LMFDB - Embedded newform 120.4.k.c.61.4

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

$q$-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	$-0.921290\pi$
$11$		−	17.8593i		−	0.489526i	0.969583	−	0.244763i	$-0.0787101\pi$
$12$	−23.3200	−	5.67247i	−0.560992	−	0.136458i
$13$		−	46.7050i		−	0.996434i	−0.867052	−	0.498217i	$-0.833988\pi$
$13$		−	46.7050i		−	0.996434i	0.867052	−	0.498217i	$-0.166012\pi$
$14$	−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	$-0.564995\pi$
$19$		−	162.197i		−	1.95845i	0.202773	−	0.979226i	$-0.435005\pi$
$20$	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	$-0.759492\pi$
$29$		−	214.174i		−	1.37142i	0.727876	−	0.685709i	$-0.240508\pi$
$30$	−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	$-0.881489\pi$
$37$		−	163.742i		−	0.727542i	0.931488	−	0.363771i	$-0.118511\pi$
$38$	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	$0.0355407\pi$
$43$			62.8357i			0.222845i	−0.993773	+	0.111423i	$0.964459\pi$
$44$	−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	$0.156380\pi$
$53$			364.051i			0.943513i	−0.881729	+	0.471757i	$0.843620\pi$
$54$	−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	$0.104033\pi$
$59$			290.985i			0.642084i	−0.947065	+	0.321042i	$0.895967\pi$
$60$	28.3624	−	116.600i	0.0610261	−	0.250883i
$61$		−	522.551i		−	1.09682i	−0.836211	−	0.548408i	$-0.815234\pi$
$61$		−	522.551i		−	1.09682i	0.836211	−	0.548408i	$-0.184766\pi$
$62$	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	$0.213561\pi$
$67$			681.913i			1.24342i	−0.783249	+	0.621708i	$0.786439\pi$
$68$	−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	$0.0581438\pi$
$83$			274.715i			0.363300i	−0.983363	+	0.181650i	$0.941856\pi$
$84$	−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	$0.0443904\pi$
$101$			282.191i			0.278010i	−0.990292	+	0.139005i	$0.955610\pi$
$102$	−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	$0.0122053\pi$
$107$			84.8590i			0.0766694i	−0.999265	+	0.0383347i	$0.987795\pi$
$108$	209.880	+	51.0522i	0.186997	+	0.0454861i
$109$			440.379i			0.386979i	0.981102	+	0.193489i	$0.0619805\pi$
$109$			440.379i			0.386979i	−0.981102	+	0.193489i	$0.938020\pi$
$110$	−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	$-0.769804\pi$
$131$		−	1984.48i		−	1.32355i	0.749703	−	0.661774i	$-0.230196\pi$
$132$	−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	$0.197236\pi$
$139$			1903.41i			1.16148i	−0.814090	+	0.580739i	$0.802764\pi$
$140$	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	$0.263477\pi$
$149$			2678.70i			1.47280i	−0.676544	+	0.736402i	$0.736523\pi$
$150$	−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	$-0.908879\pi$
$157$		−	1110.97i		−	0.564745i	0.959305	−	0.282372i	$-0.0911213\pi$
$158$	−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	$-0.699836\pi$
$163$		−	3368.46i		−	1.61864i	0.587368	−	0.809320i	$-0.300164\pi$
$164$	−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	$0.343717\pi$
$173$			4013.33i			1.76374i	−0.471489	+	0.881872i	$0.656283\pi$
$174$	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	$-0.699261\pi$
$179$		−	3881.48i		−	1.62076i	0.585906	−	0.810379i	$-0.300739\pi$
$180$	−349.800	−	85.0871i	−0.144848	−	0.0352334i
$181$		−	733.629i		−	0.301272i	−0.988589	−	0.150636i	$-0.951868\pi$
$181$		−	733.629i		−	0.301272i	0.988589	−	0.150636i	$-0.0481321\pi$
$182$	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	$-0.842849\pi$
$197$		−	2620.65i		−	0.947784i	0.880583	−	0.473892i	$-0.157151\pi$
$198$	−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	$-0.990277\pi$
$211$		−	187.219i		−	0.0610840i	0.999533	−	0.0305420i	$-0.00972333\pi$
$212$	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	$-0.906700\pi$
$227$		−	1976.34i		−	0.577862i	0.957350	−	0.288931i	$-0.0932998\pi$
$228$	−920.059	+	3782.44i	−0.267247	+	1.09868i
$229$			3669.36i			1.05886i	0.848354	+	0.529429i	$0.177594\pi$
$229$			3669.36i			1.05886i	−0.848354	+	0.529429i	$0.822406\pi$
$230$	−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	$-0.821449\pi$
$251$		−	4230.91i		−	1.06395i	0.846759	−	0.531977i	$-0.178551\pi$
$252$	−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	$-0.977625\pi$
$269$		−	619.760i		−	0.140474i	0.997530	−	0.0702368i	$-0.0223755\pi$
$270$	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	$0.00587134\pi$
