LMFDB - Embedded newform 294.3.h.g.263.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,3,Mod(263,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("294.263");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	294.h (of order $6$, degree $2$, not 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:	$8.01091977219$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.12745506816.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 8x^{6} + 55x^{4} - 72x^{2} + 81 $ x^8 - 8x^6 + 55x^4 - 72*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			263.3
Root			$-1.00781 - 0.581861i$ of defining polynomial
Character	$\chi$	$=$	294.263
Dual form			294.3.h.g.275.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(-0.0981308 + 2.99839i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-5.68986 + 3.28504i) q^{5} +(2.00000 + 3.74166i) q^{6} -2.82843i q^{8} +(-8.98074 - 0.588470i) q^{9} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(-0.0981308 + 2.99839i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-5.68986 + 3.28504i) q^{5} +(2.00000 + 3.74166i) q^{6} -2.82843i q^{8} +(-8.98074 - 0.588470i) q^{9} +(-4.64575 + 8.04668i) q^{10} +(-0.357016 - 0.206123i) q^{11} +(5.09524 + 3.16836i) q^{12} -20.5830 q^{13} +(-9.29150 - 17.3828i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(13.7524 + 7.93993i) q^{17} +(-11.4152 + 5.62962i) q^{18} +(-8.00000 - 13.8564i) q^{19} +13.1402i q^{20} -0.583005 q^{22} +(-31.1790 + 18.0012i) q^{23} +(8.48074 + 0.277556i) q^{24} +(9.08301 - 15.7322i) q^{25} +(-25.2089 + 14.5544i) q^{26} +(2.64575 - 26.8701i) q^{27} +20.8010i q^{29} +(-23.6712 - 14.7194i) q^{30} +(-2.77124 + 4.79993i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(0.653074 - 1.05025i) q^{33} +22.4575 q^{34} +(-10.0000 + 14.9666i) q^{36} +(-10.0000 - 17.3205i) q^{37} +(-19.5959 - 11.3137i) q^{38} +(2.01983 - 61.7160i) q^{39} +(9.29150 + 16.0934i) q^{40} +76.1013i q^{41} +51.7490 q^{43} +(-0.714033 + 0.412247i) q^{44} +(53.0323 - 26.1538i) q^{45} +(-25.4575 + 44.0937i) q^{46} +(7.34847 - 4.24264i) q^{47} +(10.5830 - 5.65685i) q^{48} -25.6906i q^{50} +(-25.1566 + 40.4559i) q^{51} +(-20.5830 + 35.6508i) q^{52} +(44.0908 + 25.4558i) q^{53} +(-15.7596 - 34.7798i) q^{54} +2.70850 q^{55} +(42.3320 - 22.6274i) q^{57} +(14.7085 + 25.4759i) q^{58} +(-1.42807 - 0.824494i) q^{59} +(-39.3994 - 1.28946i) q^{60} +(-33.4575 - 57.9501i) q^{61} +7.83826i q^{62} -8.00000 q^{64} +(117.114 - 67.6160i) q^{65} +(0.0572108 - 1.74808i) q^{66} +(-24.7085 + 42.7964i) q^{67} +(27.5047 - 15.8799i) q^{68} +(-50.9150 - 95.2533i) q^{69} +87.7385i q^{71} +(-1.66444 + 25.4014i) q^{72} +(-6.16601 + 10.6798i) q^{73} +(-24.4949 - 14.1421i) q^{74} +(46.2801 + 28.7782i) q^{75} -32.0000 q^{76} +(-41.1660 - 77.0146i) q^{78} +(42.4575 + 73.5386i) q^{79} +(22.7594 + 13.1402i) q^{80} +(80.3074 + 10.5698i) q^{81} +(53.8118 + 93.2047i) q^{82} -4.12247i q^{83} -104.332 q^{85} +(63.3793 - 36.5921i) q^{86} +(-62.3695 - 2.04121i) q^{87} +(-0.583005 + 1.00979i) q^{88} +(-27.0212 + 15.6007i) q^{89} +(46.4575 - 69.5312i) q^{90} +72.0047i q^{92} +(-14.1202 - 8.78030i) q^{93} +(6.00000 - 10.3923i) q^{94} +(91.0378 + 52.5607i) q^{95} +(8.96148 - 14.4115i) q^{96} +68.8340 q^{97} +(3.08497 + 2.06123i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} + 16 q^{6} - 20 q^{9}+O(q^{10}) $ 8 * q + 8 * q^4 + 16 * q^6 - 20 * q^9	$ 8 q + 8 q^{4} + 16 q^{6} - 20 q^{9} - 16 q^{10} - 80 q^{13} - 32 q^{15} - 16 q^{16} - 64 q^{19} + 80 q^{22} + 16 q^{24} - 12 q^{25} - 56 q^{30} - 128 q^{31} + 40 q^{33} - 32 q^{34} - 80 q^{36} - 80 q^{37} + 112 q^{39} + 32 q^{40} + 160 q^{43} + 112 q^{45} + 8 q^{46} - 16 q^{51} - 80 q^{52} - 152 q^{54} + 64 q^{55} + 160 q^{58} - 32 q^{60} - 56 q^{61} - 64 q^{64} + 112 q^{66} - 240 q^{67} + 16 q^{69} + 120 q^{73} + 224 q^{75} - 256 q^{76} - 160 q^{78} + 128 q^{79} + 124 q^{81} + 240 q^{82} - 496 q^{85} - 160 q^{87} + 80 q^{88} + 160 q^{90} + 280 q^{93} + 48 q^{94} - 32 q^{96} + 720 q^{97} + 448 q^{99}+O(q^{100}) $ 8 * q + 8 * q^4 + 16 * q^6 - 20 * q^9 - 16 * q^10 - 80 * q^13 - 32 * q^15 - 16 * q^16 - 64 * q^19 + 80 * q^22 + 16 * q^24 - 12 * q^25 - 56 * q^30 - 128 * q^31 + 40 * q^33 - 32 * q^34 - 80 * q^36 - 80 * q^37 + 112 * q^39 + 32 * q^40 + 160 * q^43 + 112 * q^45 + 8 * q^46 - 16 * q^51 - 80 * q^52 - 152 * q^54 + 64 * q^55 + 160 * q^58 - 32 * q^60 - 56 * q^61 - 64 * q^64 + 112 * q^66 - 240 * q^67 + 16 * q^69 + 120 * q^73 + 224 * q^75 - 256 * q^76 - 160 * q^78 + 128 * q^79 + 124 * q^81 + 240 * q^82 - 496 * q^85 - 160 * q^87 + 80 * q^88 + 160 * q^90 + 280 * q^93 + 48 * q^94 - 32 * q^96 + 720 * q^97 + 448 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$	−0.0981308	+	2.99839i	−0.0327103	+	0.999465i
$3$	−0.0981308	+	2.99839i	−0.0327103	+	0.999465i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	−5.68986	+	3.28504i	−1.13797	+	0.657008i	−0.945928	−	0.324378i	$-0.894845\pi$
$5$	−5.68986	+	3.28504i	−1.13797	+	0.657008i	−0.192044	+	0.981386i	$0.561512\pi$
$6$	2.00000	+	3.74166i	0.333333	+	0.623610i
$7$		0			0
$7$		0			0
$8$		−	2.82843i		−	0.353553i
$9$	−8.98074	−	0.588470i	−0.997860	−	0.0653855i
$10$	−4.64575	+	8.04668i	−0.464575	+	0.804668i
$11$	−0.357016	−	0.206123i	−0.0324560	−	0.0187385i	0.483684	−	0.875243i	$-0.339298\pi$
$11$	−0.357016	−	0.206123i	−0.0324560	−	0.0187385i	−0.516140	+	0.856504i	$0.672632\pi$
$12$	5.09524	+	3.16836i	0.424603	+	0.264030i
$13$	−20.5830			−1.58331			−0.791654	−	0.610970i	$-0.790780\pi$
$13$	−20.5830			−1.58331			−0.791654	+	0.610970i	$0.790780\pi$
$14$		0			0
$15$	−9.29150	−	17.3828i	−0.619434	−	1.15885i
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	13.7524	+	7.93993i	0.808962	+	0.467055i	0.846595	−	0.532237i	$-0.178648\pi$
$17$	13.7524	+	7.93993i	0.808962	+	0.467055i	−0.0376330	+	0.999292i	$0.511982\pi$
$18$	−11.4152	+	5.62962i	−0.634179	+	0.312757i
$19$	−8.00000	−	13.8564i	−0.421053	−	0.729285i	0.574990	−	0.818160i	$-0.305006\pi$
$19$	−8.00000	−	13.8564i	−0.421053	−	0.729285i	−0.996043	+	0.0888758i	$0.971673\pi$
$20$			13.1402i			0.657008i
$21$		0			0
$22$	−0.583005			−0.0265002
$23$	−31.1790	+	18.0012i	−1.35561	+	0.782660i	−0.989028	−	0.147727i	$-0.952804\pi$
$23$	−31.1790	+	18.0012i	−1.35561	+	0.782660i	−0.366579	+	0.930387i	$0.619471\pi$
$24$	8.48074	+	0.277556i	0.353364	+	0.0115648i
$25$	9.08301	−	15.7322i	0.363320	−	0.629289i
$26$	−25.2089	+	14.5544i	−0.969574	+	0.559784i
$27$	2.64575	−	26.8701i	0.0979908	−	0.995187i
$28$		0			0
$29$			20.8010i			0.717274i	0.933477	+	0.358637i	$0.116758\pi$
$29$			20.8010i			0.717274i	−0.933477	+	0.358637i	$0.883242\pi$
$30$	−23.6712	−	14.7194i	−0.789041	−	0.490647i
$31$	−2.77124	+	4.79993i	−0.0893949	+	0.154837i	−0.907256	−	0.420580i	$-0.861827\pi$
$31$	−2.77124	+	4.79993i	−0.0893949	+	0.154837i	0.817861	+	0.575416i	$0.195160\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$	0.653074	−	1.05025i	0.0197901	−	0.0318257i
$34$	22.4575			0.660515
$35$		0			0
$36$	−10.0000	+	14.9666i	−0.277778	+	0.415740i
$37$	−10.0000	−	17.3205i	−0.270270	−	0.468122i	0.698661	−	0.715453i	$-0.253780\pi$
$37$	−10.0000	−	17.3205i	−0.270270	−	0.468122i	−0.968931	+	0.247331i	$0.920446\pi$
$38$	−19.5959	−	11.3137i	−0.515682	−	0.297729i
$39$	2.01983	−	61.7160i	0.0517904	−	1.58246i
$40$	9.29150	+	16.0934i	0.232288	+	0.402334i
$41$			76.1013i			1.85613i	0.372418	+	0.928065i	$0.378529\pi$
$41$			76.1013i			1.85613i	−0.372418	+	0.928065i	$0.621471\pi$
$42$		0			0
$43$	51.7490			1.20347			0.601733	−	0.798698i	$-0.294477\pi$
$43$	51.7490			1.20347			0.601733	+	0.798698i	$0.294477\pi$
$44$	−0.714033	+	0.412247i	−0.0162280	+	0.00936925i
$45$	53.0323	−	26.1538i	1.17850	−	0.581196i
$46$	−25.4575	+	44.0937i	−0.553424	+	0.958559i
$47$	7.34847	−	4.24264i	0.156350	−	0.0902690i	−0.419784	−	0.907624i	$-0.637894\pi$
$47$	7.34847	−	4.24264i	0.156350	−	0.0902690i	0.576134	+	0.817355i	$0.304561\pi$
$48$	10.5830	−	5.65685i	0.220479	−	0.117851i
$49$		0			0
$50$		−	25.6906i		−	0.513812i
$51$	−25.1566	+	40.4559i	−0.493266	+	0.793252i
$52$	−20.5830	+	35.6508i	−0.395827	+	0.685593i
$53$	44.0908	+	25.4558i	0.831902	+	0.480299i	0.854504	−	0.519446i	$-0.173862\pi$
$53$	44.0908	+	25.4558i	0.831902	+	0.480299i	−0.0226013	+	0.999745i	$0.507195\pi$
$54$	−15.7596	−	34.7798i	−0.291845	−	0.644070i
$55$	2.70850			0.0492454
$56$		0			0
$57$	42.3320	−	22.6274i	0.742667	−	0.396972i
$58$	14.7085	+	25.4759i	0.253595	+	0.439239i
$59$	−1.42807	−	0.824494i	−0.0242045	−	0.0139745i	0.487849	−	0.872928i	$-0.337782\pi$
$59$	−1.42807	−	0.824494i	−0.0242045	−	0.0139745i	−0.512053	+	0.858954i	$0.671115\pi$
$60$	−39.3994	−	1.28946i	−0.656657	−	0.0214909i
