LMFDB - Embedded newform 210.3.f.a.181.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(181,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("210.181");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.f (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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.3317760000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.2
Root			$-1.01575 - 1.40294i$ of defining polynomial
Character	$\chi$	$=$	210.181
Dual form			210.3.f.a.181.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} +2.23607i q^{5} +2.44949i q^{6} +(1.04456 + 6.92163i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} +2.23607i q^{5} +2.44949i q^{6} +(1.04456 + 6.92163i) q^{7} -2.82843 q^{8} -3.00000 q^{9} -3.16228i q^{10} -15.9625 q^{11} -3.46410i q^{12} -6.19954i q^{13} +(-1.47723 - 9.78866i) q^{14} +3.87298 q^{15} +4.00000 q^{16} +19.7410i q^{17} +4.24264 q^{18} +29.3912i q^{19} +4.47214i q^{20} +(11.9886 - 1.80922i) q^{21} +22.5744 q^{22} +18.3412 q^{23} +4.89898i q^{24} -5.00000 q^{25} +8.76747i q^{26} +5.19615i q^{27} +(2.08911 + 13.8433i) q^{28} -53.2909 q^{29} -5.47723 q^{30} +37.4949i q^{31} -5.65685 q^{32} +27.6479i q^{33} -27.9179i q^{34} +(-15.4772 + 2.33570i) q^{35} -6.00000 q^{36} +61.0349 q^{37} -41.5654i q^{38} -10.7379 q^{39} -6.32456i q^{40} +21.3433i q^{41} +(-16.9545 + 2.55863i) q^{42} +25.9827 q^{43} -31.9250 q^{44} -6.70820i q^{45} -25.9383 q^{46} +10.3419i q^{47} -6.92820i q^{48} +(-46.8178 + 14.4601i) q^{49} +7.07107 q^{50} +34.1924 q^{51} -12.3991i q^{52} -64.7326 q^{53} -7.34847i q^{54} -35.6933i q^{55} +(-2.95445 - 19.5773i) q^{56} +50.9070 q^{57} +75.3647 q^{58} -18.0219i q^{59} +7.74597 q^{60} -91.8436i q^{61} -53.0258i q^{62} +(-3.13367 - 20.7649i) q^{63} +8.00000 q^{64} +13.8626 q^{65} -39.1000i q^{66} -18.2351 q^{67} +39.4819i q^{68} -31.7678i q^{69} +(21.8881 - 3.30318i) q^{70} +108.465 q^{71} +8.48528 q^{72} -73.5614i q^{73} -86.3164 q^{74} +8.66025i q^{75} +58.7823i q^{76} +(-16.6737 - 110.486i) q^{77} +15.1857 q^{78} -57.1904 q^{79} +8.94427i q^{80} +9.00000 q^{81} -30.1840i q^{82} +36.1402i q^{83} +(23.9772 - 3.61845i) q^{84} -44.1421 q^{85} -36.7451 q^{86} +92.3026i q^{87} +45.1488 q^{88} -133.352i q^{89} +9.48683i q^{90} +(42.9109 - 6.47576i) q^{91} +36.6823 q^{92} +64.9431 q^{93} -14.6257i q^{94} -65.7206 q^{95} +9.79796i q^{96} +29.2749i q^{97} +(66.2104 - 20.4496i) q^{98} +47.8875 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{4} - 24 q^{9}+O(q^{10}) $ 8 * q + 16 * q^4 - 24 * q^9	$ 8 q + 16 q^{4} - 24 q^{9} - 16 q^{11} + 32 q^{14} + 32 q^{16} + 96 q^{22} - 40 q^{25} - 144 q^{29} - 80 q^{35} - 48 q^{36} - 48 q^{37} - 48 q^{39} - 48 q^{42} - 64 q^{43} - 32 q^{44} + 128 q^{46} - 24 q^{49} + 128 q^{53} + 64 q^{56} + 144 q^{57} + 224 q^{58} + 64 q^{64} + 80 q^{65} - 192 q^{67} + 176 q^{71} - 160 q^{74} + 192 q^{77} - 96 q^{78} - 288 q^{79} + 72 q^{81} - 240 q^{85} - 64 q^{86} + 192 q^{88} + 64 q^{91} + 336 q^{93} + 80 q^{95} + 48 q^{99}+O(q^{100}) $ 8 * q + 16 * q^4 - 24 * q^9 - 16 * q^11 + 32 * q^14 + 32 * q^16 + 96 * q^22 - 40 * q^25 - 144 * q^29 - 80 * q^35 - 48 * q^36 - 48 * q^37 - 48 * q^39 - 48 * q^42 - 64 * q^43 - 32 * q^44 + 128 * q^46 - 24 * q^49 + 128 * q^53 + 64 * q^56 + 144 * q^57 + 224 * q^58 + 64 * q^64 + 80 * q^65 - 192 * q^67 + 176 * q^71 - 160 * q^74 + 192 * q^77 - 96 * q^78 - 288 * q^79 + 72 * q^81 - 240 * q^85 - 64 * q^86 + 192 * q^88 + 64 * q^91 + 336 * q^93 + 80 * q^95 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	2.00000			0.500000
$5$			2.23607i			0.447214i
$5$			2.23607i			0.447214i
$6$			2.44949i			0.408248i
$7$	1.04456	+	6.92163i	0.149222	+	0.988804i
$7$	1.04456	+	6.92163i	0.149222	+	0.988804i
$8$	−2.82843			−0.353553
$9$	−3.00000			−0.333333
$10$		−	3.16228i		−	0.316228i
$11$	−15.9625			−1.45114			−0.725568	−	0.688150i	$-0.758423\pi$
$11$	−15.9625			−1.45114			−0.725568	+	0.688150i	$0.758423\pi$
$12$		−	3.46410i		−	0.288675i
$13$		−	6.19954i		−	0.476887i	−0.971156	−	0.238444i	$-0.923363\pi$
$13$		−	6.19954i		−	0.476887i	0.971156	−	0.238444i	$-0.0766372\pi$
$14$	−1.47723	−	9.78866i	−0.105516	−	0.699190i
$15$	3.87298			0.258199
$16$	4.00000			0.250000
$17$			19.7410i			1.16123i	0.814177	+	0.580617i	$0.197188\pi$
$17$			19.7410i			1.16123i	−0.814177	+	0.580617i	$0.802812\pi$
$18$	4.24264			0.235702
$19$			29.3912i			1.54690i	0.633856	+	0.773451i	$0.281471\pi$
$19$			29.3912i			1.54690i	−0.633856	+	0.773451i	$0.718529\pi$
$20$			4.47214i			0.223607i
$21$	11.9886	−	1.80922i	0.570886	−	0.0861535i
$22$	22.5744			1.02611
$23$	18.3412			0.797442			0.398721	−	0.917072i	$-0.369454\pi$
$23$	18.3412			0.797442			0.398721	+	0.917072i	$0.369454\pi$
$24$			4.89898i			0.204124i
$25$	−5.00000			−0.200000
$26$			8.76747i			0.337210i
$27$			5.19615i			0.192450i
$28$	2.08911	+	13.8433i	0.0746112	+	0.494402i
$29$	−53.2909			−1.83762			−0.918809	−	0.394702i	$-0.870848\pi$
$29$	−53.2909			−1.83762			−0.918809	+	0.394702i	$0.870848\pi$
$30$	−5.47723			−0.182574
$31$			37.4949i			1.20951i	0.796411	+	0.604756i	$0.206729\pi$
$31$			37.4949i			1.20951i	−0.796411	+	0.604756i	$0.793271\pi$
$32$	−5.65685			−0.176777
$33$			27.6479i			0.837814i
$34$		−	27.9179i		−	0.821116i
$35$	−15.4772	+	2.33570i	−0.442206	+	0.0667342i
$36$	−6.00000			−0.166667
$37$	61.0349			1.64959			0.824796	−	0.565430i	$-0.191290\pi$
$37$	61.0349			1.64959			0.824796	+	0.565430i	$0.191290\pi$
$38$		−	41.5654i		−	1.09383i
$39$	−10.7379			−0.275331
$40$		−	6.32456i		−	0.158114i
$41$			21.3433i			0.520569i	0.965532	+	0.260285i	$0.0838164\pi$
$41$			21.3433i			0.520569i	−0.965532	+	0.260285i	$0.916184\pi$
$42$	−16.9545	+	2.55863i	−0.403677	+	0.0609198i
$43$	25.9827			0.604249			0.302125	−	0.953268i	$-0.402304\pi$
$43$	25.9827			0.604249			0.302125	+	0.953268i	$0.402304\pi$
$44$	−31.9250			−0.725568
$45$		−	6.70820i		−	0.149071i
$46$	−25.9383			−0.563876
$47$			10.3419i			0.220041i	0.993929	+	0.110021i	$0.0350917\pi$
$47$			10.3419i			0.220041i	−0.993929	+	0.110021i	$0.964908\pi$
$48$		−	6.92820i		−	0.144338i
$49$	−46.8178	+	14.4601i	−0.955465	+	0.295103i
$50$	7.07107			0.141421
$51$	34.1924			0.670438
$52$		−	12.3991i		−	0.238444i
$53$	−64.7326			−1.22137			−0.610685	−	0.791874i	$-0.709106\pi$
$53$	−64.7326			−1.22137			−0.610685	+	0.791874i	$0.709106\pi$
$54$		−	7.34847i		−	0.136083i
$55$		−	35.6933i		−	0.648968i
$56$	−2.95445	−	19.5773i	−0.0527581	−	0.349595i
$57$	50.9070			0.893105
$58$	75.3647			1.29939
$59$		−	18.0219i		−	0.305455i	−0.988268	−	0.152728i	$-0.951194\pi$
$59$		−	18.0219i		−	0.305455i	0.988268	−	0.152728i	$-0.0488057\pi$
$60$	7.74597			0.129099
$61$		−	91.8436i		−	1.50563i	−0.658231	−	0.752816i	$-0.728695\pi$
$61$		−	91.8436i		−	1.50563i	0.658231	−	0.752816i	$-0.271305\pi$
$62$		−	53.0258i		−	0.855255i
$63$	−3.13367	−	20.7649i	−0.0497408	−	0.329601i
$64$	8.00000			0.125000
$65$	13.8626			0.213271
$66$		−	39.1000i		−	0.592424i
