LMFDB - Embedded newform 630.3.v.c.271.5

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			271.5
Root			$1.92573 + 3.33546i$ of defining polynomial
Character	$\chi$	$=$	630.271
Dual form			630.3.v.c.451.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-1.93649 - 1.11803i) q^{5} +(-2.67372 - 6.46925i) q^{7} -2.82843 q^{8} +O(q^{10})$	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-1.93649 - 1.11803i) q^{5} +(-2.67372 - 6.46925i) q^{7} -2.82843 q^{8} +(-2.73861 + 1.58114i) q^{10} +(0.578394 + 1.00181i) q^{11} -14.8176i q^{13} +(-9.81379 - 1.29982i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-10.9271 + 6.30878i) q^{17} +(16.7162 + 9.65108i) q^{19} +4.47214i q^{20} +1.63595 q^{22} +(-12.1504 + 21.0450i) q^{23} +(2.50000 + 4.33013i) q^{25} +(-18.1477 - 10.4776i) q^{26} +(-8.53135 + 11.1003i) q^{28} -49.0382 q^{29} +(-24.9581 + 14.4096i) q^{31} +(2.82843 + 4.89898i) q^{32} +17.8439i q^{34} +(-2.05520 + 15.5170i) q^{35} +(26.6579 - 46.1728i) q^{37} +(23.6402 - 13.6487i) q^{38} +(5.47723 + 3.16228i) q^{40} +38.0398i q^{41} -63.5774 q^{43} +(1.15679 - 2.00362i) q^{44} +(17.1832 + 29.7622i) q^{46} +(-21.8175 - 12.5964i) q^{47} +(-34.7024 + 34.5940i) q^{49} +7.07107 q^{50} +(-25.6648 + 14.8176i) q^{52} +(10.4160 + 18.0411i) q^{53} -2.58666i q^{55} +(7.56243 + 18.2978i) q^{56} +(-34.6752 + 60.0593i) q^{58} +(-21.1419 + 12.2063i) q^{59} +(5.53376 + 3.19492i) q^{61} +40.7564i q^{62} +8.00000 q^{64} +(-16.5665 + 28.6941i) q^{65} +(-62.2451 - 107.812i) q^{67} +(21.8543 + 12.6176i) q^{68} +(17.5511 + 13.4892i) q^{70} +118.973 q^{71} +(-34.2336 + 19.7648i) q^{73} +(-37.7000 - 65.2983i) q^{74} -38.6043i q^{76} +(4.93448 - 6.42033i) q^{77} +(46.4356 - 80.4288i) q^{79} +(7.74597 - 4.47214i) q^{80} +(46.5891 + 26.8982i) q^{82} +5.79665i q^{83} +28.2137 q^{85} +(-44.9560 + 77.8661i) q^{86} +(-1.63595 - 2.83354i) q^{88} +(-131.622 - 75.9919i) q^{89} +(-95.8586 + 39.6181i) q^{91} +48.6014 q^{92} +(-30.8546 + 17.8139i) q^{94} +(-21.5805 - 37.3785i) q^{95} +144.310i q^{97} +(17.8305 + 66.9632i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$7$	−2.67372	−	6.46925i	−0.381960	−	0.924179i
$7$	−2.67372	−	6.46925i	−0.381960	−	0.924179i
$8$	−2.82843			−0.353553
$9$		0			0
$10$	−2.73861	+	1.58114i	−0.273861	+	0.158114i
$11$	0.578394	+	1.00181i	0.0525813	+	0.0910735i	0.891118	−	0.453772i	$-0.149922\pi$
$11$	0.578394	+	1.00181i	0.0525813	+	0.0910735i	−0.838537	+	0.544845i	$0.816588\pi$
$12$		0			0
$13$		−	14.8176i		−	1.13981i	−0.821710	−	0.569906i	$-0.806979\pi$
$13$		−	14.8176i		−	1.13981i	0.821710	−	0.569906i	$-0.193021\pi$
$14$	−9.81379	−	1.29982i	−0.700985	−	0.0928446i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−10.9271	+	6.30878i	−0.642772	+	0.371105i	−0.785682	−	0.618631i	$-0.787688\pi$
$17$	−10.9271	+	6.30878i	−0.642772	+	0.371105i	0.142909	+	0.989736i	$0.454354\pi$
$18$		0			0
$19$	16.7162	+	9.65108i	0.879798	+	0.507951i	0.870592	−	0.492006i	$-0.163736\pi$
$19$	16.7162	+	9.65108i	0.879798	+	0.507951i	0.00920603	+	0.999958i	$0.497070\pi$
$20$			4.47214i			0.223607i
$21$		0			0
$22$	1.63595			0.0743612
$23$	−12.1504	+	21.0450i	−0.528277	+	0.915002i	0.471180	+	0.882037i	$0.343828\pi$
$23$	−12.1504	+	21.0450i	−0.528277	+	0.915002i	−0.999457	+	0.0329648i	$0.989505\pi$
$24$		0			0
$25$	2.50000	+	4.33013i	0.100000	+	0.173205i
$26$	−18.1477	−	10.4776i	−0.697990	−	0.402985i
$27$		0			0
$28$	−8.53135	+	11.1003i	−0.304691	+	0.396438i
$29$	−49.0382			−1.69097			−0.845486	−	0.533998i	$-0.820689\pi$
$29$	−49.0382			−1.69097			−0.845486	+	0.533998i	$0.820689\pi$
$30$		0			0
$31$	−24.9581	+	14.4096i	−0.805100	+	0.464825i	−0.845251	−	0.534369i	$-0.820549\pi$
$31$	−24.9581	+	14.4096i	−0.805100	+	0.464825i	0.0401515	+	0.999194i	$0.487216\pi$
$32$	2.82843	+	4.89898i	0.0883883	+	0.153093i
$33$		0			0
$34$			17.8439i			0.524822i
$35$	−2.05520	+	15.5170i	−0.0587201	+	0.443342i
$36$		0			0
$37$	26.6579	−	46.1728i	0.720484	−	1.24791i	−0.240322	−	0.970693i	$-0.577253\pi$
$37$	26.6579	−	46.1728i	0.720484	−	1.24791i	0.960806	−	0.277221i	$-0.0894136\pi$
$38$	23.6402	−	13.6487i	0.622111	−	0.359176i
$39$		0			0
$40$	5.47723	+	3.16228i	0.136931	+	0.0790569i
$41$			38.0398i			0.927800i	0.885888	+	0.463900i	$0.153550\pi$
$41$			38.0398i			0.927800i	−0.885888	+	0.463900i	$0.846450\pi$
$42$		0			0
$43$	−63.5774			−1.47854			−0.739272	−	0.673407i	$-0.764830\pi$
$43$	−63.5774			−1.47854			−0.739272	+	0.673407i	$0.764830\pi$
$44$	1.15679	−	2.00362i	0.0262906	−	0.0455367i
$45$		0			0
$46$	17.1832	+	29.7622i	0.373548	+	0.647004i
$47$	−21.8175	−	12.5964i	−0.464203	−	0.268008i	0.249607	−	0.968347i	$-0.419699\pi$
$47$	−21.8175	−	12.5964i	−0.464203	−	0.268008i	−0.713810	+	0.700340i	$0.753032\pi$
$48$		0			0
$49$	−34.7024	+	34.5940i	−0.708213	+	0.705999i
$50$	7.07107			0.141421
$51$		0			0
$52$	−25.6648	+	14.8176i	−0.493553	+	0.284953i
$53$	10.4160	+	18.0411i	0.196529	+	0.340397i	0.947401	−	0.320050i	$-0.103700\pi$
$53$	10.4160	+	18.0411i	0.196529	+	0.340397i	−0.750872	+	0.660448i	$0.770366\pi$
$54$		0			0
$55$		−	2.58666i		−	0.0470301i
$56$	7.56243	+	18.2978i	0.135043	+	0.326747i
$57$		0			0
$58$	−34.6752	+	60.0593i	−0.597849	+	1.03550i
$59$	−21.1419	+	12.2063i	−0.358337	+	0.206886i	−0.668351	−	0.743846i	$-0.733000\pi$
$59$	−21.1419	+	12.2063i	−0.358337	+	0.206886i	0.310014	+	0.950732i	$0.399666\pi$
$60$		0			0
$61$	5.53376	+	3.19492i	0.0907174	+	0.0523757i	0.544672	−	0.838649i	$-0.316654\pi$
$61$	5.53376	+	3.19492i	0.0907174	+	0.0523757i	−0.453955	+	0.891025i	$0.649987\pi$
$62$			40.7564i			0.657361i
$63$		0			0
$64$	8.00000			0.125000
$65$	−16.5665	+	28.6941i	−0.254870	+	0.441448i
$66$		0			0
$67$	−62.2451	−	107.812i	−0.929031	−	1.60913i	−0.784946	−	0.619564i	$-0.787310\pi$
$67$	−62.2451	−	107.812i	−0.929031	−	1.60913i	−0.144085	−	0.989565i	$-0.546024\pi$
$68$	21.8543	+	12.6176i	0.321386	+	0.185552i
$69$		0			0
$70$	17.5511	+	13.4892i	0.250730	+	0.192704i
$71$	118.973			1.67567			0.837835	−	0.545924i	$-0.183821\pi$
$71$	118.973			1.67567			0.837835	+	0.545924i	$0.183821\pi$
$72$		0			0
$73$	−34.2336	+	19.7648i	−0.468953	+	0.270750i	−0.715801	−	0.698304i	$-0.753938\pi$
$73$	−34.2336	+	19.7648i	−0.468953	+	0.270750i	0.246848	+	0.969054i	$0.420605\pi$
$74$	−37.7000	−	65.2983i	−0.509459	−	0.882409i
$75$		0			0
$76$		−	38.6043i		−	0.507951i
$77$	4.93448	−	6.42033i	0.0640842	−	0.0833809i
$78$		0			0
$79$	46.4356	−	80.4288i	0.587792	−	1.01809i	−0.406729	−	0.913549i	$-0.633331\pi$
$79$	46.4356	−	80.4288i	0.587792	−	1.01809i	0.994521	−	0.104537i	$-0.0333360\pi$
$80$	7.74597	−	4.47214i	0.0968246	−	0.0559017i
$81$		0			0
$82$	46.5891	+	26.8982i	0.568159	+	0.328027i
$83$			5.79665i			0.0698392i	0.999390	+	0.0349196i	$0.0111175\pi$
$83$			5.79665i			0.0698392i	−0.999390	+	0.0349196i	$0.988882\pi$
$84$		0			0
$85$	28.2137			0.331926
$86$	−44.9560	+	77.8661i	−0.522744	+	0.905420i
$87$		0			0
$88$	−1.63595	−	2.83354i	−0.0185903	−	0.0321993i
$89$	−131.622	−	75.9919i	−1.47890	−	0.853842i	−0.479182	−	0.877715i	$-0.659067\pi$
