LMFDB - Embedded newform 630.3.v.c.451.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,3,Mod(271,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("630.271");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	630.v (of order $6$, degree $2$, 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:	$17.1662566547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + \cdots + 101626561 $ x^16 + 92x^14 - 112x^13 + 5846x^12 - 7728x^11 + 197216x^10 - 298200x^9 + 4836403x^8 - 6808704x^7 + 64376800x^6 - 91953512x^5 + 595763862x^4 - 630430976x^3 + 1087013404x^2 + 294123256x + 101626561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 7 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.2
Root			$-0.141814 + 0.245629i$ of defining polynomial
Character	$\chi$	$=$	630.451
Dual form			630.3.v.c.271.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(4.24494 - 5.56601i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(4.24494 - 5.56601i) q^{7} +2.82843 q^{8} +(2.73861 + 1.58114i) q^{10} +(-5.42967 + 9.40447i) q^{11} +0.772061i q^{13} +(-9.81857 - 1.26320i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-16.7760 - 9.68565i) q^{17} +(22.5766 - 13.0346i) q^{19} -4.47214i q^{20} +15.3574 q^{22} +(-6.84734 - 11.8599i) q^{23} +(2.50000 - 4.33013i) q^{25} +(0.945577 - 0.545929i) q^{26} +(5.39568 + 12.9185i) q^{28} +6.99131 q^{29} +(22.7559 + 13.1381i) q^{31} +(-2.82843 + 4.89898i) q^{32} +27.3952i q^{34} +(-1.99729 + 15.5245i) q^{35} +(-32.3004 - 55.9459i) q^{37} +(-31.9281 - 18.4337i) q^{38} +(-5.47723 + 3.16228i) q^{40} +5.54839i q^{41} -68.9320 q^{43} +(-10.8593 - 18.8089i) q^{44} +(-9.68361 + 16.7725i) q^{46} +(19.5817 - 11.3055i) q^{47} +(-12.9610 - 47.2548i) q^{49} -7.07107 q^{50} +(-1.33725 - 0.772061i) q^{52} +(37.2820 - 64.5742i) q^{53} -24.2822i q^{55} +(12.0065 - 15.7431i) q^{56} +(-4.94360 - 8.56257i) q^{58} +(-96.6595 - 55.8064i) q^{59} +(-46.9572 + 27.1108i) q^{61} -37.1603i q^{62} +8.00000 q^{64} +(-0.863190 - 1.49509i) q^{65} +(22.1273 - 38.3255i) q^{67} +(33.5521 - 19.3713i) q^{68} +(20.4259 - 8.53132i) q^{70} -31.9550 q^{71} +(-92.6322 - 53.4812i) q^{73} +(-45.6797 + 79.1195i) q^{74} +52.1384i q^{76} +(29.2968 + 70.1430i) q^{77} +(-14.8408 - 25.7050i) q^{79} +(7.74597 + 4.47214i) q^{80} +(6.79536 - 3.92330i) q^{82} -15.8151i q^{83} +43.3156 q^{85} +(48.7423 + 84.4242i) q^{86} +(-15.3574 + 26.5999i) q^{88} +(31.8358 - 18.3804i) q^{89} +(4.29730 + 3.27735i) q^{91} +27.3894 q^{92} +(-27.6926 - 15.9884i) q^{94} +(-29.1463 + 50.4828i) q^{95} +134.212i q^{97} +(-48.7102 + 49.2881i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 4 q^{7}+O(q^{10}) $ 16 * q - 16 * q^4 + 4 * q^7	$ 16 q - 16 q^{4} + 4 q^{7} + 4 q^{11} - 8 q^{14} - 32 q^{16} - 12 q^{17} - 72 q^{19} - 48 q^{22} + 12 q^{23} + 40 q^{25} + 32 q^{28} - 72 q^{29} + 120 q^{31} + 20 q^{35} + 44 q^{37} + 72 q^{38} - 56 q^{43} + 8 q^{44} + 8 q^{46} + 24 q^{47} - 40 q^{49} - 72 q^{52} - 32 q^{53} - 16 q^{56} - 88 q^{58} - 132 q^{59} + 96 q^{61} + 128 q^{64} - 20 q^{65} - 164 q^{67} + 24 q^{68} + 136 q^{71} - 348 q^{73} + 112 q^{74} - 96 q^{77} + 280 q^{79} + 264 q^{82} + 120 q^{85} + 88 q^{86} + 48 q^{88} + 300 q^{89} - 272 q^{91} - 48 q^{92} - 200 q^{95} - 384 q^{98}+O(q^{100}) $ 16 * q - 16 * q^4 + 4 * q^7 + 4 * q^11 - 8 * q^14 - 32 * q^16 - 12 * q^17 - 72 * q^19 - 48 * q^22 + 12 * q^23 + 40 * q^25 + 32 * q^28 - 72 * q^29 + 120 * q^31 + 20 * q^35 + 44 * q^37 + 72 * q^38 - 56 * q^43 + 8 * q^44 + 8 * q^46 + 24 * q^47 - 40 * q^49 - 72 * q^52 - 32 * q^53 - 16 * q^56 - 88 * q^58 - 132 * q^59 + 96 * q^61 + 128 * q^64 - 20 * q^65 - 164 * q^67 + 24 * q^68 + 136 * q^71 - 348 * q^73 + 112 * q^74 - 96 * q^77 + 280 * q^79 + 264 * q^82 + 120 * q^85 + 88 * q^86 + 48 * q^88 + 300 * q^89 - 272 * q^91 - 48 * q^92 - 200 * q^95 - 384 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$6$		0			0
$7$	4.24494	−	5.56601i	0.606420	−	0.795145i
$7$	4.24494	−	5.56601i	0.606420	−	0.795145i
$8$	2.82843			0.353553
$9$		0			0
$10$	2.73861	+	1.58114i	0.273861	+	0.158114i
$11$	−5.42967	+	9.40447i	−0.493607	+	0.854952i	−0.999973	−	0.00736658i	$-0.997655\pi$
$11$	−5.42967	+	9.40447i	−0.493607	+	0.854952i	0.506366	+	0.862319i	$0.330988\pi$
$12$		0			0
$13$			0.772061i			0.0593893i	0.999559	+	0.0296946i	$0.00945349\pi$
$13$			0.772061i			0.0593893i	−0.999559	+	0.0296946i	$0.990547\pi$
$14$	−9.81857	−	1.26320i	−0.701326	−	0.0902284i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−16.7760	−	9.68565i	−0.986826	−	0.569744i	−0.0825021	−	0.996591i	$-0.526291\pi$
$17$	−16.7760	−	9.68565i	−0.986826	−	0.569744i	−0.904324	+	0.426847i	$0.859624\pi$
$18$		0			0
$19$	22.5766	−	13.0346i	1.18824	−	0.686032i	0.230335	−	0.973111i	$-0.426018\pi$
$19$	22.5766	−	13.0346i	1.18824	−	0.686032i	0.957907	+	0.287079i	$0.0926844\pi$
$20$		−	4.47214i		−	0.223607i
$21$		0			0
$22$	15.3574			0.698065
$23$	−6.84734	−	11.8599i	−0.297711	−	0.515650i	0.677901	−	0.735153i	$-0.262890\pi$
$23$	−6.84734	−	11.8599i	−0.297711	−	0.515650i	−0.975612	+	0.219503i	$0.929556\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	0.945577	−	0.545929i	0.0363684	−	0.0209973i
$27$		0			0
$28$	5.39568	+	12.9185i	0.192703	+	0.461374i
$29$	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	$0.527359\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$		0			0
$34$			27.3952i			0.805740i
$35$	−1.99729	+	15.5245i	−0.0570655	+	0.443558i
$36$		0			0
$37$	−32.3004	−	55.9459i	−0.872984	−	1.51205i	−0.858895	−	0.512152i	$-0.828849\pi$
$37$	−32.3004	−	55.9459i	−0.872984	−	1.51205i	−0.0140890	−	0.999901i	$-0.504485\pi$
$38$	−31.9281	−	18.4337i	−0.840214	−	0.485098i
$39$		0			0
$40$	−5.47723	+	3.16228i	−0.136931	+	0.0790569i
$41$			5.54839i			0.135327i	0.997708	+	0.0676633i	$0.0215544\pi$
$41$			5.54839i			0.135327i	−0.997708	+	0.0676633i	$0.978446\pi$
$42$		0			0
$43$	−68.9320			−1.60307			−0.801535	−	0.597948i	$-0.795983\pi$
$43$	−68.9320			−1.60307			−0.801535	+	0.597948i	$0.795983\pi$
$44$	−10.8593	−	18.8089i	−0.246803	−	0.427476i
$45$		0			0
$46$	−9.68361	+	16.7725i	−0.210513	+	0.364620i
$47$	19.5817	−	11.3055i	0.416631	−	0.240542i	−0.277004	−	0.960869i	$-0.589342\pi$
$47$	19.5817	−	11.3055i	0.416631	−	0.240542i	0.693635	+	0.720327i	$0.256008\pi$
$48$		0			0
$49$	−12.9610	−	47.2548i	−0.264511	−	0.964383i
$50$	−7.07107			−0.141421
$51$		0			0
$52$	−1.33725	−	0.772061i	−0.0257163	−	0.0148473i
$53$	37.2820	−	64.5742i	0.703433	−	1.21838i	−0.263821	−	0.964572i	$-0.584983\pi$
$53$	37.2820	−	64.5742i	0.703433	−	1.21838i	0.967254	−	0.253810i	$-0.0816839\pi$
$54$		0			0
$55$		−	24.2822i		−	0.441495i
$56$	12.0065	−	15.7431i	0.214402	−	0.281126i
$57$		0			0
$58$	−4.94360	−	8.56257i	−0.0852345	−	0.147631i
$59$	−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	$0.479930\pi$
