291$	3949.13	+	5940.73i	0.795539	+	1.19674i
$292$		−	414.991i		−	0.0831696i
$293$	−8563.40			−1.70744			−0.853719	−	0.520734i	$-0.825658\pi$
$293$	−8563.40			−1.70744			−0.853719	+	0.520734i	$0.825658\pi$
$294$	−3298.49	−	3599.20i	−0.654326	−	0.713979i
$295$	1200.32			0.236898
$296$		−	9197.65i		−	1.80609i
$297$	−5760.00	+	1103.21i	−1.12535	+	0.215537i
$298$	7651.53			1.48739
$299$	328.084			0.0634569
$300$	53.7370	−	35.7219i	0.0103417	−	0.00687469i
$301$	−993.007	+	77.1885i	−0.190153	+	0.0147810i
$302$			8948.29i			1.70502i
$303$	2227.92	−	1481.02i	0.422412	−	0.280800i
$304$		−	2842.97i		−	0.536367i
$305$			2197.51i			0.412555i
$306$	−7374.25	−	3095.56i	−1.37764	−	0.578305i
$307$			4300.94i			0.799569i	0.916609	+	0.399784i	$0.130915\pi$
$307$			4300.94i			0.799569i	−0.916609	+	0.399784i	$0.869085\pi$
$308$	29.8029	+	383.405i	0.00551356	+	0.0709303i
$309$	1819.56	+	2737.20i	0.334988	+	0.503928i
$310$	−4064.34			−0.744642
$311$	207.015			0.0377452			0.0188726	−	0.999822i	$-0.493992\pi$
$311$	207.015			0.0377452			0.0188726	+	0.999822i	$0.493992\pi$
$312$	546.058	−	362.995i	0.0990848	−	0.0658671i
$313$			2048.71i			0.369967i	0.982742	+	0.184984i	$0.0592232\pi$
$313$			2048.71i			0.369967i	−0.982742	+	0.184984i	$0.940777\pi$
$314$	8378.86			1.50588
$315$	786.170	−	2373.42i	0.140621	−	0.424530i
$316$	159.456			0.0283864
$317$		−	3825.88i		−	0.677865i	−0.940811	−	0.338932i	$-0.889934\pi$
$317$		−	3825.88i		−	0.677865i	0.940811	−	0.338932i	$-0.110066\pi$
$318$	−444.893	+	295.745i	−0.0784541	+	0.0521527i
$319$	7144.95			1.25404
$320$	2698.60			0.471426
$321$	81.2628	+	122.245i	0.0141297	+	0.0212556i
$322$	3060.57	−	237.904i	0.529686	−	0.0411736i
$323$			5142.72i			0.885909i
$324$	−253.614	−	258.471i	−0.0434866	−	0.0443194i
$325$			135.546i			0.0231346i
$326$		−	2959.61i		−	0.502816i
$327$	−378.557	+	251.648i	−0.0640192	+	0.0425570i
$328$			3401.36i			0.572588i
$329$	−8323.82	+	647.027i	−1.39485	+	0.108425i
$330$	2477.48	−	1646.92i	0.413275	−	0.274726i
$331$	−482.262			−0.0800831			−0.0400415	−	0.999198i	$-0.512749\pi$
$331$	−482.262			−0.0800831			−0.0400415	+	0.999198i	$0.512749\pi$
$332$	−390.354			−0.0645285
$333$	4129.92	−	9838.30i	0.679634	−	1.61903i
$334$			7863.10i			1.28817i
$335$	1706.48			0.278313
$336$	4529.64	−	3546.45i	0.735452	−	0.575818i
$337$	−408.105			−0.0659670			−0.0329835	−	0.999456i	$-0.510501\pi$
$337$	−408.105			−0.0659670			−0.0329835	+	0.999456i	$0.510501\pi$
$338$		−	5937.52i		−	0.955499i
$339$	−5797.15	−	8720.73i	−0.928784	−	1.39718i
$340$	−268.572			−0.0428393
$341$	12404.9			1.96999
$342$	1361.41	−	3243.15i	0.215253	−	0.512776i
$343$	−6181.19	+	1465.08i	−0.973041	+	0.230633i
$344$		−	1251.67i		−	0.196179i
$345$	870.331	+	1309.25i	0.135817	+	0.204312i
$346$			2534.67i			0.393829i
$347$		−	1527.41i		−	0.236299i	−0.992996	−	0.118150i	$-0.962304\pi$
$347$		−	1527.41i		−	0.236299i	0.992996	−	0.118150i	$-0.0376963\pi$
$348$	244.227	+	367.394i	0.0376205	+	0.0565931i
$349$			3079.23i			0.472284i	0.971718	+	0.236142i	$0.0758831\pi$
$349$			3079.23i			0.472284i	−0.971718	+	0.236142i	$0.924117\pi$
$350$	98.2889	+	1264.46i	0.0150107	+	0.193109i
$351$	747.085	−	143.088i	0.113608	−	0.0217592i
$352$	−938.301			−0.142078
$353$	1297.46			0.195629			0.0978143	−	0.995205i	$-0.468815\pi$
$353$	1297.46			0.195629			0.0978143	+	0.995205i	$0.468815\pi$
$354$	1891.59	+	2845.54i	0.284002	+	0.427229i
$355$		−	2590.66i		−	0.387319i
$356$	−305.549			−0.0454889
$357$	−8193.77	+	6415.26i	−1.21473	+	0.951068i
$358$	−5221.21			−0.770809
$359$			1877.71i			0.276049i	0.990429	+	0.138024i	$0.0440752\pi$
$359$			1877.71i			0.276049i	−0.990429	+	0.138024i	$0.955925\pi$
$360$	2897.13	+	1216.16i	0.424144	+	0.178047i
$361$	4597.27			0.670253
$362$	2383.48			0.346058
$363$	−1802.01	+	1197.90i	−0.260554	+	0.173205i
$364$	−3.86549	−	49.7285i	−0.000556612	−	0.00716066i
$365$			4177.25i			0.599033i
$366$	−5209.57	+	3463.08i	−0.744012	+	0.494585i
$367$			9777.96i			1.39075i	0.718647	+	0.695375i	$0.244762\pi$
$367$			9777.96i			1.39075i	−0.718647	+	0.695375i	$0.755238\pi$
$368$			3617.35i			0.512411i
$369$	−1527.28	+	3638.28i	−0.215466	+	0.513282i
$370$			5412.46i			0.760488i
$371$	53.8710	+	693.035i	0.00753866	+	0.0969827i
$372$	424.023	+	637.864i	0.0590983	+	0.0889025i
$373$	−2397.61			−0.332825			−0.166413	−	0.986056i	$-0.553218\pi$
$373$	−2397.61			−0.332825			−0.166413	+	0.986056i	$0.553218\pi$
$374$	−12382.2			−1.71195
$375$	−540.909	+	359.572i	−0.0744865	+	0.0495153i
$376$		−	10492.1i		−	1.43906i
$377$	−926.715			−0.126600
$378$	6865.51	−	1876.55i	0.934189	−	0.255342i
$379$	−221.663			−0.0300423			−0.0150212	−	0.999887i	$-0.504782\pi$
$379$	−221.663			−0.0300423			−0.0150212	+	0.999887i	$0.504782\pi$
$380$		−	118.116i		−	0.0159454i
$381$	2714.37	−	1804.39i	0.364991	−	0.242629i
$382$	−7308.38			−0.978872
$383$	−8586.73			−1.14559			−0.572796	−	0.819698i	$-0.694141\pi$
$383$	−8586.73			−1.14559			−0.572796	+	0.819698i	$0.694141\pi$
$384$	3736.21	+	5620.43i	0.496517	+	0.746917i
$385$	−299.992	−	3859.30i	−0.0397116	−	0.510879i
$386$		−	2981.45i		−	0.393140i
$387$	562.025	−	1338.86i	0.0738226	−	0.175860i
$388$			681.937i			0.0892270i
$389$			7551.95i			0.984317i	0.870506	+	0.492158i	$0.163792\pi$
