LMFDB - Embedded newform 207.2.i.d.55.2

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			55.2
Root			$1.05639 - 1.21914i$ of defining polynomial
Character	$\chi$	$=$	207.55
Dual form			207.2.i.d.64.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.90549 - 0.559503i) q^{2} +(1.63535 - 1.05098i) q^{4} +(0.291446 + 2.02705i) q^{5} +(1.34249 - 2.93963i) q^{7} +(-0.0729013 + 0.0841325i) q^{8} +O(q^{10})$	\(q+(1.90549 - 0.559503i) q^{2} +(1.63535 - 1.05098i) q^{4} +(0.291446 + 2.02705i) q^{5} +(1.34249 - 2.93963i) q^{7} +(-0.0729013 + 0.0841325i) q^{8} +(1.68949 + 3.69946i) q^{10} +(1.55951 + 0.457915i) q^{11} +(-1.07824 - 2.36102i) q^{13} +(0.913363 - 6.35258i) q^{14} +(-1.70693 + 3.73765i) q^{16} +(-3.90777 - 2.51137i) q^{17} +(-5.38056 + 3.45787i) q^{19} +(2.60700 + 3.00863i) q^{20} +3.22785 q^{22} +(-1.37375 + 4.59487i) q^{23} +(0.773474 - 0.227113i) q^{25} +(-3.37558 - 3.89563i) q^{26} +(-0.894050 - 6.21825i) q^{28} +(-6.49822 - 4.17615i) q^{29} +(5.74006 - 6.62438i) q^{31} +(-1.12962 + 7.85671i) q^{32} +(-8.85134 - 2.59899i) q^{34} +(6.35005 + 1.86454i) q^{35} +(-1.13432 + 7.88940i) q^{37} +(-8.31792 + 9.59939i) q^{38} +(-0.191788 - 0.123254i) q^{40} +(-0.407522 - 2.83438i) q^{41} +(2.44130 + 2.81741i) q^{43} +(3.03161 - 0.890161i) q^{44} +(-0.0468192 + 9.52410i) q^{46} +8.70030 q^{47} +(-2.25516 - 2.60259i) q^{49} +(1.34678 - 0.865522i) q^{50} +(-4.24468 - 2.72789i) q^{52} +(0.624559 - 1.36759i) q^{53} +(-0.473702 + 3.29467i) q^{55} +(0.149450 + 0.327250i) q^{56} +(-14.7189 - 4.32185i) q^{58} +(-2.08771 - 4.57145i) q^{59} +(5.53965 - 6.39309i) q^{61} +(7.23127 - 15.8343i) q^{62} +(1.07383 + 7.46864i) q^{64} +(4.47166 - 2.87376i) q^{65} +(-3.57857 + 1.05076i) q^{67} -9.02995 q^{68} +13.1432 q^{70} +(-1.18331 + 0.347451i) q^{71} +(9.93598 - 6.38547i) q^{73} +(2.25270 + 15.6679i) q^{74} +(-5.16495 + 11.3097i) q^{76} +(3.43973 - 3.96966i) q^{77} +(3.73374 + 8.17574i) q^{79} +(-8.07388 - 2.37071i) q^{80} +(-2.36238 - 5.17288i) q^{82} +(-2.18254 + 15.1799i) q^{83} +(3.95177 - 8.65317i) q^{85} +(6.22822 + 4.00264i) q^{86} +(-0.152216 + 0.0978234i) q^{88} +(-1.71060 - 1.97414i) q^{89} -8.38806 q^{91} +(2.58254 + 8.95799i) q^{92} +(16.5784 - 4.86785i) q^{94} +(-8.57742 - 9.89887i) q^{95} +(-0.172893 - 1.20250i) q^{97} +(-5.75334 - 3.69745i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$

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 $

$2$	1.90549	−	0.559503i	1.34739	−	0.395628i	0.473087	−	0.881016i	$-0.343140\pi$
$2$	1.90549	−	0.559503i	1.34739	−	0.395628i	0.874299	+	0.485387i	$0.161321\pi$
$3$		0			0
$3$		0			0
$4$	1.63535	−	1.05098i	0.817675	−	0.525488i
$5$	0.291446	+	2.02705i	0.130339	+	0.906524i	0.945112	+	0.326745i	$0.105952\pi$
$5$	0.291446	+	2.02705i	0.130339	+	0.906524i	−0.814774	+	0.579779i	$0.803139\pi$
$6$		0			0
$7$	1.34249	−	2.93963i	0.507412	−	1.11108i	−0.466577	−	0.884481i	$-0.654513\pi$
$7$	1.34249	−	2.93963i	0.507412	−	1.11108i	0.973989	−	0.226597i	$-0.0727599\pi$
$8$	−0.0729013	+	0.0841325i	−0.0257745	+	0.0297453i
$9$		0			0
$10$	1.68949	+	3.69946i	0.534263	+	1.16987i
$11$	1.55951	+	0.457915i	0.470211	+	0.138067i	0.508250	−	0.861210i	$-0.330293\pi$
$11$	1.55951	+	0.457915i	0.470211	+	0.138067i	−0.0380383	+	0.999276i	$0.512111\pi$
$12$		0			0
$13$	−1.07824	−	2.36102i	−0.299050	−	0.654829i	0.699138	−	0.714986i	$-0.253567\pi$
$13$	−1.07824	−	2.36102i	−0.299050	−	0.654829i	−0.998189	+	0.0601571i	$0.980840\pi$
$14$	0.913363	−	6.35258i	0.244106	−	1.69780i
$15$		0			0
$16$	−1.70693	+	3.73765i	−0.426732	+	0.934413i
$17$	−3.90777	−	2.51137i	−0.947773	−	0.609097i	−0.0271842	−	0.999630i	$-0.508654\pi$
$17$	−3.90777	−	2.51137i	−0.947773	−	0.609097i	−0.920589	+	0.390534i	$0.872290\pi$
$18$		0			0
$19$	−5.38056	+	3.45787i	−1.23438	+	0.793290i	−0.984568	−	0.175003i	$-0.944007\pi$
$19$	−5.38056	+	3.45787i	−1.23438	+	0.793290i	−0.249816	+	0.968293i	$0.580370\pi$
$20$	2.60700	+	3.00863i	0.582942	+	0.672751i
$21$		0			0
$22$	3.22785			0.688180
$23$	−1.37375	+	4.59487i	−0.286446	+	0.958096i
$23$	−1.37375	+	4.59487i	−0.286446	+	0.958096i
$24$		0			0
$25$	0.773474	−	0.227113i	0.154695	−	0.0454225i
$26$	−3.37558	−	3.89563i	−0.662006	−	0.763995i
$27$		0			0
$28$	−0.894050	−	6.21825i	−0.168960	−	1.17514i
$29$	−6.49822	−	4.17615i	−1.20669	−	0.775492i	−0.226588	−	0.973991i	$-0.572757\pi$
$29$	−6.49822	−	4.17615i	−1.20669	−	0.775492i	−0.980101	+	0.198498i	$0.936394\pi$
$30$		0			0
$31$	5.74006	−	6.62438i	1.03094	−	1.18977i	0.0493530	−	0.998781i	$-0.484284\pi$
$31$	5.74006	−	6.62438i	1.03094	−	1.18977i	0.981592	−	0.190992i	$-0.0611705\pi$
$32$	−1.12962	+	7.85671i	−0.199691	+	1.38888i
$33$		0			0
$34$	−8.85134	−	2.59899i	−1.51799	−	0.445723i
$35$	6.35005	+	1.86454i	1.07335	+	0.315165i
$36$		0			0
$37$	−1.13432	+	7.88940i	−0.186482	+	1.29701i	0.654548	+	0.756021i	$0.272859\pi$
$37$	−1.13432	+	7.88940i	−0.186482	+	1.29701i	−0.841030	+	0.540989i	$0.818050\pi$
$38$	−8.31792	+	9.59939i	−1.34934	+	1.55723i
$39$		0			0
$40$	−0.191788	−	0.123254i	−0.0303243	−	0.0194882i
$41$	−0.407522	−	2.83438i	−0.0636443	−	0.442656i	−0.996581	−	0.0826165i	$-0.973672\pi$
$41$	−0.407522	−	2.83438i	−0.0636443	−	0.442656i	0.932937	−	0.360039i	$-0.117237\pi$
$42$		0			0
$43$	2.44130	+	2.81741i	0.372295	+	0.429651i	0.910721	−	0.413022i	$-0.135527\pi$
$43$	2.44130	+	2.81741i	0.372295	+	0.429651i	−0.538427	+	0.842672i	$0.680981\pi$
$44$	3.03161	−	0.890161i	0.457032	−	0.134197i
$45$		0			0
$46$	−0.0468192	+	9.52410i	−0.00690312	+	1.40425i
$47$	8.70030			1.26907			0.634535	−	0.772894i	$-0.281192\pi$
$47$	8.70030			1.26907			0.634535	+	0.772894i	$0.281192\pi$
$48$		0			0
$49$	−2.25516	−	2.60259i	−0.322166	−	0.371799i
$50$	1.34678	−	0.865522i	0.190463	−	0.122403i
$51$		0			0
$52$	−4.24468	−	2.72789i	−0.588631	−	0.378290i
$53$	0.624559	−	1.36759i	0.0857898	−	0.187853i	−0.861875	−	0.507121i	$-0.830710\pi$
$53$	0.624559	−	1.36759i	0.0857898	−	0.187853i	0.947665	+	0.319268i	$0.103437\pi$
$54$		0			0
$55$	−0.473702	+	3.29467i	−0.0638740	+	0.444253i
$56$	0.149450	+	0.327250i	0.0199711	+	0.0437306i
$57$		0			0
$58$	−14.7189	−	4.32185i	−1.93268	−	0.567487i
$59$	−2.08771	−	4.57145i	−0.271797	−	0.595152i	0.723682	−	0.690133i	$-0.242448\pi$
$59$	−2.08771	−	4.57145i	−0.271797	−	0.595152i	−0.995479	+	0.0949816i	$0.969721\pi$
$60$		0			0
$61$	5.53965	−	6.39309i	0.709279	−	0.818552i	−0.280696	−	0.959797i	$-0.590565\pi$
$61$	5.53965	−	6.39309i	0.709279	−	0.818552i	0.989975	+	0.141245i	$0.0451106\pi$
$62$	7.23127	−	15.8343i	0.918373	−	2.01096i
$63$		0			0
$64$	1.07383	+	7.46864i	0.134229	+	0.933580i
$65$	4.47166	−	2.87376i	0.554641	−	0.356446i
$66$		0			0
$67$	−3.57857	+	1.05076i	−0.437191	+	0.128371i	−0.492919	−	0.870075i	$-0.664070\pi$
$67$	−3.57857	+	1.05076i	−0.437191	+	0.128371i	0.0557280	+	0.998446i	$0.482252\pi$
$68$	−9.02995			−1.09504
$69$		0			0
$70$	13.1432			1.57091
$71$	−1.18331	+	0.347451i	−0.140433	+	0.0412349i	−0.351194	−	0.936303i	$-0.614224\pi$
$71$	−1.18331	+	0.347451i	−0.140433	+	0.0412349i	0.210761	+	0.977538i	$0.432406\pi$
$72$		0			0
$73$	9.93598	−	6.38547i	1.16292	−	0.747363i	0.190749	−	0.981639i	$-0.438908\pi$
$73$	9.93598	−	6.38547i	1.16292	−	0.747363i	0.972170	+	0.234276i	$0.0752721\pi$
$74$	2.25270	+	15.6679i	0.261871	+	1.82135i
$75$		0			0
$76$	−5.16495	+	11.3097i	−0.592460	+	1.29731i
$77$	3.43973	−	3.96966i	0.391994	−	0.452385i
$78$		0			0
$79$	3.73374	+	8.17574i	0.420078	+	0.919843i	0.994834	+	0.101518i	$0.0323699\pi$
$79$	3.73374	+	8.17574i	0.420078	+	0.919843i	−0.574755	+	0.818325i	$0.694903\pi$
