LMFDB - Embedded newform 552.2.f.d.277.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(277,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("552.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.f (of order $2$, degree $1$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$20$
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} - 2 x^{19} + 2 x^{18} - 2 x^{17} + x^{16} - 4 x^{15} + 16 x^{14} - 24 x^{13} + 32 x^{12} + \cdots + 1024 $ x^20 - 2x^19 + 2x^18 - 2x^17 + x^16 - 4x^15 + 16x^14 - 24x^13 + 32x^12 - 16x^11 - 16x^10 - 32x^9 + 128x^8 - 192x^7 + 256x^6 - 128x^5 + 64x^4 - 256x^3 + 512x^2 - 1024x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			277.4
Root			$1.32157 - 0.503453i$ of defining polynomial
Character	$\chi$	$=$	552.277
Dual form			552.2.f.d.277.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.32157 + 0.503453i) q^{2} +1.00000i q^{3} +(1.49307 - 1.33069i) q^{4} +2.69719i q^{5} +(-0.503453 - 1.32157i) q^{6} +1.19970 q^{7} +(-1.30325 + 2.51029i) q^{8} -1.00000 q^{9} +(-1.35791 - 3.56451i) q^{10} +3.08512i q^{11} +(1.33069 + 1.49307i) q^{12} -0.0366308i q^{13} +(-1.58548 + 0.603992i) q^{14} -2.69719 q^{15} +(0.458519 - 3.97363i) q^{16} -0.279291 q^{17} +(1.32157 - 0.503453i) q^{18} +2.99893i q^{19} +(3.58913 + 4.02710i) q^{20} +1.19970i q^{21} +(-1.55321 - 4.07718i) q^{22} +1.00000 q^{23} +(-2.51029 - 1.30325i) q^{24} -2.27484 q^{25} +(0.0184419 + 0.0484100i) q^{26} -1.00000i q^{27} +(1.79124 - 1.59643i) q^{28} -1.31147i q^{29} +(3.56451 - 1.35791i) q^{30} -3.32528 q^{31} +(1.39457 + 5.48226i) q^{32} -3.08512 q^{33} +(0.369101 - 0.140610i) q^{34} +3.23582i q^{35} +(-1.49307 + 1.33069i) q^{36} -0.965182i q^{37} +(-1.50982 - 3.96329i) q^{38} +0.0366308 q^{39} +(-6.77072 - 3.51511i) q^{40} +0.122446 q^{41} +(-0.603992 - 1.58548i) q^{42} +6.45272i q^{43} +(4.10534 + 4.60630i) q^{44} -2.69719i q^{45} +(-1.32157 + 0.503453i) q^{46} -7.33419 q^{47} +(3.97363 + 0.458519i) q^{48} -5.56072 q^{49} +(3.00635 - 1.14527i) q^{50} -0.279291i q^{51} +(-0.0487443 - 0.0546924i) q^{52} +1.48414i q^{53} +(0.503453 + 1.32157i) q^{54} -8.32115 q^{55} +(-1.56351 + 3.01159i) q^{56} -2.99893 q^{57} +(0.660262 + 1.73319i) q^{58} -0.292402i q^{59} +(-4.02710 + 3.58913i) q^{60} -10.5914i q^{61} +(4.39457 - 1.67412i) q^{62} -1.19970 q^{63} +(-4.60308 - 6.54306i) q^{64} +0.0988003 q^{65} +(4.07718 - 1.55321i) q^{66} +10.7005i q^{67} +(-0.417001 + 0.371650i) q^{68} +1.00000i q^{69} +(-1.62908 - 4.27635i) q^{70} -7.91699 q^{71} +(1.30325 - 2.51029i) q^{72} +7.30232 q^{73} +(0.485924 + 1.27555i) q^{74} -2.27484i q^{75} +(3.99066 + 4.47762i) q^{76} +3.70121i q^{77} +(-0.0484100 + 0.0184419i) q^{78} -10.5602 q^{79} +(10.7176 + 1.23671i) q^{80} +1.00000 q^{81} +(-0.161820 + 0.0616457i) q^{82} +13.9464i q^{83} +(1.59643 + 1.79124i) q^{84} -0.753301i q^{85} +(-3.24864 - 8.52769i) q^{86} +1.31147 q^{87} +(-7.74453 - 4.02068i) q^{88} +2.48847 q^{89} +(1.35791 + 3.56451i) q^{90} -0.0439460i q^{91} +(1.49307 - 1.33069i) q^{92} -3.32528i q^{93} +(9.69261 - 3.69242i) q^{94} -8.08869 q^{95} +(-5.48226 + 1.39457i) q^{96} +12.2447 q^{97} +(7.34885 - 2.79956i) q^{98} -3.08512i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9} - 12 q^{10} + 2 q^{14} + 4 q^{15} + 4 q^{16} + 32 q^{17} + 2 q^{18} + 20 q^{20} + 14 q^{22} + 20 q^{23} + 10 q^{24} - 28 q^{25} + 18 q^{28} - 22 q^{32}+ \cdots - 26 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9 - 12 * q^10 + 2 * q^14 + 4 * q^15 + 4 * q^16 + 32 * q^17 + 2 * q^18 + 20 * q^20 + 14 * q^22 + 20 * q^23 + 10 * q^24 - 28 * q^25 + 18 * q^28 - 22 * q^32 + 28 * q^33 - 26 * q^34 + 16 * q^38 + 4 * q^40 - 40 * q^41 + 14 * q^42 + 10 * q^44 - 2 * q^46 + 40 * q^47 + 12 * q^49 - 14 * q^50 + 20 * q^52 - 2 * q^54 - 8 * q^55 + 6 * q^56 - 44 * q^57 - 32 * q^58 - 24 * q^60 + 20 * q^62 + 8 * q^63 - 48 * q^64 + 8 * q^65 + 10 * q^66 + 22 * q^68 + 80 * q^70 - 40 * q^71 + 2 * q^72 - 16 * q^73 - 30 * q^74 + 44 * q^76 - 36 * q^78 - 16 * q^79 + 4 * q^80 + 20 * q^81 - 32 * q^82 + 6 * q^84 - 4 * q^86 + 8 * q^87 - 70 * q^88 - 40 * q^89 + 12 * q^90 + 64 * q^94 - 40 * q^95 + 2 * q^96 + 32 * q^97 - 26 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$1$	$-1$	$1$

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 $

$2$	−1.32157	+	0.503453i	−0.934488	+	0.355995i
$2$	−1.32157	+	0.503453i	−0.934488	+	0.355995i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.49307	−	1.33069i	0.746535	−	0.665346i
$5$			2.69719i			1.20622i	0.797658	+	0.603110i	$0.206072\pi$
$5$			2.69719i			1.20622i	−0.797658	+	0.603110i	$0.793928\pi$
$6$	−0.503453	−	1.32157i	−0.205534	−	0.539527i
$7$	1.19970			0.453444			0.226722	−	0.973960i	$-0.427199\pi$
$7$	1.19970			0.453444			0.226722	+	0.973960i	$0.427199\pi$
$8$	−1.30325	+	2.51029i	−0.460768	+	0.887520i
$9$	−1.00000			−0.333333
$10$	−1.35791	−	3.56451i	−0.429408	−	1.12720i
$11$			3.08512i			0.930198i	0.885259	+	0.465099i	$0.153981\pi$
$11$			3.08512i			0.930198i	−0.885259	+	0.465099i	$0.846019\pi$
$12$	1.33069	+	1.49307i	0.384138	+	0.431012i
$13$		−	0.0366308i		−	0.0101596i	−0.999987	−	0.00507978i	$-0.998383\pi$
$13$		−	0.0366308i		−	0.0101596i	0.999987	−	0.00507978i	$-0.00161695\pi$
$14$	−1.58548	+	0.603992i	−0.423738	+	0.161424i
$15$	−2.69719			−0.696412
$16$	0.458519	−	3.97363i	0.114630	−	0.993408i
$17$	−0.279291			−0.0677380			−0.0338690	−	0.999426i	$-0.510783\pi$
$17$	−0.279291			−0.0677380			−0.0338690	+	0.999426i	$0.510783\pi$
$18$	1.32157	−	0.503453i	0.311496	−	0.118665i
$19$			2.99893i			0.688003i	0.938969	+	0.344001i	$0.111782\pi$
$19$			2.99893i			0.688003i	−0.938969	+	0.344001i	$0.888218\pi$
$20$	3.58913	+	4.02710i	0.802554	+	0.900486i
$21$			1.19970i			0.261796i
$22$	−1.55321	−	4.07718i	−0.331146	−	0.869258i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	−2.51029	−	1.30325i	−0.512410	−	0.266025i
$25$	−2.27484			−0.454967
$26$	0.0184419	+	0.0484100i	0.00361675	+	0.00949399i
$27$		−	1.00000i		−	0.192450i
$28$	1.79124	−	1.59643i	0.338512	−	0.301697i
$29$		−	1.31147i		−	0.243533i	−0.992559	−	0.121767i	$-0.961144\pi$
$29$		−	1.31147i		−	0.243533i	0.992559	−	0.121767i	$-0.0388560\pi$
$30$	3.56451	−	1.35791i	0.650788	−	0.247919i
$31$	−3.32528			−0.597238			−0.298619	−	0.954372i	$-0.596526\pi$
$31$	−3.32528			−0.597238			−0.298619	+	0.954372i	$0.596526\pi$
$32$	1.39457	+	5.48226i	0.246528	+	0.969136i
$33$	−3.08512			−0.537050
$34$	0.369101	−	0.140610i	0.0633004	−	0.0241144i
$35$			3.23582i			0.546953i
$36$	−1.49307	+	1.33069i	−0.248845	+	0.221782i
$37$		−	0.965182i		−	0.158675i	−0.996848	−	0.0793375i	$-0.974720\pi$
$37$		−	0.965182i		−	0.158675i	0.996848	−	0.0793375i	$-0.0252805\pi$
$38$	−1.50982	−	3.96329i	−0.244925	−	0.642930i
$39$	0.0366308			0.00586563
$40$	−6.77072	−	3.51511i	−1.07055	−	0.555788i
$41$	0.122446			0.0191228			0.00956141	−	0.999954i	$-0.496956\pi$
$41$	0.122446			0.0191228			0.00956141	+	0.999954i	$0.496956\pi$
$42$	−0.603992	−	1.58548i	−0.0931980	−	0.244645i
$43$			6.45272i			0.984030i	0.870587	+	0.492015i	$0.163740\pi$
$43$			6.45272i			0.984030i	−0.870587	+	0.492015i	$0.836260\pi$
$44$	4.10534	+	4.60630i	0.618903	+	0.694425i
$45$		−	2.69719i		−	0.402073i
$46$	−1.32157	+	0.503453i	−0.194854	+	0.0742301i
$47$	−7.33419			−1.06980			−0.534901	−	0.844915i	$-0.679651\pi$
$47$	−7.33419			−1.06980			−0.534901	+	0.844915i	$0.679651\pi$
$48$	3.97363	+	0.458519i	0.573545	+	0.0661816i
$49$	−5.56072			−0.794389
$50$	3.00635	−	1.14527i	0.425161	−	0.161966i
$51$		−	0.279291i		−	0.0391086i
$52$	−0.0487443	−	0.0546924i	−0.00675962	−	0.00758447i
$53$			1.48414i			0.203863i	0.994791	+	0.101931i	$0.0325022\pi$
$53$			1.48414i			0.203863i	−0.994791	+	0.101931i	$0.967498\pi$
$54$	0.503453	+	1.32157i	0.0685112	+	0.179842i
$55$	−8.32115			−1.12202
$56$	−1.56351	+	3.01159i	−0.208933	+	0.402441i
$57$	−2.99893			−0.397218
$58$	0.660262	+	1.73319i	0.0866966	+	0.227579i
$59$		−	0.292402i		−	0.0380674i	−0.999819	−	0.0190337i	$-0.993941\pi$
$59$		−	0.292402i		−	0.0380674i	0.999819	−	0.0190337i	$-0.00605899\pi$
