LMFDB - Embedded newform 40.4.d.a.21.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [40,4,Mod(21,40)] 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("40.21"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	40.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.36007640023$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{11} + 7x^{10} - 12x^{9} + 21x^{8} - 68x^{6} + 336x^{4} - 768x^{3} + 1792x^{2} - 4096x + 4096 $ x^12 - 4x^11 + 7x^10 - 12x^9 + 21x^8 - 68x^6 + 336x^4 - 768x^3 + 1792x^2 - 4096*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.3
Root			$-0.650488 + 1.89126i$ of defining polynomial
Character	$\chi$	$=$	40.21
Dual form			40.4.d.a.21.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.54175 - 1.24077i) q^{2} +0.888401i q^{3} +(4.92097 + 6.30746i) q^{4} +5.00000i q^{5} +(1.10230 - 2.25809i) q^{6} +26.6173 q^{7} +(-4.68175 - 22.1378i) q^{8} +26.2107 q^{9} +(6.20386 - 12.7087i) q^{10} +61.7277i q^{11} +(-5.60356 + 4.37180i) q^{12} -45.0627i q^{13} +(-67.6545 - 33.0260i) q^{14} -4.44201 q^{15} +(-15.5681 + 62.0776i) q^{16} -71.8754 q^{17} +(-66.6211 - 32.5216i) q^{18} +17.6319i q^{19} +(-31.5373 + 24.6049i) q^{20} +23.6469i q^{21} +(76.5900 - 156.896i) q^{22} +43.4131 q^{23} +(19.6672 - 4.15927i) q^{24} -25.0000 q^{25} +(-55.9125 + 114.538i) q^{26} +47.2725i q^{27} +(130.983 + 167.888i) q^{28} -267.633i q^{29} +(11.2905 + 5.51152i) q^{30} +50.2133 q^{31} +(116.594 - 138.469i) q^{32} -54.8390 q^{33} +(182.689 + 89.1810i) q^{34} +133.087i q^{35} +(128.982 + 165.323i) q^{36} -75.0720i q^{37} +(21.8772 - 44.8160i) q^{38} +40.0338 q^{39} +(110.689 - 23.4087i) q^{40} -221.685 q^{41} +(29.3404 - 60.1044i) q^{42} -188.998i q^{43} +(-389.345 + 303.760i) q^{44} +131.054i q^{45} +(-110.345 - 53.8658i) q^{46} -384.142 q^{47} +(-55.1499 - 13.8307i) q^{48} +365.481 q^{49} +(63.5437 + 31.0193i) q^{50} -63.8542i q^{51} +(284.231 - 221.752i) q^{52} +247.445i q^{53} +(58.6544 - 120.155i) q^{54} -308.638 q^{55} +(-124.616 - 589.248i) q^{56} -15.6642 q^{57} +(-332.072 + 680.256i) q^{58} -518.596i q^{59} +(-21.8590 - 28.0178i) q^{60} +62.0042i q^{61} +(-127.630 - 62.3033i) q^{62} +697.660 q^{63} +(-468.162 + 207.287i) q^{64} +225.314 q^{65} +(139.387 + 68.0426i) q^{66} +558.476i q^{67} +(-353.697 - 453.351i) q^{68} +38.5683i q^{69} +(165.130 - 338.273i) q^{70} +313.194 q^{71} +(-122.712 - 580.248i) q^{72} -263.926 q^{73} +(-93.1472 + 190.814i) q^{74} -22.2100i q^{75} +(-111.213 + 86.7663i) q^{76} +1643.03i q^{77} +(-101.756 - 49.6728i) q^{78} -732.940 q^{79} +(-310.388 - 77.8405i) q^{80} +665.693 q^{81} +(563.468 + 275.061i) q^{82} -717.705i q^{83} +(-149.152 + 116.365i) q^{84} -359.377i q^{85} +(-234.503 + 480.385i) q^{86} +237.766 q^{87} +(1366.51 - 288.994i) q^{88} +1634.69 q^{89} +(162.608 - 333.106i) q^{90} -1199.45i q^{91} +(213.635 + 273.827i) q^{92} +44.6096i q^{93} +(976.392 + 476.633i) q^{94} -88.1597 q^{95} +(123.016 + 103.583i) q^{96} -1367.12 q^{97} +(-928.962 - 453.479i) q^{98} +1617.93i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 16 q^{4} - 36 q^{6} + 28 q^{7} - 40 q^{8} - 108 q^{9} + 30 q^{10} + 188 q^{12} + 68 q^{14} - 60 q^{15} - 56 q^{16} - 206 q^{18} + 20 q^{20} - 164 q^{22} + 604 q^{23} + 360 q^{24} - 300 q^{25}+ \cdots - 7266 q^{98}+O(q^{100}) $ 12 * q + 2 * q^2 + 16 * q^4 - 36 * q^6 + 28 * q^7 - 40 * q^8 - 108 * q^9 + 30 * q^10 + 188 * q^12 + 68 * q^14 - 60 * q^15 - 56 * q^16 - 206 * q^18 + 20 * q^20 - 164 * q^22 + 604 * q^23 + 360 * q^24 - 300 * q^25 - 308 * q^26 - 436 * q^28 + 40 * q^30 - 264 * q^31 + 72 * q^32 - 232 * q^33 - 180 * q^34 + 440 * q^36 + 820 * q^38 + 600 * q^39 + 120 * q^40 + 40 * q^41 + 884 * q^42 - 472 * q^44 - 1268 * q^46 - 940 * q^47 + 424 * q^48 + 1308 * q^49 - 50 * q^50 + 1024 * q^52 - 1512 * q^54 + 440 * q^55 - 728 * q^56 - 680 * q^57 - 360 * q^58 - 820 * q^60 + 592 * q^62 - 1300 * q^63 - 2048 * q^64 + 2928 * q^66 - 2344 * q^68 + 1160 * q^70 - 1592 * q^71 - 152 * q^72 + 432 * q^73 - 420 * q^74 + 2256 * q^76 + 3320 * q^78 + 2016 * q^79 + 1600 * q^80 + 2508 * q^81 + 88 * q^82 + 1048 * q^84 - 244 * q^86 - 1968 * q^87 + 4080 * q^88 - 424 * q^89 - 2250 * q^90 - 900 * q^92 + 292 * q^94 - 1520 * q^95 - 5920 * q^96 - 1584 * q^97 - 7266 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−2.54175	−	1.24077i	−0.898644	−	0.438679i
$2$	−2.54175	−	1.24077i	−0.898644	−	0.438679i
$3$			0.888401i			0.170973i	0.996339	+	0.0854865i	$0.0272444\pi$
$3$			0.888401i			0.170973i	−0.996339	+	0.0854865i	$0.972756\pi$
$4$	4.92097	+	6.30746i	0.615121	+	0.788433i
$5$			5.00000i			0.447214i
$5$			5.00000i			0.447214i
$6$	1.10230	−	2.25809i	0.0750023	−	0.153644i
$7$	26.6173			1.43720			0.718600	−	0.695424i	$-0.244783\pi$
$7$	26.6173			1.43720			0.718600	+	0.695424i	$0.244783\pi$
$8$	−4.68175	−	22.1378i	−0.206906	−	0.978361i
$9$	26.2107			0.970768
$10$	6.20386	−	12.7087i	0.196183	−	0.401886i
$11$			61.7277i			1.69196i	0.533212	+	0.845982i	$0.320985\pi$
$11$			61.7277i			1.69196i	−0.533212	+	0.845982i	$0.679015\pi$
$12$	−5.60356	+	4.37180i	−0.134801	+	0.105169i
$13$		−	45.0627i		−	0.961396i	−0.876886	−	0.480698i	$-0.840383\pi$
$13$		−	45.0627i		−	0.961396i	0.876886	−	0.480698i	$-0.159617\pi$
$14$	−67.6545	−	33.0260i	−1.29153	−	0.630470i
$15$	−4.44201			−0.0764614
$16$	−15.5681	+	62.0776i	−0.243252	+	0.969963i
$17$	−71.8754			−1.02543			−0.512716	−	0.858558i	$-0.671361\pi$
$17$	−71.8754			−1.02543			−0.512716	+	0.858558i	$0.671361\pi$
$18$	−66.6211	−	32.5216i	−0.872375	−	0.425856i
$19$			17.6319i			0.212897i	0.994318	+	0.106449i	$0.0339480\pi$
$19$			17.6319i			0.212897i	−0.994318	+	0.106449i	$0.966052\pi$
$20$	−31.5373	+	24.6049i	−0.352598	+	0.275091i
$21$			23.6469i			0.245722i
$22$	76.5900	−	156.896i	0.742229	−	1.52047i
$23$	43.4131			0.393577			0.196788	−	0.980446i	$-0.436949\pi$
$23$	43.4131			0.393577			0.196788	+	0.980446i	$0.436949\pi$
$24$	19.6672	−	4.15927i	0.167273	−	0.0353753i
$25$	−25.0000			−0.200000
$26$	−55.9125	+	114.538i	−0.421744	+	0.863952i
$27$			47.2725i			0.336948i
$28$	130.983	+	167.888i	0.884052	+	1.13314i
$29$		−	267.633i		−	1.71373i	−0.515540	−	0.856866i	$-0.672409\pi$
$29$		−	267.633i		−	1.71373i	0.515540	−	0.856866i	$-0.327591\pi$
$30$	11.2905	+	5.51152i	0.0687116	+	0.0335420i
$31$	50.2133			0.290922			0.145461	−	0.989364i	$-0.453533\pi$
$31$	50.2133			0.290922			0.145461	+	0.989364i	$0.453533\pi$
$32$	116.594	−	138.469i	0.644099	−	0.764942i
$33$	−54.8390			−0.289280
$34$	182.689	+	89.1810i	0.921498	+	0.449836i
$35$			133.087i			0.642735i
$36$	128.982	+	165.323i	0.597140	+	0.765385i
$37$		−	75.0720i		−	0.333561i	−0.985994	−	0.166781i	$-0.946663\pi$
$37$		−	75.0720i		−	0.333561i	0.985994	−	0.166781i	$-0.0533372\pi$
$38$	21.8772	−	44.8160i	0.0933935	−	0.191319i
$39$	40.0338			0.164373
$40$	110.689	−	23.4087i	0.437536	−	0.0925312i
$41$	−221.685			−0.844425			−0.422213	−	0.906497i	$-0.638746\pi$
$41$	−221.685			−0.844425			−0.422213	+	0.906497i	$0.638746\pi$
$42$	29.3404	−	60.1044i	0.107793	−	0.220817i
$43$		−	188.998i		−	0.670277i	−0.942169	−	0.335139i	$-0.891217\pi$
$43$		−	188.998i		−	0.670277i	0.942169	−	0.335139i	$-0.108783\pi$
$44$	−389.345	+	303.760i	−1.33400	+	1.04076i
$45$			131.054i			0.434141i
$46$	−110.345	−	53.8658i	−0.353685	−	0.172654i
$47$	−384.142			−1.19219			−0.596094	−	0.802914i	$-0.703282\pi$
$47$	−384.142			−1.19219			−0.596094	+	0.802914i	$0.703282\pi$
$48$	−55.1499	−	13.8307i	−0.165837	−	0.0415894i
$49$	365.481			1.06554
$50$	63.5437	+	31.0193i	0.179729	+	0.0877358i
$51$		−	63.8542i		−	0.175321i
$52$	284.231	−	221.752i	0.757996	−	0.591375i
$53$			247.445i			0.641306i	0.947197	+	0.320653i	$0.103902\pi$
$53$			247.445i			0.641306i	−0.947197	+	0.320653i	$0.896098\pi$
$54$	58.6544	−	120.155i	0.147812	−	0.302796i
$55$	−308.638			−0.756669
$56$	−124.616	−	589.248i	−0.297365	−	1.40610i
$57$	−15.6642			−0.0363997
$58$	−332.072	+	680.256i	−0.751778	+	1.54003i
$59$		−	518.596i		−	1.14433i	−0.820139	−	0.572165i	$-0.806104\pi$
$59$		−	518.596i		−	1.14433i	0.820139	−	0.572165i	$-0.193896\pi$
$60$	−21.8590	−	28.0178i	−0.0470330	−	0.0602847i
