LMFDB - Embedded newform 360.4.k.d.181.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,4,Mod(181,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, 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("360.181");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	360.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:	$21.2406876021$
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:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.11
Root			$1.74774 - 2.22383i$ of defining polynomial
Character	$\chi$	$=$	360.181
Dual form			360.4.k.d.181.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.22383 - 1.74774i) q^{2} +(1.89082 - 7.77334i) q^{4} -5.00000i q^{5} +2.94025 q^{7} +(-9.38089 - 20.5912i) q^{8} +(-8.73869 - 11.1191i) q^{10} +17.8593i q^{11} -46.7050i q^{13} +(6.53861 - 5.13879i) q^{14} +(-56.8496 - 29.3960i) q^{16} +21.6786 q^{17} -162.197i q^{19} +(-38.8667 - 9.45412i) q^{20} +(31.2134 + 39.7160i) q^{22} -160.548 q^{23} -25.0000 q^{25} +(-81.6281 - 103.864i) q^{26} +(5.55949 - 22.8556i) q^{28} +214.174i q^{29} -1.79631 q^{31} +(-177.800 + 33.9865i) q^{32} +(48.2094 - 37.8885i) q^{34} -14.7012i q^{35} -163.742i q^{37} +(-283.478 - 360.699i) q^{38} +(-102.956 + 46.9045i) q^{40} +203.616 q^{41} +62.8357i q^{43} +(138.826 + 33.7688i) q^{44} +(-357.031 + 280.596i) q^{46} -10.3285 q^{47} -334.355 q^{49} +(-55.5957 + 43.6935i) q^{50} +(-363.054 - 88.3110i) q^{52} -364.051i q^{53} +89.2965 q^{55} +(-27.5822 - 60.5434i) q^{56} +(374.320 + 476.286i) q^{58} -290.985i q^{59} -522.551i q^{61} +(-3.99469 + 3.13948i) q^{62} +(-335.998 + 386.328i) q^{64} -233.525 q^{65} +681.913i q^{67} +(40.9904 - 168.515i) q^{68} +(-25.6939 - 32.6930i) q^{70} -455.528 q^{71} +768.573 q^{73} +(-286.178 - 364.134i) q^{74} +(-1260.81 - 306.686i) q^{76} +52.5108i q^{77} +1015.12 q^{79} +(-146.980 + 284.248i) q^{80} +(452.807 - 355.867i) q^{82} -274.715i q^{83} -108.393i q^{85} +(109.820 + 139.736i) q^{86} +(367.745 - 167.536i) q^{88} +1572.69 q^{89} -137.324i q^{91} +(-303.568 + 1247.99i) q^{92} +(-22.9688 + 18.0515i) q^{94} -810.986 q^{95} +178.134 q^{97} +(-743.548 + 584.365i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} - 2 q^{4} - 28 q^{7} + 8 q^{8} - 20 q^{10} + 8 q^{14} - 22 q^{16} - 204 q^{17} + 20 q^{20} - 84 q^{22} + 328 q^{23} - 350 q^{25} + 4 q^{26} + 68 q^{28} + 596 q^{31} - 588 q^{32} + 756 q^{34}+ \cdots - 6246 q^{98}+O(q^{100}) $ 14 * q + 2 * q^2 - 2 * q^4 - 28 * q^7 + 8 * q^8 - 20 * q^10 + 8 * q^14 - 22 * q^16 - 204 * q^17 + 20 * q^20 - 84 * q^22 + 328 * q^23 - 350 * q^25 + 4 * q^26 + 68 * q^28 + 596 * q^31 - 588 * q^32 + 756 * q^34 + 1144 * q^38 + 230 * q^40 + 820 * q^41 + 2084 * q^44 - 1060 * q^46 + 104 * q^47 + 1110 * q^49 - 50 * q^50 - 1736 * q^52 - 440 * q^55 - 3812 * q^56 + 2664 * q^58 + 772 * q^62 + 2470 * q^64 + 2864 * q^68 - 1280 * q^70 - 1592 * q^71 - 2260 * q^73 - 1020 * q^74 - 2468 * q^76 - 220 * q^79 - 80 * q^80 + 3444 * q^82 + 1184 * q^86 - 500 * q^88 + 2492 * q^89 + 4536 * q^92 - 4300 * q^94 + 280 * q^95 + 3508 * q^97 - 6246 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$1$	$1$

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
$3$		0			0
$3$		0			0
$4$	1.89082	−	7.77334i	0.236353	−	0.971667i
$5$		−	5.00000i		−	0.447214i
$5$		−	5.00000i		−	0.447214i
$6$		0			0
$7$	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
$9$		0			0
$10$	−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	$0.921290\pi$
$12$		0			0
$13$		−	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
$15$		0			0
$16$	−56.8496	−	29.3960i	−0.888275	−	0.459313i
$17$	21.6786			0.309284			0.154642	−	0.987971i	$-0.450578\pi$
$17$	21.6786			0.309284			0.154642	+	0.987971i	$0.450578\pi$
$18$		0			0
$19$		−	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
$21$		0			0
$22$	31.2134	+	39.7160i	0.302487	+	0.384886i
$23$	−160.548			−1.45550			−0.727751	−	0.685842i	$-0.759434\pi$
$23$	−160.548			−1.45550			−0.727751	+	0.685842i	$0.759434\pi$
$24$		0			0
$25$	−25.0000			−0.200000
$26$	−81.6281	−	103.864i	−0.615715	−	0.783438i
$27$		0			0
$28$	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	$0.759492\pi$
$30$		0			0
$31$	−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
$33$		0			0
$34$	48.2094	−	37.8885i	0.243172	−	0.191112i
$35$		−	14.7012i		−	0.0709990i
$36$		0			0
$37$		−	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
$39$		0			0
$40$	−102.956	+	46.9045i	−0.406970	+	0.185406i
$41$	203.616			0.775596			0.387798	−	0.921744i	$-0.373236\pi$
$41$	203.616			0.775596			0.387798	+	0.921744i	$0.373236\pi$
$42$		0			0
$43$			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
$45$		0			0
$46$	−357.031	+	280.596i	−1.14438	+	0.899382i
$47$	−10.3285			−0.0320546			−0.0160273	−	0.999872i	$-0.505102\pi$
$47$	−10.3285			−0.0320546			−0.0160273	+	0.999872i	$0.505102\pi$
$48$		0			0
$49$	−334.355			−0.974796
