LMFDB - Embedded newform 448.4.i.j.65.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [448,4,Mod(65,448)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(448, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("448.65"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$N$	$=$	$448 = 2^{6} \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	448.i (of order $3$ , degree $2$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,-7,0,-3,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$26.4328556826$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.11163123.4
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{6} + 14x^{4} + 49x^{2} + 27$ x^6 + 14x^4 + 49x^2 + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$2^{6}\cdot 3$
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			65.1
Root			$2.13755i$ of defining polynomial
Character	$\chi$	$=$	448.65
Dual form			448.4.i.j.193.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.77144 - 8.26438i) q^{3} +(-7.90468 + 13.6913i) q^{5} +(-0.861792 + 18.5002i) q^{7} +(-32.0333 + 55.4834i) q^{9} +(10.8997 + 18.8788i) q^{11} -21.3423 q^{13} +150.867 q^{15} +(-37.8955 - 65.6370i) q^{17} +(-10.6432 + 18.4345i) q^{19} +(157.005 - 81.1505i) q^{21} +(51.1336 - 88.5660i) q^{23} +(-62.4679 - 108.197i) q^{25} +353.723 q^{27} -91.0008 q^{29} +(-33.4243 - 57.8926i) q^{31} +(104.015 - 180.159i) q^{33} +(-246.480 - 158.037i) q^{35} +(-84.2986 + 146.009i) q^{37} +(101.834 + 176.381i) q^{39} +101.555 q^{41} +314.402 q^{43} +(-506.426 - 877.156i) q^{45} +(-134.672 + 233.260i) q^{47} +(-341.515 - 31.8866i) q^{49} +(-361.633 + 626.366i) q^{51} +(154.430 + 267.480i) q^{53} -344.635 q^{55} +203.133 q^{57} +(-404.372 - 700.393i) q^{59} +(326.882 - 566.177i) q^{61} +(-998.847 - 640.438i) q^{63} +(168.704 - 292.204i) q^{65} +(-236.930 - 410.375i) q^{67} -975.925 q^{69} +157.998 q^{71} +(-135.038 - 233.894i) q^{73} +(-596.124 + 1032.52i) q^{75} +(-358.656 + 185.377i) q^{77} +(-162.729 + 281.854i) q^{79} +(-822.869 - 1425.25i) q^{81} +1033.08 q^{83} +1198.21 q^{85} +(434.205 + 752.065i) q^{87} +(-74.8843 + 129.703i) q^{89} +(18.3926 - 394.837i) q^{91} +(-318.964 + 552.462i) q^{93} +(-168.262 - 291.438i) q^{95} -1865.72 q^{97} -1396.62 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$6 q - 7 q^{3} - 3 q^{5} - 4 q^{7} - 18 q^{9} - 3 q^{11} + 52 q^{13} + 254 q^{15} + 31 q^{17} - 89 q^{19} + 375 q^{21} + 201 q^{23} - 300 q^{25} + 938 q^{27} - 380 q^{29} + 339 q^{31} + 105 q^{33} + 473 q^{35}+ \cdots - 4620 q^{99}+O(q^{100})$ 6 * q - 7 * q^3 - 3 * q^5 - 4 * q^7 - 18 * q^9 - 3 * q^11 + 52 * q^13 + 254 * q^15 + 31 * q^17 - 89 * q^19 + 375 * q^21 + 201 * q^23 - 300 * q^25 + 938 * q^27 - 380 * q^29 + 339 * q^31 + 105 * q^33 + 473 * q^35 - 535 * q^37 + 134 * q^39 + 116 * q^41 - 536 * q^43 - 1410 * q^45 + 205 * q^47 - 1530 * q^49 - 965 * q^51 + 757 * q^53 - 3306 * q^55 + 522 * q^57 - 1799 * q^59 + 625 * q^61 - 1714 * q^63 + 1750 * q^65 - 495 * q^67 - 1946 * q^69 + 1280 * q^71 + 443 * q^73 - 1484 * q^75 + 1131 * q^77 - 79 * q^79 - 2523 * q^81 + 4744 * q^83 + 1954 * q^85 + 910 * q^87 - 821 * q^89 + 1352 * q^91 - 1321 * q^93 + 1327 * q^95 - 684 * q^97 - 4620 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$ .

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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

)

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

$2$		0			0
$2$		0			0
$3$	−4.77144	−	8.26438i	−0.918265	−	1.59048i	−0.802050	−	0.597257i	$-0.796257\pi$
$3$	−4.77144	−	8.26438i	−0.918265	−	1.59048i	−0.116215	−	0.993224i	$-0.537076\pi$
$4$		0			0
$5$	−7.90468	+	13.6913i	−0.707016	+	1.22459i	0.258943	+	0.965893i	$0.416626\pi$
$5$	−7.90468	+	13.6913i	−0.707016	+	1.22459i	−0.965959	+	0.258695i	$0.916708\pi$
$6$		0			0
$7$	−0.861792	+	18.5002i	−0.0465324	+	0.998917i
$7$	−0.861792	+	18.5002i	−0.0465324	+	0.998917i
$8$		0			0
$9$	−32.0333	+	55.4834i	−1.18642	+	2.05494i
$10$		0			0
$11$	10.8997	+	18.8788i	0.298762	+	0.517471i	0.975853	−	0.218428i	$-0.0700929\pi$
$11$	10.8997	+	18.8788i	0.298762	+	0.517471i	−0.677091	+	0.735899i	$0.736760\pi$
$12$		0			0
$13$	−21.3423			−0.455330			−0.227665	−	0.973740i	$-0.573109\pi$
$13$	−21.3423			−0.455330			−0.227665	+	0.973740i	$0.573109\pi$
$14$		0			0
$15$	150.867			2.59691
$16$		0			0
$17$	−37.8955	−	65.6370i	−0.540648	−	0.936430i	−0.998867	−	0.0475903i	$-0.984846\pi$
$17$	−37.8955	−	65.6370i	−0.540648	−	0.936430i	0.458219	−	0.888839i	$-0.348488\pi$
$18$		0			0
$19$	−10.6432	+	18.4345i	−0.128511	+	0.222588i	−0.923100	−	0.384560i	$-0.874353\pi$
$19$	−10.6432	+	18.4345i	−0.128511	+	0.222588i	0.794589	+	0.607148i	$0.207687\pi$
$20$		0			0
$21$	157.005	−	81.1505i	1.63149	−	0.843261i
$22$		0			0
$23$	51.1336	−	88.5660i	0.463570	−	0.802926i	−0.535566	−	0.844493i	$-0.679902\pi$
$23$	51.1336	−	88.5660i	0.463570	−	0.802926i	0.999136	+	0.0415673i	$0.0132351\pi$
$24$		0			0
$25$	−62.4679	−	108.197i	−0.499743	−	0.865580i
$26$		0			0
$27$	353.723			2.52126
$28$		0			0
$29$	−91.0008			−0.582704			−0.291352	−	0.956616i	$-0.594105\pi$
$29$	−91.0008			−0.582704			−0.291352	+	0.956616i	$0.594105\pi$
$30$		0			0
$31$	−33.4243	−	57.8926i	−0.193651	−	0.335413i	0.752807	−	0.658242i	$-0.228700\pi$
$31$	−33.4243	−	57.8926i	−0.193651	−	0.335413i	−0.946457	+	0.322829i	$0.895366\pi$
$32$		0			0
$33$	104.015	−	180.159i	0.548686	−	0.950351i
$34$		0			0
$35$	−246.480	−	158.037i	−1.19036	−	0.763233i
$36$		0			0
$37$	−84.2986	+	146.009i	−0.374557	+	0.648752i	−0.990261	−	0.139226i	$-0.955539\pi$
$37$	−84.2986	+	146.009i	−0.374557	+	0.648752i	0.615704	+	0.787978i	$0.288872\pi$
$38$		0			0
$39$	101.834	+	176.381i	0.418113	+	0.724193i
$40$		0			0
$41$	101.555			0.386836			0.193418	−	0.981116i	$-0.438043\pi$
$41$	101.555			0.386836			0.193418	+	0.981116i	$0.438043\pi$
$42$		0			0
$43$	314.402			1.11502			0.557509	−	0.830171i	$-0.311757\pi$
$43$	314.402			1.11502			0.557509	+	0.830171i	$0.311757\pi$
$44$		0			0
$45$	−506.426	−	877.156i	−1.67764	−	2.90575i
$46$		0			0
$47$	−134.672	+	233.260i	−0.417957	+	0.723923i	−0.995734	−	0.0922717i	$-0.970587\pi$
$47$	−134.672	+	233.260i	−0.417957	+	0.723923i	0.577777	+	0.816195i	$0.303921\pi$
$48$		0			0
$49$	−341.515	−	31.8866i	−0.995669	−	0.0929639i
$50$		0			0
$51$	−361.633	+	626.366i	−0.992916	+	1.71978i
$52$		0			0
$53$	154.430	+	267.480i	0.400236	+	0.693230i	0.993754	−	0.111591i	$-0.0355946\pi$
