LMFDB - Embedded newform 210.3.h.a.139.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(139,210)]

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, 1, 1]))

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

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

chi := DirichletCharacter("210.139");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.h (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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 96 x^{14} - 532 x^{13} + 3236 x^{12} - 12864 x^{11} + 49526 x^{10} - 141436 x^{9} + \cdots + 33750 $ x^16 - 8x^15 + 96x^14 - 532x^13 + 3236x^12 - 12864x^11 + 49526x^10 - 141436x^9 + 362298x^8 - 722060x^7 + 1208164x^6 - 1570812x^5 + 1591101x^4 - 1183860x^3 + 619650x^2 - 202500*x + 33750
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.9
Root			$0.500000 + 1.83656i$ of defining polynomial
Character	$\chi$	$=$	210.139
Dual form			210.3.h.a.139.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +(-4.91728 + 0.905717i) q^{5} -2.44949i q^{6} +(1.91369 - 6.73333i) q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +(-4.91728 + 0.905717i) q^{5} -2.44949i q^{6} +(1.91369 - 6.73333i) q^{7} -2.82843i q^{8} +3.00000 q^{9} +(-1.28088 - 6.95409i) q^{10} +17.5116 q^{11} +3.46410 q^{12} -4.83531 q^{13} +(9.52237 + 2.70636i) q^{14} +(8.51698 - 1.56875i) q^{15} +4.00000 q^{16} +18.0284 q^{17} +4.24264i q^{18} -9.13350i q^{19} +(9.83457 - 1.81143i) q^{20} +(-3.31461 + 11.6625i) q^{21} +24.7651i q^{22} -3.72515i q^{23} +4.89898i q^{24} +(23.3594 - 8.90734i) q^{25} -6.83816i q^{26} -5.19615 q^{27} +(-3.82738 + 13.4667i) q^{28} +1.12582 q^{29} +(2.21855 + 12.0448i) q^{30} -57.0859i q^{31} +5.65685i q^{32} -30.3310 q^{33} +25.4960i q^{34} +(-3.31165 + 34.8430i) q^{35} -6.00000 q^{36} -41.3624i q^{37} +12.9167 q^{38} +8.37500 q^{39} +(2.56176 + 13.9082i) q^{40} -11.7156i q^{41} +(-16.4932 - 4.68756i) q^{42} +64.4171i q^{43} -35.0232 q^{44} +(-14.7519 + 2.71715i) q^{45} +5.26816 q^{46} +77.6614 q^{47} -6.92820 q^{48} +(-41.6756 - 25.7710i) q^{49} +(12.5969 + 33.0351i) q^{50} -31.2261 q^{51} +9.67062 q^{52} -77.5383i q^{53} -7.34847i q^{54} +(-86.1095 + 15.8606i) q^{55} +(-19.0447 - 5.41273i) q^{56} +15.8197i q^{57} +1.59215i q^{58} +87.0651i q^{59} +(-17.0340 + 3.13750i) q^{60} -5.36957i q^{61} +80.7317 q^{62} +(5.74106 - 20.2000i) q^{63} -8.00000 q^{64} +(23.7766 - 4.37942i) q^{65} -42.8945i q^{66} -47.1879i q^{67} -36.0568 q^{68} +6.45216i q^{69} +(-49.2754 - 4.68338i) q^{70} -58.3047 q^{71} -8.48528i q^{72} -53.4082 q^{73} +58.4953 q^{74} +(-40.4596 + 15.4280i) q^{75} +18.2670i q^{76} +(33.5117 - 117.911i) q^{77} +11.8440i q^{78} -74.9637 q^{79} +(-19.6691 + 3.62287i) q^{80} +9.00000 q^{81} +16.5683 q^{82} +28.7890 q^{83} +(6.62921 - 23.3250i) q^{84} +(-88.6507 + 16.3286i) q^{85} -91.0996 q^{86} -1.94997 q^{87} -49.5303i q^{88} -101.499i q^{89} +(-3.84263 - 20.8623i) q^{90} +(-9.25327 + 32.5578i) q^{91} +7.45031i q^{92} +98.8757i q^{93} +109.830i q^{94} +(8.27237 + 44.9120i) q^{95} -9.79796i q^{96} +107.830 q^{97} +(36.4457 - 58.9382i) q^{98} +52.5348 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 32 q^{4} + 48 q^{9}+O(q^{10}) $ 16 * q - 32 * q^4 + 48 * q^9	$ 16 q - 32 q^{4} + 48 q^{9} + 96 q^{11} + 16 q^{14} - 24 q^{15} + 64 q^{16} + 24 q^{21} + 24 q^{25} + 64 q^{29} + 24 q^{30} - 8 q^{35} - 96 q^{36} - 144 q^{39} - 192 q^{44} - 176 q^{46} + 224 q^{49} - 96 q^{50} - 48 q^{51} - 32 q^{56} + 48 q^{60} - 128 q^{64} + 368 q^{65} - 56 q^{70} - 384 q^{71} + 224 q^{74} - 608 q^{79} + 144 q^{81} - 48 q^{84} - 440 q^{85} + 416 q^{86} + 224 q^{91} - 560 q^{95} + 288 q^{99}+O(q^{100}) $ 16 * q - 32 * q^4 + 48 * q^9 + 96 * q^11 + 16 * q^14 - 24 * q^15 + 64 * q^16 + 24 * q^21 + 24 * q^25 + 64 * q^29 + 24 * q^30 - 8 * q^35 - 96 * q^36 - 144 * q^39 - 192 * q^44 - 176 * q^46 + 224 * q^49 - 96 * q^50 - 48 * q^51 - 32 * q^56 + 48 * q^60 - 128 * q^64 + 368 * q^65 - 56 * q^70 - 384 * q^71 + 224 * q^74 - 608 * q^79 + 144 * q^81 - 48 * q^84 - 440 * q^85 + 416 * q^86 + 224 * q^91 - 560 * q^95 + 288 * 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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−2.00000			−0.500000
$5$	−4.91728	+	0.905717i	−0.983457	+	0.181143i
$5$	−4.91728	+	0.905717i	−0.983457	+	0.181143i
$6$		−	2.44949i		−	0.408248i
$7$	1.91369	−	6.73333i	0.273384	−	0.961905i
$7$	1.91369	−	6.73333i	0.273384	−	0.961905i
$8$		−	2.82843i		−	0.353553i
$9$	3.00000			0.333333
$10$	−1.28088	−	6.95409i	−0.128088	−	0.695409i
$11$	17.5116			1.59196			0.795982	−	0.605321i	$-0.206955\pi$
$11$	17.5116			1.59196			0.795982	+	0.605321i	$0.206955\pi$
$12$	3.46410			0.288675
$13$	−4.83531			−0.371947			−0.185973	−	0.982555i	$-0.559544\pi$
$13$	−4.83531			−0.371947			−0.185973	+	0.982555i	$0.559544\pi$
$14$	9.52237	+	2.70636i	0.680170	+	0.193312i
$15$	8.51698	−	1.56875i	0.567799	−	0.104583i
$16$	4.00000			0.250000
$17$	18.0284			1.06049			0.530247	−	0.847843i	$-0.322099\pi$
$17$	18.0284			1.06049			0.530247	+	0.847843i	$0.322099\pi$
$18$			4.24264i			0.235702i
$19$		−	9.13350i		−	0.480711i	−0.970685	−	0.240355i	$-0.922736\pi$
$19$		−	9.13350i		−	0.480711i	0.970685	−	0.240355i	$-0.0772640\pi$
$20$	9.83457	−	1.81143i	0.491728	−	0.0905717i
$21$	−3.31461	+	11.6625i	−0.157838	+	0.555356i
$22$			24.7651i			1.12569i
$23$		−	3.72515i		−	0.161963i	−0.996716	−	0.0809816i	$-0.974194\pi$
$23$		−	3.72515i		−	0.161963i	0.996716	−	0.0809816i	$-0.0258055\pi$
$24$			4.89898i			0.204124i
$25$	23.3594	−	8.90734i	0.934374	−	0.356294i
$26$		−	6.83816i		−	0.263006i
$27$	−5.19615			−0.192450
$28$	−3.82738	+	13.4667i	−0.136692	+	0.480952i
$29$	1.12582			0.0388213			0.0194107	−	0.999812i	$-0.493821\pi$
$29$	1.12582			0.0388213			0.0194107	+	0.999812i	$0.493821\pi$
$30$	2.21855	+	12.0448i	0.0739515	+	0.401495i
$31$		−	57.0859i		−	1.84148i	−0.390175	−	0.920741i	$-0.627585\pi$
$31$		−	57.0859i		−	1.84148i	0.390175	−	0.920741i	$-0.372415\pi$
$32$			5.65685i			0.176777i
$33$	−30.3310			−0.919120
$34$			25.4960i			0.749882i
$35$	−3.31165	+	34.8430i	−0.0946185	+	0.995514i
$36$	−6.00000			−0.166667
$37$		−	41.3624i		−	1.11790i	−0.829200	−	0.558952i	$-0.811204\pi$
$37$		−	41.3624i		−	1.11790i	0.829200	−	0.558952i	$-0.188796\pi$
$38$	12.9167			0.339914
$39$	8.37500			0.214744
$40$	2.56176	+	13.9082i	0.0640439	+	0.347704i
$41$		−	11.7156i		−	0.285745i	−0.989741	−	0.142873i	$-0.954366\pi$
$41$		−	11.7156i		−	0.285745i	0.989741	−	0.142873i	$-0.0456340\pi$
$42$	−16.4932	−	4.68756i	−0.392696	−	0.111609i
$43$			64.4171i			1.49807i	0.662529	+	0.749036i	$0.269483\pi$
$43$			64.4171i			1.49807i	−0.662529	+	0.749036i	$0.730517\pi$
$44$	−35.0232			−0.795982
$45$	−14.7519	+	2.71715i	−0.327819	+	0.0603812i
$46$	5.26816			0.114525
$47$	77.6614			1.65237			0.826185	−	0.563399i	$-0.190507\pi$
$47$	77.6614			1.65237			0.826185	+	0.563399i	$0.190507\pi$
$48$	−6.92820			−0.144338
$49$	−41.6756	−	25.7710i	−0.850522	−	0.525939i
$50$	12.5969	+	33.0351i	0.251938	+	0.660702i
$51$	−31.2261			−0.612276
$52$	9.67062			0.185973
$53$		−	77.5383i		−	1.46299i	−0.681849	−	0.731493i	$-0.738824\pi$
$53$		−	77.5383i		−	1.46299i	0.681849	−	0.731493i	$-0.261176\pi$
$54$		−	7.34847i		−	0.136083i
$55$	−86.1095	+	15.8606i	−1.56563	+	0.288374i
$56$	−19.0447	−	5.41273i	−0.340085	−	0.0966559i
$57$			15.8197i			0.277539i
$58$			1.59215i			0.0274508i
$59$			87.0651i			1.47568i	0.674976	+	0.737839i	$0.264154\pi$
$59$			87.0651i			1.47568i	−0.674976	+	0.737839i	$0.735846\pi$
$60$	−17.0340	+	3.13750i	−0.283899	+	0.0522916i
