LMFDB - Embedded newform 136.4.c.b.69.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,4,Mod(69,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, 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("136.69");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	136.c (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:	$8.02425976078$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			69.4
Character	$\chi$	$=$	136.69
Dual form			136.4.c.b.69.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.56626 + 1.18926i) q^{2} -7.88789i q^{3} +(5.17134 - 6.10387i) q^{4} +14.0362i q^{5} +(9.38073 + 20.2424i) q^{6} -13.6466 q^{7} +(-6.01189 + 21.8142i) q^{8} -35.2189 q^{9} +O(q^{10})$	\(q+(-2.56626 + 1.18926i) q^{2} -7.88789i q^{3} +(5.17134 - 6.10387i) q^{4} +14.0362i q^{5} +(9.38073 + 20.2424i) q^{6} -13.6466 q^{7} +(-6.01189 + 21.8142i) q^{8} -35.2189 q^{9} +(-16.6927 - 36.0206i) q^{10} -23.7821i q^{11} +(-48.1467 - 40.7909i) q^{12} +81.1088i q^{13} +(35.0206 - 16.2293i) q^{14} +110.716 q^{15} +(-10.5146 - 63.1304i) q^{16} +17.0000 q^{17} +(90.3806 - 41.8843i) q^{18} +92.7147i q^{19} +(85.6755 + 72.5861i) q^{20} +107.643i q^{21} +(28.2830 + 61.0310i) q^{22} +106.498 q^{23} +(172.068 + 47.4212i) q^{24} -72.0160 q^{25} +(-96.4592 - 208.146i) q^{26} +64.8296i q^{27} +(-70.5710 + 83.2970i) q^{28} +174.650i q^{29} +(-284.127 + 131.670i) q^{30} -144.012 q^{31} +(102.061 + 149.504i) q^{32} -187.591 q^{33} +(-43.6263 + 20.2174i) q^{34} -191.547i q^{35} +(-182.129 + 214.972i) q^{36} +317.407i q^{37} +(-110.262 - 237.930i) q^{38} +639.777 q^{39} +(-306.189 - 84.3844i) q^{40} +405.570 q^{41} +(-128.015 - 276.239i) q^{42} +180.392i q^{43} +(-145.163 - 122.985i) q^{44} -494.341i q^{45} +(-273.302 + 126.654i) q^{46} -114.554 q^{47} +(-497.966 + 82.9379i) q^{48} -156.771 q^{49} +(184.812 - 85.6456i) q^{50} -134.094i q^{51} +(495.078 + 419.441i) q^{52} -373.241i q^{53} +(-77.0990 - 166.369i) q^{54} +333.811 q^{55} +(82.0417 - 297.688i) q^{56} +731.324 q^{57} +(-207.704 - 448.197i) q^{58} +176.045i q^{59} +(572.552 - 675.799i) q^{60} -562.626i q^{61} +(369.573 - 171.268i) q^{62} +480.617 q^{63} +(-439.714 - 262.289i) q^{64} -1138.46 q^{65} +(481.406 - 223.094i) q^{66} +933.658i q^{67} +(87.9127 - 103.766i) q^{68} -840.047i q^{69} +(227.798 + 491.557i) q^{70} -830.201 q^{71} +(211.732 - 768.270i) q^{72} -234.958 q^{73} +(-377.479 - 814.549i) q^{74} +568.055i q^{75} +(565.919 + 479.459i) q^{76} +324.544i q^{77} +(-1641.83 + 760.860i) q^{78} -317.026 q^{79} +(886.113 - 147.585i) q^{80} -439.541 q^{81} +(-1040.80 + 482.327i) q^{82} +198.641i q^{83} +(657.038 + 556.657i) q^{84} +238.616i q^{85} +(-214.532 - 462.932i) q^{86} +1377.62 q^{87} +(518.787 + 142.975i) q^{88} -1541.50 q^{89} +(587.898 + 1268.60i) q^{90} -1106.86i q^{91} +(550.738 - 650.052i) q^{92} +1135.95i q^{93} +(293.975 - 136.234i) q^{94} -1301.37 q^{95} +(1179.27 - 805.049i) q^{96} +180.644 q^{97} +(402.315 - 186.441i) q^{98} +837.579i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} + 5 q^{4} + 40 q^{6} + 84 q^{7} + 13 q^{8} - 216 q^{9}+O(q^{10}) $ 24 * q + q^2 + 5 * q^4 + 40 * q^6 + 84 * q^7 + 13 * q^8 - 216 * q^9	$ 24 q + q^{2} + 5 q^{4} + 40 q^{6} + 84 q^{7} + 13 q^{8} - 216 q^{9} - 16 q^{10} - 18 q^{12} + 26 q^{14} - 180 q^{15} - 103 q^{16} + 408 q^{17} - 5 q^{18} - 24 q^{20} + 172 q^{22} + 624 q^{23} - 310 q^{24} - 600 q^{25} - 180 q^{26} - 132 q^{28} - 80 q^{30} - 744 q^{31} - 39 q^{32} - 280 q^{33} + 17 q^{34} + 791 q^{36} - 162 q^{38} + 1236 q^{39} - 1396 q^{40} + 1132 q^{42} + 886 q^{44} - 1246 q^{46} - 956 q^{47} - 2226 q^{48} + 1688 q^{49} + 2505 q^{50} + 2544 q^{52} - 3264 q^{54} + 1684 q^{55} - 1100 q^{56} - 168 q^{57} + 2800 q^{58} + 2520 q^{60} - 1946 q^{62} - 2520 q^{63} - 2143 q^{64} - 72 q^{65} + 3660 q^{66} + 85 q^{68} - 5084 q^{70} + 1532 q^{71} - 2277 q^{72} + 216 q^{73} + 2188 q^{74} + 2094 q^{76} - 4748 q^{78} - 3176 q^{79} + 116 q^{80} + 2040 q^{81} + 3198 q^{82} + 5916 q^{84} - 2066 q^{86} - 236 q^{87} - 3598 q^{88} - 424 q^{89} + 2180 q^{90} + 1940 q^{92} - 2156 q^{94} - 1248 q^{95} - 4674 q^{96} - 1304 q^{97} + 3705 q^{98}+O(q^{100}) $ 24 * q + q^2 + 5 * q^4 + 40 * q^6 + 84 * q^7 + 13 * q^8 - 216 * q^9 - 16 * q^10 - 18 * q^12 + 26 * q^14 - 180 * q^15 - 103 * q^16 + 408 * q^17 - 5 * q^18 - 24 * q^20 + 172 * q^22 + 624 * q^23 - 310 * q^24 - 600 * q^25 - 180 * q^26 - 132 * q^28 - 80 * q^30 - 744 * q^31 - 39 * q^32 - 280 * q^33 + 17 * q^34 + 791 * q^36 - 162 * q^38 + 1236 * q^39 - 1396 * q^40 + 1132 * q^42 + 886 * q^44 - 1246 * q^46 - 956 * q^47 - 2226 * q^48 + 1688 * q^49 + 2505 * q^50 + 2544 * q^52 - 3264 * q^54 + 1684 * q^55 - 1100 * q^56 - 168 * q^57 + 2800 * q^58 + 2520 * q^60 - 1946 * q^62 - 2520 * q^63 - 2143 * q^64 - 72 * q^65 + 3660 * q^66 + 85 * q^68 - 5084 * q^70 + 1532 * q^71 - 2277 * q^72 + 216 * q^73 + 2188 * q^74 + 2094 * q^76 - 4748 * q^78 - 3176 * q^79 + 116 * q^80 + 2040 * q^81 + 3198 * q^82 + 5916 * q^84 - 2066 * q^86 - 236 * q^87 - 3598 * q^88 - 424 * q^89 + 2180 * q^90 + 1940 * q^92 - 2156 * q^94 - 1248 * q^95 - 4674 * q^96 - 1304 * q^97 + 3705 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	−2.56626	+	1.18926i	−0.907308	+	0.420466i
$2$	−2.56626	+	1.18926i	−0.907308	+	0.420466i
$3$		−	7.88789i		−	1.51803i	−0.651076	−	0.759013i	$-0.725682\pi$
$3$		−	7.88789i		−	1.51803i	0.651076	−	0.759013i	$-0.274318\pi$
$4$	5.17134	−	6.10387i	0.646417	−	0.762984i
$5$			14.0362i			1.25544i	0.778439	+	0.627720i	$0.216012\pi$
$5$			14.0362i			1.25544i	−0.778439	+	0.627720i	$0.783988\pi$
$6$	9.38073	+	20.2424i	0.638278	+	1.37732i
$7$	−13.6466			−0.736846			−0.368423	−	0.929658i	$-0.620102\pi$
$7$	−13.6466			−0.736846			−0.368423	+	0.929658i	$0.620102\pi$
$8$	−6.01189	+	21.8142i	−0.265691	+	0.964058i
$9$	−35.2189			−1.30440
$10$	−16.6927	−	36.0206i	−0.527869	−	1.13907i
$11$		−	23.7821i		−	0.651871i	−0.945392	−	0.325935i	$-0.894321\pi$
$11$		−	23.7821i		−	0.651871i	0.945392	−	0.325935i	$-0.105679\pi$
$12$	−48.1467	−	40.7909i	−1.15823	−	0.981278i
$13$			81.1088i			1.73042i	0.501406	+	0.865212i	$0.332816\pi$
$13$			81.1088i			1.73042i	−0.501406	+	0.865212i	$0.667184\pi$
$14$	35.0206	−	16.2293i	0.668546	−	0.309818i
$15$	110.716			1.90579
$16$	−10.5146	−	63.1304i	−0.164290	−	0.986412i
$17$	17.0000			0.242536
$17$	17.0000			0.242536
$18$	90.3806	−	41.8843i	1.18350	−	0.548457i
$19$			92.7147i			1.11949i	0.828667	+	0.559743i	$0.189100\pi$
$19$			92.7147i			1.11949i	−0.828667	+	0.559743i	$0.810900\pi$
$20$	85.6755	+	72.5861i	0.957881	+	0.811537i
$21$			107.643i			1.11855i
$22$	28.2830	+	61.0310i	0.274089	+	0.591448i
$23$	106.498			0.965497			0.482748	−	0.875759i	$-0.339639\pi$
$23$	106.498			0.965497			0.482748	+	0.875759i	$0.339639\pi$
$24$	172.068	+	47.4212i	1.46347	+	0.403325i
$25$	−72.0160			−0.576128
$26$	−96.4592	−	208.146i	−0.727584	−	1.57003i
$27$			64.8296i			0.462091i
$28$	−70.5710	+	83.2970i	−0.476309	+	0.562202i
$29$			174.650i			1.11833i	0.829055	+	0.559167i	$0.188879\pi$
$29$			174.650i			1.11833i	−0.829055	+	0.559167i	$0.811121\pi$
$30$	−284.127	+	131.670i	−1.72914	+	0.801319i
$31$	−144.012			−0.834367			−0.417184	−	0.908822i	$-0.636983\pi$
$31$	−144.012			−0.834367			−0.417184	+	0.908822i	$0.636983\pi$
$32$	102.061	+	149.504i	0.563815	+	0.825901i
$33$	−187.591			−0.989556
$34$	−43.6263	+	20.2174i	−0.220055	+	0.101978i
$35$		−	191.547i		−	0.925065i
$36$	−182.129	+	214.972i	−0.843188	+	0.995239i
$37$			317.407i			1.41031i	0.709053	+	0.705155i	$0.249123\pi$
$37$			317.407i			1.41031i	−0.709053	+	0.705155i	$0.750877\pi$
$38$	−110.262	−	237.930i	−0.470705	−	1.01572i
$39$	639.777			2.62683
$40$	−306.189	−	84.3844i	−1.21032	−	0.333559i
$41$	405.570			1.54486			0.772431	−	0.635099i	$-0.219041\pi$
$41$	405.570			1.54486			0.772431	+	0.635099i	$0.219041\pi$
$42$	−128.015	−	276.239i	−0.470312	−	1.01487i
$43$			180.392i			0.639756i	0.947459	+	0.319878i	$0.103642\pi$
$43$			180.392i			0.639756i	−0.947459	+	0.319878i	$0.896358\pi$
$44$	−145.163	−	122.985i	−0.497367	−	0.421380i
$45$		−	494.341i		−	1.63760i
$46$	−273.302	+	126.654i	−0.876003	+	0.405958i
