LMFDB - Embedded newform 105.4.b.a.41.4

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

$q$-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	$-0.808142\pi$
$2$		−	3.20688i		−	1.13380i	0.823785	−	0.566902i	$-0.191858\pi$
$3$	−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	$-0.932715\pi$
$11$		−	15.3091i		−	0.419623i	0.977742	−	0.209811i	$-0.0672850\pi$
$12$	6.70302	−	9.79447i	0.161250	−	0.235618i
$13$		−	57.4505i		−	1.22568i	−0.790205	−	0.612842i	$-0.790026\pi$
$13$		−	57.4505i		−	1.22568i	0.790205	−	0.612842i	$-0.209974\pi$
$14$	−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	$-0.809261\pi$
$19$		−	93.4201i		−	1.12800i	0.825774	−	0.564001i	$-0.190739\pi$
$20$	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	$0.128160\pi$
$23$			86.4424i			0.783674i	−0.920035	+	0.391837i	$0.871840\pi$
$24$	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	$-0.872000\pi$
$29$		−	122.241i		−	0.782747i	0.920232	−	0.391373i	$-0.128000\pi$
$30$	−68.7573	−	47.0553i	−0.418444	−	0.286369i
$31$			28.0606i			0.162575i	0.996691	+	0.0812875i	$0.0259032\pi$
$31$			28.0606i			0.162575i	−0.996691	+	0.0812875i	$0.974097\pi$
$32$			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	$0.179848\pi$
$53$			413.183i			1.07085i	−0.844583	+	0.535425i	$0.820152\pi$
$54$	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	$0.139709\pi$
$61$			404.916i			0.849904i	−0.905216	+	0.424952i	$0.860291\pi$
$62$	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	$0.0797933\pi$
$71$			296.808i			0.496122i	−0.968744	+	0.248061i	$0.920207\pi$
$72$	−461.338	+	179.191i	−0.755127	+	0.293304i
$73$		−	28.5652i		−	0.0457987i	−0.999738	−	0.0228994i	$-0.992710\pi$
$73$		−	28.5652i		−	0.0457987i	0.999738	−	0.0228994i	$-0.00728973\pi$
$74$			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	$0.307944\pi$
$97$			1573.32i			1.64687i	−0.567413	+	0.823433i	$0.692056\pi$
$98$	−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	$-0.696108\pi$
$103$		−	1706.29i		−	1.63229i	0.577849	−	0.816144i	$-0.303892\pi$
$104$	−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	$-0.791975\pi$
$107$		−	1345.87i		−	1.21599i	0.793942	−	0.607994i	$-0.208025\pi$
$108$	−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	$0.188267\pi$
$113$			1339.52i			1.11515i	−0.830128	+	0.557573i	$0.811733\pi$
$114$	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	$0.130047\pi$
$137$			1274.12i			0.794567i	−0.917696	+	0.397284i	$0.869953\pi$
$138$	−813.515	+	1188.71i	−0.501819	+	0.733259i
$139$			282.918i			0.172639i	0.996268	+	0.0863194i	$0.0275105\pi$
$139$			282.918i			0.172639i	−0.996268	+	0.0863194i	$0.972489\pi$
$140$	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	$-0.910859\pi$
$149$		−	1005.42i		−	0.552799i	0.961043	−	0.276399i	$-0.0891412\pi$
$150$	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	$-0.695222\pi$
$157$		−	3217.35i		−	1.63550i	0.575577	−	0.817748i	$-0.304778\pi$
$158$			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	$-0.812729\pi$
$179$		−	2658.16i		−	1.10995i	0.831868	−	0.554973i	$-0.187271\pi$
$180$	−111.644	−	287.433i	−0.0462302	−	0.119022i
$181$			2253.49i			0.925417i	0.886510	+	0.462709i	$0.153122\pi$
$181$			2253.49i			0.925417i	−0.886510	+	0.462709i	$0.846878\pi$
$182$	−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	$-0.659535\pi$
$191$		−	4630.03i		−	1.75402i	0.480474	−	0.877009i	$-0.340465\pi$
