LMFDB - Embedded newform 198.2.l.a.35.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,2,Mod(17,198)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("198.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	198.l (of order $10$, 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:	$1.58103796002$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.64000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 4x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			35.1
Root			$-0.831254 + 1.14412i$ of defining polynomial
Character	$\chi$	$=$	198.35
Dual form			198.2.l.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-1.05822 + 0.343836i) q^{5} +(2.97677 - 4.09718i) q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-1.05822 + 0.343836i) q^{5} +(2.97677 - 4.09718i) q^{7} +(-0.809017 + 0.587785i) q^{8} +1.11268i q^{10} +(-0.0444738 - 3.31633i) q^{11} +(-0.0598171 - 0.0194357i) q^{13} +(-2.97677 - 4.09718i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-0.486257 - 1.49654i) q^{17} +(2.74981 + 3.78479i) q^{19} +(1.05822 + 0.343836i) q^{20} +(-3.16776 - 0.982504i) q^{22} +7.56958i q^{23} +(-3.04348 + 2.21122i) q^{25} +(-0.0369690 + 0.0508834i) q^{26} +(-4.81652 + 1.56498i) q^{28} +(2.03598 + 1.47923i) q^{29} +(0.789035 - 2.42840i) q^{31} +1.00000 q^{32} -1.57356 q^{34} +(-1.74132 + 5.35922i) q^{35} +(0.513743 + 0.373256i) q^{37} +(4.44929 - 1.44566i) q^{38} +(0.654014 - 0.900173i) q^{40} +(6.87375 - 4.99407i) q^{41} +9.52398i q^{43} +(-1.91331 + 2.70911i) q^{44} +(7.19910 + 2.33913i) q^{46} +(0.490895 + 0.675659i) q^{47} +(-5.76257 - 17.7354i) q^{49} +(1.16251 + 3.57783i) q^{50} +(0.0369690 + 0.0508834i) q^{52} +(5.23082 + 1.69960i) q^{53} +(1.18733 + 3.49410i) q^{55} +5.06439i q^{56} +(2.03598 - 1.47923i) q^{58} +(-5.96143 + 8.20521i) q^{59} +(-12.2491 + 3.97997i) q^{61} +(-2.06572 - 1.50083i) q^{62} +(0.309017 - 0.951057i) q^{64} +0.0699821 q^{65} +2.91359 q^{67} +(-0.486257 + 1.49654i) q^{68} +(4.55883 + 3.31218i) q^{70} +(10.5839 - 3.43893i) q^{71} +(-4.19709 + 5.77680i) q^{73} +(0.513743 - 0.373256i) q^{74} -4.67826i q^{76} +(-13.7200 - 9.68974i) q^{77} +(10.7537 + 3.49410i) q^{79} +(-0.654014 - 0.900173i) q^{80} +(-2.62554 - 8.08058i) q^{82} +(-3.48002 - 10.7104i) q^{83} +(1.02913 + 1.41648i) q^{85} +(9.05784 + 2.94307i) q^{86} +(1.98527 + 2.65682i) q^{88} -11.4127i q^{89} +(-0.257694 + 0.187225i) q^{91} +(4.44929 - 6.12392i) q^{92} +(0.794285 - 0.258079i) q^{94} +(-4.21124 - 3.05965i) q^{95} +(1.30963 - 4.03062i) q^{97} -18.6481 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{4} - 2 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^8	$ 8 q - 2 q^{2} - 2 q^{4} - 2 q^{8} + 4 q^{11} - 2 q^{16} - 8 q^{17} - 6 q^{22} + 6 q^{25} - 20 q^{26} - 10 q^{28} + 10 q^{29} - 14 q^{31} + 8 q^{32} - 8 q^{34} + 10 q^{35} + 20 q^{38} - 10 q^{40} - 8 q^{41} - 6 q^{44} + 20 q^{46} + 20 q^{47} + 6 q^{49} - 4 q^{50} + 20 q^{52} + 30 q^{53} + 28 q^{55} + 10 q^{58} - 20 q^{59} + 20 q^{61} + 16 q^{62} - 2 q^{64} - 64 q^{65} - 56 q^{67} - 8 q^{68} + 10 q^{70} + 20 q^{71} - 10 q^{73} - 20 q^{79} + 10 q^{80} + 12 q^{82} - 12 q^{83} + 20 q^{86} - 6 q^{88} + 20 q^{92} - 20 q^{94} + 16 q^{95} - 12 q^{97} - 44 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^8 + 4 * q^11 - 2 * q^16 - 8 * q^17 - 6 * q^22 + 6 * q^25 - 20 * q^26 - 10 * q^28 + 10 * q^29 - 14 * q^31 + 8 * q^32 - 8 * q^34 + 10 * q^35 + 20 * q^38 - 10 * q^40 - 8 * q^41 - 6 * q^44 + 20 * q^46 + 20 * q^47 + 6 * q^49 - 4 * q^50 + 20 * q^52 + 30 * q^53 + 28 * q^55 + 10 * q^58 - 20 * q^59 + 20 * q^61 + 16 * q^62 - 2 * q^64 - 64 * q^65 - 56 * q^67 - 8 * q^68 + 10 * q^70 + 20 * q^71 - 10 * q^73 - 20 * q^79 + 10 * q^80 + 12 * q^82 - 12 * q^83 + 20 * q^86 - 6 * q^88 + 20 * q^92 - 20 * q^94 + 16 * q^95 - 12 * q^97 - 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$

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	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−1.05822	+	0.343836i	−0.473249	+	0.153768i	−0.535924	−	0.844266i	$-0.680037\pi$
$5$	−1.05822	+	0.343836i	−0.473249	+	0.153768i	0.0626753	+	0.998034i	$0.480037\pi$
$6$		0			0
$7$	2.97677	−	4.09718i	1.12511	−	1.54859i	0.328085	−	0.944648i	$-0.393597\pi$
$7$	2.97677	−	4.09718i	1.12511	−	1.54859i	0.797030	−	0.603939i	$-0.206403\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$		0			0
$10$			1.11268i			0.351859i
$11$	−0.0444738	−	3.31633i	−0.0134093	−	0.999910i
$11$	−0.0444738	−	3.31633i	−0.0134093	−	0.999910i
$12$		0			0
$13$	−0.0598171	−	0.0194357i	−0.0165903	−	0.00539051i	0.300710	−	0.953716i	$-0.402776\pi$
$13$	−0.0598171	−	0.0194357i	−0.0165903	−	0.00539051i	−0.317300	+	0.948325i	$0.602776\pi$
$14$	−2.97677	−	4.09718i	−0.795576	−	1.09502i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.486257	−	1.49654i	−0.117935	−	0.362965i	0.874613	−	0.484821i	$-0.161115\pi$
$17$	−0.486257	−	1.49654i	−0.117935	−	0.362965i	−0.992548	+	0.121856i	$0.961115\pi$
$18$		0			0
$19$	2.74981	+	3.78479i	0.630850	+	0.868290i	0.998086	−	0.0618372i	$-0.0196960\pi$
$19$	2.74981	+	3.78479i	0.630850	+	0.868290i	−0.367236	+	0.930128i	$0.619696\pi$
$20$	1.05822	+	0.343836i	0.236624	+	0.0768840i
$21$		0			0
$22$	−3.16776	−	0.982504i	−0.675368	−	0.209471i
$23$			7.56958i			1.57837i	0.614158	+	0.789183i	$0.289496\pi$
$23$			7.56958i			1.57837i	−0.614158	+	0.789183i	$0.710504\pi$
$24$		0			0
$25$	−3.04348	+	2.21122i	−0.608697	+	0.442244i
$26$	−0.0369690	+	0.0508834i	−0.00725021	+	0.00997906i
$27$		0			0
$28$	−4.81652	+	1.56498i	−0.910237	+	0.295754i
$29$	2.03598	+	1.47923i	0.378072	+	0.274685i	0.760550	−	0.649279i	$-0.224929\pi$
$29$	2.03598	+	1.47923i	0.378072	+	0.274685i	−0.382478	+	0.923965i	$0.624929\pi$
$30$		0			0
$31$	0.789035	−	2.42840i	0.141715	−	0.436154i	−0.854859	−	0.518860i	$-0.826356\pi$
$31$	0.789035	−	2.42840i	0.141715	−	0.436154i	0.996574	+	0.0827066i	$0.0263564\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−1.57356			−0.269863
$35$	−1.74132	+	5.35922i	−0.294336	+	0.905874i
$36$		0			0
$37$	0.513743	+	0.373256i	0.0844589	+	0.0613629i	0.629213	−	0.777233i	$-0.283377\pi$
$37$	0.513743	+	0.373256i	0.0844589	+	0.0613629i	−0.544755	+	0.838596i	$0.683377\pi$
$38$	4.44929	−	1.44566i	0.721770	−	0.234517i
$39$		0			0
$40$	0.654014	−	0.900173i	0.103409	−	0.142330i
$41$	6.87375	−	4.99407i	1.07350	−	0.779943i	0.0969614	−	0.995288i	$-0.469088\pi$
$41$	6.87375	−	4.99407i	1.07350	−	0.779943i	0.976538	+	0.215345i	$0.0690877\pi$
$42$		0			0
$43$			9.52398i			1.45239i	0.687487	+	0.726196i	$0.258714\pi$
$43$			9.52398i			1.45239i	−0.687487	+	0.726196i	$0.741286\pi$
$44$	−1.91331	+	2.70911i	−0.288442	+	0.408413i
$45$		0			0
$46$	7.19910	+	2.33913i	1.06145	+	0.344886i
$47$	0.490895	+	0.675659i	0.0716044	+	0.0985550i	0.843317	−	0.537416i	$-0.180600\pi$
$47$	0.490895	+	0.675659i	0.0716044	+	0.0985550i	−0.771713	+	0.635971i	$0.780600\pi$
$48$		0			0
$49$	−5.76257	−	17.7354i	−0.823224	−	2.53362i
$50$	1.16251	+	3.57783i	0.164403	+	0.505982i
$51$		0			0
$52$	0.0369690	+	0.0508834i	0.00512668	+	0.00705626i
$53$	5.23082	+	1.69960i	0.718508	+	0.233457i	0.645376	−	0.763865i	$-0.276701\pi$
$53$	5.23082	+	1.69960i	0.718508	+	0.233457i	0.0731319	+	0.997322i	$0.476701\pi$
$54$		0			0
$55$	1.18733	+	3.49410i	0.160100	+	0.471145i
$56$			5.06439i			0.676758i
$57$		0			0
$58$	2.03598	−	1.47923i	0.267337	−	0.194232i
$59$	−5.96143	+	8.20521i	−0.776112	+	1.06823i	0.219588	+	0.975593i	$0.429529\pi$
$59$	−5.96143	+	8.20521i	−0.776112	+	1.06823i	−0.995700	+	0.0926341i	$0.970471\pi$
$60$		0			0
$61$	−12.2491	+	3.97997i	−1.56834	+	0.509583i	−0.959019	−	0.283343i	$-0.908557\pi$
$61$	−12.2491	+	3.97997i	−1.56834	+	0.509583i	−0.609318	+	0.792926i	$0.708557\pi$
