LMFDB - Embedded newform 294.3.h.d.263.4

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			263.4
Root			$1.00781 - 0.581861i$ of defining polynomial
Character	$\chi$	$=$	294.263
Dual form			294.3.h.d.275.4

$q$-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	0.192044	−	0.981386i	$-0.438488\pi$
$5$	5.68986	−	3.28504i	1.13797	−	0.657008i	0.945928	+	0.324378i	$0.105155\pi$
$6$	−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	$-0.209220\pi$
$13$	20.5830			1.58331			0.791654	+	0.610970i	$0.209220\pi$
$14$		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	0.0376330	−	0.999292i	$-0.488018\pi$
$17$	−13.7524	−	7.93993i	−0.808962	−	0.467055i	−0.846595	+	0.532237i	$0.821352\pi$
$18$	−11.4152	+	5.62962i	−0.634179	+	0.312757i
$19$	8.00000	+	13.8564i	0.421053	+	0.729285i	0.996043	−	0.0888758i	$-0.0283274\pi$
$19$	8.00000	+	13.8564i	0.421053	+	0.729285i	−0.574990	+	0.818160i	$0.694994\pi$
$20$		−	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	−0.817861	−	0.575416i	$-0.804840\pi$
$31$	2.77124	−	4.79993i	0.0893949	−	0.154837i	0.907256	+	0.420580i	$0.138173\pi$
$32$	−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	$-0.621471\pi$
$41$		−	76.1013i		−	1.85613i	0.372418	−	0.928065i	$-0.378529\pi$
$42$		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	−0.576134	−	0.817355i	$-0.695439\pi$
$47$	−7.34847	+	4.24264i	−0.156350	+	0.0902690i	0.419784	+	0.907624i	$0.362106\pi$
$48$	−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	0.512053	−	0.858954i	$-0.328885\pi$
$59$	1.42807	+	0.824494i	0.0242045	+	0.0139745i	−0.487849	+	0.872928i	$0.662218\pi$
$60$	−39.3994	−	1.28946i	−0.656657	−	0.0214909i
$61$	33.4575	+	57.9501i	0.548484	+	0.950002i	0.998379	+	0.0569203i	$0.0181281\pi$
$61$	33.4575	+	57.9501i	0.548484	+	0.950002i	−0.449895	+	0.893082i	$0.648539\pi$
$62$		−	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	−0.820698	−	0.571363i	$-0.806415\pi$
$73$	6.16601	−	10.6798i	0.0844659	−	0.146299i	0.905163	+	0.425064i	$0.139748\pi$
$74$	−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	$0.00790577\pi$
$83$			4.12247i			0.0496683i	−0.999692	+	0.0248342i	$0.992094\pi$
$84$		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	−0.340454	−	0.940261i	$-0.610581\pi$
$89$	27.0212	−	15.6007i	0.303609	−	0.175289i	0.644063	+	0.764972i	$0.277247\pi$
$90$	−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	$-0.615456\pi$
$97$	−68.8340			−0.709629			−0.354814	+	0.934937i	$0.615456\pi$
$98$		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	0.960943	−	0.276747i	$-0.0892563\pi$
$101$	121.376	+	70.0766i	1.20174	+	0.693828i	0.240802	+	0.970574i	$0.422590\pi$
$102$	−2.20377	+	67.3365i	−0.0216056	+	0.660162i
$103$	−19.6863	−	34.0976i	−0.191129	−	0.331045i	0.754496	−	0.656305i	$-0.227881\pi$
$103$	−19.6863	−	34.0976i	−0.191129	−	0.331045i	−0.945625	+	0.325260i	$0.894548\pi$
$104$		−	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	−0.513565	−	0.858051i	$-0.671675\pi$
$131$	−3.57016	+	2.06123i	−0.0272532	+	0.0157346i	0.486312	+	0.873786i	$0.338342\pi$
$132$	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	$-0.390762\pi$
$139$	93.5425			0.672968			0.336484	+	0.941689i	$0.390762\pi$
$140$		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	−0.639271	−	0.768981i	$-0.720764\pi$
$157$	54.3725	−	94.1760i	0.346322	−	0.599847i	0.985593	+	0.169134i	$0.0540972\pi$
