LMFDB - Embedded newform 490.4.e.p.471.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,4,Mod(361,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("490.361");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$490 = 2 \cdot 5 \cdot 7^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	490.e (of order $3$ , degree $2$ , not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$28.9109359028$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{2} - x + 1$ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			471.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	490.471
Dual form			490.4.e.p.361.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} +6.00000 q^{6} -8.00000 q^{8} +(9.00000 - 15.5885i) q^{9} +(5.00000 + 8.66025i) q^{10} +(8.50000 + 14.7224i) q^{11} +(6.00000 - 10.3923i) q^{12} -81.0000 q^{13} -15.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(45.5000 + 78.8083i) q^{17} +(-18.0000 - 31.1769i) q^{18} +(-51.0000 + 88.3346i) q^{19} +20.0000 q^{20} +34.0000 q^{22} +(45.0000 - 77.9423i) q^{23} +(-12.0000 - 20.7846i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(-81.0000 + 140.296i) q^{26} +135.000 q^{27} -129.000 q^{29} +(-15.0000 + 25.9808i) q^{30} +(-58.0000 - 100.459i) q^{31} +(16.0000 + 27.7128i) q^{32} +(-25.5000 + 44.1673i) q^{33} +182.000 q^{34} -72.0000 q^{36} +(-157.000 + 271.932i) q^{37} +(102.000 + 176.669i) q^{38} +(-121.500 - 210.444i) q^{39} +(20.0000 - 34.6410i) q^{40} -124.000 q^{41} -434.000 q^{43} +(34.0000 - 58.8897i) q^{44} +(45.0000 + 77.9423i) q^{45} +(-90.0000 - 155.885i) q^{46} +(-248.500 + 430.415i) q^{47} -48.0000 q^{48} -50.0000 q^{50} +(-136.500 + 236.425i) q^{51} +(162.000 + 280.592i) q^{52} +(292.000 + 505.759i) q^{53} +(135.000 - 233.827i) q^{54} -85.0000 q^{55} -306.000 q^{57} +(-129.000 + 223.435i) q^{58} +(166.000 + 287.520i) q^{59} +(30.0000 + 51.9615i) q^{60} +(-110.000 + 190.526i) q^{61} -232.000 q^{62} +64.0000 q^{64} +(202.500 - 350.740i) q^{65} +(51.0000 + 88.3346i) q^{66} +(-192.000 - 332.554i) q^{67} +(182.000 - 315.233i) q^{68} +270.000 q^{69} -664.000 q^{71} +(-72.0000 + 124.708i) q^{72} +(-115.000 - 199.186i) q^{73} +(314.000 + 543.864i) q^{74} +(37.5000 - 64.9519i) q^{75} +408.000 q^{76} -486.000 q^{78} +(-180.500 + 312.635i) q^{79} +(-40.0000 - 69.2820i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-124.000 + 214.774i) q^{82} +1172.00 q^{83} -455.000 q^{85} +(-434.000 + 751.710i) q^{86} +(-193.500 - 335.152i) q^{87} +(-68.0000 - 117.779i) q^{88} +(-20.0000 + 34.6410i) q^{89} +180.000 q^{90} -360.000 q^{92} +(174.000 - 301.377i) q^{93} +(497.000 + 860.829i) q^{94} +(-255.000 - 441.673i) q^{95} +(-48.0000 + 83.1384i) q^{96} -175.000 q^{97} +306.000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q + 2 q^{2} + 3 q^{3} - 4 q^{4} - 5 q^{5} + 12 q^{6} - 16 q^{8} + 18 q^{9} + 10 q^{10} + 17 q^{11} + 12 q^{12} - 162 q^{13} - 30 q^{15} - 16 q^{16} + 91 q^{17} - 36 q^{18} - 102 q^{19} + 40 q^{20} + 68 q^{22}+ \cdots + 612 q^{99}+O(q^{100})$ 2 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 - 5 * q^5 + 12 * q^6 - 16 * q^8 + 18 * q^9 + 10 * q^10 + 17 * q^11 + 12 * q^12 - 162 * q^13 - 30 * q^15 - 16 * q^16 + 91 * q^17 - 36 * q^18 - 102 * q^19 + 40 * q^20 + 68 * q^22 + 90 * q^23 - 24 * q^24 - 25 * q^25 - 162 * q^26 + 270 * q^27 - 258 * q^29 - 30 * q^30 - 116 * q^31 + 32 * q^32 - 51 * q^33 + 364 * q^34 - 144 * q^36 - 314 * q^37 + 204 * q^38 - 243 * q^39 + 40 * q^40 - 248 * q^41 - 868 * q^43 + 68 * q^44 + 90 * q^45 - 180 * q^46 - 497 * q^47 - 96 * q^48 - 100 * q^50 - 273 * q^51 + 324 * q^52 + 584 * q^53 + 270 * q^54 - 170 * q^55 - 612 * q^57 - 258 * q^58 + 332 * q^59 + 60 * q^60 - 220 * q^61 - 464 * q^62 + 128 * q^64 + 405 * q^65 + 102 * q^66 - 384 * q^67 + 364 * q^68 + 540 * q^69 - 1328 * q^71 - 144 * q^72 - 230 * q^73 + 628 * q^74 + 75 * q^75 + 816 * q^76 - 972 * q^78 - 361 * q^79 - 80 * q^80 - 81 * q^81 - 248 * q^82 + 2344 * q^83 - 910 * q^85 - 868 * q^86 - 387 * q^87 - 136 * q^88 - 40 * q^89 + 360 * q^90 - 720 * q^92 + 348 * q^93 + 994 * q^94 - 510 * q^95 - 96 * q^96 - 350 * q^97 + 612 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$ .

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i	−0.684819	+	0.728714i	$0.740119\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$	6.00000			0.408248
$7$		0			0
$7$		0			0
$8$	−8.00000			−0.353553
$9$	9.00000	−	15.5885i	0.333333	−	0.577350i
$10$	5.00000	+	8.66025i	0.158114	+	0.273861i
$11$	8.50000	+	14.7224i	0.232986	+	0.403544i	0.958685	−	0.284468i	$-0.0918170\pi$
$11$	8.50000	+	14.7224i	0.232986	+	0.403544i	−0.725699	+	0.688012i	$0.758484\pi$
$12$	6.00000	−	10.3923i	0.144338	−	0.250000i
$13$	−81.0000			−1.72810			−0.864052	−	0.503402i	$-0.832081\pi$
$13$	−81.0000			−1.72810			−0.864052	+	0.503402i	$0.832081\pi$
$14$		0			0
$15$	−15.0000			−0.258199
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	45.5000	+	78.8083i	0.649139	+	1.12434i	0.983329	+	0.181837i	$0.0582042\pi$
$17$	45.5000	+	78.8083i	0.649139	+	1.12434i	−0.334189	+	0.942506i	$0.608462\pi$
$18$	−18.0000	−	31.1769i	−0.235702	−	0.408248i
$19$	−51.0000	+	88.3346i	−0.615800	+	1.06660i	0.374443	+	0.927250i	$0.377834\pi$
$19$	−51.0000	+	88.3346i	−0.615800	+	1.06660i	−0.990244	+	0.139347i	$0.955500\pi$
$20$	20.0000			0.223607
$21$		0			0
$22$	34.0000			0.329492
$23$	45.0000	−	77.9423i	0.407963	−	0.706613i	−0.586698	−	0.809806i	$-0.699573\pi$
$23$	45.0000	−	77.9423i	0.407963	−	0.706613i	0.994661	+	0.103193i	$0.0329059\pi$
$24$	−12.0000	−	20.7846i	−0.102062	−	0.176777i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	−81.0000	+	140.296i	−0.610977	+	1.05824i
$27$	135.000			0.962250
$28$		0			0
$29$	−129.000			−0.826024			−0.413012	−	0.910726i	$-0.635523\pi$
$29$	−129.000			−0.826024			−0.413012	+	0.910726i	$0.635523\pi$
$30$	−15.0000	+	25.9808i	−0.0912871	+	0.158114i
$31$	−58.0000	−	100.459i	−0.336036	−	0.582031i	0.647648	−	0.761940i	$-0.275753\pi$
$31$	−58.0000	−	100.459i	−0.336036	−	0.582031i	−0.983683	+	0.179909i	$0.942420\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$	−25.5000	+	44.1673i	−0.134515	+	0.232986i
$34$	182.000			0.918022
$35$		0			0
$36$	−72.0000			−0.333333
$37$	−157.000	+	271.932i	−0.697585	+	1.20825i	0.271717	+	0.962377i	$0.412409\pi$
$37$	−157.000	+	271.932i	−0.697585	+	1.20825i	−0.969302	+	0.245875i	$0.920925\pi$
$38$	102.000	+	176.669i	0.435436	+	0.754198i
$39$	−121.500	−	210.444i	−0.498861	−	0.864052i
$40$	20.0000	−	34.6410i	0.0790569	−	0.136931i
$41$	−124.000			−0.472330			−0.236165	−	0.971713i	$-0.575891\pi$
$41$	−124.000			−0.472330			−0.236165	+	0.971713i	$0.575891\pi$
$42$		0			0
$43$	−434.000			−1.53917			−0.769586	−	0.638543i	$-0.779537\pi$
$43$	−434.000			−1.53917			−0.769586	+	0.638543i	$0.779537\pi$
$44$	34.0000	−	58.8897i	0.116493	−	0.201772i
$45$	45.0000	+	77.9423i	0.149071	+	0.258199i
$46$	−90.0000	−	155.885i	−0.288473	−	0.499651i
$47$	−248.500	+	430.415i	−0.771222	+	1.33580i	0.165671	+	0.986181i	$0.447021\pi$
$47$	−248.500	+	430.415i	−0.771222	+	1.33580i	−0.936893	+	0.349615i	$0.886312\pi$
$48$	−48.0000			−0.144338
$49$		0			0
$50$	−50.0000			−0.141421
$51$	−136.500	+	236.425i	−0.374781	+	0.649139i
$52$	162.000	+	280.592i	0.432026	+	0.748291i
$53$	292.000	+	505.759i	0.756779	+	1.31078i	0.944485	+	0.328554i	$0.106561\pi$
$53$	292.000	+	505.759i	0.756779	+	1.31078i	−0.187706	+	0.982225i	$0.560105\pi$
$54$	135.000	−	233.827i	0.340207	−	0.589256i
$55$	−85.0000			−0.208389
$56$		0			0
$57$	−306.000			−0.711065
$58$	−129.000	+	223.435i	−0.292044	+	0.505834i
$59$	166.000	+	287.520i	0.366294	+	0.634440i	0.988983	−	0.148029i	$-0.0472930\pi$
