LMFDB - Embedded newform 245.4.e.a.116.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(116,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("245.116");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.4554679514$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			116.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	245.116
Dual form			245.4.e.a.226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 2.59808i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.50000 + 4.33013i) q^{5} +6.00000 q^{6} -21.0000 q^{8} +(11.5000 + 19.9186i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 2.59808i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.50000 + 4.33013i) q^{5} +6.00000 q^{6} -21.0000 q^{8} +(11.5000 + 19.9186i) q^{9} +(7.50000 - 12.9904i) q^{10} +(22.5000 - 38.9711i) q^{11} +(-1.00000 - 1.73205i) q^{12} -59.0000 q^{13} -10.0000 q^{15} +(35.5000 + 61.4878i) q^{16} +(-27.0000 + 46.7654i) q^{17} +(34.5000 - 59.7558i) q^{18} +(-60.5000 - 104.789i) q^{19} -5.00000 q^{20} -135.000 q^{22} +(-34.5000 - 59.7558i) q^{23} +(21.0000 - 36.3731i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(88.5000 + 153.286i) q^{26} -100.000 q^{27} -162.000 q^{29} +(15.0000 + 25.9808i) q^{30} +(-44.0000 + 76.2102i) q^{31} +(22.5000 - 38.9711i) q^{32} +(45.0000 + 77.9423i) q^{33} +162.000 q^{34} -23.0000 q^{36} +(129.500 + 224.301i) q^{37} +(-181.500 + 314.367i) q^{38} +(59.0000 - 102.191i) q^{39} +(-52.5000 - 90.9327i) q^{40} -195.000 q^{41} -286.000 q^{43} +(22.5000 + 38.9711i) q^{44} +(-57.5000 + 99.5929i) q^{45} +(-103.500 + 179.267i) q^{46} +(22.5000 + 38.9711i) q^{47} -142.000 q^{48} +75.0000 q^{50} +(-54.0000 - 93.5307i) q^{51} +(29.5000 - 51.0955i) q^{52} +(-298.500 + 517.017i) q^{53} +(150.000 + 259.808i) q^{54} +225.000 q^{55} +242.000 q^{57} +(243.000 + 420.888i) q^{58} +(-180.000 + 311.769i) q^{59} +(5.00000 - 8.66025i) q^{60} +(196.000 + 339.482i) q^{61} +264.000 q^{62} +433.000 q^{64} +(-147.500 - 255.477i) q^{65} +(135.000 - 233.827i) q^{66} +(140.000 - 242.487i) q^{67} +(-27.0000 - 46.7654i) q^{68} +138.000 q^{69} +48.0000 q^{71} +(-241.500 - 418.290i) q^{72} +(334.000 - 578.505i) q^{73} +(388.500 - 672.902i) q^{74} +(-25.0000 - 43.3013i) q^{75} +121.000 q^{76} -354.000 q^{78} +(-391.000 - 677.232i) q^{79} +(-177.500 + 307.439i) q^{80} +(-210.500 + 364.597i) q^{81} +(292.500 + 506.625i) q^{82} -768.000 q^{83} -270.000 q^{85} +(429.000 + 743.050i) q^{86} +(162.000 - 280.592i) q^{87} +(-472.500 + 818.394i) q^{88} +(-597.000 - 1034.03i) q^{89} +345.000 q^{90} +69.0000 q^{92} +(-88.0000 - 152.420i) q^{93} +(67.5000 - 116.913i) q^{94} +(302.500 - 523.945i) q^{95} +(45.0000 + 77.9423i) q^{96} -902.000 q^{97} +1035.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} - 2 q^{3} - q^{4} + 5 q^{5} + 12 q^{6} - 42 q^{8} + 23 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 - 2 * q^3 - q^4 + 5 * q^5 + 12 * q^6 - 42 * q^8 + 23 * q^9	\( 2 q - 3 q^{2} - 2 q^{3} - q^{4} + 5 q^{5} + 12 q^{6} - 42 q^{8} + 23 q^{9} + 15 q^{10} + 45 q^{11} - 2 q^{12} - 118 q^{13} - 20 q^{15} + 71 q^{16} - 54 q^{17} + 69 q^{18} - 121 q^{19} - 10 q^{20} - 270 q^{22} - 69 q^{23} + 42 q^{24} - 25 q^{25} + 177 q^{26} - 200 q^{27} - 324 q^{29} + 30 q^{30} - 88 q^{31} + 45 q^{32} + 90 q^{33} + 324 q^{34} - 46 q^{36} + 259 q^{37} - 363 q^{38} + 118 q^{39} - 105 q^{40} - 390 q^{41} - 572 q^{43} + 45 q^{44} - 115 q^{45} - 207 q^{46} + 45 q^{47} - 284 q^{48} + 150 q^{50} - 108 q^{51} + 59 q^{52} - 597 q^{53} + 300 q^{54} + 450 q^{55} + 484 q^{57} + 486 q^{58} - 360 q^{59} + 10 q^{60} + 392 q^{61} + 528 q^{62} + 866 q^{64} - 295 q^{65} + 270 q^{66} + 280 q^{67} - 54 q^{68} + 276 q^{69} + 96 q^{71} - 483 q^{72} + 668 q^{73} + 777 q^{74} - 50 q^{75} + 242 q^{76} - 708 q^{78} - 782 q^{79} - 355 q^{80} - 421 q^{81} + 585 q^{82} - 1536 q^{83} - 540 q^{85} + 858 q^{86} + 324 q^{87} - 945 q^{88} - 1194 q^{89} + 690 q^{90} + 138 q^{92} - 176 q^{93} + 135 q^{94} + 605 q^{95} + 90 q^{96} - 1804 q^{97} + 2070 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 - 2 * q^3 - q^4 + 5 * q^5 + 12 * q^6 - 42 * q^8 + 23 * q^9 + 15 * q^10 + 45 * q^11 - 2 * q^12 - 118 * q^13 - 20 * q^15 + 71 * q^16 - 54 * q^17 + 69 * q^18 - 121 * q^19 - 10 * q^20 - 270 * q^22 - 69 * q^23 + 42 * q^24 - 25 * q^25 + 177 * q^26 - 200 * q^27 - 324 * q^29 + 30 * q^30 - 88 * q^31 + 45 * q^32 + 90 * q^33 + 324 * q^34 - 46 * q^36 + 259 * q^37 - 363 * q^38 + 118 * q^39 - 105 * q^40 - 390 * q^41 - 572 * q^43 + 45 * q^44 - 115 * q^45 - 207 * q^46 + 45 * q^47 - 284 * q^48 + 150 * q^50 - 108 * q^51 + 59 * q^52 - 597 * q^53 + 300 * q^54 + 450 * q^55 + 484 * q^57 + 486 * q^58 - 360 * q^59 + 10 * q^60 + 392 * q^61 + 528 * q^62 + 866 * q^64 - 295 * q^65 + 270 * q^66 + 280 * q^67 - 54 * q^68 + 276 * q^69 + 96 * q^71 - 483 * q^72 + 668 * q^73 + 777 * q^74 - 50 * q^75 + 242 * q^76 - 708 * q^78 - 782 * q^79 - 355 * q^80 - 421 * q^81 + 585 * q^82 - 1536 * q^83 - 540 * q^85 + 858 * q^86 + 324 * q^87 - 945 * q^88 - 1194 * q^89 + 690 * q^90 + 138 * q^92 - 176 * q^93 + 135 * q^94 + 605 * q^95 + 90 * q^96 - 1804 * q^97 + 2070 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.50000	−	2.59808i	−0.530330	−	0.918559i	−0.999374	−	0.0353837i	$-0.988735\pi$
$2$	−1.50000	−	2.59808i	−0.530330	−	0.918559i	0.469044	−	0.883175i	$-0.344599\pi$
$3$	−1.00000	+	1.73205i	−0.192450	+	0.333333i	−0.946062	−	0.323987i	$-0.894977\pi$
$3$	−1.00000	+	1.73205i	−0.192450	+	0.333333i	0.753612	+	0.657320i	$0.228310\pi$
$4$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$	6.00000			0.408248
$7$		0			0
$7$		0			0
$8$	−21.0000			−0.928078
$9$	11.5000	+	19.9186i	0.425926	+	0.737725i
$10$	7.50000	−	12.9904i	0.237171	−	0.410792i
$11$	22.5000	−	38.9711i	0.616728	−	1.06820i	−0.373351	−	0.927690i	$-0.621791\pi$
$11$	22.5000	−	38.9711i	0.616728	−	1.06820i	0.990079	−	0.140514i	$-0.0448754\pi$
$12$	−1.00000	−	1.73205i	−0.0240563	−	0.0416667i
$13$	−59.0000			−1.25874			−0.629371	−	0.777105i	$-0.716688\pi$
$13$	−59.0000			−1.25874			−0.629371	+	0.777105i	$0.716688\pi$
$14$		0			0
$15$	−10.0000			−0.172133
$16$	35.5000	+	61.4878i	0.554688	+	0.960747i
$17$	−27.0000	+	46.7654i	−0.385204	+	0.667192i	−0.991797	−	0.127820i	$-0.959202\pi$
$17$	−27.0000	+	46.7654i	−0.385204	+	0.667192i	0.606594	+	0.795012i	$0.292535\pi$
$18$	34.5000	−	59.7558i	0.451763	−	0.782476i
$19$	−60.5000	−	104.789i	−0.730508	−	1.26528i	−0.956666	−	0.291186i	$-0.905950\pi$
$19$	−60.5000	−	104.789i	−0.730508	−	1.26528i	0.226158	−	0.974091i	$-0.427383\pi$
$20$	−5.00000			−0.0559017
$21$		0			0
$22$	−135.000			−1.30828
