LMFDB - Embedded newform 68.3.c.a.35.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [68,3,Mod(35,68)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(68, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("68.35");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 68 = 2^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	68.c (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:	$1.85286579765$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 8 x^{13} - 16 x^{11} + 64 x^{9} + 256 x^{7} - 1024 x^{5} - 8192 x^{3} + \cdots + 65536 $ x^16 - 2x^15 + 5x^14 - 8x^13 - 16x^11 + 64x^9 + 256x^7 - 1024x^5 - 8192x^3 + 20480x^2 - 32768x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{21} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			35.3
Root			$1.79176 - 0.888585i$ of defining polynomial
Character	$\chi$	$=$	68.35
Dual form			68.3.c.a.35.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.79176 - 0.888585i) q^{2} -0.561065i q^{3} +(2.42083 + 3.18427i) q^{4} +3.63253 q^{5} +(-0.498554 + 1.00530i) q^{6} -4.58728i q^{7} +(-1.50807 - 7.85657i) q^{8} +8.68521 q^{9} +O(q^{10})$	\(q+(-1.79176 - 0.888585i) q^{2} -0.561065i q^{3} +(2.42083 + 3.18427i) q^{4} +3.63253 q^{5} +(-0.498554 + 1.00530i) q^{6} -4.58728i q^{7} +(-1.50807 - 7.85657i) q^{8} +8.68521 q^{9} +(-6.50863 - 3.22781i) q^{10} -13.9781i q^{11} +(1.78658 - 1.35825i) q^{12} +4.17958 q^{13} +(-4.07619 + 8.21932i) q^{14} -2.03808i q^{15} +(-4.27912 + 15.4172i) q^{16} +4.12311 q^{17} +(-15.5618 - 7.71754i) q^{18} +31.5827i q^{19} +(8.79375 + 11.5669i) q^{20} -2.57376 q^{21} +(-12.4207 + 25.0454i) q^{22} -3.57847i q^{23} +(-4.40805 + 0.846126i) q^{24} -11.8047 q^{25} +(-7.48882 - 3.71391i) q^{26} -9.92255i q^{27} +(14.6071 - 11.1050i) q^{28} -8.38600 q^{29} +(-1.81101 + 3.65176i) q^{30} +38.0004i q^{31} +(21.3666 - 23.8216i) q^{32} -7.84261 q^{33} +(-7.38763 - 3.66373i) q^{34} -16.6634i q^{35} +(21.0254 + 27.6560i) q^{36} -35.8406 q^{37} +(28.0639 - 56.5887i) q^{38} -2.34501i q^{39} +(-5.47811 - 28.5392i) q^{40} +1.37979 q^{41} +(4.61157 + 2.28701i) q^{42} -13.0369i q^{43} +(44.5099 - 33.8386i) q^{44} +31.5492 q^{45} +(-3.17977 + 6.41177i) q^{46} -12.2917i q^{47} +(8.65003 + 2.40086i) q^{48} +27.9569 q^{49} +(21.1513 + 10.4895i) q^{50} -2.31333i q^{51} +(10.1181 + 13.3089i) q^{52} -64.1582 q^{53} +(-8.81702 + 17.7789i) q^{54} -50.7757i q^{55} +(-36.0403 + 6.91795i) q^{56} +17.7199 q^{57} +(15.0257 + 7.45167i) q^{58} +55.5166i q^{59} +(6.48980 - 4.93386i) q^{60} -72.4961 q^{61} +(33.7666 - 68.0878i) q^{62} -39.8415i q^{63} +(-59.4514 + 23.6966i) q^{64} +15.1824 q^{65} +(14.0521 + 6.96882i) q^{66} +109.059i q^{67} +(9.98136 + 13.1291i) q^{68} -2.00775 q^{69} +(-14.8069 + 29.8569i) q^{70} +125.437i q^{71} +(-13.0979 - 68.2359i) q^{72} +67.6229 q^{73} +(64.2178 + 31.8474i) q^{74} +6.62323i q^{75} +(-100.568 + 76.4564i) q^{76} -64.1214 q^{77} +(-2.08374 + 4.20171i) q^{78} -152.880i q^{79} +(-15.5440 + 56.0033i) q^{80} +72.5997 q^{81} +(-2.47226 - 1.22606i) q^{82} -107.373i q^{83} +(-6.23065 - 8.19555i) q^{84} +14.9773 q^{85} +(-11.5844 + 23.3591i) q^{86} +4.70509i q^{87} +(-109.820 + 21.0800i) q^{88} +33.8911 q^{89} +(-56.5288 - 28.0342i) q^{90} -19.1729i q^{91} +(11.3948 - 8.66287i) q^{92} +21.3207 q^{93} +(-10.9222 + 22.0238i) q^{94} +114.725i q^{95} +(-13.3654 - 11.9881i) q^{96} +155.225 q^{97} +(-50.0921 - 24.8420i) q^{98} -121.403i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 6 q^{4} - 6 q^{6} - 2 q^{8} - 48 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 - 6 * q^4 - 6 * q^6 - 2 * q^8 - 48 * q^9	$ 16 q - 2 q^{2} - 6 q^{4} - 6 q^{6} - 2 q^{8} - 48 q^{9} + 10 q^{10} + 6 q^{12} - 16 q^{13} - 16 q^{14} + 50 q^{16} + 58 q^{18} - 74 q^{20} + 32 q^{21} + 18 q^{22} + 86 q^{24} + 96 q^{25} - 56 q^{26} - 16 q^{28} + 16 q^{29} - 64 q^{30} - 122 q^{32} - 48 q^{33} - 18 q^{36} + 16 q^{37} + 22 q^{40} + 16 q^{41} + 8 q^{42} + 118 q^{44} - 128 q^{45} + 52 q^{46} - 106 q^{48} - 32 q^{49} - 146 q^{50} - 72 q^{52} - 16 q^{53} + 356 q^{54} + 88 q^{56} - 112 q^{57} - 214 q^{58} + 320 q^{60} + 112 q^{61} - 112 q^{62} + 42 q^{64} - 16 q^{65} + 364 q^{66} - 144 q^{69} + 136 q^{70} - 190 q^{72} + 128 q^{73} + 62 q^{74} - 112 q^{76} + 272 q^{77} - 556 q^{78} - 370 q^{80} + 384 q^{81} - 88 q^{82} + 312 q^{84} + 172 q^{86} - 250 q^{88} - 336 q^{89} - 326 q^{90} + 164 q^{92} + 16 q^{93} - 352 q^{94} + 150 q^{96} - 304 q^{97} + 110 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 6 * q^4 - 6 * q^6 - 2 * q^8 - 48 * q^9 + 10 * q^10 + 6 * q^12 - 16 * q^13 - 16 * q^14 + 50 * q^16 + 58 * q^18 - 74 * q^20 + 32 * q^21 + 18 * q^22 + 86 * q^24 + 96 * q^25 - 56 * q^26 - 16 * q^28 + 16 * q^29 - 64 * q^30 - 122 * q^32 - 48 * q^33 - 18 * q^36 + 16 * q^37 + 22 * q^40 + 16 * q^41 + 8 * q^42 + 118 * q^44 - 128 * q^45 + 52 * q^46 - 106 * q^48 - 32 * q^49 - 146 * q^50 - 72 * q^52 - 16 * q^53 + 356 * q^54 + 88 * q^56 - 112 * q^57 - 214 * q^58 + 320 * q^60 + 112 * q^61 - 112 * q^62 + 42 * q^64 - 16 * q^65 + 364 * q^66 - 144 * q^69 + 136 * q^70 - 190 * q^72 + 128 * q^73 + 62 * q^74 - 112 * q^76 + 272 * q^77 - 556 * q^78 - 370 * q^80 + 384 * q^81 - 88 * q^82 + 312 * q^84 + 172 * q^86 - 250 * q^88 - 336 * q^89 - 326 * q^90 + 164 * q^92 + 16 * q^93 - 352 * q^94 + 150 * q^96 - 304 * q^97 + 110 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/68\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$1$

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 $

$2$	−1.79176	−	0.888585i	−0.895882	−	0.444292i
$2$	−1.79176	−	0.888585i	−0.895882	−	0.444292i
$3$		−	0.561065i		−	0.187022i	−0.995618	−	0.0935108i	$-0.970191\pi$
$3$		−	0.561065i		−	0.187022i	0.995618	−	0.0935108i	$-0.0298090\pi$
$4$	2.42083	+	3.18427i	0.605209	+	0.796067i
$5$	3.63253			0.726505			0.363253	−	0.931691i	$-0.381666\pi$
$5$	3.63253			0.726505			0.363253	+	0.931691i	$0.381666\pi$
$6$	−0.498554	+	1.00530i	−0.0830923	+	0.167549i
$7$		−	4.58728i		−	0.655326i	−0.944795	−	0.327663i	$-0.893739\pi$
$7$		−	4.58728i		−	0.655326i	0.944795	−	0.327663i	$-0.106261\pi$
$8$	−1.50807	−	7.85657i	−0.188509	−	0.982071i
$9$	8.68521			0.965023
$10$	−6.50863	−	3.22781i	−0.650863	−	0.322781i
$11$		−	13.9781i		−	1.27073i	−0.772210	−	0.635367i	$-0.780849\pi$
$11$		−	13.9781i		−	1.27073i	0.772210	−	0.635367i	$-0.219151\pi$
$12$	1.78658	−	1.35825i	0.148882	−	0.113187i
$13$	4.17958			0.321506			0.160753	−	0.986995i	$-0.448608\pi$
$13$	4.17958			0.321506			0.160753	+	0.986995i	$0.448608\pi$
$14$	−4.07619	+	8.21932i	−0.291156	+	0.587094i
$15$		−	2.03808i		−	0.135872i
$16$	−4.27912	+	15.4172i	−0.267445	+	0.963573i
$17$	4.12311			0.242536
$17$	4.12311			0.242536
$18$	−15.5618	−	7.71754i	−0.864547	−	0.428752i
$19$			31.5827i			1.66224i	0.556089	+	0.831122i	$0.312301\pi$
$19$			31.5827i			1.66224i	−0.556089	+	0.831122i	$0.687699\pi$
$20$	8.79375	+	11.5669i	0.439687	+	0.578347i
$21$	−2.57376			−0.122560
$22$	−12.4207	+	25.0454i	−0.564578	+	1.13843i
$23$		−	3.57847i		−	0.155585i	−0.996970	−	0.0777927i	$-0.975213\pi$
$23$		−	3.57847i		−	0.155585i	0.996970	−	0.0777927i	$-0.0247872\pi$
$24$	−4.40805	+	0.846126i	−0.183669	+	0.0352553i
$25$	−11.8047			−0.472190
$26$	−7.48882	−	3.71391i	−0.288031	−	0.142843i
$27$		−	9.92255i		−	0.367502i
$28$	14.6071	−	11.1050i	0.521683	−	0.396609i
$29$	−8.38600			−0.289172			−0.144586	−	0.989492i	$-0.546185\pi$
$29$	−8.38600			−0.289172			−0.144586	+	0.989492i	$0.546185\pi$
$30$	−1.81101	+	3.65176i	−0.0603670	+	0.121725i
$31$			38.0004i			1.22582i	0.790153	+	0.612910i	$0.210001\pi$
$31$			38.0004i			1.22582i	−0.790153	+	0.612910i	$0.789999\pi$
$32$	21.3666	−	23.8216i	0.667707	−	0.744424i
$33$	−7.84261			−0.237655
$34$	−7.38763	−	3.66373i	−0.217283	−	0.107757i
$35$		−	16.6634i		−	0.476098i
$36$	21.0254	+	27.6560i	0.584040	+	0.768223i
$37$	−35.8406			−0.968664			−0.484332	−	0.874884i	$-0.660937\pi$
$37$	−35.8406			−0.968664			−0.484332	+	0.874884i	$0.660937\pi$
$38$	28.0639	−	56.5887i	0.738523	−	1.48918i
$39$		−	2.34501i		−	0.0601286i
$40$	−5.47811	−	28.5392i	−0.136953	−	0.713480i
$41$	1.37979			0.0336535			0.0168267	−	0.999858i	$-0.494644\pi$
$41$	1.37979			0.0336535			0.0168267	+	0.999858i	$0.494644\pi$
$42$	4.61157	+	2.28701i	0.109799	+	0.0544525i