$60$	−4.02710	+	3.58913i	−0.519896	+	0.463355i
$61$		−	10.5914i		−	1.35609i	−0.735021	−	0.678045i	$-0.762828\pi$
$61$		−	10.5914i		−	1.35609i	0.735021	−	0.678045i	$-0.237172\pi$
$62$	4.39457	−	1.67412i	0.558111	−	0.212614i
$63$	−1.19970			−0.151148
$64$	−4.60308	−	6.54306i	−0.575385	−	0.817883i
$65$	0.0988003			0.0122547
$66$	4.07718	−	1.55321i	0.501867	−	0.191187i
$67$			10.7005i			1.30728i	0.756806	+	0.653640i	$0.226759\pi$
$67$			10.7005i			1.30728i	−0.756806	+	0.653640i	$0.773241\pi$
$68$	−0.417001	+	0.371650i	−0.0505688	+	0.0450692i
$69$			1.00000i			0.120386i
$70$	−1.62908	−	4.27635i	−0.194713	−	0.511121i
$71$	−7.91699			−0.939574			−0.469787	−	0.882780i	$-0.655669\pi$
$71$	−7.91699			−0.939574			−0.469787	+	0.882780i	$0.655669\pi$
$72$	1.30325	−	2.51029i	0.153589	−	0.295840i
$73$	7.30232			0.854671			0.427336	−	0.904093i	$-0.359452\pi$
$73$	7.30232			0.854671			0.427336	+	0.904093i	$0.359452\pi$
$74$	0.485924	+	1.27555i	0.0564875	+	0.148280i
$75$		−	2.27484i		−	0.262676i
$76$	3.99066	+	4.47762i	0.457760	+	0.513618i
$77$			3.70121i			0.421793i
$78$	−0.0484100	+	0.0184419i	−0.00548136	+	0.00208813i
$79$	−10.5602			−1.18811			−0.594055	−	0.804424i	$-0.702474\pi$
$79$	−10.5602			−1.18811			−0.594055	+	0.804424i	$0.702474\pi$
$80$	10.7176	+	1.23671i	1.19827	+	0.138269i
$81$	1.00000			0.111111
$82$	−0.161820	+	0.0616457i	−0.0178700	+	0.00680763i
$83$			13.9464i			1.53082i	0.643546	+	0.765408i	$0.277463\pi$
$83$			13.9464i			1.53082i	−0.643546	+	0.765408i	$0.722537\pi$
$84$	1.59643	+	1.79124i	0.174185	+	0.195440i
$85$		−	0.753301i		−	0.0817070i
$86$	−3.24864	−	8.52769i	−0.350310	−	0.919565i
$87$	1.31147			0.140604
$88$	−7.74453	−	4.02068i	−0.825569	−	0.428606i
$89$	2.48847			0.263778			0.131889	−	0.991265i	$-0.457896\pi$
$89$	2.48847			0.263778			0.131889	+	0.991265i	$0.457896\pi$
$90$	1.35791	+	3.56451i	0.143136	+	0.375733i
$91$		−	0.0439460i		−	0.00460679i
$92$	1.49307	−	1.33069i	0.155663	−	0.138734i
$93$		−	3.32528i		−	0.344815i
$94$	9.69261	−	3.69242i	0.999717	−	0.380844i
$95$	−8.08869			−0.829883
$96$	−5.48226	+	1.39457i	−0.559531	+	0.142333i
$97$	12.2447			1.24326			0.621632	−	0.783309i	$-0.286470\pi$
$97$	12.2447			1.24326			0.621632	+	0.783309i	$0.286470\pi$
$98$	7.34885	−	2.79956i	0.742346	−	0.282798i
$99$		−	3.08512i		−	0.310066i
$100$	−3.39649	+	3.02711i	−0.339649	+	0.302711i
$101$		−	9.19144i		−	0.914582i	−0.889317	−	0.457291i	$-0.848820\pi$
$101$		−	9.19144i		−	0.914582i	0.889317	−	0.457291i	$-0.151180\pi$
$102$	0.140610	+	0.369101i	0.0139224	+	0.0365465i
$103$	13.7228			1.35215			0.676076	−	0.736832i	$-0.263679\pi$
$103$	13.7228			1.35215			0.676076	+	0.736832i	$0.263679\pi$
$104$	0.0919539	+	0.0477391i	0.00901682	+	0.00468121i
$105$	−3.23582			−0.315784
$106$	−0.747197	−	1.96139i	−0.0725741	−	0.190507i
$107$		−	11.6190i		−	1.12325i	−0.827391	−	0.561627i	$-0.810176\pi$
$107$		−	11.6190i		−	1.12325i	0.827391	−	0.561627i	$-0.189824\pi$
$108$	−1.33069	−	1.49307i	−0.128046	−	0.143671i
$109$		−	4.28843i		−	0.410758i	−0.978683	−	0.205379i	$-0.934157\pi$
$109$		−	4.28843i		−	0.410758i	0.978683	−	0.205379i	$-0.0658426\pi$
$110$	10.9969	−	4.18930i	1.04852	−	0.399434i
$111$	0.965182			0.0916111
$112$	0.550086	−	4.76717i	0.0519782	−	0.450455i
$113$	19.3075			1.81630			0.908148	−	0.418650i	$-0.137497\pi$
$113$	19.3075			1.81630			0.908148	+	0.418650i	$0.137497\pi$
$114$	3.96329	−	1.50982i	0.371196	−	0.141408i
$115$			2.69719i			0.251514i
$116$	−1.74516	−	1.95811i	−0.162034	−	0.181806i
$117$			0.0366308i			0.00338652i
$118$	0.147210	+	0.386428i	0.0135518	+	0.0355736i
$119$	−0.335065			−0.0307154
$120$	3.51511	−	6.77072i	0.320885	−	0.618079i
$121$	1.48206			0.134733
$122$	5.33227	+	13.9972i	0.482761	+	1.26725i
$123$			0.122446i			0.0110406i
$124$	−4.96488	+	4.42492i	−0.445859	+	0.397370i
$125$			7.35028i			0.657429i
$126$	1.58548	−	0.603992i	0.141246	−	0.0538079i
$127$	19.3284			1.71512			0.857561	−	0.514382i	$-0.171979\pi$
$127$	19.3284			1.71512			0.857561	+	0.514382i	$0.171979\pi$
$128$	9.37739	+	6.32965i	0.828852	+	0.559468i
$129$	−6.45272			−0.568130
$130$	−0.130571	+	0.0497413i	−0.0114518	+	0.00436260i
$131$			3.60148i			0.314663i	0.987546	+	0.157332i	$0.0502891\pi$
$131$			3.60148i			0.314663i	−0.987546	+	0.157332i	$0.949711\pi$
$132$	−4.60630	+	4.10534i	−0.400927	+	0.357324i
$133$			3.59782i			0.311971i
$134$	−5.38722	−	14.1415i	−0.465385	−	1.22164i
$135$	2.69719			0.232137
$136$	0.363986	−	0.701101i	0.0312115	−	0.0601189i
$137$	6.28115			0.536635			0.268317	−	0.963331i	$-0.413532\pi$
$137$	6.28115			0.536635			0.268317	+	0.963331i	$0.413532\pi$
$138$	−0.503453	−	1.32157i	−0.0428567	−	0.112499i
$139$			16.3829i			1.38958i	0.719213	+	0.694789i	$0.244502\pi$
$139$			16.3829i			1.38958i	−0.719213	+	0.694789i	$0.755498\pi$
$140$	4.30588	+	4.83131i	0.363913	+	0.408320i
$141$		−	7.33419i		−	0.617650i
$142$	10.4628	−	3.98583i	0.878021	−	0.334484i
$143$	0.113010			0.00945040
$144$	−0.458519	+	3.97363i	−0.0382100	+	0.331136i
$145$	3.53728			0.293755
$146$	−9.65049	+	3.67637i	−0.798680	+	0.304259i
$147$		−	5.56072i		−	0.458640i
$148$	−1.28436	−	1.44109i	−0.105574	−	0.118456i
$149$			2.75873i			0.226004i	0.993595	+	0.113002i	$0.0360466\pi$
$149$			2.75873i			0.226004i	−0.993595	+	0.113002i	$0.963953\pi$
$150$	1.14527	+	3.00635i	0.0935111	+	0.245467i
$151$	12.8704			1.04738			0.523691	−	0.851908i	$-0.324555\pi$
$151$	12.8704			1.04738			0.523691	+	0.851908i	$0.324555\pi$
$152$	−7.52818	−	3.90836i	−0.610616	−	0.317010i
$153$	0.279291			0.0225793
$154$	−1.86339	−	4.89140i	−0.150156	−	0.394160i
$155$		−	8.96891i		−	0.720400i
$156$	0.0546924	−	0.0487443i	0.00437890	−	0.00390267i
$157$		−	4.75395i		−	0.379407i	−0.981841	−	0.189703i	$-0.939247\pi$
$157$		−	4.75395i		−	0.379407i	0.981841	−	0.189703i	$-0.0607526\pi$
$158$	13.9559	−	5.31654i	1.11027	−	0.422961i
$159$	−1.48414			−0.117700
$160$	−14.7867	+	3.76143i	−1.16899	+	0.297367i
$161$	1.19970			0.0945496
$162$	−1.32157	+	0.503453i	−0.103832	+	0.0395550i
$163$		−	1.45694i		−	0.114116i	−0.998371	−	0.0570581i	$-0.981828\pi$
$163$		−	1.45694i		−	0.114116i	0.998371	−	0.0570581i	$-0.0181720\pi$
$164$	0.182820	−	0.162938i	0.0142759	−	0.0127233i
$165$		−	8.32115i		−	0.647800i
$166$	−7.02135	−	18.4311i	−0.544962	−	1.43053i
$167$	17.9505			1.38905			0.694525	−	0.719468i	$-0.255614\pi$
$167$	17.9505			1.38905			0.694525	+	0.719468i	$0.255614\pi$
$168$	−3.01159	−	1.56351i	−0.232349	−	0.120627i
$169$	12.9987			0.999897
$170$	0.379252	+	0.995537i	0.0290873	+	0.0763542i
$171$		−	2.99893i		−	0.229334i
$172$	8.58658	+	9.63436i	0.654721	+	0.734613i
$173$			1.07325i			0.0815978i	0.999167	+	0.0407989i	$0.0129903\pi$
$173$			1.07325i			0.0815978i	−0.999167	+	0.0407989i	$0.987010\pi$
$174$	−1.73319	+	0.660262i	−0.131393	+	0.0500543i
$175$	−2.72912			−0.206302
$176$	12.2591	+	1.41459i	0.924066	+	0.106628i
$177$	0.292402			0.0219782
$178$	−3.28868	+	1.25283i	−0.246497	+	0.0939035i
$179$		−	7.19320i		−	0.537645i	−0.963190	−	0.268822i	$-0.913366\pi$
$179$		−	7.19320i		−	0.537645i	0.963190	−	0.268822i	$-0.0866345\pi$
$180$	−3.58913	−	4.02710i	−0.267518	−	0.300162i
$181$		−	7.52438i		−	0.559283i	−0.960105	−	0.279641i	$-0.909784\pi$
$181$		−	7.52438i		−	0.559283i	0.960105	−	0.279641i	$-0.0902156\pi$
$182$	0.0221247	+	0.0580775i	0.00163999	+	0.00430499i
$183$	10.5914			0.782938
$184$	−1.30325	+	2.51029i	−0.0960769	+	0.185061i
$185$	2.60328			0.191397
$186$	1.67412	+	4.39457i	0.122752	+	0.322226i
$187$		−	0.861645i		−	0.0630097i
$188$	−10.9505	+	9.75955i	−0.798645	+	0.711788i
$189$		−	1.19970i		−	0.0872653i
$190$	10.6897	−	4.07228i	0.775515	−	0.295434i
$191$	−13.7860			−0.997521			−0.498760	−	0.866740i	$-0.666211\pi$
$191$	−13.7860			−0.997521			−0.498760	+	0.866740i	$0.666211\pi$
$192$	6.54306	−	4.60308i	0.472205	−	0.332199i
$193$	−21.6089			−1.55544			−0.777720	−	0.628610i	$-0.783624\pi$
$193$	−21.6089			−1.55544			−0.777720	+	0.628610i	$0.783624\pi$
