LMFDB - Embedded newform 630.3.v.c.451.1

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			451.1
Root			$0.848921 - 1.47037i$ of defining polynomial
Character	$\chi$	$=$	630.451
Dual form			630.3.v.c.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-6.38854 + 2.86123i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-6.38854 + 2.86123i) q^{7} +2.82843 q^{8} +(2.73861 + 1.58114i) q^{10} +(9.98749 - 17.2988i) q^{11} +3.49788i q^{13} +(8.02165 + 5.80113i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-15.7982 - 9.12112i) q^{17} +(-21.3143 + 12.3058i) q^{19} -4.47214i q^{20} -28.2489 q^{22} +(12.5952 + 21.8155i) q^{23} +(2.50000 - 4.33013i) q^{25} +(4.28401 - 2.47338i) q^{26} +(1.43274 - 13.9265i) q^{28} +53.1223 q^{29} +(26.0944 + 15.0656i) q^{31} +(-2.82843 + 4.89898i) q^{32} +25.7984i q^{34} +(9.17240 - 12.6833i) q^{35} +(23.3846 + 40.5034i) q^{37} +(30.1429 + 17.4030i) q^{38} +(-5.47723 + 3.16228i) q^{40} +31.5250i q^{41} +64.4116 q^{43} +(19.9750 + 34.5977i) q^{44} +(17.8123 - 30.8518i) q^{46} +(24.3029 - 14.0313i) q^{47} +(32.6268 - 36.5581i) q^{49} -7.07107 q^{50} +(-6.05851 - 3.49788i) q^{52} +(-32.4374 + 56.1833i) q^{53} +44.6654i q^{55} +(-18.0695 + 8.09277i) q^{56} +(-37.5631 - 65.0613i) q^{58} +(-86.7684 - 50.0958i) q^{59} +(6.94896 - 4.01198i) q^{61} -42.6119i q^{62} +8.00000 q^{64} +(-3.91075 - 6.77362i) q^{65} +(-8.13165 + 14.0844i) q^{67} +(31.5965 - 18.2422i) q^{68} +(-22.0197 - 2.26537i) q^{70} +107.725 q^{71} +(44.7395 + 25.8303i) q^{73} +(33.0709 - 57.2804i) q^{74} -49.2232i q^{76} +(-14.3095 + 139.091i) q^{77} +(10.9877 + 19.0313i) q^{79} +(7.74597 + 4.47214i) q^{80} +(38.6101 - 22.2916i) q^{82} -0.417479i q^{83} +40.7909 q^{85} +(-45.5459 - 78.8878i) q^{86} +(28.2489 - 48.9285i) q^{88} +(96.3110 - 55.6052i) q^{89} +(-10.0082 - 22.3463i) q^{91} -50.3807 q^{92} +(-34.3695 - 19.8432i) q^{94} +(27.5166 - 47.6601i) q^{95} +74.2244i q^{97} +(-67.8449 - 14.1090i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−6.38854	+	2.86123i	−0.912648	+	0.408747i
$7$	−6.38854	+	2.86123i	−0.912648	+	0.408747i
$8$	2.82843			0.353553
$9$		0			0
$10$	2.73861	+	1.58114i	0.273861	+	0.158114i
$11$	9.98749	−	17.2988i	0.907953	−	1.57262i	0.0910503	−	0.995846i	$-0.470978\pi$
$11$	9.98749	−	17.2988i	0.907953	−	1.57262i	0.816903	−	0.576775i	$-0.195689\pi$
$12$		0			0
$13$			3.49788i			0.269068i	0.990909	+	0.134534i	$0.0429537\pi$
$13$			3.49788i			0.269068i	−0.990909	+	0.134534i	$0.957046\pi$
$14$	8.02165	+	5.80113i	0.572975	+	0.414367i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−15.7982	−	9.12112i	−0.929308	−	0.536536i	−0.0427155	−	0.999087i	$-0.513601\pi$
$17$	−15.7982	−	9.12112i	−0.929308	−	0.536536i	−0.886593	+	0.462551i	$0.846934\pi$
$18$		0			0
$19$	−21.3143	+	12.3058i	−1.12180	+	0.647673i	−0.941861	−	0.336004i	$-0.890924\pi$
$19$	−21.3143	+	12.3058i	−1.12180	+	0.647673i	−0.179942	+	0.983677i	$0.557591\pi$
$20$		−	4.47214i		−	0.223607i
$21$		0			0
$22$	−28.2489			−1.28404
$23$	12.5952	+	21.8155i	0.547617	+	0.948500i	0.998437	+	0.0558853i	$0.0177981\pi$
$23$	12.5952	+	21.8155i	0.547617	+	0.948500i	−0.450820	+	0.892615i	$0.648869\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	4.28401	−	2.47338i	0.164770	−	0.0951299i
$27$		0			0
$28$	1.43274	−	13.9265i	0.0511694	−	0.497375i
$29$	53.1223			1.83180			0.915902	−	0.401402i	$-0.131477\pi$
$29$	53.1223			1.83180			0.915902	+	0.401402i	$0.131477\pi$
$30$		0			0
$31$	26.0944	+	15.0656i	0.841754	+	0.485987i	0.857860	−	0.513883i	$-0.171794\pi$
$31$	26.0944	+	15.0656i	0.841754	+	0.485987i	−0.0161061	+	0.999870i	$0.505127\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$		0			0
$34$			25.7984i			0.758777i
$35$	9.17240	−	12.6833i	0.262068	−	0.362381i
$36$		0			0
$37$	23.3846	+	40.5034i	0.632017	+	1.09469i	0.987139	+	0.159866i	$0.0511061\pi$
$37$	23.3846	+	40.5034i	0.632017	+	1.09469i	−0.355122	+	0.934820i	$0.615561\pi$
$38$	30.1429	+	17.4030i	0.793234	+	0.457974i
$39$		0			0
$40$	−5.47723	+	3.16228i	−0.136931	+	0.0790569i
$41$			31.5250i			0.768903i	0.923145	+	0.384452i	$0.125609\pi$
$41$			31.5250i			0.768903i	−0.923145	+	0.384452i	$0.874391\pi$
$42$		0			0
$43$	64.4116			1.49794			0.748972	−	0.662602i	$-0.230548\pi$
$43$	64.4116			1.49794			0.748972	+	0.662602i	$0.230548\pi$
$44$	19.9750	+	34.5977i	0.453977	+	0.786311i
$45$		0			0
$46$	17.8123	−	30.8518i	0.387223	−	0.670691i
$47$	24.3029	−	14.0313i	0.517083	−	0.298538i	−0.218657	−	0.975802i	$-0.570168\pi$
$47$	24.3029	−	14.0313i	0.517083	−	0.298538i	0.735740	+	0.677264i	$0.236834\pi$
$48$		0			0
$49$	32.6268	−	36.5581i	0.665852	−	0.746084i
$50$	−7.07107			−0.141421
$51$		0			0
$52$	−6.05851	−	3.49788i	−0.116510	−	0.0672670i
$53$	−32.4374	+	56.1833i	−0.612027	+	1.06006i	0.378872	+	0.925449i	$0.376312\pi$
$53$	−32.4374	+	56.1833i	−0.612027	+	1.06006i	−0.990898	+	0.134612i	$0.957021\pi$
$54$		0			0
$55$			44.6654i			0.812098i
$56$	−18.0695	+	8.09277i	−0.322670	+	0.144514i
$57$		0			0
$58$	−37.5631	−	65.0613i	−0.647640	−	1.12175i
$59$	−86.7684	−	50.0958i	−1.47065	−	0.849081i	−0.471194	−	0.882029i	$-0.656177\pi$
$59$	−86.7684	−	50.0958i	−1.47065	−	0.849081i	−0.999457	+	0.0329486i	$0.989510\pi$
$60$		0			0
$61$	6.94896	−	4.01198i	0.113917	−	0.0657702i	−0.441959	−	0.897035i	$-0.645716\pi$
$61$	6.94896	−	4.01198i	0.113917	−	0.0657702i	0.555876	+	0.831265i	$0.312383\pi$
$62$		−	42.6119i		−	0.687289i
$63$		0			0
$64$	8.00000			0.125000
$65$	−3.91075	−	6.77362i	−0.0601654	−	0.104210i
$66$		0			0
$67$	−8.13165	+	14.0844i	−0.121368	+	0.210215i	−0.920307	−	0.391196i	$-0.872061\pi$
$67$	−8.13165	+	14.0844i	−0.121368	+	0.210215i	0.798939	+	0.601411i	$0.205395\pi$
$68$	31.5965	−	18.2422i	0.464654	−	0.268268i
$69$		0			0
$70$	−22.0197	−	2.26537i	−0.314567	−	0.0323624i
$71$	107.725			1.51725			0.758625	−	0.651528i	$-0.225872\pi$
$71$	107.725			1.51725			0.758625	+	0.651528i	$0.225872\pi$
$72$		0			0
$73$	44.7395	+	25.8303i	0.612870	+	0.353840i	0.774088	−	0.633078i	$-0.218209\pi$
$73$	44.7395	+	25.8303i	0.612870	+	0.353840i	−0.161218	+	0.986919i	$0.551542\pi$
$74$	33.0709	−	57.2804i	0.446904	−	0.774060i
$75$		0			0
$76$		−	49.2232i		−	0.647673i
$77$	−14.3095	+	139.091i	−0.185838	+	1.80637i
$78$		0			0
$79$	10.9877	+	19.0313i	0.139085	+	0.240903i	0.927151	−	0.374689i	$-0.122250\pi$
$79$	10.9877	+	19.0313i	0.139085	+	0.240903i	−0.788065	+	0.615592i	$0.788917\pi$
$80$	7.74597	+	4.47214i	0.0968246	+	0.0559017i
$81$		0			0
$82$	38.6101	−	22.2916i	0.470855	−	0.271848i
$83$		−	0.417479i		−	0.00502987i	−0.999997	−	0.00251494i	$-0.999199\pi$
$83$		−	0.417479i		−	0.00502987i	0.999997	−	0.00251494i	$-0.000800530\pi$
$84$		0			0
$85$	40.7909			0.479893
$86$	−45.5459	−	78.8878i	−0.529603	−	0.917300i
$87$		0			0
$88$	28.2489	−	48.9285i	0.321010	−	0.556006i
$89$	96.3110	−	55.6052i	1.08215	−	0.624778i	0.150672	−	0.988584i	$-0.451856\pi$
$89$	96.3110	−	55.6052i	1.08215	−	0.624778i	0.931475	+	0.363806i	$0.118523\pi$
$90$		0			0
$91$	−10.0082	−	22.3463i	−0.109981	−	0.245564i
$92$	−50.3807			−0.547617