$61$		−	5.36957i		−	0.0880258i	−0.999031	−	0.0440129i	$-0.985986\pi$
$61$		−	5.36957i		−	0.0880258i	0.999031	−	0.0440129i	$-0.0140143\pi$
$62$	80.7317			1.30212
$63$	5.74106	−	20.2000i	0.0911280	−	0.320635i
$64$	−8.00000			−0.125000
$65$	23.7766	−	4.37942i	0.365794	−	0.0673757i
$66$		−	42.8945i		−	0.649916i
$67$		−	47.1879i		−	0.704297i	−0.935944	−	0.352149i	$-0.885451\pi$
$67$		−	47.1879i		−	0.704297i	0.935944	−	0.352149i	$-0.114549\pi$
$68$	−36.0568			−0.530247
$69$			6.45216i			0.0935095i
$70$	−49.2754	−	4.68338i	−0.703934	−	0.0669054i
$71$	−58.3047			−0.821193			−0.410597	−	0.911817i	$-0.634680\pi$
$71$	−58.3047			−0.821193			−0.410597	+	0.911817i	$0.634680\pi$
$72$		−	8.48528i		−	0.117851i
$73$	−53.4082			−0.731619			−0.365810	−	0.930690i	$-0.619208\pi$
$73$	−53.4082			−0.731619			−0.365810	+	0.930690i	$0.619208\pi$
$74$	58.4953			0.790477
$75$	−40.4596	+	15.4280i	−0.539461	+	0.205706i
$76$			18.2670i			0.240355i
$77$	33.5117	−	117.911i	0.435217	−	1.53132i
$78$			11.8440i			0.151847i
$79$	−74.9637			−0.948907			−0.474454	−	0.880280i	$-0.657354\pi$
$79$	−74.9637			−0.948907			−0.474454	+	0.880280i	$0.657354\pi$
$80$	−19.6691	+	3.62287i	−0.245864	+	0.0452859i
$81$	9.00000			0.111111
$82$	16.5683			0.202053
$83$	28.7890			0.346855			0.173428	−	0.984847i	$-0.444516\pi$
$83$	28.7890			0.346855			0.173428	+	0.984847i	$0.444516\pi$
$84$	6.62921	−	23.3250i	0.0789192	−	0.277678i
$85$	−88.6507	+	16.3286i	−1.04295	+	0.192101i
$86$	−91.0996			−1.05930
$87$	−1.94997			−0.0224135
$88$		−	49.5303i		−	0.562844i
$89$		−	101.499i		−	1.14043i	−0.821494	−	0.570217i	$-0.806859\pi$
$89$		−	101.499i		−	1.14043i	0.821494	−	0.570217i	$-0.193141\pi$
$90$	−3.84263	−	20.8623i	−0.0426959	−	0.231803i
$91$	−9.25327	+	32.5578i	−0.101684	+	0.357778i
$92$			7.45031i			0.0809816i
$93$			98.8757i			1.06318i
$94$			109.830i			1.16840i
$95$	8.27237	+	44.9120i	0.0870776	+	0.472758i
$96$		−	9.79796i		−	0.102062i
$97$	107.830			1.11165			0.555827	−	0.831298i	$-0.312402\pi$
$97$	107.830			1.11165			0.555827	+	0.831298i	$0.312402\pi$
$98$	36.4457	−	58.9382i	0.371895	−	0.601410i
$99$	52.5348			0.530654
$100$	−46.7187	+	17.8147i	−0.467187	+	0.178147i
$101$			52.6151i			0.520941i	0.965482	+	0.260471i	$0.0838777\pi$
$101$			52.6151i			0.520941i	−0.965482	+	0.260471i	$0.916122\pi$
$102$		−	44.1604i		−	0.432945i
$103$	72.4002			0.702915			0.351457	−	0.936204i	$-0.385686\pi$
$103$	72.4002			0.702915			0.351457	+	0.936204i	$0.385686\pi$
$104$			13.6763i			0.131503i
$105$	5.73594	−	60.3498i	0.0546280	−	0.574760i
$106$	109.656			1.03449
$107$			173.562i			1.62207i	0.584994	+	0.811037i	$0.301097\pi$
$107$			173.562i			1.62207i	−0.584994	+	0.811037i	$0.698903\pi$
$108$	10.3923			0.0962250
$109$	49.9966			0.458684			0.229342	−	0.973346i	$-0.426342\pi$
$109$	49.9966			0.458684			0.229342	+	0.973346i	$0.426342\pi$
$110$	−22.4302	−	121.777i	−0.203911	−	1.10707i
$111$			71.6418i			0.645422i
$112$	7.65475	−	26.9333i	0.0683460	−	0.240476i
$113$			70.1536i			0.620828i	0.950601	+	0.310414i	$0.100468\pi$
$113$			70.1536i			0.620828i	−0.950601	+	0.310414i	$0.899532\pi$
$114$	−22.3724			−0.196249
$115$	3.37394	+	18.3176i	0.0293386	+	0.159284i
$116$	−2.25164			−0.0194107
$117$	−14.5059			−0.123982
$118$	−123.129			−1.04346
$119$	34.5007	−	121.391i	0.289922	−	1.02009i
$120$	−4.43709	−	24.0897i	−0.0369758	−	0.200747i
$121$	185.656			1.53435
$122$	7.59373			0.0622436
$123$			20.2919i			0.164975i
$124$			114.172i			0.920741i
$125$	−106.797	+	64.9569i	−0.854376	+	0.519655i
$126$	28.5671	+	8.11909i	0.226723	+	0.0644372i
$127$			197.945i			1.55863i	0.626635	+	0.779313i	$0.284432\pi$
$127$			197.945i			1.55863i	−0.626635	+	0.779313i	$0.715568\pi$
$128$		−	11.3137i		−	0.0883883i
$129$		−	111.574i		−	0.864912i
$130$	6.19344	+	33.6252i	0.0476418	+	0.258655i
$131$			114.901i			0.877105i	0.898706	+	0.438552i	$0.144509\pi$
$131$			114.901i			0.877105i	−0.898706	+	0.438552i	$0.855491\pi$
$132$	60.6619			0.459560
$133$	−61.4989	−	17.4787i	−0.462398	−	0.131419i
$134$	66.7338			0.498013
$135$	25.5510	−	4.70625i	0.189266	−	0.0348611i
$136$		−	50.9920i		−	0.374941i
$137$		−	95.3358i		−	0.695882i	−0.937516	−	0.347941i	$-0.886881\pi$
$137$		−	95.3358i		−	0.695882i	0.937516	−	0.347941i	$-0.113119\pi$
$138$	−9.12473			−0.0661212
$139$		−	237.587i		−	1.70926i	−0.519237	−	0.854630i	$-0.673784\pi$
$139$		−	237.587i		−	1.70926i	0.519237	−	0.854630i	$-0.326216\pi$
$140$	6.62330	−	69.6860i	0.0473093	−	0.497757i
$141$	−134.513			−0.953996
$142$		−	82.4553i		−	0.580671i
$143$	−84.6740			−0.592126
$144$	12.0000			0.0833333
$145$	−5.53597	+	1.01967i	−0.0381791	+	0.00703223i
$146$		−	75.5306i		−	0.517333i
$147$	72.1842	+	44.6367i	0.491049	+	0.303651i
$148$			82.7248i			0.558952i
$149$	133.844			0.898285			0.449142	−	0.893460i	$-0.351730\pi$
$149$	133.844			0.898285			0.449142	+	0.893460i	$0.351730\pi$
$150$	−21.8184	−	57.2185i	−0.145456	−	0.381457i
$151$	155.064			1.02691			0.513456	−	0.858116i	$-0.328365\pi$
$151$	155.064			1.02691			0.513456	+	0.858116i	$0.328365\pi$
$152$	−25.8335			−0.169957
$153$	54.0852			0.353498
$154$	166.752	+	47.3928i	1.08280	+	0.307745i
$155$	51.7037	+	280.708i	0.333572	+	1.81102i
$156$	−16.7500			−0.107372
$157$	104.634			0.666459			0.333230	−	0.942846i	$-0.391862\pi$
$157$	104.634			0.666459			0.333230	+	0.942846i	$0.391862\pi$
$158$		−	106.015i		−	0.670979i
$159$			134.300i			0.844656i
$160$	−5.12351	−	27.8164i	−0.0320219	−	0.173852i
$161$	−25.0827	−	7.12878i	−0.155793	−	0.0442782i
$162$			12.7279i			0.0785674i
$163$			130.909i			0.803120i	0.915833	+	0.401560i	$0.131532\pi$
$163$			130.909i			0.803120i	−0.915833	+	0.401560i	$0.868468\pi$
$164$			23.4311i			0.142873i
$165$	149.146	−	27.4713i	0.903915	−	0.166493i
$166$			40.7138i			0.245264i
$167$	102.845			0.615838			0.307919	−	0.951413i	$-0.400367\pi$
$167$	102.845			0.615838			0.307919	+	0.951413i	$0.400367\pi$
$168$	32.9865	+	9.37512i	0.196348	+	0.0558043i
$169$	−145.620			−0.861656
$170$	−23.0922	−	125.371i	−0.135836	−	0.737477i
$171$		−	27.4005i		−	0.160237i
$172$		−	128.834i		−	0.749036i
$173$	−197.432			−1.14122			−0.570612	−	0.821220i	$-0.693294\pi$
$173$	−197.432			−1.14122			−0.570612	+	0.821220i	$0.693294\pi$
$174$		−	2.75768i		−	0.0158487i
$175$	−15.2736	−	174.332i	−0.0872776	−	0.996184i
$176$	70.0464			0.397991
$177$		−	150.801i		−	0.851984i
$178$	143.541			0.806409
$179$	−118.822			−0.663809			−0.331904	−	0.943313i	$-0.607691\pi$
$179$	−118.822			−0.663809			−0.331904	+	0.943313i	$0.607691\pi$
$180$	29.5037	−	5.43430i	0.163909	−	0.0301906i
$181$		−	14.4148i		−	0.0796399i	−0.999207	−	0.0398199i	$-0.987322\pi$
$181$		−	14.4148i		−	0.0796399i	0.999207	−	0.0398199i	$-0.0126784\pi$
$182$	−46.0436	−	13.0861i	−0.252987	−	0.0719017i
$183$			9.30038i			0.0508217i
$184$	−10.5363			−0.0572626
$185$	37.4627	+	203.391i	0.202501	+	1.09941i
$186$	−139.831			−0.751782
$187$	315.706			1.68827
$188$	−155.323			−0.826185
$189$	−9.94382	+	34.9874i	−0.0526128	+	0.185119i
$190$	−63.5152	+	11.6989i	−0.334291	+	0.0615732i
$191$	59.9375			0.313809			0.156904	−	0.987614i	$-0.449849\pi$
$191$	59.9375			0.313809			0.156904	+	0.987614i	$0.449849\pi$
$192$	13.8564			0.0721688
$193$		−	245.948i		−	1.27434i	−0.770723	−	0.637171i	$-0.780105\pi$
$193$		−	245.948i		−	1.27434i	0.770723	−	0.637171i	$-0.219895\pi$
$194$			152.495i			0.786058i
$195$	−41.1823	+	7.58538i	−0.211191	+	0.0388994i
$196$	83.3512	+	51.5420i	0.425261	+	0.262969i
$197$		−	82.0594i		−	0.416545i	−0.978071	−	0.208273i	$-0.933216\pi$