$61$	−33.4575	−	57.9501i	−0.548484	−	0.950002i	−0.998379	−	0.0569203i	$-0.981872\pi$
$61$	−33.4575	−	57.9501i	−0.548484	−	0.950002i	0.449895	−	0.893082i	$-0.351461\pi$
$62$			7.83826i			0.126424i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	117.114	−	67.6160i	1.80176	−	1.04025i
$66$	0.0572108	−	1.74808i	0.000866830	−	0.0264861i
$67$	−24.7085	+	42.7964i	−0.368784	+	0.638752i	−0.989376	−	0.145382i	$-0.953559\pi$
$67$	−24.7085	+	42.7964i	−0.368784	+	0.638752i	0.620592	+	0.784134i	$0.286892\pi$
$68$	27.5047	−	15.8799i	0.404481	−	0.233527i
$69$	−50.9150	−	95.2533i	−0.737899	−	1.38048i
$70$		0			0
$71$			87.7385i			1.23575i	0.786275	+	0.617877i	$0.212007\pi$
$71$			87.7385i			1.23575i	−0.786275	+	0.617877i	$0.787993\pi$
$72$	−1.66444	+	25.4014i	−0.0231173	+	0.352797i
$73$	−6.16601	+	10.6798i	−0.0844659	+	0.146299i	−0.905163	−	0.425064i	$-0.860252\pi$
$73$	−6.16601	+	10.6798i	−0.0844659	+	0.146299i	0.820698	+	0.571363i	$0.193585\pi$
$74$	−24.4949	−	14.1421i	−0.331012	−	0.191110i
$75$	46.2801	+	28.7782i	0.617068	+	0.383710i
$76$	−32.0000			−0.421053
$77$		0			0
$78$	−41.1660	−	77.0146i	−0.527769	−	0.987366i
$79$	42.4575	+	73.5386i	0.537437	+	0.930868i	0.999041	+	0.0437820i	$0.0139407\pi$
$79$	42.4575	+	73.5386i	0.537437	+	0.930868i	−0.461604	+	0.887086i	$0.652726\pi$
$80$	22.7594	+	13.1402i	0.284493	+	0.164252i
$81$	80.3074	+	10.5698i	0.991449	+	0.130491i
$82$	53.8118	+	93.2047i	0.656241	+	1.13664i
$83$		−	4.12247i		−	0.0496683i	−0.999692	−	0.0248342i	$-0.992094\pi$
$83$		−	4.12247i		−	0.0496683i	0.999692	−	0.0248342i	$-0.00790577\pi$
$84$		0			0
$85$	−104.332			−1.22744
$86$	63.3793	−	36.5921i	0.736969	−	0.425489i
$87$	−62.3695	−	2.04121i	−0.716891	−	0.0234622i
$88$	−0.583005	+	1.00979i	−0.00662506	+	0.0114749i
$89$	−27.0212	+	15.6007i	−0.303609	+	0.175289i	−0.644063	−	0.764972i	$-0.722753\pi$
$89$	−27.0212	+	15.6007i	−0.303609	+	0.175289i	0.340454	+	0.940261i	$0.389419\pi$
$90$	46.4575	−	69.5312i	0.516195	−	0.772569i
$91$		0			0
$92$			72.0047i			0.782660i
$93$	−14.1202	−	8.78030i	−0.151830	−	0.0944119i
$94$	6.00000	−	10.3923i	0.0638298	−	0.110556i
$95$	91.0378	+	52.5607i	0.958292	+	0.553270i
$96$	8.96148	−	14.4115i	0.0933488	−	0.150120i
$97$	68.8340			0.709629			0.354814	−	0.934937i	$-0.384544\pi$
$97$	68.8340			0.709629			0.354814	+	0.934937i	$0.384544\pi$
$98$		0			0
$99$	3.08497	+	2.06123i	0.0311614	+	0.0208206i
$100$	−18.1660	−	31.4645i	−0.181660	−	0.314645i
$101$	−121.376	−	70.0766i	−1.20174	−	0.693828i	−0.240802	−	0.970574i	$-0.577410\pi$
$101$	−121.376	−	70.0766i	−1.20174	−	0.693828i	−0.960943	+	0.276747i	$0.910744\pi$
$102$	−2.20377	+	67.3365i	−0.0216056	+	0.660162i
$103$	19.6863	+	34.0976i	0.191129	+	0.331045i	0.945625	−	0.325260i	$-0.105452\pi$
$103$	19.6863	+	34.0976i	0.191129	+	0.331045i	−0.754496	+	0.656305i	$0.772119\pi$
$104$			58.2175i			0.559784i
$105$		0			0
$106$	72.0000			0.679245
$107$	93.5369	−	54.0035i	0.874176	−	0.504706i	0.00544256	−	0.999985i	$-0.498268\pi$
$107$	93.5369	−	54.0035i	0.874176	−	0.504706i	0.868734	+	0.495279i	$0.164934\pi$
$108$	−43.8946	−	31.4526i	−0.406431	−	0.291228i
$109$	61.9150	−	107.240i	0.568028	−	0.983853i	−0.428733	−	0.903431i	$-0.641040\pi$
$109$	61.9150	−	107.240i	0.568028	−	0.983853i	0.996761	−	0.0804218i	$-0.0256267\pi$
$110$	3.31722	−	1.91520i	0.0301565	−	0.0174109i
$111$	52.9150	−	28.2843i	0.476712	−	0.254813i
$112$		0			0
$113$		−	80.4900i		−	0.712301i	−0.934429	−	0.356150i	$-0.884089\pi$
$113$		−	80.4900i		−	0.712301i	0.934429	−	0.356150i	$-0.115911\pi$
$114$	35.8459	−	57.6461i	0.314438	−	0.505667i
$115$	118.269	−	204.848i	1.02843	−	1.78129i
$116$	36.0283	+	20.8010i	0.310589	+	0.179319i
$117$	184.851	+	12.1125i	1.57992	+	0.103525i
$118$	−2.33202			−0.0197629
$119$		0			0
$120$	−49.1660	+	26.2803i	−0.409717	+	0.219003i
$121$	−60.4150	−	104.642i	−0.499298	−	0.864809i
$122$	−81.9538	−	47.3161i	−0.671753	−	0.387837i
$123$	−228.182	−	7.46788i	−1.85514	−	0.0607145i
$124$	5.54249	+	9.59987i	0.0446975	+	0.0774183i
$125$		−	44.8999i		−	0.359199i
$126$		0			0
$127$	−132.915			−1.04658			−0.523288	−	0.852156i	$-0.675295\pi$
$127$	−132.915			−1.04658			−0.523288	+	0.852156i	$0.675295\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$	−5.07817	+	155.164i	−0.0393657	+	1.20282i
$130$	95.6235	−	165.625i	0.735566	−	1.27404i
$131$	3.57016	−	2.06123i	0.0272532	−	0.0157346i	−0.486312	−	0.873786i	$-0.661658\pi$
$131$	3.57016	−	2.06123i	0.0272532	−	0.0157346i	0.513565	+	0.858051i	$0.328325\pi$
$132$	−1.16601	−	2.18141i	−0.00883341	−	0.0165258i
$133$		0			0
$134$			69.8862i			0.521539i
$135$	73.2153	+	161.578i	0.542336	+	1.19688i
$136$	22.4575	−	38.8976i	0.165129	−	0.286011i
$137$	−86.2925	−	49.8210i	−0.629872	−	0.363657i	0.150830	−	0.988560i	$-0.451805\pi$
$137$	−86.2925	−	49.8210i	−0.629872	−	0.363657i	−0.780703	+	0.624903i	$0.785139\pi$
$138$	−129.712	−	80.6586i	−0.939943	−	0.584483i
$139$	−93.5425			−0.672968			−0.336484	−	0.941689i	$-0.609238\pi$
$139$	−93.5425			−0.672968			−0.336484	+	0.941689i	$0.609238\pi$
$140$		0			0
$141$	12.0000	+	22.4499i	0.0851064	+	0.159219i
$142$	62.0405	+	107.457i	0.436905	+	0.756742i
$143$	7.34847	+	4.24264i	0.0513879	+	0.0296688i
$144$	15.9230	+	32.2871i	0.110576	+	0.224216i
$145$	−68.3320	−	118.355i	−0.471255	−	0.816238i
$146$			17.4401i			0.119453i
$147$		0			0
$148$	−40.0000			−0.270270
$149$	−43.1686	+	24.9234i	−0.289722	+	0.167271i	−0.637817	−	0.770188i	$-0.720162\pi$
$149$	−43.1686	+	24.9234i	−0.289722	+	0.167271i	0.348094	+	0.937460i	$0.386829\pi$
$150$	77.0306	+	2.52104i	0.513537	+	0.0168069i
$151$	−105.830	+	183.303i	−0.700861	+	1.21393i	0.267303	+	0.963612i	$0.413867\pi$
$151$	−105.830	+	183.303i	−0.700861	+	1.21393i	−0.968164	+	0.250315i	$0.919466\pi$
$152$	−39.1918	+	22.6274i	−0.257841	+	0.148865i
$153$	−118.834	−	79.3993i	−0.776693	−	0.518950i
$154$		0			0
$155$		−	36.4146i		−	0.234933i
$156$	−104.875	−	65.2144i	−0.672278	−	0.418041i
$157$	−54.3725	+	94.1760i	−0.346322	+	0.599847i	−0.985593	−	0.169134i	$-0.945903\pi$
$157$	−54.3725	+	94.1760i	−0.346322	+	0.599847i	0.639271	+	0.768981i	$0.279236\pi$
$158$	103.999	+	60.0440i	0.658223	+	0.380025i
$159$	−80.6533	+	129.704i	−0.507254	+	0.815746i
$160$	37.1660			0.232288
$161$		0			0
$162$	105.830	−	43.8406i	0.653272	−	0.270621i
$163$	−6.50197	−	11.2617i	−0.0398894	−	0.0690904i	0.845391	−	0.534147i	$-0.179367\pi$
$163$	−6.50197	−	11.2617i	−0.0398894	−	0.0690904i	−0.885281	+	0.465057i	$0.846034\pi$
$164$	131.811	+	76.1013i	0.803728	+	0.464032i
$165$	−0.265787	+	8.12114i	−0.00161083	+	0.0492191i
$166$	−2.91503	−	5.04897i	−0.0175604	−	0.0304155i
$167$			156.858i			0.939267i	0.882862	+	0.469633i	$0.155614\pi$
$167$			156.858i			0.939267i	−0.882862	+	0.469633i	$0.844386\pi$
$168$		0			0
$169$	254.660			1.50686
$170$	−127.780	+	73.7739i	−0.751648	+	0.433964i
$171$	63.6919	+	129.149i	0.372467	+	0.755255i
$172$	51.7490	−	89.6319i	0.300866	−	0.521116i
$173$	4.72288	−	2.72676i	0.0272999	−	0.0157616i	−0.486288	−	0.873799i	$-0.661649\pi$
$173$	4.72288	−	2.72676i	0.0272999	−	0.0157616i	0.513588	+	0.858037i	$0.328316\pi$
$174$	−77.8301	+	41.6019i	−0.447299	+	0.239091i
$175$		0			0
$176$			1.64899i			0.00936925i
$177$	2.61230	−	4.20100i	0.0147587	−	0.0237344i
$178$	−22.0627	+	38.2138i	−0.123948	+	0.214684i
$179$	−1.07105	−	0.618370i	−0.00598351	−	0.00345458i	0.497005	−	0.867748i	$-0.334433\pi$
$179$	−1.07105	−	0.618370i	−0.00598351	−	0.00345458i	−0.502989	+	0.864293i	$0.667766\pi$
$180$	7.73259	−	118.008i	0.0429588	−	0.655603i
$181$	186.915			1.03268			0.516340	−	0.856384i	$-0.327294\pi$
$181$	186.915			1.03268			0.516340	+	0.856384i	$0.327294\pi$
$182$		0			0
$183$	177.041	−	94.6321i	0.967435	−	0.517116i
$184$	50.9150	+	88.1874i	0.276712	+	0.479279i
$185$	113.797	+	65.7008i	0.615120	+	0.355140i
$186$	−23.5022	−	0.769175i	−0.126356	−	0.00413535i
$187$	−3.27321	−	5.66937i	−0.0175038	−	0.0303175i
$188$		−	16.9706i		−	0.0902690i
$189$		0			0
$190$	148.664			0.782442
$191$	−303.578	+	175.271i	−1.58941	+	0.917649i	−0.596011	+	0.802976i	$0.703249\pi$
$191$	−303.578	+	175.271i	−1.58941	+	0.917649i	−0.993403	+	0.114673i	$0.963418\pi$
$192$	0.785046	−	23.9872i	0.00408878	−	0.124933i
$193$	−135.247	+	234.255i	−0.700762	+	1.21376i	0.267437	+	0.963575i	$0.413823\pi$
$193$	−135.247	+	234.255i	−0.700762	+	1.21376i	−0.968199	+	0.250180i	$0.919510\pi$
$194$	84.3041	−	48.6730i	0.434557	−	0.250892i
$195$	191.247	+	357.790i	0.980754	+	1.83482i
$196$		0			0
$197$			63.5194i			0.322434i	0.986919	+	0.161217i	$0.0515419\pi$
$197$			63.5194i			0.322434i	−0.986919	+	0.161217i	$0.948458\pi$
$198$	5.23582	+	0.343081i	0.0264435	+	0.00173273i
