LMFDB - Embedded newform 120.4.k.c.61.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(61,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("120.61");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	120.k (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:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} + 7 x^{12} - 22 x^{11} + 70 x^{10} - 232 x^{9} + 1080 x^{8} - 4000 x^{7} + \cdots + 2097152 $ x^14 - 4x^13 + 7x^12 - 22x^11 + 70x^10 - 232x^9 + 1080x^8 - 4000x^7 + 8640x^6 - 14848x^5 + 35840x^4 - 90112x^3 + 229376x^2 - 1048576*x + 2097152
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			61.3
Root			$1.74774 - 2.22383i$ of defining polynomial
Character	$\chi$	$=$	120.61
Dual form			120.4.k.c.61.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.22383 - 1.74774i) q^{2} +3.00000i q^{3} +(1.89082 + 7.77334i) q^{4} -5.00000i q^{5} +(5.24321 - 6.67148i) q^{6} +2.94025 q^{7} +(9.38089 - 20.5912i) q^{8} -9.00000 q^{9} +(-8.73869 + 11.1191i) q^{10} +17.8593i q^{11} +(-23.3200 + 5.67247i) q^{12} +46.7050i q^{13} +(-6.53861 - 5.13879i) q^{14} +15.0000 q^{15} +(-56.8496 + 29.3960i) q^{16} -21.6786 q^{17} +(20.0145 + 15.7296i) q^{18} +162.197i q^{19} +(38.8667 - 9.45412i) q^{20} +8.82075i q^{21} +(31.2134 - 39.7160i) q^{22} +160.548 q^{23} +(61.7737 + 28.1427i) q^{24} -25.0000 q^{25} +(81.6281 - 103.864i) q^{26} -27.0000i q^{27} +(5.55949 + 22.8556i) q^{28} +214.174i q^{29} +(-33.3574 - 26.2161i) q^{30} -1.79631 q^{31} +(177.800 + 33.9865i) q^{32} -53.5779 q^{33} +(48.2094 + 37.8885i) q^{34} -14.7012i q^{35} +(-17.0174 - 69.9600i) q^{36} +163.742i q^{37} +(283.478 - 360.699i) q^{38} -140.115 q^{39} +(-102.956 - 46.9045i) q^{40} -203.616 q^{41} +(15.4164 - 19.6158i) q^{42} -62.8357i q^{43} +(-138.826 + 33.7688i) q^{44} +45.0000i q^{45} +(-357.031 - 280.596i) q^{46} +10.3285 q^{47} +(-88.1881 - 170.549i) q^{48} -334.355 q^{49} +(55.5957 + 43.6935i) q^{50} -65.0358i q^{51} +(-363.054 + 88.3110i) q^{52} -364.051i q^{53} +(-47.1889 + 60.0434i) q^{54} +89.2965 q^{55} +(27.5822 - 60.5434i) q^{56} -486.591 q^{57} +(374.320 - 476.286i) q^{58} -290.985i q^{59} +(28.3624 + 116.600i) q^{60} +522.551i q^{61} +(3.99469 + 3.13948i) q^{62} -26.4622 q^{63} +(-335.998 - 386.328i) q^{64} +233.525 q^{65} +(119.148 + 93.6401i) q^{66} -681.913i q^{67} +(-40.9904 - 168.515i) q^{68} +481.643i q^{69} +(-25.6939 + 32.6930i) q^{70} +455.528 q^{71} +(-84.4280 + 185.321i) q^{72} +768.573 q^{73} +(286.178 - 364.134i) q^{74} -75.0000i q^{75} +(-1260.81 + 306.686i) q^{76} +52.5108i q^{77} +(311.592 + 244.884i) q^{78} +1015.12 q^{79} +(146.980 + 284.248i) q^{80} +81.0000 q^{81} +(452.807 + 355.867i) q^{82} -274.715i q^{83} +(-68.5667 + 16.6785i) q^{84} +108.393i q^{85} +(-109.820 + 139.736i) q^{86} -642.522 q^{87} +(367.745 + 167.536i) q^{88} -1572.69 q^{89} +(78.6482 - 100.072i) q^{90} +137.324i q^{91} +(303.568 + 1247.99i) q^{92} -5.38893i q^{93} +(-22.9688 - 18.0515i) q^{94} +810.986 q^{95} +(-101.959 + 533.401i) q^{96} +178.134 q^{97} +(743.548 + 584.365i) q^{98} -160.734i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} - 2 q^{4} + 12 q^{6} - 28 q^{7} - 8 q^{8} - 126 q^{9} - 20 q^{10} + 12 q^{12} - 8 q^{14} + 210 q^{15} - 22 q^{16} + 204 q^{17} + 18 q^{18} - 20 q^{20} - 84 q^{22} - 328 q^{23} - 138 q^{24}+ \cdots + 6246 q^{98}+O(q^{100}) $ 14 * q - 2 * q^2 - 2 * q^4 + 12 * q^6 - 28 * q^7 - 8 * q^8 - 126 * q^9 - 20 * q^10 + 12 * q^12 - 8 * q^14 + 210 * q^15 - 22 * q^16 + 204 * q^17 + 18 * q^18 - 20 * q^20 - 84 * q^22 - 328 * q^23 - 138 * q^24 - 350 * q^25 - 4 * q^26 + 68 * q^28 - 30 * q^30 + 596 * q^31 + 588 * q^32 + 264 * q^33 + 756 * q^34 + 18 * q^36 - 1144 * q^38 + 230 * q^40 - 820 * q^41 + 768 * q^42 - 2084 * q^44 - 1060 * q^46 - 104 * q^47 - 48 * q^48 + 1110 * q^49 + 50 * q^50 - 1736 * q^52 - 108 * q^54 - 440 * q^55 + 3812 * q^56 + 168 * q^57 + 2664 * q^58 - 30 * q^60 - 772 * q^62 + 252 * q^63 + 2470 * q^64 + 972 * q^66 - 2864 * q^68 - 1280 * q^70 + 1592 * q^71 + 72 * q^72 - 2260 * q^73 + 1020 * q^74 - 2468 * q^76 - 2280 * q^78 - 220 * q^79 + 80 * q^80 + 1134 * q^81 + 3444 * q^82 - 84 * q^84 - 1184 * q^86 - 1044 * q^87 - 500 * q^88 - 2492 * q^89 + 180 * q^90 - 4536 * q^92 - 4300 * q^94 - 280 * q^95 + 1542 * q^96 + 3508 * q^97 + 6246 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−2.22383	−	1.74774i	−0.786242	−	0.617919i
$2$	−2.22383	−	1.74774i	−0.786242	−	0.617919i
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	1.89082	+	7.77334i	0.236353	+	0.971667i
$5$		−	5.00000i		−	0.447214i
$5$		−	5.00000i		−	0.447214i
$6$	5.24321	−	6.67148i	0.356756	−	0.453937i
$7$	2.94025			0.158759			0.0793793	−	0.996844i	$-0.474706\pi$
$7$	2.94025			0.158759			0.0793793	+	0.996844i	$0.474706\pi$
$8$	9.38089	−	20.5912i	0.414581	−	0.910013i
$9$	−9.00000			−0.333333
$10$	−8.73869	+	11.1191i	−0.276342	+	0.351618i
$11$			17.8593i			0.489526i	0.969583	+	0.244763i	$0.0787101\pi$
$11$			17.8593i			0.489526i	−0.969583	+	0.244763i	$0.921290\pi$
$12$	−23.3200	+	5.67247i	−0.560992	+	0.136458i
$13$			46.7050i			0.996434i	0.867052	+	0.498217i	$0.166012\pi$
$13$			46.7050i			0.996434i	−0.867052	+	0.498217i	$0.833988\pi$
$14$	−6.53861	−	5.13879i	−0.124823	−	0.0980999i
$15$	15.0000			0.258199
$16$	−56.8496	+	29.3960i	−0.888275	+	0.459313i
$17$	−21.6786			−0.309284			−0.154642	−	0.987971i	$-0.549422\pi$
$17$	−21.6786			−0.309284			−0.154642	+	0.987971i	$0.549422\pi$
$18$	20.0145	+	15.7296i	0.262081	+	0.205973i
$19$			162.197i			1.95845i	0.202773	+	0.979226i	$0.435005\pi$
$19$			162.197i			1.95845i	−0.202773	+	0.979226i	$0.564995\pi$
$20$	38.8667	−	9.45412i	0.434543	−	0.105700i
$21$			8.82075i			0.0916593i
$22$	31.2134	−	39.7160i	0.302487	−	0.384886i
$23$	160.548			1.45550			0.727751	−	0.685842i	$-0.240566\pi$
$23$	160.548			1.45550			0.727751	+	0.685842i	$0.240566\pi$
$24$	61.7737	+	28.1427i	0.525396	+	0.239358i
$25$	−25.0000			−0.200000
$26$	81.6281	−	103.864i	0.615715	−	0.783438i
$27$		−	27.0000i		−	0.192450i
$28$	5.55949	+	22.8556i	0.0375230	+	0.154260i
$29$			214.174i			1.37142i	0.727876	+	0.685709i	$0.240508\pi$
$29$			214.174i			1.37142i	−0.727876	+	0.685709i	$0.759492\pi$
$30$	−33.3574	−	26.2161i	−0.203007	−	0.159546i
$31$	−1.79631			−0.0104073			−0.00520366	−	0.999986i	$-0.501656\pi$
$31$	−1.79631			−0.0104073			−0.00520366	+	0.999986i	$0.501656\pi$
$32$	177.800	+	33.9865i	0.982217	+	0.187750i
$33$	−53.5779			−0.282628
$34$	48.2094	+	37.8885i	0.243172	+	0.191112i
$35$		−	14.7012i		−	0.0709990i
$36$	−17.0174	−	69.9600i	−0.0787843	−	0.323889i
$37$			163.742i			0.727542i	0.931488	+	0.363771i	$0.118511\pi$
$37$			163.742i			0.727542i	−0.931488	+	0.363771i	$0.881489\pi$
$38$	283.478	−	360.699i	1.21016	−	1.53982i
$39$	−140.115			−0.575291
$40$	−102.956	−	46.9045i	−0.406970	−	0.185406i
$41$	−203.616			−0.775596			−0.387798	−	0.921744i	$-0.626764\pi$
$41$	−203.616			−0.775596			−0.387798	+	0.921744i	$0.626764\pi$
$42$	15.4164	−	19.6158i	0.0566380	−	0.0720664i
$43$		−	62.8357i		−	0.222845i	−0.993773	−	0.111423i	$-0.964459\pi$
$43$		−	62.8357i		−	0.222845i	0.993773	−	0.111423i	$-0.0355407\pi$
$44$	−138.826	+	33.7688i	−0.475656	+	0.115701i
$45$			45.0000i			0.149071i
$46$	−357.031	−	280.596i	−1.14438	−	0.899382i
$47$	10.3285			0.0320546			0.0160273	−	0.999872i	$-0.494898\pi$
$47$	10.3285			0.0320546			0.0160273	+	0.999872i	$0.494898\pi$
$48$	−88.1881	−	170.549i	−0.265184	−	0.512846i
$49$	−334.355			−0.974796
$50$	55.5957	+	43.6935i	0.157248	+	0.123584i
$51$		−	65.0358i		−	0.178565i
$52$	−363.054	+	88.3110i	−0.968202	+	0.235510i
$53$		−	364.051i		−	0.943513i	−0.881729	−	0.471757i	$-0.843620\pi$
$53$		−	364.051i		−	0.943513i	0.881729	−	0.471757i	$-0.156380\pi$
$54$	−47.1889	+	60.0434i	−0.118919	+	0.151312i
$55$	89.2965			0.218923
$56$	27.5822	−	60.5434i	0.0658182	−	0.144472i
$57$	−486.591			−1.13071
$58$	374.320	−	476.286i	0.847425	−	1.07827i
$59$		−	290.985i		−	0.642084i	−0.947065	−	0.321042i	$-0.895967\pi$
$59$		−	290.985i		−	0.642084i	0.947065	−	0.321042i	$-0.104033\pi$
