LMFDB - Embedded newform 360.4.k.c.181.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [360,4,Mod(181,360)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$21.2406876021$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{11} + 7x^{10} - 12x^{9} + 21x^{8} - 68x^{6} + 336x^{4} - 768x^{3} + 1792x^{2} - 4096x + 4096 $ x^12 - 4x^11 + 7x^10 - 12x^9 + 21x^8 - 68x^6 + 336x^4 - 768x^3 + 1792x^2 - 4096*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14}\cdot 5^{4} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.2
Root			$1.71681 + 1.02595i$ of defining polynomial
Character	$\chi$	$=$	360.181
Dual form			360.4.k.c.181.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.74276 + 0.690860i) q^{2} +(7.04543 - 3.78972i) q^{4} -5.00000i q^{5} -14.6308 q^{7} +(-16.7057 + 15.2617i) q^{8} +(3.45430 + 13.7138i) q^{10} -14.9969i q^{11} +85.6955i q^{13} +(40.1288 - 10.1078i) q^{14} +(35.2761 - 53.4004i) q^{16} +91.9247 q^{17} -60.3737i q^{19} +(-18.9486 - 35.2271i) q^{20} +(10.3608 + 41.1330i) q^{22} -1.33730 q^{23} -25.0000 q^{25} +(-59.2035 - 235.042i) q^{26} +(-103.080 + 55.4467i) q^{28} -25.5118i q^{29} +73.4354 q^{31} +(-59.8615 + 170.835i) q^{32} +(-252.127 + 63.5070i) q^{34} +73.1541i q^{35} -211.259i q^{37} +(41.7098 + 165.590i) q^{38} +(76.3084 + 83.5286i) q^{40} -330.839 q^{41} -388.500i q^{43} +(-56.8342 - 105.660i) q^{44} +(3.66788 - 0.923883i) q^{46} +550.348 q^{47} -128.939 q^{49} +(68.5689 - 17.2715i) q^{50} +(324.762 + 603.761i) q^{52} -187.705i q^{53} -74.9847 q^{55} +(244.419 - 223.291i) q^{56} +(17.6251 + 69.9727i) q^{58} -779.090i q^{59} -358.850i q^{61} +(-201.415 + 50.7335i) q^{62} +(46.1625 - 509.915i) q^{64} +428.477 q^{65} +283.674i q^{67} +(647.648 - 348.369i) q^{68} +(-50.5392 - 200.644i) q^{70} +534.811 q^{71} +1016.16 q^{73} +(145.950 + 579.431i) q^{74} +(-228.799 - 425.359i) q^{76} +219.418i q^{77} +1119.59 q^{79} +(-267.002 - 176.380i) q^{80} +(907.411 - 228.563i) q^{82} -1190.49i q^{83} -459.623i q^{85} +(268.399 + 1065.56i) q^{86} +(228.879 + 250.535i) q^{88} +398.940 q^{89} -1253.80i q^{91} +(-9.42182 + 5.06797i) q^{92} +(-1509.47 + 380.213i) q^{94} -301.869 q^{95} +278.022 q^{97} +(353.648 - 89.0787i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 16 q^{4} + 28 q^{7} + 40 q^{8} + 30 q^{10} - 68 q^{14} - 56 q^{16} - 20 q^{20} - 164 q^{22} - 604 q^{23} - 300 q^{25} + 308 q^{26} - 436 q^{28} - 264 q^{31} - 72 q^{32} - 180 q^{34} - 820 q^{38}+ \cdots + 7266 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 + 16 * q^4 + 28 * q^7 + 40 * q^8 + 30 * q^10 - 68 * q^14 - 56 * q^16 - 20 * q^20 - 164 * q^22 - 604 * q^23 - 300 * q^25 + 308 * q^26 - 436 * q^28 - 264 * q^31 - 72 * q^32 - 180 * q^34 - 820 * q^38 + 120 * q^40 - 40 * q^41 + 472 * q^44 - 1268 * q^46 + 940 * q^47 + 1308 * q^49 + 50 * q^50 + 1024 * q^52 + 440 * q^55 + 728 * q^56 - 360 * q^58 - 592 * q^62 - 2048 * q^64 + 2344 * q^68 + 1160 * q^70 + 1592 * q^71 + 432 * q^73 + 420 * q^74 + 2256 * q^76 + 2016 * q^79 - 1600 * q^80 + 88 * q^82 + 244 * q^86 + 4080 * q^88 + 424 * q^89 + 900 * q^92 + 292 * q^94 + 1520 * q^95 - 1584 * q^97 + 7266 * 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 $

$2$	−2.74276	+	0.690860i	−0.969711	+	0.244256i
$2$	−2.74276	+	0.690860i	−0.969711	+	0.244256i
$3$		0			0
$3$		0			0
$4$	7.04543	−	3.78972i	0.880678	−	0.473715i
$5$		−	5.00000i		−	0.447214i
$5$		−	5.00000i		−	0.447214i
$6$		0			0
$7$	−14.6308			−0.789990			−0.394995	−	0.918683i	$-0.629254\pi$
$7$	−14.6308			−0.789990			−0.394995	+	0.918683i	$0.629254\pi$
$8$	−16.7057	+	15.2617i	−0.738296	+	0.674477i
$9$		0			0
$10$	3.45430	+	13.7138i	0.109234	+	0.433668i
$11$		−	14.9969i		−	0.411068i	−0.978650	−	0.205534i	$-0.934107\pi$
$11$		−	14.9969i		−	0.411068i	0.978650	−	0.205534i	$-0.0658931\pi$
$12$		0			0
$13$			85.6955i			1.82828i	0.405398	+	0.914140i	$0.367133\pi$
$13$			85.6955i			1.82828i	−0.405398	+	0.914140i	$0.632867\pi$
$14$	40.1288	−	10.1078i	0.766062	−	0.192960i
$15$		0			0
$16$	35.2761	−	53.4004i	0.551188	−	0.834381i
$17$	91.9247			1.31147			0.655735	−	0.754991i	$-0.272359\pi$
$17$	91.9247			1.31147			0.655735	+	0.754991i	$0.272359\pi$
$18$		0			0
$19$		−	60.3737i		−	0.728983i	−0.931207	−	0.364492i	$-0.881243\pi$
$19$		−	60.3737i		−	0.728983i	0.931207	−	0.364492i	$-0.118757\pi$
$20$	−18.9486	−	35.2271i	−0.211852	−	0.393851i
$21$		0			0
$22$	10.3608	+	41.1330i	0.100406	+	0.398617i
$23$	−1.33730			−0.0121237			−0.00606186	−	0.999982i	$-0.501930\pi$
$23$	−1.33730			−0.0121237			−0.00606186	+	0.999982i	$0.501930\pi$
$24$		0			0
$25$	−25.0000			−0.200000
$26$	−59.2035	−	235.042i	−0.446568	−	1.77290i
$27$		0			0
$28$	−103.080	+	55.4467i	−0.695727	+	0.374230i
$29$		−	25.5118i		−	0.163360i	−0.996659	−	0.0816798i	$-0.973972\pi$
$29$		−	25.5118i		−	0.163360i	0.996659	−	0.0816798i	$-0.0260285\pi$
$30$		0			0
$31$	73.4354			0.425464			0.212732	−	0.977111i	$-0.431764\pi$
$31$	73.4354			0.425464			0.212732	+	0.977111i	$0.431764\pi$
$32$	−59.8615	+	170.835i	−0.330691	+	0.943739i
$33$		0			0
$34$	−252.127	+	63.5070i	−1.27175	+	0.320334i
$35$			73.1541i			0.353294i
$36$		0			0
$37$		−	211.259i		−	0.938668i	−0.883021	−	0.469334i	$-0.844494\pi$
$37$		−	211.259i		−	0.938668i	0.883021	−	0.469334i	$-0.155506\pi$
$38$	41.7098	+	165.590i	0.178058	+	0.706903i
$39$		0			0
$40$	76.3084	+	83.5286i	0.301635	+	0.330176i
$41$	−330.839			−1.26020			−0.630102	−	0.776512i	$-0.716987\pi$
$41$	−330.839			−1.26020			−0.630102	+	0.776512i	$0.716987\pi$
$42$		0			0
$43$		−	388.500i		−	1.37781i	−0.724853	−	0.688904i	$-0.758092\pi$
$43$		−	388.500i		−	1.37781i	0.724853	−	0.688904i	$-0.241908\pi$
$44$	−56.8342	−	105.660i	−0.194729	−	0.362019i
$45$		0			0
$46$	3.66788	−	0.923883i	0.0117565	−	0.00296129i
$47$	550.348			1.70801			0.854005	−	0.520265i	$-0.174167\pi$
$47$	550.348			1.70801			0.854005	+	0.520265i	$0.174167\pi$
$48$		0			0
$49$	−128.939			−0.375915
$50$	68.5689	−	17.2715i	0.193942	−	0.0488511i
$51$		0			0
$52$	324.762	+	603.761i	0.866084	+	1.61013i
$53$		−	187.705i		−	0.486477i	−0.969966	−	0.243239i	$-0.921790\pi$
$53$		−	187.705i		−	0.486477i	0.969966	−	0.243239i	$-0.0782098\pi$
$54$		0			0
$55$	−74.9847			−0.183835
$56$	244.419	−	223.291i	0.583246	−	0.532830i
$57$		0			0
$58$	17.6251	+	69.9727i	0.0399015	+	0.158412i
$59$		−	779.090i		−	1.71913i	−0.511023	−	0.859567i	$-0.670733\pi$
$59$		−	779.090i		−	1.71913i	0.511023	−	0.859567i	$-0.329267\pi$
$60$		0			0
$61$		−	358.850i		−	0.753215i	−0.926373	−	0.376607i	$-0.877091\pi$
$61$		−	358.850i		−	0.753215i	0.926373	−	0.376607i	$-0.122909\pi$
$62$	−201.415	+	50.7335i	−0.412577	+	0.103922i
$63$		0			0
$64$	46.1625	−	509.915i	0.0901611	−	0.995927i
$65$	428.477			0.817632
$66$		0			0
$67$			283.674i			0.517258i	0.965977	+	0.258629i	$0.0832706\pi$
