LMFDB - Embedded newform 210.3.f.a.181.5

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			181.5
Root			$-1.72286 - 0.178197i$ of defining polynomial
Character	$\chi$	$=$	210.181
Dual form			210.3.f.a.181.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -2.23607i q^{5} -2.44949i q^{6} +(-1.04456 - 6.92163i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -2.23607i q^{5} -2.44949i q^{6} +(-1.04456 - 6.92163i) q^{7} +2.82843 q^{8} -3.00000 q^{9} -3.16228i q^{10} +1.00806 q^{11} -3.46410i q^{12} -7.05322i q^{13} +(-1.47723 - 9.78866i) q^{14} -3.87298 q^{15} +4.00000 q^{16} -7.09185i q^{17} -4.24264 q^{18} +4.04257i q^{19} -4.47214i q^{20} +(-11.9886 + 1.80922i) q^{21} +1.42561 q^{22} +25.4766 q^{23} -4.89898i q^{24} -5.00000 q^{25} -9.97476i q^{26} +5.19615i q^{27} +(-2.08911 - 13.8433i) q^{28} +17.2909 q^{29} -5.47723 q^{30} +23.6516i q^{31} +5.65685 q^{32} -1.74600i q^{33} -10.0294i q^{34} +(-15.4772 + 2.33570i) q^{35} -6.00000 q^{36} -29.2171 q^{37} +5.71705i q^{38} -12.2165 q^{39} -6.32456i q^{40} +5.16217i q^{41} +(-16.9545 + 2.55863i) q^{42} +45.6529 q^{43} +2.01611 q^{44} +6.70820i q^{45} +36.0294 q^{46} +61.0391i q^{47} -6.92820i q^{48} +(-46.8178 + 14.4601i) q^{49} -7.07107 q^{50} -12.2834 q^{51} -14.1064i q^{52} +74.8237 q^{53} +7.34847i q^{54} -2.25408i q^{55} +(-2.95445 - 19.5773i) q^{56} +7.00193 q^{57} +24.4531 q^{58} +50.5639i q^{59} -7.74597 q^{60} +58.0943i q^{61} +33.4485i q^{62} +(3.13367 + 20.7649i) q^{63} +8.00000 q^{64} -15.7715 q^{65} -2.46922i q^{66} -73.5827 q^{67} -14.1837i q^{68} -44.1268i q^{69} +(-21.8881 + 3.30318i) q^{70} +99.8513 q^{71} -8.48528 q^{72} -1.15350i q^{73} -41.3192 q^{74} +8.66025i q^{75} +8.08514i q^{76} +(-1.05297 - 6.97738i) q^{77} -17.2768 q^{78} -102.445 q^{79} -8.94427i q^{80} +9.00000 q^{81} +7.30042i q^{82} +83.4227i q^{83} +(-23.9772 + 3.61845i) q^{84} -15.8579 q^{85} +64.5629 q^{86} -29.9488i q^{87} +2.85121 q^{88} -69.0342i q^{89} +9.48683i q^{90} +(-48.8198 + 7.36749i) q^{91} +50.9533 q^{92} +40.9658 q^{93} +86.3223i q^{94} +9.03946 q^{95} -9.79796i q^{96} -152.172i q^{97} +(-66.2104 + 20.4496i) q^{98} -3.02417 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$11$	1.00806			0.0916414			0.0458207	−	0.998950i	$-0.485410\pi$
$11$	1.00806			0.0916414			0.0458207	+	0.998950i	$0.485410\pi$
$12$		−	3.46410i		−	0.288675i
$13$		−	7.05322i		−	0.542556i	−0.962501	−	0.271278i	$-0.912554\pi$
$13$		−	7.05322i		−	0.542556i	0.962501	−	0.271278i	$-0.0874462\pi$
$14$	−1.47723	−	9.78866i	−0.105516	−	0.699190i
$15$	−3.87298			−0.258199
$16$	4.00000			0.250000
$17$		−	7.09185i		−	0.417168i	−0.978004	−	0.208584i	$-0.933115\pi$
$17$		−	7.09185i		−	0.417168i	0.978004	−	0.208584i	$-0.0668854\pi$
$18$	−4.24264			−0.235702
$19$			4.04257i			0.212767i	0.994325	+	0.106383i	$0.0339271\pi$
$19$			4.04257i			0.212767i	−0.994325	+	0.106383i	$0.966073\pi$
$20$		−	4.47214i		−	0.223607i
$21$	−11.9886	+	1.80922i	−0.570886	+	0.0861535i
$22$	1.42561			0.0648003
$23$	25.4766			1.10768			0.553840	−	0.832623i	$-0.313162\pi$
$23$	25.4766			1.10768			0.553840	+	0.832623i	$0.313162\pi$
$24$		−	4.89898i		−	0.204124i
$25$	−5.00000			−0.200000
$26$		−	9.97476i		−	0.383645i
$27$			5.19615i			0.192450i
$28$	−2.08911	−	13.8433i	−0.0746112	−	0.494402i
$29$	17.2909			0.596239			0.298119	−	0.954529i	$-0.403641\pi$
$29$	17.2909			0.596239			0.298119	+	0.954529i	$0.403641\pi$
$30$	−5.47723			−0.182574
$31$			23.6516i			0.762956i	0.924378	+	0.381478i	$0.124585\pi$
$31$			23.6516i			0.762956i	−0.924378	+	0.381478i	$0.875415\pi$
$32$	5.65685			0.176777
$33$		−	1.74600i		−	0.0529092i
$34$		−	10.0294i		−	0.294982i
$35$	−15.4772	+	2.33570i	−0.442206	+	0.0667342i
$36$	−6.00000			−0.166667
$37$	−29.2171			−0.789651			−0.394826	−	0.918756i	$-0.629195\pi$
$37$	−29.2171			−0.789651			−0.394826	+	0.918756i	$0.629195\pi$
$38$			5.71705i			0.150449i
$39$	−12.2165			−0.313245
$40$		−	6.32456i		−	0.158114i
$41$			5.16217i			0.125907i	0.998016	+	0.0629533i	$0.0200519\pi$
$41$			5.16217i			0.125907i	−0.998016	+	0.0629533i	$0.979948\pi$
$42$	−16.9545	+	2.55863i	−0.403677	+	0.0609198i
$43$	45.6529			1.06169			0.530847	−	0.847467i	$-0.321874\pi$
$43$	45.6529			1.06169			0.530847	+	0.847467i	$0.321874\pi$
$44$	2.01611			0.0458207
$45$			6.70820i			0.149071i
$46$	36.0294			0.783248
$47$			61.0391i			1.29870i	0.760488	+	0.649352i	$0.224960\pi$
$47$			61.0391i			1.29870i	−0.760488	+	0.649352i	$0.775040\pi$
$48$		−	6.92820i		−	0.144338i
$49$	−46.8178	+	14.4601i	−0.955465	+	0.295103i
$50$	−7.07107			−0.141421
$51$	−12.2834			−0.240852
$52$		−	14.1064i		−	0.271278i
$53$	74.8237			1.41177			0.705884	−	0.708328i	$-0.250550\pi$
$53$	74.8237			1.41177			0.705884	+	0.708328i	$0.250550\pi$
$54$			7.34847i			0.136083i
$55$		−	2.25408i		−	0.0409833i
$56$	−2.95445	−	19.5773i	−0.0527581	−	0.349595i
$57$	7.00193			0.122841
$58$	24.4531			0.421604
$59$			50.5639i			0.857014i	0.903538	+	0.428507i	$0.140960\pi$
$59$			50.5639i			0.857014i	−0.903538	+	0.428507i	$0.859040\pi$
$60$	−7.74597			−0.129099
$61$			58.0943i			0.952365i	0.879346	+	0.476183i	$0.157980\pi$
$61$			58.0943i			0.952365i	−0.879346	+	0.476183i	$0.842020\pi$
$62$			33.4485i			0.539491i
$63$	3.13367	+	20.7649i	0.0497408	+	0.329601i
$64$	8.00000			0.125000
$65$	−15.7715			−0.242638
$66$		−	2.46922i		−	0.0374125i
$67$	−73.5827			−1.09825			−0.549125	−	0.835741i	$-0.685039\pi$
$67$	−73.5827			−1.09825			−0.549125	+	0.835741i	$0.685039\pi$
$68$		−	14.1837i		−	0.208584i
$69$		−	44.1268i		−	0.639519i
$70$	−21.8881	+	3.30318i	−0.312687	+	0.0471882i
$71$	99.8513			1.40636			0.703178	−	0.711013i	$-0.251764\pi$
$71$	99.8513			1.40636			0.703178	+	0.711013i	$0.251764\pi$
$72$	−8.48528			−0.117851
$73$		−	1.15350i		−	0.0158014i	−0.999969	−	0.00790069i	$-0.997485\pi$
$73$		−	1.15350i		−	0.0158014i	0.999969	−	0.00790069i	$-0.00251489\pi$
$74$	−41.3192			−0.558368
$75$			8.66025i			0.115470i
$76$			8.08514i			0.106383i
$77$	−1.05297	−	6.97738i	−0.0136749	−	0.0906154i
$78$	−17.2768			−0.221497
$79$	−102.445			−1.29677			−0.648387	−	0.761311i	$-0.724556\pi$
$79$	−102.445			−1.29677			−0.648387	+	0.761311i	$0.724556\pi$
$80$		−	8.94427i		−	0.111803i
$81$	9.00000			0.111111
$82$			7.30042i			0.0890295i
$83$			83.4227i			1.00509i	0.864550	+	0.502546i	$0.167603\pi$
$83$			83.4227i			1.00509i	−0.864550	+	0.502546i	$0.832397\pi$
$84$	−23.9772	+	3.61845i	−0.285443	+	0.0430768i
$85$	−15.8579			−0.186563
$86$	64.5629			0.750732
$87$		−	29.9488i		−	0.344239i
$88$	2.85121			0.0324001
$89$		−	69.0342i		−	0.775666i	−0.921730	−	0.387833i	$-0.873224\pi$
$89$		−	69.0342i		−	0.775666i	0.921730	−	0.387833i	$-0.126776\pi$
$90$			9.48683i			0.105409i
