LMFDB - Embedded newform 209.2.k.b.18.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,2,Mod(18,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7, 5]))

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

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

chi := DirichletCharacter("209.18");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.k (of order $10$, degree $4$, 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:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.484000000.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 16x^{4} + 66x^{2} + 121 $ x^8 + x^6 + 16x^4 + 66x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			18.2
Root			$-0.476925 - 1.46782i$ of defining polynomial
Character	$\chi$	$=$	209.18
Dual form			209.2.k.b.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.02029 + 1.46782i) q^{2} +(1.30902 + 4.02874i) q^{4} +(0.500000 - 0.363271i) q^{5} +(-1.80902 + 0.587785i) q^{7} +(-1.72553 + 5.31064i) q^{8} +(-2.42705 - 1.76336i) q^{9} +1.54336 q^{10} +(1.69098 - 2.85317i) q^{11} +(4.04057 + 2.93565i) q^{13} +(-4.51750 - 1.46782i) q^{14} +(-4.42705 + 3.21644i) q^{16} +(-2.07295 - 2.85317i) q^{17} +(-2.31504 - 7.12497i) q^{18} +(-1.97320 - 3.88671i) q^{19} +(2.11803 + 1.53884i) q^{20} +(7.60422 - 3.28216i) q^{22} -0.381966 q^{23} +(-1.42705 + 4.39201i) q^{25} +(3.85410 + 11.8617i) q^{26} +(-4.73607 - 6.51864i) q^{28} +(-0.589512 - 1.81433i) q^{29} +(-3.45106 + 4.74998i) q^{31} -2.49721 q^{32} -8.80695i q^{34} +(-0.690983 + 0.951057i) q^{35} +(3.92705 - 12.0862i) q^{36} +(3.45106 - 1.12132i) q^{37} +(1.71857 - 10.7486i) q^{38} +(1.06644 + 3.28216i) q^{40} +(-2.13287 + 6.56431i) q^{41} -9.68208i q^{43} +(13.7082 + 3.07768i) q^{44} -1.85410 q^{45} +(-0.771681 - 0.560659i) q^{46} +(0.881966 - 2.71441i) q^{47} +(-2.73607 + 1.98787i) q^{49} +(-9.32975 + 6.77846i) q^{50} +(-6.53779 + 20.1212i) q^{52} +(1.31819 - 1.81433i) q^{53} +(-0.190983 - 2.04087i) q^{55} -10.6213i q^{56} +(1.47214 - 4.53077i) q^{58} +(-9.03500 + 2.93565i) q^{59} +(6.54508 + 9.00854i) q^{61} +(-13.9443 + 4.53077i) q^{62} +(5.42705 + 1.76336i) q^{63} +(3.80902 + 2.76741i) q^{64} +3.08672 q^{65} -2.24264i q^{67} +(8.78115 - 12.0862i) q^{68} +(-2.79197 + 0.907165i) q^{70} +(7.71681 + 10.6213i) q^{71} +(13.5525 - 9.84647i) q^{72} +(-4.47214 + 1.45309i) q^{73} +(8.61803 + 2.80017i) q^{74} +(13.0756 - 13.0373i) q^{76} +(-1.38197 + 6.15537i) q^{77} +(-9.03500 - 6.56431i) q^{79} +(-1.04508 + 3.21644i) q^{80} +(2.78115 + 8.55951i) q^{81} +(-13.9443 + 10.1311i) q^{82} +(0.590170 + 0.812299i) q^{83} +(-2.07295 - 0.673542i) q^{85} +(14.2116 - 19.5606i) q^{86} +(12.2343 + 13.9034i) q^{88} -5.87130i q^{89} +(-3.74582 - 2.72150i) q^{90} +(-9.03500 - 2.93565i) q^{91} +(-0.500000 - 1.53884i) q^{92} +(5.76611 - 4.18932i) q^{94} +(-2.39853 - 1.22655i) q^{95} +(-5.58394 + 7.68563i) q^{97} -8.44549 q^{98} +(-9.13525 + 3.94298i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{4} + 4 q^{5} - 10 q^{7} - 6 q^{9} + 18 q^{11} - 22 q^{16} - 30 q^{17} - 10 q^{19} + 8 q^{20} - 12 q^{23} + 2 q^{25} + 4 q^{26} - 20 q^{28} - 10 q^{35} + 18 q^{36} + 32 q^{38} + 56 q^{44} + 12 q^{45}+ \cdots - 6 q^{99}+O(q^{100}) $ 8 * q + 6 * q^4 + 4 * q^5 - 10 * q^7 - 6 * q^9 + 18 * q^11 - 22 * q^16 - 30 * q^17 - 10 * q^19 + 8 * q^20 - 12 * q^23 + 2 * q^25 + 4 * q^26 - 20 * q^28 - 10 * q^35 + 18 * q^36 + 32 * q^38 + 56 * q^44 + 12 * q^45 + 16 * q^47 - 4 * q^49 - 6 * q^55 - 24 * q^58 + 30 * q^61 - 40 * q^62 + 30 * q^63 + 26 * q^64 + 30 * q^68 + 60 * q^74 - 20 * q^77 + 14 * q^80 - 18 * q^81 - 40 * q^82 - 40 * q^83 - 30 * q^85 - 4 * q^92 - 10 * q^95 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	2.02029	+	1.46782i	1.42856	+	1.03791i	0.990283	+	0.139068i	$0.0444107\pi$
$2$	2.02029	+	1.46782i	1.42856	+	1.03791i	0.438276	+	0.898841i	$0.355589\pi$
$3$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$3$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$4$	1.30902	+	4.02874i	0.654508	+	2.01437i
$5$	0.500000	−	0.363271i	0.223607	−	0.162460i	−0.470342	−	0.882484i	$-0.655869\pi$
$5$	0.500000	−	0.363271i	0.223607	−	0.162460i	0.693949	+	0.720024i	$0.255869\pi$
$6$		0			0
$7$	−1.80902	+	0.587785i	−0.683744	+	0.222162i	−0.630234	−	0.776405i	$-0.717041\pi$
$7$	−1.80902	+	0.587785i	−0.683744	+	0.222162i	−0.0535103	+	0.998567i	$0.517041\pi$
$8$	−1.72553	+	5.31064i	−0.610067	+	1.87759i
$9$	−2.42705	−	1.76336i	−0.809017	−	0.587785i
$10$	1.54336			0.488054
$11$	1.69098	−	2.85317i	0.509851	−	0.860263i
$11$	1.69098	−	2.85317i	0.509851	−	0.860263i
$12$		0			0
$13$	4.04057	+	2.93565i	1.12065	+	0.814202i	0.984308	−	0.176459i	$-0.0564643\pi$
$13$	4.04057	+	2.93565i	1.12065	+	0.814202i	0.136346	+	0.990661i	$0.456464\pi$
$14$	−4.51750	−	1.46782i	−1.20735	−	0.392293i
$15$		0			0
$16$	−4.42705	+	3.21644i	−1.10676	+	0.804110i
$17$	−2.07295	−	2.85317i	−0.502764	−	0.691995i	0.479914	−	0.877315i	$-0.340668\pi$
$17$	−2.07295	−	2.85317i	−0.502764	−	0.691995i	−0.982678	+	0.185320i	$0.940668\pi$
$18$	−2.31504	−	7.12497i	−0.545661	−	1.67937i
$19$	−1.97320	−	3.88671i	−0.452683	−	0.891671i
$19$	−1.97320	−	3.88671i	−0.452683	−	0.891671i
$20$	2.11803	+	1.53884i	0.473607	+	0.344095i
$21$		0			0
$22$	7.60422	−	3.28216i	1.62123	−	0.699758i
$23$	−0.381966			−0.0796454			−0.0398227	−	0.999207i	$-0.512679\pi$
$23$	−0.381966			−0.0796454			−0.0398227	+	0.999207i	$0.512679\pi$
$24$		0			0
$25$	−1.42705	+	4.39201i	−0.285410	+	0.878402i
$26$	3.85410	+	11.8617i	0.755852	+	2.32627i
$27$		0			0
$28$	−4.73607	−	6.51864i	−0.895033	−	1.23191i
$29$	−0.589512	−	1.81433i	−0.109470	−	0.336913i	0.881284	−	0.472587i	$-0.156680\pi$
$29$	−0.589512	−	1.81433i	−0.109470	−	0.336913i	−0.990753	+	0.135675i	$0.956680\pi$
$30$		0			0
$31$	−3.45106	+	4.74998i	−0.619829	+	0.853122i	−0.997340	−	0.0728834i	$-0.976780\pi$
$31$	−3.45106	+	4.74998i	−0.619829	+	0.853122i	0.377511	+	0.926005i	$0.376780\pi$
$32$	−2.49721			−0.441449
$33$		0			0
$34$		−	8.80695i		−	1.51038i
$35$	−0.690983	+	0.951057i	−0.116797	+	0.160758i
$36$	3.92705	−	12.0862i	0.654508	−	2.01437i
$37$	3.45106	−	1.12132i	0.567351	−	0.184344i	−0.0112751	−	0.999936i	$-0.503589\pi$
$37$	3.45106	−	1.12132i	0.567351	−	0.184344i	0.578626	+	0.815593i	$0.303589\pi$
$38$	1.71857	−	10.7486i	0.278789	−	1.74365i
$39$		0			0
$40$	1.06644	+	3.28216i	0.168618	+	0.518954i
$41$	−2.13287	+	6.56431i	−0.333099	+	1.02517i	0.634552	+	0.772880i	$0.281185\pi$
$41$	−2.13287	+	6.56431i	−0.333099	+	1.02517i	−0.967651	+	0.252293i	$0.918815\pi$
$42$		0			0
$43$		−	9.68208i		−	1.47650i	−0.674525	−	0.738252i	$-0.735652\pi$
$43$		−	9.68208i		−	1.47650i	0.674525	−	0.738252i	$-0.264348\pi$
$44$	13.7082	+	3.07768i	2.06659	+	0.463978i
$45$	−1.85410			−0.276393
$46$	−0.771681	−	0.560659i	−0.113778	−	0.0826647i
$47$	0.881966	−	2.71441i	0.128648	−	0.395938i	−0.865900	−	0.500217i	$-0.833254\pi$
$47$	0.881966	−	2.71441i	0.128648	−	0.395938i	0.994548	+	0.104279i	$0.0332536\pi$
$48$		0			0
$49$	−2.73607	+	1.98787i	−0.390867	+	0.283981i
$50$	−9.32975	+	6.77846i	−1.31943	+	0.958619i
$51$		0			0
$52$	−6.53779	+	20.1212i	−0.906628	+	2.79031i
$53$	1.31819	−	1.81433i	0.181067	−	0.249217i	−0.708829	−	0.705380i	$-0.750776\pi$
$53$	1.31819	−	1.81433i	0.181067	−	0.249217i	0.889897	+	0.456162i	$0.150776\pi$
$54$		0			0
$55$	−0.190983	−	2.04087i	−0.0257521	−	0.275191i
$56$		−	10.6213i		−	1.41933i
$57$		0			0
$58$	1.47214	−	4.53077i	0.193301	−	0.594919i
$59$	−9.03500	+	2.93565i	−1.17626	+	0.382189i	−0.830975	−	0.556310i	$-0.812217\pi$
$59$	−9.03500	+	2.93565i	−1.17626	+	0.382189i	−0.345282	+	0.938499i	$0.612217\pi$
$60$		0			0
$61$	6.54508	+	9.00854i	0.838012	+	1.15342i	0.986378	+	0.164492i	$0.0525986\pi$
$61$	6.54508	+	9.00854i	0.838012	+	1.15342i	−0.148366	+	0.988933i	$0.547401\pi$
$62$	−13.9443	+	4.53077i	−1.77092	+	0.575408i
$63$	5.42705	+	1.76336i	0.683744	+	0.222162i
$64$	3.80902	+	2.76741i	0.476127	+	0.345927i