$23$	−34.5000	−	59.7558i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−34.5000	−	59.7558i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$	21.0000	−	36.3731i	0.178609	−	0.309359i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	88.5000	+	153.286i	0.667549	+	1.15623i
$27$	−100.000			−0.712778
$28$		0			0
$29$	−162.000			−1.03733			−0.518666	−	0.854977i	$-0.673571\pi$
$29$	−162.000			−1.03733			−0.518666	+	0.854977i	$0.673571\pi$
$30$	15.0000	+	25.9808i	0.0912871	+	0.158114i
$31$	−44.0000	+	76.2102i	−0.254924	+	0.441541i	−0.964875	−	0.262710i	$-0.915384\pi$
$31$	−44.0000	+	76.2102i	−0.254924	+	0.441541i	0.709951	+	0.704251i	$0.248717\pi$
$32$	22.5000	−	38.9711i	0.124296	−	0.215287i
$33$	45.0000	+	77.9423i	0.237379	+	0.411152i
$34$	162.000			0.817140
$35$		0			0
$36$	−23.0000			−0.106481
$37$	129.500	+	224.301i	0.575396	+	0.996616i	0.995998	+	0.0893706i	$0.0284856\pi$
$37$	129.500	+	224.301i	0.575396	+	0.996616i	−0.420602	+	0.907245i	$0.638181\pi$
$38$	−181.500	+	314.367i	−0.774821	+	1.34203i
$39$	59.0000	−	102.191i	0.242245	−	0.419581i
$40$	−52.5000	−	90.9327i	−0.207524	−	0.359443i
$41$	−195.000			−0.742778			−0.371389	−	0.928477i	$-0.621118\pi$
$41$	−195.000			−0.742778			−0.371389	+	0.928477i	$0.621118\pi$
$42$		0			0
$43$	−286.000			−1.01429			−0.507146	−	0.861860i	$-0.669300\pi$
$43$	−286.000			−1.01429			−0.507146	+	0.861860i	$0.669300\pi$
$44$	22.5000	+	38.9711i	0.0770910	+	0.133525i
$45$	−57.5000	+	99.5929i	−0.190480	+	0.329921i
$46$	−103.500	+	179.267i	−0.331744	+	0.574598i
$47$	22.5000	+	38.9711i	0.0698290	+	0.120947i	0.898826	−	0.438306i	$-0.144421\pi$
$47$	22.5000	+	38.9711i	0.0698290	+	0.120947i	−0.828997	+	0.559253i	$0.811088\pi$
$48$	−142.000			−0.426999
$49$		0			0
$50$	75.0000			0.212132
$51$	−54.0000	−	93.5307i	−0.148265	−	0.256802i
$52$	29.5000	−	51.0955i	0.0786714	−	0.136263i
$53$	−298.500	+	517.017i	−0.773625	+	1.33996i	0.161939	+	0.986801i	$0.448225\pi$
$53$	−298.500	+	517.017i	−0.773625	+	1.33996i	−0.935564	+	0.353157i	$0.885108\pi$
$54$	150.000	+	259.808i	0.378008	+	0.654729i
$55$	225.000			0.551618
$56$		0			0
$57$	242.000			0.562345
$58$	243.000	+	420.888i	0.550129	+	0.952851i
$59$	−180.000	+	311.769i	−0.397187	+	0.687947i	−0.993378	−	0.114895i	$-0.963347\pi$
$59$	−180.000	+	311.769i	−0.397187	+	0.687947i	0.596191	+	0.802843i	$0.296680\pi$
$60$	5.00000	−	8.66025i	0.0107583	−	0.0186339i
$61$	196.000	+	339.482i	0.411397	+	0.712561i	0.995043	−	0.0994477i	$-0.0317076\pi$
$61$	196.000	+	339.482i	0.411397	+	0.712561i	−0.583646	+	0.812009i	$0.698374\pi$
$62$	264.000			0.540775
$63$		0			0
$64$	433.000			0.845703
$65$	−147.500	−	255.477i	−0.281463	−	0.487509i
$66$	135.000	−	233.827i	0.251778	−	0.436092i
$67$	140.000	−	242.487i	0.255279	−	0.442157i	−0.709692	−	0.704512i	$-0.751166\pi$
$67$	140.000	−	242.487i	0.255279	−	0.442157i	0.964971	+	0.262355i	$0.0844992\pi$
$68$	−27.0000	−	46.7654i	−0.0481505	−	0.0833990i
$69$	138.000			0.240772
$70$		0			0
$71$	48.0000			0.0802331			0.0401166	−	0.999195i	$-0.487227\pi$
$71$	48.0000			0.0802331			0.0401166	+	0.999195i	$0.487227\pi$
$72$	−241.500	−	418.290i	−0.395292	−	0.684666i
$73$	334.000	−	578.505i	0.535503	−	0.927519i	−0.463635	−	0.886026i	$-0.653455\pi$
$73$	334.000	−	578.505i	0.535503	−	0.927519i	0.999139	−	0.0414929i	$-0.0132114\pi$
$74$	388.500	−	672.902i	0.610300	−	1.05707i
$75$	−25.0000	−	43.3013i	−0.0384900	−	0.0666667i
$76$	121.000			0.182627
$77$		0			0
$78$	−354.000			−0.513880
$79$	−391.000	−	677.232i	−0.556847	−	0.964488i	−0.997757	−	0.0669365i	$-0.978678\pi$
$79$	−391.000	−	677.232i	−0.556847	−	0.964488i	0.440910	−	0.897551i	$-0.354656\pi$
$80$	−177.500	+	307.439i	−0.248064	+	0.429659i
$81$	−210.500	+	364.597i	−0.288752	+	0.500133i
$82$	292.500	+	506.625i	0.393917	+	0.682285i
$83$	−768.000			−1.01565			−0.507825	−	0.861460i	$-0.669550\pi$
$83$	−768.000			−1.01565			−0.507825	+	0.861460i	$0.669550\pi$
$84$		0			0
$85$	−270.000			−0.344537
$86$	429.000	+	743.050i	0.537910	+	0.931687i
$87$	162.000	−	280.592i	0.199635	−	0.345778i
$88$	−472.500	+	818.394i	−0.572371	+	0.991376i
$89$	−597.000	−	1034.03i	−0.711032	−	1.23154i	−0.964470	−	0.264192i	$-0.914895\pi$
$89$	−597.000	−	1034.03i	−0.711032	−	1.23154i	0.253438	−	0.967352i	$-0.418439\pi$
$90$	345.000			0.404069
$91$		0			0
$92$	69.0000			0.0781929
$93$	−88.0000	−	152.420i	−0.0981202	−	0.169949i
$94$	67.5000	−	116.913i	0.0740648	−	0.128284i
$95$	302.500	−	523.945i	0.326693	−	0.565849i
$96$	45.0000	+	77.9423i	0.0478416	+	0.0828641i
$97$	−902.000			−0.944167			−0.472084	−	0.881554i	$-0.656498\pi$
$97$	−902.000			−0.944167			−0.472084	+	0.881554i	$0.656498\pi$
$98$		0			0
$99$	1035.00			1.05072
$100$	−12.5000	−	21.6506i	−0.0125000	−	0.0216506i
$101$	342.000	−	592.361i	0.336933	−	0.583586i	−0.646921	−	0.762557i	$-0.723944\pi$
$101$	342.000	−	592.361i	0.336933	−	0.583586i	0.983854	+	0.178971i	$0.0572769\pi$
$102$	−162.000	+	280.592i	−0.157259	+	0.272380i
$103$	−758.000	−	1312.89i	−0.725126	−	1.25595i	−0.958922	−	0.283669i	$-0.908448\pi$
$103$	−758.000	−	1312.89i	−0.725126	−	1.25595i	0.233796	−	0.972286i	$-0.424885\pi$
$104$	1239.00			1.16821
$105$		0			0
$106$	1791.00			1.64111
$107$	366.000	+	633.931i	0.330678	+	0.572751i	0.982645	−	0.185496i	$-0.0593892\pi$
$107$	366.000	+	633.931i	0.330678	+	0.572751i	−0.651967	+	0.758247i	$0.726056\pi$
$108$	50.0000	−	86.6025i	0.0445486	−	0.0771605i
$109$	800.000	−	1385.64i	0.702992	−	1.21762i	−0.264420	−	0.964408i	$-0.585180\pi$
$109$	800.000	−	1385.64i	0.702992	−	1.21762i	0.967411	−	0.253210i	$-0.0814863\pi$
$110$	−337.500	−	584.567i	−0.292540	−	0.506694i
$111$	−518.000			−0.442940
$112$		0			0
$113$	−1392.00			−1.15883			−0.579417	−	0.815031i	$-0.696720\pi$
$113$	−1392.00			−1.15883			−0.579417	+	0.815031i	$0.696720\pi$
$114$	−363.000	−	628.734i	−0.298229	−	0.516547i
$115$	172.500	−	298.779i	0.139876	−	0.242272i
$116$	81.0000	−	140.296i	0.0648333	−	0.112295i
$117$	−678.500	−	1175.20i	−0.536131	−	0.928606i
$118$	1080.00			0.842560
$119$		0			0
$120$	210.000			0.159752
$121$	−347.000	−	601.022i	−0.260706	−	0.451556i
$122$	588.000	−	1018.45i	0.436353	−	0.755785i
$123$	195.000	−	337.750i	0.142948	−	0.247593i
$124$	−44.0000	−	76.2102i	−0.0318655	−	0.0551926i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	803.000			0.561061			0.280530	−	0.959845i	$-0.409490\pi$
$127$	803.000			0.561061			0.280530	+	0.959845i	$0.409490\pi$
$128$	−829.500	−	1436.74i	−0.572798	−	0.992115i
$129$	286.000	−	495.367i	0.195201	−	0.338098i
$130$	−442.500	+	766.432i	−0.298537	+	0.517081i
$131$	1009.50	+	1748.51i	0.673286	+	1.16617i	0.976967	+	0.213391i	$0.0684509\pi$
$131$	1009.50	+	1748.51i	0.673286	+	1.16617i	−0.303681	+	0.952774i	$0.598216\pi$
$132$	−90.0000			−0.0593447
$133$		0			0
$134$	−840.000			−0.541529
$135$	−250.000	−	433.013i	−0.159382	−	0.276058i
