LMFDB - Embedded newform 171.4.u.b.55.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,4,Mod(28,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("171.28");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	171.u (of order $9$, degree $6$, 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:	$10.0893266110$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			55.2
Character	$\chi$	$=$	171.55
Dual form			171.4.u.b.28.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.477474 + 2.70789i) q^{2} +(0.412858 + 0.150268i) q^{4} +(-5.11043 + 1.86004i) q^{5} +(11.7392 + 20.3328i) q^{7} +(-11.6027 + 20.0964i) q^{8} +O(q^{10})$	\(q+(-0.477474 + 2.70789i) q^{2} +(0.412858 + 0.150268i) q^{4} +(-5.11043 + 1.86004i) q^{5} +(11.7392 + 20.3328i) q^{7} +(-11.6027 + 20.0964i) q^{8} +(-2.59670 - 14.7266i) q^{10} +(23.6008 - 40.8778i) q^{11} +(-14.0615 + 11.7990i) q^{13} +(-60.6643 + 22.0800i) q^{14} +(-46.1865 - 38.7550i) q^{16} +(-16.8867 + 95.7695i) q^{17} +(-25.4519 + 78.8112i) q^{19} -2.38939 q^{20} +(99.4237 + 83.4264i) q^{22} +(-84.7939 - 30.8625i) q^{23} +(-73.0988 + 61.3372i) q^{25} +(-25.2364 - 43.7108i) q^{26} +(1.79124 + 10.1586i) q^{28} +(-16.0833 - 91.2129i) q^{29} +(-142.156 - 246.222i) q^{31} +(-15.2136 + 12.7658i) q^{32} +(-251.270 - 91.4549i) q^{34} +(-97.8122 - 82.0742i) q^{35} +232.514 q^{37} +(-201.259 - 106.551i) q^{38} +(21.9144 - 124.283i) q^{40} +(197.399 + 165.638i) q^{41} +(-75.7804 + 27.5818i) q^{43} +(15.8864 - 13.3303i) q^{44} +(124.059 - 214.877i) q^{46} +(85.6235 + 485.595i) q^{47} +(-104.116 + 180.335i) q^{49} +(-131.192 - 227.230i) q^{50} +(-7.57843 + 2.75832i) q^{52} +(106.793 + 38.8693i) q^{53} +(-44.5757 + 252.802i) q^{55} -544.824 q^{56} +254.674 q^{58} +(31.3837 - 177.986i) q^{59} +(259.591 + 94.4833i) q^{61} +(734.617 - 267.379i) q^{62} +(-268.473 - 465.008i) q^{64} +(49.9138 - 86.4532i) q^{65} +(26.9102 + 152.615i) q^{67} +(-21.3629 + 37.0017i) q^{68} +(268.951 - 225.676i) q^{70} +(577.366 - 210.144i) q^{71} +(368.338 + 309.072i) q^{73} +(-111.019 + 629.622i) q^{74} +(-22.3508 + 28.7132i) q^{76} +1108.22 q^{77} +(975.594 + 818.621i) q^{79} +(308.119 + 112.146i) q^{80} +(-542.782 + 455.448i) q^{82} +(154.093 + 266.896i) q^{83} +(-91.8370 - 520.834i) q^{85} +(-38.5053 - 218.375i) q^{86} +(547.665 + 948.584i) q^{88} +(-32.1471 + 26.9746i) q^{89} +(-404.979 - 147.400i) q^{91} +(-30.3702 - 25.4836i) q^{92} -1355.82 q^{94} +(-16.5219 - 450.101i) q^{95} +(98.6409 - 559.420i) q^{97} +(-438.614 - 368.041i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} - 24 q^{4} + 6 q^{5} + 3 q^{7} + 75 q^{8}+O(q^{10}) $ 24 * q + 6 * q^2 - 24 * q^4 + 6 * q^5 + 3 * q^7 + 75 * q^8	$ 24 q + 6 q^{2} - 24 q^{4} + 6 q^{5} + 3 q^{7} + 75 q^{8} + 75 q^{10} - 39 q^{11} - 156 q^{13} - 93 q^{14} + 504 q^{16} - 12 q^{17} + 546 q^{19} + 198 q^{20} - 6 q^{22} - 6 q^{23} - 498 q^{25} + 639 q^{26} - 1368 q^{28} + 630 q^{29} - 591 q^{31} - 147 q^{32} - 408 q^{34} - 2001 q^{35} - 72 q^{37} - 2934 q^{38} + 2886 q^{40} + 477 q^{41} + 588 q^{43} + 3423 q^{44} - 1728 q^{46} + 1242 q^{47} - 639 q^{49} + 1788 q^{50} + 2733 q^{52} + 300 q^{53} + 315 q^{55} - 4638 q^{56} - 2820 q^{58} - 2097 q^{59} - 2316 q^{61} + 1320 q^{62} - 1785 q^{64} + 2433 q^{65} + 57 q^{67} + 438 q^{68} - 213 q^{70} + 792 q^{71} + 4068 q^{73} - 4287 q^{74} + 5538 q^{76} - 3786 q^{77} + 1824 q^{79} + 2739 q^{80} + 2205 q^{82} - 1071 q^{83} - 2394 q^{85} + 5256 q^{86} + 1101 q^{88} + 3006 q^{89} - 3285 q^{91} + 1452 q^{92} - 1086 q^{94} + 3078 q^{95} - 2535 q^{97} + 2403 q^{98}+O(q^{100}) $ 24 * q + 6 * q^2 - 24 * q^4 + 6 * q^5 + 3 * q^7 + 75 * q^8 + 75 * q^10 - 39 * q^11 - 156 * q^13 - 93 * q^14 + 504 * q^16 - 12 * q^17 + 546 * q^19 + 198 * q^20 - 6 * q^22 - 6 * q^23 - 498 * q^25 + 639 * q^26 - 1368 * q^28 + 630 * q^29 - 591 * q^31 - 147 * q^32 - 408 * q^34 - 2001 * q^35 - 72 * q^37 - 2934 * q^38 + 2886 * q^40 + 477 * q^41 + 588 * q^43 + 3423 * q^44 - 1728 * q^46 + 1242 * q^47 - 639 * q^49 + 1788 * q^50 + 2733 * q^52 + 300 * q^53 + 315 * q^55 - 4638 * q^56 - 2820 * q^58 - 2097 * q^59 - 2316 * q^61 + 1320 * q^62 - 1785 * q^64 + 2433 * q^65 + 57 * q^67 + 438 * q^68 - 213 * q^70 + 792 * q^71 + 4068 * q^73 - 4287 * q^74 + 5538 * q^76 - 3786 * q^77 + 1824 * q^79 + 2739 * q^80 + 2205 * q^82 - 1071 * q^83 - 2394 * q^85 + 5256 * q^86 + 1101 * q^88 + 3006 * q^89 - 3285 * q^91 + 1452 * q^92 - 1086 * q^94 + 3078 * q^95 - 2535 * q^97 + 2403 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	−0.477474	+	2.70789i	−0.168813	+	0.957383i	0.776233	+	0.630446i	$0.217128\pi$
$2$	−0.477474	+	2.70789i	−0.168813	+	0.957383i	−0.945046	+	0.326938i	$0.893983\pi$
$3$		0			0
$3$		0			0
$4$	0.412858	+	0.150268i	0.0516073	+	0.0187835i
$5$	−5.11043	+	1.86004i	−0.457091	+	0.166367i	−0.560296	−	0.828293i	$-0.689312\pi$
$5$	−5.11043	+	1.86004i	−0.457091	+	0.166367i	0.103205	+	0.994660i	$0.467090\pi$
$6$		0			0
$7$	11.7392	+	20.3328i	0.633856	+	1.09787i	0.986756	+	0.162210i	$0.0518621\pi$
$7$	11.7392	+	20.3328i	0.633856	+	1.09787i	−0.352900	+	0.935661i	$0.614805\pi$
$8$	−11.6027	+	20.0964i	−0.512771	+	0.888146i
$9$		0			0
$10$	−2.59670	−	14.7266i	−0.0821148	−	0.465696i
$11$	23.6008	−	40.8778i	0.646901	−	1.12046i	−0.336959	−	0.941519i	$-0.609398\pi$
$11$	23.6008	−	40.8778i	0.646901	−	1.12046i	0.983859	−	0.178945i	$-0.0572685\pi$
$12$		0			0
$13$	−14.0615	+	11.7990i	−0.299997	+	0.251728i	−0.780343	−	0.625351i	$-0.784956\pi$
$13$	−14.0615	+	11.7990i	−0.299997	+	0.251728i	0.480346	+	0.877079i	$0.340511\pi$
$14$	−60.6643	+	22.0800i	−1.15809	+	0.421509i
$15$		0			0
$16$	−46.1865	−	38.7550i	−0.721663	−	0.605547i
$17$	−16.8867	+	95.7695i	−0.240920	+	1.36632i	0.588861	+	0.808235i	$0.299577\pi$
$17$	−16.8867	+	95.7695i	−0.240920	+	1.36632i	−0.829780	+	0.558090i	$0.811534\pi$
$18$		0			0
$19$	−25.4519	+	78.8112i	−0.307320	+	0.951606i
$19$	−25.4519	+	78.8112i	−0.307320	+	0.951606i
$20$	−2.38939			−0.0267142
$21$		0			0
$22$	99.4237	+	83.4264i	0.963509	+	0.808480i
$23$	−84.7939	−	30.8625i	−0.768728	−	0.279794i	−0.0722640	−	0.997386i	$-0.523022\pi$
$23$	−84.7939	−	30.8625i	−0.768728	−	0.279794i	−0.696464	+	0.717591i	$0.745245\pi$
$24$		0			0
$25$	−73.0988	+	61.3372i	−0.584791	+	0.490698i
$26$	−25.2364	−	43.7108i	−0.190357	−	0.329707i
$27$		0			0
$28$	1.79124	+	10.1586i	0.0120897	+	0.0685641i
$29$	−16.0833	−	91.2129i	−0.102986	−	0.584062i	−0.992006	−	0.126193i	$-0.959724\pi$
$29$	−16.0833	−	91.2129i	−0.102986	−	0.584062i	0.889020	−	0.457869i	$-0.151387\pi$
$30$		0			0
$31$	−142.156	−	246.222i	−0.823613	−	1.42654i	−0.902975	−	0.429693i	$-0.858622\pi$
$31$	−142.156	−	246.222i	−0.823613	−	1.42654i	0.0793624	−	0.996846i	$-0.474712\pi$
$32$	−15.2136	+	12.7658i	−0.0840443	+	0.0705215i
$33$		0			0
$34$	−251.270	−	91.4549i	−1.26743	−	0.461305i
$35$	−97.8122	−	82.0742i	−0.472380	−	0.396374i
$36$		0			0
$37$	232.514			1.03311			0.516555	−	0.856254i	$-0.327214\pi$
$37$	232.514			1.03311			0.516555	+	0.856254i	$0.327214\pi$
$38$	−201.259	−	106.551i	−0.859173	−	0.454866i
$39$		0			0
$40$	21.9144	−	124.283i	0.0866245	−	0.491272i
$41$	197.399	+	165.638i	0.751918	+	0.630934i	0.936009	−	0.351975i	$-0.114490\pi$
$41$	197.399	+	165.638i	0.751918	+	0.630934i	−0.184092	+	0.982909i	$0.558934\pi$
$42$		0			0
$43$	−75.7804	+	27.5818i	−0.268754	+	0.0978184i	−0.472882	−	0.881126i	$-0.656786\pi$
$43$	−75.7804	+	27.5818i	−0.268754	+	0.0978184i	0.204128	+	0.978944i	$0.434564\pi$
$44$	15.8864	−	13.3303i	0.0544310	−	0.0456730i
$45$		0			0
$46$	124.059	−	214.877i	0.397641	−	0.688735i
$47$	85.6235	+	485.595i	0.265734	+	1.50705i	0.766938	+	0.641721i	$0.221779\pi$
$47$	85.6235	+	485.595i	0.265734	+	1.50705i	−0.501205	+	0.865329i	$0.667110\pi$
$48$		0			0
$49$	−104.116	+	180.335i	−0.303547	+	0.525758i
$50$	−131.192	−	227.230i	−0.371066	−	0.642705i
$51$		0			0
$52$	−7.57843	+	2.75832i	−0.0202104	+	0.00735597i
$53$	106.793	+	38.8693i	0.276775	+	0.100738i	0.476679	−	0.879078i	$-0.341841\pi$
