LMFDB - Embedded newform 1050.3.q.e.649.11

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			649.11
Character	$\chi$	$=$	1050.649
Dual form			1050.3.q.e.199.11

$q$-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 $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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	0.999973	−	0.00736658i	$-0.00234488\pi$
$11$	5.42967	+	9.40447i	0.493607	+	0.854952i	−0.506366	+	0.862319i	$0.669012\pi$
$12$	−1.73205	+	3.00000i	−0.144338	+	0.250000i
$13$	−0.772061			−0.0593893			−0.0296946	−	0.999559i	$-0.509453\pi$
$13$	−0.772061			−0.0593893			−0.0296946	+	0.999559i	$0.509453\pi$
$14$	−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	0.996591	+	0.0825021i	$0.0262911\pi$
$17$	9.68565	+	16.7760i	0.569744	+	0.986826i	−0.426847	+	0.904324i	$0.640376\pi$
$18$	−3.67423	+	2.12132i	−0.204124	+	0.117851i
$19$	−22.5766	−	13.0346i	−1.18824	−	0.686032i	−0.230335	−	0.973111i	$-0.573982\pi$
$19$	−22.5766	−	13.0346i	−1.18824	−	0.686032i	−0.957907	+	0.287079i	$0.907316\pi$
$20$		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	$-0.429556\pi$
$23$	−11.8599	−	6.84734i	−0.515650	−	0.297711i	−0.735153	+	0.677901i	$0.762890\pi$
$24$	−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	−0.0858441	−	0.996309i	$-0.527359\pi$
$31$	22.7559	−	13.1381i	0.734062	−	0.423811i	0.819906	+	0.572497i	$0.194025\pi$
$32$	−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	−0.999901	−	0.0140890i	$-0.995515\pi$
$37$	−55.9459	−	32.3004i	−1.51205	−	0.872984i	−0.512152	−	0.858895i	$-0.671151\pi$
$38$	−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	$0.0215544\pi$
$41$			5.54839i			0.135327i	−0.997708	+	0.0676633i	$0.978446\pi$
$42$	−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	$-0.756008\pi$
$47$	11.3055	−	19.5817i	0.240542	−	0.416631i	0.960869	+	0.277004i	$0.0893415\pi$
$48$	−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	$-0.915017\pi$
$53$	−64.5742	+	37.2820i	−1.21838	+	0.703433i	−0.253810	+	0.967254i	$0.581684\pi$
$54$	−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	−0.656878	+	0.753997i	$0.728123\pi$
$59$	−96.6595	+	55.8064i	−1.63830	+	0.945871i	−0.981420	+	0.191874i	$0.938543\pi$
$60$		0			0
$61$	−46.9572	−	27.1108i	−0.769790	−	0.444439i	0.0630096	−	0.998013i	$-0.479930\pi$
$61$	−46.9572	−	27.1108i	−0.769790	−	0.444439i	−0.832800	+	0.553574i	$0.813263\pi$
$62$	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	$-0.773802\pi$
$67$	−38.3255	+	22.1273i	−0.572023	+	0.330258i	0.185934	+	0.982562i	$0.440469\pi$
$68$	−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	0.955760	+	0.294147i	$0.0950357\pi$
$73$	53.4812	+	92.6322i	0.732619	+	1.26893i	−0.223141	+	0.974786i	$0.571631\pi$
$74$	−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	−0.756678	−	0.653788i	$-0.773179\pi$
$79$	14.8408	−	25.7050i	0.187858	−	0.325380i	0.944536	+	0.328408i	$0.106512\pi$
$80$		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	$-0.530372\pi$
$83$	−15.8151			−0.190543			−0.0952717	+	0.995451i	$0.530372\pi$
$84$	−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	0.668074	−	0.744095i	$-0.267119\pi$
$89$	31.8358	+	18.3804i	0.357706	+	0.206521i	−0.310368	+	0.950616i	$0.600452\pi$
$90$		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	$-0.256812\pi$
$97$	134.212			1.38363			0.691813	+	0.722077i	$0.256812\pi$
$98$	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	0.331624	−	0.943412i	$-0.392404\pi$
$101$	132.760	−	76.6490i	1.31445	−	0.758901i	0.982830	+	0.184511i	$0.0590702\pi$