$89$	−131.622	−	75.9919i	−1.47890	−	0.853842i	−0.999715	+	0.0238738i	$0.992400\pi$
$90$		0			0
$91$	−95.8586	+	39.6181i	−1.05339	+	0.435363i
$92$	48.6014			0.528277
$93$		0			0
$94$	−30.8546	+	17.8139i	−0.328241	+	0.189510i
$95$	−21.5805	−	37.3785i	−0.227163	−	0.393458i
$96$		0			0
$97$			144.310i			1.48773i	0.668331	+	0.743864i	$0.267009\pi$
$97$			144.310i			1.48773i	−0.668331	+	0.743864i	$0.732991\pi$
$98$	17.8305	+	66.9632i	0.181943	+	0.683298i
$99$		0			0
$100$	5.00000	−	8.66025i	0.0500000	−	0.0866025i
$101$	33.8480	−	19.5422i	0.335129	−	0.193487i	−0.322987	−	0.946403i	$-0.604687\pi$
$101$	33.8480	−	19.5422i	0.335129	−	0.193487i	0.658116	+	0.752917i	$0.271354\pi$
$102$		0			0
$103$	32.7730	+	18.9215i	0.318185	+	0.183704i	0.650583	−	0.759435i	$-0.274525\pi$
$103$	32.7730	+	18.9215i	0.318185	+	0.183704i	−0.332398	+	0.943139i	$0.607858\pi$
$104$			41.9104i			0.402985i
$105$		0			0
$106$	29.4609			0.277933
$107$	41.5160	−	71.9079i	0.388000	−	0.672036i	−0.604180	−	0.796848i	$-0.706499\pi$
$107$	41.5160	−	71.9079i	0.388000	−	0.672036i	0.992180	+	0.124811i	$0.0398326\pi$
$108$		0			0
$109$	23.8962	+	41.3894i	0.219231	+	0.379719i	0.954573	−	0.297977i	$-0.0963118\pi$
$109$	23.8962	+	41.3894i	0.219231	+	0.379719i	−0.735342	+	0.677696i	$0.762978\pi$
$110$	−3.16800	−	1.82904i	−0.0288000	−	0.0166277i
$111$		0			0
$112$	27.7576	+	3.67646i	0.247836	+	0.0328255i
$113$	16.2283			0.143613			0.0718064	−	0.997419i	$-0.477124\pi$
$113$	16.2283			0.143613			0.0718064	+	0.997419i	$0.477124\pi$
$114$		0			0
$115$	47.0582	−	27.1690i	0.409201	−	0.236252i
$116$	49.0382	+	84.9366i	0.422743	+	0.732212i
$117$		0			0
$118$			34.5246i			0.292581i
$119$	70.0292	+	53.8224i	0.588481	+	0.452289i
$120$		0			0
$121$	59.8309	−	103.630i	0.494470	−	0.856448i
$122$	7.82592	−	4.51830i	0.0641469	−	0.0370352i
$123$		0			0
$124$	49.9162	+	28.8191i	0.402550	+	0.232412i
$125$		−	11.1803i		−	0.0894427i
$126$		0			0
$127$	80.5643			0.634365			0.317182	−	0.948365i	$-0.397263\pi$
$127$	80.5643			0.634365			0.317182	+	0.948365i	$0.397263\pi$
$128$	5.65685	−	9.79796i	0.0441942	−	0.0765466i
$129$		0			0
$130$	23.4286	+	40.5796i	0.180220	+	0.312151i
$131$	−107.981	−	62.3429i	−0.824283	−	0.475900i	0.0276082	−	0.999619i	$-0.491211\pi$
$131$	−107.981	−	62.3429i	−0.824283	−	0.475900i	−0.851891	+	0.523719i	$0.824544\pi$
$132$		0			0
$133$	17.7409	−	133.945i	0.133390	−	1.00711i
$134$	−176.056			−1.31385
$135$		0			0
$136$	30.9066	−	17.8439i	0.227254	−	0.131205i
$137$	−38.0330	−	65.8750i	−0.277613	−	0.480840i	0.693178	−	0.720766i	$-0.256210\pi$
$137$	−38.0330	−	65.8750i	−0.277613	−	0.480840i	−0.970791	+	0.239927i	$0.922877\pi$
$138$		0			0
$139$			91.7680i			0.660201i	0.943946	+	0.330101i	$0.107083\pi$
$139$			91.7680i			0.660201i	−0.943946	+	0.330101i	$0.892917\pi$
$140$	28.9314	−	11.9572i	0.206653	−	0.0854089i
$141$		0			0
$142$	84.1263	−	145.711i	0.592439	−	1.02613i
$143$	14.8444	−	8.57039i	0.103807	−	0.0599328i
$144$		0			0
$145$	94.9620	+	54.8264i	0.654911	+	0.378113i
$146$			55.9032i			0.382898i
$147$		0			0
$148$	−106.632			−0.720484
$149$	−49.4579	+	85.6637i	−0.331933	+	0.574924i	−0.982891	−	0.184190i	$-0.941034\pi$
$149$	−49.4579	+	85.6637i	−0.331933	+	0.574924i	0.650958	+	0.759114i	$0.274367\pi$
$150$		0			0
$151$	−48.8950	−	84.6886i	−0.323808	−	0.560852i	0.657462	−	0.753487i	$-0.271630\pi$
$151$	−48.8950	−	84.6886i	−0.323808	−	0.560852i	−0.981270	+	0.192635i	$0.938297\pi$
$152$	−47.2804	−	27.2974i	−0.311055	−	0.179588i
$153$		0			0
$154$	−4.37406	−	10.5833i	−0.0284030	−	0.0687230i
$155$	64.4415			0.415752
$156$		0			0
$157$	115.530	−	66.7013i	0.735860	−	0.424849i	−0.0847022	−	0.996406i	$-0.526994\pi$
$157$	115.530	−	66.7013i	0.735860	−	0.424849i	0.820562	+	0.571557i	$0.193661\pi$
$158$	−65.6698	−	113.743i	−0.415632	−	0.719895i
$159$		0			0
$160$		−	12.6491i		−	0.0790569i
$161$	168.632	+	22.3352i	1.04741	+	0.138728i
$162$		0			0
$163$	16.3746	−	28.3616i	0.100458	−	0.173998i	−0.811416	−	0.584469i	$-0.801303\pi$
$163$	16.3746	−	28.3616i	0.100458	−	0.173998i	0.911873	+	0.410472i	$0.134636\pi$
$164$	65.8869	−	38.0398i	0.401749	−	0.231950i
$165$		0			0
$166$	7.09942	+	4.09885i	0.0427676	+	0.0246919i
$167$		−	171.659i		−	1.02790i	−0.857821	−	0.513948i	$-0.828182\pi$
$167$		−	171.659i		−	1.02790i	0.857821	−	0.513948i	$-0.171818\pi$
$168$		0			0
$169$	−50.5603			−0.299173
$170$	19.9501	−	34.5546i	0.117354	−	0.203262i
$171$		0			0
$172$	63.5774	+	110.119i	0.369636	+	0.640229i
$173$	−175.336	−	101.230i	−1.01350	−	0.585145i	−0.101287	−	0.994857i	$-0.532296\pi$
$173$	−175.336	−	101.230i	−1.01350	−	0.585145i	−0.912215	+	0.409712i	$0.865629\pi$
$174$		0			0
$175$	21.3284	−	27.7507i	0.121876	−	0.158575i
$176$	−4.62715			−0.0262906
$177$		0			0
$178$	−186.141	+	107.469i	−1.04574	+	0.603757i
$179$	−39.3459	−	68.1491i	−0.219810	−	0.380721i	0.734940	−	0.678132i	$-0.237210\pi$
$179$	−39.3459	−	68.1491i	−0.219810	−	0.380721i	−0.954750	+	0.297411i	$0.903877\pi$
$180$		0			0
$181$			58.1509i			0.321276i	0.987013	+	0.160638i	$0.0513551\pi$
$181$			58.1509i			0.321276i	−0.987013	+	0.160638i	$0.948645\pi$
$182$	−19.2602	+	145.416i	−0.105825	+	0.798992i
$183$		0			0
$184$	34.3664	−	59.5244i	0.186774	−	0.323502i
$185$	−103.246	+	59.6089i	−0.558084	+	0.322210i
$186$		0			0
$187$	−12.6404	−	7.29793i	−0.0675956	−	0.0390263i
$188$			50.3854i			0.268008i
$189$		0			0
$190$	−61.0388			−0.321257
$191$	184.204	−	319.051i	0.964419	−	1.67042i	0.253251	−	0.967401i	$-0.418500\pi$
$191$	184.204	−	319.051i	0.964419	−	1.67042i	0.711168	−	0.703022i	$-0.248166\pi$
$192$		0			0
$193$	−140.409	−	243.196i	−0.727510	−	1.26008i	−0.957932	−	0.286994i	$-0.907344\pi$
$193$	−140.409	−	243.196i	−0.727510	−	1.26008i	0.230422	−	0.973091i	$-0.425989\pi$
$194$	176.742	+	102.042i	0.911044	+	0.525991i
$195$		0			0
$196$	94.6209	+	25.5124i	0.482760	+	0.130165i
$197$	−7.61779			−0.0386690			−0.0193345	−	0.999813i	$-0.506155\pi$
$197$	−7.61779			−0.0386690			−0.0193345	+	0.999813i	$0.506155\pi$
$198$		0			0
$199$	−174.795	+	100.918i	−0.878366	+	0.507125i	−0.870119	−	0.492841i	$-0.835958\pi$
$199$	−174.795	+	100.918i	−0.878366	+	0.507125i	−0.00824641	+	0.999966i	$0.502625\pi$
$200$	−7.07107	−	12.2474i	−0.0353553	−	0.0612372i
$201$		0			0
$202$		−	55.2736i		−	0.273632i
$203$	131.114	+	317.240i	0.645884	+	1.56276i
$204$		0			0
$205$	42.5298	−	73.6638i	0.207462	−	0.359335i
$206$	46.3481	−	26.7591i	0.224991	−	0.129898i
$207$		0			0
$208$	51.3296	+	29.6351i	0.246777	+	0.142477i
$209$			22.3285i			0.106835i
$210$		0			0
$211$	30.3818			0.143989			0.0719947	−	0.997405i	$-0.477064\pi$
$211$	30.3818			0.143989			0.0719947	+	0.997405i	$0.477064\pi$
$212$	20.8320	−	36.0821i	0.0982643	−	0.170199i
$213$		0			0
$214$	−58.7126	−	101.693i	−0.274358	−	0.475202i
$215$	123.117	+	71.0817i	0.572638	+	0.330613i
$216$		0			0
$217$	159.950	+	122.933i	0.737097	+	0.566512i
$218$	67.5886			0.310039
$219$		0			0
$220$	−4.48022	+	2.58666i	−0.0203646	+	0.0117575i
$221$	93.4808	+	161.914i	0.422990	+	0.732640i
$222$		0			0
$223$		−	16.7377i		−	0.0750569i	−0.999296	−	0.0375284i	$-0.988052\pi$
