LMFDB - Embedded newform 414.2.i.h.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(55,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, 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("414.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.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:	$3.30580664368$
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} + 8 x^{18} + 53 x^{16} + 358 x^{14} + 1753 x^{12} + 7149 x^{10} + 23268 x^{8} + 37292 x^{6} + \cdots + 58081 $ x^20 + 8x^18 + 53x^16 + 358x^14 + 1753x^12 + 7149x^10 + 23268x^8 + 37292x^6 + 19057x^4 - 81217*x^2 + 58081
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			163.1
Root			$0.842658 + 0.247427i$ of defining polynomial
Character	$\chi$	$=$	414.163
Dual form			414.2.i.h.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841254 - 0.540641i) q^{2} +(0.415415 + 0.909632i) q^{4} +(-1.76120 - 0.517136i) q^{5} +(-0.814622 + 0.940124i) q^{7} +(0.142315 - 0.989821i) q^{8} +O(q^{10})$	\(q+(-0.841254 - 0.540641i) q^{2} +(0.415415 + 0.909632i) q^{4} +(-1.76120 - 0.517136i) q^{5} +(-0.814622 + 0.940124i) q^{7} +(0.142315 - 0.989821i) q^{8} +(1.20203 + 1.38722i) q^{10} +(-0.0861669 + 0.0553761i) q^{11} +(2.53660 + 2.92740i) q^{13} +(1.19357 - 0.350465i) q^{14} +(-0.654861 + 0.755750i) q^{16} +(-1.27187 + 2.78502i) q^{17} +(2.06781 + 4.52787i) q^{19} +(-0.261227 - 1.81687i) q^{20} +0.102427 q^{22} +(3.69420 + 3.05825i) q^{23} +(-1.37186 - 0.881641i) q^{25} +(-0.551257 - 3.83407i) q^{26} +(-1.19357 - 0.350465i) q^{28} +(-2.79123 + 6.11195i) q^{29} +(-0.550169 + 3.82651i) q^{31} +(0.959493 - 0.281733i) q^{32} +(2.57566 - 1.65528i) q^{34} +(1.92089 - 1.23448i) q^{35} +(2.45079 - 0.719617i) q^{37} +(0.708400 - 4.92703i) q^{38} +(-0.762518 + 1.66968i) q^{40} +(1.58687 + 0.465946i) q^{41} +(-0.512056 - 3.56142i) q^{43} +(-0.0861669 - 0.0553761i) q^{44} +(-1.45434 - 4.57000i) q^{46} +1.92036 q^{47} +(0.775980 + 5.39706i) q^{49} +(0.677431 + 1.48337i) q^{50} +(-1.60911 + 3.52346i) q^{52} +(-2.71302 + 3.13099i) q^{53} +(0.180394 - 0.0529686i) q^{55} +(0.814622 + 0.940124i) q^{56} +(5.65250 - 3.63264i) q^{58} +(3.99373 + 4.60900i) q^{59} +(0.816980 - 5.68222i) q^{61} +(2.53160 - 2.92162i) q^{62} +(-0.959493 - 0.281733i) q^{64} +(-2.95361 - 6.46751i) q^{65} +(-1.30695 - 0.839923i) q^{67} -3.06169 q^{68} -2.28336 q^{70} +(7.17087 + 4.60844i) q^{71} +(-5.00506 - 10.9596i) q^{73} +(-2.45079 - 0.719617i) q^{74} +(-3.25970 + 3.76189i) q^{76} +(0.0181331 - 0.126118i) q^{77} +(-8.55951 - 9.87820i) q^{79} +(1.54417 - 0.992377i) q^{80} +(-1.08305 - 1.24990i) q^{82} +(-4.99358 + 1.46625i) q^{83} +(3.68026 - 4.24725i) q^{85} +(-1.49468 + 3.27290i) q^{86} +(0.0425496 + 0.0931707i) q^{88} +(1.13564 + 7.89854i) q^{89} -4.81849 q^{91} +(-1.24726 + 4.63080i) q^{92} +(-1.61551 - 1.03822i) q^{94} +(-1.30031 - 9.04384i) q^{95} +(-11.0078 - 3.23219i) q^{97} +(2.26507 - 4.95982i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8}+O(q^{10}) $ 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8	$ 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8} - 2 q^{10} - 2 q^{11} - 18 q^{14} - 2 q^{16} + 18 q^{17} + 16 q^{19} + 2 q^{20} + 24 q^{22} - 2 q^{23} + 38 q^{25} + 18 q^{28} - 30 q^{29} + 14 q^{31} + 2 q^{32} + 4 q^{34} + 48 q^{35} - 20 q^{37} - 16 q^{38} - 2 q^{40} - 12 q^{41} - 28 q^{43} - 2 q^{44} + 2 q^{46} + 32 q^{47} + 6 q^{49} + 6 q^{50} - 46 q^{53} - 28 q^{55} + 4 q^{56} - 14 q^{58} - 50 q^{61} + 8 q^{62} - 2 q^{64} + 16 q^{65} - 8 q^{67} - 48 q^{68} - 48 q^{70} + 12 q^{71} - 18 q^{73} + 20 q^{74} - 6 q^{76} - 4 q^{77} - 18 q^{79} + 2 q^{80} - 10 q^{82} - 44 q^{83} + 32 q^{85} + 28 q^{86} + 2 q^{88} + 44 q^{91} - 2 q^{92} + 12 q^{94} + 64 q^{95} + 14 q^{97} - 28 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8 - 2 * q^10 - 2 * q^11 - 18 * q^14 - 2 * q^16 + 18 * q^17 + 16 * q^19 + 2 * q^20 + 24 * q^22 - 2 * q^23 + 38 * q^25 + 18 * q^28 - 30 * q^29 + 14 * q^31 + 2 * q^32 + 4 * q^34 + 48 * q^35 - 20 * q^37 - 16 * q^38 - 2 * q^40 - 12 * q^41 - 28 * q^43 - 2 * q^44 + 2 * q^46 + 32 * q^47 + 6 * q^49 + 6 * q^50 - 46 * q^53 - 28 * q^55 + 4 * q^56 - 14 * q^58 - 50 * q^61 + 8 * q^62 - 2 * q^64 + 16 * q^65 - 8 * q^67 - 48 * q^68 - 48 * q^70 + 12 * q^71 - 18 * q^73 + 20 * q^74 - 6 * q^76 - 4 * q^77 - 18 * q^79 + 2 * q^80 - 10 * q^82 - 44 * q^83 + 32 * q^85 + 28 * q^86 + 2 * q^88 + 44 * q^91 - 2 * q^92 + 12 * q^94 + 64 * q^95 + 14 * q^97 - 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{1}{11}\right)$

Coefficient data

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

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

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

$2$	−0.841254	−	0.540641i	−0.594856	−	0.382291i
$2$	−0.841254	−	0.540641i	−0.594856	−	0.382291i
$3$		0			0
$3$		0			0
$4$	0.415415	+	0.909632i	0.207708	+	0.454816i
$5$	−1.76120	−	0.517136i	−0.787634	−	0.231270i	−0.136909	−	0.990584i	$-0.543717\pi$
$5$	−1.76120	−	0.517136i	−0.787634	−	0.231270i	−0.650725	+	0.759313i	$0.725535\pi$
$6$		0			0
$7$	−0.814622	+	0.940124i	−0.307898	+	0.355334i	−0.888518	−	0.458841i	$-0.848265\pi$
$7$	−0.814622	+	0.940124i	−0.307898	+	0.355334i	0.580620	+	0.814175i	$0.302810\pi$
$8$	0.142315	−	0.989821i	0.0503159	−	0.349955i
$9$		0			0
$10$	1.20203	+	1.38722i	0.380116	+	0.438678i
$11$	−0.0861669	+	0.0553761i	−0.0259803	+	0.0166965i	−0.553567	−	0.832805i	$-0.686734\pi$
$11$	−0.0861669	+	0.0553761i	−0.0259803	+	0.0166965i	0.527586	+	0.849501i	$0.323097\pi$
$12$		0			0
$13$	2.53660	+	2.92740i	0.703527	+	0.811914i	0.989225	−	0.146406i	$-0.0467707\pi$
$13$	2.53660	+	2.92740i	0.703527	+	0.811914i	−0.285697	+	0.958320i	$0.592225\pi$
$14$	1.19357	−	0.350465i	0.318996	−	0.0936657i
$15$		0			0
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	−1.27187	+	2.78502i	−0.308475	+	0.675465i	−0.998848	−	0.0479880i	$-0.984719\pi$
$17$	−1.27187	+	2.78502i	−0.308475	+	0.675465i	0.690373	+	0.723453i	$0.257446\pi$
$18$		0			0
$19$	2.06781	+	4.52787i	0.474388	+	1.03876i	0.983969	+	0.178342i	$0.0570732\pi$
$19$	2.06781	+	4.52787i	0.474388	+	1.03876i	−0.509581	+	0.860423i	$0.670200\pi$
$20$	−0.261227	−	1.81687i	−0.0584121	−	0.406265i
$21$		0			0
$22$	0.102427			0.0218375
$23$	3.69420	+	3.05825i	0.770293	+	0.637690i
$23$	3.69420	+	3.05825i	0.770293	+	0.637690i
$24$		0			0
$25$	−1.37186	−	0.881641i	−0.274372	−	0.176328i
$26$	−0.551257	−	3.83407i	−0.108110	−	0.751924i
$27$		0			0
$28$	−1.19357	−	0.350465i	−0.225564	−	0.0662316i
$29$	−2.79123	+	6.11195i	−0.518319	+	1.13496i	0.451753	+	0.892143i	$0.350799\pi$
$29$	−2.79123	+	6.11195i	−0.518319	+	1.13496i	−0.970072	+	0.242817i	$0.921929\pi$
$30$		0			0
$31$	−0.550169	+	3.82651i	−0.0988133	+	0.687261i	0.878852	+	0.477094i	$0.158310\pi$
$31$	−0.550169	+	3.82651i	−0.0988133	+	0.687261i	−0.977665	+	0.210167i	$0.932599\pi$
$32$	0.959493	−	0.281733i	0.169616	−	0.0498038i
$33$		0			0
$34$	2.57566	−	1.65528i	0.441722	−	0.283878i
$35$	1.92089	−	1.23448i	0.324689	−	0.208665i
$36$		0			0
$37$	2.45079	−	0.719617i	0.402908	−	0.118304i	−0.0739990	−	0.997258i	$-0.523576\pi$
$37$	2.45079	−	0.719617i	0.402908	−	0.118304i	0.476907	+	0.878954i	$0.341758\pi$
$38$	0.708400	−	4.92703i	0.114918	−	0.799269i
$39$		0			0
$40$	−0.762518	+	1.66968i	−0.120565	+	0.264000i
$41$	1.58687	+	0.465946i	0.247827	+	0.0727685i	0.403287	−	0.915074i	$-0.367868\pi$
$41$	1.58687	+	0.465946i	0.247827	+	0.0727685i	−0.155460	+	0.987842i	$0.549686\pi$
$42$		0			0
$43$	−0.512056	−	3.56142i	−0.0780877	−	0.543112i	−0.990886	−	0.134702i	$-0.956992\pi$
$43$	−0.512056	−	3.56142i	−0.0780877	−	0.543112i	0.912798	−	0.408410i	$-0.133917\pi$
$44$	−0.0861669	−	0.0553761i	−0.0129901	−	0.00834826i
$45$		0			0
$46$	−1.45434	−	4.57000i	−0.214430	−	0.673810i
$47$	1.92036			0.280113			0.140056	−	0.990144i	$-0.455272\pi$
$47$	1.92036			0.280113			0.140056	+	0.990144i	$0.455272\pi$
$48$		0			0
$49$	0.775980	+	5.39706i	0.110854	+	0.771008i
$50$	0.677431	+	1.48337i	0.0958032	+	0.209780i
$51$		0			0
$52$	−1.60911	+	3.52346i	−0.223143	+	0.488616i
