LMFDB - Embedded newform 1050.3.q.e.199.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(199,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1050.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.q (of order $6$, degree $2$, not 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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.5
Character	$\chi$	$=$	1050.199
Dual form			1050.3.q.e.649.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(5.56601 + 4.24494i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(5.56601 + 4.24494i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(5.42967 - 9.40447i) q^{11} +(1.73205 + 3.00000i) q^{12} +0.772061 q^{13} +(-9.81857 - 1.26320i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-9.68565 + 16.7760i) q^{17} +(3.67423 + 2.12132i) q^{18} +(-22.5766 + 13.0346i) q^{19} +(-11.1877 + 4.67280i) q^{21} +15.3574i q^{22} +(11.8599 - 6.84734i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-0.945577 + 0.545929i) q^{26} +5.19615 q^{27} +(12.9185 - 5.39568i) q^{28} +6.99131 q^{29} +(22.7559 + 13.1381i) q^{31} +(4.89898 + 2.82843i) q^{32} +(9.40447 + 16.2890i) q^{33} -27.3952i q^{34} -6.00000 q^{36} +(55.9459 - 32.3004i) q^{37} +(18.4337 - 31.9281i) q^{38} +(-0.668624 + 1.15809i) q^{39} -5.54839i q^{41} +(10.3979 - 13.6339i) q^{42} +68.9320i q^{43} +(-10.8593 - 18.8089i) q^{44} +(-9.68361 + 16.7725i) q^{46} +(-11.3055 - 19.5817i) q^{47} +6.92820 q^{48} +(12.9610 + 47.2548i) q^{49} +(-16.7760 - 29.0570i) q^{51} +(0.772061 - 1.33725i) q^{52} +(64.5742 + 37.2820i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(-12.0065 + 15.7431i) q^{56} -45.1532i q^{57} +(-8.56257 + 4.94360i) q^{58} +(-96.6595 - 55.8064i) q^{59} +(-46.9572 + 27.1108i) q^{61} -37.1603 q^{62} +(2.67965 - 20.8283i) q^{63} -8.00000 q^{64} +(-23.0362 - 13.2999i) q^{66} +(38.3255 + 22.1273i) q^{67} +(19.3713 + 33.5521i) q^{68} +23.7199i q^{69} +31.9550 q^{71} +(7.34847 - 4.24264i) q^{72} +(-53.4812 + 92.6322i) q^{73} +(-45.6797 + 79.1195i) q^{74} +52.1384i q^{76} +(70.1430 - 29.2968i) q^{77} -1.89115i q^{78} +(14.8408 + 25.7050i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(3.92330 + 6.79536i) q^{82} +15.8151 q^{83} +(-3.09419 + 24.0505i) q^{84} +(-48.7423 - 84.4242i) q^{86} +(-6.05465 + 10.4870i) q^{87} +(26.5999 + 15.3574i) q^{88} +(31.8358 - 18.3804i) q^{89} +(4.29730 + 3.27735i) q^{91} -27.3894i q^{92} +(-39.4144 + 22.7559i) q^{93} +(27.6926 + 15.9884i) q^{94} +(-8.48528 + 4.89898i) q^{96} -134.212 q^{97} +(-49.2881 - 48.7102i) q^{98} -32.5780 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} - 48 q^{9}+O(q^{10}) $ 32 * q + 32 * q^4 - 48 * q^9	$ 32 q + 32 q^{4} - 48 q^{9} - 8 q^{11} - 16 q^{14} - 64 q^{16} + 144 q^{19} - 48 q^{21} - 144 q^{29} + 240 q^{31} - 192 q^{36} - 72 q^{39} + 16 q^{44} + 16 q^{46} + 80 q^{49} - 24 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 256 q^{64} + 144 q^{66} - 272 q^{71} + 224 q^{74} - 560 q^{79} - 144 q^{81} + 48 q^{84} - 176 q^{86} + 600 q^{89} - 544 q^{91} + 48 q^{99}+O(q^{100}) $ 32 * q + 32 * q^4 - 48 * q^9 - 8 * q^11 - 16 * q^14 - 64 * q^16 + 144 * q^19 - 48 * q^21 - 144 * q^29 + 240 * q^31 - 192 * q^36 - 72 * q^39 + 16 * q^44 + 16 * q^46 + 80 * q^49 - 24 * q^51 + 32 * q^56 - 264 * q^59 + 192 * q^61 - 256 * q^64 + 144 * q^66 - 272 * q^71 + 224 * q^74 - 560 * q^79 - 144 * q^81 + 48 * q^84 - 176 * q^86 + 600 * q^89 - 544 * q^91 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		−	2.44949i		−	0.408248i
$7$	5.56601	+	4.24494i	0.795145	+	0.606420i
$7$	5.56601	+	4.24494i	0.795145	+	0.606420i
$8$			2.82843i			0.353553i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$		0			0
$11$	5.42967	−	9.40447i	0.493607	−	0.854952i	−0.506366	−	0.862319i	$-0.669012\pi$
$11$	5.42967	−	9.40447i	0.493607	−	0.854952i	0.999973	+	0.00736658i	$0.00234488\pi$
$12$	1.73205	+	3.00000i	0.144338	+	0.250000i
$13$	0.772061			0.0593893			0.0296946	−	0.999559i	$-0.490547\pi$
$13$	0.772061			0.0593893			0.0296946	+	0.999559i	$0.490547\pi$
$14$	−9.81857	−	1.26320i	−0.701326	−	0.0902284i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−9.68565	+	16.7760i	−0.569744	+	0.986826i	0.426847	+	0.904324i	$0.359624\pi$
$17$	−9.68565	+	16.7760i	−0.569744	+	0.986826i	−0.996591	+	0.0825021i	$0.973709\pi$
$18$	3.67423	+	2.12132i	0.204124	+	0.117851i
$19$	−22.5766	+	13.0346i	−1.18824	+	0.686032i	−0.957907	−	0.287079i	$-0.907316\pi$
$19$	−22.5766	+	13.0346i	−1.18824	+	0.686032i	−0.230335	+	0.973111i	$0.573982\pi$
$20$		0			0
$21$	−11.1877	+	4.67280i	−0.532748	+	0.222514i
$22$			15.3574i			0.698065i
$23$	11.8599	−	6.84734i	0.515650	−	0.297711i	−0.219503	−	0.975612i	$-0.570444\pi$
$23$	11.8599	−	6.84734i	0.515650	−	0.297711i	0.735153	+	0.677901i	$0.237110\pi$
$24$	−4.24264	−	2.44949i	−0.176777	−	0.102062i
$25$		0			0
$26$	−0.945577	+	0.545929i	−0.0363684	+	0.0209973i
$27$	5.19615			0.192450
$28$	12.9185	−	5.39568i	0.461374	−	0.192703i
$29$	6.99131			0.241080			0.120540	−	0.992708i	$-0.461537\pi$
$29$	6.99131			0.241080			0.120540	+	0.992708i	$0.461537\pi$
$30$		0			0
$31$	22.7559	+	13.1381i	0.734062	+	0.423811i	0.819906	−	0.572497i	$-0.194025\pi$
$31$	22.7559	+	13.1381i	0.734062	+	0.423811i	−0.0858441	+	0.996309i	$0.527359\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$	9.40447	+	16.2890i	0.284984	+	0.493607i
$34$		−	27.3952i		−	0.805740i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	55.9459	−	32.3004i	1.51205	−	0.872984i	0.512152	−	0.858895i	$-0.328849\pi$
$37$	55.9459	−	32.3004i	1.51205	−	0.872984i	0.999901	−	0.0140890i	$-0.00448483\pi$
$38$	18.4337	−	31.9281i	0.485098	−	0.840214i
$39$	−0.668624	+	1.15809i	−0.0171442	+	0.0296946i
$40$		0			0
$41$		−	5.54839i		−	0.135327i	−0.997708	−	0.0676633i	$-0.978446\pi$
$41$		−	5.54839i		−	0.135327i	0.997708	−	0.0676633i	$-0.0215544\pi$
$42$	10.3979	−	13.6339i	0.247570	−	0.324617i
$43$			68.9320i			1.60307i	0.597948	+	0.801535i	$0.295983\pi$
$43$			68.9320i			1.60307i	−0.597948	+	0.801535i	$0.704017\pi$
$44$	−10.8593	−	18.8089i	−0.246803	−	0.427476i
$45$		0			0
$46$	−9.68361	+	16.7725i	−0.210513	+	0.364620i
$47$	−11.3055	−	19.5817i	−0.240542	−	0.416631i	0.720327	−	0.693635i	$-0.243992\pi$
$47$	−11.3055	−	19.5817i	−0.240542	−	0.416631i	−0.960869	+	0.277004i	$0.910658\pi$
$48$	6.92820			0.144338
$49$	12.9610	+	47.2548i	0.264511	+	0.964383i
$50$		0			0
$51$	−16.7760	−	29.0570i	−0.328942	−	0.569744i
$52$	0.772061	−	1.33725i	0.0148473	−	0.0257163i
$53$	64.5742	+	37.2820i	1.21838	+	0.703433i	0.964572	−	0.263821i	$-0.0849828\pi$
$53$	64.5742	+	37.2820i	1.21838	+	0.703433i	0.253810	+	0.967254i	$0.418316\pi$
$54$	−6.36396	+	3.67423i	−0.117851	+	0.0680414i
$55$		0			0
$56$	−12.0065	+	15.7431i	−0.214402	+	0.281126i
$57$		−	45.1532i		−	0.792161i
$58$	−8.56257	+	4.94360i	−0.147631	+	0.0852345i
$59$	−96.6595	−	55.8064i	−1.63830	−	0.945871i	−0.981420	−	0.191874i	$-0.938543\pi$
$59$	−96.6595	−	55.8064i	−1.63830	−	0.945871i	−0.656878	−	0.753997i	$-0.728123\pi$
$60$		0			0
$61$	−46.9572	+	27.1108i	−0.769790	+	0.444439i	−0.832800	−	0.553574i	$-0.813263\pi$
$61$	−46.9572	+	27.1108i	−0.769790	+	0.444439i	0.0630096	+	0.998013i	$0.479930\pi$
$62$	−37.1603			−0.599359
$63$	2.67965	−	20.8283i	0.0425341	−	0.330608i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	−23.0362	−	13.2999i	−0.349033	−	0.201514i
$67$	38.3255	+	22.1273i	0.572023	+	0.330258i	0.757957	−	0.652305i	$-0.226198\pi$
$67$	38.3255	+	22.1273i	0.572023	+	0.330258i	−0.185934	+	0.982562i	$0.559531\pi$
$68$	19.3713	+	33.5521i	0.284872	+	0.493413i
$69$			23.7199i			0.343767i
$70$		0			0
$71$	31.9550			0.450071			0.225035	−	0.974351i	$-0.427750\pi$
$71$	31.9550			0.450071			0.225035	+	0.974351i	$0.427750\pi$
$72$	7.34847	−	4.24264i	0.102062	−	0.0589256i
$73$	−53.4812	+	92.6322i	−0.732619	+	1.26893i	0.223141	+	0.974786i	$0.428369\pi$