$93$		0			0
$94$	−34.3695	−	19.8432i	−0.365633	−	0.211098i
$95$	27.5166	−	47.6601i	0.289648	−	0.501686i
$96$		0			0
$97$			74.2244i			0.765200i	0.923914	+	0.382600i	$0.124971\pi$
$97$			74.2244i			0.765200i	−0.923914	+	0.382600i	$0.875029\pi$
$98$	−67.8449	−	14.1090i	−0.692295	−	0.143969i
$99$		0			0
$100$	5.00000	+	8.66025i	0.0500000	+	0.0866025i
$101$	−75.8587	−	43.7970i	−0.751076	−	0.433634i	0.0750065	−	0.997183i	$-0.476102\pi$
$101$	−75.8587	−	43.7970i	−0.751076	−	0.433634i	−0.826083	+	0.563549i	$0.809436\pi$
$102$		0			0
$103$	120.413	−	69.5206i	1.16906	−	0.674957i	0.215601	−	0.976482i	$-0.430829\pi$
$103$	120.413	−	69.5206i	1.16906	−	0.674957i	0.953458	+	0.301525i	$0.0974956\pi$
$104$			9.89350i			0.0951299i
$105$		0			0
$106$	91.7469			0.865537
$107$	76.0949	+	131.800i	0.711168	+	1.23178i	0.964419	+	0.264378i	$0.0851666\pi$
$107$	76.0949	+	131.800i	0.711168	+	1.23178i	−0.253252	+	0.967400i	$0.581500\pi$
$108$		0			0
$109$	−32.3777	+	56.0798i	−0.297043	+	0.514494i	−0.975458	−	0.220185i	$-0.929334\pi$
$109$	−32.3777	+	56.0798i	−0.297043	+	0.514494i	0.678415	+	0.734679i	$0.262667\pi$
$110$	54.7037	−	31.5832i	0.497307	−	0.287120i
$111$		0			0
$112$	22.6887	+	16.4081i	0.202577	+	0.146501i
$113$	−3.25860			−0.0288372			−0.0144186	−	0.999896i	$-0.504590\pi$
$113$	−3.25860			−0.0288372			−0.0144186	+	0.999896i	$0.504590\pi$
$114$		0			0
$115$	−48.7809	−	28.1637i	−0.424182	−	0.244902i
$116$	−53.1223	+	92.0105i	−0.457951	+	0.793194i
$117$		0			0
$118$			141.692i			1.20078i
$119$	127.025	+	13.0682i	1.06744	+	0.109817i
$120$		0			0
$121$	−139.000	−	240.755i	−1.14876	−	1.98971i
$122$	−9.82731	−	5.67380i	−0.0805517	−	0.0465066i
$123$		0			0
$124$	−52.1887	+	30.1312i	−0.420877	+	0.242993i
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	−88.5772			−0.697458			−0.348729	−	0.937224i	$-0.613387\pi$
$127$	−88.5772			−0.697458			−0.348729	+	0.937224i	$0.613387\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−5.53064	+	9.57934i	−0.0425434	+	0.0736873i
$131$	108.361	−	62.5621i	0.827181	−	0.477573i	−0.0257055	−	0.999670i	$-0.508183\pi$
$131$	108.361	−	62.5621i	0.827181	−	0.477573i	0.852887	+	0.522096i	$0.174850\pi$
$132$		0			0
$133$	100.957	−	139.601i	0.759077	−	1.04963i
$134$	22.9998			0.171640
$135$		0			0
$136$	−44.6842	−	25.7984i	−0.328560	−	0.189694i
$137$	−19.4769	+	33.7349i	−0.142167	+	0.246240i	−0.928312	−	0.371801i	$-0.878740\pi$
$137$	−19.4769	+	33.7349i	−0.142167	+	0.246240i	0.786145	+	0.618042i	$0.212074\pi$
$138$		0			0
$139$			98.9454i			0.711837i	0.934517	+	0.355919i	$0.115832\pi$
$139$			98.9454i			0.711837i	−0.934517	+	0.355919i	$0.884168\pi$
$140$	12.7958	+	28.5704i	0.0913985	+	0.204074i
$141$		0			0
$142$	−76.1729	−	131.935i	−0.536429	−	0.929122i
$143$	60.5093	+	34.9351i	0.423142	+	0.244301i
$144$		0			0
$145$	−102.871	+	59.3925i	−0.709455	+	0.409604i
$146$		−	73.0593i		−	0.500406i
$147$		0			0
$148$	−93.5385			−0.632017
$149$	−93.2324	−	161.483i	−0.625721	−	1.08378i	−0.988401	−	0.151867i	$-0.951472\pi$
$149$	−93.2324	−	161.483i	−0.625721	−	1.08378i	0.362680	−	0.931914i	$-0.381862\pi$
$150$		0			0
$151$	−77.4202	+	134.096i	−0.512716	+	0.888051i	0.487175	+	0.873304i	$0.338027\pi$
$151$	−77.4202	+	134.096i	−0.512716	+	0.888051i	−0.999891	+	0.0147462i	$0.995306\pi$
$152$	−60.2858	+	34.8060i	−0.396617	+	0.228987i
$153$		0			0
$154$	180.469	−	80.8265i	1.17188	−	0.524847i
$155$	−67.3754			−0.434680
$156$		0			0
$157$	−43.4777	−	25.1019i	−0.276928	−	0.159885i	0.355104	−	0.934827i	$-0.384446\pi$
$157$	−43.4777	−	25.1019i	−0.276928	−	0.159885i	−0.632032	+	0.774942i	$0.717779\pi$
$158$	15.5390	−	26.9143i	0.0983481	−	0.170344i
$159$		0			0
$160$		−	12.6491i		−	0.0790569i
$161$	−142.884	−	103.331i	−0.887477	−	0.641810i
$162$		0			0
$163$	57.9054	+	100.295i	0.355248	+	0.615308i	0.987160	−	0.159732i	$-0.0510631\pi$
$163$	57.9054	+	100.295i	0.355248	+	0.615308i	−0.631912	+	0.775040i	$0.717730\pi$
$164$	−54.6029	−	31.5250i	−0.332945	−	0.192226i
$165$		0			0
$166$	−0.511306	+	0.295202i	−0.00308015	+	0.00177833i
$167$			61.3210i			0.367191i	0.983002	+	0.183596i	$0.0587737\pi$
$167$			61.3210i			0.367191i	−0.983002	+	0.183596i	$0.941226\pi$
$168$		0			0
$169$	156.765			0.927602
$170$	−28.8435	−	49.9584i	−0.169668	−	0.293873i
$171$		0			0
$172$	−64.4116	+	111.564i	−0.374486	+	0.648629i
$173$	−27.4544	+	15.8508i	−0.158696	+	0.0916232i	−0.577245	−	0.816571i	$-0.695872\pi$
$173$	−27.4544	+	15.8508i	−0.158696	+	0.0916232i	0.418549	+	0.908194i	$0.362539\pi$
$174$		0			0
$175$	−3.58186	+	34.8162i	−0.0204678	+	0.198950i
$176$	−79.8999			−0.453977
$177$		0			0
$178$	−136.204	−	78.6376i	−0.765193	−	0.441784i
$179$	65.9472	−	114.224i	0.368420	−	0.638122i	−0.620899	−	0.783891i	$-0.713232\pi$
$179$	65.9472	−	114.224i	0.368420	−	0.638122i	0.989319	+	0.145768i	$0.0465655\pi$
$180$		0			0
$181$			55.1431i			0.304658i	0.988330	+	0.152329i	$0.0486773\pi$
$181$			55.1431i			0.304658i	−0.988330	+	0.152329i	$0.951323\pi$
$182$	−20.2917	+	28.0588i	−0.111493	+	0.154169i
$183$		0			0
$184$	35.6246	+	61.7035i	0.193612	+	0.335345i
$185$	−90.5683	−	52.2896i	−0.489558	−	0.282647i
$186$		0			0
$187$	−315.569	+	182.194i	−1.68754	+	0.974300i
$188$			56.1252i			0.298538i
$189$		0			0
$190$	−77.8287			−0.409625
$191$	97.5822	+	169.017i	0.510901	+	0.884907i	0.999920	+	0.0126340i	$0.00402164\pi$
$191$	97.5822	+	169.017i	0.510901	+	0.884907i	−0.489019	+	0.872273i	$0.662645\pi$
$192$		0			0
$193$	−174.380	+	302.035i	−0.903523	+	1.56495i	−0.0806348	+	0.996744i	$0.525695\pi$
$193$	−174.380	+	302.035i	−0.903523	+	1.56495i	−0.822888	+	0.568204i	$0.807639\pi$
$194$	90.9060	−	52.4846i	0.468588	−	0.270539i
$195$		0			0
$196$	30.6937	+	93.0693i	0.156601	+	0.474843i
$197$	56.3808			0.286197			0.143098	−	0.989708i	$-0.454293\pi$
$197$	56.3808			0.286197			0.143098	+	0.989708i	$0.454293\pi$
$198$		0			0
$199$	148.357	+	85.6540i	0.745513	+	0.430422i	0.824070	−	0.566487i	$-0.191698\pi$
$199$	148.357	+	85.6540i	0.745513	+	0.430422i	−0.0785571	+	0.996910i	$0.525031\pi$
$200$	7.07107	−	12.2474i	0.0353553	−	0.0612372i
$201$		0			0
$202$			123.877i			0.613251i
$203$	−339.374	+	151.995i	−1.67179	+	0.748744i
$204$		0			0
$205$	−35.2460	−	61.0479i	−0.171932	−	0.297795i
$206$	−170.290	−	98.3169i	−0.826650	−	0.477267i
$207$		0			0
$208$	12.1170	−	6.99576i	0.0582549	−	0.0336335i
$209$			491.616i			2.35223i
$210$		0			0
$211$	162.038			0.767954			0.383977	−	0.923343i	$-0.374554\pi$
$211$	162.038			0.767954			0.383977	+	0.923343i	$0.374554\pi$
$212$	−64.8748	−	112.367i	−0.306013	−	0.530031i
$213$		0			0
$214$	107.614	−	186.394i	0.502871	−	0.870999i
$215$	−124.733	+	72.0144i	−0.580151	+	0.334951i
$216$		0			0
$217$	−209.811	−	21.5851i	−0.966870	−	0.0994707i
$218$	91.5779			0.420082
$219$		0			0
$220$	−77.3627	−	44.6654i	−0.351649	−	0.203025i
$221$	31.9046	−	55.2604i	0.144365	−	0.250047i
$222$		0			0
$223$		−	365.329i		−	1.63825i	−0.573618	−	0.819123i	$-0.694461\pi$
$223$		−	365.329i		−	1.63825i	0.573618	−	0.819123i	$-0.305539\pi$