$67$			283.674i			0.517258i	−0.965977	+	0.258629i	$0.916729\pi$
$68$	647.648	−	348.369i	1.15498	−	0.621263i
$69$		0			0
$70$	−50.5392	−	200.644i	−0.0862942	−	0.342593i
$71$	534.811			0.893949			0.446975	−	0.894547i	$-0.352501\pi$
$71$	534.811			0.893949			0.446975	+	0.894547i	$0.352501\pi$
$72$		0			0
$73$	1016.16			1.62921			0.814607	−	0.580014i	$-0.196953\pi$
$73$	1016.16			1.62921			0.814607	+	0.580014i	$0.196953\pi$
$74$	145.950	+	579.431i	0.229275	+	0.910237i
$75$		0			0
$76$	−228.799	−	425.359i	−0.345330	−	0.642000i
$77$			219.418i			0.324740i
$78$		0			0
$79$	1119.59			1.59447			0.797237	−	0.603666i	$-0.206294\pi$
$79$	1119.59			1.59447			0.797237	+	0.603666i	$0.206294\pi$
$80$	−267.002	−	176.380i	−0.373146	−	0.246499i
$81$		0			0
$82$	907.411	−	228.563i	1.22203	−	0.307812i
$83$		−	1190.49i		−	1.57437i	−0.616716	−	0.787186i	$-0.711537\pi$
$83$		−	1190.49i		−	1.57437i	0.616716	−	0.787186i	$-0.288463\pi$
$84$		0			0
$85$		−	459.623i		−	0.586508i
$86$	268.399	+	1065.56i	0.336537	+	1.33607i
$87$		0			0
$88$	228.879	+	250.535i	0.277256	+	0.303490i
$89$	398.940			0.475141			0.237571	−	0.971370i	$-0.423649\pi$
$89$	398.940			0.475141			0.237571	+	0.971370i	$0.423649\pi$
$90$		0			0
$91$		−	1253.80i		−	1.44432i
$92$	−9.42182	+	5.06797i	−0.0106771	+	0.00574318i
$93$		0			0
$94$	−1509.47	+	380.213i	−1.65628	+	0.417191i
$95$	−301.869			−0.326011
$96$		0			0
$97$	278.022			0.291019			0.145510	−	0.989357i	$-0.453518\pi$
$97$	278.022			0.291019			0.145510	+	0.989357i	$0.453518\pi$
$98$	353.648	−	89.0787i	0.364529	−	0.0918195i
$99$		0			0
$100$	−176.136	+	94.7430i	−0.176136	+	0.0947430i
$101$		−	116.836i		−	0.115105i	−0.998342	−	0.0575523i	$-0.981670\pi$
$101$		−	116.836i		−	0.115105i	0.998342	−	0.0575523i	$-0.0183296\pi$
$102$		0			0
$103$	−1458.02			−1.39478			−0.697391	−	0.716691i	$-0.745656\pi$
$103$	−1458.02			−1.39478			−0.697391	+	0.716691i	$0.745656\pi$
$104$	−1307.86	−	1431.60i	−1.23313	−	1.34981i
$105$		0			0
$106$	129.678	+	514.830i	0.118825	+	0.471742i
$107$			695.124i			0.628039i	0.949417	+	0.314020i	$0.101676\pi$
$107$			695.124i			0.628039i	−0.949417	+	0.314020i	$0.898324\pi$
$108$		0			0
$109$		−	191.775i		−	0.168520i	−0.996444	−	0.0842602i	$-0.973147\pi$
$109$		−	191.775i		−	0.168520i	0.996444	−	0.0842602i	$-0.0268527\pi$
$110$	205.665	−	51.8039i	0.178267	−	0.0449028i
$111$		0			0
$112$	−516.118	+	781.292i	−0.435434	+	0.659153i
$113$	−1234.25			−1.02751			−0.513753	−	0.857938i	$-0.671745\pi$
$113$	−1234.25			−1.02751			−0.513753	+	0.857938i	$0.671745\pi$
$114$		0			0
$115$			6.68648i			0.00542189i
$116$	−96.6827	−	179.742i	−0.0773859	−	0.143867i
$117$		0			0
$118$	538.242	+	2136.85i	0.419908	+	1.66706i
$119$	−1344.93			−1.03605
$120$		0			0
$121$	1106.09			0.831023
$122$	247.915	+	984.239i	0.183977	+	0.730400i
$123$		0			0
$124$	517.384	−	278.299i	0.374697	−	0.201549i
$125$			125.000i			0.0894427i
$126$		0			0
$127$	786.958			0.549852			0.274926	−	0.961465i	$-0.411347\pi$
$127$	786.958			0.549852			0.274926	+	0.961465i	$0.411347\pi$
$128$	225.667	+	1430.46i	0.155831	+	0.987784i
$129$		0			0
$130$	−1175.21	+	296.018i	−0.792866	+	0.199711i
$131$		−	28.0441i		−	0.0187040i	−0.999956	−	0.00935201i	$-0.997023\pi$
$131$		−	28.0441i		−	0.0187040i	0.999956	−	0.00935201i	$-0.00297688\pi$
$132$		0			0
$133$			883.317i			0.575890i
$134$	−195.979	−	778.048i	−0.126343	−	0.501590i
$135$		0			0
$136$	−1535.67	+	1402.92i	−0.968253	+	0.884557i
$137$	71.4326			0.0445467			0.0222733	−	0.999752i	$-0.492910\pi$
$137$	71.4326			0.0445467			0.0222733	+	0.999752i	$0.492910\pi$
$138$		0			0
$139$		−	2343.99i		−	1.43032i	−0.698961	−	0.715160i	$-0.746354\pi$
$139$		−	2343.99i		−	1.43032i	0.698961	−	0.715160i	$-0.253646\pi$
$140$	277.234	+	515.402i	0.167361	+	0.311139i
$141$		0			0
$142$	−1466.86	+	369.479i	−0.866872	+	0.218352i
$143$	1285.17			0.751548
$144$		0			0
$145$	−127.559			−0.0730566
$146$	−2787.08	+	702.024i	−1.57987	+	0.397945i
$147$		0			0
$148$	−800.611	−	1488.41i	−0.444661	−	0.826665i
$149$			1417.40i			0.779315i	0.920960	+	0.389657i	$0.127407\pi$
$149$			1417.40i			0.779315i	−0.920960	+	0.389657i	$0.872593\pi$
$150$		0			0
$151$	1296.61			0.698786			0.349393	−	0.936976i	$-0.386388\pi$
$151$	1296.61			0.698786			0.349393	+	0.936976i	$0.386388\pi$
$152$	921.404	+	1008.59i	0.491683	+	0.538205i
$153$		0			0
$154$	−151.587	−	601.809i	−0.0793196	−	0.314904i
$155$		−	367.177i		−	0.190273i
$156$		0			0
$157$			2002.41i			1.01790i	0.860797	+	0.508948i	$0.169966\pi$
$157$			2002.41i			1.01790i	−0.860797	+	0.508948i	$0.830034\pi$
$158$	−3070.76	+	773.478i	−1.54618	+	0.389459i
$159$		0			0
$160$	854.175	+	299.307i	0.422053	+	0.147890i
$161$	19.5657			0.00957762
$162$		0			0
$163$		−	163.315i		−	0.0784774i	−0.999230	−	0.0392387i	$-0.987507\pi$
$163$		−	163.315i		−	0.0784774i	0.999230	−	0.0392387i	$-0.0124933\pi$
$164$	−2330.90	+	1253.79i	−1.10983	+	0.596977i
$165$		0			0
$166$	822.459	+	3265.21i	0.384549	+	1.52669i
$167$	243.412			0.112789			0.0563945	−	0.998409i	$-0.482040\pi$
$167$	243.412			0.112789			0.0563945	+	0.998409i	$0.482040\pi$
$168$		0			0
$169$	−5146.71			−2.34261
$170$	317.535	+	1260.63i	0.143258	+	0.568743i
$171$		0			0
$172$	−1472.31	−	2737.15i	−0.652688	−	1.21341i
$173$			1955.73i			0.859490i	0.902950	+	0.429745i	$0.141396\pi$
$173$			1955.73i			0.859490i	−0.902950	+	0.429745i	$0.858604\pi$
$174$		0			0
$175$	365.771			0.157998
$176$	−800.842	−	529.033i	−0.342987	−	0.226576i
$177$		0			0
$178$	−1094.20	+	275.611i	−0.460749	+	0.116056i
$179$		−	3978.28i		−	1.66118i	−0.556887	−	0.830588i	$-0.688005\pi$
$179$		−	3978.28i		−	1.66118i	0.556887	−	0.830588i	$-0.311995\pi$
$180$		0			0
$181$			964.412i			0.396045i	0.980197	+	0.198022i	$0.0634519\pi$
$181$			964.412i			0.396045i	−0.980197	+	0.198022i	$0.936548\pi$
$182$	866.197	+	3438.86i	0.352784	+	1.40058i
$183$		0			0
$184$	22.3405	−	20.4094i	0.00895089	−	0.00817717i
$185$	−1056.29			−0.419785
$186$		0			0
$187$		−	1378.59i		−	0.539104i
$188$	3877.43	−	2085.66i	1.50421	−	0.809110i
$189$		0			0
$190$	827.952	−	208.549i	0.316137	−	0.0796301i
$191$	908.237			0.344072			0.172036	−	0.985091i	$-0.444965\pi$
$191$	908.237			0.344072			0.172036	+	0.985091i	$0.444965\pi$
$192$		0			0
$193$	1243.86			0.463910			0.231955	−	0.972727i	$-0.425488\pi$
$193$	1243.86			0.463910			0.231955	+	0.972727i	$0.425488\pi$
$194$	−762.547	+	192.074i	−0.282205	+	0.0710831i
$195$		0			0
$196$	−908.430	+	488.642i	−0.331060	+	0.178077i
$197$			1884.72i			0.681627i	0.940131	+	0.340813i	$0.110702\pi$
$197$			1884.72i			0.681627i	−0.940131	+	0.340813i	$0.889298\pi$
$198$		0			0
$199$	−3886.45			−1.38444			−0.692219	−	0.721688i	$-0.743367\pi$
$199$	−3886.45			−1.38444			−0.692219	+	0.721688i	$0.743367\pi$
$200$	417.643	−	381.542i	0.147659	−	0.134895i
$201$		0			0
