LMFDB - Embedded newform 99.2.f.a.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(37,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("99.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.f (of order $5$, degree $4$, 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:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	99.91
Dual form			99.2.f.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 + 0.224514i) q^{2} +(-0.572949 + 1.76336i) q^{4} +(1.30902 + 0.951057i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(-0.454915 - 1.40008i) q^{8} -0.618034 q^{10} +(2.19098 + 2.48990i) q^{11} +(3.42705 - 2.48990i) q^{13} +(-0.118034 - 0.363271i) q^{14} +(-2.54508 - 1.84911i) q^{16} +(-6.35410 - 4.61653i) q^{17} +(-0.263932 - 0.812299i) q^{19} +(-2.42705 + 1.76336i) q^{20} +(-1.23607 - 0.277515i) q^{22} +4.23607 q^{23} +(-0.736068 - 2.26538i) q^{25} +(-0.500000 + 1.53884i) q^{26} +(-1.50000 - 1.08981i) q^{28} +(1.85410 - 5.70634i) q^{29} +(-4.11803 + 2.99193i) q^{31} +4.14590 q^{32} +3.00000 q^{34} +(-1.30902 + 0.951057i) q^{35} +(-0.545085 + 1.67760i) q^{37} +(0.263932 + 0.191758i) q^{38} +(0.736068 - 2.26538i) q^{40} +(1.30902 + 4.02874i) q^{41} +6.70820 q^{43} +(-5.64590 + 2.43690i) q^{44} +(-1.30902 + 0.951057i) q^{46} +(-0.336881 - 1.03681i) q^{47} +(4.85410 + 3.52671i) q^{49} +(0.736068 + 0.534785i) q^{50} +(2.42705 + 7.46969i) q^{52} +(-2.11803 + 1.53884i) q^{53} +(0.500000 + 5.34307i) q^{55} +1.47214 q^{56} +(0.708204 + 2.17963i) q^{58} +(-2.97214 + 9.14729i) q^{59} +(-6.92705 - 5.03280i) q^{61} +(0.600813 - 1.84911i) q^{62} +(3.80902 - 2.76741i) q^{64} +6.85410 q^{65} -4.85410 q^{67} +(11.7812 - 8.55951i) q^{68} +(0.190983 - 0.587785i) q^{70} +(-4.30902 - 3.13068i) q^{71} +(2.38197 - 7.33094i) q^{73} +(-0.208204 - 0.640786i) q^{74} +1.58359 q^{76} +(-3.04508 + 1.31433i) q^{77} +(-8.89919 + 6.46564i) q^{79} +(-1.57295 - 4.84104i) q^{80} +(-1.30902 - 0.951057i) q^{82} +(-6.04508 - 4.39201i) q^{83} +(-3.92705 - 12.0862i) q^{85} +(-2.07295 + 1.50609i) q^{86} +(2.48936 - 4.20025i) q^{88} +3.76393 q^{89} +(1.30902 + 4.02874i) q^{91} +(-2.42705 + 7.46969i) q^{92} +(0.336881 + 0.244758i) q^{94} +(0.427051 - 1.31433i) q^{95} +(-0.927051 + 0.673542i) q^{97} -2.29180 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 9 q^{4} + 3 q^{5} + q^{7} - 13 q^{8} + 2 q^{10} + 11 q^{11} + 7 q^{13} + 4 q^{14} + q^{16} - 12 q^{17} - 10 q^{19} - 3 q^{20} + 4 q^{22} + 8 q^{23} + 6 q^{25} - 2 q^{26} - 6 q^{28} - 6 q^{29}+ \cdots - 36 q^{98}+O(q^{100}) $ 4 * q + q^2 - 9 * q^4 + 3 * q^5 + q^7 - 13 * q^8 + 2 * q^10 + 11 * q^11 + 7 * q^13 + 4 * q^14 + q^16 - 12 * q^17 - 10 * q^19 - 3 * q^20 + 4 * q^22 + 8 * q^23 + 6 * q^25 - 2 * q^26 - 6 * q^28 - 6 * q^29 - 12 * q^31 + 30 * q^32 + 12 * q^34 - 3 * q^35 + 9 * q^37 + 10 * q^38 - 6 * q^40 + 3 * q^41 - 36 * q^44 - 3 * q^46 - 17 * q^47 + 6 * q^49 - 6 * q^50 + 3 * q^52 - 4 * q^53 + 2 * q^55 - 12 * q^56 - 24 * q^58 + 6 * q^59 - 21 * q^61 + 27 * q^62 + 13 * q^64 + 14 * q^65 - 6 * q^67 + 27 * q^68 + 3 * q^70 - 15 * q^71 + 14 * q^73 + 26 * q^74 + 60 * q^76 - q^77 - 11 * q^79 - 13 * q^80 - 3 * q^82 - 13 * q^83 - 9 * q^85 - 15 * q^86 - 37 * q^88 + 24 * q^89 + 3 * q^91 - 3 * q^92 + 17 * q^94 - 5 * q^95 + 3 * q^97 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−0.309017	+	0.224514i	−0.218508	+	0.158755i	−0.691655	−	0.722228i	$-0.743118\pi$
$2$	−0.309017	+	0.224514i	−0.218508	+	0.158755i	0.473147	+	0.880984i	$0.343118\pi$
$3$		0			0
$3$		0			0
$4$	−0.572949	+	1.76336i	−0.286475	+	0.881678i
$5$	1.30902	+	0.951057i	0.585410	+	0.425325i	0.840670	−	0.541547i	$-0.182161\pi$
$5$	1.30902	+	0.951057i	0.585410	+	0.425325i	−0.255260	+	0.966872i	$0.582161\pi$
$6$		0			0
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i	−0.992318	−	0.123716i	$-0.960519\pi$
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i	0.875520	+	0.483181i	$0.160519\pi$
$8$	−0.454915	−	1.40008i	−0.160837	−	0.495005i
$9$		0			0
$10$	−0.618034			−0.195440
$11$	2.19098	+	2.48990i	0.660606	+	0.750733i
$11$	2.19098	+	2.48990i	0.660606	+	0.750733i
$12$		0			0
$13$	3.42705	−	2.48990i	0.950493	−	0.690574i	−0.000430477	−	1.00000i	$-0.500137\pi$
$13$	3.42705	−	2.48990i	0.950493	−	0.690574i	0.950923	+	0.309426i	$0.100137\pi$
$14$	−0.118034	−	0.363271i	−0.0315459	−	0.0970883i
$15$		0			0
$16$	−2.54508	−	1.84911i	−0.636271	−	0.462278i
$17$	−6.35410	−	4.61653i	−1.54110	−	1.11967i	−0.949644	−	0.313332i	$-0.898555\pi$
$17$	−6.35410	−	4.61653i	−1.54110	−	1.11967i	−0.591452	−	0.806340i	$-0.701445\pi$
$18$		0			0
$19$	−0.263932	−	0.812299i	−0.0605502	−	0.186354i	0.916206	−	0.400707i	$-0.131236\pi$
$19$	−0.263932	−	0.812299i	−0.0605502	−	0.186354i	−0.976756	+	0.214353i	$0.931236\pi$
$20$	−2.42705	+	1.76336i	−0.542705	+	0.394298i
$21$		0			0
$22$	−1.23607	−	0.277515i	−0.263531	−	0.0591663i
$23$	4.23607			0.883281			0.441641	−	0.897192i	$-0.354397\pi$
$23$	4.23607			0.883281			0.441641	+	0.897192i	$0.354397\pi$
$24$		0			0
$25$	−0.736068	−	2.26538i	−0.147214	−	0.453077i
$26$	−0.500000	+	1.53884i	−0.0980581	+	0.301792i
$27$		0			0
$28$	−1.50000	−	1.08981i	−0.283473	−	0.205955i
$29$	1.85410	−	5.70634i	0.344298	−	1.05964i	−0.617660	−	0.786445i	$-0.711919\pi$
$29$	1.85410	−	5.70634i	0.344298	−	1.05964i	0.961958	−	0.273196i	$-0.0880806\pi$
$30$		0			0
$31$	−4.11803	+	2.99193i	−0.739621	+	0.537366i	−0.892592	−	0.450865i	$-0.851116\pi$
$31$	−4.11803	+	2.99193i	−0.739621	+	0.537366i	0.152972	+	0.988231i	$0.451116\pi$
$32$	4.14590			0.732898
$33$		0			0
$34$	3.00000			0.514496
$35$	−1.30902	+	0.951057i	−0.221264	+	0.160758i
$36$		0			0
$37$	−0.545085	+	1.67760i	−0.0896114	+	0.275796i	−0.985812	−	0.167854i	$-0.946316\pi$
$37$	−0.545085	+	1.67760i	−0.0896114	+	0.275796i	0.896201	+	0.443649i	$0.146316\pi$
$38$	0.263932	+	0.191758i	0.0428154	+	0.0311072i
$39$		0			0
$40$	0.736068	−	2.26538i	0.116383	−	0.358189i
$41$	1.30902	+	4.02874i	0.204434	+	0.629183i	0.999736	+	0.0229701i	$0.00731226\pi$
$41$	1.30902	+	4.02874i	0.204434	+	0.629183i	−0.795302	+	0.606213i	$0.792688\pi$
$42$		0			0
$43$	6.70820			1.02299			0.511496	−	0.859286i	$-0.329092\pi$
$43$	6.70820			1.02299			0.511496	+	0.859286i	$0.329092\pi$
$44$	−5.64590	+	2.43690i	−0.851151	+	0.367376i
$45$		0			0
$46$	−1.30902	+	0.951057i	−0.193004	+	0.140226i
$47$	−0.336881	−	1.03681i	−0.0491391	−	0.151235i	0.923476	−	0.383656i	$-0.125335\pi$
$47$	−0.336881	−	1.03681i	−0.0491391	−	0.151235i	−0.972615	+	0.232421i	$0.925335\pi$
$48$		0			0
$49$	4.85410	+	3.52671i	0.693443	+	0.503816i
$50$	0.736068	+	0.534785i	0.104096	+	0.0756300i
$51$		0			0
$52$	2.42705	+	7.46969i	0.336571	+	1.03586i
$53$	−2.11803	+	1.53884i	−0.290934	+	0.211376i	−0.723673	−	0.690143i	$-0.757547\pi$
$53$	−2.11803	+	1.53884i	−0.290934	+	0.211376i	0.432738	+	0.901520i	$0.357547\pi$
$54$		0			0
$55$	0.500000	+	5.34307i	0.0674200	+	0.720459i
$56$	1.47214			0.196722
$57$		0			0
$58$	0.708204	+	2.17963i	0.0929917	+	0.286199i
$59$	−2.97214	+	9.14729i	−0.386939	+	1.19088i	0.548125	+	0.836397i	$0.315342\pi$
$59$	−2.97214	+	9.14729i	−0.386939	+	1.19088i	−0.935064	+	0.354480i	$0.884658\pi$
$60$		0			0
$61$	−6.92705	−	5.03280i	−0.886918	−	0.644384i	0.0481546	−	0.998840i	$-0.484666\pi$
$61$	−6.92705	−	5.03280i	−0.886918	−	0.644384i	−0.935073	+	0.354456i	$0.884666\pi$
$62$	0.600813	−	1.84911i	0.0763033	−	0.234838i
$63$		0			0
$64$	3.80902	−	2.76741i	0.476127	−	0.345927i
$65$	6.85410			0.850147
$66$		0			0
$67$	−4.85410			−0.593023			−0.296511	−	0.955029i	$-0.595823\pi$
$67$	−4.85410			−0.593023			−0.296511	+	0.955029i	$0.595823\pi$
$68$	11.7812	−	8.55951i	1.42867	−	1.03799i
$69$		0			0
$70$	0.190983	−	0.587785i	0.0228268	−	0.0702538i
$71$	−4.30902	−	3.13068i	−0.511386	−	0.371544i	0.301963	−	0.953320i	$-0.402358\pi$