$50$	−55.5957	+	43.6935i	−0.157248	+	0.123584i
$51$		0			0
$52$	−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	$-0.156380\pi$
$54$		0			0
$55$	89.2965			0.218923
$56$	−27.5822	−	60.5434i	−0.0658182	−	0.144472i
$57$		0			0
$58$	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	$-0.104033\pi$
$60$		0			0
$61$		−	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
$63$		0			0
$64$	−335.998	+	386.328i	−0.656246	+	0.754547i
$65$	−233.525			−0.445619
$66$		0			0
$67$			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
$69$		0			0
$70$	−25.6939	−	32.6930i	−0.0438716	−	0.0558224i
$71$	−455.528			−0.761426			−0.380713	−	0.924693i	$-0.624321\pi$
$71$	−455.528			−0.761426			−0.380713	+	0.924693i	$0.624321\pi$
$72$		0			0
$73$	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
$75$		0			0
$76$	−1260.81	−	306.686i	−1.90296	−	0.462886i
$77$			52.5108i			0.0777164i
$78$		0			0
$79$	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
$81$		0			0
$82$	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	$-0.0581438\pi$
$84$		0			0
$85$		−	108.393i		−	0.138316i
$86$	109.820	+	139.736i	0.137700	+	0.175210i
$87$		0			0
$88$	367.745	−	167.536i	0.445474	−	0.202948i
$89$	1572.69			1.87309			0.936543	−	0.350553i	$-0.114006\pi$
$89$	1572.69			1.87309			0.936543	+	0.350553i	$0.114006\pi$
$90$		0			0
$91$		−	137.324i		−	0.158192i
$92$	−303.568	+	1247.99i	−0.344012	+	1.41426i
$93$		0			0
$94$	−22.9688	+	18.0515i	−0.0252027	+	0.0198072i
$95$	−810.986			−0.875846
$96$		0			0
$97$	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
$99$		0			0
$100$	−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	$-0.0443904\pi$
$102$		0			0
$103$	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
$105$		0			0
$106$	−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	$-0.0122053\pi$
$108$		0			0
$109$			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
$111$		0			0
$112$	−167.152	−	86.4316i	−0.141021	−	0.0729198i
$113$	505.336			0.420691			0.210345	−	0.977627i	$-0.432541\pi$
$113$	505.336			0.420691			0.210345	+	0.977627i	$0.432541\pi$
$114$		0			0
$115$			802.739i			0.650920i
$116$	1664.85	+	404.965i	1.33256	+	0.324139i
$117$		0			0
$118$	−508.565	−	647.100i	−0.396756	−	0.504833i
$119$	63.7404			0.0491015
$120$		0			0
$121$	1012.05			0.760365
$122$	−913.283	−	1162.06i	−0.677744	−	0.862364i
$123$		0			0
$124$	−3.39651	+	13.9633i	−0.00245980	+	0.0101125i
$125$			125.000i			0.0894427i
$126$		0			0
$127$	−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
$129$		0			0
$130$	−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	$0.769804\pi$
$132$		0			0
$133$		−	476.900i		−	0.310921i
$134$	1191.80	+	1516.46i	0.768330	+	0.977626i
$135$		0			0
$136$	−203.364	−	446.389i	−0.128223	−	0.281452i
$137$	1675.18			1.04467			0.522337	−	0.852739i	$-0.325060\pi$
$137$	1675.18			1.04467			0.522337	+	0.852739i	$0.325060\pi$
$138$		0			0
$139$			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
$141$		0			0
$142$	−1013.02	+	796.144i	−0.598665	+	0.470499i
$143$	834.119			0.487780
$144$		0			0
$145$	1070.87			0.613317
$146$	1709.17	−	1343.26i	0.968851	−	0.761433i
$147$		0			0
$148$	−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	$-0.263477\pi$
$150$		0			0
$151$	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
$153$		0			0
$154$	91.7751	+	116.775i	0.0480224	+	0.0611039i
$155$			8.98156i			0.00465430i
$156$		0			0
$157$		−	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
$159$		0			0
$160$	169.932	+	889.001i	0.0839645	+	0.439261i
$161$	−472.051			−0.231073
$162$		0			0
$163$		−	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
$165$		0			0
$166$	−480.130	−	610.920i	−0.224490	−	0.285642i
$167$	1734.65			0.803779			0.401889	−	0.915688i	$-0.368354\pi$
$167$	1734.65			0.803779			0.401889	+	0.915688i	$0.368354\pi$
$168$		0			0
$169$	15.6411			0.00711928
$170$	−189.442	−	241.047i	−0.0854681	−	0.108750i
$171$		0			0
$172$	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	$-0.343717\pi$
$174$		0			0
$175$	−73.5062			−0.0317517
$176$	524.992	−	1015.29i	0.224845	−	0.434833i
$177$		0			0
$178$	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	$0.699261\pi$
$180$		0			0
$181$		−	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
$183$		0			0
$184$	1506.08	+	3305.88i	0.603423	+	1.32452i
$185$	−818.711			−0.325366
$186$		0			0
$187$			387.164i			0.151402i
$188$	−19.5294	+	80.2870i	−0.00757621	+	0.0311465i
$189$		0			0
$190$	−1803.49	+	1417.39i	−0.688627	+	0.541202i
$191$	−21.6852			−0.00821512			−0.00410756	−	0.999992i	$-0.501307\pi$
$191$	−21.6852			−0.00821512			−0.00410756	+	0.999992i	$0.501307\pi$
$192$		0			0
$193$	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
$195$		0			0
$196$	−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	$0.842849\pi$
$198$		0			0
$199$	−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
