LMFDB - Embedded newform 105.4.b.a.41.13

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			41.13
Root			$3.20688i$ of defining polynomial
Character	$\chi$	$=$	105.41
Dual form			105.4.b.a.41.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.20688i q^{2} +(-2.93464 - 4.28811i) q^{3} -2.28410 q^{4} -5.00000 q^{5} +(13.7515 - 9.41106i) q^{6} +(18.2867 + 2.93186i) q^{7} +18.3302i q^{8} +(-9.77574 + 25.1681i) q^{9} +O(q^{10})$	\(q+3.20688i q^{2} +(-2.93464 - 4.28811i) q^{3} -2.28410 q^{4} -5.00000 q^{5} +(13.7515 - 9.41106i) q^{6} +(18.2867 + 2.93186i) q^{7} +18.3302i q^{8} +(-9.77574 + 25.1681i) q^{9} -16.0344i q^{10} +15.3091i q^{11} +(6.70302 + 9.79447i) q^{12} +57.4505i q^{13} +(-9.40212 + 58.6434i) q^{14} +(14.6732 + 21.4405i) q^{15} -77.0557 q^{16} +44.6260 q^{17} +(-80.7113 - 31.3496i) q^{18} +93.4201i q^{19} +11.4205 q^{20} +(-41.0929 - 87.0194i) q^{21} -49.0943 q^{22} -86.4424i q^{23} +(78.6020 - 53.7927i) q^{24} +25.0000 q^{25} -184.237 q^{26} +(136.612 - 31.9401i) q^{27} +(-41.7687 - 6.69666i) q^{28} +122.241i q^{29} +(-68.7573 + 47.0553i) q^{30} -28.0606i q^{31} -100.467i q^{32} +(65.6469 - 44.9266i) q^{33} +143.110i q^{34} +(-91.4336 - 14.6593i) q^{35} +(22.3288 - 57.4865i) q^{36} -142.227 q^{37} -299.587 q^{38} +(246.354 - 168.597i) q^{39} -91.6511i q^{40} -272.725 q^{41} +(279.061 - 131.780i) q^{42} +524.181 q^{43} -34.9674i q^{44} +(48.8787 - 125.841i) q^{45} +277.211 q^{46} +398.874 q^{47} +(226.131 + 330.423i) q^{48} +(325.808 + 107.228i) q^{49} +80.1721i q^{50} +(-130.961 - 191.361i) q^{51} -131.223i q^{52} -413.183i q^{53} +(102.428 + 438.099i) q^{54} -76.5453i q^{55} +(-53.7416 + 335.200i) q^{56} +(400.595 - 274.155i) q^{57} -392.014 q^{58} -651.537 q^{59} +(-33.5151 - 48.9723i) q^{60} -404.916i q^{61} +89.9870 q^{62} +(-252.556 + 431.582i) q^{63} -294.260 q^{64} -287.252i q^{65} +(144.074 + 210.522i) q^{66} +56.1055 q^{67} -101.930 q^{68} +(-370.674 + 253.678i) q^{69} +(47.0106 - 293.217i) q^{70} -296.808i q^{71} +(-461.338 - 179.191i) q^{72} +28.5652i q^{73} -456.105i q^{74} +(-73.3661 - 107.203i) q^{75} -213.381i q^{76} +(-44.8840 + 279.952i) q^{77} +(540.670 + 790.028i) q^{78} -1207.32 q^{79} +385.278 q^{80} +(-537.870 - 492.074i) q^{81} -874.598i q^{82} +88.9729 q^{83} +(93.8602 + 198.761i) q^{84} -223.130 q^{85} +1680.99i q^{86} +(524.184 - 358.735i) q^{87} -280.618 q^{88} -28.7275 q^{89} +(403.556 + 156.748i) q^{90} +(-168.437 + 1050.58i) q^{91} +197.443i q^{92} +(-120.327 + 82.3478i) q^{93} +1279.14i q^{94} -467.100i q^{95} +(-430.812 + 294.834i) q^{96} -1573.32i q^{97} +(-343.868 + 1044.83i) q^{98} +(-385.300 - 149.657i) 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 $

$2$			3.20688i			1.13380i	0.823785	+	0.566902i	$0.191858\pi$
$2$			3.20688i			1.13380i	−0.823785	+	0.566902i	$0.808142\pi$
$3$	−2.93464	−	4.28811i	−0.564772	−	0.825247i
$3$	−2.93464	−	4.28811i	−0.564772	−	0.825247i
$4$	−2.28410			−0.285512
$5$	−5.00000			−0.447214
$5$	−5.00000			−0.447214
$6$	13.7515	−	9.41106i	0.935668	−	0.640341i
$7$	18.2867	+	2.93186i	0.987390	+	0.158305i
$7$	18.2867	+	2.93186i	0.987390	+	0.158305i
$8$			18.3302i			0.810089i
$9$	−9.77574	+	25.1681i	−0.362064	+	0.932153i
$10$		−	16.0344i		−	0.507053i
$11$			15.3091i			0.419623i	0.977742	+	0.209811i	$0.0672850\pi$
$11$			15.3091i			0.419623i	−0.977742	+	0.209811i	$0.932715\pi$
$12$	6.70302	+	9.79447i	0.161250	+	0.235618i
$13$			57.4505i			1.22568i	0.790205	+	0.612842i	$0.209974\pi$
$13$			57.4505i			1.22568i	−0.790205	+	0.612842i	$0.790026\pi$
$14$	−9.40212	+	58.6434i	−0.179487	+	1.11951i
$15$	14.6732	+	21.4405i	0.252574	+	0.369062i
$16$	−77.0557			−1.20400
$17$	44.6260			0.636670			0.318335	−	0.947978i	$-0.396876\pi$
$17$	44.6260			0.636670			0.318335	+	0.947978i	$0.396876\pi$
$18$	−80.7113	−	31.3496i	−1.05688	−	0.410510i
$19$			93.4201i			1.12800i	0.825774	+	0.564001i	$0.190739\pi$
$19$			93.4201i			1.12800i	−0.825774	+	0.564001i	$0.809261\pi$
$20$	11.4205			0.127685
$21$	−41.0929	−	87.0194i	−0.427010	−	0.904247i
$22$	−49.0943			−0.475770
$23$		−	86.4424i		−	0.783674i	−0.920035	−	0.391837i	$-0.871840\pi$
$23$		−	86.4424i		−	0.783674i	0.920035	−	0.391837i	$-0.128160\pi$
$24$	78.6020	−	53.7927i	0.668523	−	0.457516i
$25$	25.0000			0.200000
$26$	−184.237			−1.38969
$27$	136.612	−	31.9401i	0.973740	−	0.227662i
$28$	−41.7687	−	6.69666i	−0.281912	−	0.0451982i
$29$			122.241i			0.782747i	0.920232	+	0.391373i	$0.128000\pi$
$29$			122.241i			0.782747i	−0.920232	+	0.391373i	$0.872000\pi$
$30$	−68.7573	+	47.0553i	−0.418444	+	0.286369i
$31$		−	28.0606i		−	0.162575i	−0.996691	−	0.0812875i	$-0.974097\pi$
$31$		−	28.0606i		−	0.162575i	0.996691	−	0.0812875i	$-0.0259032\pi$
$32$		−	100.467i		−	0.555006i
$33$	65.6469	−	44.9266i	0.346292	−	0.236991i
$34$			143.110i			0.721860i
$35$	−91.4336	−	14.6593i	−0.441574	−	0.0707963i
$36$	22.3288	−	57.4865i	0.103374	−	0.266141i
$37$	−142.227			−0.631945			−0.315972	−	0.948768i	$-0.602331\pi$
$37$	−142.227			−0.631945			−0.315972	+	0.948768i	$0.602331\pi$
$38$	−299.587			−1.27893
$39$	246.354	−	168.597i	1.01149	−	0.692233i
$40$		−	91.6511i		−	0.362283i
$41$	−272.725			−1.03884			−0.519421	−	0.854518i	$-0.673852\pi$
$41$	−272.725			−1.03884			−0.519421	+	0.854518i	$0.673852\pi$
$42$	279.061	−	131.780i	1.02524	−	0.484145i
$43$	524.181			1.85900			0.929499	−	0.368826i	$-0.120240\pi$
$43$	524.181			1.85900			0.929499	+	0.368826i	$0.120240\pi$
$44$		−	34.9674i		−	0.119808i
$45$	48.8787	−	125.841i	0.161920	−	0.416872i
$46$	277.211			0.888533
$47$	398.874			1.23791			0.618955	−	0.785426i	$-0.287556\pi$
$47$	398.874			1.23791			0.618955	+	0.785426i	$0.287556\pi$
$48$	226.131	+	330.423i	0.679983	+	0.993593i
$49$	325.808	+	107.228i	0.949879	+	0.312618i
$50$			80.1721i			0.226761i
$51$	−130.961	−	191.361i	−0.359574	−	0.525410i
$52$		−	131.223i		−	0.349948i
$53$		−	413.183i		−	1.07085i	−0.844583	−	0.535425i	$-0.820152\pi$
$53$		−	413.183i		−	1.07085i	0.844583	−	0.535425i	$-0.179848\pi$
$54$	102.428	+	438.099i	0.258124	+	1.10403i
$55$		−	76.5453i		−	0.187661i
$56$	−53.7416	+	335.200i	−0.128242	+	0.799874i
$57$	400.595	−	274.155i	0.930880	−	0.637064i
$58$	−392.014			−0.887482
$59$	−651.537			−1.43768			−0.718838	−	0.695178i	$-0.755326\pi$
$59$	−651.537			−1.43768			−0.718838	+	0.695178i	$0.755326\pi$
$60$	−33.5151	−	48.9723i	−0.0721130	−	0.105372i
$61$		−	404.916i		−	0.849904i	−0.905216	−	0.424952i	$-0.860291\pi$
$61$		−	404.916i		−	0.849904i	0.905216	−	0.424952i	$-0.139709\pi$
$62$	89.9870			0.184328
$63$	−252.556	+	431.582i	−0.505064	+	0.863082i
$64$	−294.260			−0.574727
$65$		−	287.252i		−	0.548143i
$66$	144.074	+	210.522i	0.268702	+	0.392628i
$67$	56.1055			0.102304			0.0511520	−	0.998691i	$-0.483711\pi$
$67$	56.1055			0.102304			0.0511520	+	0.998691i	$0.483711\pi$
$68$	−101.930			−0.181777
$69$	−370.674	+	253.678i	−0.646724	+	0.442597i
$70$	47.0106	−	293.217i	0.0802692	−	0.500659i
$71$		−	296.808i		−	0.496122i	−0.968744	−	0.248061i	$-0.920207\pi$
$71$		−	296.808i		−	0.496122i	0.968744	−	0.248061i	$-0.0797933\pi$
$72$	−461.338	−	179.191i	−0.755127	−	0.293304i
$73$			28.5652i			0.0457987i	0.999738	+	0.0228994i	$0.00728973\pi$
$73$			28.5652i			0.0457987i	−0.999738	+	0.0228994i	$0.992710\pi$
$74$		−	456.105i		−	0.716502i
$75$	−73.3661	−	107.203i	−0.112954	−	0.165049i
$76$		−	213.381i		−	0.322059i
$77$	−44.8840	+	279.952i	−0.0664286	+	0.414332i
$78$	540.670	+	790.028i	0.784857	+	1.14683i