$65$	3.08672			0.382861
$66$		0			0
$67$		−	2.24264i		−	0.273982i	−0.990572	−	0.136991i	$-0.956257\pi$
$67$		−	2.24264i		−	0.273982i	0.990572	−	0.136991i	$-0.0437431\pi$
$68$	8.78115	−	12.0862i	1.06487	−	1.46567i
$69$		0			0
$70$	−2.79197	+	0.907165i	−0.333704	+	0.108427i
$71$	7.71681	+	10.6213i	0.915817	+	1.26051i	0.965141	+	0.261731i	$0.0842933\pi$
$71$	7.71681	+	10.6213i	0.915817	+	1.26051i	−0.0493241	+	0.998783i	$0.515707\pi$
$72$	13.5525	−	9.84647i	1.59718	−	1.16042i
$73$	−4.47214	+	1.45309i	−0.523424	+	0.170071i	−0.558799	−	0.829303i	$-0.688738\pi$
$73$	−4.47214	+	1.45309i	−0.523424	+	0.170071i	0.0353747	+	0.999374i	$0.488738\pi$
$74$	8.61803	+	2.80017i	1.00183	+	0.325513i
$75$		0			0
$76$	13.0756	−	13.0373i	1.49987	−	1.49548i
$77$	−1.38197	+	6.15537i	−0.157490	+	0.701469i
$78$		0			0
$79$	−9.03500	−	6.56431i	−1.01652	−	0.738543i	−0.0509508	−	0.998701i	$-0.516225\pi$
$79$	−9.03500	−	6.56431i	−1.01652	−	0.738543i	−0.965566	+	0.260159i	$0.916225\pi$
$80$	−1.04508	+	3.21644i	−0.116844	+	0.359609i
$81$	2.78115	+	8.55951i	0.309017	+	0.951057i
$82$	−13.9443	+	10.1311i	−1.53989	+	1.11879i
$83$	0.590170	+	0.812299i	0.0647796	+	0.0891614i	0.840178	−	0.542311i	$-0.182451\pi$
$83$	0.590170	+	0.812299i	0.0647796	+	0.0891614i	−0.775398	+	0.631473i	$0.782451\pi$
$84$		0			0
$85$	−2.07295	−	0.673542i	−0.224843	−	0.0730559i
$86$	14.2116	−	19.5606i	1.53248	−	2.10927i
$87$		0			0
$88$	12.2343	+	13.9034i	1.30418	+	1.48211i
$89$		−	5.87130i		−	0.622356i	−0.950352	−	0.311178i	$-0.899276\pi$
$89$		−	5.87130i		−	0.622356i	0.950352	−	0.311178i	$-0.100724\pi$
$90$	−3.74582	−	2.72150i	−0.394844	−	0.286871i
$91$	−9.03500	−	2.93565i	−0.947125	−	0.307740i
$92$	−0.500000	−	1.53884i	−0.0521286	−	0.160435i
$93$		0			0
$94$	5.76611	−	4.18932i	0.594728	−	0.432095i
$95$	−2.39853	−	1.22655i	−0.246084	−	0.125841i
$96$		0			0
$97$	−5.58394	+	7.68563i	−0.566963	+	0.780357i	−0.992191	−	0.124729i	$-0.960194\pi$
$97$	−5.58394	+	7.68563i	−0.566963	+	0.780357i	0.425228	+	0.905086i	$0.360194\pi$
$98$	−8.44549			−0.853123
$99$	−9.13525	+	3.94298i	−0.918128	+	0.396285i
$100$	−19.5623			−1.95623
$101$	2.82624	−	3.88998i	0.281221	−	0.387068i	−0.644917	−	0.764253i	$-0.723108\pi$
$101$	2.82624	−	3.88998i	0.281221	−	0.387068i	0.926138	+	0.377185i	$0.123108\pi$
$102$		0			0
$103$	−12.4861	+	4.05697i	−1.23029	+	0.399745i	−0.850819	−	0.525459i	$-0.823893\pi$
$103$	−12.4861	+	4.05697i	−1.23029	+	0.399745i	−0.379469	+	0.925204i	$0.623893\pi$
$104$	−22.5623	+	16.3925i	−2.21242	+	1.60741i
$105$		0			0
$106$	5.32624	−	1.73060i	0.517330	−	0.168091i
$107$	−0.953850	+	2.93565i	−0.0922122	+	0.283800i	−0.986517	−	0.163658i	$-0.947671\pi$
$107$	−0.953850	+	2.93565i	−0.0922122	+	0.283800i	0.894305	+	0.447458i	$0.147671\pi$
$108$		0			0
$109$	−0.728677			−0.0697946			−0.0348973	−	0.999391i	$-0.511110\pi$
$109$	−0.728677			−0.0697946			−0.0348973	+	0.999391i	$0.511110\pi$
$110$	2.60980	−	4.40347i	0.248835	−	0.419855i
$111$		0			0
$112$	6.11803	−	8.42075i	0.578100	−	0.795686i
$113$	18.0700	+	5.87130i	1.69988	+	0.552325i	0.988598	−	0.150579i	$-0.0481139\pi$
$113$	18.0700	+	5.87130i	1.69988	+	0.552325i	0.711284	+	0.702904i	$0.248114\pi$
$114$		0			0
$115$	−0.190983	+	0.138757i	−0.0178093	+	0.0129392i
$116$	6.53779	−	4.74998i	0.607018	−	0.441025i
$117$	−4.63009	−	14.2499i	−0.428052	−	1.31741i
$118$	−22.5623	−	7.33094i	−2.07703	−	0.674868i
$119$	5.42705	+	3.94298i	0.497497	+	0.361453i
$120$		0			0
$121$	−5.28115	−	9.64932i	−0.480105	−	0.877211i
$122$			27.8069i			2.51752i
$123$		0			0
$124$	−23.6539	−	7.68563i	−2.12419	−	0.690190i
$125$	1.83688	+	5.65334i	0.164296	+	0.505650i
$126$	8.37590	+	11.5284i	0.746185	+	1.02704i
$127$	−2.49721	+	1.81433i	−0.221592	+	0.160996i	−0.693043	−	0.720896i	$-0.743730\pi$
$127$	−2.49721	+	1.81433i	−0.221592	+	0.160996i	0.471451	+	0.881892i	$0.343730\pi$
$128$	5.17659	+	15.9319i	0.457551	+	1.40820i
$129$		0			0
$130$	6.23607	+	4.53077i	0.546939	+	0.397375i
$131$		−	8.61251i		−	0.752478i	−0.926523	−	0.376239i	$-0.877217\pi$
$131$		−	8.61251i		−	0.752478i	0.926523	−	0.376239i	$-0.122783\pi$
$132$		0			0
$133$	5.85410	+	5.87130i	0.507615	+	0.509106i
$134$	3.29180	−	4.53077i	0.284368	−	0.391399i
$135$		0			0
$136$	18.7291	−	6.08545i	1.60601	−	0.521823i
$137$	14.4443	−	10.4944i	1.23406	−	0.896595i	0.236870	−	0.971541i	$-0.423879\pi$
$137$	14.4443	−	10.4944i	1.23406	−	0.896595i	0.997188	+	0.0749462i	$0.0238785\pi$
$138$		0			0
$139$	2.50000	−	0.812299i	0.212047	−	0.0688983i	−0.201067	−	0.979577i	$-0.564441\pi$
$139$	2.50000	−	0.812299i	0.212047	−	0.0688983i	0.413114	+	0.910679i	$0.364441\pi$
$140$	−4.73607	−	1.53884i	−0.400271	−	0.130056i
$141$		0			0
$142$			32.7849i			2.75125i
$143$	15.2084	−	6.56431i	1.27179	−	0.548935i
$144$	16.4164			1.36803
$145$	−0.953850	−	0.693013i	−0.0792129	−	0.0575516i
$146$	−11.1679	−	3.62866i	−0.924260	−	0.300310i
$147$		0			0
$148$	9.03500	+	12.4356i	0.742672	+	1.02220i
$149$	5.52786	+	7.60845i	0.452860	+	0.623309i	0.973009	−	0.230767i	$-0.0741235\pi$
$149$	5.52786	+	7.60845i	0.452860	+	0.623309i	−0.520149	+	0.854076i	$0.674124\pi$
$150$		0			0
$151$	6.53779	−	20.1212i	0.532037	−	1.63744i	−0.217927	−	0.975965i	$-0.569930\pi$
$151$	6.53779	−	20.1212i	0.532037	−	1.63744i	0.749965	−	0.661478i	$-0.230070\pi$
$152$	24.0457	−	3.77233i	1.95036	−	0.305976i
$153$			10.5801i			0.855353i
$154$	−11.8270	+	10.4071i	−0.953044	+	0.838630i
$155$			3.62866i			0.291461i
$156$		0			0
$157$	−1.04508	+	3.21644i	−0.0834069	+	0.256700i	−0.984059	−	0.177840i	$-0.943089\pi$
$157$	−1.04508	+	3.21644i	−0.0834069	+	0.256700i	0.900653	+	0.434540i	$0.143089\pi$
$158$	−8.61803	−	26.5236i	−0.685614	−	2.11010i
$159$		0			0
$160$	−1.24861	+	0.907165i	−0.0987110	+	0.0717177i
$161$	0.690983	−	0.224514i	0.0544571	−	0.0176942i
$162$	−6.94513	+	21.3749i	−0.545661	+	1.67937i
$163$	5.97214	+	4.33901i	0.467774	+	0.339858i	0.796573	−	0.604542i	$-0.206644\pi$
$163$	5.97214	+	4.33901i	0.467774	+	0.339858i	−0.328799	+	0.944400i	$0.606644\pi$
$164$	−29.2379			−2.28309
$165$		0			0
$166$			2.50734i			0.194608i
$167$	−12.1217	−	8.80695i	−0.938007	−	0.681502i	0.00993310	−	0.999951i	$-0.496838\pi$
$167$	−12.1217	−	8.80695i	−0.938007	−	0.681502i	−0.947940	+	0.318449i	$0.896838\pi$
$168$		0			0
$169$	3.69098	+	11.3597i	0.283922	+	0.873821i
$170$	−3.19931	−	4.40347i	−0.245376	−	0.337731i
$171$	−2.06459	+	12.9127i	−0.157883	+	0.987458i
$172$	39.0066	−	12.6740i	2.97422	−	0.966384i
$173$	6.17345	−	18.9999i	0.469359	−	1.44454i	−0.384059	−	0.923309i	$-0.625474\pi$
$173$	6.17345	−	18.9999i	0.469359	−	1.44454i	0.853417	−	0.521228i	$-0.174526\pi$
$174$		0			0
$175$		−	8.78402i		−	0.664010i
$176$	1.69098	+	18.0701i	0.127463	+	1.36208i
$177$		0			0
$178$	8.61803	−	11.8617i	0.645949	−	0.889072i
$179$	22.3357	+	7.25732i	1.66945	+	0.542438i	0.982820	−	0.184567i	$-0.0590884\pi$
$179$	22.3357	+	7.25732i	1.66945	+	0.542438i	0.686632	+	0.727005i	$0.259088\pi$
$180$	−2.42705	−	7.46969i	−0.180902	−	0.556758i
$181$	11.1679	+	15.3713i	0.830101	+	1.14254i	0.987904	+	0.155066i	$0.0495590\pi$
$181$	11.1679	+	15.3713i	0.830101	+	1.14254i	−0.157803	+	0.987471i	$0.550441\pi$
$182$	−13.9443	−	19.1926i	−1.03362	−	1.42265i
$183$		0			0
$184$	0.659094	−	2.02848i	0.0485891	−	0.149542i
$185$	1.31819	−	1.81433i	0.0969151	−	0.133392i
$186$		0			0
$187$	−11.6459	+	1.08981i	−0.851632	+	0.0796951i
$188$	12.0902			0.881766
$189$		0			0
$190$	−3.04536	−	5.99859i	−0.220934	−	0.435184i
$191$	−6.28115	−	19.3314i	−0.454488	−	1.39877i	−0.871735	−	0.489978i	$-0.837005\pi$
$191$	−6.28115	−	19.3314i	−0.454488	−	1.39877i	0.417247	−	0.908793i	$-0.362995\pi$
$192$		0			0
$193$	−1.54336	+	1.12132i	−0.111094	+	0.0807142i	−0.641945	−	0.766751i	$-0.721872\pi$
$193$	−1.54336	+	1.12132i	−0.111094	+	0.0807142i	0.530851	+	0.847465i	$0.321872\pi$
$194$	−22.5623	+	7.33094i	−1.61988	+	0.526331i
$195$		0			0
$196$	−11.5902	−	8.42075i	−0.827869	−	0.601482i
