LMFDB - Embedded newform 40.4.d.a.21.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,4,Mod(21,40)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.54175 + 1.24077i) q^{2} -0.888401i q^{3} +(4.92097 - 6.30746i) q^{4} -5.00000i q^{5} +(1.10230 + 2.25809i) q^{6} +26.6173 q^{7} +(-4.68175 + 22.1378i) q^{8} +26.2107 q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 12 * q + 2 * q^2 + 16 * q^4 - 36 * q^6 + 28 * q^7 - 40 * q^8 - 108 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	$-0.972756\pi$
$3$		−	0.888401i		−	0.170973i	0.996339	−	0.0854865i	$-0.0272444\pi$
$4$	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	$-0.679015\pi$
$11$		−	61.7277i		−	1.69196i	0.533212	−	0.845982i	$-0.320985\pi$
$12$	−5.60356	−	4.37180i	−0.134801	−	0.105169i
$13$			45.0627i			0.961396i	0.876886	+	0.480698i	$0.159617\pi$
$13$			45.0627i			0.961396i	−0.876886	+	0.480698i	$0.840383\pi$
$14$	−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	$-0.966052\pi$
$19$		−	17.6319i		−	0.212897i	0.994318	−	0.106449i	$-0.0339480\pi$
$20$	−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	$0.327591\pi$
$29$			267.633i			1.71373i	−0.515540	+	0.856866i	$0.672409\pi$
$30$	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	$0.0533372\pi$
$37$			75.0720i			0.333561i	−0.985994	+	0.166781i	$0.946663\pi$
$38$	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	$0.108783\pi$
$43$			188.998i			0.670277i	−0.942169	+	0.335139i	$0.891217\pi$
$44$	−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	$-0.896098\pi$
$53$		−	247.445i		−	0.641306i	0.947197	−	0.320653i	$-0.103902\pi$
$54$	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	$0.193896\pi$
$59$			518.596i			1.14433i	−0.820139	+	0.572165i	$0.806104\pi$
$60$	−21.8590	+	28.0178i	−0.0470330	+	0.0602847i
$61$		−	62.0042i		−	0.130145i	−0.997881	−	0.0650723i	$-0.979272\pi$
$61$		−	62.0042i		−	0.130145i	0.997881	−	0.0650723i	$-0.0207278\pi$
$62$	−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	$-0.829953\pi$
$67$		−	558.476i		−	1.01834i	0.860666	−	0.509169i	$-0.170047\pi$
$68$	−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	$0.157396\pi$
$83$			717.705i			0.949137i	−0.880218	+	0.474569i	$0.842604\pi$
$84$	−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	$0.00914620\pi$
$101$			58.3234i			0.0574594i	−0.999587	+	0.0287297i	$0.990854\pi$
$102$	−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	$0.0635540\pi$
$107$			439.045i			0.396674i	−0.980134	+	0.198337i	$0.936446\pi$
$108$	−298.169	−	232.627i	−0.265661	−	0.207264i
$109$			1616.51i			1.42049i	0.703955	+	0.710245i	$0.251416\pi$
$109$			1616.51i			1.42049i	−0.703955	+	0.710245i	$0.748584\pi$
$110$	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	$-0.892553\pi$
$131$		−	993.121i		−	0.662362i	0.943567	−	0.331181i	$-0.107447\pi$
$132$	−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	$-0.971962\pi$
$139$		−	288.330i		−	0.175941i	0.996123	−	0.0879707i	$-0.0280382\pi$
$140$	−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	$-0.920358\pi$
$149$		−	900.665i		−	0.495204i	0.968862	−	0.247602i	$-0.0796425\pi$
$150$	−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	$0.288597\pi$
$157$			3098.13i			1.57489i	−0.616385	+	0.787445i	$0.711403\pi$
$158$	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	$-0.672377\pi$
$163$		−	3566.57i		−	1.71383i	0.515454	−	0.856917i	$-0.327623\pi$
$164$	−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	$-0.926953\pi$
$173$		−	1035.22i		−	0.454952i	0.973784	−	0.227476i	$-0.0730473\pi$
$174$	−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	$-0.876557\pi$
$179$		−	1811.28i		−	0.756319i	0.925740	−	0.378160i	$-0.123443\pi$
$180$	−826.616	−	644.911i	−0.342291	−	0.267049i
$181$		−	2286.18i		−	0.938842i	−0.882975	−	0.469421i	$-0.844463\pi$
$181$		−	2286.18i		−	0.938842i	0.882975	−	0.469421i	$-0.155537\pi$
