LMFDB - Embedded newform 525.3.o.q.451.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,3,Mod(376,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("525.376");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	525.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.3052138789$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 24 x^{14} + 405 x^{12} - 30 x^{11} + 3324 x^{10} - 1302 x^{9} + 19731 x^{8} - 8442 x^{7} + \cdots + 22500 $ x^16 + 24x^14 + 405x^12 - 30x^11 + 3324x^10 - 1302x^9 + 19731x^8 - 8442x^7 + 60390x^6 - 35496x^5 + 130590x^4 - 44820x^3 + 77544x^2 + 20700*x + 22500
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.2
Root			$-1.46615 + 2.53945i$ of defining polynomial
Character	$\chi$	$=$	525.451
Dual form			525.3.o.q.376.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.46615 - 2.53945i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-2.29920 + 3.98234i) q^{4} -5.07890i q^{6} +(0.976973 + 6.93149i) q^{7} +1.75471 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.46615 - 2.53945i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-2.29920 + 3.98234i) q^{4} -5.07890i q^{6} +(0.976973 + 6.93149i) q^{7} +1.75471 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.31170 + 4.00398i) q^{11} +(-6.89761 + 3.98234i) q^{12} -14.9844i q^{13} +(16.1698 - 12.6436i) q^{14} +(6.62414 + 11.4734i) q^{16} +(-14.5178 - 8.38187i) q^{17} +(4.39846 - 7.61835i) q^{18} +(-15.2091 + 8.78098i) q^{19} +(-4.53739 + 11.2433i) q^{21} +13.5572 q^{22} +(-21.3463 - 36.9729i) q^{23} +(2.63206 + 1.51962i) q^{24} +(-38.0522 + 21.9694i) q^{26} +5.19615i q^{27} +(-29.8498 - 12.0463i) q^{28} -18.1470 q^{29} +(3.46723 + 2.00181i) q^{31} +(22.9334 - 39.7218i) q^{32} +(-6.93509 + 4.00398i) q^{33} +49.1564i q^{34} -13.7952 q^{36} +(-14.1759 - 24.5533i) q^{37} +(44.5977 + 25.7485i) q^{38} +(12.9769 - 22.4766i) q^{39} -44.5453i q^{41} +(35.2043 - 4.96195i) q^{42} -44.3306 q^{43} +(-10.6301 - 18.4119i) q^{44} +(-62.5939 + 108.416i) q^{46} +(-52.6502 + 30.3976i) q^{47} +22.9467i q^{48} +(-47.0910 + 13.5438i) q^{49} +(-14.5178 - 25.1456i) q^{51} +(59.6730 + 34.4522i) q^{52} +(27.0638 - 46.8759i) q^{53} +(13.1954 - 7.61835i) q^{54} +(1.71430 + 12.1627i) q^{56} -30.4182 q^{57} +(26.6063 + 46.0835i) q^{58} +(-1.54389 - 0.891363i) q^{59} +(-44.4247 + 25.6486i) q^{61} -11.7398i q^{62} +(-16.5431 + 12.9355i) q^{63} -81.5023 q^{64} +(20.3358 + 11.7409i) q^{66} +(1.41289 - 2.44721i) q^{67} +(66.7588 - 38.5432i) q^{68} -73.9459i q^{69} -19.2802 q^{71} +(2.63206 + 4.55886i) q^{72} +(85.6900 + 49.4732i) q^{73} +(-41.5680 + 71.9979i) q^{74} -80.7571i q^{76} +(-30.0120 - 12.1117i) q^{77} -76.1044 q^{78} +(59.7603 + 103.508i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-113.120 + 65.3102i) q^{82} +89.3021i q^{83} +(-34.3423 - 43.9201i) q^{84} +(64.9954 + 112.575i) q^{86} +(-27.2206 - 15.7158i) q^{87} +(-4.05635 + 7.02581i) q^{88} +(97.2388 - 56.1409i) q^{89} +(103.864 - 14.6394i) q^{91} +196.318 q^{92} +(3.46723 + 6.00542i) q^{93} +(154.386 + 89.1350i) q^{94} +(68.8003 - 39.7218i) q^{96} -115.073i q^{97} +(103.436 + 99.7281i) q^{98} -13.8702 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 24 q^{3} - 16 q^{4} + 6 q^{7} + 24 q^{9}+O(q^{10}) $ 16 * q + 24 * q^3 - 16 * q^4 + 6 * q^7 + 24 * q^9	$ 16 q + 24 q^{3} - 16 q^{4} + 6 q^{7} + 24 q^{9} - 14 q^{11} - 48 q^{12} - 30 q^{14} - 20 q^{16} + 6 q^{17} + 30 q^{19} + 6 q^{21} - 36 q^{22} - 18 q^{23} - 48 q^{26} - 168 q^{28} + 44 q^{29} + 42 q^{31} + 150 q^{32} - 42 q^{33} - 96 q^{36} + 96 q^{37} + 204 q^{38} - 18 q^{39} - 78 q^{42} - 160 q^{44} - 30 q^{46} - 138 q^{47} - 178 q^{49} + 6 q^{51} + 126 q^{52} + 150 q^{53} - 234 q^{56} + 60 q^{57} - 90 q^{58} + 402 q^{59} + 168 q^{61} + 200 q^{64} - 54 q^{66} + 174 q^{67} - 234 q^{68} + 172 q^{71} + 336 q^{73} - 450 q^{74} - 372 q^{77} - 96 q^{78} + 10 q^{79} - 72 q^{81} - 690 q^{82} - 390 q^{84} + 72 q^{86} + 66 q^{87} + 492 q^{88} - 12 q^{89} - 112 q^{91} + 204 q^{92} + 42 q^{93} + 462 q^{94} + 450 q^{96} - 198 q^{98} - 84 q^{99}+O(q^{100}) $ 16 * q + 24 * q^3 - 16 * q^4 + 6 * q^7 + 24 * q^9 - 14 * q^11 - 48 * q^12 - 30 * q^14 - 20 * q^16 + 6 * q^17 + 30 * q^19 + 6 * q^21 - 36 * q^22 - 18 * q^23 - 48 * q^26 - 168 * q^28 + 44 * q^29 + 42 * q^31 + 150 * q^32 - 42 * q^33 - 96 * q^36 + 96 * q^37 + 204 * q^38 - 18 * q^39 - 78 * q^42 - 160 * q^44 - 30 * q^46 - 138 * q^47 - 178 * q^49 + 6 * q^51 + 126 * q^52 + 150 * q^53 - 234 * q^56 + 60 * q^57 - 90 * q^58 + 402 * q^59 + 168 * q^61 + 200 * q^64 - 54 * q^66 + 174 * q^67 - 234 * q^68 + 172 * q^71 + 336 * q^73 - 450 * q^74 - 372 * q^77 - 96 * q^78 + 10 * q^79 - 72 * q^81 - 690 * q^82 - 390 * q^84 + 72 * q^86 + 66 * q^87 + 492 * q^88 - 12 * q^89 - 112 * q^91 + 204 * q^92 + 42 * q^93 + 462 * q^94 + 450 * q^96 - 198 * q^98 - 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−1.46615	−	2.53945i	−0.733076	−	1.26972i	−0.955562	−	0.294789i	$-0.904751\pi$
$2$	−1.46615	−	2.53945i	−0.733076	−	1.26972i	0.222486	−	0.974936i	$-0.428583\pi$
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$4$	−2.29920	+	3.98234i	−0.574801	+	0.995584i
$5$		0			0
$5$		0			0
$6$		−	5.07890i		−	0.846483i
$7$	0.976973	+	6.93149i	0.139568	+	0.990213i
$7$	0.976973	+	6.93149i	0.139568	+	0.990213i
$8$	1.75471			0.219338
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	−2.31170	+	4.00398i	−0.210154	+	0.363998i	−0.951763	−	0.306835i	$-0.900730\pi$
$11$	−2.31170	+	4.00398i	−0.210154	+	0.363998i	0.741608	+	0.670833i	$0.234063\pi$
$12$	−6.89761	+	3.98234i	−0.574801	+	0.331861i
$13$		−	14.9844i		−	1.15265i	−0.817221	−	0.576324i	$-0.804487\pi$
$13$		−	14.9844i		−	1.15265i	0.817221	−	0.576324i	$-0.195513\pi$
$14$	16.1698	−	12.6436i	1.15498	−	0.903113i
$15$		0			0
$16$	6.62414	+	11.4734i	0.414009	+	0.717085i
$17$	−14.5178	−	8.38187i	−0.853989	−	0.493051i	0.00800544	−	0.999968i	$-0.497452\pi$
$17$	−14.5178	−	8.38187i	−0.853989	−	0.493051i	−0.861995	+	0.506917i	$0.830785\pi$
$18$	4.39846	−	7.61835i	0.244359	−	0.423242i
$19$	−15.2091	+	8.78098i	−0.800480	+	0.462157i	−0.843639	−	0.536911i	$-0.819591\pi$
$19$	−15.2091	+	8.78098i	−0.800480	+	0.462157i	0.0431592	+	0.999068i	$0.486258\pi$
$20$		0			0
$21$	−4.53739	+	11.2433i	−0.216066	+	0.535396i
$22$	13.5572			0.616236
$23$	−21.3463	−	36.9729i	−0.928101	−	1.60752i	−0.786496	−	0.617595i	$-0.788107\pi$
$23$	−21.3463	−	36.9729i	−0.928101	−	1.60752i	−0.141605	−	0.989923i	$-0.545226\pi$
$24$	2.63206	+	1.51962i	0.109669	+	0.0633175i
$25$		0			0
$26$	−38.0522	+	21.9694i	−1.46355	+	0.844979i
$27$			5.19615i			0.192450i
$28$	−29.8498	−	12.0463i	−1.06606	−	0.430224i
$29$	−18.1470			−0.625760			−0.312880	−	0.949793i	$-0.601294\pi$
$29$	−18.1470			−0.625760			−0.312880	+	0.949793i	$0.601294\pi$
$30$		0			0
$31$	3.46723	+	2.00181i	0.111846	+	0.0645745i	0.554880	−	0.831931i	$-0.312764\pi$
$31$	3.46723	+	2.00181i	0.111846	+	0.0645745i	−0.443033	+	0.896505i	$0.646098\pi$
$32$	22.9334	−	39.7218i	0.716669	−	1.24131i
$33$	−6.93509	+	4.00398i	−0.210154	+	0.121333i
$34$			49.1564i			1.44578i
$35$		0			0
$36$	−13.7952			−0.383200
$37$	−14.1759	−	24.5533i	−0.383132	−	0.663604i	0.608376	−	0.793649i	$-0.291821\pi$
$37$	−14.1759	−	24.5533i	−0.383132	−	0.663604i	−0.991508	+	0.130045i	$0.958488\pi$
$38$	44.5977	+	25.7485i	1.17362	+	0.677593i
$39$	12.9769	−	22.4766i	0.332741	−	0.576324i
$40$		0			0
$41$		−	44.5453i		−	1.08647i	−0.839581	−	0.543235i	$-0.817199\pi$
$41$		−	44.5453i		−	1.08647i	0.839581	−	0.543235i	$-0.182801\pi$
$42$	35.2043	−	4.96195i	0.838198	−	0.118142i
$43$	−44.3306			−1.03094			−0.515472	−	0.856906i	$-0.672383\pi$
$43$	−44.3306			−1.03094			−0.515472	+	0.856906i	$0.672383\pi$
$44$	−10.6301	−	18.4119i	−0.241594	−	0.418453i
$45$		0			0
$46$	−62.5939	+	108.416i	−1.36074	+	2.35687i
$47$	−52.6502	+	30.3976i	−1.12022	+	0.646758i	−0.941456	−	0.337135i	$-0.890542\pi$
$47$	−52.6502	+	30.3976i	−1.12022	+	0.646758i	−0.178761	+	0.983893i	$0.557209\pi$
$48$			22.9467i			0.478056i
$49$	−47.0910	+	13.5438i	−0.961042	+	0.276403i
$50$		0			0
$51$	−14.5178	−	25.1456i	−0.284663	−	0.493051i
$52$	59.6730	+	34.4522i	1.14756	+	0.662543i
$53$	27.0638	−	46.8759i	0.510638	−	0.884452i	−0.489286	−	0.872124i	$-0.662742\pi$