$158$	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	$-0.844386\pi$
$167$		−	156.858i		−	0.939267i	0.882862	−	0.469633i	$-0.155614\pi$
$168$		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	−0.513588	−	0.858037i	$-0.671684\pi$
$173$	−4.72288	+	2.72676i	−0.0272999	+	0.0157616i	0.486288	+	0.873799i	$0.338351\pi$
$174$	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	$-0.672706\pi$
$181$	−186.915			−1.03268			−0.516340	+	0.856384i	$0.672706\pi$
$182$		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	−0.734038	−	0.679108i	$-0.762367\pi$
$199$	44.0000	−	76.2102i	0.221106	−	0.382966i	0.955144	+	0.296142i	$0.0957001\pi$
$200$	−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	$-0.672878\pi$
$223$	−230.494			−1.03361			−0.516803	+	0.856104i	$0.672878\pi$
$224$		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	−0.0819056	−	0.996640i	$-0.526101\pi$
$227$	−223.816	−	129.220i	−0.985974	−	0.569252i	−0.904068	+	0.427388i	$0.859434\pi$
$228$	3.14019	−	95.9486i	0.0137727	−	0.420827i
$229$	18.5425	+	32.1165i	0.0809716	+	0.140247i	0.903668	−	0.428235i	$-0.140864\pi$
$229$	18.5425	+	32.1165i	0.0809716	+	0.140247i	−0.822696	+	0.568482i	$0.807531\pi$
$230$			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	−0.699077	−	0.715046i	$-0.746406\pi$
$241$	65.0000	−	112.583i	0.269710	−	0.467151i	0.968787	+	0.247896i	$0.0797390\pi$
$242$	−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	$0.0767417\pi$
$251$			119.859i			0.477525i	−0.971078	+	0.238763i	$0.923258\pi$
$252$		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	−0.827300	−	0.561760i	$-0.810124\pi$
$257$	−193.894	+	111.945i	−0.754451	+	0.435583i	0.0728489	+	0.997343i	$0.476791\pi$
$258$	−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	0.967097	−	0.254408i	$-0.0818807\pi$
$269$	330.956	+	191.078i	1.23032	+	0.710326i	0.263224	+	0.964735i	$0.415214\pi$
$270$	203.923	+	146.121i	0.755271	+	0.541189i
$271$	−57.2288	−	99.1231i	−0.211176	−	0.365768i	0.740907	−	0.671608i	$-0.234396\pi$
$271$	−57.2288	−	99.1231i	−0.211176	−	0.365768i	−0.952083	+	0.305840i	$0.901063\pi$
$272$			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	−0.963362	−	0.268204i	$-0.913570\pi$
$283$	−70.5830	+	122.253i	−0.249410	+	0.431991i	0.713952	+	0.700194i	$0.246903\pi$
$284$	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	$0.190141\pi$
$293$			329.595i			1.12490i	−0.826832	+	0.562449i	$0.809859\pi$
$294$		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	$-0.555140\pi$
$307$	−105.830			−0.344723			−0.172362	+	0.985034i	$0.555140\pi$
$308$		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	−0.143613	−	0.989634i	$-0.545872\pi$
$311$	−333.537	−	192.568i	−1.07247	−	0.619189i	−0.928854	+	0.370445i	$0.879205\pi$
$312$	−174.559	−	5.71293i	−0.559484	−	0.0183107i
$313$	39.6640	+	68.7001i	0.126722	+	0.219489i	0.922405	−	0.386224i	$-0.126221\pi$
$313$	39.6640	+	68.7001i	0.126722	+	0.219489i	−0.795683	+	0.605714i	$0.792888\pi$
$314$		−	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	$-0.431802\pi$
$349$	148.405			0.425230			0.212615	+	0.977136i	$0.431802\pi$
$350$		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	0.687254	−	0.726417i	$-0.258816\pi$
$353$	141.830	+	81.8857i	0.401785	+	0.231971i	−0.285469	+	0.958388i	$0.592149\pi$
