LMFDB - Embedded newform 354.3.b.a.119.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,3,Mod(119,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("354.119");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	354.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.64580135835$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.19
Character	$\chi$	$=$	354.119
Dual form			354.3.b.a.119.39

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(2.95715 + 0.505227i) q^{3} -2.00000 q^{4} -6.09077i q^{5} +(0.714499 - 4.18204i) q^{6} -12.9107 q^{7} +2.82843i q^{8} +(8.48949 + 2.98806i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(2.95715 + 0.505227i) q^{3} -2.00000 q^{4} -6.09077i q^{5} +(0.714499 - 4.18204i) q^{6} -12.9107 q^{7} +2.82843i q^{8} +(8.48949 + 2.98806i) q^{9} -8.61364 q^{10} -9.79377i q^{11} +(-5.91430 - 1.01045i) q^{12} -24.3328 q^{13} +18.2585i q^{14} +(3.07722 - 18.0113i) q^{15} +4.00000 q^{16} +24.3122i q^{17} +(4.22576 - 12.0060i) q^{18} +0.781495 q^{19} +12.1815i q^{20} +(-38.1789 - 6.52284i) q^{21} -13.8505 q^{22} -14.4635i q^{23} +(-1.42900 + 8.36409i) q^{24} -12.0974 q^{25} +34.4118i q^{26} +(23.5951 + 13.1253i) q^{27} +25.8214 q^{28} -32.9290i q^{29} +(-25.4719 - 4.35184i) q^{30} +1.57730 q^{31} -5.65685i q^{32} +(4.94808 - 28.9617i) q^{33} +34.3827 q^{34} +78.6361i q^{35} +(-16.9790 - 5.97613i) q^{36} -27.3955 q^{37} -1.10520i q^{38} +(-71.9559 - 12.2936i) q^{39} +17.2273 q^{40} -72.7990i q^{41} +(-9.22469 + 53.9932i) q^{42} -2.22920 q^{43} +19.5875i q^{44} +(18.1996 - 51.7075i) q^{45} -20.4545 q^{46} -43.9337i q^{47} +(11.8286 + 2.02091i) q^{48} +117.687 q^{49} +17.1084i q^{50} +(-12.2832 + 71.8950i) q^{51} +48.6657 q^{52} -40.0392i q^{53} +(18.5619 - 33.3685i) q^{54} -59.6516 q^{55} -36.5170i q^{56} +(2.31100 + 0.394832i) q^{57} -46.5687 q^{58} +7.68115i q^{59} +(-6.15444 + 36.0226i) q^{60} +43.8960 q^{61} -2.23064i q^{62} +(-109.605 - 38.5780i) q^{63} -8.00000 q^{64} +148.206i q^{65} +(-40.9580 - 6.99763i) q^{66} -40.6775 q^{67} -48.6245i q^{68} +(7.30737 - 42.7709i) q^{69} +111.208 q^{70} +96.3569i q^{71} +(-8.45152 + 24.0119i) q^{72} -122.993 q^{73} +38.7431i q^{74} +(-35.7739 - 6.11195i) q^{75} -1.56299 q^{76} +126.445i q^{77} +(-17.3858 + 101.761i) q^{78} +18.6282 q^{79} -24.3631i q^{80} +(63.1429 + 50.7343i) q^{81} -102.953 q^{82} +42.6819i q^{83} +(76.3579 + 13.0457i) q^{84} +148.080 q^{85} +3.15256i q^{86} +(16.6366 - 97.3762i) q^{87} +27.7010 q^{88} -108.197i q^{89} +(-73.1255 - 25.7381i) q^{90} +314.154 q^{91} +28.9271i q^{92} +(4.66432 + 0.796896i) q^{93} -62.1317 q^{94} -4.75991i q^{95} +(2.85799 - 16.7282i) q^{96} +21.4884 q^{97} -166.434i q^{98} +(29.2644 - 83.1441i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9}+O(q^{10}) $ 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9	$ 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9} - 16 q^{10} + 34 q^{15} + 160 q^{16} + 16 q^{18} + 24 q^{19} - 18 q^{21} - 16 q^{22} - 16 q^{24} - 216 q^{25} - 30 q^{27} - 16 q^{28} - 64 q^{30} + 96 q^{31} + 76 q^{33} + 80 q^{34} + 48 q^{36} - 200 q^{37} - 28 q^{39} + 32 q^{40} + 48 q^{42} - 104 q^{43} + 58 q^{45} + 32 q^{46} + 288 q^{49} - 176 q^{51} - 40 q^{54} + 360 q^{55} + 214 q^{57} - 128 q^{58} - 68 q^{60} - 32 q^{61} - 132 q^{63} - 320 q^{64} - 112 q^{66} - 344 q^{67} + 88 q^{69} + 192 q^{70} - 32 q^{72} + 40 q^{73} + 28 q^{75} - 48 q^{76} + 96 q^{78} + 32 q^{79} + 336 q^{81} - 80 q^{82} + 36 q^{84} + 168 q^{85} - 162 q^{87} + 32 q^{88} + 112 q^{90} + 88 q^{91} - 316 q^{93} - 400 q^{94} + 32 q^{96} - 184 q^{97} - 148 q^{99}+O(q^{100}) $ 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9 - 16 * q^10 + 34 * q^15 + 160 * q^16 + 16 * q^18 + 24 * q^19 - 18 * q^21 - 16 * q^22 - 16 * q^24 - 216 * q^25 - 30 * q^27 - 16 * q^28 - 64 * q^30 + 96 * q^31 + 76 * q^33 + 80 * q^34 + 48 * q^36 - 200 * q^37 - 28 * q^39 + 32 * q^40 + 48 * q^42 - 104 * q^43 + 58 * q^45 + 32 * q^46 + 288 * q^49 - 176 * q^51 - 40 * q^54 + 360 * q^55 + 214 * q^57 - 128 * q^58 - 68 * q^60 - 32 * q^61 - 132 * q^63 - 320 * q^64 - 112 * q^66 - 344 * q^67 + 88 * q^69 + 192 * q^70 - 32 * q^72 + 40 * q^73 + 28 * q^75 - 48 * q^76 + 96 * q^78 + 32 * q^79 + 336 * q^81 - 80 * q^82 + 36 * q^84 + 168 * q^85 - 162 * q^87 + 32 * q^88 + 112 * q^90 + 88 * q^91 - 316 * q^93 - 400 * q^94 + 32 * q^96 - 184 * q^97 - 148 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	2.95715	+	0.505227i	0.985717	+	0.168409i
$3$	2.95715	+	0.505227i	0.985717	+	0.168409i
$4$	−2.00000			−0.500000
$5$		−	6.09077i		−	1.21815i	−0.793111	−	0.609077i	$-0.791540\pi$
$5$		−	6.09077i		−	1.21815i	0.793111	−	0.609077i	$-0.208460\pi$
$6$	0.714499	−	4.18204i	0.119083	−	0.697007i
$7$	−12.9107			−1.84439			−0.922194	−	0.386728i	$-0.873605\pi$
$7$	−12.9107			−1.84439			−0.922194	+	0.386728i	$0.873605\pi$
$8$			2.82843i			0.353553i
$9$	8.48949	+	2.98806i	0.943277	+	0.332007i
$10$	−8.61364			−0.861364
$11$		−	9.79377i		−	0.890343i	−0.895445	−	0.445171i	$-0.853143\pi$
$11$		−	9.79377i		−	0.890343i	0.895445	−	0.445171i	$-0.146857\pi$
$12$	−5.91430	−	1.01045i	−0.492859	−	0.0842045i
$13$	−24.3328			−1.87176			−0.935878	−	0.352324i	$-0.885392\pi$
$13$	−24.3328			−1.87176			−0.935878	+	0.352324i	$0.885392\pi$
$14$			18.2585i			1.30418i
$15$	3.07722	−	18.0113i	0.205148	−	1.20075i
$16$	4.00000			0.250000
$17$			24.3122i			1.43013i	0.699057	+	0.715066i	$0.253603\pi$
$17$			24.3122i			1.43013i	−0.699057	+	0.715066i	$0.746397\pi$
$18$	4.22576	−	12.0060i	0.234765	−	0.666997i
$19$	0.781495			0.0411313			0.0205657	−	0.999789i	$-0.493453\pi$
$19$	0.781495			0.0411313			0.0205657	+	0.999789i	$0.493453\pi$
$20$			12.1815i			0.609077i
$21$	−38.1789	−	6.52284i	−1.81804	−	0.310611i
$22$	−13.8505			−0.629567
$23$		−	14.4635i		−	0.628850i	−0.949282	−	0.314425i	$-0.898188\pi$
$23$		−	14.4635i		−	0.628850i	0.949282	−	0.314425i	$-0.101812\pi$
$24$	−1.42900	+	8.36409i	−0.0595415	+	0.348504i
$25$	−12.0974			−0.483897
$26$			34.4118i			1.32353i
$27$	23.5951	+	13.1253i	0.873891	+	0.486121i
$28$	25.8214			0.922194
$29$		−	32.9290i		−	1.13548i	−0.823206	−	0.567742i	$-0.807817\pi$
$29$		−	32.9290i		−	1.13548i	0.823206	−	0.567742i	$-0.192183\pi$
$30$	−25.4719	−	4.35184i	−0.849062	−	0.145061i
$31$	1.57730			0.0508807			0.0254404	−	0.999676i	$-0.491901\pi$
$31$	1.57730			0.0508807			0.0254404	+	0.999676i	$0.491901\pi$
$32$		−	5.65685i		−	0.176777i
$33$	4.94808	−	28.9617i	0.149942	−	0.877626i
$34$	34.3827			1.01126
$35$			78.6361i			2.24675i
$36$	−16.9790	−	5.97613i	−0.471638	−	0.166004i
$37$	−27.3955			−0.740419			−0.370210	−	0.928948i	$-0.620714\pi$
$37$	−27.3955			−0.740419			−0.370210	+	0.928948i	$0.620714\pi$
$38$		−	1.10520i		−	0.0290842i
$39$	−71.9559	−	12.2936i	−1.84502	−	0.315220i
$40$	17.2273			0.430682
$41$		−	72.7990i		−	1.77558i	−0.460244	−	0.887792i	$-0.652238\pi$
$41$		−	72.7990i		−	1.77558i	0.460244	−	0.887792i	$-0.347762\pi$
$42$	−9.22469	+	53.9932i	−0.219635	+	1.28555i
$43$	−2.22920			−0.0518419			−0.0259209	−	0.999664i	$-0.508252\pi$
$43$	−2.22920			−0.0518419			−0.0259209	+	0.999664i	$0.508252\pi$
$44$			19.5875i			0.445171i
$45$	18.1996	−	51.7075i	0.404436	−	1.14906i
$46$	−20.4545			−0.444664
$47$		−	43.9337i		−	0.934760i	−0.884056	−	0.467380i	$-0.845198\pi$
$47$		−	43.9337i		−	0.934760i	0.884056	−	0.467380i	$-0.154802\pi$
$48$	11.8286	+	2.02091i	0.246429	+	0.0421022i
$49$	117.687			2.40177
$50$			17.1084i			0.342167i
$51$	−12.2832	+	71.8950i	−0.240847	+	1.40971i
$52$	48.6657			0.935878
$53$		−	40.0392i		−	0.755458i	−0.925916	−	0.377729i	$-0.876705\pi$