$91$	−48.8198	+	7.36749i	−0.536481	+	0.0809614i
$92$	50.9533			0.553840
$93$	40.9658			0.440493
$94$			86.3223i			0.918323i
$95$	9.03946			0.0951522
$96$		−	9.79796i		−	0.102062i
$97$		−	152.172i		−	1.56878i	−0.620268	−	0.784390i	$-0.712976\pi$
$97$		−	152.172i		−	1.56878i	0.620268	−	0.784390i	$-0.287024\pi$
$98$	−66.2104	+	20.4496i	−0.675616	+	0.208669i
$99$	−3.02417			−0.0305471
$100$	−10.0000			−0.100000
$101$		−	66.8354i		−	0.661737i	−0.943677	−	0.330869i	$-0.892658\pi$
$101$		−	66.8354i		−	0.661737i	0.943677	−	0.330869i	$-0.107342\pi$
$102$	−17.3714			−0.170308
$103$			65.0648i			0.631697i	0.948810	+	0.315848i	$0.102289\pi$
$103$			65.0648i			0.631697i	−0.948810	+	0.315848i	$0.897711\pi$
$104$		−	19.9495i		−	0.191822i
$105$	4.04555	+	26.8073i	0.0385290	+	0.255308i
$106$	105.817			0.998270
$107$	10.8093			0.101021			0.0505106	−	0.998724i	$-0.483915\pi$
$107$	10.8093			0.101021			0.0505106	+	0.998724i	$0.483915\pi$
$108$			10.3923i			0.0962250i
$109$	−152.035			−1.39482			−0.697410	−	0.716673i	$-0.745664\pi$
$109$	−152.035			−1.39482			−0.697410	+	0.716673i	$0.745664\pi$
$110$		−	3.18775i		−	0.0289796i
$111$			50.6055i			0.455905i
$112$	−4.17822	−	27.6865i	−0.0373056	−	0.247201i
$113$	223.980			1.98212			0.991060	−	0.133419i	$-0.0425955\pi$
$113$	223.980			1.98212			0.991060	+	0.133419i	$0.0425955\pi$
$114$	9.90223			0.0868617
$115$		−	56.9675i		−	0.495370i
$116$	34.5818			0.298119
$117$			21.1597i			0.180852i
$118$			71.5081i			0.606001i
$119$	−49.0871	+	7.40784i	−0.412497	+	0.0622507i
$120$	−10.9545			−0.0912871
$121$	−119.984			−0.991602
$122$			82.1577i			0.673424i
$123$	8.94115			0.0726923
$124$			47.3033i			0.381478i
$125$			11.1803i			0.0894427i
$126$	4.43168	+	29.3660i	0.0351720	+	0.233063i
$127$	178.242			1.40348			0.701739	−	0.712434i	$-0.252407\pi$
$127$	178.242			1.40348			0.701739	+	0.712434i	$0.252407\pi$
$128$	11.3137			0.0883883
$129$		−	79.0731i		−	0.612970i
$130$	−22.3042			−0.171571
$131$		−	124.116i		−	0.947453i	−0.880672	−	0.473726i	$-0.842909\pi$
$131$		−	124.116i		−	0.947453i	0.880672	−	0.473726i	$-0.157091\pi$
$132$		−	3.49201i		−	0.0264546i
$133$	27.9811	−	4.22269i	0.210385	−	0.0317495i
$134$	−104.062			−0.776579
$135$	11.6190			0.0860663
$136$		−	20.0588i		−	0.147491i
$137$	−82.7435			−0.603967			−0.301984	−	0.953313i	$-0.597649\pi$
$137$	−82.7435			−0.603967			−0.301984	+	0.953313i	$0.597649\pi$
$138$		−	62.4048i		−	0.452209i
$139$		−	112.631i		−	0.810298i	−0.914251	−	0.405149i	$-0.867220\pi$
$139$		−	112.631i		−	0.810298i	0.914251	−	0.405149i	$-0.132780\pi$
$140$	−30.9545	+	4.67140i	−0.221103	+	0.0333671i
$141$	105.723			0.749807
$142$	141.211			0.994444
$143$		−	7.11004i		−	0.0497206i
$144$	−12.0000			−0.0833333
$145$		−	38.6637i		−	0.266646i
$146$		−	1.63130i		−	0.0111733i
$147$	25.0455	+	81.0908i	0.170378	+	0.551638i
$148$	−58.4342			−0.394826
$149$	−32.3830			−0.217336			−0.108668	−	0.994078i	$-0.534658\pi$
$149$	−32.3830			−0.217336			−0.108668	+	0.994078i	$0.534658\pi$
$150$			12.2474i			0.0816497i
$151$	−45.7944			−0.303274			−0.151637	−	0.988436i	$-0.548455\pi$
$151$	−45.7944			−0.303274			−0.151637	+	0.988436i	$0.548455\pi$
$152$			11.4341i			0.0752244i
$153$			21.2756i			0.139056i
$154$	−1.48913	−	9.86751i	−0.00966965	−	0.0640748i
$155$	52.8867			0.341204
$156$	−24.4331			−0.156622
$157$		−	251.015i		−	1.59882i	−0.600784	−	0.799411i	$-0.705145\pi$
$157$		−	251.015i		−	1.59882i	0.600784	−	0.799411i	$-0.294855\pi$
$158$	−144.879			−0.916958
$159$		−	129.598i		−	0.815084i
$160$		−	12.6491i		−	0.0790569i
$161$	−26.6118	−	176.340i	−0.165291	−	1.09528i
$162$	12.7279			0.0785674
$163$	138.555			0.850032			0.425016	−	0.905186i	$-0.360268\pi$
$163$	138.555			0.850032			0.425016	+	0.905186i	$0.360268\pi$
$164$			10.3243i			0.0629533i
$165$	−3.90418			−0.0236617
$166$			117.977i			0.710708i
$167$			180.489i			1.08077i	0.841417	+	0.540386i	$0.181722\pi$
$167$			180.489i			1.08077i	−0.841417	+	0.540386i	$0.818278\pi$
$168$	−33.9089	+	5.11726i	−0.201839	+	0.0304599i
$169$	119.252			0.705633
$170$	−22.4264			−0.131920
$171$		−	12.1277i		−	0.0709222i
$172$	91.3058			0.530847
$173$		−	292.353i		−	1.68990i	−0.534846	−	0.844950i	$-0.679630\pi$
$173$		−	292.353i		−	1.68990i	0.534846	−	0.844950i	$-0.320370\pi$
$174$		−	42.3539i		−	0.243413i
$175$	5.22278	+	34.6081i	0.0298445	+	0.197761i
$176$	4.03222			0.0229104
$177$	87.5792			0.494798
$178$		−	97.6292i		−	0.548478i
$179$	−273.253			−1.52655			−0.763277	−	0.646071i	$-0.776411\pi$
$179$	−273.253			−1.52655			−0.763277	+	0.646071i	$0.776411\pi$
$180$			13.4164i			0.0745356i
$181$		−	156.148i		−	0.862698i	−0.902185	−	0.431349i	$-0.858038\pi$
$181$		−	156.148i		−	0.862698i	0.902185	−	0.431349i	$-0.141962\pi$
$182$	−69.0416	+	10.4192i	−0.379349	+	0.0572484i
$183$	100.622			0.549848
$184$	72.0588			0.391624
$185$			65.3314i			0.353143i
$186$	57.9345			0.311476
$187$		−	7.14898i		−	0.0382299i
$188$			122.078i			0.649352i
$189$	35.9658	−	5.42767i	0.190295	−	0.0287178i
$190$	12.7837			0.0672827
$191$	−275.462			−1.44221			−0.721104	−	0.692827i	$-0.756365\pi$
$191$	−275.462			−1.44221			−0.721104	+	0.692827i	$0.756365\pi$
$192$		−	13.8564i		−	0.0721688i
$193$	−9.69062			−0.0502105			−0.0251052	−	0.999685i	$-0.507992\pi$
$193$	−9.69062			−0.0502105			−0.0251052	+	0.999685i	$0.507992\pi$
$194$		−	215.203i		−	1.10929i
$195$			27.3170i			0.140087i
$196$	−93.6356	+	28.9201i	−0.477733	+	0.147552i
$197$	−65.1041			−0.330478			−0.165239	−	0.986254i	$-0.552839\pi$
$197$	−65.1041			−0.330478			−0.165239	+	0.986254i	$0.552839\pi$
$198$	−4.27682			−0.0216001
$199$			220.166i			1.10636i	0.833062	+	0.553180i	$0.186586\pi$
$199$			220.166i			1.10636i	−0.833062	+	0.553180i	$0.813414\pi$
$200$	−14.1421			−0.0707107
$201$			127.449i			0.634074i
$202$		−	94.5196i		−	0.467919i
$203$	−18.0613	−	119.681i	−0.0889721	−	0.589563i
$204$	−24.5669			−0.120426
$205$	11.5430			0.0563072
$206$			92.0155i			0.446677i
$207$	−76.4299			−0.369227
$208$		−	28.2129i		−	0.135639i
$209$			4.07513i			0.0194982i
$210$	5.72127	+	37.9113i	0.0272441	+	0.180530i
$211$	9.08550			0.0430593			0.0215296	−	0.999768i	$-0.493146\pi$
$211$	9.08550			0.0430593			0.0215296	+	0.999768i	$0.493146\pi$
$212$	149.647			0.705884
$213$		−	172.948i		−	0.811960i
$214$	15.2866			0.0714328
$215$		−	102.083i		−	0.474804i
$216$			14.6969i			0.0680414i
$217$	163.708	−	24.7055i	0.754414	−	0.113850i
$218$	−215.010			−0.986286
$219$	−1.99792			−0.00912293
$220$		−	4.50816i		−	0.0204916i
$221$	−50.0204			−0.226337
$222$			71.5670i			0.322374i
$223$			438.428i			1.96604i	0.183489	+	0.983022i	$0.441261\pi$
$223$			438.428i			1.96604i	−0.183489	+	0.983022i	$0.558739\pi$
