LMFDB - Embedded newform 49.4.c.b.18.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,4,Mod(18,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("49.18");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	49.c (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:	$2.89109359028$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			18.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	49.18
Dual form			49.4.c.b.30.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(3.50000 - 6.06218i) q^{4} +(8.00000 + 13.8564i) q^{5} -2.00000 q^{6} +15.0000 q^{8} +(11.5000 + 19.9186i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(3.50000 - 6.06218i) q^{4} +(8.00000 + 13.8564i) q^{5} -2.00000 q^{6} +15.0000 q^{8} +(11.5000 + 19.9186i) q^{9} +(-8.00000 + 13.8564i) q^{10} +(4.00000 - 6.92820i) q^{11} +(7.00000 + 12.1244i) q^{12} -28.0000 q^{13} -32.0000 q^{15} +(-20.5000 - 35.5070i) q^{16} +(27.0000 - 46.7654i) q^{17} +(-11.5000 + 19.9186i) q^{18} +(-55.0000 - 95.2628i) q^{19} +112.000 q^{20} +8.00000 q^{22} +(-24.0000 - 41.5692i) q^{23} +(-15.0000 + 25.9808i) q^{24} +(-65.5000 + 113.449i) q^{25} +(-14.0000 - 24.2487i) q^{26} -100.000 q^{27} -110.000 q^{29} +(-16.0000 - 27.7128i) q^{30} +(6.00000 - 10.3923i) q^{31} +(80.5000 - 139.430i) q^{32} +(8.00000 + 13.8564i) q^{33} +54.0000 q^{34} +161.000 q^{36} +(123.000 + 213.042i) q^{37} +(55.0000 - 95.2628i) q^{38} +(28.0000 - 48.4974i) q^{39} +(120.000 + 207.846i) q^{40} -182.000 q^{41} +128.000 q^{43} +(-28.0000 - 48.4974i) q^{44} +(-184.000 + 318.697i) q^{45} +(24.0000 - 41.5692i) q^{46} +(162.000 + 280.592i) q^{47} +82.0000 q^{48} -131.000 q^{50} +(54.0000 + 93.5307i) q^{51} +(-98.0000 + 169.741i) q^{52} +(81.0000 - 140.296i) q^{53} +(-50.0000 - 86.6025i) q^{54} +128.000 q^{55} +220.000 q^{57} +(-55.0000 - 95.2628i) q^{58} +(405.000 - 701.481i) q^{59} +(-112.000 + 193.990i) q^{60} +(-244.000 - 422.620i) q^{61} +12.0000 q^{62} -167.000 q^{64} +(-224.000 - 387.979i) q^{65} +(-8.00000 + 13.8564i) q^{66} +(-122.000 + 211.310i) q^{67} +(-189.000 - 327.358i) q^{68} +96.0000 q^{69} -768.000 q^{71} +(172.500 + 298.779i) q^{72} +(-351.000 + 607.950i) q^{73} +(-123.000 + 213.042i) q^{74} +(-131.000 - 226.899i) q^{75} -770.000 q^{76} +56.0000 q^{78} +(-220.000 - 381.051i) q^{79} +(328.000 - 568.113i) q^{80} +(-210.500 + 364.597i) q^{81} +(-91.0000 - 157.617i) q^{82} +1302.00 q^{83} +864.000 q^{85} +(64.0000 + 110.851i) q^{86} +(110.000 - 190.526i) q^{87} +(60.0000 - 103.923i) q^{88} +(365.000 + 632.199i) q^{89} -368.000 q^{90} -336.000 q^{92} +(12.0000 + 20.7846i) q^{93} +(-162.000 + 280.592i) q^{94} +(880.000 - 1524.20i) q^{95} +(161.000 + 278.860i) q^{96} -294.000 q^{97} +184.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 2 q^{3} + 7 q^{4} + 16 q^{5} - 4 q^{6} + 30 q^{8} + 23 q^{9}+O(q^{10}) $ 2 * q + q^2 - 2 * q^3 + 7 * q^4 + 16 * q^5 - 4 * q^6 + 30 * q^8 + 23 * q^9	\( 2 q + q^{2} - 2 q^{3} + 7 q^{4} + 16 q^{5} - 4 q^{6} + 30 q^{8} + 23 q^{9} - 16 q^{10} + 8 q^{11} + 14 q^{12} - 56 q^{13} - 64 q^{15} - 41 q^{16} + 54 q^{17} - 23 q^{18} - 110 q^{19} + 224 q^{20} + 16 q^{22} - 48 q^{23} - 30 q^{24} - 131 q^{25} - 28 q^{26} - 200 q^{27} - 220 q^{29} - 32 q^{30} + 12 q^{31} + 161 q^{32} + 16 q^{33} + 108 q^{34} + 322 q^{36} + 246 q^{37} + 110 q^{38} + 56 q^{39} + 240 q^{40} - 364 q^{41} + 256 q^{43} - 56 q^{44} - 368 q^{45} + 48 q^{46} + 324 q^{47} + 164 q^{48} - 262 q^{50} + 108 q^{51} - 196 q^{52} + 162 q^{53} - 100 q^{54} + 256 q^{55} + 440 q^{57} - 110 q^{58} + 810 q^{59} - 224 q^{60} - 488 q^{61} + 24 q^{62} - 334 q^{64} - 448 q^{65} - 16 q^{66} - 244 q^{67} - 378 q^{68} + 192 q^{69} - 1536 q^{71} + 345 q^{72} - 702 q^{73} - 246 q^{74} - 262 q^{75} - 1540 q^{76} + 112 q^{78} - 440 q^{79} + 656 q^{80} - 421 q^{81} - 182 q^{82} + 2604 q^{83} + 1728 q^{85} + 128 q^{86} + 220 q^{87} + 120 q^{88} + 730 q^{89} - 736 q^{90} - 672 q^{92} + 24 q^{93} - 324 q^{94} + 1760 q^{95} + 322 q^{96} - 588 q^{97} + 368 q^{99}+O(q^{100}) \) 2 * q + q^2 - 2 * q^3 + 7 * q^4 + 16 * q^5 - 4 * q^6 + 30 * q^8 + 23 * q^9 - 16 * q^10 + 8 * q^11 + 14 * q^12 - 56 * q^13 - 64 * q^15 - 41 * q^16 + 54 * q^17 - 23 * q^18 - 110 * q^19 + 224 * q^20 + 16 * q^22 - 48 * q^23 - 30 * q^24 - 131 * q^25 - 28 * q^26 - 200 * q^27 - 220 * q^29 - 32 * q^30 + 12 * q^31 + 161 * q^32 + 16 * q^33 + 108 * q^34 + 322 * q^36 + 246 * q^37 + 110 * q^38 + 56 * q^39 + 240 * q^40 - 364 * q^41 + 256 * q^43 - 56 * q^44 - 368 * q^45 + 48 * q^46 + 324 * q^47 + 164 * q^48 - 262 * q^50 + 108 * q^51 - 196 * q^52 + 162 * q^53 - 100 * q^54 + 256 * q^55 + 440 * q^57 - 110 * q^58 + 810 * q^59 - 224 * q^60 - 488 * q^61 + 24 * q^62 - 334 * q^64 - 448 * q^65 - 16 * q^66 - 244 * q^67 - 378 * q^68 + 192 * q^69 - 1536 * q^71 + 345 * q^72 - 702 * q^73 - 246 * q^74 - 262 * q^75 - 1540 * q^76 + 112 * q^78 - 440 * q^79 + 656 * q^80 - 421 * q^81 - 182 * q^82 + 2604 * q^83 + 1728 * q^85 + 128 * q^86 + 220 * q^87 + 120 * q^88 + 730 * q^89 - 736 * q^90 - 672 * q^92 + 24 * q^93 - 324 * q^94 + 1760 * q^95 + 322 * q^96 - 588 * q^97 + 368 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.176777	+	0.306186i	0.940775	−	0.339032i	$-0.110100\pi$
$2$	0.500000	+	0.866025i	0.176777	+	0.306186i	−0.763998	+	0.645219i	$0.776766\pi$
$3$	−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	$0.228310\pi$
$4$	3.50000	−	6.06218i	0.437500	−	0.757772i
$5$	8.00000	+	13.8564i	0.715542	+	1.23935i	0.962750	+	0.270392i	$0.0871534\pi$
$5$	8.00000	+	13.8564i	0.715542	+	1.23935i	−0.247208	+	0.968962i	$0.579513\pi$
$6$	−2.00000			−0.136083
$7$		0			0
$7$		0			0
$8$	15.0000			0.662913
$9$	11.5000	+	19.9186i	0.425926	+	0.737725i
$10$	−8.00000	+	13.8564i	−0.252982	+	0.438178i
$11$	4.00000	−	6.92820i	0.109640	−	0.189903i	−0.805984	−	0.591937i	$-0.798363\pi$
$11$	4.00000	−	6.92820i	0.109640	−	0.189903i	0.915625	+	0.402034i	$0.131697\pi$
$12$	7.00000	+	12.1244i	0.168394	+	0.291667i
$13$	−28.0000			−0.597369			−0.298685	−	0.954352i	$-0.596548\pi$
$13$	−28.0000			−0.597369			−0.298685	+	0.954352i	$0.596548\pi$
$14$		0			0
$15$	−32.0000			−0.550824
$16$	−20.5000	−	35.5070i	−0.320312	−	0.554798i
$17$	27.0000	−	46.7654i	0.385204	−	0.667192i	−0.606594	−	0.795012i	$-0.707465\pi$
$17$	27.0000	−	46.7654i	0.385204	−	0.667192i	0.991797	+	0.127820i	$0.0407979\pi$
$18$	−11.5000	+	19.9186i	−0.150588	+	0.260825i
$19$	−55.0000	−	95.2628i	−0.664098	−	1.15025i	−0.979529	−	0.201303i	$-0.935482\pi$
$19$	−55.0000	−	95.2628i	−0.664098	−	1.15025i	0.315431	−	0.948949i	$-0.397851\pi$
$20$	112.000			1.25220
$21$		0			0
$22$	8.00000			0.0775275
$23$	−24.0000	−	41.5692i	−0.217580	−	0.376860i	0.736487	−	0.676451i	$-0.236483\pi$