$199$	−44.0000	+	76.2102i	−0.221106	+	0.382966i	−0.955144	−	0.296142i	$-0.904300\pi$
$199$	−44.0000	+	76.2102i	−0.221106	+	0.382966i	0.734038	+	0.679108i	$0.237633\pi$
$200$	−44.4975	−	25.6906i	−0.222487	−	0.128453i
$201$	−125.896	−	78.2855i	−0.626347	−	0.389480i
$202$	−198.207			−0.981220
$203$		0			0
$204$	44.9150	+	84.0283i	0.220172	+	0.411904i
$205$	−249.996	−	433.006i	−1.21949	−	2.11222i
$206$	48.2213	+	27.8406i	0.234084	+	0.135148i
$207$	290.603	−	143.316i	1.40388	−	0.692348i
$208$	41.1660	+	71.3016i	0.197914	+	0.342796i
$209$			6.59595i			0.0315596i
$210$		0			0
$211$	−378.745			−1.79500			−0.897500	−	0.441014i	$-0.854619\pi$
$211$	−378.745			−1.79500			−0.897500	+	0.441014i	$0.854619\pi$
$212$	88.1816	−	50.9117i	0.415951	−	0.240149i
$213$	−263.075	−	8.60985i	−1.23509	−	0.0404218i
$214$	76.3725	−	132.281i	0.356881	−	0.618136i
$215$	−294.445	+	169.998i	−1.36951	+	0.790687i
$216$	−76.0000	−	7.48331i	−0.351852	−	0.0346450i
$217$		0			0
$218$		−	175.122i		−	0.803313i
$219$	−31.4173	−	19.5362i	−0.143458	−	0.0892062i
$220$	2.70850	−	4.69126i	0.0123114	−	0.0213239i
$221$	−283.065	−	163.428i	−1.28084	−	0.739491i
$222$	44.8074	−	72.0576i	0.201835	−	0.324584i
$223$	230.494			1.03361			0.516803	−	0.856104i	$-0.327122\pi$
$223$	230.494			1.03361			0.516803	+	0.856104i	$0.327122\pi$
$224$		0			0
$225$	−90.8301	+	135.942i	−0.403689	+	0.604187i
$226$	−56.9150	−	98.5797i	−0.251836	−	0.436193i
$227$	223.816	+	129.220i	0.985974	+	0.569252i	0.904068	−	0.427388i	$-0.140566\pi$
$227$	223.816	+	129.220i	0.985974	+	0.569252i	0.0819056	+	0.996640i	$0.473899\pi$
$228$	3.14019	−	95.9486i	0.0137727	−	0.420827i
$229$	−18.5425	−	32.1165i	−0.0809716	−	0.140247i	0.822696	−	0.568482i	$-0.192469\pi$
$229$	−18.5425	−	32.1165i	−0.0809716	−	0.140247i	−0.903668	+	0.428235i	$0.859136\pi$
$230$		−	334.516i		−	1.45442i
$231$		0			0
$232$	58.8340			0.253595
$233$	−71.5955	+	41.3357i	−0.307277	+	0.177406i	−0.645707	−	0.763585i	$-0.723437\pi$
$233$	−71.5955	+	41.3357i	−0.307277	+	0.177406i	0.338430	+	0.940991i	$0.390104\pi$
$234$	234.960	−	115.874i	1.00410	−	0.495190i
$235$	−27.8745	+	48.2801i	−0.118615	+	0.205447i
$236$	−2.85613	+	1.64899i	−0.0121022	+	0.00698724i
$237$	−224.664	+	120.088i	−0.947950	+	0.506700i
$238$		0			0
$239$		−	168.469i		−	0.704891i	−0.935832	−	0.352445i	$-0.885350\pi$
$239$		−	168.469i		−	0.704891i	0.935832	−	0.352445i	$-0.114650\pi$
$240$	−41.6328	+	66.9523i	−0.173470	+	0.278968i
$241$	−65.0000	+	112.583i	−0.269710	+	0.467151i	−0.968787	−	0.247896i	$-0.920261\pi$
$241$	−65.0000	+	112.583i	−0.269710	+	0.467151i	0.699077	+	0.715046i	$0.253594\pi$
$242$	−147.986	−	85.4397i	−0.611512	−	0.353057i
$243$	−39.5730	+	239.756i	−0.162852	+	0.986651i
$244$	−133.830			−0.548484
$245$		0			0
$246$	−284.745	+	152.203i	−1.15750	+	0.618710i
$247$	164.664	+	285.206i	0.666656	+	1.15468i
$248$	13.5763	+	7.83826i	0.0547430	+	0.0316059i
$249$	12.3608	+	0.404541i	0.0496417	+	0.00162466i
$250$	−31.7490	−	54.9909i	−0.126996	−	0.219964i
$251$		−	119.859i		−	0.477525i	−0.971078	−	0.238763i	$-0.923258\pi$
$251$		−	119.859i		−	0.477525i	0.971078	−	0.238763i	$-0.0767417\pi$
$252$		0			0
$253$	14.8419			0.0586635
$254$	−162.787	+	93.9851i	−0.640894	+	0.370020i
$255$	10.2382	−	312.829i	0.0401497	−	1.22678i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	193.894	−	111.945i	0.754451	−	0.435583i	−0.0728489	−	0.997343i	$-0.523209\pi$
$257$	193.894	−	111.945i	0.754451	−	0.435583i	0.827300	+	0.561760i	$0.189876\pi$
$258$	103.498	+	193.627i	0.401155	+	0.750493i
$259$		0			0
$260$		−	270.464i		−	1.04025i
$261$	12.2407	−	186.808i	0.0468994	−	0.715739i
$262$	2.91503	−	5.04897i	0.0111261	−	0.0192709i
$263$	−185.705	−	107.217i	−0.706102	−	0.407668i	0.103514	−	0.994628i	$-0.466991\pi$
$263$	−185.705	−	107.217i	−0.706102	−	0.407668i	−0.809616	+	0.586960i	$0.800325\pi$
$264$	−2.97055	−	1.84717i	−0.0112521	−	0.00699686i
$265$	−334.494			−1.26224
$266$		0			0
$267$	−44.1255	−	82.5512i	−0.165264	−	0.309181i
$268$	49.4170	+	85.5927i	0.184392	+	0.319376i
$269$	−330.956	−	191.078i	−1.23032	−	0.710326i	−0.263224	−	0.964735i	$-0.584786\pi$
$269$	−330.956	−	191.078i	−1.23032	−	0.710326i	−0.967097	+	0.254408i	$0.918119\pi$
$270$	203.923	+	146.121i	0.755271	+	0.541189i
$271$	57.2288	+	99.1231i	0.211176	+	0.365768i	0.952083	−	0.305840i	$-0.0989373\pi$
$271$	57.2288	+	99.1231i	0.211176	+	0.365768i	−0.740907	+	0.671608i	$0.765604\pi$
$272$		−	63.5194i		−	0.233527i
$273$		0			0
$274$	−140.915			−0.514288
$275$	−6.48556	+	3.74444i	−0.0235839	+	0.0136162i
$276$	−215.899	−	7.06588i	−0.782241	−	0.0256010i
$277$	115.247	−	199.614i	0.416054	−	0.720627i	−0.579484	−	0.814983i	$-0.696746\pi$
$277$	115.247	−	199.614i	0.416054	−	0.720627i	0.995538	+	0.0943563i	$0.0300793\pi$
$278$	−114.566	+	66.1445i	−0.412107	+	0.237930i
$279$	27.7124	−	41.4762i	0.0993277	−	0.148660i
$280$		0			0
$281$			73.9458i			0.263152i	0.991306	+	0.131576i	$0.0420038\pi$
$281$			73.9458i			0.263152i	−0.991306	+	0.131576i	$0.957996\pi$
$282$	30.5714	+	19.0102i	0.108409	+	0.0674120i
$283$	70.5830	−	122.253i	0.249410	−	0.431991i	−0.713952	−	0.700194i	$-0.753097\pi$
$283$	70.5830	−	122.253i	0.249410	−	0.431991i	0.963362	+	0.268204i	$0.0864300\pi$
$284$	151.968	+	87.7385i	0.535097	+	0.308939i
$285$	−166.531	+	267.809i	−0.584320	+	0.939682i
$286$	12.0000			0.0419580
$287$		0			0
$288$	42.3320	+	28.2843i	0.146986	+	0.0982093i
$289$	−18.4150	−	31.8958i	−0.0637198	−	0.110366i
$290$	−167.379	−	96.6361i	−0.577168	−	0.333228i
$291$	−6.75473	+	206.391i	−0.0232121	+	0.709249i
$292$	12.3320	+	21.3597i	0.0422329	+	0.0731496i
$293$		−	329.595i		−	1.12490i	−0.826832	−	0.562449i	$-0.809859\pi$
$293$		−	329.595i		−	1.12490i	0.826832	−	0.562449i	$-0.190141\pi$
$294$		0			0
$295$	10.8340			0.0367254
$296$	−48.9898	+	28.2843i	−0.165506	+	0.0955550i
$297$	−6.48313	+	9.04770i	−0.0218287	+	0.0304636i
$298$	−35.2470	+	61.0497i	−0.118279	+	0.204865i
$299$	641.757	−	370.518i	2.14634	−	1.23919i
$300$	96.1255	−	51.3812i	0.320418	−	0.171271i
$301$		0			0
$302$			299.333i			0.991168i
$303$	222.028	−	357.057i	0.732766	−	1.17841i
$304$	−32.0000	+	55.4256i	−0.105263	+	0.182321i
$305$	380.737	+	219.819i	1.24832	+	0.720717i
$306$	−201.685	−	13.2156i	−0.659102	−	0.0431881i
$307$	105.830			0.344723			0.172362	−	0.985034i	$-0.444860\pi$
$307$	105.830			0.344723			0.172362	+	0.985034i	$0.444860\pi$
$308$		0			0
$309$	−104.170	+	55.6812i	−0.337120	+	0.180198i
$310$	−25.7490	−	44.5986i	−0.0830613	−	0.143866i
$311$	333.537	+	192.568i	1.07247	+	0.619189i	0.928854	−	0.370445i	$-0.120795\pi$
$311$	333.537	+	192.568i	1.07247	+	0.619189i	0.143613	+	0.989634i	$0.454128\pi$
$312$	−174.559	−	5.71293i	−0.559484	−	0.0183107i
$313$	−39.6640	−	68.7001i	−0.126722	−	0.219489i	0.795683	−	0.605714i	$-0.207112\pi$
$313$	−39.6640	−	68.7001i	−0.126722	−	0.219489i	−0.922405	+	0.386224i	$0.873779\pi$
$314$			153.789i			0.489773i
$315$		0			0
$316$	169.830			0.537437
$317$	356.089	−	205.588i	1.12331	−	0.648542i	0.181064	−	0.983471i	$-0.442046\pi$
$317$	356.089	−	205.588i	1.12331	−	0.648542i	0.942243	+	0.334929i	$0.108712\pi$
$318$	−7.06542	+	215.884i	−0.0222183	+	0.678882i
$319$	4.28757	−	7.42628i	0.0134406	−	0.0232799i
$320$	45.5189	−	26.2803i	0.142247	−	0.0821261i
$321$	152.745	+	285.760i	0.475841	+	0.890218i
$322$		0			0
$323$		−	254.078i		−	0.786618i
$324$	98.6148	−	128.527i	0.304367	−	0.396687i
$325$	−186.956	+	323.817i	−0.575248	+	0.996358i
$326$	−15.9265	−	9.19517i	−0.0488543	−	0.0282060i
$327$	315.472	+	196.169i	0.964746	+	0.599906i
$328$	215.247			0.656241
$329$		0			0
$330$	5.41699	+	10.1343i	0.0164151	+	0.0307099i
$331$	244.745	+	423.911i	0.739411	+	1.28070i	0.952761	+	0.303722i	$0.0982293\pi$
$331$	244.745	+	423.911i	0.739411	+	1.28070i	−0.213350	+	0.976976i	$0.568437\pi$
$332$	−7.14033	−	4.12247i	−0.0215070	−	0.0124171i
$333$	79.6148	+	161.436i	0.239084	+	0.484792i
$334$	110.915	+	192.110i	0.332081	+	0.575181i
$335$		−	324.674i		−	0.969176i
$336$		0			0
$337$	500.316			1.48462			0.742309	−	0.670058i	$-0.233731\pi$
$337$	500.316			1.48462			0.742309	+	0.670058i	$0.233731\pi$
$338$	311.894	−	180.072i	0.922762	−	0.532757i
$339$	241.341	+	7.89855i	0.711920	+	0.0232995i
$340$	−104.332	+	180.708i	−0.306859	+	0.531495i
$341$	1.97876	−	1.14244i	0.00580281	−	0.00335025i
$342$	169.328	+	113.137i	0.495111	+	0.330810i
$343$		0			0
$344$		−	146.368i		−	0.425489i
$345$	602.610	+	374.720i	1.74670	+	1.08614i
$346$	3.85622	−	6.67916i	0.0111451	−	0.0193039i
$347$	−167.022	−	96.4299i	−0.481330	−	0.277896i	0.239640	−	0.970862i	$-0.422970\pi$
$347$	−167.022	−	96.4299i	−0.481330	−	0.277896i	−0.720971	+	0.692966i	$0.756304\pi$
