LMFDB - Embedded newform 693.2.m.j.190.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 12 x^{18} - 3 x^{17} + 94 x^{16} - 10 x^{15} + 662 x^{14} - 153 x^{13} + 4638 x^{12} + \cdots + 121 $ x^20 + 12x^18 - 3x^17 + 94x^16 - 10x^15 + 662x^14 - 153x^13 + 4638x^12 - 1174x^11 + 15808x^10 - 3393x^9 + 26062x^8 - 15494x^7 + 11660x^6 - 33295x^5 + 67756x^4 - 43696x^3 + 13084x^2 - 1155x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.4
Root			$0.705143 + 0.512316i$ of defining polynomial
Character	$\chi$	$=$	693.190
Dual form			693.2.m.j.631.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.705143 - 0.512316i) q^{2} +(-0.383276 + 1.17960i) q^{4} +(-3.28814 - 2.38897i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(0.872746 + 2.68604i) q^{8} +O(q^{10})$	\(q+(0.705143 - 0.512316i) q^{2} +(-0.383276 + 1.17960i) q^{4} +(-3.28814 - 2.38897i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(0.872746 + 2.68604i) q^{8} -3.54252 q^{10} +(2.96738 + 1.48143i) q^{11} +(4.92697 - 3.57965i) q^{13} +(0.269341 + 0.828945i) q^{14} +(-0.0153474 - 0.0111506i) q^{16} +(1.37664 + 1.00019i) q^{17} +(1.68634 + 5.19003i) q^{19} +(4.07830 - 2.96306i) q^{20} +(2.85139 - 0.475616i) q^{22} +6.39153 q^{23} +(3.55958 + 10.9553i) q^{25} +(1.64030 - 5.04833i) q^{26} +(-1.00343 - 0.729034i) q^{28} +(-1.46763 + 4.51690i) q^{29} +(3.52981 - 2.56456i) q^{31} -5.66506 q^{32} +1.48314 q^{34} +(3.28814 - 2.38897i) q^{35} +(0.753854 - 2.32012i) q^{37} +(3.84805 + 2.79577i) q^{38} +(3.54716 - 10.9170i) q^{40} +(0.992058 + 3.05324i) q^{41} +0.127191 q^{43} +(-2.88483 + 2.93253i) q^{44} +(4.50694 - 3.27449i) q^{46} +(-2.61671 - 8.05340i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(8.12258 + 5.90140i) q^{50} +(2.33417 + 7.18385i) q^{52} +(-3.81374 + 2.77084i) q^{53} +(-6.21806 - 11.9602i) q^{55} -2.82426 q^{56} +(1.27919 + 3.93695i) q^{58} +(-1.43188 + 4.40689i) q^{59} +(-4.29654 - 3.12162i) q^{61} +(1.17516 - 3.61676i) q^{62} +(-3.96398 + 2.88000i) q^{64} -24.7522 q^{65} +14.0686 q^{67} +(-1.70746 + 1.24054i) q^{68} +(1.09470 - 3.36913i) q^{70} +(1.79507 + 1.30420i) q^{71} +(-1.72244 + 5.30112i) q^{73} +(-0.657063 - 2.02223i) q^{74} -6.76849 q^{76} +(-2.32590 + 2.36436i) q^{77} +(-5.07362 + 3.68620i) q^{79} +(0.0238261 + 0.0733293i) q^{80} +(2.26377 + 1.64472i) q^{82} +(-0.103329 - 0.0750731i) q^{83} +(-2.13717 - 6.57753i) q^{85} +(0.0896877 - 0.0651619i) q^{86} +(-1.38941 + 9.26341i) q^{88} +8.12736 q^{89} +(1.88193 + 5.79200i) q^{91} +(-2.44972 + 7.53946i) q^{92} +(-5.97104 - 4.33821i) q^{94} +(6.85391 - 21.0942i) q^{95} +(2.10118 - 1.52660i) q^{97} -0.871604 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8}+O(q^{10}) $ 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8	$ 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8} + 12 q^{10} + q^{11} + 13 q^{13} - 24 q^{16} + q^{17} + 10 q^{19} + 46 q^{20} + 26 q^{22} - 8 q^{25} + 53 q^{26} + 4 q^{28} - 3 q^{29} - 13 q^{31} - 82 q^{32} + 42 q^{34} - 5 q^{35} - 32 q^{37} - 16 q^{38} + 20 q^{40} + 3 q^{41} + 12 q^{43} - 25 q^{44} - 13 q^{46} - 20 q^{47} - 5 q^{49} + 83 q^{50} - 80 q^{52} - 3 q^{53} - 28 q^{55} + 6 q^{56} + 2 q^{58} + 9 q^{59} - 15 q^{61} + 37 q^{62} - 49 q^{64} - 58 q^{65} + 76 q^{67} - 51 q^{68} + 3 q^{70} - 37 q^{71} + 27 q^{73} + 32 q^{74} + 4 q^{76} - 6 q^{77} + 5 q^{79} - 137 q^{80} - 55 q^{82} + 42 q^{83} - 48 q^{85} - 3 q^{86} + 151 q^{88} + 18 q^{89} + 7 q^{91} - 39 q^{92} - 35 q^{94} + 96 q^{95} - 27 q^{97}+O(q^{100}) $ 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8 + 12 * q^10 + q^11 + 13 * q^13 - 24 * q^16 + q^17 + 10 * q^19 + 46 * q^20 + 26 * q^22 - 8 * q^25 + 53 * q^26 + 4 * q^28 - 3 * q^29 - 13 * q^31 - 82 * q^32 + 42 * q^34 - 5 * q^35 - 32 * q^37 - 16 * q^38 + 20 * q^40 + 3 * q^41 + 12 * q^43 - 25 * q^44 - 13 * q^46 - 20 * q^47 - 5 * q^49 + 83 * q^50 - 80 * q^52 - 3 * q^53 - 28 * q^55 + 6 * q^56 + 2 * q^58 + 9 * q^59 - 15 * q^61 + 37 * q^62 - 49 * q^64 - 58 * q^65 + 76 * q^67 - 51 * q^68 + 3 * q^70 - 37 * q^71 + 27 * q^73 + 32 * q^74 + 4 * q^76 - 6 * q^77 + 5 * q^79 - 137 * q^80 - 55 * q^82 + 42 * q^83 - 48 * q^85 - 3 * q^86 + 151 * q^88 + 18 * q^89 + 7 * q^91 - 39 * q^92 - 35 * q^94 + 96 * q^95 - 27 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	0.705143	−	0.512316i	0.498611	−	0.362262i	−0.309875	−	0.950777i	$-0.600287\pi$
$2$	0.705143	−	0.512316i	0.498611	−	0.362262i	0.808486	+	0.588515i	$0.200287\pi$
$3$		0			0
$3$		0			0
$4$	−0.383276	+	1.17960i	−0.191638	+	0.589800i
$5$	−3.28814	−	2.38897i	−1.47050	−	1.06838i	−0.980468	−	0.196677i	$-0.936985\pi$
$5$	−3.28814	−	2.38897i	−1.47050	−	1.06838i	−0.490033	−	0.871704i	$-0.663015\pi$
$6$		0			0
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$	0.872746	+	2.68604i	0.308562	+	0.949657i
$9$		0			0
$10$	−3.54252			−1.12024
$11$	2.96738	+	1.48143i	0.894699	+	0.446669i
$11$	2.96738	+	1.48143i	0.894699	+	0.446669i
$12$		0			0
$13$	4.92697	−	3.57965i	1.36649	−	0.992816i	0.368493	−	0.929631i	$-0.379874\pi$
$13$	4.92697	−	3.57965i	1.36649	−	0.992816i	0.998002	−	0.0631857i	$-0.0201260\pi$
$14$	0.269341	+	0.828945i	0.0719843	+	0.221545i
$15$		0			0
$16$	−0.0153474	−	0.0111506i	−0.00383686	−	0.00278764i
$17$	1.37664	+	1.00019i	0.333885	+	0.242582i	0.742077	−	0.670314i	$-0.233841\pi$
$17$	1.37664	+	1.00019i	0.333885	+	0.242582i	−0.408192	+	0.912896i	$0.633841\pi$
$18$		0			0
$19$	1.68634	+	5.19003i	0.386873	+	1.19067i	0.935112	+	0.354352i	$0.115298\pi$
$19$	1.68634	+	5.19003i	0.386873	+	1.19067i	−0.548239	+	0.836322i	$0.684702\pi$
$20$	4.07830	−	2.96306i	0.911935	−	0.662560i
$21$		0			0
$22$	2.85139	−	0.475616i	0.607918	−	0.101402i
$23$	6.39153			1.33273			0.666363	−	0.745627i	$-0.267850\pi$
$23$	6.39153			1.33273			0.666363	+	0.745627i	$0.267850\pi$
$24$		0			0
$25$	3.55958	+	10.9553i	0.711917	+	2.19106i
$26$	1.64030	−	5.04833i	0.321690	−	0.990059i
$27$		0			0
$28$	−1.00343	−	0.729034i	−0.189630	−	0.137774i
$29$	−1.46763	+	4.51690i	−0.272532	+	0.838767i	0.717330	+	0.696733i	$0.245364\pi$
$29$	−1.46763	+	4.51690i	−0.272532	+	0.838767i	−0.989862	+	0.142033i	$0.954636\pi$
$30$		0			0
$31$	3.52981	−	2.56456i	0.633973	−	0.460608i	−0.223801	−	0.974635i	$-0.571847\pi$
$31$	3.52981	−	2.56456i	0.633973	−	0.460608i	0.857774	+	0.514026i	$0.171847\pi$
$32$	−5.66506			−1.00145
$33$		0			0
$34$	1.48314			0.254357
$35$	3.28814	−	2.38897i	0.555797	−	0.403810i
$36$		0			0
$37$	0.753854	−	2.32012i	0.123933	−	0.381426i	−0.869772	−	0.493453i	$-0.835734\pi$
$37$	0.753854	−	2.32012i	0.123933	−	0.381426i	0.993705	+	0.112027i	$0.0357344\pi$
$38$	3.84805	+	2.79577i	0.624236	+	0.453534i
$39$		0			0
$40$	3.54716	−	10.9170i	0.560855	−	1.72613i
$41$	0.992058	+	3.05324i	0.154933	+	0.476836i	0.998154	−	0.0607314i	$-0.0193433\pi$
$41$	0.992058	+	3.05324i	0.154933	+	0.476836i	−0.843221	+	0.537568i	$0.819343\pi$
$42$		0			0
$43$	0.127191			0.0193964			0.00969821	−	0.999953i	$-0.496913\pi$
$43$	0.127191			0.0193964			0.00969821	+	0.999953i	$0.496913\pi$
$44$	−2.88483	+	2.93253i	−0.434904	+	0.442095i
$45$		0			0
$46$	4.50694	−	3.27449i	0.664512	−	0.482797i
$47$	−2.61671	−	8.05340i	−0.381686	−	1.17471i	−0.938856	−	0.344310i	$-0.888113\pi$
$47$	−2.61671	−	8.05340i	−0.381686	−	1.17471i	0.557170	−	0.830399i	$-0.311887\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	8.12258	+	5.90140i	1.14871	+	0.834584i
$51$		0			0
$52$	2.33417	+	7.18385i	0.323692	+	0.996220i
$53$	−3.81374	+	2.77084i	−0.523857	+	0.380604i	−0.818055	−	0.575140i	$-0.804948\pi$
$53$	−3.81374	+	2.77084i	−0.523857	+	0.380604i	0.294198	+	0.955745i	$0.404948\pi$
$54$		0			0
$55$	−6.21806	−	11.9602i	−0.838443	−	1.61271i
$56$	−2.82426			−0.377408
$57$		0			0
$58$	1.27919	+	3.93695i	0.167966	+	0.516946i