$80$	−8.07388	−	2.37071i	−0.902687	−	0.265053i
$81$		0			0
$82$	−2.36238	−	5.17288i	−0.260881	−	0.571249i
$83$	−2.18254	+	15.1799i	−0.239565	+	1.66621i	0.414710	+	0.909954i	$0.363883\pi$
$83$	−2.18254	+	15.1799i	−0.239565	+	1.66621i	−0.654275	+	0.756257i	$0.727026\pi$
$84$		0			0
$85$	3.95177	−	8.65317i	0.428630	−	0.938568i
$86$	6.22822	+	4.00264i	0.671607	+	0.431615i
$87$		0			0
$88$	−0.152216	+	0.0978234i	−0.0162263	+	0.0104280i
$89$	−1.71060	−	1.97414i	−0.181323	−	0.209258i	0.657810	−	0.753184i	$-0.271483\pi$
$89$	−1.71060	−	1.97414i	−0.181323	−	0.209258i	−0.839134	+	0.543925i	$0.816937\pi$
$90$		0			0
$91$	−8.38806			−0.879308
$92$	2.58254	+	8.95799i	0.269248	+	0.933935i
$93$		0			0
$94$	16.5784	−	4.86785i	1.70993	−	0.502080i
$95$	−8.57742	−	9.89887i	−0.880025	−	1.01560i
$96$		0			0
$97$	−0.172893	−	1.20250i	−0.0175546	−	0.122095i	0.979160	−	0.203091i	$-0.0650989\pi$
$97$	−0.172893	−	1.20250i	−0.0175546	−	0.122095i	−0.996714	+	0.0809964i	$0.974190\pi$
$98$	−5.75334	−	3.69745i	−0.581176	−	0.373499i
$99$		0			0
$100$	1.02621	−	1.18431i	0.102621	−	0.118431i
$101$	1.08352	−	7.53601i	0.107814	−	0.749861i	−0.862157	−	0.506641i	$-0.830887\pi$
$101$	1.08352	−	7.53601i	0.107814	−	0.749861i	0.969971	−	0.243221i	$-0.0782039\pi$
$102$		0			0
$103$	−10.4040	−	3.05489i	−1.02514	−	0.301007i	−0.274405	−	0.961614i	$-0.588481\pi$
$103$	−10.4040	−	3.05489i	−1.02514	−	0.301007i	−0.750732	+	0.660607i	$0.770299\pi$
$104$	0.277244	+	0.0814061i	0.0271860	+	0.00798253i
$105$		0			0
$106$	0.424920	−	2.95538i	0.0412719	−	0.287052i
$107$	3.00774	−	3.47111i	0.290769	−	0.335565i	−0.591505	−	0.806301i	$-0.701466\pi$
$107$	3.00774	−	3.47111i	0.290769	−	0.335565i	0.882274	+	0.470736i	$0.156012\pi$
$108$		0			0
$109$	0.710274	+	0.456465i	0.0680319	+	0.0437215i	0.574215	−	0.818705i	$-0.305307\pi$
$109$	0.710274	+	0.456465i	0.0680319	+	0.0437215i	−0.506183	+	0.862426i	$0.668944\pi$
$110$	0.940743	+	6.54301i	0.0896963	+	0.623851i
$111$		0			0
$112$	8.69580	+	10.0355i	0.821676	+	0.948264i
$113$	10.6802	−	3.13598i	1.00471	−	0.295009i	0.262321	−	0.964981i	$-0.415512\pi$
$113$	10.6802	−	3.13598i	1.00471	−	0.295009i	0.742386	+	0.669972i	$0.233694\pi$
$114$		0			0
$115$	−9.71440	−	1.44550i	−0.905873	−	0.134793i
$116$	−15.0159			−1.39419
$117$		0			0
$118$	−6.53585	−	7.54278i	−0.601674	−	0.694369i
$119$	−12.6286	+	8.11593i	−1.15766	+	0.743986i
$120$		0			0
$121$	−7.03139	−	4.51880i	−0.639217	−	0.410800i
$122$	6.97880	−	15.2814i	0.631831	−	1.38352i
$123$		0			0
$124$	2.42494	−	16.8658i	0.217766	−	1.51460i
$125$	4.93942	+	10.8158i	0.441796	+	0.967397i
$126$		0			0
$127$	17.4791	+	5.13231i	1.55102	+	0.455419i	0.941404	−	0.337281i	$-0.109507\pi$
$127$	17.4791	+	5.13231i	1.55102	+	0.455419i	0.609611	+	0.792700i	$0.291325\pi$
$128$	−0.369818	−	0.809788i	−0.0326876	−	0.0715758i
$129$		0			0
$130$	6.91283	−	7.97783i	0.606295	−	0.699702i
$131$	−0.603367	+	1.32119i	−0.0527164	+	0.115433i	−0.934157	−	0.356862i	$-0.883847\pi$
$131$	−0.603367	+	1.32119i	−0.0527164	+	0.115433i	0.881441	+	0.472294i	$0.156574\pi$
$132$		0			0
$133$	2.94156	+	20.4590i	0.255066	+	1.77402i
$134$	−6.23102	+	4.00444i	−0.538279	+	0.345931i
$135$		0			0
$136$	0.496169	−	0.145688i	0.0425461	−	0.0124927i
$137$	4.47536			0.382356			0.191178	−	0.981555i	$-0.438769\pi$
$137$	4.47536			0.382356			0.191178	+	0.981555i	$0.438769\pi$
$138$		0			0
$139$	5.81596			0.493303			0.246652	−	0.969104i	$-0.420670\pi$
$139$	5.81596			0.493303			0.246652	+	0.969104i	$0.420670\pi$
$140$	12.3441	−	3.62457i	1.04327	−	0.306332i
$141$		0			0
$142$	−2.06039	+	1.32413i	−0.172904	+	0.111119i
$143$	−0.600388	−	4.17579i	−0.0502070	−	0.349197i
$144$		0			0
$145$	6.57139	−	14.3893i	0.545724	−	1.19497i
$146$	15.3602	−	17.7267i	1.27122	−	1.46707i
$147$		0			0
$148$	6.43655	+	14.0941i	0.529081	+	1.15853i
$149$	−0.0318508	−	0.00935225i	−0.00260932	−	0.000766166i	0.280428	−	0.959875i	$-0.409524\pi$
$149$	−0.0318508	−	0.00935225i	−0.00260932	−	0.000766166i	−0.283037	+	0.959109i	$0.591342\pi$
$150$		0			0
$151$	6.25711	+	13.7012i	0.509197	+	1.11499i	0.973370	+	0.229241i	$0.0736243\pi$
$151$	6.25711	+	13.7012i	0.509197	+	1.11499i	−0.464173	+	0.885745i	$0.653648\pi$
$152$	0.101330	−	0.704763i	0.00821892	−	0.0571638i
$153$		0			0
$154$	4.33334	−	9.48870i	0.349191	−	0.764621i
$155$	15.1009	+	9.70473i	1.21293	+	0.779503i
$156$		0			0
$157$	−13.1292	+	8.43760i	−1.04782	+	0.673394i	−0.946909	−	0.321502i	$-0.895812\pi$
$157$	−13.1292	+	8.43760i	−1.04782	+	0.673394i	−0.100912	+	0.994895i	$0.532176\pi$
$158$	11.6890	+	13.4898i	0.929924	+	1.07319i
$159$		0			0
$160$	−16.2552			−1.28508
$161$	11.6630	+	10.2069i	0.919173	+	0.804413i
$162$		0			0
$163$	−13.2652	+	3.89500i	−1.03901	+	0.305080i	−0.756368	−	0.654146i	$-0.773028\pi$
$163$	−13.2652	+	3.89500i	−1.03901	+	0.305080i	−0.282640	+	0.959226i	$0.591210\pi$
$164$	−3.64531	−	4.20691i	−0.284651	−	0.328504i
$165$		0			0
$166$	4.33439	+	30.1463i	0.336414	+	2.33981i
$167$	−2.18969	−	1.40723i	−0.169443	−	0.108895i	0.453170	−	0.891424i	$-0.350293\pi$
$167$	−2.18969	−	1.40723i	−0.169443	−	0.108895i	−0.622614	+	0.782529i	$0.713929\pi$
$168$		0			0
$169$	4.10138	−	4.73324i	0.315491	−	0.364096i
$170$	2.68859	−	18.6996i	0.206206	−	1.43419i
$171$		0			0
$172$	6.95341	+	2.04170i	0.530192	+	0.155678i
$173$	−15.6378	−	4.59168i	−1.18892	−	0.349099i	−0.373314	−	0.927705i	$-0.621779\pi$
$173$	−15.6378	−	4.59168i	−1.18892	−	0.349099i	−0.815607	+	0.578606i	$0.803597\pi$
$174$		0			0
$175$	0.370751	−	2.57863i	0.0280261	−	0.194926i
$176$	−4.37350	+	5.04729i	−0.329665	+	0.380454i
$177$		0			0
$178$	−4.36407	−	2.80462i	−0.327101	−	0.210215i
$179$	−0.816896	−	5.68163i	−0.0610576	−	0.424665i	−0.997308	−	0.0733308i	$-0.976637\pi$
$179$	−0.816896	−	5.68163i	−0.0610576	−	0.424665i	0.936250	−	0.351334i	$-0.114272\pi$
$180$		0			0
$181$	−7.62337	−	8.79784i	−0.566641	−	0.653938i	0.398037	−	0.917369i	$-0.369691\pi$
$181$	−7.62337	−	8.79784i	−0.566641	−	0.653938i	−0.964678	+	0.263431i	$0.915146\pi$
$182$	−15.9834	+	4.69315i	−1.18477	+	0.347879i
$183$		0			0
$184$	−0.286430	−	0.450548i	−0.0211159	−	0.0332149i
$185$	−16.3228			−1.20008
$186$		0			0
$187$	−4.94423	−	5.70594i	−0.361558	−	0.417260i
$188$	14.2280	−	9.14381i	1.03769	−	0.666881i
$189$		0			0
$190$	−21.8827	−	14.0631i	−1.58753	−	1.02025i
$191$	−1.34149	+	2.93746i	−0.0970670	+	0.212547i	−0.951936	−	0.306297i	$-0.900910\pi$
$191$	−1.34149	+	2.93746i	−0.0970670	+	0.212547i	0.854869	+	0.518844i	$0.173637\pi$
$192$		0			0
$193$	−0.621799	+	4.32471i	−0.0447581	+	0.311299i	0.955128	+	0.296194i	$0.0957175\pi$
$193$	−0.621799	+	4.32471i	−0.0447581	+	0.311299i	−0.999886	+	0.0151054i	$0.995192\pi$
$194$	−1.00225	−	2.19462i	−0.0719572	−	0.157564i
$195$		0			0
$196$	−6.42323	−	1.88603i	−0.458802	−	0.134717i
$197$	8.92138	+	19.5351i	0.635622	+	1.39182i	0.903594	+	0.428391i	$0.140919\pi$
$197$	8.92138	+	19.5351i	0.635622	+	1.39182i	−0.267972	+	0.963427i	$0.586353\pi$
$198$		0			0
$199$	−4.15479	+	4.79488i	−0.294525	+	0.339900i	−0.883655	−	0.468138i	$-0.844925\pi$
$199$	−4.15479	+	4.79488i	−0.294525	+	0.339900i	0.589130	+	0.808038i	$0.299470\pi$
$200$	−0.0372797	+	0.0816311i	−0.00263607	+	0.00577219i
$201$		0			0
$202$	−2.15179	−	14.9660i	−0.151400	−	1.05301i
$203$	−21.0001	+	13.4960i	−1.47392	+	0.947231i
$204$		0			0
$205$	5.62666	−	1.65214i	0.392983	−	0.115390i
$206$	−21.5340			−1.50034
$207$		0			0
$208$	10.6651			0.739495
$209$	−9.97447	+	2.92877i	−0.689948	+	0.202587i
$210$		0			0
$211$	−12.4219	+	7.98305i	−0.855157	+	0.549576i	−0.893179	−	0.449701i	$-0.851530\pi$