$67$	−18.2351			−0.272166			−0.136083	−	0.990697i	$-0.543451\pi$
$67$	−18.2351			−0.272166			−0.136083	+	0.990697i	$0.543451\pi$
$68$			39.4819i			0.580617i
$69$		−	31.7678i		−	0.460403i
$70$	21.8881	−	3.30318i	0.312687	−	0.0471882i
$71$	108.465			1.52768			0.763841	−	0.645404i	$-0.223311\pi$
$71$	108.465			1.52768			0.763841	+	0.645404i	$0.223311\pi$
$72$	8.48528			0.117851
$73$		−	73.5614i		−	1.00769i	−0.863794	−	0.503845i	$-0.831918\pi$
$73$		−	73.5614i		−	1.00769i	0.863794	−	0.503845i	$-0.168082\pi$
$74$	−86.3164			−1.16644
$75$			8.66025i			0.115470i
$76$			58.7823i			0.773451i
$77$	−16.6737	−	110.486i	−0.216542	−	1.43489i
$78$	15.1857			0.194688
$79$	−57.1904			−0.723929			−0.361964	−	0.932192i	$-0.617894\pi$
$79$	−57.1904			−0.723929			−0.361964	+	0.932192i	$0.617894\pi$
$80$			8.94427i			0.111803i
$81$	9.00000			0.111111
$82$		−	30.1840i		−	0.368098i
$83$			36.1402i			0.435425i	0.976013	+	0.217712i	$0.0698594\pi$
$83$			36.1402i			0.435425i	−0.976013	+	0.217712i	$0.930141\pi$
$84$	23.9772	−	3.61845i	0.285443	−	0.0430768i
$85$	−44.1421			−0.519319
$86$	−36.7451			−0.427269
$87$			92.3026i			1.06095i
$88$	45.1488			0.513054
$89$		−	133.352i		−	1.49833i	−0.662382	−	0.749166i	$-0.730455\pi$
$89$		−	133.352i		−	1.49833i	0.662382	−	0.749166i	$-0.269545\pi$
$90$			9.48683i			0.105409i
$91$	42.9109	−	6.47576i	0.471548	−	0.0711622i
$92$	36.6823			0.398721
$93$	64.9431			0.698312
$94$		−	14.6257i		−	0.155593i
$95$	−65.7206			−0.691796
$96$			9.79796i			0.102062i
$97$			29.2749i			0.301803i	0.988549	+	0.150902i	$0.0482176\pi$
$97$			29.2749i			0.301803i	−0.988549	+	0.150902i	$0.951782\pi$
$98$	66.2104	−	20.4496i	0.675616	−	0.208669i
$99$	47.8875			0.483712
$100$	−10.0000			−0.100000
$101$			58.3844i			0.578063i	0.957320	+	0.289032i	$0.0933332\pi$
$101$			58.3844i			0.578063i	−0.957320	+	0.289032i	$0.906667\pi$
$102$	−48.3553			−0.474071
$103$			102.996i			0.999957i	0.866038	+	0.499978i	$0.166659\pi$
$103$			102.996i			0.999957i	−0.866038	+	0.499978i	$0.833341\pi$
$104$			17.5349i			0.168605i
$105$	4.04555	+	26.8073i	0.0385290	+	0.255308i
$106$	91.5457			0.863638
$107$	−58.8093			−0.549619			−0.274810	−	0.961499i	$-0.588615\pi$
$107$	−58.8093			−0.549619			−0.274810	+	0.961499i	$0.588615\pi$
$108$			10.3923i			0.0962250i
$109$	−202.689			−1.85954			−0.929768	−	0.368147i	$-0.879992\pi$
$109$	−202.689			−1.85954			−0.929768	+	0.368147i	$0.879992\pi$
$110$			50.4779i			0.458890i
$111$		−	105.716i		−	0.952392i
$112$	4.17822	+	27.6865i	0.0373056	+	0.247201i
$113$	169.018			1.49574			0.747869	−	0.663846i	$-0.231077\pi$
$113$	169.018			1.49574			0.747869	+	0.663846i	$0.231077\pi$
$114$	−71.9933			−0.631520
$115$			41.0121i			0.356627i
$116$	−106.582			−0.918809
$117$			18.5986i			0.158962i
$118$			25.4868i			0.215989i
$119$	−136.640	+	20.6205i	−1.14823	+	0.173282i
$120$	−10.9545			−0.0912871
$121$	133.802			1.10580
$122$			129.886i			1.06464i
$123$	36.9678			0.300551
$124$			74.9898i			0.604756i
$125$		−	11.1803i		−	0.0894427i
$126$	4.43168	+	29.3660i	0.0351720	+	0.233063i
$127$	−47.5171			−0.374150			−0.187075	−	0.982346i	$-0.559901\pi$
$127$	−47.5171			−0.374150			−0.187075	+	0.982346i	$0.559901\pi$
$128$	−11.3137			−0.0883883
$129$		−	45.0034i		−	0.348864i
$130$	−19.6047			−0.150805
$131$		−	13.8166i		−	0.105470i	−0.998609	−	0.0527351i	$-0.983206\pi$
$131$		−	13.8166i		−	0.105470i	0.998609	−	0.0527351i	$-0.0167939\pi$
$132$			55.2957i			0.418907i
$133$	−203.435	+	30.7007i	−1.52958	+	0.230832i
$134$	25.7883			0.192450
$135$	−11.6190			−0.0860663
$136$		−	55.8359i		−	0.410558i
$137$	113.381			0.827600			0.413800	−	0.910368i	$-0.364201\pi$
$137$	113.381			0.827600			0.413800	+	0.910368i	$0.364201\pi$
$138$			44.9265i			0.325554i
$139$			127.380i			0.916400i	0.888849	+	0.458200i	$0.151506\pi$
$139$			127.380i			0.916400i	−0.888849	+	0.458200i	$0.848494\pi$
$140$	−30.9545	+	4.67140i	−0.221103	+	0.0333671i
$141$	17.9128			0.127041
$142$	−153.393			−1.08023
$143$			98.9601i			0.692029i
$144$	−12.0000			−0.0833333
$145$		−	119.162i		−	0.821808i
$146$			104.031i			0.712544i
$147$	25.0455	+	81.0908i	0.170378	+	0.551638i
$148$	122.070			0.824796
$149$	232.201			1.55839			0.779197	−	0.626779i	$-0.215627\pi$
$149$	232.201			1.55839			0.779197	+	0.626779i	$0.215627\pi$
$150$		−	12.2474i		−	0.0816497i
$151$	−111.750			−0.740067			−0.370033	−	0.929018i	$-0.620654\pi$
$151$	−111.750			−0.740067			−0.370033	+	0.929018i	$0.620654\pi$
$152$		−	83.1307i		−	0.546913i
$153$		−	59.2229i		−	0.387078i
$154$	23.5802	+	156.252i	0.153118	+	1.01462i
$155$	−83.8411			−0.540911
$156$	−21.4758			−0.137666
$157$		−	264.635i		−	1.68557i	−0.538247	−	0.842787i	$-0.680913\pi$
$157$		−	264.635i		−	1.68557i	0.538247	−	0.842787i	$-0.319087\pi$
$158$	80.8794			0.511895
$159$			112.120i			0.705158i
$160$		−	12.6491i		−	0.0790569i
$161$	19.1584	+	126.951i	0.118996	+	0.788513i
$162$	−12.7279			−0.0785674
$163$	53.4448			0.327882			0.163941	−	0.986470i	$-0.447579\pi$
$163$	53.4448			0.327882			0.163941	+	0.986470i	$0.447579\pi$
$164$			42.6867i			0.260285i
$165$	−61.8225			−0.374682
$166$		−	51.1100i		−	0.307892i
$167$			149.019i			0.892330i	0.894951	+	0.446165i	$0.147211\pi$
$167$			149.019i			0.892330i	−0.894951	+	0.446165i	$0.852789\pi$
$168$	−33.9089	+	5.11726i	−0.201839	+	0.0304599i
$169$	130.566			0.772578
$170$	62.4264			0.367214
$171$		−	88.1735i		−	0.515634i
$172$	51.9655			0.302125
$173$			36.9558i			0.213617i	0.994280	+	0.106809i	$0.0340633\pi$
$173$			36.9558i			0.213617i	−0.994280	+	0.106809i	$0.965937\pi$
$174$		−	130.536i		−	0.750204i
$175$	−5.22278	−	34.6081i	−0.0298445	−	0.197761i
$176$	−63.8500			−0.362784
$177$	−31.2148			−0.176355
$178$			188.588i			1.05948i
$179$	118.481			0.661905			0.330952	−	0.943647i	$-0.392630\pi$
$179$	118.481			0.661905			0.330952	+	0.943647i	$0.392630\pi$
$180$		−	13.4164i		−	0.0745356i
$181$			206.745i			1.14224i	0.820868	+	0.571118i	$0.193490\pi$
$181$			206.745i			1.14224i	−0.820868	+	0.571118i	$0.806510\pi$
$182$	−60.6851	+	9.15811i	−0.333435	+	0.0503193i
$183$	−159.078			−0.869277
$184$	−51.8766			−0.281938
$185$			136.478i			0.737720i
$186$	−91.8434			−0.493781
$187$		−	315.115i		−	1.68511i
$188$			20.6839i			0.110021i
$189$	−35.9658	+	5.42767i	−0.190295	+	0.0287178i
$190$	92.9430			0.489174
$191$	188.143			0.985041			0.492520	−	0.870301i	$-0.336076\pi$
$191$	188.143			0.985041			0.492520	+	0.870301i	$0.336076\pi$
$192$		−	13.8564i		−	0.0721688i
$193$	10.2372			0.0530425			0.0265213	−	0.999648i	$-0.491557\pi$
$193$	10.2372			0.0530425			0.0265213	+	0.999648i	$0.491557\pi$
$194$		−	41.4009i		−	0.213407i
$195$		−	24.0107i		−	0.123132i
$196$	−93.6356	+	28.9201i	−0.477733	+	0.147552i
$197$	218.831			1.11082			0.555408	−	0.831578i	$-0.312562\pi$
$197$	218.831			1.11082			0.555408	+	0.831578i	$0.312562\pi$
$198$	−67.7232			−0.342036
$199$			110.865i			0.557111i	0.960420	+	0.278556i	$0.0898556\pi$
$199$			110.865i			0.557111i	−0.960420	+	0.278556i	$0.910144\pi$
