LMFDB - Embedded newform 261.3.s.a.217.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,3,Mod(10,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([0, 23]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("261.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	261.s (of order $28$, degree $12$, 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:	$7.11173489980$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{28})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			217.4
Character	$\chi$	$=$	261.217
Dual form			261.3.s.a.172.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.388927 + 3.45182i) q^{2} +(-7.86410 + 1.79493i) q^{4} +(-4.44600 - 3.54557i) q^{5} +(1.25371 - 5.49285i) q^{7} +(-4.66523 - 13.3325i) q^{8} +O(q^{10})$	\(q+(0.388927 + 3.45182i) q^{2} +(-7.86410 + 1.79493i) q^{4} +(-4.44600 - 3.54557i) q^{5} +(1.25371 - 5.49285i) q^{7} +(-4.66523 - 13.3325i) q^{8} +(10.5095 - 16.7258i) q^{10} +(6.29707 - 17.9960i) q^{11} +(6.68692 + 13.8855i) q^{13} +(19.4480 + 2.19126i) q^{14} +(15.1368 - 7.28948i) q^{16} +(-1.08221 + 1.08221i) q^{17} +(-17.6859 - 11.1128i) q^{19} +(41.3278 + 19.9024i) q^{20} +(64.5681 + 14.7372i) q^{22} +(-4.81481 - 6.03758i) q^{23} +(1.63284 + 7.15396i) q^{25} +(-45.3297 + 28.4825i) q^{26} +45.4467i q^{28} +(18.9830 - 21.9237i) q^{29} +(-5.79670 - 51.4471i) q^{31} +(0.989018 + 1.57401i) q^{32} +(-4.15651 - 3.31471i) q^{34} +(-25.0493 + 19.9761i) q^{35} +(-0.580820 - 1.65989i) q^{37} +(31.4809 - 65.3707i) q^{38} +(-26.5295 + 75.8170i) q^{40} +(-0.198543 - 0.198543i) q^{41} +(-16.5106 - 1.86030i) q^{43} +(-17.2193 + 152.825i) q^{44} +(18.9681 - 18.9681i) q^{46} +(2.91807 + 1.02108i) q^{47} +(15.5478 + 7.48743i) q^{49} +(-24.0591 + 8.41865i) q^{50} +(-77.5102 - 97.1947i) q^{52} +(-31.3688 + 39.3353i) q^{53} +(-91.8027 + 57.6835i) q^{55} +(-79.0821 + 8.91041i) q^{56} +(83.0596 + 56.9991i) q^{58} +1.15807 q^{59} +(-12.3983 - 19.7319i) q^{61} +(175.332 - 40.0183i) q^{62} +(47.4922 - 37.8737i) q^{64} +(19.5020 - 85.4439i) q^{65} +(2.18892 - 4.54533i) q^{67} +(6.56815 - 10.4531i) q^{68} +(-78.6963 - 78.6963i) q^{70} +(-12.0075 - 24.9339i) q^{71} +(-8.52973 + 75.7035i) q^{73} +(5.50374 - 2.65046i) q^{74} +(159.030 + 55.6472i) q^{76} +(-90.9547 - 57.1506i) q^{77} +(27.2780 - 9.54499i) q^{79} +(-93.1433 - 21.2594i) q^{80} +(0.608115 - 0.762553i) q^{82} +(5.13309 + 22.4895i) q^{83} +(8.64858 - 0.974461i) q^{85} -57.7154i q^{86} -269.308 q^{88} +(-8.12973 - 72.1533i) q^{89} +(84.6546 - 19.3219i) q^{91} +(48.7012 + 38.8379i) q^{92} +(-2.38966 + 10.4698i) q^{94} +(39.2304 + 112.114i) q^{95} +(65.8679 - 104.828i) q^{97} +(-19.7983 + 56.5803i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{13}{28}\right)$	$1$

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 $

$2$	0.388927	+	3.45182i	0.194464	+	1.72591i	0.589950	+	0.807440i	$0.299147\pi$
$2$	0.388927	+	3.45182i	0.194464	+	1.72591i	−0.395487	+	0.918472i	$0.629424\pi$
$3$		0			0
$3$		0			0
$4$	−7.86410	+	1.79493i	−1.96603	+	0.448733i
$5$	−4.44600	−	3.54557i	−0.889200	−	0.709113i	0.0682639	−	0.997667i	$-0.478254\pi$
$5$	−4.44600	−	3.54557i	−0.889200	−	0.709113i	−0.957464	+	0.288554i	$0.906825\pi$
$6$		0			0
$7$	1.25371	−	5.49285i	0.179101	−	0.784694i	−0.802945	−	0.596053i	$-0.796735\pi$
$7$	1.25371	−	5.49285i	0.179101	−	0.784694i	0.982046	−	0.188640i	$-0.0604081\pi$
$8$	−4.66523	−	13.3325i	−0.583154	−	1.66656i
$9$		0			0
$10$	10.5095	−	16.7258i	1.05095	−	1.67258i
$11$	6.29707	−	17.9960i	0.572461	−	1.63600i	−0.184718	−	0.982792i	$-0.559137\pi$
$11$	6.29707	−	17.9960i	0.572461	−	1.63600i	0.757179	−	0.653208i	$-0.226577\pi$
$12$		0			0
$13$	6.68692	+	13.8855i	0.514378	+	1.06812i	0.982810	+	0.184618i	$0.0591048\pi$
$13$	6.68692	+	13.8855i	0.514378	+	1.06812i	−0.468432	+	0.883499i	$0.655181\pi$
$14$	19.4480	+	2.19126i	1.38914	+	0.156518i
$15$		0			0
$16$	15.1368	−	7.28948i	0.946047	−	0.455592i
$17$	−1.08221	+	1.08221i	−0.0636597	+	0.0636597i	−0.738220	−	0.674560i	$-0.764333\pi$
$17$	−1.08221	+	1.08221i	−0.0636597	+	0.0636597i	0.674560	+	0.738220i	$0.264333\pi$
$18$		0			0
$19$	−17.6859	−	11.1128i	−0.930837	−	0.584884i	−0.0209684	−	0.999780i	$-0.506675\pi$
$19$	−17.6859	−	11.1128i	−0.930837	−	0.584884i	−0.909869	+	0.414896i	$0.863818\pi$
$20$	41.3278	+	19.9024i	2.06639	+	0.995122i
$21$		0			0
$22$	64.5681	+	14.7372i	2.93491	+	0.669875i
$23$	−4.81481	−	6.03758i	−0.209340	−	0.262504i	0.666066	−	0.745893i	$-0.267977\pi$
$23$	−4.81481	−	6.03758i	−0.209340	−	0.262504i	−0.875405	+	0.483389i	$0.839406\pi$
$24$		0			0
$25$	1.63284	+	7.15396i	0.0653138	+	0.286158i
$26$	−45.3297	+	28.4825i	−1.74345	+	1.09548i
$27$		0			0
$28$			45.4467i			1.62310i
$29$	18.9830	−	21.9237i	0.654585	−	0.755988i
$29$	18.9830	−	21.9237i	0.654585	−	0.755988i
$30$		0			0
$31$	−5.79670	−	51.4471i	−0.186990	−	1.65958i	−0.640221	−	0.768191i	$-0.721157\pi$
$31$	−5.79670	−	51.4471i	−0.186990	−	1.65958i	0.453231	−	0.891393i	$-0.350271\pi$
$32$	0.989018	+	1.57401i	0.0309068	+	0.0491879i
$33$		0			0
$34$	−4.15651	−	3.31471i	−0.122250	−	0.0974914i
$35$	−25.0493	+	19.9761i	−0.715693	+	0.570746i
$36$		0			0
$37$	−0.580820	−	1.65989i	−0.0156978	−	0.0448618i	0.935768	−	0.352617i	$-0.114708\pi$
$37$	−0.580820	−	1.65989i	−0.0156978	−	0.0448618i	−0.951466	+	0.307755i	$0.900422\pi$
$38$	31.4809	−	65.3707i	0.828444	−	1.72028i
$39$		0			0
$40$	−26.5295	+	75.8170i	−0.663238	+	1.89542i
$41$	−0.198543	−	0.198543i	−0.00484250	−	0.00484250i	0.704681	−	0.709524i	$-0.251090\pi$
$41$	−0.198543	−	0.198543i	−0.00484250	−	0.00484250i	−0.709524	+	0.704681i	$0.751090\pi$
$42$		0			0
$43$	−16.5106	−	1.86030i	−0.383969	−	0.0432629i	−0.0821293	−	0.996622i	$-0.526172\pi$
$43$	−16.5106	−	1.86030i	−0.383969	−	0.0432629i	−0.301839	+	0.953359i	$0.597601\pi$
$44$	−17.2193	+	152.825i	−0.391347	+	3.47330i
$45$		0			0
$46$	18.9681	−	18.9681i	0.412349	−	0.412349i
$47$	2.91807	+	1.02108i	0.0620866	+	0.0217250i	0.361144	−	0.932510i	$-0.382386\pi$
$47$	2.91807	+	1.02108i	0.0620866	+	0.0217250i	−0.299057	+	0.954235i	$0.596672\pi$
$48$		0			0
$49$	15.5478	+	7.48743i	0.317302	+	0.152805i
$50$	−24.0591	+	8.41865i	−0.481183	+	0.168373i
$51$		0			0
$52$	−77.5102	−	97.1947i	−1.49058	−	1.86913i
$53$	−31.3688	+	39.3353i	−0.591865	+	0.742175i	−0.984085	−	0.177696i	$-0.943136\pi$
$53$	−31.3688	+	39.3353i	−0.591865	+	0.742175i	0.392221	+	0.919871i	$0.371707\pi$
$54$		0			0
$55$	−91.8027	+	57.6835i	−1.66914	+	1.04879i
$56$	−79.0821	+	8.91041i	−1.41218	+	0.159115i
$57$		0			0
$58$	83.0596	+	56.9991i	1.43206	+	0.982744i
$59$	1.15807			0.0196282			0.00981412	−	0.999952i	$-0.496876\pi$
$59$	1.15807			0.0196282			0.00981412	+	0.999952i	$0.496876\pi$
$60$		0			0
$61$	−12.3983	−	19.7319i	−0.203252	−	0.323473i	0.729508	−	0.683972i	$-0.239749\pi$
$61$	−12.3983	−	19.7319i	−0.203252	−	0.323473i	−0.932759	+	0.360499i	$0.882606\pi$
$62$	175.332	−	40.0183i	2.82793	−	0.645457i
$63$		0			0
$64$	47.4922	−	37.8737i	0.742065	−	0.591777i
$65$	19.5020	−	85.4439i	0.300031	−	1.31452i
$66$		0			0
$67$	2.18892	−	4.54533i	0.0326704	−	0.0678408i	−0.883995	−	0.467497i	$-0.845156\pi$
$67$	2.18892	−	4.54533i	0.0326704	−	0.0678408i	0.916665	+	0.399656i	$0.130870\pi$
$68$	6.56815	−	10.4531i	0.0965904	−	0.153723i
$69$		0			0
$70$	−78.6963	−	78.6963i	−1.12423	−	1.12423i
$71$	−12.0075	−	24.9339i	−0.169120	−	0.351181i	0.799133	−	0.601155i	$-0.205292\pi$
$71$	−12.0075	−	24.9339i	−0.169120	−	0.351181i	−0.968253	+	0.249973i	$0.919578\pi$
$72$		0			0
$73$	−8.52973	+	75.7035i	−0.116846	+	1.03703i	0.789282	+	0.614030i	$0.210453\pi$
