LMFDB - Embedded newform 294.3.h.g.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			$2.23256 + 1.28897i$ of defining polynomial
Character	$\chi$	$=$	294.263
Dual form			294.3.h.g.275.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(2.54762 - 1.58418i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.790881 - 0.456615i) q^{5} +(2.00000 - 3.74166i) q^{6} -2.82843i q^{8} +(3.98074 - 8.07178i) q^{9} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(2.54762 - 1.58418i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.790881 - 0.456615i) q^{5} +(2.00000 - 3.74166i) q^{6} -2.82843i q^{8} +(3.98074 - 8.07178i) q^{9} +(0.645751 - 1.11847i) q^{10} +(12.6045 + 7.27719i) q^{11} +(-0.196262 - 5.99679i) q^{12} +0.583005 q^{13} +(1.29150 - 2.41618i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(-18.6513 - 10.7684i) q^{17} +(-0.832222 - 12.7007i) q^{18} +(-8.00000 - 13.8564i) q^{19} -1.82646i q^{20} +20.5830 q^{22} +(33.6284 - 19.4154i) q^{23} +(-4.48074 - 7.20576i) q^{24} +(-12.0830 + 20.9284i) q^{25} +(0.714033 - 0.412247i) q^{26} +(-2.64575 - 26.8701i) q^{27} +35.7676i q^{29} +(-0.126736 - 3.87243i) q^{30} +(-29.2288 + 50.6257i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(43.6398 - 1.42823i) q^{33} -30.4575 q^{34} +(-10.0000 - 14.9666i) q^{36} +(-10.0000 - 17.3205i) q^{37} +(-19.5959 - 11.3137i) q^{38} +(1.48528 - 0.923586i) q^{39} +(-1.29150 - 2.23695i) q^{40} +8.75149i q^{41} -11.7490 q^{43} +(25.2089 - 14.5544i) q^{44} +(-0.537408 - 8.20148i) q^{45} +(27.4575 - 47.5578i) q^{46} +(7.34847 - 4.24264i) q^{47} +(-10.5830 - 5.65685i) q^{48} +34.1759i q^{50} +(-64.5756 + 2.11341i) q^{51} +(0.583005 - 1.00979i) q^{52} +(44.0908 + 25.4558i) q^{53} +(-22.2404 - 31.0381i) q^{54} +13.2915 q^{55} +(-42.3320 - 22.6274i) q^{57} +(25.2915 + 43.8062i) q^{58} +(50.4179 + 29.1088i) q^{59} +(-2.89344 - 4.65313i) q^{60} +(19.4575 + 33.7014i) q^{61} +82.6714i q^{62} -8.00000 q^{64} +(0.461088 - 0.266209i) q^{65} +(52.4377 - 32.6072i) q^{66} +(-35.2915 + 61.1267i) q^{67} +(-37.3027 + 21.5367i) q^{68} +(54.9150 - 102.737i) q^{69} -17.0279i q^{71} +(-22.8305 - 11.2592i) q^{72} +(36.1660 - 62.6414i) q^{73} +(-24.4949 - 14.1421i) q^{74} +(2.37143 + 72.4592i) q^{75} -32.0000 q^{76} +(1.16601 - 2.18141i) q^{78} +(-10.4575 - 18.1129i) q^{79} +(-3.16352 - 1.82646i) q^{80} +(-49.3074 - 64.2634i) q^{81} +(6.18824 + 10.7183i) q^{82} +145.544i q^{83} -19.6680 q^{85} +(-14.3895 + 8.30781i) q^{86} +(56.6623 + 91.1222i) q^{87} +(20.5830 - 35.6508i) q^{88} +(-46.4635 + 26.8257i) q^{89} +(-6.45751 - 9.66472i) q^{90} -77.6616i q^{92} +(5.73648 + 175.279i) q^{93} +(6.00000 - 10.3923i) q^{94} +(-12.6541 - 7.30584i) q^{95} +(-16.9615 + 0.555112i) q^{96} +111.166 q^{97} +(108.915 - 72.7719i) 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
$3$	2.54762	−	1.58418i	0.849207	−	0.528060i
$3$	2.54762	−	1.58418i	0.849207	−	0.528060i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	0.790881	−	0.456615i	0.158176	−	0.0913230i	−0.418823	−	0.908068i	$-0.637557\pi$
$5$	0.790881	−	0.456615i	0.158176	−	0.0913230i	0.576999	+	0.816745i	$0.304224\pi$
$6$	2.00000	−	3.74166i	0.333333	−	0.623610i
$7$		0			0
$7$		0			0
$8$		−	2.82843i		−	0.353553i
$9$	3.98074	−	8.07178i	0.442305	−	0.896865i
$10$	0.645751	−	1.11847i	0.0645751	−	0.111847i
$11$	12.6045	+	7.27719i	1.14586	+	0.661563i	0.947875	−	0.318642i	$-0.103227\pi$
$11$	12.6045	+	7.27719i	1.14586	+	0.661563i	0.197985	+	0.980205i	$0.436560\pi$
$12$	−0.196262	−	5.99679i	−0.0163551	−	0.499732i
$13$	0.583005			0.0448466			0.0224233	−	0.999749i	$-0.492862\pi$
$13$	0.583005			0.0448466			0.0224233	+	0.999749i	$0.492862\pi$
$14$		0			0
$15$	1.29150	−	2.41618i	0.0861002	−	0.161079i
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−18.6513	−	10.7684i	−1.09714	−	0.633433i	−0.161670	−	0.986845i	$-0.551688\pi$
$17$	−18.6513	−	10.7684i	−1.09714	−	0.633433i	−0.935468	+	0.353412i	$0.885021\pi$
$18$	−0.832222	−	12.7007i	−0.0462345	−	0.705594i
$19$	−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	$0.971673\pi$
$20$		−	1.82646i		−	0.0913230i
$21$		0			0
$22$	20.5830			0.935591
$23$	33.6284	−	19.4154i	1.46211	−	0.844148i	0.462998	−	0.886359i	$-0.346774\pi$
$23$	33.6284	−	19.4154i	1.46211	−	0.844148i	0.999109	+	0.0422119i	$0.0134405\pi$
$24$	−4.48074	−	7.20576i	−0.186698	−	0.300240i
$25$	−12.0830	+	20.9284i	−0.483320	+	0.837135i
$26$	0.714033	−	0.412247i	0.0274628	−	0.0158557i
$27$	−2.64575	−	26.8701i	−0.0979908	−	0.995187i
$28$		0			0
$29$			35.7676i			1.23337i	0.787212	+	0.616683i	$0.211524\pi$
$29$			35.7676i			1.23337i	−0.787212	+	0.616683i	$0.788476\pi$
$30$	−0.126736	−	3.87243i	−0.00422454	−	0.129081i
$31$	−29.2288	+	50.6257i	−0.942863	+	1.63309i	−0.182889	+	0.983134i	$0.558545\pi$
$31$	−29.2288	+	50.6257i	−0.942863	+	1.63309i	−0.759974	+	0.649953i	$0.774788\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$	43.6398	−	1.42823i	1.32242	−	0.0432798i
$34$	−30.4575			−0.895809
$35$		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
$39$	1.48528	−	0.923586i	0.0380840	−	0.0236817i
$40$	−1.29150	−	2.23695i	−0.0322876	−	0.0559237i
$41$			8.75149i			0.213451i	0.994289	+	0.106725i	$0.0340366\pi$
$41$			8.75149i			0.213451i	−0.994289	+	0.106725i	$0.965963\pi$
$42$		0			0
$43$	−11.7490			−0.273233			−0.136616	−	0.990624i	$-0.543623\pi$
$43$	−11.7490			−0.273233			−0.136616	+	0.990624i	$0.543623\pi$
$44$	25.2089	−	14.5544i	0.572930	−	0.330781i
$45$	−0.537408	−	8.20148i	−0.0119424	−	0.182255i
$46$	27.4575	−	47.5578i	0.596902	−	1.03387i
$47$	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
$50$			34.1759i			0.683518i
$51$	−64.5756	+	2.11341i	−1.26619	+	0.0414395i
$52$	0.583005	−	1.00979i	0.0112116	−	0.0194191i
$53$	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	$0.507195\pi$
$54$	−22.2404	−	31.0381i	−0.411859	−	0.574780i
$55$	13.2915			0.241664
$56$		0			0
$57$	−42.3320	−	22.6274i	−0.742667	−	0.396972i
$58$	25.2915	+	43.8062i	0.436060	+	0.755279i
$59$	50.4179	+	29.1088i	0.854540	+	0.493369i	0.862180	−	0.506602i	$-0.169099\pi$
$59$	50.4179	+	29.1088i	0.854540	+	0.493369i	−0.00764008	+	0.999971i	$0.502432\pi$
$60$	−2.89344	−	4.65313i	−0.0482241	−	0.0775521i
$61$	19.4575	+	33.7014i	0.318976	+	0.552482i	0.980275	−	0.197640i	$-0.0633279\pi$
$61$	19.4575	+	33.7014i	0.318976	+	0.552482i	−0.661299	+	0.750122i	$0.729995\pi$