$73$	−53.4812	+	92.6322i	−0.732619	+	1.26893i	−0.955760	+	0.294147i	$0.904964\pi$
$74$	−45.6797	+	79.1195i	−0.617293	+	1.06918i
$75$		0			0
$76$			52.1384i			0.686032i
$77$	70.1430	−	29.2968i	0.910949	−	0.380478i
$78$		−	1.89115i		−	0.0242456i
$79$	14.8408	+	25.7050i	0.187858	+	0.325380i	0.944536	−	0.328408i	$-0.106512\pi$
$79$	14.8408	+	25.7050i	0.187858	+	0.325380i	−0.756678	+	0.653788i	$0.773179\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	3.92330	+	6.79536i	0.0478451	+	0.0828702i
$83$	15.8151			0.190543			0.0952717	−	0.995451i	$-0.469628\pi$
$83$	15.8151			0.190543			0.0952717	+	0.995451i	$0.469628\pi$
$84$	−3.09419	+	24.0505i	−0.0368356	+	0.286315i
$85$		0			0
$86$	−48.7423	−	84.4242i	−0.566771	−	0.981676i
$87$	−6.05465	+	10.4870i	−0.0695937	+	0.120540i
$88$	26.5999	+	15.3574i	0.302271	+	0.174516i
$89$	31.8358	−	18.3804i	0.357706	−	0.206521i	−0.310368	−	0.950616i	$-0.600452\pi$
$89$	31.8358	−	18.3804i	0.357706	−	0.206521i	0.668074	+	0.744095i	$0.267119\pi$
$90$		0			0
$91$	4.29730	+	3.27735i	0.0472231	+	0.0360148i
$92$		−	27.3894i		−	0.297711i
$93$	−39.4144	+	22.7559i	−0.423811	+	0.244687i
$94$	27.6926	+	15.9884i	0.294603	+	0.170089i
$95$		0			0
$96$	−8.48528	+	4.89898i	−0.0883883	+	0.0510310i
$97$	−134.212			−1.38363			−0.691813	−	0.722077i	$-0.743188\pi$
$97$	−134.212			−1.38363			−0.691813	+	0.722077i	$0.743188\pi$
$98$	−49.2881	−	48.7102i	−0.502940	−	0.497043i
$99$	−32.5780			−0.329071
$100$		0			0
$101$	132.760	+	76.6490i	1.31445	+	0.758901i	0.982830	−	0.184511i	$-0.0590702\pi$
$101$	132.760	+	76.6490i	1.31445	+	0.758901i	0.331624	+	0.943412i	$0.392404\pi$
$102$	41.0927	+	23.7249i	0.402870	+	0.232597i
$103$	31.6679	+	54.8504i	0.307456	+	0.532529i	0.977805	−	0.209517i	$-0.0671891\pi$
$103$	31.6679	+	54.8504i	0.307456	+	0.532529i	−0.670349	+	0.742046i	$0.733856\pi$
$104$			2.18372i			0.0209973i
$105$		0			0
$106$	−105.449			−0.994805
$107$	−37.9800	+	21.9277i	−0.354953	+	0.204932i	−0.666865	−	0.745179i	$-0.732364\pi$
$107$	−37.9800	+	21.9277i	−0.354953	+	0.204932i	0.311912	+	0.950111i	$0.399031\pi$
$108$	5.19615	−	9.00000i	0.0481125	−	0.0833333i
$109$	2.64166	−	4.57549i	0.0242354	−	0.0419770i	−0.853653	−	0.520842i	$-0.825618\pi$
$109$	2.64166	−	4.57549i	0.0242354	−	0.0419770i	0.877889	+	0.478865i	$0.158952\pi$
$110$		0			0
$111$			111.892i			1.00804i
$112$	3.57286	−	27.7711i	0.0319006	−	0.247956i
$113$			106.725i			0.944469i	0.881473	+	0.472234i	$0.156552\pi$
$113$			106.725i			0.944469i	−0.881473	+	0.472234i	$0.843448\pi$
$114$	31.9281	+	55.3011i	0.280071	+	0.485098i
$115$		0			0
$116$	6.99131	−	12.1093i	0.0602699	−	0.104391i
$117$	−1.15809	−	2.00587i	−0.00989821	−	0.0171442i
$118$	157.844			1.33766
$119$	−125.124	+	52.2607i	−1.05146	+	0.439166i
$120$		0			0
$121$	1.53727	+	2.66262i	0.0127047	+	0.0220051i
$122$	38.3404	−	66.4075i	0.314266	−	0.544324i
$123$	8.32258	+	4.80504i	0.0676633	+	0.0390654i
$124$	45.5119	−	26.2763i	0.367031	−	0.211906i
$125$		0			0
$126$	11.4460	+	27.4042i	0.0908410	+	0.217494i
$127$			203.641i			1.60348i	0.597676	+	0.801738i	$0.296091\pi$
$127$			203.641i			1.60348i	−0.597676	+	0.801738i	$0.703909\pi$
$128$	9.79796	−	5.65685i	0.0765466	−	0.0441942i
$129$	−103.398	−	59.6969i	−0.801535	−	0.462767i
$130$		0			0
$131$	−67.2791	+	38.8436i	−0.513581	+	0.296516i	−0.734304	−	0.678820i	$-0.762491\pi$
$131$	−67.2791	+	38.8436i	−0.513581	+	0.296516i	0.220724	+	0.975336i	$0.429158\pi$
$132$	37.6179			0.284984
$133$	−180.993	−	23.2854i	−1.36085	−	0.175078i
$134$	−62.5853			−0.467055
$135$		0			0
$136$	−47.4498	−	27.3952i	−0.348896	−	0.201435i
$137$	−198.326	−	114.504i	−1.44764	−	0.835794i	−0.449297	−	0.893382i	$-0.648326\pi$
$137$	−198.326	−	114.504i	−1.44764	−	0.835794i	−0.998340	+	0.0575883i	$0.981659\pi$
$138$	−16.7725	−	29.0508i	−0.121540	−	0.210513i
$139$			61.7421i			0.444188i	0.975025	+	0.222094i	$0.0712892\pi$
$139$			61.7421i			0.444188i	−0.975025	+	0.222094i	$0.928711\pi$
$140$		0			0
$141$	39.1633			0.277754
$142$	−39.1368	+	22.5956i	−0.275611	+	0.159124i
$143$	4.19204	−	7.26082i	0.0293149	−	0.0507750i
$144$	−6.00000	+	10.3923i	−0.0416667	+	0.0721688i
$145$		0			0
$146$		−	151.268i		−	1.03608i
$147$	−82.1067	−	21.4823i	−0.558549	−	0.146138i
$148$		−	129.202i		−	0.872984i
$149$	−14.6523	−	25.3785i	−0.0983373	−	0.170325i	0.812659	−	0.582739i	$-0.198019\pi$
$149$	−14.6523	−	25.3785i	−0.0983373	−	0.170325i	−0.910997	+	0.412414i	$0.864686\pi$
$150$		0			0
$151$	−81.8479	+	141.765i	−0.542039	+	0.938839i	0.456748	+	0.889596i	$0.349014\pi$
$151$	−81.8479	+	141.765i	−0.542039	+	0.938839i	−0.998787	+	0.0492431i	$0.984319\pi$
$152$	−36.8674	−	63.8563i	−0.242549	−	0.420107i
$153$	58.1139			0.379830
$154$	−65.1914	+	85.4797i	−0.423320	+	0.555063i
$155$		0			0
$156$	1.33725	+	2.31618i	0.00857210	+	0.0148473i
$157$	−104.351	+	180.741i	−0.664657	+	1.15122i	0.314722	+	0.949184i	$0.398089\pi$
$157$	−104.351	+	180.741i	−0.664657	+	1.15122i	−0.979378	+	0.202035i	$0.935245\pi$
$158$	−36.3524	−	20.9880i	−0.230078	−	0.132836i
$159$	−111.846	+	64.5742i	−0.703433	+	0.406127i
$160$		0			0
$161$	95.0792	+	12.2323i	0.590554	+	0.0759771i
$162$		−	12.7279i		−	0.0785674i
$163$	−120.523	+	69.5841i	−0.739406	+	0.426896i	−0.821853	−	0.569699i	$-0.807060\pi$
$163$	−120.523	+	69.5841i	−0.739406	+	0.426896i	0.0824475	+	0.996595i	$0.473726\pi$
$164$	−9.61009	−	5.54839i	−0.0585981	−	0.0338316i
$165$		0			0
$166$	−19.3695	+	11.1830i	−0.116683	+	0.0673672i
$167$	−54.4023			−0.325762			−0.162881	−	0.986646i	$-0.552079\pi$
$167$	−54.4023			−0.325762			−0.162881	+	0.986646i	$0.552079\pi$
$168$	−13.2167	−	31.6436i	−0.0786707	−	0.188355i
$169$	−168.404			−0.996473
$170$		0			0
$171$	67.7298	+	39.1038i	0.396081	+	0.228677i
$172$	119.394	+	68.9320i	0.694150	+	0.400768i
$173$	−31.3918	−	54.3723i	−0.181456	−	0.314291i	0.760921	−	0.648845i	$-0.224748\pi$
$173$	−31.3918	−	54.3723i	−0.181456	−	0.314291i	−0.942376	+	0.334554i	$0.891414\pi$
$174$		−	17.1251i		−	0.0984203i
$175$		0			0
$176$	−43.4374			−0.246803
$177$	167.419	−	96.6595i	0.945871	−	0.546099i
$178$	−25.9938	+	45.0226i	−0.146033	+	0.252936i
$179$	−70.3978	+	121.933i	−0.393284	+	0.681187i	−0.992880	−	0.119115i	$-0.961994\pi$
$179$	−70.3978	+	121.933i	−0.393284	+	0.681187i	0.599597	+	0.800302i	$0.295328\pi$
$180$		0			0
$181$		−	222.987i		−	1.23197i	−0.787757	−	0.615986i	$-0.788758\pi$
$181$		−	222.987i		−	1.23197i	0.787757	−	0.615986i	$-0.211242\pi$
$182$	−7.58053	−	0.975265i	−0.0416513	−	0.00535860i
$183$		−	93.9144i		−	0.513193i
$184$	19.3672	+	33.5450i	0.105257	+	0.182310i
$185$		0			0
$186$	32.1817	−	55.7404i	0.173020	−	0.299680i
$187$	105.180	+	182.177i	0.562459	+	0.974208i
$188$	−45.2219			−0.240542
$189$	28.9219	+	22.0573i	0.153026	+	0.116705i
$190$		0			0
$191$	−66.5069	−	115.193i	−0.348204	−	0.603106i	0.637727	−	0.770263i	$-0.279875\pi$
$191$	−66.5069	−	115.193i	−0.348204	−	0.603106i	−0.985930	+	0.167156i	$0.946542\pi$
$192$	6.92820	−	12.0000i	0.0360844	−	0.0625000i
$193$	247.010	+	142.611i	1.27984	+	0.738919i	0.976820	−	0.214064i	$-0.0686700\pi$
$193$	247.010	+	142.611i	1.27984	+	0.738919i	0.303025	+	0.952983i	$0.402003\pi$
$194$	164.375	−	94.9020i	0.847295	−	0.489186i
$195$		0			0
$196$	94.8087	+	24.8056i	0.483718	+	0.126559i
$197$		−	307.784i		−	1.56236i	−0.624309	−	0.781178i	$-0.714619\pi$
$197$		−	307.784i		−	1.56236i	0.624309	−	0.781178i	$-0.285381\pi$
$198$	39.8998	−	23.0362i	0.201514	−	0.116344i
$199$	8.39167	+	4.84493i	0.0421692	+	0.0243464i	0.520936	−	0.853595i	$-0.325583\pi$
$199$	8.39167	+	4.84493i	0.0421692	+	0.0243464i	−0.478767	+	0.877942i	$0.658916\pi$
$200$		0			0
$201$	−66.3818	+	38.3255i	−0.330258	+	0.190674i
$202$	−216.796			−1.07325
$203$	38.9137	+	29.6777i	0.191693	+	0.146195i
$204$	−67.1042			−0.328942
$205$		0			0
$206$	−77.5702	−	44.7852i	−0.376555	−	0.217404i
$207$	−35.5798	−	20.5420i	−0.171883	−	0.0992369i