$53$	−2.71302	+	3.13099i	−0.372662	+	0.430075i	−0.910842	−	0.412755i	$-0.864567\pi$
$53$	−2.71302	+	3.13099i	−0.372662	+	0.430075i	0.538180	+	0.842830i	$0.319112\pi$
$54$		0			0
$55$	0.180394	−	0.0529686i	0.0243244	−	0.00714228i
$56$	0.814622	+	0.940124i	0.108858	+	0.125629i
$57$		0			0
$58$	5.65250	−	3.63264i	0.742210	−	0.476989i
$59$	3.99373	+	4.60900i	0.519939	+	0.600041i	0.953616	−	0.301027i	$-0.0973295\pi$
$59$	3.99373	+	4.60900i	0.519939	+	0.600041i	−0.433677	+	0.901068i	$0.642784\pi$
$60$		0			0
$61$	0.816980	−	5.68222i	0.104604	−	0.727534i	−0.868252	−	0.496123i	$-0.834757\pi$
$61$	0.816980	−	5.68222i	0.104604	−	0.727534i	0.972856	−	0.231411i	$-0.0743343\pi$
$62$	2.53160	−	2.92162i	0.321513	−	0.371046i
$63$		0			0
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	−2.95361	−	6.46751i	−0.366351	−	0.802196i
$66$		0			0
$67$	−1.30695	−	0.839923i	−0.159669	−	0.102613i	0.458366	−	0.888763i	$-0.348435\pi$
$67$	−1.30695	−	0.839923i	−0.159669	−	0.102613i	−0.618035	+	0.786150i	$0.712071\pi$
$68$	−3.06169			−0.371285
$69$		0			0
$70$	−2.28336			−0.272914
$71$	7.17087	+	4.60844i	0.851026	+	0.546921i	0.891894	−	0.452244i	$-0.149376\pi$
$71$	7.17087	+	4.60844i	0.851026	+	0.546921i	−0.0408688	+	0.999165i	$0.513013\pi$
$72$		0			0
$73$	−5.00506	−	10.9596i	−0.585798	−	1.28272i	−0.937948	−	0.346776i	$-0.887277\pi$
$73$	−5.00506	−	10.9596i	−0.585798	−	1.28272i	0.352150	−	0.935944i	$-0.385451\pi$
$74$	−2.45079	−	0.719617i	−0.284899	−	0.0836538i
$75$		0			0
$76$	−3.25970	+	3.76189i	−0.373913	+	0.431518i
$77$	0.0181331	−	0.126118i	0.00206645	−	0.0143725i
$78$		0			0
$79$	−8.55951	−	9.87820i	−0.963020	−	1.11138i	−0.993724	−	0.111856i	$-0.964320\pi$
$79$	−8.55951	−	9.87820i	−0.963020	−	1.11138i	0.0307042	−	0.999529i	$-0.490225\pi$
$80$	1.54417	−	0.992377i	0.172643	−	0.110951i
$81$		0			0
$82$	−1.08305	−	1.24990i	−0.119603	−	0.138029i
$83$	−4.99358	+	1.46625i	−0.548117	+	0.160942i	−0.544054	−	0.839050i	$-0.683111\pi$
$83$	−4.99358	+	1.46625i	−0.548117	+	0.160942i	−0.00406256	+	0.999992i	$0.501293\pi$
$84$		0			0
$85$	3.68026	−	4.24725i	0.399180	−	0.460679i
$86$	−1.49468	+	3.27290i	−0.161176	+	0.352926i
$87$		0			0
$88$	0.0425496	+	0.0931707i	0.00453580	+	0.00993203i
$89$	1.13564	+	7.89854i	0.120377	+	0.837243i	0.957129	+	0.289661i	$0.0935426\pi$
$89$	1.13564	+	7.89854i	0.120377	+	0.837243i	−0.836752	+	0.547582i	$0.815548\pi$
$90$		0			0
$91$	−4.81849			−0.505115
$92$	−1.24726	+	4.63080i	−0.130036	+	0.482795i
$93$		0			0
$94$	−1.61551	−	1.03822i	−0.166627	−	0.107085i
$95$	−1.30031	−	9.04384i	−0.133409	−	0.927878i
$96$		0			0
$97$	−11.0078	−	3.23219i	−1.11768	−	0.328179i	−0.329823	−	0.944043i	$-0.606989\pi$
$97$	−11.0078	−	3.23219i	−1.11768	−	0.328179i	−0.787853	+	0.615863i	$0.788807\pi$
$98$	2.26507	−	4.95982i	0.228807	−	0.501017i
$99$		0			0
$100$	0.232078	−	1.61413i	0.0232078	−	0.161413i
$101$	−8.01936	+	2.35470i	−0.797956	+	0.234301i	−0.655199	−	0.755457i	$-0.727415\pi$
$101$	−8.01936	+	2.35470i	−0.797956	+	0.234301i	−0.142757	+	0.989758i	$0.545597\pi$
$102$		0			0
$103$	10.6854	−	6.86708i	1.05286	−	0.676633i	0.104727	−	0.994501i	$-0.466603\pi$
$103$	10.6854	−	6.86708i	1.05286	−	0.676633i	0.948135	+	0.317868i	$0.102967\pi$
$104$	3.25860	−	2.09417i	0.319532	−	0.205351i
$105$		0			0
$106$	3.97508	−	1.16719i	0.386094	−	0.113367i
$107$	1.49515	−	10.3990i	0.144541	−	1.00531i	−0.780423	−	0.625252i	$-0.784996\pi$
$107$	1.49515	−	10.3990i	0.144541	−	1.00531i	0.924964	−	0.380055i	$-0.124095\pi$
$108$		0			0
$109$	−2.28131	+	4.99536i	−0.218510	+	0.478469i	−0.986864	−	0.161556i	$-0.948349\pi$
$109$	−2.28131	+	4.99536i	−0.218510	+	0.478469i	0.768354	+	0.640025i	$0.221076\pi$
$110$	−0.180394	−	0.0529686i	−0.0171999	−	0.00505035i
$111$		0			0
$112$	−0.177034	−	1.23130i	−0.0167282	−	0.116347i
$113$	−15.8746	−	10.2020i	−1.49336	−	0.959723i	−0.995728	−	0.0923334i	$-0.970567\pi$
$113$	−15.8746	−	10.2020i	−1.49336	−	0.959723i	−0.497630	−	0.867390i	$-0.665796\pi$
$114$		0			0
$115$	−4.92470	−	7.29661i	−0.459230	−	0.680412i
$116$	−6.71914			−0.623857
$117$		0			0
$118$	−0.867919	−	6.03651i	−0.0798985	−	0.555706i
$119$	−1.58216	−	3.46446i	−0.145037	−	0.317586i
$120$		0			0
$121$	−4.56521	+	9.99641i	−0.415019	+	0.908764i
$122$	−3.75933	+	4.33850i	−0.340354	+	0.392789i
$123$		0			0
$124$	−3.70926	+	1.08914i	−0.333102	+	0.0978075i
$125$	7.97036	+	9.19829i	0.712891	+	0.822720i
$126$		0			0
$127$	−0.991327	+	0.637087i	−0.0879661	+	0.0565324i	−0.583884	−	0.811837i	$-0.698468\pi$
$127$	−0.991327	+	0.637087i	−0.0879661	+	0.0565324i	0.495918	+	0.868369i	$0.334832\pi$
$128$	0.654861	+	0.755750i	0.0578821	+	0.0667995i
$129$		0			0
$130$	−1.01186	+	7.03766i	−0.0887462	+	0.617243i
$131$	14.3169	−	16.5226i	1.25088	−	1.44359i	0.401449	−	0.915882i	$-0.368507\pi$
$131$	14.3169	−	16.5226i	1.25088	−	1.44359i	0.849427	−	0.527706i	$-0.176948\pi$
$132$		0			0
$133$	−5.94124	−	1.74451i	−0.515171	−	0.151268i
$134$	0.645376	+	1.41318i	0.0557520	+	0.122080i
$135$		0			0
$136$	2.57566	+	1.65528i	0.220861	+	0.141939i
$137$	−17.1557			−1.46571			−0.732855	−	0.680385i	$-0.761812\pi$
$137$	−17.1557			−1.46571			−0.732855	+	0.680385i	$0.761812\pi$
$138$		0			0
$139$	10.1346			0.859608			0.429804	−	0.902922i	$-0.358583\pi$
$139$	10.1346			0.859608			0.429804	+	0.902922i	$0.358583\pi$
$140$	1.92089	+	1.23448i	0.162345	+	0.104333i
$141$		0			0
$142$	−3.54101	−	7.75373i	−0.297155	−	0.650679i
$143$	−0.380679	−	0.111777i	−0.0318340	−	0.00934730i
$144$		0			0
$145$	8.07664	−	9.32093i	0.670728	−	0.774062i
$146$	−1.71466	+	11.9257i	−0.141906	+	0.986979i
$147$		0			0
$148$	1.67268	+	1.93038i	0.137494	+	0.158676i
$149$	0.317524	−	0.204060i	0.0260126	−	0.0167173i	−0.527570	−	0.849512i	$-0.676897\pi$
$149$	0.317524	−	0.204060i	0.0260126	−	0.0167173i	0.553582	+	0.832794i	$0.313260\pi$
$150$		0			0
$151$	10.1818	+	11.7504i	0.828580	+	0.956232i	0.999578	−	0.0290394i	$-0.00924482\pi$
$151$	10.1818	+	11.7504i	0.828580	+	0.956232i	−0.170999	+	0.985271i	$0.554699\pi$
$152$	4.77606	−	1.40238i	0.387390	−	0.113748i
$153$		0			0
$154$	−0.0834391	+	0.0962939i	−0.00672372	+	0.00775958i
$155$	2.94778	−	6.45475i	0.236772	−	0.518458i
$156$		0			0
$157$	7.46328	+	16.3423i	0.595635	+	1.30426i	0.931977	+	0.362518i	$0.118083\pi$
$157$	7.46328	+	16.3423i	0.595635	+	1.30426i	−0.336342	+	0.941740i	$0.609190\pi$
$158$	1.86016	+	12.9377i	0.147986	+	1.02927i
$159$		0			0
$160$	−1.83556			−0.145113
$161$	−5.88451	+	0.981680i	−0.463765	+	0.0773672i
$162$		0			0
$163$	−3.57981	−	2.30061i	−0.280393	−	0.180197i	0.392884	−	0.919588i	$-0.371477\pi$
$163$	−3.57981	−	2.30061i	−0.280393	−	0.180197i	−0.673277	+	0.739391i	$0.735114\pi$
$164$	0.235369	+	1.63702i	0.0183792	+	0.127830i
$165$		0			0
$166$	4.99358	+	1.46625i	0.387577	+	0.113803i
$167$	−3.07161	+	6.72588i	−0.237688	+	0.520464i	−0.990457	−	0.137820i	$-0.955990\pi$
$167$	−3.07161	+	6.72588i	−0.237688	+	0.520464i	0.752769	+	0.658285i	$0.228718\pi$
$168$		0			0
$169$	−0.285200	+	1.98361i	−0.0219384	+	0.152585i
$170$	−5.39227	+	1.58331i	−0.413568	+	0.121435i
$171$		0			0
$172$	3.02687	−	1.94525i	0.230797	−	0.148324i
$173$	12.1371	−	7.80005i	0.922768	−	0.593027i	0.00930837	−	0.999957i	$-0.497037\pi$
$173$	12.1371	−	7.80005i	0.922768	−	0.593027i	0.913459	+	0.406930i	$0.133401\pi$
$174$		0			0
$175$	1.94640	−	0.571515i	0.147134	−	0.0432024i
$176$	0.0145769	−	0.101384i	0.00109877	−	0.00764212i
$177$		0			0
$178$	3.31491	−	7.25864i	0.248463	−	0.544058i
$179$	24.8277	+	7.29007i	1.85571	+	0.544885i	0.999606	+	0.0280798i	$0.00893926\pi$
$179$	24.8277	+	7.29007i	1.85571	+	0.544885i	0.856103	+	0.516805i	$0.172879\pi$
$180$		0			0
$181$	1.94284	+	13.5128i	0.144410	+	1.00440i	0.925167	+	0.379561i	$0.123925\pi$
$181$	1.94284	+	13.5128i	0.144410	+	1.00440i	−0.780756	+	0.624835i	$0.785166\pi$
$182$	4.05357	+	2.60507i	0.300471	+	0.193101i
$183$		0			0
$184$	3.55287	−	3.22136i	0.261921	−	0.237482i
$185$	−4.68848			−0.344704
$186$		0			0
$187$	−0.0446299	−	0.310407i	−0.00326366	−	0.0226992i
$188$	0.797746	+	1.74682i	0.0581816	+	0.127400i
$189$		0			0