$194$	−16.1822	+	6.16464i	−1.16182	+	0.442596i
$195$			0.0988003i			0.00707524i
$196$	−8.30255	+	7.39960i	−0.593039	+	0.528543i
$197$		−	20.3261i		−	1.44818i	−0.689707	−	0.724089i	$-0.742261\pi$
$197$		−	20.3261i		−	1.44818i	0.689707	−	0.724089i	$-0.257739\pi$
$198$	1.55321	+	4.07718i	0.110382	+	0.289753i
$199$	13.7154			0.972259			0.486129	−	0.873887i	$-0.338408\pi$
$199$	13.7154			0.972259			0.486129	+	0.873887i	$0.338408\pi$
$200$	2.96468	−	5.71049i	0.209635	−	0.403793i
$201$	−10.7005			−0.754758
$202$	4.62746	+	12.1471i	0.325587	+	0.854666i
$203$		−	1.57337i		−	0.110429i
$204$	−0.371650	−	0.417001i	−0.0260207	−	0.0291959i
$205$			0.330260i			0.0230663i
$206$	−18.1356	+	6.90880i	−1.26357	+	0.481359i
$207$	−1.00000			−0.0695048
$208$	−0.145557	−	0.0167959i	−0.0100926	−	0.00116459i
$209$	−9.25206			−0.639978
$210$	4.27635	−	1.62908i	0.295096	−	0.112417i
$211$			17.5048i			1.20508i	0.798089	+	0.602539i	$0.205844\pi$
$211$			17.5048i			1.20508i	−0.798089	+	0.602539i	$0.794156\pi$
$212$	1.97494	+	2.21593i	0.135639	+	0.152191i
$213$		−	7.91699i		−	0.542463i
$214$	5.84963	+	15.3553i	0.399873	+	1.04967i
$215$	−17.4042			−1.18696
$216$	2.51029	+	1.30325i	0.170803	+	0.0886749i
$217$	−3.98934			−0.270814
$218$	2.15902	+	5.66745i	0.146228	+	0.383848i
$219$			7.30232i			0.493445i
$220$	−12.4241	+	11.0729i	−0.837630	+	0.746533i
$221$			0.0102307i			0.000688189i
$222$	−1.27555	+	0.485924i	−0.0856094	+	0.0326131i
$223$	19.7074			1.31970			0.659852	−	0.751396i	$-0.270619\pi$
$223$	19.7074			1.31970			0.659852	+	0.751396i	$0.270619\pi$
$224$	1.67307	+	6.57707i	0.111787	+	0.439449i
$225$	2.27484			0.151656
$226$	−25.5161	+	9.72041i	−1.69731	+	0.646592i
$227$			16.3574i			1.08568i	0.839836	+	0.542840i	$0.182651\pi$
$227$			16.3574i			1.08568i	−0.839836	+	0.542840i	$0.817349\pi$
$228$	−4.47762	+	3.99066i	−0.296538	+	0.264288i
$229$			9.50963i			0.628414i	0.949354	+	0.314207i	$0.101739\pi$
$229$			9.50963i			0.628414i	−0.949354	+	0.314207i	$0.898261\pi$
$230$	−1.35791	−	3.56451i	−0.0895378	−	0.235037i
$231$	−3.70121			−0.243522
$232$	3.29216	+	1.70917i	0.216141	+	0.112213i
$233$	−22.7838			−1.49262			−0.746308	−	0.665601i	$-0.768175\pi$
$233$	−22.7838			−1.49262			−0.746308	+	0.665601i	$0.768175\pi$
$234$	−0.0184419	−	0.0484100i	−0.00120558	−	0.00316466i
$235$		−	19.7817i		−	1.29042i
$236$	−0.389096	−	0.436576i	−0.0253280	−	0.0284187i
$237$		−	10.5602i		−	0.685956i
$238$	0.442811	−	0.168690i	0.0287032	−	0.0109345i
$239$	−16.6155			−1.07477			−0.537385	−	0.843337i	$-0.680588\pi$
$239$	−16.6155			−1.07477			−0.537385	+	0.843337i	$0.680588\pi$
$240$	−1.23671	+	10.7176i	−0.0798296	+	0.691821i
$241$	6.31610			0.406856			0.203428	−	0.979090i	$-0.434792\pi$
$241$	6.31610			0.406856			0.203428	+	0.979090i	$0.434792\pi$
$242$	−1.95864	+	0.746146i	−0.125906	+	0.0479641i
$243$			1.00000i			0.0641500i
$244$	−14.0939	−	15.8137i	−0.902268	−	1.01237i
$245$		−	14.9983i		−	0.958208i
$246$	−0.0616457	−	0.161820i	−0.00393039	−	0.0103173i
$247$	0.109853			0.00698981
$248$	4.33367	−	8.34740i	0.275188	−	0.530061i
$249$	−13.9464			−0.883817
$250$	−3.70052	−	9.71388i	−0.234042	−	0.614360i
$251$		−	20.7310i		−	1.30853i	−0.756266	−	0.654264i	$-0.772979\pi$
$251$		−	20.7310i		−	1.30853i	0.756266	−	0.654264i	$-0.227021\pi$
$252$	−1.79124	+	1.59643i	−0.112837	+	0.100566i
$253$			3.08512i			0.193960i
$254$	−25.5438	+	9.73096i	−1.60276	+	0.610575i
$255$	0.753301			0.0471735
$256$	−15.5795	−	3.64398i	−0.973720	−	0.227748i
$257$	5.82477			0.363339			0.181670	−	0.983360i	$-0.441850\pi$
$257$	5.82477			0.363339			0.181670	+	0.983360i	$0.441850\pi$
$258$	8.52769	−	3.24864i	0.530911	−	0.202251i
$259$		−	1.15793i		−	0.0719502i
$260$	0.147516	−	0.131473i	0.00914854	−	0.00815359i
$261$			1.31147i			0.0811778i
$262$	−1.81318	−	4.75960i	−0.112018	−	0.294049i
$263$	−18.1314			−1.11803			−0.559016	−	0.829157i	$-0.688821\pi$
$263$	−18.1314			−1.11803			−0.559016	+	0.829157i	$0.688821\pi$
$264$	4.02068	−	7.74453i	0.247456	−	0.476643i
$265$	−4.00302			−0.245904
$266$	−1.81133	−	4.75476i	−0.111060	−	0.291533i
$267$			2.48847i			0.152292i
$268$	14.2391	+	15.9767i	0.869793	+	0.975930i
$269$		−	5.46914i		−	0.333459i	−0.986003	−	0.166730i	$-0.946679\pi$
$269$		−	5.46914i		−	0.333459i	0.986003	−	0.166730i	$-0.0533207\pi$
$270$	−3.56451	+	1.35791i	−0.216929	+	0.0826397i
$271$	6.30219			0.382831			0.191415	−	0.981509i	$-0.438692\pi$
$271$	6.30219			0.382831			0.191415	+	0.981509i	$0.438692\pi$
$272$	−0.128060	+	1.10980i	−0.00776480	+	0.0672915i
$273$	0.0439460			0.00265973
$274$	−8.30095	+	3.16226i	−0.501479	+	0.191039i
$275$		−	7.01814i		−	0.423209i
$276$	1.33069	+	1.49307i	0.0800982	+	0.0898723i
$277$			24.5962i			1.47784i	0.673791	+	0.738922i	$0.264665\pi$
$277$			24.5962i			1.47784i	−0.673791	+	0.738922i	$0.735335\pi$
$278$	−8.24801	−	21.6511i	−0.494683	−	1.29854i
$279$	3.32528			0.199079
$280$	−8.12284	−	4.21708i	−0.485432	−	0.252019i
$281$	20.9976			1.25261			0.626306	−	0.779577i	$-0.284566\pi$
$281$	20.9976			1.25261			0.626306	+	0.779577i	$0.284566\pi$
$282$	3.69242	+	9.69261i	0.219880	+	0.577187i
$283$			6.64534i			0.395025i	0.980300	+	0.197512i	$0.0632862\pi$
$283$			6.64534i			0.395025i	−0.980300	+	0.197512i	$0.936714\pi$
$284$	−11.8206	+	10.5351i	−0.701425	+	0.625142i
$285$		−	8.08869i		−	0.479133i
$286$	−0.149351	+	0.0568954i	−0.00883129	+	0.00336429i
$287$	0.146898			0.00867113
$288$	−1.39457	−	5.48226i	−0.0821760	−	0.323045i
$289$	−16.9220			−0.995412
$290$	−4.67474	+	1.78085i	−0.274510	+	0.104575i
$291$			12.2447i			0.717799i
$292$	10.9029	−	9.71713i	0.638042	−	0.568652i
$293$			23.5701i			1.37698i	0.725246	+	0.688489i	$0.241726\pi$
$293$			23.5701i			1.37698i	−0.725246	+	0.688489i	$0.758274\pi$
$294$	2.79956	+	7.34885i	0.163274	+	0.428594i
$295$	0.788663			0.0459177
$296$	2.42288	+	1.25787i	0.140827	+	0.0731124i
$297$	3.08512			0.179017
$298$	−1.38889	−	3.64584i	−0.0804562	−	0.211198i
$299$		−	0.0366308i		−	0.00211842i
$300$	−3.02711	−	3.39649i	−0.174770	−	0.196097i
$301$			7.74133i			0.446203i
$302$	−17.0091	+	6.47966i	−0.978766	+	0.372863i
$303$	9.19144			0.528034
$304$	11.9167	+	1.37507i	0.683467	+	0.0788656i
$305$	28.5670			1.63574
$306$	−0.369101	+	0.140610i	−0.0211001	+	0.00803813i
$307$		−	14.0635i		−	0.802648i	−0.915936	−	0.401324i	$-0.868550\pi$
$307$		−	14.0635i		−	0.802648i	0.915936	−	0.401324i	$-0.131450\pi$
$308$	4.92518	+	5.52617i	0.280638	+	0.314883i
$309$			13.7228i			0.780665i
$310$	4.51542	+	11.8530i	0.256459	+	0.673205i
$311$	22.2815			1.26347			0.631734	−	0.775185i	$-0.282343\pi$
$311$	22.2815			1.26347			0.631734	+	0.775185i	$0.282343\pi$
$312$	−0.0477391	+	0.0919539i	−0.00270270	+	0.00520586i
$313$	−18.3737			−1.03854			−0.519272	−	0.854609i	$-0.673797\pi$
$313$	−18.3737			−1.03854			−0.519272	+	0.854609i	$0.673797\pi$
$314$	2.39339	+	6.28266i	0.135067	+	0.354551i
$315$		−	3.23582i		−	0.182318i
$316$	−15.7671	+	14.0523i	−0.886966	+	0.790504i
$317$		−	6.09283i		−	0.342207i	−0.985253	−	0.171104i	$-0.945267\pi$
$317$		−	6.09283i		−	0.342207i	0.985253	−	0.171104i	$-0.0547333\pi$
$318$	1.96139	−	0.747197i	0.109990	−	0.0419007i
$319$	4.04603			0.226534
$320$	17.6479	−	12.4154i	0.986547	−	0.694041i
$321$	11.6190			0.648511
$322$	−1.58548	+	0.603992i	−0.0883555	+	0.0336592i
$323$		−	0.837575i		−	0.0466039i
$324$	1.49307	−	1.33069i	0.0829484	−	0.0739273i
$325$			0.0833291i			0.00462227i
$326$	0.733500	+	1.92544i	0.0406248	+	0.106640i
$327$	4.28843			0.237151
$328$	−0.159578	+	0.307374i	−0.00881119	+	0.0169719i
$329$	−8.79883			−0.485095
$330$	4.18930	+	10.9969i	0.230614	+	0.605362i
$331$			0.142627i			0.00783948i	0.999992	+	0.00391974i	$0.00124769\pi$
$331$			0.142627i			0.00783948i	−0.999992	+	0.00391974i	$0.998752\pi$
$332$	18.5583	+	20.8229i	1.01852	+	1.14281i
$333$			0.965182i			0.0528917i
$334$	−23.7228	+	9.03723i	−1.29805	+	0.494495i
$335$	−28.8614			−1.57687
$336$	4.76717	+	0.550086i	0.260070	+	0.0300096i
$337$	18.4038			1.00252			0.501261	−	0.865296i	$-0.332870\pi$