$389$			7551.95i			0.984317i	−0.870506	+	0.492158i	$0.836208\pi$
$390$	−321.334	+	213.608i	−0.0417215	+	0.0277346i
$391$		−	6543.50i		−	0.846340i
$392$	−1233.63	−	7887.20i	−0.158948	−	1.01623i
$393$	1582.49	−	1051.97i	0.203119	−	0.135025i
$394$	−9232.25			−1.18049
$395$	−1605.06			−0.204455
$396$	−516.939	−	217.001i	−0.0655989	−	0.0275371i
$397$		−	84.7885i		−	0.0107189i	−0.999986	−	0.00535946i	$-0.998294\pi$
$397$		−	84.7885i		−	0.0107189i	0.999986	−	0.00535946i	$-0.00170598\pi$
$398$	−9942.12			−1.25214
$399$	−2821.39	−	3603.57i	−0.354000	−	0.452140i
$400$	−1494.49			−0.186811
$401$		−	939.253i		−	0.116968i	−0.998288	−	0.0584838i	$-0.981373\pi$
$401$		−	939.253i		−	0.116968i	0.998288	−	0.0584838i	$-0.0186266\pi$
$402$	2689.26	+	4045.49i	0.333652	+	0.501917i
$403$	−1608.95			−0.198877
$404$	255.743			0.0314943
$405$	2552.85	+	2601.73i	0.313215	+	0.319212i
$406$	−8644.96	+	671.991i	−1.05675	+	0.0821437i
$407$		−	16519.6i		−	2.01191i
$408$	−7239.77	−	10890.9i	−0.878486	−	1.32152i
$409$		−	11940.5i		−	1.44357i	−0.692117	−	0.721785i	$-0.743322\pi$
$409$		−	11940.5i		−	1.44357i	0.692117	−	0.721785i	$-0.256678\pi$
$410$		−	2001.57i		−	0.241099i
$411$	2183.51	+	3284.69i	0.262055	+	0.394213i
$412$			314.203i			0.0375720i
$413$	4432.66	−	344.560i	0.528128	−	0.0410525i
$414$	−1732.23	+	4126.52i	−0.205639	+	0.489873i
$415$	3929.25			0.464769
$416$	121.700			0.0143433
$417$	8554.30	+	12868.4i	1.00457	+	1.51119i
$418$		−	5445.61i		−	0.637209i
$419$	2.69075			0.000313728			0.000156864	−	1.00000i	$-0.499950\pi$
$419$	2.69075			0.000313728			0.000156864		1.00000i	$0.499950\pi$
$420$	188.192	−	147.343i	0.0218638	−	0.0171182i
$421$	−8306.10			−0.961555			−0.480777	−	0.876843i	$-0.659646\pi$
$421$	−8306.10			−0.961555			−0.480777	+	0.876843i	$0.659646\pi$
$422$			6860.92i			0.791432i
$423$	4711.14	−	11222.9i	0.541521	−	1.29001i
$424$	−873.561			−0.100056
$425$	2703.41			0.308552
$426$	6141.59	−	4082.65i	0.698500	−	0.464331i
$427$	630.813	+	8115.23i	0.0714922	+	0.919727i
$428$			14.0325i			0.00158478i
$429$	980.758	−	651.963i	0.110376	−	0.0733732i
$430$			736.561i			0.0826050i
$431$		−	1383.55i		−	0.154625i	−0.997007	−	0.0773123i	$-0.975366\pi$
$431$		−	1383.55i		−	0.154625i	0.997007	−	0.0773123i	$-0.0246338\pi$
$432$	1577.64	+	8237.10i	0.175704	+	0.917379i
$433$		−	12579.8i		−	1.39618i	−0.716008	−	0.698092i	$-0.754032\pi$
$433$		−	12579.8i		−	1.39618i	0.716008	−	0.698092i	$-0.245968\pi$
$434$	−15009.3	+	1166.70i	−1.66006	+	0.129040i
$435$	−2458.36	−	3698.14i	−0.270964	−	0.407614i
$436$	−43.4546			−0.00477316
$437$	2877.79			0.315019
$438$	−9902.85	+	6582.96i	−1.08031	+	0.718142i
$439$		−	10517.2i		−	1.14342i	−0.820456	−	0.571709i	$-0.806281\pi$
$439$		−	10517.2i		−	1.14342i	0.820456	−	0.571709i	$-0.193719\pi$
$440$	4864.60			0.527070
$441$	2221.95	−	8990.50i	0.239925	−	0.970791i
$442$	1606.00			0.172827
$443$			3275.69i			0.351316i	0.984451	+	0.175658i	$0.0562053\pi$
$443$			3275.69i			0.351316i	−0.984451	+	0.175658i	$0.943795\pi$
$444$	849.441	−	564.670i	0.0907943	−	0.0603559i
$445$	3075.62			0.327636
$446$	−11624.7			−1.23419
$447$	8035.24	+	12087.5i	0.850233	+	1.27902i
$448$	9965.70	−	774.654i	1.05097	−	0.0816941i
$449$			944.420i			0.0992649i	0.998768	+	0.0496324i	$0.0158050\pi$
$449$			944.420i			0.0992649i	−0.998768	+	0.0496324i	$0.984195\pi$
$450$	−1704.85	−	715.661i	−0.178594	−	0.0749702i
$451$			6109.08i			0.637839i
$452$		−	1001.05i		−	0.104172i
$453$	−14136.1	+	9397.03i	−1.46616	+	0.974638i
$454$			5239.39i			0.541623i
$455$	38.9095	+	500.560i	0.00400903	+	0.0515750i
$456$	4789.74	−	3184.01i	0.491887	−	0.326984i
$457$	4556.16			0.466363			0.233182	−	0.972433i	$-0.425086\pi$
$457$	4556.16			0.466363			0.233182	+	0.972433i	$0.425086\pi$
$458$	12752.4			1.30104
$459$	−2853.83	−	14900.3i	−0.290208	−	1.51522i
$460$			150.289i			0.0152332i
$461$	−13499.1			−1.36381			−0.681904	−	0.731441i	$-0.738848\pi$
$461$	−13499.1			−1.36381			−0.681904	+	0.731441i	$0.738848\pi$
$462$	8676.35	−	6793.09i	0.873724	−	0.684076i
$463$	15776.6			1.58359			0.791795	−	0.610787i	$-0.209147\pi$
$463$	15776.6			1.58359			0.791795	+	0.610787i	$0.209147\pi$
$464$		−	10217.6i		−	1.02229i
$465$	−4268.16	−	6420.66i	−0.425659	−	0.640324i
$466$	7989.97			0.794266
$467$	14478.1			1.43462			0.717308	−	0.696756i	$-0.245374\pi$
$467$	14478.1			1.43462			0.717308	+	0.696756i	$0.245374\pi$
$468$	67.0481	+	28.1454i	0.00662243	+	0.00277996i
$469$	6301.88	−	489.858i	0.620456	−	0.0482293i
$470$			6174.18i			0.605944i
$471$	8799.04	+	13236.5i	0.860803	+	1.29492i
$472$			5587.31i			0.544866i
$473$		−	2248.09i		−	0.218535i
$474$	−2529.44	−	3805.07i	−0.245107	−	0.368718i
$475$			1188.94i			0.114847i
$476$	−991.813	+	77.0956i	−0.0955035	+	0.00742368i
$477$	−934.408	−	392.246i	−0.0896931	−	0.0376514i
$478$	−6432.40			−0.615504
$479$	−7810.88			−0.745070			−0.372535	−	0.928018i	$-0.621511\pi$
$479$	−7810.88			−0.745070			−0.372535	+	0.928018i	$0.621511\pi$
$480$	322.840	+	485.653i	0.0306991	+	0.0461811i
$481$			2142.63i			0.203109i
$482$	4480.22			0.423378
$483$	3589.88	+	4585.11i	0.338189	+	0.431946i
$484$	−206.853			−0.0194265
$485$		−	6864.28i		−	0.642662i
$486$	−2144.77	+	10152.0i	−0.200183	+	0.947542i
$487$	−4283.30			−0.398552			−0.199276	−	0.979943i	$-0.563859\pi$