$277$			170.064i			0.0368886i	−0.999830	+	0.0184443i	$0.994129\pi$
$278$	−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	$-0.896847\pi$
$283$		−	3031.88i		−	0.636843i	0.947949	−	0.318422i	$-0.103153\pi$
$284$	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	$0.283846\pi$
$293$			7805.49i			1.55632i	−0.628067	+	0.778159i	$0.716154\pi$
$294$	−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	$0.266874\pi$
$307$			7999.54i			1.48716i	−0.668647	+	0.743580i	$0.733126\pi$
$308$	−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	$0.115494\pi$
$317$			4006.43i			0.709854i	−0.934894	+	0.354927i	$0.884506\pi$
$318$	−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	$0.171578\pi$
$331$			6182.22i			1.02660i	−0.858208	+	0.513302i	$0.828422\pi$
$332$	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	$0.405060\pi$
$347$			12357.0i			1.91170i	−0.293860	+	0.955849i	$0.594940\pi$
$348$	−1214.90	+	4994.54i	−0.187142	+	0.769355i
$349$			12912.3i			1.98045i	0.139469	+	0.990226i	$0.455461\pi$
$349$			12912.3i			1.98045i	−0.139469	+	0.990226i	$0.544539\pi$
$350$	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	$-0.754061\pi$
$373$		−	10056.9i		−	1.39605i	0.716071	−	0.698027i	$-0.245939\pi$
$374$	−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	$-0.919697\pi$
$379$		−	3683.45i		−	0.499225i	0.968346	−	0.249612i	$-0.0803032\pi$
$380$	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	$0.134644\pi$
$389$			6298.86i			0.820989i	−0.911863	+	0.410495i	$0.865356\pi$
$390$	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	$-0.846874\pi$
$397$		−	7320.36i		−	0.925436i	0.886505	−	0.462718i	$-0.153126\pi$
$398$	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	$-0.905879\pi$
$419$		−	4998.52i		−	0.582801i	0.956601	−	0.291401i	$-0.0941213\pi$
$420$	83.3924	−	342.833i	0.00968841	−	0.0398299i
$421$		−	3795.98i		−	0.439441i	−0.975563	−	0.219720i	$-0.929485\pi$
$421$		−	3795.98i		−	0.439441i	0.975563	−	0.219720i	$-0.0705145\pi$
$422$	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	$0.154383\pi$
$443$			8694.08i			0.932434i	−0.884670	+	0.466217i	$0.845617\pi$
$444$	−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	$-0.699560\pi$
$461$		−	16031.5i		−	1.61966i	0.586668	−	0.809828i	$-0.300440\pi$
$462$	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	$-0.943261\pi$
$467$		−	3578.77i		−	0.354616i	0.984155	−	0.177308i	$-0.0567389\pi$
$468$	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	$-0.689006\pi$
$491$		−	18035.1i		−	1.65766i	0.559498	−	0.828832i	$-0.310994\pi$
$492$	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	$0.00143332\pi$
$499$			100.386i			0.00900581i	−0.999990	+	0.00450290i	$0.998567\pi$
$500$	−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	$-0.777286\pi$
$509$		−	14790.1i		−	1.28794i	0.765051	−	0.643969i	$-0.222714\pi$
$510$	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	$-0.685604\pi$
$523$		−	19968.5i		−	1.66953i	0.550608	−	0.834764i	$-0.314396\pi$
$524$	−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	$0.0653290\pi$
$541$			5128.95i			0.407598i	−0.979013	+	0.203799i	$0.934671\pi$
$542$	−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	$0.0390326\pi$
$547$			3129.68i			0.244635i	−0.992491	+	0.122318i	$0.960967\pi$
$548$	−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	$-0.935006\pi$
$557$		−	5331.08i		−	0.405539i	0.979226	−	0.202770i	$-0.0649942\pi$
$558$	−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	$0.130169\pi$
$563$			10623.7i			0.795270i	−0.917544	+	0.397635i	$0.869831\pi$
$564$	−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	$0.0944031\pi$
$571$			7975.08i			0.584495i	−0.956343	+	0.292248i	$0.905597\pi$
$572$	−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	$0.0341423\pi$
$587$			3045.07i			0.214111i	−0.994253	+	0.107056i	$0.965858\pi$
$588$	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	$0.341432\pi$
$613$			26665.2i			1.75693i	−0.477807	+	0.878465i	$0.658568\pi$
$614$	−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	$-0.715588\pi$
$619$		−	24002.5i		−	1.55855i	0.626683	−	0.779275i	$-0.284412\pi$
$620$	−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	$0.0345496\pi$
$643$			3532.54i			0.216656i	−0.994115	+	0.108328i	$0.965450\pi$