$224$	4.05241	−	39.3901i	0.0180911	−	0.175849i
$225$		0			0
$226$	2.30418	+	3.99096i	0.0101955	+	0.0176591i
$227$	−223.325	−	128.937i	−0.983811	−	0.568004i	−0.0803928	−	0.996763i	$-0.525617\pi$
$227$	−223.325	−	128.937i	−0.983811	−	0.568004i	−0.903419	+	0.428759i	$0.858951\pi$
$228$		0			0
$229$	−13.3634	+	7.71538i	−0.0583556	+	0.0336916i	−0.528894	−	0.848688i	$-0.677393\pi$
$229$	−13.3634	+	7.71538i	−0.0583556	+	0.0336916i	0.470538	+	0.882380i	$0.344060\pi$
$230$			79.6589i			0.346343i
$231$		0			0
$232$	150.253			0.647640
$233$	−62.6734	−	108.553i	−0.268984	−	0.465895i	0.699615	−	0.714520i	$-0.253355\pi$
$233$	−62.6734	−	108.553i	−0.268984	−	0.465895i	−0.968600	+	0.248625i	$0.920021\pi$
$234$		0			0
$235$	−31.3749	+	54.3430i	−0.133510	+	0.231247i
$236$	173.537	−	100.192i	0.735326	−	0.424540i
$237$		0			0
$238$	−73.8151	−	164.814i	−0.310148	−	0.692496i
$239$	3.62565			0.0151701			0.00758503	−	0.999971i	$-0.497586\pi$
$239$	3.62565			0.0151701			0.00758503	+	0.999971i	$0.497586\pi$
$240$		0			0
$241$	83.6915	+	48.3193i	0.347268	+	0.200495i	0.663481	−	0.748193i	$-0.269078\pi$
$241$	83.6915	+	48.3193i	0.347268	+	0.200495i	−0.316213	+	0.948688i	$0.602412\pi$
$242$	−196.575	+	340.479i	−0.812295	+	1.40694i
$243$		0			0
$244$			16.0479i			0.0657702i
$245$	−22.3083	+	107.272i	−0.0910541	+	0.437846i
$246$		0			0
$247$	−43.0442	−	74.5548i	−0.174268	−	0.301841i
$248$	73.8060	+	42.6119i	0.297605	+	0.171822i
$249$		0			0
$250$	13.6931	−	7.90569i	0.0547723	−	0.0316228i
$251$			29.7311i			0.118450i	0.998245	+	0.0592252i	$0.0188630\pi$
$251$			29.7311i			0.118450i	−0.998245	+	0.0592252i	$0.981137\pi$
$252$		0			0
$253$	503.177			1.98884
$254$	62.6336	+	108.484i	0.246589	+	0.427104i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−382.457	+	220.811i	−1.48816	+	0.859189i	−0.999909	−	0.0135154i	$-0.995698\pi$
$257$	−382.457	+	220.811i	−1.48816	+	0.859189i	−0.488250	+	0.872704i	$0.662364\pi$
$258$		0			0
$259$	−265.283	−	191.848i	−1.02426	−	0.740728i
$260$	15.6430			0.0601654
$261$		0			0
$262$	−153.245	−	88.4762i	−0.584905	−	0.337695i
$263$	171.523	−	297.087i	0.652180	−	1.12961i	−0.330413	−	0.943836i	$-0.607188\pi$
$263$	171.523	−	297.087i	0.652180	−	1.12961i	0.982593	−	0.185772i	$-0.0594786\pi$
$264$		0			0
$265$		−	145.065i		−	0.547413i
$266$	−242.363	−	24.9341i	−0.911139	−	0.0937371i
$267$		0			0
$268$	−16.2633	−	28.1689i	−0.0606840	−	0.105108i
$269$	−401.274	−	231.676i	−1.49172	−	0.861247i	−0.491769	−	0.870726i	$-0.663650\pi$
$269$	−401.274	−	231.676i	−1.49172	−	0.861247i	−0.999955	+	0.00947852i	$0.996983\pi$
$270$		0			0
$271$	211.814	−	122.291i	0.781600	−	0.451257i	−0.0553967	−	0.998464i	$-0.517642\pi$
$271$	211.814	−	122.291i	0.781600	−	0.451257i	0.836997	+	0.547207i	$0.184309\pi$
$272$			72.9689i			0.268268i
$273$		0			0
$274$	55.0889			0.201054
$275$	−49.9374	−	86.4942i	−0.181591	−	0.314524i
$276$		0			0
$277$	−70.5092	+	122.126i	−0.254546	+	0.440887i	−0.964772	−	0.263087i	$-0.915259\pi$
$277$	−70.5092	+	122.126i	−0.254546	+	0.440887i	0.710226	+	0.703974i	$0.248593\pi$
$278$	121.183	−	69.9650i	0.435910	−	0.251673i
$279$		0			0
$280$	25.9435	−	35.8739i	0.0926552	−	0.128121i
$281$	−84.9953			−0.302475			−0.151237	−	0.988497i	$-0.548326\pi$
$281$	−84.9953			−0.302475			−0.151237	+	0.988497i	$0.548326\pi$
$282$		0			0
$283$	−101.047	−	58.3392i	−0.357055	−	0.206146i	0.310733	−	0.950497i	$-0.399425\pi$
$283$	−101.047	−	58.3392i	−0.357055	−	0.206146i	−0.667788	+	0.744351i	$0.732759\pi$
$284$	−107.725	+	186.585i	−0.379312	+	0.656988i
$285$		0			0
$286$		−	98.8112i		−	0.345494i
$287$	−90.2003	−	201.399i	−0.314287	−	0.701738i
$288$		0			0
$289$	21.8896	+	37.9138i	0.0757424	+	0.131190i
$290$	145.481	+	83.9937i	0.501660	+	0.289634i
$291$		0			0
$292$	−89.4789	+	51.6607i	−0.306435	+	0.176920i
$293$		−	131.882i		−	0.450110i	−0.974346	−	0.225055i	$-0.927744\pi$
$293$		−	131.882i		−	0.450110i	0.974346	−	0.225055i	$-0.0722562\pi$
$294$		0			0
$295$	224.035			0.759441
$296$	66.1417	+	114.561i	0.223452	+	0.387030i
$297$		0			0
$298$	−131.851	+	228.372i	−0.442451	+	0.766348i
$299$	−76.3080	+	44.0565i	−0.255211	+	0.147346i
$300$		0			0
$301$	−411.496	+	184.296i	−1.36710	+	0.612280i
$302$	218.977			0.725090
$303$		0			0
$304$	85.2570	+	49.2232i	0.280451	+	0.161918i
$305$	−8.97107	+	15.5383i	−0.0294133	+	0.0509454i
$306$		0			0
$307$			429.871i			1.40023i	0.714030	+	0.700115i	$0.246868\pi$
$307$			429.871i			1.40023i	−0.714030	+	0.700115i	$0.753132\pi$
$308$	−226.603	−	163.875i	−0.735723	−	0.532063i
$309$		0			0
$310$	47.6416	+	82.5176i	0.153683	+	0.266186i
$311$	217.786	+	125.739i	0.700277	+	0.404305i	0.807451	−	0.589935i	$-0.200847\pi$
$311$	217.786	+	125.739i	0.700277	+	0.404305i	−0.107174	+	0.994240i	$0.534180\pi$
$312$		0			0
$313$	11.8674	−	6.85166i	0.0379151	−	0.0218903i	−0.480923	−	0.876763i	$-0.659698\pi$
$313$	11.8674	−	6.85166i	0.0379151	−	0.0218903i	0.518838	+	0.854873i	$0.326365\pi$
$314$			70.9988i			0.226111i
$315$		0			0
$316$	−43.9509			−0.139085
$317$	−16.4651	−	28.5183i	−0.0519403	−	0.0899632i	0.838886	−	0.544307i	$-0.183207\pi$
$317$	−16.4651	−	28.5183i	−0.0519403	−	0.0899632i	−0.890827	+	0.454343i	$0.849874\pi$
$318$		0			0
$319$	530.558	−	918.954i	1.66319	−	2.88073i
$320$	−15.4919	+	8.94427i	−0.0484123	+	0.0279508i
$321$		0			0
$322$	−25.5204	+	248.063i	−0.0792560	+	0.770381i
$323$	448.970			1.39000
$324$		0			0
$325$	15.1463	+	8.74471i	0.0466039	+	0.0269068i
$326$	81.8906	−	141.839i	0.251198	−	0.435088i
$327$		0			0
$328$			89.1662i			0.271848i
$329$	−115.113	+	159.176i	−0.349888	+	0.483816i
$330$		0			0
$331$	208.940	+	361.895i	0.631240	+	1.09334i	0.987299	+	0.158876i	$0.0507869\pi$
$331$	208.940	+	361.895i	0.631240	+	1.09334i	−0.356059	+	0.934464i	$0.615880\pi$
$332$	0.723095	+	0.417479i	0.00217800	+	0.00125747i
$333$		0			0
$334$	75.1025	−	43.3605i	0.224858	−	0.129822i
$335$		−	36.3658i		−	0.108555i
$336$		0			0
$337$	−286.688			−0.850705			−0.425353	−	0.905028i	$-0.639850\pi$
$337$	−286.688			−0.850705			−0.425353	+	0.905028i	$0.639850\pi$
$338$	−110.849	−	191.997i	−0.327957	−	0.568038i
$339$		0			0
$340$	−40.7909	+	70.6519i	−0.119973	+	0.207800i
$341$	521.234	−	300.935i	1.52855	−	0.882507i
$342$		0			0
$343$	−103.836	+	326.905i	−0.302729	+	0.953077i
$344$	182.184			0.529603
$345$		0			0
$346$	38.8264	+	22.4164i	0.112215	+	0.0647874i
$347$	153.398	−	265.693i	0.442069	−	0.765685i	−0.555774	−	0.831333i	$-0.687578\pi$
$347$	153.398	−	265.693i	0.442069	−	0.765685i	0.997843	+	0.0656479i	$0.0209114\pi$
$348$		0			0
$349$		−	340.162i		−	0.974676i	−0.873214	−	0.487338i	$-0.837968\pi$
$349$		−	340.162i		−	0.974676i	0.873214	−	0.487338i	$-0.162032\pi$
$350$	45.1738	−	20.2319i	0.129068	−	0.0578055i
$351$		0			0
$352$	56.4978	+	97.8570i	0.160505	+	0.278003i
$353$	324.761	+	187.501i	0.920004	+	0.531165i	0.883636	−	0.468174i	$-0.155088\pi$
$353$	324.761	+	187.501i	0.920004	+	0.531165i	0.0363676	+	0.999338i	$0.488421\pi$
$354$		0			0
$355$	−208.608	+	120.440i	−0.587628	+	0.339267i