$136$	567.000	−	982.073i	0.357499	−	0.619206i
$137$	−30.0000	+	51.9615i	−0.0187086	+	0.0324042i	−0.875228	−	0.483710i	$-0.839289\pi$
$137$	−30.0000	+	51.9615i	−0.0187086	+	0.0324042i	0.856520	+	0.516115i	$0.172622\pi$
$138$	−207.000	−	358.535i	−0.127688	−	0.221163i
$139$	1708.00			1.04224			0.521118	−	0.853485i	$-0.325515\pi$
$139$	1708.00			1.04224			0.521118	+	0.853485i	$0.325515\pi$
$140$		0			0
$141$	−90.0000			−0.0537544
$142$	−72.0000	−	124.708i	−0.0425500	−	0.0736988i
$143$	−1327.50	+	2299.30i	−0.776302	+	1.34459i
$144$	−816.500	+	1414.22i	−0.472512	+	0.818414i
$145$	−405.000	−	701.481i	−0.231955	−	0.401757i
$146$	−2004.00			−1.13597
$147$		0			0
$148$	−259.000			−0.143849
$149$	543.000	+	940.504i	0.298552	+	0.517108i	0.975805	−	0.218643i	$-0.0701629\pi$
$149$	543.000	+	940.504i	0.298552	+	0.517108i	−0.677253	+	0.735751i	$0.736830\pi$
$150$	−75.0000	+	129.904i	−0.0408248	+	0.0707107i
$151$	1433.00	−	2482.03i	0.772291	−	1.33765i	−0.164014	−	0.986458i	$-0.552444\pi$
$151$	1433.00	−	2482.03i	0.772291	−	1.33765i	0.936305	−	0.351189i	$-0.114222\pi$
$152$	1270.50	+	2200.57i	0.677968	+	1.17428i
$153$	−1242.00			−0.656273
$154$		0			0
$155$	−440.000			−0.228011
$156$	59.0000	+	102.191i	0.0302806	+	0.0524476i
$157$	−114.500	+	198.320i	−0.0582044	+	0.100813i	−0.893659	−	0.448746i	$-0.851871\pi$
$157$	−114.500	+	198.320i	−0.0582044	+	0.100813i	0.835455	+	0.549559i	$0.185204\pi$
$158$	−1173.00	+	2031.70i	−0.590626	+	1.02299i
$159$	−597.000	−	1034.03i	−0.297768	−	0.515750i
$160$	225.000			0.111174
$161$		0			0
$162$	1263.00			0.612535
$163$	614.000	+	1063.48i	0.295044	+	0.511031i	0.974995	−	0.222226i	$-0.0713323\pi$
$163$	614.000	+	1063.48i	0.295044	+	0.511031i	−0.679951	+	0.733258i	$0.737999\pi$
$164$	97.5000	−	168.875i	0.0464236	−	0.0804080i
$165$	−225.000	+	389.711i	−0.106159	+	0.183873i
$166$	1152.00	+	1995.32i	0.538630	+	0.932934i
$167$	1929.00			0.893835			0.446918	−	0.894575i	$-0.352522\pi$
$167$	1929.00			0.893835			0.446918	+	0.894575i	$0.352522\pi$
$168$		0			0
$169$	1284.00			0.584433
$170$	405.000	+	701.481i	0.182718	+	0.316477i
$171$	1391.50	−	2410.15i	0.622285	−	1.07783i
$172$	143.000	−	247.683i	0.0633933	−	0.109800i
$173$	−349.500	−	605.352i	−0.153595	−	0.266035i	0.778951	−	0.627084i	$-0.215752\pi$
$173$	−349.500	−	605.352i	−0.153595	−	0.266035i	−0.932547	+	0.361049i	$0.882419\pi$
$174$	−972.000			−0.423489
$175$		0			0
$176$	3195.00			1.36836
$177$	−360.000	−	623.538i	−0.152877	−	0.264791i
$178$	−1791.00	+	3102.10i	−0.754164	+	1.30625i
$179$	−1558.50	+	2699.40i	−0.650770	+	1.12717i	0.332167	+	0.943221i	$0.392220\pi$
$179$	−1558.50	+	2699.40i	−0.650770	+	1.12717i	−0.982936	+	0.183945i	$0.941113\pi$
$180$	−57.5000	−	99.5929i	−0.0238100	−	0.0412401i
$181$	1798.00			0.738366			0.369183	−	0.929357i	$-0.379638\pi$
$181$	1798.00			0.738366			0.369183	+	0.929357i	$0.379638\pi$
$182$		0			0
$183$	−784.000			−0.316694
$184$	724.500	+	1254.87i	0.290276	+	0.502773i
$185$	−647.500	+	1121.50i	−0.257325	+	0.445700i
$186$	−264.000	+	457.261i	−0.104072	+	0.180258i
$187$	1215.00	+	2104.44i	0.475132	+	0.822952i
$188$	−45.0000			−0.0174572
$189$		0			0
$190$	−1815.00			−0.693021
$191$	1194.00	+	2068.07i	0.452329	+	0.783457i	0.998530	−	0.0541974i	$-0.0172600\pi$
$191$	1194.00	+	2068.07i	0.452329	+	0.783457i	−0.546201	+	0.837654i	$0.683927\pi$
$192$	−433.000	+	749.978i	−0.162756	+	0.281901i
$193$	−136.000	+	235.559i	−0.0507228	+	0.0878544i	−0.890272	−	0.455429i	$-0.849486\pi$
$193$	−136.000	+	235.559i	−0.0507228	+	0.0878544i	0.839549	+	0.543284i	$0.182819\pi$
$194$	1353.00	+	2343.46i	0.500720	+	0.867273i
$195$	590.000			0.216671
$196$		0			0
$197$	−2109.00			−0.762741			−0.381371	−	0.924422i	$-0.624548\pi$
$197$	−2109.00			−0.762741			−0.381371	+	0.924422i	$0.624548\pi$
$198$	−1552.50	−	2689.01i	−0.557229	−	0.965149i
$199$	712.000	−	1233.22i	0.253630	−	0.439300i	−0.710893	−	0.703301i	$-0.751709\pi$
$199$	712.000	−	1233.22i	0.253630	−	0.439300i	0.964522	+	0.264001i	$0.0850422\pi$
$200$	262.500	−	454.663i	0.0928078	−	0.160748i
$201$	280.000	+	484.974i	0.0982571	+	0.170186i
$202$	−2052.00			−0.714744
$203$		0			0
$204$	108.000			0.0370662
$205$	−487.500	−	844.375i	−0.166090	−	0.287677i
$206$	−2274.00	+	3938.68i	−0.769112	+	1.33214i
$207$	793.500	−	1374.38i	0.266435	−	0.461479i
$208$	−2094.50	−	3627.78i	−0.698209	−	1.20933i
$209$	−5445.00			−1.80210
$210$		0			0
$211$	−3625.00			−1.18273			−0.591363	−	0.806405i	$-0.701410\pi$
$211$	−3625.00			−1.18273			−0.591363	+	0.806405i	$0.701410\pi$
$212$	−298.500	−	517.017i	−0.0967031	−	0.167495i
$213$	−48.0000	+	83.1384i	−0.0154409	+	0.0267444i
$214$	1098.00	−	1901.79i	0.350737	−	0.607494i
$215$	−715.000	−	1238.42i	−0.226803	−	0.392834i
$216$	2100.00			0.661513
$217$		0			0
$218$	−4800.00			−1.49127
$219$	668.000	+	1157.01i	0.206115	+	0.357002i
$220$	−112.500	+	194.856i	−0.0344761	+	0.0597144i
$221$	1593.00	−	2759.16i	0.484872	−	0.839823i
$222$	777.000	+	1345.80i	0.234905	+	0.406867i
$223$	4960.00			1.48944			0.744722	−	0.667374i	$-0.232582\pi$
$223$	4960.00			1.48944			0.744722	+	0.667374i	$0.232582\pi$
$224$		0			0
$225$	−575.000			−0.170370
$226$	2088.00	+	3616.52i	0.614565	+	1.06446i
$227$	−750.000	+	1299.04i	−0.219292	+	0.379825i	−0.954592	−	0.297917i	$-0.903708\pi$
$227$	−750.000	+	1299.04i	−0.219292	+	0.379825i	0.735300	+	0.677742i	$0.237041\pi$
$228$	−121.000	+	209.578i	−0.0351466	+	0.0608757i
$229$	3046.00	+	5275.83i	0.878975	+	1.52243i	0.852467	+	0.522781i	$0.175106\pi$
$229$	3046.00	+	5275.83i	0.878975	+	1.52243i	0.0265085	+	0.999649i	$0.491561\pi$
$230$	−1035.00			−0.296721
$231$		0			0
$232$	3402.00			0.962725
$233$	−69.0000	−	119.512i	−0.0194006	−	0.0336028i	0.856162	−	0.516707i	$-0.172842\pi$
$233$	−69.0000	−	119.512i	−0.0194006	−	0.0336028i	−0.875563	+	0.483104i	$0.839509\pi$
$234$	−2035.50	+	3525.59i	−0.568653	+	0.984936i
$235$	−112.500	+	194.856i	−0.0312285	+	0.0540893i
$236$	−180.000	−	311.769i	−0.0496483	−	0.0859934i
$237$	1564.00			0.428661
$238$		0			0
$239$	−5502.00			−1.48910			−0.744550	−	0.667567i	$-0.767336\pi$
$239$	−5502.00			−1.48910			−0.744550	+	0.667567i	$0.767336\pi$
$240$	−355.000	−	614.878i	−0.0954798	−	0.165376i
$241$	1775.50	−	3075.26i	0.474564	−	0.821970i	−0.525011	−	0.851095i	$-0.675939\pi$
$241$	1775.50	−	3075.26i	0.474564	−	0.821970i	0.999576	+	0.0291256i	$0.00927228\pi$
$242$	−1041.00	+	1803.06i	−0.276521	+	0.478948i
$243$	−1771.00	−	3067.46i	−0.467530	−	0.809785i
$244$	−392.000			−0.102849
$245$		0			0
$246$	−1170.00			−0.303238
$247$	3569.50	+	6182.56i	0.919522	+	1.59266i
$248$	924.000	−	1600.41i	0.236589	−	0.409784i
$249$	768.000	−	1330.22i	0.195462	−	0.338550i
$250$	187.500	+	324.760i	0.0474342	+	0.0821584i
$251$	−7065.00			−1.77665			−0.888324	−	0.459216i	$-0.848130\pi$