$337$	18.4038			1.00252			0.501261	+	0.865296i	$0.332870\pi$
$338$	−17.1786	+	6.54421i	−0.934391	+	0.355958i
$339$			19.3075i			1.04864i
$340$	−1.00241	−	1.12473i	−0.0543634	−	0.0609971i
$341$		−	10.2589i		−	0.555549i
$342$	1.50982	+	3.96329i	0.0816418	+	0.214310i
$343$	−15.0691			−0.813655
$344$	−16.1982	−	8.40951i	−0.873347	−	0.453410i
$345$	−2.69719			−0.145212
$346$	−0.540332	−	1.41837i	−0.0290484	−	0.0762522i
$347$		−	19.1563i		−	1.02837i	−0.857680	−	0.514183i	$-0.828095\pi$
$347$		−	19.1563i		−	1.02837i	0.857680	−	0.514183i	$-0.171905\pi$
$348$	1.95811	−	1.74516i	0.104966	−	0.0935503i
$349$			28.3823i			1.51927i	0.650351	+	0.759634i	$0.274622\pi$
$349$			28.3823i			1.51927i	−0.650351	+	0.759634i	$0.725378\pi$
$350$	3.60671	−	1.37398i	0.192787	−	0.0734425i
$351$	−0.0366308			−0.00195521
$352$	−16.9134	+	4.30242i	−0.901488	+	0.229320i
$353$	30.3696			1.61641			0.808205	−	0.588901i	$-0.200439\pi$
$353$	30.3696			1.61641			0.808205	+	0.588901i	$0.200439\pi$
$354$	−0.386428	+	0.147210i	−0.0205384	+	0.00782414i
$355$		−	21.3536i		−	1.13333i
$356$	3.71547	−	3.31139i	0.196919	−	0.175503i
$357$		−	0.335065i		−	0.0177335i
$358$	3.62144	+	9.50628i	0.191399	+	0.502423i
$359$	−6.93504			−0.366018			−0.183009	−	0.983111i	$-0.558584\pi$
$359$	−6.93504			−0.366018			−0.183009	+	0.983111i	$0.558584\pi$
$360$	6.77072	+	3.51511i	0.356848	+	0.185263i
$361$	10.0064			0.526653
$362$	3.78817	+	9.94396i	0.199102	+	0.522643i
$363$			1.48206i			0.0777879i
$364$	−0.0584786	−	0.0656145i	−0.00306511	−	0.00343913i
$365$			19.6957i			1.03092i
$366$	−13.9972	+	5.33227i	−0.731646	+	0.278722i
$367$	14.5367			0.758811			0.379405	−	0.925231i	$-0.376129\pi$
$367$	14.5367			0.758811			0.379405	+	0.925231i	$0.376129\pi$
$368$	0.458519	−	3.97363i	0.0239020	−	0.207140i
$369$	−0.122446			−0.00637427
$370$	−3.44041	+	1.31063i	−0.178858	+	0.0681364i
$371$			1.78053i			0.0924404i
$372$	−4.42492	−	4.96488i	−0.229421	−	0.257417i
$373$			15.1546i			0.784674i	0.919821	+	0.392337i	$0.128333\pi$
$373$			15.1546i			0.784674i	−0.919821	+	0.392337i	$0.871667\pi$
$374$	0.433798	+	1.13872i	0.0224311	+	0.0588818i
$375$	−7.35028			−0.379567
$376$	9.55829	−	18.4109i	0.492931	−	0.949471i
$377$	−0.0480401			−0.00247419
$378$	0.603992	+	1.58548i	0.0310660	+	0.0815484i
$379$		−	20.6078i		−	1.05855i	−0.848450	−	0.529275i	$-0.822464\pi$
$379$		−	20.6078i		−	1.05855i	0.848450	−	0.529275i	$-0.177536\pi$
$380$	−12.0770	+	10.7636i	−0.619537	+	0.552159i
$381$			19.3284i			0.990226i
$382$	18.2191	−	6.94061i	0.932171	−	0.355112i
$383$	−3.98900			−0.203829			−0.101914	−	0.994793i	$-0.532497\pi$
$383$	−3.98900			−0.203829			−0.101914	+	0.994793i	$0.532497\pi$
$384$	−6.32965	+	9.37739i	−0.323009	+	0.478538i
$385$	−9.98288			−0.508775
$386$	28.5575	−	10.8790i	1.45354	−	0.553729i
$387$		−	6.45272i		−	0.328010i
$388$	18.2822	−	16.2940i	0.928140	−	0.827200i
$389$		−	36.8327i		−	1.86749i	−0.357934	−	0.933747i	$-0.616519\pi$
$389$		−	36.8327i		−	1.86749i	0.357934	−	0.933747i	$-0.383481\pi$
$390$	−0.0497413	−	0.130571i	−0.00251875	−	0.00661172i
$391$	−0.279291			−0.0141244
$392$	7.24701	−	13.9590i	0.366029	−	0.705036i
$393$	−3.60148			−0.181671
$394$	10.2333	+	26.8623i	0.515544	+	1.35330i
$395$		−	28.4827i		−	1.43312i
$396$	−4.10534	−	4.60630i	−0.206301	−	0.231475i
$397$		−	5.18791i		−	0.260374i	−0.991489	−	0.130187i	$-0.958442\pi$
$397$		−	5.18791i		−	0.260374i	0.991489	−	0.130187i	$-0.0415577\pi$
$398$	−18.1258	+	6.90506i	−0.908564	+	0.346119i
$399$	−3.59782			−0.180116
$400$	−1.04306	+	9.03937i	−0.0521528	+	0.451968i
$401$	13.1824			0.658295			0.329148	−	0.944278i	$-0.393239\pi$
$401$	13.1824			0.658295			0.329148	+	0.944278i	$0.393239\pi$
$402$	14.1415	−	5.38722i	0.705312	−	0.268690i
$403$			0.121808i			0.00606767i
$404$	−12.2310	−	13.7235i	−0.608514	−	0.682768i
$405$			2.69719i			0.134024i
$406$	0.792116	+	2.07931i	0.0393121	+	0.103194i
$407$	2.97770			0.147599
$408$	0.701101	+	0.363986i	0.0347096	+	0.0180200i
$409$	−40.0884			−1.98224			−0.991122	−	0.132958i	$-0.957553\pi$
$409$	−40.0884			−1.98224			−0.991122	+	0.132958i	$0.957553\pi$
$410$	−0.166270	−	0.436460i	−0.00821150	−	0.0215552i
$411$			6.28115i			0.309826i
$412$	20.4892	−	18.2609i	1.00943	−	0.899648i
$413$		−	0.350794i		−	0.0172615i
$414$	1.32157	−	0.503453i	0.0649514	−	0.0247434i
$415$	−37.6161			−1.84650
$416$	0.200820	−	0.0510844i	0.00984600	−	0.00250462i
$417$	−16.3829			−0.802274
$418$	12.2272	−	4.65797i	0.598052	−	0.227829i
$419$			4.46330i			0.218046i	0.994039	+	0.109023i	$0.0347723\pi$
$419$			4.46330i			0.218046i	−0.994039	+	0.109023i	$0.965228\pi$
$420$	−4.83131	+	4.30588i	−0.235744	+	0.210105i
$421$		−	26.0758i		−	1.27086i	−0.772160	−	0.635428i	$-0.780824\pi$
$421$		−	26.0758i		−	1.27086i	0.772160	−	0.635428i	$-0.219176\pi$
$422$	−8.81283	−	23.1337i	−0.429002	−	1.12613i
$423$	7.33419			0.356601
$424$	−3.72563	−	1.93421i	−0.180932	−	0.0939336i
$425$	0.635341			0.0308186
$426$	3.98583	+	10.4628i	0.193114	+	0.506925i
$427$		−	12.7065i		−	0.614910i
$428$	−15.4613	−	17.3480i	−0.747352	−	0.838548i
$429$			0.113010i			0.00545619i
$430$	23.0008	−	8.76220i	1.10920	−	0.422551i
$431$	16.5454			0.796965			0.398483	−	0.917176i	$-0.369537\pi$
$431$	16.5454			0.796965			0.398483	+	0.917176i	$0.369537\pi$
$432$	−3.97363	−	0.458519i	−0.191182	−	0.0220605i
$433$	17.3279			0.832725			0.416363	−	0.909199i	$-0.363305\pi$
$433$	17.3279			0.832725			0.416363	+	0.909199i	$0.363305\pi$
$434$	5.27217	−	2.00844i	0.253072	−	0.0964084i
$435$			3.53728i			0.169599i
$436$	−5.70658	−	6.40294i	−0.273296	−	0.306645i
$437$			2.99893i			0.143458i
$438$	−3.67637	−	9.65049i	−0.175664	−	0.461118i
$439$	−0.522509			−0.0249380			−0.0124690	−	0.999922i	$-0.503969\pi$
$439$	−0.522509			−0.0249380			−0.0124690	+	0.999922i	$0.503969\pi$
$440$	10.8445	−	20.8885i	0.516993	−	0.995818i
$441$	5.56072			0.264796
$442$	−0.00515066	−	0.0135205i	−0.000244992	−	0.000643104i
$443$		−	29.8300i		−	1.41726i	−0.705578	−	0.708632i	$-0.749313\pi$
$443$		−	29.8300i		−	1.41726i	0.705578	−	0.708632i	$-0.250687\pi$
$444$	1.44109	−	1.28436i	0.0683909	−	0.0609530i
$445$			6.71189i			0.318174i
$446$	−26.0446	+	9.92173i	−1.23325	+	0.469808i
$447$	−2.75873			−0.130483
$448$	−5.52231	−	7.84971i	−0.260905	−	0.370864i
$449$	−18.3537			−0.866167			−0.433083	−	0.901354i	$-0.642574\pi$
$449$	−18.3537			−0.866167			−0.433083	+	0.901354i	$0.642574\pi$
$450$	−3.00635	+	1.14527i	−0.141720	+	0.0539887i
$451$			0.377760i			0.0177880i
$452$	28.8274	−	25.6923i	1.35593	−	1.20846i
$453$			12.8704i			0.604706i
$454$	−8.23518	−	21.6174i	−0.386496	−	1.01455i
$455$	0.118531			0.00555681
$456$	3.90836	−	7.52818i	0.183026	−	0.352539i
$457$	2.65227			0.124068			0.0620340	−	0.998074i	$-0.480241\pi$
$457$	2.65227			0.124068			0.0620340	+	0.998074i	$0.480241\pi$
$458$	−4.78765	−	12.5676i	−0.223712	−	0.587245i
$459$			0.279291i			0.0130362i
$460$	3.58913	+	4.02710i	0.167344	+	0.187764i
$461$			16.7855i			0.781780i	0.920437	+	0.390890i	$0.127833\pi$
$461$			16.7855i			0.781780i	−0.920437	+	0.390890i	$0.872167\pi$
$462$	4.89140	−	1.86339i	0.227568	−	0.0866926i
$463$	5.48971			0.255128			0.127564	−	0.991830i	$-0.459284\pi$
$463$	5.48971			0.255128			0.127564	+	0.991830i	$0.459284\pi$
$464$	−5.21129	−	0.601333i	−0.241928	−	0.0279162i
$465$	8.96891			0.415923
$466$	30.1103	−	11.4706i	1.39483	−	0.531364i
$467$		−	30.4068i		−	1.40706i	−0.710665	−	0.703530i	$-0.751606\pi$
$467$		−	30.4068i		−	1.40706i	0.710665	−	0.703530i	$-0.248394\pi$
$468$	0.0487443	+	0.0546924i	0.00225321	+	0.00252816i
$469$			12.8374i			0.592778i
$470$	9.95916	+	26.1428i	0.459382	+	1.20588i
$471$	4.75395			0.219050
$472$	0.734012	+	0.381072i	0.0337856	+	0.0175403i
$473$	−19.9074			−0.915343
$474$	5.31654	+	13.9559i	0.244197	+	0.641017i
$475$		−	6.82208i		−	0.313019i
$476$	−0.500276	+	0.445869i	−0.0229301	+	0.0204364i
$477$		−	1.48414i		−	0.0679543i
$478$	21.9585	−	8.36514i	1.00436	−	0.382612i
$479$	17.4337			0.796566			0.398283	−	0.917263i	$-0.369606\pi$