$53$	154.430	+	267.480i	0.400236	+	0.693230i	−0.593518	+	0.804821i	$0.702261\pi$
$54$		0			0
$55$	−344.635			−0.844918
$56$		0			0
$57$	203.133			0.472029
$58$		0			0
$59$	−404.372	−	700.393i	−0.892284	−	1.54548i	−0.837131	−	0.547003i	$-0.815769\pi$
$59$	−404.372	−	700.393i	−0.892284	−	1.54548i	−0.0551526	−	0.998478i	$-0.517565\pi$
$60$		0			0
$61$	326.882	−	566.177i	0.686115	−	1.18839i	−0.286971	−	0.957939i	$-0.592648\pi$
$61$	326.882	−	566.177i	0.686115	−	1.18839i	0.973085	−	0.230446i	$-0.0740185\pi$
$62$		0			0
$63$	−998.847	−	640.438i	−1.99751	−	1.28076i
$64$		0			0
$65$	168.704	−	292.204i	0.321925	−	0.557591i
$66$		0			0
$67$	−236.930	−	410.375i	−0.432024	−	0.748288i	0.565023	−	0.825075i	$-0.308867\pi$
$67$	−236.930	−	410.375i	−0.432024	−	0.748288i	−0.997048	+	0.0767872i	$0.975534\pi$
$68$		0			0
$69$	−975.925			−1.70272
$70$		0			0
$71$	157.998			0.264098			0.132049	−	0.991243i	$-0.457844\pi$
$71$	157.998			0.264098			0.132049	+	0.991243i	$0.457844\pi$
$72$		0			0
$73$	−135.038	−	233.894i	−0.216508	−	0.375002i	0.737230	−	0.675642i	$-0.236133\pi$
$73$	−135.038	−	233.894i	−0.216508	−	0.375002i	−0.953738	+	0.300639i	$0.902800\pi$
$74$		0			0
$75$	−596.124	+	1032.52i	−0.917792	+	1.58966i
$76$		0			0
$77$	−358.656	+	185.377i	−0.530813	+	0.274359i
$78$		0			0
$79$	−162.729	+	281.854i	−0.231752	+	0.401406i	−0.958324	−	0.285684i	$-0.907779\pi$
$79$	−162.729	+	281.854i	−0.231752	+	0.401406i	0.726572	+	0.687091i	$0.241112\pi$
$80$		0			0
$81$	−822.869	−	1425.25i	−1.12876	−	1.95508i
$82$		0			0
$83$	1033.08			1.36621			0.683104	−	0.730321i	$-0.260630\pi$
$83$	1033.08			1.36621			0.683104	+	0.730321i	$0.260630\pi$
$84$		0			0
$85$	1198.21			1.52899
$86$		0			0
$87$	434.205	+	752.065i	0.535077	+	0.926780i
$88$		0			0
$89$	−74.8843	+	129.703i	−0.0891879	+	0.154478i	−0.907168	−	0.420768i	$-0.861760\pi$
$89$	−74.8843	+	129.703i	−0.0891879	+	0.154478i	0.817980	+	0.575246i	$0.195094\pi$
$90$		0			0
$91$	18.3926	−	394.837i	0.0211876	−	0.454837i
$92$		0			0
$93$	−318.964	+	552.462i	−0.355646	+	0.615996i
$94$		0			0
$95$	−168.262	−	291.438i	−0.181719	−	0.314746i
$96$		0			0
$97$	−1865.72			−1.95294			−0.976468	−	0.215663i	$-0.930809\pi$
$97$	−1865.72			−1.95294			−0.976468	+	0.215663i	$0.930809\pi$
$98$		0			0
$99$	−1396.62			−1.41783
$100$		0			0
$101$	267.275	+	462.933i	0.263315	+	0.456075i	0.967121	−	0.254317i	$-0.0818508\pi$
$101$	267.275	+	462.933i	0.263315	+	0.456075i	−0.703806	+	0.710392i	$0.748517\pi$
$102$		0			0
$103$	659.808	−	1142.82i	0.631193	−	1.09326i	−0.356115	−	0.934442i	$-0.615899\pi$
$103$	659.808	−	1142.82i	0.631193	−	1.09326i	0.987308	−	0.158816i	$-0.0507677\pi$
$104$		0			0
$105$	−130.016	+	2791.07i	−0.120840	+	2.59410i
$106$		0			0
$107$	346.778	−	600.637i	0.313311	−	0.542671i	−0.665766	−	0.746161i	$-0.731895\pi$
$107$	346.778	−	600.637i	0.313311	−	0.542671i	0.979077	+	0.203490i	$0.0652284\pi$
$108$		0			0
$109$	−982.997	−	1702.60i	−0.863798	−	1.49614i	−0.868236	−	0.496152i	$-0.834746\pi$
$109$	−982.997	−	1702.60i	−0.863798	−	1.49614i	0.00443729	−	0.999990i	$-0.498588\pi$
$110$		0			0
$111$	1608.90			1.37577
$112$		0			0
$113$	2167.14			1.80414			0.902068	−	0.431595i	$-0.142049\pi$
$113$	2167.14			1.80414			0.902068	+	0.431595i	$0.142049\pi$
$114$		0			0
$115$	808.390	+	1400.17i	0.655502	+	1.13536i
$116$		0			0
$117$	683.665	−	1184.14i	0.540212	−	0.935675i
$118$		0			0
$119$	1246.96	−	644.509i	0.960573	−	0.496488i
$120$		0			0
$121$	427.893	−	741.132i	0.321482	−	0.556824i
$122$		0			0
$123$	−484.565	−	839.291i	−0.355217	−	0.615255i
$124$		0			0
$125$	−1.01640			−0.000727276
$126$		0			0
$127$	1443.60			1.00865			0.504324	−	0.863514i	$-0.331742\pi$
$127$	1443.60			1.00865			0.504324	+	0.863514i	$0.331742\pi$
$128$		0			0
$129$	−1500.15	−	2598.33i	−1.02388	−	1.77342i
$130$		0			0
$131$	1062.64	−	1840.55i	0.708728	−	1.22755i	−0.256601	−	0.966518i	$-0.582602\pi$
$131$	1062.64	−	1840.55i	0.708728	−	1.22755i	0.965329	−	0.261036i	$-0.0840642\pi$
$132$		0			0
$133$	−331.870	−	212.788i	−0.216367	−	0.138730i
$134$		0			0
$135$	−2796.07	+	4842.93i	−1.78257	+	3.08750i
$136$		0			0
$137$	202.737	+	351.151i	0.126431	+	0.218985i	0.922291	−	0.386495i	$-0.126315\pi$
$137$	202.737	+	351.151i	0.126431	+	0.218985i	−0.795861	+	0.605480i	$0.792981\pi$
$138$		0			0
$139$	1812.24			1.10585			0.552923	−	0.833232i	$-0.313512\pi$
$139$	1812.24			1.10585			0.552923	+	0.833232i	$0.313512\pi$
$140$		0			0
$141$	2570.33			1.53518
$142$		0			0
$143$	−232.625	−	402.918i	−0.136035	−	0.235620i
$144$		0			0
$145$	719.332	−	1245.92i	0.411981	−	0.713572i
$146$		0			0
$147$	1365.99	+	2974.55i	0.766431	+	1.66896i
$148$		0			0
$149$	−1446.29	+	2505.04i	−0.795197	+	1.37732i	0.127517	+	0.991836i	$0.459299\pi$
$149$	−1446.29	+	2505.04i	−0.795197	+	1.37732i	−0.922714	+	0.385485i	$0.874034\pi$
$150$		0			0
$151$	−619.634	−	1073.24i	−0.333941	−	0.578403i	0.649340	−	0.760498i	$-0.275045\pi$
$151$	−619.634	−	1073.24i	−0.333941	−	0.578403i	−0.983281	+	0.182096i	$0.941712\pi$
$152$		0			0
$153$	4855.68			2.56574
$154$		0			0
$155$	1056.83			0.547657
$156$		0			0
$157$	−891.686	−	1544.45i	−0.453276	−	0.785096i	0.545312	−	0.838233i	$-0.316411\pi$
$157$	−891.686	−	1544.45i	−0.453276	−	0.785096i	−0.998587	+	0.0531370i	$0.983078\pi$
$158$		0			0
$159$	1473.70	−	2552.53i	0.735046	−	1.27314i
$160$		0			0
$161$	1594.42	+	1022.31i	0.780485	+	0.500429i
$162$		0			0
$163$	−639.683	+	1107.96i	−0.307385	+	0.532407i	−0.977790	−	0.209589i	$-0.932787\pi$
$163$	−639.683	+	1107.96i	−0.307385	+	0.532407i	0.670404	+	0.741996i	$0.266121\pi$
$164$		0			0
$165$	1644.40	+	2848.19i	0.775859	+	1.34383i
$166$		0			0
$167$	−971.264			−0.450052			−0.225026	−	0.974353i	$-0.572247\pi$
$167$	−971.264			−0.450052			−0.225026	+	0.974353i	$0.572247\pi$
$168$		0			0
$169$	−1741.51			−0.792675
$170$		0			0
$171$	−681.873	−	1181.04i	−0.304937	−	0.528166i
$172$		0			0
$173$	264.423	−	457.994i	0.116207	−	0.201276i	−0.802055	−	0.597250i	$-0.796260\pi$
$173$	264.423	−	457.994i	0.116207	−	0.201276i	0.918261	+	0.395975i	$0.129593\pi$
$174$		0			0
$175$	2055.51	−	1062.42i	0.887897	−	0.458924i
$176$		0			0
$177$	−3858.87	+	6683.77i	−1.63870	+	2.83832i
$178$		0			0
$179$	74.5001	+	129.038i	0.0311084	+	0.0538813i	0.881160	−	0.472817i	$-0.156763\pi$
$179$	74.5001	+	129.038i	0.0311084	+	0.0538813i	−0.850052	+	0.526699i	$0.823430\pi$