$62$	−2.06572	−	1.50083i	−0.262347	−	0.190606i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	0.0699821			0.00868022
$66$		0			0
$67$	2.91359			0.355951			0.177976	−	0.984035i	$-0.443045\pi$
$67$	2.91359			0.355951			0.177976	+	0.984035i	$0.443045\pi$
$68$	−0.486257	+	1.49654i	−0.0589673	+	0.181483i
$69$		0			0
$70$	4.55883	+	3.31218i	0.544884	+	0.395882i
$71$	10.5839	−	3.43893i	1.25608	−	0.408126i	0.395985	−	0.918257i	$-0.370403\pi$
$71$	10.5839	−	3.43893i	1.25608	−	0.408126i	0.860097	+	0.510131i	$0.170403\pi$
$72$		0			0
$73$	−4.19709	+	5.77680i	−0.491233	+	0.676124i	−0.980615	−	0.195946i	$-0.937222\pi$
$73$	−4.19709	+	5.77680i	−0.491233	+	0.676124i	0.489382	+	0.872069i	$0.337222\pi$
$74$	0.513743	−	0.373256i	0.0597214	−	0.0433902i
$75$		0			0
$76$		−	4.67826i		−	0.536633i
$77$	−13.7200	−	9.68974i	−1.56354	−	1.10425i
$78$		0			0
$79$	10.7537	+	3.49410i	1.20989	+	0.393117i	0.843390	−	0.537301i	$-0.180556\pi$
$79$	10.7537	+	3.49410i	1.20989	+	0.393117i	0.366500	+	0.930418i	$0.380556\pi$
$80$	−0.654014	−	0.900173i	−0.0731210	−	0.100642i
$81$		0			0
$82$	−2.62554	−	8.08058i	−0.289942	−	0.892350i
$83$	−3.48002	−	10.7104i	−0.381982	−	1.17562i	−0.938646	−	0.344881i	$-0.887919\pi$
$83$	−3.48002	−	10.7104i	−0.381982	−	1.17562i	0.556665	−	0.830737i	$-0.312081\pi$
$84$		0			0
$85$	1.02913	+	1.41648i	0.111625	+	0.153638i
$86$	9.05784	+	2.94307i	0.976732	+	0.317359i
$87$		0			0
$88$	1.98527	+	2.65682i	0.211630	+	0.283218i
$89$		−	11.4127i		−	1.20974i	−0.796324	−	0.604871i	$-0.793225\pi$
$89$		−	11.4127i		−	1.20974i	0.796324	−	0.604871i	$-0.206775\pi$
$90$		0			0
$91$	−0.257694	+	0.187225i	−0.0270136	+	0.0196266i
$92$	4.44929	−	6.12392i	0.463870	−	0.638463i
$93$		0			0
$94$	0.794285	−	0.258079i	0.0819242	−	0.0266188i
$95$	−4.21124	−	3.05965i	−0.432064	−	0.313913i
$96$		0			0
$97$	1.30963	−	4.03062i	0.132973	−	0.409248i	−0.862297	−	0.506404i	$-0.830975\pi$
$97$	1.30963	−	4.03062i	0.132973	−	0.409248i	0.995269	+	0.0971561i	$0.0309746\pi$
$98$	−18.6481			−1.88374
$99$		0			0
$100$	3.76195			0.376195
$101$	−3.15964	+	9.72438i	−0.314396	+	0.967612i	0.661606	+	0.749851i	$0.269875\pi$
$101$	−3.15964	+	9.72438i	−0.314396	+	0.967612i	−0.976002	+	0.217760i	$0.930125\pi$
$102$		0			0
$103$	−8.80339	−	6.39604i	−0.867424	−	0.630220i	0.0624706	−	0.998047i	$-0.480102\pi$
$103$	−8.80339	−	6.39604i	−0.867424	−	0.630220i	−0.929894	+	0.367827i	$0.880102\pi$
$104$	0.0598171	−	0.0194357i	0.00586555	−	0.00190583i
$105$		0			0
$106$	3.23282	−	4.44960i	0.314000	−	0.432183i
$107$	−7.43357	+	5.40080i	−0.718630	+	0.522115i	−0.885946	−	0.463788i	$-0.846490\pi$
$107$	−7.43357	+	5.40080i	−0.718630	+	0.522115i	0.167316	+	0.985903i	$0.446490\pi$
$108$		0			0
$109$			6.23591i			0.597292i	0.954364	+	0.298646i	$0.0965349\pi$
$109$			6.23591i			0.597292i	−0.954364	+	0.298646i	$0.903465\pi$
$110$	3.68999	−	0.0494848i	0.351827	−	0.00471820i
$111$		0			0
$112$	4.81652	+	1.56498i	0.455119	+	0.147877i
$113$	−9.30040	−	12.8009i	−0.874908	−	1.20421i	−0.977805	−	0.209515i	$-0.932811\pi$
$113$	−9.30040	−	12.8009i	−0.874908	−	1.20421i	0.102898	−	0.994692i	$-0.467189\pi$
$114$		0			0
$115$	−2.60269	−	8.01026i	−0.242702	−	0.746960i
$116$	−0.777675	−	2.39344i	−0.0722053	−	0.222225i
$117$		0			0
$118$	5.96143	+	8.20521i	0.548794	+	0.755350i
$119$	−7.57909	−	2.46259i	−0.694774	−	0.225746i
$120$		0			0
$121$	−10.9960	+	0.294979i	−0.999640	+	0.0268163i
$122$			12.8795i			1.16605i
$123$		0			0
$124$	−2.06572	+	1.50083i	−0.185507	+	0.134779i
$125$	5.73044	−	7.88728i	0.512546	−	0.705459i
$126$		0			0
$127$	−0.635021	+	0.206331i	−0.0563490	+	0.0183089i	−0.337056	−	0.941485i	$-0.609431\pi$
$127$	−0.635021	+	0.206331i	−0.0563490	+	0.0183089i	0.280707	+	0.959794i	$0.409431\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$		0			0
$130$	0.0216257	−	0.0665570i	0.00189670	−	0.00583743i
$131$	18.7827			1.64105			0.820526	−	0.571609i	$-0.193681\pi$
$131$	18.7827			1.64105			0.820526	+	0.571609i	$0.193681\pi$
$132$		0			0
$133$	23.6925			2.05440
$134$	0.900347	−	2.77098i	0.0777782	−	0.239377i
$135$		0			0
$136$	1.27304	+	0.924915i	0.109162	+	0.0793108i
$137$	−0.600713	+	0.195183i	−0.0513224	+	0.0166756i	−0.334566	−	0.942372i	$-0.608590\pi$
$137$	−0.600713	+	0.195183i	−0.0513224	+	0.0166756i	0.283243	+	0.959048i	$0.408590\pi$
$138$		0			0
$139$	7.68999	−	10.5844i	0.652257	−	0.897754i	−0.346938	−	0.937888i	$-0.612778\pi$
$139$	7.68999	−	10.5844i	0.652257	−	0.897754i	0.999194	+	0.0401338i	$0.0127784\pi$
$140$	4.55883	−	3.31218i	0.385291	−	0.279931i
$141$		0			0
$142$		−	11.1286i		−	0.933892i
$143$	−0.0617950	+	0.199237i	−0.00516756	+	0.0166611i
$144$		0			0
$145$	−2.66312	−	0.865300i	−0.221160	−	0.0718592i
$146$	4.19709	+	5.77680i	0.347354	+	0.478092i
$147$		0			0
$148$	−0.196232	−	0.603941i	−0.0161302	−	0.0496437i
$149$	1.64027	+	5.04823i	0.134376	+	0.413567i	0.995492	−	0.0948406i	$-0.0302341\pi$
$149$	1.64027	+	5.04823i	0.134376	+	0.413567i	−0.861116	+	0.508408i	$0.830234\pi$
$150$		0			0
$151$	4.41453	+	6.07608i	0.359249	+	0.494464i	0.949939	−	0.312434i	$-0.101144\pi$
$151$	4.41453	+	6.07608i	0.359249	+	0.494464i	−0.590690	+	0.806899i	$0.701144\pi$
$152$	−4.44929	−	1.44566i	−0.360885	−	0.117259i
$153$		0			0
$154$	−13.4552	+	10.0542i	−1.08425	+	0.810188i
$155$			2.84107i			0.228201i
$156$		0			0
$157$	−6.81911	+	4.95437i	−0.544224	+	0.395402i	−0.825651	−	0.564180i	$-0.809192\pi$
$157$	−6.81911	+	4.95437i	−0.544224	+	0.395402i	0.281427	+	0.959583i	$0.409192\pi$
$158$	6.64618	−	9.14768i	0.528741	−	0.727750i
$159$		0			0
$160$	−1.05822	+	0.343836i	−0.0836594	+	0.0271826i
$161$	31.0139	+	22.5329i	2.44424	+	1.77584i
$162$		0			0
$163$	2.36198	−	7.26944i	0.185005	−	0.569387i	−0.814944	−	0.579540i	$-0.803232\pi$
$163$	2.36198	−	7.26944i	0.185005	−	0.569387i	0.999948	+	0.0101538i	$0.00323211\pi$
$164$	−8.49642			−0.663459
$165$		0			0
$166$	−11.2616			−0.874068
$167$	−2.26056	+	6.95729i	−0.174927	+	0.538371i	−0.999630	−	0.0271953i	$-0.991342\pi$
$167$	−2.26056	+	6.95729i	−0.174927	+	0.538371i	0.824703	+	0.565566i	$0.191342\pi$
$168$		0			0
$169$	−10.5140	−	7.63888i	−0.808771	−	0.587606i
$170$	1.66517	−	0.541046i	0.127713	−	0.0414963i
$171$		0			0
$172$	5.59805	−	7.70506i	0.426847	−	0.587505i
$173$	−16.9823	+	12.3384i	−1.29114	+	0.938068i	−0.999828	−	0.0185595i	$-0.994092\pi$
$173$	−16.9823	+	12.3384i	−1.29114	+	0.938068i	−0.291313	+	0.956628i	$0.594092\pi$
$174$		0			0
$175$			19.0520i			1.44020i
$176$	3.14027	−	1.06710i	0.236707	−	0.0804356i
$177$		0			0
$178$	−10.8541	−	3.52671i	−0.813549	−	0.264338i
$179$	6.00243	+	8.26163i	0.448642	+	0.617503i	0.972105	−	0.234545i	$-0.0753601\pi$
$179$	6.00243	+	8.26163i	0.448642	+	0.617503i	−0.523463	+	0.852049i	$0.675360\pi$
$180$		0			0
$181$	2.93554	+	9.03468i	0.218197	+	0.671542i	0.998911	+	0.0466536i	$0.0148557\pi$
$181$	2.93554	+	9.03468i	0.218197	+	0.671542i	−0.780714	+	0.624889i	$0.785144\pi$
$182$	0.0984302	+	0.302937i	0.00729613	+	0.0224552i
$183$		0			0
$184$	−4.44929	−	6.12392i	−0.328006	−	0.451461i
$185$	−0.671990	−	0.218343i	−0.0494057	−	0.0160529i
$186$		0			0
$187$	−4.94141	+	1.67914i	−0.361351	+	0.122791i
$188$		−	0.835161i		−	0.0609103i
$189$		0			0
$190$	−4.21124	+	3.05965i	−0.305516	+	0.221970i
$191$	−9.38947	+	12.9235i	−0.679398	+	0.935111i	−0.999926	−	0.0121275i	$-0.996140\pi$
$191$	−9.38947	+	12.9235i	−0.679398	+	0.935111i	0.320528	+	0.947239i	$0.396140\pi$
$192$		0			0
$193$	14.9449	−	4.85589i	1.07576	−	0.349534i	0.283029	−	0.959111i	$-0.408661\pi$
$193$	14.9449	−	4.85589i	1.07576	−	0.349534i	0.792727	+	0.609577i	$0.208661\pi$
$194$	−3.42865	−	2.49106i	−0.246163	−	0.178848i
$195$		0			0
$196$	−5.76257	+	17.7354i	−0.411612	+	1.26681i
$197$	1.66129			0.118362			0.0591808	−	0.998247i	$-0.481151\pi$