$73$	−8.52973	+	75.7035i	−0.116846	+	1.03703i	−0.906128	+	0.423004i	$0.860976\pi$
$74$	5.50374	−	2.65046i	0.0743749	−	0.0358170i
$75$		0			0
$76$	159.030	+	55.6472i	2.09251	+	0.732200i
$77$	−90.9547	−	57.1506i	−1.18123	−	0.742216i
$78$		0			0
$79$	27.2780	−	9.54499i	0.345291	−	0.120823i	−0.152062	−	0.988371i	$-0.548591\pi$
$79$	27.2780	−	9.54499i	0.345291	−	0.120823i	0.497353	+	0.867548i	$0.334305\pi$
$80$	−93.1433	−	21.2594i	−1.16429	−	0.265742i
$81$		0			0
$82$	0.608115	−	0.762553i	0.00741604	−	0.00929942i
$83$	5.13309	+	22.4895i	0.0618444	+	0.270958i	0.996391	−	0.0848828i	$-0.0270516\pi$
$83$	5.13309	+	22.4895i	0.0618444	+	0.270958i	−0.934546	+	0.355841i	$0.884194\pi$
$84$		0			0
$85$	8.64858	−	0.974461i	0.101748	−	0.0114642i
$86$		−	57.7154i		−	0.671109i
$87$		0			0
$88$	−269.308			−3.06032
$89$	−8.12973	−	72.1533i	−0.0913453	−	0.810712i	−0.952949	−	0.303130i	$-0.901968\pi$
$89$	−8.12973	−	72.1533i	−0.0913453	−	0.810712i	0.861604	−	0.507581i	$-0.169460\pi$
$90$		0			0
$91$	84.6546	−	19.3219i	0.930271	−	0.212328i
$92$	48.7012	+	38.8379i	0.529361	+	0.422151i
$93$		0			0
$94$	−2.38966	+	10.4698i	−0.0254219	+	0.111381i
$95$	39.2304	+	112.114i	0.412951	+	1.18015i
$96$		0			0
$97$	65.8679	−	104.828i	0.679051	−	1.08070i	−0.312365	−	0.949962i	$-0.601121\pi$
$97$	65.8679	−	104.828i	0.679051	−	1.08070i	0.991416	−	0.130742i	$-0.0417358\pi$
$98$	−19.7983	+	56.5803i	−0.202024	+	0.577350i
$99$		0			0
$100$	−25.6817	−	53.3286i	−0.256817	−	0.533286i
$101$	137.817	+	15.5282i	1.36452	+	0.153745i	0.763666	−	0.645612i	$-0.223398\pi$
$101$	137.817	+	15.5282i	1.36452	+	0.153745i	0.600857	+	0.799357i	$0.294826\pi$
$102$		0			0
$103$	−86.6685	+	41.7374i	−0.841442	+	0.405217i	−0.804394	−	0.594096i	$-0.797510\pi$
$103$	−86.6685	+	41.7374i	−0.841442	+	0.405217i	−0.0370482	+	0.999313i	$0.511795\pi$
$104$	153.932	−	153.932i	1.48012	−	1.48012i
$105$		0			0
$106$	−147.979	−	92.9811i	−1.39602	−	0.877180i
$107$	−125.260	−	60.3222i	−1.17066	−	0.563759i	−0.255481	−	0.966814i	$-0.582234\pi$
$107$	−125.260	−	60.3222i	−1.17066	−	0.563759i	−0.915176	+	0.403055i	$0.867948\pi$
$108$		0			0
$109$	−120.620	−	27.5306i	−1.10660	−	0.252575i	−0.370087	−	0.928997i	$-0.620672\pi$
$109$	−120.620	−	27.5306i	−1.10660	−	0.252575i	−0.736514	+	0.676422i	$0.763529\pi$
$110$	−234.818	−	294.452i	−2.13471	−	2.67684i
$111$		0			0
$112$	−21.0630	−	92.2829i	−0.188062	−	0.823954i
$113$	−177.502	+	111.532i	−1.57082	+	0.987010i	−0.586636	+	0.809851i	$0.699548\pi$
$113$	−177.502	+	111.532i	−1.57082	+	0.987010i	−0.984182	+	0.177159i	$0.943309\pi$
$114$		0			0
$115$			43.9143i			0.381864i
$116$	−109.933	+	206.483i	−0.947695	+	1.78003i
$117$		0			0
$118$	0.450403	+	3.99744i	0.00381698	+	0.0338766i
$119$	4.58766	+	7.30123i	0.0385518	+	0.0613548i
$120$		0			0
$121$	−189.601	−	151.202i	−1.56695	−	1.24960i
$122$	63.2888	−	50.4711i	0.518761	−	0.413698i
$123$		0			0
$124$	137.930	+	394.181i	1.11234	+	3.17888i
$125$	−43.5784	+	90.4914i	−0.348627	+	0.723931i
$126$		0			0
$127$	2.47109	−	7.06196i	0.0194574	−	0.0556059i	−0.933745	−	0.357939i	$-0.883480\pi$
$127$	2.47109	−	7.06196i	0.0194574	−	0.0556059i	0.953202	+	0.302333i	$0.0977654\pi$
$128$	154.462	+	154.462i	1.20674	+	1.20674i
$129$		0			0
$130$	302.522	+	34.0861i	2.32709	+	0.262200i
$131$	2.15703	−	19.1442i	0.0164659	−	0.146139i	−0.982789	−	0.184731i	$-0.940859\pi$
$131$	2.15703	−	19.1442i	0.0164659	−	0.146139i	0.999255	+	0.0385920i	$0.0122873\pi$
$132$		0			0
$133$	−83.2139	+	83.2139i	−0.625668	+	0.625668i
$134$	16.5410	+	5.78795i	0.123440	+	0.0431937i
$135$		0			0
$136$	19.4774	+	9.37980i	0.143216	+	0.0689691i
$137$	61.9941	−	21.6927i	0.452512	−	0.158341i	−0.0943939	−	0.995535i	$-0.530091\pi$
$137$	61.9941	−	21.6927i	0.452512	−	0.158341i	0.546906	+	0.837194i	$0.315806\pi$
$138$		0			0
$139$	112.699	+	141.319i	0.810781	+	1.01669i	0.999400	+	0.0346367i	$0.0110274\pi$
$139$	112.699	+	141.319i	0.810781	+	1.01669i	−0.188619	+	0.982050i	$0.560401\pi$
$140$	161.134	−	202.056i	1.15096	−	1.44326i
$141$		0			0
$142$	81.3972	−	51.1453i	0.573220	−	0.360178i
$143$	291.992	−	32.8996i	2.04190	−	0.230067i
$144$		0			0
$145$	−162.130	+	30.1672i	−1.11814	+	0.208050i
$146$	−264.632			−1.81255
$147$		0			0
$148$	7.54701	+	12.0110i	0.0509933	+	0.0811554i
$149$	193.555	−	44.1777i	1.29903	−	0.296495i	0.483568	−	0.875307i	$-0.339341\pi$
$149$	193.555	−	44.1777i	1.29903	−	0.296495i	0.815461	+	0.578812i	$0.196484\pi$
$150$		0			0
$151$	55.9613	−	44.6277i	0.370605	−	0.295547i	−0.420422	−	0.907329i	$-0.638118\pi$
$151$	55.9613	−	44.6277i	0.370605	−	0.295547i	0.791027	+	0.611781i	$0.209547\pi$
$152$	−65.6520	+	287.640i	−0.431921	+	1.89237i
$153$		0			0
$154$	161.899	−	336.187i	1.05129	−	2.18303i
$155$	−156.637	+	249.286i	−1.01056	+	1.60830i
$156$		0			0
$157$	52.5972	+	52.5972i	0.335014	+	0.335014i	0.854487	−	0.519473i	$-0.173872\pi$
$157$	52.5972	+	52.5972i	0.335014	+	0.335014i	−0.519473	+	0.854487i	$0.673872\pi$
$158$	43.5568	+	90.4465i	0.275676	+	0.572446i
$159$		0			0
$160$	1.18359	−	10.5047i	0.00739746	−	0.0656543i
$161$	−39.1999	+	18.8777i	−0.243478	+	0.117253i
$162$		0			0
$163$	211.039	+	73.8456i	1.29471	+	0.453040i	0.887717	−	0.460389i	$-0.152290\pi$
$163$	211.039	+	73.8456i	1.29471	+	0.453040i	0.406998	+	0.913429i	$0.366576\pi$
$164$	1.91773	+	1.20499i	0.0116935	+	0.00734750i
$165$		0			0
$166$	−75.6335	+	26.4653i	−0.455623	+	0.159430i
$167$	52.3830	+	11.9561i	0.313671	+	0.0715933i	0.376458	−	0.926434i	$-0.377142\pi$
$167$	52.3830	+	11.9561i	0.313671	+	0.0715933i	−0.0627875	+	0.998027i	$0.519999\pi$
$168$		0			0
$169$	−42.7232	+	53.5732i	−0.252800	+	0.317001i
$170$	6.72733	+	29.4744i	0.0395726	+	0.173379i
$171$		0			0
$172$	133.181	−	15.0058i	0.774306	−	0.0872433i
$173$			271.306i			1.56824i	0.620606	+	0.784122i	$0.286886\pi$
$173$			271.306i			1.56824i	−0.620606	+	0.784122i	$0.713114\pi$
$174$		0			0
$175$	41.3428			0.236244
$176$	−35.8642	−	318.303i	−0.203774	−	1.80854i
$177$		0			0
$178$	245.899	−	56.1248i	1.38145	−	0.315308i
$179$	−153.672	−	122.550i	−0.858504	−	0.684634i	0.0918605	−	0.995772i	$-0.470719\pi$
$179$	−153.672	−	122.550i	−0.858504	−	0.684634i	−0.950365	+	0.311137i	$0.899290\pi$
$180$		0			0
$181$	14.9903	−	65.6768i	0.0828193	−	0.362855i	−0.916488	−	0.400062i	$-0.868989\pi$
$181$	14.9903	−	65.6768i	0.0828193	−	0.362855i	0.999308	+	0.0372064i	$0.0118459\pi$
$182$	99.6201	+	284.698i	0.547363	+	1.56427i
$183$		0			0
$184$	−58.0336	+	92.3600i	−0.315400	+	0.501956i
$185$	−3.30292	+	9.43919i	−0.0178536	+	0.0510227i
$186$		0			0
$187$	12.6607	+	26.2903i	0.0677045	+	0.140590i
$188$	−24.7808	−	2.79212i	−0.131813	−	0.0148517i
$189$		0			0
$190$	−371.740	+	179.020i	−1.95653	+	0.942213i
$191$	47.0321	−	47.0321i	0.246241	−	0.246241i	−0.573185	−	0.819426i	$-0.694292\pi$
$191$	47.0321	−	47.0321i	0.246241	−	0.246241i	0.819426	+	0.573185i	$0.194292\pi$
$192$		0			0
$193$	217.923	+	136.930i	1.12914	+	0.709483i	0.961073	−	0.276293i	$-0.0891061\pi$
$193$	217.923	+	136.930i	1.12914	+	0.709483i	0.168063	+	0.985776i	$0.446249\pi$
$194$	387.466	+	186.594i	1.99725	+	0.961824i
$195$		0			0
$196$	−135.709	−	30.9747i	−0.692393	−	0.158034i
$197$	−33.8518	−	42.4488i	−0.171837	−	0.215476i	0.688454	−	0.725280i	$-0.258290\pi$
$197$	−33.8518	−	42.4488i	−0.171837	−	0.215476i	−0.860291	+	0.509803i	$0.829718\pi$
$198$		0			0
$199$	−14.0003	−	61.3394i	−0.0703533	−	0.308238i	0.927492	−	0.373842i	$-0.121960\pi$
$199$	−14.0003	−	61.3394i	−0.0703533	−	0.308238i	−0.997846	+	0.0656039i	$0.979103\pi$
$200$	87.7622	−	55.1447i	0.438811	−	0.275723i
$201$		0			0
$202$			481.759i			2.38494i
