LMFDB - Embedded newform 209.4.d.b.208.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [209,4,Mod(208,209)] 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("209.208"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(209, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	209.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [56] 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:	$12.3313991912$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			208.9
Character	$\chi$	$=$	209.208
Dual form			209.4.d.b.208.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.05308 q^{2} -9.73675i q^{3} +8.42746 q^{4} +13.1386 q^{5} +39.4638i q^{6} +12.0311i q^{7} -1.73251 q^{8} -67.8042 q^{9} -53.2518 q^{10} +(29.5736 - 21.3635i) q^{11} -82.0560i q^{12} -47.2482 q^{13} -48.7631i q^{14} -127.927i q^{15} -60.3976 q^{16} +0.958103i q^{17} +274.816 q^{18} +(-27.3883 - 78.1593i) q^{19} +110.725 q^{20} +117.144 q^{21} +(-119.864 + 86.5881i) q^{22} -159.950 q^{23} +16.8690i q^{24} +47.6231 q^{25} +191.501 q^{26} +397.300i q^{27} +101.392i q^{28} -119.478 q^{29} +518.500i q^{30} -97.3994i q^{31} +258.657 q^{32} +(-208.011 - 287.951i) q^{33} -3.88327i q^{34} +158.072i q^{35} -571.417 q^{36} +8.05571i q^{37} +(111.007 + 316.786i) q^{38} +460.044i q^{39} -22.7628 q^{40} -494.503 q^{41} -474.794 q^{42} -184.808i q^{43} +(249.230 - 180.040i) q^{44} -890.853 q^{45} +648.289 q^{46} +39.5163 q^{47} +588.076i q^{48} +198.252 q^{49} -193.020 q^{50} +9.32880 q^{51} -398.182 q^{52} -592.067i q^{53} -1610.29i q^{54} +(388.556 - 280.687i) q^{55} -20.8441i q^{56} +(-761.018 + 266.673i) q^{57} +484.252 q^{58} +531.266i q^{59} -1078.10i q^{60} +753.580i q^{61} +394.768i q^{62} -815.762i q^{63} -565.174 q^{64} -620.776 q^{65} +(843.086 + 1167.09i) q^{66} +72.5444i q^{67} +8.07437i q^{68} +1557.39i q^{69} -640.680i q^{70} +689.847i q^{71} +117.472 q^{72} -829.355i q^{73} -32.6504i q^{74} -463.694i q^{75} +(-230.814 - 658.684i) q^{76} +(257.027 + 355.804i) q^{77} -1864.59i q^{78} +1009.06 q^{79} -793.541 q^{80} +2037.70 q^{81} +2004.26 q^{82} -762.002i q^{83} +987.227 q^{84} +12.5881i q^{85} +749.042i q^{86} +1163.32i q^{87} +(-51.2366 + 37.0125i) q^{88} +181.839i q^{89} +3610.70 q^{90} -568.449i q^{91} -1347.97 q^{92} -948.353 q^{93} -160.163 q^{94} +(-359.844 - 1026.91i) q^{95} -2518.47i q^{96} +21.7720i q^{97} -803.530 q^{98} +(-2005.22 + 1448.54i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 236 q^{4} + 16 q^{5} - 484 q^{9} + 74 q^{11} + 668 q^{16} - 264 q^{20} - 296 q^{23} + 1040 q^{25} - 672 q^{26} - 428 q^{36} + 700 q^{38} - 2472 q^{42} - 668 q^{44} + 248 q^{45} - 2284 q^{47} - 2880 q^{49}+ \cdots - 414 q^{99}+O(q^{100}) $ 56 * q + 236 * q^4 + 16 * q^5 - 484 * q^9 + 74 * q^11 + 668 * q^16 - 264 * q^20 - 296 * q^23 + 1040 * q^25 - 672 * q^26 - 428 * q^36 + 700 * q^38 - 2472 * q^42 - 668 * q^44 + 248 * q^45 - 2284 * q^47 - 2880 * q^49 - 614 * q^55 + 2112 * q^58 + 1460 * q^64 + 4964 * q^66 + 2154 * q^77 - 5680 * q^80 - 456 * q^81 + 7840 * q^82 + 10312 * q^92 - 728 * q^93 - 414 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−4.05308			−1.43298			−0.716490	−	0.697597i	$-0.754252\pi$
$2$	−4.05308			−1.43298			−0.716490	+	0.697597i	$0.754252\pi$
$3$		−	9.73675i		−	1.87384i	−0.349547	−	0.936919i	$-0.613665\pi$
$3$		−	9.73675i		−	1.87384i	0.349547	−	0.936919i	$-0.386335\pi$
$4$	8.42746			1.05343
$5$	13.1386			1.17515			0.587577	−	0.809169i	$-0.300082\pi$
$5$	13.1386			1.17515			0.587577	+	0.809169i	$0.300082\pi$
$6$			39.4638i			2.68517i
$7$			12.0311i			0.649620i	0.945779	+	0.324810i	$0.105300\pi$
$7$			12.0311i			0.649620i	−0.945779	+	0.324810i	$0.894700\pi$
$8$	−1.73251			−0.0765669
$9$	−67.8042			−2.51127
$10$	−53.2518			−1.68397
$11$	29.5736	−	21.3635i	0.810617	−	0.585577i
$11$	29.5736	−	21.3635i	0.810617	−	0.585577i
$12$		−	82.0560i		−	1.97396i
$13$	−47.2482			−1.00802			−0.504011	−	0.863697i	$-0.668143\pi$
$13$	−47.2482			−1.00802			−0.504011	+	0.863697i	$0.668143\pi$
$14$		−	48.7631i		−	0.930893i
$15$		−	127.927i		−	2.20205i
$16$	−60.3976			−0.943713
$17$			0.958103i			0.0136691i	0.999977	+	0.00683453i	$0.00217552\pi$
$17$			0.958103i			0.0136691i	−0.999977	+	0.00683453i	$0.997824\pi$
$18$	274.816			3.59860
$19$	−27.3883	−	78.1593i	−0.330700	−	0.943736i
$19$	−27.3883	−	78.1593i	−0.330700	−	0.943736i
$20$	110.725			1.23794
$21$	117.144			1.21728
$22$	−119.864	+	86.5881i	−1.16160	+	0.839120i
$23$	−159.950			−1.45008			−0.725040	−	0.688707i	$-0.758179\pi$
$23$	−159.950			−1.45008			−0.725040	+	0.688707i	$0.758179\pi$
$24$			16.8690i			0.143474i
$25$	47.6231			0.380985
$26$	191.501			1.44448
$27$			397.300i			2.83187i
$28$			101.392i			0.684331i
$29$	−119.478			−0.765049			−0.382525	−	0.923945i	$-0.624945\pi$
$29$	−119.478			−0.765049			−0.382525	+	0.923945i	$0.624945\pi$
$30$			518.500i			3.15549i
$31$		−	97.3994i		−	0.564305i	−0.959370	−	0.282152i	$-0.908952\pi$
$31$		−	97.3994i		−	0.564305i	0.959370	−	0.282152i	$-0.0910484\pi$
$32$	258.657			1.42889
$33$	−208.011	−	287.951i	−1.09728	−	1.51896i
$34$		−	3.88327i		−	0.0195875i
$35$			158.072i			0.763403i
$36$	−571.417			−2.64545
$37$			8.05571i			0.0357933i	0.999840	+	0.0178966i	$0.00569698\pi$
$37$			8.05571i			0.0357933i	−0.999840	+	0.0178966i	$0.994303\pi$
$38$	111.007	+	316.786i	0.473887	+	1.35235i
$39$			460.044i			1.88887i
$40$	−22.7628			−0.0899778
$41$	−494.503			−1.88362			−0.941810	−	0.336146i	$-0.890876\pi$
$41$	−494.503			−1.88362			−0.941810	+	0.336146i	$0.890876\pi$
$42$	−474.794			−1.74434
$43$		−	184.808i		−	0.655418i	−0.944779	−	0.327709i	$-0.893723\pi$
$43$		−	184.808i		−	0.655418i	0.944779	−	0.327709i	$-0.106277\pi$
$44$	249.230	−	180.040i	0.853930	−	0.616865i
$45$	−890.853			−2.95112
$46$	648.289			2.07793
$47$	39.5163			0.122639			0.0613196	−	0.998118i	$-0.480469\pi$
$47$	39.5163			0.122639			0.0613196	+	0.998118i	$0.480469\pi$
$48$			588.076i			1.76837i
$49$	198.252			0.577994
$50$	−193.020			−0.545944
$51$	9.32880			0.0256136
$52$	−398.182			−1.06188
$53$		−	592.067i		−	1.53446i	−0.641369	−	0.767232i	$-0.721633\pi$
$53$		−	592.067i		−	1.53446i	0.641369	−	0.767232i	$-0.278367\pi$
$54$		−	1610.29i		−	4.05801i
$55$	388.556	−	280.687i	0.952599	−	0.688143i
$56$		−	20.8441i		−	0.0497394i
$57$	−761.018	+	266.673i	−1.76841	+	0.619679i
$58$	484.252			1.09630
$59$			531.266i			1.17229i	0.810207	+	0.586143i	$0.199354\pi$
$59$			531.266i			1.17229i	−0.810207	+	0.586143i	$0.800646\pi$
$60$		−	1078.10i		−	2.31971i
$61$			753.580i			1.58174i	0.611986	+	0.790869i	$0.290371\pi$
$61$			753.580i			1.58174i	−0.611986	+	0.790869i	$0.709629\pi$
$62$			394.768i			0.808638i
$63$		−	815.762i		−	1.63137i
$64$	−565.174			−1.10386
$65$	−620.776			−1.18458
$66$	843.086	+	1167.09i	1.57237	+	2.17665i