$71$	−4.30902	−	3.13068i	−0.511386	−	0.371544i	−0.813349	+	0.581776i	$0.802358\pi$
$72$		0			0
$73$	2.38197	−	7.33094i	0.278788	−	0.858021i	−0.709404	−	0.704802i	$-0.751036\pi$
$73$	2.38197	−	7.33094i	0.278788	−	0.858021i	0.988192	−	0.153219i	$-0.0489641\pi$
$74$	−0.208204	−	0.640786i	−0.0242032	−	0.0744898i
$75$		0			0
$76$	1.58359			0.181650
$77$	−3.04508	+	1.31433i	−0.347020	+	0.149782i
$78$		0			0
$79$	−8.89919	+	6.46564i	−1.00124	+	0.727441i	−0.962353	−	0.271803i	$-0.912380\pi$
$79$	−8.89919	+	6.46564i	−1.00124	+	0.727441i	−0.0388837	+	0.999244i	$0.512380\pi$
$80$	−1.57295	−	4.84104i	−0.175861	−	0.541245i
$81$		0			0
$82$	−1.30902	−	0.951057i	−0.144557	−	0.105027i
$83$	−6.04508	−	4.39201i	−0.663534	−	0.482086i	0.204320	−	0.978904i	$-0.434502\pi$
$83$	−6.04508	−	4.39201i	−0.663534	−	0.482086i	−0.867855	+	0.496818i	$0.834502\pi$
$84$		0			0
$85$	−3.92705	−	12.0862i	−0.425948	−	1.31093i
$86$	−2.07295	+	1.50609i	−0.223532	+	0.162405i
$87$		0			0
$88$	2.48936	−	4.20025i	0.265366	−	0.447749i
$89$	3.76393			0.398976			0.199488	−	0.979900i	$-0.436072\pi$
$89$	3.76393			0.398976			0.199488	+	0.979900i	$0.436072\pi$
$90$		0			0
$91$	1.30902	+	4.02874i	0.137222	+	0.422327i
$92$	−2.42705	+	7.46969i	−0.253038	+	0.778770i
$93$		0			0
$94$	0.336881	+	0.244758i	0.0347466	+	0.0252449i
$95$	0.427051	−	1.31433i	0.0438145	−	0.134847i
$96$		0			0
$97$	−0.927051	+	0.673542i	−0.0941278	+	0.0683878i	−0.633854	−	0.773453i	$-0.718528\pi$
$97$	−0.927051	+	0.673542i	−0.0941278	+	0.0683878i	0.539726	+	0.841841i	$0.318528\pi$
$98$	−2.29180			−0.231506
$99$		0			0
$100$	4.41641			0.441641
$101$	−4.66312	+	3.38795i	−0.463998	+	0.337114i	−0.795097	−	0.606482i	$-0.792580\pi$
$101$	−4.66312	+	3.38795i	−0.463998	+	0.337114i	0.331100	+	0.943596i	$0.392580\pi$
$102$		0			0
$103$	2.14590	−	6.60440i	0.211442	−	0.650750i	−0.787946	−	0.615745i	$-0.788855\pi$
$103$	2.14590	−	6.60440i	0.211442	−	0.650750i	0.999387	−	0.0350054i	$-0.0111448\pi$
$104$	−5.04508	−	3.66547i	−0.494711	−	0.359429i
$105$		0			0
$106$	0.309017	−	0.951057i	0.0300144	−	0.0923748i
$107$	0.781153	+	2.40414i	0.0755169	+	0.232417i	0.981689	−	0.190493i	$-0.0610086\pi$
$107$	0.781153	+	2.40414i	0.0755169	+	0.232417i	−0.906172	+	0.422910i	$0.861009\pi$
$108$		0			0
$109$	−12.0000			−1.14939			−0.574696	−	0.818367i	$-0.694880\pi$
$109$	−12.0000			−1.14939			−0.574696	+	0.818367i	$0.694880\pi$
$110$	−1.35410	−	1.53884i	−0.129109	−	0.146723i
$111$		0			0
$112$	2.54508	−	1.84911i	0.240488	−	0.174725i
$113$	−1.39919	−	4.30625i	−0.131624	−	0.405098i	0.863425	−	0.504477i	$-0.168315\pi$
$113$	−1.39919	−	4.30625i	−0.131624	−	0.405098i	−0.995050	+	0.0993784i	$0.968315\pi$
$114$		0			0
$115$	5.54508	+	4.02874i	0.517082	+	0.375682i
$116$	9.00000	+	6.53888i	0.835629	+	0.607120i
$117$		0			0
$118$	−1.13525	−	3.49396i	−0.104509	−	0.321645i
$119$	6.35410	−	4.61653i	0.582480	−	0.423196i
$120$		0			0
$121$	−1.39919	+	10.9106i	−0.127199	+	0.991877i
$122$	3.27051			0.296098
$123$		0			0
$124$	−2.91641	−	8.97578i	−0.261901	−	0.806049i
$125$	3.69098	−	11.3597i	0.330132	−	1.01604i
$126$		0			0
$127$	4.61803	+	3.35520i	0.409784	+	0.297726i	0.773514	−	0.633779i	$-0.218497\pi$
$127$	4.61803	+	3.35520i	0.409784	+	0.297726i	−0.363730	+	0.931504i	$0.618497\pi$
$128$	−3.11803	+	9.59632i	−0.275598	+	0.848203i
$129$		0			0
$130$	−2.11803	+	1.53884i	−0.185764	+	0.134965i
$131$	−12.7984			−1.11820			−0.559100	−	0.829101i	$-0.688853\pi$
$131$	−12.7984			−1.11820			−0.559100	+	0.829101i	$0.688853\pi$
$132$		0			0
$133$	0.854102			0.0740600
$134$	1.50000	−	1.08981i	0.129580	−	0.0941456i
$135$		0			0
$136$	−3.57295	+	10.9964i	−0.306378	+	0.942934i
$137$	11.5172	+	8.36775i	0.983983	+	0.714905i	0.958595	−	0.284772i	$-0.0919181\pi$
$137$	11.5172	+	8.36775i	0.983983	+	0.714905i	0.0253875	+	0.999678i	$0.491918\pi$
$138$		0			0
$139$	−1.71885	+	5.29007i	−0.145791	+	0.448698i	−0.997112	−	0.0759473i	$-0.975802\pi$
$139$	−1.71885	+	5.29007i	−0.145791	+	0.448698i	0.851321	+	0.524645i	$0.175802\pi$
$140$	−0.927051	−	2.85317i	−0.0783501	−	0.241137i
$141$		0			0
$142$	2.03444			0.170727
$143$	13.7082	+	3.07768i	1.14634	+	0.257369i
$144$		0			0
$145$	7.85410	−	5.70634i	0.652248	−	0.473886i
$146$	0.909830	+	2.80017i	0.0752981	+	0.231744i
$147$		0			0
$148$	−2.64590	−	1.92236i	−0.217491	−	0.158017i
$149$	0.190983	+	0.138757i	0.0156459	+	0.0113674i	0.595581	−	0.803295i	$-0.296922\pi$
$149$	0.190983	+	0.138757i	0.0156459	+	0.0113674i	−0.579935	+	0.814663i	$0.696922\pi$
$150$		0			0
$151$	5.85410	+	18.0171i	0.476400	+	1.46621i	0.844060	+	0.536248i	$0.180159\pi$
$151$	5.85410	+	18.0171i	0.476400	+	1.46621i	−0.367660	+	0.929960i	$0.619841\pi$
$152$	−1.01722	+	0.739054i	−0.0825075	+	0.0599452i
$153$		0			0
$154$	0.645898	−	1.08981i	0.0520479	−	0.0878197i
$155$	−8.23607			−0.661537
$156$		0			0
$157$	0.708204	+	2.17963i	0.0565208	+	0.173953i	0.975331	−	0.220745i	$-0.0708490\pi$
$157$	0.708204	+	2.17963i	0.0565208	+	0.173953i	−0.918811	+	0.394699i	$0.870849\pi$
$158$	1.29837	−	3.99598i	0.103293	−	0.317903i
$159$		0			0
$160$	5.42705	+	3.94298i	0.429046	+	0.311720i
$161$	−1.30902	+	4.02874i	−0.103165	+	0.317509i
$162$		0			0
$163$	9.59017	−	6.96767i	0.751160	−	0.545750i	−0.145026	−	0.989428i	$-0.546327\pi$
$163$	9.59017	−	6.96767i	0.751160	−	0.545750i	0.896186	+	0.443678i	$0.146327\pi$
$164$	−7.85410			−0.613302
$165$		0			0
$166$	2.85410			0.221521
$167$	−13.7812	+	10.0126i	−1.06642	+	0.774798i	−0.975265	−	0.221039i	$-0.929055\pi$
$167$	−13.7812	+	10.0126i	−1.06642	+	0.774798i	−0.0911527	+	0.995837i	$0.529055\pi$
$168$		0			0
$169$	1.52786	−	4.70228i	0.117528	−	0.361714i
$170$	3.92705	+	2.85317i	0.301191	+	0.218828i
$171$		0			0
$172$	−3.84346	+	11.8290i	−0.293061	+	0.901949i
$173$	−3.40983	−	10.4944i	−0.259245	−	0.797873i	−0.992964	−	0.118420i	$-0.962217\pi$
$173$	−3.40983	−	10.4944i	−0.259245	−	0.797873i	0.733719	−	0.679453i	$-0.237783\pi$
$174$		0			0
$175$	2.38197			0.180060
$176$	−0.972136	−	10.3884i	−0.0732775	−	0.783053i
$177$		0			0
$178$	−1.16312	+	0.845055i	−0.0871795	+	0.0633396i
$179$	5.39919	+	16.6170i	0.403554	+	1.24201i	0.922096	+	0.386960i	$0.126475\pi$
$179$	5.39919	+	16.6170i	0.403554	+	1.24201i	−0.518542	+	0.855052i	$0.673525\pi$
$180$		0			0
$181$	−9.28115	−	6.74315i	−0.689863	−	0.501215i	0.186752	−	0.982407i	$-0.440204\pi$
$181$	−9.28115	−	6.74315i	−0.689863	−	0.501215i	−0.876615	+	0.481192i	$0.840204\pi$
$182$	−1.30902	−	0.951057i	−0.0970308	−	0.0704970i
$183$		0			0
$184$	−1.92705	−	5.93085i	−0.142064	−	0.437228i
$185$	−2.30902	+	1.67760i	−0.169762	+	0.123340i
$186$		0			0
$187$	−2.42705	−	25.9358i	−0.177484	−	1.89661i
$188$	2.02129			0.147417
$189$		0			0
$190$	0.163119	+	0.502029i	0.0118339	+	0.0364210i
$191$	7.16312	−	22.0458i	0.518305	−	1.59518i	−0.258882	−	0.965909i	$-0.583354\pi$
$191$	7.16312	−	22.0458i	0.518305	−	1.59518i	0.777187	−	0.629270i	$-0.216646\pi$
$192$		0			0
$193$	7.97214	+	5.79210i	0.573847	+	0.416924i	0.836501	−	0.547966i	$-0.184598\pi$
$193$	7.97214	+	5.79210i	0.573847	+	0.416924i	−0.262654	+	0.964890i	$0.584598\pi$
$194$	0.135255	−	0.416272i	0.00971074	−	0.0298866i
$195$		0			0
$196$	−9.00000	+	6.53888i	−0.642857	+	0.467063i
$197$	16.0344			1.14241			0.571203	−	0.820809i	$-0.306477\pi$
$197$	16.0344			1.14241			0.571203	+	0.820809i	$0.306477\pi$
$198$		0			0
$199$	−6.70820			−0.475532			−0.237766	−	0.971322i	$-0.576415\pi$
$199$	−6.70820			−0.475532			−0.237766	+	0.971322i	$0.576415\pi$
$200$	−2.83688	+	2.06111i	−0.200598	+	0.145743i
$201$		0			0
$202$	0.680340	−	2.09387i	0.0478685	−	0.147324i
$203$	4.85410	+	3.52671i	0.340691	+	0.247527i
$204$		0			0
$205$	−2.11803	+	6.51864i	−0.147930	+	0.455281i
$206$	0.819660	+	2.52265i	0.0571084	+	0.175762i
$207$		0			0