$201$		0			0
$202$	−493.195	−	627.543i	−0.171788	−	0.218583i
$203$			629.725i			0.217724i
$204$		0			0
$205$		−	1018.08i		−	0.346857i
$206$	2847.39	−	2237.80i	0.963044	−	0.756870i
$207$		0			0
$208$	−1372.94	+	2655.16i	−0.457675	+	0.885107i
$209$	2896.73			0.958712
$210$		0			0
$211$		−	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
$213$		0			0
$214$	−148.311	−	188.712i	−0.0473755	−	0.0602807i
$215$	314.178			0.0996594
$216$		0			0
$217$	−5.28160			−0.00165225
$218$	769.668	+	979.328i	0.239121	+	0.304259i
$219$		0			0
$220$	168.844	−	694.132i	0.0517430	−	0.212720i
$221$		−	1012.50i		−	0.308181i
$222$		0			0
$223$	−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
$225$		0			0
$226$	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	$0.906700\pi$
$228$		0			0
$229$			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
$231$		0			0
$232$	4410.11	−	2009.14i	1.24801	−	0.568563i
$233$	3950.24			1.11068			0.555341	−	0.831623i	$-0.312588\pi$
$233$	3950.24			1.11068			0.555341	+	0.831623i	$0.312588\pi$
$234$		0			0
$235$			51.6426i			0.0143353i
$236$	−2261.92	−	550.200i	−0.623892	−	0.151758i
$237$		0			0
$238$	141.748	−	111.402i	0.0386056	−	0.0303407i
$239$	−2706.48			−0.732499			−0.366250	−	0.930517i	$-0.619358\pi$
$239$	−2706.48			−0.732499			−0.366250	+	0.930517i	$0.619358\pi$
$240$		0			0
$241$	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
$243$		0			0
$244$	−4061.97	−	988.052i	−1.06574	−	0.259236i
$245$			1671.77i			0.435942i
$246$		0			0
$247$	−7575.42			−1.95147
$248$	16.8510	+	36.9883i	0.00431468	+	0.00947079i
$249$		0			0
$250$	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	$0.821449\pi$
$252$		0			0
$253$		−	2867.27i		−	0.712505i
$254$	−3915.06	+	3076.90i	−0.967136	+	0.760086i
$255$		0			0
$256$	2367.75	+	3342.30i	0.578063	+	0.815992i
$257$	−6002.97			−1.45702			−0.728511	−	0.685034i	$-0.759787\pi$
$257$	−6002.97			−1.45702			−0.728511	+	0.685034i	$0.759787\pi$
$258$		0			0
$259$		−	481.443i		−	0.115503i
$260$	−441.555	+	1815.27i	−0.105323	+	0.432993i
$261$		0			0
$262$	3468.35	+	4413.14i	0.817846	+	1.04063i
$263$	−3518.76			−0.825004			−0.412502	−	0.910957i	$-0.635345\pi$
$263$	−3518.76			−0.825004			−0.412502	+	0.910957i	$0.635345\pi$
$264$		0			0
$265$	−1820.25			−0.421952
$266$	−833.496	−	1060.54i	−0.192124	−	0.244459i
$267$		0			0
$268$	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	$0.977625\pi$
$270$		0			0
$271$	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
$273$		0			0
$274$	3725.31	−	2927.78i	0.821366	−	0.645523i
$275$		−	446.483i		−	0.0979051i
$276$		0			0
$277$			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
$279$		0			0
$280$	−302.717	+	137.911i	−0.0646100	+	0.0294348i
$281$	−2940.17			−0.624184			−0.312092	−	0.950052i	$-0.601030\pi$
$281$	−2940.17			−0.624184			−0.312092	+	0.950052i	$0.601030\pi$
$282$		0			0
$283$		−	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
$285$		0			0
$286$	1854.94	−	1457.82i	0.383513	−	0.301408i
$287$	598.681			0.123133
$288$		0			0
$289$	−4443.04			−0.904343
$290$	2381.43	−	1871.60i	0.482215	−	0.378980i
$291$		0			0
$292$	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	$-0.283846\pi$
$294$		0			0
$295$	−1454.92			−0.287149
$296$	−3371.65	+	1536.05i	−0.662072	+	0.301625i
$297$		0			0
$298$	−4681.67	−	5956.97i	−0.910073	−	1.15798i
$299$			7498.39i			1.45031i
$300$		0			0
$301$			184.752i			0.0353786i
$302$	5990.06	−	4707.67i	1.14136	−	0.897007i
$303$		0			0
$304$	−4767.95	+	9220.84i	−0.899542	+	1.73964i
$305$	−2612.76			−0.490511
$306$		0			0
$307$			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
$309$		0			0
$310$	15.6974	+	19.9734i	0.00287598	+	0.00365940i
$311$	−7248.12			−1.32155			−0.660777	−	0.750582i	$-0.729773\pi$
$311$	−7248.12			−1.32155			−0.660777	+	0.750582i	$0.729773\pi$
$312$		0			0
$313$	−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
$315$		0			0
$316$	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	$-0.115494\pi$
$318$		0			0
$319$	−3825.00			−0.671344
$320$	1931.64	+	1679.99i	0.337444	+	0.293482i
$321$		0			0
$322$	−1049.76	+	825.021i	−0.181680	+	0.142785i
$323$		−	3516.20i		−	0.605718i
$324$		0			0
$325$			1167.63i			0.199287i
$326$	−5887.19	−	7490.88i	−1.00019	−	1.27264i
$327$		0			0
$328$	−1910.10	−	4192.70i	−0.321547	−	0.705802i
$329$	−30.3684			−0.00508895
$330$		0			0
$331$			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
$333$		0			0
$334$	3857.56	−	3031.71i	0.631965	−	0.496670i
$335$	3409.56			0.556073
$336$		0			0
$337$	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
$339$		0			0
$340$	−842.575	−	204.952i	−0.134397	−	0.0326914i
$341$		−	32.0809i		−	0.00509465i
$342$		0			0
$343$	−1991.59			−0.313516
$344$	1293.86	−	589.454i	0.202792	−	0.0923874i
$345$		0			0
$346$	−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	$-0.405060\pi$