$59$	166.000	+	287.520i	0.366294	+	0.634440i	−0.622689	+	0.782470i	$0.713960\pi$
$60$	30.0000	+	51.9615i	0.0645497	+	0.111803i
$61$	−110.000	+	190.526i	−0.230886	+	0.399907i	−0.958069	−	0.286537i	$-0.907496\pi$
$61$	−110.000	+	190.526i	−0.230886	+	0.399907i	0.727183	+	0.686444i	$0.240829\pi$
$62$	−232.000			−0.475226
$63$		0			0
$64$	64.0000			0.125000
$65$	202.500	−	350.740i	0.386416	−	0.669292i
$66$	51.0000	+	88.3346i	0.0951162	+	0.164746i
$67$	−192.000	−	332.554i	−0.350098	−	0.606387i	0.636169	−	0.771550i	$-0.280518\pi$
$67$	−192.000	−	332.554i	−0.350098	−	0.606387i	−0.986266	+	0.165163i	$0.947185\pi$
$68$	182.000	−	315.233i	0.324570	−	0.562171i
$69$	270.000			0.471075
$70$		0			0
$71$	−664.000			−1.10989			−0.554946	−	0.831887i	$-0.687261\pi$
$71$	−664.000			−1.10989			−0.554946	+	0.831887i	$0.687261\pi$
$72$	−72.0000	+	124.708i	−0.117851	+	0.204124i
$73$	−115.000	−	199.186i	−0.184380	−	0.319355i	0.758987	−	0.651105i	$-0.225694\pi$
$73$	−115.000	−	199.186i	−0.184380	−	0.319355i	−0.943367	+	0.331750i	$0.892361\pi$
$74$	314.000	+	543.864i	0.493267	+	0.854364i
$75$	37.5000	−	64.9519i	0.0577350	−	0.100000i
$76$	408.000			0.615800
$77$		0			0
$78$	−486.000			−0.705496
$79$	−180.500	+	312.635i	−0.257061	+	0.445243i	−0.965453	−	0.260576i	$-0.916088\pi$
$79$	−180.500	+	312.635i	−0.257061	+	0.445243i	0.708392	+	0.705819i	$0.249421\pi$
$80$	−40.0000	−	69.2820i	−0.0559017	−	0.0968246i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	−124.000	+	214.774i	−0.166994	+	0.289242i
$83$	1172.00			1.54992			0.774962	−	0.632008i	$-0.217769\pi$
$83$	1172.00			1.54992			0.774962	+	0.632008i	$0.217769\pi$
$84$		0			0
$85$	−455.000			−0.580608
$86$	−434.000	+	751.710i	−0.544179	+	0.942546i
$87$	−193.500	−	335.152i	−0.238453	−	0.413012i
$88$	−68.0000	−	117.779i	−0.0823730	−	0.142674i
$89$	−20.0000	+	34.6410i	−0.0238202	+	0.0412578i	−0.877690	−	0.479229i	$-0.840916\pi$
$89$	−20.0000	+	34.6410i	−0.0238202	+	0.0412578i	0.853870	+	0.520487i	$0.174250\pi$
$90$	180.000			0.210819
$91$		0			0
$92$	−360.000			−0.407963
$93$	174.000	−	301.377i	0.194010	−	0.336036i
$94$	497.000	+	860.829i	0.545337	+	0.944551i
$95$	−255.000	−	441.673i	−0.275394	−	0.476997i
$96$	−48.0000	+	83.1384i	−0.0510310	+	0.0883883i
$97$	−175.000			−0.183181			−0.0915905	−	0.995797i	$-0.529195\pi$
$97$	−175.000			−0.183181			−0.0915905	+	0.995797i	$0.529195\pi$
$98$		0			0
$99$	306.000			0.310648
$100$	−50.0000	+	86.6025i	−0.0500000	+	0.0866025i
$101$	−135.000	−	233.827i	−0.133000	−	0.230363i	0.791832	−	0.610739i	$-0.209128\pi$
$101$	−135.000	−	233.827i	−0.133000	−	0.230363i	−0.924832	+	0.380377i	$0.875794\pi$
$102$	273.000	+	472.850i	0.265010	+	0.459011i
$103$	−282.500	+	489.304i	−0.270248	+	0.468083i	−0.968925	−	0.247354i	$-0.920439\pi$
$103$	−282.500	+	489.304i	−0.270248	+	0.468083i	0.698677	+	0.715437i	$0.253772\pi$
$104$	648.000			0.610977
$105$		0			0
$106$	1168.00			1.07025
$107$	603.000	−	1044.43i	0.544806	−	0.943631i	−0.453813	−	0.891097i	$-0.649937\pi$
$107$	603.000	−	1044.43i	0.544806	−	0.943631i	0.998619	−	0.0525344i	$-0.0167299\pi$
$108$	−270.000	−	467.654i	−0.240563	−	0.416667i
$109$	709.500	+	1228.89i	0.623466	+	1.07987i	0.988835	+	0.149012i	$0.0476093\pi$
$109$	709.500	+	1228.89i	0.623466	+	1.07987i	−0.365370	+	0.930863i	$0.619057\pi$
$110$	−85.0000	+	147.224i	−0.0736767	+	0.127612i
$111$	−942.000			−0.805502
$112$		0			0
$113$	−778.000			−0.647682			−0.323841	−	0.946111i	$-0.604974\pi$
$113$	−778.000			−0.647682			−0.323841	+	0.946111i	$0.604974\pi$
$114$	−306.000	+	530.008i	−0.251399	+	0.435436i
$115$	225.000	+	389.711i	0.182447	+	0.316007i
$116$	258.000	+	446.869i	0.206506	+	0.357679i
$117$	−729.000	+	1262.67i	−0.576035	+	0.997722i
$118$	664.000			0.518018
$119$		0			0
$120$	120.000			0.0912871
$121$	521.000	−	902.398i	0.391435	−	0.677985i
$122$	220.000	+	381.051i	0.163261	+	0.282777i
$123$	−186.000	−	322.161i	−0.136350	−	0.236165i
$124$	−232.000	+	401.836i	−0.168018	+	0.291015i
$125$	125.000			0.0894427
$126$		0			0
$127$	316.000			0.220791			0.110396	−	0.993888i	$-0.464788\pi$
$127$	316.000			0.220791			0.110396	+	0.993888i	$0.464788\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$	−651.000	−	1127.57i	−0.444321	−	0.769586i
$130$	−405.000	−	701.481i	−0.273237	−	0.473261i
$131$	875.000	−	1515.54i	0.583581	−	1.01079i	−0.411470	−	0.911423i	$-0.634984\pi$
$131$	875.000	−	1515.54i	0.583581	−	1.01079i	0.995051	−	0.0993684i	$-0.0316822\pi$
$132$	204.000			0.134515
$133$		0			0
$134$	−768.000			−0.495113
$135$	−337.500	+	584.567i	−0.215166	+	0.372678i
$136$	−364.000	−	630.466i	−0.229505	−	0.397515i
$137$	−24.0000	−	41.5692i	−0.0149668	−	0.0259233i	0.858445	−	0.512906i	$-0.171431\pi$
$137$	−24.0000	−	41.5692i	−0.0149668	−	0.0259233i	−0.873412	+	0.486982i	$0.838098\pi$
$138$	270.000	−	467.654i	0.166550	−	0.288473i
$139$	−38.0000			−0.0231879			−0.0115939	−	0.999933i	$-0.503691\pi$
$139$	−38.0000			−0.0231879			−0.0115939	+	0.999933i	$0.503691\pi$
$140$		0			0
$141$	−1491.00			−0.890531
$142$	−664.000	+	1150.08i	−0.392406	+	0.679667i
$143$	−688.500	−	1192.52i	−0.402624	−	0.697366i
$144$	144.000	+	249.415i	0.0833333	+	0.144338i
$145$	322.500	−	558.586i	0.184705	−	0.319918i
$146$	−460.000			−0.260753
$147$		0			0
$148$	1256.00			0.697585
$149$	1791.00	−	3102.10i	0.984728	−	1.70560i	0.341588	−	0.939850i	$-0.389035\pi$
$149$	1791.00	−	3102.10i	0.984728	−	1.70560i	0.643140	−	0.765749i	$-0.277631\pi$
$150$	−75.0000	−	129.904i	−0.0408248	−	0.0707107i
$151$	963.500	+	1668.83i	0.519262	+	0.899388i	0.999749	+	0.0223862i	$0.00712634\pi$
$151$	963.500	+	1668.83i	0.519262	+	0.899388i	−0.480488	+	0.877001i	$0.659540\pi$
$152$	408.000	−	706.677i	0.217718	−	0.377099i
$153$	1638.00			0.865519
$154$		0			0
$155$	580.000			0.300559
$156$	−486.000	+	841.777i	−0.249430	+	0.432026i
$157$	1255.00	+	2173.72i	0.637961	+	1.10498i	0.985879	+	0.167456i	$0.0535553\pi$
$157$	1255.00	+	2173.72i	0.637961	+	1.10498i	−0.347918	+	0.937525i	$0.613111\pi$
$158$	361.000	+	625.270i	0.181770	+	0.314834i
$159$	−876.000	+	1517.28i	−0.436927	+	0.756779i
$160$	−160.000			−0.0790569
$161$		0			0
$162$	−162.000			−0.0785674
$163$	935.000	−	1619.47i	0.449294	−	0.778199i	−0.549047	−	0.835792i	$-0.685009\pi$
$163$	935.000	−	1619.47i	0.449294	−	0.778199i	0.998340	+	0.0575924i	$0.0183424\pi$
$164$	248.000	+	429.549i	0.118083	+	0.204525i
$165$	−127.500	−	220.836i	−0.0601567	−	0.104195i
$166$	1172.00	−	2029.96i	0.547981	−	0.949131i
$167$	−2019.00			−0.935538			−0.467769	−	0.883851i	$-0.654942\pi$
$167$	−2019.00			−0.935538			−0.467769	+	0.883851i	$0.654942\pi$
$168$		0			0
$169$	4364.00			1.98635
$170$	−455.000	+	788.083i	−0.205276	+	0.355548i
$171$	918.000	+	1590.02i	0.410533	+	0.711065i
$172$	868.000	+	1503.42i	0.384793	+	0.666481i
$173$	−626.500	+	1085.13i	−0.275329	+	0.476884i	−0.970218	−	0.242233i	$-0.922120\pi$
$173$	−626.500	+	1085.13i	−0.275329	+	0.476884i	0.694889	+	0.719117i	$0.255453\pi$
$174$	−774.000			−0.337223
$175$		0			0
$176$	−272.000			−0.116493
$177$	−498.000	+	862.561i	−0.211480	+	0.366294i
$178$	40.0000	+	69.2820i	0.0168434	+	0.0291736i
$179$	−246.000	−	426.084i	−0.102720	−	0.177916i	0.810084	−	0.586313i	$-0.199421\pi$
$179$	−246.000	−	426.084i	−0.102720	−	0.177916i	−0.912804	+	0.408397i	$0.866088\pi$
$180$	180.000	−	311.769i	0.0745356	−	0.129099i
$181$	−4448.00			−1.82661			−0.913307	−	0.407271i	$-0.866480\pi$
$181$	−4448.00			−1.82661			−0.913307	+	0.407271i	$0.866480\pi$
$182$		0			0
$183$	−660.000			−0.266604
$184$	−360.000	+	623.538i	−0.144237	+	0.249825i
$185$	−785.000	−	1359.66i	−0.311969	−	0.540347i
$186$	−348.000	−	602.754i	−0.137186	−	0.237613i