$223$		−	16.7377i		−	0.0750569i	0.999296	−	0.0375284i	$-0.0119485\pi$
$224$	24.1303	−	31.3963i	0.107725	−	0.140162i
$225$		0			0
$226$	11.4751	−	19.8755i	0.0507748	−	0.0879446i
$227$	366.738	−	211.736i	1.61558	−	0.932758i	0.627541	−	0.778583i	$-0.284061\pi$
$227$	366.738	−	211.736i	1.61558	−	0.932758i	0.988044	−	0.154175i	$-0.0492719\pi$
$228$		0			0
$229$	−350.596	−	202.417i	−1.53099	−	0.883916i	−0.999317	−	0.0369660i	$-0.988231\pi$
$229$	−350.596	−	202.417i	−1.53099	−	0.883916i	−0.531672	−	0.846951i	$-0.678436\pi$
$230$		−	76.8456i		−	0.334111i
$231$		0			0
$232$	138.701			0.597849
$233$	138.649	−	240.147i	0.595061	−	1.03068i	−0.398478	−	0.917178i	$-0.630461\pi$
$233$	138.649	−	240.147i	0.595061	−	1.03068i	0.993538	−	0.113497i	$-0.0362053\pi$
$234$		0			0
$235$	28.1663	+	48.7855i	0.119857	+	0.207598i
$236$	42.2838	+	24.4125i	0.179169	+	0.103443i
$237$		0			0
$238$	115.437	−	47.7097i	0.485029	−	0.200461i
$239$	−290.247			−1.21442			−0.607211	−	0.794541i	$-0.707712\pi$
$239$	−290.247			−1.21442			−0.607211	+	0.794541i	$0.707712\pi$
$240$		0			0
$241$	−350.574	+	202.404i	−1.45466	+	0.839850i	−0.998741	−	0.0501703i	$-0.984024\pi$
$241$	−350.574	+	202.404i	−1.45466	+	0.839850i	−0.455922	+	0.890020i	$0.650690\pi$
$242$	−84.6137	−	146.555i	−0.349643	−	0.605600i
$243$		0			0
$244$		−	12.7797i		−	0.0523757i
$245$	105.878	−	28.1924i	0.432156	−	0.115071i
$246$		0			0
$247$	143.005	−	247.693i	0.578970	−	1.00280i
$248$	70.5922	−	40.7564i	0.284646	−	0.164340i
$249$		0			0
$250$	−13.6931	−	7.90569i	−0.0547723	−	0.0316228i
$251$			155.805i			0.620739i	0.950616	+	0.310369i	$0.100453\pi$
$251$			155.805i			0.620739i	−0.950616	+	0.310369i	$0.899547\pi$
$252$		0			0
$253$	−28.1108			−0.111110
$254$	56.9676	−	98.6707i	0.224282	−	0.388467i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	22.4315	+	12.9508i	0.0872821	+	0.0503923i	0.543006	−	0.839729i	$-0.317286\pi$
$257$	22.4315	+	12.9508i	0.0872821	+	0.0503923i	−0.455724	+	0.890121i	$0.650619\pi$
$258$		0			0
$259$	−369.980	−	49.0033i	−1.42849	−	0.189202i
$260$	66.2662			0.254870
$261$		0			0
$262$	−152.708	+	88.1662i	−0.582856	+	0.336512i
$263$	−157.902	−	273.495i	−0.600389	−	1.03990i	−0.992762	−	0.120098i	$-0.961679\pi$
$263$	−157.902	−	273.495i	−0.600389	−	1.03990i	0.392373	−	0.919806i	$-0.371654\pi$
$264$		0			0
$265$		−	46.5818i		−	0.175781i
$266$	−151.504	−	116.442i	−0.569564	−	0.437751i
$267$		0			0
$268$	−124.490	+	215.623i	−0.464516	+	0.804565i
$269$	41.4157	−	23.9114i	0.153962	−	0.0888899i	−0.421040	−	0.907042i	$-0.638335\pi$
$269$	41.4157	−	23.9114i	0.153962	−	0.0888899i	0.575002	+	0.818152i	$0.305001\pi$
$270$		0			0
$271$	294.580	+	170.076i	1.08701	+	0.627587i	0.932779	−	0.360448i	$-0.117376\pi$
$271$	294.580	+	170.076i	1.08701	+	0.627587i	0.154233	+	0.988035i	$0.450709\pi$
$272$		−	50.4703i		−	0.185552i
$273$		0			0
$274$	−107.573			−0.392604
$275$	−2.89197	+	5.00904i	−0.0105163	+	0.0182147i
$276$		0			0
$277$	−105.293	−	182.374i	−0.380121	−	0.658388i	0.610959	−	0.791663i	$-0.290784\pi$
$277$	−105.293	−	182.374i	−0.380121	−	0.658388i	−0.991079	+	0.133274i	$0.957451\pi$
$278$	112.392	+	64.8898i	0.404289	+	0.233416i
$279$		0			0
$280$	5.81299	−	43.8886i	0.0207607	−	0.156745i
$281$	−471.785			−1.67895			−0.839476	−	0.543397i	$-0.817138\pi$
$281$	−471.785			−1.67895			−0.839476	+	0.543397i	$0.817138\pi$
$282$		0			0
$283$	405.534	−	234.135i	1.43298	−	0.827333i	0.435636	−	0.900123i	$-0.356524\pi$
$283$	405.534	−	234.135i	1.43298	−	0.827333i	0.997347	+	0.0727901i	$0.0231903\pi$
$284$	−118.973	−	206.067i	−0.418917	−	0.725586i
$285$		0			0
$286$		−	24.2407i		−	0.0847578i
$287$	246.089	−	101.708i	0.857453	−	0.354383i
$288$		0			0
$289$	−64.8985	+	112.408i	−0.224562	+	0.388953i
$290$	134.297	−	77.5362i	0.463092	−	0.267366i
$291$		0			0
$292$	68.4671	+	39.5295i	0.234476	+	0.135375i
$293$		−	63.5067i		−	0.216746i	−0.994110	−	0.108373i	$-0.965436\pi$
$293$		−	63.5067i		−	0.216746i	0.994110	−	0.108373i	$-0.0345642\pi$
$294$		0			0
$295$	54.5881			0.185044
$296$	−75.3999	+	130.597i	−0.254730	+	0.441204i
$297$		0			0
$298$	69.9441	+	121.147i	0.234712	+	0.406533i
$299$	311.836	+	180.039i	1.04293	+	0.602136i
$300$		0			0
$301$	169.988	+	411.298i	0.564745	+	1.36644i
$302$	−138.296			−0.457934
$303$		0			0
$304$	−66.8646	+	38.6043i	−0.219949	+	0.126988i
$305$	−7.14406	−	12.3739i	−0.0234231	−	0.0405701i
$306$		0			0
$307$			211.610i			0.689283i	0.938734	+	0.344642i	$0.112000\pi$
$307$			211.610i			0.689283i	−0.938734	+	0.344642i	$0.888000\pi$
$308$	−16.0548	−	2.12644i	−0.0521261	−	0.00690403i
$309$		0			0
$310$	45.5670	−	78.9244i	0.146990	−	0.254595i
$311$	−58.3090	+	33.6647i	−0.187489	+	0.108247i	−0.590806	−	0.806813i	$-0.701190\pi$
$311$	−58.3090	+	33.6647i	−0.187489	+	0.108247i	0.403318	+	0.915060i	$0.367857\pi$
$312$		0			0
$313$	−119.714	−	69.1168i	−0.382472	−	0.220821i	0.296421	−	0.955057i	$-0.404207\pi$
$313$	−119.714	−	69.1168i	−0.382472	−	0.220821i	−0.678893	+	0.734237i	$0.737540\pi$
$314$		−	188.660i		−	0.600827i
$315$		0			0
$316$	−185.742			−0.587792
$317$	9.91216	−	17.1684i	0.0312686	−	0.0541589i	−0.849968	−	0.526835i	$-0.823379\pi$
$317$	9.91216	−	17.1684i	0.0312686	−	0.0541589i	0.881236	+	0.472676i	$0.156712\pi$
$318$		0			0
$319$	−28.3634	−	49.1268i	−0.0889135	−	0.154003i
$320$	−15.4919	−	8.94427i	−0.0484123	−	0.0279508i
$321$		0			0
$322$	146.596	−	190.738i	0.455267	−	0.592355i
$323$	−243.546			−0.754013
$324$		0			0
$325$	64.1619	−	37.0439i	0.197421	−	0.113981i
$326$	−23.1572	−	40.1094i	−0.0710342	−	0.123035i
$327$		0			0
$328$		−	107.593i		−	0.328027i
$329$	−23.1550	+	174.822i	−0.0703799	+	0.531374i
$330$		0			0
$331$	131.139	−	227.139i	0.396189	−	0.686220i	−0.597063	−	0.802194i	$-0.703666\pi$
$331$	131.139	−	227.139i	0.396189	−	0.686220i	0.993252	+	0.115974i	$0.0369991\pi$
$332$	10.0401	−	5.79665i	0.0302412	−	0.0174598i
$333$		0			0
$334$	−210.238	−	121.381i	−0.629455	−	0.363416i
$335$			278.368i			0.830951i
$336$		0			0
$337$	578.125			1.71550			0.857752	−	0.514063i	$-0.171860\pi$
$337$	578.125			1.71550			0.857752	+	0.514063i	$0.171860\pi$
$338$	−35.7515	+	61.9235i	−0.105774	+	0.183206i
$339$		0			0
$340$	−28.2137	−	48.8676i	−0.0829816	−	0.143728i
$341$	−28.8712	−	16.6688i	−0.0846664	−	0.0488822i
$342$		0			0
$343$	316.582	+	132.004i	0.922978	+	0.384852i
$344$	179.824			0.522744
$345$		0			0
$346$	−247.962	+	143.161i	−0.716654	+	0.413760i
$347$	229.861	+	398.131i	0.662423	+	1.14735i	0.979977	+	0.199110i	$0.0638052\pi$
$347$	229.861	+	398.131i	0.662423	+	1.14735i	−0.317554	+	0.948240i	$0.602861\pi$
$348$		0			0
$349$			389.147i			1.11504i	0.830165	+	0.557518i	$0.188246\pi$
$349$			389.147i			1.11504i	−0.830165	+	0.557518i	$0.811754\pi$
$350$	−18.9061	−	45.7445i	−0.0540173	−	0.130699i
$351$		0			0
$352$	−3.27189	+	5.66708i	−0.00929515	+	0.0160997i
$353$	−559.415	+	322.978i	−1.58475	+	0.914953i	−0.590593	+	0.806970i	$0.701106\pi$
$353$	−559.415	+	322.978i	−1.58475	+	0.914953i	−0.994153	+	0.107983i	$0.965561\pi$
$354$		0			0
$355$	−230.389	−	133.015i	−0.648984	−	0.374691i