$53$		−	40.0392i		−	0.755458i	0.925916	−	0.377729i	$-0.123295\pi$
$54$	18.5619	−	33.3685i	0.343740	−	0.617934i
$55$	−59.6516			−1.08457
$56$		−	36.5170i		−	0.652089i
$57$	2.31100	+	0.394832i	0.0405439	+	0.00692688i
$58$	−46.5687			−0.802909
$59$			7.68115i			0.130189i
$59$			7.68115i			0.130189i
$60$	−6.15444	+	36.0226i	−0.102574	+	0.600377i
$61$	43.8960			0.719606			0.359803	−	0.933028i	$-0.382844\pi$
$61$	43.8960			0.719606			0.359803	+	0.933028i	$0.382844\pi$
$62$		−	2.23064i		−	0.0359781i
$63$	−109.605	−	38.5780i	−1.73977	−	0.612350i
$64$	−8.00000			−0.125000
$65$			148.206i			2.28009i
$66$	−40.9580	−	6.99763i	−0.620575	−	0.106025i
$67$	−40.6775			−0.607127			−0.303564	−	0.952811i	$-0.598176\pi$
$67$	−40.6775			−0.607127			−0.303564	+	0.952811i	$0.598176\pi$
$68$		−	48.6245i		−	0.715066i
$69$	7.30737	−	42.7709i	0.105904	−	0.619868i
$70$	111.208			1.58869
$71$			96.3569i			1.35714i	0.734536	+	0.678570i	$0.237400\pi$
$71$			96.3569i			1.35714i	−0.734536	+	0.678570i	$0.762600\pi$
$72$	−8.45152	+	24.0119i	−0.117382	+	0.333499i
$73$	−122.993			−1.68483			−0.842417	−	0.538827i	$-0.818868\pi$
$73$	−122.993			−1.68483			−0.842417	+	0.538827i	$0.818868\pi$
$74$			38.7431i			0.523555i
$75$	−35.7739	−	6.11195i	−0.476986	−	0.0814926i
$76$	−1.56299			−0.0205657
$77$			126.445i			1.64214i
$78$	−17.3858	+	101.761i	−0.222895	+	1.30463i
$79$	18.6282			0.235800			0.117900	−	0.993025i	$-0.462384\pi$
$79$	18.6282			0.235800			0.117900	+	0.993025i	$0.462384\pi$
$80$		−	24.3631i		−	0.304538i
$81$	63.1429	+	50.7343i	0.779543	+	0.626349i
$82$	−102.953			−1.25553
$83$			42.6819i			0.514240i	0.966379	+	0.257120i	$0.0827736\pi$
$83$			42.6819i			0.514240i	−0.966379	+	0.257120i	$0.917226\pi$
$84$	76.3579	+	13.0457i	0.909022	+	0.155306i
$85$	148.080			1.74212
$86$			3.15256i			0.0366577i
$87$	16.6366	−	97.3762i	0.191226	−	1.11927i
$88$	27.7010			0.314784
$89$		−	108.197i		−	1.21570i	−0.794052	−	0.607850i	$-0.792032\pi$
$89$		−	108.197i		−	1.21570i	0.794052	−	0.607850i	$-0.207968\pi$
$90$	−73.1255	−	25.7381i	−0.812505	−	0.285979i
$91$	314.154			3.45224
$92$			28.9271i			0.314425i
$93$	4.66432	+	0.796896i	0.0501540	+	0.00856877i
$94$	−62.1317			−0.660975
$95$		−	4.75991i		−	0.0501043i
$96$	2.85799	−	16.7282i	0.0297708	−	0.174252i
$97$	21.4884			0.221530			0.110765	−	0.993847i	$-0.464670\pi$
$97$	21.4884			0.221530			0.110765	+	0.993847i	$0.464670\pi$
$98$		−	166.434i		−	1.69830i
$99$	29.2644	−	83.1441i	0.295600	−	0.839840i
$100$	24.1949			0.241949
$101$		−	110.838i		−	1.09741i	−0.836017	−	0.548704i	$-0.815122\pi$
$101$		−	110.838i		−	1.09741i	0.836017	−	0.548704i	$-0.184878\pi$
$102$	101.675	+	17.3711i	0.996812	+	0.170305i
$103$	0.913293			0.00886692			0.00443346	−	0.999990i	$-0.498589\pi$
$103$	0.913293			0.00886692			0.00443346	+	0.999990i	$0.498589\pi$
$104$		−	68.8236i		−	0.661766i
$105$	−39.7291	+	232.539i	−0.378372	+	2.21466i
$106$	−56.6240			−0.534189
$107$		−	6.14836i		−	0.0574613i	−0.999587	−	0.0287306i	$-0.990853\pi$
$107$		−	6.14836i		−	0.0574613i	0.999587	−	0.0287306i	$-0.00914651\pi$
$108$	−47.1901	−	26.2506i	−0.436946	−	0.243061i
$109$	163.358			1.49869			0.749347	−	0.662178i	$-0.230368\pi$
$109$	163.358			1.49869			0.749347	+	0.662178i	$0.230368\pi$
$110$			84.3601i			0.766910i
$111$	−81.0127	−	13.8409i	−0.729844	−	0.124693i
$112$	−51.6429			−0.461097
$113$		−	37.0904i		−	0.328233i	−0.986441	−	0.164117i	$-0.947523\pi$
$113$		−	37.0904i		−	0.328233i	0.986441	−	0.164117i	$-0.0524774\pi$
$114$	0.558377	−	3.26825i	0.00489805	−	0.0286688i
$115$	−88.0941			−0.766036
$116$			65.8581i			0.567742i
$117$	−206.573	−	72.7081i	−1.76558	−	0.621436i
$118$	10.8628			0.0920575
$119$		−	313.888i		−	2.63772i
$120$	50.9437	+	8.70369i	0.424531	+	0.0725307i
$121$	25.0821			0.207290
$122$		−	62.0783i		−	0.508838i
$123$	36.7800	−	215.278i	0.299024	−	1.75022i
$124$	−3.15461			−0.0254404
$125$		−	78.5865i		−	0.628692i
$126$	−54.5576	+	155.005i	−0.432997	+	1.23020i
$127$	49.1598			0.387085			0.193542	−	0.981092i	$-0.438002\pi$
$127$	49.1598			0.387085			0.193542	+	0.981092i	$0.438002\pi$
$128$			11.3137i			0.0883883i
$129$	−6.59208	−	1.12625i	−0.0511014	−	0.00873063i
$130$	209.594			1.61226
$131$			70.9519i			0.541617i	0.962633	+	0.270809i	$0.0872911\pi$
$131$			70.9519i			0.541617i	−0.962633	+	0.270809i	$0.912709\pi$
$132$	−9.89615	+	57.9233i	−0.0749708	+	0.438813i
$133$	−10.0897			−0.0758621
$134$			57.5267i			0.429304i
$135$	79.9430	−	143.712i	0.592170	−	1.06453i
$136$	−68.7654			−0.505628
$137$		−	98.8486i		−	0.721523i	−0.932658	−	0.360761i	$-0.882517\pi$
$137$		−	98.8486i		−	0.721523i	0.932658	−	0.360761i	$-0.117483\pi$
$138$	−60.4872	−	10.3342i	−0.438313	−	0.0748854i
$139$	91.2040			0.656144			0.328072	−	0.944653i	$-0.393601\pi$
$139$	91.2040			0.656144			0.328072	+	0.944653i	$0.393601\pi$
$140$		−	157.272i		−	1.12337i
$141$	22.1965	−	129.919i	0.157422	−	0.921409i
$142$	136.269			0.959642
$143$			238.310i			1.66650i
$144$	33.9580	+	11.9523i	0.235819	+	0.0830018i
$145$	−200.563			−1.38319
$146$			173.938i			1.19136i
$147$	348.017	+	59.4584i	2.36746	+	0.404479i
$148$	54.7910			0.370210
$149$			67.3356i			0.451917i	0.974137	+	0.225958i	$0.0725514\pi$
$149$			67.3356i			0.451917i	−0.974137	+	0.225958i	$0.927449\pi$
$150$	−8.64360	+	50.5920i	−0.0576240	+	0.337280i
$151$	−208.923			−1.38360			−0.691799	−	0.722090i	$-0.743182\pi$
$151$	−208.923			−1.38360			−0.691799	+	0.722090i	$0.743182\pi$
$152$			2.21040i			0.0145421i
$153$	−72.6465	+	206.399i	−0.474814	+	1.34901i
$154$	178.820			1.16117
$155$		−	9.60698i		−	0.0619805i
$156$	143.912	+	24.5872i	0.922511	+	0.157610i
$157$	262.211			1.67013			0.835067	−	0.550148i	$-0.185429\pi$
$157$	262.211			1.67013			0.835067	+	0.550148i	$0.185429\pi$
$158$		−	26.3443i		−	0.166736i
$159$	20.2289	−	118.402i	0.127226	−	0.744668i
$160$	−34.4546			−0.215341
$161$			186.735i			1.15984i
$162$	71.7491	−	89.2976i	0.442896	−	0.551220i
$163$	−234.337			−1.43765			−0.718825	−	0.695191i	$-0.755320\pi$
$163$	−234.337			−1.43765			−0.718825	+	0.695191i	$0.755320\pi$
$164$			145.598i			0.887792i
$165$	−176.399	−	30.1376i	−1.06908	−	0.182652i
$166$	60.3613			0.363623
$167$			13.9958i			0.0838074i	0.999122	+	0.0419037i	$0.0133423\pi$
$167$			13.9958i			0.0838074i	−0.999122	+	0.0419037i	$0.986658\pi$
$168$	18.4494	−	107.986i	0.109818	−	0.642776i
$169$	423.087			2.50347
$170$		−	209.417i		−	1.23186i
$171$	6.63450	+	2.33516i	0.0387982	+	0.0136559i
$172$	4.45840			0.0259209
$173$		−	135.756i		−	0.784718i	−0.919812	−	0.392359i	$-0.871659\pi$
$173$		−	135.756i		−	0.784718i	0.919812	−	0.392359i	$-0.128341\pi$
$174$	−137.711	−	23.5278i	−0.791441	−	0.135217i
$175$	156.186			0.892494
$176$		−	39.1751i		−	0.222586i
$177$	−3.88072	+	22.7143i	−0.0219250	+	0.128329i
$178$	−153.014			−0.859629
$179$			90.0523i			0.503086i	0.967846	+	0.251543i	$0.0809379\pi$
$179$			90.0523i			0.503086i	−0.967846	+	0.251543i	$0.919062\pi$
$180$	−36.3992	+	103.415i	−0.202218	+	0.574528i
$181$	−26.0784			−0.144080			−0.0720398	−	0.997402i	$-0.522951\pi$
$181$	−26.0784			−0.144080			−0.0720398	+	0.997402i	$0.522951\pi$
$182$		−	444.281i		−	2.44111i
$183$	129.807	+	22.1774i	0.709328	+	0.121188i
$184$	40.9091			0.222332
$185$			166.860i			0.901944i
$186$	1.12698	−	6.59635i	0.00605904	−	0.0354642i
$187$	238.109			1.27331
$188$			87.8674i			0.467380i
$189$	−304.629	−	169.457i	−1.61179	−	0.896596i
$190$	−6.73152			−0.0354291
$191$			368.538i			1.92952i	0.263130	+	0.964760i	$0.415245\pi$
$191$			368.538i			1.92952i	−0.263130	+	0.964760i	$0.584755\pi$
$192$	−23.6572	−	4.04181i	−0.123215	−	0.0210511i
