LMFDB - Embedded newform 198.3.k.a.71.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,3,Mod(53,198)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6]))

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

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

chi := DirichletCharacter("198.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	198.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:	$5.39510923433$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 14 x^{14} + 255 x^{12} + 3946 x^{10} + 33929 x^{8} + 477466 x^{6} + 3733455 x^{4} + \cdots + 214358881 $ x^16 + 14x^14 + 255x^12 + 3946x^10 + 33929x^8 + 477466x^6 + 3733455x^4 + 24801854*x^2 + 214358881
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			71.2
Root			$2.91668 - 1.57891i$ of defining polynomial
Character	$\chi$	$=$	198.71
Dual form			198.3.k.a.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34500 + 0.437016i) q^{2} +(1.61803 - 1.17557i) q^{4} +(9.21189 + 2.99313i) q^{5} +(-7.03999 + 5.11485i) q^{7} +(-1.66251 + 2.28825i) q^{8} +O(q^{10})$	\(q+(-1.34500 + 0.437016i) q^{2} +(1.61803 - 1.17557i) q^{4} +(9.21189 + 2.99313i) q^{5} +(-7.03999 + 5.11485i) q^{7} +(-1.66251 + 2.28825i) q^{8} -13.6980 q^{10} +(10.7810 - 2.18423i) q^{11} +(0.689780 + 2.12293i) q^{13} +(7.23349 - 9.95605i) q^{14} +(1.23607 - 3.80423i) q^{16} +(-6.65427 - 2.16210i) q^{17} +(-5.59212 - 4.06291i) q^{19} +(18.4238 - 5.98625i) q^{20} +(-13.5458 + 7.64924i) q^{22} +34.1701i q^{23} +(55.6748 + 40.4501i) q^{25} +(-1.85550 - 2.55388i) q^{26} +(-5.37807 + 16.5520i) q^{28} +(28.6596 + 39.4465i) q^{29} +(-2.44696 - 7.53097i) q^{31} +5.65685i q^{32} +9.89484 q^{34} +(-80.1610 + 26.0459i) q^{35} +(17.8796 - 12.9903i) q^{37} +(9.29694 + 3.02076i) q^{38} +(-22.1639 + 16.1030i) q^{40} +(37.8658 - 52.1177i) q^{41} -60.7684 q^{43} +(14.8762 - 16.2079i) q^{44} +(-14.9329 - 45.9587i) q^{46} +(31.6769 - 43.5995i) q^{47} +(8.25791 - 25.4152i) q^{49} +(-92.5597 - 30.0745i) q^{50} +(3.61174 + 2.62408i) q^{52} +(-35.8803 + 11.6582i) q^{53} +(105.851 + 12.1479i) q^{55} -24.6127i q^{56} +(-55.7858 - 40.5307i) q^{58} +(-27.4413 - 37.7697i) q^{59} +(7.79133 - 23.9792i) q^{61} +(6.58231 + 9.05977i) q^{62} +(-2.47214 - 7.60845i) q^{64} +21.6208i q^{65} -15.8370 q^{67} +(-13.3085 + 4.32420i) q^{68} +(96.4339 - 70.0633i) q^{70} +(-28.4629 - 9.24816i) q^{71} +(26.2732 - 19.0886i) q^{73} +(-18.3710 + 25.2855i) q^{74} -13.8245 q^{76} +(-64.7259 + 70.5200i) q^{77} +(-7.25774 - 22.3370i) q^{79} +(22.7731 - 31.3444i) q^{80} +(-28.1530 + 86.6461i) q^{82} +(42.5183 + 13.8150i) q^{83} +(-54.8270 - 39.8341i) q^{85} +(81.7333 - 26.5568i) q^{86} +(-12.9254 + 28.3008i) q^{88} -118.461i q^{89} +(-15.7145 - 11.4172i) q^{91} +(40.1694 + 55.2884i) q^{92} +(-23.5517 + 72.4845i) q^{94} +(-39.3532 - 54.1650i) q^{95} +(-48.5218 - 149.335i) q^{97} +37.7923i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 24 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 - 24 * q^7	$ 16 q + 8 q^{4} - 24 q^{7} - 24 q^{10} + 48 q^{13} - 16 q^{16} - 36 q^{19} + 48 q^{22} + 192 q^{25} - 32 q^{28} + 4 q^{31} - 112 q^{34} + 76 q^{37} - 72 q^{40} - 440 q^{43} - 36 q^{46} - 168 q^{49} + 24 q^{52} + 836 q^{55} - 96 q^{58} + 40 q^{61} + 32 q^{64} - 552 q^{67} + 516 q^{70} - 316 q^{73} - 288 q^{76} + 604 q^{79} - 36 q^{82} + 36 q^{85} - 16 q^{88} - 352 q^{91} - 220 q^{94} + 156 q^{97}+O(q^{100}) $ 16 * q + 8 * q^4 - 24 * q^7 - 24 * q^10 + 48 * q^13 - 16 * q^16 - 36 * q^19 + 48 * q^22 + 192 * q^25 - 32 * q^28 + 4 * q^31 - 112 * q^34 + 76 * q^37 - 72 * q^40 - 440 * q^43 - 36 * q^46 - 168 * q^49 + 24 * q^52 + 836 * q^55 - 96 * q^58 + 40 * q^61 + 32 * q^64 - 552 * q^67 + 516 * q^70 - 316 * q^73 - 288 * q^76 + 604 * q^79 - 36 * q^82 + 36 * q^85 - 16 * q^88 - 352 * q^91 - 220 * q^94 + 156 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.34500	+	0.437016i	−0.672499	+	0.218508i
$2$	−1.34500	+	0.437016i	−0.672499	+	0.218508i
$3$		0			0
$3$		0			0
$4$	1.61803	−	1.17557i	0.404508	−	0.293893i
$5$	9.21189	+	2.99313i	1.84238	+	0.598625i	0.998024	+	0.0628415i	$0.0200163\pi$
$5$	9.21189	+	2.99313i	1.84238	+	0.598625i	0.844355	+	0.535784i	$0.179984\pi$
$6$		0			0
$7$	−7.03999	+	5.11485i	−1.00571	+	0.730693i	−0.963306	−	0.268407i	$-0.913503\pi$
$7$	−7.03999	+	5.11485i	−1.00571	+	0.730693i	−0.0424073	+	0.999100i	$0.513503\pi$
$8$	−1.66251	+	2.28825i	−0.207813	+	0.286031i
$9$		0			0
$10$	−13.6980			−1.36980
$11$	10.7810	−	2.18423i	0.980087	−	0.198566i
$11$	10.7810	−	2.18423i	0.980087	−	0.198566i
$12$		0			0
$13$	0.689780	+	2.12293i	0.0530600	+	0.163302i	0.974075	−	0.226225i	$-0.0726385\pi$
$13$	0.689780	+	2.12293i	0.0530600	+	0.163302i	−0.921015	+	0.389527i	$0.872638\pi$
$14$	7.23349	−	9.95605i	0.516678	−	0.711146i
$15$		0			0
$16$	1.23607	−	3.80423i	0.0772542	−	0.237764i
$17$	−6.65427	−	2.16210i	−0.391427	−	0.127182i	0.106689	−	0.994292i	$-0.465975\pi$
$17$	−6.65427	−	2.16210i	−0.391427	−	0.127182i	−0.498117	+	0.867110i	$0.665975\pi$
$18$		0			0
$19$	−5.59212	−	4.06291i	−0.294322	−	0.213837i	0.430818	−	0.902439i	$-0.358225\pi$
$19$	−5.59212	−	4.06291i	−0.294322	−	0.213837i	−0.725140	+	0.688601i	$0.758225\pi$
$20$	18.4238	−	5.98625i	0.921189	−	0.299313i
$21$		0			0
$22$	−13.5458	+	7.64924i	−0.615719	+	0.347693i
$23$			34.1701i			1.48566i	0.669482	+	0.742828i	$0.266516\pi$
$23$			34.1701i			1.48566i	−0.669482	+	0.742828i	$0.733484\pi$
$24$		0			0
$25$	55.6748	+	40.4501i	2.22699	+	1.61800i
$26$	−1.85550	−	2.55388i	−0.0713656	−	0.0982263i
$27$		0			0
$28$	−5.37807	+	16.5520i	−0.192074	+	0.591143i
$29$	28.6596	+	39.4465i	0.988260	+	1.36022i	0.932258	+	0.361793i	$0.117835\pi$
$29$	28.6596	+	39.4465i	0.988260	+	1.36022i	0.0560020	+	0.998431i	$0.482165\pi$
$30$		0			0
$31$	−2.44696	−	7.53097i	−0.0789342	−	0.242935i	0.903801	−	0.427954i	$-0.140765\pi$
$31$	−2.44696	−	7.53097i	−0.0789342	−	0.242935i	−0.982735	+	0.185019i	$0.940765\pi$
$32$			5.65685i			0.176777i
$33$		0			0
$34$	9.89484			0.291025
$35$	−80.1610	+	26.0459i	−2.29032	+	0.744169i
$36$		0			0
$37$	17.8796	−	12.9903i	0.483231	−	0.351088i	−0.319344	−	0.947639i	$-0.603463\pi$
$37$	17.8796	−	12.9903i	0.483231	−	0.351088i	0.802575	+	0.596551i	$0.203463\pi$
$38$	9.29694	+	3.02076i	0.244656	+	0.0794936i
$39$		0			0
$40$	−22.1639	+	16.1030i	−0.554096	+	0.402575i
$41$	37.8658	−	52.1177i	0.923555	−	1.27116i	−0.0387660	−	0.999248i	$-0.512343\pi$
$41$	37.8658	−	52.1177i	0.923555	−	1.27116i	0.962321	−	0.271916i	$-0.0876573\pi$
$42$		0			0
$43$	−60.7684			−1.41322			−0.706609	−	0.707604i	$-0.749776\pi$
$43$	−60.7684			−1.41322			−0.706609	+	0.707604i	$0.749776\pi$
$44$	14.8762	−	16.2079i	0.338097	−	0.368362i
$45$		0			0
$46$	−14.9329	−	45.9587i	−0.324628	−	0.999102i
$47$	31.6769	−	43.5995i	0.673977	−	0.927649i	−0.325865	−	0.945416i	$-0.605656\pi$
$47$	31.6769	−	43.5995i	0.673977	−	0.927649i	0.999842	+	0.0177667i	$0.00565563\pi$
$48$		0			0
$49$	8.25791	−	25.4152i	0.168529	−	0.518679i
$50$	−92.5597	−	30.0745i	−1.85119	−	0.601490i
$51$		0			0
$52$	3.61174	+	2.62408i	0.0694565	+	0.0504631i
$53$	−35.8803	+	11.6582i	−0.676988	+	0.219967i	−0.627276	−	0.778797i	$-0.715830\pi$
$53$	−35.8803	+	11.6582i	−0.676988	+	0.219967i	−0.0497115	+	0.998764i	$0.515830\pi$
$54$		0			0
$55$	105.851	+	12.1479i	1.92456	+	0.220871i
$56$		−	24.6127i		−	0.439513i
$57$		0			0
$58$	−55.7858	−	40.5307i	−0.961823	−	0.698806i
$59$	−27.4413	−	37.7697i	−0.465107	−	0.640164i	0.510451	−	0.859907i	$-0.329478\pi$
$59$	−27.4413	−	37.7697i	−0.465107	−	0.640164i	−0.975558	+	0.219742i	$0.929478\pi$
$60$		0			0
$61$	7.79133	−	23.9792i	0.127727	−	0.393102i	−0.866661	−	0.498897i	$-0.833739\pi$
