LMFDB - Embedded newform 21.3.b.a.8.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,3,Mod(8,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("21.8");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	21.b (of order $2$, degree $1$, 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:	$0.572208555157$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.65856.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 14x^{2} + 21 $ x^4 + 14*x^2 + 21
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			8.2
Root			$-1.30710i$ of defining polynomial
Character	$\chi$	$=$	21.8
Dual form			21.3.b.a.8.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.30710i q^{2} +(-1.82288 - 2.38267i) q^{3} +2.29150 q^{4} +7.37953i q^{5} +(-3.11438 + 2.38267i) q^{6} -2.64575 q^{7} -8.22359i q^{8} +(-2.35425 + 8.68663i) q^{9} +O(q^{10})$	\(q-1.30710i q^{2} +(-1.82288 - 2.38267i) q^{3} +2.29150 q^{4} +7.37953i q^{5} +(-3.11438 + 2.38267i) q^{6} -2.64575 q^{7} -8.22359i q^{8} +(-2.35425 + 8.68663i) q^{9} +9.64575 q^{10} -2.61419i q^{11} +(-4.17712 - 5.45990i) q^{12} -6.35425 q^{13} +3.45825i q^{14} +(17.5830 - 13.4520i) q^{15} -1.58301 q^{16} -12.1449i q^{17} +(11.3542 + 3.07723i) q^{18} -10.2288 q^{19} +16.9102i q^{20} +(4.82288 + 6.30396i) q^{21} -3.41699 q^{22} +4.30231i q^{23} +(-19.5941 + 14.9906i) q^{24} -29.4575 q^{25} +8.30561i q^{26} +(24.9889 - 10.2252i) q^{27} -6.06275 q^{28} +17.3733i q^{29} +(-17.5830 - 22.9827i) q^{30} +39.2915 q^{31} -30.8252i q^{32} +(-6.22876 + 4.76534i) q^{33} -15.8745 q^{34} -19.5244i q^{35} +(-5.39477 + 19.9054i) q^{36} +41.0405 q^{37} +13.3700i q^{38} +(11.5830 + 15.1401i) q^{39} +60.6863 q^{40} -30.2802i q^{41} +(8.23987 - 6.30396i) q^{42} -55.8745 q^{43} -5.99042i q^{44} +(-64.1033 - 17.3733i) q^{45} +5.62352 q^{46} -39.9749i q^{47} +(2.88562 + 3.77178i) q^{48} +7.00000 q^{49} +38.5038i q^{50} +(-28.9373 + 22.1386i) q^{51} -14.5608 q^{52} +105.002i q^{53} +(-13.3654 - 32.6628i) q^{54} +19.2915 q^{55} +21.7576i q^{56} +(18.6458 + 24.3718i) q^{57} +22.7085 q^{58} +41.3640i q^{59} +(40.2915 - 30.8252i) q^{60} -20.4797 q^{61} -51.3577i q^{62} +(6.22876 - 22.9827i) q^{63} -46.6235 q^{64} -46.8914i q^{65} +(6.22876 + 8.14158i) q^{66} -27.1660 q^{67} -27.8300i q^{68} +(10.2510 - 7.84257i) q^{69} -25.5203 q^{70} -67.8049i q^{71} +(71.4353 + 19.3604i) q^{72} +60.7895 q^{73} -53.6439i q^{74} +(53.6974 + 70.1876i) q^{75} -23.4392 q^{76} +6.91650i q^{77} +(19.7895 - 15.1401i) q^{78} -63.2470 q^{79} -11.6818i q^{80} +(-69.9150 - 40.9010i) q^{81} -39.5791 q^{82} +89.9435i q^{83} +(11.0516 + 14.4455i) q^{84} +89.6235 q^{85} +73.0333i q^{86} +(41.3948 - 31.6693i) q^{87} -21.4980 q^{88} +63.1745i q^{89} +(-22.7085 + 83.7891i) q^{90} +16.8118 q^{91} +9.85875i q^{92} +(-71.6235 - 93.6188i) q^{93} -52.2510 q^{94} -75.4835i q^{95} +(-73.4464 + 56.1906i) q^{96} +19.1660 q^{97} -9.14967i q^{98} +(22.7085 + 6.15445i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 12 q^{4} + 14 q^{6} - 20 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 12 * q^4 + 14 * q^6 - 20 * q^9	$ 4 q - 2 q^{3} - 12 q^{4} + 14 q^{6} - 20 q^{9} + 28 q^{10} - 22 q^{12} - 36 q^{13} + 28 q^{15} + 36 q^{16} + 56 q^{18} + 12 q^{19} + 14 q^{21} - 56 q^{22} - 126 q^{24} - 12 q^{25} + 10 q^{27} - 56 q^{28} - 28 q^{30} + 136 q^{31} + 28 q^{33} + 116 q^{36} + 16 q^{37} + 4 q^{39} + 84 q^{40} + 70 q^{42} - 160 q^{43} - 140 q^{45} - 168 q^{46} + 38 q^{48} + 28 q^{49} - 84 q^{51} + 164 q^{52} - 154 q^{54} + 56 q^{55} + 64 q^{57} + 112 q^{58} + 140 q^{60} - 156 q^{61} - 28 q^{63} + 4 q^{64} - 28 q^{66} - 24 q^{67} + 168 q^{69} - 28 q^{70} - 32 q^{73} + 146 q^{75} - 316 q^{76} - 196 q^{78} + 128 q^{79} - 68 q^{81} + 392 q^{82} - 14 q^{84} + 168 q^{85} + 28 q^{87} + 168 q^{88} - 112 q^{90} - 28 q^{91} - 96 q^{93} - 336 q^{94} - 98 q^{96} - 8 q^{97} + 112 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 12 * q^4 + 14 * q^6 - 20 * q^9 + 28 * q^10 - 22 * q^12 - 36 * q^13 + 28 * q^15 + 36 * q^16 + 56 * q^18 + 12 * q^19 + 14 * q^21 - 56 * q^22 - 126 * q^24 - 12 * q^25 + 10 * q^27 - 56 * q^28 - 28 * q^30 + 136 * q^31 + 28 * q^33 + 116 * q^36 + 16 * q^37 + 4 * q^39 + 84 * q^40 + 70 * q^42 - 160 * q^43 - 140 * q^45 - 168 * q^46 + 38 * q^48 + 28 * q^49 - 84 * q^51 + 164 * q^52 - 154 * q^54 + 56 * q^55 + 64 * q^57 + 112 * q^58 + 140 * q^60 - 156 * q^61 - 28 * q^63 + 4 * q^64 - 28 * q^66 - 24 * q^67 + 168 * q^69 - 28 * q^70 - 32 * q^73 + 146 * q^75 - 316 * q^76 - 196 * q^78 + 128 * q^79 - 68 * q^81 + 392 * q^82 - 14 * q^84 + 168 * q^85 + 28 * q^87 + 168 * q^88 - 112 * q^90 - 28 * q^91 - 96 * q^93 - 336 * q^94 - 98 * q^96 - 8 * q^97 + 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.30710i		−	0.653548i	−0.945103	−	0.326774i	$-0.894038\pi$
$2$		−	1.30710i		−	0.653548i	0.945103	−	0.326774i	$-0.105962\pi$
$3$	−1.82288	−	2.38267i	−0.607625	−	0.794224i
$3$	−1.82288	−	2.38267i	−0.607625	−	0.794224i
$4$	2.29150			0.572876
$5$			7.37953i			1.47591i	0.674852	+	0.737953i	$0.264208\pi$
$5$			7.37953i			1.47591i	−0.674852	+	0.737953i	$0.735792\pi$
$6$	−3.11438	+	2.38267i	−0.519063	+	0.397112i
$7$	−2.64575			−0.377964
$7$	−2.64575			−0.377964
$8$		−	8.22359i		−	1.02795i
$9$	−2.35425	+	8.68663i	−0.261583	+	0.965181i
$10$	9.64575			0.964575
$11$		−	2.61419i		−	0.237654i	−0.992915	−	0.118827i	$-0.962087\pi$
$11$		−	2.61419i		−	0.237654i	0.992915	−	0.118827i	$-0.0379133\pi$
$12$	−4.17712	−	5.45990i	−0.348094	−	0.454992i
$13$	−6.35425			−0.488788			−0.244394	−	0.969676i	$-0.578589\pi$
$13$	−6.35425			−0.488788			−0.244394	+	0.969676i	$0.578589\pi$
$14$			3.45825i			0.247018i
$15$	17.5830	−	13.4520i	1.17220	−	0.896798i
$16$	−1.58301			−0.0989378
$17$		−	12.1449i		−	0.714405i	−0.934027	−	0.357202i	$-0.883731\pi$
$17$		−	12.1449i		−	0.714405i	0.934027	−	0.357202i	$-0.116269\pi$
$18$	11.3542	+	3.07723i	0.630792	+	0.170957i
$19$	−10.2288			−0.538356			−0.269178	−	0.963090i	$-0.586752\pi$
$19$	−10.2288			−0.538356			−0.269178	+	0.963090i	$0.586752\pi$
$20$			16.9102i			0.845511i
$21$	4.82288	+	6.30396i	0.229661	+	0.300188i
$22$	−3.41699			−0.155318
$23$			4.30231i			0.187057i	0.995617	+	0.0935284i	$0.0298146\pi$
$23$			4.30231i			0.187057i	−0.995617	+	0.0935284i	$0.970185\pi$
$24$	−19.5941	+	14.9906i	−0.816422	+	0.624608i
$25$	−29.4575			−1.17830
$26$			8.30561i			0.319446i
$27$	24.9889	−	10.2252i	0.925514	−	0.378713i
$28$	−6.06275			−0.216527
$29$			17.3733i			0.599078i	0.954084	+	0.299539i	$0.0968328\pi$
$29$			17.3733i			0.599078i	−0.954084	+	0.299539i	$0.903167\pi$
$30$	−17.5830	−	22.9827i	−0.586100	−	0.766089i
$31$	39.2915			1.26747			0.633734	−	0.773551i	$-0.281521\pi$
$31$	39.2915			1.26747			0.633734	+	0.773551i	$0.281521\pi$
$32$		−	30.8252i		−	0.963288i
$33$	−6.22876	+	4.76534i	−0.188750	+	0.144404i
$34$	−15.8745			−0.466897
$35$		−	19.5244i		−	0.557840i
$36$	−5.39477	+	19.9054i	−0.149855	+	0.552929i
$37$	41.0405			1.10920			0.554602	−	0.832116i	$-0.312871\pi$
$37$	41.0405			1.10920			0.554602	+	0.832116i	$0.312871\pi$
$38$			13.3700i			0.351841i
$39$	11.5830	+	15.1401i	0.297000	+	0.388207i
$40$	60.6863			1.51716
$41$		−	30.2802i		−	0.738541i	−0.929322	−	0.369270i	$-0.879608\pi$
$41$		−	30.2802i		−	0.738541i	0.929322	−	0.369270i	$-0.120392\pi$
$42$	8.23987	−	6.30396i	0.196187	−	0.150094i
$43$	−55.8745			−1.29941			−0.649704	−	0.760188i	$-0.725107\pi$
$43$	−55.8745			−1.29941			−0.649704	+	0.760188i	$0.725107\pi$
$44$		−	5.99042i		−	0.136146i
$45$	−64.1033	−	17.3733i	−1.42452	−	0.386072i
$46$	5.62352			0.122251
$47$		−	39.9749i		−	0.850530i	−0.905069	−	0.425265i	$-0.860181\pi$
$47$		−	39.9749i		−	0.850530i	0.905069	−	0.425265i	$-0.139819\pi$
$48$	2.88562	+	3.77178i	0.0601171	+	0.0785788i
$49$	7.00000			0.142857
$50$			38.5038i			0.770075i
$51$	−28.9373	+	22.1386i	−0.567397	+	0.434090i
$52$	−14.5608			−0.280015
