LMFDB - Embedded newform 294.4.e.l.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,4,Mod(67,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, 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("294.67");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$294 = 2 \cdot 3 \cdot 7^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	294.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:	$17.3465615417$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{1345})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} - x^{3} + 337x^{2} + 336x + 112896$ x^4 - x^3 + 337x^2 + 336x + 112896
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.2
Root			$9.41856 - 16.3134i$ of defining polynomial
Character	$\chi$	$=$	294.79
Dual form			294.4.e.l.67.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(10.4186 - 18.0455i) q^{5} -6.00000 q^{6} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(20.8371 + 36.0910i) q^{10} +(-7.58144 - 13.1314i) q^{11} +(6.00000 - 10.3923i) q^{12} -2.16288 q^{13} +62.5114 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-59.6742 - 103.359i) q^{17} +(-9.00000 - 15.5885i) q^{18} +(-16.7557 + 29.0217i) q^{19} -83.3485 q^{20} +30.3258 q^{22} +(-0.325758 + 0.564230i) q^{23} +(12.0000 + 20.7846i) q^{24} +(-154.593 - 267.763i) q^{25} +(2.16288 - 3.74622i) q^{26} -27.0000 q^{27} -163.208 q^{29} +(-62.5114 + 108.273i) q^{30} +(-111.663 - 193.406i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(22.7443 - 39.3943i) q^{33} +238.697 q^{34} +36.0000 q^{36} +(-84.2670 + 145.955i) q^{37} +(-33.5114 - 58.0434i) q^{38} +(-3.24432 - 5.61932i) q^{39} +(83.3485 - 144.364i) q^{40} +323.023 q^{41} +221.557 q^{43} +(-30.3258 + 52.5258i) q^{44} +(93.7670 + 162.409i) q^{45} +(-0.651517 - 1.12846i) q^{46} +(254.023 - 439.980i) q^{47} -48.0000 q^{48} +618.371 q^{50} +(179.023 - 310.076i) q^{51} +(4.32576 + 7.49243i) q^{52} +(88.2557 + 152.863i) q^{53} +(27.0000 - 46.7654i) q^{54} -315.951 q^{55} -100.534 q^{57} +(163.208 - 282.685i) q^{58} +(227.464 + 393.979i) q^{59} +(-125.023 - 216.546i) q^{60} +(19.3258 - 33.4732i) q^{61} +446.652 q^{62} +64.0000 q^{64} +(-22.5341 + 39.0302i) q^{65} +(45.4886 + 78.7886i) q^{66} +(-70.8958 - 122.795i) q^{67} +(-238.697 + 413.435i) q^{68} -1.95455 q^{69} +602.742 q^{71} +(-36.0000 + 62.3538i) q^{72} +(-551.150 - 954.619i) q^{73} +(-168.534 - 291.910i) q^{74} +(463.778 - 803.288i) q^{75} +134.045 q^{76} +12.9773 q^{78} +(58.1515 - 100.721i) q^{79} +(166.697 + 288.728i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-323.023 + 559.492i) q^{82} +568.928 q^{83} -2486.88 q^{85} +(-221.557 + 383.748i) q^{86} +(-244.812 - 424.028i) q^{87} +(-60.6515 - 105.052i) q^{88} +(-191.580 + 331.825i) q^{89} -375.068 q^{90} +2.60607 q^{92} +(334.989 - 580.217i) q^{93} +(508.045 + 879.961i) q^{94} +(349.140 + 604.728i) q^{95} +(48.0000 - 83.1384i) q^{96} -334.701 q^{97} +136.466 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 5 q^{5} - 24 q^{6} + 32 q^{8} - 18 q^{9} + 10 q^{10} - 67 q^{11} + 24 q^{12} - 82 q^{13} + 30 q^{15} - 32 q^{16} - 92 q^{17} - 36 q^{18} + 43 q^{19} - 40 q^{20} + 268 q^{22}+ \cdots + 1206 q^{99}+O(q^{100})$ 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 + 5 * q^5 - 24 * q^6 + 32 * q^8 - 18 * q^9 + 10 * q^10 - 67 * q^11 + 24 * q^12 - 82 * q^13 + 30 * q^15 - 32 * q^16 - 92 * q^17 - 36 * q^18 + 43 * q^19 - 40 * q^20 + 268 * q^22 - 148 * q^23 + 48 * q^24 - 435 * q^25 + 82 * q^26 - 108 * q^27 + 154 * q^29 - 30 * q^30 - 520 * q^31 - 64 * q^32 + 201 * q^33 + 368 * q^34 + 144 * q^36 - 7 * q^37 + 86 * q^38 - 123 * q^39 + 40 * q^40 + 852 * q^41 - 214 * q^43 - 268 * q^44 + 45 * q^45 - 296 * q^46 + 576 * q^47 - 192 * q^48 + 1740 * q^50 + 276 * q^51 + 164 * q^52 + 243 * q^53 + 108 * q^54 + 1010 * q^55 + 258 * q^57 - 154 * q^58 - 7 * q^59 - 60 * q^60 + 224 * q^61 + 2080 * q^62 + 256 * q^64 + 570 * q^65 + 402 * q^66 - 687 * q^67 - 368 * q^68 - 888 * q^69 + 944 * q^71 - 144 * q^72 - 921 * q^73 - 14 * q^74 + 1305 * q^75 - 344 * q^76 + 492 * q^78 + 526 * q^79 + 80 * q^80 - 162 * q^81 - 852 * q^82 + 442 * q^83 - 5840 * q^85 + 214 * q^86 + 231 * q^87 - 536 * q^88 + 774 * q^89 - 180 * q^90 + 1184 * q^92 + 1560 * q^93 + 1152 * q^94 + 1910 * q^95 + 192 * q^96 - 3906 * q^97 + 1206 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$ .

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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

)

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

$2$	−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
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	10.4186	−	18.0455i	0.931864	−	1.61404i	0.151732	−	0.988422i	$-0.451515\pi$
$5$	10.4186	−	18.0455i	0.931864	−	1.61404i	0.780132	−	0.625615i	$-0.215152\pi$
$6$	−6.00000			−0.408248
$7$		0			0
$7$		0			0
$8$	8.00000			0.353553
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	20.8371	+	36.0910i	0.658928	+	1.14130i
$11$	−7.58144	−	13.1314i	−0.207808	−	0.359934i	0.743216	−	0.669052i	$-0.233300\pi$
$11$	−7.58144	−	13.1314i	−0.207808	−	0.359934i	−0.951024	+	0.309118i	$0.899966\pi$
$12$	6.00000	−	10.3923i	0.144338	−	0.250000i
$13$	−2.16288			−0.0461442			−0.0230721	−	0.999734i	$-0.507345\pi$
$13$	−2.16288			−0.0461442			−0.0230721	+	0.999734i	$0.507345\pi$
$14$		0			0
$15$	62.5114			1.07602
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−59.6742	−	103.359i	−0.851361	−	1.47460i	−0.879981	−	0.475009i	$-0.842445\pi$
$17$	−59.6742	−	103.359i	−0.851361	−	1.47460i	0.0286202	−	0.999590i	$-0.490889\pi$
$18$	−9.00000	−	15.5885i	−0.117851	−	0.204124i
$19$	−16.7557	+	29.0217i	−0.202317	+	0.350423i	−0.949274	−	0.314449i	$-0.898180\pi$
$19$	−16.7557	+	29.0217i	−0.202317	+	0.350423i	0.746958	+	0.664871i	$0.231514\pi$
$20$	−83.3485			−0.931864
$21$		0			0
$22$	30.3258			0.293885
$23$	−0.325758	+	0.564230i	−0.00295327	+	0.00511522i	−0.867498	−	0.497440i	$-0.834273\pi$
$23$	−0.325758	+	0.564230i	−0.00295327	+	0.00511522i	0.864545	+	0.502555i	$0.167607\pi$
$24$	12.0000	+	20.7846i	0.102062	+	0.176777i
$25$	−154.593	−	267.763i	−1.23674	−	2.14210i
$26$	2.16288	−	3.74622i	0.0163144	−	0.0282574i
$27$	−27.0000			−0.192450
$28$		0			0
$29$	−163.208			−1.04507			−0.522535	−	0.852618i	$-0.675014\pi$
$29$	−163.208			−1.04507			−0.522535	+	0.852618i	$0.675014\pi$
$30$	−62.5114	+	108.273i	−0.380432	+	0.658928i
$31$	−111.663	−	193.406i	−0.646943	−	1.12054i	−0.983849	−	0.179000i	$-0.942714\pi$
$31$	−111.663	−	193.406i	−0.646943	−	1.12054i	0.336906	−	0.941538i	$-0.390620\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$	22.7443	−	39.3943i	0.119978	−	0.207808i
$34$	238.697			1.20401
$35$		0			0
$36$	36.0000			0.166667
$37$	−84.2670	+	145.955i	−0.374417	+	0.648509i	−0.990240	−	0.139376i	$-0.955490\pi$
$37$	−84.2670	+	145.955i	−0.374417	+	0.648509i	0.615823	+	0.787885i	$0.288824\pi$
$38$	−33.5114	−	58.0434i	−0.143059	−	0.247786i
$39$	−3.24432	−	5.61932i	−0.0133207	−	0.0230721i
$40$	83.3485	−	144.364i	0.329464	−	0.570648i
$41$	323.023			1.23043			0.615216	−	0.788359i	$-0.289069\pi$
$41$	323.023			1.23043			0.615216	+	0.788359i	$0.289069\pi$
$42$		0			0
$43$	221.557			0.785746			0.392873	−	0.919593i	$-0.371481\pi$
$43$	221.557			0.785746			0.392873	+	0.919593i	$0.371481\pi$
$44$	−30.3258	+	52.5258i	−0.103904	+	0.179967i
$45$	93.7670	+	162.409i	0.310621	+	0.538012i
$46$	−0.651517	−	1.12846i	−0.00208828	−	0.00361701i
$47$	254.023	−	439.980i	0.788362	−	1.36548i	−0.138608	−	0.990347i	$-0.544263\pi$
$47$	254.023	−	439.980i	0.788362	−	1.36548i	0.926970	−	0.375136i	$-0.122404\pi$
$48$	−48.0000			−0.144338
$49$		0			0
$50$	618.371			1.74902
$51$	179.023	−	310.076i	0.491533	−	0.851361i
$52$	4.32576	+	7.49243i	0.0115361	+	0.0199810i