$193$	−22.4169			−0.116150			−0.0580748	−	0.998312i	$-0.518496\pi$
$193$	−22.4169			−0.116150			−0.0580748	+	0.998312i	$0.518496\pi$
$194$		−	30.3892i		−	0.156646i
$195$	−74.8774	+	438.266i	−0.383987	+	2.24752i
$196$	−235.373			−1.20088
$197$			103.958i			0.527706i	0.964563	+	0.263853i	$0.0849933\pi$
$197$			103.958i			0.527706i	−0.964563	+	0.263853i	$0.915007\pi$
$198$	−117.584	−	41.3861i	−0.593856	−	0.209021i
$199$	−209.258			−1.05155			−0.525774	−	0.850624i	$-0.676224\pi$
$199$	−209.258			−1.05155			−0.525774	+	0.850624i	$0.676224\pi$
$200$		−	34.2167i		−	0.171084i
$201$	−120.290	−	20.5514i	−0.598456	−	0.102246i
$202$	−156.749			−0.775984
$203$			425.137i			2.09427i
$204$	24.5664	−	143.790i	0.120423	−	0.704853i
$205$	−443.402			−2.16293
$206$		−	1.29159i		−	0.00626986i
$207$	43.2180	−	122.788i	0.208783	−	0.593180i
$208$	−97.3313			−0.467939
$209$		−	7.65379i		−	0.0366210i
$210$	328.860	+	56.1854i	1.56600	+	0.267550i
$211$	−152.160			−0.721136			−0.360568	−	0.932733i	$-0.617417\pi$
$211$	−152.160			−0.721136			−0.360568	+	0.932733i	$0.617417\pi$
$212$			80.0785i			0.377729i
$213$	−48.6821	+	284.942i	−0.228554	+	1.33776i
$214$	−8.69509			−0.0406313
$215$			13.5775i			0.0631513i
$216$	−37.1239	+	66.7369i	−0.171870	+	0.308967i
$217$	−20.3641			−0.0938438
$218$		−	231.023i		−	1.05974i
$219$	−363.708	−	62.1393i	−1.66077	−	0.283741i
$220$	119.303			0.542287
$221$		−	591.586i		−	2.67686i
$222$	−19.5741	+	114.569i	−0.0881714	+	0.516078i
$223$	115.554			0.518179			0.259090	−	0.965853i	$-0.416577\pi$
$223$	115.554			0.518179			0.259090	+	0.965853i	$0.416577\pi$
$224$			73.0340i			0.326045i
$225$	−102.701	−	36.1479i	−0.456449	−	0.160657i
$226$	−52.4537			−0.232096
$227$		−	236.262i		−	1.04080i	−0.853923	−	0.520400i	$-0.825783\pi$
$227$		−	236.262i		−	1.04080i	0.853923	−	0.520400i	$-0.174217\pi$
$228$	−4.62200	−	0.789665i	−0.0202719	−	0.00346344i
$229$	64.8691			0.283271			0.141636	−	0.989919i	$-0.454764\pi$
$229$	64.8691			0.283271			0.141636	+	0.989919i	$0.454764\pi$
$230$			124.584i			0.541669i
$231$	−63.8832	+	373.916i	−0.276551	+	1.61868i
$232$	93.1374			0.401454
$233$			261.049i			1.12038i	0.828364	+	0.560191i	$0.189272\pi$
$233$			261.049i			1.12038i	−0.828364	+	0.560191i	$0.810728\pi$
$234$	−102.825	+	292.139i	−0.439422	+	1.24846i
$235$	−267.590			−1.13868
$236$		−	15.3623i		−	0.0650945i
$237$	55.0865	+	9.41148i	0.232433	+	0.0397109i
$238$	−443.905			−1.86515
$239$			297.679i			1.24552i	0.782413	+	0.622759i	$0.213988\pi$
$239$			297.679i			1.24552i	−0.782413	+	0.622759i	$0.786012\pi$
$240$	12.3089	−	72.0453i	0.0512870	−	0.300189i
$241$	−454.406			−1.88550			−0.942751	−	0.333499i	$-0.891771\pi$
$241$	−454.406			−1.88550			−0.942751	+	0.333499i	$0.891771\pi$
$242$		−	35.4714i		−	0.146576i
$243$	161.091	+	181.931i	0.662926	+	0.748685i
$244$	−87.7920			−0.359803
$245$		−	716.801i		−	2.92572i
$246$	−304.449	−	52.0148i	−1.23760	−	0.211442i
$247$	−19.0160			−0.0769878
$248$			4.46129i			0.0179891i
$249$	−21.5640	+	126.217i	−0.0866026	+	0.506895i
$250$	−111.138			−0.444553
$251$		−	70.7094i		−	0.281711i	−0.990030	−	0.140855i	$-0.955015\pi$
$251$		−	70.7094i		−	0.281711i	0.990030	−	0.140855i	$-0.0449852\pi$
$252$	219.211	+	77.1561i	0.869884	+	0.306175i
$253$	−141.653			−0.559892
$254$		−	69.5224i		−	0.273710i
$255$	437.896	+	74.8141i	1.71724	+	0.293389i
$256$	16.0000			0.0625000
$257$		−	379.692i		−	1.47740i	−0.674034	−	0.738700i	$-0.735440\pi$
$257$		−	379.692i		−	1.47740i	0.674034	−	0.738700i	$-0.264560\pi$
$258$	−1.59276	+	9.32261i	−0.00617349	+	0.0361342i
$259$	353.696			1.36562
$260$		−	296.411i		−	1.14004i
$261$	98.3941	−	279.551i	0.376989	−	1.07108i
$262$	100.341			0.382981
$263$			511.787i			1.94596i	0.230890	+	0.972980i	$0.425836\pi$
$263$			511.787i			1.94596i	−0.230890	+	0.972980i	$0.574164\pi$
$264$	81.9160	+	13.9953i	0.310288	+	0.0530124i
$265$	−243.870			−0.920263
$266$			14.2689i			0.0536426i
$267$	54.6641	−	319.956i	0.204735	−	1.19834i
$268$	81.3550			0.303564
$269$		−	159.744i		−	0.593844i	−0.954902	−	0.296922i	$-0.904040\pi$
$269$		−	159.744i		−	0.593844i	0.954902	−	0.296922i	$-0.0959601\pi$
$270$	−203.239	−	113.056i	−0.752739	−	0.418728i
$271$	−189.549			−0.699444			−0.349722	−	0.936854i	$-0.613724\pi$
$271$	−189.549			−0.699444			−0.349722	+	0.936854i	$0.613724\pi$
$272$			97.2490i			0.357533i
$273$	929.002	+	158.719i	3.40294	+	0.581389i
$274$	−139.793			−0.510194
$275$			118.479i			0.430834i
$276$	−14.6147	+	85.5418i	−0.0529520	+	0.309934i
$277$	79.5904			0.287330			0.143665	−	0.989626i	$-0.454111\pi$
$277$	79.5904			0.287330			0.143665	+	0.989626i	$0.454111\pi$
$278$		−	128.982i		−	0.463964i
$279$	13.3905	+	4.71308i	0.0479946	+	0.0168928i
$280$	−222.417			−0.794345
$281$		−	466.902i		−	1.66157i	−0.556592	−	0.830786i	$-0.687891\pi$
$281$		−	466.902i		−	1.66157i	0.556592	−	0.830786i	$-0.312109\pi$
$282$	−183.733	−	31.3906i	−0.651535	−	0.111314i
$283$	137.499			0.485864			0.242932	−	0.970043i	$-0.421891\pi$
$283$	137.499			0.485864			0.242932	+	0.970043i	$0.421891\pi$
$284$		−	192.714i		−	0.678570i
$285$	2.40483	−	14.0758i	0.00843801	−	0.0493886i
$286$	337.021			1.17840
$287$			939.887i			3.27487i
$288$	16.9030	−	48.0238i	0.0586911	−	0.166749i
$289$	−302.085			−1.04528
$290$			283.639i			0.978066i
$291$	63.5446	+	10.8565i	0.218366	+	0.0373077i
$292$	245.986			0.842417
$293$			283.549i			0.967744i	0.875139	+	0.483872i	$0.160770\pi$
$293$			283.549i			0.967744i	−0.875139	+	0.483872i	$0.839230\pi$
$294$	84.0868	−	492.170i	0.286010	−	1.67405i
$295$	46.7841			0.158590
$296$		−	77.4862i		−	0.261778i
$297$	128.546	−	231.085i	0.432815	−	0.778063i
$298$	95.2269			0.319553
$299$			351.939i			1.17705i
$300$	71.5479	+	12.2239i	0.238493	+	0.0407463i
$301$	28.7806			0.0956165
$302$			295.462i			0.978352i
$303$	55.9984	−	327.765i	0.184813	−	1.08173i
$304$	3.12598			0.0102828
$305$		−	267.360i		−	0.876591i
$306$	291.892	+	102.738i	0.953894	+	0.335744i
$307$	−201.147			−0.655201			−0.327601	−	0.944816i	$-0.606240\pi$
$307$	−201.147			−0.655201			−0.327601	+	0.944816i	$0.606240\pi$
$308$		−	252.889i		−	0.821069i
$309$	2.70075	+	0.461420i	0.00874028	+	0.00149327i
$310$	−13.5863			−0.0438269
$311$		−	169.903i		−	0.546313i	−0.961970	−	0.273156i	$-0.911932\pi$
$311$		−	169.903i		−	0.546313i	0.961970	−	0.273156i	$-0.0880676\pi$
$312$	34.7715	−	203.522i	0.111447	−	0.652314i
$313$	131.105			0.418867			0.209434	−	0.977823i	$-0.432838\pi$
$313$	131.105			0.418867			0.209434	+	0.977823i	$0.432838\pi$
$314$		−	370.823i		−	1.18096i
$315$	−234.970	+	667.581i	−0.745936	+	2.11930i
$316$	−37.2565			−0.117900
$317$		−	46.7749i		−	0.147555i	−0.997275	−	0.0737775i	$-0.976495\pi$
$317$		−	46.7749i		−	0.147555i	0.997275	−	0.0737775i	$-0.0235055\pi$
$318$	−167.446	−	28.6080i	−0.526559	−	0.0899622i
$319$	−322.499			−1.01097
$320$			48.7261i			0.152269i
$321$	3.10631	−	18.1816i	0.00967699	−	0.0566406i
$322$	264.083			0.820133
$323$			18.9999i			0.0588232i
$324$	−126.286	−	101.469i	−0.389771	−	0.313175i
$325$	294.365			0.905738
$326$			331.402i			1.01657i
$327$	483.073	+	82.5327i	1.47729	+	0.252393i
$328$	205.907			0.627764
$329$			567.216i			1.72406i
$330$	−42.6210	+	249.465i	−0.129154	+	0.755956i
$331$	473.871			1.43163			0.715817	−	0.698288i	$-0.246054\pi$
$331$	473.871			1.43163			0.715817	+	0.698288i	$0.246054\pi$
$332$		−	85.3638i		−	0.257120i
$333$	−232.574	−	81.8595i	−0.698420	−	0.245824i
$334$	19.7931			0.0592608
$335$			247.757i			0.739574i
$336$	−152.716	−	26.0914i	−0.454511	−	0.0776528i
$337$	0.902594			0.00267832			0.00133916	−	0.999999i	$-0.499574\pi$