$197$		−	82.0594i		−	0.416545i	0.978071	−	0.208273i	$-0.0667842\pi$
$198$			74.2954i			0.375229i
$199$		−	289.338i		−	1.45396i	−0.686658	−	0.726981i	$-0.740923\pi$
$199$		−	289.338i		−	1.45396i	0.686658	−	0.726981i	$-0.259077\pi$
$200$	−25.1938	−	66.0702i	−0.125969	−	0.330351i
$201$			81.7319i			0.406626i
$202$	−74.4089			−0.368361
$203$	2.15447	−	7.58051i	0.0106131	−	0.0373424i
$204$	62.4522			0.306138
$205$	10.6110	+	57.6087i	0.0517609	+	0.281018i
$206$			102.389i			0.497036i
$207$		−	11.1755i		−	0.0539877i
$208$	−19.3412			−0.0929867
$209$		−	159.942i		−	0.765274i
$210$	85.3475	+	8.11185i	0.406417	+	0.0386279i
$211$	33.6995			0.159713			0.0798567	−	0.996806i	$-0.474554\pi$
$211$	33.6995			0.159713			0.0798567	+	0.996806i	$0.474554\pi$
$212$			155.077i			0.731493i
$213$	100.987			0.474116
$214$	−245.454			−1.14698
$215$	−58.3437	−	316.757i	−0.271366	−	1.47329i
$216$			14.6969i			0.0680414i
$217$	−384.379	−	109.245i	−1.77133	−	0.503432i
$218$			70.7059i			0.324339i
$219$	92.5057			0.422401
$220$	172.219	−	31.7211i	0.782813	−	0.144187i
$221$	−87.1728			−0.394447
$222$	−101.317			−0.456382
$223$	10.7556			0.0482313			0.0241156	−	0.999709i	$-0.492323\pi$
$223$	10.7556			0.0482313			0.0241156	+	0.999709i	$0.492323\pi$
$224$	38.0895	+	10.8255i	0.170042	+	0.0483279i
$225$	70.0781	−	26.7220i	0.311458	−	0.118765i
$226$	−99.2121			−0.438992
$227$	−416.450			−1.83458			−0.917290	−	0.398219i	$-0.869628\pi$
$227$	−416.450			−1.83458			−0.917290	+	0.398219i	$0.869628\pi$
$228$		−	31.6394i		−	0.138769i
$229$			388.469i			1.69637i	0.529700	+	0.848185i	$0.322305\pi$
$229$			388.469i			1.69637i	−0.529700	+	0.848185i	$0.677695\pi$
$230$	−25.9051	+	4.77147i	−0.112631	+	0.0207455i
$231$	−58.0440	+	204.229i	−0.251273	+	0.884107i
$232$		−	3.18429i		−	0.0137254i
$233$			70.4036i			0.302162i	0.988521	+	0.151081i	$0.0482754\pi$
$233$			70.4036i			0.302162i	−0.988521	+	0.151081i	$0.951725\pi$
$234$		−	20.5145i		−	0.0876687i
$235$	−381.883	+	70.3393i	−1.62503	+	0.299316i
$236$		−	174.130i		−	0.737839i
$237$	129.841			0.547852
$238$	171.673	+	48.7914i	0.721315	+	0.205006i
$239$	−313.133			−1.31018			−0.655091	−	0.755550i	$-0.727370\pi$
$239$	−313.133			−1.31018			−0.655091	+	0.755550i	$0.727370\pi$
$240$	34.0679	−	6.27499i	0.141950	−	0.0261458i
$241$		−	198.727i		−	0.824595i	−0.911049	−	0.412297i	$-0.864726\pi$
$241$		−	198.727i		−	0.824595i	0.911049	−	0.412297i	$-0.135274\pi$
$242$			262.557i			1.08495i
$243$	−15.5885			−0.0641500
$244$			10.7391i			0.0440129i
$245$	228.272	+	88.9770i	0.931722	+	0.363172i
$246$	−28.6971			−0.116655
$247$			44.1633i			0.178799i
$248$	−161.463			−0.651062
$249$	−49.8640			−0.200257
$250$	−91.8629	−	151.034i	−0.367452	−	0.604135i
$251$			300.878i			1.19872i	0.800480	+	0.599359i	$0.204578\pi$
$251$			300.878i			1.19872i	−0.800480	+	0.599359i	$0.795422\pi$
$252$	−11.4821	+	40.4000i	−0.0455640	+	0.160317i
$253$		−	65.2334i		−	0.257839i
$254$	−279.937			−1.10211
$255$	153.548	−	28.2820i	0.602147	−	0.110910i
$256$	16.0000			0.0625000
$257$	−306.052			−1.19087			−0.595433	−	0.803405i	$-0.703019\pi$
$257$	−306.052			−1.19087			−0.595433	+	0.803405i	$0.703019\pi$
$258$	157.789			0.611585
$259$	−278.507	−	79.1548i	−1.07532	−	0.305617i
$260$	−47.5532	+	8.75885i	−0.182897	+	0.0336879i
$261$	3.37745			0.0129404
$262$	−162.494			−0.620207
$263$		−	286.135i		−	1.08797i	−0.839096	−	0.543984i	$-0.816915\pi$
$263$		−	286.135i		−	1.08797i	0.839096	−	0.543984i	$-0.183085\pi$
$264$			85.7889i			0.324958i
$265$	70.2278	+	381.278i	0.265010	+	1.43878i
$266$	24.7186	−	86.9726i	0.0929270	−	0.326965i
$267$			175.801i			0.658430i
$268$			94.3758i			0.352149i
$269$			188.412i			0.700415i	0.936672	+	0.350208i	$0.113889\pi$
$269$			188.412i			0.700415i	−0.936672	+	0.350208i	$0.886111\pi$
$270$	6.65564	+	36.1345i	0.0246505	+	0.133832i
$271$		−	9.59288i		−	0.0353981i	−0.999843	−	0.0176990i	$-0.994366\pi$
$271$		−	9.59288i		−	0.0353981i	0.999843	−	0.0176990i	$-0.00563408\pi$
$272$	72.1136			0.265123
$273$	16.0271	−	56.3917i	0.0587075	−	0.206563i
$274$	134.825			0.492063
$275$	409.060	−	155.982i	1.48749	−	0.567206i
$276$		−	12.9043i		−	0.0467548i
$277$			161.066i			0.581464i	0.956804	+	0.290732i	$0.0938989\pi$
$277$			161.066i			0.581464i	−0.956804	+	0.290732i	$0.906101\pi$
$278$	335.999			1.20863
$279$		−	171.258i		−	0.613827i
$280$	98.5508	+	9.36676i	0.351967	+	0.0334527i
$281$	−343.107			−1.22102			−0.610510	−	0.792008i	$-0.709036\pi$
$281$	−343.107			−1.22102			−0.610510	+	0.792008i	$0.709036\pi$
$282$		−	190.231i		−	0.674577i
$283$	324.748			1.14752			0.573759	−	0.819024i	$-0.305484\pi$
$283$	324.748			1.14752			0.573759	+	0.819024i	$0.305484\pi$
$284$	116.609			0.410597
$285$	−14.3282	−	77.7899i	−0.0502743	−	0.272947i
$286$		−	119.747i		−	0.418696i
$287$	−78.8848	−	22.4199i	−0.274860	−	0.0781182i
$288$			16.9706i			0.0589256i
$289$	36.0229			0.124647
$290$	−1.44204	−	7.82904i	−0.00497254	−	0.0269967i
$291$	−186.768			−0.641813
$292$	106.816			0.365810
$293$	−100.918			−0.344429			−0.172215	−	0.985059i	$-0.555092\pi$
$293$	−100.918			−0.344429			−0.172215	+	0.985059i	$0.555092\pi$
$294$	−63.1258	+	102.084i	−0.214714	+	0.347224i
$295$	−78.8563	−	428.124i	−0.267310	−	1.45127i
$296$	−116.991			−0.395238
$297$	−90.9929			−0.306373
$298$			189.285i			0.635183i
$299$			18.0123i			0.0602417i
$300$	80.9192	−	30.8559i	0.269731	−	0.102853i
$301$	433.742	+	123.274i	1.44100	+	0.409549i
$302$			219.293i			0.726136i
$303$		−	91.1320i		−	0.300766i
$304$		−	36.5340i		−	0.120178i
$305$	4.86332	+	26.4037i	0.0159453	+	0.0865696i
$306$			76.4880i			0.249961i
$307$	−41.3057			−0.134546			−0.0672732	−	0.997735i	$-0.521430\pi$
$307$	−41.3057			−0.134546			−0.0672732	+	0.997735i	$0.521430\pi$
$308$	−67.0235	+	235.823i	−0.217609	+	0.765659i
$309$	−125.401			−0.405828
$310$	−396.981	+	73.1201i	−1.28058	+	0.235871i
$311$			470.341i			1.51235i	0.654369	+	0.756176i	$0.272934\pi$
$311$			470.341i			1.51235i	−0.654369	+	0.756176i	$0.727066\pi$
$312$		−	23.6881i		−	0.0759233i
$313$	160.220			0.511884			0.255942	−	0.966692i	$-0.417614\pi$
$313$	160.220			0.511884			0.255942	+	0.966692i	$0.417614\pi$
$314$			147.975i			0.471258i
$315$	−9.93495	+	104.529i	−0.0315395	+	0.331838i
$316$	149.927			0.474454
$317$		−	268.766i		−	0.847843i	−0.905699	−	0.423922i	$-0.860653\pi$
$317$		−	268.766i		−	0.847843i	0.905699	−	0.423922i	$-0.139347\pi$
$318$	−189.929			−0.597262
$319$	19.7149			0.0618021
$320$	39.3383	−	7.24574i	0.122932	−	0.0226429i
$321$		−	300.618i		−	0.936505i
$322$	10.0816	−	35.4723i	0.0313094	−	0.110162i
$323$		−	164.662i		−	0.509791i
$324$	−18.0000			−0.0555556
$325$	−112.950	+	43.0697i	−0.347537	+	0.132522i
$326$	−185.133			−0.567891
$327$	−86.5967			−0.264822
$328$	−33.1366			−0.101026
$329$	148.620	−	522.920i	0.451732	−	1.58942i
$330$	38.8503	+	210.924i	0.117728	+	0.639165i
$331$	555.018			1.67679			0.838395	−	0.545063i	$-0.183494\pi$
$331$	555.018			1.67679			0.838395	+	0.545063i	$0.183494\pi$
$332$	−57.5780			−0.173428
$333$		−	124.087i		−	0.372634i
$334$			145.445i			0.435463i
$335$	42.7389	+	232.036i	0.127579	+	0.692646i
$336$	−13.2584	+	46.6499i	−0.0394596	+	0.138839i
$337$		−	47.7972i		−	0.141831i	−0.997482	−	0.0709157i	$-0.977408\pi$
$337$		−	47.7972i		−	0.141831i	0.997482	−	0.0709157i	$-0.0225921\pi$
$338$		−	205.937i		−	0.609282i
$339$		−	121.510i		−	0.358435i
$340$	177.301	−	32.6573i	0.521475	−	0.0960507i
$341$		−	999.666i		−	2.93157i
$342$	38.7502			0.113305
$343$	−253.279	+	231.298i	−0.738422	+	0.674338i