$53$			105.002i			1.98116i	0.136928	+	0.990581i	$0.456277\pi$
$53$			105.002i			1.98116i	−0.136928	+	0.990581i	$0.543723\pi$
$54$	−13.3654	−	32.6628i	−0.247507	−	0.604868i
$55$	19.2915			0.350755
$56$			21.7576i			0.388528i
$57$	18.6458	+	24.3718i	0.327118	+	0.427575i
$58$	22.7085			0.391526
$59$			41.3640i			0.701085i	0.936547	+	0.350542i	$0.114003\pi$
$59$			41.3640i			0.701085i	−0.936547	+	0.350542i	$0.885997\pi$
$60$	40.2915	−	30.8252i	0.671525	−	0.513754i
$61$	−20.4797			−0.335733			−0.167867	−	0.985810i	$-0.553688\pi$
$61$	−20.4797			−0.335733			−0.167867	+	0.985810i	$0.553688\pi$
$62$		−	51.3577i		−	0.828350i
$63$	6.22876	−	22.9827i	0.0988692	−	0.364804i
$64$	−46.6235			−0.728493
$65$		−	46.8914i		−	0.721406i
$66$	6.22876	+	8.14158i	0.0943751	+	0.123357i
$67$	−27.1660			−0.405463			−0.202731	−	0.979234i	$-0.564982\pi$
$67$	−27.1660			−0.405463			−0.202731	+	0.979234i	$0.564982\pi$
$68$		−	27.8300i		−	0.409265i
$69$	10.2510	−	7.84257i	0.148565	−	0.113660i
$70$	−25.5203			−0.364575
$71$		−	67.8049i		−	0.954999i	−0.878632	−	0.477499i	$-0.841543\pi$
$71$		−	67.8049i		−	0.954999i	0.878632	−	0.477499i	$-0.158457\pi$
$72$	71.4353	+	19.3604i	0.992157	+	0.268894i
$73$	60.7895			0.832733			0.416367	−	0.909197i	$-0.363303\pi$
$73$	60.7895			0.832733			0.416367	+	0.909197i	$0.363303\pi$
$74$		−	53.6439i		−	0.724917i
$75$	53.6974	+	70.1876i	0.715965	+	0.935834i
$76$	−23.4392			−0.308411
$77$			6.91650i			0.0898246i
$78$	19.7895	−	15.1401i	0.253712	−	0.194104i
$79$	−63.2470			−0.800596			−0.400298	−	0.916385i	$-0.631093\pi$
$79$	−63.2470			−0.800596			−0.400298	+	0.916385i	$0.631093\pi$
$80$		−	11.6818i		−	0.146023i
$81$	−69.9150	−	40.9010i	−0.863148	−	0.504950i
$82$	−39.5791			−0.482672
$83$			89.9435i			1.08366i	0.840489	+	0.541828i	$0.182268\pi$
$83$			89.9435i			1.08366i	−0.840489	+	0.541828i	$0.817732\pi$
$84$	11.0516	+	14.4455i	0.131567	+	0.171971i
$85$	89.6235			1.05439
$86$			73.0333i			0.849224i
$87$	41.3948	−	31.6693i	0.475802	−	0.364015i
$88$	−21.4980			−0.244296
$89$			63.1745i			0.709826i	0.934899	+	0.354913i	$0.115490\pi$
$89$			63.1745i			0.709826i	−0.934899	+	0.354913i	$0.884510\pi$
$90$	−22.7085	+	83.7891i	−0.252317	+	0.930990i
$91$	16.8118			0.184745
$92$			9.85875i			0.107160i
$93$	−71.6235	−	93.6188i	−0.770145	−	1.00665i
$94$	−52.2510			−0.555862
$95$		−	75.4835i		−	0.794563i
$96$	−73.4464	+	56.1906i	−0.765067	+	0.585318i
$97$	19.1660			0.197588			0.0987939	−	0.995108i	$-0.468502\pi$
$97$	19.1660			0.197588			0.0987939	+	0.995108i	$0.468502\pi$
$98$		−	9.14967i		−	0.0933639i
$99$	22.7085	+	6.15445i	0.229379	+	0.0621662i
$100$	−67.5020			−0.675020
$101$		−	98.7122i		−	0.977348i	−0.872466	−	0.488674i	$-0.837481\pi$
$101$		−	98.7122i		−	0.977348i	0.872466	−	0.488674i	$-0.162519\pi$
$102$	28.9373	+	37.8237i	0.283699	+	0.370821i
$103$	−56.2510			−0.546126			−0.273063	−	0.961996i	$-0.588037\pi$
$103$	−56.2510			−0.546126			−0.273063	+	0.961996i	$0.588037\pi$
$104$			52.2547i			0.502449i
$105$	−46.5203	+	35.5906i	−0.443050	+	0.338958i
$106$	137.247			1.29478
$107$			123.137i			1.15081i	0.817868	+	0.575406i	$0.195156\pi$
$107$			123.137i			1.15081i	−0.817868	+	0.575406i	$0.804844\pi$
$108$	57.2621	−	23.4312i	0.530205	−	0.216955i
$109$	164.539			1.50953			0.754764	−	0.655996i	$-0.227751\pi$
$109$	164.539			1.50953			0.754764	+	0.655996i	$0.227751\pi$
$110$		−	25.2158i		−	0.229235i
$111$	−74.8118	−	97.7861i	−0.673980	−	0.880956i
$112$	4.18824			0.0373950
$113$		−	144.050i		−	1.27478i	−0.770540	−	0.637391i	$-0.780014\pi$
$113$		−	144.050i		−	1.27478i	0.770540	−	0.637391i	$-0.219986\pi$
$114$	31.8562	−	24.3718i	0.279441	−	0.213787i
$115$	−31.7490			−0.276078
$116$			39.8109i			0.343197i
$117$	14.9595	−	55.1970i	0.127859	−	0.471769i
$118$	54.0667			0.458192
$119$			32.1323i			0.270020i
$120$	−110.624	−	144.595i	−0.921863	−	1.20496i
$121$	114.166			0.943521
$122$			26.7690i			0.219418i
$123$	−72.1477	+	55.1970i	−0.586567	+	0.448756i
$124$	90.0366			0.726101
$125$		−	32.8944i		−	0.263155i
$126$	−30.0405	−	8.14158i	−0.238417	−	0.0646157i
$127$	−36.5830			−0.288055			−0.144028	−	0.989574i	$-0.546005\pi$
$127$	−36.5830			−0.288055			−0.144028	+	0.989574i	$0.546005\pi$
$128$		−	62.3595i		−	0.487184i
$129$	101.852	+	133.131i	0.789553	+	1.03202i
$130$	−61.2915			−0.471473
$131$			33.6855i			0.257141i	0.991700	+	0.128570i	$0.0410389\pi$
$131$			33.6855i			0.257141i	−0.991700	+	0.128570i	$0.958961\pi$
$132$	−14.2732	+	10.9198i	−0.108130	+	0.0827257i
$133$	27.0627			0.203479
$134$			35.5086i			0.264989i
$135$	75.4575	+	184.406i	0.558945	+	1.36597i
$136$	−99.8745			−0.734371
$137$			39.9749i			0.291788i	0.989300	+	0.145894i	$0.0466058\pi$
$137$			39.9749i			0.291788i	−0.989300	+	0.145894i	$0.953394\pi$
$138$	−10.2510	−	13.3990i	−0.0742825	−	0.0970943i
$139$	−194.642			−1.40030			−0.700150	−	0.713995i	$-0.746884\pi$
$139$	−194.642			−1.40030			−0.700150	+	0.713995i	$0.746884\pi$
$140$		−	44.7402i		−	0.319573i
$141$	−95.2470	+	72.8693i	−0.675511	+	0.516803i
$142$	−88.6275			−0.624137
$143$			16.6112i			0.116162i
$144$	3.72679	−	13.7510i	0.0258805	−	0.0954929i
$145$	−128.207			−0.884183
$146$		−	79.4577i		−	0.544231i
$147$	−12.7601	−	16.6787i	−0.0868036	−	0.113461i
$148$	94.0445			0.635436
$149$		−	203.685i		−	1.36701i	−0.729945	−	0.683506i	$-0.760454\pi$
$149$		−	203.685i		−	1.36701i	0.729945	−	0.683506i	$-0.239546\pi$
$150$	91.7418	−	70.1876i	0.611612	−	0.467917i
$151$	165.749			1.09768			0.548838	−	0.835929i	$-0.315070\pi$
$151$	165.749			1.09768			0.548838	+	0.835929i	$0.315070\pi$
$152$			84.1171i			0.553402i
$153$	105.498	+	28.5921i	0.689530	+	0.186876i
$154$	9.04052			0.0587047
$155$			289.953i			1.87066i
$156$	26.5425	+	34.6936i	0.170144	+	0.222395i
$157$	−302.723			−1.92817			−0.964086	−	0.265592i	$-0.914433\pi$
$157$	−302.723			−1.92817			−0.964086	+	0.265592i	$0.914433\pi$
$158$			82.6699i			0.523227i
$159$	250.184	−	191.405i	1.57349	−	1.20380i
$160$	227.476			1.42172
$161$		−	11.3828i		−	0.0707008i
$162$	−53.4615	+	91.3856i	−0.330009	+	0.564109i
$163$	−145.041			−0.889819			−0.444910	−	0.895576i	$-0.646764\pi$
$163$	−145.041			−0.889819			−0.444910	+	0.895576i	$0.646764\pi$
$164$		−	69.3871i		−	0.423092i
$165$	−35.1660	−	45.9653i	−0.213127	−	0.278578i
$166$	117.565			0.708221
$167$			19.6594i			0.117721i	0.998266	+	0.0588604i	$0.0187467\pi$
$167$			19.6594i			0.117721i	−0.998266	+	0.0588604i	$0.981253\pi$
$168$	51.8412	−	39.6614i	0.308578	−	0.236080i
$169$	−128.624			−0.761086
$170$		−	117.146i		−	0.689097i
$171$	24.0810	−	88.8534i	0.140825	−	0.519611i
$172$	−128.037			−0.744399
$173$			19.6884i			0.113806i	0.998380	+	0.0569030i	$0.0181226\pi$
$173$			19.6884i			0.113806i	−0.998380	+	0.0569030i	$0.981877\pi$
$174$	−41.3948	−	54.1069i	−0.237901	−	0.310959i
$175$	77.9373			0.445356
$176$			4.13828i			0.0235129i
$177$	98.5568	−	75.4014i	0.556818	−	0.425997i
$178$	82.5751			0.463905
$179$		−	341.745i		−	1.90919i	−0.297910	−	0.954594i	$-0.596289\pi$
$179$		−	341.745i		−	1.90919i	0.297910	−	0.954594i	$-0.403711\pi$
$180$	−146.893	−	39.8109i	−0.816071	−	0.221171i
$181$	215.889			1.19276			0.596378	−	0.802704i	$-0.296606\pi$
$181$	215.889			1.19276			0.596378	+	0.802704i	$0.296606\pi$
$182$		−	21.9746i		−	0.120739i
$183$	37.3320	+	48.7965i	0.204000	+	0.266648i
$184$	35.3804			0.192285
$185$			302.860i			1.63708i
$186$	−122.369	+	93.6188i	−0.657896	+	0.503327i
$187$	−31.7490			−0.169781
$188$		−	91.6026i		−	0.487248i
$189$	−66.1144	+	27.0534i	−0.349812	+	0.143140i
$190$	−98.6640			−0.519284
$191$			44.7112i			0.234090i	0.993127	+	0.117045i	$0.0373422\pi$
$191$			44.7112i			0.234090i	−0.993127	+	0.117045i	$0.962658\pi$
$192$	84.9889	+	111.089i	0.442650	+	0.578586i
$193$	−145.122			−0.751925			−0.375963	−	0.926635i	$-0.622688\pi$
$193$	−145.122			−0.751925			−0.375963	+	0.926635i	$0.622688\pi$