$102$	−41.0927	+	23.7249i	−0.402870	+	0.232597i
$103$	−31.6679	+	54.8504i	−0.307456	+	0.532529i	−0.977805	−	0.209517i	$-0.932811\pi$
$103$	−31.6679	+	54.8504i	−0.307456	+	0.532529i	0.670349	+	0.742046i	$0.266144\pi$
$104$		−	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	$-0.267636\pi$
$107$	37.9800	+	21.9277i	0.354953	+	0.204932i	−0.311912	+	0.950111i	$0.600969\pi$
$108$	−5.19615	−	9.00000i	−0.0481125	−	0.0833333i
$109$	2.64166	+	4.57549i	0.0242354	+	0.0419770i	0.877889	−	0.478865i	$-0.158952\pi$
$109$	2.64166	+	4.57549i	0.0242354	+	0.0419770i	−0.853653	+	0.520842i	$0.825618\pi$
$110$		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	0.220724	−	0.975336i	$-0.429158\pi$
$131$	−67.2791	−	38.8436i	−0.513581	−	0.296516i	−0.734304	+	0.678820i	$0.762491\pi$
$132$	−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	$-0.351674\pi$
$137$	198.326	−	114.504i	1.44764	−	0.835794i	0.998340	+	0.0575883i	$0.0183411\pi$
$138$	16.7725	−	29.0508i	0.121540	−	0.210513i
$139$		−	61.7421i		−	0.444188i	−0.975025	−	0.222094i	$-0.928711\pi$
$139$		−	61.7421i		−	0.444188i	0.975025	−	0.222094i	$-0.0712892\pi$
$140$		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	−0.910997	−	0.412414i	$-0.864686\pi$
$149$	−14.6523	+	25.3785i	−0.0983373	+	0.170325i	0.812659	+	0.582739i	$0.198019\pi$
$150$		0			0
$151$	−81.8479	−	141.765i	−0.542039	−	0.938839i	−0.998787	−	0.0492431i	$-0.984319\pi$
$151$	−81.8479	−	141.765i	−0.542039	−	0.938839i	0.456748	−	0.889596i	$-0.349014\pi$
$152$	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	0.979378	+	0.202035i	$0.0647555\pi$
$157$	104.351	+	180.741i	0.664657	+	1.15122i	−0.314722	+	0.949184i	$0.601911\pi$
$158$	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	$-0.192940\pi$
$163$	120.523	+	69.5841i	0.739406	+	0.426896i	−0.0824475	+	0.996595i	$0.526274\pi$
$164$	−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	$-0.447921\pi$
$167$	54.4023			0.325762			0.162881	+	0.986646i	$0.447921\pi$
$168$	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	$-0.775252\pi$
$173$	31.3918	−	54.3723i	0.181456	−	0.314291i	0.942376	+	0.334554i	$0.108586\pi$
$174$			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	0.599597	−	0.800302i	$-0.295328\pi$
$179$	−70.3978	−	121.933i	−0.393284	−	0.681187i	−0.992880	+	0.119115i	$0.961994\pi$
$180$		0			0
$181$			222.987i			1.23197i	0.787757	+	0.615986i	$0.211242\pi$
$181$			222.987i			1.23197i	−0.787757	+	0.615986i	$0.788758\pi$
$182$	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	−0.985930	−	0.167156i	$-0.946542\pi$
$191$	−66.5069	+	115.193i	−0.348204	+	0.603106i	0.637727	+	0.770263i	$0.279875\pi$
$192$	−6.92820	−	12.0000i	−0.0360844	−	0.0625000i
$193$	−247.010	+	142.611i	−1.27984	+	0.738919i	−0.976820	−	0.214064i	$-0.931330\pi$
$193$	−247.010	+	142.611i	−1.27984	+	0.738919i	−0.303025	+	0.952983i	$0.597997\pi$
$194$	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	−0.478767	−	0.877942i	$-0.658916\pi$
$199$	8.39167	−	4.84493i	0.0421692	−	0.0243464i	0.520936	+	0.853595i	$0.325583\pi$
$200$		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	$-0.535822\pi$
$223$	−50.0854			−0.224598			−0.112299	+	0.993674i	$0.535822\pi$
$224$	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	0.977273	+	0.211985i	$0.0679927\pi$
$227$	152.594	+	264.301i	0.672221	+	1.16432i	−0.305052	+	0.952336i	$0.598674\pi$
$228$	78.2076	−	45.1532i	0.343016	−	0.198040i
$229$	353.428	+	204.052i	1.54335	+	0.891055i	0.998624	+	0.0524421i	$0.0167005\pi$