$356$			303.968i			0.853842i
$357$		0			0
$358$	−111.287			−0.310858
$359$	−33.0206	+	57.1934i	−0.0919794	+	0.159313i	−0.908344	−	0.418224i	$-0.862653\pi$
$359$	−33.0206	+	57.1934i	−0.0919794	+	0.159313i	0.816365	+	0.577537i	$0.195986\pi$
$360$		0			0
$361$	5.78661	+	10.0227i	0.0160294	+	0.0277637i
$362$	71.2200	+	41.1189i	0.196740	+	0.113588i
$363$		0			0
$364$	164.479	+	126.414i	0.451866	+	0.347291i
$365$	88.3907			0.242166
$366$		0			0
$367$	519.556	−	299.966i	1.41568	−	0.817346i	0.419768	−	0.907631i	$-0.362111\pi$
$367$	519.556	−	299.966i	1.41568	−	0.817346i	0.995916	+	0.0902858i	$0.0287781\pi$
$368$	−48.6014	−	84.1802i	−0.132069	−	0.228750i
$369$		0			0
$370$			168.599i			0.455674i
$371$	88.8627	−	115.621i	0.239522	−	0.311646i
$372$		0			0
$373$	−202.376	+	350.526i	−0.542564	+	0.939748i	0.456192	+	0.889881i	$0.349213\pi$
$373$	−202.376	+	350.526i	−0.542564	+	0.939748i	−0.998756	+	0.0498667i	$0.984120\pi$
$374$	−17.8762	+	10.3208i	−0.0477973	+	0.0275958i
$375$		0			0
$376$	61.7093	+	35.6279i	0.164120	+	0.0947550i
$377$			726.627i			1.92739i
$378$		0			0
$379$	−239.675			−0.632388			−0.316194	−	0.948695i	$-0.602405\pi$
$379$	−239.675			−0.632388			−0.316194	+	0.948695i	$0.602405\pi$
$380$	−43.1609	+	74.7569i	−0.113581	+	0.196729i
$381$		0			0
$382$	−260.504	−	451.206i	−0.681947	−	1.18117i
$383$	−553.486	−	319.555i	−1.44513	−	0.834347i	−0.446947	−	0.894561i	$-0.647489\pi$
$383$	−553.486	−	319.555i	−1.44513	−	0.834347i	−0.998186	+	0.0602133i	$0.980822\pi$
$384$		0			0
$385$	−16.7337	+	6.91600i	−0.0434642	+	0.0179636i
$386$	−397.138			−1.02885
$387$		0			0
$388$	249.952	−	144.310i	0.644205	−	0.371932i
$389$	260.797	+	451.714i	0.670429	+	1.16122i	0.977782	+	0.209622i	$0.0672234\pi$
$389$	260.797	+	451.714i	0.670429	+	1.16122i	−0.307353	+	0.951596i	$0.599443\pi$
$390$		0			0
$391$		−	306.616i		−	0.784184i
$392$	98.1533	−	97.8465i	0.250391	−	0.249608i
$393$		0			0
$394$	−5.38659	+	9.32985i	−0.0136716	+	0.0236798i
$395$	−179.844	+	103.833i	−0.455302	+	0.262869i
$396$		0			0
$397$	125.712	+	72.5800i	0.316656	+	0.182821i	0.649901	−	0.760019i	$-0.274810\pi$
$397$	125.712	+	72.5800i	0.316656	+	0.182821i	−0.333245	+	0.942840i	$0.608144\pi$
$398$			285.439i			0.717182i
$399$		0			0
$400$	−20.0000			−0.0500000
$401$	107.021	−	185.366i	0.266886	−	0.462260i	−0.701170	−	0.712994i	$-0.747339\pi$
$401$	107.021	−	185.366i	0.266886	−	0.462260i	0.968056	+	0.250734i	$0.0806719\pi$
$402$		0			0
$403$	213.515	+	369.818i	0.529813	+	0.917663i
$404$	−67.6960	−	39.0843i	−0.167564	−	0.0967434i
$405$		0			0
$406$	481.250	+	63.7410i	1.18535	+	0.156998i
$407$	61.6751			0.151536
$408$		0			0
$409$	−479.754	+	276.986i	−1.17299	+	0.677228i	−0.954383	−	0.298585i	$-0.903486\pi$
$409$	−479.754	+	276.986i	−1.17299	+	0.677228i	−0.218610	+	0.975812i	$0.570152\pi$
$410$	−60.1462	−	104.176i	−0.146698	−	0.254089i
$411$		0			0
$412$		−	75.6861i		−	0.183704i
$413$	135.493	+	104.136i	0.328070	+	0.252145i
$414$		0			0
$415$	6.48085	−	11.2252i	0.0156165	−	0.0270486i
$416$	72.5910	−	41.9104i	0.174497	−	0.100746i
$417$		0			0
$418$	27.3467	+	15.7886i	0.0654228	+	0.0377719i
$419$			268.003i			0.639626i	0.947481	+	0.319813i	$0.103620\pi$
$419$			268.003i			0.639626i	−0.947481	+	0.319813i	$0.896380\pi$
$420$		0			0
$421$	−9.12915			−0.0216844			−0.0108422	−	0.999941i	$-0.503451\pi$
$421$	−9.12915			−0.0216844			−0.0108422	+	0.999941i	$0.503451\pi$
$422$	21.4831	−	37.2099i	0.0509079	−	0.0881751i
$423$		0			0
$424$	−29.4609	−	51.0278i	−0.0694833	−	0.120349i
$425$	−54.6357	−	31.5439i	−0.128554	−	0.0742210i
$426$		0			0
$427$	5.87299	−	44.3416i	0.0137541	−	0.103845i
$428$	−166.064			−0.388000
$429$		0			0
$430$	174.114	−	100.525i	0.404916	−	0.233778i
$431$	−134.221	−	232.478i	−0.311419	−	0.539393i	0.667251	−	0.744833i	$-0.267471\pi$
$431$	−134.221	−	232.478i	−0.311419	−	0.539393i	−0.978670	+	0.205440i	$0.934137\pi$
$432$		0			0
$433$			472.254i			1.09066i	0.838223	+	0.545328i	$0.183595\pi$
$433$			472.254i			1.09066i	−0.838223	+	0.545328i	$0.816405\pi$
$434$	263.663	−	108.971i	0.607519	−	0.251086i
$435$		0			0
$436$	47.7924	−	82.7788i	0.109616	−	0.189860i
$437$	−406.215	+	234.528i	−0.929553	+	0.536678i
$438$		0			0
$439$	475.788	+	274.696i	1.08380	+	0.625731i	0.931919	−	0.362667i	$-0.118134\pi$
$439$	475.788	+	274.696i	1.08380	+	0.625731i	0.151880	+	0.988399i	$0.451467\pi$
$440$			7.31617i			0.0166277i
$441$		0			0
$442$	264.404			0.598198
$443$	235.405	−	407.734i	0.531388	−	0.920392i	−0.467940	−	0.883760i	$-0.655004\pi$
$443$	235.405	−	407.734i	0.531388	−	0.920392i	0.999329	−	0.0366317i	$-0.0116628\pi$
$444$		0			0
$445$	169.923	+	294.315i	0.381850	+	0.661383i
$446$	−20.4994	−	11.8353i	−0.0459628	−	0.0265366i
$447$		0			0
$448$	−21.3898	−	51.7540i	−0.0477450	−	0.115522i
$449$	−559.525			−1.24616			−0.623079	−	0.782159i	$-0.714118\pi$
$449$	−559.525			−1.24616			−0.623079	+	0.782159i	$0.714118\pi$
$450$		0			0
$451$	−38.1086	+	22.0020i	−0.0844980	+	0.0487849i
$452$	−16.2283	−	28.1082i	−0.0359032	−	0.0621862i
$453$		0			0
$454$		−	598.880i		−	1.31912i
$455$	229.924	+	30.4531i	0.505327	+	0.0669299i
$456$		0			0
$457$	−313.689	+	543.325i	−0.686409	+	1.18890i	0.286583	+	0.958055i	$0.407481\pi$
$457$	−313.689	+	543.325i	−0.686409	+	1.18890i	−0.972992	+	0.230840i	$0.925853\pi$
$458$	−495.818	+	286.261i	−1.08257	+	0.625023i
$459$		0			0
$460$	−94.1163	−	54.3381i	−0.204601	−	0.118126i
$461$			223.659i			0.485160i	0.970131	+	0.242580i	$0.0779936\pi$
$461$			223.659i			0.485160i	−0.970131	+	0.242580i	$0.922006\pi$
$462$		0			0
$463$	−397.204			−0.857893			−0.428946	−	0.903330i	$-0.641115\pi$
$463$	−397.204			−0.857893			−0.428946	+	0.903330i	$0.641115\pi$
$464$	98.0764	−	169.873i	0.211371	−	0.366106i
$465$		0			0
$466$	−196.079	−	339.620i	−0.420771	−	0.728797i
$467$	289.014	+	166.862i	0.618874	+	0.357307i	0.776430	−	0.630203i	$-0.217028\pi$
$467$	289.014	+	166.862i	0.618874	+	0.357307i	−0.157557	+	0.987510i	$0.550362\pi$
$468$		0			0
$469$	−531.035	+	690.937i	−1.13227	+	1.47321i
$470$	79.6663			0.169503
$471$		0			0
$472$	59.7983	−	34.5246i	0.126691	−	0.0731452i
$473$	−36.7728	−	63.6924i	−0.0777438	−	0.134656i
$474$		0			0
$475$			96.5108i			0.203181i
$476$	23.1940	−	175.117i	0.0487268	−	0.367892i
$477$		0			0
$478$	−205.235	+	355.478i	−0.429363	+	0.743678i
$479$	−527.265	+	304.417i	−1.10076	+	0.635526i	−0.936421	−	0.350878i	$-0.885883\pi$
$479$	−527.265	+	304.417i	−1.10076	+	0.635526i	−0.164341	+	0.986404i	$0.552550\pi$
$480$		0			0
$481$	−684.169	−	395.005i	−1.42239	−	0.821217i
$482$			572.484i			1.18773i
$483$		0			0
$484$	−239.324			−0.494470
$485$	161.343	−	279.454i	0.332666	−	0.576195i
$486$		0			0
$487$	159.238	+	275.809i	0.326978	+	0.566343i	0.981911	−	0.189344i	$-0.0606363\pi$
$487$	159.238	+	275.809i	0.326978	+	0.566343i	−0.654932	+	0.755687i	$0.727303\pi$
$488$	−15.6518	−	9.03659i	−0.0320734	−	0.0185176i
$489$		0			0
$490$	40.3387	−	149.609i	0.0823238	−	0.305324i
$491$	−523.303			−1.06579			−0.532895	−	0.846181i	$-0.678896\pi$