$344$	182.199			0.529649
$345$	−5.84383	−	31.7271i	−0.0169386	−	0.0919625i
$346$		−	279.211i		−	0.806967i
$347$			283.766i			0.817771i	0.912586	+	0.408885i	$0.134082\pi$
$347$			283.766i			0.817771i	−0.912586	+	0.408885i	$0.865918\pi$
$348$	3.89995			0.0112067
$349$		−	20.0321i		−	0.0573987i	−0.999588	−	0.0286993i	$-0.990863\pi$
$349$		−	20.0321i		−	0.0573987i	0.999588	−	0.0286993i	$-0.00913653\pi$
$350$	246.543	−	21.6001i	0.704408	−	0.0617146i
$351$	25.1250			0.0715812
$352$			99.0605i			0.281422i
$353$	595.015			1.68559			0.842797	−	0.538231i	$-0.180907\pi$
$353$	595.015			1.68559			0.842797	+	0.538231i	$0.180907\pi$
$354$	213.265			0.602443
$355$	286.701	−	52.8076i	0.807608	−	0.148754i
$356$			202.997i			0.570217i
$357$	−59.7570	+	210.256i	−0.167387	+	0.588952i
$358$		−	168.039i		−	0.469384i
$359$	588.390			1.63897			0.819485	−	0.573101i	$-0.194260\pi$
$359$	588.390			1.63897			0.819485	+	0.573101i	$0.194260\pi$
$360$	7.68527	+	41.7245i	0.0213480	+	0.115901i
$361$	277.579			0.768917
$362$	20.3856			0.0563139
$363$	−321.566			−0.885856
$364$	18.5065	−	65.1155i	0.0508422	−	0.178889i
$365$	262.623	−	48.3727i	0.719516	−	0.132528i
$366$	−13.1527			−0.0359364
$367$	−662.601			−1.80545			−0.902726	−	0.430215i	$-0.858438\pi$
$367$	−662.601			−1.80545			−0.902726	+	0.430215i	$0.858438\pi$
$368$		−	14.9006i		−	0.0404908i
$369$		−	35.1467i		−	0.0952485i
$370$	−287.638	+	52.9802i	−0.777400	+	0.143190i
$371$	−522.091	−	148.384i	−1.40725	−	0.399957i
$372$		−	197.751i		−	0.531590i
$373$		−	236.349i		−	0.633644i	−0.948485	−	0.316822i	$-0.897384\pi$
$373$		−	236.349i		−	0.633644i	0.948485	−	0.316822i	$-0.102616\pi$
$374$			446.476i			1.19378i
$375$	184.978	−	112.509i	0.493274	−	0.300023i
$376$		−	219.660i		−	0.584201i
$377$	−5.44368			−0.0144395
$378$	−49.4797	−	14.0627i	−0.130899	−	0.0372029i
$379$	344.235			0.908272			0.454136	−	0.890932i	$-0.349948\pi$
$379$	344.235			0.908272			0.454136	+	0.890932i	$0.349948\pi$
$380$	−16.5447	−	89.8241i	−0.0435388	−	0.236379i
$381$		−	342.852i		−	0.899873i
$382$			84.7644i			0.221896i
$383$	65.7097			0.171566			0.0857828	−	0.996314i	$-0.472661\pi$
$383$	65.7097			0.171566			0.0857828	+	0.996314i	$0.472661\pi$
$384$			19.5959i			0.0510310i
$385$	−57.9923	+	610.156i	−0.150629	+	1.58482i
$386$	347.823			0.901095
$387$			193.251i			0.499357i
$388$	−215.661			−0.555827
$389$	161.296			0.414642			0.207321	−	0.978273i	$-0.433526\pi$
$389$	161.296			0.414642			0.207321	+	0.978273i	$0.433526\pi$
$390$	−10.7274	−	58.2405i	−0.0275060	−	0.149335i
$391$		−	67.1585i		−	0.171761i
$392$	−72.8914	+	117.876i	−0.185947	+	0.300705i
$393$		−	199.014i		−	0.506397i
$394$	116.050			0.294542
$395$	368.618	−	67.8959i	0.933209	−	0.171888i
$396$	−105.070			−0.265327
$397$	−667.752			−1.68200			−0.840998	−	0.541039i	$-0.818031\pi$
$397$	−667.752			−1.68200			−0.840998	+	0.541039i	$0.818031\pi$
$398$	409.186			1.02811
$399$	106.519	+	30.2740i	0.266966	+	0.0758746i
$400$	93.4374	−	35.6294i	0.233594	−	0.0890734i
$401$	−593.826			−1.48086			−0.740431	−	0.672132i	$-0.765379\pi$
$401$	−593.826			−1.48086			−0.740431	+	0.672132i	$0.765379\pi$
$402$	−115.586			−0.287528
$403$			276.028i			0.684933i
$404$		−	105.230i		−	0.260471i
$405$	−44.2556	+	8.15146i	−0.109273	+	0.0201271i
$406$	10.7205	+	3.04687i	0.0264051	+	0.00750461i
$407$		−	724.322i		−	1.77966i
$408$			88.3207i			0.216472i
$409$			569.625i			1.39273i	0.717690	+	0.696363i	$0.245200\pi$
$409$			569.625i			1.39273i	−0.717690	+	0.696363i	$0.754800\pi$
$410$	−81.4711	+	15.0062i	−0.198710	+	0.0366005i
$411$			165.127i			0.401768i
$412$	−144.800			−0.351457
$413$	586.238	+	166.615i	1.41946	+	0.403427i
$414$	15.8045			0.0381751
$415$	−141.564	+	26.0747i	−0.341117	+	0.0628306i
$416$		−	27.3526i		−	0.0657515i
$417$			411.513i			0.986842i
$418$	226.192			0.541130
$419$		−	209.456i		−	0.499894i	−0.968260	−	0.249947i	$-0.919587\pi$
$419$		−	209.456i		−	0.499894i	0.968260	−	0.249947i	$-0.0804132\pi$
$420$	−11.4719	+	120.700i	−0.0273140	+	0.287380i
$421$	−169.713			−0.403119			−0.201560	−	0.979476i	$-0.564601\pi$
$421$	−169.713			−0.403119			−0.201560	+	0.979476i	$0.564601\pi$
$422$			47.6583i			0.112934i
$423$	232.984			0.550790
$424$	−219.311			−0.517244
$425$	421.132	−	160.585i	0.990898	−	0.377847i
$426$			142.817i			0.335251i
$427$	−36.1551	−	10.2757i	−0.0846725	−	0.0240649i
$428$		−	347.124i		−	0.811037i
$429$	146.660			0.341864
$430$	447.962	−	82.5104i	1.04177	−	0.191885i
$431$	538.427			1.24925			0.624625	−	0.780925i	$-0.285252\pi$
$431$	538.427			1.24925			0.624625	+	0.780925i	$0.285252\pi$
$432$	−20.7846			−0.0481125
$433$	−118.314			−0.273243			−0.136622	−	0.990623i	$-0.543624\pi$
$433$	−118.314			−0.273243			−0.136622	+	0.990623i	$0.543624\pi$
$434$	154.495	−	543.593i	0.355980	−	1.25252i
$435$	9.58858	−	1.76613i	0.0220427	−	0.00406006i
$436$	−99.9932			−0.229342
$437$	−34.0237			−0.0778575
$438$			130.823i			0.298682i
$439$			434.834i			0.990510i	0.868748	+	0.495255i	$0.164925\pi$
$439$			434.834i			0.990510i	−0.868748	+	0.495255i	$0.835075\pi$
$440$	44.8604	+	243.554i	0.101956	+	0.553533i
$441$	−125.027	−	77.3130i	−0.283507	−	0.175313i
$442$		−	123.281i		−	0.278916i
$443$			555.005i			1.25283i	0.779488	+	0.626417i	$0.215479\pi$
$443$			555.005i			1.25283i	−0.779488	+	0.626417i	$0.784521\pi$
$444$		−	143.284i		−	0.322711i
$445$	91.9291	+	499.098i	0.206582	+	1.12157i
$446$			15.2107i			0.0341047i
$447$	−231.825			−0.518625
$448$	−15.3095	+	53.8667i	−0.0341730	+	0.120238i
$449$	−66.8926			−0.148981			−0.0744906	−	0.997222i	$-0.523733\pi$
$449$	−66.8926			−0.148981			−0.0744906	+	0.997222i	$0.523733\pi$
$450$	37.7906	+	99.1053i	0.0839792	+	0.220234i
$451$		−	205.158i		−	0.454896i
$452$		−	140.307i		−	0.310414i
$453$	−268.578			−0.592888
$454$		−	588.949i		−	1.29724i
$455$	16.0128	−	168.477i	0.0351931	−	0.370278i
$456$	44.7449			0.0981247
$457$			750.939i			1.64319i	0.570070	+	0.821596i	$0.306916\pi$
$457$			750.939i			1.64319i	−0.570070	+	0.821596i	$0.693084\pi$
$458$	−549.378			−1.19951
$459$	−93.6783			−0.204092
$460$	−6.74787	−	36.6353i	−0.0146693	−	0.0796419i
$461$			395.377i			0.857651i	0.903387	+	0.428826i	$0.141072\pi$
$461$			395.377i			0.857651i	−0.903387	+	0.428826i	$0.858928\pi$
$462$	−288.823	−	82.0867i	−0.625158	−	0.177677i
$463$		−	423.981i		−	0.915726i	−0.889023	−	0.457863i	$-0.848615\pi$
$463$		−	423.981i		−	0.915726i	0.889023	−	0.457863i	$-0.151385\pi$
$464$	4.50327			0.00970533
$465$	−89.5535	−	486.200i	−0.192588	−	1.04559i
$466$	−99.5658			−0.213660
$467$	584.408			1.25141			0.625705	−	0.780060i	$-0.284812\pi$
$467$	584.408			1.25141			0.625705	+	0.780060i	$0.284812\pi$
$468$	29.0119			0.0619911
$469$	−317.732	−	90.3030i	−0.677467	−	0.192544i
$470$	−99.4747	−	540.064i	−0.211648	−	1.14907i
$471$	−181.232			−0.384780
$472$	246.257			0.521731
$473$			1128.05i			2.38488i
$474$			183.623i			0.387390i
$475$	−81.3552	−	213.353i	−0.171274	−	0.449164i
$476$	−69.0014	+	242.782i	−0.144961	+	0.510047i
$477$		−	232.615i		−	0.487662i
$478$		−	442.837i		−	0.926438i
$479$			734.511i			1.53343i	0.641990	+	0.766713i	$0.278109\pi$
$479$			734.511i			1.53343i	−0.641990	+	0.766713i	$0.721891\pi$
$480$	8.87418	+	48.1793i	0.0184879	+	0.100374i
$481$			200.000i			0.415801i
$482$	281.043			0.583077
$483$	43.4445	+	12.3474i	0.0899473	+	0.0255640i
$484$	−371.312			−0.767174
$485$	−530.232	+	97.6638i	−1.09326	+	0.201369i
$486$		−	22.0454i		−	0.0453609i
$487$		−	91.6643i		−	0.188222i	−0.995562	−	0.0941111i	$-0.969999\pi$