$208$	−1.54412	−	2.67450i	−0.00742366	−	0.0128582i
$209$			283.095i			1.35452i
$210$		0			0
$211$	175.954			0.833903			0.416952	−	0.908929i	$-0.363098\pi$
$211$	175.954			0.833903			0.416952	+	0.908929i	$0.363098\pi$
$212$	129.148	−	74.5639i	0.609191	−	0.351717i
$213$	−27.6739	+	47.9326i	−0.129924	+	0.225035i
$214$	31.0105	−	53.7118i	0.144909	−	0.250990i
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	70.8893	+	169.725i	0.326679	+	0.782141i
$218$			7.47174i			0.0342740i
$219$	−92.6322	−	160.444i	−0.422978	−	0.732619i
$220$		0			0
$221$	−7.47791	+	12.9521i	−0.0338367	+	0.0586069i
$222$	−79.1195	−	137.039i	−0.356394	−	0.617293i
$223$	50.0854			0.224598			0.112299	−	0.993674i	$-0.464178\pi$
$223$	50.0854			0.224598			0.112299	+	0.993674i	$0.464178\pi$
$224$	15.2613	+	36.5389i	0.0681308	+	0.163120i
$225$		0			0
$226$	−75.4659	−	130.711i	−0.333920	−	0.578366i
$227$	−152.594	+	264.301i	−0.672221	+	1.16432i	0.305052	+	0.952336i	$0.401326\pi$
$227$	−152.594	+	264.301i	−0.672221	+	1.16432i	−0.977273	+	0.211985i	$0.932007\pi$
$228$	−78.2076	−	45.1532i	−0.343016	−	0.198040i
$229$	353.428	−	204.052i	1.54335	−	0.891055i	0.544728	−	0.838613i	$-0.316633\pi$
$229$	353.428	−	204.052i	1.54335	−	0.891055i	0.998624	−	0.0524421i	$-0.0167005\pi$
$230$		0			0
$231$	−16.8004	+	130.586i	−0.0727292	+	0.565309i
$232$			19.7744i			0.0852345i
$233$	−187.762	+	108.404i	−0.805846	+	0.465255i	−0.845511	−	0.533958i	$-0.820704\pi$
$233$	−187.762	+	108.404i	−0.805846	+	0.465255i	0.0396654	+	0.999213i	$0.487371\pi$
$234$	2.83673	+	1.63779i	0.0121228	+	0.00699909i
$235$		0			0
$236$	−193.319	+	111.613i	−0.819149	+	0.472936i
$237$	−51.4100			−0.216920
$238$	116.291	−	152.482i	0.488617	−	0.640680i
$239$	389.739			1.63071			0.815354	−	0.578963i	$-0.196543\pi$
$239$	389.739			1.63071			0.815354	+	0.578963i	$0.196543\pi$
$240$		0			0
$241$	60.0686	+	34.6806i	0.249247	+	0.143903i	0.619419	−	0.785060i	$-0.287368\pi$
$241$	60.0686	+	34.6806i	0.249247	+	0.143903i	−0.370172	+	0.928963i	$0.620701\pi$
$242$	−3.76552	−	2.17402i	−0.0155600	−	0.00898356i
$243$	−7.79423	−	13.5000i	−0.0320750	−	0.0555556i
$244$			108.443i			0.444439i
$245$		0			0
$246$	−13.5907			−0.0552468
$247$	−17.4305	+	10.0635i	−0.0705688	+	0.0407429i
$248$	−37.1603	+	64.3635i	−0.149840	+	0.259530i
$249$	−13.6963	+	23.7226i	−0.0550051	+	0.0952717i
$250$		0			0
$251$		−	256.631i		−	1.02244i	−0.859451	−	0.511218i	$-0.829195\pi$
$251$		−	256.631i		−	1.02244i	0.859451	−	0.511218i	$-0.170805\pi$
$252$	−33.3961	−	25.4696i	−0.132524	−	0.101070i
$253$		−	148.715i		−	0.587808i
$254$	−143.996	−	249.409i	−0.566914	−	0.981924i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−100.458	−	173.998i	−0.390886	−	0.677034i	0.601681	−	0.798737i	$-0.294498\pi$
$257$	−100.458	−	173.998i	−0.390886	−	0.677034i	−0.992567	+	0.121703i	$0.961165\pi$
$258$	168.848			0.654451
$259$	448.509	+	57.7025i	1.73170	+	0.222789i
$260$		0			0
$261$	−10.4870	−	18.1640i	−0.0401799	−	0.0695937i
$262$	54.9331	−	95.1470i	0.209668	−	0.363156i
$263$	435.602	+	251.495i	1.65628	+	0.956256i	0.974408	+	0.224787i	$0.0721686\pi$
$263$	435.602	+	251.495i	1.65628	+	0.956256i	0.681875	+	0.731469i	$0.261165\pi$
$264$	−46.0723	+	26.5999i	−0.174516	+	0.100757i
$265$		0			0
$266$	238.135	−	99.4625i	0.895245	−	0.373919i
$267$			63.6716i			0.238470i
$268$	76.6511	−	44.2545i	0.286012	−	0.165129i
$269$	121.754	+	70.2945i	0.452616	+	0.261318i	0.708934	−	0.705275i	$-0.249176\pi$
$269$	121.754	+	70.2945i	0.452616	+	0.261318i	−0.256318	+	0.966592i	$0.582510\pi$
$270$		0			0
$271$	103.808	−	59.9334i	0.383054	−	0.221157i	−0.296092	−	0.955159i	$-0.595684\pi$
$271$	103.808	−	59.9334i	0.383054	−	0.221157i	0.679146	+	0.734003i	$0.262350\pi$
$272$	77.4852			0.284872
$273$	−8.63759	+	3.60768i	−0.0316395	+	0.0132150i
$274$	323.866			1.18199
$275$		0			0
$276$	41.0841	+	23.7199i	0.148855	+	0.0859416i
$277$	92.6706	+	53.5034i	0.334551	+	0.193153i	0.657860	−	0.753140i	$-0.271462\pi$
$277$	92.6706	+	53.5034i	0.334551	+	0.193153i	−0.323309	+	0.946293i	$0.604795\pi$
$278$	−43.6583	−	75.6183i	−0.157044	−	0.272008i
$279$		−	78.8289i		−	0.282541i
$280$		0			0
$281$	−85.5187			−0.304337			−0.152169	−	0.988355i	$-0.548626\pi$
$281$	−85.5187			−0.304337			−0.152169	+	0.988355i	$0.548626\pi$
$282$	−47.9651	+	27.6926i	−0.170089	+	0.0982008i
$283$	−196.011	+	339.501i	−0.692619	+	1.19965i	0.278358	+	0.960477i	$0.410210\pi$
$283$	−196.011	+	339.501i	−0.692619	+	1.19965i	−0.970977	+	0.239173i	$0.923124\pi$
$284$	31.9550	−	55.3477i	0.112518	−	0.194886i
$285$		0			0
$286$			11.8569i			0.0414576i
$287$	23.5526	−	30.8824i	0.0820646	−	0.107604i
$288$		−	16.9706i		−	0.0589256i
$289$	−43.1238	−	74.6926i	−0.149217	−	0.258452i
$290$		0			0
$291$	116.231	−	201.318i	0.399419	−	0.691813i
$292$	106.962	+	185.264i	0.366310	+	0.634467i
$293$	−500.595			−1.70851			−0.854257	−	0.519850i	$-0.825988\pi$
$293$	−500.595			−1.70851			−0.854257	+	0.519850i	$0.825988\pi$
$294$	115.750	−	31.7479i	0.393708	−	0.107986i
$295$		0			0
$296$	91.3593	+	158.239i	0.308646	+	0.534591i
$297$	28.2134	−	48.8671i	0.0949947	−	0.164536i
$298$	35.8906	+	20.7214i	0.120438	+	0.0695350i
$299$	9.15660	−	5.28656i	0.0306241	−	0.0176808i
$300$		0			0
$301$	−292.612	+	383.677i	−0.972133	+	1.27467i
$302$		−	231.501i		−	0.766559i
$303$	−229.947	+	132.760i	−0.758901	+	0.438151i
$304$	90.3064	+	52.1384i	0.297061	+	0.171508i
$305$		0			0
$306$	−71.1747	+	41.0927i	−0.232597	+	0.134290i
$307$	398.171			1.29698			0.648488	−	0.761225i	$-0.275402\pi$
$307$	398.171			1.29698			0.648488	+	0.761225i	$0.275402\pi$
$308$	19.3995	−	150.788i	0.0629853	−	0.489572i
$309$	−109.701			−0.355019
$310$		0			0
$311$	322.107	+	185.968i	1.03571	+	0.597969i	0.918616	−	0.395151i	$-0.129308\pi$
$311$	322.107	+	185.968i	1.03571	+	0.597969i	0.117097	+	0.993120i	$0.462641\pi$
$312$	−3.27558	−	1.89115i	−0.0104986	−	0.00606139i
$313$	−211.243	−	365.884i	−0.674899	−	1.16896i	−0.976499	−	0.215524i	$-0.930854\pi$
$313$	−211.243	−	365.884i	−0.674899	−	1.16896i	0.301600	−	0.953435i	$-0.402479\pi$
$314$		−	295.149i		−	0.939966i
$315$		0			0
$316$	59.3632			0.187858
$317$	187.219	−	108.091i	0.590597	−	0.340981i	−0.174737	−	0.984615i	$-0.555907\pi$
$317$	187.219	−	108.091i	0.590597	−	0.340981i	0.765333	+	0.643634i	$0.222574\pi$
$318$	91.3218	−	158.174i	0.287175	−	0.497402i
$319$	37.9605	−	65.7496i	0.118999	−	0.206112i
$320$		0			0
$321$		−	75.9599i		−	0.236635i
$322$	−125.097	+	52.2497i	−0.388501	+	0.162266i
$323$		−	504.995i		−	1.56345i
$324$	9.00000	+	15.5885i	0.0277778	+	0.0481125i
$325$		0			0
$326$	98.4067	−	170.445i	0.301861	−	0.522839i
$327$	4.57549	+	7.92498i	0.0139923	+	0.0242354i
$328$	15.6932			0.0478451
$329$	20.1965	−	156.983i	0.0613874	−	0.477151i
$330$		0			0
$331$	−105.730	−	183.130i	−0.319426	−	0.553262i	0.660942	−	0.750437i	$-0.270157\pi$
$331$	−105.730	−	183.130i	−0.319426	−	0.553262i	−0.980368	+	0.197175i	$0.936823\pi$
$332$	15.8151	−	27.3926i	0.0476358	−	0.0825077i
$333$	−167.838	−	96.9012i	−0.504018	−	0.290995i
$334$	66.6289	−	38.4682i	0.199488	−	0.115174i
$335$		0			0
$336$	38.5625	+	29.4098i	0.114769	+	0.0875291i
$337$			260.379i			0.772639i	0.922365	+	0.386319i	$0.126254\pi$
$337$			260.379i			0.772639i	−0.922365	+	0.386319i	$0.873746\pi$
$338$	206.252	−	119.080i	0.610213	−	0.352306i
$339$	−160.087	−	92.4265i	−0.472234	−	0.272645i
$340$		0			0
$341$	247.115	−	142.672i	0.724676	−	0.418392i
$342$	−110.602			−0.323399
$343$	−128.452	+	318.039i	−0.374496	+	0.927228i
$344$	−194.969			−0.566771
$345$		0			0
$346$	76.8940	+	44.3948i	0.222237	+	0.128309i
$347$	443.350	+	255.968i	1.27767	+	0.737661i	0.976419	−	0.215885i	$-0.0692636\pi$
$347$	443.350	+	255.968i	1.27767	+	0.737661i	0.301247	+	0.953546i	$0.402597\pi$
$348$	12.1093	+	20.9739i	0.0347968	+	0.0602699i
$349$		−	527.872i		−	1.51253i	−0.654266	−	0.756264i	$-0.727022\pi$