$197$		−	17.0130i		−	1.21213i	−0.795416	−	0.606064i	$-0.792748\pi$
$197$		−	17.0130i		−	1.21213i	0.795416	−	0.606064i	$-0.207252\pi$
$198$	−24.2434	−	5.44299i	−1.72291	−	0.386817i
$199$	5.85410			0.414986			0.207493	−	0.978236i	$-0.433470\pi$
$199$	5.85410			0.414986			0.207493	+	0.978236i	$0.433470\pi$
$200$	−20.8620	−	15.1571i	−1.47516	−	1.07177i
$201$		0			0
$202$	11.4196	−	3.71046i	0.803482	−	0.261067i
$203$	2.13287	+	2.93565i	0.149698	+	0.206042i
$204$		0			0
$205$	1.31819	+	4.05697i	0.0920663	+	0.283351i
$206$	−31.1803	−	10.1311i	−2.17244	−	0.705868i
$207$	0.927051	+	0.673542i	0.0644345	+	0.0468144i
$208$	−27.3302			−1.89501
$209$	−14.4261	−	0.942476i	−0.997873	−	0.0651924i
$210$		0			0
$211$	11.5322	+	8.37864i	0.793910	+	0.576809i	0.909121	−	0.416532i	$-0.136754\pi$
$211$	11.5322	+	8.37864i	0.793910	+	0.576809i	−0.115211	+	0.993341i	$0.536754\pi$
$212$	9.03500	+	2.93565i	0.620526	+	0.201621i
$213$		0			0
$214$	−6.23607	+	4.53077i	−0.426289	+	0.309717i
$215$	−3.51722	−	4.84104i	−0.239872	−	0.330156i
$216$		0			0
$217$	3.45106	−	10.6213i	0.234273	−	0.721019i
$218$	−1.47214	−	1.06957i	−0.0997056	−	0.0724404i
$219$		0			0
$220$	7.97214	−	3.44095i	0.537481	−	0.231989i
$221$		−	17.6139i		−	1.18484i
$222$		0			0
$223$	−20.2029	−	6.56431i	−1.35288	−	0.439579i	−0.459223	−	0.888321i	$-0.651872\pi$
$223$	−20.2029	−	6.56431i	−1.35288	−	0.439579i	−0.893661	+	0.448742i	$0.851872\pi$
$224$	4.51750	−	1.46782i	0.301838	−	0.0980731i
$225$	11.2082	−	8.14324i	0.747214	−	0.542882i
$226$	27.8885	+	38.3853i	1.85512	+	2.55335i
$227$	−0.139165	−	0.428305i	−0.00923670	−	0.0284276i	0.946332	−	0.323196i	$-0.104757\pi$
$227$	−0.139165	−	0.428305i	−0.00923670	−	0.0284276i	−0.955569	+	0.294769i	$0.904757\pi$
$228$		0			0
$229$	−17.7812	−	12.9188i	−1.17501	−	0.853696i	−0.183411	−	0.983036i	$-0.558714\pi$
$229$	−17.7812	−	12.9188i	−1.17501	−	0.853696i	−0.991600	+	0.129340i	$0.958714\pi$
$230$	−0.589512			−0.0388713
$231$		0			0
$232$	10.6525			0.699369
$233$	−11.1180	+	15.3027i	−0.728367	+	1.00251i	0.270838	+	0.962625i	$0.412699\pi$
$233$	−11.1180	+	15.3027i	−0.728367	+	1.00251i	−0.999204	+	0.0398856i	$0.987301\pi$
$234$	11.5623	−	35.5851i	0.755852	−	2.32627i
$235$	−0.545085	−	1.67760i	−0.0355574	−	0.109434i
$236$	−23.6539	−	32.5568i	−1.53974	−	2.11927i
$237$		0			0
$238$	5.17659	+	15.9319i	0.335549	+	1.03271i
$239$	6.44427	+	2.09387i	0.416845	+	0.135441i	0.509928	−	0.860217i	$-0.329672\pi$
$239$	6.44427	+	2.09387i	0.416845	+	0.135441i	−0.0930826	+	0.995658i	$0.529672\pi$
$240$		0			0
$241$	19.2490			1.23994			0.619969	−	0.784626i	$-0.287145\pi$
$241$	19.2490			1.23994			0.619969	+	0.784626i	$0.287145\pi$
$242$	3.49407	−	27.2462i	0.224607	−	1.75145i
$243$		0			0
$244$	−27.7254	+	38.1608i	−1.77494	+	2.44299i
$245$	−0.645898	+	1.98787i	−0.0412649	+	0.127000i
$246$		0			0
$247$	3.43714	−	21.4971i	0.218700	−	1.36783i
$248$	−19.2705	−	26.5236i	−1.22368	−	1.68425i
$249$		0			0
$250$	−4.58708	+	14.1176i	−0.290113	+	0.892874i
$251$	0.927051	+	0.673542i	0.0585149	+	0.0425136i	0.616658	−	0.787231i	$-0.288486\pi$
$251$	0.927051	+	0.673542i	0.0585149	+	0.0425136i	−0.558143	+	0.829745i	$0.688486\pi$
$252$			24.1724i			1.52272i
$253$	−0.645898	+	1.08981i	−0.0406073	+	0.0685160i
$254$	−7.70820			−0.483656
$255$		0			0
$256$	−10.0172	+	30.8298i	−0.626076	+	1.92686i
$257$	29.2379	−	9.49996i	1.82381	−	0.592591i	0.824152	−	0.566369i	$-0.191652\pi$
$257$	29.2379	−	9.49996i	1.82381	−	0.592591i	0.999656	−	0.0262224i	$-0.00834781\pi$
$258$		0			0
$259$	−5.58394	+	4.05697i	−0.346969	+	0.252088i
$260$	4.04057	+	12.4356i	0.250586	+	0.771224i
$261$	−1.76854	+	5.44299i	−0.109470	+	0.336913i
$262$	12.6417	−	17.3997i	0.781004	−	1.07496i
$263$		−	26.0746i		−	1.60783i	−0.594747	−	0.803913i	$-0.702748\pi$
$263$		−	26.0746i		−	1.60783i	0.594747	−	0.803913i	$-0.297252\pi$
$264$		0			0
$265$		−	1.38603i		−	0.0851429i
$266$	3.20893	+	20.4545i	0.196752	+	1.25415i
$267$		0			0
$268$	9.03500	−	2.93565i	0.551900	−	0.179323i
$269$	13.3007	+	18.3069i	0.810961	+	1.11619i	0.991174	+	0.132564i	$0.0423211\pi$
$269$	13.3007	+	18.3069i	0.810961	+	1.11619i	−0.180214	+	0.983627i	$0.557679\pi$
$270$		0			0
$271$	19.7361	−	6.41264i	1.19888	−	0.389540i	0.359532	−	0.933133i	$-0.382936\pi$
$271$	19.7361	−	6.41264i	1.19888	−	0.389540i	0.839349	+	0.543593i	$0.182936\pi$
$272$	18.3541	+	5.96361i	1.11288	+	0.361597i
$273$		0			0
$274$	44.5855			2.69351
$275$	10.1180	+	11.4984i	0.610140	+	0.693382i
$276$		0			0
$277$	−6.18034	+	8.50651i	−0.371341	+	0.511107i	−0.953265	−	0.302137i	$-0.902300\pi$
$277$	−6.18034	+	8.50651i	−0.371341	+	0.511107i	0.581924	+	0.813243i	$0.302300\pi$
$278$	6.24303	+	2.02848i	0.374432	+	0.121660i
$279$	16.7518	−	5.44299i	1.00290	−	0.325863i
$280$	−3.85840	−	5.31064i	−0.230584	−	0.317371i
$281$	−20.5672	+	14.9430i	−1.22694	+	0.891422i	−0.996657	−	0.0817027i	$-0.973964\pi$
$281$	−20.5672	+	14.9430i	−1.22694	+	0.891422i	−0.230280	+	0.973124i	$0.573964\pi$
$282$		0			0
$283$	−22.4615	−	7.29818i	−1.33520	−	0.433832i	−0.447510	−	0.894279i	$-0.647689\pi$
$283$	−22.4615	−	7.29818i	−1.33520	−	0.433832i	−0.887687	+	0.460447i	$0.847689\pi$
$284$	−32.6889	+	44.9925i	−1.93973	+	2.66981i
$285$		0			0
$286$	40.3607	+	9.06154i	2.38658	+	0.535820i
$287$		−	13.1286i		−	0.774958i
$288$	6.06086	+	4.40347i	0.357140	+	0.259477i
$289$	1.40983	−	4.33901i	0.0829312	−	0.255236i
$290$	−0.909830	−	2.80017i	−0.0534271	−	0.164432i
$291$		0			0
$292$	−11.7082	−	16.1150i	−0.685171	−	0.943057i
$293$	2.86155	+	8.80695i	0.167174	+	0.514507i	0.999190	−	0.0402438i	$-0.0128135\pi$
$293$	2.86155	+	8.80695i	0.167174	+	0.514507i	−0.832016	+	0.554751i	$0.812813\pi$
$294$		0			0
$295$	−3.45106	+	4.74998i	−0.200929	+	0.276555i
$296$			20.2622i			1.17772i
$297$		0			0
$298$			23.4852i			1.36046i
$299$	−1.54336	−	1.12132i	−0.0892549	−	0.0648475i
$300$		0			0
$301$	5.69098	+	17.5150i	0.328023	+	1.00955i
$302$	42.7426	−	31.0543i	2.45956	−	1.78698i
$303$		0			0
$304$	21.2368	+	10.8600i	1.21802	+	0.622861i
$305$	6.54508	+	2.12663i	0.374770	+	0.121770i
$306$	−15.5298	+	21.3749i	−0.887778	+	1.22192i
$307$	−21.1567			−1.20748			−0.603739	−	0.797182i	$-0.706323\pi$
$307$	−21.1567			−1.20748			−0.603739	+	0.797182i	$0.706323\pi$
$308$	−26.6074	+	2.48990i	−1.51610	+	0.141875i
$309$		0			0
$310$	−5.32624	+	7.33094i	−0.302510	+	0.416369i
$311$	−3.88197	+	11.9475i	−0.220126	+	0.677478i	0.778624	+	0.627491i	$0.215918\pi$
$311$	−3.88197	+	11.9475i	−0.220126	+	0.677478i	−0.998750	+	0.0499874i	$0.984082\pi$
$312$		0			0
$313$	−17.0172	+	12.3637i	−0.961870	+	0.698840i	−0.953584	−	0.301126i	$-0.902638\pi$
$313$	−17.0172	+	12.3637i	−0.961870	+	0.698840i	−0.00828586	+	0.999966i	$0.502638\pi$
$314$	−6.83254	+	4.96413i	−0.385583	+	0.280142i
$315$	3.35410	−	1.08981i	0.188982	−	0.0614041i
$316$	14.6189	−	44.9925i	0.822379	−	2.53102i
$317$	−2.13287	+	2.93565i	−0.119794	+	0.164882i	−0.864703	−	0.502284i	$-0.832493\pi$
$317$	−2.13287	+	2.93565i	−0.119794	+	0.164882i	0.744908	+	0.667167i	$0.232493\pi$
$318$		0			0
$319$	−6.17345	−	1.38603i	−0.345647	−	0.0776025i
$320$	2.90983			0.162664
$321$		0			0
$322$	1.72553	+	0.560659i	0.0961601	+	0.0312443i
$323$	−6.99908	+	13.6868i	−0.389439	+	0.761555i
$324$	−30.8435	+	22.4091i	−1.71353	+	1.24495i
$325$	−18.6595	+	13.5569i	−1.03504	+	0.752003i
$326$	5.69652	+	17.5321i	0.315501	+	0.971013i
$327$		0			0
$328$	−31.1803	−	22.6538i	−1.72165	−	1.25085i
$329$			5.42882i			0.299301i
$330$		0			0
$331$			8.11393i			0.445982i	0.974820	+	0.222991i	$0.0715821\pi$
$331$			8.11393i			0.445982i	−0.974820	+	0.222991i	$0.928418\pi$
$332$	−2.50000	+	3.44095i	−0.137205	+	0.188847i
$333$	−10.3532	−	3.36395i	−0.567351	−	0.184344i
$334$	−11.5623	−	35.5851i	−0.632661	−	1.94713i
$335$	−0.814685	−	1.12132i	−0.0445110	−	0.0612642i
$336$		0			0
$337$	−8.08115	−	24.8712i	−0.440208	−	1.35482i	−0.887654	−	0.460511i	$-0.847666\pi$