$208$	−13.3262			−0.924008
$209$	1.44427	−	2.43690i	0.0999024	−	0.168564i
$210$		0			0
$211$	−1.11803	+	0.812299i	−0.0769686	+	0.0559210i	−0.625604	−	0.780141i	$-0.715147\pi$
$211$	−1.11803	+	0.812299i	−0.0769686	+	0.0559210i	0.548636	+	0.836062i	$0.315147\pi$
$212$	−1.50000	−	4.61653i	−0.103020	−	0.317064i
$213$		0			0
$214$	−0.781153	−	0.567541i	−0.0533985	−	0.0387963i
$215$	8.78115	+	6.37988i	0.598870	+	0.435104i
$216$		0			0
$217$	−1.57295	−	4.84104i	−0.106779	−	0.328631i
$218$	3.70820	−	2.69417i	0.251151	−	0.182472i
$219$		0			0
$220$	−9.70820	−	2.17963i	−0.654527	−	0.146950i
$221$	−33.2705			−2.23802
$222$		0			0
$223$	−4.69098	−	14.4374i	−0.314131	−	0.966797i	−0.976110	−	0.217275i	$-0.930283\pi$
$223$	−4.69098	−	14.4374i	−0.314131	−	0.966797i	0.661979	−	0.749522i	$-0.269717\pi$
$224$	−1.28115	+	3.94298i	−0.0856006	+	0.263452i
$225$		0			0
$226$	1.39919	+	1.01657i	0.0930725	+	0.0676212i
$227$	2.83688	−	8.73102i	0.188290	−	0.579498i	−0.811699	−	0.584076i	$-0.801457\pi$
$227$	2.83688	−	8.73102i	0.188290	−	0.579498i	0.999990	+	0.00457752i	$0.00145707\pi$
$228$		0			0
$229$	6.85410	−	4.97980i	0.452932	−	0.329074i	−0.337820	−	0.941211i	$-0.609690\pi$
$229$	6.85410	−	4.97980i	0.452932	−	0.329074i	0.790752	+	0.612136i	$0.209690\pi$
$230$	−2.61803			−0.172628
$231$		0			0
$232$	−8.83282			−0.579903
$233$	−8.78115	+	6.37988i	−0.575272	+	0.417960i	−0.837017	−	0.547177i	$-0.815702\pi$
$233$	−8.78115	+	6.37988i	−0.575272	+	0.417960i	0.261744	+	0.965137i	$0.415702\pi$
$234$		0			0
$235$	0.545085	−	1.67760i	0.0355574	−	0.109434i
$236$	−14.4271	−	10.4819i	−0.939121	−	0.682311i
$237$		0			0
$238$	−0.927051	+	2.85317i	−0.0600918	+	0.184944i
$239$	−0.809017	−	2.48990i	−0.0523310	−	0.161058i	0.921476	−	0.388436i	$-0.126985\pi$
$239$	−0.809017	−	2.48990i	−0.0523310	−	0.161058i	−0.973807	+	0.227378i	$0.926985\pi$
$240$		0			0
$241$	21.7082			1.39835			0.699174	−	0.714951i	$-0.253551\pi$
$241$	21.7082			1.39835			0.699174	+	0.714951i	$0.253551\pi$
$242$	−2.01722	−	3.68571i	−0.129672	−	0.236927i
$243$		0			0
$244$	12.8435	−	9.33132i	0.822218	−	0.597376i
$245$	3.00000	+	9.23305i	0.191663	+	0.589878i
$246$		0			0
$247$	−2.92705	−	2.12663i	−0.186244	−	0.135314i
$248$	6.06231	+	4.40452i	0.384957	+	0.279687i
$249$		0			0
$250$	1.40983	+	4.33901i	0.0891655	+	0.274423i
$251$	20.2082	−	14.6821i	1.27553	−	0.926727i	0.276122	−	0.961123i	$-0.410951\pi$
$251$	20.2082	−	14.6821i	1.27553	−	0.926727i	0.999408	+	0.0343954i	$0.0109505\pi$
$252$		0			0
$253$	9.28115	+	10.5474i	0.583501	+	0.663108i
$254$	−2.18034			−0.136807
$255$		0			0
$256$	1.71885	+	5.29007i	0.107428	+	0.330629i
$257$	3.93769	−	12.1190i	0.245627	−	0.755961i	−0.749906	−	0.661544i	$-0.769901\pi$
$257$	3.93769	−	12.1190i	0.245627	−	0.755961i	0.995533	−	0.0944167i	$-0.0300986\pi$
$258$		0			0
$259$	−1.42705	−	1.03681i	−0.0886726	−	0.0644244i
$260$	−3.92705	+	12.0862i	−0.243545	+	0.749556i
$261$		0			0
$262$	3.95492	−	2.87341i	0.244335	−	0.177520i
$263$	−18.2705			−1.12661			−0.563304	−	0.826250i	$-0.690470\pi$
$263$	−18.2705			−1.12661			−0.563304	+	0.826250i	$0.690470\pi$
$264$		0			0
$265$	−4.23607			−0.260220
$266$	−0.263932	+	0.191758i	−0.0161827	+	0.0117574i
$267$		0			0
$268$	2.78115	−	8.55951i	0.169886	−	0.522855i
$269$	1.14590	+	0.832544i	0.0698666	+	0.0507611i	0.622170	−	0.782882i	$-0.286251\pi$
$269$	1.14590	+	0.832544i	0.0698666	+	0.0507611i	−0.552304	+	0.833643i	$0.686251\pi$
$270$		0			0
$271$	5.06231	−	15.5802i	0.307513	−	0.946428i	−0.671214	−	0.741263i	$-0.734227\pi$
$271$	5.06231	−	15.5802i	0.307513	−	0.946428i	0.978727	−	0.205165i	$-0.0657731\pi$
$272$	7.63525	+	23.4989i	0.462955	+	1.42483i
$273$		0			0
$274$	−5.43769			−0.328503
$275$	4.02786	−	6.79615i	0.242889	−	0.409823i
$276$		0			0
$277$	−17.9721	+	13.0575i	−1.07984	+	0.784550i	−0.977655	−	0.210215i	$-0.932584\pi$
$277$	−17.9721	+	13.0575i	−1.07984	+	0.784550i	−0.102186	+	0.994765i	$0.532584\pi$
$278$	−0.656541	−	2.02063i	−0.0393767	−	0.121189i
$279$		0			0
$280$	1.92705	+	1.40008i	0.115163	+	0.0836711i
$281$	23.6525	+	17.1845i	1.41099	+	1.02514i	0.993178	+	0.116609i	$0.0372024\pi$
$281$	23.6525	+	17.1845i	1.41099	+	1.02514i	0.417811	+	0.908534i	$0.362798\pi$
$282$		0			0
$283$	2.38197	+	7.33094i	0.141593	+	0.435779i	0.996557	−	0.0829083i	$-0.0264209\pi$
$283$	2.38197	+	7.33094i	0.141593	+	0.435779i	−0.854964	+	0.518687i	$0.826421\pi$
$284$	7.98936	−	5.80461i	0.474081	−	0.344440i
$285$		0			0
$286$	−4.92705	+	2.12663i	−0.291343	+	0.125750i
$287$	−4.23607			−0.250047
$288$		0			0
$289$	13.8090	+	42.4998i	0.812295	+	2.49999i
$290$	−1.14590	+	3.52671i	−0.0672894	+	0.207096i
$291$		0			0
$292$	11.5623	+	8.40051i	0.676633	+	0.491602i
$293$	−2.98278	+	9.18005i	−0.174256	+	0.536304i	−0.999599	−	0.0283276i	$-0.990982\pi$
$293$	−2.98278	+	9.18005i	−0.174256	+	0.536304i	0.825343	+	0.564632i	$0.190982\pi$
$294$		0			0
$295$	−12.5902	+	9.14729i	−0.733028	+	0.532576i
$296$	2.59675			0.150933
$297$		0			0
$298$	−0.0901699			−0.00522340
$299$	14.5172	−	10.5474i	0.839553	−	0.609971i
$300$		0			0
$301$	−2.07295	+	6.37988i	−0.119483	+	0.367730i
$302$	−5.85410	−	4.25325i	−0.336866	−	0.244747i
$303$		0			0
$304$	−0.830303	+	2.55541i	−0.0476212	+	0.146563i
$305$	−4.28115	−	13.1760i	−0.245138	−	0.754458i
$306$		0			0
$307$	−18.9787			−1.08317			−0.541586	−	0.840645i	$-0.682176\pi$
$307$	−18.9787			−1.08317			−0.541586	+	0.840645i	$0.682176\pi$
$308$	−0.572949	−	6.12261i	−0.0326468	−	0.348868i
$309$		0			0
$310$	2.54508	−	1.84911i	0.144551	−	0.105023i
$311$	6.07295	+	18.6906i	0.344365	+	1.05985i	0.961923	+	0.273322i	$0.0881223\pi$
$311$	6.07295	+	18.6906i	0.344365	+	1.05985i	−0.617557	+	0.786526i	$0.711878\pi$
$312$		0			0
$313$	9.28115	+	6.74315i	0.524602	+	0.381146i	0.818335	−	0.574742i	$-0.194898\pi$
$313$	9.28115	+	6.74315i	0.524602	+	0.381146i	−0.293733	+	0.955888i	$0.594898\pi$
$314$	−0.708204	−	0.514540i	−0.0399663	−	0.0290372i
$315$		0			0
$316$	−6.30244	−	19.3969i	−0.354540	−	1.09116i
$317$	−23.6074	+	17.1518i	−1.32592	+	0.963340i	−0.326085	+	0.945340i	$0.605730\pi$
$317$	−23.6074	+	17.1518i	−1.32592	+	0.963340i	−0.999838	+	0.0179992i	$0.994270\pi$
$318$		0			0
$319$	18.2705	−	7.88597i	1.02295	−	0.441529i
$320$	7.61803			0.425861
$321$		0			0
$322$	−0.500000	−	1.53884i	−0.0278639	−	0.0857563i
$323$	−2.07295	+	6.37988i	−0.115342	+	0.354986i
$324$		0			0
$325$	−8.16312	−	5.93085i	−0.452808	−	0.328985i
$326$	−1.39919	+	4.30625i	−0.0774938	+	0.238501i
$327$		0			0
$328$	5.04508	−	3.66547i	0.278568	−	0.202392i
$329$	1.09017			0.0601030
$330$		0			0
$331$	3.29180			0.180933			0.0904667	−	0.995899i	$-0.471164\pi$
$331$	3.29180			0.180933			0.0904667	+	0.995899i	$0.471164\pi$
$332$	11.2082	−	8.14324i	0.615130	−	0.446918i
$333$		0			0
$334$	2.01064	−	6.18812i	0.110017	−	0.338599i
$335$	−6.35410	−	4.61653i	−0.347162	−	0.252228i
$336$		0			0
$337$	1.29180	−	3.97574i	0.0703686	−	0.216572i	−0.909687	−	0.415294i	$-0.863679\pi$
$337$	1.29180	−	3.97574i	0.0703686	−	0.216572i	0.980056	+	0.198721i	$0.0636788\pi$
$338$	0.583592	+	1.79611i	0.0317432	+	0.0976956i
$339$		0			0
$340$	23.5623			1.27785
$341$	−16.4721	−	3.69822i	−0.892016	−	0.200270i
$342$		0			0
$343$	−10.5172	+	7.64121i	−0.567877	+	0.412586i
$344$	−3.05166	−	9.39205i	−0.164535	−	0.506386i
$345$		0			0
$346$	3.40983	+	2.47739i	0.183314	+	0.133185i
$347$	−8.47214	−	6.15537i	−0.454808	−	0.330437i	0.336683	−	0.941618i	$-0.390695\pi$
$347$	−8.47214	−	6.15537i	−0.454808	−	0.330437i	−0.791491	+	0.611181i	$0.790695\pi$
$348$		0			0
$349$	−0.218847	−	0.673542i	−0.0117146	−	0.0360539i	0.945028	−	0.326988i	$-0.106034\pi$
$349$	−0.218847	−	0.673542i	−0.0117146	−	0.0360539i	−0.956743	+	0.290935i	$0.906034\pi$
$350$	−0.736068	+	0.534785i	−0.0393445	+	0.0285854i
$351$		0			0