$47$	−114.554			−0.355520			−0.177760	−	0.984074i	$-0.556885\pi$
$47$	−114.554			−0.355520			−0.177760	+	0.984074i	$0.556885\pi$
$48$	−497.966	+	82.9379i	−1.49740	+	0.249397i
$49$	−156.771			−0.457059
$50$	184.812	−	85.6456i	0.522726	−	0.242242i
$51$		−	134.094i		−	0.368175i
$52$	495.078	+	419.441i	1.32029	+	1.11858i
$53$		−	373.241i		−	0.967332i	−0.875253	−	0.483666i	$-0.839305\pi$
$53$		−	373.241i		−	0.967332i	0.875253	−	0.483666i	$-0.160695\pi$
$54$	−77.0990	−	166.369i	−0.194293	−	0.419259i
$55$	333.811			0.818384
$56$	82.0417	−	297.688i	0.195773	−	0.710362i
$57$	731.324			1.69941
$58$	−207.704	−	448.197i	−0.470221	−	1.01467i
$59$			176.045i			0.388459i	0.980956	+	0.194229i	$0.0622206\pi$
$59$			176.045i			0.388459i	−0.980956	+	0.194229i	$0.937779\pi$
$60$	572.552	−	675.799i	1.23193	−	1.45409i
$61$		−	562.626i		−	1.18093i	−0.807062	−	0.590467i	$-0.798944\pi$
$61$		−	562.626i		−	1.18093i	0.807062	−	0.590467i	$-0.201056\pi$
$62$	369.573	−	171.268i	0.757029	−	0.350823i
$63$	480.617			0.961143
$64$	−439.714	−	262.289i	−0.858817	−	0.512283i
$65$	−1138.46			−2.17244
$66$	481.406	−	223.094i	0.897833	−	0.416075i
$67$			933.658i			1.70246i	0.524796	+	0.851228i	$0.324141\pi$
$67$			933.658i			1.70246i	−0.524796	+	0.851228i	$0.675859\pi$
$68$	87.9127	−	103.766i	0.156779	−	0.185051i
$69$		−	840.047i		−	1.46565i
$70$	227.798	+	491.557i	0.388958	+	0.839319i
$71$	−830.201			−1.38770			−0.693850	−	0.720119i	$-0.744087\pi$
$71$	−830.201			−1.38770			−0.693850	+	0.720119i	$0.744087\pi$
$72$	211.732	−	768.270i	0.346568	−	1.25752i
$73$	−234.958			−0.376709			−0.188354	−	0.982101i	$-0.560315\pi$
$73$	−234.958			−0.376709			−0.188354	+	0.982101i	$0.560315\pi$
$74$	−377.479	−	814.549i	−0.592987	−	1.27959i
$75$			568.055i			0.874578i
$76$	565.919	+	479.459i	0.854150	+	0.723654i
$77$			324.544i			0.480328i
$78$	−1641.83	+	760.860i	−2.38334	+	1.10449i
$79$	−317.026			−0.451496			−0.225748	−	0.974186i	$-0.572483\pi$
$79$	−317.026			−0.451496			−0.225748	+	0.974186i	$0.572483\pi$
$80$	886.113	−	147.585i	1.23838	−	0.206256i
$81$	−439.541			−0.602936
$82$	−1040.80	+	482.327i	−1.40167	+	0.649562i
$83$			198.641i			0.262695i	0.991336	+	0.131347i	$0.0419303\pi$
$83$			198.641i			0.262695i	−0.991336	+	0.131347i	$0.958070\pi$
$84$	657.038	+	556.657i	0.853437	+	0.723050i
$85$			238.616i			0.304489i
$86$	−214.532	−	462.932i	−0.268995	−	0.580456i
$87$	1377.62			1.69766
$88$	518.787	+	142.975i	0.628441	+	0.173196i
$89$	−1541.50			−1.83594			−0.917968	−	0.396655i	$-0.870171\pi$
$89$	−1541.50			−1.83594			−0.917968	+	0.396655i	$0.870171\pi$
$90$	587.898	+	1268.60i	0.688554	+	1.48581i
$91$		−	1106.86i		−	1.27506i
$92$	550.738	−	650.052i	0.624113	−	0.736659i
$93$			1135.95i			1.26659i
$94$	293.975	−	136.234i	0.322566	−	0.149484i
$95$	−1301.37			−1.40545
$96$	1179.27	−	805.049i	1.25374	−	0.855885i
$97$	180.644			0.189088			0.0945442	−	0.995521i	$-0.469861\pi$
$97$	180.644			0.189088			0.0945442	+	0.995521i	$0.469861\pi$
$98$	402.315	−	186.441i	0.414693	−	0.192178i
$99$			837.579i			0.850302i
$100$	−372.419	+	439.577i	−0.372419	+	0.439577i
$101$		−	643.510i		−	0.633976i	−0.948429	−	0.316988i	$-0.897328\pi$
$101$		−	643.510i		−	0.633976i	0.948429	−	0.316988i	$-0.102672\pi$
$102$	159.472	+	344.120i	0.154805	+	0.334049i
$103$	533.377			0.510244			0.255122	−	0.966909i	$-0.417884\pi$
$103$	533.377			0.510244			0.255122	+	0.966909i	$0.417884\pi$
$104$	−1769.32	−	487.617i	−1.66823	−	0.459758i
$105$	−1510.90			−1.40427
$106$	443.880	+	957.832i	0.406730	+	0.877669i
$107$			472.575i			0.426967i	0.976947	+	0.213484i	$0.0684810\pi$
$107$			472.575i			0.426967i	−0.976947	+	0.213484i	$0.931519\pi$
$108$	395.712	+	335.255i	0.352568	+	0.298703i
$109$			221.524i			0.194662i	0.995252	+	0.0973312i	$0.0310306\pi$
$109$			221.524i			0.194662i	−0.995252	+	0.0973312i	$0.968969\pi$
$110$	−856.645	+	396.988i	−0.742527	+	0.344103i
$111$	2503.68			2.14089
$112$	143.488	+	861.513i	0.121057	+	0.726833i
$113$	941.802			0.784047			0.392023	−	0.919955i	$-0.371775\pi$
$113$	941.802			0.784047			0.392023	+	0.919955i	$0.371775\pi$
$114$	−1876.76	+	869.732i	−1.54189	+	0.714543i
$115$			1494.84i			1.21212i
$116$	1066.04	+	903.174i	0.853272	+	0.722910i
$117$		−	2856.56i		−	2.25717i
$118$	−209.362	−	451.775i	−0.163334	−	0.352452i
$119$	−231.992			−0.178711
$120$	−665.615	+	2415.18i	−0.506350	+	1.83729i
$121$	765.411			0.575065
$122$	669.107	+	1443.84i	0.496542	+	1.07147i
$123$		−	3199.09i		−	2.34514i
$124$	−744.736	+	879.034i	−0.539349	+	0.636609i
$125$			743.696i			0.532145i
$126$	−1233.39	+	571.577i	−0.872053	+	0.404128i
$127$	−2113.76			−1.47690			−0.738449	−	0.674310i	$-0.764441\pi$
$127$	−2113.76			−1.47690			−0.738449	+	0.674310i	$0.764441\pi$
$128$	1440.35	+	150.166i	0.994609	+	0.103695i
$129$	1422.91			0.971166
$130$	2921.58	−	1353.92i	1.97108	−	0.913438i
$131$		−	2541.65i		−	1.69516i	−0.530671	−	0.847578i	$-0.678060\pi$
$131$		−	2541.65i		−	1.69516i	0.530671	−	0.847578i	$-0.321940\pi$
$132$	−970.095	+	1145.03i	−0.639666	+	0.755016i
$133$		−	1265.24i		−	0.824888i
$134$	−1110.36	−	2396.01i	−0.715824	−	1.54465i
$135$	−909.964			−0.580127
$136$	−102.202	+	370.841i	−0.0644394	+	0.233818i
$137$	2273.50			1.41780			0.708900	−	0.705309i	$-0.249192\pi$
$137$	2273.50			1.41780			0.708900	+	0.705309i	$0.249192\pi$
$138$	999.032	+	2155.78i	0.616255	+	1.32980i
$139$			1187.90i			0.724863i	0.932010	+	0.362431i	$0.118053\pi$
$139$			1187.90i			0.724863i	−0.932010	+	0.362431i	$0.881947\pi$
$140$	−1169.18	−	990.551i	−0.705810	−	0.597978i
$141$			903.591i			0.539689i
$142$	2130.51	−	987.323i	1.25907	−	0.583481i
$143$	1928.94			1.12801
$144$	370.312	+	2223.38i	0.214301	+	1.28668i
$145$	−2451.43			−1.40400
$146$	602.962	−	279.425i	0.341791	−	0.158393i
$147$			1236.59i			0.693827i
$148$	1937.42	+	1641.42i	1.07604	+	0.911648i
$149$			2334.00i			1.28328i	0.767005	+	0.641641i	$0.221746\pi$
$149$			2334.00i			1.28328i	−0.767005	+	0.641641i	$0.778254\pi$
$150$	−675.563	−	1457.77i	−0.367730	−	0.793512i
$151$	1236.34			0.666306			0.333153	−	0.942873i	$-0.391887\pi$
$151$	1236.34			0.666306			0.333153	+	0.942873i	$0.391887\pi$
$152$	−2022.49	−	557.391i	−1.07925	−	0.297437i
$153$	−598.721			−0.316364
$154$	−385.967	−	832.863i	−0.201961	−	0.435806i
$155$		−	2021.39i		−	1.04750i
$156$	3308.50	−	3905.12i	1.69803	−	2.00423i
$157$		−	485.746i		−	0.246922i	−0.992349	−	0.123461i	$-0.960601\pi$
$157$		−	485.746i		−	0.246922i	0.992349	−	0.123461i	$-0.0393994\pi$
$158$	813.568	−	377.025i	0.409646	−	0.189838i
$159$	−2944.09			−1.46844
$160$	−2098.48	+	1432.56i	−1.03687	+	0.707835i
$161$	−1453.34			−0.711422
$162$	1127.97	−	522.727i	0.547049	−	0.253514i
$163$			1255.49i			0.603298i	0.953419	+	0.301649i	$0.0975370\pi$
$163$			1255.49i			0.603298i	−0.953419	+	0.301649i	$0.902463\pi$
$164$	2097.34	−	2475.55i	0.998625	−	1.17871i
$165$		−	2633.07i		−	1.24233i
$166$	−236.235	−	509.763i	−0.110454	−	0.238345i
$167$	2263.46			1.04881			0.524407	−	0.851468i	$-0.324287\pi$
$167$	2263.46			1.04881			0.524407	+	0.851468i	$0.324287\pi$
$168$	−2348.13	−	647.136i	−1.07835	−	0.297188i
$169$	−4381.63			−1.99437
$170$	−283.776	−	612.350i	−0.128027	−	0.276265i
$171$		−	3265.31i		−	1.46026i
$172$	1101.09	+	932.867i	0.488124	+	0.413549i
$173$			3809.06i			1.67397i	0.547224	+	0.836986i	$0.315684\pi$
$173$			3809.06i			1.67397i	−0.547224	+	0.836986i	$0.684316\pi$
$174$	−3535.33	+	1638.35i	−1.54030	+	0.713808i
$175$	982.772			0.424518
$176$	−1501.37	+	250.059i	−0.643013	+	0.107096i
$177$	1388.62			0.589690
$178$	3955.87	−	1833.24i	1.66576	−	0.771948i
$179$		−	684.860i		−	0.285971i	−0.989725	−	0.142986i	$-0.954330\pi$
$179$		−	684.860i		−	0.285971i	0.989725	−	0.142986i	$-0.0456703\pi$
$180$	−3017.39	−	2556.40i	−1.24946	−	1.05857i
$181$		−	1233.00i		−	0.506343i	−0.967421	−	0.253172i	$-0.918526\pi$
$181$		−	1233.00i		−	0.506343i	0.967421	−	0.253172i	$-0.0814737\pi$
$182$	1316.34	+	2840.48i	0.536117	+	1.15687i
$183$	−4437.94			−1.79269
$184$	−640.256	+	2323.17i	−0.256523	+	0.930795i
$185$	−4455.21			−1.77056
$186$	−1350.94	−	2915.15i	−0.532558	−	1.14919i
$187$		−	404.296i		−	0.158102i
$188$	−592.398	+	699.224i	−0.229814	+	0.271256i