$61$	7.79133	−	23.9792i	0.127727	−	0.393102i	0.994388	+	0.105795i	$0.0337386\pi$
$62$	6.58231	+	9.05977i	0.106166	+	0.146125i
$63$		0			0
$64$	−2.47214	−	7.60845i	−0.0386271	−	0.118882i
$65$			21.6208i			0.332627i
$66$		0			0
$67$	−15.8370			−0.236373			−0.118187	−	0.992991i	$-0.537708\pi$
$67$	−15.8370			−0.236373			−0.118187	+	0.992991i	$0.537708\pi$
$68$	−13.3085	+	4.32420i	−0.195714	+	0.0635912i
$69$		0			0
$70$	96.4339	−	70.0633i	1.37763	−	1.00090i
$71$	−28.4629	−	9.24816i	−0.400886	−	0.130256i	0.101633	−	0.994822i	$-0.467593\pi$
$71$	−28.4629	−	9.24816i	−0.400886	−	0.130256i	−0.502519	+	0.864566i	$0.667593\pi$
$72$		0			0
$73$	26.2732	−	19.0886i	0.359907	−	0.261487i	−0.393107	−	0.919493i	$-0.628600\pi$
$73$	26.2732	−	19.0886i	0.359907	−	0.261487i	0.753013	+	0.658005i	$0.228600\pi$
$74$	−18.3710	+	25.2855i	−0.248257	+	0.341696i
$75$		0			0
$76$	−13.8245			−0.181901
$77$	−64.7259	+	70.5200i	−0.840595	+	0.915844i
$78$		0			0
$79$	−7.25774	−	22.3370i	−0.0918701	−	0.282747i	0.894555	−	0.446957i	$-0.147492\pi$
$79$	−7.25774	−	22.3370i	−0.0918701	−	0.282747i	−0.986425	+	0.164210i	$0.947492\pi$
$80$	22.7731	−	31.3444i	0.284663	−	0.391805i
$81$		0			0
$82$	−28.1530	+	86.6461i	−0.343330	+	1.05666i
$83$	42.5183	+	13.8150i	0.512269	+	0.166446i	0.553734	−	0.832694i	$-0.313203\pi$
$83$	42.5183	+	13.8150i	0.512269	+	0.166446i	−0.0414651	+	0.999140i	$0.513203\pi$
$84$		0			0
$85$	−54.8270	−	39.8341i	−0.645023	−	0.468637i
$86$	81.7333	−	26.5568i	0.950387	−	0.308800i
$87$		0			0
$88$	−12.9254	+	28.3008i	−0.146879	+	0.321600i
$89$		−	118.461i		−	1.33102i	−0.746389	−	0.665510i	$-0.768214\pi$
$89$		−	118.461i		−	1.33102i	0.746389	−	0.665510i	$-0.231786\pi$
$90$		0			0
$91$	−15.7145	−	11.4172i	−0.172687	−	0.125464i
$92$	40.1694	+	55.2884i	0.436623	+	0.600961i
$93$		0			0
$94$	−23.5517	+	72.4845i	−0.250550	+	0.771112i
$95$	−39.3532	−	54.1650i	−0.414244	−	0.570158i
$96$		0			0
$97$	−48.5218	−	149.335i	−0.500225	−	1.53954i	−0.808652	−	0.588287i	$-0.799803\pi$
$97$	−48.5218	−	149.335i	−0.500225	−	1.53954i	0.308427	−	0.951248i	$-0.400197\pi$
$98$			37.7923i			0.385635i
$99$		0			0
$100$	137.636			1.37636
$101$	−101.689	+	33.0408i	−1.00682	+	0.327137i	−0.765589	−	0.643330i	$-0.777552\pi$
$101$	−101.689	+	33.0408i	−1.00682	+	0.327137i	−0.241235	+	0.970467i	$0.577552\pi$
$102$		0			0
$103$	−87.7572	+	63.7593i	−0.852012	+	0.619023i	−0.925700	−	0.378259i	$-0.876523\pi$
$103$	−87.7572	+	63.7593i	−0.852012	+	0.619023i	0.0736883	+	0.997281i	$0.476523\pi$
$104$	−6.00454	−	1.95099i	−0.0577360	−	0.0187595i
$105$		0			0
$106$	43.1641	−	31.3606i	0.407209	−	0.295854i
$107$	108.931	−	149.930i	1.01804	−	1.40122i	0.104477	−	0.994527i	$-0.466683\pi$
$107$	108.931	−	149.930i	1.01804	−	1.40122i	0.913566	−	0.406689i	$-0.133317\pi$
$108$		0			0
$109$	−40.2769			−0.369512			−0.184756	−	0.982784i	$-0.559150\pi$
$109$	−40.2769			−0.369512			−0.184756	+	0.982784i	$0.559150\pi$
$110$	−147.678	+	29.9196i	−1.34253	+	0.271996i
$111$		0			0
$112$	10.7561	+	33.1040i	0.0960370	+	0.295572i
$113$	−53.7079	+	73.9225i	−0.475291	+	0.654182i	−0.977591	−	0.210511i	$-0.932487\pi$
$113$	−53.7079	+	73.9225i	−0.475291	+	0.654182i	0.502300	+	0.864693i	$0.332487\pi$
$114$		0			0
$115$	−102.275	+	314.771i	−0.889351	+	2.73714i
$116$	92.7443	+	30.1344i	0.799519	+	0.259780i
$117$		0			0
$118$	53.4144	+	38.8078i	0.452664	+	0.328880i
$119$	57.9048	−	18.8144i	0.486595	−	0.158104i
$120$		0			0
$121$	111.458	−	47.0962i	0.921143	−	0.389225i
$122$			35.6569i			0.292270i
$123$		0			0
$124$	−12.8125	−	9.30879i	−0.103326	−	0.0750709i
$125$	249.466	+	343.361i	1.99573	+	2.74689i
$126$		0			0
$127$	15.1145	−	46.5176i	0.119012	−	0.366281i	−0.873751	−	0.486374i	$-0.838319\pi$
$127$	15.1145	−	46.5176i	0.119012	−	0.366281i	0.992763	+	0.120093i	$0.0383193\pi$
$128$	6.65003	+	9.15298i	0.0519534	+	0.0715077i
$129$		0			0
$130$	−9.44862	−	29.0799i	−0.0726817	−	0.223691i
$131$		−	124.127i		−	0.947535i	−0.880650	−	0.473768i	$-0.842894\pi$
$131$		−	124.127i		−	0.947535i	0.880650	−	0.473768i	$-0.157106\pi$
$132$		0			0
$133$	60.1496			0.452253
$134$	21.3007	−	6.92103i	0.158961	−	0.0516495i
$135$		0			0
$136$	16.0102	−	11.6321i	0.117722	−	0.0855300i
$137$	90.9570	+	29.5537i	0.663920	+	0.215721i	0.621542	−	0.783381i	$-0.286507\pi$
$137$	90.9570	+	29.5537i	0.663920	+	0.215721i	0.0423782	+	0.999102i	$0.486507\pi$
$138$		0			0
$139$	−67.7574	+	49.2286i	−0.487463	+	0.354163i	−0.804208	−	0.594348i	$-0.797410\pi$
$139$	−67.7574	+	49.2286i	−0.487463	+	0.354163i	0.316745	+	0.948511i	$0.397410\pi$
$140$	−99.0845	+	136.378i	−0.707746	+	0.974129i
$141$		0			0
$142$	42.3241			0.298057
$143$	12.0735	+	21.3805i	0.0844297	+	0.149514i
$144$		0			0
$145$	145.940	+	449.159i	1.00649	+	3.09764i
$146$	−26.9953	+	37.1559i	−0.184900	+	0.254492i
$147$		0			0
$148$	13.6588	−	42.0373i	0.0922889	−	0.284036i
$149$	121.048	+	39.3307i	0.812399	+	0.263965i	0.685614	−	0.727966i	$-0.259534\pi$
$149$	121.048	+	39.3307i	0.812399	+	0.263965i	0.126786	+	0.991930i	$0.459534\pi$
$150$		0			0
$151$	−5.98602	−	4.34910i	−0.0396425	−	0.0288020i	0.567788	−	0.823175i	$-0.307800\pi$
$151$	−5.98602	−	4.34910i	−0.0396425	−	0.0288020i	−0.607430	+	0.794373i	$0.707800\pi$
$152$	18.5939	−	6.04152i	0.122328	−	0.0397468i
$153$		0			0
$154$	56.2377	−	123.135i	0.365180	−	0.799581i
$155$		−	76.6986i		−	0.494830i
$156$		0			0
$157$	−231.025	−	167.850i	−1.47150	−	1.06911i	−0.980176	−	0.198130i	$-0.936513\pi$
$157$	−231.025	−	167.850i	−1.47150	−	1.06911i	−0.491324	−	0.870977i	$-0.663487\pi$
$158$	19.5233	+	26.8715i	0.123565	+	0.170073i
$159$		0			0
$160$	−16.9317	+	52.1103i	−0.105823	+	0.325690i
$161$	−174.775	−	240.557i	−1.08556	−	1.49414i
$162$		0			0
$163$	−63.9883	−	196.936i	−0.392566	−	1.20819i	−0.930841	−	0.365425i	$-0.880924\pi$
$163$	−63.9883	−	196.936i	−0.392566	−	1.20819i	0.538275	−	0.842769i	$-0.319076\pi$
$164$		−	128.842i		−	0.785623i
$165$		0			0
$166$	−63.2244			−0.380870
$167$	79.8741	−	25.9527i	0.478288	−	0.155405i	−0.0599443	−	0.998202i	$-0.519092\pi$
$167$	79.8741	−	25.9527i	0.478288	−	0.155405i	0.538232	+	0.842797i	$0.319092\pi$
$168$		0			0
$169$	132.693	−	96.4070i	0.785165	−	0.570456i
$170$	91.1502	+	29.6165i	0.536178	+	0.174215i
$171$		0			0
$172$	−98.3253	+	71.4375i	−0.571659	+	0.415334i
$173$	60.2667	−	82.9500i	0.348362	−	0.479480i	−0.598498	−	0.801124i	$-0.704236\pi$
$173$	60.2667	−	82.9500i	0.348362	−	0.479480i	0.946860	+	0.321645i	$0.104236\pi$
$174$		0			0
$175$	−598.846			−3.42198
$176$	5.01670	−	43.7131i	0.0285040	−	0.248370i
$177$		0			0
$178$	51.7692	+	159.329i	0.290838	+	0.895108i
$179$	−68.3325	+	94.0516i	−0.381746	+	0.525428i	−0.956046	−	0.293217i	$-0.905274\pi$
$179$	−68.3325	+	94.0516i	−0.381746	+	0.525428i	0.574300	+	0.818645i	$0.305274\pi$
$180$		0			0
$181$	39.4164	−	121.311i	0.217770	−	0.670227i	−0.781175	−	0.624312i	$-0.785380\pi$
$181$	39.4164	−	121.311i	0.217770	−	0.670227i	0.998945	−	0.0459154i	$-0.0146205\pi$
$182$	26.1255	+	8.48868i	0.143547	+	0.0466411i
$183$		0			0
$184$	−78.1896	−	56.8080i	−0.424943	−	0.308739i
$185$	203.586	−	66.1491i	1.10046	−	0.357563i
$186$		0			0
$187$	−76.4619	−	8.77510i	−0.408887	−	0.0469256i
$188$		−	107.784i		−	0.573319i
$189$		0			0
$190$	76.6009	+	55.6538i	0.403163	+	0.292915i
$191$	105.281	+	144.907i	0.551209	+	0.758674i	0.990176	−	0.139829i	$-0.0446553\pi$
$191$	105.281	+	144.907i	0.551209	+	0.758674i	−0.438966	+	0.898503i	$0.644655\pi$
$192$		0			0
$193$	−50.6234	+	155.803i	−0.262297	+	0.807268i	0.730007	+	0.683440i	$0.239517\pi$
$193$	−50.6234	+	155.803i	−0.262297	+	0.807268i	−0.992304	+	0.123828i	$0.960483\pi$