$337$	0.902594			0.00267832			0.00133916	+	0.999999i	$0.499574\pi$
$338$		−	598.335i		−	1.77022i
$339$	18.7390	−	109.682i	0.0552774	−	0.323545i
$340$	−296.160			−0.871060
$341$		−	15.4477i		−	0.0453013i
$342$	3.30241	−	9.38260i	0.00965618	−	0.0274345i
$343$	−886.792			−2.58540
$344$		−	6.30513i		−	0.0183289i
$345$	−260.508	−	44.5075i	−0.755094	−	0.129007i
$346$	−191.988			−0.554880
$347$		−	553.241i		−	1.59436i	−0.603745	−	0.797178i	$-0.706325\pi$
$347$		−	553.241i		−	1.59436i	0.603745	−	0.797178i	$-0.293675\pi$
$348$	−33.2733	+	194.752i	−0.0956128	+	0.559633i
$349$	−624.016			−1.78801			−0.894005	−	0.448056i	$-0.852116\pi$
$349$	−624.016			−1.78801			−0.894005	+	0.448056i	$0.852116\pi$
$350$		−	220.881i		−	0.631089i
$351$	−574.135	−	319.375i	−1.63571	−	0.909901i
$352$	−55.4019			−0.157392
$353$		−	283.070i		−	0.801899i	−0.916100	−	0.400949i	$-0.868680\pi$
$353$		−	283.070i		−	0.801899i	0.916100	−	0.400949i	$-0.131320\pi$
$354$	32.1229	+	5.48817i	0.0907426	+	0.0155033i
$355$	586.887			1.65320
$356$			216.395i			0.607850i
$357$	158.585	−	928.216i	0.444215	−	2.60004i
$358$	127.353			0.355735
$359$		−	110.211i		−	0.306995i	−0.988149	−	0.153498i	$-0.950946\pi$
$359$		−	110.211i		−	0.306995i	0.988149	−	0.153498i	$-0.0490538\pi$
$360$	146.251	+	51.4762i	0.406253	+	0.142990i
$361$	−360.389			−0.998308
$362$			36.8804i			0.101880i
$363$	74.1715	+	12.6721i	0.204329	+	0.0349094i
$364$	−628.308			−1.72612
$365$			749.120i			2.05238i
$366$	31.3636	−	183.575i	0.0856929	−	0.501571i
$367$	−500.951			−1.36499			−0.682495	−	0.730890i	$-0.739105\pi$
$367$	−500.951			−1.36499			−0.682495	+	0.730890i	$0.739105\pi$
$368$		−	57.8542i		−	0.157212i
$369$	217.528	−	618.026i	0.589507	−	1.67487i
$370$	235.975			0.637771
$371$			516.935i			1.39336i
$372$	−9.32865	−	1.59379i	−0.0250770	−	0.00428439i
$373$	−91.0131			−0.244003			−0.122002	−	0.992530i	$-0.538931\pi$
$373$	−91.0131			−0.244003			−0.122002	+	0.992530i	$0.538931\pi$
$374$		−	336.736i		−	0.900364i
$375$	39.7040	−	232.392i	0.105877	−	0.619713i
$376$	124.263			0.330488
$377$			801.257i			2.12535i
$378$	−239.648	+	430.811i	−0.633989	+	1.13971i
$379$	621.748			1.64050			0.820248	−	0.572008i	$-0.193835\pi$
$379$	621.748			1.64050			0.820248	+	0.572008i	$0.193835\pi$
$380$			9.51981i			0.0250521i
$381$	145.373	+	24.8368i	0.381556	+	0.0651885i
$382$	521.192			1.36438
$383$		−	179.804i		−	0.469463i	−0.972060	−	0.234732i	$-0.924579\pi$
$383$		−	179.804i		−	0.469463i	0.972060	−	0.234732i	$-0.0754211\pi$
$384$	−5.71599	+	33.4564i	−0.0148854	+	0.0871259i
$385$	770.144			2.00037
$386$			31.7022i			0.0821301i
$387$	−18.9248	−	6.66099i	−0.0489012	−	0.0172119i
$388$	−42.9769			−0.110765
$389$			91.4438i			0.235074i	0.993068	+	0.117537i	$0.0374999\pi$
$389$			91.4438i			0.235074i	−0.993068	+	0.117537i	$0.962500\pi$
$390$	619.802	+	105.893i	1.58924	+	0.271520i
$391$	351.641			0.899338
$392$			332.868i			0.849152i
$393$	−35.8468	+	209.815i	−0.0912132	+	0.533882i
$394$	147.019			0.373144
$395$		−	113.460i		−	0.287241i
$396$	−58.5288	+	166.288i	−0.147800	+	0.419920i
$397$	513.496			1.29344			0.646720	−	0.762727i	$-0.276140\pi$
$397$	513.496			1.29344			0.646720	+	0.762727i	$0.276140\pi$
$398$			295.935i			0.743556i
$399$	−29.8367	−	5.09757i	−0.0747786	−	0.0127759i
$400$	−48.3897			−0.120974
$401$		−	549.823i		−	1.37113i	−0.728012	−	0.685565i	$-0.759555\pi$
$401$		−	549.823i		−	1.37113i	0.728012	−	0.685565i	$-0.240445\pi$
$402$	−29.0640	+	170.115i	−0.0722986	+	0.423172i
$403$	−38.3802			−0.0952363
$404$			221.676i			0.548704i
$405$	309.011	−	384.589i	0.762989	−	0.949602i
$406$	601.235			1.48087
$407$			268.305i			0.659227i
$408$	−203.350	−	34.7421i	−0.498406	−	0.0851523i
$409$	−181.489			−0.443739			−0.221869	−	0.975076i	$-0.571216\pi$
$409$	−181.489			−0.443739			−0.221869	+	0.975076i	$0.571216\pi$
$410$			627.065i			1.52943i
$411$	49.9410	−	292.310i	0.121511	−	0.711217i
$412$	−1.82659			−0.00443346
$413$		−	99.1691i		−	0.240119i
$414$	−173.649	−	61.1195i	−0.419441	−	0.147632i
$415$	259.966			0.626423
$416$			137.647i			0.330883i
$417$	269.704	+	46.0787i	0.646773	+	0.110501i
$418$	−10.8241			−0.0258949
$419$		−	419.792i		−	1.00189i	−0.865479	−	0.500945i	$-0.832986\pi$
$419$		−	419.792i		−	1.00189i	0.865479	−	0.500945i	$-0.167014\pi$
$420$	79.4582	−	465.078i	0.189186	−	1.10733i
$421$	69.9333			0.166112			0.0830562	−	0.996545i	$-0.473532\pi$
$421$	69.9333			0.166112			0.0830562	+	0.996545i	$0.473532\pi$
$422$			215.186i			0.509920i
$423$	131.277	−	372.975i	0.310347	−	0.881738i
$424$	113.248			0.267095
$425$		−	294.116i		−	0.692037i
$426$	402.969	+	68.8469i	0.945936	+	0.161612i
$427$	−566.728			−1.32723
$428$			12.2967i			0.0287306i
$429$	−120.401	+	704.719i	−0.280654	+	1.64270i
$430$	19.2015			0.0446547
$431$		−	338.101i		−	0.784458i	−0.919868	−	0.392229i	$-0.871704\pi$
$431$		−	338.101i		−	0.784458i	0.919868	−	0.392229i	$-0.128296\pi$
$432$	94.3803	+	52.5011i	0.218473	+	0.121530i
$433$	−82.6479			−0.190873			−0.0954364	−	0.995436i	$-0.530425\pi$
$433$	−82.6479			−0.190873			−0.0954364	+	0.995436i	$0.530425\pi$
$434$			28.7992i			0.0663576i
$435$	−593.095	−	101.330i	−1.36344	−	0.232942i
$436$	−326.715			−0.749347
$437$		−	11.3032i		−	0.0258654i
$438$	−87.8782	+	514.361i	−0.200635	+	1.17434i
$439$	−6.97355			−0.0158851			−0.00794254	−	0.999968i	$-0.502528\pi$
$439$	−6.97355			−0.0158851			−0.00794254	+	0.999968i	$0.502528\pi$
$440$		−	168.720i		−	0.383455i
$441$	999.099	+	351.655i	2.26553	+	0.797403i
$442$	−836.628			−1.89282
$443$		−	288.284i		−	0.650754i	−0.945584	−	0.325377i	$-0.894509\pi$
$443$		−	288.284i		−	0.650754i	0.945584	−	0.325377i	$-0.105491\pi$
$444$	162.025	+	27.6819i	0.364922	+	0.0623466i
$445$	−659.004			−1.48091
$446$		−	163.418i		−	0.366408i
$447$	−34.0198	+	199.122i	−0.0761068	+	0.445462i
$448$	103.286			0.230548
$449$			539.300i			1.20111i	0.799582	+	0.600557i	$0.205054\pi$
$449$			539.300i			1.20111i	−0.799582	+	0.600557i	$0.794946\pi$
$450$	−51.1209	+	145.241i	−0.113602	+	0.322758i
$451$	−712.977			−1.58088
$452$			74.1807i			0.164117i
$453$	−617.818	−	105.554i	−1.36384	−	0.233010i
$454$	−334.124			−0.735957
$455$		−	1913.44i		−	4.20536i
$456$	−1.11675	+	6.53650i	−0.00244902	+	0.0143344i
$457$	299.200			0.654705			0.327352	−	0.944902i	$-0.393844\pi$
$457$	299.200			0.654705			0.327352	+	0.944902i	$0.393844\pi$
$458$		−	91.7387i		−	0.200303i
$459$	−319.105	+	573.649i	−0.695218	+	1.24978i
$460$	176.188			0.383018
$461$			366.919i			0.795919i	0.917403	+	0.397960i	$0.130282\pi$
$461$			366.919i			0.795919i	−0.917403	+	0.397960i	$0.869718\pi$
$462$	528.797	+	90.3445i	1.14458	+	0.195551i
$463$	−481.658			−1.04030			−0.520149	−	0.854076i	$-0.674124\pi$
$463$	−481.658			−1.04030			−0.520149	+	0.854076i	$0.674124\pi$
$464$		−	131.716i		−	0.283871i
$465$	4.85370	−	28.4093i	0.0104381	−	0.0610953i
$466$	369.179			0.792229
$467$			445.588i			0.954150i	0.878863	+	0.477075i	$0.158303\pi$
$467$			445.588i			0.954150i	−0.878863	+	0.477075i	$0.841697\pi$
$468$	413.147	+	145.416i	0.882792	+	0.310718i
$469$	525.176			1.11978
$470$			378.429i			0.805169i
$471$	775.398	+	132.476i	1.64628	+	0.281266i
$472$	−21.7256			−0.0460287
$473$			21.8323i			0.0461570i
$474$	13.3098	−	77.9041i	0.0280798	−	0.164355i
$475$	−9.45409			−0.0199033
$476$			627.777i			1.31886i
$477$	119.640	−	339.913i	0.250817	−	0.712606i
$478$	420.982			0.880715
$479$		−	62.0464i		−	0.129533i	−0.997900	−	0.0647666i	$-0.979370\pi$
$479$		−	62.0464i		−	0.129533i	0.997900	−	0.0647666i	$-0.0206303\pi$
$480$	−101.887	−	17.4074i	−0.212265	−	0.0362654i
$481$	666.610			1.38588