$53$	106.793	+	38.8693i	0.276775	+	0.100738i	−0.199903	+	0.979816i	$0.564063\pi$
$54$		0			0
$55$	−44.5757	+	252.802i	−0.109283	+	0.619777i
$56$	−544.824			−1.30009
$57$		0			0
$58$	254.674			0.576557
$59$	31.3837	−	177.986i	0.0692509	−	0.392741i	−0.930406	−	0.366532i	$-0.880545\pi$
$59$	31.3837	−	177.986i	0.0692509	−	0.392741i	0.999656	−	0.0262097i	$-0.00834376\pi$
$60$		0			0
$61$	259.591	+	94.4833i	0.544872	+	0.198317i	0.599767	−	0.800175i	$-0.295260\pi$
$61$	259.591	+	94.4833i	0.544872	+	0.198317i	−0.0548947	+	0.998492i	$0.517482\pi$
$62$	734.617	−	267.379i	1.50478	−	0.547695i
$63$		0			0
$64$	−268.473	−	465.008i	−0.524361	−	0.908219i
$65$	49.9138	−	86.4532i	0.0952468	−	0.164972i
$66$		0			0
$67$	26.9102	+	152.615i	0.0490686	+	0.278282i	0.999463	−	0.0327652i	$-0.0104314\pi$
$67$	26.9102	+	152.615i	0.0490686	+	0.278282i	−0.950394	+	0.311047i	$0.899320\pi$
$68$	−21.3629	+	37.0017i	−0.0380976	+	0.0659869i
$69$		0			0
$70$	268.951	−	225.676i	0.459225	−	0.385336i
$71$	577.366	−	210.144i	0.965080	−	0.351261i	0.189058	−	0.981966i	$-0.439457\pi$
$71$	577.366	−	210.144i	0.965080	−	0.351261i	0.776022	+	0.630705i	$0.217234\pi$
$72$		0			0
$73$	368.338	+	309.072i	0.590557	+	0.495536i	0.888395	−	0.459080i	$-0.151821\pi$
$73$	368.338	+	309.072i	0.590557	+	0.495536i	−0.297838	+	0.954616i	$0.596265\pi$
$74$	−111.019	+	629.622i	−0.174402	+	0.989082i
$75$		0			0
$76$	−22.3508	+	28.7132i	−0.0337344	+	0.0433372i
$77$	1108.22			1.64017
$78$		0			0
$79$	975.594	+	818.621i	1.38940	+	1.16585i	0.965581	+	0.260104i	$0.0837568\pi$
$79$	975.594	+	818.621i	1.38940	+	1.16585i	0.423824	+	0.905745i	$0.360688\pi$
$80$	308.119	+	112.146i	0.430609	+	0.156729i
$81$		0			0
$82$	−542.782	+	455.448i	−0.730979	+	0.613364i
$83$	154.093	+	266.896i	0.203781	+	0.352960i	0.949744	−	0.313028i	$-0.101343\pi$
$83$	154.093	+	266.896i	0.203781	+	0.352960i	−0.745962	+	0.665988i	$0.768010\pi$
$84$		0			0
$85$	−91.8370	−	520.834i	−0.117190	−	0.664616i
$86$	−38.5053	−	218.375i	−0.0482807	−	0.273813i
$87$		0			0
$88$	547.665	+	948.584i	0.663424	+	1.14908i
$89$	−32.1471	+	26.9746i	−0.0382875	+	0.0321270i	−0.661731	−	0.749742i	$-0.730178\pi$
$89$	−32.1471	+	26.9746i	−0.0382875	+	0.0321270i	0.623443	+	0.781869i	$0.285733\pi$
$90$		0			0
$91$	−404.979	−	147.400i	−0.466520	−	0.169799i
$92$	−30.3702	−	25.4836i	−0.0344164	−	0.0288788i
$93$		0			0
$94$	−1355.82			−1.48768
$95$	−16.5219	−	450.101i	−0.0178433	−	0.486098i
$96$		0			0
$97$	98.6409	−	559.420i	0.103252	−	0.585572i	−0.888652	−	0.458583i	$-0.848357\pi$
$97$	98.6409	−	559.420i	0.103252	−	0.585572i	0.991904	−	0.126990i	$-0.0405316\pi$
$98$	−438.614	−	368.041i	−0.452110	−	0.379365i
$99$		0			0
$100$	−39.3965	+	14.3391i	−0.0393965	+	0.0143391i
$101$	5.35419	−	4.49270i	0.00527487	−	0.00442614i	−0.640146	−	0.768253i	$-0.721126\pi$
$101$	5.35419	−	4.49270i	0.00527487	−	0.00442614i	0.645421	+	0.763827i	$0.276682\pi$
$102$		0			0
$103$	439.531	−	761.289i	0.420468	−	0.728273i	−0.575517	−	0.817790i	$-0.695199\pi$
$103$	439.531	−	761.289i	0.420468	−	0.728273i	0.995985	+	0.0895173i	$0.0285324\pi$
$104$	−73.9669	−	419.487i	−0.0697409	−	0.395520i
$105$		0			0
$106$	−156.244	+	270.623i	−0.143168	+	0.247974i
$107$	426.585	+	738.867i	0.385416	+	0.667560i	0.991827	−	0.127591i	$-0.0407246\pi$
$107$	426.585	+	738.867i	0.385416	+	0.667560i	−0.606411	+	0.795152i	$0.707391\pi$
$108$		0			0
$109$	496.022	−	180.537i	0.435874	−	0.158645i	−0.114757	−	0.993394i	$-0.536609\pi$
$109$	496.022	−	180.537i	0.435874	−	0.158645i	0.550632	+	0.834748i	$0.314387\pi$
$110$	−663.275	−	241.412i	−0.574916	−	0.209252i
$111$		0			0
$112$	245.809	−	1394.05i	0.207382	−	1.17612i
$113$	387.539			0.322625			0.161312	−	0.986903i	$-0.448427\pi$
$113$	387.539			0.322625			0.161312	+	0.986903i	$0.448427\pi$
$114$		0			0
$115$	490.739			0.397927
$116$	7.06626	−	40.0748i	0.00565592	−	0.0320763i
$117$		0			0
$118$	466.980	+	169.967i	0.364314	+	0.132599i
$119$	−2145.50	+	780.899i	−1.65276	+	0.601554i
$120$		0			0
$121$	−448.495	−	776.815i	−0.336961	−	0.583633i
$122$	−379.798	+	657.830i	−0.281847	+	0.488173i
$123$		0			0
$124$	−21.6911	−	123.016i	−0.0157090	−	0.0890901i
$125$	599.377	−	1038.15i	0.428879	−	0.742841i
$126$		0			0
$127$	−437.956	+	367.489i	−0.306002	+	0.256767i	−0.782837	−	0.622226i	$-0.786228\pi$
$127$	−437.956	+	367.489i	−0.306002	+	0.256767i	0.476835	+	0.878993i	$0.341784\pi$
$128$	1238.08	−	450.625i	0.854937	−	0.311172i
$129$		0			0
$130$	210.273	+	176.440i	0.141863	+	0.119037i
$131$	7.61560	−	43.1902i	0.00507922	−	0.0288057i	−0.982163	−	0.188032i	$-0.939789\pi$
$131$	7.61560	−	43.1902i	0.00507922	−	0.0288057i	0.987242	+	0.159227i	$0.0509001\pi$
$132$		0			0
$133$	−1901.24	+	407.668i	−1.23954	+	0.265784i
$134$	−426.114			−0.274706
$135$		0			0
$136$	−1728.70	−	1450.55i	−1.08996	−	0.914584i
$137$	−1958.25	−	712.743i	−1.22120	−	0.444480i	−0.350624	−	0.936516i	$-0.614030\pi$
$137$	−1958.25	−	712.743i	−1.22120	−	0.444480i	−0.870575	+	0.492036i	$0.836253\pi$
$138$		0			0
$139$	1763.12	−	1479.43i	1.07587	−	0.902762i	0.0802982	−	0.996771i	$-0.474413\pi$
$139$	1763.12	−	1479.43i	1.07587	−	0.902762i	0.995571	+	0.0940092i	$0.0299683\pi$
$140$	−28.0494	−	48.5831i	−0.0169329	−	0.0293287i
$141$		0			0
$142$	293.369	+	1663.78i	0.173373	+	0.983249i
$143$	150.455	+	853.270i	0.0879835	+	0.498979i
$144$		0			0
$145$	251.853	+	436.221i	0.144243	+	0.249836i
$146$	−1012.80	+	849.844i	−0.574111	+	0.481737i
$147$		0			0
$148$	95.9953	+	34.9394i	0.0533160	+	0.0194054i
$149$	286.850	+	240.696i	0.157716	+	0.132339i	0.718231	−	0.695805i	$-0.244952\pi$
$149$	286.850	+	240.696i	0.157716	+	0.132339i	−0.560515	+	0.828144i	$0.689397\pi$
$150$		0			0
$151$	−496.496			−0.267578			−0.133789	−	0.991010i	$-0.542714\pi$
$151$	−496.496			−0.267578			−0.133789	+	0.991010i	$0.542714\pi$
$152$	−1288.51	−	1425.92i	−0.687580	−	0.760901i
$153$		0			0
$154$	−529.144	+	3000.92i	−0.276881	+	1.57027i
$155$	1184.46	+	993.882i	0.613795	+	0.515035i
$156$		0			0
$157$	−2592.46	+	943.577i	−1.31784	+	0.479654i	−0.902765	−	0.430134i	$-0.858466\pi$
$157$	−2592.46	+	943.577i	−1.31784	+	0.479654i	−0.415073	+	0.909788i	$0.636244\pi$
$158$	−2682.56	+	2250.93i	−1.35071	+	1.13338i
$159$		0			0
$160$	54.0034	−	93.5366i	0.0266834	−	0.0462170i
$161$	−367.889	−	2086.40i	−0.180085	−	1.02131i
$162$		0			0
$163$	1856.68	−	3215.87i	0.892188	−	1.54531i	0.0549404	−	0.998490i	$-0.482503\pi$
$163$	1856.68	−	3215.87i	0.892188	−	1.54531i	0.837247	−	0.546825i	$-0.184164\pi$
$164$	56.6079	+	98.0477i	0.0269533	+	0.0466844i
$165$		0			0
$166$	−796.301	+	289.830i	−0.372319	+	0.135513i
$167$	1406.58	+	511.954i	0.651764	+	0.237223i	0.646677	−	0.762764i	$-0.276158\pi$
$167$	1406.58	+	511.954i	0.651764	+	0.237223i	0.00508752	+	0.999987i	$0.498381\pi$
$168$		0			0
$169$	−322.995	+	1831.80i	−0.147017	+	0.833772i
$170$	1454.21			0.656075
$171$		0			0
$172$	−35.4312			−0.0157070
$173$	−98.3955	+	558.029i	−0.0432420	+	0.245238i	−0.998765	−	0.0496780i	$-0.984180\pi$
$173$	−98.3955	+	558.029i	−0.0432420	+	0.245238i	0.955523	+	0.294916i	$0.0952916\pi$
$174$		0			0
$175$	−2105.28	−	766.259i	−0.909395	−	0.330993i
$176$	−2674.26	+	973.350i	−1.14534	+	0.416869i
$177$		0			0
$178$	−57.6949	−	99.9304i	−0.0242945	−	0.0420792i
$179$	1443.68	−	2500.53i	0.602826	−	1.04413i	−0.389565	−	0.920999i	$-0.627374\pi$
$179$	1443.68	−	2500.53i	0.602826	−	1.04413i	0.992391	−	0.123127i	$-0.0392922\pi$
$180$		0			0
$181$	404.469	+	2293.86i	0.166099	+	0.941995i	0.947924	+	0.318497i	$0.103178\pi$
$181$	404.469	+	2293.86i	0.166099	+	0.941995i	−0.781825	+	0.623498i	$0.785711\pi$
$182$	592.510	−	1026.26i	0.241317	−	0.417974i
$183$		0			0
$184$	1604.06	−	1345.97i	0.642680	−	0.539273i
$185$	−1188.25	+	432.486i	−0.472225	+	0.171876i
$186$		0			0
$187$	3516.30	+	2950.53i	1.37507	+	1.15382i
$188$	−37.6191	+	213.348i	−0.0145939	+	0.0827661i
$189$		0			0
$190$	1226.71	+	170.172i	0.468395	+	0.0649767i
$191$	−2368.42			−0.897239			−0.448620	−	0.893723i	$-0.648084\pi$
$191$	−2368.42			−0.897239			−0.448620	+	0.893723i	$0.648084\pi$