$487$		−	91.6643i		−	0.188222i	0.995562	−	0.0941111i	$-0.0300009\pi$
$488$	−15.1875			−0.0311218
$489$		−	226.740i		−	0.463681i
$490$	−125.833	+	322.825i	−0.256801	+	0.658827i
$491$	460.086			0.937038			0.468519	−	0.883453i	$-0.344788\pi$
$491$	460.086			0.937038			0.468519	+	0.883453i	$0.344788\pi$
$492$		−	40.5839i		−	0.0824876i
$493$	20.2967			0.0411698
$494$	−62.4564			−0.126430
$495$	−258.328	+	47.5817i	−0.521876	+	0.0961246i
$496$		−	228.344i		−	0.460370i
$497$	−111.577	+	392.585i	−0.224501	+	0.789910i
$498$		−	70.5184i		−	0.141603i
$499$	−487.126			−0.976204			−0.488102	−	0.872786i	$-0.662311\pi$
$499$	−487.126			−0.976204			−0.488102	+	0.872786i	$0.662311\pi$
$500$	213.594	−	129.914i	0.427188	−	0.259828i
$501$	−178.133			−0.355554
$502$	−425.506			−0.847622
$503$	−305.145			−0.606650			−0.303325	−	0.952887i	$-0.598097\pi$
$503$	−305.145			−0.606650			−0.303325	+	0.952887i	$0.598097\pi$
$504$	−57.1342	−	16.2382i	−0.113362	−	0.0322186i
$505$	−47.6544	−	258.723i	−0.0943651	−	0.512323i
$506$	92.2539			0.182320
$507$	252.221			0.497477
$508$		−	395.891i		−	0.779313i
$509$			800.434i			1.57256i	0.617869	+	0.786281i	$0.287996\pi$
$509$			800.434i			1.57256i	−0.617869	+	0.786281i	$0.712004\pi$
$510$	39.9968	+	217.149i	0.0784251	+	0.425782i
$511$	−102.207	+	359.615i	−0.200013	+	0.703748i
$512$			22.6274i			0.0441942i
$513$			47.4591i			0.0925128i
$514$		−	432.824i		−	0.842069i
$515$	−356.012	+	65.5741i	−0.691286	+	0.127328i
$516$			223.147i			0.432456i
$517$	1359.97			2.63051
$518$	111.942	−	393.868i	0.216104	−	0.760364i
$519$	341.962			0.658886
$520$	−12.3869	−	67.2503i	−0.0238209	−	0.129328i
$521$		−	21.4194i		−	0.0411121i	−0.999789	−	0.0205560i	$-0.993456\pi$
$521$		−	21.4194i		−	0.0411121i	0.999789	−	0.0205560i	$-0.00654365\pi$
$522$			4.77644i			0.00915027i
$523$	−842.290			−1.61050			−0.805249	−	0.592937i	$-0.797968\pi$
$523$	−842.290			−1.61050			−0.805249	+	0.592937i	$0.797968\pi$
$524$		−	229.801i		−	0.438552i
$525$	26.4546	+	301.952i	0.0503897	+	0.575147i
$526$	404.657			0.769309
$527$		−	1029.17i		−	1.95288i
$528$	−121.324			−0.229780
$529$	515.123			0.973768
$530$	−539.208	+	99.3171i	−1.01737	+	0.187391i
$531$			261.195i			0.491893i
$532$	122.998	+	34.9574i	0.231199	+	0.0657093i
$533$			56.6484i			0.106282i
$534$	−248.620			−0.465580
$535$	−157.198	−	853.453i	−0.293828	−	1.59524i
$536$	−133.468			−0.249007
$537$	205.805			0.383250
$538$	−266.454			−0.495268
$539$	−729.806	−	451.291i	−1.35400	−	0.837275i
$540$	−51.1019	+	9.41249i	−0.0946332	+	0.0174305i
$541$	−15.6795			−0.0289824			−0.0144912	−	0.999895i	$-0.504613\pi$
$541$	−15.6795			−0.0289824			−0.0144912	+	0.999895i	$0.504613\pi$
$542$	13.5664			0.0250302
$543$			24.9672i			0.0459801i
$544$			101.984i			0.187471i
$545$	−245.847	+	45.2828i	−0.451096	+	0.0830877i
$546$	79.7499	+	22.6658i	0.146062	+	0.0415125i
$547$			315.792i			0.577317i	0.957432	+	0.288659i	$0.0932092\pi$
$547$			315.792i			0.577317i	−0.957432	+	0.288659i	$0.906791\pi$
$548$			190.672i			0.347941i
$549$		−	16.1087i		−	0.0293419i
$550$	220.591	+	578.498i	0.401075	+	1.05181i
$551$		−	10.2827i		−	0.0186618i
$552$	18.2495			0.0330606
$553$	−143.457	+	504.756i	−0.259416	+	0.912759i
$554$	−227.781			−0.411157
$555$	−64.8872	−	352.283i	−0.116914	−	0.634744i
$556$			475.174i			0.854630i
$557$		−	358.421i		−	0.643484i	−0.946827	−	0.321742i	$-0.895732\pi$
$557$		−	358.421i		−	0.643484i	0.946827	−	0.321742i	$-0.104268\pi$
$558$	242.195			0.434041
$559$		−	311.477i		−	0.557203i
$560$	−13.2466	+	139.372i	−0.0236546	+	0.248878i
$561$	−546.819			−0.974721
$562$		−	485.226i		−	0.863392i
$563$	622.834			1.10628			0.553138	−	0.833089i	$-0.313430\pi$
$563$	622.834			1.10628			0.553138	+	0.833089i	$0.313430\pi$
$564$	269.027			0.476998
$565$	−63.5393	−	344.965i	−0.112459	−	0.610557i
$566$			459.263i			0.811418i
$567$	17.2232	−	60.6000i	0.0303760	−	0.106878i
$568$			164.911i			0.290336i
$569$	−185.789			−0.326518			−0.163259	−	0.986583i	$-0.552201\pi$
$569$	−185.789			−0.326518			−0.163259	+	0.986583i	$0.552201\pi$
$570$	110.012	−	20.2631i	0.193003	−	0.0355493i
$571$	−486.258			−0.851589			−0.425795	−	0.904820i	$-0.640005\pi$
$571$	−486.258			−0.851589			−0.425795	+	0.904820i	$0.640005\pi$
$572$	169.348			0.296063
$573$	−103.815			−0.181178
$574$	31.7066	−	111.560i	0.0552379	−	0.194355i
$575$	−33.1812	−	87.0172i	−0.0577064	−	0.151334i
$576$	−24.0000			−0.0416667
$577$	−270.057			−0.468037			−0.234018	−	0.972232i	$-0.575188\pi$
$577$	−270.057			−0.468037			−0.234018	+	0.972232i	$0.575188\pi$
$578$			50.9440i			0.0881385i
$579$			425.994i			0.735741i
$580$	11.0719	−	2.03935i	0.0190895	−	0.00351611i
$581$	55.0932	−	193.846i	0.0948247	−	0.333642i
$582$		−	264.129i		−	0.453831i
$583$		−	1357.82i		−	2.32902i
$584$			151.061i			0.258666i
$585$	71.3298	−	13.1383i	0.121931	−	0.0224586i
$586$		−	142.719i		−	0.243548i
$587$	−400.613			−0.682476			−0.341238	−	0.939977i	$-0.610846\pi$
$587$	−400.613			−0.682476			−0.341238	+	0.939977i	$0.610846\pi$
$588$	−144.368	−	89.2734i	−0.245525	−	0.151825i
$589$	−521.395			−0.885220
$590$	605.458	−	111.520i	1.02620	−	0.189016i
$591$			142.131i			0.240493i
$592$		−	165.450i		−	0.279476i
$593$	157.686			0.265912			0.132956	−	0.991122i	$-0.457553\pi$
$593$	157.686			0.265912			0.132956	+	0.991122i	$0.457553\pi$
$594$		−	128.683i		−	0.216639i
$595$	−59.7037	+	628.163i	−0.100342	+	1.05574i
$596$	−267.689			−0.449142
$597$			501.149i			0.839445i
$598$	−25.4732			−0.0425973
$599$	−468.940			−0.782872			−0.391436	−	0.920205i	$-0.628022\pi$
$599$	−468.940			−0.782872			−0.391436	+	0.920205i	$0.628022\pi$
$600$	43.6369	+	114.437i	0.0727281	+	0.190728i
$601$			255.932i			0.425844i	0.977069	+	0.212922i	$0.0682980\pi$
$601$			255.932i			0.425844i	−0.977069	+	0.212922i	$0.931702\pi$
$602$	−174.336	+	613.404i	−0.289595	+	1.01894i
$603$		−	141.564i		−	0.234766i
$604$	−310.127			−0.513456
$605$	−912.923	+	168.152i	−1.50896	+	0.277937i
$606$	128.880			0.212673
$607$	773.553			1.27439			0.637194	−	0.770704i	$-0.280095\pi$
$607$	773.553			1.27439			0.637194	+	0.770704i	$0.280095\pi$
$608$	51.6669			0.0849785
$609$	−3.73164	+	13.1298i	−0.00612749	+	0.0215597i
$610$	−37.3405	+	6.87777i	−0.0612139	+	0.0112750i
$611$	−375.517			−0.614594
$612$	−108.170			−0.176749
$613$			443.208i			0.723015i	0.932369	+	0.361507i	$0.117738\pi$
$613$			443.208i			0.723015i	−0.932369	+	0.361507i	$0.882262\pi$
$614$		−	58.4151i		−	0.0951386i
$615$	−18.3788	−	99.7813i	−0.0298842	−	0.162246i
$616$	−333.504	−	94.7855i	−0.541402	−	0.153873i
$617$		−	363.298i		−	0.588813i	−0.955680	−	0.294407i	$-0.904878\pi$
$617$		−	363.298i		−	0.588813i	0.955680	−	0.294407i	$-0.0951220\pi$
$618$		−	177.344i		−	0.286964i
$619$		−	292.211i		−	0.472069i	−0.971745	−	0.236035i	$-0.924152\pi$
$619$		−	292.211i		−	0.472069i	0.971745	−	0.236035i	$-0.0758479\pi$
$620$	−103.407	−	561.415i	−0.166786	−	0.905509i
$621$			19.3565i			0.0311698i
$622$	−665.163			−1.06939
$623$	−683.425	−	194.237i	−1.09699	−	0.311777i
$624$	33.5000			0.0536859
$625$	466.319	−	416.139i	0.746110	−	0.665823i
$626$			226.585i			0.361956i
$627$			277.028i			0.441831i
$628$	−209.268			−0.333230
$629$		−	745.698i		−	1.18553i
$630$	−147.826	−	14.0501i	−0.234645	−	0.0223018i
$631$	189.221			0.299874			0.149937	−	0.988696i	$-0.452093\pi$
$631$	189.221			0.299874			0.149937	+	0.988696i	$0.452093\pi$
$632$			212.029i			0.335489i
$633$	−58.3693			−0.0922106
$634$	380.093			0.599516
$635$	−179.283	−	973.354i	−0.282335	−	1.53284i