$67$			72.5444i			0.132279i	0.997810	+	0.0661397i	$0.0210683\pi$
$67$			72.5444i			0.132279i	−0.997810	+	0.0661397i	$0.978932\pi$
$68$			8.07437i			0.0143994i
$69$			1557.39i			2.71721i
$70$		−	640.680i		−	1.09394i
$71$			689.847i			1.15310i	0.817063	+	0.576548i	$0.195601\pi$
$71$			689.847i			1.15310i	−0.817063	+	0.576548i	$0.804399\pi$
$72$	117.472			0.192280
$73$		−	829.355i		−	1.32971i	−0.746974	−	0.664854i	$-0.768494\pi$
$73$		−	829.355i		−	1.32971i	0.746974	−	0.664854i	$-0.231506\pi$
$74$		−	32.6504i		−	0.0512910i
$75$		−	463.694i		−	0.713904i
$76$	−230.814	−	658.684i	−0.348370	−	0.994161i
$77$	257.027	+	355.804i	0.380403	+	0.526593i
$78$		−	1864.59i		−	2.70671i
$79$	1009.06			1.43707			0.718535	−	0.695491i	$-0.244813\pi$
$79$	1009.06			1.43707			0.718535	+	0.695491i	$0.244813\pi$
$80$	−793.541			−1.10901
$81$	2037.70			2.79520
$82$	2004.26			2.69919
$83$		−	762.002i		−	1.00772i	−0.863786	−	0.503859i	$-0.831913\pi$
$83$		−	762.002i		−	1.00772i	0.863786	−	0.503859i	$-0.168087\pi$
$84$	987.227			1.28232
$85$			12.5881i			0.0160632i
$86$			749.042i			0.939201i
$87$			1163.32i			1.43358i
$88$	−51.2366	+	37.0125i	−0.0620664	+	0.0448358i
$89$			181.839i			0.216572i	0.994120	+	0.108286i	$0.0345363\pi$
$89$			181.839i			0.216572i	−0.994120	+	0.108286i	$0.965464\pi$
$90$	3610.70			4.22890
$91$		−	568.449i		−	0.654832i
$92$	−1347.97			−1.52756
$93$	−948.353			−1.05742
$94$	−160.163			−0.175739
$95$	−359.844	−	1026.91i	−0.388623	−	1.10903i
$96$		−	2518.47i		−	2.67751i
$97$			21.7720i			0.0227899i	0.999935	+	0.0113949i	$0.00362720\pi$
$97$			21.7720i			0.0227899i	−0.999935	+	0.0113949i	$0.996373\pi$
$98$	−803.530			−0.828253
$99$	−2005.22	+	1448.54i	−2.03568	+	1.47054i
$100$	401.342			0.401342
$101$		−	682.699i		−	0.672585i	−0.941758	−	0.336292i	$-0.890827\pi$
$101$		−	682.699i		−	0.672585i	0.941758	−	0.336292i	$-0.109173\pi$
$102$	−37.8104			−0.0367038
$103$		−	1371.45i		−	1.31197i	−0.754774	−	0.655984i	$-0.772254\pi$
$103$		−	1371.45i		−	1.31197i	0.754774	−	0.655984i	$-0.227746\pi$
$104$	81.8580			0.0771811
$105$	1539.11			1.43049
$106$			2399.69i			2.19886i
$107$	338.646			0.305964			0.152982	−	0.988229i	$-0.451112\pi$
$107$	338.646			0.305964			0.152982	+	0.988229i	$0.451112\pi$
$108$			3348.23i			2.98318i
$109$	284.114			0.249663			0.124831	−	0.992178i	$-0.460161\pi$
$109$	284.114			0.249663			0.124831	+	0.992178i	$0.460161\pi$
$110$	−1574.85	+	1137.65i	−1.36506	+	0.986095i
$111$	78.4364			0.0670708
$112$		−	726.652i		−	0.613055i
$113$		−	1054.94i		−	0.878231i	−0.898431	−	0.439115i	$-0.855292\pi$
$113$		−	1054.94i		−	0.878231i	0.898431	−	0.439115i	$-0.144708\pi$
$114$	3084.46	−	1080.85i	2.53409	−	0.887987i
$115$	−2101.52			−1.70407
$116$	−1006.89			−0.805927
$117$	3203.63			2.53141
$118$		−	2153.26i		−	1.67986i
$119$	−11.5271			−0.00887970
$120$			221.635i			0.168604i
$121$	418.199	−	1263.59i	0.314199	−	0.949357i
$122$		−	3054.32i		−	2.26660i
$123$			4814.85i			3.52960i
$124$		−	820.829i		−	0.594457i
$125$	−1016.62			−0.727438
$126$			3306.35i			2.33772i
$127$	−1577.83			−1.10244			−0.551221	−	0.834359i	$-0.685838\pi$
$127$	−1577.83			−1.10244			−0.551221	+	0.834359i	$0.685838\pi$
$128$	221.445			0.152915
$129$	−1799.43			−1.22815
$130$	2516.05			1.69748
$131$			1720.78i			1.14768i	0.818969	+	0.573838i	$0.194546\pi$
$131$			1720.78i			1.14768i	−0.818969	+	0.573838i	$0.805454\pi$
$132$	−1753.01	−	2426.69i	−1.15591	−	1.60013i
$133$	940.345	−	329.512i	0.613070	−	0.214830i
$134$		−	294.028i		−	0.189554i
$135$			5219.97i			3.32788i
$136$		−	1.65992i		−	0.00104660i
$137$	586.129			0.365521			0.182761	−	0.983157i	$-0.441497\pi$
$137$	586.129			0.365521			0.182761	+	0.983157i	$0.441497\pi$
$138$		−	6312.23i		−	3.89371i
$139$		−	366.282i		−	0.223508i	−0.993736	−	0.111754i	$-0.964353\pi$
$139$		−	366.282i		−	0.223508i	0.993736	−	0.111754i	$-0.0356469\pi$
$140$			1332.15i			0.804193i
$141$		−	384.760i		−	0.229806i
$142$		−	2796.01i		−	1.65236i
$143$	−1397.30	+	1009.39i	−0.817120	+	0.590275i
$144$	4095.21			2.36992
$145$	−1569.77			−0.899050
$146$			3361.44i			1.90544i
$147$		−	1930.33i		−	1.08307i
$148$			67.8892i			0.0377058i
$149$		−	1394.20i		−	0.766557i	−0.923633	−	0.383279i	$-0.874795\pi$
$149$		−	1394.20i		−	0.766557i	0.923633	−	0.383279i	$-0.125205\pi$
$150$			1879.39i			1.02301i
$151$	1241.18			0.668910			0.334455	−	0.942412i	$-0.391448\pi$
$151$	1241.18			0.668910			0.334455	+	0.942412i	$0.391448\pi$
$152$	47.4505	+	135.412i	0.0253207	+	0.0722589i
$153$		−	64.9634i		−	0.0343267i
$154$	−1041.75	−	1442.10i	−0.545109	−	0.754597i
$155$		−	1279.69i		−	0.663145i
$156$			3877.00i			1.98980i
$157$	−903.544			−0.459304			−0.229652	−	0.973273i	$-0.573759\pi$
$157$	−903.544			−0.459304			−0.229652	+	0.973273i	$0.573759\pi$
$158$	−4089.81			−2.05929
$159$	−5764.80			−2.87534
$160$	3398.39			1.67916
$161$		−	1924.38i		−	0.942001i
$162$	−8258.95			−4.00546
$163$	−3820.63			−1.83592			−0.917960	−	0.396674i	$-0.870164\pi$
$163$	−3820.63			−1.83592			−0.917960	+	0.396674i	$0.870164\pi$
$164$	−4167.40			−1.98427
$165$	−2732.98	−	3783.28i	−1.28947	−	1.78502i
$166$			3088.46i			1.44404i
$167$	1139.32			0.527925			0.263963	−	0.964533i	$-0.414970\pi$
$167$	1139.32			0.527925			0.263963	+	0.964533i	$0.414970\pi$
$168$	−202.953			−0.0932035
$169$	35.3926			0.0161095
$170$		−	51.0207i		−	0.0230183i
$171$	1857.04	+	5299.53i	0.830477	+	2.36997i
$172$		−	1557.46i		−	0.690439i
$173$	1019.26			0.447937			0.223969	−	0.974596i	$-0.428099\pi$
$173$	1019.26			0.447937			0.223969	+	0.974596i	$0.428099\pi$
$174$		−	4715.04i		−	2.05429i
$175$			572.960i			0.247495i
$176$	−1786.18	+	1290.31i	−0.764990	+	0.552617i
$177$	5172.80			2.19667
$178$		−	737.009i		−	0.310344i
$179$			3804.94i			1.58880i	0.607398	+	0.794398i	$0.292213\pi$
$179$			3804.94i			1.58880i	−0.607398	+	0.794398i	$0.707787\pi$
$180$	−7507.63			−3.10881
$181$		−	3001.64i		−	1.23265i	−0.787490	−	0.616327i	$-0.788620\pi$
$181$		−	3001.64i		−	1.23265i	0.787490	−	0.616327i	$-0.211380\pi$
$182$			2303.97i			0.938361i
$183$	7337.41			2.96392
$184$	277.115			0.111028
$185$			105.841i			0.0420626i
$186$	3843.75			1.51526
$187$	20.4685	+	28.3346i	0.00800429	+	0.0110804i
$188$	333.022			0.129192
$189$	−4779.97			−1.83964
$190$	1458.48	+	4162.13i	0.556890	+	1.58922i
$191$	−608.271			−0.230434			−0.115217	−	0.993340i	$-0.536756\pi$
$191$	−608.271			−0.230434			−0.115217	+	0.993340i	$0.536756\pi$
$192$			5502.96i			2.06845i
$193$	2508.56			0.935596			0.467798	−	0.883835i	$-0.345047\pi$
$193$	2508.56			0.935596			0.467798	+	0.883835i	$0.345047\pi$
$194$		−	88.2438i		−	0.0326574i
$195$			6044.34i			2.21971i
$196$	1670.76			0.608877
$197$		−	734.271i		−	0.265557i	−0.991146	−	0.132778i	$-0.957610\pi$
$197$		−	734.271i		−	0.265557i	0.991146	−	0.132778i	$-0.0423898\pi$