$224$	−5.90890	−	39.1546i	−0.0263790	−	0.174797i
$225$	15.0000			0.0666667
$226$	316.755			1.40157
$227$			235.641i			1.03807i	0.854754	+	0.519033i	$0.173708\pi$
$227$			235.641i			1.03807i	−0.854754	+	0.519033i	$0.826292\pi$
$228$	14.0039			0.0614205
$229$			301.350i			1.31594i	0.753044	+	0.657970i	$0.228584\pi$
$229$			301.350i			1.31594i	−0.753044	+	0.657970i	$0.771416\pi$
$230$		−	80.5642i		−	0.350279i
$231$	−12.0852	+	1.82380i	−0.0523168	+	0.00789523i
$232$	48.9061			0.210802
$233$	48.9562			0.210113			0.105056	−	0.994466i	$-0.466498\pi$
$233$	48.9562			0.210113			0.105056	+	0.994466i	$0.466498\pi$
$234$			29.9243i			0.127882i
$235$	136.488			0.580798
$236$			101.128i			0.428507i
$237$			177.440i			0.748693i
$238$	−69.4197	+	10.4763i	−0.291679	+	0.0440179i
$239$	39.0966			0.163584			0.0817921	−	0.996649i	$-0.473936\pi$
$239$	39.0966			0.163584			0.0817921	+	0.996649i	$0.473936\pi$
$240$	−15.4919			−0.0645497
$241$			163.337i			0.677745i	0.940832	+	0.338873i	$0.110046\pi$
$241$			163.337i			0.677745i	−0.940832	+	0.338873i	$0.889954\pi$
$242$	−169.683			−0.701168
$243$		−	15.5885i		−	0.0641500i
$244$			116.189i			0.476183i
$245$	32.3337	+	104.688i	0.131974	+	0.427297i
$246$	12.6447			0.0514012
$247$	28.5131			0.115438
$248$			66.8969i			0.269746i
$249$	144.492			0.580290
$250$			15.8114i			0.0632456i
$251$		−	2.50618i		−	0.00998480i	−0.999988	−	0.00499240i	$-0.998411\pi$
$251$		−	2.50618i		−	0.00998480i	0.999988	−	0.00499240i	$-0.00158914\pi$
$252$	6.26734	+	41.5298i	0.0248704	+	0.164801i
$253$	25.6819			0.101509
$254$	252.072			0.992409
$255$			27.4666i			0.107712i
$256$	16.0000			0.0625000
$257$			205.951i			0.801365i	0.916217	+	0.400682i	$0.131227\pi$
$257$			205.951i			0.801365i	−0.916217	+	0.400682i	$0.868773\pi$
$258$		−	111.826i		−	0.433435i
$259$	30.5189	+	202.230i	0.117834	+	0.780810i
$260$	−31.5430			−0.121319
$261$	−51.8728			−0.198746
$262$		−	175.527i		−	0.669950i
$263$	−431.680			−1.64137			−0.820685	−	0.571381i	$-0.806408\pi$
$263$	−431.680			−1.64137			−0.820685	+	0.571381i	$0.806408\pi$
$264$		−	4.93844i		−	0.0187062i
$265$		−	167.311i		−	0.631362i
$266$	39.5713	−	5.97178i	0.148764	−	0.0224503i
$267$	−119.571			−0.447831
$268$	−147.165			−0.549125
$269$			401.016i			1.49077i	0.666636	+	0.745384i	$0.267734\pi$
$269$			401.016i			1.49077i	−0.666636	+	0.745384i	$0.732266\pi$
$270$	16.4317			0.0608581
$271$			409.154i			1.50979i	0.655844	+	0.754897i	$0.272313\pi$
$271$			409.154i			1.50979i	−0.655844	+	0.754897i	$0.727687\pi$
$272$		−	28.3674i		−	0.104292i
$273$	12.7609	+	84.5583i	0.0467431	+	0.309737i
$274$	−117.017			−0.427070
$275$	−5.04028			−0.0183283
$276$		−	88.2537i		−	0.319760i
$277$	−311.824			−1.12572			−0.562859	−	0.826553i	$-0.690299\pi$
$277$	−311.824			−1.12572			−0.562859	+	0.826553i	$0.690299\pi$
$278$		−	159.285i		−	0.572968i
$279$		−	70.9549i		−	0.254319i
$280$	−43.7762	+	6.60635i	−0.156344	+	0.0235941i
$281$	−131.505			−0.467990			−0.233995	−	0.972238i	$-0.575180\pi$
$281$	−131.505			−0.467990			−0.233995	+	0.972238i	$0.575180\pi$
$282$	149.515			0.530194
$283$		−	50.6362i		−	0.178926i	−0.995990	−	0.0894632i	$-0.971485\pi$
$283$		−	50.6362i		−	0.178926i	0.995990	−	0.0894632i	$-0.0285151\pi$
$284$	199.703			0.703178
$285$		−	15.6568i		−	0.0549361i
$286$		−	10.0551i		−	0.0351578i
$287$	35.7306	−	5.39218i	0.124497	−	0.0187881i
$288$	−16.9706			−0.0589256
$289$	238.706			0.825971
$290$		−	54.6787i		−	0.188547i
$291$	−263.569			−0.905735
$292$		−	2.30700i		−	0.00790069i
$293$			176.891i			0.603725i	0.953351	+	0.301863i	$0.0976084\pi$
$293$			176.891i			0.603725i	−0.953351	+	0.301863i	$0.902392\pi$
$294$	35.4198	+	114.680i	0.120475	+	0.390067i
$295$	113.064			0.383269
$296$	−82.6384			−0.279184
$297$			5.23801i			0.0176364i
$298$	−45.7965			−0.153680
$299$		−	179.692i		−	0.600978i
$300$			17.3205i			0.0577350i
$301$	−47.6870	−	315.992i	−0.158429	−	1.04981i
$302$	−64.7631			−0.214447
$303$	−115.762			−0.382054
$304$			16.1703i			0.0531917i
$305$	129.903			0.425911
$306$			30.0882i			0.0983274i
$307$		−	569.023i		−	1.85349i	−0.375686	−	0.926747i	$-0.622593\pi$
$307$		−	569.023i		−	1.85349i	0.375686	−	0.926747i	$-0.377407\pi$
$308$	−2.10594	−	13.9548i	−0.00683747	−	0.0453077i
$309$	112.696			0.364710
$310$	74.7931			0.241268
$311$			322.176i			1.03593i	0.855401	+	0.517967i	$0.173311\pi$
$311$			322.176i			1.03593i	−0.855401	+	0.517967i	$0.826689\pi$
$312$	−34.5536			−0.110749
$313$			21.5138i			0.0687340i	0.999409	+	0.0343670i	$0.0109415\pi$
$313$			21.5138i			0.0687340i	−0.999409	+	0.0343670i	$0.989058\pi$
$314$		−	354.989i		−	1.13054i
$315$	46.4317	−	7.00710i	0.147402	−	0.0222447i
$316$	−204.890			−0.648387
$317$	−384.271			−1.21221			−0.606106	−	0.795384i	$-0.707269\pi$
$317$	−384.271			−1.21221			−0.606106	+	0.795384i	$0.707269\pi$
$318$		−	183.280i		−	0.576352i
$319$	17.4302			0.0546402
$320$		−	17.8885i		−	0.0559017i
$321$		−	18.7222i		−	0.0583246i
$322$	−37.6348	−	249.382i	−0.116878	−	0.774479i
$323$	28.6693			0.0887594
$324$	18.0000			0.0555556
$325$			35.2661i			0.108511i
$326$	195.947			0.601063
$327$			263.333i			0.805299i
$328$			14.6008i			0.0445147i
$329$	422.490	−	63.7588i	1.28416	−	0.193796i
$330$	−5.52135			−0.0167314
$331$	28.0523			0.0847503			0.0423751	−	0.999102i	$-0.486508\pi$
$331$	28.0523			0.0847503			0.0423751	+	0.999102i	$0.486508\pi$
$332$			166.845i			0.502546i
$333$	87.6513			0.263217
$334$			255.250i			0.764221i
$335$			164.536i			0.491152i
$336$	−47.9544	+	7.23690i	−0.142722	+	0.0215384i
$337$	−481.854			−1.42983			−0.714917	−	0.699210i	$-0.753535\pi$
$337$	−481.854			−1.42983			−0.714917	+	0.699210i	$0.753535\pi$
$338$	168.648			0.498958
$339$		−	387.944i		−	1.14438i
$340$	−31.7157			−0.0932816
$341$			23.8422i			0.0699184i
$342$		−	17.1512i		−	0.0501496i
$343$	148.991	+	308.951i	0.434376	+	0.900732i
$344$	129.126			0.375366
$345$	−98.6706			−0.286002
$346$		−	413.449i		−	1.19494i
$347$	376.261			1.08432			0.542162	−	0.840274i	$-0.317606\pi$
$347$	376.261			1.08432			0.542162	+	0.840274i	$0.317606\pi$
$348$		−	59.8975i		−	0.172119i
$349$		−	260.936i		−	0.747668i	−0.927496	−	0.373834i	$-0.878043\pi$
$349$		−	260.936i		−	0.747668i	0.927496	−	0.373834i	$-0.121957\pi$
$350$	7.38613	+	48.9433i	0.0211032	+	0.139838i
$351$	36.6496			0.104415
$352$	5.70242			0.0162001
$353$		−	142.203i		−	0.402841i	−0.979505	−	0.201421i	$-0.935444\pi$
$353$		−	142.203i		−	0.402841i	0.979505	−	0.201421i	$-0.0645558\pi$
$354$	123.856			0.349875
$355$		−	223.274i		−	0.628942i
$356$		−	138.068i		−	0.387833i
$357$	12.8308	+	85.0214i	0.0359405	+	0.238155i
$358$	−386.438			−1.07944