$180$		0			0
$181$	−3624.17			−1.48830			−0.744151	−	0.668011i	$-0.767146\pi$
$181$	−3624.17			−1.48830			−0.744151	+	0.668011i	$0.767146\pi$
$182$		0			0
$183$	−6238.80			−2.52014
$184$		0			0
$185$	−1332.71	−	2308.32i	−0.529635	−	0.917355i
$186$		0			0
$187$	826.100	−	1430.85i	0.323050	−	0.559540i
$188$		0			0
$189$	−304.836	+	6543.95i	−0.117320	+	2.51853i
$190$		0			0
$191$	1592.30	−	2757.94i	0.603218	−	1.04480i	−0.389113	−	0.921190i	$-0.627218\pi$
$191$	1592.30	−	2757.94i	0.603218	−	1.04480i	0.992330	−	0.123614i	$-0.0394484\pi$
$192$		0			0
$193$	2298.82	+	3981.67i	0.857370	+	1.48501i	0.874429	+	0.485153i	$0.161236\pi$
$193$	2298.82	+	3981.67i	0.857370	+	1.48501i	−0.0170593	+	0.999854i	$0.505430\pi$
$194$		0			0
$195$	−3219.85			−1.18245
$196$		0			0
$197$	3877.84			1.40246			0.701230	−	0.712935i	$-0.252635\pi$
$197$	3877.84			1.40246			0.701230	+	0.712935i	$0.252635\pi$
$198$		0			0
$199$	−988.062	−	1711.37i	−0.351969	−	0.609628i	0.634625	−	0.772820i	$-0.281154\pi$
$199$	−988.062	−	1711.37i	−0.351969	−	0.609628i	−0.986594	+	0.163192i	$0.947821\pi$
$200$		0			0
$201$	−2261.00	+	3916.16i	−0.793425	+	1.37425i
$202$		0			0
$203$	78.4237	−	1683.53i	0.0271146	−	0.582073i
$204$		0			0
$205$	−802.761	+	1390.42i	−0.273499	+	0.473714i
$206$		0			0
$207$	3275.96	+	5674.13i	1.09998	+	1.90521i
$208$		0			0
$209$	−464.030			−0.153577
$210$		0			0
$211$	−4169.50			−1.36038			−0.680190	−	0.733036i	$-0.738103\pi$
$211$	−4169.50			−1.36038			−0.680190	+	0.733036i	$0.738103\pi$
$212$		0			0
$213$	−753.880	−	1305.76i	−0.242512	−	0.420043i
$214$		0			0
$215$	−2485.24	+	4304.57i	−0.788336	+	1.36544i
$216$		0			0
$217$	1099.83	−	568.464i	0.344061	−	0.177834i
$218$		0			0
$219$	−1288.66	+	2232.02i	−0.397623	+	0.688703i
$220$		0			0
$221$	808.777	+	1400.84i	0.246173	+	0.426384i
$222$		0			0
$223$	−1595.43			−0.479093			−0.239547	−	0.970885i	$-0.576999\pi$
$223$	−1595.43			−0.479093			−0.239547	+	0.970885i	$0.576999\pi$
$224$		0			0
$225$	8004.21			2.37162
$226$		0			0
$227$	−428.905	−	742.885i	−0.125407	−	0.217211i	0.796485	−	0.604658i	$-0.206690\pi$
$227$	−428.905	−	742.885i	−0.125407	−	0.217211i	−0.921892	+	0.387447i	$0.873357\pi$
$228$		0			0
$229$	39.2440	−	67.9726i	0.0113245	−	0.0196146i	−0.860308	−	0.509775i	$-0.829729\pi$
$229$	39.2440	−	67.9726i	0.0113245	−	0.0196146i	0.871632	+	0.490161i	$0.163062\pi$
$230$		0			0
$231$	3243.33	+	2079.55i	0.923790	+	0.592313i
$232$		0			0
$233$	−329.882	+	571.373i	−0.0927524	+	0.160652i	−0.908668	−	0.417519i	$-0.862900\pi$
$233$	−329.882	+	571.373i	−0.0927524	+	0.160652i	0.815916	+	0.578171i	$0.196233\pi$
$234$		0			0
$235$	−2129.08	−	3687.68i	−0.591005	−	1.02365i
$236$		0			0
$237$	3105.80			0.851239
$238$		0			0
$239$	−2879.88			−0.779430			−0.389715	−	0.920935i	$-0.627427\pi$
$239$	−2879.88			−0.779430			−0.389715	+	0.920935i	$0.627427\pi$
$240$		0			0
$241$	1167.26	+	2021.75i	0.311991	+	0.540384i	0.978793	−	0.204851i	$-0.0656709\pi$
$241$	1167.26	+	2021.75i	0.311991	+	0.540384i	−0.666803	+	0.745234i	$0.732338\pi$
$242$		0			0
$243$	−3077.29	+	5330.01i	−0.812378	+	1.40708i
$244$		0			0
$245$	3136.13	−	4423.73i	0.817797	−	1.15356i
$246$		0			0
$247$	227.150	−	393.435i	0.0585150	−	0.101351i
$248$		0			0
$249$	−4929.28	−	8537.77i	−1.25454	−	2.17293i
$250$		0			0
$251$	1386.81			0.348743			0.174372	−	0.984680i	$-0.444211\pi$
$251$	1386.81			0.348743			0.174372	+	0.984680i	$0.444211\pi$
$252$		0			0
$253$	2229.37			0.553988
$254$		0			0
$255$	−5717.18	−	9902.44i	−1.40401	−	2.43182i
$256$		0			0
$257$	3026.68	−	5242.37i	0.734628	−	1.27241i	−0.220258	−	0.975442i	$-0.570690\pi$
$257$	3026.68	−	5242.37i	0.734628	−	1.27241i	0.954886	−	0.296971i	$-0.0959766\pi$
$258$		0			0
$259$	−2628.56	−	1685.37i	−0.630620	−	0.404339i
$260$		0			0
$261$	2915.06	−	5049.03i	0.691332	−	1.19742i
$262$		0			0
$263$	501.708	+	868.983i	0.117630	+	0.203741i	0.918828	−	0.394658i	$-0.129137\pi$
$263$	501.708	+	868.983i	0.117630	+	0.203741i	−0.801198	+	0.598399i	$0.795804\pi$
$264$		0			0
$265$	−4882.86			−1.13189
$266$		0			0
$267$	1429.22			0.327592
$268$		0			0
$269$	1756.03	+	3041.54i	0.398020	+	0.689391i	0.993482	−	0.113993i	$-0.0363642\pi$
$269$	1756.03	+	3041.54i	0.398020	+	0.689391i	−0.595462	+	0.803384i	$0.703031\pi$
$270$		0			0
$271$	−19.4586	+	33.7033i	−0.00436172	+	0.00755471i	−0.868198	−	0.496218i	$-0.834722\pi$
$271$	−19.4586	+	33.7033i	−0.00436172	+	0.00755471i	0.863836	+	0.503773i	$0.168055\pi$
$272$		0			0
$273$	−3350.84	+	1731.94i	−0.742865	+	0.383962i
$274$		0			0
$275$	1361.76	−	2358.64i	0.298609	−	0.517205i
$276$		0			0
$277$	−97.9751	−	169.698i	−0.0212518	−	0.0368092i	0.855204	−	0.518292i	$-0.173432\pi$
$277$	−97.9751	−	169.698i	−0.0212518	−	0.0368092i	−0.876456	+	0.481482i	$0.840099\pi$
$278$		0			0
$279$	4282.76			0.919005
$280$		0			0
$281$	809.583			0.171871			0.0859354	−	0.996301i	$-0.472612\pi$
$281$	809.583			0.171871			0.0859354	+	0.996301i	$0.472612\pi$
$282$		0			0
$283$	−1899.31	−	3289.70i	−0.398947	−	0.690997i	0.594649	−	0.803985i	$-0.297291\pi$
$283$	−1899.31	−	3289.70i	−0.398947	−	0.690997i	−0.993596	+	0.112989i	$0.963958\pi$
$284$		0			0
$285$	−1605.70	+	2781.16i	−0.333732	+	0.578041i
$286$		0			0
$287$	−87.5194	+	1878.79i	−0.0180004	+	0.386417i
$288$		0			0
$289$	−415.641	+	719.912i	−0.0846003	+	0.146532i
$290$		0			0
$291$	8902.16	+	15419.0i	1.79331	+	3.10611i
$292$		0			0
$293$	−3143.28			−0.626731			−0.313366	−	0.949633i	$-0.601457\pi$
$293$	−3143.28			−0.626731			−0.313366	+	0.949633i	$0.601457\pi$
$294$		0			0
$295$	12785.7			2.52343
$296$		0			0
$297$	3855.48	+	6677.88i	0.753257	+	1.30468i
$298$		0			0
$299$	−1091.31	+	1890.20i	−0.211077	+	0.365596i
$300$		0			0
$301$	−270.949	+	5816.49i	−0.0518845	+	1.11381i
$302$		0			0
$303$	2550.57	−	4417.72i	0.483586	−	0.837595i
$304$		0			0
$305$	5167.80	+	8950.89i	0.970188	+	1.68041i
$306$		0			0
$307$	7726.54			1.43641			0.718203	−	0.695833i	$-0.244965\pi$
$307$	7726.54			1.43641			0.718203	+	0.695833i	$0.244965\pi$
$308$		0			0
$309$	−12593.0			−2.31841
$310$		0			0
$311$	738.953	+	1279.90i	0.134734	+	0.233366i	0.925496	−	0.378758i	$-0.123649\pi$
$311$	738.953	+	1279.90i	0.134734	+	0.233366i	−0.790762	+	0.612124i	$0.790315\pi$
$312$		0			0
$313$	3410.86	−	5907.78i	0.615953	−	1.06686i	−0.374264	−	0.927322i	$-0.622105\pi$
$313$	3410.86	−	5907.78i	0.615953	−	1.06686i	0.990217	−	0.139539i	$-0.0445620\pi$