$194$	130.523	+	179.650i	0.672801	+	0.926032i
$195$		0			0
$196$	−16.5158	−	50.8305i	−0.0842644	−	0.259339i
$197$			148.625i			0.754440i	0.926124	+	0.377220i	$0.123120\pi$
$197$			148.625i			0.754440i	−0.926124	+	0.377220i	$0.876880\pi$
$198$		0			0
$199$	119.556			0.600784			0.300392	−	0.953816i	$-0.402883\pi$
$199$	119.556			0.600784			0.300392	+	0.953816i	$0.402883\pi$
$200$	−185.119	+	60.1490i	−0.925597	+	0.300745i
$201$		0			0
$202$	122.332	−	88.8797i	0.605606	−	0.439998i
$203$	−403.526	−	131.114i	−1.98781	−	0.645879i
$204$		0			0
$205$	504.810	−	366.766i	2.46249	−	1.78910i
$206$	90.1693	−	124.107i	0.437715	−	0.602463i
$207$		0			0
$208$	8.92870			0.0429265
$209$	−69.1627	−	31.5876i	−0.330922	−	0.151137i
$210$		0			0
$211$	−47.6408	−	146.623i	−0.225786	−	0.694897i	−0.998211	−	0.0597914i	$-0.980956\pi$
$211$	−47.6408	−	146.623i	−0.225786	−	0.694897i	0.772425	−	0.635106i	$-0.219044\pi$
$212$	−44.3505	+	61.0433i	−0.209201	+	0.287940i
$213$		0			0
$214$	−80.9895	+	249.260i	−0.378456	+	1.16477i
$215$	−559.792	−	181.887i	−2.60368	−	0.845988i
$216$		0			0
$217$	55.7464	+	40.5021i	0.256896	+	0.186646i
$218$	54.1723	−	17.6016i	0.248497	−	0.0807414i
$219$		0			0
$220$	185.551	−	104.779i	0.843413	−	0.476270i
$221$		−	15.6179i		−	0.0706692i
$222$		0			0
$223$	269.090	+	195.506i	1.20668	+	0.876707i	0.994925	−	0.100615i	$-0.0320812\pi$
$223$	269.090	+	195.506i	1.20668	+	0.876707i	0.211758	+	0.977322i	$0.432081\pi$
$224$	−28.9340	−	39.8242i	−0.129170	−	0.177787i
$225$		0			0
$226$	39.9316	−	122.897i	0.176688	−	0.543791i
$227$	134.012	+	184.451i	0.590360	+	0.812561i	0.994783	−	0.102011i	$-0.0325276\pi$
$227$	134.012	+	184.451i	0.590360	+	0.812561i	−0.404423	+	0.914572i	$0.632528\pi$
$228$		0			0
$229$	0.332937	+	1.02467i	0.00145387	+	0.00447456i	0.951781	−	0.306779i	$-0.0992512\pi$
$229$	0.332937	+	1.02467i	0.00145387	+	0.00447456i	−0.950327	+	0.311253i	$0.899251\pi$
$230$		−	468.062i		−	2.03505i
$231$		0			0
$232$	−137.910			−0.594440
$233$	−228.288	+	74.1751i	−0.979775	+	0.318348i	−0.754756	−	0.656006i	$-0.772245\pi$
$233$	−228.288	+	74.1751i	−0.979775	+	0.318348i	−0.225019	+	0.974354i	$0.572245\pi$
$234$		0			0
$235$	422.303	−	306.821i	1.79703	−	1.30562i
$236$	−88.8019	−	28.8535i	−0.376279	−	0.122260i
$237$		0			0
$238$	−69.6596	+	50.6107i	−0.292687	+	0.212650i
$239$	−119.235	+	164.113i	−0.498892	+	0.686665i	−0.981997	−	0.188897i	$-0.939509\pi$
$239$	−119.235	+	164.113i	−0.498892	+	0.686665i	0.483105	+	0.875562i	$0.339509\pi$
$240$		0			0
$241$	162.375			0.673753			0.336877	−	0.941549i	$-0.390629\pi$
$241$	162.375			0.673753			0.336877	+	0.941549i	$0.390629\pi$
$242$	−129.329	+	112.053i	−0.534418	+	0.463030i
$243$		0			0
$244$	−15.5827	−	47.9585i	−0.0638633	−	0.196551i
$245$	152.142	−	209.406i	0.620988	−	0.854717i
$246$		0			0
$247$	4.76792	−	14.6742i	0.0193033	−	0.0594096i
$248$	21.3008	+	6.92105i	0.0858904	+	0.0279075i
$249$		0			0
$250$	−485.586	−	352.799i	−1.94234	−	1.41119i
$251$	−202.707	+	65.8634i	−0.807597	+	0.262404i	−0.683580	−	0.729876i	$-0.739578\pi$
$251$	−202.707	+	65.8634i	−0.807597	+	0.262404i	−0.124017	+	0.992280i	$0.539578\pi$
$252$		0			0
$253$	74.6353	+	368.387i	0.295001	+	1.45607i
$254$			69.1714i			0.272328i
$255$		0			0
$256$	−12.9443	−	9.40456i	−0.0505636	−	0.0367366i
$257$	73.9975	+	101.849i	0.287928	+	0.396299i	0.928340	−	0.371733i	$-0.121236\pi$
$257$	73.9975	+	101.849i	0.287928	+	0.396299i	−0.640412	+	0.768032i	$0.721236\pi$
$258$		0			0
$259$	−59.4286	+	182.903i	−0.229454	+	0.706187i
$260$	25.4167	+	34.9831i	0.0977567	+	0.134550i
$261$		0			0
$262$	54.2455	+	166.951i	0.207044	+	0.637216i
$263$		−	329.312i		−	1.25214i	−0.779769	−	0.626068i	$-0.784663\pi$
$263$		−	329.312i		−	1.25214i	0.779769	−	0.626068i	$-0.215337\pi$
$264$		0			0
$265$	−365.420			−1.37895
$266$	−80.9011	+	26.2864i	−0.304139	+	0.0988209i
$267$		0			0
$268$	−25.6248	+	18.6175i	−0.0956151	+	0.0694684i
$269$	−68.5332	−	22.2678i	−0.254770	−	0.0827799i	0.178847	−	0.983877i	$-0.442763\pi$
$269$	−68.5332	−	22.2678i	−0.254770	−	0.0827799i	−0.433618	+	0.901097i	$0.642763\pi$
$270$		0			0
$271$	−183.385	+	133.237i	−0.676698	+	0.491650i	−0.872261	−	0.489041i	$-0.837347\pi$
$271$	−183.385	+	133.237i	−0.676698	+	0.491650i	0.195563	+	0.980691i	$0.437347\pi$
$272$	−16.4503	+	22.6418i	−0.0604789	+	0.0832420i
$273$		0			0
$274$	−135.252			−0.493622
$275$	688.580	+	314.484i	2.50393	+	1.14358i
$276$		0			0
$277$	25.7314	+	79.1932i	0.0928932	+	0.285896i	0.986699	−	0.162559i	$-0.0519746\pi$
$277$	25.7314	+	79.1932i	0.0928932	+	0.285896i	−0.893806	+	0.448454i	$0.851975\pi$
$278$	69.6198	−	95.8234i	0.250431	−	0.344688i
$279$		0			0
$280$	73.6689	−	226.730i	0.263103	−	0.809749i
$281$	−183.304	−	59.5592i	−0.652329	−	0.211955i	−0.0358882	−	0.999356i	$-0.511426\pi$
$281$	−183.304	−	59.5592i	−0.652329	−	0.211955i	−0.616441	+	0.787401i	$0.711426\pi$
$282$		0			0
$283$	395.415	+	287.286i	1.39723	+	1.01514i	0.995028	+	0.0995916i	$0.0317536\pi$
$283$	395.415	+	287.286i	1.39723	+	1.01514i	0.402198	+	0.915553i	$0.368246\pi$
$284$	−56.9258	+	18.4963i	−0.200443	+	0.0651279i
$285$		0			0
$286$	−25.5824	−	23.4805i	−0.0894489	−	0.0820995i
$287$			560.586i			1.95326i
$288$		0			0
$289$	−194.201	−	141.096i	−0.671977	−	0.488220i
$290$	−392.579	−	540.339i	−1.35372	−	1.86324i
$291$		0			0
$292$	20.0709	−	61.7719i	0.0687360	−	0.211548i
$293$	−14.9434	−	20.5679i	−0.0510015	−	0.0701976i	0.782755	−	0.622331i	$-0.213814\pi$
$293$	−14.9434	−	20.5679i	−0.0510015	−	0.0701976i	−0.833756	+	0.552133i	$0.813814\pi$
$294$		0			0
$295$	−139.737	−	430.066i	−0.473684	−	1.45785i
$296$			62.5092i			0.211180i
$297$		0			0
$298$	−179.997			−0.604016
$299$	−72.5406	+	23.5699i	−0.242611	+	0.0788290i
$300$		0			0
$301$	427.809	−	310.821i	1.42129	−	1.03263i
$302$	9.95180	+	3.23354i	0.0329530	+	0.0107071i
$303$		0			0
$304$	−22.3685	+	16.2516i	−0.0735805	+	0.0534593i
$305$	143.546	−	197.574i	0.470642	−	0.647783i
$306$		0			0
$307$	−166.206			−0.541388			−0.270694	−	0.962665i	$-0.587253\pi$
$307$	−166.206			−0.541388			−0.270694	+	0.962665i	$0.587253\pi$
$308$	−21.8274	+	190.194i	−0.0708682	+	0.617511i
$309$		0			0
$310$	33.5185	+	103.159i	0.108124	+	0.332772i
$311$	306.115	−	421.331i	0.984292	−	1.35476i	0.0498065	−	0.998759i	$-0.484140\pi$
$311$	306.115	−	421.331i	0.984292	−	1.35476i	0.934485	−	0.356002i	$-0.115860\pi$
$312$		0			0
$313$	−7.14452	+	21.9886i	−0.0228259	+	0.0702510i	−0.961821	−	0.273681i	$-0.911759\pi$
$313$	−7.14452	+	21.9886i	−0.0228259	+	0.0702510i	0.938995	+	0.343932i	$0.111759\pi$
$314$	384.082	+	124.796i	1.22319	+	0.397438i
$315$		0			0
$316$	−38.0020	−	27.6101i	−0.120260	−	0.0873737i
$317$	−59.3225	+	19.2750i	−0.187137	+	0.0608046i	−0.401086	−	0.916040i	$-0.631367\pi$
$317$	−59.3225	+	19.2750i	−0.187137	+	0.0608046i	0.213949	+	0.976845i	$0.431367\pi$
$318$		0			0
$319$	395.138	+	362.672i	1.23868	+	1.13690i
$320$		−	77.4877i		−	0.242149i
$321$		0			0
$322$	340.199	+	247.169i	1.05652	+	0.767606i
$323$	28.4270	+	39.1264i	0.0880093	+	0.121134i
$324$		0			0
$325$	−47.4692	+	146.095i	−0.146059	+	0.449523i
$326$	172.128	+	236.914i	0.528000	+	0.726730i
$327$		0			0
$328$	56.3061	+	173.292i	0.171665	+	0.528330i
$329$			468.963i			1.42542i
$330$		0			0
$331$	356.863			1.07814			0.539068	−	0.842263i	$-0.318777\pi$
$331$	356.863			1.07814			0.539068	+	0.842263i	$0.318777\pi$
$332$	85.0366	−	27.6301i	0.256134	−	0.0832231i
$333$		0			0
$334$	−96.0887	+	69.8125i	−0.287691	+	0.209019i
$335$	−145.889	−	47.4022i	−0.435489	−	0.141499i
$336$		0			0
$337$	−297.610	+	216.226i	−0.883115	+	0.641620i	−0.934074	−	0.357080i	$-0.883772\pi$
