LMFDB - Embedded newform 126.4.g.g.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,4,Mod(37,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("126.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	126.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.43424066072$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.2
Root			$9.41856 - 16.3134i$ of defining polynomial
Character	$\chi$	$=$	126.37
Dual form			126.4.g.g.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(10.4186 - 18.0455i) q^{5} +(-18.3371 + 2.59808i) q^{7} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(10.4186 - 18.0455i) q^{5} +(-18.3371 + 2.59808i) q^{7} -8.00000 q^{8} +(-20.8371 - 36.0910i) q^{10} +(7.58144 + 13.1314i) q^{11} +2.16288 q^{13} +(-13.8371 + 34.3589i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(-59.6742 - 103.359i) q^{17} +(16.7557 - 29.0217i) q^{19} -83.3485 q^{20} +30.3258 q^{22} +(0.325758 - 0.564230i) q^{23} +(-154.593 - 267.763i) q^{25} +(2.16288 - 3.74622i) q^{26} +(45.6742 + 58.3255i) q^{28} +163.208 q^{29} +(111.663 + 193.406i) q^{31} +(16.0000 + 27.7128i) q^{32} -238.697 q^{34} +(-144.163 + 357.970i) q^{35} +(-84.2670 + 145.955i) q^{37} +(-33.5114 - 58.0434i) q^{38} +(-83.3485 + 144.364i) q^{40} +323.023 q^{41} +221.557 q^{43} +(30.3258 - 52.5258i) q^{44} +(-0.651517 - 1.12846i) q^{46} +(254.023 - 439.980i) q^{47} +(329.500 - 95.2825i) q^{49} -618.371 q^{50} +(-4.32576 - 7.49243i) q^{52} +(-88.2557 - 152.863i) q^{53} +315.951 q^{55} +(146.697 - 20.7846i) q^{56} +(163.208 - 282.685i) q^{58} +(227.464 + 393.979i) q^{59} +(-19.3258 + 33.4732i) q^{61} +446.652 q^{62} +64.0000 q^{64} +(22.5341 - 39.0302i) q^{65} +(-70.8958 - 122.795i) q^{67} +(-238.697 + 413.435i) q^{68} +(475.860 + 607.668i) q^{70} -602.742 q^{71} +(551.150 + 954.619i) q^{73} +(168.534 + 291.910i) q^{74} -134.045 q^{76} +(-173.138 - 221.096i) q^{77} +(58.1515 - 100.721i) q^{79} +(166.697 + 288.728i) q^{80} +(323.023 - 559.492i) q^{82} +568.928 q^{83} -2486.88 q^{85} +(221.557 - 383.748i) q^{86} +(-60.6515 - 105.052i) q^{88} +(-191.580 + 331.825i) q^{89} +(-39.6610 + 5.61932i) q^{91} -2.60607 q^{92} +(-508.045 - 879.961i) q^{94} +(-349.140 - 604.728i) q^{95} +334.701 q^{97} +(164.466 - 665.993i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{4} + 5 q^{5} - 32 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 8 * q^4 + 5 * q^5 - 32 * q^8	$ 4 q + 4 q^{2} - 8 q^{4} + 5 q^{5} - 32 q^{8} - 10 q^{10} + 67 q^{11} + 82 q^{13} + 18 q^{14} - 32 q^{16} - 92 q^{17} - 43 q^{19} - 40 q^{20} + 268 q^{22} + 148 q^{23} - 435 q^{25} + 82 q^{26} + 36 q^{28} - 154 q^{29} + 520 q^{31} + 64 q^{32} - 368 q^{34} - 650 q^{35} - 7 q^{37} + 86 q^{38} - 40 q^{40} + 852 q^{41} - 214 q^{43} + 268 q^{44} - 296 q^{46} + 576 q^{47} + 1318 q^{49} - 1740 q^{50} - 164 q^{52} - 243 q^{53} - 1010 q^{55} - 154 q^{58} - 7 q^{59} - 224 q^{61} + 2080 q^{62} + 256 q^{64} - 570 q^{65} - 687 q^{67} - 368 q^{68} + 1390 q^{70} - 944 q^{71} + 921 q^{73} + 14 q^{74} + 344 q^{76} + 371 q^{77} + 526 q^{79} + 80 q^{80} + 852 q^{82} + 442 q^{83} - 5840 q^{85} - 214 q^{86} - 536 q^{88} + 774 q^{89} + 1345 q^{91} - 1184 q^{92} - 1152 q^{94} - 1910 q^{95} + 3906 q^{97} + 1318 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^4 + 5 * q^5 - 32 * q^8 - 10 * q^10 + 67 * q^11 + 82 * q^13 + 18 * q^14 - 32 * q^16 - 92 * q^17 - 43 * q^19 - 40 * q^20 + 268 * q^22 + 148 * q^23 - 435 * q^25 + 82 * q^26 + 36 * q^28 - 154 * q^29 + 520 * q^31 + 64 * q^32 - 368 * q^34 - 650 * q^35 - 7 * q^37 + 86 * q^38 - 40 * q^40 + 852 * q^41 - 214 * q^43 + 268 * q^44 - 296 * q^46 + 576 * q^47 + 1318 * q^49 - 1740 * q^50 - 164 * q^52 - 243 * q^53 - 1010 * q^55 - 154 * q^58 - 7 * q^59 - 224 * q^61 + 2080 * q^62 + 256 * q^64 - 570 * q^65 - 687 * q^67 - 368 * q^68 + 1390 * q^70 - 944 * q^71 + 921 * q^73 + 14 * q^74 + 344 * q^76 + 371 * q^77 + 526 * q^79 + 80 * q^80 + 852 * q^82 + 442 * q^83 - 5840 * q^85 - 214 * q^86 - 536 * q^88 + 774 * q^89 + 1345 * q^91 - 1184 * q^92 - 1152 * q^94 - 1910 * q^95 + 3906 * q^97 + 1318 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$		0			0
$3$		0			0
$4$	−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	$-0.215152\pi$
$6$		0			0
$7$	−18.3371	+	2.59808i	−0.990111	+	0.140283i
$7$	−18.3371	+	2.59808i	−0.990111	+	0.140283i
$8$	−8.00000			−0.353553
$9$		0			0
$10$	−20.8371	−	36.0910i	−0.658928	−	1.14130i
$11$	7.58144	+	13.1314i	0.207808	+	0.359934i	0.951024	−	0.309118i	$-0.100034\pi$
$11$	7.58144	+	13.1314i	0.207808	+	0.359934i	−0.743216	+	0.669052i	$0.766700\pi$
$12$		0			0
$13$	2.16288			0.0461442			0.0230721	−	0.999734i	$-0.492655\pi$
$13$	2.16288			0.0461442			0.0230721	+	0.999734i	$0.492655\pi$
$14$	−13.8371	+	34.3589i	−0.264152	+	0.655914i
$15$		0			0
$16$	−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	$-0.490889\pi$
$18$		0			0
$19$	16.7557	−	29.0217i	0.202317	−	0.350423i	−0.746958	−	0.664871i	$-0.768486\pi$
$19$	16.7557	−	29.0217i	0.202317	−	0.350423i	0.949274	+	0.314449i	$0.101820\pi$
$20$	−83.3485			−0.931864
$21$		0			0
$22$	30.3258			0.293885
$23$	0.325758	−	0.564230i	0.00295327	−	0.00511522i	−0.864545	−	0.502555i	$-0.832393\pi$
$23$	0.325758	−	0.564230i	0.00295327	−	0.00511522i	0.867498	+	0.497440i	$0.165727\pi$
$24$		0			0
$25$	−154.593	−	267.763i	−1.23674	−	2.14210i
$26$	2.16288	−	3.74622i	0.0163144	−	0.0282574i
$27$		0			0
$28$	45.6742	+	58.3255i	0.308272	+	0.393660i
$29$	163.208			1.04507			0.522535	−	0.852618i	$-0.324986\pi$
$29$	163.208			1.04507			0.522535	+	0.852618i	$0.324986\pi$
$30$		0			0
$31$	111.663	+	193.406i	0.646943	+	1.12054i	0.983849	+	0.179000i	$0.0572863\pi$