$190$	−3.79558	+	8.31116i	−0.275360	+	0.602955i
$191$	14.9471	−	17.2499i	1.08153	−	1.24816i	0.114525	−	0.993420i	$-0.463465\pi$
$191$	14.9471	−	17.2499i	1.08153	−	1.24816i	0.967010	−	0.254737i	$-0.0819891\pi$
$192$		0			0
$193$	−3.49782	+	1.02705i	−0.251779	+	0.0739289i	−0.405186	−	0.914234i	$-0.632793\pi$
$193$	−3.49782	+	1.02705i	−0.251779	+	0.0739289i	0.153408	+	0.988163i	$0.450975\pi$
$194$	7.51293	+	8.67038i	0.539397	+	0.622497i
$195$		0			0
$196$	−4.58698	+	2.94787i	−0.327642	+	0.210562i
$197$	10.6327	+	12.2708i	0.757549	+	0.874259i	0.995277	−	0.0970733i	$-0.0309481\pi$
$197$	10.6327	+	12.2708i	0.757549	+	0.874259i	−0.237728	+	0.971332i	$0.576403\pi$
$198$		0			0
$199$	−0.835603	+	5.81175i	−0.0592343	+	0.411984i	0.938533	+	0.345191i	$0.112186\pi$
$199$	−0.835603	+	5.81175i	−0.0592343	+	0.411984i	−0.997767	+	0.0667930i	$0.978723\pi$
$200$	−1.06790	+	1.23243i	−0.0755122	+	0.0871457i
$201$		0			0
$202$	8.01936	+	2.35470i	0.564240	+	0.165676i
$203$	−3.47219	−	7.60303i	−0.243700	−	0.533628i
$204$		0			0
$205$	−2.55384	−	1.64125i	−0.178368	−	0.114630i
$206$	−12.7017			−0.884972
$207$		0			0
$208$	−3.87350			−0.268579
$209$	−0.428912	−	0.275645i	−0.0296685	−	0.0190668i
$210$		0			0
$211$	10.7125	+	23.4570i	0.737476	+	1.61485i	0.787663	+	0.616106i	$0.211291\pi$
$211$	10.7125	+	23.4570i	0.737476	+	1.61485i	−0.0501875	+	0.998740i	$0.515982\pi$
$212$	−3.97508	−	1.16719i	−0.273010	−	0.0801628i
$213$		0			0
$214$	−6.87991	+	7.93984i	−0.470301	+	0.542756i
$215$	−0.939907	+	6.53720i	−0.0641011	+	0.445833i
$216$		0			0
$217$	−3.14921	−	3.63439i	−0.213783	−	0.246718i
$218$	4.61985	−	2.96900i	0.312896	−	0.201086i
$219$		0			0
$220$	0.123120	+	0.142089i	0.00830078	+	0.00957961i
$221$	−11.3791	+	3.34120i	−0.765440	+	0.224753i
$222$		0			0
$223$	5.00892	−	5.78060i	0.335422	−	0.387098i	−0.562834	−	0.826570i	$-0.690289\pi$
$223$	5.00892	−	5.78060i	0.335422	−	0.387098i	0.898256	+	0.439472i	$0.144834\pi$
$224$	−0.516761	+	1.13155i	−0.0345275	+	0.0756048i
$225$		0			0
$226$	7.83896	+	17.1649i	0.521440	+	1.14179i
$227$	1.43223	+	9.96137i	0.0950604	+	0.661160i	0.980517	+	0.196437i	$0.0629370\pi$
$227$	1.43223	+	9.96137i	0.0950604	+	0.661160i	−0.885456	+	0.464723i	$0.846154\pi$
$228$		0			0
$229$	15.6790			1.03609			0.518047	−	0.855352i	$-0.326659\pi$
$229$	15.6790			1.03609			0.518047	+	0.855352i	$0.326659\pi$
$230$	0.198072	+	8.80079i	0.0130605	+	0.580307i
$231$		0			0
$232$	5.65250	+	3.63264i	0.371105	+	0.238495i
$233$	−2.83955	−	19.7495i	−0.186025	−	1.29383i	−0.842176	−	0.539202i	$-0.818726\pi$
$233$	−2.83955	−	19.7495i	−0.186025	−	1.29383i	0.656151	−	0.754629i	$-0.272183\pi$
$234$		0			0
$235$	−3.38214	−	0.993086i	−0.220627	−	0.0647818i
$236$	−2.53344	+	5.54747i	−0.164913	+	0.361110i
$237$		0			0
$238$	−0.542025	+	3.76987i	−0.0351343	+	0.244364i
$239$	−3.48890	+	1.02443i	−0.225678	+	0.0662652i	−0.392617	−	0.919702i	$-0.628430\pi$
$239$	−3.48890	+	1.02443i	−0.225678	+	0.0662652i	0.166938	+	0.985967i	$0.446612\pi$
$240$		0			0
$241$	−3.19705	+	2.05462i	−0.205940	+	0.132350i	−0.639546	−	0.768753i	$-0.720877\pi$
$241$	−3.19705	+	2.05462i	−0.205940	+	0.132350i	0.433606	+	0.901103i	$0.357241\pi$
$242$	9.24496	−	5.94138i	0.594289	−	0.381926i
$243$		0			0
$244$	5.50812	−	1.61733i	0.352621	−	0.103539i
$245$	1.42435	−	9.90660i	0.0909987	−	0.632910i
$246$		0			0
$247$	−8.00966	+	17.5387i	−0.509642	+	1.11596i
$248$	3.70926	+	1.08914i	0.235538	+	0.0691603i
$249$		0			0
$250$	−1.73213	−	12.0472i	−0.109549	−	0.761932i
$251$	−11.8442	−	7.61182i	−0.747601	−	0.480454i	0.110538	−	0.993872i	$-0.464743\pi$
$251$	−11.8442	−	7.61182i	−0.747601	−	0.480454i	−0.858139	+	0.513418i	$0.828379\pi$
$252$		0			0
$253$	−0.487672	−	0.0589502i	−0.0306596	−	0.00370617i
$254$	1.17839			0.0739390
$255$		0			0
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−7.66024	−	16.7736i	−0.477833	−	1.04631i	−0.983054	−	0.183318i	$-0.941316\pi$
$257$	−7.66024	−	16.7736i	−0.477833	−	1.04631i	0.505221	−	0.862990i	$-0.331411\pi$
$258$		0			0
$259$	−1.31994	+	2.89026i	−0.0820171	+	0.179592i
$260$	4.65608	−	5.37340i	0.288758	−	0.333244i
$261$		0			0
$262$	−20.9770	+	6.15939i	−1.29596	+	0.380529i
$263$	6.10681	+	7.04763i	0.376562	+	0.434575i	0.912120	−	0.409923i	$-0.134444\pi$
$263$	6.10681	+	7.04763i	0.376562	+	0.434575i	−0.535558	+	0.844498i	$0.679899\pi$
$264$		0			0
$265$	6.39733	−	4.11131i	0.392985	−	0.252556i
$266$	4.05494	+	4.67965i	0.248624	+	0.286928i
$267$		0			0
$268$	0.221096	−	1.53776i	0.0135056	−	0.0939334i
$269$	−4.28051	+	4.93997i	−0.260987	+	0.301195i	−0.871086	−	0.491130i	$-0.836584\pi$
$269$	−4.28051	+	4.93997i	−0.260987	+	0.301195i	0.610099	+	0.792325i	$0.291130\pi$
$270$		0			0
$271$	−11.1395	−	3.27086i	−0.676677	−	0.198690i	−0.0747031	−	0.997206i	$-0.523801\pi$
$271$	−11.1395	−	3.27086i	−0.676677	−	0.198690i	−0.601974	+	0.798515i	$0.705619\pi$
$272$	−1.27187	−	2.78502i	−0.0771187	−	0.168866i
$273$		0			0
$274$	14.4323	+	9.27506i	0.871886	+	0.560327i
$275$	0.167031			0.0100723
$276$		0			0
$277$	−12.6946			−0.762743			−0.381372	−	0.924422i	$-0.624548\pi$
$277$	−12.6946			−0.762743			−0.381372	+	0.924422i	$0.624548\pi$
$278$	−8.52579	−	5.47919i	−0.511343	−	0.328620i
$279$		0			0
$280$	−0.948544	−	2.07702i	−0.0566863	−	0.124126i
$281$	−24.1673	−	7.09617i	−1.44170	−	0.423322i	−0.534914	−	0.844907i	$-0.679656\pi$
$281$	−24.1673	−	7.09617i	−1.44170	−	0.423322i	−0.906789	+	0.421584i	$0.861474\pi$
$282$		0			0
$283$	18.6995	−	21.5803i	1.11157	−	1.28282i	0.156093	−	0.987742i	$-0.450110\pi$
$283$	18.6995	−	21.5803i	1.11157	−	1.28282i	0.955474	−	0.295074i	$-0.0953444\pi$
$284$	−1.21310	+	8.43727i	−0.0719840	+	0.500660i
$285$		0			0
$286$	0.259816	+	0.299844i	0.0153632	+	0.0177301i
$287$	−1.73074	+	1.11228i	−0.102163	+	0.0656559i
$288$		0			0
$289$	4.99399	+	5.76337i	0.293764	+	0.339022i
$290$	−11.8338	+	3.47471i	−0.694903	+	0.204042i
$291$		0			0
$292$	7.88999	−	9.10553i	0.461727	−	0.532861i
$293$	−4.96228	+	10.8659i	−0.289899	+	0.634791i	−0.997411	−	0.0719104i	$-0.977090\pi$
$293$	−4.96228	+	10.8659i	−0.289899	+	0.634791i	0.707512	+	0.706702i	$0.249818\pi$
$294$		0			0
$295$	−4.65028	−	10.1827i	−0.270750	−	0.592859i
$296$	−0.363509	−	2.52826i	−0.0211285	−	0.146952i
$297$		0			0
$298$	−0.377442			−0.0218646
$299$	0.417983	+	18.5720i	0.0241726	+	1.07404i
$300$		0			0
$301$	3.76531	+	2.41982i	0.217029	+	0.139476i
$302$	−2.21271	−	15.3897i	−0.127327	−	0.885579i
$303$		0			0
$304$	−4.77606	−	1.40238i	−0.273926	−	0.0804319i
$305$	−4.37735	+	9.58506i	−0.250646	+	0.548839i
$306$		0			0
$307$	−1.06604	+	7.41448i	−0.0608422	+	0.423167i	0.936522	+	0.350609i	$0.114025\pi$
$307$	−1.06604	+	7.41448i	−0.0608422	+	0.423167i	−0.997364	+	0.0725579i	$0.976884\pi$
$308$	0.122254	−	0.0358970i	0.00696606	−	0.00204542i
$309$		0			0
$310$	−5.96954	+	3.83639i	−0.339047	+	0.217892i
$311$	26.4395	−	16.9916i	1.49925	−	0.963506i	0.504253	−	0.863556i	$-0.331768\pi$
$311$	26.4395	−	16.9916i	1.49925	−	0.963506i	0.994992	−	0.0999503i	$-0.0318684\pi$
$312$		0			0
$313$	26.3295	−	7.73103i	1.48823	−	0.436983i	0.566253	−	0.824231i	$-0.308392\pi$
$313$	26.3295	−	7.73103i	1.48823	−	0.436983i	0.921976	+	0.387248i	$0.126574\pi$
$314$	2.55681	−	17.7830i	0.144289	−	1.00355i
$315$		0			0
$316$	5.42978	−	11.8896i	0.305449	−	0.668840i
$317$	33.7375	+	9.90624i	1.89489	+	0.556390i	0.991952	+	0.126618i	$0.0404122\pi$
$317$	33.7375	+	9.90624i	1.89489	+	0.556390i	0.902938	+	0.429772i	$0.141406\pi$
$318$		0			0
$319$	−0.0979439	−	0.681215i	−0.00548381	−	0.0381407i
$320$	1.54417	+	0.992377i	0.0863216	+	0.0554755i
$321$		0			0
$322$	5.48110	+	2.35557i	0.305450	+	0.131271i
$323$	−15.2402			−0.847986
$324$		0			0
$325$	−0.898952	−	6.25235i	−0.0498649	−	0.346818i
$326$	1.76773	+	3.87079i	0.0979055	+	0.214383i
$327$		0			0
$328$	0.687038	−	1.50440i	0.0379353	−	0.0830667i
$329$	−1.56437	+	1.80538i	−0.0862463	+	0.0995336i
$330$		0			0
$331$	−18.8692	+	5.54049i	−1.03714	+	0.304533i	−0.755612	−	0.655019i	$-0.772660\pi$
$331$	−18.8692	+	5.54049i	−1.03714	+	0.304533i	−0.281531	+	0.959552i	$0.590842\pi$