$192$		0			0
$193$	−2094.11	−	1757.17i	−0.781022	−	0.655355i	0.162484	−	0.986711i	$-0.448049\pi$
$193$	−2094.11	−	1757.17i	−0.781022	−	0.655355i	−0.943506	+	0.331356i	$0.892494\pi$
$194$	1467.75	+	534.217i	0.543187	+	0.197704i
$195$		0			0
$196$	−70.0839	+	58.8074i	−0.0255408	+	0.0214313i
$197$	1088.18	+	1884.79i	0.393552	+	0.681652i	0.992915	−	0.118825i	$-0.0379129\pi$
$197$	1088.18	+	1884.79i	0.393552	+	0.681652i	−0.599363	+	0.800477i	$0.704580\pi$
$198$		0			0
$199$	896.373	+	5083.58i	0.319308	+	1.81088i	0.546981	+	0.837145i	$0.315777\pi$
$199$	896.373	+	5083.58i	0.319308	+	1.81088i	−0.227673	+	0.973738i	$0.573112\pi$
$200$	−384.517	−	2180.70i	−0.135947	−	0.770995i
$201$		0			0
$202$	9.60925	+	16.6437i	0.00334705	+	0.00579726i
$203$	1665.81	−	1397.78i	0.575947	−	0.483277i
$204$		0			0
$205$	−1316.89	−	479.309i	−0.448661	−	0.163299i
$206$	1851.62	+	1553.70i	0.626256	+	0.525491i
$207$		0			0
$208$	1106.72			0.368930
$209$	2620.94	+	2900.42i	0.867436	+	0.959936i
$210$		0			0
$211$	610.668	−	3463.27i	0.199242	−	1.12996i	−0.707004	−	0.707209i	$-0.749954\pi$
$211$	610.668	−	3463.27i	0.199242	−	1.12996i	0.906246	−	0.422750i	$-0.138935\pi$
$212$	38.2494	+	32.0950i	0.0123914	+	0.0103976i
$213$		0			0
$214$	−2204.45	+	802.355i	−0.704174	+	0.256298i
$215$	335.967	−	281.910i	0.106571	−	0.0894237i
$216$		0			0
$217$	3337.59	−	5780.88i	1.04410	−	1.80844i
$218$	252.037	+	1429.38i	0.0783033	+	0.444080i
$219$		0			0
$220$	−56.3914	+	97.6728i	−0.0172814	+	0.0299323i
$221$	−892.533	−	1545.91i	−0.271666	−	0.470540i
$222$		0			0
$223$	−1988.21	+	723.650i	−0.597043	+	0.217306i	−0.622824	−	0.782362i	$-0.714015\pi$
$223$	−1988.21	+	723.650i	−0.597043	+	0.217306i	0.0257814	+	0.999668i	$0.491793\pi$
$224$	−438.160	−	159.477i	−0.130695	−	0.0475693i
$225$		0			0
$226$	−185.040	+	1049.41i	−0.0544631	+	0.308875i
$227$	1257.38			0.367644			0.183822	−	0.982960i	$-0.441153\pi$
$227$	1257.38			0.367644			0.183822	+	0.982960i	$0.441153\pi$
$228$		0			0
$229$	1823.23			0.526125			0.263063	−	0.964779i	$-0.415267\pi$
$229$	1823.23			0.526125			0.263063	+	0.964779i	$0.415267\pi$
$230$	−234.315	+	1328.87i	−0.0671751	+	0.380969i
$231$		0			0
$232$	2019.66	+	735.098i	0.571541	+	0.208024i
$233$	−6446.27	+	2346.25i	−1.81248	+	0.659691i	−0.815800	+	0.578334i	$0.803703\pi$
$233$	−6446.27	+	2346.25i	−1.81248	+	0.659691i	−0.996685	+	0.0813561i	$0.974075\pi$
$234$		0			0
$235$	−1340.80	−	2322.34i	−0.372188	−	0.644649i
$236$	39.7025	−	68.7668i	0.0109509	−	0.0189675i
$237$		0			0
$238$	−1090.17	−	6182.64i	−0.296912	−	1.68387i
$239$	1965.93	−	3405.09i	0.532072	−	0.921576i	−0.467227	−	0.884138i	$-0.654747\pi$
$239$	1965.93	−	3405.09i	0.532072	−	0.921576i	0.999299	−	0.0374388i	$-0.0119199\pi$
$240$		0			0
$241$	2081.75	−	1746.80i	0.556420	−	0.466892i	−0.320688	−	0.947185i	$-0.603914\pi$
$241$	2081.75	−	1746.80i	0.556420	−	0.466892i	0.877108	+	0.480293i	$0.159470\pi$
$242$	2317.67	−	843.565i	0.615644	−	0.224076i
$243$		0			0
$244$	92.9763	+	78.0164i	0.0243942	+	0.0204692i
$245$	196.649	−	1115.25i	0.0512793	−	0.290819i
$246$		0			0
$247$	−572.002	−	1408.51i	−0.147351	−	0.362840i
$248$	6597.57			1.68930
$249$		0			0
$250$	2525.01	+	2118.74i	0.638783	+	0.536003i
$251$	3027.38	+	1101.88i	0.761302	+	0.277091i	0.693354	−	0.720597i	$-0.256132\pi$
$251$	3027.38	+	1101.88i	0.761302	+	0.277091i	0.0679486	+	0.997689i	$0.478355\pi$
$252$		0			0
$253$	−3262.79	+	2737.81i	−0.810790	+	0.680334i
$254$	−786.006	−	1361.40i	−0.194167	−	0.336307i
$255$		0			0
$256$	−116.826	−	662.555i	−0.0285220	−	0.161756i
$257$	−1218.62	−	6911.11i	−0.295779	−	1.67744i	−0.664020	−	0.747715i	$-0.731151\pi$
$257$	−1218.62	−	6911.11i	−0.295779	−	1.67744i	0.368241	−	0.929730i	$-0.379960\pi$
$258$		0			0
$259$	2729.52	+	4727.67i	0.654843	+	1.13422i
$260$	33.5984	−	28.1924i	0.00801418	−	0.00672470i
$261$		0			0
$262$	113.318	+	41.2444i	0.0267207	+	0.00972553i
$263$	107.382	+	90.1044i	0.0251767	+	0.0211258i	0.655289	−	0.755378i	$-0.272547\pi$
$263$	107.382	+	90.1044i	0.0251767	+	0.0211258i	−0.630112	+	0.776504i	$0.716991\pi$
$264$		0			0
$265$	−618.055			−0.143271
$266$	−196.126	−	5343.00i	−0.0452077	−	1.23158i
$267$		0			0
$268$	−11.8231	+	67.0521i	−0.00269481	+	0.0152831i
$269$	−2625.17	−	2202.78i	−0.595016	−	0.499278i	0.294823	−	0.955552i	$-0.404739\pi$
$269$	−2625.17	−	2202.78i	−0.595016	−	0.499278i	−0.889839	+	0.456274i	$0.849184\pi$
$270$		0			0
$271$	−3006.87	+	1094.41i	−0.674001	+	0.245316i	−0.656269	−	0.754527i	$-0.727867\pi$
$271$	−3006.87	+	1094.41i	−0.674001	+	0.245316i	−0.0177312	+	0.999843i	$0.505644\pi$
$272$	4491.49	−	3768.81i	1.00124	−	0.840138i
$273$		0			0
$274$	2865.04	−	4962.40i	0.631691	−	1.09412i
$275$	782.138	+	4435.72i	0.171508	+	0.972670i
$276$		0			0
$277$	−818.845	+	1418.28i	−0.177616	+	0.307640i	−0.941063	−	0.338230i	$-0.890172\pi$
$277$	−818.845	+	1418.28i	−0.177616	+	0.307640i	0.763447	+	0.645870i	$0.223505\pi$
$278$	3164.30	+	5480.72i	0.682669	+	1.18242i
$279$		0			0
$280$	2784.29	−	1013.40i	0.594260	−	0.216293i
$281$	−1120.25	−	407.736i	−0.237823	−	0.0865605i	0.220359	−	0.975419i	$-0.429277\pi$
$281$	−1120.25	−	407.736i	−0.237823	−	0.0865605i	−0.458182	+	0.888858i	$0.651499\pi$
$282$		0			0
$283$	−419.567	+	2379.48i	−0.0881295	+	0.499807i	0.908508	+	0.417868i	$0.137223\pi$
$283$	−419.567	+	2379.48i	−0.0881295	+	0.499807i	−0.996637	+	0.0819395i	$0.973889\pi$
$284$	269.948			0.0564031
$285$		0			0
$286$	−2382.40			−0.492567
$287$	−1050.58	+	5958.15i	−0.216076	+	1.22543i
$288$		0			0
$289$	−4269.93	−	1554.13i	−0.869108	−	0.316329i
$290$	−1301.49	+	473.705i	−0.263539	+	0.0959203i
$291$		0			0
$292$	105.627	+	182.952i	0.0211691	+	0.0366660i
$293$	−888.642	+	1539.17i	−0.177184	+	0.306892i	−0.940915	−	0.338643i	$-0.890032\pi$
$293$	−888.642	+	1539.17i	−0.177184	+	0.306892i	0.763731	+	0.645535i	$0.223366\pi$
$294$		0			0
$295$	170.677	+	967.958i	0.0336854	+	0.191040i
$296$	−2697.79	+	4672.71i	−0.529749	+	0.917552i
$297$		0			0
$298$	−788.741	+	661.833i	−0.153324	+	0.128654i
$299$	1556.48	−	566.512i	0.301049	−	0.109573i
$300$		0			0
$301$	−1450.42	−	1217.04i	−0.277743	−	0.233054i
$302$	237.064	−	1344.46i	0.0451705	−	0.256175i
$303$		0			0
$304$	4229.86	−	2653.62i	0.798024	−	0.500643i
$305$	−1502.36			−0.282049
$306$		0			0
$307$	4825.96	+	4049.46i	0.897173	+	0.752817i	0.969636	−	0.244554i	$-0.0786415\pi$
$307$	4825.96	+	4049.46i	0.897173	+	0.752817i	−0.0724631	+	0.997371i	$0.523086\pi$
$308$	457.536	+	166.529i	0.0846445	+	0.0308081i
$309$		0			0
$310$	−3256.87	+	2732.84i	−0.596703	+	0.500693i
$311$	2076.83	+	3597.17i	0.378669	+	0.655874i	0.990869	−	0.134829i	$-0.0430485\pi$
$311$	2076.83	+	3597.17i	0.378669	+	0.655874i	−0.612200	+	0.790703i	$0.709715\pi$
$312$		0			0
$313$	58.6545	+	332.646i	0.0105922	+	0.0600712i	0.989646	−	0.143532i	$-0.0458459\pi$
$313$	58.6545	+	332.646i	0.0105922	+	0.0600712i	−0.979054	+	0.203603i	$0.934735\pi$
$314$	−1317.27	−	7470.62i	−0.236745	−	1.34265i
$315$		0			0
$316$	279.769	+	484.575i	0.0498046	+	0.0862641i
$317$	4068.20	−	3413.63i	0.720799	−	0.604822i	−0.206808	−	0.978382i	$-0.566307\pi$
$317$	4068.20	−	3413.63i	0.720799	−	0.604822i	0.927606	+	0.373560i	$0.121863\pi$
$318$		0			0
$319$	−4108.16	−	1495.25i	−0.721043	−	0.262438i
$320$	2236.95	+	1877.02i	0.390779	+	0.327902i
$321$		0			0
$322$	5825.40			1.00819
$323$	−7117.91	−	3768.38i	−1.22616	−	0.649159i
$324$		0			0
$325$	304.162	−	1724.99i	0.0519135	−	0.294416i
$326$	7821.70	+	6563.18i	1.32885	+	1.11503i
$327$		0			0
$328$	−5619.10	+	2045.18i	−0.945923	+	0.344288i
$329$	−8868.38	+	7441.46i	−1.48611	+	1.24699i
$330$		0			0
$331$	−2795.49	+	4841.93i	−0.464212	+	0.804038i	−0.999166	−	0.0408431i	$-0.986996\pi$
$331$	−2795.49	+	4841.93i	−0.464212	+	0.804038i	0.534954	+	0.844881i	$0.320329\pi$
$332$	23.5124	+	133.345i	0.00388678	+	0.0220430i
$333$		0			0
$334$	−2057.92	+	3564.42i	−0.337139	+	0.583942i
$335$	−421.393	−	729.875i	−0.0687259	−	0.119037i
$336$		0			0