$43$		−	13.0369i		−	0.303184i	−0.988443	−	0.151592i	$-0.951560\pi$
$43$		−	13.0369i		−	0.303184i	0.988443	−	0.151592i	$-0.0484400\pi$
$44$	44.5099	−	33.8386i	1.01159	−	0.769059i
$45$	31.5492			0.701094
$46$	−3.17977	+	6.41177i	−0.0691254	+	0.139386i
$47$		−	12.2917i		−	0.261525i	−0.991414	−	0.130762i	$-0.958257\pi$
$47$		−	12.2917i		−	0.261525i	0.991414	−	0.130762i	$-0.0417425\pi$
$48$	8.65003	+	2.40086i	0.180209	+	0.0500180i
$49$	27.9569			0.570548
$50$	21.1513	+	10.4895i	0.423026	+	0.209790i
$51$		−	2.31333i		−	0.0453594i
$52$	10.1181	+	13.3089i	0.194578	+	0.255940i
$53$	−64.1582			−1.21053			−0.605266	−	0.796023i	$-0.706933\pi$
$53$	−64.1582			−1.21053			−0.605266	+	0.796023i	$0.706933\pi$
$54$	−8.81702	+	17.7789i	−0.163278	+	0.329238i
$55$		−	50.7757i		−	0.923195i
$56$	−36.0403	+	6.91795i	−0.643577	+	0.123535i
$57$	17.7199			0.310876
$58$	15.0257	+	7.45167i	0.259064	+	0.128477i
$59$			55.5166i			0.940960i	0.882411	+	0.470480i	$0.155919\pi$
$59$			55.5166i			0.940960i	−0.882411	+	0.470480i	$0.844081\pi$
$60$	6.48980	−	4.93386i	0.108163	−	0.0822310i
$61$	−72.4961			−1.18846			−0.594230	−	0.804295i	$-0.702543\pi$
$61$	−72.4961			−1.18846			−0.594230	+	0.804295i	$0.702543\pi$
$62$	33.7666	−	68.0878i	0.544623	−	1.09819i
$63$		−	39.8415i		−	0.632404i
$64$	−59.4514	+	23.6966i	−0.928929	+	0.370259i
$65$	15.1824			0.233576
$66$	14.0521	+	6.96882i	0.212911	+	0.105588i
$67$			109.059i			1.62774i	0.581045	+	0.813871i	$0.302644\pi$
$67$			109.059i			1.62774i	−0.581045	+	0.813871i	$0.697356\pi$
$68$	9.98136	+	13.1291i	0.146785	+	0.193075i
$69$	−2.00775			−0.0290979
$70$	−14.8069	+	29.8569i	−0.211527	+	0.426527i
$71$			125.437i			1.76672i	0.468691	+	0.883362i	$0.344726\pi$
$71$			125.437i			1.76672i	−0.468691	+	0.883362i	$0.655274\pi$
$72$	−13.0979	−	68.2359i	−0.181916	−	0.947721i
$73$	67.6229			0.926341			0.463170	−	0.886269i	$-0.346712\pi$
$73$	67.6229			0.926341			0.463170	+	0.886269i	$0.346712\pi$
$74$	64.2178	+	31.8474i	0.867809	+	0.430370i
$75$			6.62323i			0.0883097i
$76$	−100.568	+	76.4564i	−1.32326	+	1.00600i
$77$	−64.1214			−0.832745
$78$	−2.08374	+	4.20171i	−0.0267147	+	0.0538681i
$79$		−	152.880i		−	1.93519i	−0.252512	−	0.967594i	$-0.581257\pi$
$79$		−	152.880i		−	1.93519i	0.252512	−	0.967594i	$-0.418743\pi$
$80$	−15.5440	+	56.0033i	−0.194300	+	0.700041i
$81$	72.5997			0.896292
$82$	−2.47226	−	1.22606i	−0.0301495	−	0.0149520i
$83$		−	107.373i		−	1.29365i	−0.762639	−	0.646825i	$-0.776096\pi$
$83$		−	107.373i		−	1.29365i	0.762639	−	0.646825i	$-0.223904\pi$
$84$	−6.23065	−	8.19555i	−0.0741744	−	0.0975660i
$85$	14.9773			0.176203
$86$	−11.5844	+	23.3591i	−0.134702	+	0.271617i
$87$			4.70509i			0.0540815i
$88$	−109.820	+	21.0800i	−1.24795	+	0.239545i
$89$	33.8911			0.380799			0.190399	−	0.981707i	$-0.439022\pi$
$89$	33.8911			0.380799			0.190399	+	0.981707i	$0.439022\pi$
$90$	−56.5288	−	28.0342i	−0.628098	−	0.311491i
$91$		−	19.1729i		−	0.210691i
$92$	11.3948	−	8.66287i	0.123856	−	0.0941617i
$93$	21.3207			0.229255
$94$	−10.9222	+	22.0238i	−0.116194	+	0.234295i
$95$			114.725i			1.20763i
$96$	−13.3654	−	11.9881i	−0.139223	−	0.124876i
$97$	155.225			1.60026			0.800129	−	0.599828i	$-0.204764\pi$
$97$	155.225			1.60026			0.800129	+	0.599828i	$0.204764\pi$
$98$	−50.0921	−	24.8420i	−0.511144	−	0.253490i
$99$		−	121.403i		−	1.22629i
$100$	−28.5773	−	37.5895i	−0.285773	−	0.375895i
$101$	−159.125			−1.57550			−0.787749	−	0.615996i	$-0.788754\pi$
$101$	−159.125			−1.57550			−0.787749	+	0.615996i	$0.788754\pi$
$102$	−2.05559	+	4.14494i	−0.0201528	+	0.0406367i
$103$			64.0806i			0.622141i	0.950387	+	0.311071i	$0.100688\pi$
$103$			64.0806i			0.622141i	−0.950387	+	0.311071i	$0.899312\pi$
$104$	−6.30311	−	32.8372i	−0.0606068	−	0.315742i
$105$	−9.34926			−0.0890406
$106$	114.956	+	57.0100i	1.08449	+	0.537830i
$107$		−	42.4338i		−	0.396578i	−0.980144	−	0.198289i	$-0.936462\pi$
$107$		−	42.4338i		−	0.396578i	0.980144	−	0.198289i	$-0.0635385\pi$
$108$	31.5960	−	24.0208i	0.292556	−	0.222415i
$109$	78.8751			0.723625			0.361812	−	0.932251i	$-0.382158\pi$
$109$	78.8751			0.723625			0.361812	+	0.932251i	$0.382158\pi$
$110$	−45.1186	+	90.9781i	−0.410169	+	0.827074i
$111$			20.1089i			0.181161i
$112$	70.7229	+	19.6295i	0.631454	+	0.175264i
$113$	152.570			1.35018			0.675088	−	0.737737i	$-0.264105\pi$
$113$	152.570			1.35018			0.675088	+	0.737737i	$0.264105\pi$
$114$	−31.7499	−	15.7456i	−0.278508	−	0.138120i
$115$		−	12.9989i		−	0.113034i
$116$	−20.3011	−	26.7033i	−0.175010	−	0.230201i
$117$	36.3005			0.310261
$118$	49.3312	−	99.4727i	0.418061	−	0.842989i
$119$		−	18.9138i		−	0.158940i
$120$	−16.0123	+	3.07358i	−0.133436	+	0.0256131i
$121$	−74.3867			−0.614766
$122$	129.896	+	64.4189i	1.06472	+	0.528024i
$123$		−	0.774153i		−	0.00629393i
$124$	−121.004	+	91.9927i	−0.975835	+	0.741877i
$125$	−133.694			−1.06955
$126$	−35.4025	+	71.3865i	−0.280972	+	0.566560i
$127$		−	32.1074i		−	0.252814i	−0.991978	−	0.126407i	$-0.959655\pi$
$127$		−	32.1074i		−	0.252814i	0.991978	−	0.126407i	$-0.0403445\pi$
$128$	127.579	+	10.3690i	0.996713	+	0.0810079i
$129$	−7.31456			−0.0567020
$130$	−27.2033	−	13.4909i	−0.209256	−	0.103776i
$131$			51.4567i			0.392799i	0.980524	+	0.196399i	$0.0629249\pi$
$131$			51.4567i			0.392799i	−0.980524	+	0.196399i	$0.937075\pi$
$132$	−18.9857	−	24.9730i	−0.143831	−	0.189189i
$133$	144.878			1.08931
$134$	96.9079	−	195.408i	0.723194	−	1.45827i
$135$		−	36.0439i		−	0.266992i
$136$	−6.21794	−	32.3935i	−0.0457201	−	0.238187i
$137$	−197.054			−1.43835			−0.719175	−	0.694829i	$-0.755480\pi$
$137$	−197.054			−1.43835			−0.719175	+	0.694829i	$0.755480\pi$
$138$	3.59742	+	1.78406i	0.0260682	+	0.0129280i
$139$		−	77.3390i		−	0.556396i	−0.960524	−	0.278198i	$-0.910263\pi$
$139$		−	77.3390i		−	0.556396i	0.960524	−	0.278198i	$-0.0897371\pi$
$140$	53.0608	−	40.3394i	0.379006	−	0.288138i
$141$	−6.89643			−0.0489108
$142$	111.462	−	224.754i	0.784942	−	1.58278i
$143$		−	58.4225i		−	0.408549i
$144$	−37.1650	+	133.901i	−0.258091	+	0.929870i
$145$	−30.4624			−0.210085
$146$	−121.164	−	60.0887i	−0.829892	−	0.411566i
$147$		−	15.6856i		−	0.106705i
$148$	−86.7641	−	114.126i	−0.586244	−	0.771122i
$149$	85.2596			0.572212			0.286106	−	0.958198i	$-0.407639\pi$
$149$	85.2596			0.572212			0.286106	+	0.958198i	$0.407639\pi$
$150$	5.88530	−	11.8673i	0.0392353	−	0.0791151i
$151$			113.993i			0.754923i	0.926025	+	0.377461i	$0.123203\pi$
$151$			113.993i			0.754923i	−0.926025	+	0.377461i	$0.876797\pi$
$152$	248.131	−	47.6289i	1.63244	−	0.313348i
$153$	35.8100			0.234052
$154$	114.890	+	56.9773i	0.746041	+	0.369982i
$155$			138.038i			0.890565i
$156$	7.46715	−	5.67689i	0.0478664	−	0.0363903i
$157$	−208.171			−1.32593			−0.662965	−	0.748650i	$-0.730702\pi$
$157$	−208.171			−1.32593			−0.662965	+	0.748650i	$0.730702\pi$
$158$	−135.847	+	273.925i	−0.859789	+	1.73370i
$159$			35.9969i			0.226396i
$160$	77.6149	−	86.5325i	0.485093	−	0.540828i
$161$	−16.4154			−0.101959
$162$	−130.081	−	64.5109i	−0.802972	−	0.398216i
$163$			34.0535i			0.208917i	0.994529	+	0.104459i	$0.0333110\pi$
$163$			34.0535i			0.208917i	−0.994529	+	0.104459i	$0.966689\pi$
$164$	3.34025	+	4.39363i	0.0203674	+	0.0267904i
$165$	−28.4885			−0.172658
$166$	−95.4099	+	192.387i	−0.574759	+	1.15896i
$167$		−	119.136i		−	0.713390i	−0.934221	−	0.356695i	$-0.883903\pi$
$167$		−	119.136i		−	0.713390i	0.934221	−	0.356695i	$-0.116097\pi$
$168$	3.88142	+	20.2209i	0.0231037	+	0.120363i
$169$	−151.531			−0.896634
$170$	−26.8358	−	13.3086i	−0.157857	−	0.0782858i
$171$			274.302i			1.60410i
$172$	41.5130	−	31.5602i	0.241355	−	0.183490i
$173$	−205.018			−1.18508			−0.592538	−	0.805542i	$-0.701874\pi$
$173$	−205.018			−1.18508			−0.592538	+	0.805542i	$0.701874\pi$
$174$	4.18087	−	8.43041i	0.0240280	−	0.0484506i
$175$			54.1517i			0.309438i
$176$	215.502	+	59.8139i	1.22445	+	0.339852i
$177$	31.1484			0.175980
$178$	−60.7248	−	30.1151i	−0.341151	−	0.169186i
$179$			126.785i			0.708297i	0.935189	+	0.354149i	$0.115229\pi$
$179$			126.785i			0.708297i	−0.935189	+	0.354149i	$0.884771\pi$
$180$	76.3755	+	100.461i	0.424308	+	0.558118i
$181$	165.170			0.912539			0.456269	−	0.889842i	$-0.349185\pi$
$181$	165.170			0.912539			0.456269	+	0.889842i	$0.349185\pi$
$182$	−17.0367	+	34.3533i	−0.0936085	+	0.188754i