$31$	111.663	+	193.406i	0.646943	+	1.12054i	−0.336906	+	0.941538i	$0.609380\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$		0			0
$34$	−238.697			−1.20401
$35$	−144.163	+	357.970i	−0.696228	+	1.72880i
$36$		0			0
$37$	−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
$39$		0			0
$40$	−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
$45$		0			0
$46$	−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	$-0.122404\pi$
$48$		0			0
$49$	329.500	−	95.2825i	0.960641	−	0.277791i
$50$	−618.371			−1.74902
$51$		0			0
$52$	−4.32576	−	7.49243i	−0.0115361	−	0.0199810i
$53$	−88.2557	−	152.863i	−0.228733	−	0.396177i	0.728700	−	0.684833i	$-0.240125\pi$
$53$	−88.2557	−	152.863i	−0.228733	−	0.396177i	−0.957433	+	0.288656i	$0.906792\pi$
$54$		0			0
$55$	315.951			0.774596
$56$	146.697	−	20.7846i	0.350057	−	0.0495975i
$57$		0			0
$58$	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	$0.665960\pi$
$60$		0			0
$61$	−19.3258	+	33.4732i	−0.0405641	+	0.0702591i	−0.885595	−	0.464459i	$-0.846249\pi$
$61$	−19.3258	+	33.4732i	−0.0405641	+	0.0702591i	0.845031	+	0.534718i	$0.179582\pi$
$62$	446.652			0.914916
$63$		0			0
$64$	64.0000			0.125000
$65$	22.5341	−	39.0302i	0.0430001	−	0.0744784i
$66$		0			0
$67$	−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
$69$		0			0
$70$	475.860	+	607.668i	0.812516	+	1.03757i
$71$	−602.742			−1.00750			−0.503749	−	0.863850i	$-0.668046\pi$
$71$	−602.742			−1.00750			−0.503749	+	0.863850i	$0.668046\pi$
$72$		0			0
$73$	551.150	+	954.619i	0.883660	+	1.53054i	0.847242	+	0.531207i	$0.178262\pi$
$73$	551.150	+	954.619i	0.883660	+	1.53054i	0.0364183	+	0.999337i	$0.488405\pi$
$74$	168.534	+	291.910i	0.264753	+	0.458565i
$75$		0			0
$76$	−134.045			−0.202317
$77$	−173.138	−	221.096i	−0.256246	−	0.327223i
$78$		0			0
$79$	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
$81$		0			0
$82$	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
$87$		0			0
$88$	−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	$0.239942\pi$
$90$		0			0
$91$	−39.6610	+	5.61932i	−0.0456879	+	0.00647325i
$92$	−2.60607			−0.00295327
$93$		0			0
$94$	−508.045	−	879.961i	−0.557456	−	0.965543i
$95$	−349.140	−	604.728i	−0.377063	−	0.653093i
$96$		0			0
$97$	334.701			0.350348			0.175174	−	0.984538i	$-0.443951\pi$
$97$	334.701			0.350348			0.175174	+	0.984538i	$0.443951\pi$
$98$	164.466	−	665.993i	0.169526	−	0.686484i
$99$		0			0
$100$	−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	$0.835645\pi$
$102$		0			0
$103$	420.710	−	728.691i	0.402464	−	0.697088i	−0.591559	−	0.806262i	$-0.701487\pi$
$103$	420.710	−	728.691i	0.402464	−	0.697088i	0.994023	+	0.109174i	$0.0348205\pi$
$104$	−17.3030			−0.0163144
$105$		0			0
$106$	−353.023			−0.323477
$107$	−357.835	+	619.789i	−0.323301	+	0.559974i	−0.981167	−	0.193161i	$-0.938126\pi$
$107$	−357.835	+	619.789i	−0.323301	+	0.559974i	0.657866	+	0.753135i	$0.271459\pi$
$108$		0			0
$109$	−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
$111$		0			0
$112$	110.697	−	274.871i	0.0933918	−	0.231901i
$113$	−622.644			−0.518349			−0.259174	−	0.965831i	$-0.583450\pi$
$113$	−622.644			−0.518349			−0.259174	+	0.965831i	$0.583450\pi$
$114$		0			0
$115$	−6.78787	−	11.7569i	−0.00550410	−	0.00953339i
$116$	−326.417	−	565.370i	−0.261267	−	0.452529i
$117$		0			0
$118$	909.856			0.709822
$119$	1362.79	+	1740.26i	1.04980	+	1.34059i
$120$		0			0
$121$	550.544	−	953.569i	0.413632	−	0.716431i
$122$	38.6515	+	66.9464i	0.0286831	+	0.0496807i
$123$		0			0
$124$	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
$129$		0			0
$130$	−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	$0.143521\pi$
$132$		0			0
$133$	−231.850	+	575.707i	−0.151158	+	0.375339i
$134$	−283.583			−0.182820
$135$		0			0
$136$	477.394	+	826.871i	0.301001	+	0.521350i
$137$	−1300.93	−	2253.27i	−0.811283	−	1.40518i	−0.911966	−	0.410265i	$-0.865436\pi$
$137$	−1300.93	−	2253.27i	−0.811283	−	1.40518i	0.100683	−	0.994919i	$-0.467897\pi$
$138$		0			0
$139$	−2651.55			−1.61800			−0.808998	−	0.587811i	$-0.799990\pi$
$139$	−2651.55			−1.61800			−0.808998	+	0.587811i	$0.799990\pi$
$140$	1528.37	−	216.546i	0.922650	−	0.130725i
$141$		0			0
$142$	−602.742	+	1043.98i	−0.356204	+	0.616964i
$143$	16.3977	+	28.4017i	0.00958914	+	0.0166089i
$144$		0			0
$145$	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	−0.775042	−	0.631910i	$-0.782271\pi$
$149$	290.511	−	503.180i	0.159729	−	0.276659i	0.934771	+	0.355251i	$0.115605\pi$
$150$		0			0
$151$	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
$153$		0			0
$154$	−556.087	+	78.7886i	−0.290979	+	0.0412271i
$155$	4653.47			2.41145
$156$		0			0
$157$	153.466	+	265.811i	0.0780122	+	0.135121i	0.902392	−	0.430916i	$-0.141809\pi$
$157$	153.466	+	265.811i	0.0780122	+	0.135121i	−0.824380	+	0.566037i	$0.808476\pi$
$158$	−116.303	−	201.443i	−0.0585606	−	0.101430i
$159$		0			0
$160$	666.788			0.329464
$161$	−4.50756	+	11.1927i	−0.00220649	+	0.00547893i
$162$		0			0
$163$	−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
$165$		0			0
$166$	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
$171$		0			0
$172$	−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	$0.0574818\pi$
$174$		0			0
$175$	3530.45	+	4508.35i	1.52501	+	1.94742i
$176$	−242.606			−0.103904
$177$		0			0
$178$	383.159	+	663.651i	0.161343	+	0.279454i
$179$	1706.72	+	2956.12i	0.712659	+	1.23436i	0.963856	+	0.266425i	$0.0858426\pi$
$179$	1706.72	+	2956.12i	0.712659	+	1.23436i	−0.251197	+	0.967936i	$0.580824\pi$
$180$		0			0
$181$	1286.71			0.528399			0.264200	−	0.964468i	$-0.414892\pi$
$181$	1286.71			0.528399			0.264200	+	0.964468i	$0.414892\pi$
$182$	−29.9280	+	74.3142i	−0.0121891	+	0.0302667i
$183$		0			0