$479$	17.4337			0.796566			0.398283	+	0.917263i	$0.369606\pi$
$480$	−3.76143	−	14.7867i	−0.171685	−	0.674917i
$481$	−0.0353554			−0.00161207
$482$	−8.34714	+	3.17986i	−0.380202	+	0.144839i
$483$			1.19970i			0.0545882i
$484$	2.21282	−	1.97216i	0.100583	−	0.0896437i
$485$			33.0264i			1.49965i
$486$	−0.503453	−	1.32157i	−0.0228371	−	0.0599474i
$487$	−6.63631			−0.300720			−0.150360	−	0.988631i	$-0.548043\pi$
$487$	−6.63631			−0.300720			−0.150360	+	0.988631i	$0.548043\pi$
$488$	26.5874	+	13.8032i	1.20356	+	0.624843i
$489$	1.45694			0.0658851
$490$	7.55095	+	19.8213i	0.341117	+	0.895433i
$491$			11.8437i			0.534500i	0.963627	+	0.267250i	$0.0861149\pi$
$491$			11.8437i			0.534500i	−0.963627	+	0.267250i	$0.913885\pi$
$492$	0.162938	+	0.182820i	0.00734580	+	0.00824217i
$493$			0.366281i			0.0164965i
$494$	−0.145178	+	0.0553060i	−0.00653189	+	0.00248833i
$495$	8.32115			0.374008
$496$	−1.52470	+	13.2134i	−0.0684613	+	0.593301i
$497$	−9.49802			−0.426044
$498$	18.4311	−	7.02135i	0.825916	−	0.314634i
$499$			17.4583i			0.781540i	0.920488	+	0.390770i	$0.127791\pi$
$499$			17.4583i			0.781540i	−0.920488	+	0.390770i	$0.872209\pi$
$500$	9.78096	+	10.9745i	0.437418	+	0.490794i
$501$			17.9505i			0.801969i
$502$	10.4371	+	27.3973i	0.465829	+	1.22280i
$503$	−25.0051			−1.11492			−0.557460	−	0.830204i	$-0.688224\pi$
$503$	−25.0051			−1.11492			−0.557460	+	0.830204i	$0.688224\pi$
$504$	1.56351	−	3.01159i	0.0696442	−	0.134147i
$505$	24.7911			1.10319
$506$	−1.55321	−	4.07718i	−0.0690486	−	0.181253i
$507$			12.9987i			0.577291i
$508$	28.8587	−	25.7202i	1.28040	−	1.14115i
$509$			33.7255i			1.49485i	0.664344	+	0.747427i	$0.268711\pi$
$509$			33.7255i			1.49485i	−0.664344	+	0.747427i	$0.731289\pi$
$510$	−0.995537	+	0.379252i	−0.0440831	+	0.0167935i
$511$	8.76059			0.387546
$512$	22.4239	−	3.02780i	0.991007	−	0.133811i
$513$	2.99893			0.132406
$514$	−7.69782	+	2.93250i	−0.339536	+	0.129347i
$515$			37.0131i			1.63099i
$516$	−9.63436	+	8.58658i	−0.424129	+	0.378003i
$517$		−	22.6268i		−	0.995127i
$518$	0.582963	+	1.53028i	0.0256139	+	0.0672366i
$519$	−1.07325			−0.0471105
$520$	−0.128762	+	0.248017i	−0.00564657	+	0.0108763i
$521$	24.1789			1.05930			0.529649	−	0.848217i	$-0.322324\pi$
$521$	24.1789			1.05930			0.529649	+	0.848217i	$0.322324\pi$
$522$	−0.660262	−	1.73319i	−0.0288989	−	0.0758597i
$523$		−	24.3169i		−	1.06331i	−0.846962	−	0.531653i	$-0.821571\pi$
$523$		−	24.3169i		−	1.06331i	0.846962	−	0.531653i	$-0.178429\pi$
$524$	4.79246	+	5.37727i	0.209360	+	0.234907i
$525$		−	2.72912i		−	0.119109i
$526$	23.9619	−	9.12832i	1.04479	−	0.398014i
$527$	0.928721			0.0404557
$528$	−1.41459	+	12.2591i	−0.0615619	+	0.533510i
$529$	1.00000			0.0434783
$530$	5.29025	−	2.01533i	0.229794	−	0.0875404i
$531$			0.292402i			0.0126891i
$532$	4.78759	+	5.37180i	0.207568	+	0.232897i
$533$		−	0.00448529i		−	0.000194280i
$534$	−1.25283	−	3.28868i	−0.0542152	−	0.142315i
$535$	31.3387			1.35489
$536$	−26.8614	−	13.9455i	−1.16024	−	0.602353i
$537$	7.19320			0.310409
$538$	2.75345	+	7.22782i	0.118710	+	0.311614i
$539$		−	17.1555i		−	0.738938i
$540$	4.02710	−	3.58913i	0.173299	−	0.154452i
$541$		−	43.9134i		−	1.88798i	−0.329969	−	0.943992i	$-0.607038\pi$
$541$		−	43.9134i		−	1.88798i	0.329969	−	0.943992i	$-0.392962\pi$
$542$	−8.32875	+	3.17285i	−0.357751	+	0.136286i
$543$	7.52438			0.322902
$544$	−0.389492	−	1.53115i	−0.0166993	−	0.0656473i
$545$	11.5667			0.495464
$546$	−0.0580775	+	0.0221247i	−0.00248549	+	0.000946851i
$547$			41.9302i			1.79280i	0.443242	+	0.896402i	$0.353828\pi$
$547$			41.9302i			1.79280i	−0.443242	+	0.896402i	$0.646172\pi$
$548$	9.37820	−	8.35827i	0.400617	−	0.357048i
$549$			10.5914i			0.452030i
$550$	3.53330	+	9.27493i	0.150660	+	0.395484i
$551$	3.93300			0.167552
$552$	−2.51029	−	1.30325i	−0.106845	−	0.0554700i
$553$	−12.6690			−0.538741
$554$	−12.3830	−	32.5055i	−0.526105	−	1.38103i
$555$			2.60328i			0.110503i
$556$	21.8006	+	24.4608i	0.924550	+	1.03737i
$557$			39.4544i			1.67174i	0.548930	+	0.835868i	$0.315035\pi$
$557$			39.4544i			1.67174i	−0.548930	+	0.835868i	$0.684965\pi$
$558$	−4.39457	+	1.67412i	−0.186037	+	0.0708712i
$559$	0.236368			0.00999732
$560$	12.8580	+	1.48369i	0.543348	+	0.0626972i
$561$	0.861645			0.0363787
$562$	−27.7497	+	10.5713i	−1.17055	+	0.445923i
$563$			16.4558i			0.693529i	0.937952	+	0.346764i	$0.112720\pi$
$563$			16.4558i			0.693529i	−0.937952	+	0.346764i	$0.887280\pi$
$564$	−9.75955	−	10.9505i	−0.410951	−	0.461098i
$565$			52.0760i			2.19085i
$566$	−3.34562	−	8.78225i	−0.140627	−	0.369146i
$567$	1.19970			0.0503827
$568$	10.3178	−	19.8739i	0.432926	−	0.833891i
$569$	−41.2300			−1.72845			−0.864225	−	0.503106i	$-0.832191\pi$
$569$	−41.2300			−1.72845			−0.864225	+	0.503106i	$0.832191\pi$
$570$	4.07228	+	10.6897i	0.170569	+	0.447744i
$571$		−	23.3120i		−	0.975575i	−0.872962	−	0.487788i	$-0.837804\pi$
$571$		−	23.3120i		−	0.975575i	0.872962	−	0.487788i	$-0.162196\pi$
$572$	0.168732	−	0.150382i	0.00705506	−	0.00628778i
$573$		−	13.7860i		−	0.575919i
$574$	−0.194136	+	0.0739563i	−0.00810307	+	0.00308688i
$575$	−2.27484			−0.0948672
$576$	4.60308	+	6.54306i	0.191795	+	0.272628i
$577$	−22.4141			−0.933112			−0.466556	−	0.884492i	$-0.654505\pi$
$577$	−22.4141			−0.933112			−0.466556	+	0.884492i	$0.654505\pi$
$578$	22.3635	−	8.51943i	0.930200	−	0.354361i
$579$		−	21.6089i		−	0.898034i
$580$	5.28141	−	4.70703i	0.219298	−	0.195449i
$581$			16.7315i			0.694139i
$582$	−6.16464	−	16.1822i	−0.255533	−	0.670774i
$583$	−4.57876			−0.189633
$584$	−9.51674	+	18.3309i	−0.393806	+	0.758538i
$585$	−0.0988003			−0.00408489
$586$	−11.8664	−	31.1494i	−0.490197	−	1.28677i
$587$		−	0.794893i		−	0.0328087i	−0.999865	−	0.0164044i	$-0.994778\pi$
$587$		−	0.794893i		−	0.0328087i	0.999865	−	0.0164044i	$-0.00522191\pi$
$588$	−7.39960	−	8.30255i	−0.305154	−	0.342391i
$589$		−	9.97229i		−	0.410901i
$590$	−1.04227	+	0.397054i	−0.0429095	+	0.0163465i
$591$	20.3261			0.836106
$592$	−3.83528	−	0.442555i	−0.157629	−	0.0181889i
$593$	−2.49895			−0.102620			−0.0513099	−	0.998683i	$-0.516340\pi$
$593$	−2.49895			−0.102620			−0.0513099	+	0.998683i	$0.516340\pi$
$594$	−4.07718	+	1.55321i	−0.167289	+	0.0637290i
$595$		−	0.903735i		−	0.0370495i
$596$	3.67102	+	4.11898i	0.150371	+	0.168720i
$597$			13.7154i			0.561334i
$598$	0.0184419	+	0.0484100i	0.000754145	+	0.00197963i
$599$	−24.7897			−1.01288			−0.506440	−	0.862275i	$-0.669039\pi$
$599$	−24.7897			−1.01288			−0.506440	+	0.862275i	$0.669039\pi$
$600$	5.71049	+	2.96468i	0.233130	+	0.121033i
$601$	13.5250			0.551695			0.275848	−	0.961201i	$-0.411042\pi$
$601$	13.5250			0.551695			0.275848	+	0.961201i	$0.411042\pi$
$602$	−3.89739	−	10.2307i	−0.158846	−	0.416971i
$603$		−	10.7005i		−	0.435760i
$604$	19.2165	−	17.1266i	0.781907	−	0.696871i
$605$			3.99739i			0.162517i
$606$	−12.1471	+	4.62746i	−0.493442	+	0.187978i
$607$	2.33718			0.0948633			0.0474317	−	0.998874i	$-0.484896\pi$
$607$	2.33718			0.0948633			0.0474317	+	0.998874i	$0.484896\pi$
$608$	−16.4409	+	4.18223i	−0.666768	+	0.169612i
$609$	1.57337			0.0637561
$610$	−37.7532	+	14.3821i	−1.52858	+	0.582316i
$611$			0.268658i			0.0108687i
$612$	0.417001	−	0.371650i	0.0168563	−	0.0150231i
$613$		−	35.5405i		−	1.43547i	−0.696317	−	0.717734i	$-0.745179\pi$
$613$		−	35.5405i		−	1.43547i	0.696317	−	0.717734i	$-0.254821\pi$
$614$	7.08032	+	18.5859i	0.285739	+	0.750065i
$615$	−0.330260			−0.0133174
$616$	−9.29111	−	4.82361i	−0.374349	−	0.194349i
$617$	32.8959			1.32434			0.662170	−	0.749354i	$-0.269636\pi$
$617$	32.8959			1.32434			0.662170	+	0.749354i	$0.269636\pi$
$618$	−6.90880	−	18.1356i	−0.277913	−	0.729522i
$619$			6.53413i			0.262629i	0.991341	+	0.131315i	$0.0419198\pi$
$619$			6.53413i			0.262629i	−0.991341	+	0.131315i	$0.958080\pi$
$620$	−11.9349	−	13.3912i	−0.479315	−	0.537804i
$621$		−	1.00000i		−	0.0401286i
$622$	−29.4465	+	11.2177i	−1.18070	+	0.449788i
$623$	2.98542			0.119608
$624$	0.0167959	−	0.145557i	0.000672376	−	0.00582696i