$348$	−65.9050	+	105.986i	−0.189382	+	0.304557i
$349$	−148.405			−0.425230			−0.212615	−	0.977136i	$-0.568198\pi$
$349$	−148.405			−0.425230			−0.212615	+	0.977136i	$0.568198\pi$
$350$		0			0
$351$	−54.4575	+	553.067i	−0.155150	+	1.57569i
$352$	1.16601	+	2.01959i	0.00331253	+	0.00573747i
$353$	−141.830	−	81.8857i	−0.401785	−	0.231971i	0.285469	−	0.958388i	$-0.407851\pi$
$353$	−141.830	−	81.8857i	−0.401785	−	0.231971i	−0.687254	+	0.726417i	$0.741184\pi$
$354$	0.228843	−	6.99232i	0.000646449	−	0.0197523i
$355$	−288.225	−	499.220i	−0.811901	−	1.40625i
$356$			62.4029i			0.175289i
$357$		0			0
$358$	−1.74902			−0.00488552
$359$	−290.012	+	167.438i	−0.807832	+	0.466402i	−0.846202	−	0.532862i	$-0.821117\pi$
$359$	−290.012	+	167.438i	−0.807832	+	0.466402i	0.0383706	+	0.999264i	$0.487783\pi$
$360$	−73.9741	−	149.998i	−0.205484	−	0.416661i
$361$	52.5000	−	90.9327i	0.145429	−	0.251891i
$362$	228.923	−	132.169i	0.632385	−	0.365107i
$363$	319.686	−	170.879i	0.880678	−	0.470742i
$364$		0			0
$365$		−	81.0224i		−	0.221979i
$366$	149.914	−	241.087i	0.409602	−	0.658707i
$367$	163.498	−	283.187i	0.445499	−	0.771626i	−0.552588	−	0.833454i	$-0.686360\pi$
$367$	163.498	−	283.187i	0.445499	−	0.771626i	0.998087	+	0.0618281i	$0.0196930\pi$
$368$	124.716	+	72.0047i	0.338902	+	0.195665i
$369$	44.7833	−	683.446i	0.121364	−	1.85216i
$370$	185.830			0.502243
$371$		0			0
$372$	−29.3281	+	15.6765i	−0.0788389	+	0.0421412i
$373$	152.668	+	264.429i	0.409298	+	0.708924i	0.994811	−	0.101738i	$-0.0324405\pi$
$373$	152.668	+	264.429i	0.409298	+	0.708924i	−0.585514	+	0.810663i	$0.699107\pi$
$374$	−8.01770	−	4.62902i	−0.0214377	−	0.0123771i
$375$	134.628	+	4.40606i	0.359007	+	0.0117495i
$376$	−12.0000	−	20.7846i	−0.0319149	−	0.0552782i
$377$		−	428.146i		−	1.13567i
$378$		0			0
$379$	199.660			0.526808			0.263404	−	0.964686i	$-0.415155\pi$
$379$	199.660			0.526808			0.263404	+	0.964686i	$0.415155\pi$
$380$	182.076	−	105.121i	0.479146	−	0.276635i
$381$	13.0431	−	398.532i	0.0342337	−	1.04601i
$382$	−247.871	+	429.324i	−0.648876	+	1.12389i
$383$	−458.551	+	264.744i	−1.19726	+	0.691239i	−0.959944	−	0.280193i	$-0.909601\pi$
$383$	−458.551	+	264.744i	−1.19726	+	0.691239i	−0.237317	+	0.971432i	$0.576268\pi$
$384$	−16.0000	−	29.9333i	−0.0416667	−	0.0779512i
$385$		0			0
$386$			382.536i			0.991027i
$387$	−464.744	−	30.4527i	−1.20089	−	0.0786892i
$388$	68.8340	−	119.224i	0.177407	−	0.307278i
$389$	206.724	+	119.352i	0.531424	+	0.306818i	0.741596	−	0.670846i	$-0.234069\pi$
$389$	206.724	+	119.352i	0.531424	+	0.306818i	−0.210172	+	0.977664i	$0.567402\pi$
$390$	487.225	+	302.970i	1.24929	+	0.776846i
$391$	−571.712			−1.46218
$392$		0			0
$393$	5.83005	+	10.9070i	0.0148347	+	0.0277533i
$394$	44.9150	+	77.7951i	0.113998	+	0.197450i
$395$	−483.155	−	278.949i	−1.22318	−	0.706201i
$396$	6.65514	−	3.28210i	0.0168059	−	0.00828812i
$397$	160.292	+	277.633i	0.403757	+	0.699328i	0.994176	−	0.107769i	$-0.0343708\pi$
$397$	160.292	+	277.633i	0.403757	+	0.699328i	−0.590419	+	0.807097i	$0.701037\pi$
$398$			124.451i			0.312690i
$399$		0			0
$400$	−72.6640			−0.181660
$401$	−201.012	+	116.054i	−0.501276	+	0.289412i	−0.729241	−	0.684257i	$-0.760126\pi$
$401$	−201.012	+	116.054i	−0.501276	+	0.289412i	0.227964	+	0.973670i	$0.426793\pi$
$402$	−209.546	−	6.85799i	−0.521260	−	0.0170597i
$403$	57.0405	−	98.7971i	0.141540	−	0.245154i
$404$	−242.752	+	140.153i	−0.600872	+	0.346914i
$405$	−491.660	+	203.673i	−1.21398	+	0.502895i
$406$		0			0
$407$			8.24494i			0.0202578i
$408$	114.426	+	71.1535i	0.280457	+	0.174396i
$409$	264.490	−	458.110i	0.646675	−	1.12007i	−0.337237	−	0.941420i	$-0.609492\pi$
$409$	264.490	−	458.110i	0.646675	−	1.12007i	0.983912	−	0.178654i	$-0.0571744\pi$
$410$	−612.363	−	353.548i	−1.49357	−	0.862312i
$411$	157.851	−	253.850i	0.384066	−	0.617640i
$412$	78.7451			0.191129
$413$		0			0
$414$	254.575	−	381.013i	0.614916	−	0.920322i
$415$	13.5425	+	23.4563i	0.0326325	+	0.0565211i
$416$	100.836	+	58.2175i	0.242394	+	0.139946i
$417$	9.17940	−	280.477i	0.0220129	−	0.672607i
$418$	4.66404	+	8.07836i	0.0111580	+	0.0193262i
$419$		−	89.7998i		−	0.214319i	−0.994242	−	0.107160i	$-0.965824\pi$
$419$		−	89.7998i		−	0.214319i	0.994242	−	0.107160i	$-0.0341756\pi$
$420$		0			0
$421$	−777.150			−1.84596			−0.922981	−	0.384845i	$-0.874255\pi$
$421$	−777.150			−1.84596			−0.922981	+	0.384845i	$0.874255\pi$
$422$	−463.866	+	267.813i	−1.09921	+	0.634628i
$423$	−68.4914	+	33.7777i	−0.161918	+	0.0798527i
$424$	72.0000	−	124.708i	0.169811	−	0.294122i
$425$	249.826	−	144.237i	0.587825	−	0.339381i
$426$	−328.288	+	175.477i	−0.770628	+	0.411918i
$427$		0			0
$428$		−	216.014i		−	0.504706i
$429$	−13.4422	+	21.6173i	−0.0313339	+	0.0503899i
$430$	−240.413	+	416.408i	−0.559100	+	0.968390i
$431$	212.957	+	122.951i	0.494099	+	0.285268i	0.726273	−	0.687406i	$-0.241251\pi$
$431$	212.957	+	122.951i	0.494099	+	0.285268i	−0.232174	+	0.972674i	$0.574584\pi$
$432$	−98.3721	+	44.5750i	−0.227713	+	0.103183i
$433$	796.996			1.84064			0.920319	−	0.391169i	$-0.127929\pi$
$433$	796.996			1.84064			0.920319	+	0.391169i	$0.127929\pi$
$434$		0			0
$435$	361.579	−	193.272i	0.831216	−	0.444304i
$436$	−123.830	−	214.480i	−0.284014	−	0.491926i
$437$	498.863	+	288.019i	1.14156	+	0.659082i
$438$	−52.2923	−	1.71141i	−0.119389	−	0.00390733i
$439$	276.915	+	479.631i	0.630786	+	1.09255i	0.987391	+	0.158298i	$0.0506007\pi$
$439$	276.915	+	479.631i	0.630786	+	1.09255i	−0.356605	+	0.934255i	$0.616066\pi$
$440$		−	7.66079i		−	0.0174109i
$441$		0			0
$442$	−462.243			−1.04580
$443$	670.288	−	386.991i	1.51306	−	0.873568i	0.513182	−	0.858280i	$-0.328467\pi$
$443$	670.288	−	386.991i	1.51306	−	0.873568i	0.999883	−	0.0152882i	$-0.00486657\pi$
$444$	3.92523	−	119.936i	0.00884061	−	0.270126i
$445$	102.498	−	177.532i	0.230333	−	0.398948i
$446$	282.296	−	162.984i	0.632952	−	0.365435i
$447$	−70.4941	−	131.882i	−0.157705	−	0.295039i
$448$		0			0
$449$			677.174i			1.50818i	0.656770	+	0.754091i	$0.271922\pi$
$449$			677.174i			1.50818i	−0.656770	+	0.754091i	$0.728078\pi$
$450$	−15.1181	+	230.721i	−0.0335959	+	0.512713i
$451$	15.6863	−	27.1694i	0.0347811	−	0.0602426i
$452$	−139.413	−	80.4900i	−0.308435	−	0.178075i
$453$	−539.230	−	335.308i	−1.19035	−	0.740194i
$454$	365.490			0.805044
$455$		0			0
$456$	−64.0000	−	119.733i	−0.140351	−	0.262572i
$457$	−417.332	−	722.840i	−0.913199	−	1.58171i	−0.809517	−	0.587097i	$-0.800271\pi$
$457$	−417.332	−	722.840i	−0.913199	−	1.58171i	−0.103683	−	0.994610i	$-0.533063\pi$
$458$	−45.4196	−	26.2230i	−0.0991695	−	0.0572555i
$459$	249.732	−	348.520i	0.544078	−	0.759302i
$460$	−236.539	−	409.697i	−0.514214	−	0.890645i
$461$			347.150i			0.753036i	0.926409	+	0.376518i	$0.122879\pi$
$461$			347.150i			0.753036i	−0.926409	+	0.376518i	$0.877121\pi$
$462$		0			0
$463$	317.668			0.686108			0.343054	−	0.939316i	$-0.388539\pi$
$463$	317.668			0.686108			0.343054	+	0.939316i	$0.388539\pi$
$464$	72.0566	−	41.6019i	0.155294	−	0.0896593i
$465$	109.185	+	3.57339i	0.234807	+	0.00768472i
$466$	−58.4575	+	101.251i	−0.125445	+	0.217278i
$467$	−474.080	+	273.710i	−1.01516	+	0.586104i	−0.912699	−	0.408633i	$-0.866006\pi$
$467$	−474.080	+	273.710i	−1.01516	+	0.586104i	−0.102463	+	0.994737i	$0.532672\pi$
$468$	205.830	−	308.058i	0.439808	−	0.658244i
$469$		0			0
$470$			78.8410i			0.167747i
$471$	−277.041	−	172.272i	−0.588198	−	0.365758i
$472$	−2.33202	+	4.03918i	−0.00494072	+	0.00855758i
$473$	−18.4752	−	10.6667i	−0.0390597	−	0.0225511i
$474$	−190.241	+	305.939i	−0.401353	+	0.645440i
$475$	−290.656			−0.611908
$476$		0			0
$477$	−380.988	−	254.558i	−0.798717	−	0.533665i
$478$	−119.125	−	206.331i	−0.249217	−	0.431656i
$479$	−117.367	−	67.7621i	−0.245026	−	0.141466i	0.372459	−	0.928049i	$-0.378515\pi$
$479$	−117.367	−	67.7621i	−0.245026	−	0.141466i	−0.617484	+	0.786583i	$0.711848\pi$
$480$	−3.64713	+	111.438i	−0.00759819	+	0.232163i
$481$	205.830	+	356.508i	0.427921	+	0.741181i
$482$			183.848i			0.381427i
$483$		0			0
$484$	−241.660			−0.499298
$485$	−391.656	+	226.123i	−0.807538	+	0.466232i
$486$	121.066	+	321.622i	0.249108	+	0.661774i
$487$	−11.7490	+	20.3499i	−0.0241253	+	0.0417862i	−0.877836	−	0.478961i	$-0.841013\pi$
$487$	−11.7490	+	20.3499i	−0.0241253	+	0.0417862i	0.853711	+	0.520748i	$0.174347\pi$
$488$	−163.908	+	94.6321i	−0.335876	+	0.193918i
$489$	34.4052	−	18.3903i	0.0703582	−	0.0376081i
$490$		0			0
$491$			103.404i			0.210599i	0.994441	+	0.105299i	$0.0335801\pi$
$491$			103.404i			0.210599i	−0.994441	+	0.105299i	$0.966420\pi$
$492$	−241.117	+	387.755i	−0.490074	+	0.788119i
$493$	−165.158	+	286.062i	−0.335006	+	0.580248i