$211$	−12.4219	+	7.98305i	−0.855157	+	0.549576i	0.0380226	+	0.999277i	$0.487894\pi$
$212$	−0.415935	−	2.89289i	−0.0285665	−	0.198685i
$213$		0			0
$214$	3.78912	−	8.29702i	0.259019	−	0.567173i
$215$	−4.99952	+	5.76976i	−0.340965	+	0.393494i
$216$		0			0
$217$	−11.7673	−	25.7668i	−0.798817	−	1.74916i
$218$	1.60882	+	0.472391i	0.108963	+	0.0319943i
$219$		0			0
$220$	2.68795	+	5.88579i	0.181222	+	0.396820i
$221$	−1.71588	+	11.9342i	−0.115422	+	0.802780i
$222$		0			0
$223$	−8.03655	+	17.5976i	−0.538167	+	1.17842i	0.423925	+	0.905697i	$0.360652\pi$
$223$	−8.03655	+	17.5976i	−0.538167	+	1.17842i	−0.962092	+	0.272725i	$0.912075\pi$
$224$	21.5794	+	13.8682i	1.44183	+	0.926609i
$225$		0			0
$226$	18.5964	−	11.9512i	1.23701	−	0.794981i
$227$	−6.36225	−	7.34243i	−0.422277	−	0.487334i	0.504252	−	0.863557i	$-0.331768\pi$
$227$	−6.36225	−	7.34243i	−0.422277	−	0.487334i	−0.926529	+	0.376222i	$0.877223\pi$
$228$		0			0
$229$	5.31591			0.351285			0.175642	−	0.984454i	$-0.443800\pi$
$229$	5.31591			0.351285			0.175642	+	0.984454i	$0.443800\pi$
$230$	−19.3195	+	2.68085i	−1.27389	+	0.176770i
$231$		0			0
$232$	0.825079	−	0.242265i	0.0541691	−	0.0159055i
$233$	−11.0328	−	12.7325i	−0.722781	−	0.834133i	0.268858	−	0.963180i	$-0.413354\pi$
$233$	−11.0328	−	12.7325i	−0.722781	−	0.834133i	−0.991639	+	0.129046i	$0.958808\pi$
$234$		0			0
$235$	2.53567	+	17.6359i	0.165409	+	1.15044i
$236$	−8.21861	−	5.28178i	−0.534986	−	0.343815i
$237$		0			0
$238$	−19.5229	+	22.5306i	−1.26548	+	1.46044i
$239$	2.02812	−	14.1059i	0.131188	−	0.912433i	−0.812821	−	0.582513i	$-0.802069\pi$
$239$	2.02812	−	14.1059i	0.131188	−	0.912433i	0.944009	−	0.329919i	$-0.107022\pi$
$240$		0			0
$241$	−25.8093	−	7.57831i	−1.66253	−	0.488162i	−0.690558	−	0.723277i	$-0.742635\pi$
$241$	−25.8093	−	7.57831i	−1.66253	−	0.488162i	−0.971968	+	0.235115i	$0.924453\pi$
$242$	−15.9265	−	4.67645i	−1.02380	−	0.300614i
$243$		0			0
$244$	2.34028	−	16.2770i	0.149821	−	1.04203i
$245$	4.61833	−	5.32983i	0.295054	−	0.340511i
$246$		0			0
$247$	13.9656	+	8.97518i	0.888613	+	0.571077i
$248$	0.138868	+	0.965851i	0.00881815	+	0.0613316i
$249$		0			0
$250$	15.4635	+	17.8459i	0.977999	+	1.12867i
$251$	5.92489	−	1.73970i	0.373976	−	0.109809i	−0.0893429	−	0.996001i	$-0.528477\pi$
$251$	5.92489	−	1.73970i	0.373976	−	0.109809i	0.463319	+	0.886192i	$0.346659\pi$
$252$		0			0
$253$	−4.24644	+	6.53671i	−0.266971	+	0.410959i
$254$	36.1777			2.26999
$255$		0			0
$256$	−11.0402	−	12.7411i	−0.690012	−	0.796316i
$257$	8.03384	−	5.16304i	0.501137	−	0.322061i	−0.265534	−	0.964102i	$-0.585548\pi$
$257$	8.03384	−	5.16304i	0.501137	−	0.322061i	0.766671	+	0.642040i	$0.221912\pi$
$258$		0			0
$259$	21.6691	+	13.9259i	1.34646	+	0.865314i
$260$	4.29247	−	9.39920i	0.266208	−	0.582914i
$261$		0			0
$262$	−0.410502	+	2.85510i	−0.0253609	+	0.176389i
$263$	−1.19613	−	2.61917i	−0.0737568	−	0.161505i	0.869162	−	0.494527i	$-0.164659\pi$
$263$	−1.19613	−	2.61917i	−0.0737568	−	0.161505i	−0.942919	+	0.333022i	$0.891932\pi$
$264$		0			0
$265$	2.95421	+	0.867433i	0.181475	+	0.0532860i
$266$	17.0520	+	37.3387i	1.04553	+	2.28938i
$267$		0			0
$268$	−4.74788	+	5.47935i	−0.290023	+	0.334704i
$269$	−3.58458	+	7.84914i	−0.218556	+	0.478570i	−0.986873	−	0.161499i	$-0.948367\pi$
$269$	−3.58458	+	7.84914i	−0.218556	+	0.478570i	0.768317	+	0.640069i	$0.221094\pi$
$270$		0			0
$271$	1.06819	+	7.42940i	0.0648877	+	0.451304i	0.996201	+	0.0870845i	$0.0277550\pi$
$271$	1.06819	+	7.42940i	0.0648877	+	0.451304i	−0.931313	+	0.364219i	$0.881336\pi$
$272$	16.0569	−	10.3191i	0.973592	−	0.625690i
$273$		0			0
$274$	8.52776	−	2.50398i	0.515181	−	0.151271i
$275$	1.31024			0.0790106
$276$		0			0
$277$	−7.67215			−0.460975			−0.230487	−	0.973075i	$-0.574032\pi$
$277$	−7.67215			−0.460975			−0.230487	+	0.973075i	$0.574032\pi$
$278$	11.0823	−	3.25405i	0.664670	−	0.195165i
$279$		0			0
$280$	−0.619795	+	0.398318i	−0.0370398	+	0.0238041i
$281$	−3.28055	−	22.8167i	−0.195701	−	1.36113i	−0.816584	−	0.577227i	$-0.804135\pi$
$281$	−3.28055	−	22.8167i	−0.195701	−	1.36113i	0.620882	−	0.783904i	$-0.286774\pi$
$282$		0			0
$283$	3.22316	−	7.05774i	0.191597	−	0.419539i	−0.789316	−	0.613988i	$-0.789564\pi$
$283$	3.22316	−	7.05774i	0.191597	−	0.419539i	0.980913	+	0.194449i	$0.0622917\pi$
$284$	−1.56996	+	1.81184i	−0.0931602	+	0.107513i
$285$		0			0
$286$	−3.48040	−	7.62101i	−0.205800	−	0.450640i
$287$	−8.87914	−	2.60715i	−0.524119	−	0.153895i
$288$		0			0
$289$	1.90161	+	4.16395i	0.111860	+	0.244938i
$290$	4.47086	−	31.0955i	0.262538	−	1.82599i
$291$		0			0
$292$	9.53784	−	20.8849i	0.558160	−	1.22220i
$293$	−8.81117	−	5.66260i	−0.514754	−	0.330812i	0.257340	−	0.966321i	$-0.417154\pi$
$293$	−8.81117	−	5.66260i	−0.514754	−	0.330812i	−0.772094	+	0.635509i	$0.780790\pi$
$294$		0			0
$295$	8.65810	−	5.56422i	0.504094	−	0.323961i
$296$	−0.581062	−	0.670581i	−0.0337735	−	0.0389767i
$297$		0			0
$298$	−0.0659242			−0.00381888
$299$	12.3298	−	1.71094i	0.713051	−	0.0989461i
$300$		0			0
$301$	11.5596	−	3.39419i	0.666282	−	0.195638i
$302$	19.5887	+	22.6066i	1.12720	+	1.30086i
$303$		0			0
$304$	−3.74010	−	26.0130i	−0.214509	−	1.49195i
$305$	14.5736	+	9.36590i	0.834483	+	0.536290i
$306$		0			0
$307$	13.1658	−	15.1941i	0.751409	−	0.867172i	−0.243295	−	0.969952i	$-0.578228\pi$
$307$	13.1658	−	15.1941i	0.751409	−	0.867172i	0.994704	+	0.102780i	$0.0327737\pi$
$308$	1.45315	−	10.1069i	0.0828007	−	0.575892i
$309$		0			0
$310$	34.2044	+	10.0433i	1.94268	+	0.570422i
$311$	−16.3900	−	4.81254i	−0.929393	−	0.272894i	−0.218210	−	0.975902i	$-0.570022\pi$
$311$	−16.3900	−	4.81254i	−0.929393	−	0.272894i	−0.711183	+	0.703007i	$0.751840\pi$
$312$		0			0
$313$	−1.51418	+	10.5314i	−0.0855866	+	0.595268i	0.901220	+	0.433362i	$0.142673\pi$
$313$	−1.51418	+	10.5314i	−0.0855866	+	0.595268i	−0.986806	+	0.161905i	$0.948236\pi$
$314$	−20.2966	+	23.4236i	−1.14541	+	1.32187i
$315$		0			0
$316$	14.6985	+	9.44614i	0.826854	+	0.531387i
$317$	2.24495	+	15.6140i	0.126089	+	0.876969i	0.950444	+	0.310896i	$0.100629\pi$
$317$	2.24495	+	15.6140i	0.126089	+	0.876969i	−0.824355	+	0.566073i	$0.808462\pi$
$318$		0			0
$319$	−8.22175	−	9.48841i	−0.460330	−	0.531249i
$320$	−14.8263	+	4.35341i	−0.828818	+	0.243363i
$321$		0			0
$322$	27.9345	+	12.9236i	1.55673	+	0.720205i
$323$	29.7100			1.65311
$324$		0			0
$325$	−1.37021	−	1.58131i	−0.0760055	−	0.0877151i
$326$	−23.0974	+	14.8438i	−1.27925	+	0.822122i
$327$		0			0
$328$	0.268173	+	0.172344i	0.0148074	+	0.00951611i
$329$	11.6800	−	25.5757i	0.643941	−	1.41003i
$330$		0			0
$331$	1.75458	−	12.2034i	0.0964405	−	0.670759i	−0.883052	−	0.469276i	$-0.844515\pi$
$331$	1.75458	−	12.2034i	0.0964405	−	0.670759i	0.979492	−	0.201483i	$-0.0645760\pi$
$332$	12.3845	+	27.1182i	0.679687	+	1.48831i
$333$		0			0
$334$	−4.95979	−	1.45633i	−0.271388	−	0.0796866i
$335$	−3.17290	−	6.94769i	−0.173354	−	0.379593i
$336$		0			0
$337$	−19.2495	+	22.2151i	−1.04859	+	1.21013i	−0.0714669	+	0.997443i	$0.522768\pi$
$337$	−19.2495	+	22.2151i	−1.04859	+	1.21013i	−0.977120	+	0.212690i	$0.931777\pi$
$338$	5.16688	−	11.3139i	0.281041	−	0.615395i
$339$		0			0
$340$	−2.63174	−	18.3042i	−0.142726	−	0.992683i
$341$	11.9851	−	7.70236i	0.649030	−	0.417106i
$342$		0			0
$343$	11.0272	−	3.23788i	0.595413	−	0.174829i
$344$	−0.415009			−0.0223758
$345$		0			0
$346$	−32.3668			−1.74005
$347$	28.7698	−	8.44756i	1.54444	−	0.453489i	0.605008	−	0.796220i	$-0.293170\pi$
$347$	28.7698	−	8.44756i	1.54444	−	0.453489i	0.939434	+	0.342731i	$0.111352\pi$