$183$			40.6750i			0.222268i
$184$	−28.1145	+	5.39658i	−0.152796	+	0.0293293i
$185$	−130.192			−0.703740
$186$	−38.2017	−	18.9453i	−0.205385	−	0.101856i
$187$		−	57.6331i		−	0.308198i
$188$	39.1400	−	29.7561i	0.208191	−	0.158277i
$189$	−45.5175			−0.240833
$190$	101.943	−	205.560i	0.536541	−	1.08189i
$191$			233.794i			1.22405i	0.790838	+	0.612026i	$0.209645\pi$
$191$			233.794i			1.22405i	−0.790838	+	0.612026i	$0.790355\pi$
$192$	13.2953	+	33.3561i	0.0692464	+	0.173730i
$193$	−125.589			−0.650719			−0.325360	−	0.945590i	$-0.605485\pi$
$193$	−125.589			−0.650719			−0.325360	+	0.945590i	$0.605485\pi$
$194$	−278.127	−	137.931i	−1.43364	−	0.710982i
$195$		−	8.51833i		−	0.0436837i
$196$	67.6789	+	89.0221i	0.345301	+	0.454195i
$197$	−144.342			−0.732699			−0.366350	−	0.930477i	$-0.619393\pi$
$197$	−144.342			−0.732699			−0.366350	+	0.930477i	$0.619393\pi$
$198$	−107.876	+	217.525i	−0.544830	+	1.09861i
$199$		−	327.730i		−	1.64689i	−0.567399	−	0.823443i	$-0.692050\pi$
$199$		−	327.730i		−	1.64689i	0.567399	−	0.823443i	$-0.307950\pi$
$200$	17.8024	+	92.7449i	0.0890121	+	0.463724i
$201$	61.1890			0.304423
$202$	285.115	+	141.396i	1.41146	+	0.699982i
$203$			38.4689i			0.189502i
$204$	7.36626	−	5.60019i	0.0361091	−	0.0274519i
$205$	5.01213			0.0244494
$206$	56.9410	−	114.817i	0.276413	−	0.557365i
$207$		−	31.0797i		−	0.150144i
$208$	−17.8849	+	64.4373i	−0.0859852	+	0.309795i
$209$	441.465			2.11227
$210$	16.7517	+	8.30761i	0.0797698	+	0.0395600i
$211$		−	326.073i		−	1.54537i	−0.634790	−	0.772684i	$-0.718914\pi$
$211$		−	326.073i		−	1.54537i	0.634790	−	0.772684i	$-0.281086\pi$
$212$	−155.316	−	204.297i	−0.732624	−	0.963664i
$213$	70.3785			0.330416
$214$	−37.7061	+	76.0314i	−0.176197	+	0.355287i
$215$		−	47.3570i		−	0.220265i
$216$	−77.9572	+	14.9639i	−0.360913	+	0.0692774i
$217$	174.319			0.803311
$218$	−141.326	−	70.0872i	−0.648282	−	0.321501i
$219$		−	37.9408i		−	0.173246i
$220$	161.684	−	122.920i	0.734925	−	0.558726i
$221$	17.2328			0.0779767
$222$	17.8685	−	36.0304i	0.0804885	−	0.162299i
$223$		−	45.7920i		−	0.205345i	−0.994715	−	0.102673i	$-0.967261\pi$
$223$		−	45.7920i		−	0.205345i	0.994715	−	0.102673i	$-0.0327394\pi$
$224$	−109.276	−	98.0147i	−0.487840	−	0.437566i
$225$	−102.527			−0.455674
$226$	−273.369	−	135.571i	−1.20960	−	0.599873i
$227$			65.2813i			0.287583i	0.989608	+	0.143791i	$0.0459294\pi$
$227$			65.2813i			0.287583i	−0.989608	+	0.143791i	$0.954071\pi$
$228$	42.8970	+	56.4250i	0.188145	+	0.247478i
$229$	403.828			1.76344			0.881721	−	0.471772i	$-0.156385\pi$
$229$	403.828			1.76344			0.881721	+	0.471772i	$0.156385\pi$
$230$	−11.5506	+	23.2909i	−0.0502200	+	0.101265i
$231$			35.9762i			0.155741i
$232$	12.6467	+	65.8852i	0.0545116	+	0.283988i
$233$	240.929			1.03403			0.517016	−	0.855976i	$-0.327043\pi$
$233$	240.929			1.03403			0.517016	+	0.855976i	$0.327043\pi$
$234$	−65.0419	−	32.2561i	−0.277957	−	0.137846i
$235$		−	44.6498i		−	0.189999i
$236$	−176.780	+	134.397i	−0.749067	+	0.569477i
$237$	−85.7755			−0.361922
$238$	−16.8065	+	33.8891i	−0.0706157	+	0.142391i
$239$		−	283.817i		−	1.18752i	−0.804643	−	0.593759i	$-0.797643\pi$
$239$		−	283.817i		−	1.18752i	0.804643	−	0.593759i	$-0.202357\pi$
$240$	31.4215	+	8.72120i	0.130923	+	0.0363384i
$241$	143.457			0.595257			0.297629	−	0.954682i	$-0.403804\pi$
$241$	143.457			0.595257			0.297629	+	0.954682i	$0.403804\pi$
$242$	133.283	+	66.0989i	0.550758	+	0.273136i
$243$		−	130.036i		−	0.535128i
$244$	−175.501	−	230.847i	−0.719267	−	0.946094i
$245$	101.554			0.414506
$246$	−0.687900	+	1.38710i	−0.00279634	+	0.00563861i
$247$			132.002i			0.534422i
$248$	298.553	−	57.3074i	1.20384	−	0.231078i
$249$	−60.2432			−0.241940
$250$	239.548	+	118.799i	0.958194	+	0.475195i
$251$		−	422.694i		−	1.68404i	−0.539446	−	0.842020i	$-0.681366\pi$
$251$		−	422.694i		−	1.68404i	0.539446	−	0.842020i	$-0.318634\pi$
$252$	126.866	−	96.4496i	0.503436	−	0.382737i
$253$	−50.0201			−0.197708
$254$	−28.5301	+	57.5288i	−0.112323	+	0.226492i
$255$		−	8.40323i		−	0.0329539i
$256$	−219.378	−	131.944i	−0.856946	−	0.515406i
$257$	−81.4974			−0.317110			−0.158555	−	0.987350i	$-0.550684\pi$
$257$	−81.4974			−0.317110			−0.158555	+	0.987350i	$0.550684\pi$
$258$	13.1060	+	6.49961i	0.0507983	+	0.0251923i
$259$			164.411i			0.634791i
$260$	36.7542	+	48.3449i	0.141362	+	0.185942i
$261$	−72.8341			−0.279058
$262$	45.7236	−	92.1982i	0.174518	−	0.351901i
$263$		−	10.9861i		−	0.0417723i	−0.999782	−	0.0208861i	$-0.993351\pi$
$263$		−	10.9861i		−	0.0417723i	0.999782	−	0.0208861i	$-0.00664875\pi$
$264$	11.8272	+	61.6160i	0.0448001	+	0.233394i
$265$	−233.056			−0.879458
$266$	−259.588	−	128.737i	−0.975895	−	0.483973i
$267$		−	19.0151i		−	0.0712176i
$268$	−347.272	+	264.013i	−1.29579	+	0.985124i
$269$	144.027			0.535418			0.267709	−	0.963500i	$-0.413733\pi$
$269$	144.027			0.535418			0.267709	+	0.963500i	$0.413733\pi$
$270$	−32.0281	+	64.5822i	−0.118623	+	0.239193i
$271$			97.0025i			0.357943i	0.983854	+	0.178971i	$0.0572769\pi$
$271$			97.0025i			0.357943i	−0.983854	+	0.178971i	$0.942723\pi$
$272$	−17.6433	+	63.5666i	−0.0648649	+	0.233701i
$273$	−10.7572			−0.0394038
$274$	353.074	+	175.099i	1.28859	+	0.639048i
$275$			165.008i			0.600028i
$276$	−4.86043	−	6.39322i	−0.0176103	−	0.0231638i
$277$	277.278			1.00100			0.500501	−	0.865736i	$-0.333149\pi$
$277$	277.278			1.00100			0.500501	+	0.865736i	$0.333149\pi$
$278$	−68.7223	+	138.573i	−0.247202	+	0.498465i
$279$			330.042i			1.18294i
$280$	−130.917	+	25.1296i	−0.467562	+	0.0897487i
$281$	−256.738			−0.913657			−0.456829	−	0.889555i	$-0.651015\pi$
$281$	−256.738			−0.913657			−0.456829	+	0.889555i	$0.651015\pi$
$282$	12.3568	+	6.12806i	0.0438183	+	0.0217307i
$283$			478.019i			1.68911i	0.535466	+	0.844556i	$0.320136\pi$
$283$			478.019i			1.68911i	−0.535466	+	0.844556i	$0.679864\pi$
$284$	−399.426	+	303.663i	−1.40643	+	1.06924i
$285$	64.3681			0.225853
$286$	−51.9133	+	104.679i	−0.181515	+	0.366011i
$287$		−	6.32949i		−	0.0220540i
$288$	185.574	−	206.895i	0.644353	−	0.718386i
$289$	17.0000			0.0588235
$290$	54.5814	+	27.0684i	0.188212	+	0.0933393i
$291$		−	87.0913i		−	0.299283i
$292$	163.704	+	215.329i	0.560629	+	0.737429i
$293$	143.940			0.491264			0.245632	−	0.969363i	$-0.421005\pi$
$293$	143.940			0.491264			0.245632	+	0.969363i	$0.421005\pi$
$294$	−13.9380	+	28.1049i	−0.0474082	+	0.0955950i
$295$			201.666i			0.683612i
$296$	54.0502	+	281.584i	0.182602	+	0.951297i
$297$	−138.698			−0.466997
$298$	−152.765	−	75.7603i	−0.512634	−	0.254229i
$299$		−	14.9565i		−	0.0500217i
$300$	−21.0901	+	16.0337i	−0.0703005	+	0.0534458i
$301$	−59.8040			−0.198684
$302$	101.293	−	204.249i	0.335406	−	0.676322i
$303$			89.2796i			0.294652i
$304$	−486.915	−	135.146i	−1.60169	−	0.444559i
$305$	−263.344			−0.863423
$306$	−64.1631	−	31.8202i	−0.209683	−	0.103988i
$307$		−	123.260i		−	0.401499i	−0.979643	−	0.200749i	$-0.935662\pi$
$307$		−	123.260i		−	0.401499i	0.979643	−	0.200749i	$-0.0643377\pi$
$308$	−155.227	−	204.180i	−0.503984	−	0.662921i
$309$	35.9534			0.116354
$310$	122.658	−	247.331i	0.395671	−	0.797841i
$311$		−	495.048i		−	1.59179i	−0.605432	−	0.795897i	$-0.707000\pi$
$311$		−	495.048i		−	1.59179i	0.605432	−	0.795897i	$-0.293000\pi$
$312$	−18.4238	+	3.53645i	−0.0590506	+	0.0113348i
$313$	−147.536			−0.471362			−0.235681	−	0.971830i	$-0.575732\pi$
$313$	−147.536			−0.471362			−0.235681	+	0.971830i	$0.575732\pi$
$314$	372.993	+	184.978i	1.18788	+	0.589100i
$315$		−	144.725i		−	0.459445i
$316$	486.810	−	370.097i	1.54054	−	1.17119i
$317$	−231.073			−0.728936			−0.364468	−	0.931216i	$-0.618749\pi$
$317$	−231.073			−0.728936			−0.364468	+	0.931216i	$0.618749\pi$
$318$	31.9863	−	64.4979i	0.100586	−	0.202824i
$319$			117.220i			0.367461i
$320$	−215.959	+	86.0784i	−0.674872	+	0.268995i
$321$	−23.8081			−0.0741687
$322$	29.4126	+	14.5865i	0.0913434	+	0.0452997i
$323$			130.219i			0.403154i
$324$	175.752	+	231.177i	0.542444	+	0.713508i
$325$	−49.3389			−0.151812
$326$	30.2594	−	61.0158i	0.0928203	−	0.187165i
$327$		−	44.2541i		−	0.135334i
$328$	−2.08083	−	10.8404i	−0.00634398	−	0.0330501i
$329$	−56.3853			−0.171384
$330$	51.0446	+	25.3144i	0.154681	+	0.0767104i
$331$		−	430.051i		−	1.29925i	−0.760256	−	0.649624i	$-0.774927\pi$