$332$	−3.40815	−	3.93322i	−0.187047	−	0.215863i
$333$		0			0
$334$	6.22029	−	3.99753i	0.340359	−	0.218735i
$335$	1.86744	+	2.15514i	0.102029	+	0.117748i
$336$		0			0
$337$	−0.684314	+	4.75951i	−0.0372770	+	0.259267i	−0.999934	−	0.0114555i	$-0.996354\pi$
$337$	−0.684314	+	4.75951i	−0.0372770	+	0.259267i	0.962657	+	0.270723i	$0.0872626\pi$
$338$	1.31235	−	1.51453i	0.0713822	−	0.0823794i
$339$		0			0
$340$	5.39227	+	1.58331i	0.292437	+	0.0858672i
$341$	−0.164491	−	0.360185i	−0.00890768	−	0.0195051i
$342$		0			0
$343$	−13.0315	−	8.37481i	−0.703632	−	0.452197i
$344$	−3.59805			−0.193994
$345$		0			0
$346$	−14.4274			−0.775623
$347$	0.0528673	+	0.0339758i	0.00283807	+	0.00182391i	0.542059	−	0.840340i	$-0.317645\pi$
$347$	0.0528673	+	0.0339758i	0.00283807	+	0.00182391i	−0.539221	+	0.842164i	$0.681281\pi$
$348$		0			0
$349$	−3.33195	−	7.29595i	−0.178355	−	0.390543i	0.799248	−	0.601002i	$-0.205232\pi$
$349$	−3.33195	−	7.29595i	−0.178355	−	0.390543i	−0.977603	+	0.210458i	$0.932504\pi$
$350$	−1.94640	−	0.571515i	−0.104039	−	0.0305487i
$351$		0			0
$352$	−0.0670753	+	0.0774090i	−0.00357512	+	0.00412591i
$353$	1.17101	−	8.14453i	0.0623264	−	0.433489i	−0.934636	−	0.355606i	$-0.884275\pi$
$353$	1.17101	−	8.14453i	0.0623264	−	0.433489i	0.996962	−	0.0778838i	$-0.0248163\pi$
$354$		0			0
$355$	−10.2462	−	11.8247i	−0.543810	−	0.627591i
$356$	−6.71300	+	4.31418i	−0.355788	+	0.228651i
$357$		0			0
$358$	−16.9451	−	19.5557i	−0.895575	−	1.03355i
$359$	−28.4263	+	8.34671i	−1.50028	+	0.440523i	−0.925806	−	0.377999i	$-0.876612\pi$
$359$	−28.4263	+	8.34671i	−1.50028	+	0.440523i	−0.574476	+	0.818521i	$0.694794\pi$
$360$		0			0
$361$	−3.78341	+	4.36629i	−0.199127	+	0.229805i
$362$	5.67113	−	12.4180i	0.298068	−	0.652678i
$363$		0			0
$364$	−2.00167	−	4.38305i	−0.104916	−	0.229734i
$365$	3.14735	+	21.8903i	0.164740	+	1.14579i
$366$		0			0
$367$	12.5240			0.653750			0.326875	−	0.945068i	$-0.394004\pi$
$367$	12.5240			0.653750			0.326875	+	0.945068i	$0.394004\pi$
$368$	−4.73046	+	0.789155i	−0.246592	+	0.0411376i
$369$		0			0
$370$	3.94420	+	2.53478i	0.205049	+	0.131777i
$371$	−0.733435	−	5.10115i	−0.0380780	−	0.264839i
$372$		0			0
$373$	−19.8574	−	5.83067i	−1.02818	−	0.301900i	−0.276208	−	0.961098i	$-0.589078\pi$
$373$	−19.8574	−	5.83067i	−1.02818	−	0.301900i	−0.751970	+	0.659197i	$0.770896\pi$
$374$	−0.130274	+	0.285260i	−0.00673630	+	0.0147504i
$375$		0			0
$376$	0.273295	−	1.90081i	0.0140941	−	0.0980269i
$377$	−24.9723	+	7.33254i	−1.28614	+	0.377645i
$378$		0			0
$379$	4.65034	−	2.98859i	0.238872	−	0.153514i	−0.415728	−	0.909489i	$-0.636473\pi$
$379$	4.65034	−	2.98859i	0.238872	−	0.153514i	0.654600	+	0.755975i	$0.272837\pi$
$380$	7.68640	−	4.93975i	0.394304	−	0.253404i
$381$		0			0
$382$	−21.9003	+	6.43051i	−1.12052	+	0.329013i
$383$	4.99811	−	34.7626i	0.255391	−	1.77629i	−0.309281	−	0.950971i	$-0.600088\pi$
$383$	4.99811	−	34.7626i	0.255391	−	1.77629i	0.564673	−	0.825315i	$-0.309002\pi$
$384$		0			0
$385$	−0.0971563	+	0.212743i	−0.00495154	+	0.0108424i
$386$	3.49782	+	1.02705i	0.178034	+	0.0522756i
$387$		0			0
$388$	−1.63271	−	11.3558i	−0.0828885	−	0.576502i
$389$	13.8992	+	8.93246i	0.704716	+	0.452894i	0.843290	−	0.537458i	$-0.180615\pi$
$389$	13.8992	+	8.93246i	0.704716	+	0.452894i	−0.138574	+	0.990352i	$0.544252\pi$
$390$		0			0
$391$	−13.2158	+	6.39867i	−0.668354	+	0.323595i
$392$	5.45256			0.275396
$393$		0			0
$394$	−2.31071	−	16.0713i	−0.116412	−	0.809662i
$395$	9.96667	+	21.8240i	0.501477	+	1.09808i
$396$		0			0
$397$	12.9159	−	28.2818i	0.648229	−	1.41942i	−0.244867	−	0.969557i	$-0.578744\pi$
$397$	12.9159	−	28.2818i	0.648229	−	1.41942i	0.893096	−	0.449866i	$-0.148528\pi$
$398$	3.84502	−	4.43739i	0.192734	−	0.222426i
$399$		0			0
$400$	1.56468	−	0.459431i	0.0782339	−	0.0229715i
$401$	10.2080	+	11.7806i	0.509762	+	0.588297i	0.951038	−	0.309075i	$-0.100019\pi$
$401$	10.2080	+	11.7806i	0.509762	+	0.588297i	−0.441276	+	0.897372i	$0.645474\pi$
$402$		0			0
$403$	−12.5973	+	8.09577i	−0.627515	+	0.403279i
$404$	−5.47327	−	6.31649i	−0.272305	−	0.314257i
$405$		0			0
$406$	−1.18952	+	8.27329i	−0.0590348	+	0.410596i
$407$	−0.171327	+	0.197722i	−0.00849239	+	0.00980074i
$408$		0			0
$409$	−32.6538	−	9.58803i	−1.61463	−	0.474098i	−0.655061	−	0.755576i	$-0.727357\pi$
$409$	−32.6538	−	9.58803i	−1.61463	−	0.474098i	−0.959568	+	0.281478i	$0.909175\pi$
$410$	1.26110	+	2.76142i	0.0622811	+	0.136377i
$411$		0			0
$412$	10.6854	+	6.86708i	0.526431	+	0.338317i
$413$	−7.58642			−0.373303
$414$		0			0
$415$	9.55296			0.468936
$416$	3.25860	+	2.09417i	0.159766	+	0.102675i
$417$		0			0
$418$	0.211799	+	0.463775i	0.0103594	+	0.0226840i
$419$	−14.0695	−	4.13117i	−0.687339	−	0.201821i	−0.0806291	−	0.996744i	$-0.525693\pi$
$419$	−14.0695	−	4.13117i	−0.687339	−	0.201821i	−0.606710	+	0.794923i	$0.707511\pi$
$420$		0			0
$421$	9.07808	−	10.4767i	0.442439	−	0.510601i	−0.490103	−	0.871665i	$-0.663041\pi$
$421$	9.07808	−	10.4767i	0.442439	−	0.510601i	0.932541	+	0.361063i	$0.117586\pi$
$422$	3.66992	−	25.5249i	0.178649	−	1.24253i
$423$		0			0
$424$	2.71302	+	3.13099i	0.131756	+	0.152054i
$425$	4.20022	−	2.69932i	0.203740	−	0.130936i
$426$		0			0
$427$	4.67647	+	5.39693i	0.226310	+	0.261176i
$428$	10.0803	−	2.95986i	0.487252	−	0.143070i
$429$		0			0
$430$	4.32497	−	4.99129i	0.208569	−	0.240701i
$431$	−2.92787	+	6.41114i	−0.141030	+	0.308814i	−0.966946	−	0.254980i	$-0.917931\pi$
$431$	−2.92787	+	6.41114i	−0.141030	+	0.308814i	0.825916	+	0.563793i	$0.190659\pi$
$432$		0			0
$433$	−7.93087	−	17.3662i	−0.381134	−	0.834566i	−0.998840	−	0.0481571i	$-0.984665\pi$
$433$	−7.93087	−	17.3662i	−0.381134	−	0.834566i	0.617706	−	0.786409i	$-0.288062\pi$
$434$	0.684390	+	4.76004i	0.0328518	+	0.228489i
$435$		0			0
$436$	−5.49163			−0.263001
$437$	−6.20849	+	23.0507i	−0.296992	+	1.10267i
$438$		0			0
$439$	−5.77321	−	3.71021i	−0.275540	−	0.177079i	0.395572	−	0.918435i	$-0.370547\pi$
$439$	−5.77321	−	3.71021i	−0.275540	−	0.177079i	−0.671112	+	0.741356i	$0.734183\pi$
$440$	−0.0267566	−	0.186096i	−0.00127557	−	0.00887180i
$441$		0			0
$442$	11.3791	+	3.34120i	0.541248	+	0.158925i
$443$	−8.42209	+	18.4418i	−0.400145	+	0.876196i	0.597110	+	0.802159i	$0.296316\pi$
$443$	−8.42209	+	18.4418i	−0.400145	+	0.876196i	−0.997256	+	0.0740369i	$0.976412\pi$
$444$		0			0
$445$	2.08453	−	14.4982i	0.0988161	−	0.687281i
$446$	−7.33900	+	2.15493i	−0.347512	+	0.102039i
$447$		0			0
$448$	1.04649	−	0.672537i	0.0494419	−	0.0317744i
$449$	23.7362	−	15.2544i	1.12018	−	0.719897i	0.156694	−	0.987647i	$-0.449916\pi$
$449$	23.7362	−	15.2544i	1.12018	−	0.719897i	0.963488	+	0.267750i	$0.0862801\pi$
$450$		0			0
$451$	−0.162538	+	0.0477253i	−0.00765359	+	0.00224730i
$452$	2.68551	−	18.6781i	0.126316	−	0.878545i
$453$		0			0
$454$	4.18066	−	9.15436i	0.196208	−	0.429636i
$455$	8.48634	+	2.49181i	0.397846	+	0.116818i
$456$		0			0
$457$	4.24194	+	29.5034i	0.198430	+	1.38011i	0.808842	+	0.588026i	$0.200095\pi$
$457$	4.24194	+	29.5034i	0.198430	+	1.38011i	−0.610413	+	0.792084i	$0.708996\pi$
$458$	−13.1900	−	8.47669i	−0.616327	−	0.396090i
$459$		0			0
$460$	4.59144	−	7.51078i	0.214077	−	0.350192i
$461$	36.3247			1.69181			0.845905	−	0.533334i	$-0.179061\pi$
$461$	36.3247			1.69181			0.845905	+	0.533334i	$0.179061\pi$
$462$		0			0
$463$	−3.66493	−	25.4902i	−0.170324	−	1.18463i	−0.878200	−	0.478293i	$-0.841256\pi$
$463$	−3.66493	−	25.4902i	−0.170324	−	1.18463i	0.707876	−	0.706336i	$-0.249653\pi$
$464$	−2.79123	−	6.11195i	−0.129580	−	0.283740i
$465$		0			0
$466$	−8.28860	+	18.1495i	−0.383962	+	0.840759i
$467$	−4.38559	+	5.06124i	−0.202941	+	0.234206i	−0.848092	−	0.529848i	$-0.822249\pi$
$467$	−4.38559	+	5.06124i	−0.202941	+	0.234206i	0.645151	+	0.764055i	$0.276794\pi$
$468$		0			0
$469$	1.85430	−	0.544472i	0.0856236	−	0.0251414i
$470$	2.30834	+	2.66396i	0.106476	+	0.122879i
$471$		0			0
$472$	5.13046	−	3.29715i	0.236148	−	0.151763i
$473$	0.241340	+	0.278521i	0.0110968	+	0.0128064i
$474$		0			0
$475$	1.15521	−	8.03467i	0.0530047	−	0.368656i
$476$	2.49412	−	2.87837i	0.114318	−	0.131930i