$62$			82.6714i			1.33341i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	0.461088	−	0.266209i	0.00709365	−	0.00409552i
$66$	52.4377	−	32.6072i	0.794510	−	0.494049i
$67$	−35.2915	+	61.1267i	−0.526739	+	0.912338i	0.472776	+	0.881183i	$0.343252\pi$
$67$	−35.2915	+	61.1267i	−0.526739	+	0.912338i	−0.999515	+	0.0311556i	$0.990081\pi$
$68$	−37.3027	+	21.5367i	−0.548569	+	0.316716i
$69$	54.9150	−	102.737i	0.795870	−	1.48894i
$70$		0			0
$71$		−	17.0279i		−	0.239829i	−0.992784	−	0.119915i	$-0.961738\pi$
$71$		−	17.0279i		−	0.239829i	0.992784	−	0.119915i	$-0.0382621\pi$
$72$	−22.8305	−	11.2592i	−0.317090	−	0.156378i
$73$	36.1660	−	62.6414i	0.495425	−	0.858101i	−0.504561	−	0.863376i	$-0.668346\pi$
$73$	36.1660	−	62.6414i	0.495425	−	0.858101i	0.999986	+	0.00527495i	$0.00167908\pi$
$74$	−24.4949	−	14.1421i	−0.331012	−	0.191110i
$75$	2.37143	+	72.4592i	0.0316191	+	0.966123i
$76$	−32.0000			−0.421053
$77$		0			0
$78$	1.16601	−	2.18141i	0.0149489	−	0.0279667i
$79$	−10.4575	−	18.1129i	−0.132374	−	0.229278i	0.792217	−	0.610239i	$-0.208927\pi$
$79$	−10.4575	−	18.1129i	−0.132374	−	0.229278i	−0.924591	+	0.380961i	$0.875593\pi$
$80$	−3.16352	−	1.82646i	−0.0395440	−	0.0228308i
$81$	−49.3074	−	64.2634i	−0.608733	−	0.793375i
$82$	6.18824	+	10.7183i	0.0754663	+	0.130711i
$83$			145.544i			1.75354i	0.480910	+	0.876770i	$0.340306\pi$
$83$			145.544i			1.75354i	−0.480910	+	0.876770i	$0.659694\pi$
$84$		0			0
$85$	−19.6680			−0.231388
$86$	−14.3895	+	8.30781i	−0.167320	+	0.0966024i
$87$	56.6623	+	91.1222i	0.651291	+	1.04738i
$88$	20.5830	−	35.6508i	0.233898	−	0.405123i
$89$	−46.4635	+	26.8257i	−0.522061	+	0.301412i	−0.737778	−	0.675044i	$-0.764125\pi$
$89$	−46.4635	+	26.8257i	−0.522061	+	0.301412i	0.215716	+	0.976456i	$0.430791\pi$
$90$	−6.45751	−	9.66472i	−0.0717501	−	0.107386i
$91$		0			0
$92$		−	77.6616i		−	0.844148i
$93$	5.73648	+	175.279i	0.0616826	+	1.88472i
$94$	6.00000	−	10.3923i	0.0638298	−	0.110556i
$95$	−12.6541	−	7.30584i	−0.133201	−	0.0769036i
$96$	−16.9615	+	0.555112i	−0.176682	+	0.00578241i
$97$	111.166			1.14604			0.573021	−	0.819541i	$-0.305771\pi$
$97$	111.166			1.14604			0.573021	+	0.819541i	$0.305771\pi$
$98$		0			0
$99$	108.915	−	72.7719i	1.10015	−	0.735070i
$100$	24.1660	+	41.8568i	0.241660	+	0.418568i
$101$	−50.0881	−	28.9184i	−0.495921	−	0.286320i	0.231106	−	0.972929i	$-0.425766\pi$
$101$	−50.0881	−	28.9184i	−0.495921	−	0.286320i	−0.727028	+	0.686608i	$0.759099\pi$
$102$	−77.5942	+	48.2502i	−0.760727	+	0.473041i
$103$	−59.6863	−	103.380i	−0.579478	−	1.00369i	−0.995539	−	0.0943492i	$-0.969923\pi$
$103$	−59.6863	−	103.380i	−0.579478	−	1.00369i	0.416061	−	0.909337i	$-0.363410\pi$
$104$		−	1.64899i		−	0.0158557i
$105$		0			0
$106$	72.0000			0.679245
$107$	−100.885	+	58.2462i	−0.942854	+	0.544357i	−0.890854	−	0.454290i	$-0.849893\pi$
$107$	−100.885	+	58.2462i	−0.942854	+	0.544357i	−0.0520000	+	0.998647i	$0.516560\pi$
$108$	−49.1861	−	22.2875i	−0.455426	−	0.206366i
$109$	−43.9150	+	76.0631i	−0.402890	+	0.697826i	−0.994073	−	0.108711i	$-0.965328\pi$
$109$	−43.9150	+	76.0631i	−0.402890	+	0.697826i	0.591183	+	0.806537i	$0.298661\pi$
$110$	16.2787	−	9.39851i	0.147988	−	0.0854410i
$111$	−52.9150	−	28.2843i	−0.476712	−	0.254813i
$112$		0			0
$113$			69.1763i			0.612180i	0.952003	+	0.306090i	$0.0990208\pi$
$113$			69.1763i			0.612180i	−0.952003	+	0.306090i	$0.900979\pi$
$114$	−67.8459	+	2.22045i	−0.595140	+	0.0194776i
$115$	17.7307	−	30.7105i	0.154180	−	0.267048i
$116$	61.9513	+	35.7676i	0.534063	+	0.308341i
$117$	2.32079	−	4.70589i	0.0198358	−	0.0402213i
$118$	82.3320			0.697729
$119$		0			0
$120$	−6.83399	−	3.65292i	−0.0569499	−	0.0304410i
$121$	45.4150	+	78.6611i	0.375331	+	0.650092i
$122$	47.6610	+	27.5171i	0.390664	+	0.225550i
$123$	13.8639	+	22.2955i	0.112715	+	0.181264i
$124$	58.4575	+	101.251i	0.471432	+	0.816543i
$125$			44.8999i			0.359199i
$126$		0			0
$127$	−27.0850			−0.213268			−0.106634	−	0.994298i	$-0.534007\pi$
$127$	−27.0850			−0.213268			−0.106634	+	0.994298i	$0.534007\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$	−29.9320	+	18.6126i	−0.232031	+	0.144283i
$130$	0.376476	−	0.652076i	0.00289597	−	0.00501597i
$131$	−126.045	+	72.7719i	−0.962173	+	0.555511i	−0.896841	−	0.442353i	$-0.854144\pi$
$131$	−126.045	+	72.7719i	−0.962173	+	0.555511i	−0.0653318	+	0.997864i	$0.520811\pi$
$132$	41.1660	−	77.0146i	0.311864	−	0.583444i
$133$		0			0
$134$			99.8194i			0.744921i
$135$	−14.3617	−	20.0429i	−0.106383	−	0.148466i
$136$	−30.4575	+	52.7540i	−0.223952	+	0.387897i
$137$	−21.4851	−	12.4044i	−0.156825	−	0.0905431i	0.419534	−	0.907740i	$-0.362194\pi$
$137$	−21.4851	−	12.4044i	−0.156825	−	0.0905431i	−0.576359	+	0.817197i	$0.695527\pi$
$138$	−5.38885	−	164.657i	−0.0390497	−	1.19317i
$139$	−146.458			−1.05365			−0.526826	−	0.849973i	$-0.676618\pi$
$139$	−146.458			−1.05365			−0.526826	+	0.849973i	$0.676618\pi$
$140$		0			0
$141$	12.0000	−	22.4499i	0.0851064	−	0.159219i
$142$	−12.0405	−	20.8548i	−0.0847924	−	0.146865i
$143$	7.34847	+	4.24264i	0.0513879	+	0.0296688i
$144$	−35.9230	+	2.35388i	−0.249465	+	0.0163464i
$145$	16.3320	+	28.2879i	0.112635	+	0.195089i
$146$		−	102.293i		−	0.700636i
$147$		0			0
$148$	−40.0000			−0.270270
$149$	190.138	−	109.776i	1.27609	−	0.736753i	0.299966	−	0.953950i	$-0.403025\pi$
$149$	190.138	−	109.776i	1.27609	−	0.736753i	0.976128	+	0.217197i	$0.0696913\pi$
$150$	54.1408	+	87.0672i	0.360939	+	0.580448i
$151$	105.830	−	183.303i	0.700861	−	1.21393i	−0.267303	−	0.963612i	$-0.586133\pi$
$151$	105.830	−	183.303i	0.700861	−	1.21393i	0.968164	−	0.250315i	$-0.0805341\pi$
$152$	−39.1918	+	22.6274i	−0.257841	+	0.148865i
$153$	−161.166	+	107.684i	−1.05337	+	0.703814i
$154$		0			0
$155$			53.3852i			0.344420i
$156$	−0.114422	−	3.49616i	−0.000733471	−	0.0224113i
$157$	104.373	−	180.779i	0.664793	−	1.15146i	−0.314548	−	0.949242i	$-0.601853\pi$
$157$	104.373	−	180.779i	0.664793	−	1.15146i	0.979341	−	0.202214i	$-0.0648137\pi$
$158$	−25.6156	−	14.7892i	−0.162124	−	0.0936023i
$159$	152.653	−	4.99600i	0.960084	−	0.0314214i
$160$	−5.16601			−0.0322876
$161$		0			0
$162$	−105.830	−	43.8406i	−0.653272	−	0.270621i
$163$	−133.498	−	231.225i	−0.819006	−	1.41856i	−0.906415	−	0.422388i	$-0.861192\pi$
$163$	−133.498	−	231.225i	−0.819006	−	1.41856i	0.0874088	−	0.996173i	$-0.472141\pi$
$164$	15.1580	+	8.75149i	0.0924270	+	0.0533627i
$165$	33.8617	−	21.0561i	0.205222	−	0.127613i