$636$		−	268.600i		−	0.422328i
$637$	201.514	+	124.611i	0.316349	+	0.195621i
$638$			27.8810i			0.0437007i
$639$	−174.914			−0.273731
$640$	10.2470	+	55.6327i	0.0160110	+	0.0869261i
$641$	1162.94			1.81425			0.907127	−	0.420857i	$-0.138271\pi$
$641$	1162.94			1.81425			0.907127	+	0.420857i	$0.138271\pi$
$642$	425.138			0.662209
$643$	1096.08			1.70464			0.852320	−	0.523021i	$-0.175195\pi$
$643$	1096.08			1.70464			0.852320	+	0.523021i	$0.175195\pi$
$644$	50.1654	+	14.2576i	0.0778966	+	0.0221391i
$645$	101.054	+	548.640i	0.156673	+	0.850604i
$646$	232.868			0.360476
$647$	−262.877			−0.406302			−0.203151	−	0.979147i	$-0.565118\pi$
$647$	−262.877			−0.406302			−0.203151	+	0.979147i	$0.565118\pi$
$648$		−	25.4558i		−	0.0392837i
$649$			1524.65i			2.34923i
$650$	−60.9098	−	159.735i	−0.0937074	−	0.245746i
$651$	665.763	+	189.217i	1.02268	+	0.290656i
$652$		−	261.817i		−	0.401560i
$653$			242.905i			0.371983i	0.982551	+	0.185992i	$0.0595498\pi$
$653$			242.905i			0.371983i	−0.982551	+	0.185992i	$0.940450\pi$
$654$		−	122.466i		−	0.187257i
$655$	−104.068	−	564.999i	−0.158882	−	0.862594i
$656$		−	46.8622i		−	0.0714364i
$657$	−160.225			−0.243873
$658$	739.521	+	210.180i	1.12389	+	0.319422i
$659$	1176.49			1.78527			0.892634	−	0.450783i	$-0.148855\pi$
$659$	1176.49			1.78527			0.892634	+	0.450783i	$0.148855\pi$
$660$	−298.292	+	54.9426i	−0.451958	+	0.0832463i
$661$		−	246.444i		−	0.372835i	−0.982471	−	0.186418i	$-0.940312\pi$
$661$		−	246.444i		−	0.372835i	0.982471	−	0.186418i	$-0.0596877\pi$
$662$			784.914i			1.18567i
$663$	150.988			0.227734
$664$		−	81.4276i		−	0.122632i
$665$	318.238	+	30.2470i	0.478554	+	0.0454842i
$666$	175.486			0.263492
$667$		−	4.19385i		−	0.00628763i
$668$	−205.690			−0.307919
$669$	−18.6292			−0.0278464
$670$	−328.149	+	60.4420i	−0.489775	+	0.0902119i
$671$		−	94.0298i		−	0.140134i
$672$	−65.9729	−	18.7502i	−0.0981740	−	0.0279021i
$673$		−	76.3328i		−	0.113422i	−0.998391	−	0.0567109i	$-0.981939\pi$
$673$		−	76.3328i		−	0.113422i	0.998391	−	0.0567109i	$-0.0180613\pi$
$674$	67.5954			0.100290
$675$	−121.379	+	46.2839i	−0.179820	+	0.0685687i
$676$	291.240			0.430828
$677$	310.277			0.458312			0.229156	−	0.973390i	$-0.426403\pi$
$677$	310.277			0.458312			0.229156	+	0.973390i	$0.426403\pi$
$678$	171.840			0.253452
$679$	206.354	−	726.058i	0.303908	−	1.06930i
$680$	46.1843	+	250.742i	0.0679181	+	0.368738i
$681$	721.312			1.05920
$682$	1413.74			2.07293
$683$			157.333i			0.230356i	0.993345	+	0.115178i	$0.0367438\pi$
$683$			157.333i			0.230356i	−0.993345	+	0.115178i	$0.963256\pi$
$684$			54.8010i			0.0801185i
$685$	86.3473	+	468.793i	0.126054	+	0.684370i
$686$	−327.105	−	358.190i	−0.476829	−	0.522144i
$687$		−	672.848i		−	0.979400i
$688$			257.668i			0.374518i
$689$			374.921i			0.544153i
$690$	44.8689	−	8.26442i	0.0650273	−	0.0119774i
$691$		−	683.565i		−	0.989240i	−0.869109	−	0.494620i	$-0.835307\pi$
$691$		−	683.565i		−	0.989240i	0.869109	−	0.494620i	$-0.164693\pi$
$692$	394.863			0.570612
$693$	100.535	−	353.734i	0.145072	−	0.510439i
$694$	−401.306			−0.578251
$695$	215.187	+	1168.28i	0.309621	+	1.68098i
$696$			5.51536i			0.00792437i
$697$		−	211.213i		−	0.303031i
$698$	28.3297			0.0405870
$699$		−	121.943i		−	0.174453i
$700$	30.5471	+	348.664i	0.0436388	+	0.498092i
$701$	−306.153			−0.436738			−0.218369	−	0.975866i	$-0.570074\pi$
$701$	−306.153			−0.436738			−0.218369	+	0.975866i	$0.570074\pi$
$702$			35.5321i			0.0506156i
$703$	−377.784			−0.537388
$704$	−140.093			−0.198995
$705$	661.441	−	121.831i	0.938214	−	0.172810i
$706$			841.478i			1.19190i
$707$	354.275	+	100.689i	0.501096	+	0.142417i
$708$			301.602i			0.425992i
$709$	444.082			0.626350			0.313175	−	0.949695i	$-0.398607\pi$
$709$	444.082			0.626350			0.313175	+	0.949695i	$0.398607\pi$
$710$	74.6812	+	405.456i	0.105185	+	0.571065i
$711$	−224.891			−0.316302
$712$	−287.082			−0.403205
$713$	−212.654			−0.298252
$714$	−297.346	−	84.5092i	−0.416452	−	0.118360i
$715$	416.366	−	76.6907i	0.582330	−	0.107260i
$716$	237.643			0.331904
$717$	542.363			0.756434
$718$			832.109i			1.15893i
$719$			672.926i			0.935919i	0.883750	+	0.467960i	$0.155011\pi$
$719$			672.926i			0.935919i	−0.883750	+	0.467960i	$0.844989\pi$
$720$	−59.0074	+	10.8686i	−0.0819547	+	0.0150953i
$721$	138.551	−	487.495i	0.192166	−	0.676137i
$722$			392.556i			0.543707i
$723$			344.206i			0.476080i
$724$			28.8296i			0.0398199i
$725$	26.2984	−	10.0280i	0.0362736	−	0.0138318i
$726$		−	454.762i		−	0.626395i
$727$	675.927			0.929748			0.464874	−	0.885377i	$-0.346100\pi$
$727$	675.927			0.929748			0.464874	+	0.885377i	$0.346100\pi$
$728$	92.0872	+	26.1722i	0.126493	+	0.0359508i
$729$	27.0000			0.0370370
$730$	68.4094	+	371.405i	0.0937115	+	0.508775i
$731$			1161.34i			1.58870i
$732$		−	18.6008i		−	0.0254109i
$733$	−387.908			−0.529206			−0.264603	−	0.964357i	$-0.585241\pi$
$733$	−387.908			−0.529206			−0.264603	+	0.964357i	$0.585241\pi$
$734$		−	937.059i		−	1.27665i
$735$	−395.379	−	154.113i	−0.537930	−	0.209677i
$736$	21.0727			0.0286313
$737$		−	826.336i		−	1.12122i
$738$	49.7049			0.0673508
$739$	−394.643			−0.534024			−0.267012	−	0.963693i	$-0.586036\pi$
$739$	−394.643			−0.534024			−0.267012	+	0.963693i	$0.586036\pi$
$740$	−74.9253	−	406.781i	−0.101250	−	0.549705i
$741$		−	76.4931i		−	0.103230i
$742$	209.847	−	738.348i	0.282812	−	0.995079i
$743$			147.027i			0.197883i	0.995093	+	0.0989414i	$0.0315456\pi$
$743$			147.027i			0.197883i	−0.995093	+	0.0989414i	$0.968454\pi$
$744$	279.663			0.375891
$745$	−658.151	+	121.225i	−0.883424	+	0.162718i
$746$	334.248			0.448054
$747$	86.3670			0.115618
$748$	−631.412			−0.844133
$749$	1168.65	+	332.144i	1.56028	+	0.443449i
$750$	159.111	+	261.598i	0.212148	+	0.348798i
$751$	103.003			0.137154			0.0685771	−	0.997646i	$-0.478154\pi$
$751$	103.003			0.137154			0.0685771	+	0.997646i	$0.478154\pi$
$752$	310.646			0.413092
$753$		−	521.136i		−	0.692080i
$754$		−	7.69852i		−	0.0102102i
$755$	−762.492	+	140.444i	−1.00992	+	0.186018i
$756$	19.8876	−	69.9749i	0.0263064	−	0.0925593i
$757$			547.747i			0.723575i	0.932261	+	0.361788i	$0.117833\pi$
$757$			547.747i			0.723575i	−0.932261	+	0.361788i	$0.882167\pi$
$758$			486.822i			0.642246i
$759$			112.988i			0.148864i
$760$	127.030	−	23.3978i	0.167145	−	0.0307866i
$761$		−	1223.78i		−	1.60813i	−0.594544	−	0.804063i	$-0.702668\pi$
$761$		−	1223.78i		−	1.60813i	0.594544	−	0.804063i	$-0.297332\pi$
$762$	484.865			0.636306
$763$	95.6779	−	336.644i	0.125397	−	0.441211i
$764$	−119.875			−0.156904
$765$	−265.952	+	48.9859i	−0.347650	+	0.0640338i
$766$			92.9275i			0.121315i
$767$		−	420.986i		−	0.548874i
$768$	−27.7128			−0.0360844
$769$			194.874i			0.253413i	0.991940	+	0.126706i	$0.0404406\pi$
$769$			194.874i			0.253413i	−0.991940	+	0.126706i	$0.959559\pi$
$770$	−862.891	−	82.0134i	−1.12064	−	0.106511i
$771$	530.098			0.687547
$772$			491.896i			0.637171i
$773$	−1017.59			−1.31642			−0.658209	−	0.752835i	$-0.728686\pi$
$773$	−1017.59			−1.31642			−0.658209	+	0.752835i	$0.728686\pi$
$774$	−273.299			−0.353099
$775$	−508.484	−	1333.49i	−0.656108	−	1.72063i
$776$		−	304.990i		−	0.393029i
$777$	482.388	+	137.100i	0.620834	+	0.176448i
$778$			228.107i			0.293196i
$779$	−107.004			−0.137361
$780$	82.3645	−	15.1708i	0.105596	−	0.0194497i
$781$	−1021.01			−1.30731
$782$	94.9765			0.121453
$783$	−5.84992			−0.00747117
$784$	−166.702	−	103.084i	−0.212631	−	0.131485i
$785$	−514.515	+	94.7689i	−0.655434	+	0.120725i
$786$	281.448			0.358076
$787$	−222.094			−0.282203			−0.141101	−	0.989995i	$-0.545064\pi$