$331$		−	430.051i		−	1.29925i	0.760256	−	0.649624i	$-0.225073\pi$
$332$	341.904	−	259.932i	1.02983	−	0.782928i
$333$	−311.283			−0.934783
$334$	−105.863	+	213.464i	−0.316954	+	0.639113i
$335$			396.159i			1.18256i
$336$	11.0134	−	39.6801i	0.0327781	−	0.118096i
$337$	−619.723			−1.83894			−0.919470	−	0.393159i	$-0.871382\pi$
$337$	−619.723			−1.83894			−0.919470	+	0.393159i	$0.871382\pi$
$338$	271.508	+	134.648i	0.803278	+	0.398368i
$339$		−	85.6017i		−	0.252512i
$340$	36.2575	+	47.6917i	0.106640	+	0.140270i
$341$	531.173			1.55769
$342$	243.740	−	491.484i	0.712691	−	1.43709i
$343$		−	353.023i		−	1.02922i
$344$	−102.426	+	19.6606i	−0.297749	+	0.0571530i
$345$	−7.29321			−0.0211397
$346$	367.344	+	182.176i	1.06169	+	0.526520i
$347$			563.862i			1.62496i	0.582987	+	0.812481i	$0.301884\pi$
$347$			563.862i			1.62496i	−0.582987	+	0.812481i	$0.698116\pi$
$348$	−14.9823	+	11.3902i	−0.0430525	+	0.0327306i
$349$	267.184			0.765570			0.382785	−	0.923837i	$-0.374965\pi$
$349$	267.184			0.765570			0.382785	+	0.923837i	$0.374965\pi$
$350$	48.1184	−	97.0270i	0.137481	−	0.277220i
$351$		−	41.4721i		−	0.118154i
$352$	−332.980	−	298.665i	−0.945965	−	0.848479i
$353$	255.884			0.724883			0.362441	−	0.932007i	$-0.381943\pi$
$353$	255.884			0.724883			0.362441	+	0.932007i	$0.381943\pi$
$354$	−55.8106	−	27.6780i	−0.157657	−	0.0781865i
$355$			455.655i			1.28353i
$356$	82.0447	+	107.918i	0.230463	+	0.303141i
$357$	−10.6119			−0.0297252
$358$	112.659	−	227.169i	0.314691	−	0.634551i
$359$		−	32.0011i		−	0.0891394i	−0.999006	−	0.0445697i	$-0.985808\pi$
$359$		−	32.0011i		−	0.0891394i	0.999006	−	0.0445697i	$-0.0141917\pi$
$360$	−47.5785	−	247.869i	−0.132163	−	0.688525i
$361$	−636.464			−1.76306
$362$	−295.945	−	146.767i	−0.817527	−	0.405434i
$363$			41.7358i			0.114975i
$364$	61.0516	−	46.4144i	0.167724	−	0.127512i
$365$	245.642			0.672992
$366$	36.1432	−	72.8800i	0.0987519	−	0.199126i
$367$			76.5316i			0.208533i	0.994549	+	0.104266i	$0.0332495\pi$
$367$			76.5316i			0.208533i	−0.994549	+	0.104266i	$0.966751\pi$
$368$	55.1698	+	15.3127i	0.149918	+	0.0416106i
$369$	11.9838			0.0324764
$370$	233.273	+	115.686i	0.630468	+	0.312666i
$371$			294.312i			0.793293i
$372$	51.6139	+	67.8908i	0.138747	+	0.182502i
$373$	96.4987			0.258710			0.129355	−	0.991598i	$-0.458709\pi$
$373$	96.4987			0.258710			0.129355	+	0.991598i	$0.458709\pi$
$374$	−51.2119	+	103.265i	−0.136930	+	0.276109i
$375$			75.0111i			0.200030i
$376$	−96.5704	+	18.5367i	−0.256836	+	0.0492998i
$377$	−35.0499			−0.0929707
$378$	81.5566	+	40.4462i	0.215758	+	0.107000i
$379$		−	106.940i		−	0.282165i	−0.989998	−	0.141082i	$-0.954942\pi$
$379$		−	106.940i		−	0.282165i	0.989998	−	0.141082i	$-0.0450582\pi$
$380$	−365.315	+	277.730i	−0.961354	+	0.730868i
$381$	−18.0143			−0.0472817
$382$	207.746	−	418.903i	0.543837	−	1.09661i
$383$		−	508.555i		−	1.32782i	−0.747813	−	0.663910i	$-0.768896\pi$
$383$		−	508.555i		−	1.32782i	0.747813	−	0.663910i	$-0.231104\pi$
$384$	5.81769	−	71.5803i	0.0151502	−	0.186407i
$385$	−232.923			−0.604994
$386$	225.026	+	111.596i	0.582968	+	0.289110i
$387$		−	113.228i		−	0.292580i
$388$	375.774	+	494.278i	0.968490	+	1.27391i
$389$	43.6168			0.112125			0.0560627	−	0.998427i	$-0.482145\pi$
$389$	43.6168			0.112125			0.0560627	+	0.998427i	$0.482145\pi$
$390$	−7.56926	+	15.2628i	−0.0194083	+	0.0391355i
$391$		−	14.7544i		−	0.0377350i
$392$	−42.1610	−	219.645i	−0.107553	−	0.560319i
$393$	28.8705			0.0734619
$394$	258.626	+	128.260i	0.656412	+	0.325533i
$395$		−	555.340i		−	1.40592i
$396$	386.578	−	293.895i	0.976207	−	0.742160i
$397$	−240.582			−0.606001			−0.303001	−	0.952990i	$-0.597988\pi$
$397$	−240.582			−0.606001			−0.303001	+	0.952990i	$0.597988\pi$
$398$	−291.216	+	587.215i	−0.731699	+	1.47541i
$399$		−	81.2862i		−	0.203725i
$400$	50.5139	−	181.996i	0.126285	−	0.454990i
$401$	497.858			1.24154			0.620771	−	0.783992i	$-0.286820\pi$
$401$	497.858			1.24154			0.620771	+	0.783992i	$0.286820\pi$
$402$	−109.636	−	54.3716i	−0.272727	−	0.135253i
$403$			158.826i			0.394109i
$404$	−385.216	−	506.698i	−0.953505	−	1.25420i
$405$	263.720			0.651161
$406$	34.1829	−	68.9272i	0.0841943	−	0.169772i
$407$			500.982i			1.23092i
$408$	−18.1748	+	3.48867i	−0.0445462	+	0.00855066i
$409$	−53.6633			−0.131206			−0.0656030	−	0.997846i	$-0.520897\pi$
$409$	−53.6633			−0.131206			−0.0656030	+	0.997846i	$0.520897\pi$
$410$	−8.98056	−	4.45370i	−0.0219038	−	0.0108627i
$411$			110.560i			0.269003i
$412$	−204.050	+	155.128i	−0.495266	+	0.376525i
$413$	254.670			0.616635
$414$	−27.6170	+	55.6875i	−0.0667076	+	0.134511i
$415$		−	390.035i		−	0.939843i
$416$	89.3035	−	99.5641i	0.214672	−	0.239337i
$417$	−43.3922			−0.104058
$418$	−791.001	−	392.279i	−1.89235	−	0.938466i
$419$		−	525.568i		−	1.25434i	−0.778883	−	0.627170i	$-0.784213\pi$
$419$		−	525.568i		−	1.25434i	0.778883	−	0.627170i	$-0.215787\pi$
$420$	−22.6330	−	29.7705i	−0.0538881	−	0.0708822i
$421$	−18.2812			−0.0434234			−0.0217117	−	0.999764i	$-0.506912\pi$
$421$	−18.2812			−0.0434234			−0.0217117	+	0.999764i	$0.506912\pi$
$422$	−289.743	+	584.245i	−0.686595	+	1.38447i
$423$		−	106.756i		−	0.252378i
$424$	96.7552	+	504.063i	0.228196	+	1.18883i
$425$	−48.6722			−0.114523
$426$	−126.102	−	62.5373i	−0.296013	−	0.146801i
$427$			332.560i			0.778829i
$428$	135.121	−	102.725i	0.315703	−	0.240012i
$429$	−32.7788			−0.0764075
$430$	−42.0807	+	84.8525i	−0.0978620	+	0.197331i
$431$			121.865i			0.282749i	0.989956	+	0.141375i	$0.0451522\pi$
$431$			121.865i			0.282749i	−0.989956	+	0.141375i	$0.954848\pi$
$432$	152.978	+	42.4598i	0.354115	+	0.0982865i
$433$	211.366			0.488143			0.244071	−	0.969757i	$-0.421517\pi$
$433$	211.366			0.488143			0.244071	+	0.969757i	$0.421517\pi$
$434$	−312.338	−	154.897i	−0.719672	−	0.356905i
$435$			17.0914i			0.0392905i
$436$	190.944	+	251.159i	0.437944	+	0.576054i
$437$	113.017			0.258621
$438$	−33.7136	+	67.9810i	−0.0769718	+	0.155208i
$439$			357.204i			0.813677i	0.913500	+	0.406838i	$0.133369\pi$
$439$			357.204i			0.813677i	−0.913500	+	0.406838i	$0.866631\pi$
$440$	−398.923	+	76.5735i	−0.906644	+	0.174031i
$441$	242.811			0.550592
$442$	−30.8772	−	15.3128i	−0.0698579	−	0.0346444i
$443$		−	320.668i		−	0.723855i	−0.932206	−	0.361928i	$-0.882119\pi$
$443$		−	320.668i		−	0.723855i	0.932206	−	0.361928i	$-0.117881\pi$
$444$	−64.0321	+	48.6803i	−0.144216	+	0.109640i
$445$	123.110			0.276652
$446$	−40.6901	+	82.0485i	−0.0912334	+	0.183965i
$447$		−	47.8361i		−	0.107016i
$448$	108.703	+	272.720i	0.242640	+	0.608751i
$449$	−31.4336			−0.0700079			−0.0350040	−	0.999387i	$-0.511144\pi$
$449$	−31.4336			−0.0700079			−0.0350040	+	0.999387i	$0.511144\pi$
$450$	183.704	+	91.1036i	0.408230	+	0.202453i
$451$		−	19.2868i		−	0.0427646i
$452$	369.347	+	485.824i	0.817139	+	1.07483i
$453$	63.9577			0.141187
$454$	58.0080	−	116.969i	0.127771	−	0.257640i
$455$		−	69.6461i		−	0.153068i
$456$	−26.7229	−	139.218i	−0.0586029	−	0.305302i
$457$	−594.677			−1.30126			−0.650632	−	0.759393i	$-0.725496\pi$
$457$	−594.677			−1.30126			−0.650632	+	0.759393i	$0.725496\pi$
$458$	−723.565	−	358.835i	−1.57984	−	0.783484i
$459$		−	40.9117i		−	0.0891323i
$460$	41.3919	−	31.4681i	0.0899824	−	0.0684090i
$461$	100.880			0.218828			0.109414	−	0.993996i	$-0.465103\pi$
$461$	100.880			0.218828			0.109414	+	0.993996i	$0.465103\pi$
$462$	31.9679	−	64.4609i	0.0691947	−	0.139526i
$463$			439.814i			0.949922i	0.880007	+	0.474961i	$0.157538\pi$
$463$			439.814i			0.949922i	−0.880007	+	0.474961i	$0.842462\pi$
$464$	35.8847	−	129.288i	0.0773377	−	0.278639i
$465$	77.4480			0.166555
$466$	−431.689	−	214.086i	−0.926371	−	0.459413i
$467$		−	328.326i		−	0.703054i	−0.936178	−	0.351527i	$-0.885663\pi$
$467$		−	328.326i		−	0.703054i	0.936178	−	0.351527i	$-0.114337\pi$
$468$	87.8775	+	115.591i	0.187772	+	0.246988i
$469$	500.283			1.06670
$470$	−39.6752	+	80.0020i	−0.0844152	+	0.170217i
$471$			116.797i			0.247978i
$472$	436.170	−	83.7231i	0.924090	−	0.177379i
$473$	−182.231			−0.385267
$474$	153.689	+	76.2188i	0.324239	+	0.160799i
$475$		−	372.825i		−	0.784895i
$476$	60.2267	−	45.7873i	0.126527	−	0.0961918i
$477$	−557.227			−1.16819
$478$	−252.195	+	508.532i	−0.527605	+	1.06388i
$479$			189.974i			0.396604i	0.980141	+	0.198302i	$0.0635427\pi$