$187$	−773.500	+	1339.74i	−0.302481	+	0.523912i
$188$	1988.00			0.771222
$189$		0			0
$190$	−1020.00			−0.389466
$191$	−1999.50	+	3463.24i	−0.757480	+	1.31199i	0.186651	+	0.982426i	$0.440236\pi$
$191$	−1999.50	+	3463.24i	−0.757480	+	1.31199i	−0.944132	+	0.329568i	$0.893097\pi$
$192$	96.0000	+	166.277i	0.0360844	+	0.0625000i
$193$	−2440.00	−	4226.20i	−0.910026	−	1.57621i	−0.814025	−	0.580830i	$-0.802728\pi$
$193$	−2440.00	−	4226.20i	−0.910026	−	1.57621i	−0.0960015	−	0.995381i	$-0.530605\pi$
$194$	−175.000	+	303.109i	−0.0647643	+	0.112175i
$195$	1215.00			0.446195
$196$		0			0
$197$	4712.00			1.70414			0.852071	−	0.523426i	$-0.175346\pi$
$197$	4712.00			1.70414			0.852071	+	0.523426i	$0.175346\pi$
$198$	306.000	−	530.008i	0.109831	−	0.190232i
$199$	−1378.00	−	2386.77i	−0.490874	−	0.850218i	0.509071	−	0.860724i	$-0.329989\pi$
$199$	−1378.00	−	2386.77i	−0.490874	−	0.850218i	−0.999945	+	0.0105065i	$0.996656\pi$
$200$	100.000	+	173.205i	0.0353553	+	0.0612372i
$201$	576.000	−	997.661i	0.202129	−	0.350098i
$202$	−540.000			−0.188090
$203$		0			0
$204$	1092.00			0.374781
$205$	310.000	−	536.936i	0.105616	−	0.182933i
$206$	565.000	+	978.609i	0.191094	+	0.330985i
$207$	−810.000	−	1402.96i	−0.271975	−	0.471075i
$208$	648.000	−	1122.37i	0.216013	−	0.374146i
$209$	−1734.00			−0.573891
$210$		0			0
$211$	697.000			0.227410			0.113705	−	0.993515i	$-0.463728\pi$
$211$	697.000			0.227410			0.113705	+	0.993515i	$0.463728\pi$
$212$	1168.00	−	2023.04i	0.378389	−	0.655390i
$213$	−996.000	−	1725.12i	−0.320398	−	0.554946i
$214$	−1206.00	−	2088.85i	−0.385236	−	0.667248i
$215$	1085.00	−	1879.28i	0.344169	−	0.596119i
$216$	−1080.00			−0.340207
$217$		0			0
$218$	2838.00			0.881714
$219$	345.000	−	597.558i	0.106452	−	0.184380i
$220$	170.000	+	294.449i	0.0520973	+	0.0902351i
$221$	−3685.50	−	6383.47i	−1.12178	−	1.94298i
$222$	−942.000	+	1631.59i	−0.284788	+	0.493267i
$223$	−707.000			−0.212306			−0.106153	−	0.994350i	$-0.533853\pi$
$223$	−707.000			−0.212306			−0.106153	+	0.994350i	$0.533853\pi$
$224$		0			0
$225$	−450.000			−0.133333
$226$	−778.000	+	1347.54i	−0.228990	+	0.396623i
$227$	279.500	+	484.108i	0.0817228	+	0.141548i	0.903990	−	0.427554i	$-0.140624\pi$
$227$	279.500	+	484.108i	0.0817228	+	0.141548i	−0.822267	+	0.569102i	$0.807291\pi$
$228$	612.000	+	1060.02i	0.177766	+	0.307900i
$229$	1918.00	−	3322.07i	0.553472	−	0.958641i	−0.444549	−	0.895755i	$-0.646636\pi$
$229$	1918.00	−	3322.07i	0.553472	−	0.958641i	0.998021	−	0.0628865i	$-0.0200306\pi$
$230$	900.000			0.258018
$231$		0			0
$232$	1032.00			0.292044
$233$	684.000	−	1184.72i	0.192319	−	0.333106i	−0.753699	−	0.657219i	$-0.771732\pi$
$233$	684.000	−	1184.72i	0.192319	−	0.333106i	0.946018	+	0.324113i	$0.105066\pi$
$234$	1458.00	+	2525.33i	0.407318	+	0.705496i
$235$	−1242.50	−	2152.07i	−0.344901	−	0.597386i
$236$	664.000	−	1150.08i	0.183147	−	0.317220i
$237$	−1083.00			−0.296829
$238$		0			0
$239$	−3803.00			−1.02927			−0.514635	−	0.857409i	$-0.672073\pi$
$239$	−3803.00			−1.02927			−0.514635	+	0.857409i	$0.672073\pi$
$240$	120.000	−	207.846i	0.0322749	−	0.0559017i
$241$	−2825.00	−	4893.04i	−0.755080	−	1.30784i	−0.945335	−	0.326102i	$-0.894265\pi$
$241$	−2825.00	−	4893.04i	−0.755080	−	1.30784i	0.190255	−	0.981735i	$-0.439069\pi$
$242$	−1042.00	−	1804.80i	−0.276786	−	0.479408i
$243$	1944.00	−	3367.11i	0.513200	−	0.888889i
$244$	880.000			0.230886
$245$		0			0
$246$	−744.000			−0.192828
$247$	4131.00	−	7155.10i	1.06417	−	1.84319i
$248$	464.000	+	803.672i	0.118807	+	0.205779i
$249$	1758.00	+	3044.95i	0.447425	+	0.774962i
$250$	125.000	−	216.506i	0.0316228	−	0.0547723i
$251$	−1650.00			−0.414929			−0.207464	−	0.978243i	$-0.566521\pi$
$251$	−1650.00			−0.414929			−0.207464	+	0.978243i	$0.566521\pi$
$252$		0			0
$253$	1530.00			0.380199
$254$	316.000	−	547.328i	0.0780614	−	0.135206i
$255$	−682.500	−	1182.12i	−0.167607	−	0.290304i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−2905.00	+	5031.61i	−0.705093	+	1.22126i	0.261565	+	0.965186i	$0.415761\pi$
$257$	−2905.00	+	5031.61i	−0.705093	+	1.22126i	−0.966658	+	0.256071i	$0.917572\pi$
$258$	−2604.00			−0.628364
$259$		0			0
$260$	−1620.00			−0.386416
$261$	−1161.00	+	2010.91i	−0.275341	+	0.476905i
$262$	−1750.00	−	3031.09i	−0.412654	−	0.714738i
$263$	1379.00	+	2388.50i	0.323319	+	0.560004i	0.981171	−	0.193143i	$-0.0618681\pi$
$263$	1379.00	+	2388.50i	0.323319	+	0.560004i	−0.657852	+	0.753147i	$0.728535\pi$
$264$	204.000	−	353.338i	0.0475581	−	0.0823730i
$265$	−2920.00			−0.676884
$266$		0			0
$267$	−120.000			−0.0275052
$268$	−768.000	+	1330.22i	−0.175049	+	0.303193i
$269$	−93.0000	−	161.081i	−0.0210792	−	0.0365103i	0.855293	−	0.518144i	$-0.173377\pi$
$269$	−93.0000	−	161.081i	−0.0210792	−	0.0365103i	−0.876373	+	0.481634i	$0.840044\pi$
$270$	675.000	+	1169.13i	0.152145	+	0.263523i
$271$	3414.00	−	5913.22i	0.765261	−	1.32547i	−0.174847	−	0.984596i	$-0.555943\pi$
$271$	3414.00	−	5913.22i	0.765261	−	1.32547i	0.940108	−	0.340875i	$-0.110723\pi$
$272$	−1456.00			−0.324570
$273$		0			0
$274$	−96.0000			−0.0211663
$275$	212.500	−	368.061i	0.0465972	−	0.0807087i
$276$	−540.000	−	935.307i	−0.117769	−	0.203981i
$277$	4107.00	+	7113.53i	0.890851	+	1.54300i	0.838857	+	0.544352i	$0.183224\pi$
$277$	4107.00	+	7113.53i	0.890851	+	1.54300i	0.0519939	+	0.998647i	$0.483442\pi$
$278$	−38.0000	+	65.8179i	−0.00819816	+	0.0141996i
$279$	−2088.00			−0.448048
$280$		0			0
$281$	6707.00			1.42387			0.711933	−	0.702248i	$-0.247820\pi$
$281$	6707.00			1.42387			0.711933	+	0.702248i	$0.247820\pi$
$282$	−1491.00	+	2582.49i	−0.314850	+	0.545337i
$283$	2748.50	+	4760.54i	0.577319	+	0.999946i	0.995785	+	0.0917140i	$0.0292345\pi$
$283$	2748.50	+	4760.54i	0.577319	+	0.999946i	−0.418466	+	0.908232i	$0.637432\pi$
$284$	1328.00	+	2300.16i	0.277473	+	0.480597i
$285$	765.000	−	1325.02i	0.158999	−	0.275394i
$286$	−2754.00			−0.569397
$287$		0			0
$288$	576.000			0.117851
$289$	−1684.00	+	2916.77i	−0.342764	+	0.593685i
$290$	−645.000	−	1117.17i	−0.130606	−	0.226216i
$291$	−262.500	−	454.663i	−0.0528798	−	0.0915905i
$292$	−460.000	+	796.743i	−0.0921899	+	0.159678i
$293$	313.000			0.0624084			0.0312042	−	0.999513i	$-0.490066\pi$
$293$	313.000			0.0624084			0.0312042	+	0.999513i	$0.490066\pi$
$294$		0			0
$295$	−1660.00			−0.327624
$296$	1256.00	−	2175.46i	0.246634	−	0.427182i
$297$	1147.50	+	1987.53i	0.224191	+	0.388310i
$298$	−3582.00	−	6204.21i	−0.696308	−	1.20604i
$299$	−3645.00	+	6313.33i	−0.705003	+	1.22110i
$300$	−300.000			−0.0577350
$301$		0			0
$302$	3854.00			0.734347
$303$	405.000	−	701.481i	0.0767876	−	0.133000i
$304$	−816.000	−	1413.35i	−0.153950	−	0.266649i
$305$	−550.000	−	952.628i	−0.103255	−	0.178844i
$306$	1638.00	−	2837.10i	0.306007	−	0.530020i
$307$	5479.00			1.01858			0.509288	−	0.860596i	$-0.329909\pi$
$307$	5479.00			1.01858			0.509288	+	0.860596i	$0.329909\pi$
$308$		0			0
$309$	−1695.00			−0.312056
$310$	580.000	−	1004.59i	0.106264	−	0.184054i
$311$	−2211.00	−	3829.56i	−0.403133	−	0.698247i	0.590969	−	0.806694i	$-0.298745\pi$
$311$	−2211.00	−	3829.56i	−0.403133	−	0.698247i	−0.994102	+	0.108447i	$0.965412\pi$
$312$	972.000	+	1683.55i	0.176374	+	0.305489i
$313$	−137.500	+	238.157i	−0.0248305	+	0.0430078i	−0.878174	−	0.478342i	$-0.841238\pi$
$313$	−137.500	+	238.157i	−0.0248305	+	0.0430078i	0.853343	+	0.521350i	$0.174571\pi$
$314$	5020.00			0.902213
$315$		0			0
$316$	1444.00			0.257061
$317$	2053.00	−	3555.90i	0.363748	−	0.630029i	−0.624827	−	0.780763i	$-0.714830\pi$
$317$	2053.00	−	3555.90i	0.363748	−	0.630029i	0.988574	+	0.150734i	$0.0481638\pi$
$318$	1752.00	+	3034.55i	0.308954	+	0.535124i