$200$	14.1421			0.0707107
$201$			31.5841i			0.157135i
$202$		−	82.5680i		−	0.408752i
$203$	−55.6654	−	368.860i	−0.274214	−	1.81704i
$204$	68.3847			0.335219
$205$	−47.7252			−0.232806
$206$		−	145.658i		−	0.707076i
$207$	−55.0235			−0.265814
$208$		−	24.7981i		−	0.119222i
$209$		−	469.156i		−	2.24477i
$210$	−5.72127	−	37.9113i	−0.0272441	−	0.180530i
$211$	116.823			0.553665			0.276833	−	0.960918i	$-0.410715\pi$
$211$	116.823			0.553665			0.276833	+	0.960918i	$0.410715\pi$
$212$	−129.465			−0.610685
$213$		−	187.868i		−	0.882008i
$214$	83.1689			0.388640
$215$			58.0991i			0.270229i
$216$		−	14.6969i		−	0.0680414i
$217$	−259.526	+	39.1655i	−1.19597	+	0.180486i
$218$	286.646			1.31489
$219$	−127.412			−0.581790
$220$		−	71.3865i		−	0.324484i
$221$	122.385			0.553777
$222$			149.504i			0.673443i
$223$			85.7012i			0.384310i	0.981365	+	0.192155i	$0.0615477\pi$
$223$			85.7012i			0.384310i	−0.981365	+	0.192155i	$0.938452\pi$
$224$	−5.90890	−	39.1546i	−0.0263790	−	0.174797i
$225$	15.0000			0.0666667
$226$	−239.028			−1.05765
$227$			113.389i			0.499513i	0.968309	+	0.249757i	$0.0803506\pi$
$227$			113.389i			0.499513i	−0.968309	+	0.249757i	$0.919649\pi$
$228$	101.814			0.446552
$229$			49.2031i			0.214861i	0.994213	+	0.107430i	$0.0342623\pi$
$229$			49.2031i			0.214861i	−0.994213	+	0.107430i	$0.965738\pi$
$230$		−	57.9998i		−	0.252173i
$231$	−191.368	+	28.8798i	−0.828434	+	0.125021i
$232$	150.729			0.649696
$233$	−115.412			−0.495329			−0.247665	−	0.968846i	$-0.579663\pi$
$233$	−115.412			−0.495329			−0.247665	+	0.968846i	$0.579663\pi$
$234$		−	26.3024i		−	0.112403i
$235$	−23.1253			−0.0984055
$236$		−	36.0437i		−	0.152728i
$237$			99.0567i			0.417961i
$238$	193.238	−	29.1619i	0.811922	−	0.122529i
$239$	152.491			0.638039			0.319020	−	0.947748i	$-0.396646\pi$
$239$	152.491			0.638039			0.319020	+	0.947748i	$0.396646\pi$
$240$	15.4919			0.0645497
$241$		−	415.112i		−	1.72245i	−0.508220	−	0.861227i	$-0.669696\pi$
$241$		−	415.112i		−	1.72245i	0.508220	−	0.861227i	$-0.330304\pi$
$242$	−189.224			−0.781918
$243$		−	15.5885i		−	0.0641500i
$244$		−	183.687i		−	0.752816i
$245$	−32.3337	−	104.688i	−0.131974	−	0.427297i
$246$	−52.2803			−0.212522
$247$	182.211			0.737698
$248$		−	106.052i		−	0.427627i
$249$	62.5967			0.251393
$250$			15.8114i			0.0632456i
$251$			274.805i			1.09484i	0.836858	+	0.547421i	$0.184390\pi$
$251$			274.805i			1.09484i	−0.836858	+	0.547421i	$0.815610\pi$
$252$	−6.26734	−	41.5298i	−0.0248704	−	0.164801i
$253$	−292.771			−1.15720
$254$	67.1993			0.264564
$255$			76.4564i			0.299829i
$256$	16.0000			0.0625000
$257$			65.7720i			0.255922i	0.991779	+	0.127961i	$0.0408433\pi$
$257$			65.7720i			0.255922i	−0.991779	+	0.127961i	$0.959157\pi$
$258$			63.6444i			0.246684i
$259$	63.7544	+	422.461i	0.246156	+	1.63112i
$260$	27.7252			0.106635
$261$	159.873			0.612539
$262$			19.5396i			0.0745787i
$263$	−154.046			−0.585728			−0.292864	−	0.956154i	$-0.594608\pi$
$263$	−154.046			−0.585728			−0.292864	+	0.956154i	$0.594608\pi$
$264$		−	78.2000i		−	0.296212i
$265$		−	144.746i		−	0.546213i
$266$	287.700	−	43.4174i	1.08158	−	0.163223i
$267$	−230.972			−0.865062
$268$	−36.4702			−0.136083
$269$			103.741i			0.385653i	0.981233	+	0.192827i	$0.0617655\pi$
$269$			103.741i			0.385653i	−0.981233	+	0.192827i	$0.938235\pi$
$270$	16.4317			0.0608581
$271$			53.1971i			0.196299i	0.995172	+	0.0981496i	$0.0312924\pi$
$271$			53.1971i			0.196299i	−0.995172	+	0.0981496i	$0.968708\pi$
$272$			78.9639i			0.290308i
$273$	−11.2164	−	74.3238i	−0.0410855	−	0.272248i
$274$	−160.345			−0.585202
$275$	79.8125			0.290227
$276$		−	63.5356i		−	0.230202i
$277$	226.731			0.818523			0.409261	−	0.912417i	$-0.365786\pi$
$277$	226.731			0.818523			0.409261	+	0.912417i	$0.365786\pi$
$278$		−	180.142i		−	0.647993i
$279$		−	112.485i		−	0.403171i
$280$	43.7762	−	6.60635i	0.156344	−	0.0235941i
$281$	−343.766			−1.22337			−0.611683	−	0.791103i	$-0.709507\pi$
$281$	−343.766			−1.22337			−0.611683	+	0.791103i	$0.709507\pi$
$282$	−25.3325			−0.0898315
$283$		−	130.649i		−	0.461659i	−0.972994	−	0.230829i	$-0.925856\pi$
$283$		−	130.649i		−	0.461659i	0.972994	−	0.230829i	$-0.0741439\pi$
$284$	216.931			0.763841
$285$			113.831i			0.399409i
$286$		−	139.951i		−	0.489338i
$287$	−147.731	+	22.2943i	−0.514741	+	0.0776806i
$288$	16.9706			0.0589256
$289$	−100.706			−0.348462
$290$			168.521i			0.581106i
$291$	50.7056			0.174246
$292$		−	147.123i		−	0.503845i
$293$		−	137.051i		−	0.467750i	−0.972267	−	0.233875i	$-0.924859\pi$
$293$		−	137.051i		−	0.467750i	0.972267	−	0.233875i	$-0.0751406\pi$
$294$	−35.4198	−	114.680i	−0.120475	−	0.390067i
$295$	40.2981			0.136604
$296$	−172.633			−0.583219
$297$		−	82.9436i		−	0.279271i
$298$	−328.382			−1.10195
$299$		−	113.707i		−	0.380290i
$300$			17.3205i			0.0577350i
$301$	27.1404	+	179.843i	0.0901675	+	0.597484i
$302$	158.038			0.523306
$303$	101.125			0.333745
$304$			117.565i			0.386726i
$305$	205.368			0.673339
$306$			83.7538i			0.273705i
$307$		−	137.544i		−	0.448026i	−0.974586	−	0.224013i	$-0.928084\pi$
$307$		−	137.544i		−	0.448026i	0.974586	−	0.224013i	$-0.0719158\pi$
$308$	−33.3475	−	220.973i	−0.108271	−	0.717445i
$309$	178.394			0.577325
$310$	118.569			0.382481
$311$			564.525i			1.81519i	0.419845	+	0.907596i	$0.362084\pi$
$311$			564.525i			1.81519i	−0.419845	+	0.907596i	$0.637916\pi$
$312$	30.3714			0.0973442
$313$			573.653i			1.83276i	0.400312	+	0.916379i	$0.368902\pi$
$313$			573.653i			1.83276i	−0.400312	+	0.916379i	$0.631098\pi$
$314$			374.251i			1.19188i
$315$	46.4317	−	7.00710i	0.147402	−	0.0222447i
$316$	−114.381			−0.361964
$317$	−64.7265			−0.204185			−0.102092	−	0.994775i	$-0.532554\pi$
$317$	−64.7265			−0.204185			−0.102092	+	0.994775i	$0.532554\pi$
$318$		−	158.562i		−	0.498622i
$319$	850.657			2.66664
$320$			17.8885i			0.0559017i
$321$			101.861i			0.317323i
$322$	−27.0940	−	179.535i	−0.0841430	−	0.557563i
$323$	−580.210			−1.79631
$324$	18.0000			0.0555556
$325$			30.9977i			0.0953775i
$326$	−75.5823			−0.231848
$327$			351.068i			1.07360i
$328$		−	60.3681i		−	0.184049i
$329$	−71.5830	+	10.8027i	−0.217578	+	0.0328351i
$330$	87.4303			0.264940
$331$	126.403			0.381883			0.190941	−	0.981601i	$-0.438846\pi$
$331$	126.403			0.381883			0.190941	+	0.981601i	$0.438846\pi$
$332$			72.2805i			0.217712i
$333$	−183.105			−0.549864
$334$		−	210.745i		−	0.630973i
$335$		−	40.7750i		−	0.121716i
$336$	47.9544	−	7.23690i	0.142722	−	0.0215384i
$337$	73.6716			0.218610			0.109305	−	0.994008i	$-0.465137\pi$
$337$	73.6716			0.218610			0.109305	+	0.994008i	$0.465137\pi$
$338$	−184.648			−0.546295
$339$		−	292.748i		−	0.863565i
$340$	−88.2843			−0.259660
$341$		−	598.512i		−	1.75517i
$342$			124.696i			0.364608i
$343$	−148.991	−	308.951i	−0.434376	−	0.900732i
$344$	−73.4902			−0.213634
$345$	71.0350			0.205899
$346$		−	52.2634i		−	0.151050i
$347$	553.102			1.59395			0.796977	−	0.604010i	$-0.206431\pi$