$482$			642.627i			1.33325i
$483$	−94.3434	+	552.203i	−0.195328	+	1.14328i
$484$	−50.1641			−0.103645
$485$		−	130.881i		−	0.269858i
$486$	257.289	−	227.817i	0.529400	−	0.468759i
$487$	294.156			0.604016			0.302008	−	0.953305i	$-0.402343\pi$
$487$	294.156			0.604016			0.302008	+	0.953305i	$0.402343\pi$
$488$			124.157i			0.254419i
$489$	−692.970	−	118.393i	−1.41712	−	0.242113i
$490$	−1013.71			−2.06880
$491$			482.055i			0.981782i	0.871221	+	0.490891i	$0.163329\pi$
$491$			482.055i			0.981782i	−0.871221	+	0.490891i	$0.836671\pi$
$492$	−73.5600	+	430.555i	−0.149512	+	0.875112i
$493$	800.579			1.62389
$494$			26.8927i			0.0544386i
$495$	−506.411	−	178.243i	−1.02305	−	0.360086i
$496$	6.30921			0.0127202
$497$		−	1244.04i		−	2.50309i
$498$	178.498	+	30.4962i	0.358429	+	0.0612373i
$499$	68.8533			0.137982			0.0689912	−	0.997617i	$-0.478022\pi$
$499$	68.8533			0.137982			0.0689912	+	0.997617i	$0.478022\pi$
$500$			157.173i			0.314346i
$501$	−7.07107	+	41.3878i	−0.0141139	+	0.0826104i
$502$	−99.9982			−0.199200
$503$			379.875i			0.755218i	0.925965	+	0.377609i	$0.123254\pi$
$503$			379.875i			0.755218i	−0.925965	+	0.377609i	$0.876746\pi$
$504$	109.115	−	310.011i	0.216498	−	0.615101i
$505$	−675.089			−1.33681
$506$			200.327i			0.395903i
$507$	1251.13	+	213.755i	2.46772	+	0.421607i
$508$	−98.3195			−0.193542
$509$			298.523i			0.586489i	0.956038	+	0.293244i	$0.0947349\pi$
$509$			298.523i			0.586489i	−0.956038	+	0.293244i	$0.905265\pi$
$510$	105.803	−	619.278i	0.207457	−	1.21427i
$511$	1587.92			3.10749
$512$		−	22.6274i		−	0.0441942i
$513$	18.4394	+	10.2573i	0.0359443	+	0.0199948i
$514$	−536.966			−1.04468
$515$		−	5.56265i		−	0.0108013i
$516$	13.1842	+	2.25250i	0.0255507	+	0.00436532i
$517$	−430.277			−0.832257
$518$		−	500.201i		−	0.965639i
$519$	68.5877	−	401.452i	0.132154	−	0.773510i
$520$	−419.189			−0.806132
$521$		−	519.734i		−	0.997569i	−0.866726	−	0.498785i	$-0.833780\pi$
$521$		−	519.734i		−	0.997569i	0.866726	−	0.498785i	$-0.166220\pi$
$522$	−395.345	−	139.150i	−0.757365	−	0.266571i
$523$	24.5084			0.0468613			0.0234306	−	0.999725i	$-0.492541\pi$
$523$	24.5084			0.0468613			0.0234306	+	0.999725i	$0.492541\pi$
$524$		−	141.904i		−	0.270809i
$525$	461.867	+	78.9096i	0.879747	+	0.150304i
$526$	723.777			1.37600
$527$			38.3478i			0.0727662i
$528$	19.7923	−	115.847i	0.0374854	−	0.219407i
$529$	319.806			0.604548
$530$			344.884i			0.650724i
$531$	−22.9518	+	65.2090i	−0.0432236	+	0.122804i
$532$	20.1793			0.0379311
$533$			1771.41i			3.32346i
$534$	−452.486	−	77.3068i	−0.847351	−	0.144769i
$535$	−37.4482			−0.0699966
$536$		−	115.053i		−	0.214652i
$537$	−45.4968	+	266.298i	−0.0847241	+	0.495900i
$538$	−225.912			−0.419911
$539$		−	1152.59i		−	2.13839i
$540$	−159.886	+	287.424i	−0.296085	+	0.532267i
$541$	−441.492			−0.816067			−0.408034	−	0.912967i	$-0.633785\pi$
$541$	−441.492			−0.816067			−0.408034	+	0.912967i	$0.633785\pi$
$542$			268.063i			0.494581i
$543$	−77.1178	−	13.1755i	−0.142022	−	0.0242643i
$544$	137.531			0.252814
$545$		−	994.973i		−	1.82564i
$546$	224.463	−	1313.81i	0.411104	−	2.40624i
$547$	855.300			1.56362			0.781809	−	0.623517i	$-0.214297\pi$
$547$	855.300			1.56362			0.781809	+	0.623517i	$0.214297\pi$
$548$			197.697i			0.360761i
$549$	372.655	+	131.164i	0.678788	+	0.238914i
$550$	167.555			0.304646
$551$		−	25.7339i		−	0.0467040i
$552$	120.974	+	20.6684i	0.219157	+	0.0374427i
$553$	−240.504			−0.434907
$554$		−	112.558i		−	0.203173i
$555$	−84.3020	+	493.429i	−0.151895	+	0.889062i
$556$	−182.408			−0.328072
$557$		−	911.052i		−	1.63564i	−0.575474	−	0.817820i	$-0.695182\pi$
$557$		−	911.052i		−	1.63564i	0.575474	−	0.817820i	$-0.304818\pi$
$558$	6.66531	−	18.9370i	0.0119450	−	0.0339373i
$559$	54.2427			0.0970353
$560$			314.545i			0.561687i
$561$	704.123	+	120.299i	1.25512	+	0.214436i
$562$	−660.299			−1.17491
$563$		−	906.726i		−	1.61053i	−0.592918	−	0.805263i	$-0.702024\pi$
$563$		−	906.726i		−	1.61053i	0.592918	−	0.805263i	$-0.297976\pi$
$564$	−44.3930	+	259.837i	−0.0787110	+	0.460705i
$565$	−225.909			−0.399839
$566$		−	194.454i		−	0.343558i
$567$	−815.220	−	655.016i	−1.43778	−	1.15523i
$568$	−272.538			−0.479821
$569$		−	907.575i		−	1.59504i	−0.603295	−	0.797518i	$-0.706146\pi$
$569$		−	907.575i		−	1.59504i	0.603295	−	0.797518i	$-0.293854\pi$
$570$	−19.9061	−	3.40095i	−0.0349230	−	0.00596657i
$571$	−471.727			−0.826142			−0.413071	−	0.910699i	$-0.635544\pi$
$571$	−471.727			−0.826142			−0.413071	+	0.910699i	$0.635544\pi$
$572$		−	476.620i		−	0.833252i
$573$	−186.195	+	1089.82i	−0.324948	+	1.90196i
$574$	1329.20			2.31568
$575$			174.972i			0.304299i
$576$	−67.9159	−	23.9045i	−0.117910	−	0.0415009i
$577$	−510.833			−0.885325			−0.442663	−	0.896688i	$-0.645966\pi$
$577$	−510.833			−0.885325			−0.442663	+	0.896688i	$0.645966\pi$
$578$			427.213i			0.739122i
$579$	−66.2901	−	11.3256i	−0.114491	−	0.0195606i
$580$	401.126			0.691597
$581$		−	551.054i		−	0.948458i
$582$	15.3535	−	89.8656i	0.0263805	−	0.154408i
$583$	−392.135			−0.672616
$584$		−	347.876i		−	0.595678i
$585$	−442.848	+	1258.19i	−0.757005	+	2.15075i
$586$	400.999			0.684298
$587$			1161.46i			1.97863i	0.145789	+	0.989316i	$0.453428\pi$
$587$			1161.46i			1.97863i	−0.145789	+	0.989316i	$0.546572\pi$
$588$	−696.034	−	118.917i	−1.18373	−	0.202239i
$589$	1.23265			0.00209279
$590$		−	66.1627i		−	0.112140i
$591$	−52.5224	+	307.420i	−0.0888703	+	0.520169i
$592$	−109.582			−0.185105
$593$			37.4453i			0.0631455i	0.999501	+	0.0315727i	$0.0100516\pi$
$593$			37.4453i			0.0631455i	−0.999501	+	0.0315727i	$0.989948\pi$
$594$	−326.803	−	181.791i	−0.550173	−	0.306046i
$595$	−1911.82			−3.21314
$596$		−	134.671i		−	0.225958i
$597$	−618.808	−	105.723i	−1.03653	−	0.177090i
$598$	497.717			0.832303
$599$		−	1119.59i		−	1.86910i	−0.355837	−	0.934548i	$-0.615804\pi$
$599$		−	1119.59i		−	1.86910i	0.355837	−	0.934548i	$-0.384196\pi$
$600$	17.2872	−	101.184i	0.0288120	−	0.168640i
$601$	−697.826			−1.16111			−0.580554	−	0.814222i	$-0.697164\pi$
$601$	−697.826			−1.16111			−0.580554	+	0.814222i	$0.697164\pi$
$602$		−	40.7019i		−	0.0676111i
$603$	−345.331	−	121.547i	−0.572689	−	0.201571i
$604$	417.847			0.691799
$605$		−	152.769i		−	0.252511i
$606$	−463.530	−	79.1937i	−0.764901	−	0.130683i
$607$	880.704			1.45091			0.725457	−	0.688268i	$-0.241629\pi$
$607$	880.704			1.45091			0.725457	+	0.688268i	$0.241629\pi$
$608$		−	4.42081i		−	0.00727106i
$609$	−214.791	+	1257.20i	−0.352694	+	2.06436i
$610$	−378.104			−0.619843
$611$			1069.03i			1.74964i
$612$	145.293	−	412.797i	0.237407	−	0.674505i
$613$	690.322			1.12614			0.563069	−	0.826410i	$-0.309621\pi$
$613$	690.322			1.12614			0.563069	+	0.826410i	$0.309621\pi$
$614$			284.465i			0.463297i
$615$	−1311.21	−	224.018i	−2.13204	−	0.364257i
$616$	−357.639			−0.580583
$617$		−	256.727i		−	0.416089i	−0.978119	−	0.208045i	$-0.933290\pi$
$617$		−	256.727i		−	0.416089i	0.978119	−	0.208045i	$-0.0667099\pi$
$618$	0.652546	−	3.81943i	0.00105590	−	0.00618031i
$619$	957.671			1.54713			0.773563	−	0.633720i	$-0.218473\pi$
$619$	957.671			1.54713			0.773563	+	0.633720i	$0.218473\pi$
$620$			19.2140i			0.0309903i
$621$	189.838	−	341.268i	0.305697	−	0.549547i
$622$	−240.279			−0.386301
$623$			1396.90i			2.24222i
$624$	−287.823	−	49.1744i	−0.461256	−	0.0788051i
$625$	−781.088			−1.24974
$626$		−	185.411i		−	0.296184i
$627$	3.86690	−	22.6334i	0.00616730	−	0.0360979i
$628$	−524.422			−0.835067
$629$		−	666.046i		−	1.05890i
$630$	944.102	+	332.298i	1.49857	+	0.527456i
$631$	290.891			0.461001			0.230500	−	0.973072i	$-0.425964\pi$