$352$	9.08359	+	10.3229i	0.484157	+	0.550211i
$353$	12.0000			0.638696			0.319348	−	0.947638i	$-0.396536\pi$
$353$	12.0000			0.638696			0.319348	+	0.947638i	$0.396536\pi$
$354$		0			0
$355$	−2.66312	−	8.19624i	−0.141344	−	0.435011i
$356$	−2.15654	+	6.63715i	−0.114296	+	0.351768i
$357$		0			0
$358$	−5.39919	−	3.92274i	−0.285356	−	0.207323i
$359$	−1.14590	+	3.52671i	−0.0604782	+	0.186133i	−0.976731	−	0.214468i	$-0.931198\pi$
$359$	−1.14590	+	3.52671i	−0.0604782	+	0.186133i	0.916253	+	0.400600i	$0.131198\pi$
$360$		0			0
$361$	14.7812	−	10.7391i	0.777955	−	0.565218i
$362$	4.38197			0.230311
$363$		0			0
$364$	−7.85410			−0.411667
$365$	10.0902	−	7.33094i	0.528144	−	0.383719i
$366$		0			0
$367$	8.91641	−	27.4419i	0.465433	−	1.43245i	−0.393005	−	0.919536i	$-0.628564\pi$
$367$	8.91641	−	27.4419i	0.465433	−	1.43245i	0.858438	−	0.512918i	$-0.171436\pi$
$368$	−10.7812	−	7.83297i	−0.562006	−	0.408322i
$369$		0			0
$370$	0.336881	−	1.03681i	0.0175136	−	0.0539014i
$371$	−0.809017	−	2.48990i	−0.0420021	−	0.129269i
$372$		0			0
$373$	−34.8885			−1.80646			−0.903230	−	0.429156i	$-0.858811\pi$
$373$	−34.8885			−1.80646			−0.903230	+	0.429156i	$0.858811\pi$
$374$	6.57295	+	7.46969i	0.339879	+	0.386249i
$375$		0			0
$376$	−1.29837	+	0.943324i	−0.0669585	+	0.0486482i
$377$	−7.85410	−	24.1724i	−0.404507	−	1.24494i
$378$		0			0
$379$	−8.80902	−	6.40013i	−0.452489	−	0.328752i	0.338089	−	0.941114i	$-0.390220\pi$
$379$	−8.80902	−	6.40013i	−0.452489	−	0.328752i	−0.790578	+	0.612362i	$0.790220\pi$
$380$	2.07295	+	1.50609i	0.106340	+	0.0772606i
$381$		0			0
$382$	2.73607	+	8.42075i	0.139989	+	0.430843i
$383$	0.572949	−	0.416272i	0.0292763	−	0.0212705i	−0.573051	−	0.819520i	$-0.694240\pi$
$383$	0.572949	−	0.416272i	0.0292763	−	0.0212705i	0.602327	+	0.798249i	$0.294240\pi$
$384$		0			0
$385$	−5.23607	−	1.17557i	−0.266855	−	0.0599126i
$386$	−3.76393			−0.191579
$387$		0			0
$388$	−0.656541	−	2.02063i	−0.0333308	−	0.102582i
$389$	−1.77458	+	5.46158i	−0.0899745	+	0.276913i	−0.985911	−	0.167268i	$-0.946505\pi$
$389$	−1.77458	+	5.46158i	−0.0899745	+	0.276913i	0.895937	+	0.444181i	$0.146505\pi$
$390$		0			0
$391$	−26.9164	−	19.5559i	−1.36122	−	0.988985i
$392$	2.72949	−	8.40051i	0.137860	−	0.424290i
$393$		0			0
$394$	−4.95492	+	3.59996i	−0.249625	+	0.181363i
$395$	−17.7984			−0.895533
$396$		0			0
$397$	−5.29180			−0.265588			−0.132794	−	0.991144i	$-0.542395\pi$
$397$	−5.29180			−0.265588			−0.132794	+	0.991144i	$0.542395\pi$
$398$	2.07295	−	1.50609i	0.103908	−	0.0754933i
$399$		0			0
$400$	−2.31559	+	7.12667i	−0.115780	+	0.356333i
$401$	23.2082	+	16.8617i	1.15896	+	0.842035i	0.989646	−	0.143526i	$-0.0458442\pi$
$401$	23.2082	+	16.8617i	1.15896	+	0.842035i	0.169316	+	0.985562i	$0.445844\pi$
$402$		0			0
$403$	−6.66312	+	20.5070i	−0.331914	+	1.02153i
$404$	−3.30244	−	10.1639i	−0.164302	−	0.505671i
$405$		0			0
$406$	−2.29180			−0.113740
$407$	−5.37132	+	2.31838i	−0.266247	+	0.114918i
$408$		0			0
$409$	−2.00000	+	1.45309i	−0.0988936	+	0.0718504i	−0.636133	−	0.771579i	$-0.719467\pi$
$409$	−2.00000	+	1.45309i	−0.0988936	+	0.0718504i	0.537240	+	0.843430i	$0.319467\pi$
$410$	−0.809017	−	2.48990i	−0.0399545	−	0.122967i
$411$		0			0
$412$	10.4164	+	7.56796i	0.513180	+	0.372847i
$413$	−7.78115	−	5.65334i	−0.382886	−	0.278183i
$414$		0			0
$415$	−3.73607	−	11.4984i	−0.183396	−	0.564436i
$416$	14.2082	−	10.3229i	0.696615	−	0.506120i
$417$		0			0
$418$	0.100813	+	1.07730i	0.00493093	+	0.0526926i
$419$	24.4508			1.19450			0.597251	−	0.802054i	$-0.296260\pi$
$419$	24.4508			1.19450			0.597251	+	0.802054i	$0.296260\pi$
$420$		0			0
$421$	−8.50000	−	26.1603i	−0.414265	−	1.27498i	−0.912907	−	0.408168i	$-0.866168\pi$
$421$	−8.50000	−	26.1603i	−0.414265	−	1.27498i	0.498642	−	0.866808i	$-0.333832\pi$
$422$	0.163119	−	0.502029i	0.00794051	−	0.0244384i
$423$		0			0
$424$	3.11803	+	2.26538i	0.151425	+	0.110017i
$425$	−5.78115	+	17.7926i	−0.280427	+	0.863066i
$426$		0			0
$427$	6.92705	−	5.03280i	0.335223	−	0.243554i
$428$	−4.68692			−0.226551
$429$		0			0
$430$	−4.14590			−0.199933
$431$	−13.8262	+	10.0453i	−0.665986	+	0.483867i	−0.868679	−	0.495375i	$-0.835031\pi$
$431$	−13.8262	+	10.0453i	−0.665986	+	0.483867i	0.202693	+	0.979242i	$0.435031\pi$
$432$		0			0
$433$	−8.43769	+	25.9686i	−0.405490	+	1.24797i	0.514996	+	0.857193i	$0.327793\pi$
$433$	−8.43769	+	25.9686i	−0.405490	+	1.24797i	−0.920486	+	0.390776i	$0.872207\pi$
$434$	1.57295	+	1.14281i	0.0755040	+	0.0548568i
$435$		0			0
$436$	6.87539	−	21.1603i	0.329271	−	1.01339i
$437$	−1.11803	−	3.44095i	−0.0534828	−	0.164603i
$438$		0			0
$439$	36.7082			1.75199			0.875993	−	0.482323i	$-0.160207\pi$
$439$	36.7082			1.75199			0.875993	+	0.482323i	$0.160207\pi$
$440$	7.25329	−	3.13068i	0.345787	−	0.149250i
$441$		0			0
$442$	10.2812	−	7.46969i	0.489025	−	0.355297i
$443$	−5.43769	−	16.7355i	−0.258353	−	0.795128i	−0.993151	−	0.116842i	$-0.962723\pi$
$443$	−5.43769	−	16.7355i	−0.258353	−	0.795128i	0.734798	−	0.678286i	$-0.237277\pi$
$444$		0			0
$445$	4.92705	+	3.57971i	0.233565	+	0.169695i
$446$	4.69098	+	3.40820i	0.222124	+	0.161383i
$447$		0			0
$448$	1.45492	+	4.47777i	0.0687383	+	0.211555i
$449$	−21.7984	+	15.8374i	−1.02873	+	0.747415i	−0.968054	−	0.250742i	$-0.919325\pi$
$449$	−21.7984	+	15.8374i	−1.02873	+	0.747415i	−0.0606750	+	0.998158i	$0.519325\pi$
$450$		0			0
$451$	−7.16312	+	12.0862i	−0.337298	+	0.569118i
$452$	8.39512			0.394873
$453$		0			0
$454$	1.08359	+	3.33495i	0.0508555	+	0.156517i
$455$	−2.11803	+	6.51864i	−0.0992950	+	0.305598i
$456$		0			0
$457$	18.5902	+	13.5065i	0.869611	+	0.631810i	0.930483	−	0.366336i	$-0.119388\pi$
$457$	18.5902	+	13.5065i	0.869611	+	0.631810i	−0.0608712	+	0.998146i	$0.519388\pi$
$458$	−1.00000	+	3.07768i	−0.0467269	+	0.143811i
$459$		0			0
$460$	−10.2812	+	7.46969i	−0.479361	+	0.348276i
$461$	24.2705			1.13039			0.565195	−	0.824957i	$-0.308801\pi$
$461$	24.2705			1.13039			0.565195	+	0.824957i	$0.308801\pi$
$462$		0			0
$463$	35.2705			1.63916			0.819580	−	0.572965i	$-0.194207\pi$
$463$	35.2705			1.63916			0.819580	+	0.572965i	$0.194207\pi$
$464$	−15.2705	+	11.0947i	−0.708916	+	0.515057i
$465$		0			0
$466$	1.28115	−	3.94298i	0.0593483	−	0.182655i
$467$	−12.0451	−	8.75127i	−0.557380	−	0.404960i	0.273119	−	0.961980i	$-0.411945\pi$
$467$	−12.0451	−	8.75127i	−0.557380	−	0.404960i	−0.830499	+	0.557020i	$0.811945\pi$
$468$		0			0
$469$	1.50000	−	4.61653i	0.0692636	−	0.213171i
$470$	0.208204	+	0.640786i	0.00960373	+	0.0295572i
$471$		0			0
$472$	14.1591			0.651723
$473$	14.6976	+	16.7027i	0.675795	+	0.767993i
$474$		0			0
$475$	−1.64590	+	1.19581i	−0.0755190	+	0.0548678i
$476$	4.50000	+	13.8496i	0.206257	+	0.634794i
$477$		0			0
$478$	0.809017	+	0.587785i	0.0370036	+	0.0268847i
$479$	−24.7705	−	17.9968i	−1.13179	−	0.822296i	−0.145839	−	0.989308i	$-0.546588\pi$
$479$	−24.7705	−	17.9968i	−1.13179	−	0.822296i	−0.985955	+	0.167012i	$0.946588\pi$
$480$		0			0
$481$	2.30902	+	7.10642i	0.105282	+	0.324025i
$482$	−6.70820	+	4.87380i	−0.305550	+	0.221995i
$483$		0			0
$484$	−18.4377	−	8.71851i	−0.838077	−	0.396296i
$485$	−1.85410			−0.0841904
$486$		0			0
$487$	0.218847	+	0.673542i	0.00991691	+	0.0305211i	0.955893	−	0.293717i	$-0.0948922\pi$
$487$	0.218847	+	0.673542i	0.00991691	+	0.0305211i	−0.945976	+	0.324238i	$0.894892\pi$
$488$	−3.89512	+	11.9880i	−0.176324	+	0.542669i
$489$		0			0
$490$	−3.00000	−	2.17963i	−0.135526	−	0.0984655i
$491$	8.98936	−	27.6664i	0.405684	−	1.24857i	−0.514639	−	0.857407i	$-0.672074\pi$
$491$	8.98936	−	27.6664i	0.405684	−	1.24857i	0.920323	−	0.391160i	$-0.127926\pi$
$492$		0			0
$493$	−38.1246	+	27.6992i	−1.71705	+	1.24751i
$494$	1.38197			0.0621776
$495$		0			0
$496$	16.0132			0.719012
$497$	4.30902	−	3.13068i	0.193286	−	0.140430i
$498$		0			0
