LMFDB - Embedded newform 49.4.c.c.30.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,4,Mod(18,49)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [2,1,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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			30.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	49.30
Dual form			49.4.c.c.18.1

$q$-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} +(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} + 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}+ \cdots + 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

Character values

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

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

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.176777	−	0.306186i	−0.763998	−	0.645219i	$-0.776766\pi$
$2$	0.500000	−	0.866025i	0.176777	−	0.306186i	0.940775	+	0.339032i	$0.110100\pi$
$3$	1.00000	+	1.73205i	0.192450	+	0.333333i	0.946062	−	0.323987i	$-0.105023\pi$
$3$	1.00000	+	1.73205i	0.192450	+	0.333333i	−0.753612	+	0.657320i	$0.771690\pi$
$4$	3.50000	+	6.06218i	0.437500	+	0.757772i
$5$	−8.00000	+	13.8564i	−0.715542	+	1.23935i	0.247208	+	0.968962i	$0.420487\pi$
$5$	−8.00000	+	13.8564i	−0.715542	+	1.23935i	−0.962750	+	0.270392i	$0.912847\pi$
$6$	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	0.915625	−	0.402034i	$-0.131697\pi$
$11$	4.00000	+	6.92820i	0.109640	+	0.189903i	−0.805984	+	0.591937i	$0.798363\pi$
$12$	−7.00000	+	12.1244i	−0.168394	+	0.291667i
$13$	28.0000			0.597369			0.298685	−	0.954352i	$-0.403452\pi$
$13$	28.0000			0.597369			0.298685	+	0.954352i	$0.403452\pi$
$14$		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	$-0.292535\pi$
$17$	−27.0000	−	46.7654i	−0.385204	−	0.667192i	−0.991797	+	0.127820i	$0.959202\pi$
$18$	−11.5000	−	19.9186i	−0.150588	−	0.260825i
$19$	55.0000	−	95.2628i	0.664098	−	1.15025i	−0.315431	−	0.948949i	$-0.602149\pi$
$19$	55.0000	−	95.2628i	0.664098	−	1.15025i	0.979529	−	0.201303i	$-0.0645177\pi$
$20$	−112.000			−1.25220
$21$		0			0
$22$	8.00000			0.0775275
$23$	−24.0000	+	41.5692i	−0.217580	+	0.376860i	−0.954068	−	0.299591i	$-0.903150\pi$
$23$	−24.0000	+	41.5692i	−0.217580	+	0.376860i	0.736487	+	0.676451i	$0.236483\pi$
$24$	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	$-0.177734\pi$
$31$	−6.00000	−	10.3923i	−0.0347623	−	0.0602101i	−0.882883	+	0.469593i	$0.844401\pi$
$32$	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	−0.451994	−	0.892021i	$-0.649287\pi$
$37$	123.000	−	213.042i	0.546516	−	0.946593i	0.998510	−	0.0545719i	$-0.0173794\pi$
$38$	−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	$-0.387326\pi$
$41$	182.000			0.693259			0.346630	+	0.938002i	$0.387326\pi$
$42$		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	0.497226	+	0.867621i	$0.334352\pi$
$47$	−162.000	+	280.592i	−0.502769	+	0.870821i	−0.999995	+	0.00319997i	$0.998981\pi$
$48$	−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	0.951692	−	0.307055i	$-0.0993436\pi$
$53$	81.0000	+	140.296i	0.209928	+	0.363607i	−0.741763	+	0.670662i	$0.766010\pi$
$54$	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	−0.835442	−	0.549578i	$-0.814789\pi$
$59$	−405.000	−	701.481i	−0.893670	−	1.54788i	−0.0582271	−	0.998303i	$-0.518545\pi$
$60$	−112.000	−	193.990i	−0.240986	−	0.417399i
$61$	244.000	−	422.620i	0.512148	−	0.887066i	−0.487753	−	0.872982i	$-0.662183\pi$
$61$	244.000	−	422.620i	0.512148	−	0.887066i	0.999901	−	0.0140840i	$-0.00448323\pi$
$62$	−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	0.733096	−	0.680125i	$-0.238075\pi$
$67$	−122.000	−	211.310i	−0.222458	−	0.385308i	−0.955554	+	0.294817i	$0.904741\pi$
$68$	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	0.997254	+	0.0740537i	$0.0235936\pi$
$73$	351.000	+	607.950i	0.562759	+	0.974728i	−0.434495	+	0.900674i	$0.643073\pi$
$74$	−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	−0.979078	−	0.203485i	$-0.934773\pi$
$79$	−220.000	+	381.051i	−0.313316	+	0.542679i	0.665762	+	0.746164i	$0.268106\pi$
$80$	−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	$-0.830113\pi$
$83$	−1302.00			−1.72184			−0.860922	+	0.508737i	$0.830113\pi$
$84$		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	$-0.976485\pi$
$89$	−365.000	+	632.199i	−0.434718	+	0.752954i	0.562554	+	0.826760i	$0.309819\pi$