$62$		−	37.1603i		−	0.599359i
$63$		0			0
$64$	8.00000			0.125000
$65$	−0.863190	−	1.49509i	−0.0132798	−	0.0230014i
$66$		0			0
$67$	22.1273	−	38.3255i	0.330258	−	0.572023i	−0.652305	−	0.757957i	$-0.726198\pi$
$67$	22.1273	−	38.3255i	0.330258	−	0.572023i	0.982562	+	0.185934i	$0.0595310\pi$
$68$	33.5521	−	19.3713i	0.493413	−	0.284872i
$69$		0			0
$70$	20.4259	−	8.53132i	0.291798	−	0.121876i
$71$	−31.9550			−0.450071			−0.225035	−	0.974351i	$-0.572250\pi$
$71$	−31.9550			−0.450071			−0.225035	+	0.974351i	$0.572250\pi$
$72$		0			0
$73$	−92.6322	−	53.4812i	−1.26893	−	0.732619i	−0.294147	−	0.955760i	$-0.595036\pi$
$73$	−92.6322	−	53.4812i	−1.26893	−	0.732619i	−0.974786	+	0.223141i	$0.928369\pi$
$74$	−45.6797	+	79.1195i	−0.617293	+	1.06918i
$75$		0			0
$76$			52.1384i			0.686032i
$77$	29.2968	+	70.1430i	0.380478	+	0.910949i
$78$		0			0
$79$	−14.8408	−	25.7050i	−0.187858	−	0.325380i	0.756678	−	0.653788i	$-0.226821\pi$
$79$	−14.8408	−	25.7050i	−0.187858	−	0.325380i	−0.944536	+	0.328408i	$0.893488\pi$
$80$	7.74597	+	4.47214i	0.0968246	+	0.0559017i
$81$		0			0
$82$	6.79536	−	3.92330i	0.0828702	−	0.0478451i
$83$		−	15.8151i		−	0.190543i	−0.995451	−	0.0952717i	$-0.969628\pi$
$83$		−	15.8151i		−	0.190543i	0.995451	−	0.0952717i	$-0.0303720\pi$
$84$		0			0
$85$	43.3156			0.509595
$86$	48.7423	+	84.4242i	0.566771	+	0.981676i
$87$		0			0
$88$	−15.3574	+	26.5999i	−0.174516	+	0.302271i
$89$	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
$92$	27.3894			0.297711
$93$		0			0
$94$	−27.6926	−	15.9884i	−0.294603	−	0.170089i
$95$	−29.1463	+	50.4828i	−0.306803	+	0.531398i
$96$		0			0
$97$			134.212i			1.38363i	0.722077	+	0.691813i	$0.243188\pi$
$97$			134.212i			1.38363i	−0.722077	+	0.691813i	$0.756812\pi$
$98$	−48.7102	+	49.2881i	−0.497043	+	0.502940i
$99$		0			0
$100$	5.00000	+	8.66025i	0.0500000	+	0.0866025i
$101$	−132.760	−	76.6490i	−1.31445	−	0.758901i	−0.331624	−	0.943412i	$-0.607596\pi$
$101$	−132.760	−	76.6490i	−1.31445	−	0.758901i	−0.982830	+	0.184511i	$0.940930\pi$
$102$		0			0
$103$	−54.8504	+	31.6679i	−0.532529	+	0.307456i	−0.742046	−	0.670349i	$-0.766144\pi$
$103$	−54.8504	+	31.6679i	−0.532529	+	0.307456i	0.209517	+	0.977805i	$0.432811\pi$
$104$			2.18372i			0.0209973i
$105$		0			0
$106$	−105.449			−0.994805
$107$	−21.9277	−	37.9800i	−0.204932	−	0.354953i	0.745179	−	0.666865i	$-0.232364\pi$
$107$	−21.9277	−	37.9800i	−0.204932	−	0.354953i	−0.950111	+	0.311912i	$0.899031\pi$
$108$		0			0
$109$	−2.64166	+	4.57549i	−0.0242354	+	0.0419770i	−0.877889	−	0.478865i	$-0.841048\pi$
$109$	−2.64166	+	4.57549i	−0.0242354	+	0.0419770i	0.853653	+	0.520842i	$0.174382\pi$
$110$	−29.7396	+	17.1701i	−0.270360	+	0.156092i
$111$		0			0
$112$	−27.7711	−	3.57286i	−0.247956	−	0.0319006i
$113$	106.725			0.944469			0.472234	−	0.881473i	$-0.343448\pi$
$113$	106.725			0.944469			0.472234	+	0.881473i	$0.343448\pi$
$114$		0			0
$115$	26.5196	+	15.3111i	0.230606	+	0.133140i
$116$	−6.99131	+	12.1093i	−0.0602699	+	0.104391i
$117$		0			0
$118$			157.844i			1.33766i
$119$	−125.124	+	52.2607i	−1.05146	+	0.439166i
$120$		0			0
$121$	1.53727	+	2.66262i	0.0127047	+	0.0220051i
$122$	66.4075	+	38.3404i	0.544324	+	0.314266i
$123$		0			0
$124$	−45.5119	+	26.2763i	−0.367031	+	0.211906i
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	203.641			1.60348			0.801738	−	0.597676i	$-0.203909\pi$
$127$	203.641			1.60348			0.801738	+	0.597676i	$0.203909\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−1.22073	+	2.11437i	−0.00939027	+	0.0162644i
$131$	67.2791	−	38.8436i	0.513581	−	0.296516i	−0.220724	−	0.975336i	$-0.570842\pi$
$131$	67.2791	−	38.8436i	0.513581	−	0.296516i	0.734304	+	0.678820i	$0.237509\pi$
$132$		0			0
$133$	23.2854	−	180.993i	0.175078	−	1.36085i
$134$	−62.5853			−0.467055
$135$		0			0
$136$	−47.4498	−	27.3952i	−0.348896	−	0.201435i
$137$	114.504	−	198.326i	0.835794	−	1.44764i	−0.0575883	−	0.998340i	$-0.518341\pi$
$137$	114.504	−	198.326i	0.835794	−	1.44764i	0.893382	−	0.449297i	$-0.148326\pi$
$138$		0			0
$139$		−	61.7421i		−	0.444188i	−0.975025	−	0.222094i	$-0.928711\pi$
$139$		−	61.7421i		−	0.444188i	0.975025	−	0.222094i	$-0.0712892\pi$
$140$	−24.8920	−	18.9839i	−0.177800	−	0.135600i
$141$		0			0
$142$	22.5956	+	39.1368i	0.159124	+	0.275611i
$143$	−7.26082	−	4.19204i	−0.0507750	−	0.0293149i
$144$		0			0
$145$	−13.5386	+	7.81652i	−0.0933697	+	0.0539070i
$146$			151.268i			1.03608i
$147$		0			0
$148$	129.202			0.872984
$149$	−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	$0.984319\pi$
$152$	63.8563	−	36.8674i	0.420107	−	0.242549i
$153$		0			0
$154$	65.1914	−	85.4797i	0.423320	−	0.555063i
$155$	−58.7556			−0.379068
$156$		0			0
$157$	180.741	+	104.351i	1.15122	+	0.664657i	0.949184	−	0.314722i	$-0.101911\pi$
$157$	180.741	+	104.351i	1.15122	+	0.664657i	0.202035	+	0.979378i	$0.435245\pi$
$158$	−20.9880	+	36.3524i	−0.132836	+	0.230078i
$159$		0			0
$160$		−	12.6491i		−	0.0790569i
$161$	−95.0792	−	12.2323i	−0.590554	−	0.0759771i
$162$		0			0
$163$	−69.5841	−	120.523i	−0.426896	−	0.739406i	0.569699	−	0.821853i	$-0.307060\pi$
$163$	−69.5841	−	120.523i	−0.426896	−	0.739406i	−0.996595	+	0.0824475i	$0.973726\pi$
$164$	−9.61009	−	5.54839i	−0.0585981	−	0.0338316i
$165$		0			0
$166$	−19.3695	+	11.1830i	−0.116683	+	0.0673672i
$167$		−	54.4023i		−	0.325762i	−0.986646	−	0.162881i	$-0.947921\pi$
$167$		−	54.4023i		−	0.325762i	0.986646	−	0.162881i	$-0.0520787\pi$
$168$		0			0
$169$	168.404			0.996473
$170$	−30.6287	−	53.0505i	−0.180169	−	0.312062i
$171$		0			0
$172$	68.9320	−	119.394i	0.400768	−	0.694150i
$173$	−54.3723	+	31.3918i	−0.314291	+	0.181456i	−0.648845	−	0.760921i	$-0.724748\pi$
$173$	−54.3723	+	31.3918i	−0.314291	+	0.181456i	0.334554	+	0.942376i	$0.391414\pi$
$174$		0			0
$175$	−13.4892	−	32.2961i	−0.0770812	−	0.184549i
$176$	43.4374			0.246803
$177$		0			0
$178$	−45.0226	−	25.9938i	−0.252936	−	0.146033i
$179$	−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	$-0.211242\pi$
$182$	0.975265	−	7.58053i	0.00535860	−	0.0416513i
$183$		0			0
$184$	−19.3672	−	33.5450i	−0.105257	−	0.182310i
$185$	125.099	+	72.2259i	0.676210	+	0.390410i
$186$		0			0
$187$	182.177	−	105.180i	0.974208	−	0.562459i
$188$			45.2219i			0.240542i
$189$		0			0
$190$	82.4381			0.433885
$191$	66.5069	+	115.193i	0.348204	+	0.603106i	0.985930	−	0.167156i	$-0.0534585\pi$
$191$	66.5069	+	115.193i	0.348204	+	0.603106i	−0.637727	+	0.770263i	$0.720125\pi$
$192$		0			0
$193$	−142.611	+	247.010i	−0.738919	+	1.27984i	0.214064	+	0.976820i	$0.431330\pi$
$193$	−142.611	+	247.010i	−0.738919	+	1.27984i	−0.952983	+	0.303025i	$0.902003\pi$
$194$	164.375	−	94.9020i	0.847295	−	0.489186i
$195$		0			0
$196$	94.8087	+	24.8056i	0.483718	+	0.126559i
$197$	307.784			1.56236			0.781178	−	0.624309i	$-0.214619\pi$