$198$	8127.30	−	5871.04i	2.91708	−	2.10725i
$199$	1601.50			0.570488			0.285244	−	0.958455i	$-0.407925\pi$
$199$	1601.50			0.570488			0.285244	+	0.958455i	$0.407925\pi$
$200$	−82.5075			−0.0291708
$201$	706.347			0.247870
$202$			2767.03i			0.963801i
$203$		−	1437.45i		−	0.496991i
$204$	78.6181			0.0269822
$205$	−6497.08			−2.21354
$206$			5558.59i			1.88003i
$207$	10845.3			3.64154
$208$	2853.68			0.951284
$209$	−2479.73	−	1726.34i	−0.820701	−	0.571358i
$210$	−6238.14			−2.04987
$211$	4592.52			1.49840			0.749200	−	0.662344i	$-0.230438\pi$
$211$	4592.52			1.49840			0.749200	+	0.662344i	$0.230438\pi$
$212$		−	4989.62i		−	1.61645i
$213$	6716.87			2.16071
$214$	−1372.56			−0.438441
$215$		−	2428.12i		−	0.770217i
$216$		−	688.327i		−	0.216827i
$217$	1171.83			0.366584
$218$	−1151.54			−0.357761
$219$	−8075.22			−2.49166
$220$	3274.54	−	2365.48i	1.00350	−	0.724911i
$221$		−	45.2686i		−	0.0137787i
$222$	−317.909			−0.0961111
$223$		−	2843.28i		−	0.853812i	−0.904296	−	0.426906i	$-0.859604\pi$
$223$		−	2843.28i		−	0.853812i	0.904296	−	0.426906i	$-0.140396\pi$
$224$			3111.93i			0.928235i
$225$	−3229.05			−0.956755
$226$			4275.74i			1.25849i
$227$	−416.404			−0.121752			−0.0608761	−	0.998145i	$-0.519389\pi$
$227$	−416.404			−0.121752			−0.0608761	+	0.998145i	$0.519389\pi$
$228$	−6413.44	+	2247.37i	−1.86290	+	0.652789i
$229$	−807.455			−0.233005			−0.116503	−	0.993190i	$-0.537168\pi$
$229$	−807.455			−0.233005			−0.116503	+	0.993190i	$0.537168\pi$
$230$	8517.62			2.44189
$231$	3464.38	−	2502.61i	0.986750	−	0.712813i
$232$	206.996			0.0585774
$233$			6133.33i			1.72450i	0.506485	+	0.862249i	$0.330945\pi$
$233$			6133.33i			1.72450i	−0.506485	+	0.862249i	$0.669055\pi$
$234$	−12984.6			−3.62747
$235$	519.189			0.144120
$236$			4477.22i			1.23492i
$237$		−	9824.99i		−	2.69283i
$238$	46.7201			0.0127244
$239$			1193.36i			0.322978i	0.986874	+	0.161489i	$0.0516297\pi$
$239$			1193.36i			0.322978i	−0.986874	+	0.161489i	$0.948370\pi$
$240$			7726.51i			2.07810i
$241$	5885.74			1.57317			0.786584	−	0.617483i	$-0.211848\pi$
$241$	5885.74			1.57317			0.786584	+	0.617483i	$0.211848\pi$
$242$	−1694.99	+	5121.45i	−0.450241	+	1.36041i
$243$		−	9113.44i		−	2.40587i
$244$			6350.76i			1.66625i
$245$	2604.75			0.679231
$246$		−	19515.0i		−	5.05784i
$247$	1294.05	+	3692.89i	0.333353	+	0.951307i
$248$			168.746i			0.0432071i
$249$	−7419.42			−1.88830
$250$	4120.46			1.04240
$251$	−3801.45			−0.955959			−0.477979	−	0.878371i	$-0.658631\pi$
$251$	−3801.45			−0.955959			−0.477979	+	0.878371i	$0.658631\pi$
$252$		−	6874.79i		−	1.71854i
$253$	−4730.29	+	3417.09i	−1.17546	+	0.849133i
$254$	6395.09			1.57978
$255$	122.568			0.0300999
$256$	3623.86			0.884732
$257$			868.170i			0.210720i	0.994434	+	0.105360i	$0.0335994\pi$
$257$			868.170i			0.210720i	−0.994434	+	0.105360i	$0.966401\pi$
$258$	7293.24			1.75991
$259$	−96.9194			−0.0232520
$260$	−5231.56			−1.24788
$261$	8101.08			1.92124
$262$		−	6974.48i		−	1.64460i
$263$		−	4544.35i		−	1.06546i	−0.846285	−	0.532731i	$-0.821166\pi$
$263$		−	4544.35i		−	1.06546i	0.846285	−	0.532731i	$-0.178834\pi$
$264$	360.382	+	498.878i	0.0840150	+	0.116302i
$265$		−	7778.93i		−	1.80323i
$266$	−3811.30	+	1335.54i	−0.878517	+	0.307846i
$267$	1770.52			0.405821
$268$			611.365i			0.139347i
$269$		−	943.526i		−	0.213858i	−0.994267	−	0.106929i	$-0.965898\pi$
$269$		−	943.526i		−	0.213858i	0.994267	−	0.106929i	$-0.0341017\pi$
$270$		−	21157.0i		−	4.76879i
$271$		−	4321.86i		−	0.968761i	−0.874858	−	0.484380i	$-0.839045\pi$
$271$		−	4321.86i		−	0.968761i	0.874858	−	0.484380i	$-0.160955\pi$
$272$		−	57.8671i		−	0.0128997i
$273$	−5534.85			−1.22705
$274$	−2375.63			−0.523785
$275$	1408.39	−	1017.40i	0.308833	−	0.223096i
$276$			13124.8i			2.86240i
$277$		−	7413.42i		−	1.60805i	−0.594597	−	0.804024i	$-0.702688\pi$
$277$		−	7413.42i		−	1.60805i	0.594597	−	0.804024i	$-0.297312\pi$
$278$			1484.57i			0.320283i
$279$			6604.09i			1.41712i
$280$		−	273.862i		−	0.0584514i
$281$	−1157.20			−0.245669			−0.122834	−	0.992427i	$-0.539198\pi$
$281$	−1157.20			−0.245669			−0.122834	+	0.992427i	$0.539198\pi$
$282$			1559.46i			0.329307i
$283$		−	986.359i		−	0.207184i	−0.994620	−	0.103592i	$-0.966966\pi$
$283$		−	986.359i		−	0.207184i	0.994620	−	0.103592i	$-0.0330336\pi$
$284$			5813.66i			1.21471i
$285$	−9998.71	+	3503.71i	−2.07815	+	0.728217i
$286$	5663.37	−	4091.13i	1.17092	−	0.845852i
$287$		−	5949.43i		−	1.22364i
$288$	−17538.0			−3.58832
$289$	4912.08			0.999813
$290$	6362.40			1.28832
$291$	211.989			0.0427045
$292$		−	6989.35i		−	1.40076i
$293$	−1996.14			−0.398007			−0.199003	−	0.979999i	$-0.563770\pi$
$293$	−1996.14			−0.398007			−0.199003	+	0.979999i	$0.563770\pi$
$294$			7823.77i			1.55201i
$295$			6980.09i			1.37762i
$296$		−	13.9566i		−	0.00274058i
$297$	8487.74	+	11749.6i	1.65828	+	2.29556i
$298$			5650.79i			1.09846i
$299$	7557.34			1.46171
$300$		−	3907.76i		−	0.752049i
$301$	2223.45			0.425773
$302$	−5030.58			−0.958535
$303$	−6647.26			−1.26031
$304$	1654.19	+	4720.64i	0.312086	+	0.890616i
$305$			9900.99i			1.85878i
$306$			263.302i			0.0491894i
$307$	−8767.42			−1.62991			−0.814956	−	0.579523i	$-0.803239\pi$
$307$	−8767.42			−1.62991			−0.814956	+	0.579523i	$0.803239\pi$
$308$	2166.09	+	2998.52i	0.400728	+	0.554730i
$309$	−13353.4			−2.45842
$310$			5186.70i			0.950273i
$311$	948.925			0.173018			0.0865090	−	0.996251i	$-0.472429\pi$
$311$	948.925			0.173018			0.0865090	+	0.996251i	$0.472429\pi$
$312$		−	797.031i		−	0.144625i
$313$	775.879			0.140113			0.0700564	−	0.997543i	$-0.477682\pi$
$313$	775.879			0.140113			0.0700564	+	0.997543i	$0.477682\pi$
$314$	3662.14			0.658173
$315$		−	10718.0i		−	1.91711i
$316$	8503.84			1.51385
$317$		−	7674.47i		−	1.35975i	−0.733327	−	0.679876i	$-0.762034\pi$
$317$		−	7674.47i		−	1.35975i	0.733327	−	0.679876i	$-0.237966\pi$
$318$	23365.2			4.12030
$319$	−3533.39	+	2552.46i	−0.620162	+	0.447995i
$320$	−7425.61			−1.29720
$321$		−	3297.31i		−	0.573327i
$322$			7799.65i			1.34987i
$323$	74.8847	−	26.2408i	0.0129000	−	0.00452036i
$324$	17172.6			2.94455
$325$	−2250.11			−0.384041
$326$	15485.3			2.63084
$327$		−	2766.35i		−	0.467827i
$328$	856.732			0.144223
$329$			475.426i			0.0796689i
$330$	11077.0	+	15333.9i	1.84778	+	2.55789i
$331$			6740.18i			1.11926i	0.828744	+	0.559628i	$0.189056\pi$
$331$			6740.18i			1.11926i	−0.828744	+	0.559628i	$0.810944\pi$
$332$		−	6421.74i		−	1.06156i
$333$		−	546.211i		−	0.0898865i
$334$	−4617.77			−0.756506
$335$			953.133i			0.155448i
$336$	−7075.23			−1.14877
$337$	−5037.88			−0.814334			−0.407167	−	0.913354i	$-0.633483\pi$
$337$	−5037.88			−0.814334			−0.407167	+	0.913354i	$0.633483\pi$
$338$	−143.449			−0.0230846
$339$	−10271.6			−1.64566
$340$			106.086i			0.0169215i