$499$	−7.68034	+	23.6377i	−0.343819	+	1.05817i	0.618394	+	0.785868i	$0.287784\pi$
$499$	−7.68034	+	23.6377i	−0.343819	+	1.05817i	−0.962213	+	0.272298i	$0.912216\pi$
$500$	17.9164	+	13.0170i	0.801246	+	0.582139i
$501$		0			0
$502$	−2.94834	+	9.07405i	−0.131591	+	0.404995i
$503$	7.00000	+	21.5438i	0.312115	+	0.960590i	0.976926	+	0.213579i	$0.0685119\pi$
$503$	7.00000	+	21.5438i	0.312115	+	0.960590i	−0.664811	+	0.747011i	$0.731488\pi$
$504$		0			0
$505$	−9.32624			−0.415012
$506$	−5.23607	−	1.17557i	−0.232772	−	0.0522605i
$507$		0			0
$508$	−8.56231	+	6.22088i	−0.379891	+	0.276007i
$509$	1.15654	+	3.55947i	0.0512628	+	0.157771i	0.973411	−	0.229067i	$-0.0735674\pi$
$509$	1.15654	+	3.55947i	0.0512628	+	0.157771i	−0.922148	+	0.386837i	$0.873567\pi$
$510$		0			0
$511$	6.23607	+	4.53077i	0.275867	+	0.200429i
$512$	−18.0451	−	13.1105i	−0.797488	−	0.579409i
$513$		0			0
$514$	1.50407	+	4.62904i	0.0663415	+	0.204178i
$515$	9.09017	−	6.60440i	0.400561	−	0.291024i
$516$		0			0
$517$	1.84346	−	3.11044i	0.0810752	−	0.136797i
$518$	0.673762			0.0296034
$519$		0			0
$520$	−3.11803	−	9.59632i	−0.136735	−	0.420827i
$521$	2.76393	−	8.50651i	0.121090	−	0.372677i	−0.872078	−	0.489366i	$-0.837228\pi$
$521$	2.76393	−	8.50651i	0.121090	−	0.372677i	0.993168	+	0.116689i	$0.0372282\pi$
$522$		0			0
$523$	12.3541	+	8.97578i	0.540207	+	0.392483i	0.824162	−	0.566354i	$-0.191647\pi$
$523$	12.3541	+	8.97578i	0.540207	+	0.392483i	−0.283955	+	0.958838i	$0.591647\pi$
$524$	7.33282	−	22.5681i	0.320336	−	0.985891i
$525$		0			0
$526$	5.64590	−	4.10199i	0.246173	−	0.178855i
$527$	39.9787			1.74150
$528$		0			0
$529$	−5.05573			−0.219814
$530$	1.30902	−	0.951057i	0.0568601	−	0.0413113i
$531$		0			0
$532$	−0.489357	+	1.50609i	−0.0212163	+	0.0652971i
$533$	14.5172	+	10.5474i	0.628811	+	0.456858i
$534$		0			0
$535$	−1.26393	+	3.88998i	−0.0546445	+	0.168179i
$536$	2.20820	+	6.79615i	0.0953799	+	0.293549i
$537$		0			0
$538$	−0.541020			−0.0233250
$539$	1.85410	+	19.8132i	0.0798618	+	0.853414i
$540$		0			0
$541$	36.8156	−	26.7481i	1.58283	−	1.14999i	0.669462	−	0.742846i	$-0.266525\pi$
$541$	36.8156	−	26.7481i	1.58283	−	1.14999i	0.913364	−	0.407144i	$-0.133475\pi$
$542$	1.93363	+	5.95110i	0.0830565	+	0.255622i
$543$		0			0
$544$	−26.3435	−	19.1396i	−1.12947	−	0.820605i
$545$	−15.7082	−	11.4127i	−0.672866	−	0.488865i
$546$		0			0
$547$	3.62868	+	11.1679i	0.155151	+	0.477506i	0.998176	−	0.0603684i	$-0.0192275\pi$
$547$	3.62868	+	11.1679i	0.155151	+	0.477506i	−0.843025	+	0.537874i	$0.819228\pi$
$548$	−21.3541	+	15.5147i	−0.912202	+	0.662754i
$549$		0			0
$550$	0.281153	+	3.00444i	0.0119884	+	0.128110i
$551$	−5.12461			−0.218316
$552$		0			0
$553$	−3.39919	−	10.4616i	−0.144548	−	0.444873i
$554$	2.62210	−	8.06999i	0.111402	−	0.342861i
$555$		0			0
$556$	−8.34346	−	6.06188i	−0.353841	−	0.257081i
$557$	12.5557	−	38.6426i	0.532003	−	1.63734i	−0.218033	−	0.975941i	$-0.569964\pi$
$557$	12.5557	−	38.6426i	0.532003	−	1.63734i	0.750037	−	0.661396i	$-0.230036\pi$
$558$		0			0
$559$	22.9894	−	16.7027i	0.972346	−	0.706451i
$560$	5.09017			0.215099
$561$		0			0
$562$	−11.1672			−0.471059
$563$	−6.95492	+	5.05304i	−0.293115	+	0.212960i	−0.724617	−	0.689151i	$-0.757984\pi$
$563$	−6.95492	+	5.05304i	−0.293115	+	0.212960i	0.431503	+	0.902112i	$0.357984\pi$
$564$		0			0
$565$	2.26393	−	6.96767i	0.0952443	−	0.293132i
$566$	−2.38197	−	1.73060i	−0.100121	−	0.0727425i
$567$		0			0
$568$	−2.42299	+	7.45718i	−0.101666	+	0.312896i
$569$	−3.65248	−	11.2412i	−0.153120	−	0.471254i	0.844846	−	0.535010i	$-0.179692\pi$
$569$	−3.65248	−	11.2412i	−0.153120	−	0.471254i	−0.997966	+	0.0637558i	$0.979692\pi$
$570$		0			0
$571$	2.09017			0.0874709			0.0437354	−	0.999043i	$-0.486074\pi$
$571$	2.09017			0.0874709			0.0437354	+	0.999043i	$0.486074\pi$
$572$	−13.2812	+	22.4091i	−0.555313	+	0.936971i
$573$		0			0
$574$	1.30902	−	0.951057i	0.0546373	−	0.0396963i
$575$	−3.11803	−	9.59632i	−0.130031	−	0.400194i
$576$		0			0
$577$	−14.7984	−	10.7516i	−0.616064	−	0.447597i	0.235480	−	0.971879i	$-0.424334\pi$
$577$	−14.7984	−	10.7516i	−0.616064	−	0.447597i	−0.851545	+	0.524282i	$0.824334\pi$
$578$	−13.8090	−	10.0328i	−0.574379	−	0.417311i
$579$		0			0
$580$	5.56231	+	17.1190i	0.230962	+	0.710829i
$581$	6.04508	−	4.39201i	0.250792	−	0.182211i
$582$		0			0
$583$	−8.47214	−	1.90211i	−0.350880	−	0.0787775i
$584$	−11.3475			−0.469564
$585$		0			0
$586$	−1.13932	−	3.50647i	−0.0470649	−	0.144851i
$587$	−11.7812	+	36.2587i	−0.486260	+	1.49656i	0.343887	+	0.939011i	$0.388256\pi$
$587$	−11.7812	+	36.2587i	−0.486260	+	1.49656i	−0.830147	+	0.557544i	$0.811744\pi$
$588$		0			0
$589$	3.51722	+	2.55541i	0.144925	+	0.105294i
$590$	1.83688	−	5.65334i	0.0756232	−	0.232744i
$591$		0			0
$592$	4.48936	−	3.26171i	0.184511	−	0.134055i
$593$	−15.0344			−0.617391			−0.308695	−	0.951161i	$-0.599892\pi$
$593$	−15.0344			−0.617391			−0.308695	+	0.951161i	$0.599892\pi$
$594$		0			0
$595$	12.7082			0.520986
$596$	−0.354102	+	0.257270i	−0.0145046	+	0.0105382i
$597$		0			0
$598$	−2.11803	+	6.51864i	−0.0866129	+	0.266567i
$599$	−15.0902	−	10.9637i	−0.616568	−	0.447963i	0.235153	−	0.971958i	$-0.424441\pi$
$599$	−15.0902	−	10.9637i	−0.616568	−	0.447963i	−0.851721	+	0.523996i	$0.824441\pi$
$600$		0			0
$601$	8.92705	−	27.4746i	0.364142	−	1.12071i	−0.586375	−	0.810040i	$-0.699445\pi$
$601$	8.92705	−	27.4746i	0.364142	−	1.12071i	0.950517	−	0.310674i	$-0.100555\pi$
$602$	−0.791796	−	2.43690i	−0.0322712	−	0.0993205i
$603$		0			0
$604$	−35.1246			−1.42920
$605$	−12.2082	+	12.9515i	−0.496334	+	0.526554i
$606$		0			0
$607$	−2.88197	+	2.09387i	−0.116975	+	0.0849876i	−0.644735	−	0.764406i	$-0.723032\pi$
$607$	−2.88197	+	2.09387i	−0.116975	+	0.0849876i	0.527760	+	0.849394i	$0.323032\pi$
$608$	−1.09424	−	3.36771i	−0.0443771	−	0.136579i
$609$		0			0
$610$	4.28115	+	3.11044i	0.173339	+	0.125938i
$611$	−3.73607	−	2.71441i	−0.151145	−	0.109813i
$612$		0			0
$613$	−8.56231	−	26.3521i	−0.345828	−	1.06435i	−0.961139	−	0.276065i	$-0.910969\pi$
$613$	−8.56231	−	26.3521i	−0.345828	−	1.06435i	0.615311	−	0.788285i	$-0.289031\pi$
$614$	5.86475	−	4.26099i	0.236682	−	0.171959i
$615$		0			0
$616$	3.22542	+	3.66547i	0.129956	+	0.147686i
$617$	11.1803			0.450104			0.225052	−	0.974347i	$-0.427745\pi$
$617$	11.1803			0.450104			0.225052	+	0.974347i	$0.427745\pi$
$618$		0			0
$619$	−4.98278	−	15.3354i	−0.200275	−	0.616382i	−0.999874	−	0.0158490i	$-0.994955\pi$
$619$	−4.98278	−	15.3354i	−0.200275	−	0.616382i	0.799600	−	0.600533i	$-0.205045\pi$
$620$	4.71885	−	14.5231i	0.189513	−	0.583262i
$621$		0			0
$622$	−6.07295	−	4.41226i	−0.243503	−	0.176915i
$623$	−1.16312	+	3.57971i	−0.0465994	+	0.143418i
$624$		0			0
$625$	6.00000	−	4.35926i	0.240000	−	0.174370i
$626$	−4.38197			−0.175139
$627$		0			0
$628$	−4.24922			−0.169562
$629$	11.2082	−	8.14324i	0.446900	−	0.324692i
$630$		0			0
$631$	−9.95492	+	30.6381i	−0.396299	+	1.21968i	0.531646	+	0.846966i	$0.321574\pi$
$631$	−9.95492	+	30.6381i	−0.396299	+	1.21968i	−0.927945	+	0.372716i	$0.878426\pi$
$632$	13.1008	+	9.51830i	0.521122	+	0.378618i
$633$		0			0
$634$	3.44427	−	10.6004i	0.136790	−	0.420995i
$635$	2.85410	+	8.78402i	0.113262	+	0.348583i
$636$		0			0
$637$	25.4164			1.00703
$638$	−3.87539	+	6.53888i	−0.153428	+	0.258877i
$639$		0			0
$640$	−13.2082	+	9.59632i	−0.522100	+	0.379328i
$641$	4.29837	+	13.2290i	0.169776	+	0.522515i	0.999356	−	0.0358711i	$-0.0114206\pi$
$641$	4.29837	+	13.2290i	0.169776	+	0.522515i	−0.829581	+	0.558387i	$0.811421\pi$
$642$		0			0
$643$	−11.4443	−	8.31475i	−0.451318	−	0.327902i	0.338798	−	0.940859i	$-0.389980\pi$
$643$	−11.4443	−	8.31475i	−0.451318	−	0.327902i	−0.790116	+	0.612957i	$0.789980\pi$
$644$	−6.35410	−	4.61653i	−0.250387	−	0.181917i
$645$		0			0