$337$	−297.610	+	216.226i	−0.883115	+	0.641620i	0.0509590	+	0.998701i	$0.483772\pi$
$338$	−136.340	+	187.656i	−0.403373	+	0.555195i
$339$		0			0
$340$	−135.540			−0.398646
$341$	−42.8300	−	75.8464i	−0.125601	−	0.222423i
$342$		0			0
$343$	−59.9032	−	184.363i	−0.174645	−	0.537502i
$344$	101.028	−	139.053i	0.293686	−	0.404224i
$345$		0			0
$346$	−44.8080	+	137.905i	−0.129503	+	0.398569i
$347$	80.5091	+	26.1590i	0.232015	+	0.0753861i	0.422717	−	0.906262i	$-0.361076\pi$
$347$	80.5091	+	26.1590i	0.232015	+	0.0753861i	−0.190702	+	0.981648i	$0.561076\pi$
$348$		0			0
$349$	−349.764	−	254.119i	−1.00219	−	0.728134i	−0.0396337	−	0.999214i	$-0.512619\pi$
$349$	−349.764	−	254.119i	−1.00219	−	0.728134i	−0.962557	+	0.271080i	$0.912619\pi$
$350$	805.446	−	261.705i	2.30127	−	0.747729i
$351$		0			0
$352$	12.3559	+	60.9863i	0.0351019	+	0.173257i
$353$			536.582i			1.52006i	0.649887	+	0.760031i	$0.274816\pi$
$353$			536.582i			1.52006i	−0.649887	+	0.760031i	$0.725184\pi$
$354$		0			0
$355$	−234.516	−	170.386i	−0.660610	−	0.479961i
$356$	−139.259	−	191.673i	−0.391177	−	0.538409i
$357$		0			0
$358$	50.8049	−	156.361i	0.141913	−	0.436764i
$359$	−39.4089	−	54.2417i	−0.109774	−	0.151091i	0.750595	−	0.660762i	$-0.229767\pi$
$359$	−39.4089	−	54.2417i	−0.109774	−	0.151091i	−0.860369	+	0.509672i	$0.829767\pi$
$360$		0			0
$361$	−96.7906	−	297.891i	−0.268118	−	0.825182i
$362$			180.389i			0.498311i
$363$		0			0
$364$	−38.8484			−0.106726
$365$	299.160	−	97.2031i	0.819617	−	0.266310i
$366$		0			0
$367$	−375.463	+	272.790i	−1.02306	+	0.743297i	−0.966908	−	0.255126i	$-0.917883\pi$
$367$	−375.463	+	272.790i	−1.02306	+	0.743297i	−0.0561522	+	0.998422i	$0.517883\pi$
$368$	129.991	+	42.2366i	0.353236	+	0.114773i
$369$		0			0
$370$	−244.914	+	177.941i	−0.661931	+	0.480921i
$371$	192.967	−	265.596i	0.520127	−	0.715893i
$372$		0			0
$373$	300.514			0.805668			0.402834	−	0.915273i	$-0.368025\pi$
$373$	300.514			0.805668			0.402834	+	0.915273i	$0.368025\pi$
$374$	106.676	−	21.6126i	0.285230	−	0.0577877i
$375$		0			0
$376$	47.1033	+	144.969i	0.125275	+	0.385556i
$377$	−63.9732	+	88.0515i	−0.169690	+	0.233558i
$378$		0			0
$379$	−46.7487	+	143.878i	−0.123347	+	0.379624i	−0.993596	−	0.112988i	$-0.963958\pi$
$379$	−46.7487	+	143.878i	−0.123347	+	0.379624i	0.870249	+	0.492612i	$0.163958\pi$
$380$	−127.350	−	41.3784i	−0.335130	−	0.108890i
$381$		0			0
$382$	−204.929	−	148.890i	−0.536464	−	0.389764i
$383$	339.843	−	110.422i	0.887319	−	0.288307i	0.170326	−	0.985388i	$-0.445518\pi$
$383$	339.843	−	110.422i	0.887319	−	0.288307i	0.716993	+	0.697080i	$0.245518\pi$
$384$		0			0
$385$	−807.323	+	455.890i	−2.09694	+	1.18413i
$386$		−	231.677i		−	0.600200i
$387$		0			0
$388$	−254.064	−	184.588i	−0.654803	−	0.475742i
$389$	118.172	+	162.649i	0.303783	+	0.418122i	0.933430	−	0.358760i	$-0.116800\pi$
$389$	118.172	+	162.649i	0.303783	+	0.418122i	−0.629647	+	0.776882i	$0.716800\pi$
$390$		0			0
$391$	73.8792	−	227.377i	0.188949	−	0.581527i
$392$	44.4275	+	61.1492i	0.113335	+	0.155993i
$393$		0			0
$394$	−64.9513	−	199.900i	−0.164851	−	0.507360i
$395$		−	227.490i		−	0.575923i
$396$		0			0
$397$	−177.510			−0.447129			−0.223564	−	0.974689i	$-0.571769\pi$
$397$	−177.510			−0.447129			−0.223564	+	0.974689i	$0.571769\pi$
$398$	−160.802	+	52.2479i	−0.404026	+	0.131276i
$399$		0			0
$400$	222.699	−	161.800i	0.556748	−	0.404501i
$401$	−534.516	−	173.675i	−1.33296	−	0.433104i	−0.446033	−	0.895017i	$-0.647163\pi$
$401$	−534.516	−	173.675i	−1.33296	−	0.433104i	−0.886926	+	0.461912i	$0.847163\pi$
$402$		0			0
$403$	14.2998	−	10.3894i	0.0354834	−	0.0257802i
$404$	−125.695	+	173.004i	−0.311126	+	0.428228i
$405$		0			0
$406$	600.040			1.47793
$407$	164.385	−	179.100i	0.403894	−	0.440050i
$408$		0			0
$409$	202.544	+	623.367i	0.495218	+	1.52412i	0.816617	+	0.577180i	$0.195847\pi$
$409$	202.544	+	623.367i	0.495218	+	1.52412i	−0.321399	+	0.946944i	$0.604153\pi$
$410$	−518.686	+	713.910i	−1.26509	+	1.74124i
$411$		0			0
$412$	−67.0405	+	206.330i	−0.162720	+	0.500800i
$413$	386.373	+	125.540i	0.935527	+	0.303971i
$414$		0			0
$415$	350.324	+	254.525i	0.844154	+	0.613314i
$416$	−12.0091	+	3.90199i	−0.0288680	+	0.00937977i
$417$		0			0
$418$	106.828	+	12.2600i	0.255569	+	0.0293302i
$419$			741.961i			1.77079i	0.464840	+	0.885395i	$0.346112\pi$
$419$			741.961i			1.77079i	−0.464840	+	0.885395i	$0.653888\pi$
$420$		0			0
$421$	255.986	+	185.985i	0.608043	+	0.441769i	0.848725	−	0.528835i	$-0.177371\pi$
$421$	255.986	+	185.985i	0.608043	+	0.441769i	−0.240682	+	0.970604i	$0.577371\pi$
$422$	128.153	+	176.388i	0.303681	+	0.417981i
$423$		0			0
$424$	32.9745	−	101.485i	0.0777699	−	0.239351i
$425$	−283.017	−	389.540i	−0.665924	−	0.916565i
$426$		0			0
$427$	67.7994	+	208.665i	0.158781	+	0.488677i
$428$		−	370.648i		−	0.866000i
$429$		0			0
$430$	832.406			1.93583
$431$	463.450	−	150.584i	1.07529	−	0.349383i	0.282745	−	0.959195i	$-0.408755\pi$
$431$	463.450	−	150.584i	1.07529	−	0.349383i	0.792546	+	0.609812i	$0.208755\pi$
$432$		0			0
$433$	−486.468	+	353.440i	−1.12348	+	0.816258i	−0.984733	−	0.174070i	$-0.944308\pi$
$433$	−486.468	+	353.440i	−1.12348	+	0.816258i	−0.138749	+	0.990328i	$0.544308\pi$
$434$	−92.6788	−	30.1132i	−0.213546	−	0.0693852i
$435$		0			0
$436$	−65.1693	+	47.3483i	−0.149471	+	0.108597i
$437$	138.830	−	191.083i	0.317689	−	0.437261i
$438$		0			0
$439$	498.971			1.13661			0.568304	−	0.822819i	$-0.307600\pi$
$439$	498.971			1.13661			0.568304	+	0.822819i	$0.307600\pi$
$440$	−203.775	+	222.017i	−0.463125	+	0.504583i
$441$		0			0
$442$	6.82527	+	21.0060i	0.0154418	+	0.0475249i
$443$	−169.067	+	232.701i	−0.381642	+	0.525285i	−0.956019	−	0.293306i	$-0.905244\pi$
$443$	−169.067	+	232.701i	−0.381642	+	0.525285i	0.574377	+	0.818591i	$0.305244\pi$
$444$		0			0
$445$	354.568	−	1091.25i	0.796782	−	2.45224i
$446$	−447.365	−	145.358i	−1.00306	−	0.325914i
$447$		0			0
$448$	56.3199	+	40.9188i	0.125714	+	0.0913366i
$449$	−650.340	+	211.308i	−1.44842	+	0.470620i	−0.924511	−	0.381156i	$-0.875526\pi$
$449$	−650.340	+	211.308i	−1.44842	+	0.470620i	−0.523907	+	0.851775i	$0.675526\pi$
$450$		0			0
$451$	294.392	−	644.587i	0.652754	−	1.42924i
$452$			182.747i			0.404307i
$453$		0			0
$454$	−260.854	−	189.521i	−0.574568	−	0.417448i
$455$	−110.587	−	152.210i	−0.243048	−	0.334527i
$456$		0			0
$457$	−93.0878	+	286.495i	−0.203693	+	0.626903i	0.796071	+	0.605203i	$0.206908\pi$
$457$	−93.0878	+	286.495i	−0.203693	+	0.626903i	−0.999765	+	0.0217005i	$0.993092\pi$
$458$	−0.895598	−	1.23268i	−0.00195545	−	0.00269145i
$459$		0			0
$460$	204.551	+	629.543i	0.444676	+	1.36857i
$461$		−	210.253i		−	0.456080i	−0.973652	−	0.228040i	$-0.926768\pi$
$461$		−	210.253i		−	0.456080i	0.973652	−	0.228040i	$-0.0732317\pi$
$462$		0			0
$463$	−344.360			−0.743757			−0.371879	−	0.928281i	$-0.621286\pi$
$463$	−344.360			−0.743757			−0.371879	+	0.928281i	$0.621286\pi$
$464$	185.489	−	60.2689i	0.399760	−	0.129890i
$465$		0			0
$466$	274.630	−	199.531i	0.589336	−	0.428177i
$467$	234.503	+	76.1947i	0.502148	+	0.163158i	0.549129	−	0.835738i	$-0.314960\pi$
$467$	234.503	+	76.1947i	0.502148	+	0.163158i	−0.0469801	+	0.998896i	$0.514960\pi$
$468$		0			0
$469$	111.492	−	81.0040i	0.237724	−	0.172716i
$470$	−433.911	+	597.227i	−0.923214	+	1.27070i
$471$		0			0
$472$	132.048			0.279762
$473$	−655.142	+	132.732i	−1.38508	+	0.280618i
$474$		0			0
$475$	−146.995	−	452.403i	−0.309463	−	0.952428i
$476$	71.5743	−	98.5135i	0.150366	−	0.206961i
$477$		0			0
$478$	88.6508	−	272.839i	0.185462	−	0.570793i
$479$	323.334	+	105.058i	0.675018	+	0.219327i	0.626413	−	0.779491i	$-0.284522\pi$