$203$	−96.6244	−	131.757i	−0.475982	−	0.649047i
$204$		0			0
$205$	0.178774	+	1.58667i	0.000872070	+	0.00773983i
$206$	−177.778	−	282.932i	−0.862999	−	1.37345i
$207$		0			0
$208$	202.436	+	161.438i	0.973252	+	0.776143i
$209$	−311.355	+	248.297i	−1.48974	+	1.18803i
$210$		0			0
$211$	−15.5911	−	44.5567i	−0.0738913	−	0.211169i	0.901014	−	0.433791i	$-0.142824\pi$
$211$	−15.5911	−	44.5567i	−0.0738913	−	0.211169i	−0.974905	+	0.222622i	$0.928539\pi$
$212$	176.084	−	365.642i	0.830583	−	1.72472i
$213$		0			0
$214$	159.504	−	455.837i	0.745348	−	2.13008i
$215$	66.8105	+	66.8105i	0.310746	+	0.310746i
$216$		0			0
$217$	−289.859	−	32.6592i	−1.33575	−	0.150503i
$218$	48.1186	−	427.065i	0.220728	−	1.95901i
$219$		0			0
$220$	618.408	−	618.408i	2.81095	−	2.81095i
$221$	−22.2638	−	7.79044i	−0.100741	−	0.0352508i
$222$		0			0
$223$	261.957	+	126.152i	1.17469	+	0.565702i	0.916361	−	0.400354i	$-0.131113\pi$
$223$	261.957	+	126.152i	1.17469	+	0.565702i	0.258333	+	0.966056i	$0.416827\pi$
$224$	9.88576	−	3.45918i	0.0441329	−	0.0154428i
$225$		0			0
$226$	−454.025	−	569.329i	−2.00896	−	2.51915i
$227$	34.4220	−	43.1638i	0.151639	−	0.190149i	−0.700210	−	0.713937i	$-0.746910\pi$
$227$	34.4220	−	43.1638i	0.151639	−	0.190149i	0.851849	+	0.523788i	$0.175482\pi$
$228$		0			0
$229$	−221.885	+	139.419i	−0.968928	+	0.608818i	−0.920805	−	0.390024i	$-0.872467\pi$
$229$	−221.885	+	139.419i	−0.968928	+	0.608818i	−0.0481232	+	0.998841i	$0.515324\pi$
$230$	−151.584	+	17.0795i	−0.659063	+	0.0742585i
$231$		0			0
$232$	−380.856	−	150.811i	−1.64162	−	0.650046i
$233$	241.002			1.03434			0.517172	−	0.855881i	$-0.326985\pi$
$233$	241.002			1.03434			0.517172	+	0.855881i	$0.326985\pi$
$234$		0			0
$235$	−9.35344	−	14.8859i	−0.0398019	−	0.0633443i
$236$	−9.10716	+	2.07865i	−0.0385896	+	0.00880783i
$237$		0			0
$238$	−23.4183	+	18.6754i	−0.0983961	+	0.0784683i
$239$	61.9514	−	271.427i	0.259211	−	1.13568i	−0.662887	−	0.748720i	$-0.730669\pi$
$239$	61.9514	−	271.427i	0.259211	−	1.13568i	0.922098	−	0.386957i	$-0.126474\pi$
$240$		0			0
$241$	−80.8324	+	167.850i	−0.335404	+	0.696474i	−0.998651	−	0.0519267i	$-0.983464\pi$
$241$	−80.8324	+	167.850i	−0.335404	+	0.696474i	0.663247	+	0.748401i	$0.269178\pi$
$242$	448.181	−	713.276i	1.85199	−	2.94742i
$243$		0			0
$244$	132.919	+	132.919i	0.544751	+	0.544751i
$245$	−42.5784	−	88.4149i	−0.173789	−	0.360877i
$246$		0			0
$247$	36.0428	−	319.888i	0.145922	−	1.29509i
$248$	−658.874	+	317.297i	−2.65675	+	1.27942i
$249$		0			0
$250$	−329.309	−	115.230i	−1.31724	−	0.460921i
$251$	213.340	+	134.050i	0.849959	+	0.534065i	0.885145	−	0.465316i	$-0.154059\pi$
$251$	213.340	+	134.050i	0.849959	+	0.534065i	−0.0351854	+	0.999381i	$0.511202\pi$
$252$		0			0
$253$	−138.972	+	48.6282i	−0.549294	+	0.192206i
$254$	25.3377	+	5.78316i	0.0997547	+	0.0227684i
$255$		0			0
$256$	−321.607	+	403.282i	−1.25628	+	1.57532i
$257$	−25.8837	−	113.404i	−0.100715	−	0.441260i	−0.999992	−	0.00388207i	$-0.998764\pi$
$257$	−25.8837	−	113.404i	−0.100715	−	0.441260i	0.899278	−	0.437378i	$-0.144093\pi$
$258$		0			0
$259$	−9.84570	+	1.10934i	−0.0380143	+	0.00428318i
$260$			706.945i			2.71902i
$261$		0			0
$262$	66.9212			0.255424
$263$	−16.7924	−	149.037i	−0.0638495	−	0.566680i	−0.984386	−	0.176023i	$-0.943677\pi$
$263$	−16.7924	−	149.037i	−0.0638495	−	0.566680i	0.920536	−	0.390657i	$-0.127752\pi$
$264$		0			0
$265$	278.932	−	63.6643i	1.05257	−	0.240243i
$266$	−319.604	−	254.876i	−1.20152	−	0.958179i
$267$		0			0
$268$	−9.05532	+	39.6739i	−0.0337885	+	0.148037i
$269$	142.154	+	406.254i	0.528455	+	1.51024i	0.830542	+	0.556957i	$0.188031\pi$
$269$	142.154	+	406.254i	0.528455	+	1.51024i	−0.302087	+	0.953280i	$0.597683\pi$
$270$		0			0
$271$	145.351	−	231.324i	0.536349	−	0.853595i	−0.463116	−	0.886298i	$-0.653269\pi$
$271$	145.351	−	231.324i	0.536349	−	0.853595i	0.999465	+	0.0327029i	$0.0104115\pi$
$272$	−8.49243	+	24.2700i	−0.0312222	+	0.0892279i
$273$		0			0
$274$	98.9905	+	205.556i	0.361279	+	0.750204i
$275$	139.025	+	15.6643i	0.505544	+	0.0569612i
$276$		0			0
$277$	402.718	−	193.939i	1.45385	−	0.700139i	0.470595	−	0.882349i	$-0.344039\pi$
$277$	402.718	−	193.939i	1.45385	−	0.700139i	0.983260	+	0.182210i	$0.0583251\pi$
$278$	−443.978	+	443.978i	−1.59704	+	1.59704i
$279$		0			0
$280$	383.191	+	240.775i	1.36854	+	0.859911i
$281$	−146.043	−	70.3308i	−0.519728	−	0.250288i	0.155581	−	0.987823i	$-0.450275\pi$
$281$	−146.043	−	70.3308i	−0.519728	−	0.250288i	−0.675308	+	0.737536i	$0.735989\pi$
$282$		0			0
$283$	−423.259	−	96.6060i	−1.49561	−	0.341364i	−0.605037	−	0.796197i	$-0.706842\pi$
$283$	−423.259	−	96.6060i	−1.49561	−	0.341364i	−0.890577	+	0.454833i	$0.849699\pi$
$284$	139.183	+	174.530i	0.490081	+	0.614542i
$285$		0			0
$286$	227.127	+	995.109i	0.794150	+	3.47940i
$287$	−1.33948	+	0.841651i	−0.00466718	+	0.00293258i
$288$		0			0
$289$			286.658i			0.991895i
$290$	−167.189	−	547.911i	−0.576513	−	1.88935i
$291$		0			0
$292$	−68.8038	−	610.650i	−0.235629	−	2.09127i
$293$	−103.800	−	165.197i	−0.354268	−	0.563814i	0.621284	−	0.783586i	$-0.286611\pi$
$293$	−103.800	−	165.197i	−0.354268	−	0.563814i	−0.975551	+	0.219772i	$0.929469\pi$
$294$		0			0
$295$	−5.14876	−	4.10600i	−0.0174534	−	0.0139186i
$296$	−19.4207	+	15.4875i	−0.0656106	+	0.0523227i
$297$		0			0
$298$	227.773	+	650.937i	0.764337	+	2.18435i
$299$	51.6388	−	107.229i	0.172705	−	0.358625i
$300$		0			0
$301$	−30.9179	+	88.3583i	−0.102717	+	0.293549i
$302$	175.812	+	175.812i	0.582158	+	0.582158i
$303$		0			0
$304$	−348.714	−	39.2906i	−1.14708	−	0.129245i
$305$	−14.8376	+	131.687i	−0.0486477	+	0.431760i
$306$		0			0
$307$	257.664	−	257.664i	0.839297	−	0.839297i	−0.149470	−	0.988766i	$-0.547757\pi$
$307$	257.664	−	257.664i	0.839297	−	0.839297i	0.988766	+	0.149470i	$0.0477567\pi$
$308$	817.859	+	286.181i	2.65538	+	0.929159i
$309$		0			0
$310$	−921.412	−	443.729i	−2.97230	−	1.43138i
$311$	121.145	−	42.3903i	0.389532	−	0.136303i	−0.128405	−	0.991722i	$-0.540986\pi$
$311$	121.145	−	42.3903i	0.389532	−	0.136303i	0.517937	+	0.855419i	$0.326700\pi$
$312$		0			0
$313$	−32.1822	−	40.3552i	−0.102819	−	0.128930i	0.727760	−	0.685832i	$-0.240561\pi$
$313$	−32.1822	−	40.3552i	−0.102819	−	0.128930i	−0.830579	+	0.556902i	$0.811990\pi$
$314$	−161.100	+	202.013i	−0.513056	+	0.643352i
$315$		0			0
$316$	−197.384	+	124.025i	−0.624634	+	0.392484i
$317$	−9.36162	+	1.05480i	−0.0295319	+	0.00332745i	−0.126718	−	0.991939i	$-0.540444\pi$
$317$	−9.36162	+	1.05480i	−0.0295319	+	0.00332745i	0.0971862	+	0.995266i	$0.469016\pi$
$318$		0			0
$319$	−275.001	−	479.672i	−0.862072	−	1.50367i
$320$	−345.434			−1.07948
$321$		0			0
$322$	−80.4084	−	127.969i	−0.249715	−	0.397420i
$323$	31.1664	−	7.11352i	0.0964903	−	0.0220233i
$324$		0			0
$325$	−88.4178	+	70.5108i	−0.272055	+	0.216956i
$326$	−172.823	+	757.188i	−0.530133	+	2.32266i
$327$		0			0
$328$	−1.72081	+	3.57331i	−0.00524639	+	0.0108942i
$329$	9.26704	−	14.7484i	0.0281673	−	0.0448280i
$330$		0			0
$331$	258.506	+	258.506i	0.780985	+	0.780985i	0.979997	−	0.199012i	$-0.0637733\pi$
$331$	258.506	+	258.506i	0.780985	+	0.780985i	−0.199012	+	0.979997i	$0.563773\pi$
$332$	−80.7343	−	167.646i	−0.243176	−	0.504959i
$333$		0			0
$334$	−20.8971	+	185.467i	−0.0625661	+	0.555290i
$335$	−25.8477	+	12.4476i	−0.0771573	+	0.0371570i
$336$		0			0
$337$	293.050	+	102.543i	0.869584	+	0.304281i	0.727943	−	0.685637i	$-0.240476\pi$
$337$	293.050	+	102.543i	0.869584	+	0.304281i	0.141641	+	0.989918i	$0.454762\pi$
$338$	−201.541	−	126.637i	−0.596276	−	0.374665i
$339$		0			0
$340$	−66.2643	+	23.1869i	−0.194895	+	0.0681967i