$202$	80.7170	+	320.452i	0.0281150	+	0.111618i
$203$			373.259i			0.129052i
$204$		0			0
$205$			1654.20i			0.563580i
$206$	3998.98	−	1007.28i	1.35254	−	0.340684i
$207$		0			0
$208$	4576.17	+	3023.00i	1.52548	+	1.00773i
$209$	−905.421			−0.299662
$210$		0			0
$211$			3282.65i			1.07103i	0.844527	+	0.535514i	$0.179882\pi$
$211$			3282.65i			1.07103i	−0.844527	+	0.535514i	$0.820118\pi$
$212$	−711.350	−	1322.46i	−0.230451	−	0.428430i
$213$		0			0
$214$	−480.233	−	1906.56i	−0.153402	−	0.609016i
$215$	−1942.50			−0.616174
$216$		0			0
$217$	−1074.42			−0.336112
$218$	132.490	+	525.992i	0.0411621	+	0.163416i
$219$		0			0
$220$	−528.299	+	284.171i	−0.161900	+	0.0870855i
$221$			7877.53i			2.39774i
$222$		0			0
$223$	1453.07			0.436343			0.218171	−	0.975910i	$-0.429991\pi$
$223$	1453.07			0.436343			0.218171	+	0.975910i	$0.429991\pi$
$224$	875.823	−	2499.46i	0.261243	−	0.745545i
$225$		0			0
$226$	3385.24	−	852.691i	0.996383	−	0.250974i
$227$		−	4750.20i		−	1.38891i	−0.719537	−	0.694454i	$-0.755646\pi$
$227$		−	4750.20i		−	1.38891i	0.719537	−	0.694454i	$-0.244354\pi$
$228$		0			0
$229$		−	6475.51i		−	1.86862i	−0.356462	−	0.934310i	$-0.616017\pi$
$229$		−	6475.51i		−	1.86862i	0.356462	−	0.934310i	$-0.383983\pi$
$230$	−4.61942	−	18.3394i	−0.00132433	−	0.00525767i
$231$		0			0
$232$	389.353	+	426.194i	0.110182	+	0.120608i
$233$	−257.988			−0.0725379			−0.0362690	−	0.999342i	$-0.511547\pi$
$233$	−257.988			−0.0725379			−0.0362690	+	0.999342i	$0.511547\pi$
$234$		0			0
$235$		−	2751.74i		−	0.763845i
$236$	−2952.53	−	5489.02i	−0.814379	−	1.51400i
$237$		0			0
$238$	3688.83	−	929.160i	1.00467	−	0.253061i
$239$	257.014			0.0695600			0.0347800	−	0.999395i	$-0.488927\pi$
$239$	257.014			0.0695600			0.0347800	+	0.999395i	$0.488927\pi$
$240$		0			0
$241$	1194.01			0.319140			0.159570	−	0.987187i	$-0.448989\pi$
$241$	1194.01			0.319140			0.159570	+	0.987187i	$0.448989\pi$
$242$	−3033.74	+	764.154i	−0.805852	+	0.202982i
$243$		0			0
$244$	−1359.94	−	2528.25i	−0.356809	−	0.663340i
$245$			644.695i			0.168114i
$246$		0			0
$247$	5173.75			1.33279
$248$	−1226.79	+	1120.75i	−0.314118	+	0.286966i
$249$		0			0
$250$	−86.3574	−	342.845i	−0.0218469	−	0.0867336i
$251$		−	587.080i		−	0.147634i	−0.997272	−	0.0738171i	$-0.976482\pi$
$251$		−	587.080i		−	0.147634i	0.997272	−	0.0738171i	$-0.0235181\pi$
$252$		0			0
$253$			20.0553i			0.00498367i
$254$	−2158.43	+	543.677i	−0.533198	+	0.134305i
$255$		0			0
$256$	−1607.20	−	3767.51i	−0.392383	−	0.919802i
$257$	791.436			0.192095			0.0960475	−	0.995377i	$-0.469380\pi$
$257$	791.436			0.192095			0.0960475	+	0.995377i	$0.469380\pi$
$258$		0			0
$259$			3090.89i			0.741539i
$260$	3018.81	−	1623.81i	0.720071	−	0.387324i
$261$		0			0
$262$	19.3746	+	76.9182i	0.00456856	+	0.0181375i
$263$	−2705.80			−0.634398			−0.317199	−	0.948359i	$-0.602742\pi$
$263$	−2705.80			−0.634398			−0.317199	+	0.948359i	$0.602742\pi$
$264$		0			0
$265$	−938.526			−0.217559
$266$	−610.248	−	2422.72i	−0.140664	−	0.558446i
$267$		0			0
$268$	1075.04	+	1998.60i	0.245033	+	0.455538i
$269$		−	2767.26i		−	0.627222i	−0.949552	−	0.313611i	$-0.898461\pi$
$269$		−	2767.26i		−	0.627222i	0.949552	−	0.313611i	$-0.101539\pi$
$270$		0			0
$271$	400.361			0.0897423			0.0448712	−	0.998993i	$-0.485712\pi$
$271$	400.361			0.0897423			0.0448712	+	0.998993i	$0.485712\pi$
$272$	3242.74	−	4908.81i	0.722868	−	1.09427i
$273$		0			0
$274$	−195.922	+	49.3499i	−0.0431974	+	0.0108808i
$275$			374.924i			0.0822136i
$276$		0			0
$277$			6743.86i			1.46281i	0.681942	+	0.731407i	$0.261136\pi$
$277$			6743.86i			1.46281i	−0.681942	+	0.731407i	$0.738864\pi$
$278$	1619.37	+	6428.99i	0.349364	+	1.38700i
$279$		0			0
$280$	−1116.45	−	1222.09i	−0.238289	−	0.260836i
$281$	6373.81			1.35313			0.676565	−	0.736382i	$-0.263468\pi$
$281$	6373.81			1.35313			0.676565	+	0.736382i	$0.263468\pi$
$282$		0			0
$283$			2383.90i			0.500736i	0.968151	+	0.250368i	$0.0805516\pi$
$283$			2383.90i			0.500736i	−0.968151	+	0.250368i	$0.919448\pi$
$284$	3767.97	−	2026.78i	0.787281	−	0.423477i
$285$		0			0
$286$	−3524.91	+	887.872i	−0.728784	+	0.183570i
$287$	4840.45			0.995549
$288$		0			0
$289$	3537.14			0.719956
$290$	349.864	−	88.1255i	0.0708438	−	0.0178445i
$291$		0			0
$292$	7159.28	−	3850.96i	1.43481	−	0.771783i
$293$		−	748.528i		−	0.149247i	−0.997212	−	0.0746237i	$-0.976224\pi$
$293$		−	748.528i		−	0.149247i	0.997212	−	0.0746237i	$-0.0237756\pi$
$294$		0			0
$295$	−3895.45			−0.768820
$296$	3224.16	+	3529.23i	0.633110	+	0.693015i
$297$		0			0
$298$	−979.224	−	3887.58i	−0.190352	−	0.755710i
$299$		−	114.600i		−	0.0221655i
$300$		0			0
$301$			5684.08i			1.08845i
$302$	−3556.29	+	895.776i	−0.677621	+	0.170683i
$303$		0			0
$304$	−3223.98	−	2129.75i	−0.608250	−	0.401807i
$305$	−1794.25			−0.336848
$306$		0			0
$307$		−	2639.75i		−	0.490745i	−0.969429	−	0.245372i	$-0.921090\pi$
$307$		−	2639.75i		−	0.490745i	0.969429	−	0.245372i	$-0.0789102\pi$
$308$	831.531	+	1545.89i	0.153834	+	0.285991i
$309$		0			0
$310$	253.668	+	1007.08i	0.0464753	+	0.184510i
$311$	2880.46			0.525196			0.262598	−	0.964905i	$-0.415421\pi$
$311$	2880.46			0.525196			0.262598	+	0.964905i	$0.415421\pi$
$312$		0			0
$313$	−3620.24			−0.653763			−0.326882	−	0.945065i	$-0.605998\pi$
$313$	−3620.24			−0.653763			−0.326882	+	0.945065i	$0.605998\pi$
$314$	−1383.38	−	5492.12i	−0.248627	−	0.987065i
$315$		0			0
$316$	7887.97	−	4242.92i	1.40422	−	0.755326i
$317$		−	2066.64i		−	0.366164i	−0.983098	−	0.183082i	$-0.941393\pi$
$317$		−	2066.64i		−	0.366164i	0.983098	−	0.183082i	$-0.0586073\pi$
$318$		0			0
$319$	−382.599			−0.0671519
$320$	−2549.57	−	230.812i	−0.445392	−	0.0403213i
$321$		0			0
$322$	−53.6641	+	13.5172i	−0.00928752	+	0.00233939i
$323$		−	5549.83i		−	0.956040i
$324$		0			0
$325$		−	2142.39i		−	0.365656i
$326$	112.828	+	447.933i	0.0191686	+	0.0761004i
$327$		0			0
$328$	5526.91	−	5049.16i	0.930403	−	0.849979i
$329$	−8052.04			−1.34931
$330$		0			0
$331$		−	3193.53i		−	0.530309i	−0.964206	−	0.265155i	$-0.914577\pi$
$331$		−	3193.53i		−	0.530309i	0.964206	−	0.265155i	$-0.0854230\pi$
$332$	−4511.61	−	8387.48i	−0.745803	−	1.38651i
$333$		0			0
$334$	−667.619	+	168.163i	−0.109373	+	0.0275493i
$335$	1418.37			0.231325
$336$		0			0
$337$	−7803.01			−1.26130			−0.630649	−	0.776068i	$-0.717211\pi$
$337$	−7803.01			−1.26130			−0.630649	+	0.776068i	$0.717211\pi$
$338$	14116.2	−	3555.66i	2.27165	−	0.572196i
$339$		0			0
$340$	−1741.84	−	3238.24i	−0.277837	−	0.516524i
$341$		−	1101.31i		−	0.174895i
$342$		0			0
$343$	6904.86			1.08696
$344$	5929.16	+	6490.18i	0.929300	+	1.01723i
$345$		0			0
$346$	−1351.14	−	5364.10i	−0.209935	−	0.833456i
$347$			9098.25i			1.40755i	0.710423	+	0.703775i	$0.248504\pi$
$347$			9098.25i			1.40755i	−0.710423	+	0.703775i	$0.751496\pi$