$359$	214.757			0.598209			0.299104	−	0.954220i	$-0.403312\pi$
$359$	214.757			0.598209			0.299104	+	0.954220i	$0.403312\pi$
$360$			18.9737i			0.0527046i
$361$	344.658			0.954730
$362$		−	220.827i		−	0.610019i
$363$			207.818i			0.572502i
$364$	−97.6395	+	14.7350i	−0.268240	+	0.0404807i
$365$	−2.57931			−0.00706659
$366$	142.301			0.388801
$367$		−	291.094i		−	0.793172i	−0.917997	−	0.396586i	$-0.870195\pi$
$367$		−	291.094i		−	0.793172i	0.917997	−	0.396586i	$-0.129805\pi$
$368$	101.907			0.276920
$369$		−	15.4865i		−	0.0419689i
$370$			92.3926i			0.249710i
$371$	−78.1575	−	517.901i	−0.210667	−	1.39596i
$372$	81.9317			0.220246
$373$	−677.342			−1.81593			−0.907966	−	0.419044i	$-0.862365\pi$
$373$	−677.342			−1.81593			−0.907966	+	0.419044i	$0.862365\pi$
$374$		−	10.1102i		−	0.0270326i
$375$	19.3649			0.0516398
$376$			172.645i			0.459161i
$377$		−	121.957i		−	0.323493i
$378$	50.8634	−	7.67589i	0.134559	−	0.0203066i
$379$	679.912			1.79396			0.896981	−	0.442069i	$-0.145755\pi$
$379$	679.912			1.79396			0.896981	+	0.442069i	$0.145755\pi$
$380$	18.0789			0.0475761
$381$		−	308.724i		−	0.810299i
$382$	−389.562			−1.01979
$383$		−	742.938i		−	1.93979i	−0.243530	−	0.969893i	$-0.578305\pi$
$383$		−	742.938i		−	1.93979i	0.243530	−	0.969893i	$-0.421695\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	−15.6019	+	2.35451i	−0.0405244	+	0.00611562i
$386$	−13.7046			−0.0355042
$387$	−136.959			−0.353898
$388$		−	304.343i		−	0.784390i
$389$	497.964			1.28011			0.640056	−	0.768328i	$-0.278911\pi$
$389$	497.964			1.28011			0.640056	+	0.768328i	$0.278911\pi$
$390$			38.6321i			0.0990566i
$391$		−	180.677i		−	0.462088i
$392$	−132.421	+	40.8992i	−0.337808	+	0.104335i
$393$	−214.976			−0.547012
$394$	−92.0711			−0.233683
$395$			229.074i			0.579935i
$396$	−6.04833			−0.0152736
$397$			79.8232i			0.201066i	0.994934	+	0.100533i	$0.0320548\pi$
$397$			79.8232i			0.201066i	−0.994934	+	0.100533i	$0.967945\pi$
$398$			311.361i			0.782315i
$399$	−7.31391	−	48.4648i	−0.0183306	−	0.121466i
$400$	−20.0000			−0.0500000
$401$	30.9575			0.0772008			0.0386004	−	0.999255i	$-0.487710\pi$
$401$	30.9575			0.0772008			0.0386004	+	0.999255i	$0.487710\pi$
$402$			180.240i			0.448358i
$403$	166.820			0.413946
$404$		−	133.671i		−	0.330869i
$405$		−	20.1246i		−	0.0496904i
$406$	−25.5426	−	169.255i	−0.0629128	−	0.416884i
$407$	−29.4525			−0.0723648
$408$	−34.7428			−0.0851540
$409$			179.566i			0.439036i	0.975608	+	0.219518i	$0.0704484\pi$
$409$			179.566i			0.439036i	−0.975608	+	0.219518i	$0.929552\pi$
$410$	16.3242			0.0398152
$411$			143.316i			0.348701i
$412$			130.130i			0.315848i
$413$	349.984	−	52.8168i	0.847419	−	0.127886i
$414$	−108.088			−0.261083
$415$	186.539			0.449491
$416$		−	39.8991i		−	0.0959112i
$417$	−195.083			−0.467826
$418$			5.76311i			0.0137873i
$419$		−	283.259i		−	0.676035i	−0.941140	−	0.338017i	$-0.890244\pi$
$419$		−	283.259i		−	0.676035i	0.941140	−	0.338017i	$-0.109756\pi$
$420$	8.09110	+	53.6147i	0.0192645	+	0.127654i
$421$	−600.315			−1.42593			−0.712963	−	0.701202i	$-0.752647\pi$
$421$	−600.315			−1.42593			−0.712963	+	0.701202i	$0.752647\pi$
$422$	12.8488			0.0304475
$423$		−	183.117i		−	0.432901i
$424$	211.633			0.499135
$425$			35.4593i			0.0834336i
$426$		−	244.585i		−	0.574143i
$427$	402.107	−	60.6827i	0.941702	−	0.142114i
$428$	21.6185			0.0505106
$429$	−12.3150			−0.0287062
$430$		−	144.367i		−	0.335737i
$431$	267.667			0.621036			0.310518	−	0.950567i	$-0.399497\pi$
$431$	267.667			0.621036			0.310518	+	0.950567i	$0.399497\pi$
$432$			20.7846i			0.0481125i
$433$			312.397i			0.721471i	0.932668	+	0.360736i	$0.117474\pi$
$433$			312.397i			0.721471i	−0.932668	+	0.360736i	$0.882526\pi$
$434$	231.518	−	34.9388i	0.533451	−	0.0805042i
$435$	−66.9675			−0.153948
$436$	−304.071			−0.697410
$437$			102.991i			0.235677i
$438$	−2.82549			−0.00645089
$439$		−	72.4481i		−	0.165030i	−0.996590	−	0.0825150i	$-0.973705\pi$
$439$		−	72.4481i		−	0.165030i	0.996590	−	0.0825150i	$-0.0262952\pi$
$440$		−	6.37550i		−	0.0144898i
$441$	140.453	−	43.3802i	0.318488	−	0.0983677i
$442$	−70.7396			−0.160044
$443$	−279.795			−0.631591			−0.315795	−	0.948827i	$-0.602271\pi$
$443$	−279.795			−0.631591			−0.315795	+	0.948827i	$0.602271\pi$
$444$			101.211i			0.227953i
$445$	−154.365			−0.346888
$446$			620.030i			1.39020i
$447$			56.0890i			0.125479i
$448$	−8.35645	−	55.3730i	−0.0186528	−	0.123600i
$449$	−165.129			−0.367770			−0.183885	−	0.982948i	$-0.558867\pi$
$449$	−165.129			−0.367770			−0.183885	+	0.982948i	$0.558867\pi$
$450$	21.2132			0.0471405
$451$			5.20376i			0.0115383i
$452$	447.959			0.991060
$453$			79.3183i			0.175096i
$454$			333.246i			0.734023i
$455$	16.4742	+	109.164i	0.0362070	+	0.239922i
$456$	19.8045			0.0434308
$457$	−387.165			−0.847189			−0.423594	−	0.905852i	$-0.639232\pi$
$457$	−387.165			−0.847189			−0.423594	+	0.905852i	$0.639232\pi$
$458$			426.173i			0.930510i
$459$	36.8503			0.0802840
$460$		−	113.935i		−	0.247685i
$461$		−	74.1988i		−	0.160952i	−0.996757	−	0.0804759i	$-0.974356\pi$
$461$		−	74.1988i		−	0.160952i	0.996757	−	0.0804759i	$-0.0256440\pi$
$462$	−17.0910	+	2.57924i	−0.0369936	+	0.00558277i
$463$	−423.801			−0.915336			−0.457668	−	0.889123i	$-0.651315\pi$
$463$	−423.801			−0.915336			−0.457668	+	0.889123i	$0.651315\pi$
$464$	69.1637			0.149060
$465$		−	91.6024i		−	0.196994i
$466$	69.2345			0.148572
$467$		−	327.240i		−	0.700727i	−0.936614	−	0.350364i	$-0.886058\pi$
$467$		−	327.240i		−	0.700727i	0.936614	−	0.350364i	$-0.113942\pi$
$468$			42.3193i			0.0904259i
$469$	76.8613	+	509.312i	0.163883	+	1.08595i
$470$	193.023			0.410686
$471$	−434.771			−0.923080
$472$			143.016i			0.303000i
$473$	46.0207			0.0972953
$474$			250.939i			0.529406i
$475$		−	20.2128i		−	0.0425533i
$476$	−98.1743	+	14.8157i	−0.206249	+	0.0311254i
$477$	−224.471			−0.470589
$478$	55.2910			0.115671
$479$			427.880i			0.893277i	0.894715	+	0.446638i	$0.147379\pi$
$479$			427.880i			0.893277i	−0.894715	+	0.446638i	$0.852621\pi$
$480$	−21.9089			−0.0456435
$481$			206.075i			0.428430i
$482$			230.993i			0.479238i
$483$	−305.429	+	46.0930i	−0.632359	+	0.0954306i
$484$	−239.968			−0.495801
$485$	−340.266			−0.701579
$486$		−	22.0454i		−	0.0453609i
$487$	815.490			1.67452			0.837259	−	0.546807i	$-0.184157\pi$
$487$	815.490			1.67452			0.837259	+	0.546807i	$0.184157\pi$
$488$			164.315i			0.336712i
$489$		−	239.985i		−	0.490766i
$490$	45.7267	+	148.051i	0.0933198	+	0.302145i
$491$	6.57128			0.0133835			0.00669173	−	0.999978i	$-0.497870\pi$
$491$	6.57128			0.0133835			0.00669173	+	0.999978i	$0.497870\pi$
$492$	17.8823			0.0363461
$493$		−	122.625i		−	0.248732i
$494$	40.3237			0.0816268