$53$	88.2557	+	152.863i	0.228733	+	0.396177i	0.957433	−	0.288656i	$-0.0932084\pi$
$53$	88.2557	+	152.863i	0.228733	+	0.396177i	−0.728700	+	0.684833i	$0.759875\pi$
$54$	27.0000	−	46.7654i	0.0680414	−	0.117851i
$55$	−315.951			−0.774596
$56$		0			0
$57$	−100.534			−0.233615
$58$	163.208	−	282.685i	0.369488	−	0.639972i
$59$	227.464	+	393.979i	0.501920	+	0.869351i	0.999998	+	0.00221868i	$0.000706227\pi$
$59$	227.464	+	393.979i	0.501920	+	0.869351i	−0.498077	+	0.867133i	$0.665960\pi$
$60$	−125.023	−	216.546i	−0.269006	−	0.465932i
$61$	19.3258	−	33.4732i	0.0405641	−	0.0702591i	−0.845031	−	0.534718i	$-0.820418\pi$
$61$	19.3258	−	33.4732i	0.0405641	−	0.0702591i	0.885595	+	0.464459i	$0.153751\pi$
$62$	446.652			0.914916
$63$		0			0
$64$	64.0000			0.125000
$65$	−22.5341	+	39.0302i	−0.0430001	+	0.0744784i
$66$	45.4886	+	78.7886i	0.0848373	+	0.146943i
$67$	−70.8958	−	122.795i	−0.129273	−	0.223908i	0.794122	−	0.607758i	$-0.207931\pi$
$67$	−70.8958	−	122.795i	−0.129273	−	0.223908i	−0.923395	+	0.383851i	$0.874598\pi$
$68$	−238.697	+	413.435i	−0.425680	+	0.737300i
$69$	−1.95455			−0.00341015
$70$		0			0
$71$	602.742			1.00750			0.503749	−	0.863850i	$-0.331954\pi$
$71$	602.742			1.00750			0.503749	+	0.863850i	$0.331954\pi$
$72$	−36.0000	+	62.3538i	−0.0589256	+	0.102062i
$73$	−551.150	−	954.619i	−0.883660	−	1.53054i	−0.847242	−	0.531207i	$-0.821738\pi$
$73$	−551.150	−	954.619i	−0.883660	−	1.53054i	−0.0364183	−	0.999337i	$-0.511595\pi$
$74$	−168.534	−	291.910i	−0.264753	−	0.458565i
$75$	463.778	−	803.288i	0.714034	−	1.23674i
$76$	134.045			0.202317
$77$		0			0
$78$	12.9773			0.0188383
$79$	58.1515	−	100.721i	0.0828172	−	0.143444i	−0.821642	−	0.570004i	$-0.806942\pi$
$79$	58.1515	−	100.721i	0.0828172	−	0.143444i	0.904459	+	0.426561i	$0.140275\pi$
$80$	166.697	+	288.728i	0.232966	+	0.403509i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	−323.023	+	559.492i	−0.435023	+	0.753482i
$83$	568.928			0.752385			0.376193	−	0.926542i	$-0.377233\pi$
$83$	568.928			0.752385			0.376193	+	0.926542i	$0.377233\pi$
$84$		0			0
$85$	−2486.88			−3.17341
$86$	−221.557	+	383.748i	−0.277803	+	0.481169i
$87$	−244.812	−	424.028i	−0.301686	−	0.522535i
$88$	−60.6515	−	105.052i	−0.0734713	−	0.127256i
$89$	−191.580	+	331.825i	−0.228173	+	0.395207i	−0.957267	−	0.289207i	$-0.906608\pi$
$89$	−191.580	+	331.825i	−0.228173	+	0.395207i	0.729094	+	0.684414i	$0.239942\pi$
$90$	−375.068			−0.439285
$91$		0			0
$92$	2.60607			0.00295327
$93$	334.989	−	580.217i	0.373513	−	0.646943i
$94$	508.045	+	879.961i	0.557456	+	0.965543i
$95$	349.140	+	604.728i	0.377063	+	0.653093i
$96$	48.0000	−	83.1384i	0.0510310	−	0.0883883i
$97$	−334.701			−0.350348			−0.175174	−	0.984538i	$-0.556049\pi$
$97$	−334.701			−0.350348			−0.175174	+	0.984538i	$0.556049\pi$
$98$		0			0
$99$	136.466			0.138539
$100$	−618.371	+	1071.05i	−0.618371	+	1.07105i
$101$	−7.37121	−	12.7673i	−0.00726201	−	0.0125782i	0.862372	−	0.506276i	$-0.168978\pi$
$101$	−7.37121	−	12.7673i	−0.00726201	−	0.0125782i	−0.869634	+	0.493698i	$0.835645\pi$
$102$	358.045	+	620.153i	0.347566	+	0.602003i
$103$	−420.710	+	728.691i	−0.402464	+	0.697088i	−0.994023	−	0.109174i	$-0.965180\pi$
$103$	−420.710	+	728.691i	−0.402464	+	0.697088i	0.591559	+	0.806262i	$0.298513\pi$
$104$	−17.3030			−0.0163144
$105$		0			0
$106$	−353.023			−0.323477
$107$	357.835	−	619.789i	0.323301	−	0.559974i	−0.657866	−	0.753135i	$-0.728541\pi$
$107$	357.835	−	619.789i	0.323301	−	0.559974i	0.981167	+	0.193161i	$0.0618739\pi$
$108$	54.0000	+	93.5307i	0.0481125	+	0.0833333i
$109$	−300.009	−	519.632i	−0.263630	−	0.456621i	0.703574	−	0.710622i	$-0.251587\pi$
$109$	−300.009	−	519.632i	−0.263630	−	0.456621i	−0.967204	+	0.254001i	$0.918253\pi$
$110$	315.951	−	547.243i	0.273861	−	0.474341i
$111$	−505.602			−0.432339
$112$		0			0
$113$	622.644			0.518349			0.259174	−	0.965831i	$-0.416550\pi$
$113$	622.644			0.518349			0.259174	+	0.965831i	$0.416550\pi$
$114$	100.534	−	174.130i	0.0825954	−	0.143059i
$115$	6.78787	+	11.7569i	0.00550410	+	0.00953339i
$116$	326.417	+	565.370i	0.261267	+	0.452529i
$117$	9.73296	−	16.8580i	0.00769070	−	0.0133207i
$118$	−909.856			−0.709822
$119$		0			0
$120$	500.091			0.380432
$121$	550.544	−	953.569i	0.413632	−	0.716431i
$122$	38.6515	+	66.9464i	0.0286831	+	0.0496807i
$123$	484.534	+	839.238i	0.355195	+	0.615216i
$124$	−446.652	+	773.623i	−0.323472	+	0.560269i
$125$	−3837.90			−2.74618
$126$		0			0
$127$	−180.076			−0.125820			−0.0629100	−	0.998019i	$-0.520038\pi$
$127$	−180.076			−0.125820			−0.0629100	+	0.998019i	$0.520038\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$	332.335	+	575.621i	0.226825	+	0.392873i
$130$	−45.0682	−	78.0604i	−0.0304057	−	0.0526642i
$131$	108.930	−	188.672i	0.0726508	−	0.125835i	−0.827411	−	0.561596i	$-0.810187\pi$
$131$	108.930	−	188.672i	0.0726508	−	0.125835i	0.900062	+	0.435761i	$0.143521\pi$
$132$	−181.955			−0.119978
$133$		0			0
$134$	283.583			0.182820
$135$	−281.301	+	487.228i	−0.179337	+	0.310621i
$136$	−477.394	−	826.871i	−0.301001	−	0.521350i
$137$	1300.93	+	2253.27i	0.811283	+	1.40518i	0.911966	+	0.410265i	$0.134564\pi$
$137$	1300.93	+	2253.27i	0.811283	+	1.40518i	−0.100683	+	0.994919i	$0.532103\pi$
$138$	1.95455	−	3.38538i	0.00120567	−	0.00208828i
$139$	2651.55			1.61800			0.808998	−	0.587811i	$-0.200010\pi$
$139$	2651.55			1.61800			0.808998	+	0.587811i	$0.200010\pi$
$140$		0			0
$141$	1524.14			0.910322
$142$	−602.742	+	1043.98i	−0.356204	+	0.616964i
$143$	16.3977	+	28.4017i	0.00958914	+	0.0166089i
$144$	−72.0000	−	124.708i	−0.0416667	−	0.0721688i
$145$	−1700.40	+	2945.17i	−0.973863	+	1.68678i
$146$	2204.60			1.24968
$147$		0			0
$148$	674.136			0.374417
$149$	−290.511	+	503.180i	−0.159729	+	0.276659i	−0.934771	−	0.355251i	$-0.884395\pi$
$149$	−290.511	+	503.180i	−0.159729	+	0.276659i	0.775042	+	0.631910i	$0.217729\pi$
$150$	927.557	+	1606.58i	0.504898	+	0.874509i
$151$	307.695	+	532.943i	0.165827	+	0.287221i	0.936949	−	0.349467i	$-0.113637\pi$
$151$	307.695	+	532.943i	0.165827	+	0.287221i	−0.771122	+	0.636688i	$0.780304\pi$
$152$	−134.045	+	232.174i	−0.0715297	+	0.123893i
$153$	1074.14			0.567574
$154$		0			0
$155$	−4653.47			−2.41145
$156$	−12.9773	+	22.4773i	−0.00666034	+	0.0115361i
$157$	−153.466	−	265.811i	−0.0780122	−	0.135121i	0.824380	−	0.566037i	$-0.191524\pi$
$157$	−153.466	−	265.811i	−0.0780122	−	0.135121i	−0.902392	+	0.430916i	$0.858191\pi$
$158$	116.303	+	201.443i	0.0585606	+	0.101430i
$159$	−264.767	+	458.590i	−0.132059	+	0.228733i
$160$	−666.788			−0.329464
$161$		0			0
$162$	162.000			0.0785674
$163$	−1757.25	+	3043.65i	−0.844408	+	1.46256i	0.0417271	+	0.999129i	$0.486714\pi$
$163$	−1757.25	+	3043.65i	−0.844408	+	1.46256i	−0.886135	+	0.463428i	$0.846619\pi$
$164$	−646.045	−	1118.98i	−0.307608	−	0.532792i
$165$	−473.926	−	820.864i	−0.223607	−	0.387298i
$166$	−568.928	+	985.412i	−0.266008	+	0.460740i
$167$	−1123.30			−0.520502			−0.260251	−	0.965541i	$-0.583805\pi$
$167$	−1123.30			−0.520502			−0.260251	+	0.965541i	$0.583805\pi$
$168$		0			0
$169$	−2192.32			−0.997871
$170$	2486.88	−	4307.40i	1.12197	−	1.94331i
$171$	−150.801	−	261.195i	−0.0674389	−	0.116808i
$172$	−443.114	−	767.495i	−0.196437	−	0.340238i
$173$	765.299	−	1325.54i	0.336327	−	0.582536i	−0.647412	−	0.762141i	$-0.724148\pi$
$173$	765.299	−	1325.54i	0.336327	−	0.582536i	0.983739	+	0.179605i	$0.0574818\pi$
$174$	979.250			0.426648
$175$		0			0
$176$	242.606			0.103904
$177$	−682.392	+	1181.94i	−0.289784	+	0.501920i
$178$	−383.159	−	663.651i	−0.161343	−	0.279454i
$179$	−1706.72	−	2956.12i	−0.712659	−	1.23436i	−0.963856	−	0.266425i	$-0.914157\pi$
$179$	−1706.72	−	2956.12i	−0.712659	−	1.23436i	0.251197	−	0.967936i	$-0.419176\pi$
$180$	375.068	−	649.637i	0.155311	−	0.269006i