$477$		0			0
$478$	3.48890	+	1.02443i	0.159579	+	0.0468566i
$479$	6.19655	+	13.5685i	0.283127	+	0.619963i	0.996749	−	0.0805688i	$-0.0256737\pi$
$479$	6.19655	+	13.5685i	0.283127	+	0.619963i	−0.713622	+	0.700531i	$0.752946\pi$
$480$		0			0
$481$	8.32329	+	5.34905i	0.379509	+	0.243896i
$482$	3.80034			0.173101
$483$		0			0
$484$	−10.9895			−0.499523
$485$	17.7156	+	11.3851i	0.804422	+	0.516971i
$486$		0			0
$487$	6.26391	+	13.7160i	0.283845	+	0.621534i	0.996823	−	0.0796531i	$-0.0253813\pi$
$487$	6.26391	+	13.7160i	0.283845	+	0.621534i	−0.712978	+	0.701187i	$0.752654\pi$
$488$	−5.50812	−	1.61733i	−0.249341	−	0.0732131i
$489$		0			0
$490$	−6.55416	+	7.56390i	−0.296087	+	0.341702i
$491$	−0.978290	+	6.80416i	−0.0441496	+	0.307067i	0.955767	+	0.294126i	$0.0950285\pi$
$491$	−0.978290	+	6.80416i	−0.0441496	+	0.307067i	−0.999916	+	0.0129413i	$0.995881\pi$
$492$		0			0
$493$	−13.4718	−	15.5473i	−0.606738	−	0.700213i
$494$	16.2203	−	10.4241i	0.729785	−	0.469005i
$495$		0			0
$496$	−2.53160	−	2.92162i	−0.113672	−	0.131185i
$497$	−10.1741	+	2.98737i	−0.456369	+	0.134002i
$498$		0			0
$499$	−3.71720	+	4.28988i	−0.166405	+	0.192041i	−0.832827	−	0.553533i	$-0.813279\pi$
$499$	−3.71720	+	4.28988i	−0.166405	+	0.192041i	0.666423	+	0.745574i	$0.267825\pi$
$500$	−5.05605	+	11.0712i	−0.226113	+	0.495119i
$501$		0			0
$502$	5.84874	+	12.8069i	0.261042	+	0.571602i
$503$	6.03419	+	41.9687i	0.269051	+	1.87129i	0.457502	+	0.889209i	$0.348744\pi$
$503$	6.03419	+	41.9687i	0.269051	+	1.87129i	−0.188450	+	0.982083i	$0.560346\pi$
$504$		0			0
$505$	15.3414			0.682684
$506$	0.378384	+	0.313247i	0.0168212	+	0.0139255i
$507$		0			0
$508$	−0.991327	−	0.637087i	−0.0439830	−	0.0282662i
$509$	−0.522686	−	3.63536i	−0.0231676	−	0.161134i	0.974953	−	0.222410i	$-0.0713923\pi$
$509$	−0.522686	−	3.63536i	−0.0231676	−	0.161134i	−0.998121	+	0.0612754i	$0.980483\pi$
$510$		0			0
$511$	14.3806	+	4.22252i	0.636160	+	0.186793i
$512$	−0.415415	+	0.909632i	−0.0183589	+	0.0402004i
$513$		0			0
$514$	−2.62428	+	18.2523i	−0.115752	+	0.805074i
$515$	−22.3703	+	6.56853i	−0.985755	+	0.289444i
$516$		0			0
$517$	−0.165471	+	0.106342i	−0.00727742	+	0.00467691i
$518$	2.67300	−	1.71783i	0.117445	−	0.0754772i
$519$		0			0
$520$	−6.82202	+	2.00313i	−0.299165	+	0.0878429i
$521$	4.11886	−	28.6473i	0.180451	−	1.25506i	−0.675250	−	0.737589i	$-0.735964\pi$
$521$	4.11886	−	28.6473i	0.180451	−	1.25506i	0.855700	−	0.517472i	$-0.173127\pi$
$522$		0			0
$523$	6.64284	−	14.5458i	0.290471	−	0.636043i	−0.706992	−	0.707221i	$-0.749949\pi$
$523$	6.64284	−	14.5458i	0.290471	−	0.636043i	0.997464	+	0.0711780i	$0.0226758\pi$
$524$	20.9770	+	6.15939i	0.916383	+	0.269074i
$525$		0			0
$526$	−1.32714	−	9.23043i	−0.0578659	−	0.402466i
$527$	−9.95714	−	6.39907i	−0.433740	−	0.278748i
$528$		0			0
$529$	4.29415	+	22.5956i	0.186702	+	0.982417i
$530$	−7.60452			−0.330319
$531$		0			0
$532$	−0.881223	−	6.12904i	−0.0382059	−	0.265728i
$533$	2.66124	+	5.82730i	0.115271	+	0.252409i
$534$		0			0
$535$	−8.01094	+	17.5415i	−0.346343	+	0.758386i
$536$	−1.01737	+	1.17411i	−0.0439438	+	0.0507138i
$537$		0			0
$538$	6.27174	−	1.84155i	0.270394	−	0.0793948i
$539$	−0.365732	−	0.422077i	−0.0157532	−	0.0181801i
$540$		0			0
$541$	−31.5681	+	20.2876i	−1.35722	+	0.872232i	−0.998133	−	0.0610717i	$-0.980548\pi$
$541$	−31.5681	+	20.2876i	−1.35722	+	0.872232i	−0.359087	+	0.933304i	$0.616912\pi$
$542$	7.60280	+	8.77410i	0.326568	+	0.376880i
$543$		0			0
$544$	−0.435725	+	3.03053i	−0.0186815	+	0.129933i
$545$	6.60113	−	7.61811i	0.282761	−	0.326324i
$546$		0			0
$547$	11.9729	+	3.51556i	0.511924	+	0.150314i	0.527485	−	0.849565i	$-0.323135\pi$
$547$	11.9729	+	3.51556i	0.511924	+	0.150314i	−0.0155609	+	0.999879i	$0.504953\pi$
$548$	−7.12673	−	15.6054i	−0.304439	−	0.666628i
$549$		0			0
$550$	−0.140515	−	0.0903036i	−0.00599159	−	0.00385056i
$551$	−33.4458			−1.42484
$552$		0			0
$553$	16.2595			0.691425
$554$	10.6794	+	6.86321i	0.453723	+	0.291590i
$555$		0			0
$556$	4.21007	+	9.21878i	0.178547	+	0.390963i
$557$	−13.1342	−	3.85656i	−0.556515	−	0.163408i	−0.00863256	−	0.999963i	$-0.502748\pi$
$557$	−13.1342	−	3.85656i	−0.556515	−	0.163408i	−0.547883	+	0.836555i	$0.684566\pi$
$558$		0			0
$559$	9.12682	−	10.5329i	0.386023	−	0.445495i
$560$	−0.324957	+	2.26012i	−0.0137319	+	0.0955076i
$561$		0			0
$562$	16.4944	+	19.0355i	0.695774	+	0.802966i
$563$	24.0796	−	15.4750i	1.01483	−	0.652193i	0.0761932	−	0.997093i	$-0.475723\pi$
$563$	24.0796	−	15.4750i	1.01483	−	0.652193i	0.938640	+	0.344900i	$0.112087\pi$
$564$		0			0
$565$	22.6826	+	26.1771i	0.954264	+	1.10128i
$566$	−27.3982	+	8.04483i	−1.15163	+	0.338150i
$567$		0			0
$568$	5.58205	−	6.44203i	0.234218	−	0.270302i
$569$	9.46180	−	20.7185i	0.396659	−	0.868563i	−0.600939	−	0.799295i	$-0.705206\pi$
$569$	9.46180	−	20.7185i	0.396659	−	0.868563i	0.997598	−	0.0692679i	$-0.0220663\pi$
$570$		0			0
$571$	−3.49699	−	7.65734i	−0.146344	−	0.320450i	0.822237	−	0.569145i	$-0.192726\pi$
$571$	−3.49699	−	7.65734i	−0.146344	−	0.320450i	−0.968582	+	0.248695i	$0.919998\pi$
$572$	−0.0564634	−	0.392712i	−0.00236085	−	0.0164201i
$573$		0			0
$574$	2.05734			0.0858716
$575$	−2.37164	−	7.45245i	−0.0989041	−	0.310789i
$576$		0			0
$577$	14.3164	+	9.20060i	0.596000	+	0.383026i	0.803584	−	0.595191i	$-0.202924\pi$
$577$	14.3164	+	9.20060i	0.596000	+	0.383026i	−0.207584	+	0.978217i	$0.566560\pi$
$578$	−1.08530	−	7.54841i	−0.0451424	−	0.313972i
$579$		0			0
$580$	11.8338	+	3.47471i	0.491371	+	0.144279i
$581$	2.68943	−	5.88902i	0.111576	−	0.244318i
$582$		0			0
$583$	0.0603904	−	0.420024i	0.00250111	−	0.0173956i
$584$	−11.5603	+	3.39441i	−0.478369	+	0.140462i
$585$		0			0
$586$	10.0491	−	6.45815i	0.415123	−	0.266784i
$587$	−20.9570	+	13.4682i	−0.864987	+	0.555893i	−0.896215	−	0.443619i	$-0.853694\pi$
$587$	−20.9570	+	13.4682i	−0.864987	+	0.555893i	0.0312287	+	0.999512i	$0.490058\pi$
$588$		0			0
$589$	−18.4636	+	5.42140i	−0.760778	+	0.223385i
$590$	−1.59312	+	11.0804i	−0.0655875	+	0.456171i
$591$		0			0
$592$	−1.06108	+	2.32343i	−0.0436100	+	0.0954925i
$593$	10.7282	+	3.15007i	0.440552	+	0.129358i	0.494484	−	0.869187i	$-0.335357\pi$
$593$	10.7282	+	3.15007i	0.440552	+	0.129358i	−0.0539315	+	0.998545i	$0.517175\pi$
$594$		0			0
$595$	0.994918	+	6.91980i	0.0407876	+	0.283684i
$596$	0.317524	+	0.204060i	0.0130063	+	0.00835864i
$597$		0			0
$598$	9.68913	−	15.8497i	0.396218	−	0.648142i
$599$	−40.5640			−1.65740			−0.828701	−	0.559692i	$-0.810920\pi$
$599$	−40.5640			−1.65740			−0.828701	+	0.559692i	$0.810920\pi$
$600$		0			0
$601$	4.10735	+	28.5672i	0.167542	+	1.16528i	0.883944	+	0.467594i	$0.154879\pi$
$601$	4.10735	+	28.5672i	0.167542	+	1.16528i	−0.716401	+	0.697689i	$0.754212\pi$
$602$	−1.85933	−	4.07137i	−0.0757806	−	0.165936i
$603$		0			0
$604$	−6.45886	+	14.1429i	−0.262807	+	0.575468i
$605$	13.2098	−	15.2449i	0.537053	−	0.619792i
$606$		0			0
$607$	27.6606	−	8.12189i	1.12271	−	0.329657i	0.332871	−	0.942972i	$-0.391982\pi$
$607$	27.6606	−	8.12189i	1.12271	−	0.329657i	0.789839	+	0.613315i	$0.210164\pi$
$608$	3.25970	+	3.76189i	0.132198	+	0.152565i
$609$		0			0
$610$	8.86454	−	5.69689i	0.358915	−	0.230660i
$611$	4.87119	+	5.62165i	0.197067	+	0.227428i
$612$		0			0
$613$	−0.707023	+	4.91745i	−0.0285564	+	0.198614i	−0.999105	−	0.0422898i	$-0.986535\pi$
$613$	−0.707023	+	4.91745i	−0.0285564	+	0.198614i	0.970549	+	0.240904i	$0.0774438\pi$
$614$	4.90538	−	5.66111i	0.197965	−	0.228464i
$615$		0			0
$616$	−0.122254	−	0.0358970i	−0.00492575	−	0.00144633i
$617$	−10.1852	−	22.3024i	−0.410040	−	0.897862i	−0.996153	−	0.0876329i	$-0.972070\pi$
$617$	−10.1852	−	22.3024i	−0.410040	−	0.897862i	0.586113	−	0.810229i	$-0.300658\pi$
$618$		0			0
$619$	5.18118	+	3.32974i	0.208249	+	0.133834i	0.640608	−	0.767868i	$-0.278682\pi$
$619$	5.18118	+	3.32974i	0.208249	+	0.133834i	−0.432359	+	0.901702i	$0.642319\pi$
$620$	7.09600			0.284982
$621$		0			0
$622$	−31.4287			−1.26017
$623$	−8.35072	−	5.36668i	−0.334565	−	0.215012i
$624$		0			0
$625$	−5.89351	−	12.9050i	−0.235740	−	0.516200i