$348$		0			0
$349$			8700.89i			1.33452i	0.744824	+	0.667261i	$0.232533\pi$
$349$			8700.89i			1.33452i	−0.744824	+	0.667261i	$0.767467\pi$
$350$	−1003.22	+	252.696i	−0.153212	+	0.0385919i
$351$		0			0
$352$	2562.00	+	897.739i	0.387941	+	0.135937i
$353$	−1182.38			−0.178276			−0.0891382	−	0.996019i	$-0.528411\pi$
$353$	−1182.38			−0.178276			−0.0891382	+	0.996019i	$0.528411\pi$
$354$		0			0
$355$		−	2674.05i		−	0.399786i
$356$	2810.70	−	1511.87i	0.418446	−	0.225081i
$357$		0			0
$358$	2748.43	+	10911.4i	0.405752	+	1.61086i
$359$	7514.20			1.10469			0.552346	−	0.833615i	$-0.313733\pi$
$359$	7514.20			1.10469			0.552346	+	0.833615i	$0.313733\pi$
$360$		0			0
$361$	3214.01			0.468584
$362$	−666.273	−	2645.15i	−0.0967363	−	0.384049i
$363$		0			0
$364$	−4751.53	−	8833.52i	−0.684198	−	1.27198i
$365$		−	5080.80i		−	0.728606i
$366$		0			0
$367$	−7217.04			−1.02650			−0.513251	−	0.858238i	$-0.671559\pi$
$367$	−7217.04			−1.02650			−0.513251	+	0.858238i	$0.671559\pi$
$368$	−47.1745	+	71.4121i	−0.00668245	+	0.0101158i
$369$		0			0
$370$	2897.16	−	729.751i	0.407070	−	0.102535i
$371$			2746.28i			0.384312i
$372$		0			0
$373$			2350.20i			0.326244i	0.986606	+	0.163122i	$0.0521564\pi$
$373$			2350.20i			0.326244i	−0.986606	+	0.163122i	$0.947844\pi$
$374$	952.411	+	3781.13i	0.131679	+	0.522775i
$375$		0			0
$376$	−9193.96	+	8399.23i	−1.26102	+	1.15201i
$377$	2186.25			0.298667
$378$		0			0
$379$			3493.78i			0.473518i	0.971568	+	0.236759i	$0.0760852\pi$
$379$			3493.78i			0.473518i	−0.971568	+	0.236759i	$0.923915\pi$
$380$	−2126.79	+	1144.00i	−0.287111	+	0.154436i
$381$		0			0
$382$	−2491.07	+	627.464i	−0.333650	+	0.0840415i
$383$	−14241.7			−1.90004			−0.950019	−	0.312191i	$-0.898937\pi$
$383$	−14241.7			−1.90004			−0.950019	+	0.312191i	$0.898937\pi$
$384$		0			0
$385$	1097.09			0.145228
$386$	−3411.59	+	859.329i	−0.449859	+	0.113313i
$387$		0			0
$388$	1958.78	−	1053.63i	0.256294	−	0.137860i
$389$			7518.81i			0.979997i	0.871723	+	0.489998i	$0.163003\pi$
$389$			7518.81i			0.979997i	−0.871723	+	0.489998i	$0.836997\pi$
$390$		0			0
$391$	−122.930			−0.0158999
$392$	2154.02	−	1967.82i	0.277537	−	0.253546i
$393$		0			0
$394$	−1302.07	−	5169.32i	−0.166491	−	0.660981i
$395$		−	5597.94i		−	0.713071i
$396$		0			0
$397$		−	4665.28i		−	0.589782i	−0.955531	−	0.294891i	$-0.904717\pi$
$397$		−	4665.28i		−	0.589782i	0.955531	−	0.294891i	$-0.0952834\pi$
$398$	10659.6	−	2684.99i	1.34250	−	0.338157i
$399$		0			0
$400$	−881.901	+	1335.01i	−0.110238	+	0.166876i
$401$	3094.11			0.385318			0.192659	−	0.981266i	$-0.438289\pi$
$401$	3094.11			0.385318			0.192659	+	0.981266i	$0.438289\pi$
$402$		0			0
$403$			6293.08i			0.777867i
$404$	−442.774	−	823.156i	−0.0545268	−	0.101370i
$405$		0			0
$406$	−257.870	−	1023.76i	−0.0315218	−	0.125144i
$407$	−3168.24			−0.385857
$408$		0			0
$409$	7341.17			0.887525			0.443762	−	0.896144i	$-0.353643\pi$
$409$	7341.17			0.887525			0.443762	+	0.896144i	$0.353643\pi$
$410$	−1142.82	−	4537.05i	−0.137658	−	0.546510i
$411$		0			0
$412$	−10272.3	+	5525.47i	−1.22835	+	0.660729i
$413$			11398.7i			1.35810i
$414$		0			0
$415$	−5952.43			−0.704080
$416$	−14639.8	−	5129.86i	−1.72542	−	0.604596i
$417$		0			0
$418$	2483.35	−	625.519i	0.290585	−	0.0731941i
$419$			6193.33i			0.722110i	0.932544	+	0.361055i	$0.117583\pi$
$419$			6193.33i			0.722110i	−0.932544	+	0.361055i	$0.882417\pi$
$420$		0			0
$421$			4266.62i			0.493925i	0.969025	+	0.246962i	$0.0794324\pi$
$421$			4266.62i			0.493925i	−0.969025	+	0.246962i	$0.920568\pi$
$422$	−2267.85	−	9003.50i	−0.261605	−	1.03859i
$423$		0			0
$424$	2864.70	+	3135.75i	0.328118	+	0.359164i
$425$	−2298.12			−0.262294
$426$		0			0
$427$			5250.28i			0.595032i
$428$	2634.33	+	4897.45i	0.297511	+	0.553100i
$429$		0			0
$430$	5327.81	−	1342.00i	0.597511	−	0.150504i
$431$	328.807			0.0367473			0.0183736	−	0.999831i	$-0.494151\pi$
$431$	328.807			0.0367473			0.0183736	+	0.999831i	$0.494151\pi$
$432$		0			0
$433$	−6914.22			−0.767382			−0.383691	−	0.923462i	$-0.625347\pi$
$433$	−6914.22			−0.767382			−0.383691	+	0.923462i	$0.625347\pi$
$434$	2946.87	−	742.274i	0.325932	−	0.0820974i
$435$		0			0
$436$	−726.774	−	1351.14i	−0.0798306	−	0.148412i
$437$			80.7375i			0.00883798i
$438$		0			0
$439$	−11922.4			−1.29619			−0.648093	−	0.761562i	$-0.724433\pi$
$439$	−11922.4			−1.29619			−0.648093	+	0.761562i	$0.724433\pi$
$440$	1252.67	−	1144.39i	0.135725	−	0.123993i
$441$		0			0
$442$	−5442.26	−	21606.1i	−0.585661	−	2.32511i
$443$		−	6687.54i		−	0.717234i	−0.933485	−	0.358617i	$-0.883248\pi$
$443$		−	6687.54i		−	0.717234i	0.933485	−	0.358617i	$-0.116752\pi$
$444$		0			0
$445$		−	1994.70i		−	0.212490i
$446$	−3985.41	+	1003.86i	−0.423126	+	0.106579i
$447$		0			0
$448$	−675.395	+	7460.47i	−0.0712264	+	0.786773i
$449$	−3761.85			−0.395396			−0.197698	−	0.980263i	$-0.563347\pi$
$449$	−3761.85			−0.395396			−0.197698	+	0.980263i	$0.563347\pi$
$450$		0			0
$451$			4961.57i			0.518030i
$452$	−8695.79	+	4677.45i	−0.904902	+	0.486745i
$453$		0			0
$454$	3281.72	+	13028.7i	0.339249	+	1.34684i
$455$	−6268.98			−0.645921
$456$		0			0
$457$	957.270			0.0979852			0.0489926	−	0.998799i	$-0.484399\pi$
$457$	957.270			0.0979852			0.0489926	+	0.998799i	$0.484399\pi$
$458$	4473.67	+	17760.8i	0.456421	+	1.81202i
$459$		0			0
$460$	25.3399	+	47.1091i	0.00256843	+	0.00477494i
$461$		−	2903.76i		−	0.293365i	−0.989184	−	0.146683i	$-0.953140\pi$
$461$		−	2903.76i		−	0.293365i	0.989184	−	0.146683i	$-0.0468596\pi$
$462$		0			0
$463$	−6265.25			−0.628879			−0.314440	−	0.949278i	$-0.601817\pi$
$463$	−6265.25			−0.628879			−0.314440	+	0.949278i	$0.601817\pi$
$464$	−1362.34	−	899.957i	−0.136304	−	0.0900419i
$465$		0			0
$466$	707.597	−	178.233i	0.0703408	−	0.0177178i
$467$			4895.67i			0.485107i	0.970138	+	0.242553i	$0.0779849\pi$
$467$			4895.67i			0.485107i	−0.970138	+	0.242553i	$0.922015\pi$
$468$		0			0
$469$		−	4150.38i		−	0.408629i
$470$	1901.06	+	7547.35i	0.186574	+	0.740709i
$471$		0			0
$472$	11890.2	+	13015.3i	1.15952	+	1.26923i
$473$	−5826.32			−0.566373
$474$		0			0
$475$			1509.34i			0.145797i
$476$	−9475.63	+	5096.92i	−0.912426	+	0.490792i
$477$		0			0
$478$	−704.926	+	177.560i	−0.0674531	+	0.0169904i
$479$	5684.05			0.542194			0.271097	−	0.962552i	$-0.412614\pi$
$479$	5684.05			0.542194			0.271097	+	0.962552i	$0.412614\pi$
$480$		0			0
$481$	18103.9			1.71615
$482$	−3274.87	+	824.892i	−0.309474	+	0.0779518i
$483$		0			0
$484$	7792.89	−	4191.78i	0.731864	−	0.393668i
$485$		−	1390.11i		−	0.130148i
$486$		0			0
$487$	16399.6			1.52595			0.762973	−	0.646430i	$-0.223739\pi$
$487$	16399.6			1.52595			0.762973	+	0.646430i	$0.223739\pi$
$488$	5476.66	+	5994.86i	0.508026	+	0.556095i
$489$		0			0
$490$	−445.393	−	1768.24i	−0.0410629	−	0.163022i