$787$	−222.094			−0.282203			−0.141101	+	0.989995i	$0.545064\pi$
$788$			164.119i			0.208273i
$789$			495.601i			0.628138i
$790$	96.0193	+	521.304i	0.121543	+	0.659879i
$791$	472.367	+	134.252i	0.597178	+	0.169724i
$792$		−	148.591i		−	0.187615i
$793$			25.9636i			0.0327409i
$794$		−	944.344i		−	1.18935i
$795$	−121.638	−	660.392i	−0.153004	−	0.830682i
$796$			578.677i			0.726981i
$797$	−340.349			−0.427038			−0.213519	−	0.976939i	$-0.568493\pi$
$797$	−340.349			−0.427038			−0.213519	+	0.976939i	$0.568493\pi$
$798$	−42.8139	+	150.641i	−0.0536514	+	0.188773i
$799$	1400.11			1.75233
$800$	50.3875	+	132.140i	0.0629844	+	0.165176i
$801$		−	304.496i		−	0.380145i
$802$		−	839.796i		−	1.04713i
$803$	−935.263			−1.16471
$804$		−	163.464i		−	0.203313i
$805$	129.795	+	12.3364i	0.161237	+	0.0153247i
$806$	−390.363			−0.484321
$807$		−	326.339i		−	0.404385i
$808$	148.818			0.184181
$809$	−462.403			−0.571573			−0.285787	−	0.958293i	$-0.592255\pi$
$809$	−462.403			−0.571573			−0.285787	+	0.958293i	$0.592255\pi$
$810$	−11.5279	−	62.5868i	−0.0142320	−	0.0772677i
$811$			1420.09i			1.75103i	0.483190	+	0.875516i	$0.339478\pi$
$811$			1420.09i			1.75103i	−0.483190	+	0.875516i	$0.660522\pi$
$812$	−4.30893	+	15.1610i	−0.00530656	+	0.0186712i
$813$			16.6154i			0.0204371i
$814$	1024.35			1.25841
$815$	−118.566	−	643.714i	−0.145480	−	0.789833i
$816$	−124.904			−0.153069
$817$	588.354			0.720140
$818$	−805.571			−0.984806
$819$	−27.7598	+	97.6733i	−0.0338948	+	0.119259i
$820$	−21.2220	−	115.217i	−0.0258805	−	0.140509i
$821$	−651.695			−0.793782			−0.396891	−	0.917866i	$-0.629911\pi$
$821$	−651.695			−0.793782			−0.396891	+	0.917866i	$0.629911\pi$
$822$	−233.524			−0.284093
$823$		−	604.705i		−	0.734756i	−0.930072	−	0.367378i	$-0.880255\pi$
$823$		−	604.705i		−	0.734756i	0.930072	−	0.367378i	$-0.119745\pi$
$824$		−	204.779i		−	0.248518i
$825$	−708.512	+	270.168i	−0.858802	+	0.327477i
$826$	−235.630	+	829.066i	−0.285266	+	1.00371i
$827$			504.280i			0.609771i	0.952389	+	0.304885i	$0.0986181\pi$
$827$			504.280i			0.609771i	−0.952389	+	0.304885i	$0.901382\pi$
$828$			22.3509i			0.0269939i
$829$		−	814.575i		−	0.982599i	−0.870991	−	0.491300i	$-0.836522\pi$
$829$		−	814.575i		−	0.982599i	0.870991	−	0.491300i	$-0.163478\pi$
$830$	−36.8752	−	200.201i	−0.0444279	−	0.241206i
$831$		−	278.974i		−	0.335709i
$832$	38.6825			0.0464934
$833$	−751.344	−	464.610i	−0.901973	−	0.557755i
$834$	−581.967			−0.697802
$835$	−505.718	+	93.1484i	−0.605650	+	0.111555i
$836$			319.884i			0.382637i
$837$			296.627i			0.354393i
$838$	296.215			0.353478
$839$			128.459i			0.153109i	0.997065	+	0.0765547i	$0.0243920\pi$
$839$			128.459i			0.153109i	−0.997065	+	0.0765547i	$0.975608\pi$
$840$	−170.695	−	16.2237i	−0.203208	−	0.0193139i
$841$	−839.733			−0.998493
$842$		−	240.011i		−	0.285048i
$843$	594.278			0.704956
$844$	−67.3991			−0.0798567
$845$	716.054	−	131.890i	0.847401	−	0.156083i
$846$			329.489i			0.389467i
$847$	355.288	−	1250.08i	0.419466	−	1.47590i
$848$		−	310.153i		−	0.365747i
$849$	−562.480			−0.662520
$850$	227.101	+	595.570i	0.267178	+	0.700670i
$851$	−154.081			−0.181059
$852$	−201.973			−0.237058
$853$	636.175			0.745808			0.372904	−	0.927870i	$-0.378362\pi$
$853$	636.175			0.745808			0.372904	+	0.927870i	$0.378362\pi$
$854$	14.5320	−	51.1311i	0.0170164	−	0.0598725i
$855$	24.8171	+	134.736i	0.0290259	+	0.157586i
$856$	490.907			0.573490
$857$	494.679			0.577221			0.288611	−	0.957447i	$-0.406807\pi$
$857$	494.679			0.577221			0.288611	+	0.957447i	$0.406807\pi$
$858$			207.408i			0.241734i
$859$			745.414i			0.867770i	0.900968	+	0.433885i	$0.142858\pi$
$859$			745.414i			0.867770i	−0.900968	+	0.433885i	$0.857142\pi$
$860$	116.687	+	633.514i	0.135683	+	0.736645i
$861$	136.632	+	38.8325i	0.158690	+	0.0451016i
$862$			761.450i			0.883353i
$863$		−	593.451i		−	0.687661i	−0.939032	−	0.343830i	$-0.888275\pi$
$863$		−	593.451i		−	0.687661i	0.939032	−	0.343830i	$-0.111725\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	970.828	−	178.817i	1.12234	−	0.206725i
$866$		−	167.322i		−	0.193212i
$867$	−62.3935			−0.0719648
$868$	768.757	+	218.489i	0.885665	+	0.251716i
$869$	−1312.73			−1.51063
$870$	2.49768	+	13.5603i	0.00287090	+	0.0155865i
$871$			228.168i			0.261961i
$872$		−	141.412i		−	0.162169i
$873$	323.491			0.370551
$874$		−	48.1168i		−	0.0550535i
$875$	233.000	+	843.407i	0.266286	+	0.963894i
$876$	−185.011			−0.211200
$877$			291.879i			0.332815i	0.986057	+	0.166407i	$0.0532167\pi$
$877$			291.879i			0.332815i	−0.986057	+	0.166407i	$0.946783\pi$
$878$	−614.948			−0.700396
$879$	174.795			0.198856
$880$	−344.438	+	63.4422i	−0.391407	+	0.0720934i
$881$		−	1226.42i		−	1.39208i	−0.718004	−	0.696039i	$-0.754944\pi$
$881$		−	1226.42i		−	1.39208i	0.718004	−	0.696039i	$-0.245056\pi$
$882$	109.337	−	176.815i	0.123965	−	0.200470i
$883$			1132.03i			1.28202i	0.767531	+	0.641012i	$0.221485\pi$
$883$			1132.03i			1.28202i	−0.767531	+	0.641012i	$0.778515\pi$
$884$	174.346			0.197224
$885$	136.583	+	741.532i	0.154331	+	0.837889i
$886$	−784.896			−0.885887
$887$	−959.088			−1.08127			−0.540636	−	0.841257i	$-0.681816\pi$
$887$	−959.088			−1.08127			−0.540636	+	0.841257i	$0.681816\pi$
$888$	202.634			0.228191
$889$	1332.83	+	378.806i	1.49925	+	0.426103i
$890$	−705.831	+	130.007i	−0.793068	+	0.146076i
$891$	157.604			0.176885
$892$	−21.5112			−0.0241156
$893$		−	709.321i		−	0.794312i
$894$		−	327.850i		−	0.366723i
$895$	584.280	−	107.619i	0.652827	−	0.120245i
$896$	−76.1790	−	21.6509i	−0.0850212	−	0.0241640i
$897$		−	31.1982i		−	0.0347806i
$898$		−	94.6004i		−	0.105346i
$899$		−	64.2684i		−	0.0714887i
$900$	−140.156	+	53.4440i	−0.155729	+	0.0593823i
$901$		−	1397.89i		−	1.55149i
$902$	290.137			0.321660
$903$	−751.263	−	213.517i	−0.831964	−	0.236453i
$904$	198.424			0.219496
$905$	13.0558	+	70.8817i	0.0144262	+	0.0783224i
$906$		−	379.827i		−	0.419235i
$907$		−	989.799i		−	1.09129i	−0.838017	−	0.545644i	$-0.816285\pi$
$907$		−	989.799i		−	1.09129i	0.838017	−	0.545644i	$-0.183715\pi$
$908$	832.900			0.917290
$909$			157.845i			0.173647i
$910$	238.262	+	22.6456i	0.261826	+	0.0248853i
$911$	994.781			1.09197			0.545983	−	0.837796i	$-0.316156\pi$
$911$	994.781			1.09197			0.545983	+	0.837796i	$0.316156\pi$
$912$			63.2788i			0.0693846i
$913$	504.141			0.552181
$914$	−1061.99			−1.16191
$915$	−8.42351	−	45.7326i	−0.00920602	−	0.0499810i
$916$		−	776.938i		−	0.848185i
$917$	773.665	+	219.884i	0.843691	+	0.239786i
$918$		−	132.481i		−	0.144315i
$919$	−887.212			−0.965410			−0.482705	−	0.875783i	$-0.660346\pi$
$919$	−887.212			−0.965410			−0.482705	+	0.875783i	$0.660346\pi$
$920$	51.8101	−	9.54293i	0.0563153	−	0.0103728i
$921$	71.5436			0.0776804
$922$	−559.148			−0.606451
$923$	281.921			0.305440
$924$	116.088	−	408.457i	0.125636	−	0.442053i
$925$	−368.429	−	966.199i	−0.398302	−	1.04454i
$926$	599.600			0.647516
$927$	217.201			0.234305
$928$			6.36859i			0.00686270i
$929$			1224.49i			1.31808i	0.752109	+	0.659039i	$0.229037\pi$
$929$			1224.49i			1.31808i	−0.752109	+	0.659039i	$0.770963\pi$
$930$	687.591	−	126.648i	0.739345	−	0.136180i
$931$	−235.380	+	380.644i	−0.252825	+	0.408855i
$932$		−	140.807i		−	0.151081i
$933$		−	814.655i		−	0.873156i
$934$			826.478i			0.884880i
$935$	−1552.42	+	285.940i	−1.66034	+	0.305819i
$936$			41.0290i			0.0438344i
$937$	−807.001			−0.861260			−0.430630	−	0.902529i	$-0.641709\pi$
$937$	−807.001			−0.861260			−0.430630	+	0.902529i	$0.641709\pi$
$938$	127.708	−	449.341i	0.136149	−	0.479042i