$197$	1.66129			0.118362			0.0591808	+	0.998247i	$0.481151\pi$
$198$		0			0
$199$	4.02019			0.284984			0.142492	−	0.989796i	$-0.454489\pi$
$199$	4.02019			0.284984			0.142492	+	0.989796i	$0.454489\pi$
$200$	1.16251	−	3.57783i	0.0822017	−	0.252991i
$201$		0			0
$202$	8.27205	+	6.00999i	0.582019	+	0.422862i
$203$	12.1213	−	3.93845i	0.850749	−	0.276425i
$204$		0			0
$205$	−5.55678	+	7.64825i	−0.388102	+	0.534177i
$206$	−8.80339	+	6.39604i	−0.613361	+	0.445633i
$207$		0			0
$208$		−	0.0628954i		−	0.00436101i
$209$	12.4293	−	9.28760i	0.859753	−	0.642436i
$210$		0			0
$211$	2.36982	+	0.770002i	0.163145	+	0.0530091i	0.389451	−	0.921047i	$-0.372665\pi$
$211$	2.36982	+	0.770002i	0.163145	+	0.0530091i	−0.226306	+	0.974056i	$0.572665\pi$
$212$	−3.23282	−	4.44960i	−0.222031	−	0.305600i
$213$		0			0
$214$	2.83937	+	8.73868i	0.194095	+	0.597364i
$215$	−3.27468	−	10.0784i	−0.223331	−	0.687343i
$216$		0			0
$217$	−7.60081	−	10.4616i	−0.515977	−	0.710181i
$218$	5.93070	+	1.92700i	0.401678	+	0.130513i
$219$		0			0
$220$	1.09321	−	3.52468i	0.0737041	−	0.237634i
$221$			0.0989697i			0.00665742i
$222$		0			0
$223$	−12.6029	+	9.15656i	−0.843954	+	0.613169i	−0.923472	−	0.383665i	$-0.874662\pi$
$223$	−12.6029	+	9.15656i	−0.843954	+	0.613169i	0.0795182	+	0.996833i	$0.474662\pi$
$224$	2.97677	−	4.09718i	0.198894	−	0.273754i
$225$		0			0
$226$	−15.0484	+	4.88951i	−1.00100	+	0.325245i
$227$	−13.5679	−	9.85768i	−0.900535	−	0.654277i	0.0380681	−	0.999275i	$-0.487880\pi$
$227$	−13.5679	−	9.85768i	−0.900535	−	0.654277i	−0.938603	+	0.344998i	$0.887880\pi$
$228$		0			0
$229$	2.26819	−	6.98078i	0.149886	−	0.461303i	−0.847721	−	0.530443i	$-0.822026\pi$
$229$	2.26819	−	6.98078i	0.149886	−	0.461303i	0.997607	+	0.0691402i	$0.0220256\pi$
$230$	−8.42248			−0.555362
$231$		0			0
$232$	−2.51661			−0.165224
$233$	−1.29104	+	3.97341i	−0.0845789	+	0.260307i	−0.984398	−	0.175956i	$-0.943698\pi$
$233$	−1.29104	+	3.97341i	−0.0845789	+	0.260307i	0.899819	+	0.436263i	$0.143698\pi$
$234$		0			0
$235$	−0.751789	−	0.546207i	−0.0490413	−	0.0356306i
$236$	9.64580	−	3.13411i	0.627888	−	0.204013i
$237$		0			0
$238$	−4.68413	+	6.44716i	−0.303627	+	0.417907i
$239$	1.70698	−	1.24019i	0.110415	−	0.0802215i	−0.531207	−	0.847242i	$-0.678261\pi$
$239$	1.70698	−	1.24019i	0.110415	−	0.0802215i	0.641623	+	0.767020i	$0.278261\pi$
$240$		0			0
$241$		−	9.92323i		−	0.639211i	−0.947551	−	0.319606i	$-0.896450\pi$
$241$		−	9.92323i		−	0.639211i	0.947551	−	0.319606i	$-0.103550\pi$
$242$	−3.11742	+	10.5490i	−0.200396	+	0.678116i
$243$		0			0
$244$	12.2491	+	3.97997i	0.784168	+	0.254792i
$245$	12.1961	+	16.7865i	0.779179	+	1.07245i
$246$		0			0
$247$	−0.0909254	−	0.279840i	−0.00578545	−	0.0178058i
$248$	0.789035	+	2.42840i	0.0501038	+	0.154204i
$249$		0			0
$250$	−5.73044	−	7.88728i	−0.362425	−	0.498835i
$251$	0.920157	+	0.298977i	0.0580798	+	0.0188713i	0.337913	−	0.941177i	$-0.390279\pi$
$251$	0.920157	+	0.298977i	0.0580798	+	0.0188713i	−0.279833	+	0.960049i	$0.590279\pi$
$252$		0			0
$253$	25.1032	−	0.336648i	1.57822	−	0.0211649i
$254$			0.667701i			0.0418953i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−7.94128	+	10.9302i	−0.495363	+	0.681809i	−0.981366	−	0.192148i	$-0.938455\pi$
$257$	−7.94128	+	10.9302i	−0.495363	+	0.681809i	0.486003	+	0.873957i	$0.338455\pi$
$258$		0			0
$259$	3.05859	−	0.993798i	0.190052	−	0.0617516i
$260$	−0.0566167	−	0.0411345i	−0.00351122	−	0.00255105i
$261$		0			0
$262$	5.80417	−	17.8634i	0.358583	−	1.10360i
$263$	−1.86140			−0.114779			−0.0573894	−	0.998352i	$-0.518278\pi$
$263$	−1.86140			−0.114779			−0.0573894	+	0.998352i	$0.518278\pi$
$264$		0			0
$265$	−6.11972			−0.375932
$266$	7.32139	−	22.5329i	0.448903	−	1.38158i
$267$		0			0
$268$	−2.35714	−	1.71256i	−0.143985	−	0.104611i
$269$	−19.1589	+	6.22511i	−1.16814	+	0.379552i	−0.827949	−	0.560804i	$-0.810492\pi$
$269$	−19.1589	+	6.22511i	−1.16814	+	0.379552i	−0.340192	+	0.940356i	$0.610492\pi$
$270$		0			0
$271$	−2.20783	+	3.03881i	−0.134116	+	0.184595i	−0.870793	−	0.491650i	$-0.836394\pi$
$271$	−2.20783	+	3.03881i	−0.134116	+	0.184595i	0.736677	+	0.676245i	$0.236394\pi$
$272$	1.27304	−	0.924915i	0.0771892	−	0.0560812i
$273$		0			0
$274$			0.631627i			0.0381580i
$275$	7.46849	+	9.99485i	0.450367	+	0.602712i
$276$		0			0
$277$	11.9289	+	3.87594i	0.716740	+	0.232883i	0.644609	−	0.764512i	$-0.277020\pi$
$277$	11.9289	+	3.87594i	0.716740	+	0.232883i	0.0721307	+	0.997395i	$0.477020\pi$
$278$	−7.68999	−	10.5844i	−0.461215	−	0.634808i
$279$		0			0
$280$	−1.74132	−	5.35922i	−0.104064	−	0.320275i
$281$	−6.33088	−	19.4844i	−0.377668	−	1.16234i	−0.941661	−	0.336564i	$-0.890735\pi$
$281$	−6.33088	−	19.4844i	−0.377668	−	1.16234i	0.563992	−	0.825780i	$-0.309265\pi$
$282$		0			0
$283$	−6.77839	−	9.32966i	−0.402934	−	0.554591i	0.558544	−	0.829475i	$-0.311360\pi$
$283$	−6.77839	−	9.32966i	−0.402934	−	0.554591i	−0.961477	+	0.274885i	$0.911360\pi$
$284$	−10.5839	−	3.43893i	−0.628041	−	0.204063i
$285$		0			0
$286$	0.170390	+	0.120338i	0.0100754	+	0.00711575i
$287$		−	43.0292i		−	2.53993i
$288$		0			0
$289$	11.7501	−	8.53694i	0.691182	−	0.502173i
$290$	−1.64590	+	2.26538i	−0.0966505	+	0.133028i
$291$		0			0
$292$	6.79104	−	2.20654i	0.397416	−	0.129128i
$293$	−11.5578	−	8.39726i	−0.675216	−	0.490573i	0.196551	−	0.980494i	$-0.437026\pi$
$293$	−11.5578	−	8.39726i	−0.675216	−	0.490573i	−0.871767	+	0.489920i	$0.837026\pi$
$294$		0			0
$295$	3.48725	−	10.7326i	0.203035	−	0.624878i
$296$	−0.635021			−0.0369099
$297$		0			0
$298$	5.30803			0.307486
$299$	0.147120	−	0.452790i	0.00850820	−	0.0261855i
$300$		0			0
$301$	39.0214	+	28.3507i	2.24916	+	1.63411i
$302$	7.14286	−	2.32086i	0.411025	−	0.133550i
$303$		0			0
$304$	−2.74981	+	3.78479i	−0.157712	+	0.217073i
$305$	11.5937	−	8.42335i	0.663856	−	0.482320i
$306$		0			0
$307$		−	21.1447i		−	1.20679i	−0.797441	−	0.603396i	$-0.793814\pi$
$307$		−	21.1447i		−	1.20679i	0.797441	−	0.603396i	$-0.206186\pi$
$308$	5.40420	+	15.9036i	0.307933	+	0.906189i
$309$		0			0
$310$	2.70202	+	0.877940i	0.153465	+	0.0498636i
$311$	10.3251	+	14.2113i	0.585485	+	0.805852i	0.994283	−	0.106773i	$-0.0340519\pi$
$311$	10.3251	+	14.2113i	0.585485	+	0.805852i	−0.408798	+	0.912625i	$0.634052\pi$
$312$		0			0
$313$	−2.09055	−	6.43404i	−0.118165	−	0.363674i	0.874429	−	0.485153i	$-0.161236\pi$
$313$	−2.09055	−	6.43404i	−0.118165	−	0.363674i	−0.992594	+	0.121479i	$0.961236\pi$
$314$	2.60467	+	8.01635i	0.146990	+	0.452389i
$315$		0			0
$316$	−6.64618	−	9.14768i	−0.373877	−	0.514597i
$317$	−25.3393	−	8.23323i	−1.42320	−	0.462424i	−0.506579	−	0.862193i	$-0.669090\pi$
$317$	−25.3393	−	8.23323i	−1.42320	−	0.462424i	−0.916616	+	0.399769i	$0.869090\pi$
$318$		0			0
$319$	4.81505	−	6.81776i	0.269591	−	0.381721i
$320$			1.11268i			0.0622004i
$321$		0			0
$322$	31.0139	−	22.5329i	1.72834	−	1.25571i
$323$	4.32699	−	5.95560i	0.240760	−	0.331378i
$324$		0			0
$325$	0.225029	−	0.0731164i	0.0124824	−	0.00405577i
$326$	−6.18376	−	4.49276i	−0.342487	−	0.248831i
$327$		0			0
$328$	−2.62554	+	8.08058i	−0.144971	+	0.446175i
$329$	4.22958			0.233184
$330$		0			0
$331$	−11.9051			−0.654362			−0.327181	−	0.944962i	$-0.606099\pi$
$331$	−11.9051			−0.654362			−0.327181	+	0.944962i	$0.606099\pi$
$332$	−3.48002	+	10.7104i	−0.190991	+	0.587809i
$333$		0			0
$334$	5.91822	+	4.29984i	0.323831	+	0.235277i
$335$	−3.08321	+	1.00179i	−0.168453	+	0.0547339i
$336$		0			0
$337$	−14.2709	+	19.6421i	−0.777383	+	1.06998i	0.218183	+	0.975908i	$0.429987\pi$
$337$	−14.2709	+	19.6421i	−0.777383	+	1.06998i	−0.995566	+	0.0940679i	$0.970013\pi$
$338$	−10.5140	+	7.63888i	−0.571887	+	0.415500i
$339$		0			0
$340$		−	1.75086i		−	0.0949538i
$341$	−8.08846	−	2.50870i	−0.438015	−	0.135854i
$342$		0			0