$347$	553.102			1.59395			0.796977	+	0.604010i	$0.206431\pi$
$348$			184.605i			0.530475i
$349$			372.885i			1.06844i	0.845346	+	0.534219i	$0.179394\pi$
$349$			372.885i			1.06844i	−0.845346	+	0.534219i	$0.820606\pi$
$350$	7.38613	+	48.9433i	0.0211032	+	0.139838i
$351$	32.2137			0.0917770
$352$	90.2976			0.256527
$353$			486.089i			1.37702i	0.725226	+	0.688511i	$0.241735\pi$
$353$			486.089i			1.37702i	−0.725226	+	0.688511i	$0.758265\pi$
$354$	44.1444			0.124702
$355$			242.536i			0.683200i
$356$		−	266.703i		−	0.749166i
$357$	35.7158	+	236.667i	0.100044	+	0.662932i
$358$	−167.557			−0.468037
$359$	309.378			0.861776			0.430888	−	0.902405i	$-0.358200\pi$
$359$	309.378			0.861776			0.430888	+	0.902405i	$0.358200\pi$
$360$			18.9737i			0.0527046i
$361$	−502.840			−1.39291
$362$		−	292.381i		−	0.807683i
$363$		−	231.751i		−	0.638433i
$364$	85.8217	−	12.9515i	0.235774	−	0.0355811i
$365$	164.488			0.450653
$366$	224.970			0.614672
$367$		−	440.140i		−	1.19929i	−0.800266	−	0.599645i	$-0.795308\pi$
$367$		−	440.140i		−	1.19929i	0.800266	−	0.599645i	$-0.204692\pi$
$368$	73.3646			0.199360
$369$		−	64.0300i		−	0.173523i
$370$		−	193.009i		−	0.521647i
$371$	−67.6168	−	448.055i	−0.182256	−	1.20769i
$372$	129.886			0.349156
$373$	−443.742			−1.18966			−0.594829	−	0.803852i	$-0.702780\pi$
$373$	−443.742			−1.18966			−0.594829	+	0.803852i	$0.702780\pi$
$374$			445.640i			1.19155i
$375$	−19.3649			−0.0516398
$376$		−	29.2514i		−	0.0777964i
$377$			330.379i			0.876337i
$378$	50.8634	−	7.67589i	0.134559	−	0.0203066i
$379$	−443.999			−1.17150			−0.585750	−	0.810492i	$-0.699200\pi$
$379$	−443.999			−1.17150			−0.585750	+	0.810492i	$0.699200\pi$
$380$	−131.441			−0.345898
$381$			82.3020i			0.216016i
$382$	−266.074			−0.696529
$383$			580.969i			1.51689i	0.651736	+	0.758446i	$0.274041\pi$
$383$			580.969i			1.51689i	−0.651736	+	0.758446i	$0.725959\pi$
$384$			19.5959i			0.0510310i
$385$	247.055	−	37.2836i	0.641702	−	0.0968405i
$386$	−14.4776			−0.0375067
$387$	−77.9482			−0.201416
$388$			58.5498i			0.150902i
$389$	−552.150			−1.41941			−0.709704	−	0.704500i	$-0.751171\pi$
$389$	−552.150			−1.41941			−0.709704	+	0.704500i	$0.751171\pi$
$390$			33.9563i			0.0870673i
$391$			362.072i			0.926016i
$392$	132.421	−	40.8992i	0.337808	−	0.104335i
$393$	−23.9310			−0.0608933
$394$	−309.473			−0.785466
$395$		−	127.882i		−	0.323751i
$396$	95.7750			0.241856
$397$		−	169.026i		−	0.425757i	−0.977079	−	0.212879i	$-0.931716\pi$
$397$		−	169.026i		−	0.425757i	0.977079	−	0.212879i	$-0.0682839\pi$
$398$		−	156.787i		−	0.393937i
$399$	53.1752	+	352.359i	0.133271	+	0.883105i
$400$	−20.0000			−0.0500000
$401$	57.9535			0.144522			0.0722612	−	0.997386i	$-0.476978\pi$
$401$	57.9535			0.144522			0.0722612	+	0.997386i	$0.476978\pi$
$402$		−	44.6667i		−	0.111111i
$403$	232.451			0.576801
$404$			116.769i			0.289032i
$405$			20.1246i			0.0496904i
$406$	78.7227	+	521.647i	0.193898	+	1.28484i
$407$	−974.270			−2.39378
$408$	−96.7106			−0.237036
$409$			436.098i			1.06625i	0.846035	+	0.533127i	$0.178983\pi$
$409$			436.098i			1.06625i	−0.846035	+	0.533127i	$0.821017\pi$
$410$	67.4936			0.164618
$411$		−	196.382i		−	0.477815i
$412$			205.991i			0.499978i
$413$	124.741	−	18.8248i	0.302035	−	0.0455807i
$414$	77.8150			0.187959
$415$	−80.8120			−0.194728
$416$			35.0699i			0.0843026i
$417$	220.628			0.529084
$418$			663.487i			1.58729i
$419$		−	831.867i		−	1.98536i	−0.120767	−	0.992681i	$-0.538536\pi$
$419$		−	831.867i		−	1.98536i	0.120767	−	0.992681i	$-0.461464\pi$
$420$	8.09110	+	53.6147i	0.0192645	+	0.127654i
$421$	38.1367			0.0905861			0.0452930	−	0.998974i	$-0.485578\pi$
$421$	38.1367			0.0905861			0.0452930	+	0.998974i	$0.485578\pi$
$422$	−165.213			−0.391501
$423$		−	31.0258i		−	0.0733471i
$424$	183.091			0.431819
$425$		−	98.7048i		−	0.232247i
$426$			265.685i			0.623674i
$427$	635.707	−	95.9358i	1.48877	−	0.224674i
$428$	−117.619			−0.274810
$429$	171.404			0.399543
$430$		−	82.1646i		−	0.191080i
$431$	−135.897			−0.315305			−0.157653	−	0.987495i	$-0.550393\pi$
$431$	−135.897			−0.315305			−0.157653	+	0.987495i	$0.550393\pi$
$432$			20.7846i			0.0481125i
$433$			133.395i			0.308072i	0.988065	+	0.154036i	$0.0492271\pi$
$433$			133.395i			0.308072i	−0.988065	+	0.154036i	$0.950773\pi$
$434$	367.025	−	55.3884i	0.845679	−	0.127623i
$435$	−206.395			−0.474471
$436$	−405.379			−0.929768
$437$			539.068i			1.23356i
$438$	180.188			0.411388
$439$			377.550i			0.860022i	0.902824	+	0.430011i	$0.141490\pi$
$439$			377.550i			0.860022i	−0.902824	+	0.430011i	$0.858510\pi$
$440$			100.956i			0.229445i
$441$	140.453	−	43.3802i	0.318488	−	0.0983677i
$442$	−173.078			−0.391580
$443$	−219.563			−0.495628			−0.247814	−	0.968808i	$-0.579712\pi$
$443$	−219.563			−0.495628			−0.247814	+	0.968808i	$0.579712\pi$
$444$		−	211.431i		−	0.476196i
$445$	298.183			0.670074
$446$		−	121.200i		−	0.271748i
$447$		−	402.184i		−	0.899740i
$448$	8.35645	+	55.3730i	0.0186528	+	0.123600i
$449$	110.769			0.246701			0.123350	−	0.992363i	$-0.460636\pi$
$449$	110.769			0.246701			0.123350	+	0.992363i	$0.460636\pi$
$450$	−21.2132			−0.0471405
$451$		−	340.693i		−	0.755417i
$452$	338.037			0.747869
$453$			193.557i			0.427278i
$454$		−	160.357i		−	0.353209i
$455$	14.4802	+	95.9516i	0.0318247	+	0.210883i
$456$	−143.987			−0.315760
$457$	570.254			1.24782			0.623911	−	0.781496i	$-0.285543\pi$
$457$	570.254			1.24782			0.623911	+	0.781496i	$0.285543\pi$
$458$		−	69.5837i		−	0.151929i
$459$	−102.577			−0.223479
$460$			82.0242i			0.178313i
$461$			293.487i			0.636631i	0.947985	+	0.318315i	$0.103117\pi$
$461$			293.487i			0.636631i	−0.947985	+	0.318315i	$0.896883\pi$
$462$	270.636	−	40.8421i	0.585791	−	0.0884029i
$463$	633.258			1.36773			0.683864	−	0.729609i	$-0.260298\pi$
$463$	633.258			1.36773			0.683864	+	0.729609i	$0.260298\pi$
$464$	−213.164			−0.459405
$465$			145.217i			0.312295i
$466$	163.217			0.350251
$467$		−	459.735i		−	0.984444i	−0.870470	−	0.492222i	$-0.836185\pi$
$467$		−	459.735i		−	0.984444i	0.870470	−	0.492222i	$-0.163815\pi$
$468$			37.1972i			0.0794812i
$469$	−19.0476	−	126.217i	−0.0406132	−	0.269119i
$470$	32.7041			0.0695832
$471$	−458.362			−0.973167
$472$			50.9735i			0.107995i
$473$	−414.749			−0.876849
$474$		−	140.087i		−	0.295543i
$475$		−	146.956i		−	0.309381i
$476$	−273.279	+	41.2411i	−0.574116	+	0.0866409i
$477$	194.198			0.407123
$478$	−215.655			−0.451162
$479$			232.289i			0.484945i	0.970158	+	0.242473i	$0.0779585\pi$
$479$			232.289i			0.484945i	−0.970158	+	0.242473i	$0.922042\pi$
$480$	−21.9089			−0.0456435
$481$		−	378.388i		−	0.786670i
$482$			587.056i			1.21796i
$483$	219.885	−	33.1833i	0.455248	−	0.0687024i
$484$	267.603			0.552899
$485$	−65.4606			−0.134970
$486$			22.0454i			0.0453609i
$487$	−304.948			−0.626176			−0.313088	−	0.949724i	$-0.601363\pi$
$487$	−304.948			−0.626176			−0.313088	+	0.949724i	$0.601363\pi$
$488$			259.773i			0.532321i