$356$			222.421i			0.624778i
$357$		0			0
$358$	−186.527			−0.521025
$359$	−164.750	−	285.356i	−0.458915	−	0.794863i	0.539989	−	0.841672i	$-0.318428\pi$
$359$	−164.750	−	285.356i	−0.458915	−	0.794863i	−0.998904	+	0.0468084i	$0.985095\pi$
$360$		0			0
$361$	122.365	−	211.942i	0.338961	−	0.587098i
$362$	67.5362	−	38.9920i	0.186564	−	0.107713i
$363$		0			0
$364$	48.7132	+	5.01157i	0.133828	+	0.0137681i
$365$	−115.517			−0.316484
$366$		0			0
$367$	23.5163	+	13.5772i	0.0640772	+	0.0369950i	0.531696	−	0.846935i	$-0.321555\pi$
$367$	23.5163	+	13.5772i	0.0640772	+	0.0369950i	−0.467619	+	0.883930i	$0.654888\pi$
$368$	50.3807	−	87.2620i	0.136904	−	0.237125i
$369$		0			0
$370$			147.897i			0.399723i
$371$	46.4745	−	451.740i	0.125268	−	1.21763i
$372$		0			0
$373$	−63.7488	−	110.416i	−0.170908	−	0.296022i	0.767829	−	0.640654i	$-0.221337\pi$
$373$	−63.7488	−	110.416i	−0.170908	−	0.296022i	−0.938738	+	0.344633i	$0.888004\pi$
$374$	446.283	+	257.661i	1.19327	+	0.688934i
$375$		0			0
$376$	68.7390	−	39.6865i	0.182817	−	0.105549i
$377$			185.816i			0.492880i
$378$		0			0
$379$	319.795			0.843785			0.421893	−	0.906646i	$-0.361366\pi$
$379$	319.795			0.843785			0.421893	+	0.906646i	$0.361366\pi$
$380$	55.0332	+	95.3202i	0.144824	+	0.250843i
$381$		0			0
$382$	138.002	−	239.027i	0.361262	−	0.625724i
$383$	−354.155	+	204.471i	−0.924686	+	0.533867i	−0.885127	−	0.465350i	$-0.845929\pi$
$383$	−354.155	+	204.471i	−0.924686	+	0.533867i	−0.0395587	+	0.999217i	$0.512595\pi$
$384$		0			0
$385$	−127.798	−	285.346i	−0.331942	−	0.741160i
$386$	493.221			1.27777
$387$		0			0
$388$	−128.560	−	74.2244i	−0.331341	−	0.191300i
$389$	193.576	−	335.284i	0.497626	−	0.861913i	−0.502370	−	0.864652i	$-0.667539\pi$
$389$	193.576	−	335.284i	0.497626	−	0.861913i	0.999996	+	0.00273932i	$0.000871952\pi$
$390$		0			0
$391$		−	459.529i		−	1.17526i
$392$	92.2824	−	103.402i	0.235414	−	0.263780i
$393$		0			0
$394$	−39.8672	−	69.0521i	−0.101186	−	0.175259i
$395$	−42.5553	−	24.5693i	−0.107735	−	0.0622008i
$396$		0			0
$397$	26.0771	−	15.0556i	0.0656853	−	0.0379234i	−0.466798	−	0.884364i	$-0.654592\pi$
$397$	26.0771	−	15.0556i	0.0656853	−	0.0379234i	0.532483	+	0.846441i	$0.321259\pi$
$398$		−	242.266i		−	0.608709i
$399$		0			0
$400$	−20.0000			−0.0500000
$401$	68.3852	+	118.447i	0.170537	+	0.295378i	0.938608	−	0.344987i	$-0.112117\pi$
$401$	68.3852	+	118.447i	0.170537	+	0.295378i	−0.768071	+	0.640365i	$0.778783\pi$
$402$		0			0
$403$	−52.6977	+	91.2750i	−0.130763	+	0.226489i
$404$	151.717	−	87.5941i	0.375538	−	0.216817i
$405$		0			0
$406$	426.129	+	308.170i	1.04958	+	0.759038i
$407$	934.215			2.29537
$408$		0			0
$409$	−426.838	−	246.435i	−1.04361	−	0.602531i	−0.122759	−	0.992437i	$-0.539174\pi$
$409$	−426.838	−	246.435i	−1.04361	−	0.602531i	−0.920855	+	0.389906i	$0.872507\pi$
$410$	−49.8454	+	86.3348i	−0.121574	+	0.210573i
$411$		0			0
$412$			278.082i			0.674957i
$413$	697.659	+	71.7744i	1.68925	+	0.173788i
$414$		0			0
$415$	0.466756	+	0.808445i	0.00112471	+	0.00194806i
$416$	−17.1361	−	9.89350i	−0.0411924	−	0.0237825i
$417$		0			0
$418$	602.104	−	347.625i	1.44044	−	0.831638i
$419$			311.640i			0.743771i	0.928279	+	0.371885i	$0.121289\pi$
$419$			311.640i			0.743771i	−0.928279	+	0.371885i	$0.878711\pi$
$420$		0			0
$421$	−539.935			−1.28250			−0.641252	−	0.767330i	$-0.721585\pi$
$421$	−539.935			−1.28250			−0.641252	+	0.767330i	$0.721585\pi$
$422$	−114.578	−	198.456i	−0.271513	−	0.470274i
$423$		0			0
$424$	−91.7469	+	158.910i	−0.216384	+	0.374788i
$425$	−78.9912	+	45.6056i	−0.185862	+	0.107307i
$426$		0			0
$427$	−32.9145	+	45.5132i	−0.0770831	+	0.106588i
$428$	−304.380			−0.711168
$429$		0			0
$430$	176.398	+	101.844i	0.410229	+	0.236846i
$431$	−314.021	+	543.900i	−0.728586	+	1.26195i	0.228895	+	0.973451i	$0.426489\pi$
$431$	−314.021	+	543.900i	−0.728586	+	1.26195i	−0.957481	+	0.288497i	$0.906845\pi$
$432$		0			0
$433$			706.789i			1.63231i	0.577836	+	0.816153i	$0.303897\pi$
$433$			706.789i			1.63231i	−0.577836	+	0.816153i	$0.696103\pi$
$434$	121.922	+	272.228i	0.280927	+	0.627253i
$435$		0			0
$436$	−64.7554	−	112.160i	−0.148522	−	0.257247i
$437$	−536.914	−	309.987i	−1.22864	−	0.709353i
$438$		0			0
$439$	564.452	−	325.886i	1.28577	−	0.742338i	0.307871	−	0.951428i	$-0.400383\pi$
$439$	564.452	−	325.886i	1.28577	−	0.742338i	0.977896	+	0.209090i	$0.0670501\pi$
$440$			126.333i			0.287120i
$441$		0			0
$442$	−90.2398			−0.204162
$443$	−11.8129	−	20.4605i	−0.0266657	−	0.0461863i	0.852385	−	0.522915i	$-0.175156\pi$
$443$	−11.8129	−	20.4605i	−0.0266657	−	0.0461863i	−0.879050	+	0.476729i	$0.841822\pi$
$444$		0			0
$445$	−124.337	+	215.358i	−0.279409	+	0.483951i
$446$	−447.435	+	258.326i	−1.00322	+	0.579207i
$447$		0			0
$448$	−51.1083	+	22.8898i	−0.114081	+	0.0510933i
$449$	55.1499			0.122828			0.0614141	−	0.998112i	$-0.480439\pi$
$449$	55.1499			0.122828			0.0614141	+	0.998112i	$0.480439\pi$
$450$		0			0
$451$	545.346	+	314.856i	1.20919	+	0.698128i
$452$	3.25860	−	5.64407i	0.00720930	−	0.0124869i
$453$		0			0
$454$			364.689i			0.803279i
$455$	44.3648	+	32.0840i	0.0975051	+	0.0705142i
$456$		0			0
$457$	−175.386	−	303.778i	−0.383778	−	0.664723i	0.607821	−	0.794074i	$-0.292044\pi$
$457$	−175.386	−	303.778i	−0.383778	−	0.664723i	−0.991599	+	0.129351i	$0.958710\pi$
$458$	18.8987	+	10.9112i	0.0412636	+	0.0238236i
$459$		0			0
$460$	97.5619	−	56.3274i	0.212091	−	0.122451i
$461$			471.598i			1.02299i	0.859287	+	0.511494i	$0.170908\pi$
$461$			471.598i			1.02299i	−0.859287	+	0.511494i	$0.829092\pi$
$462$		0			0
$463$	387.112			0.836094			0.418047	−	0.908425i	$-0.362715\pi$
$463$	387.112			0.836094			0.418047	+	0.908425i	$0.362715\pi$
$464$	−106.245	−	184.021i	−0.228975	−	0.396597i
$465$		0			0
$466$	−88.6336	+	153.518i	−0.190201	+	0.329437i
$467$	254.045	−	146.673i	0.543994	−	0.314075i	−0.202702	−	0.979240i	$-0.564972\pi$
$467$	254.045	−	146.673i	0.543994	−	0.314075i	0.746696	+	0.665166i	$0.231639\pi$
$468$		0			0
$469$	11.6506	−	113.245i	0.0248413	−	0.241461i
$470$	88.7417			0.188812
$471$		0			0
$472$	−245.418	−	141.692i	−0.519954	−	0.300195i
$473$	643.310	−	1114.25i	1.36006	−	2.35570i
$474$		0			0
$475$			123.058i			0.259069i
$476$	−149.660	+	206.946i	−0.314412	+	0.434760i
$477$		0			0
$478$	−2.56372	−	4.44049i	−0.00536343	−	0.00928973i
$479$	660.805	+	381.516i	1.37955	+	0.796484i	0.992105	−	0.125409i	$-0.0400242\pi$
$479$	660.805	+	381.516i	1.37955	+	0.796484i	0.387445	+	0.921893i	$0.373358\pi$
$480$		0			0
$481$	−141.676	+	81.7967i	−0.294545	+	0.170056i
$482$		−	136.668i		−	0.283543i
$483$		0			0
$484$	555.999			1.14876
$485$	−82.9854	−	143.735i	−0.171104	−	0.296361i
$486$		0			0
$487$	111.944	−	193.893i	0.229865	−	0.398138i	−0.727903	−	0.685680i	$-0.759505\pi$
$487$	111.944	−	193.893i	0.229865	−	0.398138i	0.957768	+	0.287542i	$0.0928382\pi$
$488$	19.6546	−	11.3476i	0.0402759	−	0.0232533i
$489$		0			0
$490$	147.155	−	48.5310i	0.300317	−	0.0990429i
$491$	837.694			1.70610			0.853049	−	0.521830i	$-0.174751\pi$