$181$	−1286.71			−0.528399			−0.264200	−	0.964468i	$-0.585108\pi$
$181$	−1286.71			−0.528399			−0.264200	+	0.964468i	$0.585108\pi$
$182$		0			0
$183$	115.955			0.0468394
$184$	−2.60607	+	4.51384i	−0.00104414	+	0.00180850i
$185$	1755.88	+	3041.28i	0.697811	+	1.20864i
$186$	669.977	+	1160.43i	0.264114	+	0.457458i
$187$	−904.833	+	1567.22i	−0.353839	+	0.612868i
$188$	−2032.18			−0.788362
$189$		0			0
$190$	−1396.56			−0.533248
$191$	−527.648	+	913.913i	−0.199891	+	0.346222i	−0.948493	−	0.316798i	$-0.897392\pi$
$191$	−527.648	+	913.913i	−0.199891	+	0.346222i	0.748602	+	0.663020i	$0.230726\pi$
$192$	96.0000	+	166.277i	0.0360844	+	0.0625000i
$193$	2385.42	+	4131.67i	0.889670	+	1.54095i	0.840266	+	0.542175i	$0.182399\pi$
$193$	2385.42	+	4131.67i	0.889670	+	1.54095i	0.0494044	+	0.998779i	$0.484268\pi$
$194$	334.701	−	579.719i	0.123867	−	0.214543i
$195$	−135.205			−0.0496523
$196$		0			0
$197$	1622.31			0.586725			0.293363	−	0.956001i	$-0.405226\pi$
$197$	1622.31			0.586725			0.293363	+	0.956001i	$0.405226\pi$
$198$	−136.466	+	236.366i	−0.0489809	+	0.0848373i
$199$	−1775.07	−	3074.51i	−0.632318	−	1.09521i	−0.987077	−	0.160249i	$-0.948770\pi$
$199$	−1775.07	−	3074.51i	−0.632318	−	1.09521i	0.354759	−	0.934958i	$-0.384563\pi$
$200$	−1236.74	−	2142.10i	−0.437254	−	0.757347i
$201$	212.688	−	368.386i	0.0746359	−	0.129273i
$202$	29.4848			0.0102700
$203$		0			0
$204$	−1432.18			−0.491533
$205$	3365.43	−	5829.10i	1.14659	−	1.98596i
$206$	−841.420	−	1457.38i	−0.284585	−	0.492916i
$207$	−2.93183	−	5.07807i	−0.000984425	−	0.00170507i
$208$	17.3030	−	29.9697i	0.00576803	−	0.00999051i
$209$	508.129			0.168172
$210$		0			0
$211$	4653.39			1.51826			0.759129	−	0.650941i	$-0.225625\pi$
$211$	4653.39			1.51826			0.759129	+	0.650941i	$0.225625\pi$
$212$	353.023	−	611.453i	0.114367	−	0.198089i
$213$	904.114	+	1565.97i	0.290840	+	0.503749i
$214$	715.670	+	1239.58i	0.228609	+	0.395962i
$215$	2308.30	−	3998.10i	0.732209	−	1.26822i
$216$	−216.000			−0.0680414
$217$		0			0
$218$	1200.04			0.372829
$219$	1653.45	−	2863.86i	0.510181	−	0.883660i
$220$	631.901	+	1094.49i	0.193649	+	0.335410i
$221$	129.068	+	223.553i	0.0392854	+	0.0680442i
$222$	505.602	−	875.729i	0.152855	−	0.264753i
$223$	4649.53			1.39621			0.698107	−	0.715993i	$-0.254026\pi$
$223$	4649.53			1.39621			0.698107	+	0.715993i	$0.254026\pi$
$224$		0			0
$225$	2782.67			0.824495
$226$	−622.644	+	1078.45i	−0.183264	+	0.317423i
$227$	2075.86	+	3595.49i	0.606958	+	1.05128i	0.991739	+	0.128274i	$0.0409438\pi$
$227$	2075.86	+	3595.49i	0.606958	+	1.05128i	−0.384780	+	0.923008i	$0.625723\pi$
$228$	201.068	+	348.260i	0.0584038	+	0.101158i
$229$	2131.82	−	3692.41i	0.615172	−	1.06551i	−0.375182	−	0.926951i	$-0.622420\pi$
$229$	2131.82	−	3692.41i	0.615172	−	1.06551i	0.990354	−	0.138558i	$-0.0442468\pi$
$230$	−27.1515			−0.00778398
$231$		0			0
$232$	−1305.67			−0.369488
$233$	−1524.95	+	2641.29i	−0.428768	+	0.742647i	−0.996764	−	0.0803838i	$-0.974385\pi$
$233$	−1524.95	+	2641.29i	−0.428768	+	0.742647i	0.567996	+	0.823031i	$0.307719\pi$
$234$	19.4659	+	33.7159i	0.00543815	+	0.00941915i
$235$	−5293.10	−	9167.92i	−1.46929	−	2.54489i
$236$	909.856	−	1575.92i	0.250960	−	0.434676i
$237$	348.909			0.0956290
$238$		0			0
$239$	3987.20			1.07912			0.539562	−	0.841946i	$-0.318590\pi$
$239$	3987.20			1.07912			0.539562	+	0.841946i	$0.318590\pi$
$240$	−500.091	+	866.183i	−0.134503	+	0.232966i
$241$	−312.324	−	540.961i	−0.0834795	−	0.144591i	0.821263	−	0.570550i	$-0.193270\pi$
$241$	−312.324	−	540.961i	−0.0834795	−	0.144591i	−0.904742	+	0.425959i	$0.859937\pi$
$242$	1101.09	+	1907.14i	0.292482	+	0.506593i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	−154.606			−0.0405641
$245$		0			0
$246$	−1938.14			−0.502321
$247$	36.2405	−	62.7704i	0.00933574	−	0.0161700i
$248$	−893.303	−	1547.25i	−0.228729	−	0.396170i
$249$	853.392	+	1478.12i	0.217195	+	0.376193i
$250$	3837.90	−	6647.43i	0.970920	−	1.68168i
$251$	1328.78			0.334152			0.167076	−	0.985944i	$-0.446568\pi$
$251$	1328.78			0.334152			0.167076	+	0.985944i	$0.446568\pi$
$252$		0			0
$253$	9.87887			0.00245486
$254$	180.076	−	311.900i	0.0444841	−	0.0770487i
$255$	−3730.32	−	6461.10i	−0.916085	−	1.58671i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−1613.09	+	2793.96i	−0.391525	+	0.678141i	−0.992651	−	0.121013i	$-0.961386\pi$
$257$	−1613.09	+	2793.96i	−0.391525	+	0.678141i	0.601126	+	0.799154i	$0.294719\pi$
$258$	−1329.34			−0.320780
$259$		0			0
$260$	180.273			0.0430001
$261$	734.437	−	1272.08i	0.174178	−	0.301686i
$262$	217.860	+	377.344i	0.0513719	+	0.0889787i
$263$	−1625.31	−	2815.11i	−0.381067	−	0.660028i	0.610148	−	0.792288i	$-0.291110\pi$
$263$	−1625.31	−	2815.11i	−0.381067	−	0.660028i	−0.991215	+	0.132260i	$0.957777\pi$
$264$	181.955	−	315.155i	0.0424187	−	0.0734713i
$265$	3677.99			0.852593
$266$		0			0
$267$	−1149.48			−0.263471
$268$	−283.583	+	491.181i	−0.0646366	+	0.111954i
$269$	1413.02	+	2447.42i	0.320273	+	0.554729i	0.980544	−	0.196298i	$-0.0628921\pi$
$269$	1413.02	+	2447.42i	0.320273	+	0.554729i	−0.660271	+	0.751027i	$0.729559\pi$
$270$	−562.602	−	974.456i	−0.126811	−	0.219643i
$271$	−1198.38	+	2075.66i	−0.268622	+	0.465268i	−0.968506	−	0.248989i	$-0.919902\pi$
$271$	−1198.38	+	2075.66i	−0.268622	+	0.465268i	0.699884	+	0.714257i	$0.253235\pi$
$272$	1909.58			0.425680
$273$		0			0
$274$	−5203.71			−1.14733
$275$	−2344.07	+	4060.05i	−0.514010	+	0.890292i
$276$	3.90910	+	6.77076i	0.000852537	+	0.00147664i
$277$	−910.233	−	1576.57i	−0.197439	−	0.341974i	0.750258	−	0.661145i	$-0.229929\pi$
$277$	−910.233	−	1576.57i	−0.197439	−	0.341974i	−0.947697	+	0.319170i	$0.896596\pi$
$278$	−2651.55	+	4592.62i	−0.572048	+	0.990816i
$279$	2009.93			0.431296
$280$		0			0
$281$	3083.81			0.654679			0.327339	−	0.944907i	$-0.393848\pi$
$281$	3083.81			0.654679			0.327339	+	0.944907i	$0.393848\pi$
$282$	−1524.14	+	2639.88i	−0.321848	+	0.557456i
$283$	1277.38	+	2212.49i	0.268313	+	0.464732i	0.968426	−	0.249300i	$-0.0802005\pi$
$283$	1277.38	+	2212.49i	0.268313	+	0.464732i	−0.700113	+	0.714032i	$0.746867\pi$
$284$	−1205.48	−	2087.96i	−0.251875	−	0.436259i
$285$	−1047.42	+	1814.19i	−0.217698	+	0.377063i
$286$	−65.5910			−0.0135611
$287$		0			0
$288$	288.000			0.0589256
$289$	−4665.53	+	8080.94i	−0.949630	+	1.64481i
$290$	−3400.79	−	5890.34i	−0.688625	−	1.19273i
$291$	−502.051	−	869.578i	−0.101137	−	0.175174i
$292$	−2204.60	+	3818.48i	−0.441830	+	0.765272i
$293$	1846.47			0.368163			0.184081	−	0.982911i	$-0.441069\pi$
$293$	1846.47			0.368163			0.184081	+	0.982911i	$0.441069\pi$
$294$		0			0
$295$	9479.39			1.87089
$296$	−674.136	+	1167.64i	−0.132376	+	0.229282i
$297$	204.699	+	354.549i	0.0399927	+	0.0692694i
$298$	−581.023	−	1006.36i	−0.112945	−	0.195627i
$299$	0.704576	−	1.22036i	0.000136277	−	0.000236038i
$300$	−3710.23			−0.714034
$301$		0			0
$302$	−1230.78			−0.234515
$303$	22.1136	−	38.3019i	0.00419272	−	0.00726201i
$304$	−268.091	−	464.347i	−0.0505792	−	0.0876057i
$305$	−402.693	−	697.485i	−0.0756005	−	0.130944i
$306$	−1074.14	+	1860.46i	−0.200668	+	0.347566i
$307$	−7041.50			−1.30905			−0.654527	−	0.756039i	$-0.727132\pi$
$307$	−7041.50			−1.30905			−0.654527	+	0.756039i	$0.727132\pi$
$308$		0			0
$309$	−2524.26			−0.464726
$310$	4653.47	−	8060.04i	0.852578	−	1.47671i
$311$	−1343.00	−	2326.14i	−0.244869	−	0.424126i	0.717226	−	0.696841i	$-0.245412\pi$
$311$	−1343.00	−	2326.14i	−0.244869	−	0.424126i	−0.962095	+	0.272715i	$0.912078\pi$
$312$	−25.9546	−	44.9546i	−0.00470957	−	0.00815722i
$313$	1109.59	−	1921.87i	0.200377	−	0.347063i	−0.748273	−	0.663391i	$-0.769117\pi$
$313$	1109.59	−	1921.87i	0.200377	−	0.347063i	0.948650	+	0.316328i	$0.102450\pi$
$314$	613.864			0.110326
$315$		0			0
$316$	−465.212			−0.0828172