$229$	353.428	+	204.052i	1.54335	+	0.891055i	0.544728	+	0.838613i	$0.316633\pi$
$230$		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	$-0.179296\pi$
$233$	187.762	+	108.404i	0.805846	+	0.465255i	−0.0396654	+	0.999213i	$0.512629\pi$
$234$	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	−0.370172	−	0.928963i	$-0.620701\pi$
$241$	60.0686	−	34.6806i	0.249247	−	0.143903i	0.619419	+	0.785060i	$0.287368\pi$
$242$	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	$0.170805\pi$
$251$			256.631i			1.02244i	−0.859451	+	0.511218i	$0.829195\pi$
$252$	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	$-0.705502\pi$
$257$	100.458	−	173.998i	0.390886	−	0.677034i	0.992567	+	0.121703i	$0.0388355\pi$
$258$	−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	−0.681875	+	0.731469i	$0.738835\pi$
$263$	−435.602	+	251.495i	−1.65628	+	0.956256i	−0.974408	+	0.224787i	$0.927831\pi$
$264$	−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	−0.256318	−	0.966592i	$-0.582510\pi$
$269$	121.754	−	70.2945i	0.452616	−	0.261318i	0.708934	+	0.705275i	$0.249176\pi$
$270$		0			0
$271$	103.808	+	59.9334i	0.383054	+	0.221157i	0.679146	−	0.734003i	$-0.262350\pi$
$271$	103.808	+	59.9334i	0.383054	+	0.221157i	−0.296092	+	0.955159i	$0.595684\pi$
$272$	−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	$-0.728538\pi$
$277$	−92.6706	+	53.5034i	−0.334551	+	0.193153i	0.323309	+	0.946293i	$0.395205\pi$
$278$	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	0.970977	+	0.239173i	$0.0768765\pi$
$283$	196.011	+	339.501i	0.692619	+	1.19965i	−0.278358	+	0.960477i	$0.589790\pi$
$284$	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	$-0.174012\pi$
$293$	500.595			1.70851			0.854257	+	0.519850i	$0.174012\pi$
$294$	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	$-0.724598\pi$
$307$	−398.171			−1.29698			−0.648488	+	0.761225i	$0.724598\pi$
$308$	−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	0.117097	−	0.993120i	$-0.462641\pi$
$311$	322.107	−	185.968i	1.03571	−	0.597969i	0.918616	+	0.395151i	$0.129308\pi$
$312$	3.27558	−	1.89115i	0.0104986	−	0.00606139i
$313$	211.243	−	365.884i	0.674899	−	1.16896i	−0.301600	−	0.953435i	$-0.597521\pi$
$313$	211.243	−	365.884i	0.674899	−	1.16896i	0.976499	−	0.215524i	$-0.0691460\pi$
$314$			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	$-0.444093\pi$
$317$	−187.219	−	108.091i	−0.590597	−	0.340981i	−0.765333	+	0.643634i	$0.777426\pi$
$318$	−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	−0.980368	−	0.197175i	$-0.936823\pi$
$331$	−105.730	+	183.130i	−0.319426	+	0.553262i	0.660942	+	0.750437i	$0.270157\pi$
$332$	−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	$-0.930736\pi$
$347$	−443.350	+	255.968i	−1.27767	+	0.737661i	−0.301247	+	0.953546i	$0.597403\pi$
$348$	−12.1093	+	20.9739i	−0.0347968	+	0.0602699i
$349$			527.872i			1.51253i	0.654266	+	0.756264i	$0.272978\pi$
$349$			527.872i			1.51253i	−0.654266	+	0.756264i	$0.727022\pi$
$350$		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	$-0.228607\pi$
$353$	−68.2579	−	118.226i	−0.193365	−	0.334918i	−0.946363	+	0.323104i	$0.895274\pi$
$354$	−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	0.158490	+	0.987361i	$0.449338\pi$
$359$	−278.525	+	482.419i	−0.775835	+	1.34379i	−0.934324	+	0.356424i	$0.883996\pi$
$360$		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	$-0.115262\pi$
$367$	59.0110	+	102.210i	0.160793	+	0.278502i	−0.774360	+	0.632745i	$0.781928\pi$
$368$	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	$-0.473683\pi$