$631$	290.891			0.461001			0.230500	+	0.973072i	$0.425964\pi$
$632$			52.6886i			0.0833680i
$633$	−449.959	−	76.8751i	−0.710836	−	0.121446i
$634$	−66.1497			−0.104337
$635$		−	299.421i		−	0.471529i
$636$	−40.4578	+	236.804i	−0.0636129	+	0.372334i
$637$	−2863.65			−4.49552
$638$			456.083i			0.714864i
$639$	−287.921	+	818.021i	−0.450580	+	1.28016i
$640$	68.9092			0.107671
$641$			880.922i			1.37429i	0.726519	+	0.687147i	$0.241137\pi$
$641$			880.922i			1.37429i	−0.726519	+	0.687147i	$0.758863\pi$
$642$	−25.7127	−	4.39299i	−0.0400509	−	0.00684267i
$643$	439.821			0.684014			0.342007	−	0.939697i	$-0.388893\pi$
$643$	439.821			0.684014			0.342007	+	0.939697i	$0.388893\pi$
$644$		−	373.469i		−	0.579922i
$645$	−6.85973	+	40.1508i	−0.0106352	+	0.0622493i
$646$	26.8699			0.0415943
$647$		−	14.6915i		−	0.0227071i	−0.999936	−	0.0113535i	$-0.996386\pi$
$647$		−	14.6915i		−	0.0227071i	0.999936	−	0.0113535i	$-0.00361402\pi$
$648$	−143.498	+	178.595i	−0.221448	+	0.275610i
$649$	75.2274			0.115913
$650$		−	416.295i		−	0.640453i
$651$	−60.2197	−	10.2885i	−0.0925035	−	0.0158041i
$652$	468.674			0.718825
$653$		−	569.206i		−	0.871678i	−0.900025	−	0.435839i	$-0.856452\pi$
$653$		−	569.206i		−	0.871678i	0.900025	−	0.435839i	$-0.143548\pi$
$654$	116.719	−	683.169i	0.178469	−	1.04460i
$655$	432.151			0.659773
$656$		−	291.196i		−	0.443896i
$657$	−1044.15	−	367.510i	−1.58926	−	0.559377i
$658$	802.164			1.21909
$659$		−	483.041i		−	0.732991i	−0.930420	−	0.366495i	$-0.880558\pi$
$659$		−	483.041i		−	0.732991i	0.930420	−	0.366495i	$-0.119442\pi$
$660$	352.797	+	60.2751i	0.534542	+	0.0913260i
$661$	393.043			0.594619			0.297309	−	0.954781i	$-0.403911\pi$
$661$	393.043			0.594619			0.297309	+	0.954781i	$0.403911\pi$
$662$		−	670.155i		−	1.01232i
$663$	298.885	−	1749.41i	0.450807	−	2.63863i
$664$	−120.723			−0.181811
$665$			61.4538i			0.0924117i
$666$	−115.767	+	328.909i	−0.173824	+	0.493858i
$667$	−476.271			−0.714049
$668$		−	27.9917i		−	0.0419037i
$669$	341.711	+	58.3810i	0.510778	+	0.0872660i
$670$	350.382			0.522958
$671$		−	429.907i		−	0.640696i
$672$	−36.8987	+	215.973i	−0.0549088	+	0.321388i
$673$	514.250			0.764115			0.382058	−	0.924138i	$-0.375216\pi$
$673$	514.250			0.764115			0.382058	+	0.924138i	$0.375216\pi$
$674$		−	1.27646i		−	0.00189386i
$675$	−285.440	−	158.782i	−0.422874	−	0.235233i
$676$	−846.173			−1.25174
$677$		−	485.544i		−	0.717199i	−0.933492	−	0.358599i	$-0.883254\pi$
$677$		−	485.544i		−	0.717199i	0.933492	−	0.358599i	$-0.116746\pi$
$678$	−155.114	−	26.5010i	−0.228781	−	0.0390870i
$679$	−277.431			−0.408588
$680$			418.834i			0.615932i
$681$	119.366	−	698.661i	0.175280	−	1.02593i
$682$	−21.8464			−0.0320329
$683$		−	685.159i		−	1.00316i	−0.865111	−	0.501581i	$-0.832752\pi$
$683$		−	685.159i		−	1.00316i	0.865111	−	0.501581i	$-0.167248\pi$
$684$	−13.2690	−	4.67032i	−0.0193991	−	0.00682795i
$685$	−602.064			−0.878925
$686$			1254.11i			1.82815i
$687$	191.828	+	32.7736i	0.279225	+	0.0477054i
$688$	−8.91680			−0.0129605
$689$			974.268i			1.41403i
$690$	−62.9431	+	368.413i	−0.0912219	+	0.533932i
$691$	−404.275			−0.585059			−0.292529	−	0.956257i	$-0.594497\pi$
$691$	−404.275			−0.585059			−0.292529	+	0.956257i	$0.594497\pi$
$692$			271.512i			0.392359i
$693$	−377.824	+	1073.45i	−0.545201	+	1.54899i
$694$	−782.401			−1.12738
$695$		−	555.503i		−	0.799284i
$696$	275.421	+	47.0555i	0.395720	+	0.0676085i
$697$	1769.91			2.53932
$698$			882.491i			1.26431i
$699$	−131.889	+	771.961i	−0.188682	+	1.10438i
$700$	−312.373			−0.446247
$701$			1310.12i			1.86893i	0.356059	+	0.934464i	$0.384120\pi$
$701$			1310.12i			1.86893i	−0.356059	+	0.934464i	$0.615880\pi$
$702$	−451.665	+	811.949i	−0.643397	+	1.15662i
$703$	−21.4095			−0.0304544
$704$			78.3502i			0.111293i
$705$	−791.304	−	135.194i	−1.12242	−	0.191764i
$706$	−400.322			−0.567028
$707$			1431.00i			2.02404i
$708$	7.76144	−	45.4286i	0.0109625	−	0.0641647i
$709$	1116.81			1.57520			0.787598	−	0.616189i	$-0.211324\pi$
$709$	1116.81			1.57520			0.787598	+	0.616189i	$0.211324\pi$
$710$		−	829.984i		−	1.16899i
$711$	158.144	+	55.6624i	0.222425	+	0.0782874i
$712$	306.028			0.429815
$713$		−	22.8134i		−	0.0319964i
$714$	−1312.69	−	224.273i	−1.83851	−	0.314108i
$715$	1451.49			2.03006
$716$		−	180.105i		−	0.251543i
$717$	−150.395	+	880.282i	−0.209756	+	1.22773i
$718$	−155.862			−0.217078
$719$		−	347.399i		−	0.483170i	−0.970380	−	0.241585i	$-0.922333\pi$
$719$		−	347.399i		−	0.483170i	0.970380	−	0.241585i	$-0.0776672\pi$
$720$	72.7984	−	206.830i	0.101109	−	0.287264i
$721$	−11.7913			−0.0163540
$722$			509.667i			0.705911i
$723$	−1343.75	−	229.578i	−1.85857	−	0.317535i
$724$	52.1568			0.0720398
$725$			398.357i			0.549458i
$726$	17.9211	−	104.894i	0.0246847	−	0.144482i
$727$	303.082			0.416895			0.208447	−	0.978034i	$-0.433159\pi$
$727$	303.082			0.416895			0.208447	+	0.978034i	$0.433159\pi$
$728$			888.562i			1.22055i
$729$	384.454	+	619.384i	0.527372	+	0.849635i
$730$	1059.42			1.45126
$731$		−	54.1968i		−	0.0741407i
$732$	−259.614	−	44.3549i	−0.354664	−	0.0605941i
$733$	725.438			0.989683			0.494842	−	0.868983i	$-0.335226\pi$
$733$	725.438			0.989683			0.494842	+	0.868983i	$0.335226\pi$
$734$			708.452i			0.965194i
$735$	362.147	−	2119.69i	0.492717	−	2.88393i
$736$	−81.8182			−0.111166
$737$			398.386i			0.540551i
$738$	−874.021	−	307.631i	−1.18431	−	0.416844i
$739$	703.749			0.952299			0.476150	−	0.879364i	$-0.342032\pi$
$739$	703.749			0.952299			0.476150	+	0.879364i	$0.342032\pi$
$740$		−	333.719i		−	0.450972i
$741$	−56.2332	−	9.60739i	−0.0758882	−	0.0129654i
$742$	731.057			0.985252
$743$		−	781.726i		−	1.05212i	−0.850447	−	0.526060i	$-0.823669\pi$
$743$		−	781.726i		−	1.05212i	0.850447	−	0.526060i	$-0.176331\pi$
$744$	−2.25396	+	13.1927i	−0.00302952	+	0.0177321i
$745$	410.125			0.550504
$746$			128.712i			0.172536i
$747$	−127.536	+	362.348i	−0.170731	+	0.485071i
$748$	−476.217			−0.636654
$749$			79.3797i			0.105981i
$750$	−328.652	−	56.1500i	−0.438203	−	0.0748666i
$751$	160.249			0.213381			0.106691	−	0.994292i	$-0.465975\pi$
$751$	160.249			0.213381			0.106691	+	0.994292i	$0.465975\pi$
$752$		−	175.735i		−	0.233690i
$753$	35.7243	−	209.098i	0.0474426	−	0.277687i
$754$	1133.15			1.50285
$755$			1272.50i			1.68544i
$756$	609.258	+	338.913i	0.805897	+	0.448298i
$757$	840.909			1.11084			0.555422	−	0.831569i	$-0.312557\pi$
$757$	840.909			1.11084			0.555422	+	0.831569i	$0.312557\pi$
$758$		−	879.284i		−	1.16001i
$759$	−418.888	−	71.5667i	−0.551895	−	0.0942908i
$760$	13.4630			0.0177145
$761$			361.226i			0.474673i	0.971427	+	0.237337i	$0.0762744\pi$
$761$			361.226i			0.474673i	−0.971427	+	0.237337i	$0.923726\pi$
$762$	35.1246	−	205.588i	0.0460952	−	0.269801i
$763$	−2109.06			−2.76417
$764$		−	737.077i		−	0.964760i
$765$	1257.13	+	442.473i	1.64330	+	0.578396i
$766$	−254.282			−0.331961
$767$		−	186.904i		−	0.243682i
$768$	47.3144	+	8.08363i	0.0616073	+	0.0105256i
$769$	−147.034			−0.191201			−0.0956007	−	0.995420i	$-0.530477\pi$
$769$	−147.034			−0.191201			−0.0956007	+	0.995420i	$0.530477\pi$
$770$		−	1089.15i		−	1.41448i
$771$	191.831	−	1122.81i	0.248807	−	1.45630i
$772$	44.8337			0.0580748
$773$		−	199.279i		−	0.257800i	−0.991658	−	0.128900i	$-0.958855\pi$
$773$		−	199.279i		−	0.257800i	0.991658	−	0.128900i	$-0.0411446\pi$
$774$	−9.42007	+	26.7637i	−0.0121706	+	0.0345784i
$775$	−19.0813			−0.0246211
$776$			60.7785i			0.0783228i
$777$	1045.93	+	178.696i	1.34612	+	0.229983i
$778$	129.321			0.166223
$779$		−	56.8921i		−	0.0730322i
$780$	149.755	−	876.533i	0.191993	−	1.12376i
$781$	943.697			1.20832