$194$		−	25.0518i		−	0.129133i
$195$	−111.727	+	85.4772i	−0.572958	+	0.438344i
$196$	16.0405			0.0818394
$197$			87.4643i			0.443981i	0.975049	+	0.221991i	$0.0712554\pi$
$197$			87.4643i			0.443981i	−0.975049	+	0.221991i	$0.928745\pi$
$198$	8.04446	−	29.6822i	0.0406286	−	0.149910i
$199$	65.4170			0.328729			0.164364	−	0.986400i	$-0.447443\pi$
$199$	65.4170			0.328729			0.164364	+	0.986400i	$0.447443\pi$
$200$			242.247i			1.21123i
$201$	49.5203	+	64.7277i	0.246369	+	0.322028i
$202$	−129.026			−0.638743
$203$		−	45.9653i		−	0.226430i
$204$	−66.3098	+	50.7307i	−0.325048	+	0.248680i
$205$	223.454			1.09002
$206$			73.5254i			0.356919i
$207$	−37.3725	−	10.1287i	−0.180544	−	0.0489309i
$208$	10.0588			0.0483597
$209$			26.7399i			0.127942i
$210$	46.5203	+	60.8064i	0.221525	+	0.289554i
$211$	40.5830			0.192337			0.0961683	−	0.995365i	$-0.469341\pi$
$211$	40.5830			0.192337			0.0961683	+	0.995365i	$0.469341\pi$
$212$			240.611i			1.13496i
$213$	−161.557	+	123.600i	−0.758483	+	0.580281i
$214$	160.952			0.752110
$215$		−	412.328i		−	1.91780i
$216$	−84.0882	−	205.498i	−0.389297	−	0.951381i
$217$	−103.956			−0.479058
$218$		−	215.068i		−	0.986548i
$219$	−110.812	−	144.842i	−0.505990	−	0.661377i
$220$	44.2065			0.200939
$221$			77.1716i			0.349193i
$222$	−127.816	+	97.7861i	−0.575746	+	0.440478i
$223$	100.959			0.452733			0.226367	−	0.974042i	$-0.427315\pi$
$223$	100.959			0.452733			0.226367	+	0.974042i	$0.427315\pi$
$224$			81.5559i			0.364089i
$225$	69.3503	−	255.886i	0.308224	−	1.13727i
$226$	−188.288			−0.833131
$227$		−	391.279i		−	1.72370i	−0.507166	−	0.861849i	$-0.669307\pi$
$227$		−	391.279i		−	1.72370i	0.507166	−	0.861849i	$-0.330693\pi$
$228$	42.7268	+	55.8480i	0.187398	+	0.244947i
$229$	−6.81176			−0.0297457			−0.0148728	−	0.999889i	$-0.504734\pi$
$229$	−6.81176			−0.0297457			−0.0148728	+	0.999889i	$0.504734\pi$
$230$			41.4990i			0.180430i
$231$	16.4797	−	12.6079i	0.0713409	−	0.0545797i
$232$	142.871			0.615821
$233$			116.877i			0.501616i	0.968037	+	0.250808i	$0.0806963\pi$
$233$			116.877i			0.501616i	−0.968037	+	0.250808i	$0.919304\pi$
$234$	−72.1477	−	19.5535i	−0.308324	−	0.0835618i
$235$	294.996			1.25530
$236$			94.7857i			0.401634i
$237$	115.292	+	150.697i	0.486462	+	0.635852i
$238$	42.0000			0.176471
$239$		−	59.9623i		−	0.250888i	−0.992101	−	0.125444i	$-0.959964\pi$
$239$		−	59.9623i		−	0.250888i	0.992101	−	0.125444i	$-0.0400356\pi$
$240$	−27.8340	+	21.2945i	−0.115975	+	0.0887273i
$241$	134.753			0.559141			0.279570	−	0.960125i	$-0.409808\pi$
$241$	134.753			0.559141			0.279570	+	0.960125i	$0.409808\pi$
$242$		−	149.226i		−	0.616636i
$243$	29.9928	+	241.142i	0.123427	+	0.992354i
$244$	−46.9294			−0.192334
$245$			51.6567i			0.210844i
$246$	72.1477	+	94.3039i	0.293283	+	0.383349i
$247$	64.9961			0.263142
$248$		−	323.117i		−	1.30289i
$249$	214.306	−	163.956i	0.860666	−	0.658457i
$250$	−42.9961			−0.171984
$251$			268.248i			1.06872i	0.845257	+	0.534359i	$0.179447\pi$
$251$			268.248i			1.06872i	−0.845257	+	0.534359i	$0.820553\pi$
$252$	14.2732	−	52.6648i	0.0566397	−	0.208987i
$253$	11.2470			0.0444547
$254$			47.8175i			0.188258i
$255$	−163.373	−	213.543i	−0.640677	−	0.837425i
$256$	−268.004			−1.04689
$257$			234.129i			0.911007i	0.890234	+	0.455504i	$0.150541\pi$
$257$			234.129i			0.911007i	−0.890234	+	0.455504i	$0.849459\pi$
$258$	174.014	−	133.131i	0.674474	−	0.516010i
$259$	−108.583			−0.419239
$260$		−	107.452i		−	0.413276i
$261$	−150.915	−	40.9010i	−0.578218	−	0.156709i
$262$	44.0301			0.168054
$263$			250.142i			0.951111i	0.879686	+	0.475555i	$0.157753\pi$
$263$			250.142i			0.951111i	−0.879686	+	0.475555i	$0.842247\pi$
$264$	39.1882	+	51.2228i	0.148440	+	0.194026i
$265$	−774.863			−2.92401
$266$		−	35.3736i		−	0.132983i
$267$	150.524	−	115.159i	0.563761	−	0.431308i
$268$	−62.2510			−0.232280
$269$			340.684i			1.26648i	0.773955	+	0.633241i	$0.218276\pi$
$269$			340.684i			1.26648i	−0.773955	+	0.633241i	$0.781724\pi$
$270$	241.037	−	98.6301i	0.892728	−	0.365297i
$271$	−21.2994			−0.0785955			−0.0392977	−	0.999228i	$-0.512512\pi$
$271$	−21.2994			−0.0785955			−0.0392977	+	0.999228i	$0.512512\pi$
$272$			19.2254i			0.0706816i
$273$	−30.6458	−	40.0569i	−0.112255	−	0.146729i
$274$	52.2510			0.190697
$275$			77.0075i			0.280027i
$276$	23.4902	−	17.9713i	0.0851093	−	0.0651133i
$277$	−226.915			−0.819188			−0.409594	−	0.912268i	$-0.634330\pi$
$277$	−226.915			−0.819188			−0.409594	+	0.912268i	$0.634330\pi$
$278$			254.415i			0.915163i
$279$	−92.5020	+	341.311i	−0.331548	+	1.22334i
$280$	−160.561			−0.573431
$281$		−	235.489i		−	0.838039i	−0.907977	−	0.419019i	$-0.862374\pi$
$281$		−	235.489i		−	0.838039i	0.907977	−	0.419019i	$-0.137626\pi$
$282$	95.2470	+	124.497i	0.337755	+	0.441479i
$283$	368.634			1.30259			0.651297	−	0.758823i	$-0.274225\pi$
$283$	368.634			1.30259			0.651297	+	0.758823i	$0.274225\pi$
$284$		−	155.375i		−	0.547096i
$285$	−179.852	+	137.597i	−0.631061	+	0.482796i
$286$	21.7124			0.0759176
$287$			80.1138i			0.279142i
$288$	267.767	+	72.5703i	0.929748	+	0.251980i
$289$	141.502			0.489626
$290$			167.578i			0.577856i
$291$	−34.9373	−	45.6663i	−0.120059	−	0.156929i
$292$	139.299			0.477053
$293$		−	531.625i		−	1.81442i	−0.420677	−	0.907211i	$-0.638207\pi$
$293$		−	531.625i		−	1.81442i	0.420677	−	0.907211i	$-0.361793\pi$
$294$	−21.8006	+	16.6787i	−0.0741519	+	0.0567303i
$295$	−305.247			−1.03474
$296$		−	337.500i		−	1.14020i
$297$	−26.7307	−	65.3257i	−0.0900024	−	0.219952i
$298$	−266.235			−0.893407
$299$		−	27.3379i		−	0.0914312i
$300$	123.048	+	160.835i	0.410159	+	0.536117i
$301$	147.830			0.491130
$302$		−	216.650i		−	0.717383i
$303$	−235.199	+	179.940i	−0.776233	+	0.593861i
$304$	16.1922			0.0532637
$305$		−	151.131i		−	0.495511i
$306$	37.3725	−	137.896i	0.122132	−	0.450640i
$307$	567.763			1.84939			0.924696	−	0.380706i	$-0.124319\pi$
$307$	567.763			1.84939			0.924696	+	0.380706i	$0.124319\pi$
$308$			15.8492i			0.0514583i
$309$	102.539	+	134.028i	0.331840	+	0.433746i
$310$	378.996			1.22257
$311$			42.7531i			0.137470i	0.997635	+	0.0687349i	$0.0218963\pi$
$311$			42.7531i			0.137470i	−0.997635	+	0.0687349i	$0.978104\pi$
$312$	124.506	−	95.2539i	0.399057	−	0.305301i
$313$	−158.118			−0.505168			−0.252584	−	0.967575i	$-0.581280\pi$
$313$	−158.118			−0.505168			−0.252584	+	0.967575i	$0.581280\pi$
$314$			395.688i			1.26015i
$315$	169.601	+	45.9653i	0.538417	+	0.145922i
$316$	−144.931			−0.458642
$317$		−	140.944i		−	0.444619i	−0.974976	−	0.222309i	$-0.928641\pi$
$317$		−	140.944i		−	0.444619i	0.974976	−	0.222309i	$-0.0713595\pi$
$318$	−250.184	−	327.015i	−0.786743	−	1.02835i
$319$	45.4170			0.142373
$320$		−	344.060i		−	1.07519i
$321$	293.395	−	224.463i	0.914002	−	0.699262i
$322$	−14.8784			−0.0462064
$323$			124.227i			0.384604i
$324$	−160.210	−	93.7247i	−0.494477	−	0.289274i
$325$	187.180			0.575940
$326$			189.582i			0.581539i
$327$	−299.933	−	392.041i	−0.917227	−	1.19890i
$328$	−249.012			−0.759182
$329$			105.764i			0.321470i
$330$	−60.0810	+	45.9653i	−0.182064	+	0.139289i
$331$	−258.369			−0.780570			−0.390285	−	0.920694i	$-0.627623\pi$
$331$	−258.369			−0.780570			−0.390285	+	0.920694i	$0.627623\pi$
$332$			206.106i			0.620801i
$333$	−96.6196	+	356.504i	−0.290149	+	1.07058i
$334$	25.6967			0.0769362
$335$		−	200.472i		−	0.598425i
$336$	−7.63464	−	9.97920i	−0.0227221	−	0.0297000i
$337$	328.959			0.976141			0.488070	−	0.872804i	$-0.337701\pi$
$337$	328.959			0.976141			0.488070	+	0.872804i	$0.337701\pi$
$338$			168.123i			0.497406i
$339$	−343.225	+	262.586i	−1.01246	+	0.774590i
$340$	205.373			0.604037
$341$		−	102.715i		−	0.301218i
$342$	−116.140	−	31.4762i	−0.339590	−	0.0920357i
$343$	−18.5203			−0.0539949
$344$			459.489i			1.33572i
$345$	57.8745	+	75.6475i	0.167752	+	0.219268i
$346$	25.7347			0.0743776