$349$		−	527.872i		−	1.51253i	0.654266	−	0.756264i	$-0.272978\pi$
$350$		0			0
$351$	4.01174			0.0114295
$352$	53.1997	−	30.7149i	0.151136	−	0.0872582i
$353$	68.2579	−	118.226i	0.193365	−	0.334918i	−0.752998	−	0.658023i	$-0.771393\pi$
$353$	68.2579	−	118.226i	0.193365	−	0.334918i	0.946363	+	0.323104i	$0.104726\pi$
$354$	−136.697	+	236.767i	−0.386150	+	0.668832i
$355$		0			0
$356$		−	73.5216i		−	0.206521i
$357$	29.9693	−	232.945i	0.0839475	−	0.652506i
$358$		−	199.115i		−	0.556187i
$359$	−278.525	−	482.419i	−0.775835	−	1.34379i	−0.934324	−	0.356424i	$-0.883996\pi$
$359$	−278.525	−	482.419i	−0.775835	−	1.34379i	0.158490	−	0.987361i	$-0.449338\pi$
$360$		0			0
$361$	159.302	−	275.919i	0.441279	−	0.764318i
$362$	157.676	+	273.102i	0.435568	+	0.754426i
$363$	−5.32525			−0.0146701
$364$	9.97383	−	4.16579i	0.0274006	−	0.0114445i
$365$		0			0
$366$	66.4075	+	115.021i	0.181441	+	0.314266i
$367$	−59.0110	+	102.210i	−0.160793	+	0.278502i	−0.935153	−	0.354243i	$-0.884738\pi$
$367$	−59.0110	+	102.210i	−0.160793	+	0.278502i	0.774360	+	0.632745i	$0.218072\pi$
$368$	−47.4398	−	27.3894i	−0.128912	−	0.0744276i
$369$	−14.4151	+	8.32258i	−0.0390654	+	0.0225544i
$370$		0			0
$371$	201.162	+	481.625i	0.542215	+	1.29818i
$372$			91.0237i			0.244687i
$373$	275.718	−	159.186i	0.739191	−	0.426772i	−0.0825840	−	0.996584i	$-0.526317\pi$
$373$	275.718	−	159.186i	0.739191	−	0.426772i	0.821775	+	0.569812i	$0.192984\pi$
$374$	−257.637	−	148.747i	−0.688869	−	0.397719i
$375$		0			0
$376$	55.3853	−	31.9767i	0.147301	−	0.0850444i
$377$	5.39771			0.0143175
$378$	−51.0188	−	6.56377i	−0.134970	−	0.0173645i
$379$	579.699			1.52955			0.764774	−	0.644299i	$-0.222851\pi$
$379$	579.699			1.52955			0.764774	+	0.644299i	$0.222851\pi$
$380$		0			0
$381$	−305.462	−	176.359i	−0.801738	−	0.462883i
$382$	162.908	+	94.0549i	0.426461	+	0.246217i
$383$	−304.022	−	526.581i	−0.793790	−	1.37488i	−0.923605	−	0.383346i	$-0.874772\pi$
$383$	−304.022	−	526.581i	−0.793790	−	1.37488i	0.129815	−	0.991538i	$-0.458562\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−403.366			−1.04499
$387$	179.091	−	103.398i	0.462767	−	0.267178i
$388$	−134.212	+	232.462i	−0.345907	+	0.599128i
$389$	57.5081	−	99.6069i	0.147836	−	0.256059i	−0.782592	−	0.622535i	$-0.786103\pi$
$389$	57.5081	−	99.6069i	0.147836	−	0.256059i	0.930427	+	0.366476i	$0.119436\pi$
$390$		0			0
$391$			265.284i			0.678476i
$392$	−133.657	+	36.6593i	−0.340961	+	0.0935187i
$393$		−	134.558i		−	0.342387i
$394$	217.636	+	376.957i	0.552376	+	0.956744i
$395$		0			0
$396$	−32.5780	+	56.4268i	−0.0822678	+	0.142492i
$397$	−80.3952	−	139.249i	−0.202507	−	0.350752i	0.746829	−	0.665016i	$-0.231575\pi$
$397$	−80.3952	−	139.249i	−0.202507	−	0.350752i	−0.949336	+	0.314264i	$0.898242\pi$
$398$	−13.7035			−0.0344310
$399$	191.672	−	251.323i	0.480382	−	0.629883i
$400$		0			0
$401$	29.4028	+	50.9272i	0.0733238	+	0.127000i	0.900356	−	0.435154i	$-0.143306\pi$
$401$	29.4028	+	50.9272i	0.0733238	+	0.127000i	−0.827032	+	0.562154i	$0.809973\pi$
$402$	54.2005	−	93.8780i	0.134827	−	0.233527i
$403$	17.5690	+	10.1434i	0.0435954	+	0.0251698i
$404$	265.520	−	153.298i	0.657227	−	0.379450i
$405$		0			0
$406$	−68.6447	−	8.83141i	−0.169076	−	0.0217522i
$407$		−	701.523i		−	1.72364i
$408$	82.1855	−	47.4498i	0.201435	−	0.116299i
$409$	−182.052	−	105.108i	−0.445114	−	0.256987i	0.260650	−	0.965433i	$-0.416063\pi$
$409$	−182.052	−	105.108i	−0.445114	−	0.256987i	−0.705765	+	0.708446i	$0.749396\pi$
$410$		0			0
$411$	343.511	−	198.326i	0.835794	−	0.482546i
$412$	126.672			0.307456
$413$	−301.114	−	720.933i	−0.729089	−	1.74560i
$414$	58.1016			0.140342
$415$		0			0
$416$	3.78231	+	2.18372i	0.00909209	+	0.00524932i
$417$	−92.6132	−	53.4702i	−0.222094	−	0.128226i
$418$	−200.178	−	346.719i	−0.478895	−	0.829471i
$419$			690.319i			1.64754i	0.566924	+	0.823770i	$0.308133\pi$
$419$			690.319i			1.64754i	−0.566924	+	0.823770i	$0.691867\pi$
$420$		0			0
$421$	407.084			0.966945			0.483472	−	0.875360i	$-0.339375\pi$
$421$	407.084			0.966945			0.483472	+	0.875360i	$0.339375\pi$
$422$	−215.498	+	124.418i	−0.510659	+	0.294829i
$423$	−33.9164	+	58.7450i	−0.0801807	+	0.138877i
$424$	−105.449	+	182.644i	−0.248701	+	0.430763i
$425$		0			0
$426$		−	78.2735i		−	0.183741i
$427$	−376.448	−	48.4315i	−0.881611	−	0.113423i
$428$			87.7110i			0.204932i
$429$	7.26082	+	12.5761i	0.0169250	+	0.0293149i
$430$		0			0
$431$	28.0096	−	48.5141i	0.0649875	−	0.112562i	−0.831701	−	0.555224i	$-0.812633\pi$
$431$	28.0096	−	48.5141i	0.0649875	−	0.112562i	0.896688	+	0.442662i	$0.145966\pi$
$432$	−10.3923	−	18.0000i	−0.0240563	−	0.0416667i
$433$	71.4593			0.165033			0.0825165	−	0.996590i	$-0.473704\pi$
$433$	71.4593			0.165033			0.0825165	+	0.996590i	$0.473704\pi$
$434$	−206.835	−	157.743i	−0.476578	−	0.363463i
$435$		0			0
$436$	−5.28332	−	9.15098i	−0.0121177	−	0.0209885i
$437$	−178.505	+	309.179i	−0.408478	+	0.707504i
$438$	226.902	+	131.002i	0.518040	+	0.299091i
$439$	691.975	−	399.512i	1.57625	−	0.910050i	0.580878	−	0.813991i	$-0.302710\pi$
$439$	691.975	−	399.512i	1.57625	−	0.910050i	0.995376	−	0.0960592i	$-0.0306238\pi$
$440$		0			0
$441$	103.330	−	104.556i	0.234308	−	0.237088i
$442$		−	21.1507i		−	0.0478523i
$443$	703.559	−	406.200i	1.58817	−	0.916930i	0.594561	−	0.804051i	$-0.297326\pi$
$443$	703.559	−	406.200i	1.58817	−	0.916930i	0.993609	−	0.112879i	$-0.0360073\pi$
$444$	193.802	+	111.892i	0.436492	+	0.252009i
$445$		0			0
$446$	−61.3419	+	35.4157i	−0.137538	+	0.0794075i
$447$	50.7569			0.113550
$448$	−44.5281	−	33.9595i	−0.0993931	−	0.0758024i
$449$	−434.785			−0.968340			−0.484170	−	0.874974i	$-0.660878\pi$
$449$	−434.785			−0.968340			−0.484170	+	0.874974i	$0.660878\pi$
$450$		0			0
$451$	−52.1797	−	30.1259i	−0.115698	−	0.0667981i
$452$	184.853	+	106.725i	0.408967	+	0.236117i
$453$	−141.765	−	245.544i	−0.312946	−	0.542039i
$454$		−	431.601i		−	0.950663i
$455$		0			0
$456$	127.713			0.280071
$457$	−645.231	+	372.524i	−1.41188	+	0.815151i	−0.995566	−	0.0940682i	$-0.970013\pi$
$457$	−645.231	+	372.524i	−1.41188	+	0.815151i	−0.416317	+	0.909219i	$0.636680\pi$
$458$	−288.572	+	499.822i	−0.630071	+	1.09131i
$459$	−50.3281	+	87.1709i	−0.109647	+	0.189915i
$460$		0			0
$461$			516.757i			1.12095i	0.828172	+	0.560474i	$0.189381\pi$
$461$			516.757i			1.12095i	−0.828172	+	0.560474i	$0.810619\pi$
$462$	−71.7622	−	171.815i	−0.155329	−	0.371893i
$463$			538.823i			1.16376i	0.813273	+	0.581882i	$0.197684\pi$
$463$			538.823i			1.16376i	−0.813273	+	0.581882i	$0.802316\pi$
$464$	−13.9826	−	24.2186i	−0.0301350	−	0.0521953i
$465$		0			0
$466$	153.307	−	265.536i	0.328985	−	0.569819i
$467$	317.450	+	549.839i	0.679764	+	1.17739i	0.975052	+	0.221977i	$0.0712510\pi$
$467$	317.450	+	549.839i	0.679764	+	1.17739i	−0.295288	+	0.955408i	$0.595416\pi$
$468$	−4.63236			−0.00989821
$469$	119.392	+	285.850i	0.254566	+	0.609489i
$470$		0			0
$471$	−180.741	−	313.053i	−0.383740	−	0.664657i
$472$	157.844	−	273.394i	0.334416	−	0.579226i
$473$	648.269	+	374.279i	1.37055	+	0.791286i
$474$	62.9641	−	36.3524i	0.132836	−	0.0766928i
$475$		0			0
$476$	−34.6055	+	268.981i	−0.0727007	+	0.565087i
$477$		−	223.692i		−	0.468955i
$478$	−477.331	+	275.587i	−0.998600	+	0.576542i
$479$	427.580	+	246.863i	0.892650	+	0.515372i	0.874809	−	0.484469i	$-0.160987\pi$
$479$	427.580	+	246.863i	0.892650	+	0.515372i	0.0178420	+	0.999841i	$0.494320\pi$
$480$		0			0
$481$	43.1937	−	24.9379i	0.0897997	−	0.0518459i
$482$	−98.0915			−0.203509
$483$	−100.689	+	132.025i	−0.208467	+	0.273344i
$484$	6.14906			0.0127047
$485$		0			0
$486$	19.0919	+	11.0227i	0.0392837	+	0.0226805i
$487$	287.301	+	165.873i	0.589941	+	0.340603i	0.765074	−	0.643942i	$-0.222702\pi$
$487$	287.301	+	165.873i	0.589941	+	0.340603i	−0.175133	+	0.984545i	$0.556036\pi$
$488$	−76.6808	−	132.815i	−0.157133	−	0.272162i
$489$		−	241.046i		−	0.492937i
$490$		0			0