$343$	−56.1031	−	18.2290i	−3.02928	−	0.984274i
$344$	−5.59805	−	7.70506i	−0.301827	−	0.415429i
$345$		0			0
$346$	6.48666	+	19.9639i	0.348725	+	1.07327i
$347$	−5.00028	−	15.3893i	−0.268429	−	0.826139i	−0.990884	−	0.134721i	$-0.956986\pi$
$347$	−5.00028	−	15.3893i	−0.268429	−	0.826139i	0.722455	−	0.691418i	$-0.243014\pi$
$348$		0			0
$349$	−3.41409	−	4.69909i	−0.182752	−	0.251537i	0.707805	−	0.706408i	$-0.249685\pi$
$349$	−3.41409	−	4.69909i	−0.182752	−	0.251537i	−0.890557	+	0.454871i	$0.849685\pi$
$350$	18.1195	+	5.88739i	0.968530	+	0.314694i
$351$		0			0
$352$	−0.0444738	−	3.31633i	−0.00237046	−	0.176761i
$353$			23.9840i			1.27654i	0.769812	+	0.638271i	$0.220350\pi$
$353$			23.9840i			1.27654i	−0.769812	+	0.638271i	$0.779650\pi$
$354$		0			0
$355$	−10.0177	+	7.27826i	−0.531683	+	0.386290i
$356$	−6.70820	+	9.23305i	−0.355534	+	0.489351i
$357$		0			0
$358$	9.71213	−	3.15566i	0.513302	−	0.166782i
$359$	2.15196	+	1.56349i	0.113576	+	0.0825181i	0.643124	−	0.765762i	$-0.277638\pi$
$359$	2.15196	+	1.56349i	0.113576	+	0.0825181i	−0.529547	+	0.848280i	$0.677638\pi$
$360$		0			0
$361$	−0.891854	+	2.74484i	−0.0469397	+	0.144465i
$362$	9.49962			0.499289
$363$		0			0
$364$	0.318527			0.0166953
$365$	2.45517	−	7.55622i	0.128509	−	0.395511i
$366$		0			0
$367$	−20.2210	−	14.6914i	−1.05553	−	0.766884i	−0.0822701	−	0.996610i	$-0.526217\pi$
$367$	−20.2210	−	14.6914i	−1.05553	−	0.766884i	−0.973255	+	0.229726i	$0.926217\pi$
$368$	−7.19910	+	2.33913i	−0.375279	+	0.121936i
$369$		0			0
$370$	−0.415313	+	0.571629i	−0.0215911	+	0.0297176i
$371$	22.5345	−	16.3723i	1.16993	−	0.850007i
$372$		0			0
$373$			25.3171i			1.31087i	0.755251	+	0.655436i	$0.227515\pi$
$373$			25.3171i			1.31087i	−0.755251	+	0.655436i	$0.772485\pi$
$374$	0.0699821	+	5.21844i	0.00361869	+	0.269839i
$375$		0			0
$376$	−0.794285	−	0.258079i	−0.0409621	−	0.0133094i
$377$	−0.0930365	−	0.128054i	−0.00479162	−	0.00659510i
$378$		0			0
$379$	9.92771	+	30.5543i	0.509952	+	1.56947i	0.792283	+	0.610154i	$0.208892\pi$
$379$	9.92771	+	30.5543i	0.509952	+	1.56947i	−0.282331	+	0.959317i	$0.591108\pi$
$380$	1.60855	+	4.95061i	0.0825169	+	0.253961i
$381$		0			0
$382$	9.38947	+	12.9235i	0.480407	+	0.661224i
$383$	3.28969	+	1.06889i	0.168095	+	0.0546175i	0.391856	−	0.920027i	$-0.371833\pi$
$383$	3.28969	+	1.06889i	0.168095	+	0.0546175i	−0.223760	+	0.974644i	$0.571833\pi$
$384$		0			0
$385$	17.8504	+	5.53643i	0.909740	+	0.282163i
$386$		−	15.7140i		−	0.799821i
$387$		0			0
$388$	−3.42865	+	2.49106i	−0.174063	+	0.126464i
$389$	9.30681	−	12.8097i	0.471874	−	0.649479i	−0.505044	−	0.863094i	$-0.668524\pi$
$389$	9.30681	−	12.8097i	0.471874	−	0.649479i	0.976918	+	0.213615i	$0.0685238\pi$
$390$		0			0
$391$	11.3282	−	3.68076i	0.572892	−	0.186144i
$392$	15.0866	+	10.9611i	0.761988	+	0.553617i
$393$		0			0
$394$	0.513365	−	1.57998i	0.0258630	−	0.0795981i
$395$	−12.5812			−0.633028
$396$		0			0
$397$	−18.8514			−0.946123			−0.473062	−	0.881029i	$-0.656851\pi$
$397$	−18.8514			−0.946123			−0.473062	+	0.881029i	$0.656851\pi$
$398$	1.24231	−	3.82343i	0.0622712	−	0.191651i
$399$		0			0
$400$	−3.04348	−	2.21122i	−0.152174	−	0.110561i
$401$	−25.9482	+	8.43107i	−1.29579	+	0.421027i	−0.874115	−	0.485720i	$-0.838558\pi$
$401$	−25.9482	+	8.43107i	−1.29579	+	0.421027i	−0.421674	+	0.906747i	$0.638558\pi$
$402$		0			0
$403$	−0.0943956	+	0.129924i	−0.00470218	+	0.00647199i
$404$	8.27205	−	6.00999i	0.411550	−	0.299008i
$405$		0			0
$406$		−	12.7451i		−	0.632528i
$407$	1.21499	−	1.72034i	0.0602249	−	0.0852741i
$408$		0			0
$409$	−8.36713	−	2.71865i	−0.413728	−	0.134428i	0.0947545	−	0.995501i	$-0.469793\pi$
$409$	−8.36713	−	2.71865i	−0.413728	−	0.134428i	−0.508483	+	0.861072i	$0.669793\pi$
$410$	5.55678	+	7.64825i	0.274430	+	0.377720i
$411$		0			0
$412$	3.36260	+	10.3490i	0.165663	+	0.509859i
$413$	15.8724	+	48.8501i	0.781028	+	2.40376i
$414$		0			0
$415$	7.36523	+	10.1374i	0.361545	+	0.497624i
$416$	−0.0598171	−	0.0194357i	−0.00293277	−	0.000952916i
$417$		0			0
$418$	−4.99216	−	14.6910i	−0.244175	−	0.718560i
$419$		−	21.3109i		−	1.04111i	−0.853829	−	0.520553i	$-0.825726\pi$
$419$		−	21.3109i		−	1.04111i	0.853829	−	0.520553i	$-0.174274\pi$
$420$		0			0
$421$	−1.96016	+	1.42414i	−0.0955326	+	0.0694085i	−0.634526	−	0.772901i	$-0.718805\pi$
$421$	−1.96016	+	1.42414i	−0.0955326	+	0.0694085i	0.538994	+	0.842310i	$0.318805\pi$
$422$	1.46463	−	2.01589i	0.0712971	−	0.0981321i
$423$		0			0
$424$	−5.23082	+	1.69960i	−0.254031	+	0.0825397i
$425$	4.78911	+	3.47949i	0.232306	+	0.168780i
$426$		0			0
$427$	−20.1561	+	62.0342i	−0.975424	+	3.00205i
$428$	9.18839			0.444138
$429$		0			0
$430$	−10.5971			−0.511037
$431$	−1.72418	+	5.30647i	−0.0830506	+	0.255603i	−0.983956	−	0.178412i	$-0.942904\pi$
$431$	−1.72418	+	5.30647i	−0.0830506	+	0.255603i	0.900905	+	0.434016i	$0.142904\pi$
$432$		0			0
$433$	−22.2305	−	16.1514i	−1.06833	−	0.776187i	−0.0927188	−	0.995692i	$-0.529556\pi$
$433$	−22.2305	−	16.1514i	−1.06833	−	0.776187i	−0.975611	+	0.219505i	$0.929556\pi$
$434$	−12.2984	+	3.99598i	−0.590341	+	0.191813i
$435$		0			0
$436$	3.66537	−	5.04495i	0.175540	−	0.241610i
$437$	−28.6493	+	20.8149i	−1.37048	+	0.995713i
$438$		0			0
$439$		−	22.3299i		−	1.06575i	−0.846194	−	0.532875i	$-0.821112\pi$
$439$		−	22.3299i		−	1.06575i	0.846194	−	0.532875i	$-0.178888\pi$
$440$	−3.01435	−	2.12889i	−0.143704	−	0.101491i
$441$		0			0
$442$	0.0941258	+	0.0305833i	0.00447711	+	0.00145470i
$443$	−0.528036	−	0.726779i	−0.0250877	−	0.0345303i	0.796289	−	0.604917i	$-0.206794\pi$
$443$	−0.528036	−	0.726779i	−0.0250877	−	0.0345303i	−0.821377	+	0.570386i	$0.806794\pi$
$444$		0			0
$445$	3.92408	+	12.0771i	0.186019	+	0.572509i
$446$	4.81389	+	14.8156i	0.227944	+	0.701540i
$447$		0			0
$448$	−2.97677	−	4.09718i	−0.140639	−	0.193573i
$449$	11.2234	+	3.64670i	0.529664	+	0.172098i	0.561627	−	0.827391i	$-0.310176\pi$
$449$	11.2234	+	3.64670i	0.529664	+	0.172098i	−0.0319627	+	0.999489i	$0.510176\pi$
$450$		0			0
$451$	−16.8677	−	22.5735i	−0.794268	−	1.06294i
$452$			15.8228i			0.744241i
$453$		0			0
$454$	−13.5679	+	9.85768i	−0.636775	+	0.462644i
$455$	0.208321	−	0.286729i	0.00976624	−	0.0134421i
$456$		0			0
$457$	12.3809	−	4.02281i	0.579155	−	0.188179i	−0.00476697	−	0.999989i	$-0.501517\pi$
$457$	12.3809	−	4.02281i	0.579155	−	0.188179i	0.583922	+	0.811810i	$0.301517\pi$
$458$	−5.93821	−	4.31436i	−0.277474	−	0.201597i
$459$		0			0
$460$	−2.60269	+	8.01026i	−0.121351	+	0.373480i
$461$	36.3243			1.69179			0.845895	−	0.533350i	$-0.179067\pi$
$461$	36.3243			1.69179			0.845895	+	0.533350i	$0.179067\pi$
$462$		0			0
$463$	17.2988			0.803941			0.401971	−	0.915653i	$-0.368325\pi$
$463$	17.2988			0.803941			0.401971	+	0.915653i	$0.368325\pi$
$464$	−0.777675	+	2.39344i	−0.0361027	+	0.111113i
$465$		0			0
$466$	3.37999	+	2.45571i	0.156575	+	0.113758i
$467$	−30.6195	+	9.94889i	−1.41690	+	0.460380i	−0.914617	−	0.404322i	$-0.867508\pi$
$467$	−30.6195	+	9.94889i	−1.41690	+	0.460380i	−0.502286	+	0.864701i	$0.667508\pi$
$468$		0			0
$469$	8.67309	−	11.9375i	0.400486	−	0.551222i
$470$	−0.751789	+	0.546207i	−0.0346774	+	0.0251946i
$471$		0			0
$472$		−	10.1422i		−	0.466832i
$473$	31.5846	−	0.423567i	1.45226	−	0.0194756i
$474$		0			0
$475$	−16.7380	−	5.43851i	−0.767993	−	0.249536i
$476$	4.68413	+	6.44716i	0.214697	+	0.295505i
$477$		0			0
$478$	−0.652009	−	2.00668i	−0.0298222	−	0.0917833i
$479$	11.9932	+	36.9112i	0.547982	+	1.68652i	0.713792	+	0.700358i	$0.246976\pi$
$479$	11.9932	+	36.9112i	0.547982	+	1.68652i	−0.165809	+	0.986158i	$0.553024\pi$
$480$		0			0
$481$	−0.0234761	−	0.0323121i	−0.00107042	−	0.00147330i
$482$	−9.43755	−	3.06645i	−0.429869	−	0.139673i
$483$		0			0
$484$	9.06937	+	6.22467i	0.412244	+	0.282940i
$485$			4.71557i			0.214123i