$348$		0			0
$349$	7.53619	−	4.84322i	0.403403	−	0.259251i	−0.323170	−	0.946341i	$-0.604748\pi$
$349$	7.53619	−	4.84322i	0.403403	−	0.259251i	0.726573	+	0.687090i	$0.241112\pi$
$350$	−0.736287	−	5.12099i	−0.0393562	−	0.273728i
$351$		0			0
$352$	−5.35937	+	11.7354i	−0.285656	+	0.625498i
$353$	−6.27244	+	7.23878i	−0.333848	+	0.385281i	−0.897709	−	0.440588i	$-0.854770\pi$
$353$	−6.27244	+	7.23878i	−0.333848	+	0.385281i	0.563861	+	0.825870i	$0.309315\pi$
$354$		0			0
$355$	−1.04917	−	2.29737i	−0.0556843	−	0.121932i
$356$	−4.87220	−	1.43061i	−0.258226	−	0.0758221i
$357$		0			0
$358$	−4.73548	−	10.3693i	−0.250278	−	0.548032i
$359$	−2.00532	+	13.9473i	−0.105837	+	0.736111i	0.865930	+	0.500166i	$0.166728\pi$
$359$	−2.00532	+	13.9473i	−0.105837	+	0.736111i	−0.971766	+	0.235945i	$0.924181\pi$
$360$		0			0
$361$	9.10060	−	19.9275i	0.478979	−	1.04882i
$362$	−19.4487	−	12.4989i	−1.02220	−	0.656929i
$363$		0			0
$364$	−13.7174	+	8.81565i	−0.718988	+	0.462066i
$365$	15.8395	+	18.2797i	0.829075	+	0.956804i
$366$		0			0
$367$	8.38697			0.437796			0.218898	−	0.975748i	$-0.429754\pi$
$367$	8.38697			0.437796			0.218898	+	0.975748i	$0.429754\pi$
$368$	−14.8291	−	12.9777i	−0.773022	−	0.676509i
$369$		0			0
$370$	−31.1030	+	9.13266i	−1.61697	+	0.474784i
$371$	−3.18176	−	3.67195i	−0.165189	−	0.190638i
$372$		0			0
$373$	−2.53997	−	17.6659i	−0.131515	−	0.914706i	−0.943581	−	0.331141i	$-0.892566\pi$
$373$	−2.53997	−	17.6659i	−0.131515	−	0.914706i	0.812066	−	0.583565i	$-0.198343\pi$
$374$	−12.6137	−	8.10632i	−0.652238	−	0.419168i
$375$		0			0
$376$	−0.634263	+	0.731978i	−0.0327096	+	0.0377489i
$377$	−2.85333	+	19.8453i	−0.146954	+	1.02209i
$378$		0			0
$379$	21.1535	+	6.21123i	1.08658	+	0.319050i	0.775509	−	0.631336i	$-0.217493\pi$
$379$	21.1535	+	6.21123i	1.08658	+	0.319050i	0.311074	+	0.950386i	$0.399311\pi$
$380$	−24.4306	−	7.17346i	−1.25326	−	0.367991i
$381$		0			0
$382$	−0.912687	+	6.34788i	−0.0466971	+	0.324786i
$383$	−6.06799	+	7.00284i	−0.310060	+	0.357828i	−0.889296	−	0.457331i	$-0.848805\pi$
$383$	−6.06799	+	7.00284i	−0.310060	+	0.357828i	0.579236	+	0.815160i	$0.303351\pi$
$384$		0			0
$385$	9.04919	+	5.81556i	0.461190	+	0.296389i
$386$	1.23485	+	8.58860i	0.0628524	+	0.437148i
$387$		0			0
$388$	−1.54654	−	1.78480i	−0.0785135	−	0.0906094i
$389$	23.3799	−	6.86495i	1.18541	−	0.348067i	0.371150	−	0.928573i	$-0.378963\pi$
$389$	23.3799	−	6.86495i	1.18541	−	0.348067i	0.814256	+	0.580506i	$0.197145\pi$
$390$		0			0
$391$	16.9077	−	14.5057i	0.855059	−	0.733585i
$392$	0.383367			0.0193629
$393$		0			0
$394$	27.9296	+	32.2324i	1.40707	+	1.62385i
$395$	−15.4845	+	9.95126i	−0.779108	+	0.500702i
$396$		0			0
$397$	23.5996	+	15.1666i	1.18443	+	0.761188i	0.976196	−	0.216891i	$-0.0695916\pi$
$397$	23.5996	+	15.1666i	1.18443	+	0.761188i	0.208235	+	0.978079i	$0.433228\pi$
$398$	−5.23417	+	11.4612i	−0.262365	+	0.574499i
$399$		0			0
$400$	−0.471397	+	3.27864i	−0.0235699	+	0.163932i
$401$	−5.48424	−	12.0088i	−0.273870	−	0.599691i	0.721857	−	0.692042i	$-0.243289\pi$
$401$	−5.48424	−	12.0088i	−0.273870	−	0.599691i	−0.995726	+	0.0923515i	$0.970562\pi$
$402$		0			0
$403$	−21.8295	−	6.40971i	−1.08740	−	0.319290i
$404$	−6.14824	−	13.4628i	−0.305886	−	0.669798i
$405$		0			0
$406$	−32.4646	+	37.4661i	−1.61119	+	1.85941i
$407$	−5.38167	+	11.7842i	−0.266760	+	0.584122i
$408$		0			0
$409$	−2.81719	−	19.5940i	−0.139301	−	0.968861i	−0.932827	−	0.360324i	$-0.882666\pi$
$409$	−2.81719	−	19.5940i	−0.139301	−	0.968861i	0.793526	−	0.608537i	$-0.208243\pi$
$410$	9.79718	−	6.29627i	0.483848	−	0.310950i
$411$		0			0
$412$	−20.2248	+	5.93854i	−0.996405	+	0.292571i
$413$	−16.2411			−0.799172
$414$		0			0
$415$	−31.4065			−1.54168
$416$	19.7679	−	5.80437i	0.969199	−	0.284583i
$417$		0			0
$418$	−17.3676	+	11.1615i	−0.849478	+	0.545926i
$419$	0.651232	+	4.52942i	0.0318147	+	0.221276i	0.999526	−	0.0307848i	$-0.00980065\pi$
$419$	0.651232	+	4.52942i	0.0318147	+	0.221276i	−0.967711	+	0.252061i	$0.918892\pi$
$420$		0			0
$421$	2.66275	−	5.83061i	0.129774	−	0.284166i	−0.833580	−	0.552399i	$-0.813712\pi$
$421$	2.66275	−	5.83061i	0.129774	−	0.284166i	0.963354	+	0.268233i	$0.0864397\pi$
$422$	−19.2032	+	22.1617i	−0.934799	+	1.07882i
$423$		0			0
$424$	0.0695280	+	0.152245i	0.00337658	+	0.00739367i
$425$	−3.59292	−	1.05498i	−0.174282	−	0.0511739i
$426$		0			0
$427$	−11.3565	−	24.8672i	−0.549578	−	1.20341i
$428$	1.27065	−	8.83754i	0.0614190	−	0.427179i
$429$		0			0
$430$	−6.29835	+	13.7915i	−0.303734	+	0.665084i
$431$	9.49712	+	6.10343i	0.457460	+	0.293992i	0.749004	−	0.662566i	$-0.230532\pi$
$431$	9.49712	+	6.10343i	0.457460	+	0.293992i	−0.291544	+	0.956558i	$0.594169\pi$
$432$		0			0
$433$	−3.84775	+	2.47280i	−0.184911	+	0.118835i	−0.629821	−	0.776740i	$-0.716872\pi$
$433$	−3.84775	+	2.47280i	−0.184911	+	0.118835i	0.444910	+	0.895575i	$0.353236\pi$
$434$	−36.8391	−	42.5146i	−1.76833	−	2.04077i
$435$		0			0
$436$	1.64128			0.0786031
$437$	−8.49696	−	29.4732i	−0.406465	−	1.40989i
$438$		0			0
$439$	1.65787	−	0.486795i	0.0791258	−	0.0232334i	−0.241930	−	0.970294i	$-0.577780\pi$
$439$	1.65787	−	0.486795i	0.0791258	−	0.0232334i	0.321056	+	0.947060i	$0.395962\pi$
$440$	−0.242656	−	0.280039i	−0.0115682	−	0.0133504i
$441$		0			0
$442$	3.40762	+	23.7005i	0.162084	+	1.12732i
$443$	−9.26899	−	5.95682i	−0.440383	−	0.283017i	0.301601	−	0.953434i	$-0.402479\pi$
$443$	−9.26899	−	5.95682i	−0.440383	−	0.283017i	−0.741984	+	0.670417i	$0.766115\pi$
$444$		0			0
$445$	3.50313	−	4.04283i	0.166064	−	0.191648i
$446$	−5.46768	+	38.0286i	−0.258902	+	1.80070i
$447$		0			0
$448$	23.3967	+	6.86989i	1.10539	+	0.324572i
$449$	13.0534	+	3.83284i	0.616030	+	0.180883i	0.574836	−	0.818268i	$-0.305066\pi$
$449$	13.0534	+	3.83284i	0.616030	+	0.180883i	0.0411937	+	0.999151i	$0.486884\pi$
$450$		0			0
$451$	0.662368	−	4.60687i	0.0311897	−	0.216929i
$452$	14.1700	−	16.3530i	0.666500	−	0.769182i
$453$		0			0
$454$	−16.2313	−	10.4312i	−0.761774	−	0.489563i
$455$	−2.44467	−	17.0030i	−0.114608	−	0.797114i
$456$		0			0
$457$	−16.8885	−	19.4903i	−0.790009	−	0.911719i	0.207780	−	0.978176i	$-0.433376\pi$
$457$	−16.8885	−	19.4903i	−0.790009	−	0.911719i	−0.997789	+	0.0664563i	$0.978831\pi$
$458$	10.1294	−	2.97427i	0.473317	−	0.138978i
$459$		0			0
$460$	−17.4056	+	7.84571i	−0.811542	+	0.365808i
$461$	−38.6842			−1.80170			−0.900851	−	0.434129i	$-0.857056\pi$
$461$	−38.6842			−1.80170			−0.900851	+	0.434129i	$0.857056\pi$
$462$		0			0
$463$	−7.06213	−	8.15014i	−0.328205	−	0.378769i	0.567533	−	0.823351i	$-0.307898\pi$
$463$	−7.06213	−	8.15014i	−0.328205	−	0.378769i	−0.895738	+	0.444582i	$0.853352\pi$
$464$	26.7010	−	17.1597i	1.23956	−	0.796619i
$465$		0			0
$466$	−28.1467	−	18.0888i	−1.30387	−	0.837947i
$467$	−6.21336	+	13.6054i	−0.287520	+	0.629581i	−0.997187	−	0.0749564i	$-0.976118\pi$
$467$	−6.21336	+	13.6054i	−0.287520	+	0.629581i	0.709667	+	0.704538i	$0.248846\pi$
$468$		0			0
$469$	−1.71532	+	11.9303i	−0.0792061	+	0.550890i
$470$	14.6991	+	32.1864i	0.678017	+	1.48465i
$471$		0			0
$472$	0.536804	+	0.157620i	0.0247084	+	0.00725504i
$473$	2.51711	+	5.51170i	0.115737	+	0.253428i
$474$		0			0
$475$	−3.37639	+	3.89657i	−0.154920	+	0.178787i
$476$	−12.1226	+	26.5448i	−0.555638	+	1.21668i
$477$		0			0
$478$	−4.02771	−	28.0134i	−0.184223	−	1.28130i
$479$	35.8617	−	23.0469i	1.63856	−	1.05304i	0.696528	−	0.717530i	$-0.254727\pi$
$479$	35.8617	−	23.0469i	1.63856	−	1.05304i	0.942036	−	0.335511i	$-0.108909\pi$
$480$		0			0
$481$	19.8501	−	5.82852i	0.905087	−	0.265758i
$482$	−53.4196			−2.43320