$626$	−26.3295	−	7.73103i	−1.05234	−	0.308994i
$627$		0			0
$628$	−11.7651	+	13.5777i	−0.469480	+	0.541808i
$629$	−1.11295	+	7.74075i	−0.0443763	+	0.308644i
$630$		0			0
$631$	18.3428	+	21.1687i	0.730215	+	0.842712i	0.992496	−	0.122279i	$-0.0390203\pi$
$631$	18.3428	+	21.1687i	0.730215	+	0.842712i	−0.262281	+	0.964991i	$0.584475\pi$
$632$	−10.9958	+	7.06657i	−0.437390	+	0.281093i
$633$		0			0
$634$	−23.0261	−	26.5735i	−0.914484	−	1.05537i
$635$	2.07539	−	0.609390i	0.0823593	−	0.0241829i
$636$		0			0
$637$	−13.8310	+	15.9618i	−0.548003	+	0.632429i
$638$	−0.285897	+	0.626027i	−0.0113188	+	0.0247846i
$639$		0			0
$640$	−0.762518	−	1.66968i	−0.0301412	−	0.0659999i
$641$	−4.36986	−	30.3931i	−0.172599	−	1.20045i	−0.873367	−	0.487064i	$-0.838068\pi$
$641$	−4.36986	−	30.3931i	−0.172599	−	1.20045i	0.700767	−	0.713390i	$-0.252841\pi$
$642$		0			0
$643$	−8.46014			−0.333635			−0.166818	−	0.985988i	$-0.553349\pi$
$643$	−8.46014			−0.333635			−0.166818	+	0.985988i	$0.553349\pi$
$644$	−3.33748	−	4.94494i	−0.131515	−	0.194858i
$645$		0			0
$646$	12.8209	+	8.23946i	0.504430	+	0.324177i
$647$	−0.308446	−	2.14529i	−0.0121263	−	0.0843400i	0.982860	−	0.184356i	$-0.0590198\pi$
$647$	−0.308446	−	2.14529i	−0.0121263	−	0.0843400i	−0.994986	+	0.100016i	$0.968111\pi$
$648$		0			0
$649$	−0.599356	−	0.175987i	−0.0235268	−	0.00690808i
$650$	−2.62403	+	5.74582i	−0.102923	+	0.225370i
$651$		0			0
$652$	0.605597	−	4.21202i	0.0237170	−	0.164955i
$653$	−7.96236	+	2.33796i	−0.311591	+	0.0914914i	−0.433789	−	0.901014i	$-0.642824\pi$
$653$	−7.96236	+	2.33796i	−0.311591	+	0.0914914i	0.122198	+	0.992506i	$0.461006\pi$
$654$		0			0
$655$	−33.7595	+	21.6959i	−1.31909	+	0.847728i
$656$	−1.39131	+	0.894143i	−0.0543217	+	0.0349104i
$657$		0			0
$658$	2.29209	−	0.673018i	0.0893549	−	0.0262370i
$659$	5.79330	−	40.2933i	0.225675	−	1.56960i	−0.490349	−	0.871526i	$-0.663131\pi$
$659$	5.79330	−	40.2933i	0.225675	−	1.56960i	0.716024	−	0.698076i	$-0.245960\pi$
$660$		0			0
$661$	−16.1574	+	35.3799i	−0.628452	+	1.37612i	0.280758	+	0.959779i	$0.409414\pi$
$661$	−16.1574	+	35.3799i	−0.628452	+	1.37612i	−0.909210	+	0.416339i	$0.863313\pi$
$662$	18.8692	+	5.54049i	0.733371	+	0.215337i
$663$		0			0
$664$	0.740662	+	5.15142i	0.0287433	+	0.199914i
$665$	9.56159	+	6.14486i	0.370783	+	0.238287i
$666$		0			0
$667$	−29.0033	+	14.0424i	−1.12301	+	0.543725i
$668$	−7.39407			−0.286085
$669$		0			0
$670$	−0.405834	−	2.82264i	−0.0156787	−	0.109048i
$671$	0.244263	+	0.534861i	0.00942966	+	0.0206481i
$672$		0			0
$673$	17.6817	−	38.7176i	0.681580	−	1.49245i	−0.179380	−	0.983780i	$-0.557409\pi$
$673$	17.6817	−	38.7176i	0.681580	−	1.49245i	0.860960	−	0.508672i	$-0.169864\pi$
$674$	3.14887	−	3.63399i	0.121290	−	0.139976i
$675$		0			0
$676$	−1.92283	+	0.564594i	−0.0739550	+	0.0217151i
$677$	27.2058	+	31.3972i	1.04561	+	1.20669i	0.977919	+	0.208986i	$0.0670164\pi$
$677$	27.2058	+	31.3972i	1.04561	+	1.20669i	0.0676869	+	0.997707i	$0.478438\pi$
$678$		0			0
$679$	12.0059	−	7.71572i	0.460744	−	0.296102i
$680$	−3.68026	−	4.24725i	−0.141132	−	0.162874i
$681$		0			0
$682$	−0.0563520	+	0.391937i	−0.00215783	+	0.0150080i
$683$	−10.9425	+	12.6284i	−0.418705	+	0.483211i	−0.925442	−	0.378890i	$-0.876306\pi$
$683$	−10.9425	+	12.6284i	−0.418705	+	0.483211i	0.506737	+	0.862101i	$0.330851\pi$
$684$		0			0
$685$	30.2146	+	8.87182i	1.15444	+	0.338975i
$686$	6.43499	+	14.0907i	0.245689	+	0.537984i
$687$		0			0
$688$	3.02687	+	1.94525i	0.115398	+	0.0741620i
$689$	−16.0475			−0.611361
$690$		0			0
$691$	44.6532			1.69869			0.849344	−	0.527840i	$-0.176998\pi$
$691$	44.6532			1.69869			0.849344	+	0.527840i	$0.176998\pi$
$692$	12.1371	+	7.80005i	0.461384	+	0.296513i
$693$		0			0
$694$	−0.0261061	−	0.0571645i	−0.000990975	−	0.00216993i
$695$	−17.8491	−	5.24098i	−0.677056	−	0.198802i
$696$		0			0
$697$	−3.31596	+	3.82682i	−0.125601	+	0.144951i
$698$	−1.14148	+	7.93914i	−0.0432055	+	0.300501i
$699$		0			0
$700$	1.32843	+	1.53309i	0.0502100	+	0.0579454i
$701$	18.8132	−	12.0905i	0.710563	−	0.456651i	−0.134780	−	0.990876i	$-0.543033\pi$
$701$	18.8132	−	12.0905i	0.710563	−	0.456651i	0.845343	+	0.534224i	$0.179396\pi$
$702$		0			0
$703$	8.32610	+	9.60883i	0.314025	+	0.362404i
$704$	0.0982778	−	0.0288570i	0.00370398	−	0.00108759i
$705$		0			0
$706$	−5.38838	+	6.21852i	−0.202794	+	0.234037i
$707$	4.31904	−	9.45738i	0.162434	−	0.355681i
$708$		0			0
$709$	−4.19668	−	9.18946i	−0.157610	−	0.345117i	0.814310	−	0.580430i	$-0.197116\pi$
$709$	−4.19668	−	9.18946i	−0.157610	−	0.345117i	−0.971920	+	0.235313i	$0.924388\pi$
$710$	2.22671	+	15.4871i	0.0835668	+	0.581220i
$711$		0			0
$712$	7.97976			0.299054
$713$	−13.7349	+	12.4533i	−0.514375	+	0.466380i
$714$		0			0
$715$	0.612649	+	0.393726i	0.0229118	+	0.0147245i
$716$	3.68252	+	25.6125i	0.137622	+	0.957183i
$717$		0			0
$718$	28.4263	+	8.34671i	1.06086	+	0.311497i
$719$	−3.44183	+	7.53656i	−0.128359	+	0.281066i	−0.962890	−	0.269894i	$-0.913011\pi$
$719$	−3.44183	+	7.53656i	−0.128359	+	0.281066i	0.834531	+	0.550960i	$0.185738\pi$
$720$		0			0
$721$	−2.24864	+	15.6397i	−0.0837439	+	0.582452i
$722$	5.54341	−	1.62769i	0.206304	−	0.0605764i
$723$		0			0
$724$	−11.4846	+	7.38068i	−0.426820	+	0.274301i
$725$	9.21772	−	5.92387i	0.342338	−	0.220007i
$726$		0			0
$727$	14.2329	−	4.17916i	0.527869	−	0.154996i	−0.00692917	−	0.999976i	$-0.502206\pi$
$727$	14.2329	−	4.17916i	0.527869	−	0.154996i	0.534799	+	0.844980i	$0.320387\pi$
$728$	−0.685743	+	4.76945i	−0.0254153	+	0.176767i
$729$		0			0
$730$	9.18707	−	20.1169i	0.340029	−	0.744559i
$731$	10.5699	+	3.10360i	0.390942	+	0.114791i
$732$		0			0
$733$	−2.91154	−	20.2502i	−0.107540	−	0.747958i	−0.970223	−	0.242213i	$-0.922127\pi$
$733$	−2.91154	−	20.2502i	−0.107540	−	0.747958i	0.862683	−	0.505745i	$-0.168782\pi$
$734$	−10.5359	−	6.77101i	−0.388887	−	0.249923i
$735$		0			0
$736$	4.40616	+	1.89360i	0.162413	+	0.0697990i
$737$	0.159127			0.00586152
$738$		0			0
$739$	5.47357	+	38.0695i	0.201349	+	1.40041i	0.800288	+	0.599616i	$0.204680\pi$
$739$	5.47357	+	38.0695i	0.201349	+	1.40041i	−0.598940	+	0.800794i	$0.704411\pi$
$740$	−1.94767	−	4.26479i	−0.0715976	−	0.156777i
$741$		0			0
$742$	−2.14089	+	4.68789i	−0.0785944	+	0.172098i
$743$	10.9058	−	12.5859i	0.400094	−	0.461734i	−0.519576	−	0.854424i	$-0.673910\pi$
$743$	10.9058	−	12.5859i	0.400094	−	0.461734i	0.919671	+	0.392691i	$0.128456\pi$
$744$		0			0
$745$	−0.664751	+	0.195189i	−0.0243546	+	0.00715116i
$746$	13.5528	+	15.6408i	0.496204	+	0.572650i
$747$		0			0
$748$	0.263817	−	0.169545i	0.00964609	−	0.00619917i
$749$	8.55835	+	9.87686i	0.312715	+	0.360893i
$750$		0			0
$751$	2.77625	−	19.3092i	0.101307	−	0.704604i	−0.874349	−	0.485297i	$-0.838711\pi$
$751$	2.77625	−	19.3092i	0.101307	−	0.704604i	0.975656	−	0.219307i	$-0.0703796\pi$
$752$	−1.25757	+	1.45131i	−0.0458588	+	0.0529238i
$753$		0			0
$754$	24.9723	+	7.33254i	0.909439	+	0.267035i
$755$	−11.8556	−	25.9602i	−0.431470	−	0.944787i
$756$		0			0
$757$	−29.2580	−	18.8030i	−1.06340	−	0.683407i	−0.112736	−	0.993625i	$-0.535962\pi$
$757$	−29.2580	−	18.8030i	−1.06340	−	0.683407i	−0.950665	+	0.310218i	$0.899598\pi$
$758$	−5.52787			−0.200781
$759$		0			0
$760$	−9.13684			−0.331428
$761$	−1.31896	−	0.847646i	−0.0478123	−	0.0307271i	0.516516	−	0.856277i	$-0.327229\pi$
$761$	−1.31896	−	0.847646i	−0.0478123	−	0.0307271i	−0.564329	+	0.825550i	$0.690865\pi$
$762$		0			0
$763$	−2.83786	−	6.21405i	−0.102737	−	0.224964i
$764$	21.9003	+	6.43051i	0.792325	+	0.232648i
$765$		0			0
$766$	−22.9988	+	26.5420i	−0.830979	+	0.959000i
$767$	−3.36189	+	23.3824i	−0.121391	+	0.844291i
$768$		0			0
$769$	−14.9435	−	17.2457i	−0.538876	−	0.621896i	0.419379	−	0.907811i	$-0.362248\pi$
$769$	−14.9435	−	17.2457i	−0.538876	−	0.621896i	−0.958255	+	0.285915i	$0.907702\pi$
$770$	0.196750	−	0.126444i	0.00709039	−	0.00455672i
$771$		0			0
$772$	−2.38729	−	2.75508i	−0.0859204	−	0.0991574i
$773$	42.7797	−	12.5613i	1.53868	−	0.451797i	0.600985	−	0.799260i	$-0.294775\pi$
$773$	42.7797	−	12.5613i	1.53868	−	0.451797i	0.937694	+	0.347463i	$0.112957\pi$