$337$	−8.08115	−	24.8712i	−0.440208	−	1.35482i	0.447446	−	0.894311i	$-0.352334\pi$
$338$	−9.21717	+	28.3675i	−0.501348	+	1.54299i
$339$		0			0
$340$		−	9.23305i		−	0.500732i
$341$	7.71681	+	17.8786i	0.417889	+	0.968180i
$342$	−23.1246	+	23.0569i	−1.25044	+	1.24677i
$343$	11.6074	−	15.9762i	0.626740	−	0.862634i
$344$	51.4180	+	16.7067i	2.77227	+	0.900766i
$345$		0			0
$346$	40.3607	−	29.3238i	2.16980	−	1.57645i
$347$	−7.39919	−	10.1841i	−0.397209	−	0.546712i	0.562832	−	0.826572i	$-0.309712\pi$
$347$	−7.39919	−	10.1841i	−0.397209	−	0.546712i	−0.960041	+	0.279860i	$0.909712\pi$
$348$		0			0
$349$	−11.8090	−	3.83698i	−0.632122	−	0.205389i	−0.0246072	−	0.999697i	$-0.507834\pi$
$349$	−11.8090	−	3.83698i	−0.632122	−	0.205389i	−0.607515	+	0.794308i	$0.707834\pi$
$350$	12.8934	−	17.7462i	0.689181	−	0.948577i
$351$		0			0
$352$	−4.22274	+	7.12497i	−0.225073	+	0.379762i
$353$	30.7984			1.63923			0.819616	−	0.572913i	$-0.194187\pi$
$353$	30.7984			1.63923			0.819616	+	0.572913i	$0.194187\pi$
$354$		0			0
$355$	7.71681	+	2.50734i	0.409566	+	0.133076i
$356$	23.6539	−	7.68563i	1.25366	−	0.407337i
$357$		0			0
$358$	34.4721	+	47.4468i	1.82191	+	2.50764i
$359$	−14.7361	+	4.78804i	−0.777740	+	0.252703i	−0.670875	−	0.741571i	$-0.734081\pi$
$359$	−14.7361	+	4.78804i	−0.777740	+	0.252703i	−0.106865	+	0.994274i	$0.534081\pi$
$360$	3.19931	−	9.84647i	0.168618	−	0.518954i
$361$	−11.2130	+	15.3385i	−0.590156	+	0.807290i
$362$			47.4468i			2.49375i
$363$		0			0
$364$		−	40.2425i		−	2.10928i
$365$	−1.70820	+	2.35114i	−0.0894115	+	0.123064i
$366$		0			0
$367$	6.19098	+	19.0539i	0.323167	+	0.994605i	0.972261	+	0.233897i	$0.0751479\pi$
$367$	6.19098	+	19.0539i	0.323167	+	0.994605i	−0.649095	+	0.760708i	$0.724852\pi$
$368$	1.69098	−	1.22857i	0.0881486	−	0.0640437i
$369$	16.7518	−	12.1709i	0.872064	−	0.633592i
$370$	5.32624	−	1.73060i	0.276898	−	0.0899696i
$371$	−1.31819	+	4.05697i	−0.0684369	+	0.210627i
$372$		0			0
$373$	0.728677			0.0377294			0.0188647	−	0.999822i	$-0.493995\pi$
$373$	0.728677			0.0377294			0.0188647	+	0.999822i	$0.493995\pi$
$374$	−25.1277	−	14.8924i	−1.29932	−	0.770068i
$375$		0			0
$376$	12.8934	+	9.36761i	0.664926	+	0.483097i
$377$	2.94427	−	9.06154i	0.151638	−	0.466693i
$378$		0			0
$379$	16.7518	+	23.0569i	0.860483	+	1.18435i	0.981454	+	0.191697i	$0.0613990\pi$
$379$	16.7518	+	23.0569i	0.860483	+	1.18435i	−0.120972	+	0.992656i	$0.538601\pi$
$380$	1.80172	−	11.2686i	0.0924262	−	0.578068i
$381$		0			0
$382$	15.6854	−	48.2746i	0.802533	−	2.46994i
$383$	−4.26575	+	5.87130i	−0.217970	+	0.300009i	−0.903973	−	0.427588i	$-0.859363\pi$
$383$	−4.26575	+	5.87130i	−0.217970	+	0.300009i	0.686004	+	0.727598i	$0.259363\pi$
$384$		0			0
$385$	1.54508	+	3.57971i	0.0787448	+	0.182439i
$386$	−4.76393			−0.242478
$387$	−17.0729	+	23.4989i	−0.867867	+	1.19452i
$388$	−38.2729	−	12.4356i	−1.94301	−	0.631322i
$389$	−5.26393	−	16.2007i	−0.266892	−	0.821409i	−0.991252	−	0.131987i	$-0.957864\pi$
$389$	−5.26393	−	16.2007i	−0.266892	−	0.821409i	0.724360	−	0.689422i	$-0.242136\pi$
$390$		0			0
$391$	0.791796	+	1.08981i	0.0400428	+	0.0551143i
$392$	−5.83569	−	17.9604i	−0.294747	−	0.907137i
$393$		0			0
$394$	24.9721	−	34.3712i	1.25808	−	1.73159i
$395$	−6.90212			−0.347284
$396$	−27.8435	−	31.6421i	−1.39919	−	1.59008i
$397$	−2.20163			−0.110496			−0.0552482	−	0.998473i	$-0.517595\pi$
$397$	−2.20163			−0.110496			−0.0552482	+	0.998473i	$0.517595\pi$
$398$	11.8270	+	8.59279i	0.592832	+	0.430718i
$399$		0			0
$400$	−7.80902	−	24.0337i	−0.390451	−	1.20168i
$401$	−8.53149	−	11.7426i	−0.426043	−	0.586397i	0.540997	−	0.841025i	$-0.318047\pi$
$401$	−8.53149	−	11.7426i	−0.426043	−	0.586397i	−0.967039	+	0.254627i	$0.918047\pi$
$402$		0			0
$403$	−27.8885	+	9.06154i	−1.38923	+	0.451387i
$404$	19.3713	+	6.29412i	0.963759	+	0.313144i
$405$	4.50000	+	3.26944i	0.223607	+	0.162460i
$406$			9.06154i			0.449717i
$407$	2.63638	−	11.7426i	0.130680	−	0.582059i
$408$		0			0
$409$	13.0756	+	9.49996i	0.646545	+	0.469743i	0.862093	−	0.506751i	$-0.169154\pi$
$409$	13.0756	+	9.49996i	0.646545	+	0.469743i	−0.215547	+	0.976493i	$0.569154\pi$
$410$	−3.29180	+	10.1311i	−0.162570	+	0.500340i
$411$		0			0
$412$	−32.6889	−	44.9925i	−1.61047	−	2.21662i
$413$	14.6189	−	10.6213i	0.719351	−	0.522639i
$414$	0.884268	+	2.72150i	0.0434594	+	0.133754i
$415$	0.590170	+	0.191758i	0.0289703	+	0.00941302i
$416$	−10.0902	−	7.33094i	−0.494711	−	0.359429i
$417$		0			0
$418$	−27.7614	−	23.0790i	−1.35786	−	1.12883i
$419$	−5.14590			−0.251394			−0.125697	−	0.992069i	$-0.540117\pi$
$419$	−5.14590			−0.251394			−0.125697	+	0.992069i	$0.540117\pi$
$420$		0			0
$421$	−25.7868	−	8.37864i	−1.25677	−	0.408350i	−0.396429	−	0.918065i	$-0.629751\pi$
$421$	−25.7868	−	8.37864i	−1.25677	−	0.408350i	−0.860343	+	0.509715i	$0.829751\pi$
$422$	11.0000	+	33.8545i	0.535472	+	1.64801i
$423$	−6.92705	+	5.03280i	−0.336805	+	0.244703i
$424$	7.36068	+	10.1311i	0.357466	+	0.492010i
$425$	15.4894	−	5.03280i	0.751344	−	0.244127i
$426$		0			0
$427$	−17.1353	−	12.4495i	−0.829233	−	0.602473i
$428$	−13.0756			−0.632032
$429$		0			0
$430$		−	14.9430i		−	0.720613i
$431$	−2.13287	−	1.54962i	−0.102737	−	0.0746427i	0.535231	−	0.844706i	$-0.320225\pi$
$431$	−2.13287	−	1.54962i	−0.102737	−	0.0746427i	−0.637968	+	0.770063i	$0.720225\pi$
$432$		0			0
$433$	−19.3882	+	6.29960i	−0.931737	+	0.302740i	−0.735273	−	0.677771i	$-0.762946\pi$
$433$	−19.3882	+	6.29960i	−0.931737	+	0.302740i	−0.196464	+	0.980511i	$0.562946\pi$
$434$	22.5623	−	16.3925i	1.08303	−	0.786864i
$435$		0			0
$436$	−0.953850	−	2.93565i	−0.0456811	−	0.140592i
$437$	0.753696	+	1.48459i	0.0360542	+	0.0710175i
$438$		0			0
$439$	−39.6771			−1.89368			−0.946841	−	0.321701i	$-0.895746\pi$
$439$	−39.6771			−1.89368			−0.946841	+	0.321701i	$0.895746\pi$
$440$	11.1679	+	2.50734i	0.532407	+	0.119533i
$441$	10.1459			0.483138
$442$	25.8541	−	35.5851i	1.22975	−	1.69261i
$443$	−3.98936	+	12.2780i	−0.189540	+	0.583344i	−0.999997	−	0.00245390i	$-0.999219\pi$
$443$	−3.98936	+	12.2780i	−0.189540	+	0.583344i	0.810457	+	0.585798i	$0.199219\pi$
$444$		0			0
$445$	−2.13287	−	2.93565i	−0.101108	−	0.139163i
$446$	−31.1803	−	42.9161i	−1.47643	−	2.03213i
$447$		0			0
$448$	−8.51722	−	2.76741i	−0.402401	−	0.130748i
$449$	−14.6189	+	20.1212i	−0.689910	+	0.949580i	−0.999999	−	0.00112761i	$-0.999641\pi$
$449$	−14.6189	+	20.1212i	−0.689910	+	0.949580i	0.310089	+	0.950707i	$0.399641\pi$
$450$	34.5966			1.63090
$451$	15.1224	+	17.1856i	0.712088	+	0.809238i
$452$			80.4849i			3.78569i
$453$		0			0
$454$	0.347524	−	1.06957i	0.0163101	−	0.0501974i
$455$	−5.58394	+	1.81433i	−0.261779	+	0.0850571i
$456$		0			0
$457$	−16.6459	−	22.9111i	−0.778662	−	1.07174i	−0.995428	−	0.0955131i	$-0.969551\pi$
$457$	−16.6459	−	22.9111i	−0.778662	−	1.07174i	0.216766	−	0.976224i	$-0.430449\pi$
$458$	−16.9606	−	52.1992i	−0.792515	−	2.43911i
$459$		0			0
$460$	−0.809017	−	0.587785i	−0.0377206	−	0.0274056i
$461$			15.1109i			0.703785i	0.936040	+	0.351892i	$0.114462\pi$
$461$			15.1109i			0.703785i	−0.936040	+	0.351892i	$0.885538\pi$
$462$		0			0
$463$	15.3820			0.714861			0.357430	−	0.933940i	$-0.383653\pi$
$463$	15.3820			0.714861			0.357430	+	0.933940i	$0.383653\pi$
$464$	8.44549	+	6.13600i	0.392072	+	0.284857i
$465$		0			0
$466$	−44.9232	+	14.5964i	−2.08103	+	0.676167i
$467$	−10.5000	+	7.62870i	−0.485882	+	0.353014i	−0.803598	−	0.595172i	$-0.797084\pi$
$467$	−10.5000	+	7.62870i	−0.485882	+	0.353014i	0.317716	+	0.948186i	$0.397084\pi$
$468$	51.3484	−	37.3068i	2.37358	−	1.72451i
$469$	1.31819	+	4.05697i	0.0608683	+	0.187333i
$470$	1.36119	−	4.18932i	0.0627871	−	0.193239i
$471$		0			0
$472$		−	53.0472i		−	2.44169i
$473$	−27.6246	−	16.3722i	−1.27018	−	0.752796i
$474$		0			0
$475$	19.8863	−	3.11979i	0.912447	−	0.143146i
$476$	−8.78115	+	27.0256i	−0.402483	+	1.23872i
$477$	−6.39862	+	2.07904i	−0.292973	+	0.0951926i
$478$	9.94584	+	13.6893i	0.454912	+	0.626133i
