LMFDB - Embedded newform 630.3.v.c.451.6

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			451.6
Root			$-2.63284 + 4.56021i$ of defining polynomial
Character	$\chi$	$=$	630.451
Dual form			630.3.v.c.271.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(1.94434 - 6.72455i) q^{7} -2.82843 q^{8} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(1.94434 - 6.72455i) q^{7} -2.82843 q^{8} +(-2.73861 - 1.58114i) q^{10} +(-0.263223 + 0.455915i) q^{11} -4.22307i q^{13} +(9.61071 - 2.37366i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(28.8825 + 16.6753i) q^{17} +(2.75133 - 1.58848i) q^{19} -4.47214i q^{20} -0.744507 q^{22} +(5.52954 + 9.57744i) q^{23} +(2.50000 - 4.33013i) q^{25} +(5.17218 - 2.98616i) q^{26} +(9.70292 + 10.0922i) q^{28} +56.1302 q^{29} +(-1.63817 - 0.945800i) q^{31} +(2.82843 - 4.89898i) q^{32} +47.1649i q^{34} +(3.75308 + 15.1959i) q^{35} +(4.87682 + 8.44690i) q^{37} +(3.89097 + 2.24645i) q^{38} +(5.47723 - 3.16228i) q^{40} -4.07377i q^{41} +46.3519 q^{43} +(-0.526446 - 0.911831i) q^{44} +(-7.81995 + 13.5445i) q^{46} +(-54.7969 + 31.6370i) q^{47} +(-41.4391 - 26.1496i) q^{49} +7.07107 q^{50} +(7.31457 + 4.22307i) q^{52} +(-23.2606 + 40.2885i) q^{53} -1.17717i q^{55} +(-5.49942 + 19.0199i) q^{56} +(39.6900 + 68.7452i) q^{58} +(43.7614 + 25.2657i) q^{59} +(89.4583 - 51.6488i) q^{61} -2.67513i q^{62} +8.00000 q^{64} +(4.72153 + 8.17794i) q^{65} +(-4.36948 + 7.56816i) q^{67} +(-57.7649 + 33.3506i) q^{68} +(-15.9572 + 15.3417i) q^{70} -29.0608 q^{71} +(14.4912 + 8.36647i) q^{73} +(-6.89686 + 11.9457i) q^{74} +6.35393i q^{76} +(2.55403 + 2.65651i) q^{77} +(66.1473 + 114.571i) q^{79} +(7.74597 + 4.47214i) q^{80} +(4.98933 - 2.88059i) q^{82} -12.4838i q^{83} -74.5742 q^{85} +(32.7757 + 56.7692i) q^{86} +(0.744507 - 1.28952i) q^{88} +(59.1101 - 34.1272i) q^{89} +(-28.3982 - 8.21107i) q^{91} -22.1182 q^{92} +(-77.4945 - 44.7415i) q^{94} +(-3.55196 + 6.15217i) q^{95} -149.281i q^{97} +(2.72468 - 69.2429i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	1.94434	−	6.72455i	0.277762	−	0.960650i
$7$	1.94434	−	6.72455i	0.277762	−	0.960650i
$8$	−2.82843			−0.353553
$9$		0			0
$10$	−2.73861	−	1.58114i	−0.273861	−	0.158114i
$11$	−0.263223	+	0.455915i	−0.0239293	+	0.0414468i	−0.877742	−	0.479133i	$-0.840951\pi$
$11$	−0.263223	+	0.455915i	−0.0239293	+	0.0414468i	0.853813	+	0.520580i	$0.174284\pi$
$12$		0			0
$13$		−	4.22307i		−	0.324851i	−0.986721	−	0.162426i	$-0.948068\pi$
$13$		−	4.22307i		−	0.324851i	0.986721	−	0.162426i	$-0.0519318\pi$
$14$	9.61071	−	2.37366i	0.686479	−	0.169547i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	28.8825	+	16.6753i	1.69897	+	0.980900i	0.946741	+	0.321997i	$0.104354\pi$
$17$	28.8825	+	16.6753i	1.69897	+	0.980900i	0.752228	+	0.658903i	$0.228979\pi$
$18$		0			0
$19$	2.75133	−	1.58848i	0.144807	−	0.0836044i	−0.425846	−	0.904796i	$-0.640023\pi$
$19$	2.75133	−	1.58848i	0.144807	−	0.0836044i	0.570653	+	0.821191i	$0.306690\pi$
$20$		−	4.47214i		−	0.223607i
$21$		0			0
$22$	−0.744507			−0.0338412
$23$	5.52954	+	9.57744i	0.240415	+	0.416410i	0.960832	−	0.277130i	$-0.0893832\pi$
$23$	5.52954	+	9.57744i	0.240415	+	0.416410i	−0.720418	+	0.693540i	$0.756050\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	5.17218	−	2.98616i	0.198930	−	0.114852i
$27$		0			0
$28$	9.70292	+	10.0922i	0.346533	+	0.360437i
$29$	56.1302			1.93552			0.967762	−	0.251866i	$-0.0810442\pi$
$29$	56.1302			1.93552			0.967762	+	0.251866i	$0.0810442\pi$
$30$		0			0
$31$	−1.63817	−	0.945800i	−0.0528443	−	0.0305097i	0.473345	−	0.880877i	$-0.343046\pi$
$31$	−1.63817	−	0.945800i	−0.0528443	−	0.0305097i	−0.526189	+	0.850367i	$0.676380\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$		0			0
$34$			47.1649i			1.38720i
$35$	3.75308	+	15.1959i	0.107231	+	0.434168i
$36$		0			0
$37$	4.87682	+	8.44690i	0.131806	+	0.228294i	0.924373	−	0.381491i	$-0.124589\pi$
$37$	4.87682	+	8.44690i	0.131806	+	0.228294i	−0.792567	+	0.609785i	$0.791256\pi$
$38$	3.89097	+	2.24645i	0.102394	+	0.0591172i
$39$		0			0
$40$	5.47723	−	3.16228i	0.136931	−	0.0790569i
$41$		−	4.07377i		−	0.0993603i	−0.998765	−	0.0496802i	$-0.984180\pi$
$41$		−	4.07377i		−	0.0993603i	0.998765	−	0.0496802i	$-0.0158202\pi$
$42$		0			0
$43$	46.3519			1.07795			0.538975	−	0.842322i	$-0.318812\pi$
$43$	46.3519			1.07795			0.538975	+	0.842322i	$0.318812\pi$
$44$	−0.526446	−	0.911831i	−0.0119647	−	0.0207234i
$45$		0			0
$46$	−7.81995	+	13.5445i	−0.169999	+	0.294447i
$47$	−54.7969	+	31.6370i	−1.16589	+	0.673127i	−0.952709	−	0.303885i	$-0.901716\pi$
$47$	−54.7969	+	31.6370i	−1.16589	+	0.673127i	−0.213182	+	0.977012i	$0.568383\pi$
$48$		0			0
$49$	−41.4391	−	26.1496i	−0.845696	−	0.533665i
$50$	7.07107			0.141421
$51$		0			0
$52$	7.31457	+	4.22307i	0.140665	+	0.0812129i
$53$	−23.2606	+	40.2885i	−0.438878	+	0.760160i	−0.997603	−	0.0691934i	$-0.977957\pi$
$53$	−23.2606	+	40.2885i	−0.438878	+	0.760160i	0.558725	+	0.829353i	$0.311291\pi$
$54$		0			0
$55$		−	1.17717i		−	0.0214031i
$56$	−5.49942	+	19.0199i	−0.0982038	+	0.339641i
$57$		0			0
$58$	39.6900	+	68.7452i	0.684311	+	1.18526i
$59$	43.7614	+	25.2657i	0.741719	+	0.428231i	0.822694	−	0.568485i	$-0.192470\pi$
$59$	43.7614	+	25.2657i	0.741719	+	0.428231i	−0.0809752	+	0.996716i	$0.525803\pi$
$60$		0			0
$61$	89.4583	−	51.6488i	1.46653	−	0.846702i	0.467231	−	0.884135i	$-0.345252\pi$
$61$	89.4583	−	51.6488i	1.46653	−	0.846702i	0.999299	+	0.0374335i	$0.0119182\pi$
$62$		−	2.67513i		−	0.0431472i
$63$		0			0
$64$	8.00000			0.125000
$65$	4.72153	+	8.17794i	0.0726390	+	0.125814i
$66$		0			0
$67$	−4.36948	+	7.56816i	−0.0652161	+	0.112958i	−0.896790	−	0.442457i	$-0.854107\pi$
$67$	−4.36948	+	7.56816i	−0.0652161	+	0.112958i	0.831574	+	0.555414i	$0.187440\pi$
$68$	−57.7649	+	33.3506i	−0.849484	+	0.490450i
$69$		0			0
$70$	−15.9572	+	15.3417i	−0.227960	+	0.219167i
$71$	−29.0608			−0.409307			−0.204653	−	0.978835i	$-0.565607\pi$
$71$	−29.0608			−0.409307			−0.204653	+	0.978835i	$0.565607\pi$
$72$		0			0
$73$	14.4912	+	8.36647i	0.198509	+	0.114609i	0.595960	−	0.803014i	$-0.296772\pi$
$73$	14.4912	+	8.36647i	0.198509	+	0.114609i	−0.397451	+	0.917623i	$0.630105\pi$
$74$	−6.89686	+	11.9457i	−0.0932008	+	0.161429i
$75$		0			0
$76$			6.35393i			0.0836044i
$77$	2.55403	+	2.65651i	0.0331692	+	0.0345001i
$78$		0			0
$79$	66.1473	+	114.571i	0.837308	+	1.45026i	0.892137	+	0.451764i	$0.149205\pi$
$79$	66.1473	+	114.571i	0.837308	+	1.45026i	−0.0548297	+	0.998496i	$0.517462\pi$
$80$	7.74597	+	4.47214i	0.0968246	+	0.0559017i
$81$		0			0
$82$	4.98933	−	2.88059i	0.0608455	−	0.0351292i
$83$		−	12.4838i		−	0.150407i	−0.997168	−	0.0752033i	$-0.976039\pi$
$83$		−	12.4838i		−	0.150407i	0.997168	−	0.0752033i	$-0.0239606\pi$
$84$		0			0
$85$	−74.5742			−0.877344
$86$	32.7757	+	56.7692i	0.381113	+	0.660107i
$87$		0			0
$88$	0.744507	−	1.28952i	0.00846030	−	0.0146537i
$89$	59.1101	−	34.1272i	0.664158	−	0.383452i	−0.129701	−	0.991553i	$-0.541402\pi$
$89$	59.1101	−	34.1272i	0.664158	−	0.383452i	0.793860	+	0.608101i	$0.208069\pi$
$90$		0			0