$184$	−2.60607	+	4.51384i	−0.00104414	+	0.00180850i
$185$	1755.88	+	3041.28i	0.697811	+	1.20864i
$186$		0			0
$187$	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	−0.748602	−	0.663020i	$-0.769274\pi$
$191$	527.648	−	913.913i	0.199891	−	0.346222i	0.948493	+	0.316798i	$0.102608\pi$
$192$		0			0
$193$	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
$195$		0			0
$196$	−989.068	−	950.857i	−0.360448	−	0.346522i
$197$	−1622.31			−0.586725			−0.293363	−	0.956001i	$-0.594774\pi$
$197$	−1622.31			−0.586725			−0.293363	+	0.956001i	$0.594774\pi$
$198$		0			0
$199$	1775.07	+	3074.51i	0.632318	+	1.09521i	0.987077	+	0.160249i	$0.0512296\pi$
$199$	1775.07	+	3074.51i	0.632318	+	1.09521i	−0.354759	+	0.934958i	$0.615437\pi$
$200$	1236.74	+	2142.10i	0.437254	+	0.757347i
$201$		0			0
$202$	−29.4848			−0.0102700
$203$	−2992.77	+	424.028i	−1.03474	+	0.146605i
$204$		0			0
$205$	3365.43	−	5829.10i	1.14659	−	1.98596i
$206$	−841.420	−	1457.38i	−0.284585	−	0.492916i
$207$		0			0
$208$	−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
$213$		0			0
$214$	715.670	+	1239.58i	0.228609	+	0.395962i
$215$	2308.30	−	3998.10i	0.732209	−	1.26822i
$216$		0			0
$217$	−2550.06	−	3256.40i	−0.797739	−	1.01870i
$218$	−1200.04			−0.372829
$219$		0			0
$220$	−631.901	−	1094.49i	−0.193649	−	0.335410i
$221$	−129.068	−	223.553i	−0.0392854	−	0.0680442i
$222$		0			0
$223$	−4649.53			−1.39621			−0.698107	−	0.715993i	$-0.745974\pi$
$223$	−4649.53			−1.39621			−0.698107	+	0.715993i	$0.745974\pi$
$224$	−365.394	−	466.604i	−0.108991	−	0.139180i
$225$		0			0
$226$	−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	$0.625723\pi$
$228$		0			0
$229$	−2131.82	+	3692.41i	−0.615172	+	1.06551i	0.375182	+	0.926951i	$0.377580\pi$
$229$	−2131.82	+	3692.41i	−0.615172	+	1.06551i	−0.990354	+	0.138558i	$0.955753\pi$
$230$	−27.1515			−0.00778398
$231$		0			0
$232$	−1305.67			−0.369488
$233$	1524.95	−	2641.29i	0.428768	−	0.742647i	−0.567996	−	0.823031i	$-0.692281\pi$
$233$	1524.95	−	2641.29i	0.428768	−	0.742647i	0.996764	+	0.0803838i	$0.0256146\pi$
$234$		0			0
$235$	−5293.10	−	9167.92i	−1.46929	−	2.54489i
$236$	909.856	−	1575.92i	0.250960	−	0.434676i
$237$		0			0
$238$	4377.02	−	620.153i	1.19210	−	0.168901i
$239$	−3987.20			−1.07912			−0.539562	−	0.841946i	$-0.681410\pi$
$239$	−3987.20			−1.07912			−0.539562	+	0.841946i	$0.681410\pi$
$240$		0			0
$241$	312.324	+	540.961i	0.0834795	+	0.144591i	0.904742	−	0.425959i	$-0.140063\pi$
$241$	312.324	+	540.961i	0.0834795	+	0.144591i	−0.821263	+	0.570550i	$0.806730\pi$
$242$	−1101.09	−	1907.14i	−0.292482	−	0.506593i
$243$		0			0
$244$	154.606			0.0405641
$245$	1713.50	−	6938.69i	0.446822	−	1.80937i
$246$		0			0
$247$	36.2405	−	62.7704i	0.00933574	−	0.0161700i
$248$	−893.303	−	1547.25i	−0.228729	−	0.396170i
$249$		0			0
$250$	−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
$255$		0			0
$256$	−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	$0.294719\pi$
$258$		0			0
$259$	1166.01	−	2895.32i	0.279740	−	0.694620i
$260$	−180.273			−0.0430001
$261$		0			0
$262$	−217.860	−	377.344i	−0.0513719	−	0.0889787i
$263$	1625.31	+	2815.11i	0.381067	+	0.660028i	0.991215	−	0.132260i	$-0.0422233\pi$
$263$	1625.31	+	2815.11i	0.381067	+	0.660028i	−0.610148	+	0.792288i	$0.708890\pi$
$264$		0			0
$265$	−3677.99			−0.852593
$266$	765.303	+	977.283i	0.176405	+	0.225267i
$267$		0			0
$268$	−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	$0.729559\pi$
$270$		0			0
$271$	1198.38	−	2075.66i	0.268622	−	0.465268i	−0.699884	−	0.714257i	$-0.746765\pi$
$271$	1198.38	−	2075.66i	0.268622	−	0.465268i	0.968506	+	0.248989i	$0.0800983\pi$
$272$	1909.58			0.425680
$273$		0			0
$274$	−5203.71			−1.14733
$275$	2344.07	−	4060.05i	0.514010	−	0.890292i
$276$		0			0
$277$	−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
$279$		0			0
$280$	1153.30	−	2863.76i	0.246154	−	0.611223i
$281$	−3083.81			−0.654679			−0.327339	−	0.944907i	$-0.606152\pi$
$281$	−3083.81			−0.654679			−0.327339	+	0.944907i	$0.606152\pi$
$282$		0			0
$283$	−1277.38	−	2212.49i	−0.268313	−	0.464732i	0.700113	−	0.714032i	$-0.253133\pi$
$283$	−1277.38	−	2212.49i	−0.268313	−	0.464732i	−0.968426	+	0.249300i	$0.919800\pi$
$284$	1205.48	+	2087.96i	0.251875	+	0.436259i
$285$		0			0
$286$	65.5910			0.0135611
$287$	−5923.31	+	839.238i	−1.21826	+	0.172608i
$288$		0			0
$289$	−4665.53	+	8080.94i	−0.949630	+	1.64481i
$290$	−3400.79	−	5890.34i	−0.688625	−	1.19273i
$291$		0			0
$292$	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
$297$		0			0
$298$	−581.023	−	1006.36i	−0.112945	−	0.195627i
$299$	0.704576	−	1.22036i	0.000136277	−	0.000236038i
$300$		0			0
$301$	−4062.71	+	575.621i	−0.777977	+	0.110227i
$302$	1230.78			0.234515
$303$		0			0
$304$	268.091	+	464.347i	0.0505792	+	0.0876057i
$305$	402.693	+	697.485i	0.0756005	+	0.130944i
$306$		0			0
$307$	7041.50			1.30905			0.654527	−	0.756039i	$-0.272868\pi$
$307$	7041.50			1.30905			0.654527	+	0.756039i	$0.272868\pi$
$308$	−419.621	+	1041.96i	−0.0776303	+	0.192764i
$309$		0			0
$310$	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	$0.912078\pi$
$312$		0			0
$313$	−1109.59	+	1921.87i	−0.200377	+	0.347063i	−0.948650	−	0.316328i	$-0.897550\pi$
$313$	−1109.59	+	1921.87i	−0.200377	+	0.347063i	0.748273	+	0.663391i	$0.230883\pi$
$314$	613.864			0.110326
$315$		0			0
$316$	−465.212			−0.0828172
$317$	1110.63	−	1923.67i	0.196780	−	0.340833i	−0.750703	−	0.660640i	$-0.770285\pi$
$317$	1110.63	−	1923.67i	0.196780	−	0.340833i	0.947483	+	0.319807i	$0.103618\pi$
$318$		0			0
$319$	1237.35	+	2143.16i	0.217174	+	0.376157i
$320$	666.788	−	1154.91i	0.116483	−	0.201755i
$321$		0			0
$322$	14.8788	+	19.0000i	0.00257503	+	0.00328829i