$79$	−1207.32			−1.71941			−0.859707	−	0.510787i	$-0.829354\pi$
$79$	−1207.32			−1.71941			−0.859707	+	0.510787i	$0.829354\pi$
$80$	385.278			0.538443
$81$	−537.870	−	492.074i	−0.737819	−	0.674999i
$82$		−	874.598i		−	1.17784i
$83$	88.9729			0.117663			0.0588316	−	0.998268i	$-0.481263\pi$
$83$	88.9729			0.117663			0.0588316	+	0.998268i	$0.481263\pi$
$84$	93.8602	+	198.761i	0.121917	+	0.258174i
$85$	−223.130			−0.284728
$86$			1680.99i			2.10774i
$87$	524.184	−	358.735i	0.645959	−	0.442074i
$88$	−280.618			−0.339932
$89$	−28.7275			−0.0342147			−0.0171073	−	0.999854i	$-0.505446\pi$
$89$	−28.7275			−0.0342147			−0.0171073	+	0.999854i	$0.505446\pi$
$90$	403.556	+	156.748i	0.472651	+	0.183586i
$91$	−168.437	+	1050.58i	−0.194033	+	1.21023i
$92$			197.443i			0.223749i
$93$	−120.327	+	82.3478i	−0.134165	+	0.0918179i
$94$			1279.14i			1.40355i
$95$		−	467.100i		−	0.504458i
$96$	−430.812	+	294.834i	−0.458017	+	0.313452i
$97$		−	1573.32i		−	1.64687i	−0.567413	−	0.823433i	$-0.692056\pi$
$97$		−	1573.32i		−	1.64687i	0.567413	−	0.823433i	$-0.307944\pi$
$98$	−343.868	+	1044.83i	−0.354448	+	1.07698i
$99$	−385.300	−	149.657i	−0.391153	−	0.151931i
$100$	−57.1025			−0.0571025
$101$	1079.31			1.06332			0.531661	−	0.846957i	$-0.321568\pi$
$101$	1079.31			1.06332			0.531661	+	0.846957i	$0.321568\pi$
$102$	613.673	−	419.978i	0.595712	−	0.407686i
$103$			1706.29i			1.63229i	0.577849	+	0.816144i	$0.303892\pi$
$103$			1706.29i			1.63229i	−0.577849	+	0.816144i	$0.696108\pi$
$104$	−1053.08			−0.992914
$105$	205.464	+	435.097i	0.190965	+	0.404392i
$106$	1325.03			1.21413
$107$			1345.87i			1.21599i	0.793942	+	0.607994i	$0.208025\pi$
$107$			1345.87i			1.21599i	−0.793942	+	0.607994i	$0.791975\pi$
$108$	−312.035	+	72.9543i	−0.278015	+	0.0650003i
$109$	1564.32			1.37463			0.687316	−	0.726358i	$-0.258789\pi$
$109$	1564.32			1.37463			0.687316	+	0.726358i	$0.258789\pi$
$110$	245.472			0.212771
$111$	417.385	+	609.884i	0.356905	+	0.521510i
$112$	−1409.10	−	225.916i	−1.18881	−	0.190599i
$113$		−	1339.52i		−	1.11515i	−0.830128	−	0.557573i	$-0.811733\pi$
$113$		−	1339.52i		−	1.11515i	0.830128	−	0.557573i	$-0.188267\pi$
$114$	879.182	+	1284.66i	0.722306	+	1.05544i
$115$			432.212i			0.350469i
$116$		−	279.212i		−	0.223484i
$117$	−1445.92	−	561.621i	−1.14253	−	0.443777i
$118$		−	2089.40i		−	1.63004i
$119$	816.064	+	130.837i	0.628642	+	0.100788i
$120$	−393.010	+	268.963i	−0.298973	+	0.204607i
$121$	1096.63			0.823917
$122$	1298.52			0.963625
$123$	800.351	+	1169.48i	0.586709	+	0.857301i
$124$			64.0931i			0.0464172i
$125$	−125.000			−0.0894427
$126$	−1384.03	−	809.916i	−0.978566	−	0.572643i
$127$	−1506.06			−1.05229			−0.526146	−	0.850394i	$-0.676364\pi$
$127$	−1506.06			−1.05229			−0.526146	+	0.850394i	$0.676364\pi$
$128$		−	1747.39i		−	1.20663i
$129$	−1538.28	−	2247.75i	−1.04991	−	1.53413i
$130$	921.185			0.621487
$131$	2328.40			1.55293			0.776464	−	0.630161i	$-0.217011\pi$
$131$	2328.40			1.55293			0.776464	+	0.630161i	$0.217011\pi$
$132$	−149.944	+	102.617i	−0.0988708	+	0.0676640i
$133$	−273.894	+	1708.35i	−0.178569	+	1.11378i
$134$			179.924i			0.115993i
$135$	−683.060	+	159.700i	−0.435470	+	0.101814i
$136$			818.005i			0.515760i
$137$		−	1274.12i		−	0.794567i	−0.917696	−	0.397284i	$-0.869953\pi$
$137$		−	1274.12i		−	0.794567i	0.917696	−	0.397284i	$-0.130047\pi$
$138$	−813.515	−	1188.71i	−0.501819	−	0.733259i
$139$		−	282.918i		−	0.172639i	−0.996268	−	0.0863194i	$-0.972489\pi$
$139$		−	282.918i		−	0.172639i	0.996268	−	0.0863194i	$-0.0275105\pi$
$140$	208.843	+	33.4833i	0.126075	+	0.0202132i
$141$	−1170.55	−	1710.42i	−0.699137	−	1.02158i
$142$	951.829			0.562505
$143$	−879.512			−0.514325
$144$	753.276	−	1939.35i	0.435924	−	1.12231i
$145$		−	611.207i		−	0.350055i
$146$	−91.6054			−0.0519268
$147$	−496.326	−	1711.78i	−0.278478	−	0.960443i
$148$	324.860			0.180428
$149$			1005.42i			0.552799i	0.961043	+	0.276399i	$0.0891412\pi$
$149$			1005.42i			0.552799i	−0.961043	+	0.276399i	$0.910859\pi$
$150$	343.787	−	235.276i	0.187134	−	0.128068i
$151$	1845.90			0.994818			0.497409	−	0.867516i	$-0.334285\pi$
$151$	1845.90			0.994818			0.497409	+	0.867516i	$0.334285\pi$
$152$	−1712.41			−0.913782
$153$	−436.252	+	1123.15i	−0.230516	+	0.593474i
$154$	−897.775	−	143.938i	−0.469771	−	0.0753170i
$155$			140.303i			0.0727058i
$156$	−562.697	+	385.092i	−0.288794	+	0.197641i
$157$			3217.35i			1.63550i	0.575577	+	0.817748i	$0.304778\pi$
$157$			3217.35i			1.63550i	−0.575577	+	0.817748i	$0.695222\pi$
$158$		−	3871.72i		−	1.94948i
$159$	−1771.77	+	1212.54i	−0.883715	+	0.604786i
$160$			502.334i			0.248206i
$161$	253.437	−	1580.75i	0.124060	−	0.773792i
$162$	1578.02	−	1724.89i	0.765317	−	0.836542i
$163$	−1131.54			−0.543734			−0.271867	−	0.962335i	$-0.587641\pi$
$163$	−1131.54			−0.543734			−0.271867	+	0.962335i	$0.587641\pi$
$164$	622.932			0.296602
$165$	−328.234	+	224.633i	−0.154867	+	0.105986i
$166$			285.326i			0.133407i
$167$	1558.76			0.722277			0.361139	−	0.932512i	$-0.382388\pi$
$167$	1558.76			0.722277			0.361139	+	0.932512i	$0.382388\pi$
$168$	1595.09	−	753.242i	0.732521	−	0.345916i
$169$	−1103.56			−0.502302
$170$		−	715.552i		−	0.322826i
$171$	−2351.21	−	913.250i	−1.05147	−	0.408409i
$172$	−1197.28			−0.530767
$173$	3704.95			1.62822			0.814111	−	0.580709i	$-0.197225\pi$
$173$	3704.95			1.62822			0.814111	+	0.580709i	$0.197225\pi$
$174$	1150.42	+	1681.00i	0.501225	+	0.732392i
$175$	457.168	+	73.2964i	0.197478	+	0.0316611i
$176$		−	1179.65i		−	0.505224i
$177$	1912.03	+	2793.86i	0.811960	+	1.18644i
$178$		−	92.1256i		−	0.0387927i
$179$			2658.16i			1.10995i	0.831868	+	0.554973i	$0.187271\pi$
$179$			2658.16i			1.10995i	−0.831868	+	0.554973i	$0.812729\pi$
$180$	−111.644	+	287.433i	−0.0462302	+	0.119022i
$181$		−	2253.49i		−	0.925417i	−0.886510	−	0.462709i	$-0.846878\pi$
$181$		−	2253.49i		−	0.925417i	0.886510	−	0.462709i	$-0.153122\pi$
$182$	−3369.09	−	540.157i	−1.37216	−	0.219995i
$183$	−1736.32	+	1188.28i	−0.701380	+	0.480002i
$184$	1584.51			0.634845
$185$	711.134			0.282614
$186$	−264.080	−	385.874i	−0.104104	−	0.152116i
$187$			683.182i			0.267162i
$188$	−911.068			−0.353439
$189$	2591.83	−	183.553i	0.997502	−	0.0706428i
$190$	1497.94			0.571957
$191$			4630.03i			1.75402i	0.480474	+	0.877009i	$0.340465\pi$
$191$			4630.03i			1.75402i	−0.480474	+	0.877009i	$0.659535\pi$
$192$	863.549	+	1261.82i	0.324590	+	0.474292i
$193$	654.637			0.244154			0.122077	−	0.992521i	$-0.461044\pi$
$193$	654.637			0.244154			0.122077	+	0.992521i	$0.461044\pi$
$194$	5045.44			1.86723
$195$	−1231.77	+	842.983i	−0.452353	+	0.309576i
$196$	−744.179	−	244.920i	−0.271202	−	0.0892565i
$197$		−	1141.81i		−	0.412947i	−0.978452	−	0.206474i	$-0.933801\pi$
$197$		−	1141.81i		−	0.412947i	0.978452	−	0.206474i	$-0.0661988\pi$
$198$	479.933	−	1235.61i	0.172259	−	0.443491i
$199$		−	5121.28i		−	1.82431i	−0.409846	−	0.912155i	$-0.634418\pi$
$199$		−	5121.28i		−	1.82431i	0.409846	−	0.912155i	$-0.365582\pi$
$200$			458.256i			0.162018i
$201$	−164.650	−	240.586i	−0.0577785	−	0.0844261i
$202$			3461.22i			1.20560i
$203$	−358.394	+	2235.40i	−0.123913	+	0.772877i
$204$	299.129	+	437.088i	0.102663	+	0.150011i
$205$	1363.63			0.464584
$206$	−5471.87			−1.85069
$207$	2175.59	+	845.038i	0.730504	+	0.283740i
$208$		−	4426.89i		−	1.47572i
$209$	−1430.17			−0.473336
$210$	−1395.31	+	658.900i	−0.458501	+	0.216516i
$211$	−2033.51			−0.663473			−0.331737	−	0.943372i	$-0.607635\pi$