$53$	27.0638	−	46.8759i	0.510638	−	0.884452i	0.999924	−	0.0123280i	$-0.00392424\pi$
$54$	13.1954	−	7.61835i	0.244359	−	0.141081i
$55$		0			0
$56$	1.71430	+	12.1627i	0.0306125	+	0.217192i
$57$	−30.4182			−0.533653
$58$	26.6063	+	46.0835i	0.458730	+	0.794543i
$59$	−1.54389	−	0.891363i	−0.0261675	−	0.0151078i	0.486859	−	0.873480i	$-0.338142\pi$
$59$	−1.54389	−	0.891363i	−0.0261675	−	0.0151078i	−0.513027	+	0.858373i	$0.671476\pi$
$60$		0			0
$61$	−44.4247	+	25.6486i	−0.728274	+	0.420469i	−0.817790	−	0.575516i	$-0.804801\pi$
$61$	−44.4247	+	25.6486i	−0.728274	+	0.420469i	0.0895167	+	0.995985i	$0.471468\pi$
$62$		−	11.7398i		−	0.189352i
$63$	−16.5431	+	12.9355i	−0.262588	+	0.205325i
$64$	−81.5023			−1.27347
$65$		0			0
$66$	20.3358	+	11.7409i	0.308118	+	0.177892i
$67$	1.41289	−	2.44721i	0.0210880	−	0.0365255i	−0.855289	−	0.518152i	$-0.826620\pi$
$67$	1.41289	−	2.44721i	0.0210880	−	0.0365255i	0.876377	+	0.481626i	$0.159954\pi$
$68$	66.7588	−	38.5432i	0.981748	−	0.566812i
$69$		−	73.9459i		−	1.07168i
$70$		0			0
$71$	−19.2802			−0.271553			−0.135776	−	0.990740i	$-0.543353\pi$
$71$	−19.2802			−0.271553			−0.135776	+	0.990740i	$0.543353\pi$
$72$	2.63206	+	4.55886i	0.0365564	+	0.0633175i
$73$	85.6900	+	49.4732i	1.17384	+	0.677714i	0.954581	−	0.297953i	$-0.0963039\pi$
$73$	85.6900	+	49.4732i	1.17384	+	0.677714i	0.219255	+	0.975667i	$0.429637\pi$
$74$	−41.5680	+	71.9979i	−0.561729	+	0.972944i
$75$		0			0
$76$		−	80.7571i		−	1.06259i
$77$	−30.0120	−	12.1117i	−0.389766	−	0.157295i
$78$	−76.1044			−0.975697
$79$	59.7603	+	103.508i	0.756459	+	1.31023i	0.944646	+	0.328093i	$0.106406\pi$
$79$	59.7603	+	103.508i	0.756459	+	1.31023i	−0.188186	+	0.982133i	$0.560261\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−113.120	+	65.3102i	−1.37952	+	0.796465i
$83$			89.3021i			1.07593i	0.842968	+	0.537964i	$0.180806\pi$
$83$			89.3021i			1.07593i	−0.842968	+	0.537964i	$0.819194\pi$
$84$	−34.3423	−	43.9201i	−0.408837	−	0.522858i
$85$		0			0
$86$	64.9954	+	112.575i	0.755761	+	1.30902i
$87$	−27.2206	−	15.7158i	−0.312880	−	0.180641i
$88$	−4.05635	+	7.02581i	−0.0460949	+	0.0798387i
$89$	97.2388	−	56.1409i	1.09257	−	0.630796i	0.158311	−	0.987389i	$-0.449395\pi$
$89$	97.2388	−	56.1409i	1.09257	−	0.630796i	0.934260	+	0.356593i	$0.116062\pi$
$90$		0			0
$91$	103.864	−	14.6394i	1.14137	−	0.160872i
$92$	196.318			2.13389
$93$	3.46723	+	6.00542i	0.0372821	+	0.0645745i
$94$	154.386	+	89.1350i	1.64241	+	0.948245i
$95$		0			0
$96$	68.8003	−	39.7218i	0.716669	−	0.413769i
$97$		−	115.073i		−	1.18632i	−0.805083	−	0.593162i	$-0.797880\pi$
$97$		−	115.073i		−	1.18632i	0.805083	−	0.593162i	$-0.202120\pi$
$98$	103.436	+	99.7281i	1.05547	+	1.01763i
$99$	−13.8702			−0.140103
$100$		0			0
$101$	14.2439	+	8.22372i	0.141029	+	0.0814230i	0.568854	−	0.822438i	$-0.307387\pi$
$101$	14.2439	+	8.22372i	0.141029	+	0.0814230i	−0.427825	+	0.903861i	$0.640720\pi$
$102$	−42.5707	+	73.7346i	−0.417359	+	0.722888i
$103$	−128.202	+	74.0173i	−1.24468	+	0.718615i	−0.970043	−	0.242934i	$-0.921890\pi$
$103$	−128.202	+	74.0173i	−1.24468	+	0.718615i	−0.274634	+	0.961549i	$0.588557\pi$
$104$		−	26.2933i		−	0.252820i
$105$		0			0
$106$	−158.719			−1.49735
$107$	64.9595	+	112.513i	0.607099	+	1.05153i	0.991716	+	0.128449i	$0.0410000\pi$
$107$	64.9595	+	112.513i	0.607099	+	1.05153i	−0.384618	+	0.923076i	$0.625667\pi$
$108$	−20.6928	−	11.9470i	−0.191600	−	0.110620i
$109$	−33.9234	+	58.7570i	−0.311223	+	0.539055i	−0.978628	−	0.205641i	$-0.934072\pi$
$109$	−33.9234	+	58.7570i	−0.311223	+	0.539055i	0.667404	+	0.744696i	$0.267405\pi$
$110$		0			0
$111$		−	49.1067i		−	0.442403i
$112$	−73.0558	+	57.1243i	−0.652284	+	0.510039i
$113$	−34.3029			−0.303565			−0.151783	−	0.988414i	$-0.548501\pi$
$113$	−34.3029			−0.303565			−0.151783	+	0.988414i	$0.548501\pi$
$114$	44.5977	+	77.2455i	0.391208	+	0.677593i
$115$		0			0
$116$	41.7237	−	72.2676i	0.359687	−	0.622997i
$117$	38.9307	−	22.4766i	0.332741	−	0.192108i
$118$			5.22749i			0.0443008i
$119$	43.9153	−	108.819i	0.369036	−	0.914445i
$120$		0			0
$121$	49.8121	+	86.2771i	0.411670	+	0.713034i
$122$	130.267	+	75.2095i	1.06776	+	0.616471i
$123$	38.5773	−	66.8179i	0.313637	−	0.543235i
$124$	−15.9437	+	9.20513i	−0.128579	+	0.0742349i
$125$		0			0
$126$	57.1037	+	23.0449i	0.453204	+	0.182896i
$127$	−122.729			−0.966374			−0.483187	−	0.875517i	$-0.660521\pi$
$127$	−122.729			−0.966374			−0.483187	+	0.875517i	$0.660521\pi$
$128$	27.7611	+	48.0837i	0.216884	+	0.375654i
$129$	−66.4959	−	38.3914i	−0.515472	−	0.297608i
$130$		0			0
$131$	−136.182	+	78.6246i	−1.03956	+	0.600188i	−0.919707	−	0.392605i	$-0.871574\pi$
$131$	−136.182	+	78.6246i	−1.03956	+	0.600188i	−0.119848	+	0.992792i	$0.538241\pi$
$132$		−	36.8238i		−	0.278968i
$133$	−75.7242	−	96.8430i	−0.569355	−	0.728143i
$134$	−8.28607			−0.0618364
$135$		0			0
$136$	−25.4745	−	14.7077i	−0.187313	−	0.108145i
$137$	40.1055	−	69.4647i	0.292741	−	0.507042i	−0.681716	−	0.731617i	$-0.738766\pi$
$137$	40.1055	−	69.4647i	0.292741	−	0.507042i	0.974457	+	0.224575i	$0.0720994\pi$
$138$	−187.782	+	108.416i	−1.36074	+	0.785622i
$139$		−	251.236i		−	1.80746i	−0.428107	−	0.903728i	$-0.640819\pi$
$139$		−	251.236i		−	1.80746i	0.428107	−	0.903728i	$-0.359181\pi$
$140$		0			0
$141$	−105.300			−0.746811
$142$	28.2677	+	48.9612i	0.199069	+	0.344797i
$143$	59.9973	+	34.6395i	0.419562	+	0.242234i
$144$	−19.8724	+	34.4201i	−0.138003	+	0.239028i
$145$		0			0
$146$		−	290.141i		−	1.98726i
$147$	−82.3658	−	20.4664i	−0.560312	−	0.139227i
$148$	130.373			0.880898
$149$	−144.514	−	250.305i	−0.969890	−	1.67990i	−0.695860	−	0.718177i	$-0.744977\pi$
$149$	−144.514	−	250.305i	−0.969890	−	1.67990i	−0.274030	−	0.961721i	$-0.588357\pi$
$150$		0			0
$151$	26.9221	−	46.6305i	0.178292	−	0.308811i	−0.763004	−	0.646394i	$-0.776276\pi$
$151$	26.9221	−	46.6305i	0.178292	−	0.308811i	0.941296	+	0.337583i	$0.109609\pi$
$152$	−26.6875	+	15.4081i	−0.175576	+	0.101369i
$153$		−	50.2912i		−	0.328701i
$154$	13.2450	+	93.9715i	0.0860066	+	0.610205i
$155$		0			0
$156$	59.6730	+	103.357i	0.382519	+	0.662543i
$157$	−22.9328	−	13.2403i	−0.146069	−	0.0843328i	0.425184	−	0.905107i	$-0.360209\pi$
$157$	−22.9328	−	13.2403i	−0.146069	−	0.0843328i	−0.571253	+	0.820774i	$0.693543\pi$
$158$	175.235	−	303.516i	1.10908	−	1.92099i
$159$	81.1915	−	46.8759i	0.510638	−	0.294817i
$160$		0			0
$161$	235.423	−	184.083i	1.46225	−	1.14337i
$162$	26.3907			0.162906
$163$	−43.3489	−	75.0826i	−0.265944	−	0.460629i	0.701866	−	0.712309i	$-0.252350\pi$
$163$	−43.3489	−	75.0826i	−0.265944	−	0.460629i	−0.967811	+	0.251680i	$0.919017\pi$
$164$	177.394	+	102.419i	1.08167	+	0.624504i
$165$		0			0
$166$	226.778	−	130.930i	1.36613	−	0.788737i
$167$			40.5216i			0.242644i	0.992613	+	0.121322i	$0.0387134\pi$
$167$			40.5216i			0.242644i	−0.992613	+	0.121322i	$0.961287\pi$
$168$	−7.96178	+	19.7287i	−0.0473916	+	0.117433i
$169$	−55.5330			−0.328598
$170$		0			0
$171$	−45.6273	−	26.3430i	−0.266827	−	0.154052i
$172$	101.925	−	176.539i	0.592588	−	1.02639i
$173$	146.824	−	84.7690i	0.848695	−	0.489994i	−0.0115151	−	0.999934i	$-0.503665\pi$
$173$	146.824	−	84.7690i	0.848695	−	0.489994i	0.860210	+	0.509939i	$0.170332\pi$
$174$			92.1670i			0.529695i
$175$		0			0
$176$	−61.2521			−0.348023
$177$	−1.54389	−	2.67409i	−0.00872252	−	0.0151078i
$178$	−285.134	−	164.622i	−1.60187	−	0.924843i
$179$	−97.4232	+	168.742i	−0.544264	+	0.942692i	0.454389	+	0.890803i	$0.349858\pi$
$179$	−97.4232	+	168.742i	−0.544264	+	0.942692i	−0.998653	+	0.0518889i	$0.983476\pi$
$180$		0			0
$181$		−	52.1881i		−	0.288332i	−0.989554	−	0.144166i	$-0.953950\pi$
$181$		−	52.1881i		−	0.288332i	0.989554	−	0.144166i	$-0.0460499\pi$
$182$	−189.457	−	242.295i	−1.04097	−	1.33129i
$183$	−88.8494			−0.485516
$184$	−37.4566	−	64.8767i	−0.203568	−	0.352591i
$185$		0			0
$186$	10.1670	−	17.6097i	0.0546612	−	0.0946760i
$187$	67.1216	−	38.7527i	0.358939	−	0.207234i
$188$		−	279.561i		−	1.48703i
$189$	−36.0171	+	5.07650i	−0.190566	+	0.0268598i
$190$		0			0
$191$	−35.6031	−	61.6663i	−0.186404	−	0.322860i	0.757645	−	0.652667i	$-0.226350\pi$
$191$	−35.6031	−	61.6663i	−0.186404	−	0.322860i	−0.944049	+	0.329806i	$0.893017\pi$
$192$	−122.254	−	70.5831i	−0.636737	−	0.367620i