$90$	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	$-0.450826\pi$
$97$	294.000			0.307744			0.153872	+	0.988091i	$0.450826\pi$
$98$		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	$-0.0566106\pi$
$101$	344.000	+	595.825i	0.338904	+	0.586999i	−0.645323	+	0.763910i	$0.723277\pi$
$102$	−54.0000	−	93.5307i	−0.0524196	−	0.0907934i
$103$	−694.000	+	1202.04i	−0.663901	+	1.14991i	0.315680	+	0.948866i	$0.397767\pi$
$103$	−694.000	+	1202.04i	−0.663901	+	1.14991i	−0.979582	+	0.201046i	$0.935566\pi$
$104$	420.000			0.396004
$105$		0			0
$106$	162.000			0.148442
$107$	−122.000	+	211.310i	−0.110226	+	0.190917i	−0.915861	−	0.401495i	$-0.868491\pi$
$107$	−122.000	+	211.310i	−0.110226	+	0.190917i	0.805635	+	0.592412i	$0.201824\pi$
$108$	350.000	+	606.218i	0.311840	+	0.540123i
$109$	−45.0000	−	77.9423i	−0.0395433	−	0.0684910i	0.845576	−	0.533854i	$-0.179257\pi$
$109$	−45.0000	−	77.9423i	−0.0395433	−	0.0684910i	−0.885120	+	0.465363i	$0.845924\pi$
$110$	−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	$-0.711723\pi$
$131$	559.000	−	968.216i	0.372825	−	0.645752i	0.989999	+	0.141075i	$0.0450559\pi$
$132$	−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	−0.965208	−	0.261482i	$-0.915789\pi$
$137$	−1137.00	−	1969.34i	−0.709054	−	1.22812i	0.256154	−	0.966636i	$-0.417545\pi$
$138$	−48.0000	+	83.1384i	−0.0296089	+	0.0512842i
$139$	−210.000			−0.128144			−0.0640718	−	0.997945i	$-0.520409\pi$
$139$	−210.000			−0.128144			−0.0640718	+	0.997945i	$0.520409\pi$
$140$		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	−0.445519	−	0.895272i	$-0.646981\pi$
$149$	1005.00	−	1740.71i	0.552569	−	0.957078i	0.998088	−	0.0618054i	$-0.0196858\pi$
$150$	−131.000	−	226.899i	−0.0713074	−	0.123508i
$151$	−556.000	−	963.020i	−0.299647	−	0.519003i	0.676408	−	0.736527i	$-0.263535\pi$
$151$	−556.000	−	963.020i	−0.299647	−	0.519003i	−0.976055	+	0.217524i	$0.930202\pi$
$152$	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	$-0.176700\pi$
$157$	−62.0000	−	107.387i	−0.0315168	−	0.0545887i	−0.881354	+	0.472457i	$0.843367\pi$
$158$	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	−0.999797	−	0.0201478i	$-0.993586\pi$
$163$	−1004.00	+	1738.98i	−0.482450	+	0.835628i	0.517347	+	0.855776i	$0.326920\pi$
$164$	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	$-0.267076\pi$
$167$	2884.00			1.33635			0.668176	+	0.744004i	$0.267076\pi$
$168$		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	$-0.996180\pi$
$173$	−1114.00	+	1929.50i	−0.489571	+	0.847963i	0.510357	+	0.859963i	$0.329513\pi$
$174$	−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	0.938840	−	0.344354i	$-0.111902\pi$
$179$	410.000	+	710.141i	0.171200	+	0.296527i	−0.767640	+	0.640882i	$0.778569\pi$
$180$	−1288.00	+	2230.88i	−0.533344	+	0.923778i
$181$	3892.00			1.59829			0.799144	−	0.601140i	$-0.205287\pi$
$181$	3892.00			1.59829			0.799144	+	0.601140i	$0.205287\pi$
$182$		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	0.224533	−	0.974466i	$-0.427914\pi$
$191$	2524.00	−	4371.70i	0.956179	−	1.65615i	0.731646	−	0.681684i	$-0.238752\pi$
$192$	−167.000	−	289.252i	−0.0627718	−	0.108724i
$193$	1481.00	+	2565.17i	0.552356	+	0.956709i	0.998104	+	0.0615502i	$0.0196044\pi$
$193$	1481.00	+	2565.17i	0.552356	+	0.956709i	−0.445748	+	0.895159i	$0.647062\pi$
$194$	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	$-0.274149\pi$
$199$	−930.000	−	1610.81i	−0.331286	−	0.573805i	−0.982764	+	0.184863i	$0.940816\pi$
$200$	−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	$-0.803588\pi$
$223$	−5432.00			−1.63118			−0.815591	+	0.578629i	$0.803588\pi$
$224$		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	$-0.0699756\pi$
$227$	1023.00	+	1771.89i	0.299114	+	0.518081i	−0.676819	+	0.736149i	$0.736642\pi$
$228$	770.000	+	1333.68i	0.223660	+	0.387391i
$229$	1490.00	−	2580.76i	0.429965	−	0.744721i	−0.566905	−	0.823783i	$-0.691859\pi$
$229$	1490.00	−	2580.76i	0.429965	−	0.744721i	0.996870	+	0.0790622i	$0.0251926\pi$
$230$	−768.000			−0.220176
$231$		0			0
$232$	−1650.00			−0.466930
$233$	−2229.00	+	3860.74i	−0.626724	+	1.08552i	0.361481	+	0.932379i	$0.382271\pi$
$233$	−2229.00	+	3860.74i	−0.626724	+	1.08552i	−0.988205	+	0.153138i	$0.951062\pi$
$234$	−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	$-0.312145\pi$
$241$	−1651.00	−	2859.62i	−0.441287	−	0.764332i	−0.997785	+	0.0665168i	$0.978811\pi$