$337$	8251.69	−	3003.37i	1.33382	−	0.485472i	0.425961	−	0.904742i	$-0.359936\pi$
$337$	8251.69	−	3003.37i	1.33382	−	0.485472i	0.907862	+	0.419270i	$0.137714\pi$
$338$	−4806.08	−	1749.27i	−0.773422	−	0.281502i
$339$		0			0
$340$	40.3490	−	228.830i	0.00643597	−	0.0365002i
$341$	−13420.0			−2.13118
$342$		0			0
$343$	3164.11			0.498093
$344$	324.960	−	1842.94i	0.0509322	−	0.288851i
$345$		0			0
$346$	−1464.10	−	532.888i	−0.227487	−	0.0827984i
$347$	−1363.50	+	496.273i	−0.210941	+	0.0767762i	−0.445329	−	0.895367i	$-0.646913\pi$
$347$	−1363.50	+	496.273i	−0.210941	+	0.0767762i	0.234389	+	0.972143i	$0.424691\pi$
$348$		0			0
$349$	3391.17	+	5873.67i	0.520129	+	0.900890i	0.999726	+	0.0234010i	$0.00744943\pi$
$349$	3391.17	+	5873.67i	0.520129	+	0.900890i	−0.479597	+	0.877489i	$0.659217\pi$
$350$	3080.16	−	5335.00i	0.470404	−	0.814764i
$351$		0			0
$352$	162.782	+	923.182i	0.0246486	+	0.139789i
$353$	5155.16	−	8928.99i	0.777284	−	1.34630i	−0.156218	−	0.987723i	$-0.549930\pi$
$353$	5155.16	−	8928.99i	0.777284	−	1.34630i	0.933502	−	0.358573i	$-0.116737\pi$
$354$		0			0
$355$	−2559.71	+	2147.85i	−0.382691	+	0.321116i
$356$	−17.3256	+	6.30601i	−0.00257937	+	0.000938813i
$357$		0			0
$358$	6081.84	+	5103.27i	0.897864	+	0.753398i
$359$	−1862.89	+	10565.0i	−0.273870	+	1.55320i	0.468657	+	0.883380i	$0.344738\pi$
$359$	−1862.89	+	10565.0i	−0.273870	+	1.55320i	−0.742528	+	0.669815i	$0.766373\pi$
$360$		0			0
$361$	−5563.40	−	4011.79i	−0.811109	−	0.584895i
$362$	−6404.63			−0.929890
$363$		0			0
$364$	−145.049	−	121.711i	−0.0208864	−	0.0175257i
$365$	−2457.25	−	894.366i	−0.352379	−	0.128256i
$366$		0			0
$367$	2814.42	−	2361.58i	0.400304	−	0.335895i	−0.420307	−	0.907382i	$-0.638078\pi$
$367$	2814.42	−	2361.58i	0.400304	−	0.335895i	0.820611	+	0.571487i	$0.193633\pi$
$368$	2720.25	+	4711.62i	0.385334	+	0.667419i
$369$		0			0
$370$	−603.768	−	3424.14i	−0.0848336	−	0.481115i
$371$	463.333	+	2627.69i	0.0648384	+	0.367717i
$372$		0			0
$373$	−1353.85	−	2344.94i	−0.187935	−	0.325513i	0.756626	−	0.653847i	$-0.226846\pi$
$373$	−1353.85	−	2344.94i	−0.187935	−	0.325513i	−0.944562	+	0.328334i	$0.893513\pi$
$374$	−9668.65	+	8112.96i	−1.33678	+	1.12169i
$375$		0			0
$376$	−10752.2	−	3913.48i	−1.47474	−	0.536762i
$377$	1302.38	+	1092.83i	0.177920	+	0.149293i
$378$		0			0
$379$	−12094.2			−1.63915			−0.819573	−	0.572974i	$-0.805790\pi$
$379$	−12094.2			−1.63915			−0.819573	+	0.572974i	$0.805790\pi$
$380$	60.8145	−	188.310i	0.00820979	−	0.0254214i
$381$		0			0
$382$	1130.86	−	6413.41i	0.151465	−	0.859002i
$383$	4039.50	+	3389.54i	0.538926	+	0.452213i	0.871170	−	0.490981i	$-0.163361\pi$
$383$	4039.50	+	3389.54i	0.538926	+	0.452213i	−0.332244	+	0.943193i	$0.607806\pi$
$384$		0			0
$385$	−5663.46	+	2061.33i	−0.749705	+	0.272870i
$386$	5758.09	−	4831.61i	0.759273	−	0.637105i
$387$		0			0
$388$	124.788	−	216.139i	0.0163277	−	0.0282803i
$389$	1156.94	+	6561.34i	0.150795	+	0.855201i	0.962530	+	0.271175i	$0.0874123\pi$
$389$	1156.94	+	6561.34i	0.150795	+	0.855201i	−0.811735	+	0.584026i	$0.801477\pi$
$390$		0			0
$391$	4387.58	−	7599.51i	0.567492	−	0.982925i
$392$	−2416.06	−	4184.74i	−0.311300	−	0.539187i
$393$		0			0
$394$	−5623.37	+	2046.74i	−0.719038	+	0.261709i
$395$	−6508.38	−	2368.86i	−0.829043	−	0.301747i
$396$		0			0
$397$	1129.71	−	6406.89i	0.142817	−	0.809956i	−0.826277	−	0.563264i	$-0.809545\pi$
$397$	1129.71	−	6406.89i	0.142817	−	0.809956i	0.969094	−	0.246692i	$-0.0793435\pi$
$398$	−14193.8			−1.78761
$399$		0			0
$400$	5753.30			0.719163
$401$	593.766	−	3367.41i	0.0739432	−	0.419353i	−0.925256	−	0.379343i	$-0.876150\pi$
$401$	593.766	−	3367.41i	0.0739432	−	0.419353i	0.999199	−	0.0400098i	$-0.0127389\pi$
$402$		0			0
$403$	4904.11	+	1784.95i	0.606181	+	0.220632i
$404$	2.88563	−	1.05028i	0.000355360	−	0.000129341i
$405$		0			0
$406$	2989.66	+	5178.24i	0.365454	+	0.632985i
$407$	5487.51	−	9504.65i	0.668319	−	1.15756i
$408$		0			0
$409$	230.257	+	1305.85i	0.0278373	+	0.157873i	0.995558	−	0.0941529i	$-0.0300142\pi$
$409$	230.257	+	1305.85i	0.0278373	+	0.157873i	−0.967720	+	0.252026i	$0.918903\pi$
$410$	1926.70	−	3337.14i	0.232080	−	0.401974i
$411$		0			0
$412$	295.861	−	248.257i	0.0353787	−	0.0296863i
$413$	3987.37	−	1451.28i	0.475074	−	0.172913i
$414$		0			0
$415$	−1283.92	−	1077.34i	−0.151868	−	0.127432i
$416$	63.3035	−	359.012i	0.00746084	−	0.0423126i
$417$		0			0
$418$	−9105.46	+	5712.33i	−1.06546	+	0.668420i
$419$	2455.32			0.286277			0.143139	−	0.989703i	$-0.454281\pi$
$419$	2455.32			0.286277			0.143139	+	0.989703i	$0.454281\pi$
$420$		0			0
$421$	−715.441	−	600.326i	−0.0828230	−	0.0694967i	0.600436	−	0.799673i	$-0.294994\pi$
$421$	−715.441	−	600.326i	−0.0828230	−	0.0694967i	−0.683259	+	0.730176i	$0.739438\pi$
$422$	9086.58	+	3307.24i	1.04817	+	0.381503i
$423$		0			0
$424$	−2020.22	+	1695.16i	−0.231392	+	0.194161i
$425$	−4639.83	−	8036.42i	−0.529564	−	0.917233i
$426$		0			0
$427$	1126.27	+	6387.37i	0.127644	+	0.723903i
$428$	65.0910	+	369.149i	0.00735115	+	0.0416904i
$429$		0			0
$430$	602.965	+	1044.37i	0.0676223	+	0.117125i
$431$	−807.361	+	677.456i	−0.0902302	+	0.0757121i	−0.686787	−	0.726859i	$-0.740979\pi$
$431$	−807.361	+	677.456i	−0.0902302	+	0.0757121i	0.596557	+	0.802571i	$0.296535\pi$
$432$		0			0
$433$	8600.27	+	3130.24i	0.954509	+	0.347413i	0.771879	−	0.635769i	$-0.219317\pi$
$433$	8600.27	+	3130.24i	0.954509	+	0.347413i	0.182630	+	0.983182i	$0.441539\pi$
$434$	14060.4	+	11798.0i	1.55511	+	1.30489i
$435$		0			0
$436$	231.916			0.0254742
$437$	4590.48	−	5897.20i	0.502499	−	0.645541i
$438$		0			0
$439$	281.660	−	1597.38i	0.0306217	−	0.173664i	−0.965661	−	0.259804i	$-0.916342\pi$
$439$	281.660	−	1597.38i	0.0306217	−	0.173664i	0.996283	+	0.0861398i	$0.0274532\pi$
$440$	−4563.21	−	3828.99i	−0.494415	−	0.414864i
$441$		0			0
$442$	4612.32	−	1678.75i	0.496348	−	0.180656i
$443$	7978.73	−	6694.95i	0.855713	−	0.718028i	−0.105327	−	0.994438i	$-0.533589\pi$
$443$	7978.73	−	6694.95i	0.855713	−	0.718028i	0.961040	+	0.276409i	$0.0891446\pi$
$444$		0			0
$445$	114.111	−	197.647i	0.0121560	−	0.0210547i
$446$	−1010.24	−	5729.38i	−0.107257	−	0.608283i
$447$		0			0
$448$	6303.30	−	10917.6i	0.664738	−	1.15136i
$449$	−6677.63	−	11566.0i	−0.701864	−	1.21566i	−0.967811	−	0.251677i	$-0.919018\pi$
$449$	−6677.63	−	11566.0i	−0.701864	−	1.21566i	0.265947	−	0.963988i	$-0.414315\pi$
$450$		0			0
$451$	11429.7	−	4160.07i	1.19335	−	0.434346i
$452$	159.998	+	58.2347i	0.0166498	+	0.00606002i
$453$		0			0
$454$	−600.366	+	3404.85i	−0.0620630	+	0.351977i
$455$	2343.79			0.241491
$456$		0			0
$457$	−17571.0			−1.79855			−0.899275	−	0.437384i	$-0.855905\pi$
$457$	−17571.0			−1.79855			−0.899275	+	0.437384i	$0.855905\pi$
$458$	−870.546	+	4937.11i	−0.0888165	+	0.503703i
$459$		0			0
$460$	202.606	+	73.7424i	0.0205359	+	0.00747447i
$461$	−9777.28	+	3558.64i	−0.987794	+	0.359528i	−0.784866	−	0.619666i	$-0.787268\pi$
$461$	−9777.28	+	3558.64i	−0.987794	+	0.359528i	−0.202928	+	0.979194i	$0.565046\pi$
$462$		0			0
$463$	−2012.85	−	3486.36i	−0.202041	−	0.349946i	0.747145	−	0.664661i	$-0.231424\pi$
$463$	−2012.85	−	3486.36i	−0.202041	−	0.349946i	−0.949186	+	0.314716i	$0.898091\pi$
$464$	−2792.13	+	4836.11i	−0.279356	+	0.483859i
$465$		0			0
$466$	−3275.46	−	18576.0i	−0.325607	−	1.84661i
$467$	−3336.14	+	5778.36i	−0.330574	+	0.572571i	−0.982624	−	0.185605i	$-0.940576\pi$
$467$	−3336.14	+	5778.36i	−0.330574	+	0.572571i	0.652051	+	0.758175i	$0.273909\pi$
$468$		0			0
$469$	−2787.20	+	2338.74i	−0.274415	+	0.230262i
$470$	6928.83	−	2521.89i	0.680006	−	0.247502i
$471$		0			0
$472$	3212.74	+	2695.81i	0.313302	+	0.262891i
$473$	−660.995	+	3748.69i	−0.0642549	+	0.364408i
$474$		0			0
$475$	−2973.55	−	7322.15i	−0.287233	−	0.707291i
$476$	−1003.13			−0.0965935
$477$		0			0
$478$	8281.92	+	6949.35i	0.792481	+	0.664971i
$479$	5473.84	+	1992.31i	0.522142	+	0.190044i	0.589626	−	0.807676i	$-0.299275\pi$
$479$	5473.84	+	1992.31i	0.522142	+	0.190044i	−0.0674844	+	0.997720i	$0.521497\pi$
$480$		0			0