$373$	−275.718	−	159.186i	−0.739191	−	0.426772i	−0.821775	+	0.569812i	$0.807016\pi$
$374$	−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	−0.129815	−	0.991538i	$-0.541438\pi$
$383$	304.022	−	526.581i	0.793790	−	1.37488i	0.923605	−	0.383346i	$-0.125228\pi$
$384$		−	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	0.930427	−	0.366476i	$-0.119436\pi$
$389$	57.5081	+	99.6069i	0.147836	+	0.256059i	−0.782592	+	0.622535i	$0.786103\pi$
$390$		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	$-0.768425\pi$
$397$	80.3952	−	139.249i	0.202507	−	0.350752i	0.949336	+	0.314264i	$0.101758\pi$
$398$	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	−0.827032	−	0.562154i	$-0.809973\pi$
$401$	29.4028	−	50.9272i	0.0733238	−	0.127000i	0.900356	+	0.435154i	$0.143306\pi$
$402$	−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	−0.705765	−	0.708446i	$-0.749396\pi$
$409$	−182.052	+	105.108i	−0.445114	+	0.256987i	0.260650	+	0.965433i	$0.416063\pi$
$410$		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	$-0.691867\pi$
$419$		−	690.319i		−	1.64754i	0.566924	−	0.823770i	$-0.308133\pi$
$420$		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	0.896688	−	0.442662i	$-0.145966\pi$
$431$	28.0096	+	48.5141i	0.0649875	+	0.112562i	−0.831701	+	0.555224i	$0.812633\pi$
$432$	10.3923	−	18.0000i	0.0240563	−	0.0416667i
$433$	−71.4593			−0.165033			−0.0825165	−	0.996590i	$-0.526296\pi$
$433$	−71.4593			−0.165033			−0.0825165	+	0.996590i	$0.526296\pi$
$434$	−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	0.995376	+	0.0960592i	$0.0306238\pi$
$439$	691.975	+	399.512i	1.57625	+	0.910050i	0.580878	+	0.813991i	$0.302710\pi$
$440$		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	−0.993609	−	0.112879i	$-0.963993\pi$
$443$	−703.559	−	406.200i	−1.58817	−	0.916930i	−0.594561	−	0.804051i	$-0.702674\pi$
$444$	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	$-0.0299872\pi$
$457$	645.231	+	372.524i	1.41188	+	0.815151i	0.416317	+	0.909219i	$0.363320\pi$
$458$	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	$-0.810619\pi$
$461$		−	516.757i		−	1.12095i	0.828172	−	0.560474i	$-0.189381\pi$
$462$	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	0.295288	+	0.955408i	$0.404584\pi$
$467$	−317.450	+	549.839i	−0.679764	+	1.17739i	−0.975052	+	0.221977i	$0.928749\pi$
$468$	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	0.0178420	−	0.999841i	$-0.494320\pi$
$479$	427.580	−	246.863i	0.892650	−	0.515372i	0.874809	+	0.484469i	$0.160987\pi$
$480$		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	$-0.777298\pi$
$487$	−287.301	+	165.873i	−0.589941	+	0.340603i	0.175133	+	0.984545i	$0.443964\pi$
$488$	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	0.494137	+	0.869384i	$0.335484\pi$
$499$	−252.414	+	437.194i	−0.505840	+	0.876141i	−0.999977	+	0.00675693i	$0.997849\pi$
$500$		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	$-0.630994\pi$
$503$	−402.412			−0.800024			−0.400012	+	0.916510i	$0.630994\pi$
$504$	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	0.0408910	−	0.999164i	$-0.486980\pi$
$509$	−409.218	−	236.262i	−0.803965	−	0.464169i	−0.844856	+	0.534994i	$0.820314\pi$
$510$		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	−0.452993	−	0.891514i	$-0.649644\pi$
$521$	48.2368	−	27.8496i	0.0925851	−	0.0534540i	0.545578	+	0.838060i	$0.316310\pi$
$522$	−25.6877	+	14.8308i	−0.0492102	+	0.0284115i
$523$	265.238	−	459.405i	0.507146	−	0.878403i	−0.492819	−	0.870132i	$-0.664034\pi$