$189$		−	884.701i		−	0.340490i
$190$	3339.64	−	1547.66i	1.27517	−	0.590942i
$191$	910.302			0.344854			0.172427	−	0.985022i	$-0.444839\pi$
$191$	910.302			0.344854			0.172427	+	0.985022i	$0.444839\pi$
$192$	−2068.91	+	3468.42i	−0.777658	+	1.30371i
$193$	1022.20			0.381240			0.190620	−	0.981664i	$-0.438950\pi$
$193$	1022.20			0.381240			0.190620	+	0.981664i	$0.438950\pi$
$194$	−463.577	+	214.832i	−0.171561	+	0.0795052i
$195$			8980.07i			3.29783i
$196$	−810.716	+	956.911i	−0.295450	+	0.348729i
$197$		−	1982.25i		−	0.716902i	−0.933548	−	0.358451i	$-0.883305\pi$
$197$		−	1982.25i		−	0.716902i	0.933548	−	0.358451i	$-0.116695\pi$
$198$	−996.097	−	2149.44i	−0.357523	−	0.771486i
$199$	2123.70			0.756509			0.378254	−	0.925702i	$-0.376524\pi$
$199$	2123.70			0.756509			0.378254	+	0.925702i	$0.376524\pi$
$200$	432.953	−	1570.97i	0.153072	−	0.555421i
$201$	7364.60			2.58437
$202$	765.299	+	1651.41i	0.266565	+	0.575212i
$203$		−	2383.37i		−	0.824040i
$204$	−818.494	−	693.446i	−0.280912	−	0.237995i
$205$			5692.67i			1.93948i
$206$	−1368.78	+	634.322i	−0.462949	+	0.214540i
$207$	−3750.75			−1.25940
$208$	5120.43	−	852.824i	1.70691	−	0.284292i
$209$	2204.95			0.729759
$210$	3877.35	−	1796.85i	1.27411	−	0.590449i
$211$		−	4710.20i		−	1.53679i	−0.639974	−	0.768396i	$-0.721055\pi$
$211$		−	4710.20i		−	1.53679i	0.639974	−	0.768396i	$-0.278945\pi$
$212$	−2278.22	−	1930.16i	−0.738059	−	0.625300i
$213$			6548.54i			2.10657i
$214$	−562.013	−	1212.75i	−0.179525	−	0.387391i
$215$	−2532.02			−0.803175
$216$	−1414.20	−	389.748i	−0.445483	−	0.122773i
$217$	1965.28			0.614800
$218$	−263.450	−	568.488i	−0.0818489	−	0.176619i
$219$			1853.32i			0.571853i
$220$	1726.25	−	2037.54i	0.529017	−	0.624414i
$221$			1378.85i			0.419690i
$222$	−6425.07	+	2977.51i	−1.94244	+	0.900170i
$223$	−3281.34			−0.985357			−0.492678	−	0.870212i	$-0.663982\pi$
$223$	−3281.34			−0.985357			−0.492678	+	0.870212i	$0.663982\pi$
$224$	−1392.79	−	2040.22i	−0.415444	−	0.608562i
$225$	2536.32			0.751503
$226$	−2416.91	+	1120.04i	−0.711372	+	0.329665i
$227$		−	4190.90i		−	1.22537i	−0.790326	−	0.612686i	$-0.790089\pi$
$227$		−	4190.90i		−	1.22537i	0.790326	−	0.612686i	$-0.209911\pi$
$228$	3781.92	−	4463.91i	1.09853	−	1.29662i
$229$		−	3767.13i		−	1.08707i	−0.839387	−	0.543534i	$-0.817086\pi$
$229$		−	3767.13i		−	1.08707i	0.839387	−	0.543534i	$-0.182914\pi$
$230$	−1777.74	−	3836.13i	−0.509656	−	1.09977i
$231$	2559.97			0.729150
$232$	−3809.84	−	1049.98i	−1.07814	−	0.297131i
$233$	5818.16			1.63588			0.817941	−	0.575302i	$-0.195115\pi$
$233$	5818.16			1.63588			0.817941	+	0.575302i	$0.195115\pi$
$234$	3397.18	+	7330.66i	0.949063	+	2.04795i
$235$		−	1607.91i		−	0.446334i
$236$	1074.55	+	910.386i	0.296388	+	0.251106i
$237$			2500.66i			0.685382i
$238$	595.350	−	275.898i	0.162146	−	0.0751420i
$239$	4888.45			1.32304			0.661522	−	0.749926i	$-0.269911\pi$
$239$	4888.45			1.32304			0.661522	+	0.749926i	$0.269911\pi$
$240$	−1164.14	−	6989.57i	−0.313103	−	1.87989i
$241$	−619.409			−0.165559			−0.0827793	−	0.996568i	$-0.526380\pi$
$241$	−619.409			−0.165559			−0.0827793	+	0.996568i	$0.526380\pi$
$242$	−1964.24	+	910.271i	−0.521761	+	0.241795i
$243$			5217.45i			1.37736i
$244$	−3434.20	−	2909.53i	−0.901034	−	0.763375i
$245$		−	2200.48i		−	0.573809i
$246$	3804.54	+	8209.68i	0.986052	+	2.12777i
$247$	−7519.98			−1.93718
$248$	865.787	−	3141.51i	0.221684	−	0.804379i
$249$	1566.86			0.398777
$250$	−884.445	−	1908.51i	−0.223749	−	0.482820i
$251$		−	5420.98i		−	1.36322i	−0.731714	−	0.681612i	$-0.761279\pi$
$251$		−	5420.98i		−	1.36322i	0.731714	−	0.681612i	$-0.238721\pi$
$252$	2485.43	−	2933.62i	0.621299	−	0.733337i
$253$		−	2532.75i		−	0.629379i
$254$	5424.45	−	2513.80i	1.34000	−	0.620985i
$255$	1882.18			0.462222
$256$	−3874.89	+	1327.58i	−0.946017	+	0.324116i
$257$	6669.51			1.61880			0.809402	−	0.587255i	$-0.199792\pi$
$257$	6669.51			1.61880			0.809402	+	0.587255i	$0.199792\pi$
$258$	−3651.56	+	1692.21i	−0.881147	+	0.408342i
$259$		−	4331.52i		−	1.03918i
$260$	−5887.37	+	6949.03i	−1.40430	+	1.65754i
$261$		−	6150.98i		−	1.45876i
$262$	3022.68	+	6522.53i	0.712755	+	1.53803i
$263$	−698.624			−0.163798			−0.0818992	−	0.996641i	$-0.526099\pi$
$263$	−698.624			−0.163798			−0.0818992	+	0.996641i	$0.526099\pi$
$264$	1127.78	−	4092.13i	0.262916	−	0.953990i
$265$	5238.90			1.21443
$266$	1504.69	+	3246.92i	0.346837	+	0.748427i
$267$			12159.2i			2.78700i
$268$	5698.93	+	4828.26i	1.29895	+	1.10050i
$269$		−	2004.26i		−	0.454282i	−0.973862	−	0.227141i	$-0.927062\pi$
$269$		−	2004.26i		−	0.454282i	0.973862	−	0.227141i	$-0.0729378\pi$
$270$	2335.20	−	1082.18i	0.526354	−	0.243924i
$271$	1382.90			0.309982			0.154991	−	0.987916i	$-0.450465\pi$
$271$	1382.90			0.309982			0.154991	+	0.987916i	$0.450465\pi$
$272$	−178.748	−	1073.22i	−0.0398462	−	0.239240i
$273$	−8730.77			−1.93557
$274$	−5834.39	+	2703.78i	−1.28638	+	0.596137i
$275$			1712.69i			0.375561i
$276$	−5127.54	−	4344.17i	−1.11827	−	0.947420i
$277$			5647.52i			1.22500i	0.790469	+	0.612502i	$0.209837\pi$
$277$			5647.52i			1.22500i	−0.790469	+	0.612502i	$0.790163\pi$
$278$	−1412.71	−	3048.44i	−0.304780	−	0.657674i
$279$	5071.95			1.08835
$280$	4178.43	+	1151.56i	0.891817	+	0.245781i
$281$	−3711.09			−0.787847			−0.393923	−	0.919143i	$-0.628882\pi$
$281$	−3711.09			−0.787847			−0.393923	+	0.919143i	$0.628882\pi$
$282$	−1074.60	−	2318.85i	−0.226921	−	0.489664i
$283$			7125.83i			1.49677i	0.663263	+	0.748386i	$0.269171\pi$
$283$			7125.83i			1.49677i	−0.663263	+	0.748386i	$0.730829\pi$
$284$	−4293.25	+	5067.44i	−0.897033	+	1.05879i
$285$			10265.0i			2.13350i
$286$	−4950.15	+	2294.00i	−1.02346	+	0.474291i
$287$	−5534.64			−1.13832
$288$	−3594.48	−	5265.37i	−0.735441	−	1.07731i
$289$	289.000			0.0588235
$290$	6291.00	−	2915.38i	1.27386	−	0.590335i
$291$		−	1424.90i		−	0.287041i
$292$	−1215.05	+	1434.15i	−0.243511	+	0.287423i
$293$		−	2551.66i		−	0.508770i	−0.967103	−	0.254385i	$-0.918127\pi$
$293$		−	2551.66i		−	0.508770i	0.967103	−	0.254385i	$-0.0818730\pi$
$294$	−1470.63	−	3173.42i	−0.291730	−	0.629515i
$295$	−2471.00			−0.487686
$296$	−6923.97	−	1908.22i	−1.35962	−	0.374706i
$297$	1541.78			0.301224
$298$	−2775.73	−	5989.65i	−0.539576	−	1.16433i
$299$			8637.94i			1.67072i
$300$	3467.34	+	2937.60i	0.667289	+	0.565342i
$301$		−	2461.73i		−	0.471401i
$302$	−3172.77	+	1470.33i	−0.604545	+	0.280159i
$303$	−5075.94			−0.962393
$304$	5853.12	−	974.856i	1.10427	−	0.183921i
$305$	7897.16			1.48259
$306$	1536.47	−	712.033i	0.287040	−	0.133020i
$307$		−	9808.57i		−	1.82347i	−0.410782	−	0.911734i	$-0.634744\pi$
$307$		−	9808.57i		−	1.82347i	0.410782	−	0.911734i	$-0.365256\pi$
$308$	1980.98	+	1678.33i	0.366483	+	0.310492i
$309$		−	4207.22i		−	0.774564i
$310$	2403.96	+	5187.41i	0.440437	+	0.950404i
$311$	5323.36			0.970611			0.485305	−	0.874345i	$-0.338708\pi$
$311$	5323.36			0.970611			0.485305	+	0.874345i	$0.338708\pi$
$312$	−3846.27	+	13956.2i	−0.697924	+	2.53242i
$313$	−7566.43			−1.36639			−0.683195	−	0.730236i	$-0.739410\pi$
$313$	−7566.43			−1.36639			−0.683195	+	0.730236i	$0.739410\pi$
$314$	577.677	+	1246.55i	0.103822	+	0.224034i
$315$			6746.05i			1.20666i
$316$	−1639.45	+	1935.08i	−0.291854	+	0.344484i
$317$			8035.97i			1.42380i	0.702280	+	0.711901i	$0.252166\pi$
$317$			8035.97i			1.42380i	−0.702280	+	0.711901i	$0.747834\pi$
$318$	7555.28	−	3501.28i	1.33232	−	0.617427i
$319$	4153.55			0.729009
$320$	3681.55	−	6171.94i	0.643140	−	1.07819i
$321$	3727.62			0.648147
$322$	3729.63	−	1728.39i	0.645479	−	0.299129i
$323$			1576.15i			0.271515i
$324$	−2273.01	+	2682.90i	−0.389748	+	0.460031i
$325$		−	5841.13i		−	0.996947i
$326$	−1493.10	−	3221.91i	−0.253666	−	0.547377i
$327$	1747.36			0.295502
$328$	−2438.24	+	8847.16i	−0.410455	+	1.48934i
$329$	1563.27			0.261963
$330$	3131.40	+	6757.13i	0.522357	+	1.12717i
$331$			891.471i			0.148035i	0.997257	+	0.0740176i	$0.0235821\pi$
$331$			891.471i			0.148035i	−0.997257	+	0.0740176i	$0.976418\pi$
$332$	1212.48	+	1027.24i	0.200432	+	0.169810i
$333$		−	11178.7i		−	1.83961i
$334$	−5808.63	+	2691.84i	−0.951598	+	0.440991i
$335$	−13105.1			−2.13733