$23$	−24.0000	−	41.5692i	−0.217580	−	0.376860i	−0.954068	+	0.299591i	$0.903150\pi$
$24$	−15.0000	+	25.9808i	−0.127578	+	0.220971i
$25$	−65.5000	+	113.449i	−0.524000	+	0.907595i
$26$	−14.0000	−	24.2487i	−0.105601	−	0.182906i
$27$	−100.000			−0.712778
$28$		0			0
$29$	−110.000			−0.704362			−0.352181	−	0.935932i	$-0.614560\pi$
$29$	−110.000			−0.704362			−0.352181	+	0.935932i	$0.614560\pi$
$30$	−16.0000	−	27.7128i	−0.0973729	−	0.168655i
$31$	6.00000	−	10.3923i	0.0347623	−	0.0602101i	−0.848121	−	0.529803i	$-0.822266\pi$
$31$	6.00000	−	10.3923i	0.0347623	−	0.0602101i	0.882883	+	0.469593i	$0.155599\pi$
$32$	80.5000	−	139.430i	0.444704	−	0.770250i
$33$	8.00000	+	13.8564i	0.0422006	+	0.0730937i
$34$	54.0000			0.272380
$35$		0			0
$36$	161.000			0.745370
$37$	123.000	+	213.042i	0.546516	+	0.946593i	0.998510	+	0.0545719i	$0.0173794\pi$
$37$	123.000	+	213.042i	0.546516	+	0.946593i	−0.451994	+	0.892021i	$0.649287\pi$
$38$	55.0000	−	95.2628i	0.234794	−	0.406675i
$39$	28.0000	−	48.4974i	0.114964	−	0.199123i
$40$	120.000	+	207.846i	0.474342	+	0.821584i
$41$	−182.000			−0.693259			−0.346630	−	0.938002i	$-0.612674\pi$
$41$	−182.000			−0.693259			−0.346630	+	0.938002i	$0.612674\pi$
$42$		0			0
$43$	128.000			0.453949			0.226975	−	0.973901i	$-0.427117\pi$
$43$	128.000			0.453949			0.226975	+	0.973901i	$0.427117\pi$
$44$	−28.0000	−	48.4974i	−0.0959354	−	0.166165i
$45$	−184.000	+	318.697i	−0.609536	+	1.05575i
$46$	24.0000	−	41.5692i	0.0769262	−	0.133240i
$47$	162.000	+	280.592i	0.502769	+	0.870821i	0.999995	+	0.00319997i	$0.00101858\pi$
$47$	162.000	+	280.592i	0.502769	+	0.870821i	−0.497226	+	0.867621i	$0.665648\pi$
$48$	82.0000			0.246577
$49$		0			0
$50$	−131.000			−0.370524
$51$	54.0000	+	93.5307i	0.148265	+	0.256802i
$52$	−98.0000	+	169.741i	−0.261349	+	0.452670i
$53$	81.0000	−	140.296i	0.209928	−	0.363607i	−0.741763	−	0.670662i	$-0.766010\pi$
$53$	81.0000	−	140.296i	0.209928	−	0.363607i	0.951692	+	0.307055i	$0.0993436\pi$
$54$	−50.0000	−	86.6025i	−0.126003	−	0.218243i
$55$	128.000			0.313809
$56$		0			0
$57$	220.000			0.511223
$58$	−55.0000	−	95.2628i	−0.124515	−	0.215666i
$59$	405.000	−	701.481i	0.893670	−	1.54788i	0.0582271	−	0.998303i	$-0.481455\pi$
$59$	405.000	−	701.481i	0.893670	−	1.54788i	0.835442	−	0.549578i	$-0.185211\pi$
$60$	−112.000	+	193.990i	−0.240986	+	0.417399i
$61$	−244.000	−	422.620i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−244.000	−	422.620i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$	12.0000			0.0245807
$63$		0			0
$64$	−167.000			−0.326172
$65$	−224.000	−	387.979i	−0.427443	−	0.740353i
$66$	−8.00000	+	13.8564i	−0.0149202	+	0.0258425i
$67$	−122.000	+	211.310i	−0.222458	+	0.385308i	−0.955554	−	0.294817i	$-0.904741\pi$
$67$	−122.000	+	211.310i	−0.222458	+	0.385308i	0.733096	+	0.680125i	$0.238075\pi$
$68$	−189.000	−	327.358i	−0.337053	−	0.583793i
$69$	96.0000			0.167493
$70$		0			0
$71$	−768.000			−1.28373			−0.641865	−	0.766818i	$-0.721839\pi$
$71$	−768.000			−1.28373			−0.641865	+	0.766818i	$0.721839\pi$
$72$	172.500	+	298.779i	0.282352	+	0.489047i
$73$	−351.000	+	607.950i	−0.562759	+	0.974728i	0.434495	+	0.900674i	$0.356927\pi$
$73$	−351.000	+	607.950i	−0.562759	+	0.974728i	−0.997254	+	0.0740537i	$0.976406\pi$
$74$	−123.000	+	213.042i	−0.193222	+	0.334671i
$75$	−131.000	−	226.899i	−0.201688	−	0.349333i
$76$	−770.000			−1.16217
$77$		0			0
$78$	56.0000			0.0812917
$79$	−220.000	−	381.051i	−0.313316	−	0.542679i	0.665762	−	0.746164i	$-0.268106\pi$
$79$	−220.000	−	381.051i	−0.313316	−	0.542679i	−0.979078	+	0.203485i	$0.934773\pi$
$80$	328.000	−	568.113i	0.458394	−	0.793962i
$81$	−210.500	+	364.597i	−0.288752	+	0.500133i
$82$	−91.0000	−	157.617i	−0.122552	−	0.212266i
$83$	1302.00			1.72184			0.860922	−	0.508737i	$-0.169887\pi$
$83$	1302.00			1.72184			0.860922	+	0.508737i	$0.169887\pi$
$84$		0			0
$85$	864.000			1.10252
$86$	64.0000	+	110.851i	0.0802476	+	0.138993i
$87$	110.000	−	190.526i	0.135554	−	0.234787i
$88$	60.0000	−	103.923i	0.0726821	−	0.125889i
$89$	365.000	+	632.199i	0.434718	+	0.752954i	0.997273	−	0.0738062i	$-0.0235146\pi$
$89$	365.000	+	632.199i	0.434718	+	0.752954i	−0.562554	+	0.826760i	$0.690181\pi$
$90$	−368.000			−0.431007
$91$		0			0
$92$	−336.000			−0.380765
$93$	12.0000	+	20.7846i	0.0133800	+	0.0231749i
$94$	−162.000	+	280.592i	−0.177756	+	0.307882i
$95$	880.000	−	1524.20i	0.950380	−	1.64611i
$96$	161.000	+	278.860i	0.171167	+	0.296469i
$97$	−294.000			−0.307744			−0.153872	−	0.988091i	$-0.549174\pi$
$97$	−294.000			−0.307744			−0.153872	+	0.988091i	$0.549174\pi$
$98$		0			0
$99$	184.000			0.186795
$100$	458.500	+	794.145i	0.458500	+	0.794145i
$101$	−344.000	+	595.825i	−0.338904	+	0.586999i	−0.984227	−	0.176911i	$-0.943389\pi$
$101$	−344.000	+	595.825i	−0.338904	+	0.586999i	0.645323	+	0.763910i	$0.276723\pi$
$102$	−54.0000	+	93.5307i	−0.0524196	+	0.0907934i
$103$	694.000	+	1202.04i	0.663901	+	1.14991i	0.979582	+	0.201046i	$0.0644339\pi$
$103$	694.000	+	1202.04i	0.663901	+	1.14991i	−0.315680	+	0.948866i	$0.602233\pi$
$104$	−420.000			−0.396004
$105$		0			0
$106$	162.000			0.148442
$107$	−122.000	−	211.310i	−0.110226	−	0.190917i	0.805635	−	0.592412i	$-0.201824\pi$
$107$	−122.000	−	211.310i	−0.110226	−	0.190917i	−0.915861	+	0.401495i	$0.868491\pi$
$108$	−350.000	+	606.218i	−0.311840	+	0.540123i
$109$	−45.0000	+	77.9423i	−0.0395433	+	0.0684910i	−0.885120	−	0.465363i	$-0.845924\pi$
$109$	−45.0000	+	77.9423i	−0.0395433	+	0.0684910i	0.845576	+	0.533854i	$0.179257\pi$
$110$	64.0000	+	110.851i	0.0554742	+	0.0960841i
$111$	−492.000			−0.420708
$112$		0			0
$113$	1318.00			1.09723			0.548615	−	0.836075i	$-0.315155\pi$
$113$	1318.00			1.09723			0.548615	+	0.836075i	$0.315155\pi$
$114$	110.000	+	190.526i	0.0903723	+	0.156529i
$115$	384.000	−	665.108i	0.311376	−	0.539318i
$116$	−385.000	+	666.840i	−0.308158	+	0.533746i
$117$	−322.000	−	557.720i	−0.254435	−	0.440695i
$118$	810.000			0.631920
$119$		0			0
$120$	−480.000			−0.365148
$121$	633.500	+	1097.25i	0.475958	+	0.824383i
$122$	244.000	−	422.620i	0.181071	−	0.313625i
$123$	182.000	−	315.233i	0.133418	−	0.231086i
$124$	−42.0000	−	72.7461i	−0.0304170	−	0.0526838i
$125$	−96.0000			−0.0686920
$126$		0			0
$127$	−1776.00			−1.24090			−0.620451	−	0.784245i	$-0.713050\pi$
$127$	−1776.00			−1.24090			−0.620451	+	0.784245i	$0.713050\pi$
$128$	−727.500	−	1260.07i	−0.502363	−	0.870119i
$129$	−128.000	+	221.703i	−0.0873626	+	0.151316i
$130$	224.000	−	387.979i	0.151124	−	0.261754i
$131$	−559.000	−	968.216i	−0.372825	−	0.645752i	0.617174	−	0.786827i	$-0.288277\pi$
$131$	−559.000	−	968.216i	−0.372825	−	0.645752i	−0.989999	+	0.141075i	$0.954944\pi$
$132$	112.000			0.0738511
$133$		0			0
$134$	−244.000			−0.157301
$135$	−800.000	−	1385.64i	−0.510022	−	0.883385i