$166$	102.915	+	178.254i	0.619970	+	1.07382i
$167$			7.19124i			0.0430613i	0.999768	+	0.0215307i	$0.00685395\pi$
$167$			7.19124i			0.0430613i	−0.999768	+	0.0215307i	$0.993146\pi$
$168$		0			0
$169$	−168.660			−0.997989
$170$	−24.0883	+	13.9074i	−0.141696	+	0.0818080i
$171$	−143.692	+	9.41551i	−0.840303	+	0.0550615i
$172$	−11.7490	+	20.3499i	−0.0683082	+	0.118313i
$173$	166.741	−	96.2682i	0.963823	−	0.556464i	0.0664755	−	0.997788i	$-0.478825\pi$
$173$	166.741	−	96.2682i	0.963823	−	0.556464i	0.897348	+	0.441325i	$0.145491\pi$
$174$	133.830	+	71.5352i	0.769138	+	0.411122i
$175$		0			0
$176$		−	58.2175i		−	0.330781i
$177$	174.559	−	5.71293i	0.986210	−	0.0322765i
$178$	−37.9373	+	65.7093i	−0.213131	+	0.369153i
$179$	37.8134	+	21.8316i	0.211248	+	0.121964i	0.601891	−	0.798578i	$-0.294414\pi$
$179$	37.8134	+	21.8316i	0.211248	+	0.121964i	−0.390643	+	0.920542i	$0.627747\pi$
$180$	−14.7428	−	7.27067i	−0.0819044	−	0.0403926i
$181$	81.0850			0.447983			0.223992	−	0.974591i	$-0.428091\pi$
$181$	81.0850			0.447983			0.223992	+	0.974591i	$0.428091\pi$
$182$		0			0
$183$	102.959	+	55.0342i	0.562620	+	0.300733i
$184$	−54.9150	−	95.1156i	−0.298451	−	0.516933i
$185$	−15.8176	−	9.13230i	−0.0855006	−	0.0493638i
$186$	130.966	+	210.615i	0.704121	+	1.13234i
$187$	−156.727	−	271.459i	−0.838111	−	1.45165i
$188$		−	16.9706i		−	0.0902690i
$189$		0			0
$190$	−20.6640			−0.108758
$191$	46.3818	−	26.7785i	0.242837	−	0.140202i	−0.373643	−	0.927573i	$-0.621892\pi$
$191$	46.3818	−	26.7785i	0.242837	−	0.140202i	0.616480	+	0.787371i	$0.288558\pi$
$192$	−20.3810	+	12.6734i	−0.106151	+	0.0660075i
$193$	55.2470	−	95.6907i	0.286254	−	0.495807i	−0.686658	−	0.726980i	$-0.740923\pi$
$193$	55.2470	−	95.6907i	0.286254	−	0.495807i	0.972913	+	0.231174i	$0.0742565\pi$
$194$	136.150	−	78.6062i	0.701804	−	0.405187i
$195$	0.752953	−	1.40865i	0.00386130	−	0.00722382i
$196$		0			0
$197$		−	86.1469i		−	0.437294i	−0.975804	−	0.218647i	$-0.929836\pi$
$197$		−	86.1469i		−	0.437294i	0.975804	−	0.218647i	$-0.0701643\pi$
$198$	81.9356	−	166.142i	0.413816	−	0.839099i
$199$	−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	$0.237633\pi$
$200$	59.1944	+	34.1759i	0.295972	+	0.170879i
$201$	6.92637	+	211.636i	0.0344595	+	1.05291i
$202$	−81.7935			−0.404918
$203$		0			0
$204$	−60.9150	+	113.962i	−0.298603	+	0.558635i
$205$	3.99606	+	6.92138i	0.0194930	+	0.0337628i
$206$	−146.201	−	84.4091i	−0.709713	−	0.409753i
$207$	−22.8507	−	348.729i	−0.110390	−	1.68468i
$208$	−1.16601	−	2.01959i	−0.00560582	−	0.00970956i
$209$		−	232.870i		−	1.11421i
$210$		0			0
$211$	−61.2549			−0.290308			−0.145154	−	0.989409i	$-0.546368\pi$
$211$	−61.2549			−0.290308			−0.145154	+	0.989409i	$0.546368\pi$
$212$	88.1816	−	50.9117i	0.415951	−	0.240149i
$213$	−26.9752	−	43.3805i	−0.126644	−	0.203664i
$214$	−82.3725	+	142.673i	−0.384918	+	0.666698i
$215$	−9.29207	+	5.36478i	−0.0432189	+	0.0249525i
$216$	−76.0000	+	7.48331i	−0.351852	+	0.0346450i
$217$		0			0
$218$			124.210i			0.569773i
$219$	−7.09800	−	216.880i	−0.0324109	−	0.990319i
$220$	13.2915	−	23.0216i	0.0604159	−	0.104643i
$221$	−10.8738	−	6.27801i	−0.0492029	−	0.0284073i
$222$	−84.8074	+	2.77556i	−0.382015	+	0.0125025i
$223$	−150.494			−0.674861			−0.337431	−	0.941350i	$-0.609558\pi$
$223$	−150.494			−0.674861			−0.337431	+	0.941350i	$0.609558\pi$
$224$		0			0
$225$	120.830	+	180.842i	0.537022	+	0.803742i
$226$	48.9150	+	84.7233i	0.216438	+	0.374882i
$227$	−165.028	−	95.2792i	−0.726997	−	0.419732i	0.0903255	−	0.995912i	$-0.471209\pi$
$227$	−165.028	−	95.2792i	−0.726997	−	0.419732i	−0.817323	+	0.576180i	$0.804543\pi$
$228$	−81.5239	+	50.6938i	−0.357561	+	0.222341i
$229$	−71.4575	−	123.768i	−0.312042	−	0.540472i	0.666763	−	0.745270i	$-0.267679\pi$
$229$	−71.4575	−	123.768i	−0.312042	−	0.540472i	−0.978804	+	0.204798i	$0.934346\pi$
$230$		−	50.1501i		−	0.218044i
$231$		0			0
$232$	101.166			0.436060
$233$	−6.78813	+	3.91913i	−0.0291336	+	0.0168203i	−0.514496	−	0.857493i	$-0.672021\pi$
$233$	−6.78813	+	3.91913i	−0.0291336	+	0.0168203i	0.485362	+	0.874313i	$0.338688\pi$
$234$	−0.485190	−	7.40457i	−0.00207346	−	0.0316434i
$235$	3.87451	−	6.71084i	0.0164873	−	0.0285568i
$236$	100.836	−	58.2175i	0.427270	−	0.246684i
$237$	−55.3360	−	29.5783i	−0.233485	−	0.124803i
$238$		0			0
$239$		−	213.369i		−	0.892756i	−0.894844	−	0.446378i	$-0.852714\pi$
$239$		−	213.369i		−	0.892756i	0.894844	−	0.446378i	$-0.147286\pi$
$240$	−10.9529	+	0.358464i	−0.0456371	+	0.00149360i
$241$	−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	$0.253594\pi$
$242$	111.244	+	64.2265i	0.459684	+	0.265399i
$243$	−227.421	−	85.6068i	−0.935890	−	0.352291i
$244$	77.8301			0.318976
$245$		0			0
$246$	32.7451	+	17.5030i	0.133110	+	0.0711503i
$247$	−4.66404	−	8.07836i	−0.0188828	−	0.0327059i
$248$	143.191	+	82.6714i	0.577383	+	0.333352i
$249$	230.568	+	370.790i	0.925975	+	1.48912i
$250$	31.7490	+	54.9909i	0.126996	+	0.219964i
$251$		−	389.258i		−	1.55083i	−0.631453	−	0.775415i	$-0.717541\pi$
$251$		−	389.258i		−	1.55083i	0.631453	−	0.775415i	$-0.282459\pi$
$252$		0			0
$253$	565.158			2.23383
$254$	−33.1722	+	19.1520i	−0.130599	+	0.0754015i
$255$	−50.1065	+	31.1576i	−0.196496	+	0.122187i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	291.105	−	168.070i	1.13270	−	0.653967i	0.188091	−	0.982152i	$-0.439770\pi$
$257$	291.105	−	168.070i	1.13270	−	0.653967i	0.944614	+	0.328184i	$0.106437\pi$
$258$	−23.4980	+	43.9608i	−0.0910776	+	0.170391i
$259$		0			0
$260$		−	1.06484i		−	0.00409552i
$261$	288.708	+	142.381i	1.10616	+	0.545523i
$262$	−102.915	+	178.254i	−0.392805	+	0.680359i
$263$	−380.127	−	219.467i	−1.44535	−	0.834473i	−0.447151	−	0.894458i	$-0.647561\pi$
$263$	−380.127	−	219.467i	−1.44535	−	0.834473i	−0.998199	+	0.0599849i	$0.980895\pi$
$264$	−4.03965	−	123.432i	−0.0153017	−	0.467545i
$265$	46.4941			0.175449
$266$		0			0
$267$	−75.8745	+	141.948i	−0.284174	+	0.531641i
$268$	70.5830	+	122.253i	0.263369	+	0.456169i
$269$	12.5228	+	7.23004i	0.0465531	+	0.0268775i	0.523096	−	0.852274i	$-0.324777\pi$
$269$	12.5228	+	7.23004i	0.0465531	+	0.0268775i	−0.476543	+	0.879151i	$0.658110\pi$
$270$	−31.7620	−	14.3922i	−0.117637	−	0.0533043i
$271$	30.7712	+	53.2974i	0.113547	+	0.196669i	0.917198	−	0.398432i	$-0.130445\pi$
$271$	30.7712	+	53.2974i	0.113547	+	0.196669i	−0.803651	+	0.595101i	$0.797112\pi$
$272$			86.1469i			0.316716i