$314$		0			0
$315$	16664.0	−	8613.06i	2.98067	−	1.54061i
$316$		0			0
$317$	−368.611	+	638.453i	−0.0653099	+	0.113120i	−0.896831	−	0.442372i	$-0.854137\pi$
$317$	−368.611	+	638.453i	−0.0653099	+	0.113120i	0.831521	+	0.555493i	$0.187470\pi$
$318$		0			0
$319$	−991.882	−	1717.99i	−0.174090	−	0.301533i
$320$		0			0
$321$	−6618.53			−1.15081
$322$		0			0
$323$	1613.32			0.277917
$324$		0			0
$325$	1333.21	+	2309.18i	0.227548	+	0.394124i
$326$		0			0
$327$	−9380.63	+	16247.7i	−1.58639	+	2.74771i
$328$		0			0
$329$	−4199.29	−	2692.49i	−0.703691	−	0.451190i
$330$		0			0
$331$	1832.14	−	3173.36i	0.304241	−	0.526960i	−0.672851	−	0.739778i	$-0.734931\pi$
$331$	1832.14	−	3173.36i	0.304241	−	0.526960i	0.977092	+	0.212818i	$0.0682640\pi$
$332$		0			0
$333$	−5400.73	−	9354.34i	−0.888764	−	1.53938i
$334$		0			0
$335$	7491.42			1.22179
$336$		0			0
$337$	−3269.01			−0.528411			−0.264206	−	0.964466i	$-0.585110\pi$
$337$	−3269.01			−0.528411			−0.264206	+	0.964466i	$0.585110\pi$
$338$		0			0
$339$	−10340.4	−	17910.1i	−1.65667	−	2.86944i
$340$		0			0
$341$	728.630	−	1262.02i	0.115711	−	0.200418i
$342$		0			0
$343$	884.224	−	6290.61i	0.139194	−	0.990265i
$344$		0			0
$345$	7714.37	−	13361.7i	1.20385	−	2.08513i
$346$		0			0
$347$	4521.27	+	7831.07i	0.699465	+	1.21151i	0.968652	+	0.248422i	$0.0799118\pi$
$347$	4521.27	+	7831.07i	0.699465	+	1.21151i	−0.269187	+	0.963088i	$0.586755\pi$
$348$		0			0
$349$	5151.89			0.790185			0.395092	−	0.918641i	$-0.370713\pi$
$349$	5151.89			0.790185			0.395092	+	0.918641i	$0.370713\pi$
$350$		0			0
$351$	−7549.26			−1.14800
$352$		0			0
$353$	−1071.18	−	1855.33i	−0.161510	−	0.279743i	0.773901	−	0.633307i	$-0.218303\pi$
$353$	−1071.18	−	1855.33i	−0.161510	−	0.279743i	−0.935410	+	0.353564i	$0.884970\pi$
$354$		0			0
$355$	−1248.93	+	2163.20i	−0.186722	+	0.323411i
$356$		0			0
$357$	−11276.2	−	7230.07i	−1.67171	−	1.07187i
$358$		0			0
$359$	714.986	−	1238.39i	0.105113	−	0.182061i	−0.808671	−	0.588261i	$-0.799813\pi$
$359$	714.986	−	1238.39i	0.105113	−	0.182061i	0.913784	+	0.406200i	$0.133146\pi$
$360$		0			0
$361$	3202.95	+	5547.66i	0.466970	+	0.808815i
$362$		0			0
$363$	−8166.67			−1.18082
$364$		0			0
$365$	4269.74			0.612297
$366$		0			0
$367$	1510.16	+	2615.67i	0.214794	+	0.372034i	0.953209	−	0.302312i	$-0.0977586\pi$
$367$	1510.16	+	2615.67i	0.214794	+	0.372034i	−0.738415	+	0.674347i	$0.764425\pi$
$368$		0			0
$369$	−3253.15	+	5634.62i	−0.458949	+	0.794924i
$370$		0			0
$371$	−5081.52	+	2626.47i	−0.711103	+	0.367545i
$372$		0			0
$373$	−823.554	+	1426.44i	−0.114322	+	0.198011i	−0.917508	−	0.397716i	$-0.869803\pi$
$373$	−823.554	+	1426.44i	−0.114322	+	0.198011i	0.803187	+	0.595727i	$0.203136\pi$
$374$		0			0
$375$	4.84969	+	8.39991i	0.000667832	+	0.00115672i
$376$		0			0
$377$	1942.17			0.265323
$378$		0			0
$379$	4385.44			0.594366			0.297183	−	0.954821i	$-0.403953\pi$
$379$	4385.44			0.594366			0.297183	+	0.954821i	$0.403953\pi$
$380$		0			0
$381$	−6888.03	−	11930.4i	−0.926206	−	1.60424i
$382$		0			0
$383$	7194.48	−	12461.2i	0.959845	−	1.66250i	0.236975	−	0.971516i	$-0.423844\pi$
$383$	7194.48	−	12461.2i	0.959845	−	1.66250i	0.722870	−	0.690984i	$-0.242823\pi$
$384$		0			0
$385$	297.003	−	6375.81i	0.0393161	−	0.844003i
$386$		0			0
$387$	−10071.3	+	17444.1i	−1.32288	+	2.29130i
$388$		0			0
$389$	−1332.78	−	2308.44i	−0.173714	−	0.300881i	0.766002	−	0.642839i	$-0.222243\pi$
$389$	−1332.78	−	2308.44i	−0.173714	−	0.300881i	−0.939715	+	0.341957i	$0.888910\pi$
$390$		0			0
$391$	−7750.94			−1.00251
$392$		0			0
$393$	−20281.3			−2.60320
$394$		0			0
$395$	−2572.64	−	4455.94i	−0.327705	−	0.567601i
$396$		0			0
$397$	−2228.85	+	3860.49i	−0.281771	+	0.488041i	−0.971821	−	0.235720i	$-0.924255\pi$
$397$	−2228.85	+	3860.49i	−0.281771	+	0.488041i	0.690050	+	0.723762i	$0.257588\pi$
$398$		0			0
$399$	−175.059	+	3758.01i	−0.0219646	+	0.471518i
$400$		0			0
$401$	6656.90	−	11530.1i	0.829001	−	1.43587i	−0.0698209	−	0.997560i	$-0.522243\pi$
$401$	6656.90	−	11530.1i	0.829001	−	1.43587i	0.898822	−	0.438313i	$-0.144424\pi$
$402$		0			0
$403$	713.351	+	1235.56i	0.0881750	+	0.152724i
$404$		0			0
$405$	26018.1			3.19222
$406$		0			0
$407$	−3675.32			−0.447614
$408$		0			0
$409$	2046.12	+	3543.98i	0.247369	+	0.428456i	0.962795	−	0.270233i	$-0.0871007\pi$
$409$	2046.12	+	3543.98i	0.247369	+	0.428456i	−0.715426	+	0.698688i	$0.753767\pi$
$410$		0			0
$411$	1934.70	−	3351.00i	0.232194	−	0.402172i
$412$		0			0
$413$	13305.9	−	6877.37i	1.58533	−	0.819402i
$414$		0			0
$415$	−8166.16	+	14144.2i	−0.965931	+	1.67304i
$416$		0			0
$417$	−8647.02	−	14977.1i	−1.01546	−	1.75883i
$418$		0			0
$419$	−8297.69			−0.967467			−0.483733	−	0.875215i	$-0.660720\pi$
$419$	−8297.69			−0.967467			−0.483733	+	0.875215i	$0.660720\pi$
$420$		0			0
$421$	−14729.2			−1.70512			−0.852561	−	0.522627i	$-0.824952\pi$
$421$	−14729.2			−1.70512			−0.852561	+	0.522627i	$0.824952\pi$
$422$		0			0
$423$	−8628.01	−	14944.2i	−0.991746	−	1.71775i
$424$		0			0
$425$	−4734.50	+	8200.40i	−0.540370	+	0.935948i
$426$		0			0
$427$	10192.7	+	6535.31i	1.15517	+	0.740670i
$428$		0			0
$429$	−2219.91	+	3845.00i	−0.249833	+	0.432723i
$430$		0			0
$431$	−2470.26	−	4278.61i	−0.276074	−	0.478175i	0.694331	−	0.719656i	$-0.255700\pi$
$431$	−2470.26	−	4278.61i	−0.276074	−	0.478175i	−0.970406	+	0.241481i	$0.922367\pi$
$432$		0			0
$433$	−8291.22			−0.920209			−0.460105	−	0.887865i	$-0.652188\pi$
$433$	−8291.22			−0.920209			−0.460105	+	0.887865i	$0.652188\pi$
$434$		0			0
$435$	−13729.0			−1.51323
$436$		0			0
$437$	1088.45	+	1885.25i	0.119148	+	0.206370i
$438$		0			0
$439$	−4048.86	+	7012.82i	−0.440185	+	0.762423i	−0.997703	−	0.0677419i	$-0.978421\pi$
$439$	−4048.86	+	7012.82i	−0.440185	+	0.762423i	0.557518	+	0.830165i	$0.311754\pi$
$440$		0			0
$441$	12709.0	−	17926.9i	1.37232	−	1.93575i
$442$		0			0
$443$	−3229.58	+	5593.79i	−0.346370	+	0.599930i	−0.985602	−	0.169084i	$-0.945919\pi$
$443$	−3229.58	+	5593.79i	−0.346370	+	0.599930i	0.639232	+	0.769014i	$0.279252\pi$
$444$		0			0
$445$	−1183.87	−	2050.53i	−0.126114	−	0.218437i
$446$		0			0
$447$	27603.5			2.92080
$448$		0			0
$449$	4951.16			0.520401			0.260200	−	0.965555i	$-0.416211\pi$
$449$	4951.16			0.520401			0.260200	+	0.965555i	$0.416211\pi$
$450$		0			0
$451$	1106.92	+	1917.24i	0.115572	+	0.200176i
$452$		0			0
$453$	−5913.09	+	10241.8i	−0.613292	+	1.06225i