$487$	−4283.30			−0.398552			−0.199276	+	0.979943i	$0.563859\pi$
$488$	−10229.1			−0.948875
$489$	4675.46	−	3108.03i	0.432375	−	0.287424i
$490$	725.944	+	4641.32i	0.0669282	+	0.427905i
$491$		−	3680.77i		−	0.338312i	−0.985589	−	0.169156i	$-0.945896\pi$
$491$		−	3680.77i		−	0.338312i	0.985589	−	0.169156i	$-0.0541041\pi$
$492$	−314.130	+	208.819i	−0.0287847	+	0.0191347i
$493$			18482.9i			1.68850i
$494$			706.307i			0.0643284i
$495$	5203.44	+	2184.30i	0.472479	+	0.198337i
$496$		−	17739.7i		−	1.60592i
$497$	−743.669	−	9567.09i	−0.0671190	−	0.863466i
$498$	6192.14	+	9314.93i	0.557182	+	0.838176i
$499$	−6002.76			−0.538518			−0.269259	−	0.963068i	$-0.586779\pi$
$499$	−6002.76			−0.538518			−0.269259	+	0.963068i	$0.586779\pi$
$500$	−62.0910			−0.00555359
$501$	−12421.7	+	8257.41i	−1.10771	+	0.736355i
$502$		−	500.784i		−	0.0445241i
$503$	−19748.2			−1.75056			−0.875278	−	0.483621i	$-0.839321\pi$
$503$	−19748.2			−1.75056			−0.875278	+	0.483621i	$0.839321\pi$
$504$	11047.9	+	3659.51i	0.976417	+	0.323428i
$505$	−2574.28			−0.226839
$506$			6928.89i			0.608749i
$507$	9379.82	−	6235.28i	0.821642	−	0.546190i
$508$	311.583			0.0272131
$509$	8250.81			0.718489			0.359244	−	0.933243i	$-0.383034\pi$
$509$	8250.81			0.718489			0.359244	+	0.933243i	$0.383034\pi$
$510$	4260.33	+	6408.87i	0.369903	+	0.556450i
$511$	1199.11	+	15426.2i	0.103807	+	1.33545i
$512$			12472.4i			1.07658i
$513$	6553.05	−	1255.10i	0.563985	−	0.108019i
$514$		−	8603.73i		−	0.738316i
$515$		−	3162.73i		−	0.270614i
$516$	115.597	−	76.8437i	0.00986217	−	0.00655592i
$517$		−	18844.5i		−	1.60305i
$518$	1553.69	+	19987.8i	0.131786	+	1.69539i
$519$	−4004.15	+	2661.78i	−0.338657	+	0.225124i
$520$	−630.949			−0.0532095
$521$	11902.2			1.00086			0.500428	−	0.865778i	$-0.333176\pi$
$521$	11902.2			1.00086			0.500428	+	0.865778i	$0.333176\pi$
$522$	4892.90	−	11655.9i	0.410261	−	0.977325i
$523$			2508.97i			0.209770i	0.994484	+	0.104885i	$0.0334474\pi$
$523$			2508.97i			0.209770i	−0.994484	+	0.104885i	$0.966553\pi$
$524$	181.654			0.0151442
$525$	−1894.31	+	1483.14i	−0.157475	+	0.123294i
$526$	18119.3			1.50198
$527$			32089.8i			2.65247i
$528$	7188.33	+	10813.5i	0.592484	+	0.891283i
$529$	8505.35			0.699051
$530$	514.057			0.0421306
$531$	−2508.81	+	5976.48i	−0.205034	+	0.488432i
$532$	−33.9062	−	436.193i	−0.00276319	−	0.0355477i
$533$		−	792.360i		−	0.0643920i
$534$	4846.89	+	7291.25i	0.392782	+	0.590867i
$535$		−	141.249i		−	0.0114145i
$536$			7943.44i			0.640120i
$537$	−5483.05	−	8248.23i	−0.440616	−	0.662826i
$538$		−	18664.6i		−	1.49570i
$539$	−2215.68	−	14166.0i	−0.177062	−	1.13204i
$540$	65.5458	+	342.225i	0.00522341	+	0.0272722i
$541$	7355.65			0.584555			0.292277	−	0.956334i	$-0.405587\pi$
$541$	7355.65			0.584555			0.292277	+	0.956334i	$0.405587\pi$
$542$	1689.57			0.133899
$543$	2503.01	+	3765.31i	0.197816	+	0.297578i
$544$		−	2427.25i		−	0.191300i
$545$	437.408			0.0343789
$546$	−1125.34	+	881.079i	−0.0882054	+	0.0690599i
$547$	−16439.1			−1.28498			−0.642489	−	0.766295i	$-0.722098\pi$
$547$	−16439.1			−1.28498			−0.642489	+	0.766295i	$0.722098\pi$
$548$			377.050i			0.0293919i
$549$	−10941.6	−	4593.08i	−0.850596	−	0.357063i
$550$	−2862.63			−0.221933
$551$	−8128.67			−0.628481
$552$	−6094.39	+	4051.27i	−0.469917	+	0.312380i
$553$	−5927.36	+	460.746i	−0.455799	+	0.0354302i
$554$		−	21891.6i		−	1.67885i
$555$	−8550.36	+	5683.89i	−0.653950	+	0.434716i
$556$			1477.16i			0.112672i
$557$			1852.31i			0.140907i	0.997515	+	0.0704534i	$0.0224446\pi$
$557$			1852.31i			0.140907i	−0.997515	+	0.0704534i	$0.977555\pi$
$558$	8494.98	−	20236.7i	0.644482	−	1.53529i
$559$			291.582i			0.0220619i
$560$	−5519.00	+	429.003i	−0.416465	+	0.0323727i
$561$	−13003.1	−	19560.8i	−0.978596	−	1.47212i
$562$	8135.39			0.610624
$563$	−1276.99			−0.0955924			−0.0477962	−	0.998857i	$-0.515220\pi$
$563$	−1276.99			−0.0955924			−0.0477962	+	0.998857i	$0.515220\pi$
$564$	968.985	−	644.137i	0.0723433	−	0.0480906i
$565$			10076.5i			0.750302i
$566$	−9720.89			−0.721907
$567$	10174.3	+	8875.15i	0.753580	+	0.657357i
$568$	12059.2			0.890831
$569$			23460.1i			1.72847i	0.503087	+	0.864236i	$0.332198\pi$
$569$			23460.1i			1.72847i	−0.503087	+	0.864236i	$0.667802\pi$
$570$	−2818.58	+	1873.67i	−0.207118	+	0.137683i
$571$	−14492.3			−1.06215			−0.531073	−	0.847326i	$-0.678211\pi$
$571$	−14492.3			−1.06215			−0.531073	+	0.847326i	$0.678211\pi$
$572$	112.581			0.00822947
$573$	−7674.88	−	11545.4i	−0.559551	−	0.841741i
$574$	−574.566	−	7391.62i	−0.0417803	−	0.537492i
$575$		−	1512.79i		−	0.109718i
$576$	−5640.41	+	13436.6i	−0.408016	+	0.971976i
$577$			9876.48i			0.712588i	0.934374	+	0.356294i	$0.115960\pi$
$577$			9876.48i			0.712588i	−0.934374	+	0.356294i	$0.884040\pi$
$578$		−	18573.2i		−	1.33658i
$579$	4709.96	−	3130.97i	0.338064	−	0.224730i
$580$		−	424.510i		−	0.0303911i
$581$	14510.4	−	1127.92i	1.03613	−	0.0805405i
$582$	16272.9	−	10817.5i	1.15899	−	0.770445i
$583$	−1568.98			−0.111459
$584$	−19444.5			−1.37777
$585$	−674.897	−	283.308i	−0.0476984	−	0.0200228i
$586$			23457.0i			1.65358i
$587$	5989.36			0.421137			0.210568	−	0.977579i	$-0.432469\pi$
$587$	5989.36			0.421137			0.210568	+	0.977579i	$0.432469\pi$
$588$	652.679	−	598.148i	0.0457756	−	0.0419511i
$589$	−14112.9			−0.987285
$590$		−	3287.92i		−	0.229426i