$61$			62.0042i			0.130145i	0.997881	+	0.0650723i	$0.0207278\pi$
$61$			62.0042i			0.130145i	−0.997881	+	0.0650723i	$0.979272\pi$
$62$	−127.630	−	62.3033i	−0.261435	−	0.127621i
$63$	697.660			1.39519
$64$	−468.162	+	207.287i	−0.914380	+	0.404858i
$65$	225.314			0.429949
$66$	139.387	+	68.0426i	0.259960	+	0.126901i
$67$			558.476i			1.01834i	0.860666	+	0.509169i	$0.170047\pi$
$67$			558.476i			1.01834i	−0.860666	+	0.509169i	$0.829953\pi$
$68$	−353.697	−	453.351i	−0.630765	−	0.808484i
$69$			38.5683i			0.0672910i
$70$	165.130	−	338.273i	0.281955	−	0.577590i
$71$	313.194			0.523512			0.261756	−	0.965134i	$-0.415699\pi$
$71$	313.194			0.523512			0.261756	+	0.965134i	$0.415699\pi$
$72$	−122.712	−	580.248i	−0.200858	−	0.949762i
$73$	−263.926			−0.423153			−0.211576	−	0.977361i	$-0.567860\pi$
$73$	−263.926			−0.423153			−0.211576	+	0.977361i	$0.567860\pi$
$74$	−93.1472	+	190.814i	−0.146326	+	0.299753i
$75$		−	22.2100i		−	0.0341946i
$76$	−111.213	+	86.7663i	−0.167855	+	0.130958i
$77$			1643.03i			2.43169i
$78$	−101.756	−	49.6728i	−0.147712	−	0.0721069i
$79$	−732.940			−1.04383			−0.521913	−	0.852999i	$-0.674781\pi$
$79$	−732.940			−1.04383			−0.521913	+	0.852999i	$0.674781\pi$
$80$	−310.388	−	77.8405i	−0.433781	−	0.108785i
$81$	665.693			0.913159
$82$	563.468	+	275.061i	0.758837	+	0.370432i
$83$		−	717.705i		−	0.949137i	−0.880218	−	0.474569i	$-0.842604\pi$
$83$		−	717.705i		−	0.949137i	0.880218	−	0.474569i	$-0.157396\pi$
$84$	−149.152	+	116.365i	−0.193735	+	0.151149i
$85$		−	359.377i		−	0.458587i
$86$	−234.503	+	480.385i	−0.294037	+	0.602341i
$87$	237.766			0.293002
$88$	1366.51	−	288.994i	1.65535	−	0.350077i
$89$	1634.69			1.94693			0.973463	−	0.228845i	$-0.0734949\pi$
$89$	1634.69			1.94693			0.973463	+	0.228845i	$0.0734949\pi$
$90$	162.608	−	333.106i	0.190448	−	0.390138i
$91$		−	1199.45i		−	1.38172i
$92$	213.635	+	273.827i	0.242097	+	0.310309i
$93$			44.6096i			0.0497398i
$94$	976.392	+	476.633i	1.07135	+	0.522988i
$95$	−88.1597			−0.0952105
$96$	123.016	+	103.583i	0.130784	+	0.110124i
$97$	−1367.12			−1.43103			−0.715516	−	0.698596i	$-0.753809\pi$
$97$	−1367.12			−1.43103			−0.715516	+	0.698596i	$0.753809\pi$
$98$	−928.962	−	453.479i	−0.957544	−	0.467432i
$99$			1617.93i			1.64250i
$100$	−123.024	−	157.687i	−0.123024	−	0.157687i
$101$		−	58.3234i		−	0.0574594i	−0.999587	−	0.0287297i	$-0.990854\pi$
$101$		−	58.3234i		−	0.0574594i	0.999587	−	0.0287297i	$-0.00914620\pi$
$102$	−79.2285	+	162.301i	−0.0769097	+	0.157551i
$103$	−9.69032			−0.00927005			−0.00463503	−	0.999989i	$-0.501475\pi$
$103$	−9.69032			−0.00927005			−0.00463503	+	0.999989i	$0.501475\pi$
$104$	−997.588	+	210.972i	−0.940592	+	0.198919i
$105$	−118.234			−0.109890
$106$	307.023	−	628.944i	0.281328	−	0.576306i
$107$		−	439.045i		−	0.396674i	−0.980134	−	0.198337i	$-0.936446\pi$
$107$		−	439.045i		−	0.396674i	0.980134	−	0.198337i	$-0.0635540\pi$
$108$	−298.169	+	232.627i	−0.265661	+	0.207264i
$109$		−	1616.51i		−	1.42049i	−0.703955	−	0.710245i	$-0.748584\pi$
$109$		−	1616.51i		−	1.42049i	0.703955	−	0.710245i	$-0.251416\pi$
$110$	784.481	+	382.950i	0.679976	+	0.331935i
$111$	66.6941			0.0570299
$112$	−414.381	+	1652.34i	−0.349601	+	1.39403i
$113$	−1281.25			−1.06663			−0.533316	−	0.845916i	$-0.679054\pi$
$113$	−1281.25			−1.06663			−0.533316	+	0.845916i	$0.679054\pi$
$114$	39.8146	+	19.4358i	0.0327103	+	0.0159678i
$115$			217.066i			0.176013i
$116$	1688.08	−	1317.01i	1.35116	−	1.05415i
$117$		−	1181.13i		−	0.933293i
$118$	−643.459	+	1318.14i	−0.501993	+	1.02834i
$119$	−1913.13			−1.47375
$120$	20.7964	+	98.3362i	0.0158203	+	0.0748069i
$121$	−2479.31			−1.86274
$122$	76.9330	−	157.599i	0.0570917	−	0.116954i
$123$		−	196.946i		−	0.144374i
$124$	247.098	+	316.718i	0.178952	+	0.229372i
$125$		−	125.000i		−	0.0894427i
$126$	−1773.28	−	865.636i	−1.25378	−	0.612040i
$127$	235.326			0.164423			0.0822117	−	0.996615i	$-0.473802\pi$
$127$	235.326			0.164423			0.0822117	+	0.996615i	$0.473802\pi$
$128$	1447.15	+	54.0113i	0.999304	+	0.0372966i
$129$	167.906			0.114599
$130$	−572.690	−	279.563i	−0.386371	−	0.188610i
$131$			993.121i			0.662362i	0.943567	+	0.331181i	$0.107447\pi$
$131$			993.121i			0.662362i	−0.943567	+	0.331181i	$0.892553\pi$
$132$	−269.861	−	345.895i	−0.177942	−	0.228078i
$133$			469.315i			0.305976i
$134$	692.941	−	1419.51i	0.446724	−	0.915124i
$135$	−236.363			−0.150688
$136$	336.503	+	1591.16i	0.212168	+	1.00324i
$137$	2070.09			1.29095			0.645474	−	0.763782i	$-0.276660\pi$
$137$	2070.09			1.29095			0.645474	+	0.763782i	$0.276660\pi$
$138$	47.8545	−	98.0309i	0.0295191	−	0.0604706i
$139$			288.330i			0.175941i	0.996123	+	0.0879707i	$0.0280382\pi$
$139$			288.330i			0.175941i	−0.996123	+	0.0879707i	$0.971962\pi$
$140$	−839.438	+	654.915i	−0.506753	+	0.395360i
$141$		−	341.272i		−	0.203832i
$142$	−796.061	−	388.603i	−0.470450	−	0.229654i
$143$	2781.62			1.62665
$144$	−408.052	+	1627.10i	−0.236141	+	0.941609i
$145$	1338.17			0.766404
$146$	670.832	+	327.471i	0.380264	+	0.185628i
$147$			324.694i			0.182179i
$148$	473.514	−	369.427i	0.262990	−	0.205181i
$149$			900.665i			0.495204i	0.968862	+	0.247602i	$0.0796425\pi$
$149$			900.665i			0.495204i	−0.968862	+	0.247602i	$0.920358\pi$
$150$	−27.5576	+	56.4523i	−0.0150005	+	0.0307288i
$151$	2005.71			1.08094			0.540472	−	0.841362i	$-0.318246\pi$
$151$	2005.71			1.08094			0.540472	+	0.841362i	$0.318246\pi$
$152$	390.332	−	82.5483i	0.208290	−	0.0440497i
$153$	−1883.91			−0.995457
$154$	2038.62	−	4176.16i	1.06673	−	2.18522i
$155$			251.067i			0.130104i
$156$	197.005	+	252.511i	0.101109	+	0.129597i
$157$		−	3098.13i		−	1.57489i	−0.616385	−	0.787445i	$-0.711403\pi$
$157$		−	3098.13i		−	1.57489i	0.616385	−	0.787445i	$-0.288597\pi$
$158$	1862.95	+	909.412i	0.938027	+	0.457905i
$159$	−219.831			−0.109646
$160$	692.346	+	582.972i	0.342092	+	0.288050i
$161$	1155.54			0.565648
$162$	−1692.02	−	825.973i	−0.820605	−	0.400584i
$163$			3566.57i			1.71383i	0.515454	+	0.856917i	$0.327623\pi$
$163$			3566.57i			1.71383i	−0.515454	+	0.856917i	$0.672377\pi$
$164$	−1090.91	−	1398.27i	−0.519424	−	0.665772i
$165$		−	274.195i		−	0.129370i
$166$	−890.509	+	1824.23i	−0.416367	+	0.852936i
$167$	1326.87			0.614830			0.307415	−	0.951576i	$-0.400536\pi$
$167$	1326.87			0.614830			0.307415	+	0.951576i	$0.400536\pi$
$168$	523.489	−	110.709i	0.240405	−	0.0508414i
$169$	166.353			0.0757180
$170$	−445.905	+	913.446i	−0.201173	+	0.412106i
$171$			462.146i			0.206674i
$172$	1192.10	−	930.054i	0.528469	−	0.412302i
$173$			1035.22i			0.454952i	0.973784	+	0.227476i	$0.0730473\pi$
$173$			1035.22i			0.454952i	−0.973784	+	0.227476i	$0.926953\pi$
$174$	−604.340	−	295.013i	−0.263304	−	0.128534i
$175$	−665.433			−0.287440
$176$	−3831.91	−	960.983i	−1.64114	−	0.411573i
$177$	460.721			0.195649
$178$	−4154.96	−	2028.27i	−1.74959	−	0.854076i
$179$			1811.28i			0.756319i	0.925740	+	0.378160i	$0.123443\pi$
$179$			1811.28i			0.756319i	−0.925740	+	0.378160i	$0.876557\pi$
$180$	−826.616	+	644.911i	−0.342291	+	0.267049i
$181$			2286.18i			0.938842i	0.882975	+	0.469421i	$0.155537\pi$
$181$			2286.18i			0.938842i	−0.882975	+	0.469421i	$0.844463\pi$
$182$	−1488.24	+	3048.70i	−0.606131	+	1.24167i
$183$	−55.0846			−0.0222512
$184$	−203.249	−	961.070i	−0.0814334	−	0.385060i
$185$	375.360			0.149173
$186$	55.3503	−	113.386i	0.0218198	−	0.0446983i
$187$		−	4436.70i		−	1.73499i
$188$	−1890.35	−	2422.96i	−0.733341	−	0.939960i
$189$			1258.27i			0.484262i
$190$	224.080	+	109.386i	0.0855603	+	0.0417669i
$191$	−2392.90			−0.906513			−0.453256	−	0.891380i	$-0.649738\pi$
$191$	−2392.90			−0.906513			−0.453256	+	0.891380i	$0.649738\pi$
$192$	−184.154	−	415.916i	−0.0692197	−	0.156334i
$193$	−638.414			−0.238104			−0.119052	−	0.992888i	$-0.537985\pi$
$193$	−638.414			−0.238104			−0.119052	+	0.992888i	$0.537985\pi$
$194$	3474.88	+	1696.29i	1.28599	+	0.627764i
$195$			200.169i			0.0735097i
$196$	1798.52	+	2305.26i	0.655438	+	0.840109i
$197$			654.303i			0.236635i	0.992976	+	0.118318i	$0.0377501\pi$
$197$			654.303i			0.236635i	−0.992976	+	0.118318i	$0.962250\pi$
$198$	2007.48	−	4112.37i	0.720532	−	1.47603i