$273$		0			0
$274$	−35.0850			−0.128047
$275$	−304.600	+	175.861i	−1.10764	+	0.639493i
$276$	−123.030	−	197.852i	−0.445761	−	0.716856i
$277$	−75.2470	+	130.332i	−0.271650	+	0.470512i	−0.969284	−	0.245942i	$-0.920903\pi$
$277$	−75.2470	+	130.332i	−0.271650	+	0.470512i	0.697634	+	0.716454i	$0.254236\pi$
$278$	−179.373	+	103.561i	−0.645227	+	0.372522i
$279$	292.288	+	437.456i	1.04763	+	1.56794i
$280$		0			0
$281$		−	300.220i		−	1.06840i	−0.845359	−	0.534199i	$-0.820613\pi$
$281$		−	300.220i		−	1.06840i	0.845359	−	0.534199i	$-0.179387\pi$
$282$	−1.17757	−	35.9807i	−0.00417578	−	0.127591i
$283$	49.4170	−	85.5927i	0.174618	−	0.302448i	−0.765411	−	0.643542i	$-0.777464\pi$
$283$	49.4170	−	85.5927i	0.174618	−	0.302448i	0.940029	+	0.341094i	$0.110798\pi$
$284$	−29.4931	−	17.0279i	−0.103849	−	0.0599573i
$285$	−43.8116	+	1.43386i	−0.153725	+	0.00503107i
$286$	12.0000			0.0419580
$287$		0			0
$288$	−42.3320	+	28.2843i	−0.146986	+	0.0982093i
$289$	87.4150	+	151.407i	0.302474	+	0.523901i
$290$	40.0051	+	23.0970i	0.137949	+	0.0796447i
$291$	283.209	−	176.107i	0.973226	−	0.605179i
$292$	−72.3320	−	125.283i	−0.247712	−	0.429050i
$293$			7.15424i			0.0244172i	0.999925	+	0.0122086i	$0.00388621\pi$
$293$			7.15424i			0.0244172i	−0.999925	+	0.0122086i	$0.996114\pi$
$294$		0			0
$295$	53.1660			0.180224
$296$	−48.9898	+	28.2843i	−0.165506	+	0.0955550i
$297$	162.190	−	357.936i	0.546095	−	1.20517i
$298$	155.247	−	268.896i	0.520963	−	0.902335i
$299$	19.6056	−	11.3193i	0.0655704	−	0.0378571i
$300$	127.875	+	68.3518i	0.426248	+	0.227839i
$301$		0			0
$302$		−	299.333i		−	0.991168i
$303$	−173.417	+	5.67556i	−0.572334	+	0.0187312i
$304$	−32.0000	+	55.4256i	−0.105263	+	0.182321i
$305$	30.7771	+	17.7692i	0.100909	+	0.0582596i
$306$	−121.243	+	245.846i	−0.396220	+	0.803420i
$307$	−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
$309$	−315.830	−	168.818i	−1.02210	−	0.546337i
$310$	37.7490	+	65.3832i	0.121771	+	0.210914i
$311$	229.845	+	132.701i	0.739053	+	0.426692i	0.821725	−	0.569885i	$-0.193012\pi$
$311$	229.845	+	132.701i	0.739053	+	0.426692i	−0.0826721	+	0.996577i	$0.526345\pi$
$312$	−2.61230	−	4.20100i	−0.00837274	−	0.0134647i
$313$	129.664	+	224.585i	0.414262	+	0.717523i	0.995351	−	0.0963173i	$-0.0307064\pi$
$313$	129.664	+	224.585i	0.414262	+	0.717523i	−0.581089	+	0.813840i	$0.697373\pi$
$314$		−	295.210i		−	0.940160i
$315$		0			0
$316$	−41.8301			−0.132374
$317$	−32.7559	+	18.9116i	−0.103331	+	0.0596581i	−0.550775	−	0.834654i	$-0.685668\pi$
$317$	−32.7559	+	18.9116i	−0.103331	+	0.0596581i	0.447444	+	0.894312i	$0.352334\pi$
$318$	183.429	−	114.061i	0.576820	−	0.358683i
$319$	−260.288	+	450.831i	−0.815948	+	1.41326i
$320$	−6.32704	+	3.65292i	−0.0197720	+	0.0114154i
$321$	−164.745	+	308.210i	−0.513225	+	0.960155i
$322$		0			0
$323$			344.587i			1.06683i
$324$	−160.615	+	21.1396i	−0.495725	+	0.0652456i
$325$	−7.04446	+	12.2014i	−0.0216752	+	0.0375426i
$326$	−327.002	−	188.795i	−1.00307	−	0.579125i
$327$	8.61883	+	263.349i	0.0263573	+	0.805349i
$328$	24.7530			0.0754663
$329$		0			0
$330$	26.5830	−	49.7322i	0.0805546	−	0.150704i
$331$	−72.7451	−	125.998i	−0.219774	−	0.380659i	0.734965	−	0.678105i	$-0.237199\pi$
$331$	−72.7451	−	125.998i	−0.219774	−	0.380659i	−0.954739	+	0.297446i	$0.903865\pi$
$332$	252.089	+	145.544i	0.759305	+	0.438385i
$333$	−179.615	+	11.7694i	−0.539384	+	0.0353435i
$334$	5.08497	+	8.80743i	0.0152245	+	0.0263696i
$335$			64.4585i			0.192414i
$336$		0			0
$337$	−600.316			−1.78135			−0.890677	−	0.454637i	$-0.849769\pi$
$337$	−600.316			−1.78135			−0.890677	+	0.454637i	$0.849769\pi$
$338$	−206.566	+	119.261i	−0.611141	+	0.352842i
$339$	109.588	+	176.235i	0.323268	+	0.519867i
$340$	−19.6680	+	34.0659i	−0.0578470	+	0.100194i
$341$	−736.826	+	425.407i	−2.16078	+	1.24753i
$342$	−169.328	+	113.137i	−0.495111	+	0.330810i
$343$		0			0
$344$			33.2312i			0.0966024i
$345$	−3.47986	−	106.327i	−0.0100866	−	0.308195i
$346$	136.144	−	235.808i	0.393479	−	0.681526i
$347$	27.4007	+	15.8198i	0.0789644	+	0.0455901i	0.538962	−	0.842330i	$-0.318817\pi$
$347$	27.4007	+	15.8198i	0.0789644	+	0.0455901i	−0.459998	+	0.887920i	$0.652150\pi$
$348$	214.491	−	7.01980i	0.616353	−	0.0201718i
$349$	592.405			1.69744			0.848718	−	0.528846i	$-0.177375\pi$
$349$	592.405			1.69744			0.848718	+	0.528846i	$0.177375\pi$
$350$		0			0
$351$	−1.54249	−	15.6654i	−0.00439455	−	0.0446307i
$352$	−41.1660	−	71.3016i	−0.116949	−	0.202561i
$353$	538.648	+	310.988i	1.52591	+	0.880987i	0.999527	+	0.0307412i	$0.00978678\pi$
$353$	538.648	+	310.988i	1.52591	+	0.880987i	0.526386	+	0.850245i	$0.323547\pi$
$354$	209.751	−	130.429i	0.592516	−	0.368443i
$355$	−7.77518	−	13.4670i	−0.0219019	−	0.0379352i
$356$			107.303i			0.301412i
$357$		0			0
$358$	61.7490			0.172483
$359$	−432.588	+	249.755i	−1.20498	+	0.695696i	−0.961658	−	0.274250i	$-0.911570\pi$
$359$	−432.588	+	249.755i	−1.20498	+	0.695696i	−0.243322	+	0.969946i	$0.578237\pi$
$360$	−23.1973	+	1.52002i	−0.0644369	+	0.00422228i
$361$	52.5000	−	90.9327i	0.145429	−	0.251891i
$362$	99.3084	−	57.3357i	0.274333	−	0.158386i
$363$	240.314	+	128.453i	0.662021	+	0.353865i
$364$		0			0
$365$		−	66.0558i		−	0.180975i
$366$	165.014	−	5.40055i	0.450858	−	0.0147556i
$367$	36.5020	−	63.2233i	0.0994604	−	0.172270i	−0.812001	−	0.583656i	$-0.801622\pi$
$367$	36.5020	−	63.2233i	0.0994604	−	0.172270i	0.911461	+	0.411386i	$0.134955\pi$
$368$	−134.514	−	77.6616i	−0.365527	−	0.211037i
$369$	70.6401	+	34.8374i	0.191437	+	0.0944103i
$370$	−25.8301			−0.0698110
$371$		0			0
$372$	309.328	+	165.343i	0.831527	+	0.444470i
$373$	237.332	+	411.071i	0.636279	+	1.10207i	0.986243	+	0.165304i	$0.0528606\pi$
$373$	237.332	+	411.071i	0.636279	+	1.10207i	−0.349964	+	0.936763i	$0.613806\pi$
$374$	−383.901	−	221.645i	−1.02647	−	0.592634i
$375$	71.1296	+	114.388i	0.189679	+	0.305034i
$376$	−12.0000	−	20.7846i	−0.0319149	−	0.0552782i
$377$			20.8527i			0.0553122i
$378$		0			0
$379$	−223.660			−0.590132			−0.295066	−	0.955477i	$-0.595342\pi$
$379$	−223.660			−0.590132			−0.295066	+	0.955477i	$0.595342\pi$
$380$	−25.3082	+	14.6117i	−0.0666005	+	0.0384518i
$381$	−69.0022	+	42.9075i	−0.181108	+	0.112618i
$382$	37.8706	−	65.5938i	0.0991376	−	0.171711i
$383$	448.753	−	259.088i	1.17168	−	0.676469i	0.217604	−	0.976037i	$-0.430176\pi$
$383$	448.753	−	259.088i	1.17168	−	0.676469i	0.954075	+	0.299568i	$0.0968426\pi$