$211$	−2033.51			−0.663473			−0.331737	+	0.943372i	$0.607635\pi$
$212$			943.751i			0.305741i
$213$	−1272.75	+	871.026i	−0.409423	+	0.280196i
$214$	−4316.06			−1.37869
$215$	−2620.91			−0.831369
$216$	585.469	+	2504.13i	0.184426	+	0.788816i
$217$	82.2696	−	513.136i	0.0257365	−	0.160525i
$218$			5016.60i			1.55856i
$219$	122.491	−	83.8288i	0.0377953	−	0.0258659i
$220$			174.837i			0.0535796i
$221$			2563.79i			0.780357i
$222$	−1955.83	+	1338.51i	−0.591291	+	0.404660i
$223$		−	2820.01i		−	0.846823i	−0.905937	−	0.423412i	$-0.860832\pi$
$223$		−	2820.01i		−	0.846823i	0.905937	−	0.423412i	$-0.139168\pi$
$224$	294.554	−	1837.21i	0.0878604	−	0.548007i
$225$	−244.393	+	629.203i	−0.0724129	+	0.186431i
$226$	4295.68			1.26436
$227$	6086.04			1.77949			0.889745	−	0.456457i	$-0.150882\pi$
$227$	6086.04			1.77949			0.889745	+	0.456457i	$0.150882\pi$
$228$	−915.000	+	626.197i	−0.265778	+	0.181890i
$229$			1166.01i			0.336473i	0.985747	+	0.168236i	$0.0538072\pi$
$229$			1166.01i			0.336473i	−0.985747	+	0.168236i	$0.946193\pi$
$230$	−1386.05			−0.397364
$231$	1332.18	−	629.093i	0.379443	−	0.179183i
$232$	−2240.71			−0.634095
$233$		−	1232.20i		−	0.346455i	−0.984882	−	0.173227i	$-0.944580\pi$
$233$		−	1232.20i		−	0.346455i	0.984882	−	0.173227i	$-0.0554195\pi$
$234$	1801.05	−	4636.90i	0.503156	−	1.29540i
$235$	−1994.37			−0.553610
$236$	1488.18			0.410474
$237$	3543.04	+	5177.10i	0.971078	+	1.41894i
$238$	−419.579	+	2617.02i	−0.114274	+	0.712757i
$239$		−	3757.25i		−	1.01689i	−0.861095	−	0.508444i	$-0.830221\pi$
$239$		−	3757.25i		−	1.01689i	0.861095	−	0.508444i	$-0.169779\pi$
$240$	−1130.65	−	1652.12i	−0.304098	−	0.444348i
$241$		−	3743.42i		−	1.00056i	−0.865863	−	0.500280i	$-0.833230\pi$
$241$		−	3743.42i		−	1.00056i	0.865863	−	0.500280i	$-0.166770\pi$
$242$			3516.77i			0.934160i
$243$	−531.610	+	3750.51i	−0.140341	+	0.990103i
$244$			924.868i			0.242658i
$245$	−1629.04	−	536.141i	−0.424799	−	0.139807i
$246$	−3750.37	+	2566.63i	−0.972012	+	0.665214i
$247$	−5367.03			−1.38257
$248$	514.357			0.131700
$249$	−261.104	−	381.525i	−0.0664529	−	0.0971012i
$250$		−	400.860i		−	0.101411i
$251$	−341.806			−0.0859546			−0.0429773	−	0.999076i	$-0.513684\pi$
$251$	−341.806			−0.0859546			−0.0429773	+	0.999076i	$0.513684\pi$
$252$	576.862	−	985.775i	0.144202	−	0.246421i
$253$	1323.35			0.328847
$254$		−	4829.76i		−	1.19309i
$255$	654.807	+	956.806i	0.160806	+	0.234971i
$256$	3249.60			0.793360
$257$	−4540.24			−1.10199			−0.550996	−	0.834508i	$-0.685752\pi$
$257$	−4540.24			−1.10199			−0.550996	+	0.834508i	$0.685752\pi$
$258$	7208.26	−	4933.10i	1.73940	−	1.19039i
$259$	−2600.86	−	416.989i	−0.623976	−	0.100040i
$260$			656.113i			0.156502i
$261$	−3076.59	−	1195.00i	−0.729640	−	0.283405i
$262$			7466.92i			1.76072i
$263$			2522.63i			0.591452i	0.955273	+	0.295726i	$0.0955616\pi$
$263$			2522.63i			0.591452i	−0.955273	+	0.295726i	$0.904438\pi$
$264$	823.515	+	1203.32i	0.191984	+	0.280528i
$265$			2065.91i			0.478898i
$266$	−5478.47	−	878.347i	−1.26281	−	0.202462i
$267$	84.3048	+	123.186i	0.0193235	+	0.0282355i
$268$	−128.150			−0.0292091
$269$	−2316.59			−0.525075			−0.262538	−	0.964922i	$-0.584559\pi$
$269$	−2316.59			−0.525075			−0.262538	+	0.964922i	$0.584559\pi$
$270$	−512.141	−	2190.49i	−0.115437	−	0.493738i
$271$		−	2752.52i		−	0.616987i	−0.951226	−	0.308494i	$-0.900175\pi$
$271$		−	2752.52i		−	0.616987i	0.951226	−	0.308494i	$-0.0998248\pi$
$272$	−3438.69			−0.766548
$273$	4999.31	−	2360.81i	1.10832	−	0.523379i
$274$	4085.96			0.900884
$275$			382.726i			0.0839246i
$276$	846.657	−	579.425i	0.184648	−	0.126367i
$277$	−1107.41			−0.240209			−0.120104	−	0.992761i	$-0.538323\pi$
$277$	−1107.41			−0.240209			−0.120104	+	0.992761i	$0.538323\pi$
$278$	907.285			0.195739
$279$	706.232	+	274.313i	0.151545	+	0.0588626i
$280$	268.708	−	1676.00i	0.0573513	−	0.357715i
$281$		−	5582.76i		−	1.18519i	−0.805499	−	0.592597i	$-0.798103\pi$
$281$		−	5582.76i		−	1.18519i	0.805499	−	0.592597i	$-0.201897\pi$
$282$	5485.10	−	3753.83i	1.15827	−	0.792685i
$283$			3142.41i			0.660059i	0.943971	+	0.330029i	$0.107059\pi$
$283$			3142.41i			0.660059i	−0.943971	+	0.330029i	$0.892941\pi$
$284$			677.940i			0.141649i
$285$	−2002.98	+	1370.77i	−0.416302	+	0.284904i
$286$		−	2820.49i		−	0.583144i
$287$	−4987.25	−	799.592i	−1.02574	−	0.164454i
$288$	2528.56	+	982.137i	0.517350	+	0.200948i
$289$	−2921.52			−0.594651
$290$	1960.07			0.396894
$291$	−6746.55	+	4617.12i	−1.35907	+	0.930105i
$292$		−	65.2459i		−	0.0130761i
$293$	−2093.25			−0.417368			−0.208684	−	0.977983i	$-0.566918\pi$
$293$	−2093.25			−0.417368			−0.208684	+	0.977983i	$0.566918\pi$
$294$	5489.47	−	1591.66i	1.08895	−	0.315740i
$295$	3257.68			0.642948
$296$		−	2607.05i		−	0.511931i
$297$	488.972	+	2091.40i	0.0955322	+	0.408604i
$298$	−3224.26			−0.626766
$299$	4966.16			0.960537
$300$	167.575	+	244.862i	0.0322499	+	0.0471236i
$301$	9585.56	+	1536.82i	1.83556	+	0.294289i
$302$			5919.60i			1.12793i
$303$	−3167.39	−	4628.20i	−0.600535	−	0.877502i
$304$		−	7198.55i		−	1.35811i
$305$			2024.58i			0.380089i
$306$	−3601.82	−	1399.01i	−0.672884	−	0.261360i
$307$		−	1154.31i		−	0.214593i	−0.994227	−	0.107297i	$-0.965781\pi$
$307$		−	1154.31i		−	0.214593i	0.994227	−	0.107297i	$-0.0342195\pi$
$308$	102.519	−	639.439i	0.0189662	−	0.118297i
$309$	7316.75	−	5007.35i	1.34704	−	0.921871i
$310$	−449.935			−0.0824341
$311$	4682.28			0.853723			0.426861	−	0.904317i	$-0.359619\pi$
$311$	4682.28			0.853723			0.426861	+	0.904317i	$0.359619\pi$
$312$	3090.42	+	4515.72i	0.560770	+	0.819399i
$313$			1740.67i			0.314340i	0.987572	+	0.157170i	$0.0502371\pi$
$313$			1740.67i			0.314340i	−0.987572	+	0.157170i	$0.949763\pi$
$314$	−10317.7			−1.85433
$315$	1262.78	−	2157.91i	0.225871	−	0.385982i
$316$	2757.63			0.490914
$317$		−	9835.66i		−	1.74267i	−0.490691	−	0.871334i	$-0.663255\pi$
$317$		−	9835.66i		−	1.74267i	0.490691	−	0.871334i	$-0.336745\pi$
$318$	−3888.49	−	5681.87i	−0.685709	−	1.00196i
$319$	−1871.40			−0.328459
$320$	1471.30			0.257026
$321$	5771.26	−	3949.66i	1.00349	−	0.686756i
$322$	5069.28	+	812.743i	0.877328	+	0.140660i
$323$			4168.97i			0.718166i
$324$	1228.55	+	1123.95i	0.210656	+	0.192721i
$325$			1436.26i			0.245137i
$326$		−	3628.70i		−	0.616489i
$327$	−4590.73	−	6707.99i	−0.776355	−	1.13441i
$328$		−	4999.11i		−	0.841555i
$329$	7294.10	+	1169.44i	1.22230	+	0.195968i
$330$	−720.372	−	1052.61i	−0.120167	−	0.175589i
$331$	704.817			0.117040			0.0585200	−	0.998286i	$-0.481362\pi$
$331$	704.817			0.117040			0.0585200	+	0.998286i	$0.481362\pi$
$332$	−203.223			−0.0335943
$333$	1390.37	−	3579.58i	0.228805	−	0.589069i
$334$			4998.75i			0.818921i
$335$	−280.527			−0.0457518
$336$	3166.44	+	6705.34i	0.514118	+	1.08871i
$337$	2740.29			0.442948			0.221474	−	0.975166i	$-0.428913\pi$
$337$	2740.29			0.442948			0.221474	+	0.975166i	$0.428913\pi$
$338$		−	3538.98i		−	0.569513i
$339$	−5744.01	+	3931.01i	−0.920270	+	0.629803i
$340$	509.651			0.0812933
$341$	429.581			0.0682202
$342$	2928.69	−	7540.05i	0.463056	−	1.19216i
$343$	5643.59	+	2916.07i	0.888412	+	0.459047i
$344$			9608.36i			1.50595i
$345$	1853.37	−	1268.39i	0.289224	−	0.197935i
$346$			11881.4i			1.84609i
$347$		−	4295.37i		−	0.664517i	−0.943188	−	0.332258i	$-0.892189\pi$
$347$		−	4295.37i		−	0.664517i	0.943188	−	0.332258i	$-0.107811\pi$
$348$	−1197.29	+	819.386i	−0.184429	+	0.126218i