$336$	6795.52	−	1131.82i	1.10335	−	0.183767i
$337$	211.947			0.0342597			0.0171298	−	0.999853i	$-0.494547\pi$
$337$	211.947			0.0342597			0.0171298	+	0.999853i	$0.494547\pi$
$338$	11244.4	−	5210.88i	1.80951	−	0.838564i
$339$		−	7428.84i		−	1.19020i
$340$	1456.48	+	1233.96i	0.232320	+	0.196827i
$341$			3424.92i			0.543900i
$342$	3883.29	+	8379.62i	0.613989	+	1.32491i
$343$	6820.16			1.07363
$344$	−3935.10	−	1084.50i	−0.616762	−	0.169977i
$345$	11791.1			1.84003
$346$	−4529.95	−	9775.01i	−0.703848	−	1.51881i
$347$			1599.19i			0.247404i	0.992319	+	0.123702i	$0.0394767\pi$
$347$			1599.19i			0.247404i	−0.992319	+	0.123702i	$0.960523\pi$
$348$	7124.14	−	8408.83i	1.09740	−	1.29529i
$349$			5976.55i			0.916669i	0.888780	+	0.458334i	$0.151554\pi$
$349$			5976.55i			0.916669i	−0.888780	+	0.458334i	$0.848446\pi$
$350$	−2522.04	+	1168.77i	−0.385168	+	0.178495i
$351$	−5258.25			−0.799614
$352$	3555.52	−	2427.23i	0.538381	−	0.367534i
$353$	−3807.53			−0.574092			−0.287046	−	0.957917i	$-0.592673\pi$
$353$	−3807.53			−0.574092			−0.287046	+	0.957917i	$0.592673\pi$
$354$	−3563.56	+	1651.43i	−0.535031	+	0.247945i
$355$		−	11652.9i		−	1.74217i
$356$	−7971.59	+	9409.10i	−1.18678	+	1.40079i
$357$			1829.93i			0.271288i
$358$	814.475	+	1757.53i	0.120241	+	0.259464i
$359$	−2799.25			−0.411528			−0.205764	−	0.978602i	$-0.565968\pi$
$359$	−2799.25			−0.411528			−0.205764	+	0.978602i	$0.565968\pi$
$360$	10783.6	+	2971.92i	1.57874	+	0.435095i
$361$	−1737.02			−0.253247
$362$	1466.35	+	3164.19i	0.212900	+	0.459409i
$363$		−	6037.48i		−	0.872963i
$364$	−6756.11	−	5723.93i	−0.972848	−	0.824218i
$365$		−	3297.92i		−	0.472935i
$366$	11388.9	−	5277.85i	1.62652	−	0.753764i
$367$	−158.223			−0.0225045			−0.0112523	−	0.999937i	$-0.503582\pi$
$367$	−158.223			−0.0225045			−0.0112523	+	0.999937i	$0.503582\pi$
$368$	−1119.78	−	6723.28i	−0.158622	−	0.952378i
$369$	−14283.7			−2.01512
$370$	11433.2	−	5298.39i	1.60644	−	0.744459i
$371$			5093.46i			0.712775i
$372$	6933.72	+	5874.40i	0.966389	+	0.818746i
$373$		−	3.31916i		−	0.000460749i	−1.00000		0.000230374i	$-0.999927\pi$
$373$		−	3.31916i		−	0.000460749i	1.00000		0.000230374i	$-7.33305e-5\pi$
$374$	480.812	+	1037.53i	0.0664764	+	0.143447i
$375$	5866.19			0.807810
$376$	688.687	−	2498.90i	0.0944584	−	0.342742i
$377$	−14165.6			−1.93519
$378$	1052.14	+	2270.37i	0.143164	+	0.308929i
$379$		−	4532.29i		−	0.614269i	−0.951666	−	0.307135i	$-0.900630\pi$
$379$		−	4532.29i		−	0.614269i	0.951666	−	0.307135i	$-0.0993702\pi$
$380$	−6729.80	+	7943.38i	−0.908504	+	1.07233i
$381$			16673.1i			2.24197i
$382$	−2336.07	+	1082.58i	−0.312889	+	0.144999i
$383$	−7133.15			−0.951663			−0.475832	−	0.879536i	$-0.657853\pi$
$383$	−7133.15			−0.951663			−0.475832	+	0.879536i	$0.657853\pi$
$384$	1184.50	−	11361.3i	0.157412	−	1.50984i
$385$	−4555.38			−0.603023
$386$	−2623.22	+	1215.65i	−0.345902	+	0.160298i
$387$		−	6353.20i		−	0.834499i
$388$	934.168	−	1102.63i	0.122230	−	0.144271i
$389$			2165.68i			0.282274i	0.989990	+	0.141137i	$0.0450758\pi$
$389$			2165.68i			0.282274i	−0.989990	+	0.141137i	$0.954924\pi$
$390$	−10679.6	−	23045.1i	−1.38662	−	2.99214i
$391$	1810.47			0.234167
$392$	942.491	−	3419.83i	0.121436	−	0.440631i
$393$	−20048.3			−2.57329
$394$	2357.41	+	5086.97i	0.301433	+	0.650451i
$395$		−	4449.85i		−	0.566825i
$396$	5112.48	+	4331.40i	0.648767	+	0.549649i
$397$		−	8450.03i		−	1.06825i	−0.845406	−	0.534124i	$-0.820641\pi$
$397$		−	8450.03i		−	1.06825i	0.845406	−	0.534124i	$-0.179359\pi$
$398$	−5449.96	+	2525.63i	−0.686387	+	0.318086i
$399$	−9980.06			−1.25220
$400$	757.218	+	4546.40i	0.0946523	+	0.568300i
$401$	4837.50			0.602428			0.301214	−	0.953557i	$-0.402608\pi$
$401$	4837.50			0.602428			0.301214	+	0.953557i	$0.402608\pi$
$402$	−18899.4	+	8758.40i	−2.34482	+	1.08664i
$403$		−	11680.7i		−	1.44381i
$404$	−3927.90	−	3327.81i	−0.483714	−	0.409813i
$405$		−	6169.50i		−	0.756950i
$406$	2834.44	+	6116.35i	0.346481	+	0.747658i
$407$	7548.62			0.919339
$408$	2925.15	+	806.160i	0.354943	+	0.0978207i
$409$	−8388.38			−1.01413			−0.507064	−	0.861908i	$-0.669269\pi$
$409$	−8388.38			−1.01413			−0.507064	+	0.861908i	$0.669269\pi$
$410$	−6770.05	−	14608.9i	−0.815485	−	1.75971i
$411$		−	17933.2i		−	2.15226i
$412$	2758.27	−	3255.67i	0.329831	−	0.389309i
$413$		−	2402.40i		−	0.286234i
$414$	9625.38	−	4460.60i	1.14266	−	0.529533i
$415$	−2788.17			−0.329797
$416$	−12126.1	+	8278.07i	−1.42916	+	0.975639i
$417$	9369.99			1.10036
$418$	−5658.47	+	2622.25i	−0.662117	+	0.306839i
$419$			5077.94i			0.592061i	0.955179	+	0.296030i	$0.0956629\pi$
$419$			5077.94i			0.592061i	−0.955179	+	0.296030i	$0.904337\pi$
$420$	−7813.36	+	9222.34i	−0.907746	+	1.07144i
$421$			13393.6i			1.55051i	0.631646	+	0.775257i	$0.282380\pi$
$421$			13393.6i			1.55051i	−0.631646	+	0.775257i	$0.717620\pi$
$422$	5601.63	+	12087.6i	0.646169	+	1.39434i
$423$	4034.47			0.463741
$424$	8141.94	+	2243.89i	0.932565	+	0.257011i
$425$	−1224.27			−0.139732
$426$	−7787.90	−	16805.2i	−0.885739	−	1.91130i
$427$			7677.92i			0.870165i
$428$	2884.54	+	2443.84i	0.325769	+	0.275999i
$429$		−	15215.3i		−	1.71235i
$430$	6497.82	−	3011.23i	0.728727	−	0.337708i
$431$	9585.00			1.07121			0.535607	−	0.844467i	$-0.320083\pi$
$431$	9585.00			1.07121			0.535607	+	0.844467i	$0.320083\pi$
$432$	4092.72	−	681.656i	0.455812	−	0.0759171i
$433$	7851.33			0.871387			0.435694	−	0.900095i	$-0.356503\pi$
$433$	7851.33			0.871387			0.435694	+	0.900095i	$0.356503\pi$
$434$	−5043.40	+	2337.22i	−0.557813	+	0.258502i
$435$			19336.6i			2.13131i
$436$	1352.16	+	1145.58i	0.148524	+	0.125833i
$437$			9873.96i			1.08086i
$438$	−2204.08	−	4756.10i	−0.240445	−	0.518847i
$439$	11378.2			1.23702			0.618509	−	0.785778i	$-0.287737\pi$
$439$	11378.2			1.23702			0.618509	+	0.785778i	$0.287737\pi$
$440$	−2006.84	+	7281.81i	−0.217437	+	0.788970i
$441$	5521.30			0.596188
$442$	−1639.81	−	3538.48i	−0.176465	−	0.380788i
$443$		−	15405.2i		−	1.65219i	−0.563529	−	0.826096i	$-0.690557\pi$
$443$		−	15405.2i		−	1.65219i	0.563529	−	0.826096i	$-0.309443\pi$
$444$	12947.4	−	15282.1i	1.38391	−	1.63346i
$445$		−	21636.8i		−	2.30491i
$446$	8420.75	−	3902.35i	0.894022	−	0.414309i
$447$	18410.4			1.94806
$448$	6000.59	+	3579.34i	0.632815	+	0.377473i
$449$	14558.6			1.53020			0.765101	−	0.643910i	$-0.222689\pi$
$449$	14558.6			1.53020			0.765101	+	0.643910i	$0.222689\pi$
$450$	−6508.85	+	3016.34i	−0.681845	+	0.315981i
$451$		−	9645.30i		−	1.00705i
$452$	4870.38	−	5748.64i	0.506821	−	0.598216i
$453$		−	9752.15i		−	1.01147i
$454$	4984.05	+	10754.9i	0.515227	+	1.11179i
$455$	15536.1			1.60076
$456$	−4396.64	+	15953.2i	−0.451517	+	1.63833i
$457$	−14551.1			−1.48944			−0.744719	−	0.667378i	$-0.767417\pi$
$457$	−14551.1			−1.48944			−0.744719	+	0.667378i	$0.767417\pi$
$458$	4480.08	+	9667.41i	0.457075	+	0.986306i
$459$			1102.10i			0.112074i
$460$	9124.29	+	7730.30i	0.924831	+	0.783537i
$461$		−	4243.77i		−	0.428746i	−0.976752	−	0.214373i	$-0.931229\pi$
$461$		−	4243.77i		−	0.428746i	0.976752	−	0.214373i	$-0.0687708\pi$
$462$	−6569.54	+	3044.46i	−0.661564	+	0.306583i
$463$	−5921.02			−0.594327			−0.297163	−	0.954827i	$-0.596041\pi$
$463$	−5921.02			−0.594327			−0.297163	+	0.954827i	$0.596041\pi$
$464$	11025.7	−	1836.37i	1.10314	−	0.183731i
$465$	−15944.5			−1.59013
$466$	−14930.9	+	6919.29i	−1.48425	+	0.687833i
$467$			9981.84i			0.989089i	0.869152	+	0.494544i	$0.164665\pi$
$467$			9981.84i			0.989089i	−0.869152	+	0.494544i	$0.835335\pi$
$468$	−17436.1	−	14772.2i	−1.72219	−	1.45907i
$469$		−	12741.2i		−	1.25445i
$470$	1912.22	+	4126.31i	0.187668	+	0.404963i
$471$	−3831.51			−0.374834
$472$	−3840.26	−	1058.36i	−0.374497	−	0.103210i
$473$	4290.10			0.417038
$474$	−2973.93	−	6417.34i	−0.288180	−	0.621853i
$475$		−	6676.95i		−	0.644967i
$476$	−1199.71	+	1416.05i	−0.115522	+	0.136354i
$477$			13145.1i			1.26179i
$478$	−12545.0	+	5813.62i	−1.20041	+	0.556295i
$479$	−8759.26			−0.835534			−0.417767	−	0.908554i	$-0.637187\pi$
$479$	−8759.26			−0.835534			−0.417767	+	0.908554i	$0.637187\pi$
$480$	11299.9	+	16552.6i	1.07451	+	1.57399i
$481$	−25744.5			−2.44044
$482$	1589.56	−	736.636i	0.150213	−	0.0696118i
