LMFDB - Embedded newform 207.2.i.d.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(55,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("207.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.i (of order $11$, degree $10$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
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} - 7 x^{19} + 24 x^{18} - 70 x^{17} + 209 x^{16} - 527 x^{15} + 1115 x^{14} - 2187 x^{13} + \cdots + 529 $ x^20 - 7x^19 + 24x^18 - 70x^17 + 209x^16 - 527x^15 + 1115x^14 - 2187x^13 + 4165x^12 - 7040x^11 + 10649x^10 - 13519x^9 + 15111x^8 - 12101x^7 + 8244x^6 - 2837x^5 + 1859x^4 - 1730x^3 + 1957x^2 - 1656*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 69)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			73.1
Root			$2.55199 + 0.749331i$ of defining polynomial
Character	$\chi$	$=$	207.73
Dual form			207.2.i.d.190.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.236364 + 0.517565i) q^{2} +(1.09772 - 1.26683i) q^{4} +(-2.27341 - 1.46103i) q^{5} +(-0.481879 - 3.35154i) q^{7} +(2.00700 + 0.589308i) q^{8} +O(q^{10})$	\(q+(0.236364 + 0.517565i) q^{2} +(1.09772 - 1.26683i) q^{4} +(-2.27341 - 1.46103i) q^{5} +(-0.481879 - 3.35154i) q^{7} +(2.00700 + 0.589308i) q^{8} +(0.218827 - 1.52197i) q^{10} +(1.86448 - 4.08263i) q^{11} +(-0.891052 + 6.19740i) q^{13} +(1.62074 - 1.04159i) q^{14} +(-0.307736 - 2.14035i) q^{16} +(2.00981 + 2.31944i) q^{17} +(-0.686559 + 0.792332i) q^{19} +(-4.34644 + 1.27623i) q^{20} +2.55372 q^{22} +(3.18128 + 3.58879i) q^{23} +(0.956704 + 2.09489i) q^{25} +(-3.41817 + 1.00367i) q^{26} +(-4.77480 - 3.06858i) q^{28} +(-1.45248 - 1.67625i) q^{29} +(6.22433 + 1.82763i) q^{31} +(4.55438 - 2.92692i) q^{32} +(-0.725416 + 1.58844i) q^{34} +(-3.80120 + 8.32347i) q^{35} +(0.235181 - 0.151142i) q^{37} +(-0.572361 - 0.168060i) q^{38} +(-3.70173 - 4.27203i) q^{40} +(-1.19434 - 0.767558i) q^{41} +(-1.76507 + 0.518271i) q^{43} +(-3.12534 - 6.84355i) q^{44} +(-1.10549 + 2.49478i) q^{46} -4.74565 q^{47} +(-4.28417 + 1.25794i) q^{49} +(-0.858110 + 0.990312i) q^{50} +(6.87295 + 7.93180i) q^{52} +(0.768306 + 5.34369i) q^{53} +(-10.2036 + 6.55744i) q^{55} +(1.00796 - 7.01051i) q^{56} +(0.524255 - 1.14796i) q^{58} +(-1.54995 + 10.7801i) q^{59} +(-4.49474 - 1.31978i) q^{61} +(0.525291 + 3.65348i) q^{62} +(-1.04683 - 0.672754i) q^{64} +(11.0803 - 12.7874i) q^{65} +(-0.0835538 - 0.182957i) q^{67} +5.14454 q^{68} -5.20640 q^{70} +(1.25365 + 2.74512i) q^{71} +(7.91764 - 9.13745i) q^{73} +(0.133814 + 0.0859970i) q^{74} +(0.250104 + 1.73951i) q^{76} +(-14.5816 - 4.28153i) q^{77} +(-1.10543 + 7.68843i) q^{79} +(-2.42751 + 5.31551i) q^{80} +(0.114961 - 0.799573i) q^{82} +(12.4179 - 7.98047i) q^{83} +(-1.18034 - 8.20944i) q^{85} +(-0.685438 - 0.791037i) q^{86} +(6.14793 - 7.09509i) q^{88} +(-0.838282 + 0.246142i) q^{89} +21.2002 q^{91} +(8.03854 - 0.0906751i) q^{92} +(-1.12170 - 2.45618i) q^{94} +(2.71845 - 0.798210i) q^{95} +(9.73536 + 6.25653i) q^{97} +(-1.66369 - 1.92000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8}+O(q^{10}) $ 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 10 * q^8	$ 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8} - 18 q^{10} + 16 q^{11} + 14 q^{13} + 22 q^{14} - 8 q^{16} - 11 q^{17} - 11 q^{19} - 57 q^{20} + 26 q^{22} - 4 q^{25} + 14 q^{26} - 14 q^{28} - 12 q^{29} + 41 q^{31} + 46 q^{32} - 3 q^{34} + 26 q^{35} - 18 q^{37} - 70 q^{38} - 13 q^{40} - 10 q^{43} + 3 q^{44} - 24 q^{46} - 18 q^{47} - 10 q^{49} - 33 q^{50} + 61 q^{52} + 20 q^{53} - 17 q^{55} - 6 q^{56} - 37 q^{58} - 40 q^{59} - 12 q^{61} + 89 q^{62} - 2 q^{64} + 51 q^{65} - 47 q^{67} + 12 q^{68} + 32 q^{70} + 47 q^{71} + 39 q^{73} + 50 q^{74} - 39 q^{76} - 22 q^{77} - 2 q^{79} - 12 q^{80} + 26 q^{82} + 52 q^{83} + 35 q^{85} - 34 q^{86} + 30 q^{88} - 36 q^{89} + 8 q^{91} + 19 q^{92} + 21 q^{94} - 89 q^{95} - 85 q^{98}+O(q^{100}) $ 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 10 * q^8 - 18 * q^10 + 16 * q^11 + 14 * q^13 + 22 * q^14 - 8 * q^16 - 11 * q^17 - 11 * q^19 - 57 * q^20 + 26 * q^22 - 4 * q^25 + 14 * q^26 - 14 * q^28 - 12 * q^29 + 41 * q^31 + 46 * q^32 - 3 * q^34 + 26 * q^35 - 18 * q^37 - 70 * q^38 - 13 * q^40 - 10 * q^43 + 3 * q^44 - 24 * q^46 - 18 * q^47 - 10 * q^49 - 33 * q^50 + 61 * q^52 + 20 * q^53 - 17 * q^55 - 6 * q^56 - 37 * q^58 - 40 * q^59 - 12 * q^61 + 89 * q^62 - 2 * q^64 + 51 * q^65 - 47 * q^67 + 12 * q^68 + 32 * q^70 + 47 * q^71 + 39 * q^73 + 50 * q^74 - 39 * q^76 - 22 * q^77 - 2 * q^79 - 12 * q^80 + 26 * q^82 + 52 * q^83 + 35 * q^85 - 34 * q^86 + 30 * q^88 - 36 * q^89 + 8 * q^91 + 19 * q^92 + 21 * q^94 - 89 * q^95 - 85 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	0.236364	+	0.517565i	0.167135	+	0.365974i	0.974604	−	0.223936i	$-0.0718907\pi$
$2$	0.236364	+	0.517565i	0.167135	+	0.365974i	−0.807469	+	0.589910i	$0.799163\pi$
$3$		0			0
$3$		0			0
$4$	1.09772	−	1.26683i	0.548858	−	0.633416i
$5$	−2.27341	−	1.46103i	−1.01670	−	0.653393i	−0.0775811	−	0.996986i	$-0.524720\pi$
$5$	−2.27341	−	1.46103i	−1.01670	−	0.653393i	−0.939119	+	0.343593i	$0.888356\pi$
$6$		0			0
$7$	−0.481879	−	3.35154i	−0.182133	−	1.26676i	−0.851707	−	0.524018i	$-0.824432\pi$
$7$	−0.481879	−	3.35154i	−0.182133	−	1.26676i	0.669574	−	0.742745i	$-0.266477\pi$
$8$	2.00700	+	0.589308i	0.709581	+	0.208352i
$9$		0			0
$10$	0.218827	−	1.52197i	0.0691990	−	0.481290i
$11$	1.86448	−	4.08263i	0.562161	−	1.23096i	−0.388707	−	0.921362i	$-0.627078\pi$
$11$	1.86448	−	4.08263i	0.562161	−	1.23096i	0.950867	−	0.309599i	$-0.100195\pi$
$12$		0			0
$13$	−0.891052	+	6.19740i	−0.247133	+	1.71885i	0.367488	+	0.930028i	$0.380218\pi$
$13$	−0.891052	+	6.19740i	−0.247133	+	1.71885i	−0.614621	+	0.788822i	$0.710691\pi$
$14$	1.62074	−	1.04159i	0.433161	−	0.278376i
$15$		0			0
$16$	−0.307736	−	2.14035i	−0.0769340	−	0.535088i
$17$	2.00981	+	2.31944i	0.487450	+	0.562548i	0.945183	−	0.326542i	$-0.105884\pi$
$17$	2.00981	+	2.31944i	0.487450	+	0.562548i	−0.457732	+	0.889090i	$0.651338\pi$
$18$		0			0
$19$	−0.686559	+	0.792332i	−0.157507	+	0.181773i	−0.829018	−	0.559221i	$-0.811100\pi$
$19$	−0.686559	+	0.792332i	−0.157507	+	0.181773i	0.671511	+	0.740995i	$0.265646\pi$
$20$	−4.34644	+	1.27623i	−0.971894	+	0.285374i
$21$		0			0
$22$	2.55372			0.544455
$23$	3.18128	+	3.58879i	0.663343	+	0.748315i
$23$	3.18128	+	3.58879i	0.663343	+	0.748315i
$24$		0			0
$25$	0.956704	+	2.09489i	0.191341	+	0.418978i
$26$	−3.41817	+	1.00367i	−0.670358	+	0.196835i
$27$		0			0
$28$	−4.77480	−	3.06858i	−0.902353	−	0.579907i
$29$	−1.45248	−	1.67625i	−0.269719	−	0.311272i	0.604691	−	0.796460i	$-0.293297\pi$
$29$	−1.45248	−	1.67625i	−0.269719	−	0.311272i	−0.874410	+	0.485188i	$0.838751\pi$
$30$		0			0
$31$	6.22433	+	1.82763i	1.11792	+	0.328252i	0.787951	−	0.615739i	$-0.211142\pi$
$31$	6.22433	+	1.82763i	1.11792	+	0.328252i	0.329973	+	0.943990i	$0.392960\pi$
$32$	4.55438	−	2.92692i	0.805108	−	0.517412i
$33$		0			0
$34$	−0.725416	+	1.58844i	−0.124408	+	0.272415i
$35$	−3.80120	+	8.32347i	−0.642520	+	1.40692i
$36$		0			0
$37$	0.235181	−	0.151142i	0.0386635	−	0.0248475i	−0.521166	−	0.853455i	$-0.674503\pi$
$37$	0.235181	−	0.151142i	0.0386635	−	0.0248475i	0.559830	+	0.828608i	$0.310867\pi$
$38$	−0.572361	−	0.168060i	−0.0928492	−	0.0272630i
$39$		0			0
$40$	−3.70173	−	4.27203i	−0.585295	−	0.675467i
$41$	−1.19434	−	0.767558i	−0.186525	−	0.119872i	0.444046	−	0.896004i	$-0.353543\pi$
$41$	−1.19434	−	0.767558i	−0.186525	−	0.119872i	−0.630571	+	0.776132i	$0.717179\pi$
$42$		0			0
$43$	−1.76507	+	0.518271i	−0.269171	+	0.0790356i	−0.413533	−	0.910489i	$-0.635705\pi$
$43$	−1.76507	+	0.518271i	−0.269171	+	0.0790356i	0.144362	+	0.989525i	$0.453887\pi$
$44$	−3.12534	−	6.84355i	−0.471163	−	1.03170i
$45$		0			0
$46$	−1.10549	+	2.49478i	−0.162996	+	0.367835i
$47$	−4.74565			−0.692225			−0.346112	−	0.938193i	$-0.612498\pi$
$47$	−4.74565			−0.692225			−0.346112	+	0.938193i	$0.612498\pi$
$48$		0			0
$49$	−4.28417	+	1.25794i	−0.612024	+	0.179706i
$50$	−0.858110	+	0.990312i	−0.121355	+	0.140051i
$51$		0			0