$347$			128.635i			0.370707i	0.982672	+	0.185353i	$0.0593430\pi$
$347$			128.635i			0.370707i	−0.982672	+	0.185353i	$0.940657\pi$
$348$	94.8562	−	72.5703i	0.272575	−	0.208535i
$349$	−73.4837			−0.210555			−0.105277	−	0.994443i	$-0.533573\pi$
$349$	−73.4837			−0.210555			−0.105277	+	0.994443i	$0.533573\pi$
$350$		−	101.871i		−	0.291061i
$351$	−158.786	+	64.9737i	−0.452381	+	0.185110i
$352$	−80.5830			−0.228929
$353$		−	239.685i		−	0.678995i	−0.940607	−	0.339498i	$-0.889743\pi$
$353$		−	239.685i		−	0.678995i	0.940607	−	0.339498i	$-0.110257\pi$
$354$	−98.5568	−	128.823i	−0.278409	−	0.363907i
$355$	500.369			1.40949
$356$			144.765i			0.406642i
$357$	76.5608	−	58.5732i	0.214456	−	0.164071i
$358$	−446.693			−1.24775
$359$			180.215i			0.501992i	0.967988	+	0.250996i	$0.0807581\pi$
$359$			180.215i			0.501992i	−0.967988	+	0.250996i	$0.919242\pi$
$360$	−142.871	+	527.159i	−0.396863	+	1.46433i
$361$	−256.373			−0.710173
$362$		−	282.187i		−	0.779523i
$363$	−208.110	−	272.020i	−0.573307	−	0.749367i
$364$	38.5242			0.105836
$365$			448.598i			1.22904i
$366$	63.7817	−	48.7965i	0.174267	−	0.133324i
$367$	229.786			0.626119			0.313059	−	0.949734i	$-0.398646\pi$
$367$	229.786			0.626119			0.313059	+	0.949734i	$0.398646\pi$
$368$		−	6.81057i		−	0.0185070i
$369$	263.033	+	71.2871i	0.712826	+	0.193190i
$370$	395.867			1.06991
$371$		−	277.808i		−	0.748809i
$372$	−164.125	−	214.528i	−0.441198	−	0.576687i
$373$	441.749			1.18431			0.592157	−	0.805823i	$-0.298277\pi$
$373$	441.749			1.18431			0.592157	+	0.805823i	$0.298277\pi$
$374$			41.4990i			0.110960i
$375$	−78.3765	+	59.9623i	−0.209004	+	0.159900i
$376$	−328.737			−0.874301
$377$		−	110.394i		−	0.292822i
$378$	35.3614	+	86.4178i	0.0935487	+	0.228618i
$379$	−421.203			−1.11135			−0.555676	−	0.831399i	$-0.687541\pi$
$379$	−421.203			−1.11135			−0.555676	+	0.831399i	$0.687541\pi$
$380$		−	172.971i		−	0.455186i
$381$	66.6863	+	87.1653i	0.175030	+	0.228780i
$382$	58.4418			0.152989
$383$			595.591i			1.55507i	0.628841	+	0.777534i	$0.283530\pi$
$383$			595.591i			1.55507i	−0.628841	+	0.777534i	$0.716470\pi$
$384$	−148.582	+	113.674i	−0.386933	+	0.296025i
$385$	−51.0405			−0.132573
$386$			189.688i			0.491419i
$387$	131.542	−	485.361i	0.339903	−	1.25416i
$388$	43.9190			0.113193
$389$		−	367.347i		−	0.944336i	−0.881509	−	0.472168i	$-0.843472\pi$
$389$		−	367.347i		−	0.944336i	0.881509	−	0.472168i	$-0.156528\pi$
$390$	111.727	+	146.038i	0.286479	+	0.374455i
$391$	52.2510			0.133634
$392$		−	57.5651i		−	0.146850i
$393$	80.2614	−	61.4044i	0.204227	−	0.156245i
$394$	114.324			0.290163
$395$		−	466.734i		−	1.18160i
$396$	52.0366	+	14.1029i	0.131406	+	0.0356135i
$397$	408.346			1.02858			0.514290	−	0.857616i	$-0.328055\pi$
$397$	408.346			1.02858			0.514290	+	0.857616i	$0.328055\pi$
$398$		−	85.5062i		−	0.214840i
$399$	−49.3320	−	64.4816i	−0.123639	−	0.161608i
$400$	46.6314			0.116578
$401$		−	238.817i		−	0.595555i	−0.954635	−	0.297777i	$-0.903755\pi$
$401$		−	238.817i		−	0.595555i	0.954635	−	0.297777i	$-0.0962453\pi$
$402$	84.6052	−	64.7277i	0.210461	−	0.161014i
$403$	−249.668			−0.619524
$404$		−	226.199i		−	0.559899i
$405$	301.830	−	515.940i	0.745259	−	1.27393i
$406$	−60.0810			−0.147983
$407$		−	107.288i		−	0.263606i
$408$	182.059	+	237.968i	0.446223	+	0.583255i
$409$	−649.365			−1.58769			−0.793844	−	0.608121i	$-0.791924\pi$
$409$	−649.365			−1.58769			−0.793844	+	0.608121i	$0.791924\pi$
$410$		−	292.075i		−	0.712378i
$411$	95.2470	−	72.8693i	0.231745	−	0.177297i
$412$	−128.899			−0.312862
$413$		−	109.439i		−	0.264985i
$414$	−13.2392	+	48.8495i	−0.0319787	+	0.117994i
$415$	−663.741			−1.59938
$416$			195.871i			0.470844i
$417$	354.808	+	463.768i	0.850858	+	1.11215i
$418$	34.9516			0.0836163
$419$		−	11.5178i		−	0.0274888i	−0.999906	−	0.0137444i	$-0.995625\pi$
$419$		−	11.5178i		−	0.0274888i	0.999906	−	0.0137444i	$-0.00437512\pi$
$420$	−106.601	+	81.5559i	−0.253813	+	0.194181i
$421$	−83.9921			−0.199506			−0.0997531	−	0.995012i	$-0.531805\pi$
$421$	−83.9921			−0.199506			−0.0997531	+	0.995012i	$0.531805\pi$
$422$		−	53.0458i		−	0.125701i
$423$	347.247	+	94.1108i	0.820915	+	0.222484i
$424$	863.490			2.03653
$425$			357.758i			0.841783i
$426$	161.557	+	211.170i	0.379241	+	0.495705i
$427$	54.1843			0.126895
$428$			282.168i			0.659272i
$429$	39.5791	−	30.2802i	0.0922589	−	0.0705832i
$430$	−538.952			−1.25338
$431$			694.004i			1.61022i	0.593127	+	0.805109i	$0.297893\pi$
$431$			694.004i			1.61022i	−0.593127	+	0.805109i	$0.702107\pi$
$432$	−39.5575	+	16.1866i	−0.0915684	+	0.0374690i
$433$	116.834			0.269824			0.134912	−	0.990858i	$-0.456925\pi$
$433$	116.834			0.269824			0.134912	+	0.990858i	$0.456925\pi$
$434$			135.880i			0.313087i
$435$	233.705	+	305.474i	0.537252	+	0.702239i
$436$	377.041			0.864772
$437$		−	44.0072i		−	0.100703i
$438$	−189.322	+	144.842i	−0.432241	+	0.330688i
$439$	−528.073			−1.20290			−0.601450	−	0.798910i	$-0.705410\pi$
$439$	−528.073			−1.20290			−0.601450	+	0.798910i	$0.705410\pi$
$440$		−	158.645i		−	0.360558i
$441$	−16.4797	+	60.8064i	−0.0373690	+	0.137883i
$442$	100.871			0.228214
$443$			272.252i			0.614564i	0.951619	+	0.307282i	$0.0994194\pi$
$443$			272.252i			0.614564i	−0.951619	+	0.307282i	$0.900581\pi$
$444$	−171.431	−	224.077i	−0.386107	−	0.504678i
$445$	−466.199			−1.04764
$446$		−	131.964i		−	0.295883i
$447$	−485.314	+	371.292i	−1.08571	+	0.830631i
$448$	123.354			0.275344
$449$		−	525.770i		−	1.17098i	−0.810680	−	0.585490i	$-0.800902\pi$
$449$		−	525.770i		−	1.17098i	0.810680	−	0.585490i	$-0.199098\pi$
$450$	−334.468	−	90.6474i	−0.743262	−	0.201439i
$451$	−79.1581			−0.175517
$452$		−	330.092i		−	0.730292i
$453$	−302.140	−	394.925i	−0.666975	−	0.871800i
$454$	−511.439			−1.12652
$455$			124.063i			0.272666i
$456$	200.423	−	153.335i	0.439525	−	0.336261i
$457$	−513.786			−1.12426			−0.562129	−	0.827050i	$-0.690017\pi$
$457$	−513.786			−1.12426			−0.562129	+	0.827050i	$0.690017\pi$
$458$			8.90362i			0.0194402i
$459$	−124.184	−	303.487i	−0.270554	−	0.661192i
$460$	−72.7530			−0.158159
$461$			687.879i			1.49214i	0.665865	+	0.746072i	$0.268063\pi$
$461$			687.879i			1.49214i	−0.665865	+	0.746072i	$0.731937\pi$
$462$	−16.4797	−	21.5406i	−0.0356704	−	0.0466246i
$463$	781.061			1.68696			0.843479	−	0.537162i	$-0.180504\pi$
$463$	781.061			1.68696			0.843479	+	0.537162i	$0.180504\pi$
$464$		−	27.5020i		−	0.0592715i
$465$	690.863	−	528.548i	1.48573	−	1.13666i
$466$	152.769			0.327830
$467$			163.353i			0.349792i	0.984587	+	0.174896i	$0.0559589\pi$
$467$			163.353i			0.349792i	−0.984587	+	0.174896i	$0.944041\pi$
$468$	34.2797	−	126.484i	0.0732472	−	0.270265i
$469$	71.8745			0.153251
$470$		−	385.588i		−	0.820400i
$471$	551.826	+	721.289i	1.17161	+	1.53140i
$472$	340.161			0.720679
$473$			146.067i			0.308809i
$474$	196.975	−	150.697i	0.415560	−	0.317926i
$475$	301.314			0.634345
$476$			73.6313i			0.154688i
$477$	−912.110	−	247.200i	−1.91218	−	0.518239i
$478$	−78.3765			−0.163968
$479$			700.159i			1.46171i	0.682533	+	0.730855i	$0.260878\pi$
$479$			700.159i			1.46171i	−0.682533	+	0.730855i	$0.739122\pi$
$480$	−414.660	−	542.000i	−0.863875	−	1.12917i
$481$	−260.782			−0.542166
$482$		−	176.135i		−	0.365425i
$483$	−27.1216	+	20.7495i	−0.0561523	+	0.0429596i
$484$	261.612			0.540520
$485$			141.436i			0.291621i
$486$	315.195	−	39.2035i	0.648550	−	0.0806656i
$487$	86.5909			0.177805			0.0889023	−	0.996040i	$-0.471664\pi$
$487$	86.5909			0.177805			0.0889023	+	0.996040i	$0.471664\pi$
$488$			168.417i			0.345117i
$489$	264.391	+	345.584i	0.540677	+	0.706716i
$490$	67.5203			0.137796
$491$		−	741.494i		−	1.51017i	−0.655627	−	0.755085i	$-0.727596\pi$
$491$		−	741.494i		−	1.51017i	0.655627	−	0.755085i	$-0.272404\pi$
$492$	−165.327	+	126.484i	−0.336030	+	0.257081i
$493$	210.996			0.427984
$494$		−	84.9560i		−	0.171976i