$197$	307.784			1.56236			0.781178	+	0.624309i	$0.214619\pi$
$198$		0			0
$199$	−8.39167	−	4.84493i	−0.0421692	−	0.0243464i	0.478767	−	0.877942i	$-0.341084\pi$
$199$	−8.39167	−	4.84493i	−0.0421692	−	0.0243464i	−0.520936	+	0.853595i	$0.674417\pi$
$200$	7.07107	−	12.2474i	0.0353553	−	0.0612372i
$201$		0			0
$202$			216.796i			1.07325i
$203$	29.6777	−	38.9137i	0.146195	−	0.191693i
$204$		0			0
$205$	−6.20329	−	10.7444i	−0.0302599	−	0.0524117i
$206$	77.5702	+	44.7852i	0.376555	+	0.217404i
$207$		0			0
$208$	2.67450	−	1.54412i	0.0128582	−	0.00742366i
$209$			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	$0.363098\pi$
$212$	74.5639	+	129.148i	0.351717	+	0.609191i
$213$		0			0
$214$	−31.0105	+	53.7118i	−0.144909	+	0.250990i
$215$	133.486	−	77.0684i	0.620867	−	0.358457i
$216$		0			0
$217$	169.725	−	70.8893i	0.782141	−	0.326679i
$218$	7.47174			0.0342740
$219$		0			0
$220$	42.0581	+	24.2822i	0.191173	+	0.110374i
$221$	7.47791	−	12.9521i	0.0338367	−	0.0586069i
$222$		0			0
$223$			50.0854i			0.224598i	0.993674	+	0.112299i	$0.0358215\pi$
$223$			50.0854i			0.224598i	−0.993674	+	0.112299i	$0.964178\pi$
$224$	15.2613	+	36.5389i	0.0681308	+	0.163120i
$225$		0			0
$226$	−75.4659	−	130.711i	−0.333920	−	0.578366i
$227$	−264.301	−	152.594i	−1.16432	−	0.672221i	−0.211985	−	0.977273i	$-0.567993\pi$
$227$	−264.301	−	152.594i	−1.16432	−	0.672221i	−0.952336	+	0.305052i	$0.901326\pi$
$228$		0			0
$229$	−353.428	+	204.052i	−1.54335	+	0.891055i	−0.544728	+	0.838613i	$0.683367\pi$
$229$	−353.428	+	204.052i	−1.54335	+	0.891055i	−0.998624	+	0.0524421i	$0.983299\pi$
$230$		−	43.3064i		−	0.188289i
$231$		0			0
$232$	19.7744			0.0852345
$233$	108.404	+	187.762i	0.465255	+	0.805846i	0.999213	−	0.0396654i	$-0.0126292\pi$
$233$	108.404	+	187.762i	0.465255	+	0.805846i	−0.533958	+	0.845511i	$0.679296\pi$
$234$		0			0
$235$	−25.2798	+	43.7859i	−0.107574	+	0.186323i
$236$	193.319	−	111.613i	0.819149	−	0.472936i
$237$		0			0
$238$	152.482	+	116.291i	0.640680	+	0.488617i
$239$	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	$0.620701\pi$
$242$	2.17402	−	3.76552i	0.00898356	−	0.0155600i
$243$		0			0
$244$		−	108.443i		−	0.444439i
$245$	77.9313	+	77.0176i	0.318087	+	0.314357i
$246$		0			0
$247$	10.0635	+	17.4305i	0.0407429	+	0.0705688i
$248$	64.3635	+	37.1603i	0.259530	+	0.149840i
$249$		0			0
$250$	13.6931	−	7.90569i	0.0547723	−	0.0316228i
$251$			256.631i			1.02244i	0.859451	+	0.511218i	$0.170805\pi$
$251$			256.631i			1.02244i	−0.859451	+	0.511218i	$0.829195\pi$
$252$		0			0
$253$	148.715			0.587808
$254$	−143.996	−	249.409i	−0.566914	−	0.981924i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	173.998	−	100.458i	0.677034	−	0.390886i	−0.121703	−	0.992567i	$-0.538835\pi$
$257$	173.998	−	100.458i	0.677034	−	0.390886i	0.798737	+	0.601681i	$0.205502\pi$
$258$		0			0
$259$	−448.509	−	57.7025i	−1.73170	−	0.222789i
$260$	3.45276			0.0132798
$261$		0			0
$262$	−95.1470	−	54.9331i	−0.363156	−	0.209668i
$263$	251.495	−	435.602i	0.956256	−	1.65628i	0.224787	−	0.974408i	$-0.427831\pi$
$263$	251.495	−	435.602i	0.956256	−	1.65628i	0.731469	−	0.681875i	$-0.238835\pi$
$264$		0			0
$265$			166.730i			0.629170i
$266$	−238.135	+	99.4625i	−0.895245	+	0.373919i
$267$		0			0
$268$	44.2545	+	76.6511i	0.165129	+	0.286012i
$269$	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	$0.262350\pi$
$272$			77.4852i			0.284872i
$273$		0			0
$274$	−323.866			−1.18199
$275$	27.1484	+	47.0224i	0.0987214	+	0.170990i
$276$		0			0
$277$	53.5034	−	92.6706i	0.193153	−	0.334551i	−0.753140	−	0.657860i	$-0.771462\pi$
$277$	53.5034	−	92.6706i	0.193153	−	0.334551i	0.946293	+	0.323309i	$0.104795\pi$
$278$	−75.6183	+	43.6583i	−0.272008	+	0.157044i
$279$		0			0
$280$	−5.64919	+	43.9100i	−0.0201757	+	0.156821i
$281$	85.5187			0.304337			0.152169	−	0.988355i	$-0.451374\pi$
$281$	85.5187			0.304337			0.152169	+	0.988355i	$0.451374\pi$
$282$		0			0
$283$	−339.501	−	196.011i	−1.19965	−	0.692619i	−0.239173	−	0.970977i	$-0.576876\pi$
$283$	−339.501	−	196.011i	−1.19965	−	0.692619i	−0.960477	+	0.278358i	$0.910210\pi$
$284$	31.9550	−	55.3477i	0.112518	−	0.194886i
$285$		0			0
$286$			11.8569i			0.0414576i
$287$	30.8824	+	23.5526i	0.107604	+	0.0820646i
$288$		0			0
$289$	43.1238	+	74.6926i	0.149217	+	0.258452i
$290$	19.1465	+	11.0542i	0.0660224	+	0.0381180i
$291$		0			0
$292$	185.264	−	106.962i	0.634467	−	0.366310i
$293$			500.595i			1.70851i	0.519850	+	0.854257i	$0.325988\pi$
$293$			500.595i			1.70851i	−0.519850	+	0.854257i	$0.674012\pi$
$294$		0			0
$295$	249.574			0.846013
$296$	−91.3593	−	158.239i	−0.308646	−	0.534591i
$297$		0			0
$298$	−20.7214	+	35.8906i	−0.0695350	+	0.120438i
$299$	9.15660	−	5.28656i	0.0306241	−	0.0176808i
$300$		0			0
$301$	−292.612	+	383.677i	−0.972133	+	1.27467i
$302$	231.501			0.766559
$303$		0			0
$304$	−90.3064	−	52.1384i	−0.297061	−	0.171508i
$305$	60.6215	−	104.999i	0.198759	−	0.344261i
$306$		0			0
$307$		−	398.171i		−	1.29698i	−0.761225	−	0.648488i	$-0.775402\pi$
$307$		−	398.171i		−	1.29698i	0.761225	−	0.648488i	$-0.224598\pi$
$308$	−150.788	−	19.3995i	−0.489572	−	0.0629853i
$309$		0			0
$310$	41.5465	+	71.9606i	0.134021	+	0.232131i
$311$	−322.107	−	185.968i	−1.03571	−	0.597969i	−0.117097	−	0.993120i	$-0.537359\pi$
$311$	−322.107	−	185.968i	−1.03571	−	0.597969i	−0.918616	+	0.395151i	$0.870692\pi$
$312$		0			0
$313$	365.884	−	211.243i	1.16896	−	0.674899i	0.215524	−	0.976499i	$-0.430854\pi$
$313$	365.884	−	211.243i	1.16896	−	0.674899i	0.953435	+	0.301600i	$0.0975207\pi$
$314$		−	295.149i		−	0.939966i
$315$		0			0
$316$	59.3632			0.187858
$317$	108.091	+	187.219i	0.340981	+	0.590597i	0.984615	−	0.174737i	$-0.0559075\pi$
$317$	108.091	+	187.219i	0.340981	+	0.590597i	−0.643634	+	0.765333i	$0.722574\pi$
$318$		0			0
$319$	−37.9605	+	65.7496i	−0.118999	+	0.206112i
$320$	−15.4919	+	8.94427i	−0.0484123	+	0.0279508i
$321$		0			0
$322$	52.2497	+	125.097i	0.162266	+	0.388501i
$323$	−504.995			−1.56345
$324$		0			0
$325$	3.34312	+	1.93015i	0.0102865	+	0.00593893i
$326$	−98.4067	+	170.445i	−0.301861	+	0.522839i
$327$		0			0
$328$			15.6932i			0.0478451i
$329$	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	$0.936823\pi$
$332$	27.3926	+	15.8151i	0.0825077	+	0.0476358i
$333$		0			0
$334$	−66.6289	+	38.4682i	−0.199488	+	0.115174i
$335$			98.9561i			0.295391i
$336$		0			0
$337$	260.379			0.772639			0.386319	−	0.922365i	$-0.373746\pi$
$337$	260.379			0.772639			0.386319	+	0.922365i	$0.373746\pi$
$338$	−119.080	−	206.252i	−0.352306	−	0.610213i
$339$		0			0
$340$	−43.3156	+	75.0247i	−0.127399	+	0.220661i
$341$	−247.115	+	142.672i	−0.724676	+	0.418392i
$342$		0			0
$343$	−318.039	−	128.452i	−0.927228	−	0.374496i
$344$	−194.969			−0.566771
$345$		0			0
$346$	76.8940	+	44.3948i	0.222237	+	0.128309i