$251$	−7065.00			−1.77665			−0.888324	+	0.459216i	$0.848130\pi$
$252$		0			0
$253$	−3105.00			−0.771580
$254$	−1204.50	−	2086.26i	−0.297547	−	0.515367i
$255$	270.000	−	467.654i	0.0663061	−	0.114846i
$256$	−756.500	+	1310.30i	−0.184692	+	0.319897i
$257$	−2040.00	−	3533.38i	−0.495143	−	0.857613i	0.504842	−	0.863212i	$-0.331551\pi$
$257$	−2040.00	−	3533.38i	−0.495143	−	0.857613i	−0.999984	+	0.00559954i	$0.998218\pi$
$258$	−1716.00			−0.414083
$259$		0			0
$260$	295.000			0.0703659
$261$	−1863.00	−	3226.81i	−0.441827	−	0.765267i
$262$	3028.50	−	5245.52i	0.714127	−	1.23690i
$263$	1644.00	−	2847.49i	0.385450	−	0.667619i	−0.606381	−	0.795174i	$-0.707380\pi$
$263$	1644.00	−	2847.49i	0.385450	−	0.667619i	0.991832	+	0.127555i	$0.0407128\pi$
$264$	−945.000	−	1636.79i	−0.220306	−	0.381581i
$265$	−2985.00			−0.691951
$266$		0			0
$267$	2388.00			0.547353
$268$	140.000	+	242.487i	0.0319099	+	0.0552696i
$269$	−1632.00	+	2826.71i	−0.369906	+	0.640697i	−0.989551	−	0.144186i	$-0.953944\pi$
$269$	−1632.00	+	2826.71i	−0.369906	+	0.640697i	0.619644	+	0.784883i	$0.287277\pi$
$270$	−750.000	+	1299.04i	−0.169050	+	0.292803i
$271$	−1376.00	−	2383.30i	−0.308436	−	0.534226i	0.669585	−	0.742736i	$-0.266472\pi$
$271$	−1376.00	−	2383.30i	−0.308436	−	0.534226i	−0.978020	+	0.208510i	$0.933139\pi$
$272$	−3834.00			−0.854671
$273$		0			0
$274$	180.000			0.0396869
$275$	562.500	+	974.279i	0.123346	+	0.213641i
$276$	−69.0000	+	119.512i	−0.0150482	+	0.0260643i
$277$	2345.00	−	4061.66i	0.508655	−	0.881016i	−0.491295	−	0.870993i	$-0.663476\pi$
$277$	2345.00	−	4061.66i	0.508655	−	0.881016i	0.999950	−	0.0100228i	$-0.00319040\pi$
$278$	−2562.00	−	4437.51i	−0.552729	−	0.957354i
$279$	−2024.00			−0.434314
$280$		0			0
$281$	7821.00			1.66036			0.830181	−	0.557494i	$-0.188237\pi$
$281$	7821.00			1.66036			0.830181	+	0.557494i	$0.188237\pi$
$282$	135.000	+	233.827i	0.0285076	+	0.0493765i
$283$	−329.000	+	569.845i	−0.0691061	+	0.119695i	−0.898508	−	0.438957i	$-0.855348\pi$
$283$	−329.000	+	569.845i	−0.0691061	+	0.119695i	0.829402	+	0.558652i	$0.188681\pi$
$284$	−24.0000	+	41.5692i	−0.00501457	+	0.00868549i
$285$	605.000	+	1047.89i	0.125744	+	0.217795i
$286$	7965.00			1.64678
$287$		0			0
$288$	1035.00			0.211764
$289$	998.500	+	1729.45i	0.203236	+	0.352016i
$290$	−1215.00	+	2104.44i	−0.246025	+	0.426128i
$291$	902.000	−	1562.31i	0.181705	−	0.314722i
$292$	334.000	+	578.505i	0.0669379	+	0.115940i
$293$	5997.00			1.19573			0.597864	−	0.801597i	$-0.296016\pi$
$293$	5997.00			1.19573			0.597864	+	0.801597i	$0.296016\pi$
$294$		0			0
$295$	−1800.00			−0.355254
$296$	−2719.50	−	4710.31i	−0.534013	−	0.924937i
$297$	−2250.00	+	3897.11i	−0.439590	+	0.761392i
$298$	1629.00	−	2821.51i	0.316663	−	0.548476i
$299$	2035.50	+	3525.59i	0.393699	+	0.681907i
$300$	50.0000			0.00962250
$301$		0			0
$302$	−8598.00			−1.63828
$303$	684.000	+	1184.72i	0.129686	+	0.224622i
$304$	4295.50	−	7440.02i	0.810407	−	1.40367i
$305$	−980.000	+	1697.41i	−0.183982	+	0.318667i
$306$	1863.00	+	3226.81i	0.348041	+	0.602825i
$307$	6226.00			1.15745			0.578724	−	0.815523i	$-0.303551\pi$
$307$	6226.00			1.15745			0.578724	+	0.815523i	$0.303551\pi$
$308$		0			0
$309$	3032.00			0.558202
$310$	660.000	+	1143.15i	0.120921	+	0.209441i
$311$	2340.00	−	4053.00i	0.426653	−	0.738985i	−0.569920	−	0.821700i	$-0.693026\pi$
$311$	2340.00	−	4053.00i	0.426653	−	0.738985i	0.996573	+	0.0827149i	$0.0263591\pi$
$312$	−1239.00	+	2146.01i	−0.224822	+	0.389404i
$313$	514.000	+	890.274i	0.0928211	+	0.160771i	0.908697	−	0.417456i	$-0.137078\pi$
$313$	514.000	+	890.274i	0.0928211	+	0.160771i	−0.815876	+	0.578227i	$0.803745\pi$
$314$	687.000			0.123470
$315$		0			0
$316$	782.000			0.139212
$317$	−4311.00	−	7466.87i	−0.763817	−	1.32297i	−0.940870	−	0.338768i	$-0.889990\pi$
$317$	−4311.00	−	7466.87i	−0.763817	−	1.32297i	0.177053	−	0.984201i	$-0.443344\pi$
$318$	−1791.00	+	3102.10i	−0.315831	+	0.547036i
$319$	−3645.00	+	6313.33i	−0.639752	+	1.10808i
$320$	1082.50	+	1874.94i	0.189105	+	0.327539i
$321$	−1464.00			−0.254556
$322$		0			0
$323$	6534.00			1.12558
$324$	−210.500	−	364.597i	−0.0360940	−	0.0625166i
$325$	737.500	−	1277.39i	0.125874	−	0.218021i
$326$	1842.00	−	3190.44i	0.312942	−	0.542031i
$327$	1600.00	+	2771.28i	0.270582	+	0.468661i
$328$	4095.00			0.689355
$329$		0			0
$330$	1350.00			0.225197
$331$	999.500	+	1731.18i	0.165974	+	0.287476i	0.937001	−	0.349327i	$-0.113590\pi$
$331$	999.500	+	1731.18i	0.165974	+	0.287476i	−0.771027	+	0.636803i	$0.780256\pi$
$332$	384.000	−	665.108i	0.0634781	−	0.109947i
$333$	−2978.50	+	5158.91i	−0.490153	+	0.848969i
$334$	−2893.50	−	5011.69i	−0.474028	−	0.821040i
$335$	1400.00			0.228329
$336$		0			0
$337$	5114.00			0.826639			0.413319	−	0.910586i	$-0.364369\pi$
$337$	5114.00			0.826639			0.413319	+	0.910586i	$0.364369\pi$
$338$	−1926.00	−	3335.93i	−0.309943	−	0.536836i
$339$	1392.00	−	2411.01i	0.223018	−	0.386278i
$340$	135.000	−	233.827i	0.0215335	−	0.0372972i
$341$	1980.00	+	3429.46i	0.314437	+	0.544621i
$342$	−8349.00			−1.32006
$343$		0			0
$344$	6006.00			0.941342
$345$	345.000	+	597.558i	0.0538382	+	0.0932505i
$346$	−1048.50	+	1816.06i	−0.162912	+	0.282173i
$347$	−2160.00	+	3741.23i	−0.334164	+	0.578789i	−0.983324	−	0.181863i	$-0.941787\pi$
$347$	−2160.00	+	3741.23i	−0.334164	+	0.578789i	0.649160	+	0.760652i	$0.275121\pi$
$348$	162.000	+	280.592i	0.0249543	+	0.0432222i
$349$	−7922.00			−1.21506			−0.607529	−	0.794298i	$-0.707839\pi$
$349$	−7922.00			−1.21506			−0.607529	+	0.794298i	$0.707839\pi$
$350$		0			0
$351$	5900.00			0.897204
$352$	−1012.50	−	1753.70i	−0.153314	−	0.265547i
$353$	414.000	−	717.069i	0.0624221	−	0.108118i	−0.833125	−	0.553084i	$-0.813451\pi$
$353$	414.000	−	717.069i	0.0624221	−	0.108118i	0.895548	+	0.444966i	$0.146784\pi$
$354$	−1080.00	+	1870.61i	−0.162151	+	0.280853i
$355$	120.000	+	207.846i	0.0179407	+	0.0310742i
$356$	1194.00			0.177758
$357$		0			0
$358$	9351.00			1.38049
$359$	675.000	+	1169.13i	0.0992344	+	0.171879i	0.911368	−	0.411593i	$-0.135027\pi$
$359$	675.000	+	1169.13i	0.0992344	+	0.171879i	−0.812134	+	0.583472i	$0.801694\pi$
$360$	1207.50	−	2091.45i	0.176780	−	0.306192i
$361$	−3891.00	+	6739.41i	−0.567284	+	0.982564i
$362$	−2697.00	−	4671.34i	−0.391578	−	0.678233i
$363$	1388.00			0.200692
$364$		0			0
$365$	3340.00			0.478969
$366$	1176.00	+	2036.89i	0.167952	+	0.290902i
$367$	1400.50	−	2425.74i	0.199198	−	0.345020i	−0.749071	−	0.662490i	$-0.769500\pi$
$367$	1400.50	−	2425.74i	0.199198	−	0.345020i	0.948268	+	0.317470i	$0.102833\pi$
$368$	2449.50	−	4242.66i	0.346981	−	0.600989i
$369$	−2242.50	−	3884.12i	−0.316368	−	0.547966i
$370$	3885.00			0.545869
$371$		0			0
$372$	176.000			0.0245300