$495$			6.76224i			0.0136611i
$496$			94.6066i			0.190739i
$497$	−104.300	−	691.134i	−0.209860	−	1.39061i
$498$	204.343			0.410327
$499$	−468.850			−0.939579			−0.469790	−	0.882778i	$-0.655670\pi$
$499$	−468.850			−0.939579			−0.469790	+	0.882778i	$0.655670\pi$
$500$			22.3607i			0.0447214i
$501$	312.616			0.623984
$502$		−	3.54428i		−	0.00706032i
$503$			567.093i			1.12742i	0.825972	+	0.563711i	$0.190627\pi$
$503$			567.093i			1.12742i	−0.825972	+	0.563711i	$0.809373\pi$
$504$	8.86335	+	58.7319i	0.0175860	+	0.116532i
$505$	−149.449			−0.295938
$506$	36.3197			0.0717780
$507$		−	206.551i		−	0.407398i
$508$	356.483			0.701739
$509$			464.735i			0.913036i	0.889714	+	0.456518i	$0.150904\pi$
$509$			464.735i			0.913036i	−0.889714	+	0.456518i	$0.849096\pi$
$510$			38.8437i			0.0761641i
$511$	−7.98410	+	1.20490i	−0.0156245	+	0.00235792i
$512$	22.6274			0.0441942
$513$	−21.0058			−0.0409470
$514$			291.258i			0.566651i
$515$	145.489			0.282503
$516$		−	158.146i		−	0.306485i
$517$			61.5308i			0.119015i
$518$	43.1602	+	285.996i	0.0833209	+	0.552116i
$519$	−506.370			−0.975664
$520$	−44.6085			−0.0857856
$521$			925.284i			1.77598i	0.459866	+	0.887988i	$0.347897\pi$
$521$			925.284i			1.77598i	−0.459866	+	0.887988i	$0.652103\pi$
$522$	−73.3592			−0.140535
$523$		−	743.118i		−	1.42088i	−0.703760	−	0.710438i	$-0.748497\pi$
$523$		−	743.118i		−	1.42088i	0.703760	−	0.710438i	$-0.251503\pi$
$524$		−	248.233i		−	0.473726i
$525$	59.9430	−	9.04612i	0.114177	−	0.0172307i
$526$	−610.488			−1.16062
$527$	167.734			0.318281
$528$		−	6.98402i		−	0.0132273i
$529$	120.059			0.226955
$530$		−	236.613i		−	0.446440i
$531$		−	151.692i		−	0.285671i
$532$	55.9623	−	8.44538i	0.105192	−	0.0158748i
$533$	36.4100			0.0683114
$534$	−169.099			−0.316664
$535$		−	24.1703i		−	0.0451781i
$536$	−208.123			−0.388290
$537$			473.288i			0.881357i
$538$			567.123i			1.05413i
$539$	−47.1950	+	14.5765i	−0.0875602	+	0.0270437i
$540$	23.2379			0.0430331
$541$	224.274			0.414555			0.207277	−	0.978282i	$-0.433540\pi$
$541$	224.274			0.414555			0.207277	+	0.978282i	$0.433540\pi$
$542$			578.631i			1.06759i
$543$	−270.457			−0.498079
$544$		−	40.1176i		−	0.0737455i
$545$			339.961i			0.623782i
$546$	18.0466	+	119.584i	0.0330524	+	0.219017i
$547$	636.899			1.16435			0.582175	−	0.813064i	$-0.302202\pi$
$547$	636.899			1.16435			0.582175	+	0.813064i	$0.302202\pi$
$548$	−165.487			−0.301984
$549$		−	174.283i		−	0.317455i
$550$	−7.12803			−0.0129601
$551$			69.8997i			0.126860i
$552$		−	124.810i		−	0.226104i
$553$	107.010	+	709.087i	0.193508	+	1.28226i
$554$	−440.986			−0.796003
$555$	113.157			0.203887
$556$		−	225.263i		−	0.405149i
$557$	715.978			1.28542			0.642709	−	0.766111i	$-0.277811\pi$
$557$	715.978			1.28542			0.642709	+	0.766111i	$0.277811\pi$
$558$		−	100.345i		−	0.179830i
$559$		−	322.000i		−	0.576029i
$560$	−61.9089	+	9.34279i	−0.110552	+	0.0166836i
$561$	−12.3824			−0.0220720
$562$	−185.976			−0.330919
$563$		−	911.747i		−	1.61944i	−0.586813	−	0.809722i	$-0.699618\pi$
$563$		−	911.747i		−	1.61944i	0.586813	−	0.809722i	$-0.300382\pi$
$564$	211.446			0.374904
$565$		−	500.833i		−	0.886431i
$566$		−	71.6103i		−	0.126520i
$567$	−9.40101	−	62.2946i	−0.0165803	−	0.109867i
$568$	282.422			0.497222
$569$	83.3213			0.146435			0.0732173	−	0.997316i	$-0.476673\pi$
$569$	83.3213			0.146435			0.0732173	+	0.997316i	$0.476673\pi$
$570$		−	22.1421i		−	0.0388457i
$571$	112.867			0.197666			0.0988328	−	0.995104i	$-0.468489\pi$
$571$	112.867			0.197666			0.0988328	+	0.995104i	$0.468489\pi$
$572$		−	14.2201i		−	0.0248603i
$573$			477.114i			0.832659i
$574$	50.5307	−	7.62570i	0.0880327	−	0.0132852i
$575$	−127.383			−0.221536
$576$	−24.0000			−0.0416667
$577$			187.954i			0.325743i	0.986647	+	0.162872i	$0.0520757\pi$
$577$			187.954i			0.325743i	−0.986647	+	0.162872i	$0.947924\pi$
$578$	337.581			0.584050
$579$			16.7846i			0.0289890i
$580$		−	77.3274i		−	0.133323i
$581$	577.420	−	87.1397i	0.993839	−	0.149982i
$582$	−372.743			−0.640452
$583$	75.4264			0.129376
$584$		−	3.26259i		−	0.00558663i
$585$	47.3145			0.0808794
$586$			250.162i			0.426898i
$587$		−	137.244i		−	0.233806i	−0.993143	−	0.116903i	$-0.962703\pi$
$587$		−	137.244i		−	0.233806i	0.993143	−	0.116903i	$-0.0372967\pi$
$588$	50.0911	+	162.182i	0.0851889	+	0.275819i
$589$	−95.6134			−0.162332
$590$	159.897			0.271012
$591$			112.764i			0.190801i
$592$	−116.868			−0.197413
$593$		−	691.207i		−	1.16561i	−0.812612	−	0.582805i	$-0.801955\pi$
$593$		−	691.207i		−	1.16561i	0.812612	−	0.582805i	$-0.198045\pi$
$594$			7.40767i			0.0124708i
$595$	16.5644	+	109.762i	0.0278394	+	0.184474i
$596$	−64.7660			−0.108668
$597$	381.338			0.638758
$598$		−	254.123i		−	0.424956i
$599$	−915.774			−1.52884			−0.764419	−	0.644720i	$-0.776974\pi$
$599$	−915.774			−1.52884			−0.764419	+	0.644720i	$0.776974\pi$
$600$			24.4949i			0.0408248i
$601$		−	178.510i		−	0.297022i	−0.988911	−	0.148511i	$-0.952552\pi$
$601$		−	178.510i		−	0.297022i	0.988911	−	0.148511i	$-0.0474480\pi$
$602$	−67.4396	−	446.880i	−0.112026	−	0.742326i
$603$	220.748			0.366083
$604$	−91.5889			−0.151637
$605$			268.292i			0.443458i
$606$	−163.713			−0.270153
$607$			673.634i			1.10978i	0.831925	+	0.554888i	$0.187239\pi$
$607$			673.634i			1.10978i	−0.831925	+	0.554888i	$0.812761\pi$
$608$			22.8682i			0.0376122i
$609$	−207.294	+	31.2832i	−0.340384	+	0.0513681i
$610$	183.710			0.301164
$611$	430.522			0.704619
$612$			42.5511i			0.0695280i
$613$	859.658			1.40238			0.701189	−	0.712976i	$-0.252653\pi$
$613$	859.658			1.40238			0.701189	+	0.712976i	$0.252653\pi$
$614$		−	804.720i		−	1.31062i
$615$		−	19.9930i		−	0.0325090i
$616$	−2.97825	−	19.7350i	−0.00483482	−	0.0320374i
$617$	−695.263			−1.12684			−0.563422	−	0.826169i	$-0.690516\pi$
$617$	−695.263			−1.12684			−0.563422	+	0.826169i	$0.690516\pi$
$618$	159.376			0.257889
$619$		−	1036.53i		−	1.67452i	−0.546808	−	0.837258i	$-0.684157\pi$
$619$		−	1036.53i		−	1.67452i	0.546808	−	0.837258i	$-0.315843\pi$
$620$	105.773			0.170602
$621$			132.381i			0.213173i
$622$			455.625i			0.732516i
$623$	−477.829	+	72.1102i	−0.766981	+	0.115747i
$624$	−48.8662			−0.0783112
$625$	25.0000			0.0400000
$626$			30.4250i			0.0486023i
$627$	7.05834			0.0112573
$628$		−	502.030i		−	0.799411i
$629$			207.203i			0.329417i
$630$	65.6643	−	9.90953i	0.104229	−	0.0157294i
$631$	702.851			1.11387			0.556934	−	0.830557i	$-0.311978\pi$
$631$	702.851			1.11387			0.556934	+	0.830557i	$0.311978\pi$
$632$	−289.759			−0.458479
$633$		−	15.7366i		−	0.0248603i
$634$	−543.442			−0.857164
$635$		−	398.561i		−	0.627655i
$636$		−	259.197i		−	0.407542i
$637$	101.990	+	330.216i	0.160110	+	0.518393i