$348$		0			0
$349$			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
$351$		0			0
$352$	−606.974	−	3175.39i	−0.0919087	−	0.480820i
$353$	−1085.49			−0.163669			−0.0818343	−	0.996646i	$-0.526078\pi$
$353$	−1085.49			−0.163669			−0.0818343	+	0.996646i	$0.526078\pi$
$354$		0			0
$355$			2277.64i			0.340520i
$356$	2973.68	−	12225.0i	0.442709	−	1.82002i
$357$		0			0
$358$	6783.82	+	8631.75i	1.00150	+	1.27431i
$359$	−12270.1			−1.80387			−0.901936	−	0.431869i	$-0.857854\pi$
$359$	−12270.1			−1.80387			−0.901936	+	0.431869i	$0.857854\pi$
$360$		0			0
$361$	−19448.9			−2.83553
$362$	−1282.19	−	1631.46i	−0.186161	−	0.236873i
$363$		0			0
$364$	−1067.47	−	259.656i	−0.153710	−	0.0373892i
$365$		−	3842.86i		−	0.551081i
$366$		0			0
$367$	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
$369$		0			0
$370$	−1820.67	+	1430.89i	−0.255817	+	0.201050i
$371$		−	1070.40i		−	0.149791i
$372$		0			0
$373$		−	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
$375$		0			0
$376$	96.8907	+	212.677i	0.0132892	+	0.0291701i
$377$	10003.0			1.36653
$378$		0			0
$379$		−	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
$381$		0			0
$382$	−48.2242	+	37.9001i	−0.00645908	+	0.00507628i
$383$	−7961.76			−1.06221			−0.531105	−	0.847306i	$-0.678223\pi$
$383$	−7961.76			−1.06221			−0.531105	+	0.847306i	$0.678223\pi$
$384$		0			0
$385$	262.554			0.0347558
$386$	2934.67	−	2306.40i	0.386971	−	0.304126i
$387$		0			0
$388$	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	$-0.134644\pi$
$390$		0			0
$391$	−3480.45			−0.450163
$392$	3136.55	+	6884.78i	0.404132	+	0.887076i
$393$		0			0
$394$	4580.21	+	5827.87i	0.585654	+	0.745188i
$395$		−	5075.59i		−	0.646533i
$396$		0			0
$397$		−	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
$399$		0			0
$400$	1421.24	+	734.901i	0.177655	+	0.0918626i
$401$	2292.02			0.285432			0.142716	−	0.989764i	$-0.454417\pi$
$401$	2292.02			0.285432			0.142716	+	0.989764i	$0.454417\pi$
$402$		0			0
$403$			83.8968i			0.0103702i
$404$	−2193.56	−	533.573i	−0.270133	−	0.0657085i
$405$		0			0
$406$	1100.59	+	1400.40i	0.134536	+	0.171184i
$407$	2924.32			0.356150
$408$		0			0
$409$	−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
$411$		0			0
$412$	2421.01	−	9952.99i	0.289502	−	1.19017i
$413$		−	855.567i		−	0.101936i
$414$		0			0
$415$	−1373.58			−0.162473
$416$	1587.34	+	8304.16i	0.187081	+	0.978714i
$417$		0			0
$418$	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	$0.905879\pi$
$420$		0			0
$421$		−	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
$423$		0			0
$424$	−7496.25	+	3415.12i	−0.858609	+	0.391162i
$425$	−541.965			−0.0618568
$426$		0			0
$427$		−	1536.43i		−	0.174129i
$428$	−659.638	−	160.453i	−0.0744972	−	0.0181210i
$429$		0			0
$430$	698.678	−	549.101i	0.0783564	−	0.0615814i
$431$	8423.43			0.941398			0.470699	−	0.882294i	$-0.344002\pi$
$431$	8423.43			0.941398			0.470699	+	0.882294i	$0.344002\pi$
$432$		0			0
$433$	−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
$435$		0			0
$436$	3423.22	+	832.679i	0.376015	+	0.0914636i
$437$			26040.4i			2.85053i
$438$		0			0
$439$	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
$441$		0			0
$442$	−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	$-0.154383\pi$
$444$		0			0
$445$		−	7863.44i		−	0.837669i
$446$	−7811.57	+	6139.23i	−0.829347	+	0.651795i
$447$		0			0
$448$	−987.917	+	1135.90i	−0.104185	+	0.119791i
$449$	−10748.7			−1.12976			−0.564878	−	0.825174i	$-0.691077\pi$
$449$	−10748.7			−1.12976			−0.564878	+	0.825174i	$0.691077\pi$
$450$		0			0
$451$			3636.44i			0.379674i
$452$	955.502	−	3928.15i	0.0994315	−	0.408771i
$453$		0			0
$454$	3454.13	+	4395.05i	0.357072	+	0.454339i
$455$	−686.622			−0.0707458
$456$		0			0
$457$	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
$459$		0			0
$460$	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	$0.699560\pi$
$462$		0			0
$463$	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
$465$		0			0
$466$	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	$0.943261\pi$
$468$		0			0
$469$			2004.99i			0.197403i
$470$	90.2577	+	114.844i	0.00885803	+	0.0112710i
$471$		0			0
$472$	−5991.73	+	2729.69i	−0.584305	+	0.266196i
$473$	−1122.20			−0.109088
$474$		0			0
$475$			4054.93i			0.391690i
$476$	120.522	−	495.476i	0.0116053	−	0.0477103i
$477$		0			0
$478$	−6018.74	+	4730.21i	−0.575922	+	0.452625i
$479$	7375.39			0.703529			0.351764	−	0.936089i	$-0.385582\pi$
$479$	7375.39			0.703529			0.351764	+	0.936089i	$0.385582\pi$
$480$		0			0
$481$	−7647.58			−0.724947
$482$	16539.1	−	12998.3i	1.56294	−	1.22833i
$483$		0			0
$484$	1913.60	−	7866.97i	0.179714	−	0.738821i
$485$		−	890.670i		−	0.0833881i
$486$		0			0
$487$	−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
$489$		0			0
$490$	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	$0.689006\pi$
$492$		0			0
$493$			4642.99i			0.424158i