$199$	−1637.06			−0.583155			−0.291578	−	0.956547i	$-0.594180\pi$
$199$	−1637.06			−0.583155			−0.291578	+	0.956547i	$0.594180\pi$
$200$	117.044	+	553.444i	0.0413812	+	0.195672i
$201$	−496.151			−0.174108
$202$	−72.3661	+	148.243i	−0.0252062	+	0.0516355i
$203$		−	7123.67i		−	2.46297i
$204$	402.758	−	314.225i	0.138229	−	0.107844i
$205$		−	1108.43i		−	0.377638i
$206$	24.6304	+	12.0235i	0.00833048	+	0.00406658i
$207$	1137.89			0.382072
$208$	2797.39	+	701.541i	0.932519	+	0.233861i
$209$	−1088.38			−0.360214
$210$	300.522	+	146.702i	0.0987523	+	0.0482066i
$211$			2769.26i			0.903524i	0.892139	+	0.451762i	$0.149204\pi$
$211$			2769.26i			0.903524i	−0.892139	+	0.451762i	$0.850796\pi$
$212$	−1560.75	+	1217.67i	−0.505627	+	0.394481i
$213$			278.242i			0.0895063i
$214$	−544.755	+	1115.94i	−0.174012	+	0.356468i
$215$	944.990			0.299757
$216$	1046.51	−	221.318i	0.329657	−	0.0697166i
$217$	1336.54			0.418113
$218$	−2005.72	+	4108.76i	−0.623139	+	1.27651i
$219$		−	234.472i		−	0.0723477i
$220$	−1518.80	−	1946.72i	−0.465443	−	0.596582i
$221$			3238.90i			0.985846i
$222$	−169.520	−	82.7521i	−0.0512496	−	0.0250178i
$223$	−4312.57			−1.29503			−0.647514	−	0.762054i	$-0.724191\pi$
$223$	−4312.57			−1.29503			−0.647514	+	0.762054i	$0.724191\pi$
$224$	3103.43	−	3685.68i	0.925699	−	1.09937i
$225$	−655.269			−0.194154
$226$	3256.60	+	1589.73i	0.958523	+	0.467909i
$227$		−	575.097i		−	0.168152i	−0.996459	−	0.0840761i	$-0.973206\pi$
$227$		−	575.097i		−	0.168152i	0.996459	−	0.0840761i	$-0.0267939\pi$
$228$	−77.0833	−	98.8016i	−0.0223902	−	0.0286987i
$229$		−	2396.42i		−	0.691529i	−0.938321	−	0.345765i	$-0.887620\pi$
$229$		−	2396.42i		−	0.691529i	0.938321	−	0.345765i	$-0.112380\pi$
$230$	269.329	−	551.726i	0.0772132	−	0.158173i
$231$	−1459.67			−0.415753
$232$	−5924.80	+	1252.99i	−1.67665	+	0.354581i
$233$	3307.22			0.929885			0.464943	−	0.885341i	$-0.346075\pi$
$233$	3307.22			0.929885			0.464943	+	0.885341i	$0.346075\pi$
$234$	−1465.51	+	3002.13i	−0.409416	+	0.838698i
$235$		−	1920.71i		−	0.533163i
$236$	3271.02	−	2551.99i	0.902227	−	0.703901i
$237$		−	651.145i		−	0.178466i
$238$	4862.69	+	2373.76i	1.32438	+	0.646504i
$239$	−1534.33			−0.415262			−0.207631	−	0.978207i	$-0.566575\pi$
$239$	−1534.33			−0.415262			−0.207631	+	0.978207i	$0.566575\pi$
$240$	69.1536	−	275.749i	0.0185994	−	0.0741648i
$241$	−461.143			−0.123257			−0.0616283	−	0.998099i	$-0.519629\pi$
$241$	−461.143			−0.123257			−0.0616283	+	0.998099i	$0.519629\pi$
$242$	6301.77	+	3076.25i	1.67394	+	0.817145i
$243$			1867.76i			0.493074i
$244$	−391.089	+	305.121i	−0.102610	+	0.0800547i
$245$			1827.41i			0.476526i
$246$	−244.365	+	500.586i	−0.0633338	+	0.129741i
$247$	794.543			0.204678
$248$	−235.086	−	1111.61i	−0.0601935	−	0.284627i
$249$	637.611			0.162277
$250$	−155.096	+	317.719i	−0.0392367	+	0.0803771i
$251$		−	6200.39i		−	1.55922i	−0.626263	−	0.779612i	$-0.715416\pi$
$251$		−	6200.39i		−	1.55922i	0.626263	−	0.779612i	$-0.284584\pi$
$252$	3433.16	+	4400.46i	0.858210	+	1.10001i
$253$			2679.79i			0.665917i
$254$	−598.139	−	291.986i	−0.147758	−	0.0721291i
$255$	319.271			0.0784060
$256$	−3611.27	−	1932.86i	−0.881657	−	0.471890i
$257$	−2381.71			−0.578082			−0.289041	−	0.957317i	$-0.593336\pi$
$257$	−2381.71			−0.578082			−0.289041	+	0.957317i	$0.593336\pi$
$258$	−426.775	−	208.333i	−0.102984	−	0.0502723i
$259$		−	1998.22i		−	0.479394i
$260$	1108.76	+	1421.16i	0.264471	+	0.338986i
$261$		−	7014.86i		−	1.66364i
$262$	1232.24	−	2524.26i	0.290564	−	0.595227i
$263$	−420.996			−0.0987061			−0.0493531	−	0.998781i	$-0.515716\pi$
$263$	−420.996			−0.0987061			−0.0493531	+	0.998781i	$0.515716\pi$
$264$	256.742	+	1214.01i	0.0598538	+	0.283020i
$265$	−1237.23			−0.286801
$266$	582.313	−	1192.88i	0.134225	−	0.274963i
$267$			1452.26i			0.332872i
$268$	−3522.56	+	2748.24i	−0.802891	+	0.626402i
$269$			6748.92i			1.52970i	0.644209	+	0.764849i	$0.277187\pi$
$269$			6748.92i			1.52970i	−0.644209	+	0.764849i	$0.722813\pi$
$270$	600.774	+	293.272i	0.135415	+	0.0661036i
$271$	5718.47			1.28182			0.640908	−	0.767618i	$-0.278558\pi$
$271$	5718.47			1.28182			0.640908	+	0.767618i	$0.278558\pi$
$272$	1118.96	−	4461.86i	0.249438	−	0.994631i
$273$	1065.59			0.236236
$274$	−5261.65	−	2568.51i	−1.16010	−	0.566312i
$275$		−	1543.19i		−	0.338393i
$276$	−243.268	+	189.793i	−0.0530544	+	0.0413921i
$277$			6245.97i			1.35481i	0.735608	+	0.677407i	$0.236897\pi$
$277$			6245.97i			1.35481i	−0.735608	+	0.677407i	$0.763103\pi$
$278$	357.752	−	732.863i	0.0771818	−	0.158109i
$279$	1316.13			0.282418
$280$	2946.24	−	623.078i	0.628827	−	0.132986i
$281$	2883.17			0.612084			0.306042	−	0.952018i	$-0.400995\pi$
$281$	2883.17			0.612084			0.306042	+	0.952018i	$0.400995\pi$
$282$	−423.441	+	867.428i	−0.0894168	+	0.183172i
$283$			7520.83i			1.57974i	0.613273	+	0.789871i	$0.289852\pi$
$283$			7520.83i			1.57974i	−0.613273	+	0.789871i	$0.710148\pi$
$284$	1541.22	+	1975.46i	0.322023	+	0.412754i
$285$		−	78.3212i		−	0.0162784i
$286$	−7070.17	−	3451.35i	−1.46178	−	0.713576i
$287$	−5900.67			−1.21361
$288$	3056.03	−	3629.38i	0.625271	−	0.742581i
$289$	253.072			0.0515107
$290$	−3401.28	−	1660.36i	−0.688724	−	0.336205i
$291$		−	1214.55i		−	0.244668i
$292$	−1298.77	−	1664.70i	−0.260290	−	0.333627i
$293$		−	6762.89i		−	1.34844i	−0.738531	−	0.674219i	$-0.764480\pi$
$293$		−	6762.89i		−	1.34844i	0.738531	−	0.674219i	$-0.235520\pi$
$294$	402.871	−	825.291i	0.0799182	−	0.163714i
$295$	2592.98			0.511760
$296$	−1661.93	+	351.468i	−0.326343	+	0.0690158i
$297$	−2918.02			−0.570104
$298$	1117.52	−	2289.26i	0.217236	−	0.445012i
$299$		−	1956.31i		−	0.378383i
$300$	140.089	−	109.295i	0.0269601	−	0.0210338i
$301$		−	5030.62i		−	0.963323i
$302$	−5098.01	−	2488.63i	−0.971383	−	0.474187i
$303$	51.8146			0.00982400
$304$	−1094.55	−	274.496i	−0.206502	−	0.0517876i
$305$	−310.021			−0.0582024
$306$	4788.42	+	2337.50i	0.894561	+	0.436686i
$307$			10085.5i			1.87495i	0.348058	+	0.937473i	$0.386841\pi$
$307$			10085.5i			1.87495i	−0.348058	+	0.937473i	$0.613159\pi$
$308$	−10363.3	+	8085.28i	−1.91722	+	1.49578i
$309$		−	8.60889i		−	0.00158493i
$310$	311.516	−	638.148i	0.0570740	−	0.116917i
$311$	−7683.50			−1.40094			−0.700469	−	0.713683i	$-0.747026\pi$
$311$	−7683.50			−1.40094			−0.700469	+	0.713683i	$0.747026\pi$
$312$	−187.428	−	886.259i	−0.0340097	−	0.160816i
$313$	1253.17			0.226304			0.113152	−	0.993578i	$-0.463905\pi$
$313$	1253.17			0.226304			0.113152	+	0.993578i	$0.463905\pi$
$314$	−3844.07	+	7874.67i	−0.690872	+	1.41527i
$315$			3488.30i			0.623947i
$316$	−3606.78	−	4622.99i	−0.642079	−	0.822986i
$317$		−	958.616i		−	0.169846i	−0.996388	−	0.0849231i	$-0.972936\pi$
$317$		−	958.616i		−	0.169846i	0.996388	−	0.0849231i	$-0.0270645\pi$
$318$	558.755	+	272.760i	0.0985327	+	0.0480994i
$319$	16520.4			2.89957
$320$	−1036.44	−	2340.81i	−0.181058	−	0.408923i
$321$	390.048			0.0678204
$322$	−2937.09	−	1433.76i	−0.508316	−	0.248138i
$323$		−	1267.30i		−	0.218312i
$324$	3275.86	+	4198.83i	0.561704	+	0.719964i
$325$			1126.57i			0.192279i
$326$	4425.29	−	9065.31i	0.751823	−	1.54013i
$327$	1436.11			0.242865
$328$	1037.87	+	4907.62i	0.174717	+	0.826152i
$329$	−10224.8			−1.71341
$330$	−340.213	+	696.934i	−0.0567519	+	0.116257i
$331$			4252.70i			0.706192i	0.935587	+	0.353096i	$0.114871\pi$
$331$			4252.70i			0.706192i	−0.935587	+	0.353096i	$0.885129\pi$
$332$	4526.90	−	3531.81i	0.748331	−	0.583835i
$333$		−	1967.69i		−	0.323811i
$334$	−3372.58	−	1646.35i	−0.552513	−	0.269713i
$335$	−2792.38			−0.455415
$336$	−1467.94	−	368.137i	−0.238342	−	0.0597723i
$337$	7662.86			1.23864			0.619321	−	0.785138i	$-0.287408\pi$
$337$	7662.86			1.23864			0.619321	+	0.785138i	$0.287408\pi$
$338$	−422.826	−	206.406i	−0.0680435	−	0.0332159i
$339$		−	1138.26i		−	0.182365i
$340$	2266.76	−	1768.48i	0.361565	−	0.282087i
$341$			3099.55i			0.492229i
$342$	573.418	−	1174.66i	0.0906635	−	0.185726i
$343$	598.394			0.0941990
$344$	−4184.00	+	884.841i	−0.655773	+	0.138684i
$345$	−192.841			−0.0300934
$346$	1284.48	−	2631.28i	0.199578	−	0.408840i
$347$			3626.75i			0.561078i	0.959843	+	0.280539i	$0.0905132\pi$