$341$	−962.344	−	219.649i	−2.82212	−	0.644131i
$342$		0			0
$343$	232.748	−	291.856i	0.678564	−	0.850893i
$344$	52.2235	+	228.806i	0.151813	+	0.665135i
$345$		0			0
$346$	−936.501	+	105.518i	−2.70665	+	0.304966i
$347$			110.260i			0.317751i	0.987299	+	0.158876i	$0.0507869\pi$
$347$			110.260i			0.317751i	−0.987299	+	0.158876i	$0.949213\pi$
$348$		0			0
$349$	−132.174			−0.378722			−0.189361	−	0.981908i	$-0.560642\pi$
$349$	−132.174			−0.378722			−0.189361	+	0.981908i	$0.560642\pi$
$350$	16.0793	+	142.708i	0.0459409	+	0.407737i
$351$		0			0
$352$	34.5538	−	7.88669i	0.0981643	−	0.0224054i
$353$	50.9851	+	40.6592i	0.144434	+	0.115182i	0.693041	−	0.720898i	$-0.256270\pi$
$353$	50.9851	+	40.6592i	0.144434	+	0.115182i	−0.548608	+	0.836080i	$0.684842\pi$
$354$		0			0
$355$	−35.0192	+	153.429i	−0.0986457	+	0.432195i
$356$	193.443	+	552.829i	0.543380	+	1.55289i
$357$		0			0
$358$	363.252	−	578.112i	1.01467	−	1.61484i
$359$	109.932	−	314.168i	0.306218	−	0.875120i	−0.683227	−	0.730206i	$-0.739424\pi$
$359$	109.932	−	314.168i	0.306218	−	0.875120i	0.989444	−	0.144914i	$-0.0462904\pi$
$360$		0			0
$361$	32.6651	+	67.8297i	0.0904850	+	0.187894i
$362$	232.535	+	26.2004i	0.642361	+	0.0723767i
$363$		0			0
$364$	−631.051	+	303.898i	−1.73366	+	0.834885i
$365$	306.335	−	306.335i	0.839274	−	0.839274i
$366$		0			0
$367$	156.576	+	98.3835i	0.426639	+	0.268075i	0.728190	−	0.685375i	$-0.240362\pi$
$367$	156.576	+	98.3835i	0.426639	+	0.268075i	−0.301552	+	0.953450i	$0.597505\pi$
$368$	−116.891	−	56.2919i	−0.317640	−	0.152967i
$369$		0			0
$370$	−33.8670	−	7.72992i	−0.0915324	−	0.0208917i
$371$	176.736	+	221.619i	0.476376	+	0.597357i
$372$		0			0
$373$	−132.214	−	579.268i	−0.354462	−	1.55300i	−0.766751	−	0.641945i	$-0.778128\pi$
$373$	−132.214	−	579.268i	−0.354462	−	1.55300i	0.412289	−	0.911053i	$-0.364729\pi$
$374$	−85.8253	+	53.9276i	−0.229480	+	0.144192i
$375$		0			0
$376$		−	43.6686i		−	0.116140i
$377$	431.359	+	116.987i	1.14419	+	0.310310i
$378$		0			0
$379$	50.6720	+	449.726i	0.133699	+	1.18661i	0.864002	+	0.503489i	$0.167951\pi$
$379$	50.6720	+	449.726i	0.133699	+	1.18661i	−0.730302	+	0.683124i	$0.760621\pi$
$380$	−509.749	−	811.260i	−1.34144	−	2.13490i
$381$		0			0
$382$	180.638	+	144.054i	0.472875	+	0.377105i
$383$	546.226	−	435.601i	1.42618	−	1.13734i	0.457443	−	0.889239i	$-0.348765\pi$
$383$	546.226	−	435.601i	1.42618	−	1.13734i	0.968734	−	0.248100i	$-0.0798062\pi$
$384$		0			0
$385$	201.753	+	576.577i	0.524034	+	1.49760i
$386$	−387.903	+	805.488i	−1.00493	+	2.08676i
$387$		0			0
$388$	−329.833	+	942.609i	−0.850085	+	2.42940i
$389$	−290.889	−	290.889i	−0.747786	−	0.747786i	0.226277	−	0.974063i	$-0.427345\pi$
$389$	−290.889	−	290.889i	−0.747786	−	0.747786i	−0.974063	+	0.226277i	$0.927345\pi$
$390$		0			0
$391$	11.7446	+	1.32330i	0.0300374	+	0.00338440i
$392$	27.2918	−	242.221i	0.0696218	−	0.617911i
$393$		0			0
$394$	133.360	−	133.360i	0.338477	−	0.338477i
$395$	−155.120	−	54.2790i	−0.392710	−	0.137415i
$396$		0			0
$397$	−331.592	−	159.686i	−0.835245	−	0.402233i	−0.0331653	−	0.999450i	$-0.510559\pi$
$397$	−331.592	−	159.686i	−0.835245	−	0.402233i	−0.802080	+	0.597217i	$0.796273\pi$
$398$	206.288	−	72.1831i	0.518310	−	0.181365i
$399$		0			0
$400$	76.8646	+	96.3851i	0.192161	+	0.240963i
$401$	337.498	−	423.209i	0.841641	−	1.05538i	−0.156068	−	0.987746i	$-0.549882\pi$
$401$	337.498	−	423.209i	0.841641	−	1.05538i	0.997710	−	0.0676387i	$-0.0215465\pi$
$402$		0			0
$403$	675.608	−	424.513i	1.67645	−	1.05338i
$404$	−1111.68	+	125.256i	−2.75168	+	0.310040i
$405$		0			0
$406$	417.220	−	384.774i	1.02764	−	0.947719i
$407$	−33.5288			−0.0823803
$408$		0			0
$409$	70.7312	+	112.568i	0.172937	+	0.275227i	0.921935	−	0.387345i	$-0.126608\pi$
$409$	70.7312	+	112.568i	0.172937	+	0.275227i	−0.748998	+	0.662572i	$0.769465\pi$
$410$	−5.40736	+	1.23419i	−0.0131887	+	0.00301023i
$411$		0			0
$412$	606.655	−	483.791i	1.47246	−	1.17425i
$413$	1.45188	−	6.36109i	0.00351544	−	0.0154022i
$414$		0			0
$415$	56.9164	−	118.188i	0.137148	−	0.284791i
$416$	−15.2425	+	24.2583i	−0.0366407	+	0.0583133i
$417$		0			0
$418$	−978.173	−	978.173i	−2.34013	−	2.34013i
$419$	236.230	+	490.537i	0.563795	+	1.17073i	0.966800	+	0.255535i	$0.0822517\pi$
$419$	236.230	+	490.537i	0.563795	+	1.17073i	−0.403004	+	0.915198i	$0.632034\pi$
$420$		0			0
$421$	12.9846	−	115.241i	0.0308422	−	0.273732i	−0.968821	−	0.247764i	$-0.920304\pi$
$421$	12.9846	−	115.241i	0.0308422	−	0.273732i	0.999663	−	0.0259687i	$-0.00826704\pi$
$422$	147.738	−	71.1469i	0.350090	−	0.168594i
$423$		0			0
$424$	670.779	+	234.716i	1.58203	+	0.553575i
$425$	−9.50920	−	5.97503i	−0.0223746	−	0.0140589i
$426$		0			0
$427$	−123.928	+	43.3643i	−0.290230	+	0.101556i
$428$	1093.33	+	249.546i	2.55452	+	0.583052i
$429$		0			0
$430$	−204.634	+	256.602i	−0.475892	+	0.596750i
$431$	−99.9880	−	438.076i	−0.231991	−	1.01642i	−0.947986	−	0.318312i	$-0.896884\pi$
$431$	−99.9880	−	438.076i	−0.231991	−	1.01642i	0.715995	−	0.698105i	$-0.245973\pi$
$432$		0			0
$433$	−23.7882	+	2.68029i	−0.0549382	+	0.00619004i	−0.139391	−	0.990237i	$-0.544514\pi$
$433$	−23.7882	+	2.68029i	−0.0549382	+	0.00619004i	0.0844526	+	0.996427i	$0.473086\pi$
$434$		−	1013.24i		−	2.33466i
$435$		0			0
$436$	997.980			2.28895
$437$	18.0599	+	160.286i	0.0413270	+	0.366787i
$438$		0			0
$439$	467.042	−	106.599i	1.06388	−	0.242823i	0.345458	−	0.938434i	$-0.387724\pi$
$439$	467.042	−	106.599i	1.06388	−	0.242823i	0.718418	+	0.695612i	$0.244866\pi$
$440$	1197.34	+	954.850i	2.72124	+	2.17011i
$441$		0			0
$442$	18.2322	−	79.8806i	0.0412494	−	0.180725i
$443$	−122.406	−	349.816i	−0.276311	−	0.789653i	−0.995493	−	0.0948309i	$-0.969769\pi$
$443$	−122.406	−	349.816i	−0.276311	−	0.789653i	0.719182	−	0.694822i	$-0.244517\pi$
$444$		0			0
$445$	−219.680	+	349.618i	−0.493662	+	0.785659i
$446$	−333.571	+	953.292i	−0.747917	+	2.13742i
$447$		0			0
$448$	−148.494	−	308.350i	−0.331459	−	0.688282i
$449$	−320.265	−	36.0852i	−0.713285	−	0.0803679i	−0.252138	−	0.967691i	$-0.581134\pi$
$449$	−320.265	−	36.0852i	−0.713285	−	0.0803679i	−0.461148	+	0.887323i	$0.652562\pi$
$450$		0			0
$451$	−4.82321	+	2.32274i	−0.0106945	+	0.00515019i
$452$	1195.70	−	1195.70i	2.64536	−	2.64536i
$453$		0			0
$454$	162.382	+	102.031i	0.357669	+	0.224738i
$455$	−444.881	−	214.244i	−0.977761	−	0.470865i
$456$		0			0
$457$	−259.574	−	59.2460i	−0.567995	−	0.129641i	−0.0711271	−	0.997467i	$-0.522660\pi$
$457$	−259.574	−	59.2460i	−0.567995	−	0.129641i	−0.496868	+	0.867826i	$0.665517\pi$
$458$	−567.548	−	711.682i	−1.23919	−	1.55389i
$459$		0			0
$460$	−78.8231	−	345.347i	−0.171355	−	0.750754i
$461$	476.625	−	299.484i	1.03389	−	0.649639i	0.0955801	−	0.995422i	$-0.469529\pi$
$461$	476.625	−	299.484i	1.03389	−	0.649639i	0.938315	+	0.345783i	$0.112387\pi$
$462$		0			0
$463$		−	475.767i		−	1.02757i	−0.857918	−	0.513787i	$-0.828242\pi$
$463$		−	475.767i		−	1.02757i	0.857918	−	0.513787i	$-0.171758\pi$
$464$	127.528	−	470.229i	0.274846	−	1.01342i
$465$		0			0
$466$	93.7323	+	831.897i	0.201142	+	1.78519i
$467$	446.325	+	710.323i	0.955729	+	1.52103i	0.850095	+	0.526629i	$0.176544\pi$
$467$	446.325	+	710.323i	0.955729	+	1.52103i	0.105633	+	0.994405i	$0.466313\pi$
$468$		0			0
$469$	−22.2226	−	17.7219i	−0.0473829	−	0.0377866i
$470$	47.7457	−	38.0760i	0.101587	−	0.0810127i
$471$		0			0
$472$	−5.40265	−	15.4399i	−0.0114463	−	0.0327116i
$473$	−137.447	+	285.411i	−0.290585	+	0.603406i
$474$		0			0
$475$	50.6221	−	144.670i	0.106573	−	0.304568i
$476$	−49.1831	−	49.1831i	−0.103326	−	0.103326i
$477$		0			0
$478$	961.011	+	108.280i	2.01048	+	0.226527i