$523$	265.238	−	459.405i	0.507146	−	0.878403i	0.999966	−	0.00827171i	$-0.00263300\pi$
$524$		−	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	−0.994942	−	0.100449i	$-0.967972\pi$
$541$	−222.070	+	384.636i	−0.410480	+	0.710972i	0.584462	+	0.811421i	$0.301306\pi$
$542$	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	$-0.535028\pi$
$557$	387.702	−	223.840i	0.696054	−	0.401867i	0.805876	+	0.592084i	$0.201695\pi$
$558$	−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	0.946963	+	0.321343i	$0.104134\pi$
$563$	423.248	+	733.087i	0.751773	+	1.30211i	−0.195190	+	0.980765i	$0.562532\pi$
$564$	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	−0.670219	−	0.742164i	$-0.733800\pi$
$569$	175.038	−	303.174i	0.307623	−	0.532819i	0.977842	+	0.209345i	$0.0671331\pi$
$570$		0			0
$571$	382.891	+	663.186i	0.670562	+	1.16145i	0.977745	+	0.209797i	$0.0672803\pi$
$571$	382.891	+	663.186i	0.670562	+	1.16145i	−0.307183	+	0.951650i	$0.599386\pi$
$572$	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	$-0.195994\pi$
$577$	−53.0857	−	91.9471i	−0.0920029	−	0.159354i	−0.908354	+	0.418203i	$0.862660\pi$
$578$	−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	$-0.739646\pi$
$587$	−802.707			−1.36747			−0.683737	+	0.729729i	$0.739646\pi$
$588$	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	$-0.856173\pi$
$593$	−42.5138	+	73.6360i	−0.0716927	+	0.124175i	0.827951	+	0.560801i	$0.189507\pi$
$594$		−	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	0.978125	−	0.208017i	$-0.0667011\pi$
$599$	185.040	+	320.498i	0.308914	+	0.535055i	−0.669211	+	0.743072i	$0.733368\pi$
$600$		0			0
$601$			462.547i			0.769628i	0.922994	+	0.384814i	$0.125734\pi$
$601$			462.547i			0.769628i	−0.922994	+	0.384814i	$0.874266\pi$
$602$	−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	−0.427756	−	0.903894i	$-0.640696\pi$
$607$	345.333	−	598.134i	0.568918	−	0.985394i	0.996673	−	0.0814998i	$-0.0259710\pi$
$608$	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	$-0.641106\pi$
$613$	85.1695	−	49.1726i	0.138939	−	0.0802163i	0.567858	+	0.823126i	$0.307772\pi$
$614$	−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	−0.405054	−	0.914293i	$-0.632747\pi$
$619$	114.032	−	65.8365i	0.184220	−	0.106359i	0.589274	+	0.807933i	$0.299414\pi$
$620$		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	0.999839	−	0.0179287i	$-0.00570718\pi$
$641$	310.496	+	537.795i	0.484393	+	0.838993i	−0.515446	+	0.856922i	$0.672374\pi$
$642$	−53.7118	+	93.0316i	−0.0836632	+	0.144909i
$643$	75.8433			0.117952			0.0589761	−	0.998259i	$-0.481216\pi$
$643$	75.8433			0.117952			0.0589761	+	0.998259i	$0.481216\pi$
$644$	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	$-0.127766\pi$
$647$	78.8723	+	136.611i	0.121905	+	0.211145i	−0.798614	+	0.601843i	$0.794433\pi$
$648$	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	$-0.519022\pi$
$653$	−623.004	−	359.691i	−0.954064	−	0.550829i	−0.894341	+	0.447386i	$0.852355\pi$
$654$	−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	0.579083	−	0.815268i	$-0.303411\pi$
$661$	1040.86	−	600.938i	1.57467	−	0.909135i	0.995585	−	0.0938667i	$-0.0299227\pi$
$662$	−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	$-0.687783\pi$
$677$	298.889	−	517.691i	0.441491	−	0.764685i	0.997800	+	0.0662906i	$0.0211164\pi$
$678$	−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	$-0.791883\pi$
$683$	−453.453	+	261.801i	−0.663913	+	0.383310i	0.129853	+	0.991533i	$0.458549\pi$
$684$	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	0.618120	−	0.786083i	$-0.287894\pi$