$347$	−255.968	+	443.350i	−0.737661	+	1.27767i	0.215885	+	0.976419i	$0.430736\pi$
$347$	−255.968	+	443.350i	−0.737661	+	1.27767i	−0.953546	+	0.301247i	$0.902597\pi$
$348$		0			0
$349$			527.872i			1.51253i	0.654266	+	0.756264i	$0.272978\pi$
$349$			527.872i			1.51253i	−0.654266	+	0.756264i	$0.727022\pi$
$350$	−30.0162	+	39.3577i	−0.0857607	+	0.112450i
$351$		0			0
$352$	−30.7149	−	53.1997i	−0.0872582	−	0.151136i
$353$	−118.226	−	68.2579i	−0.334918	−	0.193365i	0.323104	−	0.946363i	$-0.395274\pi$
$353$	−118.226	−	68.2579i	−0.334918	−	0.193365i	−0.658023	+	0.752998i	$0.728607\pi$
$354$		0			0
$355$	61.8807	−	35.7268i	0.174312	−	0.100639i
$356$			73.5216i			0.206521i
$357$		0			0
$358$	199.115			0.556187
$359$	−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
$362$	−273.102	+	157.676i	−0.754426	+	0.435568i
$363$		0			0
$364$	−9.97383	+	4.16579i	−0.0274006	+	0.0114445i
$365$	239.175			0.655274
$366$		0			0
$367$	102.210	+	59.0110i	0.278502	+	0.160793i	0.632745	−	0.774360i	$-0.281928\pi$
$367$	102.210	+	59.0110i	0.278502	+	0.160793i	−0.354243	+	0.935153i	$0.615262\pi$
$368$	−27.3894	+	47.4398i	−0.0744276	+	0.128912i
$369$		0			0
$370$		−	204.286i		−	0.552124i
$371$	−201.162	−	481.625i	−0.542215	−	1.29818i
$372$		0			0
$373$	159.186	+	275.718i	0.426772	+	0.739191i	0.996584	−	0.0825840i	$-0.0263173\pi$
$373$	159.186	+	275.718i	0.426772	+	0.739191i	−0.569812	+	0.821775i	$0.692984\pi$
$374$	−257.637	−	148.747i	−0.688869	−	0.397719i
$375$		0			0
$376$	55.3853	−	31.9767i	0.147301	−	0.0850444i
$377$			5.39771i			0.0143175i
$378$		0			0
$379$	−579.699			−1.52955			−0.764774	−	0.644299i	$-0.777149\pi$
$379$	−579.699			−1.52955			−0.764774	+	0.644299i	$0.777149\pi$
$380$	−58.2925	−	100.966i	−0.153401	−	0.265699i
$381$		0			0
$382$	94.0549	−	162.908i	0.246217	−	0.426461i
$383$	−526.581	+	304.022i	−1.37488	+	0.793790i	−0.991538	−	0.129815i	$-0.958562\pi$
$383$	−526.581	+	304.022i	−1.37488	+	0.793790i	−0.383346	+	0.923605i	$0.625228\pi$
$384$		0			0
$385$	−135.155	−	103.077i	−0.351053	−	0.267731i
$386$	403.366			1.04499
$387$		0			0
$388$	−232.462	−	134.212i	−0.599128	−	0.345907i
$389$	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
$392$	−36.6593	−	133.657i	−0.0935187	−	0.340961i
$393$		0			0
$394$	−217.636	−	376.957i	−0.552376	−	0.956744i
$395$	57.4781	+	33.1850i	0.145514	+	0.0840127i
$396$		0			0
$397$	−139.249	+	80.3952i	−0.350752	+	0.202507i	−0.665016	−	0.746829i	$-0.731575\pi$
$397$	−139.249	+	80.3952i	−0.350752	+	0.202507i	0.314264	+	0.949336i	$0.398242\pi$
$398$			13.7035i			0.0344310i
$399$		0			0
$400$	−20.0000			−0.0500000
$401$	−29.4028	−	50.9272i	−0.0733238	−	0.127000i	0.827032	−	0.562154i	$-0.190027\pi$
$401$	−29.4028	−	50.9272i	−0.0733238	−	0.127000i	−0.900356	+	0.435154i	$0.856694\pi$
$402$		0			0
$403$	−10.1434	+	17.5690i	−0.0251698	+	0.0435954i
$404$	265.520	−	153.298i	0.657227	−	0.379450i
$405$		0			0
$406$	−68.6447	−	8.83141i	−0.169076	−	0.0217522i
$407$	701.523			1.72364
$408$		0			0
$409$	182.052	+	105.108i	0.445114	+	0.256987i	0.705765	−	0.708446i	$-0.250604\pi$
$409$	182.052	+	105.108i	0.445114	+	0.256987i	−0.260650	+	0.965433i	$0.583937\pi$
$410$	−8.77277	+	15.1949i	−0.0213970	+	0.0370607i
$411$		0			0
$412$		−	126.672i		−	0.307456i
$413$	−720.933	+	301.114i	−1.74560	+	0.729089i
$414$		0			0
$415$	17.6818	+	30.6258i	0.0426068	+	0.0737971i
$416$	−3.78231	−	2.18372i	−0.00909209	−	0.00524932i
$417$		0			0
$418$	346.719	−	200.178i	0.829471	−	0.478895i
$419$			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	$0.339375\pi$
$422$	−124.418	−	215.498i	−0.294829	−	0.510659i
$423$		0			0
$424$	105.449	−	182.644i	0.248701	−	0.430763i
$425$	−83.8802	+	48.4283i	−0.197365	+	0.113949i
$426$		0			0
$427$	−48.4315	+	376.448i	−0.113423	+	0.881611i
$428$	87.7110			0.204932
$429$		0			0
$430$	−188.778	−	108.991i	−0.439019	−	0.253468i
$431$	−28.0096	+	48.5141i	−0.0649875	+	0.112562i	−0.896688	−	0.442662i	$-0.854034\pi$
$431$	−28.0096	+	48.5141i	−0.0649875	+	0.112562i	0.831701	+	0.555224i	$0.187367\pi$
$432$		0			0
$433$			71.4593i			0.165033i	0.996590	+	0.0825165i	$0.0262957\pi$
$433$			71.4593i			0.165033i	−0.996590	+	0.0825165i	$0.973704\pi$
$434$	−206.835	−	157.743i	−0.476578	−	0.363463i
$435$		0			0
$436$	−5.28332	−	9.15098i	−0.0121177	−	0.0209885i
$437$	−309.179	−	178.505i	−0.707504	−	0.408478i
$438$		0			0
$439$	−691.975	+	399.512i	−1.57625	+	0.910050i	−0.580878	+	0.813991i	$0.697290\pi$
$439$	−691.975	+	399.512i	−1.57625	+	0.910050i	−0.995376	+	0.0960592i	$0.969376\pi$
$440$		−	68.6806i		−	0.156092i
$441$		0			0
$442$	−21.1507			−0.0478523
$443$	−406.200	−	703.559i	−0.916930	−	1.58817i	−0.804051	−	0.594561i	$-0.797326\pi$
$443$	−406.200	−	703.559i	−0.916930	−	1.58817i	−0.112879	−	0.993609i	$-0.536007\pi$
$444$		0			0
$445$	−41.0998	+	71.1870i	−0.0923592	+	0.159971i
$446$	61.3419	−	35.4157i	0.137538	−	0.0794075i
$447$		0			0
$448$	33.9595	−	44.5281i	0.0758024	−	0.0993931i
$449$	−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
$452$	−106.725	+	184.853i	−0.236117	+	0.408967i
$453$		0			0
$454$			431.601i			0.950663i
$455$	−11.9859	−	1.54203i	−0.0263426	−	0.00338908i
$456$		0			0
$457$	372.524	+	645.231i	0.815151	+	1.41188i	0.909219	+	0.416317i	$0.136680\pi$
$457$	372.524	+	645.231i	0.815151	+	1.41188i	−0.0940682	+	0.995566i	$0.529987\pi$
$458$	499.822	+	288.572i	1.09131	+	0.630071i
$459$		0			0
$460$	−53.0393	+	30.6223i	−0.115303	+	0.0665701i
$461$		−	516.757i		−	1.12095i	−0.828172	−	0.560474i	$-0.810619\pi$
$461$		−	516.757i		−	1.12095i	0.828172	−	0.560474i	$-0.189381\pi$
$462$		0			0
$463$	−538.823			−1.16376			−0.581882	−	0.813273i	$-0.697684\pi$
$463$	−538.823			−1.16376			−0.581882	+	0.813273i	$0.697684\pi$
$464$	−13.9826	−	24.2186i	−0.0301350	−	0.0521953i
$465$		0			0
$466$	153.307	−	265.536i	0.328985	−	0.569819i
$467$	−549.839	+	317.450i	−1.17739	+	0.679764i	−0.955408	−	0.295288i	$-0.904584\pi$
$467$	−549.839	+	317.450i	−1.17739	+	0.679764i	−0.221977	+	0.975052i	$0.571251\pi$
$468$		0			0
$469$	−119.392	−	285.850i	−0.254566	−	0.609489i
$470$	71.5021			0.152132
$471$		0			0
$472$	−273.394	−	157.844i	−0.579226	−	0.334416i
$473$	374.279	−	648.269i	0.791286	−	1.37055i
$474$		0			0
$475$		−	130.346i		−	0.274413i
$476$	34.6055	−	268.981i	0.0727007	−	0.565087i
$477$		0			0
$478$	−275.587	−	477.331i	−0.576542	−	0.998600i
$479$	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
$482$		−	98.0915i		−	0.203509i
$483$		0			0
$484$	−6.14906			−0.0127047
$485$	−150.053	−	259.900i	−0.309388	−	0.535876i
$486$		0			0
$487$	165.873	−	287.301i	0.340603	−	0.589941i	−0.643942	−	0.765074i	$-0.722702\pi$
$487$	165.873	−	287.301i	0.340603	−	0.589941i	0.984545	+	0.175133i	$0.0560356\pi$
$488$	−132.815	+	76.6808i	−0.272162	+	0.157133i