$495$	−45.4170	+	167.578i	−0.0917515	+	0.338542i
$496$	−62.1987			−0.125401
$497$			179.395i			0.360956i
$498$	−214.306	−	280.118i	−0.430333	−	0.562486i
$499$	379.814			0.761151			0.380575	−	0.924750i	$-0.375726\pi$
$499$	379.814			0.761151			0.380575	+	0.924750i	$0.375726\pi$
$500$		−	75.3775i		−	0.150755i
$501$	46.8419	−	35.8366i	0.0934967	−	0.0715302i
$502$	350.626			0.698458
$503$		−	465.808i		−	0.926059i	−0.886343	−	0.463029i	$-0.846762\pi$
$503$		−	465.808i		−	0.926059i	0.886343	−	0.463029i	$-0.153238\pi$
$504$	−189.000	−	51.2228i	−0.375000	−	0.101632i
$505$	728.450			1.44247
$506$		−	14.7010i		−	0.0290533i
$507$	234.465	+	306.468i	0.462455	+	0.604473i
$508$	−83.8301			−0.165020
$509$		−	750.503i		−	1.47447i	−0.675639	−	0.737233i	$-0.736132\pi$
$509$		−	750.503i		−	1.47447i	0.675639	−	0.737233i	$-0.263868\pi$
$510$	−279.122	+	213.543i	−0.547297	+	0.418713i
$511$	−160.834			−0.314744
$512$			100.868i			0.197009i
$513$	−255.605	+	104.592i	−0.498256	+	0.203882i
$514$	306.029			0.595387
$515$		−	415.106i		−	0.806031i
$516$	233.395	+	305.069i	0.452315	+	0.591219i
$517$	−104.502			−0.202131
$518$			141.928i			0.273993i
$519$	46.9111	−	35.8896i	0.0903875	−	0.0691514i
$520$	−385.616			−0.741569
$521$		−	726.946i		−	1.39529i	−0.716443	−	0.697645i	$-0.754231\pi$
$521$		−	726.946i		−	1.39529i	0.716443	−	0.697645i	$-0.245769\pi$
$522$	−53.4615	+	197.260i	−0.102417	+	0.377893i
$523$	−624.707			−1.19447			−0.597234	−	0.802067i	$-0.703734\pi$
$523$	−624.707			−1.19447			−0.597234	+	0.802067i	$0.703734\pi$
$524$			77.1903i			0.147310i
$525$	−142.070	−	185.699i	−0.270609	−	0.353712i
$526$	326.959			0.621596
$527$		−	477.190i		−	0.905485i
$528$	9.86015	−	7.54356i	0.0186745	−	0.0142871i
$529$	510.490			0.965010
$530$			1012.82i			1.91098i
$531$	−359.314	−	97.3812i	−0.676674	−	0.183392i
$532$	62.0144			0.116568
$533$			192.408i			0.360990i
$534$	−150.524	−	196.749i	−0.281881	−	0.368445i
$535$	−908.693			−1.69849
$536$			223.402i			0.416795i
$537$	−814.265	+	622.958i	−1.51632	+	1.16007i
$538$	445.306			0.827706
$539$		−	18.2993i		−	0.0339505i
$540$	172.911	+	422.568i	0.320206	+	0.782533i
$541$	−291.757			−0.539292			−0.269646	−	0.962960i	$-0.586907\pi$
$541$	−291.757			−0.539292			−0.269646	+	0.962960i	$0.586907\pi$
$542$			27.8403i			0.0513659i
$543$	−393.539	−	514.392i	−0.724749	−	0.947315i
$544$	−374.369			−0.688178
$545$			1214.22i			2.22792i
$546$	−52.3582	+	40.0569i	−0.0958941	+	0.0733643i
$547$	204.952			0.374683			0.187342	−	0.982295i	$-0.440013\pi$
$547$	204.952			0.374683			0.187342	+	0.982295i	$0.440013\pi$
$548$			91.6026i			0.167158i
$549$	48.2144	−	177.900i	0.0878222	−	0.324044i
$550$	100.656			0.183011
$551$		−	177.707i		−	0.322517i
$552$	−64.4941	−	84.2999i	−0.116837	−	0.152717i
$553$	167.336			0.302597
$554$			296.599i			0.535378i
$555$	721.616	−	552.076i	1.30021	−	0.994731i
$556$	−446.022			−0.802198
$557$			503.883i			0.904637i	0.891857	+	0.452318i	$0.149403\pi$
$557$			503.883i			0.904637i	−0.891857	+	0.452318i	$0.850597\pi$
$558$	446.125	+	120.909i	0.799508	+	0.216683i
$559$	355.041			0.635135
$560$			30.9072i			0.0551915i
$561$	57.8745	+	75.6475i	0.103163	+	0.134844i
$562$	−307.806			−0.547698
$563$		−	108.735i		−	0.193135i	−0.995326	−	0.0965674i	$-0.969214\pi$
$563$		−	108.735i		−	0.193135i	0.995326	−	0.0965674i	$-0.0307863\pi$
$564$	−218.259	+	166.980i	−0.386984	+	0.296064i
$565$	1063.02			1.88146
$566$		−	481.840i		−	0.851307i
$567$	184.978	+	108.214i	0.326239	+	0.190853i
$568$	−557.600			−0.981690
$569$			434.871i			0.764273i	0.924106	+	0.382136i	$0.124812\pi$
$569$			434.871i			0.764273i	−0.924106	+	0.382136i	$0.875188\pi$
$570$	179.852	+	235.084i	0.315530	+	0.412428i
$571$	119.122			0.208619			0.104310	−	0.994545i	$-0.466737\pi$
$571$	119.122			0.208619			0.104310	+	0.994545i	$0.466737\pi$
$572$			38.0646i			0.0665466i
$573$	106.532	−	81.5029i	0.185920	−	0.142239i
$574$	104.716			0.182433
$575$		−	126.735i		−	0.220409i
$576$	109.763	−	405.001i	0.190561	−	0.703127i
$577$	−655.417			−1.13590			−0.567952	−	0.823061i	$-0.692264\pi$
$577$	−655.417			−1.13590			−0.567952	+	0.823061i	$0.692264\pi$
$578$		−	184.957i		−	0.319994i
$579$	264.539	+	345.777i	0.456889	+	0.597197i
$580$	−293.786			−0.506527
$581$		−	237.968i		−	0.409584i
$582$	−59.6902	+	45.6663i	−0.102560	+	0.0784645i
$583$	274.494			0.470830
$584$		−	499.908i		−	0.856007i
$585$	407.328	+	110.394i	0.696287	+	0.188708i
$586$	−694.885			−1.18581
$587$		−	736.236i		−	1.25424i	−0.778925	−	0.627118i	$-0.784235\pi$
$587$		−	736.236i		−	1.25424i	0.778925	−	0.627118i	$-0.215765\pi$
$588$	−29.2399	−	38.2193i	−0.0497277	−	0.0649988i
$589$	−401.903			−0.682348
$590$			398.987i			0.676249i
$591$	208.399	−	159.437i	0.352620	−	0.269774i
$592$	−64.9674			−0.109742
$593$		−	832.884i		−	1.40453i	−0.711917	−	0.702263i	$-0.752173\pi$
$593$		−	832.884i		−	1.40453i	0.711917	−	0.702263i	$-0.247827\pi$
$594$	−85.3869	+	34.9396i	−0.143749	+	0.0588209i
$595$	−237.122			−0.398524
$596$		−	466.744i		−	0.783127i
$597$	−119.247	−	155.867i	−0.199744	−	0.261084i
$598$	−35.7333			−0.0597546
$599$		−	69.3290i		−	0.115741i	−0.998324	−	0.0578706i	$-0.981569\pi$
$599$		−	69.3290i		−	0.115741i	0.998324	−	0.0578706i	$-0.0184311\pi$
$600$	577.194	−	441.585i	0.961990	−	0.735976i
$601$	−161.720			−0.269085			−0.134543	−	0.990908i	$-0.542957\pi$
$601$	−161.720			−0.269085			−0.134543	+	0.990908i	$0.542957\pi$
$602$		−	193.228i		−	0.320977i
$603$	63.9555	−	235.981i	0.106062	−	0.391345i
$604$	379.814			0.628832
$605$			842.492i			1.39255i
$606$	235.199	+	307.427i	0.388117	+	0.507305i
$607$	929.608			1.53148			0.765740	−	0.643151i	$-0.222373\pi$
$607$	929.608			1.53148			0.765740	+	0.643151i	$0.222373\pi$
$608$			315.304i			0.518592i
$609$	−109.520	+	83.7891i	−0.179836	+	0.137585i
$610$	−197.542			−0.323840
$611$			254.010i			0.415729i
$612$	241.749	+	65.5188i	0.395015	+	0.107057i
$613$	297.940			0.486036			0.243018	−	0.970022i	$-0.421863\pi$
$613$	297.940			0.486036			0.243018	+	0.970022i	$0.421863\pi$
$614$		−	742.121i		−	1.20867i
$615$	−407.328	−	532.417i	−0.662322	−	0.865718i
$616$	56.8784			0.0923351
$617$			975.575i			1.58116i	0.612360	+	0.790579i	$0.290220\pi$
$617$			975.575i			1.58116i	−0.612360	+	0.790579i	$0.709780\pi$
$618$	175.187	−	134.028i	0.283474	−	0.216873i
$619$	357.034			0.576792			0.288396	−	0.957511i	$-0.406878\pi$
$619$	357.034			0.576792			0.288396	+	0.957511i	$0.406878\pi$
$620$			664.428i			1.07166i
$621$	43.9921	+	107.510i	0.0708408	+	0.173124i
$622$	55.8824			0.0898431
$623$		−	167.144i		−	0.268289i
$624$	−18.3360	−	23.9668i	−0.0293845	−	0.0384084i
$625$	−493.693			−0.789908
$626$			206.675i			0.330151i
$627$	63.7124	−	48.7435i	0.101615	−	0.0777409i
$628$	−693.690			−1.10460
$629$		−	498.432i		−	0.792420i
$630$	60.0810	−	221.685i	0.0953667	−	0.351881i
$631$	−813.223			−1.28879			−0.644393	−	0.764695i	$-0.722890\pi$
$631$	−813.223			−1.28879			−0.644393	+	0.764695i	$0.722890\pi$
$632$			520.118i			0.822971i
$633$	−73.9778	−	96.6960i	−0.116869	−	0.152758i
$634$	−184.227			−0.290579
$635$		−	269.966i		−	0.425143i
$636$	573.298	−	438.605i	0.901412	−	0.689630i
$637$	−44.4797			−0.0698269
$638$		−	59.3643i		−	0.0930475i
$639$	588.996	+	159.630i	0.921747	+	0.249812i
$640$	460.184			0.719038
$641$		−	646.727i		−	1.00893i	−0.863431	−	0.504467i	$-0.831689\pi$
$641$		−	646.727i		−	1.00893i	0.863431	−	0.504467i	$-0.168311\pi$
$642$	−293.395	−	383.495i	−0.457001	−	0.597344i
$643$	144.561			0.224822			0.112411	−	0.993662i	$-0.464143\pi$
$643$	144.561			0.224822			0.112411	+	0.993662i	$0.464143\pi$
$644$		−	26.0838i		−	0.0405028i
$645$	−982.442	+	751.622i	−1.52317	+	1.16531i
$646$	162.376			0.251357
$647$			716.654i			1.10766i	0.832631	+	0.553828i	$0.186834\pi$
$647$			716.654i			1.10766i	−0.832631	+	0.553828i	$0.813166\pi$