$52$	6.87295	+	7.93180i	0.953106	+	1.09994i
$53$	0.768306	+	5.34369i	0.105535	+	0.734012i	0.972035	+	0.234835i	$0.0754550\pi$
$53$	0.768306	+	5.34369i	0.105535	+	0.734012i	−0.866500	+	0.499177i	$0.833636\pi$
$54$		0			0
$55$	−10.2036	+	6.55744i	−1.37585	+	0.884205i
$56$	1.00796	−	7.01051i	0.134694	−	0.936819i
$57$		0			0
$58$	0.524255	−	1.14796i	0.0688380	−	0.150734i
$59$	−1.54995	+	10.7801i	−0.201786	+	1.40346i	0.597193	+	0.802097i	$0.296283\pi$
$59$	−1.54995	+	10.7801i	−0.201786	+	1.40346i	−0.798980	+	0.601358i	$0.794627\pi$
$60$		0			0
$61$	−4.49474	−	1.31978i	−0.575493	−	0.168980i	−0.0189815	−	0.999820i	$-0.506042\pi$
$61$	−4.49474	−	1.31978i	−0.575493	−	0.168980i	−0.556512	+	0.830840i	$0.687861\pi$
$62$	0.525291	+	3.65348i	0.0667121	+	0.463993i
$63$		0			0
$64$	−1.04683	−	0.672754i	−0.130853	−	0.0840943i
$65$	11.0803	−	12.7874i	1.37435	−	1.58608i
$66$		0			0
$67$	−0.0835538	−	0.182957i	−0.0102077	−	0.0223518i	0.904459	−	0.426560i	$-0.140275\pi$
$67$	−0.0835538	−	0.182957i	−0.0102077	−	0.0223518i	−0.914667	+	0.404208i	$0.867547\pi$
$68$	5.14454			0.623868
$69$		0			0
$70$	−5.20640			−0.622284
$71$	1.25365	+	2.74512i	0.148781	+	0.325786i	0.969319	−	0.245807i	$-0.0790530\pi$
$71$	1.25365	+	2.74512i	0.148781	+	0.325786i	−0.820537	+	0.571593i	$0.806326\pi$
$72$		0			0
$73$	7.91764	−	9.13745i	0.926690	−	1.06946i	−0.0707172	−	0.997496i	$-0.522529\pi$
$73$	7.91764	−	9.13745i	0.926690	−	1.06946i	0.997407	−	0.0719611i	$-0.0229257\pi$
$74$	0.133814	+	0.0859970i	0.0155556	+	0.00999695i
$75$		0			0
$76$	0.250104	+	1.73951i	0.0286889	+	0.199535i
$77$	−14.5816	−	4.28153i	−1.66172	−	0.487926i
$78$		0			0
$79$	−1.10543	+	7.68843i	−0.124371	+	0.865016i	0.828142	+	0.560518i	$0.189398\pi$
$79$	−1.10543	+	7.68843i	−0.124371	+	0.865016i	−0.952513	+	0.304498i	$0.901511\pi$
$80$	−2.42751	+	5.31551i	−0.271404	+	0.594292i
$81$		0			0
$82$	0.114961	−	0.799573i	0.0126954	−	0.0882981i
$83$	12.4179	−	7.98047i	1.36304	−	0.875971i	0.364562	−	0.931179i	$-0.381219\pi$
$83$	12.4179	−	7.98047i	1.36304	−	0.875971i	0.998475	+	0.0552086i	$0.0175824\pi$
$84$		0			0
$85$	−1.18034	−	8.20944i	−0.128026	−	0.890439i
$86$	−0.685438	−	0.791037i	−0.0739127	−	0.0852997i
$87$		0			0
$88$	6.14793	−	7.09509i	0.655371	−	0.756339i
$89$	−0.838282	+	0.246142i	−0.0888577	+	0.0260910i	−0.325859	−	0.945418i	$-0.605654\pi$
$89$	−0.838282	+	0.246142i	−0.0888577	+	0.0260910i	0.237002	+	0.971509i	$0.423835\pi$
$90$		0			0
$91$	21.2002			2.22239
$92$	8.03854	−	0.0906751i	0.838076	−	0.00945354i
$93$		0			0
$94$	−1.12170	−	2.45618i	−0.115695	−	0.253336i
$95$	2.71845	−	0.798210i	0.278907	−	0.0818946i
$96$		0			0
$97$	9.73536	+	6.25653i	0.988476	+	0.635255i	0.931737	−	0.363134i	$-0.118293\pi$
$97$	9.73536	+	6.25653i	0.988476	+	0.635255i	0.0567390	+	0.998389i	$0.481930\pi$
$98$	−1.66369	−	1.92000i	−0.168058	−	0.193949i
$99$		0			0
$100$	3.70406	+	1.08761i	0.370406	+	0.108761i
$101$	−7.93886	+	5.10200i	−0.789947	+	0.507668i	−0.872321	−	0.488934i	$-0.837386\pi$
$101$	−7.93886	+	5.10200i	−0.789947	+	0.507668i	0.0823744	+	0.996601i	$0.473750\pi$
$102$		0			0
$103$	1.66695	−	3.65011i	0.164250	−	0.359656i	−0.809555	−	0.587044i	$-0.800291\pi$
$103$	1.66695	−	3.65011i	0.164250	−	0.359656i	0.973804	+	0.227388i	$0.0730186\pi$
$104$	−5.44052	+	11.9131i	−0.533487	+	1.16817i
$105$		0			0
$106$	−2.58410	+	1.66070i	−0.250990	+	0.161302i
$107$	3.52529	+	1.03512i	0.340803	+	0.100069i	0.447655	−	0.894206i	$-0.352259\pi$
$107$	3.52529	+	1.03512i	0.340803	+	0.100069i	−0.106853	+	0.994275i	$0.534077\pi$
$108$		0			0
$109$	−8.78273	−	10.1358i	−0.841233	−	0.970835i	0.158631	−	0.987338i	$-0.449292\pi$
$109$	−8.78273	−	10.1358i	−0.841233	−	0.970835i	−0.999864	+	0.0165033i	$0.994747\pi$
$110$	−5.80566	−	3.73107i	−0.553548	−	0.355744i
$111$		0			0
$112$	−7.02518	+	2.06278i	−0.663817	+	0.194914i
$113$	−0.288666	−	0.632091i	−0.0271554	−	0.0594621i	0.895568	−	0.444924i	$-0.146769\pi$
$113$	−0.288666	−	0.632091i	−0.0271554	−	0.0594621i	−0.922724	+	0.385462i	$0.874042\pi$
$114$		0			0
$115$	−1.98902	−	12.8068i	−0.185477	−	1.19424i
$116$	−3.71794			−0.345202
$117$		0			0
$118$	−5.94578	+	1.74584i	−0.547353	+	0.160717i
$119$	6.80522	−	7.85365i	0.623834	−	0.719943i
$120$		0			0
$121$	−5.98816	−	6.91070i	−0.544378	−	0.628246i
$122$	−0.379326	−	2.63827i	−0.0343425	−	0.238858i
$123$		0			0
$124$	9.14785	−	5.87897i	0.821501	−	0.527947i
$125$	−1.03724	+	7.21419i	−0.0927739	+	0.645257i
$126$		0			0
$127$	−4.54632	+	9.95505i	−0.403421	+	0.883368i	0.593491	+	0.804840i	$0.297749\pi$
$127$	−4.54632	+	9.95505i	−0.403421	+	0.883368i	−0.996912	+	0.0785275i	$0.974978\pi$
$128$	1.64169	−	11.4182i	0.145106	−	1.00924i
$129$		0			0
$130$	9.23729	+	2.71231i	0.810164	+	0.237886i
$131$	−0.503437	−	3.50148i	−0.0439855	−	0.305926i	−0.999924	−	0.0123577i	$-0.996066\pi$
$131$	−0.503437	−	3.50148i	−0.0439855	−	0.305926i	0.955938	−	0.293568i	$-0.0948428\pi$
$132$		0			0
$133$	2.98637	+	1.91922i	0.258951	+	0.166418i
$134$	0.0749432	−	0.0864890i	0.00647410	−	0.00747152i
$135$		0			0
$136$	2.66682	+	5.83951i	0.228678	+	0.500734i
$137$	−12.7925			−1.09294			−0.546469	−	0.837479i	$-0.684028\pi$
$137$	−12.7925			−1.09294			−0.546469	+	0.837479i	$0.684028\pi$
$138$		0			0
$139$	8.21741			0.696992			0.348496	−	0.937310i	$-0.386693\pi$
$139$	8.21741			0.696992			0.348496	+	0.937310i	$0.386693\pi$
$140$	6.37179	+	13.9523i	0.538515	+	1.17918i
$141$		0			0
$142$	−1.12446	+	1.29769i	−0.0943625	+	0.108900i
$143$	23.6404	+	15.1928i	1.97691	+	1.27048i
$144$		0			0
$145$	0.853026	+	5.93293i	0.0708399	+	0.492703i
$146$	6.60067	+	1.93813i	0.546275	+	0.160401i
$147$		0			0
$148$	0.0666909	−	0.463846i	0.00548196	−	0.0381279i
$149$	7.73403	−	16.9352i	0.633597	−	1.38738i	−0.271608	−	0.962408i	$-0.587555\pi$
$149$	7.73403	−	16.9352i	0.633597	−	1.38738i	0.905205	−	0.424975i	$-0.139717\pi$
$150$		0			0
$151$	0.778374	−	5.41371i	0.0633432	−	0.440562i	−0.933327	−	0.359027i	$-0.883109\pi$
$151$	0.778374	−	5.41371i	0.0633432	−	0.440562i	0.996670	−	0.0815349i	$-0.0259822\pi$
$152$	−1.84485	+	1.18561i	−0.149637	+	0.0961659i
$153$		0			0
$154$	−1.23058	−	8.55890i	−0.0991633	−	0.689696i
$155$	−11.4802	−	13.2489i	−0.922115	−	1.06418i
$156$		0			0
$157$	−10.7637	+	12.4219i	−0.859033	+	0.991377i	0.140966	+	0.990014i	$0.454979\pi$
$157$	−10.7637	+	12.4219i	−0.859033	+	0.991377i	−0.999999	+	0.00136270i	$0.999566\pi$
$158$	−4.24055	+	1.24514i	−0.337360	+	0.0990577i
$159$		0			0
$160$	−14.6303			−1.15663
$161$	10.4950	−	12.3916i	0.827121	−	0.976592i
$162$		0			0
$163$	4.16078	+	9.11084i	0.325898	+	0.713616i	0.999680	−	0.0253139i	$-0.00805853\pi$
$163$	4.16078	+	9.11084i	0.325898	+	0.713616i	−0.673782	+	0.738930i	$0.735331\pi$
$164$	−2.28342	+	0.670472i	−0.178305	+	0.0523551i
$165$		0			0
$166$	7.06554	+	4.54075i	0.548393	+	0.352430i
$167$	−4.84536	−	5.59184i	−0.374945	−	0.432709i	0.536646	−	0.843807i	$-0.319691\pi$
$167$	−4.84536	−	5.59184i	−0.374945	−	0.432709i	−0.911591	+	0.411098i	$0.865145\pi$
$168$		0			0
$169$	−25.1404	−	7.38190i	−1.93388	−	0.567838i
$170$	3.96993	−	2.55132i	0.304480	−	0.195677i
$171$		0			0
$172$	−1.28098	+	2.80496i	−0.0976740	+	0.213876i
$173$	−2.33259	+	5.10767i	−0.177344	+	0.388329i	−0.977340	−	0.211677i	$-0.932108\pi$
$173$	−2.33259	+	5.10767i	−0.177344	+	0.388329i	0.799996	+	0.600005i	$0.204835\pi$
$174$		0			0
$175$	6.56009	−	4.21591i	0.495896	−	0.318693i
$176$	−9.31204	−	2.73426i	−0.701921	−	0.206103i
$177$		0			0
$178$	−0.325534	−	0.375686i	−0.0243998	−	0.0281589i
$179$	−18.1247	−	11.6480i	−1.35470	−	0.870614i	−0.356726	−	0.934209i	$-0.616107\pi$
$179$	−18.1247	−	11.6480i	−1.35470	−	0.870614i	−0.997976	+	0.0635946i	$0.979744\pi$
$180$		0			0
$181$	−9.84568	+	2.89095i	−0.731824	+	0.214883i	−0.626353	−	0.779540i	$-0.715453\pi$
$181$	−9.84568	+	2.89095i	−0.731824	+	0.214883i	−0.105471	+	0.994422i	$0.533635\pi$
$182$	5.01097	+	10.9725i	0.371438	+	0.813335i
$183$		0			0
$184$	4.26992	+	9.07745i	0.314783	+	0.669199i
$185$	−0.755486			−0.0555444
$186$		0			0
$187$	13.2167	−	3.88077i	0.966499	−	0.283790i