$489$		−	92.5690i		−	0.189303i
$490$	45.7267	+	148.051i	0.0933198	+	0.302145i
$491$	−666.975			−1.35840			−0.679201	−	0.733953i	$-0.737673\pi$
$491$	−666.975			−1.35840			−0.679201	+	0.733953i	$0.737673\pi$
$492$	73.9355			0.150275
$493$		−	1052.01i		−	2.13390i
$494$	−257.686			−0.521632
$495$			107.080i			0.216323i
$496$			149.980i			0.302378i
$497$	113.298	+	750.757i	0.227964	+	1.51058i
$498$	−88.5252			−0.177761
$499$	963.488			1.93084			0.965419	−	0.260705i	$-0.0839549\pi$
$499$	963.488			1.93084			0.965419	+	0.260705i	$0.0839549\pi$
$500$		−	22.3607i		−	0.0447214i
$501$	258.109			0.515187
$502$		−	388.633i		−	0.774170i
$503$		−	335.211i		−	0.666424i	−0.942852	−	0.333212i	$-0.891867\pi$
$503$		−	335.211i		−	0.666424i	0.942852	−	0.333212i	$-0.108133\pi$
$504$	8.86335	+	58.7319i	0.0175860	+	0.116532i
$505$	−130.551			−0.258518
$506$	414.041			0.818262
$507$		−	226.147i		−	0.446048i
$508$	−95.0342			−0.187075
$509$		−	906.823i		−	1.78158i	−0.454417	−	0.890789i	$-0.650152\pi$
$509$		−	906.823i		−	1.78158i	0.454417	−	0.890789i	$-0.349848\pi$
$510$		−	108.126i		−	0.212011i
$511$	509.164	−	76.8390i	0.996407	−	0.150370i
$512$	−22.6274			−0.0441942
$513$	−152.721			−0.297702
$514$		−	93.0157i		−	0.180964i
$515$	−230.305			−0.447194
$516$		−	90.0068i		−	0.174432i
$517$		−	165.083i		−	0.319310i
$518$	−90.1623	−	597.450i	−0.174059	−	1.15338i
$519$	64.0094			0.123332
$520$	−39.2093			−0.0754025
$521$		−	218.031i		−	0.418486i	−0.977864	−	0.209243i	$-0.932900\pi$
$521$		−	218.031i		−	0.418486i	0.977864	−	0.209243i	$-0.0670999\pi$
$522$	−226.094			−0.433131
$523$			239.568i			0.458066i	0.973419	+	0.229033i	$0.0735563\pi$
$523$			239.568i			0.458066i	−0.973419	+	0.229033i	$0.926444\pi$
$524$		−	27.6332i		−	0.0527351i
$525$	−59.9430	+	9.04612i	−0.114177	+	0.0172307i
$526$	217.855			0.414172
$527$	−740.185			−1.40453
$528$			110.591i			0.209454i
$529$	−192.602			−0.364087
$530$			204.702i			0.386231i
$531$			54.0656i			0.101818i
$532$	−406.869	+	61.4014i	−0.764792	+	0.115416i
$533$	132.319			0.248253
$534$	326.643			0.611691
$535$		−	131.502i		−	0.245797i
$536$	51.5767			0.0962252
$537$		−	205.215i		−	0.382151i
$538$		−	146.711i		−	0.272698i
$539$	747.330	−	230.819i	1.38651	−	0.428235i
$540$	−23.2379			−0.0430331
$541$	−228.274			−0.421949			−0.210974	−	0.977492i	$-0.567664\pi$
$541$	−228.274			−0.421949			−0.210974	+	0.977492i	$0.567664\pi$
$542$		−	75.2320i		−	0.138804i
$543$	358.092			0.659470
$544$		−	111.672i		−	0.205279i
$545$		−	453.227i		−	0.831609i
$546$	15.8623	+	105.110i	0.0290519	+	0.192509i
$547$	−898.348			−1.64232			−0.821159	−	0.570699i	$-0.806672\pi$
$547$	−898.348			−1.64232			−0.821159	+	0.570699i	$0.806672\pi$
$548$	226.762			0.413800
$549$			275.531i			0.501877i
$550$	−112.872			−0.205222
$551$		−	1566.28i		−	2.84262i
$552$			89.8530i			0.162777i
$553$	−59.7386	−	395.850i	−0.108026	−	0.715824i
$554$	−320.646			−0.578783
$555$	236.387			0.425923
$556$			254.759i			0.458200i
$557$	185.202			0.332500			0.166250	−	0.986084i	$-0.446834\pi$
$557$	185.202			0.332500			0.166250	+	0.986084i	$0.446834\pi$
$558$			159.077i			0.285085i
$559$		−	161.081i		−	0.288159i
$560$	−61.9089	+	9.34279i	−0.110552	+	0.0166836i
$561$	−545.796			−0.972898
$562$	486.159			0.865051
$563$			42.3604i			0.0752405i	0.999292	+	0.0376203i	$0.0119777\pi$
$563$			42.3604i			0.0752405i	−0.999292	+	0.0376203i	$0.988022\pi$
$564$	35.8255			0.0635205
$565$			377.937i			0.668914i
$566$			184.766i			0.326442i
$567$	9.40101	+	62.2946i	0.0165803	+	0.109867i
$568$	−306.787			−0.540117
$569$	−339.139			−0.596027			−0.298013	−	0.954562i	$-0.596324\pi$
$569$	−339.139			−0.596027			−0.298013	+	0.954562i	$0.596324\pi$
$570$		−	160.982i		−	0.282425i
$571$	922.951			1.61638			0.808188	−	0.588924i	$-0.200448\pi$
$571$	922.951			1.61638			0.808188	+	0.588924i	$0.200448\pi$
$572$			197.920i			0.346014i
$573$		−	325.873i		−	0.568714i
$574$	208.923	−	31.5289i	0.363977	−	0.0549285i
$575$	−91.7058			−0.159488
$576$	−24.0000			−0.0416667
$577$		−	606.088i		−	1.05041i	−0.850975	−	0.525206i	$-0.823988\pi$
$577$		−	606.088i		−	1.05041i	0.850975	−	0.525206i	$-0.176012\pi$
$578$	142.419			0.246400
$579$		−	17.7314i		−	0.0306241i
$580$		−	238.324i		−	0.410904i
$581$	−250.149	+	37.7505i	−0.430549	+	0.0649751i
$582$	−71.7085			−0.123211
$583$	1033.29			1.77237
$584$			208.063i			0.356272i
$585$	−41.5878			−0.0710902
$586$			193.819i			0.330749i
$587$		−	210.428i		−	0.358481i	−0.983805	−	0.179240i	$-0.942636\pi$
$587$		−	210.428i		−	0.358481i	0.983805	−	0.179240i	$-0.0573640\pi$
$588$	50.0911	+	162.182i	0.0851889	+	0.275819i
$589$	−1102.02			−1.87100
$590$	−56.9901			−0.0965934
$591$		−	379.026i		−	0.641330i
$592$	244.140			0.412398
$593$			520.732i			0.878132i	0.898455	+	0.439066i	$0.144691\pi$
$593$			520.732i			0.878132i	−0.898455	+	0.439066i	$0.855309\pi$
$594$			117.300i			0.197475i
$595$	−46.1089	−	305.535i	−0.0774940	−	0.513505i
$596$	464.402			0.779197
$597$	192.024			0.321648
$598$			160.806i			0.268906i
$599$	−336.725			−0.562145			−0.281073	−	0.959686i	$-0.590690\pi$
$599$	−336.725			−0.562145			−0.281073	+	0.959686i	$0.590690\pi$
$600$		−	24.4949i		−	0.0408248i
$601$			992.938i			1.65214i	0.563566	+	0.826071i	$0.309429\pi$
$601$			992.938i			1.65214i	−0.563566	+	0.826071i	$0.690571\pi$
$602$	−38.3823	−	254.336i	−0.0637581	−	0.422485i
$603$	54.7053			0.0907220
$604$	−223.500			−0.370033
$605$			299.190i			0.494528i
$606$	−143.012			−0.235993
$607$			678.834i			1.11834i	0.829052	+	0.559171i	$0.188881\pi$
$607$			678.834i			1.11834i	−0.829052	+	0.559171i	$0.811119\pi$
$608$		−	166.261i		−	0.273456i
$609$	−638.884	+	96.4152i	−1.04907	+	0.158317i
$610$	−290.435			−0.476123
$611$	64.1152			0.104935
$612$		−	118.446i		−	0.193539i
$613$	212.334			0.346385			0.173193	−	0.984888i	$-0.444592\pi$
$613$	212.334			0.346385			0.173193	+	0.984888i	$0.444592\pi$
$614$			194.517i			0.316802i
$615$			82.6624i			0.134410i
$616$	47.1604	+	312.503i	0.0765592	+	0.507310i
$617$	283.176			0.458957			0.229478	−	0.973314i	$-0.426298\pi$
$617$	283.176			0.458957			0.229478	+	0.973314i	$0.426298\pi$
$618$	−252.287			−0.408231
$619$		−	502.207i		−	0.811320i	−0.914024	−	0.405660i	$-0.867042\pi$
$619$		−	502.207i		−	0.811320i	0.914024	−	0.405660i	$-0.132958\pi$
$620$	−167.682			−0.270455
$621$			95.3035i			0.153468i
$622$		−	798.358i		−	1.28353i
$623$	923.009	−	139.293i	1.48156	−	0.223585i
$624$	−42.9516			−0.0688328
$625$	25.0000			0.0400000
$626$		−	811.268i		−	1.29596i
$627$	−812.603			−1.29602
$628$		−	529.270i		−	0.842787i
$629$			1204.89i			1.91556i
$630$	−65.6643	+	9.90953i	−0.104229	+	0.0157294i
$631$	−246.851			−0.391206			−0.195603	−	0.980683i	$-0.562666\pi$
$631$	−246.851			−0.391206			−0.195603	+	0.980683i	$0.562666\pi$
$632$	161.759			0.255948
$633$		−	202.344i		−	0.319659i
$634$	91.5371			0.144380
$635$		−	106.251i		−	0.167325i
$636$			224.240i			0.352579i
$637$	89.6456	+	290.249i	0.140731	+	0.455649i