$454$		0			0
$455$	5260.44	+	3372.88i	0.542007	+	0.347523i
$456$		0			0
$457$	−7908.74	+	13698.3i	−0.809530	+	1.40215i	0.103660	+	0.994613i	$0.466945\pi$
$457$	−7908.74	+	13698.3i	−0.809530	+	1.40215i	−0.913190	+	0.407534i	$0.866389\pi$
$458$		0			0
$459$	−13404.5	−	23217.3i	−1.36311	−	2.36098i
$460$		0			0
$461$	−8584.25			−0.867263			−0.433632	−	0.901090i	$-0.642768\pi$
$461$	−8584.25			−0.867263			−0.433632	+	0.901090i	$0.642768\pi$
$462$		0			0
$463$	−15304.5			−1.53620			−0.768101	−	0.640329i	$-0.778798\pi$
$463$	−15304.5			−1.53620			−0.768101	+	0.640329i	$0.778798\pi$
$464$		0			0
$465$	−5042.62	−	8734.07i	−0.502894	−	0.871038i
$466$		0			0
$467$	4270.87	−	7397.37i	0.423196	−	0.732996i	−0.573054	−	0.819517i	$-0.694242\pi$
$467$	4270.87	−	7397.37i	0.423196	−	0.732996i	0.996250	+	0.0865210i	$0.0275750\pi$
$468$		0			0
$469$	7796.20	−	4029.60i	0.767580	−	0.396737i
$470$		0			0
$471$	−8509.26	+	14738.5i	−0.832454	+	1.44185i
$472$		0			0
$473$	3426.88	+	5935.54i	0.333125	+	0.576990i
$474$		0			0
$475$	2659.43			0.256890
$476$		0			0
$477$	−19787.6			−1.89939
$478$		0			0
$479$	−1149.11	−	1990.31i	−0.109612	−	0.189853i	0.806001	−	0.591914i	$-0.201627\pi$
$479$	−1149.11	−	1990.31i	−0.109612	−	0.189853i	−0.915613	+	0.402061i	$0.868294\pi$
$480$		0			0
$481$	1799.13	−	3116.18i	0.170547	−	0.295396i
$482$		0			0
$483$	841.044	−	18054.8i	0.0792315	−	1.70087i
$484$		0			0
$485$	14747.9	−	25544.1i	1.38076	−	2.39154i
$486$		0			0
$487$	−5509.61	−	9542.92i	−0.512657	−	0.887948i	−0.999892	−	0.0146775i	$-0.995328\pi$
$487$	−5509.61	−	9542.92i	−0.512657	−	0.887948i	0.487235	−	0.873271i	$-0.338005\pi$
$488$		0			0
$489$	12208.8			1.12904
$490$		0			0
$491$	−17105.3			−1.57221			−0.786103	−	0.618096i	$-0.787904\pi$
$491$	−17105.3			−1.57221			−0.786103	+	0.618096i	$0.787904\pi$
$492$		0			0
$493$	3448.52	+	5973.02i	0.315038	+	0.545662i
$494$		0			0
$495$	11039.8	−	19121.5i	1.00243	−	1.73626i
$496$		0			0
$497$	−136.162	+	2923.00i	−0.0122891	+	0.263812i
$498$		0			0
$499$	−646.501	+	1119.77i	−0.0579987	+	0.100457i	−0.893567	−	0.448930i	$-0.851805\pi$
$499$	−646.501	+	1119.77i	−0.0579987	+	0.100457i	0.835568	+	0.549387i	$0.185139\pi$
$500$		0			0
$501$	4634.33	+	8026.90i	0.413267	+	0.715799i
$502$		0			0
$503$	−258.772			−0.0229385			−0.0114692	−	0.999934i	$-0.503651\pi$
$503$	−258.772			−0.0229385			−0.0114692	+	0.999934i	$0.503651\pi$
$504$		0			0
$505$	−8450.88			−0.744672
$506$		0			0
$507$	8309.50	+	14392.5i	0.727885	+	1.26073i
$508$		0			0
$509$	8132.50	−	14085.9i	0.708186	−	1.22661i	−0.257343	−	0.966320i	$-0.582847\pi$
$509$	8132.50	−	14085.9i	0.708186	−	1.22661i	0.965529	−	0.260294i	$-0.0838195\pi$
$510$		0			0
$511$	4443.45	−	2296.67i	0.384671	−	0.198823i
$512$		0			0
$513$	−3764.74	+	6520.72i	−0.324010	+	0.561202i
$514$		0			0
$515$	10431.1	+	18067.3i	0.892527	+	1.54590i
$516$		0			0
$517$	−5871.56			−0.499479
$518$		0			0
$519$	−5046.72			−0.426833
$520$		0			0
$521$	8322.36	+	14414.8i	0.699826	+	1.21213i	0.968526	+	0.248911i	$0.0800725\pi$
$521$	8322.36	+	14414.8i	0.699826	+	1.21213i	−0.268700	+	0.963224i	$0.586594\pi$
$522$		0			0
$523$	−5137.18	+	8897.85i	−0.429509	+	0.743931i	−0.996830	−	0.0795658i	$-0.974647\pi$
$523$	−5137.18	+	8897.85i	−0.429509	+	0.743931i	0.567321	+	0.823497i	$0.307980\pi$
$524$		0			0
$525$	−18588.0	−	11918.2i	−1.54523	−	0.990769i
$526$		0			0
$527$	−2533.26	+	4387.74i	−0.209394	+	0.362681i
$528$		0			0
$529$	854.204	+	1479.52i	0.0702066	+	0.121601i
$530$		0			0
$531$	51813.5			4.23449
$532$		0			0
$533$	−2167.42			−0.176138
$534$		0			0
$535$	5482.34	+	9495.69i	0.443032	+	0.767354i
$536$		0			0
$537$	710.946	−	1231.39i	0.0571314	−	0.0989546i
$538$		0			0
$539$	−3120.43	−	6794.96i	−0.249362	−	0.543005i
$540$		0			0
$541$	8718.16	−	15100.3i	0.692833	−	1.20002i	−0.278072	−	0.960560i	$-0.589696\pi$
$541$	8718.16	−	15100.3i	0.692833	−	1.20002i	0.970906	−	0.239462i	$-0.0769711\pi$
$542$		0			0
$543$	17292.5	+	29951.6i	1.36666	+	2.36712i
$544$		0			0
$545$	31081.1			2.44288
$546$		0			0
$547$	−3708.40			−0.289871			−0.144936	−	0.989441i	$-0.546297\pi$
$547$	−3708.40			−0.289871			−0.144936	+	0.989441i	$0.546297\pi$
$548$		0			0
$549$	20942.3	+	36273.1i	1.62804	+	2.81985i
$550$		0			0
$551$	968.538	−	1677.56i	0.0748840	−	0.129703i
$552$		0			0
$553$	−5074.12	−	3253.41i	−0.390187	−	0.250179i
$554$		0			0
$555$	−12717.9	+	22028.0i	−0.972691	+	1.68475i
$556$		0			0
$557$	9960.80	+	17252.6i	0.757725	+	1.31242i	0.944008	+	0.329922i	$0.107022\pi$
$557$	9960.80	+	17252.6i	0.757725	+	1.31242i	−0.186284	+	0.982496i	$0.559644\pi$
$558$		0			0
$559$	−6710.05			−0.507701
$560$		0			0
$561$	−15766.8			−1.18658
$562$		0			0
$563$	3426.37	+	5934.65i	0.256491	+	0.444255i	0.965299	−	0.261146i	$-0.0841004\pi$
$563$	3426.37	+	5934.65i	0.256491	+	0.444255i	−0.708809	+	0.705401i	$0.750767\pi$
$564$		0			0
$565$	−17130.5	+	29671.0i	−1.27555	+	2.20932i
$566$		0			0
$567$	27076.6	−	13995.0i	2.00548	−	1.03657i
$568$		0			0
$569$	2736.52	−	4739.79i	0.201618	−	0.349213i	−0.747432	−	0.664339i	$-0.768713\pi$
$569$	2736.52	−	4739.79i	0.201618	−	0.349213i	0.949050	+	0.315125i	$0.102047\pi$
$570$		0			0
$571$	−10803.5	−	18712.2i	−0.791792	−	1.37142i	−0.924857	−	0.380316i	$-0.875815\pi$
$571$	−10803.5	−	18712.2i	−0.791792	−	1.37142i	0.133065	−	0.991107i	$-0.457518\pi$
$572$		0			0
$573$	−30390.2			−2.21565
$574$		0			0
$575$	−12776.8			−0.926662
$576$		0			0
$577$	−580.448	−	1005.37i	−0.0418794	−	0.0725372i	0.844326	−	0.535830i	$-0.180001\pi$
$577$	−580.448	−	1005.37i	−0.0418794	−	0.0725372i	−0.886205	+	0.463293i	$0.846668\pi$
$578$		0			0
$579$	21937.3	−	37996.6i	1.57458	−	2.72726i
$580$		0			0
$581$	−890.300	+	19112.2i	−0.0635729	+	1.36473i
$582$		0			0
$583$	−3366.47	+	5830.90i	−0.239151	+	0.414222i
$584$		0			0
$585$	10808.3	+	18720.5i	0.763877	+	1.32307i
$586$		0			0
$587$	6275.52			0.441258			0.220629	−	0.975358i	$-0.429189\pi$
$587$	6275.52			0.441258			0.220629	+	0.975358i	$0.429189\pi$
$588$		0			0
$589$	1422.96			0.0995453
$590$		0			0
$591$	−18502.9	−	32047.9i	−1.28783	−	2.23058i
$592$		0			0
$593$	−7013.59	+	12147.9i	−0.485689	+	0.841238i	−0.999865	−	0.0164467i	$-0.994765\pi$
$593$	−7013.59	+	12147.9i	−0.485689	+	0.841238i	0.514176	+	0.857685i	$0.328098\pi$
$594$		0			0
$595$	−1032.61	+	22167.1i	−0.0711474	+	1.52733i
$596$		0			0
$597$	−9428.96	+	16331.4i	−0.646401	+	1.11960i