$188$	−5.20938	+	6.01194i	−0.379933	+	0.438466i
$189$		0			0
$190$	1.05567	+	1.21831i	0.0765863	+	0.0883853i
$191$	1.20256	+	8.36400i	0.0870143	+	0.605198i	0.985940	+	0.167097i	$0.0534394\pi$
$191$	1.20256	+	8.36400i	0.0870143	+	0.605198i	−0.898926	+	0.438100i	$0.855651\pi$
$192$		0			0
$193$	0.329863	−	0.211990i	0.0237440	−	0.0152594i	−0.528715	−	0.848799i	$-0.677326\pi$
$193$	0.329863	−	0.211990i	0.0237440	−	0.0152594i	0.552459	+	0.833540i	$0.313690\pi$
$194$	−0.937075	+	6.51750i	−0.0672780	+	0.467929i
$195$		0			0
$196$	−3.10919	+	6.80819i	−0.222085	+	0.486299i
$197$	−3.21162	+	22.3373i	−0.228818	+	1.59146i	0.474281	+	0.880373i	$0.342708\pi$
$197$	−3.21162	+	22.3373i	−0.228818	+	1.59146i	−0.703099	+	0.711092i	$0.748201\pi$
$198$		0			0
$199$	−12.8230	−	3.76518i	−0.908999	−	0.266906i	−0.206380	−	0.978472i	$-0.566168\pi$
$199$	−12.8230	−	3.76518i	−0.908999	−	0.266906i	−0.702620	+	0.711566i	$0.747986\pi$
$200$	0.685568	+	4.76823i	0.0484770	+	0.337165i
$201$		0			0
$202$	−4.51708	−	2.90295i	−0.317820	−	0.204251i
$203$	−4.91810	+	5.67580i	−0.345183	+	0.398363i
$204$		0			0
$205$	1.59381	+	3.48995i	0.111316	+	0.243749i
$206$	2.28318			0.159076
$207$		0			0
$208$	13.5388			0.938749
$209$	1.95473	+	4.28025i	0.135211	+	0.296071i
$210$		0			0
$211$	0.366068	−	0.422465i	0.0252011	−	0.0290837i	−0.743009	−	0.669281i	$-0.766602\pi$
$211$	0.366068	−	0.422465i	0.0252011	−	0.0290837i	0.768210	+	0.640198i	$0.221148\pi$
$212$	7.61293	+	4.89254i	0.522858	+	0.336021i
$213$		0			0
$214$	0.297510	+	2.06923i	0.0203374	+	0.141450i
$215$	4.76994	+	1.40058i	0.325307	+	0.0955188i
$216$		0			0
$217$	3.12600	−	21.7418i	0.212207	−	1.47593i
$218$	3.17002	−	6.94137i	0.214701	−	0.470129i
$219$		0			0
$220$	−2.89346	+	20.1244i	−0.195077	+	1.35679i
$221$	−16.1654	+	10.3889i	−1.08740	+	0.698830i
$222$		0			0
$223$	4.22619	+	29.3938i	0.283007	+	1.96836i	0.247049	+	0.969003i	$0.420539\pi$
$223$	4.22619	+	29.3938i	0.283007	+	1.96836i	0.0359582	+	0.999353i	$0.488552\pi$
$224$	−12.0044	−	13.8538i	−0.802075	−	0.925644i
$225$		0			0
$226$	0.258918	−	0.298807i	0.0172229	−	0.0198763i
$227$	−23.6710	+	6.95043i	−1.57110	+	0.461316i	−0.947321	−	0.320285i	$-0.896221\pi$
$227$	−23.6710	+	6.95043i	−1.57110	+	0.461316i	−0.623778	+	0.781602i	$0.714403\pi$
$228$		0			0
$229$	−28.4810			−1.88207			−0.941037	−	0.338302i	$-0.890147\pi$
$229$	−28.4810			−1.88207			−0.941037	+	0.338302i	$0.890147\pi$
$230$	6.15819	−	4.05650i	0.406059	−	0.267478i
$231$		0			0
$232$	−1.92730	−	4.22019i	−0.126533	−	0.277069i
$233$	−14.4529	+	4.24374i	−0.946839	+	0.278017i	−0.718470	−	0.695558i	$-0.755157\pi$
$233$	−14.4529	+	4.24374i	−0.946839	+	0.278017i	−0.228369	+	0.973575i	$0.573339\pi$
$234$		0			0
$235$	10.7888	+	6.93355i	0.703785	+	0.452295i
$236$	11.9552	+	13.7971i	0.778219	+	0.898112i
$237$		0			0
$238$	5.67328	+	1.66583i	0.367744	+	0.107979i
$239$	22.6822	−	14.5770i	1.46719	−	0.942907i	0.468975	−	0.883211i	$-0.344623\pi$
$239$	22.6822	−	14.5770i	1.46719	−	0.942907i	0.998217	−	0.0596958i	$-0.0190131\pi$
$240$		0			0
$241$	8.76904	−	19.2015i	0.564864	−	1.23688i	−0.384624	−	0.923074i	$-0.625669\pi$
$241$	8.76904	−	19.2015i	0.564864	−	1.23688i	0.949487	−	0.313806i	$-0.101604\pi$
$242$	2.16135	−	4.73270i	0.138937	−	0.304229i
$243$		0			0
$244$	−6.60589	+	4.24535i	−0.422899	+	0.271780i
$245$	11.5776	+	3.39948i	0.739664	+	0.217185i
$246$		0			0
$247$	−4.29864	−	4.96089i	−0.273516	−	0.315654i
$248$	11.4152	+	7.33610i	0.724865	+	0.465843i
$249$		0			0
$250$	−3.97898	+	1.16833i	−0.251653	+	0.0738919i
$251$	0.966692	+	2.11676i	0.0610170	+	0.133609i	0.937684	−	0.347489i	$-0.112966\pi$
$251$	0.966692	+	2.11676i	0.0610170	+	0.133609i	−0.876667	+	0.481098i	$0.840238\pi$
$252$		0			0
$253$	20.5832	−	6.29679i	1.29405	−	0.395876i
$254$	−6.22697			−0.390715
$255$		0			0
$256$	3.90978	−	1.14801i	0.244361	−	0.0717509i
$257$	17.4817	−	20.1749i	1.09048	−	1.25848i	0.126651	−	0.991947i	$-0.459577\pi$
$257$	17.4817	−	20.1749i	1.09048	−	1.25848i	0.963826	−	0.266531i	$-0.0858773\pi$
$258$		0			0
$259$	−0.619886	−	0.715387i	−0.0385179	−	0.0444520i
$260$	−4.03641	−	28.0738i	−0.250327	−	1.74107i
$261$		0			0
$262$	1.69325	−	1.08819i	0.104609	−	0.0672283i
$263$	1.42355	−	9.90102i	0.0877800	−	0.610523i	−0.897684	−	0.440639i	$-0.854752\pi$
$263$	1.42355	−	9.90102i	0.0877800	−	0.610523i	0.985464	−	0.169884i	$-0.0543392\pi$
$264$		0			0
$265$	6.06062	−	13.2709i	0.372301	−	0.815225i
$266$	−0.287452	+	1.99927i	−0.0176248	+	0.122583i
$267$		0			0
$268$	−0.323495	−	0.0949866i	−0.0197606	−	0.00580223i
$269$	−2.49684	−	17.3659i	−0.152235	−	1.05882i	−0.912463	−	0.409160i	$-0.865822\pi$
$269$	−2.49684	−	17.3659i	−0.152235	−	1.05882i	0.760228	−	0.649657i	$-0.225087\pi$
$270$		0			0
$271$	0.958576	+	0.616040i	0.0582294	+	0.0374217i	0.569432	−	0.822039i	$-0.307163\pi$
$271$	0.958576	+	0.616040i	0.0582294	+	0.0374217i	−0.511202	+	0.859460i	$0.670800\pi$
$272$	4.34593	−	5.01547i	0.263511	−	0.304108i
$273$		0			0
$274$	−3.02369	−	6.62096i	−0.182668	−	0.399987i
$275$	10.3364			0.623309
$276$		0			0
$277$	−21.3674			−1.28384			−0.641920	−	0.766772i	$-0.721862\pi$
$277$	−21.3674			−1.28384			−0.641920	+	0.766772i	$0.721862\pi$
$278$	1.94230	+	4.25304i	0.116491	+	0.255080i
$279$		0			0
$280$	−12.5341	+	14.4651i	−0.749055	+	0.864455i
$281$	10.4177	+	6.69502i	0.621465	+	0.399391i	0.813141	−	0.582067i	$-0.197756\pi$
$281$	10.4177	+	6.69502i	0.621465	+	0.399391i	−0.191676	+	0.981458i	$0.561392\pi$
$282$		0			0
$283$	1.01281	+	7.04422i	0.0602051	+	0.418735i	0.997528	+	0.0702729i	$0.0223870\pi$
$283$	1.01281	+	7.04422i	0.0602051	+	0.418735i	−0.937323	+	0.348462i	$0.886704\pi$
$284$	4.85376	+	1.42519i	0.288018	+	0.0845697i
$285$		0			0
$286$	−2.27550	+	15.8264i	−0.134553	+	0.935837i
$287$	−1.99697	+	4.37276i	−0.117878	+	0.258116i
$288$		0			0
$289$	1.07887	−	7.50369i	0.0634628	−	0.441393i
$290$	−2.86905	+	1.84383i	−0.168476	+	0.108273i
$291$		0			0
$292$	−2.88429	−	20.0606i	−0.168790	−	1.17396i
$293$	−11.7773	−	13.5917i	−0.688038	−	0.794038i	0.299046	−	0.954239i	$-0.403331\pi$
$293$	−11.7773	−	13.5917i	−0.688038	−	0.794038i	−0.987085	+	0.160200i	$0.948786\pi$
$294$		0			0
$295$	19.2738	−	22.2432i	1.12216	−	1.29505i
$296$	0.561077	−	0.164747i	0.0326119	−	0.00957573i
$297$		0			0
$298$	10.5931			0.613641
$299$	−25.0759	+	16.5179i	−1.45018	+	0.955255i
$300$		0			0
$301$	2.58756	+	5.66596i	0.149144	+	0.326580i
$302$	2.98593	−	0.876747i	0.171821	−	0.0504511i
$303$		0			0
$304$	1.90715	+	1.22565i	0.109382	+	0.0702958i
$305$	8.29016	+	9.56736i	0.474693	+	0.547825i
$306$		0			0
$307$	−1.75668	−	0.515809i	−0.100259	−	0.0294388i	0.231218	−	0.972902i	$-0.425729\pi$
$307$	−1.75668	−	0.515809i	−0.100259	−	0.0294388i	−0.331477	+	0.943463i	$0.607547\pi$
$308$	−21.4304	+	13.7725i	−1.22111	+	0.784760i
$309$		0			0
$310$	4.14365	−	9.07333i	0.235344	−	0.515330i
$311$	3.84938	−	8.42896i	0.218278	−	0.477963i	−0.768539	−	0.639803i	$-0.779016\pi$
$311$	3.84938	−	8.42896i	0.218278	−	0.477963i	0.986817	+	0.161841i	$0.0517431\pi$
$312$		0			0
$313$	11.7077	−	7.52409i	0.661759	−	0.425287i	−0.166187	−	0.986094i	$-0.553146\pi$
$313$	11.7077	−	7.52409i	0.661759	−	0.425287i	0.827946	+	0.560808i	$0.189509\pi$
$314$	−8.97329	−	2.63479i	−0.506392	−	0.148690i
$315$		0			0
$316$	8.52650	+	9.84011i	0.479653	+	0.553549i
$317$	22.7584	+	14.6259i	1.27824	+	0.821473i	0.990669	−	0.136287i	$-0.0435169\pi$
$317$	22.7584	+	14.6259i	1.27824	+	0.821473i	0.287568	+	0.957760i	$0.407153\pi$
$318$		0			0
$319$	−9.55163	+	2.80461i	−0.534789	+	0.157028i
$320$	1.39695	+	3.05889i	0.0780918	+	0.170997i
$321$		0			0
$322$	8.89407	+	2.50292i	0.495647	+	0.139482i
$323$	−3.21762			−0.179033
$324$		0			0
$325$	−13.8353	+	4.06242i	−0.767447	+	0.225343i
$326$	−3.73199	+	4.30695i	−0.206696	+	0.238540i
$327$		0			0
$328$	−1.94472	−	2.24432i	−0.107379	−	0.123922i
$329$	2.28683	+	15.9053i	0.126077	+	0.876885i
$330$		0			0
$331$	13.8155	−	8.87867i	0.759367	−	0.488016i	−0.102761	−	0.994706i	$-0.532768\pi$
$331$	13.8155	−	8.87867i	0.759367	−	0.488016i	0.862128	+	0.506690i	$0.169131\pi$