$483$			11463.8i			1.07996i
$484$	3958.20	−	4671.97i	0.371732	−	0.438765i
$485$			2535.56i			0.237389i
$486$	−6204.89	−	13389.3i	−0.579135	−	1.24969i
$487$	15218.5			1.41605			0.708026	−	0.706187i	$-0.249586\pi$
$487$	15218.5			1.41605			0.708026	+	0.706187i	$0.249586\pi$
$488$	12273.2	+	3382.45i	1.13849	+	0.313763i
$489$	9903.17			0.915822
$490$	2616.93	+	5646.99i	0.241267	+	0.520622i
$491$			5169.37i			0.475134i	0.971371	+	0.237567i	$0.0763499\pi$
$491$			5169.37i			0.475134i	−0.971371	+	0.237567i	$0.923650\pi$
$492$	−19526.8	−	16543.6i	−1.78931	−	1.51594i
$493$			2969.05i			0.271236i
$494$	19298.2	−	8943.18i	1.75762	−	0.814520i
$495$	−11756.5			−1.06750
$496$	1514.23	+	9091.56i	0.137078	+	0.823030i
$497$	11329.4			1.02252
$498$	−4020.95	+	1863.40i	−0.361814	+	0.167672i
$499$			6037.42i			0.541628i	0.962632	+	0.270814i	$0.0872928\pi$
$499$			6037.42i			0.541628i	−0.962632	+	0.270814i	$0.912707\pi$
$500$	4539.42	+	3845.90i	0.406019	+	0.343988i
$501$		−	17854.0i		−	1.59213i
$502$	6446.94	+	13911.6i	0.573189	+	1.23686i
$503$	−5548.00			−0.491795			−0.245898	−	0.969296i	$-0.579083\pi$
$503$	−5548.00			−0.491795			−0.245898	+	0.969296i	$0.579083\pi$
$504$	−2889.42	+	10484.2i	−0.255367	+	0.926598i
$505$	9032.46			0.795919
$506$	3012.10	+	6499.69i	0.264632	+	0.571041i
$507$			34561.8i			3.02750i
$508$	−10931.0	+	12902.1i	−0.954691	+	1.12685i
$509$			4524.35i			0.393985i	0.980405	+	0.196992i	$0.0631174\pi$
$509$			4524.35i			0.393985i	−0.980405	+	0.196992i	$0.936883\pi$
$510$	−4830.15	+	2238.39i	−0.419378	+	0.194349i
$511$	3206.37			0.277576
$512$	8365.12	−	8015.14i	0.722050	−	0.691841i
$513$	−6010.66			−0.517304
$514$	−17115.7	+	7931.76i	−1.46875	+	0.680652i
$515$			7486.61i			0.640581i
$516$	7358.36	−	8685.28i	0.627778	−	0.740984i
$517$			2724.34i			0.231753i
$518$	5151.29	+	11115.8i	0.436940	+	0.942857i
$519$	30045.4			2.54113
$520$	6844.31	−	24834.6i	0.577198	−	2.09436i
$521$	3454.19			0.290462			0.145231	−	0.989398i	$-0.453607\pi$
$521$	3454.19			0.290462			0.145231	+	0.989398i	$0.453607\pi$
$522$	7315.09	+	15785.0i	0.613358	+	1.32354i
$523$			13016.3i			1.08827i	0.838999	+	0.544133i	$0.183141\pi$
$523$			13016.3i			1.08827i	−0.838999	+	0.544133i	$0.816859\pi$
$524$	−15513.9	−	13143.7i	−1.29338	−	1.09578i
$525$		−	7752.00i		−	0.644429i
$526$	1792.85	−	830.843i	0.148616	−	0.0688717i
$527$	−2448.21			−0.202364
$528$	1972.44	+	11842.7i	0.162574	+	0.976110i
$529$	−825.116			−0.0678159
$530$	−13444.4	+	6230.40i	−1.10186	+	0.510625i
$531$		−	6200.09i		−	0.506706i
$532$	−7722.86	−	6542.97i	−0.629376	−	0.533221i
$533$			32895.3i			2.67327i
$534$	−14460.4	−	31203.5i	−1.17184	−	2.52867i
$535$	−6633.17			−0.536032
$536$	−20367.0	−	5613.05i	−1.64127	−	0.452327i
$537$	−5402.10			−0.434112
$538$	2383.58	+	5143.44i	0.191010	+	0.412174i
$539$			3728.35i			0.297943i
$540$	−4705.73	+	5554.30i	−0.375004	+	0.442628i
$541$			523.986i			0.0416413i	0.999783	+	0.0208206i	$0.00662789\pi$
$541$			523.986i			0.0416413i	−0.999783	+	0.0208206i	$0.993372\pi$
$542$	−3548.87	+	1644.62i	−0.281249	+	0.130337i
$543$	−9725.76			−0.768642
$544$	1735.04	+	2541.57i	0.136745	+	0.200311i
$545$	−3109.37			−0.244387
$546$	22405.4	−	10383.1i	1.75616	−	0.813840i
$547$			10726.2i			0.838428i	0.907888	+	0.419214i	$0.137694\pi$
$547$			10726.2i			0.838428i	−0.907888	+	0.419214i	$0.862306\pi$
$548$	11757.1	−	13877.2i	0.916490	−	1.08176i
$549$			19815.1i			1.54041i
$550$	−2036.83	−	4395.21i	−0.157911	−	0.340750i
$551$	−16192.6			−1.25196
$552$	18324.9	+	5050.27i	1.41297	+	0.389409i
$553$	4326.31			0.332683
$554$	−6716.35	−	14493.0i	−0.515073	−	1.11146i
$555$			35142.2i			2.68775i
$556$	7250.76	+	6143.00i	0.553059	+	0.468564i
$557$		−	19279.3i		−	1.46659i	−0.679911	−	0.733295i	$-0.737982\pi$
$557$		−	19279.3i		−	1.46659i	0.679911	−	0.733295i	$-0.262018\pi$
$558$	−13015.9	+	6031.86i	−0.987470	+	0.457614i
$559$	−14631.4			−1.10705
$560$	−12092.4	+	2014.03i	−0.912495	+	0.151979i
$561$	−3189.04			−0.240003
$562$	9523.60	−	4413.44i	0.714820	−	0.331263i
$563$			21661.9i			1.62156i	0.585351	+	0.810780i	$0.300957\pi$
$563$			21661.9i			1.62156i	−0.585351	+	0.810780i	$0.699043\pi$
$564$	5515.41	+	4672.77i	0.411774	+	0.348864i
$565$			13219.4i			0.984323i
$566$	−8474.44	−	18286.7i	−0.629342	−	1.35803i
$567$	5998.22			0.444271
$568$	4991.08	−	18110.1i	0.368699	−	1.33782i
$569$	20149.5			1.48455			0.742277	−	0.670093i	$-0.233746\pi$
$569$	20149.5			1.48455			0.742277	+	0.670093i	$0.233746\pi$
$570$	−12207.8	−	26342.7i	−0.897065	−	1.93575i
$571$			6882.54i			0.504423i	0.967672	+	0.252211i	$0.0811578\pi$
$571$			6882.54i			0.504423i	−0.967672	+	0.252211i	$0.918842\pi$
$572$	9975.18	−	11774.0i	0.729167	−	0.860656i
$573$		−	7180.37i		−	0.523498i
$574$	14203.3	−	6582.10i	1.03281	−	0.478627i
$575$	−7669.58			−0.556250
$576$	15486.2	+	9237.51i	1.12024	+	0.668223i
$577$	2754.11			0.198709			0.0993547	−	0.995052i	$-0.468322\pi$
$577$	2754.11			0.198709			0.0993547	+	0.995052i	$0.468322\pi$
$578$	−741.648	+	343.695i	−0.0533711	+	0.0247333i
$579$		−	8062.97i		−	0.578732i
$580$	−12677.2	+	14963.2i	−0.907570	+	1.07123i
$581$		−	2710.76i		−	0.193565i
$582$	1694.57	+	3656.65i	0.120691	+	0.260435i
$583$	−8876.46			−0.630575
$584$	1412.54	−	5125.40i	0.100088	−	0.363169i
$585$	40095.3			2.83374
$586$	3034.58	+	6548.21i	0.213920	+	0.461611i
$587$		−	10822.8i		−	0.760998i	−0.924781	−	0.380499i	$-0.875752\pi$
$587$		−	10822.8i		−	0.760998i	0.924781	−	0.380499i	$-0.124248\pi$
$588$	7548.01	+	6394.84i	0.529379	+	0.448501i
$589$		−	13352.1i		−	0.934062i
$590$	6341.23	−	2938.66i	0.442482	−	0.205055i
$591$	−15635.8			−1.08828
$592$	20038.1	−	3337.41i	1.39115	−	0.231700i
$593$	−16058.9			−1.11207			−0.556036	−	0.831158i	$-0.687678\pi$
$593$	−16058.9			−1.11207			−0.556036	+	0.831158i	$0.687678\pi$
$594$	−3956.61	+	1833.58i	−0.273303	+	0.126654i
$595$		−	3256.29i		−	0.224361i
$596$	14246.5	+	12069.9i	0.979124	+	0.829535i
$597$		−	16751.5i		−	1.14840i
$598$	−10272.7	−	22167.2i	−0.702480	−	1.51586i
$599$	−13884.3			−0.947071			−0.473536	−	0.880775i	$-0.657023\pi$
$599$	−13884.3			−0.947071			−0.473536	+	0.880775i	$0.657023\pi$
$600$	−12391.6	−	3415.09i	−0.843144	−	0.232367i
$601$	−10479.8			−0.711284			−0.355642	−	0.934622i	$-0.615738\pi$
$601$	−10479.8			−0.711284			−0.355642	+	0.934622i	$0.615738\pi$
$602$	2927.63	+	6317.43i	0.198208	+	0.427706i
$603$		−	32882.4i		−	2.22069i
$604$	6393.55	−	7546.49i	0.430712	−	0.508381i
$605$			10743.5i			0.721959i
$606$	13026.2	−	6036.59i	0.873187	−	0.404653i
$607$	782.802			0.0523442			0.0261721	−	0.999657i	$-0.491668\pi$
$607$	782.802			0.0523442			0.0261721	+	0.999657i	$0.491668\pi$
$608$	−13861.2	+	9462.59i	−0.924584	+	0.631182i
$609$	−18799.8			−1.25091
$610$	−20266.1	+	9391.75i	−1.34517	+	0.623379i
$611$		−	9291.35i		−	0.615201i
$612$	−3096.19	+	3654.52i	−0.204503	+	0.241381i
$613$		−	15748.5i		−	1.03764i	−0.854883	−	0.518821i	$-0.826371\pi$
$613$		−	15748.5i		−	1.03764i	0.854883	−	0.518821i	$-0.173629\pi$
$614$	11664.9	+	25171.3i	0.766706	+	1.65445i
$615$	44903.2			2.94418
$616$	−7079.66	−	1951.13i	−0.463064	−	0.127619i
$617$	18340.0			1.19666			0.598332	−	0.801248i	$-0.295830\pi$
$617$	18340.0			1.19666			0.598332	+	0.801248i	$0.295830\pi$
$618$	5003.47	+	10796.8i	0.325678	+	0.702769i
$619$			8956.52i			0.581572i	0.956788	+	0.290786i	$0.0939167\pi$
$619$			8956.52i			0.581572i	−0.956788	+	0.290786i	$0.906083\pi$
$620$	−12338.3	−	10453.3i	−0.799225	−	0.677120i
$621$			6904.24i			0.446147i
$622$	−13661.1	+	6330.84i	−0.880643	+	0.408109i
$623$	21036.1			1.35280
$624$	−6726.99	−	40389.4i	−0.431563	−	2.59114i
$625$	−19440.7			−1.24420
$626$	19417.4	−	8998.43i	1.23974	−	0.574520i
$627$		−	17392.4i		−	1.10779i
$628$	−2964.93	−	2511.96i	−0.188398	−	0.159615i
$629$			5395.93i			0.342050i
$630$	−8022.79	−	17312.1i	−0.507358	−	1.09481i
$631$	12675.2			0.799672			0.399836	−	0.916587i	$-0.369067\pi$
$631$	12675.2			0.799672			0.399836	+	0.916587i	$0.369067\pi$
$632$	1905.92	−	6915.64i	0.119958	−	0.435268i
$633$	−37153.5			−2.33289
$634$	−9556.84	−	20622.4i	−0.598660	−	1.29183i
$635$		−	29669.3i		−	1.85416i