$491$	−523.303			−1.06579			−0.532895	+	0.846181i	$0.678896\pi$
$492$		0			0
$493$	535.847	−	309.371i	1.08691	−	0.627528i
$494$	−202.240	−	350.290i	−0.409393	−	0.709090i
$495$		0			0
$496$		−	115.277i		−	0.232412i
$497$	−318.100	−	769.663i	−0.640039	−	1.54862i
$498$		0			0
$499$	391.909	−	678.806i	0.785388	−	1.36033i	−0.143379	−	0.989668i	$-0.545797\pi$
$499$	391.909	−	678.806i	0.785388	−	1.36033i	0.928767	−	0.370664i	$-0.120870\pi$
$500$	−19.3649	+	11.1803i	−0.0387298	+	0.0223607i
$501$		0			0
$502$	190.822	+	110.171i	0.380123	+	0.219464i
$503$		−	58.0772i		−	0.115462i	−0.998332	−	0.0577308i	$-0.981613\pi$
$503$		−	58.0772i		−	0.115462i	0.998332	−	0.0577308i	$-0.0183865\pi$
$504$		0			0
$505$	−87.3952			−0.173060
$506$	−19.8773	+	34.4286i	−0.0392833	+	0.0680406i
$507$		0			0
$508$	−80.5643	−	139.541i	−0.158591	−	0.274688i
$509$	811.110	+	468.295i	1.59354	+	0.920029i	0.992694	+	0.120662i	$0.0385017\pi$
$509$	811.110	+	468.295i	1.59354	+	0.920029i	0.600843	+	0.799367i	$0.294832\pi$
$510$		0			0
$511$	219.394	+	168.620i	0.429343	+	0.329981i
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	31.7229	−	18.3152i	0.0617178	−	0.0356328i
$515$	−42.3098	−	73.2827i	−0.0821549	−	0.142297i
$516$		0			0
$517$		−	29.1426i		−	0.0563687i
$518$	−321.632	+	418.480i	−0.620910	+	0.807876i
$519$		0			0
$520$	46.8573	−	81.1592i	0.0901101	−	0.156075i
$521$	607.133	−	350.528i	1.16532	−	0.672799i	0.212749	−	0.977107i	$-0.431758\pi$
$521$	607.133	−	350.528i	1.16532	−	0.672799i	0.952574	+	0.304308i	$0.0984251\pi$
$522$		0			0
$523$	−594.464	−	343.214i	−1.13664	−	0.656241i	−0.191046	−	0.981581i	$-0.561188\pi$
$523$	−594.464	−	343.214i	−1.13664	−	0.656241i	−0.945597	+	0.325340i	$0.894521\pi$
$524$			249.372i			0.475900i
$525$		0			0
$526$	−446.615			−0.849078
$527$	181.814	−	314.910i	0.344997	−	0.597553i
$528$		0			0
$529$	−30.7626	−	53.2824i	−0.0581524	−	0.100723i
$530$	−57.0509	−	32.9383i	−0.107643	−	0.0621478i
$531$		0			0
$532$	−249.741	+	103.217i	−0.469438	+	0.194017i
$533$	563.657			1.05752
$534$		0			0
$535$	−160.791	+	92.8327i	−0.300544	+	0.173519i
$536$	176.056	+	304.937i	0.328462	+	0.568913i
$537$		0			0
$538$		−	67.6316i		−	0.125709i
$539$	−54.7282	−	14.7562i	−0.101537	−	0.0273770i
$540$		0			0
$541$	−398.250	+	689.789i	−0.736136	+	1.27503i	0.218087	+	0.975929i	$0.430018\pi$
$541$	−398.250	+	689.789i	−0.736136	+	1.27503i	−0.954223	+	0.299096i	$0.903315\pi$
$542$	416.599	−	240.524i	0.768634	−	0.443771i
$543$		0			0
$544$	−61.8132	−	35.6879i	−0.113627	−	0.0656027i
$545$		−	106.867i		−	0.196086i
$546$		0			0
$547$	−395.055			−0.722221			−0.361111	−	0.932523i	$-0.617602\pi$
$547$	−395.055			−0.722221			−0.361111	+	0.932523i	$0.617602\pi$
$548$	−76.0659	+	131.750i	−0.138806	+	0.240420i
$549$		0			0
$550$	4.08986	+	7.08385i	0.00743612	+	0.0128797i
$551$	−819.730	−	473.271i	−1.48771	−	0.858932i
$552$		0			0
$553$	−644.470	−	85.3592i	−1.16541	−	0.154357i
$554$	−297.815			−0.537572
$555$		0			0
$556$	158.947	−	91.7680i	0.285876	−	0.165050i
$557$	−20.8443	−	36.1034i	−0.0374224	−	0.0648175i	0.846708	−	0.532059i	$-0.178581\pi$
$557$	−20.8443	−	36.1034i	−0.0374224	−	0.0648175i	−0.884130	+	0.467241i	$0.845248\pi$
$558$		0			0
$559$			942.063i			1.68526i
$560$	−49.6419	−	38.1534i	−0.0886463	−	0.0681310i
$561$		0			0
$562$	−333.603	+	577.817i	−0.593599	+	1.02814i
$563$	640.642	−	369.875i	1.13791	−	0.656972i	0.191996	−	0.981396i	$-0.438504\pi$
$563$	640.642	−	369.875i	1.13791	−	0.656972i	0.945912	+	0.324424i	$0.105170\pi$
$564$		0			0
$565$	−31.4259	−	18.1437i	−0.0556210	−	0.0321128i
$566$		−	662.234i		−	1.17003i
$567$		0			0
$568$	−336.505			−0.592439
$569$	2.38030	−	4.12281i	0.00418331	−	0.00724570i	−0.863926	−	0.503618i	$-0.832002\pi$
$569$	2.38030	−	4.12281i	0.00418331	−	0.00724570i	0.868109	+	0.496373i	$0.165335\pi$
$570$		0			0
$571$	−399.848	−	692.557i	−0.700260	−	1.21289i	−0.968375	−	0.249498i	$-0.919734\pi$
$571$	−399.848	−	692.557i	−0.700260	−	1.21289i	0.268116	−	0.963387i	$-0.413599\pi$
$572$	−29.6887	−	17.1408i	−0.0519033	−	0.0299664i
$573$		0			0
$574$	49.4451	−	373.315i	0.0861412	−	0.650374i
$575$	−121.504			−0.211311
$576$		0			0
$577$	−148.871	+	85.9510i	−0.258009	+	0.148962i	−0.623426	−	0.781882i	$-0.714260\pi$
$577$	−148.871	+	85.9510i	−0.258009	+	0.148962i	0.365417	+	0.930844i	$0.380926\pi$
$578$	91.7804	+	158.968i	0.158790	+	0.275032i
$579$		0			0
$580$		−	219.305i		−	0.378113i
$581$	37.5000	−	15.4986i	0.0645439	−	0.0266758i
$582$		0			0
$583$	−12.0491	+	20.8697i	−0.0206675	+	0.0357971i
$584$	96.8271	−	55.9032i	0.165800	−	0.0957246i
$585$		0			0
$586$	−77.7795	−	44.9060i	−0.132730	−	0.0766314i
$587$			724.352i			1.23399i	0.786967	+	0.616994i	$0.211650\pi$
$587$			724.352i			1.23399i	−0.786967	+	0.616994i	$0.788350\pi$
$588$		0			0
$589$	−556.271			−0.944433
$590$	38.5996	−	66.8565i	0.0654231	−	0.113316i
$591$		0			0
$592$	106.632	+	184.691i	0.180121	+	0.311979i
$593$	894.293	+	516.320i	1.50808	+	0.870692i	0.999956	+	0.00940925i	$0.00299510\pi$
$593$	894.293	+	516.320i	1.50808	+	0.870692i	0.508127	+	0.861282i	$0.330338\pi$
$594$		0			0
$595$	−75.4357	−	182.522i	−0.126783	−	0.306759i
$596$	197.832			0.331933
$597$		0			0
$598$	441.003	−	254.613i	0.737464	−	0.425775i
$599$	−212.436	−	367.949i	−0.354650	−	0.614272i	0.632408	−	0.774636i	$-0.282067\pi$
$599$	−212.436	−	367.949i	−0.354650	−	0.614272i	−0.987058	+	0.160363i	$0.948733\pi$
$600$		0			0
$601$		−	749.418i		−	1.24695i	−0.781843	−	0.623476i	$-0.785720\pi$
$601$		−	749.418i		−	1.24695i	0.781843	−	0.623476i	$-0.214280\pi$
$602$	623.935	+	82.6395i	1.03644	+	0.137275i
$603$		0			0
$604$	−97.7900	+	169.377i	−0.161904	+	0.280426i
$605$	−231.724	+	133.786i	−0.383015	+	0.221134i
$606$		0			0
$607$	−205.133	−	118.434i	−0.337945	−	0.195113i	0.321418	−	0.946938i	$-0.395841\pi$
$607$	−205.133	−	118.434i	−0.337945	−	0.195113i	−0.659363	+	0.751825i	$0.729174\pi$
$608$			109.189i			0.179588i
$609$		0			0
$610$	−20.2064			−0.0331253
$611$	−186.647	+	323.283i	−0.305478	+	0.529104i
$612$		0			0
$613$	469.189	+	812.659i	0.765398	+	1.32571i	0.940036	+	0.341075i	$0.110791\pi$
$613$	469.189	+	812.659i	0.765398	+	1.32571i	−0.174638	+	0.984633i	$0.555876\pi$
$614$	259.168	+	149.631i	0.422098	+	0.243698i
$615$		0			0
$616$	−13.9568	+	18.1594i	−0.0226572	+	0.0294796i
$617$	−225.176			−0.364952			−0.182476	−	0.983210i	$-0.558411\pi$
$617$	−225.176			−0.364952			−0.182476	+	0.983210i	$0.558411\pi$
$618$		0			0
$619$	916.115	−	528.919i	1.47999	−	0.854473i	0.480248	−	0.877133i	$-0.340547\pi$
$619$	916.115	−	528.919i	1.47999	−	0.854473i	0.999743	+	0.0226591i	$0.00721323\pi$
$620$	−64.4415	−	111.616i	−0.103938	−	0.180026i
$621$		0			0
$622$			95.2182i			0.153084i
$623$	−139.691	+	1054.68i	−0.224222	+	1.69290i
$624$		0			0
$625$	−12.5000	+	21.6506i	−0.0200000	+	0.0346410i
$626$	−169.301	+	97.7460i	−0.270449	+	0.156144i
$627$		0			0
$628$	−231.060	−	133.403i	−0.367930	−	0.212424i
$629$			672.716i			1.06950i
$630$		0			0
$631$	877.283			1.39031			0.695153	−	0.718862i	$-0.255336\pi$
$631$	877.283			1.39031			0.695153	+	0.718862i	$0.255336\pi$