$782$		−	497.296i		−	0.635928i
$783$	432.203	−	776.963i	0.551983	−	0.992290i
$784$	470.746			0.600441
$785$		−	1597.07i		−	2.03448i
$786$	296.724	+	50.6950i	0.377511	+	0.0644975i
$787$	224.633			0.285430			0.142715	−	0.989764i	$-0.454417\pi$
$787$	224.633			0.285430			0.142715	+	0.989764i	$0.454417\pi$
$788$		−	207.916i		−	0.263853i
$789$	−258.569	+	1513.43i	−0.327717	+	1.91817i
$790$	−160.457			−0.203110
$791$			478.863i			0.605390i
$792$	235.167	+	82.7723i	0.296928	+	0.104510i
$793$	−1068.11			−1.34693
$794$		−	726.193i		−	0.914600i
$795$	−721.160	−	123.210i	−0.907119	−	0.154981i
$796$	418.516			0.525774
$797$			874.178i			1.09684i	0.836205	+	0.548418i	$0.184770\pi$
$797$			874.178i			1.09684i	−0.836205	+	0.548418i	$0.815230\pi$
$798$	−7.20905	+	42.1954i	−0.00903390	+	0.0528765i
$799$	1068.13			1.33683
$800$			68.4334i			0.0855418i
$801$	323.300	−	918.540i	0.403621	−	1.14674i
$802$	−777.567			−0.969535
$803$			1204.56i			1.50008i
$804$	240.579	+	41.1027i	0.299228	+	0.0511228i
$805$	1137.36			1.41287
$806$			54.2779i			0.0673423i
$807$	80.7069	−	472.387i	0.100009	−	0.585362i
$808$	313.498			0.387992
$809$		−	85.8800i		−	0.106156i	−0.998590	−	0.0530779i	$-0.983097\pi$
$809$		−	85.8800i		−	0.106156i	0.998590	−	0.0530779i	$-0.0169032\pi$
$810$	−543.891	−	437.007i	−0.671470	−	0.539515i
$811$	−95.2249			−0.117417			−0.0587083	−	0.998275i	$-0.518698\pi$
$811$	−95.2249			−0.117417			−0.0587083	+	0.998275i	$0.518698\pi$
$812$		−	850.275i		−	1.04714i
$813$	−560.526	−	95.7653i	−0.689454	−	0.117793i
$814$	379.441			0.466144
$815$			1427.29i			1.75128i
$816$	−49.1328	+	287.580i	−0.0602117	+	0.352426i
$817$	−1.74211			−0.00213232
$818$			256.664i			0.313771i
$819$	2667.01	+	938.713i	3.25642	+	1.14617i
$820$	886.803			1.08147
$821$		−	444.587i		−	0.541519i	−0.962647	−	0.270759i	$-0.912725\pi$
$821$		−	444.587i		−	0.541519i	0.962647	−	0.270759i	$-0.0872748\pi$
$822$	−413.389	−	70.6272i	−0.502907	−	0.0859211i
$823$	−992.886			−1.20642			−0.603212	−	0.797581i	$-0.706113\pi$
$823$	−992.886			−1.20642			−0.603212	+	0.797581i	$0.706113\pi$
$824$			2.58318i			0.00313493i
$825$	−59.8590	+	350.362i	−0.0725564	+	0.424681i
$826$	−140.246			−0.169790
$827$			434.277i			0.525124i	0.964915	+	0.262562i	$0.0845674\pi$
$827$			434.277i			0.525124i	−0.964915	+	0.262562i	$0.915433\pi$
$828$	−86.4360	+	245.576i	−0.104391	+	0.296590i
$829$	−611.091			−0.737142			−0.368571	−	0.929600i	$-0.620153\pi$
$829$	−611.091			−0.737142			−0.368571	+	0.929600i	$0.620153\pi$
$830$		−	367.647i		−	0.442948i
$831$	235.361	+	40.2112i	0.283226	+	0.0483889i
$832$	194.663			0.233970
$833$			2861.22i			3.43484i
$834$	65.1652	−	381.419i	0.0781357	−	0.457337i
$835$	85.2454			0.102090
$836$			15.3076i			0.0183105i
$837$	37.2166	+	20.7025i	0.0444642	+	0.0247342i
$838$	−593.675			−0.708443
$839$		−	800.909i		−	0.954599i	−0.878741	−	0.477300i	$-0.841616\pi$
$839$		−	800.909i		−	0.954599i	0.878741	−	0.477300i	$-0.158384\pi$
$840$	−657.720	−	112.371i	−0.782999	−	0.133775i
$841$	−243.322			−0.289324
$842$		−	98.9006i		−	0.117459i
$843$	235.891	−	1380.70i	0.279824	−	1.63784i
$844$	304.319			0.360568
$845$		−	2576.92i		−	3.04961i
$846$	−527.466	−	185.653i	−0.623483	−	0.219448i
$847$	−323.827			−0.382323
$848$		−	160.157i		−	0.188864i
$849$	406.607	+	69.4684i	0.478924	+	0.0818238i
$850$	−415.942			−0.489344
$851$			396.236i			0.465613i
$852$	97.3642	−	569.884i	0.114277	−	0.668878i
$853$	−950.425			−1.11421			−0.557107	−	0.830440i	$-0.688089\pi$
$853$	−950.425			−1.11421			−0.557107	+	0.830440i	$0.688089\pi$
$854$			801.475i			0.938495i
$855$	14.2229	−	40.4092i	0.0166350	−	0.0472622i
$856$	17.3902			0.0203156
$857$		−	436.330i		−	0.509137i	−0.967055	−	0.254568i	$-0.918067\pi$
$857$		−	436.330i		−	0.509137i	0.967055	−	0.254568i	$-0.0819334\pi$
$858$	996.624	+	170.272i	1.16157	+	0.198453i
$859$	94.3926			0.109887			0.0549433	−	0.998489i	$-0.482502\pi$
$859$	94.3926			0.109887			0.0549433	+	0.998489i	$0.482502\pi$
$860$		−	27.1551i		−	0.0315757i
$861$	−474.856	+	2779.39i	−0.551517	+	3.22809i
$862$	−478.147			−0.554695
$863$		−	487.347i		−	0.564713i	−0.959310	−	0.282356i	$-0.908884\pi$
$863$		−	487.347i		−	0.564713i	0.959310	−	0.282356i	$-0.0911161\pi$
$864$	74.2478	−	133.474i	0.0859349	−	0.154484i
$865$	−826.860			−0.955907
$866$			116.882i			0.134967i
$867$	−893.311	−	152.621i	−1.03035	−	0.176034i
$868$	40.7282			0.0469219
$869$		−	182.441i		−	0.209943i
$870$	−143.302	+	838.764i	−0.164715	+	0.964096i
$871$	989.799			1.13639
$872$			462.045i			0.529868i
$873$	182.426	+	64.2088i	0.208964	+	0.0735496i
$874$	−15.9851			−0.0182896
$875$			1014.61i			1.15955i
$876$	727.417	+	124.279i	0.830385	+	0.141870i
$877$	1527.91			1.74220			0.871102	−	0.491102i	$-0.163406\pi$
$877$	1527.91			1.74220			0.871102	+	0.491102i	$0.163406\pi$
$878$			9.86209i			0.0112324i
$879$	−143.257	+	838.497i	−0.162977	+	0.953922i
$880$	−238.606			−0.271143
$881$		−	1224.15i		−	1.38950i	−0.719249	−	0.694752i	$-0.755514\pi$
$881$		−	1224.15i		−	1.38950i	0.719249	−	0.694752i	$-0.244486\pi$
$882$	497.315	−	1412.94i	0.563849	−	1.60197i
$883$	−247.887			−0.280732			−0.140366	−	0.990100i	$-0.544828\pi$
$883$	−247.887			−0.280732			−0.140366	+	0.990100i	$0.544828\pi$
$884$			1183.17i			1.33843i
$885$	138.348	+	23.6366i	0.156325	+	0.0267080i
$886$	−407.695			−0.460152
$887$			617.752i			0.696451i	0.937411	+	0.348226i	$0.113216\pi$
$887$			617.752i			0.696451i	−0.937411	+	0.348226i	$0.886784\pi$
$888$	39.1481	−	229.138i	0.0440857	−	0.258039i
$889$	−634.688			−0.713934
$890$			931.973i			1.04716i
$891$	496.880	−	618.407i	0.557666	−	0.694060i
$892$	−231.108			−0.259090
$893$		−	34.3340i		−	0.0384479i
$894$	281.600	+	48.1112i	0.314989	+	0.0538157i
$895$	548.488			0.612835
$896$		−	146.068i		−	0.163022i
$897$	−177.809	+	1040.74i	−0.198226	+	1.16024i
$898$	762.685			0.849315
$899$		−	51.9391i		−	0.0577743i
$900$	205.402	+	72.2958i	0.228225	+	0.0803287i
$901$	973.444			1.08040
$902$			1008.30i			1.11785i
$903$	85.1085	+	14.5407i	0.0942508	+	0.0161027i
$904$	104.907			0.116048
$905$			158.837i			0.175511i
$906$	−149.275	+	873.727i	−0.164763	+	0.964379i
$907$	−1441.01			−1.58877			−0.794384	−	0.607416i	$-0.792206\pi$
$907$	−1441.01			−1.58877			−0.794384	+	0.607416i	$0.792206\pi$
$908$			472.523i			0.520400i
$909$	331.191	−	940.959i	0.364347	−	1.03516i
$910$	−2706.01			−2.97364
$911$		−	1677.23i		−	1.84108i	−0.390646	−	0.920541i	$-0.627748\pi$
$911$		−	1677.23i		−	1.84108i	0.390646	−	0.920541i	$-0.372252\pi$
$912$	9.24400	+	1.57933i	0.0101360	+	0.00173172i
$913$	418.017			0.457850
$914$		−	423.133i		−	0.462946i
$915$	135.078	−	790.625i	0.147626	−	0.864071i
$916$	−129.738			−0.141636
$917$		−	916.039i		−	0.998952i
$918$	811.262	+	451.283i	0.883728	+	0.491593i
$919$	−628.997			−0.684437			−0.342218	−	0.939620i	$-0.611178\pi$
$919$	−628.997			−0.684437			−0.342218	+	0.939620i	$0.611178\pi$
$920$		−	249.168i		−	0.270834i
$921$	−594.822	−	101.625i	−0.645843	−	0.110342i
$922$	518.902			0.562800
$923$		−	2344.64i		−	2.54023i
$924$	127.766	−	747.831i	0.138275	−	0.809341i
$925$	331.415			0.358287
$926$			681.167i			0.735601i
$927$	7.75339	+	2.72898i	0.00836396	+	0.00294388i
$928$	−186.275			−0.200727
$929$		−	213.387i		−	0.229696i	−0.993383	−	0.114848i	$-0.963362\pi$
$929$		−	213.387i		−	0.229696i	0.993383	−	0.114848i	$-0.0366381\pi$
$930$	−40.1768	−	6.86418i	−0.0432009	−	0.00738083i
$931$	91.9715			0.0987878
$932$		−	522.098i		−	0.560191i
$933$	85.8396	−	502.430i	0.0920039	−	0.538510i
$934$	630.157			0.674686
$935$		−	1450.26i		−	1.55108i
$936$	205.649	−	584.278i	0.219711	−	0.624228i