$349$			6410.35i			0.983205i	0.870820	+	0.491602i	$0.163589\pi$
$349$			6410.35i			0.983205i	−0.870820	+	0.491602i	$0.836411\pi$
$350$	−235.053	+	1466.08i	−0.0358975	+	0.223901i
$351$	1834.97	+	7848.42i	0.279042	+	1.19350i
$352$	1538.05			0.232893
$353$	−9590.74			−1.44607			−0.723036	−	0.690810i	$-0.757254\pi$
$353$	−9590.74			−1.44607			−0.723036	+	0.690810i	$0.757254\pi$
$354$	−8959.58	+	6131.65i	−1.34519	+	0.920603i
$355$			1484.04i			0.221872i
$356$	65.6164			0.00976871
$357$	−1833.81	−	3883.33i	−0.271864	−	0.575707i
$358$	−8524.42			−1.25846
$359$		−	2245.22i		−	0.330078i	−0.986287	−	0.165039i	$-0.947225\pi$
$359$		−	2245.22i		−	0.330078i	0.986287	−	0.165039i	$-0.0527750\pi$
$360$	2306.69	+	895.957i	0.337703	+	0.131170i
$361$	−1868.31			−0.272389
$362$	7226.68			1.04924
$363$	−3218.23	−	4702.48i	−0.465325	−	0.679934i
$364$	384.726	−	2399.63i	0.0553987	−	0.345535i
$365$		−	142.826i		−	0.0204818i
$366$	−3810.68	−	5568.18i	−0.544229	−	0.795228i
$367$		−	428.510i		−	0.0609483i	−0.999536	−	0.0304741i	$-0.990298\pi$
$367$		−	428.510i		−	0.0609483i	0.999536	−	0.0304741i	$-0.00970172\pi$
$368$			6660.88i			0.943539i
$369$	2666.09	−	6863.99i	0.376128	−	0.968360i
$370$			2280.52i			0.320429i
$371$	1211.39	−	7555.76i	0.169521	−	1.05735i
$372$	274.838	−	188.091i	0.0383057	−	0.0262152i
$373$	−1679.09			−0.233082			−0.116541	−	0.993186i	$-0.537181\pi$
$373$	−1679.09			−0.233082			−0.116541	+	0.993186i	$0.537181\pi$
$374$	−2190.88			−0.302909
$375$	366.830	+	536.013i	0.0505148	+	0.0738123i
$376$			7311.45i			1.00282i
$377$	−7022.83			−0.959401
$378$	588.632	+	8311.69i	0.0800951	+	1.13097i
$379$	−5793.77			−0.785239			−0.392620	−	0.919701i	$-0.628431\pi$
$379$	−5793.77			−0.785239			−0.392620	+	0.919701i	$0.628431\pi$
$380$			1066.90i			0.144029i
$381$	4419.75	+	6458.15i	0.594306	+	0.868401i
$382$	−14848.0			−1.98871
$383$	9073.39			1.21052			0.605259	−	0.796028i	$-0.293069\pi$
$383$	9073.39			1.21052			0.605259	+	0.796028i	$0.293069\pi$
$384$	−7493.01	+	5127.97i	−0.995771	+	0.681473i
$385$	224.420	−	1399.76i	0.0297078	−	0.185295i
$386$			2099.34i			0.276823i
$387$	−5124.26	+	13192.7i	−0.673077	+	1.73287i
$388$			3593.61i			0.470201i
$389$			6411.91i			0.835724i	0.908510	+	0.417862i	$0.137220\pi$
$389$			6411.91i			0.835724i	−0.908510	+	0.417862i	$0.862780\pi$
$390$	−2703.35	−	3950.14i	−0.350999	−	0.512880i
$391$		−	3857.58i		−	0.498942i
$392$	−1965.52	+	5972.14i	−0.253249	+	0.769486i
$393$	−6833.04	−	9984.45i	−0.877051	−	1.28155i
$394$	3661.65			0.468201
$395$	6036.58			0.768945
$396$	880.064	+	341.832i	0.111679	+	0.0433781i
$397$		−	12017.0i		−	1.51919i	−0.650397	−	0.759595i	$-0.725397\pi$
$397$		−	12017.0i		−	1.51919i	0.650397	−	0.759595i	$-0.274603\pi$
$398$	16423.3			2.06841
$399$	8129.36	−	3838.90i	1.01999	−	0.481668i
$400$	−1926.39			−0.240799
$401$		−	1300.39i		−	0.161941i	−0.996716	−	0.0809707i	$-0.974198\pi$
$401$		−	1300.39i		−	0.161941i	0.996716	−	0.0809707i	$-0.0258020\pi$
$402$	771.532	−	528.012i	0.0957227	−	0.0655095i
$403$	1612.09			0.199266
$404$	−2465.25			−0.303591
$405$	2689.35	+	2460.37i	0.329963	+	0.301869i
$406$	−7168.65	−	1149.33i	−0.876291	−	0.140493i
$407$		−	2177.36i		−	0.265178i
$408$	3507.69	−	2400.55i	0.425629	−	0.291287i
$409$		−	12304.0i		−	1.48752i	−0.668447	−	0.743760i	$-0.733040\pi$
$409$		−	12304.0i		−	1.48752i	0.668447	−	0.743760i	$-0.266960\pi$
$410$			4372.99i			0.526748i
$411$	−5463.58	+	3739.10i	−0.655714	+	0.448750i
$412$		−	3897.33i		−	0.466038i
$413$	−11914.5	−	1910.21i	−1.41955	−	0.227592i
$414$	−2709.94	+	6976.88i	−0.321706	+	0.828248i
$415$	−444.864			−0.0526206
$416$	5771.87			0.680262
$417$	−1213.18	+	830.263i	−0.142470	+	0.0975016i
$418$		−	4586.40i		−	0.536670i
$419$	−11004.6			−1.28308			−0.641541	−	0.767088i	$-0.721705\pi$
$419$	−11004.6			−1.28308			−0.641541	+	0.767088i	$0.721705\pi$
$420$	−469.301	−	993.805i	−0.0545228	−	0.115459i
$421$	2739.12			0.317094			0.158547	−	0.987351i	$-0.449319\pi$
$421$	2739.12			0.317094			0.158547	+	0.987351i	$0.449319\pi$
$422$		−	6521.24i		−	0.752249i
$423$	−3899.29	+	10038.9i	−0.448203	+	1.15392i
$424$	7573.73			0.867484
$425$	1115.65			0.127334
$426$	−2793.28	−	4081.55i	−0.317687	−	0.464206i
$427$	1187.15	−	7404.58i	0.134544	−	0.839187i
$428$		−	3074.11i		−	0.347179i
$429$	2581.06	+	3771.44i	0.290477	+	0.424445i
$430$		−	8404.94i		−	0.942610i
$431$			3943.99i			0.440778i	0.975412	+	0.220389i	$0.0707327\pi$
$431$			3943.99i			0.440778i	−0.975412	+	0.220389i	$0.929267\pi$
$432$	−10526.7	+	2461.17i	−1.17238	+	0.274104i
$433$			1159.29i			0.128665i	0.997929	+	0.0643324i	$0.0204918\pi$
$433$			1159.29i			0.128665i	−0.997929	+	0.0643324i	$0.979508\pi$
$434$	1645.57	+	263.829i	0.182004	+	0.0291802i
$435$	−2620.92	+	1793.67i	−0.288882	+	0.197701i
$436$	−3573.07			−0.392475
$437$	8075.46			0.883985
$438$	268.829	+	392.814i	0.0293268	+	0.0428524i
$439$			15277.3i			1.66093i	0.557072	+	0.830464i	$0.311925\pi$
$439$			15277.3i			1.66093i	−0.557072	+	0.830464i	$0.688075\pi$
$440$	1403.09			0.152022
$441$	−5883.75	+	7151.76i	−0.635325	+	0.772244i
$442$	−8221.76			−0.884772
$443$			17219.2i			1.84674i	0.383908	+	0.923371i	$0.374578\pi$
$443$			17219.2i			1.84674i	−0.383908	+	0.923371i	$0.625422\pi$
$444$	−953.349	−	1393.04i	−0.101901	−	0.148898i
$445$	143.637			0.0153013
$446$	9043.43			0.960132
$447$	4311.34	−	2950.54i	0.456195	−	0.312205i
$448$	−5381.06	−	862.729i	−0.567480	−	0.0909824i
$449$			922.113i			0.0969202i	0.998825	+	0.0484601i	$0.0154314\pi$
$449$			922.113i			0.0969202i	−0.998825	+	0.0484601i	$0.984569\pi$
$450$	−2017.78	−	783.741i	−0.211376	−	0.0821020i
$451$		−	4175.16i		−	0.435922i
$452$			3059.60i			0.318388i
$453$	−5417.07	−	7915.44i	−0.561846	−	0.820971i
$454$			19517.2i			2.01759i
$455$	842.183	−	5252.91i	0.0867740	−	0.541231i
$456$	5025.32	+	7343.00i	0.516079	+	0.754096i
$457$	1859.90			0.190378			0.0951888	−	0.995459i	$-0.469655\pi$
$457$	1859.90			0.190378			0.0951888	+	0.995459i	$0.469655\pi$
$458$	−3739.27			−0.381495
$459$	6096.45	−	1425.36i	0.619952	−	0.144946i
$460$		−	987.216i		−	0.100063i
$461$	4560.89			0.460785			0.230392	−	0.973098i	$-0.425999\pi$
$461$	4560.89			0.460785			0.230392	+	0.973098i	$0.425999\pi$
$462$	2017.43	+	4272.16i	0.203159	+	0.430214i
$463$	12103.4			1.21488			0.607442	−	0.794364i	$-0.292196\pi$
$463$	12103.4			1.21488			0.607442	+	0.794364i	$0.292196\pi$
$464$		−	9419.40i		−	0.942424i
$465$	601.634	−	411.739i	0.0600002	−	0.0410622i
$466$	3951.51			0.392812
$467$	9975.42			0.988452			0.494226	−	0.869333i	$-0.335451\pi$
$467$	9975.42			0.988452			0.494226	+	0.869333i	$0.335451\pi$
$468$	3302.63	+	1282.80i	0.326205	+	0.126704i
$469$	1025.98	+	164.493i	0.101014	+	0.0161953i
$470$		−	6395.71i		−	0.627686i
$471$	13796.4	−	9441.79i	1.34969	−	0.923683i
$472$		−	11942.8i		−	1.16465i
$473$			8024.72i			0.780078i
$474$	−16602.4	+	11362.1i	−1.60880	+	1.10101i
$475$			2335.50i			0.225600i
$476$	−1863.97	−	298.845i	−0.179485	−	0.0287763i
$477$	10399.0	+	4039.17i	0.998196	+	0.387716i
$478$	12049.1			1.15295
$479$	12884.7			1.22906			0.614529	−	0.788894i	$-0.289346\pi$
$479$	12884.7			1.22906			0.614529	+	0.788894i	$0.289346\pi$
$480$	2154.06	−	1474.17i	0.204831	−	0.140180i
$481$		−	8171.00i		−	0.774565i
$482$	12004.7			1.13444
$483$	−7522.17	+	3552.17i	−0.708635	+	0.334636i
$484$	−2504.82			−0.235238
$485$			7866.58i			0.736501i
$486$	−12027.4	−	1704.81i	−1.12258	−	0.159119i