$591$	−9695.23	−	14584.7i	−0.674803	−	1.01512i
$592$	−23623.9			−1.64009
$593$	18499.7			1.28110			0.640550	−	0.767917i	$-0.278707\pi$
$593$	18499.7			1.28110			0.640550	+	0.767917i	$0.278707\pi$
$594$	3021.91	+	15777.9i	0.208738	+	1.08985i
$595$	9983.45	−	776.034i	0.687868	−	0.0534694i
$596$			1387.53i			0.0953614i
$597$	−10440.7	−	15706.1i	−0.715761	−	1.07673i
$598$		−	898.692i		−	0.0614553i
$599$		−	1322.48i		−	0.0902085i	−0.998982	−	0.0451043i	$-0.985638\pi$
$599$		−	1322.48i		−	0.0902085i	0.998982	−	0.0451043i	$-0.0143620\pi$
$600$	−1673.76	−	2517.86i	−0.113885	−	0.171319i
$601$			19711.3i			1.33784i	0.743336	+	0.668918i	$0.233242\pi$
$601$			19711.3i			1.33784i	−0.743336	+	0.668918i	$0.766758\pi$
$602$	211.435	+	2720.06i	0.0143147	+	0.184155i
$603$	−3566.76	+	8496.73i	−0.240878	+	0.573820i
$604$	−1622.68			−0.109315
$605$	2082.16			0.139920
$606$	−4056.83	−	6102.75i	−0.271943	−	0.409088i
$607$		−	5424.27i		−	0.362709i	−0.983418	−	0.181355i	$-0.941952\pi$
$607$		−	5424.27i		−	0.362709i	0.983418	−	0.181355i	$-0.0580482\pi$
$608$	1067.49			0.0712045
$609$	−10140.1	−	12951.2i	−0.674707	−	0.861757i
$610$	6019.45			0.399542
$611$			2444.17i			0.161834i
$612$	561.349	−	1337.25i	0.0370771	−	0.0883251i
$613$	−24401.3			−1.60776			−0.803882	−	0.594789i	$-0.797236\pi$
$613$	−24401.3			−1.60776			−0.803882	+	0.594789i	$0.797236\pi$
$614$	11781.2			0.774348
$615$	3161.99	−	2101.95i	0.207323	−	0.137819i
$616$	17964.5	−	1396.42i	1.17502	−	0.0913366i
$617$		−	16370.8i		−	1.06817i	−0.845430	−	0.534086i	$-0.820656\pi$
$617$		−	16370.8i		−	1.06817i	0.845430	−	0.534086i	$-0.179344\pi$
$618$	7497.76	−	4984.17i	0.488032	−	0.324422i
$619$			20112.1i			1.30593i	0.757386	+	0.652967i	$0.226476\pi$
$619$			20112.1i			1.30593i	−0.757386	+	0.652967i	$0.773524\pi$
$620$		−	737.028i		−	0.0477415i
$621$	−8337.98	+	1596.96i	−0.538795	+	0.103195i
$622$		−	567.058i		−	0.0365546i
$623$	11358.0	−	882.878i	0.730414	−	0.0567765i
$624$	−932.341	−	1402.53i	−0.0598133	−	0.0899781i
$625$	625.000			0.0400000
$626$	5611.84			0.358297
$627$	8602.71	−	5718.69i	0.547941	−	0.364247i
$628$			1519.42i			0.0965470i
$629$	42733.8			2.70892
$630$	−6501.29	−	2153.48i	−0.411139	−	0.136185i
$631$	5655.53			0.356804			0.178402	−	0.983958i	$-0.442907\pi$
$631$	5655.53			0.356804			0.178402	+	0.983958i	$0.442907\pi$
$632$		−	7471.36i		−	0.470245i
$633$	−10838.6	+	7204.98i	−0.680559	+	0.452405i
$634$	−10479.9			−0.656483
$635$	−3136.35			−0.196004
$636$	−53.6304	−	80.6770i	−0.00334368	−	0.00502995i
$637$	287.379	+	1837.35i	0.0178750	+	0.114284i
$638$		−	19571.5i		−	1.21449i
$639$	12899.2	+	5414.81i	0.798564	+	0.335221i
$640$		−	6494.19i		−	0.401102i
$641$		−	16810.4i		−	1.03584i	−0.855430	−	0.517919i	$-0.826707\pi$
$641$		−	16810.4i		−	1.03584i	0.855430	−	0.517919i	$-0.173293\pi$
$642$	334.854	−	222.596i	0.0205851	−	0.0136841i
$643$		−	6183.50i		−	0.379243i	−0.981857	−	0.189622i	$-0.939274\pi$
$643$		−	6183.50i		−	0.379243i	0.981857	−	0.189622i	$-0.0607261\pi$
$644$	43.1416	+	555.004i	0.00263978	+	0.0339600i
$645$	−1163.58	+	773.498i	−0.0710327	+	0.0472193i
$646$	14087.0			0.857964
$647$	14545.4			0.883829			0.441915	−	0.897057i	$-0.354299\pi$
$647$	14545.4			0.883829			0.441915	+	0.897057i	$0.354299\pi$
$648$	−12110.7	+	11883.2i	−0.734187	+	0.720392i
$649$			10035.2i			0.606958i
$650$	371.289			0.0224049
$651$	−17605.0	−	22485.7i	−1.05990	−	1.35374i
$652$	536.696			0.0322372
$653$		−	20772.5i		−	1.24486i	−0.782677	−	0.622428i	$-0.786146\pi$
$653$		−	20772.5i		−	1.24486i	0.782677	−	0.622428i	$-0.213854\pi$
$654$	689.316	+	1036.95i	0.0412147	+	0.0619998i
$655$	−1828.50			−0.109077
$656$	8736.30			0.519962
$657$	−20798.9	−	8730.96i	−1.23507	−	0.518459i
$658$	1772.34	+	22800.7i	0.105005	+	1.35086i
$659$			23686.4i			1.40014i	0.714076	+	0.700068i	$0.246847\pi$
$659$			23686.4i			1.40014i	−0.714076	+	0.700068i	$0.753153\pi$
$660$	298.652	+	449.266i	0.0176136	+	0.0264964i
$661$		−	13232.2i		−	0.778625i	−0.921106	−	0.389312i	$-0.872713\pi$
$661$		−	13232.2i		−	0.778625i	0.921106	−	0.389312i	$-0.127287\pi$
$662$			1321.02i			0.0775570i
$663$	1686.53	+	2537.08i	0.0987927	+	0.148615i
$664$			18290.1i			1.06897i
$665$	341.295	+	4390.66i	0.0199020	+	0.256034i
$666$	−26949.2	−	11312.7i	−1.56796	−	0.658197i
$667$	10342.8			0.600411
$668$	−1425.89			−0.0825890
$669$	−12207.7	−	18364.2i	−0.705496	−	1.06129i
$670$		−	4674.41i		−	0.269535i
$671$	−18372.2			−1.05701
$672$	1331.63	+	1700.80i	0.0764417	+	0.0976337i
$673$	−25868.1			−1.48164			−0.740820	−	0.671703i	$-0.765563\pi$
$673$	−25868.1			−1.48164			−0.740820	+	0.671703i	$0.765563\pi$
$674$			1117.88i			0.0638862i
$675$	−659.776	−	3444.79i	−0.0376219	−	0.196430i
$676$	1076.71			0.0612602
$677$	−29641.7			−1.68275			−0.841376	−	0.540450i	$-0.818254\pi$
$677$	−29641.7			−1.68275			−0.841376	+	0.540450i	$0.818254\pi$
$678$	−23887.9	+	15879.6i	−1.35311	+	0.899488i
$679$	−1970.44	−	25349.2i	−0.111368	−	1.43271i
$680$			12584.0i			0.709669i
$681$	−8276.94	+	5502.13i	−0.465746	+	0.309607i
$682$		−	33979.8i		−	1.90785i
$683$		−	21482.5i		−	1.20352i	−0.798677	−	0.601761i	$-0.794466\pi$
$683$		−	21482.5i		−	1.20352i	0.798677	−	0.601761i	$-0.205534\pi$
$684$	588.112	+	246.878i	0.0328758	+	0.0138006i
$685$		−	3795.33i		−	0.211697i