$691$	170.271	+	98.3059i	0.246412	+	0.142266i	−0.371708	+	0.928350i	$0.621228\pi$
$692$	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	−0.739068	−	0.673631i	$-0.764734\pi$
$709$	151.618	−	262.609i	0.213847	−	0.370394i	0.952915	+	0.303237i	$0.0980672\pi$
$710$		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	0.580325	−	0.814385i	$-0.302926\pi$
$719$	118.785	+	68.5808i	0.165209	+	0.0953835i	−0.415116	+	0.909769i	$0.636259\pi$
$720$		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	$-0.670232\pi$
$727$	−741.058			−1.01934			−0.509669	+	0.860371i	$0.670232\pi$
$728$	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	$-0.802059\pi$
$733$	71.9021	−	124.538i	0.0980929	−	0.169902i	0.910895	+	0.412638i	$0.135392\pi$
$734$			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	−0.965842	−	0.259133i	$-0.916563\pi$
$739$	−522.722	−	905.381i	−0.707337	−	1.22514i	0.258505	−	0.966010i	$-0.416770\pi$
$740$		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	−0.914078	−	0.405539i	$-0.867084\pi$
$751$	−79.4795	+	137.663i	−0.105832	+	0.183306i	0.808246	+	0.588845i	$0.200417\pi$
$752$	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	−0.319585	−	0.947558i	$-0.603544\pi$
$761$	−989.290	−	571.167i	−1.29999	−	0.750548i	−0.980401	+	0.197010i	$0.936877\pi$
$762$	−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	$0.0346159\pi$
$769$			166.927i			0.217070i	−0.994093	+	0.108535i	$0.965384\pi$
$770$		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	$-0.237056\pi$
$773$	−169.546	−	293.663i	−0.219336	−	0.379901i	−0.954605	+	0.297874i	$0.903722\pi$
$774$	−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	$-0.0954910\pi$
$787$	174.514	+	302.268i	0.221746	+	0.384076i	−0.733592	+	0.679590i	$0.762158\pi$
$788$	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	$-0.527532\pi$
$797$	−137.702			−0.172776			−0.0863878	+	0.996262i	$0.527532\pi$
$798$	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	−0.994747	−	0.102362i	$-0.967360\pi$
$809$	−474.092	−	821.151i	−0.586022	−	1.01502i	0.408726	−	0.912657i	$-0.365973\pi$
$810$		0			0
$811$			434.987i			0.536359i	0.963369	+	0.268180i	$0.0864221\pi$
$811$			434.987i			0.536359i	−0.963369	+	0.268180i	$0.913578\pi$
$812$	−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	0.385646	+	0.922647i	$0.373979\pi$
$821$	−497.701	+	862.043i	−0.606213	+	1.04999i	−0.991859	+	0.127344i	$0.959355\pi$
$822$	280.476	+	485.798i	0.341211	+	0.590996i
$823$	−203.545	+	117.517i	−0.247321	+	0.142791i	−0.618537	−	0.785756i	$-0.712274\pi$
$823$	−203.545	+	117.517i	−0.247321	+	0.142791i	0.371216	+	0.928547i	$0.378941\pi$
$824$	−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	−0.672593	+	0.740013i	$0.734819\pi$
$829$	−1367.65	+	789.613i	−1.64976	+	0.952489i	−0.977166	+	0.212476i	$0.931847\pi$
$830$		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	$-0.903190\pi$
$839$		−	502.512i		−	0.598942i	0.954105	−	0.299471i	$-0.0968102\pi$
$840$		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	$-0.672541\pi$
$853$	−880.120			−1.03179			−0.515897	+	0.856651i	$0.672541\pi$
$854$	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	$-0.235150\pi$
$857$	−182.962	−	316.900i	−0.213492	−	0.369778i	−0.952805	+	0.303583i	$0.901817\pi$
$858$	17.7853	−	10.2684i	0.0207288	−	0.0119678i
$859$	957.688	+	552.921i	1.11489	+	0.643680i	0.940091	−	0.340924i	$-0.110740\pi$
$859$	957.688	+	552.921i	1.11489	+	0.643680i	0.174796	+	0.984605i	$0.444073\pi$