$648$	−336.353	+	574.953i	−0.519063	+	0.887273i
$649$	108.133			0.166615
$650$		−	244.663i		−	0.376404i
$651$	189.498	+	247.692i	0.291088	+	0.380479i
$652$	−332.361			−0.509756
$653$		−	378.999i		−	0.580397i	−0.956966	−	0.290199i	$-0.906279\pi$
$653$		−	378.999i		−	0.580397i	0.956966	−	0.290199i	$-0.0937214\pi$
$654$	−512.435	+	392.041i	−0.783540	+	0.599452i
$655$	−248.583			−0.379516
$656$			47.9337i			0.0730696i
$657$	−143.114	+	528.056i	−0.217829	+	0.803738i
$658$	138.243			0.210096
$659$			710.721i			1.07848i	0.842151	+	0.539242i	$0.181289\pi$
$659$			710.721i			1.07848i	−0.842151	+	0.539242i	$0.818711\pi$
$660$	−80.5830	−	105.330i	−0.122095	−	0.159590i
$661$	91.5045			0.138433			0.0692167	−	0.997602i	$-0.477950\pi$
$661$	91.5045			0.138433			0.0692167	+	0.997602i	$0.477950\pi$
$662$			337.712i			0.510139i
$663$	183.875	−	140.674i	0.277337	−	0.212178i
$664$	739.659			1.11394
$665$			199.710i			0.300316i
$666$	465.984	+	126.291i	0.699676	+	0.189626i
$667$	−74.7451			−0.112062
$668$			45.0495i			0.0674394i
$669$	−184.037	−	240.553i	−0.275092	−	0.359571i
$670$	−262.037			−0.391099
$671$			53.5379i			0.0797883i
$672$	194.321	−	148.666i	0.289168	−	0.221230i
$673$	645.806			0.959594			0.479797	−	0.877380i	$-0.340710\pi$
$673$	645.806			0.959594			0.479797	+	0.877380i	$0.340710\pi$
$674$		−	429.981i		−	0.637954i
$675$	−736.110	+	301.210i	−1.09053	+	0.446237i
$676$	−294.741			−0.436008
$677$			335.571i			0.495674i	0.968802	+	0.247837i	$0.0797198\pi$
$677$			335.571i			0.495674i	−0.968802	+	0.247837i	$0.920280\pi$
$678$	343.225	+	448.627i	0.506231	+	0.661692i
$679$	−50.7085			−0.0746811
$680$		−	737.027i		−	1.08386i
$681$	−932.290	+	713.254i	−1.36900	+	1.04736i
$682$	−134.259			−0.196860
$683$			113.336i			0.165939i	0.996552	+	0.0829694i	$0.0264404\pi$
$683$			113.336i			0.165939i	−0.996552	+	0.0829694i	$0.973560\pi$
$684$	55.1818	−	203.608i	0.0806751	−	0.297672i
$685$	−294.996			−0.430651
$686$			24.2077i			0.0352882i
$687$	12.4170	+	16.2302i	0.0180742	+	0.0236247i
$688$	88.4496			0.128561
$689$		−	667.206i		−	0.968369i
$690$	98.8784	−	75.6475i	0.143302	−	0.109634i
$691$	565.667			0.818620			0.409310	−	0.912395i	$-0.365769\pi$
$691$	565.667			0.818620			0.409310	+	0.912395i	$0.365769\pi$
$692$			45.1161i			0.0651967i
$693$	−60.0810	−	16.2832i	−0.0866970	−	0.0234966i
$694$	168.138			0.242274
$695$		−	1436.37i		−	2.06671i
$696$	−260.435	−	340.414i	−0.374189	−	0.489100i
$697$	−367.749			−0.527617
$698$			96.0501i			0.137608i
$699$	278.478	−	213.051i	0.398395	−	0.304794i
$700$	178.593			0.255133
$701$			872.955i			1.24530i	0.782501	+	0.622650i	$0.213944\pi$
$701$			872.955i			1.24530i	−0.782501	+	0.622650i	$0.786056\pi$
$702$	84.9268	+	207.548i	0.120978	+	0.295652i
$703$	−419.793			−0.597146
$704$			121.883i			0.173129i
$705$	−537.741	−	702.879i	−0.762753	−	0.996991i
$706$	−313.292			−0.443756
$707$			261.168i			0.369403i
$708$	225.843	−	172.783i	0.318988	−	0.244043i
$709$	1092.04			1.54025			0.770125	−	0.637894i	$-0.220194\pi$
$709$	1092.04			1.54025			0.770125	+	0.637894i	$0.220194\pi$
$710$		−	654.029i		−	0.921168i
$711$	148.899	−	549.404i	0.209422	−	0.772720i
$712$	519.522			0.729665
$713$			169.044i			0.237088i
$714$	−76.5608	−	100.072i	−0.107228	−	0.140157i
$715$	−122.583			−0.171445
$716$		−	783.109i		−	1.09373i
$717$	−142.871	+	109.304i	−0.199262	+	0.152446i
$718$	235.558			0.328076
$719$			901.769i			1.25420i	0.778939	+	0.627099i	$0.215758\pi$
$719$			901.769i			1.25420i	−0.778939	+	0.627099i	$0.784242\pi$
$720$	101.476	+	27.5020i	0.140939	+	0.0381972i
$721$	148.826			0.206416
$722$			335.103i			0.464132i
$723$	−245.638	−	321.072i	−0.339748	−	0.444083i
$724$	494.710			0.683301
$725$		−	511.773i		−	0.705894i
$726$	−355.556	+	272.020i	−0.489747	+	0.374683i
$727$	297.506			0.409224			0.204612	−	0.978843i	$-0.434407\pi$
$727$	297.506			0.409224			0.204612	+	0.978843i	$0.434407\pi$
$728$		−	138.253i		−	0.189908i
$729$	519.889	−	511.035i	0.713153	−	0.701008i
$730$	586.361			0.803234
$731$			678.589i			0.928302i
$732$	85.5464	+	111.817i	0.116867	+	0.152756i
$733$	456.966			0.623419			0.311709	−	0.950177i	$-0.399098\pi$
$733$	456.966			0.623419			0.311709	+	0.950177i	$0.399098\pi$
$734$		−	300.352i		−	0.409198i
$735$	123.081	−	94.1638i	0.167457	−	0.128114i
$736$	132.620			0.180190
$737$			71.0171i			0.0963597i
$738$	93.1790	−	343.809i	0.126259	−	0.465865i
$739$	−332.199			−0.449525			−0.224762	−	0.974414i	$-0.572161\pi$
$739$	−332.199			−0.449525			−0.224762	+	0.974414i	$0.572161\pi$
$740$			694.004i			0.937844i
$741$	−118.480	−	154.864i	−0.159892	−	0.208994i
$742$	−363.122			−0.489382
$743$		−	64.5346i		−	0.0868568i	−0.999057	−	0.0434284i	$-0.986172\pi$
$743$		−	64.5346i		−	0.0868568i	0.999057	−	0.0434284i	$-0.0138280\pi$
$744$	−769.882	+	589.003i	−1.03479	+	0.791670i
$745$	1503.10			2.01758
$746$		−	577.408i		−	0.774005i
$747$	−781.306	−	211.749i	−1.04592	−	0.283466i
$748$	−72.7530			−0.0972633
$749$		−	325.790i		−	0.434966i
$750$	78.3765	+	102.446i	0.104502	+	0.136594i
$751$	−611.668			−0.814471			−0.407236	−	0.913323i	$-0.633507\pi$
$751$	−611.668			−0.814471			−0.407236	+	0.913323i	$0.633507\pi$
$752$			63.2805i			0.0841496i
$753$	639.148	−	488.983i	0.848802	−	0.649380i
$754$	−144.295			−0.191373
$755$			1223.15i			1.62007i
$756$	−151.501	+	61.9930i	−0.200399	+	0.0820014i
$757$	−207.357			−0.273919			−0.136960	−	0.990577i	$-0.543733\pi$
$757$	−207.357			−0.273919			−0.136960	+	0.990577i	$0.543733\pi$
$758$			550.552i			0.726322i
$759$	−20.5020	−	26.7980i	−0.0270118	−	0.0353070i
$760$	−620.745			−0.816770
$761$			337.770i			0.443851i	0.975064	+	0.221925i	$0.0712341\pi$
$761$			337.770i			0.443851i	−0.975064	+	0.221925i	$0.928766\pi$
$762$	113.933	−	87.1653i	0.149519	−	0.114390i
$763$	−435.328			−0.570548
$764$			102.456i			0.134104i
$765$	−210.996	+	778.526i	−0.275812	+	1.01768i
$766$	778.494			1.01631
$767$		−	262.837i		−	0.342682i
$768$	488.538	+	638.565i	0.636117	+	0.831465i
$769$	−1042.22			−1.35529			−0.677646	−	0.735388i	$-0.737000\pi$
$769$	−1042.22			−1.35529			−0.677646	+	0.735388i	$0.737000\pi$
$770$			66.7148i			0.0866426i
$771$	557.852	−	426.788i	0.723544	−	0.553551i
$772$	−332.546			−0.430760
$773$			291.448i			0.377035i	0.982070	+	0.188517i	$0.0603682\pi$
$773$			291.448i			0.377035i	−0.982070	+	0.188517i	$0.939632\pi$
$774$	−634.413	−	171.939i	−0.819655	−	0.222143i
$775$	−1157.43			−1.49346
$776$		−	157.613i		−	0.203110i
$777$	197.933	+	258.718i	0.254740	+	0.332970i
$778$	−480.157			−0.617168
$779$			309.729i			0.397598i
$780$	−256.022	+	195.871i	−0.328234	+	0.251117i
$781$	−177.255			−0.226959
$782$		−	68.2970i		−	0.0873363i
$783$	177.646	+	434.138i	0.226878	+	0.554455i
$784$	−11.0810			−0.0141340
$785$		−	2233.95i		−	2.84580i
$786$	−80.2614	−	104.909i	−0.102114	−	0.133472i
$787$	293.889			0.373429			0.186715	−	0.982414i	$-0.440216\pi$
$787$	293.889			0.373429			0.186715	+	0.982414i	$0.440216\pi$
$788$			200.425i			0.254346i
$789$	596.006	−	455.978i	0.755395	−	0.577919i
$790$	−610.065			−0.772235
$791$			381.122i			0.481822i
$792$	50.6117	−	186.745i	0.0639037	−	0.235790i
$793$	130.133			0.164103
$794$		−	533.748i		−	0.672226i
$795$	1412.48	+	1846.24i	1.77670	+	2.32232i
$796$	149.903			0.188321
$797$		−	568.764i		−	0.713631i	−0.934175	−	0.356816i	$-0.883862\pi$
$797$		−	568.764i		−	0.713631i	0.934175	−	0.356816i	$-0.116138\pi$
$798$	−84.2836	+	64.4816i	−0.105619	+	0.0808041i
$799$	−485.490			−0.607622
$800$			908.035i			1.13504i
$801$	−548.774	−	148.729i	−0.685111	−	0.185679i
$802$	−312.157			−0.389223
$803$		−	158.915i		−	0.197902i
$804$	113.476	+	148.324i	0.141139	+	0.184482i
$805$	84.0000			0.104348
$806$			326.340i			0.404888i
$807$	811.737	−	621.024i	1.00587	−	0.769546i
$808$	−811.768			−1.00466