$341$	−2080.80	−	2880.45i	−0.330444	−	0.457435i
$342$	−7526.74	−	21479.4i	−1.19006	−	3.39612i
$343$			6511.87i			1.02510i
$344$			320.182i			0.0501833i
$345$			20461.9i			3.19314i
$346$	−4131.16			−0.641885
$347$			8884.41i			1.37447i	0.726437	+	0.687233i	$0.241175\pi$
$347$			8884.41i			1.37447i	−0.726437	+	0.687233i	$0.758825\pi$
$348$			9803.85i			1.51018i
$349$		−	11049.4i		−	1.69474i	−0.531005	−	0.847368i	$-0.678186\pi$
$349$		−	11049.4i		−	1.69474i	0.531005	−	0.847368i	$-0.321814\pi$
$350$		−	2322.25i		−	0.354656i
$351$		−	18771.7i		−	2.85459i
$352$	7649.41	−	5525.82i	1.15828	−	0.836724i
$353$	5142.39			0.775359			0.387680	−	0.921794i	$-0.373277\pi$
$353$	5142.39			0.775359			0.387680	+	0.921794i	$0.373277\pi$
$354$	−20965.8			−3.14779
$355$			9063.64i			1.35506i
$356$			1532.44i			0.228144i
$357$			112.236i			0.0166391i
$358$		−	15421.7i		−	2.27671i
$359$		−	3498.61i		−	0.514344i	−0.966366	−	0.257172i	$-0.917209\pi$
$359$		−	3498.61i		−	0.514344i	0.966366	−	0.257172i	$-0.0827907\pi$
$360$	1543.41			0.225958
$361$	−5358.76	+	4281.30i	−0.781275	+	0.624187i
$362$			12165.9i			1.76637i
$363$	−12303.3	−	4071.90i	−1.77894	−	0.588758i
$364$		−	4790.58i		−	0.689821i
$365$		−	10896.6i		−	1.56261i
$366$	−29739.1			−4.24724
$367$	12669.8			1.80206			0.901031	−	0.433755i	$-0.142812\pi$
$367$	12669.8			1.80206			0.901031	+	0.433755i	$0.142812\pi$
$368$	9660.59			1.36846
$369$	33529.4			4.73027
$370$		−	428.982i		−	0.0602748i
$371$	7123.23			0.996819
$372$	−7992.21			−1.11392
$373$	467.050			0.0648337			0.0324168	−	0.999474i	$-0.489680\pi$
$373$	467.050			0.0648337			0.0324168	+	0.999474i	$0.489680\pi$
$374$	−82.9603	−	114.842i	−0.0114700	−	0.0158780i
$375$			9898.62i			1.36310i
$376$	−68.4624			−0.00939010
$377$	5645.10			0.771187
$378$	19373.6			2.63617
$379$			4957.34i			0.671877i	0.941884	+	0.335939i	$0.109053\pi$
$379$			4957.34i			0.671877i	−0.941884	+	0.335939i	$0.890947\pi$
$380$	−3032.57	−	8654.20i	−0.409388	−	1.16829i
$381$			15363.0i			2.06580i
$382$	2465.37			0.330208
$383$		−	14936.6i		−	1.99275i	−0.0850591	−	0.996376i	$-0.527108\pi$
$383$		−	14936.6i		−	1.99275i	0.0850591	−	0.996376i	$-0.472892\pi$
$384$		−	2156.15i		−	0.286538i
$385$	3376.98	+	4674.77i	0.447031	+	0.618827i
$386$	−10167.4			−1.34069
$387$			12530.8i			1.64593i
$388$			183.483i			0.0240076i
$389$	−5974.28			−0.778684			−0.389342	−	0.921093i	$-0.627298\pi$
$389$	−5974.28			−0.778684			−0.389342	+	0.921093i	$0.627298\pi$
$390$		−	24498.2i		−	3.18080i
$391$		−	153.248i		−	0.0198212i
$392$	−343.473			−0.0442552
$393$	16754.8			2.15056
$394$			2976.06i			0.380537i
$395$	13257.7			1.68878
$396$	−16898.9	+	12207.5i	−2.14445	+	1.54911i
$397$	5566.41			0.703703			0.351851	−	0.936056i	$-0.385552\pi$
$397$	5566.41			0.703703			0.351851	+	0.936056i	$0.385552\pi$
$398$	−6491.00			−0.817498
$399$	−3208.38	−	9155.90i	−0.402556	−	1.14879i
$400$	−2876.32			−0.359540
$401$		−	5351.76i		−	0.666469i	−0.942844	−	0.333234i	$-0.891860\pi$
$401$		−	5351.76i		−	0.666469i	0.942844	−	0.333234i	$-0.108140\pi$
$402$	−2862.88			−0.355193
$403$			4601.95i			0.568832i
$404$		−	5753.41i		−	0.708522i
$405$	26772.5			3.28478
$406$			5826.10i			0.712179i
$407$	172.098	+	238.237i	0.0209597	+	0.0290146i
$408$	−16.1623			−0.00196115
$409$	−11165.8			−1.34991			−0.674955	−	0.737858i	$-0.735837\pi$
$409$	−11165.8			−1.34991			−0.674955	+	0.737858i	$0.735837\pi$
$410$	26333.2			3.17196
$411$		−	5706.99i		−	0.684927i
$412$		−	11557.8i		−	1.38207i
$413$	−6391.73			−0.761541
$414$	−43956.7			−5.21825
$415$		−	10011.7i		−	1.18422i
$416$	−12221.1			−1.44035
$417$	−3566.39			−0.418818
$418$	10050.5	+	6997.01i	1.17605	+	0.818744i
$419$	6501.08			0.757992			0.378996	−	0.925398i	$-0.376269\pi$
$419$	6501.08			0.757992			0.378996	+	0.925398i	$0.376269\pi$
$420$	12970.8			1.50693
$421$		−	659.285i		−	0.0763220i	−0.999272	−	0.0381610i	$-0.987850\pi$
$421$		−	659.285i		−	0.0763220i	0.999272	−	0.0381610i	$-0.0121500\pi$
$422$	−18613.9			−2.14718
$423$	−2679.37			−0.307980
$424$			1025.76i			0.117489i
$425$			45.6278i			0.00520771i
$426$	−27224.0			−3.09626
$427$	−9066.42			−1.02753
$428$	2853.93			0.322313
$429$	9828.16	+	13605.2i	1.10608	+	1.53115i
$430$			9841.38i			1.10371i
$431$	−5383.08			−0.601610			−0.300805	−	0.953686i	$-0.597255\pi$
$431$	−5383.08			−0.601610			−0.300805	+	0.953686i	$0.597255\pi$
$432$		−	23996.0i		−	2.67247i
$433$			95.9011i			0.0106437i	0.999986	+	0.00532184i	$0.00169400\pi$
$433$			95.9011i			0.0106437i	−0.999986	+	0.00532184i	$0.998306\pi$
$434$	−4749.50			−0.525307
$435$			15284.4i			1.68467i
$436$	2394.36			0.263002
$437$	4380.75	+	12501.6i	0.479542	+	1.36849i
$438$	32729.5			3.57049
$439$	15353.8			1.66924			0.834619	−	0.550828i	$-0.185688\pi$
$439$	15353.8			1.66924			0.834619	+	0.550828i	$0.185688\pi$
$440$	−673.178	+	486.293i	−0.0729375	+	0.0526889i
$441$	−13442.3			−1.45150
$442$			183.477i			0.0197446i
$443$	6845.15			0.734137			0.367069	−	0.930194i	$-0.380361\pi$
$443$	6845.15			0.734137			0.367069	+	0.930194i	$0.380361\pi$
$444$	661.019			0.0706545
$445$			2389.12i			0.254506i
$446$			11524.0i			1.22350i
$447$	−13574.9			−1.43640
$448$		−	6799.69i		−	0.717087i
$449$		−	7700.03i		−	0.809324i	−0.914466	−	0.404662i	$-0.867389\pi$
$449$		−	7700.03i		−	0.809324i	0.914466	−	0.404662i	$-0.132611\pi$
$450$	13087.6			1.37101
$451$	−14624.3	+	10564.3i	−1.52689	+	1.10300i
$452$		−	8890.43i		−	0.925156i
$453$		−	12085.0i		−	1.25343i
$454$	1687.72			0.174468
$455$		−	7468.64i		−	0.769528i
$456$	1318.47	−	462.014i	0.135401	−	0.0474469i
$457$		−	17323.6i		−	1.77322i	−0.462514	−	0.886612i	$-0.653053\pi$
$457$		−	17323.6i		−	1.77322i	0.462514	−	0.886612i	$-0.346947\pi$
$458$	3272.68			0.333892
$459$	−380.654			−0.0387090
$460$	−17710.4			−1.79512
$461$		−	9501.13i		−	0.959895i	−0.877297	−	0.479948i	$-0.840656\pi$
$461$		−	9501.13i		−	0.959895i	0.877297	−	0.479948i	$-0.159344\pi$
$462$	−14041.4	+	10143.3i	−1.41399	+	1.02145i
$463$	7661.20			0.768998			0.384499	−	0.923125i	$-0.374374\pi$
$463$	7661.20			0.768998			0.384499	+	0.923125i	$0.374374\pi$
$464$	7216.16			0.721987
$465$	−12460.0			−1.24263
$466$		−	24858.9i		−	2.47117i
$467$	−17173.8			−1.70173			−0.850863	−	0.525387i	$-0.823921\pi$
$467$	−17173.8			−1.70173			−0.850863	+	0.525387i	$0.823921\pi$
$468$	26998.4			2.66667
$469$	−872.792			−0.0859313
$470$	−2104.31			−0.206521
$471$			8797.58i			0.860661i
$472$		−	920.424i		−	0.0897583i
$473$	−3948.16	−	5465.45i	−0.383798	−	0.531293i
$474$			39821.5i			3.85878i
$475$	−1304.32	−	3722.19i	−0.125992	−	0.359549i
$476$	−97.1438			−0.00935416
$477$			40144.6i			3.85345i
$478$		−	4836.77i		−	0.462822i
$479$			16898.5i			1.61193i	0.591966	+	0.805963i	$0.298352\pi$
$479$			16898.5i			1.61193i	−0.591966	+	0.805963i	$0.701648\pi$