$494$	403.343	+	232.870i	0.816484	+	0.471397i
$495$	−24.3243	−	1.59387i	−0.0491400	−	0.00321994i
$496$	22.1699			0.0446975
$497$		0			0
$498$	15.4249	−	8.24494i	0.0309736	−	0.0165561i
$499$	32.1699	+	55.7200i	0.0644688	+	0.111663i	0.896458	−	0.443128i	$-0.146131\pi$
$499$	32.1699	+	55.7200i	0.0644688	+	0.111663i	−0.831989	+	0.554792i	$0.812798\pi$
$500$	−77.7689	−	44.8999i	−0.155538	−	0.0897998i
$501$	−470.321	−	15.3926i	−0.938764	−	0.0307237i
$502$	−84.7530	−	146.796i	−0.168831	−	0.292423i
$503$			546.940i			1.08736i	0.839294	+	0.543678i	$0.182969\pi$
$503$			546.940i			1.08736i	−0.839294	+	0.543678i	$0.817031\pi$
$504$		0			0
$505$	920.818			1.82340
$506$	18.1775	−	10.4948i	0.0359239	−	0.0207407i
$507$	−24.9900	+	763.571i	−0.0492899	+	1.50606i
$508$	−132.915	+	230.216i	−0.261644	+	0.453180i
$509$	−55.0318	+	31.7727i	−0.108118	+	0.0624217i	−0.553084	−	0.833126i	$-0.686549\pi$
$509$	−55.0318	+	31.7727i	−0.108118	+	0.0624217i	0.444966	+	0.895547i	$0.353216\pi$
$510$	−208.664	−	390.375i	−0.409145	−	0.765441i
$511$		0			0
$512$			22.6274i			0.0441942i
$513$	−393.488	+	178.300i	−0.767034	+	0.347563i
$514$	158.314	−	274.207i	0.308003	−	0.533477i
$515$	−224.024	−	129.340i	−0.434999	−	0.251147i
$516$	263.674	+	163.960i	0.510996	+	0.317751i
$517$	−3.49803			−0.00676602
$518$		0			0
$519$	7.71243	+	14.4286i	0.0148602	+	0.0278009i
$520$	−191.247	−	331.250i	−0.367783	−	0.637018i
$521$	556.245	+	321.148i	1.06765	+	0.616408i	0.927538	−	0.373728i	$-0.121921\pi$
$521$	556.245	+	321.148i	1.06765	+	0.616408i	0.140111	+	0.990136i	$0.455254\pi$
$522$	−117.101	−	237.448i	−0.224332	−	0.454881i
$523$	−56.1882	−	97.3209i	−0.107434	−	0.186082i	0.807296	−	0.590147i	$-0.200930\pi$
$523$	−56.1882	−	97.3209i	−0.107434	−	0.186082i	−0.914730	+	0.404065i	$0.867597\pi$
$524$		−	8.24494i		−	0.0157346i
$525$		0			0
$526$	−303.255			−0.576530
$527$	−76.2223	+	44.0070i	−0.144634	+	0.0835047i
$528$	−4.94432	−	0.161816i	−0.00936424	−	0.000306471i
$529$	383.585	−	664.389i	0.725113	−	1.25593i
$530$	−409.670	+	236.523i	−0.772962	+	0.446270i
$531$	12.3399	+	8.24494i	0.0232390	+	0.0155272i
$532$		0			0
$533$		−	1566.39i		−	2.93883i
$534$	−112.415	−	69.9028i	−0.210515	−	0.130904i
$535$	−354.808	+	614.545i	−0.663192	+	1.14868i
$536$	121.046	+	69.8862i	0.225833	+	0.130385i
$537$	1.95922	−	3.15075i	0.00364846	−	0.00586731i
$538$	−540.450			−1.00455
$539$		0			0
$540$	353.077	+	34.7656i	0.653846	+	0.0643808i
$541$	16.5751	+	28.7090i	0.0306380	+	0.0530665i	0.880938	−	0.473232i	$-0.156913\pi$
$541$	16.5751	+	28.7090i	0.0306380	+	0.0530665i	−0.850300	+	0.526299i	$0.823579\pi$
$542$	140.181	+	80.9337i	0.258637	+	0.149324i
$543$	−18.3421	+	560.445i	−0.0337792	+	1.03213i
$544$	−44.9150	−	77.7951i	−0.0825644	−	0.143006i
$545$			813.574i			1.49280i
$546$		0			0
$547$	−919.911			−1.68174			−0.840869	−	0.541238i	$-0.817956\pi$
$547$	−919.911			−1.68174			−0.840869	+	0.541238i	$0.817956\pi$
$548$	−172.585	+	99.6420i	−0.314936	+	0.181828i
$549$	266.371	+	540.124i	0.485194	+	0.983832i
$550$	−5.29544	+	9.17197i	−0.00962807	+	0.0166763i
$551$	288.227	−	166.408i	0.523097	−	0.302010i
$552$	−269.417	+	144.009i	−0.488074	+	0.260887i
$553$		0			0
$554$		−	325.968i		−	0.588390i
$555$	−208.164	+	334.762i	−0.375070	+	0.603174i
$556$	−93.5425	+	162.020i	−0.168242	+	0.291403i
$557$	628.190	+	362.686i	1.12781	+	0.651141i	0.943383	−	0.331705i	$-0.107624\pi$
$557$	628.190	+	362.686i	1.12781	+	0.651141i	0.184427	+	0.982846i	$0.440957\pi$
$558$	4.61258	−	70.3934i	0.00826627	−	0.126153i
$559$	−1065.15			−1.90546
$560$		0			0
$561$	17.3202	−	9.25804i	0.0308738	−	0.0165027i
$562$	52.2876	+	90.5647i	0.0930384	+	0.161147i
$563$	−631.136	−	364.386i	−1.12102	−	0.647223i	−0.179361	−	0.983783i	$-0.557403\pi$
$563$	−631.136	−	364.386i	−1.12102	−	0.647223i	−0.941662	+	0.336561i	$0.890736\pi$
$564$	50.8844	+	1.66533i	0.0902206	+	0.00295272i
$565$	264.413	+	457.977i	0.467988	+	0.810578i
$566$		−	199.639i		−	0.352719i
$567$		0			0
$568$	248.162			0.436905
$569$	−144.664	+	83.5218i	−0.254242	+	0.146787i	−0.621705	−	0.783251i	$-0.713560\pi$
$569$	−144.664	+	83.5218i	−0.254242	+	0.146787i	0.367463	+	0.930038i	$0.380227\pi$
$570$	−14.5885	+	445.753i	−0.0255939	+	0.782024i
$571$	36.4575	−	63.1463i	0.0638485	−	0.110589i	−0.832334	−	0.554274i	$-0.812996\pi$
$571$	36.4575	−	63.1463i	0.0638485	−	0.110589i	0.896183	+	0.443685i	$0.146329\pi$
$572$	14.6969	−	8.48528i	0.0256939	−	0.0148344i
$573$	−495.741	−	927.447i	−0.865168	−	1.61858i
$574$		0			0
$575$			654.019i			1.13742i
$576$	71.8459	+	4.70776i	0.124733	+	0.00817319i
$577$	276.077	−	478.180i	0.478470	−	0.828734i	−0.521225	−	0.853419i	$-0.674525\pi$
$577$	276.077	−	478.180i	0.478470	−	0.828734i	0.999695	+	0.0246850i	$0.00785826\pi$
$578$	−45.1074	−	26.0428i	−0.0780405	−	0.0450567i
$579$	−689.116	−	428.512i	−1.19018	−	0.740089i
$580$	−273.328			−0.471255
$581$		0			0
$582$	137.668	+	257.553i	0.236543	+	0.442531i
$583$	−10.4941	−	18.1763i	−0.0180002	−	0.0311772i
$584$	30.2072	+	17.4401i	0.0517246	+	0.0298632i
$585$	−1091.56	+	538.324i	−1.86592	+	0.920212i
$586$	−233.059	−	403.670i	−0.397711	−	0.688856i
$587$			1115.21i			1.89985i	0.312474	+	0.949926i	$0.398842\pi$
$587$			1115.21i			1.89985i	−0.312474	+	0.949926i	$0.601158\pi$
$588$		0			0
$589$	88.6798			0.150560
$590$	13.2689	−	7.66079i	0.0224896	−	0.0129844i
$591$	−190.456	−	6.23321i	−0.322261	−	0.0105469i
$592$	−40.0000	+	69.2820i	−0.0675676	+	0.117030i
$593$	−829.224	+	478.753i	−1.39835	+	0.807340i	−0.994220	−	0.107359i	$-0.965761\pi$
$593$	−829.224	+	478.753i	−1.39835	+	0.807340i	−0.404134	+	0.914700i	$0.632427\pi$
$594$	−1.54249	+	15.6654i	−0.00259678	+	0.0263727i
$595$		0			0
$596$			99.6937i			0.167271i
$597$	−224.191	−	139.408i	−0.375529	−	0.233514i
$598$	523.992	−	907.581i	0.876241	−	1.51769i
$599$	−528.316	−	305.024i	−0.881997	−	0.509221i	−0.0106810	−	0.999943i	$-0.503400\pi$
$599$	−528.316	−	305.024i	−0.881997	−	0.509221i	−0.871316	+	0.490721i	$0.836733\pi$
$600$	81.3972	−	130.900i	0.135662	−	0.218166i
$601$	974.470			1.62142			0.810708	−	0.585451i	$-0.199083\pi$
$601$	974.470			1.62142			0.810708	+	0.585451i	$0.199083\pi$
$602$		0			0
$603$	247.085	−	369.803i	0.409759	−	0.613272i
$604$	211.660	+	366.606i	0.350431	+	0.606964i
$605$	687.506	+	396.932i	1.13637	+	0.656086i
$606$	19.4502	−	594.301i	0.0320960	−	0.980695i
$607$	−548.073	−	949.291i	−0.902921	−	1.56391i	−0.823684	−	0.567050i	$-0.808085\pi$
$607$	−548.073	−	949.291i	−0.902921	−	1.56391i	−0.0792376	−	0.996856i	$-0.525249\pi$
$608$			90.5097i			0.148865i
$609$		0			0
$610$	621.741			1.01925
$611$	−151.254	+	87.3263i	−0.247551	+	0.142924i
$612$	−256.358	+	126.427i	−0.418885	+	0.206580i
$613$	155.583	−	269.478i	0.253806	−	0.439605i	−0.710765	−	0.703430i	$-0.751651\pi$
$613$	155.583	−	269.478i	0.253806	−	0.439605i	0.964570	+	0.263825i	$0.0849842\pi$
$614$	129.615	−	74.8331i	0.211099	−	0.121878i
$615$	1322.85	−	707.096i	2.15098	−	1.14975i
$616$		0			0
$617$			905.503i			1.46759i	0.679371	+	0.733795i	$0.262253\pi$
$617$			905.503i			1.46759i	−0.679371	+	0.733795i	$0.737747\pi$
$618$	−88.2091	+	141.855i	−0.142733	+	0.229538i
$619$	27.3987	−	47.4559i	0.0442628	−	0.0766655i	−0.843045	−	0.537843i	$-0.819239\pi$
$619$	27.3987	−	47.4559i	0.0442628	−	0.0766655i	0.887308	+	0.461177i	$0.152573\pi$
$620$	−63.0719	−	36.4146i	−0.101729	−	0.0587332i
$621$	401.201	+	885.407i	0.646056	+	1.42578i
$622$	544.664			0.875666
$623$		0			0
$624$	−217.830	+	116.435i	−0.349087	+	0.186595i
$625$	374.573	+	648.780i	0.599317	+	1.03805i
$626$	−97.1567	−	56.0934i	−0.155202	−	0.0896061i
$627$	−19.7773	−	0.647266i	−0.0315427	−	0.00103232i
$628$	108.745	+	188.352i	0.173161	+	0.299924i
$629$		−	317.597i		−	0.504924i
$630$		0			0
$631$	181.490			0.287623			0.143812	−	0.989605i	$-0.454064\pi$
$631$	181.490			0.287623			0.143812	+	0.989605i	$0.454064\pi$
$632$	207.998	−	120.088i	0.329112	−	0.190013i
$633$	37.1666	−	1135.63i	0.0587149	−	1.79404i
$634$	290.745	−	503.585i	0.458588	−	0.794298i
$635$	756.268	−	436.631i	1.19097	−	0.687609i
$636$	144.000	+	269.399i	0.226415	+	0.423584i
$637$		0			0
$638$		−	12.1271i		−	0.0190079i
$639$	51.6315	−	787.957i	0.0808004	−	1.23311i
$640$	37.1660	−	64.3734i	0.0580719	−	0.100583i
$641$	−725.401	−	418.811i	−1.13167	−	0.653371i	−0.187316	−	0.982300i	$-0.559979\pi$
$641$	−725.401	−	418.811i	−1.13167	−	0.653371i	−0.944355	+	0.328929i	$0.893312\pi$
$642$	389.136	+	241.976i	0.606132	+	0.376909i
$643$	−59.0118			−0.0917758			−0.0458879	−	0.998947i	$-0.514612\pi$
$643$	−59.0118			−0.0917758			−0.0458879	+	0.998947i	$0.514612\pi$
$644$		0			0
$645$	−480.826	−	899.543i	−0.745467	−	1.39464i