$332$	3.52136	−	24.4916i	0.193260	−	1.34415i
$333$		0			0
$334$	1.74887	−	3.82949i	0.0956940	−	0.209541i
$335$	−0.0773544	+	0.538012i	−0.00422632	+	0.0293947i
$336$		0			0
$337$	15.9032	+	4.66961i	0.866305	+	0.254370i	0.684543	−	0.728972i	$-0.260002\pi$
$337$	15.9032	+	4.66961i	0.866305	+	0.254370i	0.181762	+	0.983343i	$0.441820\pi$
$338$	−2.12168	−	14.7566i	−0.115404	−	0.802654i
$339$		0			0
$340$	−11.6957	−	7.51634i	−0.634286	−	0.407631i
$341$	19.0667	−	22.0041i	1.03252	−	1.19159i
$342$		0			0
$343$	−3.56568	−	7.80775i	−0.192529	−	0.421579i
$344$	−3.84791			−0.207466
$345$		0			0
$346$	−3.19489			−0.171758
$347$	0.0775703	+	0.169855i	0.00416419	+	0.00911830i	0.911703	−	0.410851i	$-0.134768\pi$
$347$	0.0775703	+	0.169855i	0.00416419	+	0.00911830i	−0.907538	+	0.419969i	$0.862041\pi$
$348$		0			0
$349$	−6.88632	+	7.94723i	−0.368616	+	0.425406i	−0.909508	−	0.415686i	$-0.863541\pi$
$349$	−6.88632	+	7.94723i	−0.368616	+	0.425406i	0.540892	+	0.841092i	$0.318087\pi$
$350$	3.73258	+	2.39878i	0.199515	+	0.128220i
$351$		0			0
$352$	−3.45802	−	24.0510i	−0.184313	−	1.28192i
$353$	−19.8284	−	5.82213i	−1.05536	−	0.309881i	−0.292377	−	0.956303i	$-0.594446\pi$
$353$	−19.8284	−	5.82213i	−1.05536	−	0.309881i	−0.762980	+	0.646422i	$0.776264\pi$
$354$		0			0
$355$	1.16064	−	8.07241i	0.0616002	−	0.428439i
$356$	−0.608375	+	1.33216i	−0.0322438	+	0.0706041i
$357$		0			0
$358$	1.74459	−	12.1339i	0.0922043	−	0.641295i
$359$	−13.1887	+	8.47588i	−0.696074	+	0.447340i	−0.840241	−	0.542214i	$-0.817586\pi$
$359$	−13.1887	+	8.47588i	−0.696074	+	0.447340i	0.144166	+	0.989553i	$0.453950\pi$
$360$		0			0
$361$	2.54756	+	17.7186i	0.134082	+	0.932560i
$362$	−3.82342	−	4.41246i	−0.200954	−	0.231914i
$363$		0			0
$364$	23.2718	−	26.8571i	1.21978	−	1.40770i
$365$	−31.3502	+	9.20524i	−1.64094	+	0.481824i
$366$		0			0
$367$	5.44563			0.284259			0.142130	−	0.989848i	$-0.454605\pi$
$367$	5.44563			0.284259			0.142130	+	0.989848i	$0.454605\pi$
$368$	6.70228	−	7.91347i	0.349381	−	0.412518i
$369$		0			0
$370$	−0.178570	−	0.391013i	−0.00928339	−	0.0203278i
$371$	17.5394	−	5.15002i	0.910598	−	0.267376i
$372$		0			0
$373$	−3.38805	−	2.17737i	−0.175427	−	0.112740i	0.449981	−	0.893038i	$-0.351431\pi$
$373$	−3.38805	−	2.17737i	−0.175427	−	0.112740i	−0.625407	+	0.780298i	$0.715067\pi$
$374$	5.13249	+	5.92321i	0.265395	+	0.306282i
$375$		0			0
$376$	−9.52451	−	2.79665i	−0.491189	−	0.144226i
$377$	11.6826	−	7.50798i	0.601687	−	0.386681i
$378$		0			0
$379$	−4.63145	+	10.1415i	−0.237902	+	0.520932i	−0.990494	−	0.137555i	$-0.956076\pi$
$379$	−4.63145	+	10.1415i	−0.237902	+	0.520932i	0.752593	+	0.658486i	$0.228803\pi$
$380$	1.97289	−	4.32003i	0.101207	−	0.221613i
$381$		0			0
$382$	−4.04467	+	2.59935i	−0.206943	+	0.132994i
$383$	−14.4041	−	4.22944i	−0.736017	−	0.216114i	−0.107822	−	0.994170i	$-0.534388\pi$
$383$	−14.4041	−	4.22944i	−0.736017	−	0.216114i	−0.628195	+	0.778056i	$0.716206\pi$
$384$		0			0
$385$	26.8944	+	31.0378i	1.37067	+	1.58183i
$386$	0.187686	+	0.120619i	0.00955297	+	0.00613932i
$387$		0			0
$388$	18.6126	−	5.46516i	0.944913	−	0.277452i
$389$	13.7756	+	30.1644i	0.698452	+	1.52940i	0.841838	+	0.539730i	$0.181474\pi$
$389$	13.7756	+	30.1644i	0.698452	+	1.52940i	−0.143387	+	0.989667i	$0.545799\pi$
$390$		0			0
$391$	−1.93023	+	14.5916i	−0.0976159	+	0.737929i
$392$	−9.33963			−0.471723
$393$		0			0
$394$	−12.3201	+	3.61751i	−0.620677	+	0.182247i
$395$	13.7461	−	15.8639i	0.691643	−	0.798199i
$396$		0			0
$397$	4.36833	+	5.04133i	0.219240	+	0.253017i	0.854706	−	0.519112i	$-0.173737\pi$
$397$	4.36833	+	5.04133i	0.219240	+	0.253017i	−0.635466	+	0.772129i	$0.719192\pi$
$398$	−1.08217	−	7.52669i	−0.0542445	−	0.377279i
$399$		0			0
$400$	4.18939	−	2.69236i	0.209469	−	0.134618i
$401$	−0.886108	+	6.16302i	−0.0442501	+	0.307766i	0.955661	+	0.294468i	$0.0951423\pi$
$401$	−0.886108	+	6.16302i	−0.0442501	+	0.307766i	−0.999912	+	0.0132987i	$0.995767\pi$
$402$		0			0
$403$	−16.8728	+	36.9462i	−0.840492	+	1.84042i
$404$	−2.25125	+	15.6578i	−0.112004	+	0.779002i
$405$		0			0
$406$	−4.10005	−	1.20388i	−0.203482	−	0.0597478i
$407$	−0.178567	−	1.24196i	−0.00885122	−	0.0615616i
$408$		0			0
$409$	−1.64881	−	1.05962i	−0.0815282	−	0.0523950i	0.499242	−	0.866463i	$-0.333612\pi$
$409$	−1.64881	−	1.05962i	−0.0815282	−	0.0523950i	−0.580770	+	0.814068i	$0.697248\pi$
$410$	−1.42956	+	1.64980i	−0.0706008	+	0.0814776i
$411$		0			0
$412$	−2.79424	−	6.11853i	−0.137662	−	0.301439i
$413$	36.8770			1.81460
$414$		0			0
$415$	−39.8906			−1.95815
$416$	14.0811	+	30.8334i	0.690384	+	1.51173i
$417$		0			0
$418$	−1.75328	+	2.02339i	−0.0857558	+	0.0989675i
$419$	−6.95250	−	4.46810i	−0.339652	−	0.218281i	0.359684	−	0.933074i	$-0.382884\pi$
$419$	−6.95250	−	4.46810i	−0.339652	−	0.218281i	−0.699336	+	0.714793i	$0.746521\pi$
$420$		0			0
$421$	0.252051	+	1.75305i	0.0122842	+	0.0854385i	0.995041	−	0.0994630i	$-0.0317125\pi$
$421$	0.252051	+	1.75305i	0.0122842	+	0.0854385i	−0.982757	+	0.184901i	$0.940803\pi$
$422$	0.305178	+	0.0896084i	0.0148558	+	0.00436207i
$423$		0			0
$424$	−1.60709	+	11.1775i	−0.0780470	+	0.542829i
$425$	−2.93618	+	6.42935i	−0.142426	+	0.311869i
$426$		0			0
$427$	−2.25736	+	15.7003i	−0.109241	+	0.759790i
$428$	5.18109	−	3.32968i	0.250437	−	0.160946i
$429$		0			0
$430$	0.402550	+	2.79980i	0.0194127	+	0.135018i
$431$	17.5221	+	20.2215i	0.844008	+	0.974037i	0.999906	−	0.0137365i	$-0.00437262\pi$
$431$	17.5221	+	20.2215i	0.844008	+	0.974037i	−0.155898	+	0.987773i	$0.549827\pi$
$432$		0			0
$433$	−16.0940	+	18.5735i	−0.773428	+	0.892583i	−0.996617	−	0.0821919i	$-0.973808\pi$
$433$	−16.0940	+	18.5735i	−0.773428	+	0.892583i	0.223189	+	0.974775i	$0.428353\pi$
$434$	11.9917	−	3.52107i	0.575618	−	0.169017i
$435$		0			0
$436$	−22.4813			−1.07666
$437$	−5.02765	+	0.0567122i	−0.240505	+	0.00271291i
$438$		0			0
$439$	2.32447	+	5.08987i	0.110941	+	0.242926i	0.956956	−	0.290232i	$-0.0937324\pi$
$439$	2.32447	+	5.08987i	0.110941	+	0.242926i	−0.846016	+	0.533158i	$0.821005\pi$
$440$	−24.3429	+	7.14772i	−1.16050	+	0.340754i
$441$		0			0
$442$	−9.19781	−	5.91108i	−0.437495	−	0.281161i
$443$	8.19690	+	9.45973i	0.389447	+	0.449445i	0.916289	−	0.400518i	$-0.131170\pi$
$443$	8.19690	+	9.45973i	0.389447	+	0.449445i	−0.526842	+	0.849963i	$0.676624\pi$
$444$		0			0
$445$	2.26538	+	0.665175i	0.107389	+	0.0315323i
$446$	−14.2143	+	9.13497i	−0.673066	+	0.432553i
$447$		0			0
$448$	−1.75032	+	3.83267i	−0.0826948	+	0.181076i
$449$	3.38548	−	7.41317i	0.159771	−	0.349849i	−0.812769	−	0.582586i	$-0.802041\pi$
$449$	3.38548	−	7.41317i	0.159771	−	0.349849i	0.972540	+	0.232737i	$0.0747682\pi$
$450$		0			0
$451$	−5.36049	+	3.44497i	−0.252415	+	0.162218i
$452$	−1.11763	−	0.328165i	−0.0525687	−	0.0154356i
$453$		0			0
$454$	−9.19227	−	10.6084i	−0.431414	−	0.497879i
$455$	−48.1968	−	30.9742i	−2.25950	−	1.45209i
$456$		0			0
$457$	17.3676	−	5.09960i	0.812424	−	0.238549i	0.150973	−	0.988538i	$-0.451759\pi$
$457$	17.3676	−	5.09960i	0.812424	−	0.238549i	0.661451	+	0.749989i	$0.269941\pi$
$458$	−6.73187	−	14.7407i	−0.314560	−	0.688790i
$459$		0			0
$460$	−18.4074	−	11.5384i	−0.858249	−	0.537982i
$461$	−13.1011			−0.610180			−0.305090	−	0.952324i	$-0.598687\pi$
$461$	−13.1011			−0.610180			−0.305090	+	0.952324i	$0.598687\pi$
$462$		0			0
$463$	18.6776	−	5.48425i	0.868023	−	0.254875i	0.182749	−	0.983160i	$-0.441501\pi$
$463$	18.6776	−	5.48425i	0.868023	−	0.254875i	0.685274	+	0.728285i	$0.259682\pi$
$464$	−3.14079	+	3.62466i	−0.145807	+	0.168271i
$465$		0			0
$466$	−5.61255	−	6.47723i	−0.259996	−	0.300052i
$467$	−0.170185	−	1.18366i	−0.00787520	−	0.0547732i	0.985505	−	0.169647i	$-0.0542627\pi$
$467$	−0.170185	−	1.18366i	−0.00787520	−	0.0547732i	−0.993380	+	0.114874i	$0.963354\pi$
$468$		0			0
$469$	−0.572926	+	0.368197i	−0.0264553	+	0.0170018i
$470$	−1.03847	+	7.22275i	−0.0479013	+	0.333161i
$471$		0			0
$472$	−9.46357	+	20.7223i	−0.435596	+	0.953822i
$473$	−1.17502	+	8.17244i	−0.0540274	+	0.375769i
$474$		0			0
$475$	−2.31668	−	0.680239i	−0.106297	−	0.0312115i