$937$	−847.045			−0.903996			−0.451998	−	0.892019i	$-0.649289\pi$
$937$	−847.045			−0.903996			−0.451998	+	0.892019i	$0.649289\pi$
$938$		−	742.711i		−	0.791802i
$939$	387.699	+	66.2380i	0.412885	+	0.0705410i
$940$	535.180			0.569341
$941$		−	649.303i		−	0.690014i	−0.938600	−	0.345007i	$-0.887877\pi$
$941$		−	649.303i		−	0.690014i	0.938600	−	0.345007i	$-0.112123\pi$
$942$	187.349	−	1096.58i	0.198885	−	1.16410i
$943$	−1052.93			−1.11658
$944$			30.7246i			0.0325472i
$945$	−1032.12	+	1855.42i	−1.09219	+	1.96341i
$946$	30.8755			0.0326379
$947$			1199.84i			1.26700i	0.773745	+	0.633498i	$0.218381\pi$
$947$			1199.84i			1.26700i	−0.773745	+	0.633498i	$0.781619\pi$
$948$	−110.173	−	18.8230i	−0.116216	−	0.0198554i
$949$	2992.76			3.15360
$950$			13.3701i			0.0140738i
$951$	23.6319	−	138.321i	0.0248496	−	0.145447i
$952$	887.810			0.932574
$953$			1116.32i			1.17138i	0.810537	+	0.585688i	$0.199175\pi$
$953$			1116.32i			1.17138i	−0.810537	+	0.585688i	$0.800825\pi$
$954$	−480.709	−	169.196i	−0.503888	−	0.177355i
$955$	2244.68			2.35045
$956$		−	595.358i		−	0.622759i
$957$	−953.680	−	162.935i	−0.996531	−	0.170256i
$958$	−87.7469			−0.0915938
$959$			1276.21i			1.33077i
$960$	−24.6177	+	144.091i	−0.0256435	+	0.150094i
$961$	−958.512			−0.997411
$962$		−	942.729i		−	0.979968i
$963$	18.3717	−	52.1964i	0.0190776	−	0.0542019i
$964$	908.812			0.942751
$965$			136.536i			0.141488i
$966$	780.933	+	133.422i	0.808419	+	0.138118i
$967$	−608.301			−0.629060			−0.314530	−	0.949248i	$-0.601847\pi$
$967$	−608.301			−0.629060			−0.314530	+	0.949248i	$0.601847\pi$
$968$			70.9428i			0.0732880i
$969$	−9.59926	+	56.1856i	−0.00990636	+	0.0579831i
$970$	−185.094			−0.190818
$971$			1217.25i			1.25361i	0.779177	+	0.626804i	$0.215637\pi$
$971$			1217.25i			1.25361i	−0.779177	+	0.626804i	$0.784363\pi$
$972$	−322.182	−	363.861i	−0.331463	−	0.374343i
$973$	−1177.51			−1.21018
$974$		−	415.999i		−	0.427104i
$975$	870.481	+	148.721i	0.892801	+	0.152534i
$976$	175.584			0.179902
$977$			683.352i			0.699439i	0.936854	+	0.349719i	$0.113723\pi$
$977$			683.352i			0.699439i	−0.936854	+	0.349719i	$0.886277\pi$
$978$	−167.433	+	980.007i	−0.171200	+	1.00205i
$979$	−1059.66			−1.08239
$980$			1433.60i			1.46286i
$981$	1386.82	+	488.123i	1.41368	+	0.497577i
$982$	681.729			0.694225
$983$		−	977.431i		−	0.994334i	−0.867655	−	0.497167i	$-0.834374\pi$
$983$		−	977.431i		−	0.994334i	0.867655	−	0.497167i	$-0.165626\pi$
$984$	608.897	+	104.030i	0.618798	+	0.105721i
$985$	633.184			0.642826
$986$		−	1132.19i		−	1.14827i
$987$	−286.573	+	1677.34i	−0.290347	+	1.69944i
$988$	38.0320			0.0384939
$989$			32.2421i			0.0326007i
$990$	−252.073	+	716.174i	−0.254619	+	0.723408i
$991$	738.198			0.744902			0.372451	−	0.928052i	$-0.378517\pi$
$991$	738.198			0.744902			0.372451	+	0.928052i	$0.378517\pi$
$992$		−	8.92257i		−	0.00899453i
$993$	1401.31	+	239.412i	1.41119	+	0.241100i
$994$	−1759.33			−1.76995
$995$			1274.54i			1.28095i
$996$	43.1281	−	252.434i	0.0433013	−	0.253448i
$997$	−616.825			−0.618681			−0.309341	−	0.950951i	$-0.600108\pi$
$997$	−616.825			−0.618681			−0.309341	+	0.950951i	$0.600108\pi$
$998$		−	97.3732i		−	0.0975683i
$999$	−646.399	−	359.574i	−0.647046	−	0.359934i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.3.b.a.119.19	✓	40
3.2	odd	2	inner	354.3.b.a.119.39	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.3.b.a.119.19	✓	40	1.1	even	1	trivial
354.3.b.a.119.39	yes	40	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	354.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(2.95715 + 0.505227i) q^{3} -2.00000 q^{4} -6.09077i q^{5} +(0.714499 - 4.18204i) q^{6} -12.9107 q^{7} +2.82843i q^{8} +(8.48949 + 2.98806i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(2.95715 + 0.505227i) q^{3} -2.00000 q^{4} -6.09077i q^{5} +(0.714499 - 4.18204i) q^{6} -12.9107 q^{7} +2.82843i q^{8} +(8.48949 + 2.98806i) q^{9} -8.61364 q^{10} -9.79377i q^{11} +(-5.91430 - 1.01045i) q^{12} -24.3328 q^{13} +18.2585i q^{14} +(3.07722 - 18.0113i) q^{15} +4.00000 q^{16} +24.3122i q^{17} +(4.22576 - 12.0060i) q^{18} +0.781495 q^{19} +12.1815i q^{20} +(-38.1789 - 6.52284i) q^{21} -13.8505 q^{22} -14.4635i q^{23} +(-1.42900 + 8.36409i) q^{24} -12.0974 q^{25} +34.4118i q^{26} +(23.5951 + 13.1253i) q^{27} +25.8214 q^{28} -32.9290i q^{29} +(-25.4719 - 4.35184i) q^{30} +1.57730 q^{31} -5.65685i q^{32} +(4.94808 - 28.9617i) q^{33} +34.3827 q^{34} +78.6361i q^{35} +(-16.9790 - 5.97613i) q^{36} -27.3955 q^{37} -1.10520i q^{38} +(-71.9559 - 12.2936i) q^{39} +17.2273 q^{40} -72.7990i q^{41} +(-9.22469 + 53.9932i) q^{42} -2.22920 q^{43} +19.5875i q^{44} +(18.1996 - 51.7075i) q^{45} -20.4545 q^{46} -43.9337i q^{47} +(11.8286 + 2.02091i) q^{48} +117.687 q^{49} +17.1084i q^{50} +(-12.2832 + 71.8950i) q^{51} +48.6657 q^{52} -40.0392i q^{53} +(18.5619 - 33.3685i) q^{54} -59.6516 q^{55} -36.5170i q^{56} +(2.31100 + 0.394832i) q^{57} -46.5687 q^{58} +7.68115i q^{59} +(-6.15444 + 36.0226i) q^{60} +43.8960 q^{61} -2.23064i q^{62} +(-109.605 - 38.5780i) q^{63} -8.00000 q^{64} +148.206i q^{65} +(-40.9580 - 6.99763i) q^{66} -40.6775 q^{67} -48.6245i q^{68} +(7.30737 - 42.7709i) q^{69} +111.208 q^{70} +96.3569i q^{71} +(-8.45152 + 24.0119i) q^{72} -122.993 q^{73} +38.7431i q^{74} +(-35.7739 - 6.11195i) q^{75} -1.56299 q^{76} +126.445i q^{77} +(-17.3858 + 101.761i) q^{78} +18.6282 q^{79} -24.3631i q^{80} +(63.1429 + 50.7343i) q^{81} -102.953 q^{82} +42.6819i q^{83} +(76.3579 + 13.0457i) q^{84} +148.080 q^{85} +3.15256i q^{86} +(16.6366 - 97.3762i) q^{87} +27.7010 q^{88} -108.197i q^{89} +(-73.1255 - 25.7381i) q^{90} +314.154 q^{91} +28.9271i q^{92} +(4.66432 + 0.796896i) q^{93} -62.1317 q^{94} -4.75991i q^{95} +(2.85799 - 16.7282i) q^{96} +21.4884 q^{97} -166.434i q^{98} +(29.2644 - 83.1441i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9}+O(q^{10}) \) 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9	\( 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9} - 16 q^{10} + 34 q^{15} + 160 q^{16} + 16 q^{18} + 24 q^{19} - 18 q^{21} - 16 q^{22} - 16 q^{24} - 216 q^{25} - 30 q^{27} - 16 q^{28} - 64 q^{30} + 96 q^{31} + 76 q^{33} + 80 q^{34} + 48 q^{36} - 200 q^{37} - 28 q^{39} + 32 q^{40} + 48 q^{42} - 104 q^{43} + 58 q^{45} + 32 q^{46} + 288 q^{49} - 176 q^{51} - 40 q^{54} + 360 q^{55} + 214 q^{57} - 128 q^{58} - 68 q^{60} - 32 q^{61} - 132 q^{63} - 320 q^{64} - 112 q^{66} - 344 q^{67} + 88 q^{69} + 192 q^{70} - 32 q^{72} + 40 q^{73} + 28 q^{75} - 48 q^{76} + 96 q^{78} + 32 q^{79} + 336 q^{81} - 80 q^{82} + 36 q^{84} + 168 q^{85} - 162 q^{87} + 32 q^{88} + 112 q^{90} + 88 q^{91} - 316 q^{93} - 400 q^{94} + 32 q^{96} - 184 q^{97} - 148 q^{99}+O(q^{100}) \) 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9 - 16 * q^10 + 34 * q^15 + 160 * q^16 + 16 * q^18 + 24 * q^19 - 18 * q^21 - 16 * q^22 - 16 * q^24 - 216 * q^25 - 30 * q^27 - 16 * q^28 - 64 * q^30 + 96 * q^31 + 76 * q^33 + 80 * q^34 + 48 * q^36 - 200 * q^37 - 28 * q^39 + 32 * q^40 + 48 * q^42 - 104 * q^43 + 58 * q^45 + 32 * q^46 + 288 * q^49 - 176 * q^51 - 40 * q^54 + 360 * q^55 + 214 * q^57 - 128 * q^58 - 68 * q^60 - 32 * q^61 - 132 * q^63 - 320 * q^64 - 112 * q^66 - 344 * q^67 + 88 * q^69 + 192 * q^70 - 32 * q^72 + 40 * q^73 + 28 * q^75 - 48 * q^76 + 96 * q^78 + 32 * q^79 + 336 * q^81 - 80 * q^82 + 36 * q^84 + 168 * q^85 - 162 * q^87 + 32 * q^88 + 112 * q^90 + 88 * q^91 - 316 * q^93 - 400 * q^94 + 32 * q^96 - 184 * q^97 - 148 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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