$136$	405.000	−	701.481i	0.255356	−	0.442290i
$137$	−1137.00	+	1969.34i	−0.709054	+	1.22812i	0.256154	+	0.966636i	$0.417545\pi$
$137$	−1137.00	+	1969.34i	−0.709054	+	1.22812i	−0.965208	+	0.261482i	$0.915789\pi$
$138$	48.0000	+	83.1384i	0.0296089	+	0.0512842i
$139$	210.000			0.128144			0.0640718	−	0.997945i	$-0.479591\pi$
$139$	210.000			0.128144			0.0640718	+	0.997945i	$0.479591\pi$
$140$		0			0
$141$	−648.000			−0.387032
$142$	−384.000	−	665.108i	−0.226934	−	0.393060i
$143$	−112.000	+	193.990i	−0.0654959	+	0.113442i
$144$	471.500	−	816.662i	0.272859	−	0.472605i
$145$	−880.000	−	1524.20i	−0.504000	−	0.872954i
$146$	−702.000			−0.397931
$147$		0			0
$148$	1722.00			0.956402
$149$	1005.00	+	1740.71i	0.552569	+	0.957078i	0.998088	+	0.0618054i	$0.0196858\pi$
$149$	1005.00	+	1740.71i	0.552569	+	0.957078i	−0.445519	+	0.895272i	$0.646981\pi$
$150$	131.000	−	226.899i	0.0713074	−	0.123508i
$151$	−556.000	+	963.020i	−0.299647	+	0.519003i	−0.976055	−	0.217524i	$-0.930202\pi$
$151$	−556.000	+	963.020i	−0.299647	+	0.519003i	0.676408	+	0.736527i	$0.263535\pi$
$152$	−825.000	−	1428.94i	−0.440239	−	0.762516i
$153$	1242.00			0.656273
$154$		0			0
$155$	192.000			0.0994956
$156$	−196.000	−	339.482i	−0.100593	−	0.174233i
$157$	62.0000	−	107.387i	0.0315168	−	0.0545887i	−0.849837	−	0.527046i	$-0.823300\pi$
$157$	62.0000	−	107.387i	0.0315168	−	0.0545887i	0.881354	+	0.472457i	$0.156633\pi$
$158$	220.000	−	381.051i	0.110774	−	0.191866i
$159$	162.000	+	280.592i	0.0808015	+	0.139952i
$160$	2576.00			1.27282
$161$		0			0
$162$	−421.000			−0.204178
$163$	−1004.00	−	1738.98i	−0.482450	−	0.835628i	0.517347	−	0.855776i	$-0.326920\pi$
$163$	−1004.00	−	1738.98i	−0.482450	−	0.835628i	−0.999797	+	0.0201478i	$0.993586\pi$
$164$	−637.000	+	1103.32i	−0.303301	+	0.525333i
$165$	−128.000	+	221.703i	−0.0603926	+	0.104603i
$166$	651.000	+	1127.57i	0.304382	+	0.527205i
$167$	−2884.00			−1.33635			−0.668176	−	0.744004i	$-0.732924\pi$
$167$	−2884.00			−1.33635			−0.668176	+	0.744004i	$0.732924\pi$
$168$		0			0
$169$	−1413.00			−0.643150
$170$	432.000	+	748.246i	0.194899	+	0.337576i
$171$	1265.00	−	2191.04i	0.565713	−	0.979844i
$172$	448.000	−	775.959i	0.198603	−	0.343990i
$173$	1114.00	+	1929.50i	0.489571	+	0.847963i	0.999928	−	0.0120003i	$-0.00381992\pi$
$173$	1114.00	+	1929.50i	0.489571	+	0.847963i	−0.510357	+	0.859963i	$0.670487\pi$
$174$	220.000			0.0958515
$175$		0			0
$176$	−328.000			−0.140477
$177$	810.000	+	1402.96i	0.343974	+	0.595780i
$178$	−365.000	+	632.199i	−0.153696	+	0.266209i
$179$	410.000	−	710.141i	0.171200	−	0.296527i	−0.767640	−	0.640882i	$-0.778569\pi$
$179$	410.000	−	710.141i	0.171200	−	0.296527i	0.938840	+	0.344354i	$0.111902\pi$
$180$	1288.00	+	2230.88i	0.533344	+	0.923778i
$181$	−3892.00			−1.59829			−0.799144	−	0.601140i	$-0.794713\pi$
$181$	−3892.00			−1.59829			−0.799144	+	0.601140i	$0.794713\pi$
$182$		0			0
$183$	976.000			0.394251
$184$	−360.000	−	623.538i	−0.144237	−	0.249825i
$185$	−1968.00	+	3408.68i	−0.782109	+	1.35465i
$186$	−12.0000	+	20.7846i	−0.00473055	+	0.00819356i
$187$	−216.000	−	374.123i	−0.0844678	−	0.146303i
$188$	2268.00			0.879845
$189$		0			0
$190$	1760.00			0.672020
$191$	2524.00	+	4371.70i	0.956179	+	1.65615i	0.731646	+	0.681684i	$0.238752\pi$
$191$	2524.00	+	4371.70i	0.956179	+	1.65615i	0.224533	+	0.974466i	$0.427914\pi$
$192$	167.000	−	289.252i	0.0627718	−	0.108724i
$193$	1481.00	−	2565.17i	0.552356	−	0.956709i	−0.445748	−	0.895159i	$-0.647062\pi$
$193$	1481.00	−	2565.17i	0.552356	−	0.956709i	0.998104	−	0.0615502i	$-0.0196044\pi$
$194$	−147.000	−	254.611i	−0.0544020	−	0.0942270i
$195$	896.000			0.329046
$196$		0			0
$197$	3334.00			1.20577			0.602887	−	0.797826i	$-0.294017\pi$
$197$	3334.00			1.20577			0.602887	+	0.797826i	$0.294017\pi$
$198$	92.0000	+	159.349i	0.0330210	+	0.0571940i
$199$	930.000	−	1610.81i	0.331286	−	0.573805i	−0.651478	−	0.758667i	$-0.725851\pi$
$199$	930.000	−	1610.81i	0.331286	−	0.573805i	0.982764	+	0.184863i	$0.0591841\pi$
$200$	−982.500	+	1701.74i	−0.347366	+	0.601656i
$201$	−244.000	−	422.620i	−0.0856240	−	0.148305i
$202$	−688.000			−0.239641
$203$		0			0
$204$	756.000			0.259464
$205$	−1456.00	−	2521.87i	−0.496056	−	0.859194i
$206$	−694.000	+	1202.04i	−0.234725	+	0.406555i
$207$	552.000	−	956.092i	0.185346	−	0.321029i
$208$	574.000	+	994.197i	0.191345	+	0.331419i
$209$	−880.000			−0.291248
$210$		0			0
$211$	−4268.00			−1.39252			−0.696259	−	0.717791i	$-0.745153\pi$
$211$	−4268.00			−1.39252			−0.696259	+	0.717791i	$0.745153\pi$
$212$	−567.000	−	982.073i	−0.183687	−	0.318156i
$213$	768.000	−	1330.22i	0.247054	−	0.427910i
$214$	122.000	−	211.310i	0.0389708	−	0.0674994i
$215$	1024.00	+	1773.62i	0.324820	+	0.562604i
$216$	−1500.00			−0.472510
$217$		0			0
$218$	−90.0000			−0.0279613
$219$	−702.000	−	1215.90i	−0.216606	−	0.375173i
$220$	448.000	−	775.959i	0.137292	−	0.237796i
$221$	−756.000	+	1309.43i	−0.230109	+	0.398560i
$222$	−246.000	−	426.084i	−0.0743713	−	0.128815i
$223$	5432.00			1.63118			0.815591	−	0.578629i	$-0.196412\pi$
$223$	5432.00			1.63118			0.815591	+	0.578629i	$0.196412\pi$
$224$		0			0
$225$	−3013.00			−0.892741
$226$	659.000	+	1141.42i	0.193965	+	0.335957i
$227$	−1023.00	+	1771.89i	−0.299114	+	0.518081i	−0.975934	−	0.218068i	$-0.930024\pi$
$227$	−1023.00	+	1771.89i	−0.299114	+	0.518081i	0.676819	+	0.736149i	$0.263358\pi$
$228$	770.000	−	1333.68i	0.223660	−	0.387391i
$229$	−1490.00	−	2580.76i	−0.429965	−	0.744721i	0.566905	−	0.823783i	$-0.308141\pi$
$229$	−1490.00	−	2580.76i	−0.429965	−	0.744721i	−0.996870	+	0.0790622i	$0.974807\pi$
$230$	768.000			0.220176
$231$		0			0
$232$	−1650.00			−0.466930
$233$	−2229.00	−	3860.74i	−0.626724	−	1.08552i	−0.988205	−	0.153138i	$-0.951062\pi$
$233$	−2229.00	−	3860.74i	−0.626724	−	1.08552i	0.361481	−	0.932379i	$-0.382271\pi$
$234$	322.000	−	557.720i	0.0899564	−	0.155809i
$235$	−2592.00	+	4489.48i	−0.719504	+	1.24622i
$236$	−2835.00	−	4910.36i	−0.781961	−	1.35440i
$237$	880.000			0.241190
$238$		0			0
$239$	4440.00			1.20167			0.600836	−	0.799372i	$-0.294834\pi$
$239$	4440.00			1.20167			0.600836	+	0.799372i	$0.294834\pi$
$240$	656.000	+	1136.23i	0.176436	+	0.305596i
$241$	1651.00	−	2859.62i	0.441287	−	0.764332i	−0.556498	−	0.830849i	$-0.687855\pi$
$241$	1651.00	−	2859.62i	0.441287	−	0.764332i	0.997785	+	0.0665168i	$0.0211886\pi$
$242$	−633.500	+	1097.25i	−0.168277	+	0.291464i
$243$	−1771.00	−	3067.46i	−0.467530	−	0.809785i
$244$	−3416.00			−0.896258
$245$		0			0
$246$	364.000			0.0943406
$247$	1540.00	+	2667.36i	0.396712	+	0.687125i
$248$	90.0000	−	155.885i	0.0230444	−	0.0399140i
$249$	−1302.00	+	2255.13i	−0.331369	+	0.573948i
$250$	−48.0000	−	83.1384i	−0.0121431	−	0.0210325i