$483$		0			0
$484$	−16.2479			−0.738542
$485$	2.38713	−	0.700926i	0.108394	−	0.0318274i
$486$		0			0
$487$	−27.7611	+	17.8410i	−1.25797	+	0.808451i	−0.988006	−	0.154418i	$-0.950650\pi$
$487$	−27.7611	+	17.8410i	−1.25797	+	0.808451i	−0.269968	+	0.962869i	$0.587013\pi$
$488$	0.134020	+	0.932129i	0.00606680	+	0.0421955i
$489$		0			0
$490$	5.81813	−	12.7399i	0.262836	−	0.575531i
$491$	19.9564	−	23.0310i	0.900622	−	1.03937i	−0.0983997	−	0.995147i	$-0.531372\pi$
$491$	19.9564	−	23.0310i	0.900622	−	1.03937i	0.999022	−	0.0442260i	$-0.0140822\pi$
$492$		0			0
$493$	14.9057	+	32.6389i	0.671318	+	1.46998i
$494$	31.6331	+	9.28831i	1.42324	+	0.417901i
$495$		0			0
$496$	14.9617	+	32.7617i	0.671802	+	1.47104i
$497$	−0.567198	+	3.94495i	−0.0254423	+	0.176955i
$498$		0			0
$499$	−11.1079	+	24.3229i	−0.497258	+	1.08884i	0.480092	+	0.877218i	$0.340603\pi$
$499$	−11.1079	+	24.3229i	−0.497258	+	1.08884i	−0.977351	+	0.211626i	$0.932124\pi$
$500$	19.4449	+	12.4965i	0.869601	+	0.558858i
$501$		0			0
$502$	10.3165	−	6.62999i	0.460446	−	0.295911i
$503$	19.8916	+	22.9561i	0.886922	+	1.02356i	0.999552	+	0.0299259i	$0.00952712\pi$
$503$	19.8916	+	22.9561i	0.886922	+	1.02356i	−0.112630	+	0.993637i	$0.535927\pi$
$504$		0			0
$505$	15.5917			0.693820
$506$	−4.43424	+	14.8315i	−0.197126	+	0.659342i
$507$		0			0
$508$	33.9783	−	9.97693i	1.50754	−	0.442655i
$509$	10.9695	+	12.6595i	0.486215	+	0.561122i	0.944850	−	0.327503i	$-0.106207\pi$
$509$	10.9695	+	12.6595i	0.486215	+	0.561122i	−0.458635	+	0.888625i	$0.651662\pi$
$510$		0			0
$511$	−5.43202	−	37.7806i	−0.240299	−	1.67131i
$512$	−26.6678	−	17.1384i	−1.17856	−	0.757417i
$513$		0			0
$514$	12.4197	−	14.3331i	0.547809	−	0.632205i
$515$	3.16021	−	21.9798i	0.139256	−	0.968545i
$516$		0			0
$517$	13.5683	+	3.98400i	0.596731	+	0.175216i
$518$	49.0820	+	14.4118i	2.15654	+	0.633217i
$519$		0			0
$520$	−0.0842127	+	0.585712i	−0.00369297	+	0.0256852i
$521$	−7.75531	+	8.95011i	−0.339766	+	0.392111i	−0.899760	−	0.436386i	$-0.856258\pi$
$521$	−7.75531	+	8.95011i	−0.339766	+	0.392111i	0.559993	+	0.828497i	$0.310804\pi$
$522$		0			0
$523$	7.30361	+	4.69375i	0.319365	+	0.205243i	0.690494	−	0.723338i	$-0.257393\pi$
$523$	7.30361	+	4.69375i	0.319365	+	0.205243i	−0.371130	+	0.928581i	$0.621029\pi$
$524$	0.401822	+	2.79473i	0.0175537	+	0.122088i
$525$		0			0
$526$	−3.74466	−	4.32156i	−0.163275	−	0.188429i
$527$	−39.0671	+	11.4711i	−1.70179	+	0.499690i
$528$		0			0
$529$	−19.2256	−	12.6244i	−0.835898	−	0.548885i
$530$	6.11455			0.265599
$531$		0			0
$532$	26.3124	+	30.3661i	1.14079	+	1.31654i
$533$	−6.25262	+	4.01832i	−0.270831	+	0.174053i
$534$		0			0
$535$	7.91271	+	5.08519i	0.342096	+	0.219852i
$536$	0.172479	−	0.377676i	0.00744994	−	0.0163131i
$537$		0			0
$538$	−2.43877	+	16.9621i	−0.105143	+	0.731286i
$539$	−2.32519	−	5.09145i	−0.100153	−	0.219304i
$540$		0			0
$541$	30.6995	+	9.01419i	1.31988	+	0.387550i	0.864448	−	0.502723i	$-0.167668\pi$
$541$	30.6995	+	9.01419i	1.31988	+	0.387550i	0.455427	+	0.890273i	$0.349486\pi$
$542$	6.19219	+	13.5590i	0.265977	+	0.582409i
$543$		0			0
$544$	24.1454	−	27.8653i	1.03523	−	1.19471i
$545$	−0.718272	+	1.57280i	−0.0307674	+	0.0673712i
$546$		0			0
$547$	−2.94629	−	20.4919i	−0.125974	−	0.876169i	−0.950584	−	0.310467i	$-0.899514\pi$
$547$	−2.94629	−	20.4919i	−0.125974	−	0.876169i	0.824610	−	0.565702i	$-0.191395\pi$
$548$	7.31877	−	4.70349i	0.312643	−	0.200923i
$549$		0			0
$550$	2.49666	−	0.733085i	0.106458	−	0.0312588i
$551$	49.4047			2.10471
$552$		0			0
$553$	29.0462			1.23517
$554$	−14.6192	+	4.29259i	−0.621111	+	0.182375i
$555$		0			0
$556$	9.51113	−	6.11243i	0.403362	−	0.259225i
$557$	−3.33433	−	23.1908i	−0.141280	−	0.982625i	−0.929918	−	0.367767i	$-0.880122\pi$
$557$	−3.33433	−	23.1908i	−0.141280	−	0.982625i	0.788638	−	0.614858i	$-0.210787\pi$
$558$		0			0
$559$	4.01965	−	8.80180i	0.170013	−	0.372277i
$560$	−17.8081	+	20.5516i	−0.752529	+	0.868464i
$561$		0			0
$562$	−19.0171	−	41.6416i	−0.802187	−	1.75654i
$563$	−18.3162	−	5.37813i	−0.771937	−	0.226661i	−0.128035	−	0.991770i	$-0.540867\pi$
$563$	−18.3162	−	5.37813i	−0.771937	−	0.226661i	−0.643901	+	0.765109i	$0.722685\pi$
$564$		0			0
$565$	9.46949	+	20.7353i	0.398384	+	0.872340i
$566$	2.19288	−	15.2518i	0.0921737	−	0.641082i
$567$		0			0
$568$	0.0570329	−	0.124885i	0.00239305	−	0.00524004i
$569$	−12.8432	−	8.25385i	−0.538417	−	0.346020i	0.243003	−	0.970026i	$-0.421868\pi$
$569$	−12.8432	−	8.25385i	−0.538417	−	0.346020i	−0.781419	+	0.624006i	$0.785504\pi$
$570$		0			0
$571$	27.3906	−	17.6029i	1.14626	−	0.736658i	0.177371	−	0.984144i	$-0.443241\pi$
$571$	27.3906	−	17.6029i	1.14626	−	0.736658i	0.968891	+	0.247486i	$0.0796045\pi$
$572$	−5.37050	−	6.19788i	−0.224552	−	0.259147i
$573$		0			0
$574$	−18.3778			−0.767076
$575$	−0.0190048	+	3.86601i	−0.000792554	+	0.161224i
$576$		0			0
$577$	−37.1531	+	10.9091i	−1.54670	+	0.454153i	−0.940113	−	0.340863i	$-0.889281\pi$
$577$	−37.1531	+	10.9091i	−1.54670	+	0.454153i	−0.606589	+	0.795015i	$0.707463\pi$
$578$	5.95325	+	6.87042i	0.247623	+	0.285772i
$579$		0			0
$580$	−4.37632	−	30.4380i	−0.181717	−	1.26387i
$581$	41.6933	+	26.7947i	1.72973	+	1.11163i
$582$		0			0
$583$	1.60025	−	1.84679i	0.0662756	−	0.0764862i
$584$	−0.187120	+	1.30145i	−0.00774308	+	0.0538543i
$585$		0			0
$586$	−19.9579	−	5.86016i	−0.824452	−	0.242081i
$587$	−4.61318	−	1.35455i	−0.190406	−	0.0559083i	0.185139	−	0.982712i	$-0.440726\pi$
$587$	−4.61318	−	1.35455i	−0.190406	−	0.0559083i	−0.375545	+	0.926804i	$0.622545\pi$
$588$		0			0
$589$	−7.97843	+	55.4912i	−0.328746	+	2.28648i
$590$	13.3847	−	15.4468i	0.551041	−	0.635935i
$591$		0			0
$592$	−27.5516	−	17.7063i	−1.13236	−	0.727726i
$593$	−4.47077	−	31.0949i	−0.183593	−	1.27691i	−0.848182	−	0.529706i	$-0.822302\pi$
$593$	−4.47077	−	31.0949i	−0.183593	−	1.27691i	0.664589	−	0.747209i	$-0.268607\pi$
$594$		0			0
$595$	−20.1320	−	23.2335i	−0.825330	−	0.952481i
$596$	−0.0619163	+	0.0181803i	−0.00253619	+	0.000744692i
$597$		0			0
$598$	22.5371	−	10.1587i	0.921610	−	0.415422i
$599$	−38.0521			−1.55477			−0.777384	−	0.629026i	$-0.783454\pi$
$599$	−38.0521			−1.55477			−0.777384	+	0.629026i	$0.783454\pi$
$600$		0			0
$601$	4.36534	+	5.03788i	0.178066	+	0.205499i	0.837765	−	0.546031i	$-0.183862\pi$
$601$	4.36534	+	5.03788i	0.178066	+	0.205499i	−0.659699	+	0.751530i	$0.729316\pi$
$602$	20.1276	−	12.9352i	0.820340	−	0.527200i
$603$		0			0
$604$	24.6322	+	15.8301i	1.00227	+	0.644119i
$605$	7.11056	−	15.5700i	0.289085	−	0.633009i
$606$		0			0
$607$	−0.942420	+	6.55468i	−0.0382517	+	0.266046i	−0.999968	−	0.00800074i	$-0.997453\pi$
$607$	−0.942420	+	6.55468i	−0.0382517	+	0.266046i	0.961716	+	0.274047i	$0.0883623\pi$
$608$	−21.0895	−	46.1796i	−0.855292	−	1.87283i
$609$		0			0
$610$	33.0102	+	9.69266i	1.33654	+	0.392444i
$611$	−9.38103	−	20.5416i	−0.379516	−	0.831024i
$612$		0			0
$613$	−19.4706	+	22.4703i	−0.786410	+	0.907565i	−0.997555	−	0.0698897i	$-0.977735\pi$
$613$	−19.4706	+	22.4703i	−0.786410	+	0.907565i	0.211145	+	0.977455i	$0.432281\pi$
$614$	16.5861	−	36.3185i	0.669361	−	1.46570i
$615$		0			0
$616$	0.0832169	+	0.578786i	0.00335291	+	0.0233200i
$617$	−40.9365	+	26.3083i	−1.64804	+	1.05913i	−0.715156	+	0.698965i	$0.753644\pi$
$617$	−40.9365	+	26.3083i	−1.64804	+	1.05913i	−0.932888	+	0.360168i	$0.882719\pi$
$618$		0			0
$619$	−25.4383	+	7.46935i	−1.02245	+	0.300219i	−0.749638	−	0.661849i	$-0.769772\pi$
$619$	−25.4383	+	7.46935i	−1.02245	+	0.300219i	−0.272813	+	0.962067i	$0.587954\pi$
$620$	34.8946			1.40140
$621$		0			0