$487$	7849.39			0.730369			0.365185	−	0.930935i	$-0.381006\pi$
$487$	7849.39			0.730369			0.365185	+	0.930935i	$0.381006\pi$
$488$	7422.19			0.688498
$489$	3320.65	+	4852.15i	0.307086	+	0.448715i
$490$	1719.34	−	5224.15i	0.158514	−	0.481639i
$491$		−	5583.66i		−	0.513212i	−0.966516	−	0.256606i	$-0.917396\pi$
$491$		−	5583.66i		−	0.513212i	0.966516	−	0.256606i	$-0.0826043\pi$
$492$	−1828.08	−	2671.20i	−0.167513	−	0.244770i
$493$			5455.15i			0.498352i
$494$		−	17211.4i		−	1.56757i
$495$	1926.50	+	748.286i	0.174929	+	0.0679454i
$496$			2162.23i			0.195740i
$497$	870.199	−	5427.65i	0.0785388	−	0.489866i
$498$	1223.51	−	837.329i	0.110094	−	0.0753446i
$499$	−4776.41			−0.428500			−0.214250	−	0.976779i	$-0.568731\pi$
$499$	−4776.41			−0.428500			−0.214250	+	0.976779i	$0.568731\pi$
$500$	285.512			0.0255370
$501$	−4574.40	−	6684.12i	−0.407922	−	0.596057i
$502$		−	1096.13i		−	0.0974557i
$503$	−8948.14			−0.793197			−0.396598	−	0.917992i	$-0.629809\pi$
$503$	−8948.14			−0.793197			−0.396598	+	0.917992i	$0.629809\pi$
$504$	−7910.99	−	4629.40i	−0.699173	−	0.409147i
$505$	−5396.55			−0.475532
$506$			4243.83i			0.372849i
$507$	3238.55	+	4732.18i	0.283687	+	0.414523i
$508$	3439.99			0.300443
$509$	−895.199			−0.0779548			−0.0389774	−	0.999240i	$-0.512410\pi$
$509$	−895.199			−0.0779548			−0.0389774	+	0.999240i	$0.512410\pi$
$510$	−3068.36	+	2099.89i	−0.266411	+	0.182323i
$511$	−83.7492	+	522.365i	−0.00725019	+	0.0452212i
$512$		−	3558.05i		−	0.307119i
$513$	2983.85	+	12762.3i	0.256803	+	1.09838i
$514$		−	14560.0i		−	1.24944i
$515$		−	8531.44i		−	0.729981i
$516$	3513.60	+	5134.07i	0.299762	+	0.438014i
$517$			6106.39i			0.519456i
$518$	1337.23	−	8340.66i	0.113426	−	0.707467i
$519$	−10872.7	−	15887.2i	−0.919575	−	1.34368i
$520$	5265.40			0.444044
$521$	−20660.5			−1.73734			−0.868668	−	0.495395i	$-0.835023\pi$
$521$	−20660.5			−1.73734			−0.868668	+	0.495395i	$0.835023\pi$
$522$	3832.23	−	9866.26i	0.321326	−	0.827269i
$523$			11928.6i			0.997322i	0.866797	+	0.498661i	$0.166175\pi$
$523$			11928.6i			0.997322i	−0.866797	+	0.498661i	$0.833825\pi$
$524$	−5318.31			−0.443380
$525$	−1027.32	−	2175.48i	−0.0854019	−	0.180849i
$526$	−8089.78			−0.670591
$527$		−	1252.23i		−	0.103507i
$528$	−5058.46	+	3461.85i	−0.416934	+	0.285337i
$529$	4694.71			0.385856
$530$	−6625.15			−0.542977
$531$	6369.25	−	16398.0i	0.520531	−	1.34013i
$532$	625.602	−	3902.04i	0.0509836	−	0.317998i
$533$		−	15668.2i		−	1.27329i
$534$	−395.044	+	270.356i	−0.0320136	+	0.0219091i
$535$		−	6729.37i		−	0.543806i
$536$			1028.43i			0.0828754i
$537$	11398.5	−	7800.76i	0.915980	−	0.626867i
$538$		−	7429.04i		−	0.595332i
$539$	−1641.56	+	4987.82i	−0.131182	+	0.398591i
$540$	1560.18	−	364.772i	0.124332	−	0.0290690i
$541$	−7501.05			−0.596110			−0.298055	−	0.954549i	$-0.596338\pi$
$541$	−7501.05			−0.596110			−0.298055	+	0.954549i	$0.596338\pi$
$542$	8827.00			0.699543
$543$	−9663.20	+	6613.19i	−0.763698	+	0.522650i
$544$		−	4483.43i		−	0.353356i
$545$	−7821.61			−0.614754
$546$	7570.83	+	16032.2i	0.593410	+	1.25662i
$547$	2636.92			0.206118			0.103059	−	0.994675i	$-0.467137\pi$
$547$	2636.92			0.206118			0.103059	+	0.994675i	$0.467137\pi$
$548$			2910.22i			0.226859i
$549$	10191.0	+	3958.35i	0.792240	+	0.307720i
$550$	−1227.36			−0.0951541
$551$	−11419.8			−0.882940
$552$	−4649.97	−	6794.55i	−0.358543	−	0.523904i
$553$	−22077.9	−	3539.68i	−1.69773	−	0.272193i
$554$		−	3551.34i		−	0.272350i
$555$	−2086.93	−	3049.42i	−0.159613	−	0.233226i
$556$			646.213i			0.0492905i
$557$		−	5826.60i		−	0.443233i	−0.975134	−	0.221617i	$-0.928867\pi$
$557$		−	5826.60i		−	0.443233i	0.975134	−	0.221617i	$-0.0711334\pi$
$558$	−879.689	+	2264.80i	−0.0667387	+	0.171822i
$559$			30114.5i			2.27854i
$560$	7045.48	+	1129.58i	0.531653	+	0.0852384i
$561$	2929.56	−	2004.90i	0.220474	−	0.150885i
$562$	17903.3			1.34378
$563$	−332.705			−0.0249056			−0.0124528	−	0.999922i	$-0.503964\pi$
$563$	−332.705			−0.0249056			−0.0124528	+	0.999922i	$0.503964\pi$
$564$	2673.66	+	3906.76i	0.199612	+	0.291674i
$565$			6697.60i			0.498708i
$566$	−10077.3			−0.748377
$567$	−8393.19	−	10575.4i	−0.621659	−	0.783288i
$568$	5440.56			0.401903
$569$			18283.4i			1.34707i	0.739156	+	0.673534i	$0.235224\pi$
$569$			18283.4i			1.34707i	−0.739156	+	0.673534i	$0.764776\pi$
$570$	−4395.91	−	6423.31i	−0.323025	−	0.472005i
$571$	−11317.3			−0.829449			−0.414725	−	0.909947i	$-0.636122\pi$
$571$	−11317.3			−0.829449			−0.414725	+	0.909947i	$0.636122\pi$
$572$	2008.89			0.146846
$573$	19854.1	−	13587.5i	1.44750	−	0.990621i
$574$	2564.20	−	15993.5i	0.186459	−	1.16299i
$575$		−	2161.06i		−	0.156735i
$576$	2876.61	−	7405.98i	0.208088	−	0.535734i
$577$			765.268i			0.0552141i	0.999619	+	0.0276070i	$0.00878871\pi$
$577$			765.268i			0.0552141i	−0.999619	+	0.0276070i	$0.991211\pi$
$578$		−	9368.97i		−	0.674218i
$579$	−1921.13	−	2807.15i	−0.137892	−	0.201488i
$580$			1396.06i			0.0999451i
$581$	1627.02	+	260.856i	0.116179	+	0.0186267i
$582$	−14806.6	−	21635.4i	−1.05456	−	1.54092i
$583$	6325.44			0.449353
$584$	−523.607			−0.0371011
$585$	7229.61	+	2808.10i	0.510953	+	0.198463i
$586$		−	6712.80i		−	0.473214i
$587$	11666.1			0.820290			0.410145	−	0.912020i	$-0.365478\pi$
$587$	11666.1			0.820290			0.410145	+	0.912020i	$0.365478\pi$
$588$	1133.66	+	3909.87i	0.0795089	+	0.274218i
$589$	2621.42			0.183385
$590$			10447.0i			0.728977i
$591$	−4896.20	+	3350.81i	−0.340783	+	0.233221i
$592$	10959.4			0.760858
$593$	−5438.09			−0.376586			−0.188293	−	0.982113i	$-0.560295\pi$
$593$	−5438.09			−0.376586			−0.188293	+	0.982113i	$0.560295\pi$
$594$	−6706.87	+	1568.08i	−0.463277	+	0.108315i
$595$	−4080.32	−	654.186i	−0.281137	−	0.0450739i
$596$		−	2296.47i		−	0.157831i
$597$	−21960.6	+	15029.1i	−1.50551	+	1.03032i
$598$			15925.9i			1.08906i
$599$		−	12956.1i		−	0.883761i	−0.897074	−	0.441881i	$-0.854311\pi$
$599$		−	12956.1i		−	0.883761i	0.897074	−	0.441881i	$-0.145689\pi$
$600$	1965.05	−	1344.82i	0.133705	−	0.0915032i
$601$			15357.7i			1.04235i	0.853450	+	0.521174i	$0.174506\pi$
$601$			15357.7i			1.04235i	−0.853450	+	0.521174i	$0.825494\pi$
$602$	−4928.42	+	30739.8i	−0.333667	+	2.08116i
$603$	−548.472	+	1412.07i	−0.0370407	+	0.0953631i
$604$	−4216.23			−0.284033
$605$	−5483.16			−0.368467
$606$	14842.1	−	10157.5i	0.994916	−	0.680889i
$607$			11256.0i			0.752662i	0.926485	+	0.376331i	$0.122815\pi$
$607$			11256.0i			0.752662i	−0.926485	+	0.376331i	$0.877185\pi$
$608$	9385.62			0.626048
$609$	10637.4	−	5023.25i	0.707797	−	0.334241i
$610$	−6492.59			−0.430946
$611$			22915.5i			1.51729i
$612$	996.443	−	2565.39i	0.0658151	−	0.169444i
$613$	−5382.76			−0.354662			−0.177331	−	0.984151i	$-0.556746\pi$
$613$	−5382.76			−0.354662			−0.177331	+	0.984151i	$0.556746\pi$
$614$	3701.75			0.243307
$615$	−4001.76	−	5847.38i	−0.262384	−	0.383397i
$616$	−5131.59	−	822.733i	−0.335646	−	0.0538131i
$617$			30519.0i			1.99133i	0.0930124	+	0.995665i	$0.470350\pi$
$617$			30519.0i			1.99133i	−0.0930124	+	0.995665i	$0.529650\pi$
$618$	16058.0	+	23464.0i	1.04522	+	1.52728i
$619$			10618.9i			0.689517i	0.938691	+	0.344759i	$0.112039\pi$
$619$			10618.9i			0.689517i	−0.938691	+	0.344759i	$0.887961\pi$
$620$		−	320.466i		−	0.0207584i
$621$	−2760.98	−	11809.1i	−0.178413	−	0.763095i
$622$			15015.5i			0.967954i
$623$	−525.331	−	84.2248i	−0.0337832	−	0.00541637i
$624$	−18983.0	+	12991.3i	−1.21783	+	0.833445i
$625$	625.000			0.0400000
$626$	−5582.13			−0.356401