$632$	−131.340	+	227.487i	−0.207816	+	0.359948i
$633$		0			0
$634$	−14.0179	−	24.2797i	−0.0221103	−	0.0382961i
$635$	−156.012	−	90.0736i	−0.245688	−	0.141848i
$636$		0			0
$637$	512.598	+	514.205i	0.804707	+	0.807230i
$638$	−80.2238			−0.125743
$639$		0			0
$640$	−21.9089	+	12.6491i	−0.0342327	+	0.0197642i
$641$	26.8684	+	46.5374i	0.0419163	+	0.0726012i	0.886222	−	0.463260i	$-0.153320\pi$
$641$	26.8684	+	46.5374i	0.0419163	+	0.0726012i	−0.844306	+	0.535861i	$0.819987\pi$
$642$		0			0
$643$		−	99.7799i		−	0.155179i	−0.996985	−	0.0775893i	$-0.975278\pi$
$643$		−	99.7799i		−	0.155179i	0.996985	−	0.0775893i	$-0.0247223\pi$
$644$	−129.947	−	314.415i	−0.201781	−	0.488222i
$645$		0			0
$646$	−172.213	+	298.282i	−0.266584	+	0.461737i
$647$	657.905	−	379.842i	1.01685	−	0.587081i	0.103663	−	0.994612i	$-0.466944\pi$
$647$	657.905	−	379.842i	1.01685	−	0.587081i	0.913191	+	0.407531i	$0.133610\pi$
$648$		0			0
$649$	−24.4567	−	14.1201i	−0.0376836	−	0.0217567i
$650$		−	104.776i		−	0.161194i
$651$		0			0
$652$	−65.4983			−0.100458
$653$	574.896	−	995.749i	0.880392	−	1.52488i	0.0294854	−	0.999565i	$-0.490613\pi$
$653$	574.896	−	995.749i	0.880392	−	1.52488i	0.850906	−	0.525318i	$-0.176054\pi$
$654$		0			0
$655$	139.403	+	241.453i	0.212829	+	0.368631i
$656$	−131.774	−	76.0796i	−0.200875	−	0.115975i
$657$		0			0
$658$	197.740	+	151.977i	0.300516	+	0.230968i
$659$	−213.700			−0.324280			−0.162140	−	0.986768i	$-0.551840\pi$
$659$	−213.700			−0.324280			−0.162140	+	0.986768i	$0.551840\pi$
$660$		0			0
$661$	665.936	−	384.479i	1.00747	−	0.581662i	0.0970187	−	0.995283i	$-0.469069\pi$
$661$	665.936	−	384.479i	1.00747	−	0.581662i	0.910449	+	0.413621i	$0.135736\pi$
$662$	−185.458	−	321.223i	−0.280148	−	0.485231i
$663$		0			0
$664$		−	16.3954i		−	0.0246919i
$665$	−184.111	+	239.549i	−0.276858	+	0.360224i
$666$		0			0
$667$	595.832	−	1032.01i	0.893301	−	1.54724i
$668$	−297.322	+	171.659i	−0.445092	+	0.256974i
$669$		0			0
$670$	340.930	+	196.836i	0.508851	+	0.293785i
$671$			7.39169i			0.0110159i
$672$		0			0
$673$	−1299.78			−1.93133			−0.965664	−	0.259796i	$-0.916345\pi$
$673$	−1299.78			−1.93133			−0.965664	+	0.259796i	$0.916345\pi$
$674$	408.796	−	708.056i	0.606523	−	1.05053i
$675$		0			0
$676$	50.5603	+	87.5730i	0.0747933	+	0.129546i
$677$	−1073.60	−	619.840i	−1.58581	−	0.915569i	−0.993986	−	0.109504i	$-0.965074\pi$
$677$	−1073.60	−	619.840i	−1.58581	−	0.915569i	−0.591826	−	0.806066i	$-0.701593\pi$
$678$		0			0
$679$	933.575	−	385.844i	1.37493	−	0.568253i
$680$	−79.8005			−0.117354
$681$		0			0
$682$	−40.8301	+	23.5733i	−0.0598682	+	0.0345649i
$683$	−233.043	−	403.643i	−0.341205	−	0.590985i	0.643452	−	0.765487i	$-0.277502\pi$
$683$	−233.043	−	403.643i	−0.341205	−	0.590985i	−0.984657	+	0.174502i	$0.944168\pi$
$684$		0			0
$685$			170.089i			0.248304i
$686$	385.528	−	294.391i	0.561995	−	0.429141i
$687$		0			0
$688$	127.155	−	220.239i	0.184818	−	0.320114i
$689$	267.325	−	154.340i	0.387989	−	0.224006i
$690$		0			0
$691$	−93.9272	−	54.2289i	−0.135929	−	0.0784788i	0.430493	−	0.902594i	$-0.358340\pi$
$691$	−93.9272	−	54.2289i	−0.135929	−	0.0784788i	−0.566423	+	0.824115i	$0.691673\pi$
$692$			404.921i			0.585145i
$693$		0			0
$694$	650.145			0.936808
$695$	102.600	−	177.708i	0.147626	−	0.255695i
$696$		0			0
$697$	−239.985	−	415.666i	−0.344311	−	0.596364i
$698$	476.606	+	275.169i	0.682817	+	0.394224i
$699$		0			0
$700$	−69.3940	−	9.19115i	−0.0991342	−	0.0131302i
$701$	−528.400			−0.753780			−0.376890	−	0.926258i	$-0.623007\pi$
$701$	−528.400			−0.753780			−0.376890	+	0.926258i	$0.623007\pi$
$702$		0			0
$703$	891.235	−	514.555i	1.26776	−	0.731942i
$704$	4.62715	+	8.01446i	0.00657266	+	0.0113842i
$705$		0			0
$706$			913.521i			1.29394i
$707$	−216.923	−	166.721i	−0.306822	−	0.235815i
$708$		0			0
$709$	466.779	−	808.484i	0.658362	−	1.14032i	−0.322678	−	0.946509i	$-0.604583\pi$
$709$	466.779	−	808.484i	0.658362	−	1.14032i	0.981040	−	0.193808i	$-0.0620837\pi$
$710$	−325.820	+	188.112i	−0.458901	+	0.264947i
$711$		0			0
$712$	372.283	+	214.938i	0.522869	+	0.301879i
$713$		−	700.326i		−	0.982224i
$714$		0			0
$715$	−38.3280			−0.0536055
$716$	−78.6918	+	136.298i	−0.109905	+	0.190361i
$717$		0			0
$718$	46.6982	+	80.8836i	0.0650392	+	0.112651i
$719$	−557.452	−	321.845i	−0.775316	−	0.447629i	0.0594517	−	0.998231i	$-0.481065\pi$
$719$	−557.452	−	321.845i	−0.775316	−	0.447629i	−0.834768	+	0.550602i	$0.814398\pi$
$720$		0			0
$721$	34.7821	−	262.608i	0.0482414	−	0.364227i
$722$	16.3670			0.0226690
$723$		0			0
$724$	100.720	−	58.1509i	0.139116	−	0.0803189i
$725$	−122.595	−	212.342i	−0.169097	−	0.292885i
$726$		0			0
$727$			317.353i			0.436524i	0.975890	+	0.218262i	$0.0700388\pi$
$727$			317.353i			0.436524i	−0.975890	+	0.218262i	$0.929961\pi$
$728$	271.129	−	112.057i	0.372430	−	0.153924i
$729$		0			0
$730$	62.5016	−	108.256i	0.0856187	−	0.148296i
$731$	694.719	−	401.096i	0.950368	−	0.548695i
$732$		0			0
$733$	−727.023	−	419.747i	−0.991846	−	0.572643i	−0.0860205	−	0.996293i	$-0.527415\pi$
$733$	−727.023	−	419.747i	−0.991846	−	0.572643i	−0.905826	+	0.423651i	$0.860748\pi$
$734$		−	848.431i		−	1.15590i
$735$		0			0
$736$	−137.466			−0.186774
$737$	72.0044	−	124.715i	0.0976993	−	0.169220i
$738$		0			0
$739$	459.403	+	795.709i	0.621654	+	1.07674i	0.989178	+	0.146723i	$0.0468725\pi$
$739$	459.403	+	795.709i	0.621654	+	1.07674i	−0.367523	+	0.930014i	$0.619794\pi$
$740$	206.491	+	119.218i	0.279042	+	0.161105i
$741$		0			0
$742$	−78.7703	−	190.590i	−0.106160	−	0.256860i
$743$	1034.18			1.39190			0.695952	−	0.718088i	$-0.254983\pi$
$743$	1034.18			1.39190			0.695952	+	0.718088i	$0.254983\pi$
$744$		0			0
$745$	191.550	−	110.591i	0.257114	−	0.148445i
$746$	286.203	+	495.719i	0.383651	+	0.664502i
$747$		0			0
$748$			29.1917i			0.0390263i
$749$	−576.193	−	76.3160i	−0.769283	−	0.101891i
$750$		0			0
$751$	340.948	−	590.540i	0.453992	−	0.786338i	−0.544637	−	0.838672i	$-0.683333\pi$
$751$	340.948	−	590.540i	0.453992	−	0.786338i	0.998630	+	0.0523339i	$0.0166660\pi$
$752$	87.2701	−	50.3854i	0.116051	−	0.0670019i
$753$		0			0
$754$	889.932	+	513.803i	1.18028	+	0.681436i
$755$			218.665i			0.289623i
$756$		0			0
$757$	183.172			0.241971			0.120985	−	0.992654i	$-0.461395\pi$
$757$	183.172			0.241971			0.120985	+	0.992654i	$0.461395\pi$
$758$	−169.476	+	293.541i	−0.223583	+	0.387257i
$759$		0			0
$760$	61.0388	+	105.722i	0.0803142	+	0.139108i
$761$	673.743	+	388.985i	0.885338	+	0.511150i	0.872415	−	0.488766i	$-0.162553\pi$
$761$	673.743	+	388.985i	0.885338	+	0.511150i	0.0129235	+	0.999916i	$0.495886\pi$
$762$		0			0
$763$	203.867	−	265.254i	0.267191	−	0.347646i
$764$	−736.816			−0.964419
$765$		0			0
$766$	−782.747	+	451.919i	−1.02186	+	0.589973i
$767$	180.867	+	313.271i	0.235811	+	0.408437i
$768$		0			0
$769$		−	302.546i		−	0.393428i	−0.980461	−	0.196714i	$-0.936973\pi$
$769$		−	302.546i		−	0.393428i	0.980461	−	0.196714i	$-0.0630271\pi$
$770$	−3.36220	+	25.3849i	−0.00436649	+	0.0329674i
$771$		0			0
$772$	−280.819	+	486.393i	−0.363755	+	0.630042i