$476$	−2.47905	−	17.2421i	−0.113627	−	0.790293i
$477$		0			0
$478$	12.9058	+	8.29405i	0.590297	+	0.379361i
$479$	−11.4506	+	13.2147i	−0.523192	+	0.603796i	−0.954427	−	0.298444i	$-0.903533\pi$
$479$	−11.4506	+	13.2147i	−0.523192	+	0.603796i	0.431235	+	0.902240i	$0.358078\pi$
$480$		0			0
$481$	0.727128	+	1.59219i	0.0331542	+	0.0725975i
$482$	12.0107			0.547073
$483$		0			0
$484$	−15.3280			−0.696727
$485$	−12.9915	−	28.4473i	−0.589912	−	1.29173i
$486$		0			0
$487$	14.7431	−	17.0144i	0.668073	−	0.770997i	−0.316001	−	0.948759i	$-0.602340\pi$
$487$	14.7431	−	17.0144i	0.668073	−	0.770997i	0.984074	+	0.177762i	$0.0568856\pi$
$488$	−8.24319	−	5.29758i	−0.373152	−	0.239810i
$489$		0			0
$490$	0.977068	+	6.79565i	0.0441394	+	0.306996i
$491$	28.2419	+	8.29258i	1.27454	+	0.374239i	0.847887	−	0.530176i	$-0.177874\pi$
$491$	28.2419	+	8.29258i	1.27454	+	0.374239i	0.426653	+	0.904415i	$0.359693\pi$
$492$		0			0
$493$	0.968762	−	6.73789i	0.0436309	−	0.303459i
$494$	1.55154	−	3.39740i	0.0698071	−	0.152856i
$495$		0			0
$496$	1.99632	−	13.8847i	0.0896373	−	0.623441i
$497$	8.59627	−	5.52449i	0.385595	−	0.247807i
$498$		0			0
$499$	1.84778	+	12.8516i	0.0827180	+	0.575317i	0.988459	+	0.151486i	$0.0484058\pi$
$499$	1.84778	+	12.8516i	0.0827180	+	0.575317i	−0.905741	+	0.423831i	$0.860685\pi$
$500$	8.00057	+	9.23315i	0.357796	+	0.412919i
$501$		0			0
$502$	−0.867069	+	1.00065i	−0.0386992	+	0.0446613i
$503$	−0.705392	+	0.207122i	−0.0314519	+	0.00923510i	−0.297421	−	0.954747i	$-0.596126\pi$
$503$	−0.705392	+	0.207122i	−0.0314519	+	0.00923510i	0.265969	+	0.963982i	$0.414308\pi$
$504$		0			0
$505$	25.5025			1.13485
$506$	8.12411	+	9.16478i	0.361161	+	0.407424i
$507$		0			0
$508$	7.62081	+	16.6872i	0.338119	+	0.740377i
$509$	2.65234	−	0.778796i	0.117563	−	0.0345195i	−0.222422	−	0.974950i	$-0.571396\pi$
$509$	2.65234	−	0.778796i	0.117563	−	0.0345195i	0.339985	+	0.940431i	$0.389578\pi$
$510$		0			0
$511$	−34.4399	−	22.1332i	−1.52353	−	0.979114i
$512$	−13.5901	−	15.6839i	−0.600605	−	0.693136i
$513$		0			0
$514$	14.5739	+	4.27928i	0.642826	+	0.188751i
$515$	−9.12259	+	5.86273i	−0.401989	+	0.258343i
$516$		0			0
$517$	−8.84816	+	19.3748i	−0.389142	+	0.852101i
$518$	0.223740	−	0.489923i	0.00983059	−	0.0215260i
$519$		0			0
$520$	29.7739	−	19.1345i	1.30567	−	0.839104i
$521$	−15.7236	−	4.61686i	−0.688862	−	0.202268i	−0.0814765	−	0.996675i	$-0.525964\pi$
$521$	−15.7236	−	4.61686i	−0.688862	−	0.202268i	−0.607386	+	0.794407i	$0.707782\pi$
$522$		0			0
$523$	−16.2792	−	18.7872i	−0.711839	−	0.821506i	0.278462	−	0.960447i	$-0.410176\pi$
$523$	−16.2792	−	18.7872i	−0.711839	−	0.821506i	−0.990301	+	0.138941i	$0.955630\pi$
$524$	−4.98842	−	3.20586i	−0.217920	−	0.140049i
$525$		0			0
$526$	5.46090	−	1.60346i	0.238106	−	0.0699143i
$527$	8.27064	+	18.1102i	0.360275	+	0.788892i
$528$		0			0
$529$	−2.75887	+	22.8339i	−0.119951	+	0.992780i
$530$	8.30107			0.360575
$531$		0			0
$532$	5.70952	−	1.67647i	0.247539	−	0.0726840i
$533$	5.82109	−	6.71790i	0.252139	−	0.290984i
$534$		0			0
$535$	−6.50209	−	7.50381i	−0.281110	−	0.324418i
$536$	−0.0598742	−	0.416434i	−0.00258617	−	0.0179872i
$537$		0			0
$538$	8.39781	−	5.39695i	0.362055	−	0.232679i
$539$	−2.85200	+	19.8361i	−0.122844	+	0.854401i
$540$		0			0
$541$	15.9154	−	34.8498i	0.684255	−	1.49831i	−0.173815	−	0.984778i	$-0.555609\pi$
$541$	15.9154	−	34.8498i	0.684255	−	1.49831i	0.858070	−	0.513532i	$-0.171663\pi$
$542$	−0.0922675	+	0.641735i	−0.00396323	+	0.0275649i
$543$		0			0
$544$	15.9423	+	4.68107i	0.683519	+	0.200699i
$545$	5.15800	+	35.8747i	0.220945	+	1.53670i
$546$		0			0
$547$	−15.8646	−	10.1956i	−0.678323	−	0.435932i	0.155594	−	0.987821i	$-0.450271\pi$
$547$	−15.8646	−	10.1956i	−0.678323	−	0.435932i	−0.833917	+	0.551889i	$0.813907\pi$
$548$	−14.0426	+	16.2060i	−0.599868	+	0.692285i
$549$		0			0
$550$	2.44316	+	5.34976i	0.104176	+	0.228115i
$551$	2.32536			0.0990637
$552$		0			0
$553$	26.3008			1.11842
$554$	−5.05047	−	11.0590i	−0.214574	−	0.469851i
$555$		0			0
$556$	9.02038	−	10.4101i	0.382549	−	0.441486i
$557$	−19.1542	−	12.3096i	−0.811588	−	0.521576i	0.0677904	−	0.997700i	$-0.478405\pi$
$557$	−19.1542	−	12.3096i	−0.811588	−	0.521576i	−0.879378	+	0.476124i	$0.842041\pi$
$558$		0			0
$559$	−1.63917	−	11.4007i	−0.0693294	−	0.482196i
$560$	18.9849	+	5.57447i	0.802259	+	0.235564i
$561$		0			0
$562$	−1.00275	+	6.97427i	−0.0422984	+	0.294192i
$563$	7.56278	−	16.5602i	0.318733	−	0.697928i	−0.680666	−	0.732594i	$-0.738309\pi$
$563$	7.56278	−	16.5602i	0.318733	−	0.697928i	0.999399	+	0.0346659i	$0.0110367\pi$
$564$		0			0
$565$	−0.267248	+	1.85875i	−0.0112432	+	0.0781983i
$566$	−3.40645	+	2.18919i	−0.143184	+	0.0920186i
$567$		0			0
$568$	0.898361	+	6.24824i	0.0376944	+	0.262170i
$569$	−20.6338	−	23.8127i	−0.865013	−	0.998279i	−0.999972	−	0.00742738i	$-0.997636\pi$
$569$	−20.6338	−	23.8127i	−0.865013	−	0.998279i	0.134959	−	0.990851i	$-0.456910\pi$
$570$		0			0
$571$	−3.16999	+	3.65836i	−0.132660	+	0.153098i	−0.818193	−	0.574944i	$-0.805024\pi$
$571$	−3.16999	+	3.65836i	−0.132660	+	0.153098i	0.685533	+	0.728042i	$0.259569\pi$
$572$	45.1971	−	13.2711i	1.88979	−	0.554891i
$573$		0			0
$574$	−2.73520			−0.114165
$575$	−4.47458	+	10.0978i	−0.186603	+	0.421109i
$576$		0			0
$577$	10.4429	+	22.8667i	0.434743	+	0.951954i	0.992534	+	0.121972i	$0.0389218\pi$
$577$	10.4429	+	22.8667i	0.434743	+	0.951954i	−0.557791	+	0.829982i	$0.688351\pi$
$578$	4.13865	−	1.21522i	0.172145	−	0.0505464i
$579$		0			0
$580$	8.45240	+	5.43203i	0.350967	+	0.225553i
$581$	−32.7308	−	37.7733i	−1.35790	−	1.56710i
$582$		0			0
$583$	23.2488	+	6.82646i	0.962867	+	0.282723i
$584$	21.2755	−	13.6729i	0.880385	−	0.565789i
$585$		0			0
$586$	4.25088	−	9.30812i	0.175602	−	0.384515i
$587$	−12.9330	+	28.3194i	−0.533804	+	1.16887i	0.430140	+	0.902762i	$0.358464\pi$
$587$	−12.9330	+	28.3194i	−0.533804	+	1.16887i	−0.963944	+	0.266106i	$0.914263\pi$
$588$		0			0
$589$	−5.72146	+	3.67696i	−0.235749	+	0.151507i
$590$	16.0679	+	4.71796i	0.661505	+	0.194235i
$591$		0			0
$592$	−0.395870	−	0.456858i	−0.0162702	−	0.0187768i
$593$	21.7689	+	13.9900i	0.893941	+	0.574501i	0.904988	−	0.425438i	$-0.139880\pi$
$593$	21.7689	+	13.9900i	0.893941	+	0.574501i	−0.0110463	+	0.999939i	$0.503516\pi$
$594$		0			0
$595$	−26.9455	+	7.91191i	−1.10466	+	0.324357i
$596$	−12.9642	−	28.3877i	−0.531036	−	1.16281i
$597$		0			0
$598$	−14.4761	−	9.07416i	−0.591972	−	0.371070i
$599$	43.7707			1.78842			0.894210	−	0.447647i	$-0.147738\pi$
$599$	43.7707			1.78842			0.894210	+	0.447647i	$0.147738\pi$
$600$		0			0
$601$	−12.5602	+	3.68802i	−0.512342	+	0.150437i	−0.527677	−	0.849445i	$-0.676937\pi$
$601$	−12.5602	+	3.68802i	−0.512342	+	0.150437i	0.0153345	+	0.999882i	$0.495119\pi$
$602$	−2.32090	+	2.67846i	−0.0945927	+	0.109166i
$603$		0			0
$604$	−6.00383	−	6.92879i	−0.244292	−	0.281928i
$605$	3.51678	+	24.4597i	0.142977	+	0.994430i
$606$		0			0
$607$	10.2332	−	6.57650i	0.415354	−	0.266932i	−0.316231	−	0.948682i	$-0.602417\pi$
$607$	10.2332	−	6.57650i	0.415354	−	0.266932i	0.731585	+	0.681750i	$0.238781\pi$
$608$	−0.807758	+	5.61808i	−0.0327589	+	0.227843i
$609$		0			0
$610$	−2.99223	+	6.55207i	−0.121152	+	0.265286i
$611$	4.22862	−	29.4107i	0.171072	−	1.18983i
$612$		0			0
$613$	−40.9582	−	12.0264i	−1.65429	−	0.485742i	−0.684360	−	0.729144i	$-0.739918\pi$
$613$	−40.9582	−	12.0264i	−1.65429	−	0.485742i	−0.969925	+	0.243402i	$0.921736\pi$
$614$	−0.148252	−	1.03112i	−0.00598297	−	0.0416125i
$615$		0			0
$616$	−26.7420	−	17.1861i	−1.07747	−	0.692446i
$617$	0.260539	−	0.300678i	0.0104889	−	0.0121048i	−0.750481	−	0.660892i	$-0.770178\pi$
$617$	0.260539	−	0.300678i	0.0104889	−	0.0121048i	0.760970	+	0.648787i	$0.224724\pi$
$618$		0			0
$619$	−12.4831	−	27.3343i	−0.501740	−	1.09866i	−0.975900	−	0.218219i	$-0.929975\pi$
$619$	−12.4831	−	27.3343i	−0.501740	−	1.09866i	0.474160	−	0.880439i	$-0.342752\pi$
$620$	−29.3862			−1.18018
$621$		0			0
$622$	5.27239			0.211403
$623$	1.22890	+	2.69092i	0.0492350	+	0.107810i
$624$		0			0
$625$	20.4390	−	23.5878i	0.817559	−	0.943514i