$646$	−0.791796	−	2.43690i	−0.0311528	−	0.0958785i
$647$	12.9164	−	9.38432i	0.507796	−	0.368936i	−0.304191	−	0.952611i	$-0.598386\pi$
$647$	12.9164	−	9.38432i	0.507796	−	0.368936i	0.811987	+	0.583676i	$0.198386\pi$
$648$		0			0
$649$	−29.2877	+	12.6412i	−1.14964	+	0.496212i
$650$	3.85410			0.151170
$651$		0			0
$652$	6.79180	+	20.9030i	0.265987	+	0.818625i
$653$	1.04508	−	3.21644i	0.0408973	−	0.125869i	−0.928523	−	0.371274i	$-0.878921\pi$
$653$	1.04508	−	3.21644i	0.0408973	−	0.125869i	0.969421	+	0.245405i	$0.0789210\pi$
$654$		0			0
$655$	−16.7533	−	12.1720i	−0.654605	−	0.475598i
$656$	4.11803	−	12.6740i	0.160782	−	0.494837i
$657$		0			0
$658$	−0.336881	+	0.244758i	−0.0131330	+	0.00954168i
$659$	0.875388			0.0341003			0.0170501	−	0.999855i	$-0.494573\pi$
$659$	0.875388			0.0341003			0.0170501	+	0.999855i	$0.494573\pi$
$660$		0			0
$661$	16.4377			0.639352			0.319676	−	0.947527i	$-0.396426\pi$
$661$	16.4377			0.639352			0.319676	+	0.947527i	$0.396426\pi$
$662$	−1.01722	+	0.739054i	−0.0395354	+	0.0287242i
$663$		0			0
$664$	−3.39919	+	10.4616i	−0.131914	+	0.405990i
$665$	1.11803	+	0.812299i	0.0433555	+	0.0314996i
$666$		0			0
$667$	7.85410	−	24.1724i	0.304112	−	0.935961i
$668$	−9.75987	−	30.0378i	−0.377621	−	1.16220i
$669$		0			0
$670$	3.00000			0.115900
$671$	−2.64590	−	28.2744i	−0.102144	−	1.09152i
$672$		0			0
$673$	14.4271	−	10.4819i	0.556122	−	0.404046i	−0.273916	−	0.961754i	$-0.588319\pi$
$673$	14.4271	−	10.4819i	0.556122	−	0.404046i	0.830038	+	0.557707i	$0.188319\pi$
$674$	0.493422	+	1.51860i	0.0190059	+	0.0584942i
$675$		0			0
$676$	7.41641	+	5.38834i	0.285246	+	0.207244i
$677$	18.1803	+	13.2088i	0.698727	+	0.507655i	0.879517	−	0.475867i	$-0.157866\pi$
$677$	18.1803	+	13.2088i	0.698727	+	0.507655i	−0.180790	+	0.983522i	$0.557866\pi$
$678$		0			0
$679$	−0.354102	−	1.08981i	−0.0135892	−	0.0418232i
$680$	−15.1353	+	10.9964i	−0.580411	+	0.421693i
$681$		0			0
$682$	5.92047	−	2.55541i	0.226707	−	0.0978517i
$683$	49.0689			1.87757			0.938784	−	0.344505i	$-0.111953\pi$
$683$	49.0689			1.87757			0.938784	+	0.344505i	$0.111953\pi$
$684$		0			0
$685$	7.11803	+	21.9071i	0.271966	+	0.837026i
$686$	1.53444	−	4.72253i	0.0585853	−	0.180307i
$687$		0			0
$688$	−17.0729	−	12.4042i	−0.650900	−	0.472907i
$689$	−3.42705	+	10.5474i	−0.130560	+	0.401823i
$690$		0			0
$691$	−26.4164	+	19.1926i	−1.00493	+	0.730123i	−0.963139	−	0.269004i	$-0.913306\pi$
$691$	−26.4164	+	19.1926i	−1.00493	+	0.730123i	−0.0417884	+	0.999126i	$0.513306\pi$
$692$	20.4590			0.777734
$693$		0			0
$694$	4.00000			0.151838
$695$	−7.28115	+	5.29007i	−0.276190	+	0.200664i
$696$		0			0
$697$	10.2812	−	31.6421i	0.389426	−	1.19853i
$698$	0.218847	+	0.159002i	0.00828348	+	0.00601830i
$699$		0			0
$700$	−1.36475	+	4.20025i	−0.0515825	+	0.158755i
$701$	3.15248	+	9.70232i	0.119067	+	0.366452i	0.992774	−	0.120002i	$-0.0382902\pi$
$701$	3.15248	+	9.70232i	0.119067	+	0.366452i	−0.873706	+	0.486454i	$0.838290\pi$
$702$		0			0
$703$	1.50658			0.0568217
$704$	15.2361	+	3.42071i	0.574231	+	0.128923i
$705$		0			0
$706$	−3.70820	+	2.69417i	−0.139560	+	0.101396i
$707$	−1.78115	−	5.48183i	−0.0669872	−	0.206165i
$708$		0			0
$709$	32.5344	+	23.6377i	1.22186	+	0.887731i	0.996253	−	0.0864884i	$-0.0275645\pi$
$709$	32.5344	+	23.6377i	1.22186	+	0.887731i	0.225604	+	0.974219i	$0.427565\pi$
$710$	2.66312	+	1.93487i	0.0999451	+	0.0726143i
$711$		0			0
$712$	−1.71227	−	5.26982i	−0.0641700	−	0.197495i
$713$	−17.4443	+	12.6740i	−0.653293	+	0.474645i
$714$		0			0
$715$	15.0172	+	17.0660i	0.561612	+	0.638233i
$716$	−32.3951			−1.21066
$717$		0			0
$718$	−0.437694	−	1.34708i	−0.0163346	−	0.0502727i
$719$	−14.3647	+	44.2101i	−0.535715	+	1.64876i	0.206385	+	0.978471i	$0.433830\pi$
$719$	−14.3647	+	44.2101i	−0.535715	+	1.64876i	−0.742100	+	0.670289i	$0.766170\pi$
$720$		0			0
$721$	5.61803	+	4.08174i	0.209227	+	0.152012i
$722$	−2.15654	+	6.63715i	−0.0802582	+	0.247009i
$723$		0			0
$724$	17.2082	−	12.5025i	0.639538	−	0.464651i
$725$	−14.2918			−0.530784
$726$		0			0
$727$	−15.8541			−0.587996			−0.293998	−	0.955806i	$-0.594986\pi$
$727$	−15.8541			−0.587996			−0.293998	+	0.955806i	$0.594986\pi$
$728$	5.04508	−	3.66547i	0.186983	−	0.135851i
$729$		0			0
$730$	−1.47214	+	4.53077i	−0.0544862	+	0.167691i
$731$	−42.6246	−	30.9686i	−1.57653	−	1.14541i
$732$		0			0
$733$	−15.3262	+	47.1693i	−0.566088	+	1.74224i	0.0986105	+	0.995126i	$0.468560\pi$
$733$	−15.3262	+	47.1693i	−0.566088	+	1.74224i	−0.664698	+	0.747112i	$0.731440\pi$
$734$	3.40576	+	10.4819i	0.125709	+	0.386893i
$735$		0			0
$736$	17.5623			0.647355
$737$	−10.6353	−	12.0862i	−0.391755	−	0.445202i
$738$		0			0
$739$	−2.42705	+	1.76336i	−0.0892805	+	0.0648661i	−0.631530	−	0.775351i	$-0.717573\pi$
$739$	−2.42705	+	1.76336i	−0.0892805	+	0.0648661i	0.542250	+	0.840218i	$0.317573\pi$
$740$	−1.63525	−	5.03280i	−0.0601132	−	0.185009i
$741$		0			0
$742$	0.809017	+	0.587785i	0.0296999	+	0.0215783i
$743$	−5.75329	−	4.18001i	−0.211068	−	0.153350i	0.477229	−	0.878779i	$-0.341641\pi$
$743$	−5.75329	−	4.18001i	−0.211068	−	0.153350i	−0.688297	+	0.725429i	$0.741641\pi$
$744$		0			0
$745$	0.118034	+	0.363271i	0.00432443	+	0.0133092i
$746$	10.7812	−	7.83297i	0.394726	−	0.286785i
$747$		0			0
$748$	47.1246	+	10.5801i	1.72305	+	0.386848i
$749$	−2.52786			−0.0923661
$750$		0			0
$751$	7.06231	+	21.7355i	0.257707	+	0.793141i	0.993284	+	0.115700i	$0.0369111\pi$
$751$	7.06231	+	21.7355i	0.257707	+	0.793141i	−0.735577	+	0.677441i	$0.763089\pi$
$752$	−1.05979	+	3.26171i	−0.0386467	+	0.118942i
$753$		0			0
$754$	7.85410	+	5.70634i	0.286030	+	0.207813i
$755$	−9.47214	+	29.1522i	−0.344726	+	1.06096i
$756$		0			0
$757$	−4.04508	+	2.93893i	−0.147021	+	0.106817i	−0.658864	−	0.752262i	$-0.728963\pi$
$757$	−4.04508	+	2.93893i	−0.147021	+	0.106817i	0.511843	+	0.859079i	$0.328963\pi$
$758$	4.15905			0.151064
$759$		0			0
$760$	−2.03444			−0.0737970
$761$	34.5517	−	25.1033i	1.25250	−	0.909992i	0.254133	−	0.967169i	$-0.418210\pi$
$761$	34.5517	−	25.1033i	1.25250	−	0.909992i	0.998364	+	0.0571772i	$0.0182100\pi$
$762$		0			0
$763$	3.70820	−	11.4127i	0.134246	−	0.413167i
$764$	34.7705	+	25.2623i	1.25795	+	0.913956i
$765$		0			0
$766$	−0.0835921	+	0.257270i	−0.00302031	+	0.00929555i
$767$	12.5902	+	38.7486i	0.454605	+	1.39913i
$768$		0			0
$769$	3.50658			0.126450			0.0632252	−	0.997999i	$-0.479861\pi$
$769$	3.50658			0.126450			0.0632252	+	0.997999i	$0.479861\pi$
$770$	1.88197	−	0.812299i	0.0678213	−	0.0292732i
$771$		0			0
$772$	−14.7812	+	10.7391i	−0.531985	+	0.386510i
$773$	−1.48936	−	4.58377i	−0.0535684	−	0.164867i	0.920693	−	0.390287i	$-0.127624\pi$
$773$	−1.48936	−	4.58377i	−0.0535684	−	0.164867i	−0.974262	+	0.225421i	$0.927624\pi$
$774$		0			0
$775$	9.80902	+	7.12667i	0.352350	+	0.255997i
$776$	1.36475	+	0.991545i	0.0489915	+	0.0355944i
$777$		0			0
$778$	−0.677827	−	2.08614i	−0.0243013	−	0.0747917i
$779$	2.92705	−	2.12663i	0.104872	−	0.0761943i
$780$		0			0
$781$	−1.64590	−	17.5883i	−0.0588949	−	0.629358i
$782$	12.7082			0.454444
$783$		0			0
$784$	−5.83282	−	17.9516i	−0.208315	−	0.641127i
$785$	−1.14590	+	3.52671i	−0.0408989	+	0.125874i
$786$		0			0
$787$	−3.00000	−	2.17963i	−0.106938	−	0.0776953i	0.533031	−	0.846096i	$-0.321053\pi$
$787$	−3.00000	−	2.17963i	−0.106938	−	0.0776953i	−0.639969	+	0.768400i	$0.721053\pi$
$788$	−9.18692	+	28.2744i	−0.327270	+	1.00723i
$789$		0			0
$790$	5.50000	−	3.99598i	0.195681	−	0.142171i
$791$	4.52786			0.160992
$792$		0			0
$793$	−36.2705			−1.28800
$794$	1.63525	−	1.18808i	0.0580330	−	0.0421635i
$795$		0			0
$796$	3.84346	−	11.8290i	0.136228	−	0.419266i
$797$	−39.2705	−	28.5317i	−1.39103	−	1.01064i	−0.995751	−	0.0920845i	$-0.970647\pi$
$797$	−39.2705	−	28.5317i	−1.39103	−	1.01064i	−0.395282	−	0.918560i	$-0.629353\pi$