$773$	110.995	−	64.0833i	0.143591	−	0.0829020i	−0.426484	−	0.904495i	$-0.640248\pi$
$773$	110.995	−	64.0833i	0.143591	−	0.0829020i	0.570074	+	0.821593i	$0.306914\pi$
$774$		0			0
$775$	−124.790	−	72.0478i	−0.161020	−	0.0929649i
$776$		−	408.169i		−	0.525991i
$777$		0			0
$778$	737.645			0.948130
$779$	−367.125	+	635.879i	−0.471277	+	0.816277i
$780$		0			0
$781$	68.8130	+	119.188i	0.0881089	+	0.152609i
$782$	−375.526	−	216.810i	−0.480213	−	0.277251i
$783$		0			0
$784$	−50.4321	−	189.401i	−0.0643267	−	0.241582i
$785$	−298.297			−0.379996
$786$		0			0
$787$	−466.311	+	269.225i	−0.592518	+	0.342090i	−0.766092	−	0.642731i	$-0.777801\pi$
$787$	−466.311	+	269.225i	−0.592518	+	0.342090i	0.173575	+	0.984821i	$0.444468\pi$
$788$	7.61779	+	13.1944i	0.00966725	+	0.0167442i
$789$		0			0
$790$			293.684i			0.371752i
$791$	−43.3898	−	104.985i	−0.0548544	−	0.132724i
$792$		0			0
$793$	47.3409	−	81.9969i	0.0596985	−	0.103401i
$794$	177.784	−	102.644i	0.223909	−	0.129274i
$795$		0			0
$796$	349.589	+	201.836i	0.439183	+	0.253562i
$797$		−	207.481i		−	0.260328i	−0.991492	−	0.130164i	$-0.958450\pi$
$797$		−	207.481i		−	0.260328i	0.991492	−	0.130164i	$-0.0415504\pi$
$798$		0			0
$799$	317.871			0.397836
$800$	−14.1421	+	24.4949i	−0.0176777	+	0.0306186i
$801$		0			0
$802$	−151.351	−	262.148i	−0.188717	−	0.326867i
$803$	−39.6010	−	22.8636i	−0.0493163	−	0.0284728i
$804$		0			0
$805$	−301.584	−	231.789i	−0.374638	−	0.287936i
$806$	603.911			0.749269
$807$		0			0
$808$	−95.7366	+	55.2736i	−0.118486	+	0.0684079i
$809$	722.858	+	1252.03i	0.893520	+	1.54762i	0.835625	+	0.549300i	$0.185106\pi$
$809$	722.858	+	1252.03i	0.893520	+	1.54762i	0.0578954	+	0.998323i	$0.481561\pi$
$810$		0			0
$811$		−	207.868i		−	0.256310i	−0.991754	−	0.128155i	$-0.959094\pi$
$811$		−	207.868i		−	0.256310i	0.991754	−	0.128155i	$-0.0409055\pi$
$812$	418.362	−	544.337i	0.515224	−	0.670366i
$813$		0			0
$814$	43.6109	−	75.5363i	0.0535760	−	0.0927964i
$815$	−63.4185	+	36.6147i	−0.0778141	+	0.0449260i
$816$		0			0
$817$	−1062.77	−	613.591i	−1.30082	−	0.751029i
$818$			783.435i			0.957745i
$819$		0			0
$820$	−170.119			−0.207462
$821$	307.642	−	532.851i	0.374716	−	0.649027i	−0.615568	−	0.788083i	$-0.711074\pi$
$821$	307.642	−	532.851i	0.374716	−	0.649027i	0.990285	+	0.139056i	$0.0444068\pi$
$822$		0			0
$823$	167.804	+	290.645i	0.203893	+	0.353153i	0.949779	−	0.312920i	$-0.101307\pi$
$823$	167.804	+	290.645i	0.203893	+	0.353153i	−0.745886	+	0.666073i	$0.767974\pi$
$824$	−92.6961	−	53.5181i	−0.112495	−	0.0649492i
$825$		0			0
$826$	223.348	−	92.3091i	0.270397	−	0.111754i
$827$	1453.38			1.75741			0.878707	−	0.477362i	$-0.158407\pi$
$827$	1453.38			1.75741			0.878707	+	0.477362i	$0.158407\pi$
$828$		0			0
$829$	−11.2468	+	6.49333i	−0.0135667	+	0.00783273i	−0.506768	−	0.862082i	$-0.669160\pi$
$829$	−11.2468	+	6.49333i	−0.0135667	+	0.00783273i	0.493201	+	0.869915i	$0.335827\pi$
$830$	−9.16531	−	15.8748i	−0.0110425	−	0.0191262i
$831$		0			0
$832$		−	118.541i		−	0.142477i
$833$	160.952	−	596.943i	0.193220	−	0.716618i
$834$		0			0
$835$	−191.920	+	332.416i	−0.229845	+	0.398103i
$836$	38.6741	−	22.3285i	0.0462609	−	0.0267087i
$837$		0			0
$838$	328.236	+	189.507i	0.391689	+	0.226142i
$839$		−	940.714i		−	1.12123i	−0.828076	−	0.560616i	$-0.810564\pi$
$839$		−	940.714i		−	1.12123i	0.828076	−	0.560616i	$-0.189436\pi$
$840$		0			0
$841$	1563.74			1.85939
$842$	−6.45529	+	11.1809i	−0.00766661	+	0.0132790i
$843$		0			0
$844$	−30.3818	−	52.6228i	−0.0359973	−	0.0623492i
$845$	97.9096	+	56.5281i	0.115869	+	0.0668972i
$846$		0			0
$847$	−830.381	−	109.983i	−0.980379	−	0.129850i
$848$	−83.3281			−0.0982643
$849$		0			0
$850$	−77.2665	+	44.6098i	−0.0909018	+	0.0524822i
$851$	647.806	+	1122.03i	0.761230	+	1.31849i
$852$		0			0
$853$		−	1176.97i		−	1.37980i	−0.723903	−	0.689902i	$-0.757654\pi$
$853$		−	1176.97i		−	1.37980i	0.723903	−	0.689902i	$-0.242346\pi$
$854$	−50.1543	−	38.5472i	−0.0587287	−	0.0451372i
$855$		0			0
$856$	−117.425	+	203.386i	−0.137179	+	0.237601i
$857$	−415.523	+	239.902i	−0.484858	+	0.279933i	−0.722439	−	0.691435i	$-0.756979\pi$
$857$	−415.523	+	239.902i	−0.484858	+	0.279933i	0.237581	+	0.971368i	$0.423645\pi$
$858$		0			0
$859$	1185.54	+	684.470i	1.38014	+	0.796821i	0.992175	−	0.124855i	$-0.0398465\pi$
$859$	1185.54	+	684.470i	1.38014	+	0.796821i	0.387960	+	0.921676i	$0.373180\pi$
$860$		−	284.327i		−	0.330613i
$861$		0			0
$862$	−379.635			−0.440412
$863$	42.7677	−	74.0758i	0.0495570	−	0.0858352i	−0.840183	−	0.542303i	$-0.817552\pi$
$863$	42.7677	−	74.0758i	0.0495570	−	0.0858352i	0.889740	+	0.456468i	$0.150886\pi$
$864$		0			0
$865$	226.358	+	392.063i	0.261685	+	0.453252i
$866$	578.391	+	333.934i	0.667888	+	0.385605i
$867$		0			0
$868$	52.9762	−	399.975i	0.0610324	−	0.460800i
$869$	107.432			0.123627
$870$		0			0
$871$	−1597.51	+	922.321i	−1.83411	+	1.05892i
$872$	−67.5886	−	117.067i	−0.0775099	−	0.134251i
$873$		0			0
$874$			663.346i			0.758977i
$875$	−72.3284	+	29.8931i	−0.0826611	+	0.0341636i
$876$		0			0
$877$	236.635	−	409.863i	0.269823	−	0.467347i	−0.698993	−	0.715128i	$-0.746368\pi$
$877$	236.635	−	409.863i	0.269823	−	0.467347i	0.968816	+	0.247781i	$0.0797015\pi$
$878$	672.865	−	388.479i	0.766361	−	0.442459i
$879$		0			0
$880$	8.96044	+	5.17331i	0.0101823	+	0.00587877i
$881$			442.658i			0.502449i	0.967929	+	0.251225i	$0.0808333\pi$
$881$			442.658i			0.502449i	−0.967929	+	0.251225i	$0.919167\pi$
$882$		0			0
$883$	432.227			0.489498			0.244749	−	0.969586i	$-0.421294\pi$
$883$	432.227			0.489498			0.244749	+	0.969586i	$0.421294\pi$
$884$	186.962	−	323.827i	0.211495	−	0.366320i
$885$		0			0
$886$	−332.913	−	576.622i	−0.375748	−	0.650815i
$887$	−451.613	−	260.739i	−0.509146	−	0.293956i	0.223337	−	0.974741i	$-0.428305\pi$
$887$	−451.613	−	260.739i	−0.509146	−	0.293956i	−0.732483	+	0.680786i	$0.761638\pi$
$888$		0			0
$889$	−215.407	−	521.191i	−0.242302	−	0.586266i
$890$	480.615			0.540017
$891$		0			0
$892$	−28.9905	+	16.7377i	−0.0325006	+	0.0187642i
$893$	−243.137	−	421.125i	−0.272270	−	0.471585i
$894$		0			0
$895$			175.960i			0.196604i
$896$	−78.5103	−	10.3986i	−0.0876231	−	0.0116056i
$897$		0			0
$898$	−395.644	+	685.275i	−0.440583	+	0.763113i
$899$	1223.90	−	706.619i	1.36140	−	0.786005i
$900$		0			0
$901$	−227.634	−	131.425i	−0.252646	−	0.145865i
$902$			62.2311i			0.0689923i
$903$		0			0
$904$	−45.9004			−0.0507748
$905$	65.0147	−	112.609i	0.0718394	−	0.124430i
$906$		0			0
$907$	−633.871	−	1097.90i	−0.698865	−	1.21047i	−0.968860	−	0.247608i	$-0.920355\pi$
$907$	−633.871	−	1097.90i	−0.698865	−	1.21047i	0.269995	−	0.962862i	$-0.412978\pi$
$908$	−733.475	−	423.472i	−0.807792	−	0.466379i
$909$		0			0
$910$	199.878	−	260.064i	0.219646	−	0.285785i
$911$	−789.834			−0.866997			−0.433498	−	0.901154i	$-0.642721\pi$
$911$	−789.834			−0.866997			−0.433498	+	0.901154i	$0.642721\pi$
$912$		0			0
$913$	−5.80713	+	3.35275i	−0.00636049	+	0.00367223i
$914$	443.623	+	768.378i	0.485364	+	0.840676i
$915$		0			0
$916$			809.668i			0.883916i
$917$	−114.601	+	865.244i	−0.124973	+	0.943560i