$182$	−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	$-0.962250\pi$
$197$		−	654.303i		−	0.236635i	0.992976	−	0.118318i	$-0.0377501\pi$
$198$	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	$-0.850796\pi$
$211$		−	2769.26i		−	0.903524i	0.892139	−	0.451762i	$-0.149204\pi$
$212$	−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	$0.0267939\pi$
$227$			575.097i			0.168152i	−0.996459	+	0.0840761i	$0.973206\pi$
$228$	−77.0833	+	98.8016i	−0.0223902	+	0.0286987i
$229$			2396.42i			0.691529i	0.938321	+	0.345765i	$0.112380\pi$
$229$			2396.42i			0.691529i	−0.938321	+	0.345765i	$0.887620\pi$
$230$	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	$0.284584\pi$
$251$			6200.39i			1.55922i	−0.626263	+	0.779612i	$0.715416\pi$
$252$	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	$-0.722813\pi$
$269$		−	6748.92i		−	1.52970i	0.644209	−	0.764849i	$-0.277187\pi$
$270$	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	$-0.763103\pi$
$277$		−	6245.97i		−	1.35481i	0.735608	−	0.677407i	$-0.236897\pi$
$278$	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	$-0.710148\pi$
$283$		−	7520.83i		−	1.57974i	0.613273	−	0.789871i	$-0.289852\pi$
$284$	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	$0.235520\pi$
$293$			6762.89i			1.34844i	−0.738531	+	0.674219i	$0.764480\pi$
$294$	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	$-0.613159\pi$
$307$		−	10085.5i		−	1.87495i	0.348058	−	0.937473i	$-0.386841\pi$
$308$	−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	$0.0270645\pi$
$317$			958.616i			0.169846i	−0.996388	+	0.0849231i	$0.972936\pi$
$318$	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	$-0.885129\pi$
$331$		−	4252.70i		−	0.706192i	0.935587	−	0.353096i	$-0.114871\pi$
$332$	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	$-0.909487\pi$
$347$		−	3626.75i		−	0.561078i	0.959843	−	0.280539i	$-0.0905132\pi$
$348$	1170.04	−	1499.70i	0.180232	−	0.231012i
$349$			8867.03i			1.36000i	0.733210	+	0.680002i	$0.238021\pi$
$349$			8867.03i			1.36000i	−0.733210	+	0.680002i	$0.761979\pi$
$350$	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	$0.00598028\pi$
$373$			270.669i			0.0375730i	−0.999824	+	0.0187865i	$0.994020\pi$
$374$	−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	$0.194223\pi$
$379$			8455.66i			1.14601i	−0.819551	+	0.573006i	$0.805777\pi$
$380$	−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	$-0.985823\pi$
$389$		−	683.173i		−	0.0890443i	0.999008	−	0.0445222i	$-0.0141765\pi$
$390$	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	$-0.947870\pi$
$397$		−	2579.34i		−	0.326079i	0.986620	−	0.163040i	$-0.0521298\pi$
$398$	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	$0.0758037\pi$
$419$			4046.49i			0.471799i	−0.971777	+	0.235900i	$0.924196\pi$
$420$	−581.827	+	745.758i	−0.0675959	+	0.0866411i
$421$		−	3305.28i		−	0.382636i	−0.981528	−	0.191318i	$-0.938724\pi$
$421$		−	3305.28i		−	0.382636i	0.981528	−	0.191318i	$-0.0612761\pi$
$422$	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	$-0.848558\pi$
$443$		−	8541.25i		−	0.916042i	0.888941	−	0.458021i	$-0.151442\pi$
$444$	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	$-0.870179\pi$
$461$		−	7851.78i		−	0.793262i	0.917978	−	0.396631i	$-0.129821\pi$
$462$	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	$0.285041\pi$
$467$			15753.8i			1.56102i	−0.625142	+	0.780511i	$0.714959\pi$
$468$	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	$-0.683070\pi$
$491$		−	18259.0i		−	1.67824i	0.543945	−	0.839121i	$-0.316930\pi$
$492$	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	$-0.989581\pi$
$499$		−	729.599i		−	0.0654536i	0.999464	−	0.0327268i	$-0.0104191\pi$
$500$	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	$0.0862247\pi$
$509$			6145.59i			0.535164i	−0.963535	+	0.267582i	$0.913775\pi$