$625$	−31.1993			−1.24797
$626$	24.2821	−	9.25030i	0.970507	−	0.369716i
$627$		−	9.25206i		−	0.369492i
$628$	−6.32604	−	7.09798i	−0.252437	−	0.283240i
$629$			0.269567i			0.0107483i
$630$	1.62908	+	4.27635i	0.0649042	+	0.170374i
$631$	−36.3203			−1.44589			−0.722945	−	0.690906i	$-0.757212\pi$
$631$	−36.3203			−1.44589			−0.722945	+	0.690906i	$0.757212\pi$
$632$	13.7625	−	26.5090i	0.547444	−	1.05447i
$633$	−17.5048			−0.695752
$634$	3.06745	+	8.05207i	0.121824	+	0.319789i
$635$			52.1325i			2.06882i
$636$	−2.21593	+	1.97494i	−0.0878674	+	0.0783114i
$637$			0.203694i			0.00807064i
$638$	−5.34709	+	2.03698i	−0.211693	+	0.0806450i
$639$	7.91699			0.313191
$640$	−17.0723	+	25.2926i	−0.674841	+	0.999778i
$641$	−26.1925			−1.03454			−0.517271	−	0.855822i	$-0.673052\pi$
$641$	−26.1925			−1.03454			−0.517271	+	0.855822i	$0.673052\pi$
$642$	−15.3553	+	5.84963i	−0.606025	+	0.230867i
$643$		−	17.6245i		−	0.695041i	−0.937672	−	0.347520i	$-0.887024\pi$
$643$		−	17.6245i		−	0.695041i	0.937672	−	0.347520i	$-0.112976\pi$
$644$	1.79124	−	1.59643i	0.0705846	−	0.0629082i
$645$		−	17.4042i		−	0.685290i
$646$	0.421680	+	1.10691i	0.0165908	+	0.0435508i
$647$	32.6508			1.28364			0.641818	−	0.766857i	$-0.278180\pi$
$647$	32.6508			1.28364			0.641818	+	0.766857i	$0.278180\pi$
$648$	−1.30325	+	2.51029i	−0.0511965	+	0.0986134i
$649$	0.902093			0.0354102
$650$	−0.0419523	−	0.110125i	−0.00164550	−	0.00431945i
$651$		−	3.98934i		−	0.156354i
$652$	−1.93874	−	2.17531i	−0.0759268	−	0.0851918i
$653$			18.5941i			0.727644i	0.931468	+	0.363822i	$0.118528\pi$
$653$			18.5941i			0.727644i	−0.931468	+	0.363822i	$0.881472\pi$
$654$	−5.66745	+	2.15902i	−0.221615	+	0.0844245i
$655$	−9.71389			−0.379553
$656$	0.0561438	−	0.486555i	0.00219205	−	0.0189968i
$657$	−7.30232			−0.284890
$658$	11.6282	−	4.42980i	0.453316	−	0.172691i
$659$		−	18.8820i		−	0.735540i	−0.929917	−	0.367770i	$-0.880121\pi$
$659$		−	18.8820i		−	0.735540i	0.929917	−	0.367770i	$-0.119879\pi$
$660$	−11.0729	−	12.4241i	−0.431011	−	0.483606i
$661$		−	21.1981i		−	0.824509i	−0.911069	−	0.412254i	$-0.864742\pi$
$661$		−	21.1981i		−	0.824509i	0.911069	−	0.412254i	$-0.135258\pi$
$662$	−0.0718058	−	0.188491i	−0.00279081	−	0.00732589i
$663$	−0.0102307			−0.000397326
$664$	−35.0094	−	18.1756i	−1.35863	−	0.705352i
$665$	−9.70401			−0.376305
$666$	−0.485924	−	1.27555i	−0.0188292	−	0.0494266i
$667$		−	1.31147i		−	0.0507802i
$668$	26.8014	−	23.8866i	1.03698	−	0.924199i
$669$			19.7074i			0.761931i
$670$	38.1422	−	14.5303i	1.47356	−	0.561356i
$671$	32.6757			1.26143
$672$	−6.57707	+	1.67307i	−0.253716	+	0.0645401i
$673$	−43.9854			−1.69551			−0.847756	−	0.530387i	$-0.822047\pi$
$673$	−43.9854			−1.69551			−0.847756	+	0.530387i	$0.822047\pi$
$674$	−24.3219	+	9.26546i	−0.936844	+	0.356892i
$675$			2.27484i			0.0875585i
$676$	19.4079	−	17.2972i	0.746458	−	0.665277i
$677$			20.3589i			0.782455i	0.920294	+	0.391228i	$0.127949\pi$
$677$			20.3589i			0.782455i	−0.920294	+	0.391228i	$0.872051\pi$
$678$	−9.72041	−	25.5161i	−0.373310	−	0.979940i
$679$	14.6900			0.563751
$680$	1.89100	+	0.981740i	0.0725166	+	0.0376480i
$681$	−16.3574			−0.626817
$682$	5.16486	+	13.5578i	0.197773	+	0.519154i
$683$			22.8765i			0.875345i	0.899134	+	0.437673i	$0.144197\pi$
$683$			22.8765i			0.875345i	−0.899134	+	0.437673i	$0.855803\pi$
$684$	−3.99066	−	4.47762i	−0.152587	−	0.171206i
$685$			16.9415i			0.647300i
$686$	19.9148	−	7.58658i	0.760351	−	0.289657i
$687$	−9.50963			−0.362815
$688$	25.6407	+	2.95870i	0.977544	+	0.112799i
$689$	0.0543654			0.00207116
$690$	3.56451	−	1.35791i	0.135699	−	0.0516947i
$691$			38.6280i			1.46948i	0.678350	+	0.734739i	$0.262695\pi$
$691$			38.6280i			1.46948i	−0.678350	+	0.734739i	$0.737305\pi$
$692$	1.42817	+	1.60244i	0.0542908	+	0.0609157i
$693$		−	3.70121i		−	0.140598i
$694$	9.64432	+	25.3164i	0.366093	+	0.960996i
$695$	−44.1878			−1.67614
$696$	−1.70917	+	3.29216i	−0.0647859	+	0.124789i
$697$	−0.0341980			−0.00129534
$698$	−14.2891	−	37.5090i	−0.540852	−	1.41974i
$699$		−	22.7838i		−	0.861762i
$700$	−4.07477	+	3.63162i	−0.154012	+	0.137262i
$701$		−	19.3933i		−	0.732476i	−0.930521	−	0.366238i	$-0.880646\pi$
$701$		−	19.3933i		−	0.732476i	0.930521	−	0.366238i	$-0.119354\pi$
$702$	0.0484100	−	0.0184419i	0.00182712	−	0.000696044i
$703$	2.89452			0.109169
$704$	20.1861	−	14.2010i	0.760793	−	0.535222i
$705$	19.7817			0.745022
$706$	−40.1354	+	15.2897i	−1.51052	+	0.575434i
$707$		−	11.0270i		−	0.414712i
$708$	0.436576	−	0.389096i	0.0164075	−	0.0146231i
$709$		−	4.08674i		−	0.153481i	−0.997051	−	0.0767404i	$-0.975549\pi$
$709$		−	4.08674i		−	0.153481i	0.997051	−	0.0767404i	$-0.0244513\pi$
$710$	10.7505	+	28.2202i	0.403461	+	1.05909i
$711$	10.5602			0.396037
$712$	−3.24310	+	6.24678i	−0.121540	+	0.234108i
$713$	−3.32528			−0.124533
$714$	0.168690	+	0.442811i	0.00631305	+	0.0165718i
$715$			0.304810i			0.0113993i
$716$	−9.57193	−	10.7400i	−0.357720	−	0.401371i
$717$		−	16.6155i		−	0.620518i
$718$	9.16511	−	3.49147i	0.342039	−	0.130300i
$719$	41.6385			1.55286			0.776428	−	0.630206i	$-0.217030\pi$
$719$	41.6385			1.55286			0.776428	+	0.630206i	$0.217030\pi$
$720$	−10.7176	−	1.23671i	−0.399423	−	0.0460896i
$721$	16.4633			0.613125
$722$	−13.2241	+	5.03775i	−0.492150	+	0.187486i
$723$			6.31610i			0.234898i
$724$	−10.0126	−	11.2344i	−0.372116	−	0.417524i
$725$			2.98337i			0.110800i
$726$	−0.746146	−	1.95864i	−0.0276921	−	0.0726918i
$727$	−49.0589			−1.81950			−0.909748	−	0.415162i	$-0.863725\pi$
$727$	−49.0589			−1.81950			−0.909748	+	0.415162i	$0.863725\pi$
$728$	0.110317	+	0.0572726i	0.00408862	+	0.00212267i
$729$	−1.00000			−0.0370370
$730$	−9.91587	−	26.0292i	−0.367003	−	0.963384i
$731$		−	1.80219i		−	0.0666563i
$732$	15.8137	−	14.0939i	0.584491	−	0.520925i
$733$		−	16.3492i		−	0.603871i	−0.953328	−	0.301936i	$-0.902367\pi$
$733$		−	16.3492i		−	0.603871i	0.953328	−	0.301936i	$-0.0976328\pi$
$734$	−19.2112	+	7.31855i	−0.709099	+	0.270133i
$735$	14.9983			0.553221
$736$	1.39457	+	5.48226i	0.0514047	+	0.202079i
$737$	−33.0124			−1.21603
$738$	0.161820	−	0.0616457i	0.00595668	−	0.00226921i
$739$			33.0831i			1.21698i	0.793560	+	0.608492i	$0.208225\pi$
$739$			33.0831i			1.21698i	−0.793560	+	0.608492i	$0.791775\pi$
$740$	3.88688	−	3.46416i	0.142885	−	0.127345i
$741$			0.109853i			0.00403557i
$742$	−0.896412	−	2.35308i	−0.0329083	−	0.0863844i
$743$	9.15454			0.335847			0.167924	−	0.985800i	$-0.446294\pi$
$743$	9.15454			0.335847			0.167924	+	0.985800i	$0.446294\pi$
$744$	8.34740	+	4.33367i	0.306031	+	0.158880i
$745$	−7.44082			−0.272610
$746$	−7.62962	−	20.0278i	−0.279340	−	0.733269i
$747$		−	13.9464i		−	0.510272i
$748$	−1.14658	−	1.28650i	−0.0419233	−	0.0470390i
$749$		−	13.9393i		−	0.509333i
$750$	9.71388	−	3.70052i	0.354701	−	0.135124i
$751$	6.15690			0.224669			0.112334	−	0.993670i	$-0.464167\pi$
$751$	6.15690			0.224669			0.112334	+	0.993670i	$0.464167\pi$
$752$	−3.36287	+	29.1434i	−0.122631	+	1.06275i
$753$	20.7310			0.755479
$754$	0.0634882	−	0.0241859i	0.00231210	−	0.000880800i
$755$			34.7140i			1.26337i
$756$	−1.59643	−	1.79124i	−0.0580616	−	0.0651467i
$757$			8.78191i			0.319184i	0.987183	+	0.159592i	$0.0510178\pi$
$757$			8.78191i			0.319184i	−0.987183	+	0.159592i	$0.948982\pi$
$758$	10.3750	+	27.2345i	0.376839	+	0.989203i
$759$	−3.08512			−0.111983
$760$	10.5416	−	20.3049i	0.382384	−	0.736538i
$761$	−18.6171			−0.674870			−0.337435	−	0.941349i	$-0.609559\pi$
$761$	−18.6171			−0.674870			−0.337435	+	0.941349i	$0.609559\pi$
$762$	−9.73096	−	25.5438i	−0.352515	−	0.925354i
$763$		−	5.14484i		−	0.186256i
$764$	−20.5835	+	18.3449i	−0.744684	+	0.663696i
$765$			0.753301i			0.0272357i
$766$	5.27173	−	2.00827i	0.190475	−	0.0725619i
$767$	−0.0107109			−0.000386748
$768$	3.64398	−	15.5795i	0.131491	−	0.562178i
$769$	−24.5966			−0.886975			−0.443487	−	0.896281i	$-0.646259\pi$
$769$	−24.5966			−0.886975			−0.443487	+	0.896281i	$0.646259\pi$
$770$	13.1930	−	5.02591i	0.475444	−	0.181121i
$771$			5.82477i			0.209774i