$193$	−170.319	+	295.002i	−0.882484	+	1.52851i	−0.0339131	+	0.999425i	$0.510797\pi$
$193$	−170.319	+	295.002i	−0.882484	+	1.52851i	−0.848571	+	0.529082i	$0.822536\pi$
$194$	−292.223	+	168.715i	−1.50630	+	0.869665i
$195$		0			0
$196$	54.3361	−	218.672i	0.277225	−	1.11567i
$197$	−57.0319			−0.289502			−0.144751	−	0.989468i	$-0.546238\pi$
$197$	−57.0319			−0.289502			−0.144751	+	0.989468i	$0.546238\pi$
$198$	20.3358	+	35.2226i	0.102706	+	0.177892i
$199$	−108.667	−	62.7389i	−0.546065	−	0.315271i	0.201468	−	0.979495i	$-0.435429\pi$
$199$	−108.667	−	62.7389i	−0.546065	−	0.315271i	−0.747533	+	0.664224i	$0.768762\pi$
$200$		0			0
$201$	4.23868	−	2.44721i	0.0210880	−	0.0121752i
$202$		−	48.2289i		−	0.238757i
$203$	−17.7292	−	125.786i	−0.0873358	−	0.619635i
$204$	133.518			0.654498
$205$		0			0
$206$	375.926	+	217.041i	1.82489	+	1.05360i
$207$	64.0390	−	110.919i	0.309367	−	0.535840i
$208$	171.922	−	99.2590i	0.826546	−	0.477207i
$209$		−	81.1959i		−	0.388497i
$210$		0			0
$211$	168.745			0.799738			0.399869	−	0.916572i	$-0.369056\pi$
$211$	168.745			0.799738			0.399869	+	0.916572i	$0.369056\pi$
$212$	124.450	+	215.555i	0.587031	+	1.01677i
$213$	−28.9203	−	16.6972i	−0.135776	−	0.0783905i
$214$	190.481	−	329.923i	0.890099	−	1.54170i
$215$		0			0
$216$			9.11773i			0.0422117i
$217$	−10.4881	+	25.9888i	−0.0483323	+	0.119764i
$218$	198.947			0.912602
$219$	85.6900	+	148.419i	0.391279	+	0.677714i
$220$		0			0
$221$	−125.597	+	217.541i	−0.568314	+	0.984349i
$222$	−124.704	+	71.9979i	−0.561729	+	0.324315i
$223$		−	304.803i		−	1.36683i	−0.730029	−	0.683416i	$-0.760494\pi$
$223$		−	304.803i		−	1.36683i	0.730029	−	0.683416i	$-0.239506\pi$
$224$	297.737	+	120.156i	1.32918	+	0.536409i
$225$		0			0
$226$	50.2932	+	87.1104i	0.222536	+	0.385444i
$227$	−226.804	−	130.945i	−0.999137	−	0.576852i	−0.0911440	−	0.995838i	$-0.529052\pi$
$227$	−226.804	−	130.945i	−0.999137	−	0.576852i	−0.907993	+	0.418986i	$0.862386\pi$
$228$	69.9377	−	121.136i	0.306744	−	0.531296i
$229$	170.565	−	98.4758i	0.744826	−	0.430025i	−0.0789956	−	0.996875i	$-0.525171\pi$
$229$	170.565	−	98.4758i	0.744826	−	0.430025i	0.823821	+	0.566850i	$0.191838\pi$
$230$		0			0
$231$	−34.5289	−	44.1587i	−0.149476	−	0.191163i
$232$	−31.8427			−0.137253
$233$	121.332	+	210.153i	0.520737	+	0.901944i	0.999709	+	0.0241133i	$0.00767625\pi$
$233$	121.332	+	210.153i	0.520737	+	0.901944i	−0.478972	+	0.877830i	$0.658990\pi$
$234$	−114.157	−	65.9083i	−0.487849	−	0.281660i
$235$		0			0
$236$	7.09941	−	4.09885i	0.0300823	−	0.0173680i
$237$			207.016i			0.873484i
$238$	−340.727	+	48.0244i	−1.43163	+	0.201783i
$239$	286.679			1.19949			0.599746	−	0.800190i	$-0.295268\pi$
$239$	286.679			1.19949			0.599746	+	0.800190i	$0.295268\pi$
$240$		0			0
$241$	34.8904	+	20.1440i	0.144773	+	0.0835849i	0.570637	−	0.821202i	$-0.306696\pi$
$241$	34.8904	+	20.1440i	0.144773	+	0.0835849i	−0.425864	+	0.904787i	$0.640030\pi$
$242$	146.064	−	252.991i	0.603571	−	1.04542i
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$		−	235.885i		−	0.966743i
$245$		0			0
$246$	−226.241			−0.919679
$247$	131.578	+	227.900i	0.532705	+	0.922671i
$248$	6.08398	+	3.51259i	0.0245322	+	0.0141637i
$249$	−77.3379	+	133.953i	−0.310594	+	0.537964i
$250$		0			0
$251$		−	231.058i		−	0.920550i	−0.887776	−	0.460275i	$-0.847751\pi$
$251$		−	231.058i		−	0.920550i	0.887776	−	0.460275i	$-0.152249\pi$
$252$	−13.4776	−	95.6214i	−0.0534824	−	0.379450i
$253$	197.385			0.780178
$254$	179.940	+	311.665i	0.708425	+	1.22703i
$255$		0			0
$256$	−81.6006	+	141.336i	−0.318752	+	0.552095i
$257$	−98.6720	+	56.9683i	−0.383938	+	0.221666i	−0.679530	−	0.733648i	$-0.737816\pi$
$257$	−98.6720	+	56.9683i	−0.383938	+	0.221666i	0.295592	+	0.955314i	$0.404483\pi$
$258$			225.151i			0.872677i
$259$	156.342	−	122.248i	0.603636	−	0.471999i
$260$		0			0
$261$	−27.2206	−	47.1474i	−0.104293	−	0.180641i
$262$	399.326	+	230.551i	1.52415	+	0.879966i
$263$	−99.9012	+	173.034i	−0.379853	+	0.657924i	−0.991041	−	0.133562i	$-0.957359\pi$
$263$	−99.9012	+	173.034i	−0.379853	+	0.657924i	0.611188	+	0.791485i	$0.290692\pi$
$264$	−12.1691	+	7.02581i	−0.0460949	+	0.0266129i
$265$		0			0
$266$	−134.905	+	334.284i	−0.507161	+	1.25671i
$267$	194.478			0.728381
$268$	6.49706	+	11.2532i	0.0242428	+	0.0419897i
$269$	0.129042	+	0.0745024i	0.000479710	+	0.000276960i	0.500240	−	0.865887i	$-0.333245\pi$
$269$	0.129042	+	0.0745024i	0.000479710	+	0.000276960i	−0.499760	+	0.866164i	$0.666579\pi$
$270$		0			0
$271$	69.2668	−	39.9912i	0.255597	−	0.147569i	−0.366727	−	0.930328i	$-0.619522\pi$
$271$	69.2668	−	39.9912i	0.255597	−	0.147569i	0.622324	+	0.782759i	$0.286189\pi$
$272$		−	222.091i		−	0.816510i
$273$	168.475	+	67.9901i	0.617123	+	0.249048i
$274$	−235.203			−0.858405
$275$		0			0
$276$	294.477	+	170.017i	1.06695	+	0.616002i
$277$	95.6786	−	165.720i	0.345410	−	0.598268i	−0.640018	−	0.768360i	$-0.721073\pi$
$277$	95.6786	−	165.720i	0.345410	−	0.598268i	0.985428	+	0.170092i	$0.0544065\pi$
$278$	−638.002	+	368.351i	−2.29497	+	1.32500i
$279$			12.0108i			0.0430496i
$280$		0			0
$281$	−442.495			−1.57471			−0.787357	−	0.616497i	$-0.788551\pi$
$281$	−442.495			−1.57471			−0.787357	+	0.616497i	$0.788551\pi$
$282$	154.386	+	267.405i	0.547469	+	0.948245i
$283$	370.302	+	213.794i	1.30849	+	0.755455i	0.981843	−	0.189693i	$-0.0607492\pi$
$283$	370.302	+	213.794i	1.30849	+	0.755455i	0.326643	+	0.945148i	$0.394083\pi$
$284$	44.3292	−	76.7804i	0.156089	−	0.270353i
$285$		0			0
$286$		−	203.147i		−	0.710304i
$287$	308.765	−	43.5195i	1.07584	−	0.151636i
$288$	137.601			0.477780
$289$	−3.98857	−	6.90841i	−0.0138013	−	0.0239045i
$290$		0			0
$291$	99.6565	−	172.610i	0.342462	−	0.593162i
$292$	−394.037	+	227.498i	−1.34944	+	0.779102i
$293$			231.320i			0.789488i	0.918791	+	0.394744i	$0.129167\pi$
$293$			231.320i			0.789488i	−0.918791	+	0.394744i	$0.870833\pi$
$294$	68.7873	+	239.171i	0.233971	+	0.813506i
$295$		0			0
$296$	−24.8745	−	43.0839i	−0.0840355	−	0.145554i
$297$	−20.8053	−	12.0119i	−0.0700514	−	0.0404442i
$298$	−423.758	+	733.970i	−1.42201	+	2.46299i
$299$	−554.018	+	319.863i	−1.85290	+	1.06977i
$300$		0			0
$301$	−43.3098	−	307.277i	−0.143886	−	1.02085i
$302$	−157.888			−0.522807
$303$	14.2439	+	24.6712i	0.0470096	+	0.0814230i
$304$	−201.495	−	116.333i	−0.662811	−	0.382674i
$305$		0			0
$306$	−127.712	+	73.7346i	−0.417359	+	0.240963i
$307$			136.146i			0.443474i	0.975107	+	0.221737i	$0.0711726\pi$
$307$			136.146i			0.443474i	−0.975107	+	0.221737i	$0.928827\pi$
$308$	117.237	−	91.6705i	0.380638	−	0.297631i
$309$	−256.403			−0.829785
$310$		0			0
$311$	−160.355	−	92.5809i	−0.515610	−	0.297688i	0.219527	−	0.975607i	$-0.429549\pi$
$311$	−160.355	−	92.5809i	−0.515610	−	0.297688i	−0.735137	+	0.677919i	$0.762882\pi$
$312$	22.7707	−	39.4399i	0.0729829	−	0.126410i
$313$	283.997	−	163.966i	0.907340	−	0.523853i	0.0277655	−	0.999614i	$-0.491161\pi$
$313$	283.997	−	163.966i	0.907340	−	0.523853i	0.879574	+	0.475762i	$0.157827\pi$
$314$			77.6489i			0.247289i
$315$		0			0
$316$	−549.604			−1.73925
$317$	235.116	+	407.233i	0.741691	+	1.28465i	0.951725	+	0.306952i	$0.0993091\pi$
$317$	235.116	+	407.233i	0.741691	+	1.28465i	−0.210034	+	0.977694i	$0.567358\pi$
$318$	−238.078	−	137.454i	−0.748673	−	0.432247i
$319$	41.9505	−	72.6603i	0.131506	−	0.227775i
$320$		0			0
$321$			225.026i			0.701017i
$322$	−812.636	−	327.950i	−2.52371	−	1.01848i
$323$	294.404			0.911468
$324$	−20.6928	−	35.8410i	−0.0638667	−	0.110620i
$325$		0			0
$326$	−127.112	+	220.165i	−0.389915	+	0.675352i
$327$	−101.770	+	58.7570i	−0.311223	+	0.179685i
$328$		−	78.1639i		−	0.238305i
$329$	−262.138	−	335.247i	−0.796773	−	1.01899i
$330$		0			0
$331$	288.752	+	500.133i	0.872362	+	1.51097i	0.859547	+	0.511057i	$0.170746\pi$
$331$	288.752	+	500.133i	0.872362	+	1.51097i	0.0128148	+	0.999918i	$0.495921\pi$
$332$	−355.631	−	205.324i	−1.07118	−	0.618444i
$333$	42.5276	−	73.6600i	0.127711	−	0.221201i
$334$	102.903	−	59.4108i	0.308091	−	0.177877i
$335$		0			0
$336$	−159.055	+	22.4183i	−0.473377	+	0.0667212i
$337$	388.265			1.15212			0.576061	−	0.817406i	$-0.304589\pi$
$337$	388.265			1.15212			0.576061	+	0.817406i	$0.304589\pi$
$338$	81.4198	+	141.023i	0.240887	+	0.417229i