$373$	−3301.00	−	5717.50i	−0.458229	−	0.793675i	0.540639	−	0.841255i	$-0.318183\pi$
$373$	−3301.00	−	5717.50i	−0.458229	−	0.793675i	−0.998867	+	0.0475795i	$0.984849\pi$
$374$	3645.00	−	6313.33i	0.503953	−	0.872872i
$375$	125.000	−	216.506i	0.0172133	−	0.0298142i
$376$	−472.500	−	818.394i	−0.0648067	−	0.112249i
$377$	9558.00			1.30573
$378$		0			0
$379$	−8305.00			−1.12559			−0.562796	−	0.826596i	$-0.690274\pi$
$379$	−8305.00			−1.12559			−0.562796	+	0.826596i	$0.690274\pi$
$380$	302.500	+	523.945i	0.0408366	+	0.0707311i
$381$	−803.000	+	1390.84i	−0.107976	+	0.187020i
$382$	3582.00	−	6204.21i	0.479767	−	0.830981i
$383$	472.500	+	818.394i	0.0630382	+	0.109185i	0.895822	−	0.444413i	$-0.146588\pi$
$383$	472.500	+	818.394i	0.0630382	+	0.109185i	−0.832784	+	0.553598i	$0.813254\pi$
$384$	3318.00			0.440940
$385$		0			0
$386$	816.000			0.107599
$387$	−3289.00	−	5696.72i	−0.432014	−	0.748270i
$388$	451.000	−	781.155i	0.0590105	−	0.102209i
$389$	−6018.00	+	10423.5i	−0.784382	+	1.35859i	0.144985	+	0.989434i	$0.453687\pi$
$389$	−6018.00	+	10423.5i	−0.784382	+	1.35859i	−0.929367	+	0.369156i	$0.879647\pi$
$390$	−885.000	−	1532.86i	−0.114907	−	0.199025i
$391$	3726.00			0.481923
$392$		0			0
$393$	−4038.00			−0.518296
$394$	3163.50	+	5479.34i	0.404505	+	0.700623i
$395$	1955.00	−	3386.16i	0.249030	−	0.431332i
$396$	−517.500	+	896.336i	−0.0656701	+	0.113744i
$397$	−1349.00	−	2336.54i	−0.170540	−	0.295384i	0.768069	−	0.640367i	$-0.221218\pi$
$397$	−1349.00	−	2336.54i	−0.170540	−	0.295384i	−0.938609	+	0.344983i	$0.887885\pi$
$398$	−4272.00			−0.538030
$399$		0			0
$400$	−1775.00			−0.221875
$401$	−3526.50	−	6108.08i	−0.439165	−	0.760655i	0.558461	−	0.829531i	$-0.311392\pi$
$401$	−3526.50	−	6108.08i	−0.439165	−	0.760655i	−0.997625	+	0.0688756i	$0.978059\pi$
$402$	840.000	−	1454.92i	0.104217	−	0.180510i
$403$	2596.00	−	4496.40i	0.320883	−	0.555786i
$404$	342.000	+	592.361i	0.0421167	+	0.0729482i
$405$	−2105.00			−0.258267
$406$		0			0
$407$	11655.0			1.41945
$408$	1134.00	+	1964.15i	0.137601	+	0.238333i
$409$	−5435.00	+	9413.70i	−0.657074	+	1.13809i	0.324295	+	0.945956i	$0.394873\pi$
$409$	−5435.00	+	9413.70i	−0.657074	+	1.13809i	−0.981369	+	0.192130i	$0.938460\pi$
$410$	−1462.50	+	2533.12i	−0.176165	+	0.305127i
$411$	−60.0000	−	103.923i	−0.00720093	−	0.0124724i
$412$	1516.00			0.181281
$413$		0			0
$414$	−4761.00			−0.565194
$415$	−1920.00	−	3325.54i	−0.227106	−	0.393360i
$416$	−1327.50	+	2299.30i	−0.156457	+	0.270991i
$417$	−1708.00	+	2958.34i	−0.200578	+	0.347412i
$418$	8167.50	+	14146.5i	0.955707	+	1.65533i
$419$	9729.00			1.13435			0.567175	−	0.823597i	$-0.308036\pi$
$419$	9729.00			1.13435			0.567175	+	0.823597i	$0.308036\pi$
$420$		0			0
$421$	−12550.0			−1.45285			−0.726425	−	0.687246i	$-0.758819\pi$
$421$	−12550.0			−1.45285			−0.726425	+	0.687246i	$0.758819\pi$
$422$	5437.50	+	9418.03i	0.627235	+	1.08640i
$423$	−517.500	+	896.336i	−0.0594840	+	0.103029i
$424$	6268.50	−	10857.4i	0.717984	−	1.24358i
$425$	−675.000	−	1169.13i	−0.0770407	−	0.133438i
$426$	288.000			0.0327550
$427$		0			0
$428$	−732.000			−0.0826695
$429$	−2655.00	−	4598.59i	−0.298799	−	0.517534i
$430$	−2145.00	+	3715.25i	−0.240561	+	0.416663i
$431$	−1494.00	+	2587.68i	−0.166969	+	0.289198i	−0.937353	−	0.348382i	$-0.886731\pi$
$431$	−1494.00	+	2587.68i	−0.166969	+	0.289198i	0.770384	+	0.637580i	$0.220065\pi$
$432$	−3550.00	−	6148.78i	−0.395369	−	0.684799i
$433$	−16616.0			−1.84414			−0.922072	−	0.387019i	$-0.873505\pi$
$433$	−16616.0			−1.84414			−0.922072	+	0.387019i	$0.873505\pi$
$434$		0			0
$435$	1620.00			0.178559
$436$	800.000	+	1385.64i	0.0878740	+	0.152202i
$437$	−4174.50	+	7230.45i	−0.456964	+	0.791485i
$438$	2004.00	−	3471.03i	0.218618	−	0.378658i
$439$	3673.00	+	6361.82i	0.399323	+	0.691647i	0.993642	−	0.112581i	$-0.0359119\pi$
$439$	3673.00	+	6361.82i	0.399323	+	0.691647i	−0.594320	+	0.804229i	$0.702579\pi$
$440$	−4725.00			−0.511944
$441$		0			0
$442$	−9558.00			−1.02857
$443$	−6.00000	−	10.3923i	−0.000643496	−	0.00111457i	0.865703	−	0.500557i	$-0.166871\pi$
$443$	−6.00000	−	10.3923i	−0.000643496	−	0.00111457i	−0.866347	+	0.499443i	$0.833538\pi$
$444$	259.000	−	448.601i	0.0276838	−	0.0479497i
$445$	2985.00	−	5170.17i	0.317983	−	0.550763i
$446$	−7440.00	−	12886.5i	−0.789897	−	1.36814i
$447$	−2172.00			−0.229826
$448$		0			0
$449$	9669.00			1.01628			0.508138	−	0.861275i	$-0.330334\pi$
$449$	9669.00			1.01628			0.508138	+	0.861275i	$0.330334\pi$
$450$	862.500	+	1493.89i	0.0903525	+	0.156495i
$451$	−4387.50	+	7599.37i	−0.458092	+	0.793438i
$452$	696.000	−	1205.51i	0.0724272	−	0.125448i
$453$	2866.00	+	4964.06i	0.297255	+	0.514860i
$454$	4500.00			0.465188
$455$		0			0
$456$	−5082.00			−0.521900
$457$	4817.00	+	8343.29i	0.493063	+	0.854010i	0.999968	−	0.00799181i	$-0.00254390\pi$
$457$	4817.00	+	8343.29i	0.493063	+	0.854010i	−0.506905	+	0.862002i	$0.669211\pi$
$458$	9138.00	−	15827.5i	0.932294	−	1.61478i
$459$	2700.00	−	4676.54i	0.274565	−	0.475560i
$460$	172.500	+	298.779i	0.0174845	+	0.0302840i
$461$	342.000			0.0345521			0.0172761	−	0.999851i	$-0.494501\pi$
$461$	342.000			0.0345521			0.0172761	+	0.999851i	$0.494501\pi$
$462$		0			0
$463$	2411.00			0.242006			0.121003	−	0.992652i	$-0.461389\pi$
$463$	2411.00			0.242006			0.121003	+	0.992652i	$0.461389\pi$
$464$	−5751.00	−	9961.02i	−0.575395	−	0.996614i
$465$	440.000	−	762.102i	0.0438807	−	0.0760035i
$466$	−207.000	+	358.535i	−0.0205774	+	0.0356412i
$467$	−603.000	−	1044.43i	−0.0597506	−	0.103491i	0.834603	−	0.550852i	$-0.185697\pi$
$467$	−603.000	−	1044.43i	−0.0597506	−	0.103491i	−0.894353	+	0.447361i	$0.852364\pi$
$468$	1357.00			0.134033
$469$		0			0
$470$	675.000			0.0662456
$471$	−229.000	−	396.640i	−0.0224029	−	0.0388030i
$472$	3780.00	−	6547.15i	0.368620	−	0.638468i
$473$	−6435.00	+	11145.7i	−0.625543	+	1.08347i
$474$	−2346.00	−	4063.39i	−0.227332	−	0.393751i
$475$	3025.00			0.292203
$476$		0			0
$477$	−13731.0			−1.31803
$478$	8253.00	+	14294.6i	0.789714	+	1.36783i
$479$	−216.000	+	374.123i	−0.0206039	+	0.0356871i	−0.876144	−	0.482050i	$-0.839892\pi$
$479$	−216.000	+	374.123i	−0.0206039	+	0.0356871i	0.855540	+	0.517737i	$0.173226\pi$
$480$	−225.000	+	389.711i	−0.0213954	+	0.0370579i
$481$	−7640.50	−	13233.7i	−0.724276	−	1.25448i
$482$	−10653.0			−1.00670
$483$		0			0
$484$	694.000			0.0651766
$485$	−2255.00	−	3905.77i	−0.211122	−	0.365674i
$486$	−5313.00	+	9202.39i	−0.495890	+	0.858907i
$487$	5948.00	−	10302.2i	0.553449	−	0.958602i	−0.444574	−	0.895742i	$-0.646645\pi$
$487$	5948.00	−	10302.2i	0.553449	−	0.958602i	0.998022	−	0.0628592i	$-0.0200219\pi$
$488$	−4116.00	−	7129.12i	−0.381809	−	0.661312i
$489$	−2456.00			−0.227125
$490$		0			0
$491$	−12276.0			−1.12833			−0.564163	−	0.825663i	$-0.690801\pi$