$480$		−	33089.2i		−	3.14648i
$481$		−	380.618i		−	0.0360804i
$482$	−23855.4			−2.25432
$483$	−18737.2			−1.76516
$484$	3524.36	−	10648.9i	0.330988	−	1.00008i
$485$			286.054i			0.0267816i
$486$			36937.5i			3.44757i
$487$		−	19679.2i		−	1.83111i	−0.402197	−	0.915553i	$-0.631753\pi$
$487$		−	19679.2i		−	1.83111i	0.402197	−	0.915553i	$-0.368247\pi$
$488$		−	1305.58i		−	0.121109i
$489$			37200.5i			3.44021i
$490$	−10557.3			−0.973324
$491$		−	3584.46i		−	0.329459i	−0.986339	−	0.164730i	$-0.947325\pi$
$491$		−	3584.46i		−	0.329459i	0.986339	−	0.164730i	$-0.0526751\pi$
$492$			40576.9i			3.71819i
$493$		−	114.472i		−	0.0104575i
$494$	−5244.88	−	14967.6i	−0.477689	−	1.36320i
$495$	−26345.8	+	19031.8i	−2.39223	+	1.72811i
$496$			5882.70i			0.532542i
$497$	−8299.65			−0.749074
$498$	30071.5			2.70590
$499$	−16750.4			−1.50271			−0.751353	−	0.659900i	$-0.770598\pi$
$499$	−16750.4			−1.50271			−0.751353	+	0.659900i	$0.770598\pi$
$500$	−8567.56			−0.766306
$501$		−	11093.3i		−	0.989246i
$502$	15407.6			1.36987
$503$			9773.12i			0.866326i	0.901316	+	0.433163i	$0.142603\pi$
$503$			9773.12i			0.866326i	−0.901316	+	0.433163i	$0.857397\pi$
$504$			1413.32i			0.124909i
$505$		−	8969.71i		−	0.790390i
$506$	19172.3	−	13849.7i	1.68441	−	1.21679i
$507$		−	344.609i		−	0.0301866i
$508$	−13297.1			−1.16135
$509$		−	13011.0i		−	1.13301i	−0.824058	−	0.566505i	$-0.808295\pi$
$509$		−	13011.0i		−	1.13301i	0.824058	−	0.566505i	$-0.191705\pi$
$510$	−496.776			−0.0431326
$511$	9978.08			0.863805
$512$	−16459.4			−1.42072
$513$	31052.7	−	10881.4i	2.67254	−	0.936500i
$514$		−	3518.76i		−	0.301957i
$515$		−	18018.9i		−	1.54176i
$516$	−15164.6			−1.29377
$517$	1168.64	−	844.207i	0.0994134	−	0.0718147i
$518$	392.822			0.0333197
$519$		−	9924.31i		−	0.839362i
$520$	1075.50			0.0906997
$521$		−	7101.57i		−	0.597170i	−0.954383	−	0.298585i	$-0.903485\pi$
$521$		−	7101.57i		−	0.597170i	0.954383	−	0.298585i	$-0.0965146\pi$
$522$	−32834.3			−2.75310
$523$	−7482.66			−0.625610			−0.312805	−	0.949817i	$-0.601269\pi$
$523$	−7482.66			−0.625610			−0.312805	+	0.949817i	$0.601269\pi$
$524$			14501.8i			1.20900i
$525$	5578.77			0.463766
$526$			18418.6i			1.52679i
$527$	93.3187			0.00771352
$528$	12563.4	+	17391.6i	1.03551	+	1.43347i
$529$	13416.9			1.10273
$530$			31528.6i			2.58399i
$531$		−	36022.1i		−	2.94392i
$532$	7924.72	−	2776.95i	0.645827	−	0.226308i
$533$	23364.4			1.89873
$534$	−7176.07			−0.581534
$535$	4449.34			0.359555
$536$		−	125.684i		−	0.0101282i
$537$	37047.7			2.97714
$538$			3824.18i			0.306454i
$539$	5863.03	−	4235.36i	0.468531	−	0.338460i
$540$			43991.1i			3.50569i
$541$			2894.87i			0.230056i	0.993362	+	0.115028i	$0.0366957\pi$
$541$			2894.87i			0.230056i	−0.993362	+	0.115028i	$0.963304\pi$
$542$			17516.8i			1.38821i
$543$	−29226.2			−2.30979
$544$			247.820i			0.0195316i
$545$	3732.87			0.293392
$546$	22433.2			1.75834
$547$	−2495.97			−0.195101			−0.0975503	−	0.995231i	$-0.531101\pi$
$547$	−2495.97			−0.195101			−0.0975503	+	0.995231i	$0.531101\pi$
$548$	4939.58			0.385052
$549$		−	51095.9i		−	3.97217i
$550$	−5708.31	+	4123.59i	−0.442551	+	0.319692i
$551$	3272.29	+	9338.29i	0.253002	+	0.722004i
$552$		−	2698.19i		−	0.208049i
$553$			12140.2i			0.933549i
$554$			30047.2i			2.30430i
$555$	1030.55			0.0788184
$556$		−	3086.82i		−	0.235451i
$557$		−	3223.89i		−	0.245244i	−0.992453	−	0.122622i	$-0.960870\pi$
$557$		−	3223.89i		−	0.245244i	0.992453	−	0.122622i	$-0.0391302\pi$
$558$		−	26766.9i		−	2.03071i
$559$			8731.86i			0.660676i
$560$		−	9547.20i		−	0.720434i
$561$	275.887	−	199.296i	0.0207628	−	0.0149987i
$562$	4690.23			0.352038
$563$	4454.35			0.333443			0.166722	−	0.986004i	$-0.446682\pi$
$563$	4454.35			0.333443			0.166722	+	0.986004i	$0.446682\pi$
$564$		−	3242.55i		−	0.242085i
$565$		−	13860.4i		−	1.03206i
$566$			3997.79i			0.296890i
$567$			24515.8i			1.81582i
$568$		−	1195.17i		−	0.0882890i
$569$	2584.93			0.190450			0.0952249	−	0.995456i	$-0.469643\pi$
$569$	2584.93			0.190450			0.0952249	+	0.995456i	$0.469643\pi$
$570$	40525.6	−	14200.8i	2.97795	−	1.04352i
$571$		−	9971.66i		−	0.730825i	−0.930846	−	0.365412i	$-0.880928\pi$
$571$		−	9971.66i		−	0.730825i	0.930846	−	0.365412i	$-0.119072\pi$
$572$	−11775.7	+	8506.58i	−0.860780	+	0.621814i
$573$			5922.58i			0.431796i
$574$			24113.5i			1.75345i
$575$	−7617.30			−0.552458
$576$	38321.2			2.77208
$577$	−945.316			−0.0682045			−0.0341023	−	0.999418i	$-0.510857\pi$
$577$	−945.316			−0.0682045			−0.0341023	+	0.999418i	$0.510857\pi$
$578$	−19909.1			−1.43271
$579$		−	24425.2i		−	1.75315i
$580$	−13229.2			−0.947088
$581$	9167.75			0.654634
$582$	−859.207			−0.0611947
$583$	−12648.6	−	17509.6i	−0.898547	−	1.24386i
$584$			1436.87i			0.101812i
$585$	42091.2			2.97480
$586$	8090.53			0.570336
$587$	−3174.26			−0.223196			−0.111598	−	0.993753i	$-0.535597\pi$
$587$	−3174.26			−0.223196			−0.111598	+	0.993753i	$0.535597\pi$
$588$		−	16267.7i		−	1.14094i
$589$	−7612.67	+	2667.60i	−0.532555	+	0.186616i
$590$		−	28290.9i		−	1.97410i
$591$	−7149.41			−0.497610
$592$		−	486.546i		−	0.0337786i
$593$			23485.4i			1.62636i	0.582014	+	0.813179i	$0.302265\pi$
$593$			23485.4i			1.62636i	−0.582014	+	0.813179i	$0.697735\pi$
$594$	−34401.5	−	47622.1i	−2.37628	−	3.28949i
$595$	−151.450			−0.0104350
$596$		−	11749.5i		−	0.807516i
$597$		−	15593.4i		−	1.06900i
$598$	−30630.5			−2.09461
$599$		−	14333.6i		−	0.977724i	−0.872361	−	0.488862i	$-0.837412\pi$
$599$		−	14333.6i		−	0.977724i	0.872361	−	0.488862i	$-0.162588\pi$
$600$			803.355i			0.0546614i
$601$	11369.1			0.771640			0.385820	−	0.922574i	$-0.373919\pi$
$601$	11369.1			0.771640			0.385820	+	0.922574i	$0.373919\pi$
$602$	−9011.83			−0.610124
$603$		−	4918.82i		−	0.332189i
$604$	10460.0			0.704651
$605$	5494.56	−	16601.9i	0.369232	−	1.11564i
$606$	26941.9			1.80601
$607$	−1676.08			−0.112076			−0.0560379	−	0.998429i	$-0.517847\pi$
$607$	−1676.08			−0.112076			−0.0560379	+	0.998429i	$0.517847\pi$
$608$	−7084.16	−	20216.4i	−0.472534	−	1.34849i
$609$	−13996.1			−0.931281
$610$		−	40129.5i		−	2.66360i
$611$	−1867.07			−0.123623
$612$		−	547.476i		−	0.0361608i
$613$			11116.4i			0.732441i	0.930528	+	0.366220i	$0.119348\pi$
$613$			11116.4i			0.732441i	−0.930528	+	0.366220i	$0.880652\pi$
$614$	35535.1			2.33563
$615$			63260.5i			4.14782i
$616$	−445.303	−	616.435i	−0.0291262	−	0.0403196i
$617$	4591.68			0.299601			0.149801	−	0.988716i	$-0.452137\pi$
$617$	4591.68			0.299601			0.149801	+	0.988716i	$0.452137\pi$
$618$	54122.6			3.52286
$619$	22283.3			1.44692			0.723459	−	0.690367i	$-0.242551\pi$
$619$	22283.3			1.44692			0.723459	+	0.690367i	$0.242551\pi$
$620$		−	10784.6i		−	0.698578i
$621$		−	63548.1i		−	4.10643i
$622$	−3846.07			−0.247931
$623$	−2187.73			−0.140690
$624$		−	27785.6i		−	1.78255i