$491$	−744.294			−1.51587			−0.757937	−	0.652328i	$-0.773793\pi$
$491$	−744.294			−1.51587			−0.757937	+	0.652328i	$0.773793\pi$
$492$	16.6452	−	9.61009i	0.0338316	−	0.0195327i
$493$	−67.7154	+	117.287i	−0.137354	+	0.237904i
$494$	14.2319	−	24.6505i	0.0288096	−	0.0498997i
$495$		0			0
$496$		−	105.105i		−	0.211906i
$497$	177.862	+	135.647i	0.357872	+	0.272932i
$498$		−	38.7389i		−	0.0777890i
$499$	−252.414	−	437.194i	−0.505840	−	0.876141i	−0.999977	−	0.00675693i	$-0.997849\pi$
$499$	−252.414	−	437.194i	−0.505840	−	0.876141i	0.494137	−	0.869384i	$-0.335484\pi$
$500$		0			0
$501$	47.1138	−	81.6034i	0.0940394	−	0.162881i
$502$	181.466	+	314.308i	0.361486	+	0.626111i
$503$	402.412			0.800024			0.400012	−	0.916510i	$-0.369006\pi$
$503$	402.412			0.800024			0.400012	+	0.916510i	$0.369006\pi$
$504$	58.9114	+	7.57919i	0.116888	+	0.0150381i
$505$		0			0
$506$	105.158	+	182.138i	0.207821	+	0.359957i
$507$	145.842	−	252.606i	0.287657	−	0.498236i
$508$	352.717	+	203.641i	0.694325	+	0.400869i
$509$	−409.218	+	236.262i	−0.803965	+	0.464169i	−0.844856	−	0.534994i	$-0.820314\pi$
$509$	−409.218	+	236.262i	−0.803965	+	0.464169i	0.0408910	+	0.999164i	$0.486980\pi$
$510$		0			0
$511$	−690.895	+	288.568i	−1.35204	+	0.564712i
$512$		−	22.6274i		−	0.0441942i
$513$	−117.311	+	67.7298i	−0.228677	+	0.132027i
$514$	246.070	+	142.069i	0.478735	+	0.276398i
$515$		0			0
$516$	−206.796	+	119.394i	−0.400768	+	0.231383i
$517$	−245.540			−0.474933
$518$	−590.111	+	246.473i	−1.13921	+	0.475817i
$519$	108.745			0.209527
$520$		0			0
$521$	48.2368	+	27.8496i	0.0925851	+	0.0534540i	0.545578	−	0.838060i	$-0.316310\pi$
$521$	48.2368	+	27.8496i	0.0925851	+	0.0534540i	−0.452993	+	0.891514i	$0.649644\pi$
$522$	25.6877	+	14.8308i	0.0492102	+	0.0284115i
$523$	−265.238	−	459.405i	−0.507146	−	0.878403i	−0.999966	−	0.00827171i	$-0.997367\pi$
$523$	−265.238	−	459.405i	−0.507146	−	0.878403i	0.492819	−	0.870132i	$-0.335966\pi$
$524$			155.374i			0.296516i
$525$		0			0
$526$	−711.336			−1.35235
$527$	−440.812	+	254.503i	−0.836456	+	0.482928i
$528$	37.6179	−	65.1561i	0.0712460	−	0.123402i
$529$	−170.728	+	295.709i	−0.322737	+	0.558997i
$530$		0			0
$531$			334.838i			0.630581i
$532$	−221.324	+	290.203i	−0.416023	+	0.545495i
$533$		−	4.28369i		−	0.00803694i
$534$	−45.0226	−	77.9815i	−0.0843120	−	0.146033i
$535$		0			0
$536$	−62.5853	+	108.401i	−0.116764	+	0.202241i
$537$	−121.933	−	211.193i	−0.227062	−	0.393284i
$538$	−198.823			−0.369559
$539$	514.780	+	134.686i	0.955065	+	0.249882i
$540$		0			0
$541$	−222.070	−	384.636i	−0.410480	−	0.710972i	0.584462	−	0.811421i	$-0.301306\pi$
$541$	−222.070	−	384.636i	−0.410480	−	0.710972i	−0.994942	+	0.100449i	$0.967972\pi$
$542$	−84.7586	+	146.806i	−0.156381	+	0.270860i
$543$	334.480	+	193.112i	0.615986	+	0.355640i
$544$	−94.8996	+	54.7903i	−0.174448	+	0.100718i
$545$		0			0
$546$	8.02783	−	10.5262i	0.0147030	−	0.0192787i
$547$		−	308.345i		−	0.563702i	−0.959458	−	0.281851i	$-0.909052\pi$
$547$		−	308.345i		−	0.563702i	0.959458	−	0.281851i	$-0.0909484\pi$
$548$	−396.653	+	229.008i	−0.723819	+	0.417897i
$549$	140.872	+	81.3323i	0.256597	+	0.148146i
$550$		0			0
$551$	−157.840	+	91.1289i	−0.286461	+	0.165388i
$552$	−67.0900			−0.121540
$553$	−26.5121	+	206.073i	−0.0479422	+	0.372645i
$554$	−151.330			−0.273160
$555$		0			0
$556$	106.940	+	61.7421i	0.192339	+	0.111047i
$557$	−387.702	−	223.840i	−0.696054	−	0.401867i	0.109822	−	0.993951i	$-0.464972\pi$
$557$	−387.702	−	223.840i	−0.696054	−	0.401867i	−0.805876	+	0.592084i	$0.798305\pi$
$558$	55.7404	+	96.5452i	0.0998932	+	0.173020i
$559$			53.2197i			0.0952052i
$560$		0			0
$561$	−364.354			−0.649472
$562$	104.739	−	60.4709i	0.186368	−	0.107599i
$563$	−423.248	+	733.087i	−0.751773	+	1.30211i	0.195190	+	0.980765i	$0.437468\pi$
$563$	−423.248	+	733.087i	−0.751773	+	1.30211i	−0.946963	+	0.321343i	$0.895866\pi$
$564$	39.1633	−	67.8328i	0.0694385	−	0.120271i
$565$		0			0
$566$		−	554.403i		−	0.979511i
$567$	−58.1331	+	24.2806i	−0.102527	+	0.0428229i
$568$			90.3825i			0.159124i
$569$	175.038	+	303.174i	0.307623	+	0.532819i	0.977842	−	0.209345i	$-0.0671331\pi$
$569$	175.038	+	303.174i	0.307623	+	0.532819i	−0.670219	+	0.742164i	$0.733800\pi$
$570$		0			0
$571$	382.891	−	663.186i	0.670562	−	1.16145i	−0.307183	−	0.951650i	$-0.599386\pi$
$571$	382.891	−	663.186i	0.670562	−	1.16145i	0.977745	−	0.209797i	$-0.0672803\pi$
$572$	−8.38408	−	14.5216i	−0.0146575	−	0.0253875i
$573$	230.387			0.402071
$574$	−7.00871	+	54.4772i	−0.0122103	+	0.0949081i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	53.0857	−	91.9471i	0.0920029	−	0.159354i	−0.816351	−	0.577556i	$-0.804006\pi$
$577$	53.0857	−	91.9471i	0.0920029	−	0.159354i	0.908354	+	0.418203i	$0.137340\pi$
$578$	105.631	+	60.9862i	0.182753	+	0.105512i
$579$	−427.834	+	247.010i	−0.738919	+	0.426615i
$580$		0			0
$581$	88.0271	+	67.1341i	0.151510	+	0.115549i
$582$			328.750i			0.564863i
$583$	701.234	−	404.858i	1.20280	−	0.694439i
$584$	−262.003	−	151.268i	−0.448636	−	0.259020i
$585$		0			0
$586$	613.101	−	353.974i	1.04625	−	0.604051i
$587$	802.707			1.36747			0.683737	−	0.729729i	$-0.260354\pi$
$587$	802.707			1.36747			0.683737	+	0.729729i	$0.260354\pi$
$588$	−119.315	+	120.731i	−0.202917	+	0.205324i
$589$	−685.002			−1.16299
$590$		0			0
$591$	461.676	+	266.549i	0.781178	+	0.451013i
$592$	−223.784	−	129.202i	−0.378013	−	0.218246i
$593$	42.5138	+	73.6360i	0.0716927	+	0.124175i	0.899643	−	0.436626i	$-0.143827\pi$
$593$	42.5138	+	73.6360i	0.0716927	+	0.124175i	−0.827951	+	0.560801i	$0.810493\pi$
$594$			79.7996i			0.134343i
$595$		0			0
$596$	−58.6090			−0.0983373
$597$	−14.5348	+	8.39167i	−0.0243464	+	0.0140564i
$598$	−7.47633	+	12.9494i	−0.0125022	+	0.0216545i
$599$	185.040	−	320.498i	0.308914	−	0.535055i	−0.669211	−	0.743072i	$-0.733368\pi$
$599$	185.040	−	320.498i	0.308914	−	0.535055i	0.978125	+	0.208017i	$0.0667011\pi$
$600$		0			0
$601$		−	462.547i		−	0.769628i	−0.922994	−	0.384814i	$-0.874266\pi$
$601$		−	462.547i		−	0.769628i	0.922994	−	0.384814i	$-0.125734\pi$
$602$	87.0748	−	676.814i	0.144643	−	1.12428i
$603$		−	132.764i		−	0.220172i
$604$	163.696	+	283.529i	0.271020	+	0.469420i
$605$		0			0
$606$	187.751	−	325.194i	0.309820	−	0.536624i
$607$	−345.333	−	598.134i	−0.568918	−	0.985394i	−0.996673	−	0.0814998i	$-0.974029\pi$
$607$	−345.333	−	598.134i	−0.568918	−	0.985394i	0.427756	−	0.903894i	$-0.359304\pi$
$608$	−147.470			−0.242549
$609$	−78.2168	+	32.6690i	−0.128435	+	0.0536436i
$610$		0			0
$611$	−8.72851	−	15.1182i	−0.0142856	−	0.0247434i
$612$	58.1139	−	100.656i	0.0949574	−	0.164471i
$613$	−85.1695	−	49.1726i	−0.138939	−	0.0802163i	0.428919	−	0.903343i	$-0.358894\pi$
$613$	−85.1695	−	49.1726i	−0.138939	−	0.0802163i	−0.567858	+	0.823126i	$0.692228\pi$
$614$	−487.658	+	281.550i	−0.794232	+	0.458550i
$615$		0			0
$616$	82.8639	+	198.394i	0.134519	+	0.322069i
$617$		−	794.667i		−	1.28795i	−0.765045	−	0.643976i	$-0.777283\pi$
$617$		−	794.667i		−	1.28795i	0.765045	−	0.643976i	$-0.222717\pi$
$618$	134.356	−	77.5702i	0.217404	−	0.125518i
$619$	114.032	+	65.8365i	0.184220	+	0.106359i	0.589274	−	0.807933i	$-0.299414\pi$
$619$	114.032	+	65.8365i	0.184220	+	0.106359i	−0.405054	+	0.914293i	$0.632747\pi$
$620$		0			0
$621$	61.6261	−	35.5798i	0.0992369	−	0.0572944i
$622$	−525.998			−0.845656
$623$	255.222	+	32.8353i	0.409666	+	0.0527052i
$624$	5.34899			0.00857210
$625$		0			0
$626$	517.438	+	298.743i	0.826579	+	0.477225i
$627$	−424.642	−	245.167i	−0.677260	−	0.391016i
$628$	208.702	+	361.483i	0.332328	+	0.575609i
$629$			1251.40i			1.98951i
$630$		0			0
$631$	−1086.67			−1.72213			−0.861067	−	0.508492i	$-0.830203\pi$
$631$	−1086.67			−1.72213			−0.861067	+	0.508492i	$0.830203\pi$
$632$	−72.7047	+	41.9761i	−0.115039	+	0.0664179i
$633$	−152.380	+	263.930i	−0.240727	+	0.416952i
$634$	−152.864	+	264.768i	−0.241110	+	0.417615i