$772$	−32.2636	+	28.7548i	−1.16119	+	1.03491i
$773$		−	20.6191i		−	0.741618i	−0.928709	−	0.370809i	$-0.879080\pi$
$773$		−	20.6191i		−	0.741618i	0.928709	−	0.370809i	$-0.120920\pi$
$774$	3.24864	+	8.52769i	0.116770	+	0.306522i
$775$	7.56447			0.271724
$776$	−15.9579	+	30.7378i	−0.572857	+	1.10342i
$777$	1.15793			0.0415405
$778$	18.5435	+	48.6769i	0.664818	+	1.74515i
$779$			0.367207i			0.0131566i
$780$	0.131473	+	0.147516i	0.00470748	+	0.00528191i
$781$		−	24.4248i		−	0.873989i
$782$	0.369101	−	0.140610i	0.0131990	−	0.00502820i
$783$	−1.31147			−0.0468680
$784$	−2.54970	+	22.0963i	−0.0910606	+	0.789152i
$785$	12.8223			0.457648
$786$	4.75960	−	1.81318i	0.169769	−	0.0646739i
$787$		−	10.1637i		−	0.362297i	−0.983456	−	0.181148i	$-0.942019\pi$
$787$		−	10.1637i		−	0.362297i	0.983456	−	0.181148i	$-0.0579814\pi$
$788$	−27.0478	−	30.3484i	−0.963539	−	1.08112i
$789$		−	18.1314i		−	0.645496i
$790$	14.3397	+	37.6418i	0.510184	+	1.33924i
$791$	23.1632			0.823588
$792$	7.74453	+	4.02068i	0.275190	+	0.142869i
$793$	−0.387972			−0.0137773
$794$	2.61187	+	6.85616i	0.0926917	+	0.243316i
$795$		−	4.00302i		−	0.141972i
$796$	20.4781	−	18.2510i	0.725825	−	0.646888i
$797$			27.7332i			0.982360i	0.871058	+	0.491180i	$0.163434\pi$
$797$			27.7332i			0.982360i	−0.871058	+	0.491180i	$0.836566\pi$
$798$	4.75476	−	1.81133i	0.168317	−	0.0641205i
$799$	2.04837			0.0724663
$800$	−3.17243	−	12.4712i	−0.112162	−	0.440925i
$801$	−2.48847			−0.0879259
$802$	−17.4213	+	6.63669i	−0.615169	+	0.234350i
$803$			22.5285i			0.795013i
$804$	−15.9767	+	14.2391i	−0.563453	+	0.502175i
$805$			3.23582i			0.114048i
$806$	−0.0613244	−	0.160977i	−0.00216006	−	0.00567017i
$807$	5.46914			0.192523
$808$	23.0731	+	11.9787i	0.811710	+	0.421411i
$809$	−23.6857			−0.832745			−0.416373	−	0.909194i	$-0.636699\pi$
$809$	−23.6857			−0.832745			−0.416373	+	0.909194i	$0.636699\pi$
$810$	−1.35791	−	3.56451i	−0.0477120	−	0.125244i
$811$		−	33.9216i		−	1.19115i	−0.803300	−	0.595574i	$-0.796925\pi$
$811$		−	33.9216i		−	1.19115i	0.803300	−	0.595574i	$-0.203075\pi$
$812$	−2.09367	−	2.34915i	−0.0734733	−	0.0824390i
$813$			6.30219i			0.221027i
$814$	−3.93523	+	1.49913i	−0.137930	+	0.0525445i
$815$	3.92964			0.137649
$816$	−1.10980	−	0.128060i	−0.0388508	−	0.00448301i
$817$	−19.3513			−0.677015
$818$	52.9794	−	20.1826i	1.85238	−	0.705669i
$819$			0.0439460i			0.00153560i
$820$	0.439474	+	0.493101i	0.0153471	+	0.0172198i
$821$		−	11.7295i		−	0.409361i	−0.978829	−	0.204680i	$-0.934385\pi$
$821$		−	11.7295i		−	0.409361i	0.978829	−	0.204680i	$-0.0656155\pi$
$822$	−3.16226	−	8.30095i	−0.110297	−	0.289529i
$823$	−21.7912			−0.759592			−0.379796	−	0.925070i	$-0.624006\pi$
$823$	−21.7912			−0.759592			−0.379796	+	0.925070i	$0.624006\pi$
$824$	−17.8843	+	34.4483i	−0.623029	+	1.20006i
$825$	7.01814			0.244340
$826$	0.176608	+	0.463597i	0.00614499	+	0.0161306i
$827$		−	40.1470i		−	1.39605i	−0.716074	−	0.698024i	$-0.754063\pi$
$827$		−	40.1470i		−	1.39605i	0.716074	−	0.698024i	$-0.245937\pi$
$828$	−1.49307	+	1.33069i	−0.0518878	+	0.0462447i
$829$		−	8.43995i		−	0.293132i	−0.989201	−	0.146566i	$-0.953178\pi$
$829$		−	8.43995i		−	0.293132i	0.989201	−	0.146566i	$-0.0468220\pi$
$830$	49.7121	−	18.9379i	1.72553	−	0.657345i
$831$	−24.5962			−0.853234
$832$	−0.239678	+	0.168615i	−0.00830933	+	0.00584566i
$833$	1.55306			0.0538103
$834$	21.6511	−	8.24801i	0.749715	−	0.285605i
$835$			48.4159i			1.67550i
$836$	−13.8140	+	12.3116i	−0.477766	+	0.425807i
$837$			3.32528i			0.114938i
$838$	−2.24706	−	5.89854i	−0.0776234	−	0.203762i
$839$	−4.94829			−0.170834			−0.0854169	−	0.996345i	$-0.527222\pi$
$839$	−4.94829			−0.170834			−0.0854169	+	0.996345i	$0.527222\pi$
$840$	4.21708	−	8.12284i	0.145503	−	0.280264i
$841$	27.2801			0.940691
$842$	13.1279	+	34.4609i	0.452418	+	1.18760i
$843$			20.9976i			0.723196i
$844$	23.2935	+	26.1359i	0.801794	+	0.899634i
$845$			35.0599i			1.20610i
$846$	−9.69261	+	3.69242i	−0.333239	+	0.126948i
$847$	1.77803			0.0610937
$848$	5.89744	+	0.680509i	0.202519	+	0.0233688i
$849$	−6.64534			−0.228068
$850$	−0.839645	+	0.319864i	−0.0287996	+	0.0109713i
$851$		−	0.965182i		−	0.0330860i
$852$	−10.5351	−	11.8206i	−0.360926	−	0.404968i
$853$			27.0000i			0.924463i	0.886759	+	0.462231i	$0.152951\pi$
$853$			27.0000i			0.924463i	−0.886759	+	0.462231i	$0.847049\pi$
$854$	6.39712	+	16.7925i	0.218905	+	0.574626i
$855$	8.08869			0.276628
$856$	29.1671	+	15.1425i	0.996910	+	0.517560i
$857$	46.0104			1.57169			0.785843	−	0.618426i	$-0.212229\pi$
$857$	46.0104			1.57169			0.785843	+	0.618426i	$0.212229\pi$
$858$	−0.0568954	−	0.149351i	−0.00194238	−	0.00509874i
$859$			9.27196i			0.316355i	0.987411	+	0.158178i	$0.0505619\pi$
$859$			9.27196i			0.316355i	−0.987411	+	0.158178i	$0.949438\pi$
$860$	−25.9857	+	23.1596i	−0.886106	+	0.789737i
$861$			0.146898i			0.00500628i
$862$	−21.8659	+	8.32984i	−0.744755	+	0.283716i
$863$	−35.5800			−1.21116			−0.605579	−	0.795785i	$-0.707059\pi$
$863$	−35.5800			−1.21116			−0.605579	+	0.795785i	$0.707059\pi$
$864$	5.48226	−	1.39457i	0.186510	−	0.0474443i
$865$	−2.89476			−0.0984249
$866$	−22.8999	+	8.72378i	−0.778172	+	0.296446i
$867$		−	16.9220i		−	0.574701i
$868$	−5.95636	+	5.30858i	−0.202172	+	0.180185i
$869$		−	32.5793i		−	1.10518i
$870$	−1.78085	−	4.67474i	−0.0603766	−	0.158489i
$871$	0.391970			0.0132814
$872$	10.7652	+	5.58890i	0.364556	+	0.189264i
$873$	−12.2447			−0.414421
$874$	−1.50982	−	3.96329i	−0.0510705	−	0.134060i
$875$			8.81814i			0.298107i
$876$	9.71713	+	10.9029i	0.328311	+	0.368374i
$877$		−	9.91363i		−	0.334760i	−0.985892	−	0.167380i	$-0.946469\pi$
$877$		−	9.91363i		−	0.334760i	0.985892	−	0.167380i	$-0.0535306\pi$
$878$	0.690530	−	0.263059i	0.0233042	−	0.00887780i
$879$	−23.5701			−0.794999
$880$	−3.81541	+	33.0652i	−0.128617	+	1.11463i
$881$	49.0720			1.65328			0.826639	−	0.562732i	$-0.190250\pi$
$881$	49.0720			1.65328			0.826639	+	0.562732i	$0.190250\pi$
$882$	−7.34885	+	2.79956i	−0.247449	+	0.0942661i
$883$		−	4.34547i		−	0.146237i	−0.997323	−	0.0731183i	$-0.976705\pi$
$883$		−	4.34547i		−	0.146237i	0.997323	−	0.0731183i	$-0.0232951\pi$
$884$	0.0136139	+	0.0152751i	0.000457884	+	0.000513757i
$885$			0.788663i			0.0265106i
$886$	15.0180	+	39.4223i	0.504539	+	1.32442i
$887$	−11.4503			−0.384463			−0.192232	−	0.981350i	$-0.561572\pi$
$887$	−11.4503			−0.384463			−0.192232	+	0.981350i	$0.561572\pi$
$888$	−1.25787	+	2.42288i	−0.0422115	+	0.0813067i
$889$	23.1883			0.777712
$890$	−3.37912	−	8.87020i	−0.113268	−	0.297330i
$891$			3.08512i			0.103355i
$892$	29.4245	−	26.2244i	0.985205	−	0.878059i
$893$		−	21.9948i		−	0.736026i
$894$	3.64584	−	1.38889i	0.121935	−	0.0464514i
$895$	19.4014			0.648518
$896$	11.2501	+	7.59369i	0.375838	+	0.253687i
$897$	0.0366308			0.00122307
$898$	24.2557	−	9.24024i	0.809422	−	0.308351i
$899$			4.36100i			0.145447i
$900$	3.39649	−	3.02711i	0.113216	−	0.100904i
$901$		−	0.414508i		−	0.0138093i
$902$	−0.190184	−	0.499234i	−0.00633244	−	0.0166227i
$903$	−7.74133			−0.257615
$904$	−25.1625	+	48.4673i	−0.836892	+	1.61200i
$905$	20.2947			0.674618
$906$	−6.47966	−	17.0091i	−0.215272	−	0.565091i
$907$		−	45.2916i		−	1.50388i	−0.659229	−	0.751942i	$-0.729117\pi$
$907$		−	45.2916i		−	1.50388i	0.659229	−	0.751942i	$-0.270883\pi$
$908$	21.7667	+	24.4228i	0.722352	+	0.810498i
$909$			9.19144i			0.304861i
$910$	−0.156646	+	0.0596746i	−0.00519277	+	0.00197820i
$911$	22.6911			0.751791			0.375896	−	0.926662i	$-0.377335\pi$
$911$	22.6911			0.751791			0.375896	+	0.926662i	$0.377335\pi$
$912$	−1.37507	+	11.9167i	−0.0455331	+	0.394600i
$913$	−43.0262			−1.42396
$914$	−3.50515	+	1.33529i	−0.115940	+	0.0441676i
$915$			28.5670i			0.944396i
$916$	12.6544	+	14.1986i	0.418113	+	0.469133i
$917$			4.32070i			0.142682i
$918$	−0.140610	−	0.369101i	−0.00464082	−	0.0121822i
$919$	−39.0435			−1.28793			−0.643963	−	0.765057i	$-0.722711\pi$
$919$	−39.0435			−1.28793			−0.643963	+	0.765057i	$0.722711\pi$
$920$	−6.77072	−	3.51511i	−0.223224	−	0.115890i