$489$		0			0
$490$	39.2211	−	149.906i	0.0800430	−	0.305930i
$491$	744.294			1.51587			0.757937	−	0.652328i	$-0.226207\pi$
$491$	744.294			1.51587			0.757937	+	0.652328i	$0.226207\pi$
$492$		0			0
$493$	−117.287	−	67.7154i	−0.237904	−	0.137354i
$494$	14.2319	−	24.6505i	0.0288096	−	0.0498997i
$495$		0			0
$496$		−	105.105i		−	0.211906i
$497$	−135.647	+	177.862i	−0.272932	+	0.357872i
$498$		0			0
$499$	252.414	+	437.194i	0.505840	+	0.876141i	0.999977	+	0.00675693i	$0.00215081\pi$
$499$	252.414	+	437.194i	0.505840	+	0.876141i	−0.494137	+	0.869384i	$0.664516\pi$
$500$	−19.3649	−	11.1803i	−0.0387298	−	0.0223607i
$501$		0			0
$502$	314.308	−	181.466i	0.626111	−	0.361486i
$503$		−	402.412i		−	0.800024i	−0.916510	−	0.400012i	$-0.869006\pi$
$503$		−	402.412i		−	0.800024i	0.916510	−	0.400012i	$-0.130994\pi$
$504$		0			0
$505$	342.785			0.678781
$506$	−105.158	−	182.138i	−0.207821	−	0.359957i
$507$		0			0
$508$	−203.641	+	352.717i	−0.400869	+	0.694325i
$509$	−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
$512$	22.6274			0.0441942
$513$		0			0
$514$	−246.070	−	142.069i	−0.478735	−	0.276398i
$515$	70.8116	−	122.649i	0.137498	−	0.238154i
$516$		0			0
$517$			245.540i			0.474933i
$518$	246.473	+	590.111i	0.475817	+	1.13921i
$519$		0			0
$520$	−2.44147	−	4.22875i	−0.00469513	−	0.00813221i
$521$	−48.2368	−	27.8496i	−0.0925851	−	0.0534540i	0.452993	−	0.891514i	$-0.350356\pi$
$521$	−48.2368	−	27.8496i	−0.0925851	−	0.0534540i	−0.545578	+	0.838060i	$0.683690\pi$
$522$		0			0
$523$	459.405	−	265.238i	0.878403	−	0.507146i	0.00827171	−	0.999966i	$-0.497367\pi$
$523$	459.405	−	265.238i	0.878403	−	0.507146i	0.870132	+	0.492819i	$0.164034\pi$
$524$			155.374i			0.296516i
$525$		0			0
$526$	−711.336			−1.35235
$527$	−254.503	−	440.812i	−0.482928	−	0.836456i
$528$		0			0
$529$	170.728	−	295.709i	0.322737	−	0.558997i
$530$	204.202	−	117.896i	0.385286	−	0.222445i
$531$		0			0
$532$	290.203	+	221.324i	0.545495	+	0.416023i
$533$	−4.28369			−0.00803694
$534$		0			0
$535$	84.9258	+	49.0319i	0.158740	+	0.0916485i
$536$	62.5853	−	108.401i	0.116764	−	0.202241i
$537$		0			0
$538$		−	198.823i		−	0.369559i
$539$	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	$0.967972\pi$
$542$	−146.806	−	84.7586i	−0.270860	−	0.156381i
$543$		0			0
$544$	94.8996	−	54.7903i	0.174448	−	0.100718i
$545$		−	11.8139i		−	0.0216768i
$546$		0			0
$547$	−308.345			−0.563702			−0.281851	−	0.959458i	$-0.590948\pi$
$547$	−308.345			−0.563702			−0.281851	+	0.959458i	$0.590948\pi$
$548$	229.008	+	396.653i	0.417897	+	0.723819i
$549$		0			0
$550$	38.3936	−	66.4997i	0.0698065	−	0.120908i
$551$	157.840	−	91.1289i	0.286461	−	0.165388i
$552$		0			0
$553$	−206.073	−	26.5121i	−0.372645	−	0.0479422i
$554$	−151.330			−0.273160
$555$		0			0
$556$	106.940	+	61.7421i	0.192339	+	0.111047i
$557$	223.840	−	387.702i	0.401867	−	0.696054i	−0.592084	−	0.805876i	$-0.701695\pi$
$557$	223.840	−	387.702i	0.401867	−	0.696054i	0.993951	+	0.109822i	$0.0350281\pi$
$558$		0			0
$559$		−	53.2197i		−	0.0952052i
$560$	57.7731	−	24.1302i	0.103166	−	0.0430897i
$561$		0			0
$562$	−60.4709	−	104.739i	−0.107599	−	0.186368i
$563$	733.087	+	423.248i	1.30211	+	0.751773i	0.980765	−	0.195190i	$-0.0625324\pi$
$563$	733.087	+	423.248i	1.30211	+	0.751773i	0.321343	+	0.946963i	$0.395866\pi$
$564$		0			0
$565$	−206.672	+	119.322i	−0.365791	+	0.211190i
$566$			554.403i			0.979511i
$567$		0			0
$568$	−90.3825			−0.159124
$569$	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	$-0.0672803\pi$
$572$	14.5216	−	8.38408i	0.0253875	−	0.0146575i
$573$		0			0
$574$	7.00871	−	54.4772i	0.0122103	−	0.0949081i
$575$	−68.4734			−0.119084
$576$		0			0
$577$	−91.9471	−	53.0857i	−0.159354	−	0.0920029i	0.418203	−	0.908354i	$-0.362660\pi$
$577$	−91.9471	−	53.0857i	−0.159354	−	0.0920029i	−0.577556	+	0.816351i	$0.695994\pi$
$578$	60.9862	−	105.631i	0.105512	−	0.182753i
$579$		0			0
$580$		−	31.2661i		−	0.0539070i
$581$	−88.0271	−	67.1341i	−0.151510	−	0.115549i
$582$		0			0
$583$	404.858	+	701.234i	0.694439	+	1.20280i
$584$	−262.003	−	151.268i	−0.448636	−	0.259020i
$585$		0			0
$586$	613.101	−	353.974i	1.04625	−	0.604051i
$587$			802.707i			1.36747i	0.729729	+	0.683737i	$0.239646\pi$
$587$			802.707i			1.36747i	−0.729729	+	0.683737i	$0.760354\pi$
$588$		0			0
$589$	685.002			1.16299
$590$	−176.475	−	305.664i	−0.299111	−	0.518075i
$591$		0			0
$592$	−129.202	+	223.784i	−0.218246	+	0.378013i
$593$	73.6360	−	42.5138i	0.124175	−	0.0716927i	−0.436626	−	0.899643i	$-0.643827\pi$
$593$	73.6360	−	42.5138i	0.124175	−	0.0716927i	0.560801	+	0.827951i	$0.310493\pi$
$594$		0			0
$595$	183.872	−	241.095i	0.309028	−	0.405202i
$596$	58.6090			0.0983373
$597$		0			0
$598$	−12.9494	−	7.47633i	−0.0216545	−	0.0125022i
$599$	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	$-0.125734\pi$
$602$	676.814	+	87.0748i	1.12428	+	0.144643i
$603$		0			0
$604$	−163.696	−	283.529i	−0.271020	−	0.469420i
$605$	−5.95381	−	3.43743i	−0.00984100	−	0.00568170i
$606$		0			0
$607$	−598.134	+	345.333i	−0.985394	+	0.568918i	−0.903894	−	0.427756i	$-0.859304\pi$
$607$	−598.134	+	345.333i	−0.985394	+	0.568918i	−0.0814998	+	0.996673i	$0.525971\pi$
$608$			147.470i			0.242549i
$609$		0			0
$610$	−171.463			−0.281088
$611$	8.72851	+	15.1182i	0.0142856	+	0.0247434i
$612$		0			0
$613$	49.1726	−	85.1695i	0.0802163	−	0.138939i	−0.823126	−	0.567858i	$-0.807772\pi$
$613$	49.1726	−	85.1695i	0.0802163	−	0.138939i	0.903343	+	0.428919i	$0.141106\pi$
$614$	−487.658	+	281.550i	−0.794232	+	0.458550i
$615$		0			0
$616$	82.8639	+	198.394i	0.134519	+	0.322069i
$617$	794.667			1.28795			0.643976	−	0.765045i	$-0.277283\pi$
$617$	794.667			1.28795			0.643976	+	0.765045i	$0.277283\pi$
$618$		0			0
$619$	−114.032	−	65.8365i	−0.184220	−	0.106359i	0.405054	−	0.914293i	$-0.367253\pi$
$619$	−114.032	−	65.8365i	−0.184220	−	0.106359i	−0.589274	+	0.807933i	$0.700586\pi$
$620$	58.7556	−	101.768i	0.0947670	−	0.164141i
$621$		0			0
$622$			525.998i			0.845656i
$623$	32.8353	−	255.222i	0.0527052	−	0.409666i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	−517.438	−	298.743i	−0.826579	−	0.477225i
$627$		0			0
$628$	−361.483	+	208.702i	−0.575609	+	0.332328i
$629$			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	$0.830203\pi$
$632$	−41.9761	−	72.7047i	−0.0664179	−	0.115039i
$633$		0			0
$634$	152.864	−	264.768i	0.241110	−	0.417615i
$635$	−394.350	+	227.678i	−0.621023	+	0.358548i
$636$		0			0
$637$	36.4835	−	10.0067i	0.0572740	−	0.0157091i
$638$	107.369			0.168289
$639$		0			0
$640$	21.9089	+	12.6491i	0.0342327	+	0.0197642i
$641$	−310.496	+	537.795i	−0.484393	+	0.838993i	−0.999839	−	0.0179287i	$-0.994293\pi$
$641$	−310.496	+	537.795i	−0.484393	+	0.838993i	0.515446	+	0.856922i	$0.327626\pi$
$642$		0			0