$59$	−1.43188	+	4.40689i	−0.186416	+	0.573728i	−0.999970	−	0.00776089i	$-0.997530\pi$
$59$	−1.43188	+	4.40689i	−0.186416	+	0.573728i	0.813554	+	0.581489i	$0.197530\pi$
$60$		0			0
$61$	−4.29654	−	3.12162i	−0.550115	−	0.399682i	0.277713	−	0.960664i	$-0.410424\pi$
$61$	−4.29654	−	3.12162i	−0.550115	−	0.399682i	−0.827828	+	0.560982i	$0.810424\pi$
$62$	1.17516	−	3.61676i	0.149245	−	0.459329i
$63$		0			0
$64$	−3.96398	+	2.88000i	−0.495498	+	0.360000i
$65$	−24.7522			−3.07014
$66$		0			0
$67$	14.0686			1.71876			0.859379	−	0.511340i	$-0.170851\pi$
$67$	14.0686			1.71876			0.859379	+	0.511340i	$0.170851\pi$
$68$	−1.70746	+	1.24054i	−0.207060	+	0.150438i
$69$		0			0
$70$	1.09470	−	3.36913i	0.130841	−	0.402689i
$71$	1.79507	+	1.30420i	0.213036	+	0.154780i	0.689186	−	0.724584i	$-0.257968\pi$
$71$	1.79507	+	1.30420i	0.213036	+	0.154780i	−0.476150	+	0.879364i	$0.657968\pi$
$72$		0			0
$73$	−1.72244	+	5.30112i	−0.201596	+	0.620449i	0.798240	+	0.602340i	$0.205765\pi$
$73$	−1.72244	+	5.30112i	−0.201596	+	0.620449i	−0.999836	+	0.0181095i	$0.994235\pi$
$74$	−0.657063	−	2.02223i	−0.0763820	−	0.235080i
$75$		0			0
$76$	−6.76849			−0.776400
$77$	−2.32590	+	2.36436i	−0.265061	+	0.269444i
$78$		0			0
$79$	−5.07362	+	3.68620i	−0.570827	+	0.414730i	−0.835406	−	0.549634i	$-0.814767\pi$
$79$	−5.07362	+	3.68620i	−0.570827	+	0.414730i	0.264579	+	0.964364i	$0.414767\pi$
$80$	0.0238261	+	0.0733293i	0.00266384	+	0.00819846i
$81$		0			0
$82$	2.26377	+	1.64472i	0.249991	+	0.181629i
$83$	−0.103329	−	0.0750731i	−0.0113419	−	0.00824034i	0.582100	−	0.813117i	$-0.302231\pi$
$83$	−0.103329	−	0.0750731i	−0.0113419	−	0.00824034i	−0.593442	+	0.804877i	$0.702231\pi$
$84$		0			0
$85$	−2.13717	−	6.57753i	−0.231809	−	0.713433i
$86$	0.0896877	−	0.0651619i	0.00967127	−	0.00702659i
$87$		0			0
$88$	−1.38941	+	9.26341i	−0.148112	+	0.987483i
$89$	8.12736			0.861498			0.430749	−	0.902472i	$-0.358249\pi$
$89$	8.12736			0.861498			0.430749	+	0.902472i	$0.358249\pi$
$90$		0			0
$91$	1.88193	+	5.79200i	0.197280	+	0.607166i
$92$	−2.44972	+	7.53946i	−0.255401	+	0.786043i
$93$		0			0
$94$	−5.97104	−	4.33821i	−0.615866	−	0.447453i
$95$	6.85391	−	21.0942i	0.703196	−	2.16422i
$96$		0			0
$97$	2.10118	−	1.52660i	0.213343	−	0.155003i	−0.475982	−	0.879455i	$-0.657907\pi$
$97$	2.10118	−	1.52660i	0.213343	−	0.155003i	0.689325	+	0.724452i	$0.257907\pi$
$98$	−0.871604			−0.0880453
$99$		0			0
$100$	−14.2872			−1.42872
$101$	−4.87492	+	3.54184i	−0.485073	+	0.352426i	−0.803286	−	0.595593i	$-0.796917\pi$
$101$	−4.87492	+	3.54184i	−0.485073	+	0.352426i	0.318214	+	0.948019i	$0.396917\pi$
$102$		0			0
$103$	3.98440	−	12.2627i	0.392595	−	1.20828i	−0.538224	−	0.842802i	$-0.680905\pi$
$103$	3.98440	−	12.2627i	0.392595	−	1.20828i	0.930819	−	0.365481i	$-0.119095\pi$
$104$	13.9151	+	10.1099i	1.36448	+	0.991355i
$105$		0			0
$106$	−1.26968	+	3.90768i	−0.123322	+	0.379547i
$107$	1.65250	+	5.08587i	0.159753	+	0.491669i	0.998611	−	0.0526805i	$-0.0167765\pi$
$107$	1.65250	+	5.08587i	0.159753	+	0.491669i	−0.838858	+	0.544350i	$0.816776\pi$
$108$		0			0
$109$	−1.44173			−0.138093			−0.0690465	−	0.997613i	$-0.521996\pi$
$109$	−1.44173			−0.138093			−0.0690465	+	0.997613i	$0.521996\pi$
$110$	−10.5120	−	5.24800i	−1.00228	−	0.500377i
$111$		0			0
$112$	0.0153474	−	0.0111506i	0.00145020	−	0.00105363i
$113$	−6.03121	−	18.5621i	−0.567368	−	1.74618i	−0.660808	−	0.750555i	$-0.729786\pi$
$113$	−6.03121	−	18.5621i	−0.567368	−	1.74618i	0.0934402	−	0.995625i	$-0.470214\pi$
$114$		0			0
$115$	−21.0163	−	15.2692i	−1.95978	−	1.42386i
$116$	−4.76563	−	3.46243i	−0.442478	−	0.321479i
$117$		0			0
$118$	1.24804	+	3.84106i	0.114891	+	0.353598i
$119$	−1.37664	+	1.00019i	−0.126197	+	0.0916873i
$120$		0			0
$121$	6.61071	+	8.79196i	0.600974	+	0.799269i
$122$	−4.62893			−0.419083
$123$		0			0
$124$	1.67227	+	5.14670i	0.150174	+	0.462188i
$125$	8.18766	−	25.1990i	0.732327	−	2.25387i
$126$		0			0
$127$	0.519157	+	0.377189i	0.0460677	+	0.0334701i	0.610581	−	0.791954i	$-0.290936\pi$
$127$	0.519157	+	0.377189i	0.0460677	+	0.0334701i	−0.564513	+	0.825424i	$0.690936\pi$
$128$	2.18150	−	6.71397i	0.192819	−	0.593436i
$129$		0			0
$130$	−17.4539	+	12.6810i	−1.53081	+	1.11220i
$131$	13.9987			1.22307			0.611537	−	0.791216i	$-0.290552\pi$
$131$	13.9987			1.22307			0.611537	+	0.791216i	$0.290552\pi$
$132$		0			0
$133$	−5.45712			−0.473192
$134$	9.92039	−	7.20759i	0.856992	−	0.622641i
$135$		0			0
$136$	−1.48509	+	4.57062i	−0.127345	+	0.391928i
$137$	−2.18449	−	1.58712i	−0.186633	−	0.135597i	0.490545	−	0.871416i	$-0.336798\pi$
$137$	−2.18449	−	1.58712i	−0.186633	−	0.135597i	−0.677179	+	0.735819i	$0.736798\pi$
$138$		0			0
$139$	−0.637168	+	1.96100i	−0.0540439	+	0.166330i	−0.974435	−	0.224668i	$-0.927870\pi$
$139$	−0.637168	+	1.96100i	−0.0540439	+	0.166330i	0.920391	+	0.390998i	$0.127870\pi$
$140$	1.55777	+	4.79433i	0.131656	+	0.405195i
$141$		0			0
$142$	1.93395			0.162293
$143$	19.9232	−	3.32322i	1.66606	−	0.277902i
$144$		0			0
$145$	15.6165	−	11.3461i	1.29688	−	0.942239i
$146$	1.50128	+	4.62048i	0.124247	+	0.382394i
$147$		0			0
$148$	2.44789	+	1.77849i	0.201215	+	0.146191i
$149$	8.15727	+	5.92661i	0.668270	+	0.485526i	0.869446	−	0.494029i	$-0.164476\pi$
$149$	8.15727	+	5.92661i	0.668270	+	0.485526i	−0.201176	+	0.979555i	$0.564476\pi$
$150$		0			0
$151$	−4.62410	−	14.2315i	−0.376304	−	1.15815i	−0.942595	−	0.333939i	$-0.891622\pi$
$151$	−4.62410	−	14.2315i	−0.376304	−	1.15815i	0.566290	−	0.824206i	$-0.308378\pi$
$152$	−12.4688	+	9.05915i	−1.01136	+	0.734794i
$153$		0			0
$154$	−0.428790	+	2.85881i	−0.0345529	+	0.230369i
$155$	−17.7332			−1.42436
$156$		0			0
$157$	6.01162	+	18.5019i	0.479780	+	1.47661i	0.839401	+	0.543512i	$0.182906\pi$
$157$	6.01162	+	18.5019i	0.479780	+	1.47661i	−0.359622	+	0.933098i	$0.617094\pi$
$158$	−1.68913	+	5.19860i	−0.134380	+	0.413578i
$159$		0			0
$160$	18.6275	+	13.5337i	1.47264	+	1.06993i
$161$	−1.97509	+	6.07871i	−0.155659	+	0.479069i
$162$		0			0
$163$	−9.79754	+	7.11833i	−0.767403	+	0.557551i	−0.901172	−	0.433462i	$-0.857292\pi$
$163$	−9.79754	+	7.11833i	−0.767403	+	0.557551i	0.133769	+	0.991013i	$0.457292\pi$
$164$	−3.98184			−0.310929
$165$		0			0
$166$	−0.111323			−0.00864034
$167$	−10.6531	+	7.73994i	−0.824363	+	0.598935i	−0.917959	−	0.396675i	$-0.870164\pi$
$167$	−10.6531	+	7.73994i	−0.824363	+	0.598935i	0.0935958	+	0.995610i	$0.470164\pi$
$168$		0			0
$169$	7.44388	−	22.9099i	0.572606	−	1.76230i
$170$	−4.87678	−	3.54319i	−0.374032	−	0.271750i
$171$		0			0
$172$	−0.0487491	+	0.150034i	−0.00371709	+	0.0114400i
$173$	4.54809	+	13.9976i	0.345785	+	1.06422i	0.961162	+	0.275984i	$0.0890036\pi$
$173$	4.54809	+	13.9976i	0.345785	+	1.06422i	−0.615377	+	0.788233i	$0.710996\pi$
$174$		0			0
$175$	−11.5191			−0.870759
$176$	−0.0290229	−	0.0558242i	−0.00218768	−	0.00420791i
$177$		0			0
$178$	5.73095	−	4.16378i	0.429553	−	0.312088i
$179$	3.61252	+	11.1182i	0.270013	+	0.831014i	0.990496	+	0.137541i	$0.0439200\pi$
$179$	3.61252	+	11.1182i	0.270013	+	0.831014i	−0.720483	+	0.693472i	$0.756080\pi$
$180$		0			0
$181$	−15.9378	−	11.5795i	−1.18465	−	0.860698i	−0.191961	−	0.981403i	$-0.561485\pi$
$181$	−15.9378	−	11.5795i	−1.18465	−	0.860698i	−0.992689	+	0.120704i	$0.961485\pi$
$182$	4.29436	+	3.12004i	0.318319	+	0.231273i
$183$		0			0
$184$	5.57818	+	17.1679i	0.411229	+	1.26563i
$185$	−8.02149	+	5.82796i	−0.589752	+	0.428480i
$186$		0			0
$187$	2.60331	+	5.00735i	0.190373	+	0.366174i
$188$	10.5027			0.765989
$189$		0			0
$190$	−5.97390	−	18.3858i	−0.433392	−	1.33384i
$191$	−2.15136	+	6.62120i	−0.155667	+	0.479093i	−0.998228	−	0.0595077i	$-0.981047\pi$
$191$	−2.15136	+	6.62120i	−0.155667	+	0.479093i	0.842561	+	0.538601i	$0.181047\pi$
$192$		0			0
$193$	−13.6427	−	9.91199i	−0.982022	−	0.713481i	−0.0238626	−	0.999715i	$-0.507596\pi$