$481$	−3269.50	+	2743.44i	−0.309930	+	0.260062i
$482$	3736.15	+	6471.20i	0.353064	+	0.611525i
$483$		0			0
$484$	−68.4341	−	388.109i	−0.00642694	−	0.0364490i
$485$	536.449	+	3042.35i	0.0502245	+	0.284838i
$486$		0			0
$487$	−1435.60	−	2486.53i	−0.133579	−	0.231366i	0.791475	−	0.611202i	$-0.209314\pi$
$487$	−1435.60	−	2486.53i	−0.133579	−	0.231366i	−0.925054	+	0.379836i	$0.875980\pi$
$488$	−4910.73	+	4120.59i	−0.455529	+	0.382234i
$489$		0			0
$490$	2926.08	+	1065.01i	0.269769	+	0.0981879i
$491$	8671.93	+	7276.61i	0.797064	+	0.668816i	0.947483	−	0.319806i	$-0.103618\pi$
$491$	8671.93	+	7276.61i	0.797064	+	0.668816i	−0.150419	+	0.988622i	$0.548062\pi$
$492$		0			0
$493$	9007.01			0.822830
$494$	4087.22	−	876.388i	0.372252	−	0.0798190i
$495$		0			0
$496$	−2976.64	+	16881.4i	−0.269466	+	1.52822i
$497$	11050.6	+	9272.57i	0.997360	+	0.836885i
$498$		0			0
$499$	702.905	−	255.837i	0.0630588	−	0.0229515i	−0.310298	−	0.950639i	$-0.600429\pi$
$499$	702.905	−	255.837i	0.0630588	−	0.0229515i	0.373357	+	0.927688i	$0.378207\pi$
$500$	403.459	−	338.542i	0.0360864	−	0.0302801i
$501$		0			0
$502$	−4429.26	+	7671.71i	−0.393800	+	0.682082i
$503$	−571.219	−	3239.54i	−0.0506350	−	0.287165i	0.948967	−	0.315375i	$-0.102130\pi$
$503$	−571.219	−	3239.54i	−0.0506350	−	0.287165i	−0.999602	+	0.0282100i	$0.991019\pi$
$504$		0			0
$505$	−19.0056	+	32.9187i	−0.00167473	+	0.00290072i
$506$	−5855.78	−	10142.5i	−0.514469	−	0.891086i
$507$		0			0
$508$	−236.035	+	85.9099i	−0.0206149	+	0.00750322i
$509$	1780.26	+	647.963i	0.155027	+	0.0564253i	0.418368	−	0.908278i	$-0.362602\pi$
$509$	1780.26	+	647.963i	0.155027	+	0.0564253i	−0.263341	+	0.964703i	$0.584824\pi$
$510$		0			0
$511$	−1960.33	+	11117.6i	−0.169707	+	0.962454i
$512$	12390.2			1.06948
$513$		0			0
$514$	19296.4			1.65589
$515$	−830.159	+	4708.06i	−0.0710314	+	0.402839i
$516$		0			0
$517$	21870.8	+	7960.33i	1.86050	+	0.677166i
$518$	−14105.3	+	5133.90i	−1.19643	+	0.435465i
$519$		0			0
$520$	1158.27	+	2006.18i	0.0976796	+	0.169186i
$521$	6557.36	−	11357.7i	0.551407	−	0.955065i	−0.446767	−	0.894651i	$-0.647425\pi$
$521$	6557.36	−	11357.7i	0.551407	−	0.955065i	0.998173	−	0.0604141i	$-0.0192421\pi$
$522$		0			0
$523$	−892.891	−	5063.83i	−0.0746527	−	0.423377i	−0.999113	−	0.0420993i	$-0.986595\pi$
$523$	−892.891	−	5063.83i	−0.0746527	−	0.423377i	0.924461	−	0.381277i	$-0.124516\pi$
$524$	9.63427	−	16.6870i	0.000803197	−	0.00139118i
$525$		0			0
$526$	−295.265	+	247.757i	−0.0244756	+	0.0205375i
$527$	25981.1	−	9456.34i	2.14754	−	0.781641i
$528$		0			0
$529$	−3082.95	−	2586.90i	−0.253386	−	0.212616i
$530$	295.105	−	1673.62i	0.0241859	−	0.137165i
$531$		0			0
$532$	−846.202	−	117.387i	−0.0689615	−	0.00956647i
$533$	−4730.10			−0.384397
$534$		0			0
$535$	−3554.36	−	2982.46i	−0.287230	−	0.241015i
$536$	−3379.25	−	1229.95i	−0.272316	−	0.0991149i
$537$		0			0
$538$	7218.33	−	6056.90i	0.578447	−	0.485375i
$539$	4914.46	+	8512.10i	0.392729	+	0.680226i
$540$		0			0
$541$	−3801.70	−	21560.5i	−0.302122	−	1.71342i	−0.636753	−	0.771068i	$-0.719723\pi$
$541$	−3801.70	−	21560.5i	−0.302122	−	1.71342i	0.334632	−	0.942349i	$-0.391388\pi$
$542$	−1527.84	−	8664.82i	−0.121082	−	0.686689i
$543$		0			0
$544$	−965.662	−	1672.57i	−0.0761073	−	0.131822i
$545$	−2199.08	+	1845.25i	−0.172841	+	0.145031i
$546$		0			0
$547$	16584.9	+	6036.43i	1.29638	+	0.471845i	0.895817	−	0.444424i	$-0.146591\pi$
$547$	16584.9	+	6036.43i	1.29638	+	0.471845i	0.400565	+	0.916268i	$0.368814\pi$
$548$	−701.375	−	588.523i	−0.0546738	−	0.0458768i
$549$		0			0
$550$	−12384.9			−0.960171
$551$	7597.94	+	1054.00i	0.587447	+	0.0814918i
$552$		0			0
$553$	−5192.22	+	29446.5i	−0.399269	+	2.26437i
$554$	−3449.57	−	2894.53i	−0.264546	−	0.221980i
$555$		0			0
$556$	950.230	−	345.855i	0.0724797	−	0.0263805i
$557$	−5123.81	+	4299.39i	−0.389772	+	0.327057i	−0.816524	−	0.577311i	$-0.804102\pi$
$557$	−5123.81	+	4299.39i	−0.389772	+	0.327057i	0.426753	+	0.904368i	$0.359658\pi$
$558$		0			0
$559$	740.150	−	1281.98i	0.0560018	−	0.0969980i
$560$	1336.81	+	7581.43i	0.100876	+	0.572097i
$561$		0			0
$562$	1638.99	−	2838.82i	0.123019	−	0.213075i
$563$	3043.88	+	5272.16i	0.227859	+	0.394663i	0.957173	−	0.289516i	$-0.0934943\pi$
$563$	3043.88	+	5272.16i	0.227859	+	0.394663i	−0.729315	+	0.684178i	$0.760161\pi$
$564$		0			0
$565$	−1980.49	+	720.839i	−0.147469	+	0.0536742i
$566$	−6243.04	−	2272.28i	−0.463630	−	0.168748i
$567$		0			0
$568$	−2475.85	+	14041.2i	−0.182895	+	1.03725i
$569$	−15509.6			−1.14270			−0.571350	−	0.820706i	$-0.693580\pi$
$569$	−15509.6			−1.14270			−0.571350	+	0.820706i	$0.693580\pi$
$570$		0			0
$571$	−5985.24			−0.438660			−0.219330	−	0.975651i	$-0.570387\pi$
$571$	−5985.24			−0.438660			−0.219330	+	0.975651i	$0.570387\pi$
$572$	−66.1029	+	374.888i	−0.00483199	+	0.0274036i
$573$		0			0
$574$	−15632.4	−	5689.72i	−1.13673	−	0.413736i
$575$	8091.35	−	2945.01i	0.586840	−	0.213592i
$576$		0			0
$577$	−6754.38	−	11698.9i	−0.487328	−	0.844077i	0.512566	−	0.858648i	$-0.328695\pi$
$577$	−6754.38	−	11698.9i	−0.487328	−	0.844077i	−0.999894	+	0.0145707i	$0.995362\pi$
$578$	6247.18	−	10820.4i	0.449565	−	0.778669i
$579$		0			0
$580$	38.4292	+	217.943i	0.00275118	+	0.0156027i
$581$	−3617.84	+	6266.28i	−0.258336	+	0.447451i
$582$		0			0
$583$	4109.28	−	3448.10i	0.291919	−	0.244949i
$584$	−10485.0	+	3816.21i	−0.742929	+	0.270404i
$585$		0			0
$586$	−3743.60	−	3141.26i	−0.263903	−	0.221441i
$587$	−308.492	+	1749.54i	−0.0216914	+	0.123018i	−0.993731	−	0.111800i	$-0.964338\pi$
$587$	−308.492	+	1749.54i	−0.0216914	+	0.123018i	0.972039	+	0.234818i	$0.0754494\pi$
$588$		0			0
$589$	23023.2	−	4936.67i	1.61062	−	0.345351i
$590$	−2702.62			−0.188585
$591$		0			0
$592$	−10739.0	−	9011.09i	−0.745558	−	0.625597i
$593$	8376.07	+	3048.64i	0.580040	+	0.211117i	0.615343	−	0.788259i	$-0.289017\pi$
$593$	8376.07	+	3048.64i	0.580040	+	0.211117i	−0.0353030	+	0.999377i	$0.511240\pi$
$594$		0			0
$595$	9511.94	−	7981.46i	0.655381	−	0.549930i
$596$	82.2595	+	142.478i	0.00565349	+	0.00979213i
$597$		0			0
$598$	790.874	+	4485.27i	0.0540823	+	0.306716i
$599$	−3509.08	−	19901.0i	−0.239361	−	1.35748i	−0.833233	−	0.552922i	$-0.813513\pi$
$599$	−3509.08	−	19901.0i	−0.239361	−	1.35748i	0.593872	−	0.804559i	$-0.297598\pi$
$600$		0			0
$601$	−3014.26	−	5220.85i	−0.204583	−	0.354347i	0.745417	−	0.666598i	$-0.232250\pi$
$601$	−3014.26	−	5220.85i	−0.204583	−	0.354347i	−0.950000	+	0.312251i	$0.898917\pi$
$602$	3988.16	−	3346.46i	0.270009	−	0.226564i
$603$		0			0
$604$	−204.982	−	74.6074i	−0.0138090	−	0.00502605i
$605$	3736.91	+	3135.64i	0.251119	+	0.210714i
$606$		0			0
$607$	−3058.64			−0.204524			−0.102262	−	0.994757i	$-0.532608\pi$
$607$	−3058.64			−0.204524			−0.102262	+	0.994757i	$0.532608\pi$
$608$	−618.868	−	1523.92i	−0.0412803	−	0.101650i
$609$		0			0
$610$	717.339	−	4068.23i	0.0476135	−	0.270029i
$611$	−6933.55	−	5817.94i	−0.459086	−	0.385219i
$612$		0			0
$613$	−17448.7	+	6350.79i	−1.14966	+	0.418444i	−0.845395	−	0.534142i	$-0.820635\pi$
$613$	−17448.7	+	6350.79i	−1.14966	+	0.418444i	−0.304270	+	0.952586i	$0.598413\pi$
$614$	−13269.8	+	11134.6i	−0.872189	+	0.731853i
$615$		0			0
$616$	−12858.3	+	22271.2i	−0.841030	+	1.45671i
$617$	−4417.45	−	25052.6i	−0.288233	−	1.63465i	−0.693504	−	0.720453i	$-0.743934\pi$
$617$	−4417.45	−	25052.6i	−0.288233	−	1.63465i	0.405271	−	0.914197i	$-0.367177\pi$
$618$		0			0
$619$	−4466.62	+	7736.41i	−0.290030	+	0.502346i	−0.973816	−	0.227336i	$-0.926999\pi$
$619$	−4466.62	+	7736.41i	−0.290030	+	0.502346i	0.683787	+	0.729682i	$0.260332\pi$
$620$	339.666	+	588.319i	0.0220021	+	0.0381088i
$621$		0			0
$622$	−10732.4	+	3906.26i	−0.691847	+	0.251812i
$623$	−925.851	−	336.982i	−0.0595400	−	0.0216708i
$624$		0			0
$625$	939.203	−	5326.49i	0.0601090	−	0.340895i
$626$	−928.776			−0.0592993
$627$		0			0
$628$	−1212.11			−0.0770196
$629$	−3926.41	+	22267.8i	−0.248897	+	1.41156i
$630$		0			0
$631$	2045.40	+	744.466i	0.129043	+	0.0469679i	0.405735	−	0.913991i	$-0.367016\pi$