$347$			3626.75i			0.561078i	−0.959843	+	0.280539i	$0.909487\pi$
$348$	1170.04	+	1499.70i	0.180232	+	0.231012i
$349$		−	8867.03i		−	1.36000i	−0.733210	−	0.680002i	$-0.761979\pi$
$349$		−	8867.03i		−	1.36000i	0.733210	−	0.680002i	$-0.238021\pi$
$350$	1691.36	+	825.650i	0.258306	+	0.126094i
$351$	2130.23			0.323940
$352$	8547.39	+	7197.10i	1.29425	+	1.08979i
$353$	8775.59			1.32317			0.661583	−	0.749872i	$-0.269885\pi$
$353$	8775.59			1.32317			0.661583	+	0.749872i	$0.269885\pi$
$354$	−1171.04	−	571.650i	−0.175819	−	0.0858273i
$355$			1565.97i			0.234121i
$356$	8044.24	+	10310.7i	1.19760	+	1.53502i
$357$		−	1699.63i		−	0.251971i
$358$	2247.38	−	4603.81i	0.331782	−	0.679662i
$359$	7668.51			1.12738			0.563688	−	0.825988i	$-0.309382\pi$
$359$	7668.51			1.12738			0.563688	+	0.825988i	$0.309382\pi$
$360$	2901.24	−	613.561i	0.424746	−	0.0898263i
$361$	6548.11			0.954675
$362$	2836.63	−	5810.89i	0.411850	−	0.843684i
$363$		−	2202.62i		−	0.318478i
$364$	7565.47	−	5902.45i	1.08939	−	0.849924i
$365$		−	1319.63i		−	0.189240i
$366$	140.011	+	68.3474i	0.0199959	+	0.00976114i
$367$	−8276.28			−1.17716			−0.588581	−	0.808438i	$-0.700313\pi$
$367$	−8276.28			−1.17716			−0.588581	+	0.808438i	$0.700313\pi$
$368$	−675.860	+	2694.99i	−0.0957382	+	0.381755i
$369$	−5810.54			−0.819741
$370$	−954.071	−	465.736i	−0.134053	−	0.0654391i
$371$			6586.33i			0.921685i
$372$	−281.373	+	219.522i	−0.0392164	+	0.0305960i
$373$		−	270.669i		−	0.0375730i	−0.999824	−	0.0187865i	$-0.994020\pi$
$373$		−	270.669i		−	0.0375730i	0.999824	−	0.0187865i	$-0.00598028\pi$
$374$	−5504.93	+	11277.0i	−0.761105	+	1.55914i
$375$	111.050			0.0152923
$376$	1798.46	+	8504.05i	0.246671	+	1.16639i
$377$	−12060.3			−1.64757
$378$	1561.22	−	3198.20i	0.212435	−	0.435179i
$379$		−	8455.66i		−	1.14601i	−0.819551	−	0.573006i	$-0.805777\pi$
$379$		−	8455.66i		−	1.14601i	0.819551	−	0.573006i	$-0.194223\pi$
$380$	−433.831	−	556.064i	−0.0585660	−	0.0750671i
$381$			209.064i			0.0281120i
$382$	6082.14	+	2969.04i	0.814632	+	0.397668i
$383$	−6527.25			−0.870827			−0.435414	−	0.900231i	$-0.643398\pi$
$383$	−6527.25			−0.870827			−0.435414	+	0.900231i	$0.643398\pi$
$384$	−47.9837	+	1285.65i	−0.00637672	+	0.170854i
$385$	−8215.13			−1.08748
$386$	1622.69	+	792.126i	0.213971	+	0.104451i
$387$		−	4953.78i		−	0.650684i
$388$	−6727.57	−	8623.07i	−0.880259	−	1.12827i
$389$			683.173i			0.0890443i	0.999008	+	0.0445222i	$0.0141765\pi$
$389$			683.173i			0.0890443i	−0.999008	+	0.0445222i	$0.985823\pi$
$390$	248.364	−	508.779i	0.0322472	−	0.0660590i
$391$	−3120.34			−0.403586
$392$	−1711.09	−	8090.95i	−0.220467	−	1.04249i
$393$	−882.290			−0.113246
$394$	811.840	−	1663.07i	0.103807	−	0.212651i
$395$		−	3664.70i		−	0.466813i
$396$	−10205.0	+	7961.78i	−1.29500	+	1.01034i
$397$			2579.34i			0.326079i	0.986620	+	0.163040i	$0.0521298\pi$
$397$			2579.34i			0.326079i	−0.986620	+	0.163040i	$0.947870\pi$
$398$	4160.99	+	2031.21i	0.524049	+	0.255818i
$399$	−416.940			−0.0523136
$400$	389.203	−	1551.94i	0.0486503	−	0.193993i
$401$	−8344.02			−1.03910			−0.519552	−	0.854439i	$-0.673901\pi$
$401$	−8344.02			−1.03910			−0.519552	+	0.854439i	$0.673901\pi$
$402$	1261.09	+	615.610i	0.156461	+	0.0763777i
$403$		−	2262.75i		−	0.279691i
$404$	367.873	−	287.008i	0.0453028	−	0.0353445i
$405$			3328.47i			0.408377i
$406$	−8838.85	+	18106.6i	−1.08046	+	2.21334i
$407$	4634.02			0.564373
$408$	−1413.59	+	298.949i	−0.171527	+	0.0362750i
$409$	1939.68			0.234501			0.117251	−	0.993102i	$-0.462592\pi$
$409$	1939.68			0.234501			0.117251	+	0.993102i	$0.462592\pi$
$410$	−1375.30	+	2817.34i	−0.165662	+	0.339362i
$411$			1839.07i			0.220717i
$412$	−47.6858	−	61.1213i	−0.00570221	−	0.00730881i
$413$		−	13803.6i		−	1.64463i
$414$	−2892.23	−	1411.86i	−0.343346	−	0.167607i
$415$	3588.53			0.424467
$416$	−6239.80	−	5254.06i	−0.735412	−	0.619234i
$417$	−256.153			−0.0300812
$418$	2766.39	+	1350.43i	0.323704	+	0.158018i
$419$		−	4046.49i		−	0.471799i	−0.971777	−	0.235900i	$-0.924196\pi$
$419$		−	4046.49i		−	0.471799i	0.971777	−	0.235900i	$-0.0758037\pi$
$420$	−581.827	−	745.758i	−0.0675959	−	0.0866411i
$421$			3305.28i			0.382636i	0.981528	+	0.191318i	$0.0612761\pi$
$421$			3305.28i			0.382636i	−0.981528	+	0.191318i	$0.938724\pi$
$422$	3436.02	−	7038.76i	0.396357	−	0.811946i
$423$	−10068.6			−1.15734
$424$	5477.89	−	1158.48i	0.627429	−	0.132690i
$425$	1796.88			0.205086
$426$	345.235	−	707.222i	0.0392645	−	0.0804343i
$427$			1650.38i			0.187044i
$428$	2769.26	−	2160.53i	0.312750	−	0.244002i
$429$			2471.19i			0.278113i
$430$	−2401.93	−	1172.52i	−0.269375	−	0.131497i
$431$	−2953.12			−0.330038			−0.165019	−	0.986290i	$-0.552769\pi$
$431$	−2953.12			−0.330038			−0.165019	+	0.986290i	$0.552769\pi$
$432$	−2934.57	−	735.943i	−0.326827	−	0.0819632i
$433$	1380.70			0.153239			0.0766193	−	0.997060i	$-0.475587\pi$
$433$	1380.70			0.153239			0.0766193	+	0.997060i	$0.475587\pi$
$434$	−3397.16	−	1658.35i	−0.375735	−	0.183417i
$435$			1188.83i			0.131034i
$436$	10196.1	−	7954.79i	1.11996	−	0.873774i
$437$			765.458i			0.0837914i
$438$	−290.926	+	595.968i	−0.0317374	+	0.0650148i
$439$	−14233.4			−1.54743			−0.773717	−	0.633532i	$-0.781605\pi$
$439$	−14233.4			−1.54743			−0.773717	+	0.633532i	$0.781605\pi$
$440$	1444.97	+	6832.57i	0.156559	+	0.740295i
$441$	9579.54			1.03440
$442$	4018.74	−	8232.47i	0.432470	−	0.885924i
$443$			8541.25i			0.916042i	0.888941	+	0.458021i	$0.151442\pi$
$443$			8541.25i			0.916042i	−0.888941	+	0.458021i	$0.848558\pi$
$444$	328.200	+	420.670i	0.0350803	+	0.0449643i
$445$			8173.43i			0.870692i
$446$	10961.5	+	5350.92i	1.16377	+	0.568101i
$447$	−800.152			−0.0846664
$448$	−12461.2	+	5517.42i	−1.31415	+	0.581861i
$449$	9994.76			1.05052			0.525258	−	0.850943i	$-0.323969\pi$
$449$	9994.76			1.05052			0.525258	+	0.850943i	$0.323969\pi$
$450$	1665.53	+	813.039i	0.174475	+	0.0851712i
$451$		−	13684.1i		−	1.42874i
$452$	−6304.97	−	8081.41i	−0.656108	−	0.840968i
$453$			1781.88i			0.184812i
$454$	−713.564	+	1461.75i	−0.0737648	+	0.151109i
$455$	5997.24			0.617923
$456$	73.3361	+	346.772i	0.00753131	+	0.0356120i
$457$	6435.58			0.658739			0.329370	−	0.944201i	$-0.393164\pi$
$457$	6435.58			0.658739			0.329370	+	0.944201i	$0.393164\pi$
$458$	−2973.42	+	6091.11i	−0.303359	+	0.621438i
$459$		−	3397.73i		−	0.345517i
$460$	−1369.13	+	1068.17i	−0.138774	+	0.108269i
$461$			7851.78i			0.793262i	0.917978	+	0.396631i	$0.129821\pi$
$461$			7851.78i			0.793262i	−0.917978	+	0.396631i	$0.870179\pi$
$462$	3710.10	+	1811.11i	0.373614	+	0.182382i
$463$	7073.58			0.710016			0.355008	−	0.934863i	$-0.384478\pi$
$463$	7073.58			0.710016			0.355008	+	0.934863i	$0.384478\pi$
$464$	16614.0	+	4166.54i	1.66226	+	0.416868i
$465$	−223.048			−0.0222443
$466$	−8406.12	−	4103.51i	−0.835635	−	0.407921i
$467$		−	15753.8i		−	1.56102i	−0.625142	−	0.780511i	$-0.714959\pi$
$467$		−	15753.8i		−	1.56102i	0.625142	−	0.780511i	$-0.285041\pi$
$468$	7449.91	−	5812.29i	0.735838	−	0.574088i
$469$			14865.1i			1.46356i
$470$	−2383.16	+	4881.96i	−0.233887	+	0.479124i
$471$	2752.38			0.269264
$472$	−11480.6	+	2427.94i	−1.11957	+	0.236769i
$473$	11666.4			1.13408
$474$	−807.923	+	1655.05i	−0.0782893	+	0.160377i
$475$		−	440.799i		−	0.0425794i
$476$	−9414.46	−	12067.0i	−0.906535	−	1.16195i
$477$			6485.73i			0.622560i
$478$	3899.88	+	1903.75i	0.373172	+	0.182167i
$479$	14747.9			1.40678			0.703391	−	0.710803i	$-0.251668\pi$
$479$	14747.9			1.40678			0.703391	+	0.710803i	$0.251668\pi$
$480$	−517.913	+	615.082i	−0.0492487	+	0.0584886i
$481$	−3382.95			−0.320684
$482$	1172.11	+	572.173i	0.110764	+	0.0540701i
$483$			1026.58i			0.0967106i
$484$	−12200.6	−	15638.1i	−1.14581	−	1.46864i
$485$		−	6835.61i		−	0.639977i
$486$	2317.46	−	4747.38i	0.216301	−	0.443097i
$487$	5631.77			0.524024			0.262012	−	0.965065i	$-0.415614\pi$
$487$	5631.77			0.524024			0.262012	+	0.965065i	$0.415614\pi$
$488$	1372.63	−	290.288i	0.127328	−	0.0269277i
$489$	−3168.54			−0.293019
$490$	2267.40	−	4644.81i	0.209042	−	0.428227i
$491$			18259.0i			1.67824i	0.543945	+	0.839121i	$0.316930\pi$
$491$			18259.0i			1.67824i	−0.543945	+	0.839121i	$0.683070\pi$