$339$	−51.4543	−	29.7072i	−0.151783	−	0.0876317i
$340$		0			0
$341$	−16.0304	+	9.25515i	−0.0470099	+	0.0271412i
$342$			154.491i			0.451728i
$343$	−139.885	−	313.179i	−0.407828	−	0.913059i
$344$	−77.7872			−0.226126
$345$		0			0
$346$	−430.533	−	248.569i	−1.24432	−	0.718406i
$347$	−143.160	+	247.961i	−0.412566	+	0.714585i	−0.995170	−	0.0981715i	$-0.968701\pi$
$347$	−143.160	+	247.961i	−0.412566	+	0.714585i	0.582604	+	0.812756i	$0.302034\pi$
$348$	125.171	−	72.2676i	0.359687	−	0.207666i
$349$			141.867i			0.406497i	0.979127	+	0.203248i	$0.0651499\pi$
$349$			141.867i			0.406497i	−0.979127	+	0.203248i	$0.934850\pi$
$350$		0			0
$351$	77.8614			0.221827
$352$	106.030	+	183.650i	0.301222	+	0.521732i
$353$	−526.791	−	304.143i	−1.49232	−	0.861594i	−0.492363	−	0.870390i	$-0.663867\pi$
$353$	−526.791	−	304.143i	−1.49232	−	0.861594i	−0.999961	+	0.00879590i	$0.997200\pi$
$354$	−4.52714	+	7.84124i	−0.0127885	+	0.0221504i
$355$		0			0
$356$			516.317i			1.45033i
$357$	160.113	−	125.197i	0.448496	−	0.350691i
$358$	571.349			1.59595
$359$	−89.0088	−	154.168i	−0.247935	−	0.429436i	0.715018	−	0.699107i	$-0.246419\pi$
$359$	−89.0088	−	154.168i	−0.247935	−	0.429436i	−0.962953	+	0.269670i	$0.913085\pi$
$360$		0			0
$361$	−26.2886	+	45.5332i	−0.0728216	+	0.126131i
$362$	−132.529	+	76.5156i	−0.366102	+	0.211369i
$363$			172.554i			0.475356i
$364$	−180.506	+	447.282i	−0.495897	+	1.22880i
$365$		0			0
$366$	130.267	+	225.628i	0.355920	+	0.616471i
$367$	227.793	+	131.516i	0.620689	+	0.358355i	0.777137	−	0.629331i	$-0.216671\pi$
$367$	227.793	+	131.516i	0.620689	+	0.358355i	−0.156448	+	0.987686i	$0.550004\pi$
$368$	282.802	−	489.828i	0.768485	−	1.33105i
$369$	115.732	−	66.8179i	0.313637	−	0.181078i
$370$		0			0
$371$	351.361	+	141.796i	0.947064	+	0.382200i
$372$	−31.8875			−0.0857191
$373$	229.871	+	398.149i	0.616277	+	1.06742i	0.990159	+	0.139946i	$0.0446930\pi$
$373$	229.871	+	398.149i	0.616277	+	1.06742i	−0.373882	+	0.927476i	$0.621974\pi$
$374$	−196.821	−	113.635i	−0.526259	−	0.303836i
$375$		0			0
$376$	−92.3857	+	53.3389i	−0.245707	+	0.141859i
$377$			271.923i			0.721281i
$378$	65.6980	+	84.0206i	0.173804	+	0.222277i
$379$	270.666			0.714160			0.357080	−	0.934074i	$-0.383772\pi$
$379$	270.666			0.714160			0.357080	+	0.934074i	$0.383772\pi$
$380$		0			0
$381$	−184.094	−	106.287i	−0.483187	−	0.278968i
$382$	−104.399	+	180.824i	−0.273296	+	0.473362i
$383$	−268.825	+	155.206i	−0.701893	+	0.405238i	−0.808052	−	0.589111i	$-0.799478\pi$
$383$	−268.825	+	155.206i	−0.701893	+	0.405238i	0.106159	+	0.994349i	$0.466145\pi$
$384$			96.1674i			0.250436i
$385$		0			0
$386$	998.856			2.58771
$387$	−66.4959	−	115.174i	−0.171824	−	0.297608i
$388$	458.261	+	264.577i	1.18108	+	0.681899i
$389$	−62.5903	+	108.410i	−0.160901	+	0.278688i	−0.935192	−	0.354141i	$-0.884773\pi$
$389$	−62.5903	+	108.410i	−0.160901	+	0.278688i	0.774291	+	0.632829i	$0.218107\pi$
$390$		0			0
$391$			715.688i			1.83041i
$392$	−82.6310	+	23.7653i	−0.210793	+	0.0606258i
$393$	−272.364			−0.693037
$394$	83.6174	+	144.830i	0.212227	+	0.367588i
$395$		0			0
$396$	31.8904	−	55.2357i	0.0805312	−	0.139484i
$397$	19.7194	−	11.3850i	0.0496710	−	0.0286776i	−0.474959	−	0.880008i	$-0.657537\pi$
$397$	19.7194	−	11.3850i	0.0496710	−	0.0286776i	0.524630	+	0.851330i	$0.324204\pi$
$398$			367.939i			0.924469i
$399$	−29.7178	−	210.844i	−0.0744806	−	0.528430i
$400$		0			0
$401$	−293.273	−	507.963i	−0.731354	−	1.26674i	−0.956305	−	0.292372i	$-0.905556\pi$
$401$	−293.273	−	507.963i	−0.731354	−	1.26674i	0.224951	−	0.974370i	$-0.427778\pi$
$402$	−12.4291	−	7.17595i	−0.0309182	−	0.0178506i
$403$	29.9959	−	51.9545i	0.0744316	−	0.128919i
$404$	−65.4992	+	37.8160i	−0.162127	+	0.0936039i
$405$		0			0
$406$	−293.434	+	229.444i	−0.722743	+	0.565132i
$407$	131.081			0.322067
$408$	−25.4745	−	44.1232i	−0.0624376	−	0.108145i
$409$	96.5354	+	55.7348i	0.236028	+	0.136271i	0.613350	−	0.789811i	$-0.289822\pi$
$409$	96.5354	+	55.7348i	0.236028	+	0.136271i	−0.377322	+	0.926082i	$0.623155\pi$
$410$		0			0
$411$	120.316	−	69.4647i	0.292741	−	0.169014i
$412$		−	680.723i		−	1.65224i
$413$	4.67014	−	11.5723i	0.0113078	−	0.0280200i
$414$	−375.564			−0.907158
$415$		0			0
$416$	−595.209	−	343.644i	−1.43079	−	0.826068i
$417$	217.577	−	376.855i	0.521768	−	0.903728i
$418$	−206.193	+	119.046i	−0.493285	+	0.284798i
$419$			401.778i			0.958898i	0.877570	+	0.479449i	$0.159163\pi$
$419$			401.778i			0.958898i	−0.877570	+	0.479449i	$0.840837\pi$
$420$		0			0
$421$	−19.0197			−0.0451775			−0.0225888	−	0.999745i	$-0.507191\pi$
$421$	−19.0197			−0.0451775			−0.0225888	+	0.999745i	$0.507191\pi$
$422$	−247.405	−	428.519i	−0.586269	−	1.01545i
$423$	−157.951	−	91.1928i	−0.373406	−	0.215586i
$424$	47.4891	−	82.2536i	0.112003	−	0.193994i
$425$		0			0
$426$			97.9223i			0.229865i
$427$	−221.185	−	282.871i	−0.517997	−	0.662462i
$428$	−597.421			−1.39584
$429$	59.9973	+	103.918i	0.139854	+	0.242234i
$430$		0			0
$431$	118.794	−	205.757i	0.275624	−	0.477395i	−0.694668	−	0.719330i	$-0.744449\pi$
$431$	118.794	−	205.757i	0.275624	−	0.477395i	0.970292	+	0.241935i	$0.0777822\pi$
$432$	−59.6173	+	34.4201i	−0.138003	+	0.0796761i
$433$		−	650.720i		−	1.50282i	−0.659837	−	0.751409i	$-0.729375\pi$
$433$		−	650.720i		−	1.50282i	0.659837	−	0.751409i	$-0.270625\pi$
$434$	81.3744	−	11.4695i	0.187499	−	0.0264274i
$435$		0			0
$436$	−155.993	−	270.188i	−0.357783	−	0.619698i
$437$	649.317	+	374.884i	1.48585	+	0.857857i
$438$	251.269	−	435.211i	0.573674	−	0.993632i
$439$	335.581	−	193.748i	0.764421	−	0.441339i	−0.0664598	−	0.997789i	$-0.521170\pi$
$439$	335.581	−	193.748i	0.764421	−	0.441339i	0.830881	+	0.556450i	$0.187837\pi$
$440$		0			0
$441$	−105.824	−	102.031i	−0.239964	−	0.231362i
$442$	736.580			1.66647
$443$	54.0584	+	93.6319i	0.122028	+	0.211359i	0.920567	−	0.390584i	$-0.127727\pi$
$443$	54.0584	+	93.6319i	0.122028	+	0.211359i	−0.798539	+	0.601943i	$0.794394\pi$
$444$	195.559	+	112.906i	0.440449	+	0.254293i
$445$		0			0
$446$	−774.033	+	446.888i	−1.73550	+	1.00199i
$447$		−	500.610i		−	1.11993i
$448$	−79.6256	−	564.932i	−0.177736	−	1.26101i
$449$	659.524			1.46887			0.734436	−	0.678678i	$-0.237447\pi$
$449$	659.524			1.46887			0.734436	+	0.678678i	$0.237447\pi$
$450$		0			0
$451$	178.358	+	102.975i	0.395473	+	0.228326i
$452$	78.8693	−	136.606i	0.174490	−	0.302225i
$453$	80.7663	−	46.6305i	0.178292	−	0.102937i
$454$			767.943i			1.69150i
$455$		0			0
$456$	−53.3751			−0.117051
$457$	−344.514	−	596.716i	−0.753860	−	1.30572i	−0.945939	−	0.324344i	$-0.894857\pi$
$457$	−344.514	−	596.716i	−0.753860	−	1.30572i	0.192080	−	0.981379i	$-0.438477\pi$
$458$	−500.149	−	288.761i	−1.09203	−	0.630482i
$459$	43.5535	−	75.4368i	0.0948877	−	0.164350i
$460$		0			0
$461$			175.860i			0.381476i	0.981641	+	0.190738i	$0.0610880\pi$
$461$			175.860i			0.381476i	−0.981641	+	0.190738i	$0.938912\pi$
$462$	−61.5142	+	152.428i	−0.133148	+	0.329930i
$463$	−622.892			−1.34534			−0.672670	−	0.739943i	$-0.734853\pi$
$463$	−622.892			−1.34534			−0.672670	+	0.739943i	$0.734853\pi$
$464$	−120.209	−	208.207i	−0.259070	−	0.448723i
$465$		0			0
$466$	355.782	−	616.232i	0.763480	−	1.32239i
$467$	−447.999	+	258.652i	−0.959312	+	0.553859i	−0.895961	−	0.444132i	$-0.853512\pi$
$467$	−447.999	+	258.652i	−0.959312	+	0.553859i	−0.0633508	+	0.997991i	$0.520179\pi$
$468$			206.713i			0.441695i
$469$	18.3431	+	7.40261i	0.0391112	+	0.0157838i
$470$		0			0
$471$	−22.9328	−	39.7208i	−0.0486896	−	0.0843328i
$472$	−2.70907	−	1.56408i	−0.00573955	−	0.00331373i
$473$	102.479	−	177.499i	0.216657	−	0.375262i
$474$	525.706	−	303.516i	1.10908	−	0.640330i
$475$		0			0
$476$	332.384	+	425.082i	0.698285	+	0.893030i
$477$	162.383			0.340426
$478$	−420.315	−	728.006i	−0.879319	−	1.52303i
$479$	28.6151	+	16.5210i	0.0597393	+	0.0344905i	0.529572	−	0.848265i	$-0.322352\pi$
$479$	28.6151	+	16.5210i	0.0597393	+	0.0344905i	−0.469833	+	0.882755i	$0.655686\pi$
$480$		0			0
$481$	−367.918	+	212.417i	−0.764902	+	0.441616i
$482$		−	118.136i		−	0.245096i
$483$	512.555	−	72.2431i	1.06119	−	0.149572i
$484$	−458.113			−0.946514
$485$		0			0
$486$	39.5861	+	22.8550i	0.0814529	+	0.0470268i
$487$	−25.1665	+	43.5897i	−0.0516767	+	0.0895066i	−0.890707	−	0.454579i	$-0.849790\pi$