$636$	−15224.9	+	17970.3i	−0.949222	+	1.12039i
$637$		−	12715.5i		−	0.790906i
$638$	−10659.1	+	4939.63i	−0.661436	+	0.306523i
$639$	29238.8			1.81012
$640$	−2107.77	+	20217.1i	−0.130183	+	1.24867i
$641$	8289.63			0.510797			0.255398	−	0.966836i	$-0.417793\pi$
$641$	8289.63			0.510797			0.255398	+	0.966836i	$0.417793\pi$
$642$	−9566.02	+	4433.10i	−0.588070	+	0.272524i
$643$		−	11350.7i		−	0.696158i	−0.937465	−	0.348079i	$-0.886834\pi$
$643$		−	11350.7i		−	0.696158i	0.937465	−	0.348079i	$-0.113166\pi$
$644$	−7515.69	+	8870.98i	−0.459875	+	0.542804i
$645$			19972.3i			1.21924i
$646$	−1874.45	−	4044.80i	−0.114163	−	0.246348i
$647$	6903.05			0.419454			0.209727	−	0.977760i	$-0.432742\pi$
$647$	6903.05			0.419454			0.209727	+	0.977760i	$0.432742\pi$
$648$	2642.47	−	9588.21i	0.160195	−	0.581266i
$649$	4186.71			0.253225
$650$	6946.61	+	14989.8i	0.419182	+	0.904538i
$651$		−	15501.9i		−	0.933282i
$652$	7663.35	+	6492.56i	0.460307	+	0.389982i
$653$		−	2726.04i		−	0.163366i	−0.996658	−	0.0816831i	$-0.973970\pi$
$653$		−	2726.04i		−	0.163366i	0.996658	−	0.0816831i	$-0.0260295\pi$
$654$	−4484.18	+	2078.06i	−0.268112	+	0.124249i
$655$	35675.3			2.12816
$656$	−4264.39	−	25603.8i	−0.253806	−	1.52387i
$657$	8274.95			0.491380
$658$	−4011.75	+	1859.13i	−0.237682	+	0.110147i
$659$		−	3361.65i		−	0.198712i	−0.995052	−	0.0993561i	$-0.968322\pi$
$659$		−	3361.65i		−	0.198712i	0.995052	−	0.0993561i	$-0.0316783\pi$
$660$	−16071.9	−	13616.5i	−0.947877	−	0.803062i
$661$			2623.17i			0.154356i	0.997017	+	0.0771780i	$0.0245910\pi$
$661$			2623.17i			0.154356i	−0.997017	+	0.0771780i	$0.975409\pi$
$662$	−1060.19	−	2287.74i	−0.0622438	−	0.134314i
$663$	10876.2			0.637100
$664$	−4333.18	−	1194.21i	−0.253253	−	0.0697955i
$665$	17759.2			1.03560
$666$	13294.4	+	28687.5i	0.773494	+	1.66910i
$667$			18599.9i			1.07975i
$668$	11705.1	−	13815.9i	0.677972	−	0.800229i
$669$			25882.8i			1.49580i
$670$	33630.9	−	15585.3i	1.93922	−	0.898674i
$671$	−13380.4			−0.769816
$672$	−16093.0	+	10986.2i	−0.923813	+	0.630655i
$673$	29899.5			1.71254			0.856272	−	0.516525i	$-0.172775\pi$
$673$	29899.5			1.71254			0.856272	+	0.516525i	$0.172775\pi$
$674$	−543.911	+	252.060i	−0.0310841	+	0.0144050i
$675$		−	4668.77i		−	0.266224i
$676$	−22658.9	+	26744.9i	−1.28919	+	1.52167i
$677$			15936.3i			0.904699i	0.891841	+	0.452349i	$0.149414\pi$
$677$			15936.3i			0.904699i	−0.891841	+	0.452349i	$0.850586\pi$
$678$	8834.80	+	19064.3i	0.500440	+	1.07988i
$679$	−2465.16			−0.139329
$680$	−5205.21	−	1434.53i	−0.293545	−	0.0808998i
$681$	−33057.4			−1.86015
$682$	−4073.11	−	8789.22i	−0.228691	−	0.493485i
$683$		−	12301.8i		−	0.689186i	−0.938752	−	0.344593i	$-0.888017\pi$
$683$		−	12301.8i		−	0.689186i	0.938752	−	0.344593i	$-0.111983\pi$
$684$	−19931.0	−	16886.0i	−1.11416	−	0.943936i
$685$			31911.5i			1.77996i
$686$	−17502.3	+	8110.93i	−0.974111	+	0.451424i
$687$	−29714.7			−1.65020
$688$	11388.2	−	1896.74i	0.631063	−	0.105106i
$689$	30273.1			1.67390
$690$	−30259.0	+	14022.7i	−1.66948	+	0.773671i
$691$		−	14776.5i		−	0.813495i	−0.913541	−	0.406748i	$-0.866663\pi$
$691$		−	14776.5i		−	0.813495i	0.913541	−	0.406748i	$-0.133337\pi$
$692$	23250.0	+	19697.9i	1.27721	+	1.08208i
$693$		−	11430.1i		−	0.626541i
$694$	−1901.85	−	4103.94i	−0.104025	−	0.224472i
$695$	−16673.6			−0.910022
$696$	−8282.11	+	30051.6i	−0.451052	+	1.63664i
$697$	6894.68			0.374684
$698$	−7107.65	−	15337.4i	−0.385428	−	0.831701i
$699$		−	45893.1i		−	2.48331i
$700$	5082.24	−	5998.72i	0.274415	−	0.323900i
$701$		−	1133.13i		−	0.0610524i	−0.999534	−	0.0305262i	$-0.990282\pi$
$701$		−	1133.13i		−	0.0610524i	0.999534	−	0.0305262i	$-0.00971830\pi$
$702$	13494.0	−	6253.41i	0.725496	−	0.336210i
$703$	−29428.3			−1.57882
$704$	−6237.78	+	10457.3i	−0.333942	+	0.559837i
$705$	−12683.0			−0.677546
$706$	9771.11	−	4528.14i	0.520879	−	0.241386i
$707$			8781.70i			0.467143i
$708$	7181.03	−	8475.97i	0.381186	−	0.449924i
$709$			5866.05i			0.310725i	0.987858	+	0.155363i	$0.0496546\pi$
$709$			5866.05i			0.310725i	−0.987858	+	0.155363i	$0.950345\pi$
$710$	13858.3	+	29904.3i	0.732525	+	1.58069i
$711$	11165.3			0.588932
$712$	9267.31	−	33626.4i	0.487791	−	1.76995i
$713$	−15337.1			−0.805579
$714$	−2176.25	−	4696.06i	−0.114067	−	0.246142i
$715$			27075.0i			1.41615i
$716$	−4180.30	−	3541.64i	−0.218192	−	0.184857i
$717$		−	38559.6i		−	2.00842i
$718$	7183.58	−	3329.02i	0.373383	−	0.173034i
$719$	−22225.4			−1.15281			−0.576404	−	0.817165i	$-0.695545\pi$
$719$	−22225.4			−1.15281			−0.576404	+	0.817165i	$0.695545\pi$
$720$	−31207.9	+	5197.78i	−1.61535	+	0.269042i
$721$	−7278.77			−0.375971
$722$	4457.64	−	2065.76i	0.229773	−	0.106482i
$723$			4885.83i			0.251322i
$724$	−7526.07	−	6376.25i	−0.386332	−	0.327309i
$725$		−	12577.6i		−	0.644304i
$726$	7180.12	+	15493.7i	0.367051	+	0.792047i
$727$	−32369.6			−1.65134			−0.825669	−	0.564155i	$-0.809202\pi$
$727$	−32369.6			−1.65134			−0.825669	+	0.564155i	$0.809202\pi$
$728$	24145.1	+	6654.30i	1.22923	+	0.338770i
$729$	29287.1			1.48794
$730$	3922.08	+	8463.31i	0.198853	+	0.429098i
$731$			3066.66i			0.155164i
$732$	−22950.1	+	27088.6i	−1.15882	+	1.36779i
$733$		−	22168.7i		−	1.11708i	−0.829478	−	0.558540i	$-0.811362\pi$
$733$		−	22168.7i		−	1.11708i	0.829478	−	0.558540i	$-0.188638\pi$
$734$	406.040	−	188.167i	0.0204185	−	0.00946238i
$735$	−17357.1			−0.871058
$736$	10869.4	+	15921.9i	0.544361	+	0.797405i
$737$	22204.4			1.10978
$738$	36655.6	−	16987.0i	1.82834	−	0.847290i
$739$		−	17907.0i		−	0.891368i	−0.895190	−	0.445684i	$-0.852960\pi$
$739$		−	17907.0i		−	0.891368i	0.895190	−	0.445684i	$-0.147040\pi$
$740$	−23039.4	+	27194.0i	−1.14452	+	1.35091i
$741$			59316.8i			2.94070i
$742$	−6057.43	−	13071.1i	−0.299697	−	0.646706i
$743$	−5143.09			−0.253946			−0.126973	−	0.991906i	$-0.540526\pi$
$743$	−5143.09			−0.253946			−0.126973	+	0.991906i	$0.540526\pi$
$744$	−24779.9	−	6829.24i	−1.22107	−	0.336521i
$745$	−32760.6			−1.61108
$746$	3.94733	+	8.51780i	0.000193729	+	0.000418041i
$747$		−	6995.90i		−	0.342659i
$748$	−2467.77	−	2090.75i	−0.120629	−	0.102200i
$749$		−	6449.02i		−	0.314609i
$750$	−15054.1	+	6976.41i	−0.732933	+	0.339657i
$751$	−3265.94			−0.158689			−0.0793447	−	0.996847i	$-0.525283\pi$
$751$	−3265.94			−0.158689			−0.0793447	+	0.996847i	$0.525283\pi$
$752$	1204.49	+	7231.85i	0.0584085	+	0.350689i
$753$	−42760.1			−2.06941
$754$	36352.7	−	16846.6i	1.75582	−	0.813683i
$755$			17353.6i			0.836507i
$756$	−5400.11	−	4575.09i	−0.259788	−	0.220098i
$757$			16450.7i			0.789841i	0.918715	+	0.394920i	$0.129228\pi$
$757$			16450.7i			0.789841i	−0.918715	+	0.394920i	$0.870772\pi$
$758$	5390.06	+	11631.0i	0.258279	+	0.557332i
$759$	−19978.1			−0.955414
$760$	7823.67	−	28388.2i	0.373414	−	1.35493i
$761$	23296.6			1.10972			0.554862	−	0.831943i	$-0.312771\pi$
$761$	23296.6			1.10972			0.554862	+	0.831943i	$0.312771\pi$
$762$	−19828.6	−	42787.5i	−0.942671	−	2.03416i
$763$		−	3023.05i		−	0.143436i
$764$	4707.48	−	5556.37i	0.222920	−	0.263118i
$765$		−	8403.79i		−	0.397176i
$766$	18305.5	−	8483.15i	0.863452	−	0.400142i
$767$	−14278.8			−0.672198
$768$	10471.8	+	30564.7i	0.492016	+	1.43608i
$769$	8413.53			0.394538			0.197269	−	0.980349i	$-0.436793\pi$
$769$	8413.53			0.394538			0.197269	+	0.980349i	$0.436793\pi$
$770$	11690.3	−	5417.52i	0.547127	−	0.253550i
$771$		−	52608.4i		−	2.45739i
$772$	5286.12	−	6239.35i	0.246440	−	0.290880i
$773$			4242.38i			0.197397i	0.995117	+	0.0986985i	$0.0314679\pi$
$773$			4242.38i			0.197397i	−0.995117	+	0.0986985i	$0.968532\pi$
$774$	7555.59	+	16303.9i	0.350878	+	0.757148i
$775$	10371.2			0.480703
$776$	−1086.01	+	3940.58i	−0.0502390	+	0.182292i
$777$	−34166.6			−1.57750
$778$	−2575.55	−	5557.69i	−0.118686	−	0.256109i
$779$			37602.3i			1.72945i
$780$	54813.2	+	46438.9i	2.51619	+	2.13177i
$781$			19743.9i			0.904601i
$782$	−4646.13	+	2153.12i	−0.212462	+	0.0984594i
$783$	−11322.5			−0.516772
$784$	1648.38	+	9897.02i	0.0750903	+	0.450848i
$785$	6818.05			0.309996
$786$	51449.1	−	23842.6i	2.33477	−	1.08198i
$787$			42437.9i			1.92217i	0.276251	+	0.961085i	$0.410908\pi$
$787$			42437.9i			1.92217i	−0.276251	+	0.961085i	$0.589092\pi$