$627$	4197.05	+	6132.74i	0.267327	+	0.390619i
$628$		−	7348.76i		−	0.466954i
$629$	−6347.02			−0.402340
$630$	6920.16	+	4049.58i	0.437628	+	0.256094i
$631$	−1407.82			−0.0888187			−0.0444094	−	0.999013i	$-0.514141\pi$
$631$	−1407.82			−0.0888187			−0.0444094	+	0.999013i	$0.514141\pi$
$632$		−	22130.4i		−	1.39288i
$633$	5967.64	+	8719.92i	0.374711	+	0.547529i
$634$	31541.8			1.97584
$635$	7530.30			0.470600
$636$	4046.90	−	2769.57i	0.252312	−	0.172674i
$637$	−6160.31	+	18717.9i	−0.383172	+	1.16425i
$638$		−	6001.36i		−	0.372408i
$639$	7470.11	+	2901.52i	0.462462	+	0.179628i
$640$			8736.96i			0.539623i
$641$			6584.65i			0.405738i	0.979206	+	0.202869i	$0.0650266\pi$
$641$			6584.65i			0.405738i	−0.979206	+	0.202869i	$0.934973\pi$
$642$	12666.1	+	18507.7i	0.778647	+	1.13776i
$643$		−	26506.6i		−	1.62569i	−0.582479	−	0.812846i	$-0.697917\pi$
$643$		−	26506.6i		−	1.62569i	0.582479	−	0.812846i	$-0.302083\pi$
$644$	−578.875	+	3610.59i	−0.0354206	+	0.220927i
$645$	7691.42	+	11238.7i	0.469534	+	0.686084i
$646$	−13369.4			−0.814259
$647$	−32595.6			−1.98062			−0.990312	−	0.138858i	$-0.955657\pi$
$647$	−32595.6			−1.98062			−0.990312	+	0.138858i	$0.955657\pi$
$648$	9019.83	−	9859.28i	0.546809	−	0.597699i
$649$		−	9974.41i		−	0.603282i
$650$	−4605.92			−0.277937
$651$	−2441.81	+	1153.09i	−0.147008	+	0.0694211i
$652$	2584.54			0.155243
$653$			125.561i			0.00752462i	0.999993	+	0.00376231i	$0.00119758\pi$
$653$			125.561i			0.00752462i	−0.999993	+	0.00376231i	$0.998802\pi$
$654$	21511.7	−	14721.9i	1.28620	−	0.880234i
$655$	−11642.0			−0.694491
$656$	21015.0			1.25076
$657$	−718.934	−	279.246i	−0.0426914	−	0.0165821i
$658$	−3750.26	+	23391.3i	−0.222189	+	1.38585i
$659$			16830.1i			0.994851i	0.867507	+	0.497426i	$0.165721\pi$
$659$			16830.1i			0.994851i	−0.867507	+	0.497426i	$0.834279\pi$
$660$	749.720	−	513.084i	0.0442164	−	0.0302603i
$661$		−	13389.8i		−	0.787899i	−0.919132	−	0.393950i	$-0.871108\pi$
$661$		−	13389.8i		−	0.787899i	0.919132	−	0.393950i	$-0.128892\pi$
$662$			2260.27i			0.132701i
$663$	10993.8	−	7523.80i	0.643987	−	0.440724i
$664$			1630.89i			0.0953177i
$665$	1369.47	−	8541.74i	0.0798584	−	0.498097i
$666$	11479.3	+	4458.76i	0.667889	+	0.259420i
$667$	10566.8			0.613418
$668$	−3560.36			−0.206219
$669$	−12092.5	+	8275.71i	−0.698838	+	0.478262i
$670$		−	899.618i		−	0.0518736i
$671$	6198.87			0.356639
$672$	−8742.56	+	4128.47i	−0.501862	+	0.236993i
$673$	11754.9			0.673279			0.336640	−	0.941634i	$-0.390710\pi$
$673$	11754.9			0.673279			0.336640	+	0.941634i	$0.390710\pi$
$674$			8787.81i			0.502216i
$675$	3415.30	−	798.502i	0.194748	−	0.0455324i
$676$	2520.64			0.143414
$677$	−28677.3			−1.62800			−0.814002	−	0.580862i	$-0.802715\pi$
$677$	−28677.3			−1.62800			−0.814002	+	0.580862i	$0.802715\pi$
$678$	−12606.3	−	18420.4i	−0.714074	−	1.04341i
$679$	4612.74	−	28770.8i	0.260708	−	1.62610i
$680$		−	4090.02i		−	0.230655i
$681$	−17860.3	−	26097.6i	−1.00501	−	1.46852i
$682$			1377.62i			0.0773484i
$683$		−	20988.8i		−	1.17586i	−0.808911	−	0.587931i	$-0.799943\pi$
$683$		−	20988.8i		−	1.17586i	0.808911	−	0.587931i	$-0.200057\pi$
$684$	5370.40	+	2085.95i	0.300208	+	0.116606i
$685$			6370.62i			0.355341i
$686$	−9351.51	+	18098.3i	−0.520470	+	1.00729i
$687$	4999.99	−	3421.83i	0.277673	−	0.190031i
$688$	−40391.1			−2.23822
$689$	23737.6			1.31252
$690$	4067.57	+	5943.55i	0.224420	+	0.327923i
$691$			12727.8i			0.700707i	0.936618	+	0.350354i	$0.113939\pi$
$691$			12727.8i			0.700707i	−0.936618	+	0.350354i	$0.886061\pi$
$692$	−8462.48			−0.464878
$693$	−6607.11	−	3866.39i	−0.362169	−	0.211936i
$694$	13774.7			0.753432
$695$			1414.59i			0.0772064i
$696$	6575.69	+	9608.42i	0.358119	+	0.523285i
$697$	−12170.6			−0.661400
$698$	−20557.3			−1.11476
$699$	−5283.80	+	3616.06i	−0.285911	+	0.195668i
$700$	−1044.22	−	167.416i	−0.0563824	−	0.00903963i
$701$		−	1253.07i		−	0.0675146i	−0.999430	−	0.0337573i	$-0.989253\pi$
$701$		−	1253.07i		−	0.0675146i	0.999430	−	0.0337573i	$-0.0107473\pi$
$702$	−25169.0	+	5884.55i	−1.35319	+	0.316379i
$703$		−	13286.8i		−	0.712835i
$704$		−	4504.85i		−	0.241169i
$705$	5852.77	+	8552.08i	0.312664	+	0.456865i
$706$		−	30756.4i		−	1.63956i
$707$	19737.1	+	3164.39i	1.04991	+	0.168330i
$708$	−4367.26	−	6381.46i	−0.231825	−	0.338743i
$709$	−28060.2			−1.48635			−0.743176	−	0.669095i	$-0.766682\pi$
$709$	−28060.2			−1.48635			−0.743176	+	0.669095i	$0.766682\pi$
$710$	−4759.15			−0.251560
$711$	11802.4	−	30385.9i	0.622539	−	1.60276i
$712$		−	526.581i		−	0.0277169i
$713$	−2425.62			−0.127406
$714$	12453.4	−	5880.82i	0.652740	−	0.308241i
$715$	4397.56			0.230013
$716$		−	6071.51i		−	0.316904i
$717$	−16111.5	+	11026.2i	−0.839184	+	0.574311i
$718$	7200.15			0.374244
$719$	−20672.4			−1.07225			−0.536127	−	0.844137i	$-0.680113\pi$
$719$	−20672.4			−1.07225			−0.536127	+	0.844137i	$0.680113\pi$
$720$	−3766.38	+	9696.74i	−0.194951	+	0.501911i
$721$	−5002.59	+	31202.4i	−0.258400	+	1.61170i
$722$		−	5991.47i		−	0.308836i
$723$	−16052.2	+	10985.6i	−0.825709	+	0.565089i
$724$			5147.19i			0.264218i
$725$			3056.04i			0.156549i
$726$	15080.3	−	10320.5i	0.770913	−	0.527588i
$727$		−	31607.4i		−	1.61245i	−0.591607	−	0.806226i	$-0.701506\pi$
$727$		−	31607.4i		−	1.61245i	0.591607	−	0.806226i	$-0.298494\pi$
$728$	−19257.4	−	3087.48i	−0.980393	−	0.157184i
$729$	17642.7	−	8726.80i	0.896340	−	0.443367i
$730$	458.027			0.0232224
$731$	23392.1			1.18357
$732$	3965.93	−	2714.16i	0.200253	−	0.137047i
$733$		−	11958.1i		−	0.602570i	−0.953534	−	0.301285i	$-0.902584\pi$
$733$		−	11958.1i		−	0.602570i	0.953534	−	0.301285i	$-0.0974156\pi$
$734$	1374.18			0.0691034
$735$	2481.63	+	8558.89i	0.124539	+	0.429523i
$736$	−8684.59			−0.434943
$737$			858.921i			0.0429291i
$738$	22012.0	+	8549.84i	1.09793	+	0.426455i
$739$	−4584.07			−0.228184			−0.114092	−	0.993470i	$-0.536396\pi$
$739$	−4584.07			−0.228184			−0.114092	+	0.993470i	$0.536396\pi$
$740$	−1624.30			−0.0806899
$741$	15750.3	+	23014.4i	0.780840	+	1.14097i
$742$	24230.4	+	3884.80i	1.19882	+	0.192204i
$743$		−	7821.64i		−	0.386202i	−0.981179	−	0.193101i	$-0.938146\pi$
$743$		−	7821.64i		−	0.386202i	0.981179	−	0.193101i	$-0.0618545\pi$
$744$	−1509.45	−	2205.62i	−0.0743807	−	0.108685i
$745$		−	5027.09i		−	0.247219i
$746$		−	5384.63i		−	0.264270i
$747$	−869.776	+	2239.28i	−0.0426016	+	0.109680i
$748$		−	1560.46i		−	0.0762780i
$749$	−3945.91	+	24611.6i	−0.192497	+	1.20065i
$750$	−1718.93	+	1176.38i	−0.0836887	+	0.0572739i
$751$	−12029.5			−0.584504			−0.292252	−	0.956341i	$-0.594405\pi$
$751$	−12029.5			−0.584504			−0.292252	+	0.956341i	$0.594405\pi$
$752$	−30735.5			−1.49044
$753$	1003.08	+	1465.70i	0.0485448	+	0.0709337i
$754$		−	22521.4i		−	1.08777i
$755$	−9229.52			−0.444896
$756$	−5920.00	+	419.252i	−0.284799	+	0.0201694i
$757$	28867.8			1.38602			0.693010	−	0.720928i	$-0.256284\pi$
$757$	28867.8			1.38602			0.693010	+	0.720928i	$0.256284\pi$
$758$		−	18579.9i		−	0.890308i
$759$	−3883.57	−	5674.67i	−0.185724	−	0.271380i
$760$	8562.06			0.408656
$761$	−20308.0			−0.967364			−0.483682	−	0.875244i	$-0.660701\pi$
$761$	−20308.0			−0.967364			−0.483682	+	0.875244i	$0.660701\pi$
$762$	−20710.5	+	14173.6i	−0.984597	+	0.673827i
$763$	28606.3	+	4586.37i	1.35730	+	0.217612i
$764$		−	10575.5i		−	0.500794i
$765$	2181.26	−	5615.77i	0.103090	−	0.265410i
$766$			29097.3i			1.37249i
$767$		−	37431.1i		−	1.76214i
$768$	−9536.42	−	13934.6i	−0.448068	−	0.654718i