$91$	−28.3982	−	8.21107i	−0.312068	−	0.0902315i
$92$	−22.1182			−0.240415
$93$		0			0
$94$	−77.4945	−	44.7415i	−0.824409	−	0.475973i
$95$	−3.55196	+	6.15217i	−0.0373890	+	0.0647597i
$96$		0			0
$97$		−	149.281i		−	1.53898i	−0.638659	−	0.769490i	$-0.720510\pi$
$97$		−	149.281i		−	1.53898i	0.638659	−	0.769490i	$-0.279490\pi$
$98$	2.72468	−	69.2429i	0.0278029	−	0.706560i
$99$		0			0
$100$	5.00000	+	8.66025i	0.0500000	+	0.0866025i
$101$	−83.7839	−	48.3726i	−0.829543	−	0.478937i	0.0241531	−	0.999708i	$-0.492311\pi$
$101$	−83.7839	−	48.3726i	−0.829543	−	0.478937i	−0.853696	+	0.520771i	$0.825644\pi$
$102$		0			0
$103$	90.7268	−	52.3811i	0.880843	−	0.508555i	0.00990642	−	0.999951i	$-0.496847\pi$
$103$	90.7268	−	52.3811i	0.880843	−	0.508555i	0.870936	+	0.491396i	$0.163513\pi$
$104$			11.9446i			0.114852i
$105$		0			0
$106$	−65.7908			−0.620668
$107$	−62.3022	−	107.911i	−0.582263	−	1.00851i	−0.995211	−	0.0977548i	$-0.968834\pi$
$107$	−62.3022	−	107.911i	−0.582263	−	1.00851i	0.412947	−	0.910755i	$-0.364499\pi$
$108$		0			0
$109$	−42.3042	+	73.2731i	−0.388112	+	0.672230i	−0.992196	−	0.124691i	$-0.960206\pi$
$109$	−42.3042	+	73.2731i	−0.388112	+	0.672230i	0.604083	+	0.796921i	$0.293539\pi$
$110$	1.44173	−	0.832384i	0.0131066	−	0.00756712i
$111$		0			0
$112$	−27.1832	+	6.71372i	−0.242707	+	0.0599439i
$113$	116.241			1.02868			0.514340	−	0.857586i	$-0.328037\pi$
$113$	116.241			1.02868			0.514340	+	0.857586i	$0.328037\pi$
$114$		0			0
$115$	−21.4158	−	12.3644i	−0.186224	−	0.107517i
$116$	−56.1302	+	97.2204i	−0.483881	+	0.838107i
$117$		0			0
$118$			71.4621i			0.605611i
$119$	168.291	−	161.799i	1.41421	−	1.35966i
$120$		0			0
$121$	60.3614	+	104.549i	0.498855	+	0.864042i
$122$	126.513	+	73.0424i	1.03699	+	0.598708i
$123$		0			0
$124$	3.27635	−	1.89160i	0.0264222	−	0.0152548i
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	−81.3744			−0.640743			−0.320372	−	0.947292i	$-0.603808\pi$
$127$	−81.3744			−0.640743			−0.320372	+	0.947292i	$0.603808\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−6.67726	+	11.5654i	−0.0513635	+	0.0889642i
$131$	−208.389	+	120.313i	−1.59075	+	0.918421i	−0.597574	+	0.801814i	$0.703869\pi$
$131$	−208.389	+	120.313i	−1.59075	+	0.918421i	−0.993178	+	0.116608i	$0.962798\pi$
$132$		0			0
$133$	−5.33231	−	21.5900i	−0.0400926	−	0.162331i
$134$	−12.3588			−0.0922295
$135$		0			0
$136$	−81.6919	−	47.1649i	−0.600676	−	0.346800i
$137$	116.831	−	202.357i	0.852778	−	1.47706i	−0.0259125	−	0.999664i	$-0.508249\pi$
$137$	116.831	−	202.357i	0.852778	−	1.47706i	0.878691	−	0.477391i	$-0.158418\pi$
$138$		0			0
$139$		−	211.491i		−	1.52152i	−0.649033	−	0.760760i	$-0.724826\pi$
$139$		−	211.491i		−	1.52152i	0.649033	−	0.760760i	$-0.275174\pi$
$140$	−30.0731	−	8.69534i	−0.214808	−	0.0621096i
$141$		0			0
$142$	−20.5491	−	35.5920i	−0.144712	−	0.250648i
$143$	1.92536	+	1.11161i	0.0134641	+	0.00777348i
$144$		0			0
$145$	−108.696	+	62.7555i	−0.749625	+	0.432796i
$146$			23.6640i			0.162082i
$147$		0			0
$148$	−19.5073			−0.131806
$149$	72.0402	+	124.777i	0.483491	+	0.837431i	0.999820	−	0.0189590i	$-0.00603520\pi$
$149$	72.0402	+	124.777i	0.483491	+	0.837431i	−0.516329	+	0.856390i	$0.672702\pi$
$150$		0			0
$151$	−46.7563	+	80.9842i	−0.309644	+	0.536319i	−0.978285	−	0.207267i	$-0.933543\pi$
$151$	−46.7563	+	80.9842i	−0.309644	+	0.536319i	0.668640	+	0.743586i	$0.266877\pi$
$152$	−7.78195	+	4.49291i	−0.0511970	+	0.0295586i
$153$		0			0
$154$	−1.44757	+	5.00647i	−0.00939982	+	0.0325095i
$155$	4.22975			0.0272887
$156$		0			0
$157$	−148.286	−	85.6127i	−0.944494	−	0.545304i	−0.0531280	−	0.998588i	$-0.516919\pi$
$157$	−148.286	−	85.6127i	−0.944494	−	0.545304i	−0.891366	+	0.453284i	$0.850252\pi$
$158$	−93.5464	+	162.027i	−0.592066	+	1.02549i
$159$		0			0
$160$			12.6491i			0.0790569i
$161$	75.1553	−	18.5619i	0.466803	−	0.115291i
$162$		0			0
$163$	−46.5064	−	80.5515i	−0.285316	−	0.494181i	0.687370	−	0.726307i	$-0.258765\pi$
$163$	−46.5064	−	80.5515i	−0.285316	−	0.494181i	−0.972686	+	0.232126i	$0.925432\pi$
$164$	7.05598	+	4.07377i	0.0430243	+	0.0248401i
$165$		0			0
$166$	15.2894	−	8.82735i	0.0921049	−	0.0531768i
$167$		−	104.991i		−	0.628688i	−0.949309	−	0.314344i	$-0.898216\pi$
$167$		−	104.991i		−	0.628688i	0.949309	−	0.314344i	$-0.101784\pi$
$168$		0			0
$169$	151.166			0.894472
$170$	−52.7319	−	91.3344i	−0.310188	−	0.537261i
$171$		0			0
$172$	−46.3519	+	80.2838i	−0.269488	+	0.466766i
$173$	−176.805	+	102.079i	−1.02200	+	0.590049i	−0.914681	−	0.404176i	$-0.867558\pi$
$173$	−176.805	+	102.079i	−1.02200	+	0.590049i	−0.107314	+	0.994225i	$0.534225\pi$
$174$		0			0
$175$	−24.2573	−	25.2306i	−0.138613	−	0.144175i
$176$	2.10578			0.0119647
$177$		0			0
$178$	83.5943	+	48.2632i	0.469631	+	0.271141i
$179$	−97.9495	+	169.653i	−0.547204	+	0.947785i	0.451261	+	0.892392i	$0.350974\pi$
$179$	−97.9495	+	169.653i	−0.547204	+	0.947785i	−0.998465	+	0.0553926i	$0.982359\pi$
$180$		0			0
$181$			119.031i			0.657632i	0.944394	+	0.328816i	$0.106650\pi$
$181$			119.031i			0.657632i	−0.944394	+	0.328816i	$0.893350\pi$
$182$	−10.0241	−	40.5867i	−0.0550776	−	0.223004i
$183$		0			0
$184$	−15.6399	−	27.0891i	−0.0849994	−	0.147223i
$185$	−18.8878	−	10.9049i	−0.102096	−	0.0589454i
$186$		0			0
$187$	−15.2050	+	8.77864i	−0.0813104	+	0.0469446i
$188$		−	126.548i		−	0.673127i
$189$		0			0
$190$	−10.0464			−0.0528760
$191$	−32.8657	−	56.9250i	−0.172072	−	0.298037i	0.767072	−	0.641561i	$-0.221713\pi$
$191$	−32.8657	−	56.9250i	−0.172072	−	0.298037i	−0.939144	+	0.343524i	$0.888379\pi$
$192$		0			0
$193$	48.4350	−	83.8919i	0.250959	−	0.434673i	−0.712831	−	0.701335i	$-0.752588\pi$
$193$	48.4350	−	83.8919i	0.250959	−	0.434673i	0.963790	+	0.266662i	$0.0859209\pi$
$194$	182.831	−	105.558i	0.942429	−	0.544112i
$195$		0			0
$196$	86.7315	−	45.6251i	0.442508	−	0.232781i
$197$	−186.672			−0.947574			−0.473787	−	0.880640i	$-0.657113\pi$
$197$	−186.672			−0.947574			−0.473787	+	0.880640i	$0.657113\pi$
$198$		0			0
$199$	99.8454	+	57.6458i	0.501736	+	0.289677i	0.729430	−	0.684055i	$-0.239785\pi$
$199$	99.8454	+	57.6458i	0.501736	+	0.289677i	−0.227694	+	0.973733i	$0.573119\pi$
$200$	−7.07107	+	12.2474i	−0.0353553	+	0.0612372i
$201$		0			0
$202$		−	136.818i		−	0.677319i
$203$	109.136	−	377.450i	0.537616	−	1.85936i
$204$		0			0
$205$	4.55462	+	7.88883i	0.0222176	+	0.0384821i
$206$	128.307	+	74.0781i	0.622850	+	0.359602i
$207$		0			0
$208$	−14.6291	+	8.44614i	−0.0703324	+	0.0406064i
$209$			1.67250i			0.00800239i
$210$		0			0
$211$	139.433			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$211$	139.433			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$212$	−46.5211	−	80.5769i	−0.219439	−	0.380080i
$213$		0			0
$214$	88.1086	−	152.609i	0.411722	−	0.713124i
$215$	−89.7600	+	51.8230i	−0.417488	+	0.241037i
$216$		0			0
$217$	−9.54524	+	9.17703i	−0.0439873	+	0.0422905i
$218$	−119.654			−0.548874
$219$		0			0
$220$	2.03892	+	1.17717i	0.00926780	+	0.00535076i
$221$	70.4209	−	121.973i	0.318647	−	0.551912i
$222$		0			0
$223$		−	258.055i		−	1.15720i	−0.815612	−	0.578599i	$-0.803600\pi$