$479$	323.334	+	105.058i	0.675018	+	0.219327i	0.0486053	+	0.998818i	$0.484522\pi$
$480$		0			0
$481$	39.9103	+	28.9965i	0.0829736	+	0.0602838i
$482$	−218.393	+	70.9603i	−0.453098	+	0.147221i
$483$		0			0
$484$	124.978	−	207.230i	0.258220	−	0.428162i
$485$		−	1520.89i		−	3.13585i
$486$		0			0
$487$	−147.251	−	106.984i	−0.302363	−	0.219679i	0.426250	−	0.904605i	$-0.359834\pi$
$487$	−147.251	−	106.984i	−0.302363	−	0.219679i	−0.728612	+	0.684926i	$0.759834\pi$
$488$	41.9172	+	57.6941i	0.0858960	+	0.118226i
$489$		0			0
$490$	−113.117	+	348.138i	−0.230851	+	0.710487i
$491$	−556.488	−	765.940i	−1.13338	−	1.55996i	−0.781490	−	0.623918i	$-0.785540\pi$
$491$	−556.488	−	765.940i	−1.13338	−	1.55996i	−0.351888	−	0.936042i	$-0.614460\pi$
$492$		0			0
$493$	−105.421	−	324.452i	−0.213836	−	0.658118i
$494$			21.8204i			0.0441708i
$495$		0			0
$496$	−31.6741			−0.0638591
$497$	247.682	−	80.4767i	0.498353	−	0.161925i
$498$		0			0
$499$	−626.492	+	455.173i	−1.25549	+	0.912170i	−0.998527	−	0.0542504i	$-0.982723\pi$
$499$	−626.492	+	455.173i	−1.25549	+	0.912170i	−0.256967	+	0.966420i	$0.582723\pi$
$500$	807.290	+	262.304i	1.61458	+	0.524609i
$501$		0			0
$502$	243.857	−	177.172i	0.485770	−	0.352933i
$503$	−253.245	+	348.562i	−0.503469	+	0.692966i	−0.982801	−	0.184668i	$-0.940879\pi$
$503$	−253.245	+	348.562i	−0.503469	+	0.692966i	0.479332	+	0.877634i	$0.340879\pi$
$504$		0			0
$505$	−1035.65			−2.05078
$506$	−261.375	−	462.862i	−0.516552	−	0.914747i
$507$		0			0
$508$	−30.2290	−	93.0353i	−0.0595059	−	0.183140i
$509$	139.366	−	191.821i	0.273803	−	0.376858i	−0.649866	−	0.760049i	$-0.725175\pi$
$509$	139.366	−	191.821i	0.273803	−	0.376858i	0.923669	+	0.383191i	$0.125175\pi$
$510$		0			0
$511$	−87.3276	+	268.767i	−0.170896	+	0.525963i
$512$	21.5200	+	6.99226i	0.0420312	+	0.0136568i
$513$		0			0
$514$	−144.036	−	104.648i	−0.280226	−	0.203596i
$515$	−999.250	+	324.676i	−1.94029	+	0.630439i
$516$		0			0
$517$	246.276	−	539.234i	0.476356	−	1.04301i
$518$		−	271.975i		−	0.525047i
$519$		0			0
$520$	−49.4736	−	35.9447i	−0.0951416	−	0.0691244i
$521$	16.3590	+	22.5163i	0.0313993	+	0.0432174i	0.824428	−	0.565967i	$-0.191497\pi$
$521$	16.3590	+	22.5163i	0.0313993	+	0.0432174i	−0.793029	+	0.609184i	$0.791497\pi$
$522$		0			0
$523$	126.172	−	388.319i	0.241247	−	0.742483i	−0.754984	−	0.655744i	$-0.772355\pi$
$523$	126.172	−	388.319i	0.241247	−	0.742483i	0.996231	−	0.0867394i	$-0.0276448\pi$
$524$	−145.920	−	200.842i	−0.278474	−	0.383286i
$525$		0			0
$526$	143.914	+	442.923i	0.273602	+	0.842059i
$527$			55.4037i			0.105130i
$528$		0			0
$529$	−638.595			−1.20717
$530$	491.489	−	159.695i	0.927338	−	0.301311i
$531$		0			0
$532$	97.3241	−	70.7101i	0.182940	−	0.132914i
$533$	136.761	+	44.4364i	0.256587	+	0.0833703i
$534$		0			0
$535$	1452.22	−	1055.10i	2.71443	−	1.97215i
$536$	26.3292	−	36.2390i	0.0491216	−	0.0676101i
$537$		0			0
$538$	101.908			0.189421
$539$	33.5155	−	292.038i	0.0621809	−	0.541814i
$540$		0			0
$541$	93.7157	+	288.427i	0.173227	+	0.533137i	0.999548	−	0.0300618i	$-0.00957041\pi$
$541$	93.7157	+	288.427i	0.173227	+	0.533137i	−0.826321	+	0.563199i	$0.809570\pi$
$542$	188.426	−	259.346i	0.347649	−	0.478498i
$543$		0			0
$544$	12.2307	−	37.6422i	0.0224829	−	0.0691952i
$545$	−371.026	−	120.554i	−0.680782	−	0.221199i
$546$		0			0
$547$	−523.360	−	380.243i	−0.956782	−	0.695143i	−0.00438064	−	0.999990i	$-0.501394\pi$
$547$	−523.360	−	380.243i	−0.956782	−	0.695143i	−0.952401	+	0.304848i	$0.901394\pi$
$548$	181.914	−	59.1075i	0.331960	−	0.107860i
$549$		0			0
$550$	−1063.57	−	122.060i	−1.93377	−	0.221927i
$551$		−	337.031i		−	0.611671i
$552$		0			0
$553$	165.345	+	120.130i	0.298996	+	0.217234i
$554$	−69.2174	−	95.2695i	−0.124941	−	0.171967i
$555$		0			0
$556$	−51.7620	+	159.307i	−0.0930972	+	0.286524i
$557$	−33.6544	−	46.3213i	−0.0604208	−	0.0831621i	0.777737	−	0.628589i	$-0.216367\pi$
$557$	−33.6544	−	46.3213i	−0.0604208	−	0.0831621i	−0.838158	+	0.545427i	$0.816367\pi$
$558$		0			0
$559$	−41.9168	−	129.007i	−0.0749854	−	0.230781i
$560$			337.145i			0.602045i
$561$		0			0
$562$	272.572			0.485004
$563$	441.664	−	143.505i	0.784482	−	0.254894i	0.110730	−	0.993851i	$-0.464681\pi$
$563$	441.664	−	143.505i	0.784482	−	0.254894i	0.673753	+	0.738957i	$0.264681\pi$
$564$		0			0
$565$	−716.011	+	520.212i	−1.26728	+	0.920730i
$566$	−657.381	−	213.596i	−1.16145	−	0.377378i
$567$		0			0
$568$	68.4819	−	49.7550i	0.120567	−	0.0875968i
$569$	463.656	−	638.168i	0.814861	−	1.12156i	−0.175694	−	0.984445i	$-0.556217\pi$
$569$	463.656	−	638.168i	0.814861	−	1.12156i	0.990555	−	0.137115i	$-0.0437830\pi$
$570$		0			0
$571$	964.425			1.68901			0.844505	−	0.535547i	$-0.179895\pi$
$571$	964.425			1.68901			0.844505	+	0.535547i	$0.179895\pi$
$572$	44.6696	+	20.4012i	0.0780937	+	0.0356665i
$573$		0			0
$574$	−244.985	−	753.987i	−0.426803	−	1.31357i
$575$	−1382.18	+	1902.41i	−2.40380	+	3.30854i
$576$		0			0
$577$	21.4850	−	66.1241i	0.0372358	−	0.114600i	−0.930711	−	0.365756i	$-0.880811\pi$
$577$	21.4850	−	66.1241i	0.0372358	−	0.114600i	0.967947	+	0.251156i	$0.0808106\pi$
$578$	322.861	+	104.904i	0.558583	+	0.181495i
$579$		0			0
$580$	764.154	+	555.190i	1.31751	+	0.957225i
$581$	−369.990	+	120.217i	−0.636816	+	0.206914i
$582$		0			0
$583$	−361.360	+	204.058i	−0.619829	+	0.350013i
$584$			91.8544i			0.157285i
$585$		0			0
$586$	29.0874	+	21.1332i	0.0496372	+	0.0360635i
$587$	394.778	+	543.365i	0.672535	+	0.925664i	0.999814	−	0.0192631i	$-0.00613200\pi$
$587$	394.778	+	543.365i	0.672535	+	0.925664i	−0.327280	+	0.944927i	$0.606132\pi$
$588$		0			0
$589$	−16.9140	+	52.0559i	−0.0287164	+	0.0883801i
$590$	375.891	+	517.370i	0.637104	+	0.876898i
$591$		0			0
$592$	−27.3175	−	84.0747i	−0.0461445	−	0.142018i
$593$		−	175.258i		−	0.295545i	−0.989021	−	0.147772i	$-0.952790\pi$
$593$		−	175.258i		−	0.295545i	0.989021	−	0.147772i	$-0.0472103\pi$
$594$		0			0
$595$	589.727			0.991137
$596$	242.095	−	78.6614i	0.406200	−	0.131982i
$597$		0			0
$598$	87.2664	−	63.4028i	0.145930	−	0.106025i
$599$	590.954	+	192.013i	0.986568	+	0.320555i	0.757486	−	0.652852i	$-0.226427\pi$
$599$	590.954	+	192.013i	0.986568	+	0.320555i	0.229082	+	0.973407i	$0.426427\pi$
$600$		0			0
$601$	−11.1676	+	8.11373i	−0.0185817	+	0.0135004i	−0.597037	−	0.802213i	$-0.703656\pi$
$601$	−11.1676	+	8.11373i	−0.0185817	+	0.0135004i	0.578456	+	0.815714i	$0.303656\pi$
$602$	−439.568	+	605.013i	−0.730179	+	1.00501i
$603$		0			0
$604$	−14.7983			−0.0245004
$605$	1167.71	−	100.236i	1.93009	−	0.165680i
$606$		0			0
$607$	−150.273	−	462.493i	−0.247567	−	0.761932i	−0.995204	−	0.0978243i	$-0.968812\pi$
$607$	−150.273	−	462.493i	−0.247567	−	0.761932i	0.747637	−	0.664108i	$-0.231188\pi$
$608$	22.9833	−	31.6338i	0.0378015	−	0.0520293i
$609$		0			0
$610$	−106.726	+	328.468i	−0.174960	+	0.538472i
$611$	114.409	+	37.1736i	0.187248	+	0.0608406i
$612$		0			0
$613$	223.605	+	162.459i	0.364772	+	0.265022i	0.755040	−	0.655679i	$-0.227618\pi$
$613$	223.605	+	162.459i	0.364772	+	0.265022i	−0.390268	+	0.920701i	$0.627618\pi$
$614$	223.547	−	72.6348i	0.364083	−	0.118298i
$615$		0			0
$616$	−53.7598	−	265.349i	−0.0872724	−	0.430761i
$617$		−	5.53948i		−	0.00897808i	−0.999990	−	0.00448904i	$-0.998571\pi$
$617$		−	5.53948i		−	0.00897808i	0.999990	−	0.00448904i	$-0.00142891\pi$
$618$		0			0
$619$	179.838	+	130.660i	0.290530	+	0.211083i	0.723497	−	0.690327i	$-0.242533\pi$
$619$	179.838	+	130.660i	0.290530	+	0.211083i	−0.432967	+	0.901410i	$0.642533\pi$
$620$	−90.1646	−	124.101i	−0.145427	−	0.200163i
$621$		0			0
$622$	−227.595	+	700.466i	−0.365908	+	1.12615i
$623$	605.909	+	833.962i	0.972567	+	1.33862i
$624$		0			0