$788$	−12099.4	−	10250.9i	−0.546985	−	0.463418i
$789$			5510.67i			0.248650i
$790$	5292.01	+	11419.4i	0.238331	+	0.514285i
$791$	−12852.4			−0.577722
$792$	−18271.1	−	5035.44i	−0.819740	−	0.225917i
$793$	45633.9			2.04352
$794$	10049.3	+	21684.9i	0.449162	+	0.969231i
$795$		−	41323.9i		−	1.84353i
$796$	10982.4	−	12962.8i	0.489020	−	0.577204i
$797$		−	14533.4i		−	0.645921i	−0.946412	−	0.322960i	$-0.895322\pi$
$797$		−	14533.4i		−	0.645921i	0.946412	−	0.322960i	$-0.104678\pi$
$798$	25611.4	−	11868.9i	1.13613	−	0.526508i
$799$	−1947.42			−0.0862263
$800$	−7350.05	−	10766.7i	−0.324830	−	0.475825i
$801$	54289.8			2.39480
$802$	−12414.3	+	5753.04i	−0.546588	+	0.253300i
$803$			5587.79i			0.245565i
$804$	38084.8	−	44952.6i	1.67058	−	1.97184i
$805$		−	20399.4i		−	0.893147i
$806$	13891.3	+	29975.6i	0.607073	+	1.30998i
$807$	−15809.4			−0.689612
$808$	14037.6	+	3868.71i	0.611190	+	0.168442i
$809$	−33745.5			−1.46654			−0.733268	−	0.679940i	$-0.762006\pi$
$809$	−33745.5			−1.46654			−0.733268	+	0.679940i	$0.762006\pi$
$810$	7337.12	+	15832.5i	0.318272	+	0.686787i
$811$		−	37911.4i		−	1.64149i	−0.571295	−	0.820744i	$-0.693559\pi$
$811$		−	37911.4i		−	1.64149i	0.571295	−	0.820744i	$-0.306441\pi$
$812$	−14547.8	−	12325.2i	−0.628729	−	0.532673i
$813$		−	10908.2i		−	0.470560i
$814$	−19371.7	+	8977.25i	−0.834124	+	0.386551i
$815$	−17622.4			−0.757404
$816$	−8465.42	+	1409.94i	−0.363173	+	0.0604876i
$817$	−16725.0			−0.716197
$818$	21526.7	−	9975.94i	0.920127	−	0.426406i
$819$			38982.2i			1.66319i
$820$	34747.4	+	29438.7i	1.47979	+	1.25371i
$821$			10077.5i			0.428388i	0.976791	+	0.214194i	$0.0687125\pi$
$821$			10077.5i			0.428388i	−0.976791	+	0.214194i	$0.931288\pi$
$822$	21327.1	+	46021.1i	0.904951	+	1.95276i
$823$	45305.9			1.91891			0.959455	−	0.281862i	$-0.0909520\pi$
$823$	45305.9			1.91891			0.959455	+	0.281862i	$0.0909520\pi$
$824$	−3206.60	+	11635.2i	−0.135567	+	0.491905i
$825$	13509.5			0.570111
$826$	2857.08	+	6165.19i	0.120352	+	0.259702i
$827$		−	25463.0i		−	1.07066i	−0.844643	−	0.535330i	$-0.820187\pi$
$827$		−	25463.0i		−	1.07066i	0.844643	−	0.535330i	$-0.179813\pi$
$828$	−19396.4	+	22894.1i	−0.814095	+	0.960900i
$829$		−	5536.37i		−	0.231949i	−0.993252	−	0.115975i	$-0.963001\pi$
$829$		−	5536.37i		−	0.231949i	0.993252	−	0.115975i	$-0.0369991\pi$
$830$	7155.15	−	3315.85i	0.299228	−	0.138668i
$831$	44547.0			1.85959
$832$	21273.9	−	35664.7i	0.886466	−	1.48612i
$833$	−2665.11			−0.110853
$834$	−24045.8	+	11143.3i	−0.998366	+	0.462664i
$835$			31770.5i			1.31672i
$836$	11402.5	−	13458.8i	0.471729	−	0.556795i
$837$		−	9336.26i		−	0.385554i
$838$	−6038.97	−	13031.3i	−0.248941	−	0.537181i
$839$	5691.61			0.234203			0.117101	−	0.993120i	$-0.462640\pi$
$839$	5691.61			0.234203			0.117101	+	0.993120i	$0.462640\pi$
$840$	9083.36	−	32959.0i	0.373102	−	1.35380i
$841$	−6113.63			−0.250672
$842$	−15928.5	−	34371.5i	−0.651938	−	1.40679i
$843$			29272.7i			1.19597i
$844$	−28750.4	−	24358.0i	−1.17255	−	0.993409i
$845$		−	61501.6i		−	2.50381i
$846$	−10353.5	+	4798.02i	−0.420756	+	0.194987i
$847$	−10445.2			−0.423734
$848$	−23562.9	+	3924.47i	−0.954188	+	0.158923i
$849$	56207.8			2.27214
$850$	3141.80	−	1455.97i	0.126780	−	0.0587524i
$851$			33803.3i			1.36165i
$852$	39971.5	+	33864.7i	1.60728	+	1.36172i
$853$		−	13395.7i		−	0.537701i	−0.963182	−	0.268850i	$-0.913356\pi$
$853$		−	13395.7i		−	0.537701i	0.963182	−	0.268850i	$-0.0866437\pi$
$854$	−9131.02	−	19703.5i	−0.365875	−	0.789508i
$855$	45832.6			1.83327
$856$	−10308.8	−	2841.07i	−0.411621	−	0.113441i
$857$	−11513.9			−0.458935			−0.229468	−	0.973316i	$-0.573698\pi$
$857$	−11513.9			−0.458935			−0.229468	+	0.973316i	$0.573698\pi$
$858$	18094.8	+	39046.2i	0.719986	+	1.55363i
$859$		−	9878.11i		−	0.392359i	−0.980568	−	0.196180i	$-0.937146\pi$
$859$		−	9878.11i		−	0.392359i	0.980568	−	0.196180i	$-0.0628536\pi$
$860$	−13093.9	+	15455.2i	−0.519186	+	0.612810i
$861$			43656.6i			1.72801i
$862$	−24597.6	+	11399.0i	−0.971921	+	0.450409i
$863$	−48500.5			−1.91307			−0.956533	−	0.291623i	$-0.905805\pi$
$863$	−48500.5			−1.91307			−0.956533	+	0.291623i	$0.905805\pi$
$864$	−9692.29	+	6616.59i	−0.381642	+	0.260534i
$865$	−53464.8			−2.10157
$866$	−20148.5	+	9337.25i	−0.790617	+	0.366389i
$867$		−	2279.60i		−	0.0892956i
$868$	10163.1	−	11995.8i	0.397417	−	0.469083i
$869$			7539.54i			0.294317i
$870$	−22996.2	−	49622.7i	−0.896143	−	1.93376i
$871$	−75727.9			−2.94597
$872$	−4832.37	−	1331.78i	−0.187666	−	0.0517200i
$873$	−6362.06			−0.246647
$874$	−11742.7	−	25339.1i	−0.454464	−	0.980673i
$875$		−	10148.9i		−	0.392109i
$876$	11312.4	+	9584.15i	0.436315	+	0.369656i
$877$		−	34861.3i		−	1.34228i	−0.741329	−	0.671142i	$-0.765804\pi$
$877$		−	34861.3i		−	1.34228i	0.741329	−	0.671142i	$-0.234196\pi$
$878$	−29199.3	+	13531.6i	−1.12236	+	0.520124i
$879$	−20127.2			−0.772325
$880$	−3509.89	−	21073.6i	−0.134453	−	0.807264i
$881$	19255.3			0.736354			0.368177	−	0.929756i	$-0.379982\pi$
$881$	19255.3			0.736354			0.368177	+	0.929756i	$0.379982\pi$
$882$	−14169.1	+	6566.25i	−0.540927	+	0.250677i
$883$			45822.7i			1.74638i	0.487378	+	0.873191i	$0.337954\pi$
$883$			45822.7i			1.74638i	−0.487378	+	0.873191i	$0.662046\pi$
$884$	8416.32	+	7130.49i	0.320217	+	0.271294i
$885$			19491.0i			0.740320i
$886$	18320.7	+	39533.6i	0.694691	+	1.49905i
$887$	−36147.0			−1.36832			−0.684160	−	0.729332i	$-0.739831\pi$
$887$	−36147.0			−1.36832			−0.684160	+	0.729332i	$0.739831\pi$
$888$	−15051.8	+	54615.6i	−0.568814	+	2.06394i
$889$	28845.6			1.08825
$890$	25731.7	+	55525.6i	0.969134	+	2.09126i
$891$			10453.2i			0.393037i
$892$	−16968.9	+	20028.9i	−0.636951	+	0.751812i
$893$		−	10620.9i		−	0.397999i
$894$	−47245.7	+	21894.7i	−1.76749	+	0.819091i
$895$	9612.86			0.359020
$896$	−19655.8	−	2049.26i	−0.732873	−	0.0764072i
$897$	68135.2			2.53620
$898$	−37361.0	+	17313.9i	−1.38837	+	0.643398i
$899$		−	25151.8i		−	0.933102i
$900$	13116.2	−	15481.4i	0.485784	−	0.573385i
$901$		−	6345.10i		−	0.234613i
$902$	11470.7	+	24752.3i	0.423430	+	0.913705i
$903$	−19417.9			−0.715599
$904$	−5662.01	+	20544.6i	−0.208314	+	0.755867i
$905$	17306.7			0.635683
$906$	11597.8	+	25026.5i	0.425289	+	0.917715i
$907$			41102.7i			1.50473i	0.658744	+	0.752367i	$0.271088\pi$
$907$			41102.7i			1.50473i	−0.658744	+	0.752367i	$0.728912\pi$
$908$	−25580.7	−	21672.5i	−0.934940	−	0.792102i
$909$			22663.7i			0.826960i
$910$	−39869.6	+	18476.4i	−1.45238	+	0.673063i
$911$	3741.54			0.136073			0.0680366	−	0.997683i	$-0.478327\pi$
$911$	3741.54			0.136073			0.0680366	+	0.997683i	$0.478327\pi$
$912$	−7689.56	−	46168.8i	−0.279196	−	1.67632i
$913$	4724.09			0.171243
$914$	37341.9	−	17305.0i	1.35138	−	0.626258i
$915$		−	62291.9i		−	2.25061i
$916$	−22994.1	−	19481.1i	−0.829416	−	0.702699i
$917$			34684.9i			1.24907i
$918$	−1310.68	−	2828.28i	−0.0471231	−	0.101685i
$919$	44209.7			1.58688			0.793441	−	0.608647i	$-0.208288\pi$
$919$	44209.7			1.58688			0.793441	+	0.608647i	$0.208288\pi$
$920$	−32608.6	−	8986.79i	−1.16856	−	0.322050i
$921$	−77368.9			−2.76807
$922$	5046.93	+	10890.6i	0.180273	+	0.389005i
$923$		−	67336.6i		−	2.40131i
$924$	13238.5	−	15625.7i	0.471335	−	0.556330i
$925$		−	22858.4i		−	0.812519i
$926$	15194.9	−	7041.62i	0.539237	−	0.249894i
$927$	−18784.9			−0.665564
$928$	−26110.9	+	17825.0i	−0.923634	+	0.630533i
$929$	−21198.8			−0.748664			−0.374332	−	0.927295i	$-0.622128\pi$
$929$	−21198.8			−0.748664			−0.374332	+	0.927295i	$0.622128\pi$
$930$	40917.7	−	18962.1i	1.44274	−	0.668595i
$931$		−	14535.0i		−	0.511670i
$932$	30087.7	−	35513.3i	1.05746	−	1.24815i
$933$		−	41990.1i		−	1.47341i
$934$	−11871.0	−	25615.9i	−0.415878	−	0.897408i
$935$	5674.79			0.198487
$936$	62313.4	+	17173.3i	2.17604	+	0.599709i
$937$	12461.7			0.434478			0.217239	−	0.976118i	$-0.430295\pi$
$937$	12461.7			0.434478			0.217239	+	0.976118i	$0.430295\pi$
$938$	15152.6	+	32697.3i	0.527452	+	1.13817i
$939$			59683.2i			2.07422i
$940$	−9814.48	−	8315.04i	−0.340546	−	0.288518i
$941$			34591.9i			1.19837i	0.800612	+	0.599183i	$0.204508\pi$
$941$			34591.9i			1.19837i	−0.800612	+	0.599183i	$0.795492\pi$
$942$	9832.64	−	4556.65i	0.340090	−	0.157605i