$323$	−3999.53			−0.688978
$324$		0			0
$325$	−334.366	−	579.138i	−0.0570685	−	0.0988455i
$326$	3514.50	+	6087.29i	0.597086	+	1.03418i
$327$		0			0
$328$	−2584.18			−0.435023
$329$	−3514.94	+	8727.94i	−0.589012	+	1.46257i
$330$		0			0
$331$	−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
$333$		0			0
$334$	−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
$339$		0			0
$340$	4973.76	+	8614.80i	0.793353	+	1.37413i
$341$	−1693.13	+	2932.59i	−0.268880	+	0.465714i
$342$		0			0
$343$	−5794.53	+	2603.27i	−0.912173	+	0.409806i
$344$	−1772.45			−0.277803
$345$		0			0
$346$	−1530.60	−	2651.07i	−0.237819	−	0.411915i
$347$	−3112.32	−	5390.69i	−0.481493	−	0.833970i	0.518282	−	0.855210i	$-0.326572\pi$
$347$	−3112.32	−	5390.69i	−0.481493	−	0.833970i	−0.999774	+	0.0212401i	$0.993239\pi$
$348$		0			0
$349$	9732.21			1.49270			0.746352	−	0.665552i	$-0.231804\pi$
$349$	9732.21			1.49270			0.746352	+	0.665552i	$0.231804\pi$
$350$	11339.1	−	1606.58i	1.73172	−	0.245357i
$351$		0			0
$352$	−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	$0.799057\pi$
$354$		0			0
$355$	−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	−0.996315	−	0.0857714i	$-0.972665\pi$
$359$	−2883.25	+	4993.93i	−0.423877	+	0.734177i	0.572438	+	0.819948i	$0.305998\pi$
$360$		0			0
$361$	2867.99	+	4967.51i	0.418136	+	0.724233i
$362$	1286.71	−	2228.64i	0.186817	−	0.323577i
$363$		0			0
$364$	98.7879	+	126.151i	0.0142250	+	0.0181651i
$365$	22968.7			3.29381
$366$		0			0
$367$	−5772.67	−	9998.56i	−0.821065	−	1.42213i	−0.904890	−	0.425646i	$-0.860047\pi$
$367$	−5772.67	−	9998.56i	−0.821065	−	1.42213i	0.0838244	−	0.996481i	$-0.473287\pi$
$368$	5.21213	+	9.02768i	0.000738319	+	0.00127881i
$369$		0			0
$370$	7023.53			0.986854
$371$	2015.51	+	2573.78i	0.282048	+	0.360172i
$372$		0			0
$373$	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
$375$		0			0
$376$	−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
$381$		0			0
$382$	−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	$0.0727130\pi$
$384$		0			0
$385$	−5793.63	+	820.864i	−0.766937	+	0.108663i
$386$	9541.68			1.25818
$387$		0			0
$388$	−669.402	−	1159.44i	−0.0875869	−	0.151705i
$389$	−6573.46	−	11385.6i	−0.856781	−	1.48399i	−0.874983	−	0.484154i	$-0.839128\pi$
$389$	−6573.46	−	11385.6i	−0.856781	−	1.48399i	0.0182021	−	0.999834i	$-0.494206\pi$
$390$		0			0
$391$	−77.7575			−0.0100572
$392$	−2636.00	+	762.260i	−0.339638	+	0.0982141i
$393$		0			0
$394$	−1622.31	+	2809.92i	−0.207439	+	0.359294i
$395$	−1211.71	−	2098.74i	−0.154349	−	0.267340i
$396$		0			0
$397$	4239.02	−	7342.20i	0.535895	−	0.928198i	−0.463224	−	0.886241i	$-0.653308\pi$
$397$	4239.02	−	7342.20i	0.535895	−	0.928198i	0.999119	−	0.0419565i	$-0.0133591\pi$
$398$	7100.27			0.894232
$399$		0			0
$400$	4946.97			0.618371
$401$	1401.50	−	2427.47i	0.174533	−	0.302299i	−0.765467	−	0.643475i	$-0.777492\pi$
$401$	1401.50	−	2427.47i	0.174533	−	0.302299i	0.939999	+	0.341176i	$0.110825\pi$
$402$		0			0
$403$	241.513	+	418.313i	0.0298527	+	0.0517064i
$404$	−29.4848	+	51.0692i	−0.00363100	+	0.00628908i
$405$		0			0
$406$	−2258.33	+	5607.66i	−0.276057	+	0.685476i
$407$	−2555.46			−0.311227
$408$		0			0
$409$	3192.69	+	5529.91i	0.385987	+	0.668548i	0.991906	−	0.126978i	$-0.0405278\pi$
$409$	3192.69	+	5529.91i	0.385987	+	0.668548i	−0.605919	+	0.795526i	$0.707194\pi$
$410$	−6730.86	−	11658.2i	−0.810765	−	1.40429i
$411$		0			0
$412$	−3365.68			−0.402464
$413$	−5194.62	−	6633.48i	−0.618912	−	0.790344i
$414$		0			0
$415$	5927.41	−	10266.6i	0.701121	−	1.21438i
$416$	34.6061	+	59.9395i	0.00407861	+	0.00706436i
$417$		0			0
$418$	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
$423$		0			0
$424$	706.045	+	1222.91i	0.0808693	+	0.140070i
$425$	−18450.4	+	31957.1i	−2.10583	+	3.64740i
$426$		0			0
$427$	267.413	−	664.012i	0.0303068	−	0.0752548i
$428$	2862.68			0.323301
$429$		0			0
$430$	−4616.61	−	7996.20i	−0.517750	−	0.896769i
$431$	3495.97	+	6055.19i	0.390707	+	0.676725i	0.992543	−	0.121895i	$-0.0388972\pi$
$431$	3495.97	+	6055.19i	0.390707	+	0.676725i	−0.601836	+	0.798620i	$0.705564\pi$
$432$		0			0
$433$	−7699.26			−0.854510			−0.427255	−	0.904131i	$-0.640519\pi$
$433$	−7699.26			−0.854510			−0.427255	+	0.904131i	$0.640519\pi$
$434$	−8190.30	+	1160.43i	−0.905869	+	0.128347i
$435$		0			0
$436$	−1200.04	+	2078.53i	−0.131815	+	0.228310i
$437$	−10.9166	−	18.9081i	−0.00119499	−	0.00206979i
$438$		0			0
$439$	−4706.16	+	8151.31i	−0.511646	+	0.886198i	0.488262	+	0.872697i	$0.337631\pi$
$439$	−4706.16	+	8151.31i	−0.511646	+	0.886198i	−0.999909	+	0.0135008i	$0.995702\pi$
$440$	−2527.61			−0.273861
$441$		0			0
$442$	−516.273			−0.0555579
$443$	−3129.09	+	5419.74i	−0.335593	+	0.581263i	−0.983598	−	0.180372i	$-0.942270\pi$
$443$	−3129.09	+	5419.74i	−0.335593	+	0.581263i	0.648006	+	0.761635i	$0.275603\pi$
$444$		0			0
$445$	3991.97	+	6914.29i	0.425252	+	0.736559i
$446$	−4649.53	+	8053.23i	−0.493636	+	0.855003i
$447$		0			0
$448$	−1173.58	+	166.277i	−0.123764	+	0.0175354i
$449$	11633.8			1.22279			0.611396	−	0.791325i	$-0.290608\pi$
$449$	11633.8			1.22279			0.611396	+	0.791325i	$0.290608\pi$
$450$		0			0
$451$	2448.98	+	4241.75i	0.255694	+	0.442874i
$452$	1245.29	+	2156.90i	0.129587	+	0.224452i
$453$		0			0
$454$	8303.43			0.858369
$455$	−311.807	+	774.246i	−0.0321269	+	0.0797741i
$456$		0			0
$457$	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
$459$		0			0
$460$	−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
$465$		0			0
$466$	−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	$-0.114282\pi$
$468$		0			0
$469$	1619.06	+	2067.52i	0.159405	+	0.203559i
$470$	−21172.4			−2.07789