$319$	−1096.50	−	1899.19i	−0.192452	−	0.333337i
$320$	−160.000	+	277.128i	−0.0279508	+	0.0484123i
$321$	3618.00			0.629087
$322$		0			0
$323$	−9282.00			−1.59896
$324$	−162.000	+	280.592i	−0.0277778	+	0.0481125i
$325$	1012.50	+	1753.70i	0.172810	+	0.299316i
$326$	−1870.00	−	3238.94i	−0.317699	−	0.550270i
$327$	−2128.50	+	3686.67i	−0.359958	+	0.623466i
$328$	992.000			0.166994
$329$		0			0
$330$	−510.000			−0.0850745
$331$	−4130.00	+	7153.37i	−0.685817	+	1.18787i	0.287363	+	0.957822i	$0.407222\pi$
$331$	−4130.00	+	7153.37i	−0.685817	+	1.18787i	−0.973179	+	0.230048i	$0.926112\pi$
$332$	−2344.00	−	4059.93i	−0.387481	−	0.671137i
$333$	2826.00	+	4894.78i	0.465057	+	0.805502i
$334$	−2019.00	+	3497.01i	−0.330763	+	0.572898i
$335$	1920.00			0.313137
$336$		0			0
$337$	9946.00			1.60769			0.803847	−	0.594836i	$-0.202783\pi$
$337$	9946.00			1.60769			0.803847	+	0.594836i	$0.202783\pi$
$338$	4364.00	−	7558.67i	0.702279	−	1.21638i
$339$	−1167.00	−	2021.30i	−0.186970	−	0.323841i
$340$	910.000	+	1576.17i	0.145152	+	0.251411i
$341$	986.000	−	1707.80i	0.156583	−	0.271210i
$342$	3672.00			0.580582
$343$		0			0
$344$	3472.00			0.544179
$345$	−675.000	+	1169.13i	−0.105336	+	0.182447i
$346$	1253.00	+	2170.26i	0.194687	+	0.337208i
$347$	4399.00	+	7619.29i	0.680550	+	1.17875i	0.974813	+	0.223022i	$0.0715922\pi$
$347$	4399.00	+	7619.29i	0.680550	+	1.17875i	−0.294264	+	0.955724i	$0.595074\pi$
$348$	−774.000	+	1340.61i	−0.119226	+	0.206506i
$349$	−1838.00			−0.281908			−0.140954	−	0.990016i	$-0.545017\pi$
$349$	−1838.00			−0.281908			−0.140954	+	0.990016i	$0.545017\pi$
$350$		0			0
$351$	−10935.0			−1.66287
$352$	−272.000	+	471.118i	−0.0411865	+	0.0713371i
$353$	−1132.50	−	1961.55i	−0.170756	−	0.295758i	0.767928	−	0.640536i	$-0.221288\pi$
$353$	−1132.50	−	1961.55i	−0.170756	−	0.295758i	−0.938684	+	0.344778i	$0.887954\pi$
$354$	996.000	+	1725.12i	0.149539	+	0.259009i
$355$	1660.00	−	2875.20i	0.248179	−	0.429859i
$356$	160.000			0.0238202
$357$		0			0
$358$	−984.000			−0.145268
$359$	−2068.00	+	3581.88i	−0.304025	+	0.526586i	−0.977044	−	0.213039i	$-0.931664\pi$
$359$	−2068.00	+	3581.88i	−0.304025	+	0.526586i	0.673019	+	0.739625i	$0.264997\pi$
$360$	−360.000	−	623.538i	−0.0527046	−	0.0912871i
$361$	−1772.50	−	3070.06i	−0.258420	−	0.447596i
$362$	−4448.00	+	7704.16i	−0.645806	+	1.11857i
$363$	3126.00			0.451990
$364$		0			0
$365$	1150.00			0.164914
$366$	−660.000	+	1143.15i	−0.0942589	+	0.163261i
$367$	5015.50	+	8687.10i	0.713370	+	1.23559i	0.963585	+	0.267403i	$0.0861656\pi$
$367$	5015.50	+	8687.10i	0.713370	+	1.23559i	−0.250214	+	0.968191i	$0.580501\pi$
$368$	720.000	+	1247.08i	0.101991	+	0.176653i
$369$	−1116.00	+	1932.97i	−0.157443	+	0.272700i
$370$	−3140.00			−0.441191
$371$		0			0
$372$	−1392.00			−0.194010
$373$	−1396.00	+	2417.94i	−0.193786	+	0.335647i	−0.946502	−	0.322698i	$-0.895410\pi$
$373$	−1396.00	+	2417.94i	−0.193786	+	0.335647i	0.752716	+	0.658345i	$0.228743\pi$
$374$	1547.00	+	2679.48i	0.213886	+	0.370462i
$375$	187.500	+	324.760i	0.0258199	+	0.0447214i
$376$	1988.00	−	3443.32i	0.272668	−	0.472275i
$377$	10449.0			1.42746
$378$		0			0
$379$	9948.00			1.34827			0.674135	−	0.738608i	$-0.264517\pi$
$379$	9948.00			1.34827			0.674135	+	0.738608i	$0.264517\pi$
$380$	−1020.00	+	1766.69i	−0.137697	+	0.238498i
$381$	474.000	+	820.992i	0.0637369	+	0.110396i
$382$	3999.00	+	6926.47i	0.535619	+	0.927720i
$383$	−1350.00	+	2338.27i	−0.180109	+	0.311958i	−0.941918	−	0.335844i	$-0.890978\pi$
$383$	−1350.00	+	2338.27i	−0.180109	+	0.311958i	0.761808	+	0.647802i	$0.224312\pi$
$384$	384.000			0.0510310
$385$		0			0
$386$	−9760.00			−1.28697
$387$	−3906.00	+	6765.39i	−0.513057	+	0.888641i
$388$	350.000	+	606.218i	0.0457953	+	0.0793197i
$389$	315.500	+	546.462i	0.0411221	+	0.0712255i	0.885854	−	0.463964i	$-0.153573\pi$
$389$	315.500	+	546.462i	0.0411221	+	0.0712255i	−0.844732	+	0.535190i	$0.820240\pi$
$390$	1215.00	−	2104.44i	0.157754	−	0.273237i
$391$	8190.00			1.05930
$392$		0			0
$393$	5250.00			0.673861
$394$	4712.00	−	8161.42i	0.602505	−	1.04357i
$395$	−902.500	−	1563.18i	−0.114961	−	0.199119i
$396$	−612.000	−	1060.02i	−0.0776620	−	0.134515i
$397$	6569.50	−	11378.7i	0.830513	−	1.43849i	−0.0671186	−	0.997745i	$-0.521381\pi$
$397$	6569.50	−	11378.7i	0.830513	−	1.43849i	0.897632	−	0.440746i	$-0.145286\pi$
$398$	−5512.00			−0.694200
$399$		0			0
$400$	400.000			0.0500000
$401$	443.500	−	768.165i	0.0552303	−	0.0956616i	−0.837088	−	0.547068i	$-0.815744\pi$
$401$	443.500	−	768.165i	0.0552303	−	0.0956616i	0.892319	+	0.451406i	$0.149077\pi$
$402$	−1152.00	−	1995.32i	−0.142927	−	0.247556i
$403$	4698.00	+	8137.17i	0.580705	+	1.00581i
$404$	−540.000	+	935.307i	−0.0665000	+	0.115181i
$405$	405.000			0.0496904
$406$		0			0
$407$	−5338.00			−0.650110
$408$	1092.00	−	1891.40i	0.132505	−	0.229505i
$409$	2595.00	+	4494.67i	0.313727	+	0.543392i	0.979166	−	0.203061i	$-0.0650889\pi$
$409$	2595.00	+	4494.67i	0.313727	+	0.543392i	−0.665439	+	0.746452i	$0.731756\pi$
$410$	−620.000	−	1073.87i	−0.0746820	−	0.129353i
$411$	72.0000	−	124.708i	0.00864111	−	0.0149668i
$412$	2260.00			0.270248
$413$		0			0
$414$	−3240.00			−0.384631
$415$	−2930.00	+	5074.91i	−0.346574	+	0.600283i
$416$	−1296.00	−	2244.74i	−0.152744	−	0.264561i
$417$	−57.0000	−	98.7269i	−0.00669377	−	0.0115939i
$418$	−1734.00	+	3003.38i	−0.202901	+	0.351435i
$419$	−5712.00			−0.665989			−0.332995	−	0.942929i	$-0.608059\pi$
$419$	−5712.00			−0.665989			−0.332995	+	0.942929i	$0.608059\pi$
$420$		0			0
$421$	−11155.0			−1.29136			−0.645679	−	0.763609i	$-0.723425\pi$
$421$	−11155.0			−1.29136			−0.645679	+	0.763609i	$0.723425\pi$
$422$	697.000	−	1207.24i	0.0804015	−	0.139259i
$423$	4473.00	+	7747.46i	0.514148	+	0.890531i
$424$	−2336.00	−	4046.07i	−0.267562	−	0.463431i
$425$	1137.50	−	1970.21i	0.129828	−	0.224869i
$426$	−3984.00			−0.453111
$427$		0			0
$428$	−4824.00			−0.544806
$429$	2065.50	−	3577.55i	0.232455	−	0.402624i
$430$	−2170.00	−	3758.55i	−0.243364	−	0.421520i
$431$	−4249.50	−	7360.35i	−0.474922	−	0.822588i	0.524666	−	0.851308i	$-0.324190\pi$
$431$	−4249.50	−	7360.35i	−0.474922	−	0.822588i	−0.999587	+	0.0287199i	$0.990857\pi$
$432$	−1080.00	+	1870.61i	−0.120281	+	0.208333i
$433$	5102.00			0.566251			0.283125	−	0.959083i	$-0.408629\pi$
$433$	5102.00			0.566251			0.283125	+	0.959083i	$0.408629\pi$
$434$		0			0
$435$	1935.00			0.213279
$436$	2838.00	−	4915.56i	0.311733	−	0.539937i
$437$	4590.00	+	7950.11i	0.502447	+	0.870264i
$438$	−690.000	−	1195.12i	−0.0752728	−	0.130376i
$439$	−7847.00	+	13591.4i	−0.853114	+	1.47764i	0.0252705	+	0.999681i	$0.491955\pi$
$439$	−7847.00	+	13591.4i	−0.853114	+	1.47764i	−0.878384	+	0.477955i	$0.841378\pi$
$440$	680.000			0.0736767
$441$		0			0
$442$	−14742.0			−1.58644
$443$	−4571.00	+	7917.20i	−0.490236	+	0.849115i	−0.999937	−	0.0112375i	$-0.996423\pi$
$443$	−4571.00	+	7917.20i	−0.490236	+	0.849115i	0.509700	+	0.860352i	$0.329756\pi$
$444$	1884.00	+	3263.18i	0.201375	+	0.348792i
$445$	−100.000	−	173.205i	−0.0106527	−	0.0184510i
$446$	−707.000	+	1224.56i	−0.0750615	+	0.130010i
$447$	10746.0			1.13707
$448$		0			0
$449$	−17145.0			−1.80205			−0.901027	−	0.433762i	$-0.857186\pi$
$449$	−17145.0			−1.80205			−0.901027	+	0.433762i	$0.857186\pi$
$450$	−450.000	+	779.423i	−0.0471405	+	0.0816497i
$451$	−1054.00	−	1825.58i	−0.110046	−	0.190606i
$452$	1556.00	+	2695.07i	0.161921	+	0.280455i
$453$	−2890.50	+	5006.49i	−0.299796	+	0.519262i
$454$	1118.00			0.115573
$455$		0			0
$456$	2448.00			0.251399
$457$	5092.00	−	8819.60i	0.521212	−	0.902765i	−0.478484	−	0.878096i	$-0.658814\pi$
$457$	5092.00	−	8819.60i	0.521212	−	0.902765i	0.999696	−	0.0246688i	$-0.00785311\pi$