$622$	−33.9237			−1.36022
$623$	−8.09971	+	2.37829i	−0.324508	+	0.0952841i
$624$		0			0
$625$	−17.0939	+	10.9856i	−0.683755	+	0.439422i
$626$	3.00707	+	20.9146i	0.120187	+	0.835916i
$627$		0			0
$628$	−12.6031	+	27.5969i	−0.502917	+	1.10123i
$629$	24.2459	−	27.9812i	0.966746	−	1.11568i
$630$		0			0
$631$	12.5343	+	27.4463i	0.498982	+	1.09262i	0.976799	+	0.214159i	$0.0687012\pi$
$631$	12.5343	+	27.4463i	0.498982	+	1.09262i	−0.477816	+	0.878460i	$0.658572\pi$
$632$	−0.960040	−	0.281893i	−0.0381883	−	0.0112131i
$633$		0			0
$634$	13.0138	+	28.4963i	0.516844	+	1.13173i
$635$	−5.30926	+	36.9267i	−0.210692	+	1.46539i
$636$		0			0
$637$	−3.71317	+	8.13070i	−0.147121	+	0.322150i
$638$	−20.9753	−	13.4800i	−0.830419	−	0.533678i
$639$		0			0
$640$	1.53370	−	0.985648i	0.0606247	−	0.0389612i
$641$	−28.2677	−	32.6226i	−1.11651	−	1.28852i	−0.953334	−	0.301918i	$-0.902373\pi$
$641$	−28.2677	−	32.6226i	−1.11651	−	1.28852i	−0.163171	−	0.986598i	$-0.552172\pi$
$642$		0			0
$643$	−7.57458			−0.298712			−0.149356	−	0.988783i	$-0.547720\pi$
$643$	−7.57458			−0.298712			−0.149356	+	0.988783i	$0.547720\pi$
$644$	29.8003	+	4.43426i	1.17429	+	0.174734i
$645$		0			0
$646$	56.6121	−	16.6228i	2.22737	−	0.654016i
$647$	16.9543	+	19.5663i	0.666541	+	0.769230i	0.983831	−	0.179099i	$-0.0573182\pi$
$647$	16.9543	+	19.5663i	0.666541	+	0.769230i	−0.317290	+	0.948329i	$0.602773\pi$
$648$		0			0
$649$	−1.16248	−	8.08523i	−0.0456314	−	0.317373i
$650$	−3.49567	−	2.24653i	−0.137111	−	0.0881162i
$651$		0			0
$652$	−17.5996	+	20.3111i	−0.689255	+	0.795442i
$653$	−6.40456	+	44.5447i	−0.250630	+	1.74317i	0.343819	+	0.939036i	$0.388279\pi$
$653$	−6.40456	+	44.5447i	−0.250630	+	1.74317i	−0.594449	+	0.804134i	$0.702630\pi$
$654$		0			0
$655$	−2.85397	−	0.838000i	−0.111514	−	0.0327434i
$656$	11.2895	+	3.31491i	0.440782	+	0.129425i
$657$		0			0
$658$	7.94653	−	55.2693i	0.309788	−	2.15462i
$659$	−20.2462	+	23.3653i	−0.788679	+	0.910184i	−0.997704	−	0.0677265i	$-0.978425\pi$
$659$	−20.2462	+	23.3653i	−0.788679	+	0.910184i	0.209025	+	0.977910i	$0.432971\pi$
$660$		0			0
$661$	−9.43193	−	6.06153i	−0.366860	−	0.235766i	0.344203	−	0.938895i	$-0.388149\pi$
$661$	−9.43193	−	6.06153i	−0.366860	−	0.235766i	−0.711062	+	0.703129i	$0.751786\pi$
$662$	−3.48449	−	24.2351i	−0.135428	−	0.941926i
$663$		0			0
$664$	−1.11801	−	1.29026i	−0.0433873	−	0.0500716i
$665$	−40.6141	+	11.9254i	−1.57495	+	0.462447i
$666$		0			0
$667$	28.1158	−	24.1215i	1.08865	−	0.933988i
$668$	−5.05988			−0.195773
$669$		0			0
$670$	−9.93320	−	11.4635i	−0.383753	−	0.442874i
$671$	11.5667	−	7.43344i	0.446526	−	0.286965i
$672$		0			0
$673$	5.55352	+	3.56903i	0.214073	+	0.137576i	0.643283	−	0.765628i	$-0.277572\pi$
$673$	5.55352	+	3.56903i	0.214073	+	0.137576i	−0.429211	+	0.903204i	$0.641208\pi$
$674$	−24.2503	+	53.1008i	−0.934088	+	2.04537i
$675$		0			0
$676$	1.73267	−	12.0510i	0.0666410	−	0.463498i
$677$	12.0749	+	26.4404i	0.464076	+	1.01619i	0.986539	+	0.163524i	$0.0522860\pi$
$677$	12.0749	+	26.4404i	0.464076	+	1.01619i	−0.522463	+	0.852662i	$0.674987\pi$
$678$		0			0
$679$	−3.76701	−	1.10609i	−0.144565	−	0.0424480i
$680$	0.439924	+	0.963299i	0.0168703	+	0.0369408i
$681$		0			0
$682$	18.5280	−	21.3825i	0.709475	−	0.818778i
$683$	5.13709	−	11.2487i	0.196565	−	0.430418i	−0.785525	−	0.618830i	$-0.787607\pi$
$683$	5.13709	−	11.2487i	0.196565	−	0.430418i	0.982090	+	0.188412i	$0.0603341\pi$
$684$		0			0
$685$	1.30432	+	9.07177i	0.0498357	+	0.346615i
$686$	19.2006	−	12.3395i	0.733084	−	0.471124i
$687$		0			0
$688$	−14.6976	+	4.31561i	−0.560341	+	0.164531i
$689$	−3.90234			−0.148667
$690$		0			0
$691$	28.7504			1.09372			0.546858	−	0.837225i	$-0.315824\pi$
$691$	28.7504			1.09372			0.546858	+	0.837225i	$0.315824\pi$
$692$	−30.3991	+	8.92597i	−1.15560	+	0.339314i
$693$		0			0
$694$	50.0941	−	32.1935i	1.90155	−	1.22205i
$695$	1.69504	+	11.7892i	0.0642964	+	0.447191i
$696$		0			0
$697$	−5.52567	+	12.0995i	−0.209300	+	0.458303i
$698$	11.6504	−	13.4452i	0.440973	−	0.508910i
$699$		0			0
$700$	−2.10377	−	4.60661i	−0.0795149	−	0.174113i
$701$	27.4145	+	8.04963i	1.03543	+	0.304030i	0.754918	−	0.655819i	$-0.227677\pi$
$701$	27.4145	+	8.04963i	1.03543	+	0.304030i	0.280515	+	0.959850i	$0.409495\pi$
$702$		0			0
$703$	−21.1772	−	46.3717i	−0.798715	−	1.74894i
$704$	−1.74535	+	12.1392i	−0.0657804	+	0.457513i
$705$		0			0
$706$	−7.90196	+	17.3029i	−0.297394	+	0.651202i
$707$	−20.6985	−	13.3021i	−0.778448	−	0.500278i
$708$		0			0
$709$	23.0015	−	14.7822i	0.863840	−	0.555156i	−0.0320229	−	0.999487i	$-0.510195\pi$
$709$	23.0015	−	14.7822i	0.863840	−	0.555156i	0.895863	+	0.444331i	$0.146559\pi$
$710$	−3.28457	−	3.79060i	−0.123268	−	0.142259i
$711$		0			0
$712$	0.290794			0.0108980
$713$	22.5528	+	35.4750i	0.844608	+	1.32855i
$714$		0			0
$715$	8.28955	−	2.43403i	0.310012	−	0.0910276i
$716$	−7.30717	−	8.43292i	−0.273082	−	0.315153i
$717$		0			0
$718$	3.98244	+	27.6985i	0.148623	+	1.03370i
$719$	28.0260	+	18.0112i	1.04519	+	0.671704i	0.946266	−	0.323391i	$-0.104823\pi$
$719$	28.0260	+	18.0112i	1.04519	+	0.671704i	0.0989264	+	0.995095i	$0.468459\pi$
$720$		0			0
$721$	−22.9475	+	26.4828i	−0.854610	+	0.986272i
$722$	6.19161	−	43.0636i	0.230428	−	1.60266i
$723$		0			0
$724$	−21.7132	−	6.37557i	−0.806965	−	0.236946i
$725$	−5.97466	−	1.75432i	−0.221893	−	0.0651538i
$726$		0			0
$727$	3.27954	−	22.8097i	0.121632	−	0.845966i	−0.834076	−	0.551649i	$-0.813999\pi$
$727$	3.27954	−	22.8097i	0.121632	−	0.845966i	0.955708	−	0.294317i	$-0.0950921\pi$
$728$	0.611500	−	0.705709i	0.0226637	−	0.0261553i
$729$		0			0
$730$	40.4095	+	25.9696i	1.49562	+	0.961179i
$731$	−2.46447	−	17.1408i	−0.0911518	−	0.633975i
$732$		0			0
$733$	6.62114	+	7.64120i	0.244557	+	0.282234i	0.864736	−	0.502226i	$-0.167485\pi$
$733$	6.62114	+	7.64120i	0.244557	+	0.282234i	−0.620179	+	0.784460i	$0.712940\pi$
$734$	15.9813	−	4.69254i	0.589881	−	0.173205i
$735$		0			0
$736$	−34.5488	−	15.9836i	−1.27348	−	0.589164i
$737$	−6.06199			−0.223296
$738$		0			0
$739$	−3.15006	−	3.63536i	−0.115877	−	0.133729i	0.694847	−	0.719157i	$-0.255472\pi$
$739$	−3.15006	−	3.63536i	−0.115877	−	0.133729i	−0.810724	+	0.585428i	$0.800926\pi$
$740$	−26.6935	+	17.1549i	−0.981272	+	0.630626i
$741$		0			0
$742$	−8.11730	−	5.21667i	−0.297995	−	0.191510i
$743$	11.0854	−	24.2735i	0.406682	−	0.890510i	−0.589867	−	0.807501i	$-0.700820\pi$
$743$	11.0854	−	24.2735i	0.406682	−	0.890510i	0.996549	−	0.0830089i	$-0.0264530\pi$
$744$		0			0
$745$	0.00967469	−	0.0672889i	0.000354453	−	0.00246528i
$746$	−14.7240	−	32.2411i	−0.539085	−	1.18043i
$747$		0			0
$748$	−14.0823	−	4.13495i	−0.514902	−	0.151189i
$749$	−6.16596	−	13.5016i	−0.225299	−	0.493337i
$750$		0			0
$751$	−13.6470	+	15.7495i	−0.497987	+	0.574707i	−0.947982	−	0.318323i	$-0.896880\pi$
$751$	−13.6470	+	15.7495i	−0.497987	+	0.574707i	0.449995	+	0.893031i	$0.351426\pi$
$752$	−14.8508	+	32.5187i	−0.541552	+	1.18583i
$753$		0			0
$754$	5.66653	+	39.4116i	0.206363	+	1.43529i
$755$	−25.9493	+	16.6766i	−0.944393	+	0.606925i
$756$		0			0
$757$	−14.0513	+	4.12582i	−0.510701	+	0.149955i	−0.526923	−	0.849913i	$-0.676654\pi$
$757$	−14.0513	+	4.12582i	−0.510701	+	0.149955i	0.0162217	+	0.999868i	$0.494836\pi$
$758$	43.7831			1.59027
$759$		0			0
$760$	1.45812			0.0528916
$761$	23.8070	−	6.99036i	0.863003	−	0.253400i	0.179866	−	0.983691i	$-0.442434\pi$
$761$	23.8070	−	6.99036i	0.863003	−	0.253400i	0.683137	+	0.730291i	$0.260615\pi$
$762$		0			0
$763$	2.29537	−	1.47515i	0.0830982	−	0.0534039i
$764$	0.893388	+	6.21365i	0.0323217	+	0.224802i