$491$		−	10721.8i		−	0.985472i	−0.870179	−	0.492736i	$-0.835997\pi$
$491$		−	10721.8i		−	0.985472i	0.870179	−	0.492736i	$-0.164003\pi$
$492$		0			0
$493$		−	2345.17i		−	0.214241i
$494$	−14190.3	+	3574.34i	−1.29242	+	0.325541i
$495$		0			0
$496$	2590.51	−	3921.48i	0.234511	−	0.354999i
$497$	−7824.73			−0.706211
$498$		0			0
$499$		−	11116.5i		−	0.997281i	−0.866809	−	0.498640i	$-0.833833\pi$
$499$		−	11116.5i		−	0.997281i	0.866809	−	0.498640i	$-0.166167\pi$
$500$	473.715	+	880.678i	0.0423703	+	0.0787703i
$501$		0			0
$502$	405.590	+	1610.22i	0.0360605	+	0.143162i
$503$	6432.33			0.570186			0.285093	−	0.958500i	$-0.407976\pi$
$503$	6432.33			0.570186			0.285093	+	0.958500i	$0.407976\pi$
$504$		0			0
$505$	−584.178			−0.0514764
$506$	−13.8554	−	55.0069i	−0.00121729	−	0.00483272i
$507$		0			0
$508$	5544.45	−	2982.35i	0.484243	−	0.260473i
$509$			9622.35i			0.837924i	0.908004	+	0.418962i	$0.137606\pi$
$509$			9622.35i			0.837924i	−0.908004	+	0.418962i	$0.862394\pi$
$510$		0			0
$511$	−14867.3			−1.28706
$512$	7010.98	+	9223.01i	0.605165	+	0.796100i
$513$		0			0
$514$	−2170.72	+	546.771i	−0.186277	+	0.0469203i
$515$			7290.08i			0.623766i
$516$		0			0
$517$		−	8253.53i		−	0.702108i
$518$	−2135.37	−	8477.56i	−0.181125	−	0.719078i
$519$		0			0
$520$	−7158.02	+	6539.28i	−0.603654	+	0.551474i
$521$	19725.1			1.65868			0.829338	−	0.558747i	$-0.188718\pi$
$521$	19725.1			1.65868			0.829338	+	0.558747i	$0.188718\pi$
$522$		0			0
$523$		−	4068.08i		−	0.340123i	−0.985433	−	0.170062i	$-0.945603\pi$
$523$		−	4068.08i		−	0.340123i	0.985433	−	0.170062i	$-0.0543967\pi$
$524$	−106.279	−	197.583i	−0.00886037	−	0.0164722i
$525$		0			0
$526$	7421.35	−	1869.33i	0.615183	−	0.154955i
$527$	6750.52			0.557984
$528$		0			0
$529$	−12165.2			−0.999853
$530$	2574.15	−	648.390i	0.210970	−	0.0531401i
$531$		0			0
$532$	3347.52	+	6223.35i	0.272808	+	0.507174i
$533$		−	28351.4i		−	2.30401i
$534$		0			0
$535$	3475.62			0.280868
$536$	−4329.34	−	4738.98i	−0.348878	−	0.381889i
$537$		0			0
$538$	1911.79	+	7589.92i	0.153203	+	0.608224i
$539$			1933.69i			0.154527i
$540$		0			0
$541$		−	13192.1i		−	1.04837i	−0.851603	−	0.524187i	$-0.824369\pi$
$541$		−	13192.1i		−	1.04837i	0.851603	−	0.524187i	$-0.175631\pi$
$542$	−1098.09	+	276.593i	−0.0870241	+	0.0219201i
$543$		0			0
$544$	−5502.75	+	15704.0i	−0.433692	+	1.23769i
$545$	−958.875			−0.0753646
$546$		0			0
$547$			2125.25i			0.166123i	0.996544	+	0.0830614i	$0.0264697\pi$
$547$			2125.25i			0.166123i	−0.996544	+	0.0830614i	$0.973530\pi$
$548$	503.273	−	270.709i	0.0392313	−	0.0211024i
$549$		0			0
$550$	−259.020	−	1028.32i	−0.0200811	−	0.0797234i
$551$	−1540.24			−0.119086
$552$		0			0
$553$	−16380.5			−1.25962
$554$	−4659.06	−	18496.8i	−0.357301	−	1.41851i
$555$		0			0
$556$	−8883.06	−	16514.4i	−0.677564	−	1.25965i
$557$		−	18387.1i		−	1.39872i	−0.714769	−	0.699360i	$-0.753468\pi$
$557$		−	18387.1i		−	1.39872i	0.714769	−	0.699360i	$-0.246532\pi$
$558$		0			0
$559$	33292.7			2.51902
$560$	3906.46	+	2580.59i	0.294782	+	0.194732i
$561$		0			0
$562$	−17481.8	+	4403.41i	−1.31215	+	0.330510i
$563$			22098.7i			1.65426i	0.562008	+	0.827132i	$0.310029\pi$
$563$			22098.7i			1.65426i	−0.562008	+	0.827132i	$0.689971\pi$
$564$		0			0
$565$			6171.23i			0.459515i
$566$	−1646.94	−	6538.46i	−0.122308	−	0.485569i
$567$		0			0
$568$	−8934.40	+	8162.11i	−0.659999	+	0.602948i
$569$	19489.2			1.43591			0.717954	−	0.696091i	$-0.245079\pi$
$569$	19489.2			1.43591			0.717954	+	0.696091i	$0.245079\pi$
$570$		0			0
$571$		−	1501.40i		−	0.110038i	−0.998485	−	0.0550189i	$-0.982478\pi$
$571$		−	1501.40i		−	0.110038i	0.998485	−	0.0550189i	$-0.0175219\pi$
$572$	9054.57	−	4870.43i	0.661872	−	0.356019i
$573$		0			0
$574$	−13276.2	+	3344.07i	−0.965395	+	0.243169i
$575$	33.4324			0.00242474
$576$		0			0
$577$	15875.8			1.14544			0.572718	−	0.819753i	$-0.305889\pi$
$577$	15875.8			1.14544			0.572718	+	0.819753i	$0.305889\pi$
$578$	−9701.52	+	2443.67i	−0.698149	+	0.175853i
$579$		0			0
$580$	−898.709	+	483.413i	−0.0643394	+	0.0346080i
$581$			17417.8i			1.24374i
$582$		0			0
$583$	−2815.00			−0.199975
$584$	−16975.7	+	15508.3i	−1.20284	+	1.09887i
$585$		0			0
$586$	517.128	+	2053.03i	0.0364545	+	0.144727i
$587$			5444.12i			0.382799i	0.981512	+	0.191399i	$0.0613025\pi$
$587$			5444.12i			0.382799i	−0.981512	+	0.191399i	$0.938697\pi$
$588$		0			0
$589$		−	4433.57i		−	0.310156i
$590$	10684.3	−	2691.21i	0.745533	−	0.187789i
$591$		0			0
$592$	−11281.3	−	7452.38i	−0.783207	−	0.517383i
$593$	−28383.8			−1.96557			−0.982787	−	0.184744i	$-0.940854\pi$
$593$	−28383.8			−1.96557			−0.982787	+	0.184744i	$0.940854\pi$
$594$		0			0
$595$			6724.67i			0.463335i
$596$	5371.55	+	9986.18i	0.369173	+	0.686326i
$597$		0			0
$598$	79.1726	+	314.320i	0.00541406	+	0.0214942i
$599$	2045.77			0.139546			0.0697729	−	0.997563i	$-0.477773\pi$
$599$	2045.77			0.139546			0.0697729	+	0.997563i	$0.477773\pi$
$600$		0			0
$601$	13847.5			0.939851			0.469926	−	0.882706i	$-0.344281\pi$
$601$	13847.5			0.939851			0.469926	+	0.882706i	$0.344281\pi$
$602$	−3926.90	−	15590.0i	−0.265861	−	1.05549i
$603$		0			0
$604$	9135.18	−	4913.79i	0.615406	−	0.331025i
$605$		−	5530.46i		−	0.371645i
$606$		0			0
$607$	11611.0			0.776405			0.388202	−	0.921574i	$-0.373096\pi$
$607$	11611.0			0.776405			0.388202	+	0.921574i	$0.373096\pi$
$608$	10313.9	+	3614.06i	0.687970	+	0.241068i
$609$		0			0
$610$	4921.20	−	1239.58i	0.326645	−	0.0822770i
$611$			47162.3i			3.12272i
$612$		0			0
$613$		−	21644.9i		−	1.42615i	−0.701087	−	0.713076i	$-0.747301\pi$
$613$		−	21644.9i		−	1.42615i	0.701087	−	0.713076i	$-0.252699\pi$
$614$	1823.70	+	7240.20i	0.119867	+	0.475881i
$615$		0			0
$616$	−3348.68	−	3665.53i	−0.219030	−	0.239754i
$617$	3432.62			0.223974			0.111987	−	0.993710i	$-0.464278\pi$
$617$	3432.62			0.223974			0.111987	+	0.993710i	$0.464278\pi$
$618$		0			0
$619$			2936.25i			0.190659i	0.995446	+	0.0953295i	$0.0303905\pi$
$619$			2936.25i			0.190659i	−0.995446	+	0.0953295i	$0.969610\pi$
$620$	−1391.50	−	2586.92i	−0.0901353	−	0.167570i
$621$		0			0
$622$	−7900.40	+	1989.99i	−0.509288	+	0.128282i
$623$	−5836.82			−0.375357
$624$		0			0
$625$	625.000			0.0400000
$626$	9929.43	−	2501.08i	0.633961	−	0.159685i
$627$		0			0
$628$	7588.57	+	14107.8i	0.482193	+	0.896439i
$629$		−	19419.9i		−	1.23104i
$630$		0			0
$631$	−18455.3			−1.16433			−0.582167	−	0.813069i	$-0.697795\pi$
$631$	−18455.3			−1.16433			−0.582167	+	0.813069i	$0.697795\pi$
$632$	−18703.5	+	17086.8i	−1.17719	+	1.07544i
$633$		0			0
$634$	1427.76	+	5668.28i	0.0894376	+	0.355073i
$635$		−	3934.79i		−	0.245901i
$636$		0			0
$637$		−	11049.5i		−	0.687278i
$638$	1049.38	−	264.323i	0.0651179	−	0.0164022i
$639$		0			0
$640$	7152.32	−	1128.34i	0.441750	−	0.0696896i
$641$	14764.4			0.909761			0.454880	−	0.890552i	$-0.349682\pi$