$223$		−	258.055i		−	1.15720i	0.815612	−	0.578599i	$-0.196400\pi$
$224$	−27.4440	−	28.5452i	−0.122518	−	0.127434i
$225$		0			0
$226$	82.1947	+	142.365i	0.363693	+	0.629935i
$227$	−286.682	−	165.516i	−1.26292	−	0.729146i	−0.289280	−	0.957245i	$-0.593416\pi$
$227$	−286.682	−	165.516i	−1.26292	−	0.729146i	−0.973638	+	0.228099i	$0.926749\pi$
$228$		0			0
$229$	211.516	−	122.119i	0.923653	−	0.533271i	0.0388541	−	0.999245i	$-0.487629\pi$
$229$	211.516	−	122.119i	0.923653	−	0.533271i	0.884799	+	0.465974i	$0.154296\pi$
$230$		−	34.9719i		−	0.152052i
$231$		0			0
$232$	−158.760			−0.684311
$233$	105.745	+	183.155i	0.453840	+	0.786074i	0.998621	−	0.0525044i	$-0.0167204\pi$
$233$	105.745	+	183.155i	0.453840	+	0.786074i	−0.544781	+	0.838579i	$0.683387\pi$
$234$		0			0
$235$	70.7425	−	122.530i	0.301032	−	0.521402i
$236$	−87.5228	+	50.5313i	−0.370859	+	0.214116i
$237$		0			0
$238$	317.162	+	91.7044i	1.33262	+	0.385313i
$239$	−344.134			−1.43989			−0.719946	−	0.694030i	$-0.755833\pi$
$239$	−344.134			−1.43989			−0.719946	+	0.694030i	$0.755833\pi$
$240$		0			0
$241$	−148.392	−	85.6742i	−0.615735	−	0.355495i	0.159472	−	0.987203i	$-0.449021\pi$
$241$	−148.392	−	85.6742i	−0.615735	−	0.355495i	−0.775207	+	0.631708i	$0.782354\pi$
$242$	−85.3639	+	147.855i	−0.352744	+	0.610970i
$243$		0			0
$244$			206.595i			0.846702i
$245$	109.483	+	4.30810i	0.446868	+	0.0175841i
$246$		0			0
$247$	−6.70827	−	11.6191i	−0.0271590	−	0.0470408i
$248$	4.63346	+	2.67513i	0.0186833	+	0.0107868i
$249$		0			0
$250$	−13.6931	+	7.90569i	−0.0547723	+	0.0316228i
$251$		−	327.538i		−	1.30493i	−0.757818	−	0.652467i	$-0.773734\pi$
$251$		−	327.538i		−	1.30493i	0.757818	−	0.652467i	$-0.226266\pi$
$252$		0			0
$253$	−5.82200			−0.0230119
$254$	−57.5404	−	99.6629i	−0.226537	−	0.392374i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	190.836	−	110.179i	0.742552	−	0.428713i	−0.0804442	−	0.996759i	$-0.525634\pi$
$257$	190.836	−	110.179i	0.742552	−	0.428713i	0.822997	+	0.568046i	$0.192301\pi$
$258$		0			0
$259$	66.2837	−	16.3708i	0.255922	−	0.0632077i
$260$	−18.8861			−0.0726390
$261$		0			0
$262$	−294.706	−	170.149i	−1.12483	−	0.649422i
$263$	66.5976	−	115.350i	0.253223	−	0.438594i	−0.711189	−	0.703001i	$-0.751843\pi$
$263$	66.5976	−	115.350i	0.253223	−	0.438594i	0.964411	+	0.264407i	$0.0851761\pi$
$264$		0			0
$265$		−	104.024i		−	0.392545i
$266$	22.6718	−	21.7972i	0.0852322	−	0.0819443i
$267$		0			0
$268$	−8.73896	−	15.1363i	−0.0326080	−	0.0564788i
$269$	22.9633	+	13.2578i	0.0853653	+	0.0492857i	0.542075	−	0.840330i	$-0.317639\pi$
$269$	22.9633	+	13.2578i	0.0853653	+	0.0492857i	−0.456710	+	0.889616i	$0.650972\pi$
$270$		0			0
$271$	−92.6776	+	53.5074i	−0.341984	+	0.197444i	−0.661149	−	0.750255i	$-0.729931\pi$
$271$	−92.6776	+	53.5074i	−0.341984	+	0.197444i	0.319165	+	0.947699i	$0.396598\pi$
$272$		−	133.402i		−	0.490450i
$273$		0			0
$274$	330.447			1.20601
$275$	1.31611	+	2.27958i	0.00478587	+	0.00828937i
$276$		0			0
$277$	−220.191	+	381.381i	−0.794912	+	1.37683i	0.127983	+	0.991776i	$0.459150\pi$
$277$	−220.191	+	381.381i	−0.794912	+	1.37683i	−0.922895	+	0.385052i	$0.874184\pi$
$278$	259.023	−	149.547i	0.931737	−	0.537939i
$279$		0			0
$280$	−10.6153	−	42.9804i	−0.0379119	−	0.153501i
$281$	−322.069			−1.14615			−0.573076	−	0.819502i	$-0.694250\pi$
$281$	−322.069			−1.14615			−0.573076	+	0.819502i	$0.694250\pi$
$282$		0			0
$283$	−59.3514	−	34.2665i	−0.209722	−	0.121083i	0.391460	−	0.920195i	$-0.371970\pi$
$283$	−59.3514	−	34.2665i	−0.209722	−	0.121083i	−0.601182	+	0.799112i	$0.705303\pi$
$284$	29.0608	−	50.3347i	0.102327	−	0.177235i
$285$		0			0
$286$			3.14410i			0.0109934i
$287$	−27.3943	−	7.92079i	−0.0954505	−	0.0275986i
$288$		0			0
$289$	411.631	+	712.966i	1.42433	+	2.46701i
$290$	−153.719	−	88.7496i	−0.530065	−	0.306033i
$291$		0			0
$292$	−28.9823	+	16.7329i	−0.0992545	+	0.0573046i
$293$			147.510i			0.503448i	0.967799	+	0.251724i	$0.0809975\pi$
$293$			147.510i			0.503448i	−0.967799	+	0.251724i	$0.919003\pi$
$294$		0			0
$295$	−112.991			−0.383022
$296$	−13.7937	−	23.8914i	−0.0466004	−	0.0807143i
$297$		0			0
$298$	−101.880	+	176.462i	−0.341880	+	0.592153i
$299$	40.4462	−	23.3516i	0.135272	−	0.0780991i
$300$		0			0
$301$	90.1237	−	311.695i	0.299414	−	1.03553i
$302$	−132.247			−0.437903
$303$		0			0
$304$	−11.0053	−	6.35393i	−0.0362018	−	0.0209011i
$305$	−115.490	+	200.035i	−0.378657	+	0.655852i
$306$		0			0
$307$		−	376.010i		−	1.22479i	−0.790553	−	0.612394i	$-0.790207\pi$
$307$		−	376.010i		−	1.22479i	0.790553	−	0.612394i	$-0.209793\pi$
$308$	−7.15524	+	1.76720i	−0.0232313	+	0.00573767i
$309$		0			0
$310$	2.99088	+	5.18036i	0.00964801	+	0.0167108i
$311$	337.599	+	194.913i	1.08553	+	0.626730i	0.932383	−	0.361473i	$-0.117726\pi$
$311$	337.599	+	194.913i	1.08553	+	0.626730i	0.153146	+	0.988204i	$0.451059\pi$
$312$		0			0
$313$	−123.890	+	71.5282i	−0.395816	+	0.228524i	−0.684677	−	0.728847i	$-0.740057\pi$
$313$	−123.890	+	71.5282i	−0.395816	+	0.228524i	0.288861	+	0.957371i	$0.406723\pi$
$314$		−	242.149i		−	0.771176i
$315$		0			0
$316$	−264.589			−0.837308
$317$	192.222	+	332.938i	0.606378	+	1.05028i	0.991832	+	0.127551i	$0.0407117\pi$
$317$	192.222	+	332.938i	0.606378	+	1.05028i	−0.385454	+	0.922727i	$0.625955\pi$
$318$		0			0
$319$	−14.7747	+	25.5906i	−0.0463158	+	0.0802214i
$320$	−15.4919	+	8.94427i	−0.0484123	+	0.0279508i
$321$		0			0
$322$	75.8764	+	78.9208i	0.235641	+	0.245096i
$323$	105.954			0.328030
$324$		0			0
$325$	−18.2864	−	10.5577i	−0.0562659	−	0.0324851i
$326$	65.7700	−	113.917i	0.201749	−	0.349439i
$327$		0			0
$328$			11.5224i			0.0351292i
$329$	106.201	+	429.997i	0.322799	+	1.30698i
$330$		0			0
$331$	−96.9539	−	167.929i	−0.292912	−	0.507338i	0.681585	−	0.731739i	$-0.261291\pi$
$331$	−96.9539	−	167.929i	−0.292912	−	0.507338i	−0.974497	+	0.224400i	$0.927958\pi$
$332$	21.6225	+	12.4838i	0.0651280	+	0.0376017i
$333$		0			0
$334$	128.587	−	74.2397i	0.384991	−	0.222275i
$335$		−	19.5409i		−	0.0583310i
$336$		0			0
$337$	125.477			0.372337			0.186168	−	0.982518i	$-0.440393\pi$
$337$	125.477			0.372337			0.186168	+	0.982518i	$0.440393\pi$
$338$	106.890	+	185.139i	0.316243	+	0.547750i
$339$		0			0
$340$	74.5742	−	129.166i	0.219336	−	0.379901i
$341$	0.862410	−	0.497912i	0.00252906	−	0.00146015i
$342$		0			0
$343$	−256.416	+	227.816i	−0.747568	+	0.664186i
$344$	−131.103			−0.381113
$345$		0			0
$346$	−250.040	−	144.361i	−0.722660	−	0.417228i
$347$	−251.798	+	436.128i	−0.725644	+	1.25685i	0.233065	+	0.972461i	$0.425125\pi$
$347$	−251.798	+	436.128i	−0.725644	+	1.25685i	−0.958708	+	0.284391i	$0.908209\pi$
$348$		0			0
$349$			47.7682i			0.136872i	0.997656	+	0.0684358i	$0.0218008\pi$
$349$			47.7682i			0.136872i	−0.997656	+	0.0684358i	$0.978199\pi$
$350$	13.7485	−	47.5497i	0.0392815	−	0.135856i
$351$		0			0
$352$	1.48901	+	2.57905i	0.00423015	+	0.00732684i
$353$	−28.5012	−	16.4552i	−0.0807399	−	0.0466152i	0.459087	−	0.888392i	$-0.348177\pi$
$353$	−28.5012	−	16.4552i	−0.0807399	−	0.0466152i	−0.539826	+	0.841776i	$0.681510\pi$
$354$		0			0