$494$	−16846.4	+	13239.9i	−1.53433	+	1.20585i
$495$		0			0
$496$	102.120	+	52.8044i	0.00924456	+	0.00478022i
$497$	−1339.37			−0.120883
$498$		0			0
$499$			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
$501$		0			0
$502$	7394.51	+	9408.81i	0.657437	+	0.836525i
$503$	−188.469			−0.0167066			−0.00835331	−	0.999965i	$-0.502659\pi$
$503$	−188.469			−0.0167066			−0.00835331	+	0.999965i	$0.502659\pi$
$504$		0			0
$505$	−1410.95			−0.124330
$506$	−5011.24	−	6376.32i	−0.440270	−	0.560202i
$507$		0			0
$508$	−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	$0.777286\pi$
$510$		0			0
$511$	2259.79			0.195631
$512$	11106.9	+	3294.50i	0.958714	+	0.284371i
$513$		0			0
$514$	−13349.6	+	10491.6i	−1.14557	+	0.900321i
$515$		−	6402.00i		−	0.547779i
$516$		0			0
$517$		−	184.460i		−	0.0156916i
$518$	−841.436	−	1070.65i	−0.0713717	−	0.0908137i
$519$		0			0
$520$	2190.67	+	4808.57i	0.184745	+	0.405519i
$521$	20291.3			1.70630			0.853148	−	0.521669i	$-0.174690\pi$
$521$	20291.3			1.70630			0.853148	+	0.521669i	$0.174690\pi$
$522$		0			0
$523$		−	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
$525$		0			0
$526$	−7825.12	+	6149.87i	−0.648653	+	0.509785i
$527$	−38.9415			−0.00321882
$528$		0			0
$529$	13608.6			1.11848
$530$	−4047.93	+	3181.33i	−0.331756	+	0.260732i
$531$		0			0
$532$	−3707.11	−	901.734i	−0.302112	−	0.0734871i
$533$		−	9509.88i		−	0.772831i
$534$		0			0
$535$	−424.295			−0.0342876
$536$	14041.4	−	6396.95i	1.13152	−	0.515496i
$537$		0			0
$538$	1083.18	+	1378.24i	0.0868013	+	0.110446i
$539$		−	5971.35i		−	0.477188i
$540$		0			0
$541$			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
$543$		0			0
$544$	−3854.46	+	736.778i	−0.303784	+	0.0580682i
$545$	2201.90			0.173062
$546$		0			0
$547$			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
$549$		0			0
$550$	−780.335	−	992.901i	−0.0604974	−	0.0769771i
$551$	34738.4			2.68585
$552$		0			0
$553$	2984.70			0.229516
$554$	297.227	+	378.193i	0.0227942	+	0.0290034i
$555$		0			0
$556$	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	$0.935006\pi$
$558$		0			0
$559$	2934.74			0.222051
$560$	−432.158	+	835.760i	−0.0326107	+	0.0630666i
$561$		0			0
$562$	−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	$-0.130169\pi$
$564$		0			0
$565$		−	2526.68i		−	0.188139i
$566$	−5298.93	−	6742.38i	−0.393517	−	0.500713i
$567$		0			0
$568$	4273.26	+	9379.88i	0.315673	+	0.692907i
$569$	24063.9			1.77296			0.886478	−	0.462771i	$-0.153145\pi$
$569$	24063.9			1.77296			0.886478	+	0.462771i	$0.153145\pi$
$570$		0			0
$571$			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
$573$		0			0
$574$	1331.36	−	1046.34i	0.0968120	−	0.0760859i
$575$	4013.70			0.291100
$576$		0			0
$577$	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
$579$		0			0
$580$	2024.83	−	8324.23i	0.144959	−	0.595940i
$581$		−	807.731i		−	0.0576770i
$582$		0			0
$583$	6501.69			0.461874
$584$	−7209.90	−	15825.9i	−0.510869	−	1.12137i
$585$		0			0
$586$	−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	$-0.0341423\pi$
$588$		0			0
$589$			291.357i			0.0203822i
$590$	−3235.50	+	2542.82i	−0.225768	+	0.177435i
$591$		0			0
$592$	−4813.37	+	9308.67i	−0.334169	+	0.646257i
$593$	−19029.4			−1.31778			−0.658890	−	0.752239i	$-0.728974\pi$
$593$	−19029.4			−1.31778			−0.658890	+	0.752239i	$0.728974\pi$
$594$		0			0
$595$		−	318.702i		−	0.0219589i
$596$	−20822.5	−	5064.95i	−1.43108	−	0.348102i
$597$		0			0
$598$	13105.2	+	16675.1i	0.896174	+	1.14030i
$599$	−5789.36			−0.394903			−0.197451	−	0.980313i	$-0.563266\pi$
$599$	−5789.36			−0.394903			−0.197451	+	0.980313i	$0.563266\pi$
$600$		0			0
$601$	−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
$603$		0			0
$604$	5093.09	−	20938.1i	0.343104	−	1.41053i
$605$		−	5060.23i		−	0.340045i
$606$		0			0
$607$	−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
$609$		0			0
$610$	−5810.32	+	4566.41i	−0.385661	+	0.303096i
$611$			482.393i			0.0319403i
$612$		0			0
$613$			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
$615$		0			0
$616$	1081.26	−	492.598i	0.0707229	−	0.0322197i
$617$	−21929.0			−1.43084			−0.715421	−	0.698694i	$-0.753765\pi$
$617$	−21929.0			−1.43084			−0.715421	+	0.698694i	$0.753765\pi$
$618$		0			0
$619$		−	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
$621$		0			0
$622$	−16118.6	+	12667.8i	−1.03906	+	0.816613i
$623$	4624.10			0.297368
$624$		0			0
$625$	625.000			0.0400000
$626$	−14926.0	+	11730.6i	−0.952977	+	0.748958i
$627$		0			0
$628$	−8635.93	−	2100.64i	−0.548744	−	0.133479i
$629$		−	3549.70i		−	0.225017i
$630$		0			0
$631$	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
$633$		0			0
$634$	−7002.19	−	8909.62i	−0.438632	−	0.558117i
$635$			8802.52i			0.550106i
$636$		0			0
$637$			15616.1i			0.971320i
$638$	−8506.14	+	6685.09i	−0.527839	+	0.414836i
$639$		0			0
$640$	7231.82	+	360.003i	0.446661	+	0.0222350i