$251$	−1582.00			−0.397829			−0.198914	−	0.980017i	$-0.563742\pi$
$251$	−1582.00			−0.397829			−0.198914	+	0.980017i	$0.563742\pi$
$252$		0			0
$253$	−384.000			−0.0954224
$254$	−888.000	−	1538.06i	−0.219363	−	0.379947i
$255$	−864.000	+	1496.49i	−0.212180	+	0.367506i
$256$	59.5000	−	103.057i	0.0145264	−	0.0251604i
$257$	1177.00	+	2038.62i	0.285678	+	0.494809i	0.972773	−	0.231758i	$-0.0744479\pi$
$257$	1177.00	+	2038.62i	0.285678	+	0.494809i	−0.687095	+	0.726567i	$0.741115\pi$
$258$	−256.000			−0.0617747
$259$		0			0
$260$	−3136.00			−0.748025
$261$	−1265.00	−	2191.04i	−0.300006	−	0.519625i
$262$	559.000	−	968.216i	0.131813	−	0.228308i
$263$	1936.00	−	3353.25i	0.453912	−	0.786199i	−0.544713	−	0.838623i	$-0.683361\pi$
$263$	1936.00	−	3353.25i	0.453912	−	0.786199i	0.998625	+	0.0524239i	$0.0166947\pi$
$264$	120.000	+	207.846i	0.0279753	+	0.0484547i
$265$	2592.00			0.600850
$266$		0			0
$267$	−1460.00			−0.334646
$268$	854.000	+	1479.17i	0.194651	+	0.337145i
$269$	90.0000	−	155.885i	0.0203992	−	0.0353325i	−0.855646	−	0.517562i	$-0.826840\pi$
$269$	90.0000	−	155.885i	0.0203992	−	0.0353325i	0.876045	+	0.482230i	$0.160173\pi$
$270$	800.000	−	1385.64i	0.180320	−	0.312324i
$271$	1016.00	+	1759.76i	0.227740	+	0.394458i	0.957138	−	0.289632i	$-0.0935330\pi$
$271$	1016.00	+	1759.76i	0.227740	+	0.394458i	−0.729398	+	0.684090i	$0.760200\pi$
$272$	−2214.00			−0.493542
$273$		0			0
$274$	−2274.00			−0.501377
$275$	524.000	+	907.595i	0.114903	+	0.199018i
$276$	336.000	−	581.969i	0.0732783	−	0.126922i
$277$	2713.00	−	4699.05i	0.588478	−	1.01927i	−0.405954	−	0.913893i	$-0.633061\pi$
$277$	2713.00	−	4699.05i	0.588478	−	1.01927i	0.994432	−	0.105380i	$-0.0336059\pi$
$278$	105.000	+	181.865i	0.0226528	+	0.0392358i
$279$	276.000			0.0592247
$280$		0			0
$281$	842.000			0.178753			0.0893764	−	0.995998i	$-0.471513\pi$
$281$	842.000			0.178753			0.0893764	+	0.995998i	$0.471513\pi$
$282$	−324.000	−	561.184i	−0.0684182	−	0.118504i
$283$	−1891.00	+	3275.31i	−0.397202	+	0.687975i	−0.993380	−	0.114878i	$-0.963352\pi$
$283$	−1891.00	+	3275.31i	−0.397202	+	0.687975i	0.596177	+	0.802853i	$0.296686\pi$
$284$	−2688.00	+	4655.75i	−0.561632	+	0.972775i
$285$	1760.00	+	3048.41i	0.365801	+	0.633587i
$286$	−224.000			−0.0463126
$287$		0			0
$288$	3703.00			0.757644
$289$	998.500	+	1729.45i	0.203236	+	0.352016i
$290$	880.000	−	1524.20i	0.178191	−	0.308636i
$291$	294.000	−	509.223i	0.0592254	−	0.102581i
$292$	2457.00	+	4255.65i	0.492415	+	0.852887i
$293$	4312.00			0.859760			0.429880	−	0.902886i	$-0.358556\pi$
$293$	4312.00			0.859760			0.429880	+	0.902886i	$0.358556\pi$
$294$		0			0
$295$	12960.0			2.55783
$296$	1845.00	+	3195.63i	0.362292	+	0.627508i
$297$	−400.000	+	692.820i	−0.0781493	+	0.135359i
$298$	−1005.00	+	1740.71i	−0.195363	+	0.338378i
$299$	672.000	+	1163.94i	0.129976	+	0.225125i
$300$	−1834.00			−0.352953
$301$		0			0
$302$	−1112.00			−0.211882
$303$	−688.000	−	1191.65i	−0.130444	−	0.225936i
$304$	−2255.00	+	3905.77i	−0.425438	+	0.736880i
$305$	3904.00	−	6761.93i	0.732926	−	1.26946i
$306$	621.000	+	1075.60i	0.116014	+	0.200942i
$307$	−2674.00			−0.497112			−0.248556	−	0.968618i	$-0.579956\pi$
$307$	−2674.00			−0.497112			−0.248556	+	0.968618i	$0.579956\pi$
$308$		0			0
$309$	−2776.00			−0.511072
$310$	96.0000	+	166.277i	0.0175885	+	0.0304642i
$311$	−1884.00	+	3263.18i	−0.343511	+	0.594978i	−0.985082	−	0.172085i	$-0.944950\pi$
$311$	−1884.00	+	3263.18i	−0.343511	+	0.594978i	0.641571	+	0.767063i	$0.278283\pi$
$312$	420.000	−	727.461i	0.0762110	−	0.132001i
$313$	1219.00	+	2111.37i	0.220134	+	0.381283i	0.954849	−	0.297093i	$-0.0960172\pi$
$313$	1219.00	+	2111.37i	0.220134	+	0.381283i	−0.734714	+	0.678376i	$0.762684\pi$
$314$	124.000			0.0222857
$315$		0			0
$316$	−3080.00			−0.548302
$317$	1593.00	+	2759.16i	0.282245	+	0.488863i	0.971937	−	0.235239i	$-0.0755874\pi$
$317$	1593.00	+	2759.16i	0.282245	+	0.488863i	−0.689692	+	0.724103i	$0.742254\pi$
$318$	−162.000	+	280.592i	−0.0285676	+	0.0494806i
$319$	−440.000	+	762.102i	−0.0772266	+	0.133760i
$320$	−1336.00	−	2314.02i	−0.233390	−	0.404243i
$321$	488.000			0.0848520
$322$		0			0
$323$	−5940.00			−1.02325
$324$	1473.50	+	2552.18i	0.252658	+	0.437616i
$325$	1834.00	−	3176.58i	0.313022	−	0.542169i
$326$	1004.00	−	1738.98i	0.170572	−	0.295439i
$327$	−90.0000	−	155.885i	−0.0152202	−	0.0263622i
$328$	−2730.00			−0.459570
$329$		0			0
$330$	−256.000			−0.0427040
$331$	−4336.00	−	7510.17i	−0.720025	−	1.24712i	−0.960989	−	0.276585i	$-0.910797\pi$
$331$	−4336.00	−	7510.17i	−0.720025	−	1.24712i	0.240965	−	0.970534i	$-0.422536\pi$
$332$	4557.00	−	7892.96i	0.753307	−	1.30477i
$333$	−2829.00	+	4899.97i	−0.465550	+	0.806357i
$334$	−1442.00	−	2497.62i	−0.236236	−	0.409172i
$335$	−3904.00			−0.636711
$336$		0			0
$337$	814.000			0.131577			0.0657884	−	0.997834i	$-0.479044\pi$
$337$	814.000			0.131577			0.0657884	+	0.997834i	$0.479044\pi$
$338$	−706.500	−	1223.69i	−0.113694	−	0.196924i
$339$	−1318.00	+	2282.84i	−0.211162	+	0.365743i
$340$	3024.00	−	5237.72i	0.482351	−	0.835457i
$341$	−48.0000	−	83.1384i	−0.00762271	−	0.0132029i
$342$	2530.00			0.400020
$343$		0			0
$344$	1920.00			0.300929
$345$	768.000	+	1330.22i	0.119848	+	0.207584i
$346$	−1114.00	+	1929.50i	−0.173090	+	0.299800i
$347$	−4672.00	+	8092.14i	−0.722784	+	1.25190i	0.237095	+	0.971486i	$0.423805\pi$
$347$	−4672.00	+	8092.14i	−0.722784	+	1.25190i	−0.959880	+	0.280413i	$0.909529\pi$
$348$	−770.000	−	1333.68i	−0.118610	−	0.205439i
$349$	5180.00			0.794496			0.397248	−	0.917711i	$-0.369965\pi$
$349$	5180.00			0.794496			0.397248	+	0.917711i	$0.369965\pi$
$350$		0			0
$351$	2800.00			0.425792
$352$	−644.000	−	1115.44i	−0.0975151	−	0.168901i
$353$	6089.00	−	10546.5i	0.918087	−	1.59017i	0.115770	−	0.993276i	$-0.463067\pi$
$353$	6089.00	−	10546.5i	0.918087	−	1.59017i	0.802317	−	0.596898i	$-0.203600\pi$
$354$	−810.000	+	1402.96i	−0.121613	+	0.210640i
$355$	−6144.00	−	10641.7i	−0.918562	−	1.59100i
$356$	5110.00			0.760757
$357$		0			0
$358$	820.000			0.121057
$359$	−220.000	−	381.051i	−0.0323431	−	0.0560198i	0.849401	−	0.527748i	$-0.176964\pi$
$359$	−220.000	−	381.051i	−0.0323431	−	0.0560198i	−0.881744	+	0.471729i	$0.843630\pi$
$360$	−2760.00	+	4780.46i	−0.404069	+	0.699868i
$361$	−2620.50	+	4538.84i	−0.382053	+	0.661735i
$362$	−1946.00	−	3370.57i	−0.282540	−	0.489374i
$363$	−2534.00			−0.366393
$364$		0			0
$365$	−11232.0			−1.61071
$366$	488.000	+	845.241i	0.0696944	+	0.120714i
$367$	−4908.00	+	8500.91i	−0.698080	+	1.20911i	0.271051	+	0.962565i	$0.412629\pi$
$367$	−4908.00	+	8500.91i	−0.698080	+	1.20911i	−0.969131	+	0.246546i	$0.920704\pi$
$368$	−984.000	+	1704.34i	−0.139387	+	0.241426i
$369$	−2093.00	−	3625.18i	−0.295277	−	0.511435i