$491$	837.694			1.70610			0.853049	+	0.521830i	$0.174751\pi$
$492$		0			0
$493$	−839.239	−	484.535i	−1.70231	−	0.982829i
$494$	−60.8737	+	105.436i	−0.123226	+	0.213434i
$495$		0			0
$496$		−	120.525i		−	0.242993i
$497$	−688.203	+	308.225i	−1.38471	+	0.620171i
$498$		0			0
$499$	−87.3234	−	151.249i	−0.174997	−	0.303103i	0.765163	−	0.643836i	$-0.222658\pi$
$499$	−87.3234	−	151.249i	−0.174997	−	0.303103i	−0.940160	+	0.340733i	$0.889325\pi$
$500$	−19.3649	−	11.1803i	−0.0387298	−	0.0223607i
$501$		0			0
$502$	36.4130	−	21.0230i	0.0725358	−	0.0418786i
$503$			747.962i			1.48700i	0.668734	+	0.743501i	$0.266836\pi$
$503$			747.962i			1.48700i	−0.668734	+	0.743501i	$0.733164\pi$
$504$		0			0
$505$	195.866			0.387854
$506$	−355.800	−	616.263i	−0.703162	−	1.21791i
$507$		0			0
$508$	88.5772	−	153.420i	0.174365	−	0.302008i
$509$	203.021	−	117.214i	0.398863	−	0.230284i	−0.287130	−	0.957892i	$-0.592701\pi$
$509$	203.021	−	117.214i	0.398863	−	0.230284i	0.685993	+	0.727608i	$0.259368\pi$
$510$		0			0
$511$	−359.726	−	37.0083i	−0.703965	−	0.0724233i
$512$	22.6274			0.0441942
$513$		0			0
$514$	540.875	+	312.275i	1.05229	+	0.607538i
$515$	−155.453	+	269.252i	−0.301850	+	0.522819i
$516$		0			0
$517$		−	560.549i		−	1.08423i
$518$	−47.3821	+	460.561i	−0.0914712	+	0.889114i
$519$		0			0
$520$	−11.0613	−	19.1587i	−0.0212717	−	0.0368436i
$521$	−186.068	−	107.427i	−0.357137	−	0.206193i	0.310687	−	0.950512i	$-0.399441\pi$
$521$	−186.068	−	107.427i	−0.357137	−	0.206193i	−0.667824	+	0.744319i	$0.732774\pi$
$522$		0			0
$523$	801.108	−	462.520i	1.53176	−	0.884360i	0.532475	−	0.846446i	$-0.321262\pi$
$523$	801.108	−	462.520i	1.53176	−	0.884360i	0.999281	−	0.0379137i	$-0.0120712\pi$
$524$			250.248i			0.477573i
$525$		0			0
$526$	−485.141			−0.922321
$527$	−274.830	−	476.020i	−0.521499	−	0.903263i
$528$		0			0
$529$	−52.7773	+	91.4130i	−0.0997681	+	0.172803i
$530$	−177.667	+	102.576i	−0.335221	+	0.193540i
$531$		0			0
$532$	140.839	+	314.464i	0.264734	+	0.591098i
$533$	−110.271			−0.206887
$534$		0			0
$535$	−294.714	−	170.153i	−0.550868	−	0.318044i
$536$	−22.9998	+	39.8368i	−0.0429100	+	0.0743224i
$537$		0			0
$538$			655.277i			1.21799i
$539$	−306.553	−	929.528i	−0.568744	−	1.72454i
$540$		0			0
$541$	57.1560	+	98.9971i	0.105649	+	0.182989i	0.914003	−	0.405707i	$-0.132975\pi$
$541$	57.1560	+	98.9971i	0.105649	+	0.182989i	−0.808354	+	0.588696i	$0.799641\pi$
$542$	−299.550	−	172.945i	−0.552675	−	0.319087i
$543$		0			0
$544$	89.3683	−	51.5968i	0.164280	−	0.0948471i
$545$		−	144.797i		−	0.265683i
$546$		0			0
$547$	−57.7698			−0.105612			−0.0528060	−	0.998605i	$-0.516817\pi$
$547$	−57.7698			−0.105612			−0.0528060	+	0.998605i	$0.516817\pi$
$548$	−38.9538	−	67.4699i	−0.0710835	−	0.123120i
$549$		0			0
$550$	−70.6222	+	122.321i	−0.128404	+	0.222402i
$551$	−1132.26	+	653.712i	−2.05492	+	1.18641i
$552$		0			0
$553$	−124.648	−	90.1438i	−0.225404	−	0.163009i
$554$	199.430			0.359982
$555$		0			0
$556$	−171.378	−	98.9454i	−0.308235	−	0.177959i
$557$	−203.076	+	351.738i	−0.364589	+	0.631487i	−0.988710	−	0.149841i	$-0.952124\pi$
$557$	−203.076	+	351.738i	−0.364589	+	0.631487i	0.624121	+	0.781328i	$0.285457\pi$
$558$		0			0
$559$			225.304i			0.403049i
$560$	−62.2812	−	6.40743i	−0.111216	−	0.0114418i
$561$		0			0
$562$	60.1008	+	104.098i	0.106941	+	0.185227i
$563$	370.911	+	214.146i	0.658813	+	0.380366i	0.791824	−	0.610749i	$-0.209131\pi$
$563$	370.911	+	214.146i	0.658813	+	0.380366i	−0.133012	+	0.991114i	$0.542465\pi$
$564$		0			0
$565$	6.31026	−	3.64323i	0.0111686	−	0.00644819i
$566$			165.008i			0.291534i
$567$		0			0
$568$	304.691			0.536429
$569$	−457.897	−	793.100i	−0.804739	−	1.39385i	−0.916467	−	0.400110i	$-0.868972\pi$
$569$	−457.897	−	793.100i	−0.804739	−	1.39385i	0.111728	−	0.993739i	$-0.464362\pi$
$570$		0			0
$571$	356.947	−	618.250i	0.625125	−	1.08275i	−0.363391	−	0.931637i	$-0.618381\pi$
$571$	356.947	−	618.250i	0.625125	−	1.08275i	0.988517	−	0.151112i	$-0.0482855\pi$
$572$	−121.019	+	69.8701i	−0.211571	+	0.122151i
$573$		0			0
$574$	−182.881	+	252.883i	−0.318608	+	0.440562i
$575$	125.952			0.219047
$576$		0			0
$577$	−75.8591	−	43.7973i	−0.131472	−	0.0759052i	0.432822	−	0.901480i	$-0.357518\pi$
$577$	−75.8591	−	43.7973i	−0.131472	−	0.0759052i	−0.564293	+	0.825574i	$0.690851\pi$
$578$	30.9565	−	53.6183i	0.0535580	−	0.0927652i
$579$		0			0
$580$		−	237.570i		−	0.409604i
$581$	1.19450	+	2.66708i	0.00205594	+	0.00459050i
$582$		0			0
$583$	647.937	+	1122.26i	1.11138	+	1.92497i
$584$	126.542	+	73.0593i	0.216682	+	0.125101i
$585$		0			0
$586$	−161.522	+	93.2548i	−0.275635	+	0.159138i
$587$			169.908i			0.289452i	0.989472	+	0.144726i	$0.0462300\pi$
$587$			169.908i			0.289452i	−0.989472	+	0.144726i	$0.953770\pi$
$588$		0			0
$589$	−741.576			−1.25904
$590$	−158.417	−	274.386i	−0.268503	−	0.465061i
$591$		0			0
$592$	93.5385	−	162.014i	0.158004	−	0.273671i
$593$	−173.424	+	100.126i	−0.292452	+	0.168847i	−0.639047	−	0.769168i	$-0.720671\pi$
$593$	−173.424	+	100.126i	−0.292452	+	0.168847i	0.346595	+	0.938015i	$0.387338\pi$
$594$		0			0
$595$	−260.594	+	116.712i	−0.437973	+	0.196155i
$596$	372.930			0.625721
$597$		0			0
$598$	107.916	+	62.3053i	0.180461	+	0.104189i
$599$	−350.201	+	606.566i	−0.584643	+	1.01263i	0.410277	+	0.911961i	$0.365432\pi$
$599$	−350.201	+	606.566i	−0.584643	+	1.01263i	−0.994920	+	0.100671i	$0.967901\pi$
$600$		0			0
$601$			1039.21i			1.72914i	0.502515	+	0.864569i	$0.332408\pi$
$601$			1039.21i			1.72914i	−0.502515	+	0.864569i	$0.667592\pi$
$602$	516.687	+	373.660i	0.858285	+	0.620698i
$603$		0			0
$604$	−154.840	−	268.191i	−0.256358	−	0.444025i
$605$	538.344	+	310.813i	0.889825	+	0.513740i
$606$		0			0
$607$	52.9655	−	30.5796i	0.0872578	−	0.0503783i	−0.455736	−	0.890115i	$-0.650624\pi$
$607$	52.9655	−	30.5796i	0.0872578	−	0.0503783i	0.542994	+	0.839737i	$0.317291\pi$
$608$		−	139.224i		−	0.228987i
$609$		0			0
$610$	25.3740			0.0415967
$611$	49.0798	+	85.0087i	0.0803270	+	0.139130i
$612$		0			0
$613$	261.359	−	452.688i	0.426361	−	0.738479i	−0.570185	−	0.821516i	$-0.693129\pi$
$613$	261.359	−	452.688i	0.426361	−	0.738479i	0.996546	+	0.0830371i	$0.0264620\pi$
$614$	526.482	−	303.965i	0.857462	−	0.495056i
$615$		0			0
$616$	−40.4734	+	393.408i	−0.0657036	+	0.638649i
$617$	608.200			0.985738			0.492869	−	0.870104i	$-0.335948\pi$
$617$	608.200			0.985738			0.492869	+	0.870104i	$0.335948\pi$
$618$		0			0
$619$	902.671	+	521.157i	1.45827	+	0.841934i	0.998927	−	0.0463229i	$-0.0147503\pi$
$619$	902.671	+	521.157i	1.45827	+	0.841934i	0.459346	+	0.888257i	$0.348084\pi$
$620$	67.3754	−	116.698i	0.108670	−	0.188222i
$621$		0			0
$622$		−	355.643i		−	0.571774i
$623$	−456.187	+	630.804i	−0.732243	+	1.01253i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	−16.7831	−	9.68972i	−0.0268100	−	0.0154788i
$627$		0			0
$628$	86.9554	−	50.2037i	0.138464	−	0.0799423i
$629$		−	853.176i		−	1.35640i
$630$		0			0
$631$	−235.274			−0.372859			−0.186430	−	0.982468i	$-0.559692\pi$
$631$	−235.274			−0.372859			−0.186430	+	0.982468i	$0.559692\pi$