$487$	−25.1665	+	43.5897i	−0.0516767	+	0.0895066i	0.839030	+	0.544085i	$0.183123\pi$
$488$	−77.9523	+	45.0058i	−0.159738	+	0.0922250i
$489$		−	150.165i		−	0.307086i
$490$		0			0
$491$	498.996			1.01628			0.508142	−	0.861273i	$-0.330332\pi$
$491$	498.996			1.01628			0.508142	+	0.861273i	$0.330332\pi$
$492$	177.394	+	307.256i	0.360557	+	0.624504i
$493$	263.456	+	152.106i	0.534393	+	0.308532i
$494$	385.827	−	668.271i	0.781026	−	1.35278i
$495$		0			0
$496$			53.0411i			0.106938i
$497$	−18.8363	−	133.641i	−0.0378999	−	0.268895i
$498$	453.556			0.910755
$499$	−148.580	−	257.349i	−0.297756	−	0.515729i	0.677866	−	0.735185i	$-0.262905\pi$
$499$	−148.580	−	257.349i	−0.297756	−	0.515729i	−0.975622	+	0.219457i	$0.929572\pi$
$500$		0			0
$501$	−35.0927	+	60.7824i	−0.0700453	+	0.121322i
$502$	−586.761	+	338.766i	−1.16885	+	0.674833i
$503$			11.3379i			0.0225406i	0.999936	+	0.0112703i	$0.00358753\pi$
$503$			11.3379i			0.0225406i	−0.999936	+	0.0112703i	$0.996412\pi$
$504$	−29.0283	+	22.6980i	−0.0575957	+	0.0450357i
$505$		0			0
$506$	−289.396	−	501.249i	−0.571930	−	0.990611i
$507$	−83.2995	−	48.0930i	−0.164299	−	0.0948580i
$508$	282.180	−	488.750i	0.555472	−	0.962106i
$509$	245.448	−	141.710i	0.482217	−	0.278408i	−0.239123	−	0.970989i	$-0.576860\pi$
$509$	245.448	−	141.710i	0.482217	−	0.278408i	0.721340	+	0.692581i	$0.243527\pi$
$510$		0			0
$511$	−259.206	+	642.293i	−0.507252	+	1.25693i
$512$	700.644			1.36845
$513$	−45.6273	−	79.0289i	−0.0889422	−	0.154052i
$514$	289.336	+	167.048i	0.562911	+	0.324997i
$515$		0			0
$516$	305.775	−	176.539i	0.592588	−	0.342131i
$517$		−	281.080i		−	0.543676i
$518$	−539.663	−	217.788i	−1.04182	−	0.420440i
$519$	293.649			0.565797
$520$		0			0
$521$	−203.962	−	117.757i	−0.391482	−	0.226022i	0.291320	−	0.956626i	$-0.405905\pi$
$521$	−203.962	−	117.757i	−0.391482	−	0.226022i	−0.682802	+	0.730604i	$0.739239\pi$
$522$	−79.8190	+	138.250i	−0.152910	+	0.264848i
$523$	423.006	−	244.223i	0.808807	−	0.466965i	−0.0377341	−	0.999288i	$-0.512014\pi$
$523$	423.006	−	244.223i	0.808807	−	0.466965i	0.846542	+	0.532323i	$0.178681\pi$
$524$		−	723.096i		−	1.37995i
$525$		0			0
$526$	585.881			1.11384
$527$	−33.5578	−	58.1238i	−0.0636770	−	0.110292i
$528$	−91.8781	−	53.0458i	−0.174012	−	0.100466i
$529$	−646.832	+	1120.35i	−1.22274	+	2.11785i
$530$		0			0
$531$		−	5.34818i		−	0.0100719i
$532$	559.767	−	78.8975i	1.05219	−	0.148303i
$533$	−667.485			−1.25232
$534$	−285.134	−	493.866i	−0.533958	−	0.924843i
$535$		0			0
$536$	2.47922	−	4.29413i	0.00462540	−	0.00801144i
$537$	−292.270	+	168.742i	−0.544264	+	0.314231i
$538$		−	0.436927i		−	0.000812132i
$539$	54.6314	−	219.861i	0.101357	−	0.407904i
$540$		0			0
$541$	−344.329	−	596.395i	−0.636468	−	1.10239i	−0.986202	−	0.165546i	$-0.947062\pi$
$541$	−344.329	−	596.395i	−0.636468	−	1.10239i	0.349734	−	0.936849i	$-0.386272\pi$
$542$	−203.111	−	117.266i	−0.374744	−	0.216359i
$543$	45.1962	−	78.2821i	0.0832342	−	0.144166i
$544$	−665.887	+	384.450i	−1.22406	+	0.706709i
$545$		0			0
$546$	−74.3519	−	527.517i	−0.136176	−	0.966148i
$547$	−835.239			−1.52694			−0.763472	−	0.645840i	$-0.776507\pi$
$547$	−835.239			−1.52694			−0.763472	+	0.645840i	$0.776507\pi$
$548$	184.421	+	319.427i	0.336535	+	0.582896i
$549$	−133.274	−	76.9458i	−0.242758	−	0.140156i
$550$		0			0
$551$	276.000	−	159.349i	0.500908	−	0.289199i
$552$		−	129.753i		−	0.235060i
$553$	−659.079	+	515.352i	−1.19182	+	0.931921i
$554$	−561.118			−1.01285
$555$		0			0
$556$	1000.51	+	577.643i	1.79947	+	1.03893i
$557$	−29.8727	+	51.7410i	−0.0536314	+	0.0928923i	−0.891595	−	0.452834i	$-0.850413\pi$
$557$	−29.8727	+	51.7410i	−0.0536314	+	0.0928923i	0.837963	+	0.545727i	$0.183746\pi$
$558$	30.5009	−	17.6097i	0.0546612	−	0.0315587i
$559$			664.269i			1.18832i
$560$		0			0
$561$	134.243			0.239293
$562$	648.764	+	1123.69i	1.15439	+	1.99945i
$563$	337.650	+	194.943i	0.599734	+	0.346257i	0.768937	−	0.639325i	$-0.220786\pi$
$563$	337.650	+	194.943i	0.599734	+	0.346257i	−0.169203	+	0.985581i	$0.554119\pi$
$564$	242.107	−	419.342i	0.429268	−	0.743514i
$565$		0			0
$566$		−	1253.82i		−	2.21522i
$567$	−58.4220	−	23.5769i	−0.103037	−	0.0415819i
$568$	−33.8312			−0.0595619
$569$	169.757	+	294.029i	0.298343	+	0.516746i	0.975757	−	0.218856i	$-0.0702326\pi$
$569$	169.757	+	294.029i	0.298343	+	0.516746i	−0.677414	+	0.735602i	$0.736899\pi$
$570$		0			0
$571$	75.4413	−	130.668i	0.132121	−	0.228841i	−0.792373	−	0.610037i	$-0.791154\pi$
$571$	75.4413	−	130.668i	0.132121	−	0.228841i	0.924494	+	0.381196i	$0.124488\pi$
$572$	−275.892	+	159.286i	−0.482329	+	0.278473i
$573$		−	123.333i		−	0.215240i
$574$	−563.212	−	720.287i	−0.981206	−	1.25486i
$575$		0			0
$576$	−122.254	−	211.749i	−0.212246	−	0.367620i
$577$	−131.454	−	75.8951i	−0.227823	−	0.131534i	0.381744	−	0.924268i	$-0.375324\pi$
$577$	−131.454	−	75.8951i	−0.227823	−	0.131534i	−0.609568	+	0.792734i	$0.708657\pi$
$578$	−11.6957	+	20.2576i	−0.0202348	+	0.0350477i
$579$	−510.958	+	295.002i	−0.882484	+	0.509502i
$580$		0			0
$581$	−618.996	+	87.2457i	−1.06540	+	0.150165i
$582$	−584.446			−1.00420
$583$	125.127	+	216.726i	0.214626	+	0.371743i
$584$	150.361	+	86.8109i	0.257467	+	0.148649i
$585$		0			0
$586$	587.426	−	339.150i	1.00243	−	0.578755i
$587$		−	75.3253i		−	0.128322i	−0.997940	−	0.0641612i	$-0.979563\pi$
$587$		−	75.3253i		−	0.128322i	0.997940	−	0.0641612i	$-0.0204372\pi$
$588$	270.880	−	280.952i	0.460680	−	0.477809i
$589$	−70.3114			−0.119374
$590$		0			0
$591$	−85.5478	−	49.3910i	−0.144751	−	0.0835720i
$592$	187.806	−	325.290i	0.317240	−	0.549476i
$593$	−277.335	+	160.120i	−0.467682	+	0.270016i	−0.715269	−	0.698849i	$-0.753696\pi$
$593$	−277.335	+	160.120i	−0.467682	+	0.270016i	0.247587	+	0.968866i	$0.420362\pi$
$594$			70.4453i			0.118595i
$595$		0			0
$596$	1329.06			2.22997
$597$	−108.667	−	188.217i	−0.182022	−	0.315271i
$598$	1624.55	+	937.934i	2.71664	+	1.56845i
$599$	−27.5526	+	47.7225i	−0.0459976	+	0.0796703i	−0.888108	−	0.459636i	$-0.847980\pi$
$599$	−27.5526	+	47.7225i	−0.0459976	+	0.0796703i	0.842110	+	0.539306i	$0.181313\pi$
$600$		0			0
$601$			310.393i			0.516462i	0.966083	+	0.258231i	$0.0831395\pi$
$601$			310.393i			0.516462i	−0.966083	+	0.258231i	$0.916860\pi$
$602$	−716.816	+	560.498i	−1.19072	+	0.931060i
$603$	8.47737			0.0140587
$604$	123.799	+	214.426i	0.204965	+	0.355010i
$605$		0			0
$606$	41.7674	−	72.3433i	0.0689232	−	0.119378i
$607$	809.176	−	467.178i	1.33307	−	0.769651i	0.347305	−	0.937752i	$-0.387097\pi$
$607$	809.176	−	467.178i	1.33307	−	0.769651i	0.985770	+	0.168101i	$0.0537636\pi$
$608$			805.512i			1.32486i
$609$	82.3401	−	204.033i	0.135205	−	0.335029i
$610$		0			0
$611$	455.491	+	788.933i	0.745484	+	1.29122i
$612$	200.277	+	115.630i	0.327249	+	0.188937i
$613$	−135.611	+	234.885i	−0.221225	+	0.383172i	−0.955180	−	0.296025i	$-0.904339\pi$
$613$	−135.611	+	234.885i	−0.221225	+	0.383172i	0.733955	+	0.679198i	$0.237672\pi$
$614$	345.737	−	199.611i	0.563090	−	0.325100i
$615$		0			0
$616$	−52.6622	−	21.2525i	−0.0854907	−	0.0345009i
$617$	−837.065			−1.35667			−0.678335	−	0.734753i	$-0.737298\pi$
$617$	−837.065			−1.35667			−0.678335	+	0.734753i	$0.737298\pi$
$618$	375.926	+	651.124i	0.608295	+	1.05360i
$619$	−619.694	−	357.781i	−1.00112	−	0.577998i	−0.0925415	−	0.995709i	$-0.529499\pi$
$619$	−619.694	−	357.781i	−1.00112	−	0.577998i	−0.908580	+	0.417711i	$0.862832\pi$
$620$		0			0
$621$	192.117	−	110.919i	0.309367	−	0.178613i
$622$			542.951i			0.872911i
$623$	484.139	+	619.162i	0.777110	+	0.993839i
$624$	343.843			0.551031
$625$		0			0
$626$	−832.767	−	480.798i	−1.33030	−	0.768048i
$627$	70.3177	−	121.794i	0.112149	−	0.194249i
$628$	105.454	−	60.8841i	0.167921	−	0.0969491i
$629$			475.281i			0.755614i
$630$		0			0
$631$	1189.05			1.88439			0.942194	−	0.335067i	$-0.108759\pi$
$631$	1189.05			1.88439			0.942194	+	0.335067i	$0.108759\pi$
$632$	104.862	+	181.626i	0.165921	+	0.287383i
$633$	253.117	+	146.137i	0.399869	+	0.230865i
$634$	689.431	−	1194.13i	1.08743	−	1.88349i
$635$		0			0
$636$			431.109i			0.677845i
$637$	202.945	+	705.632i	0.318595	+	1.10774i
$638$	−246.023			−0.385616
$639$	−28.9203	−	50.0915i	−0.0452588	−	0.0783905i
$640$		0			0