$626$	6.66148	+	4.28108i	0.266246	+	0.171106i
$627$		0			0
$628$	3.92105	+	27.2715i	0.156467	+	1.08825i
$629$	0.823234	+	0.241723i	0.0328245	+	0.00963814i
$630$		0			0
$631$	3.43513	−	23.8919i	0.136750	−	0.951120i	−0.799720	−	0.600373i	$-0.795019\pi$
$631$	3.43513	−	23.8919i	0.136750	−	0.951120i	0.936470	−	0.350747i	$-0.114072\pi$
$632$	−6.74945	+	14.7792i	−0.268479	+	0.587886i
$633$		0			0
$634$	−2.19060	+	15.2360i	−0.0869999	+	0.605098i
$635$	24.8803	−	15.9896i	0.987344	−	0.634528i
$636$		0			0
$637$	−3.97858	−	27.6716i	−0.157637	−	1.09639i
$638$	−3.70923	−	4.28068i	−0.146850	−	0.169474i
$639$		0			0
$640$	−20.4146	+	23.5597i	−0.806958	+	0.931279i
$641$	31.6282	−	9.28689i	1.24924	−	0.366810i	0.410761	−	0.911743i	$-0.365263\pi$
$641$	31.6282	−	9.28689i	1.24924	−	0.366810i	0.838479	+	0.544933i	$0.183445\pi$
$642$		0			0
$643$	7.50786			0.296081			0.148040	−	0.988981i	$-0.452703\pi$
$643$	7.50786			0.296081			0.148040	+	0.988981i	$0.452703\pi$
$644$	−4.17751	−	26.8978i	−0.164617	−	1.05992i
$645$		0			0
$646$	−0.760529	−	1.66533i	−0.0299226	−	0.0655214i
$647$	13.2481	−	3.88998i	0.520835	−	0.152931i	−0.0107395	−	0.999942i	$-0.503419\pi$
$647$	13.2481	−	3.88998i	0.520835	−	0.152931i	0.531575	+	0.847011i	$0.321600\pi$
$648$		0			0
$649$	41.1215	+	26.4272i	1.61416	+	1.03736i
$650$	−5.37274	−	6.20048i	−0.210736	−	0.243203i
$651$		0			0
$652$	16.1093	+	4.73011i	0.630888	+	0.185245i
$653$	−20.0883	+	12.9100i	−0.786116	+	0.505206i	−0.871058	−	0.491180i	$-0.836566\pi$
$653$	−20.0883	+	12.9100i	−0.786116	+	0.505206i	0.0849423	+	0.996386i	$0.472929\pi$
$654$		0			0
$655$	−3.97126	+	8.69584i	−0.155170	+	0.339775i
$656$	−1.27530	+	2.79252i	−0.0497922	+	0.109030i
$657$		0			0
$658$	−7.69147	+	4.94301i	−0.299845	+	0.192699i
$659$	19.8085	+	5.81631i	0.771631	+	0.226571i	0.643768	−	0.765220i	$-0.277370\pi$
$659$	19.8085	+	5.81631i	0.771631	+	0.226571i	0.127863	+	0.991792i	$0.459188\pi$
$660$		0			0
$661$	30.0235	+	34.6490i	1.16778	+	1.34769i	0.926076	+	0.377338i	$0.123161\pi$
$661$	30.0235	+	34.6490i	1.16778	+	1.34769i	0.241703	+	0.970350i	$0.422294\pi$
$662$	7.86076	+	5.05181i	0.305517	+	0.196344i
$663$		0			0
$664$	29.6256	−	8.69885i	1.14969	−	0.337581i
$665$	−3.98520	−	8.72636i	−0.154539	−	0.338394i
$666$		0			0
$667$	1.39497	−	10.5453i	0.0540134	−	0.408315i
$668$	−12.4027			−0.479877
$669$		0			0
$670$	−0.296740	+	0.0871307i	−0.0114641	+	0.00336615i
$671$	−13.7685	+	15.8897i	−0.531527	+	0.613415i
$672$		0			0
$673$	−22.7553	−	26.2610i	−0.877153	−	1.01229i	−0.999803	−	0.0198386i	$-0.993685\pi$
$673$	−22.7553	−	26.2610i	−0.877153	−	1.01229i	0.122650	−	0.992450i	$-0.460861\pi$
$674$	1.34213	+	9.33469i	0.0516967	+	0.359559i
$675$		0			0
$676$	−36.9487	+	23.7455i	−1.42110	+	0.913288i
$677$	4.44431	−	30.9109i	0.170809	−	1.18800i	−0.706372	−	0.707841i	$-0.749669\pi$
$677$	4.44431	−	30.9109i	0.170809	−	1.18800i	0.877181	−	0.480161i	$-0.159422\pi$
$678$		0			0
$679$	16.2778	−	35.6433i	0.624683	−	1.36787i
$680$	2.46895	−	17.1719i	0.0946798	−	0.658513i
$681$		0			0
$682$	15.8952	+	4.66726i	0.608659	+	0.178719i
$683$	3.56583	+	24.8009i	0.136443	+	0.948980i	0.936902	+	0.349592i	$0.113680\pi$
$683$	3.56583	+	24.8009i	0.136443	+	0.948980i	−0.800459	+	0.599387i	$0.795411\pi$
$684$		0			0
$685$	29.0826	+	18.6903i	1.11119	+	0.714119i
$686$	3.19822	−	3.69094i	0.122109	−	0.140921i
$687$		0			0
$688$	1.65246	+	3.61838i	0.0629994	+	0.137949i
$689$	−33.8016			−1.28774
$690$		0			0
$691$	47.0943			1.79155			0.895775	−	0.444507i	$-0.146621\pi$
$691$	47.0943			1.79155			0.895775	+	0.444507i	$0.146621\pi$
$692$	3.91003	+	8.56177i	0.148637	+	0.325470i
$693$		0			0
$694$	−0.0695763	+	0.0802953i	−0.00264108	+	0.00304797i
$695$	−18.6815	−	12.0059i	−0.708631	−	0.455410i
$696$		0			0
$697$	−0.620095	−	4.31286i	−0.0234878	−	0.163361i
$698$	−5.74089	−	1.68568i	−0.217296	−	0.0638038i
$699$		0			0
$700$	1.86026	−	12.9384i	0.0703113	−	0.489026i
$701$	−10.6225	+	23.2601i	−0.401207	+	0.878522i	0.595939	+	0.803030i	$0.296780\pi$
$701$	−10.6225	+	23.2601i	−0.401207	+	0.878522i	−0.997146	+	0.0754920i	$0.975947\pi$
$702$		0			0
$703$	−0.0417114	+	0.290109i	−0.00157317	+	0.0109417i
$704$	−4.69839	+	3.01947i	−0.177077	+	0.113801i
$705$		0			0
$706$	−1.67338	−	11.6386i	−0.0629784	−	0.438025i
$707$	20.9251	+	24.1489i	0.786970	+	0.908212i
$708$		0			0
$709$	13.9512	−	16.1005i	0.523947	−	0.604667i	−0.430668	−	0.902511i	$-0.641722\pi$
$709$	13.9512	−	16.1005i	0.523947	−	0.604667i	0.954615	+	0.297843i	$0.0962674\pi$
$710$	4.45233	−	1.30732i	0.167093	−	0.0490629i
$711$		0			0
$712$	−1.82748			−0.0684878
$713$	13.2424	+	28.1521i	0.495931	+	1.05430i
$714$		0			0
$715$	−31.5472	−	69.0787i	−1.17980	−	2.58340i
$716$	−34.6518	+	10.1747i	−1.29500	+	0.380246i
$717$		0			0
$718$	−7.50415	−	4.82263i	−0.280053	−	0.179979i
$719$	−11.0585	−	12.7622i	−0.412412	−	0.475949i	0.511098	−	0.859522i	$-0.329239\pi$
$719$	−11.0585	−	12.7622i	−0.412412	−	0.475949i	−0.923510	+	0.383573i	$0.874693\pi$
$720$		0			0
$721$	−13.0368	−	3.82794i	−0.485515	−	0.142560i
$722$	−8.56839	+	5.50657i	−0.318883	+	0.204933i
$723$		0			0
$724$	−7.14541	+	15.6463i	−0.265557	+	0.581489i
$725$	2.12197	−	4.64646i	0.0788079	−	0.172565i
$726$		0			0
$727$	−39.3725	+	25.3032i	−1.46024	+	0.938442i	−0.461563	+	0.887107i	$0.652711\pi$
$727$	−39.3725	+	25.3032i	−1.46024	+	0.938442i	−0.998681	+	0.0513351i	$0.983652\pi$
$728$	42.5488	+	12.4935i	1.57696	+	0.463038i
$729$		0			0
$730$	−12.1744	−	14.0500i	−0.450593	−	0.520012i
$731$	−4.74955	−	3.05235i	−0.175669	−	0.112895i
$732$		0			0
$733$	1.17020	−	0.343601i	0.0432223	−	0.0126912i	−0.260050	−	0.965595i	$-0.583739\pi$
$733$	1.17020	−	0.343601i	0.0432223	−	0.0126912i	0.303272	+	0.952904i	$0.401921\pi$
$734$	1.28715	+	2.81846i	0.0475096	+	0.104031i
$735$		0			0
$736$	24.9929	+	7.03336i	0.921250	+	0.259253i
$737$	−0.902732			−0.0332526
$738$		0			0
$739$	27.8695	−	8.18321i	1.02519	−	0.301024i	0.274439	−	0.961604i	$-0.411508\pi$
$739$	27.8695	−	8.18321i	1.02519	−	0.301024i	0.750756	+	0.660580i	$0.229690\pi$
$740$	−0.829309	+	0.957074i	−0.0304860	+	0.0351827i
$741$		0			0
$742$	6.81114	+	7.86047i	0.250045	+	0.288567i
$743$	−3.79826	−	26.4174i	−0.139344	−	0.969162i	−0.932764	−	0.360487i	$-0.882610\pi$
$743$	−3.79826	−	26.4174i	−0.139344	−	0.969162i	0.793420	−	0.608675i	$-0.208299\pi$
$744$		0			0
$745$	−42.3255	+	27.2009i	−1.55068	+	0.996565i
$746$	0.326116	−	2.26819i	0.0119400	−	0.0830442i
$747$		0			0
$748$	9.59188	−	21.0033i	0.350714	−	0.767956i
$749$	1.77048	−	12.3140i	0.0646919	−	0.449942i
$750$		0			0
$751$	−1.31007	−	0.384670i	−0.0478050	−	0.0140368i	0.257743	−	0.966214i	$-0.417021\pi$
$751$	−1.31007	−	0.384670i	−0.0478050	−	0.0140368i	−0.305548	+	0.952177i	$0.598840\pi$
$752$	1.46041	+	10.1574i	0.0532556	+	0.370401i
$753$		0			0
$754$	6.64722	+	4.27191i	0.242077	+	0.155574i
$755$	−9.67917	+	11.1704i	−0.352261	+	0.406531i
$756$		0			0
$757$	21.6745	+	47.4605i	0.787773	+	1.72498i	0.682918	+	0.730495i	$0.260711\pi$
$757$	21.6745	+	47.4605i	0.787773	+	1.72498i	0.104855	+	0.994488i	$0.466562\pi$
$758$	−6.34357			−0.230409
$759$		0			0
$760$	5.92632			0.214970
$761$	−9.05143	−	19.8199i	−0.328114	−	0.718470i	0.671635	−	0.740883i	$-0.265593\pi$
$761$	−9.05143	−	19.8199i	−0.328114	−	0.718470i	−0.999749	+	0.0224126i	$0.992865\pi$
$762$		0			0
$763$	−29.7384	+	34.3199i	−1.07660	+	1.24246i
$764$	11.9158	+	7.65785i	0.431100	+	0.277051i
$765$		0			0
$766$	−1.21561	−	8.45476i	−0.0439218	−	0.305483i
$767$	−65.4278	−	19.2113i	−2.36246	−	0.693681i
$768$		0			0
$769$	−5.35823	+	37.2673i	−0.193223	+	1.34389i	0.630186	+	0.776444i	$0.282979\pi$
$769$	−5.35823	+	37.2673i	−0.193223	+	1.34389i	−0.823409	+	0.567449i	$0.807931\pi$
$770$	−9.70721	+	21.2558i	−0.349823	+	0.766007i
$771$		0			0
$772$	0.0935400	−	0.650585i	0.00336658	−	0.0234151i
$773$	−1.53486	+	0.986395i	−0.0552051	+	0.0354782i	−0.567952	−	0.823061i	$-0.692264\pi$
$773$	−1.53486	+	0.986395i	−0.0552051	+	0.0354782i	0.512747	+	0.858540i	$0.328628\pi$
$774$		0			0