$686$	4013.17	+	16931.6i	0.223358	+	0.942348i
$687$	13391.9	+	20145.6i	0.743714	+	1.11878i
$688$	−3214.88			−0.178149
$689$	203.500			0.0112521
$690$	3586.31	−	2384.02i	0.197868	−	0.131533i
$691$		−	30709.9i		−	1.69068i	−0.534229	−	0.845340i	$-0.679398\pi$
$691$		−	30709.9i		−	1.69068i	0.534229	−	0.845340i	$-0.320602\pi$
$692$	−459.637			−0.0252497
$693$	19842.9	+	6572.74i	1.08769	+	0.360285i
$694$	−4183.91			−0.228846
$695$		−	14868.9i		−	0.811524i
$696$	17214.3	−	11443.3i	0.937512	−	0.623215i
$697$	−15803.3			−0.858812
$698$	8434.65			0.457387
$699$	8390.65	+	12622.2i	0.454025	+	0.682996i
$700$	−229.297	+	17.8237i	−0.0123809	+	0.000962389i
$701$			21707.5i			1.16959i	0.811182	+	0.584794i	$0.198825\pi$
$701$			21707.5i			1.16959i	−0.811182	+	0.584794i	$0.801175\pi$
$702$	−391.948	−	2046.42i	−0.0210728	−	0.110025i
$703$			18794.1i			1.00829i
$704$			22561.5i			1.20784i
$705$	−9753.67	+	6483.80i	−0.521056	+	0.346375i
$706$		−	3554.02i		−	0.189458i
$707$	−9506.58	+	738.966i	−0.505703	+	0.0393093i
$708$	−516.011	+	343.020i	−0.0273911	+	0.0182083i
$709$	10863.4			0.575433			0.287716	−	0.957716i	$-0.407104\pi$
$709$	10863.4			0.575433			0.287716	+	0.957716i	$0.407104\pi$
$710$	−7096.37			−0.375101
$711$	3354.78	−	7991.77i	0.176954	−	0.421540i
$712$			14316.6i			0.753562i
$713$	17957.0			0.943189
$714$	17572.7	+	22444.4i	0.921069	+	1.17642i
$715$	−1133.23			−0.0592732
$716$		−	946.815i		−	0.0494192i
$717$	−6754.97	−	10161.6i	−0.351840	−	0.529277i
$718$	5143.43			0.267341
$719$	−11005.7			−0.570851			−0.285426	−	0.958401i	$-0.592135\pi$
$719$	−11005.7			−0.570851			−0.285426	+	0.958401i	$0.592135\pi$
$720$	3123.66	−	7441.19i	0.161683	−	0.385162i
$721$	−907.884	−	11679.7i	−0.0468951	−	0.603292i
$722$		−	12592.9i		−	0.649111i
$723$	4704.89	+	7077.64i	0.242015	+	0.364067i
$724$			432.220i			0.0221869i
$725$			4273.06i			0.218893i
$726$	3281.29	+	4936.09i	0.167741	+	0.252335i
$727$			20004.8i			1.02055i	0.860013	+	0.510273i	$0.170456\pi$
$727$			20004.8i			1.02055i	−0.860013	+	0.510273i	$0.829544\pi$
$728$	−2330.04	+	181.119i	−0.118622	+	0.00922075i
$729$	−18290.0	+	7272.92i	−0.929230	+	0.369503i
$730$	11442.4			0.580138
$731$	5815.48			0.294245
$732$	−627.995	−	944.702i	−0.0317095	−	0.0477011i
$733$		−	24555.3i		−	1.23734i	−0.785650	−	0.618671i	$-0.787671\pi$
$733$		−	24555.3i		−	1.23734i	0.785650	−	0.618671i	$-0.212329\pi$
$734$	26783.9			1.34688
$735$	−6569.78	+	6020.88i	−0.329701	+	0.302155i
$736$	−1358.25			−0.0680242
$737$			14267.0i			0.713067i
$738$	9966.01	+	4183.53i	0.497092	+	0.208669i
$739$	7887.23			0.392607			0.196303	−	0.980543i	$-0.437106\pi$
$739$	7887.23			0.392607			0.196303	+	0.980543i	$0.437106\pi$
$740$	−981.496			−0.0487574
$741$	−1115.79	+	741.727i	−0.0553166	+	0.0367719i
$742$	1898.37	−	147.564i	0.0939236	−	0.00730087i
$743$			27562.8i			1.36094i	0.732775	+	0.680471i	$0.238225\pi$
$743$			27562.8i			1.36094i	−0.732775	+	0.680471i	$0.761775\pi$
$744$	29887.3	−	19867.7i	1.47274	−	0.979013i
$745$		−	13966.7i		−	0.686845i
$746$			6567.57i			0.322327i
$747$	−8212.62	+	19564.1i	−0.402254	+	0.958251i
$748$		−	2245.38i		−	0.109759i
$749$	−40.5467	−	521.621i	−0.00197803	−	0.0254467i
$750$	984.943	+	1481.66i	0.0479534	+	0.0721370i
$751$	30649.5			1.48924			0.744618	−	0.667490i	$-0.232631\pi$
$751$	30649.5			1.48924			0.744618	+	0.667490i	$0.232631\pi$
$752$	−26948.6			−1.30680
$753$	791.115	−	525.898i	0.0382866	−	0.0254512i
$754$			2538.47i			0.122607i
$755$	16333.7			0.787344
$756$	340.293	+	1244.99i	0.0163708	+	0.0598940i
$757$	−27581.2			−1.32425			−0.662125	−	0.749393i	$-0.730345\pi$
$757$	−27581.2			−1.32425			−0.662125	+	0.749393i	$0.730345\pi$
$758$			607.180i			0.0290947i
$759$	−10945.9	+	7276.36i	−0.523468	+	0.347978i
$760$	−5534.37			−0.264148
$761$	17361.2			0.826993			0.413497	−	0.910506i	$-0.364307\pi$
$761$	17361.2			0.826993			0.413497	+	0.910506i	$0.364307\pi$
$762$	−4942.61	−	7435.23i	−0.234976	−	0.353478i
$763$	1615.31	−	125.561i	0.0766424	−	0.00595757i
$764$		−	1325.30i		−	0.0627588i
$765$	−5650.46	+	13460.5i	−0.267049	+	0.636166i
$766$			23520.9i			1.10946i
$767$		−	1301.58i		−	0.0612745i
$768$	−3288.61	+	2186.12i	−0.154515	+	0.102715i
$769$			23167.4i			1.08639i	0.839605	+	0.543197i	$0.182786\pi$
$769$			23167.4i			1.08639i	−0.839605	+	0.543197i	$0.817214\pi$
$770$	−10571.4	+	821.740i	−0.494764	+	0.0384590i
$771$	13591.8	−	9035.19i	0.634884	−	0.422042i
$772$	540.656			0.0252055
$773$	25590.9			1.19074			0.595370	−	0.803452i	$-0.297006\pi$
$773$	25590.9			1.19074			0.595370	+	0.803452i	$0.297006\pi$
$774$	−3667.41	−	1539.50i	−0.170313	−	0.0714940i
$775$			7418.82i			0.343861i
$776$	31952.3			1.47812
$777$	−29944.1	+	23444.5i	−1.38255	+	1.08246i
$778$	20686.4			0.953269
$779$		−	6950.19i		−	0.319661i
$780$	−38.7357	−	58.2707i	−0.00177816	−	0.00267491i
$781$	21659.1			0.992349
$782$	−17924.0			−0.819644
$783$	23551.7	−	4510.82i	1.07493	−	0.205879i
$784$	−20258.0	+	3168.54i	−0.922834	+	0.144340i
$785$		−	15294.3i		−	0.695384i
$786$	−2881.55	−	4334.76i	−0.130765	−	0.196712i
$787$		−	39888.6i		−	1.80670i	−0.428902	−	0.903351i	$-0.641099\pi$
$787$		−	39888.6i		−	1.80670i	0.428902	−	0.903351i	$-0.358901\pi$
$788$		−	1674.18i		−	0.0756853i
$789$	19028.0	+	28624.1i	0.858573	+	1.29156i