$625$	−19309.9			−1.23584
$626$	−3144.70			−0.200779
$627$	−16809.0	+	24144.5i	−1.07063	+	1.53786i
$628$	−7614.58			−0.483845
$629$	−7.71820			−0.000489260
$630$			43440.8i			2.74718i
$631$	−17212.6			−1.08593			−0.542965	−	0.839755i	$-0.682698\pi$
$631$	−17212.6			−1.08593			−0.542965	+	0.839755i	$0.682698\pi$
$632$	−1748.21			−0.110032
$633$		−	44716.2i		−	2.80776i
$634$			31105.3i			1.94850i
$635$	−20730.6			−1.29554
$636$	−48582.6			−3.02897
$637$	−9367.04			−0.582631
$638$	14321.1	−	10345.3i	0.888679	−	0.641968i
$639$		−	46774.6i		−	2.89573i
$640$	2909.48			0.179699
$641$			17870.1i			1.10113i	0.834791	+	0.550567i	$0.185589\pi$
$641$			17870.1i			1.10113i	−0.834791	+	0.550567i	$0.814411\pi$
$642$			13364.3i			0.821567i
$643$	32551.1			1.99641			0.998204	−	0.0599079i	$-0.0190807\pi$
$643$	32551.1			1.99641			0.998204	+	0.0599079i	$0.0190807\pi$
$644$		−	16217.6i		−	0.992334i
$645$	−23642.0			−1.44326
$646$	−303.514	+	106.356i	−0.0184854	+	0.00647759i
$647$	−14621.7			−0.888467			−0.444233	−	0.895911i	$-0.646524\pi$
$647$	−14621.7			−0.888467			−0.444233	+	0.895911i	$0.646524\pi$
$648$	−3530.33			−0.214019
$649$	11349.7	+	15711.5i	0.686464	+	0.950275i
$650$	9119.86			0.550324
$651$		−	11409.8i		−	0.686919i
$652$	−32198.2			−1.93402
$653$	−23216.1			−1.39130			−0.695648	−	0.718383i	$-0.744883\pi$
$653$	−23216.1			−1.39130			−0.695648	+	0.718383i	$0.744883\pi$
$654$			11212.2i			0.670387i
$655$			22608.7i			1.34870i
$656$	29866.8			1.77760
$657$			56233.7i			3.33925i
$658$		−	1926.94i		−	0.114164i
$659$	−17952.4			−1.06119			−0.530597	−	0.847624i	$-0.678032\pi$
$659$	−17952.4			−1.06119			−0.530597	+	0.847624i	$0.678032\pi$
$660$	−23032.1	−	31883.4i	−1.35837	−	1.88039i
$661$			2816.64i			0.165741i	0.996560	+	0.0828704i	$0.0264087\pi$
$661$			2816.64i			0.165741i	−0.996560	+	0.0828704i	$0.973591\pi$
$662$		−	27318.5i		−	1.60387i
$663$	−440.769			−0.0258191
$664$			1320.18i			0.0771578i
$665$	12354.8	−	4329.33i	0.720451	−	0.252458i
$666$			2213.84i			0.128806i
$667$	19110.4			1.10938
$668$	9601.60			0.556133
$669$	−27684.3			−1.59990
$670$		−	3863.13i		−	0.222755i
$671$	16099.1	+	22286.1i	0.926229	+	1.28218i
$672$	30300.1			1.73936
$673$	−7907.31			−0.452904			−0.226452	−	0.974022i	$-0.572713\pi$
$673$	−7907.31			−0.452904			−0.226452	+	0.974022i	$0.572713\pi$
$674$	20418.9			1.16692
$675$			18920.7i			1.07890i
$676$	298.270			0.0169703
$677$	9243.78			0.524767			0.262384	−	0.964964i	$-0.415491\pi$
$677$	9243.78			0.524767			0.262384	+	0.964964i	$0.415491\pi$
$678$	41631.8			2.35820
$679$	−261.942			−0.0148047
$680$		−	21.8091i		−	0.00122991i
$681$			4054.42i			0.228144i
$682$	8433.63	+	11674.7i	0.473520	+	0.655495i
$683$		−	2785.59i		−	0.156058i	−0.996951	−	0.0780291i	$-0.975137\pi$
$683$		−	2785.59i		−	0.156058i	0.996951	−	0.0780291i	$-0.0248627\pi$
$684$	15650.1	+	44661.6i	0.874851	+	2.49661i
$685$	7700.92			0.429543
$686$		−	26393.1i		−	1.46894i
$687$			7861.99i			0.436614i
$688$			11162.0i			0.618527i
$689$			27974.1i			1.54677i
$690$		−	82933.9i		−	4.57571i
$691$	15223.4			0.838097			0.419048	−	0.907964i	$-0.362364\pi$
$691$	15223.4			0.838097			0.419048	+	0.907964i	$0.362364\pi$
$692$	8589.80			0.471871
$693$	−17427.5	−	24125.0i	−0.955293	−	1.32242i
$694$		−	36009.2i		−	1.96958i
$695$		−	4812.44i		−	0.262656i
$696$		−	2015.47i		−	0.109765i
$697$		−	473.785i		−	0.0257473i
$698$			44784.3i			2.42852i
$699$	59718.7			3.23143
$700$			4828.59i			0.260720i
$701$			28942.7i			1.55941i	0.626145	+	0.779707i	$0.284632\pi$
$701$			28942.7i			1.55941i	−0.626145	+	0.779707i	$0.715368\pi$
$702$			76083.3i			4.09057i
$703$	629.629	−	220.632i	0.0337794	−	0.0118368i
$704$	−16714.3	+	12074.1i	−0.894805	+	0.646393i
$705$		−	5055.21i		−	0.270057i
$706$	−20842.5			−1.11107
$707$	8213.64			0.436925
$708$	43593.5			2.31405
$709$	−1559.41			−0.0826023			−0.0413011	−	0.999147i	$-0.513150\pi$
$709$	−1559.41			−0.0826023			−0.0413011	+	0.999147i	$0.513150\pi$
$710$		−	36735.6i		−	1.94178i
$711$	−68418.7			−3.60887
$712$		−	315.039i		−	0.0165823i
$713$			15579.0i			0.818287i
$714$		−	454.902i		−	0.0238435i
$715$	−18358.6	+	13262.0i	−0.960241	+	0.693663i
$716$			32065.9i			1.67369i
$717$	11619.4			0.605209
$718$			14180.1i			0.737045i
$719$	20008.0			1.03779			0.518897	−	0.854837i	$-0.326343\pi$
$719$	20008.0			1.03779			0.518897	+	0.854837i	$0.326343\pi$
$720$	53805.4			2.78501
$721$	16500.1			0.852281
$722$	21719.5	−	17352.5i	1.11955	−	0.894448i
$723$		−	57307.9i		−	2.94786i
$724$		−	25296.2i		−	1.29852i
$725$	−5689.89			−0.291472
$726$	49866.2	+	16503.7i	2.54919	+	0.843679i
$727$	−18557.5			−0.946713			−0.473356	−	0.880871i	$-0.656958\pi$
$727$	−18557.5			−0.946713			−0.473356	+	0.880871i	$0.656958\pi$
$728$			984.845i			0.0501384i
$729$	−33717.4			−1.71302
$730$			44164.7i			2.23919i
$731$	177.065			0.00895895
$732$	61835.7			3.12229
$733$			24386.2i			1.22882i	0.788987	+	0.614410i	$0.210606\pi$
$733$			24386.2i			1.22882i	−0.788987	+	0.614410i	$0.789394\pi$
$734$	−51351.6			−2.58232
$735$		−	25361.8i		−	1.27277i
$736$	−41372.0			−2.07200
$737$	1549.81	+	2145.40i	0.0774597	+	0.107228i
$738$	−135897.			−6.77839
$739$			27215.5i			1.35472i	0.735652	+	0.677360i	$0.236876\pi$
$739$			27215.5i			1.35472i	−0.735652	+	0.677360i	$0.763124\pi$
$740$			891.969i			0.0443101i
$741$	35956.7	−	12599.8i	1.78259	−	0.624650i
$742$	−28871.0			−1.42842
$743$	11437.1			0.564720			0.282360	−	0.959309i	$-0.408883\pi$
$743$	11437.1			0.564720			0.282360	+	0.959309i	$0.408883\pi$
$744$	1643.03			0.0809630
$745$		−	18317.8i		−	0.900822i
$746$	−1892.99			−0.0929053
$747$			51667.0i			2.53065i
$748$	172.497	+	238.788i	0.00843197	+	0.0116724i
$749$			4074.30i			0.198761i
$750$		−	40119.9i		−	1.95329i
$751$			865.514i			0.0420546i	0.999779	+	0.0210273i	$0.00669370\pi$
$751$			865.514i			0.0420546i	−0.999779	+	0.0210273i	$0.993306\pi$
$752$	−2386.69			−0.115736
$753$			37013.8i			1.79131i
$754$	−22880.0			−1.10510
$755$	16307.3			0.786072
$756$	−40283.0			−1.93793
$757$	8593.54			0.412599			0.206299	−	0.978489i	$-0.433858\pi$
$757$	8593.54			0.412599			0.206299	+	0.978489i	$0.433858\pi$
$758$		−	20092.5i		−	0.962787i
$759$	33271.3	+	46057.7i	1.59114	+	2.20262i
$760$	623.434	+	1779.12i	0.0297557	+	0.0849153i
$761$			34933.7i			1.66406i	0.554734	+	0.832028i	$0.312820\pi$
$761$			34933.7i			1.66406i	−0.554734	+	0.832028i	$0.687180\pi$
$762$		−	62267.4i		−	2.96025i
$763$			3418.22i			0.162186i
$764$	−5126.18			−0.242747
$765$		−	853.529i		−	0.0403391i
$766$			60539.2i			2.85557i
$767$		−	25101.4i		−	1.18169i
$768$		−	35284.6i		−	1.65784i
$769$		−	3451.84i		−	0.161868i	−0.996719	−	0.0809339i	$-0.974210\pi$
$769$		−	3451.84i		−	0.161868i	0.996719	−	0.0809339i	$-0.0257903\pi$