$492$	1242.23	−	969.163i	0.113829	−	0.0888074i
$493$			19236.2i			1.75731i
$494$	−2019.53	−	985.847i	−0.183933	−	0.0897882i
$495$	−8089.64			−0.734550
$496$	−781.726	+	3117.12i	−0.0707672	+	0.282183i
$497$	8336.39			0.752391
$498$	−1620.65	−	791.129i	−0.145829	−	0.0711875i
$499$			729.599i			0.0654536i	0.999464	+	0.0327268i	$0.0104191\pi$
$499$			729.599i			0.0654536i	−0.999464	+	0.0327268i	$0.989581\pi$
$500$	788.433	−	615.121i	0.0705195	−	0.0550181i
$501$			1178.80i			0.105119i
$502$	−7693.27	+	15759.8i	−0.683999	+	1.40119i
$503$	1551.81			0.137558			0.0687790	−	0.997632i	$-0.478090\pi$
$503$	1551.81			0.137558			0.0687790	+	0.997632i	$0.478090\pi$
$504$	−3266.27	−	15444.6i	−0.288673	−	1.36500i
$505$	291.617			0.0256966
$506$	3325.01	−	6811.36i	0.292124	−	0.598423i
$507$			147.788i			0.0129457i
$508$	1158.03	+	1484.31i	0.101140	+	0.129637i
$509$		−	6145.59i		−	0.535164i	−0.963535	−	0.267582i	$-0.913775\pi$
$509$		−	6145.59i		−	0.535164i	0.963535	−	0.267582i	$-0.0862247\pi$
$510$	−811.507	−	396.143i	−0.0704591	−	0.0343951i
$511$	−7024.99			−0.608155
$512$	6780.69	+	9393.61i	0.585287	+	0.810826i
$513$	−833.506			−0.0717353
$514$	6053.71	+	2955.16i	0.519490	+	0.253593i
$515$		−	48.4516i		−	0.00414569i
$516$	826.261	+	1059.06i	0.0704925	+	0.0903538i
$517$		−	23712.2i		−	2.01714i
$518$	−2479.33	+	5078.96i	−0.210300	+	0.430804i
$519$	−919.695			−0.0777845
$520$	−1054.86	−	4987.94i	−0.0889591	−	0.420646i
$521$	588.432			0.0494812			0.0247406	−	0.999694i	$-0.492124\pi$
$521$	588.432			0.0494812			0.0247406	+	0.999694i	$0.492124\pi$
$522$	−8703.84	+	17830.0i	−0.729802	+	1.49502i
$523$		−	866.147i		−	0.0724168i	−0.999344	−	0.0362084i	$-0.988472\pi$
$523$		−	866.147i		−	0.0724168i	0.999344	−	0.0362084i	$-0.0115280\pi$
$524$	−6264.07	+	4887.12i	−0.522228	+	0.407433i
$525$		−	591.172i		−	0.0491445i
$526$	1070.07	+	522.360i	0.0887016	+	0.0433003i
$527$	−3609.10			−0.298321
$528$	853.739	−	3404.27i	0.0703678	−	0.280591i
$529$	−10282.3			−0.845097
$530$	3144.72	+	1535.12i	0.257732	+	0.125814i
$531$		−	13592.8i		−	1.11088i
$532$	−2960.19	+	2309.49i	−0.241241	+	0.188212i
$533$			9989.74i			0.811827i
$534$	1801.92	−	3691.27i	0.146024	−	0.299133i
$535$	2195.22			0.177398
$536$	12363.4	−	2614.64i	0.996303	−	0.210700i
$537$	−1609.14			−0.129310
$538$	8373.87	−	17154.1i	0.671047	−	1.37465i
$539$			22560.3i			1.80286i
$540$	−1163.13	−	1490.85i	−0.0926912	−	0.118807i
$541$		−	10380.3i		−	0.824926i	−0.910974	−	0.412463i	$-0.864669\pi$
$541$		−	10380.3i		−	0.824926i	0.910974	−	0.412463i	$-0.135331\pi$
$542$	−14534.9	−	7095.31i	−1.15190	−	0.562306i
$543$	−2031.05			−0.160517
$544$	−8380.27	+	9952.53i	−0.660480	+	0.784396i
$545$	8082.54			0.635262
$546$	−2708.47	−	1322.16i	−0.212292	−	0.103632i
$547$		−	1208.43i		−	0.0944584i	−0.998884	−	0.0472292i	$-0.984961\pi$
$547$		−	1208.43i		−	0.0944584i	0.998884	−	0.0472292i	$-0.0150391\pi$
$548$	10186.9	+	13057.0i	0.794090	+	1.01783i
$549$			1625.18i			0.126340i
$550$	−1914.75	+	3922.41i	−0.148446	+	0.304094i
$551$	4718.89			0.364849
$552$	853.816	−	180.567i	0.0658348	−	0.0139229i
$553$	−19508.9			−1.50019
$554$	7749.82	−	15875.7i	0.594329	−	1.21750i
$555$			333.470i			0.0255046i
$556$	−1818.63	+	1418.86i	−0.138718	+	0.108225i
$557$			10284.9i			0.782379i	0.920310	+	0.391190i	$0.127936\pi$
$557$			10284.9i			0.782379i	−0.920310	+	0.391190i	$0.872064\pi$
$558$	−3345.27	−	1633.01i	−0.253793	−	0.123891i
$559$	−8516.76			−0.644402
$560$	−8261.70	−	2071.91i	−0.623430	−	0.156346i
$561$	3941.57			0.296637
$562$	−7328.29	−	3577.36i	−0.550045	−	0.268508i
$563$		−	18420.7i		−	1.37894i	−0.724316	−	0.689469i	$-0.757844\pi$
$563$		−	18420.7i		−	1.37894i	0.724316	−	0.689469i	$-0.242156\pi$
$564$	2152.56	−	1679.39i	0.160708	−	0.125381i
$565$		−	6406.23i		−	0.477013i
$566$	9331.63	−	19116.1i	0.693000	−	1.41963i
$567$	17719.0			1.31239
$568$	−1466.30	−	6933.43i	−0.108318	−	0.512183i
$569$	−13111.3			−0.966002			−0.483001	−	0.875620i	$-0.660453\pi$
$569$	−13111.3			−0.966002			−0.483001	+	0.875620i	$0.660453\pi$
$570$	−97.1788	+	199.073i	−0.00714100	+	0.0146285i
$571$		−	12226.6i		−	0.896088i	−0.894012	−	0.448044i	$-0.852121\pi$
$571$		−	12226.6i		−	0.896088i	0.894012	−	0.448044i	$-0.147879\pi$
$572$	13688.3	+	17544.9i	1.00058	+	1.28250i
$573$		−	2125.85i		−	0.154989i
$574$	14998.0	+	7321.38i	1.09060	+	0.532384i
$575$	−1085.33			−0.0787153
$576$	−12270.9	+	5433.15i	−0.887651	+	0.393023i
$577$	3294.12			0.237671			0.118836	−	0.992914i	$-0.462084\pi$
$577$	3294.12			0.237671			0.118836	+	0.992914i	$0.462084\pi$
$578$	−643.246	−	314.005i	−0.0462898	−	0.0225967i
$579$		−	567.168i		−	0.0407093i
$580$	6585.07	+	8440.42i	0.471431	+	0.604258i
$581$		−	19103.4i		−	1.36410i
$582$	−1506.98	+	3087.09i	−0.107331	+	0.219869i
$583$	−15274.2			−1.08507
$584$	1235.63	+	5842.73i	0.0875529	+	0.413996i
$585$	5905.64			0.417381
$586$	−8391.21	+	17189.6i	−0.591532	+	1.21177i
$587$			16607.6i			1.16775i	0.811844	+	0.583874i	$0.198464\pi$
$587$			16607.6i			1.16775i	−0.811844	+	0.583874i	$0.801536\pi$
$588$	−2048.00	+	1597.81i	−0.143636	+	0.112062i
$589$			885.358i			0.0619364i
$590$	−6590.70	−	3217.30i	−0.459890	−	0.224498i
$591$	−581.284			−0.0404582
$592$	4660.29	+	1168.73i	0.323542	+	0.0811393i
$593$	−15288.4			−1.05872			−0.529359	−	0.848398i	$-0.677567\pi$
$593$	−15288.4			−1.05872			−0.529359	+	0.848398i	$0.677567\pi$
$594$	7416.88	+	3620.60i	0.512320	+	0.250093i
$595$		−	9565.65i		−	0.659081i
$596$	−5680.91	+	4432.15i	−0.390435	+	0.304610i
$597$		−	1454.36i		−	0.0997038i
$598$	−2427.34	+	4972.46i	−0.165989	+	0.340032i
$599$	−23543.0			−1.60591			−0.802955	−	0.596040i	$-0.796740\pi$
$599$	−23543.0			−1.60591			−0.802955	+	0.596040i	$0.796740\pi$
$600$	−491.681	+	103.982i	−0.0334546	+	0.00707507i
$601$	−15689.7			−1.06488			−0.532442	−	0.846467i	$-0.678725\pi$
$601$	−15689.7			−1.06488			−0.532442	+	0.846467i	$0.678725\pi$
$602$	−6241.85	+	12786.6i	−0.422590	+	0.865684i
$603$			14638.1i			0.988571i
$604$	9870.05	+	12650.9i	0.664911	+	0.852251i
$605$		−	12396.5i		−	0.833043i
$606$	−131.700	−	64.2901i	−0.00882827	−	0.00430958i
$607$	−26462.9			−1.76952			−0.884759	−	0.466048i	$-0.845677\pi$
$607$	−26462.9			−1.76952			−0.884759	+	0.466048i	$0.845677\pi$
$608$	2441.48	+	2055.79i	0.162854	+	0.137127i
$609$	6328.68			0.421102
$610$	787.995	+	384.665i	0.0523032	+	0.0255322i
$611$			17310.5i			1.14617i
$612$	−9270.65	−	11882.7i	−0.612327	−	0.784850i
$613$		−	18256.6i		−	1.20290i	−0.798912	−	0.601448i	$-0.794591\pi$
$613$		−	18256.6i		−	1.20290i	0.798912	−	0.601448i	$-0.205409\pi$
$614$	12513.8	−	25634.7i	0.822500	−	1.68491i
$615$	984.728			0.0645659
$616$	36372.9	−	7692.23i	2.37907	−	0.503131i
$617$	393.579			0.0256805			0.0128403	−	0.999918i	$-0.495913\pi$
$617$	393.579			0.0256805			0.0128403	+	0.999918i	$0.495913\pi$
$618$	−10.6817	+	21.8816i	−0.000695275	+	0.00142429i
$619$			23039.6i			1.49602i	0.663685	+	0.748012i	$0.268991\pi$
$619$			23039.6i			1.49602i	−0.663685	+	0.748012i	$0.731009\pi$
$620$	−1583.59	+	1235.49i	−0.102578	+	0.0800299i
$621$			2052.25i			0.132615i
$622$	19529.5	+	9533.47i	1.25894	+	0.614562i
$623$	43511.0			2.79812
$624$	−623.250	+	2485.20i	−0.0399839	+	0.159435i
$625$	625.000			0.0400000
$626$	−3185.24	−	1554.90i	−0.203367	−	0.0992750i
$627$		−	966.918i		−	0.0615869i
$628$	19541.3	−	15245.8i	1.24169	−	0.968749i
$629$			5395.83i			0.342044i
$630$	4328.18	−	8866.38i	0.273713	−	0.560706i
$631$	28960.4			1.82709			0.913547	−	0.406734i	$-0.133332\pi$
$631$	28960.4			1.82709			0.913547	+	0.406734i	$0.133332\pi$
$632$	3431.44	+	16225.7i	0.215974	+	1.02124i
$633$	−2460.21			−0.154478
$634$	−1189.42	+	2436.56i	−0.0745080	+	0.152631i
$635$			1176.63i			0.0735324i
$636$	−1081.78	−	1386.57i	−0.0674456	−	0.0864485i
$637$		−	16469.6i		−	1.02441i
$638$	−41990.6	−	20498.0i	−2.60568	−	1.27198i
$639$	8209.05			0.508208
$640$	−270.057	+	7235.74i	−0.0166796	+	0.446902i
$641$	−7160.30			−0.441209			−0.220604	−	0.975363i	$-0.570803\pi$
$641$	−7160.30			−0.441209			−0.220604	+	0.975363i	$0.570803\pi$
$642$	−991.404	−	483.961i	−0.0609464	−	0.0297514i