$479$	22.5238	+	31.0013i	1.02914	+	1.41649i	0.905592	+	0.424149i	$0.139427\pi$
$479$	22.5238	+	31.0013i	1.02914	+	1.41649i	0.123546	+	0.992339i	$0.460573\pi$
$480$		0			0
$481$	17.2361	+	5.60034i	0.785897	+	0.255353i
$482$	38.8885	+	28.2542i	1.77132	+	1.28694i
$483$		0			0
$484$	31.9615	−	33.9075i	1.45280	−	1.54125i
$485$			5.87130i			0.266602i
$486$		0			0
$487$	21.5211	+	6.99262i	0.975212	+	0.316866i	0.752918	−	0.658114i	$-0.228646\pi$
$487$	21.5211	+	6.99262i	0.975212	+	0.316866i	0.222294	+	0.974980i	$0.428646\pi$
$488$	−59.1348	+	19.2141i	−2.67691	+	0.869780i
$489$		0			0
$490$	−4.22274	+	3.06800i	−0.190764	+	0.138598i
$491$	−19.0451	+	6.18812i	−0.859493	+	0.279266i	−0.705417	−	0.708793i	$-0.749240\pi$
$491$	−19.0451	+	6.18812i	−0.859493	+	0.279266i	−0.154076	+	0.988059i	$0.549240\pi$
$492$		0			0
$493$	−3.95457	+	5.44299i	−0.178105	+	0.245140i
$494$	38.4980	−	38.3853i	1.73211	−	1.72704i
$495$	−3.13525	+	5.29007i	−0.140919	+	0.237771i
$496$		−	32.1285i		−	1.44261i
$497$	−20.2029	−	14.6782i	−0.906223	−	0.658409i
$498$		0			0
$499$	−9.22542	−	28.3929i	−0.412987	−	1.27104i	−0.914039	−	0.405626i	$-0.867054\pi$
$499$	−9.22542	−	28.3929i	−0.412987	−	1.27104i	0.501053	−	0.865417i	$-0.332946\pi$
$500$	−20.3713	+	14.8006i	−0.911033	+	0.661904i
$501$		0			0
$502$	0.884268	+	2.72150i	0.0394668	+	0.121466i
$503$	39.2705	+	12.7598i	1.75099	+	0.568930i	0.996204	−	0.0870469i	$-0.0277430\pi$
$503$	39.2705	+	12.7598i	1.75099	+	0.568930i	0.754781	+	0.655977i	$0.227743\pi$
$504$	−18.7291	+	25.7784i	−0.834260	+	1.14826i
$505$		−	2.97168i		−	0.132238i
$506$	−2.90455	+	1.25367i	−0.129123	+	0.0557325i
$507$		0			0
$508$	−10.5784	−	7.68563i	−0.469339	−	0.340995i
$509$	−1.31819	−	0.428305i	−0.0584277	−	0.0189843i	0.279657	−	0.960100i	$-0.409779\pi$
$509$	−1.31819	−	0.428305i	−0.0584277	−	0.0189843i	−0.338085	+	0.941116i	$0.609779\pi$
$510$		0			0
$511$	7.23607	−	5.25731i	0.320105	−	0.232570i
$512$	−38.3855	+	27.8887i	−1.69641	+	1.23252i
$513$		0			0
$514$	73.0132	+	23.7234i	3.22047	+	1.04639i
$515$	−4.76925	+	6.56431i	−0.210158	+	0.289258i
$516$		0			0
$517$	−6.25329	−	7.10642i	−0.275019	−	0.312540i
$518$	−17.2361			−0.757309
$519$		0			0
$520$	−5.32624	+	16.3925i	−0.233571	+	0.718858i
$521$	−26.2903	+	8.54224i	−1.15180	+	0.374242i	−0.821821	−	0.569746i	$-0.807042\pi$
$521$	−26.2903	+	8.54224i	−1.15180	+	0.374242i	−0.329979	+	0.943988i	$0.607042\pi$
$522$	−11.5623	+	8.40051i	−0.506068	+	0.367680i
$523$	10.5784	−	7.68563i	0.462559	−	0.336069i	−0.331975	−	0.943288i	$-0.607715\pi$
$523$	10.5784	−	7.68563i	0.462559	−	0.336069i	0.794534	+	0.607219i	$0.207715\pi$
$524$	34.6976	−	11.2739i	1.51577	−	0.492504i
$525$		0			0
$526$	38.2729	−	52.6781i	1.66878	−	2.29687i
$527$	20.7064			0.901984
$528$		0			0
$529$	−22.8541			−0.993657
$530$	2.03444	−	2.80017i	0.0883705	−	0.121632i
$531$	27.1050	+	8.80695i	1.17626	+	0.382189i
$532$	−15.9908	+	31.2703i	−0.693290	+	1.35574i
$533$	−27.8885	+	20.2622i	−1.20799	+	0.877654i
$534$		0			0
$535$	0.589512	+	1.81433i	0.0254868	+	0.0784404i
$536$	11.9098	+	3.86974i	0.514426	+	0.167147i
$537$		0			0
$538$			56.5084i			2.43625i
$539$	1.04508	+	11.1679i	0.0450150	+	0.481036i
$540$		0			0
$541$	22.7254	−	31.2789i	0.977042	−	1.34478i	0.0386346	−	0.999253i	$-0.487699\pi$
$541$	22.7254	−	31.2789i	0.977042	−	1.34478i	0.938408	−	0.345530i	$-0.112301\pi$
$542$	49.2851	+	16.0137i	2.11698	+	0.687848i
$543$		0			0
$544$	5.17659	+	7.12497i	0.221945	+	0.305481i
$545$	−0.364338	+	0.264707i	−0.0156065	+	0.0113388i
$546$		0			0
$547$	−3.90141	+	12.0073i	−0.166812	+	0.513395i	−0.999165	−	0.0408506i	$-0.986993\pi$
$547$	−3.90141	+	12.0073i	−0.166812	+	0.513395i	0.832353	+	0.554246i	$0.186993\pi$
$548$	61.1869	+	44.4549i	2.61378	+	1.89902i
$549$		−	33.4055i		−	1.42571i
$550$	3.56365	+	38.0816i	0.151954	+	1.62381i
$551$	−5.88854	+	5.87130i	−0.250860	+	0.250126i
$552$		0			0
$553$	20.2029	+	6.56431i	0.859113	+	0.279143i
$554$	−24.9721	+	8.11393i	−1.06096	+	0.344728i
$555$		0			0
$556$	6.54508	+	9.00854i	0.277573	+	0.382047i
$557$	15.4271	−	5.01255i	0.653665	−	0.212389i	0.0366356	−	0.999329i	$-0.488336\pi$
$557$	15.4271	−	5.01255i	0.653665	−	0.212389i	0.617030	+	0.786940i	$0.288336\pi$
$558$	41.8328	+	13.5923i	1.77092	+	0.575408i
$559$	28.4232	−	39.1212i	1.20217	−	1.65465i
$560$		−	6.43288i		−	0.271839i
$561$		0			0
$562$	−63.4853			−2.67797
$563$	2.86155	+	2.07904i	0.120600	+	0.0876210i	0.646450	−	0.762956i	$-0.276253\pi$
$563$	2.86155	+	2.07904i	0.120600	+	0.0876210i	−0.525850	+	0.850577i	$0.676253\pi$
$564$		0			0
$565$	11.1679	−	3.62866i	0.469836	−	0.152659i
$566$	−34.6662	−	47.7139i	−1.45713	−	2.00557i
$567$	−10.0623	−	13.8496i	−0.422577	−	0.581628i
$568$	−69.7214	+	22.6538i	−2.92544	+	0.950534i
$569$	0.814685	−	2.50734i	0.0341534	−	0.105113i	−0.932527	−	0.361101i	$-0.882401\pi$
$569$	0.814685	−	2.50734i	0.0341534	−	0.105113i	0.966680	+	0.255988i	$0.0824008\pi$
$570$		0			0
$571$			3.91023i			0.163638i	0.996647	+	0.0818190i	$0.0260729\pi$
$571$			3.91023i			0.163638i	−0.996647	+	0.0818190i	$0.973927\pi$
$572$	46.3540	+	52.6781i	1.93816	+	2.20258i
$573$		0			0
$574$	19.2705	−	26.5236i	0.804336	−	1.10707i
$575$	0.545085	−	1.67760i	0.0227316	−	0.0699607i
$576$	−4.36475	−	13.4333i	−0.181864	−	0.559721i
$577$	8.38197	−	6.08985i	0.348946	−	0.253524i	−0.399481	−	0.916742i	$-0.630810\pi$
$577$	8.38197	−	6.08985i	0.348946	−	0.253524i	0.748427	+	0.663218i	$0.230810\pi$
$578$	9.21717	−	6.69666i	0.383384	−	0.278544i
$579$		0			0
$580$	1.54336	−	4.74998i	0.0640846	−	0.197232i
$581$	−1.54508	−	1.12257i	−0.0641009	−	0.0465720i
$582$		0			0
$583$	−2.94756	−	6.82902i	−0.122075	−	0.282829i
$584$		−	26.2572i		−	1.08653i
$585$	−7.49164	−	5.44299i	−0.309741	−	0.225040i
$586$	−7.14590	+	21.9928i	−0.295194	+	0.908515i
$587$	−3.05573	−	9.40456i	−0.126123	−	0.388168i	0.867981	−	0.496598i	$-0.165418\pi$
$587$	−3.05573	−	9.40456i	−0.126123	−	0.388168i	−0.994104	+	0.108430i	$0.965418\pi$
$588$		0			0
$589$	25.2714	+	4.04060i	1.04129	+	0.166490i
$590$	−13.9443	+	4.53077i	−0.574077	+	0.186529i
$591$		0			0
$592$	−11.6714	+	16.0643i	−0.479691	+	0.660237i
$593$		−	18.7436i		−	0.769708i	−0.922977	−	0.384854i	$-0.874252\pi$
$593$		−	18.7436i		−	0.769708i	0.922977	−	0.384854i	$-0.125748\pi$
$594$		0			0
$595$	4.14590			0.169965
$596$	−23.4164	+	32.2299i	−0.959173	+	1.32019i
$597$		0			0
$598$	−1.47214	−	4.53077i	−0.0602001	−	0.185277i
$599$	2.13287	+	2.93565i	0.0871469	+	0.119947i	0.850364	−	0.526194i	$-0.176382\pi$
$599$	2.13287	+	2.93565i	0.0871469	+	0.119947i	−0.763218	+	0.646142i	$0.776382\pi$
$600$		0			0
$601$	−6.90212	−	21.2426i	−0.281544	−	0.866502i	−0.987413	−	0.158160i	$-0.949444\pi$
$601$	−6.90212	−	21.2426i	−0.281544	−	0.866502i	0.705870	−	0.708341i	$-0.250556\pi$
$602$	−14.2116	+	43.7388i	−0.579221	+	1.78266i
$603$	−3.95457	+	5.44299i	−0.161042	+	0.221656i
$604$	89.6213			3.64664
$605$	−6.14590	−	2.90617i	−0.249866	−	0.118153i
$606$		0			0
$607$	8.67066	+	6.29960i	0.351931	+	0.255693i	0.749679	−	0.661802i	$-0.230208\pi$
$607$	8.67066	+	6.29960i	0.351931	+	0.255693i	−0.397748	+	0.917495i	$0.630208\pi$
$608$	4.92750	+	9.70593i	0.199837	+	0.393627i
$609$		0			0
$610$	10.1014	+	13.9034i	0.408995	+	0.562934i
$611$	11.5322	−	8.37864i	0.466543	−	0.338964i
$612$	−42.6246	+	13.8496i	−1.72300	+	0.559836i
$613$	−23.4787	−	7.62870i	−0.948296	−	0.308120i	−0.206273	−	0.978494i	$-0.566134\pi$
$613$	−23.4787	−	7.62870i	−0.948296	−	0.308120i	−0.742023	+	0.670374i	$0.766134\pi$
$614$	−42.7426	−	31.0543i	−1.72495	−	1.25325i
$615$		0			0
$616$	−30.3043	−	17.9604i	−1.22100	−	0.723645i
$617$	−28.8328			−1.16077			−0.580383	−	0.814344i	$-0.697097\pi$
$617$	−28.8328			−1.16077			−0.580383	+	0.814344i	$0.697097\pi$
$618$		0			0
$619$	−3.88197	+	11.9475i	−0.156029	+	0.480209i	−0.998264	−	0.0589025i	$-0.981240\pi$
$619$	−3.88197	+	11.9475i	−0.156029	+	0.480209i	0.842234	+	0.539112i	$0.181240\pi$