$317$	−1110.63	+	1923.67i	−0.196780	+	0.340833i	−0.947483	−	0.319807i	$-0.896382\pi$
$317$	−1110.63	+	1923.67i	−0.196780	+	0.340833i	0.750703	+	0.660640i	$0.229715\pi$
$318$	−529.534	−	917.180i	−0.0933799	−	0.161739i
$319$	1237.35	+	2143.16i	0.217174	+	0.376157i
$320$	666.788	−	1154.91i	0.116483	−	0.201755i
$321$	2147.01			0.373316
$322$		0			0
$323$	3999.53			0.688978
$324$	−162.000	+	280.592i	−0.0277778	+	0.0481125i
$325$	334.366	+	579.138i	0.0570685	+	0.0988455i
$326$	−3514.50	−	6087.29i	−0.597086	−	1.03418i
$327$	900.028	−	1558.89i	0.152207	−	0.263630i
$328$	2584.18			0.435023
$329$		0			0
$330$	1895.70			0.316228
$331$	−2077.03	+	3597.52i	−0.344906	+	0.597394i	−0.985337	−	0.170622i	$-0.945422\pi$
$331$	−2077.03	+	3597.52i	−0.344906	+	0.597394i	0.640431	+	0.768016i	$0.278756\pi$
$332$	−1137.86	−	1970.82i	−0.188096	−	0.325792i
$333$	−758.403	−	1313.59i	−0.124806	−	0.216170i
$334$	1123.30	−	1945.62i	0.184025	−	0.318741i
$335$	−2954.53			−0.481860
$336$		0			0
$337$	−254.167			−0.0410841			−0.0205420	−	0.999789i	$-0.506539\pi$
$337$	−254.167			−0.0410841			−0.0205420	+	0.999789i	$0.506539\pi$
$338$	2192.32	−	3797.21i	0.352801	−	0.611069i
$339$	933.966	+	1617.68i	0.149634	+	0.259174i
$340$	4973.76	+	8614.80i	0.793353	+	1.37413i
$341$	−1693.13	+	2932.59i	−0.268880	+	0.465714i
$342$	603.205			0.0953730
$343$		0			0
$344$	1772.45			0.277803
$345$	−20.3636	+	35.2708i	−0.00317780	+	0.00550410i
$346$	1530.60	+	2651.07i	0.237819	+	0.411915i
$347$	3112.32	+	5390.69i	0.481493	+	0.833970i	0.999774	−	0.0212401i	$-0.00676143\pi$
$347$	3112.32	+	5390.69i	0.481493	+	0.833970i	−0.518282	+	0.855210i	$0.673428\pi$
$348$	−979.250	+	1696.11i	−0.150843	+	0.261267i
$349$	−9732.21			−1.49270			−0.746352	−	0.665552i	$-0.768196\pi$
$349$	−9732.21			−1.49270			−0.746352	+	0.665552i	$0.768196\pi$
$350$		0			0
$351$	58.3977			0.00888046
$352$	−242.606	+	420.206i	−0.0367356	+	0.0636280i
$353$	712.807	+	1234.62i	0.107476	+	0.186153i	0.914747	−	0.404027i	$-0.132390\pi$
$353$	712.807	+	1234.62i	0.107476	+	0.186153i	−0.807271	+	0.590180i	$0.799057\pi$
$354$	−1364.78	−	2363.88i	−0.204908	−	0.354911i
$355$	6279.71	−	10876.8i	0.938852	−	1.62614i
$356$	1532.64			0.228173
$357$		0			0
$358$	6826.86			1.00785
$359$	2883.25	−	4993.93i	0.423877	−	0.734177i	−0.572438	−	0.819948i	$-0.694002\pi$
$359$	2883.25	−	4993.93i	0.423877	−	0.734177i	0.996315	+	0.0857714i	$0.0273355\pi$
$360$	750.136	+	1299.27i	0.109821	+	0.190216i
$361$	2867.99	+	4967.51i	0.418136	+	0.724233i
$362$	1286.71	−	2228.64i	0.186817	−	0.323577i
$363$	3303.26			0.477621
$364$		0			0
$365$	−22968.7			−3.29381
$366$	−115.955	+	200.839i	−0.0165602	+	0.0286831i
$367$	5772.67	+	9998.56i	0.821065	+	1.42213i	0.904890	+	0.425646i	$0.139953\pi$
$367$	5772.67	+	9998.56i	0.821065	+	1.42213i	−0.0838244	+	0.996481i	$0.526713\pi$
$368$	−5.21213	−	9.02768i	−0.000738319	−	0.00127881i
$369$	−1453.60	+	2517.71i	−0.205072	+	0.355195i
$370$	−7023.53			−0.986854
$371$		0			0
$372$	−2679.91			−0.373513
$373$	3239.79	−	5611.47i	0.449731	−	0.778957i	−0.548637	−	0.836061i	$-0.684853\pi$
$373$	3239.79	−	5611.47i	0.449731	−	0.778957i	0.998368	+	0.0571033i	$0.0181864\pi$
$374$	−1809.67	−	3134.43i	−0.250202	−	0.433363i
$375$	−5756.85	−	9971.15i	−0.792753	−	1.37309i
$376$	2032.18	−	3519.84i	0.278728	−	0.482771i
$377$	353.000			0.0482239
$378$		0			0
$379$	611.996			0.0829449			0.0414725	−	0.999140i	$-0.486795\pi$
$379$	611.996			0.0829449			0.0414725	+	0.999140i	$0.486795\pi$
$380$	1396.56	−	2418.91i	0.188532	−	0.326546i
$381$	−270.114	−	467.851i	−0.0363211	−	0.0629100i
$382$	−1055.30	−	1827.83i	−0.141345	−	0.244816i
$383$	2180.41	−	3776.57i	0.290897	−	0.503848i	−0.683125	−	0.730301i	$-0.739380\pi$
$383$	2180.41	−	3776.57i	0.290897	−	0.503848i	0.974022	+	0.226453i	$0.0727130\pi$
$384$	−384.000			−0.0510310
$385$		0			0
$386$	−9541.68			−1.25818
$387$	−997.006	+	1726.86i	−0.130958	+	0.226825i
$388$	669.402	+	1159.44i	0.0875869	+	0.151705i
$389$	6573.46	+	11385.6i	0.856781	+	1.48399i	0.874983	+	0.484154i	$0.160872\pi$
$389$	6573.46	+	11385.6i	0.856781	+	1.48399i	−0.0182021	+	0.999834i	$0.505794\pi$
$390$	135.205	−	234.181i	0.0175547	−	0.0304057i
$391$	77.7575			0.0100572
$392$		0			0
$393$	653.580			0.0838899
$394$	−1622.31	+	2809.92i	−0.207439	+	0.359294i
$395$	−1211.71	−	2098.74i	−0.154349	−	0.267340i
$396$	−272.932	−	472.732i	−0.0346347	−	0.0599891i
$397$	−4239.02	+	7342.20i	−0.535895	+	0.928198i	0.463224	+	0.886241i	$0.346692\pi$
$397$	−4239.02	+	7342.20i	−0.535895	+	0.928198i	−0.999119	+	0.0419565i	$0.986641\pi$
$398$	7100.27			0.894232
$399$		0			0
$400$	4946.97			0.618371
$401$	−1401.50	+	2427.47i	−0.174533	+	0.302299i	−0.939999	−	0.341176i	$-0.889175\pi$
$401$	−1401.50	+	2427.47i	−0.174533	+	0.302299i	0.765467	+	0.643475i	$0.222508\pi$
$402$	425.375	+	736.771i	0.0527756	+	0.0914100i
$403$	241.513	+	418.313i	0.0298527	+	0.0517064i
$404$	−29.4848	+	51.0692i	−0.00363100	+	0.00628908i
$405$	−1687.81			−0.207081
$406$		0			0
$407$	2555.46			0.311227
$408$	1432.18	−	2480.61i	0.173783	−	0.301001i
$409$	−3192.69	−	5529.91i	−0.385987	−	0.668548i	0.605919	−	0.795526i	$-0.292806\pi$
$409$	−3192.69	−	5529.91i	−0.385987	−	0.668548i	−0.991906	+	0.126978i	$0.959472\pi$
$410$	6730.86	+	11658.2i	0.810765	+	1.40429i
$411$	−3902.78	+	6759.82i	−0.468395	+	0.811283i
$412$	3365.68			0.402464
$413$		0			0
$414$	11.7273			0.00139219
$415$	5927.41	−	10266.6i	0.701121	−	1.21438i
$416$	34.6061	+	59.9395i	0.00407861	+	0.00706436i
$417$	3977.32	+	6888.93i	0.467075	+	0.808998i
$418$	−508.129	+	880.105i	−0.0594579	+	0.102984i
$419$	−4831.66			−0.563346			−0.281673	−	0.959510i	$-0.590889\pi$
$419$	−4831.66			−0.563346			−0.281673	+	0.959510i	$0.590889\pi$
$420$		0			0
$421$	7475.37			0.865385			0.432693	−	0.901542i	$-0.357564\pi$
$421$	7475.37			0.865385			0.432693	+	0.901542i	$0.357564\pi$
$422$	−4653.39	+	8059.90i	−0.536785	+	0.929739i
$423$	2286.20	+	3959.82i	0.262787	+	0.455161i
$424$	706.045	+	1222.91i	0.0808693	+	0.140070i
$425$	−18450.4	+	31957.1i	−2.10583	+	3.64740i
$426$	−3616.45			−0.411309
$427$		0			0
$428$	−2862.68			−0.323301
$429$	−49.1932	+	85.2051i	−0.00553630	+	0.00958914i
$430$	4616.61	+	7996.20i	0.517750	+	0.896769i
$431$	−3495.97	−	6055.19i	−0.390707	−	0.676725i	0.601836	−	0.798620i	$-0.294436\pi$
$431$	−3495.97	−	6055.19i	−0.390707	−	0.676725i	−0.992543	+	0.121895i	$0.961103\pi$
$432$	216.000	−	374.123i	0.0240563	−	0.0416667i
$433$	7699.26			0.854510			0.427255	−	0.904131i	$-0.359481\pi$
$433$	7699.26			0.854510			0.427255	+	0.904131i	$0.359481\pi$
$434$		0			0
$435$	−10202.4			−1.12452
$436$	−1200.04	+	2078.53i	−0.131815	+	0.228310i
$437$	−10.9166	−	18.9081i	−0.00119499	−	0.00206979i
$438$	3306.90	+	5727.71i	0.360753	+	0.624842i
$439$	4706.16	−	8151.31i	0.511646	−	0.886198i	−0.488262	−	0.872697i	$-0.662369\pi$
$439$	4706.16	−	8151.31i	0.511646	−	0.886198i	0.999909	−	0.0135008i	$-0.00429758\pi$
$440$	−2527.61			−0.273861
$441$		0			0
$442$	−516.273			−0.0555579
$443$	3129.09	−	5419.74i	0.335593	−	0.581263i	−0.648006	−	0.761635i	$-0.724397\pi$
$443$	3129.09	−	5419.74i	0.335593	−	0.581263i	0.983598	+	0.180372i	$0.0577301\pi$
$444$	1011.20	+	1751.46i	0.108085	+	0.187208i
$445$	3991.97	+	6914.29i	0.425252	+	0.736559i
$446$	−4649.53	+	8053.23i	−0.493636	+	0.855003i
$447$	−1743.07			−0.184439
$448$		0			0
$449$	−11633.8			−1.22279			−0.611396	−	0.791325i	$-0.709392\pi$
$449$	−11633.8			−1.22279			−0.611396	+	0.791325i	$0.709392\pi$
$450$	−2782.67	+	4819.73i	−0.291503	+	0.504898i
$451$	−2448.98	−	4241.75i	−0.255694	−	0.442874i
$452$	−1245.29	−	2156.90i	−0.129587	−	0.224452i
$453$	−923.085	+	1598.83i	−0.0957402	+	0.165827i
$454$	−8303.43			−0.858369
$455$		0			0
$456$	−804.273			−0.0825954