$479$			189.974i			0.396604i	−0.980141	+	0.198302i	$0.936457\pi$
$480$	−48.5503	−	43.5470i	−0.101147	−	0.0907229i
$481$	−149.798			−0.311431
$482$	−257.041	−	127.474i	−0.533280	−	0.264468i
$483$			9.21012i			0.0190686i
$484$	−180.078	−	236.867i	−0.372062	−	0.489395i
$485$	563.859			1.16260
$486$	−115.548	+	232.994i	−0.237753	+	0.479411i
$487$			823.337i			1.69063i	0.534269	+	0.845315i	$0.320587\pi$
$487$			823.337i			1.69063i	−0.534269	+	0.845315i	$0.679413\pi$
$488$	109.329	+	569.571i	0.224036	+	1.16715i
$489$	19.1062			0.0390720
$490$	−181.961	−	90.2394i	−0.371349	−	0.184162i
$491$			142.182i			0.289577i	0.989463	+	0.144788i	$0.0462501\pi$
$491$			142.182i			0.289577i	−0.989463	+	0.144788i	$0.953750\pi$
$492$	2.46511	−	1.87410i	0.00501039	−	0.00380914i
$493$	−34.5764			−0.0701346
$494$	117.295	−	236.517i	0.237439	−	0.478779i
$495$		−	440.998i		−	0.890905i
$496$	−585.859	−	162.608i	−1.18117	−	0.327840i
$497$	575.417			1.15778
$498$	107.942	+	53.5312i	0.216750	+	0.107492i
$499$			172.104i			0.344899i	0.985018	+	0.172449i	$0.0551681\pi$
$499$			172.104i			0.344899i	−0.985018	+	0.172449i	$0.944832\pi$
$500$	−323.652	−	425.718i	−0.647303	−	0.851436i
$501$	−66.8431			−0.133419
$502$	−375.600	+	757.368i	−0.748206	+	1.50870i
$503$		−	893.998i		−	1.77733i	−0.458555	−	0.888666i	$-0.651633\pi$
$503$		−	893.998i		−	1.77733i	0.458555	−	0.888666i	$-0.348367\pi$
$504$	−313.017	+	60.0838i	−0.621066	+	0.119214i
$505$	−578.027			−1.14461
$506$	89.6242	+	44.4471i	0.177123	+	0.0878401i
$507$			85.0188i			0.167690i
$508$	102.239	−	77.7267i	0.201257	−	0.153005i
$509$	127.126			0.249756			0.124878	−	0.992172i	$-0.460146\pi$
$509$	127.126			0.249756			0.124878	+	0.992172i	$0.460146\pi$
$510$	−7.46698	+	15.0566i	−0.0146411	+	0.0295228i
$511$		−	310.205i		−	0.607055i
$512$	275.831	+	431.348i	0.538732	+	0.842477i
$513$	313.380			0.610878
$514$	146.024	+	72.4173i	0.284094	+	0.140890i
$515$			232.774i			0.451989i
$516$	−17.7073	−	23.2915i	−0.0343165	−	0.0451386i
$517$	−171.814			−0.332329
$518$	146.093	−	294.585i	0.282033	−	0.568697i
$519$			115.029i			0.221635i
$520$	−22.8962	−	119.282i	−0.0440312	−	0.229388i
$521$	429.975			0.825288			0.412644	−	0.910892i	$-0.364605\pi$
$521$	429.975			0.825288			0.412644	+	0.910892i	$0.364605\pi$
$522$	130.502	+	64.7193i	0.250003	+	0.123983i
$523$			461.286i			0.882000i	0.897507	+	0.441000i	$0.145376\pi$
$523$			461.286i			0.882000i	−0.897507	+	0.441000i	$0.854624\pi$
$524$	−163.852	+	124.568i	−0.312694	+	0.237725i
$525$	30.3826			0.0578716
$526$	−9.76209	+	19.6845i	−0.0185591	+	0.0374230i
$527$			156.680i			0.297305i
$528$	33.5595	−	120.911i	0.0635596	−	0.228998i
$529$	516.195			0.975793
$530$	417.582	+	207.090i	0.787890	+	0.390736i
$531$			482.173i			0.908048i
$532$	350.727	+	461.332i	0.659261	+	0.867165i
$533$	5.76695			0.0108198
$534$	−16.8965	+	34.0706i	−0.0316414	+	0.0638026i
$535$		−	154.142i		−	0.288116i
$536$	856.828	−	164.468i	1.59856	−	0.306844i
$537$	71.1347			0.132467
$538$	−258.063	−	127.980i	−0.479671	−	0.237882i
$539$		−	390.783i		−	0.725015i
$540$	114.773	−	87.2564i	0.212544	−	0.161586i
$541$	377.902			0.698524			0.349262	−	0.937025i	$-0.386432\pi$
$541$	377.902			0.698524			0.349262	+	0.937025i	$0.386432\pi$
$542$	86.1949	−	173.805i	0.159031	−	0.320674i
$543$		−	92.6708i		−	0.170664i
$544$	88.0969	−	98.2188i	0.161943	−	0.180549i
$545$	286.516			0.525717
$546$	19.2744	+	9.55872i	0.0353012	+	0.0175068i
$547$		−	373.853i		−	0.683461i	−0.939798	−	0.341731i	$-0.888987\pi$
$547$		−	373.853i		−	0.683461i	0.939798	−	0.341731i	$-0.111013\pi$
$548$	−477.035	−	627.473i	−0.870502	−	1.14502i
$549$	−629.644			−1.14689
$550$	146.623	−	295.655i	0.266588	−	0.537554i
$551$		−	264.852i		−	0.480675i
$552$	3.02783	+	15.7740i	0.00548521	+	0.0285762i
$553$	−701.302			−1.26818
$554$	−496.816	−	246.385i	−0.896780	−	0.444738i
$555$			73.0461i			0.131615i
$556$	246.268	−	187.225i	0.442928	−	0.336736i
$557$	−864.284			−1.55168			−0.775838	−	0.630932i	$-0.782673\pi$
$557$	−864.284			−1.55168			−0.775838	+	0.630932i	$0.782673\pi$
$558$	293.270	−	591.356i	0.525573	−	1.05978i
$559$		−	54.4888i		−	0.0974756i
$560$	256.903	+	71.3048i	0.458755	+	0.127330i
$561$	−32.3359			−0.0576398
$562$	460.013	+	228.133i	0.818529	+	0.405931i
$563$		−	466.096i		−	0.827879i	−0.910304	−	0.413940i	$-0.864152\pi$
$563$		−	466.096i		−	0.827879i	0.910304	−	0.413940i	$-0.135848\pi$
$564$	−16.6951	−	21.9601i	−0.0296013	−	0.0389363i
$565$	554.215			0.980911
$566$	424.760	−	856.497i	0.750460	−	1.51325i
$567$		−	333.035i		−	0.587363i
$568$	985.508	−	189.169i	1.73505	−	0.333043i
$569$	−667.111			−1.17243			−0.586214	−	0.810156i	$-0.699382\pi$
$569$	−667.111			−1.17243			−0.586214	+	0.810156i	$0.699382\pi$
$570$	−115.332	−	57.1965i	−0.202338	−	0.100345i
$571$		−	342.187i		−	0.599276i	−0.954053	−	0.299638i	$-0.903134\pi$
$571$		−	342.187i		−	0.599276i	0.954053	−	0.299638i	$-0.0968659\pi$
$572$	186.033	−	141.431i	0.325232	−	0.247257i
$573$	131.174			0.228924
$574$	−5.62429	+	11.3410i	−0.00979841	+	0.0197578i
$575$			42.2429i			0.0734659i
$576$	−516.348	+	205.809i	−0.896437	+	0.357308i
$577$	374.914			0.649764			0.324882	−	0.945755i	$-0.394675\pi$
$577$	374.914			0.649764			0.324882	+	0.945755i	$0.394675\pi$
$578$	−30.4600	−	15.1059i	−0.0526989	−	0.0261348i
$579$			70.4635i			0.121699i
$580$	−73.7444	−	97.0003i	−0.127145	−	0.167242i
$581$	−492.550			−0.847762
$582$	−77.3880	+	156.047i	−0.132969	+	0.268122i
$583$			896.808i			1.53826i
$584$	−101.980	−	531.284i	−0.174624	−	0.909733i
$585$	131.863			0.225406
$586$	−257.907	−	127.903i	−0.440114	−	0.218265i
$587$			565.147i			0.962771i	0.876509	+	0.481386i	$0.159866\pi$
$587$			565.147i			0.962771i	−0.876509	+	0.481386i	$0.840134\pi$
$588$	49.9472	−	37.9723i	0.0849442	−	0.0645787i
$589$	−1200.15			−2.03761
$590$	179.197	−	361.337i	0.303724	−	0.612436i
$591$			80.9851i			0.137031i
$592$	153.366	−	552.560i	0.259064	−	0.933379i
$593$	580.473			0.978875			0.489437	−	0.872038i	$-0.337202\pi$
$593$	580.473			0.978875			0.489437	+	0.872038i	$0.337202\pi$
$594$	248.514	+	123.245i	0.418374	+	0.207483i
$595$		−	68.7050i		−	0.115471i
$596$	206.399	+	271.489i	0.346308	+	0.455519i
$597$	−183.878			−0.308003
$598$	−13.2901	+	26.7985i	−0.0222242	+	0.0448135i
$599$		−	630.273i		−	1.05221i	−0.850420	−	0.526104i	$-0.823652\pi$
$599$		−	630.273i		−	1.05221i	0.850420	−	0.526104i	$-0.176348\pi$
$600$	52.0359	−	9.98831i	0.0867265	−	0.0166472i
$601$	511.744			0.851488			0.425744	−	0.904844i	$-0.360012\pi$
$601$	511.744			0.851488			0.425744	+	0.904844i	$0.360012\pi$
$602$	107.155	+	53.1409i	0.177998	+	0.0882740i
$603$			947.198i			1.57081i
$604$	−362.985	+	275.959i	−0.600969	+	0.456886i
$605$	−270.212			−0.446631
$606$	79.3325	−	159.968i	0.130912	−	0.263974i
$607$		−	466.021i		−	0.767745i	−0.923386	−	0.383873i	$-0.874590\pi$
$607$		−	466.021i		−	0.767745i	0.923386	−	0.383873i	$-0.125410\pi$
$608$	752.348	+	674.815i	1.23741	+	1.10989i
$609$	21.5836			0.0354410
$610$	471.850	+	234.003i	0.773525	+	0.383612i
$611$		−	51.3740i		−	0.0840819i
$612$	86.6901	+	114.029i	0.141651	+	0.186321i
$613$	23.1027			0.0376880			0.0188440	−	0.999822i	$-0.494001\pi$
$613$	23.1027			0.0376880			0.0188440	+	0.999822i	$0.494001\pi$
$614$	−109.527	+	220.853i	−0.178383	+	0.359695i
$615$		−	2.81213i		−	0.00457257i
$616$	96.6996	+	503.774i	0.156980	+	0.817815i
$617$	−826.024			−1.33877			−0.669387	−	0.742913i	$-0.733443\pi$
$617$	−826.024			−1.33877			−0.669387	+	0.742913i	$0.733443\pi$
$618$	−64.4199	−	31.9476i	−0.104239	−	0.0516952i
$619$			37.8170i			0.0610936i	0.999533	+	0.0305468i	$0.00972487\pi$
$619$			37.8170i			0.0610936i	−0.999533	+	0.0305468i	$0.990275\pi$
$620$	−439.549	+	334.166i	−0.708949	+	0.538978i
$621$	−35.5075			−0.0571779
$622$	−439.892	+	887.009i	−0.707222	+	1.42606i
$623$		−	155.468i		−	0.249547i
$624$	36.1535	+	10.0346i	0.0579383	+	0.0160811i
$625$	−190.529			−0.304847
$626$	264.350	+	131.099i	0.422285	+	0.209423i
$627$		−	247.690i		−	0.395041i
$628$	−503.947	−	662.872i	−0.802464	−	1.05553i
$629$	−147.774			−0.234936
$630$	−128.601	+	259.313i	−0.204128	+	0.411609i
$631$			299.759i			0.475053i	0.971381	+	0.237527i	$0.0763367\pi$