$486$		0			0
$487$	21.8852	−	15.9005i	0.991712	−	0.720521i	0.0314168	−	0.999506i	$-0.489998\pi$
$487$	21.8852	−	15.9005i	0.991712	−	0.720521i	0.960295	+	0.278985i	$0.0899981\pi$
$488$	7.57036	−	10.4197i	0.342694	−	0.471678i
$489$		0			0
$490$	19.7337	−	6.41186i	0.891477	−	0.289658i
$491$	0.368179	+	0.267498i	0.0166157	+	0.0120720i	0.596062	−	0.802938i	$-0.296731\pi$
$491$	0.368179	+	0.267498i	0.0166157	+	0.0120720i	−0.579446	+	0.815010i	$0.696731\pi$
$492$		0			0
$493$	1.22372	−	3.76622i	0.0551135	−	0.169622i
$494$	−0.294241			−0.0132385
$495$		0			0
$496$	2.55337			0.114650
$497$	17.4161	−	53.6012i	0.781218	−	2.40434i
$498$		0			0
$499$	−8.44213	−	6.13357i	−0.377922	−	0.274576i	0.382566	−	0.923928i	$-0.375040\pi$
$499$	−8.44213	−	6.13357i	−0.377922	−	0.274576i	−0.760488	+	0.649352i	$0.775040\pi$
$500$	−9.27205	+	3.01267i	−0.414659	+	0.134731i
$501$		0			0
$502$	0.568689	−	0.782733i	0.0253818	−	0.0349351i
$503$	34.3387	−	24.9485i	1.53109	−	1.11240i	0.575458	−	0.817831i	$-0.304824\pi$
$503$	34.3387	−	24.9485i	1.53109	−	1.11240i	0.955630	−	0.294570i	$-0.0951763\pi$
$504$		0			0
$505$		−	11.3769i		−	0.506265i
$506$	7.43714	−	23.9786i	0.330621	−	1.06598i
$507$		0			0
$508$	0.635021	+	0.206331i	0.0281745	+	0.00915446i
$509$	−2.25909	−	3.10937i	−0.100132	−	0.137820i	0.756011	−	0.654559i	$-0.227146\pi$
$509$	−2.25909	−	3.10937i	−0.100132	−	0.137820i	−0.856143	+	0.516739i	$0.827146\pi$
$510$		0			0
$511$	11.1748	+	34.3925i	0.494344	+	1.52143i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$		0			0
$514$	7.94128	+	10.9302i	0.350275	+	0.482112i
$515$	11.5151	+	3.74148i	0.507415	+	0.164869i
$516$		0			0
$517$	2.21887	−	1.65802i	0.0975860	−	0.0729195i
$518$		−	3.21600i		−	0.141303i
$519$		0			0
$520$	−0.0566167	+	0.0411345i	−0.00248281	+	0.00180387i
$521$	−8.49738	+	11.6956i	−0.372277	+	0.512396i	−0.953518	−	0.301336i	$-0.902567\pi$
$521$	−8.49738	+	11.6956i	−0.372277	+	0.512396i	0.581241	+	0.813732i	$0.302567\pi$
$522$		0			0
$523$	19.6461	−	6.38340i	0.859063	−	0.279126i	0.153826	−	0.988098i	$-0.450841\pi$
$523$	19.6461	−	6.38340i	0.859063	−	0.279126i	0.705237	+	0.708972i	$0.250841\pi$
$524$	−15.1955	−	11.0402i	−0.663819	−	0.482293i
$525$		0			0
$526$	−0.575204	+	1.77030i	−0.0250801	+	0.0771886i
$527$	−4.01789			−0.175022
$528$		0			0
$529$	−34.2986			−1.49124
$530$	−1.89110	+	5.82020i	−0.0821441	+	0.252813i
$531$		0			0
$532$	−19.1677	−	13.9261i	−0.831023	−	0.603774i
$533$	−0.508231	+	0.165134i	−0.0220139	+	0.00715276i
$534$		0			0
$535$	6.00934	−	8.27114i	0.259806	−	0.357593i
$536$	−2.35714	+	1.71256i	−0.101813	+	0.0739714i
$537$		0			0
$538$			20.1449i			0.868508i
$539$	−58.5599	+	19.8993i	−2.52236	+	0.857124i
$540$		0			0
$541$	5.61053	+	1.82297i	0.241215	+	0.0783757i	0.427130	−	0.904190i	$-0.359525\pi$
$541$	5.61053	+	1.82297i	0.241215	+	0.0783757i	−0.185914	+	0.982566i	$0.559525\pi$
$542$	2.20783	+	3.03881i	0.0948343	+	0.130528i
$543$		0			0
$544$	−0.486257	−	1.49654i	−0.0208481	−	0.0641638i
$545$	−2.14413	−	6.59894i	−0.0918443	−	0.282668i
$546$		0			0
$547$	10.1696	+	13.9973i	0.434822	+	0.598481i	0.969052	−	0.246858i	$-0.0793982\pi$
$547$	10.1696	+	13.9973i	0.434822	+	0.598481i	−0.534229	+	0.845340i	$0.679398\pi$
$548$	0.600713	+	0.195183i	0.0256612	+	0.00833782i
$549$		0			0
$550$	11.8136	−	4.01437i	0.503732	−	0.171174i
$551$			11.7733i			0.501562i
$552$		0			0
$553$	46.3274	−	33.6588i	1.97004	−	1.43132i
$554$	7.37248	−	10.1474i	0.313227	−	0.431120i
$555$		0			0
$556$	−12.4427	+	4.04287i	−0.527687	+	0.171456i
$557$	0.465691	+	0.338345i	0.0197320	+	0.0143361i	0.597608	−	0.801789i	$-0.296118\pi$
$557$	0.465691	+	0.338345i	0.0197320	+	0.0143361i	−0.577876	+	0.816125i	$0.696118\pi$
$558$		0			0
$559$	0.185106	−	0.569696i	0.00782913	−	0.0240956i
$560$	−5.63502			−0.238123
$561$		0			0
$562$	−20.4871			−0.864198
$563$	0.418386	−	1.28766i	0.0176329	−	0.0542684i	−0.941853	−	0.336025i	$-0.890917\pi$
$563$	0.418386	−	1.28766i	0.0176329	−	0.0542684i	0.959486	+	0.281757i	$0.0909172\pi$
$564$		0			0
$565$	14.2432	+	10.3483i	0.599218	+	0.435357i
$566$	−10.9677	+	3.56361i	−0.461006	+	0.149790i
$567$		0			0
$568$	−6.54123	+	9.00323i	−0.274464	+	0.377767i
$569$	−7.84462	+	5.69945i	−0.328864	+	0.238933i	−0.739948	−	0.672664i	$-0.765150\pi$
$569$	−7.84462	+	5.69945i	−0.328864	+	0.238933i	0.411085	+	0.911597i	$0.365150\pi$
$570$		0			0
$571$		−	3.56124i		−	0.149033i	−0.997220	−	0.0745166i	$-0.976259\pi$
$571$		−	3.56124i		−	0.149033i	0.997220	−	0.0745166i	$-0.0237414\pi$
$572$	0.167102	−	0.124864i	0.00698688	−	0.00522084i
$573$		0			0
$574$	−40.9232	−	13.2968i	−1.70810	−	0.554996i
$575$	−16.7380	−	23.0379i	−0.698024	−	0.960747i
$576$		0			0
$577$	2.09235	+	6.43958i	0.0871055	+	0.268083i	0.985116	−	0.171891i	$-0.0549876\pi$
$577$	2.09235	+	6.43958i	0.0871055	+	0.268083i	−0.898010	+	0.439974i	$0.854988\pi$
$578$	−4.48813	−	13.8131i	−0.186682	−	0.574547i
$579$		0			0
$580$	1.64590	+	2.26538i	0.0683422	+	0.0940650i
$581$	−54.2416	−	17.6242i	−2.25032	−	0.731174i
$582$		0			0
$583$	5.40378	−	17.4227i	0.223802	−	0.721574i
$584$		−	7.14052i		−	0.295477i
$585$		0			0
$586$	−11.5578	+	8.39726i	−0.477450	+	0.346888i
$587$	−12.1041	+	16.6598i	−0.499588	+	0.687624i	−0.982120	−	0.188254i	$-0.939717\pi$
$587$	−12.1041	+	16.6598i	−0.499588	+	0.687624i	0.482532	+	0.875878i	$0.339717\pi$
$588$		0			0
$589$	11.3607	−	3.69131i	0.468109	−	0.152098i
$590$	−9.12973	−	6.63314i	−0.375865	−	0.273082i
$591$		0			0
$592$	−0.196232	+	0.603941i	−0.00806510	+	0.0248218i
$593$	4.06096			0.166764			0.0833818	−	0.996518i	$-0.473428\pi$
$593$	4.06096			0.166764			0.0833818	+	0.996518i	$0.473428\pi$
$594$		0			0
$595$	8.86705			0.363513
$596$	1.64027	−	5.04823i	0.0671881	−	0.206784i
$597$		0			0
$598$	−0.385166	−	0.279840i	−0.0157506	−	0.0114435i
$599$	37.3606	−	12.1392i	1.52651	−	0.495994i	0.578894	−	0.815403i	$-0.303484\pi$
$599$	37.3606	−	12.1392i	1.52651	−	0.495994i	0.947617	+	0.319409i	$0.103484\pi$
$600$		0			0
$601$	−9.67461	+	13.3160i	−0.394635	+	0.543169i	−0.959387	−	0.282092i	$-0.908972\pi$
$601$	−9.67461	+	13.3160i	−0.394635	+	0.543169i	0.564752	+	0.825261i	$0.308972\pi$
$602$	39.0214	−	28.3507i	1.59039	−	1.15549i
$603$		0			0
$604$		−	7.51045i		−	0.305596i
$605$	11.5348	−	4.09298i	0.468955	−	0.166403i
$606$		0			0
$607$	13.8300	+	4.49363i	0.561341	+	0.182391i	0.575924	−	0.817503i	$-0.304642\pi$
$607$	13.8300	+	4.49363i	0.561341	+	0.182391i	−0.0145836	+	0.999894i	$0.504642\pi$
$608$	2.74981	+	3.78479i	0.111520	+	0.153494i
$609$		0			0
$610$	−4.42842	−	13.6293i	−0.179301	−	0.551833i
$611$	−0.0162320	−	0.0499569i	−0.000656675	−	0.00202104i
$612$		0			0
$613$	−8.59574	−	11.8310i	−0.347179	−	0.477850i	0.599342	−	0.800493i	$-0.295429\pi$
$613$	−8.59574	−	11.8310i	−0.347179	−	0.477850i	−0.946521	+	0.322642i	$0.895429\pi$
$614$	−20.1098	−	6.53408i	−0.811566	−	0.263694i
$615$		0			0
$616$	16.7952	−	0.225233i	0.676697	−	0.00907488i
$617$			18.6554i			0.751040i	0.926814	+	0.375520i	$0.122536\pi$
$617$			18.6554i			0.751040i	−0.926814	+	0.375520i	$0.877464\pi$
$618$		0			0
$619$	18.4543	−	13.4078i	0.741740	−	0.538906i	−0.151516	−	0.988455i	$-0.548415\pi$
$619$	18.4543	−	13.4078i	0.741740	−	0.538906i	0.893256	+	0.449549i	$0.148415\pi$
$620$	1.66994	−	2.29848i	0.0670665	−	0.0923091i
$621$		0			0
$622$	16.7064	−	5.42825i	0.669867	−	0.217653i
$623$	−46.7598	−	33.9730i	−1.87339	−	1.36110i
$624$		0			0
$625$	2.46041	−	7.57238i	0.0984166	−	0.302895i
$626$	−6.76515			−0.270390
$627$		0			0
$628$	8.42888			0.336349
$629$	0.308784	−	0.950338i	0.0123120	−	0.0378925i
$630$		0			0
$631$	20.8933	+	15.1799i	0.831749	+	0.604301i	0.920054	−	0.391792i	$-0.128145\pi$
$631$	20.8933	+	15.1799i	0.831749	+	0.604301i	−0.0883046	+	0.996094i	$0.528145\pi$