$457$	6552.31	−	11348.9i	0.670688	−	1.16167i	−0.307022	−	0.951703i	$-0.599332\pi$
$457$	6552.31	−	11348.9i	0.670688	−	1.16167i	0.977709	−	0.209963i	$-0.0673343\pi$
$458$	4263.63	+	7384.83i	0.434992	+	0.753429i
$459$	1611.20	+	2790.69i	0.163844	+	0.283787i
$460$	27.1515	−	47.0277i	0.00275205	−	0.00476669i
$461$	2594.63			0.262134			0.131067	−	0.991373i	$-0.458160\pi$
$461$	2594.63			0.262134			0.131067	+	0.991373i	$0.458160\pi$
$462$		0			0
$463$	−14136.2			−1.41893			−0.709465	−	0.704741i	$-0.751063\pi$
$463$	−14136.2			−1.41893			−0.709465	+	0.704741i	$0.751063\pi$
$464$	1305.67	−	2261.48i	0.130634	−	0.226264i
$465$	−6980.20	−	12090.1i	−0.696127	−	1.20573i
$466$	−3049.90	−	5282.58i	−0.303184	−	0.525131i
$467$	7795.12	−	13501.5i	0.772409	−	1.33785i	−0.163830	−	0.986489i	$-0.552385\pi$
$467$	7795.12	−	13501.5i	0.772409	−	1.33785i	0.936239	−	0.351363i	$-0.114282\pi$
$468$	−77.8637			−0.00769070
$469$		0			0
$470$	21172.4			2.07789
$471$	460.398	−	797.432i	0.0450404	−	0.0780122i
$472$	1819.71	+	3151.83i	0.177456	+	0.307362i
$473$	−1679.72	−	2909.36i	−0.163285	−	0.282817i
$474$	−348.909	+	604.328i	−0.0338100	+	0.0585606i
$475$	10361.2			1.00085
$476$		0			0
$477$	−1588.60			−0.152489
$478$	−3987.20	+	6906.04i	−0.381528	+	0.660826i
$479$	−4226.75	−	7320.95i	−0.403184	−	0.698336i	0.590924	−	0.806727i	$-0.298763\pi$
$479$	−4226.75	−	7320.95i	−0.403184	−	0.698336i	−0.994108	+	0.108391i	$0.965430\pi$
$480$	−1000.18	−	1732.37i	−0.0951080	−	0.164732i
$481$	182.259	−	315.683i	0.0172772	−	0.0299249i
$482$	1249.30			0.118058
$483$		0			0
$484$	−4404.35			−0.413632
$485$	−3487.10	+	6039.83i	−0.326476	+	0.565474i
$486$	243.000	+	420.888i	0.0226805	+	0.0392837i
$487$	2005.53	+	3473.69i	0.186611	+	0.323219i	0.944118	−	0.329607i	$-0.106916\pi$
$487$	2005.53	+	3473.69i	0.186611	+	0.323219i	−0.757507	+	0.652827i	$0.773583\pi$
$488$	154.606	−	267.786i	0.0143416	−	0.0248403i
$489$	−10543.5			−0.975038
$490$		0			0
$491$	13927.9			1.28016			0.640079	−	0.768309i	$-0.278902\pi$
$491$	13927.9			1.28016			0.640079	+	0.768309i	$0.278902\pi$
$492$	1938.14	−	3356.95i	0.177597	−	0.307608i
$493$	9739.33	+	16869.0i	0.889731	+	1.54106i
$494$	72.4810	+	125.541i	0.00660137	+	0.0114339i
$495$	1421.78	−	2462.59i	0.129099	−	0.223607i
$496$	3573.21			0.323472
$497$		0			0
$498$	−3413.57			−0.307160
$499$	1973.77	−	3418.68i	0.177071	−	0.306695i	−0.763805	−	0.645447i	$-0.776671\pi$
$499$	1973.77	−	3418.68i	0.177071	−	0.306695i	0.940876	+	0.338751i	$0.110005\pi$
$500$	7675.80	+	13294.9i	0.686544	+	1.18913i
$501$	−1684.95	−	2918.43i	−0.150256	−	0.260251i
$502$	−1328.78	+	2301.52i	−0.118141	+	0.204625i
$503$	13725.3			1.21666			0.608331	−	0.793684i	$-0.291839\pi$
$503$	13725.3			1.21666			0.608331	+	0.793684i	$0.291839\pi$
$504$		0			0
$505$	−307.190			−0.0270688
$506$	−9.87887	+	17.1107i	−0.000867924	+	0.00150329i
$507$	−3288.48	−	5695.82i	−0.288060	−	0.498935i
$508$	360.152	+	623.801i	0.0314550	+	0.0544817i
$509$	3915.05	−	6781.07i	0.340926	−	0.590502i	−0.643679	−	0.765296i	$-0.722593\pi$
$509$	3915.05	−	6781.07i	0.340926	−	0.590502i	0.984605	+	0.174794i	$0.0559259\pi$
$510$	14921.3			1.29554
$511$		0			0
$512$	512.000			0.0441942
$513$	452.403	−	783.586i	0.0389359	−	0.0674389i
$514$	−3226.18	−	5587.91i	−0.276850	−	0.479518i
$515$	8766.39	+	15183.8i	0.750084	+	1.29918i
$516$	1329.34	−	2302.49i	0.113413	−	0.196437i
$517$	−7703.43			−0.655312
$518$		0			0
$519$	4591.80			0.388357
$520$	−180.273	+	312.241i	−0.0152028	+	0.0263321i
$521$	−2953.69	−	5115.95i	−0.248376	−	0.430199i	0.714700	−	0.699431i	$-0.246563\pi$
$521$	−2953.69	−	5115.95i	−0.248376	−	0.430199i	−0.963075	+	0.269232i	$0.913230\pi$
$522$	1468.87	+	2544.17i	0.123163	+	0.213324i
$523$	3954.03	−	6848.58i	0.330588	−	0.572595i	−0.652039	−	0.758185i	$-0.726086\pi$
$523$	3954.03	−	6848.58i	0.330588	−	0.572595i	0.982627	+	0.185590i	$0.0594196\pi$
$524$	−871.439			−0.0726508
$525$		0			0
$526$	6501.23			0.538911
$527$	−13326.8	+	23082.7i	−1.10156	+	1.90797i
$528$	363.909	+	630.309i	0.0299945	+	0.0519520i
$529$	6083.29	+	10536.6i	0.499983	+	0.865995i
$530$	−3677.99	+	6370.46i	−0.301437	+	0.522104i
$531$	−4094.35			−0.334613
$532$		0			0
$533$	−698.659			−0.0567773
$534$	1149.48	−	1990.95i	0.0931512	−	0.161343i
$535$	−7456.26	−	12914.6i	−0.602546	−	1.04364i
$536$	−567.167	−	982.362i	−0.0457050	−	0.0791633i
$537$	5120.15	−	8868.36i	0.411454	−	0.712659i
$538$	−5652.08			−0.452934
$539$		0			0
$540$	2250.41			0.179337
$541$	1970.52	−	3413.04i	0.156598	−	0.271235i	−0.777042	−	0.629449i	$-0.783281\pi$
$541$	1970.52	−	3413.04i	0.156598	−	0.271235i	0.933640	+	0.358214i	$0.116614\pi$
$542$	−2396.77	−	4151.33i	−0.189945	−	0.328994i
$543$	−1930.06	−	3342.97i	−0.152536	−	0.264200i
$544$	−1909.58	+	3307.48i	−0.150501	+	0.260675i
$545$	−12502.7			−0.982670
$546$		0			0
$547$	−1828.71			−0.142943			−0.0714717	−	0.997443i	$-0.522770\pi$
$547$	−1828.71			−0.142943			−0.0714717	+	0.997443i	$0.522770\pi$
$548$	5203.71	−	9013.09i	0.405642	−	0.702592i
$549$	173.932	+	301.259i	0.0135214	+	0.0234197i
$550$	−4688.14	−	8120.10i	−0.363460	−	0.629532i
$551$	2734.67	−	4736.58i	0.211435	−	0.366216i
$552$	−15.6364			−0.00120567
$553$		0			0
$554$	3640.93			0.279221
$555$	−5267.65	+	9123.83i	−0.402881	+	0.697811i
$556$	−5303.10	−	9185.24i	−0.404499	−	0.700613i
$557$	−11266.0	−	19513.3i	−0.857011	−	1.48439i	−0.874767	−	0.484544i	$-0.838985\pi$
$557$	−11266.0	−	19513.3i	−0.857011	−	1.48439i	0.0177556	−	0.999842i	$-0.494348\pi$
$558$	−2009.93	+	3481.30i	−0.152486	+	0.264114i
$559$	−479.201			−0.0362577
$560$		0			0
$561$	−5429.00			−0.408579
$562$	−3083.81	+	5341.32i	−0.231464	+	0.400907i
$563$	11677.9	+	20226.6i	0.874179	+	1.51412i	0.857635	+	0.514260i	$0.171933\pi$
$563$	11677.9	+	20226.6i	0.874179	+	1.51412i	0.0165446	+	0.999863i	$0.494733\pi$
$564$	−3048.27	−	5279.76i	−0.227581	−	0.394181i
$565$	6487.05	−	11235.9i	0.483031	−	0.836634i
$566$	−5109.54			−0.379452
$567$		0			0
$568$	4821.94			0.356204
$569$	10443.8	−	18089.2i	0.769468	−	1.33276i	−0.168384	−	0.985721i	$-0.553855\pi$
$569$	10443.8	−	18089.2i	0.769468	−	1.33276i	0.937852	−	0.347036i	$-0.112812\pi$
$570$	−2094.84	−	3628.37i	−0.153935	−	0.266624i
$571$	−11872.6	−	20564.0i	−0.870147	−	1.50714i	−0.861844	−	0.507173i	$-0.830690\pi$
$571$	−11872.6	−	20564.0i	−0.870147	−	1.50714i	−0.00830301	−	0.999966i	$-0.502643\pi$
$572$	65.5910	−	113.607i	0.00479457	−	0.00830444i
$573$	−3165.89			−0.230815
$574$		0			0
$575$	201.440			0.0146098
$576$	−288.000	+	498.831i	−0.0208333	+	0.0360844i
$577$	1227.20	+	2125.57i	0.0885422	+	0.153360i	0.906895	−	0.421356i	$-0.138446\pi$
$577$	1227.20	+	2125.57i	0.0885422	+	0.153360i	−0.818353	+	0.574716i	$0.805113\pi$
$578$	−9331.06	−	16161.9i	−0.671490	−	1.16305i
$579$	−7156.26	+	12395.0i	−0.513651	+	0.889670i
$580$	13603.2			0.973863
$581$		0			0
$582$	2008.20			0.143029
$583$	1338.21	−	2317.85i	0.0950652	−	0.164658i
$584$	−4409.20	−	7636.95i	−0.312421	−	0.541129i
$585$	−202.807	−	351.272i	−0.0143334	−	0.0248261i
$586$	−1846.47	+	3198.17i	−0.130165	+	0.225453i
$587$	−18567.5			−1.30556			−0.652780	−	0.757547i	$-0.726397\pi$
$587$	−18567.5			−1.30556			−0.652780	+	0.757547i	$0.726397\pi$
$588$		0			0
$589$	7483.95			0.523550
$590$	−9479.39	+	16418.8i	−0.661458	+	1.14568i
$591$	2433.47	+	4214.89i	0.169373	+	0.293363i
$592$	−1348.27	−	2335.28i	−0.0936042	−	0.162127i
$593$	8556.47	−	14820.2i	0.592533	−	1.02630i	−0.401357	−	0.915922i	$-0.631461\pi$
$593$	8556.47	−	14820.2i	0.592533	−	1.02630i	0.993890	−	0.110375i	$-0.0352053\pi$
$594$	−818.795			−0.0565582
$595$		0			0
$596$	2324.09			0.159729
$597$	5325.20	−	9223.52i	0.365069	−	0.632318i
$598$	1.40915	+	2.44072i	9.63621e−5	+	0.000166904i
$599$	−11632.4	−	20147.9i	−0.793469	−	1.37433i	−0.923807	−	0.382859i	$-0.874940\pi$