$60$	28.3624	+	116.600i	0.0610261	+	0.250883i
$61$			522.551i			1.09682i	0.836211	+	0.548408i	$0.184766\pi$
$61$			522.551i			1.09682i	−0.836211	+	0.548408i	$0.815234\pi$
$62$	3.99469	+	3.13948i	0.00818268	+	0.00643088i
$63$	−26.4622			−0.0529195
$64$	−335.998	−	386.328i	−0.656246	−	0.754547i
$65$	233.525			0.445619
$66$	119.148	+	93.6401i	0.222214	+	0.174641i
$67$		−	681.913i		−	1.24342i	−0.783249	−	0.621708i	$-0.786439\pi$
$67$		−	681.913i		−	1.24342i	0.783249	−	0.621708i	$-0.213561\pi$
$68$	−40.9904	−	168.515i	−0.0731002	−	0.300521i
$69$			481.643i			0.840334i
$70$	−25.6939	+	32.6930i	−0.0438716	+	0.0558224i
$71$	455.528			0.761426			0.380713	−	0.924693i	$-0.375679\pi$
$71$	455.528			0.761426			0.380713	+	0.924693i	$0.375679\pi$
$72$	−84.4280	+	185.321i	−0.138194	+	0.303338i
$73$	768.573			1.23226			0.616128	−	0.787646i	$-0.288701\pi$
$73$	768.573			1.23226			0.616128	+	0.787646i	$0.288701\pi$
$74$	286.178	−	364.134i	0.449562	−	0.572024i
$75$		−	75.0000i		−	0.115470i
$76$	−1260.81	+	306.686i	−1.90296	+	0.462886i
$77$			52.5108i			0.0777164i
$78$	311.592	+	244.884i	0.452318	+	0.355483i
$79$	1015.12			1.44569			0.722846	−	0.691009i	$-0.242834\pi$
$79$	1015.12			1.44569			0.722846	+	0.691009i	$0.242834\pi$
$80$	146.980	+	284.248i	0.205411	+	0.397248i
$81$	81.0000			0.111111
$82$	452.807	+	355.867i	0.609806	+	0.479256i
$83$		−	274.715i		−	0.363300i	−0.983363	−	0.181650i	$-0.941856\pi$
$83$		−	274.715i		−	0.363300i	0.983363	−	0.181650i	$-0.0581438\pi$
$84$	−68.5667	+	16.6785i	−0.0890623	+	0.0216639i
$85$			108.393i			0.138316i
$86$	−109.820	+	139.736i	−0.137700	+	0.175210i
$87$	−642.522			−0.791788
$88$	367.745	+	167.536i	0.445474	+	0.202948i
$89$	−1572.69			−1.87309			−0.936543	−	0.350553i	$-0.885994\pi$
$89$	−1572.69			−1.87309			−0.936543	+	0.350553i	$0.885994\pi$
$90$	78.6482	−	100.072i	0.0921139	−	0.117206i
$91$			137.324i			0.158192i
$92$	303.568	+	1247.99i	0.344012	+	1.41426i
$93$		−	5.38893i		−	0.00600867i
$94$	−22.9688	−	18.0515i	−0.0252027	−	0.0198072i
$95$	810.986			0.875846
$96$	−101.959	+	533.401i	−0.108398	+	0.567083i
$97$	178.134			0.186462			0.0932308	−	0.995645i	$-0.470281\pi$
$97$	178.134			0.186462			0.0932308	+	0.995645i	$0.470281\pi$
$98$	743.548	+	584.365i	0.766425	+	0.602345i
$99$		−	160.734i		−	0.163175i
$100$	−47.2706	−	194.333i	−0.0472706	−	0.194333i
$101$		−	282.191i		−	0.278010i	−0.990292	−	0.139005i	$-0.955610\pi$
$101$		−	282.191i		−	0.278010i	0.990292	−	0.139005i	$-0.0443904\pi$
$102$	−113.665	+	144.628i	−0.110339	+	0.140395i
$103$	1280.40			1.22487			0.612435	−	0.790521i	$-0.290190\pi$
$103$	1280.40			1.22487			0.612435	+	0.790521i	$0.290190\pi$
$104$	961.714	+	438.135i	0.906767	+	0.413102i
$105$	44.1037			0.0409913
$106$	−636.265	+	809.586i	−0.583014	+	0.741830i
$107$		−	84.8590i		−	0.0766694i	−0.999265	−	0.0383347i	$-0.987795\pi$
$107$		−	84.8590i		−	0.0766694i	0.999265	−	0.0383347i	$-0.0122053\pi$
$108$	209.880	−	51.0522i	0.186997	−	0.0454861i
$109$		−	440.379i		−	0.386979i	−0.981102	−	0.193489i	$-0.938020\pi$
$109$		−	440.379i		−	0.386979i	0.981102	−	0.193489i	$-0.0619805\pi$
$110$	−198.580	−	156.067i	−0.172126	−	0.135276i
$111$	−491.226			−0.420046
$112$	−167.152	+	86.4316i	−0.141021	+	0.0729198i
$113$	−505.336			−0.420691			−0.210345	−	0.977627i	$-0.567459\pi$
$113$	−505.336			−0.420691			−0.210345	+	0.977627i	$0.567459\pi$
$114$	1082.10	+	850.434i	0.889014	+	0.698688i
$115$		−	802.739i		−	0.650920i
$116$	−1664.85	+	404.965i	−1.33256	+	0.324139i
$117$		−	420.345i		−	0.332145i
$118$	−508.565	+	647.100i	−0.396756	+	0.504833i
$119$	−63.7404			−0.0491015
$120$	140.713	−	308.868i	0.107044	−	0.234964i
$121$	1012.05			0.760365
$122$	913.283	−	1162.06i	0.677744	−	0.862364i
$123$		−	610.848i		−	0.447791i
$124$	−3.39651	−	13.9633i	−0.00245980	−	0.0101125i
$125$			125.000i			0.0894427i
$126$	58.8475	+	46.2491i	0.0416075	+	0.0327000i
$127$	−1760.50			−1.23007			−0.615037	−	0.788498i	$-0.710859\pi$
$127$	−1760.50			−1.23007			−0.615037	+	0.788498i	$0.710859\pi$
$128$	72.0006	+	1446.36i	0.0497189	+	0.998763i
$129$	188.507			0.128660
$130$	−519.320	−	408.141i	−0.350364	−	0.275356i
$131$			1984.48i			1.32355i	0.749703	+	0.661774i	$0.230196\pi$
$131$			1984.48i			1.32355i	−0.749703	+	0.661774i	$0.769804\pi$
$132$	−101.306	−	416.479i	−0.0667999	−	0.274620i
$133$			476.900i			0.310921i
$134$	−1191.80	+	1516.46i	−0.768330	+	0.977626i
$135$	−135.000			−0.0860663
$136$	−203.364	+	446.389i	−0.128223	+	0.281452i
$137$	−1675.18			−1.04467			−0.522337	−	0.852739i	$-0.674940\pi$
$137$	−1675.18			−1.04467			−0.522337	+	0.852739i	$0.674940\pi$
$138$	841.787	−	1071.09i	0.519258	−	0.660706i
$139$		−	1903.41i		−	1.16148i	−0.814090	−	0.580739i	$-0.802764\pi$
$139$		−	1903.41i		−	1.16148i	0.814090	−	0.580739i	$-0.197236\pi$
$140$	114.278	−	27.7975i	0.0689874	−	0.0167808i
$141$			30.9855i			0.0185068i
$142$	−1013.02	−	796.144i	−0.598665	−	0.470499i
$143$	−834.119			−0.487780
$144$	511.646	−	264.564i	0.296092	−	0.153104i
$145$	1070.87			0.613317
$146$	−1709.17	−	1343.26i	−0.968851	−	0.761433i
$147$		−	1003.06i		−	0.562799i
$148$	−1272.82	+	309.607i	−0.706928	+	0.171957i
$149$		−	2678.70i		−	1.47280i	−0.676544	−	0.736402i	$-0.736523\pi$
$149$		−	2678.70i		−	1.47280i	0.676544	−	0.736402i	$-0.263477\pi$
$150$	−131.080	+	166.787i	−0.0713511	+	0.0907874i
$151$	2693.58			1.45166			0.725829	−	0.687875i	$-0.241456\pi$
$151$	2693.58			1.45166			0.725829	+	0.687875i	$0.241456\pi$
$152$	3339.84	+	1521.55i	1.78222	+	0.811936i
$153$	195.107			0.103095
$154$	91.7751	−	116.775i	0.0480224	−	0.0611039i
$155$			8.98156i			0.00465430i
$156$	−264.933	−	1089.16i	−0.135972	−	0.558992i
$157$			1110.97i			0.564745i	0.959305	+	0.282372i	$0.0911213\pi$
$157$			1110.97i			0.564745i	−0.959305	+	0.282372i	$0.908879\pi$
$158$	−2257.45	−	1774.16i	−1.13666	−	0.893320i
$159$	1092.15			0.544738
$160$	169.932	−	889.001i	0.0839645	−	0.439261i
$161$	472.051			0.231073
$162$	−180.130	−	141.567i	−0.0873602	−	0.0686576i
$163$			3368.46i			1.61864i	0.587368	+	0.809320i	$0.300164\pi$
$163$			3368.46i			1.61864i	−0.587368	+	0.809320i	$0.699836\pi$
$164$	−385.002	−	1582.77i	−0.183314	−	0.753622i
$165$			267.890i			0.126395i
$166$	−480.130	+	610.920i	−0.224490	+	0.285642i
$167$	−1734.65			−0.803779			−0.401889	−	0.915688i	$-0.631646\pi$
$167$	−1734.65			−0.803779			−0.401889	+	0.915688i	$0.631646\pi$
$168$	181.630	+	82.7465i	0.0834111	+	0.0380002i
$169$	15.6411			0.00711928
$170$	189.442	−	241.047i	0.0854681	−	0.108750i
$171$		−	1459.77i		−	0.652817i
$172$	488.443	−	118.811i	0.216531	−	0.0526701i
$173$		−	4013.33i		−	1.76374i	−0.471489	−	0.881872i	$-0.656283\pi$
$173$		−	4013.33i		−	1.76374i	0.471489	−	0.881872i	$-0.343717\pi$
$174$	1428.86	+	1122.96i	0.622537	+	0.489261i
$175$	−73.5062			−0.0317517
$176$	−524.992	−	1015.29i	−0.224845	−	0.434833i
$177$	872.954			0.370707
$178$	3497.39	+	2748.65i	1.47270	+	1.15741i
$179$			3881.48i			1.62076i	0.585906	+	0.810379i	$0.300739\pi$
$179$			3881.48i			1.62076i	−0.585906	+	0.810379i	$0.699261\pi$
$180$	−349.800	+	85.0871i	−0.144848	+	0.0352334i
$181$			733.629i			0.301272i	0.988589	+	0.150636i	$0.0481321\pi$
$181$			733.629i			0.301272i	−0.988589	+	0.150636i	$0.951868\pi$
$182$	240.007	−	305.386i	0.0977500	−	0.124378i
$183$	−1567.65			−0.633248
$184$	1506.08	−	3305.88i	0.603423	−	1.32452i
$185$	818.711			0.325366
$186$	−9.41844	+	11.9841i	−0.00371287	+	0.00472427i
$187$		−	387.164i		−	0.151402i
$188$	19.5294	+	80.2870i	0.00757621	+	0.0311465i
$189$		−	79.3867i		−	0.0305531i
$190$	−1803.49	−	1417.39i	−0.688627	−	0.541202i
$191$	21.6852			0.00821512			0.00410756	−	0.999992i	$-0.498693\pi$
$191$	21.6852			0.00821512			0.00410756	+	0.999992i	$0.498693\pi$
$192$	1158.98	−	1007.99i	0.435638	−	0.378884i
$193$	1319.65			0.492179			0.246089	−	0.969247i	$-0.420854\pi$
$193$	1319.65			0.492179			0.246089	+	0.969247i	$0.420854\pi$
$194$	−396.139	−	311.332i	−0.146604	−	0.115218i
$195$			700.575i			0.257278i
$196$	−632.206	−	2599.05i	−0.230396	−	0.947177i