$643$			1843.33i			0.113054i	0.998401	+	0.0565270i	$0.0180027\pi$
$643$			1843.33i			0.113054i	−0.998401	+	0.0565270i	$0.981997\pi$
$644$	5686.38	+	7288.53i	0.347942	+	0.445976i
$645$			839.531i			0.0512504i
$646$	−1572.43	+	3221.17i	−0.0957687	+	0.196184i
$647$	28494.4			1.73142			0.865712	−	0.500542i	$-0.166866\pi$
$647$	28494.4			1.73142			0.865712	+	0.500542i	$0.166866\pi$
$648$	−3116.61	−	14737.0i	−0.188938	−	0.893399i
$649$	32011.7			1.93616
$650$	1397.81	−	2863.45i	0.0843489	−	0.172790i
$651$			1187.39i			0.0714860i
$652$	−22496.0	+	17551.0i	−1.35124	+	1.05422i
$653$		−	15898.2i		−	0.952746i	−0.879243	−	0.476373i	$-0.841951\pi$
$653$		−	15898.2i		−	0.952746i	0.879243	−	0.476373i	$-0.158049\pi$
$654$	−3650.23	−	1781.88i	−0.218249	−	0.106540i
$655$	−4965.61			−0.296217
$656$	3451.22	−	13761.7i	0.205408	−	0.819061i
$657$	−6917.69			−0.410783
$658$	25988.9	+	12686.7i	1.53975	+	0.751639i
$659$		−	6729.26i		−	0.397776i	−0.980022	−	0.198888i	$-0.936267\pi$
$659$		−	6729.26i		−	0.397776i	0.980022	−	0.198888i	$-0.0637331\pi$
$660$	1729.47	−	1349.30i	0.101999	−	0.0795782i
$661$			24516.3i			1.44262i	0.692611	+	0.721311i	$0.256460\pi$
$661$			24516.3i			1.44262i	−0.692611	+	0.721311i	$0.743540\pi$
$662$	5276.63	−	10809.3i	0.309792	−	0.634615i
$663$	−2877.44			−0.168553
$664$	−15888.4	+	3360.12i	−0.928599	+	0.196382i
$665$	−2346.58			−0.136837
$666$	−2441.46	+	5001.38i	−0.142049	+	0.290990i
$667$		−	11618.8i		−	0.674485i
$668$	6529.51	+	8369.20i	0.378195	+	0.484752i
$669$		−	3831.29i		−	0.221415i
$670$	7097.53	+	3464.71i	0.409256	+	0.199781i
$671$	−3827.37			−0.220200
$672$	3274.36	+	2757.09i	0.187963	+	0.158270i
$673$	−8192.84			−0.469258			−0.234629	−	0.972085i	$-0.575388\pi$
$673$	−8192.84			−0.469258			−0.234629	+	0.972085i	$0.575388\pi$
$674$	−19477.1	−	9507.86i	−1.11310	−	0.543367i
$675$		−	1181.81i		−	0.0673896i
$676$	818.616	+	1049.26i	0.0465758	+	0.0596986i
$677$			5219.11i			0.296287i	0.988966	+	0.148144i	$0.0473298\pi$
$677$			5219.11i			0.296287i	−0.988966	+	0.148144i	$0.952670\pi$
$678$	−1412.32	+	2893.17i	−0.0799998	+	0.163881i
$679$	−36389.1			−2.05668
$680$	−7955.81	+	1682.51i	−0.448664	+	0.0948844i
$681$	510.917			0.0287495
$682$	3845.84	−	7878.28i	0.215931	−	0.442339i
$683$			7903.11i			0.442759i	0.975188	+	0.221379i	$0.0710559\pi$
$683$			7903.11i			0.442759i	−0.975188	+	0.221379i	$0.928944\pi$
$684$	−2914.97	+	2274.21i	−0.162948	+	0.127129i
$685$			10350.5i			0.577330i
$686$	−1520.97	−	742.471i	−0.0846513	−	0.0413231i
$687$	2128.99			0.118233
$688$	11732.6	+	2942.34i	0.650144	+	0.163046i
$689$	11150.6			0.616549
$690$	490.154	+	239.272i	0.0270433	+	0.0132014i
$691$		−	13969.2i		−	0.769051i	−0.923114	−	0.384526i	$-0.874365\pi$
$691$		−	13969.2i		−	0.769051i	0.923114	−	0.384526i	$-0.125635\pi$
$692$	−6529.64	+	5094.31i	−0.358699	+	0.279851i
$693$			43064.9i			2.36061i
$694$	4499.97	−	9218.28i	0.246133	−	0.504209i
$695$	−1441.65			−0.0786834
$696$	−1113.16	−	5263.60i	−0.0606238	−	0.286661i
$697$	15933.7			0.865900
$698$	−11002.0	+	22537.8i	−0.596605	+	1.22216i
$699$			2938.14i			0.158985i
$700$	−3274.58	−	4197.19i	−0.176810	−	0.226627i
$701$		−	1929.28i		−	0.103948i	−0.998648	−	0.0519742i	$-0.983449\pi$
$701$		−	1929.28i		−	0.103948i	0.998648	−	0.0519742i	$-0.0165514\pi$
$702$	−5414.50	−	2643.13i	−0.291107	−	0.142106i
$703$	1323.67			0.0710142
$704$	−12795.3	−	28898.6i	−0.685004	−	1.54710i
$705$	1706.36			0.0911564
$706$	−22305.3	−	10888.5i	−1.18905	−	0.580445i
$707$		−	1552.41i		−	0.0825806i
$708$	2267.20	+	2905.98i	0.120348	+	0.154256i
$709$		−	33077.6i		−	1.75213i	−0.482197	−	0.876063i	$-0.660161\pi$
$709$		−	33077.6i		−	1.75213i	0.482197	−	0.876063i	$-0.339839\pi$
$710$	1943.01	−	3980.31i	0.102704	−	0.210392i
$711$	−19210.9			−1.01331
$712$	−7653.19	−	36188.3i	−0.402831	−	1.90480i
$713$	2179.92			0.114500
$714$	−2108.85	+	4320.03i	−0.110535	+	0.226433i
$715$			13908.1i			0.727458i
$716$	−11424.6	+	8913.24i	−0.596307	+	0.465228i
$717$		−	1363.10i		−	0.0709985i
$718$	−19491.4	−	9514.87i	−1.01311	−	0.494557i
$719$	−5643.22			−0.292707			−0.146354	−	0.989232i	$-0.546754\pi$
$719$	−5643.22			−0.292707			−0.146354	+	0.989232i	$0.546754\pi$
$720$	−8135.51	−	2040.26i	−0.421101	−	0.105605i
$721$	−257.930			−0.0133229
$722$	−16643.7	−	8124.72i	−0.857913	−	0.418796i
$723$		−	409.680i		−	0.0210735i
$724$	−14420.0	+	11250.2i	−0.740213	+	0.577502i
$725$			6690.83i			0.342746i
$726$	−2732.95	+	5598.51i	−0.139710	+	0.286198i
$727$	17112.0			0.872969			0.436484	−	0.899712i	$-0.356223\pi$
$727$	17112.0			0.872969			0.436484	+	0.899712i	$0.356223\pi$
$728$	−26553.1	+	5615.52i	−1.35182	+	0.285886i
$729$	16314.4			0.828857
$730$	−1637.36	+	3354.16i	−0.0830155	+	0.170059i
$731$			13584.3i			0.687324i
$732$	−271.070	−	347.444i	−0.0136872	−	0.0175436i
$733$			20314.2i			1.02363i	0.859095	+	0.511817i	$0.171027\pi$
$733$			20314.2i			1.02363i	−0.859095	+	0.511817i	$0.828973\pi$
$734$	21036.2	+	10269.0i	1.05785	+	0.516396i
$735$	−1623.47			−0.0814730
$736$	5061.73	−	6011.39i	0.253502	−	0.301063i
$737$	−34473.4			−1.72299
$738$	14768.9	+	7209.55i	0.736655	+	0.359603i
$739$			5845.97i			0.290998i	0.989358	+	0.145499i	$0.0464788\pi$
$739$			5845.97i			0.290998i	−0.989358	+	0.145499i	$0.953521\pi$
$740$	1847.14	+	2367.57i	0.0917595	+	0.117613i
$741$			705.873i			0.0349945i
$742$	8172.13	−	16740.8i	0.404324	−	0.828267i
$743$	4964.00			0.245103			0.122551	−	0.992462i	$-0.460892\pi$
$743$	4964.00			0.245103			0.122551	+	0.992462i	$0.460892\pi$
$744$	987.557	−	208.851i	0.0486634	−	0.0102915i
$745$	−4503.32			−0.221462
$746$	−335.839	+	687.973i	−0.0164825	+	0.0337647i
$747$		−	18811.6i		−	0.921393i
$748$	27984.3	−	21832.9i	1.36793	−	1.06723i
$749$		−	11686.2i		−	0.570099i
$750$	−282.262	−	137.788i	−0.0137423	−	0.00670841i
$751$	30765.7			1.49488			0.747441	−	0.664329i	$-0.231282\pi$
$751$	30765.7			1.49488			0.747441	+	0.664329i	$0.231282\pi$
$752$	5980.36	−	23846.6i	0.290002	−	1.15638i
$753$	5508.44			0.266585
$754$	30654.2	+	14964.0i	1.48058	+	0.722756i
$755$			10028.6i			0.483413i
$756$	−7936.47	+	6191.89i	−0.381808	+	0.297880i
$757$			34346.8i			1.64908i	0.565801	+	0.824542i	$0.308567\pi$
$757$			34346.8i			1.64908i	−0.565801	+	0.824542i	$0.691433\pi$
$758$	−10491.5	+	21492.2i	−0.502731	+	1.02986i
$759$	−2380.73			−0.113854
$760$	412.742	+	1951.66i	0.0196996	+	0.0931502i
$761$	−12083.9			−0.575610			−0.287805	−	0.957689i	$-0.592926\pi$
$761$	−12083.9			−0.575610			−0.287805	+	0.957689i	$0.592926\pi$
$762$	259.400	−	531.387i	0.0123321	−	0.0252626i
$763$		−	43027.1i		−	2.04153i
$764$	−11775.4	−	15093.1i	−0.557615	−	0.714724i
$765$		−	9419.54i		−	0.445182i
$766$	16590.6	+	8098.82i	0.782563	+	0.382014i
$767$	−23369.3			−1.10015
$768$	1717.16	−	3208.26i	0.0806805	−	0.150740i
$769$	9054.84			0.424611			0.212305	−	0.977203i	$-0.431903\pi$
$769$	9054.84			0.424611			0.212305	+	0.977203i	$0.431903\pi$
$770$	20880.8	+	10193.1i	0.977261	+	0.477057i
$771$		−	2115.92i		−	0.0988364i
$772$	−3141.62	−	4026.77i	−0.146463	−	0.187729i
$773$		−	13846.2i		−	0.644260i	−0.946695	−	0.322130i	$-0.895601\pi$
$773$		−	13846.2i		−	0.644260i	0.946695	−	0.322130i	$-0.104399\pi$
$774$	−6146.51	+	12591.3i	−0.285442	+	0.584733i
$775$	−1255.33			−0.0581844
$776$	6400.52	+	30265.0i	0.296089	+	1.40007i
$777$	1775.22			0.0819634
$778$	847.662	−	1736.45i	0.0390619	−	0.0800191i
$779$		−	3908.74i		−	0.179776i
$780$	−1262.56	+	985.025i	−0.0579574	+	0.0452174i
$781$			19332.8i			0.885762i
$782$	7931.11	+	3871.63i	0.362680	+	0.177045i
$783$	12651.7			0.577438
$784$	−5689.85	+	22688.2i	−0.259195	+	1.03354i
$785$	15490.7			0.704312
$786$	2242.56	+	1094.72i	0.101768	+	0.0496786i
$787$		−	9393.21i		−	0.425454i	−0.977112	−	0.212727i	$-0.931766\pi$
$787$		−	9393.21i		−	0.425454i	0.977112	−	0.212727i	$-0.0682344\pi$
$788$	−4126.99	+	3219.80i	−0.186571	+	0.145559i
$789$		−	374.013i		−	0.0168761i
$790$	−4547.06	+	9314.75i	−0.204781	+	0.419499i
$791$	−34103.3			−1.53296
$792$	35817.3	−	7574.73i	1.60696	−	0.339844i
$793$	2794.08			0.125120
$794$	3200.37	−	6556.04i	0.143044	−	0.293029i
$795$		−	1099.15i		−	0.0490352i