$598$		0			0
$599$	−11413.5	−	19768.7i	−0.778535	−	1.34846i	−0.932786	−	0.360431i	$-0.882630\pi$
$599$	−11413.5	−	19768.7i	−0.778535	−	1.34846i	0.154251	−	0.988032i	$-0.450704\pi$
$600$		0			0
$601$	−14056.5			−0.954036			−0.477018	−	0.878894i	$-0.658282\pi$
$601$	−14056.5			−0.954036			−0.477018	+	0.878894i	$0.658282\pi$
$602$		0			0
$603$	30358.6			2.05025
$604$		0			0
$605$	6764.71	+	11716.8i	0.454586	+	0.787366i
$606$		0			0
$607$	−10251.2	+	17755.5i	−0.685472	+	1.18727i	0.287816	+	0.957686i	$0.407071\pi$
$607$	−10251.2	+	17755.5i	−0.685472	+	1.18727i	−0.973288	+	0.229587i	$0.926262\pi$
$608$		0			0
$609$	−14287.6	+	7384.76i	−0.950674	+	0.491372i
$610$		0			0
$611$	2874.22	−	4978.29i	0.190308	−	0.329624i
$612$		0			0
$613$	−6248.46	−	10822.7i	−0.411702	−	0.713088i	0.583374	−	0.812203i	$-0.301732\pi$
$613$	−6248.46	−	10822.7i	−0.411702	−	0.713088i	−0.995076	+	0.0991154i	$0.968399\pi$
$614$		0			0
$615$	15321.3			1.00458
$616$		0			0
$617$	3715.94			0.242460			0.121230	−	0.992624i	$-0.461316\pi$
$617$	3715.94			0.242460			0.121230	+	0.992624i	$0.461316\pi$
$618$		0			0
$619$	−748.648	−	1296.70i	−0.0486118	−	0.0841981i	0.840696	−	0.541508i	$-0.182146\pi$
$619$	−748.648	−	1296.70i	−0.0486118	−	0.0841981i	−0.889307	+	0.457310i	$0.848813\pi$
$620$		0			0
$621$	18087.1	−	31327.8i	1.16878	−	2.02439i
$622$		0			0
$623$	−2335.00	−	1497.15i	−0.150160	−	0.0962795i
$624$		0			0
$625$	7816.52	−	13538.6i	0.500257	−	0.866471i
$626$		0			0
$627$	2214.09	+	3834.92i	0.141025	+	0.244262i
$628$		0			0
$629$	12778.2			0.810014
$630$		0			0
$631$	27717.6			1.74869			0.874343	−	0.485309i	$-0.161293\pi$
$631$	27717.6			1.74869			0.874343	+	0.485309i	$0.161293\pi$
$632$		0			0
$633$	19894.5	+	34458.3i	1.24919	+	2.16366i
$634$		0			0
$635$	−11411.2	+	19764.7i	−0.713131	+	1.23518i
$636$		0			0
$637$	7288.71	+	680.534i	0.453358	+	0.0423293i
$638$		0			0
$639$	−5061.22	+	8766.28i	−0.313331	+	0.542706i
$640$		0			0
$641$	−5939.27	−	10287.1i	−0.365971	−	0.633880i	0.622961	−	0.782253i	$-0.285930\pi$
$641$	−5939.27	−	10287.1i	−0.365971	−	0.633880i	−0.988931	+	0.148373i	$0.952596\pi$
$642$		0			0
$643$	−21166.1			−1.29815			−0.649073	−	0.760726i	$-0.724843\pi$
$643$	−21166.1			−1.29815			−0.649073	+	0.760726i	$0.724843\pi$
$644$		0			0
$645$	47432.8			2.89560
$646$		0			0
$647$	8956.31	+	15512.8i	0.544218	+	0.942613i	0.998656	+	0.0518345i	$0.0165068\pi$
$647$	8956.31	+	15512.8i	0.544218	+	0.942613i	−0.454438	+	0.890778i	$0.650160\pi$
$648$		0			0
$649$	8815.07	−	15268.1i	0.533161	−	0.923462i
$650$		0			0
$651$	−9945.78	−	6377.01i	−0.598780	−	0.383924i
$652$		0			0
$653$	−2303.47	+	3989.73i	−0.138043	+	0.239097i	−0.926756	−	0.375665i	$-0.877414\pi$
$653$	−2303.47	+	3989.73i	−0.138043	+	0.239097i	0.788713	+	0.614761i	$0.210748\pi$
$654$		0			0
$655$	16799.7	+	29097.9i	1.00216	+	1.73580i
$656$		0			0
$657$	17302.9			1.02748
$658$		0			0
$659$	−6753.57			−0.399213			−0.199607	−	0.979876i	$-0.563966\pi$
$659$	−6753.57			−0.399213			−0.199607	+	0.979876i	$0.563966\pi$
$660$		0			0
$661$	−15944.4	−	27616.5i	−0.938223	−	1.62505i	−0.768783	−	0.639510i	$-0.779137\pi$
$661$	−15944.4	−	27616.5i	−0.938223	−	1.62505i	−0.169440	−	0.985541i	$-0.554196\pi$
$662$		0			0
$663$	7718.07	−	13368.1i	0.452104	−	0.783067i
$664$		0			0
$665$	5536.67	−	2861.72i	0.322861	−	0.166876i
$666$		0			0
$667$	−4653.20	+	8059.58i	−0.270124	+	0.467868i
$668$		0			0
$669$	7612.49	+	13185.2i	0.439934	+	0.761988i
$670$		0			0
$671$	14251.7			0.819940
$672$		0			0
$673$	4332.88			0.248173			0.124086	−	0.992271i	$-0.460400\pi$
$673$	4332.88			0.248173			0.124086	+	0.992271i	$0.460400\pi$
$674$		0			0
$675$	−22096.3	−	38271.9i	−1.25998	−	2.18235i
$676$		0			0
$677$	−742.064	+	1285.29i	−0.0421268	+	0.0729658i	−0.886320	−	0.463073i	$-0.846747\pi$
$677$	−742.064	+	1285.29i	−0.0421268	+	0.0729658i	0.844193	+	0.536039i	$0.180080\pi$
$678$		0			0
$679$	1607.86	−	34516.1i	0.0908747	−	1.95082i
$680$		0			0
$681$	−4092.99	+	7089.26i	−0.230314	+	0.398915i
$682$		0			0
$683$	−1853.16	−	3209.76i	−0.103820	−	0.179822i	0.809435	−	0.587209i	$-0.199773\pi$
$683$	−1853.16	−	3209.76i	−0.103820	−	0.179822i	−0.913255	+	0.407387i	$0.866440\pi$
$684$		0			0
$685$	−6410.29			−0.357554
$686$		0			0
$687$	−749.001			−0.0415956
$688$		0			0
$689$	−3295.88	−	5708.63i	−0.182240	−	0.315648i
$690$		0			0
$691$	−12901.6	+	22346.3i	−0.710276	+	1.23023i	0.254477	+	0.967079i	$0.418097\pi$
$691$	−12901.6	+	22346.3i	−0.710276	+	1.23023i	−0.964753	+	0.263156i	$0.915237\pi$
$692$		0			0
$693$	1203.59	−	25837.7i	0.0659750	−	1.41629i
$694$		0			0
$695$	−14325.2	+	24812.0i	−0.781850	+	1.35420i
$696$		0			0
$697$	−3848.49	−	6665.78i	−0.209142	−	0.362244i
$698$		0			0
$699$	6296.06			0.340685
$700$		0			0
$701$	16440.9			0.885827			0.442914	−	0.896564i	$-0.353945\pi$
$701$	16440.9			0.885827			0.442914	+	0.896564i	$0.353945\pi$
$702$		0			0
$703$	−1794.41	−	3108.01i	−0.0962695	−	0.166744i
$704$		0			0
$705$	−20317.6	+	35191.1i	−1.08540	+	1.87996i
$706$		0			0
$707$	−8794.69	+	4545.68i	−0.467834	+	0.241808i
$708$		0			0
$709$	8310.79	−	14394.7i	0.440223	−	0.762489i	−0.557482	−	0.830189i	$-0.688233\pi$
$709$	8310.79	−	14394.7i	0.440223	−	0.762489i	0.997706	+	0.0676995i	$0.0215659\pi$
$710$		0			0
$711$	−10425.5	−	18057.5i	−0.549910	−	0.952473i
$712$		0			0
$713$	−6836.42			−0.359083
$714$		0			0
$715$	7355.29			0.384717
$716$		0			0
$717$	13741.2	+	23800.4i	0.715723	+	1.23967i
$718$		0			0
$719$	−8713.36	+	15092.0i	−0.451952	+	0.782804i	−0.998507	−	0.0546192i	$-0.982606\pi$
$719$	−8713.36	+	15092.0i	−0.451952	+	0.782804i	0.546555	+	0.837423i	$0.315939\pi$
$720$		0			0
$721$	20573.8	+	13191.5i	1.06270	+	0.681381i
$722$		0			0
$723$	11139.0	−	19293.3i	0.572980	−	0.992430i
$724$		0			0
$725$	5684.62	+	9846.06i	0.291202	+	0.504377i
$726$		0			0
$727$	−19950.2			−1.01776			−0.508879	−	0.860838i	$-0.669940\pi$
$727$	−19950.2			−1.01776			−0.508879	+	0.860838i	$0.669940\pi$
$728$		0			0
$729$	14297.4			0.726385
$730$		0			0
$731$	−11914.4	−	20636.4i	−0.602832	−	1.04414i
$732$		0			0
$733$	−6353.15	+	11004.0i	−0.320135	+	0.554490i	−0.980516	−	0.196441i	$-0.937062\pi$
$733$	−6353.15	+	11004.0i	−0.320135	+	0.554490i	0.660381	+	0.750931i	$0.270395\pi$
$734$		0			0
$735$	−51523.2	−	4810.64i	−2.58566	−	0.241419i
$736$		0			0
$737$	5164.94	−	8945.93i	0.258145	−	0.447120i
$738$		0			0