$774$		0			0
$775$	4.12836	−	4.76438i	0.148295	−	0.171142i
$776$	−4.76587	+	10.4358i	−0.171085	+	0.374623i
$777$		0			0
$778$	−6.86348	−	15.0289i	−0.246068	−	0.538813i
$779$	1.17159	+	8.14861i	0.0419767	+	0.291954i
$780$		0			0
$781$	−0.873089			−0.0312416
$782$	14.5773	+	1.76211i	0.521282	+	0.0630130i
$783$		0			0
$784$	−4.58698	−	2.94787i	−0.163821	−	0.105281i
$785$	−4.69316	−	32.6417i	−0.167506	−	1.16503i
$786$		0			0
$787$	−36.2415	−	10.6415i	−1.29187	−	0.379327i	−0.437605	−	0.899167i	$-0.644173\pi$
$787$	−36.2415	−	10.6415i	−1.29187	−	0.379327i	−0.854264	+	0.519840i	$0.825991\pi$
$788$	−6.74493	+	14.7693i	−0.240278	+	0.526136i
$789$		0			0
$790$	3.41443	−	23.7479i	0.121480	−	0.844911i
$791$	22.5230	−	6.61334i	0.800824	−	0.235143i
$792$		0			0
$793$	18.7065	−	12.0219i	0.664286	−	0.426911i
$794$	−26.1558	+	16.8093i	−0.928235	+	0.596540i
$795$		0			0
$796$	−5.63367	+	1.65420i	−0.199680	+	0.0586314i
$797$	−1.68840	+	11.7431i	−0.0598061	+	0.415960i	0.937821	+	0.347118i	$0.112840\pi$
$797$	−1.68840	+	11.7431i	−0.0598061	+	0.415960i	−0.997628	+	0.0688425i	$0.978069\pi$
$798$		0			0
$799$	−2.44245	+	5.34823i	−0.0864078	+	0.189207i
$800$	−1.56468	−	0.459431i	−0.0553197	−	0.0162433i
$801$		0			0
$802$	−2.21841	−	15.4293i	−0.0783346	−	0.544829i
$803$	1.03817	+	0.667190i	0.0366362	+	0.0235446i
$804$		0			0
$805$	10.8715	+	1.31416i	0.383170	+	0.0463179i
$806$	14.9744			0.527451
$807$		0			0
$808$	1.18945	+	8.27284i	0.0418449	+	0.291038i
$809$	3.12011	+	6.83209i	0.109697	+	0.240204i	0.956517	−	0.291676i	$-0.0942130\pi$
$809$	3.12011	+	6.83209i	0.109697	+	0.240204i	−0.846820	+	0.531880i	$0.821486\pi$
$810$		0			0
$811$	11.1976	−	24.5193i	0.393201	−	0.860990i	−0.604714	−	0.796443i	$-0.706712\pi$
$811$	11.1976	−	24.5193i	0.393201	−	0.860990i	0.997915	−	0.0645471i	$-0.0205603\pi$
$812$	5.47356	−	6.31683i	0.192084	−	0.221677i
$813$		0			0
$814$	0.251027	−	0.0737081i	0.00879848	−	0.00258347i
$815$	5.11505	+	5.90309i	0.179173	+	0.206776i
$816$		0			0
$817$	15.0668	−	9.68287i	0.527122	−	0.338761i
$818$	22.2865	+	25.7200i	0.779229	+	0.899278i
$819$		0			0
$820$	0.432032	−	3.00485i	0.0150872	−	0.104934i
$821$	25.8018	−	29.7769i	0.900490	−	1.03922i	−0.0985372	−	0.995133i	$-0.531416\pi$
$821$	25.8018	−	29.7769i	0.900490	−	1.03922i	0.999028	−	0.0440880i	$-0.0140382\pi$
$822$		0			0
$823$	−46.8553	−	13.7580i	−1.63327	−	0.479572i	−0.668731	−	0.743504i	$-0.733162\pi$
$823$	−46.8553	−	13.7580i	−1.63327	−	0.479572i	−0.964541	+	0.263932i	$0.914981\pi$
$824$	−5.27649	−	11.5539i	−0.183815	−	0.402500i
$825$		0			0
$826$	6.38210	+	4.10153i	0.222062	+	0.142710i
$827$	−20.7802			−0.722599			−0.361299	−	0.932450i	$-0.617667\pi$
$827$	−20.7802			−0.722599			−0.361299	+	0.932450i	$0.617667\pi$
$828$		0			0
$829$	11.8167			0.410410			0.205205	−	0.978719i	$-0.434214\pi$
$829$	11.8167			0.410410			0.205205	+	0.978719i	$0.434214\pi$
$830$	−8.03646	−	5.16472i	−0.278950	−	0.179270i
$831$		0			0
$832$	−1.60911	−	3.52346i	−0.0557859	−	0.122154i
$833$	−16.0178	−	4.70326i	−0.554985	−	0.162958i
$834$		0			0
$835$	8.88792	−	10.2572i	0.307579	−	0.354965i
$836$	0.0725591	−	0.504660i	0.00250951	−	0.0174540i
$837$		0			0
$838$	9.60252	+	11.0819i	0.331714	+	0.382818i
$839$	−22.7258	+	14.6050i	−0.784581	+	0.504220i	−0.870551	−	0.492078i	$-0.836237\pi$
$839$	−22.7258	+	14.6050i	−0.784581	+	0.504220i	0.0859701	+	0.996298i	$0.472601\pi$
$840$		0			0
$841$	−10.5740	−	12.2030i	−0.364619	−	0.420793i
$842$	−13.3011	+	3.90555i	−0.458386	+	0.134594i
$843$		0			0
$844$	−16.8871	+	19.4888i	−0.581279	+	0.670831i
$845$	1.52809	−	3.34605i	0.0525679	−	0.115108i
$846$		0			0
$847$	−5.67895	−	12.4352i	−0.195131	−	0.427277i
$848$	−0.589595	−	4.10073i	−0.0202468	−	0.140820i
$849$		0			0
$850$	−4.99281			−0.171252
$851$	11.2545	+	4.83674i	0.385798	+	0.165801i
$852$		0			0
$853$	−18.0919	−	11.6270i	−0.619456	−	0.398100i	0.192936	−	0.981211i	$-0.438199\pi$
$853$	−18.0919	−	11.6270i	−0.619456	−	0.398100i	−0.812392	+	0.583111i	$0.801835\pi$
$854$	−1.01629	−	7.06847i	−0.0347768	−	0.241878i
$855$		0			0
$856$	−10.0803	−	2.95986i	−0.344539	−	0.101166i
$857$	15.9916	−	35.0167i	0.546263	−	1.19615i	−0.412243	−	0.911074i	$-0.635255\pi$
$857$	15.9916	−	35.0167i	0.546263	−	1.19615i	0.958505	−	0.285074i	$-0.0920182\pi$
$858$		0			0
$859$	4.18290	−	29.0927i	0.142719	−	0.992631i	−0.785038	−	0.619447i	$-0.787357\pi$
$859$	4.18290	−	29.0927i	0.142719	−	0.992631i	0.927757	−	0.373184i	$-0.121734\pi$
$860$	−6.33689	+	1.86068i	−0.216086	+	0.0634487i
$861$		0			0
$862$	5.92920	−	3.81047i	0.201949	−	0.129785i
$863$	23.5450	−	15.1314i	0.801481	−	0.515080i	−0.0746179	−	0.997212i	$-0.523774\pi$
$863$	23.5450	−	15.1314i	0.801481	−	0.515080i	0.876099	+	0.482132i	$0.160137\pi$
$864$		0			0
$865$	−25.4096	+	7.46094i	−0.863953	+	0.253679i
$866$	−2.71700	+	18.8971i	−0.0923273	+	0.642150i
$867$		0			0
$868$	1.99772	−	4.37441i	0.0678072	−	0.148477i
$869$	1.28456	+	0.377182i	0.0435758	+	0.0127950i
$870$		0			0
$871$	−0.856416	−	5.95650i	−0.0290185	−	0.201828i
$872$	4.61985	+	2.96900i	0.156448	+	0.100543i
$873$		0			0
$874$	17.6851	−	16.0349i	0.598207	−	0.542390i
$875$	−15.1404			−0.511838
$876$		0			0
$877$	0.956541	+	6.65289i	0.0323001	+	0.224652i	0.999577	−	0.0290695i	$-0.00925441\pi$
$877$	0.956541	+	6.65289i	0.0323001	+	0.224652i	−0.967277	+	0.253722i	$0.918345\pi$
$878$	2.85084	+	6.24246i	0.0962111	+	0.210673i
$879$		0			0
$880$	−0.0781022	+	0.171020i	−0.00263283	+	0.00576508i
$881$	1.74069	−	2.00886i	0.0586454	−	0.0676803i	−0.725669	−	0.688044i	$-0.758470\pi$
$881$	1.74069	−	2.00886i	0.0586454	−	0.0676803i	0.784314	+	0.620364i	$0.213015\pi$
$882$		0			0
$883$	44.4323	−	13.0465i	1.49527	−	0.439049i	0.571048	−	0.820917i	$-0.306537\pi$
$883$	44.4323	−	13.0465i	1.49527	−	0.439049i	0.924217	+	0.381867i	$0.124719\pi$
$884$	−7.76630	−	8.96279i	−0.261209	−	0.301451i
$885$		0			0
$886$	17.0555	−	10.9609i	0.572991	−	0.368239i
$887$	−8.40574	−	9.70074i	−0.282237	−	0.325719i	0.596875	−	0.802334i	$-0.296409\pi$
$887$	−8.40574	−	9.70074i	−0.282237	−	0.325719i	−0.879112	+	0.476615i	$0.841863\pi$
$888$		0			0
$889$	0.208616	−	1.45096i	0.00699676	−	0.0486635i
$890$	−9.59194	+	11.0697i	−0.321523	+	0.371057i
$891$		0			0
$892$	7.33900	+	2.15493i	0.245728	+	0.0721522i
$893$	3.97093	+	8.69513i	0.132882	+	0.290971i
$894$		0			0
$895$	−39.9567	−	25.6786i	−1.33560	−	0.858340i
$896$	−1.24396			−0.0415579
$897$		0			0
$898$	−28.2153			−0.941557
$899$	−21.8518	−	14.0433i	−0.728797	−	0.468370i
$900$		0			0
$901$	−5.26924	−	11.5380i	−0.175544	−	0.384387i
$902$	0.162538	+	0.0477253i	0.00541191	+	0.00158908i
$903$		0			0
$904$	−12.3573	+	14.2611i	−0.410999	+	0.474318i
$905$	3.56620	−	24.8034i	0.118544	−	0.824494i
$906$		0			0
$907$	14.4045	+	16.6237i	0.478293	+	0.551979i	0.942700	−	0.333643i	$-0.108278\pi$
$907$	14.4045	+	16.6237i	0.478293	+	0.551979i	−0.464407	+	0.885622i	$0.653732\pi$
$908$	−8.46621	+	5.44091i	−0.280961	+	0.180563i
$909$		0			0
$910$	−5.79199	−	6.68431i	−0.192003	−	0.221583i
$911$	−25.1179	+	7.37527i	−0.832192	+	0.244354i	−0.669958	−	0.742399i	$-0.733688\pi$
$911$	−25.1179	+	7.37527i	−0.832192	+	0.244354i	−0.162234	+	0.986752i	$0.551870\pi$
$912$		0			0
$913$	0.349086	−	0.402867i	0.0115531	−	0.0133329i
$914$	12.3822	−	27.1132i	0.409566	−	0.896824i
$915$		0			0
$916$	6.51328	+	14.2621i	0.215205	+	0.471233i
$917$	3.87042	+	26.9194i	0.127813	+	0.888956i
$918$		0			0
$919$	−56.1530			−1.85232			−0.926158	−	0.377135i	$-0.876909\pi$
$919$	−56.1530			−1.85232			−0.926158	+	0.377135i	$0.876909\pi$
$920$	−7.92320	+	3.83615i	−0.261220	+	0.126474i
$921$		0			0
$922$	−30.5583	−	19.6386i	−1.00638	−	0.646763i
$923$	4.69893	+	32.6818i	0.154667	+	1.07573i
$924$		0			0
$925$	−3.99659	−	1.17350i	−0.131407	−	0.0385846i
$926$	−10.6979	+	23.4251i	−0.351555	+	0.769797i
$927$		0			0
$928$	−0.956234	+	6.65075i	−0.0313899	+	0.218322i
$929$	1.34669	−	0.395425i	0.0441836	−	0.0129735i	−0.259566	−	0.965725i	$-0.583580\pi$
$929$	1.34669	−	0.395425i	0.0441836	−	0.0129735i	0.303750	+	0.952752i	$0.401761\pi$