$775$	2.12616	+	14.7878i	0.0763740	+	0.531193i
$776$	15.8518	+	18.2940i	0.569047	+	0.656715i
$777$		0			0
$778$	−12.3560	+	14.2596i	−0.442983	+	0.511230i
$779$	1.42815	−	0.419342i	0.0511687	−	0.0150245i
$780$		0			0
$781$	13.5447			0.484668
$782$	−8.00833	+	2.44991i	−0.286377	+	0.0876085i
$783$		0			0
$784$	4.01084	+	8.78251i	0.143244	+	0.313661i
$785$	42.6190	−	12.5141i	1.52114	−	0.446646i
$786$		0			0
$787$	−24.2453	−	15.5815i	−0.864250	−	0.555420i	0.0317386	−	0.999496i	$-0.489896\pi$
$787$	−24.2453	−	15.5815i	−0.864250	−	0.555420i	−0.895989	+	0.444076i	$0.853532\pi$
$788$	24.7721	+	28.5886i	0.882471	+	1.01843i
$789$		0			0
$790$	11.4597	+	3.36487i	0.407717	+	0.119717i
$791$	−1.97938	+	1.27207i	−0.0703785	+	0.0452295i
$792$		0			0
$793$	12.1842	−	26.6798i	0.432675	−	0.947426i
$794$	−1.57670	+	3.45248i	−0.0559549	+	0.122524i
$795$		0			0
$796$	−18.8459	+	12.1115i	−0.667974	+	0.429281i
$797$	−0.861256	−	0.252887i	−0.0305072	−	0.00895773i	0.266443	−	0.963851i	$-0.414151\pi$
$797$	−0.861256	−	0.252887i	−0.0305072	−	0.00895773i	−0.296951	+	0.954893i	$0.595970\pi$
$798$		0			0
$799$	−9.53786	−	11.0073i	−0.337425	−	0.389409i
$800$	10.4888	+	6.74072i	0.370834	+	0.238320i
$801$		0			0
$802$	−3.39920	+	0.998096i	−0.120030	+	0.0352440i
$803$	−22.5426	−	49.3614i	−0.795511	−	1.74193i
$804$		0			0
$805$	−41.9639	+	12.8376i	−1.47903	+	0.452465i
$806$	−23.1102			−0.814021
$807$		0			0
$808$	−18.9399	+	5.56127i	−0.666304	+	0.195645i
$809$	−24.6586	+	28.4575i	−0.866949	+	1.00051i	0.133006	+	0.991115i	$0.457537\pi$
$809$	−24.6586	+	28.4575i	−0.866949	+	1.00051i	−0.999956	+	0.00939782i	$0.997009\pi$
$810$		0			0
$811$	13.4067	+	15.4722i	0.470775	+	0.543303i	0.940627	−	0.339442i	$-0.110238\pi$
$811$	13.4067	+	15.4722i	0.470775	+	0.543303i	−0.469852	+	0.882745i	$0.655693\pi$
$812$	1.79160	+	12.4608i	0.0628727	+	0.437289i
$813$		0			0
$814$	0.600587	−	0.385974i	0.0210506	−	0.0135284i
$815$	3.85207	−	26.7917i	0.134932	−	0.938473i
$816$		0			0
$817$	0.801182	−	1.75434i	0.0280298	−	0.0613767i
$818$	0.158705	−	1.10382i	0.00554901	−	0.0385942i
$819$		0			0
$820$	6.17073	+	1.81189i	0.215491	+	0.0632739i
$821$	−2.30296	−	16.0174i	−0.0803739	−	0.559013i	−0.989725	−	0.142983i	$-0.954330\pi$
$821$	−2.30296	−	16.0174i	−0.0803739	−	0.559013i	0.909351	−	0.416029i	$-0.136579\pi$
$822$		0			0
$823$	−15.0421	−	9.66699i	−0.524336	−	0.336970i	0.251549	−	0.967844i	$-0.419060\pi$
$823$	−15.0421	−	9.66699i	−0.524336	−	0.336970i	−0.775885	+	0.630874i	$0.782696\pi$
$824$	5.49660	−	6.34342i	0.191483	−	0.220984i
$825$		0			0
$826$	8.71639	+	19.0862i	0.303282	+	0.664095i
$827$	8.08676			0.281204			0.140602	−	0.990066i	$-0.455096\pi$
$827$	8.08676			0.281204			0.140602	+	0.990066i	$0.455096\pi$
$828$		0			0
$829$	−37.2365			−1.29328			−0.646639	−	0.762796i	$-0.723826\pi$
$829$	−37.2365			−1.29328			−0.646639	+	0.762796i	$0.723826\pi$
$830$	−9.42870	−	20.6460i	−0.327275	−	0.716632i
$831$		0			0
$832$	5.10211	−	5.88814i	0.176884	−	0.204135i
$833$	−11.5281	−	7.40865i	−0.399425	−	0.256695i
$834$		0			0
$835$	2.84563	+	19.7918i	0.0984769	+	0.684922i
$836$	7.56809	+	2.22219i	0.261748	+	0.0768562i
$837$		0			0
$838$	0.669211	−	4.65446i	0.0231175	−	0.160786i
$839$	14.4379	−	31.6145i	0.498451	−	1.09145i	−0.478519	−	0.878077i	$-0.658826\pi$
$839$	14.4379	−	31.6145i	0.498451	−	1.09145i	0.976970	−	0.213377i	$-0.0684464\pi$
$840$		0			0
$841$	3.42701	−	23.8354i	0.118173	−	0.821910i
$842$	−0.847742	+	0.544810i	−0.0292151	+	0.0187754i
$843$		0			0
$844$	−0.133353	−	0.927493i	−0.00459021	−	0.0319256i
$845$	46.3693	+	53.5131i	1.59515	+	1.84090i
$846$		0			0
$847$	−20.2759	+	23.3997i	−0.696689	+	0.804022i
$848$	11.2009	−	3.28889i	0.384642	−	0.112941i
$849$		0			0
$850$	−4.02161			−0.137940
$851$	1.29059	+	0.363192i	0.0442410	+	0.0124501i
$852$		0			0
$853$	−11.7305	−	25.6863i	−0.401646	−	0.879482i	−0.997101	−	0.0760933i	$-0.975755\pi$
$853$	−11.7305	−	25.6863i	−0.401646	−	0.879482i	0.595455	−	0.803389i	$-0.296972\pi$
$854$	−8.65948	+	2.54265i	−0.296321	+	0.0870078i
$855$		0			0
$856$	6.46525	+	4.15496i	0.220978	+	0.142014i
$857$	−4.86922	−	5.61938i	−0.166330	−	0.191954i	0.666466	−	0.745536i	$-0.267806\pi$
$857$	−4.86922	−	5.61938i	−0.166330	−	0.191954i	−0.832795	+	0.553581i	$0.813261\pi$
$858$		0			0
$859$	−39.2382	−	11.5214i	−1.33879	−	0.393104i	−0.467551	−	0.883966i	$-0.654864\pi$
$859$	−39.2382	−	11.5214i	−1.33879	−	0.393104i	−0.871237	+	0.490862i	$0.836682\pi$
$860$	7.01034	−	4.50527i	0.239051	−	0.153628i
$861$		0			0
$862$	−6.32437	+	13.8484i	−0.215409	+	0.471680i
$863$	8.82000	−	19.3131i	0.300236	−	0.657426i	−0.698044	−	0.716055i	$-0.745946\pi$
$863$	8.82000	−	19.3131i	0.300236	−	0.657426i	0.998280	+	0.0586297i	$0.0186731\pi$
$864$		0			0
$865$	12.7654	−	8.20383i	0.434037	−	0.278939i
$866$	−13.4170	−	3.93959i	−0.455928	−	0.133873i
$867$		0			0
$868$	−24.1118	−	27.8264i	−0.818406	−	0.944491i
$869$	29.3280	+	18.8480i	0.994884	+	0.639373i
$870$		0			0
$871$	1.20831	−	0.354792i	0.0409421	−	0.0120217i
$872$	−11.6538	−	25.5183i	−0.394648	−	0.864158i
$873$		0			0
$874$	−1.21771	−	2.58873i	−0.0411896	−	0.0875651i
$875$	24.6785			0.834285
$876$		0			0
$877$	−17.9522	+	5.27124i	−0.606203	+	0.177997i	−0.570407	−	0.821362i	$-0.693215\pi$
$877$	−17.9522	+	5.27124i	−0.606203	+	0.177997i	−0.0357955	+	0.999359i	$0.511396\pi$
$878$	−2.08492	+	2.40612i	−0.0703626	+	0.0812028i
$879$		0			0
$880$	17.1752	+	19.8213i	0.578977	+	0.668175i
$881$	5.10803	+	35.5271i	0.172094	+	1.19694i	0.874451	+	0.485114i	$0.161222\pi$
$881$	5.10803	+	35.5271i	0.172094	+	1.19694i	−0.702357	+	0.711825i	$0.747869\pi$
$882$		0			0
$883$	5.34188	−	3.43302i	0.179769	−	0.115530i	−0.447662	−	0.894203i	$-0.647743\pi$
$883$	5.34188	−	3.43302i	0.179769	−	0.115530i	0.627430	+	0.778673i	$0.284107\pi$
$884$	−4.58406	+	31.8828i	−0.154179	+	1.07234i
$885$		0			0
$886$	−2.95857	+	6.47837i	−0.0993951	+	0.217645i
$887$	2.27527	−	15.8248i	0.0763960	−	0.531346i	−0.915303	−	0.402766i	$-0.868049\pi$
$887$	2.27527	−	15.8248i	0.0763960	−	0.531346i	0.991699	−	0.128580i	$-0.0410420\pi$
$888$		0			0
$889$	35.5555	+	10.4400i	1.19249	+	0.350148i
$890$	0.191183	+	1.32970i	0.00640845	+	0.0445718i
$891$		0			0
$892$	41.8762	+	26.9122i	1.40212	+	0.901087i
$893$	3.25817	−	3.76013i	0.109031	−	0.125828i
$894$		0			0
$895$	24.1867	+	52.9615i	0.808472	+	1.77031i
$896$	−39.0597			−1.30489
$897$		0			0
$898$	4.63700			0.154739
$899$	−5.97715	−	13.0881i	−0.199349	−	0.436514i
$900$		0			0
$901$	−10.8502	+	12.5218i	−0.361473	+	0.417163i
$902$	−3.05002	−	1.96013i	−0.101555	−	0.0652652i
$903$		0			0
$904$	−0.206856	−	1.43872i	−0.00687994	−	0.0478511i
$905$	26.6070	+	7.81253i	0.884448	+	0.259697i
$906$		0			0
$907$	3.33936	−	23.2257i	0.110881	−	0.771198i	−0.856184	−	0.516671i	$-0.827171\pi$
$907$	3.33936	−	23.2257i	0.110881	−	0.771198i	0.967066	−	0.254527i	$-0.0819197\pi$
$908$	−17.1790	+	37.6168i	−0.570105	+	1.24836i
$909$		0			0
$910$	4.63917	−	32.2662i	0.153787	−	1.06961i
$911$	−23.3996	+	15.0380i	−0.775263	+	0.498231i	−0.867458	−	0.497510i	$-0.834248\pi$
$911$	−23.3996	+	15.0380i	−0.775263	+	0.498231i	0.0921956	+	0.995741i	$0.470611\pi$
$912$		0			0
$913$	−9.42854	−	65.5770i	−0.312039	−	2.17028i
$914$	6.74446	+	7.78352i	0.223087	+	0.257456i
$915$		0			0
$916$	−31.2640	+	36.0806i	−1.03299	+	1.19214i
$917$	−11.4928	+	3.37458i	−0.379525	+	0.111438i
$918$		0			0
$919$	38.7863			1.27944			0.639720	−	0.768608i	$-0.279050\pi$
$919$	38.7863			1.27944			0.639720	+	0.768608i	$0.279050\pi$
$920$	3.55516	−	26.8753i	0.117210	−	0.886051i
$921$		0			0
$922$	−3.09663	−	6.78068i	−0.101982	−	0.223310i
$923$	−18.1297	+	5.32336i	−0.596746	+	0.175220i
$924$		0			0
$925$	0.541624	+	0.348080i	0.0178085	+	0.0114448i
$926$	7.25317	+	8.37060i	0.238354	+	0.275075i
$927$		0			0
$928$	−11.5214	−	3.38299i	−0.378208	−	0.111052i
$929$	27.2494	−	17.5121i	0.894023	−	0.574554i	−0.0109891	−	0.999940i	$-0.503498\pi$
$929$	27.2494	−	17.5121i	0.894023	−	0.574554i	0.905012	+	0.425386i	$0.139862\pi$
$930$		0			0
$931$	1.94462	−	4.25813i	0.0637325	−	0.139555i