$809$		−	183.697i		−	0.227067i	−0.993534	−	0.113534i	$-0.963783\pi$
$809$		−	183.697i		−	0.227067i	0.993534	−	0.113534i	$-0.0362169\pi$
$810$	−674.383	−	394.521i	−0.832572	−	0.487062i
$811$	−544.663			−0.671594			−0.335797	−	0.941934i	$-0.609006\pi$
$811$	−544.663			−0.671594			−0.335797	+	0.941934i	$0.609006\pi$
$812$		−	105.330i		−	0.129716i
$813$	38.8261	+	50.7494i	0.0477566	+	0.0624224i
$814$	−140.235			−0.172279
$815$		−	1070.33i		−	1.31329i
$816$	45.8078	−	35.0455i	0.0561370	−	0.0429479i
$817$	571.527			0.699543
$818$			848.781i			1.03763i
$819$	−39.5791	+	146.038i	−0.0483261	+	0.178312i
$820$	512.044			0.624444
$821$			1188.78i			1.44797i	0.689818	+	0.723983i	$0.257691\pi$
$821$			1188.78i			1.44797i	−0.689818	+	0.723983i	$0.742309\pi$
$822$	−95.2470	−	124.497i	−0.115872	−	0.151456i
$823$	1265.15			1.53724			0.768621	−	0.639704i	$-0.220943\pi$
$823$	1265.15			1.53724			0.768621	+	0.639704i	$0.220943\pi$
$824$			462.585i			0.561390i
$825$	183.484	−	140.375i	0.222404	−	0.170152i
$826$	−143.047			−0.173180
$827$		−	790.941i		−	0.956398i	−0.878252	−	0.478199i	$-0.841290\pi$
$827$		−	790.941i		−	0.956398i	0.878252	−	0.478199i	$-0.158710\pi$
$828$	−85.6393	−	23.2099i	−0.103429	−	0.0280313i
$829$	99.1961			0.119658			0.0598288	−	0.998209i	$-0.480945\pi$
$829$	99.1961			0.119658			0.0598288	+	0.998209i	$0.480945\pi$
$830$			867.573i			1.04527i
$831$	413.638	+	540.664i	0.497759	+	0.650619i
$832$	296.257			0.356079
$833$		−	85.0141i		−	0.102058i
$834$	606.188	−	463.768i	0.726844	−	0.556076i
$835$	−145.077			−0.173745
$836$			61.2746i			0.0732950i
$837$	981.851	−	401.765i	1.17306	−	0.480006i
$838$	−15.0549			−0.0179652
$839$			243.824i			0.290612i	0.989387	+	0.145306i	$0.0464167\pi$
$839$			243.824i			0.290612i	−0.989387	+	0.145306i	$0.953583\pi$
$840$	292.682	+	382.564i	0.348431	+	0.455433i
$841$	539.170			0.641106
$842$			109.786i			0.130387i
$843$	−561.093	+	429.267i	−0.665591	+	0.509214i
$844$	92.9961			0.110185
$845$		−	949.182i		−	1.12329i
$846$	123.012	−	453.885i	0.145404	−	0.536507i
$847$	−302.055			−0.356617
$848$		−	166.218i		−	0.196012i
$849$	−671.974	−	878.334i	−0.791489	−	1.03455i
$850$	467.624			0.550145
$851$			176.569i			0.207484i
$852$	−370.208	+	283.230i	−0.434516	+	0.332429i
$853$	−1122.06			−1.31543			−0.657713	−	0.753268i	$-0.728476\pi$
$853$	−1122.06			−1.31543			−0.657713	+	0.753268i	$0.728476\pi$
$854$		−	70.8240i		−	0.0829321i
$855$	655.697	+	177.707i	0.766897	+	0.207844i
$856$	1012.63			1.18298
$857$		−	871.489i		−	1.01691i	−0.861090	−	0.508453i	$-0.830217\pi$
$857$		−	871.489i		−	1.01691i	0.861090	−	0.508453i	$-0.169783\pi$
$858$	−39.5791	−	51.7336i	−0.0461295	−	0.0602956i
$859$	−1674.92			−1.94985			−0.974925	−	0.222533i	$-0.928568\pi$
$859$	−1674.92			−1.94985			−0.974925	+	0.222533i	$0.928568\pi$
$860$		−	944.850i		−	1.09866i
$861$	190.885	−	146.038i	0.221701	−	0.169614i
$862$	907.129			1.05235
$863$		−	1320.74i		−	1.53041i	−0.643787	−	0.765205i	$-0.722638\pi$
$863$		−	1320.74i		−	1.53041i	0.643787	−	0.765205i	$-0.277362\pi$
$864$	−315.195	−	770.288i	−0.364810	−	0.891537i
$865$	−145.292			−0.167967
$866$		−	152.713i		−	0.176343i
$867$	−257.940	−	337.153i	−0.297509	−	0.388873i
$868$	−238.214			−0.274441
$869$			165.340i			0.190264i
$870$	399.284	−	305.474i	0.458947	−	0.351120i
$871$	172.620			0.198186
$872$		−	1353.10i		−	1.55172i
$873$	−45.1216	+	166.488i	−0.0516856	+	0.190708i
$874$	−57.5217			−0.0658142
$875$			87.0303i			0.0994632i
$876$	−253.925	−	331.905i	−0.289869	−	0.378887i
$877$	−344.790			−0.393147			−0.196573	−	0.980489i	$-0.562981\pi$
$877$	−344.790			−0.393147			−0.196573	+	0.980489i	$0.562981\pi$
$878$			690.242i			0.786152i
$879$	−1266.69	+	969.087i	−1.44106	+	1.10249i
$880$	−30.5385			−0.0347029
$881$			518.737i			0.588805i	0.955682	+	0.294403i	$0.0951206\pi$
$881$			518.737i			0.588805i	−0.955682	+	0.294403i	$0.904879\pi$
$882$	79.4797	+	21.5406i	0.0901131	+	0.0244224i
$883$	−584.008			−0.661391			−0.330695	−	0.943738i	$-0.607283\pi$
$883$	−584.008			−0.661391			−0.330695	+	0.943738i	$0.607283\pi$
$884$			176.839i			0.200044i
$885$	556.427	+	727.303i	0.628732	+	0.821812i
$886$	355.859			0.401646
$887$			263.213i			0.296745i	0.988932	+	0.148373i	$0.0474035\pi$
$887$			263.213i			0.296745i	−0.988932	+	0.148373i	$0.952597\pi$
$888$	−804.153	+	615.221i	−0.905577	+	0.692817i
$889$	96.7895			0.108875
$890$			609.366i			0.684681i
$891$	−106.923	+	182.771i	−0.120003	+	0.205130i
$892$	231.349			0.259360
$893$			408.893i			0.457887i
$894$	485.314	+	634.351i	0.542857	+	0.709565i
$895$	2521.92			2.81778
$896$			164.988i			0.184138i
$897$	−65.1373	+	49.8336i	−0.0726168	+	0.0555559i
$898$	−687.231			−0.765291
$899$			682.621i			0.759312i
$900$	158.916	−	586.365i	0.176574	−	0.651516i
$901$	1275.23			1.41535
$902$			103.467i			0.114709i
$903$	−269.476	−	352.230i	−0.298423	−	0.390067i
$904$	−1184.61			−1.31041
$905$			1593.16i			1.76040i
$906$	−516.205	+	394.925i	−0.569763	+	0.435900i
$907$	−1501.72			−1.65570			−0.827849	−	0.560951i	$-0.810435\pi$
$907$	−1501.72			−1.65570			−0.827849	+	0.560951i	$0.810435\pi$
$908$		−	896.618i		−	0.987464i
$909$	857.476	+	232.393i	0.943318	+	0.255658i
$910$	162.162			0.178200
$911$			879.178i			0.965069i	0.875877	+	0.482534i	$0.160284\pi$
$911$			879.178i			0.965069i	−0.875877	+	0.482534i	$0.839716\pi$
$912$	−29.5163	−	38.5806i	−0.0323644	−	0.0423033i
$913$	235.129			0.257535
$914$			671.567i			0.734756i
$915$	−360.095	+	275.493i	−0.393547	+	0.301085i
$916$	−15.6092			−0.0170406
$917$		−	89.1234i		−	0.0971901i
$918$	−396.686	+	162.321i	−0.432120	+	0.176820i
$919$	76.9882			0.0837739			0.0418869	−	0.999122i	$-0.486663\pi$
$919$	76.9882			0.0837739			0.0418869	+	0.999122i	$0.486663\pi$
$920$			261.091i			0.283795i
$921$	−1034.96	−	1352.79i	−1.12374	−	1.46883i
$922$	899.123			0.975188
$923$			430.849i			0.466792i
$924$	37.7634	−	28.8911i	0.0408694	−	0.0312674i
$925$	−1208.95			−1.30697
$926$		−	1020.92i		−	1.10251i
$927$	132.429	−	488.631i	0.142857	−	0.527110i
$928$	535.535			0.577085
$929$			1629.76i			1.75431i	0.480204	+	0.877157i	$0.340563\pi$
$929$			1629.76i			1.75431i	−0.480204	+	0.877157i	$0.659437\pi$
$930$	−690.863	−	903.023i	−0.742863	−	0.970993i
$931$	−71.6013			−0.0769079
$932$			267.823i			0.287364i
$933$	101.867	−	77.9336i	0.109182	−	0.0835301i
$934$	213.517			0.228605
$935$		−	234.293i		−	0.250581i
$936$	−453.918	−	123.021i	−0.484955	−	0.131432i
$937$	−497.720			−0.531185			−0.265592	−	0.964085i	$-0.585568\pi$
$937$	−497.720			−0.531185			−0.265592	+	0.964085i	$0.585568\pi$
$938$		−	93.9468i		−	0.100157i
$939$	288.229	+	376.742i	0.306953	+	0.401217i
$940$	675.984			0.719132
$941$		−	238.894i		−	0.253873i	−0.991911	−	0.126936i	$-0.959486\pi$
$941$		−	238.894i		−	0.253873i	0.991911	−	0.126936i	$-0.0405144\pi$
$942$	942.793	−	721.289i	1.00084	−	0.765700i
$943$	130.275			0.138149
$944$		−	65.4794i		−	0.0693638i
$945$	−199.642	−	487.893i	−0.211261	−	0.516289i
$946$	190.923			0.201821
$947$		−	667.910i		−	0.705291i	−0.935757	−	0.352645i	$-0.885282\pi$
$947$		−	667.910i		−	0.705291i	0.935757	−	0.352645i	$-0.114718\pi$
$948$	264.191	+	345.322i	0.278682	+	0.364264i
$949$	−386.272			−0.407030
$950$		−	393.846i		−	0.414574i
$951$	−335.824	+	256.924i	−0.353127	+	0.270162i
$952$	264.243			0.277566
$953$		−	11.3247i		−	0.0118832i	−0.999982	−	0.00594162i	$-0.998109\pi$
$953$		−	11.3247i		−	0.0118832i	0.999982	−	0.00594162i	$-0.00189129\pi$
$954$	−323.114	+	1192.21i	−0.338694	+	1.24970i
$955$	−329.948			−0.345495
$956$		−	137.404i		−	0.143728i
$957$	−82.7895	−	108.214i	−0.0865094	−	0.113076i
$958$	915.174			0.955296
$959$		−	105.764i		−	0.110285i
$960$	−819.782	+	627.178i	−0.853939	+	0.653311i
$961$	582.822			0.606475
$962$			340.866i			0.354331i
$963$	−1069.64	−	289.895i	−1.11074	−	0.301033i
$964$	308.787			0.320318
$965$		−	1070.93i		−	1.10977i