$641$	14764.4			0.909761			0.454880	+	0.890552i	$0.349682\pi$
$642$		0			0
$643$		−	21285.4i		−	1.30547i	−0.757588	−	0.652733i	$-0.773622\pi$
$643$		−	21285.4i		−	1.30547i	0.757588	−	0.652733i	$-0.226378\pi$
$644$	137.849	−	74.1487i	0.00843480	−	0.00453706i
$645$		0			0
$646$	3834.16	+	15221.8i	0.233518	+	0.927083i
$647$	−18831.7			−1.14428			−0.572140	−	0.820156i	$-0.693887\pi$
$647$	−18831.7			−1.14428			−0.572140	+	0.820156i	$0.693887\pi$
$648$		0			0
$649$	−11684.0			−0.706681
$650$	1480.09	+	5876.04i	0.0893136	+	0.354581i
$651$		0			0
$652$	−618.918	−	1150.62i	−0.0371759	−	0.0691134i
$653$		−	26184.9i		−	1.56921i	−0.619996	−	0.784605i	$-0.712866\pi$
$653$		−	26184.9i		−	1.56921i	0.619996	−	0.784605i	$-0.287134\pi$
$654$		0			0
$655$	−140.221			−0.00836469
$656$	−11670.7	+	17666.9i	−0.694610	+	1.05149i
$657$		0			0
$658$	22084.8	−	5562.83i	1.30844	−	0.329577i
$659$		−	5338.89i		−	0.315590i	−0.987472	−	0.157795i	$-0.949561\pi$
$659$		−	5338.89i		−	0.315590i	0.987472	−	0.157795i	$-0.0504385\pi$
$660$		0			0
$661$			23161.9i			1.36293i	0.731852	+	0.681464i	$0.238656\pi$
$661$			23161.9i			1.36293i	−0.731852	+	0.681464i	$0.761344\pi$
$662$	2206.28	+	8759.08i	0.129531	+	0.514247i
$663$		0			0
$664$	18168.8	+	19887.9i	1.06188	+	1.16235i
$665$	4416.59			0.257546
$666$		0			0
$667$			34.1169i			0.00198052i
$668$	1714.94	−	922.461i	0.0993308	−	0.0534298i
$669$		0			0
$670$	−3890.24	+	979.894i	−0.224318	+	0.0565024i
$671$	−5381.66			−0.309622
$672$		0			0
$673$	3571.25			0.204549			0.102275	−	0.994756i	$-0.467388\pi$
$673$	3571.25			0.204549			0.102275	+	0.994756i	$0.467388\pi$
$674$	21401.8	−	5390.79i	1.22309	−	0.308079i
$675$		0			0
$676$	−36260.8	+	19504.6i	−2.06308	+	1.10973i
$677$			1010.61i			0.0573721i	0.999588	+	0.0286861i	$0.00913231\pi$
$677$			1010.61i			0.0573721i	−0.999588	+	0.0286861i	$0.990868\pi$
$678$		0			0
$679$	−4067.69			−0.229902
$680$	7014.62	+	7678.34i	0.395586	+	0.433016i
$681$		0			0
$682$	760.848	+	3020.62i	0.0427190	+	0.169597i
$683$		−	24805.2i		−	1.38967i	−0.719168	−	0.694836i	$-0.755477\pi$
$683$		−	24805.2i		−	1.38967i	0.719168	−	0.694836i	$-0.244523\pi$
$684$		0			0
$685$		−	357.163i		−	0.0199219i
$686$	−18938.3	+	4770.29i	−1.05404	+	0.265496i
$687$		0			0
$688$	−20746.1	−	13704.8i	−1.14962	−	0.759431i
$689$	16085.5			0.889417
$690$		0			0
$691$			12948.4i			0.712854i	0.934323	+	0.356427i	$0.116005\pi$
$691$			12948.4i			0.712854i	−0.934323	+	0.356427i	$0.883995\pi$
$692$	7411.68	+	13779.0i	0.407153	+	0.756934i
$693$		0			0
$694$	−6285.61	−	24954.3i	−0.343802	−	1.36492i
$695$	−11719.9			−0.639659
$696$		0			0
$697$	−30412.3			−1.65272
$698$	−6011.09	−	23864.4i	−0.325965	−	1.29410i
$699$		0			0
$700$	2577.01	−	1386.17i	0.139145	−	0.0748460i
$701$		−	27490.7i		−	1.48118i	−0.671954	−	0.740592i	$-0.734545\pi$
$701$		−	27490.7i		−	1.48118i	0.671954	−	0.740592i	$-0.265455\pi$
$702$		0			0
$703$	−12754.5			−0.684273
$704$	−7647.16	−	692.296i	−0.409394	−	0.0370623i
$705$		0			0
$706$	3242.97	−	816.856i	0.172877	−	0.0435450i
$707$			1709.40i			0.0909316i
$708$		0			0
$709$		−	11490.7i		−	0.608663i	−0.952566	−	0.304332i	$-0.901567\pi$
$709$		−	11490.7i		−	0.608663i	0.952566	−	0.304332i	$-0.0984331\pi$
$710$	1847.40	+	7334.28i	0.0976501	+	0.387677i
$711$		0			0
$712$	−6664.58	+	6088.49i	−0.350795	+	0.320472i
$713$	−98.2048			−0.00515820
$714$		0			0
$715$		−	6425.85i		−	0.336102i
$716$	−15076.6	−	28028.7i	−0.786924	−	1.46296i
$717$		0			0
$718$	−20609.6	+	5191.26i	−1.07123	+	0.269827i
$719$	−30178.1			−1.56530			−0.782652	−	0.622459i	$-0.786134\pi$
$719$	−30178.1			−1.56530			−0.782652	+	0.622459i	$0.786134\pi$
$720$		0			0
$721$	21332.0			1.10186
$722$	−8815.26	+	2220.43i	−0.454391	+	0.114454i
$723$		0			0
$724$	3654.85	+	6794.69i	0.187612	+	0.348788i
$725$			637.796i			0.0326719i
$726$		0			0
$727$	24019.3			1.22535			0.612674	−	0.790336i	$-0.290094\pi$
$727$	24019.3			1.22535			0.612674	+	0.790336i	$0.290094\pi$
$728$	19135.0	+	20945.6i	0.974163	+	1.06634i
$729$		0			0
$730$	3510.12	+	13935.4i	0.177966	+	0.706538i
$731$		−	35712.7i		−	1.80695i
$732$		0			0
$733$		−	14231.8i		−	0.717142i	−0.933502	−	0.358571i	$-0.883264\pi$
$733$		−	14231.8i		−	0.717142i	0.933502	−	0.358571i	$-0.116736\pi$
$734$	19794.6	−	4985.96i	0.995411	−	0.250729i
$735$		0			0
$736$	80.0525	−	228.457i	0.00400920	−	0.0114416i
$737$	4254.24			0.212628
$738$		0			0
$739$			34171.8i			1.70099i	0.525985	+	0.850494i	$0.323697\pi$
$739$			34171.8i			1.70099i	−0.525985	+	0.850494i	$0.676303\pi$
$740$	−7442.04	+	4003.06i	−0.369696	+	0.198859i
$741$		0			0
$742$	−1897.30	−	7532.38i	−0.0938705	−	0.372672i
$743$	1648.56			0.0813994			0.0406997	−	0.999171i	$-0.487041\pi$
$743$	1648.56			0.0813994			0.0406997	+	0.999171i	$0.487041\pi$
$744$		0			0
$745$	7087.00			0.348520
$746$	−1623.66	−	6446.04i	−0.0796870	−	0.316362i
$747$		0			0
$748$	−5224.47	−	9712.75i	−0.255382	−	0.474777i
$749$		−	10170.2i		−	0.496145i
$750$		0			0
$751$	7622.18			0.370356			0.185178	−	0.982705i	$-0.440714\pi$
$751$	7622.18			0.370356			0.185178	+	0.982705i	$0.440714\pi$
$752$	19414.1	−	29388.8i	0.941435	−	1.42513i
$753$		0			0
$754$	−5996.35	+	1510.39i	−0.289621	+	0.0729512i
$755$		−	6483.06i		−	0.312507i
$756$		0			0
$757$		−	1436.99i		−	0.0689939i	−0.999405	−	0.0344970i	$-0.989017\pi$
$757$		−	1436.99i		−	0.0689939i	0.999405	−	0.0344970i	$-0.0109829\pi$
$758$	−2413.71	−	9582.59i	−0.115660	−	0.459176i
$759$		0			0
$760$	5042.93	−	4607.02i	0.240693	−	0.219887i
$761$	4491.30			0.213942			0.106971	−	0.994262i	$-0.465885\pi$
$761$	4491.30			0.213942			0.106971	+	0.994262i	$0.465885\pi$
$762$		0			0
$763$			2805.83i			0.133129i
$764$	6398.92	−	3441.96i	0.303017	−	0.162992i
$765$		0			0
$766$	39061.4	−	9838.99i	1.84249	−	0.464095i
$767$	66764.5			3.14306
$768$		0			0
$769$	7977.22			0.374078			0.187039	−	0.982353i	$-0.440111\pi$
$769$	7977.22			0.374078			0.187039	+	0.982353i	$0.440111\pi$
$770$	−3009.05	+	757.934i	−0.140829	+	0.0354728i
$771$		0			0
$772$	8763.49	−	4713.86i	0.408556	−	0.219761i
$773$			21972.3i			1.02237i	0.859472	+	0.511183i	$0.170792\pi$
$773$			21972.3i			1.02237i	−0.859472	+	0.511183i	$0.829208\pi$
$774$		0			0
$775$	−1835.88			−0.0850928
$776$	−4644.56	+	4243.08i	−0.214858	+	0.196286i
$777$		0			0
$778$	−5194.44	−	20622.3i	−0.239370	−	0.950314i
$779$			19974.0i			0.918668i
$780$		0			0
$781$		−	8020.53i		−	0.367474i
$782$	337.168	−	84.9277i	0.0154183	−	0.00388364i
$783$		0			0
$784$	−4548.46	+	6885.39i	−0.207200	+	0.313656i
$785$	10012.1			0.455217
$786$		0			0
$787$		−	14770.5i		−	0.669010i	−0.942394	−	0.334505i	$-0.891431\pi$
$787$		−	14770.5i		−	0.669010i	0.942394	−	0.334505i	$-0.108569\pi$
$788$	7142.54	+	13278.6i	0.322897	+	0.600294i
$789$		0			0
$790$	3867.39	+	15353.8i	0.174172	+	0.691472i