$620$	−14.6189	+	4.74998i	−0.587111	+	0.190764i
$621$		0			0
$622$	−25.3795	+	18.4393i	−1.01762	+	0.739347i
$623$	3.45106	+	10.6213i	0.138264	+	0.425532i
$624$		0			0
$625$	−15.7082	−	11.4127i	−0.628328	−	0.456507i
$626$	−52.5275			−2.09942
$627$		0			0
$628$	−14.3262			−0.571679
$629$	−10.3532	−	7.52203i	−0.412809	−	0.299923i
$630$	8.37590	+	2.72150i	0.333704	+	0.108427i
$631$	12.3607	+	38.0423i	0.492071	+	1.51444i	0.821472	+	0.570248i	$0.193153\pi$
$631$	12.3607	+	38.0423i	0.492071	+	1.51444i	−0.329401	+	0.944190i	$0.606847\pi$
$632$	50.4508	−	36.6547i	2.00683	−	1.45805i
$633$		0			0
$634$	−8.61803	+	2.80017i	−0.342266	+	0.111209i
$635$	−0.589512	+	1.81433i	−0.0233941	+	0.0719995i
$636$		0			0
$637$	−16.8910			−0.669245
$638$	−10.4377	−	11.8617i	−0.413232	−	0.469609i
$639$		−	39.3859i		−	1.55808i
$640$	8.37590	+	6.08545i	0.331087	+	0.240549i
$641$	2.13287	+	0.693013i	0.0842434	+	0.0273724i	0.350835	−	0.936437i	$-0.385898\pi$
$641$	2.13287	+	0.693013i	0.0842434	+	0.0273724i	−0.266592	+	0.963809i	$0.585898\pi$
$642$		0			0
$643$	10.3090	−	7.48994i	0.406548	−	0.295374i	−0.365655	−	0.930751i	$-0.619155\pi$
$643$	10.3090	−	7.48994i	0.406548	−	0.295374i	0.772203	+	0.635376i	$0.219155\pi$
$644$	1.80902	+	2.48990i	0.0712853	+	0.0981157i
$645$		0			0
$646$	−34.2300	+	17.3779i	−1.34676	+	0.683723i
$647$	−2.47214	−	1.79611i	−0.0971897	−	0.0706124i	0.538129	−	0.842862i	$-0.319131\pi$
$647$	−2.47214	−	1.79611i	−0.0971897	−	0.0706124i	−0.635319	+	0.772250i	$0.719131\pi$
$648$	−50.2554			−1.97422
$649$	−6.90212	+	30.7425i	−0.270932	+	1.20675i
$650$	−57.5967			−2.25913
$651$		0			0
$652$	−9.66312	+	29.7400i	−0.378437	+	1.16471i
$653$	0.972136	+	2.99193i	0.0380426	+	0.117083i	0.968274	−	0.249889i	$-0.0803943\pi$
$653$	0.972136	+	2.99193i	0.0380426	+	0.117083i	−0.930232	+	0.366973i	$0.880394\pi$
$654$		0			0
$655$	−3.12868	−	4.30625i	−0.122248	−	0.168259i
$656$	−11.6714	−	35.9208i	−0.455691	−	1.40247i
$657$	13.4164	+	4.35926i	0.523424	+	0.170071i
$658$	−7.96856	+	10.9678i	−0.310647	+	0.427569i
$659$	28.5092			1.11056			0.555280	−	0.831663i	$-0.312611\pi$
$659$	28.5092			1.11056			0.555280	+	0.831663i	$0.312611\pi$
$660$		0			0
$661$		−	20.3859i		−	0.792921i	−0.918052	−	0.396461i	$-0.870238\pi$
$661$		−	20.3859i		−	0.792921i	0.918052	−	0.396461i	$-0.129762\pi$
$662$	−11.9098	+	16.3925i	−0.462889	+	0.637112i
$663$		0			0
$664$	−5.33218	+	1.73253i	−0.206929	+	0.0672353i
$665$	5.05992	+	0.809022i	0.196215	+	0.0313725i
$666$	−15.9787	−	21.9928i	−0.619163	−	0.852204i
$667$	0.225173	+	0.693013i	0.00871875	+	0.0268336i
$668$	19.6134	−	60.3637i	0.758864	−	2.33554i
$669$		0			0
$670$		−	3.46120i		−	0.133718i
$671$	36.7705	−	3.44095i	1.41951	−	0.132837i
$672$		0			0
$673$	7.49164	+	5.44299i	0.288781	+	0.209812i	0.722739	−	0.691122i	$-0.242883\pi$
$673$	7.49164	+	5.44299i	0.288781	+	0.209812i	−0.433957	+	0.900933i	$0.642883\pi$
$674$	20.1803	−	62.1087i	0.777318	−	2.39234i
$675$		0			0
$676$	−40.9336	+	29.7400i	−1.57437	+	1.14385i
$677$	−17.1161	+	12.4356i	−0.657827	+	0.477939i	−0.865928	−	0.500168i	$-0.833272\pi$
$677$	−17.1161	+	12.4356i	−0.657827	+	0.477939i	0.208101	+	0.978107i	$0.433272\pi$
$678$		0			0
$679$	5.58394	−	17.1856i	0.214292	−	0.659522i
$680$	7.15388	−	9.84647i	0.274339	−	0.377595i
$681$		0			0
$682$	−10.6525	+	47.4468i	−0.407904	+	1.81683i
$683$		−	29.3565i		−	1.12329i	−0.827377	−	0.561647i	$-0.810168\pi$
$683$		−	29.3565i		−	1.12329i	0.827377	−	0.561647i	$-0.189832\pi$
$684$	−54.7244	+	8.58525i	−2.09244	+	0.328265i
$685$	3.40983	−	10.4944i	0.130283	−	0.400970i
$686$	46.9005	−	15.2389i	1.79067	−	0.581824i
$687$		0			0
$688$	31.1418	+	42.8631i	1.18727	+	1.63414i
$689$	10.6525	−	3.46120i	0.405827	−	0.131861i
$690$		0			0
$691$	−14.2082	−	10.3229i	−0.540506	−	0.392700i	0.283767	−	0.958893i	$-0.408416\pi$
$691$	−14.2082	−	10.3229i	−0.540506	−	0.392700i	−0.824273	+	0.566193i	$0.808416\pi$
$692$	84.6269			3.21703
$693$	14.2082	−	12.5025i	0.539725	−	0.474930i
$694$		−	31.4355i		−	1.19328i
$695$	0.954915	−	1.31433i	0.0362220	−	0.0498553i
$696$		0			0
$697$	23.1504	−	7.52203i	0.876885	−	0.284917i
$698$	−18.2256	−	25.0854i	−0.689849	−	0.949495i
$699$		0			0
$700$	35.3885	−	11.4984i	1.33756	−	0.434600i
$701$	18.3541	+	5.96361i	0.693225	+	0.225242i	0.634376	−	0.773025i	$-0.281257\pi$
$701$	18.3541	+	5.96361i	0.693225	+	0.225242i	0.0588487	+	0.998267i	$0.481257\pi$
$702$		0			0
$703$	−11.1679	−	11.2007i	−0.421204	−	0.422441i
$704$	14.3369	−	6.18812i	0.540342	−	0.233224i
$705$		0			0
$706$	62.2216	+	45.2066i	2.34174	+	1.70137i
$707$	−2.82624	+	8.69827i	−0.106292	+	0.327132i
$708$		0			0
$709$	−22.9721	+	16.6902i	−0.862737	+	0.626815i	−0.928628	−	0.371012i	$-0.879011\pi$
$709$	−22.9721	+	16.6902i	−0.862737	+	0.626815i	0.0658914	+	0.997827i	$0.479011\pi$
$710$	11.9098	+	16.3925i	0.446968	+	0.615199i
$711$	10.3532	+	31.8638i	0.388275	+	1.19499i
$712$	31.1803	+	10.1311i	1.16853	+	0.379679i
$713$	1.31819	−	1.81433i	0.0493665	−	0.0679472i
$714$		0			0
$715$	5.21960	−	8.80695i	0.195202	−	0.329361i
$716$			99.4849i			3.71792i
$717$		0			0
$718$	−36.7991	−	11.9567i	−1.37333	−	0.446222i
$719$	0.302439	+	0.930812i	0.0112791	+	0.0347134i	0.956538	−	0.291609i	$-0.0941905\pi$
$719$	0.302439	+	0.930812i	0.0112791	+	0.0347134i	−0.945259	+	0.326322i	$0.894191\pi$
$720$	8.20820	−	5.96361i	0.305902	−	0.222251i
$721$	20.2029	−	14.6782i	0.752394	−	0.546646i
$722$	−45.1676	+	14.5295i	−1.68096	+	0.540733i
$723$		0			0
$724$	−47.3079	+	65.1137i	−1.75818	+	2.41993i
$725$	8.80982			0.327189
$726$		0			0
$727$	35.2148			1.30604			0.653022	−	0.757339i	$-0.273501\pi$
$727$	35.2148			1.30604			0.653022	+	0.757339i	$0.273501\pi$
$728$	31.1803	−	42.9161i	1.15562	−	1.59057i
$729$	8.34346	−	25.6785i	0.309017	−	0.951057i
$730$	−6.90212	+	2.24264i	−0.255459	+	0.0830037i
$731$	−27.6246	+	20.0705i	−1.02173	+	0.742333i
$732$		0			0
$733$	32.6631	−	10.6129i	1.20644	−	0.391996i	0.364313	−	0.931276i	$-0.381304\pi$
$733$	32.6631	−	10.6129i	1.20644	−	0.391996i	0.842126	+	0.539280i	$0.181304\pi$
$734$	−15.4602	+	47.5816i	−0.570646	+	1.75627i
$735$		0			0
$736$	0.953850			0.0351594
$737$	−6.39862	−	3.79226i	−0.235696	−	0.139690i
$738$	51.7082			1.90341
$739$	−7.82624	+	10.7719i	−0.287893	+	0.396250i	−0.928328	−	0.371762i	$-0.878754\pi$
$739$	−7.82624	+	10.7719i	−0.287893	+	0.396250i	0.640435	+	0.768012i	$0.278754\pi$
$740$	9.03500	+	2.93565i	0.332133	+	0.107917i
$741$		0			0
$742$	−8.61803	+	6.26137i	−0.316378	+	0.229862i
$743$	20.9315	−	15.2077i	0.767904	−	0.557915i	−0.133420	−	0.991060i	$-0.542596\pi$
$743$	20.9315	−	15.2077i	0.767904	−	0.557915i	0.901324	+	0.433145i	$0.142596\pi$
$744$		0			0
$745$	5.52786	+	1.79611i	0.202525	+	0.0658044i
$746$	1.47214	+	1.06957i	0.0538987	+	0.0391597i
$747$		−	3.01217i		−	0.110210i
$748$	−19.6353	−	45.4917i	−0.717936	−	1.66334i
$749$		−	5.87130i		−	0.214533i
$750$		0			0
$751$	6.90212	+	2.24264i	0.251862	+	0.0818350i	0.432227	−	0.901765i	$-0.357728\pi$
$751$	6.90212	+	2.24264i	0.251862	+	0.0818350i	−0.180365	+	0.983600i	$0.557728\pi$
$752$	4.82624	+	14.8536i	0.175995	+	0.541656i
$753$		0			0
$754$	19.2490	−	13.9852i	0.701008	−	0.509312i
$755$	−4.04057	−	12.4356i	−0.147052	−	0.452578i
$756$		0			0
$757$	2.85410	+	2.07363i	0.103734	+	0.0753672i	0.638443	−	0.769669i	$-0.279579\pi$
$757$	2.85410	+	2.07363i	0.103734	+	0.0753672i	−0.534709	+	0.845036i	$0.679579\pi$
$758$			71.1702i			2.58502i
$759$		0			0
$760$	10.6525	−	10.6213i	0.386406	−	0.385274i
$761$	4.47214	−	6.15537i	0.162115	−	0.223132i	−0.720230	−	0.693735i	$-0.755964\pi$
$761$	4.47214	−	6.15537i	0.162115	−	0.223132i	0.882345	+	0.470603i	$0.155964\pi$
$762$		0			0
$763$	1.31819	−	0.428305i	0.0477216	−	0.0155057i
$764$	69.6591	−	50.6103i	2.52018	−	1.83102i
$765$	3.84346	+	5.29007i	0.138961	+	0.191263i
$766$	−17.2361	+	5.60034i	−0.622764	+	0.202348i
$767$	−45.1246	−	14.6619i	−1.62936	−	0.529410i