$599$	−11632.4	−	20147.9i	−0.793469	−	1.37433i	0.130338	−	0.991470i	$-0.458394\pi$
$600$	3710.23	−	6426.30i	0.252449	−	0.437254i
$601$	−25322.3			−1.71867			−0.859334	−	0.511416i	$-0.829121\pi$
$601$	−25322.3			−1.71867			−0.859334	+	0.511416i	$0.829121\pi$
$602$		0			0
$603$	1276.13			0.0861821
$604$	1230.78	−	2131.77i	0.0829135	−	0.143610i
$605$	−11471.7	−	19869.6i	−0.770897	−	1.33523i
$606$	44.2272	+	76.6038i	0.00296470	+	0.00513501i
$607$	−10867.2	+	18822.5i	−0.726665	+	1.25862i	0.231620	+	0.972806i	$0.425597\pi$
$607$	−10867.2	+	18822.5i	−0.726665	+	1.25862i	−0.958285	+	0.285814i	$0.907736\pi$
$608$	1072.36			0.0715297
$609$		0			0
$610$	1610.77			0.106915
$611$	−549.420	+	951.624i	−0.0363784	+	0.0630092i
$612$	−2148.27	−	3720.92i	−0.141893	−	0.245767i
$613$	6786.19	+	11754.0i	0.447131	+	0.774454i	0.998198	−	0.0600072i	$-0.0191124\pi$
$613$	6786.19	+	11754.0i	0.447131	+	0.774454i	−0.551067	+	0.834461i	$0.685779\pi$
$614$	7041.50	−	12196.2i	0.462820	−	0.801628i
$615$	20192.6			1.32397
$616$		0			0
$617$	−8497.12			−0.554427			−0.277213	−	0.960808i	$-0.589411\pi$
$617$	−8497.12			−0.554427			−0.277213	+	0.960808i	$0.589411\pi$
$618$	2524.26	−	4372.15i	0.164305	−	0.284585i
$619$	−11491.5	−	19903.8i	−0.746173	−	1.29241i	−0.949645	−	0.313329i	$-0.898556\pi$
$619$	−11491.5	−	19903.8i	−0.746173	−	1.29241i	0.203472	−	0.979081i	$-0.434777\pi$
$620$	9306.93	+	16120.1i	0.602863	+	1.04419i
$621$	8.79548	−	15.2342i	0.000568358	−	0.000984425i
$622$	5371.98			0.346297
$623$		0			0
$624$	103.818			0.00666034
$625$	−20661.3	+	35786.4i	−1.32232	+	2.29033i
$626$	2219.19	+	3843.75i	0.141688	+	0.245411i
$627$	762.193	+	1320.16i	0.0485471	+	0.0840861i
$628$	−613.864	+	1063.24i	−0.0390061	+	0.0675605i
$629$	20114.3			1.27505
$630$		0			0
$631$	−15717.9			−0.991635			−0.495817	−	0.868427i	$-0.665131\pi$
$631$	−15717.9			−0.991635			−0.495817	+	0.868427i	$0.665131\pi$
$632$	465.212	−	805.771i	0.0292803	−	0.0507150i
$633$	6980.08	+	12089.9i	0.438283	+	0.759129i
$634$	−2221.26	−	3847.34i	−0.139144	−	0.241005i
$635$	−1876.13	+	3249.55i	−0.117247	+	0.203078i
$636$	2118.14			0.132059
$637$		0			0
$638$	−4949.42			−0.307131
$639$	−2712.34	+	4697.91i	−0.167916	+	0.290840i
$640$	1333.58	+	2309.82i	0.0823660	+	0.142662i
$641$	−14553.7	−	25207.7i	−0.896780	−	1.55327i	−0.831587	−	0.555395i	$-0.812567\pi$
$641$	−14553.7	−	25207.7i	−0.896780	−	1.55327i	−0.0651930	−	0.997873i	$-0.520766\pi$
$642$	−2147.01	+	3718.73i	−0.131987	+	0.228609i
$643$	3112.26			0.190880			0.0954398	−	0.995435i	$-0.469574\pi$
$643$	3112.26			0.190880			0.0954398	+	0.995435i	$0.469574\pi$
$644$		0			0
$645$	13849.8			0.845482
$646$	−3999.53	+	6927.39i	−0.243590	+	0.421911i
$647$	−3928.80	−	6804.87i	−0.238728	−	0.413489i	0.721622	−	0.692288i	$-0.243397\pi$
$647$	−3928.80	−	6804.87i	−0.238728	−	0.413489i	−0.960349	+	0.278799i	$0.910064\pi$
$648$	−324.000	−	561.184i	−0.0196419	−	0.0340207i
$649$	3449.01	−	5973.86i	0.208606	−	0.361317i
$650$	−1337.46			−0.0807071
$651$		0			0
$652$	14058.0			0.844408
$653$	9761.01	−	16906.6i	0.584958	−	1.01318i	−0.409923	−	0.912120i	$-0.634444\pi$
$653$	9761.01	−	16906.6i	0.584958	−	1.01318i	0.994881	−	0.101057i	$-0.0322224\pi$
$654$	1800.06	+	3117.79i	0.107627	+	0.186415i
$655$	−2269.79	−	3931.38i	−0.135401	−	0.234522i
$656$	−2584.18	+	4475.93i	−0.153804	+	0.266396i
$657$	9920.69			0.589107
$658$		0			0
$659$	664.061			0.0392536			0.0196268	−	0.999807i	$-0.493752\pi$
$659$	664.061			0.0392536			0.0196268	+	0.999807i	$0.493752\pi$
$660$	−1895.70	+	3283.46i	−0.111803	+	0.193649i
$661$	7960.82	+	13788.5i	0.468442	+	0.811365i	0.999349	−	0.0360650i	$-0.0114823\pi$
$661$	7960.82	+	13788.5i	0.468442	+	0.811365i	−0.530908	+	0.847430i	$0.678149\pi$
$662$	−4154.06	−	7195.04i	−0.243885	−	0.422422i
$663$	−387.205	+	670.658i	−0.0226814	+	0.0392854i
$664$	4551.42			0.266008
$665$		0			0
$666$	3033.61			0.176502
$667$	53.1665	−	92.0870i	0.00308638	−	0.00534576i
$668$	2246.61	+	3891.24i	0.130125	+	0.225384i
$669$	6974.30	+	12079.8i	0.403052	+	0.698107i
$670$	2954.53	−	5117.40i	0.170363	−	0.295078i
$671$	−586.068			−0.0337182
$672$		0			0
$673$	24631.0			1.41078			0.705391	−	0.708819i	$-0.250771\pi$
$673$	24631.0			1.41078			0.705391	+	0.708819i	$0.250771\pi$
$674$	254.167	−	440.230i	0.0145254	−	0.0251588i
$675$	4174.01	+	7229.59i	0.238011	+	0.412247i
$676$	4384.64	+	7594.43i	0.249468	+	0.432091i
$677$	8546.39	−	14802.8i	0.485177	−	0.840350i	−0.514678	−	0.857383i	$-0.672089\pi$
$677$	8546.39	−	14802.8i	0.485177	−	0.840350i	0.999855	+	0.0170329i	$0.00542200\pi$
$678$	−3735.86			−0.211615
$679$		0			0
$680$	−19895.0			−1.12197
$681$	−6227.57	+	10786.5i	−0.350428	+	0.606958i
$682$	−3386.26	−	5865.18i	−0.190127	−	0.329310i
$683$	9581.79	+	16596.1i	0.536804	+	0.929771i	0.999074	+	0.0430322i	$0.0137018\pi$
$683$	9581.79	+	16596.1i	0.536804	+	0.929771i	−0.462270	+	0.886739i	$0.652965\pi$
$684$	−603.205	+	1044.78i	−0.0337194	+	0.0584038i
$685$	54215.2			3.02402
$686$		0			0
$687$	12790.9			0.710339
$688$	−1772.45	+	3069.98i	−0.0982183	+	0.170119i
$689$	−190.886	−	330.625i	−0.0105547	−	0.0182813i
$690$	−40.7272	−	70.5416i	−0.00224704	−	0.00389199i
$691$	4047.94	−	7011.23i	0.222852	−	0.385991i	−0.732821	−	0.680422i	$-0.761797\pi$
$691$	4047.94	−	7011.23i	0.222852	−	0.385991i	0.955673	+	0.294431i	$0.0951300\pi$
$692$	−6122.39			−0.336327
$693$		0			0
$694$	−12449.3			−0.680934
$695$	27625.3	−	47848.5i	1.50775	−	2.61150i
$696$	−1958.50	−	3392.22i	−0.106662	−	0.184744i
$697$	−19276.1	−	33387.2i	−1.04754	−	1.81439i
$698$	9732.21	−	16856.7i	0.527750	−	0.914090i
$699$	−9149.70			−0.495098
$700$		0			0
$701$	12354.7			0.665664			0.332832	−	0.942986i	$-0.391996\pi$
$701$	12354.7			0.665664			0.332832	+	0.942986i	$0.391996\pi$
$702$	−58.3977	+	101.148i	−0.00313972	+	0.00543815i
$703$	−2823.90	−	4891.14i	−0.151501	−	0.262408i
$704$	−485.212	−	840.412i	−0.0259760	−	0.0449918i
$705$	15879.3	−	27503.8i	0.848297	−	1.46929i
$706$	−2851.23			−0.151993
$707$		0			0
$708$	5459.14			0.289784
$709$	−1914.41	+	3315.85i	−0.101406	+	0.175641i	−0.912264	−	0.409602i	$-0.865668\pi$
$709$	−1914.41	+	3315.85i	−0.101406	+	0.175641i	0.810858	+	0.585243i	$0.199001\pi$
$710$	12559.4	+	21753.5i	0.663868	+	1.14985i
$711$	523.364	+	906.492i	0.0276057	+	0.0478145i
$712$	−1532.64	+	2654.60i	−0.0806713	+	0.139727i
$713$	145.500			0.00764241
$714$		0			0
$715$	683.363			0.0357431
$716$	−6826.86	+	11824.5i	−0.356329	+	0.617181i
$717$	5980.81	+	10359.1i	0.311516	+	0.539562i
$718$	5766.49	+	9987.86i	0.299726	+	0.519141i
$719$	611.500	−	1059.15i	0.0317178	−	0.0549368i	−0.849731	−	0.527217i	$-0.823236\pi$
$719$	611.500	−	1059.15i	0.0317178	−	0.0549368i	0.881449	+	0.472280i	$0.156569\pi$
$720$	−3000.55			−0.155311
$721$		0			0
$722$	−11472.0			−0.591333
$723$	936.972	−	1622.88i	0.0481969	−	0.0834795i
$724$	2573.42	+	4457.29i	0.132100	+	0.228804i
$725$	25230.8	+	43701.1i	1.29248	+	2.23864i
$726$	−3303.26	+	5721.42i	−0.168864	+	0.292482i
$727$	−6368.21			−0.324875			−0.162437	−	0.986719i	$-0.551936\pi$
$727$	−6368.21			−0.324875			−0.162437	+	0.986719i	$0.551936\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	22968.7	−	39783.0i	1.16454	−	2.01704i
$731$	−13221.2	−	22899.9i	−0.668954	−	1.15866i
$732$	−231.909	−	401.678i	−0.0117098	−	0.0202820i
$733$	−12577.0	+	21784.0i	−0.633753	+	1.09769i	0.353024	+	0.935614i	$0.385153\pi$
$733$	−12577.0	+	21784.0i	−0.633753	+	1.09769i	−0.986778	+	0.162079i	$0.948180\pi$
$734$	−23090.7			−1.16116
$735$		0			0
$736$	20.8485			0.00104414
$737$	−1074.98	+	1861.93i	−0.0537281	+	0.0930597i
$738$	−2907.20	−	5035.43i	−0.145008	−	0.251161i
$739$	5369.55	+	9300.34i	0.267283	+	0.462948i	0.968159	−	0.250335i	$-0.0805408\pi$