$790$			4396.61i			0.198006i
$791$	2892.53	+	37211.5i	0.130021	+	1.67268i
$792$	−10167.6	+	24221.3i	−0.456175	+	1.08670i
$793$	2382.92			0.106709
$794$	−232.253			−0.0103808
$795$	539.836	+	812.084i	0.0240830	+	0.0362285i
$796$		−	1802.90i		−	0.0802792i
$797$	−27354.4			−1.21574			−0.607869	−	0.794037i	$-0.707976\pi$
$797$	−27354.4			−1.21574			−0.607869	+	0.794037i	$0.707976\pi$
$798$	−9870.92	+	7728.38i	−0.437878	+	0.342834i
$799$	48747.9			2.15842
$800$		−	561.154i		−	0.0247997i
$801$	−6428.42	+	15313.8i	−0.283567	+	0.675513i
$802$	−2572.81			−0.113278
$803$	−34923.7			−1.53478
$804$	−733.609	+	487.670i	−0.0321796	+	0.0213915i
$805$	−434.257	−	5586.60i	−0.0190131	−	0.244598i
$806$			4407.25i			0.192604i
$807$	29485.4	−	19600.6i	1.28617	−	0.854986i
$808$		−	11982.9i		−	0.521730i
$809$		−	18570.3i		−	0.807044i	−0.914970	−	0.403522i	$-0.867786\pi$
$809$		−	18570.3i		−	0.807044i	0.914970	−	0.403522i	$-0.132214\pi$
$810$	7126.69	−	6992.78i	0.309144	−	0.303335i
$811$		−	8683.46i		−	0.375977i	−0.982171	−	0.187989i	$-0.939803\pi$
$811$		−	8683.46i		−	0.375977i	0.982171	−	0.187989i	$-0.0601968\pi$
$812$	−121.859	−	1567.68i	−0.00526651	−	0.0677521i
$813$	1774.30	+	2669.11i	0.0765406	+	0.115141i
$814$	−45250.7			−1.94845
$815$	−5402.31			−0.232190
$816$	−27972.9	+	18595.1i	−1.20006	+	0.797745i
$817$			2557.61i			0.109522i
$818$	−32707.6			−1.39804
$819$	−2573.66	−	852.498i	−0.109806	−	0.0363720i
$820$	362.965			0.0154577
$821$		−	22095.2i		−	0.939256i	−0.882864	−	0.469628i	$-0.844388\pi$
$821$		−	22095.2i		−	0.939256i	0.882864	−	0.469628i	$-0.155612\pi$
$822$	8997.45	−	5981.10i	0.381779	−	0.253789i
$823$	38298.6			1.62212			0.811060	−	0.584963i	$-0.198891\pi$
$823$	38298.6			1.62212			0.811060	+	0.584963i	$0.198891\pi$
$824$	14722.1			0.622412
$825$	−3006.19	−	4522.25i	−0.126863	−	0.190842i
$826$	−943.821	−	12142.0i	−0.0397575	−	0.511469i
$827$		−	11902.0i		−	0.500451i	−0.968188	−	0.250225i	$-0.919495\pi$
$827$		−	11902.0i		−	0.500451i	0.968188	−	0.250225i	$-0.0805047\pi$
$828$	−748.303	−	314.123i	−0.0314074	−	0.0131842i
$829$			28692.3i			1.20208i	0.799218	+	0.601041i	$0.205247\pi$
$829$			28692.3i			1.20208i	−0.799218	+	0.601041i	$0.794753\pi$
$830$		−	10763.0i		−	0.450109i
$831$	34583.3	−	22989.4i	1.44366	−	0.959681i
$832$		−	2926.28i		−	0.121936i
$833$	36645.3	−	5731.65i	1.52423	−	0.238403i
$834$	35249.1	−	23432.0i	1.46352	−	0.972884i
$835$	14352.9			0.594851
$836$	987.506			0.0408536
$837$	40890.0	−	7831.61i	1.68861	−	0.323417i
$838$		−	7.37054i		−	0.000303832i
$839$	−21919.1			−0.901944			−0.450972	−	0.892538i	$-0.648923\pi$
$839$	−21919.1			−0.901944			−0.450972	+	0.892538i	$0.648923\pi$
$840$	−6903.82	−	8817.77i	−0.283577	−	0.362193i
$841$	−4825.46			−0.197854
$842$			22752.2i			0.931225i
$843$	8543.36	+	12851.9i	0.349050	+	0.525081i
$844$	−1244.16			−0.0507414
$845$	−10838.0			−0.441230
$846$	−30741.8	−	12904.8i	−1.24932	−	0.524440i
$847$	7689.22	−	597.698i	0.311930	−	0.0242469i
$848$			2243.72i			0.0908603i
$849$	−10208.4	−	15356.6i	−0.412663	−	0.620774i
$850$		−	7405.21i		−	0.298819i
$851$		−	23913.2i		−	0.963260i
$852$	740.348	+	1113.72i	0.0297698	+	0.0447832i
$853$			24530.2i			0.984638i	0.870415	+	0.492319i	$0.163851\pi$
$853$			24530.2i			0.984638i	−0.870415	+	0.492319i	$0.836149\pi$
$854$	22229.3	−	1727.93i	0.890716	−	0.0692371i
$855$	−5919.86	−	2485.04i	−0.236789	−	0.0993994i
$856$	657.496			0.0262532
$857$	28659.6			1.14235			0.571175	−	0.820828i	$-0.306488\pi$
$857$	28659.6			1.14235			0.571175	+	0.820828i	$0.306488\pi$
$858$	−1785.86	−	2686.50i	−0.0710587	−	0.106895i
$859$		−	22404.8i		−	0.889921i	−0.895550	−	0.444961i	$-0.853218\pi$
$859$		−	22404.8i		−	0.889921i	0.895550	−	0.444961i	$-0.146782\pi$
$860$	−133.568			−0.00529608
$861$	11073.6	−	8669.97i	0.438311	−	0.343173i
$862$	−3789.83			−0.149747
$863$			16914.4i			0.667177i	0.942719	+	0.333588i	$0.108260\pi$
$863$			16914.4i			0.667177i	−0.942719	+	0.333588i	$0.891740\pi$
$864$	−3092.89	+	592.377i	−0.121785	+	0.0233253i
$865$	4626.65			0.181862
$866$	−34458.8			−1.35214
$867$	29341.0	−	19504.6i	1.14933	−	0.764025i
$868$	−211.569	−	2721.78i	−0.00827319	−	0.106432i
$869$		−	13419.1i		−	0.523833i
$870$	−10130.0	+	6733.95i	−0.394757	+	0.262417i
$871$		−	1850.46i		−	0.0719865i
$872$			2036.08i			0.0790714i
$873$	34177.9	+	14347.2i	1.32503	+	0.556219i
$874$		−	7882.87i		−	0.305083i
$875$	2308.07	−	179.411i	0.0891737	−	0.00693165i
$876$	−1193.75	−	1795.78i	−0.0460425	−	0.0692624i
$877$	−4271.24			−0.164458			−0.0822289	−	0.996613i	$-0.526204\pi$
$877$	−4271.24			−0.164458			−0.0822289	+	0.996613i	$0.526204\pi$
$878$	−28808.9			−1.10735
$879$	−37056.2	+	24633.3i	−1.42193	+	0.945233i
$880$		−	12494.6i		−	0.478628i
$881$	−12389.8			−0.473806			−0.236903	−	0.971533i	$-0.576132\pi$
$881$	−12389.8			−0.473806			−0.236903	+	0.971533i	$0.576132\pi$
$882$	−24626.9	−	6086.38i	−0.940170	−	0.232357i
$883$	−35283.7			−1.34472			−0.672361	−	0.740223i	$-0.734720\pi$
$883$	−35283.7			−1.34472			−0.672361	+	0.740223i	$0.734720\pi$
$884$			291.231i			0.0110805i
$885$	5194.09	−	3452.80i	0.197285	−	0.131146i
$886$	8972.82			0.340234
$887$	−26285.9			−0.995034			−0.497517	−	0.867454i	$-0.665755\pi$
$887$	−26285.9			−0.995034			−0.497517	+	0.867454i	$0.665755\pi$