$197$			2620.65i			0.947784i	0.880583	+	0.473892i	$0.157151\pi$
$197$			2620.65i			0.947784i	−0.880583	+	0.473892i	$0.842849\pi$
$198$	−280.920	+	357.444i	−0.100829	+	0.128295i
$199$	−3324.94			−1.18442			−0.592209	−	0.805785i	$-0.701744\pi$
$199$	−3324.94			−1.18442			−0.592209	+	0.805785i	$0.701744\pi$
$200$	−234.522	+	514.781i	−0.0829162	+	0.182003i
$201$	2045.74			0.717887
$202$	−493.195	+	627.543i	−0.171788	+	0.218583i
$203$			629.725i			0.217724i
$204$	505.545	−	122.971i	0.173506	−	0.0422044i
$205$			1018.08i			0.346857i
$206$	−2847.39	−	2237.80i	−0.963044	−	0.756870i
$207$	−1444.93			−0.485167
$208$	−1372.94	−	2655.16i	−0.457675	−	0.885107i
$209$	−2896.73			−0.958712
$210$	−98.0791	−	77.0818i	−0.0322291	−	0.0253293i
$211$			187.219i			0.0610840i	0.999533	+	0.0305420i	$0.00972333\pi$
$211$			187.219i			0.0610840i	−0.999533	+	0.0305420i	$0.990277\pi$
$212$	2829.89	−	688.356i	0.916781	−	0.223002i
$213$			1366.58i			0.439609i
$214$	−148.311	+	188.712i	−0.0473755	+	0.0602807i
$215$	−314.178			−0.0996594
$216$	−555.963	−	253.284i	−0.175132	−	0.0797861i
$217$	−5.28160			−0.00165225
$218$	−769.668	+	979.328i	−0.239121	+	0.304259i
$219$			2305.72i			0.711443i
$220$	168.844	+	694.132i	0.0517430	+	0.212720i
$221$		−	1012.50i		−	0.308181i
$222$	1092.40	+	858.535i	0.330258	+	0.259554i
$223$	−3512.67			−1.05482			−0.527412	−	0.849610i	$-0.676838\pi$
$223$	−3512.67			−1.05482			−0.527412	+	0.849610i	$0.676838\pi$
$224$	522.777	+	99.9287i	0.155935	+	0.0298070i
$225$	225.000			0.0666667
$226$	1123.78	+	883.196i	0.330765	+	0.259953i
$227$			1976.34i			0.577862i	0.957350	+	0.288931i	$0.0932998\pi$
$227$			1976.34i			0.577862i	−0.957350	+	0.288931i	$0.906700\pi$
$228$	−920.059	−	3782.44i	−0.267247	−	1.09868i
$229$		−	3669.36i		−	1.05886i	−0.848354	−	0.529429i	$-0.822406\pi$
$229$		−	3669.36i		−	1.05886i	0.848354	−	0.529429i	$-0.177594\pi$
$230$	−1402.98	+	1785.15i	−0.402216	+	0.511781i
$231$	−157.532			−0.0448696
$232$	4410.11	+	2009.14i	1.24801	+	0.568563i
$233$	−3950.24			−1.11068			−0.555341	−	0.831623i	$-0.687412\pi$
$233$	−3950.24			−1.11068			−0.555341	+	0.831623i	$0.687412\pi$
$234$	−734.653	+	934.775i	−0.205238	+	0.261146i
$235$		−	51.6426i		−	0.0143353i
$236$	2261.92	−	550.200i	0.623892	−	0.151758i
$237$			3045.35i			0.834671i
$238$	141.748	+	111.402i	0.0386056	+	0.0303407i
$239$	2706.48			0.732499			0.366250	−	0.930517i	$-0.380642\pi$
$239$	2706.48			0.732499			0.366250	+	0.930517i	$0.380642\pi$
$240$	−852.744	+	440.940i	−0.229352	+	0.118594i
$241$	7437.22			1.98786			0.993928	−	0.110029i	$-0.0350945\pi$
$241$	7437.22			1.98786			0.993928	+	0.110029i	$0.0350945\pi$
$242$	−2250.61	−	1768.79i	−0.597831	−	0.469844i
$243$			243.000i			0.0641500i
$244$	−4061.97	+	988.052i	−1.06574	+	0.259236i
$245$			1671.77i			0.435942i
$246$	−1067.60	+	1358.42i	−0.276698	+	0.352072i
$247$	−7575.42			−1.95147
$248$	−16.8510	+	36.9883i	−0.00431468	+	0.00947079i
$249$	824.146			0.209751
$250$	218.467	−	277.979i	0.0552683	−	0.0703236i
$251$			4230.91i			1.06395i	0.846759	+	0.531977i	$0.178551\pi$
$251$			4230.91i			1.06395i	−0.846759	+	0.531977i	$0.821449\pi$
$252$	−50.0354	−	205.700i	−0.0125077	−	0.0514202i
$253$			2867.27i			0.712505i
$254$	3915.06	+	3076.90i	0.967136	+	0.760086i
$255$	−325.179			−0.0798568
$256$	2367.75	−	3342.30i	0.578063	−	0.815992i
$257$	6002.97			1.45702			0.728511	−	0.685034i	$-0.240213\pi$
$257$	6002.97			1.45702			0.728511	+	0.685034i	$0.240213\pi$
$258$	−419.207	−	329.461i	−0.101158	−	0.0795013i
$259$			481.443i			0.115503i
$260$	441.555	+	1815.27i	0.105323	+	0.432993i
$261$		−	1927.57i		−	0.457139i
$262$	3468.35	−	4413.14i	0.817846	−	1.04063i
$263$	3518.76			0.825004			0.412502	−	0.910957i	$-0.364655\pi$
$263$	3518.76			0.825004			0.412502	+	0.910957i	$0.364655\pi$
$264$	−502.609	+	1103.24i	−0.117172	+	0.257195i
$265$	−1820.25			−0.421952
$266$	833.496	−	1060.54i	0.192124	−	0.244459i
$267$		−	4718.06i		−	1.08143i
$268$	5300.74	−	1289.38i	1.20819	−	0.293885i
$269$			619.760i			0.140474i	0.997530	+	0.0702368i	$0.0223755\pi$
$269$			619.760i			0.140474i	−0.997530	+	0.0702368i	$0.977625\pi$
$270$	300.217	+	235.945i	0.0676689	+	0.0531820i
$271$	3575.48			0.801457			0.400728	−	0.916197i	$-0.368757\pi$
$271$	3575.48			0.801457			0.400728	+	0.916197i	$0.368757\pi$
$272$	1232.42	−	637.264i	0.274729	−	0.142058i
$273$	−411.973			−0.0913324
$274$	3725.31	+	2927.78i	0.821366	+	0.645523i
$275$		−	446.483i		−	0.0979051i
$276$	−3743.98	+	910.703i	−0.816525	+	0.198615i
$277$		−	170.064i		−	0.0368886i	−0.999830	−	0.0184443i	$-0.994129\pi$
$277$		−	170.064i		−	0.0368886i	0.999830	−	0.0184443i	$-0.00587134\pi$
$278$	−3326.67	+	4232.87i	−0.717699	+	0.913203i
$279$	16.1668			0.00346911
$280$	−302.717	−	137.911i	−0.0646100	−	0.0294348i
$281$	2940.17			0.624184			0.312092	−	0.950052i	$-0.398970\pi$
$281$	2940.17			0.624184			0.312092	+	0.950052i	$0.398970\pi$
$282$	54.1546	−	68.9065i	0.0114357	−	0.0145508i
$283$			3031.88i			0.636843i	0.947949	+	0.318422i	$0.103153\pi$
$283$			3031.88i			0.636843i	−0.947949	+	0.318422i	$0.896847\pi$
$284$	861.323	+	3540.97i	0.179965	+	0.739853i
$285$			2432.96i			0.505670i
$286$	1854.94	+	1457.82i	0.383513	+	0.301408i
$287$	−598.681			−0.123133
$288$	−1600.20	−	305.878i	−0.327406	−	0.0625835i
$289$	−4443.04			−0.904343
$290$	−2381.43	−	1871.60i	−0.482215	−	0.378980i
$291$			534.402i			0.107654i
$292$	1453.24	+	5974.37i	0.291247	+	1.19734i
$293$		−	7805.49i		−	1.55632i	−0.628067	−	0.778159i	$-0.716154\pi$
$293$		−	7805.49i		−	1.55632i	0.628067	−	0.778159i	$-0.283846\pi$
$294$	−1753.09	+	2230.64i	−0.347764	+	0.442496i
$295$	−1454.92			−0.287149
$296$	3371.65	+	1536.05i	0.662072	+	0.301625i
$297$	482.201			0.0942093
$298$	−4681.67	+	5956.97i	−0.910073	+	1.15798i
$299$			7498.39i			1.45031i
$300$	583.000	−	141.812i	0.112198	−	0.0272917i
$301$		−	184.752i		−	0.0353786i
$302$	−5990.06	−	4707.67i	−1.14136	−	0.897007i
$303$	846.572			0.160509
$304$	−4767.95	−	9220.84i	−0.899542	−	1.73964i
$305$	2612.76			0.490511
$306$	−433.885	−	340.996i	−0.0810574	−	0.0637041i
$307$		−	7999.54i		−	1.48716i	−0.668647	−	0.743580i	$-0.733126\pi$
$307$		−	7999.54i		−	1.48716i	0.668647	−	0.743580i	$-0.266874\pi$
$308$	−408.184	+	99.2887i	−0.0755145	+	0.0183685i
$309$			3841.20i			0.707179i
$310$	15.6974	−	19.9734i	0.00287598	−	0.00365940i
$311$	7248.12			1.32155			0.660777	−	0.750582i	$-0.270227\pi$
$311$	7248.12			1.32155			0.660777	+	0.750582i	$0.270227\pi$
$312$	−1314.40	+	2885.14i	−0.238505	+	0.523522i
$313$	−6711.86			−1.21207			−0.606033	−	0.795440i	$-0.707240\pi$
$313$	−6711.86			−1.21207			−0.606033	+	0.795440i	$0.707240\pi$
$314$	1941.68	−	2470.60i	0.348966	−	0.444026i
$315$			132.311i			0.0236663i
$316$	1919.41	+	7890.86i	0.341694	+	1.40473i
$317$		−	4006.43i		−	0.709854i	−0.934894	−	0.354927i	$-0.884506\pi$
$317$		−	4006.43i		−	0.709854i	0.934894	−	0.354927i	$-0.115494\pi$
$318$	−2428.76	−	1908.80i	−0.428296	−	0.336604i
$319$	−3825.00			−0.671344
$320$	−1931.64	+	1679.99i	−0.337444	+	0.293482i
$321$	254.577			0.0442651
$322$	−1049.76	−	825.021i	−0.181680	−	0.142785i
$323$		−	3516.20i		−	0.605718i
$324$	153.157	+	629.640i	0.0262614	+	0.107963i
$325$		−	1167.63i		−	0.199287i
$326$	5887.19	−	7490.88i	1.00019	−	1.27264i
$327$	1321.14			0.223422
$328$	−1910.10	+	4192.70i	−0.321547	+	0.705802i
$329$	30.3684			0.00508895
$330$	468.201	−	595.740i	0.0781018	−	0.0993770i
$331$		−	6182.22i		−	1.02660i	−0.858208	−	0.513302i	$-0.828422\pi$
$331$		−	6182.22i		−	1.02660i	0.858208	−	0.513302i	$-0.171578\pi$
$332$	2135.45	−	519.438i	0.353007	−	0.0858671i
$333$		−	1473.68i		−	0.242514i
$334$	3857.56	+	3031.71i	0.631965	+	0.496670i
$335$	−3409.56			−0.556073
$336$	−259.295	−	501.456i	−0.0421003	−	0.0814186i
$337$	7794.12			1.25986			0.629930	−	0.776652i	$-0.283084\pi$
$337$	7794.12			1.25986			0.629930	+	0.776652i	$0.283084\pi$
$338$	−34.7830	−	27.3365i	−0.00559748	−	0.00439914i
$339$		−	1516.01i		−	0.242886i
$340$	−842.575	+	204.952i	−0.134397	+	0.0326914i