$635$		0			0
$636$			258.297i			0.406127i
$637$	10.0067	+	36.4835i	0.0157091	+	0.0572740i
$638$			107.369i			0.168289i
$639$	−47.9326	−	83.0216i	−0.0750118	−	0.129924i
$640$		0			0
$641$	310.496	−	537.795i	0.484393	−	0.838993i	−0.515446	−	0.856922i	$-0.672374\pi$
$641$	310.496	−	537.795i	0.484393	−	0.838993i	0.999839	+	0.0179287i	$0.00570718\pi$
$642$	53.7118	+	93.0316i	0.0836632	+	0.144909i
$643$	−75.8433			−0.117952			−0.0589761	−	0.998259i	$-0.518784\pi$
$643$	−75.8433			−0.117952			−0.0589761	+	0.998259i	$0.518784\pi$
$644$	116.266	−	152.450i	0.180538	−	0.236723i
$645$		0			0
$646$	357.085	+	618.490i	0.552763	+	0.957414i
$647$	−78.8723	+	136.611i	−0.121905	+	0.211145i	−0.920519	−	0.390698i	$-0.872234\pi$
$647$	−78.8723	+	136.611i	−0.121905	+	0.211145i	0.798614	+	0.601843i	$0.205567\pi$
$648$	−22.0454	−	12.7279i	−0.0340207	−	0.0196419i
$649$	−1049.66	+	606.021i	−1.61735	+	0.933777i
$650$		0			0
$651$	−315.979	−	40.6519i	−0.485374	−	0.0624453i
$652$			278.336i			0.426896i
$653$	623.004	−	359.691i	0.954064	−	0.550829i	0.0597229	−	0.998215i	$-0.480978\pi$
$653$	623.004	−	359.691i	0.954064	−	0.550829i	0.894341	+	0.447386i	$0.147645\pi$
$654$	−11.2076	−	6.47072i	−0.0171370	−	0.00989407i
$655$		0			0
$656$	−19.2202	+	11.0968i	−0.0292991	+	0.0169158i
$657$	320.887			0.488413
$658$	86.2681	+	206.545i	0.131106	+	0.313898i
$659$	10.5090			0.0159469			0.00797343	−	0.999968i	$-0.497462\pi$
$659$	10.5090			0.0159469			0.00797343	+	0.999968i	$0.497462\pi$
$660$		0			0
$661$	1040.86	+	600.938i	1.57467	+	0.909135i	0.995585	+	0.0938667i	$0.0299227\pi$
$661$	1040.86	+	600.938i	1.57467	+	0.909135i	0.579083	+	0.815268i	$0.303411\pi$
$662$	258.985	+	149.525i	0.391215	+	0.225868i
$663$	−12.9521	−	22.4337i	−0.0195356	−	0.0338367i
$664$			44.7318i			0.0673672i
$665$		0			0
$666$	274.078			0.411529
$667$	82.9166	−	47.8719i	0.124313	−	0.0717720i
$668$	−54.4023	+	94.2275i	−0.0814405	+	0.141059i
$669$	−43.3753	+	75.1282i	−0.0648360	+	0.112299i
$670$		0			0
$671$			588.810i			0.877512i
$672$	−68.0251	−	8.75169i	−0.101228	−	0.0130234i
$673$		−	1070.49i		−	1.59062i	−0.606203	−	0.795310i	$-0.707308\pi$
$673$		−	1070.49i		−	1.59062i	0.606203	−	0.795310i	$-0.292692\pi$
$674$	−184.116	−	318.898i	−0.273169	−	0.473143i
$675$		0			0
$676$	−168.404	+	291.684i	−0.249118	+	0.431485i
$677$	−298.889	−	517.691i	−0.441491	−	0.764685i	0.556309	−	0.830975i	$-0.312217\pi$
$677$	−298.889	−	517.691i	−0.441491	−	0.764685i	−0.997800	+	0.0662906i	$0.978884\pi$
$678$	261.422			0.385578
$679$	−747.024	−	569.720i	−1.10018	−	0.839058i
$680$		0			0
$681$	−264.301	−	457.782i	−0.388107	−	0.672221i
$682$	−201.768	+	349.473i	−0.295848	+	0.512424i
$683$	453.453	+	261.801i	0.663913	+	0.383310i	0.793766	−	0.608223i	$-0.208117\pi$
$683$	453.453	+	261.801i	0.663913	+	0.383310i	−0.129853	+	0.991533i	$0.541451\pi$
$684$	135.460	−	78.2076i	0.198040	−	0.114339i
$685$		0			0
$686$	−67.5667	−	480.346i	−0.0984937	−	0.700214i
$687$			706.855i			1.02890i
$688$	238.788	−	137.864i	0.347075	−	0.200384i
$689$	49.8552	+	28.7839i	0.0723588	+	0.0417764i
$690$		0			0
$691$	170.271	−	98.3059i	0.246412	−	0.142266i	−0.371708	−	0.928350i	$-0.621228\pi$
$691$	170.271	−	98.3059i	0.246412	−	0.142266i	0.618120	+	0.786083i	$0.287894\pi$
$692$	−125.567			−0.181456
$693$	−181.330	−	138.292i	−0.261659	−	0.199555i
$694$	−723.988			−1.04321
$695$		0			0
$696$	−29.6616	−	17.1251i	−0.0426173	−	0.0246051i
$697$	93.0800	+	53.7398i	0.133544	+	0.0771015i
$698$	373.262	+	646.509i	0.534760	+	0.926231i
$699$		−	375.524i		−	0.537231i
$700$		0			0
$701$	132.968			0.189683			0.0948414	−	0.995492i	$-0.469766\pi$
$701$	132.968			0.189683			0.0948414	+	0.995492i	$0.469766\pi$
$702$	−4.91336	+	2.83673i	−0.00699909	+	0.00404093i
$703$	−842.046	+	1458.47i	−1.19779	+	2.07463i
$704$	−43.4374	+	75.2358i	−0.0617008	+	0.106869i
$705$		0			0
$706$			193.062i			0.273460i
$707$	413.573	+	990.186i	0.584969	+	1.40055i
$708$		−	386.638i		−	0.546099i
$709$	151.618	+	262.609i	0.213847	+	0.370394i	0.952915	−	0.303237i	$-0.0980672\pi$
$709$	151.618	+	262.609i	0.213847	+	0.370394i	−0.739068	+	0.673631i	$0.764734\pi$
$710$		0			0
$711$	44.5224	−	77.1150i	0.0626194	−	0.108460i
$712$	51.9877	+	90.0453i	0.0730164	+	0.126468i
$713$	359.846			0.504692
$714$	128.012	+	306.489i	0.179289	+	0.429257i
$715$		0			0
$716$	140.796	+	243.865i	0.196642	+	0.340594i
$717$	−337.524	+	584.608i	−0.470745	+	0.815354i
$718$	682.243	+	393.893i	0.950200	+	0.548598i
$719$	118.785	−	68.5808i	0.165209	−	0.0953835i	−0.415116	−	0.909769i	$-0.636259\pi$
$719$	118.785	−	68.5808i	0.165209	−	0.0953835i	0.580325	+	0.814385i	$0.302926\pi$
$720$		0			0
$721$	−56.5726	+	439.727i	−0.0784640	+	0.609884i
$722$			450.574i			0.624063i
$723$	−104.042	+	60.0686i	−0.143903	+	0.0830824i
$724$	−386.225	−	222.987i	−0.533460	−	0.307993i
$725$		0			0
$726$	6.52207	−	3.76552i	0.00898356	−	0.00518666i
$727$	741.058			1.01934			0.509669	−	0.860371i	$-0.329768\pi$
$727$	741.058			1.01934			0.509669	+	0.860371i	$0.329768\pi$
$728$	−9.26974	+	12.1546i	−0.0127332	+	0.0166959i
$729$	27.0000			0.0370370
$730$		0			0
$731$	−1156.41	−	667.652i	−1.58195	−	0.913340i
$732$	−162.665	−	93.9144i	−0.222219	−	0.128298i
$733$	−71.9021	−	124.538i	−0.0980929	−	0.169902i	0.812802	−	0.582540i	$-0.197941\pi$
$733$	−71.9021	−	124.538i	−0.0980929	−	0.169902i	−0.910895	+	0.412638i	$0.864608\pi$
$734$		−	166.908i		−	0.227396i
$735$		0			0
$736$	77.4688			0.105257
$737$	416.190	−	240.288i	0.564709	−	0.326035i
$738$	11.7699	−	20.3861i	0.0159484	−	0.0276234i
$739$	−522.722	+	905.381i	−0.707337	+	1.22514i	0.258505	+	0.966010i	$0.416770\pi$
$739$	−522.722	+	905.381i	−0.707337	+	1.22514i	−0.965842	+	0.259133i	$0.916563\pi$
$740$		0			0
$741$		−	34.8610i		−	0.0470459i
$742$	−586.932	−	447.626i	−0.791014	−	0.603269i
$743$		−	660.175i		−	0.888526i	−0.895896	−	0.444263i	$-0.853466\pi$
$743$		−	660.175i		−	0.888526i	0.895896	−	0.444263i	$-0.146534\pi$
$744$	−64.3635	−	111.481i	−0.0865101	−	0.149840i
$745$		0			0
$746$	−225.123	+	389.925i	−0.301774	+	0.522687i
$747$	−23.7226	−	41.0888i	−0.0317572	−	0.0550051i
$748$	420.720			0.562459
$749$	−304.479	−	39.1724i	−0.406514	−	0.0522996i
$750$		0			0
$751$	−79.4795	−	137.663i	−0.105832	−	0.183306i	0.808246	−	0.588845i	$-0.200417\pi$
$751$	−79.4795	−	137.663i	−0.105832	−	0.183306i	−0.914078	+	0.405539i	$0.867084\pi$
$752$	−45.2219	+	78.3266i	−0.0601355	+	0.104158i
$753$	384.947	+	222.249i	0.511218	+	0.295152i
$754$	−6.61082	+	3.81676i	−0.00876767	+	0.00506202i
$755$		0			0
$756$	67.1263	−	28.0368i	0.0887914	−	0.0370857i
$757$		−	777.212i		−	1.02670i	−0.858179	−	0.513350i	$-0.828404\pi$
$757$		−	777.212i		−	1.02670i	0.858179	−	0.513350i	$-0.171596\pi$
$758$	−709.983	+	409.909i	−0.936653	+	0.540777i
$759$	223.073	+	128.791i	0.293904	+	0.169686i
$760$		0			0
$761$	−989.290	+	571.167i	−1.29999	+	0.750548i	−0.980401	−	0.197010i	$-0.936877\pi$
$761$	−989.290	+	571.167i	−1.29999	+	0.750548i	−0.319585	+	0.947558i	$0.603544\pi$
$762$	498.817			0.654616
$763$	34.1262	−	14.2536i	0.0447263	−	0.0186809i
$764$	−266.028			−0.348204
$765$		0			0
$766$	744.698	+	429.951i	0.972190	+	0.561294i
$767$	−74.6270	−	43.0859i	−0.0972973	−	0.0561746i
$768$	−13.8564	−	24.0000i	−0.0180422	−	0.0312500i
$769$		−	166.927i		−	0.217070i	−0.994093	−	0.108535i	$-0.965384\pi$
$769$		−	166.927i		−	0.217070i	0.994093	−	0.108535i	$-0.0346159\pi$
$770$		0			0
$771$	347.995			0.451356
$772$	494.020	−	285.223i	0.639922	−	0.369459i
$773$	169.546	−	293.663i	0.219336	−	0.379901i	−0.735269	−	0.677775i	$-0.762944\pi$
$773$	169.546	−	293.663i	0.219336	−	0.379901i	0.954605	+	0.297874i	$0.0962777\pi$
$774$	−146.227	+	253.272i	−0.188924	+	0.327225i
$775$		0			0
$776$		−	379.608i		−	0.489186i
$777$	−474.974	+	622.792i	−0.611292	+	0.801534i
$778$			162.657i			0.209071i
$779$	72.3210	+	125.264i	0.0928383	+	0.160801i