$638$	24.6500			0.0386364
$639$	−299.554			−0.468786
$640$		−	25.2982i		−	0.0395285i
$641$	−421.315			−0.657277			−0.328639	−	0.944456i	$-0.606590\pi$
$641$	−421.315			−0.657277			−0.328639	+	0.944456i	$0.606590\pi$
$642$		−	26.4772i		−	0.0412417i
$643$		−	414.352i		−	0.644404i	−0.946671	−	0.322202i	$-0.895577\pi$
$643$		−	414.352i		−	0.644404i	0.946671	−	0.322202i	$-0.104423\pi$
$644$	−53.2236	−	352.680i	−0.0826453	−	0.547639i
$645$	−176.813			−0.274128
$646$	40.5445			0.0627624
$647$		−	116.692i		−	0.180358i	−0.995926	−	0.0901790i	$-0.971256\pi$
$647$		−	116.692i		−	0.180358i	0.995926	−	0.0901790i	$-0.0287439\pi$
$648$	25.4558			0.0392837
$649$			50.9712i			0.0785380i
$650$			49.8738i			0.0767289i
$651$	−42.7911	−	283.550i	−0.0657314	−	0.435561i
$652$	277.110			0.425016
$653$	168.591			0.258178			0.129089	−	0.991633i	$-0.458795\pi$
$653$	168.591			0.258178			0.129089	+	0.991633i	$0.458795\pi$
$654$			372.409i			0.569433i
$655$	−277.533			−0.423714
$656$			20.6487i			0.0314767i
$657$			3.46050i			0.00526713i
$658$	597.491	−	90.1685i	0.908041	−	0.137034i
$659$	−1009.52			−1.53189			−0.765946	−	0.642904i	$-0.777729\pi$
$659$	−1009.52			−1.53189			−0.765946	+	0.642904i	$0.777729\pi$
$660$	−7.80837			−0.0118309
$661$			646.529i			0.978107i	0.872254	+	0.489054i	$0.162658\pi$
$661$			646.529i			0.978107i	−0.872254	+	0.489054i	$0.837342\pi$
$662$	39.6720			0.0599275
$663$			86.6379i			0.130676i
$664$			235.955i			0.355354i
$665$	−9.44222	−	62.5677i	−0.0141988	−	0.0940868i
$666$	123.958			0.186123
$667$	440.515			0.660442
$668$			360.978i			0.540386i
$669$	759.379			1.13510
$670$			232.689i			0.347297i
$671$			58.5623i			0.0872761i
$672$	−67.8178	+	10.2345i	−0.100919	+	0.0152299i
$673$	−840.576			−1.24900			−0.624500	−	0.781025i	$-0.714697\pi$
$673$	−840.576			−1.24900			−0.624500	+	0.781025i	$0.714697\pi$
$674$	−681.444			−1.01104
$675$		−	25.9808i		−	0.0384900i
$676$	238.504			0.352817
$677$			379.146i			0.560038i	0.959994	+	0.280019i	$0.0903408\pi$
$677$			379.146i			0.560038i	−0.959994	+	0.280019i	$0.909659\pi$
$678$		−	548.635i		−	0.809197i
$679$	−1053.27	+	158.952i	−1.55121	+	0.234097i
$680$	−44.8528			−0.0659600
$681$	408.142			0.599327
$682$			33.7179i			0.0494398i
$683$	−115.942			−0.169754			−0.0848770	−	0.996391i	$-0.527050\pi$
$683$	−115.942			−0.169754			−0.0848770	+	0.996391i	$0.527050\pi$
$684$		−	24.2554i		−	0.0354611i
$685$			185.020i			0.270102i
$686$	210.705	+	436.923i	0.307150	+	0.636914i
$687$	521.954			0.759758
$688$	182.612			0.265424
$689$		−	527.748i		−	0.765962i
$690$	−139.541			−0.202234
$691$			112.794i			0.163233i	0.996664	+	0.0816167i	$0.0260083\pi$
$691$			112.794i			0.163233i	−0.996664	+	0.0816167i	$0.973992\pi$
$692$		−	584.705i		−	0.844950i
$693$	3.15891	+	20.9322i	0.00455832	+	0.0302051i
$694$	532.113			0.766733
$695$	−251.852			−0.362377
$696$		−	84.7079i		−	0.121707i
$697$	36.6094			0.0525242
$698$		−	369.020i		−	0.528681i
$699$		−	84.7947i		−	0.121309i
$700$	10.4456	+	69.2163i	0.0149222	+	0.0988804i
$701$	192.764			0.274985			0.137492	−	0.990503i	$-0.456096\pi$
$701$	192.764			0.274985			0.137492	+	0.990503i	$0.456096\pi$
$702$	51.8304			0.0738325
$703$		−	118.112i		−	0.168012i
$704$	8.06445			0.0114552
$705$		−	236.403i		−	0.335324i
$706$		−	201.105i		−	0.284852i
$707$	−462.610	+	69.8134i	−0.654328	+	0.0987459i
$708$	175.158			0.247399
$709$	−317.352			−0.447604			−0.223802	−	0.974635i	$-0.571847\pi$
$709$	−317.352			−0.447604			−0.223802	+	0.974635i	$0.571847\pi$
$710$		−	315.758i		−	0.444729i
$711$	307.336			0.432258
$712$		−	195.258i		−	0.274239i
$713$			602.564i			0.845111i
$714$	18.1454	+	120.238i	0.0254138	+	0.168401i
$715$	−15.8985			−0.0222357
$716$	−546.506			−0.763277
$717$		−	67.7173i		−	0.0944454i
$718$	303.712			0.422998
$719$			668.666i			0.929995i	0.885312	+	0.464997i	$0.153945\pi$
$719$			668.666i			0.929995i	−0.885312	+	0.464997i	$0.846055\pi$
$720$			26.8328i			0.0372678i
$721$	450.354	−	67.9638i	0.624624	−	0.0942633i
$722$	487.420			0.675096
$723$	282.907			0.391296
$724$		−	312.297i		−	0.431349i
$725$	−86.4546			−0.119248
$726$			293.899i			0.404820i
$727$			164.229i			0.225900i	0.993601	+	0.112950i	$0.0360300\pi$
$727$			164.229i			0.225900i	−0.993601	+	0.112950i	$0.963970\pi$
$728$	−138.083	+	20.8384i	−0.189675	+	0.0286242i
$729$	−27.0000			−0.0370370
$730$	−3.64769			−0.00499683
$731$		−	323.764i		−	0.442905i
$732$	201.244			0.274924
$733$		−	986.499i		−	1.34584i	−0.739717	−	0.672919i	$-0.765040\pi$
$733$		−	986.499i		−	1.34584i	0.739717	−	0.672919i	$-0.234960\pi$
$734$		−	411.669i		−	0.560858i
$735$	181.325	−	56.0035i	0.246700	−	0.0761953i
$736$	144.118			0.195812
$737$	−74.1755			−0.100645
$738$		−	21.9012i		−	0.0296765i
$739$	−645.708			−0.873759			−0.436880	−	0.899520i	$-0.643916\pi$
$739$	−645.708			−0.873759			−0.436880	+	0.899520i	$0.643916\pi$
$740$			130.663i			0.176571i
$741$		−	49.3862i		−	0.0666480i
$742$	−110.531	−	732.423i	−0.148964	−	0.987093i
$743$	45.9927			0.0619013			0.0309507	−	0.999521i	$-0.490147\pi$
$743$	45.9927			0.0619013			0.0309507	+	0.999521i	$0.490147\pi$
$744$	115.869			0.155738
$745$			72.4106i			0.0971955i
$746$	−957.907			−1.28406
$747$		−	250.268i		−	0.335031i
$748$		−	14.2980i		−	0.0191149i
$749$	−11.2909	−	74.8177i	−0.0150746	−	0.0998902i
$750$	27.3861			0.0365148
$751$	638.813			0.850616			0.425308	−	0.905049i	$-0.360166\pi$
$751$	638.813			0.850616			0.425308	+	0.905049i	$0.360166\pi$
$752$			244.156i			0.324676i
$753$	−4.34084			−0.00576472
$754$		−	172.473i		−	0.228744i
$755$			102.399i			0.135628i
$756$	71.9316	−	10.8553i	0.0951477	−	0.0143589i
$757$	−1133.23			−1.49700			−0.748502	−	0.663133i	$-0.769226\pi$
$757$	−1133.23			−1.49700			−0.748502	+	0.663133i	$0.769226\pi$
$758$	961.540			1.26852
$759$		−	44.4823i		−	0.0586065i
$760$	25.5674			0.0336414
$761$			846.462i			1.11230i	0.831081	+	0.556151i	$0.187722\pi$
$761$			846.462i			1.11230i	−0.831081	+	0.556151i	$0.812278\pi$
$762$		−	436.601i		−	0.572968i
$763$	158.809	+	1052.33i	0.208138	+	1.37920i
$764$	−550.923			−0.721104
$765$	47.5736			0.0621877
$766$		−	1050.67i		−	1.37164i
$767$	356.638			0.464978
$768$		−	27.7128i		−	0.0360844i
$769$		−	894.921i		−	1.16375i	−0.813280	−	0.581873i	$-0.802320\pi$
$769$		−	894.921i		−	1.16375i	0.813280	−	0.581873i	$-0.197680\pi$
$770$	−22.0644	+	3.32979i	−0.0286551	+	0.00432440i
$771$	356.717			0.462668
$772$	−19.3812			−0.0251052
$773$			104.513i			0.135204i	0.997712	+	0.0676019i	$0.0215348\pi$
$773$			104.513i			0.135204i	−0.997712	+	0.0676019i	$0.978465\pi$
$774$	−193.689			−0.250244
$775$		−	118.258i		−	0.152591i
$776$		−	430.406i		−	0.554647i