$641$	−10005.0			−0.616496			−0.308248	−	0.951306i	$-0.599743\pi$
$641$	−10005.0			−0.616496			−0.308248	+	0.951306i	$0.599743\pi$
$642$		0			0
$643$			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
$645$		0			0
$646$	−6145.40	−	7819.44i	−0.374284	−	0.476241i
$647$	4225.62			0.256764			0.128382	−	0.991725i	$-0.459022\pi$
$647$	4225.62			0.256764			0.128382	+	0.991725i	$0.459022\pi$
$648$		0			0
$649$	5196.78			0.314317
$650$	2040.70	+	2596.60i	0.123143	+	0.156688i
$651$		0			0
$652$	−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	$-0.0938394\pi$
$654$		0			0
$655$	9922.41			0.591909
$656$	−11575.5	−	5985.50i	−0.688943	−	0.356241i
$657$		0			0
$658$	−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	$-0.0828587\pi$
$660$		0			0
$661$			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
$663$		0			0
$664$	−5656.73	+	2577.07i	−0.330608	+	0.150617i
$665$	−2384.50			−0.139048
$666$		0			0
$667$		−	34385.2i		−	1.99610i
$668$	3279.91	−	13484.0i	0.189975	−	0.781005i
$669$		0			0
$670$	7582.28	−	5959.02i	0.437208	−	0.343608i
$671$	9332.40			0.536920
$672$		0			0
$673$	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
$675$		0			0
$676$	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	$0.904674\pi$
$678$		0			0
$679$	523.758			0.0296024
$680$	−2231.94	+	1016.82i	−0.125869	+	0.0573432i
$681$		0			0
$682$	−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	$-0.265317\pi$
$684$		0			0
$685$		−	8375.90i		−	0.467192i
$686$	−4428.96	+	3480.78i	−0.246499	+	0.193727i
$687$		0			0
$688$	1847.12	−	3572.18i	0.102356	−	0.197948i
$689$	−17003.0			−0.940149
$690$		0			0
$691$			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
$693$		0			0
$694$	−21596.8	−	27479.9i	−1.18127	−	1.50306i
$695$	9517.07			0.519429
$696$		0			0
$697$	4414.10			0.239880
$698$	22567.3	+	28714.7i	1.22376	+	1.55712i
$699$		0			0
$700$	−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	$-0.0483014\pi$
$702$		0			0
$703$	−26558.5			−1.42485
$704$	−6899.55	−	6000.69i	−0.369370	−	0.321249i
$705$		0			0
$706$	−2413.95	+	1897.16i	−0.128683	+	0.101134i
$707$		−	829.711i		−	0.0441365i
$708$		0			0
$709$		−	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
$711$		0			0
$712$	−14753.2	−	32383.6i	−0.776545	−	1.70453i
$713$	288.394			0.0151479
$714$		0			0
$715$		−	4170.60i		−	0.218142i
$716$	30172.1	+	7339.20i	1.57484	+	0.383071i
$717$		0			0
$718$	−27286.6	+	21444.9i	−1.41828	+	1.11465i
$719$	4998.44			0.259263			0.129632	−	0.991562i	$-0.458621\pi$
$719$	4998.44			0.259263			0.129632	+	0.991562i	$0.458621\pi$
$720$		0			0
$721$	3764.70			0.194459
$722$	−43251.1	+	33991.6i	−2.22941	+	1.75213i
$723$		0			0
$724$	−5702.74	−	1387.16i	−0.292736	−	0.0712065i
$725$		−	5354.35i		−	0.274284i
$726$		0			0
$727$	−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
$729$		0			0
$730$	−6716.32	−	8545.87i	−0.340523	−	0.433283i
$731$			1362.19i			0.0689225i
$732$		0			0
$733$		−	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
$735$		0			0
$736$	28545.4	−	5456.45i	1.42962	−	0.273271i
$737$	−12178.5			−0.608684
$738$		0			0
$739$		−	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
$741$		0			0
$742$	−1870.78	−	2380.38i	−0.0925585	−	0.117772i
$743$	−3157.00			−0.155880			−0.0779401	−	0.996958i	$-0.524834\pi$
$743$	−3157.00			−0.155880			−0.0779401	+	0.996958i	$0.524834\pi$
$744$		0			0
$745$	−13393.5			−0.658658
$746$	−17576.9	−	22364.9i	−0.862648	−	1.09764i
$747$		0			0
$748$	3009.56	+	732.060i	0.147113	+	0.0357844i
$749$		−	249.507i		−	0.0121719i
$750$		0			0
$751$	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
$753$		0			0
$754$	22245.0	−	17482.6i	1.07442	−	0.844403i
$755$		−	13467.9i		−	0.649202i
$756$		0			0
$757$			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
$759$		0			0
$760$	7607.77	+	16699.2i	0.363109	+	0.797031i
$761$	−29909.5			−1.42473			−0.712363	−	0.701811i	$-0.752375\pi$
$761$	−29909.5			−1.42473			−0.712363	+	0.701811i	$0.752375\pi$
$762$		0			0
$763$			1294.82i			0.0614362i
$764$	−41.0030	+	168.567i	−0.00194167	+	0.00798237i
$765$		0			0
$766$	−17705.6	+	13915.1i	−0.835155	+	0.656360i
$767$	−13590.4			−0.639794
$768$		0			0
$769$	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
$771$		0			0
$772$	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	$0.941629\pi$
$774$		0			0
$775$	44.9078			0.00208146
$776$	−1671.06	−	3668.00i	−0.0773034	−	0.169682i
$777$		0			0
$778$	−11008.8	−	14007.6i	−0.507305	−	0.645496i
$779$		−	33025.9i		−	1.51897i
$780$		0			0
$781$		−	8135.41i		−	0.372737i
$782$	−7739.92	+	6082.91i	−0.353937	+	0.278164i
$783$		0			0
$784$	19007.9	+	9828.71i	0.865886	+	0.447736i
$785$	−5554.84			−0.252561
$786$		0			0
$787$			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
$789$		0			0
$790$	−8870.80	−	11287.2i	−0.399505	−	0.508332i
$791$	1485.81			0.0667882
$792$		0			0