$384$	−16.0000	+	29.9333i	−0.0416667	+	0.0779512i
$385$		0			0
$386$		−	156.262i		−	0.404824i
$387$	−46.7698	+	94.8355i	−0.120852	+	0.245053i
$388$	111.166	−	192.545i	0.286510	−	0.496250i
$389$	38.2249	+	22.0691i	0.0982644	+	0.0567330i	0.548327	−	0.836264i	$-0.315265\pi$
$389$	38.2249	+	22.0691i	0.0982644	+	0.0567330i	−0.450062	+	0.892997i	$0.648598\pi$
$390$	−0.0738878	−	2.25765i	−0.000189456	−	0.00578885i
$391$	−836.288			−2.13884
$392$		0			0
$393$	−205.830	+	385.073i	−0.523741	+	0.979829i
$394$	−60.9150	−	105.508i	−0.154607	−	0.267787i
$395$	−16.5413	−	9.55012i	−0.0418767	−	0.0241775i
$396$	−17.1296	−	261.418i	−0.0432566	−	0.660147i
$397$	149.708	+	259.303i	0.377099	+	0.653155i	0.990639	−	0.136509i	$-0.0435881\pi$
$397$	149.708	+	259.303i	0.377099	+	0.653155i	−0.613539	+	0.789664i	$0.710255\pi$
$398$			124.451i			0.312690i
$399$		0			0
$400$	96.6640			0.241660
$401$	−239.896	+	138.504i	−0.598245	+	0.345397i	−0.768351	−	0.640029i	$-0.778922\pi$
$401$	−239.896	+	138.504i	−0.598245	+	0.345397i	0.170106	+	0.985426i	$0.445589\pi$
$402$	158.132	+	254.302i	0.393363	+	0.632592i
$403$	−17.0405	+	29.5150i	−0.0422842	+	0.0732383i
$404$	−100.176	+	57.8367i	−0.247961	+	0.143160i
$405$	−68.3399	−	28.3101i	−0.168740	−	0.0699016i
$406$		0			0
$407$		−	291.088i		−	0.715203i
$408$	5.97764	+	182.647i	0.0146511	+	0.447665i
$409$	−370.490	+	641.708i	−0.905844	+	1.56897i	−0.0860635	+	0.996290i	$0.527429\pi$
$409$	−370.490	+	641.708i	−0.905844	+	1.56897i	−0.819780	+	0.572678i	$0.805905\pi$
$410$	9.78832	+	5.65129i	0.0238739	+	0.0137836i
$411$	−74.3866	+	2.43451i	−0.180989	+	0.00592338i
$412$	−238.745			−0.579478
$413$		0			0
$414$	−274.575	−	410.946i	−0.663225	−	0.992624i
$415$	66.4575	+	115.108i	0.160139	+	0.277368i
$416$	−2.85613	−	1.64899i	−0.00686570	−	0.00396391i
$417$	−373.118	+	232.015i	−0.894768	+	0.556391i
$418$	−164.664	−	285.206i	−0.393933	−	0.682312i
$419$			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
$421$	281.150			0.667815			0.333908	−	0.942606i	$-0.391633\pi$
$421$	281.150			0.667815			0.333908	+	0.942606i	$0.391633\pi$
$422$	−75.0217	+	43.3138i	−0.177776	+	0.102639i
$423$	−4.99333	−	76.2041i	−0.0118046	−	0.180152i
$424$	72.0000	−	124.708i	0.169811	−	0.294122i
$425$	450.729	−	260.228i	1.06054	−	0.612302i
$426$	−63.7124	−	34.0557i	−0.149560	−	0.0799430i
$427$		0			0
$428$			232.985i			0.544357i
$429$	25.4422	−	0.832667i	0.0593059	−	0.00194095i
$430$	−7.58694	+	13.1410i	−0.0176441	+	0.0305604i
$431$	485.148	+	280.100i	1.12563	+	0.649885i	0.942833	−	0.333266i	$-0.108151\pi$
$431$	485.148	+	280.100i	1.12563	+	0.649885i	0.182800	+	0.983150i	$0.441484\pi$
$432$	−87.7891	+	62.9053i	−0.203216	+	0.145614i
$433$	543.004			1.25405			0.627025	−	0.778999i	$-0.284272\pi$
$433$	543.004			1.25405			0.627025	+	0.778999i	$0.284272\pi$
$434$		0			0
$435$	86.4209	+	46.1939i	0.198669	+	0.106193i
$436$	87.8301	+	152.126i	0.201445	+	0.348913i
$437$	−538.055	−	310.646i	−1.23125	−	0.710861i
$438$	−162.051	−	260.604i	−0.369978	−	0.594985i
$439$	171.085	+	296.328i	0.389715	+	0.675007i	0.992411	−	0.122964i	$-0.0392401\pi$
$439$	171.085	+	296.328i	0.389715	+	0.675007i	−0.602696	+	0.797971i	$0.705907\pi$
$440$		−	37.5940i		−	0.0854410i
$441$		0			0
$442$	−17.7569			−0.0401740
$443$	346.251	−	199.908i	0.781604	−	0.451259i	−0.0553944	−	0.998465i	$-0.517642\pi$
$443$	346.251	−	199.908i	0.781604	−	0.451259i	0.836998	+	0.547205i	$0.184308\pi$
$444$	−101.905	+	63.3672i	−0.229515	+	0.142719i
$445$	−24.4980	+	42.4318i	−0.0550518	+	0.0953524i
$446$	−184.317	+	106.415i	−0.413267	+	0.238600i
$447$	310.494	−	580.881i	0.694618	−	1.29951i
$448$		0			0
$449$			737.040i			1.64151i	0.571277	+	0.820757i	$0.306448\pi$
$449$			737.040i			1.64151i	−0.571277	+	0.820757i	$0.693552\pi$
$450$	275.860	+	136.045i	0.613023	+	0.302323i
$451$	−63.6863	+	110.308i	−0.141211	+	0.244585i
$452$	119.817	+	69.1763i	0.265082	+	0.153045i
$453$	−20.7704	−	634.641i	−0.0458507	−	1.40097i
$454$	−269.490			−0.593591
$455$		0			0
$456$	−64.0000	+	119.733i	−0.140351	+	0.262572i
$457$	−332.668	−	576.198i	−0.727939	−	1.26083i	−0.957753	−	0.287592i	$-0.907145\pi$
$457$	−332.668	−	576.198i	−0.727939	−	1.26083i	0.229814	−	0.973235i	$-0.426188\pi$
$458$	−175.034	−	101.056i	−0.382171	−	0.220647i
$459$	−240.000	+	529.653i	−0.522875	+	1.15393i
$460$	−35.4615	−	61.4210i	−0.0770901	−	0.133524i
$461$		−	318.865i		−	0.691682i	−0.938293	−	0.345841i	$-0.887594\pi$
$461$		−	318.865i		−	0.691682i	0.938293	−	0.345841i	$-0.112406\pi$
$462$		0			0
$463$	402.332			0.868968			0.434484	−	0.900680i	$-0.356931\pi$
$463$	402.332			0.868968			0.434484	+	0.900680i	$0.356931\pi$
$464$	123.903	−	71.5352i	0.267031	−	0.154171i
$465$	84.5718	+	136.005i	0.181875	+	0.292484i
$466$	−5.54249	+	9.59987i	−0.0118937	+	0.0206006i
$467$	−603.695	+	348.544i	−1.29271	+	0.746346i	−0.979134	−	0.203217i	$-0.934860\pi$
$467$	−603.695	+	348.544i	−1.29271	+	0.746346i	−0.313575	+	0.949563i	$0.601527\pi$
$468$	−5.83005	−	8.72562i	−0.0124574	−	0.0186445i
$469$		0			0
$470$		−	10.9588i		−	0.0233165i
$471$	−20.4843	−	625.900i	−0.0434911	−	1.32887i
$472$	82.3320	−	142.603i	0.174432	−	0.302126i
$473$	−148.090	−	85.4998i	−0.313087	−	0.180761i
$474$	−88.6875	+	2.90254i	−0.187104	+	0.00612351i
$475$	386.656			0.814013
$476$		0			0
$477$	380.988	−	254.558i	0.798717	−	0.533665i
$478$	−150.875	−	261.322i	−0.315637	−	0.546699i
$479$	141.862	+	81.9042i	0.296163	+	0.170990i	0.640718	−	0.767776i	$-0.278637\pi$
$479$	141.862	+	81.9042i	0.296163	+	0.170990i	−0.344555	+	0.938766i	$0.611970\pi$
$480$	−13.1610	+	8.18390i	−0.0274188	+	0.0170498i
$481$	−5.83005	−	10.0979i	−0.0121207	−	0.0209937i
$482$			183.848i			0.381427i
$483$		0			0
$484$	181.660			0.375331
$485$	87.9190	−	50.7601i	0.181276	−	0.104660i
$486$	−339.066	+	55.9647i	−0.697667	+	0.115154i
$487$	51.7490	−	89.6319i	0.106261	−	0.184049i	−0.807992	−	0.589194i	$-0.799445\pi$
$487$	51.7490	−	89.6319i	0.106261	−	0.184049i	0.914253	+	0.405145i	$0.132779\pi$
$488$	95.3220	−	55.0342i	0.195332	−	0.112775i
$489$	−706.405	−	377.589i	−1.44459	−	0.772167i
$490$		0			0
$491$		−	570.094i		−	1.16109i	−0.814229	−	0.580544i	$-0.802840\pi$
$491$		−	570.094i		−	1.16109i	0.814229	−	0.580544i	$-0.197160\pi$
$492$	52.4808	−	1.71758i	0.106668	−	0.00349102i
$493$	385.158	−	667.113i	0.781254	−	1.35317i
$494$	−11.4245	−	6.59595i	−0.0231266	−	0.0133521i