$638$	−1203.01			−1.88560
$639$	−325.396			−0.509227
$640$		−	25.2982i		−	0.0395285i
$641$	366.399			0.571606			0.285803	−	0.958288i	$-0.407740\pi$
$641$	366.399			0.571606			0.285803	+	0.958288i	$0.407740\pi$
$642$		−	144.053i		−	0.224381i
$643$		−	529.036i		−	0.822763i	−0.911463	−	0.411381i	$-0.865046\pi$
$643$		−	529.036i		−	0.822763i	0.911463	−	0.411381i	$-0.134954\pi$
$644$	38.3167	+	253.901i	0.0594981	+	0.394257i
$645$	100.631			0.156017
$646$	820.540			1.27019
$647$		−	361.039i		−	0.558020i	−0.960288	−	0.279010i	$-0.909994\pi$
$647$		−	361.039i		−	0.558020i	0.960288	−	0.279010i	$-0.0900062\pi$
$648$	−25.4558			−0.0392837
$649$			287.674i			0.443257i
$650$		−	43.8373i		−	0.0674421i
$651$	67.8367	+	449.512i	0.104204	+	0.690494i
$652$	106.890			0.163941
$653$	1216.58			1.86306			0.931532	−	0.363658i	$-0.118472\pi$
$653$	1216.58			1.86306			0.931532	+	0.363658i	$0.118472\pi$
$654$		−	496.485i		−	0.759152i
$655$	30.8949			0.0471677
$656$			85.3734i			0.130142i
$657$			220.684i			0.335897i
$658$	101.234	−	15.2774i	0.153851	−	0.0232179i
$659$	331.022			0.502310			0.251155	−	0.967947i	$-0.419190\pi$
$659$	331.022			0.502310			0.251155	+	0.967947i	$0.419190\pi$
$660$	−123.645			−0.187341
$661$			970.308i			1.46794i	0.679182	+	0.733970i	$0.262335\pi$
$661$			970.308i			1.46794i	−0.679182	+	0.733970i	$0.737665\pi$
$662$	−178.761			−0.270032
$663$		−	211.977i		−	0.319724i
$664$		−	102.220i		−	0.153946i
$665$	−68.6489	−	454.893i	−0.103231	−	0.684050i
$666$	258.949			0.388813
$667$	−977.417			−1.46539
$668$			298.038i			0.446165i
$669$	148.439			0.221882
$670$			57.6645i			0.0860664i
$671$			1466.05i			2.18488i
$672$	−67.8178	+	10.2345i	−0.100919	+	0.0152299i
$673$	886.937			1.31789			0.658943	−	0.752193i	$-0.271004\pi$
$673$	886.937			1.31789			0.658943	+	0.752193i	$0.271004\pi$
$674$	−104.187			−0.154581
$675$		−	25.9808i		−	0.0384900i
$676$	261.132			0.386289
$677$		−	13.9949i		−	0.0206720i	−0.999947	−	0.0103360i	$-0.996710\pi$
$677$		−	13.9949i		−	0.0206720i	0.999947	−	0.0103360i	$-0.00329010\pi$
$678$			414.009i			0.610633i
$679$	−202.630	+	30.5793i	−0.298424	+	0.0450357i
$680$	124.853			0.183607
$681$	196.396			0.288394
$682$			846.424i			1.24109i
$683$	1080.03			1.58130			0.790651	−	0.612267i	$-0.209742\pi$
$683$	1080.03			1.58130			0.790651	+	0.612267i	$0.209742\pi$
$684$		−	176.347i		−	0.257817i
$685$			253.528i			0.370114i
$686$	210.705	+	436.923i	0.307150	+	0.636914i
$687$	85.2223			0.124050
$688$	103.931			0.151062
$689$			401.312i			0.582456i
$690$	−100.459			−0.145592
$691$		−	810.183i		−	1.17248i	−0.810138	−	0.586240i	$-0.800608\pi$
$691$		−	810.183i		−	1.17248i	0.810138	−	0.586240i	$-0.199392\pi$
$692$			73.9117i			0.106809i
$693$	50.0212	+	331.459i	0.0721807	+	0.478297i
$694$	−782.204			−1.12710
$695$	−284.829			−0.409827
$696$		−	261.071i		−	0.375102i
$697$	−421.338			−0.604502
$698$		−	527.339i		−	0.755500i
$699$			199.899i			0.285978i
$700$	−10.4456	−	69.2163i	−0.0149222	−	0.0988804i
$701$	588.867			0.840039			0.420019	−	0.907515i	$-0.362023\pi$
$701$	588.867			0.840039			0.420019	+	0.907515i	$0.362023\pi$
$702$	−45.5571			−0.0648962
$703$			1793.89i			2.55176i
$704$	−127.700			−0.181392
$705$			40.0542i			0.0568144i
$706$		−	687.433i		−	0.973701i
$707$	−404.115	+	60.9858i	−0.571591	+	0.0862599i
$708$	−62.4295			−0.0881773
$709$	−1141.19			−1.60958			−0.804789	−	0.593561i	$-0.797722\pi$
$709$	−1141.19			−1.60958			−0.804789	+	0.593561i	$0.797722\pi$
$710$		−	342.998i		−	0.483096i
$711$	171.571			0.241310
$712$			377.175i			0.529740i
$713$			687.700i			0.964516i
$714$	−50.5098	−	334.697i	−0.0707420	−	0.468764i
$715$	−221.282			−0.309485
$716$	236.962			0.330952
$717$		−	264.123i		−	0.368372i
$718$	−437.526			−0.609368
$719$			28.4620i			0.0395856i	0.999804	+	0.0197928i	$0.00630065\pi$
$719$			28.4620i			0.0395856i	−0.999804	+	0.0197928i	$0.993699\pi$
$720$		−	26.8328i		−	0.0372678i
$721$	−712.897	+	107.585i	−0.988761	+	0.149216i
$722$	711.123			0.984935
$723$	−718.994			−0.994460
$724$			413.489i			0.571118i
$725$	266.455			0.367524
$726$			327.746i			0.451440i
$727$			821.139i			1.12949i	0.825266	+	0.564745i	$0.191025\pi$
$727$			821.139i			1.12949i	−0.825266	+	0.564745i	$0.808975\pi$
$728$	−121.370	+	18.3162i	−0.166717	+	0.0251597i
$729$	−27.0000			−0.0370370
$730$	−232.621			−0.318660
$731$			512.924i			0.701674i
$732$	−318.155			−0.434639
$733$			1135.68i			1.54936i	0.632353	+	0.774680i	$0.282089\pi$
$733$			1135.68i			1.54936i	−0.632353	+	0.774680i	$0.717911\pi$
$734$			622.451i			0.848026i
$735$	−181.325	+	56.0035i	−0.246700	+	0.0761953i
$736$	−103.753			−0.140969
$737$	291.078			0.394950
$738$			90.5521i			0.122699i
$739$	449.526			0.608289			0.304145	−	0.952626i	$-0.401629\pi$
$739$	449.526			0.608289			0.304145	+	0.952626i	$0.401629\pi$
$740$			272.956i			0.368860i
$741$		−	315.600i		−	0.425910i
$742$	95.6246	+	633.645i	0.128874	+	0.853969i
$743$	27.5435			0.0370707			0.0185353	−	0.999828i	$-0.494100\pi$
$743$	27.5435			0.0370707			0.0185353	+	0.999828i	$0.494100\pi$
$744$	−183.687			−0.246891
$745$			519.217i			0.696935i
$746$	627.547			0.841215
$747$		−	108.421i		−	0.145142i
$748$		−	630.231i		−	0.842554i
$749$	−61.4296	−	407.056i	−0.0820155	−	0.543466i
$750$	27.3861			0.0365148
$751$	−1424.00			−1.89614			−0.948070	−	0.318062i	$-0.896968\pi$
$751$	−1424.00			−1.89614			−0.948070	+	0.318062i	$0.896968\pi$
$752$			41.3678i			0.0550103i
$753$	475.976			0.632107
$754$		−	467.226i		−	0.619664i
$755$		−	249.881i		−	0.330968i
$756$	−71.9316	+	10.8553i	−0.0951477	+	0.0143589i
$757$	47.2357			0.0623985			0.0311992	−	0.999513i	$-0.490067\pi$
$757$	47.2357			0.0623985			0.0311992	+	0.999513i	$0.490067\pi$
$758$	627.909			0.828376
$759$			507.094i			0.668108i
$760$	185.886			0.244587
$761$		−	64.6316i		−	0.0849299i	−0.999098	−	0.0424649i	$-0.986479\pi$
$761$		−	64.6316i		−	0.0849299i	0.999098	−	0.0424649i	$-0.0135211\pi$
$762$		−	116.393i		−	0.152746i
$763$	−211.720	−	1402.94i	−0.277484	−	1.83872i
$764$	376.286			0.492520
$765$	132.426			0.173106
$766$		−	821.615i		−	1.07260i
$767$	−111.727			−0.145668
$768$		−	27.7128i		−	0.0360844i
$769$		−	931.435i		−	1.21123i	−0.795758	−	0.605615i	$-0.792927\pi$
$769$		−	931.435i		−	1.21123i	0.795758	−	0.605615i	$-0.207073\pi$
$770$	−349.389	+	52.7270i	−0.453752	+	0.0684766i
$771$	113.920			0.147757
$772$	20.4744			0.0265213
$773$			1232.95i			1.59501i	0.603309	+	0.797507i	$0.293848\pi$
$773$			1232.95i			1.59501i	−0.603309	+	0.797507i	$0.706152\pi$
$774$	110.235			0.142423
$775$		−	187.474i		−	0.241903i
$776$		−	82.8019i		−	0.106703i
$777$	731.724	−	110.426i	0.941729	−	0.142118i
$778$	780.858			1.00367
$779$	−627.305			−0.805270
$780$		−	48.0214i		−	0.0615659i
$781$	−1731.38			−2.21688
$782$		−	512.047i		−	0.654792i
$783$		−	276.908i		−	0.353650i
$784$	−187.271	+	57.8402i	−0.238866	+	0.0737758i
$785$	591.742			0.753812
$786$	33.8436			0.0430580