$471$		0			0
$472$	−1819.71	−	3151.83i	−0.177456	−	0.307362i
$473$	1679.72	+	2909.36i	0.163285	+	0.282817i
$474$		0			0
$475$	−10361.2			−1.00085
$476$	3302.88	−	8201.37i	0.318040	−	0.789725i
$477$		0			0
$478$	−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	$0.965430\pi$
$480$		0			0
$481$	−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
$486$		0			0
$487$	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
$489$		0			0
$490$	−10304.7	−	9906.56i	−0.950035	−	0.913332i
$491$	−13927.9			−1.28016			−0.640079	−	0.768309i	$-0.721098\pi$
$491$	−13927.9			−1.28016			−0.640079	+	0.768309i	$0.721098\pi$
$492$		0			0
$493$	−9739.33	−	16869.0i	−0.889731	−	1.54106i
$494$	−72.4810	−	125.541i	−0.00660137	−	0.0114339i
$495$		0			0
$496$	−3573.21			−0.323472
$497$	11052.6	−	1565.97i	0.997535	−	0.141335i
$498$		0			0
$499$	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
$501$		0			0
$502$	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
$507$		0			0
$508$	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	$0.0559259\pi$
$510$		0			0
$511$	−12586.7	−	16073.0i	−1.08963	−	1.39145i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	3226.18	+	5587.91i	0.276850	+	0.479518i
$515$	−8766.39	−	15183.8i	−0.750084	−	1.29918i
$516$		0			0
$517$	7703.43			0.655312
$518$	−3848.83	−	4914.92i	−0.326463	−	0.416890i
$519$		0			0
$520$	−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	$0.913230\pi$
$522$		0			0
$523$	−3954.03	+	6848.58i	−0.330588	+	0.572595i	−0.982627	−	0.185590i	$-0.940580\pi$
$523$	−3954.03	+	6848.58i	−0.330588	+	0.572595i	0.652039	+	0.758185i	$0.273914\pi$
$524$	−871.439			−0.0726508
$525$		0			0
$526$	6501.23			0.538911
$527$	13326.8	−	23082.7i	1.10156	−	1.90797i
$528$		0			0
$529$	6083.29	+	10536.6i	0.499983	+	0.865995i
$530$	−3677.99	+	6370.46i	−0.301437	+	0.522104i
$531$		0			0
$532$	2458.01	−	348.260i	0.200316	−	0.0283816i
$533$	698.659			0.0567773
$534$		0			0
$535$	7456.26	+	12914.6i	0.602546	+	1.04364i
$536$	567.167	+	982.362i	0.0457050	+	0.0791633i
$537$		0			0
$538$	5652.08			0.452934
$539$	3749.28	+	3604.43i	0.299616	+	0.288040i
$540$		0			0
$541$	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
$543$		0			0
$544$	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
$549$		0			0
$550$	−4688.14	−	8120.10i	−0.363460	−	0.629532i
$551$	2734.67	−	4736.58i	0.211435	−	0.366216i
$552$		0			0
$553$	−804.650	+	1998.02i	−0.0618756	+	0.153643i
$554$	−3640.93			−0.279221
$555$		0			0
$556$	5303.10	+	9185.24i	0.404499	+	0.700613i
$557$	11266.0	+	19513.3i	0.857011	+	1.48439i	0.874767	+	0.484544i	$0.161015\pi$
$557$	11266.0	+	19513.3i	0.857011	+	1.48439i	−0.0177556	+	0.999842i	$0.505652\pi$
$558$		0			0
$559$	479.201			0.0362577
$560$	−3806.88	−	4861.34i	−0.287268	−	0.366838i
$561$		0			0
$562$	−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	$0.494733\pi$
$564$		0			0
$565$	−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	$0.446145\pi$
$569$	−10443.8	+	18089.2i	−0.769468	+	1.33276i	−0.937852	+	0.347036i	$0.887188\pi$
$570$		0			0
$571$	−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
$573$		0			0
$574$	−4469.70	+	11098.7i	−0.325021	+	0.807058i
$575$	−201.440			−0.0146098
$576$		0			0
$577$	−1227.20	−	2125.57i	−0.0885422	−	0.153360i	0.818353	−	0.574716i	$-0.194887\pi$
$577$	−1227.20	−	2125.57i	−0.0885422	−	0.153360i	−0.906895	+	0.421356i	$0.861554\pi$
$578$	9331.06	+	16161.9i	0.671490	+	1.16305i
$579$		0			0
$580$	−13603.2			−0.973863
$581$	−10432.5	+	1478.12i	−0.744945	+	0.105547i
$582$		0			0
$583$	1338.21	−	2317.85i	0.0950652	−	0.164658i
$584$	−4409.20	−	7636.95i	−0.312421	−	0.541129i
$585$		0			0
$586$	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
$591$		0			0
$592$	−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	$-0.0352053\pi$
$594$		0			0
$595$	45602.2	−	6461.10i	3.14203	−	0.445175i
$596$	−2324.09			−0.159729
$597$		0			0
$598$	−1.40915	−	2.44072i	−9.63621e−5	−	0.000166904i
$599$	11632.4	+	20147.9i	0.793469	+	1.37433i	0.923807	+	0.382859i	$0.125060\pi$
$599$	11632.4	+	20147.9i	0.793469	+	1.37433i	−0.130338	+	0.991470i	$0.541606\pi$
$600$		0			0
$601$	25322.3			1.71867			0.859334	−	0.511416i	$-0.170879\pi$
$601$	25322.3			1.71867			0.859334	+	0.511416i	$0.170879\pi$
$602$	−3065.71	+	7612.45i	−0.207556	+	0.515382i
$603$		0			0
$604$	1230.78	−	2131.77i	0.0829135	−	0.143610i
$605$	−11471.7	−	19869.6i	−0.770897	−	1.33523i
$606$		0			0
$607$	10867.2	−	18822.5i	0.726665	−	1.25862i	−0.231620	−	0.972806i	$-0.574403\pi$
$607$	10867.2	−	18822.5i	0.726665	−	1.25862i	0.958285	−	0.285814i	$-0.0922639\pi$
$608$	1072.36			0.0715297
$609$		0			0
$610$	1610.77			0.106915
$611$	549.420	−	951.624i	0.0363784	−	0.0630092i
$612$		0			0
$613$	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
$615$		0			0
$616$	1385.11	+	1768.76i	0.0905966	+	0.115691i
$617$	8497.12			0.554427			0.277213	−	0.960808i	$-0.410589\pi$
$617$	8497.12			0.554427			0.277213	+	0.960808i	$0.410589\pi$
$618$		0			0
$619$	11491.5	+	19903.8i	0.746173	+	1.29241i	0.949645	+	0.313329i	$0.101444\pi$
$619$	11491.5	+	19903.8i	0.746173	+	1.29241i	−0.203472	+	0.979081i	$0.565223\pi$
$620$	−9306.93	−	16120.1i	−0.602863	−	1.04419i
$621$		0			0
$622$	−5371.98			−0.346297
$623$	2650.91	−	6582.46i	0.170476	−	0.423308i
$624$		0			0
$625$	−20661.3	+	35786.4i	−1.32232	+	2.29033i
$626$	2219.19	+	3843.75i	0.141688	+	0.245411i
$627$		0			0
$628$	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
$633$		0			0
$634$	−2221.26	−	3847.34i	−0.139144	−	0.241005i
$635$	−1876.13	+	3249.55i	−0.117247	+	0.203078i
$636$		0			0
$637$	712.669	−	206.084i	0.0443280	−	0.0128185i
$638$	4949.42			0.307131