$632$	31.0780	+	53.8287i	0.0491741	+	0.0851720i
$633$		0			0
$634$	−23.2851	+	40.3310i	−0.0367273	+	0.0636136i
$635$	171.529	−	99.0323i	0.270124	−	0.155956i
$636$		0			0
$637$	127.876	+	114.125i	0.200747	+	0.179159i
$638$	−1500.65			−2.35211
$639$		0			0
$640$	21.9089	+	12.6491i	0.0342327	+	0.0197642i
$641$	−58.4900	+	101.308i	−0.0912481	+	0.158046i	−0.908037	−	0.418891i	$-0.862419\pi$
$641$	−58.4900	+	101.308i	−0.0912481	+	0.158046i	0.816788	+	0.576937i	$0.195752\pi$
$642$		0			0
$643$		−	874.209i		−	1.35958i	−0.733408	−	0.679789i	$-0.762071\pi$
$643$		−	874.209i		−	1.35958i	0.733408	−	0.679789i	$-0.237929\pi$
$644$	321.859	−	144.151i	0.499781	−	0.223837i
$645$		0			0
$646$	−317.470	−	549.874i	−0.491439	−	0.851198i
$647$	10.1185	+	5.84189i	0.0156390	+	0.00902920i	0.507799	−	0.861476i	$-0.330459\pi$
$647$	10.1185	+	5.84189i	0.0156390	+	0.00902920i	−0.492160	+	0.870505i	$0.663793\pi$
$648$		0			0
$649$	−1733.20	+	1000.66i	−2.67057	+	1.54185i
$650$		−	24.7338i		−	0.0380519i
$651$		0			0
$652$	−231.622			−0.355248
$653$	319.067	+	552.641i	0.488618	+	0.846311i	0.999914	−	0.0130935i	$-0.00416791\pi$
$653$	319.067	+	552.641i	0.488618	+	0.846311i	−0.511296	+	0.859404i	$0.670835\pi$
$654$		0			0
$655$	−139.893	+	242.302i	−0.213577	+	0.369927i
$656$	109.206	−	63.0500i	0.166472	−	0.0961129i
$657$		0			0
$658$	276.347	+	28.4303i	0.419980	+	0.0432071i
$659$	−870.363			−1.32073			−0.660367	−	0.750943i	$-0.729599\pi$
$659$	−870.363			−1.32073			−0.660367	+	0.750943i	$0.729599\pi$
$660$		0			0
$661$	417.571	+	241.085i	0.631727	+	0.364728i	0.781420	−	0.624005i	$-0.214495\pi$
$661$	417.571	+	241.085i	0.631727	+	0.364728i	−0.149694	+	0.988732i	$0.547829\pi$
$662$	295.486	−	511.797i	0.446354	−	0.773108i
$663$		0			0
$664$		−	1.18081i		−	0.00177833i
$665$	−39.4242	+	383.210i	−0.0592846	+	0.576255i
$666$		0			0
$667$	669.085	+	1158.89i	1.00313	+	1.73747i
$668$	−106.211	−	61.3210i	−0.158999	−	0.0917978i
$669$		0			0
$670$	−44.5389	+	25.7145i	−0.0664759	+	0.0383799i
$671$		−	160.279i		−	0.238865i
$672$		0			0
$673$	−399.323			−0.593347			−0.296674	−	0.954979i	$-0.595877\pi$
$673$	−399.323			−0.593347			−0.296674	+	0.954979i	$0.595877\pi$
$674$	202.719	+	351.119i	0.300770	+	0.520948i
$675$		0			0
$676$	−156.765	+	271.525i	−0.231901	+	0.401664i
$677$	−122.405	+	70.6707i	−0.180805	+	0.104388i	−0.587671	−	0.809100i	$-0.699955\pi$
$677$	−122.405	+	70.6707i	−0.180805	+	0.104388i	0.406866	+	0.913488i	$0.366622\pi$
$678$		0			0
$679$	−212.373	−	474.185i	−0.312773	−	0.698358i
$680$	115.374			0.169668
$681$		0			0
$682$	−737.137	−	425.586i	−1.08085	−	0.624026i
$683$	494.088	−	855.785i	0.723408	−	1.25298i	−0.236218	−	0.971700i	$-0.575908\pi$
$683$	494.088	−	855.785i	0.723408	−	1.25298i	0.959626	−	0.281279i	$-0.0907587\pi$
$684$		0			0
$685$		−	87.1032i		−	0.127158i
$686$	473.799	−	103.984i	0.690669	−	0.151580i
$687$		0			0
$688$	−128.823	−	223.128i	−0.187243	−	0.324314i
$689$	−196.522	−	113.462i	−0.285228	−	0.164677i
$690$		0			0
$691$	303.829	−	175.415i	0.439694	−	0.253857i	−0.263774	−	0.964585i	$-0.584967\pi$
$691$	303.829	−	175.415i	0.439694	−	0.253857i	0.703468	+	0.710727i	$0.251634\pi$
$692$		−	63.4033i		−	0.0916232i
$693$		0			0
$694$	−433.875			−0.625180
$695$	−110.624	−	191.607i	−0.159172	−	0.275693i
$696$		0			0
$697$	287.543	−	498.040i	0.412544	−	0.714548i
$698$	−416.611	+	240.531i	−0.596864	+	0.344600i
$699$		0			0
$700$	−56.7216	−	41.0202i	−0.0810309	−	0.0586003i
$701$	−307.500			−0.438659			−0.219330	−	0.975651i	$-0.570387\pi$
$701$	−307.500			−0.438659			−0.219330	+	0.975651i	$0.570387\pi$
$702$		0			0
$703$	−996.852	−	575.533i	−1.41800	−	0.818681i
$704$	79.8999	−	138.391i	0.113494	−	0.196578i
$705$		0			0
$706$		−	530.333i		−	0.751180i
$707$	609.939	+	62.7500i	0.862715	+	0.0887552i
$708$		0			0
$709$	49.0712	+	84.9938i	0.0692118	+	0.119878i	0.898555	−	0.438862i	$-0.144618\pi$
$709$	49.0712	+	84.9938i	0.0692118	+	0.119878i	−0.829343	+	0.558740i	$0.811285\pi$
$710$	295.016	+	170.328i	0.415516	+	0.239898i
$711$		0			0
$712$	272.409	−	157.275i	0.382597	−	0.220892i
$713$			759.016i			1.06454i
$714$		0			0
$715$	−156.234			−0.218510
$716$	131.894	+	228.448i	0.184210	+	0.319061i
$717$		0			0
$718$	−232.992	+	403.554i	−0.324502	+	0.562053i
$719$	−612.340	+	353.535i	−0.851655	+	0.491703i	−0.861209	−	0.508251i	$-0.830292\pi$
$719$	−612.340	+	353.535i	−0.851655	+	0.491703i	0.00955403	+	0.999954i	$0.496959\pi$
$720$		0			0
$721$	−570.349	+	788.664i	−0.791053	+	1.09385i
$722$	−346.100			−0.479363
$723$		0			0
$724$	−95.5106	−	55.1431i	−0.131921	−	0.0761645i
$725$	132.806	−	230.026i	0.183180	−	0.317278i
$726$		0			0
$727$		−	1353.85i		−	1.86225i	−0.364705	−	0.931123i	$-0.618830\pi$
$727$		−	1353.85i		−	1.86225i	0.364705	−	0.931123i	$-0.381170\pi$
$728$	−28.3076	−	63.2050i	−0.0388840	−	0.0868201i
$729$		0			0
$730$	81.6827	+	141.479i	0.111894	+	0.193806i
$731$	−1017.59	−	587.506i	−1.39205	−	0.803701i
$732$		0			0
$733$	−478.941	+	276.517i	−0.653398	+	0.377240i	−0.789757	−	0.613420i	$-0.789793\pi$
$733$	−478.941	+	276.517i	−0.653398	+	0.377240i	0.136359	+	0.990660i	$0.456460\pi$
$734$		−	38.4020i		−	0.0523188i
$735$		0			0
$736$	−142.498			−0.193612
$737$	162.429	+	281.336i	0.220393	+	0.381732i
$738$		0			0
$739$	−466.739	+	808.416i	−0.631582	+	1.09393i	0.355646	+	0.934621i	$0.384261\pi$
$739$	−466.739	+	808.416i	−0.631582	+	1.09393i	−0.987228	+	0.159312i	$0.949072\pi$
$740$	181.137	−	104.579i	0.244779	−	0.141323i
$741$		0			0
$742$	−586.128	+	262.509i	−0.789930	+	0.353785i
$743$	−554.921			−0.746865			−0.373432	−	0.927657i	$-0.621819\pi$
$743$	−554.921			−0.746865			−0.373432	+	0.927657i	$0.621819\pi$
$744$		0			0
$745$	361.088	+	208.474i	0.484681	+	0.279831i
$746$	−90.1544	+	156.152i	−0.120850	+	0.209319i
$747$		0			0
$748$		−	728.776i		−	0.974300i
$749$	−863.246	−	624.286i	−1.15253	−	0.833492i
$750$		0			0
$751$	−363.974	−	630.421i	−0.484652	−	0.839442i	0.515192	−	0.857075i	$-0.327721\pi$
$751$	−363.974	−	630.421i	−0.484652	−	0.839442i	−0.999845	+	0.0176322i	$0.994387\pi$
$752$	−97.2117	−	56.1252i	−0.129271	−	0.0746345i
$753$		0			0
$754$	227.577	−	131.391i	0.301826	−	0.174259i
$755$		−	346.233i		−	0.458587i
$756$		0			0
$757$	667.167			0.881330			0.440665	−	0.897672i	$-0.354743\pi$
$757$	667.167			0.881330			0.440665	+	0.897672i	$0.354743\pi$
$758$	−226.129	−	391.667i	−0.298323	−	0.516711i
$759$		0			0
$760$	77.8287	−	134.803i	0.102406	−	0.177373i
$761$	630.061	−	363.766i	0.827938	−	0.478010i	−0.0252080	−	0.999682i	$-0.508025\pi$
$761$	630.061	−	363.766i	0.827938	−	0.478010i	0.853146	+	0.521672i	$0.174691\pi$
$762$		0			0
$763$	46.3890	−	450.908i	0.0607981	−	0.590967i
$764$	−390.329			−0.510901
$765$		0			0
$766$	500.850	+	289.166i	0.653851	+	0.377501i
$767$	175.229	−	303.506i	0.228460	−	0.395705i
$768$		0			0
$769$			1374.28i			1.78709i	0.448969	+	0.893547i	$0.351791\pi$
$769$			1374.28i			1.78709i	−0.448969	+	0.893547i	$0.648209\pi$
$770$	−259.110	+	358.290i	−0.336506	+	0.465312i
$771$		0			0