$777$	350.272	−	52.8603i	0.450801	−	0.0680313i
$778$	704.227			0.905176
$779$	−20.8684			−0.0267888
$780$			54.6340i			0.0700436i
$781$	100.656			0.128881
$782$		−	255.515i		−	0.326746i
$783$			89.8463i			0.114746i
$784$	−187.271	+	57.8402i	−0.238866	+	0.0737758i
$785$	−561.287			−0.715015
$786$	−304.022			−0.386796
$787$			349.479i			0.444065i	0.975039	+	0.222032i	$0.0712691\pi$
$787$			349.479i			0.444065i	−0.975039	+	0.222032i	$0.928731\pi$
$788$	−130.208			−0.165239
$789$			747.692i			0.947645i
$790$			323.960i			0.410076i
$791$	−233.959	−	1550.30i	−0.295776	−	1.95993i
$792$	−8.55364			−0.0108000
$793$	409.752			0.516711
$794$			112.887i			0.142175i
$795$	−289.791			−0.364517
$796$			440.332i			0.553180i
$797$		−	606.585i		−	0.761085i	−0.924763	−	0.380543i	$-0.875737\pi$
$797$		−	606.585i		−	0.761085i	0.924763	−	0.380543i	$-0.124263\pi$
$798$	−10.3434	−	68.5395i	−0.0129617	−	0.0858891i
$799$	432.880			0.541778
$800$	−28.2843			−0.0353553
$801$			207.103i			0.258555i
$802$	43.7805			0.0545892
$803$		−	1.16279i		−	0.00144806i
$804$			254.898i			0.317037i
$805$	−394.308	+	59.5058i	−0.489823	+	0.0739202i
$806$	235.920			0.292704
$807$	694.581			0.860695
$808$		−	189.039i		−	0.233959i
$809$	−157.390			−0.194548			−0.0972742	−	0.995258i	$-0.531012\pi$
$809$	−157.390			−0.194548			−0.0972742	+	0.995258i	$0.531012\pi$
$810$		−	28.4605i		−	0.0351364i
$811$		−	443.035i		−	0.546283i	−0.961974	−	0.273141i	$-0.911937\pi$
$811$		−	443.035i		−	0.546283i	0.961974	−	0.273141i	$-0.0880626\pi$
$812$	−36.1227	−	239.363i	−0.0444861	−	0.294782i
$813$	708.676			0.871680
$814$	−41.6521			−0.0511696
$815$		−	309.819i		−	0.380146i
$816$	−49.1338			−0.0602130
$817$			184.555i			0.225893i
$818$			253.944i			0.310445i
$819$	146.459	−	22.1025i	0.178827	−	0.0269871i
$820$	23.0859			0.0281536
$821$	768.304			0.935815			0.467907	−	0.883777i	$-0.345008\pi$
$821$	768.304			0.935815			0.467907	+	0.883777i	$0.345008\pi$
$822$			202.679i			0.246569i
$823$	−1094.49			−1.32988			−0.664938	−	0.746899i	$-0.731542\pi$
$823$	−1094.49			−1.32988			−0.664938	+	0.746899i	$0.731542\pi$
$824$			184.031i			0.223339i
$825$			8.73002i			0.0105818i
$826$	494.952	−	74.6942i	0.599216	−	0.0904288i
$827$	1258.41			1.52165			0.760826	−	0.648956i	$-0.224794\pi$
$827$	1258.41			1.52165			0.760826	+	0.648956i	$0.224794\pi$
$828$	−152.860			−0.184613
$829$			182.499i			0.220143i	0.993924	+	0.110072i	$0.0351081\pi$
$829$			182.499i			0.220143i	−0.993924	+	0.110072i	$0.964892\pi$
$830$	263.806			0.317838
$831$			540.095i			0.649934i
$832$		−	56.4258i		−	0.0678195i
$833$	102.549	+	332.025i	0.123108	+	0.398589i
$834$	−275.890			−0.330803
$835$	403.585			0.483336
$836$			8.15027i			0.00974912i
$837$	−122.898			−0.146831
$838$		−	400.588i		−	0.478029i
$839$			1157.55i			1.37968i	0.723963	+	0.689839i	$0.242319\pi$
$839$			1157.55i			1.37968i	−0.723963	+	0.689839i	$0.757681\pi$
$840$	11.4425	+	75.8226i	0.0136221	+	0.0902650i
$841$	−542.024			−0.644499
$842$	−848.973			−1.00828
$843$			227.774i			0.270194i
$844$	18.1710			0.0215296
$845$		−	266.656i		−	0.315569i
$846$		−	258.967i		−	0.306108i
$847$	125.330	+	830.483i	0.147969	+	0.980500i
$848$	299.295			0.352942
$849$	−87.7044			−0.103303
$850$			50.1470i			0.0589964i
$851$	−744.354			−0.874681
$852$		−	345.895i		−	0.405980i
$853$			1038.69i			1.21769i	0.793290	+	0.608844i	$0.208366\pi$
$853$			1038.69i			1.21769i	−0.793290	+	0.608844i	$0.791634\pi$
$854$	568.665	−	85.8184i	0.665884	−	0.100490i
$855$	−27.1184			−0.0317174
$856$	30.5732			0.0357164
$857$		−	1206.41i		−	1.40771i	−0.710344	−	0.703854i	$-0.751461\pi$
$857$		−	1206.41i		−	1.40771i	0.710344	−	0.703854i	$-0.248539\pi$
$858$	−17.4160			−0.0202983
$859$		−	333.020i		−	0.387683i	−0.981033	−	0.193841i	$-0.937905\pi$
$859$		−	333.020i		−	0.387683i	0.981033	−	0.193841i	$-0.0620947\pi$
$860$		−	204.166i		−	0.237402i
$861$	−9.33953	−	61.8873i	−0.0108473	−	0.0718784i
$862$	378.538			0.439139
$863$	683.072			0.791508			0.395754	−	0.918357i	$-0.370483\pi$
$863$	683.072			0.791508			0.395754	+	0.918357i	$0.370483\pi$
$864$			29.3939i			0.0340207i
$865$	−653.720			−0.755746
$866$			441.796i			0.510157i
$867$		−	413.450i		−	0.476875i
$868$	327.416	−	49.4109i	0.377207	−	0.0569250i
$869$	−103.270			−0.118838
$870$	−94.7063			−0.108858
$871$			518.995i			0.595861i
$872$	−430.021			−0.493143
$873$			456.515i			0.522926i
$874$			145.651i			0.166649i
$875$	77.3861	−	11.6785i	0.0884413	−	0.0133468i
$876$	−3.99584			−0.00456146
$877$	−792.582			−0.903743			−0.451871	−	0.892083i	$-0.649243\pi$
$877$	−792.582			−0.903743			−0.451871	+	0.892083i	$0.649243\pi$
$878$		−	102.457i		−	0.116694i
$879$	306.385			0.348561
$880$		−	9.01633i		−	0.0102458i
$881$		−	260.584i		−	0.295782i	−0.989004	−	0.147891i	$-0.952752\pi$
$881$		−	260.584i		−	0.295782i	0.989004	−	0.147891i	$-0.0472485\pi$
$882$	198.631	−	61.3488i	0.225205	−	0.0695565i
$883$	25.2235			0.0285657			0.0142828	−	0.999898i	$-0.495453\pi$
$883$	25.2235			0.0285657			0.0142828	+	0.999898i	$0.495453\pi$
$884$	−100.041			−0.113168
$885$		−	195.833i		−	0.221280i
$886$	−395.690			−0.446602
$887$			1430.63i			1.61289i	0.591308	+	0.806446i	$0.298612\pi$
$887$			1430.63i			1.61289i	−0.591308	+	0.806446i	$0.701388\pi$
$888$			143.134i			0.161187i
$889$	−186.184	−	1233.72i	−0.209430	−	1.38776i
$890$	−218.305			−0.245287
$891$	9.07250			0.0101824
$892$			876.855i			0.983022i
$893$	−246.755			−0.276321
$894$			79.3219i			0.0887269i
$895$			611.013i			0.682696i
$896$	−11.8178	−	78.3093i	−0.0131895	−	0.0873987i
$897$	−311.236			−0.346975
$898$	−233.528			−0.260053
$899$			408.959i			0.454904i
$900$	30.0000			0.0333333
$901$		−	530.638i		−	0.588944i
$902$			7.35923i			0.00815879i
$903$	−547.314	+	82.5963i	−0.606107	+	0.0914688i
$904$	633.510			0.700785
$905$	−349.158			−0.385810
$906$			112.173i			0.123811i
$907$	−1208.91			−1.33287			−0.666436	−	0.745563i	$-0.732181\pi$
$907$	−1208.91			−1.33287			−0.666436	+	0.745563i	$0.732181\pi$
$908$			471.282i			0.519033i
$909$			200.506i			0.220579i
$910$	23.2980	+	154.382i	0.0256022	+	0.169650i
$911$	604.287			0.663323			0.331661	−	0.943398i	$-0.392391\pi$
$911$	604.287			0.663323			0.331661	+	0.943398i	$0.392391\pi$
$912$	28.0077			0.0307102
$913$			84.0947i			0.0921081i
$914$	−547.534			−0.599053
$915$		−	224.998i		−	0.245900i
$916$			602.700i			0.657970i
$917$	−859.087	+	129.646i	−0.936845	+	0.141381i
$918$	52.1143			0.0567693
$919$	264.211			0.287498			0.143749	−	0.989614i	$-0.454084\pi$
$919$	264.211			0.287498			0.143749	+	0.989614i	$0.454084\pi$
$920$		−	161.128i		−	0.175140i
$921$	−985.576			−1.07012
$922$		−	104.933i		−	0.113810i
$923$		−	704.274i		−	0.763027i