$341$		−	32.0809i		−	0.00509465i
$342$	−2551.30	+	3246.29i	−0.403388	+	0.513272i
$343$	−1991.59			−0.313516
$344$	−1293.86	−	589.454i	−0.202792	−	0.0923874i
$345$	2408.22			0.375809
$346$	−7014.24	+	8924.95i	−1.08985	+	1.38673i
$347$		−	12357.0i		−	1.91170i	−0.293860	−	0.955849i	$-0.594940\pi$
$347$		−	12357.0i		−	1.91170i	0.293860	−	0.955849i	$-0.405060\pi$
$348$	−1214.90	−	4994.54i	−0.187142	−	0.769355i
$349$		−	12912.3i		−	1.98045i	−0.139469	−	0.990226i	$-0.544539\pi$
$349$		−	12912.3i		−	1.98045i	0.139469	−	0.990226i	$-0.455461\pi$
$350$	163.465	+	128.470i	0.0249645	+	0.0196200i
$351$	1261.04			0.191764
$352$	−606.974	+	3175.39i	−0.0919087	+	0.480820i
$353$	1085.49			0.163669			0.0818343	−	0.996646i	$-0.473922\pi$
$353$	1085.49			0.163669			0.0818343	+	0.996646i	$0.473922\pi$
$354$	−1941.30	−	1525.69i	−0.291466	−	0.229067i
$355$		−	2277.64i		−	0.340520i
$356$	−2973.68	−	12225.0i	−0.442709	−	1.82002i
$357$		−	191.221i		−	0.0283488i
$358$	6783.82	−	8631.75i	1.00150	−	1.27431i
$359$	12270.1			1.80387			0.901936	−	0.431869i	$-0.142146\pi$
$359$	12270.1			1.80387			0.901936	+	0.431869i	$0.142146\pi$
$360$	926.605	+	422.140i	0.135657	+	0.0618021i
$361$	−19448.9			−2.83553
$362$	1282.19	−	1631.46i	0.186161	−	0.236873i
$363$			3036.14i			0.438997i
$364$	−1067.47	+	259.656i	−0.153710	+	0.0373892i
$365$		−	3842.86i		−	0.551081i
$366$	3486.19	+	2739.85i	0.497886	+	0.391296i
$367$	2883.50			0.410130			0.205065	−	0.978748i	$-0.434259\pi$
$367$	2883.50			0.410130			0.205065	+	0.978748i	$0.434259\pi$
$368$	−9127.07	+	4719.47i	−1.29288	+	0.668531i
$369$	1832.54			0.258532
$370$	−1820.67	−	1430.89i	−0.255817	−	0.201050i
$371$		−	1070.40i		−	0.149791i
$372$	41.8900	−	10.1895i	0.00583843	−	0.00142017i
$373$			10056.9i			1.39605i	0.716071	+	0.698027i	$0.245939\pi$
$373$			10056.9i			1.39605i	−0.716071	+	0.698027i	$0.754061\pi$
$374$	−676.662	+	860.987i	−0.0935544	+	0.119039i
$375$	−375.000			−0.0516398
$376$	96.8907	−	212.677i	0.0132892	−	0.0291701i
$377$	−10003.0			−1.36653
$378$	−138.747	+	176.542i	−0.0188793	+	0.0240221i
$379$			3683.45i			0.499225i	0.968346	+	0.249612i	$0.0803032\pi$
$379$			3683.45i			0.499225i	−0.968346	+	0.249612i	$0.919697\pi$
$380$	1533.43	+	6304.07i	0.207009	+	0.851031i
$381$		−	5281.51i		−	0.710184i
$382$	−48.2242	−	37.9001i	−0.00645908	−	0.00507628i
$383$	7961.76			1.06221			0.531105	−	0.847306i	$-0.321777\pi$
$383$	7961.76			1.06221			0.531105	+	0.847306i	$0.321777\pi$
$384$	−4339.09	+	216.002i	−0.576636	+	0.0287052i
$385$	262.554			0.0347558
$386$	−2934.67	−	2306.40i	−0.386971	−	0.304126i
$387$			565.521i			0.0742818i
$388$	336.820	+	1384.70i	0.0440707	+	0.181179i
$389$		−	6298.86i		−	0.820989i	−0.911863	−	0.410495i	$-0.865356\pi$
$389$		−	6298.86i		−	0.820989i	0.911863	−	0.410495i	$-0.134644\pi$
$390$	1224.42	−	1557.96i	0.158977	−	0.202283i
$391$	−3480.45			−0.450163
$392$	−3136.55	+	6884.78i	−0.404132	+	0.887076i
$393$	−5953.44			−0.764151
$394$	4580.21	−	5827.87i	0.585654	−	0.745188i
$395$		−	5075.59i		−	0.646533i
$396$	1249.44	−	303.919i	0.158552	−	0.0385669i
$397$			7320.36i			0.925436i	0.886505	+	0.462718i	$0.153126\pi$
$397$			7320.36i			0.925436i	−0.886505	+	0.462718i	$0.846874\pi$
$398$	7394.10	+	5811.13i	0.931239	+	0.731874i
$399$	−1430.70			−0.179510
$400$	1421.24	−	734.901i	0.177655	−	0.0918626i
$401$	−2292.02			−0.285432			−0.142716	−	0.989764i	$-0.545583\pi$
$401$	−2292.02			−0.285432			−0.142716	+	0.989764i	$0.545583\pi$
$402$	−4549.37	−	3575.41i	−0.564433	−	0.443596i
$403$		−	83.8968i		−	0.0103702i
$404$	2193.56	−	533.573i	0.270133	−	0.0657085i
$405$		−	405.000i		−	0.0496904i
$406$	1100.59	−	1400.40i	0.134536	−	0.171184i
$407$	−2924.32			−0.356150
$408$	−1339.17	−	610.093i	−0.162497	−	0.0740297i
$409$	−7748.03			−0.936712			−0.468356	−	0.883540i	$-0.655154\pi$
$409$	−7748.03			−0.936712			−0.468356	+	0.883540i	$0.655154\pi$
$410$	1779.34	−	2264.03i	0.214330	−	0.272714i
$411$		−	5025.54i		−	0.603142i
$412$	2421.01	+	9952.99i	0.289502	+	1.19017i
$413$		−	855.567i		−	0.101936i
$414$	3213.28	+	2525.36i	0.381459	+	0.299794i
$415$	−1373.58			−0.162473
$416$	−1587.34	+	8304.16i	−0.187081	+	0.978714i
$417$	5710.24			0.670580
$418$	6441.83	+	5062.72i	0.753780	+	0.592406i
$419$			4998.52i			0.582801i	0.956601	+	0.291401i	$0.0941213\pi$
$419$			4998.52i			0.582801i	−0.956601	+	0.291401i	$0.905879\pi$
$420$	83.3924	+	342.833i	0.00968841	+	0.0398299i
$421$			3795.98i			0.439441i	0.975563	+	0.219720i	$0.0705145\pi$
$421$			3795.98i			0.439441i	−0.975563	+	0.219720i	$0.929485\pi$
$422$	327.211	−	416.344i	0.0377449	−	0.0480268i
$423$	−92.9566			−0.0106849
$424$	−7496.25	−	3415.12i	−0.858609	−	0.391162i
$425$	541.965			0.0618568
$426$	2388.43	−	3039.05i	0.271643	−	0.345639i
$427$			1536.43i			0.174129i
$428$	659.638	−	160.453i	0.0744972	−	0.0181210i
$429$		−	2502.36i		−	0.281620i
$430$	698.678	+	549.101i	0.0783564	+	0.0615814i
$431$	−8423.43			−0.941398			−0.470699	−	0.882294i	$-0.655998\pi$
$431$	−8423.43			−0.941398			−0.470699	+	0.882294i	$0.655998\pi$
$432$	793.693	+	1534.94i	0.0883948	+	0.170949i
$433$	−2521.08			−0.279805			−0.139902	−	0.990165i	$-0.544679\pi$
$433$	−2521.08			−0.279805			−0.139902	+	0.990165i	$0.544679\pi$
$434$	11.7454	+	9.23086i	0.00129907	+	0.00102096i
$435$			3212.61i			0.354099i
$436$	3423.22	−	832.679i	0.376015	−	0.0914636i
$437$			26040.4i			2.85053i
$438$	4029.79	−	5127.52i	0.439614	−	0.559366i
$439$	10195.5			1.10844			0.554220	−	0.832370i	$-0.313017\pi$
$439$	10195.5			1.10844			0.554220	+	0.832370i	$0.313017\pi$
$440$	837.681	−	1838.73i	0.0907611	−	0.199222i
$441$	3009.19			0.324932
$442$	−1769.58	+	2251.62i	−0.190431	+	0.242305i
$443$		−	8694.08i		−	0.932434i	−0.884670	−	0.466217i	$-0.845617\pi$
$443$		−	8694.08i		−	0.932434i	0.884670	−	0.466217i	$-0.154383\pi$
$444$	−928.822	−	3818.47i	−0.0992792	−	0.408145i
$445$			7863.44i			0.837669i
$446$	7811.57	+	6139.23i	0.829347	+	0.651795i
$447$	8036.10			0.850324
$448$	−987.917	−	1135.90i	−0.104185	−	0.119791i
$449$	10748.7			1.12976			0.564878	−	0.825174i	$-0.308923\pi$
$449$	10748.7			1.12976			0.564878	+	0.825174i	$0.308923\pi$
$450$	−500.361	−	393.241i	−0.0524161	−	0.0411946i
$451$		−	3636.44i		−	0.379674i
$452$	−955.502	−	3928.15i	−0.0994315	−	0.408771i
$453$			8080.74i			0.838116i
$454$	3454.13	−	4395.05i	0.357072	−	0.454339i
$455$	686.622			0.0707458
$456$	−4564.66	+	10019.5i	−0.468772	+	1.02896i
$457$	15551.7			1.59185			0.795925	−	0.605395i	$-0.206985\pi$
$457$	15551.7			1.59185			0.795925	+	0.605395i	$0.206985\pi$
$458$	−6413.09	+	8160.03i	−0.654288	+	0.832518i
$459$			585.322i			0.0595217i
$460$	6239.96	−	1517.84i	0.632478	−	0.153847i
$461$			16031.5i			1.61966i	0.586668	+	0.809828i	$0.300440\pi$
$461$			16031.5i			1.61966i	−0.586668	+	0.809828i	$0.699560\pi$
$462$	350.325	+	275.325i	0.0352783	+	0.0277257i
$463$	16487.8			1.65498			0.827488	−	0.561484i	$-0.189769\pi$
$463$	16487.8			1.65498			0.827488	+	0.561484i	$0.189769\pi$
$464$	−6295.86	−	12175.7i	−0.629910	−	1.21820i
$465$	−26.9447			−0.00268716
$466$	8784.65	+	6903.98i	0.873264	+	0.686311i
$467$			3578.77i			0.354616i	0.984155	+	0.177308i	$0.0567389\pi$
$467$			3578.77i			0.354616i	−0.984155	+	0.177308i	$0.943261\pi$
$468$	3267.49	−	794.799i	0.322734	−	0.0785034i
$469$		−	2004.99i		−	0.197403i
$470$	−90.2577	+	114.844i	−0.00885803	+	0.0112710i
$471$	−3332.90			−0.326055
$472$	−5991.73	−	2729.69i	−0.584305	−	0.266196i
$473$	1122.20			0.109088
$474$	5322.48	−	6772.34i	0.515759	−	0.656253i
$475$		−	4054.93i		−	0.391690i
$476$	−120.522	−	495.476i	−0.0116053	−	0.0477103i
$477$			3276.46i			0.314504i
$478$	−6018.74	−	4730.21i	−0.575922	−	0.452625i
$479$	−7375.39			−0.703529			−0.351764	−	0.936089i	$-0.614418\pi$
$479$	−7375.39			−0.703529			−0.351764	+	0.936089i	$0.614418\pi$
$480$	2667.00	+	509.797i	0.253607	+	0.0484770i
$481$	−7647.58			−0.724947
$482$	−16539.1	−	12998.3i	−1.56294	−	1.22833i
$483$			1416.15i			0.133410i
$484$	1913.60	+	7866.97i	0.179714	+	0.738821i