$458$	−3836.00	−	6644.15i	−0.391364	−	0.677862i
$459$	6142.50	+	10639.1i	0.624635	+	1.08190i
$460$	900.000	−	1558.85i	0.0912233	−	0.158003i
$461$	−9152.00			−0.924623			−0.462311	−	0.886718i	$-0.652980\pi$
$461$	−9152.00			−0.924623			−0.462311	+	0.886718i	$0.652980\pi$
$462$		0			0
$463$	−1084.00			−0.108807			−0.0544036	−	0.998519i	$-0.517326\pi$
$463$	−1084.00			−0.108807			−0.0544036	+	0.998519i	$0.517326\pi$
$464$	1032.00	−	1787.48i	0.103253	−	0.178839i
$465$	870.000	+	1506.88i	0.0867641	+	0.150280i
$466$	−1368.00	−	2369.45i	−0.135990	−	0.235542i
$467$	−9641.50	+	16699.6i	−0.955365	+	1.65474i	−0.221834	+	0.975084i	$0.571204\pi$
$467$	−9641.50	+	16699.6i	−0.955365	+	1.65474i	−0.733531	+	0.679656i	$0.762129\pi$
$468$	5832.00			0.576035
$469$		0			0
$470$	−4970.00			−0.487764
$471$	−3765.00	+	6521.17i	−0.368327	+	0.637961i
$472$	−1328.00	−	2300.16i	−0.129505	−	0.224308i
$473$	−3689.00	−	6389.54i	−0.358605	−	0.621123i
$474$	−1083.00	+	1875.81i	−0.104945	+	0.181770i
$475$	2550.00			0.246320
$476$		0			0
$477$	10512.0			1.00904
$478$	−3803.00	+	6586.99i	−0.363902	+	0.630297i
$479$	2559.00	+	4432.32i	0.244100	+	0.422793i	0.961878	−	0.273479i	$-0.0881743\pi$
$479$	2559.00	+	4432.32i	0.244100	+	0.422793i	−0.717779	+	0.696272i	$0.754841\pi$
$480$	−240.000	−	415.692i	−0.0228218	−	0.0395285i
$481$	12717.0	−	22026.5i	1.20550	−	2.08799i
$482$	−11300.0			−1.06784
$483$		0			0
$484$	−4168.00			−0.391435
$485$	437.500	−	757.772i	0.0409605	−	0.0709457i
$486$	−3888.00	−	6734.21i	−0.362887	−	0.628539i
$487$	−1459.00	−	2527.06i	−0.135757	−	0.235138i	0.790129	−	0.612940i	$-0.210013\pi$
$487$	−1459.00	−	2527.06i	−0.135757	−	0.235138i	−0.925886	+	0.377802i	$0.876680\pi$
$488$	880.000	−	1524.20i	0.0816306	−	0.141388i
$489$	5610.00			0.518800
$490$		0			0
$491$	−18627.0			−1.71207			−0.856033	−	0.516921i	$-0.827078\pi$
$491$	−18627.0			−1.71207			−0.856033	+	0.516921i	$0.827078\pi$
$492$	−744.000	+	1288.65i	−0.0681750	+	0.118083i
$493$	−5869.50	−	10166.3i	−0.536205	−	0.928734i
$494$	−8262.00	−	14310.2i	−0.752480	−	1.30333i
$495$	−765.000	+	1325.02i	−0.0694630	+	0.120313i
$496$	1856.00			0.168018
$497$		0			0
$498$	7032.00			0.632754
$499$	−6421.50	+	11122.4i	−0.576084	+	0.997806i	0.419839	+	0.907599i	$0.362086\pi$
$499$	−6421.50	+	11122.4i	−0.576084	+	0.997806i	−0.995923	+	0.0902079i	$0.971247\pi$
$500$	−250.000	−	433.013i	−0.0223607	−	0.0387298i
$501$	−3028.50	−	5245.52i	−0.270067	−	0.467769i
$502$	−1650.00	+	2857.88i	−0.146699	+	0.254091i
$503$	−18837.0			−1.66978			−0.834891	−	0.550415i	$-0.814469\pi$
$503$	−18837.0			−1.66978			−0.834891	+	0.550415i	$0.814469\pi$
$504$		0			0
$505$	1350.00			0.118959
$506$	1530.00	−	2650.04i	0.134421	−	0.232823i
$507$	6546.00	+	11338.0i	0.573408	+	0.993173i
$508$	−632.000	−	1094.66i	−0.0551978	−	0.0956053i
$509$	3871.00	−	6704.77i	0.337090	−	0.583858i	−0.646794	−	0.762665i	$-0.723891\pi$
$509$	3871.00	−	6704.77i	0.337090	−	0.583858i	0.983884	+	0.178807i	$0.0572238\pi$
$510$	−2730.00			−0.237032
$511$		0			0
$512$	−512.000			−0.0441942
$513$	−6885.00	+	11925.2i	−0.592554	+	1.02633i
$514$	5810.00	+	10063.2i	0.498576	+	0.863559i
$515$	−1412.50	−	2446.52i	−0.120859	−	0.209333i
$516$	−2604.00	+	4510.26i	−0.222160	+	0.384793i
$517$	−8449.00			−0.718736
$518$		0			0
$519$	−3759.00			−0.317923
$520$	−1620.00	+	2805.92i	−0.136619	+	0.236630i
$521$	−307.000	−	531.740i	−0.0258156	−	0.0447139i	0.852829	−	0.522190i	$-0.174885\pi$
$521$	−307.000	−	531.740i	−0.0258156	−	0.0447139i	−0.878645	+	0.477476i	$0.841552\pi$
$522$	2322.00	+	4021.82i	0.194696	+	0.337223i
$523$	−8918.00	+	15446.4i	−0.745616	+	1.29144i	0.204291	+	0.978910i	$0.434511\pi$
$523$	−8918.00	+	15446.4i	−0.745616	+	1.29144i	−0.949907	+	0.312534i	$0.898822\pi$
$524$	−7000.00			−0.583581
$525$		0			0
$526$	5516.00			0.457242
$527$	5278.00	−	9141.76i	0.436268	−	0.755639i
$528$	−408.000	−	706.677i	−0.0336286	−	0.0582465i
$529$	2033.50	+	3522.13i	0.167132	+	0.289482i
$530$	−2920.00	+	5057.59i	−0.239315	+	0.414505i
$531$	5976.00			0.488392
$532$		0			0
$533$	10044.0			0.816236
$534$	−120.000	+	207.846i	−0.00972455	+	0.0168434i
$535$	3015.00	+	5222.13i	0.243645	+	0.422005i
$536$	1536.00	+	2660.43i	0.123778	+	0.214390i
$537$	738.000	−	1278.25i	0.0593055	−	0.102720i
$538$	−372.000			−0.0298105
$539$		0			0
$540$	2700.00			0.215166
$541$	−11731.5	+	20319.6i	−0.932304	+	1.61480i	−0.152932	+	0.988237i	$0.548872\pi$
$541$	−11731.5	+	20319.6i	−0.932304	+	1.61480i	−0.779372	+	0.626562i	$0.784462\pi$
$542$	−6828.00	−	11826.4i	−0.541121	−	0.937249i
$543$	−6672.00	−	11556.2i	−0.527298	−	0.913307i
$544$	−1456.00	+	2521.87i	−0.114753	+	0.198758i
$545$	−7095.00			−0.557645
$546$		0			0
$547$	−1860.00			−0.145389			−0.0726946	−	0.997354i	$-0.523160\pi$
$547$	−1860.00			−0.145389			−0.0726946	+	0.997354i	$0.523160\pi$
$548$	−96.0000	+	166.277i	−0.00748342	+	0.0129617i
$549$	1980.00	+	3429.46i	0.153924	+	0.266604i
$550$	−425.000	−	736.122i	−0.0329492	−	0.0570697i
$551$	6579.00	−	11395.2i	0.508666	−	0.881035i
$552$	−2160.00			−0.166550
$553$		0			0
$554$	16428.0			1.25985
$555$	2355.00	−	4078.98i	0.180116	−	0.311969i
$556$	76.0000	+	131.636i	0.00579697	+	0.0100407i
$557$	−5144.00	−	8909.67i	−0.391307	−	0.677764i	0.601315	−	0.799012i	$-0.294644\pi$
$557$	−5144.00	−	8909.67i	−0.391307	−	0.677764i	−0.992622	+	0.121248i	$0.961310\pi$
$558$	−2088.00	+	3616.52i	−0.158409	+	0.274372i
$559$	35154.0			2.65985
$560$		0			0
$561$	−4641.00			−0.349275
$562$	6707.00	−	11616.9i	0.503412	−	0.871936i
$563$	1178.00	+	2040.36i	0.0881826	+	0.152737i	0.906743	−	0.421684i	$-0.138561\pi$
$563$	1178.00	+	2040.36i	0.0881826	+	0.152737i	−0.818560	+	0.574421i	$0.805227\pi$
$564$	2982.00	+	5164.98i	0.222633	+	0.385611i
$565$	1945.00	−	3368.84i	0.144826	−	0.250846i
$566$	10994.0			0.816453
$567$		0			0
$568$	5312.00			0.392406
$569$	7659.00	−	13265.8i	0.564292	−	0.977382i	−0.432823	−	0.901479i	$-0.642483\pi$
$569$	7659.00	−	13265.8i	0.564292	−	0.977382i	0.997115	−	0.0759032i	$-0.0241840\pi$
$570$	−1530.00	−	2650.04i	−0.112429	−	0.194733i
$571$	6582.00	+	11400.4i	0.482396	+	0.835534i	0.999796	−	0.0202094i	$-0.00643329\pi$
$571$	6582.00	+	11400.4i	0.482396	+	0.835534i	−0.517400	+	0.855744i	$0.673100\pi$
$572$	−2754.00	+	4770.07i	−0.201312	+	0.348683i
$573$	−11997.0			−0.874663
$574$		0			0
$575$	−2250.00			−0.163185
$576$	576.000	−	997.661i	0.0416667	−	0.0721688i
$577$	−4479.50	−	7758.72i	−0.323196	−	0.559792i	0.657950	−	0.753062i	$-0.271424\pi$
$577$	−4479.50	−	7758.72i	−0.323196	−	0.559792i	−0.981146	+	0.193270i	$0.938091\pi$
$578$	3368.00	+	5833.55i	0.242371	+	0.419799i
$579$	7320.00	−	12678.6i	0.525404	−	0.910026i
$580$	−2580.00			−0.184705
$581$		0			0
$582$	−1050.00			−0.0747833
$583$	−4964.00	+	8597.90i	−0.352638	+	0.610787i
$584$	920.000	+	1593.49i	0.0651881	+	0.112909i
$585$	−3645.00	−	6313.33i	−0.257611	−	0.446195i
$586$	313.000	−	542.132i	0.0220647	−	0.0382172i
$587$	16952.0			1.19197			0.595983	−	0.802997i	$-0.296763\pi$
$587$	16952.0			1.19197			0.595983	+	0.802997i	$0.296763\pi$
$588$		0			0
$589$	11832.0			0.827723
$590$	−1660.00	+	2875.20i	−0.115832	+	0.200628i
$591$	7068.00	+	12242.1i	0.491944	+	0.852071i
$592$	−2512.00	−	4350.91i	−0.174396	−	0.302063i
$593$	−5035.50	+	8721.74i	−0.348707	+	0.603978i	−0.986020	−	0.166627i	$-0.946712\pi$
$593$	−5035.50	+	8721.74i	−0.348707	+	0.603978i	0.637313	+	0.770605i	$0.280046\pi$
$594$	4590.00			0.317054
$595$		0			0
$596$	−14328.0			−0.984728
$597$	4134.00	−	7160.30i	0.283406	−	0.490874i
$598$	7290.00	+	12626.7i	0.498512	+	0.863448i
$599$	1414.50	+	2449.99i	0.0964856	+	0.167118i	0.910228	−	0.414108i	$-0.135906\pi$