$192$	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	$0.0661988\pi$
$197$			1141.81i			0.412947i	−0.978452	+	0.206474i	$0.933801\pi$
$198$	479.933	+	1235.61i	0.172259	+	0.443491i
$199$			5121.28i			1.82431i	0.409846	+	0.912155i	$0.365582\pi$
$199$			5121.28i			1.82431i	−0.409846	+	0.912155i	$0.634418\pi$
$200$		−	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	$0.139168\pi$
$223$			2820.01i			0.846823i	−0.905937	+	0.423412i	$0.860832\pi$
$224$	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	$-0.946193\pi$
$229$		−	1166.01i		−	0.336473i	0.985747	−	0.168236i	$-0.0538072\pi$
$230$	−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	$0.0554195\pi$
$233$			1232.20i			0.346455i	−0.984882	+	0.173227i	$0.944580\pi$
$234$	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	$0.169779\pi$
$239$			3757.25i			1.01689i	−0.861095	+	0.508444i	$0.830221\pi$
$240$	−1130.65	+	1652.12i	−0.304098	+	0.444348i
$241$			3743.42i			1.00056i	0.865863	+	0.500280i	$0.166770\pi$
$241$			3743.42i			1.00056i	−0.865863	+	0.500280i	$0.833230\pi$
$242$		−	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	$-0.904438\pi$
$263$		−	2522.63i		−	0.591452i	0.955273	−	0.295726i	$-0.0955616\pi$
$264$	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	$0.0998248\pi$
$271$			2752.52i			0.616987i	−0.951226	+	0.308494i	$0.900175\pi$
$272$	−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	$0.201897\pi$
$281$			5582.76i			1.18519i	−0.805499	+	0.592597i	$0.798103\pi$
$282$	5485.10	+	3753.83i	1.15827	+	0.792685i
$283$		−	3142.41i		−	0.660059i	−0.943971	−	0.330029i	$-0.892941\pi$
$283$		−	3142.41i		−	0.660059i	0.943971	−	0.330029i	$-0.107059\pi$
$284$		−	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	$0.0342195\pi$
$307$			1154.31i			0.214593i	−0.994227	+	0.107297i	$0.965781\pi$
$308$	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	$-0.949763\pi$
$313$		−	1740.67i		−	0.314340i	0.987572	−	0.157170i	$-0.0502371\pi$
$314$	−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	$0.336745\pi$
$317$			9835.66i			1.74267i	−0.490691	+	0.871334i	$0.663255\pi$
$318$	−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	$0.107811\pi$
$347$			4295.37i			0.664517i	−0.943188	+	0.332258i	$0.892189\pi$
$348$	−1197.29	−	819.386i	−0.184429	−	0.126218i
$349$		−	6410.35i		−	0.983205i	−0.870820	−	0.491602i	$-0.836411\pi$
$349$		−	6410.35i		−	0.983205i	0.870820	−	0.491602i	$-0.163589\pi$
$350$	−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	$0.0527750\pi$
$359$			2245.22i			0.330078i	−0.986287	+	0.165039i	$0.947225\pi$
$360$	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	$0.00970172\pi$
$367$			428.510i			0.0609483i	−0.999536	+	0.0304741i	$0.990298\pi$
$368$		−	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	$-0.862780\pi$
$389$		−	6411.91i		−	0.835724i	0.908510	−	0.417862i	$-0.137220\pi$
$390$	−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	$0.274603\pi$
$397$			12017.0i			1.51919i	−0.650397	+	0.759595i	$0.725397\pi$
$398$	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	$0.0258020\pi$
$401$			1300.39i			0.161941i	−0.996716	+	0.0809707i	$0.974198\pi$
$402$	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	$0.266960\pi$
$409$			12304.0i			1.48752i	−0.668447	+	0.743760i	$0.733040\pi$
$410$		−	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	$-0.929267\pi$