$769$		−	23443.7i		−	1.09935i	−0.835378	−	0.549676i	$-0.814751\pi$
$769$		−	23443.7i		−	1.09935i	0.835378	−	0.549676i	$-0.185249\pi$
$770$	4488.87	+	719.688i	0.210088	+	0.0336828i
$771$	13324.0	+	19469.0i	0.622375	+	0.909416i
$772$	−1495.26			−0.0697091
$773$	30076.2			1.39944			0.699718	−	0.714419i	$-0.253309\pi$
$773$	30076.2			1.39944			0.699718	+	0.714419i	$0.253309\pi$
$774$	−42307.3	−	16432.9i	−1.96474	−	0.763137i
$775$		−	701.514i		−	0.0325150i
$776$	28839.2			1.33411
$777$	5844.51	+	12376.5i	0.269846	+	0.571434i
$778$	−20562.2			−0.947548
$779$		−	25478.0i		−	1.17182i
$780$	2813.48	−	1925.46i	0.129152	−	0.0883878i
$781$	4543.85			0.208184
$782$	12370.8			0.565702
$783$	3904.40	+	16699.6i	0.178202	+	0.762192i
$784$	−25105.4	−	8262.54i	−1.14365	−	0.376391i
$785$		−	16086.8i		−	0.731416i
$786$	32019.0	−	21912.7i	1.45303	−	0.994404i
$787$		−	19430.6i		−	0.880082i	−0.897978	−	0.440041i	$-0.854964\pi$
$787$		−	19430.6i		−	0.880082i	0.897978	−	0.440041i	$-0.145036\pi$
$788$			2608.01i			0.117902i
$789$	10817.3	−	7403.02i	0.488094	−	0.334036i
$790$			19358.6i			0.871834i
$791$	3927.28	−	24495.4i	0.176534	−	1.10108i
$792$	2743.25	−	7062.64i	0.123077	−	0.316869i
$793$	23262.6			1.04171
$794$	38537.3			1.72246
$795$	8858.86	−	6062.72i	0.395209	−	0.270469i
$796$			11697.5i			0.520863i
$797$	−34333.6			−1.52592			−0.762959	−	0.646447i	$-0.776254\pi$
$797$	−34333.6			−1.52592			−0.762959	+	0.646447i	$0.776254\pi$
$798$	12310.9	+	26069.9i	0.546117	+	1.15647i
$799$	17800.2			0.788141
$800$		−	2511.67i		−	0.111001i
$801$	280.832	−	723.016i	0.0123879	−	0.0318933i
$802$	4170.21			0.183610
$803$	−437.307			−0.0192182
$804$	376.076	+	549.523i	0.0164965	+	0.0241047i
$805$	−1267.18	+	7903.74i	−0.0554812	+	0.346050i
$806$			5169.80i			0.225928i
$807$	6798.38	+	9933.80i	0.296548	+	0.433317i
$808$			19784.0i			0.861385i
$809$			788.890i			0.0342842i	0.999853	+	0.0171421i	$0.00545676\pi$
$809$			788.890i			0.0342842i	−0.999853	+	0.0171421i	$0.994543\pi$
$810$	−7890.12	+	8624.43i	−0.342260	+	0.374113i
$811$		−	144.246i		−	0.00624558i	−0.999995	−	0.00312279i	$-0.999006\pi$
$811$		−	144.246i		−	0.00624558i	0.999995	−	0.00312279i	$-0.000994016\pi$
$812$	818.609	−	5105.87i	0.0353787	−	0.220666i
$813$	−11803.1	+	8077.66i	−0.509167	+	0.348457i
$814$	6982.53			0.300661
$815$	5657.68			0.243165
$816$	10091.3	+	14745.5i	0.432925	+	0.632591i
$817$			48969.1i			2.09695i
$818$	39457.6			1.68656
$819$	−24794.6	−	14509.4i	−1.05787	−	0.619049i
$820$	−3114.66			−0.132645
$821$			36695.4i			1.55990i	0.625842	+	0.779950i	$0.284756\pi$
$821$			36695.4i			1.55990i	−0.625842	+	0.779950i	$0.715244\pi$
$822$	−11990.8	−	17521.1i	−0.508794	−	0.743451i
$823$	31577.4			1.33745			0.668723	−	0.743512i	$-0.266841\pi$
$823$	31577.4			1.33745			0.668723	+	0.743512i	$0.266841\pi$
$824$	−31276.6			−1.32230
$825$	1641.17	−	1123.17i	0.0692585	−	0.0473983i
$826$	6125.83	−	38208.3i	0.258045	−	1.60949i
$827$			35653.9i			1.49916i	0.661913	+	0.749581i	$0.269745\pi$
$827$			35653.9i			1.49916i	−0.661913	+	0.749581i	$0.730255\pi$
$828$	−4969.28	−	1930.15i	−0.208568	−	0.0810114i
$829$		−	15354.0i		−	0.643267i	−0.946864	−	0.321633i	$-0.895768\pi$
$829$		−	15354.0i		−	0.643267i	0.946864	−	0.321633i	$-0.104232\pi$
$830$		−	1426.63i		−	0.0596614i
$831$	3249.86	+	4748.70i	0.135663	+	0.198232i
$832$		−	16905.4i		−	0.704434i
$833$	14539.5	+	4785.16i	0.604760	+	0.199035i
$834$	−2662.56	−	3890.53i	−0.110548	−	0.161533i
$835$	−7793.79			−0.323012
$836$	3266.66			0.135143
$837$	−896.257	−	3833.41i	−0.0370122	−	0.158306i
$838$		−	35290.6i		−	1.45477i
$839$	−5106.22			−0.210115			−0.105057	−	0.994466i	$-0.533503\pi$
$839$	−5106.22			−0.210115			−0.105057	+	0.994466i	$0.533503\pi$
$840$	−7975.43	+	3766.21i	−0.327593	+	0.154698i
$841$	9446.03			0.387307
$842$			8784.04i			0.359523i
$843$	−23939.5	+	16383.4i	−0.978078	+	0.669365i
$844$	4644.75			0.189430
$845$	5517.79			0.224636
$846$	−32193.6	−	12504.6i	−1.30832	−	0.508175i
$847$	20053.8	+	3215.17i	0.813527	+	0.130430i
$848$			31838.1i			1.28930i
$849$	13475.0	−	9221.84i	0.544711	−	0.372783i
$850$			3577.76i			0.144372i
$851$			12294.4i			0.495238i
$852$	2907.08	−	1989.51i	0.116895	−	0.0799994i
$853$		−	29250.9i		−	1.17413i	−0.809540	−	0.587064i	$-0.800284\pi$
$853$		−	29250.9i		−	1.17413i	0.809540	−	0.587064i	$-0.199716\pi$
$854$	23745.6	+	3807.07i	0.951474	+	0.152547i
$855$	11756.0	+	4566.25i	0.470232	+	0.182646i
$856$	−24670.2			−0.985058
$857$	−39247.1			−1.56436			−0.782180	−	0.623053i	$-0.785892\pi$
$857$	−39247.1			−1.56436			−0.782180	+	0.623053i	$0.785892\pi$
$858$	−12094.6	+	8277.14i	−0.481238	+	0.329344i
$859$			2660.13i			0.105660i	0.998604	+	0.0528302i	$0.0168242\pi$
$859$			2660.13i			0.105660i	−0.998604	+	0.0528302i	$0.983176\pi$
$860$	5986.41			0.237366
$861$	11207.1	+	23732.4i	0.443596	+	0.939370i
$862$	−12647.9			−0.499756
$863$		−	34109.2i		−	1.34541i	−0.739909	−	0.672707i	$-0.765132\pi$
$863$		−	34109.2i		−	1.34541i	0.739909	−	0.672707i	$-0.234868\pi$
$864$	−3208.92	−	13725.0i	−0.126354	−	0.540432i
$865$	−18524.8			−0.728163
$866$	−3717.70			−0.145881
$867$	8573.62	+	12527.8i	0.335842	+	0.490734i
$868$	−187.912	+	1172.05i	−0.00734810	+	0.0458319i
$869$		−	18482.9i		−	0.721506i
$870$	−5752.11	−	8404.99i	−0.224155	−	0.327535i
$871$			3223.29i			0.125393i
$872$			28674.4i			1.11357i
$873$	39597.4	+	15380.3i	1.53513	+	0.596272i
$874$			25897.1i			1.00227i
$875$	−2285.84	−	366.482i	−0.0883149	−	0.0141593i
$876$	−279.781	+	191.473i	−0.0107910	+	0.00738503i
$877$	15198.7			0.585204			0.292602	−	0.956234i	$-0.405479\pi$
$877$	15198.7			0.585204			0.292602	+	0.956234i	$0.405479\pi$
$878$	−48992.6			−1.88317
$879$	6142.93	+	8976.07i	0.235718	+	0.344431i
$880$			5898.25i			0.225943i
$881$	23822.7			0.911020			0.455510	−	0.890231i	$-0.349457\pi$
$881$	23822.7			0.911020			0.455510	+	0.890231i	$0.349457\pi$
$882$	−22934.8	−	18868.5i	−0.875574	−	0.720335i
$883$	−16687.1			−0.635976			−0.317988	−	0.948095i	$-0.603007\pi$
$883$	−16687.1			−0.635976			−0.317988	+	0.948095i	$0.603007\pi$
$884$		−	5855.94i		−	0.222802i
$885$	−9560.14	−	13969.3i	−0.363119	−	0.530591i
$886$	−55219.8			−2.09384
$887$	47390.4			1.79393			0.896963	−	0.442105i	$-0.145768\pi$
$887$	47390.4			1.79393			0.896963	+	0.442105i	$0.145768\pi$
$888$	−11179.3	+	7650.76i	−0.422470	+	0.289125i
$889$	−27540.9	−	4415.55i	−1.03902	−	0.166584i
$890$			460.628i			0.0173486i
$891$	7533.19	−	8234.28i	0.283245	−	0.309606i
$892$			6441.18i			0.241779i
$893$			37262.9i			1.39637i
$894$	9462.04	+	13826.0i	0.353980	+	0.517236i
$895$		−	13290.8i		−	0.496383i
$896$	5123.11	−	31954.1i	0.191017	−	1.19142i
$897$	−14573.9	−	21295.4i	−0.542485	−	0.792680i
$898$	−2957.11			−0.109889
$899$	3430.16			0.127255
$900$	558.219	−	1437.16i	0.0206748	−	0.0532283i
$901$		−	18438.7i		−	0.681778i
$902$	13389.3			0.494250
$903$	−21540.1	−	45613.9i	−0.793810	−	1.68099i
$904$	24553.7			0.903367
$905$			11267.4i			0.413859i
$906$	25383.9	−	17371.9i	0.930820	−	0.637023i
$907$	−37478.0			−1.37203			−0.686017	−	0.727585i	$-0.740643\pi$
$907$	−37478.0			−1.37203			−0.686017	+	0.727585i	$0.740643\pi$
$908$	−13901.1			−0.508067
$909$	−10551.1	+	27164.2i	−0.384991	+	0.991178i
$910$	16845.5	+	2700.78i	0.613650	+	0.0983847i
$911$		−	35733.3i		−	1.29956i	−0.760123	−	0.649779i	$-0.774862\pi$
$911$		−	35733.3i		−	1.29956i	0.760123	−	0.649779i	$-0.225138\pi$