$479$	−67.6166	+	600.114i	−0.141162	+	1.25285i	0.700818	+	0.713340i	$0.252818\pi$
$479$	−67.6166	+	600.114i	−0.141162	+	1.25285i	−0.841981	+	0.539508i	$0.818610\pi$
$480$		0			0
$481$	19.1645	−	19.1645i	0.0398431	−	0.0398431i
$482$	−610.827	−	213.738i	−1.26728	−	0.443439i
$483$		0			0
$484$	1762.44	+	848.746i	3.64140	+	1.75361i
$485$	−664.524	+	232.527i	−1.37015	+	0.479437i
$486$		0			0
$487$	−154.254	−	193.429i	−0.316744	−	0.397185i	0.597817	−	0.801633i	$-0.296035\pi$
$487$	−154.254	−	193.429i	−0.316744	−	0.397185i	−0.914561	+	0.404448i	$0.867464\pi$
$488$	−205.233	+	257.354i	−0.420559	+	0.527365i
$489$		0			0
$490$	288.633	−	181.360i	0.589046	−	0.370122i
$491$	−713.303	+	80.3699i	−1.45276	+	0.163686i	−0.802783	−	0.596272i	$-0.796648\pi$
$491$	−713.303	+	80.3699i	−1.45276	+	0.163686i	−0.649972	+	0.759958i	$0.725220\pi$
$492$		0			0
$493$	3.18246	+	44.2697i	0.00645530	+	0.0897966i
$494$	1118.22			2.26360
$495$		0			0
$496$	−462.766	−	736.487i	−0.932995	−	1.48485i
$497$	−152.012	+	34.6957i	−0.305859	+	0.0698103i
$498$		0			0
$499$	−321.823	+	256.645i	−0.644936	+	0.514319i	−0.890454	−	0.455073i	$-0.849613\pi$
$499$	−321.823	+	256.645i	−0.644936	+	0.514319i	0.245519	+	0.969392i	$0.421042\pi$
$500$	180.279	−	789.854i	0.360558	−	1.57971i
$501$		0			0
$502$	−379.744	+	788.547i	−0.756462	+	1.57081i
$503$	242.724	−	386.293i	0.482552	−	0.767977i	−0.513372	−	0.858166i	$-0.671604\pi$
$503$	242.724	−	386.293i	0.482552	−	0.767977i	0.995925	+	0.0901884i	$0.0287469\pi$
$504$		0			0
$505$	−557.677	−	557.677i	−1.10431	−	1.10431i
$506$	−221.906	−	460.792i	−0.438549	−	0.910656i
$507$		0			0
$508$	−6.75715	+	59.9714i	−0.0133015	+	0.118054i
$509$	−99.8145	+	48.0681i	−0.196099	+	0.0944364i	−0.529356	−	0.848400i	$-0.677567\pi$
$509$	−99.8145	+	48.0681i	−0.196099	+	0.0944364i	0.333257	+	0.942836i	$0.391852\pi$
$510$		0			0
$511$	405.134	+	141.763i	0.792827	+	0.277422i
$512$	−777.298	−	488.409i	−1.51816	−	0.953923i
$513$		0			0
$514$	381.383	−	133.452i	0.741991	−	0.259634i
$515$	533.311	+	121.725i	1.03555	+	0.236359i
$516$		0			0
$517$	36.7506	−	46.0838i	0.0710843	−	0.0891369i
$518$	−7.65852	−	33.5542i	−0.0147848	−	0.0647764i
$519$		0			0
$520$	−1230.16	+	138.606i	−2.36569	+	0.266549i
$521$			119.063i			0.228527i	0.993450	+	0.114263i	$0.0364508\pi$
$521$			119.063i			0.228527i	−0.993450	+	0.114263i	$0.963549\pi$
$522$		0			0
$523$	−995.924			−1.90425			−0.952126	−	0.305705i	$-0.901108\pi$
$523$	−995.924			−1.90425			−0.952126	+	0.305705i	$0.901108\pi$
$524$	17.3993	+	154.423i	0.0332049	+	0.294701i
$525$		0			0
$526$	507.918	−	115.929i	0.965623	−	0.220397i
$527$	61.9500	+	49.4035i	0.117552	+	0.0937448i
$528$		0			0
$529$	104.444	−	457.597i	0.197436	−	0.865023i
$530$	328.242	+	938.061i	0.619324	+	1.76993i
$531$		0			0
$532$	505.040	−	803.766i	0.949323	−	1.51084i
$533$	1.42923	−	4.08451i	0.00268148	−	0.00766324i
$534$		0			0
$535$	343.031	+	712.311i	0.641179	+	1.33142i
$536$	−70.8123	−	7.97863i	−0.132112	−	0.0148855i
$537$		0			0
$538$	−1347.03	+	648.695i	−2.50377	+	1.20575i
$539$	232.649	−	232.649i	0.431632	−	0.431632i
$540$		0			0
$541$	−416.895	−	261.953i	−0.770601	−	0.484201i	0.0884564	−	0.996080i	$-0.471807\pi$
$541$	−416.895	−	261.953i	−0.770601	−	0.484201i	−0.859057	+	0.511879i	$0.828949\pi$
$542$	855.021	+	411.756i	1.57753	+	0.759698i
$543$		0			0
$544$	−2.77375	−	0.633090i	−0.00509880	−	0.00116377i
$545$	438.663	+	550.066i	0.804886	+	1.00929i
$546$		0			0
$547$	145.992	+	639.634i	0.266896	+	1.16935i	0.913602	+	0.406609i	$0.133289\pi$
$547$	145.992	+	639.634i	0.266896	+	1.16935i	−0.646706	+	0.762739i	$0.723854\pi$
$548$	−448.591	+	281.869i	−0.818597	+	0.514359i
$549$		0			0
$550$			485.981i			0.883602i
$551$	−579.364	+	176.786i	−1.05148	+	0.320846i
$552$		0			0
$553$	−18.2306	−	161.801i	−0.0329667	−	0.292587i
$554$	826.069	+	1314.68i	1.49110	+	2.37307i
$555$		0			0
$556$	−1139.93	−	909.065i	−2.05024	−	1.63501i
$557$	456.764	−	364.257i	0.820043	−	0.653962i	−0.120849	−	0.992671i	$-0.538562\pi$
$557$	456.764	−	364.257i	0.820043	−	0.653962i	0.940891	+	0.338709i	$0.109990\pi$
$558$		0			0
$559$	−84.5740	−	241.699i	−0.151295	−	0.432377i
$560$	−233.549	+	484.970i	−0.417052	+	0.866017i
$561$		0			0
$562$	185.969	−	531.470i	0.330906	−	0.945676i
$563$	−240.446	−	240.446i	−0.427080	−	0.427080i	0.460552	−	0.887633i	$-0.347651\pi$
$563$	−240.446	−	240.446i	−0.427080	−	0.427080i	−0.887633	+	0.460552i	$0.847651\pi$
$564$		0			0
$565$	1184.62	+	133.475i	2.09667	+	0.236238i
$566$	168.850	−	1498.59i	0.298322	−	2.64768i
$567$		0			0
$568$	−276.412	+	276.412i	−0.486641	+	0.486641i
$569$	70.7181	+	24.7453i	0.124285	+	0.0434891i	0.391705	−	0.920091i	$-0.371885\pi$
$569$	70.7181	+	24.7453i	0.124285	+	0.0434891i	−0.267420	+	0.963580i	$0.586171\pi$
$570$		0			0
$571$	−396.867	−	191.121i	−0.695038	−	0.334713i	0.0527893	−	0.998606i	$-0.483189\pi$
$571$	−396.867	−	191.121i	−0.695038	−	0.334713i	−0.747828	+	0.663893i	$0.768903\pi$
$572$	−2237.20	+	782.831i	−3.91119	+	1.36859i
$573$		0			0
$574$	−3.42619	−	4.29631i	−0.00596897	−	0.00748486i
$575$	35.3308	−	44.3034i	0.0614448	−	0.0770494i
$576$		0			0
$577$	−711.295	+	446.936i	−1.23275	+	0.774586i	−0.981150	−	0.193246i	$-0.938099\pi$
$577$	−711.295	+	446.936i	−1.23275	+	0.774586i	−0.251597	+	0.967832i	$0.580956\pi$
$578$	−989.491	+	111.489i	−1.71192	+	0.192887i
$579$		0			0
$580$	1220.86	−	528.250i	2.10493	−	0.910776i
$581$	129.967			0.223696
$582$		0			0
$583$	510.346	+	812.210i	0.875378	+	1.39316i
$584$	1049.11	−	239.452i	1.79642	−	0.410020i
$585$		0			0
$586$	529.861	−	422.550i	0.904200	−	0.721075i
$587$	−260.514	+	1141.39i	−0.443806	+	1.94444i	−0.149292	+	0.988793i	$0.547699\pi$
$587$	−260.514	+	1141.39i	−0.443806	+	1.94444i	−0.294514	+	0.955647i	$0.595158\pi$
$588$		0			0
$589$	−469.201	+	974.306i	−0.796606	+	1.65417i
$590$	12.1707	−	19.3695i	0.0206283	−	0.0328297i
$591$		0			0
$592$	−20.8914	−	20.8914i	−0.0352896	−	0.0352896i
$593$	158.384	+	328.888i	0.267089	+	0.554617i	0.990776	−	0.135512i	$-0.0432680\pi$
$593$	158.384	+	328.888i	0.267089	+	0.554617i	−0.723686	+	0.690129i	$0.757554\pi$
$594$		0			0
$595$	5.49023	−	48.7271i	0.00922727	−	0.0818943i
$596$	−1442.84	+	694.836i	−2.42088	+	1.16583i
$597$		0			0
$598$	390.219	+	136.544i	0.652540	+	0.228334i
$599$	−221.090	−	138.920i	−0.369098	−	0.231920i	0.334692	−	0.942328i	$-0.391368\pi$
$599$	−221.090	−	138.920i	−0.369098	−	0.231920i	−0.703790	+	0.710408i	$0.748511\pi$
$600$		0			0
$601$	−942.786	+	329.895i	−1.56869	+	0.548910i	−0.968083	−	0.250631i	$-0.919362\pi$
$601$	−942.786	+	329.895i	−1.56869	+	0.548910i	−0.600612	+	0.799541i	$0.705076\pi$
$602$	−317.022	−	72.3582i	−0.526615	−	0.120196i
$603$		0			0
$604$	−359.982	+	451.403i	−0.595997	+	0.747356i
$605$	306.870	+	1344.49i	0.507223	+	2.22229i
$606$		0			0
$607$	784.036	−	88.3397i	1.29166	−	0.145535i	0.560735	−	0.827995i	$-0.310519\pi$
$607$	784.036	−	88.3397i	1.29166	−	0.145535i	0.730922	+	0.682460i	$0.239090\pi$
$608$		−	38.8286i		−	0.0638628i
$609$		0			0
$610$	−460.331			−0.754640
$611$	5.33470	+	47.3468i	0.00873110	+	0.0774907i
$612$		0			0
$613$	−541.445	+	123.581i	−0.883270	+	0.201601i	−0.640016	−	0.768362i	$-0.721072\pi$
$613$	−541.445	+	123.581i	−0.883270	+	0.201601i	−0.243255	+	0.969962i	$0.578215\pi$
$614$	989.623	+	789.198i	1.61176	+	1.28534i
$615$		0			0
$616$	−337.634	+	1479.27i	−0.548107	+	2.40141i
$617$	−310.899	−	888.498i	−0.503888	−	1.44003i	−0.862267	−	0.506454i	$-0.830956\pi$
$617$	−310.899	−	888.498i	−0.503888	−	1.44003i	0.358379	−	0.933576i	$-0.383330\pi$
$618$		0			0