$599$	1414.50	+	2449.99i	0.0964856	+	0.167118i	−0.813742	+	0.581226i	$0.802573\pi$
$600$	−300.000	+	519.615i	−0.0204124	+	0.0353553i
$601$	−7662.00			−0.520032			−0.260016	−	0.965604i	$-0.583728\pi$
$601$	−7662.00			−0.520032			−0.260016	+	0.965604i	$0.583728\pi$
$602$		0			0
$603$	−6912.00			−0.466797
$604$	3854.00	−	6675.32i	0.259631	−	0.449694i
$605$	2605.00	+	4511.99i	0.175055	+	0.303204i
$606$	−810.000	−	1402.96i	−0.0542970	−	0.0940452i
$607$	−453.500	+	785.485i	−0.0303245	+	0.0525236i	−0.880789	−	0.473508i	$-0.842987\pi$
$607$	−453.500	+	785.485i	−0.0303245	+	0.0525236i	0.850465	+	0.526032i	$0.176321\pi$
$608$	−3264.00			−0.217718
$609$		0			0
$610$	−2200.00			−0.146025
$611$	20128.5	−	34863.6i	1.33275	−	2.30840i
$612$	−3276.00	−	5674.20i	−0.216380	−	0.374781i
$613$	14823.0	+	25674.2i	0.976664	+	1.69163i	0.674329	+	0.738431i	$0.264433\pi$
$613$	14823.0	+	25674.2i	0.976664	+	1.69163i	0.302335	+	0.953202i	$0.402234\pi$
$614$	5479.00	−	9489.91i	0.360121	−	0.623748i
$615$	1860.00			0.121955
$616$		0			0
$617$	11006.0			0.718128			0.359064	−	0.933313i	$-0.383096\pi$
$617$	11006.0			0.718128			0.359064	+	0.933313i	$0.383096\pi$
$618$	−1695.00	+	2935.83i	−0.110328	+	0.191094i
$619$	−10549.0	−	18271.4i	−0.684976	−	1.18641i	−0.973444	−	0.228924i	$-0.926479\pi$
$619$	−10549.0	−	18271.4i	−0.684976	−	1.18641i	0.288468	−	0.957489i	$-0.406854\pi$
$620$	−1160.00	−	2009.18i	−0.0751399	−	0.130146i
$621$	6075.00	−	10522.2i	0.392563	−	0.679938i
$622$	−8844.00			−0.570116
$623$		0			0
$624$	3888.00			0.249430
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	275.000	+	476.314i	0.0175578	+	0.0304111i
$627$	−2601.00	−	4505.06i	−0.165668	−	0.286946i
$628$	5020.00	−	8694.90i	0.318981	−	0.552491i
$629$	−28574.0			−1.81132
$630$		0			0
$631$	21707.0			1.36948			0.684740	−	0.728787i	$-0.259916\pi$
$631$	21707.0			1.36948			0.684740	+	0.728787i	$0.259916\pi$
$632$	1444.00	−	2501.08i	0.0908849	−	0.157417i
$633$	1045.50	+	1810.86i	0.0656475	+	0.113705i
$634$	−4106.00	−	7111.80i	−0.257208	−	0.445498i
$635$	−790.000	+	1368.32i	−0.0493704	+	0.0855120i
$636$	7008.00			0.436927
$637$		0			0
$638$	−4386.00			−0.272168
$639$	−5976.00	+	10350.7i	−0.369964	+	0.640796i
$640$	320.000	+	554.256i	0.0197642	+	0.0342327i
$641$	−5545.00	−	9604.22i	−0.341676	−	0.591800i	0.643068	−	0.765809i	$-0.277661\pi$
$641$	−5545.00	−	9604.22i	−0.341676	−	0.591800i	−0.984744	+	0.174009i	$0.944328\pi$
$642$	3618.00	−	6266.56i	0.222416	−	0.385236i
$643$	−995.000			−0.0610248			−0.0305124	−	0.999534i	$-0.509714\pi$
$643$	−995.000			−0.0610248			−0.0305124	+	0.999534i	$0.509714\pi$
$644$		0			0
$645$	6510.00			0.397412
$646$	−9282.00	+	16076.9i	−0.565318	+	0.979159i
$647$	10396.0	+	18006.4i	0.631699	+	1.09413i	0.987204	+	0.159460i	$0.0509753\pi$
$647$	10396.0	+	18006.4i	0.631699	+	1.09413i	−0.355506	+	0.934674i	$0.615691\pi$
$648$	324.000	+	561.184i	0.0196419	+	0.0340207i
$649$	−2822.00	+	4887.85i	−0.170683	+	0.295631i
$650$	4050.00			0.244391
$651$		0			0
$652$	−7480.00			−0.449294
$653$	5249.00	−	9091.53i	0.314562	−	0.544838i	−0.664782	−	0.747037i	$-0.731476\pi$
$653$	5249.00	−	9091.53i	0.314562	−	0.544838i	0.979344	+	0.202199i	$0.0648089\pi$
$654$	4257.00	+	7373.34i	0.254529	+	0.440857i
$655$	4375.00	+	7577.72i	0.260985	+	0.452040i
$656$	992.000	−	1718.19i	0.0590413	−	0.102263i
$657$	−4140.00			−0.245840
$658$		0			0
$659$	−6749.00			−0.398943			−0.199472	−	0.979904i	$-0.563923\pi$
$659$	−6749.00			−0.398943			−0.199472	+	0.979904i	$0.563923\pi$
$660$	−510.000	+	883.346i	−0.0300784	+	0.0520973i
$661$	−6200.00	−	10738.7i	−0.364829	−	0.631903i	0.623920	−	0.781489i	$-0.285539\pi$
$661$	−6200.00	−	10738.7i	−0.364829	−	0.631903i	−0.988749	+	0.149586i	$0.952206\pi$
$662$	8260.00	+	14306.7i	0.484946	+	0.839950i
$663$	11056.5	−	19150.4i	0.647660	−	1.12178i
$664$	−9376.00			−0.547981
$665$		0			0
$666$	11304.0			0.657689
$667$	−5805.00	+	10054.6i	−0.336987	+	0.583679i
$668$	4038.00	+	6994.02i	0.233885	+	0.405100i
$669$	−1060.50	−	1836.84i	−0.0612874	−	0.106153i
$670$	1920.00	−	3325.54i	0.110711	−	0.191756i
$671$	−3740.00			−0.215173
$672$		0			0
$673$	16024.0			0.917801			0.458900	−	0.888488i	$-0.348244\pi$
$673$	16024.0			0.917801			0.458900	+	0.888488i	$0.348244\pi$
$674$	9946.00	−	17227.0i	0.568406	−	0.984508i
$675$	−1687.50	−	2922.84i	−0.0962250	−	0.166667i
$676$	−8728.00	−	15117.3i	−0.496586	−	0.860113i
$677$	−9367.50	+	16225.0i	−0.531791	+	0.921088i	0.467521	+	0.883982i	$0.345147\pi$
$677$	−9367.50	+	16225.0i	−0.531791	+	0.921088i	−0.999311	+	0.0371063i	$0.988186\pi$
$678$	−4668.00			−0.264415
$679$		0			0
$680$	3640.00			0.205276
$681$	−838.500	+	1452.32i	−0.0471827	+	0.0817228i
$682$	−1972.00	−	3415.60i	−0.110721	−	0.191775i
$683$	6422.00	+	11123.2i	0.359782	+	0.623160i	0.987924	−	0.154938i	$-0.0495178\pi$
$683$	6422.00	+	11123.2i	0.359782	+	0.623160i	−0.628142	+	0.778098i	$0.716184\pi$
$684$	3672.00	−	6360.09i	0.205267	−	0.355532i
$685$	240.000			0.0133868
$686$		0			0
$687$	11508.0			0.639094
$688$	3472.00	−	6013.68i	0.192396	−	0.333240i
$689$	−23652.0	−	40966.5i	−1.30779	−	2.26516i
$690$	1350.00	+	2338.27i	0.0744835	+	0.129009i
$691$	−12998.0	+	22513.2i	−0.715582	+	1.23942i	0.247153	+	0.968977i	$0.420505\pi$
$691$	−12998.0	+	22513.2i	−0.715582	+	1.23942i	−0.962735	+	0.270448i	$0.912828\pi$
$692$	5012.00			0.275329
$693$		0			0
$694$	17596.0			0.962442
$695$	95.0000	−	164.545i	0.00518497	−	0.00898063i
$696$	1548.00	+	2681.21i	0.0843057	+	0.146022i
$697$	−5642.00	−	9772.23i	−0.306608	−	0.531061i
$698$	−1838.00	+	3183.51i	−0.0996695	+	0.172633i
$699$	4104.00			0.222071
$700$		0			0
$701$	25435.0			1.37042			0.685212	−	0.728344i	$-0.259710\pi$
$701$	25435.0			1.37042			0.685212	+	0.728344i	$0.259710\pi$
$702$	−10935.0	+	18940.0i	−0.587913	+	1.01830i
$703$	−16014.0	−	27737.1i	−0.859146	−	1.48808i
$704$	544.000	+	942.236i	0.0291233	+	0.0504430i
$705$	3727.50	−	6456.22i	0.199129	−	0.344901i
$706$	−4530.00			−0.241486
$707$		0			0
$708$	3984.00			0.211480
$709$	−1911.50	+	3310.82i	−0.101252	+	0.175374i	−0.912201	−	0.409743i	$-0.865618\pi$
$709$	−1911.50	+	3310.82i	−0.101252	+	0.175374i	0.810949	+	0.585117i	$0.198952\pi$
$710$	−3320.00	−	5750.41i	−0.175489	−	0.303956i
$711$	3249.00	+	5627.43i	0.171374	+	0.296829i
$712$	160.000	−	277.128i	0.00842170	−	0.0145868i
$713$	−10440.0			−0.548361
$714$		0			0
$715$	6885.00			0.360118
$716$	−984.000	+	1704.34i	−0.0513601	+	0.0889582i
$717$	−5704.50	−	9880.48i	−0.297125	−	0.514635i
$718$	4136.00	+	7163.76i	0.214978	+	0.372353i
$719$	−10545.0	+	18264.5i	−0.546957	+	0.947357i	0.451524	+	0.892259i	$0.350881\pi$
$719$	−10545.0	+	18264.5i	−0.546957	+	0.947357i	−0.998481	+	0.0550984i	$0.982453\pi$
$720$	−1440.00			−0.0745356
$721$		0			0
$722$	−7090.00			−0.365460
$723$	8475.00	−	14679.1i	0.435946	−	0.755080i
$724$	8896.00	+	15408.3i	0.456654	+	0.790947i
$725$	1612.50	+	2792.93i	0.0826024	+	0.143072i
$726$	3126.00	−	5414.39i	0.159803	−	0.276786i
$727$	−7992.00			−0.407712			−0.203856	−	0.979001i	$-0.565347\pi$
$727$	−7992.00			−0.407712			−0.203856	+	0.979001i	$0.565347\pi$
$728$		0			0
$729$	9477.00			0.481481
$730$	1150.00	−	1991.86i	0.0583060	−	0.100989i
$731$	−19747.0	−	34202.8i	−0.999137	−	1.73056i
$732$	1320.00	+	2286.31i	0.0666511	+	0.115443i
$733$	18482.5	−	32012.6i	0.931332	−	1.61312i	0.150286	−	0.988643i	$-0.451981\pi$
$733$	18482.5	−	32012.6i	0.931332	−	1.61312i	0.781047	−	0.624473i	$-0.214686\pi$
$734$	20062.0			1.00886
$735$		0			0
$736$	2880.00			0.144237
$737$	3264.00	−	5653.41i	0.163136	−	0.282559i
$738$	2232.00	+	3865.94i	0.111329	+	0.192828i