$242$	−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	$-0.436258\pi$
$251$	1582.00			0.397829			0.198914	+	0.980017i	$0.436258\pi$
$252$		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	$-0.925552\pi$
$257$	−1177.00	+	2038.62i	−0.285678	+	0.494809i	0.687095	+	0.726567i	$0.258885\pi$
$258$	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	0.998625	−	0.0524239i	$-0.0166947\pi$
$263$	1936.00	+	3353.25i	0.453912	+	0.786199i	−0.544713	+	0.838623i	$0.683361\pi$
$264$	−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	$-0.173160\pi$
$269$	−90.0000	−	155.885i	−0.0203992	−	0.0353325i	−0.876045	+	0.482230i	$0.839827\pi$
$270$	800.000	+	1385.64i	0.180320	+	0.312324i
$271$	−1016.00	+	1759.76i	−0.227740	+	0.394458i	−0.957138	−	0.289632i	$-0.906467\pi$
$271$	−1016.00	+	1759.76i	−0.227740	+	0.394458i	0.729398	+	0.684090i	$0.239800\pi$
$272$	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	0.994432	+	0.105380i	$0.0336059\pi$
$277$	2713.00	+	4699.05i	0.588478	+	1.01927i	−0.405954	+	0.913893i	$0.633061\pi$
$278$	−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	$-0.0366478\pi$
$283$	1891.00	+	3275.31i	0.397202	+	0.687975i	−0.596177	+	0.802853i	$0.703314\pi$
$284$	−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	$-0.641444\pi$
$293$	−4312.00			−0.859760			−0.429880	+	0.902886i	$0.641444\pi$
$294$		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	$-0.420044\pi$
$307$	2674.00			0.497112			0.248556	+	0.968618i	$0.420044\pi$
$308$		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	$-0.0550505\pi$
$311$	1884.00	+	3263.18i	0.343511	+	0.594978i	−0.641571	+	0.767063i	$0.721717\pi$
$312$	420.000	+	727.461i	0.0762110	+	0.132001i
$313$	−1219.00	+	2111.37i	−0.220134	+	0.381283i	−0.954849	−	0.297093i	$-0.903983\pi$
$313$	−1219.00	+	2111.37i	−0.220134	+	0.381283i	0.734714	+	0.678376i	$0.237316\pi$
$314$	−124.000			−0.0222857
$315$		0			0
$316$	−3080.00			−0.548302
$317$	1593.00	−	2759.16i	0.282245	−	0.488863i	−0.689692	−	0.724103i	$-0.742254\pi$
$317$	1593.00	−	2759.16i	0.282245	−	0.488863i	0.971937	+	0.235239i	$0.0755874\pi$
$318$	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	0.240965	+	0.970534i	$0.422536\pi$
$331$	−4336.00	+	7510.17i	−0.720025	+	1.24712i	−0.960989	+	0.276585i	$0.910797\pi$
$332$	−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	−0.959880	−	0.280413i	$-0.909529\pi$
$347$	−4672.00	−	8092.14i	−0.722784	−	1.25190i	0.237095	−	0.971486i	$-0.423805\pi$
$348$	770.000	−	1333.68i	0.118610	−	0.205439i
$349$	−5180.00			−0.794496			−0.397248	−	0.917711i	$-0.630035\pi$
$349$	−5180.00			−0.794496			−0.397248	+	0.917711i	$0.630035\pi$
$350$		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	−0.802317	−	0.596898i	$-0.796400\pi$
$353$	−6089.00	−	10546.5i	−0.918087	−	1.59017i	−0.115770	−	0.993276i	$-0.536933\pi$
$354$	−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	−0.881744	−	0.471729i	$-0.843630\pi$
$359$	−220.000	+	381.051i	−0.0323431	+	0.0560198i	0.849401	+	0.527748i	$0.176964\pi$
$360$	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	0.969131	+	0.246546i	$0.0792955\pi$
$367$	4908.00	+	8500.91i	0.698080	+	1.20911i	−0.271051	+	0.962565i	$0.587371\pi$
$368$	−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	−0.850279	−	0.526333i	$-0.823567\pi$
$373$	221.000	−	382.783i	0.0306781	−	0.0531361i	0.880957	+	0.473197i	$0.156900\pi$
$374$	−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	$-0.981009\pi$
$383$	−3354.00	+	5809.30i	−0.447471	+	0.775043i	0.550750	+	0.834670i	$0.314342\pi$
$384$	−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	0.861980	+	0.506943i	$0.169225\pi$
$389$	6675.00	+	11561.4i	0.870015	+	1.50691i	0.00803563	+	0.999968i	$0.497442\pi$
$390$	−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	$-0.806017\pi$
$397$	678.000	−	1174.33i	0.0857125	−	0.148458i	0.905695	+	0.423931i	$0.139350\pi$
$398$	−1860.00			−0.234255
$399$		0			0
$400$	5371.00			0.671375
$401$	−3111.00	+	5388.41i	−0.387421	+	0.671033i	−0.992102	−	0.125435i	$-0.959967\pi$
$401$	−3111.00	+	5388.41i	−0.387421	+	0.671033i	0.604681	+	0.796468i	$0.293301\pi$
$402$	−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	$-0.267434\pi$
$409$	−2575.00	−	4460.03i	−0.311309	−	0.539204i	−0.978646	+	0.205552i	$0.934101\pi$
$410$	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	$-0.457004\pi$