$643$		−	75.8433i		−	0.117952i	−0.998259	−	0.0589761i	$-0.981216\pi$
$643$		−	75.8433i		−	0.117952i	0.998259	−	0.0589761i	$-0.0187836\pi$
$644$	116.266	−	152.450i	0.180538	−	0.236723i
$645$		0			0
$646$	357.085	+	618.490i	0.552763	+	0.957414i
$647$	−136.611	−	78.8723i	−0.211145	−	0.121905i	0.390698	−	0.920519i	$-0.372234\pi$
$647$	−136.611	−	78.8723i	−0.211145	−	0.121905i	−0.601843	+	0.798614i	$0.705567\pi$
$648$		0			0
$649$	1049.66	−	606.021i	1.61735	−	0.933777i
$650$		−	5.45929i		−	0.00839891i
$651$		0			0
$652$	278.336			0.426896
$653$	−359.691	−	623.004i	−0.550829	−	0.954064i	−0.998215	−	0.0597229i	$-0.980978\pi$
$653$	−359.691	−	623.004i	−0.550829	−	0.954064i	0.447386	−	0.894341i	$-0.352355\pi$
$654$		0			0
$655$	−86.8569	+	150.441i	−0.132606	+	0.229680i
$656$	19.2202	−	11.0968i	0.0292991	−	0.0169158i
$657$		0			0
$658$	−206.545	+	86.2681i	−0.313898	+	0.131106i
$659$	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	$0.303411\pi$
$662$	−149.525	+	258.985i	−0.225868	+	0.391215i
$663$		0			0
$664$		−	44.7318i		−	0.0673672i
$665$	157.264	+	376.525i	0.236487	+	0.566203i
$666$		0			0
$667$	−47.8719	−	82.9166i	−0.0717720	−	0.124313i
$668$	94.2275	+	54.4023i	0.141059	+	0.0814405i
$669$		0			0
$670$	121.196	−	69.9725i	0.180890	−	0.104437i
$671$		−	588.810i		−	0.877512i
$672$		0			0
$673$	1070.49			1.59062			0.795310	−	0.606203i	$-0.207308\pi$
$673$	1070.49			1.59062			0.795310	+	0.606203i	$0.207308\pi$
$674$	−184.116	−	318.898i	−0.273169	−	0.473143i
$675$		0			0
$676$	−168.404	+	291.684i	−0.249118	+	0.431485i
$677$	517.691	−	298.889i	0.764685	−	0.441491i	−0.0662906	−	0.997800i	$-0.521116\pi$
$677$	517.691	−	298.889i	0.764685	−	0.441491i	0.830975	+	0.556309i	$0.187783\pi$
$678$		0			0
$679$	747.024	+	569.720i	1.10018	+	0.839058i
$680$	122.515			0.180169
$681$		0			0
$682$	349.473	+	201.768i	0.512424	+	0.295848i
$683$	261.801	−	453.453i	0.383310	−	0.663913i	−0.608223	−	0.793766i	$-0.708117\pi$
$683$	261.801	−	453.453i	0.383310	−	0.663913i	0.991533	+	0.129853i	$0.0414506\pi$
$684$		0			0
$685$			512.076i			0.747557i
$686$	67.5667	+	480.346i	0.0984937	+	0.700214i
$687$		0			0
$688$	137.864	+	238.788i	0.200384	+	0.347075i
$689$	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	$0.287894\pi$
$692$		−	125.567i		−	0.181456i
$693$		0			0
$694$	723.988			1.04321
$695$	69.0298	+	119.563i	0.0993234	+	0.172033i
$696$		0			0
$697$	53.7398	−	93.0800i	0.0771015	−	0.133544i
$698$	646.509	−	373.262i	0.926231	−	0.534760i
$699$		0			0
$700$	69.4278	+	8.93216i	0.0991825	+	0.0127602i
$701$	−132.968			−0.189683			−0.0948414	−	0.995492i	$-0.530234\pi$
$701$	−132.968			−0.189683			−0.0948414	+	0.995492i	$0.530234\pi$
$702$		0			0
$703$	−1458.47	−	842.046i	−2.07463	−	1.19779i
$704$	−43.4374	+	75.2358i	−0.0617008	+	0.106869i
$705$		0			0
$706$			193.062i			0.273460i
$707$	−990.186	+	413.573i	−1.40055	+	0.584969i
$708$		0			0
$709$	−151.618	−	262.609i	−0.213847	−	0.370394i	0.739068	−	0.673631i	$-0.235266\pi$
$709$	−151.618	−	262.609i	−0.213847	−	0.370394i	−0.952915	+	0.303237i	$0.901933\pi$
$710$	−87.5125	−	50.5254i	−0.123257	−	0.0711625i
$711$		0			0
$712$	90.0453	−	51.9877i	0.126468	−	0.0730164i
$713$		−	359.846i		−	0.504692i
$714$		0			0
$715$	18.7474			0.0262201
$716$	−140.796	−	243.865i	−0.196642	−	0.340594i
$717$		0			0
$718$	−393.893	+	682.243i	−0.548598	+	0.950200i
$719$	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
$722$	−450.574			−0.624063
$723$		0			0
$724$	386.225	+	222.987i	0.533460	+	0.307993i
$725$	17.4783	−	30.2733i	0.0241080	−	0.0417562i
$726$		0			0
$727$		−	741.058i		−	1.01934i	−0.860371	−	0.509669i	$-0.829768\pi$
$727$		−	741.058i		−	1.01934i	0.860371	−	0.509669i	$-0.170232\pi$
$728$	12.1546	+	9.26974i	0.0166959	+	0.0127332i
$729$		0			0
$730$	−169.122	−	292.929i	−0.231675	−	0.401272i
$731$	1156.41	+	667.652i	1.58195	+	0.913340i
$732$		0			0
$733$	124.538	−	71.9021i	0.169902	−	0.0980929i	−0.412638	−	0.910895i	$-0.635392\pi$
$733$	124.538	−	71.9021i	0.169902	−	0.0980929i	0.582540	+	0.812802i	$0.302059\pi$
$734$		−	166.908i		−	0.227396i
$735$		0			0
$736$	77.4688			0.105257
$737$	240.288	+	416.190i	0.326035	+	0.564709i
$738$		0			0
$739$	522.722	−	905.381i	0.707337	−	1.22514i	−0.258505	−	0.966010i	$-0.583230\pi$
$739$	522.722	−	905.381i	0.707337	−	1.22514i	0.965842	−	0.259133i	$-0.0834368\pi$
$740$	−250.198	+	144.452i	−0.338105	+	0.195205i
$741$		0			0
$742$	−447.626	+	586.932i	−0.603269	+	0.791014i
$743$	−660.175			−0.888526			−0.444263	−	0.895896i	$-0.646534\pi$
$743$	−660.175			−0.888526			−0.444263	+	0.895896i	$0.646534\pi$
$744$		0			0
$745$	56.7480	+	32.7634i	0.0761717	+	0.0439778i
$746$	225.123	−	389.925i	0.301774	−	0.522687i
$747$		0			0
$748$			420.720i			0.562459i
$749$	−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	$0.867084\pi$
$752$	−78.3266	−	45.2219i	−0.104158	−	0.0601355i
$753$		0			0
$754$	6.61082	−	3.81676i	0.00876767	−	0.00506202i
$755$		−	366.035i		−	0.484815i
$756$		0			0
$757$	−777.212			−1.02670			−0.513350	−	0.858179i	$-0.671596\pi$
$757$	−777.212			−1.02670			−0.513350	+	0.858179i	$0.671596\pi$
$758$	409.909	+	709.983i	0.540777	+	0.936653i
$759$		0			0
$760$	−82.4381	+	142.787i	−0.108471	+	0.187878i
$761$	989.290	−	571.167i	1.29999	−	0.750548i	0.319585	−	0.947558i	$-0.396456\pi$
$761$	989.290	−	571.167i	1.29999	−	0.750548i	0.980401	+	0.197010i	$0.0631231\pi$
$762$		0			0
$763$	14.2536	+	34.1262i	0.0186809	+	0.0447263i
$764$	−266.028			−0.348204
$765$		0			0
$766$	744.698	+	429.951i	0.972190	+	0.561294i
$767$	43.0859	−	74.6270i	0.0561746	−	0.0972973i
$768$		0			0
$769$			166.927i			0.217070i	0.994093	+	0.108535i	$0.0346159\pi$
$769$			166.927i			0.217070i	−0.994093	+	0.108535i	$0.965384\pi$
$770$	−30.6733	+	238.417i	−0.0398354	+	0.309632i
$771$		0			0
$772$	−285.223	−	494.020i	−0.369459	−	0.639922i
$773$	−293.663	−	169.546i	−0.379901	−	0.219336i	0.297874	−	0.954605i	$-0.403722\pi$
$773$	−293.663	−	169.546i	−0.379901	−	0.219336i	−0.677775	+	0.735269i	$0.737056\pi$
$774$		0			0
$775$	113.780	−	65.6907i	0.146812	−	0.0847622i
$776$			379.608i			0.489186i
$777$		0			0
$778$	−162.657			−0.209071
$779$	72.3210	+	125.264i	0.0928383	+	0.160801i
$780$		0			0
$781$	173.505	−	300.520i	0.222158	−	0.384789i
$782$	324.905	−	187.584i	0.415480	−	0.239877i
$783$		0			0
$784$	−137.773	+	139.408i	−0.175731	+	0.177816i
$785$	−466.672			−0.594487
$786$		0			0
$787$	302.268	+	174.514i	0.384076	+	0.221746i	0.679590	−	0.733592i	$-0.262158\pi$
$787$	302.268	+	174.514i	0.384076	+	0.221746i	−0.295514	+	0.955338i	$0.595491\pi$
$788$	−307.784	+	533.098i	−0.390589	+	0.676520i
$789$		0			0
$790$		−	93.8614i		−	0.118812i
$791$	453.041	−	594.033i	0.572744	−	0.750989i
$792$		0			0
$793$	−20.9311	−	36.2538i	−0.0263949	−	0.0457173i