$966$	27.1216	+	35.4504i	0.0280761	+	0.0366982i
$967$	830.324			0.858660			0.429330	−	0.903148i	$-0.358750\pi$
$967$	830.324			0.858660			0.429330	+	0.903148i	$0.358750\pi$
$968$		−	938.855i		−	0.969891i
$969$	295.992	−	226.450i	0.305461	−	0.233695i
$970$	184.871			0.190588
$971$		−	1217.58i		−	1.25394i	−0.779044	−	0.626970i	$-0.784295\pi$
$971$		−	1217.58i		−	1.25394i	0.779044	−	0.626970i	$-0.215705\pi$
$972$	68.7286	+	552.577i	0.0707085	+	0.568495i
$973$	514.974			0.529264
$974$		−	113.183i		−	0.116204i
$975$	−341.207	−	445.989i	−0.349955	−	0.457425i
$976$	32.4195			0.0332167
$977$			424.579i			0.434574i	0.976108	+	0.217287i	$0.0697207\pi$
$977$			424.579i			0.434574i	−0.976108	+	0.217287i	$0.930279\pi$
$978$	451.711	−	345.584i	0.461872	−	0.353358i
$979$	165.150			0.168693
$980$			118.372i			0.120787i
$981$	−387.365	+	1429.29i	−0.394867	+	1.45697i
$982$	−969.203			−0.986968
$983$			76.7273i			0.0780542i	0.999238	+	0.0390271i	$0.0124259\pi$
$983$			76.7273i			0.0780542i	−0.999238	+	0.0390271i	$0.987574\pi$
$984$	453.918	+	593.313i	0.461298	+	0.602961i
$985$	−645.446			−0.655275
$986$		−	275.792i		−	0.279708i
$987$	252.000	−	192.794i	0.255319	−	0.195333i
$988$	148.939			0.150748
$989$		−	240.389i		−	0.243063i
$990$	219.041	+	59.3643i	0.221253	+	0.0599640i
$991$	181.271			0.182917			0.0914585	−	0.995809i	$-0.470847\pi$
$991$	181.271			0.182917			0.0914585	+	0.995809i	$0.470847\pi$
$992$		−	1211.17i		−	1.22094i
$993$	470.974	+	615.608i	0.474294	+	0.619947i
$994$	234.486			0.235902
$995$			482.747i			0.485173i
$996$	491.082	−	375.705i	0.493055	−	0.377214i
$997$	−1184.43			−1.18800			−0.593998	−	0.804466i	$-0.702451\pi$
$997$	−1184.43			−1.18800			−0.593998	+	0.804466i	$0.702451\pi$
$998$		−	496.453i		−	0.497448i
$999$	1025.56	−	419.649i	1.02658	−	0.420069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.3.b.a.8.2	✓	4
3.2	odd	2	inner	21.3.b.a.8.3	yes	4
4.3	odd	2		336.3.d.c.113.4		4
5.2	odd	4		525.3.f.a.449.6		8
5.3	odd	4		525.3.f.a.449.3		8
5.4	even	2		525.3.c.a.176.3		4
7.2	even	3		147.3.h.e.116.2		8
7.3	odd	6		147.3.h.c.128.3		8
7.4	even	3		147.3.h.e.128.3		8
7.5	odd	6		147.3.h.c.116.2		8
7.6	odd	2		147.3.b.f.50.2		4
8.3	odd	2		1344.3.d.b.449.1		4
8.5	even	2		1344.3.d.f.449.4		4
9.2	odd	6		567.3.r.c.134.3		8
9.4	even	3		567.3.r.c.512.3		8
9.5	odd	6		567.3.r.c.512.2		8
9.7	even	3		567.3.r.c.134.2		8
12.11	even	2		336.3.d.c.113.3		4
15.2	even	4		525.3.f.a.449.4		8
15.8	even	4		525.3.f.a.449.5		8
15.14	odd	2		525.3.c.a.176.2		4
21.2	odd	6		147.3.h.e.116.3		8
21.5	even	6		147.3.h.c.116.3		8
21.11	odd	6		147.3.h.e.128.2		8
21.17	even	6		147.3.h.c.128.2		8
21.20	even	2		147.3.b.f.50.3		4
24.5	odd	2		1344.3.d.f.449.3		4
24.11	even	2		1344.3.d.b.449.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.b.a.8.2	✓	4	1.1	even	1	trivial
21.3.b.a.8.3	yes	4	3.2	odd	2	inner
147.3.b.f.50.2		4	7.6	odd	2
147.3.b.f.50.3		4	21.20	even	2
147.3.h.c.116.2		8	7.5	odd	6
147.3.h.c.116.3		8	21.5	even	6
147.3.h.c.128.2		8	21.17	even	6
147.3.h.c.128.3		8	7.3	odd	6
147.3.h.e.116.2		8	7.2	even	3
147.3.h.e.116.3		8	21.2	odd	6
147.3.h.e.128.2		8	21.11	odd	6
147.3.h.e.128.3		8	7.4	even	3
336.3.d.c.113.3		4	12.11	even	2
336.3.d.c.113.4		4	4.3	odd	2
525.3.c.a.176.2		4	15.14	odd	2
525.3.c.a.176.3		4	5.4	even	2
525.3.f.a.449.3		8	5.3	odd	4
525.3.f.a.449.4		8	15.2	even	4
525.3.f.a.449.5		8	15.8	even	4
525.3.f.a.449.6		8	5.2	odd	4
567.3.r.c.134.2		8	9.7	even	3
567.3.r.c.134.3		8	9.2	odd	6
567.3.r.c.512.2		8	9.5	odd	6
567.3.r.c.512.3		8	9.4	even	3
1344.3.d.b.449.1		4	8.3	odd	2
1344.3.d.b.449.2		4	24.11	even	2
1344.3.d.f.449.3		4	24.5	odd	2
1344.3.d.f.449.4		4	8.5	even	2

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	21.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.30710i q^{2} +(-1.82288 - 2.38267i) q^{3} +2.29150 q^{4} +7.37953i q^{5} +(-3.11438 + 2.38267i) q^{6} -2.64575 q^{7} -8.22359i q^{8} +(-2.35425 + 8.68663i) q^{9} +O(q^{10})\)	\(q-1.30710i q^{2} +(-1.82288 - 2.38267i) q^{3} +2.29150 q^{4} +7.37953i q^{5} +(-3.11438 + 2.38267i) q^{6} -2.64575 q^{7} -8.22359i q^{8} +(-2.35425 + 8.68663i) q^{9} +9.64575 q^{10} -2.61419i q^{11} +(-4.17712 - 5.45990i) q^{12} -6.35425 q^{13} +3.45825i q^{14} +(17.5830 - 13.4520i) q^{15} -1.58301 q^{16} -12.1449i q^{17} +(11.3542 + 3.07723i) q^{18} -10.2288 q^{19} +16.9102i q^{20} +(4.82288 + 6.30396i) q^{21} -3.41699 q^{22} +4.30231i q^{23} +(-19.5941 + 14.9906i) q^{24} -29.4575 q^{25} +8.30561i q^{26} +(24.9889 - 10.2252i) q^{27} -6.06275 q^{28} +17.3733i q^{29} +(-17.5830 - 22.9827i) q^{30} +39.2915 q^{31} -30.8252i q^{32} +(-6.22876 + 4.76534i) q^{33} -15.8745 q^{34} -19.5244i q^{35} +(-5.39477 + 19.9054i) q^{36} +41.0405 q^{37} +13.3700i q^{38} +(11.5830 + 15.1401i) q^{39} +60.6863 q^{40} -30.2802i q^{41} +(8.23987 - 6.30396i) q^{42} -55.8745 q^{43} -5.99042i q^{44} +(-64.1033 - 17.3733i) q^{45} +5.62352 q^{46} -39.9749i q^{47} +(2.88562 + 3.77178i) q^{48} +7.00000 q^{49} +38.5038i q^{50} +(-28.9373 + 22.1386i) q^{51} -14.5608 q^{52} +105.002i q^{53} +(-13.3654 - 32.6628i) q^{54} +19.2915 q^{55} +21.7576i q^{56} +(18.6458 + 24.3718i) q^{57} +22.7085 q^{58} +41.3640i q^{59} +(40.2915 - 30.8252i) q^{60} -20.4797 q^{61} -51.3577i q^{62} +(6.22876 - 22.9827i) q^{63} -46.6235 q^{64} -46.8914i q^{65} +(6.22876 + 8.14158i) q^{66} -27.1660 q^{67} -27.8300i q^{68} +(10.2510 - 7.84257i) q^{69} -25.5203 q^{70} -67.8049i q^{71} +(71.4353 + 19.3604i) q^{72} +60.7895 q^{73} -53.6439i q^{74} +(53.6974 + 70.1876i) q^{75} -23.4392 q^{76} +6.91650i q^{77} +(19.7895 - 15.1401i) q^{78} -63.2470 q^{79} -11.6818i q^{80} +(-69.9150 - 40.9010i) q^{81} -39.5791 q^{82} +89.9435i q^{83} +(11.0516 + 14.4455i) q^{84} +89.6235 q^{85} +73.0333i q^{86} +(41.3948 - 31.6693i) q^{87} -21.4980 q^{88} +63.1745i q^{89} +(-22.7085 + 83.7891i) q^{90} +16.8118 q^{91} +9.85875i q^{92} +(-71.6235 - 93.6188i) q^{93} -52.2510 q^{94} -75.4835i q^{95} +(-73.4464 + 56.1906i) q^{96} +19.1660 q^{97} -9.14967i q^{98} +(22.7085 + 6.15445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 12 q^{4} + 14 q^{6} - 20 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 12 * q^4 + 14 * q^6 - 20 * q^9	\( 4 q - 2 q^{3} - 12 q^{4} + 14 q^{6} - 20 q^{9} + 28 q^{10} - 22 q^{12} - 36 q^{13} + 28 q^{15} + 36 q^{16} + 56 q^{18} + 12 q^{19} + 14 q^{21} - 56 q^{22} - 126 q^{24} - 12 q^{25} + 10 q^{27} - 56 q^{28} - 28 q^{30} + 136 q^{31} + 28 q^{33} + 116 q^{36} + 16 q^{37} + 4 q^{39} + 84 q^{40} + 70 q^{42} - 160 q^{43} - 140 q^{45} - 168 q^{46} + 38 q^{48} + 28 q^{49} - 84 q^{51} + 164 q^{52} - 154 q^{54} + 56 q^{55} + 64 q^{57} + 112 q^{58} + 140 q^{60} - 156 q^{61} - 28 q^{63} + 4 q^{64} - 28 q^{66} - 24 q^{67} + 168 q^{69} - 28 q^{70} - 32 q^{73} + 146 q^{75} - 316 q^{76} - 196 q^{78} + 128 q^{79} - 68 q^{81} + 392 q^{82} - 14 q^{84} + 168 q^{85} + 28 q^{87} + 168 q^{88} - 112 q^{90} - 28 q^{91} - 96 q^{93} - 336 q^{94} - 98 q^{96} - 8 q^{97} + 112 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 12 * q^4 + 14 * q^6 - 20 * q^9 + 28 * q^10 - 22 * q^12 - 36 * q^13 + 28 * q^15 + 36 * q^16 + 56 * q^18 + 12 * q^19 + 14 * q^21 - 56 * q^22 - 126 * q^24 - 12 * q^25 + 10 * q^27 - 56 * q^28 - 28 * q^30 + 136 * q^31 + 28 * q^33 + 116 * q^36 + 16 * q^37 + 4 * q^39 + 84 * q^40 + 70 * q^42 - 160 * q^43 - 140 * q^45 - 168 * q^46 + 38 * q^48 + 28 * q^49 - 84 * q^51 + 164 * q^52 - 154 * q^54 + 56 * q^55 + 64 * q^57 + 112 * q^58 + 140 * q^60 - 156 * q^61 - 28 * q^63 + 4 * q^64 - 28 * q^66 - 24 * q^67 + 168 * q^69 - 28 * q^70 - 32 * q^73 + 146 * q^75 - 316 * q^76 - 196 * q^78 + 128 * q^79 - 68 * q^81 + 392 * q^82 - 14 * q^84 + 168 * q^85 + 28 * q^87 + 168 * q^88 - 112 * q^90 - 28 * q^91 - 96 * q^93 - 336 * q^94 - 98 * q^96 - 8 * q^97 + 112 * q^99

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