$632$	−10.7537	+	3.49410i	−0.427761	+	0.138988i
$633$		0			0
$634$	−15.6605	+	21.5549i	−0.621959	+	0.856053i
$635$	0.601047	−	0.436686i	0.0238518	−	0.0173293i
$636$		0			0
$637$			1.17288i			0.0464711i
$638$	−4.99614	−	6.68619i	−0.197799	−	0.264709i
$639$		0			0
$640$	1.05822	+	0.343836i	0.0418297	+	0.0135913i
$641$	−18.0683	−	24.8689i	−0.713656	−	0.982264i	−0.999711	−	0.0240504i	$-0.992344\pi$
$641$	−18.0683	−	24.8689i	−0.713656	−	0.982264i	0.286054	−	0.958213i	$-0.407656\pi$
$642$		0			0
$643$	−6.52664	−	20.0869i	−0.257386	−	0.792151i	−0.993350	−	0.115132i	$-0.963271\pi$
$643$	−6.52664	−	20.0869i	−0.257386	−	0.792151i	0.735965	−	0.677020i	$-0.236729\pi$
$644$	−11.8463	−	36.4590i	−0.466808	−	1.43669i
$645$		0			0
$646$	−4.32699	−	5.95560i	−0.170243	−	0.234320i
$647$	31.4151	+	10.2074i	1.23506	+	0.401294i	0.852543	−	0.522657i	$-0.175059\pi$
$647$	31.4151	+	10.2074i	1.23506	+	0.401294i	0.382512	+	0.923950i	$0.375059\pi$
$648$		0			0
$649$	27.4763	+	19.4051i	1.07854	+	0.761718i
$650$		−	0.236610i		−	0.00928059i
$651$		0			0
$652$	−6.18376	+	4.49276i	−0.242175	+	0.175950i
$653$	15.5572	−	21.4126i	0.608799	−	0.837939i	−0.387679	−	0.921794i	$-0.626723\pi$
$653$	15.5572	−	21.4126i	0.608799	−	0.837939i	0.996478	+	0.0838550i	$0.0267233\pi$
$654$		0			0
$655$	−19.8762	+	6.45816i	−0.776626	+	0.252341i
$656$	6.87375	+	4.99407i	0.268375	+	0.194986i
$657$		0			0
$658$	1.30701	−	4.02257i	0.0509526	−	0.156816i
$659$	27.4209			1.06817			0.534084	−	0.845432i	$-0.320657\pi$
$659$	27.4209			1.06817			0.534084	+	0.845432i	$0.320657\pi$
$660$		0			0
$661$	−48.5993			−1.89029			−0.945146	−	0.326647i	$-0.894081\pi$
$661$	−48.5993			−1.89029			−0.945146	+	0.326647i	$0.894081\pi$
$662$	−3.67887	+	11.3224i	−0.142983	+	0.440057i
$663$		0			0
$664$	9.11081	+	6.61939i	0.353568	+	0.256882i
$665$	−25.0718	+	8.14633i	−0.972244	+	0.315901i
$666$		0			0
$667$	−11.1971	+	15.4115i	−0.433554	+	0.596736i
$668$	5.91822	−	4.29984i	0.228983	−	0.166366i
$669$		0			0
$670$			3.24187i			0.125245i
$671$	13.7437	+	40.4450i	0.530568	+	1.56136i
$672$		0			0
$673$	23.5194	+	7.64193i	0.906607	+	0.294575i	0.724962	−	0.688789i	$-0.241858\pi$
$673$	23.5194	+	7.64193i	0.906607	+	0.294575i	0.181646	+	0.983364i	$0.441858\pi$
$674$	14.2709	+	19.6421i	0.549693	+	0.756587i
$675$		0			0
$676$	4.01600	+	12.3600i	0.154461	+	0.475384i
$677$	6.57404	+	20.2328i	0.252661	+	0.777611i	0.994281	+	0.106791i	$0.0340576\pi$
$677$	6.57404	+	20.2328i	0.252661	+	0.777611i	−0.741620	+	0.670820i	$0.765942\pi$
$678$		0			0
$679$	−12.6157	−	17.3640i	−0.484146	−	0.666370i
$680$	−1.66517	−	0.541046i	−0.0638563	−	0.0207482i
$681$		0			0
$682$	−4.88539	+	6.91736i	−0.187071	+	0.264879i
$683$		−	24.5172i		−	0.938124i	−0.883165	−	0.469062i	$-0.844592\pi$
$683$		−	24.5172i		−	0.938124i	0.883165	−	0.469062i	$-0.155408\pi$
$684$		0			0
$685$	0.568573	−	0.413093i	0.0217241	−	0.0157835i
$686$	−34.6736	+	47.7241i	−1.32385	+	1.82212i
$687$		0			0
$688$	−9.05784	+	2.94307i	−0.345327	+	0.112204i
$689$	−0.279859	−	0.203330i	−0.0106618	−	0.00774625i
$690$		0			0
$691$	9.69552	−	29.8397i	0.368835	−	1.13516i	−0.578710	−	0.815534i	$-0.696444\pi$
$691$	9.69552	−	29.8397i	0.368835	−	1.13516i	0.947545	−	0.319624i	$-0.103556\pi$
$692$	20.9913			0.797969
$693$		0			0
$694$	−16.1812			−0.614231
$695$	−4.49840	+	13.8447i	−0.170634	+	0.525158i
$696$		0			0
$697$	−10.8163	−	7.85847i	−0.409695	−	0.297661i
$698$	−5.52411	+	1.79489i	−0.209091	+	0.0679377i
$699$		0			0
$700$	11.1985	−	15.4134i	0.423263	−	0.582572i
$701$	11.7991	−	8.57257i	0.445647	−	0.323781i	−0.342228	−	0.939617i	$-0.611181\pi$
$701$	11.7991	−	8.57257i	0.445647	−	0.323781i	0.787875	+	0.615836i	$0.211181\pi$
$702$		0			0
$703$			2.97079i			0.112046i
$704$	−3.16776	−	0.982504i	−0.119389	−	0.0370295i
$705$		0			0
$706$	22.8102	+	7.41148i	0.858473	+	0.278935i
$707$	30.4370	+	41.8929i	1.14470	+	1.57554i
$708$		0			0
$709$	1.02926	+	3.16773i	0.0386546	+	0.118967i	0.968522	−	0.248929i	$-0.0800785\pi$
$709$	1.02926	+	3.16773i	0.0386546	+	0.118967i	−0.929867	+	0.367895i	$0.880078\pi$
$710$	3.82641	+	11.7765i	0.143603	+	0.441963i
$711$		0			0
$712$	6.70820	+	9.23305i	0.251401	+	0.346023i
$713$	18.3820	+	5.97267i	0.688411	+	0.223678i
$714$		0			0
$715$	−0.00311237	−	0.232084i	−0.000116396	−	0.00867944i
$716$		−	10.2119i		−	0.381638i
$717$		0			0
$718$	2.15196	−	1.56349i	0.0803106	−	0.0583491i
$719$	−5.32392	+	7.32775i	−0.198549	+	0.273279i	−0.896669	−	0.442702i	$-0.854020\pi$
$719$	−5.32392	+	7.32775i	−0.198549	+	0.273279i	0.698120	+	0.715981i	$0.254020\pi$
$720$		0			0
$721$	−52.4114	+	17.0295i	−1.95190	+	0.634212i
$722$	2.33490	+	1.69641i	0.0868961	+	0.0631337i
$723$		0			0
$724$	2.93554	−	9.03468i	0.109099	−	0.335771i
$725$	−9.46737			−0.351609
$726$		0			0
$727$	12.1618			0.451056			0.225528	−	0.974237i	$-0.427589\pi$
$727$	12.1618			0.451056			0.225528	+	0.974237i	$0.427589\pi$
$728$	0.0984302	−	0.302937i	0.00364807	−	0.0112276i
$729$		0			0
$730$	−6.42771	−	4.67000i	−0.237900	−	0.172845i
$731$	14.2531	−	4.63110i	0.527168	−	0.171287i
$732$		0			0
$733$	0.259338	−	0.356948i	0.00957886	−	0.0131842i	−0.804201	−	0.594358i	$-0.797406\pi$
$733$	0.259338	−	0.356948i	0.00957886	−	0.0131842i	0.813780	+	0.581174i	$0.197406\pi$
$734$	−20.2210	+	14.6914i	−0.746369	+	0.542269i
$735$		0			0
$736$			7.56958i			0.279018i
$737$	−0.129578	−	9.66240i	−0.00477307	−	0.355919i
$738$		0			0
$739$	24.1982	+	7.86248i	0.890146	+	0.289226i	0.718164	−	0.695874i	$-0.244983\pi$
$739$	24.1982	+	7.86248i	0.890146	+	0.289226i	0.171982	+	0.985100i	$0.444983\pi$
$740$	0.415313	+	0.571629i	0.0152672	+	0.0210135i
$741$		0			0
$742$	−8.60742	−	26.4909i	−0.315988	−	0.972512i
$743$	3.95806	+	12.1817i	0.145207	+	0.446902i	0.997038	−	0.0769161i	$-0.0245073\pi$
$743$	3.95806	+	12.1817i	0.145207	+	0.446902i	−0.851830	+	0.523818i	$0.824507\pi$
$744$		0			0
$745$	−3.47152	−	4.77814i	−0.127187	−	0.175058i
$746$	24.0780	+	7.82343i	0.881559	+	0.286436i
$747$		0			0
$748$	4.98466	+	1.54603i	0.182257	+	0.0565284i
$749$			46.5336i			1.70030i
$750$		0			0
$751$	−19.8533	+	14.4243i	−0.724459	+	0.526350i	−0.887806	−	0.460219i	$-0.847771\pi$
$751$	−19.8533	+	14.4243i	−0.724459	+	0.526350i	0.163347	+	0.986569i	$0.447771\pi$
$752$	−0.490895	+	0.675659i	−0.0179011	+	0.0246388i
$753$		0			0
$754$	−0.150536	+	0.0489122i	−0.00548221	+	0.00178128i
$755$	−6.76070	−	4.91194i	−0.246047	−	0.178764i
$756$		0			0
$757$	−5.80929	+	17.8792i	−0.211142	+	0.649829i	0.788263	+	0.615339i	$0.210981\pi$
$757$	−5.80929	+	17.8792i	−0.211142	+	0.649829i	−0.999405	+	0.0344905i	$0.989019\pi$
$758$	32.1267			1.16690
$759$		0			0
$760$	5.20538			0.188819
$761$	9.76094	−	30.0411i	0.353834	−	1.08899i	−0.602849	−	0.797855i	$-0.705968\pi$
$761$	9.76094	−	30.0411i	0.353834	−	1.08899i	0.956683	−	0.291133i	$-0.0940322\pi$
$762$		0			0
$763$	25.5496	+	18.5629i	0.924958	+	0.672022i
$764$	15.1925	−	4.93634i	0.549645	−	0.178590i
$765$		0			0
$766$	2.03314	−	2.79838i	0.0734604	−	0.101110i
$767$	0.516070	−	0.374947i	0.0186342	−	0.0135385i
$768$		0			0
$769$		−	5.02784i		−	0.181309i	−0.995882	−	0.0906544i	$-0.971104\pi$
$769$		−	5.02784i		−	0.181309i	0.995882	−	0.0906544i	$-0.0288958\pi$
$770$	10.7815	−	15.2659i	0.388539	−	0.550144i
$771$		0			0
$772$	−14.9449	−	4.85589i	−0.537878	−	0.174767i
$773$	−14.3183	−	19.7074i	−0.514993	−	0.708828i	0.469758	−	0.882795i	$-0.344341\pi$
$773$	−14.3183	−	19.7074i	−0.514993	−	0.708828i	−0.984751	+	0.173968i	$0.944341\pi$
$774$		0			0
$775$	2.96832	+	9.13553i	0.106625	+	0.328158i
$776$	1.30963	+	4.03062i	0.0470129	+	0.144691i
$777$		0			0
$778$	−9.30681	−	12.8097i	−0.333665	−	0.459251i
$779$	37.8030	+	12.2829i	1.35443	+	0.440082i
$780$		0			0
$781$	−11.8753	−	34.9468i	−0.424932	−	1.25050i