$355$	56.2760	−	32.4909i	0.158524	−	0.0915238i
$356$			136.509i			0.383452i
$357$		0			0
$358$	−277.043			−0.773863
$359$	133.898	+	231.919i	0.372976	+	0.646013i	0.990022	−	0.140914i	$-0.0450040\pi$
$359$	133.898	+	231.919i	0.372976	+	0.646013i	−0.617046	+	0.786927i	$0.711671\pi$
$360$		0			0
$361$	−175.453	+	303.894i	−0.486021	+	0.841812i
$362$	−145.783	+	84.1679i	−0.402716	+	0.232508i
$363$		0			0
$364$	42.6202	−	40.9761i	0.117089	−	0.112572i
$365$	−37.4160			−0.102510
$366$		0			0
$367$	−137.458	−	79.3613i	−0.374545	−	0.216243i	0.300897	−	0.953657i	$-0.402714\pi$
$367$	−137.458	−	79.3613i	−0.374545	−	0.216243i	−0.675442	+	0.737413i	$0.736047\pi$
$368$	22.1182	−	38.3098i	0.0601037	−	0.104103i
$369$		0			0
$370$		−	30.8437i		−	0.0833614i
$371$	225.695	+	234.751i	0.608343	+	0.632752i
$372$		0			0
$373$	−207.172	−	358.832i	−0.555421	−	0.962017i	−0.997871	−	0.0652235i	$-0.979224\pi$
$373$	−207.172	−	358.832i	−0.555421	−	0.962017i	0.442450	−	0.896793i	$-0.354109\pi$
$374$	−21.5032	−	12.4149i	−0.0574951	−	0.0331948i
$375$		0			0
$376$	154.989	−	89.4829i	0.412205	−	0.237986i
$377$		−	237.042i		−	0.628758i
$378$		0			0
$379$	−72.8000			−0.192084			−0.0960422	−	0.995377i	$-0.530618\pi$
$379$	−72.8000			−0.192084			−0.0960422	+	0.995377i	$0.530618\pi$
$380$	−7.10391	−	12.3043i	−0.0186945	−	0.0323798i
$381$		0			0
$382$	46.4791	−	80.5042i	0.121673	−	0.210744i
$383$	246.830	−	142.507i	0.644464	−	0.372082i	−0.141868	−	0.989886i	$-0.545311\pi$
$383$	246.830	−	142.507i	0.644464	−	0.372082i	0.786332	+	0.617804i	$0.211977\pi$
$384$		0			0
$385$	−7.91593	−	2.28881i	−0.0205608	−	0.00594497i
$386$	136.995			0.354909
$387$		0			0
$388$	258.562	+	149.281i	0.666398	+	0.384745i
$389$	−48.5692	+	84.1242i	−0.124856	+	0.216258i	−0.921677	−	0.387959i	$-0.873180\pi$
$389$	−48.5692	+	84.1242i	−0.124856	+	0.216258i	0.796820	+	0.604216i	$0.206514\pi$
$390$		0			0
$391$			368.827i			0.943291i
$392$	117.207	+	73.9622i	0.298999	+	0.188679i
$393$		0			0
$394$	−131.997	−	228.626i	−0.335018	−	0.580268i
$395$	−256.187	−	147.910i	−0.648576	−	0.374455i
$396$		0			0
$397$	−685.636	+	395.852i	−1.72704	+	0.997108i	−0.825522	+	0.564371i	$0.809119\pi$
$397$	−685.636	+	395.852i	−1.72704	+	0.997108i	−0.901520	+	0.432737i	$0.857548\pi$
$398$			163.047i			0.409665i
$399$		0			0
$400$	−20.0000			−0.0500000
$401$	251.613	+	435.807i	0.627464	+	1.08680i	0.988059	+	0.154077i	$0.0492405\pi$
$401$	251.613	+	435.807i	0.627464	+	1.08680i	−0.360594	+	0.932723i	$0.617426\pi$
$402$		0			0
$403$	−3.99418	+	6.91812i	−0.00991112	+	0.0171666i
$404$	167.568	−	96.7453i	0.414772	−	0.239468i
$405$		0			0
$406$	539.451	−	133.234i	1.32870	−	0.328162i
$407$	−5.13476			−0.0126161
$408$		0			0
$409$	649.395	+	374.928i	1.58776	+	0.916696i	0.993675	+	0.112296i	$0.0358204\pi$
$409$	649.395	+	374.928i	1.58776	+	0.916696i	0.594088	+	0.804400i	$0.297513\pi$
$410$	−6.44120	+	11.1565i	−0.0157102	+	0.0272109i
$411$		0			0
$412$			209.525i			0.508555i
$413$	254.987	−	245.151i	0.617402	−	0.593585i
$414$		0			0
$415$	13.9573	+	24.1747i	0.0336319	+	0.0582522i
$416$	−20.6887	−	11.9446i	−0.0497325	−	0.0287131i
$417$		0			0
$418$	−2.04839	+	1.18264i	−0.00490044	+	0.00282927i
$419$			465.759i			1.11160i	0.831317	+	0.555799i	$0.187587\pi$
$419$			465.759i			1.11160i	−0.831317	+	0.555799i	$0.812413\pi$
$420$		0			0
$421$	345.980			0.821805			0.410902	−	0.911679i	$-0.365214\pi$
$421$	345.980			0.821805			0.410902	+	0.911679i	$0.365214\pi$
$422$	98.5939	+	170.770i	0.233635	+	0.404667i
$423$		0			0
$424$	65.7908	−	113.953i	0.155167	−	0.268757i
$425$	144.412	−	83.3765i	0.339794	−	0.196180i
$426$		0			0
$427$	−173.378	−	701.990i	−0.406037	−	1.64400i
$428$	249.209			0.582263
$429$		0			0
$430$	−126.940	−	73.2888i	−0.295209	−	0.170439i
$431$	247.300	−	428.336i	0.573782	−	0.993819i	−0.422391	−	0.906414i	$-0.638809\pi$
$431$	247.300	−	428.336i	0.573782	−	0.993819i	0.996173	−	0.0874056i	$-0.0278576\pi$
$432$		0			0
$433$			730.022i			1.68596i	0.537943	+	0.842981i	$0.319201\pi$
$433$			730.022i			1.68596i	−0.537943	+	0.842981i	$0.680799\pi$
$434$	−17.9890	−	5.20135i	−0.0414494	−	0.0119847i
$435$		0			0
$436$	−84.6085	−	146.546i	−0.194056	−	0.336115i
$437$	30.4272	+	17.5672i	0.0696275	+	0.0401994i
$438$		0			0
$439$	−321.631	+	185.694i	−0.732645	+	0.422993i	−0.819389	−	0.573238i	$-0.805687\pi$
$439$	−321.631	+	185.694i	−0.732645	+	0.422993i	0.0867437	+	0.996231i	$0.472354\pi$
$440$			3.32953i			0.00756712i
$441$		0			0
$442$	199.180			0.450635
$443$	204.354	+	353.951i	0.461295	+	0.798987i	0.999026	−	0.0441299i	$-0.0140515\pi$
$443$	204.354	+	353.951i	0.461295	+	0.798987i	−0.537731	+	0.843117i	$0.680718\pi$
$444$		0			0
$445$	−76.3108	+	132.174i	−0.171485	+	0.297021i
$446$	316.052	−	182.473i	0.708636	−	0.409131i
$447$		0			0
$448$	15.5547	−	53.7964i	0.0347203	−	0.120081i
$449$	−725.469			−1.61574			−0.807872	−	0.589358i	$-0.799381\pi$
$449$	−725.469			−1.61574			−0.807872	+	0.589358i	$0.799381\pi$
$450$		0			0
$451$	1.85730	+	1.07231i	0.00411817	+	0.00237763i
$452$	−116.241	+	201.335i	−0.257170	+	0.445432i
$453$		0			0
$454$		−	468.150i		−	1.03117i
$455$	64.1732	−	15.8495i	0.141040	−	0.0348341i
$456$		0			0
$457$	−200.765	−	347.736i	−0.439311	−	0.760909i	0.558325	−	0.829622i	$-0.311444\pi$
$457$	−200.765	−	347.736i	−0.439311	−	0.760909i	−0.997636	+	0.0687128i	$0.978111\pi$
$458$	299.129	+	172.702i	0.653121	+	0.377080i
$459$		0			0
$460$	42.8316	−	24.7288i	0.0931122	−	0.0537584i
$461$		−	653.050i		−	1.41659i	−0.705915	−	0.708297i	$-0.749464\pi$
$461$		−	653.050i		−	1.41659i	0.705915	−	0.708297i	$-0.250536\pi$
$462$		0			0
$463$	−869.580			−1.87814			−0.939072	−	0.343722i	$-0.888312\pi$
$463$	−869.580			−1.87814			−0.939072	+	0.343722i	$0.888312\pi$
$464$	−112.260	−	194.441i	−0.241941	−	0.419053i
$465$		0			0
$466$	−149.546	+	259.021i	−0.320913	+	0.555838i
$467$	−640.168	+	369.601i	−1.37081	+	0.791437i	−0.991030	−	0.133641i	$-0.957333\pi$
$467$	−640.168	+	369.601i	−1.37081	+	0.791437i	−0.379779	+	0.925077i	$0.624000\pi$
$468$		0			0
$469$	42.3967	+	44.0978i	0.0903981	+	0.0940252i
$470$	200.090			0.425723
$471$		0			0
$472$	−123.776	−	71.4621i	−0.262237	−	0.151403i
$473$	−12.2009	+	21.1325i	−0.0257947	+	0.0446777i
$474$		0			0
$475$		−	15.8848i		−	0.0334417i
$476$	111.953	+	453.288i	0.235196	+	0.952285i
$477$		0			0
$478$	−243.339	−	421.476i	−0.509078	−	0.881750i
$479$	525.006	+	303.112i	1.09605	+	0.632802i	0.935180	−	0.354174i	$-0.115238\pi$
$479$	525.006	+	303.112i	1.09605	+	0.632802i	0.160866	+	0.986976i	$0.448571\pi$
$480$		0			0
$481$	35.6718	−	20.5951i	0.0741618	−	0.0428173i
$482$		−	242.323i		−	0.502745i
$483$		0			0
$484$	−241.446			−0.498855
$485$	166.901	+	289.082i	0.344126	+	0.596044i
$486$		0			0
$487$	−324.788	+	562.549i	−0.666916	+	1.15513i	0.311846	+	0.950133i	$0.399053\pi$
$487$	−324.788	+	562.549i	−0.666916	+	1.15513i	−0.978762	+	0.205000i	$0.934281\pi$
$488$	−253.026	+	146.085i	−0.518497	+	0.299354i
$489$		0			0
$490$	72.1396	+	137.135i	0.147224	+	0.279866i
$491$	−266.629			−0.543033			−0.271516	−	0.962434i	$-0.587525\pi$