$780$		0			0
$781$	173.505	−	300.520i	0.222158	−	0.384789i
$782$	−187.584	−	324.905i	−0.239877	−	0.415480i
$783$	36.3279			0.0463958
$784$	137.773	−	139.408i	0.175731	−	0.177816i
$785$		0			0
$786$	95.1470	+	164.799i	0.121052	+	0.209668i
$787$	−174.514	+	302.268i	−0.221746	+	0.384076i	−0.955338	−	0.295514i	$-0.904509\pi$
$787$	−174.514	+	302.268i	−0.221746	+	0.384076i	0.733592	+	0.679590i	$0.237842\pi$
$788$	−533.098	−	307.784i	−0.676520	−	0.390589i
$789$	−754.486	+	435.602i	−0.956256	+	0.552094i
$790$		0			0
$791$	−453.041	+	594.033i	−0.572744	+	0.750989i
$792$		−	92.1446i		−	0.116344i
$793$	−36.2538	+	20.9311i	−0.0457173	+	0.0263949i
$794$	196.927	+	113.696i	0.248019	+	0.143194i
$795$		0			0
$796$	16.7833	−	9.68987i	0.0210846	−	0.0121732i
$797$	137.702			0.172776			0.0863878	−	0.996262i	$-0.472468\pi$
$797$	137.702			0.172776			0.0863878	+	0.996262i	$0.472468\pi$
$798$	−57.0374	+	443.340i	−0.0714755	+	0.555564i
$799$	438.004			0.548190
$800$		0			0
$801$	−95.5074	−	55.1412i	−0.119235	−	0.0688405i
$802$	−72.0219	−	41.5819i	−0.0898029	−	0.0518477i
$803$	580.771	+	1005.92i	0.723252	+	1.25271i
$804$			153.302i			0.190674i
$805$		0			0
$806$	−28.6900			−0.0355955
$807$	−210.884	+	121.754i	−0.261318	+	0.150872i
$808$	−216.796	+	375.502i	−0.268312	+	0.464730i
$809$	−474.092	+	821.151i	−0.586022	+	1.01502i	0.408726	+	0.912657i	$0.365973\pi$
$809$	−474.092	+	821.151i	−0.586022	+	1.01502i	−0.994747	+	0.102362i	$0.967360\pi$
$810$		0			0
$811$		−	434.987i		−	0.536359i	−0.963369	−	0.268180i	$-0.913578\pi$
$811$		−	434.987i		−	0.536359i	0.963369	−	0.268180i	$-0.0864221\pi$
$812$	90.3169	−	37.7229i	0.111228	−	0.0464568i
$813$			207.615i			0.255370i
$814$	496.052	+	859.186i	0.609400	+	1.05551i
$815$		0			0
$816$	−67.1042	+	116.228i	−0.0822355	+	0.142436i
$817$	−898.502	−	1556.25i	−1.09976	−	1.90484i
$818$	297.289			0.363434
$819$	2.06885	−	16.0807i	0.00252607	−	0.0196346i
$820$		0			0
$821$	−497.701	−	862.043i	−0.606213	−	1.04999i	−0.991859	−	0.127344i	$-0.959355\pi$
$821$	−497.701	−	862.043i	−0.606213	−	1.04999i	0.385646	−	0.922647i	$-0.373979\pi$
$822$	−280.476	+	485.798i	−0.341211	+	0.590996i
$823$	203.545	+	117.517i	0.247321	+	0.142791i	0.618537	−	0.785756i	$-0.287726\pi$
$823$	203.545	+	117.517i	0.247321	+	0.142791i	−0.371216	+	0.928547i	$0.621059\pi$
$824$	−155.140	+	89.5704i	−0.188277	+	0.108702i
$825$		0			0
$826$	878.564	+	670.039i	1.06364	+	0.811186i
$827$			267.742i			0.323751i	0.986811	+	0.161876i	$0.0517543\pi$
$827$			267.742i			0.323751i	−0.986811	+	0.161876i	$0.948246\pi$
$828$	−71.1597	+	41.0841i	−0.0859416	+	0.0496184i
$829$	−1367.65	−	789.613i	−1.64976	−	0.952489i	−0.977166	−	0.212476i	$-0.931847\pi$
$829$	−1367.65	−	789.613i	−1.64976	−	0.952489i	−0.672593	−	0.740013i	$-0.734819\pi$
$830$		0			0
$831$	−160.510	+	92.6706i	−0.193153	+	0.111517i
$832$	−6.17648			−0.00742366
$833$	−918.284	−	240.258i	−1.10238	−	0.288425i
$834$	151.237			0.181339
$835$		0			0
$836$	490.334	+	283.095i	0.586524	+	0.338630i
$837$	118.243	+	68.2678i	0.141270	+	0.0815625i
$838$	−488.129	−	845.465i	−0.582493	−	1.00891i
$839$			502.512i			0.598942i	0.954105	+	0.299471i	$0.0968102\pi$
$839$			502.512i			0.598942i	−0.954105	+	0.299471i	$0.903190\pi$
$840$		0			0
$841$	−792.122			−0.941881
$842$	−498.574	+	287.852i	−0.592130	+	0.341867i
$843$	74.0614	−	128.278i	0.0878545	−	0.152169i
$844$	175.954	−	304.761i	0.208476	−	0.361091i
$845$		0			0
$846$		−	95.9301i		−	0.113393i
$847$	−2.74622	+	21.3458i	−0.00324229	+	0.0252016i
$848$		−	298.256i		−	0.351717i
$849$	−339.501	−	588.033i	−0.399884	−	0.692619i
$850$		0			0
$851$	442.344	−	766.162i	0.519793	−	0.900308i
$852$	55.3477	+	95.8651i	0.0649621	+	0.112518i
$853$	880.120			1.03179			0.515897	−	0.856651i	$-0.327459\pi$
$853$	880.120			1.03179			0.515897	+	0.856651i	$0.327459\pi$
$854$	495.299	−	206.873i	0.579975	−	0.242240i
$855$		0			0
$856$	−62.0210	−	107.424i	−0.0724545	−	0.125495i
$857$	182.962	−	316.900i	0.213492	−	0.369778i	−0.739313	−	0.673362i	$-0.764850\pi$
$857$	182.962	−	316.900i	0.213492	−	0.369778i	0.952805	+	0.303583i	$0.0981831\pi$
$858$	−17.7853	−	10.2684i	−0.0207288	−	0.0119678i
$859$	957.688	−	552.921i	1.11489	−	0.643680i	0.174796	−	0.984605i	$-0.444073\pi$
$859$	957.688	−	552.921i	1.11489	−	0.643680i	0.940091	+	0.340924i	$0.110740\pi$
$860$		0			0
$861$	25.9265	+	62.0738i	0.0301121	+	0.0720950i
$862$			79.2231i			0.0919062i
$863$	−848.741	+	490.021i	−0.983477	+	0.567811i	−0.903318	−	0.428971i	$-0.858876\pi$
$863$	−848.741	+	490.021i	−0.983477	+	0.567811i	−0.0801589	+	0.996782i	$0.525543\pi$
$864$	25.4558	+	14.6969i	0.0294628	+	0.0170103i
$865$		0			0
$866$	−87.5194	+	50.5293i	−0.101062	+	0.0583480i
$867$	149.385			0.172301
$868$	364.861	+	46.9408i	0.420347	+	0.0540793i
$869$	322.323			0.370912
$870$		0			0
$871$	29.5896	+	17.0836i	0.0339720	+	0.0196138i
$872$	12.9414	+	7.47174i	0.0148411	+	0.00856851i
$873$	201.318	+	348.692i	0.230604	+	0.399419i
$874$		−	504.888i		−	0.577675i
$875$		0			0
$876$	−370.529			−0.422978
$877$	1204.77	−	695.577i	1.37374	−	0.793132i	0.382347	−	0.924019i	$-0.375116\pi$
$877$	1204.77	−	695.577i	1.37374	−	0.793132i	0.991397	+	0.130887i	$0.0417825\pi$
$878$	−564.995	+	978.601i	−0.643503	+	1.11458i
$879$	433.528	−	750.892i	0.493206	−	0.854257i
$880$		0			0
$881$			234.790i			0.266504i	0.991082	+	0.133252i	$0.0425419\pi$
$881$			234.790i			0.266504i	−0.991082	+	0.133252i	$0.957458\pi$
$882$	−52.6206	+	201.120i	−0.0596606	+	0.228027i
$883$		−	977.996i		−	1.10758i	−0.832655	−	0.553791i	$-0.813180\pi$
$883$		−	977.996i		−	1.10758i	0.832655	−	0.553791i	$-0.186820\pi$
$884$	14.9558	+	25.9042i	0.0169184	+	0.0293034i
$885$		0			0
$886$	−574.454	+	994.983i	−0.648367	+	1.12301i
$887$	690.695	+	1196.32i	0.778686	+	1.34872i	0.932699	+	0.360655i	$0.117447\pi$
$887$	690.695	+	1196.32i	0.778686	+	1.34872i	−0.154013	+	0.988069i	$0.549220\pi$
$888$	−316.478			−0.356394
$889$	−864.445	+	1133.47i	−0.972379	+	1.27500i
$890$		0			0
$891$	48.8671	+	84.6403i	0.0548452	+	0.0949947i
$892$	50.0854	−	86.7505i	0.0561496	−	0.0972539i
$893$	510.478	+	294.725i	0.571644	+	0.330039i
$894$	−62.1643	+	35.8906i	−0.0695350	+	0.0401460i
$895$		0			0
$896$	78.5486	+	10.1056i	0.0876658	+	0.0112786i
$897$			18.3132i			0.0204160i
$898$	532.501	−	307.439i	0.592985	−	0.342360i
$899$	159.094	+	91.8528i	0.176967	+	0.102172i
$900$		0			0
$901$	−1250.89	+	722.200i	−1.38833	+	0.801554i
$902$	85.2090			0.0944668
$903$	−322.105	−	771.192i	−0.356706	−	0.854033i
$904$	−301.864			−0.333920
$905$		0			0
$906$	347.251	+	200.486i	0.383280	+	0.221287i
$907$	906.269	+	523.235i	0.999194	+	0.576885i	0.908010	−	0.418949i	$-0.137601\pi$
$907$	906.269	+	523.235i	0.999194	+	0.576885i	0.0911843	+	0.995834i	$0.470935\pi$
$908$	305.188	+	528.601i	0.336110	+	0.582160i
$909$		−	459.894i		−	0.505934i
$910$		0			0
$911$	−942.221			−1.03427			−0.517136	−	0.855903i	$-0.673002\pi$
$911$	−942.221			−1.03427			−0.517136	+	0.855903i	$0.673002\pi$
$912$	−156.415	+	90.3064i	−0.171508	+	0.0990202i
$913$	85.8708	−	148.733i	0.0940535	−	0.162905i
$914$	526.829	−	912.494i	0.576399	−	0.998352i
$915$		0			0
$916$		−	816.206i		−	0.891055i
$917$	−539.365	−	69.3914i	−0.588184	−	0.0756722i
$918$		−	142.349i		−	0.155065i
$919$	218.878	+	379.108i	0.238170	+	0.412522i	0.960189	−	0.279350i	$-0.0901191\pi$
$919$	218.878	+	379.108i	0.238170	+	0.412522i	−0.722019	+	0.691873i	$0.756786\pi$
$920$		0			0
$921$	−344.827	+	597.257i	−0.374405	+	0.648488i
$922$	−365.403	−	632.896i	−0.396315	−	0.686438i
$923$	24.6712			0.0267294
$924$	209.382	+	159.686i	0.226604	+	0.172820i
$925$		0			0
$926$	−381.005	−	659.921i	−0.411453	−	0.712657i
$927$	95.0038	−	164.551i	0.102485	−	0.177510i
$928$	34.2503	+	19.7744i	0.0369076	+	0.0213086i
$929$	1326.88	−	766.072i	1.42828	−	0.824620i	0.431299	−	0.902209i	$-0.358056\pi$