$798$		0			0
$799$	−2.64590	+	8.14324i	−0.0936051	+	0.288087i
$800$	−3.05166	−	9.39205i	−0.107893	−	0.332059i
$801$		0			0
$802$	−10.9574			−0.386920
$803$	23.4721	−	10.1311i	0.828314	−	0.357519i
$804$		0			0
$805$	−5.54508	+	4.02874i	−0.195439	+	0.141994i
$806$	−2.54508	−	7.83297i	−0.0896468	−	0.275904i
$807$		0			0
$808$	6.86475	+	4.98753i	0.241501	+	0.175461i
$809$	12.8713	+	9.35156i	0.452532	+	0.328783i	0.790594	−	0.612340i	$-0.209772\pi$
$809$	12.8713	+	9.35156i	0.452532	+	0.328783i	−0.338063	+	0.941124i	$0.609772\pi$
$810$		0			0
$811$	5.07953	+	15.6332i	0.178366	+	0.548955i	0.999771	−	0.0213905i	$-0.00680931\pi$
$811$	5.07953	+	15.6332i	0.178366	+	0.548955i	−0.821405	+	0.570346i	$0.806809\pi$
$812$	−9.00000	+	6.53888i	−0.315838	+	0.229470i
$813$		0			0
$814$	1.13932	−	1.92236i	0.0399332	−	0.0673786i
$815$	19.1803			0.671858
$816$		0			0
$817$	−1.77051	−	5.44907i	−0.0619423	−	0.190639i
$818$	0.291796	−	0.898056i	0.0102024	−	0.0313998i
$819$		0			0
$820$	−10.2812	−	7.46969i	−0.359033	−	0.260853i
$821$	2.65654	−	8.17599i	0.0927139	−	0.285344i	−0.893937	−	0.448192i	$-0.852068\pi$
$821$	2.65654	−	8.17599i	0.0927139	−	0.285344i	0.986651	+	0.162848i	$0.0520680\pi$
$822$		0			0
$823$	−20.8992	+	15.1841i	−0.728500	+	0.529286i	−0.889089	−	0.457735i	$-0.848661\pi$
$823$	−20.8992	+	15.1841i	−0.728500	+	0.529286i	0.160589	+	0.987021i	$0.448661\pi$
$824$	−10.2229			−0.356132
$825$		0			0
$826$	3.67376			0.127827
$827$	16.7082	−	12.1392i	0.581001	−	0.422122i	−0.258084	−	0.966123i	$-0.583091\pi$
$827$	16.7082	−	12.1392i	0.581001	−	0.422122i	0.839085	+	0.544000i	$0.183091\pi$
$828$		0			0
$829$	13.1008	−	40.3202i	0.455010	−	1.40038i	−0.416113	−	0.909313i	$-0.636608\pi$
$829$	13.1008	−	40.3202i	0.455010	−	1.40038i	0.871123	−	0.491064i	$-0.163392\pi$
$830$	3.73607	+	2.71441i	0.129681	+	0.0942186i
$831$		0			0
$832$	6.16312	−	18.9681i	0.213668	−	0.657602i
$833$	−14.5623	−	44.8182i	−0.504554	−	1.55286i
$834$		0			0
$835$	−27.5623			−0.953833
$836$	3.46962	+	3.94298i	0.119999	+	0.136371i
$837$		0			0
$838$	−7.55573	+	5.48956i	−0.261008	+	0.189634i
$839$	−11.0729	−	34.0790i	−0.382281	−	1.17654i	−0.938434	−	0.345459i	$-0.887723\pi$
$839$	−11.0729	−	34.0790i	−0.382281	−	1.17654i	0.556153	−	0.831080i	$-0.312277\pi$
$840$		0			0
$841$	−5.66312	−	4.11450i	−0.195280	−	0.141879i
$842$	8.50000	+	6.17561i	0.292929	+	0.212826i
$843$		0			0
$844$	−0.791796	−	2.43690i	−0.0272547	−	0.0838815i
$845$	6.47214	−	4.70228i	0.222648	−	0.161763i
$846$		0			0
$847$	−9.94427	−	4.70228i	−0.341689	−	0.161572i
$848$	8.23607			0.282828
$849$		0			0
$850$	−2.20820	−	6.79615i	−0.0757408	−	0.233106i
$851$	−2.30902	+	7.10642i	−0.0791521	+	0.243605i
$852$		0			0
$853$	1.75329	+	1.27384i	0.0600315	+	0.0436154i	0.617396	−	0.786652i	$-0.288188\pi$
$853$	1.75329	+	1.27384i	0.0600315	+	0.0436154i	−0.557365	+	0.830268i	$0.688188\pi$
$854$	−1.01064	+	3.11044i	−0.0345835	+	0.106437i
$855$		0			0
$856$	3.01064	−	2.18736i	0.102902	−	0.0747624i
$857$	−32.2361			−1.10116			−0.550582	−	0.834781i	$-0.685594\pi$
$857$	−32.2361			−1.10116			−0.550582	+	0.834781i	$0.685594\pi$
$858$		0			0
$859$	−7.58359			−0.258749			−0.129374	−	0.991596i	$-0.541297\pi$
$859$	−7.58359			−0.258749			−0.129374	+	0.991596i	$0.541297\pi$
$860$	−16.2812	+	11.8290i	−0.555183	+	0.403364i
$861$		0			0
$862$	2.01722	−	6.20837i	0.0687068	−	0.211458i
$863$	29.0344	+	21.0948i	0.988344	+	0.718074i	0.959558	−	0.281512i	$-0.0908358\pi$
$863$	29.0344	+	21.0948i	0.988344	+	0.718074i	0.0287861	+	0.999586i	$0.490836\pi$
$864$		0			0
$865$	5.51722	−	16.9803i	0.187591	−	0.577346i
$866$	−3.22291	−	9.91910i	−0.109519	−	0.337065i
$867$		0			0
$868$	9.43769			0.320336
$869$	−35.5967	−	7.99197i	−1.20754	−	0.271109i
$870$		0			0
$871$	−16.6353	+	12.0862i	−0.563664	+	0.409526i
$872$	5.45898	+	16.8010i	0.184864	+	0.568954i
$873$		0			0
$874$	1.11803	+	0.812299i	0.0378181	+	0.0274764i
$875$	9.66312	+	7.02067i	0.326673	+	0.237342i
$876$		0			0
$877$	−12.3779	−	38.0953i	−0.417972	−	1.28639i	−0.909565	−	0.415561i	$-0.863585\pi$
$877$	−12.3779	−	38.0953i	−0.417972	−	1.28639i	0.491593	−	0.870825i	$-0.336415\pi$
$878$	−11.3435	+	8.24151i	−0.382823	+	0.278137i
$879$		0			0
$880$	8.60739	−	14.5231i	0.290155	−	0.489574i
$881$	−30.7984			−1.03762			−0.518812	−	0.854888i	$-0.673625\pi$
$881$	−30.7984			−1.03762			−0.518812	+	0.854888i	$0.673625\pi$
$882$		0			0
$883$	5.85410	+	18.0171i	0.197006	+	0.606323i	0.999947	+	0.0102644i	$0.00326732\pi$
$883$	5.85410	+	18.0171i	0.197006	+	0.606323i	−0.802941	+	0.596058i	$0.796733\pi$
$884$	19.0623	−	58.6677i	0.641135	−	1.97321i
$885$		0			0
$886$	5.43769	+	3.95072i	0.182683	+	0.132727i
$887$	−9.42047	+	28.9932i	−0.316309	+	0.973498i	0.658904	+	0.752227i	$0.271020\pi$
$887$	−9.42047	+	28.9932i	−0.316309	+	0.973498i	−0.975212	+	0.221270i	$0.928980\pi$
$888$		0			0
$889$	−4.61803	+	3.35520i	−0.154884	+	0.112530i
$890$	−2.32624			−0.0779757
$891$		0			0
$892$	28.1459			0.942394
$893$	−0.753289	+	0.547296i	−0.0252079	+	0.0183146i
$894$		0			0
$895$	−8.73607	+	26.8869i	−0.292015	+	0.898728i
$896$	−8.16312	−	5.93085i	−0.272711	−	0.198136i
$897$		0			0
$898$	3.18034	−	9.78808i	0.106129	−	0.326632i
$899$	9.43769	+	29.0462i	0.314765	+	0.968746i
$900$		0			0
$901$	20.5623			0.685030
$902$	−0.500000	−	5.34307i	−0.0166482	−	0.177905i
$903$		0			0
$904$	−5.39261	+	3.91796i	−0.179356	+	0.130309i
$905$	−5.73607	−	17.6538i	−0.190673	−	0.586832i
$906$		0			0
$907$	−25.3992	−	18.4536i	−0.843366	−	0.612741i	0.0799428	−	0.996799i	$-0.474526\pi$
$907$	−25.3992	−	18.4536i	−0.843366	−	0.612741i	−0.923309	+	0.384058i	$0.874526\pi$
$908$	13.7705	+	10.0049i	0.456990	+	0.332023i
$909$		0			0
$910$	−0.809017	−	2.48990i	−0.0268187	−	0.0825393i
$911$	−8.57295	+	6.22861i	−0.284034	+	0.206363i	−0.720675	−	0.693273i	$-0.756168\pi$
$911$	−8.57295	+	6.22861i	−0.284034	+	0.206363i	0.436641	+	0.899636i	$0.356168\pi$
$912$		0			0
$913$	−2.30902	−	24.6745i	−0.0764173	−	0.816606i
$914$	−8.77709			−0.290320
$915$		0			0
$916$	4.85410	+	14.9394i	0.160384	+	0.493611i
$917$	3.95492	−	12.1720i	0.130603	−	0.401954i
$918$		0			0
$919$	4.57295	+	3.32244i	0.150848	+	0.109597i	0.660649	−	0.750695i	$-0.270281\pi$
$919$	4.57295	+	3.32244i	0.150848	+	0.109597i	−0.509801	+	0.860292i	$0.670281\pi$
$920$	3.11803	−	9.59632i	0.102799	−	0.316381i
$921$		0			0
$922$	−7.50000	+	5.44907i	−0.246999	+	0.179456i
$923$	−22.5623			−0.742647
$924$		0			0
$925$	4.20163			0.138149
$926$	−10.8992	+	7.91872i	−0.358170	+	0.260225i
$927$		0			0
$928$	7.68692	−	23.6579i	0.252335	−	0.776609i
$929$	0.572949	+	0.416272i	0.0187978	+	0.0136574i	0.597145	−	0.802134i	$-0.296302\pi$
$929$	0.572949	+	0.416272i	0.0187978	+	0.0136574i	−0.578347	+	0.815791i	$0.696302\pi$
$930$		0			0
$931$	1.58359	−	4.87380i	0.0519001	−	0.159732i
$932$	−6.21885	−	19.1396i	−0.203705	−	0.626940i
$933$		0			0
$934$	5.68692			0.186082
$935$	21.4894	−	36.2587i	0.702777	−	1.18578i
$936$		0			0
$937$	−8.37132	+	6.08212i	−0.273479	+	0.198694i	−0.716068	−	0.698030i	$-0.754060\pi$
$937$	−8.37132	+	6.08212i	−0.273479	+	0.198694i	0.442589	+	0.896725i	$0.354060\pi$
$938$	0.572949	+	1.76336i	0.0187074	+	0.0575756i
$939$		0			0
$940$	2.64590	+	1.92236i	0.0862997	+	0.0627004i
$941$	33.5344	+	24.3642i	1.09319	+	0.794250i	0.979935	−	0.199316i	$-0.0638719\pi$
$941$	33.5344	+	24.3642i	1.09319	+	0.794250i	0.113256	+	0.993566i	$0.463872\pi$
$942$		0			0
$943$	5.54508	+	17.0660i	0.180573	+	0.555746i
$944$	24.4787	−	17.7848i	0.796714	−	0.578847i
$945$		0			0
$946$	−8.29180	−	1.86162i	−0.269590	−	0.0605266i
$947$	−41.3951			−1.34516			−0.672580	−	0.740024i	$-0.734814\pi$
$947$	−41.3951			−1.34516			−0.672580	+	0.740024i	$0.734814\pi$
$948$		0			0
$949$	−10.0902	−	31.0543i	−0.327541	−	1.00807i