$739$	−7756.39	−	13434.5i	−0.386094	−	0.668734i	0.605826	−	0.795597i	$-0.292843\pi$
$739$	−7756.39	−	13434.5i	−0.386094	−	0.668734i	−0.991920	+	0.126863i	$0.959509\pi$
$740$		0			0
$741$	−4335.33			−0.214929
$742$		0			0
$743$	1559.42			0.0769981			0.0384991	−	0.999259i	$-0.487742\pi$
$743$	1559.42			0.0769981			0.0384991	+	0.999259i	$0.487742\pi$
$744$		0			0
$745$	−22864.8	−	39603.1i	−1.12443	−	1.94758i
$746$		0			0
$747$	−33093.0	+	57318.7i	−1.62090	+	2.80747i
$748$		0			0
$749$	10813.1	+	6933.09i	0.527504	+	0.338224i
$750$		0			0
$751$	5173.64	−	8961.01i	0.251383	−	0.435408i	−0.712524	−	0.701648i	$-0.752448\pi$
$751$	5173.64	−	8961.01i	0.251383	−	0.435408i	0.963907	+	0.266240i	$0.0857812\pi$
$752$		0			0
$753$	−6617.08	−	11461.1i	−0.320239	−	0.554670i
$754$		0			0
$755$	19592.0			0.944406
$756$		0			0
$757$	−40281.7			−1.93403			−0.967017	−	0.254711i	$-0.918020\pi$
$757$	−40281.7			−1.93403			−0.967017	+	0.254711i	$0.918020\pi$
$758$		0			0
$759$	−10637.3	−	18424.3i	−0.508708	−	0.881108i
$760$		0			0
$761$	−4288.89	+	7428.57i	−0.204300	+	0.353858i	−0.949909	−	0.312525i	$-0.898825\pi$
$761$	−4288.89	+	7428.57i	−0.204300	+	0.353858i	0.745610	+	0.666383i	$0.232158\pi$
$762$		0			0
$763$	32345.6	−	16718.3i	1.53472	−	0.793243i
$764$		0			0
$765$	−38382.6	+	66480.6i	−1.81402	+	3.14197i
$766$		0			0
$767$	8630.22	+	14948.0i	0.406283	+	0.703703i
$768$		0			0
$769$	−10747.8			−0.504001			−0.252000	−	0.967727i	$-0.581088\pi$
$769$	−10747.8			−0.504001			−0.252000	+	0.967727i	$0.581088\pi$
$770$		0			0
$771$	−57766.6			−2.69833
$772$		0			0
$773$	−5894.46	−	10209.5i	−0.274268	−	0.475046i	0.695682	−	0.718350i	$-0.255102\pi$
$773$	−5894.46	−	10209.5i	−0.274268	−	0.475046i	−0.969950	+	0.243304i	$0.921769\pi$
$774$		0			0
$775$	−4175.89	+	7232.85i	−0.193551	+	0.335241i
$776$		0			0
$777$	−1386.54	+	29765.0i	−0.0640178	+	1.37428i
$778$		0			0
$779$	−1080.87	+	1872.12i	−0.0497127	+	0.0861050i
$780$		0			0
$781$	1722.14	+	2982.83i	0.0789025	+	0.136663i
$782$		0			0
$783$	−32189.1			−1.46915
$784$		0			0
$785$	28194.0			1.28189
$786$		0			0
$787$	−5656.26	−	9796.93i	−0.256193	−	0.443739i	0.709026	−	0.705182i	$-0.249135\pi$
$787$	−5656.26	−	9796.93i	−0.256193	−	0.443739i	−0.965219	+	0.261443i	$0.915802\pi$
$788$		0			0
$789$	4787.74	−	8292.61i	0.216031	−	0.374176i
$790$		0			0
$791$	−1867.62	+	40092.5i	−0.0839507	+	1.80218i
$792$		0			0
$793$	−6976.42	+	12083.5i	−0.312408	+	0.541107i
$794$		0			0
$795$	23298.3	+	40353.9i	1.03938	+	1.80026i
$796$		0			0
$797$	32275.4			1.43444			0.717222	−	0.696845i	$-0.245413\pi$
$797$	32275.4			1.43444			0.717222	+	0.696845i	$0.245413\pi$
$798$		0			0
$799$	20413.9			0.903871
$800$		0			0
$801$	−4797.59	−	8309.67i	−0.211629	−	0.366551i
$802$		0			0
$803$	2943.76	−	5098.74i	0.129369	−	0.224073i
$804$		0			0
$805$	−26600.1	+	13748.7i	−1.16464	+	0.601961i
$806$		0			0
$807$	16757.6	−	29025.1i	0.730975	−	1.26609i
$808$		0			0
$809$	5155.40	+	8929.42i	0.224047	+	0.388061i	0.956033	−	0.293258i	$-0.0947396\pi$
$809$	5155.40	+	8929.42i	0.224047	+	0.388061i	−0.731986	+	0.681320i	$0.761406\pi$
$810$		0			0
$811$	−13890.7			−0.601439			−0.300720	−	0.953713i	$-0.597227\pi$
$811$	−13890.7			−0.601439			−0.300720	+	0.953713i	$0.597227\pi$
$812$		0			0
$813$	371.382			0.0160208
$814$		0			0
$815$	−10113.0	−	17516.2i	−0.434653	−	0.752840i
$816$		0			0
$817$	−3346.23	+	5795.85i	−0.143292	+	0.248190i
$818$		0			0
$819$	21317.7	+	13668.4i	0.909524	+	0.583166i
$820$		0			0
$821$	−15805.4	+	27375.7i	−0.671878	+	1.16373i	0.305493	+	0.952194i	$0.401179\pi$
$821$	−15805.4	+	27375.7i	−0.671878	+	1.16373i	−0.977371	+	0.211532i	$0.932155\pi$
$822$		0			0
$823$	−5754.38	−	9966.87i	−0.243724	−	0.422143i	0.718048	−	0.695994i	$-0.245036\pi$
$823$	−5754.38	−	9966.87i	−0.243724	−	0.422143i	−0.961772	+	0.273851i	$0.911702\pi$
$824$		0			0
$825$	−25990.3			−1.09681
$826$		0			0
$827$	42336.9			1.78017			0.890083	−	0.455798i	$-0.150646\pi$
$827$	42336.9			1.78017			0.890083	+	0.455798i	$0.150646\pi$
$828$		0			0
$829$	−17964.3	−	31115.1i	−0.752625	−	1.30358i	−0.946546	−	0.322567i	$-0.895454\pi$
$829$	−17964.3	−	31115.1i	−0.752625	−	1.30358i	0.193922	−	0.981017i	$-0.437879\pi$
$830$		0			0
$831$	−934.965	+	1619.41i	−0.0390296	+	0.0676012i
$832$		0			0
$833$	10848.9	+	23624.3i	0.451252	+	0.982635i
$834$		0			0
$835$	7677.53	−	13297.9i	0.318194	−	0.551128i
$836$		0			0
$837$	−11822.9	−	20477.9i	−0.488244	−	0.845664i
$838$		0			0
$839$	1043.87			0.0429541			0.0214771	−	0.999769i	$-0.493163\pi$
$839$	1043.87			0.0429541			0.0214771	+	0.999769i	$0.493163\pi$
$840$		0			0
$841$	−16107.9			−0.660456
$842$		0			0
$843$	−3862.88	−	6690.70i	−0.157823	−	0.273357i
$844$		0			0
$845$	13766.0	−	23843.5i	0.560434	−	0.970700i
$846$		0			0
$847$	13342.3	+	8554.81i	0.541261	+	0.347044i
$848$		0			0
$849$	−18124.9	+	31393.2i	−0.732678	+	1.26904i
$850$		0			0
$851$	8620.99	+	14932.0i	0.347266	+	0.601483i
$852$		0			0
$853$	23453.0			0.941403			0.470702	−	0.882292i	$-0.344001\pi$
$853$	23453.0			0.941403			0.470702	+	0.882292i	$0.344001\pi$
$854$		0			0
$855$	21560.0			0.862380
$856$		0			0
$857$	−19931.7	−	34522.8i	−0.794464	−	1.37605i	−0.923179	−	0.384370i	$-0.874419\pi$
$857$	−19931.7	−	34522.8i	−0.794464	−	1.37605i	0.128716	−	0.991682i	$-0.458915\pi$
$858$		0			0
$859$	−3953.97	+	6848.47i	−0.157052	+	0.272022i	−0.933804	−	0.357784i	$-0.883532\pi$
$859$	−3953.97	+	6848.47i	−0.157052	+	0.272022i	0.776752	+	0.629806i	$0.216866\pi$
$860$		0			0
$861$	15944.6	−	8241.25i	0.631117	−	0.326203i
$862$		0			0
$863$	−3384.84	+	5862.71i	−0.133512	+	0.231250i	−0.925028	−	0.379898i	$-0.875959\pi$
$863$	−3384.84	+	5862.71i	−0.133512	+	0.231250i	0.791516	+	0.611149i	$0.209292\pi$
$864$		0			0
$865$	4180.36	+	7240.60i	0.164320	+	0.284610i
$866$		0			0
$867$	7932.84			0.310742
$868$		0			0
$869$	−7094.78			−0.276955
$870$		0			0
$871$	5056.63	+	8758.34i	0.196713	+	0.340718i
$872$		0			0
$873$	59765.1	−	103516.i	2.31700	−	4.01316i
$874$		0			0
$875$	0.875924	−	18.8036i	3.38419e−5	−	0.000726488i
$876$		0			0
$877$	8658.83	−	14997.5i	0.333396	−	0.577458i	−0.649780	−	0.760123i	$-0.725139\pi$
$877$	8658.83	−	14997.5i	0.333396	−	0.577458i	0.983175	+	0.182664i	$0.0584722\pi$
$878$		0			0
$879$	14998.0	+	25977.3i	0.575505	+	0.996804i
$880$		0			0
$881$	33759.7			1.29103			0.645513	−	0.763750i	$-0.276644\pi$