$739$	1652.50	+	2862.21i	0.0822574	+	0.142474i	0.904219	−	0.427069i	$-0.140454\pi$
$739$	1652.50	+	2862.21i	0.0822574	+	0.142474i	−0.821962	+	0.569543i	$0.807120\pi$
$740$	−3140.00	+	5438.64i	−0.155985	+	0.270173i
$741$	24786.0			1.22879
$742$		0			0
$743$	−2208.00			−0.109022			−0.0545112	−	0.998513i	$-0.517360\pi$
$743$	−2208.00			−0.109022			−0.0545112	+	0.998513i	$0.517360\pi$
$744$	−1392.00	+	2411.01i	−0.0685930	+	0.118807i
$745$	8955.00	+	15510.5i	0.440384	+	0.762767i
$746$	2792.00	+	4835.89i	0.137027	+	0.237338i
$747$	10548.0	−	18269.7i	0.516641	−	0.894849i
$748$	6188.00			0.302481
$749$		0			0
$750$	750.000			0.0365148
$751$	5775.50	−	10003.5i	0.280627	−	0.486060i	−0.690912	−	0.722939i	$-0.742791\pi$
$751$	5775.50	−	10003.5i	0.280627	−	0.486060i	0.971539	+	0.236878i	$0.0761242\pi$
$752$	−3976.00	−	6886.63i	−0.192806	−	0.333949i
$753$	−2475.00	−	4286.83i	−0.119780	−	0.207464i
$754$	10449.0	−	18098.2i	0.504682	−	0.874135i
$755$	−9635.00			−0.464442
$756$		0			0
$757$	9688.00			0.465147			0.232574	−	0.972579i	$-0.425285\pi$
$757$	9688.00			0.465147			0.232574	+	0.972579i	$0.425285\pi$
$758$	9948.00	−	17230.4i	0.476686	−	0.825644i
$759$	2295.00	+	3975.06i	0.109754	+	0.190099i
$760$	2040.00	+	3533.38i	0.0973665	+	0.168644i
$761$	3507.00	−	6074.30i	0.167055	−	0.289347i	−0.770328	−	0.637647i	$-0.779908\pi$
$761$	3507.00	−	6074.30i	0.167055	−	0.289347i	0.937383	+	0.348300i	$0.113241\pi$
$762$	1896.00			0.0901376
$763$		0			0
$764$	15996.0			0.757480
$765$	−4095.00	+	7092.75i	−0.193536	+	0.335214i
$766$	2700.00	+	4676.54i	0.127356	+	0.220588i
$767$	−13446.0	−	23289.2i	−0.632995	−	1.09638i
$768$	384.000	−	665.108i	0.0180422	−	0.0312500i
$769$	−6278.00			−0.294396			−0.147198	−	0.989107i	$-0.547025\pi$
$769$	−6278.00			−0.294396			−0.147198	+	0.989107i	$0.547025\pi$
$770$		0			0
$771$	−17430.0			−0.814171
$772$	−9760.00	+	16904.8i	−0.455013	+	0.788106i
$773$	−10675.5	−	18490.5i	−0.496728	−	0.860359i	0.503264	−	0.864132i	$-0.332132\pi$
$773$	−10675.5	−	18490.5i	−0.496728	−	0.860359i	−0.999993	+	0.00377362i	$0.998799\pi$
$774$	7812.00	+	13530.8i	0.362786	+	0.628364i
$775$	−1450.00	+	2511.47i	−0.0672071	+	0.116406i
$776$	1400.00			0.0647643
$777$		0			0
$778$	1262.00			0.0581554
$779$	6324.00	−	10953.5i	0.290861	−	0.503786i
$780$	−2430.00	−	4208.88i	−0.111549	−	0.193208i
$781$	−5644.00	−	9775.69i	−0.258589	−	0.447890i
$782$	8190.00	−	14185.5i	0.374519	−	0.648686i
$783$	−17415.0			−0.794842
$784$		0			0
$785$	−12550.0			−0.570610
$786$	5250.00	−	9093.27i	0.238246	−	0.412654i
$787$	12983.5	+	22488.1i	0.588071	+	1.01857i	0.994485	+	0.104880i	$0.0334457\pi$
$787$	12983.5	+	22488.1i	0.588071	+	1.01857i	−0.406414	+	0.913689i	$0.633221\pi$
$788$	−9424.00	−	16322.8i	−0.426036	−	0.737915i
$789$	−4137.00	+	7165.49i	−0.186668	+	0.323319i
$790$	−3610.00			−0.162580
$791$		0			0
$792$	−2448.00			−0.109831
$793$	8910.00	−	15432.6i	0.398995	−	0.691080i
$794$	−13139.0	−	22757.4i	−0.587262	−	1.01717i
$795$	−4380.00	−	7586.38i	−0.195399	−	0.338442i
$796$	−5512.00	+	9547.06i	−0.245437	+	0.425109i
$797$	−8595.00			−0.381996			−0.190998	−	0.981590i	$-0.561172\pi$
$797$	−8595.00			−0.381996			−0.190998	+	0.981590i	$0.561172\pi$
$798$		0			0
$799$	−45227.0			−2.00252
$800$	400.000	−	692.820i	0.0176777	−	0.0306186i
$801$	360.000	+	623.538i	0.0158801	+	0.0275052i
$802$	−887.000	−	1536.33i	−0.0390537	−	0.0676430i
$803$	1955.00	−	3386.16i	0.0859159	−	0.148811i
$804$	−4608.00			−0.202129
$805$		0			0
$806$	18792.0			0.821241
$807$	279.000	−	483.242i	0.0121701	−	0.0210792i
$808$	1080.00	+	1870.61i	0.0470226	+	0.0814455i
$809$	6835.50	+	11839.4i	0.297062	+	0.514527i	0.975463	−	0.220166i	$-0.0706598\pi$
$809$	6835.50	+	11839.4i	0.297062	+	0.514527i	−0.678400	+	0.734693i	$0.737326\pi$
$810$	405.000	−	701.481i	0.0175682	−	0.0304290i
$811$	−11986.0			−0.518971			−0.259485	−	0.965747i	$-0.583553\pi$
$811$	−11986.0			−0.518971			−0.259485	+	0.965747i	$0.583553\pi$
$812$		0			0
$813$	20484.0			0.883647
$814$	−5338.00	+	9245.69i	−0.229849	+	0.398110i
$815$	4675.00	+	8097.34i	0.200930	+	0.348021i
$816$	−2184.00	−	3782.80i	−0.0936952	−	0.162285i
$817$	22134.0	−	38337.2i	0.947822	−	1.64168i
$818$	10380.0			0.443677
$819$		0			0
$820$	−2480.00			−0.105616
$821$	6475.50	−	11215.9i	0.275270	−	0.476781i	−0.694933	−	0.719074i	$-0.744566\pi$
$821$	6475.50	−	11215.9i	0.275270	−	0.476781i	0.970203	+	0.242293i	$0.0778995\pi$
$822$	−144.000	−	249.415i	−0.00611019	−	0.0105832i
$823$	6394.00	+	11074.7i	0.270815	+	0.469066i	0.969071	−	0.246783i	$-0.0793735\pi$
$823$	6394.00	+	11074.7i	0.270815	+	0.469066i	−0.698256	+	0.715848i	$0.746040\pi$
$824$	2260.00	−	3914.43i	0.0955471	−	0.165492i
$825$	1275.00			0.0538058
$826$		0			0
$827$	24662.0			1.03698			0.518490	−	0.855084i	$-0.326495\pi$
$827$	24662.0			1.03698			0.518490	+	0.855084i	$0.326495\pi$
$828$	−3240.00	+	5611.84i	−0.135988	+	0.235538i
$829$	−2062.00	−	3571.49i	−0.0863887	−	0.149630i	0.819593	−	0.572946i	$-0.194199\pi$
$829$	−2062.00	−	3571.49i	−0.0863887	−	0.149630i	−0.905982	+	0.423316i	$0.860866\pi$
$830$	5860.00	+	10149.8i	0.245065	+	0.424464i
$831$	−12321.0	+	21340.6i	−0.514333	+	0.890851i
$832$	−5184.00			−0.216013
$833$		0			0
$834$	−228.000			−0.00946642
$835$	5047.50	−	8742.53i	0.209193	−	0.362332i
$836$	3468.00	+	6006.75i	0.143473	+	0.248502i
$837$	−7830.00	−	13562.0i	−0.323351	−	0.560060i
$838$	−5712.00	+	9893.47i	−0.235463	+	0.407833i
$839$	−33154.0			−1.36425			−0.682123	−	0.731237i	$-0.738943\pi$
$839$	−33154.0			−1.36425			−0.682123	+	0.731237i	$0.738943\pi$
$840$		0			0
$841$	−7748.00			−0.317684
$842$	−11155.0	+	19321.0i	−0.456564	+	0.790792i
$843$	10060.5	+	17425.3i	0.411034	+	0.711933i
$844$	−1394.00	−	2414.48i	−0.0568524	−	0.0984713i
$845$	−10910.0	+	18896.7i	−0.444160	+	0.769308i
$846$	17892.0			0.727115
$847$		0			0
$848$	−9344.00			−0.378389
$849$	−8245.50	+	14281.6i	−0.333315	+	0.577319i
$850$	−2275.00	−	3940.42i	−0.0918022	−	0.159006i
$851$	14130.0	+	24473.9i	0.569178	+	0.985845i
$852$	−3984.00	+	6900.49i	−0.160199	+	0.277473i
$853$	12050.0			0.483686			0.241843	−	0.970315i	$-0.422248\pi$
$853$	12050.0			0.483686			0.241843	+	0.970315i	$0.422248\pi$
$854$		0			0
$855$	−9180.00			−0.367192
$856$	−4824.00	+	8355.41i	−0.192618	+	0.333624i
$857$	−7635.00	−	13224.2i	−0.304325	−	0.527107i	0.672786	−	0.739837i	$-0.265098\pi$
$857$	−7635.00	−	13224.2i	−0.304325	−	0.527107i	−0.977111	+	0.212731i	$0.931764\pi$
$858$	−4131.00	−	7155.10i	−0.164371	−	0.284698i
$859$	6282.00	−	10880.7i	0.249522	−	0.432184i	−0.713872	−	0.700277i	$-0.753060\pi$
$859$	6282.00	−	10880.7i	0.249522	−	0.432184i	0.963393	+	0.268093i	$0.0863933\pi$
$860$	−8680.00			−0.344169
$861$		0			0
$862$	−16998.0			−0.671641
$863$	−6488.00	+	11237.5i	−0.255914	+	0.443257i	−0.965143	−	0.261721i	$-0.915710\pi$
$863$	−6488.00	+	11237.5i	−0.255914	+	0.443257i	0.709229	+	0.704978i	$0.249043\pi$
$864$	2160.00	+	3741.23i	0.0850517	+	0.147314i
$865$	−3132.50	−	5425.65i	−0.123131	−	0.213269i
$866$	5102.00	−	8836.92i	0.200200	−	0.346756i
$867$	−10104.0			−0.395790
$868$		0			0
$869$	−6137.00			−0.239567
$870$	1935.00	−	3351.52i	0.0754053	−	0.130606i
$871$	15552.0	+	26936.9i	0.605005	+	1.04790i
$872$	−5676.00	−	9831.12i	−0.220428	−	0.381793i
$873$	−1575.00	+	2727.98i	−0.0610603	+	0.105760i
$874$	18360.0			0.710568
$875$		0			0
$876$	−2760.00			−0.106452
$877$	7817.00	−	13539.4i	0.300982	−	0.521316i	−0.675377	−	0.737473i	$-0.736019\pi$
$877$	7817.00	−	13539.4i	0.300982	−	0.521316i	0.976359	+	0.216157i	$0.0693522\pi$
$878$	15694.0	+	27182.8i	0.603242	+	1.04485i
$879$	469.500	+	813.198i	0.0180157	+	0.0312042i
$880$	680.000	−	1177.79i	0.0260486	−	0.0451176i