$491$	−266.629			−0.543033			−0.271516	+	0.962434i	$0.587525\pi$
$492$		0			0
$493$	1621.18	+	935.988i	3.28839	+	1.89856i
$494$	9.48693	−	16.4318i	0.0192043	−	0.0332628i
$495$		0			0
$496$			7.56640i			0.0152548i
$497$	−56.5039	+	195.421i	−0.113690	+	0.393200i
$498$		0			0
$499$	340.553	+	589.855i	0.682471	+	1.18207i	0.974225	+	0.225581i	$0.0724279\pi$
$499$	340.553	+	589.855i	0.682471	+	1.18207i	−0.291754	+	0.956493i	$0.594239\pi$
$500$	−19.3649	−	11.1803i	−0.0387298	−	0.0223607i
$501$		0			0
$502$	401.151	−	231.604i	0.799105	−	0.461364i
$503$		−	453.326i		−	0.901245i	−0.892715	−	0.450622i	$-0.851202\pi$
$503$		−	453.326i		−	0.901245i	0.892715	−	0.450622i	$-0.148798\pi$
$504$		0			0
$505$	216.329			0.428374
$506$	−4.11678	−	7.13047i	−0.00813592	−	0.0140918i
$507$		0			0
$508$	81.3744	−	140.945i	0.160186	−	0.277450i
$509$	43.5300	−	25.1321i	0.0855206	−	0.0493754i	−0.456630	−	0.889657i	$-0.650944\pi$
$509$	43.5300	−	25.1321i	0.0855206	−	0.0493754i	0.542150	+	0.840281i	$0.317610\pi$
$510$		0			0
$511$	84.4364	−	81.1792i	0.165238	−	0.158863i
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	269.883	+	155.817i	0.525064	+	0.303146i
$515$	−117.128	+	202.871i	−0.227433	+	0.393925i
$516$		0			0
$517$		−	33.3103i		−	0.0644300i
$518$	66.9197	+	69.6048i	0.129189	+	0.134372i
$519$		0			0
$520$	−13.3545	−	23.1307i	−0.0256818	−	0.0444821i
$521$	89.2971	+	51.5557i	0.171396	+	0.0989553i	0.583244	−	0.812297i	$-0.301783\pi$
$521$	89.2971	+	51.5557i	0.171396	+	0.0989553i	−0.411848	+	0.911252i	$0.635117\pi$
$522$		0			0
$523$	−317.716	+	183.434i	−0.607488	+	0.350733i	−0.771982	−	0.635645i	$-0.780734\pi$
$523$	−317.716	+	183.434i	−0.607488	+	0.350733i	0.164494	+	0.986378i	$0.447401\pi$
$524$		−	481.253i		−	0.918421i
$525$		0			0
$526$	188.366			0.358111
$527$	−31.5430	−	54.6341i	−0.0598539	−	0.103670i
$528$		0			0
$529$	203.348	−	352.210i	0.384402	−	0.665803i
$530$	127.403	−	73.5563i	0.240384	−	0.138786i
$531$		0			0
$532$	42.7273	+	12.3542i	0.0803145	+	0.0232222i
$533$	−17.2038			−0.0322773
$534$		0			0
$535$	241.295	+	139.312i	0.451019	+	0.260396i
$536$	12.3588	−	21.4060i	0.0230574	−	0.0399365i
$537$		0			0
$538$			37.4988i			0.0697005i
$539$	22.8297	−	12.0096i	0.0423557	−	0.0222812i
$540$		0			0
$541$	266.559	+	461.693i	0.492714	+	0.853407i	0.999965	−	0.00839227i	$-0.00267137\pi$
$541$	266.559	+	461.693i	0.492714	+	0.853407i	−0.507250	+	0.861799i	$0.669338\pi$
$542$	−131.066	−	75.6709i	−0.241819	−	0.139614i
$543$		0			0
$544$	163.384	−	94.3297i	0.300338	−	0.173400i
$545$		−	189.190i		−	0.347138i
$546$		0			0
$547$	69.6218			0.127279			0.0636396	−	0.997973i	$-0.479729\pi$
$547$	69.6218			0.127279			0.0636396	+	0.997973i	$0.479729\pi$
$548$	233.661	+	404.713i	0.426389	+	0.738528i
$549$		0			0
$550$	−1.86127	+	3.22381i	−0.00338412	+	0.00586147i
$551$	154.433	−	89.1619i	0.280277	−	0.161818i
$552$		0			0
$553$	899.048	−	222.047i	1.62576	−	0.401532i
$554$	−622.793			−1.12418
$555$		0			0
$556$	366.314	+	211.491i	0.658838	+	0.380380i
$557$	8.43122	−	14.6033i	0.0151368	−	0.0262178i	−0.858358	−	0.513052i	$-0.828515\pi$
$557$	8.43122	−	14.6033i	0.0151368	−	0.0262178i	0.873495	+	0.486834i	$0.161848\pi$
$558$		0			0
$559$		−	195.747i		−	0.350174i
$560$	45.1339	−	43.3928i	0.0805962	−	0.0774871i
$561$		0			0
$562$	−227.737	−	394.452i	−0.405226	−	0.701872i
$563$	−793.093	−	457.892i	−1.40869	−	0.813308i	−0.413428	−	0.910537i	$-0.635669\pi$
$563$	−793.093	−	457.892i	−1.40869	−	0.813308i	−0.995262	+	0.0972290i	$0.969002\pi$
$564$		0			0
$565$	−225.099	+	129.961i	−0.398406	+	0.230020i
$566$		−	96.9204i		−	0.171237i
$567$		0			0
$568$	82.1963			0.144712
$569$	203.828	+	353.040i	0.358221	+	0.620456i	0.987664	−	0.156590i	$-0.0500502\pi$
$569$	203.828	+	353.040i	0.358221	+	0.620456i	−0.629443	+	0.777047i	$0.716717\pi$
$570$		0			0
$571$	447.910	−	775.803i	0.784431	−	1.35867i	−0.144908	−	0.989445i	$-0.546289\pi$
$571$	447.910	−	775.803i	0.784431	−	1.35867i	0.929339	−	0.369229i	$-0.120378\pi$
$572$	−3.85072	+	2.22322i	−0.00673203	+	0.00388674i
$573$		0			0
$574$	−9.66974	−	39.1519i	−0.0168462	−	0.0682088i
$575$	55.2954			0.0961659
$576$		0			0
$577$	590.115	+	340.703i	1.02273	+	0.590473i	0.914893	−	0.403695i	$-0.132274\pi$
$577$	590.115	+	340.703i	1.02273	+	0.590473i	0.107836	+	0.994169i	$0.465608\pi$
$578$	−582.134	+	1008.29i	−1.00715	+	1.74444i
$579$		0			0
$580$		−	251.022i		−	0.432796i
$581$	−83.9476	−	24.2726i	−0.144488	−	0.0417773i
$582$		0			0
$583$	−12.2454	−	21.2097i	−0.0210041	−	0.0363802i
$584$	−40.9872	−	23.6640i	−0.0701835	−	0.0405205i
$585$		0			0
$586$	−180.662	+	104.305i	−0.308297	+	0.177996i
$587$		−	833.001i		−	1.41908i	−0.704665	−	0.709541i	$-0.748903\pi$
$587$		−	833.001i		−	1.41908i	0.704665	−	0.709541i	$-0.251097\pi$
$588$		0			0
$589$	−6.00955			−0.0102030
$590$	−79.8970	−	138.386i	−0.135419	−	0.234552i
$591$		0			0
$592$	19.5073	−	33.7876i	0.0329515	−	0.0570736i
$593$	−270.842	+	156.371i	−0.456731	+	0.263694i	−0.710669	−	0.703527i	$-0.751608\pi$
$593$	−270.842	+	156.371i	−0.456731	+	0.263694i	0.253938	+	0.967221i	$0.418274\pi$
$594$		0			0
$595$	−144.997	+	501.478i	−0.243693	+	0.842820i
$596$	−288.161			−0.483491
$597$		0			0
$598$	57.1996	+	33.0242i	0.0956514	+	0.0552244i
$599$	107.121	−	185.540i	0.178834	−	0.309749i	−0.762648	−	0.646814i	$-0.776101\pi$
$599$	107.121	−	185.540i	0.178834	−	0.309749i	0.941481	+	0.337065i	$0.109434\pi$
$600$		0			0
$601$		−	176.849i		−	0.294257i	−0.989117	−	0.147129i	$-0.952997\pi$
$601$		−	176.849i		−	0.294257i	0.989117	−	0.147129i	$-0.0470031\pi$
$602$	445.474	−	110.023i	0.739991	−	0.182763i
$603$		0			0
$604$	−93.5125	−	161.968i	−0.154822	−	0.268160i
$605$	−233.779	−	134.972i	−0.386411	−	0.223095i
$606$		0			0
$607$	32.1304	−	18.5505i	0.0529331	−	0.0305609i	−0.473300	−	0.880901i	$-0.656937\pi$
$607$	32.1304	−	18.5505i	0.0529331	−	0.0305609i	0.526233	+	0.850340i	$0.323604\pi$
$608$		−	17.9716i		−	0.0295586i
$609$		0			0
$610$	−326.656			−0.535501
$611$	133.605	+	231.411i	0.218666	+	0.378741i
$612$		0			0
$613$	449.860	−	779.180i	0.733866	−	1.27109i	−0.221353	−	0.975194i	$-0.571047\pi$
$613$	449.860	−	779.180i	0.733866	−	1.27109i	0.955219	−	0.295899i	$-0.0956192\pi$
$614$	460.516	−	265.879i	0.750027	−	0.433028i
$615$		0			0
$616$	−7.22389	−	7.51374i	−0.0117271	−	0.0121976i
$617$	626.244			1.01498			0.507491	−	0.861657i	$-0.330573\pi$
$617$	626.244			1.01498			0.507491	+	0.861657i	$0.330573\pi$
$618$		0			0
$619$	−776.375	−	448.240i	−1.25424	−	0.724136i	−0.282291	−	0.959329i	$-0.591094\pi$
$619$	−776.375	−	448.240i	−1.25424	−	0.724136i	−0.971949	+	0.235193i	$0.924428\pi$
$620$	−4.22975	+	7.32614i	−0.00682217	+	0.0118164i
$621$		0			0
$622$			551.298i			0.886331i
$623$	−114.560	−	463.843i	−0.183885	−	0.744532i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	−175.207	−	101.156i	−0.279884	−	0.161591i
$627$		0			0
$628$	296.571	−	171.225i	0.472247	−	0.272652i
$629$			325.290i			0.517153i
$630$		0			0
$631$	−500.730			−0.793550			−0.396775	−	0.917916i	$-0.629871\pi$
$631$	−500.730			−0.793550			−0.396775	+	0.917916i	$0.629871\pi$