$631$	2045.40	+	744.466i	0.129043	+	0.0469679i	−0.276691	+	0.960959i	$0.589238\pi$
$632$	−27770.9	+	10107.8i	−1.74789	+	0.636180i
$633$		0			0
$634$	7301.27	+	12646.2i	0.457367	+	0.792182i
$635$	1554.60	−	2692.64i	0.0971533	−	0.168274i
$636$		0			0
$637$	−663.741	−	3764.26i	−0.0412847	−	0.234137i
$638$	6010.50	−	10410.5i	0.372975	−	0.646012i
$639$		0			0
$640$	−5488.95	+	4605.77i	−0.339015	+	0.284467i
$641$	−15117.7	+	5502.41i	−0.931536	+	0.339051i	−0.762818	−	0.646613i	$-0.776185\pi$
$641$	−15117.7	+	5502.41i	−0.931536	+	0.339051i	−0.168718	+	0.985664i	$0.553963\pi$
$642$		0			0
$643$	−11391.2	−	9558.35i	−0.698639	−	0.586228i	0.222747	−	0.974876i	$-0.428498\pi$
$643$	−11391.2	−	9558.35i	−0.698639	−	0.586228i	−0.921386	+	0.388648i	$0.872942\pi$
$644$	161.634	−	916.670i	0.00989015	−	0.0560898i
$645$		0			0
$646$	13603.0	−	17475.2i	0.828486	−	1.06432i
$647$	17908.3			1.08817			0.544086	−	0.839029i	$-0.316876\pi$
$647$	17908.3			1.08817			0.544086	+	0.839029i	$0.316876\pi$
$648$		0			0
$649$	−6534.97	−	5483.49i	−0.395254	−	0.331658i
$650$	4525.85	+	1647.28i	0.273105	+	0.0994022i
$651$		0			0
$652$	1249.79	−	1048.70i	0.0750698	−	0.0629910i
$653$	7139.51	+	12366.0i	0.427857	+	0.741070i	0.996682	−	0.0813882i	$-0.0259354\pi$
$653$	7139.51	+	12366.0i	0.427857	+	0.741070i	−0.568825	+	0.822458i	$0.692602\pi$
$654$		0			0
$655$	41.4167	+	234.886i	0.00247067	+	0.0140118i
$656$	−2697.88	−	15300.4i	−0.160571	−	0.910644i
$657$		0			0
$658$	−15916.2	−	27567.7i	−0.942977	−	1.63328i
$659$	−14665.1	+	12305.5i	−0.866876	+	0.727395i	−0.963438	−	0.267932i	$-0.913660\pi$
$659$	−14665.1	+	12305.5i	−0.866876	+	0.727395i	0.0965620	+	0.995327i	$0.469215\pi$
$660$		0			0
$661$	2596.82	+	945.165i	0.152806	+	0.0556167i	0.417291	−	0.908773i	$-0.362980\pi$
$661$	2596.82	+	945.165i	0.152806	+	0.0556167i	−0.264485	+	0.964390i	$0.585202\pi$
$662$	−11776.6	−	9881.77i	−0.691408	−	0.580160i
$663$		0			0
$664$	−7151.56			−0.417973
$665$	8957.88	−	5619.75i	0.522363	−	0.327706i
$666$		0			0
$667$	−1451.29	+	8230.67i	−0.0842491	+	0.477800i
$668$	503.788	+	422.729i	0.0291799	+	0.0244848i
$669$		0			0
$670$	2177.62	−	792.590i	0.125566	−	0.0457021i
$671$	9988.81	−	8381.61i	0.574685	−	0.482218i
$672$		0			0
$673$	10446.1	−	18093.1i	0.598315	−	1.03631i	−0.394754	−	0.918787i	$-0.629170\pi$
$673$	10446.1	−	18093.1i	0.598315	−	1.03631i	0.993070	−	0.117526i	$-0.0374964\pi$
$674$	4192.83	+	23778.7i	0.239617	+	1.35893i
$675$		0			0
$676$	−408.612	+	707.737i	−0.0232483	+	0.0402672i
$677$	−12848.3	−	22253.9i	−0.729395	−	1.26335i	−0.957139	−	0.289628i	$-0.906469\pi$
$677$	−12848.3	−	22253.9i	−0.729395	−	1.26335i	0.227745	−	0.973721i	$-0.426865\pi$
$678$		0			0
$679$	12532.6	−	4561.48i	0.708330	−	0.257811i
$680$	11532.5	+	4197.47i	0.650367	+	0.236714i
$681$		0			0
$682$	6407.69	−	36339.8i	0.359770	−	2.04036i
$683$	−26695.9			−1.49559			−0.747796	−	0.663929i	$-0.768888\pi$
$683$	−26695.9			−1.49559			−0.747796	+	0.663929i	$0.768888\pi$
$684$		0			0
$685$	11333.2			0.632146
$686$	−1510.78	+	8568.05i	−0.0840843	+	0.476866i
$687$		0			0
$688$	4568.96	+	1662.97i	0.253183	+	0.0921512i
$689$	−1960.29	+	713.486i	−0.108390	+	0.0394509i
$690$		0			0
$691$	16838.1	+	29164.4i	0.926991	+	1.60560i	0.788327	+	0.615256i	$0.210947\pi$
$691$	16838.1	+	29164.4i	0.926991	+	1.60560i	0.138664	+	0.990340i	$0.455719\pi$
$692$	−124.477	+	215.601i	−0.00683803	+	0.0118438i
$693$		0			0
$694$	−692.818	−	3929.16i	−0.0378948	−	0.214912i
$695$	−6258.49	+	10840.0i	−0.341580	+	0.591634i
$696$		0			0
$697$	−19196.5	+	16107.8i	−1.04321	+	0.875359i
$698$	−17524.4	+	6378.38i	−0.950301	+	0.345881i
$699$		0			0
$700$	−754.037	−	632.712i	−0.0407142	−	0.0341633i
$701$	2244.79	−	12730.8i	0.120948	−	0.685930i	−0.862684	−	0.505743i	$-0.831218\pi$
$701$	2244.79	−	12730.8i	0.120948	−	0.685930i	0.983632	−	0.180187i	$-0.0576704\pi$
$702$		0			0
$703$	−5917.93	+	18324.7i	−0.317495	+	0.983114i
$704$	−25344.7			−1.35684
$705$		0			0
$706$	21717.3	+	18223.0i	1.15771	+	0.971431i
$707$	154.203	+	56.1254i	0.00820284	+	0.00298559i
$708$		0			0
$709$	−11565.1	+	9704.25i	−0.612603	+	0.514035i	−0.895469	−	0.445125i	$-0.853159\pi$
$709$	−11565.1	+	9704.25i	−0.612603	+	0.514035i	0.282866	+	0.959160i	$0.408715\pi$
$710$	−4593.95	−	7956.96i	−0.242828	−	0.420590i
$711$		0			0
$712$	−169.101	−	959.020i	−0.00890075	−	0.0504787i
$713$	4454.97	+	25265.4i	0.233997	+	1.32706i
$714$		0			0
$715$	−2356.01	−	4080.73i	−0.123230	−	0.213441i
$716$	971.786	−	815.425i	0.0507226	−	0.0425613i
$717$		0			0
$718$	−27719.3	−	10089.0i	−1.44077	−	0.524398i
$719$	8869.03	+	7442.00i	0.460027	+	0.386008i	0.843141	−	0.537693i	$-0.180704\pi$
$719$	8869.03	+	7442.00i	0.460027	+	0.386008i	−0.383114	+	0.923701i	$0.625148\pi$
$720$		0			0
$721$	20638.9			1.06607
$722$	13519.9	−	13149.5i	0.696894	−	0.677805i
$723$		0			0
$724$	−177.705	+	1007.82i	−0.00912205	+	0.0517337i
$725$	6770.41	+	5681.05i	0.346823	+	0.291019i
$726$		0			0
$727$	3836.36	−	1396.32i	0.195712	−	0.0712334i	−0.242305	−	0.970200i	$-0.577903\pi$
$727$	3836.36	−	1396.32i	0.195712	−	0.0712334i	0.438017	+	0.898967i	$0.355681\pi$
$728$	7661.06	−	6428.39i	0.390024	−	0.327269i
$729$		0			0
$730$	3595.12	−	6226.93i	0.182276	−	0.315711i
$731$	−1361.81	−	7723.22i	−0.0689035	−	0.390771i
$732$		0			0
$733$	−17806.4	+	30841.6i	−0.897263	+	1.55411i	−0.0662848	+	0.997801i	$0.521115\pi$
$733$	−17806.4	+	30841.6i	−0.897263	+	1.55411i	−0.830978	+	0.556305i	$0.812219\pi$
$734$	5051.08	+	8748.74i	0.254004	+	0.439948i
$735$		0			0
$736$	1684.01	−	612.928i	0.0843387	−	0.0306968i
$737$	6873.66	+	2501.81i	0.343548	+	0.125041i
$738$		0			0
$739$	505.438	−	2866.48i	0.0251594	−	0.142686i	−0.969640	−	0.244535i	$-0.921365\pi$
$739$	505.438	−	2866.48i	0.0251594	−	0.142686i	0.994800	+	0.101849i	$0.0324758\pi$
$740$	−555.566			−0.0275987
$741$		0			0
$742$	−7336.73			−0.362991
$743$	−6796.69	+	38546.0i	−0.335594	+	1.90325i	0.0856930	+	0.996322i	$0.472690\pi$
$743$	−6796.69	+	38546.0i	−0.335594	+	1.90325i	−0.421287	+	0.906927i	$0.638422\pi$
$744$		0			0
$745$	−1913.63	−	696.505i	−0.0941075	−	0.0342523i
$746$	6996.27	−	2546.44i	0.343367	−	0.124975i
$747$		0			0
$748$	1008.36	+	1746.54i	0.0492907	+	0.0853740i
$749$	−10015.5	+	17347.4i	−0.488597	+	0.846274i
$750$		0			0
$751$	3986.93	+	22611.0i	0.193722	+	1.09865i	0.914227	+	0.405202i	$0.132799\pi$
$751$	3986.93	+	22611.0i	0.193722	+	1.09865i	−0.720505	+	0.693449i	$0.756090\pi$
$752$	14864.6	−	25746.3i	0.720820	−	1.24850i
$753$		0			0
$754$	−3581.10	+	3004.90i	−0.172966	+	0.145135i
$755$	2537.31	−	923.504i	0.122307	−	0.0445162i
$756$		0			0
$757$	7376.48	+	6189.60i	0.354165	+	0.297180i	0.802460	−	0.596706i	$-0.203524\pi$
$757$	7376.48	+	6189.60i	0.354165	+	0.297180i	−0.448295	+	0.893886i	$0.647969\pi$
$758$	5774.66	−	32749.7i	0.276709	−	1.56929i
$759$		0			0
$760$	9237.12	+	4890.35i	0.440876	+	0.233410i
$761$	−18187.4			−0.866350			−0.433175	−	0.901310i	$-0.642607\pi$
$761$	−18187.4			−0.866350			−0.433175	+	0.901310i	$0.642607\pi$
$762$		0			0
$763$	9493.73	+	7966.18i	0.450454	+	0.377975i
$764$	−977.820	−	355.897i	−0.0463040	−	0.0168533i
$765$		0			0
$766$	−11107.3	+	9320.09i	−0.523918	+	0.439620i
$767$	1658.75	+	2873.05i	0.0780888	+	0.135254i
$768$		0			0
$769$	−2426.76	−	13762.9i	−0.113799	−	0.645385i	−0.987338	−	0.158631i	$-0.949292\pi$
$769$	−2426.76	−	13762.9i	−0.113799	−	0.645385i	0.873539	−	0.486754i	$-0.161819\pi$
$770$	−2877.70	−	16320.2i	−0.134682	−	0.763819i
$771$		0			0
$772$	−600.524	−	1040.14i	−0.0279965	−	0.0484914i
$773$	15491.5	−	12998.9i	0.720816	−	0.604837i	−0.206795	−	0.978384i	$-0.566303\pi$
$773$	15491.5	−	12998.9i	0.720816	−	0.604837i	0.927611	+	0.373548i	$0.121859\pi$
$774$		0			0
$775$	25494.0	+	9279.05i	1.18164	+	0.430082i
$776$	10097.9	+	8473.11i	0.467129	+	0.391968i
$777$		0			0
$778$	−18319.8			−0.844211
$779$	−18078.3	+	11341.5i	−0.831480	+	0.521631i
$780$		0			0
$781$	5036.07	−	28561.0i	0.230736	−	1.30857i
$782$	18483.7	+	15509.6i	0.845236	+	0.709237i