$510$	−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	$0.0115280\pi$
$523$			866.147i			0.0724168i	−0.999344	+	0.0362084i	$0.988472\pi$
$524$	−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	$0.135331\pi$
$541$			10380.3i			0.824926i	−0.910974	+	0.412463i	$0.864669\pi$
$542$	−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	$0.0150391\pi$
$547$			1208.43i			0.0944584i	−0.998884	+	0.0472292i	$0.984961\pi$
$548$	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	$-0.872064\pi$
$557$		−	10284.9i		−	0.782379i	0.920310	−	0.391190i	$-0.127936\pi$
$558$	−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	$0.242156\pi$
$563$			18420.7i			1.37894i	−0.724316	+	0.689469i	$0.757844\pi$
$564$	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	$0.147879\pi$
$571$			12226.6i			0.896088i	−0.894012	+	0.448044i	$0.852121\pi$
$572$	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	$-0.801536\pi$
$587$		−	16607.6i		−	1.16775i	0.811844	−	0.583874i	$-0.198464\pi$
$588$	−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	$0.205409\pi$
$613$			18256.6i			1.20290i	−0.798912	+	0.601448i	$0.794591\pi$
$614$	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	$-0.731009\pi$
$619$		−	23039.6i		−	1.49602i	0.663685	−	0.748012i	$-0.268991\pi$
$620$	−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	$-0.981997\pi$
$643$		−	1843.33i		−	0.113054i	0.998401	−	0.0565270i	$-0.0180027\pi$
$644$	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	$0.158049\pi$
$653$			15898.2i			0.952746i	−0.879243	+	0.476373i	$0.841951\pi$
$654$	−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	$0.0637331\pi$
$659$			6729.26i			0.397776i	−0.980022	+	0.198888i	$0.936267\pi$
$660$	1729.47	+	1349.30i	0.101999	+	0.0795782i
$661$		−	24516.3i		−	1.44262i	−0.692611	−	0.721311i	$-0.743540\pi$
$661$		−	24516.3i		−	1.44262i	0.692611	−	0.721311i	$-0.256460\pi$
$662$	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	$-0.952670\pi$
$677$		−	5219.11i		−	0.296287i	0.988966	−	0.148144i	$-0.0473298\pi$
$678$	−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	$-0.928944\pi$
$683$		−	7903.11i		−	0.442759i	0.975188	−	0.221379i	$-0.0710559\pi$
$684$	−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	$0.125635\pi$
$691$			13969.2i			0.769051i	−0.923114	+	0.384526i	$0.874365\pi$
$692$	−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	$0.0165514\pi$
$701$			1929.28i			0.103948i	−0.998648	+	0.0519742i	$0.983449\pi$
$702$	−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	$0.339839\pi$
$709$			33077.6i			1.75213i	−0.482197	+	0.876063i	$0.660161\pi$
$710$	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	$-0.828973\pi$
$733$		−	20314.2i		−	1.02363i	0.859095	−	0.511817i	$-0.171027\pi$
$734$	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	$-0.953521\pi$
$739$		−	5845.97i		−	0.290998i	0.989358	−	0.145499i	$-0.0464788\pi$
$740$	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	$-0.691433\pi$
$757$		−	34346.8i		−	1.64908i	0.565801	−	0.824542i	$-0.308567\pi$
$758$	−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	$0.104399\pi$
$773$			13846.2i			0.644260i	−0.946695	+	0.322130i	$0.895601\pi$
$774$	−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	$0.0682344\pi$
$787$			9393.21i			0.425454i	−0.977112	+	0.212727i	$0.931766\pi$
$788$	−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	$0.0563290\pi$
$797$			7921.92i			0.352081i	−0.984383	+	0.176041i	$0.943671\pi$
$798$	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	$0.215821\pi$
$811$			28973.7i			1.25451i	−0.778816	+	0.627253i	$0.784179\pi$
$812$	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	$-0.924006\pi$
$821$		−	11126.0i		−	0.472960i	0.971636	−	0.236480i	$-0.0759937\pi$
$822$	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	$-0.706499\pi$
$827$		−	37902.1i		−	1.59369i	0.604181	−	0.796847i	$-0.293501\pi$