$793$	−24405.8			−1.09291
$794$	−12794.1	−	16279.2i	−0.571845	−	0.727617i
$795$		0			0
$796$	−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	$-0.0196416\pi$
$798$		0			0
$799$	−223.908			−0.00991399
$800$	4445.01	−	849.661i	0.196443	−	0.0375501i
$801$		0			0
$802$	5097.06	−	4005.85i	0.224418	−	0.176374i
$803$			13726.2i			0.603220i
$804$		0			0
$805$			2360.25i			0.103339i
$806$	146.630	+	186.572i	0.00640795	+	0.00815350i
$807$		0			0
$808$	−5810.65	+	2647.20i	−0.252993	+	0.115258i
$809$	4977.21			0.216303			0.108152	−	0.994134i	$-0.465507\pi$
$809$	4977.21			0.216303			0.108152	+	0.994134i	$0.465507\pi$
$810$		0			0
$811$			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
$813$		0			0
$814$	6503.19	−	5110.95i	0.280020	−	0.220072i
$815$	−16842.3			−0.723878
$816$		0			0
$817$	10191.8			0.436432
$818$	−17230.3	+	13541.5i	−0.736483	+	0.578812i
$819$		0			0
$820$	−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	$-0.00723765\pi$
$822$		0			0
$823$	−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
$825$		0			0
$826$	−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	$0.999290\pi$
$828$		0			0
$829$			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
$831$		0			0
$832$	18043.5	+	15692.8i	0.751857	+	0.653905i
$833$	−7248.34			−0.301489
$834$		0			0
$835$		−	8673.24i		−	0.359461i
$836$	5477.20	−	22517.2i	0.226594	−	0.931549i
$837$		0			0
$838$	8736.11	+	11115.9i	0.360124	+	0.458223i
$839$	29684.4			1.22148			0.610738	−	0.791833i	$-0.290873\pi$
$839$	29684.4			1.22148			0.610738	+	0.791833i	$0.290873\pi$
$840$		0			0
$841$	−21481.5			−0.880786
$842$	−6634.37	−	8441.60i	−0.271539	−	0.345507i
$843$		0			0
$844$	−1455.32	−	353.999i	−0.0593533	−	0.0144374i
$845$		−	78.2053i		−	0.00318384i
$846$		0			0
$847$	2975.67			0.120714
$848$	−10701.6	+	20696.1i	−0.433368	+	0.838099i
$849$		0			0
$850$	−1205.24	+	947.212i	−0.0486344	+	0.0382225i
$851$			26288.4i			1.05894i
$852$		0			0
$853$		−	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
$855$		0			0
$856$	−1747.35	+	796.053i	−0.0697701	+	0.0317857i
$857$	34610.8			1.37956			0.689779	−	0.724020i	$-0.257708\pi$
$857$	34610.8			1.37956			0.689779	+	0.724020i	$0.257708\pi$
$858$		0			0
$859$		−	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
$861$		0			0
$862$	18732.3	−	14722.0i	0.740167	−	0.581707i
$863$	38597.5			1.52245			0.761224	−	0.648488i	$-0.224599\pi$
$863$	38597.5			1.52245			0.761224	+	0.648488i	$0.224599\pi$
$864$		0			0
$865$	−20066.6			−0.788770
$866$	−5606.46	+	4406.19i	−0.219994	+	0.172897i
$867$		0			0
$868$	−9.98658	+	41.0557i	−0.000390514	+	0.00160544i
$869$			18129.3i			0.707704i
$870$		0			0
$871$	31848.7			1.23898
$872$	9067.95	−	4131.15i	0.352155	−	0.160434i
$873$		0			0
$874$	45511.8	+	57909.4i	1.76140	+	2.24121i
$875$			367.531i			0.0141998i
$876$		0			0
$877$			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
$879$		0			0
$880$	−5076.47	−	2624.96i	−0.194463	−	0.100554i
$881$	−28819.4			−1.10210			−0.551050	−	0.834472i	$-0.685773\pi$
$881$	−28819.4			−1.10210			−0.551050	+	0.834472i	$0.685773\pi$
$882$		0			0
$883$			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
$885$		0			0
$886$	−15195.0	−	19334.1i	−0.576168	−	0.733119i
$887$	−25787.8			−0.976178			−0.488089	−	0.872794i	$-0.662306\pi$
$887$	−25787.8			−0.976178			−0.488089	+	0.872794i	$0.662306\pi$
$888$		0			0
$889$	−5176.32			−0.195285
$890$	−13743.2	−	17486.9i	−0.517612	−	0.658611i
$891$		0			0
$892$	−6641.84	+	27305.2i	−0.249311	+	1.02494i
$893$			1675.26i			0.0627775i
$894$		0			0
$895$	19407.4			0.724825
$896$	−211.700	+	4252.67i	−0.00789330	+	0.158562i
$897$		0			0
$898$	−23903.2	+	18785.8i	−0.888262	+	0.698098i
$899$		−	384.723i		−	0.0142728i
$900$		0			0
$901$		−	7892.10i		−	0.291814i
$902$	6355.54	+	8086.81i	0.234608	+	0.298516i
$903$		0			0
$904$	−4740.51	−	10405.5i	−0.174410	−	0.382834i
$905$	−3668.14			−0.134733
$906$		0			0
$907$			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
$909$		0			0
$910$	−1526.93	+	1200.04i	−0.0556233	+	0.0437151i
$911$	−20391.9			−0.741616			−0.370808	−	0.928710i	$-0.620919\pi$
$911$	−20391.9			−0.741616			−0.370808	+	0.928710i	$0.620919\pi$
$912$		0			0
$913$	4906.22			0.177845
$914$	34584.2	−	27180.2i	1.25158	−	0.983634i
$915$		0			0
$916$	28523.2	+	6938.12i	1.02886	+	0.250264i
$917$			5834.87i			0.210125i
$918$		0			0
$919$	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
$921$		0			0
$922$	28018.9	+	35651.3i	1.00082	+	1.27344i
$923$			21275.4i			0.758711i
$924$		0			0
$925$			4093.55i			0.145508i
$926$	36666.1	−	28816.4i	1.30121	−	1.02264i
$927$		0			0
$928$	−7279.02	−	38080.2i	−0.257484	−	1.34703i
$929$	22104.8			0.780663			0.390332	−	0.920674i	$-0.372360\pi$
$929$	22104.8			0.780663			0.390332	+	0.920674i	$0.372360\pi$
$930$		0			0
$931$			54231.4i			1.90909i
$932$	7469.20	−	30706.5i	0.262513	−	1.07921i