$495$	52.9100	−	107.286i	0.106889	−	0.216740i
$496$	233.830			0.471432
$497$		0			0
$498$	544.575	+	291.088i	1.09352	+	0.584513i
$499$	243.830	+	422.326i	0.488637	+	0.846345i	0.999915	−	0.0130711i	$-0.00416078\pi$
$499$	243.830	+	422.326i	0.488637	+	0.846345i	−0.511277	+	0.859416i	$0.670827\pi$
$500$	77.7689	+	44.8999i	0.155538	+	0.0897998i
$501$	11.3922	+	18.3205i	0.0227390	+	0.0365680i
$502$	−275.247	−	476.742i	−0.548301	−	0.949685i
$503$			97.9412i			0.194714i	0.995250	+	0.0973571i	$0.0310389\pi$
$503$			97.9412i			0.194714i	−0.995250	+	0.0973571i	$0.968961\pi$
$504$		0			0
$505$	−52.8182			−0.104591
$506$	692.175	−	399.627i	1.36793	−	0.789777i
$507$	−429.682	+	267.188i	−0.847499	+	0.526998i
$508$	−27.0850	+	46.9126i	−0.0533169	+	0.0923475i
$509$	275.486	−	159.052i	0.541230	−	0.312479i	−0.204347	−	0.978898i	$-0.565507\pi$
$509$	275.486	−	159.052i	0.541230	−	0.312479i	0.745577	+	0.666419i	$0.232174\pi$
$510$	−39.3360	+	73.5908i	−0.0771293	+	0.144296i
$511$		0			0
$512$			22.6274i			0.0441942i
$513$	−351.156	+	251.621i	−0.684515	+	0.490489i
$514$	237.686	−	411.685i	0.462425	−	0.800943i
$515$	−94.4094	−	54.5073i	−0.183319	−	0.105839i
$516$	2.30588	+	70.4564i	0.00446876	+	0.136543i
$517$	123.498			0.238874
$518$		0			0
$519$	272.288	−	509.403i	0.524639	−	0.981509i
$520$	−0.752953	−	1.30415i	−0.00144799	−	0.00250799i
$521$	−629.730	−	363.575i	−1.20870	−	0.697840i	−0.246221	−	0.969214i	$-0.579189\pi$
$521$	−629.730	−	363.575i	−1.20870	−	0.697840i	−0.962474	+	0.271373i	$0.912522\pi$
$522$	454.273	−	29.7666i	0.870255	−	0.0570241i
$523$	−103.812	−	179.807i	−0.198493	−	0.343800i	0.749547	−	0.661951i	$-0.230271\pi$
$523$	−103.812	−	179.807i	−0.198493	−	0.343800i	−0.948040	+	0.318151i	$0.896938\pi$
$524$			291.088i			0.555511i
$525$		0			0
$526$	−620.745			−1.18012
$527$	1090.31	−	629.491i	2.06890	−	1.19448i
$528$	−92.2271	−	148.316i	−0.174673	−	0.280902i
$529$	489.415	−	847.692i	0.925170	−	1.60244i
$530$	56.9434	−	32.8763i	0.107440	−	0.0620307i
$531$	435.660	−	291.088i	0.820452	−	0.548188i
$532$		0			0
$533$			5.10216i			0.00957254i
$534$	7.44562	+	227.502i	0.0139431	+	0.426033i
$535$	−53.1922	+	92.1316i	−0.0994246	+	0.172209i
$536$	172.892	+	99.8194i	0.322560	+	0.186230i
$537$	130.919	−	4.28470i	0.243798	−	0.00797896i
$538$	20.4496			0.0380105
$539$		0			0
$540$	−49.0771	+	4.83236i	−0.0908835	+	0.00894882i
$541$	−512.575	−	887.806i	−0.947459	−	1.64105i	−0.750752	−	0.660584i	$-0.770309\pi$
$541$	−512.575	−	887.806i	−0.947459	−	1.64105i	−0.196707	−	0.980462i	$-0.563025\pi$
$542$	75.3738	+	43.5171i	0.139066	+	0.0802899i
$543$	206.574	−	128.453i	0.380430	−	0.236562i
$544$	60.9150	+	105.508i	0.111976	+	0.193948i
$545$			80.2091i			0.147173i
$546$		0			0
$547$	−560.089			−1.02393			−0.511964	−	0.859007i	$-0.671082\pi$
$547$	−560.089			−1.02393			−0.511964	+	0.859007i	$0.671082\pi$
$548$	−42.9701	+	24.8088i	−0.0784127	+	0.0452716i
$549$	349.486	−	22.9003i	0.636586	−	0.0417128i
$550$	−248.705	+	430.769i	−0.452190	+	0.783216i
$551$	495.610	−	286.141i	0.899474	−	0.519312i
$552$	−290.583	−	155.323i	−0.526418	−	0.281383i
$553$		0			0
$554$			212.831i			0.384171i
$555$	−54.7645	+	1.79232i	−0.0986748	+	0.00322941i
$556$	−146.458	+	253.672i	−0.263413	+	0.456244i
$557$	498.575	+	287.853i	0.895108	+	0.516791i	0.875610	−	0.483019i	$-0.160460\pi$
$557$	498.575	+	287.853i	0.895108	+	0.516791i	0.0194983	+	0.999810i	$0.493793\pi$
$558$	667.306	+	329.093i	1.19589	+	0.589773i
$559$	−6.84974			−0.0122536
$560$		0			0
$561$	−829.320	−	443.290i	−1.47829	−	0.790179i
$562$	−212.288	−	367.693i	−0.377736	−	0.654258i
$563$	405.783	+	234.279i	0.720751	+	0.416126i	0.815029	−	0.579420i	$-0.196721\pi$
$563$	405.783	+	234.279i	0.720751	+	0.416126i	−0.0942781	+	0.995546i	$0.530054\pi$
$564$	−26.8844	−	43.2346i	−0.0476675	−	0.0766570i
$565$	31.5869	+	54.7102i	0.0559061	+	0.0968322i
$566$		−	139.772i		−	0.246948i
$567$		0			0
$568$	−48.1621			−0.0847924
$569$	438.603	−	253.227i	0.770831	−	0.445039i	−0.0623401	−	0.998055i	$-0.519856\pi$
$569$	438.603	−	253.227i	0.770831	−	0.445039i	0.833171	+	0.553016i	$0.186523\pi$
$570$	−52.6441	+	32.7356i	−0.0923581	+	0.0574308i
$571$	−16.4575	+	28.5052i	−0.0288223	+	0.0499216i	−0.880077	−	0.474831i	$-0.842509\pi$
$571$	−16.4575	+	28.5052i	−0.0288223	+	0.0499216i	0.851254	+	0.524753i	$0.175842\pi$
$572$	14.6969	−	8.48528i	0.0256939	−	0.0148344i
$573$	75.7411	−	141.699i	0.132183	−	0.247293i
$574$		0			0
$575$			938.385i			1.63197i
$576$	−31.8459	+	64.5743i	−0.0552881	+	0.112108i
$577$	−126.077	+	218.372i	−0.218505	+	0.378461i	−0.954351	−	0.298688i	$-0.903451\pi$
$577$	−126.077	+	218.372i	−0.218505	+	0.378461i	0.735846	+	0.677148i	$0.236785\pi$
$578$	214.122	+	123.624i	0.370454	+	0.213882i
$579$	−10.8429	−	331.305i	−0.0187269	−	0.572202i
$580$	65.3281			0.112635
$581$		0			0
$582$	222.332	−	415.945i	0.382014	−	0.714682i
$583$	370.494	+	641.715i	0.635496	+	1.10071i
$584$	−177.177	−	102.293i	−0.303384	−	0.175159i
$585$	−0.313312	−	4.78151i	−0.000535576	−	0.00817352i
$586$	5.05881	+	8.76211i	0.00863278	+	0.0149524i
$587$			366.882i			0.625012i	0.949916	+	0.312506i	$0.101168\pi$
$587$			366.882i			0.625012i	−0.949916	+	0.312506i	$0.898832\pi$
$588$		0			0
$589$	935.320			1.58798
$590$	65.1148	−	37.5940i	0.110364	−	0.0637187i
$591$	−136.472	−	219.469i	−0.230917	−	0.371353i
$592$	−40.0000	+	69.2820i	−0.0675676	+	0.117030i
$593$	−537.591	+	310.378i	−0.906562	+	0.523404i	−0.879323	−	0.476225i	$-0.842005\pi$
$593$	−537.591	+	310.378i	−0.906562	+	0.523404i	−0.0272383	+	0.999629i	$0.508671\pi$
$594$	−54.4575	−	553.067i	−0.0916793	−	0.931088i
$595$		0			0
$596$		−	439.105i		−	0.736753i
$597$	8.63551	+	263.859i	0.0144648	+	0.441974i
$598$	16.0079	−	27.7265i	0.0267690	−	0.0463653i
$599$	−22.8187	−	13.1744i	−0.0380947	−	0.0219940i	0.480832	−	0.876813i	$-0.340335\pi$
$599$	−22.8187	−	13.1744i	−0.0380947	−	0.0219940i	−0.518926	+	0.854819i	$0.673668\pi$
$600$	204.946	−	6.70742i	0.341576	−	0.0111790i
$601$	−930.470			−1.54820			−0.774102	−	0.633061i	$-0.781798\pi$
$601$	−930.470			−1.54820			−0.774102	+	0.633061i	$0.781798\pi$
$602$		0			0
$603$	352.915	+	528.195i	0.585265	+	0.875945i
$604$	−211.660	−	366.606i	−0.350431	−	0.606964i
$605$	71.8357	+	41.4744i	0.118737	+	0.0685527i
$606$	−208.379	+	129.576i	−0.343859	+	0.213821i
$607$	108.073	+	187.188i	0.178045	+	0.308383i	0.941211	−	0.337820i	$-0.109689\pi$