$370$	−3936.00			−0.553035
$371$		0			0
$372$	168.000			0.0234150
$373$	221.000	+	382.783i	0.0306781	+	0.0531361i	0.880957	−	0.473197i	$-0.156900\pi$
$373$	221.000	+	382.783i	0.0306781	+	0.0531361i	−0.850279	+	0.526333i	$0.823567\pi$
$374$	216.000	−	374.123i	0.0298639	−	0.0517258i
$375$	96.0000	−	166.277i	0.0132198	−	0.0228973i
$376$	2430.00	+	4208.88i	0.333292	+	0.577278i
$377$	3080.00			0.420764
$378$		0			0
$379$	−3960.00			−0.536706			−0.268353	−	0.963321i	$-0.586479\pi$
$379$	−3960.00			−0.536706			−0.268353	+	0.963321i	$0.586479\pi$
$380$	−6160.00	−	10669.4i	−0.831582	−	1.44034i
$381$	1776.00	−	3076.12i	0.238812	−	0.413634i
$382$	−2524.00	+	4371.70i	−0.338060	+	0.585538i
$383$	3354.00	+	5809.30i	0.447471	+	0.775043i	0.998221	−	0.0596280i	$-0.0189914\pi$
$383$	3354.00	+	5809.30i	0.447471	+	0.775043i	−0.550750	+	0.834670i	$0.685658\pi$
$384$	2910.00			0.386720
$385$		0			0
$386$	2962.00			0.390575
$387$	1472.00	+	2549.58i	0.193349	+	0.334890i
$388$	−1029.00	+	1782.28i	−0.134638	+	0.233200i
$389$	6675.00	−	11561.4i	0.870015	−	1.50691i	0.00803563	−	0.999968i	$-0.497442\pi$
$389$	6675.00	−	11561.4i	0.870015	−	1.50691i	0.861980	−	0.506943i	$-0.169225\pi$
$390$	448.000	+	775.959i	0.0581676	+	0.100749i
$391$	−2592.00			−0.335251
$392$		0			0
$393$	2236.00			0.287001
$394$	1667.00	+	2887.33i	0.213153	+	0.369192i
$395$	3520.00	−	6096.82i	0.448381	−	0.776618i
$396$	644.000	−	1115.44i	0.0817228	−	0.141548i
$397$	−678.000	−	1174.33i	−0.0857125	−	0.148458i	0.819982	−	0.572389i	$-0.193983\pi$
$397$	−678.000	−	1174.33i	−0.0857125	−	0.148458i	−0.905695	+	0.423931i	$0.860650\pi$
$398$	1860.00			0.234255
$399$		0			0
$400$	5371.00			0.671375
$401$	−3111.00	−	5388.41i	−0.387421	−	0.671033i	0.604681	−	0.796468i	$-0.293301\pi$
$401$	−3111.00	−	5388.41i	−0.387421	−	0.671033i	−0.992102	+	0.125435i	$0.959967\pi$
$402$	244.000	−	422.620i	0.0302727	−	0.0524338i
$403$	−168.000	+	290.985i	−0.0207659	+	0.0359677i
$404$	2408.00	+	4170.78i	0.296541	+	0.513624i
$405$	−6736.00			−0.826456
$406$		0			0
$407$	1968.00			0.239681
$408$	810.000	+	1402.96i	0.0982867	+	0.170238i
$409$	2575.00	−	4460.03i	0.311309	−	0.539204i	−0.667337	−	0.744756i	$-0.732566\pi$
$409$	2575.00	−	4460.03i	0.311309	−	0.539204i	0.978646	+	0.205552i	$0.0658991\pi$
$410$	1456.00	−	2521.87i	0.175382	−	0.303771i
$411$	−2274.00	−	3938.68i	−0.272915	−	0.472703i
$412$	9716.00			1.16183
$413$		0			0
$414$	1104.00			0.131060
$415$	10416.0	+	18041.0i	1.23205	+	2.13398i
$416$	−2254.00	+	3904.04i	−0.265653	+	0.460124i
$417$	−210.000	+	363.731i	−0.0246613	+	0.0427146i
$418$	−440.000	−	762.102i	−0.0514859	−	0.0891762i
$419$	−2310.00			−0.269334			−0.134667	−	0.990891i	$-0.542996\pi$
$419$	−2310.00			−0.269334			−0.134667	+	0.990891i	$0.542996\pi$
$420$		0			0
$421$	1262.00			0.146095			0.0730476	−	0.997328i	$-0.476727\pi$
$421$	1262.00			0.146095			0.0730476	+	0.997328i	$0.476727\pi$
$422$	−2134.00	−	3696.20i	−0.246165	−	0.426370i
$423$	−3726.00	+	6453.62i	−0.428284	+	0.741810i
$424$	1215.00	−	2104.44i	0.139164	−	0.241039i
$425$	3537.00	+	6126.26i	0.403693	+	0.699218i
$426$	1536.00			0.174694
$427$		0			0
$428$	−1708.00			−0.192896
$429$	−224.000	−	387.979i	−0.0252094	−	0.0436639i
$430$	−1024.00	+	1773.62i	−0.114841	+	0.198911i
$431$	2244.00	−	3886.72i	0.250788	−	0.434378i	−0.712955	−	0.701210i	$-0.752644\pi$
$431$	2244.00	−	3886.72i	0.250788	−	0.434378i	0.963743	+	0.266832i	$0.0859769\pi$
$432$	2050.00	+	3550.70i	0.228312	+	0.395448i
$433$	−17038.0			−1.89098			−0.945490	−	0.325652i	$-0.894416\pi$
$433$	−17038.0			−1.89098			−0.945490	+	0.325652i	$0.894416\pi$
$434$		0			0
$435$	3520.00			0.387979
$436$	315.000	+	545.596i	0.0346004	+	0.0599296i
$437$	−2640.00	+	4572.61i	−0.288989	+	0.500544i
$438$	702.000	−	1215.90i	0.0765819	−	0.132644i
$439$	8100.00	+	14029.6i	0.880619	+	1.52528i	0.850654	+	0.525727i	$0.176206\pi$
$439$	8100.00	+	14029.6i	0.880619	+	1.52528i	0.0299658	+	0.999551i	$0.490460\pi$
$440$	1920.00			0.208028
$441$		0			0
$442$	−1512.00			−0.162712
$443$	4386.00	+	7596.77i	0.470395	+	0.814749i	0.999427	−	0.0338535i	$-0.0107780\pi$
$443$	4386.00	+	7596.77i	0.470395	+	0.814749i	−0.529031	+	0.848602i	$0.677445\pi$
$444$	−1722.00	+	2982.59i	−0.184060	+	0.318801i
$445$	−5840.00	+	10115.2i	−0.622118	+	1.07754i
$446$	2716.00	+	4704.25i	0.288355	+	0.499446i
$447$	−4020.00			−0.425368
$448$		0			0
$449$	2130.00			0.223877			0.111939	−	0.993715i	$-0.464294\pi$
$449$	2130.00			0.223877			0.111939	+	0.993715i	$0.464294\pi$
$450$	−1506.50	−	2609.33i	−0.157816	−	0.273345i
$451$	−728.000	+	1260.93i	−0.0760093	+	0.131652i
$452$	4613.00	−	7989.95i	0.480038	−	0.831451i
$453$	−1112.00	−	1926.04i	−0.115334	−	0.199764i
$454$	−2046.00			−0.211506
$455$		0			0
$456$	3300.00			0.338896
$457$	−5267.00	−	9122.71i	−0.539124	−	0.933791i	−0.998951	−	0.0457824i	$-0.985422\pi$
$457$	−5267.00	−	9122.71i	−0.539124	−	0.933791i	0.459827	−	0.888009i	$-0.347911\pi$
$458$	1490.00	−	2580.76i	0.152016	−	0.263299i
$459$	−2700.00	+	4676.54i	−0.274565	+	0.475560i
$460$	−2688.00	−	4655.75i	−0.272454	−	0.471903i
$461$	9268.00			0.936342			0.468171	−	0.883638i	$-0.344913\pi$
$461$	9268.00			0.936342			0.468171	+	0.883638i	$0.344913\pi$
$462$		0			0
$463$	−9392.00			−0.942728			−0.471364	−	0.881939i	$-0.656238\pi$
$463$	−9392.00			−0.942728			−0.471364	+	0.881939i	$0.656238\pi$
$464$	2255.00	+	3905.77i	0.225616	+	0.390778i
$465$	−192.000	+	332.554i	−0.0191479	+	0.0331652i
$466$	2229.00	−	3860.74i	0.221580	−	0.383788i
$467$	−5403.00	−	9358.27i	−0.535377	−	0.927300i	−0.999145	−	0.0413434i	$-0.986836\pi$
$467$	−5403.00	−	9358.27i	−0.535377	−	0.927300i	0.463768	−	0.885957i	$-0.346497\pi$
$468$	−4508.00			−0.445261
$469$		0			0
$470$	−5184.00			−0.508766
$471$	124.000	+	214.774i	0.0121308	+	0.0210112i
$472$	6075.00	−	10522.2i	0.592425	−	1.02611i
$473$	512.000	−	886.810i	0.0497712	−	0.0862063i
$474$	440.000	+	762.102i	0.0426369	+	0.0738492i
$475$	14410.0			1.39195
$476$		0			0
$477$	3726.00			0.357656
$478$	2220.00	+	3845.15i	0.212428	+	0.367936i
$479$	2470.00	−	4278.17i	0.235610	−	0.408088i	−0.723840	−	0.689968i	$-0.757625\pi$
$479$	2470.00	−	4278.17i	0.235610	−	0.408088i	0.959450	+	0.281880i	$0.0909579\pi$
$480$	−2576.00	+	4461.76i	−0.244954	+	0.424272i
$481$	−3444.00	−	5965.18i	−0.326472	−	0.565466i
$482$	3302.00			0.312037
$483$		0			0
$484$	8869.00			0.832926
$485$	−2352.00	−	4073.78i	−0.220204	−	0.381404i
$486$	1771.00	−	3067.46i	0.165297	−	0.286302i
$487$	2608.00	−	4517.19i	0.242669	−	0.420315i	−0.718805	−	0.695212i	$-0.755310\pi$
$487$	2608.00	−	4517.19i	0.242669	−	0.420315i	0.961474	+	0.274897i	$0.0886438\pi$
$488$	−3660.00	−	6339.31i	−0.339509	−	0.588047i
$489$	4016.00			0.371390