$632$	−187.093	−	324.054i	−0.296033	−	0.512744i
$633$		0			0
$634$	−271.843	+	470.846i	−0.428774	+	0.742659i
$635$	157.581	−	90.9793i	0.248159	−	0.143275i
$636$		0			0
$637$	−110.431	+	175.000i	−0.173362	+	0.274726i
$638$	−41.7893			−0.0655005
$639$		0			0
$640$	−21.9089	−	12.6491i	−0.0342327	−	0.0197642i
$641$	310.289	−	537.436i	0.484070	−	0.838434i	−0.515763	−	0.856732i	$-0.672491\pi$
$641$	310.289	−	537.436i	0.484070	−	0.838434i	0.999833	+	0.0182978i	$0.00582469\pi$
$642$		0			0
$643$		−	1127.93i		−	1.75417i	−0.480334	−	0.877086i	$-0.659484\pi$
$643$		−	1127.93i		−	1.75417i	0.480334	−	0.877086i	$-0.340516\pi$
$644$	−43.0051	+	148.735i	−0.0667782	+	0.230954i
$645$		0			0
$646$	74.9206	+	129.766i	0.115976	+	0.200877i
$647$	117.130	+	67.6248i	0.181035	+	0.104521i	0.587779	−	0.809022i	$-0.300003\pi$
$647$	117.130	+	67.6248i	0.181035	+	0.104521i	−0.406744	+	0.913542i	$0.633336\pi$
$648$		0			0
$649$	−23.0380	+	13.3010i	−0.0354977	+	0.0204946i
$650$		−	29.8616i		−	0.0459409i
$651$		0			0
$652$	186.026			0.285316
$653$	−195.145	−	338.001i	−0.298843	−	0.517612i	0.677028	−	0.735957i	$-0.263267\pi$
$653$	−195.145	−	338.001i	−0.298843	−	0.517612i	−0.975872	+	0.218345i	$0.929934\pi$
$654$		0			0
$655$	269.028	−	465.971i	0.410730	−	0.711406i
$656$	−14.1120	+	8.14755i	−0.0215121	+	0.0124200i
$657$		0			0
$658$	−451.542	+	434.123i	−0.686233	+	0.659761i
$659$	864.853			1.31237			0.656186	−	0.754599i	$-0.272169\pi$
$659$	864.853			1.31237			0.656186	+	0.754599i	$0.272169\pi$
$660$		0			0
$661$	−873.134	−	504.104i	−1.32093	−	0.762638i	−0.337052	−	0.941486i	$-0.609430\pi$
$661$	−873.134	−	504.104i	−1.32093	−	0.762638i	−0.983877	+	0.178848i	$0.942763\pi$
$662$	137.113	−	237.487i	0.207120	−	0.358742i
$663$		0			0
$664$			35.3094i			0.0531768i
$665$	34.4644	+	35.8472i	0.0518261	+	0.0539055i
$666$		0			0
$667$	310.374	+	537.584i	0.465328	+	0.805973i
$668$	181.849	+	104.991i	0.272230	+	0.157172i
$669$		0			0
$670$	23.9326	−	13.8175i	0.0357203	−	0.0206231i
$671$			54.3806i			0.0810441i
$672$		0			0
$673$	−109.959			−0.163386			−0.0816928	−	0.996658i	$-0.526033\pi$
$673$	−109.959			−0.163386			−0.0816928	+	0.996658i	$0.526033\pi$
$674$	88.7259	+	153.678i	0.131641	+	0.228009i
$675$		0			0
$676$	−151.166	+	261.827i	−0.223618	+	0.387318i
$677$	−146.213	+	84.4163i	−0.215972	+	0.124692i	−0.604084	−	0.796921i	$-0.706461\pi$
$677$	−146.213	+	84.4163i	−0.215972	+	0.124692i	0.388112	+	0.921612i	$0.373128\pi$
$678$		0			0
$679$	−1003.85	−	290.253i	−1.47842	−	0.427471i
$680$	210.928			0.310188
$681$		0			0
$682$	1.21963	+	0.704155i	0.00178832	+	0.00103248i
$683$	−218.065	+	377.700i	−0.319276	+	0.553002i	−0.980337	−	0.197330i	$-0.936773\pi$
$683$	−218.065	+	377.700i	−0.319276	+	0.553002i	0.661061	+	0.750332i	$0.270106\pi$
$684$		0			0
$685$			522.482i			0.762748i
$686$	−460.329	−	152.954i	−0.671034	−	0.222965i
$687$		0			0
$688$	−92.7038	−	160.568i	−0.134744	−	0.233383i
$689$	170.141	+	98.2309i	0.246939	+	0.142570i
$690$		0			0
$691$	−59.2770	+	34.2236i	−0.0857843	+	0.0495276i	−0.542279	−	0.840199i	$-0.682438\pi$
$691$	−59.2770	+	34.2236i	−0.0857843	+	0.0495276i	0.456494	+	0.889726i	$0.349105\pi$
$692$		−	408.314i		−	0.590049i
$693$		0			0
$694$	−712.193			−1.02622
$695$	236.454	+	409.551i	0.340222	+	0.589282i
$696$		0			0
$697$	67.9314	−	117.661i	0.0974625	−	0.168810i
$698$	−58.5039	+	33.7772i	−0.0838164	+	0.0483914i
$699$		0			0
$700$	67.9580	−	16.7843i	0.0970828	−	0.0239776i
$701$	−1283.41			−1.83083			−0.915414	−	0.402514i	$-0.868136\pi$
$701$	−1283.41			−1.83083			−0.915414	+	0.402514i	$0.868136\pi$
$702$		0			0
$703$	26.8355	+	15.4935i	0.0381728	+	0.0220391i
$704$	−2.10578	+	3.64732i	−0.00299117	+	0.00518086i
$705$		0			0
$706$		−	46.5422i		−	0.0659238i
$707$	−488.188	+	469.356i	−0.690507	+	0.663870i
$708$		0			0
$709$	−86.2000	−	149.303i	−0.121580	−	0.210582i	0.798811	−	0.601582i	$-0.205463\pi$
$709$	−86.2000	−	149.303i	−0.121580	−	0.210582i	−0.920391	+	0.391000i	$0.872129\pi$
$710$	79.5862	+	45.9491i	0.112093	+	0.0647171i
$711$		0			0
$712$	−167.189	+	96.5264i	−0.234815	+	0.135571i
$713$		−	20.9194i		−	0.0293399i
$714$		0			0
$715$	−4.97126			−0.00695282
$716$	−195.899	−	339.307i	−0.273602	−	0.473892i
$717$		0			0
$718$	−189.361	+	327.983i	−0.263734	+	0.456801i
$719$	435.015	−	251.156i	0.605028	−	0.349313i	−0.165989	−	0.986128i	$-0.553082\pi$
$719$	435.015	−	251.156i	0.605028	−	0.349313i	0.771017	+	0.636815i	$0.219748\pi$
$720$		0			0
$721$	−175.836	−	711.943i	−0.243878	−	0.987439i
$722$	−496.257			−0.687337
$723$		0			0
$724$	−206.168	−	119.031i	−0.284763	−	0.164408i
$725$	140.326	−	243.051i	0.193552	−	0.335243i
$726$		0			0
$727$		−	748.693i		−	1.02984i	−0.857238	−	0.514920i	$-0.827822\pi$
$727$		−	748.693i		−	1.02984i	0.857238	−	0.514920i	$-0.172178\pi$
$728$	80.3223	+	23.2244i	0.110333	+	0.0319017i
$729$		0			0
$730$	−26.4571	−	45.8251i	−0.0362426	−	0.0627741i
$731$	1338.76	+	772.931i	1.83140	+	1.05736i
$732$		0			0
$733$	−812.761	+	469.248i	−1.10881	+	0.640175i	−0.938522	−	0.345219i	$-0.887805\pi$
$733$	−812.761	+	469.248i	−1.10881	+	0.640175i	−0.170293	+	0.985394i	$0.554471\pi$
$734$		−	224.468i		−	0.305814i
$735$		0			0
$736$	62.5596			0.0849994
$737$	−2.30029	−	3.98422i	−0.00312116	−	0.00540600i
$738$		0			0
$739$	−106.820	+	185.018i	−0.144547	+	0.250363i	−0.929204	−	0.369567i	$-0.879506\pi$
$739$	−106.820	+	185.018i	−0.144547	+	0.250363i	0.784657	+	0.619931i	$0.212839\pi$
$740$	37.7757	−	21.8098i	0.0510482	−	0.0294727i
$741$		0			0
$742$	−127.919	+	442.413i	−0.172398	+	0.596244i
$743$	−544.013			−0.732184			−0.366092	−	0.930579i	$-0.619304\pi$
$743$	−544.013			−0.732184			−0.366092	+	0.930579i	$0.619304\pi$
$744$		0			0
$745$	−279.010	−	161.087i	−0.374511	−	0.216224i
$746$	292.985	−	507.465i	0.392742	−	0.680249i
$747$		0			0
$748$		−	35.1146i		−	0.0469446i
$749$	−846.786	+	209.140i	−1.13056	+	0.279225i
$750$		0			0
$751$	−294.705	−	510.443i	−0.392416	−	0.679685i	0.600351	−	0.799736i	$-0.295027\pi$
$751$	−294.705	−	510.443i	−0.392416	−	0.679685i	−0.992768	+	0.120051i	$0.961694\pi$
$752$	219.187	+	126.548i	0.291473	+	0.168282i
$753$		0			0
$754$	290.316	−	167.614i	0.385034	−	0.222299i
$755$		−	209.100i		−	0.276954i
$756$		0			0
$757$	−448.997			−0.593127			−0.296564	−	0.955013i	$-0.595841\pi$
$757$	−448.997			−0.593127			−0.296564	+	0.955013i	$0.595841\pi$
$758$	−51.4774	−	89.1614i	−0.0679121	−	0.117627i
$759$		0			0
$760$	10.0464	−	17.4010i	0.0132190	−	0.0228960i
$761$	−371.914	+	214.725i	−0.488718	+	0.282161i	−0.724042	−	0.689756i	$-0.757718\pi$
$761$	−371.914	+	214.725i	−0.488718	+	0.282161i	0.235325	+	0.971917i	$0.424385\pi$
$762$		0			0
$763$	410.475	+	426.944i	0.537975	+	0.559560i
$764$	131.463			0.172072
$765$		0			0
$766$	349.070	+	201.536i	0.455705	+	0.263101i
$767$	106.699	−	184.807i	0.139112	−	0.240948i
$768$		0			0
$769$			32.5790i			0.0423655i	0.999776	+	0.0211827i	$0.00674318\pi$
$769$			32.5790i			0.0423655i	−0.999776	+	0.0211827i	$0.993257\pi$
$770$	−2.79419	−	11.3134i	−0.00362882	−	0.0146928i