$607$	108.073	+	187.188i	0.178045	+	0.308383i	−0.763166	+	0.646202i	$0.776356\pi$
$608$			90.5097i			0.148865i
$609$		0			0
$610$	50.2589			0.0823916
$611$	4.28420	−	2.47348i	0.00701178	−	0.00404825i
$612$	25.3474	+	386.831i	0.0414173	+	0.632077i
$613$	134.417	−	232.817i	0.219277	−	0.379799i	−0.735310	−	0.677731i	$-0.762963\pi$
$613$	134.417	−	232.817i	0.219277	−	0.379799i	0.954587	+	0.297932i	$0.0962967\pi$
$614$	−129.615	+	74.8331i	−0.211099	+	0.121878i
$615$	21.1452	+	11.3026i	0.0343824	+	0.0183782i
$616$		0			0
$617$			531.338i			0.861163i	0.902552	+	0.430582i	$0.141692\pi$
$617$			531.338i			0.861163i	−0.902552	+	0.430582i	$0.858308\pi$
$618$	−506.184	+	16.5663i	−0.819068	+	0.0268063i
$619$	212.601	−	368.236i	0.343459	−	0.594889i	−0.641613	−	0.767028i	$-0.721735\pi$
$619$	212.601	−	368.236i	0.343459	−	0.594889i	0.985073	+	0.172139i	$0.0550679\pi$
$620$	92.4658	+	53.3852i	0.149138	+	0.0861051i
$621$	−610.665	−	852.230i	−0.983358	−	1.37235i
$622$	375.336			0.603434
$623$		0			0
$624$	−6.16995	−	3.29798i	−0.00988774	−	0.00528522i
$625$	−281.573	−	487.699i	−0.450517	−	0.780318i
$626$	317.611	+	183.373i	0.507365	+	0.292928i
$627$	−368.908	−	593.265i	−0.588371	−	0.946196i
$628$	−208.745	−	361.557i	−0.332397	−	0.575728i
$629$			430.734i			0.684792i
$630$		0			0
$631$	−453.490			−0.718685			−0.359342	−	0.933206i	$-0.616999\pi$
$631$	−453.490			−0.718685			−0.359342	+	0.933206i	$0.616999\pi$
$632$	−51.2311	+	29.5783i	−0.0810619	+	0.0468011i
$633$	−156.054	+	97.0389i	−0.246531	+	0.153300i
$634$	−26.7451	+	46.3238i	−0.0421847	+	0.0730660i
$635$	−21.4210	+	12.3674i	−0.0337338	+	0.0194762i
$636$	144.000	−	269.399i	0.226415	−	0.423584i
$637$		0			0
$638$			736.204i			1.15393i
$639$	−137.445	−	67.7835i	−0.215094	−	0.106077i
$640$	−5.16601	+	8.94779i	−0.00807189	+	0.0139809i
$641$	−401.364	−	231.728i	−0.626153	−	0.361510i	0.153108	−	0.988210i	$-0.451072\pi$
$641$	−401.364	−	231.728i	−0.626153	−	0.361510i	−0.779261	+	0.626700i	$0.784405\pi$
$642$	16.1666	+	493.971i	0.0251816	+	0.769425i
$643$	−820.988			−1.27681			−0.638405	−	0.769701i	$-0.720405\pi$
$643$	−820.988			−1.27681			−0.638405	+	0.769701i	$0.720405\pi$
$644$		0			0
$645$	−15.1739	+	28.3877i	−0.0235254	+	0.0440120i
$646$	243.660	+	422.032i	0.377183	+	0.653300i
$647$	−863.133	−	498.330i	−1.33405	−	0.770216i	−0.348136	−	0.937444i	$-0.613185\pi$
$647$	−863.133	−	498.330i	−1.33405	−	0.770216i	−0.985918	+	0.167228i	$0.946518\pi$
$648$	−181.764	+	139.462i	−0.280500	+	0.215220i
$649$	423.660	+	733.801i	0.652789	+	1.13066i
$650$			19.9247i			0.0306534i
$651$		0			0
$652$	−533.992			−0.819006
$653$	−309.692	+	178.801i	−0.474261	+	0.273815i	−0.718022	−	0.696021i	$-0.754952\pi$
$653$	−309.692	+	178.801i	−0.474261	+	0.273815i	0.243761	+	0.969835i	$0.421619\pi$
$654$	196.772	+	316.441i	0.300874	+	0.483855i
$655$	−66.4575	+	115.108i	−0.101462	+	0.175737i
$656$	30.3161	−	17.5030i	0.0462135	−	0.0266814i
$657$	−361.660	−	541.283i	−0.550472	−	0.823871i
$658$		0			0
$659$		−	131.562i		−	0.199640i	−0.995006	−	0.0998198i	$-0.968173\pi$
$659$		−	131.562i		−	0.199640i	0.995006	−	0.0998198i	$-0.0318266\pi$
$660$	−2.60861	−	79.7063i	−0.00395244	−	0.120767i
$661$	−125.458	+	217.299i	−0.189800	+	0.328742i	−0.945183	−	0.326540i	$-0.894117\pi$
$661$	−125.458	+	217.299i	−0.189800	+	0.328742i	0.755384	+	0.655283i	$0.227450\pi$
$662$	−178.188	−	102.877i	−0.269167	−	0.155403i
$663$	−37.6479	+	1.23213i	−0.0567842	+	0.00185842i
$664$	411.660			0.619970
$665$		0			0
$666$	−211.660	+	141.421i	−0.317808	+	0.212344i
$667$	694.442	+	1202.81i	1.04114	+	1.80331i
$668$	12.4556	+	7.19124i	0.0186461	+	0.0107653i
$669$	−383.402	+	238.410i	−0.573097	+	0.356368i
$670$	45.5791	+	78.9453i	0.0680285	+	0.117829i
$671$			566.384i			0.844090i
$672$		0			0
$673$	196.502			0.291979			0.145990	−	0.989286i	$-0.453363\pi$
$673$	196.502			0.291979			0.145990	+	0.989286i	$0.453363\pi$
$674$	−735.234	+	424.488i	−1.09085	+	0.629804i
$675$	594.315	+	269.300i	0.880467	+	0.398963i
$676$	−168.660	+	292.128i	−0.249497	+	0.432142i
$677$	−46.9245	+	27.0919i	−0.0693125	+	0.0400176i	−0.534256	−	0.845323i	$-0.679408\pi$
$677$	−46.9245	+	27.0919i	−0.0693125	+	0.0400176i	0.464943	+	0.885340i	$0.346075\pi$
$678$	258.834	+	138.353i	0.381761	+	0.204060i
$679$		0			0
$680$			55.6294i			0.0818080i
$681$	−571.369	+	18.6996i	−0.839015	+	0.0274591i
$682$	−601.616	+	1042.03i	−0.882134	+	1.52790i
$683$	648.659	+	374.503i	0.949720	+	0.548321i	0.892994	−	0.450069i	$-0.148601\pi$
$683$	648.659	+	374.503i	0.949720	+	0.548321i	0.0567258	+	0.998390i	$0.481934\pi$
$684$	−127.384	+	258.297i	−0.186233	+	0.377627i
$685$	−22.6562			−0.0330747
$686$		0			0
$687$	−378.118	−	202.112i	−0.550390	−	0.294196i
$688$	23.4980	+	40.6998i	0.0341541	+	0.0591567i
$689$	25.7052	+	14.8409i	0.0373079	+	0.0215398i
$690$	−79.4468	−	127.763i	−0.115140	−	0.185164i
$691$	237.569	+	411.481i	0.343804	+	0.595486i	0.985136	−	0.171778i	$-0.0549510\pi$
$691$	237.569	+	411.481i	0.343804	+	0.595486i	−0.641332	+	0.767264i	$0.721618\pi$
$692$		−	385.073i		−	0.556464i
$693$		0			0
$694$	44.7451			0.0644742
$695$	−115.830	+	66.8747i	−0.166662	+	0.0962226i
$696$	257.733	−	160.265i	0.370305	−	0.230266i
$697$	94.2392	−	163.227i	0.135207	−	0.234185i
$698$	725.545	−	418.894i	1.03946	−	0.600134i
$699$	−11.0850	+	20.7381i	−0.0158583	+	0.0296682i
$700$		0			0
$701$		−	1251.49i		−	1.78529i	−0.450760	−	0.892645i	$-0.648847\pi$
$701$		−	1251.49i		−	1.78529i	0.450760	−	0.892645i	$-0.351153\pi$
$702$	−12.9663	−	18.0954i	−0.0184704	−	0.0257769i
$703$	−160.000	+	277.128i	−0.227596	+	0.394208i
$704$	−100.836	−	58.2175i	−0.143233	−	0.0826954i
$705$	−0.760417	−	23.2346i	−0.00107861	−	0.0329569i
$706$	879.608			1.24590
$707$		0			0
$708$	164.664	−	308.058i	0.232576	−	0.435110i
$709$	8.25492	+	14.2979i	0.0116430	+	0.0201664i	0.871788	−	0.489883i	$-0.162960\pi$
$709$	8.25492	+	14.2979i	0.0116430	+	0.0201664i	−0.860145	+	0.510049i	$0.829627\pi$
$710$	−19.0452	−	10.9958i	−0.0268243	−	0.0154870i
$711$	−187.832	+	12.3079i	−0.264181	+	0.0173106i
$712$	75.8745	+	131.419i	0.106565	+	0.184577i
$713$			2269.95i			3.18366i
$714$		0			0
$715$	7.74902			0.0108378
$716$	75.6268	−	43.6631i	0.105624	−	0.0609820i
$717$	−338.015	−	543.583i	−0.471429	−	0.758135i
$718$	−353.207	+	611.772i	−0.491931	+	0.852050i