$939$	−277.508			−0.295536
$940$	763.766	−	140.679i	0.812517	−	0.149658i
$941$		−	1246.48i		−	1.32464i	−0.749223	−	0.662318i	$-0.769573\pi$
$941$		−	1246.48i		−	1.32464i	0.749223	−	0.662318i	$-0.230427\pi$
$942$		−	256.300i		−	0.272081i
$943$	−43.6423			−0.0462802
$944$			348.260i			0.368920i
$945$	17.2078	−	181.049i	0.0182093	−	0.191587i
$946$	−1595.30			−1.68636
$947$			675.978i			0.713810i	0.934141	+	0.356905i	$0.116168\pi$
$947$			675.978i			0.713810i	−0.934141	+	0.356905i	$0.883832\pi$
$948$	−259.682			−0.273926
$949$	258.245			0.272123
$950$	301.726	−	115.054i	0.317607	−	0.121109i
$951$			465.517i			0.489502i
$952$	−343.346	−	97.5828i	−0.360658	−	0.102503i
$953$			1098.24i			1.15240i	0.817308	+	0.576201i	$0.195466\pi$
$953$			1098.24i			1.15240i	−0.817308	+	0.576201i	$0.804534\pi$
$954$	328.967			0.344829
$955$	−294.730	+	54.2864i	−0.308618	+	0.0568444i
$956$	626.267			0.655091
$957$	−34.1472			−0.0356815
$958$	−1038.76			−1.08430
$959$	−641.928	−	182.443i	−0.669372	−	0.190243i
$960$	−68.1359	+	12.5500i	−0.0709749	+	0.0130729i
$961$	−2297.80			−2.39105
$962$	−282.843			−0.294015
$963$			520.686i			0.540692i
$964$			397.455i			0.412297i
$965$	222.759	+	1209.40i	0.230839	+	1.25326i
$966$	−17.4619	+	61.4398i	−0.0180765	+	0.0636023i
$967$			1345.41i			1.39132i	0.718370	+	0.695661i	$0.244889\pi$
$967$			1345.41i			1.39132i	−0.718370	+	0.695661i	$0.755111\pi$
$968$		−	525.114i		−	0.542474i
$969$			285.204i			0.294328i
$970$	−138.118	−	749.862i	−0.142389	−	0.773054i
$971$			1230.36i			1.26710i	0.773701	+	0.633551i	$0.218403\pi$
$971$			1230.36i			1.26710i	−0.773701	+	0.633551i	$0.781597\pi$
$972$	31.1769			0.0320750
$973$	−1599.75	−	454.668i	−1.64415	−	0.467284i
$974$	129.633			0.133093
$975$	195.635	−	74.5990i	0.200651	−	0.0765118i
$976$		−	21.4783i		−	0.0220065i
$977$		−	228.116i		−	0.233487i	−0.993162	−	0.116743i	$-0.962755\pi$
$977$		−	228.116i		−	0.233487i	0.993162	−	0.116743i	$-0.0372455\pi$
$978$	320.659			0.327872
$979$		−	1777.40i		−	1.81553i
$980$	−456.544	−	177.954i	−0.465861	−	0.181586i
$981$	149.990			0.152895
$982$			650.659i			0.662586i
$983$	1721.09			1.75085			0.875425	−	0.483354i	$-0.160582\pi$
$983$	1721.09			1.75085			0.875425	+	0.483354i	$0.160582\pi$
$984$	57.3943			0.0583275
$985$	74.3227	+	403.510i	0.0754545	+	0.409654i
$986$			28.7039i			0.0291114i
$987$	−257.417	+	905.724i	−0.260807	+	0.917654i
$988$		−	88.3266i		−	0.0893994i
$989$	239.964			0.242633
$990$	−67.2906	−	365.332i	−0.0679703	−	0.369022i
$991$	−1911.05			−1.92841			−0.964205	−	0.265159i	$-0.914576\pi$
$991$	−1911.05			−1.92841			−0.964205	+	0.265159i	$0.914576\pi$
$992$	322.927			0.325531
$993$	−961.319			−0.968095
$994$	−555.199	−	157.794i	−0.558550	−	0.158746i
$995$	262.059	+	1422.76i	0.263376	+	1.42991i
$996$	99.7280			0.100129
$997$	31.3627			0.0314571			0.0157285	−	0.999876i	$-0.494993\pi$
$997$	31.3627			0.0314571			0.0157285	+	0.999876i	$0.494993\pi$
$998$		−	688.900i		−	0.690281i
$999$			214.925i			0.215141i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.h.a.139.9	yes	16
3.2	odd	2		630.3.h.e.559.8		16
4.3	odd	2		1680.3.bd.a.769.10		16
5.2	odd	4		1050.3.f.e.601.8		16
5.3	odd	4		1050.3.f.e.601.9		16
5.4	even	2	inner	210.3.h.a.139.8	yes	16
7.6	odd	2	inner	210.3.h.a.139.16	yes	16
15.14	odd	2		630.3.h.e.559.9		16
20.19	odd	2		1680.3.bd.a.769.8		16
21.20	even	2		630.3.h.e.559.1		16
28.27	even	2		1680.3.bd.a.769.7		16
35.13	even	4		1050.3.f.e.601.13		16
35.27	even	4		1050.3.f.e.601.4		16
35.34	odd	2	inner	210.3.h.a.139.1	✓	16
105.104	even	2		630.3.h.e.559.16		16
140.139	even	2		1680.3.bd.a.769.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.h.a.139.1	✓	16	35.34	odd	2	inner
210.3.h.a.139.8	yes	16	5.4	even	2	inner
210.3.h.a.139.9	yes	16	1.1	even	1	trivial
210.3.h.a.139.16	yes	16	7.6	odd	2	inner
630.3.h.e.559.1		16	21.20	even	2
630.3.h.e.559.8		16	3.2	odd	2
630.3.h.e.559.9		16	15.14	odd	2
630.3.h.e.559.16		16	105.104	even	2
1050.3.f.e.601.4		16	35.27	even	4
1050.3.f.e.601.8		16	5.2	odd	4
1050.3.f.e.601.9		16	5.3	odd	4
1050.3.f.e.601.13		16	35.13	even	4
1680.3.bd.a.769.7		16	28.27	even	2
1680.3.bd.a.769.8		16	20.19	odd	2
1680.3.bd.a.769.9		16	140.139	even	2
1680.3.bd.a.769.10		16	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.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +(-4.91728 + 0.905717i) q^{5} -2.44949i q^{6} +(1.91369 - 6.73333i) q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +(-4.91728 + 0.905717i) q^{5} -2.44949i q^{6} +(1.91369 - 6.73333i) q^{7} -2.82843i q^{8} +3.00000 q^{9} +(-1.28088 - 6.95409i) q^{10} +17.5116 q^{11} +3.46410 q^{12} -4.83531 q^{13} +(9.52237 + 2.70636i) q^{14} +(8.51698 - 1.56875i) q^{15} +4.00000 q^{16} +18.0284 q^{17} +4.24264i q^{18} -9.13350i q^{19} +(9.83457 - 1.81143i) q^{20} +(-3.31461 + 11.6625i) q^{21} +24.7651i q^{22} -3.72515i q^{23} +4.89898i q^{24} +(23.3594 - 8.90734i) q^{25} -6.83816i q^{26} -5.19615 q^{27} +(-3.82738 + 13.4667i) q^{28} +1.12582 q^{29} +(2.21855 + 12.0448i) q^{30} -57.0859i q^{31} +5.65685i q^{32} -30.3310 q^{33} +25.4960i q^{34} +(-3.31165 + 34.8430i) q^{35} -6.00000 q^{36} -41.3624i q^{37} +12.9167 q^{38} +8.37500 q^{39} +(2.56176 + 13.9082i) q^{40} -11.7156i q^{41} +(-16.4932 - 4.68756i) q^{42} +64.4171i q^{43} -35.0232 q^{44} +(-14.7519 + 2.71715i) q^{45} +5.26816 q^{46} +77.6614 q^{47} -6.92820 q^{48} +(-41.6756 - 25.7710i) q^{49} +(12.5969 + 33.0351i) q^{50} -31.2261 q^{51} +9.67062 q^{52} -77.5383i q^{53} -7.34847i q^{54} +(-86.1095 + 15.8606i) q^{55} +(-19.0447 - 5.41273i) q^{56} +15.8197i q^{57} +1.59215i q^{58} +87.0651i q^{59} +(-17.0340 + 3.13750i) q^{60} -5.36957i q^{61} +80.7317 q^{62} +(5.74106 - 20.2000i) q^{63} -8.00000 q^{64} +(23.7766 - 4.37942i) q^{65} -42.8945i q^{66} -47.1879i q^{67} -36.0568 q^{68} +6.45216i q^{69} +(-49.2754 - 4.68338i) q^{70} -58.3047 q^{71} -8.48528i q^{72} -53.4082 q^{73} +58.4953 q^{74} +(-40.4596 + 15.4280i) q^{75} +18.2670i q^{76} +(33.5117 - 117.911i) q^{77} +11.8440i q^{78} -74.9637 q^{79} +(-19.6691 + 3.62287i) q^{80} +9.00000 q^{81} +16.5683 q^{82} +28.7890 q^{83} +(6.62921 - 23.3250i) q^{84} +(-88.6507 + 16.3286i) q^{85} -91.0996 q^{86} -1.94997 q^{87} -49.5303i q^{88} -101.499i q^{89} +(-3.84263 - 20.8623i) q^{90} +(-9.25327 + 32.5578i) q^{91} +7.45031i q^{92} +98.8757i q^{93} +109.830i q^{94} +(8.27237 + 44.9120i) q^{95} -9.79796i q^{96} +107.830 q^{97} +(36.4457 - 58.9382i) q^{98} +52.5348 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{4} + 48 q^{9}+O(q^{10}) \) 16 * q - 32 * q^4 + 48 * q^9	\( 16 q - 32 q^{4} + 48 q^{9} + 96 q^{11} + 16 q^{14} - 24 q^{15} + 64 q^{16} + 24 q^{21} + 24 q^{25} + 64 q^{29} + 24 q^{30} - 8 q^{35} - 96 q^{36} - 144 q^{39} - 192 q^{44} - 176 q^{46} + 224 q^{49} - 96 q^{50} - 48 q^{51} - 32 q^{56} + 48 q^{60} - 128 q^{64} + 368 q^{65} - 56 q^{70} - 384 q^{71} + 224 q^{74} - 608 q^{79} + 144 q^{81} - 48 q^{84} - 440 q^{85} + 416 q^{86} + 224 q^{91} - 560 q^{95} + 288 q^{99}+O(q^{100}) \) 16 * q - 32 * q^4 + 48 * q^9 + 96 * q^11 + 16 * q^14 - 24 * q^15 + 64 * q^16 + 24 * q^21 + 24 * q^25 + 64 * q^29 + 24 * q^30 - 8 * q^35 - 96 * q^36 - 144 * q^39 - 192 * q^44 - 176 * q^46 + 224 * q^49 - 96 * q^50 - 48 * q^51 - 32 * q^56 + 48 * q^60 - 128 * q^64 + 368 * q^65 - 56 * q^70 - 384 * q^71 + 224 * q^74 - 608 * q^79 + 144 * q^81 - 48 * q^84 - 440 * q^85 + 416 * q^86 + 224 * q^91 - 560 * q^95 + 288 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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