$419$	2310.00			0.269334			0.134667	+	0.990891i	$0.457004\pi$
$420$		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	0.963743	−	0.266832i	$-0.0859769\pi$
$431$	2244.00	+	3886.72i	0.250788	+	0.434378i	−0.712955	+	0.701210i	$0.752644\pi$
$432$	−2050.00	+	3550.70i	−0.228312	+	0.395448i
$433$	17038.0			1.89098			0.945490	−	0.325652i	$-0.105584\pi$
$433$	17038.0			1.89098			0.945490	+	0.325652i	$0.105584\pi$
$434$		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	−0.0299658	+	0.999551i	$0.509540\pi$
$439$	−8100.00	+	14029.6i	−0.880619	+	1.52528i	−0.850654	+	0.525727i	$0.823794\pi$
$440$	−1920.00			−0.208028
$441$		0			0
$442$	−1512.00			−0.162712
$443$	4386.00	−	7596.77i	0.470395	−	0.814749i	−0.529031	−	0.848602i	$-0.677445\pi$
$443$	4386.00	−	7596.77i	0.470395	−	0.814749i	0.999427	+	0.0338535i	$0.0107780\pi$
$444$	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	0.459827	+	0.888009i	$0.347911\pi$
$457$	−5267.00	+	9122.71i	−0.539124	+	0.933791i	−0.998951	+	0.0457824i	$0.985422\pi$
$458$	−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	$-0.655087\pi$
$461$	−9268.00			−0.936342			−0.468171	+	0.883638i	$0.655087\pi$
$462$		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	−0.463768	−	0.885957i	$-0.653503\pi$
$467$	5403.00	−	9358.27i	0.535377	−	0.927300i	0.999145	−	0.0413434i	$-0.0131638\pi$
$468$	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	$-0.242375\pi$
$479$	−2470.00	−	4278.17i	−0.235610	−	0.408088i	−0.959450	+	0.281880i	$0.909042\pi$
$480$	−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	0.961474	−	0.274897i	$-0.0886438\pi$
$487$	2608.00	+	4517.19i	0.242669	+	0.420315i	−0.718805	+	0.695212i	$0.755310\pi$
$488$	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	0.0217362	+	0.999764i	$0.493081\pi$
$499$	−9530.00	+	16506.4i	−0.854953	+	1.48082i	−0.876689	+	0.481058i	$0.840253\pi$
$500$	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	$-0.308528\pi$
$503$	12768.0			1.13180			0.565902	+	0.824473i	$0.308528\pi$
$504$		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	$-0.756359\pi$
$509$	2750.00	−	4763.14i	0.239473	−	0.414779i	0.960563	+	0.278062i	$0.0896921\pi$
$510$	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	$-0.0668311\pi$
$521$	3669.00	+	6354.89i	0.308526	+	0.534382i	−0.669514	+	0.742799i	$0.733498\pi$
$522$	1265.00	+	2191.04i	0.106068	+	0.183715i
$523$	8791.00	−	15226.5i	0.734997	−	1.27305i	−0.219727	−	0.975561i	$-0.570517\pi$
$523$	8791.00	−	15226.5i	0.734997	−	1.27305i	0.954725	−	0.297491i	$-0.0961499\pi$
$524$	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	−0.832088	−	0.554644i	$-0.812855\pi$
$541$	809.000	−	1401.23i	0.0642914	−	0.111356i	0.896379	+	0.443288i	$0.146188\pi$
$542$	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	0.763841	−	0.645405i	$-0.223311\pi$
$557$	−2327.00	−	4030.48i	−0.177016	−	0.306601i	−0.940857	+	0.338803i	$0.889978\pi$
$558$	−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	$-0.289783\pi$
$563$	−5039.00	−	8727.80i	−0.377209	−	0.653345i	−0.990655	+	0.136392i	$0.956449\pi$
$564$	−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	−0.735883	−	0.677109i	$-0.763233\pi$
$569$	2965.00	−	5135.53i	0.218452	−	0.378370i	0.954335	+	0.298739i	$0.0965659\pi$
$570$	1760.00	+	3048.41i	0.129330	+	0.224007i
$571$	9524.00	+	16496.1i	0.698016	+	1.20900i	0.969153	+	0.246458i	$0.0792668\pi$
$571$	9524.00	+	16496.1i	0.698016	+	1.20900i	−0.271138	+	0.962541i	$0.587400\pi$
$572$	−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	0.999775	+	0.0212070i	$0.00675092\pi$
$577$	7183.00	+	12441.3i	0.518253	+	0.897641i	−0.481522	+	0.876434i	$0.659916\pi$
$578$	−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	$-0.540689\pi$
$587$	−3626.00			−0.254959			−0.127480	+	0.991841i	$0.540689\pi$
$588$		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	$-0.821626\pi$
$593$	531.000	−	919.719i	0.0367716	−	0.0636903i	0.883826	+	0.467817i	$0.154959\pi$
$594$	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	0.985873	−	0.167496i	$-0.0535682\pi$
$599$	5100.00	+	8833.46i	0.347880	+	0.602547i	−0.637992	+	0.770043i	$0.720235\pi$
$600$	1965.00	−	3403.48i	0.133701	−	0.231577i
$601$	−25158.0			−1.70751			−0.853757	−	0.520671i	$-0.825682\pi$
$601$	−25158.0			−1.70751			−0.853757	+	0.520671i	$0.825682\pi$
$602$		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	0.0157413	+	0.999876i	$0.494989\pi$