$485$		−	890.670i		−	0.0833881i
$486$	424.700	−	540.390i	0.0396395	−	0.0504374i
$487$	−3961.33			−0.368594			−0.184297	−	0.982871i	$-0.559001\pi$
$487$	−3961.33			−0.368594			−0.184297	+	0.982871i	$0.559001\pi$
$488$	10760.0	+	4902.00i	0.998117	+	0.454719i
$489$	−10105.4			−0.934522
$490$	2921.82	−	3717.74i	0.269377	−	0.342756i
$491$			18035.1i			1.65766i	0.559498	+	0.828832i	$0.310994\pi$
$491$			18035.1i			1.65766i	−0.559498	+	0.828832i	$0.689006\pi$
$492$	4748.32	−	1155.00i	0.435104	−	0.105837i
$493$		−	4642.99i		−	0.424158i
$494$	16846.4	+	13239.9i	1.53433	+	1.20585i
$495$	−803.669			−0.0729742
$496$	102.120	−	52.8044i	0.00924456	−	0.00478022i
$497$	1339.37			0.120883
$498$	−1832.76	−	1440.39i	−0.164915	−	0.129609i
$499$		−	100.386i		−	0.00900581i	−0.999990	−	0.00450290i	$-0.998567\pi$
$499$		−	100.386i		−	0.00900581i	0.999990	−	0.00450290i	$-0.00143332\pi$
$500$	−971.667	+	236.353i	−0.0869086	+	0.0211401i
$501$		−	5203.94i		−	0.464062i
$502$	7394.51	−	9408.81i	0.657437	−	0.836525i
$503$	188.469			0.0167066			0.00835331	−	0.999965i	$-0.497341\pi$
$503$	188.469			0.0167066			0.00835331	+	0.999965i	$0.497341\pi$
$504$	−248.239	+	544.890i	−0.0219394	+	0.0481574i
$505$	−1410.95			−0.124330
$506$	5011.24	−	6376.32i	0.440270	−	0.560202i
$507$			46.9232i			0.00411032i
$508$	−3328.80	−	13685.0i	−0.290732	−	1.19522i
$509$			14790.1i			1.28794i	0.765051	+	0.643969i	$0.222714\pi$
$509$			14790.1i			1.28794i	−0.765051	+	0.643969i	$0.777286\pi$
$510$	723.142	+	568.327i	0.0627868	+	0.0493450i
$511$	2259.79			0.195631
$512$	−11106.9	+	3294.50i	−0.958714	+	0.284371i
$513$	4379.32			0.376904
$514$	−13349.6	−	10491.6i	−1.14557	−	0.900321i
$515$		−	6402.00i		−	0.547779i
$516$	356.433	+	1465.33i	0.0304091	+	0.125014i
$517$			184.460i			0.0156916i
$518$	841.436	−	1070.65i	0.0713717	−	0.0908137i
$519$	12040.0			1.01830
$520$	2190.67	−	4808.57i	0.184745	−	0.405519i
$521$	−20291.3			−1.70630			−0.853148	−	0.521669i	$-0.825310\pi$
$521$	−20291.3			−1.70630			−0.853148	+	0.521669i	$0.825310\pi$
$522$	−3368.88	+	4286.58i	−0.282475	+	0.359422i
$523$			19968.5i			1.66953i	0.550608	+	0.834764i	$0.314396\pi$
$523$			19968.5i			1.66953i	−0.550608	+	0.834764i	$0.685604\pi$
$524$	−15426.0	+	3752.30i	−1.28605	+	0.312825i
$525$		−	220.519i		−	0.0183319i
$526$	−7825.12	−	6149.87i	−0.648653	−	0.509785i
$527$	38.9415			0.00321882
$528$	3045.88	−	1574.98i	0.251051	−	0.129815i
$529$	13608.6			1.11848
$530$	4047.93	+	3181.33i	0.331756	+	0.260732i
$531$			2618.86i			0.214028i
$532$	−3707.11	+	901.734i	−0.302112	+	0.0734871i
$533$		−	9509.88i		−	0.772831i
$534$	−8245.94	+	10492.2i	−0.668234	+	0.850263i
$535$	−424.295			−0.0342876
$536$	−14041.4	−	6396.95i	−1.13152	−	0.515496i
$537$	−11644.4			−0.935745
$538$	1083.18	−	1378.24i	0.0868013	−	0.110446i
$539$		−	5971.35i		−	0.477188i
$540$	−255.261	−	1049.40i	−0.0203420	−	0.0836278i
$541$		−	5128.95i		−	0.407598i	−0.979013	−	0.203799i	$-0.934671\pi$
$541$		−	5128.95i		−	0.407598i	0.979013	−	0.203799i	$-0.0653290\pi$
$542$	−7951.25	−	6249.00i	−0.630139	−	0.495235i
$543$	−2200.89			−0.173939
$544$	−3854.46	−	736.778i	−0.303784	−	0.0580682i
$545$	−2201.90			−0.173062
$546$	916.158	+	720.021i	0.0718094	+	0.0564360i
$547$		−	3129.68i		−	0.244635i	−0.992491	−	0.122318i	$-0.960967\pi$
$547$		−	3129.68i		−	0.244635i	0.992491	−	0.122318i	$-0.0390326\pi$
$548$	−3167.47	−	13021.7i	−0.246912	−	1.01507i
$549$		−	4702.96i		−	0.365606i
$550$	−780.335	+	992.901i	−0.0604974	+	0.0769771i
$551$	−34738.4			−2.68585
$552$	9917.63	+	4518.25i	0.764715	+	0.348386i
$553$	2984.70			0.229516
$554$	−297.227	+	378.193i	−0.0227942	+	0.0290034i
$555$			2456.13i			0.187850i
$556$	14795.9	−	3599.02i	1.12857	−	0.274519i
$557$			5331.08i			0.405539i	0.979226	+	0.202770i	$0.0649942\pi$
$557$			5331.08i			0.405539i	−0.979226	+	0.202770i	$0.935006\pi$
$558$	−35.9522	−	28.2553i	−0.00272756	−	0.00214363i
$559$	2934.74			0.222051
$560$	432.158	+	835.760i	0.0326107	+	0.0630666i
$561$	1161.49			0.0874123
$562$	−6538.43	−	5138.65i	−0.490760	−	0.385695i
$563$		−	10623.7i		−	0.795270i	−0.917544	−	0.397635i	$-0.869831\pi$
$563$		−	10623.7i		−	0.795270i	0.917544	−	0.397635i	$-0.130169\pi$
$564$	−240.861	+	58.5882i	−0.0179824	+	0.00437413i
$565$			2526.68i			0.188139i
$566$	5298.93	−	6742.38i	0.393517	−	0.500713i
$567$	238.160			0.0176398
$568$	4273.26	−	9379.88i	0.315673	−	0.692907i
$569$	−24063.9			−1.77296			−0.886478	−	0.462771i	$-0.846855\pi$
$569$	−24063.9			−1.77296			−0.886478	+	0.462771i	$0.846855\pi$
$570$	4252.17	−	5410.48i	0.312463	−	0.397579i
$571$		−	7975.08i		−	0.584495i	−0.956343	−	0.292248i	$-0.905597\pi$
$571$		−	7975.08i		−	0.584495i	0.956343	−	0.292248i	$-0.0944031\pi$
$572$	−1577.17	−	6483.89i	−0.115288	−	0.473960i
$573$			65.0557i			0.00474300i
$574$	1331.36	+	1046.34i	0.0968120	+	0.0760859i
$575$	−4013.70			−0.291100
$576$	3023.98	+	3476.95i	0.218749	+	0.251516i
$577$	9639.60			0.695497			0.347749	−	0.937588i	$-0.386946\pi$
$577$	9639.60			0.695497			0.347749	+	0.937588i	$0.386946\pi$
$578$	9880.56	+	7765.27i	0.711033	+	0.558811i
$579$			3958.95i			0.284159i
$580$	2024.83	+	8324.23i	0.144959	+	0.595940i
$581$		−	807.731i		−	0.0576770i
$582$	933.995	−	1188.42i	0.0665212	−	0.0846418i
$583$	6501.69			0.461874
$584$	7209.90	−	15825.9i	0.510869	−	1.12137i
$585$	−2101.73			−0.148540
$586$	−13641.9	+	17358.1i	−0.961679	+	1.22364i
$587$		−	3045.07i		−	0.214111i	−0.994253	−	0.107056i	$-0.965858\pi$
$587$		−	3045.07i		−	0.214111i	0.994253	−	0.107056i	$-0.0341423\pi$
$588$	7797.16	−	1896.62i	0.546853	−	0.133019i
$589$		−	291.357i		−	0.0203822i
$590$	3235.50	+	2542.82i	0.225768	+	0.177435i
$591$	−7861.95			−0.547204
$592$	−4813.37	−	9308.67i	−0.334169	−	0.646257i
$593$	19029.4			1.31778			0.658890	−	0.752239i	$-0.271026\pi$
$593$	19029.4			1.31778			0.658890	+	0.752239i	$0.271026\pi$
$594$	−1072.33	−	842.761i	−0.0740713	−	0.0582137i
$595$			318.702i			0.0219589i
$596$	20822.5	−	5064.95i	1.43108	−	0.348102i
$597$		−	9974.83i		−	0.683824i
$598$	13105.2	−	16675.1i	0.896174	−	1.14030i
$599$	5789.36			0.394903			0.197451	−	0.980313i	$-0.436734\pi$
$599$	5789.36			0.394903			0.197451	+	0.980313i	$0.436734\pi$
$600$	−1544.34	−	703.567i	−0.105079	−	0.0478717i
$601$	−8009.05			−0.543587			−0.271794	−	0.962356i	$-0.587617\pi$
$601$	−8009.05			−0.543587			−0.271794	+	0.962356i	$0.587617\pi$
$602$	−322.899	+	410.858i	−0.0218611	+	0.0278161i
$603$			6137.21i			0.414472i
$604$	5093.09	+	20938.1i	0.343104	+	1.41053i
$605$		−	5060.23i		−	0.340045i
$606$	−1882.63	−	1479.59i	−0.126199	−	0.0991816i
$607$	−6351.98			−0.424743			−0.212371	−	0.977189i	$-0.568119\pi$
$607$	−6351.98			−0.424743			−0.212371	+	0.977189i	$0.568119\pi$
$608$	−5512.51	+	28838.7i	−0.367700	+	1.92362i
$609$	−1889.17			−0.125703
$610$	−5810.32	−	4566.41i	−0.385661	−	0.303096i
$611$			482.393i			0.0319403i
$612$	368.913	+	1516.63i	0.0243667	+	0.100174i
$613$		−	26665.2i		−	1.75693i	−0.477807	−	0.878465i	$-0.658568\pi$
$613$		−	26665.2i		−	1.75693i	0.477807	−	0.878465i	$-0.341432\pi$
$614$	−13981.1	+	17789.6i	−0.918944	+	1.16927i
$615$	−3054.24			−0.200258
$616$	1081.26	+	492.598i	0.0707229	+	0.0322197i
$617$	21929.0			1.43084			0.715421	−	0.698694i	$-0.246235\pi$
$617$	21929.0			1.43084			0.715421	+	0.698694i	$0.246235\pi$
$618$	6713.41	−	8542.17i	0.436979	−	0.556014i
$619$			24002.5i			1.55855i	0.626683	+	0.779275i	$0.284412\pi$
$619$			24002.5i			1.55855i	−0.626683	+	0.779275i	$0.715588\pi$
$620$	−69.8167	+	16.9825i	−0.00452243	+	0.00110006i
$621$		−	4334.79i		−	0.280111i
$622$	−16118.6	−	12667.8i	−1.03906	−	0.816613i
$623$	−4624.10			−0.297368
$624$	7965.48	−	4118.83i	0.511017	−	0.264239i
$625$	625.000			0.0400000
$626$	14926.0	+	11730.6i	0.952977	+	0.748958i
$627$		−	8690.18i		−	0.553513i
$628$	−8635.93	+	2100.64i	−0.548744	+	0.133479i
$629$		−	3549.70i		−	0.225017i
$630$	231.245	−	294.237i	0.0146239	−	0.0186075i
$631$	19328.2			1.21940			0.609702	−	0.792631i	$-0.291289\pi$
$631$	19328.2			1.21940			0.609702	+	0.792631i	$0.291289\pi$