$770$	−13687.2	−	18947.2i	−0.640587	−	0.886767i
$771$	8453.15			0.394854
$772$	21140.8			0.985587
$773$			13690.3i			0.637005i	0.947922	+	0.318503i	$0.103180\pi$
$773$			13690.3i			0.637005i	−0.947922	+	0.318503i	$0.896820\pi$
$774$		−	50788.2i		−	2.35859i
$775$		−	4638.46i		−	0.214992i
$776$		−	37.7203i		−	0.00174495i
$777$			943.679i			0.0435705i
$778$	24214.2			1.11584
$779$	13543.6	+	38650.0i	0.622914	+	1.77764i
$780$			50938.4i			2.33832i
$781$	14737.6	+	20401.3i	0.675226	+	0.934719i
$782$			621.127i			0.0284034i
$783$		−	47468.5i		−	2.16652i
$784$	−11973.9			−0.545460
$785$	−11871.3			−0.539752
$786$	−67908.7			−3.08171
$787$	9829.57			0.445218			0.222609	−	0.974908i	$-0.428543\pi$
$787$	9829.57			0.445218			0.222609	+	0.974908i	$0.428543\pi$
$788$		−	6188.04i		−	0.279746i
$789$	−44247.2			−1.99650
$790$	−53734.5			−2.41998
$791$	12692.1			0.570516
$792$	3474.06	−	2509.61i	0.155865	−	0.112595i
$793$		−	35605.3i		−	1.59443i
$794$	−22561.1			−1.00839
$795$	−75741.5			−3.37896
$796$	13496.5			0.600970
$797$			27232.7i			1.21033i	0.796100	+	0.605165i	$0.206893\pi$
$797$			27232.7i			1.21033i	−0.796100	+	0.605165i	$0.793107\pi$
$798$	13003.8	+	37109.6i	0.576854	+	1.64620i
$799$			37.8606i			0.00167636i
$800$	12318.0			0.544385
$801$		−	12329.5i		−	0.543871i
$802$			21691.1i			0.955037i
$803$	−17717.9	−	24527.0i	−0.778646	−	1.07788i
$804$	5952.71			0.261114
$805$		−	25283.6i		−	1.10700i
$806$		−	18652.1i		−	0.815125i
$807$	−9186.87			−0.400735
$808$			1182.78i			0.0514977i
$809$		−	10496.9i		−	0.456183i	−0.973640	−	0.228092i	$-0.926751\pi$
$809$		−	10496.9i		−	0.456183i	0.973640	−	0.228092i	$-0.0732485\pi$
$810$	−108511.			−4.70703
$811$	20308.5			0.879320			0.439660	−	0.898164i	$-0.355099\pi$
$811$	20308.5			0.879320			0.439660	+	0.898164i	$0.355099\pi$
$812$		−	12114.1i		−	0.523547i
$813$	−42080.8			−1.81530
$814$	−697.529	−	965.592i	−0.0300349	−	0.0415774i
$815$	−50197.8			−2.15749
$816$	−563.438			−0.0241719
$817$	−14444.5	+	5061.58i	−0.618542	+	0.216747i
$818$	45255.9			1.93440
$819$			38543.3i			1.64446i
$820$	−54753.9			−2.33182
$821$		−	25716.8i		−	1.09321i	−0.837392	−	0.546603i	$-0.815921\pi$
$821$		−	25716.8i		−	1.09321i	0.837392	−	0.546603i	$-0.184079\pi$
$822$			23130.9i			0.981487i
$823$	255.413			0.0108179			0.00540894	−	0.999985i	$-0.498278\pi$
$823$	255.413			0.0108179			0.00540894	+	0.999985i	$0.498278\pi$
$824$			2376.05i			0.100453i
$825$	−9906.14	−	13713.1i	−0.418046	−	0.578702i
$826$	25906.2			1.09127
$827$	6085.54			0.255883			0.127941	−	0.991782i	$-0.459163\pi$
$827$	6085.54			0.255883			0.127941	+	0.991782i	$0.459163\pi$
$828$	91398.0			3.83611
$829$		−	28705.8i		−	1.20265i	−0.799006	−	0.601323i	$-0.794641\pi$
$829$		−	28705.8i		−	1.20265i	0.799006	−	0.601323i	$-0.205359\pi$
$830$			40578.0i			1.69697i
$831$	−72182.6			−3.01322
$832$	26703.5			1.11271
$833$			189.946i			0.00790063i
$834$	14454.9			0.600158
$835$	14969.1			0.620393
$836$	−20897.8	−	14548.7i	−0.864553	−	0.601886i
$837$	38696.8			1.59804
$838$	−26349.4			−1.08619
$839$			19745.6i			0.812509i	0.913760	+	0.406255i	$0.133165\pi$
$839$			19745.6i			0.812509i	−0.913760	+	0.406255i	$0.866835\pi$
$840$	−2666.53			−0.109528
$841$	−10114.1			−0.414700
$842$			2672.13i			0.109368i
$843$			11267.4i			0.460343i
$844$	38703.3			1.57846
$845$	465.010			0.0189312
$846$	10859.7			0.441329
$847$	15202.5	+	5031.41i	0.616722	+	0.204110i
$848$			35759.4i			1.44809i
$849$	−9603.93			−0.388228
$850$		−	184.933i		−	0.00746254i
$851$		−	1288.51i		−	0.0519031i
$852$	56606.1			2.27617
$853$			25810.8i			1.03604i	0.855367	+	0.518022i	$0.173331\pi$
$853$			25810.8i			1.03604i	−0.855367	+	0.518022i	$0.826669\pi$
$854$	36746.9			1.47243
$855$	24398.9	+	69628.5i	0.975937	+	2.78508i
$856$	−586.709			−0.0234267
$857$	−18403.9			−0.733564			−0.366782	−	0.930307i	$-0.619541\pi$
$857$	−18403.9			−0.733564			−0.366782	+	0.930307i	$0.619541\pi$
$858$	−39834.3	−	55142.8i	−1.58499	−	2.19411i
$859$	−10981.3			−0.436177			−0.218089	−	0.975929i	$-0.569982\pi$
$859$	−10981.3			−0.436177			−0.218089	+	0.975929i	$0.569982\pi$
$860$		−	20462.9i		−	0.811371i
$861$	−57928.1			−2.29290
$862$	21818.0			0.862095
$863$			4.23317i			0.000166974i	1.00000		8.34871e-5i	$2.65748e-5\pi$
$863$			4.23317i			0.000166974i	−1.00000		8.34871e-5i	$0.999973\pi$
$864$			102764.i			4.04643i
$865$	13391.7			0.526395
$866$		−	388.695i		−	0.0152522i
$867$		−	47827.7i		−	1.87349i
$868$	9875.51			0.386171
$869$	29841.7	−	21557.2i	1.16491	−	0.841515i
$870$		−	61949.1i		−	2.41410i
$871$		−	3427.59i		−	0.133341i
$872$	−492.231			−0.0191159
$873$		−	1476.24i		−	0.0572314i
$874$	−17755.5	−	50669.8i	−0.687174	−	1.96102i
$875$		−	12231.2i		−	0.472558i
$876$	−68053.5			−2.62479
$877$	−30293.8			−1.16642			−0.583210	−	0.812321i	$-0.698204\pi$
$877$	−30293.8			−1.16642			−0.583210	+	0.812321i	$0.698204\pi$
$878$	−62230.0			−2.39198
$879$			19436.0i			0.745800i
$880$	−23467.9	+	16952.8i	−0.898980	+	0.649409i
$881$	−8046.92			−0.307727			−0.153864	−	0.988092i	$-0.549172\pi$
$881$	−8046.92			−0.307727			−0.153864	+	0.988092i	$0.549172\pi$
$882$	54482.7			2.07997
$883$	22050.2			0.840370			0.420185	−	0.907438i	$-0.361965\pi$
$883$	22050.2			0.840370			0.420185	+	0.907438i	$0.361965\pi$
$884$		−	381.499i		−	0.0145149i
$885$	67963.4			2.58143
$886$	−27743.9			−1.05200
$887$	41377.1			1.56630			0.783150	−	0.621833i	$-0.213612\pi$
$887$	41377.1			1.56630			0.783150	+	0.621833i	$0.213612\pi$
$888$	−135.892			−0.00513540
$889$		−	18983.1i		−	0.716169i
$890$		−	9683.28i		−	0.364701i
$891$	60262.1	−	43532.4i	2.26583	−	1.63680i
$892$		−	23961.6i		−	0.899433i
$893$	−1082.28	−	3088.57i	−0.0405568	−	0.115739i
$894$	55020.3			2.05834
$895$			49991.6i			1.86708i
$896$			2664.23i			0.0993368i
$897$		−	73583.9i		−	2.73901i
$898$			31208.8i			1.15975i
$899$			11637.0i			0.431721i
$900$	−27212.7			−1.00788
$901$	567.261			0.0209747
$902$	59273.3	−	42818.1i	2.18801	−	1.58058i
$903$		−	21649.2i		−	0.797829i
$904$			1827.69i			0.0672434i
$905$		−	39437.4i		−	1.44856i
$906$			48981.5i			1.79614i
$907$		−	24232.9i		−	0.887144i	−0.896239	−	0.443572i	$-0.853711\pi$
$907$		−	24232.9i		−	0.887144i	0.896239	−	0.443572i	$-0.146289\pi$
$908$	−3509.23			−0.128258
$909$			46289.9i			1.68904i
$910$			30271.0i			1.10272i
$911$		−	24336.1i		−	0.885063i	−0.896753	−	0.442532i	$-0.854080\pi$
$911$		−	24336.1i		−	0.885063i	0.896753	−	0.442532i	$-0.145920\pi$
$912$	45963.7	−	16106.4i	1.66887	−	0.584799i
$913$	−16279.1	−	22535.2i	−0.590097	−	0.816873i
$914$			70213.9i			2.54099i
$915$	96403.4			3.48306
$916$	−6804.79			−0.245455
$917$	−20703.0			−0.745554
$918$	1542.82			0.0554692
$919$		−	28780.1i		−	1.03304i	−0.856274	−	0.516522i	$-0.827226\pi$
$919$		−	28780.1i		−	1.03304i	0.856274	−	0.516522i	$-0.172774\pi$