$828$	5599.53	−	7177.20i	0.235020	−	0.301238i
$829$		−	38596.7i		−	1.61703i	−0.588474	−	0.808516i	$-0.700271\pi$
$829$		−	38596.7i		−	1.61703i	0.588474	−	0.808516i	$-0.299729\pi$
$830$	−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	$0.268591\pi$
$853$			37228.6i			1.49435i	−0.664625	+	0.747177i	$0.731409\pi$
$854$	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	$0.125784\pi$
$859$			19383.6i			0.769918i	−0.922934	+	0.384959i	$0.874216\pi$
$860$	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	$0.0514139\pi$
$877$			8353.53i			0.321640i	−0.986984	+	0.160820i	$0.948586\pi$
$878$	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	$-0.775547\pi$
$883$		−	34012.6i		−	1.29628i	0.761521	−	0.648140i	$-0.224453\pi$
$884$	−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	$-0.908291\pi$
$907$		−	15523.0i		−	0.568284i	0.958782	−	0.284142i	$-0.0917088\pi$
$908$	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	$-0.921963\pi$
$941$		−	14012.2i		−	0.485426i	0.970098	−	0.242713i	$-0.0780373\pi$
$942$	−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	$-0.762412\pi$
$947$		−	39575.5i		−	1.35801i	0.734135	−	0.679003i	$-0.237588\pi$
$948$	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	$0.198933\pi$
$971$			35405.1i			1.17014i	−0.810983	+	0.585069i	$0.801067\pi$
$972$	−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	$0.0939605\pi$
$997$			18316.5i			0.581835i	−0.956748	+	0.290917i	$0.906039\pi$
$998$	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.21.4	yes	12
3.2	odd	2		360.4.k.c.181.9		12
4.3	odd	2		160.4.d.a.81.7		12
5.2	odd	4		200.4.f.b.149.5		12
5.3	odd	4		200.4.f.c.149.8		12
5.4	even	2		200.4.d.b.101.9		12
8.3	odd	2		160.4.d.a.81.6		12
8.5	even	2	inner	40.4.d.a.21.3	✓	12
12.11	even	2		1440.4.k.c.721.7		12
16.3	odd	4		1280.4.a.ba.1.4		6
16.5	even	4		1280.4.a.bb.1.4		6
16.11	odd	4		1280.4.a.bd.1.3		6
16.13	even	4		1280.4.a.bc.1.3		6
20.3	even	4		800.4.f.b.49.8		12
20.7	even	4		800.4.f.c.49.5		12
20.19	odd	2		800.4.d.d.401.6		12
24.5	odd	2		360.4.k.c.181.10		12
24.11	even	2		1440.4.k.c.721.1		12
40.3	even	4		800.4.f.c.49.6		12
40.13	odd	4		200.4.f.b.149.6		12
40.19	odd	2		800.4.d.d.401.7		12
40.27	even	4		800.4.f.b.49.7		12
40.29	even	2		200.4.d.b.101.10		12
40.37	odd	4		200.4.f.c.149.7		12

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

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

\(f(q)\)	\(=\)	\(q+(-2.54175 + 1.24077i) q^{2} -0.888401i q^{3} +(4.92097 - 6.30746i) q^{4} -5.00000i q^{5} +(1.10230 + 2.25809i) q^{6} +26.6173 q^{7} +(-4.68175 + 22.1378i) q^{8} +26.2107 q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 16 q^{4} - 36 q^{6} + 28 q^{7} - 40 q^{8} - 108 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 + 16 * q^4 - 36 * q^6 + 28 * q^7 - 40 * q^8 - 108 * q^9	\( 12 q + 2 q^{2} + 16 q^{4} - 36 q^{6} + 28 q^{7} - 40 q^{8} - 108 q^{9} + 30 q^{10} + 188 q^{12} + 68 q^{14} - 60 q^{15} - 56 q^{16} - 206 q^{18} + 20 q^{20} - 164 q^{22} + 604 q^{23} + 360 q^{24} - 300 q^{25} - 308 q^{26} - 436 q^{28} + 40 q^{30} - 264 q^{31} + 72 q^{32} - 232 q^{33} - 180 q^{34} + 440 q^{36} + 820 q^{38} + 600 q^{39} + 120 q^{40} + 40 q^{41} + 884 q^{42} - 472 q^{44} - 1268 q^{46} - 940 q^{47} + 424 q^{48} + 1308 q^{49} - 50 q^{50} + 1024 q^{52} - 1512 q^{54} + 440 q^{55} - 728 q^{56} - 680 q^{57} - 360 q^{58} - 820 q^{60} + 592 q^{62} - 1300 q^{63} - 2048 q^{64} + 2928 q^{66} - 2344 q^{68} + 1160 q^{70} - 1592 q^{71} - 152 q^{72} + 432 q^{73} - 420 q^{74} + 2256 q^{76} + 3320 q^{78} + 2016 q^{79} + 1600 q^{80} + 2508 q^{81} + 88 q^{82} + 1048 q^{84} - 244 q^{86} - 1968 q^{87} + 4080 q^{88} - 424 q^{89} - 2250 q^{90} - 900 q^{92} + 292 q^{94} - 1520 q^{95} - 5920 q^{96} - 1584 q^{97} - 7266 q^{98}+O(q^{100}) \) 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

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