$932$	−10.4890	+	22.9678i	−0.343580	+	0.752335i
$933$		0			0
$934$	0.572395	−	0.367856i	0.0187293	−	0.0120366i
$935$	−35.7169	−	10.4874i	−1.16807	−	0.342975i
$936$		0			0
$937$	0.936770	+	1.08109i	0.0306029	+	0.0353177i	0.770845	−	0.637023i	$-0.219834\pi$
$937$	0.936770	+	1.08109i	0.0306029	+	0.0353177i	−0.740242	+	0.672341i	$0.765289\pi$
$938$	−0.325985	−	0.209498i	−0.0106438	−	0.00684035i
$939$		0			0
$940$	20.6267	−	6.05655i	0.672769	−	0.197543i
$941$	0.263641	+	0.577294i	0.00859446	+	0.0188192i	0.913881	−	0.405983i	$-0.133071\pi$
$941$	0.263641	+	0.577294i	0.00859446	+	0.0188192i	−0.905286	+	0.424802i	$0.860344\pi$
$942$		0			0
$943$	−1.04494	−	6.72807i	−0.0340279	−	0.219096i
$944$	23.5503			0.766496
$945$		0			0
$946$	−4.50750	+	1.32352i	−0.146551	+	0.0430314i
$947$	−21.7906	+	25.1476i	−0.708098	+	0.817188i	−0.989823	−	0.142307i	$-0.954548\pi$
$947$	−21.7906	+	25.1476i	−0.708098	+	0.817188i	0.281725	+	0.959495i	$0.409093\pi$
$948$		0			0
$949$	49.5734	+	57.2108i	1.60922	+	1.85714i
$950$	−0.195512	−	1.35982i	−0.00634325	−	0.0441183i
$951$		0			0
$952$	18.2863	−	11.7519i	0.592662	−	0.380881i
$953$	−5.69080	+	39.5804i	−0.184343	+	1.28214i	0.662003	+	0.749502i	$0.269707\pi$
$953$	−5.69080	+	39.5804i	−0.184343	+	1.28214i	−0.846346	+	0.532634i	$0.821202\pi$
$954$		0			0
$955$	9.48615	−	20.7718i	0.306965	−	0.672159i
$956$	6.43206	−	44.7360i	0.208028	−	1.44686i
$957$		0			0
$958$	−9.54599	−	2.80295i	−0.308417	−	0.0905594i
$959$	6.16444	+	42.8746i	0.199060	+	1.38449i
$960$		0			0
$961$	9.32324	+	5.99169i	0.300750	+	0.193280i
$962$	−0.652193	+	0.752671i	−0.0210276	+	0.0242671i
$963$		0			0
$964$	−14.6992	−	32.1867i	−0.473429	−	1.03666i
$965$	−1.05964			−0.0341109
$966$		0			0
$967$	50.8204			1.63427			0.817136	−	0.576444i	$-0.195560\pi$
$967$	50.8204			1.63427			0.817136	+	0.576444i	$0.195560\pi$
$968$	−7.94569	−	17.3986i	−0.255384	−	0.559213i
$969$		0			0
$970$	11.6526	−	13.4478i	0.374143	−	0.431784i
$971$	−36.1031	−	23.2020i	−1.15860	−	0.744589i	−0.187269	−	0.982309i	$-0.559964\pi$
$971$	−36.1031	−	23.2020i	−1.15860	−	0.744589i	−0.971334	+	0.237720i	$0.923600\pi$
$972$		0			0
$973$	−3.95980	−	27.5410i	−0.126945	−	0.882923i
$974$	12.2908	+	3.60891i	0.393823	+	0.115637i
$975$		0			0
$976$	−1.44159	+	10.0265i	−0.0461442	+	0.320940i
$977$	−4.38860	+	9.60970i	−0.140404	+	0.307442i	−0.966751	−	0.255719i	$-0.917688\pi$
$977$	−4.38860	+	9.60970i	−0.140404	+	0.307442i	0.826347	+	0.563161i	$0.190415\pi$
$978$		0			0
$979$	−0.558050	+	3.88132i	−0.0178354	+	0.124048i
$980$	17.0155	−	10.9352i	0.543539	−	0.349311i
$981$		0			0
$982$	2.38343	+	16.5771i	0.0760582	+	0.528996i
$983$	31.0101	+	35.7876i	0.989068	+	1.14145i	0.989946	+	0.141446i	$0.0451752\pi$
$983$	31.0101	+	35.7876i	0.989068	+	1.14145i	−0.000877467		1.00000i	$0.500279\pi$
$984$		0			0
$985$	39.9368	−	46.0895i	1.27249	−	1.46853i
$986$	3.71627	−	1.09120i	0.118350	−	0.0347508i
$987$		0			0
$988$	−11.0033			−0.350062
$989$	−7.47516	−	4.68570i	−0.237696	−	0.148997i
$990$		0			0
$991$	10.0139	+	21.9274i	0.318102	+	0.696546i	0.999370	−	0.0354879i	$-0.0112985\pi$
$991$	10.0139	+	21.9274i	0.318102	+	0.696546i	−0.681268	+	0.732034i	$0.738571\pi$
$992$	33.6973	−	9.89442i	1.06989	−	0.314148i
$993$		0			0
$994$	4.89113	+	3.14334i	0.155137	+	0.0997006i
$995$	23.6509	+	27.2946i	0.749785	+	0.865298i
$996$		0			0
$997$	−27.1075	−	7.95949i	−0.858504	−	0.252079i	−0.177285	−	0.984160i	$-0.556732\pi$
$997$	−27.1075	−	7.95949i	−0.858504	−	0.252079i	−0.681219	+	0.732080i	$0.738550\pi$
$998$	−6.21479	+	3.99400i	−0.196726	+	0.126428i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.i.d.73.1		20
3.2	odd	2		69.2.e.c.4.2	✓	20
23.6	even	11	inner	207.2.i.d.190.1		20
23.11	odd	22		4761.2.a.bu.1.5		10
23.12	even	11		4761.2.a.bt.1.5		10
69.11	even	22		1587.2.a.t.1.6		10
69.29	odd	22		69.2.e.c.52.2	yes	20
69.35	odd	22		1587.2.a.u.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.c.4.2	✓	20	3.2	odd	2
69.2.e.c.52.2	yes	20	69.29	odd	22
207.2.i.d.73.1		20	1.1	even	1	trivial
207.2.i.d.190.1		20	23.6	even	11	inner
1587.2.a.t.1.6		10	69.11	even	22
1587.2.a.u.1.6		10	69.35	odd	22
4761.2.a.bt.1.5		10	23.12	even	11
4761.2.a.bu.1.5		10	23.11	odd	22

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.236364 + 0.517565i) q^{2} +(1.09772 - 1.26683i) q^{4} +(-2.27341 - 1.46103i) q^{5} +(-0.481879 - 3.35154i) q^{7} +(2.00700 + 0.589308i) q^{8} +O(q^{10})\)	\(q+(0.236364 + 0.517565i) q^{2} +(1.09772 - 1.26683i) q^{4} +(-2.27341 - 1.46103i) q^{5} +(-0.481879 - 3.35154i) q^{7} +(2.00700 + 0.589308i) q^{8} +(0.218827 - 1.52197i) q^{10} +(1.86448 - 4.08263i) q^{11} +(-0.891052 + 6.19740i) q^{13} +(1.62074 - 1.04159i) q^{14} +(-0.307736 - 2.14035i) q^{16} +(2.00981 + 2.31944i) q^{17} +(-0.686559 + 0.792332i) q^{19} +(-4.34644 + 1.27623i) q^{20} +2.55372 q^{22} +(3.18128 + 3.58879i) q^{23} +(0.956704 + 2.09489i) q^{25} +(-3.41817 + 1.00367i) q^{26} +(-4.77480 - 3.06858i) q^{28} +(-1.45248 - 1.67625i) q^{29} +(6.22433 + 1.82763i) q^{31} +(4.55438 - 2.92692i) q^{32} +(-0.725416 + 1.58844i) q^{34} +(-3.80120 + 8.32347i) q^{35} +(0.235181 - 0.151142i) q^{37} +(-0.572361 - 0.168060i) q^{38} +(-3.70173 - 4.27203i) q^{40} +(-1.19434 - 0.767558i) q^{41} +(-1.76507 + 0.518271i) q^{43} +(-3.12534 - 6.84355i) q^{44} +(-1.10549 + 2.49478i) q^{46} -4.74565 q^{47} +(-4.28417 + 1.25794i) q^{49} +(-0.858110 + 0.990312i) q^{50} +(6.87295 + 7.93180i) q^{52} +(0.768306 + 5.34369i) q^{53} +(-10.2036 + 6.55744i) q^{55} +(1.00796 - 7.01051i) q^{56} +(0.524255 - 1.14796i) q^{58} +(-1.54995 + 10.7801i) q^{59} +(-4.49474 - 1.31978i) q^{61} +(0.525291 + 3.65348i) q^{62} +(-1.04683 - 0.672754i) q^{64} +(11.0803 - 12.7874i) q^{65} +(-0.0835538 - 0.182957i) q^{67} +5.14454 q^{68} -5.20640 q^{70} +(1.25365 + 2.74512i) q^{71} +(7.91764 - 9.13745i) q^{73} +(0.133814 + 0.0859970i) q^{74} +(0.250104 + 1.73951i) q^{76} +(-14.5816 - 4.28153i) q^{77} +(-1.10543 + 7.68843i) q^{79} +(-2.42751 + 5.31551i) q^{80} +(0.114961 - 0.799573i) q^{82} +(12.4179 - 7.98047i) q^{83} +(-1.18034 - 8.20944i) q^{85} +(-0.685438 - 0.791037i) q^{86} +(6.14793 - 7.09509i) q^{88} +(-0.838282 + 0.246142i) q^{89} +21.2002 q^{91} +(8.03854 - 0.0906751i) q^{92} +(-1.12170 - 2.45618i) q^{94} +(2.71845 - 0.798210i) q^{95} +(9.73536 + 6.25653i) q^{97} +(-1.66369 - 1.92000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8}+O(q^{10}) \) 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 10 * q^8	\( 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8} - 18 q^{10} + 16 q^{11} + 14 q^{13} + 22 q^{14} - 8 q^{16} - 11 q^{17} - 11 q^{19} - 57 q^{20} + 26 q^{22} - 4 q^{25} + 14 q^{26} - 14 q^{28} - 12 q^{29} + 41 q^{31} + 46 q^{32} - 3 q^{34} + 26 q^{35} - 18 q^{37} - 70 q^{38} - 13 q^{40} - 10 q^{43} + 3 q^{44} - 24 q^{46} - 18 q^{47} - 10 q^{49} - 33 q^{50} + 61 q^{52} + 20 q^{53} - 17 q^{55} - 6 q^{56} - 37 q^{58} - 40 q^{59} - 12 q^{61} + 89 q^{62} - 2 q^{64} + 51 q^{65} - 47 q^{67} + 12 q^{68} + 32 q^{70} + 47 q^{71} + 39 q^{73} + 50 q^{74} - 39 q^{76} - 22 q^{77} - 2 q^{79} - 12 q^{80} + 26 q^{82} + 52 q^{83} + 35 q^{85} - 34 q^{86} + 30 q^{88} - 36 q^{89} + 8 q^{91} + 19 q^{92} + 21 q^{94} - 89 q^{95} - 85 q^{98}+O(q^{100}) \) 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 10 * q^8 - 18 * q^10 + 16 * q^11 + 14 * q^13 + 22 * q^14 - 8 * q^16 - 11 * q^17 - 11 * q^19 - 57 * q^20 + 26 * q^22 - 4 * q^25 + 14 * q^26 - 14 * q^28 - 12 * q^29 + 41 * q^31 + 46 * q^32 - 3 * q^34 + 26 * q^35 - 18 * q^37 - 70 * q^38 - 13 * q^40 - 10 * q^43 + 3 * q^44 - 24 * q^46 - 18 * q^47 - 10 * q^49 - 33 * q^50 + 61 * q^52 + 20 * q^53 - 17 * q^55 - 6 * q^56 - 37 * q^58 - 40 * q^59 - 12 * q^61 + 89 * q^62 - 2 * q^64 + 51 * q^65 - 47 * q^67 + 12 * q^68 + 32 * q^70 + 47 * q^71 + 39 * q^73 + 50 * q^74 - 39 * q^76 - 22 * q^77 - 2 * q^79 - 12 * q^80 + 26 * q^82 + 52 * q^83 + 35 * q^85 - 34 * q^86 + 30 * q^88 - 36 * q^89 + 8 * q^91 + 19 * q^92 + 21 * q^94 - 89 * q^95 - 85 * q^98

Introduction

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