$646$	−179.660	−	311.180i	−0.278112	−	0.481703i
$647$	−474.288	−	273.831i	−0.733058	−	0.423231i	0.0864819	−	0.996253i	$-0.472438\pi$
$647$	−474.288	−	273.831i	−0.733058	−	0.423231i	−0.819540	+	0.573022i	$0.805771\pi$
$648$	29.8959	−	227.144i	0.0461356	−	0.350530i
$649$	0.339895	+	0.588716i	0.000523721	+	0.000907112i
$650$			528.790i			0.813523i
$651$		0			0
$652$	−26.0079			−0.0398894
$653$	662.419	−	382.448i	1.01442	−	0.585678i	0.101940	−	0.994791i	$-0.467495\pi$
$653$	662.419	−	382.448i	1.01442	−	0.585678i	0.912484	+	0.409113i	$0.134162\pi$
$654$	525.085	+	17.1849i	0.802883	+	0.0262766i
$655$	−13.5425	+	23.4563i	−0.0206756	+	0.0358111i
$656$	263.623	−	152.203i	0.401864	−	0.232016i
$657$	61.6601	−	92.2844i	0.0938510	−	0.140463i
$658$		0			0
$659$			1050.80i			1.59454i	0.603623	+	0.797270i	$0.293723\pi$
$659$			1050.80i			1.59454i	−0.603623	+	0.797270i	$0.706277\pi$
$660$	13.8004	+	8.58150i	0.0209098	+	0.0130023i
$661$	−72.5425	+	125.647i	−0.109747	+	0.190087i	−0.915668	−	0.401936i	$-0.868337\pi$
$661$	−72.5425	+	125.647i	−0.109747	+	0.190087i	0.805921	+	0.592023i	$0.201671\pi$
$662$	599.501	+	346.122i	0.905590	+	0.522843i
$663$	517.798	−	832.703i	0.780992	−	1.25596i
$664$	−11.6601			−0.0175604
$665$		0			0
$666$	211.660	+	141.421i	0.317808	+	0.212344i
$667$	−374.442	−	648.552i	−0.561382	−	0.972342i
$668$	271.685	+	156.858i	0.406714	+	0.234817i
$669$	−22.6186	+	691.112i	−0.0338095	+	1.03305i
$670$	−229.579	−	397.643i	−0.342655	−	0.593496i
$671$			27.5855i			0.0411111i
$672$		0			0
$673$	323.498			0.480681			0.240340	−	0.970689i	$-0.422741\pi$
$673$	323.498			0.480681			0.240340	+	0.970689i	$0.422741\pi$
$674$	612.760	−	353.777i	0.909139	−	0.524892i
$675$	−398.694	−	285.684i	−0.590658	−	0.423236i
$676$	254.660	−	441.084i	0.376716	−	0.652491i
$677$	−144.136	+	83.2168i	−0.212903	+	0.122920i	−0.602660	−	0.797998i	$-0.705892\pi$
$677$	−144.136	+	83.2168i	−0.212903	+	0.122920i	0.389757	+	0.920918i	$0.372559\pi$
$678$	301.166	−	160.980i	0.444198	−	0.237434i
$679$		0			0
$680$			295.096i			0.433964i
$681$	−409.417	+	658.408i	−0.601199	+	0.966826i
$682$	1.61565	−	2.79839i	0.00236899	−	0.00410321i
$683$	843.081	+	486.753i	1.23438	+	0.712669i	0.967940	−	0.251183i	$-0.0808195\pi$
$683$	843.081	+	486.753i	1.23438	+	0.712669i	0.266439	+	0.963852i	$0.414153\pi$
$684$	287.384	+	18.8310i	0.420152	+	0.0275307i
$685$	654.656			0.955702
$686$		0			0
$687$	98.1176	−	52.4461i	0.142820	−	0.0763407i
$688$	−103.498	−	179.264i	−0.150433	−	0.260558i
$689$	−907.521	−	523.958i	−1.31716	−	0.760461i
$690$	1003.01	+	32.8263i	1.45364	+	0.0475744i
$691$	634.431	+	1098.87i	0.918135	+	1.59026i	0.802245	+	0.596995i	$0.203639\pi$
$691$	634.431	+	1098.87i	0.918135	+	1.59026i	0.115890	+	0.993262i	$0.463028\pi$
$692$		−	10.9070i		−	0.0157616i
$693$		0			0
$694$	−272.745			−0.393004
$695$	532.244	−	307.291i	0.765818	−	0.442145i
$696$	−5.77343	+	176.408i	−0.00829515	+	0.253459i
$697$	−604.239	+	1046.57i	−0.866914	+	1.50154i
$698$	−181.758	+	104.938i	−0.260399	+	0.150341i
$699$	−116.915	−	218.728i	−0.167260	−	0.312916i
$700$		0			0
$701$			798.940i			1.13971i	0.821744	+	0.569857i	$0.193002\pi$
$701$			798.940i			1.13971i	−0.821744	+	0.569857i	$0.806998\pi$
$702$	324.381	+	715.873i	0.462081	+	1.01976i
$703$	−160.000	+	277.128i	−0.227596	+	0.394208i
$704$	2.85613	+	1.64899i	0.00405700	+	0.00234231i
$705$	−142.027	−	88.3165i	−0.201457	−	0.125272i
$706$	−231.608			−0.328056
$707$		0			0
$708$	−4.66404	−	8.72562i	−0.00658763	−	0.0123243i
$709$	325.745	+	564.207i	0.459443	+	0.795779i	0.998932	−	0.0462143i	$-0.0147157\pi$
$709$	325.745	+	564.207i	0.459443	+	0.795779i	−0.539489	+	0.841993i	$0.681382\pi$
$710$	−706.004	−	407.611i	−0.994371	−	0.574101i
$711$	−338.025	−	685.416i	−0.475422	−	0.964017i
$712$	44.1255	+	76.4276i	0.0619740	+	0.107342i
$713$		−	199.543i		−	0.279863i
$714$		0			0
$715$	−55.7490			−0.0779707
$716$	−2.14210	+	1.23674i	−0.00299176	+	0.00172729i
$717$	505.136	+	16.5320i	0.704514	+	0.0230572i
$718$	−236.793	+	410.138i	−0.329796	+	0.571223i
$719$	−760.879	+	439.294i	−1.05825	+	0.610979i	−0.924947	−	0.380097i	$-0.875891\pi$
$719$	−760.879	+	439.294i	−1.05825	+	0.610979i	−0.133299	+	0.991076i	$0.542557\pi$
$720$	−196.664	−	131.402i	−0.273145	−	0.182502i
$721$		0			0
$722$		−	148.492i		−	0.205668i
$723$	−331.191	−	205.944i	−0.458078	−	0.284846i
$724$	186.915	−	323.746i	0.258170	−	0.447163i
$725$	327.245	+	188.935i	0.451373	+	0.260600i
$726$	270.704	−	435.336i	0.372871	−	0.599637i
$727$	−442.782			−0.609053			−0.304527	−	0.952504i	$-0.598498\pi$
$727$	−442.782			−0.609053			−0.304527	+	0.952504i	$0.598498\pi$
$728$		0			0
$729$	−715.000	−	142.183i	−0.980796	−	0.195038i
$730$	−57.2915	−	99.2318i	−0.0784815	−	0.135934i
$731$	711.671	+	410.884i	0.973558	+	0.562084i
$732$	13.1328	−	401.275i	0.0179410	−	0.548190i
$733$	481.280	+	833.601i	0.656589	+	1.13725i	0.981493	+	0.191498i	$0.0613347\pi$
$733$	481.280	+	833.601i	0.656589	+	1.13725i	−0.324904	+	0.945747i	$0.605332\pi$
$734$		−	462.442i		−	0.630030i
$735$		0			0
$736$	203.660			0.276712
$737$	17.6427	−	10.1860i	0.0239385	−	0.0138209i
$738$	−428.421	−	868.714i	−0.580517	−	1.17712i
$739$	−612.405	+	1060.72i	−0.828694	+	1.43534i	0.0703683	+	0.997521i	$0.477583\pi$
$739$	−612.405	+	1060.72i	−0.828694	+	1.43534i	−0.899063	+	0.437820i	$0.855751\pi$
$740$	227.594	−	131.402i	0.307560	−	0.177570i
$741$	−871.320	+	465.740i	−1.17587	+	0.628529i
$742$		0			0
$743$		−	1447.24i		−	1.94783i	−0.226908	−	0.973916i	$-0.572862\pi$
$743$		−	1447.24i		−	1.94783i	0.226908	−	0.973916i	$-0.427138\pi$
$744$	−24.8344	+	39.9378i	−0.0333796	+	0.0536799i
$745$	163.749	−	283.622i	0.219797	−	0.380700i
$746$	373.959	+	215.905i	0.501285	+	0.289417i
$747$	−2.42595	+	37.0228i	−0.00324759	+	0.0495620i
$748$	−13.0928			−0.0175038
$749$		0			0
$750$	168.000	−	89.7998i	0.224000	−	0.119733i
$751$	342.458	+	593.154i	0.456002	+	0.789819i	0.998745	−	0.0500800i	$-0.0159476\pi$
$751$	342.458	+	593.154i	0.456002	+	0.789819i	−0.542743	+	0.839899i	$0.682614\pi$
$752$	−29.3939	−	16.9706i	−0.0390876	−	0.0225672i
$753$	359.384	+	11.7618i	0.477269	+	0.0156200i
$754$	−302.745	−	524.370i	−0.401519	−	0.695451i
$755$		−	1390.62i		−	1.84189i
$756$		0			0
$757$	−907.135			−1.19833			−0.599164	−	0.800626i	$-0.704500\pi$
$757$	−907.135			−1.19833			−0.599164	+	0.800626i	$0.704500\pi$
$758$	244.533	−	141.181i	0.322602	−	0.186255i
$759$	−1.45644	+	44.5018i	−0.00191890	+	0.0586321i
$760$	148.664	−	257.494i	0.195611	−	0.338807i
$761$	1257.04	−	725.754i	1.65183	−	0.953685i	0.675511	−	0.737350i	$-0.263923\pi$
$761$	1257.04	−	725.754i	1.65183	−	0.953685i	0.976319	−	0.216335i	$-0.0694102\pi$
$762$	−265.830	−	497.322i	−0.348858	−	0.652654i
$763$		0			0
$764$			701.084i			0.917649i
$765$	936.979	+	61.3962i	1.22481	+	0.0802565i
$766$	−374.405	+	648.489i	−0.488780	+	0.846591i
$767$	29.3939	+	16.9706i	0.0383232	+	0.0221259i
$768$	−40.7619	−	25.3469i	−0.0530754	−	0.0330038i
$769$	1089.32			1.41654			0.708271	−	0.705941i	$-0.249476\pi$
$769$	1089.32			1.41654			0.708271	+	0.705941i	$0.249476\pi$
$770$		0			0
$771$	316.627	+	592.356i	0.410671	+	0.768295i
$772$	270.494	+	468.510i	0.350381	+	0.606878i
$773$	−882.985	−	509.792i	−1.14228	−	0.659498i	−0.195288	−	0.980746i	$-0.562564\pi$
$773$	−882.985	−	509.792i	−1.14228	−	0.659498i	−0.946995	+	0.321248i	$0.895898\pi$
$774$	−590.727	+	291.327i	−0.763213	+	0.376392i
$775$	50.3424	+	87.1957i	0.0649580	+	0.112511i
$776$		−	194.692i		−	0.250892i
$777$		0			0
$778$	337.579			0.433906
$779$	1054.49	−	608.811i	1.35365	−	0.781528i
$780$	810.958	+	26.5409i	1.03969	+	0.0340267i
$781$	18.0850	−	31.3241i	0.0231562	−	0.0401077i
$782$	−700.202	+	404.262i	−0.895399	+	0.516959i
$783$	558.923	+	55.0342i	0.713822	+	0.0702863i
$784$		0			0
$785$		−	714.464i		−	0.910146i
$786$	14.8528	+	9.23586i	0.0188966	+	0.0117505i
$787$	−633.501	+	1097.26i	−0.804956	+	1.39423i	0.111364	+	0.993780i	$0.464478\pi$
$787$	−633.501	+	1097.26i	−0.804956	+	1.39423i	−0.916321	+	0.400445i	$0.868855\pi$
$788$	110.019	+	63.5194i	0.139618	+	0.0806084i
$789$	339.702	−	546.295i	0.430547	−	0.692390i
$790$	−788.988			−0.998719
$791$		0			0
$792$	5.83005	−	8.72562i	0.00736118	−	0.0110172i
$793$	688.656	+	1192.79i	0.868419	+	1.50415i
$794$	392.632	+	226.686i	0.494499	+	0.285499i
$795$	32.8242	−	1002.95i	0.0412883	−	1.26157i
$796$	88.0000	+	152.420i	0.110553	+	0.191483i
$797$			922.123i			1.15699i	0.815685	+	0.578496i	$0.196360\pi$
$797$			922.123i			1.15699i	−0.815685	+	0.578496i	$0.803640\pi$
$798$		0			0
$799$	134.745			0.168642
$800$	−88.9949	+	51.3812i	−0.111244	+	0.0642265i
$801$	251.851	−	124.205i	0.314421	−	0.155062i