$632$	9522.71	−	20902.5i	0.599356	−	1.31560i
$633$	−561.658			−0.0352669
$634$	−7002.19	+	8909.62i	−0.438632	+	0.558117i
$635$			8802.52i			0.550106i
$636$	2065.07	+	8489.67i	0.128750	+	0.529304i
$637$		−	15616.1i		−	0.971320i
$638$	8506.14	+	6685.09i	0.527839	+	0.414836i
$639$	−4099.75			−0.253809
$640$	7231.82	−	360.003i	0.446661	−	0.0222350i
$641$	10005.0			0.616496			0.308248	−	0.951306i	$-0.400257\pi$
$641$	10005.0			0.616496			0.308248	+	0.951306i	$0.400257\pi$
$642$	−566.136	−	444.934i	−0.0348031	−	0.0273522i
$643$		−	3532.54i		−	0.216656i	−0.994115	−	0.108328i	$-0.965450\pi$
$643$		−	3532.54i		−	0.216656i	0.994115	−	0.108328i	$-0.0345496\pi$
$644$	892.564	+	3669.41i	0.0546149	+	0.224526i
$645$		−	942.535i		−	0.0575384i
$646$	−6145.40	+	7819.44i	−0.374284	+	0.476241i
$647$	−4225.62			−0.256764			−0.128382	−	0.991725i	$-0.540978\pi$
$647$	−4225.62			−0.256764			−0.128382	+	0.991725i	$0.540978\pi$
$648$	759.852	−	1667.89i	0.0460645	−	0.101113i
$649$	5196.78			0.314317
$650$	−2040.70	+	2596.60i	−0.123143	+	0.156688i
$651$		−	15.8448i		−	0.000953928i
$652$	−26184.2	+	6369.17i	−1.57278	+	0.382570i
$653$		−	9696.74i		−	0.581107i	−0.956859	−	0.290553i	$-0.906161\pi$
$653$		−	9696.74i		−	0.581107i	0.956859	−	0.290553i	$-0.0938394\pi$
$654$	−2937.98	−	2309.00i	−0.175664	−	0.138057i
$655$	9922.41			0.591909
$656$	11575.5	−	5985.50i	0.688943	−	0.356241i
$657$	−6917.15			−0.410752
$658$	−67.5341	−	53.0760i	−0.00400115	−	0.00314456i
$659$		−	8708.23i		−	0.514757i	−0.966311	−	0.257378i	$-0.917141\pi$
$659$		−	8708.23i		−	0.514757i	0.966311	−	0.257378i	$-0.0828587\pi$
$660$	−2082.40	+	506.532i	−0.122814	+	0.0298738i
$661$		−	7496.13i		−	0.441098i	−0.975376	−	0.220549i	$-0.929215\pi$
$661$		−	7496.13i		−	0.441098i	0.975376	−	0.220549i	$-0.0707849\pi$
$662$	−10804.9	+	13748.2i	−0.634357	+	0.807159i
$663$	3037.50			0.177928
$664$	−5656.73	−	2577.07i	−0.330608	−	0.150617i
$665$	2384.50			0.139048
$666$	−2575.60	+	3277.21i	−0.149854	+	0.190675i
$667$			34385.2i			1.99610i
$668$	−3279.91	−	13484.0i	−0.189975	−	0.781005i
$669$		−	10538.0i		−	0.609003i
$670$	7582.28	+	5959.02i	0.437208	+	0.343608i
$671$	−9332.40			−0.536920
$672$	−299.786	+	1568.33i	−0.0172091	+	0.0900293i
$673$	21372.6			1.22415			0.612076	−	0.790799i	$-0.290335\pi$
$673$	21372.6			1.22415			0.612076	+	0.790799i	$0.290335\pi$
$674$	−17332.8	−	13622.1i	−0.990554	−	0.778491i
$675$			675.000i			0.0384900i
$676$	29.5745	+	121.583i	0.00168266	+	0.00691757i
$677$			10393.5i			0.590038i	0.955491	+	0.295019i	$0.0953260\pi$
$677$			10393.5i			0.590038i	−0.955491	+	0.295019i	$0.904674\pi$
$678$	−2649.59	+	3371.34i	−0.150084	+	0.190967i
$679$	523.758			0.0296024
$680$	2231.94	+	1016.82i	0.125869	+	0.0573432i
$681$	−5929.03			−0.333629
$682$	−56.0690	+	71.3423i	−0.00314808	+	0.00400563i
$683$		−	26428.3i		−	1.48060i	−0.672276	−	0.740300i	$-0.734683\pi$
$683$		−	26428.3i		−	1.48060i	0.672276	−	0.740300i	$-0.265317\pi$
$684$	11347.3	−	2760.18i	0.634321	−	0.154295i
$685$			8375.90i			0.467192i
$686$	4428.96	+	3480.78i	0.246499	+	0.193727i
$687$	11008.1			0.611332
$688$	1847.12	+	3572.18i	0.102356	+	0.197948i
$689$	17003.0			0.940149
$690$	−5355.46	−	4208.93i	−0.295477	−	0.232219i
$691$		−	14709.1i		−	0.809783i	−0.914365	−	0.404891i	$-0.867309\pi$
$691$		−	14709.1i		−	0.809783i	0.914365	−	0.404891i	$-0.132691\pi$
$692$	31196.9	−	7588.49i	1.71377	−	0.416866i
$693$		−	472.597i		−	0.0259055i
$694$	−21596.8	+	27479.9i	−1.18127	+	1.50306i
$695$	−9517.07			−0.519429
$696$	−6027.43	+	13230.3i	−0.328260	+	0.720537i
$697$	4414.10			0.239880
$698$	−22567.3	+	28714.7i	−1.22376	+	1.55712i
$699$		−	11850.7i		−	0.641252i
$700$	−138.987	−	571.389i	−0.00750461	−	0.0308521i
$701$		−	5611.11i		−	0.302323i	−0.988509	−	0.151162i	$-0.951699\pi$
$701$		−	5611.11i		−	0.302323i	0.988509	−	0.151162i	$-0.0483014\pi$
$702$	−2804.33	−	2203.96i	−0.150773	−	0.118494i
$703$	−26558.5			−1.42485
$704$	6899.55	−	6000.69i	0.369370	−	0.321249i
$705$	154.928			0.00827647
$706$	−2413.95	−	1897.16i	−0.128683	−	0.101134i
$707$		−	829.711i		−	0.0441365i
$708$	1650.60	+	6785.76i	0.0876178	+	0.360204i
$709$			13261.2i			0.702449i	0.936291	+	0.351224i	$0.114235\pi$
$709$			13261.2i			0.702449i	−0.936291	+	0.351224i	$0.885765\pi$
$710$	−3980.72	+	5065.08i	−0.210414	+	0.267731i
$711$	−9136.06			−0.481897
$712$	−14753.2	+	32383.6i	−0.776545	+	1.70453i
$713$	−288.394			−0.0151479
$714$	−334.205	+	425.243i	−0.0175172	+	0.0222890i
$715$			4170.60i			0.218142i
$716$	−30172.1	+	7339.20i	−1.57484	+	0.383071i
$717$			8119.43i			0.422909i
$718$	−27286.6	−	21444.9i	−1.41828	−	1.11465i
$719$	−4998.44			−0.259263			−0.129632	−	0.991562i	$-0.541379\pi$
$719$	−4998.44			−0.259263			−0.129632	+	0.991562i	$0.541379\pi$
$720$	−1322.82	−	2558.23i	−0.0684703	−	0.132416i
$721$	3764.70			0.194459
$722$	43251.1	+	33991.6i	2.22941	+	1.75213i
$723$			22311.7i			1.14769i
$724$	−5702.74	+	1387.16i	−0.292736	+	0.0712065i
$725$		−	5354.35i		−	0.274284i
$726$	5306.37	−	6751.84i	0.271264	−	0.345158i
$727$	−1317.31			−0.0672026			−0.0336013	−	0.999435i	$-0.510698\pi$
$727$	−1317.31			−0.0672026			−0.0336013	+	0.999435i	$0.510698\pi$
$728$	2827.68	+	1288.23i	0.143957	+	0.0655835i
$729$	−729.000			−0.0370370
$730$	−6716.32	+	8545.87i	−0.340523	+	0.433283i
$731$			1362.19i			0.0689225i
$732$	−2964.16	−	12185.9i	−0.149670	−	0.615306i
$733$			15742.0i			0.793239i	0.917983	+	0.396619i	$0.129817\pi$
$733$			15742.0i			0.793239i	−0.917983	+	0.396619i	$0.870183\pi$
$734$	−6412.41	−	5039.61i	−0.322461	−	0.253427i
$735$	−5015.32			−0.251691
$736$	28545.4	+	5456.45i	1.42962	+	0.273271i
$737$	12178.5			0.608684
$738$	−4075.26	−	3202.80i	−0.203269	−	0.159752i
$739$			4513.21i			0.224656i	0.993671	+	0.112328i	$0.0358308\pi$
$739$			4513.21i			0.224656i	−0.993671	+	0.112328i	$0.964169\pi$
$740$	1548.04	+	6364.11i	0.0769013	+	0.316148i
$741$		−	22726.3i		−	1.12668i
$742$	−1870.78	+	2380.38i	−0.0925585	+	0.117772i
$743$	3157.00			0.155880			0.0779401	−	0.996958i	$-0.475166\pi$
$743$	3157.00			0.155880			0.0779401	+	0.996958i	$0.475166\pi$
$744$	−110.965	−	50.5530i	−0.00546797	−	0.00249108i
$745$	−13393.5			−0.658658
$746$	17576.9	−	22364.9i	0.862648	−	1.09764i
$747$			2472.44i			0.121100i
$748$	3009.56	−	732.060i	0.147113	−	0.0357844i
$749$		−	249.507i		−	0.0121719i
$750$	833.936	+	655.402i	0.0406014	+	0.0319092i
$751$	2252.87			0.109465			0.0547326	−	0.998501i	$-0.482569\pi$
$751$	2252.87			0.109465			0.0547326	+	0.998501i	$0.482569\pi$
$752$	−587.172	+	303.617i	−0.0284733	+	0.0147231i
$753$	−12692.7			−0.614274
$754$	22245.0	+	17482.6i	1.07442	+	0.844403i
$755$		−	13467.9i		−	0.649202i
$756$	617.100	−	150.106i	0.0296874	−	0.00722131i
$757$		−	26431.9i		−	1.26907i	−0.772895	−	0.634534i	$-0.781192\pi$
$757$		−	26431.9i		−	1.26907i	0.772895	−	0.634534i	$-0.218808\pi$
$758$	6437.71	−	8191.36i	0.308480	−	0.392511i
$759$	−8601.82			−0.411365
$760$	7607.77	−	16699.2i	0.363109	−	0.797031i
$761$	29909.5			1.42473			0.712363	−	0.701811i	$-0.247625\pi$
$761$	29909.5			1.42473			0.712363	+	0.701811i	$0.247625\pi$
$762$	−9230.70	+	11745.2i	−0.438836	+	0.558376i
$763$		−	1294.82i		−	0.0614362i
$764$	41.0030	+	168.567i	0.00194167	+	0.00798237i
$765$		−	975.536i		−	0.0461053i
$766$	−17705.6	−	13915.1i	−0.835155	−	0.656360i
$767$	13590.4			0.639794
$768$	10026.9	+	7103.24i	0.471113	+	0.333745i
$769$	25085.4			1.17634			0.588168	−	0.808739i	$-0.299850\pi$
$769$	25085.4			1.17634			0.588168	+	0.808739i	$0.299850\pi$
$770$	−583.875	−	458.876i	−0.0273265	−	0.0214763i
$771$			18008.9i			0.841212i
$772$	2495.22	+	10258.1i	0.116328	+	0.478234i
$773$			7838.06i			0.364703i	0.983233	+	0.182352i	$0.0583709\pi$
$773$			7838.06i			0.364703i	−0.983233	+	0.182352i	$0.941629\pi$
$774$	988.382	−	1257.62i	0.0459001	−	0.0584034i
$775$	44.9078			0.00208146
$776$	1671.06	−	3668.00i	0.0773034	−	0.169682i
$777$	−1444.33			−0.0666859
$778$	−11008.8	+	14007.6i	−0.507305	+	0.645496i
$779$		−	33025.9i		−	1.51897i