$639$		0			0
$640$	−1333.58	−	2309.82i	−0.0823660	−	0.142662i
$641$	14553.7	+	25207.7i	0.896780	+	1.55327i	0.831587	+	0.555395i	$0.187433\pi$
$641$	14553.7	+	25207.7i	0.896780	+	1.55327i	0.0651930	+	0.997873i	$0.479234\pi$
$642$		0			0
$643$	−3112.26			−0.190880			−0.0954398	−	0.995435i	$-0.530426\pi$
$643$	−3112.26			−0.190880			−0.0954398	+	0.995435i	$0.530426\pi$
$644$	47.7878	−	6.77076i	0.00292407	−	0.000414294i
$645$		0			0
$646$	−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	$0.910064\pi$
$648$		0			0
$649$	−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	$0.365556\pi$
$653$	−9761.01	+	16906.6i	−0.584958	+	1.01318i	−0.994881	+	0.101057i	$0.967778\pi$
$654$		0			0
$655$	−2269.79	−	3931.38i	−0.135401	−	0.234522i
$656$	−2584.18	+	4475.93i	−0.153804	+	0.266396i
$657$		0			0
$658$	11602.3	+	14816.0i	0.687393	+	0.877793i
$659$	−664.061			−0.0392536			−0.0196268	−	0.999807i	$-0.506248\pi$
$659$	−664.061			−0.0392536			−0.0196268	+	0.999807i	$0.506248\pi$
$660$		0			0
$661$	−7960.82	−	13788.5i	−0.468442	−	0.811365i	0.530908	−	0.847430i	$-0.321851\pi$
$661$	−7960.82	−	13788.5i	−0.468442	−	0.811365i	−0.999349	+	0.0360650i	$0.988518\pi$
$662$	4154.06	+	7195.04i	0.243885	+	0.422422i
$663$		0			0
$664$	−4551.42			−0.266008
$665$	7973.36	+	10181.9i	0.464953	+	0.593739i
$666$		0			0
$667$	53.1665	−	92.0870i	0.00308638	−	0.00534576i
$668$	2246.61	+	3891.24i	0.130125	+	0.225384i
$669$		0			0
$670$	−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
$675$		0			0
$676$	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	$0.00542200\pi$
$678$		0			0
$679$	−6137.45	+	869.578i	−0.346883	+	0.0491478i
$680$	19895.0			1.12197
$681$		0			0
$682$	3386.26	+	5865.18i	0.190127	+	0.329310i
$683$	−9581.79	−	16596.1i	−0.536804	−	0.929771i	−0.999074	−	0.0430322i	$-0.986298\pi$
$683$	−9581.79	−	16596.1i	−0.536804	−	0.929771i	0.462270	−	0.886739i	$-0.347035\pi$
$684$		0			0
$685$	−54215.2			−3.02402
$686$	−1285.53	+	12639.7i	−0.0715478	+	0.703478i
$687$		0			0
$688$	−1772.45	+	3069.98i	−0.0982183	+	0.170119i
$689$	−190.886	−	330.625i	−0.0105547	−	0.0182813i
$690$		0			0
$691$	−4047.94	+	7011.23i	−0.222852	+	0.385991i	−0.955673	−	0.294431i	$-0.904870\pi$
$691$	−4047.94	+	7011.23i	−0.222852	+	0.385991i	0.732821	+	0.680422i	$0.238203\pi$
$692$	−6122.39			−0.336327
$693$		0			0
$694$	−12449.3			−0.680934
$695$	−27625.3	+	47848.5i	−1.50775	+	2.61150i
$696$		0			0
$697$	−19276.1	−	33387.2i	−1.04754	−	1.81439i
$698$	9732.21	−	16856.7i	0.527750	−	0.914090i
$699$		0			0
$700$	8556.48	−	21246.6i	0.462006	−	1.14721i
$701$	−12354.7			−0.665664			−0.332832	−	0.942986i	$-0.608004\pi$
$701$	−12354.7			−0.665664			−0.332832	+	0.942986i	$0.608004\pi$
$702$		0			0
$703$	2823.90	+	4891.14i	0.151501	+	0.262408i
$704$	485.212	+	840.412i	0.0259760	+	0.0449918i
$705$		0			0
$706$	2851.23			0.151993
$707$	168.337	+	214.965i	0.00895470	+	0.0114350i
$708$		0			0
$709$	−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
$711$		0			0
$712$	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
$717$		0			0
$718$	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	$0.156569\pi$
$720$		0			0
$721$	−5821.42	+	14455.1i	−0.300695	+	0.746654i
$722$	11472.0			0.591333
$723$		0			0
$724$	−2573.42	−	4457.29i	−0.132100	−	0.228804i
$725$	−25230.8	−	43701.1i	−1.29248	−	2.23864i
$726$		0			0
$727$	6368.21			0.324875			0.162437	−	0.986719i	$-0.448064\pi$
$727$	6368.21			0.324875			0.162437	+	0.986719i	$0.448064\pi$
$728$	317.288	−	44.9546i	0.0161531	−	0.00228864i
$729$		0			0
$730$	22968.7	−	39783.0i	1.16454	−	2.01704i
$731$	−13221.2	−	22899.9i	−0.668954	−	1.15866i
$732$		0			0
$733$	12577.0	−	21784.0i	0.633753	−	1.09769i	−0.353024	−	0.935614i	$-0.614847\pi$
$733$	12577.0	−	21784.0i	0.633753	−	1.09769i	0.986778	−	0.162079i	$-0.0518199\pi$
$734$	−23090.7			−1.16116
$735$		0			0
$736$	20.8485			0.00104414
$737$	1074.98	−	1861.93i	0.0537281	−	0.0930597i
$738$		0			0
$739$	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
$741$		0			0
$742$	6473.42	−	917.180i	0.320279	−	0.0453783i
$743$	−28166.3			−1.39074			−0.695370	−	0.718652i	$-0.744760\pi$
$743$	−28166.3			−1.39074			−0.695370	+	0.718652i	$0.744760\pi$
$744$		0			0
$745$	−6053.42	−	10484.8i	−0.297691	−	0.515617i
$746$	−6479.57	−	11222.9i	−0.318008	−	0.550806i
$747$		0			0
$748$	−7238.67			−0.353839
$749$	4951.41	−	12294.8i	0.241549	−	0.599791i
$750$		0			0
$751$	−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
$753$		0			0
$754$	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
$759$		0			0
$760$	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	$0.131486\pi$
$762$		0			0
$763$	6851.35	+	8749.10i	0.325079	+	0.415123i
$764$	−4221.18			−0.199891
$765$		0			0
$766$	−4360.81	−	7553.15i	−0.205695	−	0.356274i
$767$	491.977	+	852.129i	0.0231607	+	0.0401155i
$768$		0			0
$769$	33276.8			1.56046			0.780228	−	0.625495i	$-0.215103\pi$
$769$	33276.8			1.56046			0.780228	+	0.625495i	$0.215103\pi$
$770$	−4371.85	+	10855.7i	−0.204611	+	0.508069i
$771$		0			0
$772$	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	$-0.345853\pi$
$774$		0			0
$775$	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
$780$		0			0
$781$	−4569.66	−	7914.88i	−0.209366	−	0.362633i
$782$	−77.7575	+	134.680i	−0.00355576	+	0.00615876i
$783$		0			0
$784$	−1315.73	+	5327.95i	−0.0599366	+	0.242709i
$785$	6395.58			0.290787
$786$		0			0
$787$	6757.23	+	11703.9i	0.306060	+	0.530112i	0.977497	−	0.210950i	$-0.0676558\pi$
$787$	6757.23	+	11703.9i	0.306060	+	0.530112i	−0.671437	+	0.741062i	$0.734322\pi$
$788$	3244.62	+	5619.85i	0.146681	+	0.254059i
$789$		0			0
$790$	−4846.84			−0.218282