$796$	−8055.91	−	10325.7i	−0.358711	−	0.459779i
$797$		−	7921.92i		−	0.352081i	−0.984383	−	0.176041i	$-0.943671\pi$
$797$		−	7921.92i		−	0.352081i	0.984383	−	0.176041i	$-0.0563290\pi$
$798$	1059.76	+	517.328i	0.0470113	+	0.0229489i
$799$	27610.4			1.22251
$800$	−2914.86	+	3461.73i	−0.128820	+	0.152988i
$801$	42846.3			1.89001
$802$	21208.4	+	10353.0i	0.933784	+	0.455833i
$803$		−	16291.5i		−	0.715959i
$804$	−2441.54	−	3129.45i	−0.107098	−	0.137273i
$805$			5777.71i			0.252966i
$806$	−2807.55	+	5751.34i	−0.122695	+	0.251343i
$807$	−5995.75			−0.261537
$808$	−1291.15	+	273.056i	−0.0562160	+	0.0118887i
$809$	8042.02			0.349496			0.174748	−	0.984613i	$-0.444089\pi$
$809$	8042.02			0.349496			0.174748	+	0.984613i	$0.444089\pi$
$810$	4129.87	−	8460.12i	0.179147	−	0.366986i
$811$		−	28973.7i		−	1.25451i	−0.778816	−	0.627253i	$-0.784179\pi$
$811$		−	28973.7i		−	1.25451i	0.778816	−	0.627253i	$-0.215821\pi$
$812$	44932.3	−	35055.4i	1.94189	−	1.51503i
$813$			5080.29i			0.219156i
$814$	−11778.5	−	5749.76i	−0.507170	−	0.247579i
$815$	−17832.8			−0.766450
$816$	3963.92	+	994.089i	0.170055	+	0.0426471i
$817$	3332.40			0.142700
$818$	−4930.18	−	2406.70i	−0.210733	−	0.102871i
$819$		−	31438.4i		−	1.34133i
$820$	6991.36	−	5454.53i	0.297742	−	0.232293i
$821$			11126.0i			0.472960i	0.971636	+	0.236480i	$0.0759937\pi$
$821$			11126.0i			0.472960i	−0.971636	+	0.236480i	$0.924006\pi$
$822$	2281.87	−	4674.46i	0.0968240	−	0.198346i
$823$	3077.71			0.130355			0.0651775	−	0.997874i	$-0.479239\pi$
$823$	3077.71			0.130355			0.0651775	+	0.997874i	$0.479239\pi$
$824$	45.3676	+	214.522i	0.00191803	+	0.00906946i
$825$	1370.97			0.0578560
$826$	−17127.2	+	35085.4i	−0.721465	+	1.47794i
$827$			37902.1i			1.59369i	0.604181	+	0.796847i	$0.293501\pi$
$827$			37902.1i			1.59369i	−0.604181	+	0.796847i	$0.706499\pi$
$828$	5599.53	+	7177.20i	0.235020	+	0.301238i
$829$			38596.7i			1.61703i	0.588474	+	0.808516i	$0.299729\pi$
$829$			38596.7i			1.61703i	−0.588474	+	0.808516i	$0.700271\pi$
$830$	−9121.13	−	4452.54i	−0.381445	−	0.186205i
$831$	−5548.92			−0.231637
$832$	9340.92	+	21096.7i	0.389228	+	0.879081i
$833$	−26269.1			−1.09264
$834$	651.076	+	317.827i	0.0270323	+	0.0131960i
$835$			6634.37i			0.274960i
$836$	−5355.88	−	6864.91i	−0.221575	−	0.284005i
$837$			2373.71i			0.0980255i
$838$	−5020.77	+	10285.2i	−0.206968	+	0.423979i
$839$	−7585.24			−0.312123			−0.156062	−	0.987747i	$-0.549880\pi$
$839$	−7585.24			−0.312123			−0.156062	+	0.987747i	$0.549880\pi$
$840$	553.543	+	2617.44i	0.0227370	+	0.107512i
$841$	−47238.4			−1.93687
$842$	4101.10	−	8401.20i	0.167854	−	0.343853i
$843$			2561.41i			0.104650i
$844$	−17467.0	+	13627.4i	−0.712368	+	0.555777i
$845$			831.763i			0.0338621i
$846$	25592.0	+	12492.9i	1.04004	+	0.507700i
$847$	−65992.5			−2.67713
$848$	−15360.8	−	3852.26i	−0.622044	−	0.155999i
$849$	−6681.52			−0.270093
$850$	−4567.23	−	2229.52i	−0.184300	−	0.0899671i
$851$		−	3259.11i		−	0.131282i
$852$	−1755.00	+	1369.22i	−0.0705697	+	0.0550572i
$853$		−	37228.6i		−	1.49435i	−0.664625	−	0.747177i	$-0.731409\pi$
$853$		−	37228.6i		−	1.49435i	0.664625	−	0.747177i	$-0.268591\pi$
$854$	2047.75	−	4194.86i	0.0820522	−	0.168086i
$855$	−2310.73			−0.0924273
$856$	−9719.48	+	2055.50i	−0.388090	+	0.0820741i
$857$	7510.28			0.299354			0.149677	−	0.988735i	$-0.452177\pi$
$857$	7510.28			0.299354			0.149677	+	0.988735i	$0.452177\pi$
$858$	3066.19	−	6281.15i	0.122002	−	0.249924i
$859$		−	19383.6i		−	0.769918i	−0.922934	−	0.384959i	$-0.874216\pi$
$859$		−	19383.6i		−	0.769918i	0.922934	−	0.384959i	$-0.125784\pi$
$860$	4650.27	+	5960.49i	0.184387	+	0.236338i
$861$		−	5242.16i		−	0.207494i
$862$	7506.08	+	3664.14i	0.296587	+	0.144781i
$863$	7835.20			0.309054			0.154527	−	0.987989i	$-0.450615\pi$
$863$	7835.20			0.309054			0.154527	+	0.987989i	$0.450615\pi$
$864$	6545.79	+	5511.71i	0.257746	+	0.217028i
$865$	−5176.12			−0.203461
$866$	−3509.40	−	1713.14i	−0.137707	−	0.0672226i
$867$			224.830i			0.00880694i
$868$	6577.09	+	8430.20i	0.257190	+	0.329654i
$869$		−	45242.7i		−	1.76611i
$870$	1475.06	−	3021.70i	0.0574820	−	0.117753i
$871$	25166.4			0.979026
$872$	−35785.9	+	7568.09i	−1.38975	+	0.293908i
$873$	−35833.3			−1.38920
$874$	949.759	−	1945.60i	0.0367575	−	0.0752986i
$875$		−	3327.16i		−	0.128547i
$876$	1478.92	−	1153.83i	0.0570413	−	0.0445026i
$877$		−	8353.53i		−	0.321640i	−0.986984	−	0.160820i	$-0.948586\pi$
$877$		−	8353.53i		−	0.321640i	0.986984	−	0.160820i	$-0.0514139\pi$
$878$	36177.7	+	17660.4i	1.39059	+	0.678827i
$879$	6008.16			0.230546
$880$	4804.92	−	19159.5i	0.184061	−	0.733941i
$881$	17964.9			0.687008			0.343504	−	0.939151i	$-0.388386\pi$
$881$	17964.9			0.687008			0.343504	+	0.939151i	$0.388386\pi$
$882$	−24348.8	−	11886.0i	−0.929553	−	0.453768i
$883$			34012.6i			1.29628i	0.761521	+	0.648140i	$0.224453\pi$
$883$			34012.6i			1.29628i	−0.761521	+	0.648140i	$0.775547\pi$
$884$	−20429.2	+	15938.5i	−0.777273	+	0.606415i
$885$			2303.61i			0.0874971i
$886$	10597.7	−	21709.7i	0.401849	−	0.823196i
$887$	32352.3			1.22467			0.612335	−	0.790598i	$-0.290230\pi$
$887$	32352.3			1.22467			0.612335	+	0.790598i	$0.290230\pi$
$888$	−312.245	−	1476.46i	−0.0117998	−	0.0557958i
$889$	6263.74			0.236309
$890$	10141.4	−	20774.8i	0.381954	−	0.782442i
$891$			41091.7i			1.54503i
$892$	−21222.0	−	27201.4i	−0.796599	−	1.02104i
$893$		−	6773.17i		−	0.253814i
$894$	2033.79	+	992.806i	0.0760850	+	0.0371414i
$895$	−9056.38			−0.338236
$896$	38519.2	+	1437.64i	1.43620	+	0.0536027i
$897$	1737.99			0.0646933
$898$	−25404.2	−	12401.2i	−0.944040	−	0.460840i
$899$		−	13438.7i		−	0.498562i
$900$	−3224.56	−	4133.08i	−0.119428	−	0.153077i
$901$		−	17785.2i		−	0.657616i
$902$	−16978.9	+	34781.6i	−0.626757	+	1.28392i
$903$	4469.21			0.164702
$904$	5998.47	+	28363.9i	0.220693	+	1.04355i
$905$	−11430.9			−0.419863
$906$	2210.90	−	4529.08i	0.0810732	−	0.166080i
$907$			15523.0i			0.568284i	0.958782	+	0.284142i	$0.0917088\pi$
$907$			15523.0i			0.568284i	−0.958782	+	0.284142i	$0.908291\pi$
$908$	3627.40	−	2830.04i	0.132577	−	0.103434i
$909$		−	1528.70i		−	0.0557797i
$910$	−15243.5	−	7441.21i	−0.555293	−	0.271070i
$911$	8000.66			0.290970			0.145485	−	0.989360i	$-0.453526\pi$
$911$	8000.66			0.290970			0.145485	+	0.989360i	$0.453526\pi$
$912$	243.863	−	972.400i	0.00885427	−	0.0353063i
$913$	44302.3			1.60591
$914$	−16357.6	−	7985.09i	−0.591972	−	0.288975i
$915$		−	275.423i		−	0.00995104i
$916$	15115.4	−	11792.7i	0.545224	−	0.425374i
$917$			26434.2i			0.951946i
$918$	−4215.81	+	8636.17i	−0.151571	+	0.310497i
$919$	−23631.8			−0.848251			−0.424125	−	0.905603i	$-0.639418\pi$
$919$	−23631.8			−0.848251			−0.424125	+	0.905603i	$0.639418\pi$
$920$	4805.35	−	1016.25i	0.172204	−	0.0364181i
$921$	−8959.95			−0.320565
$922$	9742.27	−	19957.2i	0.347987	−	0.712860i
$923$		−	14113.4i		−	0.503302i
$924$	−7182.97	−	9206.78i	−0.255739	−	0.327793i
$925$			1876.80i			0.0667122i
$926$	−17979.3	−	8776.70i	−0.638051	−	0.311469i
$927$	−253.991			−0.00899908
$928$	−37059.0	−	31204.5i	−1.31091	−	1.10381i
$929$	−7564.75			−0.267160			−0.133580	−	0.991038i	$-0.542647\pi$
$929$	−7564.75			−0.267160			−0.133580	+	0.991038i	$0.542647\pi$
$930$	566.932	+	276.752i	0.0199897	+	0.00975811i
$931$			6444.15i			0.226851i
$932$	16274.7	+	20860.2i	0.571992	+	0.733152i
$933$		−	6826.03i		−	0.239522i
$934$	−19546.8	+	40042.1i	−0.684788	+	1.40280i
$935$	22183.5			0.775913
$936$	−26147.5	+	5529.74i	−0.913097	+	0.193104i
$937$	6226.13			0.217074			0.108537	−	0.994092i	$-0.465383\pi$
$937$	6226.13			0.217074			0.108537	+	0.994092i	$0.465383\pi$
$938$	18444.2	−	37783.4i	0.642031	−	1.31522i
$939$			1113.32i			0.0386919i
$940$	12114.8	−	9451.76i	0.420363	−	0.327960i
$941$			14012.2i			0.485426i	0.970098	+	0.242713i	$0.0780373\pi$
$941$			14012.2i			0.485426i	−0.970098	+	0.242713i	$0.921963\pi$
$942$	−6995.87	−	3415.08i	−0.241972	−	0.118120i
$943$	−9624.05			−0.332346
$944$	32193.2	+	8073.56i	1.10996	+	0.278360i
$945$	−6291.33			−0.216568
$946$	−29653.1	−	14475.4i	−1.01914	−	0.497499i
$947$			39575.5i			1.35801i	0.734135	+	0.679003i	$0.237588\pi$