$929$	1326.88	−	766.072i	1.42828	−	0.824620i	0.996985	+	0.0775890i	$0.0247222\pi$
$930$		0			0
$931$	−908.563	−	897.910i	−0.975900	−	0.964457i
$932$			433.618i			0.465255i
$933$	−557.905	+	322.107i	−0.597969	+	0.345238i
$934$	−777.590	−	448.942i	−0.832537	−	0.480666i
$935$		0			0
$936$	5.67346	−	3.27558i	0.00606139	−	0.00349955i
$937$	987.468			1.05386			0.526931	−	0.849908i	$-0.323343\pi$
$937$	987.468			1.05386			0.526931	+	0.849908i	$0.323343\pi$
$938$	−348.351	−	265.671i	−0.371376	−	0.283231i
$939$	731.768			0.779306
$940$		0			0
$941$	1441.57	+	832.293i	1.53196	+	0.884477i	0.999271	+	0.0381649i	$0.0121512\pi$
$941$	1441.57	+	832.293i	1.53196	+	0.884477i	0.532687	+	0.846312i	$0.321182\pi$
$942$	442.724	+	255.607i	0.469983	+	0.271345i
$943$	−37.9917	−	65.8036i	−0.0402881	−	0.0697811i
$944$			446.451i			0.472936i
$945$		0			0
$946$	−1058.62			−1.11905
$947$	−591.674	+	341.603i	−0.624788	+	0.360721i	−0.778731	−	0.627358i	$-0.784136\pi$
$947$	−591.674	+	341.603i	−0.624788	+	0.360721i	0.153943	+	0.988080i	$0.450803\pi$
$948$	−51.4100	+	89.0448i	−0.0542300	+	0.0939291i
$949$	−41.2907	+	71.5176i	−0.0435097	+	0.0753610i
$950$		0			0
$951$			374.438i			0.393731i
$952$	−147.816	−	353.903i	−0.155269	−	0.371747i
$953$		−	705.451i		−	0.740243i	−0.928983	−	0.370121i	$-0.879316\pi$
$953$		−	705.451i		−	0.740243i	0.928983	−	0.370121i	$-0.120684\pi$
$954$	158.174	+	273.965i	0.165801	+	0.287175i
$955$		0			0
$956$	389.739	−	675.048i	0.407677	−	0.706117i
$957$	65.7496	+	113.882i	0.0687038	+	0.118999i
$958$	−698.235			−0.728846
$959$	−617.826	−	1479.21i	−0.644240	−	1.54245i
$960$		0			0
$961$	−135.278	−	234.309i	−0.140768	−	0.243818i
$962$	−35.2675	+	61.0851i	−0.0366606	+	0.0634980i
$963$	113.940	+	65.7832i	0.118318	+	0.0683107i
$964$	120.137	−	69.3612i	0.124624	−	0.0719515i
$965$		0			0
$966$	29.9629	−	232.895i	0.0310175	−	0.241093i
$967$		−	187.828i		−	0.194238i	−0.995273	−	0.0971188i	$-0.969037\pi$
$967$		−	187.828i		−	0.194238i	0.995273	−	0.0971188i	$-0.0309627\pi$
$968$	−7.53103	+	4.34804i	−0.00777999	+	0.00449178i
$969$	757.492	+	437.338i	0.781725	+	0.451329i
$970$		0			0
$971$	244.015	−	140.882i	0.251303	−	0.145090i	−0.369058	−	0.929406i	$-0.620320\pi$
$971$	244.015	−	140.882i	0.251303	−	0.145090i	0.620361	+	0.784317i	$0.286986\pi$
$972$	−31.1769			−0.0320750
$973$	−262.091	+	343.658i	−0.269364	+	0.353194i
$974$	−469.161			−0.481685
$975$		0			0
$976$	187.829	+	108.443i	0.192448	+	0.111110i
$977$	−751.877	−	434.096i	−0.769577	−	0.444316i	0.0631464	−	0.998004i	$-0.479886\pi$
$977$	−751.877	−	434.096i	−0.769577	−	0.444316i	−0.832724	+	0.553689i	$0.813220\pi$
$978$	170.445	+	295.220i	0.174280	+	0.301861i
$979$		−	399.199i		−	0.407762i
$980$		0			0
$981$	−15.8500			−0.0161569
$982$	911.571	−	526.296i	0.928280	−	0.535943i
$983$	−17.2202	+	29.8262i	−0.0175180	+	0.0303420i	−0.874652	−	0.484752i	$-0.838910\pi$
$983$	−17.2202	+	29.8262i	−0.0175180	+	0.0303420i	0.857134	+	0.515094i	$0.172243\pi$
$984$	−13.5907	+	23.5398i	−0.0138117	+	0.0239226i
$985$		0			0
$986$		−	191.528i		−	0.194248i
$987$	217.983	+	166.246i	0.220855	+	0.168435i
$988$			40.2540i			0.0407429i
$989$	472.001	+	817.530i	0.477251	+	0.826623i
$990$		0			0
$991$	225.801	−	391.098i	0.227851	−	0.394650i	−0.729320	−	0.684173i	$-0.760163\pi$
$991$	225.801	−	391.098i	0.227851	−	0.394650i	0.957171	+	0.289523i	$0.0934967\pi$
$992$	74.3206	+	128.727i	0.0749199	+	0.129765i
$993$	366.259			0.368841
$994$	−313.753	−	40.3655i	−0.315647	−	0.0406092i
$995$		0			0
$996$	27.3926	+	47.4453i	0.0275026	+	0.0476358i
$997$	815.641	−	1412.73i	0.818095	−	1.41698i	−0.0889893	−	0.996033i	$-0.528364\pi$
$997$	815.641	−	1412.73i	0.818095	−	1.41698i	0.907084	−	0.420949i	$-0.138303\pi$
$998$	618.286	+	356.968i	0.619525	+	0.357683i
$999$	290.704	−	167.838i	0.290995	−	0.168006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.q.e.199.5		32
5.2	odd	4		1050.3.p.i.451.2		16
5.3	odd	4		210.3.o.b.31.8	✓	16
5.4	even	2	inner	1050.3.q.e.199.11		32
7.5	odd	6	inner	1050.3.q.e.649.11		32
15.8	even	4		630.3.v.c.451.2		16
35.3	even	12		1470.3.f.d.391.1		16
35.12	even	12		1050.3.p.i.901.2		16
35.18	odd	12		1470.3.f.d.391.7		16
35.19	odd	6	inner	1050.3.q.e.649.5		32
35.33	even	12		210.3.o.b.61.8	yes	16
105.68	odd	12		630.3.v.c.271.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.8	✓	16	5.3	odd	4
210.3.o.b.61.8	yes	16	35.33	even	12
630.3.v.c.271.2		16	105.68	odd	12
630.3.v.c.451.2		16	15.8	even	4
1050.3.p.i.451.2		16	5.2	odd	4
1050.3.p.i.901.2		16	35.12	even	12
1050.3.q.e.199.5		32	1.1	even	1	trivial
1050.3.q.e.199.11		32	5.4	even	2	inner
1050.3.q.e.649.5		32	35.19	odd	6	inner
1050.3.q.e.649.11		32	7.5	odd	6	inner
1470.3.f.d.391.1		16	35.3	even	12
1470.3.f.d.391.7		16	35.18	odd	12

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(5.56601 + 4.24494i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(5.56601 + 4.24494i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(5.42967 - 9.40447i) q^{11} +(1.73205 + 3.00000i) q^{12} +0.772061 q^{13} +(-9.81857 - 1.26320i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-9.68565 + 16.7760i) q^{17} +(3.67423 + 2.12132i) q^{18} +(-22.5766 + 13.0346i) q^{19} +(-11.1877 + 4.67280i) q^{21} +15.3574i q^{22} +(11.8599 - 6.84734i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-0.945577 + 0.545929i) q^{26} +5.19615 q^{27} +(12.9185 - 5.39568i) q^{28} +6.99131 q^{29} +(22.7559 + 13.1381i) q^{31} +(4.89898 + 2.82843i) q^{32} +(9.40447 + 16.2890i) q^{33} -27.3952i q^{34} -6.00000 q^{36} +(55.9459 - 32.3004i) q^{37} +(18.4337 - 31.9281i) q^{38} +(-0.668624 + 1.15809i) q^{39} -5.54839i q^{41} +(10.3979 - 13.6339i) q^{42} +68.9320i q^{43} +(-10.8593 - 18.8089i) q^{44} +(-9.68361 + 16.7725i) q^{46} +(-11.3055 - 19.5817i) q^{47} +6.92820 q^{48} +(12.9610 + 47.2548i) q^{49} +(-16.7760 - 29.0570i) q^{51} +(0.772061 - 1.33725i) q^{52} +(64.5742 + 37.2820i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(-12.0065 + 15.7431i) q^{56} -45.1532i q^{57} +(-8.56257 + 4.94360i) q^{58} +(-96.6595 - 55.8064i) q^{59} +(-46.9572 + 27.1108i) q^{61} -37.1603 q^{62} +(2.67965 - 20.8283i) q^{63} -8.00000 q^{64} +(-23.0362 - 13.2999i) q^{66} +(38.3255 + 22.1273i) q^{67} +(19.3713 + 33.5521i) q^{68} +23.7199i q^{69} +31.9550 q^{71} +(7.34847 - 4.24264i) q^{72} +(-53.4812 + 92.6322i) q^{73} +(-45.6797 + 79.1195i) q^{74} +52.1384i q^{76} +(70.1430 - 29.2968i) q^{77} -1.89115i q^{78} +(14.8408 + 25.7050i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(3.92330 + 6.79536i) q^{82} +15.8151 q^{83} +(-3.09419 + 24.0505i) q^{84} +(-48.7423 - 84.4242i) q^{86} +(-6.05465 + 10.4870i) q^{87} +(26.5999 + 15.3574i) q^{88} +(31.8358 - 18.3804i) q^{89} +(4.29730 + 3.27735i) q^{91} -27.3894i q^{92} +(-39.4144 + 22.7559i) q^{93} +(27.6926 + 15.9884i) q^{94} +(-8.48528 + 4.89898i) q^{96} -134.212 q^{97} +(-49.2881 - 48.7102i) q^{98} -32.5780 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} - 48 q^{9}+O(q^{10}) \) 32 * q + 32 * q^4 - 48 * q^9	\( 32 q + 32 q^{4} - 48 q^{9} - 8 q^{11} - 16 q^{14} - 64 q^{16} + 144 q^{19} - 48 q^{21} - 144 q^{29} + 240 q^{31} - 192 q^{36} - 72 q^{39} + 16 q^{44} + 16 q^{46} + 80 q^{49} - 24 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 256 q^{64} + 144 q^{66} - 272 q^{71} + 224 q^{74} - 560 q^{79} - 144 q^{81} + 48 q^{84} - 176 q^{86} + 600 q^{89} - 544 q^{91} + 48 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 - 48 * q^9 - 8 * q^11 - 16 * q^14 - 64 * q^16 + 144 * q^19 - 48 * q^21 - 144 * q^29 + 240 * q^31 - 192 * q^36 - 72 * q^39 + 16 * q^44 + 16 * q^46 + 80 * q^49 - 24 * q^51 + 32 * q^56 - 264 * q^59 + 192 * q^61 - 256 * q^64 + 144 * q^66 - 272 * q^71 + 224 * q^74 - 560 * q^79 - 144 * q^81 + 48 * q^84 - 176 * q^86 + 600 * q^89 - 544 * q^91 + 48 * q^99

Introduction

L-functions

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