$794$	196.927	+	113.696i	0.248019	+	0.143194i
$795$		0			0
$796$	16.7833	−	9.68987i	0.0210846	−	0.0121732i
$797$			137.702i			0.172776i	0.996262	+	0.0863878i	$0.0275324\pi$
$797$			137.702i			0.172776i	−0.996262	+	0.0863878i	$0.972468\pi$
$798$		0			0
$799$	−438.004			−0.548190
$800$	14.1421	+	24.4949i	0.0176777	+	0.0306186i
$801$		0			0
$802$	−41.5819	+	72.0219i	−0.0518477	+	0.0898029i
$803$	1005.92	−	580.771i	1.25271	−	0.723252i
$804$		0			0
$805$	197.796	−	82.6140i	0.245710	−	0.102626i
$806$	28.6900			0.0355955
$807$		0			0
$808$	−375.502	−	216.796i	−0.464730	−	0.268312i
$809$	−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	$-0.0864221\pi$
$812$	37.7229	+	90.3169i	0.0464568	+	0.111228i
$813$		0			0
$814$	−496.052	−	859.186i	−0.609400	−	1.05551i
$815$	269.498	+	155.595i	0.330672	+	0.190914i
$816$		0			0
$817$	−1556.25	+	898.502i	−1.90484	+	1.09976i
$818$		−	297.289i		−	0.363434i
$819$		0			0
$820$	24.8131			0.0302599
$821$	497.701	+	862.043i	0.606213	+	1.04999i	0.991859	+	0.127344i	$0.0406453\pi$
$821$	497.701	+	862.043i	0.606213	+	1.04999i	−0.385646	+	0.922647i	$0.626021\pi$
$822$		0			0
$823$	−117.517	+	203.545i	−0.142791	+	0.247321i	−0.928547	−	0.371216i	$-0.878941\pi$
$823$	−117.517	+	203.545i	−0.142791	+	0.247321i	0.785756	+	0.618537i	$0.212274\pi$
$824$	−155.140	+	89.5704i	−0.188277	+	0.108702i
$825$		0			0
$826$	878.564	+	670.039i	1.06364	+	0.811186i
$827$	−267.742			−0.323751			−0.161876	−	0.986811i	$-0.551754\pi$
$827$	−267.742			−0.323751			−0.161876	+	0.986811i	$0.551754\pi$
$828$		0			0
$829$	1367.65	+	789.613i	1.64976	+	0.952489i	0.977166	+	0.212476i	$0.0681527\pi$
$829$	1367.65	+	789.613i	1.64976	+	0.952489i	0.672593	+	0.740013i	$0.265181\pi$
$830$	25.0059	−	43.3114i	0.0301275	−	0.0521824i
$831$		0			0
$832$			6.17648i			0.00742366i
$833$	−240.258	+	918.284i	−0.288425	+	1.10238i
$834$		0			0
$835$	60.8236	+	105.350i	0.0728426	+	0.126167i
$836$	−490.334	−	283.095i	−0.586524	−	0.338630i
$837$		0			0
$838$	845.465	−	488.129i	1.00891	−	0.582493i
$839$			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
$842$	−287.852	−	498.574i	−0.341867	−	0.592130i
$843$		0			0
$844$	−175.954	+	304.761i	−0.208476	+	0.361091i
$845$	−326.113	+	188.281i	−0.385932	+	0.222818i
$846$		0			0
$847$	21.3458	+	2.74622i	0.0252016	+	0.00324229i
$848$	−298.256			−0.351717
$849$		0			0
$850$	118.625	+	68.4879i	0.139558	+	0.0805740i
$851$	−442.344	+	766.162i	−0.519793	+	0.900308i
$852$		0			0
$853$			880.120i			1.03179i	0.856651	+	0.515897i	$0.172541\pi$
$853$			880.120i			1.03179i	−0.856651	+	0.515897i	$0.827459\pi$
$854$	495.299	−	206.873i	0.579975	−	0.242240i
$855$		0			0
$856$	−62.0210	−	107.424i	−0.0724545	−	0.125495i
$857$	316.900	+	182.962i	0.369778	+	0.213492i	0.673362	−	0.739313i	$-0.264850\pi$
$857$	316.900	+	182.962i	0.369778	+	0.213492i	−0.303583	+	0.952805i	$0.598183\pi$
$858$		0			0
$859$	−957.688	+	552.921i	−1.11489	+	0.643680i	−0.940091	−	0.340924i	$-0.889260\pi$
$859$	−957.688	+	552.921i	−1.11489	+	0.643680i	−0.174796	+	0.984605i	$0.555927\pi$
$860$			308.273i			0.358457i
$861$		0			0
$862$	79.2231			0.0919062
$863$	490.021	+	848.741i	0.567811	+	0.983477i	0.996782	+	0.0801589i	$0.0255428\pi$
$863$	490.021	+	848.741i	0.567811	+	0.983477i	−0.428971	+	0.903318i	$0.641124\pi$
$864$		0			0
$865$	70.1943	−	121.580i	0.0811495	−	0.140555i
$866$	87.5194	−	50.5293i	0.101062	−	0.0583480i
$867$		0			0
$868$	−46.9408	+	364.861i	−0.0540793	+	0.420347i
$869$	322.323			0.370912
$870$		0			0
$871$	29.5896	+	17.0836i	0.0339720	+	0.0196138i
$872$	−7.47174	+	12.9414i	−0.00856851	+	0.0148411i
$873$		0			0
$874$			504.888i			0.577675i
$875$	62.2299	+	47.4598i	0.0711199	+	0.0542398i
$876$		0			0
$877$	−695.577	−	1204.77i	−0.793132	−	1.37374i	−0.924019	−	0.382347i	$-0.875116\pi$
$877$	−695.577	−	1204.77i	−0.793132	−	1.37374i	0.130887	−	0.991397i	$-0.458218\pi$
$878$	978.601	+	564.995i	1.11458	+	0.643503i
$879$		0			0
$880$	−84.1162	+	48.5645i	−0.0955865	+	0.0551869i
$881$		−	234.790i		−	0.266504i	−0.991082	−	0.133252i	$-0.957458\pi$
$881$		−	234.790i		−	0.266504i	0.991082	−	0.133252i	$-0.0425419\pi$
$882$		0			0
$883$	977.996			1.10758			0.553791	−	0.832655i	$-0.313180\pi$
$883$	977.996			1.10758			0.553791	+	0.832655i	$0.313180\pi$
$884$	14.9558	+	25.9042i	0.0169184	+	0.0293034i
$885$		0			0
$886$	−574.454	+	994.983i	−0.648367	+	1.12301i
$887$	−1196.32	+	690.695i	−1.34872	+	0.778686i	−0.988069	−	0.154013i	$-0.950780\pi$
$887$	−1196.32	+	690.695i	−1.34872	+	0.778686i	−0.360655	+	0.932699i	$0.617447\pi$
$888$		0			0
$889$	864.445	−	1133.47i	0.972379	−	1.27500i
$890$	116.248			0.130616
$891$		0			0
$892$	−86.7505	−	50.0854i	−0.0972539	−	0.0561496i
$893$	294.725	−	510.478i	0.330039	−	0.571644i
$894$		0			0
$895$		−	314.828i		−	0.351764i
$896$	−78.5486	−	10.1056i	−0.0876658	−	0.0112786i
$897$		0			0
$898$	307.439	+	532.501i	0.342360	+	0.592985i
$899$	159.094	+	91.8528i	0.176967	+	0.102172i
$900$		0			0
$901$	−1250.89	+	722.200i	−1.38833	+	0.801554i
$902$			85.2090i			0.0944668i
$903$		0			0
$904$	301.864			0.333920
$905$	249.307	+	431.812i	0.275477	+	0.477141i
$906$		0			0
$907$	523.235	−	906.269i	0.576885	−	0.999194i	−0.418949	−	0.908010i	$-0.637601\pi$
$907$	523.235	−	906.269i	0.576885	−	0.999194i	0.995834	−	0.0911843i	$-0.0290652\pi$
$908$	528.601	−	305.188i	0.582160	−	0.336110i
$909$		0			0
$910$	6.58670	+	15.7700i	0.00723813	+	0.0173297i
$911$	942.221			1.03427			0.517136	−	0.855903i	$-0.326998\pi$
$911$	942.221			1.03427			0.517136	+	0.855903i	$0.326998\pi$
$912$		0			0
$913$	148.733	+	85.8708i	0.162905	+	0.0940535i
$914$	526.829	−	912.494i	0.576399	−	0.998352i
$915$		0			0
$916$		−	816.206i		−	0.891055i
$917$	69.3914	−	539.365i	0.0756722	−	0.588184i
$918$		0			0
$919$	−218.878	−	379.108i	−0.238170	−	0.412522i	0.722019	−	0.691873i	$-0.243214\pi$
$919$	−218.878	−	379.108i	−0.238170	−	0.412522i	−0.960189	+	0.279350i	$0.909881\pi$
$920$	75.0089	+	43.3064i	0.0815314	+	0.0470722i
$921$		0			0
$922$	−632.896	+	365.403i	−0.686438	+	0.396315i
$923$		−	24.6712i		−	0.0267294i
$924$		0			0
$925$	−323.004			−0.349194
$926$	381.005	+	659.921i	0.411453	+	0.712657i
$927$		0			0
$928$	−19.7744	+	34.2503i	−0.0213086	+	0.0369076i
$929$	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
$932$	−433.618			−0.465255
$933$		0			0
$934$	777.590	+	448.942i	0.832537	+	0.480666i
$935$	−235.189	+	407.360i	−0.251539	+	0.435679i
$936$		0			0
$937$		−	987.468i		−	1.05386i	−0.849908	−	0.526931i	$-0.823343\pi$
$937$		−	987.468i		−	1.05386i	0.849908	−	0.526931i	$-0.176657\pi$
$938$	−265.671	+	348.351i	−0.283231	+	0.371376i
$939$		0			0
$940$	−50.5596	−	87.5718i	−0.0537868	−	0.0931615i
$941$	−1441.57	−	832.293i	−1.53196	−	0.884477i	−0.999271	−	0.0381649i	$-0.987849\pi$