$771$		0			0
$772$	96.8700	+	167.784i	0.125479	+	0.217337i
$773$	−1076.93	−	621.768i	−1.39319	−	0.804357i	−0.399520	−	0.916724i	$-0.630823\pi$
$773$	−1076.93	−	621.768i	−1.39319	−	0.804357i	−0.993667	+	0.112367i	$0.964157\pi$
$774$		0			0
$775$	−8.19087	+	4.72900i	−0.0105689	+	0.00610194i
$776$			422.231i			0.544112i
$777$		0			0
$778$	−137.374			−0.176574
$779$	−6.47112	−	11.2083i	−0.00830696	−	0.0143881i
$780$		0			0
$781$	7.64946	−	13.2493i	0.00979444	−	0.0169645i
$782$	−451.719	+	260.800i	−0.577645	+	0.333504i
$783$		0			0
$784$	−7.70657	+	195.848i	−0.00982981	+	0.249807i
$785$	382.872			0.487735
$786$		0			0
$787$	165.088	+	95.3138i	0.209769	+	0.121110i	0.601204	−	0.799096i	$-0.294688\pi$
$787$	165.088	+	95.3138i	0.209769	+	0.121110i	−0.391435	+	0.920206i	$0.628021\pi$
$788$	186.672	−	323.325i	0.236893	−	0.410311i
$789$		0			0
$790$		−	418.352i		−	0.529560i
$791$	226.011	−	781.667i	0.285729	−	0.988202i
$792$		0			0
$793$	−218.116	−	377.789i	−0.275052	−	0.476405i
$794$	−969.635	−	559.819i	−1.22120	−	0.705062i
$795$		0			0
$796$	−199.691	+	115.292i	−0.250868	+	0.144839i
$797$		−	387.796i		−	0.486570i	−0.969955	−	0.243285i	$-0.921775\pi$
$797$		−	387.796i		−	0.486570i	0.969955	−	0.243285i	$-0.0782250\pi$
$798$		0			0
$799$	−2110.23			−2.64108
$800$	−14.1421	−	24.4949i	−0.0176777	−	0.0306186i
$801$		0			0
$802$	−355.835	+	616.324i	−0.443684	+	0.768484i
$803$	−7.62881	+	4.40449i	−0.00950038	+	0.00548505i
$804$		0			0
$805$	−124.785	+	119.971i	−0.155012	+	0.149032i
$806$	−11.2972			−0.0140164
$807$		0			0
$808$	236.977	+	136.818i	0.293288	+	0.169330i
$809$	182.613	−	316.295i	0.225727	−	0.390970i	−0.730811	−	0.682580i	$-0.760858\pi$
$809$	182.613	−	316.295i	0.225727	−	0.390970i	0.956537	+	0.291610i	$0.0941911\pi$
$810$		0			0
$811$		−	944.189i		−	1.16423i	−0.813107	−	0.582114i	$-0.802226\pi$
$811$		−	944.189i		−	1.16423i	0.813107	−	0.582114i	$-0.197774\pi$
$812$	544.627	+	566.479i	0.670723	+	0.697635i
$813$		0			0
$814$	−3.63082	−	6.28877i	−0.00446047	−	0.00772576i
$815$	180.119	+	103.992i	0.221005	+	0.127597i
$816$		0			0
$817$	127.529	−	73.6292i	0.156095	−	0.0901214i
$818$			1060.46i			1.29640i
$819$		0			0
$820$	−18.2185			−0.0222176
$821$	−342.337	−	592.946i	−0.416976	−	0.722224i	0.578657	−	0.815571i	$-0.303577\pi$
$821$	−342.337	−	592.946i	−0.416976	−	0.722224i	−0.995634	+	0.0933467i	$0.970243\pi$
$822$		0			0
$823$	522.835	−	905.578i	0.635280	−	1.10034i	−0.351176	−	0.936310i	$-0.614218\pi$
$823$	522.835	−	905.578i	0.635280	−	1.10034i	0.986456	−	0.164028i	$-0.0524486\pi$
$824$	−256.614	+	148.156i	−0.311425	+	0.179801i
$825$		0			0
$826$	480.550	+	138.946i	0.581780	+	0.168216i
$827$	−830.505			−1.00424			−0.502119	−	0.864798i	$-0.667446\pi$
$827$	−830.505			−1.00424			−0.502119	+	0.864798i	$0.667446\pi$
$828$		0			0
$829$	−621.983	−	359.102i	−0.750280	−	0.433175i	0.0755148	−	0.997145i	$-0.475940\pi$
$829$	−621.983	−	359.102i	−0.750280	−	0.433175i	−0.825795	+	0.563970i	$0.809273\pi$
$830$	−19.7385	+	34.1882i	−0.0237814	+	0.0411906i
$831$		0			0
$832$		−	33.7846i		−	0.0406064i
$833$	−760.812	−	1446.27i	−0.913339	−	1.73622i
$834$		0			0
$835$	117.383	+	203.314i	0.140579	+	0.243490i
$836$	−2.89685	−	1.67250i	−0.00346514	−	0.00200060i
$837$		0			0
$838$	−570.436	+	329.342i	−0.680712	+	0.393009i
$839$		−	55.2900i		−	0.0658999i	−0.999457	−	0.0329499i	$-0.989510\pi$
$839$		−	55.2900i		−	0.0658999i	0.999457	−	0.0329499i	$-0.0104902\pi$
$840$		0			0
$841$	2309.60			2.74625
$842$	244.645	+	423.737i	0.290552	+	0.503251i
$843$		0			0
$844$	−139.433	+	241.505i	−0.165205	+	0.286143i
$845$	−292.731	+	169.008i	−0.346427	+	0.200010i
$846$		0			0
$847$	820.408	−	202.625i	0.968605	−	0.239226i
$848$	186.084			0.219439
$849$		0			0
$850$	204.230	+	117.912i	0.240270	+	0.138720i
$851$	−53.9331	+	93.4149i	−0.0633761	+	0.109771i
$852$		0			0
$853$			21.9601i			0.0257445i	0.999917	+	0.0128723i	$0.00409748\pi$
$853$			21.9601i			0.0257445i	−0.999917	+	0.0128723i	$0.995903\pi$
$854$	737.162	−	708.725i	0.863187	−	0.829889i
$855$		0			0
$856$	176.217	+	305.217i	0.205861	+	0.356562i
$857$	1399.33	+	807.903i	1.63282	+	0.942711i	0.983217	+	0.182441i	$0.0583997\pi$
$857$	1399.33	+	807.903i	1.63282	+	0.942711i	0.649607	+	0.760271i	$0.274934\pi$
$858$		0			0
$859$	772.149	−	445.801i	0.898893	−	0.518976i	0.0220523	−	0.999757i	$-0.492980\pi$
$859$	772.149	−	445.801i	0.898893	−	0.518976i	0.876841	+	0.480781i	$0.159647\pi$
$860$		−	207.292i		−	0.241037i
$861$		0			0
$862$	699.470			0.811450
$863$	−448.173	−	776.259i	−0.519320	−	0.899489i	−0.999748	−	0.0224544i	$-0.992852\pi$
$863$	−448.173	−	776.259i	−0.519320	−	0.899489i	0.480428	−	0.877034i	$-0.340481\pi$
$864$		0			0
$865$	228.255	−	395.349i	0.263878	−	0.457050i
$866$	−894.090	+	516.203i	−1.03244	+	0.596078i
$867$		0			0
$868$	−6.34984	−	25.7099i	−0.00731548	−	0.0296197i
$869$	−69.6459			−0.0801449
$870$		0			0
$871$	31.9609	+	18.4526i	0.0366944	+	0.0211855i
$872$	119.654	−	207.248i	0.137218	−	0.237669i
$873$		0			0
$874$			49.6874i			0.0568506i
$875$	75.1827	+	21.7383i	0.0859231	+	0.0248438i
$876$		0			0
$877$	168.885	+	292.517i	0.192571	+	0.333543i	0.946102	−	0.323870i	$-0.104984\pi$
$877$	168.885	+	292.517i	0.192571	+	0.333543i	−0.753530	+	0.657413i	$0.771651\pi$
$878$	−454.855	−	262.611i	−0.518059	−	0.299101i
$879$		0			0
$880$	−4.07783	+	2.35434i	−0.00463390	+	0.00267538i
$881$			301.377i			0.342085i	0.985264	+	0.171042i	$0.0547135\pi$
$881$			301.377i			0.342085i	−0.985264	+	0.171042i	$0.945287\pi$
$882$		0			0
$883$	38.3679			0.0434518			0.0217259	−	0.999764i	$-0.493084\pi$
$883$	38.3679			0.0434518			0.0217259	+	0.999764i	$0.493084\pi$
$884$	140.842	+	243.945i	0.159323	+	0.275956i
$885$		0			0
$886$	−289.000	+	500.563i	−0.326185	+	0.564969i
$887$	−572.834	+	330.726i	−0.645811	+	0.372859i	−0.786849	−	0.617145i	$-0.788289\pi$
$887$	−572.834	+	330.726i	−0.645811	+	0.372859i	0.141038	+	0.990004i	$0.454956\pi$
$888$		0			0
$889$	−158.219	+	547.206i	−0.177974	+	0.615530i
$890$	−215.840			−0.242516
$891$		0			0
$892$	446.965	+	258.055i	0.501082	+	0.289300i
$893$	−100.510	+	174.088i	−0.112553	+	0.194947i
$894$		0			0
$895$		−	438.043i		−	0.489434i
$896$	76.8857	−	18.9893i	0.0858099	−	0.0211934i
$897$		0			0
$898$	−512.984	−	888.515i	−0.571252	−	0.989437i
$899$	−91.9510	−	53.0880i	−0.102281	−	0.0590522i
$900$		0			0
$901$	−1343.64	+	775.753i	−1.49128	+	0.860991i
$902$			3.03295i			0.00336247i
$903$		0			0
$904$	−328.779			−0.363693
$905$	−133.081	−	230.503i	−0.147051	−	0.254700i
$906$		0			0
$907$	484.152	−	838.576i	0.533795	−	0.924560i	−0.465426	−	0.885087i	$-0.654099\pi$
$907$	484.152	−	838.576i	0.533795	−	0.924560i	0.999221	−	0.0394729i	$-0.0125679\pi$
$908$	573.365	−	331.032i	0.631459	−	0.364573i
$909$		0			0
$910$	64.7889	+	67.3885i	0.0711966	+	0.0740533i
$911$	−220.674			−0.242233			−0.121116	−	0.992638i	$-0.538647\pi$
$911$	−220.674			−0.242233			−0.121116	+	0.992638i	$0.538647\pi$
$912$		0			0
$913$	5.69153	+	3.28601i	0.00623388	+	0.00359913i
$914$	283.925	−	491.772i	0.310640	−	0.538044i