$933$		0			0
$934$	6254.76	+	7958.57i	0.219124	+	0.278814i
$935$	1935.82			0.0677093
$936$		0			0
$937$	−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
$939$		0			0
$940$	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	$0.674784\pi$
$942$		0			0
$943$	−32690.1			−1.12888
$944$	−8553.79	+	16542.3i	−0.294917	+	0.570347i
$945$		0			0
$946$	−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	$0.913709\pi$
$948$		0			0
$949$		−	35896.2i		−	1.22786i
$950$	7086.95	+	9017.47i	0.242033	+	0.307963i
$951$		0			0
$952$	−597.942	−	1312.49i	−0.0203565	−	0.0446830i
$953$	25045.9			0.851327			0.425664	−	0.904881i	$-0.360041\pi$
$953$	25045.9			0.851327			0.425664	+	0.904881i	$0.360041\pi$
$954$		0			0
$955$			108.426i			0.00367392i
$956$	−5117.47	+	21038.4i	−0.173128	+	0.711746i
$957$		0			0
$958$	16401.6	−	12890.3i	0.553144	−	0.434724i
$959$	4925.45			0.165851
$960$		0			0
$961$	−29787.8			−0.999892
$962$	−17006.9	+	13366.0i	−0.569984	+	0.447958i
$963$		0			0
$964$	14062.5	−	57812.0i	0.469836	−	1.93154i
$965$		−	6598.25i		−	0.220109i
$966$		0			0
$967$	−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
$969$		0			0
$970$	−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	$0.979785\pi$
$972$		0			0
$973$			5596.51i			0.184395i
$974$	−8809.33	+	6923.37i	−0.289804	+	0.227761i
$975$		0			0
$976$	−15360.9	+	29706.8i	−0.503782	+	0.974275i
$977$	43474.6			1.42362			0.711810	−	0.702372i	$-0.247876\pi$
$977$	43474.6			1.42362			0.711810	+	0.702372i	$0.247876\pi$
$978$		0			0
$979$			28087.1i			0.916924i
$980$	12995.3	+	3161.03i	0.423590	+	0.103036i
$981$		0			0
$982$	31520.6	+	40107.0i	1.02430	+	1.30332i
$983$	−17053.6			−0.553333			−0.276667	−	0.960966i	$-0.589230\pi$
$983$	−17053.6			−0.553333			−0.276667	+	0.960966i	$0.589230\pi$
$984$		0			0
$985$	13103.2			0.423862
$986$	8114.73	+	10325.2i	0.262095	+	0.333491i
$987$		0			0
$988$	−14323.8	+	58886.3i	−0.461235	+	1.89618i
$989$		−	10088.1i		−	0.324352i
$990$		0			0
$991$	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
$993$		0			0
$994$	−2978.52	+	2340.86i	−0.0950432	+	0.0746958i
$995$			16624.7i			0.529687i
$996$		0			0
$997$		−	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
$999$		0			0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	360.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.22383 - 1.74774i) q^{2} +(1.89082 - 7.77334i) q^{4} -5.00000i q^{5} +2.94025 q^{7} +(-9.38089 - 20.5912i) q^{8} +(-8.73869 - 11.1191i) q^{10} +17.8593i q^{11} -46.7050i q^{13} +(6.53861 - 5.13879i) q^{14} +(-56.8496 - 29.3960i) q^{16} +21.6786 q^{17} -162.197i q^{19} +(-38.8667 - 9.45412i) q^{20} +(31.2134 + 39.7160i) q^{22} -160.548 q^{23} -25.0000 q^{25} +(-81.6281 - 103.864i) q^{26} +(5.55949 - 22.8556i) q^{28} +214.174i q^{29} -1.79631 q^{31} +(-177.800 + 33.9865i) q^{32} +(48.2094 - 37.8885i) q^{34} -14.7012i q^{35} -163.742i q^{37} +(-283.478 - 360.699i) q^{38} +(-102.956 + 46.9045i) q^{40} +203.616 q^{41} +62.8357i q^{43} +(138.826 + 33.7688i) q^{44} +(-357.031 + 280.596i) q^{46} -10.3285 q^{47} -334.355 q^{49} +(-55.5957 + 43.6935i) q^{50} +(-363.054 - 88.3110i) q^{52} -364.051i q^{53} +89.2965 q^{55} +(-27.5822 - 60.5434i) q^{56} +(374.320 + 476.286i) q^{58} -290.985i q^{59} -522.551i q^{61} +(-3.99469 + 3.13948i) q^{62} +(-335.998 + 386.328i) q^{64} -233.525 q^{65} +681.913i q^{67} +(40.9904 - 168.515i) q^{68} +(-25.6939 - 32.6930i) q^{70} -455.528 q^{71} +768.573 q^{73} +(-286.178 - 364.134i) q^{74} +(-1260.81 - 306.686i) q^{76} +52.5108i q^{77} +1015.12 q^{79} +(-146.980 + 284.248i) q^{80} +(452.807 - 355.867i) q^{82} -274.715i q^{83} -108.393i q^{85} +(109.820 + 139.736i) q^{86} +(367.745 - 167.536i) q^{88} +1572.69 q^{89} -137.324i q^{91} +(-303.568 + 1247.99i) q^{92} +(-22.9688 + 18.0515i) q^{94} -810.986 q^{95} +178.134 q^{97} +(-743.548 + 584.365i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} - 2 q^{4} - 28 q^{7} + 8 q^{8} - 20 q^{10} + 8 q^{14} - 22 q^{16} - 204 q^{17} + 20 q^{20} - 84 q^{22} + 328 q^{23} - 350 q^{25} + 4 q^{26} + 68 q^{28} + 596 q^{31} - 588 q^{32} + 756 q^{34}+ \cdots - 6246 q^{98}+O(q^{100}) \) 14 * q + 2 * q^2 - 2 * q^4 - 28 * q^7 + 8 * q^8 - 20 * q^10 + 8 * q^14 - 22 * q^16 - 204 * q^17 + 20 * q^20 - 84 * q^22 + 328 * q^23 - 350 * q^25 + 4 * q^26 + 68 * q^28 + 596 * q^31 - 588 * q^32 + 756 * q^34 + 1144 * q^38 + 230 * q^40 + 820 * q^41 + 2084 * q^44 - 1060 * q^46 + 104 * q^47 + 1110 * q^49 - 50 * q^50 - 1736 * q^52 - 440 * q^55 - 3812 * q^56 + 2664 * q^58 + 772 * q^62 + 2470 * q^64 + 2864 * q^68 - 1280 * q^70 - 1592 * q^71 - 2260 * q^73 - 1020 * q^74 - 2468 * q^76 - 220 * q^79 - 80 * q^80 + 3444 * q^82 + 1184 * q^86 - 500 * q^88 + 2492 * q^89 + 4536 * q^92 - 4300 * q^94 + 280 * q^95 + 3508 * q^97 - 6246 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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