$791$	18058.0			0.811720
$792$		0			0
$793$	30751.8			1.37709
$794$	3223.05	+	12795.7i	0.144058	+	0.571918i
$795$		0			0
$796$	−27381.7	+	14728.5i	−1.21924	+	0.655829i
$797$			33342.5i			1.48187i	0.671576	+	0.740936i	$0.265618\pi$
$797$			33342.5i			1.48187i	−0.671576	+	0.740936i	$0.734382\pi$
$798$		0			0
$799$	50590.5			2.24001
$800$	1496.54	−	4270.88i	0.0661382	−	0.188748i
$801$		0			0
$802$	−8486.39	+	2137.60i	−0.373647	+	0.0941161i
$803$		−	15239.3i		−	0.669718i
$804$		0			0
$805$		−	97.8287i		−	0.00428324i
$806$	−4347.63	−	17260.4i	−0.189999	−	0.754307i
$807$		0			0
$808$	1783.11	+	1951.82i	0.0776355	+	0.0849813i
$809$	−27061.3			−1.17605			−0.588026	−	0.808842i	$-0.700095\pi$
$809$	−27061.3			−1.17605			−0.588026	+	0.808842i	$0.700095\pi$
$810$		0			0
$811$		−	36672.2i		−	1.58784i	−0.608025	−	0.793918i	$-0.708038\pi$
$811$		−	36672.2i		−	1.58784i	0.608025	−	0.793918i	$-0.291962\pi$
$812$	1414.55	+	2629.77i	0.0611341	+	0.113654i
$813$		0			0
$814$	8689.70	−	2188.81i	0.374169	−	0.0942477i
$815$	−816.575			−0.0350962
$816$		0			0
$817$	−23455.2			−1.00440
$818$	−20135.0	+	5071.72i	−0.860642	+	0.216783i
$819$		0			0
$820$	6268.93	+	11654.5i	0.266976	+	0.496333i
$821$		−	24984.9i		−	1.06209i	−0.847342	−	0.531047i	$-0.821799\pi$
$821$		−	24984.9i		−	1.06209i	0.847342	−	0.531047i	$-0.178201\pi$
$822$		0			0
$823$	−30397.5			−1.28747			−0.643737	−	0.765247i	$-0.722617\pi$
$823$	−30397.5			−1.28747			−0.643737	+	0.765247i	$0.722617\pi$
$824$	24357.2	−	22251.8i	1.02976	−	0.940749i
$825$		0			0
$826$	−7874.92	−	31263.9i	−0.331723	−	1.31696i
$827$			21641.5i			0.909972i	0.890498	+	0.454986i	$0.150356\pi$
$827$			21641.5i			0.909972i	−0.890498	+	0.454986i	$0.849644\pi$
$828$		0			0
$829$		−	36955.2i		−	1.54826i	−0.633028	−	0.774129i	$-0.718188\pi$
$829$		−	36955.2i		−	1.54826i	0.633028	−	0.774129i	$-0.281812\pi$
$830$	16326.1	−	4112.29i	0.682754	−	0.171976i
$831$		0			0
$832$	43697.4	+	3955.91i	1.82083	+	0.164840i
$833$	−11852.7			−0.493002
$834$		0			0
$835$		−	1217.06i		−	0.0504407i
$836$	−6379.08	+	3431.29i	−0.263906	+	0.141954i
$837$		0			0
$838$	−4278.72	−	16986.8i	−0.176380	−	0.700238i
$839$	4786.98			0.196978			0.0984891	−	0.995138i	$-0.468599\pi$
$839$	4786.98			0.196978			0.0984891	+	0.995138i	$0.468599\pi$
$840$		0			0
$841$	23738.1			0.973314
$842$	−2947.63	−	11702.3i	−0.120644	−	0.478964i
$843$		0			0
$844$	12440.3	+	23127.6i	0.507362	+	0.943230i
$845$			25733.6i			1.04765i
$846$		0			0
$847$	−16183.0			−0.656500
$848$	−10023.5	−	6621.50i	−0.405907	−	0.268141i
$849$		0			0
$850$	6303.17	−	1587.68i	0.254349	−	0.0640669i
$851$			282.515i			0.0113801i
$852$		0			0
$853$		−	4074.67i		−	0.163557i	−0.996651	−	0.0817785i	$-0.973940\pi$
$853$		−	4074.67i		−	0.163557i	0.996651	−	0.0817785i	$-0.0260600\pi$
$854$	−3627.20	−	14400.2i	−0.145340	−	0.577009i
$855$		0			0
$856$	−10608.8	−	11612.6i	−0.423598	−	0.463679i
$857$	6011.57			0.239616			0.119808	−	0.992797i	$-0.461772\pi$
$857$	6011.57			0.239616			0.119808	+	0.992797i	$0.461772\pi$
$858$		0			0
$859$			16761.1i			0.665752i	0.942971	+	0.332876i	$0.108019\pi$
$859$			16761.1i			0.665752i	−0.942971	+	0.332876i	$0.891981\pi$
$860$	−13685.7	+	7361.53i	−0.542651	+	0.291891i
$861$		0			0
$862$	−901.837	+	227.159i	−0.0356342	+	0.00897573i
$863$	−25926.9			−1.02267			−0.511334	−	0.859382i	$-0.670848\pi$
$863$	−25926.9			−1.02267			−0.511334	+	0.859382i	$0.670848\pi$
$864$		0			0
$865$	9778.67			0.384375
$866$	18964.0	−	4776.76i	0.744138	−	0.187437i
$867$		0			0
$868$	−7569.75	+	4071.75i	−0.296007	+	0.159221i
$869$		−	16790.4i		−	0.655438i
$870$		0			0
$871$	−24309.6			−0.945692
$872$	2926.81	+	3203.74i	0.113663	+	0.124418i
$873$		0			0
$874$	−55.7783	−	221.443i	−0.00215873	−	0.00857029i
$875$		−	1828.85i		−	0.0706589i
$876$		0			0
$877$			26838.9i			1.03339i	0.856169	+	0.516697i	$0.172839\pi$
$877$			26838.9i			1.03339i	−0.856169	+	0.516697i	$0.827161\pi$
$878$	32700.3	−	8236.71i	1.25692	−	0.316601i
$879$		0			0
$880$	−2645.17	+	4004.21i	−0.101328	+	0.153389i
$881$	16191.5			0.619190			0.309595	−	0.950869i	$-0.399807\pi$
$881$	16191.5			0.619190			0.309595	+	0.950869i	$0.399807\pi$
$882$		0			0
$883$			22021.1i			0.839263i	0.907695	+	0.419631i	$0.137841\pi$
$883$			22021.1i			0.839263i	−0.907695	+	0.419631i	$0.862159\pi$
$884$	29853.6	+	55500.5i	1.13584	+	2.11163i
$885$		0			0
$886$	4620.15	+	18342.3i	0.175189	+	0.695510i
$887$	8897.22			0.336797			0.168399	−	0.985719i	$-0.446140\pi$
$887$	8897.22			0.336797			0.168399	+	0.985719i	$0.446140\pi$
$888$		0			0
$889$	−11513.8			−0.434378
$890$	1378.06	+	5470.98i	0.0519018	+	0.206053i
$891$		0			0
$892$	10237.5	−	5506.71i	0.384278	−	0.206702i
$893$		−	33226.5i		−	1.24511i
$894$		0			0
$895$	−19891.4			−0.742900
$896$	−3301.70	−	20928.9i	−0.123105	−	0.780340i
$897$		0			0
$898$	10317.8	−	2598.91i	0.383420	−	0.0965777i
$899$		−	1873.47i		−	0.0695036i
$900$		0			0
$901$		−	17254.7i		−	0.638001i
$902$	−3427.75	−	13608.4i	−0.126532	−	0.502339i
$903$		0			0
$904$	20619.0	−	18836.7i	0.758603	−	0.693029i
$905$	4822.06			0.177117
$906$		0			0
$907$			15822.5i			0.579246i	0.957141	+	0.289623i	$0.0935299\pi$
$907$			15822.5i			0.579246i	−0.957141	+	0.289623i	$0.906470\pi$
$908$	−18001.9	−	33467.2i	−0.657946	−	1.22318i
$909$		0			0
$910$	17194.3	−	4330.98i	0.626357	−	0.157770i
$911$	−4136.51			−0.150438			−0.0752188	−	0.997167i	$-0.523966\pi$
$911$	−4136.51			−0.150438			−0.0752188	+	0.997167i	$0.523966\pi$
$912$		0			0
$913$	−17853.7			−0.647174
$914$	−2625.56	+	661.339i	−0.0950173	+	0.0239334i
$915$		0			0
$916$	−24540.4	−	45622.7i	−0.885193	−	1.64565i
$917$			410.309i			0.0147760i
$918$		0			0
$919$	−8655.85			−0.310697			−0.155348	−	0.987860i	$-0.549650\pi$
$919$	−8655.85			−0.310697			−0.155348	+	0.987860i	$0.549650\pi$
$920$	−102.047	−	111.702i	−0.00365694	−	0.00400296i
$921$		0			0
$922$	2006.09	+	7964.30i	0.0716562	+	0.284480i
$923$			45830.9i			1.63439i
$924$		0			0
$925$			5281.47i			0.187734i
$926$	17184.1	−	4328.41i	0.609831	−	0.153607i
$927$		0			0
$928$	4358.31	+	1527.18i	0.154169	+	0.0540216i
$929$	19787.3			0.698817			0.349409	−	0.936970i	$-0.386382\pi$
$929$	19787.3			0.698817			0.349409	+	0.936970i	$0.386382\pi$
$930$		0			0
$931$			7784.52i			0.274036i
$932$	−1817.63	+	977.701i	−0.0638826	+	0.0343623i
$933$		0			0
$934$	−3382.22	−	13427.6i	−0.118490	−	0.470413i
$935$	−6892.95			−0.241095
$936$		0			0
$937$	−21427.2			−0.747061			−0.373531	−	0.927618i	$-0.621853\pi$
$937$	−21427.2			−0.747061			−0.373531	+	0.927618i	$0.621853\pi$
$938$	2867.33	+	11383.5i	0.0998099	+	0.396252i
$939$		0			0
$940$	−10428.3	−	19387.2i	−0.361845	−	0.672702i
$941$			40905.9i			1.41710i	0.705659	+	0.708552i	$0.250651\pi$
$941$			40905.9i			1.41710i	−0.705659	+	0.708552i	$0.749349\pi$