$881$	−8896.00			−0.340197			−0.170099	−	0.985427i	$-0.554409\pi$
$881$	−8896.00			−0.340197			−0.170099	+	0.985427i	$0.554409\pi$
$882$		0			0
$883$	−33456.0			−1.27507			−0.637533	−	0.770423i	$-0.720045\pi$
$883$	−33456.0			−1.27507			−0.637533	+	0.770423i	$0.720045\pi$
$884$	−14742.0	+	25533.9i	−0.560890	+	0.971491i
$885$	−2490.00	−	4312.81i	−0.0945768	−	0.163812i
$886$	9142.00	+	15834.4i	0.346650	+	0.600415i
$887$	−4144.00	+	7177.62i	−0.156868	+	0.271703i	−0.933738	−	0.357958i	$-0.883473\pi$
$887$	−4144.00	+	7177.62i	−0.156868	+	0.271703i	0.776870	+	0.629661i	$0.216806\pi$
$888$	7536.00			0.284788
$889$		0			0
$890$	−400.000			−0.0150652
$891$	688.500	−	1192.52i	0.0258873	−	0.0448382i
$892$	1414.00	+	2449.12i	0.0530765	+	0.0919312i
$893$	−25347.0	−	43902.3i	−0.949838	−	1.64517i
$894$	10746.0	−	18612.6i	0.402013	−	0.696308i
$895$	2460.00			0.0918757
$896$		0			0
$897$	−21870.0			−0.814067
$898$	−17145.0	+	29696.0i	−0.637123	+	1.10353i
$899$	7482.00	+	12959.2i	0.277574	+	0.480772i
$900$	900.000	+	1558.85i	0.0333333	+	0.0577350i
$901$	−26572.0	+	46024.1i	−0.982510	+	1.70176i
$902$	−4216.00			−0.155629
$903$		0			0
$904$	6224.00			0.228990
$905$	11120.0	−	19260.4i	0.408443	−	0.707445i
$906$	5781.00	+	10013.0i	0.211988	+	0.367173i
$907$	−7699.00	−	13335.1i	−0.281853	−	0.488185i	0.689988	−	0.723821i	$-0.257616\pi$
$907$	−7699.00	−	13335.1i	−0.281853	−	0.488185i	−0.971841	+	0.235636i	$0.924283\pi$
$908$	1118.00	−	1936.43i	0.0408614	−	0.0707740i
$909$	−4860.00			−0.177333
$910$		0			0
$911$	22656.0			0.823959			0.411980	−	0.911193i	$-0.364838\pi$
$911$	22656.0			0.823959			0.411980	+	0.911193i	$0.364838\pi$
$912$	2448.00	−	4240.06i	0.0888831	−	0.153950i
$913$	9962.00	+	17254.7i	0.361111	+	0.625462i
$914$	−10184.0	−	17639.2i	−0.368552	−	0.638351i
$915$	1650.00	−	2857.88i	0.0596146	−	0.103255i
$916$	−15344.0			−0.553472
$917$		0			0
$918$	24570.0			0.883367
$919$	−4574.50	+	7923.27i	−0.164199	+	0.284401i	−0.936371	−	0.351013i	$-0.885837\pi$
$919$	−4574.50	+	7923.27i	−0.164199	+	0.284401i	0.772172	+	0.635414i	$0.219171\pi$
$920$	−1800.00	−	3117.69i	−0.0645046	−	0.111725i
$921$	8218.50	+	14234.9i	0.294038	+	0.509288i
$922$	−9152.00	+	15851.7i	−0.326904	+	0.566214i
$923$	53784.0			1.91801
$924$		0			0
$925$	7850.00			0.279034
$926$	−1084.00	+	1877.54i	−0.0384692	+	0.0666306i
$927$	5085.00	+	8807.48i	0.180165	+	0.312056i
$928$	−2064.00	−	3574.95i	−0.0730109	−	0.126459i
$929$	13636.0	−	23618.2i	0.481574	−	0.834111i	−0.518202	−	0.855258i	$-0.673398\pi$
$929$	13636.0	−	23618.2i	0.481574	−	0.834111i	0.999776	+	0.0211469i	$0.00673177\pi$
$930$	3480.00			0.122703
$931$		0			0
$932$	−5472.00			−0.192319
$933$	6633.00	−	11488.7i	0.232749	−	0.403133i
$934$	19283.0	+	33399.1i	0.675545	+	1.17008i
$935$	−3867.50	−	6698.71i	−0.135274	−	0.234301i
$936$	5832.00	−	10101.3i	0.203659	−	0.352748i
$937$	44177.0			1.54023			0.770117	−	0.637902i	$-0.220198\pi$
$937$	44177.0			1.54023			0.770117	+	0.637902i	$0.220198\pi$
$938$		0			0
$939$	−825.000			−0.0286718
$940$	−4970.00	+	8608.29i	−0.172451	+	0.298693i
$941$	1118.00	+	1936.43i	0.0387309	+	0.0670839i	0.884741	−	0.466083i	$-0.154335\pi$
$941$	1118.00	+	1936.43i	0.0387309	+	0.0670839i	−0.846010	+	0.533167i	$0.821002\pi$
$942$	7530.00	+	13042.3i	0.260447	+	0.451107i
$943$	−5580.00	+	9664.84i	−0.192693	+	0.333755i
$944$	−5312.00			−0.183147
$945$		0			0
$946$	−14756.0			−0.507145
$947$	8732.00	−	15124.3i	0.299632	−	0.518979i	−0.676419	−	0.736517i	$-0.736469\pi$
$947$	8732.00	−	15124.3i	0.299632	−	0.518979i	0.976052	+	0.217538i	$0.0698026\pi$
$948$	2166.00	+	3751.62i	0.0742072	+	0.128531i
$949$	9315.00	+	16134.1i	0.318628	+	0.551879i
$950$	2550.00	−	4416.73i	0.0870873	−	0.150840i
$951$	12318.0			0.420019
$952$		0			0
$953$	−18336.0			−0.623254			−0.311627	−	0.950204i	$-0.600874\pi$
$953$	−18336.0			−0.623254			−0.311627	+	0.950204i	$0.600874\pi$
$954$	10512.0	−	18207.3i	0.356749	−	0.617907i
$955$	−9997.50	−	17316.2i	−0.338756	−	0.586742i
$956$	7606.00	+	13174.0i	0.257318	+	0.445687i
$957$	3289.50	−	5697.58i	0.111112	−	0.192452i
$958$	10236.0			0.345209
$959$		0			0
$960$	−960.000			−0.0322749
$961$	8167.50	−	14146.5i	0.274160	−	0.474859i
$962$	−25434.0	−	44053.0i	−0.852417	−	1.47643i
$963$	−10854.0	−	18799.7i	−0.363204	−	0.629087i
$964$	−11300.0	+	19572.2i	−0.377540	+	0.653918i
$965$	24400.0			0.813952
$966$		0			0
$967$	−46802.0			−1.55641			−0.778206	−	0.628009i	$-0.783870\pi$
$967$	−46802.0			−1.55641			−0.778206	+	0.628009i	$0.783870\pi$
$968$	−4168.00	+	7219.19i	−0.138393	+	0.239704i
$969$	−13923.0	−	24115.3i	−0.461580	−	0.799480i
$970$	−875.000	−	1515.54i	−0.0289635	−	0.0501662i
$971$	−22512.0	+	38991.9i	−0.744021	+	1.28868i	0.206630	+	0.978419i	$0.433750\pi$
$971$	−22512.0	+	38991.9i	−0.744021	+	1.28868i	−0.950651	+	0.310263i	$0.899583\pi$
$972$	−15552.0			−0.513200
$973$		0			0
$974$	−5836.00			−0.191989
$975$	−3037.50	+	5261.10i	−0.0997722	+	0.172810i
$976$	−1760.00	−	3048.41i	−0.0577215	−	0.0999766i
$977$	−6393.00	−	11073.0i	−0.209345	−	0.362596i	0.742163	−	0.670219i	$-0.233800\pi$
$977$	−6393.00	−	11073.0i	−0.209345	−	0.362596i	−0.951508	+	0.307623i	$0.900467\pi$
$978$	5610.00	−	9716.81i	0.183423	−	0.317699i
$979$	−680.000			−0.0221991
$980$		0			0
$981$	25542.0			0.831288
$982$	−18627.0	+	32262.9i	−0.605307	+	1.04842i
$983$	−16769.5	−	29045.6i	−0.544114	−	0.942433i	−0.998662	−	0.0517108i	$-0.983533\pi$
$983$	−16769.5	−	29045.6i	−0.544114	−	0.942433i	0.454548	−	0.890722i	$-0.349801\pi$
$984$	1488.00	+	2577.29i	0.0482070	+	0.0834970i
$985$	−11780.0	+	20403.6i	−0.381058	+	0.660012i
$986$	−23478.0			−0.758308
$987$		0			0
$988$	−33048.0			−1.06417
$989$	−19530.0	+	33827.0i	−0.627925	+	1.08760i
$990$	1530.00	+	2650.04i	0.0491178	+	0.0850745i
$991$	9100.00	+	15761.7i	0.291696	+	0.505233i	0.974211	−	0.225639i	$-0.0724470\pi$
$991$	9100.00	+	15761.7i	0.291696	+	0.505233i	−0.682515	+	0.730872i	$0.739114\pi$
$992$	1856.00	−	3214.69i	0.0594033	−	0.102890i
$993$	−24780.0			−0.791913
$994$		0			0
$995$	13780.0			0.439051
$996$	7032.00	−	12179.8i	0.223712	−	0.387481i
$997$	16299.5	+	28231.6i	0.517764	+	0.896793i	0.999787	+	0.0206346i	$0.00656867\pi$
$997$	16299.5	+	28231.6i	0.517764	+	0.896793i	−0.482023	+	0.876158i	$0.660098\pi$
$998$	12843.0	+	22244.7i	0.407353	+	0.705556i
$999$	−21195.0	+	36710.8i	−0.671251	+	1.16264i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.e.p.471.1		2
7.2	even	3		70.4.a.b.1.1	✓	1
7.3	odd	6		490.4.e.l.361.1		2
7.4	even	3	inner	490.4.e.p.361.1		2
7.5	odd	6		490.4.a.f.1.1		1
7.6	odd	2		490.4.e.l.471.1		2
21.2	odd	6		630.4.a.m.1.1		1
28.23	odd	6		560.4.a.k.1.1		1
35.2	odd	12		350.4.c.j.99.1		2
35.9	even	6		350.4.a.t.1.1		1
35.19	odd	6		2450.4.a.ba.1.1		1
35.23	odd	12		350.4.c.j.99.2		2
56.37	even	6		2240.4.a.w.1.1		1
56.51	odd	6		2240.4.a.p.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.a.b.1.1	✓	1	7.2	even	3
350.4.a.t.1.1		1	35.9	even	6
350.4.c.j.99.1		2	35.2	odd	12
350.4.c.j.99.2		2	35.23	odd	12
490.4.a.f.1.1		1	7.5	odd	6
490.4.e.l.361.1		2	7.3	odd	6
490.4.e.l.471.1		2	7.6	odd	2
490.4.e.p.361.1		2	7.4	even	3	inner
490.4.e.p.471.1		2	1.1	even	1	trivial
560.4.a.k.1.1		1	28.23	odd	6
630.4.a.m.1.1		1	21.2	odd	6
2240.4.a.p.1.1		1	56.51	odd	6
2240.4.a.w.1.1		1	56.37	even	6
2450.4.a.ba.1.1		1	35.19	odd	6

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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Newspace parameters

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	490.4.e.p.471.1

Level	$490$
Weight	$4$
Character	490.471
Analytic conductor	$28.911$
Analytic rank	$0$
Dimension	$2$
Inner twists	$2$