$619$	102.702	−	163.450i	0.165916	−	0.264055i	−0.753409	−	0.657552i	$-0.771592\pi$
$619$	102.702	−	163.450i	0.165916	−	0.264055i	0.919326	+	0.393497i	$0.128735\pi$
$620$	784.358	−	2241.57i	1.26509	−	3.61543i
$621$		0			0
$622$	193.440	+	401.683i	0.310997	+	0.645792i
$623$	−406.520	−	45.8038i	−0.652520	−	0.0735214i
$624$		0			0
$625$	679.874	−	327.410i	1.08780	−	0.523856i
$626$	126.782	−	126.782i	0.202528	−	0.202528i
$627$		0			0
$628$	−508.038	−	319.222i	−0.808978	−	0.508315i
$629$	2.42492	+	1.16778i	0.00385521	+	0.00185657i
$630$		0			0
$631$	1062.78	+	242.573i	1.68428	+	0.384427i	0.954256	−	0.298991i	$-0.0966501\pi$
$631$	1062.78	+	242.573i	1.68428	+	0.384427i	0.730028	+	0.683418i	$0.239507\pi$
$632$	−254.516	−	319.153i	−0.402716	−	0.504990i
$633$		0			0
$634$	−7.28197	−	31.9044i	−0.0114858	−	0.0503224i
$635$	−36.0251	+	22.6360i	−0.0567324	+	0.0356473i
$636$		0			0
$637$			265.957i			0.417515i
$638$	1548.79	−	1135.81i	2.42757	−	1.78027i
$639$		0			0
$640$	−139.083	−	1234.40i	−0.217317	−	1.92874i
$641$	194.352	+	309.310i	0.303202	+	0.482543i	0.963223	−	0.268704i	$-0.0865954\pi$
$641$	194.352	+	309.310i	0.303202	+	0.482543i	−0.660021	+	0.751247i	$0.729453\pi$
$642$		0			0
$643$	340.752	+	271.740i	0.529940	+	0.422613i	0.851561	−	0.524255i	$-0.175656\pi$
$643$	340.752	+	271.740i	0.529940	+	0.422613i	−0.321621	+	0.946869i	$0.604228\pi$
$644$	274.388	−	218.817i	0.426069	−	0.339778i
$645$		0			0
$646$	36.6760	+	104.814i	0.0567740	+	0.162251i
$647$	−278.913	+	579.169i	−0.431087	+	0.895161i	0.566388	+	0.824139i	$0.308340\pi$
$647$	−278.913	+	579.169i	−0.431087	+	0.895161i	−0.997475	+	0.0710220i	$0.977374\pi$
$648$		0			0
$649$	7.29243	−	20.8406i	0.0112364	−	0.0321118i
$650$	−277.779	−	277.779i	−0.427352	−	0.427352i
$651$		0			0
$652$	−1792.18	−	201.930i	−2.74874	−	0.309708i
$653$	−32.7552	+	290.711i	−0.0501612	+	0.445193i	0.943379	+	0.331716i	$0.107627\pi$
$653$	−32.7552	+	290.711i	−0.0501612	+	0.445193i	−0.993541	+	0.113477i	$0.963801\pi$
$654$		0			0
$655$	−77.4671	+	77.4671i	−0.118270	+	0.118270i
$656$	−4.45256	−	1.55802i	−0.00678744	−	0.00237503i
$657$		0			0
$658$	54.5131	+	26.2521i	0.0828466	+	0.0398968i
$659$	−65.2168	+	22.8203i	−0.0989632	+	0.0346287i	−0.379307	−	0.925271i	$-0.623837\pi$
$659$	−65.2168	+	22.8203i	−0.0989632	+	0.0346287i	0.280343	+	0.959900i	$0.409552\pi$
$660$		0			0
$661$	515.047	+	645.849i	0.779194	+	0.977078i	0.999998	+	0.00176027i	$0.000560312\pi$
$661$	515.047	+	645.849i	0.779194	+	0.977078i	−0.220804	+	0.975318i	$0.570868\pi$
$662$	−791.777	+	992.857i	−1.19604	+	1.49978i
$663$		0			0
$664$	275.894	−	173.356i	0.415503	−	0.261078i
$665$	665.009	−	74.9285i	1.00001	−	0.112675i
$666$		0			0
$667$	−223.765	−	9.05292i	−0.335480	−	0.0135726i
$668$	−433.406			−0.648811
$669$		0			0
$670$	−53.0198	−	84.3805i	−0.0791340	−	0.125941i
$671$	−433.168	+	98.8677i	−0.645555	+	0.147344i
$672$		0			0
$673$	716.861	−	571.677i	1.06517	−	0.849446i	0.0761326	−	0.997098i	$-0.475743\pi$
$673$	716.861	−	571.677i	1.06517	−	0.849446i	0.989039	+	0.147651i	$0.0471713\pi$
$674$	−239.984	+	1051.44i	−0.356059	+	1.56000i
$675$		0			0
$676$	239.820	−	497.990i	0.354763	−	0.736672i
$677$	214.274	−	341.016i	0.316506	−	0.503716i	−0.650146	−	0.759809i	$-0.725292\pi$
$677$	214.274	−	341.016i	0.316506	−	0.503716i	0.966652	+	0.256093i	$0.0824353\pi$
$678$		0			0
$679$	−493.227	−	493.227i	−0.726402	−	0.726402i
$680$	−53.3396	−	110.761i	−0.0784406	−	0.162884i
$681$		0			0
$682$	383.907	−	3407.27i	0.562913	−	4.99599i
$683$	289.662	−	139.494i	0.424102	−	0.204237i	−0.209644	−	0.977778i	$-0.567231\pi$
$683$	289.662	−	139.494i	0.424102	−	0.204237i	0.633746	+	0.773541i	$0.281516\pi$
$684$		0			0
$685$	−352.539	−	123.359i	−0.514655	−	0.180086i
$686$	1097.96	+	689.893i	1.60052	+	1.00567i
$687$		0			0
$688$	−263.478	+	92.1950i	−0.382963	+	0.134004i
$689$	−755.952	−	172.541i	−1.09717	−	0.250422i
$690$		0			0
$691$	−601.397	+	754.128i	−0.870328	+	1.09136i	0.124742	+	0.992189i	$0.460190\pi$
$691$	−601.397	+	754.128i	−0.870328	+	1.09136i	−0.995071	+	0.0991680i	$0.968382\pi$
$692$	−486.976	−	2133.58i	−0.703722	−	3.08321i
$693$		0			0
$694$	−380.597	+	42.8829i	−0.548410	+	0.0617910i
$695$		−	1027.89i		−	1.47897i
$696$		0			0
$697$	0.429731			0.000616544
$698$	−51.4060	−	456.241i	−0.0736476	−	0.653640i
$699$		0			0
$700$	−325.124	+	74.2074i	−0.464462	+	0.106011i
$701$	−236.940	−	188.954i	−0.338004	−	0.269549i	0.439747	−	0.898122i	$-0.355068\pi$
$701$	−236.940	−	188.954i	−0.338004	−	0.269549i	−0.777751	+	0.628573i	$0.783639\pi$
$702$		0			0
$703$	−8.17366	+	35.8111i	−0.0116268	+	0.0509405i
$704$	−382.514	−	1093.16i	−0.543344	−	1.55279i
$705$		0			0
$706$	−120.519	+	191.805i	−0.170707	+	0.271678i
$707$	258.076	−	737.540i	0.365030	−	1.04320i
$708$		0			0
$709$	−412.716	−	857.013i	−0.582109	−	1.20876i	−0.959237	−	0.282601i	$-0.908803\pi$
$709$	−412.716	−	857.013i	−0.582109	−	1.20876i	0.377128	−	0.926161i	$-0.376912\pi$
$710$	−543.231	−	61.2074i	−0.765114	−	0.0862076i
$711$		0			0
$712$	−924.055	+	445.001i	−1.29783	+	0.625002i
$713$	−282.706	+	282.706i	−0.396502	+	0.396502i
$714$		0			0
$715$	−1414.84	−	889.005i	−1.97880	−	1.24336i
$716$	1428.46	+	687.911i	1.99506	+	0.960770i
$717$		0			0
$718$	1127.21	+	257.278i	1.56993	+	0.358326i
$719$	79.2834	+	99.4183i	0.110269	+	0.138273i	0.833903	−	0.551911i	$-0.186101\pi$
$719$	79.2834	+	99.4183i	0.110269	+	0.138273i	−0.723634	+	0.690184i	$0.757530\pi$
$720$		0			0
$721$	120.600	+	528.384i	0.167268	+	0.732849i
$722$	−221.432	+	139.135i	−0.306692	+	0.192708i
$723$		0			0
$724$			543.396i			0.750546i
$725$	187.837	+	100.005i	0.259086	+	0.137938i
$726$		0			0
$727$	−64.0613	−	568.559i	−0.0881173	−	0.782062i	−0.957600	−	0.288100i	$-0.906977\pi$
$727$	−64.0613	−	568.559i	−0.0881173	−	0.782062i	0.869483	−	0.493963i	$-0.164452\pi$
$728$	−652.541	−	1038.51i	−0.896348	−	1.42653i
$729$		0			0
$730$	1176.56	+	938.272i	1.61172	+	1.28530i
$731$	19.8813	−	15.8548i	0.0271974	−	0.0216892i
$732$		0			0
$733$	22.0048	+	62.8862i	0.0300202	+	0.0857928i	0.957918	−	0.287041i	$-0.0926717\pi$
$733$	22.0048	+	62.8862i	0.0300202	+	0.0857928i	−0.927898	+	0.372834i	$0.878386\pi$
$734$	−278.706	+	578.738i	−0.379708	+	0.788472i
$735$		0			0
$736$	4.74130	−	13.5499i	0.00644198	−	0.0184101i
$737$	−68.0140	−	68.0140i	−0.0922850	−	0.0922850i
$738$		0			0
$739$	−995.614	−	112.179i	−1.34724	−	0.151798i	−0.591309	−	0.806445i	$-0.701389\pi$
$739$	−995.614	−	112.179i	−1.34724	−	0.151798i	−0.755935	+	0.654647i	$0.772817\pi$
$740$	9.03178	−	80.1593i	0.0122051	−	0.108323i
$741$		0			0
$742$	−696.254	+	696.254i	−0.938347	+	0.938347i
$743$	1074.63	+	376.031i	1.44634	+	0.506098i	0.935423	−	0.353530i	$-0.115019\pi$
$743$	1074.63	+	376.031i	1.44634	+	0.506098i	0.510921	+	0.859628i	$0.329304\pi$
$744$		0			0
$745$	−1017.18	−	489.849i	−1.36534	−	0.657515i
$746$	1948.11	−	681.673i	2.61141	−	0.913771i
$747$		0			0
$748$	−146.755	−	184.024i	−0.196196	−	0.246022i
$749$	−488.381	+	612.410i	−0.652044	+	0.817637i
$750$		0			0
$751$	297.047	−	186.647i	0.395535	−	0.248531i	−0.319549	−	0.947570i	$-0.603531\pi$
$751$	297.047	−	186.647i	0.395535	−	0.248531i	0.715084	+	0.699039i	$0.246389\pi$
$752$	51.6132	−	5.81542i	0.0686346	−	0.00773327i
$753$		0			0
$754$	−236.050	+	1534.47i	−0.313064	+	2.03511i
$755$	−407.034			−0.539118
$756$		0			0
$757$	−4.92720	−	7.84159i	−0.00650884	−	0.0103588i	0.843454	−	0.537202i	$-0.180519\pi$
$757$	−4.92720	−	7.84159i	−0.00650884	−	0.0103588i	−0.849963	+	0.526843i	$0.823376\pi$
$758$	−1532.67	+	349.822i	−2.02199	+	0.461506i
$759$		0			0
$760$	1311.74	−	1046.07i	1.72597	−	1.37641i