$881$	33759.7			1.29103			0.645513	+	0.763750i	$0.276644\pi$
$882$		0			0
$883$	20233.7			0.771142			0.385571	−	0.922678i	$-0.374004\pi$
$883$	20233.7			0.771142			0.385571	+	0.922678i	$0.374004\pi$
$884$		0			0
$885$	−61006.3	−	105666.i	−2.31718	−	4.01347i
$886$		0			0
$887$	13903.3	−	24081.3i	0.526300	−	0.911579i	−0.473230	−	0.880939i	$-0.656912\pi$
$887$	13903.3	−	24081.3i	0.526300	−	0.911579i	0.999530	−	0.0306400i	$-0.00975453\pi$
$888$		0			0
$889$	−1244.08	+	26706.8i	−0.0469348	+	1.00756i
$890$		0			0
$891$	17938.1	−	31069.6i	0.674464	−	1.16821i
$892$		0			0
$893$	−2866.69	−	4965.25i	−0.107424	−	0.186065i
$894$		0			0
$895$	−2355.60			−0.0879765
$896$		0			0
$897$	20828.5			0.775298
$898$		0			0
$899$	3041.64	+	5268.27i	0.112841	+	0.195447i
$900$		0			0
$901$	11704.4	−	20272.6i	0.432774	−	0.749587i
$902$		0			0
$903$	49362.5	−	25513.8i	1.81914	−	0.940252i
$904$		0			0
$905$	28647.9	−	49619.7i	1.05225	−	1.82256i
$906$		0			0
$907$	−9596.46	−	16621.6i	−0.351318	−	0.608500i	0.635163	−	0.772378i	$-0.280933\pi$
$907$	−9596.46	−	16621.6i	−0.351318	−	0.608500i	−0.986481	+	0.163878i	$0.947600\pi$
$908$		0			0
$909$	−34246.8			−1.24961
$910$		0			0
$911$	−39131.9			−1.42316			−0.711579	−	0.702607i	$-0.752019\pi$
$911$	−39131.9			−1.42316			−0.711579	+	0.702607i	$0.752019\pi$
$912$		0			0
$913$	11260.3	+	19503.4i	0.408171	+	0.706973i
$914$		0			0
$915$	49315.7	−	85417.3i	1.78178	−	3.08613i
$916$		0			0
$917$	33134.7	+	21245.2i	1.19325	+	0.765082i
$918$		0			0
$919$	25239.1	−	43715.4i	0.905942	−	1.56914i	0.0862946	−	0.996270i	$-0.472497\pi$
$919$	25239.1	−	43715.4i	0.905942	−	1.56914i	0.819648	−	0.572868i	$-0.194169\pi$
$920$		0			0
$921$	−36866.7	−	63855.1i	−1.31900	−	2.28458i
$922$		0			0
$923$	−3372.05			−0.120252
$924$		0			0
$925$	21063.8			0.748729
$926$		0			0
$927$	42271.7	+	73216.8i	1.49772	+	2.59413i
$928$		0			0
$929$	−9546.23	+	16534.5i	−0.337138	+	0.583941i	−0.983893	−	0.178757i	$-0.942792\pi$
$929$	−9546.23	+	16534.5i	−0.337138	+	0.583941i	0.646755	+	0.762698i	$0.276126\pi$
$930$		0			0
$931$	4222.62	−	5956.29i	0.148647	−	0.209677i
$932$		0			0
$933$	7051.74	−	12214.0i	0.247442	−	0.428583i
$934$		0			0
$935$	13060.1	+	22620.8i	0.456803	+	0.791207i
$936$		0			0
$937$	−19922.3			−0.694592			−0.347296	−	0.937756i	$-0.612900\pi$
$937$	−19922.3			−0.694592			−0.347296	+	0.937756i	$0.612900\pi$
$938$		0			0
$939$	−65098.9			−2.26243
$940$		0			0
$941$	7662.52	+	13271.9i	0.265453	+	0.459778i	0.967682	−	0.252173i	$-0.0811452\pi$
$941$	7662.52	+	13271.9i	0.265453	+	0.459778i	−0.702229	+	0.711951i	$0.747812\pi$
$942$		0			0
$943$	5192.89	−	8994.34i	0.179325	−	0.310600i
$944$		0			0
$945$	−87185.5	−	55901.4i	−3.00121	−	1.92431i
$946$		0			0
$947$	1130.28	−	1957.70i	0.0387848	−	0.0671772i	−0.845981	−	0.533212i	$-0.820985\pi$
$947$	1130.28	−	1957.70i	0.0387848	−	0.0671772i	0.884766	+	0.466035i	$0.154318\pi$
$948$		0			0
$949$	2882.03	+	4991.82i	0.0985824	+	0.170750i
$950$		0			0
$951$	7035.22			0.239887
$952$		0			0
$953$	24905.1			0.846543			0.423272	−	0.906003i	$-0.360882\pi$
$953$	24905.1			0.846543			0.423272	+	0.906003i	$0.360882\pi$
$954$		0			0
$955$	25173.2	+	43601.3i	0.852969	+	1.47739i
$956$		0			0
$957$	−9465.41	+	16394.6i	−0.319721	+	0.553774i
$958$		0			0
$959$	−6671.09	+	3448.06i	−0.224630	+	0.116104i
$960$		0			0
$961$	12661.1	−	21929.7i	0.424999	−	0.736119i
$962$		0			0
$963$	22216.9	+	38480.8i	0.743437	+	1.28767i
$964$		0			0
$965$	−72685.6			−2.42470
$966$		0			0
$967$	−28438.6			−0.945734			−0.472867	−	0.881134i	$-0.656781\pi$
$967$	−28438.6			−0.945734			−0.472867	+	0.881134i	$0.656781\pi$
$968$		0			0
$969$	−7697.84	−	13333.1i	−0.255202	−	0.442022i
$970$		0			0
$971$	−7640.18	+	13233.2i	−0.252508	+	0.437356i	−0.964216	−	0.265119i	$-0.914589\pi$
$971$	−7640.18	+	13233.2i	−0.252508	+	0.437356i	0.711708	+	0.702476i	$0.247922\pi$
$972$		0			0
$973$	−1561.78	+	33526.9i	−0.0514576	+	1.10465i
$974$		0			0
$975$	12722.6	−	22036.3i	0.417898	−	0.723821i
$976$		0			0
$977$	15541.7	+	26919.1i	0.508930	+	0.881493i	0.999947	+	0.0103424i	$0.00329213\pi$
$977$	15541.7	+	26919.1i	0.508930	+	0.881493i	−0.491017	+	0.871150i	$0.663375\pi$
$978$		0			0
$979$	−3264.87			−0.106584
$980$		0			0
$981$	125955.			4.09931
$982$		0			0
$983$	4753.07	+	8232.56i	0.154221	+	0.267119i	0.932775	−	0.360459i	$-0.117380\pi$
$983$	4753.07	+	8232.56i	0.154221	+	0.267119i	−0.778554	+	0.627578i	$0.784047\pi$
$984$		0			0
$985$	−30653.1	+	53092.6i	−0.991561	+	1.71743i
$986$		0			0
$987$	−2215.09	+	47551.6i	−0.0714357	+	1.53352i
$988$		0			0
$989$	16076.5	−	27845.3i	0.516889	−	0.895277i
$990$		0			0
$991$	−20656.6	−	35778.2i	−0.662137	−	1.14686i	−0.980053	−	0.198736i	$-0.936316\pi$
$991$	−20656.6	−	35778.2i	−0.662137	−	1.14686i	0.317916	−	0.948119i	$-0.397017\pi$
$992$		0			0
$993$	−34967.8			−1.11749
$994$		0			0
$995$	31241.2			0.995391
$996$		0			0
$997$	14889.5	+	25789.3i	0.472973	+	0.819213i	0.999521	−	0.0309318i	$-0.00984748\pi$
$997$	14889.5	+	25789.3i	0.472973	+	0.819213i	−0.526549	+	0.850145i	$0.676514\pi$
$998$		0			0
$999$	−29818.4	+	51646.9i	−0.944355	+	1.63567i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.4.i.j.65.1		6
4.3	odd	2		448.4.i.m.65.3		6
7.4	even	3	inner	448.4.i.j.193.1		6
8.3	odd	2		112.4.i.e.65.1		6
8.5	even	2		56.4.i.b.9.3	✓	6
24.5	odd	2		504.4.s.h.289.1		6
28.11	odd	6		448.4.i.m.193.3		6
56.5	odd	6		392.4.a.l.1.3		3
56.11	odd	6		112.4.i.e.81.1		6
56.13	odd	2		392.4.i.m.177.1		6
56.19	even	6		784.4.a.bb.1.1		3
56.37	even	6		392.4.a.i.1.1		3
56.45	odd	6		392.4.i.m.361.1		6
56.51	odd	6		784.4.a.be.1.3		3
56.53	even	6		56.4.i.b.25.3	yes	6
168.53	odd	6		504.4.s.h.361.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.4.i.b.9.3	✓	6	8.5	even	2
56.4.i.b.25.3	yes	6	56.53	even	6
112.4.i.e.65.1		6	8.3	odd	2
112.4.i.e.81.1		6	56.11	odd	6
392.4.a.i.1.1		3	56.37	even	6
392.4.a.l.1.3		3	56.5	odd	6
392.4.i.m.177.1		6	56.13	odd	2
392.4.i.m.361.1		6	56.45	odd	6
448.4.i.j.65.1		6	1.1	even	1	trivial
448.4.i.j.193.1		6	7.4	even	3	inner
448.4.i.m.65.3		6	4.3	odd	2
448.4.i.m.193.3		6	28.11	odd	6
504.4.s.h.289.1		6	24.5	odd	2
504.4.s.h.361.1		6	168.53	odd	6
784.4.a.bb.1.1		3	56.19	even	6
784.4.a.be.1.3		3	56.51	odd	6

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	448.4.i.j.65.1

Level	$448$
Weight	$4$
Character	448.65
Analytic conductor	$26.433$
Analytic rank	$0$
Dimension	$6$
Inner twists	$2$