$947$			39575.5i			1.35801i	−0.734135	+	0.679003i	$0.762412\pi$
$948$	4107.07	−	3204.27i	0.140708	−	0.109778i
$949$			11893.2i			0.406817i
$950$	−546.931	+	1120.40i	−0.0186787	+	0.0382637i
$951$	851.636			0.0290391
$952$	8956.79	+	42352.4i	0.304928	+	1.44186i
$953$	36806.3			1.25107			0.625537	−	0.780194i	$-0.284880\pi$
$953$	36806.3			1.25107			0.625537	+	0.780194i	$0.284880\pi$
$954$	8047.31	−	16485.1i	0.273104	−	0.559460i
$955$		−	11964.5i		−	0.405405i
$956$	−7550.39	−	9677.73i	−0.255436	−	0.327406i
$957$			14676.7i			0.495748i
$958$	−37485.4	−	18298.8i	−1.26420	−	0.617126i
$959$	55100.3			1.85535
$960$	2079.58	−	920.771i	0.0699148	−	0.0309560i
$961$	−27269.6			−0.915364
$962$	8598.60	+	4197.47i	0.288181	+	0.140678i
$963$		−	11507.7i		−	0.385078i
$964$	−2269.27	−	2908.64i	−0.0758177	−	0.0971795i
$965$		−	3192.07i		−	0.106483i
$966$	1273.76	−	2609.32i	0.0424249	−	0.0869084i
$967$	33422.7			1.11148			0.555740	−	0.831356i	$-0.312435\pi$
$967$	33422.7			1.11148			0.555740	+	0.831356i	$0.312435\pi$
$968$	11607.5	+	54886.3i	0.385412	+	1.82243i
$969$	1125.87			0.0373254
$970$	−8481.43	+	17374.4i	−0.280745	+	0.575112i
$971$		−	35405.1i		−	1.17014i	−0.810983	−	0.585069i	$-0.801067\pi$
$971$		−	35405.1i		−	1.17014i	0.810983	−	0.585069i	$-0.198933\pi$
$972$	−11780.8	+	9191.19i	−0.388755	+	0.303300i
$973$			7674.58i			0.252863i
$974$	−14314.5	−	6987.74i	−0.470911	−	0.229878i
$975$	−1000.84			−0.0328745
$976$	−3849.07	−	965.287i	−0.126235	−	0.0316579i
$977$	−45772.5			−1.49887			−0.749433	−	0.662080i	$-0.769674\pi$
$977$	−45772.5			−1.49887			−0.749433	+	0.662080i	$0.769674\pi$
$978$	8053.64	+	3931.44i	0.263320	+	0.128541i
$979$			100905.i			3.29413i
$980$	−11526.3	+	8992.62i	−0.375708	+	0.293121i
$981$		−	42369.9i		−	1.37897i
$982$	22655.2	−	46409.8i	0.736210	−	1.50814i
$983$	−18452.9			−0.598736			−0.299368	−	0.954138i	$-0.596776\pi$
$983$	−18452.9			−0.598736			−0.299368	+	0.954138i	$0.596776\pi$
$984$	−4359.94	+	922.050i	−0.141250	+	0.0298718i
$985$	−3271.51			−0.105826
$986$	23867.8	−	48893.7i	0.770897	−	1.57920i
$987$		−	9083.75i		−	0.292947i
$988$	3909.92	+	5011.55i	0.125902	+	0.161375i
$989$		−	8205.00i		−	0.263806i
$990$	20561.8	+	10037.4i	0.660099	+	0.322232i
$991$	34921.1			1.11938			0.559689	−	0.828703i	$-0.310920\pi$
$991$	34921.1			1.11938			0.559689	+	0.828703i	$0.310920\pi$
$992$	5854.59	−	6953.00i	0.187383	−	0.222538i
$993$	−3778.10			−0.120740
$994$	−21189.0	−	10343.6i	−0.676131	−	0.330058i
$995$		−	8185.29i		−	0.260795i
$996$	3137.66	+	4021.70i	0.0998199	+	0.127944i
$997$		−	18316.5i		−	0.581835i	−0.956748	−	0.290917i	$-0.906039\pi$
$997$		−	18316.5i		−	0.581835i	0.956748	−	0.290917i	$-0.0939605\pi$
$998$	905.266	−	1854.46i	0.0287131	−	0.0588195i
$999$	3548.84			0.112393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.4.d.a.21.3	✓	12
3.2	odd	2		360.4.k.c.181.10		12
4.3	odd	2		160.4.d.a.81.6		12
5.2	odd	4		200.4.f.c.149.7		12
5.3	odd	4		200.4.f.b.149.6		12
5.4	even	2		200.4.d.b.101.10		12
8.3	odd	2		160.4.d.a.81.7		12
8.5	even	2	inner	40.4.d.a.21.4	yes	12
12.11	even	2		1440.4.k.c.721.1		12
16.3	odd	4		1280.4.a.bd.1.3		6
16.5	even	4		1280.4.a.bc.1.3		6
16.11	odd	4		1280.4.a.ba.1.4		6
16.13	even	4		1280.4.a.bb.1.4		6
20.3	even	4		800.4.f.c.49.6		12
20.7	even	4		800.4.f.b.49.7		12
20.19	odd	2		800.4.d.d.401.7		12
24.5	odd	2		360.4.k.c.181.9		12
24.11	even	2		1440.4.k.c.721.7		12
40.3	even	4		800.4.f.b.49.8		12
40.13	odd	4		200.4.f.c.149.8		12
40.19	odd	2		800.4.d.d.401.6		12
40.27	even	4		800.4.f.c.49.5		12
40.29	even	2		200.4.d.b.101.9		12
40.37	odd	4		200.4.f.b.149.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.d.a.21.3	✓	12	1.1	even	1	trivial
40.4.d.a.21.4	yes	12	8.5	even	2	inner
160.4.d.a.81.6		12	4.3	odd	2
160.4.d.a.81.7		12	8.3	odd	2
200.4.d.b.101.9		12	40.29	even	2
200.4.d.b.101.10		12	5.4	even	2
200.4.f.b.149.5		12	40.37	odd	4
200.4.f.b.149.6		12	5.3	odd	4
200.4.f.c.149.7		12	5.2	odd	4
200.4.f.c.149.8		12	40.13	odd	4
360.4.k.c.181.9		12	24.5	odd	2
360.4.k.c.181.10		12	3.2	odd	2
800.4.d.d.401.6		12	40.19	odd	2
800.4.d.d.401.7		12	20.19	odd	2
800.4.f.b.49.7		12	20.7	even	4
800.4.f.b.49.8		12	40.3	even	4
800.4.f.c.49.5		12	40.27	even	4
800.4.f.c.49.6		12	20.3	even	4
1280.4.a.ba.1.4		6	16.11	odd	4
1280.4.a.bb.1.4		6	16.13	even	4
1280.4.a.bc.1.3		6	16.5	even	4
1280.4.a.bd.1.3		6	16.3	odd	4
1440.4.k.c.721.1		12	12.11	even	2
1440.4.k.c.721.7		12	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	40.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.54175 - 1.24077i) q^{2} +0.888401i q^{3} +(4.92097 + 6.30746i) q^{4} +5.00000i q^{5} +(1.10230 - 2.25809i) q^{6} +26.6173 q^{7} +(-4.68175 - 22.1378i) q^{8} +26.2107 q^{9} +(6.20386 - 12.7087i) q^{10} +61.7277i q^{11} +(-5.60356 + 4.37180i) q^{12} -45.0627i q^{13} +(-67.6545 - 33.0260i) q^{14} -4.44201 q^{15} +(-15.5681 + 62.0776i) q^{16} -71.8754 q^{17} +(-66.6211 - 32.5216i) q^{18} +17.6319i q^{19} +(-31.5373 + 24.6049i) q^{20} +23.6469i q^{21} +(76.5900 - 156.896i) q^{22} +43.4131 q^{23} +(19.6672 - 4.15927i) q^{24} -25.0000 q^{25} +(-55.9125 + 114.538i) q^{26} +47.2725i q^{27} +(130.983 + 167.888i) q^{28} -267.633i q^{29} +(11.2905 + 5.51152i) q^{30} +50.2133 q^{31} +(116.594 - 138.469i) q^{32} -54.8390 q^{33} +(182.689 + 89.1810i) q^{34} +133.087i q^{35} +(128.982 + 165.323i) q^{36} -75.0720i q^{37} +(21.8772 - 44.8160i) q^{38} +40.0338 q^{39} +(110.689 - 23.4087i) q^{40} -221.685 q^{41} +(29.3404 - 60.1044i) q^{42} -188.998i q^{43} +(-389.345 + 303.760i) q^{44} +131.054i q^{45} +(-110.345 - 53.8658i) q^{46} -384.142 q^{47} +(-55.1499 - 13.8307i) q^{48} +365.481 q^{49} +(63.5437 + 31.0193i) q^{50} -63.8542i q^{51} +(284.231 - 221.752i) q^{52} +247.445i q^{53} +(58.6544 - 120.155i) q^{54} -308.638 q^{55} +(-124.616 - 589.248i) q^{56} -15.6642 q^{57} +(-332.072 + 680.256i) q^{58} -518.596i q^{59} +(-21.8590 - 28.0178i) q^{60} +62.0042i q^{61} +(-127.630 - 62.3033i) q^{62} +697.660 q^{63} +(-468.162 + 207.287i) q^{64} +225.314 q^{65} +(139.387 + 68.0426i) q^{66} +558.476i q^{67} +(-353.697 - 453.351i) q^{68} +38.5683i q^{69} +(165.130 - 338.273i) q^{70} +313.194 q^{71} +(-122.712 - 580.248i) q^{72} -263.926 q^{73} +(-93.1472 + 190.814i) q^{74} -22.2100i q^{75} +(-111.213 + 86.7663i) q^{76} +1643.03i q^{77} +(-101.756 - 49.6728i) q^{78} -732.940 q^{79} +(-310.388 - 77.8405i) q^{80} +665.693 q^{81} +(563.468 + 275.061i) q^{82} -717.705i q^{83} +(-149.152 + 116.365i) q^{84} -359.377i q^{85} +(-234.503 + 480.385i) q^{86} +237.766 q^{87} +(1366.51 - 288.994i) q^{88} +1634.69 q^{89} +(162.608 - 333.106i) q^{90} -1199.45i q^{91} +(213.635 + 273.827i) q^{92} +44.6096i q^{93} +(976.392 + 476.633i) q^{94} -88.1597 q^{95} +(123.016 + 103.583i) q^{96} -1367.12 q^{97} +(-928.962 - 453.479i) q^{98} +1617.93i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 16 q^{4} - 36 q^{6} + 28 q^{7} - 40 q^{8} - 108 q^{9} + 30 q^{10} + 188 q^{12} + 68 q^{14} - 60 q^{15} - 56 q^{16} - 206 q^{18} + 20 q^{20} - 164 q^{22} + 604 q^{23} + 360 q^{24} - 300 q^{25}+ \cdots - 7266 q^{98}+O(q^{100}) \) 12 * q + 2 * q^2 + 16 * q^4 - 36 * q^6 + 28 * q^7 - 40 * q^8 - 108 * q^9 + 30 * q^10 + 188 * q^12 + 68 * q^14 - 60 * q^15 - 56 * q^16 - 206 * q^18 + 20 * q^20 - 164 * q^22 + 604 * q^23 + 360 * q^24 - 300 * q^25 - 308 * q^26 - 436 * q^28 + 40 * q^30 - 264 * q^31 + 72 * q^32 - 232 * q^33 - 180 * q^34 + 440 * q^36 + 820 * q^38 + 600 * q^39 + 120 * q^40 + 40 * q^41 + 884 * q^42 - 472 * q^44 - 1268 * q^46 - 940 * q^47 + 424 * q^48 + 1308 * q^49 - 50 * q^50 + 1024 * q^52 - 1512 * q^54 + 440 * q^55 - 728 * q^56 - 680 * q^57 - 360 * q^58 - 820 * q^60 + 592 * q^62 - 1300 * q^63 - 2048 * q^64 + 2928 * q^66 - 2344 * q^68 + 1160 * q^70 - 1592 * q^71 - 152 * q^72 + 432 * q^73 - 420 * q^74 + 2256 * q^76 + 3320 * q^78 + 2016 * q^79 + 1600 * q^80 + 2508 * q^81 + 88 * q^82 + 1048 * q^84 - 244 * q^86 - 1968 * q^87 + 4080 * q^88 - 424 * q^89 - 2250 * q^90 - 900 * q^92 + 292 * q^94 - 1520 * q^95 - 5920 * q^96 - 1584 * q^97 - 7266 * q^98

Introduction

L-functions

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