$761$	298.503	−	1307.83i	0.392251	−	1.71856i	−0.264438	−	0.964403i	$-0.585186\pi$
$761$	298.503	−	1307.83i	0.392251	−	1.71856i	0.656689	−	0.754162i	$-0.271957\pi$
$762$		0			0
$763$	−302.443	+	628.030i	−0.396387	+	0.823106i
$764$	−285.446	+	454.284i	−0.373620	+	0.594613i
$765$		0			0
$766$	1716.06	+	1716.06i	2.24029	+	2.24029i
$767$	7.74390	+	16.0804i	0.0100963	+	0.0209653i
$768$		0			0
$769$	−107.950	+	958.085i	−0.140377	+	1.24588i	0.704025	+	0.710175i	$0.251384\pi$
$769$	−107.950	+	958.085i	−0.140377	+	1.24588i	−0.844403	+	0.535709i	$0.820044\pi$
$770$	−1911.78	+	920.663i	−2.48283	+	1.19567i
$771$		0			0
$772$	−1959.55	−	685.677i	−2.53828	−	0.888182i
$773$	−951.174	−	597.662i	−1.23050	−	0.773172i	−0.249722	−	0.968318i	$-0.580339\pi$
$773$	−951.174	−	597.662i	−1.23050	−	0.773172i	−0.980774	+	0.195145i	$0.937482\pi$
$774$		0			0
$775$	358.585	−	125.474i	0.462691	−	0.161902i
$776$	−1704.91	−	389.134i	−2.19705	−	0.501461i
$777$		0			0
$778$	890.962	−	1117.23i	1.14520	−	1.43603i
$779$	1.30504	+	5.71777i	0.00167528	+	0.00733988i
$780$		0			0
$781$	−524.322	+	59.0769i	−0.671347	+	0.0756426i
$782$			41.0550i			0.0525000i
$783$		0			0
$784$	289.923			0.369799
$785$	−47.3602	−	420.334i	−0.0603315	−	0.535457i
$786$		0			0
$787$	−29.9939	+	6.84590i	−0.0381116	+	0.00869873i	−0.241534	−	0.970392i	$-0.577651\pi$
$787$	−29.9939	+	6.84590i	−0.0381116	+	0.00869873i	0.203423	+	0.979091i	$0.434793\pi$
$788$	342.407	+	273.060i	0.434526	+	0.346523i
$789$		0			0
$790$	127.031	−	556.558i	0.160799	−	0.704504i
$791$	390.094	+	1114.82i	0.493165	+	1.40939i
$792$		0			0
$793$	191.080	−	304.103i	0.240959	−	0.383484i
$794$	422.244	−	1206.70i	0.531793	−	1.51978i
$795$		0			0
$796$	220.200	+	457.250i	0.276633	+	0.574434i
$797$	250.368	+	28.2097i	0.314138	+	0.0353948i	0.267626	−	0.963523i	$-0.413761\pi$
$797$	250.368	+	28.2097i	0.314138	+	0.0353948i	0.0465118	+	0.998918i	$0.485189\pi$
$798$		0			0
$799$	−4.26300	+	2.05295i	−0.00533542	+	0.00256940i
$800$	−9.64551	+	9.64551i	−0.0120569	+	0.0120569i
$801$		0			0
$802$	1592.11	+	1000.39i	1.98517	+	1.24736i
$803$	1308.65	+	630.211i	1.62970	+	0.784821i
$804$		0			0
$805$	241.215	+	55.0557i	0.299646	+	0.0683922i
$806$	1728.10	+	2166.97i	2.14405	+	2.68855i
$807$		0			0
$808$	−435.918	−	1909.88i	−0.539502	−	2.36371i
$809$	−525.861	+	330.420i	−0.650013	+	0.408430i	−0.816285	−	0.577650i	$-0.803970\pi$
$809$	−525.861	+	330.420i	−0.650013	+	0.408430i	0.166272	+	0.986080i	$0.446827\pi$
$810$		0			0
$811$		−	1519.25i		−	1.87330i	−0.350268	−	0.936650i	$-0.613909\pi$
$811$		−	1519.25i		−	1.87330i	0.350268	−	0.936650i	$-0.386091\pi$
$812$	996.358	+	862.713i	1.22704	+	1.06245i
$813$		0			0
$814$	−13.0403	−	115.735i	−0.0160200	−	0.142181i
$815$	−676.453	−	1076.57i	−0.830003	−	1.32094i
$816$		0			0
$817$	271.333	+	216.381i	0.332108	+	0.264848i
$818$	−361.056	+	287.932i	−0.441388	+	0.351995i
$819$		0			0
$820$	−4.25386	−	12.1568i	−0.00518763	−	0.0148254i
$821$	−58.4187	+	121.308i	−0.0711555	+	0.147756i	−0.933513	−	0.358545i	$-0.883273\pi$
$821$	−58.4187	+	121.308i	−0.0711555	+	0.147756i	0.862357	+	0.506301i	$0.168987\pi$
$822$		0			0
$823$	6.13993	−	17.5469i	0.00746042	−	0.0213207i	−0.940093	−	0.340918i	$-0.889262\pi$
$823$	6.13993	−	17.5469i	0.00746042	−	0.0213207i	0.947553	+	0.319598i	$0.103548\pi$
$824$	960.790	+	960.790i	1.16601	+	1.16601i
$825$		0			0
$826$	22.5220	+	2.53762i	0.0272664	+	0.00307218i
$827$	5.49058	−	48.7303i	0.00663916	−	0.0589241i	−0.989956	−	0.141377i	$-0.954847\pi$
$827$	5.49058	−	48.7303i	0.00663916	−	0.0589241i	0.996595	+	0.0824532i	$0.0262755\pi$
$828$		0			0
$829$	860.091	−	860.091i	1.03750	−	1.03750i	0.0382351	−	0.999269i	$-0.487826\pi$
$829$	860.091	−	860.091i	1.03750	−	1.03750i	0.999269	−	0.0382351i	$-0.0121736\pi$
$830$	430.101	+	150.499i	0.518194	+	0.181324i
$831$		0			0
$832$	843.473	+	406.195i	1.01379	+	0.488215i
$833$	−24.9291	+	8.72305i	−0.0299268	+	0.0104719i
$834$		0			0
$835$	−190.504	−	238.884i	−0.228148	−	0.286089i
$836$	2002.85	−	2511.50i	2.39576	−	3.00418i
$837$		0			0
$838$	−1601.37	+	1006.21i	−1.91094	+	1.20073i
$839$	−1245.92	+	140.381i	−1.48501	+	0.167320i	−0.816914	−	0.576760i	$-0.804317\pi$
$839$	−1245.92	+	140.381i	−1.48501	+	0.167320i	−0.668091	+	0.744079i	$0.732888\pi$
$840$		0			0
$841$	−120.294	−	832.352i	−0.143037	−	0.989717i
$842$	402.843			0.478435
$843$		0			0
$844$	202.586	+	322.414i	0.240031	+	0.382007i
$845$	379.895	−	86.7085i	0.449579	−	0.102614i
$846$		0			0
$847$	−1068.23	+	851.888i	−1.26120	+	1.00577i
$848$	−188.089	+	824.071i	−0.221803	+	0.971782i
$849$		0			0
$850$	16.9263	−	35.1479i	0.0199133	−	0.0413505i
$851$	−7.22517	+	11.4988i	−0.00849021	+	0.0135121i
$852$		0			0
$853$	573.655	+	573.655i	0.672514	+	0.672514i	0.958295	−	0.285781i	$-0.0922529\pi$
$853$	573.655	+	573.655i	0.672514	+	0.672514i	−0.285781	+	0.958295i	$0.592253\pi$
$854$	−197.885	−	410.912i	−0.231715	−	0.481162i
$855$		0			0
$856$	−219.875	+	1951.44i	−0.256863	+	2.27973i
$857$	451.731	−	217.542i	0.527107	−	0.253841i	−0.151351	−	0.988480i	$-0.548363\pi$
$857$	451.731	−	217.542i	0.527107	−	0.253841i	0.678459	+	0.734639i	$0.262648\pi$
$858$		0			0
$859$	1157.72	+	405.103i	1.34775	+	0.471598i	0.905139	−	0.425115i	$-0.139767\pi$
$859$	1157.72	+	405.103i	1.34775	+	0.471598i	0.442611	+	0.896714i	$0.354052\pi$
$860$	−645.325	−	405.484i	−0.750378	−	0.471494i
$861$		0			0
$862$	1473.27	−	515.520i	1.70913	−	0.598051i
$863$	1110.33	+	253.426i	1.28660	+	0.293658i	0.810502	−	0.585736i	$-0.199194\pi$
$863$	1110.33	+	253.426i	1.28660	+	0.293658i	0.476096	+	0.879393i	$0.342052\pi$
$864$		0			0
$865$	961.934	−	1206.23i	1.11206	−	1.39448i
$866$	−18.5038	−	81.0703i	−0.0213669	−	0.0936147i
$867$		0			0
$868$	2338.10	−	263.441i	2.69366	−	0.303503i
$869$		−	551.000i		−	0.634063i
$870$		0			0
$871$	77.7515			0.0892669
$872$	195.667	+	1736.59i	0.224389	+	1.99150i
$873$		0			0
$874$	−546.255	+	124.679i	−0.625006	+	0.142654i
$875$	442.422	+	352.820i	0.505625	+	0.403222i
$876$		0			0
$877$	−320.746	+	1405.28i	−0.365731	+	1.60237i	0.372639	+	0.927976i	$0.378453\pi$
$877$	−320.746	+	1405.28i	−0.365731	+	1.60237i	−0.738370	+	0.674396i	$0.764404\pi$
$878$	549.607	+	1570.69i	0.625976	+	1.78894i
$879$		0			0
$880$	−969.113	+	1542.33i	−1.10126	+	1.75265i
$881$	−325.085	+	929.039i	−0.368995	+	1.05453i	0.598387	+	0.801207i	$0.295808\pi$
$881$	−325.085	+	929.039i	−0.368995	+	1.05453i	−0.967382	+	0.253320i	$0.918477\pi$
$882$		0			0
$883$	712.448	+	1479.41i	0.806849	+	1.67544i	0.735043	+	0.678021i	$0.237162\pi$
$883$	712.448	+	1479.41i	0.806849	+	1.67544i	0.0718062	+	0.997419i	$0.477124\pi$
$884$	189.068	+	21.3029i	0.213878	+	0.0240982i
$885$		0			0
$886$	1159.90	−	558.577i	1.30914	−	0.630448i
$887$	−279.467	+	279.467i	−0.315070	+	0.315070i	−0.846870	−	0.531800i	$-0.821516\pi$
$887$	−279.467	+	279.467i	−0.315070	+	0.315070i	0.531800	+	0.846870i	$0.321516\pi$
$888$		0			0
$889$	−35.6923	−	22.4269i	−0.0401488	−	0.0252272i
$890$	−1292.26	−	622.319i	−1.45198	−	0.699235i
$891$		0			0
$892$	−2286.49	−	521.876i	−2.56333	−	0.585063i
$893$	−40.2617	−	50.4866i	−0.0450859	−	0.0565359i
$894$		0			0
$895$	248.719	+	1089.71i	0.277899	+	1.21755i
$896$	1042.09	−	654.788i	1.16305	−	0.730791i
$897$		0			0
$898$		−	1119.53i		−	1.24670i
$899$	−1237.95	−	849.534i	−1.37703	−	0.944976i
$900$		0			0
$901$	−8.62139	−	76.5170i	−0.00956869	−	0.0849245i
$902$	−9.89355	−	15.7455i	−0.0109685	−	0.0174562i
$903$		0			0
$904$	2315.09	+	1846.22i	2.56094	+	2.04228i
$905$	−299.508	+	238.850i	−0.330948	+	0.263922i
$906$		0			0