$787$		−	545.472i		−	0.693103i	−0.938031	−	0.346552i	$-0.887353\pi$
$787$		−	545.472i		−	0.693103i	0.938031	−	0.346552i	$-0.112647\pi$
$788$	437.662			0.555408
$789$			266.816i			0.338170i
$790$			180.852i			0.228926i
$791$	176.549	+	1169.88i	0.223198	+	1.47899i
$792$	−135.446			−0.171018
$793$	−569.387			−0.718017
$794$			239.038i			0.301056i
$795$	−250.708			−0.315356
$796$			221.730i			0.278556i
$797$			46.3471i			0.0581519i	0.999577	+	0.0290759i	$0.00925646\pi$
$797$			46.3471i			0.0581519i	−0.999577	+	0.0290759i	$0.990744\pi$
$798$	−75.2011	−	498.311i	−0.0942369	−	0.624450i
$799$	−204.160			−0.255519
$800$	28.2843			0.0353553
$801$			400.055i			0.499444i
$802$	−81.9586			−0.102193
$803$			1174.22i			1.46230i
$804$			63.1683i			0.0785675i
$805$	−283.870	+	42.8394i	−0.352634	+	0.0532167i
$806$	−328.735			−0.407860
$807$	179.684			0.222657
$808$		−	165.136i		−	0.204376i
$809$	−996.788			−1.23212			−0.616062	−	0.787698i	$-0.711273\pi$
$809$	−996.788			−1.23212			−0.616062	+	0.787698i	$0.711273\pi$
$810$		−	28.4605i		−	0.0351364i
$811$		−	524.649i		−	0.646917i	−0.946242	−	0.323458i	$-0.895154\pi$
$811$		−	524.649i		−	0.646917i	0.946242	−	0.323458i	$-0.104846\pi$
$812$	−111.331	−	737.720i	−0.137107	−	0.908522i
$813$	92.1400			0.113333
$814$	1377.83			1.69266
$815$			119.506i			0.146633i
$816$	136.769			0.167610
$817$			763.662i			0.934715i
$818$		−	616.735i		−	0.753955i
$819$	−128.733	+	19.4273i	−0.157183	+	0.0237207i
$820$	−95.4503			−0.116403
$821$	89.8739			0.109469			0.0547344	−	0.998501i	$-0.482569\pi$
$821$	89.8739			0.109469			0.0547344	+	0.998501i	$0.482569\pi$
$822$			277.726i			0.337866i
$823$	−601.322			−0.730647			−0.365323	−	0.930881i	$-0.619042\pi$
$823$	−601.322			−0.730647			−0.365323	+	0.930881i	$0.619042\pi$
$824$		−	291.315i		−	0.353538i
$825$		−	138.239i		−	0.167563i
$826$	−176.410	+	26.6223i	−0.213571	+	0.0322304i
$827$	742.670			0.898029			0.449014	−	0.893525i	$-0.351775\pi$
$827$	742.670			0.898029			0.449014	+	0.893525i	$0.351775\pi$
$828$	−110.047			−0.132907
$829$		−	1323.55i		−	1.59657i	−0.602282	−	0.798283i	$-0.705742\pi$
$829$		−	1323.55i		−	1.59657i	0.602282	−	0.798283i	$-0.294258\pi$
$830$	114.285			0.137693
$831$		−	392.709i		−	0.472574i
$832$		−	49.5963i		−	0.0596109i
$833$	−285.455	−	924.229i	−0.342684	−	1.10952i
$834$	−312.015			−0.374119
$835$	−333.217			−0.399062
$836$		−	938.313i		−	1.12238i
$837$	−194.829			−0.232771
$838$			1176.44i			1.40386i
$839$		−	206.287i		−	0.245872i	−0.992415	−	0.122936i	$-0.960769\pi$
$839$		−	206.287i		−	0.245872i	0.992415	−	0.122936i	$-0.0392310\pi$
$840$	−11.4425	−	75.8226i	−0.0136221	−	0.0902650i
$841$	1998.92			2.37684
$842$	−53.9335			−0.0640540
$843$			595.420i			0.706311i
$844$	233.647			0.276833
$845$			291.954i			0.345508i
$846$			43.8771i			0.0518642i
$847$	139.763	+	926.125i	0.165010	+	1.09342i
$848$	−258.930			−0.305342
$849$	−226.291			−0.266539
$850$			139.590i			0.164223i
$851$	1119.45			1.31545
$852$		−	375.735i		−	0.441004i
$853$		−	1220.74i		−	1.43112i	−0.698554	−	0.715558i	$-0.746173\pi$
$853$		−	1220.74i		−	1.43112i	0.698554	−	0.715558i	$-0.253827\pi$
$854$	−899.025	+	135.674i	−1.05272	+	0.158868i
$855$	197.162			0.230599
$856$	166.338			0.194320
$857$		−	1031.50i		−	1.20362i	−0.798641	−	0.601808i	$-0.794447\pi$
$857$		−	1031.50i		−	1.20362i	0.798641	−	0.601808i	$-0.205553\pi$
$858$	−242.402			−0.282520
$859$		−	263.066i		−	0.306247i	−0.988207	−	0.153124i	$-0.951067\pi$
$859$		−	263.066i		−	0.306247i	0.988207	−	0.153124i	$-0.0489333\pi$
$860$			116.198i			0.135114i
$861$	38.6149	+	255.877i	0.0448489	+	0.297186i
$862$	192.187			0.222954
$863$	811.835			0.940713			0.470356	−	0.882477i	$-0.344125\pi$
$863$	811.835			0.940713			0.470356	+	0.882477i	$0.344125\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	−82.6357			−0.0955326
$866$		−	188.649i		−	0.217840i
$867$			174.427i			0.201185i
$868$	−519.051	+	78.3310i	−0.597985	+	0.0902431i
$869$	912.902			1.05052
$870$	291.886			0.335502
$871$			113.049i			0.129792i
$872$	573.292			0.657445
$873$		−	87.8247i		−	0.100601i
$874$		−	762.357i		−	0.872262i
$875$	77.3861	−	11.6785i	0.0884413	−	0.0133468i
$876$	−254.824			−0.290895
$877$	1294.40			1.47595			0.737973	−	0.674830i	$-0.235783\pi$
$877$	1294.40			1.47595			0.737973	+	0.674830i	$0.235783\pi$
$878$		−	533.936i		−	0.608127i
$879$	−237.379			−0.270055
$880$		−	142.773i		−	0.162242i
$881$		−	1592.39i		−	1.80748i	−0.428084	−	0.903739i	$-0.640811\pi$
$881$		−	1592.39i		−	1.80748i	0.428084	−	0.903739i	$-0.359189\pi$
$882$	−198.631	+	61.3488i	−0.225205	+	0.0695565i
$883$	760.044			0.860752			0.430376	−	0.902650i	$-0.358381\pi$
$883$	760.044			0.860752			0.430376	+	0.902650i	$0.358381\pi$
$884$	244.770			0.276889
$885$		−	69.7984i		−	0.0788682i
$886$	310.509			0.350462
$887$		−	219.050i		−	0.246956i	−0.992347	−	0.123478i	$-0.960595\pi$
$887$		−	219.050i		−	0.246956i	0.992347	−	0.123478i	$-0.0394049\pi$
$888$			299.009i			0.336722i
$889$	−49.6343	−	328.896i	−0.0558316	−	0.369961i
$890$	−421.695			−0.473814
$891$	−143.663			−0.161237
$892$			171.402i			0.192155i
$893$	−303.962			−0.340383
$894$			568.774i			0.636212i
$895$			264.932i			0.296013i
$896$	−11.8178	−	78.3093i	−0.0131895	−	0.0873987i
$897$	−196.946			−0.219560
$898$	−156.651			−0.174444
$899$		−	1998.14i		−	2.22262i
$900$	30.0000			0.0333333
$901$		−	1277.88i		−	1.41829i
$902$			481.813i			0.534161i
$903$	311.497	−	47.0086i	0.344958	−	0.0520582i
$904$	−478.056			−0.528823
$905$	−462.295			−0.510823
$906$		−	273.731i		−	0.302131i
$907$	−41.6200			−0.0458875			−0.0229438	−	0.999737i	$-0.507304\pi$
$907$	−41.6200			−0.0458875			−0.0229438	+	0.999737i	$0.507304\pi$
$908$			226.779i			0.249757i
$909$		−	175.153i		−	0.192688i
$910$	−20.4782	−	135.696i	−0.0225035	−	0.149117i
$911$	−522.703			−0.573769			−0.286884	−	0.957965i	$-0.592620\pi$
$911$	−522.703			−0.573769			−0.286884	+	0.957965i	$0.592620\pi$
$912$	203.628			0.223276
$913$		−	576.889i		−	0.631861i
$914$	−806.461			−0.882343
$915$		−	355.709i		−	0.388753i
$916$			98.4062i			0.107430i
$917$	95.6333	−	14.4322i	0.104289	−	0.0157385i
$918$	145.066			0.158024
$919$	−1356.85			−1.47644			−0.738222	−	0.674557i	$-0.764334\pi$
$919$	−1356.85			−1.47644			−0.738222	+	0.674557i	$0.764334\pi$
$920$		−	116.000i		−	0.126087i
$921$	−238.233			−0.258668
$922$		−	415.053i		−	0.450166i
$923$		−	672.435i		−	0.728532i
$924$	−382.736	+	57.7595i	−0.414217	+	0.0625103i
$925$	−305.175			−0.329918
$926$	−895.562			−0.967130
$927$		−	308.987i		−	0.333319i
$928$	301.459			0.324848
$929$			274.165i			0.295118i	0.989053	+	0.147559i	$0.0471416\pi$
$929$			274.165i			0.295118i	−0.989053	+	0.147559i	$0.952858\pi$
$930$		−	205.368i		−	0.220826i
$931$	−424.998	−	1376.03i	−0.456496	−	1.47801i
$932$	−230.823			−0.247665
$933$	977.785			1.04800
$934$			650.164i			0.696107i
$935$	704.619			0.753603
$936$		−	52.6048i		−	0.0562017i
$937$			938.107i			1.00118i	0.865684	+	0.500591i	$0.166884\pi$