$930$		0			0
$931$	−22.8326	+	14.6736i	−0.748308	+	0.480908i
$932$	16.7852	−	10.7872i	0.549817	−	0.353346i
$933$		0			0
$934$	6.42570	−	1.88676i	0.210255	−	0.0617366i
$935$	−0.0819206	+	0.569770i	−0.00267909	+	0.0186335i
$936$		0			0
$937$	−3.02034	+	6.61361i	−0.0986701	+	0.216057i	−0.952529	−	0.304446i	$-0.901529\pi$
$937$	−3.02034	+	6.61361i	−0.0986701	+	0.216057i	0.853859	+	0.520504i	$0.174256\pi$
$938$	−1.85430	−	0.544472i	−0.0605450	−	0.0177776i
$939$		0			0
$940$	−0.501649	−	3.48905i	−0.0163620	−	0.113800i
$941$	20.3975	+	13.1087i	0.664939	+	0.427330i	0.829098	−	0.559104i	$-0.188855\pi$
$941$	20.3975	+	13.1087i	0.664939	+	0.427330i	−0.164159	+	0.986434i	$0.552491\pi$
$942$		0			0
$943$	4.43721	+	6.57433i	0.144495	+	0.214090i
$944$	−6.09859			−0.198492
$945$		0			0
$946$	−0.0524482	−	0.364785i	−0.00170524	−	0.0118602i
$947$	−9.93354	−	21.7514i	−0.322797	−	0.706826i	0.676772	−	0.736193i	$-0.263378\pi$
$947$	−9.93354	−	21.7514i	−0.322797	−	0.706826i	−0.999569	+	0.0293667i	$0.990651\pi$
$948$		0			0
$949$	19.3871	−	42.4519i	0.629332	−	1.37805i
$950$	−5.31569	+	6.13464i	−0.172464	+	0.199034i
$951$		0			0
$952$	−3.65436	+	1.07302i	−0.118438	+	0.0347767i
$953$	−11.8897	−	13.7215i	−0.385146	−	0.444482i	0.529761	−	0.848147i	$-0.322282\pi$
$953$	−11.8897	−	13.7215i	−0.385146	−	0.444482i	−0.914907	+	0.403665i	$0.867736\pi$
$954$		0			0
$955$	−35.2454	+	22.6509i	−1.14052	+	0.732965i
$956$	−2.38120	−	2.74805i	−0.0770136	−	0.0888784i
$957$		0			0
$958$	2.12284	−	14.7647i	0.0685859	−	0.477025i
$959$	13.9754	−	16.1285i	0.451289	−	0.520816i
$960$		0			0
$961$	15.4048	+	4.52326i	0.496929	+	0.145911i
$962$	−4.11008	−	8.99982i	−0.132514	−	0.290166i
$963$		0			0
$964$	−3.19705	−	2.05462i	−0.102970	−	0.0661748i
$965$	6.69150			0.215407
$966$		0			0
$967$	40.5149			1.30287			0.651436	−	0.758704i	$-0.274167\pi$
$967$	40.5149			1.30287			0.651436	+	0.758704i	$0.274167\pi$
$968$	9.24496	+	5.94138i	0.297144	+	0.190963i
$969$		0			0
$970$	−8.74803	−	19.1555i	−0.280882	−	0.615046i
$971$	2.72734	+	0.800819i	0.0875245	+	0.0256995i	0.325202	−	0.945645i	$-0.394568\pi$
$971$	2.72734	+	0.800819i	0.0875245	+	0.0256995i	−0.237677	+	0.971344i	$0.576386\pi$
$972$		0			0
$973$	−8.25589	+	9.52781i	−0.264672	+	0.305447i
$974$	2.14592	−	14.9252i	0.0687597	−	0.478234i
$975$		0			0
$976$	3.75933	+	4.33850i	0.120333	+	0.138872i
$977$	−4.53478	+	2.91432i	−0.145080	+	0.0932375i	−0.611167	−	0.791501i	$-0.709300\pi$
$977$	−4.53478	+	2.91432i	−0.145080	+	0.0932375i	0.466087	+	0.884739i	$0.345663\pi$
$978$		0			0
$979$	−0.535245	−	0.617705i	−0.0171065	−	0.0197419i
$980$	9.60306	−	2.81971i	0.306759	−	0.0900724i
$981$		0			0
$982$	4.50159	−	5.19512i	0.143652	−	0.165783i
$983$	−14.8903	+	32.6052i	−0.474927	+	1.03994i	0.508901	+	0.860825i	$0.330052\pi$
$983$	−14.8903	+	32.6052i	−0.474927	+	1.03994i	−0.983827	+	0.179119i	$0.942675\pi$
$984$		0			0
$985$	−12.3807	−	27.1099i	−0.394482	−	0.863794i
$986$	2.92770	+	20.3626i	0.0932368	+	0.648476i
$987$		0			0
$988$	−19.2811			−0.613413
$989$	9.00011	−	14.7226i	0.286187	−	0.468151i
$990$		0			0
$991$	−21.1975	−	13.6228i	−0.673362	−	0.432743i	0.158774	−	0.987315i	$-0.449246\pi$
$991$	−21.1975	−	13.6228i	−0.673362	−	0.432743i	−0.832136	+	0.554572i	$0.812882\pi$
$992$	0.550169	+	3.82651i	0.0174679	+	0.121492i
$993$		0			0
$994$	10.1741	+	2.98737i	0.322701	+	0.0947537i
$995$	4.47713	−	9.80355i	0.141935	−	0.310793i
$996$		0			0
$997$	−0.984656	+	6.84843i	−0.0311844	+	0.216892i	−0.999455	−	0.0330121i	$-0.989490\pi$
$997$	−0.984656	+	6.84843i	−0.0311844	+	0.216892i	0.968271	+	0.249904i	$0.0803991\pi$
$998$	5.44639	−	1.59920i	0.172402	−	0.0506219i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.h.163.1	yes	20
3.2	odd	2		414.2.i.g.163.2	yes	20
23.9	even	11		9522.2.a.cg.1.9		10
23.12	even	11	inner	414.2.i.h.127.1	yes	20
23.14	odd	22		9522.2.a.ch.1.2		10
69.14	even	22		9522.2.a.ci.1.9		10
69.32	odd	22		9522.2.a.cj.1.2		10
69.35	odd	22		414.2.i.g.127.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.i.g.127.2	✓	20	69.35	odd	22
414.2.i.g.163.2	yes	20	3.2	odd	2
414.2.i.h.127.1	yes	20	23.12	even	11	inner
414.2.i.h.163.1	yes	20	1.1	even	1	trivial
9522.2.a.cg.1.9		10	23.9	even	11
9522.2.a.ch.1.2		10	23.14	odd	22
9522.2.a.ci.1.9		10	69.14	even	22
9522.2.a.cj.1.2		10	69.32	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.841254 - 0.540641i) q^{2} +(0.415415 + 0.909632i) q^{4} +(-1.76120 - 0.517136i) q^{5} +(-0.814622 + 0.940124i) q^{7} +(0.142315 - 0.989821i) q^{8} +O(q^{10})\)	\(q+(-0.841254 - 0.540641i) q^{2} +(0.415415 + 0.909632i) q^{4} +(-1.76120 - 0.517136i) q^{5} +(-0.814622 + 0.940124i) q^{7} +(0.142315 - 0.989821i) q^{8} +(1.20203 + 1.38722i) q^{10} +(-0.0861669 + 0.0553761i) q^{11} +(2.53660 + 2.92740i) q^{13} +(1.19357 - 0.350465i) q^{14} +(-0.654861 + 0.755750i) q^{16} +(-1.27187 + 2.78502i) q^{17} +(2.06781 + 4.52787i) q^{19} +(-0.261227 - 1.81687i) q^{20} +0.102427 q^{22} +(3.69420 + 3.05825i) q^{23} +(-1.37186 - 0.881641i) q^{25} +(-0.551257 - 3.83407i) q^{26} +(-1.19357 - 0.350465i) q^{28} +(-2.79123 + 6.11195i) q^{29} +(-0.550169 + 3.82651i) q^{31} +(0.959493 - 0.281733i) q^{32} +(2.57566 - 1.65528i) q^{34} +(1.92089 - 1.23448i) q^{35} +(2.45079 - 0.719617i) q^{37} +(0.708400 - 4.92703i) q^{38} +(-0.762518 + 1.66968i) q^{40} +(1.58687 + 0.465946i) q^{41} +(-0.512056 - 3.56142i) q^{43} +(-0.0861669 - 0.0553761i) q^{44} +(-1.45434 - 4.57000i) q^{46} +1.92036 q^{47} +(0.775980 + 5.39706i) q^{49} +(0.677431 + 1.48337i) q^{50} +(-1.60911 + 3.52346i) q^{52} +(-2.71302 + 3.13099i) q^{53} +(0.180394 - 0.0529686i) q^{55} +(0.814622 + 0.940124i) q^{56} +(5.65250 - 3.63264i) q^{58} +(3.99373 + 4.60900i) q^{59} +(0.816980 - 5.68222i) q^{61} +(2.53160 - 2.92162i) q^{62} +(-0.959493 - 0.281733i) q^{64} +(-2.95361 - 6.46751i) q^{65} +(-1.30695 - 0.839923i) q^{67} -3.06169 q^{68} -2.28336 q^{70} +(7.17087 + 4.60844i) q^{71} +(-5.00506 - 10.9596i) q^{73} +(-2.45079 - 0.719617i) q^{74} +(-3.25970 + 3.76189i) q^{76} +(0.0181331 - 0.126118i) q^{77} +(-8.55951 - 9.87820i) q^{79} +(1.54417 - 0.992377i) q^{80} +(-1.08305 - 1.24990i) q^{82} +(-4.99358 + 1.46625i) q^{83} +(3.68026 - 4.24725i) q^{85} +(-1.49468 + 3.27290i) q^{86} +(0.0425496 + 0.0931707i) q^{88} +(1.13564 + 7.89854i) q^{89} -4.81849 q^{91} +(-1.24726 + 4.63080i) q^{92} +(-1.61551 - 1.03822i) q^{94} +(-1.30031 - 9.04384i) q^{95} +(-11.0078 - 3.23219i) q^{97} +(2.26507 - 4.95982i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8}+O(q^{10}) \) 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8	\( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8} - 2 q^{10} - 2 q^{11} - 18 q^{14} - 2 q^{16} + 18 q^{17} + 16 q^{19} + 2 q^{20} + 24 q^{22} - 2 q^{23} + 38 q^{25} + 18 q^{28} - 30 q^{29} + 14 q^{31} + 2 q^{32} + 4 q^{34} + 48 q^{35} - 20 q^{37} - 16 q^{38} - 2 q^{40} - 12 q^{41} - 28 q^{43} - 2 q^{44} + 2 q^{46} + 32 q^{47} + 6 q^{49} + 6 q^{50} - 46 q^{53} - 28 q^{55} + 4 q^{56} - 14 q^{58} - 50 q^{61} + 8 q^{62} - 2 q^{64} + 16 q^{65} - 8 q^{67} - 48 q^{68} - 48 q^{70} + 12 q^{71} - 18 q^{73} + 20 q^{74} - 6 q^{76} - 4 q^{77} - 18 q^{79} + 2 q^{80} - 10 q^{82} - 44 q^{83} + 32 q^{85} + 28 q^{86} + 2 q^{88} + 44 q^{91} - 2 q^{92} + 12 q^{94} + 64 q^{95} + 14 q^{97} - 28 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8 - 2 * q^10 - 2 * q^11 - 18 * q^14 - 2 * q^16 + 18 * q^17 + 16 * q^19 + 2 * q^20 + 24 * q^22 - 2 * q^23 + 38 * q^25 + 18 * q^28 - 30 * q^29 + 14 * q^31 + 2 * q^32 + 4 * q^34 + 48 * q^35 - 20 * q^37 - 16 * q^38 - 2 * q^40 - 12 * q^41 - 28 * q^43 - 2 * q^44 + 2 * q^46 + 32 * q^47 + 6 * q^49 + 6 * q^50 - 46 * q^53 - 28 * q^55 + 4 * q^56 - 14 * q^58 - 50 * q^61 + 8 * q^62 - 2 * q^64 + 16 * q^65 - 8 * q^67 - 48 * q^68 - 48 * q^70 + 12 * q^71 - 18 * q^73 + 20 * q^74 - 6 * q^76 - 4 * q^77 - 18 * q^79 + 2 * q^80 - 10 * q^82 - 44 * q^83 + 32 * q^85 + 28 * q^86 + 2 * q^88 + 44 * q^91 - 2 * q^92 + 12 * q^94 + 64 * q^95 + 14 * q^97 - 28 * q^98

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