$641$	−100.442	+	173.971i	−0.156696	+	0.271406i	−0.933675	−	0.358121i	$-0.883418\pi$
$641$	−100.442	+	173.971i	−0.156696	+	0.271406i	0.776979	+	0.629526i	$0.216751\pi$
$642$	571.443	−	329.923i	0.890099	−	0.513899i
$643$		−	844.066i		−	1.31270i	−0.754456	−	0.656350i	$-0.772099\pi$
$643$		−	844.066i		−	1.31270i	0.754456	−	0.656350i	$-0.227901\pi$
$644$	191.798	+	1360.78i	0.297822	+	2.11301i
$645$		0			0
$646$	−431.641	−	747.625i	−0.668175	−	1.15731i
$647$	−166.365	−	96.0508i	−0.257133	−	0.148456i	0.365893	−	0.930657i	$-0.380764\pi$
$647$	−166.365	−	96.0508i	−0.257133	−	0.148456i	−0.623026	+	0.782201i	$0.714097\pi$
$648$	−7.89618	+	13.6766i	−0.0121855	+	0.0211058i
$649$	7.13799	−	4.12112i	0.0109984	−	0.00634996i
$650$		0			0
$651$	−38.2391	+	29.9002i	−0.0587391	+	0.0459297i
$652$	398.672			0.611460
$653$	−352.318	−	610.233i	−0.539538	−	0.934507i	−0.998929	−	0.0462731i	$-0.985266\pi$
$653$	−352.318	−	610.233i	−0.539538	−	0.934507i	0.459391	−	0.888234i	$-0.348068\pi$
$654$	298.421	+	172.293i	0.456301	+	0.263445i
$655$		0			0
$656$	511.084	−	295.074i	0.779091	−	0.449808i
$657$			296.839i			0.451810i
$658$	−467.007	+	1157.21i	−0.709737	+	1.75868i
$659$	400.255			0.607367			0.303684	−	0.952773i	$-0.401783\pi$
$659$	400.255			0.607367			0.303684	+	0.952773i	$0.401783\pi$
$660$		0			0
$661$	−709.224	−	409.471i	−1.07296	−	0.619472i	−0.143969	−	0.989582i	$-0.545986\pi$
$661$	−709.224	−	409.471i	−1.07296	−	0.619472i	−0.928988	+	0.370111i	$0.879320\pi$
$662$	846.708	−	1466.54i	1.27901	−	2.21532i
$663$	−376.792	+	217.541i	−0.568314	+	0.328116i
$664$			156.699i			0.235992i
$665$		0			0
$666$	−249.408			−0.374486
$667$	387.373	+	670.949i	0.580769	+	1.00592i
$668$	−161.371	−	93.1673i	−0.241573	−	0.139472i
$669$	263.968	−	457.205i	0.394570	−	0.683416i
$670$		0			0
$671$		−	237.167i		−	0.353453i
$672$	342.547	+	438.081i	0.509743	+	0.651906i
$673$	−29.8403			−0.0443393			−0.0221696	−	0.999754i	$-0.507057\pi$
$673$	−29.8403			−0.0443393			−0.0221696	+	0.999754i	$0.507057\pi$
$674$	−569.256	−	985.980i	−0.844593	−	1.46288i
$675$		0			0
$676$	127.682	−	221.151i	0.188878	−	0.327147i
$677$	−1064.66	+	614.684i	−1.57262	+	0.907953i	−0.576774	+	0.816904i	$0.695689\pi$
$677$	−1064.66	+	614.684i	−1.57262	+	0.907953i	−0.995846	+	0.0910491i	$0.970978\pi$
$678$			174.221i			0.256963i
$679$	797.630	−	112.424i	1.17471	−	0.165572i
$680$		0			0
$681$	−226.804	−	392.836i	−0.333046	−	0.576852i
$682$	47.0060	+	27.1389i	0.0689237	+	0.0397931i
$683$	−349.893	+	606.033i	−0.512289	+	0.887310i	0.487610	+	0.873062i	$0.337869\pi$
$683$	−349.893	+	606.033i	−0.512289	+	0.887310i	−0.999898	+	0.0142484i	$0.995464\pi$
$684$	209.813	−	121.136i	0.306744	−	0.177099i
$685$		0			0
$686$	−590.210	+	814.399i	−0.860364	+	1.18717i
$687$	341.130			0.496550
$688$	−293.652	−	508.621i	−0.426820	−	0.739274i
$689$	−702.409	−	405.536i	−1.01946	−	0.588586i
$690$		0			0
$691$	585.332	−	337.941i	0.847079	−	0.489061i	−0.0125851	−	0.999921i	$-0.504006\pi$
$691$	585.332	−	337.941i	0.847079	−	0.489061i	0.859664	+	0.510859i	$0.170673\pi$
$692$			779.605i			1.12660i
$693$	−13.5508	−	96.1410i	−0.0195538	−	0.138732i
$694$	839.579			1.20977
$695$		0			0
$696$	−47.7641	−	27.5766i	−0.0686266	−	0.0396216i
$697$	−373.373	+	646.700i	−0.535685	+	0.927834i
$698$	360.265	−	207.999i	0.516139	−	0.297993i
$699$			420.306i			0.601296i
$700$		0			0
$701$	1206.42			1.72100			0.860499	−	0.509452i	$-0.170152\pi$
$701$	1206.42			1.72100			0.860499	+	0.509452i	$0.170152\pi$
$702$	−114.157	−	197.725i	−0.162616	−	0.281660i
$703$	431.205	+	248.956i	0.613378	+	0.354134i
$704$	188.409	−	326.334i	0.267626	−	0.463542i
$705$		0			0
$706$			1783.68i			2.52646i
$707$	−43.0867	+	106.766i	−0.0609430	+	0.151012i
$708$	14.1988			0.0200548
$709$	380.628	+	659.267i	0.536852	+	0.929855i	0.999071	+	0.0430891i	$0.0137199\pi$
$709$	380.628	+	659.267i	0.536852	+	0.929855i	−0.462219	+	0.886766i	$0.652947\pi$
$710$		0			0
$711$	−179.281	+	310.524i	−0.252153	+	0.436742i
$712$	170.626	−	98.5108i	0.239643	−	0.138358i
$713$		−	170.925i		−	0.239727i
$714$	−552.681	−	223.041i	−0.774062	−	0.312383i
$715$		0			0
$716$	−447.991	−	775.944i	−0.625686	−	1.08372i
$717$	430.018	+	248.271i	0.599746	+	0.346264i
$718$	−261.001	+	452.067i	−0.363511	+	0.629619i
$719$	700.739	−	404.572i	0.974602	−	0.562687i	0.0739657	−	0.997261i	$-0.476434\pi$
$719$	700.739	−	404.572i	0.974602	−	0.562687i	0.900636	+	0.434574i	$0.143101\pi$
$720$		0			0
$721$	−638.300	−	816.316i	−0.885298	−	1.13220i
$722$	154.172			0.213535
$723$	34.8904	+	60.4319i	0.0482577	+	0.0835849i
$724$	207.830	+	119.991i	0.287059	+	0.165733i
$725$		0			0
$726$	438.193	−	252.991i	0.603571	−	0.348472i
$727$		−	1106.13i		−	1.52150i	−0.649043	−	0.760751i	$-0.724831\pi$
$727$		−	1106.13i		−	1.52150i	0.649043	−	0.760751i	$-0.275169\pi$
$728$	182.252	−	25.6878i	0.250346	−	0.0352855i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	643.584	+	371.573i	0.880416	+	0.508308i
$732$	204.283	−	353.828i	0.279075	−	0.483372i
$733$	−144.898	+	83.6571i	−0.197678	+	0.114130i	−0.595572	−	0.803302i	$-0.703075\pi$
$733$	−144.898	+	83.6571i	−0.197678	+	0.114130i	0.397894	+	0.917432i	$0.369741\pi$
$734$		−	771.292i		−	1.05081i
$735$		0			0
$736$	−1958.18			−2.66057
$737$	6.53237	+	11.3144i	0.00886346	+	0.0153520i
$738$	−339.361	−	195.930i	−0.459839	−	0.265488i
$739$	−529.900	+	917.813i	−0.717050	+	1.24197i	0.245114	+	0.969494i	$0.421175\pi$
$739$	−529.900	+	917.813i	−0.717050	+	1.24197i	−0.962164	+	0.272472i	$0.912159\pi$
$740$		0			0
$741$			455.800i			0.615114i
$742$	−155.064	−	1100.16i	−0.208981	−	1.48269i
$743$	214.079			0.288128			0.144064	−	0.989568i	$-0.453983\pi$
$743$	214.079			0.288128			0.144064	+	0.989568i	$0.453983\pi$
$744$	6.08398	+	10.5378i	0.00817739	+	0.0141637i
$745$		0			0
$746$	674.052	−	1167.49i	0.903555	−	1.56500i
$747$	−232.014	+	133.953i	−0.310594	+	0.179321i
$748$			356.401i			0.476472i
$749$	−716.420	+	560.189i	−0.956502	+	0.747915i
$750$		0			0
$751$	−34.1405	−	59.1330i	−0.0454600	−	0.0787391i	0.842400	−	0.538853i	$-0.181142\pi$
$751$	−34.1405	−	59.1330i	−0.0454600	−	0.0787391i	−0.887860	+	0.460114i	$0.847809\pi$
$752$	−697.525	−	402.716i	−0.927560	−	0.535527i
$753$	200.102	−	346.587i	0.265740	−	0.460275i
$754$	690.535	−	398.680i	0.915829	−	0.528754i
$755$		0			0
$756$	62.5942	−	155.104i	0.0827966	−	0.205164i
$757$	205.800			0.271862			0.135931	−	0.990718i	$-0.456597\pi$
$757$	205.800			0.271862			0.135931	+	0.990718i	$0.456597\pi$
$758$	−396.838	−	687.344i	−0.523533	−	0.906786i
$759$	296.078	+	170.940i	0.390089	+	0.225218i
$760$		0			0
$761$	−830.500	+	479.489i	−1.09133	+	0.630078i	−0.933929	−	0.357457i	$-0.883644\pi$
$761$	−830.500	+	479.489i	−1.09133	+	0.630078i	−0.157397	+	0.987535i	$0.550310\pi$
$762$			623.330i			0.818019i
$763$	−440.416	−	177.735i	−0.577216	−	0.232943i
$764$	327.435			0.428580
$765$		0			0
$766$	788.276	+	455.112i	1.02908	+	0.594140i
$767$	−13.3566	+	23.1342i	−0.0174140	+	0.0301620i
$768$	−244.802	+	141.336i	−0.318752	+	0.184032i
$769$			96.6414i			0.125671i	0.998024	+	0.0628357i	$0.0200144\pi$
$769$			96.6414i			0.125671i	−0.998024	+	0.0628357i	$0.979986\pi$
$770$		0			0
$771$	−197.344			−0.255958
$772$	−783.198	−	1356.54i	−1.01450	−	1.75717i
$773$	−384.244	−	221.844i	−0.497082	−	0.286990i	0.230426	−	0.973090i	$-0.425988\pi$
$773$	−384.244	−	221.844i	−0.497082	−	0.286990i	−0.727508	+	0.686100i	$0.759321\pi$
$774$	−194.986	+	337.726i	−0.251920	+	0.436339i
$775$		0			0
$776$		−	201.920i		−	0.260206i
$777$	340.382	−	47.9759i	0.438073	−	0.0617450i
$778$	367.068			0.471809
$779$	391.151	+	677.494i	0.502120	+	0.869697i
$780$		0			0
$781$	44.5701	−	77.1976i	0.0570679	−	0.0988445i
$782$	1817.45	−	1049.31i	2.32411	−	1.34183i
$783$		−	94.2948i		−	0.120428i
$784$	−467.330	−	450.576i	−0.596084	−	0.574715i
$785$		0			0
$786$	399.326	+	691.654i	0.508049	+	0.879966i
$787$	−765.896	−	442.190i	−0.973184	−	0.561868i	−0.0729786	−	0.997334i	$-0.523250\pi$
$787$	−765.896	−	442.190i	−0.973184	−	0.561868i	−0.900205	+	0.435465i	$0.856584\pi$
$788$	131.128	−	227.120i	0.166406	−	0.288223i
$789$	−299.704	+	173.034i	−0.379853	+	0.219308i
$790$		0			0
$791$	−33.5130	−	237.770i	−0.0423679	−	0.300594i
$792$	−24.3381			−0.0307299