$772$	−348.760	−	604.070i	−0.451761	−	0.782474i
$773$	−80.2556	−	46.3356i	−0.103824	−	0.0599425i	0.447189	−	0.894439i	$-0.352425\pi$
$773$	−80.2556	−	46.3356i	−0.103824	−	0.0599425i	−0.551013	+	0.834497i	$0.685758\pi$
$774$		0			0
$775$	130.472	−	75.3280i	0.168351	−	0.0971974i
$776$			209.938i			0.270539i
$777$		0			0
$778$	−547.517			−0.703749
$779$	−387.940	−	671.932i	−0.497998	−	0.862558i
$780$		0			0
$781$	1075.90	−	1863.51i	1.37759	−	2.38606i
$782$	−562.805	+	324.936i	−0.719700	+	0.415519i
$783$		0			0
$784$	−191.894	−	39.9062i	−0.244763	−	0.0509008i
$785$	112.259			0.143005
$786$		0			0
$787$	724.193	+	418.113i	0.920195	+	0.531275i	0.883697	−	0.468059i	$-0.155047\pi$
$787$	724.193	+	418.113i	0.920195	+	0.531275i	0.0364974	+	0.999334i	$0.488380\pi$
$788$	−56.3808	+	97.6544i	−0.0715492	+	0.123927i
$789$		0			0
$790$			69.4925i			0.0879652i
$791$	20.8177	−	9.32360i	0.0263182	−	0.0117871i
$792$		0			0
$793$	14.0334	+	24.3066i	0.0176967	+	0.0306515i
$794$	−36.8785	−	21.2918i	−0.0464465	−	0.0268159i
$795$		0			0
$796$	−296.714	+	171.308i	−0.372757	+	0.215211i
$797$			130.279i			0.163462i	0.996654	+	0.0817310i	$0.0260448\pi$
$797$			130.279i			0.163462i	−0.996654	+	0.0817310i	$0.973955\pi$
$798$		0			0
$799$	−511.924			−0.640706
$800$	14.1421	+	24.4949i	0.0176777	+	0.0306186i
$801$		0			0
$802$	96.7113	−	167.509i	0.120588	−	0.208864i
$803$	893.670	−	515.960i	1.11291	−	0.642541i
$804$		0			0
$805$	392.221	+	40.3514i	0.487232	+	0.0501259i
$806$	149.052			0.184927
$807$		0			0
$808$	−214.561	−	123.877i	−0.265546	−	0.153313i
$809$	310.782	−	538.290i	0.384156	−	0.665377i	−0.607496	−	0.794323i	$-0.707826\pi$
$809$	310.782	−	538.290i	0.384156	−	0.665377i	0.991652	+	0.128946i	$0.0411592\pi$
$810$		0			0
$811$			445.846i			0.549748i	0.961480	+	0.274874i	$0.0886361\pi$
$811$			445.846i			0.549748i	−0.961480	+	0.274874i	$0.911364\pi$
$812$	76.1107	−	739.808i	0.0937324	−	0.911093i
$813$		0			0
$814$	−660.590	−	1144.17i	−0.811535	−	1.40562i
$815$	−224.267	−	129.480i	−0.275174	−	0.158872i
$816$		0			0
$817$	−1372.89	+	792.636i	−1.68040	+	0.970178i
$818$			697.023i			0.852107i
$819$		0			0
$820$	140.984			0.171932
$821$	628.622	+	1088.81i	0.765678	+	1.32619i	0.939887	+	0.341485i	$0.110930\pi$
$821$	628.622	+	1088.81i	0.765678	+	1.32619i	−0.174209	+	0.984709i	$0.555737\pi$
$822$		0			0
$823$	−60.1709	+	104.219i	−0.0731117	+	0.126633i	−0.900264	−	0.435345i	$-0.856626\pi$
$823$	−60.1709	+	104.219i	−0.0731117	+	0.126633i	0.827152	+	0.561978i	$0.189960\pi$
$824$	340.580	−	196.634i	0.413325	−	0.238633i
$825$		0			0
$826$	−405.414	−	905.206i	−0.490816	−	1.09589i
$827$	−151.053			−0.182652			−0.0913258	−	0.995821i	$-0.529110\pi$
$827$	−151.053			−0.182652			−0.0913258	+	0.995821i	$0.529110\pi$
$828$		0			0
$829$	217.640	+	125.654i	0.262533	+	0.151573i	0.625489	−	0.780233i	$-0.284899\pi$
$829$	217.640	+	125.654i	0.262533	+	0.151573i	−0.362957	+	0.931806i	$0.618233\pi$
$830$	0.660093	−	1.14331i	0.000795292	−	0.00137749i
$831$		0			0
$832$			27.9831i			0.0336335i
$833$	−848.896	+	279.961i	−1.01908	+	0.336088i
$834$		0			0
$835$	−68.5589	−	118.748i	−0.0821065	−	0.142213i
$836$	−851.503	−	491.616i	−1.01854	−	0.588057i
$837$		0			0
$838$	381.679	−	220.363i	0.455465	−	0.262963i
$839$			499.592i			0.595461i	0.954650	+	0.297730i	$0.0962297\pi$
$839$			499.592i			0.595461i	−0.954650	+	0.297730i	$0.903770\pi$
$840$		0			0
$841$	1980.98			2.35550
$842$	381.791	+	661.282i	0.453434	+	0.785371i
$843$		0			0
$844$	−162.038	+	280.658i	−0.191988	+	0.332534i
$845$	−303.574	+	175.268i	−0.359259	+	0.207418i
$846$		0			0
$847$	1576.86	+	1140.36i	1.86170	+	1.34635i
$848$	259.499			0.306013
$849$		0			0
$850$	111.710	+	64.4960i	0.131424	+	0.0758777i
$851$	−589.068	+	1020.30i	−0.692206	+	1.19894i
$852$		0			0
$853$			1265.99i			1.48416i	0.670310	+	0.742082i	$0.266161\pi$
$853$			1265.99i			1.48416i	−0.670310	+	0.742082i	$0.733839\pi$
$854$	79.0162	+	8.12911i	0.0925248	+	0.00951886i
$855$		0			0
$856$	215.229	+	372.788i	0.251436	+	0.435499i
$857$	−320.100	−	184.810i	−0.373513	−	0.215648i	0.301479	−	0.953473i	$-0.402520\pi$
$857$	−320.100	−	184.810i	−0.373513	−	0.215648i	−0.674992	+	0.737825i	$0.735853\pi$
$858$		0			0
$859$	−1089.49	+	629.015i	−1.26832	+	0.732264i	−0.974670	−	0.223649i	$-0.928203\pi$
$859$	−1089.49	+	629.015i	−1.26832	+	0.732264i	−0.293649	+	0.955913i	$0.594870\pi$
$860$		−	288.057i		−	0.334951i
$861$		0			0
$862$	888.184			1.03038
$863$	−118.333	−	204.959i	−0.137118	−	0.237496i	0.789286	−	0.614025i	$-0.210451\pi$
$863$	−118.333	−	204.959i	−0.137118	−	0.237496i	−0.926405	+	0.376530i	$0.877117\pi$
$864$		0			0
$865$	35.4435	−	61.3900i	0.0409752	−	0.0709711i
$866$	865.636	−	499.775i	0.999579	−	0.577107i
$867$		0			0
$868$	247.197	−	341.818i	0.284790	−	0.393799i
$869$	438.959			0.505132
$870$		0			0
$871$	−49.2657	−	28.4436i	−0.0565622	−	0.0326562i
$872$	−91.5779	+	158.618i	−0.105021	+	0.181901i
$873$		0			0
$874$			876.777i			1.00318i
$875$	−31.9895	−	71.4260i	−0.0365594	−	0.0816297i
$876$		0			0
$877$	−402.766	−	697.611i	−0.459254	−	0.795451i	0.539668	−	0.841878i	$-0.318550\pi$
$877$	−402.766	−	697.611i	−0.459254	−	0.795451i	−0.998922	+	0.0464269i	$0.985217\pi$
$878$	−798.256	−	460.873i	−0.909175	−	0.524912i
$879$		0			0
$880$	154.725	−	89.3308i	0.175824	−	0.101512i
$881$		−	763.260i		−	0.866356i	−0.901308	−	0.433178i	$-0.857392\pi$
$881$		−	763.260i		−	0.866356i	0.901308	−	0.433178i	$-0.142608\pi$
$882$		0			0
$883$	574.986			0.651173			0.325587	−	0.945512i	$-0.394438\pi$
$883$	574.986			0.651173			0.325587	+	0.945512i	$0.394438\pi$
$884$	63.8092	+	110.521i	0.0721823	+	0.125023i
$885$		0			0
$886$	−16.7060	+	28.9356i	−0.0188555	+	0.0326587i
$887$	332.122	−	191.751i	0.374433	−	0.216179i	−0.300960	−	0.953637i	$-0.597307\pi$
$887$	332.122	−	191.751i	0.374433	−	0.216179i	0.675393	+	0.737458i	$0.263974\pi$
$888$		0			0
$889$	565.879	−	253.440i	0.636534	−	0.285084i
$890$	351.678			0.395144
$891$		0			0
$892$	632.768	+	365.329i	0.709381	+	0.409561i
$893$	−345.332	+	598.133i	−0.386710	+	0.669802i
$894$		0			0
$895$			294.925i			0.329525i
$896$	64.1732	+	46.4091i	0.0716219	+	0.0517958i
$897$		0			0
$898$	−38.9968	−	67.5445i	−0.0434263	−	0.0752166i
$899$	1386.19	+	800.319i	1.54193	+	0.890232i
$900$		0			0
$901$	1024.91	−	591.731i	1.13752	−	0.656749i
$902$		−	890.547i		−	0.987302i
$903$		0			0
$904$	−9.21672			−0.0101955
$905$	−61.6518	−	106.784i	−0.0681236	−	0.117993i
$906$		0			0
$907$	581.220	−	1006.70i	0.640816	−	1.10993i	−0.344435	−	0.938810i	$-0.611930\pi$
$907$	581.220	−	1006.70i	0.640816	−	1.10993i	0.985251	−	0.171115i	$-0.0547371\pi$
$908$	446.650	−	257.874i	0.491906	−	0.284002i
$909$		0			0
$910$	7.92399	−	77.0224i	0.00870768	−	0.0846400i
$911$	−1070.03			−1.17457			−0.587284	−	0.809381i	$-0.699803\pi$
$911$	−1070.03			−1.17457			−0.587284	+	0.809381i	$0.699803\pi$
$912$		0			0
$913$	−7.22190	−	4.16957i	−0.00791008	−	0.00456689i
$914$	−248.034	+	429.607i	−0.271372	+	0.470030i
$915$		0			0
$916$		−	30.8615i		−	0.0336916i