$193$	−13.6427	−	9.91199i	−0.982022	−	0.713481i	−0.958160	+	0.286234i	$0.907596\pi$
$194$	0.699533	−	2.15294i	0.0502235	−	0.154572i
$195$		0			0
$196$	1.00343	−	0.729034i	0.0716735	−	0.0520738i
$197$	−6.42145			−0.457510			−0.228755	−	0.973484i	$-0.573465\pi$
$197$	−6.42145			−0.457510			−0.228755	+	0.973484i	$0.573465\pi$
$198$		0			0
$199$	−13.2645			−0.940297			−0.470149	−	0.882587i	$-0.655800\pi$
$199$	−13.2645			−0.940297			−0.470149	+	0.882587i	$0.655800\pi$
$200$	−26.3196	+	19.1223i	−1.86108	+	1.35215i
$201$		0			0
$202$	−1.62297	+	4.99500i	−0.114192	+	0.351447i
$203$	−3.84230	−	2.79160i	−0.269677	−	0.195932i
$204$		0			0
$205$	4.03209	−	12.4095i	0.281613	−	0.866716i
$206$	−3.47282	−	10.6882i	−0.241963	−	0.744685i
$207$		0			0
$208$	−0.115531			−0.00801067
$209$	−2.68466	+	17.8990i	−0.185702	+	1.23810i
$210$		0			0
$211$	−2.35552	+	1.71139i	−0.162161	+	0.117817i	−0.665906	−	0.746035i	$-0.731955\pi$
$211$	−2.35552	+	1.71139i	−0.162161	+	0.117817i	0.503746	+	0.863852i	$0.331955\pi$
$212$	−1.80678	−	5.56068i	−0.124090	−	0.381909i
$213$		0			0
$214$	3.77082	+	2.73966i	0.257768	+	0.187279i
$215$	−0.418221	−	0.303855i	−0.0285224	−	0.0207228i
$216$		0			0
$217$	1.34827	+	4.14954i	0.0915264	+	0.281689i
$218$	−1.01663	+	0.738623i	−0.0688547	+	0.0500259i
$219$		0			0
$220$	16.4914	−	2.75080i	1.11185	−	0.185459i
$221$	10.3630			0.697091
$222$		0			0
$223$	−1.03697	−	3.19146i	−0.0694406	−	0.213716i	0.910314	−	0.413918i	$-0.135840\pi$
$223$	−1.03697	−	3.19146i	−0.0694406	−	0.213716i	−0.979755	+	0.200202i	$0.935840\pi$
$224$	1.75060	−	5.38780i	0.116967	−	0.359987i
$225$		0			0
$226$	−13.7625	−	9.99908i	−0.915471	−	0.665129i
$227$	−1.03147	+	3.17454i	−0.0684612	+	0.210702i	−0.979434	−	0.201764i	$-0.935332\pi$
$227$	−1.03147	+	3.17454i	−0.0684612	+	0.210702i	0.910973	+	0.412466i	$0.135332\pi$
$228$		0			0
$229$	−5.50248	+	3.99778i	−0.363614	+	0.264181i	−0.754558	−	0.656234i	$-0.772149\pi$
$229$	−5.50248	+	3.99778i	−0.363614	+	0.264181i	0.390944	+	0.920414i	$0.372149\pi$
$230$	−22.6421			−1.49298
$231$		0			0
$232$	−13.4134			−0.880634
$233$	5.00420	−	3.63576i	0.327836	−	0.238187i	−0.411676	−	0.911330i	$-0.635056\pi$
$233$	5.00420	−	3.63576i	0.327836	−	0.238187i	0.739512	+	0.673144i	$0.235056\pi$
$234$		0			0
$235$	−10.6353	+	32.7319i	−0.693767	+	2.13520i
$236$	−4.64956	−	3.37811i	−0.302661	−	0.219896i
$237$		0			0
$238$	−0.458317	+	1.41055i	−0.0297082	+	0.0914326i
$239$	−6.32817	−	19.4761i	−0.409335	−	1.25980i	−0.917220	−	0.398380i	$-0.869573\pi$
$239$	−6.32817	−	19.4761i	−0.409335	−	1.25980i	0.507885	−	0.861425i	$-0.330427\pi$
$240$		0			0
$241$	1.04113			0.0670653			0.0335326	−	0.999438i	$-0.489324\pi$
$241$	1.04113			0.0670653			0.0335326	+	0.999438i	$0.489324\pi$
$242$	9.16576	+	2.81281i	0.589197	+	0.180814i
$243$		0			0
$244$	5.32902	−	3.87176i	0.341155	−	0.247864i
$245$	1.25596	+	3.86544i	0.0802402	+	0.246954i
$246$		0			0
$247$	26.8870	+	19.5346i	1.71078	+	1.24295i
$248$	9.96913	+	7.24299i	0.633040	+	0.459931i
$249$		0			0
$250$	−7.13640	−	21.9636i	−0.451346	−	1.38910i
$251$	5.36621	−	3.89878i	0.338712	−	0.246089i	−0.405406	−	0.914137i	$-0.632870\pi$
$251$	5.36621	−	3.89878i	0.338712	−	0.246089i	0.744118	+	0.668048i	$0.232870\pi$
$252$		0			0
$253$	18.9661	+	9.46863i	1.19239	+	0.595287i
$254$	0.559320			0.0350948
$255$		0			0
$256$	−4.92962	−	15.1718i	−0.308101	−	0.948238i
$257$	−0.890729	+	2.74138i	−0.0555622	+	0.171003i	−0.974986	−	0.222264i	$-0.928655\pi$
$257$	−0.890729	+	2.74138i	−0.0555622	+	0.171003i	0.919424	+	0.393267i	$0.128655\pi$
$258$		0			0
$259$	1.97362	+	1.43392i	0.122635	+	0.0890992i
$260$	9.48693	−	29.1978i	0.588354	−	1.81077i
$261$		0			0
$262$	9.87109	−	7.17177i	0.609838	−	0.443073i
$263$	21.1018			1.30119			0.650595	−	0.759425i	$-0.274520\pi$
$263$	21.1018			1.30119			0.650595	+	0.759425i	$0.274520\pi$
$264$		0			0
$265$	19.1596			1.17696
$266$	−3.84805	+	2.79577i	−0.235939	+	0.171420i
$267$		0			0
$268$	−5.39216	+	16.5954i	−0.329379	+	1.01372i
$269$	−13.8597	−	10.0696i	−0.845040	−	0.613957i	0.0787342	−	0.996896i	$-0.474912\pi$
$269$	−13.8597	−	10.0696i	−0.845040	−	0.613957i	−0.923774	+	0.382938i	$0.874912\pi$
$270$		0			0
$271$	5.05547	−	15.5591i	0.307098	−	0.945151i	−0.671788	−	0.740744i	$-0.734473\pi$
$271$	5.05547	−	15.5591i	0.307098	−	0.945151i	0.978886	−	0.204407i	$-0.0655266\pi$
$272$	−0.00997527	−	0.0307007i	−0.000604839	−	0.00186150i
$273$		0			0
$274$	−2.35348			−0.142179
$275$	−5.66686	+	37.7818i	−0.341725	+	2.27833i
$276$		0			0
$277$	2.00516	−	1.45684i	0.120479	−	0.0875329i	−0.525914	−	0.850538i	$-0.676277\pi$
$277$	2.00516	−	1.45684i	0.120479	−	0.0875329i	0.646393	+	0.763005i	$0.276277\pi$
$278$	0.555358	+	1.70922i	0.0333082	+	0.102512i
$279$		0			0
$280$	9.28658	+	6.74709i	0.554979	+	0.403216i
$281$	19.5740	+	14.2214i	1.16769	+	0.848375i	0.990730	−	0.135843i	$-0.0433744\pi$
$281$	19.5740	+	14.2214i	1.16769	+	0.848375i	0.176958	+	0.984218i	$0.443374\pi$
$282$		0			0
$283$	−9.01893	−	27.7574i	−0.536119	−	1.65001i	−0.741218	−	0.671265i	$-0.765751\pi$
$283$	−9.01893	−	27.7574i	−0.536119	−	1.65001i	0.205098	−	0.978741i	$-0.434249\pi$
$284$	−2.22644	+	1.61760i	−0.132115	+	0.0959872i
$285$		0			0
$286$	12.3462	−	12.5503i	0.730044	−	0.742116i
$287$	−3.21037			−0.189502
$288$		0			0
$289$	−4.35852	−	13.4142i	−0.256384	−	0.789068i
$290$	5.19910	−	16.0012i	0.305302	−	0.939622i
$291$		0			0
$292$	−5.59304	−	4.06358i	−0.327308	−	0.237803i
$293$	8.40272	−	25.8609i	0.490892	−	1.51081i	−0.332369	−	0.943149i	$-0.607848\pi$
$293$	8.40272	−	25.8609i	0.490892	−	1.51081i	0.823262	−	0.567662i	$-0.192152\pi$
$294$		0			0
$295$	15.2362	−	11.0697i	0.887085	−	0.644505i
$296$	6.88986			0.400465
$297$		0			0
$298$	8.78834			0.509095
$299$	31.4909	−	22.8794i	1.82116	−	1.32315i
$300$		0			0
$301$	−0.0393041	+	0.120966i	−0.00226545	+	0.00697234i
$302$	−10.5517	−	7.66625i	−0.607182	−	0.441143i
$303$		0			0
$304$	0.0319907	−	0.0984573i	0.00183479	−	0.00564691i
$305$	6.67015	+	20.5286i	0.381932	+	1.17547i
$306$		0			0
$307$	−9.95364			−0.568084			−0.284042	−	0.958812i	$-0.591676\pi$
$307$	−9.95364			−0.568084			−0.284042	+	0.958812i	$0.591676\pi$
$308$	−1.89754	−	3.64983i	−0.108122	−	0.207969i
$309$		0			0
$310$	−12.5044	+	9.08500i	−0.710204	+	0.515993i
$311$	−5.01864	−	15.4458i	−0.284581	−	0.875850i	−0.986524	−	0.163617i	$-0.947684\pi$
$311$	−5.01864	−	15.4458i	−0.284581	−	0.875850i	0.701943	−	0.712233i	$-0.252316\pi$
$312$		0			0
$313$	−13.4417	−	9.76594i	−0.759768	−	0.552004i	0.139071	−	0.990282i	$-0.455588\pi$
$313$	−13.4417	−	9.76594i	−0.759768	−	0.552004i	−0.898839	+	0.438279i	$0.855588\pi$
$314$	13.7179	+	9.96661i	0.774144	+	0.562448i
$315$		0			0
$316$	−2.40365	−	7.39768i	−0.135216	−	0.416152i
$317$	6.55305	−	4.76107i	0.368056	−	0.267408i	−0.388348	−	0.921513i	$-0.626954\pi$
$317$	6.55305	−	4.76107i	0.368056	−	0.267408i	0.756404	+	0.654104i	$0.226954\pi$
$318$		0			0
$319$	−11.0465	+	11.2292i	−0.618485	+	0.628713i
$320$	19.9144			1.11325
$321$		0			0
$322$	1.72150	+	5.29823i	0.0959354	+	0.295259i
$323$	−2.86952	+	8.83148i	−0.159664	+	0.491397i
$324$		0			0
$325$	56.7540	+	41.2342i	3.14815	+	2.28726i
$326$	−3.26183	+	10.0389i	−0.180656	+	0.556002i
$327$		0			0
$328$	−7.33530	+	5.32941i	−0.405024	+	0.294267i
$329$	8.46784			0.466847
$330$		0			0
$331$	−6.64605			−0.365300			−0.182650	−	0.983178i	$-0.558468\pi$
$331$	−6.64605			−0.365300			−0.182650	+	0.983178i	$0.558468\pi$
$332$	0.128160	−	0.0931136i	0.00703369	−	0.00511027i
$333$		0			0
$334$	−3.54667	+	10.9155i	−0.194065	+	0.597271i
$335$	−46.2596	−	33.6096i	−2.52743	−	1.83629i
$336$		0			0
$337$	−6.47454	+	19.9266i	−0.352691	+	1.08547i	0.604646	+	0.796494i	$0.293315\pi$