$783$		0			0
$784$	11797.7	−	4294.00i	0.537430	−	0.195608i
$785$	11493.5	−	9644.17i	0.522573	−	0.438491i
$786$		0			0
$787$	3258.28	−	5643.50i	0.147579	−	0.255615i	−0.782753	−	0.622333i	$-0.786185\pi$
$787$	3258.28	−	5643.50i	0.147579	−	0.255615i	0.930332	+	0.366718i	$0.119518\pi$
$788$	166.041	+	941.667i	0.00750632	+	0.0425705i
$789$		0			0
$790$	9522.18	−	16492.9i	0.428840	−	0.742774i
$791$	4549.38	+	7879.76i	0.204497	+	0.354200i
$792$		0			0
$793$	−4765.05	+	1734.34i	−0.213382	+	0.0776647i
$794$	16809.7	+	6118.24i	0.751329	+	0.273461i
$795$		0			0
$796$	−393.825	+	2233.49i	−0.0175361	+	0.0994524i
$797$	21628.0			0.961235			0.480618	−	0.876930i	$-0.340413\pi$
$797$	21628.0			0.961235			0.480618	+	0.876930i	$0.340413\pi$
$798$		0			0
$799$	−47951.1			−2.12314
$800$	329.083	−	1866.32i	0.0145436	−	0.0824806i
$801$		0			0
$802$	8835.07	+	3215.70i	0.388999	+	0.141584i
$803$	21327.2	−	7762.48i	0.937262	−	0.341136i
$804$		0			0
$805$	5760.87	+	9978.12i	0.252229	+	0.436873i
$806$	−7175.03	+	12427.5i	−0.313560	+	0.543102i
$807$		0			0
$808$	28.1643	+	159.728i	0.00122626	+	0.00695446i
$809$	11239.6	−	19467.5i	0.488459	−	0.846035i	−0.511453	−	0.859311i	$-0.670893\pi$
$809$	11239.6	−	19467.5i	0.488459	−	0.846035i	0.999912	+	0.0132758i	$0.00422596\pi$
$810$		0			0
$811$	320.403	−	268.850i	0.0138728	−	0.0116407i	−0.635825	−	0.771833i	$-0.719340\pi$
$811$	320.403	−	268.850i	0.0138728	−	0.0116407i	0.649698	+	0.760193i	$0.274895\pi$
$812$	897.786	−	326.768i	0.0388007	−	0.0141223i
$813$		0			0
$814$	23117.4	+	19397.8i	0.995411	+	0.835249i
$815$	−3506.79	+	19888.0i	−0.150721	+	0.854780i
$816$		0			0
$817$	−244.996	−	6674.36i	−0.0104912	−	0.285809i
$818$	−3646.04			−0.155844
$819$		0			0
$820$	−471.664	−	395.773i	−0.0200868	−	0.0168549i
$821$	35130.4	+	12786.4i	1.49338	+	0.543544i	0.954336	−	0.298737i	$-0.0965652\pi$
$821$	35130.4	+	12786.4i	1.49338	+	0.543544i	0.539039	+	0.842281i	$0.318787\pi$
$822$		0			0
$823$	10803.6	−	9065.33i	0.457583	−	0.383958i	−0.384658	−	0.923059i	$-0.625680\pi$
$823$	10803.6	−	9065.33i	0.457583	−	0.383958i	0.842241	+	0.539101i	$0.181236\pi$
$824$	10199.5	+	17666.0i	0.431208	+	0.746875i
$825$		0			0
$826$	2026.05	+	11490.3i	0.0853455	+	0.484018i
$827$	−7514.64	−	42617.7i	−0.315973	−	1.79197i	−0.566710	−	0.823917i	$-0.691784\pi$
$827$	−7514.64	−	42617.7i	−0.315973	−	1.79197i	0.250737	−	0.968055i	$-0.419327\pi$
$828$		0			0
$829$	−13342.5	−	23109.9i	−0.558993	−	0.968204i	−0.997581	−	0.0695155i	$-0.977855\pi$
$829$	−13342.5	−	23109.9i	−0.558993	−	0.968204i	0.438588	−	0.898688i	$-0.355479\pi$
$830$	3530.34	−	2962.31i	0.147639	−	0.123883i
$831$		0			0
$832$	9261.78	+	3371.01i	0.385931	+	0.140467i
$833$	−15512.4	−	13016.5i	−0.645226	−	0.541409i
$834$		0			0
$835$	−8140.50			−0.337381
$836$	646.234	+	1591.31i	0.0267350	+	0.0658331i
$837$		0			0
$838$	−1172.35	+	6648.73i	−0.0483272	+	0.274077i
$839$	−23549.6	−	19760.5i	−0.969039	−	0.813120i	0.0133609	−	0.999911i	$-0.495747\pi$
$839$	−23549.6	−	19760.5i	−0.969039	−	0.813120i	−0.982400	+	0.186791i	$0.940191\pi$
$840$		0			0
$841$	14857.0	−	5407.52i	0.609170	−	0.221720i
$842$	1967.22	−	1650.69i	0.0805166	−	0.0675614i
$843$		0			0
$844$	772.538	−	1338.08i	0.0315069	−	0.0545716i
$845$	−1756.58	−	9962.06i	−0.0715127	−	0.405568i
$846$		0			0
$847$	10529.9	−	18238.3i	0.427169	−	0.739878i
$848$	−3425.99	−	5933.99i	−0.138737	−	0.240299i
$849$		0			0
$850$	23977.1	−	8726.97i	0.967540	−	0.352156i
$851$	−19715.8	−	7175.95i	−0.794181	−	0.289058i
$852$		0			0
$853$	−1637.01	+	9283.93i	−0.0657093	+	0.372656i	0.934166	+	0.356840i	$0.116146\pi$
$853$	−1637.01	+	9283.93i	−0.0657093	+	0.372656i	−0.999875	+	0.0158164i	$0.994965\pi$
$854$	−17834.1			−0.714601
$855$		0			0
$856$	−19798.1			−0.790521
$857$	6156.15	−	34913.3i	0.245379	−	1.39162i	−0.574230	−	0.818694i	$-0.694699\pi$
$857$	6156.15	−	34913.3i	0.245379	−	1.39162i	0.819610	−	0.572922i	$-0.194190\pi$
$858$		0			0
$859$	−2974.86	−	1082.76i	−0.118162	−	0.0430074i	0.282263	−	0.959337i	$-0.408915\pi$
$859$	−2974.86	−	1082.76i	−0.118162	−	0.0430074i	−0.400424	+	0.916330i	$0.631137\pi$
$860$	181.069	−	65.9037i	0.00717953	−	0.00261314i
$861$		0			0
$862$	−1448.98	−	2509.71i	−0.0572535	−	0.0991660i
$863$	−8473.77	+	14677.0i	−0.334241	+	0.578923i	−0.983339	−	0.181782i	$-0.941813\pi$
$863$	−8473.77	+	14677.0i	−0.334241	+	0.578923i	0.649097	+	0.760705i	$0.275147\pi$
$864$		0			0
$865$	−535.115	−	3034.79i	−0.0210340	−	0.119290i
$866$	−12582.7	+	21794.0i	−0.493740	+	0.855183i
$867$		0			0
$868$	2246.63	−	1885.15i	0.0878522	−	0.0737167i
$869$	56488.2	−	20560.0i	2.20510	−	0.802590i
$870$		0			0
$871$	−2179.11	−	1828.49i	−0.0847718	−	0.0711320i
$872$	−2127.03	+	12063.0i	−0.0826037	+	0.468469i
$873$		0			0
$874$	13777.1	+	15246.3i	0.533202	+	0.590060i
$875$	28144.8			1.08739
$876$		0			0
$877$	−13543.5	−	11364.3i	−0.521472	−	0.437567i	0.343672	−	0.939090i	$-0.388329\pi$
$877$	−13543.5	−	11364.3i	−0.521472	−	0.437567i	−0.865145	+	0.501522i	$0.832774\pi$
$878$	4191.03	+	1525.41i	0.161094	+	0.0586334i
$879$		0			0
$880$	11856.1	−	9948.47i	0.454170	−	0.381094i
$881$	13438.4	+	23276.0i	0.513907	+	0.890113i	0.999870	+	0.0161337i	$0.00513575\pi$
$881$	13438.4	+	23276.0i	0.513907	+	0.890113i	−0.485963	+	0.873980i	$0.661531\pi$
$882$		0			0
$883$	−6839.72	−	38790.0i	−0.260674	−	1.47835i	−0.781077	−	0.624434i	$-0.785330\pi$
$883$	−6839.72	−	38790.0i	−0.260674	−	1.47835i	0.520403	−	0.853921i	$-0.325782\pi$
$884$	−136.188	−	772.362i	−0.00518157	−	0.0293861i
$885$		0			0
$886$	14319.5	+	24802.2i	0.542973	+	0.940457i
$887$	−12259.4	+	10286.9i	−0.464072	+	0.389402i	−0.844627	−	0.535356i	$-0.820177\pi$
$887$	−12259.4	+	10286.9i	−0.464072	+	0.389402i	0.380555	+	0.924758i	$0.375733\pi$
$888$		0			0
$889$	−12613.3	−	4590.88i	−0.475858	−	0.173198i
$890$	480.721	+	403.373i	0.0181054	+	0.0151922i
$891$		0			0
$892$	−929.591			−0.0348935
$893$	−40449.6	−	5611.25i	−1.51578	−	0.210272i
$894$		0			0
$895$	−2726.74	+	15464.1i	−0.101838	+	0.577551i
$896$	23696.5	+	19883.8i	0.883533	+	0.741372i
$897$		0			0
$898$	34507.8	−	12559.8i	1.28234	−	0.466734i
$899$	−20172.2	+	16926.5i	−0.748367	+	0.627955i
$900$		0			0
$901$	−5525.87	+	9571.10i	−0.204321	+	0.353895i
$902$	5807.62	+	32936.7i	0.214382	+	1.21582i
$903$		0			0
$904$	−4496.49	+	7788.15i	−0.165433	+	0.286538i
$905$	−6333.69	−	10970.3i	−0.232640	−	0.402944i
$906$		0			0
$907$	−3270.13	+	1190.23i	−0.119717	+	0.0435733i	−0.401184	−	0.915998i	$-0.631401\pi$
$907$	−3270.13	+	1190.23i	−0.119717	+	0.0435733i	0.281467	+	0.959571i	$0.409179\pi$
$908$	519.120	+	188.944i	0.0189731	+	0.00690565i
$909$		0			0
$910$	−1119.10	+	6346.71i	−0.0407667	+	0.231199i
$911$	18185.1			0.661359			0.330680	−	0.943743i	$-0.392722\pi$
$911$	18185.1			0.661359			0.330680	+	0.943743i	$0.392722\pi$
$912$		0			0
$913$	14546.8			0.527305
$914$	8389.70	−	47580.3i	0.303618	−	1.72190i
$915$		0			0
$916$	752.737	+	273.974i	0.0271519	+	0.00988247i
$917$	967.581	−	352.171i	0.0348444	−	0.0126823i
$918$		0			0
$919$	−8934.27	−	15474.6i	−0.320690	−	0.555452i	0.659940	−	0.751318i	$-0.270582\pi$
$919$	−8934.27	−	15474.6i	−0.320690	−	0.555452i	−0.980631	+	0.195866i	$0.937248\pi$
$920$	−5693.89	+	9862.11i	−0.204046	+	0.353418i
$921$		0			0
$922$	−4968.00	−	28174.9i	−0.177454	−	1.00639i
$923$	−5639.15	+	9767.30i	−0.201100	+	0.348315i
$924$		0			0
$925$	−16996.5	+	14261.8i	−0.604153	+	0.506944i
$926$	10401.8	−	3785.93i	0.369139	−	0.134356i
$927$		0			0
$928$	1409.09	+	1182.36i	0.0498443	+	0.0418244i
$929$	−2814.85	+	15963.8i	−0.0994105	+	0.563785i	0.893896	+	0.448275i	$0.147961\pi$
$929$	−2814.85	+	15963.8i	−0.0994105	+	0.563785i	−0.993306	+	0.115510i	$0.963150\pi$
$930$		0			0
$931$	−11562.4	−	12795.4i	−0.407029	−	0.450433i
$932$	−3013.96			−0.105929
$933$		0			0
$934$	−14054.2	−	11792.9i	−0.492365	−	0.413143i
$935$	−23457.9	−	8537.99i	−0.820488	−	0.298633i
$936$		0			0
$937$	14567.9	−	12223.9i	0.507910	−	0.426187i	−0.352483	−	0.935818i	$-0.614662\pi$