$793$	384.330	+	665.678i	0.484653	+	0.839443i
$794$	−57.8232	−	33.3842i	−0.0728252	−	0.0420457i
$795$		0			0
$796$	499.695	−	288.499i	0.627757	−	0.362436i
$797$		−	428.625i		−	0.537798i	−0.963168	−	0.268899i	$-0.913340\pi$
$797$		−	428.625i		−	0.537798i	0.963168	−	0.268899i	$-0.0866597\pi$
$798$	−491.856	+	384.595i	−0.616361	+	0.481949i
$799$	1019.16			1.27554
$800$		0			0
$801$	291.716	+	168.423i	0.364190	+	0.210265i
$802$	−859.965	+	1489.50i	−1.07228	+	1.85724i
$803$	−396.179	+	228.734i	−0.493373	+	0.284849i
$804$			22.5065i			0.0279931i
$805$		0			0
$806$	−175.914			−0.218256
$807$	0.129042	+	0.223507i	0.000159903	+	0.000276960i
$808$	24.9939	+	14.4302i	0.0309330	+	0.0178592i
$809$	−160.168	+	277.419i	−0.197982	+	0.342916i	−0.947874	−	0.318645i	$-0.896772\pi$
$809$	−160.168	+	277.419i	−0.197982	+	0.342916i	0.749892	+	0.661561i	$0.230106\pi$
$810$		0			0
$811$		−	347.835i		−	0.428896i	−0.976735	−	0.214448i	$-0.931205\pi$
$811$		−	347.835i		−	0.428896i	0.976735	−	0.214448i	$-0.0687952\pi$
$812$	541.685	+	218.604i	0.667100	+	0.269217i
$813$	138.534			0.170398
$814$	−192.185	−	332.874i	−0.236100	−	0.408937i
$815$		0			0
$816$	192.336	−	333.136i	0.235706	−	0.408255i
$817$	674.229	−	389.266i	0.825250	−	0.476458i
$818$		−	326.862i		−	0.399587i
$819$	193.831	+	247.888i	0.236668	+	0.302672i
$820$		0			0
$821$	112.413	+	194.706i	0.136922	+	0.237157i	0.926330	−	0.376713i	$-0.122946\pi$
$821$	112.413	+	194.706i	0.136922	+	0.237157i	−0.789408	+	0.613869i	$0.789612\pi$
$822$	−352.804	−	203.692i	−0.429202	−	0.247800i
$823$	424.260	−	734.840i	0.515504	−	0.892880i	−0.484334	−	0.874883i	$-0.660938\pi$
$823$	424.260	−	734.840i	0.515504	−	0.892880i	0.999838	−	0.0179964i	$-0.00572875\pi$
$824$	−224.957	+	129.879i	−0.273005	+	0.157620i
$825$		0			0
$826$	−36.2343	+	5.10712i	−0.0438672	+	0.00618295i
$827$	−395.332			−0.478031			−0.239016	−	0.971016i	$-0.576825\pi$
$827$	−395.332			−0.478031			−0.239016	+	0.971016i	$0.576825\pi$
$828$	294.477	+	510.050i	0.355649	+	0.616002i
$829$	−481.780	−	278.156i	−0.581158	−	0.335532i	0.180435	−	0.983587i	$-0.442249\pi$
$829$	−481.780	−	278.156i	−0.581158	−	0.335532i	−0.761593	+	0.648055i	$0.775583\pi$
$830$		0			0
$831$	287.036	−	165.720i	0.345410	−	0.199423i
$832$			1221.27i			1.46787i
$833$	797.181	+	198.085i	0.957000	+	0.237797i
$834$	−1276.00			−1.52998
$835$		0			0
$836$	323.349	+	186.686i	0.386782	+	0.223308i
$837$	−10.4017	+	18.0163i	−0.0124274	+	0.0215248i
$838$	1020.30	−	589.068i	1.21754	−	0.702945i
$839$		−	587.010i		−	0.699654i	−0.936814	−	0.349827i	$-0.886240\pi$
$839$		−	587.010i		−	0.699654i	0.936814	−	0.349827i	$-0.113760\pi$
$840$		0			0
$841$	−511.685			−0.608424
$842$	27.8858	+	48.2997i	0.0331186	+	0.0573631i
$843$	−663.742	−	383.212i	−0.787357	−	0.454581i
$844$	−387.978	+	671.998i	−0.459690	+	0.796207i
$845$		0			0
$846$			534.810i			0.632163i
$847$	−549.364	+	429.562i	−0.648599	+	0.507158i
$848$	717.099			0.845636
$849$	370.302	+	641.381i	0.436162	+	0.755455i
$850$		0			0
$851$	−605.206	+	1048.25i	−0.711170	+	1.23178i
$852$	132.987	−	76.7804i	0.156089	−	0.0901178i
$853$		−	1119.14i		−	1.31201i	−0.754757	−	0.656005i	$-0.772245\pi$
$853$		−	1119.14i		−	1.31201i	0.754757	−	0.656005i	$-0.227755\pi$
$854$	−394.047	+	976.420i	−0.461413	+	1.14335i
$855$		0			0
$856$	113.985	+	197.428i	0.133160	+	0.230640i
$857$	517.735	+	298.914i	0.604125	+	0.348792i	0.770663	−	0.637244i	$-0.219925\pi$
$857$	517.735	+	298.914i	0.604125	+	0.348792i	−0.166538	+	0.986035i	$0.553259\pi$
$858$	175.930	−	304.720i	0.205047	−	0.355152i
$859$	−604.204	+	348.837i	−0.703381	+	0.406097i	−0.808605	−	0.588351i	$-0.799777\pi$
$859$	−604.204	+	348.837i	−0.703381	+	0.406097i	0.105224	+	0.994448i	$0.466444\pi$
$860$		0			0
$861$	500.837	+	202.119i	0.581692	+	0.234749i
$862$	−696.680			−0.808213
$863$	295.718	+	512.198i	0.342662	+	0.593508i	0.984926	−	0.172975i	$-0.0553380\pi$
$863$	295.718	+	512.198i	0.342662	+	0.593508i	−0.642264	+	0.766484i	$0.722005\pi$
$864$	206.401	+	119.166i	0.238890	+	0.137923i
$865$		0			0
$866$	−1652.47	+	954.054i	−1.90816	+	1.10168i
$867$		−	13.8168i		−	0.0159364i
$868$	−79.3818	−	101.521i	−0.0914537	−	0.116959i
$869$	−552.591			−0.635893
$870$		0			0
$871$	−36.6700	−	21.1714i	−0.0421010	−	0.0243070i
$872$	−59.5256	+	103.101i	−0.0682633	+	0.118235i
$873$	298.969	−	172.610i	0.342462	−	0.197721i
$874$		−	2198.55i		−	2.51550i
$875$		0			0
$876$	−788.075			−0.899629
$877$	−452.691	−	784.084i	−0.516182	−	0.894053i	−0.999824	−	0.0187869i	$-0.994020\pi$
$877$	−452.691	−	784.084i	−0.516182	−	0.894053i	0.483642	−	0.875266i	$-0.339314\pi$
$878$	−984.025	−	568.127i	−1.12076	−	0.647070i
$879$	−200.329	+	346.980i	−0.227906	+	0.394744i
$880$		0			0
$881$			129.395i			0.146872i	0.997300	+	0.0734362i	$0.0233965\pi$
$881$			129.395i			0.146872i	−0.997300	+	0.0734362i	$0.976603\pi$
$882$	−103.947	+	418.328i	−0.117854	+	0.474294i
$883$	22.6993			0.0257070			0.0128535	−	0.999917i	$-0.495908\pi$
$883$	22.6993			0.0257070			0.0128535	+	0.999917i	$0.495908\pi$
$884$	−577.548	−	1000.34i	−0.653335	−	1.13161i
$885$		0			0
$886$	158.516	−	274.557i	0.178912	−	0.309884i
$887$	303.675	−	175.327i	0.342362	−	0.197663i	−0.318954	−	0.947770i	$-0.603332\pi$
$887$	303.675	−	175.327i	0.342362	−	0.197663i	0.661316	+	0.750107i	$0.269998\pi$
$888$		−	86.1679i		−	0.0970359i
$889$	−119.903	−	850.698i	−0.134874	−	0.956915i
$890$		0			0
$891$	−20.8053	−	36.0358i	−0.0233505	−	0.0404442i
$892$	1213.83	+	700.805i	1.36080	+	0.785656i
$893$	533.842	−	924.641i	0.597807	−	1.03543i
$894$	−1271.27	+	733.970i	−1.42201	+	0.820996i
$895$		0			0
$896$	−306.170	+	239.403i	−0.341707	+	0.267190i
$897$	−1108.04			−1.23527
$898$	−966.962	−	1674.83i	−1.07680	−	1.86506i
$899$	−62.9200	−	36.3269i	−0.0699889	−	0.0404081i
$900$		0			0
$901$	−785.816	+	453.691i	−0.872160	+	0.503542i
$902$		−	603.909i		−	0.669522i
$903$	201.145	−	498.423i	0.222752	−	0.551963i
$904$	−60.1915			−0.0665835
$905$		0			0
$906$	−236.831	−	136.735i	−0.261403	−	0.150921i
$907$	−172.405	+	298.615i	−0.190083	+	0.329233i	−0.945278	−	0.326267i	$-0.894209\pi$
$907$	−172.405	+	298.615i	−0.190083	+	0.329233i	0.755195	+	0.655501i	$0.227542\pi$
$908$	1042.94	−	602.140i	1.14861	−	0.663150i
$909$			49.3423i			0.0542820i
$910$		0			0
$911$	350.988			0.385278			0.192639	−	0.981270i	$-0.438295\pi$
$911$	350.988			0.385278			0.192639	+	0.981270i	$0.438295\pi$
$912$	−201.495	−	348.999i	−0.220937	−	0.382674i
$913$	−357.563	−	206.439i	−0.391636	−	0.226111i
$914$	−1010.22	+	1749.75i	−1.10527	+	1.91439i
$915$		0			0
$916$			905.663i			0.988715i
$917$	−678.031	−	867.128i	−0.739402	−	0.945614i
$918$	−255.424			−0.278240
$919$	−624.787	−	1082.16i	−0.679855	−	1.17754i	−0.975024	−	0.222098i	$-0.928709\pi$
$919$	−624.787	−	1082.16i	−0.679855	−	1.17754i	0.295169	−	0.955445i	$-0.404624\pi$
$920$		0			0
$921$	−117.906	+	204.220i	−0.128020	+	0.221737i
$922$	446.588	−	257.838i	0.484369	−	0.279651i
$923$			288.903i			0.313005i
$924$	255.244	−	35.9759i	0.276238	−	0.0389349i
$925$		0			0
$926$	913.255	+	1581.80i	0.986236	+	1.70821i
$927$	−384.605	−	222.052i	−0.414892	−	0.239538i
$928$	−416.174	+	720.834i	−0.448463	+	0.776761i
$929$	102.213	−	59.0125i	0.110024	−	0.0635226i	−0.443978	−	0.896038i	$-0.646433\pi$
$929$	102.213	−	59.0125i	0.110024	−	0.0635226i	0.554002	+	0.832515i	$0.313100\pi$
$930$		0			0
$931$	597.286	−	619.494i	0.641553	−	0.665407i
$932$	−1115.87			−1.19728
$933$	−160.355	−	277.743i	−0.171870	−	0.297688i
$934$	1313.67	+	758.447i	1.40650	+	0.812041i
$935$		0			0
$936$	68.3120	−	39.4399i	0.0729829	−	0.0421367i
$937$		−	64.6493i		−	0.0689961i	−0.999405	−	0.0344980i	$-0.989017\pi$
$937$		−	64.6493i		−	0.0689961i	0.999405	−	0.0344980i	$-0.0109832\pi$
$938$	−8.09527	−	57.4348i	−0.00863035	−	0.0612311i
$939$	567.995			0.604893
$940$		0			0
$941$	−1102.55	−	636.557i	−1.17168	−	0.676468i	−0.217603	−	0.976037i	$-0.569824\pi$
$941$	−1102.55	−	636.557i	−1.17168	−	0.676468i	−0.954075	+	0.299569i	$0.903157\pi$
$942$	−67.2459	+	116.473i	−0.0713863	+	0.123645i
$943$	−1646.97	+	950.878i	−1.74652	+	1.00835i
$944$		−	23.6181i		−	0.0250191i
$945$		0			0
$946$	−600.999			−0.635305
$947$	587.133	+	1016.94i	0.619993	+	1.07386i	0.989486	+	0.144626i	$0.0461978\pi$