$942$		0			0
$943$	442.430			0.0152784
$944$	−41603.7	−	27483.2i	−1.43441	−	0.947567i
$945$		0			0
$946$	15980.2	−	4025.17i	0.549218	−	0.138340i
$947$		−	4430.18i		−	0.152019i	−0.997107	−	0.0760093i	$-0.975782\pi$
$947$		−	4430.18i		−	0.152019i	0.997107	−	0.0760093i	$-0.0242179\pi$
$948$		0			0
$949$			87080.3i			2.97866i
$950$	−1042.74	−	4139.76i	−0.0356117	−	0.141381i
$951$		0			0
$952$	22468.1	−	20525.9i	0.764911	−	0.698792i
$953$	12381.1			0.420844			0.210422	−	0.977611i	$-0.432516\pi$
$953$	12381.1			0.420844			0.210422	+	0.977611i	$0.432516\pi$
$954$		0			0
$955$		−	4541.19i		−	0.153874i
$956$	1810.77	−	974.010i	0.0612600	−	0.0329516i
$957$		0			0
$958$	−15590.0	+	3926.88i	−0.525771	+	0.132434i
$959$	−1045.12			−0.0351915
$960$		0			0
$961$	−24398.2			−0.818980
$962$	−49654.6	+	12507.3i	−1.66417	+	0.419179i
$963$		0			0
$964$	8412.29	−	4524.95i	0.281060	−	0.151181i
$965$		−	6219.28i		−	0.207467i
$966$		0			0
$967$	51294.8			1.70582			0.852911	−	0.522056i	$-0.174835\pi$
$967$	51294.8			1.70582			0.852911	+	0.522056i	$0.174835\pi$
$968$	−18478.1	+	16880.8i	−0.613541	+	0.560506i
$969$		0			0
$970$	960.371	+	3812.74i	0.0317893	+	0.126206i
$971$			11036.3i			0.364750i	0.983229	+	0.182375i	$0.0583785\pi$
$971$			11036.3i			0.364750i	−0.983229	+	0.182375i	$0.941621\pi$
$972$		0			0
$973$			34294.5i			1.12994i
$974$	−44980.1	+	11329.8i	−1.47973	+	0.372721i
$975$		0			0
$976$	−19162.7	−	12658.8i	−0.628468	−	0.415163i
$977$	−24788.2			−0.811713			−0.405857	−	0.913937i	$-0.633027\pi$
$977$	−24788.2			−0.811713			−0.405857	+	0.913937i	$0.633027\pi$
$978$		0			0
$979$		−	5982.88i		−	0.195315i
$980$	2443.21	+	4542.15i	0.0796383	+	0.148055i
$981$		0			0
$982$	7407.24	+	29407.2i	0.240707	+	0.955623i
$983$	−28853.0			−0.936183			−0.468091	−	0.883680i	$-0.655058\pi$
$983$	−28853.0			−0.936183			−0.468091	+	0.883680i	$0.655058\pi$
$984$		0			0
$985$	9423.58			0.304833
$986$	1620.18	+	6432.22i	0.0523297	+	0.207752i
$987$		0			0
$988$	36451.3	−	19607.1i	1.17376	−	0.631360i
$989$			519.540i			0.0167041i
$990$		0			0
$991$	−50061.0			−1.60468			−0.802342	−	0.596865i	$-0.796413\pi$
$991$	−50061.0			−1.60468			−0.802342	+	0.596865i	$0.796413\pi$
$992$	−4395.95	+	12545.3i	−0.140697	+	0.401527i
$993$		0			0
$994$	21461.3	−	5405.79i	0.684821	−	0.172496i
$995$			19432.2i			0.619139i
$996$		0			0
$997$		−	7718.06i		−	0.245169i	−0.992458	−	0.122584i	$-0.960882\pi$
$997$		−	7718.06i		−	0.245169i	0.992458	−	0.122584i	$-0.0391182\pi$
$998$	7679.94	+	30489.9i	0.243592	+	0.967074i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.4.k.c.181.2		12
3.2	odd	2		40.4.d.a.21.11	✓	12
4.3	odd	2		1440.4.k.c.721.5		12
8.3	odd	2		1440.4.k.c.721.11		12
8.5	even	2	inner	360.4.k.c.181.1		12
12.11	even	2		160.4.d.a.81.9		12
15.2	even	4		200.4.f.c.149.6		12
15.8	even	4		200.4.f.b.149.7		12
15.14	odd	2		200.4.d.b.101.2		12
24.5	odd	2		40.4.d.a.21.12	yes	12
24.11	even	2		160.4.d.a.81.4		12
48.5	odd	4		1280.4.a.bc.1.2		6
48.11	even	4		1280.4.a.ba.1.5		6
48.29	odd	4		1280.4.a.bb.1.5		6
48.35	even	4		1280.4.a.bd.1.2		6
60.23	odd	4		800.4.f.c.49.3		12
60.47	odd	4		800.4.f.b.49.10		12
60.59	even	2		800.4.d.d.401.4		12
120.29	odd	2		200.4.d.b.101.1		12
120.53	even	4		200.4.f.c.149.5		12
120.59	even	2		800.4.d.d.401.9		12
120.77	even	4		200.4.f.b.149.8		12
120.83	odd	4		800.4.f.b.49.9		12
120.107	odd	4		800.4.f.c.49.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.d.a.21.11	✓	12	3.2	odd	2
40.4.d.a.21.12	yes	12	24.5	odd	2
160.4.d.a.81.4		12	24.11	even	2
160.4.d.a.81.9		12	12.11	even	2
200.4.d.b.101.1		12	120.29	odd	2
200.4.d.b.101.2		12	15.14	odd	2
200.4.f.b.149.7		12	15.8	even	4
200.4.f.b.149.8		12	120.77	even	4
200.4.f.c.149.5		12	120.53	even	4
200.4.f.c.149.6		12	15.2	even	4
360.4.k.c.181.1		12	8.5	even	2	inner
360.4.k.c.181.2		12	1.1	even	1	trivial
800.4.d.d.401.4		12	60.59	even	2
800.4.d.d.401.9		12	120.59	even	2
800.4.f.b.49.9		12	120.83	odd	4
800.4.f.b.49.10		12	60.47	odd	4
800.4.f.c.49.3		12	60.23	odd	4
800.4.f.c.49.4		12	120.107	odd	4
1280.4.a.ba.1.5		6	48.11	even	4
1280.4.a.bb.1.5		6	48.29	odd	4
1280.4.a.bc.1.2		6	48.5	odd	4
1280.4.a.bd.1.2		6	48.35	even	4
1440.4.k.c.721.5		12	4.3	odd	2
1440.4.k.c.721.11		12	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-2.74276 + 0.690860i) q^{2} +(7.04543 - 3.78972i) q^{4} -5.00000i q^{5} -14.6308 q^{7} +(-16.7057 + 15.2617i) q^{8} +(3.45430 + 13.7138i) q^{10} -14.9969i q^{11} +85.6955i q^{13} +(40.1288 - 10.1078i) q^{14} +(35.2761 - 53.4004i) q^{16} +91.9247 q^{17} -60.3737i q^{19} +(-18.9486 - 35.2271i) q^{20} +(10.3608 + 41.1330i) q^{22} -1.33730 q^{23} -25.0000 q^{25} +(-59.2035 - 235.042i) q^{26} +(-103.080 + 55.4467i) q^{28} -25.5118i q^{29} +73.4354 q^{31} +(-59.8615 + 170.835i) q^{32} +(-252.127 + 63.5070i) q^{34} +73.1541i q^{35} -211.259i q^{37} +(41.7098 + 165.590i) q^{38} +(76.3084 + 83.5286i) q^{40} -330.839 q^{41} -388.500i q^{43} +(-56.8342 - 105.660i) q^{44} +(3.66788 - 0.923883i) q^{46} +550.348 q^{47} -128.939 q^{49} +(68.5689 - 17.2715i) q^{50} +(324.762 + 603.761i) q^{52} -187.705i q^{53} -74.9847 q^{55} +(244.419 - 223.291i) q^{56} +(17.6251 + 69.9727i) q^{58} -779.090i q^{59} -358.850i q^{61} +(-201.415 + 50.7335i) q^{62} +(46.1625 - 509.915i) q^{64} +428.477 q^{65} +283.674i q^{67} +(647.648 - 348.369i) q^{68} +(-50.5392 - 200.644i) q^{70} +534.811 q^{71} +1016.16 q^{73} +(145.950 + 579.431i) q^{74} +(-228.799 - 425.359i) q^{76} +219.418i q^{77} +1119.59 q^{79} +(-267.002 - 176.380i) q^{80} +(907.411 - 228.563i) q^{82} -1190.49i q^{83} -459.623i q^{85} +(268.399 + 1065.56i) q^{86} +(228.879 + 250.535i) q^{88} +398.940 q^{89} -1253.80i q^{91} +(-9.42182 + 5.06797i) q^{92} +(-1509.47 + 380.213i) q^{94} -301.869 q^{95} +278.022 q^{97} +(353.648 - 89.0787i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 16 q^{4} + 28 q^{7} + 40 q^{8} + 30 q^{10} - 68 q^{14} - 56 q^{16} - 20 q^{20} - 164 q^{22} - 604 q^{23} - 300 q^{25} + 308 q^{26} - 436 q^{28} - 264 q^{31} - 72 q^{32} - 180 q^{34} - 820 q^{38}+ \cdots + 7266 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 + 16 * q^4 + 28 * q^7 + 40 * q^8 + 30 * q^10 - 68 * q^14 - 56 * q^16 - 20 * q^20 - 164 * q^22 - 604 * q^23 - 300 * q^25 + 308 * q^26 - 436 * q^28 - 264 * q^31 - 72 * q^32 - 180 * q^34 - 820 * q^38 + 120 * q^40 - 40 * q^41 + 472 * q^44 - 1268 * q^46 + 940 * q^47 + 1308 * q^49 + 50 * q^50 + 1024 * q^52 + 440 * q^55 + 728 * q^56 - 360 * q^58 - 592 * q^62 - 2048 * q^64 + 2344 * q^68 + 1160 * q^70 + 1592 * q^71 + 432 * q^73 + 420 * q^74 + 2256 * q^76 + 2016 * q^79 - 1600 * q^80 + 88 * q^82 + 244 * q^86 + 4080 * q^88 + 424 * q^89 + 900 * q^92 + 292 * q^94 + 1520 * q^95 - 1584 * q^97 + 7266 * q^98

Introduction

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