$924$	−24.1704	+	3.64760i	−0.0261584	+	0.00394762i
$925$	146.086			0.157930
$926$	−599.345			−0.647240
$927$		−	195.194i		−	0.210566i
$928$	97.8122			0.105401
$929$			828.146i			0.891439i	0.895173	+	0.445719i	$0.147052\pi$
$929$			828.146i			0.891439i	−0.895173	+	0.445719i	$0.852948\pi$
$930$		−	129.545i		−	0.139296i
$931$	−58.4558	−	189.264i	−0.0627881	−	0.203291i
$932$	97.9124			0.105056
$933$	558.024			0.598097
$934$		−	462.787i		−	0.495489i
$935$	−15.9856			−0.0170969
$936$			59.8486i			0.0639408i
$937$		−	396.006i		−	0.422632i	−0.977418	−	0.211316i	$-0.932225\pi$
$937$		−	396.006i		−	0.422632i	0.977418	−	0.211316i	$-0.0677749\pi$
$938$	108.698	+	720.276i	0.115883	+	0.767885i
$939$	37.2629			0.0396836
$940$	272.975			0.290399
$941$			457.424i			0.486105i	0.970013	+	0.243052i	$0.0781487\pi$
$941$			457.424i			0.486105i	−0.970013	+	0.243052i	$0.921851\pi$
$942$	−614.859			−0.652716
$943$			131.515i			0.139464i
$944$			202.255i			0.214254i
$945$	−12.1366	−	80.4220i	−0.0128430	−	0.0851027i
$946$	65.0830			0.0687981
$947$	203.596			0.214991			0.107495	−	0.994206i	$-0.465717\pi$
$947$	203.596			0.214991			0.107495	+	0.994206i	$0.465717\pi$
$948$			354.881i			0.374347i
$949$	−8.13590			−0.00857313
$950$		−	28.5853i		−	0.0300898i
$951$			665.578i			0.699871i
$952$	−138.839	+	20.9525i	−0.145840	+	0.0220090i
$953$	119.616			0.125516			0.0627578	−	0.998029i	$-0.480010\pi$
$953$	119.616			0.125516			0.0627578	+	0.998029i	$0.480010\pi$
$954$	−317.450			−0.332757
$955$			615.951i			0.644975i
$956$	78.1932			0.0817921
$957$		−	30.1900i		−	0.0315465i
$958$			605.113i			0.631642i
$959$	86.4303	+	572.720i	0.0901254	+	0.597205i
$960$	−30.9839			−0.0322749
$961$	401.600			0.417898
$962$			291.434i			0.302946i
$963$	−32.4278			−0.0336737
$964$			326.673i			0.338873i
$965$			21.6689i			0.0224548i
$966$	−431.943	+	65.1853i	−0.447145	+	0.0674796i
$967$	427.535			0.442126			0.221063	−	0.975260i	$-0.429047\pi$
$967$	427.535			0.442126			0.221063	+	0.975260i	$0.429047\pi$
$968$	−339.366			−0.350584
$969$		−	49.6567i		−	0.0512453i
$970$	−481.209			−0.496092
$971$		−	6.82181i		−	0.00702555i	−0.999994	−	0.00351278i	$-0.998882\pi$
$971$		−	6.82181i		−	0.00702555i	0.999994	−	0.00351278i	$-0.00111815\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	−779.593	+	117.650i	−0.801226	+	0.120915i
$974$	1153.28			1.18406
$975$	61.0827			0.0626489
$976$			232.377i			0.238091i
$977$	251.640			0.257564			0.128782	−	0.991673i	$-0.458893\pi$
$977$	251.640			0.257564			0.128782	+	0.991673i	$0.458893\pi$
$978$		−	339.390i		−	0.347024i
$979$		−	69.5904i		−	0.0710831i
$980$	64.6673	+	209.376i	0.0659871	+	0.213649i
$981$	456.106			0.464940
$982$	9.29320			0.00946354
$983$			743.441i			0.756298i	0.925745	+	0.378149i	$0.123439\pi$
$983$			743.441i			0.756298i	−0.925745	+	0.378149i	$0.876561\pi$
$984$	25.2894			0.0257006
$985$			145.577i			0.147794i
$986$		−	173.417i		−	0.175880i
$987$	−110.433	−	731.774i	−0.111888	−	0.741412i
$988$	57.0263			0.0577189
$989$	1163.08			1.17602
$990$			9.56326i			0.00965986i
$991$	−579.815			−0.585080			−0.292540	−	0.956253i	$-0.594501\pi$
$991$	−579.815			−0.585080			−0.292540	+	0.956253i	$0.594501\pi$
$992$			133.794i			0.134873i
$993$		−	48.5881i		−	0.0489306i
$994$	−147.503	−	977.410i	−0.148393	−	0.983310i
$995$	492.306			0.494780
$996$	288.985			0.290145
$997$			723.701i			0.725878i	0.931813	+	0.362939i	$0.118227\pi$
$997$			723.701i			0.725878i	−0.931813	+	0.362939i	$0.881773\pi$
$998$	−663.054			−0.664383
$999$		−	151.817i		−	0.151968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.f.a.181.5	✓	8
3.2	odd	2		630.3.f.c.181.3		8
4.3	odd	2		1680.3.s.a.1441.5		8
5.2	odd	4		1050.3.h.b.349.12		16
5.3	odd	4		1050.3.h.b.349.5		16
5.4	even	2		1050.3.f.b.601.4		8
7.6	odd	2	inner	210.3.f.a.181.8	yes	8
21.20	even	2		630.3.f.c.181.1		8
28.27	even	2		1680.3.s.a.1441.3		8
35.13	even	4		1050.3.h.b.349.4		16
35.27	even	4		1050.3.h.b.349.13		16
35.34	odd	2		1050.3.f.b.601.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.f.a.181.5	✓	8	1.1	even	1	trivial
210.3.f.a.181.8	yes	8	7.6	odd	2	inner
630.3.f.c.181.1		8	21.20	even	2
630.3.f.c.181.3		8	3.2	odd	2
1050.3.f.b.601.2		8	35.34	odd	2
1050.3.f.b.601.4		8	5.4	even	2
1050.3.h.b.349.4		16	35.13	even	4
1050.3.h.b.349.5		16	5.3	odd	4
1050.3.h.b.349.12		16	5.2	odd	4
1050.3.h.b.349.13		16	35.27	even	4
1680.3.s.a.1441.3		8	28.27	even	2
1680.3.s.a.1441.5		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)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -2.23607i q^{5} -2.44949i q^{6} +(-1.04456 - 6.92163i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -2.23607i q^{5} -2.44949i q^{6} +(-1.04456 - 6.92163i) q^{7} +2.82843 q^{8} -3.00000 q^{9} -3.16228i q^{10} +1.00806 q^{11} -3.46410i q^{12} -7.05322i q^{13} +(-1.47723 - 9.78866i) q^{14} -3.87298 q^{15} +4.00000 q^{16} -7.09185i q^{17} -4.24264 q^{18} +4.04257i q^{19} -4.47214i q^{20} +(-11.9886 + 1.80922i) q^{21} +1.42561 q^{22} +25.4766 q^{23} -4.89898i q^{24} -5.00000 q^{25} -9.97476i q^{26} +5.19615i q^{27} +(-2.08911 - 13.8433i) q^{28} +17.2909 q^{29} -5.47723 q^{30} +23.6516i q^{31} +5.65685 q^{32} -1.74600i q^{33} -10.0294i q^{34} +(-15.4772 + 2.33570i) q^{35} -6.00000 q^{36} -29.2171 q^{37} +5.71705i q^{38} -12.2165 q^{39} -6.32456i q^{40} +5.16217i q^{41} +(-16.9545 + 2.55863i) q^{42} +45.6529 q^{43} +2.01611 q^{44} +6.70820i q^{45} +36.0294 q^{46} +61.0391i q^{47} -6.92820i q^{48} +(-46.8178 + 14.4601i) q^{49} -7.07107 q^{50} -12.2834 q^{51} -14.1064i q^{52} +74.8237 q^{53} +7.34847i q^{54} -2.25408i q^{55} +(-2.95445 - 19.5773i) q^{56} +7.00193 q^{57} +24.4531 q^{58} +50.5639i q^{59} -7.74597 q^{60} +58.0943i q^{61} +33.4485i q^{62} +(3.13367 + 20.7649i) q^{63} +8.00000 q^{64} -15.7715 q^{65} -2.46922i q^{66} -73.5827 q^{67} -14.1837i q^{68} -44.1268i q^{69} +(-21.8881 + 3.30318i) q^{70} +99.8513 q^{71} -8.48528 q^{72} -1.15350i q^{73} -41.3192 q^{74} +8.66025i q^{75} +8.08514i q^{76} +(-1.05297 - 6.97738i) q^{77} -17.2768 q^{78} -102.445 q^{79} -8.94427i q^{80} +9.00000 q^{81} +7.30042i q^{82} +83.4227i q^{83} +(-23.9772 + 3.61845i) q^{84} -15.8579 q^{85} +64.5629 q^{86} -29.9488i q^{87} +2.85121 q^{88} -69.0342i q^{89} +9.48683i q^{90} +(-48.8198 + 7.36749i) q^{91} +50.9533 q^{92} +40.9658 q^{93} +86.3223i q^{94} +9.03946 q^{95} -9.79796i q^{96} -152.172i q^{97} +(-66.2104 + 20.4496i) q^{98} -3.02417 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) 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

Modular forms

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Database

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