$947$	587.133	+	1016.94i	0.619993	+	1.07386i	−0.369494	+	0.929233i	$0.620469\pi$
$948$	−824.406	−	475.971i	−0.869627	−	0.502079i
$949$	741.327	−	1284.02i	0.781166	−	1.35302i
$950$		0			0
$951$			814.466i			0.856431i
$952$	77.0585	−	190.945i	0.0809438	−	0.200573i
$953$	−734.690			−0.770923			−0.385462	−	0.922724i	$-0.625958\pi$
$953$	−734.690			−0.770923			−0.385462	+	0.922724i	$0.625958\pi$
$954$	−238.078	−	412.363i	−0.249558	−	0.432247i
$955$		0			0
$956$	−659.133	+	1141.65i	−0.689469	+	1.19420i
$957$	125.851	−	72.6603i	0.131506	−	0.0759251i
$958$		−	96.8889i		−	0.101137i
$959$	520.676	+	210.126i	0.542936	+	0.219109i
$960$		0			0
$961$	−472.486	−	818.369i	−0.491660	−	0.851581i
$962$	1078.85	+	622.872i	1.12146	+	0.647476i
$963$	−194.879	+	337.540i	−0.202366	+	0.350508i
$964$	−160.440	+	92.6301i	−0.166432	+	0.0960893i
$965$		0			0
$966$	−934.941	−	1195.69i	−0.967848	−	1.23777i
$967$	686.621			0.710053			0.355027	−	0.934856i	$-0.384472\pi$
$967$	686.621			0.710053			0.355027	+	0.934856i	$0.384472\pi$
$968$	87.4057	+	151.391i	0.0902951	+	0.156396i
$969$	441.606	+	254.962i	0.455734	+	0.263118i
$970$		0			0
$971$	687.799	−	397.101i	0.708341	−	0.408961i	−0.102105	−	0.994774i	$-0.532558\pi$
$971$	687.799	−	397.101i	0.708341	−	0.408961i	0.810447	+	0.585813i	$0.199225\pi$
$972$		−	71.6821i		−	0.0737470i
$973$	1741.44	−	245.451i	1.78977	−	0.252262i
$974$	147.592			0.151532
$975$		0			0
$976$	−588.551	−	339.800i	−0.603024	−	0.348156i
$977$	−376.672	+	652.415i	−0.385540	+	0.667774i	−0.991844	−	0.127459i	$-0.959318\pi$
$977$	−376.672	+	652.415i	−0.385540	+	0.667774i	0.606304	+	0.795233i	$0.292651\pi$
$978$	−381.337	+	220.165i	−0.389915	+	0.225117i
$979$			519.123i			0.530258i
$980$		0			0
$981$	−203.540			−0.207482
$982$	−731.604	−	1267.17i	−0.745014	−	1.29040i
$983$	166.533	+	96.1480i	0.169413	+	0.0978108i	0.582309	−	0.812967i	$-0.302149\pi$
$983$	166.533	+	96.1480i	0.169413	+	0.0978108i	−0.412896	+	0.910778i	$0.635483\pi$
$984$	67.6920	−	117.246i	0.0687926	−	0.119152i
$985$		0			0
$986$		−	892.043i		−	0.904709i
$987$	−102.876	−	729.888i	−0.104231	−	0.739502i
$988$	−1210.10			−1.22480
$989$	946.296	+	1639.03i	0.956821	+	1.65726i
$990$		0			0
$991$	5.63896	−	9.76696i	0.00569017	−	0.00985567i	−0.863166	−	0.504920i	$-0.831522\pi$
$991$	5.63896	−	9.76696i	0.00569017	−	0.00985567i	0.868856	+	0.495064i	$0.164855\pi$
$992$	159.031	−	91.8166i	0.160314	−	0.0925571i
$993$			1000.27i			1.00732i
$994$	−311.757	+	243.771i	−0.313639	+	0.245243i
$995$		0			0
$996$	−355.631	−	615.971i	−0.357059	−	0.618444i
$997$	−899.370	−	519.252i	−0.902077	−	0.520814i	−0.0242032	−	0.999707i	$-0.507705\pi$
$997$	−899.370	−	519.252i	−0.902077	−	0.520814i	−0.877873	+	0.478893i	$0.841038\pi$
$998$	−435.682	+	754.624i	−0.436556	+	0.756136i
$999$	127.583	−	73.6600i	0.127711	−	0.0737338i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.o.q.451.2		16
5.2	odd	4		105.3.r.a.94.14	yes	32
5.3	odd	4		105.3.r.a.94.3	yes	32
5.4	even	2		525.3.o.p.451.7		16
7.5	odd	6	inner	525.3.o.q.376.2		16
15.2	even	4		315.3.bi.e.199.3		32
15.8	even	4		315.3.bi.e.199.14		32
35.3	even	12		735.3.e.a.244.23		32
35.12	even	12		105.3.r.a.19.3	✓	32
35.17	even	12		735.3.e.a.244.16		32
35.18	odd	12		735.3.e.a.244.15		32
35.19	odd	6		525.3.o.p.376.7		16
35.32	odd	12		735.3.e.a.244.24		32
35.33	even	12		105.3.r.a.19.14	yes	32
105.47	odd	12		315.3.bi.e.19.14		32
105.68	odd	12		315.3.bi.e.19.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.r.a.19.3	✓	32	35.12	even	12
105.3.r.a.19.14	yes	32	35.33	even	12
105.3.r.a.94.3	yes	32	5.3	odd	4
105.3.r.a.94.14	yes	32	5.2	odd	4
315.3.bi.e.19.3		32	105.68	odd	12
315.3.bi.e.19.14		32	105.47	odd	12
315.3.bi.e.199.3		32	15.2	even	4
315.3.bi.e.199.14		32	15.8	even	4
525.3.o.p.376.7		16	35.19	odd	6
525.3.o.p.451.7		16	5.4	even	2
525.3.o.q.376.2		16	7.5	odd	6	inner
525.3.o.q.451.2		16	1.1	even	1	trivial
735.3.e.a.244.15		32	35.18	odd	12
735.3.e.a.244.16		32	35.17	even	12
735.3.e.a.244.23		32	35.3	even	12
735.3.e.a.244.24		32	35.32	odd	12

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.46615 - 2.53945i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-2.29920 + 3.98234i) q^{4} -5.07890i q^{6} +(0.976973 + 6.93149i) q^{7} +1.75471 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.46615 - 2.53945i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-2.29920 + 3.98234i) q^{4} -5.07890i q^{6} +(0.976973 + 6.93149i) q^{7} +1.75471 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.31170 + 4.00398i) q^{11} +(-6.89761 + 3.98234i) q^{12} -14.9844i q^{13} +(16.1698 - 12.6436i) q^{14} +(6.62414 + 11.4734i) q^{16} +(-14.5178 - 8.38187i) q^{17} +(4.39846 - 7.61835i) q^{18} +(-15.2091 + 8.78098i) q^{19} +(-4.53739 + 11.2433i) q^{21} +13.5572 q^{22} +(-21.3463 - 36.9729i) q^{23} +(2.63206 + 1.51962i) q^{24} +(-38.0522 + 21.9694i) q^{26} +5.19615i q^{27} +(-29.8498 - 12.0463i) q^{28} -18.1470 q^{29} +(3.46723 + 2.00181i) q^{31} +(22.9334 - 39.7218i) q^{32} +(-6.93509 + 4.00398i) q^{33} +49.1564i q^{34} -13.7952 q^{36} +(-14.1759 - 24.5533i) q^{37} +(44.5977 + 25.7485i) q^{38} +(12.9769 - 22.4766i) q^{39} -44.5453i q^{41} +(35.2043 - 4.96195i) q^{42} -44.3306 q^{43} +(-10.6301 - 18.4119i) q^{44} +(-62.5939 + 108.416i) q^{46} +(-52.6502 + 30.3976i) q^{47} +22.9467i q^{48} +(-47.0910 + 13.5438i) q^{49} +(-14.5178 - 25.1456i) q^{51} +(59.6730 + 34.4522i) q^{52} +(27.0638 - 46.8759i) q^{53} +(13.1954 - 7.61835i) q^{54} +(1.71430 + 12.1627i) q^{56} -30.4182 q^{57} +(26.6063 + 46.0835i) q^{58} +(-1.54389 - 0.891363i) q^{59} +(-44.4247 + 25.6486i) q^{61} -11.7398i q^{62} +(-16.5431 + 12.9355i) q^{63} -81.5023 q^{64} +(20.3358 + 11.7409i) q^{66} +(1.41289 - 2.44721i) q^{67} +(66.7588 - 38.5432i) q^{68} -73.9459i q^{69} -19.2802 q^{71} +(2.63206 + 4.55886i) q^{72} +(85.6900 + 49.4732i) q^{73} +(-41.5680 + 71.9979i) q^{74} -80.7571i q^{76} +(-30.0120 - 12.1117i) q^{77} -76.1044 q^{78} +(59.7603 + 103.508i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-113.120 + 65.3102i) q^{82} +89.3021i q^{83} +(-34.3423 - 43.9201i) q^{84} +(64.9954 + 112.575i) q^{86} +(-27.2206 - 15.7158i) q^{87} +(-4.05635 + 7.02581i) q^{88} +(97.2388 - 56.1409i) q^{89} +(103.864 - 14.6394i) q^{91} +196.318 q^{92} +(3.46723 + 6.00542i) q^{93} +(154.386 + 89.1350i) q^{94} +(68.8003 - 39.7218i) q^{96} -115.073i q^{97} +(103.436 + 99.7281i) q^{98} -13.8702 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 24 q^{3} - 16 q^{4} + 6 q^{7} + 24 q^{9}+O(q^{10}) \) 16 * q + 24 * q^3 - 16 * q^4 + 6 * q^7 + 24 * q^9	\( 16 q + 24 q^{3} - 16 q^{4} + 6 q^{7} + 24 q^{9} - 14 q^{11} - 48 q^{12} - 30 q^{14} - 20 q^{16} + 6 q^{17} + 30 q^{19} + 6 q^{21} - 36 q^{22} - 18 q^{23} - 48 q^{26} - 168 q^{28} + 44 q^{29} + 42 q^{31} + 150 q^{32} - 42 q^{33} - 96 q^{36} + 96 q^{37} + 204 q^{38} - 18 q^{39} - 78 q^{42} - 160 q^{44} - 30 q^{46} - 138 q^{47} - 178 q^{49} + 6 q^{51} + 126 q^{52} + 150 q^{53} - 234 q^{56} + 60 q^{57} - 90 q^{58} + 402 q^{59} + 168 q^{61} + 200 q^{64} - 54 q^{66} + 174 q^{67} - 234 q^{68} + 172 q^{71} + 336 q^{73} - 450 q^{74} - 372 q^{77} - 96 q^{78} + 10 q^{79} - 72 q^{81} - 690 q^{82} - 390 q^{84} + 72 q^{86} + 66 q^{87} + 492 q^{88} - 12 q^{89} - 112 q^{91} + 204 q^{92} + 42 q^{93} + 462 q^{94} + 450 q^{96} - 198 q^{98} - 84 q^{99}+O(q^{100}) \) 16 * q + 24 * q^3 - 16 * q^4 + 6 * q^7 + 24 * q^9 - 14 * q^11 - 48 * q^12 - 30 * q^14 - 20 * q^16 + 6 * q^17 + 30 * q^19 + 6 * q^21 - 36 * q^22 - 18 * q^23 - 48 * q^26 - 168 * q^28 + 44 * q^29 + 42 * q^31 + 150 * q^32 - 42 * q^33 - 96 * q^36 + 96 * q^37 + 204 * q^38 - 18 * q^39 - 78 * q^42 - 160 * q^44 - 30 * q^46 - 138 * q^47 - 178 * q^49 + 6 * q^51 + 126 * q^52 + 150 * q^53 - 234 * q^56 + 60 * q^57 - 90 * q^58 + 402 * q^59 + 168 * q^61 + 200 * q^64 - 54 * q^66 + 174 * q^67 - 234 * q^68 + 172 * q^71 + 336 * q^73 - 450 * q^74 - 372 * q^77 - 96 * q^78 + 10 * q^79 - 72 * q^81 - 690 * q^82 - 390 * q^84 + 72 * q^86 + 66 * q^87 + 492 * q^88 - 12 * q^89 - 112 * q^91 + 204 * q^92 + 42 * q^93 + 462 * q^94 + 450 * q^96 - 198 * q^98 - 84 * q^99

Introduction

L-functions

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