$860$		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	$-0.141124\pi$
$863$	848.741	+	490.021i	0.983477	+	0.567811i	0.0801589	+	0.996782i	$0.474457\pi$
$864$	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	$-0.624884\pi$
$877$	−1204.77	−	695.577i	−1.37374	−	0.793132i	−0.991397	+	0.130887i	$0.958218\pi$
$878$	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	$-0.957458\pi$
$881$		−	234.790i		−	0.266504i	0.991082	−	0.133252i	$-0.0425419\pi$
$882$	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	0.154013	+	0.988069i	$0.450780\pi$
$887$	−690.695	+	1196.32i	−0.778686	+	1.34872i	−0.932699	+	0.360655i	$0.882553\pi$
$888$	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	$-0.862399\pi$
$907$	−906.269	+	523.235i	−0.999194	+	0.576885i	−0.0911843	+	0.995834i	$0.529065\pi$
$908$	−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	−0.722019	−	0.691873i	$-0.756786\pi$
$919$	218.878	−	379.108i	0.238170	−	0.412522i	0.960189	+	0.279350i	$0.0901191\pi$
$920$		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	0.996985	−	0.0775890i	$-0.0247222\pi$
$929$	1326.88	+	766.072i	1.42828	+	0.824620i	0.431299	+	0.902209i	$0.358056\pi$
$930$		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	$-0.676657\pi$
$937$	−987.468			−1.05386			−0.526931	+	0.849908i	$0.676657\pi$
$938$	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	0.532687	−	0.846312i	$-0.321182\pi$
$941$	1441.57	−	832.293i	1.53196	−	0.884477i	0.999271	−	0.0381649i	$-0.0121512\pi$
$942$	−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	$-0.215864\pi$
$947$	591.674	+	341.603i	0.624788	+	0.360721i	−0.153943	+	0.988080i	$0.549197\pi$
$948$	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	0.620361	−	0.784317i	$-0.286986\pi$
$971$	244.015	+	140.882i	0.251303	+	0.145090i	−0.369058	+	0.929406i	$0.620320\pi$
$972$	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	$-0.520114\pi$
$977$	751.877	−	434.096i	0.769577	−	0.444316i	0.832724	+	0.553689i	$0.186780\pi$
$978$	−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	$-0.161090\pi$
$983$	17.2202	+	29.8262i	0.0175180	+	0.0303420i	−0.857134	+	0.515094i	$0.827757\pi$
$984$	−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	0.957171	−	0.289523i	$-0.0934967\pi$
$991$	225.801	+	391.098i	0.227851	+	0.394650i	−0.729320	+	0.684173i	$0.760163\pi$
$992$	−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	−0.907084	−	0.420949i	$-0.861697\pi$
$997$	−815.641	−	1412.73i	−0.818095	−	1.41698i	0.0889893	−	0.996033i	$-0.471636\pi$
$998$	−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.649.11		32
5.2	odd	4		1050.3.p.i.901.2		16
5.3	odd	4		210.3.o.b.61.8	yes	16
5.4	even	2	inner	1050.3.q.e.649.5		32
7.3	odd	6	inner	1050.3.q.e.199.5		32
15.8	even	4		630.3.v.c.271.2		16
35.3	even	12		210.3.o.b.31.8	✓	16
35.17	even	12		1050.3.p.i.451.2		16
35.23	odd	12		1470.3.f.d.391.1		16
35.24	odd	6	inner	1050.3.q.e.199.11		32
35.33	even	12		1470.3.f.d.391.7		16
105.38	odd	12		630.3.v.c.451.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.8	✓	16	35.3	even	12
210.3.o.b.61.8	yes	16	5.3	odd	4
630.3.v.c.271.2		16	15.8	even	4
630.3.v.c.451.2		16	105.38	odd	12
1050.3.p.i.451.2		16	35.17	even	12
1050.3.p.i.901.2		16	5.2	odd	4
1050.3.q.e.199.5		32	7.3	odd	6	inner
1050.3.q.e.199.11		32	35.24	odd	6	inner
1050.3.q.e.649.5		32	5.4	even	2	inner
1050.3.q.e.649.11		32	1.1	even	1	trivial
1470.3.f.d.391.1		16	35.23	odd	12
1470.3.f.d.391.7		16	35.33	even	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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