$431$		−	3943.99i		−	0.440778i	0.975412	−	0.220389i	$-0.0707327\pi$
$432$	−10526.7	−	2461.17i	−1.17238	−	0.274104i
$433$		−	1159.29i		−	0.128665i	−0.997929	−	0.0643324i	$-0.979508\pi$
$433$		−	1159.29i		−	0.128665i	0.997929	−	0.0643324i	$-0.0204918\pi$
$434$	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	$-0.688075\pi$
$439$		−	15277.3i		−	1.66093i	0.557072	−	0.830464i	$-0.311925\pi$
$440$	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	$-0.625422\pi$
$443$		−	17219.2i		−	1.84674i	0.383908	−	0.923371i	$-0.374578\pi$
$444$	−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	$-0.984569\pi$
$449$		−	922.113i		−	0.0969202i	0.998825	−	0.0484601i	$-0.0154314\pi$
$450$	−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	$0.0826043\pi$
$491$			5583.66i			0.513212i	−0.966516	+	0.256606i	$0.917396\pi$
$492$	−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	$-0.833825\pi$
$523$		−	11928.6i		−	0.997322i	0.866797	−	0.498661i	$-0.166175\pi$
$524$	−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	$0.0711334\pi$
$557$			5826.60i			0.443233i	−0.975134	+	0.221617i	$0.928867\pi$
$558$	−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	$-0.764776\pi$
$569$		−	18283.4i		−	1.34707i	0.739156	−	0.673534i	$-0.235224\pi$
$570$	−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	$-0.991211\pi$
$577$		−	765.268i		−	0.0552141i	0.999619	−	0.0276070i	$-0.00878871\pi$
$578$			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	$0.145689\pi$
$599$			12956.1i			0.883761i	−0.897074	+	0.441881i	$0.854311\pi$
$600$	1965.05	+	1344.82i	0.133705	+	0.0915032i
$601$		−	15357.7i		−	1.04235i	−0.853450	−	0.521174i	$-0.825494\pi$
$601$		−	15357.7i		−	1.04235i	0.853450	−	0.521174i	$-0.174506\pi$
$602$	−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	$-0.877185\pi$
$607$		−	11256.0i		−	0.752662i	0.926485	−	0.376331i	$-0.122815\pi$
$608$	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	$-0.529650\pi$
$617$		−	30519.0i		−	1.99133i	0.0930124	−	0.995665i	$-0.470350\pi$
$618$	16058.0	−	23464.0i	1.04522	−	1.52728i
$619$		−	10618.9i		−	0.689517i	−0.938691	−	0.344759i	$-0.887961\pi$
$619$		−	10618.9i		−	0.689517i	0.938691	−	0.344759i	$-0.112039\pi$
$620$			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	$-0.934973\pi$
$641$		−	6584.65i		−	0.405738i	0.979206	−	0.202869i	$-0.0650266\pi$
$642$	12666.1	−	18507.7i	0.778647	−	1.13776i
$643$			26506.6i			1.62569i	0.582479	+	0.812846i	$0.302083\pi$
$643$			26506.6i			1.62569i	−0.582479	+	0.812846i	$0.697917\pi$
$644$	−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	$-0.998802\pi$
$653$		−	125.561i		−	0.00752462i	0.999993	−	0.00376231i	$-0.00119758\pi$
$654$	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	$-0.834279\pi$
$659$		−	16830.1i		−	0.994851i	0.867507	−	0.497426i	$-0.165721\pi$
$660$	749.720	+	513.084i	0.0442164	+	0.0302603i
$661$			13389.8i			0.787899i	0.919132	+	0.393950i	$0.128892\pi$
$661$			13389.8i			0.787899i	−0.919132	+	0.393950i	$0.871108\pi$
$662$		−	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	$0.200057\pi$
$683$			20988.8i			1.17586i	−0.808911	+	0.587931i	$0.799943\pi$
$684$	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	$-0.886061\pi$
$691$		−	12727.8i		−	0.700707i	0.936618	−	0.350354i	$-0.113939\pi$
$692$	−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	$0.0107473\pi$
$701$			1253.07i			0.0675146i	−0.999430	+	0.0337573i	$0.989253\pi$