$337$	−6.47454	+	19.9266i	−0.352691	+	1.08547i	−0.957336	+	0.288976i	$0.906685\pi$
$338$	−6.48811	−	19.9684i	−0.352907	−	1.08614i
$339$		0			0
$340$	8.57798			0.465207
$341$	14.2735	−	2.38084i	0.772955	−	0.128930i
$342$		0			0
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	0.111005	+	0.341639i	0.00598500	+	0.0184199i
$345$		0			0
$346$	10.3782	+	7.54023i	0.557938	+	0.405365i
$347$	−14.3901	−	10.4550i	−0.772500	−	0.561254i	0.130219	−	0.991485i	$-0.458432\pi$
$347$	−14.3901	−	10.4550i	−0.772500	−	0.561254i	−0.902719	+	0.430231i	$0.858432\pi$
$348$		0			0
$349$	3.62603	+	11.1598i	0.194097	+	0.597368i	0.999986	+	0.00530193i	$0.00168767\pi$
$349$	3.62603	+	11.1598i	0.194097	+	0.597368i	−0.805889	+	0.592066i	$0.798312\pi$
$350$	−8.12258	+	5.90140i	−0.434170	+	0.315443i
$351$		0			0
$352$	−16.8104	−	8.39241i	−0.895998	−	0.447317i
$353$	−15.2682			−0.812642			−0.406321	−	0.913730i	$-0.633189\pi$
$353$	−15.2682			−0.812642			−0.406321	+	0.913730i	$0.633189\pi$
$354$		0			0
$355$	−2.78676	−	8.57677i	−0.147906	−	0.455208i
$356$	−3.11502	+	9.58704i	−0.165096	+	0.508112i
$357$		0			0
$358$	8.24338	+	5.98917i	0.435676	+	0.316537i
$359$	−2.08338	+	6.41200i	−0.109957	+	0.338412i	−0.990862	−	0.134881i	$-0.956935\pi$
$359$	−2.08338	+	6.41200i	−0.109957	+	0.338412i	0.880905	+	0.473293i	$0.156935\pi$
$360$		0			0
$361$	−8.72130	+	6.33640i	−0.459016	+	0.333495i
$362$	−17.1708			−0.902478
$363$		0			0
$364$	−7.55354			−0.395913
$365$	18.3279	−	13.3160i	0.959324	−	0.696989i
$366$		0			0
$367$	−6.48141	+	19.9477i	−0.338327	+	1.04126i	0.626733	+	0.779234i	$0.284392\pi$
$367$	−6.48141	+	19.9477i	−0.338327	+	1.04126i	−0.965060	+	0.262029i	$0.915608\pi$
$368$	−0.0980937	−	0.0712692i	−0.00511349	−	0.00371516i
$369$		0			0
$370$	−2.67054	+	8.21908i	−0.138835	+	0.427290i
$371$	−1.45672	−	4.48332i	−0.0756290	−	0.232762i
$372$		0			0
$373$	29.1253			1.50805			0.754027	−	0.656844i	$-0.228109\pi$
$373$	29.1253			1.50805			0.754027	+	0.656844i	$0.228109\pi$
$374$	4.40105	+	2.19718i	0.227573	+	0.113613i
$375$		0			0
$376$	19.3480	−	14.0571i	0.997796	−	0.724942i
$377$	8.93795	+	27.5082i	0.460328	+	1.41674i
$378$		0			0
$379$	−25.8362	−	18.7711i	−1.32712	−	0.964207i	−0.999814	−	0.0192874i	$-0.993860\pi$
$379$	−25.8362	−	18.7711i	−1.32712	−	0.964207i	−0.327303	−	0.944919i	$-0.606140\pi$
$380$	22.2558	+	16.1698i	1.14170	+	0.829491i
$381$		0			0
$382$	1.87513	+	5.77107i	0.0959402	+	0.295273i
$383$	2.90411	−	2.10996i	0.148393	−	0.107814i	−0.511111	−	0.859514i	$-0.670766\pi$
$383$	2.90411	−	2.10996i	0.148393	−	0.107814i	0.659505	+	0.751700i	$0.270766\pi$
$384$		0			0
$385$	13.2963	−	2.21784i	0.677641	−	0.113031i
$386$	−14.6981			−0.748115
$387$		0			0
$388$	0.995445	+	3.06367i	0.0505361	+	0.155534i
$389$	−3.23572	+	9.95853i	−0.164058	+	0.504917i	−0.998966	−	0.0454722i	$-0.985521\pi$
$389$	−3.23572	+	9.95853i	−0.164058	+	0.504917i	0.834908	+	0.550389i	$0.185521\pi$
$390$		0			0
$391$	8.79886	+	6.39275i	0.444977	+	0.323295i
$392$	0.872746	−	2.68604i	0.0440803	−	0.135665i
$393$		0			0
$394$	−4.52804	+	3.28981i	−0.228119	+	0.165738i
$395$	25.4890			1.28249
$396$		0			0
$397$	17.7269			0.889686			0.444843	−	0.895609i	$-0.353259\pi$
$397$	17.7269			0.889686			0.444843	+	0.895609i	$0.353259\pi$
$398$	−9.35338	+	6.79563i	−0.468843	+	0.340634i
$399$		0			0
$400$	0.0675270	−	0.207827i	0.00337635	−	0.0103913i
$401$	6.53714	+	4.74951i	0.326449	+	0.237179i	0.738922	−	0.673791i	$-0.235335\pi$
$401$	6.53714	+	4.74951i	0.326449	+	0.237179i	−0.412473	+	0.910970i	$0.635335\pi$
$402$		0			0
$403$	8.21104	−	25.2710i	0.409021	−	1.25884i
$404$	−2.30952	−	7.10796i	−0.114903	−	0.353634i
$405$		0			0
$406$	−4.13955			−0.205442
$407$	5.67408	−	5.76791i	0.281254	−	0.285905i
$408$		0			0
$409$	−32.1090	+	23.3286i	−1.58769	+	1.15352i	−0.680539	+	0.732712i	$0.738254\pi$
$409$	−32.1090	+	23.3286i	−1.58769	+	1.15352i	−0.907148	+	0.420811i	$0.861746\pi$
$410$	−3.51438	−	10.8162i	−0.173563	−	0.534172i
$411$		0			0
$412$	12.9380	+	9.40001i	0.637409	+	0.463105i
$413$	−3.74872	−	2.72361i	−0.184463	−	0.134020i
$414$		0			0
$415$	0.160413	+	0.493702i	0.00787438	+	0.0242349i
$416$	−27.9116	+	20.2789i	−1.36848	+	0.994257i
$417$		0			0
$418$	7.27688	+	13.9967i	0.355924	+	0.684603i
$419$	−16.1715			−0.790028			−0.395014	−	0.918675i	$-0.629260\pi$
$419$	−16.1715			−0.790028			−0.395014	+	0.918675i	$0.629260\pi$
$420$		0			0
$421$	7.66622	+	23.5942i	0.373629	+	1.14991i	0.944399	+	0.328802i	$0.106645\pi$
$421$	7.66622	+	23.5942i	0.373629	+	1.14991i	−0.570770	+	0.821110i	$0.693355\pi$
$422$	−0.784207	+	2.41354i	−0.0381746	+	0.117489i
$423$		0			0
$424$	−10.7710	−	7.82559i	−0.523086	−	0.380044i
$425$	−6.05708	+	18.6418i	−0.293811	+	0.904259i
$426$		0			0
$427$	4.29654	−	3.12162i	0.207924	−	0.151066i
$428$	−6.63265			−0.320601
$429$		0			0
$430$	−0.450576			−0.0217287
$431$	17.7030	−	12.8620i	0.852724	−	0.619540i	−0.0731719	−	0.997319i	$-0.523312\pi$
$431$	17.7030	−	12.8620i	0.852724	−	0.619540i	0.925896	+	0.377779i	$0.123312\pi$
$432$		0			0
$433$	12.1579	−	37.4183i	0.584273	−	1.79821i	−0.0178973	−	0.999840i	$-0.505697\pi$
$433$	12.1579	−	37.4183i	0.584273	−	1.79821i	0.602170	−	0.798368i	$-0.294303\pi$
$434$	3.07660	+	2.23528i	0.147682	+	0.107297i
$435$		0			0
$436$	0.552581	−	1.70067i	0.0264638	−	0.0814473i
$437$	10.7783	+	33.1722i	0.515596	+	1.58684i
$438$		0			0
$439$	9.59194			0.457799			0.228899	−	0.973450i	$-0.426487\pi$
$439$	9.59194			0.457799			0.228899	+	0.973450i	$0.426487\pi$
$440$	26.6986	−	27.1401i	1.27281	−	1.29385i
$441$		0			0
$442$	7.30740	−	5.30914i	0.347577	−	0.252530i
$443$	0.194414	+	0.598344i	0.00923687	+	0.0284282i	0.955569	−	0.294768i	$-0.0952425\pi$
$443$	0.194414	+	0.598344i	0.00923687	+	0.0284282i	−0.946332	+	0.323197i	$0.895242\pi$
$444$		0			0
$445$	−26.7239	−	19.4160i	−1.26683	−	0.920409i
$446$	−2.36625	−	1.71918i	−0.112045	−	0.0814055i
$447$		0			0
$448$	−1.51411	−	4.65994i	−0.0715348	−	0.220162i
$449$	−14.0254	+	10.1901i	−0.661900	+	0.480899i	−0.867304	−	0.497779i	$-0.834149\pi$
$449$	−14.0254	+	10.1901i	−0.661900	+	0.480899i	0.205404	+	0.978677i	$0.434149\pi$
$450$		0			0
$451$	−1.57936	+	10.5298i	−0.0743690	+	0.495829i
$452$	24.2075			1.13863
$453$		0			0
$454$	0.899035	+	2.76695i	0.0421938	+	0.129859i
$455$	7.64886	−	23.5408i	0.358584	−	1.10361i
$456$		0			0
$457$	23.5549	+	17.1136i	1.10185	+	0.800541i	0.981361	−	0.192174i	$-0.0615539\pi$
$457$	23.5549	+	17.1136i	1.10185	+	0.800541i	0.120489	+	0.992715i	$0.461554\pi$
$458$	−1.83190	+	5.63801i	−0.0855991	+	0.263447i
$459$		0			0
$460$	26.0666	−	18.9385i	1.21536	−	0.883011i
$461$	−15.1850			−0.707236			−0.353618	−	0.935390i	$-0.615049\pi$
$461$	−15.1850			−0.707236			−0.353618	+	0.935390i	$0.615049\pi$
$462$		0			0
$463$	17.8886			0.831355			0.415677	−	0.909512i	$-0.363545\pi$
$463$	17.8886			0.831355			0.415677	+	0.909512i	$0.363545\pi$
$464$	0.0728903	−	0.0529579i	0.00338385	−	0.00245851i
$465$		0			0
$466$	1.66601	−	5.12747i	0.0771766	−	0.237525i
$467$	−24.5214	−	17.8158i	−1.13472	−	0.824419i	−0.148341	−	0.988936i	$-0.547393\pi$
$467$	−24.5214	−	17.8158i	−1.13472	−	0.824419i	−0.986374	+	0.164517i	$0.947393\pi$
$468$		0			0
$469$	−4.34745	+	13.3801i	−0.200746	+	0.617834i
$470$	9.26973	+	28.5293i	0.427581	+	1.31596i
$471$		0			0
$472$	−13.0867			−0.602366
$473$	0.377424	+	0.188425i	0.0173540	+	0.00866377i
$474$		0			0
$475$	−50.8555	+	36.9487i	−2.33341	+	1.69532i
$476$	−0.652191	−	2.00724i	−0.0298931	−	0.0920016i
$477$		0			0
$478$	−14.4402	−	10.4914i	−0.660479	−	0.479866i
$479$	−6.42966	−	4.67142i	−0.293779	−	0.213443i	0.431126	−	0.902292i	$-0.358116\pi$
$479$	−6.42966	−	4.67142i	−0.293779	−	0.213443i	−0.724905	+	0.688849i	$0.758116\pi$
$480$		0			0
$481$	−4.59102	−	14.1297i	−0.209333	−	0.644259i