$631$			299.759i			0.475053i	−0.971381	+	0.237527i	$0.923663\pi$
$632$	−1201.11	+	230.554i	−1.90049	+	0.364800i
$633$	−182.948			−0.289017
$634$	414.028	+	205.328i	0.653040	+	0.323861i
$635$		−	116.631i		−	0.183671i
$636$	−114.624	+	87.1425i	−0.180226	+	0.137017i
$637$	116.848			0.183435
$638$	104.160	−	210.031i	0.163260	−	0.329202i
$639$			1089.45i			1.70493i
$640$	463.435	+	37.6657i	0.724118	+	0.0588527i
$641$	−849.517			−1.32530			−0.662650	−	0.748930i	$-0.730568\pi$
$641$	−849.517			−1.32530			−0.662650	+	0.748930i	$0.730568\pi$
$642$	42.6586	+	21.1556i	0.0664464	+	0.0329526i
$643$		−	421.551i		−	0.655600i	−0.944747	−	0.327800i	$-0.893693\pi$
$643$		−	421.551i		−	0.655600i	0.944747	−	0.327800i	$-0.106307\pi$
$644$	−39.7390	−	52.2711i	−0.0617066	−	0.0811663i
$645$	−26.5703			−0.0411943
$646$	115.710	−	233.321i	0.179118	−	0.361178i
$647$			1244.19i			1.92301i	0.274788	+	0.961505i	$0.411392\pi$
$647$			1244.19i			1.92301i	−0.274788	+	0.961505i	$0.588608\pi$
$648$	−109.486	−	570.384i	−0.168959	−	0.880223i
$649$	776.016			1.19571
$650$	88.4036	+	43.8418i	0.136006	+	0.0674489i
$651$		−	97.8040i		−	0.150237i
$652$	−108.435	+	82.4378i	−0.166312	+	0.126438i
$653$	−318.048			−0.487057			−0.243528	−	0.969894i	$-0.578305\pi$
$653$	−318.048			−0.487057			−0.243528	+	0.969894i	$0.578305\pi$
$654$	−39.3235	+	79.2928i	−0.0601276	+	0.121243i
$655$			186.918i			0.285371i
$656$	−5.90430	+	21.2725i	−0.00900045	+	0.0324276i
$657$	587.319			0.893940
$658$	101.029	+	50.1032i	0.153540	+	0.0761446i
$659$			1077.30i			1.63475i	0.576107	+	0.817374i	$0.304571\pi$
$659$			1077.30i			1.63475i	−0.576107	+	0.817374i	$0.695429\pi$
$660$	−68.9659	−	90.7150i	−0.104494	−	0.137447i
$661$	218.740			0.330923			0.165462	−	0.986216i	$-0.447089\pi$
$661$	218.740			0.330923			0.165462	+	0.986216i	$0.447089\pi$
$662$	−382.137	+	770.549i	−0.577246	+	1.16397i
$663$		−	9.66874i		−	0.0145833i
$664$	−843.583	+	161.926i	−1.27046	+	0.243865i
$665$	526.275			0.791391
$666$	557.745	+	276.601i	0.837455	+	0.415317i
$667$			30.0090i			0.0449910i
$668$	379.361	−	288.409i	0.567906	−	0.431750i
$669$	−25.6923			−0.0384040
$670$	352.021	−	709.823i	0.525404	−	1.05944i
$671$			1013.36i			1.51022i
$672$	−54.9926	+	61.3110i	−0.0818343	+	0.0912367i
$673$	507.759			0.754471			0.377236	−	0.926117i	$-0.376875\pi$
$673$	507.759			0.754471			0.377236	+	0.926117i	$0.376875\pi$
$674$	1110.40	+	550.676i	1.64747	+	0.817027i
$675$			117.133i			0.173531i
$676$	−366.832	−	482.516i	−0.542651	−	0.713781i
$677$	−606.960			−0.896544			−0.448272	−	0.893897i	$-0.647960\pi$
$677$	−606.960			−0.896544			−0.448272	+	0.893897i	$0.647960\pi$
$678$	−76.0643	+	153.378i	−0.112189	+	0.226221i
$679$		−	712.060i		−	1.04869i
$680$	−22.5868	−	117.670i	−0.0332159	−	0.173044i
$681$	36.6270			0.0537842
$682$	−951.736	−	471.992i	−1.39551	−	0.692071i
$683$		−	324.368i		−	0.474917i	−0.971398	−	0.237458i	$-0.923686\pi$
$683$		−	324.368i		−	0.474917i	0.971398	−	0.237458i	$-0.0763143\pi$
$684$	−873.451	+	664.039i	−1.27697	+	0.970818i
$685$	−715.804			−1.04497
$686$	−313.691	+	632.533i	−0.457275	+	0.922060i
$687$		−	226.574i		−	0.329802i
$688$	200.992	+	55.7866i	0.292140	+	0.0810851i
$689$	−268.154			−0.389193
$690$	13.0677	+	6.48064i	0.0189387	+	0.00939223i
$691$		−	604.456i		−	0.874755i	−0.899278	−	0.437378i	$-0.855907\pi$
$691$		−	604.456i		−	0.874755i	0.899278	−	0.437378i	$-0.144093\pi$
$692$	−496.315	−	652.833i	−0.717219	−	0.943400i
$693$	−556.907			−0.803618
$694$	501.039	−	1010.31i	0.721959	−	1.45577i
$695$		−	280.936i		−	0.404225i
$696$	36.9659	−	7.09562i	0.0531119	−	0.0101949i
$697$	5.68903			0.00816216
$698$	−478.730	−	237.415i	−0.685860	−	0.340137i
$699$		−	135.177i		−	0.193386i
$700$	−172.433	+	131.092i	−0.246334	+	0.187275i
$701$	576.049			0.821754			0.410877	−	0.911691i	$-0.365223\pi$
$701$	576.049			0.821754			0.410877	+	0.911691i	$0.365223\pi$
$702$	−36.8514	+	74.3081i	−0.0524949	+	0.105852i
$703$		−	1131.94i		−	1.61016i
$704$	331.232	+	831.017i	0.470500	+	1.18042i
$705$	−25.0515			−0.0355340
$706$	−458.483	−	227.374i	−0.649409	−	0.322060i
$707$			729.952i			1.03246i
$708$	75.4052	+	99.1850i	0.106505	+	0.140092i
$709$	720.109			1.01567			0.507834	−	0.861455i	$-0.330446\pi$
$709$	720.109			1.01567			0.507834	+	0.861455i	$0.330446\pi$
$710$	404.888	−	816.426i	0.570265	−	1.14990i
$711$		−	1327.79i		−	1.86750i
$712$	−51.1102	−	266.268i	−0.0717840	−	0.373972i
$713$	135.983			0.190720
$714$	19.0140	+	9.42956i	0.0266303	+	0.0132067i
$715$		−	212.221i		−	0.296813i
$716$	−403.718	+	306.926i	−0.563852	+	0.428668i
$717$	−159.240			−0.222091
$718$	−28.4356	+	57.3383i	−0.0396040	+	0.0798584i
$719$			250.539i			0.348455i	0.984705	+	0.174228i	$0.0557428\pi$
$719$			250.539i			0.348455i	−0.984705	+	0.174228i	$0.944257\pi$
$720$	−135.003	+	486.400i	−0.187504	+	0.675556i
$721$	293.956			0.407705
$722$	1140.39	+	565.552i	1.57949	+	0.783313i
$723$		−	80.4887i		−	0.111326i
$724$	399.848	+	525.944i	0.552276	+	0.726442i
$725$	98.9946			0.136544
$726$	37.0858	−	74.7806i	0.0510823	−	0.103004i
$727$		−	1065.72i		−	1.46591i	−0.680276	−	0.732956i	$-0.738140\pi$
$727$		−	1065.72i		−	1.46591i	0.680276	−	0.732956i	$-0.261860\pi$
$728$	−150.633	+	28.9141i	−0.206914	+	0.0397172i
$729$	580.438			0.796212
$730$	−440.132	−	218.274i	−0.602921	−	0.299005i
$731$		−	53.7526i		−	0.0735330i
$732$	−129.520	+	98.4675i	−0.176940	+	0.134518i
$733$	111.085			0.151549			0.0757745	−	0.997125i	$-0.475857\pi$
$733$	111.085			0.151549			0.0757745	+	0.997125i	$0.475857\pi$
$734$	68.0048	−	137.127i	0.0926496	−	0.186821i
$735$		−	56.9784i		−	0.0775217i
$736$	−85.2447	−	76.4598i	−0.115822	−	0.103886i
$737$	1524.43			2.06843
$738$	−21.4721	−	10.6486i	−0.0290950	−	0.0144290i
$739$			50.3154i			0.0680858i	0.999420	+	0.0340429i	$0.0108383\pi$
$739$			50.3154i			0.0680858i	−0.999420	+	0.0340429i	$0.989162\pi$
$740$	−315.173	−	414.566i	−0.425909	−	0.560224i
$741$	74.0618			0.0999484
$742$	261.521	−	527.337i	0.352454	−	0.710696i
$743$			547.420i			0.736769i	0.929673	+	0.368385i	$0.120089\pi$
$743$			547.420i			0.736769i	−0.929673	+	0.368385i	$0.879911\pi$
$744$	−32.1532	−	167.508i	−0.0432166	−	0.225145i
$745$	309.708			0.415715
$746$	−172.903	−	85.7473i	−0.231773	−	0.114943i
$747$		−	932.556i		−	1.24840i
$748$	183.519	−	139.520i	0.245347	−	0.186524i
$749$	−194.656			−0.259888
$750$	66.6538	−	134.402i	0.0888717	−	0.179203i
$751$			145.853i			0.194211i	0.995274	+	0.0971056i	$0.0309585\pi$
$751$			145.853i			0.194211i	−0.995274	+	0.0971056i	$0.969042\pi$
$752$	189.503	+	52.5976i	0.251998	+	0.0699436i
$753$	−237.159			−0.314952
$754$	62.8012	+	31.1448i	0.0832907	+	0.0413062i
$755$			414.084i			0.548456i
$756$	−110.190	−	144.940i	−0.145754	−	0.191719i
$757$	871.192			1.15085			0.575424	−	0.817855i	$-0.304837\pi$
$757$	871.192			1.15085			0.575424	+	0.817855i	$0.304837\pi$
$758$	−95.0256	+	191.612i	−0.125364	+	0.252786i
$759$			28.0645i			0.0369756i
$760$	901.344	−	173.013i	1.18598	−	0.227649i
$761$	226.790			0.298015			0.149008	−	0.988836i	$-0.452392\pi$
$761$	226.790			0.298015			0.149008	+	0.988836i	$0.452392\pi$
$762$	32.2774	+	16.0073i	0.0423588	+	0.0210069i
$763$		−	361.822i		−	0.474210i
$764$	−744.462	+	565.976i	−0.974427	+	0.740807i
$765$	130.081			0.170040
$766$	−451.894	+	911.210i	−0.589940	+	1.18957i
$767$			232.036i			0.302524i
$768$	−74.0291	+	123.085i	−0.0963920	+	0.160267i
$769$	64.6796			0.0841087			0.0420544	−	0.999115i	$-0.486610\pi$
$769$	64.6796			0.0841087			0.0420544	+	0.999115i	$0.486610\pi$
$770$	417.342	+	206.971i	0.542003	+	0.268794i
$771$			45.7253i			0.0593065i
$772$	−304.030	−	399.908i	−0.393821	−	0.518016i
$773$	−1305.30			−1.68862			−0.844308	−	0.535859i	$-0.819988\pi$
$773$	−1305.30			−1.68862			−0.844308	+	0.535859i	$0.819988\pi$
$774$	−100.613	+	202.878i	−0.129991	+	0.262117i
$775$		−	448.585i		−	0.578820i
$776$	−234.090	−	1219.54i	−0.301663	−	1.57157i
$777$	92.2451			0.118720
$778$	−78.1509	−	38.7572i	−0.100451	−	0.0498164i
$779$			43.5775i			0.0559403i
$780$	27.1246	−	20.6215i	0.0347752	−	0.0264378i
$781$	1753.37			2.24504
$782$	−13.1105	+	26.4364i	−0.0167654	+	0.0338061i
$783$			83.2105i			0.106271i
$784$	−119.631	+	431.016i	−0.152590	+	0.549765i
$785$	−756.187			−0.963295
$786$	−51.7292	−	25.6539i	−0.0658132	−	0.0326386i