$780$	−5445.81	+	1324.66i	−0.249989	+	0.0608084i
$781$			8135.41i			0.372737i
$782$	7739.92	+	6082.91i	0.353937	+	0.278164i
$783$	5782.70			0.263929
$784$	19007.9	−	9828.71i	0.865886	−	0.447736i
$785$	5554.84			0.252561
$786$	13239.4	+	10405.1i	0.600808	+	0.472183i
$787$		−	591.082i		−	0.0267723i	−0.999910	−	0.0133861i	$-0.995739\pi$
$787$		−	591.082i		−	0.0267723i	0.999910	−	0.0133861i	$-0.00426107\pi$
$788$	−20371.2	+	4955.18i	−0.920931	+	0.224012i
$789$			10556.3i			0.476316i
$790$	−8870.80	+	11287.2i	−0.399505	+	0.508332i
$791$	−1485.81			−0.0667882
$792$	−3309.71	−	1507.83i	−0.148491	−	0.0676493i
$793$	−24405.8			−1.09291
$794$	12794.1	−	16279.2i	0.571845	−	0.727617i
$795$		−	5460.76i		−	0.243614i
$796$	−6286.88	−	25845.9i	−0.279940	−	1.15086i
$797$		−	2775.04i		−	0.123334i	−0.998097	−	0.0616668i	$-0.980358\pi$
$797$		−	2775.04i		−	0.123334i	0.998097	−	0.0616668i	$-0.0196416\pi$
$798$	3181.63	+	2500.49i	0.141139	+	0.110923i
$799$	−223.908			−0.00991399
$800$	−4445.01	−	849.661i	−0.196443	−	0.0375501i
$801$	14154.2			0.624362
$802$	5097.06	+	4005.85i	0.224418	+	0.176374i
$803$			13726.2i			0.603220i
$804$	3868.13	+	15902.2i	0.169675	+	0.697547i
$805$		−	2360.25i		−	0.103339i
$806$	−146.630	+	186.572i	−0.00640795	+	0.00815350i
$807$	−1859.28			−0.0811025
$808$	−5810.65	−	2647.20i	−0.252993	−	0.115258i
$809$	−4977.21			−0.216303			−0.108152	−	0.994134i	$-0.534493\pi$
$809$	−4977.21			−0.216303			−0.108152	+	0.994134i	$0.534493\pi$
$810$	−707.834	+	900.650i	−0.0307046	+	0.0390687i
$811$		−	6737.08i		−	0.291703i	−0.989307	−	0.145851i	$-0.953408\pi$
$811$		−	6737.08i		−	0.291703i	0.989307	−	0.145851i	$-0.0465921\pi$
$812$	−4895.06	+	1190.70i	−0.211556	+	0.0514598i
$813$			10726.4i			0.462721i
$814$	6503.19	+	5110.95i	0.280020	+	0.220072i
$815$	16842.3			0.723878
$816$	1911.79	+	3697.25i	0.0820173	+	0.158615i
$817$	10191.8			0.436432
$818$	17230.3	+	13541.5i	0.736483	+	0.578812i
$819$		−	1235.92i		−	0.0527308i
$820$	−7913.87	+	1925.01i	−0.337030	+	0.0819807i
$821$		−	1069.68i		−	0.0454716i	−0.999742	−	0.0227358i	$-0.992762\pi$
$821$		−	1069.68i		−	0.0454716i	0.999742	−	0.0227358i	$-0.00723765\pi$
$822$	−8783.33	+	11175.9i	−0.372693	+	0.474216i
$823$	−21261.4			−0.900518			−0.450259	−	0.892898i	$-0.648668\pi$
$823$	−21261.4			−0.900518			−0.450259	+	0.892898i	$0.648668\pi$
$824$	12011.3	−	26365.0i	0.507808	−	1.11465i
$825$	1339.45			0.0565256
$826$	−1495.31	+	1902.63i	−0.0629884	+	0.0801466i
$827$			106.022i			0.00445796i	0.999998	+	0.00222898i	$0.000709508\pi$
$827$			106.022i			0.00445796i	−0.999998	+	0.00222898i	$0.999290\pi$
$828$	−2732.11	−	11231.9i	−0.114671	−	0.471421i
$829$		−	411.629i		−	0.0172454i	−0.999963	−	0.00862272i	$-0.997255\pi$
$829$		−	411.629i		−	0.0172454i	0.999963	−	0.00862272i	$-0.00274473\pi$
$830$	3054.60	+	2400.65i	0.127743	+	0.100395i
$831$	510.191			0.0212976
$832$	18043.5	−	15692.8i	0.751857	−	0.653905i
$833$	7248.34			0.301489
$834$	−12698.6	−	9980.01i	−0.527238	−	0.414364i
$835$			8673.24i			0.359461i
$836$	−5477.20	−	22517.2i	−0.226594	−	0.931549i
$837$			48.5004i			0.00200289i
$838$	8736.11	−	11115.9i	0.360124	−	0.458223i
$839$	−29684.4			−1.22148			−0.610738	−	0.791833i	$-0.709127\pi$
$839$	−29684.4			−1.22148			−0.610738	+	0.791833i	$0.709127\pi$
$840$	413.732	−	908.150i	0.0169942	−	0.0373026i
$841$	−21481.5			−0.880786
$842$	6634.37	−	8441.60i	0.271539	−	0.345507i
$843$			8820.51i			0.360373i
$844$	−1455.32	+	353.999i	−0.0593533	+	0.0144374i
$845$		−	78.2053i		−	0.00318384i
$846$	206.720	+	162.464i	0.00840090	+	0.00660239i
$847$	2975.67			0.120714
$848$	10701.6	+	20696.1i	0.433368	+	0.838099i
$849$	−9095.64			−0.367681
$850$	−1205.24	−	947.212i	−0.0486344	−	0.0382225i
$851$			26288.4i			1.05894i
$852$	−10622.9	+	2583.97i	−0.427154	+	0.103903i
$853$			19661.9i			0.789227i	0.918847	+	0.394614i	$0.129122\pi$
$853$			19661.9i			0.789227i	−0.918847	+	0.394614i	$0.870878\pi$
$854$	2685.28	−	3416.76i	0.107598	−	0.136908i
$855$	−7298.87			−0.291949
$856$	−1747.35	−	796.053i	−0.0697701	−	0.0317857i
$857$	−34610.8			−1.37956			−0.689779	−	0.724020i	$-0.742292\pi$
$857$	−34610.8			−1.37956			−0.689779	+	0.724020i	$0.742292\pi$
$858$	−4373.47	+	5564.81i	−0.174018	+	0.221421i
$859$			13980.2i			0.555295i	0.960683	+	0.277648i	$0.0895548\pi$
$859$			13980.2i			0.555295i	−0.960683	+	0.277648i	$0.910445\pi$
$860$	−594.056	−	2442.21i	−0.0235548	−	0.0968358i
$861$		−	1796.04i		−	0.0710906i
$862$	18732.3	+	14722.0i	0.740167	+	0.581707i
$863$	−38597.5			−1.52245			−0.761224	−	0.648488i	$-0.775401\pi$
$863$	−38597.5			−1.52245			−0.761224	+	0.648488i	$0.775401\pi$
$864$	917.634	−	4800.61i	0.0361326	−	0.189028i
$865$	−20066.6			−0.788770
$866$	5606.46	+	4406.19i	0.219994	+	0.172897i
$867$		−	13329.1i		−	0.522123i
$868$	−9.98658	−	41.0557i	−0.000390514	−	0.00160544i
$869$			18129.3i			0.707704i
$870$	5614.80	−	7144.29i	0.218804	−	0.278407i
$871$	31848.7			1.23898
$872$	−9067.95	−	4131.15i	−0.352155	−	0.160434i
$873$	−1603.21			−0.0621538
$874$	45511.8	−	57909.4i	1.76140	−	2.24121i
$875$			367.531i			0.0141998i
$876$	−17923.1	+	4359.71i	−0.691286	+	0.168152i
$877$		−	47471.5i		−	1.82782i	−0.405915	−	0.913911i	$-0.633047\pi$
$877$		−	47471.5i		−	1.82782i	0.405915	−	0.913911i	$-0.366953\pi$
$878$	−22673.1	−	17819.1i	−0.871502	−	0.684925i
$879$	23416.5			0.898541
$880$	−5076.47	+	2624.96i	−0.194463	+	0.100554i
$881$	28819.4			1.10210			0.551050	−	0.834472i	$-0.314227\pi$
$881$	28819.4			1.10210			0.551050	+	0.834472i	$0.314227\pi$
$882$	−6691.93	−	5259.28i	−0.255475	−	0.200782i
$883$		−	11414.0i		−	0.435009i	−0.976059	−	0.217504i	$-0.930208\pi$
$883$		−	11414.0i		−	0.435009i	0.976059	−	0.217504i	$-0.0697916\pi$
$884$	7870.50	−	1914.46i	0.299450	−	0.0728395i
$885$		−	4364.77i		−	0.165785i
$886$	−15195.0	+	19334.1i	−0.576168	+	0.733119i
$887$	25787.8			0.976178			0.488089	−	0.872794i	$-0.337694\pi$
$887$	25787.8			0.976178			0.488089	+	0.872794i	$0.337694\pi$
$888$	−4608.14	+	10115.0i	−0.174143	+	0.382247i
$889$	−5176.32			−0.195285
$890$	13743.2	−	17486.9i	0.517612	−	0.658611i
$891$			1446.60i			0.0543917i
$892$	−6641.84	−	27305.2i	−0.249311	−	1.02494i
$893$			1675.26i			0.0627775i
$894$	−17870.9	−	14045.0i	−0.668560	−	0.525431i
$895$	19407.4			0.724825
$896$	211.700	+	4252.67i	0.00789330	+	0.158562i
$897$	−22495.2			−0.837338
$898$	−23903.2	−	18785.8i	−0.888262	−	0.698098i
$899$		−	384.723i		−	0.0142728i
$900$	425.435	+	1749.00i	0.0157569	+	0.0647778i
$901$			7892.10i			0.291814i
$902$	−6355.54	+	8086.81i	−0.234608	+	0.298516i
$903$	554.257			0.0204258
$904$	−4740.51	+	10405.5i	−0.174410	+	0.382834i
$905$	3668.14			0.134733
$906$	14123.0	−	17970.2i	0.517887	−	0.658962i
$907$		−	1475.86i		−	0.0540301i	−0.999635	−	0.0270150i	$-0.991400\pi$
$907$		−	1475.86i		−	0.0540301i	0.999635	−	0.0270150i	$-0.00860020\pi$
$908$	−15362.8	+	3736.92i	−0.561489	+	0.136579i
$909$			2539.72i			0.0926700i
$910$	−1526.93	−	1200.04i	−0.0556233	−	0.0437151i
$911$	20391.9			0.741616			0.370808	−	0.928710i	$-0.379081\pi$
$911$	20391.9			0.741616			0.370808	+	0.928710i	$0.379081\pi$
$912$	27662.5	−	14303.9i	1.00438	−	0.519351i
$913$	4906.22			0.177845
$914$	−34584.2	−	27180.2i	−1.25158	−	0.983634i
$915$			7838.27i			0.283197i
$916$	28523.2	−	6938.12i	1.02886	−	0.250264i
$917$			5834.87i			0.210125i
$918$	1022.99	−	1301.66i	0.0367796	−	0.0467985i
$919$	10447.6			0.375011			0.187506	−	0.982264i	$-0.439960\pi$
$919$	10447.6			0.375011			0.187506	+	0.982264i	$0.439960\pi$
$920$	−16529.4	−	7530.41i	−0.592345	−	0.269859i
$921$	23998.6			0.858612
$922$	28018.9	−	35651.3i	1.00082	−	1.27344i
$923$			21275.4i			0.758711i
$924$	−297.866	−	1224.55i	−0.0106051	−	0.0435983i
$925$		−	4093.55i		−	0.145508i
$926$	−36666.1	−	28816.4i	−1.30121	−	1.02264i
$927$	−11523.6			−0.408290
$928$	−7279.02	+	38080.2i	−0.257484	+	1.34703i
$929$	−22104.8			−0.780663			−0.390332	−	0.920674i	$-0.627640\pi$
$929$	−22104.8			−0.780663			−0.390332	+	0.920674i	$0.627640\pi$