$607$	−12832.0	+	22225.7i	−0.858047	+	1.48618i	−0.873789	+	0.486306i	$0.838344\pi$
$608$	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	−0.988242	−	0.152896i	$-0.951140\pi$
$613$	−9509.00	−	16470.1i	−0.626533	−	1.08519i	0.361709	−	0.932291i	$-0.382193\pi$
$614$	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	−0.991554	−	0.129694i	$-0.958600\pi$
$619$	−9365.00	−	16220.7i	−0.608096	−	1.05325i	0.383459	−	0.923558i	$-0.374733\pi$
$620$	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	−0.999997	−	0.00260525i	$-0.999171\pi$
$641$	−8151.00	−	14117.9i	−0.502255	−	0.869930i	0.497742	−	0.867325i	$-0.334163\pi$
$642$	−244.000	+	422.620i	−0.0149999	+	0.0259805i
$643$	4718.00			0.289362			0.144681	−	0.989478i	$-0.453784\pi$
$643$	4718.00			0.289362			0.144681	+	0.989478i	$0.453784\pi$
$644$		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	0.982816	+	0.184586i	$0.0590944\pi$
$647$	10718.0	+	18564.1i	0.651264	+	1.12802i	−0.331552	+	0.943437i	$0.607572\pi$
$648$	−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	−0.925054	−	0.379836i	$-0.875981\pi$
$653$	−2229.00	+	3860.74i	−0.133580	+	0.231367i	0.791474	+	0.611202i	$0.209314\pi$
$654$	−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	$-0.236836\pi$
$661$	−3716.00	−	6436.30i	−0.218662	−	0.378734i	−0.954399	+	0.298533i	$0.903503\pi$
$662$	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	−0.380389	−	0.924827i	$-0.624210\pi$
$677$	10758.0	−	18633.4i	0.610729	−	1.05781i	0.991118	−	0.132987i	$-0.0424568\pi$
$678$	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	−0.999965	−	0.00837480i	$-0.997334\pi$
$683$	−9054.00	−	15682.0i	−0.507235	−	0.878557i	0.492730	−	0.870182i	$-0.335999\pi$
$684$	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	$-0.743856\pi$
$691$	5039.00	−	8727.80i	0.277413	−	0.480494i	0.970741	+	0.240128i	$0.0771895\pi$
$692$	−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	−0.942004	−	0.335601i	$-0.891061\pi$
$709$	−3405.00	+	5897.63i	−0.180363	+	0.312398i	0.761641	+	0.647999i	$0.224394\pi$
$710$	−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	$-0.873561\pi$
$719$	−2430.00	+	4208.88i	−0.126041	+	0.218310i	0.796098	+	0.605167i	$0.206894\pi$
$720$	−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	$-0.613078\pi$
$727$	−13636.0			−0.695641			−0.347821	+	0.937561i	$0.613078\pi$
$728$		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	$-0.850086\pi$
$733$	−1044.00	+	1808.26i	−0.0526071	+	0.0911182i	0.838523	+	0.544867i	$0.183420\pi$
$734$	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	0.923067	−	0.384639i	$-0.125674\pi$
$739$	2580.00	+	4468.69i	0.128426	+	0.222440i	−0.794641	+	0.607080i	$0.792341\pi$
$740$	−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	−0.586360	−	0.810050i	$-0.699440\pi$
$751$	8404.00	−	14556.2i	0.408344	−	0.707272i	0.994704	+	0.102778i	$0.0327731\pi$
$752$	−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	$-0.889899\pi$
$761$	−3711.00	+	6427.64i	−0.176772	+	0.306178i	0.764001	+	0.645215i	$0.223232\pi$
$762$	−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	$-0.395198\pi$
$769$	13790.0			0.646658			0.323329	+	0.946287i	$0.395198\pi$
$770$		0			0
$771$	−4708.00			−0.219915
$772$	−10367.0	+	17956.2i	−0.483312	+	0.837120i
$773$	3116.00	+	5397.07i	0.144987	+	0.251124i	0.929368	−	0.369155i	$-0.120353\pi$
$773$	3116.00	+	5397.07i	0.144987	+	0.251124i	−0.784381	+	0.620279i	$0.787019\pi$
$774$	−1472.00	−	2549.58i	−0.0683591	−	0.118401i
$775$	−786.000	+	1361.39i	−0.0364309	+	0.0631002i
$776$	4410.00			0.204007
$777$		0			0
$778$	13350.0			0.615194
$779$	10010.0	−	17337.8i	0.460392	−	0.797423i
$780$	−3136.00	−	5431.71i	−0.143957	−	0.249342i
$781$	−3072.00	−	5320.86i	−0.140749	−	0.243784i
$782$	1296.00	−	2244.74i	0.0592645	−	0.102649i
$783$	−11000.0			−0.502054
$784$		0			0
$785$	1984.00			0.0902064
$786$	1118.00	−	1936.43i	0.0507350	−	0.0878757i
$787$	883.000	+	1529.40i	0.0399943	+	0.0692722i	0.885330	−	0.464964i	$-0.153933\pi$
$787$	883.000	+	1529.40i	0.0399943	+	0.0692722i	−0.845335	+	0.534236i	$0.820599\pi$
$788$	11669.0	+	20211.3i	0.527527	+	0.913703i
$789$	−3872.00	+	6706.50i	−0.174711	+	0.302608i
$790$	−7040.00			−0.317053
$791$		0			0
$792$	2760.00			0.123829
$793$	6832.00	−	11833.4i	0.305941	−	0.529906i
$794$	−678.000	−	1174.33i	−0.0303039	−	0.0524879i