$918$		0			0
$919$	506.816	−	877.831i	0.551486	−	0.955202i	−0.446681	−	0.894693i	$-0.647394\pi$
$919$	506.816	−	877.831i	0.551486	−	0.955202i	0.998168	−	0.0605090i	$-0.0192724\pi$
$920$	−133.101	+	76.8456i	−0.144675	+	0.0835279i
$921$		0			0
$922$	273.925	+	158.151i	0.297098	+	0.171530i
$923$		−	1762.88i		−	1.90995i
$924$		0			0
$925$	266.579			0.288194
$926$	−280.866	+	486.474i	−0.303311	+	0.525350i
$927$		0			0
$928$	−138.701	−	240.237i	−0.149462	−	0.258876i
$929$	−546.568	−	315.561i	−0.588340	−	0.339678i	0.176101	−	0.984372i	$-0.443652\pi$
$929$	−546.568	−	315.561i	−0.588340	−	0.339678i	−0.764441	+	0.644694i	$0.776985\pi$
$930$		0			0
$931$	−913.960	+	243.362i	−0.981697	+	0.261399i
$932$	−554.596			−0.595061
$933$		0			0
$934$	408.727	−	235.979i	0.437610	−	0.252654i
$935$	16.3187	+	28.2647i	0.0174531	+	0.0302297i
$936$		0			0
$937$			867.113i			0.925414i	0.886511	+	0.462707i	$0.153122\pi$
$937$			867.113i			0.925414i	−0.886511	+	0.462707i	$0.846878\pi$
$938$	470.724	+	1138.95i	0.501838	+	1.21423i
$939$		0			0
$940$	56.3326	−	97.5709i	0.0599283	−	0.103799i
$941$	1151.28	−	664.692i	1.22346	−	0.706367i	0.257809	−	0.966196i	$-0.416999\pi$
$941$	1151.28	−	664.692i	1.22346	−	0.706367i	0.965655	+	0.259829i	$0.0836661\pi$
$942$		0			0
$943$	−800.550	−	462.197i	−0.848939	−	0.490135i
$944$		−	97.6502i		−	0.103443i
$945$		0			0
$946$	−104.009			−0.109946
$947$	−770.741	+	1334.96i	−0.813877	+	1.40968i	0.0962547	+	0.995357i	$0.469314\pi$
$947$	−770.741	+	1334.96i	−0.813877	+	1.40968i	−0.910132	+	0.414319i	$0.864020\pi$
$948$		0			0
$949$	292.866	+	507.258i	0.308604	+	0.534519i
$950$	118.201	+	68.2434i	0.124422	+	0.0718352i
$951$		0			0
$952$	−198.073	−	152.233i	−0.208059	−	0.159908i
$953$	114.779			0.120439			0.0602196	−	0.998185i	$-0.480820\pi$
$953$	114.779			0.120439			0.0602196	+	0.998185i	$0.480820\pi$
$954$		0			0
$955$	−713.419	+	411.893i	−0.747036	+	0.431301i
$956$	290.247	+	502.722i	0.303605	+	0.525860i
$957$		0			0
$958$			861.020i			0.898769i
$959$	−324.472	+	422.176i	−0.338345	+	0.440225i
$960$		0			0
$961$	−65.2290	+	112.980i	−0.0678761	+	0.117565i
$962$	−967.561	+	558.622i	−1.00578	+	0.580688i
$963$		0			0
$964$	701.147	+	404.808i	0.727331	+	0.419925i
$965$			627.930i			0.650705i
$966$		0			0
$967$	−881.904			−0.912000			−0.456000	−	0.889980i	$-0.650718\pi$
$967$	−881.904			−0.912000			−0.456000	+	0.889980i	$0.650718\pi$
$968$	−169.227	+	293.110i	−0.174822	+	0.302800i
$969$		0			0
$970$	−228.174	−	395.208i	−0.235230	−	0.407431i
$971$	−407.102	−	235.041i	−0.419261	−	0.242060i	0.275500	−	0.961301i	$-0.411157\pi$
$971$	−407.102	−	235.041i	−0.419261	−	0.242060i	−0.694761	+	0.719241i	$0.744490\pi$
$972$		0			0
$973$	593.670	−	245.362i	0.610144	−	0.252171i
$974$	450.394			0.462417
$975$		0			0
$976$	−22.1350	+	12.7797i	−0.0226794	+	0.0130939i
$977$	−527.971	−	914.472i	−0.540400	−	0.936000i	−0.998881	−	0.0472957i	$-0.984940\pi$
$977$	−527.971	−	914.472i	−0.540400	−	0.936000i	0.458481	−	0.888704i	$-0.348394\pi$
$978$		0			0
$979$		−	175.813i		−	0.179584i
$980$	−154.709	−	155.194i	−0.157866	−	0.158361i
$981$		0			0
$982$	−370.031	+	640.913i	−0.376814	+	0.652661i
$983$	128.137	−	73.9799i	0.130353	−	0.0752593i	−0.433406	−	0.901199i	$-0.642688\pi$
$983$	128.137	−	73.9799i	0.130353	−	0.0752593i	0.563758	+	0.825940i	$0.309355\pi$
$984$		0			0
$985$	14.7518	+	8.51695i	0.0149764	+	0.00864665i
$986$		−	875.034i		−	0.887458i
$987$		0			0
$988$	−572.022			−0.578970
$989$	772.489	−	1337.99i	0.781081	−	1.35287i
$990$		0			0
$991$	653.220	+	1131.41i	0.659153	+	1.14169i	0.980835	+	0.194839i	$0.0624183\pi$
$991$	653.220	+	1131.41i	0.659153	+	1.14169i	−0.321682	+	0.946848i	$0.604248\pi$
$992$	−141.184	−	81.5128i	−0.142323	−	0.0821702i
$993$		0			0
$994$	−1167.57	−	154.643i	−1.17462	−	0.155577i
$995$	451.318			0.453586
$996$		0			0
$997$	−306.223	+	176.798i	−0.307145	+	0.177330i	−0.645648	−	0.763635i	$-0.723413\pi$
$997$	−306.223	+	176.798i	−0.307145	+	0.177330i	0.338503	+	0.940965i	$0.390079\pi$
$998$	−554.242	−	959.976i	−0.555353	−	0.961900i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.v.c.271.5		16
3.2	odd	2		210.3.o.b.61.3	yes	16
7.3	odd	6	inner	630.3.v.c.451.5		16
15.2	even	4		1050.3.q.e.649.6		32
15.8	even	4		1050.3.q.e.649.14		32
15.14	odd	2		1050.3.p.i.901.8		16
21.2	odd	6		1470.3.f.d.391.10		16
21.5	even	6		1470.3.f.d.391.16		16
21.17	even	6		210.3.o.b.31.3	✓	16
105.17	odd	12		1050.3.q.e.199.13		32
105.38	odd	12		1050.3.q.e.199.6		32
105.59	even	6		1050.3.p.i.451.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.3	✓	16	21.17	even	6
210.3.o.b.61.3	yes	16	3.2	odd	2
630.3.v.c.271.5		16	1.1	even	1	trivial
630.3.v.c.451.5		16	7.3	odd	6	inner
1050.3.p.i.451.8		16	105.59	even	6
1050.3.p.i.901.8		16	15.14	odd	2
1050.3.q.e.199.6		32	105.38	odd	12
1050.3.q.e.199.13		32	105.17	odd	12
1050.3.q.e.649.6		32	15.2	even	4
1050.3.q.e.649.14		32	15.8	even	4
1470.3.f.d.391.10		16	21.2	odd	6
1470.3.f.d.391.16		16	21.5	even	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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-1.93649 - 1.11803i) q^{5} +(-2.67372 - 6.46925i) q^{7} -2.82843 q^{8} +O(q^{10})\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-1.93649 - 1.11803i) q^{5} +(-2.67372 - 6.46925i) q^{7} -2.82843 q^{8} +(-2.73861 + 1.58114i) q^{10} +(0.578394 + 1.00181i) q^{11} -14.8176i q^{13} +(-9.81379 - 1.29982i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-10.9271 + 6.30878i) q^{17} +(16.7162 + 9.65108i) q^{19} +4.47214i q^{20} +1.63595 q^{22} +(-12.1504 + 21.0450i) q^{23} +(2.50000 + 4.33013i) q^{25} +(-18.1477 - 10.4776i) q^{26} +(-8.53135 + 11.1003i) q^{28} -49.0382 q^{29} +(-24.9581 + 14.4096i) q^{31} +(2.82843 + 4.89898i) q^{32} +17.8439i q^{34} +(-2.05520 + 15.5170i) q^{35} +(26.6579 - 46.1728i) q^{37} +(23.6402 - 13.6487i) q^{38} +(5.47723 + 3.16228i) q^{40} +38.0398i q^{41} -63.5774 q^{43} +(1.15679 - 2.00362i) q^{44} +(17.1832 + 29.7622i) q^{46} +(-21.8175 - 12.5964i) q^{47} +(-34.7024 + 34.5940i) q^{49} +7.07107 q^{50} +(-25.6648 + 14.8176i) q^{52} +(10.4160 + 18.0411i) q^{53} -2.58666i q^{55} +(7.56243 + 18.2978i) q^{56} +(-34.6752 + 60.0593i) q^{58} +(-21.1419 + 12.2063i) q^{59} +(5.53376 + 3.19492i) q^{61} +40.7564i q^{62} +8.00000 q^{64} +(-16.5665 + 28.6941i) q^{65} +(-62.2451 - 107.812i) q^{67} +(21.8543 + 12.6176i) q^{68} +(17.5511 + 13.4892i) q^{70} +118.973 q^{71} +(-34.2336 + 19.7648i) q^{73} +(-37.7000 - 65.2983i) q^{74} -38.6043i q^{76} +(4.93448 - 6.42033i) q^{77} +(46.4356 - 80.4288i) q^{79} +(7.74597 - 4.47214i) q^{80} +(46.5891 + 26.8982i) q^{82} +5.79665i q^{83} +28.2137 q^{85} +(-44.9560 + 77.8661i) q^{86} +(-1.63595 - 2.83354i) q^{88} +(-131.622 - 75.9919i) q^{89} +(-95.8586 + 39.6181i) q^{91} +48.6014 q^{92} +(-30.8546 + 17.8139i) q^{94} +(-21.5805 - 37.3785i) q^{95} +144.310i q^{97} +(17.8305 + 66.9632i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 4 q^{7}+O(q^{10}) \) 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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