$920$	3640.90			0.130475
$921$			85366.1i			3.05419i
$922$			38508.8i			1.37551i
$923$		−	32594.0i		−	1.16235i
$924$	29195.9	−	21090.6i	1.03947	−	0.750900i
$925$			383.638i			0.0136367i
$926$	−31051.5			−1.10196
$927$			92990.0i			3.29470i
$928$	−30903.7			−1.09317
$929$	−44906.5			−1.58594			−0.792968	−	0.609264i	$-0.791465\pi$
$929$	−44906.5			−1.58594			−0.792968	+	0.609264i	$0.791465\pi$
$930$	50501.6			1.78066
$931$	−5429.78	−	15495.2i	−0.191143	−	0.545473i
$932$			51688.4i			1.81664i
$933$		−	9239.44i		−	0.324208i
$934$	69606.6			2.43854
$935$	268.927	+	372.277i	0.00940626	+	0.0130211i
$936$	−5550.32			−0.193822
$937$		−	36946.9i		−	1.28816i	−0.764959	−	0.644079i	$-0.777241\pi$
$937$		−	36946.9i		−	1.28816i	0.764959	−	0.644079i	$-0.222759\pi$
$938$	3537.50			0.123138
$939$		−	7554.54i		−	0.262549i
$940$	4375.44			0.151820
$941$	−50341.3			−1.74397			−0.871987	−	0.489529i	$-0.837169\pi$
$941$	−50341.3			−1.74397			−0.871987	+	0.489529i	$0.837169\pi$
$942$		−	35657.3i		−	1.23331i
$943$	79095.6			2.73140
$944$		−	32087.2i		−	1.10630i
$945$	−62802.2			−2.16186
$946$	16002.2	+	22151.9i	0.549975	+	0.761332i
$947$	−30092.3			−1.03260			−0.516298	−	0.856409i	$-0.672690\pi$
$947$	−30092.3			−1.03260			−0.516298	+	0.856409i	$0.672690\pi$
$948$		−	82799.7i		−	2.83672i
$949$			39185.5i			1.34037i
$950$	5286.49	+	15086.3i	0.180544	+	0.515227i
$951$	−74724.4			−2.54795
$952$	19.9708			0.000679891
$953$	−25981.2			−0.883121			−0.441560	−	0.897232i	$-0.645575\pi$
$953$	−25981.2			−0.883121			−0.441560	+	0.897232i	$0.645575\pi$
$954$		−	162709.i		−	5.52192i
$955$	−7991.84			−0.270796
$956$			10057.0i			0.340236i
$957$	24852.7	+	34403.7i	0.839470	+	1.16208i
$958$		−	68491.0i		−	2.30986i
$959$			7051.80i			0.237450i
$960$			72301.2i			2.43074i
$961$	20304.4			0.681560
$962$			1542.67i			0.0517025i
$963$	−22961.7			−0.768358
$964$	49601.8			1.65723
$965$	32959.0			1.09947
$966$	75943.2			2.52943
$967$			3607.67i			0.119974i	0.998199	+	0.0599870i	$0.0191059\pi$
$967$			3607.67i			0.119974i	−0.998199	+	0.0599870i	$0.980894\pi$
$968$	−724.535	+	2189.19i	−0.0240573	+	0.0726893i
$969$	−255.500	−	729.133i	−0.00847042	−	0.0241725i
$970$		−	1159.40i		−	0.0383774i
$971$			28727.2i			0.949432i	0.880139	+	0.474716i	$0.157449\pi$
$971$			28727.2i			0.949432i	−0.880139	+	0.474716i	$0.842551\pi$
$972$		−	76803.1i		−	2.53442i
$973$	4406.79			0.145195
$974$			79761.3i			2.62394i
$975$			21908.7i			0.719631i
$976$		−	45514.4i		−	1.49271i
$977$		−	26468.1i		−	0.866725i	−0.901220	−	0.433363i	$-0.857327\pi$
$977$		−	26468.1i		−	0.866725i	0.901220	−	0.433363i	$-0.142673\pi$
$978$		−	150777.i		−	4.92976i
$979$	3884.73	+	5377.65i	0.126820	+	0.175557i
$980$	21951.4			0.715524
$981$	−19264.1			−0.626969
$982$			14528.1i			0.472108i
$983$			20458.5i			0.663809i	0.943313	+	0.331905i	$0.107691\pi$
$983$			20458.5i			0.663809i	−0.943313	+	0.331905i	$0.892309\pi$
$984$		−	8341.78i		−	0.270250i
$985$		−	9647.30i		−	0.312070i
$986$			463.963i			0.0149854i
$987$	4629.10			0.149287
$988$	10905.5	+	31121.6i	0.351165	+	1.00214i
$989$			29560.0i			0.950409i
$990$	106781.	−	77137.3i	3.42802	−	2.47635i
$991$		−	43093.8i		−	1.38135i	−0.723165	−	0.690676i	$-0.757313\pi$
$991$		−	43093.8i		−	1.38135i	0.723165	−	0.690676i	$-0.242687\pi$
$992$		−	25193.0i		−	0.806329i
$993$	65627.4			2.09730
$994$	33639.1			1.07341
$995$	21041.4			0.670411
$996$	−62526.8			−1.98920
$997$		−	42881.8i		−	1.36217i	−0.732205	−	0.681084i	$-0.761509\pi$
$997$		−	42881.8i		−	1.36217i	0.732205	−	0.681084i	$-0.238491\pi$
$998$	67890.7			2.15335
$999$	−3200.54			−0.101362

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	209.4.d.b.208.9	✓	56
11.10	odd	2	inner	209.4.d.b.208.47	yes	56
19.18	odd	2	inner	209.4.d.b.208.48	yes	56
209.208	even	2	inner	209.4.d.b.208.10	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.4.d.b.208.9	✓	56	1.1	even	1	trivial
209.4.d.b.208.10	yes	56	209.208	even	2	inner
209.4.d.b.208.47	yes	56	11.10	odd	2	inner
209.4.d.b.208.48	yes	56	19.18	odd	2	inner

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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	209.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.05308 q^{2} -9.73675i q^{3} +8.42746 q^{4} +13.1386 q^{5} +39.4638i q^{6} +12.0311i q^{7} -1.73251 q^{8} -67.8042 q^{9} -53.2518 q^{10} +(29.5736 - 21.3635i) q^{11} -82.0560i q^{12} -47.2482 q^{13} -48.7631i q^{14} -127.927i q^{15} -60.3976 q^{16} +0.958103i q^{17} +274.816 q^{18} +(-27.3883 - 78.1593i) q^{19} +110.725 q^{20} +117.144 q^{21} +(-119.864 + 86.5881i) q^{22} -159.950 q^{23} +16.8690i q^{24} +47.6231 q^{25} +191.501 q^{26} +397.300i q^{27} +101.392i q^{28} -119.478 q^{29} +518.500i q^{30} -97.3994i q^{31} +258.657 q^{32} +(-208.011 - 287.951i) q^{33} -3.88327i q^{34} +158.072i q^{35} -571.417 q^{36} +8.05571i q^{37} +(111.007 + 316.786i) q^{38} +460.044i q^{39} -22.7628 q^{40} -494.503 q^{41} -474.794 q^{42} -184.808i q^{43} +(249.230 - 180.040i) q^{44} -890.853 q^{45} +648.289 q^{46} +39.5163 q^{47} +588.076i q^{48} +198.252 q^{49} -193.020 q^{50} +9.32880 q^{51} -398.182 q^{52} -592.067i q^{53} -1610.29i q^{54} +(388.556 - 280.687i) q^{55} -20.8441i q^{56} +(-761.018 + 266.673i) q^{57} +484.252 q^{58} +531.266i q^{59} -1078.10i q^{60} +753.580i q^{61} +394.768i q^{62} -815.762i q^{63} -565.174 q^{64} -620.776 q^{65} +(843.086 + 1167.09i) q^{66} +72.5444i q^{67} +8.07437i q^{68} +1557.39i q^{69} -640.680i q^{70} +689.847i q^{71} +117.472 q^{72} -829.355i q^{73} -32.6504i q^{74} -463.694i q^{75} +(-230.814 - 658.684i) q^{76} +(257.027 + 355.804i) q^{77} -1864.59i q^{78} +1009.06 q^{79} -793.541 q^{80} +2037.70 q^{81} +2004.26 q^{82} -762.002i q^{83} +987.227 q^{84} +12.5881i q^{85} +749.042i q^{86} +1163.32i q^{87} +(-51.2366 + 37.0125i) q^{88} +181.839i q^{89} +3610.70 q^{90} -568.449i q^{91} -1347.97 q^{92} -948.353 q^{93} -160.163 q^{94} +(-359.844 - 1026.91i) q^{95} -2518.47i q^{96} +21.7720i q^{97} -803.530 q^{98} +(-2005.22 + 1448.54i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 236 q^{4} + 16 q^{5} - 484 q^{9} + 74 q^{11} + 668 q^{16} - 264 q^{20} - 296 q^{23} + 1040 q^{25} - 672 q^{26} - 428 q^{36} + 700 q^{38} - 2472 q^{42} - 668 q^{44} + 248 q^{45} - 2284 q^{47} - 2880 q^{49}+ \cdots - 414 q^{99}+O(q^{100}) \) 56 * q + 236 * q^4 + 16 * q^5 - 484 * q^9 + 74 * q^11 + 668 * q^16 - 264 * q^20 - 296 * q^23 + 1040 * q^25 - 672 * q^26 - 428 * q^36 + 700 * q^38 - 2472 * q^42 - 668 * q^44 + 248 * q^45 - 2284 * q^47 - 2880 * q^49 - 614 * q^55 + 2112 * q^58 + 1460 * q^64 + 4964 * q^66 + 2154 * q^77 - 5680 * q^80 - 456 * q^81 + 7840 * q^82 + 10312 * q^92 - 728 * q^93 - 414 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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