$782$		−	11.9112i		−	0.425943i
$783$		0			0
$784$	15.0866	−	10.9611i	0.538807	−	0.391466i
$785$	5.51261	−	7.58745i	0.196753	−	0.270808i
$786$		0			0
$787$	19.2668	−	6.26017i	0.686788	−	0.223151i	0.0552234	−	0.998474i	$-0.482413\pi$
$787$	19.2668	−	6.26017i	0.686788	−	0.223151i	0.631565	+	0.775323i	$0.282413\pi$
$788$	−1.34401	−	0.976479i	−0.0478783	−	0.0347856i
$789$		0			0
$790$	−3.88780	+	11.9654i	−0.138322	+	0.425710i
$791$	−80.1327			−2.84919
$792$		0			0
$793$	0.810059			0.0287660
$794$	−5.82539	+	17.9287i	−0.206735	+	0.636266i
$795$		0			0
$796$	−3.25240	−	2.36301i	−0.115278	−	0.0837546i
$797$	33.8547	−	11.0001i	1.19920	−	0.389642i	0.359731	−	0.933056i	$-0.382868\pi$
$797$	33.8547	−	11.0001i	1.19920	−	0.389642i	0.839465	+	0.543414i	$0.182868\pi$
$798$		0			0
$799$	0.772453	−	1.06319i	0.0273274	−	0.0376130i
$800$	−3.04348	+	2.21122i	−0.107603	+	0.0781785i
$801$		0			0
$802$			27.2835i			0.963414i
$803$	19.3444	+	13.6620i	0.682650	+	0.482122i
$804$		0			0
$805$	−40.5671	−	13.1810i	−1.42980	−	0.464571i
$806$	0.0943956	+	0.129924i	0.00332494	+	0.00457639i
$807$		0			0
$808$	−3.15964	−	9.72438i	−0.111156	−	0.342102i
$809$	−0.572465	−	1.76187i	−0.0201268	−	0.0619439i	0.940489	−	0.339825i	$-0.110368\pi$
$809$	−0.572465	−	1.76187i	−0.0201268	−	0.0619439i	−0.960615	+	0.277881i	$0.910368\pi$
$810$		0			0
$811$	6.39976	+	8.80852i	0.224726	+	0.309309i	0.906460	−	0.422291i	$-0.138774\pi$
$811$	6.39976	+	8.80852i	0.224726	+	0.309309i	−0.681734	+	0.731600i	$0.738774\pi$
$812$	−12.1213	−	3.93845i	−0.425374	−	0.138213i
$813$		0			0
$814$	−1.26069	−	1.68714i	−0.0441871	−	0.0591342i
$815$			8.50478i			0.297909i
$816$		0			0
$817$	−36.0463	+	26.1891i	−1.26110	+	0.916242i
$818$	−5.17117	+	7.11751i	−0.180806	+	0.248858i
$819$		0			0
$820$	8.99106	−	2.92137i	0.313981	−	0.102019i
$821$	22.4036	+	16.2771i	0.781890	+	0.568076i	0.905546	−	0.424249i	$-0.139462\pi$
$821$	22.4036	+	16.2771i	0.781890	+	0.568076i	−0.123656	+	0.992325i	$0.539462\pi$
$822$		0			0
$823$	−10.8951	+	33.5317i	−0.379780	+	1.16884i	0.560416	+	0.828211i	$0.310641\pi$
$823$	−10.8951	+	33.5317i	−0.379780	+	1.16884i	−0.940197	+	0.340632i	$0.889359\pi$
$824$	10.8816			0.379078
$825$		0			0
$826$	51.3640			1.78718
$827$	−7.35517	+	22.6369i	−0.255764	+	0.787162i	0.737914	+	0.674895i	$0.235811\pi$
$827$	−7.35517	+	22.6369i	−0.255764	+	0.787162i	−0.993678	+	0.112267i	$0.964189\pi$
$828$		0			0
$829$	−3.97218	−	2.88596i	−0.137960	−	0.100233i	0.516665	−	0.856188i	$-0.327173\pi$
$829$	−3.97218	−	2.88596i	−0.137960	−	0.100233i	−0.654625	+	0.755954i	$0.727173\pi$
$830$	11.9172	−	3.87213i	0.413652	−	0.134404i
$831$		0			0
$832$	−0.0369690	+	0.0508834i	−0.00128167	+	0.00176407i
$833$	−23.7397	+	17.2479i	−0.822530	+	0.597603i
$834$		0			0
$835$		−	8.13958i		−	0.281682i
$836$	−15.5146	+	0.208060i	−0.536585	+	0.00719590i
$837$		0			0
$838$	−20.2679	−	6.58544i	−0.700143	−	0.227490i
$839$	−7.18368	−	9.88748i	−0.248008	−	0.341354i	0.666804	−	0.745233i	$-0.267662\pi$
$839$	−7.18368	−	9.88748i	−0.248008	−	0.341354i	−0.914812	+	0.403879i	$0.867662\pi$
$840$		0			0
$841$	−7.00439	−	21.5573i	−0.241531	−	0.743355i
$842$	0.748716	+	2.30431i	0.0258025	+	0.0794118i
$843$		0			0
$844$	−1.46463	−	2.01589i	−0.0504147	−	0.0693899i
$845$	13.7526	+	4.46850i	0.473105	+	0.153721i
$846$		0			0
$847$	−31.5242	+	45.9308i	−1.08318	+	1.57820i
$848$			5.50001i			0.188871i
$849$		0			0
$850$	4.78911	−	3.47949i	0.164265	−	0.119346i
$851$	−2.82539	+	3.88882i	−0.0968532	+	0.133307i
$852$		0			0
$853$	−20.0559	+	6.51657i	−0.686703	+	0.223123i	−0.631527	−	0.775353i	$-0.717572\pi$
$853$	−20.0559	+	6.51657i	−0.686703	+	0.223123i	−0.0551751	+	0.998477i	$0.517572\pi$
$854$	52.7695	+	38.3393i	1.80573	+	1.31194i
$855$		0			0
$856$	2.83937	−	8.73868i	0.0970477	−	0.298682i
$857$	−20.1075			−0.686859			−0.343430	−	0.939178i	$-0.611589\pi$
$857$	−20.1075			−0.686859			−0.343430	+	0.939178i	$0.611589\pi$
$858$		0			0
$859$	1.81545			0.0619423			0.0309712	−	0.999520i	$-0.490140\pi$
$859$	1.81545			0.0619423			0.0309712	+	0.999520i	$0.490140\pi$
$860$	−3.27468	+	10.0784i	−0.111666	+	0.343672i
$861$		0			0
$862$	4.51395	+	3.27958i	0.153746	+	0.111703i
$863$	−24.3727	+	7.91917i	−0.829656	+	0.269572i	−0.692900	−	0.721033i	$-0.743667\pi$
$863$	−24.3727	+	7.91917i	−0.829656	+	0.269572i	−0.136756	+	0.990605i	$0.543667\pi$
$864$		0			0
$865$	13.7286	−	18.8958i	0.466786	−	0.642476i
$866$	−22.2305	+	16.1514i	−0.755424	+	0.548847i
$867$		0			0
$868$			12.9313i			0.438916i
$869$	11.1093	−	35.8183i	0.376858	−	1.21505i
$870$		0			0
$871$	−0.174282	−	0.0566277i	−0.00590533	−	0.00191876i
$872$	−3.66537	−	5.04495i	−0.124125	−	0.170844i
$873$		0			0
$874$	10.9430	+	33.6792i	0.370154	+	1.13922i
$875$	−15.2573	−	46.9573i	−0.515792	−	1.58745i
$876$		0			0
$877$	−6.62225	−	9.11475i	−0.223618	−	0.307783i	0.682437	−	0.730945i	$-0.260920\pi$
$877$	−6.62225	−	9.11475i	−0.223618	−	0.307783i	−0.906054	+	0.423162i	$0.860920\pi$
$878$	−21.2370	−	6.90033i	−0.716715	−	0.232875i
$879$		0			0
$880$	−2.95618	+	2.20896i	−0.0996529	+	0.0744640i
$881$		−	21.8680i		−	0.736751i	−0.929677	−	0.368376i	$-0.879914\pi$
$881$		−	21.8680i		−	0.736751i	0.929677	−	0.368376i	$-0.120086\pi$
$882$		0			0
$883$	−32.3684	+	23.5170i	−1.08928	+	0.791411i	−0.979278	−	0.202520i	$-0.935087\pi$
$883$	−32.3684	+	23.5170i	−1.08928	+	0.791411i	−0.110005	+	0.993931i	$0.535087\pi$
$884$	0.0581729	−	0.0800682i	0.00195657	−	0.00269298i
$885$		0			0
$886$	−0.854379	+	0.277605i	−0.0287034	+	0.00932631i
$887$	−2.81693	−	2.04662i	−0.0945831	−	0.0687187i	0.539489	−	0.841993i	$-0.318618\pi$
$887$	−2.81693	−	2.04662i	−0.0945831	−	0.0687187i	−0.634072	+	0.773274i	$0.718618\pi$
$888$		0			0
$889$	−1.04494	+	3.21600i	−0.0350462	+	0.107861i
$890$	12.6986			0.425658
$891$		0			0
$892$	15.5781			0.521592
$893$	−1.20736	+	3.71587i	−0.0404027	+	0.124347i
$894$		0			0
$895$	−9.19251	−	6.67875i	−0.307272	−	0.223246i
$896$	−4.81652	+	1.56498i	−0.160909	+	0.0522824i
$897$		0			0
$898$	6.93643	−	9.54717i	0.231472	−	0.318593i
$899$	5.19862	−	3.77702i	0.173384	−	0.125971i
$900$		0			0
$901$		−	8.65459i		−	0.288326i
$902$	−26.6811	+	9.06652i	−0.888382	+	0.301882i
$903$		0			0
$904$	15.0484	+	4.88951i	0.500501	+	0.162623i
$905$	−6.21289	−	8.55130i	−0.206523	−	0.284255i
$906$		0			0
$907$	8.30714	+	25.5667i	0.275834	+	0.848930i	0.988998	+	0.147932i	$0.0472617\pi$
$907$	8.30714	+	25.5667i	0.275834	+	0.848930i	−0.713163	+	0.700998i	$0.752738\pi$
$908$	5.18249	+	15.9501i	0.171987	+	0.529321i
$909$		0			0
$910$	−0.208321	−	0.286729i	−0.00690578	−	0.00950498i
$911$	−49.8636	−	16.2017i	−1.65205	−	0.536785i	−0.672871	−	0.739760i	$-0.734939\pi$
$911$	−49.8636	−	16.2017i	−1.65205	−	0.536785i	−0.979184	+	0.202975i	$0.934939\pi$
$912$		0			0
$913$	−35.3644	+	12.0172i	−1.17039	+	0.397712i
$914$		−	13.0181i		−	0.430599i
$915$		0			0
$916$	−5.93821	+	4.31436i	−0.196204	+	0.142550i
$917$	55.9118	−	76.9561i	1.84637	−	2.54131i
$918$		0			0
$919$	3.86354	−	1.25534i	0.127446	−	0.0414099i	−0.244599	−	0.969624i	$-0.578656\pi$
$919$	3.86354	−	1.25534i	0.127446	−	0.0414099i	0.372046	+	0.928214i	$0.378656\pi$
$920$	6.81393	+	4.95061i	0.224649	+	0.163217i
$921$		0			0
$922$	11.2248	−	34.5464i	0.369670	−	1.13773i
$923$	−0.699938			−0.0230387
$924$		0			0
$925$	−2.38892			−0.0785473
$926$	5.34561	−	16.4521i	0.175668	−	0.540649i
$927$		0			0
$928$	2.03598	+	1.47923i	0.0668343	+	0.0485580i
$929$	1.95021	−	0.633660i	0.0639842	−	0.0207897i	−0.276850	−	0.960913i	$-0.589291\pi$
$929$	1.95021	−	0.633660i	0.0639842	−	0.0207897i	0.340834	+	0.940123i	$0.389291\pi$
$930$		0			0
$931$	51.2786	−	70.5790i	1.68059	−	2.31313i
$932$	3.37999	−	2.45571i	0.110715	−	0.0804393i
$933$		0			0