$791$	11417.5	−	1617.68i	0.513223	−	0.0727155i
$792$		0			0
$793$	−41.7993	+	72.3985i	−0.00187180	+	0.00324205i
$794$	−8478.04	−	14684.4i	−0.378935	−	0.656335i
$795$		0			0
$796$	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
$801$		0			0
$802$	−2803.00	−	4854.94i	−0.123413	−	0.213758i
$803$	−8357.02	+	14474.8i	−0.367264	+	0.636119i
$804$		0			0
$805$	155.015	+	197.953i	0.00678705	+	0.00866698i
$806$	966.053			0.0422181
$807$		0			0
$808$	58.9697	+	102.138i	0.00256751	+	0.00444705i
$809$	11784.0	+	20410.5i	0.512117	+	0.887013i	0.999901	+	0.0140486i	$0.00447194\pi$
$809$	11784.0	+	20410.5i	0.512117	+	0.887013i	−0.487784	+	0.872964i	$0.662195\pi$
$810$		0			0
$811$	−6704.22			−0.290280			−0.145140	−	0.989411i	$-0.546363\pi$
$811$	−6704.22			−0.290280			−0.145140	+	0.989411i	$0.546363\pi$
$812$	7454.42	+	9519.21i	0.322166	+	0.411402i
$813$		0			0
$814$	−2555.46	+	4426.19i	−0.110035	+	0.190587i
$815$	36616.0	+	63420.8i	1.57375	+	2.72581i
$816$		0			0
$817$	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	$-0.658677\pi$
$821$	12269.7	−	21251.8i	0.521579	−	0.903401i	0.999685	−	0.0250988i	$-0.00799003\pi$
$822$		0			0
$823$	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
$825$		0			0
$826$	−16684.1	+	2363.88i	−0.702803	+	0.0995760i
$827$	−31244.9			−1.31377			−0.656887	−	0.753989i	$-0.728127\pi$
$827$	−31244.9			−1.31377			−0.656887	+	0.753989i	$0.728127\pi$
$828$		0			0
$829$	−2115.75	−	3664.58i	−0.0886405	−	0.153530i	0.818296	−	0.574797i	$-0.194919\pi$
$829$	−2115.75	−	3664.58i	−0.0886405	−	0.153530i	−0.906937	+	0.421267i	$0.861586\pi$
$830$	−11854.8	−	20533.2i	−0.495767	−	0.858694i
$831$		0			0
$832$	138.424			0.00576803
$833$	−29510.9	−	28370.8i	−1.22748	−	1.18006i
$834$		0			0
$835$	−11703.2	+	20270.5i	−0.485037	+	0.840109i
$836$	−1016.26	−	1760.21i	−0.0420431	−	0.0728207i
$837$		0			0
$838$	−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
$843$		0			0
$844$	−9306.77	−	16119.8i	−0.379564	−	0.657425i
$845$	−22840.8	+	39561.5i	−0.929880	+	1.61060i
$846$		0			0
$847$	−7617.94	+	18916.1i	−0.309038	+	0.767372i
$848$	2824.18			0.114367
$849$		0			0
$850$	36900.8	+	63914.1i	1.48904	+	2.57910i
$851$	54.9014	+	95.0920i	0.00221151	+	0.00383045i
$852$		0			0
$853$	−19944.4			−0.800565			−0.400282	−	0.916392i	$-0.631088\pi$
$853$	−19944.4			−0.800565			−0.400282	+	0.916392i	$0.631088\pi$
$854$	−882.689	−	1127.18i	−0.0353689	−	0.0451656i
$855$		0			0
$856$	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	$0.744103\pi$
$858$		0			0
$859$	2078.58	−	3600.21i	0.0825614	−	0.143000i	−0.821788	−	0.569793i	$-0.807023\pi$
$859$	2078.58	−	3600.21i	0.0825614	−	0.143000i	0.904349	+	0.426793i	$0.140357\pi$
$860$	−18466.4			−0.732209
$861$		0			0
$862$	13983.9			0.552543
$863$	−8118.96	+	14062.5i	−0.320246	+	0.554683i	−0.980539	−	0.196326i	$-0.937099\pi$
$863$	−8118.96	+	14062.5i	−0.320246	+	0.554683i	0.660292	+	0.751009i	$0.270432\pi$
$864$		0			0
$865$	−15946.6	−	27620.4i	−0.626823	−	1.08569i
$866$	−7699.26	+	13335.5i	−0.302115	+	0.523278i
$867$		0			0
$868$	−6180.37	+	15346.5i	−0.241677	+	0.600107i
$869$	1763.49			0.0688403
$870$		0			0
$871$	−153.339	−	265.591i	−0.00596521	−	0.0103320i
$872$	2400.08	+	4157.05i	0.0932074	+	0.161440i
$873$		0			0
$874$	−43.6664			−0.00168998
$875$	70376.0	−	9971.15i	2.71902	−	0.385242i
$876$		0			0
$877$	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
$879$		0			0
$880$	−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
$885$		0			0
$886$	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	$-0.0121659\pi$
$888$		0			0
$889$	3302.07	−	467.851i	0.124576	−	0.0176504i
$890$	15967.9			0.601398
$891$		0			0
$892$	9299.07	+	16106.5i	0.349054	+	0.604579i
$893$	−8512.65	−	14744.3i	−0.318998	−	0.552520i
$894$		0			0
$895$	71126.1			2.65641
$896$	−885.576	+	2198.97i	−0.0330190	+	0.0819893i
$897$		0			0
$898$	11633.8	−	20150.4i	0.432322	−	0.748804i
$899$	18224.3	+	31565.4i	0.676101	+	1.17104i
$900$		0			0
$901$	−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
$906$		0			0
$907$	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
$909$		0			0
$910$	1029.23	+	1314.31i	0.0374929	+	0.0478780i
$911$	−29647.3			−1.07822			−0.539110	−	0.842235i	$-0.681239\pi$
$911$	−29647.3			−1.07822			−0.539110	+	0.842235i	$0.681239\pi$
$912$		0			0
$913$	4313.29	+	7470.84i	0.156352	+	0.270809i
$914$	−13104.6	−	22697.9i	−0.474248	−	0.821421i
$915$		0			0
$916$	17054.5			0.615172
$917$	−1507.28	+	3742.71i	−0.0542799	+	0.134782i
$918$		0			0
$919$	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
$921$		0			0
$922$	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
$927$		0			0
$928$	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	$0.923397\pi$
$930$		0			0
$931$	2755.74	−	11159.2i	0.0970093	−	0.392832i
$932$	−12199.6			−0.428768
$933$		0			0
$934$	−15590.2	−	27003.1i	−0.546176	−	0.946004i
$935$	−18854.1	−	32656.3i	−0.659461	−	1.14222i
$936$		0			0
$937$	9716.23			0.338757			0.169379	−	0.985551i	$-0.445824\pi$
$937$	9716.23			0.338757			0.169379	+	0.985551i	$0.445824\pi$
$938$	5200.10	−	736.771i	0.181012	−	0.0256465i
$939$		0			0
$940$	−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	$0.872001\pi$
$942$		0			0
$943$	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	−0.708436	−	0.705775i	$-0.750599\pi$
$947$	7489.62	−	12972.4i	0.257001	−	0.445139i	0.965437	+	0.260636i	$0.0839323\pi$
$948$		0			0
$949$	1192.07	+	2064.73i	0.0407758	+	0.0706258i
$950$	−10361.2	+	17946.2i	−0.353855	+	0.612896i
$951$		0			0
$952$	−10902.3	−	13922.1i	−0.371161	−	0.473969i
$953$	−29393.3			−0.999100			−0.499550	−	0.866285i	$-0.666501\pi$
$953$	−29393.3			−0.999100			−0.499550	+	0.866285i	$0.666501\pi$