$702$	−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	$0.298494\pi$
$727$			31607.4i			1.61245i	−0.591607	+	0.806226i	$0.701506\pi$
$728$	−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	$0.0974156\pi$
$733$			11958.1i			0.602570i	−0.953534	+	0.301285i	$0.902584\pi$
$734$	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	$0.0618545\pi$
$743$			7821.64i			0.386202i	−0.981179	+	0.193101i	$0.938146\pi$
$744$	−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	$0.185249\pi$
$769$			23443.7i			1.09935i	−0.835378	+	0.549676i	$0.814751\pi$
$770$	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	$0.145036\pi$
$787$			19430.6i			0.880082i	−0.897978	+	0.440041i	$0.854964\pi$
$788$		−	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	$-0.994543\pi$
$809$		−	788.890i		−	0.0342842i	0.999853	−	0.0171421i	$-0.00545676\pi$
$810$	−7890.12	−	8624.43i	−0.342260	−	0.374113i
$811$			144.246i			0.00624558i	0.999995	+	0.00312279i	$0.000994016\pi$
$811$			144.246i			0.00624558i	−0.999995	+	0.00312279i	$0.999006\pi$
$812$	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	$-0.715244\pi$
$821$		−	36695.4i		−	1.55990i	0.625842	−	0.779950i	$-0.284756\pi$
$822$	−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	$-0.730255\pi$
$827$		−	35653.9i		−	1.49916i	0.661913	−	0.749581i	$-0.269745\pi$
$828$	−4969.28	+	1930.15i	−0.208568	+	0.0810114i
$829$			15354.0i			0.643267i	0.946864	+	0.321633i	$0.104232\pi$
$829$			15354.0i			0.643267i	−0.946864	+	0.321633i	$0.895768\pi$
$830$			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	$0.199716\pi$
$853$			29250.9i			1.17413i	−0.809540	+	0.587064i	$0.800284\pi$
$854$	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	$-0.983176\pi$
$859$		−	2660.13i		−	0.105660i	0.998604	−	0.0528302i	$-0.0168242\pi$
$860$	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	$0.234868\pi$
$863$			34109.2i			1.34541i	−0.739909	+	0.672707i	$0.765132\pi$
$864$	−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	$0.225138\pi$
$911$			35733.3i			1.29956i	−0.760123	+	0.649779i	$0.774862\pi$
$912$	−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	$-0.796302\pi$
$937$		−	34254.6i		−	1.19429i	0.802134	−	0.597144i	$-0.203698\pi$
$938$	−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	$0.322036\pi$
$947$			49410.2i			1.69548i	−0.530415	+	0.847738i	$0.677964\pi$
$948$	−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	$-0.989288\pi$
$953$		−	1979.72i		−	0.0672922i	0.999434	−	0.0336461i	$-0.0107119\pi$
$954$	−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	$-0.937153\pi$
$977$		−	11980.7i		−	0.392321i	0.980572	−	0.196160i	$-0.0628473\pi$
$978$	−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	$-0.966641\pi$
$997$		−	6586.26i		−	0.209217i	0.994513	−	0.104608i	$-0.0333589\pi$
$998$			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.41.4	✓	16
3.2	odd	2		105.4.b.b.41.13	yes	16
7.6	odd	2		105.4.b.b.41.4	yes	16
21.20	even	2	inner	105.4.b.a.41.13	yes	16

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

\(f(q)\)	\(=\)	\(q-3.20688i q^{2} +(-2.93464 + 4.28811i) q^{3} -2.28410 q^{4} -5.00000 q^{5} +(13.7515 + 9.41106i) q^{6} +(18.2867 - 2.93186i) q^{7} -18.3302i q^{8} +(-9.77574 - 25.1681i) q^{9} +O(q^{10})\)	\(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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