$625$	738.688	+	2273.45i	1.18190	+	3.63752i
$626$		−	32.6968i		−	0.0522313i
$627$		0			0
$628$	−571.126			−0.909437
$629$	−147.062	+	47.7832i	−0.233802	+	0.0759669i
$630$		0			0
$631$	−430.323	+	312.648i	−0.681971	+	0.495481i	−0.874011	−	0.485906i	$-0.838490\pi$
$631$	−430.323	+	312.648i	−0.681971	+	0.495481i	0.192040	+	0.981387i	$0.438490\pi$
$632$	63.1787	+	20.5280i	0.0999662	+	0.0324810i
$633$		0			0
$634$	71.3651	−	51.8498i	0.112563	−	0.0817820i
$635$	278.466	−	383.276i	0.438530	−	0.603584i
$636$		0			0
$637$	59.6508			0.0936434
$638$	−689.953	−	315.111i	−1.08143	−	0.493905i
$639$		0			0
$640$	33.8634	+	104.221i	0.0529115	+	0.162845i
$641$	490.893	−	675.656i	0.765824	−	1.05407i	−0.230884	−	0.972981i	$-0.574162\pi$
$641$	490.893	−	675.656i	0.765824	−	1.05407i	0.996707	−	0.0810844i	$-0.0258383\pi$
$642$		0			0
$643$	−19.4435	+	59.8410i	−0.0302388	+	0.0930653i	−0.965037	−	0.262114i	$-0.915580\pi$
$643$	−19.4435	+	59.8410i	−0.0302388	+	0.0930653i	0.934798	+	0.355180i	$0.115580\pi$
$644$	−565.584	−	183.769i	−0.878236	−	0.285356i
$645$		0			0
$646$	−55.3331	−	40.2019i	−0.0856550	−	0.0622320i
$647$	−136.229	+	44.2635i	−0.210555	+	0.0684135i	−0.412395	−	0.911005i	$-0.635308\pi$
$647$	−136.229	+	44.2635i	−0.210555	+	0.0684135i	0.201840	+	0.979418i	$0.435308\pi$
$648$		0			0
$649$	−378.341	−	347.256i	−0.582960	−	0.535062i
$650$		−	217.242i		−	0.334219i
$651$		0			0
$652$	−335.047	−	243.426i	−0.513876	−	0.373353i
$653$	−446.819	−	614.994i	−0.684256	−	0.941798i	0.315719	−	0.948853i	$-0.397754\pi$
$653$	−446.819	−	614.994i	−0.684256	−	0.941798i	−0.999975	+	0.00705462i	$0.997754\pi$
$654$		0			0
$655$	371.528	−	1143.45i	0.567219	−	1.74572i
$656$	−151.463	−	208.471i	−0.230889	−	0.317791i
$657$		0			0
$658$	−204.944	−	630.754i	−0.311466	−	0.958592i
$659$			995.342i			1.51038i	0.655505	+	0.755191i	$0.272456\pi$
$659$			995.342i			1.51038i	−0.655505	+	0.755191i	$0.727544\pi$
$660$		0			0
$661$	−163.048			−0.246669			−0.123334	−	0.992365i	$-0.539359\pi$
$661$	−163.048			−0.246669			−0.123334	+	0.992365i	$0.539359\pi$
$662$	−479.979	+	155.955i	−0.725044	+	0.235581i
$663$		0			0
$664$	−102.299	+	74.3247i	−0.154065	+	0.111935i
$665$	554.092	+	180.035i	0.833221	+	0.270730i
$666$		0			0
$667$	−1347.89	+	979.300i	−2.02082	+	1.46822i
$668$	98.7298	−	135.890i	0.147799	−	0.203428i
$669$		0			0
$670$	216.936			0.323785
$671$	31.6218	−	275.537i	0.0471264	−	0.410637i
$672$		0			0
$673$	−201.075	−	618.844i	−0.298774	−	0.919531i	−0.981928	−	0.189257i	$-0.939392\pi$
$673$	−201.075	−	618.844i	−0.298774	−	0.919531i	0.683154	−	0.730274i	$-0.260608\pi$
$674$	305.790	−	420.884i	0.453694	−	0.624456i
$675$		0			0
$676$	101.368	−	311.980i	0.149953	−	0.461508i
$677$	824.416	+	267.869i	1.21775	+	0.395670i	0.846261	−	0.532768i	$-0.178848\pi$
$677$	824.416	+	267.869i	1.21775	+	0.395670i	0.371487	+	0.928438i	$0.378848\pi$
$678$		0			0
$679$	1105.42	+	803.134i	1.62801	+	1.18282i
$680$	182.300	−	59.2330i	0.268089	−	0.0871074i
$681$		0			0
$682$	90.7523	+	83.2958i	0.133068	+	0.122135i
$683$		−	489.451i		−	0.716620i	−0.933603	−	0.358310i	$-0.883353\pi$
$683$		−	489.451i		−	0.716620i	0.933603	−	0.358310i	$-0.116647\pi$
$684$		0			0
$685$	749.429	+	544.492i	1.09406	+	0.794878i
$686$	161.139	+	221.789i	0.234897	+	0.323308i
$687$		0			0
$688$	−75.1139	+	231.177i	−0.109177	+	0.336013i
$689$	−49.4991	−	68.1297i	−0.0718419	−	0.0988820i
$690$		0			0
$691$	243.136	+	748.297i	0.351862	+	1.08292i	0.957807	+	0.287412i	$0.0927950\pi$
$691$	243.136	+	748.297i	0.351862	+	1.08292i	−0.605945	+	0.795506i	$0.707205\pi$
$692$		−	205.064i		−	0.296335i
$693$		0			0
$694$	−119.716			−0.172502
$695$	−771.521	+	250.682i	−1.11010	+	0.360694i
$696$		0			0
$697$	−364.653	+	264.936i	−0.523175	+	0.380109i
$698$	581.486	+	188.936i	0.833075	+	0.270682i
$699$		0			0
$700$	−968.953	+	703.986i	−1.38422	+	1.00569i
$701$	−492.664	+	678.094i	−0.702802	+	0.967324i	0.297120	+	0.954840i	$0.403974\pi$
$701$	−492.664	+	678.094i	−0.702802	+	0.967324i	−0.999922	+	0.0124840i	$0.996026\pi$
$702$		0			0
$703$	−152.763			−0.217301
$704$	−43.2706	−	76.6267i	−0.0614639	−	0.108845i
$705$		0			0
$706$	−234.495	−	721.701i	−0.332146	−	1.02224i
$707$	546.892	−	752.733i	0.773539	−	1.06469i
$708$		0			0
$709$	131.441	−	404.535i	0.185390	−	0.570571i	−0.814565	−	0.580072i	$-0.803024\pi$
$709$	131.441	−	404.535i	0.185390	−	0.570571i	0.999955	+	0.00950122i	$0.00302438\pi$
$710$	389.885	+	126.681i	0.549134	+	0.178425i
$711$		0			0
$712$	271.067	+	196.942i	0.380712	+	0.276604i
$713$	257.334	−	83.6129i	0.360917	−	0.117269i
$714$		0			0
$715$	47.2247	+	233.093i	0.0660485	+	0.326004i
$716$			232.508i			0.324732i
$717$		0			0
$718$	76.7093	+	55.7326i	0.106837	+	0.0776219i
$719$	−205.764	−	283.210i	−0.286181	−	0.393894i	0.641588	−	0.767050i	$-0.278276\pi$
$719$	−205.764	−	283.210i	−0.286181	−	0.393894i	−0.927769	+	0.373155i	$0.878276\pi$
$720$		0			0
$721$	291.690	−	897.730i	0.404563	−	1.24512i
$722$	260.366	+	358.363i	0.360618	+	0.496348i
$723$		0			0
$724$	−78.8327	−	242.622i	−0.108885	−	0.335114i
$725$			3355.46i			4.62821i
$726$		0			0
$727$	235.723			0.324240			0.162120	−	0.986771i	$-0.448167\pi$
$727$	235.723			0.324240			0.162120	+	0.986771i	$0.448167\pi$
$728$	52.2509	−	16.9774i	0.0717733	−	0.0233205i
$729$		0			0
$730$	−359.890	+	261.476i	−0.493001	+	0.358186i
$731$	404.369	+	131.387i	0.553172	+	0.179737i
$732$		0			0
$733$	−193.726	+	140.750i	−0.264292	+	0.192019i	−0.712037	−	0.702142i	$-0.752227\pi$
$733$	−193.726	+	140.750i	−0.264292	+	0.192019i	0.447745	+	0.894161i	$0.352227\pi$
$734$	385.783	−	530.985i	0.525590	−	0.723413i
$735$		0			0
$736$	−193.295			−0.262629
$737$	−170.738	+	34.5917i	−0.231667	+	0.0469358i
$738$		0			0
$739$	204.544	+	629.522i	0.276785	+	0.851857i	0.988742	+	0.149633i	$0.0478094\pi$
$739$	204.544	+	629.522i	0.276785	+	0.851857i	−0.711956	+	0.702224i	$0.752191\pi$
$740$	251.646	−	346.361i	0.340062	−	0.468056i
$741$		0			0
$742$	−143.470	+	441.556i	−0.193356	+	0.595089i
$743$	850.914	+	276.479i	1.14524	+	0.372111i	0.819349	−	0.573296i	$-0.194335\pi$
$743$	850.914	+	276.479i	1.14524	+	0.372111i	0.325892	+	0.945407i	$0.394335\pi$
$744$		0			0
$745$	997.355	+	724.621i	1.33873	+	0.972645i
$746$	−404.191	+	131.330i	−0.541811	+	0.176045i
$747$		0			0
$748$	−134.034	+	75.6880i	−0.179189	+	0.101187i
$749$			1612.67i			2.15310i
$750$		0			0
$751$	301.695	+	219.194i	0.401724	+	0.291869i	0.770243	−	0.637751i	$-0.220135\pi$
$751$	301.695	+	219.194i	0.401724	+	0.291869i	−0.368519	+	0.929620i	$0.620135\pi$
$752$	−126.708	−	174.398i	−0.168494	−	0.231912i
$753$		0			0
$754$	47.5638	−	146.386i	0.0630820	−	0.194146i
$755$	−42.1252	−	57.9803i	−0.0557949	−	0.0767951i
$756$		0			0
$757$	−240.125	−	739.028i	−0.317206	−	0.976260i	−0.974837	−	0.222919i	$-0.928441\pi$
$757$	−240.125	−	739.028i	−0.317206	−	0.976260i	0.657631	−	0.753340i	$-0.271559\pi$
$758$		−	213.945i		−	0.282249i
$759$		0			0
$760$	189.368			0.249168
$761$	−1293.58	+	420.310i	−1.69984	+	0.552313i	−0.988591	−	0.150623i	$-0.951872\pi$
$761$	−1293.58	+	420.310i	−1.69984	+	0.552313i	−0.711253	+	0.702936i	$0.751872\pi$
$762$		0			0
$763$	283.549	−	206.010i	0.371623	−	0.270000i
$764$	340.696	+	110.699i	0.445938	+	0.144894i
$765$		0			0
$766$	−408.832	+	297.034i	−0.533723	+	0.387773i
$767$	61.2538	−	84.3086i	0.0798615	−	0.109920i
$768$		0			0
$769$	306.481			0.398545			0.199273	−	0.979944i	$-0.436142\pi$
$769$	306.481			0.398545			0.199273	+	0.979944i	$0.436142\pi$
$770$	886.616	−	965.984i	1.15145	−	1.25452i
$771$		0			0
$772$	101.247	+	311.605i	0.131149	+	0.403634i