$768$		0			0
$769$			33.2340i			1.19845i	0.800581	+	0.599224i	$0.204524\pi$
$769$			33.2340i			1.19845i	−0.800581	+	0.599224i	$0.795476\pi$
$770$	−2.13287	+	9.49996i	−0.0768634	+	0.342355i
$771$		0			0
$772$	−6.53779	−	4.74998i	−0.235300	−	0.170956i
$773$	−37.4582	−	12.1709i	−1.34728	−	0.437757i	−0.455502	−	0.890235i	$-0.650540\pi$
$773$	−37.4582	−	12.1709i	−1.34728	−	0.437757i	−0.891776	+	0.452478i	$0.850540\pi$
$774$	−68.9845	+	22.4144i	−2.47960	+	0.805670i
$775$	−15.9371	−	21.9356i	−0.572478	−	0.787949i
$776$	−31.1803	−	42.9161i	−1.11931	−	1.54060i
$777$		0			0
$778$	13.1452	−	40.4566i	0.471277	−	1.45044i
$779$	29.7221	−	4.66285i	1.06491	−	0.167064i
$780$		0			0
$781$	43.3533	−	4.05697i	1.55130	−	0.145170i
$782$			3.36395i			0.120295i
$783$		0			0
$784$	5.71885	−	17.6008i	0.204245	−	0.628600i
$785$	0.645898	+	1.98787i	0.0230531	+	0.0709501i
$786$		0			0
$787$	−40.5449	+	29.4576i	−1.44527	+	1.05005i	−0.458362	+	0.888766i	$0.651564\pi$
$787$	−40.5449	+	29.4576i	−1.44527	+	1.05005i	−0.986908	+	0.161284i	$0.948436\pi$
$788$	68.5410	−	22.2703i	2.44167	−	0.793348i
$789$		0			0
$790$	−13.9443	−	10.1311i	−0.496115	−	0.360449i
$791$	−36.1400			−1.28499
$792$	−5.17659	−	55.3178i	−0.183942	−	1.96563i
$793$			55.6137i			1.97490i
$794$	−4.44792	−	3.23160i	−0.157851	−	0.114685i
$795$		0			0
$796$	7.66312	+	23.5847i	0.271612	+	0.835936i
$797$	−10.6644	−	14.6782i	−0.377751	−	0.519930i	0.577236	−	0.816578i	$-0.304131\pi$
$797$	−10.6644	−	14.6782i	−0.377751	−	0.519930i	−0.954987	+	0.296647i	$0.904131\pi$
$798$		0			0
$799$	−9.57295	+	3.11044i	−0.338667	+	0.110039i
$800$	3.56365	−	10.9678i	0.125994	−	0.387770i
$801$	−10.3532	+	14.2499i	−0.365812	+	0.503497i
$802$		−	36.2461i		−	1.27990i
$803$	−3.41641	+	15.2169i	−0.120562	+	0.536993i
$804$		0			0
$805$	0.263932	−	0.363271i	0.00930238	−	0.0128036i
$806$	−69.6436	−	22.6286i	−2.45309	−	0.797058i
$807$		0			0
$808$	15.7815	+	21.7214i	0.555192	+	0.764157i
$809$	−6.77051	−	9.31881i	−0.238038	−	0.327632i	0.673239	−	0.739425i	$-0.264903\pi$
$809$	−6.77051	−	9.31881i	−0.238038	−	0.327632i	−0.911277	+	0.411793i	$0.864903\pi$
$810$	4.29233	+	13.2104i	0.150817	+	0.464167i
$811$	−11.6182	+	35.7572i	−0.407971	+	1.25561i	0.510418	+	0.859926i	$0.329491\pi$
$811$	−11.6182	+	35.7572i	−0.407971	+	1.25561i	−0.918389	+	0.395679i	$0.870509\pi$
$812$	−9.03500	+	12.4356i	−0.317066	+	0.436404i
$813$		0			0
$814$	22.5623	−	19.8537i	0.790808	−	0.695871i
$815$	4.56231			0.159811
$816$		0			0
$817$	−37.6314	+	19.1047i	−1.31656	+	0.668388i
$818$	12.4721	+	38.3853i	0.436078	+	1.34211i
$819$	16.7518	+	23.0569i	0.585356	+	0.805673i
$820$	−14.6189	+	10.6213i	−0.510515	+	0.370911i
$821$	28.3541	−	9.21281i	0.989565	−	0.321529i	0.230877	−	0.972983i	$-0.425841\pi$
$821$	28.3541	−	9.21281i	0.989565	−	0.321529i	0.758688	+	0.651454i	$0.225841\pi$
$822$		0			0
$823$	−7.97214	−	5.79210i	−0.277891	−	0.201900i	0.440106	−	0.897946i	$-0.354941\pi$
$823$	−7.97214	−	5.79210i	−0.277891	−	0.201900i	−0.717997	+	0.696046i	$0.754941\pi$
$824$		−	73.3094i		−	2.55385i
$825$		0			0
$826$	45.1246			1.57009
$827$	26.1511	+	18.9999i	0.909364	+	0.660692i	0.940854	−	0.338812i	$-0.110025\pi$
$827$	26.1511	+	18.9999i	0.909364	+	0.660692i	−0.0314897	+	0.999504i	$0.510025\pi$
$828$	−1.50000	+	4.61653i	−0.0521286	+	0.160435i
$829$	30.5561	−	9.92826i	1.06126	−	0.344823i	0.274179	−	0.961679i	$-0.411594\pi$
$829$	30.5561	−	9.92826i	1.06126	−	0.344823i	0.787076	+	0.616856i	$0.211594\pi$
$830$	0.910846	+	1.25367i	0.0316159	+	0.0435156i
$831$		0			0
$832$	7.26646	+	22.3639i	0.251919	+	0.775328i
$833$	11.3435	+	3.68571i	0.393028	+	0.127702i
$834$		0			0
$835$	−9.26017			−0.320461
$836$	−15.0870	−	59.3526i	−0.521794	−	2.05275i
$837$		0			0
$838$	−10.3962	−	7.55327i	−0.359130	−	0.260924i
$839$	4.76925	+	1.54962i	0.164653	+	0.0534989i	0.390183	−	0.920737i	$-0.372412\pi$
$839$	4.76925	+	1.54962i	0.164653	+	0.0534989i	−0.225531	+	0.974236i	$0.572412\pi$
$840$		0			0
$841$	20.5172	−	14.9066i	0.707490	−	0.514022i
$842$	−39.7984	−	54.7778i	−1.37154	−	1.88777i
$843$		0			0
$844$	−18.6595	+	57.4281i	−0.642287	+	1.97676i
$845$	5.97214	+	4.33901i	0.205448	+	0.149267i
$846$	−21.3819			−0.735125
$847$	15.2254	+	14.3516i	0.523152	+	0.493127i
$848$			12.2720i			0.421423i
$849$		0			0
$850$	38.6802	+	12.5680i	1.32672	+	0.431078i
$851$	−1.31819	+	0.428305i	−0.0451869	+	0.0146821i
$852$		0			0
$853$	−2.07295	−	2.85317i	−0.0709764	−	0.0976907i	0.772053	−	0.635558i	$-0.219230\pi$
$853$	−2.07295	−	2.85317i	−0.0709764	−	0.0976907i	−0.843029	+	0.537868i	$0.819230\pi$
$854$	−16.3445	−	50.3031i	−0.559296	−	1.72134i
$855$	3.65852	+	7.20635i	0.125119	+	0.246452i
$856$	−13.9443	−	10.1311i	−0.476605	−	0.346274i
$857$	−46.8575			−1.60062			−0.800311	−	0.599585i	$-0.795332\pi$
$857$	−46.8575			−1.60062			−0.800311	+	0.599585i	$0.795332\pi$
$858$		0			0
$859$	20.9230			0.713883			0.356942	−	0.934127i	$-0.383820\pi$
$859$	20.9230			0.713883			0.356942	+	0.934127i	$0.383820\pi$
$860$	14.8992	−	20.5070i	0.508058	−	0.699282i
$861$		0			0
$862$	−2.03444	−	6.26137i	−0.0692934	−	0.213263i
$863$	−12.9896	−	17.8786i	−0.442170	−	0.608595i	0.528523	−	0.848919i	$-0.322746\pi$
$863$	−12.9896	−	17.8786i	−0.442170	−	0.608595i	−0.970693	+	0.240325i	$0.922746\pi$
$864$		0			0
$865$	−3.81540	−	11.7426i	−0.129728	−	0.399260i
$866$	−48.4164	−	15.7314i	−1.64526	−	0.534576i
$867$		0			0
$868$	47.3079			1.60573
$869$	−34.0071	+	14.6782i	−1.15361	+	0.497925i
$870$		0			0
$871$	6.58359	−	9.06154i	0.223077	−	0.307038i
$872$	1.25735	−	3.86974i	0.0425794	−	0.131046i
$873$	27.1050	−	8.80695i	0.917365	−	0.298070i
$874$	−0.656435	+	4.10559i	−0.0222042	+	0.138874i
$875$	−6.64590	−	9.14729i	−0.224672	−	0.309235i
$876$		0			0
$877$	10.2140	−	31.4355i	0.344903	−	1.06150i	−0.616733	−	0.787173i	$-0.711544\pi$
$877$	10.2140	−	31.4355i	0.344903	−	1.06150i	0.961636	−	0.274330i	$-0.0884559\pi$
$878$	−80.1591	−	58.2390i	−2.70524	−	1.96547i
$879$		0			0
$880$	7.40983	+	8.42075i	0.249785	+	0.283863i
$881$	−13.4164			−0.452010			−0.226005	−	0.974126i	$-0.572567\pi$
$881$	−13.4164			−0.452010			−0.226005	+	0.974126i	$0.572567\pi$
$882$	20.4976	+	14.8924i	0.690191	+	0.501453i
$883$	−12.3926	+	38.1405i	−0.417045	+	1.28353i	0.493365	+	0.869822i	$0.335767\pi$
$883$	−12.3926	+	38.1405i	−0.417045	+	1.28353i	−0.910409	+	0.413709i	$0.864233\pi$
$884$	70.9618	−	23.0569i	2.38670	−	0.775487i
$885$		0			0
$886$	−26.0816	+	18.9494i	−0.876227	+	0.636616i
$887$	−7.35247	−	22.6286i	−0.246872	−	0.759793i	−0.995323	−	0.0966034i	$-0.969202\pi$
$887$	−7.35247	−	22.6286i	−0.246872	−	0.759793i	0.748451	−	0.663190i	$-0.230798\pi$
$888$		0			0
$889$	3.45106	−	4.74998i	0.115745	−	0.159309i
$890$		−	9.06154i		−	0.303743i
$891$	29.1246	+	6.53888i	0.975711	+	0.219061i
$892$		−	89.9849i		−	3.01292i
$893$	−12.2904	+	1.92814i	−0.411283	+	0.0645227i
$894$		0			0
$895$	13.8042	−	4.48527i	0.461425	−	0.149926i
$896$	−18.7291	−	25.7784i	−0.625695	−	0.861195i
$897$		0			0
$898$	−59.0689	+	19.1926i	−1.97115	+	0.640467i
$899$	10.6525	+	3.46120i	0.355280	+	0.115437i
$900$	47.4787	+	34.4953i	1.58262	+	1.14984i
$901$	−7.90913			−0.263491
$902$	5.32624	+	56.9169i	0.177344	+	1.89513i
$903$		0			0
$904$	−62.3607	+	85.8321i	−2.07409	+	2.85473i
$905$	11.1679	+	3.62866i	0.371233	+	0.120621i
$906$		0			0
$907$	−18.5735	−	25.5642i	−0.616723	−	0.848846i	0.380386	−	0.924828i	$-0.375791\pi$
$907$	−18.5735	−	25.5642i	−0.616723	−	0.848846i	−0.997109	+	0.0759814i	$0.975791\pi$
$908$	1.54336	−	1.12132i	0.0512183	−	0.0372122i
$909$	−13.7188	+	4.45752i	−0.455025	+	0.147847i
$910$	−13.9443	−	4.53077i	−0.462248	−	0.150194i
$911$	−2.94756	+	4.05697i	−0.0976570	+	0.134413i	−0.855049	−	0.518547i	$-0.826473\pi$
$911$	−2.94756	+	4.05697i	−0.0976570	+	0.134413i	0.757392	+	0.652960i	$0.226473\pi$
$912$		0			0
$913$	3.31559	−	0.310271i	0.109730	−	0.0102685i
$914$		−	70.7203i		−	2.33922i
$915$		0			0