$954$		0			0
$955$	−10994.7	−	19043.3i	−0.372543	−	0.645264i
$956$	7974.41	+	13812.1i	0.269781	+	0.467275i
$957$		0			0
$958$	−16907.0			−0.570189
$959$	29709.5	+	37938.6i	1.00038	+	1.27748i
$960$		0			0
$961$	−10041.7	+	17392.7i	−0.337072	+	0.583825i
$962$	364.519	+	631.365i	0.0122168	+	0.0211601i
$963$		0			0
$964$	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
$969$		0			0
$970$	−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	$0.217847\pi$
$972$		0			0
$973$	48621.8	−	6888.93i	1.60200	−	0.226977i
$974$	8022.14			0.263907
$975$		0			0
$976$	−309.212	−	535.571i	−0.0101410	−	0.0175648i
$977$	10652.8	+	18451.3i	0.348838	+	0.604205i	0.986043	−	0.166489i	$-0.0532431\pi$
$977$	10652.8	+	18451.3i	0.348838	+	0.604205i	−0.637205	+	0.770694i	$0.719910\pi$
$978$		0			0
$979$	−5809.79			−0.189665
$980$	−27463.3	+	7941.65i	−0.895187	+	0.258864i
$981$		0			0
$982$	−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	$-0.373421\pi$
$984$		0			0
$985$	−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
$990$		0			0
$991$	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
$993$		0			0
$994$	8340.22	−	20709.6i	0.266132	−	0.660833i
$995$	73974.6			2.35694
$996$		0			0
$997$	17186.9	+	29768.6i	0.545953	+	0.945618i	0.998546	+	0.0539007i	$0.0171655\pi$
$997$	17186.9	+	29768.6i	0.545953	+	0.945618i	−0.452594	+	0.891717i	$0.649501\pi$
$998$	−3947.55	−	6837.36i	−0.125208	−	0.216866i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.e.c.25.1	✓	4	21.11	odd	6
42.4.e.c.37.1	yes	4	3.2	odd	2
126.4.g.g.37.2		4	1.1	even	1	trivial
126.4.g.g.109.2		4	7.4	even	3	inner
294.4.a.m.1.1		2	21.5	even	6
294.4.a.n.1.2		2	21.2	odd	6
294.4.e.l.67.2		4	21.17	even	6
294.4.e.l.79.2		4	21.20	even	2
336.4.q.j.193.1		4	84.11	even	6
336.4.q.j.289.1		4	12.11	even	2
882.4.a.v.1.1		2	7.2	even	3
882.4.a.z.1.2		2	7.5	odd	6
882.4.g.bf.361.1		4	7.3	odd	6
882.4.g.bf.667.1		4	7.6	odd	2
2352.4.a.bq.1.2		2	84.23	even	6
2352.4.a.ca.1.1		2	84.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(10.4186 - 18.0455i) q^{5} +(-18.3371 + 2.59808i) q^{7} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(10.4186 - 18.0455i) q^{5} +(-18.3371 + 2.59808i) q^{7} -8.00000 q^{8} +(-20.8371 - 36.0910i) q^{10} +(7.58144 + 13.1314i) q^{11} +2.16288 q^{13} +(-13.8371 + 34.3589i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(-59.6742 - 103.359i) q^{17} +(16.7557 - 29.0217i) q^{19} -83.3485 q^{20} +30.3258 q^{22} +(0.325758 - 0.564230i) q^{23} +(-154.593 - 267.763i) q^{25} +(2.16288 - 3.74622i) q^{26} +(45.6742 + 58.3255i) q^{28} +163.208 q^{29} +(111.663 + 193.406i) q^{31} +(16.0000 + 27.7128i) q^{32} -238.697 q^{34} +(-144.163 + 357.970i) q^{35} +(-84.2670 + 145.955i) q^{37} +(-33.5114 - 58.0434i) q^{38} +(-83.3485 + 144.364i) q^{40} +323.023 q^{41} +221.557 q^{43} +(30.3258 - 52.5258i) q^{44} +(-0.651517 - 1.12846i) q^{46} +(254.023 - 439.980i) q^{47} +(329.500 - 95.2825i) q^{49} -618.371 q^{50} +(-4.32576 - 7.49243i) q^{52} +(-88.2557 - 152.863i) q^{53} +315.951 q^{55} +(146.697 - 20.7846i) q^{56} +(163.208 - 282.685i) q^{58} +(227.464 + 393.979i) q^{59} +(-19.3258 + 33.4732i) q^{61} +446.652 q^{62} +64.0000 q^{64} +(22.5341 - 39.0302i) q^{65} +(-70.8958 - 122.795i) q^{67} +(-238.697 + 413.435i) q^{68} +(475.860 + 607.668i) q^{70} -602.742 q^{71} +(551.150 + 954.619i) q^{73} +(168.534 + 291.910i) q^{74} -134.045 q^{76} +(-173.138 - 221.096i) q^{77} +(58.1515 - 100.721i) q^{79} +(166.697 + 288.728i) q^{80} +(323.023 - 559.492i) q^{82} +568.928 q^{83} -2486.88 q^{85} +(221.557 - 383.748i) q^{86} +(-60.6515 - 105.052i) q^{88} +(-191.580 + 331.825i) q^{89} +(-39.6610 + 5.61932i) q^{91} -2.60607 q^{92} +(-508.045 - 879.961i) q^{94} +(-349.140 - 604.728i) q^{95} +334.701 q^{97} +(164.466 - 665.993i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{4} + 5 q^{5} - 32 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 8 * q^4 + 5 * q^5 - 32 * q^8	\( 4 q + 4 q^{2} - 8 q^{4} + 5 q^{5} - 32 q^{8} - 10 q^{10} + 67 q^{11} + 82 q^{13} + 18 q^{14} - 32 q^{16} - 92 q^{17} - 43 q^{19} - 40 q^{20} + 268 q^{22} + 148 q^{23} - 435 q^{25} + 82 q^{26} + 36 q^{28} - 154 q^{29} + 520 q^{31} + 64 q^{32} - 368 q^{34} - 650 q^{35} - 7 q^{37} + 86 q^{38} - 40 q^{40} + 852 q^{41} - 214 q^{43} + 268 q^{44} - 296 q^{46} + 576 q^{47} + 1318 q^{49} - 1740 q^{50} - 164 q^{52} - 243 q^{53} - 1010 q^{55} - 154 q^{58} - 7 q^{59} - 224 q^{61} + 2080 q^{62} + 256 q^{64} - 570 q^{65} - 687 q^{67} - 368 q^{68} + 1390 q^{70} - 944 q^{71} + 921 q^{73} + 14 q^{74} + 344 q^{76} + 371 q^{77} + 526 q^{79} + 80 q^{80} + 852 q^{82} + 442 q^{83} - 5840 q^{85} - 214 q^{86} - 536 q^{88} + 774 q^{89} + 1345 q^{91} - 1184 q^{92} - 1152 q^{94} - 1910 q^{95} + 3906 q^{97} + 1318 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^4 + 5 * q^5 - 32 * q^8 - 10 * q^10 + 67 * q^11 + 82 * q^13 + 18 * q^14 - 32 * q^16 - 92 * q^17 - 43 * q^19 - 40 * q^20 + 268 * q^22 + 148 * q^23 - 435 * q^25 + 82 * q^26 + 36 * q^28 - 154 * q^29 + 520 * q^31 + 64 * q^32 - 368 * q^34 - 650 * q^35 - 7 * q^37 + 86 * q^38 - 40 * q^40 + 852 * q^41 - 214 * q^43 + 268 * q^44 - 296 * q^46 + 576 * q^47 + 1318 * q^49 - 1740 * q^50 - 164 * q^52 - 243 * q^53 - 1010 * q^55 - 154 * q^58 - 7 * q^59 - 224 * q^61 + 2080 * q^62 + 256 * q^64 - 570 * q^65 - 687 * q^67 - 368 * q^68 + 1390 * q^70 - 944 * q^71 + 921 * q^73 + 14 * q^74 + 344 * q^76 + 371 * q^77 + 526 * q^79 + 80 * q^80 + 852 * q^82 + 442 * q^83 - 5840 * q^85 - 214 * q^86 - 536 * q^88 + 774 * q^89 + 1345 * q^91 - 1184 * q^92 - 1152 * q^94 - 1910 * q^95 + 3906 * q^97 + 1318 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more