$915$		0			0
$916$			488.476i			0.533271i
$917$	403.874	+	1635.25i	0.440430	+	1.78326i
$918$		0			0
$919$	574.019	+	994.231i	0.624613	+	1.08186i	0.988616	+	0.150464i	$0.0480766\pi$
$919$	574.019	+	994.231i	0.624613	+	1.08186i	−0.364002	+	0.931398i	$0.618590\pi$
$920$	60.5731	+	34.9719i	0.0658403	+	0.0380129i
$921$		0			0
$922$	799.819	−	461.776i	0.867483	−	0.500841i
$923$			122.726i			0.132964i
$924$		0			0
$925$	48.7682			0.0527223
$926$	−614.886	−	1065.01i	−0.664024	−	1.15012i
$927$		0			0
$928$	158.760	−	274.981i	0.171078	−	0.296315i
$929$	264.398	−	152.650i	0.284605	−	0.164317i	−0.350901	−	0.936412i	$-0.614125\pi$
$929$	264.398	−	152.650i	0.284605	−	0.164317i	0.635506	+	0.772096i	$0.280791\pi$
$930$		0			0
$931$	−155.551	−	6.12088i	−0.167079	−	0.00657452i
$932$	−422.979			−0.453840
$933$		0			0
$934$	−905.334	−	522.695i	−0.969308	−	0.559630i
$935$	19.6296	−	33.9995i	0.0209943	−	0.0363631i
$936$		0			0
$937$			12.4049i			0.0132390i	0.999978	+	0.00661948i	$0.00210706\pi$
$937$			12.4049i			0.0132390i	−0.999978	+	0.00661948i	$0.997893\pi$
$938$	−24.0296	+	83.1070i	−0.0256179	+	0.0886002i
$939$		0			0
$940$	141.485	+	245.059i	0.150516	+	0.260701i
$941$	250.409	+	144.573i	0.266109	+	0.153638i	0.627118	−	0.778924i	$-0.284234\pi$
$941$	250.409	+	144.573i	0.266109	+	0.153638i	−0.361009	+	0.932562i	$0.617568\pi$
$942$		0			0
$943$	39.0163	−	22.5261i	0.0413747	−	0.0238877i
$944$		−	202.125i		−	0.214116i
$945$		0			0
$946$	−34.5093			−0.0364792
$947$	−713.478	−	1235.78i	−0.753409	−	1.30494i	−0.946161	−	0.323695i	$-0.895075\pi$
$947$	−713.478	−	1235.78i	−0.753409	−	1.30494i	0.192752	−	0.981247i	$-0.438259\pi$
$948$		0			0
$949$	35.3322	−	61.1972i	0.0372310	−	0.0644859i
$950$	19.4549	−	11.2323i	0.0204788	−	0.0118234i
$951$		0			0
$952$	−475.999	+	457.637i	−0.499999	+	0.480711i
$953$	668.525			0.701495			0.350747	−	0.936470i	$-0.385928\pi$
$953$	668.525			0.701495			0.350747	+	0.936470i	$0.385928\pi$
$954$		0			0
$955$	127.288	+	73.4899i	0.133286	+	0.0769528i
$956$	344.134	−	596.058i	0.359973	−	0.623491i
$957$		0			0
$958$			857.331i			0.894918i
$959$	−1133.60	−	1179.08i	−1.18206	−	1.22949i
$960$		0			0
$961$	−478.711	−	829.152i	−0.498138	−	0.862801i
$962$	50.4476	+	29.1259i	0.0524403	+	0.0302764i
$963$		0			0
$964$	296.784	−	171.348i	0.307867	−	0.177747i
$965$			216.608i			0.224464i
$966$		0			0
$967$	1647.14			1.70335			0.851676	−	0.524069i	$-0.175586\pi$
$967$	1647.14			1.70335			0.851676	+	0.524069i	$0.175586\pi$
$968$	−170.728	−	295.709i	−0.176372	−	0.305485i
$969$		0			0
$970$	−236.034	+	408.823i	−0.243334	+	0.421467i
$971$	−1138.76	+	657.466i	−1.17277	+	0.677102i	−0.954332	−	0.298748i	$-0.903431\pi$
$971$	−1138.76	+	657.466i	−1.17277	+	0.677102i	−0.218443	+	0.975850i	$0.570098\pi$
$972$		0			0
$973$	−1422.18	−	411.210i	−1.46165	−	0.422621i
$974$	−918.639			−0.943161
$975$		0			0
$976$	−357.833	−	206.595i	−0.366633	−	0.211675i
$977$	778.021	−	1347.57i	0.796337	−	1.37930i	−0.125650	−	0.992075i	$-0.540102\pi$
$977$	778.021	−	1347.57i	0.796337	−	1.37930i	0.921987	−	0.387221i	$-0.126565\pi$
$978$		0			0
$979$			35.9323i			0.0367030i
$980$	−116.944	+	185.321i	−0.119331	+	0.189103i
$981$		0			0
$982$	−188.535	−	326.553i	−0.191991	−	0.332538i
$983$	1188.87	+	686.397i	1.20944	+	0.698268i	0.962636	−	0.270799i	$-0.0872879\pi$
$983$	1188.87	+	686.397i	1.20944	+	0.698268i	0.246799	+	0.969067i	$0.420621\pi$
$984$		0			0
$985$	361.489	−	208.706i	0.366994	−	0.211884i
$986$			2647.37i			2.68496i
$987$		0			0
$988$	26.8331			0.0271590
$989$	256.304	+	443.932i	0.259155	+	0.448870i
$990$		0			0
$991$	−321.812	+	557.395i	−0.324735	+	0.562457i	−0.981459	−	0.191674i	$-0.938608\pi$
$991$	−321.812	+	557.395i	−0.324735	+	0.562457i	0.656724	+	0.754131i	$0.271942\pi$
$992$	−9.26691	+	5.35025i	−0.00934165	+	0.00539340i
$993$		0			0
$994$	−279.295	+	68.9803i	−0.280981	+	0.0693967i
$995$	−257.800			−0.259095
$996$		0			0
$997$	610.431	+	352.433i	0.612268	+	0.353493i	0.773853	−	0.633366i	$-0.218327\pi$
$997$	610.431	+	352.433i	0.612268	+	0.353493i	−0.161584	+	0.986859i	$0.551660\pi$
$998$	−481.615	+	834.181i	−0.482580	+	0.835853i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.v.c.451.6		16
3.2	odd	2		210.3.o.b.31.4	✓	16
7.5	odd	6	inner	630.3.v.c.271.6		16
15.2	even	4		1050.3.q.e.199.12		32
15.8	even	4		1050.3.q.e.199.4		32
15.14	odd	2		1050.3.p.i.451.6		16
21.5	even	6		210.3.o.b.61.4	yes	16
21.11	odd	6		1470.3.f.d.391.15		16
21.17	even	6		1470.3.f.d.391.9		16
105.47	odd	12		1050.3.q.e.649.4		32
105.68	odd	12		1050.3.q.e.649.12		32
105.89	even	6		1050.3.p.i.901.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.4	✓	16	3.2	odd	2
210.3.o.b.61.4	yes	16	21.5	even	6
630.3.v.c.271.6		16	7.5	odd	6	inner
630.3.v.c.451.6		16	1.1	even	1	trivial
1050.3.p.i.451.6		16	15.14	odd	2
1050.3.p.i.901.6		16	105.89	even	6
1050.3.q.e.199.4		32	15.8	even	4
1050.3.q.e.199.12		32	15.2	even	4
1050.3.q.e.649.4		32	105.47	odd	12
1050.3.q.e.649.12		32	105.68	odd	12
1470.3.f.d.391.9		16	21.17	even	6
1470.3.f.d.391.15		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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(1.94434 - 6.72455i) q^{7} -2.82843 q^{8} +O(q^{10})\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(1.94434 - 6.72455i) q^{7} -2.82843 q^{8} +(-2.73861 - 1.58114i) q^{10} +(-0.263223 + 0.455915i) q^{11} -4.22307i q^{13} +(9.61071 - 2.37366i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(28.8825 + 16.6753i) q^{17} +(2.75133 - 1.58848i) q^{19} -4.47214i q^{20} -0.744507 q^{22} +(5.52954 + 9.57744i) q^{23} +(2.50000 - 4.33013i) q^{25} +(5.17218 - 2.98616i) q^{26} +(9.70292 + 10.0922i) q^{28} +56.1302 q^{29} +(-1.63817 - 0.945800i) q^{31} +(2.82843 - 4.89898i) q^{32} +47.1649i q^{34} +(3.75308 + 15.1959i) q^{35} +(4.87682 + 8.44690i) q^{37} +(3.89097 + 2.24645i) q^{38} +(5.47723 - 3.16228i) q^{40} -4.07377i q^{41} +46.3519 q^{43} +(-0.526446 - 0.911831i) q^{44} +(-7.81995 + 13.5445i) q^{46} +(-54.7969 + 31.6370i) q^{47} +(-41.4391 - 26.1496i) q^{49} +7.07107 q^{50} +(7.31457 + 4.22307i) q^{52} +(-23.2606 + 40.2885i) q^{53} -1.17717i q^{55} +(-5.49942 + 19.0199i) q^{56} +(39.6900 + 68.7452i) q^{58} +(43.7614 + 25.2657i) q^{59} +(89.4583 - 51.6488i) q^{61} -2.67513i q^{62} +8.00000 q^{64} +(4.72153 + 8.17794i) q^{65} +(-4.36948 + 7.56816i) q^{67} +(-57.7649 + 33.3506i) q^{68} +(-15.9572 + 15.3417i) q^{70} -29.0608 q^{71} +(14.4912 + 8.36647i) q^{73} +(-6.89686 + 11.9457i) q^{74} +6.35393i q^{76} +(2.55403 + 2.65651i) q^{77} +(66.1473 + 114.571i) q^{79} +(7.74597 + 4.47214i) q^{80} +(4.98933 - 2.88059i) q^{82} -12.4838i q^{83} -74.5742 q^{85} +(32.7757 + 56.7692i) q^{86} +(0.744507 - 1.28952i) q^{88} +(59.1101 - 34.1272i) q^{89} +(-28.3982 - 8.21107i) q^{91} -22.1182 q^{92} +(-77.4945 - 44.7415i) q^{94} +(-3.55196 + 6.15217i) q^{95} -149.281i q^{97} +(2.72468 - 69.2429i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 4 q^{7}+O(q^{10}) \) 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

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