$490$		0			0
$491$	4412.00			0.405521			0.202760	−	0.979228i	$-0.435009\pi$
$491$	4412.00			0.405521			0.202760	+	0.979228i	$0.435009\pi$
$492$	−1274.00	−	2206.63i	−0.116741	−	0.202201i
$493$	−2970.00	+	5144.19i	−0.271323	+	0.469945i
$494$	−1540.00	+	2667.36i	−0.140259	+	0.242935i
$495$	1472.00	+	2549.58i	0.133660	+	0.231505i
$496$	−492.000			−0.0445392
$497$		0			0
$498$	−2604.00			−0.234313
$499$	−9530.00	−	16506.4i	−0.854953	−	1.48082i	−0.876689	−	0.481058i	$-0.840253\pi$
$499$	−9530.00	−	16506.4i	−0.854953	−	1.48082i	0.0217362	−	0.999764i	$-0.493081\pi$
$500$	−336.000	+	581.969i	−0.0300528	+	0.0520529i
$501$	2884.00	−	4995.23i	0.257181	−	0.445450i
$502$	−791.000	−	1370.05i	−0.0703268	−	0.121810i
$503$	−12768.0			−1.13180			−0.565902	−	0.824473i	$-0.691472\pi$
$503$	−12768.0			−1.13180			−0.565902	+	0.824473i	$0.691472\pi$
$504$		0			0
$505$	−11008.0			−0.969999
$506$	−192.000	−	332.554i	−0.0168685	−	0.0292170i
$507$	1413.00	−	2447.39i	0.123774	−	0.214383i
$508$	−6216.00	+	10766.4i	−0.542894	+	0.940321i
$509$	−2750.00	−	4763.14i	−0.239473	−	0.414779i	0.721090	−	0.692841i	$-0.243641\pi$
$509$	−2750.00	−	4763.14i	−0.239473	−	0.414779i	−0.960563	+	0.278062i	$0.910308\pi$
$510$	−1728.00			−0.150034
$511$		0			0
$512$	−11521.0			−0.994455
$513$	5500.00	+	9526.28i	0.473355	+	0.819874i
$514$	−1177.00	+	2038.62i	−0.101002	+	0.174941i
$515$	−11104.0	+	19232.7i	−0.950098	+	1.64562i
$516$	896.000	+	1551.92i	0.0764422	+	0.132402i
$517$	2592.00			0.220495
$518$		0			0
$519$	−4456.00			−0.376872
$520$	−3360.00	−	5819.69i	−0.283357	−	0.490789i
$521$	−3669.00	+	6354.89i	−0.308526	+	0.534382i	−0.978040	−	0.208417i	$-0.933169\pi$
$521$	−3669.00	+	6354.89i	−0.308526	+	0.534382i	0.669514	+	0.742799i	$0.266502\pi$
$522$	1265.00	−	2191.04i	0.106068	−	0.183715i
$523$	−8791.00	−	15226.5i	−0.734997	−	1.27305i	−0.954725	−	0.297491i	$-0.903850\pi$
$523$	−8791.00	−	15226.5i	−0.734997	−	1.27305i	0.219727	−	0.975561i	$-0.429483\pi$
$524$	−7826.00			−0.652444
$525$		0			0
$526$	3872.00			0.320964
$527$	−324.000	−	561.184i	−0.0267811	−	0.0463863i
$528$	328.000	−	568.113i	0.0270348	−	0.0468256i
$529$	4931.50	−	8541.61i	0.405318	−	0.702031i
$530$	1296.00	+	2244.74i	0.106216	+	0.183972i
$531$	18630.0			1.52255
$532$		0			0
$533$	5096.00			0.414132
$534$	−730.000	−	1264.40i	−0.0591577	−	0.102464i
$535$	1952.00	−	3380.96i	0.157743	−	0.273218i
$536$	−1830.00	+	3169.65i	−0.147470	+	0.255426i
$537$	820.000	+	1420.28i	0.0658950	+	0.114133i
$538$	180.000			0.0144244
$539$		0			0
$540$	−11200.0			−0.892539
$541$	809.000	+	1401.23i	0.0642914	+	0.111356i	0.896379	−	0.443288i	$-0.146188\pi$
$541$	809.000	+	1401.23i	0.0642914	+	0.111356i	−0.832088	+	0.554644i	$0.812855\pi$
$542$	−1016.00	+	1759.76i	−0.0805183	+	0.139462i
$543$	3892.00	−	6741.14i	0.307591	−	0.532763i
$544$	−4347.00	−	7529.22i	−0.342603	−	0.593406i
$545$	−1440.00			−0.113179
$546$		0			0
$547$	16144.0			1.26192			0.630958	−	0.775817i	$-0.282662\pi$
$547$	16144.0			1.26192			0.630958	+	0.775817i	$0.282662\pi$
$548$	7959.00	+	13785.4i	0.620423	+	1.07460i
$549$	5612.00	−	9720.27i	0.436274	−	0.755648i
$550$	−524.000	+	907.595i	−0.0406244	+	0.0703636i
$551$	6050.00	+	10478.9i	0.467765	+	0.810193i
$552$	1440.00			0.111033
$553$		0			0
$554$	5426.00			0.416117
$555$	−3936.00	−	6817.35i	−0.301034	−	0.521406i
$556$	735.000	−	1273.06i	0.0560628	−	0.0971037i
$557$	−2327.00	+	4030.48i	−0.177016	+	0.306601i	−0.940857	−	0.338803i	$-0.889978\pi$
$557$	−2327.00	+	4030.48i	−0.177016	+	0.306601i	0.763841	+	0.645405i	$0.223311\pi$
$558$	138.000	+	239.023i	0.0104695	+	0.0181338i
$559$	−3584.00			−0.271175
$560$		0			0
$561$	864.000			0.0650234
$562$	421.000	+	729.193i	0.0315993	+	0.0547316i
$563$	5039.00	−	8727.80i	0.377209	−	0.653345i	−0.613446	−	0.789736i	$-0.710217\pi$
$563$	5039.00	−	8727.80i	0.377209	−	0.653345i	0.990655	+	0.136392i	$0.0435506\pi$
$564$	−2268.00	+	3928.29i	−0.169326	+	0.293282i
$565$	10544.0	+	18262.7i	0.785114	+	1.35986i
$566$	−3782.00			−0.280865
$567$		0			0
$568$	−11520.0			−0.851001
$569$	2965.00	+	5135.53i	0.218452	+	0.378370i	0.954335	−	0.298739i	$-0.0965659\pi$
$569$	2965.00	+	5135.53i	0.218452	+	0.378370i	−0.735883	+	0.677109i	$0.763233\pi$
$570$	−1760.00	+	3048.41i	−0.129330	+	0.224007i
$571$	9524.00	−	16496.1i	0.698016	−	1.20900i	−0.271138	−	0.962541i	$-0.587400\pi$
$571$	9524.00	−	16496.1i	0.698016	−	1.20900i	0.969153	−	0.246458i	$-0.0792668\pi$
$572$	784.000	+	1357.93i	0.0573089	+	0.0992619i
$573$	−10096.0			−0.736067
$574$		0			0
$575$	6288.00			0.456048
$576$	−1920.50	−	3326.40i	−0.138925	−	0.240625i
$577$	−7183.00	+	12441.3i	−0.518253	+	0.897641i	0.481522	+	0.876434i	$0.340084\pi$
$577$	−7183.00	+	12441.3i	−0.518253	+	0.897641i	−0.999775	+	0.0212070i	$0.993249\pi$
$578$	−998.500	+	1729.45i	−0.0718549	+	0.124456i
$579$	2962.00	+	5130.33i	0.212602	+	0.368237i
$580$	−12320.0			−0.882000
$581$		0			0
$582$	588.000			0.0418787
$583$	−648.000	−	1122.37i	−0.0460333	−	0.0797320i
$584$	−5265.00	+	9119.25i	−0.373060	+	0.646159i
$585$	5152.00	−	8923.53i	0.364118	−	0.630671i
$586$	2156.00	+	3734.30i	0.151986	+	0.263247i
$587$	3626.00			0.254959			0.127480	−	0.991841i	$-0.459311\pi$
$587$	3626.00			0.254959			0.127480	+	0.991841i	$0.459311\pi$
$588$		0			0
$589$	−1320.00			−0.0923424
$590$	6480.00	+	11223.7i	0.452165	+	0.783173i
$591$	−3334.00	+	5774.66i	−0.232051	+	0.401925i
$592$	5043.00	−	8734.73i	0.350112	−	0.606411i
$593$	−531.000	−	919.719i	−0.0367716	−	0.0636903i	0.847054	−	0.531507i	$-0.178374\pi$
$593$	−531.000	−	919.719i	−0.0367716	−	0.0636903i	−0.883826	+	0.467817i	$0.845041\pi$
$594$	−800.000			−0.0552599
$595$		0			0
$596$	14070.0			0.966996
$597$	1860.00	+	3221.61i	0.127512	+	0.220857i
$598$	−672.000	+	1163.94i	−0.0459534	+	0.0795936i
$599$	5100.00	−	8833.46i	0.347880	−	0.602547i	−0.637992	−	0.770043i	$-0.720235\pi$
$599$	5100.00	−	8833.46i	0.347880	−	0.602547i	0.985873	+	0.167496i	$0.0535682\pi$
$600$	−1965.00	−	3403.48i	−0.133701	−	0.231577i
$601$	25158.0			1.70751			0.853757	−	0.520671i	$-0.174318\pi$
$601$	25158.0			1.70751			0.853757	+	0.520671i	$0.174318\pi$
$602$		0			0
$603$	−5612.00			−0.379002
$604$	3892.00	+	6741.14i	0.262191	+	0.454128i
$605$	−10136.0	+	17556.1i	−0.681136	+	1.17976i
$606$	688.000	−	1191.65i	0.0461190	−	0.0798804i
$607$	12832.0	+	22225.7i	0.858047	+	1.48618i	0.873789	+	0.486306i	$0.161656\pi$
$607$	12832.0	+	22225.7i	0.858047	+	1.48618i	−0.0157413	+	0.999876i	$0.505011\pi$
$608$	−17710.0			−1.18131
$609$		0			0
$610$	7808.00			0.518257
$611$	−4536.00	−	7856.58i	−0.300339	−	0.520202i
$612$	4347.00	−	7529.22i	0.287119	−	0.497305i
$613$	−9509.00	+	16470.1i	−0.626533	+	1.08519i	0.361709	+	0.932291i	$0.382193\pi$