$491$	−12276.0			−1.12833			−0.564163	+	0.825663i	$0.690801\pi$
$492$	195.000	+	337.750i	0.0178685	+	0.0309491i
$493$	4374.00	−	7575.99i	0.399584	−	0.692100i
$494$	10708.5	−	18547.7i	0.975300	−	1.68927i
$495$	2587.50	+	4481.68i	0.234948	+	0.406943i
$496$	−6248.00			−0.565612
$497$		0			0
$498$	−4608.00			−0.414637
$499$	5438.00	+	9418.89i	0.487852	+	0.844985i	0.999902	−	0.0139706i	$-0.00444712\pi$
$499$	5438.00	+	9418.89i	0.487852	+	0.844985i	−0.512050	+	0.858956i	$0.671114\pi$
$500$	62.5000	−	108.253i	0.00559017	−	0.00968246i
$501$	−1929.00	+	3341.13i	−0.172019	+	0.297945i
$502$	10597.5	+	18355.4i	0.942210	+	1.63196i
$503$	−12000.0			−1.06372			−0.531862	−	0.846831i	$-0.678508\pi$
$503$	−12000.0			−1.06372			−0.531862	+	0.846831i	$0.678508\pi$
$504$		0			0
$505$	3420.00			0.301362
$506$	4657.50	+	8067.03i	0.409192	+	0.708741i
$507$	−1284.00	+	2223.95i	−0.112474	+	0.194811i
$508$	−401.500	+	695.418i	−0.0350663	+	0.0607366i
$509$	−5841.00	−	10116.9i	−0.508640	−	0.880990i	−0.999950	−	0.0100055i	$-0.996815\pi$
$509$	−5841.00	−	10116.9i	−0.508640	−	0.880990i	0.491310	−	0.870985i	$-0.336518\pi$
$510$	−1620.00			−0.140656
$511$		0			0
$512$	−8733.00			−0.753804
$513$	6050.00	+	10478.9i	0.520690	+	0.901862i
$514$	−6120.00	+	10600.2i	−0.525178	+	0.909635i
$515$	3790.00	−	6564.47i	0.324286	−	0.561680i
$516$	286.000	+	495.367i	0.0244001	+	0.0422622i
$517$	2025.00			0.172262
$518$		0			0
$519$	1398.00			0.118238
$520$	3097.50	+	5365.03i	0.261220	+	0.452446i
$521$	4804.50	−	8321.64i	0.404010	−	0.699765i	−0.590196	−	0.807260i	$-0.700950\pi$
$521$	4804.50	−	8321.64i	0.404010	−	0.699765i	0.994206	+	0.107495i	$0.0342829\pi$
$522$	−5589.00	+	9680.43i	−0.468628	+	0.811688i
$523$	10594.0	+	18349.3i	0.885742	+	1.53415i	0.844860	+	0.534987i	$0.179683\pi$
$523$	10594.0	+	18349.3i	0.885742	+	1.53415i	0.0408820	+	0.999164i	$0.486983\pi$
$524$	−2019.00			−0.168321
$525$		0			0
$526$	−9864.00			−0.817663
$527$	−2376.00	−	4115.35i	−0.196395	−	0.340166i
$528$	−3195.00	+	5533.90i	−0.263342	+	0.456122i
$529$	3703.00	−	6413.78i	0.304348	−	0.527146i
$530$	4477.50	+	7755.26i	0.366963	+	0.635598i
$531$	−8280.00			−0.676688
$532$		0			0
$533$	11505.0			0.934966
$534$	−3582.00	−	6204.21i	−0.290278	−	0.502776i
$535$	−1830.00	+	3169.65i	−0.147884	+	0.256142i
$536$	−2940.00	+	5092.23i	−0.236919	+	0.410356i
$537$	−3117.00	−	5398.80i	−0.250481	−	0.433846i
$538$	9792.00			0.784690
$539$		0			0
$540$	500.000			0.0398455
$541$	−4036.00	−	6990.56i	−0.320742	−	0.555541i	0.659900	−	0.751354i	$-0.270599\pi$
$541$	−4036.00	−	6990.56i	−0.320742	−	0.555541i	−0.980641	+	0.195813i	$0.937265\pi$
$542$	−4128.00	+	7149.91i	−0.327145	+	0.566632i
$543$	−1798.00	+	3114.23i	−0.142099	+	0.246122i
$544$	1215.00	+	2104.44i	0.0957586	+	0.165859i
$545$	8000.00			0.628775
$546$		0			0
$547$	344.000			0.0268892			0.0134446	−	0.999910i	$-0.495720\pi$
$547$	344.000			0.0268892			0.0134446	+	0.999910i	$0.495720\pi$
$548$	−30.0000	−	51.9615i	−0.00233857	−	0.00405052i
$549$	−4508.00	+	7808.09i	−0.350449	+	0.606996i
$550$	1687.50	−	2922.84i	0.130828	−	0.226600i
$551$	9801.00	+	16975.8i	0.757780	+	1.31251i
$552$	−2898.00			−0.223455
$553$		0			0
$554$	−14070.0			−1.07902
$555$	−1295.00	−	2243.01i	−0.0990445	−	0.171550i
$556$	−854.000	+	1479.17i	−0.0651397	+	0.112825i
$557$	−9181.50	+	15902.8i	−0.698443	+	1.20974i	0.270563	+	0.962702i	$0.412790\pi$
$557$	−9181.50	+	15902.8i	−0.698443	+	1.20974i	−0.969006	+	0.247036i	$0.920543\pi$
$558$	3036.00	+	5258.51i	0.230330	+	0.398943i
$559$	16874.0			1.27673
$560$		0			0
$561$	−4860.00			−0.365756
$562$	−11731.5	−	20319.6i	−0.880540	−	1.52514i
$563$	−3147.00	+	5450.76i	−0.235578	+	0.408033i	−0.959440	−	0.281912i	$-0.909032\pi$
$563$	−3147.00	+	5450.76i	−0.235578	+	0.408033i	0.723863	+	0.689944i	$0.242365\pi$
$564$	45.0000	−	77.9423i	0.00335965	−	0.00581908i
$565$	−3480.00	−	6027.54i	−0.259123	−	0.448815i
$566$	1974.00			0.146596
$567$		0			0
$568$	−1008.00			−0.0744626
$569$	−5866.50	−	10161.1i	−0.432226	−	0.748637i	0.564839	−	0.825201i	$-0.308938\pi$
$569$	−5866.50	−	10161.1i	−0.432226	−	0.748637i	−0.997065	+	0.0765642i	$0.975605\pi$
$570$	1815.00	−	3143.67i	0.133372	−	0.231007i
$571$	−526.000	+	911.059i	−0.0385506	+	0.0667717i	−0.884657	−	0.466242i	$-0.845607\pi$
$571$	−526.000	+	911.059i	−0.0385506	+	0.0667717i	0.846106	+	0.533014i	$0.178941\pi$
$572$	−1327.50	−	2299.30i	−0.0970377	−	0.168074i
$573$	−4776.00			−0.348203
$574$		0			0
$575$	1725.00			0.125109
$576$	4979.50	+	8624.75i	0.360207	+	0.623897i
$577$	−6578.00	+	11393.4i	−0.474603	+	0.822036i	−0.999577	−	0.0290821i	$-0.990742\pi$
$577$	−6578.00	+	11393.4i	−0.474603	+	0.822036i	0.524974	+	0.851118i	$0.324075\pi$
$578$	2995.50	−	5188.36i	0.215565	−	0.373369i
$579$	−272.000	−	471.118i	−0.0195232	−	0.0338152i
$580$	810.000			0.0579887
$581$		0			0
$582$	−5412.00			−0.385455
$583$	13432.5	+	23265.8i	0.954232	+	1.65278i
$584$	−7014.00	+	12148.6i	−0.496989	+	0.860810i
$585$	3392.50	−	5875.98i	0.239765	−	0.415285i
$586$	−8995.50	−	15580.7i	−0.634131	−	1.09835i
$587$	13368.0			0.939960			0.469980	−	0.882677i	$-0.344261\pi$
$587$	13368.0			0.939960			0.469980	+	0.882677i	$0.344261\pi$
$588$		0			0
$589$	10648.0			0.744895
$590$	2700.00	+	4676.54i	0.188402	+	0.326322i
$591$	2109.00	−	3652.90i	0.146790	−	0.254247i
$592$	−9194.50	+	15925.3i	−0.638330	+	1.10562i
$593$	13332.0	+	23091.7i	0.923237	+	1.59909i	0.794372	+	0.607431i	$0.207800\pi$
$593$	13332.0	+	23091.7i	0.923237	+	1.59909i	0.128865	+	0.991662i	$0.458867\pi$
$594$	13500.0			0.932511
$595$		0			0
$596$	−1086.00			−0.0746381
$597$	1424.00	+	2466.44i	0.0976222	+	0.169087i
$598$	6106.50	−	10576.8i	0.417581	−	0.723271i
$599$	−3807.00	+	6593.92i	−0.259682	+	0.449783i	−0.966157	−	0.257955i	$-0.916951\pi$
$599$	−3807.00	+	6593.92i	−0.259682	+	0.449783i	0.706474	+	0.707739i	$0.250285\pi$
$600$	525.000	+	909.327i	0.0357217	+	0.0618718i
$601$	−6410.00			−0.435057			−0.217529	−	0.976054i	$-0.569800\pi$
$601$	−6410.00			−0.435057			−0.217529	+	0.976054i	$0.569800\pi$
$602$		0			0
$603$	6440.00			0.434921
$604$	1433.00	+	2482.03i	0.0965363	+	0.167206i
$605$	1735.00	−	3005.11i	0.116591	−	0.201942i
$606$	2052.00	−	3554.17i	0.137552	−	0.238248i
$607$	−10734.5	−	18592.7i	−0.717792	−	1.24325i	−0.961873	−	0.273498i	$-0.911819\pi$
$607$	−10734.5	−	18592.7i	−0.717792	−	1.24325i	0.244080	−	0.969755i	$-0.421514\pi$
$608$	−5445.00			−0.363197
$609$		0			0
$610$	5880.00			0.390286
$611$	−1327.50	−	2299.30i	−0.0878967	−	0.152242i
$612$	621.000	−	1075.60i	0.0410171	−	0.0710436i
$613$	−1868.50	+	3236.34i	−0.123113	+	0.213237i	−0.920994	−	0.389578i	$-0.872621\pi$
$613$	−1868.50	+	3236.34i	−0.123113	+	0.213237i	0.797881	+	0.602815i	$0.205954\pi$