$482$	0.734147	−	0.533389i	0.0334395	−	0.0242952i
$483$		0			0
$484$	−12.9047	+	4.42826i	−0.586578	+	0.201285i
$485$	−10.5560			−0.479323
$486$		0			0
$487$	−3.14304	−	9.67329i	−0.142425	−	0.438338i	0.854246	−	0.519869i	$-0.174019\pi$
$487$	−3.14304	−	9.67329i	−0.142425	−	0.438338i	−0.996671	+	0.0815305i	$0.974019\pi$
$488$	4.63499	−	14.2650i	0.209816	−	0.645747i
$489$		0			0
$490$	2.86596	+	2.08224i	0.129471	+	0.0940660i
$491$	−0.332923	+	1.02463i	−0.0150246	+	0.0462409i	−0.958288	−	0.285805i	$-0.907739\pi$
$491$	−0.332923	+	1.02463i	−0.0150246	+	0.0462409i	0.943263	+	0.332046i	$0.107739\pi$
$492$		0			0
$493$	−6.53816	+	4.75025i	−0.294464	+	0.213940i
$494$	28.9671			1.30329
$495$		0			0
$496$	−0.0827699			−0.00371648
$497$	−1.79507	+	1.30420i	−0.0805201	+	0.0585013i
$498$		0			0
$499$	10.6969	−	32.9217i	0.478859	−	1.47378i	−0.361823	−	0.932247i	$-0.617845\pi$
$499$	10.6969	−	32.9217i	0.478859	−	1.47378i	0.840682	−	0.541530i	$-0.182155\pi$
$500$	26.5867	+	19.3163i	1.18899	+	0.863853i
$501$		0			0
$502$	1.78654	−	5.49840i	0.0797371	−	0.245405i
$503$	−0.852636	−	2.62414i	−0.0380172	−	0.117005i	0.930247	−	0.366934i	$-0.119593\pi$
$503$	−0.852636	−	2.62414i	−0.0380172	−	0.117005i	−0.968264	+	0.249929i	$0.919593\pi$
$504$		0			0
$505$	24.4908			1.08982
$506$	18.2247	−	3.03991i	0.810189	−	0.135141i
$507$		0			0
$508$	−0.643913	+	0.467830i	−0.0285690	+	0.0207566i
$509$	−4.50899	−	13.8773i	−0.199858	−	0.615099i	−0.999885	−	0.0151357i	$-0.995182\pi$
$509$	−4.50899	−	13.8773i	−0.199858	−	0.615099i	0.800028	−	0.599963i	$-0.204818\pi$
$510$		0			0
$511$	−4.50940	−	3.27627i	−0.199484	−	0.144934i
$512$	0.173635	+	0.126153i	0.00767364	+	0.00557523i
$513$		0			0
$514$	0.776364	+	2.38940i	0.0342439	+	0.105392i
$515$	−42.3966	+	30.8029i	−1.86822	+	1.35734i
$516$		0			0
$517$	4.16580	−	27.7740i	0.183212	−	1.22150i
$518$	2.12630			0.0934242
$519$		0			0
$520$	−21.6024	−	66.4854i	−0.947329	−	2.91558i
$521$	4.24334	−	13.0597i	0.185904	−	0.572154i	−0.814059	−	0.580783i	$-0.802747\pi$
$521$	4.24334	−	13.0597i	0.185904	−	0.572154i	0.999963	+	0.00862850i	$0.00274657\pi$
$522$		0			0
$523$	−6.10491	−	4.43548i	−0.266949	−	0.193950i	0.446256	−	0.894905i	$-0.352757\pi$
$523$	−6.10491	−	4.43548i	−0.266949	−	0.193950i	−0.713205	+	0.700956i	$0.752757\pi$
$524$	−5.36537	+	16.5129i	−0.234387	+	0.721369i
$525$		0			0
$526$	14.8798	−	10.8108i	0.648788	−	0.471372i
$527$	7.42434			0.323409
$528$		0			0
$529$	17.8517			0.776160
$530$	13.5102	−	9.81576i	0.586847	−	0.426369i
$531$		0			0
$532$	2.09158	−	6.43722i	0.0906815	−	0.279089i
$533$	15.8174	+	11.4920i	0.685126	+	0.497774i
$534$		0			0
$535$	6.71635	−	20.6708i	0.290373	−	0.893677i
$536$	12.2783	+	37.7888i	0.530344	+	1.63223i
$537$		0			0
$538$	−14.9319			−0.643760
$539$	−1.52990	−	2.94269i	−0.0658974	−	0.126751i
$540$		0			0
$541$	1.63162	−	1.18544i	0.0701486	−	0.0509659i	−0.552158	−	0.833739i	$-0.686196\pi$
$541$	1.63162	−	1.18544i	0.0701486	−	0.0509659i	0.622307	+	0.782773i	$0.286196\pi$
$542$	−4.40637	−	13.5614i	−0.189270	−	0.582513i
$543$		0			0
$544$	−7.79877	−	5.66614i	−0.334370	−	0.242934i
$545$	4.74062	+	3.44426i	0.203066	+	0.147536i
$546$		0			0
$547$	12.7165	+	39.1373i	0.543718	+	1.67339i	0.724019	+	0.689780i	$0.242293\pi$
$547$	12.7165	+	39.1373i	0.543718	+	1.67339i	−0.180301	+	0.983612i	$0.557707\pi$
$548$	2.70943	−	1.96852i	0.115741	−	0.0840908i
$549$		0			0
$550$	15.3603	+	29.5448i	0.654964	+	1.25979i
$551$	−25.9177			−1.10413
$552$		0			0
$553$	−1.93795	−	5.96440i	−0.0824100	−	0.253632i
$554$	0.667566	−	2.05456i	0.0283622	−	0.0872897i
$555$		0			0
$556$	−2.06899	−	1.50321i	−0.0877446	−	0.0637502i
$557$	5.70473	−	17.5574i	0.241717	−	0.743930i	−0.754442	−	0.656367i	$-0.772092\pi$
$557$	5.70473	−	17.5574i	0.241717	−	0.743930i	0.996159	−	0.0875624i	$-0.0279077\pi$
$558$		0			0
$559$	0.626665	−	0.455299i	0.0265051	−	0.0192571i
$560$	−0.0771030			−0.00325819
$561$		0			0
$562$	21.0883			0.889557
$563$	−23.0694	+	16.7609i	−0.972260	+	0.706388i	−0.955966	−	0.293479i	$-0.905187\pi$
$563$	−23.0694	+	16.7609i	−0.972260	+	0.706388i	−0.0162945	+	0.999867i	$0.505187\pi$
$564$		0			0
$565$	−24.5130	+	75.4433i	−1.03127	+	3.17392i
$566$	−20.5802	−	14.9524i	−0.865050	−	0.628496i
$567$		0			0
$568$	−1.93648	+	5.95987i	−0.0812528	+	0.250070i
$569$	−5.48146	−	16.8702i	−0.229795	−	0.707235i	−0.997769	−	0.0667550i	$-0.978735\pi$
$569$	−5.48146	−	16.8702i	−0.229795	−	0.707235i	0.767975	−	0.640480i	$-0.221265\pi$
$570$		0			0
$571$	−20.8488			−0.872496			−0.436248	−	0.899827i	$-0.643693\pi$
$571$	−20.8488			−0.872496			−0.436248	+	0.899827i	$0.643693\pi$
$572$	−3.71600	+	24.7751i	−0.155374	+	1.03590i
$573$		0			0
$574$	−2.26377	+	1.64472i	−0.0944878	+	0.0686494i
$575$	22.7512	+	70.0210i	0.948791	+	2.92008i
$576$		0			0
$577$	−17.2311	−	12.5191i	−0.717339	−	0.521178i	0.168194	−	0.985754i	$-0.446207\pi$
$577$	−17.2311	−	12.5191i	−0.717339	−	0.521178i	−0.885533	+	0.464576i	$0.846207\pi$
$578$	−9.94567	−	7.22595i	−0.413685	−	0.300560i
$579$		0			0
$580$	7.39840	+	22.7699i	0.307202	+	0.945470i
$581$	0.103329	−	0.0750731i	0.00428682	−	0.00311456i
$582$		0			0
$583$	−15.4216	+	2.57235i	−0.638699	+	0.106536i
$584$	−15.7422			−0.651419
$585$		0			0
$586$	−7.32385	−	22.5405i	−0.302545	−	0.931139i
$587$	−9.01940	+	27.7589i	−0.372271	+	1.14573i	0.573031	+	0.819534i	$0.305767\pi$
$587$	−9.01940	+	27.7589i	−0.372271	+	1.14573i	−0.945302	+	0.326197i	$0.894233\pi$
$588$		0			0
$589$	19.2626	+	13.9951i	0.793702	+	0.576658i
$590$	5.07248	−	15.6115i	0.208831	−	0.642714i
$591$		0			0
$592$	−0.0374404	+	0.0272021i	−0.00153879	+	0.00111800i
$593$	37.3094			1.53212			0.766058	−	0.642772i	$-0.222216\pi$
$593$	37.3094			1.53212			0.766058	+	0.642772i	$0.222216\pi$
$594$		0			0
$595$	6.91602			0.283529
$596$	−10.1175	+	7.35080i	−0.414430	+	0.301101i
$597$		0			0
$598$	10.4840	−	32.2666i	0.428724	−	1.31948i
$599$	−4.00761	−	2.91170i	−0.163747	−	0.118969i	0.502894	−	0.864348i	$-0.332269\pi$
$599$	−4.00761	−	2.91170i	−0.163747	−	0.118969i	−0.666641	+	0.745379i	$0.732269\pi$
$600$		0			0
$601$	9.10277	−	28.0155i	0.371310	−	1.14277i	−0.574625	−	0.818417i	$-0.694852\pi$
$601$	9.10277	−	28.0155i	0.371310	−	1.14277i	0.945935	−	0.324357i	$-0.105148\pi$
$602$	0.0342576	+	0.105434i	0.00139624	+	0.00429718i
$603$		0			0
$604$	18.5598			0.755189
$605$	−0.733195	−	44.7020i	−0.0298086	−	1.81739i
$606$		0			0
$607$	21.3116	−	15.4838i	0.865011	−	0.628467i	−0.0642329	−	0.997935i	$-0.520460\pi$
$607$	21.3116	−	15.4838i	0.865011	−	0.628467i	0.929243	+	0.369468i	$0.120460\pi$
$608$	−9.55323	−	29.4018i	−0.387435	−	1.19240i
$609$		0			0
$610$	15.2206	+	11.0584i	0.616262	+	0.447741i
$611$	−41.7208	−	30.3119i	−1.68784	−	1.22629i
$612$		0			0
$613$	14.8974	+	45.8494i	0.601699	+	1.85184i	0.518062	+	0.855343i	$0.326653\pi$
$613$	14.8974	+	45.8494i	0.601699	+	1.85184i	0.0836366	+	0.996496i	$0.473347\pi$
$614$	−7.01873	+	5.09941i	−0.283253	+	0.205795i
$615$		0			0
$616$	−8.38067	−	4.18396i	−0.337667	−	0.168577i
$617$	29.2376			1.17706			0.588532	−	0.808474i	$-0.299706\pi$
$617$	29.2376			1.17706			0.588532	+	0.808474i	$0.299706\pi$
$618$		0			0
$619$	1.89856	+	5.84318i	0.0763097	+	0.234857i	0.981934	−	0.189224i	$-0.0605972\pi$
$619$	1.89856	+	5.84318i	0.0763097	+	0.234857i	−0.905624	+	0.424081i	$0.860597\pi$
$620$	6.79670	−	20.9181i	0.272962	−	0.840090i
$621$		0			0
$622$	−11.4520	−	8.32035i	−0.459183	−	0.333616i
$623$	−2.51149	+	7.72958i	−0.100621	+	0.309679i
$624$		0			0
$625$	−40.5264	+	29.4442i	−1.62106	+	1.17777i
$626$	−14.4815			−0.578799
$627$		0			0
$628$	−24.1289			−0.962849
$629$	3.35835	−	2.43999i	0.133906	−	0.0972886i
$630$		0			0
$631$	12.5351	−	38.5792i	0.499016	−	1.53581i	−0.311587	−	0.950217i	$-0.600861\pi$