$613$	−9509.00	+	16470.1i	−0.626533	+	1.08519i	−0.988242	+	0.152896i	$0.951140\pi$
$614$	−1337.00	−	2315.75i	−0.0878777	−	0.152209i
$615$	5824.00			0.381864
$616$		0			0
$617$	17334.0			1.13102			0.565511	−	0.824741i	$-0.308679\pi$
$617$	17334.0			1.13102			0.565511	+	0.824741i	$0.308679\pi$
$618$	−1388.00	−	2404.09i	−0.0903455	−	0.156483i
$619$	9365.00	−	16220.7i	0.608096	−	1.05325i	−0.383459	−	0.923558i	$-0.625267\pi$
$619$	9365.00	−	16220.7i	0.608096	−	1.05325i	0.991554	−	0.129694i	$-0.0413996\pi$
$620$	672.000	−	1163.94i	0.0435293	−	0.0753950i
$621$	2400.00	+	4156.92i	0.155086	+	0.268618i
$622$	−3768.00			−0.242899
$623$		0			0
$624$	−2296.00			−0.147297
$625$	7419.50	+	12851.0i	0.474848	+	0.822461i
$626$	−1219.00	+	2111.37i	−0.0778291	+	0.134804i
$627$	880.000	−	1524.20i	0.0560507	−	0.0970827i
$628$	−434.000	−	751.710i	−0.0275772	−	0.0477651i
$629$	13284.0			0.842079
$630$		0			0
$631$	−6928.00			−0.437083			−0.218541	−	0.975828i	$-0.570130\pi$
$631$	−6928.00			−0.437083			−0.218541	+	0.975828i	$0.570130\pi$
$632$	−3300.00	−	5715.77i	−0.207701	−	0.359748i
$633$	4268.00	−	7392.39i	0.267990	−	0.464173i
$634$	−1593.00	+	2759.16i	−0.0997888	+	0.172839i
$635$	−14208.0	−	24609.0i	−0.887917	−	1.53792i
$636$	2268.00			0.141403
$637$		0			0
$638$	−880.000			−0.0546074
$639$	−8832.00	−	15297.5i	−0.546774	−	0.947040i
$640$	11640.0	−	20161.1i	0.718924	−	1.24521i
$641$	−8151.00	+	14117.9i	−0.502255	+	0.869930i	0.497742	+	0.867325i	$0.334163\pi$
$641$	−8151.00	+	14117.9i	−0.502255	+	0.869930i	−0.999997	+	0.00260525i	$0.999171\pi$
$642$	244.000	+	422.620i	0.0149999	+	0.0259805i
$643$	−4718.00			−0.289362			−0.144681	−	0.989478i	$-0.546216\pi$
$643$	−4718.00			−0.289362			−0.144681	+	0.989478i	$0.546216\pi$
$644$		0			0
$645$	−4096.00			−0.250046
$646$	−2970.00	−	5144.19i	−0.180887	−	0.313306i
$647$	−10718.0	+	18564.1i	−0.651264	+	1.12802i	0.331552	+	0.943437i	$0.392428\pi$
$647$	−10718.0	+	18564.1i	−0.651264	+	1.12802i	−0.982816	+	0.184586i	$0.940906\pi$
$648$	−3157.50	+	5468.95i	−0.191417	+	0.331544i
$649$	−3240.00	−	5611.84i	−0.195965	−	0.339421i
$650$	3668.00			0.221340
$651$		0			0
$652$	−14056.0			−0.844287
$653$	−2229.00	−	3860.74i	−0.133580	−	0.231367i	0.791474	−	0.611202i	$-0.209314\pi$
$653$	−2229.00	−	3860.74i	−0.133580	−	0.231367i	−0.925054	+	0.379836i	$0.875981\pi$
$654$	90.0000	−	155.885i	0.00538116	−	0.00932044i
$655$	8944.00	−	15491.5i	0.533544	−	0.924124i
$656$	3731.00	+	6462.28i	0.222060	+	0.384618i
$657$	−16146.0			−0.958775
$658$		0			0
$659$	−26640.0			−1.57473			−0.787365	−	0.616487i	$-0.788555\pi$
$659$	−26640.0			−1.57473			−0.787365	+	0.616487i	$0.788555\pi$
$660$	896.000	+	1551.92i	0.0528436	+	0.0915277i
$661$	3716.00	−	6436.30i	0.218662	−	0.378734i	−0.735737	−	0.677267i	$-0.763164\pi$
$661$	3716.00	−	6436.30i	0.218662	−	0.378734i	0.954399	+	0.298533i	$0.0964974\pi$
$662$	4336.00	−	7510.17i	0.254567	−	0.440923i
$663$	−1512.00	−	2618.86i	−0.0885690	−	0.153406i
$664$	19530.0			1.14143
$665$		0			0
$666$	−5658.00			−0.329194
$667$	2640.00	+	4572.61i	0.153255	+	0.265446i
$668$	−10094.0	+	17483.3i	−0.584654	+	1.01265i
$669$	−5432.00	+	9408.50i	−0.313921	+	0.543727i
$670$	−1952.00	−	3380.96i	−0.112556	−	0.194952i
$671$	−3904.00			−0.224608
$672$		0			0
$673$	58.0000			0.00332204			0.00166102	−	0.999999i	$-0.499471\pi$
$673$	58.0000			0.00332204			0.00166102	+	0.999999i	$0.499471\pi$
$674$	407.000	+	704.945i	0.0232597	+	0.0402870i
$675$	6550.00	−	11344.9i	0.373496	−	0.646914i
$676$	−4945.50	+	8565.86i	−0.281378	+	0.487361i
$677$	−10758.0	−	18633.4i	−0.610729	−	1.05781i	−0.991118	−	0.132987i	$-0.957543\pi$
$677$	−10758.0	−	18633.4i	−0.610729	−	1.05781i	0.380389	−	0.924827i	$-0.375790\pi$
$678$	−2636.00			−0.149314
$679$		0			0
$680$	12960.0			0.730873
$681$	−2046.00	−	3543.78i	−0.115129	−	0.199409i
$682$	48.0000	−	83.1384i	0.00269504	−	0.00466794i
$683$	−9054.00	+	15682.0i	−0.507235	+	0.878557i	0.492730	+	0.870182i	$0.335999\pi$
$683$	−9054.00	+	15682.0i	−0.507235	+	0.878557i	−0.999965	+	0.00837480i	$0.997334\pi$
$684$	−8855.00	−	15337.3i	−0.494999	−	0.857364i
$685$	−36384.0			−2.02943
$686$		0			0
$687$	5960.00			0.330987
$688$	−2624.00	−	4544.90i	−0.145406	−	0.251850i
$689$	−2268.00	+	3928.29i	−0.125405	+	0.217208i
$690$	−768.000	+	1330.22i	−0.0423728	+	0.0733919i
$691$	−5039.00	−	8727.80i	−0.277413	−	0.480494i	0.693328	−	0.720622i	$-0.256144\pi$
$691$	−5039.00	−	8727.80i	−0.277413	−	0.480494i	−0.970741	+	0.240128i	$0.922810\pi$
$692$	15596.0			0.856750
$693$		0			0
$694$	−9344.00			−0.511086
$695$	1680.00	+	2909.85i	0.0916921	+	0.158815i
$696$	1650.00	−	2857.88i	0.0898608	−	0.155643i
$697$	−4914.00	+	8511.30i	−0.267046	+	0.462537i
$698$	2590.00	+	4486.01i	0.140448	+	0.243264i
$699$	8916.00			0.482452
$700$		0			0
$701$	18762.0			1.01089			0.505443	−	0.862860i	$-0.331329\pi$
$701$	18762.0			1.01089			0.505443	+	0.862860i	$0.331329\pi$
$702$	1400.00	+	2424.87i	0.0752701	+	0.130372i
$703$	13530.0	−	23434.6i	0.725880	−	1.25726i
$704$	−668.000	+	1157.01i	−0.0357616	+	0.0619410i
$705$	−5184.00	−	8978.95i	−0.276937	−	0.479669i
$706$	12178.0			0.649186
$707$		0			0
$708$	11340.0			0.601954
$709$	−3405.00	−	5897.63i	−0.180363	−	0.312398i	0.761641	−	0.647999i	$-0.224394\pi$
$709$	−3405.00	−	5897.63i	−0.180363	−	0.312398i	−0.942004	+	0.335601i	$0.891061\pi$
$710$	6144.00	−	10641.7i	0.324761	−	0.562502i
$711$	5060.00	−	8764.18i	0.266898	−	0.462282i
$712$	5475.00	+	9482.98i	0.288180	+	0.499143i
$713$	−576.000			−0.0302544
$714$		0			0
$715$	−3584.00			−0.187460
$716$	−2870.00	−	4970.99i	−0.149800	−	0.259462i
$717$	−4440.00	+	7690.31i	−0.231262	+	0.400557i
$718$	220.000	−	381.051i	0.0114350	−	0.0198060i
$719$	2430.00	+	4208.88i	0.126041	+	0.218310i	0.922140	−	0.386858i	$-0.126439\pi$
$719$	2430.00	+	4208.88i	0.126041	+	0.218310i	−0.796098	+	0.605167i	$0.793106\pi$
$720$	15088.0			0.780967
$721$		0			0
$722$	−5241.00			−0.270152
$723$	3302.00	+	5719.23i	0.169852	+	0.294192i
$724$	−13622.0	+	23594.0i	−0.699251	+	1.21114i
$725$	7205.00	−	12479.4i	0.369085	−	0.639275i
$726$	−1267.00	−	2194.51i	−0.0647697	−	0.112184i
$727$	13636.0			0.695641			0.347821	−	0.937561i	$-0.386922\pi$
$727$	13636.0			0.695641			0.347821	+	0.937561i	$0.386922\pi$
$728$		0			0
$729$	−4283.00			−0.217599
$730$	−5616.00	−	9727.20i	−0.284736	−	0.493178i
$731$	3456.00	−	5985.97i	0.174863	−	0.302871i
$732$	3416.00	−	5916.69i	0.172485	−	0.298753i
$733$	1044.00	+	1808.26i	0.0526071	+	0.0911182i	0.891130	−	0.453749i	$-0.149914\pi$
$733$	1044.00	+	1808.26i	0.0526071	+	0.0911182i	−0.838523	+	0.544867i	$0.816580\pi$
$734$	−9816.00			−0.493617
$735$		0			0
$736$	−7728.00			−0.387035
$737$	976.000	+	1690.48i	0.0487808	+	0.0844908i