$773$	186.486	−	256.675i	0.241249	−	0.332051i	−0.671173	−	0.741300i	$-0.734209\pi$
$773$	186.486	−	256.675i	0.241249	−	0.332051i	0.912423	+	0.409249i	$0.134209\pi$
$774$		0			0
$775$	168.394	−	518.265i	0.217283	−	0.668729i
$776$	422.383	+	137.241i	0.544308	+	0.176856i
$777$		0			0
$778$	−230.021	−	167.120i	−0.295657	−	0.214807i
$779$	−423.499	+	137.603i	−0.543645	+	0.176641i
$780$		0			0
$781$	−327.058	−	37.5345i	−0.418768	−	0.0480596i
$782$			338.108i			0.432363i
$783$		0			0
$784$	−86.4780	−	62.8299i	−0.110304	−	0.0801402i
$785$	−1625.79	−	2237.70i	−2.07107	−	2.85058i
$786$		0			0
$787$	189.559	−	583.403i	0.240863	−	0.741300i	−0.755427	−	0.655233i	$-0.772570\pi$
$787$	189.559	−	583.403i	0.240863	−	0.741300i	0.996289	−	0.0860663i	$-0.0274297\pi$
$788$	174.719	+	240.480i	0.221724	+	0.305177i
$789$		0			0
$790$	99.4166	+	305.973i	0.125844	+	0.387308i
$791$		−	795.122i		−	1.00521i
$792$		0			0
$793$	56.2804			0.0709715
$794$	238.750	−	77.5747i	0.300693	−	0.0977012i
$795$		0			0
$796$	193.446	−	140.546i	0.243022	−	0.176566i
$797$	−1214.99	−	394.776i	−1.52446	−	0.495327i	−0.577421	−	0.816447i	$-0.695941\pi$
$797$	−1214.99	−	394.776i	−1.52446	−	0.495327i	−0.947039	+	0.321120i	$0.895941\pi$
$798$		0			0
$799$	−305.053	+	221.634i	−0.381794	+	0.277389i
$800$	−228.820	+	314.944i	−0.286025	+	0.393680i
$801$		0			0
$802$	794.821			0.991049
$803$	241.556	−	263.180i	0.300817	−	0.327746i
$804$		0			0
$805$	−889.991	−	2739.11i	−1.10558	−	3.40262i
$806$	−14.6929	+	20.2230i	−0.0182294	+	0.0250906i
$807$		0			0
$808$	93.4536	−	287.621i	0.115660	−	0.355966i
$809$	−362.334	−	117.729i	−0.447878	−	0.145525i	0.0763892	−	0.997078i	$-0.475661\pi$
$809$	−362.334	−	117.729i	−0.447878	−	0.145525i	−0.524268	+	0.851554i	$0.675661\pi$
$810$		0			0
$811$	−989.907	−	719.209i	−1.22060	−	0.886818i	−0.224451	−	0.974485i	$-0.572059\pi$
$811$	−989.907	−	719.209i	−1.22060	−	0.886818i	−0.996150	+	0.0876674i	$0.972059\pi$
$812$	−807.052	+	262.227i	−0.993906	+	0.322940i
$813$		0			0
$814$	−142.828	+	312.729i	−0.175464	+	0.384187i
$815$		−	2005.68i		−	2.46095i
$816$		0			0
$817$	339.824	+	246.896i	0.415941	+	0.302199i
$818$	−544.842	−	749.911i	−0.666066	−	0.916762i
$819$		0			0
$820$	385.641	−	1186.88i	0.470294	−	1.44741i
$821$	−11.5022	−	15.8314i	−0.0140100	−	0.0192831i	0.801955	−	0.597385i	$-0.203794\pi$
$821$	−11.5022	−	15.8314i	−0.0140100	−	0.0192831i	−0.815965	+	0.578102i	$0.803794\pi$
$822$		0			0
$823$	−263.945	−	812.340i	−0.320711	−	0.987048i	−0.973339	−	0.229369i	$-0.926334\pi$
$823$	−263.945	−	812.340i	−0.320711	−	0.987048i	0.652628	−	0.757678i	$-0.273666\pi$
$824$		−	306.810i		−	0.372343i
$825$		0			0
$826$	−574.533			−0.695561
$827$	1009.87	−	328.125i	1.22112	−	0.396766i	0.373630	−	0.927578i	$-0.378113\pi$
$827$	1009.87	−	328.125i	1.22112	−	0.396766i	0.847490	+	0.530812i	$0.178113\pi$
$828$		0			0
$829$	17.4887	−	12.7063i	0.0210962	−	0.0153273i	−0.577187	−	0.816612i	$-0.695850\pi$
$829$	17.4887	−	12.7063i	0.0210962	−	0.0153273i	0.598283	+	0.801285i	$0.295850\pi$
$830$	−582.416	−	189.238i	−0.701706	−	0.227998i
$831$		0			0
$832$	14.4469	−	10.4963i	0.0173641	−	0.0126158i
$833$	−109.901	+	151.265i	−0.131934	+	0.181591i
$834$		0			0
$835$	813.471			0.974217
$836$	−149.041	+	30.1958i	−0.178279	+	0.0361194i
$837$		0			0
$838$	−324.249	−	997.935i	−0.386932	−	1.19085i
$839$	242.628	−	333.949i	0.289188	−	0.398033i	−0.639562	−	0.768739i	$-0.720884\pi$
$839$	242.628	−	333.949i	0.289188	−	0.398033i	0.928750	+	0.370707i	$0.120884\pi$
$840$		0			0
$841$	−474.772	+	1461.20i	−0.564533	+	1.73745i
$842$	−425.579	−	138.279i	−0.505438	−	0.164227i
$843$		0			0
$844$	−249.450	−	181.236i	−0.295557	−	0.214735i
$845$	1510.91	−	490.925i	1.78806	−	0.580976i
$846$		0			0
$847$	−543.775	+	901.649i	−0.642001	+	1.06452i
$848$			150.907i			0.177957i
$849$		0			0
$850$	550.893	+	400.247i	0.648109	+	0.470879i
$851$	443.878	+	610.946i	0.521596	+	0.717915i
$852$		0			0
$853$	5.91770	−	18.2128i	0.00693751	−	0.0213515i	−0.947528	−	0.319673i	$-0.896427\pi$
$853$	5.91770	−	18.2128i	0.00693751	−	0.0213515i	0.954465	+	0.298322i	$0.0964269\pi$
$854$	−182.380	−	251.024i	−0.213560	−	0.293940i
$855$		0			0
$856$	161.979	+	498.520i	0.189228	+	0.582383i
$857$			554.266i			0.646751i	0.946271	+	0.323375i	$0.104818\pi$
$857$			554.266i			0.646751i	−0.946271	+	0.323375i	$0.895182\pi$
$858$		0			0
$859$	−105.229			−0.122501			−0.0612506	−	0.998122i	$-0.519509\pi$
$859$	−105.229			−0.122501			−0.0612506	+	0.998122i	$0.519509\pi$
$860$	−1119.58	+	363.775i	−1.30184	+	0.422994i
$861$		0			0
$862$	−557.532	+	405.070i	−0.646788	+	0.469919i
$863$	1461.17	+	474.764i	1.69313	+	0.550132i	0.987386	−	0.158331i	$-0.0506113\pi$
$863$	1461.17	+	474.764i	1.69313	+	0.550132i	0.705748	+	0.708463i	$0.250611\pi$
$864$		0			0
$865$	803.450	−	583.741i	0.928844	−	0.674845i
$866$	499.839	−	687.969i	0.577181	−	0.794422i
$867$		0			0
$868$	137.813			0.158770
$869$	−127.035	−	224.962i	−0.146185	−	0.258875i
$870$		0			0
$871$	−10.9241	−	33.6208i	−0.0125420	−	0.0386002i
$872$	66.9606	−	92.1633i	0.0767897	−	0.105692i
$873$		0			0
$874$	−103.220	+	317.677i	−0.118100	+	0.363475i
$875$	−3512.48	−	1141.27i	−4.01426	−	1.30431i
$876$		0			0
$877$	−612.966	−	445.346i	−0.698935	−	0.507806i	0.180650	−	0.983547i	$-0.442180\pi$
$877$	−612.966	−	445.346i	−0.698935	−	0.507806i	−0.879585	+	0.475741i	$0.842180\pi$
$878$	−671.114	+	218.058i	−0.764367	+	0.248358i
$879$		0			0
$880$	177.052	−	387.665i	0.201195	−	0.440528i
$881$			843.725i			0.957690i	0.877899	+	0.478845i	$0.158944\pi$
$881$			843.725i			0.957690i	−0.877899	+	0.478845i	$0.841056\pi$
$882$		0			0
$883$	−356.535	−	259.038i	−0.403777	−	0.293361i	0.367301	−	0.930102i	$-0.380282\pi$
$883$	−356.535	−	259.038i	−0.403777	−	0.293361i	−0.771078	+	0.636741i	$0.780282\pi$
$884$	−18.3599	−	25.2703i	−0.0207691	−	0.0285863i
$885$		0			0
$886$	125.701	−	386.867i	0.141875	−	0.436645i
$887$	313.953	+	432.119i	0.353949	+	0.487169i	0.948450	−	0.316926i	$-0.102651\pi$
$887$	313.953	+	432.119i	0.353949	+	0.487169i	−0.594502	+	0.804094i	$0.702651\pi$
$888$		0			0
$889$	131.525	+	404.792i	0.147947	+	0.455334i
$890$			1622.68i			1.82323i
$891$		0			0
$892$	665.228			0.745771
$893$	−354.282	+	115.113i	−0.396732	+	0.128906i
$894$		0			0
$895$	−910.980	+	661.866i	−1.01785	+	0.739515i
$896$	−93.6323	−	30.4230i	−0.104500	−	0.0339542i
$897$		0			0
$898$	782.360	−	568.418i	0.871225	−	0.632982i
$899$	226.942	−	312.358i	0.252438	−	0.347451i
$900$		0			0
$901$	263.964			0.292967
$902$	−114.262	+	995.622i	−0.126676	+	1.10379i
$903$		0			0
$904$	−79.8632	−	245.794i	−0.0883442	−	0.271896i
$905$	726.199	−	999.527i	0.802430	−	1.10445i
$906$		0			0
$907$	303.622	−	934.451i	0.334754	−	1.03027i	−0.632090	−	0.774895i	$-0.717803\pi$
$907$	303.622	−	934.451i	0.334754	−	1.03027i	0.966843	−	0.255370i	$-0.0821974\pi$
$908$	433.671	+	140.908i	0.477612	+	0.155185i
$909$		0			0
$910$	215.257	+	156.394i	0.236547	+	0.171861i
$911$	−1094.72	+	355.696i	−1.20167	+	0.390446i	−0.840375	−	0.542006i	$-0.817665\pi$
$911$	−1094.72	+	355.696i	−1.20167	+	0.390446i	−0.361295	+	0.932452i	$0.617665\pi$
$912$		0			0
$913$	488.563	+	56.0696i	0.535119	+	0.0614125i
$914$		−	426.016i		−	0.466100i
$915$		0			0
$916$	1.74328	+	1.26657i	0.00190314	+	0.00138271i
$917$	634.892	+	873.854i	0.692358	+	0.952949i
$918$		0			0
$919$	−317.967	+	978.602i	−0.345992	+	1.06486i	0.615058	+	0.788482i	$0.289133\pi$
$919$	−317.967	+	978.602i	−0.345992	+	1.06486i	−0.961050	+	0.276373i	$0.910867\pi$
$920$	−550.240	−	757.341i	−0.598087	−	0.823197i
$921$		0			0
$922$	91.8839	+	282.790i	0.0996572	+	0.306713i
$923$		−	66.8039i		−	0.0723769i