$795$	−2592.00	−	4489.48i	−0.115634	−	0.200283i
$796$	6510.00	−	11275.7i	0.289875	−	0.502079i
$797$	1204.00			0.0535105			0.0267552	−	0.999642i	$-0.491483\pi$
$797$	1204.00			0.0535105			0.0267552	+	0.999642i	$0.491483\pi$
$798$		0			0
$799$	17496.0			0.774673
$800$	10545.5	−	18265.3i	0.466050	−	0.807222i
$801$	8395.00	+	14540.6i	0.370316	+	0.641405i
$802$	3111.00	+	5388.41i	0.136974	+	0.237246i
$803$	−2808.00	+	4863.60i	−0.123402	+	0.213739i
$804$	3416.00			0.149842
$805$		0			0
$806$	−336.000			−0.0146837
$807$	180.000	−	311.769i	0.00785167	−	0.0135995i
$808$	5160.00	+	8937.38i	0.224664	+	0.389129i
$809$	3525.00	+	6105.48i	0.153192	+	0.265336i	0.932399	−	0.361430i	$-0.117711\pi$
$809$	3525.00	+	6105.48i	0.153192	+	0.265336i	−0.779207	+	0.626766i	$0.784378\pi$
$810$	3368.00	−	5833.55i	0.146098	−	0.253049i
$811$	23282.0			1.00807			0.504033	−	0.863684i	$-0.331849\pi$
$811$	23282.0			1.00807			0.504033	+	0.863684i	$0.331849\pi$
$812$		0			0
$813$	−4064.00			−0.175315
$814$	984.000	−	1704.34i	0.0423700	−	0.0733870i
$815$	−16064.0	−	27823.7i	−0.690426	−	1.19585i
$816$	2214.00	+	3834.76i	0.0949822	+	0.164514i
$817$	7040.00	−	12193.6i	0.301467	−	0.522156i
$818$	−5150.00			−0.220129
$819$		0			0
$820$	−20384.0			−0.868098
$821$	−5071.00	+	8783.23i	−0.215565	+	0.373370i	−0.953447	−	0.301560i	$-0.902493\pi$
$821$	−5071.00	+	8783.23i	−0.215565	+	0.373370i	0.737882	+	0.674930i	$0.235826\pi$
$822$	−2274.00	−	3938.68i	−0.0964901	−	0.167126i
$823$	4596.00	+	7960.51i	0.194662	+	0.337164i	0.946790	−	0.321853i	$-0.104306\pi$
$823$	4596.00	+	7960.51i	0.194662	+	0.337164i	−0.752128	+	0.659017i	$0.770972\pi$
$824$	−10410.0	+	18030.6i	−0.440109	+	0.762291i
$825$	2096.00			0.0884525
$826$		0			0
$827$	−46716.0			−1.96430			−0.982149	−	0.188104i	$-0.939766\pi$
$827$	−46716.0			−1.96430			−0.982149	+	0.188104i	$0.939766\pi$
$828$	−3864.00	+	6692.64i	−0.162178	+	0.280900i
$829$	−5620.00	−	9734.13i	−0.235453	−	0.407817i	0.723951	−	0.689851i	$-0.242324\pi$
$829$	−5620.00	−	9734.13i	−0.235453	−	0.407817i	−0.959404	+	0.282034i	$0.908991\pi$
$830$	−10416.0	−	18041.0i	−0.435596	−	0.754474i
$831$	−5426.00	+	9398.11i	−0.226505	+	0.392319i
$832$	−4676.00			−0.194845
$833$		0			0
$834$	−420.000			−0.0174381
$835$	−23072.0	+	39961.9i	−0.956215	+	1.65621i
$836$	3080.00	+	5334.72i	0.127421	+	0.220700i
$837$	−600.000	−	1039.23i	−0.0247778	−	0.0429164i
$838$	1155.00	−	2000.52i	0.0476119	−	0.0824663i
$839$	700.000			0.0288042			0.0144021	−	0.999896i	$-0.495416\pi$
$839$	700.000			0.0288042			0.0144021	+	0.999896i	$0.495416\pi$
$840$		0			0
$841$	−12289.0			−0.503875
$842$	631.000	−	1092.92i	0.0258262	−	0.0447324i
$843$	842.000	+	1458.39i	0.0344010	+	0.0595842i
$844$	−14938.0	−	25873.4i	−0.609226	−	1.05521i
$845$	11304.0	−	19579.1i	0.460200	−	0.797091i
$846$	7452.00			0.302843
$847$		0			0
$848$	−6642.00			−0.268971
$849$	−3782.00	+	6550.62i	−0.152883	+	0.264802i
$850$	3537.00	+	6126.26i	0.142727	+	0.247211i
$851$	5904.00	+	10226.0i	0.237822	+	0.411920i
$852$	5376.00	−	9311.51i	0.216172	−	0.374421i
$853$	−37492.0			−1.50493			−0.752463	−	0.658635i	$-0.771134\pi$
$853$	−37492.0			−1.50493			−0.752463	+	0.658635i	$0.771134\pi$
$854$		0			0
$855$	40480.0			1.61917
$856$	−1830.00	+	3169.65i	−0.0730702	+	0.126561i
$857$	−14447.0	−	25022.9i	−0.575846	−	0.997395i	−0.995949	−	0.0899183i	$-0.971339\pi$
$857$	−14447.0	−	25022.9i	−0.575846	−	0.997395i	0.420103	−	0.907476i	$-0.361994\pi$
$858$	224.000	+	387.979i	0.00891286	+	0.0154375i
$859$	1385.00	−	2398.89i	0.0550123	−	0.0952841i	−0.837208	−	0.546885i	$-0.815814\pi$
$859$	1385.00	−	2398.89i	0.0550123	−	0.0952841i	0.892220	+	0.451601i	$0.149147\pi$
$860$	−14336.0			−0.568434
$861$		0			0
$862$	4488.00			0.177334
$863$	−8844.00	+	15318.3i	−0.348845	+	0.604217i	−0.986045	−	0.166482i	$-0.946759\pi$
$863$	−8844.00	+	15318.3i	−0.348845	+	0.604217i	0.637200	+	0.770699i	$0.280093\pi$
$864$	8050.00	+	13943.0i	0.316975	+	0.549017i
$865$	−17824.0	−	30872.1i	−0.700618	−	1.21351i
$866$	8519.00	−	14755.3i	0.334281	−	0.578992i
$867$	3994.00			0.156451
$868$		0			0
$869$	−3520.00			−0.137408
$870$	1760.00	−	3048.41i	0.0685857	−	0.118794i
$871$	−3416.00	−	5916.69i	−0.132889	−	0.230171i
$872$	−675.000	−	1169.13i	−0.0262137	−	0.0454035i
$873$	3381.00	−	5856.06i	0.131076	−	0.227031i
$874$	5280.00			0.204346
$875$		0			0