$354$	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	−0.998087	−	0.0618281i	$-0.980307\pi$
$367$	−163.498	+	283.187i	−0.445499	+	0.771626i	0.552588	+	0.833454i	$0.313640\pi$
$368$	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	0.237317	−	0.971432i	$-0.423732\pi$
$383$	458.551	−	264.744i	1.19726	−	0.691239i	0.959944	+	0.280193i	$0.0903986\pi$
$384$	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	0.590419	−	0.807097i	$-0.298963\pi$
$397$	−160.292	−	277.633i	−0.403757	−	0.699328i	−0.994176	+	0.107769i	$0.965629\pi$
$398$		−	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	$0.390508\pi$
$409$	−264.490	+	458.110i	−0.646675	+	1.12007i	−0.983912	+	0.178654i	$0.942826\pi$
$410$	−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	$0.0341756\pi$
$419$			89.7998i			0.214319i	−0.994242	+	0.107160i	$0.965824\pi$
$420$		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	$-0.872071\pi$
$433$	−796.996			−1.84064			−0.920319	+	0.391169i	$0.872071\pi$
$434$		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	$-0.949399\pi$
$439$	−276.915	−	479.631i	−0.630786	−	1.09255i	0.356605	−	0.934255i	$-0.383934\pi$
$440$			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	$-0.877121\pi$
$461$		−	347.150i		−	0.753036i	0.926409	−	0.376518i	$-0.122879\pi$
$462$		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	0.102463	−	0.994737i	$-0.467328\pi$
$467$	474.080	−	273.710i	1.01516	−	0.586104i	0.912699	+	0.408633i	$0.133994\pi$
$468$	−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	0.617484	−	0.786583i	$-0.288152\pi$
$479$	117.367	+	67.7621i	0.245026	+	0.141466i	−0.372459	+	0.928049i	$0.621485\pi$
$480$	−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	$-0.817031\pi$
$503$		−	546.940i		−	1.08736i	0.839294	−	0.543678i	$-0.182969\pi$
$504$		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	−0.444966	−	0.895547i	$-0.646784\pi$
$509$	55.0318	−	31.7727i	0.108118	−	0.0624217i	0.553084	+	0.833126i	$0.313451\pi$
$510$	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	−0.140111	−	0.990136i	$-0.544746\pi$
$521$	−556.245	−	321.148i	−1.06765	−	0.616408i	−0.927538	+	0.373728i	$0.878079\pi$
$522$	−117.101	−	237.448i	−0.224332	−	0.454881i
$523$	56.1882	+	97.3209i	0.107434	+	0.186082i	0.914730	−	0.404065i	$-0.132403\pi$
$523$	56.1882	+	97.3209i	0.107434	+	0.186082i	−0.807296	+	0.590147i	$0.799070\pi$
$524$			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	0.941662	−	0.336561i	$-0.109264\pi$
$563$	631.136	+	364.386i	1.12102	+	0.647223i	0.179361	+	0.983783i	$0.442597\pi$
$564$	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	−0.999695	−	0.0246850i	$-0.992142\pi$
$577$	−276.077	+	478.180i	−0.478470	+	0.828734i	0.521225	+	0.853419i	$0.325475\pi$
$578$	−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	$-0.601158\pi$
$587$		−	1115.21i		−	1.89985i	0.312474	−	0.949926i	$-0.398842\pi$
$588$		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	0.404134	−	0.914700i	$-0.367573\pi$
$593$	829.224	−	478.753i	1.39835	−	0.807340i	0.994220	+	0.107359i	$0.0342395\pi$
$594$	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	$-0.800917\pi$
$601$	−974.470			−1.62142			−0.810708	+	0.585451i	$0.800917\pi$
$602$		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	$0.191915\pi$
$607$	548.073	+	949.291i	0.902921	+	1.56391i	0.0792376	+	0.996856i	$0.474751\pi$