$930$	59.9203	+	47.0922i	0.00211276	+	0.00166045i
$931$		−	54231.4i		−	1.90909i
$932$	−7469.20	−	30706.5i	−0.262513	−	1.07921i
$933$			21744.4i			0.763000i
$934$	6254.76	−	7958.57i	0.219124	−	0.278814i
$935$	−1935.82			−0.0677093
$936$	−8655.43	−	3943.21i	−0.302256	−	0.137701i
$937$	−40032.2			−1.39572			−0.697862	−	0.716232i	$-0.745865\pi$
$937$	−40032.2			−1.39572			−0.697862	+	0.716232i	$0.745865\pi$
$938$	−3504.20	+	4458.76i	−0.121979	+	0.155206i
$939$		−	20135.6i		−	0.699786i
$940$	401.435	−	97.6470i	0.0139291	−	0.00338818i
$941$			49244.9i			1.70599i	0.521919	+	0.852995i	$0.325216\pi$
$941$			49244.9i			1.70599i	−0.521919	+	0.852995i	$0.674784\pi$
$942$	7411.81	+	5825.04i	0.256358	+	0.201476i
$943$	−32690.1			−1.12888
$944$	8553.79	+	16542.3i	0.294917	+	0.570347i
$945$	−396.934			−0.0136638
$946$	−2495.58	−	1961.31i	−0.0857699	−	0.0674078i
$947$			15607.6i			0.535565i	0.963479	+	0.267782i	$0.0862908\pi$
$947$			15607.6i			0.535565i	−0.963479	+	0.267782i	$0.913709\pi$
$948$	−23672.6	+	5758.23i	−0.811022	+	0.197277i
$949$			35896.2i			1.22786i
$950$	−7086.95	+	9017.47i	−0.242033	+	0.307963i
$951$	12019.3			0.409834
$952$	−597.942	+	1312.49i	−0.0203565	+	0.0446830i
$953$	−25045.9			−0.851327			−0.425664	−	0.904881i	$-0.639959\pi$
$953$	−25045.9			−0.851327			−0.425664	+	0.904881i	$0.639959\pi$
$954$	5726.39	−	7286.27i	0.194338	−	0.247277i
$955$		−	108.426i		−	0.00367392i
$956$	5117.47	+	21038.4i	0.173128	+	0.711746i
$957$		−	11475.0i		−	0.387601i
$958$	16401.6	+	12890.3i	0.553144	+	0.434724i
$959$	−4925.45			−0.165851
$960$	−5039.97	−	5794.92i	−0.169442	−	0.194823i
$961$	−29787.8			−0.999892
$962$	17006.9	+	13366.0i	0.569984	+	0.447958i
$963$			763.731i			0.0255565i
$964$	14062.5	+	57812.0i	0.469836	+	1.93154i
$965$		−	6598.25i		−	0.220109i
$966$	2475.06	−	3149.28i	0.0824367	−	0.104893i
$967$	−38342.2			−1.27508			−0.637540	−	0.770417i	$-0.720048\pi$
$967$	−38342.2			−1.27508			−0.637540	+	0.770417i	$0.720048\pi$
$968$	9493.89	−	20839.3i	0.315233	−	0.691941i
$969$	10548.6			0.349711
$970$	−1556.66	+	1980.70i	−0.0515271	+	0.0655632i
$971$			3840.52i			0.126929i	0.997984	+	0.0634646i	$0.0202150\pi$
$971$			3840.52i			0.126929i	−0.997984	+	0.0634646i	$0.979785\pi$
$972$	−1888.92	+	459.470i	−0.0623325	+	0.0151620i
$973$		−	5596.51i		−	0.184395i
$974$	8809.33	+	6923.37i	0.289804	+	0.227761i
$975$	3502.88			0.115058
$976$	−15360.9	−	29706.8i	−0.503782	−	0.974275i
$977$	−43474.6			−1.42362			−0.711810	−	0.702372i	$-0.752124\pi$
$977$	−43474.6			−1.42362			−0.711810	+	0.702372i	$0.752124\pi$
$978$	22472.6	+	17661.6i	0.734760	+	0.577459i
$979$		−	28087.1i		−	0.916924i
$980$	−12995.3	+	3161.03i	−0.423590	+	0.103036i
$981$			3963.41i			0.128993i
$982$	31520.6	−	40107.0i	1.02430	−	1.30332i
$983$	17053.6			0.553333			0.276667	−	0.960966i	$-0.410770\pi$
$983$	17053.6			0.553333			0.276667	+	0.960966i	$0.410770\pi$
$984$	−12578.1	−	5730.29i	−0.407495	−	0.185645i
$985$	13103.2			0.423862
$986$	−8114.73	+	10325.2i	−0.262095	+	0.333491i
$987$			91.1052i			0.00293811i
$988$	−14323.8	−	58886.3i	−0.461235	−	1.89618i
$989$		−	10088.1i		−	0.324352i
$990$	1787.22	+	1404.60i	0.0573754	+	0.0450921i
$991$	32082.1			1.02838			0.514188	−	0.857677i	$-0.328093\pi$
$991$	32082.1			1.02838			0.514188	+	0.857677i	$0.328093\pi$
$992$	−319.385	−	61.0503i	−0.0102222	−	0.00195398i
$993$	18546.7			0.592710
$994$	−2978.52	−	2340.86i	−0.0950432	−	0.0746958i
$995$			16624.7i			0.529687i
$996$	1558.31	+	6406.36i	0.0495754	+	0.203809i
$997$			4324.24i			0.137362i	0.997639	+	0.0686810i	$0.0218791\pi$
$997$			4324.24i			0.137362i	−0.997639	+	0.0686810i	$0.978121\pi$
$998$	−175.449	+	223.241i	−0.00556486	+	0.00708074i
$999$	4421.04			0.140015

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.k.c.61.3	✓	14
3.2	odd	2		360.4.k.d.181.12		14
4.3	odd	2		480.4.k.c.241.3		14
8.3	odd	2		480.4.k.c.241.10		14
8.5	even	2	inner	120.4.k.c.61.4	yes	14
12.11	even	2		1440.4.k.d.721.10		14
24.5	odd	2		360.4.k.d.181.11		14
24.11	even	2		1440.4.k.d.721.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.k.c.61.3	✓	14	1.1	even	1	trivial
120.4.k.c.61.4	yes	14	8.5	even	2	inner
360.4.k.d.181.11		14	24.5	odd	2
360.4.k.d.181.12		14	3.2	odd	2
480.4.k.c.241.3		14	4.3	odd	2
480.4.k.c.241.10		14	8.3	odd	2
1440.4.k.d.721.3		14	24.11	even	2
1440.4.k.d.721.10		14	12.11	even	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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.22383 - 1.74774i) q^{2} +3.00000i q^{3} +(1.89082 + 7.77334i) q^{4} -5.00000i q^{5} +(5.24321 - 6.67148i) q^{6} +2.94025 q^{7} +(9.38089 - 20.5912i) q^{8} -9.00000 q^{9} +(-8.73869 + 11.1191i) q^{10} +17.8593i q^{11} +(-23.3200 + 5.67247i) q^{12} +46.7050i q^{13} +(-6.53861 - 5.13879i) q^{14} +15.0000 q^{15} +(-56.8496 + 29.3960i) q^{16} -21.6786 q^{17} +(20.0145 + 15.7296i) q^{18} +162.197i q^{19} +(38.8667 - 9.45412i) q^{20} +8.82075i q^{21} +(31.2134 - 39.7160i) q^{22} +160.548 q^{23} +(61.7737 + 28.1427i) q^{24} -25.0000 q^{25} +(81.6281 - 103.864i) q^{26} -27.0000i q^{27} +(5.55949 + 22.8556i) q^{28} +214.174i q^{29} +(-33.3574 - 26.2161i) q^{30} -1.79631 q^{31} +(177.800 + 33.9865i) q^{32} -53.5779 q^{33} +(48.2094 + 37.8885i) q^{34} -14.7012i q^{35} +(-17.0174 - 69.9600i) q^{36} +163.742i q^{37} +(283.478 - 360.699i) q^{38} -140.115 q^{39} +(-102.956 - 46.9045i) q^{40} -203.616 q^{41} +(15.4164 - 19.6158i) q^{42} -62.8357i q^{43} +(-138.826 + 33.7688i) q^{44} +45.0000i q^{45} +(-357.031 - 280.596i) q^{46} +10.3285 q^{47} +(-88.1881 - 170.549i) q^{48} -334.355 q^{49} +(55.5957 + 43.6935i) q^{50} -65.0358i q^{51} +(-363.054 + 88.3110i) q^{52} -364.051i q^{53} +(-47.1889 + 60.0434i) q^{54} +89.2965 q^{55} +(27.5822 - 60.5434i) q^{56} -486.591 q^{57} +(374.320 - 476.286i) q^{58} -290.985i q^{59} +(28.3624 + 116.600i) q^{60} +522.551i q^{61} +(3.99469 + 3.13948i) q^{62} -26.4622 q^{63} +(-335.998 - 386.328i) q^{64} +233.525 q^{65} +(119.148 + 93.6401i) q^{66} -681.913i q^{67} +(-40.9904 - 168.515i) q^{68} +481.643i q^{69} +(-25.6939 + 32.6930i) q^{70} +455.528 q^{71} +(-84.4280 + 185.321i) q^{72} +768.573 q^{73} +(286.178 - 364.134i) q^{74} -75.0000i q^{75} +(-1260.81 + 306.686i) q^{76} +52.5108i q^{77} +(311.592 + 244.884i) q^{78} +1015.12 q^{79} +(146.980 + 284.248i) q^{80} +81.0000 q^{81} +(452.807 + 355.867i) q^{82} -274.715i q^{83} +(-68.5667 + 16.6785i) q^{84} +108.393i q^{85} +(-109.820 + 139.736i) q^{86} -642.522 q^{87} +(367.745 + 167.536i) q^{88} -1572.69 q^{89} +(78.6482 - 100.072i) q^{90} +137.324i q^{91} +(303.568 + 1247.99i) q^{92} -5.38893i q^{93} +(-22.9688 - 18.0515i) q^{94} +810.986 q^{95} +(-101.959 + 533.401i) q^{96} +178.134 q^{97} +(743.548 + 584.365i) q^{98} -160.734i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} - 2 q^{4} + 12 q^{6} - 28 q^{7} - 8 q^{8} - 126 q^{9} - 20 q^{10} + 12 q^{12} - 8 q^{14} + 210 q^{15} - 22 q^{16} + 204 q^{17} + 18 q^{18} - 20 q^{20} - 84 q^{22} - 328 q^{23} - 138 q^{24}+ \cdots + 6246 q^{98}+O(q^{100}) \) 14 * q - 2 * q^2 - 2 * q^4 + 12 * q^6 - 28 * q^7 - 8 * q^8 - 126 * q^9 - 20 * q^10 + 12 * q^12 - 8 * q^14 + 210 * q^15 - 22 * q^16 + 204 * q^17 + 18 * q^18 - 20 * q^20 - 84 * q^22 - 328 * q^23 - 138 * q^24 - 350 * q^25 - 4 * q^26 + 68 * q^28 - 30 * q^30 + 596 * q^31 + 588 * q^32 + 264 * q^33 + 756 * q^34 + 18 * q^36 - 1144 * q^38 + 230 * q^40 - 820 * q^41 + 768 * q^42 - 2084 * q^44 - 1060 * q^46 - 104 * q^47 - 48 * q^48 + 1110 * q^49 + 50 * q^50 - 1736 * q^52 - 108 * q^54 - 440 * q^55 + 3812 * q^56 + 168 * q^57 + 2664 * q^58 - 30 * q^60 - 772 * q^62 + 252 * q^63 + 2470 * q^64 + 972 * q^66 - 2864 * q^68 - 1280 * q^70 + 1592 * q^71 + 72 * q^72 - 2260 * q^73 + 1020 * q^74 - 2468 * q^76 - 2280 * q^78 - 220 * q^79 + 80 * q^80 + 1134 * q^81 + 3444 * q^82 - 84 * q^84 - 1184 * q^86 - 1044 * q^87 - 500 * q^88 - 2492 * q^89 + 180 * q^90 - 4536 * q^92 - 4300 * q^94 - 280 * q^95 + 1542 * q^96 + 3508 * q^97 + 6246 * q^98

Introduction

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