$943$	43192.5			1.49156
$944$	11113.8	−	1851.03i	0.383180	−	0.0638200i
$945$	12417.9			0.427464
$946$	−11009.5	+	5102.03i	−0.378382	+	0.175350i
$947$		−	7015.40i		−	0.240729i	−0.992730	−	0.120364i	$-0.961594\pi$
$947$		−	7015.40i		−	0.240729i	0.992730	−	0.120364i	$-0.0384063\pi$
$948$	15263.7	+	12931.8i	0.522936	+	0.443043i
$949$		−	19057.1i		−	0.651866i
$950$	7940.61	+	17134.8i	0.271187	+	0.585184i
$951$	63386.9			2.16137
$952$	1394.71	−	5060.70i	0.0474819	−	0.172288i
$953$	6101.32			0.207388			0.103694	−	0.994609i	$-0.466934\pi$
$953$	6101.32			0.207388			0.103694	+	0.994609i	$0.466934\pi$
$954$	−15632.9	−	33733.8i	−0.530540	−	1.14483i
$955$			12777.2i			0.432944i
$956$	25279.8	−	29838.5i	0.855238	−	1.00946i
$957$		−	32762.7i		−	1.10665i
$958$	22478.5	−	10417.0i	0.758087	−	0.351314i
$959$	−31025.5			−1.04470
$960$	−48683.6	−	29039.6i	−1.63672	−	0.976303i
$961$	−9051.43			−0.303831
$962$	66067.0	−	30616.9i	2.21423	−	1.02612i
$963$		−	16643.5i		−	0.556937i
$964$	−3203.17	+	3780.79i	−0.107020	+	0.126319i
$965$			14347.8i			0.478623i
$966$	−13633.4	−	29418.9i	−0.454085	−	0.979854i
$967$	46946.0			1.56120			0.780601	−	0.625030i	$-0.214913\pi$
$967$	46946.0			1.56120			0.780601	+	0.625030i	$0.214913\pi$
$968$	−4601.57	+	16696.8i	−0.152789	+	0.554396i
$969$	12432.5			0.412167
$970$	−3015.43	−	6506.88i	−0.0998140	−	0.215385i
$971$		−	11698.2i		−	0.386624i	−0.981137	−	0.193312i	$-0.938077\pi$
$971$		−	11698.2i		−	0.386624i	0.981137	−	0.193312i	$-0.0619230\pi$
$972$	31846.7	+	26981.2i	1.05091	+	0.890352i
$973$		−	16210.7i		−	0.534112i
$974$	−39054.6	+	18098.7i	−1.28480	+	0.595401i
$975$	−46074.2			−1.51339
$976$	−35518.8	+	5915.78i	−1.16489	+	0.194016i
$977$	−42119.4			−1.37924			−0.689621	−	0.724171i	$-0.742223\pi$
$977$	−42119.4			−1.37924			−0.689621	+	0.724171i	$0.742223\pi$
$978$	−25414.1	+	11777.4i	−0.830933	+	0.385072i
$979$			36660.0i			1.19679i
$980$	−13431.4	−	11379.4i	−0.437808	−	0.370920i
$981$		−	7801.84i		−	0.253918i
$982$	−6147.71	−	13265.9i	−0.199777	−	0.431093i
$983$	55335.3			1.79545			0.897723	−	0.440561i	$-0.145220\pi$
$983$	55335.3			1.79545			0.897723	+	0.440561i	$0.145220\pi$
$984$	69785.4	+	19232.6i	2.26085	+	0.623082i
$985$	27823.4			0.900027
$986$	−3530.96	−	7619.34i	−0.114045	−	0.246095i
$987$		−	12330.9i		−	0.397667i
$988$	−38888.3	+	45901.0i	−1.25223	+	1.47804i
$989$			19211.4i			0.617682i
$990$	30170.1	−	13981.5i	0.968554	−	0.448848i
$991$	−39869.2			−1.27799			−0.638994	−	0.769211i	$-0.720649\pi$
$991$	−39869.2			−1.27799			−0.638994	+	0.769211i	$0.720649\pi$
$992$	−14698.1	−	21530.4i	−0.470428	−	0.689105i
$993$	7031.83			0.224721
$994$	−29074.1	+	13473.6i	−0.927742	+	0.429935i
$995$			29808.8i			0.949751i
$996$	8102.74	−	9563.90i	0.257776	−	0.304261i
$997$		−	3724.66i		−	0.118316i	−0.998249	−	0.0591580i	$-0.981158\pi$
$997$		−	3724.66i		−	0.118316i	0.998249	−	0.0591580i	$-0.0188416\pi$
$998$	−7180.05	−	15493.6i	−0.227736	−	0.491423i
$999$	−20577.4			−0.651692

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.4.c.b.69.4	yes	24
4.3	odd	2		544.4.c.a.273.21		24
8.3	odd	2		544.4.c.a.273.4		24
8.5	even	2	inner	136.4.c.b.69.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.c.b.69.3	✓	24	8.5	even	2	inner
136.4.c.b.69.4	yes	24	1.1	even	1	trivial
544.4.c.a.273.4		24	8.3	odd	2
544.4.c.a.273.21		24	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	136.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.56626 + 1.18926i) q^{2} -7.88789i q^{3} +(5.17134 - 6.10387i) q^{4} +14.0362i q^{5} +(9.38073 + 20.2424i) q^{6} -13.6466 q^{7} +(-6.01189 + 21.8142i) q^{8} -35.2189 q^{9} +O(q^{10})\)	\(q+(-2.56626 + 1.18926i) q^{2} -7.88789i q^{3} +(5.17134 - 6.10387i) q^{4} +14.0362i q^{5} +(9.38073 + 20.2424i) q^{6} -13.6466 q^{7} +(-6.01189 + 21.8142i) q^{8} -35.2189 q^{9} +(-16.6927 - 36.0206i) q^{10} -23.7821i q^{11} +(-48.1467 - 40.7909i) q^{12} +81.1088i q^{13} +(35.0206 - 16.2293i) q^{14} +110.716 q^{15} +(-10.5146 - 63.1304i) q^{16} +17.0000 q^{17} +(90.3806 - 41.8843i) q^{18} +92.7147i q^{19} +(85.6755 + 72.5861i) q^{20} +107.643i q^{21} +(28.2830 + 61.0310i) q^{22} +106.498 q^{23} +(172.068 + 47.4212i) q^{24} -72.0160 q^{25} +(-96.4592 - 208.146i) q^{26} +64.8296i q^{27} +(-70.5710 + 83.2970i) q^{28} +174.650i q^{29} +(-284.127 + 131.670i) q^{30} -144.012 q^{31} +(102.061 + 149.504i) q^{32} -187.591 q^{33} +(-43.6263 + 20.2174i) q^{34} -191.547i q^{35} +(-182.129 + 214.972i) q^{36} +317.407i q^{37} +(-110.262 - 237.930i) q^{38} +639.777 q^{39} +(-306.189 - 84.3844i) q^{40} +405.570 q^{41} +(-128.015 - 276.239i) q^{42} +180.392i q^{43} +(-145.163 - 122.985i) q^{44} -494.341i q^{45} +(-273.302 + 126.654i) q^{46} -114.554 q^{47} +(-497.966 + 82.9379i) q^{48} -156.771 q^{49} +(184.812 - 85.6456i) q^{50} -134.094i q^{51} +(495.078 + 419.441i) q^{52} -373.241i q^{53} +(-77.0990 - 166.369i) q^{54} +333.811 q^{55} +(82.0417 - 297.688i) q^{56} +731.324 q^{57} +(-207.704 - 448.197i) q^{58} +176.045i q^{59} +(572.552 - 675.799i) q^{60} -562.626i q^{61} +(369.573 - 171.268i) q^{62} +480.617 q^{63} +(-439.714 - 262.289i) q^{64} -1138.46 q^{65} +(481.406 - 223.094i) q^{66} +933.658i q^{67} +(87.9127 - 103.766i) q^{68} -840.047i q^{69} +(227.798 + 491.557i) q^{70} -830.201 q^{71} +(211.732 - 768.270i) q^{72} -234.958 q^{73} +(-377.479 - 814.549i) q^{74} +568.055i q^{75} +(565.919 + 479.459i) q^{76} +324.544i q^{77} +(-1641.83 + 760.860i) q^{78} -317.026 q^{79} +(886.113 - 147.585i) q^{80} -439.541 q^{81} +(-1040.80 + 482.327i) q^{82} +198.641i q^{83} +(657.038 + 556.657i) q^{84} +238.616i q^{85} +(-214.532 - 462.932i) q^{86} +1377.62 q^{87} +(518.787 + 142.975i) q^{88} -1541.50 q^{89} +(587.898 + 1268.60i) q^{90} -1106.86i q^{91} +(550.738 - 650.052i) q^{92} +1135.95i q^{93} +(293.975 - 136.234i) q^{94} -1301.37 q^{95} +(1179.27 - 805.049i) q^{96} +180.644 q^{97} +(402.315 - 186.441i) q^{98} +837.579i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} + 5 q^{4} + 40 q^{6} + 84 q^{7} + 13 q^{8} - 216 q^{9}+O(q^{10}) \) 24 * q + q^2 + 5 * q^4 + 40 * q^6 + 84 * q^7 + 13 * q^8 - 216 * q^9	\( 24 q + q^{2} + 5 q^{4} + 40 q^{6} + 84 q^{7} + 13 q^{8} - 216 q^{9} - 16 q^{10} - 18 q^{12} + 26 q^{14} - 180 q^{15} - 103 q^{16} + 408 q^{17} - 5 q^{18} - 24 q^{20} + 172 q^{22} + 624 q^{23} - 310 q^{24} - 600 q^{25} - 180 q^{26} - 132 q^{28} - 80 q^{30} - 744 q^{31} - 39 q^{32} - 280 q^{33} + 17 q^{34} + 791 q^{36} - 162 q^{38} + 1236 q^{39} - 1396 q^{40} + 1132 q^{42} + 886 q^{44} - 1246 q^{46} - 956 q^{47} - 2226 q^{48} + 1688 q^{49} + 2505 q^{50} + 2544 q^{52} - 3264 q^{54} + 1684 q^{55} - 1100 q^{56} - 168 q^{57} + 2800 q^{58} + 2520 q^{60} - 1946 q^{62} - 2520 q^{63} - 2143 q^{64} - 72 q^{65} + 3660 q^{66} + 85 q^{68} - 5084 q^{70} + 1532 q^{71} - 2277 q^{72} + 216 q^{73} + 2188 q^{74} + 2094 q^{76} - 4748 q^{78} - 3176 q^{79} + 116 q^{80} + 2040 q^{81} + 3198 q^{82} + 5916 q^{84} - 2066 q^{86} - 236 q^{87} - 3598 q^{88} - 424 q^{89} + 2180 q^{90} + 1940 q^{92} - 2156 q^{94} - 1248 q^{95} - 4674 q^{96} - 1304 q^{97} + 3705 q^{98}+O(q^{100}) \) 24 * q + q^2 + 5 * q^4 + 40 * q^6 + 84 * q^7 + 13 * q^8 - 216 * q^9 - 16 * q^10 - 18 * q^12 + 26 * q^14 - 180 * q^15 - 103 * q^16 + 408 * q^17 - 5 * q^18 - 24 * q^20 + 172 * q^22 + 624 * q^23 - 310 * q^24 - 600 * q^25 - 180 * q^26 - 132 * q^28 - 80 * q^30 - 744 * q^31 - 39 * q^32 - 280 * q^33 + 17 * q^34 + 791 * q^36 - 162 * q^38 + 1236 * q^39 - 1396 * q^40 + 1132 * q^42 + 886 * q^44 - 1246 * q^46 - 956 * q^47 - 2226 * q^48 + 1688 * q^49 + 2505 * q^50 + 2544 * q^52 - 3264 * q^54 + 1684 * q^55 - 1100 * q^56 - 168 * q^57 + 2800 * q^58 + 2520 * q^60 - 1946 * q^62 - 2520 * q^63 - 2143 * q^64 - 72 * q^65 + 3660 * q^66 + 85 * q^68 - 5084 * q^70 + 1532 * q^71 - 2277 * q^72 + 216 * q^73 + 2188 * q^74 + 2094 * q^76 - 4748 * q^78 - 3176 * q^79 + 116 * q^80 + 2040 * q^81 + 3198 * q^82 + 5916 * q^84 - 2066 * q^86 - 236 * q^87 - 3598 * q^88 - 424 * q^89 + 2180 * q^90 + 1940 * q^92 - 2156 * q^94 - 1248 * q^95 - 4674 * q^96 - 1304 * q^97 + 3705 * q^98

Introduction

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