$608$		−	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	−0.887308	−	0.461177i	$-0.847427\pi$
$619$	−27.3987	+	47.4559i	−0.0442628	+	0.0766655i	0.843045	+	0.537843i	$0.180761\pi$
$620$	−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	$-0.485388\pi$
$643$	59.0118			0.0917758			0.0458879	+	0.998947i	$0.485388\pi$
$644$		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	0.819540	−	0.573022i	$-0.194229\pi$
$647$	474.288	+	273.831i	0.733058	+	0.423231i	−0.0864819	+	0.996253i	$0.527562\pi$
$648$	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	−0.805921	−	0.592023i	$-0.798329\pi$
$661$	72.5425	−	125.647i	0.109747	−	0.190087i	0.915668	+	0.401936i	$0.131663\pi$
$662$	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	−0.389757	−	0.920918i	$-0.627441\pi$
$677$	144.136	−	83.2168i	0.212903	−	0.122920i	0.602660	+	0.797998i	$0.294108\pi$
$678$	−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	$-0.796361\pi$
$691$	−634.431	−	1098.87i	−0.918135	−	1.59026i	−0.115890	−	0.993262i	$-0.536972\pi$
$692$			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	0.133299	−	0.991076i	$-0.457443\pi$
$719$	760.879	−	439.294i	1.05825	−	0.610979i	0.924947	+	0.380097i	$0.124109\pi$
$720$	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	$-0.401502\pi$
$727$	442.782			0.609053			0.304527	+	0.952504i	$0.401502\pi$
$728$		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	$-0.938665\pi$
$733$	−481.280	−	833.601i	−0.656589	−	1.13725i	0.324904	−	0.945747i	$-0.394668\pi$
$734$			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	$0.736077\pi$
$761$	−1257.04	+	725.754i	−1.65183	+	0.953685i	−0.976319	+	0.216335i	$0.930590\pi$
$762$	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	$-0.750524\pi$
$769$	−1089.32			−1.41654			−0.708271	+	0.705941i	$0.750524\pi$
$770$		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	0.946995	−	0.321248i	$-0.104102\pi$
$773$	882.985	+	509.792i	1.14228	+	0.659498i	0.195288	+	0.980746i	$0.437436\pi$
$774$	−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	$-0.535522\pi$
$787$	633.501	−	1097.26i	0.804956	−	1.39423i	0.916321	−	0.400445i	$-0.131145\pi$
$788$	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	$-0.803640\pi$
$797$		−	922.123i		−	1.15699i	0.815685	−	0.578496i	$-0.196360\pi$
$798$		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	$-0.328147\pi$
$811$	833.778			1.02809			0.514043	+	0.857764i	$0.328147\pi$
$812$		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	$-0.509470\pi$
$829$	705.288	−	1221.59i	0.850769	−	1.47358i	0.880515	−	0.474018i	$-0.157197\pi$
$830$	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	$-0.942802\pi$
$839$		−	299.906i		−	0.357456i	0.983899	−	0.178728i	$-0.0571982\pi$
$840$		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	$-0.502568\pi$
$853$	−13.7648			−0.0161369			−0.00806844	+	0.999967i	$0.502568\pi$
$854$		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	0.622127	−	0.782916i	$-0.286269\pi$
$857$	218.677	+	126.253i	0.255166	+	0.147320i	−0.366962	+	0.930236i	$0.619602\pi$
$858$	−1.17757	+	35.9807i	−0.00137246	+	0.0419356i
$859$	−337.255	−	584.143i	−0.392613	−	0.680026i	0.600180	−	0.799865i	$-0.295096\pi$
$859$	−337.255	−	584.143i	−0.392613	−	0.680026i	−0.992793	+	0.119839i	$0.961762\pi$