$876$	−9828.00			−0.379061
$877$	16783.0	−	29069.0i	0.646205	−	1.11926i	−0.337817	−	0.941212i	$-0.609688\pi$
$877$	16783.0	−	29069.0i	0.646205	−	1.11926i	0.984022	−	0.178048i	$-0.0569782\pi$
$878$	8100.00	+	14029.6i	0.311346	+	0.539267i
$879$	−4312.00	−	7468.60i	−0.165461	−	0.286587i
$880$	2624.00	−	4544.90i	0.100517	−	0.174101i
$881$	−16758.0			−0.640853			−0.320426	−	0.947273i	$-0.603826\pi$
$881$	−16758.0			−0.640853			−0.320426	+	0.947273i	$0.603826\pi$
$882$		0			0
$883$	11468.0			0.437066			0.218533	−	0.975830i	$-0.429873\pi$
$883$	11468.0			0.437066			0.218533	+	0.975830i	$0.429873\pi$
$884$	5292.00	−	9166.01i	0.201345	−	0.348740i
$885$	12960.0	+	22447.4i	0.492255	+	0.852611i
$886$	−4386.00	−	7596.77i	−0.166310	−	0.288057i
$887$	25178.0	−	43609.6i	0.953094	−	1.65081i	0.214424	−	0.976741i	$-0.431213\pi$
$887$	25178.0	−	43609.6i	0.953094	−	1.65081i	0.738670	−	0.674067i	$-0.235454\pi$
$888$	7380.00			0.278893
$889$		0			0
$890$	−11680.0			−0.439904
$891$	1684.00	−	2916.77i	0.0633178	−	0.109670i
$892$	−19012.0	−	32929.7i	−0.713642	−	1.23606i
$893$	17820.0	+	30865.1i	0.667776	+	1.15662i
$894$	2010.00	−	3481.42i	0.0751951	−	0.130242i
$895$	−13120.0			−0.490004
$896$		0			0
$897$	−2688.00			−0.100055
$898$	1065.00	−	1844.63i	0.0395763	−	0.0685481i
$899$	660.000	+	1143.15i	0.0244852	+	0.0424097i
$900$	−10545.5	−	18265.3i	−0.390574	−	0.676494i
$901$	4374.00	−	7575.99i	0.161730	−	0.280125i
$902$	1456.00			0.0537467
$903$		0			0
$904$	19770.0			0.727368
$905$	−31136.0	+	53929.1i	−1.14364	+	1.98085i
$906$	−1112.00	−	1926.04i	−0.0407767	−	0.0706274i
$907$	4358.00	+	7548.28i	0.159542	+	0.276336i	0.934704	−	0.355428i	$-0.115665\pi$
$907$	4358.00	+	7548.28i	0.159542	+	0.276336i	−0.775161	+	0.631763i	$0.782331\pi$
$908$	−7161.00	+	12403.2i	−0.261725	+	0.453321i
$909$	15824.0			0.577392
$910$		0			0
$911$	7632.00			0.277563			0.138781	−	0.990323i	$-0.455682\pi$
$911$	7632.00			0.277563			0.138781	+	0.990323i	$0.455682\pi$
$912$	−4510.00	+	7811.55i	−0.163751	+	0.283625i
$913$	−5208.00	−	9020.52i	−0.188784	−	0.326983i
$914$	5267.00	+	9122.71i	0.190609	+	0.330145i
$915$	−7808.00	+	13523.9i	−0.282103	+	0.488617i
$916$	20860.0			0.752439
$917$		0			0
$918$	−5400.00			−0.194147
$919$	11540.0	−	19987.9i	0.414221	−	0.717453i	−0.581125	−	0.813814i	$-0.697387\pi$
$919$	11540.0	−	19987.9i	0.414221	−	0.717453i	0.995346	+	0.0963618i	$0.0307206\pi$
$920$	−5760.00	−	9976.61i	−0.206415	−	0.357521i
$921$	2674.00	+	4631.50i	0.0956692	+	0.165704i
$922$	−4634.00	+	8026.32i	−0.165523	+	0.286695i
$923$	−21504.0			−0.766861
$924$		0			0
$925$	−32226.0			−1.14550
$926$	−4696.00	+	8133.71i	−0.166652	+	0.288650i
$927$	15962.0	+	27647.0i	0.565546	+	0.979554i
$928$	−8855.00	−	15337.3i	−0.313232	−	0.542534i
$929$	−22555.0	+	39066.4i	−0.796561	+	1.37968i	0.125282	+	0.992121i	$0.460017\pi$
$929$	−22555.0	+	39066.4i	−0.796561	+	1.37968i	−0.921843	+	0.387564i	$0.873317\pi$
$930$	384.000			0.0135396
$931$		0			0
$932$	−31206.0			−1.09677
$933$	−3768.00	+	6526.37i	−0.132217	+	0.229007i
$934$	−5403.00	−	9358.27i	−0.189284	−	0.327850i
$935$	3456.00	+	5985.97i	0.120881	+	0.209371i
$936$	4830.00	−	8365.81i	0.168668	−	0.292142i
$937$	16674.0			0.581340			0.290670	−	0.956823i	$-0.406122\pi$
$937$	16674.0			0.581340			0.290670	+	0.956823i	$0.406122\pi$
$938$		0			0
$939$	−4876.00			−0.169459
$940$	18144.0	−	31426.3i	0.629566	−	1.09044i
$941$	−21916.0	−	37959.6i	−0.759236	−	1.31504i	−0.943241	−	0.332110i	$-0.892239\pi$
$941$	−21916.0	−	37959.6i	−0.759236	−	1.31504i	0.184005	−	0.982925i	$-0.441094\pi$
$942$	−124.000	−	214.774i	−0.00428889	−	0.00742858i
$943$	−4368.00	+	7565.60i	−0.150840	+	0.261262i
$944$	33210.0			1.14501
$945$		0			0
$946$	1024.00			0.0351936
$947$	368.000	−	637.395i	0.0126277	−	0.0218717i	−0.859643	−	0.510896i	$-0.829314\pi$
$947$	368.000	−	637.395i	0.0126277	−	0.0218717i	0.872270	+	0.489024i	$0.162647\pi$
$948$	−3080.00	−	5334.72i	−0.105521	−	0.182767i
$949$	9828.00	+	17022.6i	0.336175	+	0.582273i
$950$	−7205.00	+	12479.4i	−0.246064	+	0.426196i
$951$	6372.00			0.217273
$952$		0			0
$953$	38138.0			1.29634			0.648169	−	0.761496i	$-0.275535\pi$
$953$	38138.0			1.29634			0.648169	+	0.761496i	$0.275535\pi$
$954$	1863.00	−	3226.81i	0.0632252	−	0.109509i
$955$	40384.0	+	69947.1i	1.36837	+	2.37009i
$956$	15540.0	+	26916.1i	0.525732	+	0.910594i