$739$	5369.55	+	9300.34i	0.267283	+	0.462948i	−0.700876	+	0.713283i	$0.747207\pi$
$740$	7023.53	−	12165.1i	0.348906	−	0.604322i
$741$	217.443			0.0107800
$742$		0			0
$743$	28166.3			1.39074			0.695370	−	0.718652i	$-0.255240\pi$
$743$	28166.3			1.39074			0.695370	+	0.718652i	$0.255240\pi$
$744$	2679.91	−	4641.74i	0.132057	−	0.228729i
$745$	6053.42	+	10484.8i	0.297691	+	0.515617i
$746$	6479.57	+	11222.9i	0.318008	+	0.550806i
$747$	−2560.18	+	4434.36i	−0.125398	+	0.217195i
$748$	7238.67			0.353839
$749$		0			0
$750$	23027.4			1.12112
$751$	−14328.5	+	24817.7i	−0.696211	+	1.20587i	0.273559	+	0.961855i	$0.411799\pi$
$751$	−14328.5	+	24817.7i	−0.696211	+	1.20587i	−0.969771	+	0.244018i	$0.921534\pi$
$752$	4064.36	+	7039.68i	0.197091	+	0.341371i
$753$	1993.18	+	3452.28i	0.0964613	+	0.167076i
$754$	−353.000	+	611.414i	−0.0170497	+	0.0295310i
$755$	12823.0			0.618113
$756$		0			0
$757$	−23604.1			−1.13330			−0.566648	−	0.823960i	$-0.691760\pi$
$757$	−23604.1			−1.13330			−0.566648	+	0.823960i	$0.691760\pi$
$758$	−611.996	+	1060.01i	−0.0293255	+	0.0507932i
$759$	14.8183	+	25.6661i	0.000708657	+	0.00122743i
$760$	2793.12	+	4837.83i	0.133312	+	0.230903i
$761$	2315.48	−	4010.54i	0.110297	−	0.191041i	−0.805593	−	0.592470i	$-0.798153\pi$
$761$	2315.48	−	4010.54i	0.110297	−	0.191041i	0.915890	+	0.401429i	$0.131486\pi$
$762$	1080.45			0.0513658
$763$		0			0
$764$	4221.18			0.199891
$765$	11191.0	−	19383.3i	0.528902	−	0.916085i
$766$	4360.81	+	7553.15i	0.205695	+	0.356274i
$767$	−491.977	−	852.129i	−0.0231607	−	0.0401155i
$768$	384.000	−	665.108i	0.0180422	−	0.0312500i
$769$	−33276.8			−1.56046			−0.780228	−	0.625495i	$-0.784897\pi$
$769$	−33276.8			−1.56046			−0.780228	+	0.625495i	$0.784897\pi$
$770$		0			0
$771$	−9678.55			−0.452094
$772$	9541.68	−	16526.7i	0.444835	−	0.770477i
$773$	−11469.4	−	19865.6i	−0.533668	−	0.924340i	−0.999227	−	0.0393231i	$-0.987480\pi$
$773$	−11469.4	−	19865.6i	−0.533668	−	0.924340i	0.465558	−	0.885017i	$-0.345853\pi$
$774$	−1994.01	−	3453.73i	−0.0926011	−	0.160390i
$775$	−34524.6	+	59798.3i	−1.60020	+	2.77164i
$776$	−2677.61			−0.123867
$777$		0			0
$778$	−26293.8			−1.21167
$779$	−5412.47	+	9374.67i	−0.248937	+	0.431171i
$780$	270.409	+	468.362i	0.0124131	+	0.0215001i
$781$	−4569.66	−	7914.88i	−0.209366	−	0.362633i
$782$	−77.7575	+	134.680i	−0.00355576	+	0.00615876i
$783$	4406.62			0.201124
$784$		0			0
$785$	−6395.58			−0.290787
$786$	−653.580	+	1132.03i	−0.0296596	+	0.0513719i
$787$	−6757.23	−	11703.9i	−0.306060	−	0.530112i	0.671437	−	0.741062i	$-0.265678\pi$
$787$	−6757.23	−	11703.9i	−0.306060	−	0.530112i	−0.977497	+	0.210950i	$0.932344\pi$
$788$	−3244.62	−	5619.85i	−0.146681	−	0.254059i
$789$	4875.92	−	8445.34i	0.220009	−	0.381067i
$790$	4846.84			0.218282
$791$		0			0
$792$	1091.73			0.0489809
$793$	−41.7993	+	72.3985i	−0.00187180	+	0.00324205i
$794$	−8478.04	−	14684.4i	−0.378935	−	0.656335i
$795$	5516.98	+	9555.69i	0.246122	+	0.426296i
$796$	−7100.27	+	12298.0i	−0.316159	+	0.547603i
$797$	−10473.4			−0.465480			−0.232740	−	0.972539i	$-0.574769\pi$
$797$	−10473.4			−0.465480			−0.232740	+	0.972539i	$0.574769\pi$
$798$		0			0
$799$	−60634.5			−2.68472
$800$	−4946.97	+	8568.40i	−0.218627	+	0.378673i
$801$	−1724.22	−	2986.43i	−0.0760576	−	0.131736i
$802$	−2803.00	−	4854.94i	−0.123413	−	0.213758i
$803$	−8357.02	+	14474.8i	−0.367264	+	0.636119i
$804$	−1701.50			−0.0746359
$805$		0			0
$806$	−966.053			−0.0422181
$807$	−4239.06	+	7342.27i	−0.184910	+	0.320273i
$808$	−58.9697	−	102.138i	−0.00256751	−	0.00444705i
$809$	−11784.0	−	20410.5i	−0.512117	−	0.887013i	−0.999901	−	0.0140486i	$-0.995528\pi$
$809$	−11784.0	−	20410.5i	−0.512117	−	0.887013i	0.487784	−	0.872964i	$-0.337805\pi$
$810$	1687.81	−	2923.37i	0.0732142	−	0.126811i
$811$	6704.22			0.290280			0.145140	−	0.989411i	$-0.453637\pi$
$811$	6704.22			0.290280			0.145140	+	0.989411i	$0.453637\pi$
$812$		0			0
$813$	−7190.31			−0.310178
$814$	−2555.46	+	4426.19i	−0.110035	+	0.190587i
$815$	36616.0	+	63420.8i	1.57375	+	2.72581i
$816$	2864.36	+	4961.22i	0.122883	+	0.212840i
$817$	−3712.34	+	6429.95i	−0.158970	+	0.275343i
$818$	12770.8			0.545867
$819$		0			0
$820$	−26923.5			−1.14659
$821$	−12269.7	+	21251.8i	−0.521579	+	0.903401i	0.478106	+	0.878302i	$0.341323\pi$
$821$	−12269.7	+	21251.8i	−0.521579	+	0.903401i	−0.999685	+	0.0250988i	$0.992010\pi$
$822$	−7805.57	−	13519.6i	−0.331205	−	0.573664i
$823$	15558.5	+	26948.1i	0.658973	+	1.14137i	0.980882	+	0.194604i	$0.0623421\pi$
$823$	15558.5	+	26948.1i	0.658973	+	1.14137i	−0.321909	+	0.946771i	$0.604325\pi$
$824$	−3365.68	+	5829.53i	−0.142293	+	0.246458i
$825$	−14064.4			−0.593528
$826$		0			0
$827$	31244.9			1.31377			0.656887	−	0.753989i	$-0.271873\pi$
$827$	31244.9			1.31377			0.656887	+	0.753989i	$0.271873\pi$
$828$	−11.7273	+	20.3123i	−0.000492212	+	0.000852537i
$829$	2115.75	+	3664.58i	0.0886405	+	0.153530i	0.906937	−	0.421267i	$-0.138414\pi$
$829$	2115.75	+	3664.58i	0.0886405	+	0.153530i	−0.818296	+	0.574797i	$0.805081\pi$
$830$	11854.8	+	20533.2i	0.495767	+	0.858694i
$831$	2730.70	−	4729.71i	0.113991	−	0.197439i
$832$	−138.424			−0.00576803
$833$		0			0
$834$	−15909.3			−0.660544
$835$	−11703.2	+	20270.5i	−0.485037	+	0.840109i
$836$	−1016.26	−	1760.21i	−0.0420431	−	0.0728207i
$837$	3014.90	+	5221.96i	0.124504	+	0.215648i
$838$	4831.66	−	8368.68i	0.199173	−	0.344978i
$839$	38670.4			1.59124			0.795621	−	0.605795i	$-0.207145\pi$
$839$	38670.4			1.59124			0.795621	+	0.605795i	$0.207145\pi$
$840$		0			0
$841$	2247.96			0.0921710
$842$	−7475.37	+	12947.7i	−0.305960	+	0.529938i
$843$	4625.72	+	8011.97i	0.188989	+	0.327339i
$844$	−9306.77	−	16119.8i	−0.379564	−	0.657425i
$845$	−22840.8	+	39561.5i	−0.929880	+	1.61060i
$846$	−9144.82			−0.371637
$847$		0			0
$848$	−2824.18			−0.114367
$849$	−3832.15	+	6637.48i	−0.154911	+	0.268313i
$850$	−36900.8	−	63914.1i	−1.48904	−	2.57910i
$851$	−54.9014	−	95.0920i	−0.00221151	−	0.00383045i
$852$	3616.45	−	6263.88i	0.145420	−	0.251875i
$853$	19944.4			0.800565			0.400282	−	0.916392i	$-0.368912\pi$
$853$	19944.4			0.800565			0.400282	+	0.916392i	$0.368912\pi$
$854$		0			0
$855$	−6284.52			−0.251376
$856$	2862.68	−	4958.31i	0.114304	−	0.197981i
$857$	6941.10	+	12022.3i	0.276667	+	0.479201i	0.970554	−	0.240882i	$-0.0774368\pi$
$857$	6941.10	+	12022.3i	0.276667	+	0.479201i	−0.693887	+	0.720084i	$0.744103\pi$
$858$	−98.3864	−	170.410i	−0.00391475	−	0.00678055i
$859$	−2078.58	+	3600.21i	−0.0825614	+	0.143000i	−0.904349	−	0.426793i	$-0.859643\pi$
$859$	−2078.58	+	3600.21i	−0.0825614	+	0.143000i	0.821788	+	0.569793i	$0.192977\pi$
$860$	−18466.4			−0.732209
$861$		0			0
$862$	13983.9			0.552543
$863$	8118.96	−	14062.5i	0.320246	−	0.554683i	−0.660292	−	0.751009i	$-0.729568\pi$
$863$	8118.96	−	14062.5i	0.320246	−	0.554683i	0.980539	+	0.196326i	$0.0629009\pi$
$864$	432.000	+	748.246i	0.0170103	+	0.0294628i
$865$	−15946.6	−	27620.4i	−0.626823	−	1.08569i
$866$	−7699.26	+	13335.5i	−0.302115	+	0.523278i
$867$	−27993.2			−1.09654
$868$		0			0
$869$	−1763.49			−0.0688403
$870$	10202.4	−	17671.0i	0.397578	−	0.688625i
$871$	153.339	+	265.591i	0.00596521	+	0.0103320i
$872$	−2400.08	−	4157.05i	−0.0932074	−	0.161440i
$873$	1506.15	−	2608.73i	0.0583913	−	0.101137i
$874$	43.6664			0.00168998
$875$		0			0
$876$	−13227.6			−0.510181
$877$	8244.70	−	14280.2i	0.317450	−	0.549840i	−0.662505	−	0.749057i	$-0.730507\pi$
$877$	8244.70	−	14280.2i	0.317450	−	0.549840i	0.979955	+	0.199218i	$0.0638401\pi$
$878$	9412.32	+	16302.6i	0.361789	+	0.626636i
$879$	2769.70	+	4797.26i	0.106279	+	0.184081i
$880$	2527.61	−	4377.94i	0.0968245	−	0.167705i
$881$	−45411.7			−1.73662			−0.868309	−	0.496023i	$-0.834793\pi$
$881$	−45411.7			−1.73662			−0.868309	+	0.496023i	$0.834793\pi$