$907$	−412.469	−	1178.77i	−0.454761	−	1.29963i	−0.911964	−	0.410271i	$-0.865434\pi$
$907$	−412.469	−	1178.77i	−0.454761	−	1.29963i	0.457203	−	0.889363i	$-0.348851\pi$
$908$	−193.222	+	401.230i	−0.212800	+	0.441883i
$909$		0			0
$910$	566.504	−	1618.98i	0.622532	−	1.77909i
$911$	982.420	+	982.420i	1.07840	+	1.07840i	0.996653	+	0.0817436i	$0.0260488\pi$
$911$	982.420	+	982.420i	1.07840	+	1.07840i	0.0817436	+	0.996653i	$0.473951\pi$
$912$		0			0
$913$	437.045	+	49.2431i	0.478691	+	0.0539355i
$914$	103.552	−	919.045i	0.113295	−	1.00552i
$915$		0			0
$916$	1494.68	−	1494.68i	1.63174	−	1.63174i
$917$	−102.452	−	35.8495i	−0.111725	−	0.0390943i
$918$		0			0
$919$	70.0984	+	33.7576i	0.0762769	+	0.0367330i	0.471633	−	0.881795i	$-0.343665\pi$
$919$	70.0984	+	33.7576i	0.0762769	+	0.0367330i	−0.395356	+	0.918528i	$0.629379\pi$
$920$	585.486	−	204.870i	0.636398	−	0.222685i
$921$		0			0
$922$	1219.14	+	1528.75i	1.32227	+	1.65808i
$923$	265.926	−	333.461i	0.288111	−	0.361280i
$924$		0			0
$925$	10.9264	−	6.86550i	0.0118123	−	0.00742216i
$926$	1642.26	−	185.039i	1.77350	−	0.199826i
$927$		0			0
$928$	53.2826	+	8.19654i	0.0574166	+	0.00883248i
$929$	−1069.35			−1.15108			−0.575539	−	0.817774i	$-0.695208\pi$
$929$	−1069.35			−1.15108			−0.575539	+	0.817774i	$0.695208\pi$
$930$		0			0
$931$	−191.771	−	305.201i	−0.205984	−	0.327821i
$932$	−1895.27	+	432.582i	−2.03355	+	0.464144i
$933$		0			0
$934$	−2278.32	+	1816.90i	−2.43932	+	1.94529i
$935$	36.9243	−	161.776i	0.0394913	−	0.173023i
$936$		0			0
$937$	−257.680	+	535.079i	−0.275006	+	0.571055i	−0.992031	−	0.125992i	$-0.959789\pi$
$937$	−257.680	+	535.079i	−0.275006	+	0.571055i	0.717026	+	0.697047i	$0.245503\pi$
$938$	52.5300	−	83.6010i	0.0560021	−	0.0891269i
$939$		0			0
$940$	100.276	+	100.276i	0.106676	+	0.106676i
$941$	219.225	+	455.225i	0.232970	+	0.483767i	0.984377	−	0.176072i	$-0.0563390\pi$
$941$	219.225	+	455.225i	0.232970	+	0.483767i	−0.751408	+	0.659838i	$0.770625\pi$
$942$		0			0
$943$	−0.242772	+	2.15466i	−0.000257447	+	0.00228490i
$944$	17.5294	−	8.44170i	0.0185692	−	0.00894248i
$945$		0			0
$946$	−1038.65	−	363.438i	−1.09793	−	0.384184i
$947$	−661.273	−	415.505i	−0.698282	−	0.438759i	0.135556	−	0.990770i	$-0.456718\pi$
$947$	−661.273	−	415.505i	−0.698282	−	0.438759i	−0.833837	+	0.552010i	$0.813861\pi$
$948$		0			0
$949$	−1108.22	+	387.783i	−1.16778	+	0.408623i
$950$	519.062	+	118.473i	0.546381	+	0.124708i
$951$		0			0
$952$	75.9408	−	95.2267i	0.0797697	−	0.100028i
$953$	114.757	+	502.782i	0.120416	+	0.527578i	0.998771	+	0.0495684i	$0.0157846\pi$
$953$	114.757	+	502.782i	0.120416	+	0.527578i	−0.878354	+	0.478010i	$0.841358\pi$
$954$		0			0
$955$	−375.860	+	42.3492i	−0.393570	+	0.0443447i
$956$			2245.73i			2.34909i
$957$		0			0
$958$	−2097.79			−2.18975
$959$	−41.4322	−	367.721i	−0.0432036	−	0.383442i
$960$		0			0
$961$	−1676.30	+	382.604i	−1.74433	+	0.398131i
$962$	73.6061	+	58.6989i	0.0765136	+	0.0610176i
$963$		0			0
$964$	334.395	−	1465.08i	0.346883	−	1.51979i
$965$	−483.391	−	1381.45i	−0.500924	−	1.43156i
$966$		0			0
$967$	−116.344	+	185.160i	−0.120314	+	0.191479i	−0.901451	−	0.432880i	$-0.857497\pi$
$967$	−116.344	+	185.160i	−0.120314	+	0.191479i	0.781137	+	0.624360i	$0.214640\pi$
$968$	−1131.36	+	3233.24i	−1.16876	+	3.34012i
$969$		0			0
$970$	−1061.09	−	2203.38i	−1.09391	−	2.27153i
$971$	−838.831	−	94.5135i	−0.863883	−	0.0973363i	−0.331108	−	0.943593i	$-0.607422\pi$
$971$	−838.831	−	94.5135i	−0.863883	−	0.0973363i	−0.532775	+	0.846257i	$0.678851\pi$
$972$		0			0
$973$	917.539	−	441.863i	0.943000	−	0.454125i
$974$	607.689	−	607.689i	0.623911	−	0.623911i
$975$		0			0
$976$	−331.506	−	208.299i	−0.339657	−	0.213421i
$977$	−1555.05	−	748.872i	−1.59166	−	0.766502i	−0.592423	−	0.805627i	$-0.701829\pi$
$977$	−1555.05	−	748.872i	−1.59166	−	0.766502i	−0.999234	+	0.0391251i	$0.987543\pi$
$978$		0			0
$979$	−1349.66	−	308.052i	−1.37862	−	0.314660i
$980$	493.539	+	618.879i	0.503611	+	0.631509i
$981$		0			0
$982$	−554.845	−	2430.94i	−0.565016	−	2.47550i
$983$	594.731	−	373.694i	0.605016	−	0.380157i	−0.194411	−	0.980920i	$-0.562280\pi$
$983$	594.731	−	373.694i	0.605016	−	0.380157i	0.799427	+	0.600763i	$0.205137\pi$
$984$		0			0
$985$			308.751i			0.313453i
$986$	−151.574	+	28.2030i	−0.153726	+	0.0286034i
$987$		0			0
$988$	290.733	+	2580.33i	0.294265	+	2.61167i
$989$	68.2639	+	108.641i	0.0690232	+	0.109850i
$990$		0			0
$991$	−1115.14	−	889.298i	−1.12527	−	0.897375i	−0.129717	−	0.991551i	$-0.541407\pi$
$991$	−1115.14	−	889.298i	−1.12527	−	0.897375i	−0.995556	+	0.0941765i	$0.969978\pi$
$992$	75.2454	−	60.0062i	0.0758522	−	0.0604901i
$993$		0			0
$994$	−178.885	−	511.224i	−0.179965	−	0.514310i
$995$	−155.237	+	322.354i	−0.156017	+	0.323974i
$996$		0			0
$997$	595.003	−	1700.42i	0.596793	−	1.70554i	−0.106204	−	0.994344i	$-0.533870\pi$
$997$	595.003	−	1700.42i	0.596793	−	1.70554i	0.702997	−	0.711193i	$-0.251845\pi$
$998$	−1011.06	−	1011.06i	−1.01309	−	1.01309i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.3.s.a.217.4		48
3.2	odd	2		29.3.f.a.14.1	✓	48
29.27	odd	28	inner	261.3.s.a.172.4		48
87.56	even	28		29.3.f.a.27.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.f.a.14.1	✓	48	3.2	odd	2
29.3.f.a.27.1	yes	48	87.56	even	28
261.3.s.a.172.4		48	29.27	odd	28	inner
261.3.s.a.217.4		48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	261.s (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.388927 + 3.45182i) q^{2} +(-7.86410 + 1.79493i) q^{4} +(-4.44600 - 3.54557i) q^{5} +(1.25371 - 5.49285i) q^{7} +(-4.66523 - 13.3325i) q^{8} +O(q^{10})\)	\(q+(0.388927 + 3.45182i) q^{2} +(-7.86410 + 1.79493i) q^{4} +(-4.44600 - 3.54557i) q^{5} +(1.25371 - 5.49285i) q^{7} +(-4.66523 - 13.3325i) q^{8} +(10.5095 - 16.7258i) q^{10} +(6.29707 - 17.9960i) q^{11} +(6.68692 + 13.8855i) q^{13} +(19.4480 + 2.19126i) q^{14} +(15.1368 - 7.28948i) q^{16} +(-1.08221 + 1.08221i) q^{17} +(-17.6859 - 11.1128i) q^{19} +(41.3278 + 19.9024i) q^{20} +(64.5681 + 14.7372i) q^{22} +(-4.81481 - 6.03758i) q^{23} +(1.63284 + 7.15396i) q^{25} +(-45.3297 + 28.4825i) q^{26} +45.4467i q^{28} +(18.9830 - 21.9237i) q^{29} +(-5.79670 - 51.4471i) q^{31} +(0.989018 + 1.57401i) q^{32} +(-4.15651 - 3.31471i) q^{34} +(-25.0493 + 19.9761i) q^{35} +(-0.580820 - 1.65989i) q^{37} +(31.4809 - 65.3707i) q^{38} +(-26.5295 + 75.8170i) q^{40} +(-0.198543 - 0.198543i) q^{41} +(-16.5106 - 1.86030i) q^{43} +(-17.2193 + 152.825i) q^{44} +(18.9681 - 18.9681i) q^{46} +(2.91807 + 1.02108i) q^{47} +(15.5478 + 7.48743i) q^{49} +(-24.0591 + 8.41865i) q^{50} +(-77.5102 - 97.1947i) q^{52} +(-31.3688 + 39.3353i) q^{53} +(-91.8027 + 57.6835i) q^{55} +(-79.0821 + 8.91041i) q^{56} +(83.0596 + 56.9991i) q^{58} +1.15807 q^{59} +(-12.3983 - 19.7319i) q^{61} +(175.332 - 40.0183i) q^{62} +(47.4922 - 37.8737i) q^{64} +(19.5020 - 85.4439i) q^{65} +(2.18892 - 4.54533i) q^{67} +(6.56815 - 10.4531i) q^{68} +(-78.6963 - 78.6963i) q^{70} +(-12.0075 - 24.9339i) q^{71} +(-8.52973 + 75.7035i) q^{73} +(5.50374 - 2.65046i) q^{74} +(159.030 + 55.6472i) q^{76} +(-90.9547 - 57.1506i) q^{77} +(27.2780 - 9.54499i) q^{79} +(-93.1433 - 21.2594i) q^{80} +(0.608115 - 0.762553i) q^{82} +(5.13309 + 22.4895i) q^{83} +(8.64858 - 0.974461i) q^{85} -57.7154i q^{86} -269.308 q^{88} +(-8.12973 - 72.1533i) q^{89} +(84.6546 - 19.3219i) q^{91} +(48.7012 + 38.8379i) q^{92} +(-2.38966 + 10.4698i) q^{94} +(39.2304 + 112.114i) q^{95} +(65.8679 - 104.828i) q^{97} +(-19.7983 + 56.5803i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Introduction

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