$941$	−1441.57	−	832.293i	−1.53196	−	0.884477i	−0.532687	−	0.846312i	$-0.678818\pi$
$942$		0			0
$943$	65.8036	−	37.9917i	0.0697811	−	0.0402881i
$944$			446.451i			0.472936i
$945$		0			0
$946$	−1058.62			−1.11905
$947$	−341.603	−	591.674i	−0.360721	−	0.624788i	0.627358	−	0.778731i	$-0.284136\pi$
$947$	−341.603	−	591.674i	−0.360721	−	0.624788i	−0.988080	+	0.153943i	$0.950803\pi$
$948$		0			0
$949$	41.2907	−	71.5176i	0.0435097	−	0.0753610i
$950$	−159.641	+	92.1686i	−0.168043	+	0.0970196i
$951$		0			0
$952$	−353.903	+	147.816i	−0.371747	+	0.155269i
$953$	−705.451			−0.740243			−0.370121	−	0.928983i	$-0.620684\pi$
$953$	−705.451			−0.740243			−0.370121	+	0.928983i	$0.620684\pi$
$954$		0			0
$955$	−257.580	−	148.714i	−0.269717	−	0.155721i
$956$	−389.739	+	675.048i	−0.407677	+	0.706117i
$957$		0			0
$958$		−	698.235i		−	0.728846i
$959$	−617.826	−	1479.21i	−0.644240	−	1.54245i
$960$		0			0
$961$	−135.278	−	234.309i	−0.140768	−	0.243818i
$962$	−61.0851	−	35.2675i	−0.0634980	−	0.0366606i
$963$		0			0
$964$	−120.137	+	69.3612i	−0.124624	+	0.0719515i
$965$		−	637.777i		−	0.660909i
$966$		0			0
$967$	−187.828			−0.194238			−0.0971188	−	0.995273i	$-0.530963\pi$
$967$	−187.828			−0.194238			−0.0971188	+	0.995273i	$0.530963\pi$
$968$	4.34804	+	7.53103i	0.00449178	+	0.00777999i
$969$		0			0
$970$	−212.207	+	367.554i	−0.218771	+	0.378922i
$971$	−244.015	+	140.882i	−0.251303	+	0.145090i	−0.620361	−	0.784317i	$-0.713014\pi$
$971$	−244.015	+	140.882i	−0.251303	+	0.145090i	0.369058	+	0.929406i	$0.379680\pi$
$972$		0			0
$973$	−343.658	−	262.091i	−0.353194	−	0.269364i
$974$	−469.161			−0.481685
$975$		0			0
$976$	187.829	+	108.443i	0.192448	+	0.111110i
$977$	434.096	−	751.877i	0.444316	−	0.769577i	−0.553689	−	0.832724i	$-0.686780\pi$
$977$	434.096	−	751.877i	0.444316	−	0.769577i	0.998004	+	0.0631464i	$0.0201135\pi$
$978$		0			0
$979$			399.199i			0.407762i
$980$	−211.330	+	57.9635i	−0.215643	+	0.0591464i
$981$		0			0
$982$	−526.296	−	911.571i	−0.535943	−	0.928280i
$983$	29.8262	+	17.2202i	0.0303420	+	0.0175180i	0.515094	−	0.857134i	$-0.327757\pi$
$983$	29.8262	+	17.2202i	0.0303420	+	0.0175180i	−0.484752	+	0.874652i	$0.661090\pi$
$984$		0			0
$985$	−596.021	+	344.113i	−0.605098	+	0.349353i
$986$			191.528i			0.194248i
$987$		0			0
$988$	−40.2540			−0.0407429
$989$	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	$0.0934967\pi$
$992$	−128.727	+	74.3206i	−0.129765	+	0.0749199i
$993$		0			0
$994$	313.753	+	40.3655i	0.315647	+	0.0406092i
$995$	21.6672			0.0217761
$996$		0			0
$997$	−1412.73	−	815.641i	−1.41698	−	0.818095i	−0.420949	−	0.907084i	$-0.638303\pi$
$997$	−1412.73	−	815.641i	−1.41698	−	0.818095i	−0.996033	+	0.0889893i	$0.971636\pi$
$998$	356.968	−	618.286i	0.357683	−	0.619525i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.v.c.451.2		16
3.2	odd	2		210.3.o.b.31.8	✓	16
7.5	odd	6	inner	630.3.v.c.271.2		16
15.2	even	4		1050.3.q.e.199.5		32
15.8	even	4		1050.3.q.e.199.11		32
15.14	odd	2		1050.3.p.i.451.2		16
21.5	even	6		210.3.o.b.61.8	yes	16
21.11	odd	6		1470.3.f.d.391.7		16
21.17	even	6		1470.3.f.d.391.1		16
105.47	odd	12		1050.3.q.e.649.11		32
105.68	odd	12		1050.3.q.e.649.5		32
105.89	even	6		1050.3.p.i.901.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.8	✓	16	3.2	odd	2
210.3.o.b.61.8	yes	16	21.5	even	6
630.3.v.c.271.2		16	7.5	odd	6	inner
630.3.v.c.451.2		16	1.1	even	1	trivial
1050.3.p.i.451.2		16	15.14	odd	2
1050.3.p.i.901.2		16	105.89	even	6
1050.3.q.e.199.5		32	15.2	even	4
1050.3.q.e.199.11		32	15.8	even	4
1050.3.q.e.649.5		32	105.68	odd	12
1050.3.q.e.649.11		32	105.47	odd	12
1470.3.f.d.391.1		16	21.17	even	6
1470.3.f.d.391.7		16	21.11	odd	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	630.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(4.24494 - 5.56601i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(4.24494 - 5.56601i) q^{7} +2.82843 q^{8} +(2.73861 + 1.58114i) q^{10} +(-5.42967 + 9.40447i) q^{11} +0.772061i q^{13} +(-9.81857 - 1.26320i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-16.7760 - 9.68565i) q^{17} +(22.5766 - 13.0346i) q^{19} -4.47214i q^{20} +15.3574 q^{22} +(-6.84734 - 11.8599i) q^{23} +(2.50000 - 4.33013i) q^{25} +(0.945577 - 0.545929i) q^{26} +(5.39568 + 12.9185i) q^{28} +6.99131 q^{29} +(22.7559 + 13.1381i) q^{31} +(-2.82843 + 4.89898i) q^{32} +27.3952i q^{34} +(-1.99729 + 15.5245i) q^{35} +(-32.3004 - 55.9459i) q^{37} +(-31.9281 - 18.4337i) q^{38} +(-5.47723 + 3.16228i) q^{40} +5.54839i q^{41} -68.9320 q^{43} +(-10.8593 - 18.8089i) q^{44} +(-9.68361 + 16.7725i) q^{46} +(19.5817 - 11.3055i) q^{47} +(-12.9610 - 47.2548i) q^{49} -7.07107 q^{50} +(-1.33725 - 0.772061i) q^{52} +(37.2820 - 64.5742i) q^{53} -24.2822i q^{55} +(12.0065 - 15.7431i) q^{56} +(-4.94360 - 8.56257i) q^{58} +(-96.6595 - 55.8064i) q^{59} +(-46.9572 + 27.1108i) q^{61} -37.1603i q^{62} +8.00000 q^{64} +(-0.863190 - 1.49509i) q^{65} +(22.1273 - 38.3255i) q^{67} +(33.5521 - 19.3713i) q^{68} +(20.4259 - 8.53132i) q^{70} -31.9550 q^{71} +(-92.6322 - 53.4812i) q^{73} +(-45.6797 + 79.1195i) q^{74} +52.1384i q^{76} +(29.2968 + 70.1430i) q^{77} +(-14.8408 - 25.7050i) q^{79} +(7.74597 + 4.47214i) q^{80} +(6.79536 - 3.92330i) q^{82} -15.8151i q^{83} +43.3156 q^{85} +(48.7423 + 84.4242i) q^{86} +(-15.3574 + 26.5999i) q^{88} +(31.8358 - 18.3804i) q^{89} +(4.29730 + 3.27735i) q^{91} +27.3894 q^{92} +(-27.6926 - 15.9884i) q^{94} +(-29.1463 + 50.4828i) q^{95} +134.212i q^{97} +(-48.7102 + 49.2881i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 4 q^{7}+O(q^{10}) \) 16 * q - 16 * q^4 + 4 * q^7	\( 16 q - 16 q^{4} + 4 q^{7} + 4 q^{11} - 8 q^{14} - 32 q^{16} - 12 q^{17} - 72 q^{19} - 48 q^{22} + 12 q^{23} + 40 q^{25} + 32 q^{28} - 72 q^{29} + 120 q^{31} + 20 q^{35} + 44 q^{37} + 72 q^{38} - 56 q^{43} + 8 q^{44} + 8 q^{46} + 24 q^{47} - 40 q^{49} - 72 q^{52} - 32 q^{53} - 16 q^{56} - 88 q^{58} - 132 q^{59} + 96 q^{61} + 128 q^{64} - 20 q^{65} - 164 q^{67} + 24 q^{68} + 136 q^{71} - 348 q^{73} + 112 q^{74} - 96 q^{77} + 280 q^{79} + 264 q^{82} + 120 q^{85} + 88 q^{86} + 48 q^{88} + 300 q^{89} - 272 q^{91} - 48 q^{92} - 200 q^{95} - 384 q^{98}+O(q^{100}) \) 16 * q - 16 * q^4 + 4 * q^7 + 4 * q^11 - 8 * q^14 - 32 * q^16 - 12 * q^17 - 72 * q^19 - 48 * q^22 + 12 * q^23 + 40 * q^25 + 32 * q^28 - 72 * q^29 + 120 * q^31 + 20 * q^35 + 44 * q^37 + 72 * q^38 - 56 * q^43 + 8 * q^44 + 8 * q^46 + 24 * q^47 - 40 * q^49 - 72 * q^52 - 32 * q^53 - 16 * q^56 - 88 * q^58 - 132 * q^59 + 96 * q^61 + 128 * q^64 - 20 * q^65 - 164 * q^67 + 24 * q^68 + 136 * q^71 - 348 * q^73 + 112 * q^74 - 96 * q^77 + 280 * q^79 + 264 * q^82 + 120 * q^85 + 88 * q^86 + 48 * q^88 + 300 * q^89 - 272 * q^91 - 48 * q^92 - 200 * q^95 - 384 * q^98

Introduction

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