$937$	14567.9	−	12223.9i	0.507910	−	0.426187i	0.860393	+	0.509631i	$0.170218\pi$
$938$	−5002.22	−	8664.10i	−0.174124	−	0.301592i
$939$		0			0
$940$	−204.588	−	1160.27i	−0.00709885	−	0.0402596i
$941$	6801.96	+	38575.8i	0.235640	+	1.33638i	0.841261	+	0.540630i	$0.181814\pi$
$941$	6801.96	+	38575.8i	0.235640	+	1.33638i	−0.605620	+	0.795754i	$0.707075\pi$
$942$		0			0
$943$	−11626.3	−	20137.3i	−0.401489	−	0.695399i
$944$	−8347.34	+	7004.25i	−0.287799	+	0.241492i
$945$		0			0
$946$	−9835.43	−	3579.80i	−0.338031	−	0.123033i
$947$	−36536.0	−	30657.4i	−1.25371	−	1.05199i	−0.996323	−	0.0856775i	$-0.972695\pi$
$947$	−36536.0	−	30657.4i	−1.25371	−	1.05199i	−0.257385	−	0.966309i	$-0.582861\pi$
$948$		0			0
$949$	−8826.14			−0.301906
$950$	21247.4	−	4555.90i	0.725638	−	0.155593i
$951$		0			0
$952$	9200.31	−	52177.5i	0.313218	−	1.77635i
$953$	−8730.52	−	7325.78i	−0.296757	−	0.249009i	0.482236	−	0.876041i	$-0.339825\pi$
$953$	−8730.52	−	7325.78i	−0.296757	−	0.249009i	−0.778993	+	0.627033i	$0.784269\pi$
$954$		0			0
$955$	12103.6	−	4405.36i	0.410120	−	0.149271i
$956$	1323.32	−	1110.40i	0.0447692	−	0.0375658i
$957$		0			0
$958$	−8008.58	+	13871.3i	−0.270089	+	0.467808i
$959$	−8496.09	−	48183.7i	−0.286082	−	1.62245i
$960$		0			0
$961$	−25521.2	+	44204.0i	−0.856675	+	1.48381i
$962$	−5867.83	−	10163.4i	−0.196659	−	0.340624i
$963$		0			0
$964$	1121.95	−	408.358i	0.0374852	−	0.0136435i
$965$	13970.2	+	5084.74i	0.466028	+	0.169620i
$966$		0			0
$967$	−1305.96	+	7406.47i	−0.0434300	+	0.246304i	−0.998792	−	0.0491331i	$-0.984354\pi$
$967$	−1305.96	+	7406.47i	−0.0434300	+	0.246304i	0.955362	+	0.295437i	$0.0954653\pi$
$968$	20815.0			0.691135
$969$		0			0
$970$	−8494.50			−0.281177
$971$	−84.9728	+	481.905i	−0.00280835	+	0.0159269i	−0.986180	−	0.165679i	$-0.947018\pi$
$971$	−84.9728	+	481.905i	−0.00280835	+	0.0159269i	0.983371	+	0.181606i	$0.0581295\pi$
$972$		0			0
$973$	50778.7	+	18481.9i	1.67306	+	0.608945i
$974$	7418.70	−	2700.19i	0.244056	−	0.0888291i
$975$		0			0
$976$	−8327.87	−	14424.3i	−0.273124	−	0.473064i
$977$	8975.95	−	15546.8i	0.293926	−	0.509096i	−0.680808	−	0.732462i	$-0.738371\pi$
$977$	8975.95	−	15546.8i	0.293926	−	0.509096i	0.974735	+	0.223366i	$0.0717046\pi$
$978$		0			0
$979$	343.965	+	1950.72i	0.0112290	+	0.0636827i
$980$	248.775	−	430.890i	0.00810899	−	0.0140452i
$981$		0			0
$982$	−23844.9	+	20008.2i	−0.774868	+	0.650192i
$983$	−17320.0	+	6303.96i	−0.561976	+	0.204542i	−0.607359	−	0.794427i	$-0.707771\pi$
$983$	−17320.0	+	6303.96i	−0.561976	+	0.204542i	0.0453837	+	0.998970i	$0.485549\pi$
$984$		0			0
$985$	−9066.86	−	7608.00i	−0.293294	−	0.246102i
$986$	−4300.61	+	24390.0i	−0.138904	+	0.787764i
$987$		0			0
$988$	−24.5009	−	667.470i	−0.000788944	−	0.0214930i
$989$	7276.96			0.233968
$990$		0			0
$991$	10549.6	+	8852.13i	0.338161	+	0.283751i	0.796015	−	0.605276i	$-0.206937\pi$
$991$	10549.6	+	8852.13i	0.338161	+	0.283751i	−0.457854	+	0.889027i	$0.651382\pi$
$992$	5305.92	+	1931.20i	0.169822	+	0.0618100i
$993$		0			0
$994$	−30385.5	+	25496.4i	−0.969587	+	0.813580i
$995$	−14036.5	−	24312.0i	−0.447224	−	0.774616i
$996$		0			0
$997$	6089.47	+	34535.1i	0.193436	+	1.09703i	0.914629	+	0.404295i	$0.132483\pi$
$997$	6089.47	+	34535.1i	0.193436	+	1.09703i	−0.721193	+	0.692734i	$0.756406\pi$
$998$	357.158	+	2025.54i	0.0113283	+	0.0642460i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.4.u.b.55.2		24
3.2	odd	2		19.4.e.a.17.3	yes	24
19.9	even	9	inner	171.4.u.b.28.2		24
57.35	odd	18		361.4.a.n.1.9		12
57.41	even	18		361.4.a.m.1.4		12
57.47	odd	18		19.4.e.a.9.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.4.e.a.9.3	✓	24	57.47	odd	18
19.4.e.a.17.3	yes	24	3.2	odd	2
171.4.u.b.28.2		24	19.9	even	9	inner
171.4.u.b.55.2		24	1.1	even	1	trivial
361.4.a.m.1.4		12	57.41	even	18
361.4.a.n.1.9		12	57.35	odd	18

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	171.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.477474 + 2.70789i) q^{2} +(0.412858 + 0.150268i) q^{4} +(-5.11043 + 1.86004i) q^{5} +(11.7392 + 20.3328i) q^{7} +(-11.6027 + 20.0964i) q^{8} +O(q^{10})\)	\(q+(-0.477474 + 2.70789i) q^{2} +(0.412858 + 0.150268i) q^{4} +(-5.11043 + 1.86004i) q^{5} +(11.7392 + 20.3328i) q^{7} +(-11.6027 + 20.0964i) q^{8} +(-2.59670 - 14.7266i) q^{10} +(23.6008 - 40.8778i) q^{11} +(-14.0615 + 11.7990i) q^{13} +(-60.6643 + 22.0800i) q^{14} +(-46.1865 - 38.7550i) q^{16} +(-16.8867 + 95.7695i) q^{17} +(-25.4519 + 78.8112i) q^{19} -2.38939 q^{20} +(99.4237 + 83.4264i) q^{22} +(-84.7939 - 30.8625i) q^{23} +(-73.0988 + 61.3372i) q^{25} +(-25.2364 - 43.7108i) q^{26} +(1.79124 + 10.1586i) q^{28} +(-16.0833 - 91.2129i) q^{29} +(-142.156 - 246.222i) q^{31} +(-15.2136 + 12.7658i) q^{32} +(-251.270 - 91.4549i) q^{34} +(-97.8122 - 82.0742i) q^{35} +232.514 q^{37} +(-201.259 - 106.551i) q^{38} +(21.9144 - 124.283i) q^{40} +(197.399 + 165.638i) q^{41} +(-75.7804 + 27.5818i) q^{43} +(15.8864 - 13.3303i) q^{44} +(124.059 - 214.877i) q^{46} +(85.6235 + 485.595i) q^{47} +(-104.116 + 180.335i) q^{49} +(-131.192 - 227.230i) q^{50} +(-7.57843 + 2.75832i) q^{52} +(106.793 + 38.8693i) q^{53} +(-44.5757 + 252.802i) q^{55} -544.824 q^{56} +254.674 q^{58} +(31.3837 - 177.986i) q^{59} +(259.591 + 94.4833i) q^{61} +(734.617 - 267.379i) q^{62} +(-268.473 - 465.008i) q^{64} +(49.9138 - 86.4532i) q^{65} +(26.9102 + 152.615i) q^{67} +(-21.3629 + 37.0017i) q^{68} +(268.951 - 225.676i) q^{70} +(577.366 - 210.144i) q^{71} +(368.338 + 309.072i) q^{73} +(-111.019 + 629.622i) q^{74} +(-22.3508 + 28.7132i) q^{76} +1108.22 q^{77} +(975.594 + 818.621i) q^{79} +(308.119 + 112.146i) q^{80} +(-542.782 + 455.448i) q^{82} +(154.093 + 266.896i) q^{83} +(-91.8370 - 520.834i) q^{85} +(-38.5053 - 218.375i) q^{86} +(547.665 + 948.584i) q^{88} +(-32.1471 + 26.9746i) q^{89} +(-404.979 - 147.400i) q^{91} +(-30.3702 - 25.4836i) q^{92} -1355.82 q^{94} +(-16.5219 - 450.101i) q^{95} +(98.6409 - 559.420i) q^{97} +(-438.614 - 368.041i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} - 24 q^{4} + 6 q^{5} + 3 q^{7} + 75 q^{8}+O(q^{10}) \) 24 * q + 6 * q^2 - 24 * q^4 + 6 * q^5 + 3 * q^7 + 75 * q^8	\( 24 q + 6 q^{2} - 24 q^{4} + 6 q^{5} + 3 q^{7} + 75 q^{8} + 75 q^{10} - 39 q^{11} - 156 q^{13} - 93 q^{14} + 504 q^{16} - 12 q^{17} + 546 q^{19} + 198 q^{20} - 6 q^{22} - 6 q^{23} - 498 q^{25} + 639 q^{26} - 1368 q^{28} + 630 q^{29} - 591 q^{31} - 147 q^{32} - 408 q^{34} - 2001 q^{35} - 72 q^{37} - 2934 q^{38} + 2886 q^{40} + 477 q^{41} + 588 q^{43} + 3423 q^{44} - 1728 q^{46} + 1242 q^{47} - 639 q^{49} + 1788 q^{50} + 2733 q^{52} + 300 q^{53} + 315 q^{55} - 4638 q^{56} - 2820 q^{58} - 2097 q^{59} - 2316 q^{61} + 1320 q^{62} - 1785 q^{64} + 2433 q^{65} + 57 q^{67} + 438 q^{68} - 213 q^{70} + 792 q^{71} + 4068 q^{73} - 4287 q^{74} + 5538 q^{76} - 3786 q^{77} + 1824 q^{79} + 2739 q^{80} + 2205 q^{82} - 1071 q^{83} - 2394 q^{85} + 5256 q^{86} + 1101 q^{88} + 3006 q^{89} - 3285 q^{91} + 1452 q^{92} - 1086 q^{94} + 3078 q^{95} - 2535 q^{97} + 2403 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 - 24 * q^4 + 6 * q^5 + 3 * q^7 + 75 * q^8 + 75 * q^10 - 39 * q^11 - 156 * q^13 - 93 * q^14 + 504 * q^16 - 12 * q^17 + 546 * q^19 + 198 * q^20 - 6 * q^22 - 6 * q^23 - 498 * q^25 + 639 * q^26 - 1368 * q^28 + 630 * q^29 - 591 * q^31 - 147 * q^32 - 408 * q^34 - 2001 * q^35 - 72 * q^37 - 2934 * q^38 + 2886 * q^40 + 477 * q^41 + 588 * q^43 + 3423 * q^44 - 1728 * q^46 + 1242 * q^47 - 639 * q^49 + 1788 * q^50 + 2733 * q^52 + 300 * q^53 + 315 * q^55 - 4638 * q^56 - 2820 * q^58 - 2097 * q^59 - 2316 * q^61 + 1320 * q^62 - 1785 * q^64 + 2433 * q^65 + 57 * q^67 + 438 * q^68 - 213 * q^70 + 792 * q^71 + 4068 * q^73 - 4287 * q^74 + 5538 * q^76 - 3786 * q^77 + 1824 * q^79 + 2739 * q^80 + 2205 * q^82 - 1071 * q^83 - 2394 * q^85 + 5256 * q^86 + 1101 * q^88 + 3006 * q^89 - 3285 * q^91 + 1452 * q^92 - 1086 * q^94 + 3078 * q^95 - 2535 * q^97 + 2403 * q^98

Introduction

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