$802$	−164.125	+	284.274i	−0.204645	+	0.354456i
$803$	4.40273	−	2.54192i	0.00548286	−	0.00316553i
$804$	−261.490	+	139.772i	−0.325237	+	0.173846i
$805$		0			0
$806$		−	161.335i		−	0.200167i
$807$	605.404	−	973.587i	0.750190	−	1.20643i
$808$	−198.207	+	343.304i	−0.245305	+	0.424881i
$809$	−612.155	−	353.428i	−0.756681	−	0.436870i	0.0714221	−	0.997446i	$-0.477246\pi$
$809$	−612.155	−	353.428i	−0.756681	−	0.436870i	−0.828103	+	0.560576i	$0.810580\pi$
$810$	−458.140	+	597.103i	−0.565605	+	0.737164i
$811$	−833.778			−1.02809			−0.514043	−	0.857764i	$-0.671853\pi$
$811$	−833.778			−1.02809			−0.514043	+	0.857764i	$0.671853\pi$
$812$		0			0
$813$	−302.826	+	161.867i	−0.372480	+	0.199099i
$814$	5.83005	+	10.0979i	0.00716223	+	0.0124053i
$815$	73.9906	+	42.7185i	0.0907860	+	0.0524153i
$816$	190.456	+	6.23321i	0.233402	+	0.00763874i
$817$	−413.992	−	717.055i	−0.506722	−	0.877669i
$818$		−	748.091i		−	0.914537i
$819$		0			0
$820$	−999.984			−1.21949
$821$	217.598	−	125.630i	0.265040	−	0.153021i	−0.361591	−	0.932337i	$-0.617766\pi$
$821$	217.598	−	125.630i	0.265040	−	0.153021i	0.626632	+	0.779316i	$0.284433\pi$
$822$	13.8281	−	422.519i	0.0168225	−	0.514013i
$823$	−19.4615	+	33.7082i	−0.0236470	+	0.0409577i	−0.877607	−	0.479381i	$-0.840861\pi$
$823$	−19.4615	+	33.7082i	−0.0236470	+	0.0409577i	0.853960	+	0.520339i	$0.174194\pi$
$824$	96.4426	−	55.6812i	0.117042	−	0.0675742i
$825$	−10.5909	−	19.8137i	−0.0128374	−	0.0240166i
$826$		0			0
$827$		−	108.007i		−	0.130601i	−0.997866	−	0.0653005i	$-0.979199\pi$
$827$		−	108.007i		−	0.130601i	0.997866	−	0.0653005i	$-0.0208006\pi$
$828$	42.3726	−	646.656i	0.0511746	−	0.780985i
$829$	−705.288	+	1221.59i	−0.850769	+	1.47358i	0.0297462	+	0.999557i	$0.490530\pi$
$829$	−705.288	+	1221.59i	−0.850769	+	1.47358i	−0.880515	+	0.474018i	$0.842803\pi$
$830$	33.1722	+	19.1520i	0.0399665	+	0.0230747i
$831$	587.211	+	365.144i	0.706632	+	0.439404i
$832$	164.664			0.197914
$833$		0			0
$834$	−187.085	−	350.004i	−0.224323	−	0.419669i
$835$	−515.284	−	892.497i	−0.617106	−	1.06886i
$836$	11.4245	+	6.59595i	0.0136657	+	0.00788989i
$837$	121.642	+	87.1629i	0.145332	+	0.104137i
$838$	−63.4980	−	109.982i	−0.0757733	−	0.131243i
$839$			299.906i			0.357456i	0.983899	+	0.178728i	$0.0571982\pi$
$839$			299.906i			0.357456i	−0.983899	+	0.178728i	$0.942802\pi$
$840$		0			0
$841$	408.320			0.485517
$842$	−951.811	+	549.528i	−1.13042	+	0.652646i
$843$	−221.719	−	7.25636i	−0.263011	−	0.00860778i
$844$	−378.745	+	656.006i	−0.448750	+	0.777258i
$845$	−1448.98	+	836.569i	−1.71477	+	0.990023i
$846$	−60.0000	+	89.7998i	−0.0709220	+	0.106146i
$847$		0			0
$848$		−	203.647i		−	0.240149i
$849$	359.637	+	223.633i	0.423601	+	0.263407i
$850$	203.982	−	353.307i	0.239978	−	0.415655i
$851$	623.579	+	360.024i	0.732760	+	0.423059i
$852$	−277.987	+	447.049i	−0.326276	+	0.524705i
$853$	13.7648			0.0161369			0.00806844	−	0.999967i	$-0.497432\pi$
$853$	13.7648			0.0161369			0.00806844	+	0.999967i	$0.497432\pi$
$854$		0			0
$855$	−786.656	−	525.607i	−0.920066	−	0.614745i
$856$	−152.745	−	264.562i	−0.178441	−	0.309068i
$857$	−218.677	−	126.253i	−0.255166	−	0.147320i	0.366962	−	0.930236i	$-0.380398\pi$
$857$	−218.677	−	126.253i	−0.255166	−	0.147320i	−0.622127	+	0.782916i	$0.713731\pi$
$858$	−1.17757	+	35.9807i	−0.00137246	+	0.0419356i
$859$	337.255	+	584.143i	0.392613	+	0.680026i	0.992793	−	0.119839i	$-0.0382377\pi$
$859$	337.255	+	584.143i	0.392613	+	0.680026i	−0.600180	+	0.799865i	$0.704904\pi$
$860$			679.991i			0.790687i
$861$		0			0
$862$	347.757			0.403430
$863$	−413.716	+	238.859i	−0.479392	+	0.276777i	−0.720163	−	0.693805i	$-0.755933\pi$
$863$	−413.716	+	238.859i	−0.479392	+	0.276777i	0.240771	+	0.970582i	$0.422600\pi$
$864$	−88.9615	+	124.153i	−0.102965	+	0.143695i
$865$	−17.9150	+	31.0297i	−0.0207110	+	0.0358725i
$866$	976.117	−	563.561i	1.12716	−	0.650764i
$867$	97.4432	−	52.0856i	0.112391	−	0.0600756i
$868$		0			0
$869$		−	35.0060i		−	0.0402830i
$870$	306.178	−	492.384i	0.351929	−	0.565959i
$871$	508.575	−	880.878i	0.583898	−	1.01134i
$872$	−303.320	−	175.122i	−0.347845	−	0.200828i
$873$	−618.180	−	40.5067i	−0.708110	−	0.0463994i
$874$	814.640			0.932083
$875$		0			0
$876$	−65.2549	+	34.8802i	−0.0744919	+	0.0398176i
$877$	−766.571	−	1327.74i	−0.874083	−	1.51396i	−0.857736	−	0.514091i	$-0.828130\pi$
$877$	−766.571	−	1327.74i	−0.874083	−	1.51396i	−0.0163476	−	0.999866i	$-0.505204\pi$
$878$	678.301	+	391.617i	0.772552	+	0.446033i
$879$	988.256	+	32.3434i	1.12430	+	0.0367957i
$880$	−5.41699	−	9.38251i	−0.00615568	−	0.0106619i
$881$			1368.30i			1.55313i	0.630039	+	0.776563i	$0.283039\pi$
$881$			1368.30i			1.55313i	−0.630039	+	0.776563i	$0.716961\pi$
$882$		0			0
$883$	944.486			1.06963			0.534817	−	0.844968i	$-0.320381\pi$
$883$	944.486			1.06963			0.534817	+	0.844968i	$0.320381\pi$
$884$	−566.130	+	326.855i	−0.640418	+	0.369746i
$885$	−1.06315	+	32.4846i	−0.00120130	+	0.0367057i
$886$	547.288	−	947.930i	0.617706	−	1.06990i
$887$	1149.10	−	663.432i	1.29549	−	0.747951i	0.315868	−	0.948803i	$-0.397704\pi$
$887$	1149.10	−	663.432i	1.29549	−	0.747951i	0.979622	+	0.200852i	$0.0643711\pi$
$888$	−80.0000	−	149.666i	−0.0900901	−	0.168543i
$889$		0			0
$890$		−	289.908i		−	0.325740i
$891$	−26.4924	−	20.3268i	−0.0297333	−	0.0228135i
$892$	230.494	−	399.227i	0.258401	−	0.447564i
$893$	−117.576	−	67.8823i	−0.131664	−	0.0760160i
$894$	−179.592	−	111.675i	−0.200886	−	0.124917i
$895$	8.12549			0.00907876
$896$		0			0
$897$	1047.98	+	1960.60i	1.16832	+	2.18573i
$898$	478.834	+	829.365i	0.533223	+	0.923569i
$899$	−99.8432	−	57.6445i	−0.111060	−	0.0641207i
$900$	144.628	+	293.264i	0.160698	+	0.325849i
$901$	404.235	+	700.156i	0.448652	+	0.777088i
$902$		−	44.3675i		−	0.0491879i
$903$		0			0
$904$	−227.660			−0.251836
$905$	−1063.52	+	614.024i	−1.17516	+	0.678479i
$906$	−897.517	−	29.3737i	−0.990637	−	0.0324213i
$907$	609.822	−	1056.24i	0.672351	−	1.16455i	−0.304885	−	0.952389i	$-0.598618\pi$
$907$	609.822	−	1056.24i	0.672351	−	1.16455i	0.977236	−	0.212157i	$-0.0680487\pi$
$908$	447.632	−	258.441i	0.492987	−	0.284626i
$909$	1048.81	+	700.766i	1.15381	+	0.770920i
$910$		0			0
$911$		−	63.8282i		−	0.0700639i	−0.999386	−	0.0350320i	$-0.988847\pi$
$911$		−	63.8282i		−	0.0700639i	0.999386	−	0.0350320i	$-0.0111533\pi$
$912$	−163.048	−	101.388i	−0.178780	−	0.111171i
$913$	−0.849738	+	1.47179i	−0.000930710	+	0.00161204i
$914$	−1022.25	−	590.197i	−1.11844	−	0.645729i
$915$	−696.465	+	1120.03i	−0.761164	+	1.22408i
$916$	−74.1699			−0.0809716
$917$		0			0
$918$	59.4170	−	603.435i	0.0647244	−	0.657336i
$919$	−490.693	−	849.905i	−0.533942	−	0.924815i	−0.999214	−	0.0396468i	$-0.987377\pi$
$919$	−490.693	−	849.905i	−0.533942	−	0.924815i	0.465272	−	0.885168i	$-0.345957\pi$
$920$	−579.399	−	334.516i	−0.629781	−	0.363604i
$921$	−10.3852	+	317.320i	−0.0112760	+	0.344539i
$922$	245.472	+	425.170i	0.266238	+	0.461139i
$923$		−	1805.92i		−	1.95658i
$924$		0			0
$925$	−363.320			−0.392779
$926$	389.062	−	224.625i	0.420154	−	0.242576i
$927$	−156.732	−	317.807i	−0.169074	−	0.342833i
$928$	58.8340	−	101.903i	0.0633987	−	0.109810i
$929$	295.255	−	170.465i	0.317820	−	0.183493i	−0.332600	−	0.943068i	$-0.607926\pi$
$929$	295.255	−	170.465i	0.317820	−	0.183493i	0.650420	+	0.759574i	$0.274593\pi$
$930$	136.251	−	72.8292i	0.146506	−	0.0783110i
$931$		0			0
$932$			165.343i			0.177406i
$933$	−610.125	+	981.179i	−0.653938	+	1.05164i
$934$	−387.085	+	670.451i	−0.414438	+	0.717827i
$935$	37.2482	+	21.5053i	0.0398377	+	0.0230003i
$936$	34.2592	−	522.837i	0.0366018	−	0.558586i
$937$	−1010.00			−1.07791			−0.538954	−	0.842335i	$-0.681180\pi$
$937$	−1010.00			−1.07791			−0.538954	+	0.842335i	$0.681180\pi$
$938$		0			0
$939$	209.882	−	112.187i	0.223517	−	0.119475i
$940$	55.7490	+	96.5601i	0.0593075	+	0.102724i
$941$	250.331	+	144.529i	0.266027	+	0.153591i	0.627081	−	0.778954i	$-0.284250\pi$
$941$	250.331	+	144.529i	0.266027	+	0.153591i	−0.361054	+	0.932545i	$0.617583\pi$
$942$	−461.119	−	15.0914i	−0.489511	−	0.0160206i
$943$	−1369.91	−	2372.76i	−1.45272	−	2.51618i
$944$			6.59595i			0.00698724i
$945$		0			0
$946$	−30.1699			−0.0318921
$947$	−717.116	+	414.027i	−0.757250	+	0.437199i	−0.828308	−	0.560274i	$-0.810696\pi$
$947$	−717.116	+	414.027i	−0.757250	+	0.437199i	0.0710573	+	0.997472i	$0.477363\pi$
$948$	−16.6656	+	509.218i	−0.0175797	+	0.537149i
$949$	126.915	−	219.823i	0.133736	−	0.231637i
$950$	−355.980	+	205.525i	−0.374715	+	0.216342i
$951$	581.490	+	1087.87i	0.611451	+	1.14392i
$952$		0			0
$953$			102.785i			0.107854i	0.998545	+	0.0539269i	$0.0171738\pi$
$953$			102.785i			0.107854i	−0.998545	+	0.0539269i	$0.982826\pi$