$860$		−	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	$-0.716961\pi$
$881$		−	1368.30i		−	1.55313i	0.630039	−	0.776563i	$-0.283039\pi$
$882$		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	−0.979622	−	0.200852i	$-0.935629\pi$
$887$	−1149.10	+	663.432i	−1.29549	+	0.747951i	−0.315868	+	0.948803i	$0.602296\pi$
$888$	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	−0.650420	−	0.759574i	$-0.725407\pi$
$929$	−295.255	+	170.465i	−0.317820	+	0.183493i	0.332600	+	0.943068i	$0.392074\pi$
$930$	−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	$-0.318820\pi$
$937$	1010.00			1.07791			0.538954	+	0.842335i	$0.318820\pi$
$938$		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	0.361054	−	0.932545i	$-0.382417\pi$
$941$	−250.331	−	144.529i	−0.266027	−	0.153591i	−0.627081	+	0.778954i	$0.715750\pi$
$942$	−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	0.328305	−	0.944572i	$-0.393523\pi$
$971$	1272.48	−	734.664i	1.31048	−	0.756606i	0.982176	+	0.187966i	$0.0601894\pi$
$972$	−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	$-0.916510\pi$
$983$	−1644.81	−	949.630i	−1.67325	−	0.966053i	−0.707456	−	0.706758i	$-0.750157\pi$
$984$	−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	$0.379424\pi$
$997$	−617.871	+	1070.18i	−0.619730	+	1.07340i	−0.989535	+	0.144294i	$0.953909\pi$
$998$	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.d.263.4		8
3.2	odd	2	inner	294.3.h.d.263.2		8
7.2	even	3	inner	294.3.h.d.275.2		8
7.3	odd	6		294.3.b.h.197.4		4
7.4	even	3		42.3.b.a.29.3	yes	4
7.5	odd	6		294.3.h.g.275.1		8
7.6	odd	2		294.3.h.g.263.3		8
21.2	odd	6	inner	294.3.h.d.275.4		8
21.5	even	6		294.3.h.g.275.3		8
21.11	odd	6		42.3.b.a.29.1	✓	4
21.17	even	6		294.3.b.h.197.2		4
21.20	even	2		294.3.h.g.263.1		8
28.11	odd	6		336.3.d.b.113.3		4
35.4	even	6		1050.3.e.a.701.2		4
35.18	odd	12		1050.3.c.a.449.5		8
35.32	odd	12		1050.3.c.a.449.3		8
56.11	odd	6		1344.3.d.e.449.2		4
56.53	even	6		1344.3.d.c.449.3		4
63.4	even	3		1134.3.q.a.1079.2		8
63.11	odd	6		1134.3.q.a.701.2		8
63.25	even	3		1134.3.q.a.701.3		8
63.32	odd	6		1134.3.q.a.1079.3		8
84.11	even	6		336.3.d.b.113.4		4
105.32	even	12		1050.3.c.a.449.8		8
105.53	even	12		1050.3.c.a.449.2		8
105.74	odd	6		1050.3.e.a.701.4		4
168.11	even	6		1344.3.d.e.449.1		4
168.53	odd	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	21.11	odd	6
42.3.b.a.29.3	yes	4	7.4	even	3
294.3.b.h.197.2		4	21.17	even	6
294.3.b.h.197.4		4	7.3	odd	6
294.3.h.d.263.2		8	3.2	odd	2	inner
294.3.h.d.263.4		8	1.1	even	1	trivial
294.3.h.d.275.2		8	7.2	even	3	inner
294.3.h.d.275.4		8	21.2	odd	6	inner
294.3.h.g.263.1		8	21.20	even	2
294.3.h.g.263.3		8	7.6	odd	2
294.3.h.g.275.1		8	7.5	odd	6
294.3.h.g.275.3		8	21.5	even	6
336.3.d.b.113.3		4	28.11	odd	6
336.3.d.b.113.4		4	84.11	even	6
1050.3.c.a.449.2		8	105.53	even	12
1050.3.c.a.449.3		8	35.32	odd	12
1050.3.c.a.449.5		8	35.18	odd	12
1050.3.c.a.449.8		8	105.32	even	12
1050.3.e.a.701.2		4	35.4	even	6
1050.3.e.a.701.4		4	105.74	odd	6
1134.3.q.a.701.2		8	63.11	odd	6
1134.3.q.a.701.3		8	63.25	even	3
1134.3.q.a.1079.2		8	63.4	even	3
1134.3.q.a.1079.3		8	63.32	odd	6
1344.3.d.c.449.3		4	56.53	even	6
1344.3.d.c.449.4		4	168.53	odd	6
1344.3.d.e.449.1		4	168.11	even	6
1344.3.d.e.449.2		4	56.11	odd	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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more