$765$		0			0
$766$	−7.64440	+	16.7389i	−0.276204	+	0.604801i
$767$	−8.54222	+	9.85825i	−0.308442	+	0.355961i
$768$		0			0
$769$	−11.3732	−	24.9037i	−0.410126	−	0.898052i	−0.996142	−	0.0877520i	$-0.972032\pi$
$769$	−11.3732	−	24.9037i	−0.410126	−	0.898052i	0.586016	−	0.810300i	$-0.300696\pi$
$770$	20.4970	+	6.01846i	0.738660	+	0.216890i
$771$		0			0
$772$	3.52830	+	7.72591i	0.126986	+	0.278062i
$773$	−1.28113	+	8.91045i	−0.0460790	+	0.320487i	0.953725	+	0.300681i	$0.0972139\pi$
$773$	−1.28113	+	8.91045i	−0.0460790	+	0.320487i	−0.999804	+	0.0198058i	$0.993695\pi$
$774$		0			0
$775$	2.93531	−	6.42742i	0.105439	−	0.230880i
$776$	0.113773	+	0.0731176i	0.00408422	+	0.00262477i
$777$		0			0
$778$	40.7092	−	26.1622i	1.45950	−	0.937960i
$779$	11.9936	+	13.8414i	0.429716	+	0.495919i
$780$		0			0
$781$	−2.00449			−0.0717264
$782$	24.1015	−	37.1004i	0.861868	−	1.32671i
$783$		0			0
$784$	13.5770	−	3.98656i	0.484892	−	0.142377i
$785$	−20.9299	−	24.1544i	−0.747019	−	0.862106i
$786$		0			0
$787$	3.09178	+	21.5038i	0.110210	+	0.766528i	0.967714	+	0.252050i	$0.0811049\pi$
$787$	3.09178	+	21.5038i	0.110210	+	0.766528i	−0.857504	+	0.514477i	$0.827986\pi$
$788$	35.1205	+	22.5706i	1.25111	+	0.804043i
$789$		0			0
$790$	−23.9378	+	27.6256i	−0.851667	+	0.982876i
$791$	5.11935	−	35.6058i	0.182023	−	1.26600i
$792$		0			0
$793$	−21.0673	−	6.18592i	−0.748122	−	0.219668i
$794$	53.4546	+	15.6957i	1.89703	+	0.557020i
$795$		0			0
$796$	−1.75523	+	12.2079i	−0.0622125	+	0.432697i
$797$	18.8971	−	21.8084i	0.669369	−	0.772493i	−0.314909	−	0.949122i	$-0.601974\pi$
$797$	18.8971	−	21.8084i	0.669369	−	0.772493i	0.984277	+	0.176629i	$0.0565193\pi$
$798$		0			0
$799$	−33.9988	−	21.8497i	−1.20279	−	0.772986i
$800$	0.910622	+	6.33352i	0.0321954	+	0.223924i
$801$		0			0
$802$	−17.1691	−	19.8142i	−0.606263	−	0.699665i
$803$	18.4193	−	5.40840i	0.650003	−	0.190858i
$804$		0			0
$805$	−17.2907	+	26.6162i	−0.609416	+	0.938099i
$806$	−45.1821			−1.59147
$807$		0			0
$808$	0.555034	+	0.640544i	0.0195260	+	0.0225342i
$809$	−29.2641	+	18.8069i	−1.02887	+	0.661215i	−0.942210	−	0.335023i	$-0.891256\pi$
$809$	−29.2641	+	18.8069i	−1.02887	+	0.661215i	−0.0866604	+	0.996238i	$0.527620\pi$
$810$		0			0
$811$	9.27718	+	5.96208i	0.325766	+	0.209357i	0.693293	−	0.720656i	$-0.256159\pi$
$811$	9.27718	+	5.96208i	0.325766	+	0.209357i	−0.367527	+	0.930013i	$0.619796\pi$
$812$	−20.1586	+	44.1413i	−0.707430	+	1.54905i
$813$		0			0
$814$	−3.66143	+	25.4658i	−0.128333	+	0.892576i
$815$	−11.7614	−	25.7540i	−0.411985	−	0.902122i
$816$		0			0
$817$	−22.8778	−	6.71752i	−0.800392	−	0.235016i
$818$	−16.3310	−	35.7600i	−0.571001	−	1.25032i
$819$		0			0
$820$	7.46520	−	8.61530i	0.260696	−	0.300860i
$821$	−5.73009	+	12.5471i	−0.199981	+	0.437898i	−0.982879	−	0.184252i	$-0.941014\pi$
$821$	−5.73009	+	12.5471i	−0.199981	+	0.437898i	0.782898	+	0.622151i	$0.213741\pi$
$822$		0			0
$823$	3.55362	+	24.7160i	0.123871	+	0.861545i	0.953104	+	0.302642i	$0.0978686\pi$
$823$	3.55362	+	24.7160i	0.123871	+	0.861545i	−0.829233	+	0.558903i	$0.811222\pi$
$824$	1.01548	−	0.652610i	0.0353760	−	0.0227347i
$825$		0			0
$826$	−30.9473	+	9.08695i	−1.07679	+	0.316175i
$827$	29.2203			1.01609			0.508045	−	0.861331i	$-0.330369\pi$
$827$	29.2203			1.01609			0.508045	+	0.861331i	$0.330369\pi$
$828$		0			0
$829$	16.9029			0.587063			0.293531	−	0.955949i	$-0.405169\pi$
$829$	16.9029			0.587063			0.293531	+	0.955949i	$0.405169\pi$
$830$	−59.8448	+	17.5720i	−2.07724	+	0.609934i
$831$		0			0
$832$	16.4758	−	10.5883i	0.571195	−	0.367084i
$833$	2.27657	+	15.8339i	0.0788783	+	0.548611i
$834$		0			0
$835$	2.21435	−	4.84875i	0.0766307	−	0.167798i
$836$	−13.2337	+	15.2725i	−0.457696	+	0.528210i
$837$		0			0
$838$	3.77514	+	8.26640i	0.130410	+	0.285558i
$839$	−1.52515	−	0.447825i	−0.0526540	−	0.0154606i	0.255299	−	0.966862i	$-0.417826\pi$
$839$	−1.52515	−	0.447825i	−0.0526540	−	0.0154606i	−0.307953	+	0.951401i	$0.599644\pi$
$840$		0			0
$841$	12.7396	+	27.8958i	0.439296	+	0.961925i
$842$	1.81161	−	12.6000i	0.0624320	−	0.434224i
$843$		0			0
$844$	−11.9241	+	26.1102i	−0.410445	+	0.898749i
$845$	10.7899	+	6.93422i	0.371182	+	0.238544i
$846$		0			0
$847$	−22.7232	+	14.6033i	−0.780777	+	0.501775i
$848$	4.04551	+	4.66877i	0.138923	+	0.160326i
$849$		0			0
$850$	−7.43654			−0.255071
$851$	−34.6925	−	16.0501i	−1.18924	−	0.550191i
$852$		0			0
$853$	−17.4876	+	5.13482i	−0.598764	+	0.175813i	−0.567049	−	0.823684i	$-0.691915\pi$
$853$	−17.4876	+	5.13482i	−0.598764	+	0.175813i	−0.0317146	+	0.999497i	$0.510097\pi$
$854$	−35.5529	−	41.0302i	−1.21660	−	1.40403i
$855$		0			0
$856$	0.0727658	+	0.506097i	0.00248708	+	0.0172980i
$857$	25.8396	+	16.6061i	0.882665	+	0.567254i	0.901602	−	0.432566i	$-0.142392\pi$
$857$	25.8396	+	16.6061i	0.882665	+	0.567254i	−0.0189372	+	0.999821i	$0.506028\pi$
$858$		0			0
$859$	−7.22996	+	8.34382i	−0.246683	+	0.284687i	−0.865565	−	0.500797i	$-0.833040\pi$
$859$	−7.22996	+	8.34382i	−0.246683	+	0.284687i	0.618882	+	0.785484i	$0.287586\pi$
$860$	−2.11210	+	14.6899i	−0.0720219	+	0.500923i
$861$		0			0
$862$	21.5116	+	6.31637i	0.732687	+	0.215136i
$863$	15.3401	+	4.50427i	0.522184	+	0.153327i	0.532193	−	0.846623i	$-0.321368\pi$
$863$	15.3401	+	4.50427i	0.522184	+	0.153327i	−0.0100093	+	0.999950i	$0.503186\pi$
$864$		0			0
$865$	4.74999	−	33.0369i	0.161504	−	1.12329i
$866$	−5.94832	+	6.86473i	−0.202132	+	0.233273i
$867$		0			0
$868$	−46.3239	−	29.7706i	−1.57234	−	1.01048i
$869$	2.07902	+	14.4599i	0.0705261	+	0.490520i
$870$		0			0
$871$	6.33943	+	7.31609i	0.214803	+	0.247896i
$872$	−0.0901835	+	0.0264803i	−0.00305400	+	0.000896735i
$873$		0			0
$874$	−32.6812	−	51.4069i	−1.10546	−	1.73886i
$875$	38.4257			1.29903
$876$		0			0
$877$	21.6818	+	25.0221i	0.732143	+	0.844938i	0.992711	−	0.120518i	$-0.0384554\pi$
$877$	21.6818	+	25.0221i	0.732143	+	0.844938i	−0.260569	+	0.965455i	$0.583910\pi$
$878$	2.88670	−	1.85517i	0.0974213	−	0.0626088i
$879$		0			0
$880$	−11.5058	−	7.39430i	−0.387859	−	0.249262i
$881$	13.8057	−	30.2303i	0.465126	−	1.01848i	−0.521163	−	0.853457i	$-0.674502\pi$
$881$	13.8057	−	30.2303i	0.465126	−	1.01848i	0.986289	−	0.165027i	$-0.0527711\pi$
$882$		0			0
$883$	4.21852	−	29.3404i	0.141964	−	0.987384i	−0.786931	−	0.617041i	$-0.788331\pi$
$883$	4.21852	−	29.3404i	0.141964	−	0.987384i	0.928895	−	0.370343i	$-0.120760\pi$
$884$	9.73647	+	21.3199i	0.327473	+	0.717066i
$885$		0			0
$886$	−20.9948	−	6.16464i	−0.705336	−	0.207105i
$887$	−4.09687	−	8.97089i	−0.137559	−	0.301213i	0.828298	−	0.560288i	$-0.189310\pi$
$887$	−4.09687	−	8.97089i	−0.137559	−	0.301213i	−0.965857	+	0.259075i	$0.916582\pi$
$888$		0			0
$889$	38.5525	−	44.4920i	1.29301	−	1.49221i
$890$	4.41321	−	9.66359i	0.147931	−	0.323924i
$891$		0			0
$892$	5.35207	+	37.2244i	0.179200	+	1.24637i
$893$	−46.8125	+	30.0845i	−1.56652	+	1.00674i
$894$		0			0
$895$	11.2789	−	3.31178i	0.377011	−	0.110700i
$896$	−2.87695			−0.0961123
$897$		0			0
$898$	27.0177			0.901593
$899$	−64.9646	+	19.0753i	−2.16669	+	0.636198i
$900$		0			0
$901$	−5.87517	+	3.77574i	−0.195730	+	0.125788i
$902$	−1.31542	−	9.14895i	−0.0437987	−	0.304627i
$903$		0			0
$904$	−0.514760	+	1.12717i	−0.0171207	+	0.0374890i
$905$	15.6119	−	18.0171i	0.518956	−	0.598907i
$906$		0			0
$907$	16.2239	+	35.5254i	0.538705	+	1.17960i	0.961860	+	0.273543i	$0.0881955\pi$
$907$	16.2239	+	35.5254i	0.538705	+	1.17960i	−0.423154	+	0.906058i	$0.639077\pi$
$908$	−18.1212	−	5.32087i	−0.601374	−	0.176579i
$909$		0			0
$910$	−14.1715	−	31.0313i	−0.469782	−	1.02868i