$912$	−30868.2	+	21125.2i	−1.12078	+	0.767022i
$913$			1362.09i			0.0493742i
$914$			5964.49i			0.215851i
$915$	8681.61	−	5941.41i	0.313667	−	0.214663i
$916$		−	2663.29i		−	0.0960672i
$917$	42578.9	+	6826.55i	1.53335	+	0.245837i
$918$	4570.96	+	19550.6i	0.164340	+	0.702904i
$919$	−865.364			−0.0310617			−0.0155309	−	0.999879i	$-0.504944\pi$
$919$	−865.364			−0.0310617			−0.0155309	+	0.999879i	$0.504944\pi$
$920$	−7922.55			−0.283912
$921$	−4949.82	+	3387.50i	−0.177092	+	0.121196i
$922$			14626.2i			0.522440i
$923$	17051.8			0.608089
$924$	−3042.84	+	1436.91i	−0.108336	+	0.0511590i
$925$	−3555.67			−0.126389
$926$			38814.1i			1.37744i
$927$	−42944.1	−	16680.2i	−1.52154	−	0.590993i
$928$	12281.2			0.434429
$929$	−16444.6			−0.580765			−0.290382	−	0.956911i	$-0.593782\pi$
$929$	−16444.6			−0.580765			−0.290382	+	0.956911i	$0.593782\pi$
$930$	1320.40	+	1929.37i	0.0465565	+	0.0680285i
$931$	−10017.3	+	30437.1i	−0.352634	+	1.07147i
$932$			2814.46i			0.0989171i
$933$	−13740.8	−	20078.1i	−0.482159	−	0.704532i
$934$			31990.0i			1.12071i
$935$		−	3415.91i		−	0.119478i
$936$	10294.6	−	26504.1i	0.359499	−	0.925548i
$937$			34254.6i			1.19429i	0.802134	+	0.597144i	$0.203698\pi$
$937$			34254.6i			1.19429i	−0.802134	+	0.597144i	$0.796302\pi$
$938$	−527.510	+	3290.21i	−0.0183623	+	0.114530i
$939$	7464.19	−	5108.25i	0.259408	−	0.177531i
$940$	4555.34			0.158063
$941$	3170.55			0.109838			0.0549188	−	0.998491i	$-0.482510\pi$
$941$	3170.55			0.109838			0.0549188	+	0.998491i	$0.482510\pi$
$942$	30278.7	+	44243.3i	1.04728	+	1.53028i
$943$			23575.0i			0.814113i
$944$	50204.6			1.73095
$945$	−12959.1	+	917.763i	−0.446096	+	0.0315924i
$946$	−25734.3			−0.884456
$947$		−	49410.2i		−	1.69548i	−0.530415	−	0.847738i	$-0.677964\pi$
$947$		−	49410.2i		−	1.69548i	0.530415	−	0.847738i	$-0.322036\pi$
$948$	−8092.66	−	11825.0i	−0.277255	−	0.405125i
$949$	−1641.09			−0.0561348
$950$	−7489.68			−0.255787
$951$	−42176.4	+	28864.2i	−1.43813	+	0.984211i
$952$	−2398.27	+	14958.6i	−0.0816476	+	0.509256i
$953$			1979.72i			0.0672922i	0.999434	+	0.0336461i	$0.0107119\pi$
$953$			1979.72i			0.0672922i	−0.999434	+	0.0336461i	$0.989288\pi$
$954$	−12953.1	+	33348.5i	−0.439595	+	1.13176i
$955$		−	23150.2i		−	0.784421i
$956$			8581.94i			0.290334i
$957$	5491.89	+	8024.77i	0.185504	+	0.271059i
$958$			41319.9i			1.39351i
$959$	3735.55	−	23299.5i	0.125784	−	0.784548i
$960$	−4317.74	−	6309.10i	−0.145161	−	0.212110i
$961$	29003.6			0.973569
$962$	26203.4			0.878205
$963$	−33873.2	−	13156.9i	−1.13349	−	0.440266i
$964$			8550.35i			0.285673i
$965$	−3273.19			−0.109189
$966$	−11391.4	−	24122.7i	−0.379412	−	0.803453i
$967$	−23286.6			−0.774403			−0.387201	−	0.921995i	$-0.626558\pi$
$967$	−23286.6			−0.774403			−0.387201	+	0.921995i	$0.626558\pi$
$968$			20101.5i			0.667446i
$969$	17877.0	−	12234.4i	0.592664	−	0.405600i
$970$	−25227.2			−0.835048
$971$	−35942.3			−1.18789			−0.593946	−	0.804505i	$-0.702431\pi$
$971$	−35942.3			−1.18789			−0.593946	+	0.804505i	$0.702431\pi$
$972$	1214.25	−	8566.53i	0.0400691	−	0.282687i
$973$	829.475	−	5173.64i	0.0273296	−	0.170462i
$974$			25172.1i			0.828096i
$975$	6158.85	−	4214.92i	0.202298	−	0.138447i
$976$			31201.0i			1.02328i
$977$			11980.7i			0.392321i	0.980572	+	0.196160i	$0.0628473\pi$
$977$			11980.7i			0.392321i	−0.980572	+	0.196160i	$0.937153\pi$
$978$	−15560.3	+	10648.9i	−0.508755	+	0.348176i
$979$		−	439.790i		−	0.0143573i
$980$	3720.89	+	1224.60i	0.121285	+	0.0399167i
$981$	−15292.4	+	39371.1i	−0.497705	+	1.28137i
$982$	17906.1			0.581882
$983$	34449.2			1.11776			0.558880	−	0.829248i	$-0.311231\pi$
$983$	34449.2			1.11776			0.558880	+	0.829248i	$0.311231\pi$
$984$	−21436.7	+	14670.6i	−0.694490	+	0.475287i
$985$			5709.05i			0.184676i
$986$	−17494.0			−0.565034
$987$	−16390.9	−	34709.8i	−0.528600	−	1.11938i
$988$	12258.8			0.394742
$989$		−	45311.5i		−	1.45685i
$990$	−2399.67	+	6178.06i	−0.0770368	+	0.198335i
$991$	57013.4			1.82754			0.913769	−	0.406235i	$-0.133159\pi$
$991$	57013.4			1.82754			0.913769	+	0.406235i	$0.133159\pi$
$992$	−2819.16			−0.0902301
$993$	−2068.39	−	3022.33i	−0.0661010	−	0.0965869i
$994$	17405.8	+	2790.63i	0.555412	+	0.0890476i
$995$			25606.4i			0.815856i
$996$	596.387	+	871.442i	0.0189731	+	0.0277236i
$997$			6586.26i			0.209217i	0.994513	+	0.104608i	$0.0333589\pi$
$997$			6586.26i			0.209217i	−0.994513	+	0.104608i	$0.966641\pi$
$998$		−	15317.4i		−	0.485836i
$999$	−19429.9	+	4542.74i	−0.615350	+	0.143870i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.b.a.41.13	yes	16
3.2	odd	2		105.4.b.b.41.4	yes	16
7.6	odd	2		105.4.b.b.41.13	yes	16
21.20	even	2	inner	105.4.b.a.41.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.b.a.41.4	✓	16	21.20	even	2	inner
105.4.b.a.41.13	yes	16	1.1	even	1	trivial
105.4.b.b.41.4	yes	16	3.2	odd	2
105.4.b.b.41.13	yes	16	7.6	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)

\(f(q)\)	\(=\)	\(q+3.20688i q^{2} +(-2.93464 - 4.28811i) q^{3} -2.28410 q^{4} -5.00000 q^{5} +(13.7515 - 9.41106i) q^{6} +(18.2867 + 2.93186i) q^{7} +18.3302i q^{8} +(-9.77574 + 25.1681i) q^{9} +O(q^{10})\)	\(q+3.20688i q^{2} +(-2.93464 - 4.28811i) q^{3} -2.28410 q^{4} -5.00000 q^{5} +(13.7515 - 9.41106i) q^{6} +(18.2867 + 2.93186i) q^{7} +18.3302i q^{8} +(-9.77574 + 25.1681i) q^{9} -16.0344i q^{10} +15.3091i q^{11} +(6.70302 + 9.79447i) q^{12} +57.4505i q^{13} +(-9.40212 + 58.6434i) q^{14} +(14.6732 + 21.4405i) q^{15} -77.0557 q^{16} +44.6260 q^{17} +(-80.7113 - 31.3496i) q^{18} +93.4201i q^{19} +11.4205 q^{20} +(-41.0929 - 87.0194i) q^{21} -49.0943 q^{22} -86.4424i q^{23} +(78.6020 - 53.7927i) q^{24} +25.0000 q^{25} -184.237 q^{26} +(136.612 - 31.9401i) q^{27} +(-41.7687 - 6.69666i) q^{28} +122.241i q^{29} +(-68.7573 + 47.0553i) q^{30} -28.0606i q^{31} -100.467i q^{32} +(65.6469 - 44.9266i) q^{33} +143.110i q^{34} +(-91.4336 - 14.6593i) q^{35} +(22.3288 - 57.4865i) q^{36} -142.227 q^{37} -299.587 q^{38} +(246.354 - 168.597i) q^{39} -91.6511i q^{40} -272.725 q^{41} +(279.061 - 131.780i) q^{42} +524.181 q^{43} -34.9674i q^{44} +(48.8787 - 125.841i) q^{45} +277.211 q^{46} +398.874 q^{47} +(226.131 + 330.423i) q^{48} +(325.808 + 107.228i) q^{49} +80.1721i q^{50} +(-130.961 - 191.361i) q^{51} -131.223i q^{52} -413.183i q^{53} +(102.428 + 438.099i) q^{54} -76.5453i q^{55} +(-53.7416 + 335.200i) q^{56} +(400.595 - 274.155i) q^{57} -392.014 q^{58} -651.537 q^{59} +(-33.5151 - 48.9723i) q^{60} -404.916i q^{61} +89.9870 q^{62} +(-252.556 + 431.582i) q^{63} -294.260 q^{64} -287.252i q^{65} +(144.074 + 210.522i) q^{66} +56.1055 q^{67} -101.930 q^{68} +(-370.674 + 253.678i) q^{69} +(47.0106 - 293.217i) q^{70} -296.808i q^{71} +(-461.338 - 179.191i) q^{72} +28.5652i q^{73} -456.105i q^{74} +(-73.3661 - 107.203i) q^{75} -213.381i q^{76} +(-44.8840 + 279.952i) q^{77} +(540.670 + 790.028i) q^{78} -1207.32 q^{79} +385.278 q^{80} +(-537.870 - 492.074i) q^{81} -874.598i q^{82} +88.9729 q^{83} +(93.8602 + 198.761i) q^{84} -223.130 q^{85} +1680.99i q^{86} +(524.184 - 358.735i) q^{87} -280.618 q^{88} -28.7275 q^{89} +(403.556 + 156.748i) q^{90} +(-168.437 + 1050.58i) q^{91} +197.443i q^{92} +(-120.327 + 82.3478i) q^{93} +1279.14i q^{94} -467.100i q^{95} +(-430.812 + 294.834i) q^{96} -1573.32i q^{97} +(-343.868 + 1044.83i) q^{98} +(-385.300 - 149.657i) 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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