$921$	14.0635			0.463409
$922$	−8.45072	−	22.1832i	−0.278310	−	0.730564i
$923$			0.290006i			0.00954566i
$924$	−5.52617	+	4.92518i	−0.181798	+	0.162026i
$925$			2.19563i			0.0721920i
$926$	−7.25501	+	2.76381i	−0.238414	+	0.0908244i
$927$	−13.7228			−0.450717
$928$	7.18980	−	1.82894i	0.236017	−	0.0600378i
$929$	2.68826			0.0881990			0.0440995	−	0.999027i	$-0.485958\pi$
$929$	2.68826			0.0881990			0.0440995	+	0.999027i	$0.485958\pi$
$930$	−11.8530	+	4.51542i	−0.388675	+	0.148067i
$931$		−	16.6762i		−	0.546541i
$932$	−34.0178	+	30.3182i	−1.11429	+	0.993106i
$933$			22.2815i			0.729464i
$934$	15.3084	+	40.1846i	0.500907	+	1.31488i
$935$	2.32402			0.0760036
$936$	−0.0919539	−	0.0477391i	−0.00300561	−	0.00156040i
$937$	10.7840			0.352298			0.176149	−	0.984363i	$-0.443636\pi$
$937$	10.7840			0.352298			0.176149	+	0.984363i	$0.443636\pi$
$938$	−6.46304	−	16.9655i	−0.211026	−	0.553944i
$939$		−	18.3737i		−	0.599604i
$940$	−26.3234	−	29.5355i	−0.858573	−	0.963342i
$941$		−	56.8767i		−	1.85413i	−0.374904	−	0.927063i	$-0.622324\pi$
$941$		−	56.8767i		−	1.85413i	0.374904	−	0.927063i	$-0.377676\pi$
$942$	−6.28266	+	2.39339i	−0.204700	+	0.0779809i
$943$	0.122446			0.00398738
$944$	−1.16190	−	0.134072i	−0.0378165	−	0.00436366i
$945$	3.23582			0.105261
$946$	26.3089	−	10.0224i	0.855377	−	0.325857i
$947$		−	55.3235i		−	1.79777i	−0.438184	−	0.898886i	$-0.644378\pi$
$947$		−	55.3235i		−	1.79777i	0.438184	−	0.898886i	$-0.355622\pi$
$948$	−14.0523	−	15.7671i	−0.456398	−	0.512090i
$949$		−	0.267490i		−	0.00868309i
$950$	3.43460	+	9.01583i	0.111433	+	0.292512i
$951$	6.09283			0.197573
$952$	0.436674	−	0.841110i	0.0141527	−	0.0272605i
$953$	11.5435			0.373932			0.186966	−	0.982366i	$-0.440135\pi$
$953$	11.5435			0.373932			0.186966	+	0.982366i	$0.440135\pi$
$954$	0.747197	+	1.96139i	0.0241914	+	0.0635025i
$955$		−	37.1835i		−	1.20323i
$956$	−24.8082	+	22.1102i	−0.802353	+	0.715093i
$957$			4.04603i			0.130790i
$958$	−23.0398	+	8.77704i	−0.744381	+	0.283573i
$959$	7.53549			0.243334
$960$	12.4154	+	17.6479i	0.400705	+	0.569583i
$961$	−19.9425			−0.643307
$962$	0.0467245	−	0.0177998i	0.00150646	−	0.000573888i
$963$			11.6190i			0.374418i
$964$	9.43038	−	8.40478i	0.303732	−	0.270700i
$965$		−	58.2833i		−	1.87620i
$966$	−0.603992	−	1.58548i	−0.0194331	−	0.0510121i
$967$	−55.0285			−1.76960			−0.884798	−	0.465975i	$-0.845704\pi$
$967$	−55.0285			−1.76960			−0.884798	+	0.465975i	$0.845704\pi$
$968$	−1.93149	+	3.72039i	−0.0620805	+	0.119578i
$969$	0.837575			0.0269068
$970$	−16.6272	−	43.6465i	−0.533868	−	1.40140i
$971$		−	4.42957i		−	0.142152i	−0.997471	−	0.0710759i	$-0.977357\pi$
$971$		−	4.42957i		−	0.142152i	0.997471	−	0.0710759i	$-0.0226433\pi$
$972$	1.33069	+	1.49307i	0.0426820	+	0.0478903i
$973$			19.6546i			0.630096i
$974$	8.77032	−	3.34107i	0.281019	−	0.107055i
$975$	−0.0833291			−0.00266867
$976$	−42.0863	−	4.85636i	−1.34715	−	0.155448i
$977$	22.6814			0.725642			0.362821	−	0.931859i	$-0.381814\pi$
$977$	22.6814			0.725642			0.362821	+	0.931859i	$0.381814\pi$
$978$	−1.92544	+	0.733500i	−0.0615688	+	0.0234547i
$979$			7.67723i			0.245365i
$980$	−19.9581	−	22.3936i	−0.637539	−	0.715336i
$981$			4.28843i			0.136919i
$982$	−5.96276	−	15.6523i	−0.190279	−	0.499484i
$983$	39.9862			1.27536			0.637680	−	0.770301i	$-0.279894\pi$
$983$	39.9862			1.27536			0.637680	+	0.770301i	$0.279894\pi$
$984$	−0.307374	−	0.159578i	−0.00979873	−	0.00508715i
$985$	54.8235			1.74682
$986$	−0.184405	−	0.484064i	−0.00587266	−	0.0154158i
$987$		−	8.79883i		−	0.280070i
$988$	0.164019	−	0.146181i	0.00521814	−	0.00465064i
$989$			6.45272i			0.205185i
$990$	−10.9969	+	4.18930i	−0.349506	+	0.133145i
$991$	−14.0401			−0.445998			−0.222999	−	0.974819i	$-0.571585\pi$
$991$	−14.0401			−0.445998			−0.222999	+	0.974819i	$0.571585\pi$
$992$	−4.63734	−	18.2300i	−0.147236	−	0.578804i
$993$	−0.142627			−0.00452612
$994$	12.5522	−	4.78180i	0.398133	−	0.151670i
$995$			36.9930i			1.17276i
$996$	−20.8229	+	18.5583i	−0.659800	+	0.588044i
$997$		−	17.4381i		−	0.552271i	−0.961119	−	0.276135i	$-0.910946\pi$
$997$		−	17.4381i		−	0.552271i	0.961119	−	0.276135i	$-0.0890538\pi$
$998$	−8.78942	−	23.0723i	−0.278224	−	0.730339i
$999$	−0.965182			−0.0305370

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.f.d.277.4	yes	20
4.3	odd	2		2208.2.f.d.1105.9		20
8.3	odd	2		2208.2.f.d.1105.12		20
8.5	even	2	inner	552.2.f.d.277.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.f.d.277.3	✓	20	8.5	even	2	inner
552.2.f.d.277.4	yes	20	1.1	even	1	trivial
2208.2.f.d.1105.9		20	4.3	odd	2
2208.2.f.d.1105.12		20	8.3	odd	2

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32157 + 0.503453i) q^{2} +1.00000i q^{3} +(1.49307 - 1.33069i) q^{4} +2.69719i q^{5} +(-0.503453 - 1.32157i) q^{6} +1.19970 q^{7} +(-1.30325 + 2.51029i) q^{8} -1.00000 q^{9} +(-1.35791 - 3.56451i) q^{10} +3.08512i q^{11} +(1.33069 + 1.49307i) q^{12} -0.0366308i q^{13} +(-1.58548 + 0.603992i) q^{14} -2.69719 q^{15} +(0.458519 - 3.97363i) q^{16} -0.279291 q^{17} +(1.32157 - 0.503453i) q^{18} +2.99893i q^{19} +(3.58913 + 4.02710i) q^{20} +1.19970i q^{21} +(-1.55321 - 4.07718i) q^{22} +1.00000 q^{23} +(-2.51029 - 1.30325i) q^{24} -2.27484 q^{25} +(0.0184419 + 0.0484100i) q^{26} -1.00000i q^{27} +(1.79124 - 1.59643i) q^{28} -1.31147i q^{29} +(3.56451 - 1.35791i) q^{30} -3.32528 q^{31} +(1.39457 + 5.48226i) q^{32} -3.08512 q^{33} +(0.369101 - 0.140610i) q^{34} +3.23582i q^{35} +(-1.49307 + 1.33069i) q^{36} -0.965182i q^{37} +(-1.50982 - 3.96329i) q^{38} +0.0366308 q^{39} +(-6.77072 - 3.51511i) q^{40} +0.122446 q^{41} +(-0.603992 - 1.58548i) q^{42} +6.45272i q^{43} +(4.10534 + 4.60630i) q^{44} -2.69719i q^{45} +(-1.32157 + 0.503453i) q^{46} -7.33419 q^{47} +(3.97363 + 0.458519i) q^{48} -5.56072 q^{49} +(3.00635 - 1.14527i) q^{50} -0.279291i q^{51} +(-0.0487443 - 0.0546924i) q^{52} +1.48414i q^{53} +(0.503453 + 1.32157i) q^{54} -8.32115 q^{55} +(-1.56351 + 3.01159i) q^{56} -2.99893 q^{57} +(0.660262 + 1.73319i) q^{58} -0.292402i q^{59} +(-4.02710 + 3.58913i) q^{60} -10.5914i q^{61} +(4.39457 - 1.67412i) q^{62} -1.19970 q^{63} +(-4.60308 - 6.54306i) q^{64} +0.0988003 q^{65} +(4.07718 - 1.55321i) q^{66} +10.7005i q^{67} +(-0.417001 + 0.371650i) q^{68} +1.00000i q^{69} +(-1.62908 - 4.27635i) q^{70} -7.91699 q^{71} +(1.30325 - 2.51029i) q^{72} +7.30232 q^{73} +(0.485924 + 1.27555i) q^{74} -2.27484i q^{75} +(3.99066 + 4.47762i) q^{76} +3.70121i q^{77} +(-0.0484100 + 0.0184419i) q^{78} -10.5602 q^{79} +(10.7176 + 1.23671i) q^{80} +1.00000 q^{81} +(-0.161820 + 0.0616457i) q^{82} +13.9464i q^{83} +(1.59643 + 1.79124i) q^{84} -0.753301i q^{85} +(-3.24864 - 8.52769i) q^{86} +1.31147 q^{87} +(-7.74453 - 4.02068i) q^{88} +2.48847 q^{89} +(1.35791 + 3.56451i) q^{90} -0.0439460i q^{91} +(1.49307 - 1.33069i) q^{92} -3.32528i q^{93} +(9.69261 - 3.69242i) q^{94} -8.08869 q^{95} +(-5.48226 + 1.39457i) q^{96} +12.2447 q^{97} +(7.34885 - 2.79956i) q^{98} -3.08512i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9} - 12 q^{10} + 2 q^{14} + 4 q^{15} + 4 q^{16} + 32 q^{17} + 2 q^{18} + 20 q^{20} + 14 q^{22} + 20 q^{23} + 10 q^{24} - 28 q^{25} + 18 q^{28} - 22 q^{32}+ \cdots - 26 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9 - 12 * q^10 + 2 * q^14 + 4 * q^15 + 4 * q^16 + 32 * q^17 + 2 * q^18 + 20 * q^20 + 14 * q^22 + 20 * q^23 + 10 * q^24 - 28 * q^25 + 18 * q^28 - 22 * q^32 + 28 * q^33 - 26 * q^34 + 16 * q^38 + 4 * q^40 - 40 * q^41 + 14 * q^42 + 10 * q^44 - 2 * q^46 + 40 * q^47 + 12 * q^49 - 14 * q^50 + 20 * q^52 - 2 * q^54 - 8 * q^55 + 6 * q^56 - 44 * q^57 - 32 * q^58 - 24 * q^60 + 20 * q^62 + 8 * q^63 - 48 * q^64 + 8 * q^65 + 10 * q^66 + 22 * q^68 + 80 * q^70 - 40 * q^71 + 2 * q^72 - 16 * q^73 - 30 * q^74 + 44 * q^76 - 36 * q^78 - 16 * q^79 + 4 * q^80 + 20 * q^81 - 32 * q^82 + 6 * q^84 - 4 * q^86 + 8 * q^87 - 70 * q^88 - 40 * q^89 + 12 * q^90 + 64 * q^94 - 40 * q^95 + 2 * q^96 + 32 * q^97 - 26 * q^98

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