$631$	12.5351	−	38.5792i	0.499016	−	1.53581i	0.810603	−	0.585596i	$-0.199139\pi$
$632$	−14.3292	−	10.4108i	−0.569987	−	0.414120i
$633$		0			0
$634$	2.18166	−	6.71447i	0.0866449	−	0.266666i
$635$	−0.805964	−	2.48050i	−0.0319837	−	0.0984357i
$636$		0			0
$637$	−6.09006			−0.241297
$638$	−2.03647	+	13.5775i	−0.0806248	+	0.537537i
$639$		0			0
$640$	−23.2126	+	16.8649i	−0.917557	+	0.666644i
$641$	−7.27011	−	22.3751i	−0.287152	−	0.883763i	−0.985745	−	0.168244i	$-0.946190\pi$
$641$	−7.27011	−	22.3751i	−0.287152	−	0.883763i	0.698593	−	0.715519i	$-0.253810\pi$
$642$		0			0
$643$	17.0009	+	12.3519i	0.670452	+	0.487112i	0.870176	−	0.492740i	$-0.164005\pi$
$643$	17.0009	+	12.3519i	0.670452	+	0.487112i	−0.199725	+	0.979852i	$0.564005\pi$
$644$	−6.41345	−	4.65964i	−0.252725	−	0.183616i
$645$		0			0
$646$	2.50109	+	7.69755i	0.0984040	+	0.302856i
$647$	0.366260	−	0.266103i	0.0143992	−	0.0104616i	−0.580562	−	0.814216i	$-0.697167\pi$
$647$	0.366260	−	0.266103i	0.0143992	−	0.0104616i	0.594962	+	0.803754i	$0.297167\pi$
$648$		0			0
$649$	−10.7775	+	10.9557i	−0.423052	+	0.430048i
$650$	61.1446			2.39829
$651$		0			0
$652$	−4.64163	−	14.2855i	−0.181780	−	0.559462i
$653$	6.81098	−	20.9620i	0.266534	−	0.820308i	−0.724802	−	0.688957i	$-0.758069\pi$
$653$	6.81098	−	20.9620i	0.266534	−	0.820308i	0.991336	−	0.131350i	$-0.0419312\pi$
$654$		0			0
$655$	−46.0297	−	33.4426i	−1.79853	−	1.30671i
$656$	0.0188198	−	0.0579215i	0.000734791	−	0.00226145i
$657$		0			0
$658$	5.97104	−	4.33821i	0.232775	−	0.169121i
$659$	−18.3859			−0.716215			−0.358107	−	0.933680i	$-0.616578\pi$
$659$	−18.3859			−0.716215			−0.358107	+	0.933680i	$0.616578\pi$
$660$		0			0
$661$	−45.9605			−1.78766			−0.893829	−	0.448408i	$-0.851991\pi$
$661$	−45.9605			−1.78766			−0.893829	+	0.448408i	$0.851991\pi$
$662$	−4.68641	+	3.40488i	−0.182143	+	0.132334i
$663$		0			0
$664$	0.111469	−	0.343066i	0.00432583	−	0.0133135i
$665$	17.9438	+	13.0369i	0.695829	+	0.505550i
$666$		0			0
$667$	−9.38040	+	28.8699i	−0.363210	+	1.11785i
$668$	−5.04697	−	15.5330i	−0.195273	−	0.600988i
$669$		0			0
$670$	−49.8384			−1.92542
$671$	−8.12500	−	15.6281i	−0.313662	−	0.603315i
$672$		0			0
$673$	−24.0603	+	17.4808i	−0.927457	+	0.673837i	−0.945369	−	0.326003i	$-0.894298\pi$
$673$	−24.0603	+	17.4808i	−0.927457	+	0.673837i	0.0179118	+	0.999840i	$0.494298\pi$
$674$	5.64324	+	17.3681i	0.217369	+	0.668994i
$675$		0			0
$676$	24.1715	+	17.5616i	0.929672	+	0.675446i
$677$	22.4767	+	16.3303i	0.863851	+	0.627624i	0.928930	−	0.370256i	$-0.120730\pi$
$677$	22.4767	+	16.3303i	0.863851	+	0.627624i	−0.0650791	+	0.997880i	$0.520730\pi$
$678$		0			0
$679$	0.802581	+	2.47009i	0.0308002	+	0.0947933i
$680$	15.8023	−	11.4810i	0.605989	−	0.440277i
$681$		0			0
$682$	8.84513	−	8.99139i	0.338697	−	0.344298i
$683$	−40.8297			−1.56231			−0.781153	−	0.624339i	$-0.785368\pi$
$683$	−40.8297			−1.56231			−0.781153	+	0.624339i	$0.785368\pi$
$684$		0			0
$685$	3.39130	+	10.4374i	0.129575	+	0.398791i
$686$	0.269341	−	0.828945i	0.0102835	−	0.0316493i
$687$		0			0
$688$	−0.00195205	−	0.00141825i	−7.44213e−5	−	5.40703e-5i
$689$	−8.87151	+	27.3037i	−0.337977	+	1.04019i
$690$		0			0
$691$	−30.5934	+	22.2274i	−1.16383	+	0.845571i	−0.990257	−	0.139250i	$-0.955531\pi$
$691$	−30.5934	+	22.2274i	−1.16383	+	0.845571i	−0.173572	+	0.984821i	$0.555531\pi$
$692$	−18.2547			−0.693941
$693$		0			0
$694$	−15.5033			−0.588498
$695$	6.77988	−	4.92587i	0.257175	−	0.186849i
$696$		0			0
$697$	−1.68811	+	5.19547i	−0.0639418	+	0.196792i
$698$	8.27419	+	6.01155i	0.313183	+	0.227541i
$699$		0			0
$700$	4.41497	−	13.5879i	0.166870	−	0.513574i
$701$	−8.47498	−	26.0833i	−0.320096	−	0.985153i	−0.973606	−	0.228235i	$-0.926704\pi$
$701$	−8.47498	−	26.0833i	−0.320096	−	0.985153i	0.653510	−	0.756918i	$-0.273296\pi$
$702$		0			0
$703$	13.3128			0.502100
$704$	−16.0292	+	2.67369i	−0.604123	+	0.100769i
$705$		0			0
$706$	−10.7662	+	7.82213i	−0.405192	+	0.294390i
$707$	−1.86205	−	5.73081i	−0.0700297	−	0.215529i
$708$		0			0
$709$	25.7623	+	18.7174i	0.967522	+	0.702946i	0.954885	−	0.296974i	$-0.0959775\pi$
$709$	25.7623	+	18.7174i	0.967522	+	0.702946i	0.0126366	+	0.999920i	$0.495978\pi$
$710$	−6.35908	−	4.62014i	−0.238652	−	0.173391i
$711$		0			0
$712$	7.09312	+	21.8304i	0.265826	+	0.818128i
$713$	22.5609	−	16.3915i	0.844913	−	0.613865i
$714$		0			0
$715$	−73.4494	−	36.6688i	−2.74685	−	1.37134i
$716$	−14.4996			−0.541877
$717$		0			0
$718$	1.81589	+	5.58873i	0.0677683	+	0.208569i
$719$	4.71151	−	14.5005i	0.175710	−	0.540778i	−0.823956	−	0.566654i	$-0.808237\pi$
$719$	4.71151	−	14.5005i	0.175710	−	0.540778i	0.999665	+	0.0258760i	$0.00823749\pi$
$720$		0			0
$721$	10.4313	+	7.57878i	0.388482	+	0.282249i
$722$	−2.90352	+	8.93613i	−0.108058	+	0.332568i
$723$		0			0
$724$	19.7678	−	14.3621i	0.734664	−	0.533765i
$725$	−54.7080			−2.03180
$726$		0			0
$727$	−33.7158			−1.25045			−0.625225	−	0.780445i	$-0.714993\pi$
$727$	−33.7158			−1.25045			−0.625225	+	0.780445i	$0.714993\pi$
$728$	−13.9151	+	10.1099i	−0.515726	+	0.374697i
$729$		0			0
$730$	6.10177	−	18.7793i	0.225837	−	0.695054i
$731$	0.175096	+	0.127215i	0.00647617	+	0.00470521i
$732$		0			0
$733$	−1.39567	+	4.29543i	−0.0515503	+	0.158655i	−0.973518	−	0.228612i	$-0.926581\pi$
$733$	−1.39567	+	4.29543i	−0.0515503	+	0.158655i	0.921967	+	0.387268i	$0.126581\pi$
$734$	5.64923	+	17.3865i	0.208517	+	0.641749i
$735$		0			0
$736$	−36.2084			−1.33466
$737$	41.7470	+	20.8417i	1.53777	+	0.767715i
$738$		0			0
$739$	−8.12253	+	5.90136i	−0.298792	+	0.217085i	−0.727072	−	0.686561i	$-0.759120\pi$
$739$	−8.12253	+	5.90136i	−0.298792	+	0.217085i	0.428280	+	0.903646i	$0.359120\pi$
$740$	−3.80022	−	11.6959i	−0.139699	−	0.429949i
$741$		0			0
$742$	−3.32407	−	2.41508i	−0.122030	−	0.0886603i
$743$	−12.7037	−	9.22981i	−0.466055	−	0.338609i	0.329847	−	0.944035i	$-0.393003\pi$
$743$	−12.7037	−	9.22981i	−0.466055	−	0.338609i	−0.795902	+	0.605426i	$0.793003\pi$
$744$		0			0
$745$	−12.6638	−	38.9750i	−0.463964	−	1.42793i
$746$	20.5375	−	14.9214i	0.751932	−	0.546311i
$747$		0			0
$748$	−6.90446	+	1.15167i	−0.252452	+	0.0421094i
$749$	−5.34760			−0.195397
$750$		0			0
$751$	5.95724	+	18.3345i	0.217383	+	0.669036i	0.998976	+	0.0452468i	$0.0144074\pi$
$751$	5.95724	+	18.3345i	0.217383	+	0.669036i	−0.781593	+	0.623789i	$0.785593\pi$
$752$	−0.0496402	+	0.152777i	−0.00181019	+	0.00557120i
$753$		0			0
$754$	20.3954	+	14.8181i	0.742758	+	0.539645i
$755$	−18.7940	+	57.8421i	−0.683985	+	2.10509i
$756$		0			0
$757$	−30.3730	+	22.0673i	−1.10393	+	0.802049i	−0.981696	−	0.190453i	$-0.939004\pi$
$757$	−30.3730	+	22.0673i	−1.10393	+	0.802049i	−0.122229	+	0.992502i	$0.539004\pi$
$758$	−27.8350			−1.01101
$759$		0			0
$760$	62.6414			2.27224
$761$	−31.3469	+	22.7749i	−1.13633	+	0.825588i	−0.986603	−	0.163140i	$-0.947838\pi$
$761$	−31.3469	+	22.7749i	−1.13633	+	0.825588i	−0.149722	+	0.988728i	$0.547838\pi$
$762$		0			0
$763$	0.445520	−	1.37117i	0.0161289	−	0.0496397i
$764$	−6.98581	−	5.07549i	−0.252738	−	0.183625i
$765$		0			0
$766$	0.966847	−	2.97565i	0.0349336	−	0.107515i
$767$	8.72027	+	26.8382i	0.314871	+	0.969072i
$768$		0			0
$769$	−24.0014			−0.865513			−0.432756	−	0.901511i	$-0.642459\pi$
$769$	−24.0014			−0.865513			−0.432756	+	0.901511i	$0.642459\pi$
$770$	8.23954	−	8.37579i	0.296932	−	0.301842i
$771$		0			0
$772$	16.9211	−	12.2939i	0.609004	−	0.442467i
$773$	12.1355	+	37.3493i	0.436485	+	1.34336i	0.891557	+	0.452908i	$0.149613\pi$
$773$	12.1355	+	37.3493i	0.436485	+	1.34336i	−0.455072	+	0.890455i	$0.650387\pi$
$774$		0			0
$775$	40.6601	+	29.5413i	1.46055	+	1.06116i
$776$	5.93430	+	4.31152i	0.213029	+	0.154775i
$777$		0			0
$778$	2.82027	+	8.67989i	0.101112	+	0.311189i
$779$	−14.1735	+	10.2976i	−0.507817	+	0.368950i