$738$	2093.00	−	3625.18i	0.104396	−	0.180820i
$739$	2580.00	−	4468.69i	0.128426	−	0.222440i	−0.794641	−	0.607080i	$-0.792341\pi$
$739$	2580.00	−	4468.69i	0.128426	−	0.222440i	0.923067	+	0.384639i	$0.125674\pi$
$740$	13776.0	+	23860.7i	0.684346	+	1.18532i
$741$	−6160.00			−0.305389
$742$		0			0
$743$	−28152.0			−1.39004			−0.695018	−	0.718992i	$-0.744604\pi$
$743$	−28152.0			−1.39004			−0.695018	+	0.718992i	$0.744604\pi$
$744$	180.000	+	311.769i	0.00886979	+	0.0153629i
$745$	−16080.0	+	27851.4i	−0.790773	+	1.36966i
$746$	−221.000	+	382.783i	−0.0108464	+	0.0187864i
$747$	14973.0	+	25934.0i	0.733378	+	1.27025i
$748$	−3024.00			−0.147819
$749$		0			0
$750$	192.000			0.00934780
$751$	8404.00	+	14556.2i	0.408344	+	0.707272i	0.994704	−	0.102778i	$-0.0327731\pi$
$751$	8404.00	+	14556.2i	0.408344	+	0.707272i	−0.586360	+	0.810050i	$0.699440\pi$
$752$	6642.00	−	11504.3i	0.322086	−	0.557870i
$753$	1582.00	−	2740.10i	0.0765621	−	0.132610i
$754$	1540.00	+	2667.36i	0.0743813	+	0.128832i
$755$	−17792.0			−0.857639
$756$		0			0
$757$	21674.0			1.04063			0.520314	−	0.853975i	$-0.325815\pi$
$757$	21674.0			1.04063			0.520314	+	0.853975i	$0.325815\pi$
$758$	−1980.00	−	3429.46i	−0.0948771	−	0.164332i
$759$	384.000	−	665.108i	0.0183641	−	0.0318075i
$760$	13200.0	−	22863.1i	0.630019	−	1.09122i
$761$	3711.00	+	6427.64i	0.176772	+	0.306178i	0.940773	−	0.339037i	$-0.110101\pi$
$761$	3711.00	+	6427.64i	0.176772	+	0.306178i	−0.764001	+	0.645215i	$0.776768\pi$
$762$	3552.00			0.168865
$763$		0			0
$764$	35336.0			1.67331
$765$	9936.00	+	17209.7i	0.469591	+	0.813355i
$766$	−3354.00	+	5809.30i	−0.158205	+	0.274019i
$767$	−11340.0	+	19641.5i	−0.533851	+	0.924657i
$768$	119.000	+	206.114i	0.00559120	+	0.00968424i
$769$	−13790.0			−0.646658			−0.323329	−	0.946287i	$-0.604802\pi$
$769$	−13790.0			−0.646658			−0.323329	+	0.946287i	$0.604802\pi$
$770$		0			0
$771$	−4708.00			−0.219915
$772$	−10367.0	−	17956.2i

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	49.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(3.50000 - 6.06218i) q^{4} +(8.00000 + 13.8564i) q^{5} -2.00000 q^{6} +15.0000 q^{8} +(11.5000 + 19.9186i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(3.50000 - 6.06218i) q^{4} +(8.00000 + 13.8564i) q^{5} -2.00000 q^{6} +15.0000 q^{8} +(11.5000 + 19.9186i) q^{9} +(-8.00000 + 13.8564i) q^{10} +(4.00000 - 6.92820i) q^{11} +(7.00000 + 12.1244i) q^{12} -28.0000 q^{13} -32.0000 q^{15} +(-20.5000 - 35.5070i) q^{16} +(27.0000 - 46.7654i) q^{17} +(-11.5000 + 19.9186i) q^{18} +(-55.0000 - 95.2628i) q^{19} +112.000 q^{20} +8.00000 q^{22} +(-24.0000 - 41.5692i) q^{23} +(-15.0000 + 25.9808i) q^{24} +(-65.5000 + 113.449i) q^{25} +(-14.0000 - 24.2487i) q^{26} -100.000 q^{27} -110.000 q^{29} +(-16.0000 - 27.7128i) q^{30} +(6.00000 - 10.3923i) q^{31} +(80.5000 - 139.430i) q^{32} +(8.00000 + 13.8564i) q^{33} +54.0000 q^{34} +161.000 q^{36} +(123.000 + 213.042i) q^{37} +(55.0000 - 95.2628i) q^{38} +(28.0000 - 48.4974i) q^{39} +(120.000 + 207.846i) q^{40} -182.000 q^{41} +128.000 q^{43} +(-28.0000 - 48.4974i) q^{44} +(-184.000 + 318.697i) q^{45} +(24.0000 - 41.5692i) q^{46} +(162.000 + 280.592i) q^{47} +82.0000 q^{48} -131.000 q^{50} +(54.0000 + 93.5307i) q^{51} +(-98.0000 + 169.741i) q^{52} +(81.0000 - 140.296i) q^{53} +(-50.0000 - 86.6025i) q^{54} +128.000 q^{55} +220.000 q^{57} +(-55.0000 - 95.2628i) q^{58} +(405.000 - 701.481i) q^{59} +(-112.000 + 193.990i) q^{60} +(-244.000 - 422.620i) q^{61} +12.0000 q^{62} -167.000 q^{64} +(-224.000 - 387.979i) q^{65} +(-8.00000 + 13.8564i) q^{66} +(-122.000 + 211.310i) q^{67} +(-189.000 - 327.358i) q^{68} +96.0000 q^{69} -768.000 q^{71} +(172.500 + 298.779i) q^{72} +(-351.000 + 607.950i) q^{73} +(-123.000 + 213.042i) q^{74} +(-131.000 - 226.899i) q^{75} -770.000 q^{76} +56.0000 q^{78} +(-220.000 - 381.051i) q^{79} +(328.000 - 568.113i) q^{80} +(-210.500 + 364.597i) q^{81} +(-91.0000 - 157.617i) q^{82} +1302.00 q^{83} +864.000 q^{85} +(64.0000 + 110.851i) q^{86} +(110.000 - 190.526i) q^{87} +(60.0000 - 103.923i) q^{88} +(365.000 + 632.199i) q^{89} -368.000 q^{90} -336.000 q^{92} +(12.0000 + 20.7846i) q^{93} +(-162.000 + 280.592i) q^{94} +(880.000 - 1524.20i) q^{95} +(161.000 + 278.860i) q^{96} -294.000 q^{97} +184.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 2 q^{3} + 7 q^{4} + 16 q^{5} - 4 q^{6} + 30 q^{8} + 23 q^{9}+O(q^{10}) \) 2 * q + q^2 - 2 * q^3 + 7 * q^4 + 16 * q^5 - 4 * q^6 + 30 * q^8 + 23 * q^9	\( 2 q + q^{2} - 2 q^{3} + 7 q^{4} + 16 q^{5} - 4 q^{6} + 30 q^{8} + 23 q^{9} - 16 q^{10} + 8 q^{11} + 14 q^{12} - 56 q^{13} - 64 q^{15} - 41 q^{16} + 54 q^{17} - 23 q^{18} - 110 q^{19} + 224 q^{20} + 16 q^{22} - 48 q^{23} - 30 q^{24} - 131 q^{25} - 28 q^{26} - 200 q^{27} - 220 q^{29} - 32 q^{30} + 12 q^{31} + 161 q^{32} + 16 q^{33} + 108 q^{34} + 322 q^{36} + 246 q^{37} + 110 q^{38} + 56 q^{39} + 240 q^{40} - 364 q^{41} + 256 q^{43} - 56 q^{44} - 368 q^{45} + 48 q^{46} + 324 q^{47} + 164 q^{48} - 262 q^{50} + 108 q^{51} - 196 q^{52} + 162 q^{53} - 100 q^{54} + 256 q^{55} + 440 q^{57} - 110 q^{58} + 810 q^{59} - 224 q^{60} - 488 q^{61} + 24 q^{62} - 334 q^{64} - 448 q^{65} - 16 q^{66} - 244 q^{67} - 378 q^{68} + 192 q^{69} - 1536 q^{71} + 345 q^{72} - 702 q^{73} - 246 q^{74} - 262 q^{75} - 1540 q^{76} + 112 q^{78} - 440 q^{79} + 656 q^{80} - 421 q^{81} - 182 q^{82} + 2604 q^{83} + 1728 q^{85} + 128 q^{86} + 220 q^{87} + 120 q^{88} + 730 q^{89} - 736 q^{90} - 672 q^{92} + 24 q^{93} - 324 q^{94} + 1760 q^{95} + 322 q^{96} - 588 q^{97} + 368 q^{99}+O(q^{100}) \) 2 * q + q^2 - 2 * q^3 + 7 * q^4 + 16 * q^5 - 4 * q^6 + 30 * q^8 + 23 * q^9 - 16 * q^10 + 8 * q^11 + 14 * q^12 - 56 * q^13 - 64 * q^15 - 41 * q^16 + 54 * q^17 - 23 * q^18 - 110 * q^19 + 224 * q^20 + 16 * q^22 - 48 * q^23 - 30 * q^24 - 131 * q^25 - 28 * q^26 - 200 * q^27 - 220 * q^29 - 32 * q^30 + 12 * q^31 + 161 * q^32 + 16 * q^33 + 108 * q^34 + 322 * q^36 + 246 * q^37 + 110 * q^38 + 56 * q^39 + 240 * q^40 - 364 * q^41 + 256 * q^43 - 56 * q^44 - 368 * q^45 + 48 * q^46 + 324 * q^47 + 164 * q^48 - 262 * q^50 + 108 * q^51 - 196 * q^52 + 162 * q^53 - 100 * q^54 + 256 * q^55 + 440 * q^57 - 110 * q^58 + 810 * q^59 - 224 * q^60 - 488 * q^61 + 24 * q^62 - 334 * q^64 - 448 * q^65 - 16 * q^66 - 244 * q^67 - 378 * q^68 + 192 * q^69 - 1536 * q^71 + 345 * q^72 - 702 * q^73 - 246 * q^74 - 262 * q^75 - 1540 * q^76 + 112 * q^78 - 440 * q^79 + 656 * q^80 - 421 * q^81 - 182 * q^82 + 2604 * q^83 + 1728 * q^85 + 128 * q^86 + 220 * q^87 + 120 * q^88 + 730 * q^89 - 736 * q^90 - 672 * q^92 + 24 * q^93 - 324 * q^94 + 1760 * q^95 + 322 * q^96 - 588 * q^97 + 368 * q^99

Introduction

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