$924$		0			0
$925$	1520.90			1.64421
$926$	463.163	−	150.491i	0.500176	−	0.162517i
$927$		0			0
$928$	−223.143	+	162.123i	−0.240456	+	0.174701i
$929$	−511.021	−	166.041i	−0.550077	−	0.178731i	0.0207747	−	0.999784i	$-0.493387\pi$
$929$	−511.021	−	166.041i	−0.550077	−	0.178731i	−0.570851	+	0.821053i	$0.693387\pi$
$930$		0			0
$931$	−149.439	+	108.574i	−0.160515	+	0.116621i
$932$	−282.179	+	388.386i	−0.302767	+	0.416723i
$933$		0			0
$934$	−348.705			−0.373345
$935$	−678.094	−	309.695i	−0.725234	−	0.331225i
$936$		0			0
$937$	−410.291	−	1262.75i	−0.437878	−	1.34765i	−0.890109	−	0.455748i	$-0.849372\pi$
$937$	−410.291	−	1262.75i	−0.437878	−	1.34765i	0.452231	−	0.891901i	$-0.350628\pi$
$938$	−114.557	+	157.674i	−0.122129	+	0.168096i
$939$		0			0
$940$	322.611	−	992.894i	0.343203	−	1.05627i
$941$	1102.47	+	358.215i	1.17160	+	0.380674i	0.829238	−	0.558895i	$-0.188775\pi$
$941$	1102.47	+	358.215i	1.17160	+	0.380674i	0.342357	+	0.939570i	$0.388775\pi$
$942$		0			0
$943$	1780.87	+	1293.88i	1.88851	+	1.37209i
$944$	−177.604	+	57.7070i	−0.188140	+	0.0611302i
$945$		0			0
$946$	823.158	−	464.832i	0.870145	−	0.491365i
$947$		−	242.837i		−	0.256427i	−0.991747	−	0.128214i	$-0.959076\pi$
$947$		−	242.837i		−	0.256427i	0.991747	−	0.128214i	$-0.0409243\pi$
$948$		0			0
$949$	58.6464	+	42.6091i	0.0617981	+	0.0448989i
$950$	395.415	+	544.242i	0.416226	+	0.572886i
$951$		0			0
$952$	−53.2152	+	163.780i	−0.0558983	+	0.172037i
$953$	−311.782	−	429.131i	−0.327158	−	0.450294i	0.613478	−	0.789712i	$-0.289770\pi$
$953$	−311.782	−	429.131i	−0.327158	−	0.450294i	−0.940636	+	0.339418i	$0.889770\pi$
$954$		0			0
$955$	536.113	+	1649.99i	0.561375	+	1.72773i
$956$			405.710i			0.424383i
$957$		0			0
$958$	−480.795			−0.501874
$959$	−791.500	+	257.174i	−0.825339	+	0.268169i
$960$		0			0
$961$	726.737	−	528.006i	0.756230	−	0.549434i
$962$	−66.3512	−	21.5588i	−0.0689721	−	0.0224104i
$963$		0			0
$964$	262.728	−	190.883i	0.272539	−	0.198011i
$965$	−932.674	+	1283.72i	−0.966502	+	1.33028i
$966$		0			0
$967$	275.752			0.285163			0.142581	−	0.989783i	$-0.454460\pi$
$967$	275.752			0.285163			0.142581	+	0.989783i	$0.454460\pi$
$968$	−77.5326	+	333.342i	−0.0800957	+	0.344361i
$969$		0			0
$970$	664.653	+	2045.59i	0.685209	+	2.10886i
$971$	−728.042	+	1002.06i	−0.749786	+	1.03199i	0.248210	+	0.968706i	$0.420158\pi$
$971$	−728.042	+	1002.06i	−0.749786	+	1.03199i	−0.997995	+	0.0632850i	$0.979842\pi$
$972$		0			0
$973$	225.214	−	693.138i	0.231464	−	0.712372i
$974$	244.805	+	79.5420i	0.251340	+	0.0816653i
$975$		0			0
$976$	−81.5918	−	59.2799i	−0.0835982	−	0.0607376i
$977$	−305.204	+	99.1669i	−0.312389	+	0.101501i	−0.461016	−	0.887392i	$-0.652515\pi$
$977$	−305.204	+	99.1669i	−0.312389	+	0.101501i	0.148626	+	0.988893i	$0.452515\pi$
$978$		0			0
$979$	−258.745	−	1277.12i	−0.264296	−	1.30452i
$980$		−	517.679i		−	0.528244i
$981$		0			0
$982$	1083.20	+	786.993i	1.10306	+	0.801419i
$983$	−458.327	−	630.833i	−0.466253	−	0.641742i	0.509538	−	0.860448i	$-0.329816\pi$
$983$	−458.327	−	630.833i	−0.466253	−	0.641742i	−0.975791	+	0.218706i	$0.929816\pi$
$984$		0			0
$985$	−444.852	+	1369.11i	−0.451627	+	1.38996i
$986$	283.582	+	390.317i	0.287608	+	0.395859i
$987$		0			0
$988$	−9.53585	−	29.3483i	−0.00965167	−	0.0297048i
$989$		−	2076.46i		−	2.09956i
$990$		0			0
$991$	−1400.10			−1.41281			−0.706407	−	0.707806i	$-0.749685\pi$
$991$	−1400.10			−1.41281			−0.706407	+	0.707806i	$0.749685\pi$
$992$	42.6016	−	13.8421i	0.0429452	−	0.0139537i
$993$		0			0
$994$	−297.962	+	216.482i	−0.299760	+	0.217788i
$995$	1101.34	+	357.846i	1.10687	+	0.359644i
$996$		0			0
$997$	−1042.15	+	757.167i	−1.04529	+	0.759445i	−0.971311	−	0.237815i	$-0.923569\pi$
$997$	−1042.15	+	757.167i	−1.04529	+	0.759445i	−0.0739763	+	0.997260i	$0.523569\pi$
$998$	643.711	−	885.993i	0.645001	−	0.887768i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.3.k.a.71.2	yes	16
3.2	odd	2	inner	198.3.k.a.71.3	yes	16
11.3	even	5		2178.3.c.p.485.8		8
11.8	odd	10		2178.3.c.m.485.4		8
11.9	even	5	inner	198.3.k.a.53.3	yes	16
33.8	even	10		2178.3.c.m.485.5		8
33.14	odd	10		2178.3.c.p.485.1		8
33.20	odd	10	inner	198.3.k.a.53.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.3.k.a.53.2	✓	16	33.20	odd	10	inner
198.3.k.a.53.3	yes	16	11.9	even	5	inner
198.3.k.a.71.2	yes	16	1.1	even	1	trivial
198.3.k.a.71.3	yes	16	3.2	odd	2	inner
2178.3.c.m.485.4		8	11.8	odd	10
2178.3.c.m.485.5		8	33.8	even	10
2178.3.c.p.485.1		8	33.14	odd	10
2178.3.c.p.485.8		8	11.3	even	5

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:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	198.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34500 + 0.437016i) q^{2} +(1.61803 - 1.17557i) q^{4} +(9.21189 + 2.99313i) q^{5} +(-7.03999 + 5.11485i) q^{7} +(-1.66251 + 2.28825i) q^{8} +O(q^{10})\)	\(q+(-1.34500 + 0.437016i) q^{2} +(1.61803 - 1.17557i) q^{4} +(9.21189 + 2.99313i) q^{5} +(-7.03999 + 5.11485i) q^{7} +(-1.66251 + 2.28825i) q^{8} -13.6980 q^{10} +(10.7810 - 2.18423i) q^{11} +(0.689780 + 2.12293i) q^{13} +(7.23349 - 9.95605i) q^{14} +(1.23607 - 3.80423i) q^{16} +(-6.65427 - 2.16210i) q^{17} +(-5.59212 - 4.06291i) q^{19} +(18.4238 - 5.98625i) q^{20} +(-13.5458 + 7.64924i) q^{22} +34.1701i q^{23} +(55.6748 + 40.4501i) q^{25} +(-1.85550 - 2.55388i) q^{26} +(-5.37807 + 16.5520i) q^{28} +(28.6596 + 39.4465i) q^{29} +(-2.44696 - 7.53097i) q^{31} +5.65685i q^{32} +9.89484 q^{34} +(-80.1610 + 26.0459i) q^{35} +(17.8796 - 12.9903i) q^{37} +(9.29694 + 3.02076i) q^{38} +(-22.1639 + 16.1030i) q^{40} +(37.8658 - 52.1177i) q^{41} -60.7684 q^{43} +(14.8762 - 16.2079i) q^{44} +(-14.9329 - 45.9587i) q^{46} +(31.6769 - 43.5995i) q^{47} +(8.25791 - 25.4152i) q^{49} +(-92.5597 - 30.0745i) q^{50} +(3.61174 + 2.62408i) q^{52} +(-35.8803 + 11.6582i) q^{53} +(105.851 + 12.1479i) q^{55} -24.6127i q^{56} +(-55.7858 - 40.5307i) q^{58} +(-27.4413 - 37.7697i) q^{59} +(7.79133 - 23.9792i) q^{61} +(6.58231 + 9.05977i) q^{62} +(-2.47214 - 7.60845i) q^{64} +21.6208i q^{65} -15.8370 q^{67} +(-13.3085 + 4.32420i) q^{68} +(96.4339 - 70.0633i) q^{70} +(-28.4629 - 9.24816i) q^{71} +(26.2732 - 19.0886i) q^{73} +(-18.3710 + 25.2855i) q^{74} -13.8245 q^{76} +(-64.7259 + 70.5200i) q^{77} +(-7.25774 - 22.3370i) q^{79} +(22.7731 - 31.3444i) q^{80} +(-28.1530 + 86.6461i) q^{82} +(42.5183 + 13.8150i) q^{83} +(-54.8270 - 39.8341i) q^{85} +(81.7333 - 26.5568i) q^{86} +(-12.9254 + 28.3008i) q^{88} -118.461i q^{89} +(-15.7145 - 11.4172i) q^{91} +(40.1694 + 55.2884i) q^{92} +(-23.5517 + 72.4845i) q^{94} +(-39.3532 - 54.1650i) q^{95} +(-48.5218 - 149.335i) q^{97} +37.7923i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 24 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 - 24 * q^7	\( 16 q + 8 q^{4} - 24 q^{7} - 24 q^{10} + 48 q^{13} - 16 q^{16} - 36 q^{19} + 48 q^{22} + 192 q^{25} - 32 q^{28} + 4 q^{31} - 112 q^{34} + 76 q^{37} - 72 q^{40} - 440 q^{43} - 36 q^{46} - 168 q^{49} + 24 q^{52} + 836 q^{55} - 96 q^{58} + 40 q^{61} + 32 q^{64} - 552 q^{67} + 516 q^{70} - 316 q^{73} - 288 q^{76} + 604 q^{79} - 36 q^{82} + 36 q^{85} - 16 q^{88} - 352 q^{91} - 220 q^{94} + 156 q^{97}+O(q^{100}) \) 16 * q + 8 * q^4 - 24 * q^7 - 24 * q^10 + 48 * q^13 - 16 * q^16 - 36 * q^19 + 48 * q^22 + 192 * q^25 - 32 * q^28 + 4 * q^31 - 112 * q^34 + 76 * q^37 - 72 * q^40 - 440 * q^43 - 36 * q^46 - 168 * q^49 + 24 * q^52 + 836 * q^55 - 96 * q^58 + 40 * q^61 + 32 * q^64 - 552 * q^67 + 516 * q^70 - 316 * q^73 - 288 * q^76 + 604 * q^79 - 36 * q^82 + 36 * q^85 - 16 * q^88 - 352 * q^91 - 220 * q^94 + 156 * q^97

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