$780$		0			0
$781$	3.39459	+	6.52934i	0.121468	+	0.233638i
$782$	9.47956			0.338988
$783$		0			0
$784$	0.00586220	+	0.0180420i	0.000209364	+	0.000644357i
$785$	24.4334	−	75.1983i	0.872066	−	2.68394i
$786$		0			0
$787$	−20.5681	−	14.9436i	−0.733172	−	0.532681i	0.157393	−	0.987536i	$-0.449691\pi$
$787$	−20.5681	−	14.9436i	−0.733172	−	0.532681i	−0.890565	+	0.454855i	$0.849691\pi$
$788$	2.46119	−	7.57475i	0.0876761	−	0.269839i
$789$		0			0
$790$	17.9734	−	13.0584i	0.639465	−	0.464598i
$791$	19.5174			0.693959
$792$		0			0
$793$	−32.3432			−1.14854
$794$	12.5000	−	9.08176i	0.443607	−	0.322300i
$795$		0			0
$796$	5.08397	−	15.6468i	0.180197	−	0.554588i
$797$	−29.7416	−	21.6085i	−1.05350	−	0.765413i	−0.0806252	−	0.996744i	$-0.525692\pi$
$797$	−29.7416	−	21.6085i	−1.05350	−	0.765413i	−0.972875	+	0.231332i	$0.925692\pi$
$798$		0			0
$799$	4.45265	−	13.7039i	0.157524	−	0.484808i
$800$	−20.1653	−	62.0623i	−0.712950	−	2.19424i
$801$		0			0
$802$	7.04287			0.248692
$803$	−12.9644	+	13.1788i	−0.457503	+	0.465069i
$804$		0			0
$805$	21.0163	−	15.2692i	0.740726	−	0.538169i
$806$	−7.15678	−	22.0263i	−0.252087	−	0.775844i
$807$		0			0
$808$	−13.7681	−	10.0031i	−0.484359	−	0.351907i
$809$	−32.7478	−	23.7926i	−1.15135	−	0.836505i	−0.162690	−	0.986677i	$-0.552017\pi$
$809$	−32.7478	−	23.7926i	−1.15135	−	0.836505i	−0.988660	+	0.150172i	$0.952017\pi$
$810$		0			0
$811$	−2.95118	−	9.08279i	−0.103630	−	0.318940i	0.885777	−	0.464112i	$-0.153626\pi$
$811$	−2.95118	−	9.08279i	−0.103630	−	0.318940i	−0.989406	+	0.145172i	$0.953626\pi$
$812$	4.76563	−	3.46243i	0.167241	−	0.121508i
$813$		0			0
$814$	1.04604	−	6.97412i	0.0366638	−	0.244443i
$815$	49.2212			1.72414
$816$		0			0
$817$	0.214487	+	0.660124i	0.00750395	+	0.0230948i
$818$	−10.6898	+	32.8999i	−0.373761	+	1.15032i
$819$		0			0
$820$	13.0928	+	9.51251i	0.457222	+	0.332191i
$821$	11.2046	−	34.4843i	0.391044	−	1.20351i	−0.540956	−	0.841051i	$-0.681938\pi$
$821$	11.2046	−	34.4843i	0.391044	−	1.20351i	0.932000	−	0.362458i	$-0.118062\pi$
$822$		0			0
$823$	33.7670	−	24.5332i	1.17704	−	0.855173i	0.185209	−	0.982699i	$-0.440704\pi$
$823$	33.7670	−	24.5332i	1.17704	−	0.855173i	0.991835	+	0.127526i	$0.0407037\pi$
$824$	36.4155			1.26859
$825$		0			0
$826$	−4.03873			−0.140525
$827$	22.8676	−	16.6143i	0.795183	−	0.577735i	−0.114314	−	0.993445i	$-0.536467\pi$
$827$	22.8676	−	16.6143i	0.795183	−	0.577735i	0.909497	+	0.415710i	$0.136467\pi$
$828$		0			0
$829$	−0.621234	+	1.91196i	−0.0215764	+	0.0664052i	−0.961265	−	0.275626i	$-0.911115\pi$
$829$	−0.621234	+	1.91196i	−0.0215764	+	0.0664052i	0.939689	+	0.342031i	$0.111115\pi$
$830$	0.366046	+	0.265948i	0.0127056	+	0.00923118i
$831$		0			0
$832$	−9.22101	+	28.3794i	−0.319681	+	0.983877i
$833$	−0.525831	−	1.61834i	−0.0182190	−	0.0560722i
$834$		0			0
$835$	53.5195			1.85212
$836$	−20.0847	−	10.0271i	−0.694644	−	0.346794i
$837$		0			0
$838$	−11.4032	+	8.28491i	−0.393917	+	0.286197i
$839$	7.48127	+	23.0250i	0.258282	+	0.794911i	0.993165	+	0.116717i	$0.0372370\pi$
$839$	7.48127	+	23.0250i	0.258282	+	0.794911i	−0.734883	+	0.678194i	$0.762763\pi$
$840$		0			0
$841$	5.21307	+	3.78752i	0.179761	+	0.130604i
$842$	17.4935	+	12.7098i	0.602865	+	0.438007i
$843$		0			0
$844$	−1.11594	−	3.43451i	−0.0384122	−	0.118221i
$845$	−79.2076	+	57.5477i	−2.72483	+	1.97970i
$846$		0			0
$847$	−10.4045	+	3.57030i	−0.357502	+	0.122677i
$848$	0.0894276			0.00307096
$849$		0			0
$850$	5.27938	+	16.2482i	0.181081	+	0.557310i
$851$	4.81828	−	14.8291i	0.165169	−	0.508337i
$852$		0			0
$853$	−16.2959	−	11.8397i	−0.557963	−	0.405384i	0.272750	−	0.962085i	$-0.412067\pi$
$853$	−16.2959	−	11.8397i	−0.557963	−	0.405384i	−0.830713	+	0.556701i	$0.812067\pi$
$854$	1.43042	−	4.40237i	0.0489479	−	0.150646i
$855$		0			0
$856$	−12.2186	+	8.87734i	−0.417623	+	0.303421i
$857$	26.6092			0.908953			0.454477	−	0.890759i	$-0.349826\pi$
$857$	26.6092			0.908953			0.454477	+	0.890759i	$0.349826\pi$
$858$		0			0
$859$	14.4645			0.493522			0.246761	−	0.969076i	$-0.420634\pi$
$859$	14.4645			0.493522			0.246761	+	0.969076i	$0.420634\pi$
$860$	0.518722	−	0.376874i	0.0176883	−	0.0128513i
$861$		0			0
$862$	5.89374	−	18.1391i	0.200742	−	0.617819i
$863$	22.9456	+	16.6710i	0.781078	+	0.567487i	0.905302	−	0.424768i	$-0.139644\pi$
$863$	22.9456	+	16.6710i	0.781078	+	0.567487i	−0.124224	+	0.992254i	$0.539644\pi$
$864$		0			0
$865$	18.4851	−	56.8913i	0.628512	−	1.93436i
$866$	−10.5969	−	32.6139i	−0.360098	−	1.10827i
$867$		0			0
$868$	−5.41156			−0.183680
$869$	−20.5162	+	3.42214i	−0.695965	+	0.116088i
$870$		0			0
$871$	69.3157	−	50.3608i	2.34867	−	1.70641i
$872$	−1.25827	−	3.87255i	−0.0426103	−	0.131141i
$873$		0			0
$874$	24.5949	+	17.8692i	0.831935	+	0.604436i
$875$	21.4356	+	15.5739i	0.724655	+	0.526493i
$876$		0			0
$877$	3.13396	+	9.64535i	0.105826	+	0.325700i	0.989924	−	0.141603i	$-0.0452256\pi$
$877$	3.13396	+	9.64535i	0.105826	+	0.325700i	−0.884097	+	0.467303i	$0.845226\pi$
$878$	6.76369	−	4.91411i	0.228263	−	0.165843i
$879$		0			0
$880$	−0.0379312	+	0.252893i	−0.00127866	+	0.00852501i
$881$	3.71883			0.125291			0.0626453	−	0.998036i	$-0.480046\pi$
$881$	3.71883			0.125291			0.0626453	+	0.998036i	$0.480046\pi$
$882$		0			0
$883$	5.35542	+	16.4823i	0.180224	+	0.554673i	0.999833	−	0.0182500i	$-0.00580947\pi$
$883$	5.35542	+	16.4823i	0.180224	+	0.554673i	−0.819609	+	0.572923i	$0.805809\pi$
$884$	−3.97189	+	12.2242i	−0.133589	+	0.411145i
$885$		0			0
$886$	0.443631	+	0.322316i	0.0149041	+	0.0108284i
$887$	1.67084	−	5.14232i	0.0561014	−	0.172662i	−0.919079	−	0.394072i	$-0.871066\pi$
$887$	1.67084	−	5.14232i	0.0561014	−	0.172662i	0.975181	+	0.221410i	$0.0710659\pi$
$888$		0			0
$889$	−0.519157	+	0.377189i	−0.0174120	+	0.0126505i
$890$	−28.7913			−0.965087
$891$		0			0
$892$	4.16210			0.139357
$893$	37.3847	−	27.1616i	1.25103	−	0.908927i
$894$		0			0
$895$	14.6826	−	45.1884i	0.490786	−	1.51048i
$896$	5.71124	+	4.14946i	0.190799	+	0.138624i
$897$		0			0
$898$	−4.66939	+	14.3709i	−0.155819	+	0.479563i
$899$	6.40339	+	19.7076i	0.213565	+	0.657286i
$900$		0			0
$901$	−8.02152			−0.267236
$902$	4.28092	+	8.23414i	0.142539	+	0.274167i
$903$		0			0
$904$	44.5949	−	32.4001i	1.48320	−	1.07761i
$905$	24.7427	+	76.1501i	0.822474	+	2.53132i
$906$		0			0
$907$	8.65808	+	6.29046i	0.287487	+	0.208871i	0.722176	−	0.691709i	$-0.243142\pi$
$907$	8.65808	+	6.29046i	0.287487	+	0.208871i	−0.434690	+	0.900580i	$0.643142\pi$
$908$	−3.34936	−	2.43345i	−0.111152	−	0.0807569i
$909$		0			0
$910$	−6.66678	−	20.5182i	−0.221002	−	0.680173i
$911$	−22.3053	+	16.2057i	−0.739007	+	0.536920i	−0.892400	−	0.451245i	$-0.850980\pi$
$911$	−22.3053	+	16.2057i	−0.739007	+	0.536920i	0.153393	+	0.988165i	$0.450980\pi$
$912$		0			0
$913$	−0.195402	−	0.375846i	−0.00646685	−	0.0124387i
$914$	25.3771			0.839400
$915$		0			0
$916$	−2.60682	−	8.02298i	−0.0861319	−	0.265087i
$917$	−4.32584	+	13.3136i	−0.142852	+	0.439653i
$918$		0			0
$919$	−29.4499	−	21.3966i	−0.971464	−	0.705810i	−0.0156789	−	0.999877i	$-0.504991\pi$
$919$	−29.4499	−	21.3966i	−0.971464	−	0.705810i	−0.955785	+	0.294067i	$0.904991\pi$
$920$	22.6718	−	69.7765i	0.747466	−	2.30046i
$921$		0			0
$922$	−10.7076	+	7.77952i	−0.352636	+	0.256205i
$923$	13.5128			0.444781
$924$		0			0
$925$	28.1010			0.923956
$926$	12.6140	−	9.16463i	0.414523	−	0.301168i
$927$		0			0
$928$	8.31421	−	25.5885i	0.272927	−	0.839984i
$929$	21.2287	+	15.4235i	0.696491	+	0.506030i	0.878787	−	0.477214i	$-0.158353\pi$
$929$	21.2287	+	15.4235i	0.696491	+	0.506030i	−0.182297	+	0.983244i	$0.558353\pi$
$930$		0			0
$931$	1.68634	−	5.19003i	0.0552676	−	0.170096i
$932$	2.37076	+	7.29646i	0.0776569	+	0.239003i
$933$		0			0
$934$	−26.4184			−0.864437
$935$	3.40237	−	22.6841i	0.111270	−	0.741850i