$934$			32.1953i			1.05346i
$935$	4.65173	−	3.47593i	0.152128	−	0.113675i
$936$		0			0
$937$	32.4341	+	10.5385i	1.05958	+	0.344278i	0.786420	−	0.617692i	$-0.211932\pi$
$937$	32.4341	+	10.5385i	1.05958	+	0.344278i	0.273157	+	0.961969i	$0.411932\pi$
$938$	−8.67309	−	11.9375i	−0.283186	−	0.389772i
$939$		0			0
$940$	0.287158	+	0.883781i	0.00936606	+	0.0288258i
$941$	−15.8259	−	48.7070i	−0.515908	−	1.58780i	−0.781623	−	0.623751i	$-0.785608\pi$
$941$	−15.8259	−	48.7070i	−0.515908	−	1.58780i	0.265715	−	0.964052i	$-0.414392\pi$
$942$		0			0
$943$	37.8030	+	52.0314i	1.23104	+	1.69438i
$944$	−9.64580	−	3.13411i	−0.313944	−	0.102007i
$945$		0			0
$946$	9.35735	−	30.1696i	0.304234	−	0.980900i
$947$			24.0021i			0.779964i	0.920823	+	0.389982i	$0.127519\pi$
$947$			24.0021i			0.779964i	−0.920823	+	0.389982i	$0.872481\pi$
$948$		0			0
$949$	0.363334	−	0.263978i	0.0117943	−	0.00856908i
$950$	−10.3447	+	14.2382i	−0.335625	+	0.461948i
$951$		0			0
$952$	7.57909	−	2.46259i	0.245640	−	0.0798132i
$953$	42.1151	+	30.5984i	1.36424	+	0.991180i	0.998162	+	0.0605973i	$0.0193005\pi$
$953$	42.1151	+	30.5984i	1.36424	+	0.991180i	0.366081	+	0.930583i	$0.380699\pi$
$954$		0			0
$955$	5.49254	−	16.9043i	0.177734	−	0.547010i
$956$	−2.10995			−0.0682405
$957$		0			0
$958$	38.8107			1.25392
$959$	−0.988485	+	3.04224i	−0.0319198	+	0.0982392i
$960$		0			0
$961$	19.8050	+	14.3892i	0.638870	+	0.464166i
$962$	−0.0379851	+	0.0123421i	−0.00122469	+	0.000397926i
$963$		0			0
$964$	−5.83273	+	8.02806i	−0.187859	+	0.258566i
$965$	−14.1453	+	10.2772i	−0.455353	+	0.330834i
$966$		0			0
$967$		−	43.0557i		−	1.38458i	−0.721620	−	0.692289i	$-0.756602\pi$
$967$		−	43.0557i		−	1.38458i	0.721620	−	0.692289i	$-0.243398\pi$
$968$	8.72260	−	6.70196i	0.280355	−	0.215409i
$969$		0			0
$970$	4.48477	+	1.45719i	0.143997	+	0.0467876i
$971$	−6.25870	−	8.61436i	−0.200851	−	0.276448i	0.696696	−	0.717367i	$-0.254653\pi$
$971$	−6.25870	−	8.61436i	−0.200851	−	0.276448i	−0.897547	+	0.440919i	$0.854653\pi$
$972$		0			0
$973$	−20.4747	−	63.0146i	−0.656388	−	2.02015i
$974$	−8.35940	−	25.7276i	−0.267852	−	0.824365i
$975$		0			0
$976$	−7.57036	−	10.4197i	−0.242321	−	0.333527i
$977$	−7.94989	−	2.58307i	−0.254339	−	0.0826399i	0.179072	−	0.983836i	$-0.442690\pi$
$977$	−7.94989	−	2.58307i	−0.254339	−	0.0826399i	−0.433412	+	0.901196i	$0.642690\pi$
$978$		0			0
$979$	−37.8482	+	0.507565i	−1.20963	+	0.0162218i
$980$		−	20.7492i		−	0.662810i
$981$		0			0
$982$	0.368179	−	0.267498i	0.0117491	−	0.00853619i
$983$	−3.25522	+	4.48042i	−0.103825	+	0.142903i	−0.857768	−	0.514037i	$-0.828149\pi$
$983$	−3.25522	+	4.48042i	−0.103825	+	0.142903i	0.753943	+	0.656940i	$0.228149\pi$
$984$		0			0
$985$	−1.75800	+	0.571209i	−0.0560145	+	0.0182002i
$986$	−3.20374	−	2.32765i	−0.102028	−	0.0741275i
$987$		0			0
$988$	−0.0909254	+	0.279840i	−0.00289272	+	0.00890289i
$989$	−72.0925			−2.29241
$990$		0			0
$991$	54.1183			1.71912			0.859562	−	0.511032i	$-0.170737\pi$
$991$	54.1183			1.71912			0.859562	+	0.511032i	$0.170737\pi$
$992$	0.789035	−	2.42840i	0.0250519	−	0.0771018i
$993$		0			0
$994$	−45.5959	−	33.1273i	−1.44621	−	1.05074i
$995$	−4.25423	+	1.38228i	−0.134868	+	0.0438213i
$996$		0			0
$997$	−26.4174	+	36.3604i	−0.836647	+	1.15155i	0.150002	+	0.988686i	$0.452072\pi$
$997$	−26.4174	+	36.3604i	−0.836647	+	1.15155i	−0.986649	+	0.162860i	$0.947928\pi$
$998$	−8.44213	+	6.13357i	−0.267231	+	0.194155i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.2.l.a.35.1	yes	8
3.2	odd	2		198.2.l.b.35.2	yes	8
4.3	odd	2		1584.2.cd.a.1025.1		8
11.4	even	5		2178.2.b.j.2177.6		8
11.6	odd	10		198.2.l.b.17.2	yes	8
11.7	odd	10		2178.2.b.i.2177.6		8
12.11	even	2		1584.2.cd.b.1025.2		8
33.17	even	10	inner	198.2.l.a.17.1	✓	8
33.26	odd	10		2178.2.b.i.2177.3		8
33.29	even	10		2178.2.b.j.2177.3		8
44.39	even	10		1584.2.cd.b.17.2		8
132.83	odd	10		1584.2.cd.a.17.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.2.l.a.17.1	✓	8	33.17	even	10	inner
198.2.l.a.35.1	yes	8	1.1	even	1	trivial
198.2.l.b.17.2	yes	8	11.6	odd	10
198.2.l.b.35.2	yes	8	3.2	odd	2
1584.2.cd.a.17.1		8	132.83	odd	10
1584.2.cd.a.1025.1		8	4.3	odd	2
1584.2.cd.b.17.2		8	44.39	even	10
1584.2.cd.b.1025.2		8	12.11	even	2
2178.2.b.i.2177.3		8	33.26	odd	10
2178.2.b.i.2177.6		8	11.7	odd	10
2178.2.b.j.2177.3		8	33.29	even	10
2178.2.b.j.2177.6		8	11.4	even	5

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:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	198.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-1.05822 + 0.343836i) q^{5} +(2.97677 - 4.09718i) q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-1.05822 + 0.343836i) q^{5} +(2.97677 - 4.09718i) q^{7} +(-0.809017 + 0.587785i) q^{8} +1.11268i q^{10} +(-0.0444738 - 3.31633i) q^{11} +(-0.0598171 - 0.0194357i) q^{13} +(-2.97677 - 4.09718i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-0.486257 - 1.49654i) q^{17} +(2.74981 + 3.78479i) q^{19} +(1.05822 + 0.343836i) q^{20} +(-3.16776 - 0.982504i) q^{22} +7.56958i q^{23} +(-3.04348 + 2.21122i) q^{25} +(-0.0369690 + 0.0508834i) q^{26} +(-4.81652 + 1.56498i) q^{28} +(2.03598 + 1.47923i) q^{29} +(0.789035 - 2.42840i) q^{31} +1.00000 q^{32} -1.57356 q^{34} +(-1.74132 + 5.35922i) q^{35} +(0.513743 + 0.373256i) q^{37} +(4.44929 - 1.44566i) q^{38} +(0.654014 - 0.900173i) q^{40} +(6.87375 - 4.99407i) q^{41} +9.52398i q^{43} +(-1.91331 + 2.70911i) q^{44} +(7.19910 + 2.33913i) q^{46} +(0.490895 + 0.675659i) q^{47} +(-5.76257 - 17.7354i) q^{49} +(1.16251 + 3.57783i) q^{50} +(0.0369690 + 0.0508834i) q^{52} +(5.23082 + 1.69960i) q^{53} +(1.18733 + 3.49410i) q^{55} +5.06439i q^{56} +(2.03598 - 1.47923i) q^{58} +(-5.96143 + 8.20521i) q^{59} +(-12.2491 + 3.97997i) q^{61} +(-2.06572 - 1.50083i) q^{62} +(0.309017 - 0.951057i) q^{64} +0.0699821 q^{65} +2.91359 q^{67} +(-0.486257 + 1.49654i) q^{68} +(4.55883 + 3.31218i) q^{70} +(10.5839 - 3.43893i) q^{71} +(-4.19709 + 5.77680i) q^{73} +(0.513743 - 0.373256i) q^{74} -4.67826i q^{76} +(-13.7200 - 9.68974i) q^{77} +(10.7537 + 3.49410i) q^{79} +(-0.654014 - 0.900173i) q^{80} +(-2.62554 - 8.08058i) q^{82} +(-3.48002 - 10.7104i) q^{83} +(1.02913 + 1.41648i) q^{85} +(9.05784 + 2.94307i) q^{86} +(1.98527 + 2.65682i) q^{88} -11.4127i q^{89} +(-0.257694 + 0.187225i) q^{91} +(4.44929 - 6.12392i) q^{92} +(0.794285 - 0.258079i) q^{94} +(-4.21124 - 3.05965i) q^{95} +(1.30963 - 4.03062i) q^{97} -18.6481 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{4} - 2 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^8	\( 8 q - 2 q^{2} - 2 q^{4} - 2 q^{8} + 4 q^{11} - 2 q^{16} - 8 q^{17} - 6 q^{22} + 6 q^{25} - 20 q^{26} - 10 q^{28} + 10 q^{29} - 14 q^{31} + 8 q^{32} - 8 q^{34} + 10 q^{35} + 20 q^{38} - 10 q^{40} - 8 q^{41} - 6 q^{44} + 20 q^{46} + 20 q^{47} + 6 q^{49} - 4 q^{50} + 20 q^{52} + 30 q^{53} + 28 q^{55} + 10 q^{58} - 20 q^{59} + 20 q^{61} + 16 q^{62} - 2 q^{64} - 64 q^{65} - 56 q^{67} - 8 q^{68} + 10 q^{70} + 20 q^{71} - 10 q^{73} - 20 q^{79} + 10 q^{80} + 12 q^{82} - 12 q^{83} + 20 q^{86} - 6 q^{88} + 20 q^{92} - 20 q^{94} + 16 q^{95} - 12 q^{97} - 44 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^8 + 4 * q^11 - 2 * q^16 - 8 * q^17 - 6 * q^22 + 6 * q^25 - 20 * q^26 - 10 * q^28 + 10 * q^29 - 14 * q^31 + 8 * q^32 - 8 * q^34 + 10 * q^35 + 20 * q^38 - 10 * q^40 - 8 * q^41 - 6 * q^44 + 20 * q^46 + 20 * q^47 + 6 * q^49 - 4 * q^50 + 20 * q^52 + 30 * q^53 + 28 * q^55 + 10 * q^58 - 20 * q^59 + 20 * q^61 + 16 * q^62 - 2 * q^64 - 64 * q^65 - 56 * q^67 - 8 * q^68 + 10 * q^70 + 20 * q^71 - 10 * q^73 - 20 * q^79 + 10 * q^80 + 12 * q^82 - 12 * q^83 + 20 * q^86 - 6 * q^88 + 20 * q^92 - 20 * q^94 + 16 * q^95 - 12 * q^97 - 44 * q^98

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