$916$	28.7705	−	88.5465i	0.950604	−	2.92566i
$917$	5.06231	+	15.5802i	0.167172	+	0.514503i
$918$		0			0
$919$	−6.77051	−	9.31881i	−0.223339	−	0.307399i	0.682613	−	0.730780i	$-0.260843\pi$
$919$	−6.77051	−	9.31881i	−0.223339	−	0.307399i	−0.905952	+	0.423381i	$0.860843\pi$
$920$	−0.407343	−	1.25367i	−0.0134297	−	0.0413323i
$921$		0			0
$922$	−22.1802	+	30.5284i	−0.730464	+	1.00540i
$923$			65.5699i			2.15826i
$924$		0			0
$925$			16.7573i			0.550976i
$926$	31.0760	+	22.5780i	1.02122	+	0.741960i
$927$	37.4582	+	12.1709i	1.23029	+	0.399745i
$928$	1.47214	+	4.53077i	0.0483252	+	0.148730i
$929$	−17.9271	+	13.0248i	−0.588167	+	0.427329i	−0.841659	−	0.540009i	$-0.818421\pi$
$929$	−17.9271	+	13.0248i	−0.588167	+	0.427329i	0.253492	+	0.967338i	$0.418421\pi$
$930$		0			0
$931$	13.1251	+	6.71182i	0.430157	+	0.219971i
$932$	−76.2041	−	24.7602i	−2.49615	−	0.811048i
$933$		0			0
$934$	−32.4106			−1.06051
$935$	−5.42705	+	4.77553i	−0.177484	+	0.156176i
$936$	83.6656			2.73470
$937$	14.1074	−	19.4172i	0.460868	−	0.634331i	−0.513820	−	0.857898i	$-0.671770\pi$
$937$	14.1074	−	19.4172i	0.460868	−	0.634331i	0.974689	+	0.223567i	$0.0717702\pi$
$938$	−3.29180	+	10.1311i	−0.107481	+	0.330792i
$939$		0			0
$940$	6.04508	−	4.39201i	0.197169	−	0.143252i
$941$	15.5728	−	11.3143i	0.507658	−	0.368835i	−0.304276	−	0.952584i	$-0.598415\pi$
$941$	15.5728	−	11.3143i	0.507658	−	0.368835i	0.811935	+	0.583749i	$0.198415\pi$
$942$		0			0
$943$	0.814685	−	2.50734i	0.0265298	−	0.0816503i
$944$	30.5561	−	42.0568i	0.994515	−	1.36883i
$945$		0			0
$946$	−31.7781	−	73.6247i	−1.03319	−	2.39374i
$947$	7.67376			0.249364			0.124682	−	0.992197i	$-0.460209\pi$
$947$	7.67376			0.249364			0.124682	+	0.992197i	$0.460209\pi$
$948$		0			0
$949$	−22.3357	−	7.25732i	−0.725049	−	0.235583i
$950$	44.7554	+	22.8867i	1.45206	+	0.742544i
$951$		0			0
$952$	−30.3043	+	22.0174i	−0.982168	+	0.713587i
$953$	−9.76367	−	30.0495i	−0.316276	−	0.973399i	−0.975226	−	0.221212i	$-0.928999\pi$
$953$	−9.76367	−	30.0495i	−0.316276	−	0.973399i	0.658949	−	0.752187i	$-0.271001\pi$
$954$	−15.9787	−	5.19180i	−0.517330	−	0.168091i
$955$	−10.1631	−	7.38394i	−0.328871	−	0.238939i
$956$			28.7032i			0.928328i
$957$		0			0
$958$			95.6926i			3.09169i
$959$	−19.9615	+	27.4746i	−0.644590	+	0.887202i
$960$		0			0
$961$	−1.07295	−	3.30220i	−0.0346113	−	0.106523i
$962$	26.6015	+	36.6138i	0.857666	+	1.18048i
$963$	7.49164	−	5.44299i	0.241415	−	0.175398i
$964$	25.1973	+	77.5493i	0.811550	+	2.49769i
$965$	−0.364338	+	1.12132i	−0.0117285	+	0.0360965i
$966$		0			0
$967$			19.6417i			0.631634i	0.948820	+	0.315817i	$0.102278\pi$
$967$			19.6417i			0.631634i	−0.948820	+	0.315817i	$0.897722\pi$
$968$	60.3569	−	11.3961i	1.93994	−	0.366284i
$969$		0			0
$970$	−8.61803	+	11.8617i	−0.276708	+	0.380856i
$971$	−5.08043	−	1.65073i	−0.163039	−	0.0529745i	0.226360	−	0.974044i	$-0.427317\pi$
$971$	−5.08043	−	1.65073i	−0.163039	−	0.0529745i	−0.389399	+	0.921069i	$0.627317\pi$
$972$		0			0
$973$	−4.04508	+	2.93893i	−0.129679	+	0.0942177i
$974$	33.2148	+	45.7162i	1.06427	+	1.46484i
$975$		0			0
$976$	−57.9508	−	18.8294i	−1.85496	−	0.602714i
$977$	16.4406	−	22.6286i	0.525982	−	0.723952i	−0.460529	−	0.887645i	$-0.652340\pi$
$977$	16.4406	−	22.6286i	0.525982	−	0.723952i	0.986511	+	0.163692i	$0.0523404\pi$
$978$		0			0
$979$	−16.7518	−	9.92826i	−0.535390	−	0.317309i
$980$	−8.85410			−0.282834
$981$	1.76854	+	1.28492i	0.0564650	+	0.0410242i
$982$	−47.5596	−	15.4531i	−1.51769	−	0.493127i
$983$	21.0176	−	6.82902i	0.670356	−	0.217812i	0.0459877	−	0.998942i	$-0.485356\pi$
$983$	21.0176	−	6.82902i	0.670356	−	0.217812i	0.624368	+	0.781130i	$0.285356\pi$
$984$		0			0
$985$	−6.18034	−	8.50651i	−0.196922	−	0.271040i
$986$	−15.9787	+	5.19180i	−0.508866	+	0.165341i
$987$		0			0
$988$	91.1057	−	14.2928i	2.89846	−	0.454714i
$989$			3.69822i			0.117597i
$990$	−14.0990	+	6.08545i	−0.448096	+	0.193408i
$991$		−	17.6139i		−	0.559524i	−0.960069	−	0.279762i	$-0.909744\pi$
$991$		−	17.6139i		−	0.559524i	0.960069	−	0.279762i	$-0.0902555\pi$
$992$	8.61803	−	11.8617i	0.273623	−	0.376610i
$993$		0			0
$994$	−19.2705	−	59.3085i	−0.611223	−	1.88115i
$995$	2.92705	−	2.12663i	0.0927938	−	0.0674186i
$996$		0			0
$997$	31.4058	−	10.2044i	0.994631	−	0.323175i	0.233913	−	0.972258i	$-0.424847\pi$
$997$	31.4058	−	10.2044i	0.994631	−	0.323175i	0.760718	+	0.649083i	$0.224847\pi$
$998$	23.0378	−	70.9032i	0.729250	−	2.24440i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	209.2.k.b.18.2	yes	8
11.8	odd	10	inner	209.2.k.b.151.1	yes	8
19.18	odd	2	inner	209.2.k.b.18.1	✓	8
209.151	even	10	inner	209.2.k.b.151.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.k.b.18.1	✓	8	19.18	odd	2	inner
209.2.k.b.18.2	yes	8	1.1	even	1	trivial
209.2.k.b.151.1	yes	8	11.8	odd	10	inner
209.2.k.b.151.2	yes	8	209.151	even	10	inner

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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.02029 + 1.46782i) q^{2} +(1.30902 + 4.02874i) q^{4} +(0.500000 - 0.363271i) q^{5} +(-1.80902 + 0.587785i) q^{7} +(-1.72553 + 5.31064i) q^{8} +(-2.42705 - 1.76336i) q^{9} +1.54336 q^{10} +(1.69098 - 2.85317i) q^{11} +(4.04057 + 2.93565i) q^{13} +(-4.51750 - 1.46782i) q^{14} +(-4.42705 + 3.21644i) q^{16} +(-2.07295 - 2.85317i) q^{17} +(-2.31504 - 7.12497i) q^{18} +(-1.97320 - 3.88671i) q^{19} +(2.11803 + 1.53884i) q^{20} +(7.60422 - 3.28216i) q^{22} -0.381966 q^{23} +(-1.42705 + 4.39201i) q^{25} +(3.85410 + 11.8617i) q^{26} +(-4.73607 - 6.51864i) q^{28} +(-0.589512 - 1.81433i) q^{29} +(-3.45106 + 4.74998i) q^{31} -2.49721 q^{32} -8.80695i q^{34} +(-0.690983 + 0.951057i) q^{35} +(3.92705 - 12.0862i) q^{36} +(3.45106 - 1.12132i) q^{37} +(1.71857 - 10.7486i) q^{38} +(1.06644 + 3.28216i) q^{40} +(-2.13287 + 6.56431i) q^{41} -9.68208i q^{43} +(13.7082 + 3.07768i) q^{44} -1.85410 q^{45} +(-0.771681 - 0.560659i) q^{46} +(0.881966 - 2.71441i) q^{47} +(-2.73607 + 1.98787i) q^{49} +(-9.32975 + 6.77846i) q^{50} +(-6.53779 + 20.1212i) q^{52} +(1.31819 - 1.81433i) q^{53} +(-0.190983 - 2.04087i) q^{55} -10.6213i q^{56} +(1.47214 - 4.53077i) q^{58} +(-9.03500 + 2.93565i) q^{59} +(6.54508 + 9.00854i) q^{61} +(-13.9443 + 4.53077i) q^{62} +(5.42705 + 1.76336i) q^{63} +(3.80902 + 2.76741i) q^{64} +3.08672 q^{65} -2.24264i q^{67} +(8.78115 - 12.0862i) q^{68} +(-2.79197 + 0.907165i) q^{70} +(7.71681 + 10.6213i) q^{71} +(13.5525 - 9.84647i) q^{72} +(-4.47214 + 1.45309i) q^{73} +(8.61803 + 2.80017i) q^{74} +(13.0756 - 13.0373i) q^{76} +(-1.38197 + 6.15537i) q^{77} +(-9.03500 - 6.56431i) q^{79} +(-1.04508 + 3.21644i) q^{80} +(2.78115 + 8.55951i) q^{81} +(-13.9443 + 10.1311i) q^{82} +(0.590170 + 0.812299i) q^{83} +(-2.07295 - 0.673542i) q^{85} +(14.2116 - 19.5606i) q^{86} +(12.2343 + 13.9034i) q^{88} -5.87130i q^{89} +(-3.74582 - 2.72150i) q^{90} +(-9.03500 - 2.93565i) q^{91} +(-0.500000 - 1.53884i) q^{92} +(5.76611 - 4.18932i) q^{94} +(-2.39853 - 1.22655i) q^{95} +(-5.58394 + 7.68563i) q^{97} -8.44549 q^{98} +(-9.13525 + 3.94298i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{4} + 4 q^{5} - 10 q^{7} - 6 q^{9} + 18 q^{11} - 22 q^{16} - 30 q^{17} - 10 q^{19} + 8 q^{20} - 12 q^{23} + 2 q^{25} + 4 q^{26} - 20 q^{28} - 10 q^{35} + 18 q^{36} + 32 q^{38} + 56 q^{44} + 12 q^{45}+ \cdots - 6 q^{99}+O(q^{100}) \) 8 * q + 6 * q^4 + 4 * q^5 - 10 * q^7 - 6 * q^9 + 18 * q^11 - 22 * q^16 - 30 * q^17 - 10 * q^19 + 8 * q^20 - 12 * q^23 + 2 * q^25 + 4 * q^26 - 20 * q^28 - 10 * q^35 + 18 * q^36 + 32 * q^38 + 56 * q^44 + 12 * q^45 + 16 * q^47 - 4 * q^49 - 6 * q^55 - 24 * q^58 + 30 * q^61 - 40 * q^62 + 30 * q^63 + 26 * q^64 + 30 * q^68 + 60 * q^74 - 20 * q^77 + 14 * q^80 - 18 * q^81 - 40 * q^82 - 40 * q^83 - 30 * q^85 - 4 * q^92 - 10 * q^95 - 6 * q^99

Introduction

L-functions

Modular forms

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Database

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