$954$	−646.613	−	42.3698i	−0.677792	−	0.0444128i
$955$	1151.55	−	1994.53i	1.20581	−	2.08852i
$956$	−291.797	−	168.469i	−0.305227	−	0.176223i
$957$	21.8462	+	13.5846i	0.0228278	+	0.0141949i
$958$	−191.660			−0.200063
$959$		0			0
$960$	74.3320	+	139.062i	0.0774292	+	0.144857i
$961$	465.140	+	805.647i	0.484017	+	0.838342i
$962$	504.179	+	291.088i	0.524094	+	0.302586i
$963$	−871.810	+	429.948i	−0.905306	+	0.446467i
$964$	130.000	+	225.167i	0.134855	+	0.233575i
$965$		−	1777.17i		−	1.84163i
$966$		0			0
$967$	−184.753			−0.191058			−0.0955289	−	0.995427i	$-0.530454\pi$
$967$	−184.753			−0.191058			−0.0955289	+	0.995427i	$0.530454\pi$
$968$	−295.972	+	170.879i	−0.305756	+	0.176528i
$969$	761.825	+	24.9328i	0.786198	+	0.0257305i
$970$	−319.786	+	553.885i	−0.329676	+	0.571015i
$971$	−1272.48	+	734.664i	−1.31048	+	0.756606i	−0.982176	−	0.187966i	$-0.939811\pi$
$971$	−1272.48	+	734.664i	−1.31048	+	0.756606i	−0.328305	+	0.944572i	$0.606477\pi$
$972$	375.697	+	308.299i	0.386519	+	0.317180i
$973$		0			0
$974$			33.2312i			0.0341183i
$975$	−952.584	−	592.343i	−0.977009	−	0.607531i
$976$	−133.830	+	231.800i	−0.137121	+	0.237500i
$977$	−574.237	−	331.536i	−0.587756	−	0.339341i	0.176454	−	0.984309i	$-0.443537\pi$
$977$	−574.237	−	331.536i	−0.587756	−	0.339341i	−0.764210	+	0.644968i	$0.776871\pi$
$978$	29.1336	−	46.8516i	0.0297890	−	0.0479055i
$979$	12.8627			0.0131386
$980$		0			0
$981$	−619.150	+	926.659i	−0.631142	+	0.944607i
$982$	73.1176	+	126.643i	0.0744579	+	0.128965i
$983$	1644.81	+	949.630i	1.67325	+	0.966053i	0.965798	+	0.259296i	$0.0834904\pi$
$983$	1644.81	+	949.630i	1.67325	+	0.966053i	0.707456	+	0.706758i	$0.249843\pi$
$984$	−21.1224	+	645.396i	−0.0214658	+	0.655890i
$985$	−208.664	−	361.417i	−0.211842	−	0.366921i
$986$			467.138i			0.473771i
$987$		0			0
$988$	658.656			0.666656
$989$	−1613.48	+	931.543i	−1.63143	+	0.941904i
$990$	−30.9181	+	15.2478i	−0.0312304	+	0.0154018i
$991$	128.863	−	223.197i	0.130033	−	0.225224i	−0.793656	−	0.608367i	$-0.791825\pi$
$991$	128.863	−	223.197i	0.130033	−	0.225224i	0.923689	+	0.383143i	$0.125158\pi$
$992$	27.1525	−	15.6765i	0.0273715	−	0.0158029i
$993$	−1295.07	+	692.244i	−1.30420	+	0.697123i
$994$		0			0
$995$		−	578.167i		−	0.581073i
$996$	13.0615	−	21.0050i	0.0131139	−	0.0210893i
$997$	617.871	−	1070.18i	0.619730	−	1.07340i	−0.369805	−	0.929109i	$-0.620576\pi$
$997$	617.871	−	1070.18i	0.619730	−	1.07340i	0.989535	−	0.144294i	$-0.0460911\pi$
$998$	78.8000	+	45.4952i	0.0789579	+	0.0455863i
$999$	−491.861	+	222.875i	−0.492353	+	0.223098i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.3.h.g.263.3		8
3.2	odd	2	inner	294.3.h.g.263.1		8
7.2	even	3	inner	294.3.h.g.275.1		8
7.3	odd	6		42.3.b.a.29.3	yes	4
7.4	even	3		294.3.b.h.197.4		4
7.5	odd	6		294.3.h.d.275.2		8
7.6	odd	2		294.3.h.d.263.4		8
21.2	odd	6	inner	294.3.h.g.275.3		8
21.5	even	6		294.3.h.d.275.4		8
21.11	odd	6		294.3.b.h.197.2		4
21.17	even	6		42.3.b.a.29.1	✓	4
21.20	even	2		294.3.h.d.263.2		8
28.3	even	6		336.3.d.b.113.3		4
35.3	even	12		1050.3.c.a.449.5		8
35.17	even	12		1050.3.c.a.449.3		8
35.24	odd	6		1050.3.e.a.701.2		4
56.3	even	6		1344.3.d.e.449.2		4
56.45	odd	6		1344.3.d.c.449.3		4
63.31	odd	6		1134.3.q.a.1079.2		8
63.38	even	6		1134.3.q.a.701.2		8
63.52	odd	6		1134.3.q.a.701.3		8
63.59	even	6		1134.3.q.a.1079.3		8
84.59	odd	6		336.3.d.b.113.4		4
105.17	odd	12		1050.3.c.a.449.8		8
105.38	odd	12		1050.3.c.a.449.2		8
105.59	even	6		1050.3.e.a.701.4		4
168.59	odd	6		1344.3.d.e.449.1		4
168.101	even	6		1344.3.d.c.449.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.b.a.29.1	✓	4	21.17	even	6
42.3.b.a.29.3	yes	4	7.3	odd	6
294.3.b.h.197.2		4	21.11	odd	6
294.3.b.h.197.4		4	7.4	even	3
294.3.h.d.263.2		8	21.20	even	2
294.3.h.d.263.4		8	7.6	odd	2
294.3.h.d.275.2		8	7.5	odd	6
294.3.h.d.275.4		8	21.5	even	6
294.3.h.g.263.1		8	3.2	odd	2	inner
294.3.h.g.263.3		8	1.1	even	1	trivial
294.3.h.g.275.1		8	7.2	even	3	inner
294.3.h.g.275.3		8	21.2	odd	6	inner
336.3.d.b.113.3		4	28.3	even	6
336.3.d.b.113.4		4	84.59	odd	6
1050.3.c.a.449.2		8	105.38	odd	12
1050.3.c.a.449.3		8	35.17	even	12
1050.3.c.a.449.5		8	35.3	even	12
1050.3.c.a.449.8		8	105.17	odd	12
1050.3.e.a.701.2		4	35.24	odd	6
1050.3.e.a.701.4		4	105.59	even	6
1134.3.q.a.701.2		8	63.38	even	6
1134.3.q.a.701.3		8	63.52	odd	6
1134.3.q.a.1079.2		8	63.31	odd	6
1134.3.q.a.1079.3		8	63.59	even	6
1344.3.d.c.449.3		4	56.45	odd	6
1344.3.d.c.449.4		4	168.101	even	6
1344.3.d.e.449.1		4	168.59	odd	6
1344.3.d.e.449.2		4	56.3	even	6

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	294.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(-0.0981308 + 2.99839i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-5.68986 + 3.28504i) q^{5} +(2.00000 + 3.74166i) q^{6} -2.82843i q^{8} +(-8.98074 - 0.588470i) q^{9} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(-0.0981308 + 2.99839i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-5.68986 + 3.28504i) q^{5} +(2.00000 + 3.74166i) q^{6} -2.82843i q^{8} +(-8.98074 - 0.588470i) q^{9} +(-4.64575 + 8.04668i) q^{10} +(-0.357016 - 0.206123i) q^{11} +(5.09524 + 3.16836i) q^{12} -20.5830 q^{13} +(-9.29150 - 17.3828i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(13.7524 + 7.93993i) q^{17} +(-11.4152 + 5.62962i) q^{18} +(-8.00000 - 13.8564i) q^{19} +13.1402i q^{20} -0.583005 q^{22} +(-31.1790 + 18.0012i) q^{23} +(8.48074 + 0.277556i) q^{24} +(9.08301 - 15.7322i) q^{25} +(-25.2089 + 14.5544i) q^{26} +(2.64575 - 26.8701i) q^{27} +20.8010i q^{29} +(-23.6712 - 14.7194i) q^{30} +(-2.77124 + 4.79993i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(0.653074 - 1.05025i) q^{33} +22.4575 q^{34} +(-10.0000 + 14.9666i) q^{36} +(-10.0000 - 17.3205i) q^{37} +(-19.5959 - 11.3137i) q^{38} +(2.01983 - 61.7160i) q^{39} +(9.29150 + 16.0934i) q^{40} +76.1013i q^{41} +51.7490 q^{43} +(-0.714033 + 0.412247i) q^{44} +(53.0323 - 26.1538i) q^{45} +(-25.4575 + 44.0937i) q^{46} +(7.34847 - 4.24264i) q^{47} +(10.5830 - 5.65685i) q^{48} -25.6906i q^{50} +(-25.1566 + 40.4559i) q^{51} +(-20.5830 + 35.6508i) q^{52} +(44.0908 + 25.4558i) q^{53} +(-15.7596 - 34.7798i) q^{54} +2.70850 q^{55} +(42.3320 - 22.6274i) q^{57} +(14.7085 + 25.4759i) q^{58} +(-1.42807 - 0.824494i) q^{59} +(-39.3994 - 1.28946i) q^{60} +(-33.4575 - 57.9501i) q^{61} +7.83826i q^{62} -8.00000 q^{64} +(117.114 - 67.6160i) q^{65} +(0.0572108 - 1.74808i) q^{66} +(-24.7085 + 42.7964i) q^{67} +(27.5047 - 15.8799i) q^{68} +(-50.9150 - 95.2533i) q^{69} +87.7385i q^{71} +(-1.66444 + 25.4014i) q^{72} +(-6.16601 + 10.6798i) q^{73} +(-24.4949 - 14.1421i) q^{74} +(46.2801 + 28.7782i) q^{75} -32.0000 q^{76} +(-41.1660 - 77.0146i) q^{78} +(42.4575 + 73.5386i) q^{79} +(22.7594 + 13.1402i) q^{80} +(80.3074 + 10.5698i) q^{81} +(53.8118 + 93.2047i) q^{82} -4.12247i q^{83} -104.332 q^{85} +(63.3793 - 36.5921i) q^{86} +(-62.3695 - 2.04121i) q^{87} +(-0.583005 + 1.00979i) q^{88} +(-27.0212 + 15.6007i) q^{89} +(46.4575 - 69.5312i) q^{90} +72.0047i q^{92} +(-14.1202 - 8.78030i) q^{93} +(6.00000 - 10.3923i) q^{94} +(91.0378 + 52.5607i) q^{95} +(8.96148 - 14.4115i) q^{96} +68.8340 q^{97} +(3.08497 + 2.06123i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} + 16 q^{6} - 20 q^{9}+O(q^{10}) \) 8 * q + 8 * q^4 + 16 * q^6 - 20 * q^9	\( 8 q + 8 q^{4} + 16 q^{6} - 20 q^{9} - 16 q^{10} - 80 q^{13} - 32 q^{15} - 16 q^{16} - 64 q^{19} + 80 q^{22} + 16 q^{24} - 12 q^{25} - 56 q^{30} - 128 q^{31} + 40 q^{33} - 32 q^{34} - 80 q^{36} - 80 q^{37} + 112 q^{39} + 32 q^{40} + 160 q^{43} + 112 q^{45} + 8 q^{46} - 16 q^{51} - 80 q^{52} - 152 q^{54} + 64 q^{55} + 160 q^{58} - 32 q^{60} - 56 q^{61} - 64 q^{64} + 112 q^{66} - 240 q^{67} + 16 q^{69} + 120 q^{73} + 224 q^{75} - 256 q^{76} - 160 q^{78} + 128 q^{79} + 124 q^{81} + 240 q^{82} - 496 q^{85} - 160 q^{87} + 80 q^{88} + 160 q^{90} + 280 q^{93} + 48 q^{94} - 32 q^{96} + 720 q^{97} + 448 q^{99}+O(q^{100}) \) 8 * q + 8 * q^4 + 16 * q^6 - 20 * q^9 - 16 * q^10 - 80 * q^13 - 32 * q^15 - 16 * q^16 - 64 * q^19 + 80 * q^22 + 16 * q^24 - 12 * q^25 - 56 * q^30 - 128 * q^31 + 40 * q^33 - 32 * q^34 - 80 * q^36 - 80 * q^37 + 112 * q^39 + 32 * q^40 + 160 * q^43 + 112 * q^45 + 8 * q^46 - 16 * q^51 - 80 * q^52 - 152 * q^54 + 64 * q^55 + 160 * q^58 - 32 * q^60 - 56 * q^61 - 64 * q^64 + 112 * q^66 - 240 * q^67 + 16 * q^69 + 120 * q^73 + 224 * q^75 - 256 * q^76 - 160 * q^78 + 128 * q^79 + 124 * q^81 + 240 * q^82 - 496 * q^85 - 160 * q^87 + 80 * q^88 + 160 * q^90 + 280 * q^93 + 48 * q^94 - 32 * q^96 + 720 * q^97 + 448 * q^99

Introduction

L-functions

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