$950$	0.240133	−	0.739054i	0.00779095	−	0.0239781i
$951$		0			0
$952$	−9.35410	−	6.79615i	−0.303168	−	0.220265i
$953$	−13.1803	+	40.5649i	−0.426953	+	1.31403i	0.474159	+	0.880439i	$0.342752\pi$
$953$	−13.1803	+	40.5649i	−0.426953	+	1.31403i	−0.901112	+	0.433587i	$0.857248\pi$
$954$		0			0
$955$	30.3435	−	22.0458i	0.981891	−	0.713386i
$956$	4.85410			0.156993
$957$		0			0
$958$	11.6950			0.377850
$959$	−11.5172	+	8.36775i	−0.371910	+	0.270209i
$960$		0			0
$961$	−1.57295	+	4.84104i	−0.0507403	+	0.156163i
$962$	−2.30902	−	1.67760i	−0.0744457	−	0.0540880i
$963$		0			0
$964$	−12.4377	+	38.2793i	−0.400591	+	1.23289i
$965$	4.92705	+	15.1639i	0.158607	+	0.488143i
$966$		0			0
$967$	−20.9230			−0.672838			−0.336419	−	0.941712i	$-0.609216\pi$
$967$	−20.9230			−0.672838			−0.336419	+	0.941712i	$0.609216\pi$
$968$	15.9123	−	3.00444i	0.511442	−	0.0965663i
$969$		0			0
$970$	0.572949	−	0.416272i	0.0183963	−	0.0133657i
$971$	12.9787	+	39.9444i	0.416507	+	1.28188i	0.910896	+	0.412635i	$0.135392\pi$
$971$	12.9787	+	39.9444i	0.416507	+	1.28188i	−0.494389	+	0.869240i	$0.664608\pi$
$972$		0			0
$973$	−4.50000	−	3.26944i	−0.144263	−	0.104813i
$974$	−0.218847	−	0.159002i	−0.00701231	−	0.00509474i
$975$		0			0
$976$	8.32373	+	25.6178i	0.266436	+	0.820006i
$977$	39.3156	−	28.5645i	1.25782	−	0.913858i	0.259169	−	0.965832i	$-0.416551\pi$
$977$	39.3156	−	28.5645i	1.25782	−	0.913858i	0.998648	+	0.0519742i	$0.0165514\pi$
$978$		0			0
$979$	8.24671	+	9.37181i	0.263566	+	0.299524i
$980$	−18.0000			−0.574989
$981$		0			0
$982$	3.43363	+	10.5676i	0.109571	+	0.337226i
$983$	13.5623	−	41.7405i	0.432570	−	1.33131i	−0.462986	−	0.886366i	$-0.653222\pi$
$983$	13.5623	−	41.7405i	0.432570	−	1.33131i	0.895556	−	0.444949i	$-0.146778\pi$
$984$		0			0
$985$	20.9894	+	15.2497i	0.668777	+	0.485895i
$986$	5.56231	−	17.1190i	0.177140	−	0.545181i
$987$		0			0
$988$	5.42705	−	3.94298i	0.172657	−	0.125443i
$989$	28.4164			0.903589
$990$		0			0
$991$	−38.7426			−1.23070			−0.615350	−	0.788254i	$-0.710985\pi$
$991$	−38.7426			−1.23070			−0.615350	+	0.788254i	$0.710985\pi$
$992$	−17.0729	+	12.4042i	−0.542067	+	0.393834i
$993$		0			0
$994$	−0.628677	+	1.93487i	−0.0199404	+	0.0613703i
$995$	−8.78115	−	6.37988i	−0.278381	−	0.202256i
$996$		0			0
$997$	−14.1525	+	43.5568i	−0.448213	+	1.37946i	0.430708	+	0.902492i	$0.358264\pi$
$997$	−14.1525	+	43.5568i	−0.448213	+	1.37946i	−0.878921	+	0.476967i	$0.841736\pi$
$998$	−2.93363	−	9.02878i	−0.0928624	−	0.285801i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.f.a.91.1		4
3.2	odd	2		33.2.e.b.25.1	yes	4
9.2	odd	6		891.2.n.c.190.1		8
9.4	even	3		891.2.n.b.784.1		8
9.5	odd	6		891.2.n.c.784.1		8
9.7	even	3		891.2.n.b.190.1		8
11.2	odd	10		1089.2.a.l.1.2		2
11.4	even	5	inner	99.2.f.a.37.1		4
11.9	even	5		1089.2.a.t.1.1		2
12.11	even	2		528.2.y.b.289.1		4
15.2	even	4		825.2.bx.d.124.2		8
15.8	even	4		825.2.bx.d.124.1		8
15.14	odd	2		825.2.n.c.751.1		4
33.2	even	10		363.2.a.i.1.1		2
33.5	odd	10		363.2.e.k.130.1		4
33.8	even	10		363.2.e.b.148.1		4
33.14	odd	10		363.2.e.k.148.1		4
33.17	even	10		363.2.e.b.130.1		4
33.20	odd	10		363.2.a.d.1.2		2
33.26	odd	10		33.2.e.b.4.1	✓	4
33.29	even	10		363.2.e.f.202.1		4
33.32	even	2		363.2.e.f.124.1		4
99.4	even	15		891.2.n.b.136.1		8
99.59	odd	30		891.2.n.c.136.1		8
99.70	even	15		891.2.n.b.433.1		8
99.92	odd	30		891.2.n.c.433.1		8
132.35	odd	10		5808.2.a.ci.1.2		2
132.59	even	10		528.2.y.b.433.1		4
132.119	even	10		5808.2.a.cj.1.2		2
165.59	odd	10		825.2.n.c.301.1		4
165.92	even	20		825.2.bx.d.499.1		8
165.119	odd	10		9075.2.a.cb.1.1		2
165.134	even	10		9075.2.a.u.1.2		2
165.158	even	20		825.2.bx.d.499.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.b.4.1	✓	4	33.26	odd	10
33.2.e.b.25.1	yes	4	3.2	odd	2
99.2.f.a.37.1		4	11.4	even	5	inner
99.2.f.a.91.1		4	1.1	even	1	trivial
363.2.a.d.1.2		2	33.20	odd	10
363.2.a.i.1.1		2	33.2	even	10
363.2.e.b.130.1		4	33.17	even	10
363.2.e.b.148.1		4	33.8	even	10
363.2.e.f.124.1		4	33.32	even	2
363.2.e.f.202.1		4	33.29	even	10
363.2.e.k.130.1		4	33.5	odd	10
363.2.e.k.148.1		4	33.14	odd	10
528.2.y.b.289.1		4	12.11	even	2
528.2.y.b.433.1		4	132.59	even	10
825.2.n.c.301.1		4	165.59	odd	10
825.2.n.c.751.1		4	15.14	odd	2
825.2.bx.d.124.1		8	15.8	even	4
825.2.bx.d.124.2		8	15.2	even	4
825.2.bx.d.499.1		8	165.92	even	20
825.2.bx.d.499.2		8	165.158	even	20
891.2.n.b.136.1		8	99.4	even	15
891.2.n.b.190.1		8	9.7	even	3
891.2.n.b.433.1		8	99.70	even	15
891.2.n.b.784.1		8	9.4	even	3
891.2.n.c.136.1		8	99.59	odd	30
891.2.n.c.190.1		8	9.2	odd	6
891.2.n.c.433.1		8	99.92	odd	30
891.2.n.c.784.1		8	9.5	odd	6
1089.2.a.l.1.2		2	11.2	odd	10
1089.2.a.t.1.1		2	11.9	even	5
5808.2.a.ci.1.2		2	132.35	odd	10
5808.2.a.cj.1.2		2	132.119	even	10
9075.2.a.u.1.2		2	165.134	even	10
9075.2.a.cb.1.1		2	165.119	odd	10

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.224514i) q^{2} +(-0.572949 + 1.76336i) q^{4} +(1.30902 + 0.951057i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(-0.454915 - 1.40008i) q^{8} -0.618034 q^{10} +(2.19098 + 2.48990i) q^{11} +(3.42705 - 2.48990i) q^{13} +(-0.118034 - 0.363271i) q^{14} +(-2.54508 - 1.84911i) q^{16} +(-6.35410 - 4.61653i) q^{17} +(-0.263932 - 0.812299i) q^{19} +(-2.42705 + 1.76336i) q^{20} +(-1.23607 - 0.277515i) q^{22} +4.23607 q^{23} +(-0.736068 - 2.26538i) q^{25} +(-0.500000 + 1.53884i) q^{26} +(-1.50000 - 1.08981i) q^{28} +(1.85410 - 5.70634i) q^{29} +(-4.11803 + 2.99193i) q^{31} +4.14590 q^{32} +3.00000 q^{34} +(-1.30902 + 0.951057i) q^{35} +(-0.545085 + 1.67760i) q^{37} +(0.263932 + 0.191758i) q^{38} +(0.736068 - 2.26538i) q^{40} +(1.30902 + 4.02874i) q^{41} +6.70820 q^{43} +(-5.64590 + 2.43690i) q^{44} +(-1.30902 + 0.951057i) q^{46} +(-0.336881 - 1.03681i) q^{47} +(4.85410 + 3.52671i) q^{49} +(0.736068 + 0.534785i) q^{50} +(2.42705 + 7.46969i) q^{52} +(-2.11803 + 1.53884i) q^{53} +(0.500000 + 5.34307i) q^{55} +1.47214 q^{56} +(0.708204 + 2.17963i) q^{58} +(-2.97214 + 9.14729i) q^{59} +(-6.92705 - 5.03280i) q^{61} +(0.600813 - 1.84911i) q^{62} +(3.80902 - 2.76741i) q^{64} +6.85410 q^{65} -4.85410 q^{67} +(11.7812 - 8.55951i) q^{68} +(0.190983 - 0.587785i) q^{70} +(-4.30902 - 3.13068i) q^{71} +(2.38197 - 7.33094i) q^{73} +(-0.208204 - 0.640786i) q^{74} +1.58359 q^{76} +(-3.04508 + 1.31433i) q^{77} +(-8.89919 + 6.46564i) q^{79} +(-1.57295 - 4.84104i) q^{80} +(-1.30902 - 0.951057i) q^{82} +(-6.04508 - 4.39201i) q^{83} +(-3.92705 - 12.0862i) q^{85} +(-2.07295 + 1.50609i) q^{86} +(2.48936 - 4.20025i) q^{88} +3.76393 q^{89} +(1.30902 + 4.02874i) q^{91} +(-2.42705 + 7.46969i) q^{92} +(0.336881 + 0.244758i) q^{94} +(0.427051 - 1.31433i) q^{95} +(-0.927051 + 0.673542i) q^{97} -2.29180 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 9 q^{4} + 3 q^{5} + q^{7} - 13 q^{8} + 2 q^{10} + 11 q^{11} + 7 q^{13} + 4 q^{14} + q^{16} - 12 q^{17} - 10 q^{19} - 3 q^{20} + 4 q^{22} + 8 q^{23} + 6 q^{25} - 2 q^{26} - 6 q^{28} - 6 q^{29}+ \cdots - 36 q^{98}+O(q^{100}) \) 4 * q + q^2 - 9 * q^4 + 3 * q^5 + q^7 - 13 * q^8 + 2 * q^10 + 11 * q^11 + 7 * q^13 + 4 * q^14 + q^16 - 12 * q^17 - 10 * q^19 - 3 * q^20 + 4 * q^22 + 8 * q^23 + 6 * q^25 - 2 * q^26 - 6 * q^28 - 6 * q^29 - 12 * q^31 + 30 * q^32 + 12 * q^34 - 3 * q^35 + 9 * q^37 + 10 * q^38 - 6 * q^40 + 3 * q^41 - 36 * q^44 - 3 * q^46 - 17 * q^47 + 6 * q^49 - 6 * q^50 + 3 * q^52 - 4 * q^53 + 2 * q^55 - 12 * q^56 - 24 * q^58 + 6 * q^59 - 21 * q^61 + 27 * q^62 + 13 * q^64 + 14 * q^65 - 6 * q^67 + 27 * q^68 + 3 * q^70 - 15 * q^71 + 14 * q^73 + 26 * q^74 + 60 * q^76 - q^77 - 11 * q^79 - 13 * q^80 - 3 * q^82 - 13 * q^83 - 9 * q^85 - 15 * q^86 - 37 * q^88 + 24 * q^89 + 3 * q^91 - 3 * q^92 + 17 * q^94 - 5 * q^95 + 3 * q^97 - 36 * q^98

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