$917$	−513.262	+	709.725i	−0.559719	+	0.773964i
$918$		0			0
$919$	−583.360	−	1010.41i	−0.634777	−	1.09947i	−0.986562	−	0.163386i	$-0.947759\pi$
$919$	−583.360	−	1010.41i	−0.634777	−	1.09947i	0.351785	−	0.936081i	$-0.385575\pi$
$920$	−137.973	−	79.6589i	−0.149971	−	0.0865858i
$921$		0			0
$922$	577.587	−	333.470i	0.626450	−	0.361681i
$923$			376.808i			0.408243i
$924$		0			0
$925$	233.846			0.252807
$926$	−273.729	−	474.113i	−0.295604	−	0.512001i
$927$		0			0
$928$	−150.253	+	260.245i	−0.161910	+	0.280437i
$929$	−194.325	+	112.194i	−0.209177	+	0.120768i	−0.600929	−	0.799303i	$-0.705202\pi$
$929$	−194.325	+	112.194i	−0.209177	+	0.120768i	0.391752	+	0.920071i	$0.371869\pi$
$930$		0			0
$931$	−245.539	+	1180.71i	−0.263737	+	1.26821i
$932$	250.694			0.268984
$933$		0			0
$934$	−359.274	−	207.427i	−0.384662	−	0.222084i
$935$	407.398	−	705.635i	0.435720	−	0.754689i
$936$		0			0
$937$		−	644.185i		−	0.687497i	−0.939062	−	0.343749i	$-0.888303\pi$
$937$		−	644.185i		−	0.687497i	0.939062	−	0.343749i	$-0.111697\pi$
$938$	−146.935	+	65.8076i	−0.156647	+	0.0701573i
$939$		0			0
$940$	−62.7499	−	108.686i	−0.0667552	−	0.115623i
$941$	266.097	+	153.631i	0.282781	+	0.163264i	0.634682	−	0.772774i	$-0.281131\pi$
$941$	266.097	+	153.631i	0.282781	+	0.163264i	−0.351901	+	0.936037i	$0.614465\pi$
$942$		0			0
$943$	−687.734	+	397.063i	−0.729305	+	0.421064i
$944$			400.766i			0.424540i
$945$		0			0
$946$	−1819.56			−1.92342
$947$	−490.755	−	850.013i	−0.518221	−	0.897585i	−0.999776	−	0.0211694i	$-0.993261\pi$
$947$	−490.755	−	850.013i	−0.518221	−	0.897585i	0.481555	−	0.876416i	$-0.340072\pi$
$948$		0			0
$949$	−90.3515	+	156.493i	−0.0952071	+	0.164903i
$950$	150.715	−	87.0151i	0.158647	−	0.0915948i
$951$		0			0
$952$	359.281	+	36.9625i	0.377397	+	0.0388262i
$953$	−1258.67			−1.32075			−0.660375	−	0.750936i	$-0.729603\pi$
$953$	−1258.67			−1.32075			−0.660375	+	0.750936i	$0.729603\pi$
$954$		0			0
$955$	−377.934	−	218.200i	−0.395743	−	0.228482i
$956$	−3.62565	+	6.27980i	−0.00379252	+	0.00656883i
$957$		0			0
$958$		−	1079.09i		−	1.12640i
$959$	27.9054	−	271.245i	0.0290984	−	0.282841i
$960$		0			0
$961$	−26.5559	−	45.9962i	−0.0276336	−	0.0478628i
$962$	200.360	+	115.678i	0.208275	+	0.120247i
$963$		0			0
$964$	−167.383	+	96.6387i	−0.173634	+	0.100248i
$965$		−	779.851i		−	0.808135i
$966$		0			0
$967$	−992.744			−1.02662			−0.513311	−	0.858202i	$-0.671581\pi$
$967$	−992.744			−1.02662			−0.513311	+	0.858202i	$0.671581\pi$
$968$	−393.151	−	680.957i	−0.406147	−	0.703468i
$969$		0			0
$970$	−117.359	+	203.272i	−0.120989	+	0.209559i
$971$	309.667	−	178.787i	0.318916	−	0.184126i	−0.331993	−	0.943282i	$-0.607721\pi$
$971$	309.667	−	178.787i	0.318916	−	0.184126i	0.650909	+	0.759155i	$0.274388\pi$
$972$		0			0
$973$	−283.105	−	632.116i	−0.290961	−	0.649657i
$974$	−316.626			−0.325078
$975$		0			0
$976$	−27.7958	−	16.0479i	−0.0284793	−	0.0164426i
$977$	−438.673	+	759.804i	−0.449000	+	0.777691i	−0.998321	−	0.0579204i	$-0.981553\pi$
$977$	−438.673	+	759.804i	−0.449000	+	0.777691i	0.549321	+	0.835611i	$0.314886\pi$
$978$		0			0
$979$		−	2221.43i		−	2.26908i
$980$	−163.493	−	145.911i	−0.166829	−	0.148889i
$981$		0			0
$982$	−592.339	−	1025.96i	−0.603197	−	1.04477i
$983$	1247.26	+	720.104i	1.26883	+	0.732557i	0.974766	−	0.223229i	$-0.0716599\pi$
$983$	1247.26	+	720.104i	1.26883	+	0.732557i	0.294061	+	0.955787i	$0.404993\pi$
$984$		0			0
$985$	−109.181	+	63.0356i	−0.110844	+	0.0639956i
$986$			1370.47i			1.38993i
$987$		0			0
$988$	172.177			0.174268
$989$	811.276	+	1405.17i	0.820299	+	1.42080i
$990$		0			0
$991$	−577.181	+	999.706i	−0.582423	+	1.00879i	0.412769	+	0.910836i	$0.364562\pi$
$991$	−577.181	+	999.706i	−0.582423	+	1.00879i	−0.995191	+	0.0979496i	$0.968772\pi$
$992$	−147.612	+	85.2239i	−0.148802	+	0.0859111i
$993$		0			0
$994$	864.130	+	624.925i	0.869346	+	0.628697i
$995$	−383.057			−0.384981
$996$		0			0
$997$	1407.21	+	812.451i	1.41144	+	0.814896i	0.995524	−	0.0945072i	$-0.0301275\pi$
$997$	1407.21	+	812.451i	1.41144	+	0.814896i	0.415916	+	0.909403i	$0.363461\pi$
$998$	−123.494	+	213.898i	−0.123741	+	0.214326i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.v.c.451.1		16
3.2	odd	2		210.3.o.b.31.7	✓	16
7.5	odd	6	inner	630.3.v.c.271.1		16
15.2	even	4		1050.3.q.e.199.1		32
15.8	even	4		1050.3.q.e.199.10		32
15.14	odd	2		1050.3.p.i.451.4		16
21.5	even	6		210.3.o.b.61.7	yes	16
21.11	odd	6		1470.3.f.d.391.8		16
21.17	even	6		1470.3.f.d.391.2		16
105.47	odd	12		1050.3.q.e.649.10		32
105.68	odd	12		1050.3.q.e.649.1		32
105.89	even	6		1050.3.p.i.901.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.7	✓	16	3.2	odd	2
210.3.o.b.61.7	yes	16	21.5	even	6
630.3.v.c.271.1		16	7.5	odd	6	inner
630.3.v.c.451.1		16	1.1	even	1	trivial
1050.3.p.i.451.4		16	15.14	odd	2
1050.3.p.i.901.4		16	105.89	even	6
1050.3.q.e.199.1		32	15.2	even	4
1050.3.q.e.199.10		32	15.8	even	4
1050.3.q.e.649.1		32	105.68	odd	12
1050.3.q.e.649.10		32	105.47	odd	12
1470.3.f.d.391.2		16	21.17	even	6
1470.3.f.d.391.8		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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-6.38854 + 2.86123i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-6.38854 + 2.86123i) q^{7} +2.82843 q^{8} +(2.73861 + 1.58114i) q^{10} +(9.98749 - 17.2988i) q^{11} +3.49788i q^{13} +(8.02165 + 5.80113i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-15.7982 - 9.12112i) q^{17} +(-21.3143 + 12.3058i) q^{19} -4.47214i q^{20} -28.2489 q^{22} +(12.5952 + 21.8155i) q^{23} +(2.50000 - 4.33013i) q^{25} +(4.28401 - 2.47338i) q^{26} +(1.43274 - 13.9265i) q^{28} +53.1223 q^{29} +(26.0944 + 15.0656i) q^{31} +(-2.82843 + 4.89898i) q^{32} +25.7984i q^{34} +(9.17240 - 12.6833i) q^{35} +(23.3846 + 40.5034i) q^{37} +(30.1429 + 17.4030i) q^{38} +(-5.47723 + 3.16228i) q^{40} +31.5250i q^{41} +64.4116 q^{43} +(19.9750 + 34.5977i) q^{44} +(17.8123 - 30.8518i) q^{46} +(24.3029 - 14.0313i) q^{47} +(32.6268 - 36.5581i) q^{49} -7.07107 q^{50} +(-6.05851 - 3.49788i) q^{52} +(-32.4374 + 56.1833i) q^{53} +44.6654i q^{55} +(-18.0695 + 8.09277i) q^{56} +(-37.5631 - 65.0613i) q^{58} +(-86.7684 - 50.0958i) q^{59} +(6.94896 - 4.01198i) q^{61} -42.6119i q^{62} +8.00000 q^{64} +(-3.91075 - 6.77362i) q^{65} +(-8.13165 + 14.0844i) q^{67} +(31.5965 - 18.2422i) q^{68} +(-22.0197 - 2.26537i) q^{70} +107.725 q^{71} +(44.7395 + 25.8303i) q^{73} +(33.0709 - 57.2804i) q^{74} -49.2232i q^{76} +(-14.3095 + 139.091i) q^{77} +(10.9877 + 19.0313i) q^{79} +(7.74597 + 4.47214i) q^{80} +(38.6101 - 22.2916i) q^{82} -0.417479i q^{83} +40.7909 q^{85} +(-45.5459 - 78.8878i) q^{86} +(28.2489 - 48.9285i) q^{88} +(96.3110 - 55.6052i) q^{89} +(-10.0082 - 22.3463i) q^{91} -50.3807 q^{92} +(-34.3695 - 19.8432i) q^{94} +(27.5166 - 47.6601i) q^{95} +74.2244i q^{97} +(-67.8449 - 14.1090i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 4 q^{7}+O(q^{10}) \) 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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