$957$	880.000	−	1524.20i	0.0297245	−	0.0514844i
$958$	−4940.00			−0.166601
$959$		0			0
$960$	5344.00			0.179663
$961$	14823.5	−	25675.1i	0.497583	−	0.861839i
$962$	−3444.00	−	5965.18i	−0.115425	−	0.199922i
$963$	2806.00	+	4860.13i	0.0938962	+	0.162633i
$964$	11557.0	−	20017.3i	0.386126	−	0.668791i
$965$	−47392.0			−1.58094
$966$		0			0
$967$	26224.0			0.872086			0.436043	−	0.899926i	$-0.356380\pi$
$967$	26224.0			0.872086			0.436043	+	0.899926i	$0.356380\pi$
$968$	9502.50	−	16458.8i	0.315519	−	0.546494i
$969$	−5940.00	−	10288.4i	−0.196925	−	0.341084i
$970$	2352.00	+	4073.78i	0.0778538	+	0.134847i
$971$	−9381.00	+	16248.4i	−0.310042	+	0.537008i	−0.978371	−	0.206857i	$-0.933676\pi$
$971$	−9381.00	+	16248.4i	−0.310042	+	0.537008i	0.668329	+	0.743866i	$0.267010\pi$
$972$	24794.0			0.818177
$973$		0			0
$974$	5216.00			0.171593
$975$	3668.00	−	6353.16i	0.120482	−	0.208681i
$976$	10004.0	+	17327.4i	0.328095	+	0.568276i
$977$	−19197.0	−	33250.2i	−0.628625	−	1.08881i	−0.987828	−	0.155551i	$-0.950285\pi$
$977$	−19197.0	−	33250.2i	−0.628625	−	1.08881i	0.359203	−	0.933259i	$-0.383049\pi$
$978$	−2008.00	+	3477.96i	−0.0656531	+	0.113715i
$979$	−5840.00			−0.190651
$980$		0			0
$981$	−2070.00			−0.0673700
$982$	2206.00	−	3820.90i	0.0716866	−	0.124165i
$983$	−2694.00	−	4666.14i	−0.0874112	−	0.151401i	0.819005	−	0.573787i	$-0.194526\pi$
$983$	−2694.00	−	4666.14i	−0.0874112	−	0.151401i	−0.906416	+	0.422386i	$0.861193\pi$
$984$	2730.00	+	4728.50i	0.0884443	+	0.153190i
$985$	−26672.0	+	46197.3i	−0.862782	+	1.49438i
$986$	5940.00			0.191854
$987$		0			0
$988$	21560.0			0.694246
$989$	−3072.00	+	5320.86i	−0.0987704	+	0.171075i
$990$	1472.00	+	2549.58i	0.0472558	+	0.0818494i
$991$	−12736.0	−	22059.4i	−0.408247	−	0.707104i	0.586447	−	0.809988i	$-0.300526\pi$
$991$	−12736.0	−	22059.4i	−0.408247	−	0.707104i	−0.994693	+	0.102884i	$0.967193\pi$
$992$	966.000	−	1673.16i	0.0309179	−	0.0535513i
$993$	−17344.0			−0.554275
$994$		0			0
$995$	29760.0			0.948196
$996$	9114.00	−	15785.9i	0.289948	−	0.502205i
$997$	8548.00	+	14805.6i	0.271532	+	0.470308i	0.969254	−	0.246061i	$-0.0791362\pi$
$997$	8548.00	+	14805.6i	0.271532	+	0.470308i	−0.697722	+	0.716369i	$0.745803\pi$
$998$	9530.00	+	16506.4i	0.302271	+	0.523549i
$999$	12300.0	−	21304.2i	0.389544	−	0.674711i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.4.c.c.30.1		2
3.2	odd	2		441.4.e.h.226.1		2
7.2	even	3		7.4.a.a.1.1	✓	1
7.3	odd	6		49.4.c.b.18.1		2
7.4	even	3	inner	49.4.c.c.18.1		2
7.5	odd	6		49.4.a.b.1.1		1
7.6	odd	2		49.4.c.b.30.1		2
21.2	odd	6		63.4.a.b.1.1		1
21.5	even	6		441.4.a.i.1.1		1
21.11	odd	6		441.4.e.h.361.1		2
21.17	even	6		441.4.e.e.361.1		2
21.20	even	2		441.4.e.e.226.1		2
28.19	even	6		784.4.a.g.1.1		1
28.23	odd	6		112.4.a.f.1.1		1
35.2	odd	12		175.4.b.b.99.1		2
35.9	even	6		175.4.a.b.1.1		1
35.19	odd	6		1225.4.a.j.1.1		1
35.23	odd	12		175.4.b.b.99.2		2
56.37	even	6		448.4.a.i.1.1		1
56.51	odd	6		448.4.a.e.1.1		1
77.65	odd	6		847.4.a.b.1.1		1
84.23	even	6		1008.4.a.c.1.1		1
91.51	even	6		1183.4.a.b.1.1		1
105.44	odd	6		1575.4.a.e.1.1		1
119.16	even	6		2023.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.4.a.a.1.1	✓	1	7.2	even	3
49.4.a.b.1.1		1	7.5	odd	6
49.4.c.b.18.1		2	7.3	odd	6
49.4.c.b.30.1		2	7.6	odd	2
49.4.c.c.18.1		2	7.4	even	3	inner
49.4.c.c.30.1		2	1.1	even	1	trivial
63.4.a.b.1.1		1	21.2	odd	6
112.4.a.f.1.1		1	28.23	odd	6
175.4.a.b.1.1		1	35.9	even	6
175.4.b.b.99.1		2	35.2	odd	12
175.4.b.b.99.2		2	35.23	odd	12
441.4.a.i.1.1		1	21.5	even	6
441.4.e.e.226.1		2	21.20	even	2
441.4.e.e.361.1		2	21.17	even	6
441.4.e.h.226.1		2	3.2	odd	2
441.4.e.h.361.1		2	21.11	odd	6
448.4.a.e.1.1		1	56.51	odd	6
448.4.a.i.1.1		1	56.37	even	6
784.4.a.g.1.1		1	28.19	even	6
847.4.a.b.1.1		1	77.65	odd	6
1008.4.a.c.1.1		1	84.23	even	6
1183.4.a.b.1.1		1	91.51	even	6
1225.4.a.j.1.1		1	35.19	odd	6
1575.4.a.e.1.1		1	105.44	odd	6
2023.4.a.a.1.1		1	119.16	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 2 q^{3} + 7 q^{4} - 16 q^{5} + 4 q^{6} + 30 q^{8} + 23 q^{9} + 16 q^{10} + 8 q^{11} - 14 q^{12} + 56 q^{13} - 64 q^{15} - 41 q^{16} - 54 q^{17} - 23 q^{18} + 110 q^{19} - 224 q^{20} + 16 q^{22}+ \cdots + 368 q^{99}+O(q^{100}) \) 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

L-functions

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Database

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