$888$	−26457.7	−	39800.8i	−0.999846	−	1.50408i
$889$	−11582.3	+	900.313i	−0.436959	+	0.0339657i
$890$		−	8424.76i		−	0.317302i
$891$	−21751.7	+	21343.0i	−0.817854	+	0.802487i
$892$		−	2108.03i		−	0.0791279i
$893$			21439.0i			0.803392i
$894$	33110.3	−	22010.2i	1.23867	−	0.823414i
$895$			9530.51i			0.355944i
$896$	−1864.21	−	23982.5i	−0.0695075	−	0.894194i
$897$	1419.71	−	943.760i	0.0528459	−	0.0351296i
$898$	2586.96			0.0961338
$899$	−50721.7			−1.88172
$900$	129.778	−	309.157i	0.00480659	−	0.0114503i
$901$		−	4058.71i		−	0.150072i
$902$	16734.0			0.617719
$903$	−4074.98	+	3190.48i	−0.150174	+	0.117577i
$904$	−46904.6			−1.72569
$905$		−	4350.67i		−	0.159802i
$906$	25740.4	+	38721.7i	0.943895	+	1.41991i
$907$	−36682.7			−1.34292			−0.671460	−	0.741041i	$-0.734333\pi$
$907$	−36682.7			−1.34292			−0.671460	+	0.741041i	$0.734333\pi$
$908$	−950.110			−0.0347252
$909$	5380.56	−	12817.6i	0.196328	−	0.467692i
$910$	1371.14	−	106.581i	0.0499481	−	0.00388257i
$911$			49888.7i			1.81437i	0.420737	+	0.907183i	$0.361772\pi$
$911$			49888.7i			1.81437i	−0.420737	+	0.907183i	$0.638228\pi$
$912$	−8178.03	−	12302.3i	−0.296931	−	0.446678i
$913$			32850.3i			1.19079i
$914$		−	12480.3i		−	0.451653i
$915$	6321.32	+	9509.25i	0.228389	+	0.343569i
$916$			2312.51i			0.0834144i
$917$	−6752.50	+	524.886i	−0.243170	+	0.0189021i
$918$	−40815.0	+	7817.24i	−1.46742	+	0.281054i
$919$	332.180			0.0119234			0.00596170	−	0.999982i	$-0.498102\pi$
$919$	332.180			0.0119234			0.00596170	+	0.999982i	$0.498102\pi$
$920$	7041.83			0.252350
$921$	12372.0	+	18611.4i	0.442639	+	0.665869i
$922$			36976.9i			1.32079i
$923$	−2809.23			−0.100181
$924$	1231.86	+	1573.37i	0.0438584	+	0.0560174i
$925$	9879.61			0.351178
$926$		−	43215.5i		−	1.53364i
$927$	15747.5	+	6610.49i	0.557946	+	0.234215i
$928$	3836.55			0.135712
$929$	18054.6			0.637624			0.318812	−	0.947818i	$-0.396716\pi$
$929$	18054.6			0.637624			0.318812	+	0.947818i	$0.396716\pi$
$930$	−17587.5	+	11691.4i	−0.620127	+	0.412232i
$931$	2520.74	+	16116.3i	0.0887369	+	0.567338i
$932$			1448.90i			0.0509231i
$933$	895.811	−	595.494i	0.0314336	−	0.0208956i
$934$		−	39658.5i		−	1.38936i
$935$			22601.7i			0.790541i
$936$	1318.76	−	3141.55i	0.0460524	−	0.109706i
$937$		−	38254.6i		−	1.33375i	−0.745170	−	0.666875i	$-0.767632\pi$
$937$		−	38254.6i		−	1.33375i	0.745170	−	0.666875i	$-0.232368\pi$
$938$	−1341.82	−	17262.2i	−0.0467080	−	0.600885i
$939$	5893.26	+	8865.32i	0.204813	+	0.308103i
$940$	−1119.62			−0.0388491
$941$	−54622.4			−1.89228			−0.946141	−	0.323754i	$-0.895055\pi$
$941$	−54622.4			−1.89228			−0.946141	+	0.323754i	$0.895055\pi$
$942$	36257.6	−	24102.4i	1.25407	−	0.833651i
$943$			8843.29i			0.305384i
$944$	14350.8			0.494788
$945$	−3425.35	−	12531.9i	−0.117912	−	0.431389i
$946$	−6157.99			−0.211642
$947$		−	23956.8i		−	0.822061i	−0.911621	−	0.411031i	$-0.865169\pi$
$947$		−	23956.8i		−	0.822061i	0.911621	−	0.411031i	$-0.134831\pi$
$948$	690.011	−	458.688i	0.0236398	−	0.0157147i
$949$	4529.68			0.154942
$950$	3256.76			0.111225
$951$	−11005.4	−	16555.7i	−0.375264	−	0.564515i
$952$	3612.33	+	46471.6i	0.122979	+	1.58209i
$953$		−	19456.1i		−	0.661328i	−0.943749	−	0.330664i	$-0.892727\pi$
$953$		−	19456.1i		−	0.661328i	0.943749	−	0.330664i	$-0.107273\pi$
$954$	−1074.44	+	2559.54i	−0.0364637	+	0.0868639i
$955$			13340.3i			0.452023i
$956$		−	1166.45i		−	0.0394620i
$957$	30918.1	−	20553.0i	1.04435	−	0.694236i
$958$			21395.6i			0.721568i
$959$	−1089.48	−	14015.8i	−0.0366852	−	0.471944i
$960$	11677.6	−	7762.73i	0.392596	−	0.260980i
$961$	−58271.3			−1.95600
$962$	5869.11			0.196702
$963$	703.293	+	295.228i	0.0235341	+	0.00987913i
$964$			812.442i			0.0271442i
$965$	−5442.17			−0.181544
$966$	12559.6	−	9833.45i	0.418321	−	0.327522i
$967$	18173.5			0.604363			0.302182	−	0.953250i	$-0.402285\pi$
$967$	18173.5			0.604363			0.302182	+	0.953250i	$0.402285\pi$
$968$			9692.15i			0.321816i
$969$	14793.4	+	22254.0i	0.490437	+	0.737771i
$970$	−18802.7			−0.622390
$971$	−31591.5			−1.04410			−0.522050	−	0.852915i	$-0.674833\pi$
$971$	−31591.5			−1.04410			−0.522050	+	0.852915i	$0.674833\pi$
$972$	−1840.97	−	388.933i	−0.0607501	−	0.0128344i
$973$	−4268.23	−	54909.5i	−0.140630	−	1.80917i
$974$			11732.9i			0.385981i
$975$	389.909	+	586.545i	0.0128073	+	0.0192661i
$976$			26273.2i			0.861666i
$977$			52487.7i			1.71876i	0.511336	+	0.859381i	$0.329151\pi$
$977$			52487.7i			1.71876i	−0.511336	+	0.859381i	$0.670849\pi$
$978$	−8513.56	−	12807.1i	−0.278357	−	0.418737i
$979$			25713.6i			0.839437i
$980$	−841.656	+	131.643i	−0.0274344	+	0.00429099i
$981$	−914.238	+	2177.90i	−0.0297547	+	0.0708817i
$982$	−10082.4			−0.327640
$983$	33261.8			1.07923			0.539617	−	0.841911i	$-0.318569\pi$
$983$	33261.8			1.07923			0.539617	+	0.841911i	$0.318569\pi$
$984$	9784.27	+	14718.6i	0.316983	+	0.476842i
$985$			16852.0i			0.545127i
$986$	50628.6			1.63524
$987$	−34158.2	+	26744.0i	−1.10159	+	0.862482i
$988$	−128.082			−0.00412431
$989$		−	3254.26i		−	0.104630i
$990$	5983.25	−	14253.3i	0.192081	−	0.457576i
$991$	19900.3			0.637895			0.318947	−	0.947772i	$-0.396671\pi$
$991$	19900.3			0.637895			0.318947	+	0.947772i	$0.396671\pi$
$992$	6660.96			0.213191
$993$	−2086.88	+	1387.26i	−0.0666919	+	0.0443338i