$787$			660.975i			0.839867i	0.907555	+	0.419934i	$0.137947\pi$
$787$			660.975i			0.839867i	−0.907555	+	0.419934i	$0.862053\pi$
$788$	−349.427	−	459.623i	−0.443436	−	0.583278i
$789$	−6.16392			−0.00781232
$790$	−493.467	+	995.038i	−0.624641	+	1.25954i
$791$		−	699.881i		−	0.884806i
$792$	−953.807	+	183.084i	−1.20430	+	0.231166i
$793$	−303.003			−0.382097
$794$	431.067	+	213.778i	0.542905	+	0.269242i
$795$			130.760i			0.164478i
$796$	1043.58	−	793.381i	1.31103	−	0.996709i
$797$	802.901			1.00740			0.503702	−	0.863877i	$-0.331971\pi$
$797$	802.901			1.00740			0.503702	+	0.863877i	$0.331971\pi$
$798$	−72.2297	+	145.646i	−0.0905134	+	0.182513i
$799$		−	50.6799i		−	0.0634291i
$800$	−252.228	+	281.208i	−0.315285	+	0.351509i
$801$	294.351			0.367479
$802$	−892.044	−	442.389i	−1.11227	−	0.551607i
$803$		−	945.238i		−	1.17713i
$804$	148.129	+	194.842i	0.184239	+	0.242341i
$805$	−59.6295			−0.0740739
$806$	141.130	−	284.578i	0.175099	−	0.353075i
$807$		−	80.8087i		−	0.100135i
$808$	239.972	+	1250.18i	0.296996	+	1.54725i
$809$	341.831			0.422535			0.211267	−	0.977428i	$-0.432241\pi$
$809$	341.831			0.422535			0.211267	+	0.977428i	$0.432241\pi$
$810$	−472.524	−	234.338i	−0.583363	−	0.289306i
$811$			1007.12i			1.24182i	0.783881	+	0.620911i	$0.213237\pi$
$811$			1007.12i			1.24182i	−0.783881	+	0.620911i	$0.786763\pi$
$812$	−122.495	+	93.1269i	−0.150856	+	0.114688i
$813$	54.4247			0.0669430
$814$	445.165	−	897.642i	0.546886	−	1.10275i
$815$			123.700i			0.151779i
$816$	35.6650	+	9.89902i	0.0437071	+	0.0121311i
$817$	411.741			0.503966
$818$	96.1519	+	47.6844i	0.117545	+	0.0582938i
$819$		−	166.521i		−	0.203322i
$820$	12.1335	+	15.9600i	0.0147970	+	0.0194634i
$821$	−1130.16			−1.37657			−0.688283	−	0.725442i	$-0.741635\pi$
$821$	−1130.16			−1.37657			−0.688283	+	0.725442i	$0.741635\pi$
$822$	98.2420	−	198.098i	0.119516	−	0.240995i
$823$			389.250i			0.472964i	0.971636	+	0.236482i	$0.0759945\pi$
$823$			389.250i			0.472964i	−0.971636	+	0.236482i	$0.924005\pi$
$824$	503.454	−	96.6381i	0.610987	−	0.117279i
$825$	92.5800			0.112218
$826$	−456.309	−	226.296i	−0.552432	−	0.273966i
$827$		−	173.744i		−	0.210089i	−0.994468	−	0.105044i	$-0.966502\pi$
$827$		−	173.744i		−	0.210089i	0.994468	−	0.105044i	$-0.0334985\pi$
$828$	98.9661	−	75.2389i	0.119524	−	0.0908682i
$829$	−1083.04			−1.30645			−0.653224	−	0.757165i	$-0.726584\pi$
$829$	−1083.04			−1.30645			−0.653224	+	0.757165i	$0.726584\pi$
$830$	−346.579	+	698.851i	−0.417565	+	0.841989i
$831$		−	155.571i		−	0.187209i
$832$	−248.482	+	99.0416i	−0.298656	+	0.119040i
$833$	115.269			0.138378
$834$	77.7486	+	38.5577i	0.0932237	+	0.0462322i
$835$		−	432.765i		−	0.518282i
$836$	1068.71	+	1405.74i	1.27837	+	1.68151i
$837$	377.061			0.450491
$838$	−467.012	+	941.694i	−0.557293	+	1.12374i
$839$			106.196i			0.126575i	0.997995	+	0.0632875i	$0.0201585\pi$
$839$			106.196i			0.126575i	−0.997995	+	0.0632875i	$0.979841\pi$
$840$	14.0994	+	73.4531i	0.0167849	+	0.0874442i
$841$	−770.675			−0.916379
$842$	32.7556	+	16.2444i	0.0389022	+	0.0192927i
$843$			144.046i			0.170874i
$844$	1038.30	−	789.368i	1.23022	−	0.935270i
$845$	−550.441			−0.651409
$846$	−94.8615	+	191.281i	−0.112129	+	0.226101i
$847$			341.233i			0.402872i
$848$	274.541	−	989.138i	0.323751	−	1.16644i
$849$	268.200			0.315901
$850$	87.2091	+	43.2494i	0.102599	+	0.0508816i
$851$			128.254i			0.150710i
$852$	170.375	+	224.104i	0.199970	+	0.263033i
$853$	443.180			0.519554			0.259777	−	0.965669i	$-0.416351\pi$
$853$	443.180			0.519554			0.259777	+	0.965669i	$0.416351\pi$
$854$	295.508	−	595.869i	0.346028	−	0.697739i
$855$			996.409i			1.16539i
$856$	−333.385	+	63.9933i	−0.389468	+	0.0747585i
$857$	−363.895			−0.424615			−0.212307	−	0.977203i	$-0.568098\pi$
$857$	−363.895			−0.424615			−0.212307	+	0.977203i	$0.568098\pi$
$858$	58.7319	+	29.1267i	0.0684521	+	0.0339472i
$859$		−	56.5417i		−	0.0658227i	−0.999458	−	0.0329114i	$-0.989522\pi$
$859$		−	56.5417i		−	0.0658227i	0.999458	−	0.0329114i	$-0.0104779\pi$
$860$	150.797	−	114.643i	0.175346	−	0.133306i
$861$	−3.55126			−0.00412457
$862$	108.287	−	218.353i	0.125623	−	0.253310i
$863$			672.942i			0.779770i	0.920863	+	0.389885i	$0.127485\pi$
$863$			672.942i			0.779770i	−0.920863	+	0.389885i	$0.872515\pi$
$864$	−236.371	−	212.011i	−0.273577	−	0.245384i
$865$	−744.734			−0.860965
$866$	−378.718	−	187.817i	−0.437318	−	0.216878i
$867$		−	9.53810i		−	0.0110013i
$868$	421.996	+	555.077i	0.486171	+	0.639490i
$869$	−2136.97			−2.45911
$870$	15.1871	−	30.6237i	0.0174565	−	0.0351996i
$871$			455.820i			0.523329i
$872$	−118.949	−	619.688i	−0.136410	−	0.710651i
$873$	1348.16			1.54429
$874$	−202.501	−	100.426i	−0.231694	−	0.114903i
$875$			613.293i			0.700906i
$876$	120.814	−	91.8485i	0.137915	−	0.104850i
$877$	−116.130			−0.132417			−0.0662084	−	0.997806i	$-0.521090\pi$
$877$	−116.130			−0.132417			−0.0662084	+	0.997806i	$0.521090\pi$
$878$	317.406	−	640.025i	0.361510	−	0.728958i
$879$		−	80.7598i		−	0.0918770i
$880$	782.818	+	217.276i	0.889566	+	0.246904i
$881$	−1387.76			−1.57521			−0.787605	−	0.616181i	$-0.788679\pi$
$881$	−1387.76			−1.57521			−0.787605	+	0.616181i	$0.788679\pi$
$882$	−435.060	−	215.758i	−0.493266	−	0.244624i
$883$			476.174i			0.539269i	0.962963	+	0.269634i	$0.0869028\pi$
$883$			476.174i			0.539269i	−0.962963	+	0.269634i	$0.913097\pi$
$884$	41.7179	+	54.8740i	0.0471921	+	0.0620746i
$885$	113.148			0.127850
$886$	−284.941	+	574.561i	−0.321603	+	0.648489i
$887$			1384.64i			1.56104i	0.625130	+	0.780521i	$0.285046\pi$
$887$			1384.64i			1.56104i	−0.625130	+	0.780521i	$0.714954\pi$
$888$	157.987	−	30.3257i	0.177913	−	0.0341505i
$889$	−147.286			−0.165676
$890$	−220.585	−	109.394i	−0.247848	−	0.122914i
$891$		−	1014.80i		−	1.13895i
$892$	145.814	−	110.855i	0.163469	−	0.124277i
$893$	388.204			0.434719
$894$	−42.5065	+	85.7111i	−0.0475464	+	0.0958737i
$895$			460.551i			0.514582i
$896$	47.5656	−	585.242i	0.0530866	−	0.653172i
$897$	−8.39156			−0.00935513
$898$	56.3215	+	27.9314i	0.0627189	+	0.0311040i
$899$		−	318.672i		−	0.354473i
$900$	−248.200	−	326.472i	−0.275778	−	0.362747i
$901$	−264.531			−0.293597
$902$	−17.1380	+	34.5575i	−0.0190000	+	0.0383120i
$903$			33.5539i			0.0371583i
$904$	−230.087	−	1198.68i	−0.254521	−	1.32597i
$905$	599.983			0.662964
$906$	−114.597	−	56.8318i	−0.126487	−	0.0627283i
$907$		−	1014.45i		−	1.11847i	−0.829010	−	0.559234i	$-0.811095\pi$
$907$		−	1014.45i		−	1.11847i	0.829010	−	0.559234i	$-0.188905\pi$
$908$	−207.873	+	158.035i	−0.228935	+	0.174048i
$909$	−1382.04			−1.52039
$910$	−61.8864	+	124.789i	−0.0680071	+	0.137131i
$911$		−	1260.63i		−	1.38379i	−0.722000	−	0.691893i	$-0.756777\pi$
$911$		−	1260.63i		−	1.38379i	0.722000	−	0.691893i	$-0.243223\pi$
$912$	−75.8257	+	273.191i	−0.0831422	+	0.299552i
$913$	−1500.87			−1.64389
$914$	1065.52	+	528.421i	1.16578	+	0.578141i
$915$			147.753i			0.161479i
$916$	977.601	+	1285.90i	1.06725	+	1.40382i
$917$	236.046			0.257411
$918$	−36.3535	+	73.3041i	−0.0396008	+	0.0798520i
$919$		−	758.349i		−	0.825189i	−0.910915	−	0.412595i	$-0.864623\pi$
$919$		−	758.349i		−	0.825189i	0.910915	−	0.412595i	$-0.135377\pi$
$920$	−102.127	+	19.6032i	−0.111007	+	0.0213079i
$921$	−69.1569			−0.0750889
$922$	−180.752	−	89.6400i	−0.196044	−	0.0972234i
$923$			524.276i			0.568013i
$924$	−114.558	+	87.0925i	−0.123981	+	0.0942560i
$925$	423.089			0.457393
$926$	390.812	−	788.043i	0.422043	−	0.851018i
$927$			556.553i			0.600381i
$928$	−179.181	+	199.768i	−0.193083	+	0.215267i
$929$	1282.78			1.38082			0.690412	−	0.723417i	$-0.257429\pi$
$929$	1282.78			1.38082			0.690412	+	0.723417i	$0.257429\pi$
$930$	−138.769	−	68.8191i	−0.149214	−	0.0739991i
$931$			882.952i			0.948391i
$932$	583.250	+	767.184i	0.625805	+	0.823159i
$933$	−277.754			−0.297700
$934$	−291.746	+	588.283i	−0.312361	+	0.629853i
$935$		−	209.354i		−	0.223908i
$936$	−54.7438	−	285.197i	−0.0584869	−	0.304698i
$937$	1552.93			1.65734			0.828670	−	0.559737i	$-0.189098\pi$
$937$	1552.93			1.65734			0.828670	+	0.559737i	$0.189098\pi$
$938$	−896.389	−	444.544i	−0.955639	−	0.473927i
$939$			82.7775i			0.0881549i
$940$	142.177	−	108.090i	0.151252	−	0.114989i
$941$	−889.670			−0.945452			−0.472726	−	0.881210i	$-0.656730\pi$