$644$	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	$0.0938394\pi$
$653$			9696.74i			0.581107i	−0.956859	+	0.290553i	$0.906161\pi$
$654$	−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	$0.0828587\pi$
$659$			8708.23i			0.514757i	−0.966311	+	0.257378i	$0.917141\pi$
$660$	−2082.40	−	506.532i	−0.122814	−	0.0298738i
$661$			7496.13i			0.441098i	0.975376	+	0.220549i	$0.0707849\pi$
$661$			7496.13i			0.441098i	−0.975376	+	0.220549i	$0.929215\pi$
$662$	−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	$-0.904674\pi$
$677$		−	10393.5i		−	0.590038i	0.955491	−	0.295019i	$-0.0953260\pi$
$678$	−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	$0.265317\pi$
$683$			26428.3i			1.48060i	−0.672276	+	0.740300i	$0.734683\pi$
$684$	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	$0.132691\pi$
$691$			14709.1i			0.809783i	−0.914365	+	0.404891i	$0.867309\pi$
$692$	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	$0.0483014\pi$
$701$			5611.11i			0.302323i	−0.988509	+	0.151162i	$0.951699\pi$
$702$	−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	$-0.885765\pi$
$709$		−	13261.2i		−	0.702449i	0.936291	−	0.351224i	$-0.114235\pi$
$710$	−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	$-0.870183\pi$
$733$		−	15742.0i		−	0.793239i	0.917983	−	0.396619i	$-0.129817\pi$
$734$	−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	$-0.964169\pi$
$739$		−	4513.21i		−	0.224656i	0.993671	−	0.112328i	$-0.0358308\pi$
$740$	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	$0.218808\pi$
$757$			26431.9i			1.26907i	−0.772895	+	0.634534i	$0.781192\pi$
$758$	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	$-0.941629\pi$
$773$		−	7838.06i		−	0.364703i	0.983233	−	0.182352i	$-0.0583709\pi$
$774$	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	$0.00426107\pi$
$787$			591.082i			0.0267723i	−0.999910	+	0.0133861i	$0.995739\pi$
$788$	−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	$0.0196416\pi$
$797$			2775.04i			0.123334i	−0.998097	+	0.0616668i	$0.980358\pi$
$798$	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	$0.0465921\pi$
$811$			6737.08i			0.291703i	−0.989307	+	0.145851i	$0.953408\pi$
$812$	−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	$0.00723765\pi$
$821$			1069.68i			0.0454716i	−0.999742	+	0.0227358i	$0.992762\pi$
$822$	−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	$-0.999290\pi$
$827$		−	106.022i		−	0.00445796i	0.999998	−	0.00222898i	$-0.000709508\pi$
$828$	−2732.11	+	11231.9i	−0.114671	+	0.471421i
$829$			411.629i			0.0172454i	0.999963	+	0.00862272i	$0.00274473\pi$
$829$			411.629i			0.0172454i	−0.999963	+	0.00862272i	$0.997255\pi$
$830$	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	$-0.870878\pi$
$853$		−	19661.9i		−	0.789227i	0.918847	−	0.394614i	$-0.129122\pi$
$854$	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	$-0.910445\pi$
$859$		−	13980.2i		−	0.555295i	0.960683	−	0.277648i	$-0.0895548\pi$
$860$	−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	$0.366953\pi$
$877$			47471.5i			1.82782i	−0.405915	+	0.913911i	$0.633047\pi$
$878$	−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	$0.0697916\pi$
$883$			11414.0i			0.435009i	−0.976059	+	0.217504i	$0.930208\pi$
$884$	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	$0.00860020\pi$
$907$			1475.86i			0.0540301i	−0.999635	+	0.0270150i	$0.991400\pi$
$908$	−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	$-0.674784\pi$
$941$		−	49244.9i		−	1.70599i	0.521919	−	0.852995i	$-0.325216\pi$
$942$	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	$-0.913709\pi$
$947$		−	15607.6i		−	0.535565i	0.963479	−	0.267782i	$-0.0862908\pi$
$948$	−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	$-0.979785\pi$
$971$		−	3840.52i		−	0.126929i	0.997984	−	0.0634646i	$-0.0202150\pi$
$972$	−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	$-0.978121\pi$
$997$		−	4324.24i		−	0.137362i	0.997639	−	0.0686810i	$-0.0218791\pi$
$998$	−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.61.4	yes	14
3.2	odd	2		360.4.k.d.181.11		14
4.3	odd	2		480.4.k.c.241.10		14
8.3	odd	2		480.4.k.c.241.3		14
8.5	even	2	inner	120.4.k.c.61.3	✓	14
12.11	even	2		1440.4.k.d.721.3		14
24.5	odd	2		360.4.k.d.181.12		14
24.11	even	2		1440.4.k.d.721.10		14

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more