$994$	−26206.3	+	2037.07i	−0.836230	+	0.0650018i
$995$			18147.8i			0.578215i
$996$	−1689.17	+	1122.88i	−0.0537383	+	0.0357228i
$997$		−	20578.8i		−	0.653698i	−0.945076	−	0.326849i	$-0.894013\pi$
$997$		−	20578.8i		−	0.653698i	0.945076	−	0.326849i	$-0.105987\pi$
$998$			16442.8i			0.521531i
$999$	−10429.3	−	54453.1i	−0.330299	−	1.72454i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.b.a.41.5	✓	16
3.2	odd	2		105.4.b.b.41.12	yes	16
7.6	odd	2		105.4.b.b.41.5	yes	16
21.20	even	2	inner	105.4.b.a.41.12	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.b.a.41.5	✓	16	1.1	even	1	trivial
105.4.b.a.41.12	yes	16	21.20	even	2	inner
105.4.b.b.41.5	yes	16	7.6	odd	2
105.4.b.b.41.12	yes	16	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.73921i q^{2} +(4.32728 - 2.87658i) q^{3} +0.496728 q^{4} -5.00000 q^{5} +(-7.87955 - 11.8533i) q^{6} +(-18.4646 + 1.43529i) q^{7} -23.2743i q^{8} +(10.4506 - 24.8955i) q^{9} +O(q^{10})\)	\(q-2.73921i q^{2} +(4.32728 - 2.87658i) q^{3} +0.496728 q^{4} -5.00000 q^{5} +(-7.87955 - 11.8533i) q^{6} +(-18.4646 + 1.43529i) q^{7} -23.2743i q^{8} +(10.4506 - 24.8955i) q^{9} +13.6961i q^{10} -41.8023i q^{11} +(2.14948 - 1.42888i) q^{12} +5.42185i q^{13} +(3.93155 + 50.5783i) q^{14} +(-21.6364 + 14.3829i) q^{15} -59.7794 q^{16} +108.136 q^{17} +(-68.1939 - 28.6264i) q^{18} +47.5577i q^{19} -2.48364 q^{20} +(-75.7725 + 59.3256i) q^{21} -114.505 q^{22} -60.5116i q^{23} +(-66.9504 - 100.714i) q^{24} +25.0000 q^{25} +14.8516 q^{26} +(-26.3910 - 137.792i) q^{27} +(-9.17187 + 0.712948i) q^{28} +170.922i q^{29} +(39.3977 + 59.2666i) q^{30} +296.753i q^{31} -22.4462i q^{32} +(-120.247 - 180.890i) q^{33} -296.208i q^{34} +(92.3228 - 7.17644i) q^{35} +(5.19112 - 12.3663i) q^{36} +395.184 q^{37} +130.271 q^{38} +(15.5964 + 23.4618i) q^{39} +116.372i q^{40} -146.142 q^{41} +(162.505 + 207.557i) q^{42} +53.7791 q^{43} -20.7644i q^{44} +(-52.2531 + 124.477i) q^{45} -165.754 q^{46} +450.800 q^{47} +(-258.682 + 171.960i) q^{48} +(338.880 - 53.0039i) q^{49} -68.4803i q^{50} +(467.936 - 311.063i) q^{51} +2.69318i q^{52} -37.5333i q^{53} +(-377.440 + 72.2906i) q^{54} +209.011i q^{55} +(33.4053 + 429.750i) q^{56} +(136.803 + 205.795i) q^{57} +468.192 q^{58} -240.063 q^{59} +(-10.7474 + 7.14438i) q^{60} -439.503i q^{61} +812.868 q^{62} +(-157.234 + 474.684i) q^{63} -539.720 q^{64} -27.1092i q^{65} +(-495.496 + 329.383i) q^{66} -341.296 q^{67} +53.7144 q^{68} +(-174.066 - 261.850i) q^{69} +(-19.6578 - 252.892i) q^{70} +518.133i q^{71} +(-579.425 - 243.231i) q^{72} -835.450i q^{73} -1082.49i q^{74} +(108.182 - 71.9144i) q^{75} +23.6233i q^{76} +(59.9983 + 771.861i) q^{77} +(64.2669 - 42.7217i) q^{78} +321.013 q^{79} +298.897 q^{80} +(-510.569 - 520.346i) q^{81} +400.314i q^{82} -785.850 q^{83} +(-37.6383 + 29.4687i) q^{84} -540.682 q^{85} -147.312i q^{86} +(491.671 + 739.628i) q^{87} -972.920 q^{88} -615.123 q^{89} +(340.970 + 143.132i) q^{90} +(-7.78191 - 100.112i) q^{91} -30.0578i q^{92} +(853.632 + 1284.13i) q^{93} -1234.84i q^{94} -237.788i q^{95} +(-64.5681 - 97.1307i) q^{96} +1372.86i q^{97} +(-145.189 - 928.263i) q^{98} +(-1040.69 - 436.860i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} - 64 q^{4} - 80 q^{5} - 28 q^{6} - 4 q^{7} - 22 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 - 64 * q^4 - 80 * q^5 - 28 * q^6 - 4 * q^7 - 22 * q^9	\( 16 q - 2 q^{3} - 64 q^{4} - 80 q^{5} - 28 q^{6} - 4 q^{7} - 22 q^{9} - 66 q^{12} - 90 q^{14} + 10 q^{15} + 376 q^{16} - 72 q^{17} - 182 q^{18} + 320 q^{20} - 74 q^{21} - 276 q^{22} + 526 q^{24} + 400 q^{25} + 696 q^{26} - 128 q^{27} + 10 q^{28} + 140 q^{30} - 502 q^{33} + 20 q^{35} + 996 q^{36} - 812 q^{37} - 1200 q^{38} - 594 q^{39} - 936 q^{41} - 1834 q^{42} - 548 q^{43} + 110 q^{45} + 1224 q^{46} + 912 q^{47} + 1850 q^{48} + 328 q^{49} + 750 q^{51} - 2950 q^{54} + 1254 q^{56} + 432 q^{57} + 576 q^{58} - 552 q^{59} + 330 q^{60} - 1860 q^{62} - 898 q^{63} - 4000 q^{64} + 1378 q^{66} + 1004 q^{67} + 3828 q^{68} + 1988 q^{69} + 450 q^{70} + 1988 q^{72} - 50 q^{75} + 1152 q^{77} + 1446 q^{78} + 1292 q^{79} - 1880 q^{80} - 2950 q^{81} - 1752 q^{83} + 1068 q^{84} + 360 q^{85} + 1910 q^{87} - 912 q^{88} + 6096 q^{89} + 910 q^{90} - 552 q^{91} - 1080 q^{93} - 9546 q^{96} - 4824 q^{98} + 2530 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 - 64 * q^4 - 80 * q^5 - 28 * q^6 - 4 * q^7 - 22 * q^9 - 66 * q^12 - 90 * q^14 + 10 * q^15 + 376 * q^16 - 72 * q^17 - 182 * q^18 + 320 * q^20 - 74 * q^21 - 276 * q^22 + 526 * q^24 + 400 * q^25 + 696 * q^26 - 128 * q^27 + 10 * q^28 + 140 * q^30 - 502 * q^33 + 20 * q^35 + 996 * q^36 - 812 * q^37 - 1200 * q^38 - 594 * q^39 - 936 * q^41 - 1834 * q^42 - 548 * q^43 + 110 * q^45 + 1224 * q^46 + 912 * q^47 + 1850 * q^48 + 328 * q^49 + 750 * q^51 - 2950 * q^54 + 1254 * q^56 + 432 * q^57 + 576 * q^58 - 552 * q^59 + 330 * q^60 - 1860 * q^62 - 898 * q^63 - 4000 * q^64 + 1378 * q^66 + 1004 * q^67 + 3828 * q^68 + 1988 * q^69 + 450 * q^70 + 1988 * q^72 - 50 * q^75 + 1152 * q^77 + 1446 * q^78 + 1292 * q^79 - 1880 * q^80 - 2950 * q^81 - 1752 * q^83 + 1068 * q^84 + 360 * q^85 + 1910 * q^87 - 912 * q^88 + 6096 * q^89 + 910 * q^90 - 552 * q^91 - 1080 * q^93 - 9546 * q^96 - 4824 * q^98 + 2530 * q^99

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