$941$	−889.670			−0.945452			−0.472726	+	0.881210i	$0.656730\pi$
$942$	103.784	−	209.273i	0.110175	−	0.222159i
$943$		−	4.93754i		−	0.00523599i
$944$	−855.909	−	237.562i	−0.906684	−	0.251655i
$945$	−165.344			−0.174967
$946$	326.515	+	161.928i	0.345153	+	0.171171i
$947$		−	1236.34i		−	1.30554i	−0.757557	−	0.652769i	$-0.773607\pi$
$947$		−	1236.34i		−	1.30554i	0.757557	−	0.652769i	$-0.226393\pi$
$948$	−207.648	−	273.132i	−0.219038	−	0.288114i
$949$	282.635			0.297824
$950$	−331.287	+	668.015i	−0.348723	+	0.703174i
$951$			129.647i			0.136327i
$952$	−148.598	+	28.5234i	−0.156090	+	0.0299616i
$953$	18.5950			0.0195120			0.00975601	−	0.999952i	$-0.496895\pi$
$953$	18.5950			0.0195120			0.00975601	+	0.999952i	$0.496895\pi$
$954$	998.419	+	495.143i	1.04656	+	0.519018i
$955$			849.263i			0.889280i
$956$	903.748	−	687.073i	0.945343	−	0.718696i
$957$	65.7681			0.0687232
$958$	168.808	−	340.388i	0.176208	−	0.355311i
$959$			903.942i			0.942588i
$960$	48.2955	+	121.167i	0.0503079	+	0.126216i
$961$	−483.032			−0.502635
$962$	268.404	+	133.109i	0.279006	+	0.138367i
$963$		−	368.547i		−	0.382707i
$964$	347.286	+	456.805i	0.360255	+	0.473865i
$965$	−456.205			−0.472751
$966$	8.18397	−	16.5024i	0.00847202	−	0.0170832i
$967$		−	540.325i		−	0.558765i	−0.960180	−	0.279382i	$-0.909870\pi$
$967$		−	540.325i		−	0.558765i	0.960180	−	0.279382i	$-0.0901297\pi$
$968$	112.181	+	584.424i	0.115889	+	0.603744i
$969$	73.0611			0.0753984
$970$	−1010.30	−	501.036i	−1.04155	−	0.516532i
$971$			1484.57i			1.52891i	0.644678	+	0.764454i	$0.276991\pi$
$971$			1484.57i			1.52891i	−0.644678	+	0.764454i	$0.723009\pi$
$972$	414.070	−	314.796i	0.425998	−	0.323864i
$973$	−354.776			−0.364620
$974$	731.604	−	1475.22i	0.751134	−	1.51460i
$975$			27.6823i			0.0283921i
$976$	310.220	−	1117.68i	0.317848	−	1.14517i
$977$	292.663			0.299552			0.149776	−	0.988720i	$-0.452145\pi$
$977$	292.663			0.299552			0.149776	+	0.988720i	$0.452145\pi$
$978$	−34.2338	−	16.9775i	−0.0350039	−	0.0173594i
$979$		−	473.732i		−	0.483894i
$980$	245.846	+	323.375i	0.250863	+	0.329975i
$981$	685.047			0.698315
$982$	126.341	−	254.757i	0.128657	−	0.259427i
$983$			1541.91i			1.56858i	0.620396	+	0.784289i	$0.286972\pi$
$983$			1541.91i			1.56858i	−0.620396	+	0.784289i	$0.713028\pi$
$984$	−6.08219	+	1.16748i	−0.00618108	+	0.00118646i
$985$	−524.325			−0.532310
$986$	61.9527	+	30.7240i	0.0628323	+	0.0311603i
$987$			31.6358i			0.0320525i
$988$	−420.330	+	319.555i	−0.425435	+	0.323437i
$989$	−46.6522			−0.0471711
$990$	−391.864	+	790.164i	−0.395822	+	0.798145i
$991$		−	1027.68i		−	1.03701i	−0.855073	−	0.518507i	$-0.826488\pi$
$991$		−	1027.68i		−	1.03701i	0.855073	−	0.518507i	$-0.173512\pi$
$992$	905.230	+	811.941i	0.912530	+	0.818489i
$993$	−241.286			−0.242987
$994$	−1031.01	−	511.306i	−1.03723	−	0.514393i
$995$		−	1190.49i		−	1.19647i
$996$	−145.839	−	191.830i	−0.146424	−	0.192601i
$997$	−1325.66			−1.32965			−0.664825	−	0.747000i	$-0.731494\pi$
$997$	−1325.66			−1.32965			−0.664825	+	0.747000i	$0.731494\pi$
$998$	152.929	−	308.370i	0.153236	−	0.308988i
$999$			355.630i			0.355986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	68.3.c.a.35.3	✓	16
3.2	odd	2		612.3.f.a.307.14		16
4.3	odd	2	inner	68.3.c.a.35.4	yes	16
8.3	odd	2		1088.3.d.d.511.8		16
8.5	even	2		1088.3.d.d.511.9		16
12.11	even	2		612.3.f.a.307.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
68.3.c.a.35.3	✓	16	1.1	even	1	trivial
68.3.c.a.35.4	yes	16	4.3	odd	2	inner
612.3.f.a.307.13		16	12.11	even	2
612.3.f.a.307.14		16	3.2	odd	2
1088.3.d.d.511.8		16	8.3	odd	2
1088.3.d.d.511.9		16	8.5	even	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:	\( N \)	\(=\)	\( 68 = 2^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	68.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.79176 - 0.888585i) q^{2} -0.561065i q^{3} +(2.42083 + 3.18427i) q^{4} +3.63253 q^{5} +(-0.498554 + 1.00530i) q^{6} -4.58728i q^{7} +(-1.50807 - 7.85657i) q^{8} +8.68521 q^{9} +O(q^{10})\)	\(q+(-1.79176 - 0.888585i) q^{2} -0.561065i q^{3} +(2.42083 + 3.18427i) q^{4} +3.63253 q^{5} +(-0.498554 + 1.00530i) q^{6} -4.58728i q^{7} +(-1.50807 - 7.85657i) q^{8} +8.68521 q^{9} +(-6.50863 - 3.22781i) q^{10} -13.9781i q^{11} +(1.78658 - 1.35825i) q^{12} +4.17958 q^{13} +(-4.07619 + 8.21932i) q^{14} -2.03808i q^{15} +(-4.27912 + 15.4172i) q^{16} +4.12311 q^{17} +(-15.5618 - 7.71754i) q^{18} +31.5827i q^{19} +(8.79375 + 11.5669i) q^{20} -2.57376 q^{21} +(-12.4207 + 25.0454i) q^{22} -3.57847i q^{23} +(-4.40805 + 0.846126i) q^{24} -11.8047 q^{25} +(-7.48882 - 3.71391i) q^{26} -9.92255i q^{27} +(14.6071 - 11.1050i) q^{28} -8.38600 q^{29} +(-1.81101 + 3.65176i) q^{30} +38.0004i q^{31} +(21.3666 - 23.8216i) q^{32} -7.84261 q^{33} +(-7.38763 - 3.66373i) q^{34} -16.6634i q^{35} +(21.0254 + 27.6560i) q^{36} -35.8406 q^{37} +(28.0639 - 56.5887i) q^{38} -2.34501i q^{39} +(-5.47811 - 28.5392i) q^{40} +1.37979 q^{41} +(4.61157 + 2.28701i) q^{42} -13.0369i q^{43} +(44.5099 - 33.8386i) q^{44} +31.5492 q^{45} +(-3.17977 + 6.41177i) q^{46} -12.2917i q^{47} +(8.65003 + 2.40086i) q^{48} +27.9569 q^{49} +(21.1513 + 10.4895i) q^{50} -2.31333i q^{51} +(10.1181 + 13.3089i) q^{52} -64.1582 q^{53} +(-8.81702 + 17.7789i) q^{54} -50.7757i q^{55} +(-36.0403 + 6.91795i) q^{56} +17.7199 q^{57} +(15.0257 + 7.45167i) q^{58} +55.5166i q^{59} +(6.48980 - 4.93386i) q^{60} -72.4961 q^{61} +(33.7666 - 68.0878i) q^{62} -39.8415i q^{63} +(-59.4514 + 23.6966i) q^{64} +15.1824 q^{65} +(14.0521 + 6.96882i) q^{66} +109.059i q^{67} +(9.98136 + 13.1291i) q^{68} -2.00775 q^{69} +(-14.8069 + 29.8569i) q^{70} +125.437i q^{71} +(-13.0979 - 68.2359i) q^{72} +67.6229 q^{73} +(64.2178 + 31.8474i) q^{74} +6.62323i q^{75} +(-100.568 + 76.4564i) q^{76} -64.1214 q^{77} +(-2.08374 + 4.20171i) q^{78} -152.880i q^{79} +(-15.5440 + 56.0033i) q^{80} +72.5997 q^{81} +(-2.47226 - 1.22606i) q^{82} -107.373i q^{83} +(-6.23065 - 8.19555i) q^{84} +14.9773 q^{85} +(-11.5844 + 23.3591i) q^{86} +4.70509i q^{87} +(-109.820 + 21.0800i) q^{88} +33.8911 q^{89} +(-56.5288 - 28.0342i) q^{90} -19.1729i q^{91} +(11.3948 - 8.66287i) q^{92} +21.3207 q^{93} +(-10.9222 + 22.0238i) q^{94} +114.725i q^{95} +(-13.3654 - 11.9881i) q^{96} +155.225 q^{97} +(-50.0921 - 24.8420i) q^{98} -121.403i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 6 q^{4} - 6 q^{6} - 2 q^{8} - 48 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 - 6 * q^4 - 6 * q^6 - 2 * q^8 - 48 * q^9	\( 16 q - 2 q^{2} - 6 q^{4} - 6 q^{6} - 2 q^{8} - 48 q^{9} + 10 q^{10} + 6 q^{12} - 16 q^{13} - 16 q^{14} + 50 q^{16} + 58 q^{18} - 74 q^{20} + 32 q^{21} + 18 q^{22} + 86 q^{24} + 96 q^{25} - 56 q^{26} - 16 q^{28} + 16 q^{29} - 64 q^{30} - 122 q^{32} - 48 q^{33} - 18 q^{36} + 16 q^{37} + 22 q^{40} + 16 q^{41} + 8 q^{42} + 118 q^{44} - 128 q^{45} + 52 q^{46} - 106 q^{48} - 32 q^{49} - 146 q^{50} - 72 q^{52} - 16 q^{53} + 356 q^{54} + 88 q^{56} - 112 q^{57} - 214 q^{58} + 320 q^{60} + 112 q^{61} - 112 q^{62} + 42 q^{64} - 16 q^{65} + 364 q^{66} - 144 q^{69} + 136 q^{70} - 190 q^{72} + 128 q^{73} + 62 q^{74} - 112 q^{76} + 272 q^{77} - 556 q^{78} - 370 q^{80} + 384 q^{81} - 88 q^{82} + 312 q^{84} + 172 q^{86} - 250 q^{88} - 336 q^{89} - 326 q^{90} + 164 q^{92} + 16 q^{93} - 352 q^{94} + 150 q^{96} - 304 q^{97} + 110 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 6 * q^4 - 6 * q^6 - 2 * q^8 - 48 * q^9 + 10 * q^10 + 6 * q^12 - 16 * q^13 - 16 * q^14 + 50 * q^16 + 58 * q^18 - 74 * q^20 + 32 * q^21 + 18 * q^22 + 86 * q^24 + 96 * q^25 - 56 * q^26 - 16 * q^28 + 16 * q^29 - 64 * q^30 - 122 * q^32 - 48 * q^33 - 18 * q^36 + 16 * q^37 + 22 * q^40 + 16 * q^41 + 8 * q^42 + 118 * q^44 - 128 * q^45 + 52 * q^46 - 106 * q^48 - 32 * q^49 - 146 * q^50 - 72 * q^52 - 16 * q^53 + 356 * q^54 + 88 * q^56 - 112 * q^57 - 214 * q^58 + 320 * q^60 + 112 * q^61 - 112 * q^62 + 42 * q^64 - 16 * q^65 + 364 * q^66 - 144 * q^69 + 136 * q^70 - 190 * q^72 + 128 * q^73 + 62 * q^74 - 112 * q^76 + 272 * q^77 - 556 * q^78 - 370 * q^80 + 384 * q^81 - 88 * q^82 + 312 * q^84 + 172 * q^86 - 250 * q^88 - 336 * q^89 - 326 * q^90 + 164 * q^92 + 16 * q^93 - 352 * q^94 + 150 * q^96 - 304 * q^97 + 110 * q^98

Introduction

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