$936$		0			0
$937$	−19.3192	+	14.0362i	−0.631131	+	0.458544i	−0.856792	−	0.515662i	$-0.827546\pi$
$937$	−19.3192	+	14.0362i	−0.631131	+	0.458544i	0.225661	+	0.974206i	$0.427546\pi$
$938$	3.78925	+	11.6621i	0.123724	+	0.380782i
$939$		0			0
$940$	−34.5344	−	25.0907i	−1.12639	−	0.818369i
$941$	14.3837	+	10.4504i	0.468896	+	0.340673i	0.797011	−	0.603965i	$-0.206413\pi$
$941$	14.3837	+	10.4504i	0.468896	+	0.340673i	−0.328115	+	0.944638i	$0.606413\pi$
$942$		0			0
$943$	6.34077	+	19.5149i	0.206484	+	0.635492i
$944$	0.0711151	−	0.0516681i	0.00231460	−	0.00168165i
$945$		0			0
$946$	0.362671	−	0.0604940i	0.0117914	−	0.00196683i
$947$	−31.7071			−1.03034			−0.515171	−	0.857088i	$-0.672271\pi$
$947$	−31.7071			−1.03034			−0.515171	+	0.857088i	$0.672271\pi$
$948$		0			0
$949$	10.4898	+	32.2842i	0.340512	+	1.04799i
$950$	−16.9310	+	52.1082i	−0.549313	+	1.69061i
$951$		0			0
$952$	−3.88801	−	2.82480i	−0.126011	−	0.0915523i
$953$	1.01423	−	3.12149i	0.0328543	−	0.101115i	−0.933285	−	0.359138i	$-0.883071\pi$
$953$	1.01423	−	3.12149i	0.0328543	−	0.101115i	0.966139	+	0.258023i	$0.0830709\pi$
$954$		0			0
$955$	22.8918	−	16.6319i	0.740762	−	0.538195i
$956$	25.3995			0.821478
$957$		0			0
$958$	−6.92707			−0.223804
$959$	2.18449	−	1.58712i	0.0705407	−	0.0512508i
$960$		0			0
$961$	−3.69691	+	11.3779i	−0.119255	+	0.367030i
$962$	−10.4762	−	7.61141i	−0.337766	−	0.245402i
$963$		0			0
$964$	−0.399041	+	1.22812i	−0.0128522	+	0.0395551i
$965$	21.1796	+	65.1840i	0.681795	+	2.09835i
$966$		0			0
$967$	−3.83683			−0.123384			−0.0616921	−	0.998095i	$-0.519650\pi$
$967$	−3.83683			−0.123384			−0.0616921	+	0.998095i	$0.519650\pi$
$968$	−17.8460	+	25.4297i	−0.573593	+	0.817343i
$969$		0			0
$970$	−7.44348	+	5.40800i	−0.238996	+	0.173641i
$971$	−13.6977	−	42.1573i	−0.439581	−	1.35289i	−0.888319	−	0.459228i	$-0.848126\pi$
$971$	−13.6977	−	42.1573i	−0.439581	−	1.35289i	0.448738	−	0.893663i	$-0.351874\pi$
$972$		0			0
$973$	−1.66813	−	1.21197i	−0.0534777	−	0.0388538i
$974$	−7.17207	−	5.21082i	−0.229808	−	0.166965i
$975$		0			0
$976$	0.0311330	+	0.0958176i	0.000996544	+	0.00306705i
$977$	7.84564	−	5.70019i	0.251004	−	0.182365i	−0.455168	−	0.890406i	$-0.650421\pi$
$977$	7.84564	−	5.70019i	0.251004	−	0.182365i	0.706172	+	0.708041i	$0.250421\pi$
$978$		0			0
$979$	24.1170	+	12.0401i	0.770782	+	0.384804i
$980$	−5.04106			−0.161031
$981$		0			0
$982$	0.290177	+	0.893073i	0.00925992	+	0.0284991i
$983$	−8.86112	+	27.2717i	−0.282626	+	0.869833i	0.704474	+	0.709730i	$0.251183\pi$
$983$	−8.86112	+	27.2717i	−0.282626	+	0.869833i	−0.987100	+	0.160104i	$0.948817\pi$
$984$		0			0
$985$	21.1146	+	15.3407i	0.672768	+	0.488795i
$986$	−2.17670	+	6.69921i	−0.0693204	+	0.213346i
$987$		0			0
$988$	−33.3481	+	24.2288i	−1.06095	+	0.770822i
$989$	0.812944			0.0258501
$990$		0			0
$991$	−14.0455			−0.446170			−0.223085	−	0.974799i	$-0.571613\pi$
$991$	−14.0455			−0.446170			−0.223085	+	0.974799i	$0.571613\pi$
$992$	−19.9966	+	14.5284i	−0.634893	+	0.461277i
$993$		0			0
$994$	−0.597622	+	1.83929i	−0.0189554	+	0.0583388i
$995$	43.6156	+	31.6886i	1.38271	+	1.00460i
$996$		0			0
$997$	−11.1896	+	34.4379i	−0.354377	+	1.09066i	0.601993	+	0.798501i	$0.294374\pi$
$997$	−11.1896	+	34.4379i	−0.354377	+	1.09066i	−0.956370	+	0.292159i	$0.905626\pi$
$998$	−9.32347	−	28.6947i	−0.295129	−	0.908314i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.j.190.4		20
3.2	odd	2		231.2.j.g.190.2	yes	20
11.2	odd	10		7623.2.a.cy.1.7		10
11.4	even	5	inner	693.2.m.j.631.4		20
11.9	even	5		7623.2.a.cx.1.4		10
33.2	even	10		2541.2.a.br.1.4		10
33.20	odd	10		2541.2.a.bq.1.7		10
33.26	odd	10		231.2.j.g.169.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.169.2	✓	20	33.26	odd	10
231.2.j.g.190.2	yes	20	3.2	odd	2
693.2.m.j.190.4		20	1.1	even	1	trivial
693.2.m.j.631.4		20	11.4	even	5	inner
2541.2.a.bq.1.7		10	33.20	odd	10
2541.2.a.br.1.4		10	33.2	even	10
7623.2.a.cx.1.4		10	11.9	even	5
7623.2.a.cy.1.7		10	11.2	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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.705143 - 0.512316i) q^{2} +(-0.383276 + 1.17960i) q^{4} +(-3.28814 - 2.38897i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(0.872746 + 2.68604i) q^{8} +O(q^{10})\)	\(q+(0.705143 - 0.512316i) q^{2} +(-0.383276 + 1.17960i) q^{4} +(-3.28814 - 2.38897i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(0.872746 + 2.68604i) q^{8} -3.54252 q^{10} +(2.96738 + 1.48143i) q^{11} +(4.92697 - 3.57965i) q^{13} +(0.269341 + 0.828945i) q^{14} +(-0.0153474 - 0.0111506i) q^{16} +(1.37664 + 1.00019i) q^{17} +(1.68634 + 5.19003i) q^{19} +(4.07830 - 2.96306i) q^{20} +(2.85139 - 0.475616i) q^{22} +6.39153 q^{23} +(3.55958 + 10.9553i) q^{25} +(1.64030 - 5.04833i) q^{26} +(-1.00343 - 0.729034i) q^{28} +(-1.46763 + 4.51690i) q^{29} +(3.52981 - 2.56456i) q^{31} -5.66506 q^{32} +1.48314 q^{34} +(3.28814 - 2.38897i) q^{35} +(0.753854 - 2.32012i) q^{37} +(3.84805 + 2.79577i) q^{38} +(3.54716 - 10.9170i) q^{40} +(0.992058 + 3.05324i) q^{41} +0.127191 q^{43} +(-2.88483 + 2.93253i) q^{44} +(4.50694 - 3.27449i) q^{46} +(-2.61671 - 8.05340i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(8.12258 + 5.90140i) q^{50} +(2.33417 + 7.18385i) q^{52} +(-3.81374 + 2.77084i) q^{53} +(-6.21806 - 11.9602i) q^{55} -2.82426 q^{56} +(1.27919 + 3.93695i) q^{58} +(-1.43188 + 4.40689i) q^{59} +(-4.29654 - 3.12162i) q^{61} +(1.17516 - 3.61676i) q^{62} +(-3.96398 + 2.88000i) q^{64} -24.7522 q^{65} +14.0686 q^{67} +(-1.70746 + 1.24054i) q^{68} +(1.09470 - 3.36913i) q^{70} +(1.79507 + 1.30420i) q^{71} +(-1.72244 + 5.30112i) q^{73} +(-0.657063 - 2.02223i) q^{74} -6.76849 q^{76} +(-2.32590 + 2.36436i) q^{77} +(-5.07362 + 3.68620i) q^{79} +(0.0238261 + 0.0733293i) q^{80} +(2.26377 + 1.64472i) q^{82} +(-0.103329 - 0.0750731i) q^{83} +(-2.13717 - 6.57753i) q^{85} +(0.0896877 - 0.0651619i) q^{86} +(-1.38941 + 9.26341i) q^{88} +8.12736 q^{89} +(1.88193 + 5.79200i) q^{91} +(-2.44972 + 7.53946i) q^{92} +(-5.97104 - 4.33821i) q^{94} +(6.85391 - 21.0942i) q^{95} +(2.10118 - 1.52660i) q^{97} -0.871604 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8}+O(q^{10}) \) 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8	\( 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8} + 12 q^{10} + q^{11} + 13 q^{13} - 24 q^{16} + q^{17} + 10 q^{19} + 46 q^{20} + 26 q^{22} - 8 q^{25} + 53 q^{26} + 4 q^{28} - 3 q^{29} - 13 q^{31} - 82 q^{32} + 42 q^{34} - 5 q^{35} - 32 q^{37} - 16 q^{38} + 20 q^{40} + 3 q^{41} + 12 q^{43} - 25 q^{44} - 13 q^{46} - 20 q^{47} - 5 q^{49} + 83 q^{50} - 80 q^{52} - 3 q^{53} - 28 q^{55} + 6 q^{56} + 2 q^{58} + 9 q^{59} - 15 q^{61} + 37 q^{62} - 49 q^{64} - 58 q^{65} + 76 q^{67} - 51 q^{68} + 3 q^{70} - 37 q^{71} + 27 q^{73} + 32 q^{74} + 4 q^{76} - 6 q^{77} + 5 q^{79} - 137 q^{80} - 55 q^{82} + 42 q^{83} - 48 q^{85} - 3 q^{86} + 151 q^{88} + 18 q^{89} + 7 q^{91} - 39 q^{92} - 35 q^{94} + 96 q^{95} - 27 q^{97}+O(q^{100}) \) 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8 + 12 * q^10 + q^11 + 13 * q^13 - 24 * q^16 + q^17 + 10 * q^19 + 46 * q^20 + 26 * q^22 - 8 * q^25 + 53 * q^26 + 4 * q^28 - 3 * q^29 - 13 * q^31 - 82 * q^32 + 42 * q^34 - 5 * q^35 - 32 * q^37 - 16 * q^38 + 20 * q^40 + 3 * q^41 + 12 * q^43 - 25 * q^44 - 13 * q^46 - 20 * q^47 - 5 * q^49 + 83 * q^50 - 80 * q^52 - 3 * q^53 - 28 * q^55 + 6 * q^56 + 2 * q^58 + 9 * q^59 - 15 * q^61 + 37 * q^62 - 49 * q^64 - 58 * q^65 + 76 * q^67 - 51 * q^68 + 3 * q^70 - 37 * q^71 + 27 * q^73 + 32 * q^74 + 4 * q^76 - 6 * q^77 + 5 * q^79 - 137 * q^80 - 55 * q^82 + 42 * q^83 - 48 * q^85 - 3 * q^86 + 151 * q^88 + 18 * q^89 + 7 * q^91 - 39 * q^92 - 35 * q^94 + 96 * q^95 - 27 * q^97

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