$614$	−9339.00	−	16175.6i	−0.613830	−	1.06318i
$615$	1950.00			0.127856
$616$		0			0
$617$	18078.0			1.17957			0.589784	−	0.807561i	$-0.299213\pi$
$617$	18078.0			1.17957			0.589784	+	0.807561i	$0.299213\pi$
$618$	−4548.00	−	7877.37i	−0.296031	−	0.512741i
$619$	6143.50	−	10640.9i	0.398915	−	0.690940i	−0.594678	−	0.803964i	$-0.702720\pi$
$619$	6143.50	−	10640.9i	0.398915	−	0.690940i	0.993592	+	0.113024i	$0.0360537\pi$
$620$	220.000	−	381.051i	0.0142507	−	0.0246829i
$621$	3450.00	+	5975.58i	0.222937	+	0.386138i
$622$	−14040.0			−0.905069
$623$		0			0
$624$	8378.00			0.537481
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	1542.00	−	2670.82i	0.0984516	−	0.170523i
$627$	5445.00	−	9431.02i	0.346814	−	0.600699i
$628$	−114.500	−	198.320i	−0.00727555	−	0.0126016i
$629$	−13986.0			−0.886579
$630$		0			0
$631$	−9580.00			−0.604396			−0.302198	−	0.953245i	$-0.597720\pi$
$631$	−9580.00			−0.604396			−0.302198	+	0.953245i	$0.597720\pi$
$632$	8211.00	+	14221.9i	0.516798	+	0.895120i
$633$	3625.00	−	6278.68i	0.227616	−	0.394242i
$634$	−12933.0	+	22400.6i	−0.810150	+	1.40322i
$635$	2007.50	+	3477.09i	0.125457	+	0.217298i
$636$	1194.00			0.0744421
$637$		0			0
$638$	21870.0			1.35712
$639$	552.000	+	956.092i	0.0341734	+	0.0591900i
$640$	4147.50	−	7183.68i	0.256163	−	0.443687i
$641$	−5389.50	+	9334.89i	−0.332094	+	0.575204i	−0.982922	−	0.184021i	$-0.941089\pi$
$641$	−5389.50	+	9334.89i	−0.332094	+	0.575204i	0.650828	+	0.759225i	$0.274422\pi$
$642$	2196.00	+	3803.58i	0.134999	+	0.233825i
$643$	−8882.00			−0.544746			−0.272373	−	0.962192i	$-0.587809\pi$
$643$	−8882.00			−0.544746			−0.272373	+	0.962192i	$0.587809\pi$
$644$		0			0
$645$	2860.00			0.174593
$646$	−9801.00	−	16975.8i	−0.596928	−	1.03391i
$647$	−5509.50	+	9542.73i	−0.334777	+	0.579851i	−0.983442	−	0.181223i	$-0.941994\pi$
$647$	−5509.50	+	9542.73i	−0.334777	+	0.579851i	0.648665	+	0.761074i	$0.275328\pi$
$648$	4420.50	−	7656.53i	0.267984	−	0.464162i
$649$	8100.00	+	14029.6i	0.489912	+	0.848552i
$650$	−4425.00			−0.267020
$651$		0			0
$652$	−1228.00			−0.0737610
$653$	−11161.5	−	19332.3i	−0.668887	−	1.15855i	−0.978216	−	0.207591i	$-0.933438\pi$
$653$	−11161.5	−	19332.3i	−0.668887	−	1.15855i	0.309329	−	0.950955i	$-0.399896\pi$
$654$	4800.00	−	8313.84i	0.286995	−	0.497090i
$655$	−5047.50	+	8742.53i	−0.301103	+	0.521525i
$656$	−6922.50	−	11990.1i	−0.412009	−	0.713621i
$657$	15364.0			0.912339
$658$		0			0
$659$	−11856.0			−0.700826			−0.350413	−	0.936595i	$-0.613959\pi$
$659$	−11856.0			−0.700826			−0.350413	+	0.936595i	$0.613959\pi$
$660$	−225.000	−	389.711i	−0.0132699	−	0.0229841i
$661$	−16622.0	+	28790.1i	−0.978095	+	1.69411i	−0.308777	+	0.951134i	$0.599920\pi$
$661$	−16622.0	+	28790.1i	−0.978095	+	1.69411i	−0.669318	+	0.742976i	$0.733414\pi$
$662$	2998.50	−	5193.55i	0.176042	−	0.304914i
$663$	3186.00	+	5518.31i	0.186627	+	0.323248i
$664$	16128.0			0.942602
$665$		0			0
$666$	17871.0			1.03977
$667$	5589.00	+	9680.43i	0.324448	+	0.561961i
$668$	−964.500	+	1670.56i	−0.0558647	+	0.0967605i
$669$	−4960.00	+	8590.97i	−0.286644	+	0.496482i
$670$	−2100.00	−	3637.31i	−0.121090	−	0.209733i
$671$	17640.0			1.01488
$672$		0			0
$673$	−12322.0			−0.705763			−0.352881	−	0.935668i	$-0.614798\pi$
$673$	−12322.0			−0.705763			−0.352881	+	0.935668i	$0.614798\pi$
$674$	−7671.00	−	13286.6i	−0.438392	−	0.759316i
$675$	1250.00	−	2165.06i	0.0712778	−	0.123457i
$676$	−642.000	+	1111.98i	−0.0365271	+	0.0632668i
$677$	−6298.50	−	10909.3i	−0.357564	−	0.619320i	0.629989	−	0.776604i	$-0.283059\pi$
$677$	−6298.50	−	10909.3i	−0.357564	−	0.619320i	−0.987553	+	0.157285i	$0.949726\pi$
$678$	−8352.00			−0.473092
$679$		0			0
$680$	5670.00			0.319757
$681$	−1500.00	−	2598.08i	−0.0844055	−	0.146195i
$682$	5940.00	−	10288.4i	0.333511	−	0.577658i
$683$	4170.00	−	7222.65i	0.233617	−	0.404637i	−0.725253	−	0.688483i	$-0.758277\pi$
$683$	4170.00	−	7222.65i	0.233617	−	0.404637i	0.958870	+	0.283846i	$0.0916104\pi$
$684$	1391.50	+	2410.15i	0.0777856	+	0.134729i
$685$	−300.000			−0.0167334
$686$		0			0
$687$	−12184.0			−0.676636
$688$	−10153.0	−	17585.5i	−0.562616	−	0.974479i
$689$	17611.5	−	30504.0i	0.973795	−	1.68666i
$690$	1035.00	−	1792.67i	0.0571040	−	0.0989071i
$691$	−10100.0	−	17493.7i	−0.556038	−	0.963086i	−0.997822	−	0.0659643i	$-0.978988\pi$
$691$	−10100.0	−	17493.7i	−0.556038	−	0.963086i	0.441784	−	0.897121i	$-0.354346\pi$
$692$	699.000			0.0383988
$693$		0			0
$694$	12960.0			0.708869
$695$	4270.00	+	7395.86i	0.233051	+	0.403656i
$696$	−3402.00	+	5892.44i	−0.185277	+	0.320908i
$697$	5265.00	−	9119.25i	0.286121	−	0.495576i
$698$	11883.0	+	20582.0i	0.644381	+	1.11610i
$699$	276.000			0.0149346
$700$		0			0
$701$	474.000			0.0255388			0.0127694	−	0.999918i	$-0.495935\pi$
$701$	474.000			0.0255388			0.0127694	+	0.999918i	$0.495935\pi$
$702$	−8850.00	−	15328.6i	−0.475814	−	0.824135i
$703$	15669.5	−	27140.4i	0.840663	−	1.45607i
$704$	9742.50	−	16874.5i	0.521569	−	0.903383i
$705$	−225.000	−	389.711i	−0.0120198	−	0.0208190i
$706$	−2484.00			−0.132417
$707$		0			0
$708$	720.000			0.0382193
$709$	12563.0	+	21759.8i	0.665463	+	1.15262i	0.979160	+	0.203093i	$0.0650993\pi$
$709$	12563.0	+	21759.8i	0.665463	+	1.15262i	−0.313696	+	0.949523i	$0.601567\pi$
$710$	360.000	−	623.538i	0.0190290	−	0.0329591i
$711$	8993.00	−	15576.3i	0.474351	−	0.821601i
$712$	12537.0	+	21714.7i	0.659893	+	1.14297i
$713$	6072.00			0.318932
$714$		0			0
$715$	−13275.0			−0.694345
$716$	−1558.50	−	2699.40i	−0.0813462	−	0.140896i
$717$	5502.00	−	9529.74i	0.286577	−	0.496367i
$718$	2025.00	−	3507.40i	0.105254	−	0.182305i
$719$	−3648.00	−	6318.52i	−0.189218	−	0.327734i	0.755772	−	0.654835i	$-0.227262\pi$
$719$	−3648.00	−	6318.52i	−0.189218	−	0.327734i	−0.944990	+	0.327100i	$0.893928\pi$
$720$	−8165.00			−0.422627
$721$		0			0
$722$	23346.0			1.20339
$723$	3551.00	+	6150.51i	0.182660	+	0.316376i
$724$	−899.000	+	1557.11i	−0.0461479	+	0.0799305i
$725$	2025.00	−	3507.40i	0.103733	−	0.179671i
$726$	−2082.00	−	3606.13i	−0.106433	−	0.184347i
$727$	15421.0			0.786703			0.393352	−	0.919388i	$-0.371316\pi$
$727$	15421.0			0.786703			0.393352	+	0.919388i	$0.371316\pi$
$728$		0			0
$729$	−4283.00			−0.217599
$730$	−5010.00	−	8677.57i	−0.254012	−	0.439961i
$731$	7722.00	−	13374.9i	0.390709	−	0.676728i
$732$	392.000	−	678.964i	0.0197934	−	0.0342831i
$733$	−14583.5	−	25259.4i	−0.734862	−	1.27282i	−0.954784	−	0.297301i	$-0.903914\pi$
$733$	−14583.5	−	25259.4i	−0.734862	−	1.27282i	0.219922	−	0.975517i	$-0.429420\pi$
$734$	−8403.00			−0.422562
$735$		0			0
$736$	−3105.00			−0.155505
$737$	−6300.00	−	10911.9i	−0.314876	−	0.545381i
$738$	−6727.50	+	11652.4i	−0.335559	+	0.581206i
$739$	6690.50	−	11588.3i	0.333037	−	0.576836i	−0.650069	−	0.759875i	$-0.725260\pi$