$937$			938.107i			1.00118i	−0.865684	+	0.500591i	$0.833116\pi$
$938$	26.9374	+	178.497i	0.0287179	+	0.190296i
$939$	993.596			1.05814
$940$	−46.2506			−0.0492027
$941$			595.662i			0.633010i	0.948591	+	0.316505i	$0.102509\pi$
$941$			595.662i			0.633010i	−0.948591	+	0.316505i	$0.897491\pi$
$942$	648.221			0.688133
$943$			391.462i			0.415124i
$944$		−	72.0874i		−	0.0763638i
$945$	−12.1366	−	80.4220i	−0.0128430	−	0.0851027i
$946$	586.544			0.620026
$947$	−114.789			−0.121213			−0.0606067	−	0.998162i	$-0.519304\pi$
$947$	−114.789			−0.121213			−0.0606067	+	0.998162i	$0.519304\pi$
$948$			198.113i			0.208980i
$949$	−456.046			−0.480555
$950$			207.827i			0.218765i
$951$			112.110i			0.117886i
$952$	386.475	−	58.3237i	0.405961	−	0.0612644i
$953$	349.928			0.367186			0.183593	−	0.983002i	$-0.441227\pi$
$953$	349.928			0.367186			0.183593	+	0.983002i	$0.441227\pi$
$954$	−274.637			−0.287879
$955$			420.700i			0.440524i
$956$	304.983			0.319020
$957$		−	1473.38i		−	1.53958i
$958$		−	328.506i		−	0.342908i
$959$	118.433	+	784.782i	0.123496	+	0.818334i
$960$	30.9839			0.0322749
$961$	−444.867			−0.462921
$962$			535.122i			0.556259i
$963$	176.428			0.183206
$964$		−	830.223i		−	0.861227i
$965$			22.8911i			0.0237213i
$966$	−310.964	+	46.9282i	−0.321909	+	0.0485800i
$967$	246.460			0.254871			0.127436	−	0.991847i	$-0.459325\pi$
$967$	246.460			0.254871			0.127436	+	0.991847i	$0.459325\pi$
$968$	−378.448			−0.390959
$969$			1004.95i			1.03710i
$970$	92.5753			0.0954385
$971$			1064.63i			1.09642i	0.836339	+	0.548212i	$0.184691\pi$
$971$			1064.63i			1.09642i	−0.836339	+	0.548212i	$0.815309\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	−881.674	+	133.055i	−0.906140	+	0.136747i
$974$	431.261			0.442773
$975$	53.6896			0.0550662
$976$		−	367.374i		−	0.376408i
$977$	344.273			0.352377			0.176189	−	0.984356i	$-0.443623\pi$
$977$	344.273			0.352377			0.176189	+	0.984356i	$0.443623\pi$
$978$			130.912i			0.133857i
$979$			2128.62i			2.17428i
$980$	−64.6673	−	209.376i	−0.0659871	−	0.213649i
$981$	608.068			0.619845
$982$	943.245			0.960535
$983$			25.5898i			0.0260324i	0.999915	+	0.0130162i	$0.00414329\pi$
$983$			25.5898i			0.0260324i	−0.999915	+	0.0130162i	$0.995857\pi$
$984$	−104.561			−0.106261
$985$			489.320i			0.496772i
$986$			1487.77i			1.50890i
$987$	18.7109	+	123.985i	0.0189573	+	0.125619i
$988$	364.423			0.368849
$989$	476.553			0.481854
$990$		−	151.434i		−	0.152963i
$991$	406.270			0.409960			0.204980	−	0.978766i	$-0.434287\pi$
$991$	406.270			0.409960			0.204980	+	0.978766i	$0.434287\pi$
$992$		−	212.103i		−	0.213814i
$993$		−	218.937i		−	0.220480i
$994$	−160.228	−	1061.73i	−0.161195	−	1.06814i
$995$	−247.902			−0.249148
$996$	125.193			0.125696
$997$		−	557.561i		−	0.559239i	−0.960111	−	0.279620i	$-0.909792\pi$
$997$		−	557.561i		−	0.559239i	0.960111	−	0.279620i	$-0.0902083\pi$
$998$	−1362.58			−1.36531
$999$			317.147i			0.317464i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.f.a.181.2	✓	8
3.2	odd	2		630.3.f.c.181.6		8
4.3	odd	2		1680.3.s.a.1441.8		8
5.2	odd	4		1050.3.h.b.349.1		16
5.3	odd	4		1050.3.h.b.349.16		16
5.4	even	2		1050.3.f.b.601.7		8
7.6	odd	2	inner	210.3.f.a.181.3	yes	8
21.20	even	2		630.3.f.c.181.8		8
28.27	even	2		1680.3.s.a.1441.2		8
35.13	even	4		1050.3.h.b.349.9		16
35.27	even	4		1050.3.h.b.349.8		16
35.34	odd	2		1050.3.f.b.601.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.f.a.181.2	✓	8	1.1	even	1	trivial
210.3.f.a.181.3	yes	8	7.6	odd	2	inner
630.3.f.c.181.6		8	3.2	odd	2
630.3.f.c.181.8		8	21.20	even	2
1050.3.f.b.601.5		8	35.34	odd	2
1050.3.f.b.601.7		8	5.4	even	2
1050.3.h.b.349.1		16	5.2	odd	4
1050.3.h.b.349.8		16	35.27	even	4
1050.3.h.b.349.9		16	35.13	even	4
1050.3.h.b.349.16		16	5.3	odd	4
1680.3.s.a.1441.2		8	28.27	even	2
1680.3.s.a.1441.8		8	4.3	odd	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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} +2.23607i q^{5} +2.44949i q^{6} +(1.04456 + 6.92163i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} +2.23607i q^{5} +2.44949i q^{6} +(1.04456 + 6.92163i) q^{7} -2.82843 q^{8} -3.00000 q^{9} -3.16228i q^{10} -15.9625 q^{11} -3.46410i q^{12} -6.19954i q^{13} +(-1.47723 - 9.78866i) q^{14} +3.87298 q^{15} +4.00000 q^{16} +19.7410i q^{17} +4.24264 q^{18} +29.3912i q^{19} +4.47214i q^{20} +(11.9886 - 1.80922i) q^{21} +22.5744 q^{22} +18.3412 q^{23} +4.89898i q^{24} -5.00000 q^{25} +8.76747i q^{26} +5.19615i q^{27} +(2.08911 + 13.8433i) q^{28} -53.2909 q^{29} -5.47723 q^{30} +37.4949i q^{31} -5.65685 q^{32} +27.6479i q^{33} -27.9179i q^{34} +(-15.4772 + 2.33570i) q^{35} -6.00000 q^{36} +61.0349 q^{37} -41.5654i q^{38} -10.7379 q^{39} -6.32456i q^{40} +21.3433i q^{41} +(-16.9545 + 2.55863i) q^{42} +25.9827 q^{43} -31.9250 q^{44} -6.70820i q^{45} -25.9383 q^{46} +10.3419i q^{47} -6.92820i q^{48} +(-46.8178 + 14.4601i) q^{49} +7.07107 q^{50} +34.1924 q^{51} -12.3991i q^{52} -64.7326 q^{53} -7.34847i q^{54} -35.6933i q^{55} +(-2.95445 - 19.5773i) q^{56} +50.9070 q^{57} +75.3647 q^{58} -18.0219i q^{59} +7.74597 q^{60} -91.8436i q^{61} -53.0258i q^{62} +(-3.13367 - 20.7649i) q^{63} +8.00000 q^{64} +13.8626 q^{65} -39.1000i q^{66} -18.2351 q^{67} +39.4819i q^{68} -31.7678i q^{69} +(21.8881 - 3.30318i) q^{70} +108.465 q^{71} +8.48528 q^{72} -73.5614i q^{73} -86.3164 q^{74} +8.66025i q^{75} +58.7823i q^{76} +(-16.6737 - 110.486i) q^{77} +15.1857 q^{78} -57.1904 q^{79} +8.94427i q^{80} +9.00000 q^{81} -30.1840i q^{82} +36.1402i q^{83} +(23.9772 - 3.61845i) q^{84} -44.1421 q^{85} -36.7451 q^{86} +92.3026i q^{87} +45.1488 q^{88} -133.352i q^{89} +9.48683i q^{90} +(42.9109 - 6.47576i) q^{91} +36.6823 q^{92} +64.9431 q^{93} -14.6257i q^{94} -65.7206 q^{95} +9.79796i q^{96} +29.2749i q^{97} +(66.2104 - 20.4496i) q^{98} +47.8875 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) 8 * q + 16 * q^4 - 24 * q^9	\( 8 q + 16 q^{4} - 24 q^{9} - 16 q^{11} + 32 q^{14} + 32 q^{16} + 96 q^{22} - 40 q^{25} - 144 q^{29} - 80 q^{35} - 48 q^{36} - 48 q^{37} - 48 q^{39} - 48 q^{42} - 64 q^{43} - 32 q^{44} + 128 q^{46} - 24 q^{49} + 128 q^{53} + 64 q^{56} + 144 q^{57} + 224 q^{58} + 64 q^{64} + 80 q^{65} - 192 q^{67} + 176 q^{71} - 160 q^{74} + 192 q^{77} - 96 q^{78} - 288 q^{79} + 72 q^{81} - 240 q^{85} - 64 q^{86} + 192 q^{88} + 64 q^{91} + 336 q^{93} + 80 q^{95} + 48 q^{99}+O(q^{100}) \) 8 * q + 16 * q^4 - 24 * q^9 - 16 * q^11 + 32 * q^14 + 32 * q^16 + 96 * q^22 - 40 * q^25 - 144 * q^29 - 80 * q^35 - 48 * q^36 - 48 * q^37 - 48 * q^39 - 48 * q^42 - 64 * q^43 - 32 * q^44 + 128 * q^46 - 24 * q^49 + 128 * q^53 + 64 * q^56 + 144 * q^57 + 224 * q^58 + 64 * q^64 + 80 * q^65 - 192 * q^67 + 176 * q^71 - 160 * q^74 + 192 * q^77 - 96 * q^78 - 288 * q^79 + 72 * q^81 - 240 * q^85 - 64 * q^86 + 192 * q^88 + 64 * q^91 + 336 * q^93 + 80 * q^95 + 48 * q^99

Introduction

L-functions

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