$882$		0			0
$883$	−2206.85			−0.0841070			−0.0420535	−	0.999115i	$-0.513390\pi$
$883$	−2206.85			−0.0841070			−0.0420535	+	0.999115i	$0.513390\pi$
$884$	516.273	−	894.211i	0.0196427	−	0.0340221i
$885$	14219.1	+	24628.2i	0.540078	+	0.935443i
$886$	6258.18	+	10839.5i	0.237300	+	0.411015i
$887$	14073.1	−	24375.3i	0.532727	−	0.922710i	−0.466543	−	0.884498i	$-0.654501\pi$
$887$	14073.1	−	24375.3i	0.532727	−	0.922710i	0.999270	−	0.0382111i	$-0.0121659\pi$
$888$	−4044.82			−0.152855
$889$		0			0
$890$	−15967.9			−0.601398
$891$	−614.097	+	1063.65i	−0.0230898	+	0.0399927i
$892$	−9299.07	−	16106.5i	−0.349054	−	0.604579i
$893$	8512.65	+	14744.3i	0.318998	+	0.552520i
$894$	1743.07	−	3019.08i	0.0652091	−	0.112945i
$895$	−71126.1			−2.65641
$896$		0			0
$897$	4.22746			0.000157359
$898$	11633.8	−	20150.4i	0.432322	−	0.748804i
$899$	18224.3	+	31565.4i	0.676101	+	1.17104i
$900$	−5565.34	−	9639.45i	−0.206124	−	0.357017i
$901$	10533.2	−	18244.0i	0.389469	−	0.674579i
$902$	9795.91			0.361605
$903$		0			0
$904$	4981.15			0.183264
$905$	−13405.6	+	23219.3i	−0.492396	+	0.852856i
$906$	−1846.17	−	3197.66i	−0.0676986	−	0.117257i
$907$	2521.12	+	4366.71i	0.0922960	+	0.159861i	0.908477	−	0.417935i	$-0.137246\pi$
$907$	2521.12	+	4366.71i	0.0922960	+	0.159861i	−0.816181	+	0.577797i	$0.803913\pi$
$908$	8303.43	−	14382.0i	0.303479	−	0.525641i
$909$	132.682			0.00484134
$910$		0			0
$911$	29647.3			1.07822			0.539110	−	0.842235i	$-0.318761\pi$
$911$	29647.3			1.07822			0.539110	+	0.842235i	$0.318761\pi$
$912$	804.273	−	1393.04i	0.0292019	−	0.0505792i
$913$	−4313.29	−	7470.84i	−0.156352	−	0.270809i
$914$	13104.6	+	22697.9i	0.474248	+	0.821421i
$915$	1208.08	−	2092.46i	0.0436480	−	0.0756005i
$916$	−17054.5			−0.615172
$917$		0			0
$918$	−6444.82			−0.231711
$919$	5945.64	−	10298.1i	0.213415	−	0.369646i	−0.739366	−	0.673304i	$-0.764875\pi$
$919$	5945.64	−	10298.1i	0.213415	−	0.369646i	0.952781	+	0.303658i	$0.0982080\pi$
$920$	54.3029	+	94.0554i	0.00194599	+	0.00337056i
$921$	−10562.2	−	18294.3i	−0.377891	−	0.654527i
$922$	−2594.63	+	4494.03i	−0.0926785	+	0.160524i
$923$	−1303.66			−0.0464902
$924$		0			0
$925$	52108.3			1.85223
$926$	14136.2	−	24484.6i	0.501667	−	0.868913i
$927$	−3786.39	−	6558.22i	−0.134155	−	0.232363i
$928$	2611.33	+	4522.96i	0.0923720	+	0.159993i
$929$	−19594.3	+	33938.3i	−0.691999	+	1.19858i	0.279183	+	0.960238i	$0.409937\pi$
$929$	−19594.3	+	33938.3i	−0.691999	+	1.19858i	−0.971182	+	0.238340i	$0.923397\pi$
$930$	27920.8			0.984472
$931$		0			0
$932$	12199.6			0.428768
$933$	4028.99	−	6978.41i	0.141375	−	0.244869i
$934$	15590.2	+	27003.1i	0.546176	+	0.946004i
$935$	18854.1	+	32656.3i	0.659461	+	1.14222i
$936$	77.8637	−	134.864i	0.00271907	−	0.00470957i
$937$	−9716.23			−0.338757			−0.169379	−	0.985551i	$-0.554176\pi$
$937$	−9716.23			−0.338757			−0.169379	+	0.985551i	$0.554176\pi$
$938$		0			0
$939$	6657.57			0.231375
$940$	−21172.4	+	36671.7i	−0.734647	+	1.27245i
$941$	−3497.93	−	6058.60i	−0.121179	−	0.209888i	0.799054	−	0.601259i	$-0.205334\pi$
$941$	−3497.93	−	6058.60i	−0.121179	−	0.209888i	−0.920233	+	0.391371i	$0.872001\pi$
$942$	920.795	+	1594.86i	0.0318483	+	0.0551629i
$943$	−105.227	+	182.259i	−0.00363380	+	0.00629393i
$944$	−7278.85			−0.250960
$945$		0			0
$946$	6718.88			0.230919
$947$	−7489.62	+	12972.4i	−0.257001	+	0.445139i	−0.965437	−	0.260636i	$-0.916068\pi$
$947$	−7489.62	+	12972.4i	−0.257001	+	0.445139i	0.708436	+	0.705775i	$0.249401\pi$
$948$	−697.818	−	1208.66i	−0.0239073	−	0.0414086i
$949$	1192.07	+	2064.73i	0.0407758	+	0.0706258i
$950$	−10361.2	+	17946.2i	−0.353855	+	0.612896i
$951$	−6663.78			−0.227222
$952$		0			0
$953$	29393.3			0.999100			0.499550	−	0.866285i	$-0.333499\pi$
$953$	29393.3			0.999100			0.499550	+	0.866285i	$0.333499\pi$
$954$	1588.60	−	2751.54i	0.0539129	−	0.0933799i
$955$	10994.7	+	19043.3i	0.372543	+	0.645264i
$956$	−7974.41	−	13812.1i	−0.269781	−	0.467275i
$957$	−3712.06	+	6429.48i	−0.125386	+	0.217174i
$958$	16907.0			0.570189
$959$		0			0
$960$	4000.73			0.134503
$961$	−10041.7	+	17392.7i	−0.337072	+	0.583825i
$962$	364.519	+	631.365i	0.0122168	+	0.0211601i
$963$	3220.52	+	5578.10i	0.107767	+	0.186658i
$964$	−1249.30	+	2163.84i	−0.0417397	+	0.0722953i
$965$	99410.6			3.31621
$966$		0			0
$967$	−7133.95			−0.237241			−0.118621	−	0.992940i	$-0.537847\pi$
$967$	−7133.95			−0.237241			−0.118621	+	0.992940i	$0.537847\pi$
$968$	4404.35	−	7628.56i	0.146241	−	0.253297i
$969$	5999.30	+	10391.1i	0.198891	+	0.344489i
$970$	−6974.20	−	12079.7i	−0.230854	−	0.399850i
$971$	−4844.06	+	8390.16i	−0.160096	+	0.277295i	−0.934903	−	0.354903i	$-0.884514\pi$
$971$	−4844.06	+	8390.16i	−0.160096	+	0.277295i	0.774807	+	0.632198i	$0.217847\pi$
$972$	−972.000			−0.0320750
$973$		0			0
$974$	−8022.14			−0.263907
$975$	−1003.10	+	1737.41i	−0.0329485	+	0.0570685i
$976$	309.212	+	535.571i	0.0101410	+	0.0175648i
$977$	−10652.8	−	18451.3i	−0.348838	−	0.604205i	0.637205	−	0.770694i	$-0.280090\pi$
$977$	−10652.8	−	18451.3i	−0.348838	−	0.604205i	−0.986043	+	0.166489i	$0.946757\pi$
$978$	10543.5	−	18261.9i	0.344728	−	0.597086i
$979$	5809.79			0.189665
$980$		0			0
$981$	5400.17			0.175753
$982$	−13927.9	+	24123.8i	−0.452604	+	0.783933i
$983$	−18640.4	−	32286.1i	−0.604818	−	1.04758i	−0.992080	−	0.125606i	$-0.959913\pi$
$983$	−18640.4	−	32286.1i	−0.604818	−	1.04758i	0.387262	−	0.921970i	$-0.373421\pi$
$984$	3876.27	+	6713.90i	0.125580	+	0.217512i
$985$	16902.1	−	29275.4i	0.546748	−	0.946996i
$986$	−38957.3			−1.25827
$987$		0			0
$988$	−289.924			−0.00933574
$989$	−72.1740	+	125.009i	−0.00232052	+	0.00401927i
$990$	2843.56	+	4925.18i	0.0912870	+	0.158114i
$991$	25698.5	+	44511.2i	0.823755	+	1.42678i	0.902867	+	0.429919i	$0.141458\pi$
$991$	25698.5	+	44511.2i	0.823755	+	1.42678i	−0.0791128	+	0.996866i	$0.525209\pi$
$992$	−3573.21	+	6188.98i	−0.114365	+	0.198085i
$993$	−12462.2			−0.398263
$994$		0			0
$995$	−73974.6			−2.35694
$996$	3413.57	−	5912.47i	0.108597	−	0.188096i
$997$	−17186.9	−	29768.6i	−0.545953	−	0.945618i	−0.998546	−	0.0539007i	$-0.982835\pi$
$997$	−17186.9	−	29768.6i	−0.545953	−	0.945618i	0.452594	−	0.891717i	$-0.350499\pi$
$998$	3947.55	+	6837.36i	0.125208	+	0.216866i
$999$	2275.21	−	3940.78i	0.0720565	−	0.124806i

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	294.4.e.l.79.2		4
3.2	odd	2		882.4.g.bf.667.1		4
7.2	even	3		294.4.a.m.1.1		2
7.3	odd	6		42.4.e.c.25.1	✓	4
7.4	even	3	inner	294.4.e.l.67.2		4
7.5	odd	6		294.4.a.n.1.2		2
7.6	odd	2		42.4.e.c.37.1	yes	4
21.2	odd	6		882.4.a.z.1.2		2
21.5	even	6		882.4.a.v.1.1		2
21.11	odd	6		882.4.g.bf.361.1		4
21.17	even	6		126.4.g.g.109.2		4
21.20	even	2		126.4.g.g.37.2		4
28.3	even	6		336.4.q.j.193.1		4
28.19	even	6		2352.4.a.bq.1.2		2
28.23	odd	6		2352.4.a.ca.1.1		2
28.27	even	2		336.4.q.j.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.e.c.25.1	✓	4	7.3	odd	6
42.4.e.c.37.1	yes	4	7.6	odd	2
126.4.g.g.37.2		4	21.20	even	2
126.4.g.g.109.2		4	21.17	even	6
294.4.a.m.1.1		2	7.2	even	3
294.4.a.n.1.2		2	7.5	odd	6
294.4.e.l.67.2		4	7.4	even	3	inner
294.4.e.l.79.2		4	1.1	even	1	trivial
336.4.q.j.193.1		4	28.3	even	6
336.4.q.j.289.1		4	28.27	even	2
882.4.a.v.1.1		2	21.5	even	6
882.4.a.z.1.2		2	21.2	odd	6
882.4.g.bf.361.1		4	21.11	odd	6
882.4.g.bf.667.1		4	3.2	odd	2
2352.4.a.bq.1.2		2	28.19	even	6
2352.4.a.ca.1.1		2	28.23	odd	6

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Hilbert	Bianchi

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

Introduction

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

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	294.4.e.l.79.2

Level	$294$
Weight	$4$
Character	294.79
Analytic conductor	$17.347$
Analytic rank	$0$
Dimension	$4$
Inner twists	$2$