$739$	6690.50	−	11588.3i	0.333037	−	0.576836i	0.983106	+	0.183039i	$0.0585934\pi$
$740$	−647.500	−	1121.50i	−0.0321656	−	0.0557125i
$741$	−14278.0			−0.707848
$742$		0			0
$743$	5487.00			0.270927			0.135463	−	0.990782i	$-0.456748\pi$
$743$	5487.00			0.270927			0.135463	+	0.990782i	$0.456748\pi$
$744$	1848.00	+	3200.83i	0.0910631	+	0.157726i
$745$	−2715.00	+	4702.52i	−0.133517	+	0.231258i
$746$	−9903.00	+	17152.5i	−0.486025	+	0.841820i
$747$	−8832.00	−	15297.5i	−0.432592	−	0.749271i
$748$	−2430.00			−0.118783
$749$		0			0
$750$	−750.000			−0.0365148
$751$	−3319.00	−	5748.68i	−0.161268	−	0.279324i	0.774056	−	0.633117i	$-0.218225\pi$
$751$	−3319.00	−	5748.68i	−0.161268	−	0.279324i	−0.935324	+	0.353793i	$0.884892\pi$
$752$	−1597.50	+	2766.95i	−0.0774665	+	0.134176i
$753$	7065.00	−	12236.9i	0.341916	−	0.592216i
$754$	−14337.0	−	24832.4i	−0.692470	−	1.19939i
$755$	14330.0			0.690758
$756$		0			0
$757$	14846.0			0.712797			0.356398	−	0.934334i	$-0.384005\pi$
$757$	14846.0			0.712797			0.356398	+	0.934334i	$0.384005\pi$
$758$	12457.5	+	21577.0i	0.596935	+	1.03392i
$759$	3105.00	−	5378.02i	0.148491	−	0.257193i
$760$	−6352.50	+	11002.9i	−0.303197	+	0.525152i
$761$	−1825.50	−	3161.86i	−0.0869571	−	0.150614i	0.819266	−	0.573413i	$-0.194381\pi$
$761$	−1825.50	−	3161.86i	−0.0869571	−	0.150614i	−0.906223	+	0.422799i	$0.861048\pi$
$762$	4818.00			0.229052
$763$		0			0
$764$	−2388.00			−0.113082
$765$	−3105.00	−	5378.02i	−0.146747	−	0.254173i
$766$	1417.50	−	2455.18i	0.0668621	−	0.115809i
$767$	10620.0	−	18394.4i	0.499956	−	0.865949i
$768$	−1513.00	−	2620.59i	−0.0710881	−	0.123128i
$769$	−29855.0			−1.40000			−0.699999	−	0.714144i	$-0.746816\pi$
$769$	−29855.0			−1.40000			−0.699999	+	0.714144i	$0.746816\pi$
$770$		0			0
$771$	8160.00			0.381161
$772$	−136.000	−	235.559i	−0.00634035	−

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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 2.59808i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.50000 + 4.33013i) q^{5} +6.00000 q^{6} -21.0000 q^{8} +(11.5000 + 19.9186i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 2.59808i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.50000 + 4.33013i) q^{5} +6.00000 q^{6} -21.0000 q^{8} +(11.5000 + 19.9186i) q^{9} +(7.50000 - 12.9904i) q^{10} +(22.5000 - 38.9711i) q^{11} +(-1.00000 - 1.73205i) q^{12} -59.0000 q^{13} -10.0000 q^{15} +(35.5000 + 61.4878i) q^{16} +(-27.0000 + 46.7654i) q^{17} +(34.5000 - 59.7558i) q^{18} +(-60.5000 - 104.789i) q^{19} -5.00000 q^{20} -135.000 q^{22} +(-34.5000 - 59.7558i) q^{23} +(21.0000 - 36.3731i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(88.5000 + 153.286i) q^{26} -100.000 q^{27} -162.000 q^{29} +(15.0000 + 25.9808i) q^{30} +(-44.0000 + 76.2102i) q^{31} +(22.5000 - 38.9711i) q^{32} +(45.0000 + 77.9423i) q^{33} +162.000 q^{34} -23.0000 q^{36} +(129.500 + 224.301i) q^{37} +(-181.500 + 314.367i) q^{38} +(59.0000 - 102.191i) q^{39} +(-52.5000 - 90.9327i) q^{40} -195.000 q^{41} -286.000 q^{43} +(22.5000 + 38.9711i) q^{44} +(-57.5000 + 99.5929i) q^{45} +(-103.500 + 179.267i) q^{46} +(22.5000 + 38.9711i) q^{47} -142.000 q^{48} +75.0000 q^{50} +(-54.0000 - 93.5307i) q^{51} +(29.5000 - 51.0955i) q^{52} +(-298.500 + 517.017i) q^{53} +(150.000 + 259.808i) q^{54} +225.000 q^{55} +242.000 q^{57} +(243.000 + 420.888i) q^{58} +(-180.000 + 311.769i) q^{59} +(5.00000 - 8.66025i) q^{60} +(196.000 + 339.482i) q^{61} +264.000 q^{62} +433.000 q^{64} +(-147.500 - 255.477i) q^{65} +(135.000 - 233.827i) q^{66} +(140.000 - 242.487i) q^{67} +(-27.0000 - 46.7654i) q^{68} +138.000 q^{69} +48.0000 q^{71} +(-241.500 - 418.290i) q^{72} +(334.000 - 578.505i) q^{73} +(388.500 - 672.902i) q^{74} +(-25.0000 - 43.3013i) q^{75} +121.000 q^{76} -354.000 q^{78} +(-391.000 - 677.232i) q^{79} +(-177.500 + 307.439i) q^{80} +(-210.500 + 364.597i) q^{81} +(292.500 + 506.625i) q^{82} -768.000 q^{83} -270.000 q^{85} +(429.000 + 743.050i) q^{86} +(162.000 - 280.592i) q^{87} +(-472.500 + 818.394i) q^{88} +(-597.000 - 1034.03i) q^{89} +345.000 q^{90} +69.0000 q^{92} +(-88.0000 - 152.420i) q^{93} +(67.5000 - 116.913i) q^{94} +(302.500 - 523.945i) q^{95} +(45.0000 + 77.9423i) q^{96} -902.000 q^{97} +1035.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} - 2 q^{3} - q^{4} + 5 q^{5} + 12 q^{6} - 42 q^{8} + 23 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 - 2 * q^3 - q^4 + 5 * q^5 + 12 * q^6 - 42 * q^8 + 23 * q^9	\( 2 q - 3 q^{2} - 2 q^{3} - q^{4} + 5 q^{5} + 12 q^{6} - 42 q^{8} + 23 q^{9} + 15 q^{10} + 45 q^{11} - 2 q^{12} - 118 q^{13} - 20 q^{15} + 71 q^{16} - 54 q^{17} + 69 q^{18} - 121 q^{19} - 10 q^{20} - 270 q^{22} - 69 q^{23} + 42 q^{24} - 25 q^{25} + 177 q^{26} - 200 q^{27} - 324 q^{29} + 30 q^{30} - 88 q^{31} + 45 q^{32} + 90 q^{33} + 324 q^{34} - 46 q^{36} + 259 q^{37} - 363 q^{38} + 118 q^{39} - 105 q^{40} - 390 q^{41} - 572 q^{43} + 45 q^{44} - 115 q^{45} - 207 q^{46} + 45 q^{47} - 284 q^{48} + 150 q^{50} - 108 q^{51} + 59 q^{52} - 597 q^{53} + 300 q^{54} + 450 q^{55} + 484 q^{57} + 486 q^{58} - 360 q^{59} + 10 q^{60} + 392 q^{61} + 528 q^{62} + 866 q^{64} - 295 q^{65} + 270 q^{66} + 280 q^{67} - 54 q^{68} + 276 q^{69} + 96 q^{71} - 483 q^{72} + 668 q^{73} + 777 q^{74} - 50 q^{75} + 242 q^{76} - 708 q^{78} - 782 q^{79} - 355 q^{80} - 421 q^{81} + 585 q^{82} - 1536 q^{83} - 540 q^{85} + 858 q^{86} + 324 q^{87} - 945 q^{88} - 1194 q^{89} + 690 q^{90} + 138 q^{92} - 176 q^{93} + 135 q^{94} + 605 q^{95} + 90 q^{96} - 1804 q^{97} + 2070 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 - 2 * q^3 - q^4 + 5 * q^5 + 12 * q^6 - 42 * q^8 + 23 * q^9 + 15 * q^10 + 45 * q^11 - 2 * q^12 - 118 * q^13 - 20 * q^15 + 71 * q^16 - 54 * q^17 + 69 * q^18 - 121 * q^19 - 10 * q^20 - 270 * q^22 - 69 * q^23 + 42 * q^24 - 25 * q^25 + 177 * q^26 - 200 * q^27 - 324 * q^29 + 30 * q^30 - 88 * q^31 + 45 * q^32 + 90 * q^33 + 324 * q^34 - 46 * q^36 + 259 * q^37 - 363 * q^38 + 118 * q^39 - 105 * q^40 - 390 * q^41 - 572 * q^43 + 45 * q^44 - 115 * q^45 - 207 * q^46 + 45 * q^47 - 284 * q^48 + 150 * q^50 - 108 * q^51 + 59 * q^52 - 597 * q^53 + 300 * q^54 + 450 * q^55 + 484 * q^57 + 486 * q^58 - 360 * q^59 + 10 * q^60 + 392 * q^61 + 528 * q^62 + 866 * q^64 - 295 * q^65 + 270 * q^66 + 280 * q^67 - 54 * q^68 + 276 * q^69 + 96 * q^71 - 483 * q^72 + 668 * q^73 + 777 * q^74 - 50 * q^75 + 242 * q^76 - 708 * q^78 - 782 * q^79 - 355 * q^80 - 421 * q^81 + 585 * q^82 - 1536 * q^83 - 540 * q^85 + 858 * q^86 + 324 * q^87 - 945 * q^88 - 1194 * q^89 + 690 * q^90 + 138 * q^92 - 176 * q^93 + 135 * q^94 + 605 * q^95 + 90 * q^96 - 1804 * q^97 + 2070 * q^99

Introduction

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