$911$	1.22251	−	8.50273i	0.0405035	−	0.281708i	−0.959496	−	0.281721i	$-0.909095\pi$
$911$	1.22251	−	8.50273i	0.0405035	−	0.281708i	1.00000		1.24817e-5i	$3.97304e-6\pi$
$912$		0			0
$913$	−10.3548	+	22.6739i	−0.342694	+	0.750395i
$914$	−43.0857	−	27.6895i	−1.42515	−	0.915888i
$915$		0			0
$916$	8.69337	−	5.58689i	0.287237	−	0.184596i
$917$	3.07380	+	3.54736i	0.101506	+	0.117144i
$918$		0			0
$919$	6.75276			0.222753			0.111377	−	0.993778i	$-0.464474\pi$
$919$	6.75276			0.222753			0.111377	+	0.993778i	$0.464474\pi$
$920$	0.829805	−	0.711919i	0.0273579	−	0.0234713i
$921$		0			0
$922$	−73.7124	+	21.6439i	−2.42759	+	0.712804i
$923$	2.09623	+	2.41918i	0.0689984	+	0.0796284i
$924$		0			0
$925$	0.914411	+	6.35987i	0.0300656	+	0.209111i
$926$	−18.0169	−	11.5787i	−0.592071	−	0.380501i
$927$		0			0
$928$	40.1514	−	46.3372i	1.31803	−	1.52109i
$929$	−6.07703	+	42.2667i	−0.199381	+	1.38673i	0.606705	+	0.794927i	$0.292491\pi$
$929$	−6.07703	+	42.2667i	−0.199381	+	1.38673i	−0.806086	+	0.591798i	$0.798418\pi$
$930$		0			0
$931$	21.1334	+	6.20534i	0.692620	+	0.203372i
$932$	−31.4240	−	9.22691i	−1.02933	−	0.302238i
$933$		0			0
$934$	−4.22727	+	29.4013i	−0.138320	+	0.962040i
$935$	10.1253	−	11.6852i	0.331131	−	0.382146i
$936$		0			0
$937$	6.25612	+	4.02056i	0.204378	+	0.131346i	0.638826	−	0.769351i	$-0.279420\pi$
$937$	6.25612	+	4.02056i	0.204378	+	0.131346i	−0.434448	+	0.900697i	$0.643057\pi$
$938$	3.40652	+	23.6928i	0.111227	+	0.773599i
$939$		0			0
$940$	22.6817	+	26.1760i	0.739794	+	0.853768i
$941$	44.5812	−	13.0902i	1.45330	−	0.426729i	0.542672	−	0.839945i	$-0.317413\pi$
$941$	44.5812	−	13.0902i	1.45330	−	0.426729i	0.910633	+	0.413216i	$0.135595\pi$
$942$		0			0
$943$	13.5834	+	2.02121i	0.442338	+	0.0658196i
$944$	20.6500			0.672101
$945$		0			0
$946$	7.88014	+	9.09417i	0.256206	+	0.295677i
$947$	9.34041	−	6.00272i	0.303522	−	0.195062i	−0.380010	−	0.924983i	$-0.624079\pi$
$947$	9.34041	−	6.00272i	0.303522	−	0.195062i	0.683532	+	0.729921i	$0.260443\pi$
$948$		0			0
$949$	−25.7896	−	16.5740i	−0.837166	−	0.538014i
$950$	−4.25355	+	9.31398i	−0.138003	+	0.302185i
$951$		0			0
$952$	0.237829	−	1.65414i	0.00770810	−	0.0536110i
$953$	−9.39201	−	20.5656i	−0.304237	−	0.666187i	0.694332	−	0.719654i	$-0.255700\pi$
$953$	−9.39201	−	20.5656i	−0.304237	−	0.666187i	−0.998570	+	0.0534679i	$0.982973\pi$
$954$		0			0
$955$	−6.34535	−	1.86316i	−0.205331	−	0.0602905i
$956$	−11.5082	−	25.1995i	−0.372203	−	0.815011i
$957$		0			0
$958$	55.4394	−	63.9805i	1.79117	−	2.06712i
$959$	6.00810	−	13.1559i	0.194012	−	0.424827i
$960$		0			0
$961$	−6.52238	−	45.3641i	−0.210399	−	1.46336i
$962$	34.5632	−	22.2124i	1.11436	−	0.716156i
$963$		0			0
$964$	−50.1719	+	14.7318i	−1.61593	+	0.474479i
$965$	−8.94762			−0.288034
$966$		0			0
$967$	0.0544688			0.00175160			0.000875800	−	1.00000i	$-0.499721\pi$
$967$	0.0544688			0.00175160			0.000875800		1.00000i	$0.499721\pi$
$968$	0.892775	−	0.262142i	0.0286949	−	0.00842558i
$969$		0			0
$970$	4.15649	−	2.67122i	0.133457	−	0.0857676i
$971$	−6.92603	−	48.1716i	−0.222267	−	1.54590i	−0.729433	−	0.684052i	$-0.760216\pi$
$971$	−6.92603	−	48.1716i	−0.222267	−	1.54590i	0.507166	−	0.861848i	$-0.330693\pi$
$972$		0			0
$973$	7.80785	−	17.0968i	0.250308	−	0.548098i
$974$	−42.9164	+	49.5282i	−1.37513	+	1.58699i
$975$		0			0
$976$	14.4394	+	31.6178i	0.462193	+	1.01206i
$977$	52.8998	+	15.5328i	1.69241	+	0.496938i	0.979009	−	0.203815i	$-0.0653341\pi$
$977$	52.8998	+	15.5328i	1.69241	+	0.496938i	0.713404	+	0.700753i	$0.247152\pi$
$978$		0			0
$979$	−1.76372	−	3.86201i	−0.0563687	−	0.123430i
$980$	1.95106	−	13.5699i	0.0623242	−	0.433474i
$981$		0			0
$982$	25.1410	−	55.0510i	0.802280	−	1.75675i
$983$	40.3538	+	25.9338i	1.28709	+	0.827160i	0.991744	−	0.128232i	$-0.0409303\pi$
$983$	40.3538	+	25.9338i	1.28709	+	0.827160i	0.295341	+	0.955392i	$0.404567\pi$
$984$		0			0
$985$	−36.9985	+	23.7775i	−1.17887	+	0.757614i
$986$	46.6642	+	53.8533i	1.48609	+	1.71504i
$987$		0			0
$988$	32.2714			1.02669
$989$	−16.2993	+	7.34704i	−0.518289	+	0.233622i
$990$		0			0
$991$	25.2051	−	7.40089i	0.800667	−	0.235097i	0.144295	−	0.989535i	$-0.453908\pi$
$991$	25.2051	−	7.40089i	0.800667	−	0.235097i	0.656372	+	0.754438i	$0.272090\pi$
$992$	45.5617	+	52.5810i	1.44659	+	1.66945i
$993$		0			0
$994$	1.12642	+	7.83442i	0.0357279	+	0.248493i
$995$	−10.9304	−	7.02452i	−0.346516	−	0.222692i
$996$		0			0
$997$	−15.6901	+	18.1074i	−0.496912	+	0.573467i	−0.947699	−	0.319164i	$-0.896598\pi$
$997$	−15.6901	+	18.1074i	−0.496912	+	0.573467i	0.450787	+	0.892631i	$0.351143\pi$
$998$	−7.55728	+	52.5621i	−0.239222	+	1.66382i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.i.d.55.2		20
3.2	odd	2		69.2.e.c.55.1	✓	20
23.8	even	11		4761.2.a.bt.1.2		10
23.15	odd	22		4761.2.a.bu.1.2		10
23.18	even	11	inner	207.2.i.d.64.2		20
69.8	odd	22		1587.2.a.u.1.9		10
69.38	even	22		1587.2.a.t.1.9		10
69.41	odd	22		69.2.e.c.64.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.c.55.1	✓	20	3.2	odd	2
69.2.e.c.64.1	yes	20	69.41	odd	22
207.2.i.d.55.2		20	1.1	even	1	trivial
207.2.i.d.64.2		20	23.18	even	11	inner
1587.2.a.t.1.9		10	69.38	even	22
1587.2.a.u.1.9		10	69.8	odd	22
4761.2.a.bt.1.2		10	23.8	even	11
4761.2.a.bu.1.2		10	23.15	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)

\(f(q)\)	\(=\)	\(q+(1.90549 - 0.559503i) q^{2} +(1.63535 - 1.05098i) q^{4} +(0.291446 + 2.02705i) q^{5} +(1.34249 - 2.93963i) q^{7} +(-0.0729013 + 0.0841325i) q^{8} +O(q^{10})\)	\(q+(1.90549 - 0.559503i) q^{2} +(1.63535 - 1.05098i) q^{4} +(0.291446 + 2.02705i) q^{5} +(1.34249 - 2.93963i) q^{7} +(-0.0729013 + 0.0841325i) q^{8} +(1.68949 + 3.69946i) q^{10} +(1.55951 + 0.457915i) q^{11} +(-1.07824 - 2.36102i) q^{13} +(0.913363 - 6.35258i) q^{14} +(-1.70693 + 3.73765i) q^{16} +(-3.90777 - 2.51137i) q^{17} +(-5.38056 + 3.45787i) q^{19} +(2.60700 + 3.00863i) q^{20} +3.22785 q^{22} +(-1.37375 + 4.59487i) q^{23} +(0.773474 - 0.227113i) q^{25} +(-3.37558 - 3.89563i) q^{26} +(-0.894050 - 6.21825i) q^{28} +(-6.49822 - 4.17615i) q^{29} +(5.74006 - 6.62438i) q^{31} +(-1.12962 + 7.85671i) q^{32} +(-8.85134 - 2.59899i) q^{34} +(6.35005 + 1.86454i) q^{35} +(-1.13432 + 7.88940i) q^{37} +(-8.31792 + 9.59939i) q^{38} +(-0.191788 - 0.123254i) q^{40} +(-0.407522 - 2.83438i) q^{41} +(2.44130 + 2.81741i) q^{43} +(3.03161 - 0.890161i) q^{44} +(-0.0468192 + 9.52410i) q^{46} +8.70030 q^{47} +(-2.25516 - 2.60259i) q^{49} +(1.34678 - 0.865522i) q^{50} +(-4.24468 - 2.72789i) q^{52} +(0.624559 - 1.36759i) q^{53} +(-0.473702 + 3.29467i) q^{55} +(0.149450 + 0.327250i) q^{56} +(-14.7189 - 4.32185i) q^{58} +(-2.08771 - 4.57145i) q^{59} +(5.53965 - 6.39309i) q^{61} +(7.23127 - 15.8343i) q^{62} +(1.07383 + 7.46864i) q^{64} +(4.47166 - 2.87376i) q^{65} +(-3.57857 + 1.05076i) q^{67} -9.02995 q^{68} +13.1432 q^{70} +(-1.18331 + 0.347451i) q^{71} +(9.93598 - 6.38547i) q^{73} +(2.25270 + 15.6679i) q^{74} +(-5.16495 + 11.3097i) q^{76} +(3.43973 - 3.96966i) q^{77} +(3.73374 + 8.17574i) q^{79} +(-8.07388 - 2.37071i) q^{80} +(-2.36238 - 5.17288i) q^{82} +(-2.18254 + 15.1799i) q^{83} +(3.95177 - 8.65317i) q^{85} +(6.22822 + 4.00264i) q^{86} +(-0.152216 + 0.0978234i) q^{88} +(-1.71060 - 1.97414i) q^{89} -8.38806 q^{91} +(2.58254 + 8.95799i) q^{92} +(16.5784 - 4.86785i) q^{94} +(-8.57742 - 9.89887i) q^{95} +(-0.172893 - 1.20250i) q^{97} +(-5.75334 - 3.69745i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8}+O(q^{10}) \) 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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