$719$	−1149.72	+	663.793i	−1.59906	+	0.923217i	−0.607390	+	0.794404i	$0.707783\pi$
$719$	−1149.72	+	663.793i	−1.59906	+	0.923217i	−0.991669	+	0.128813i	$0.958883\pi$
$720$	−27.3360	+	18.2646i	−0.0379666	+	0.0253675i
$721$		0			0
$722$		−	148.492i		−	0.205668i
$723$	12.7570	+	389.791i	0.0176445	+	0.539130i
$724$	81.0850	−	140.443i	0.111996	−	0.193982i
$725$	−748.558	−	432.180i	−1.03249	−	0.596110i
$726$	385.153	−	12.6052i	0.530514	−	0.0173625i
$727$	202.782			0.278929			0.139465	−	0.990227i	$-0.455462\pi$
$727$	202.782			0.278929			0.139465	+	0.990227i	$0.455462\pi$
$728$		0			0
$729$	−715.000	+	142.183i	−0.980796	+	0.195038i
$730$	−46.7085	−	80.9015i	−0.0639842	−	0.110824i
$731$	219.135	+	126.518i	0.299774	+	0.173075i
$732$	198.281	−	123.297i	0.270876	−	0.168438i
$733$	−291.280	−	504.511i	−0.397380	−	0.688283i	0.596022	−	0.802968i	$-0.296747\pi$
$733$	−291.280	−	504.511i	−0.397380	−	0.688283i	−0.993402	+	0.114686i	$0.963414\pi$
$734$		−	103.243i		−	0.140658i
$735$		0			0
$736$	−219.660			−0.298451
$737$	−889.661	+	513.646i	−1.20714	+	0.696942i
$738$	111.150	−	7.28318i	0.150610	−	0.00986881i
$739$	128.405	−	222.404i	0.173755	−	0.300953i	−0.765975	−	0.642871i	$-0.777743\pi$
$739$	128.405	−	222.404i	0.173755	−	0.300953i	0.939730	+	0.341918i	$0.111076\pi$
$740$	−31.6352	+	18.2646i	−0.0427503	+	0.0246819i
$741$	−24.6798	−	13.1919i	−0.0333061	−	0.0178028i
$742$		0			0
$743$			573.256i			0.771542i	0.922595	+	0.385771i	$0.126064\pi$
$743$			573.256i			0.771542i	−0.922595	+	0.385771i	$0.873936\pi$
$744$	495.763	−	16.2252i	0.666348	−	0.0218081i
$745$	100.251	−	173.640i	0.134565	−	0.233074i
$746$	581.342	+	335.638i	0.779279	+	0.449917i
$747$	1174.80	+	579.372i	1.57269	+	0.775599i
$748$	−626.907			−0.838111
$749$		0			0
$750$	168.000	+	89.7998i	0.224000	+	0.119733i
$751$	289.542	+	501.502i	0.385543	+	0.667779i	0.991844	−	0.127455i	$-0.0406809\pi$
$751$	289.542	+	501.502i	0.385543	+	0.667779i	−0.606302	+	0.795235i	$0.707348\pi$
$752$	−29.3939	−	16.9706i	−0.0390876	−	0.0225672i
$753$	−616.655	−	991.682i	−0.818931	−	1.31697i
$754$	14.7451	+	25.5392i	0.0195558	+	0.0338717i
$755$		−	193.294i		−	0.256019i
$756$		0			0
$757$	1167.13			1.54179			0.770895	−	0.636963i	$-0.219809\pi$
$757$	1167.13			1.54179			0.770895	+	0.636963i	$0.219809\pi$
$758$	−273.927	+	158.152i	−0.361381	+	0.208643i
$759$	1439.81	−	895.313i	1.89698	−	1.17960i
$760$	−20.6640	+	35.7912i	−0.0271895	+	0.0470936i
$761$	−693.660	+	400.485i	−0.911511	+	0.526261i	−0.880917	−	0.473271i	$-0.843073\pi$
$761$	−693.660	+	400.485i	−0.911511	+	0.526261i	−0.0305942	+	0.999532i	$0.509740\pi$
$762$	−54.1699	+	101.343i	−0.0710892	+	0.132996i
$763$		0			0
$764$		−	107.114i		−	0.140202i
$765$	−78.2931	+	158.756i	−0.102344	+	0.207524i
$766$	366.405	−	634.632i	0.478336	−	0.828502i
$767$	29.3939	+	16.9706i	0.0383232	+	0.0221259i
$768$	1.57009	+	47.9743i	0.00204439	+	0.0624666i
$769$	242.680			0.315578			0.157789	−	0.987473i	$-0.449563\pi$
$769$	242.680			0.315578			0.157789	+	0.987473i	$0.449563\pi$
$770$		0			0
$771$	475.373	−	889.341i	0.616566	−	1.15349i
$772$	−110.494	−	191.381i	−0.143127	−	0.247903i
$773$	1093.64	+	631.414i	1.41480	+	0.816836i	0.995836	−	0.0911667i	$-0.0290596\pi$
$773$	1093.64	+	631.414i	1.41480	+	0.816836i	0.418965	+	0.908002i	$0.362393\pi$
$774$	9.77779	+	149.221i	0.0126328	+	0.192791i
$775$	−706.342	−	1223.42i	−0.911410	−	1.57861i
$776$		−	314.425i		−	0.405187i
$777$		0			0
$778$	62.4209			0.0802326
$779$	121.264	−	70.0119i	0.155667	−	0.0898741i
$780$	−1.68689	−	2.71280i	−0.00216268	−	0.00347795i
$781$	123.915	−	214.627i	0.158662	−	0.274811i
$782$	−1024.24	+	591.345i	−1.30977	+	0.756195i
$783$	961.077	−	94.6321i	1.22743	−	0.120858i
$784$		0			0
$785$		−	190.632i		−	0.242844i
$786$	20.1983	+	617.160i	0.0256975	+	0.785190i
$787$	673.501	−	1166.54i	0.855782	−	1.48226i	−0.0201353	−	0.999797i	$-0.506410\pi$
$787$	673.501	−	1166.54i	0.855782	−	1.48226i	0.875917	−	0.482461i	$-0.160257\pi$
$788$	−149.211	−	86.1469i	−0.189354	−	0.109323i
$789$	−1316.09	+	43.0728i	−1.66805	+	0.0545917i
$790$	−27.0118			−0.0341922
$791$		0			0
$792$	−205.830	−	308.058i	−0.259886	−	0.388962i
$793$	11.3438	+	19.6481i	0.0143050	+	0.0247769i
$794$	366.709	+	211.720i	0.461851	+	0.266650i
$795$	118.449	−	73.6551i	0.148993	−	0.0926479i
$796$	88.0000	+	152.420i	0.110553	+	0.191483i
$797$		−	1210.62i		−	1.51897i	−0.650523	−	0.759487i	$-0.725450\pi$
$797$		−	1210.62i		−	1.51897i	0.650523	−	0.759487i	$-0.274550\pi$
$798$		0			0
$799$	−182.745			−0.228717
$800$	118.389	−	68.3518i	0.147986	−	0.0854397i
$801$	31.5722	+	481.829i	0.0394160	+	0.601534i
$802$	−195.875	+	339.265i	−0.244233	+	0.423023i
$803$	911.706	−	526.374i	1.13538	−	0.655509i
$804$	373.490	+	199.639i	0.464540	+	0.248307i
$805$		0			0
$806$			48.1979i			0.0597988i
$807$	43.3570	−	1.41898i	0.0537262	−	0.00175834i
$808$	−81.7935	+	141.670i	−0.101230	+	0.175335i
$809$	269.226	+	155.438i	0.332789	+	0.192136i	0.657079	−	0.753822i	$-0.271792\pi$
$809$	269.226	+	155.438i	0.332789	+	0.192136i	−0.324290	+	0.945958i	$0.605125\pi$
$810$	−103.717	+	13.6509i	−0.128046	+	0.0168530i
$811$	65.7777			0.0811069			0.0405535	−	0.999177i	$-0.487088\pi$
$811$	65.7777			0.0811069			0.0405535	+	0.999177i	$0.487088\pi$
$812$		0			0
$813$	162.826	+	87.0342i	0.200278	+	0.107053i
$814$	−205.830	−	356.508i	−0.252862	−	0.437971i
$815$	−211.162	−	121.914i	−0.259094	−	0.149588i
$816$	136.472	+	219.469i	0.167245	+	0.268958i
$817$	93.9921	+	162.799i	0.115045	+	0.199265i
$818$			1047.90i			1.28106i
$819$		0			0
$820$	15.9843			0.0194930
$821$	321.290	−	185.497i	0.391340	−	0.225940i	−0.291401	−	0.956601i	$-0.594121\pi$
$821$	321.290	−	185.497i	0.391340	−	0.225940i	0.682740	+	0.730661i	$0.260788\pi$
$822$	−89.3832	+	55.5810i	−0.108739	+	0.0676167i
$823$	−220.539	+	381.984i	−0.267969	+	0.464136i	−0.968337	−	0.249646i	$-0.919686\pi$
$823$	−220.539	+	381.984i	−0.267969	+	0.464136i	0.700368	+	0.713782i	$0.253019\pi$
$824$	−292.402	+	168.818i	−0.354857	+	0.204877i
$825$	−497.409	+	930.567i	−0.602920	+	1.12796i
$826$		0			0
$827$			116.492i			0.140861i	0.997517	+	0.0704307i	$0.0224374\pi$
$827$			116.492i			0.140861i	−0.997517	+	0.0704307i	$0.977563\pi$
$828$	−626.867	−	309.151i	−0.757086	−	0.373370i
$829$	−440.712	+	763.336i	−0.531619	+	0.920792i	0.467699	+	0.883888i	$0.345083\pi$
$829$	−440.712	+	763.336i	−0.531619	+	0.920792i	−0.999319	+	0.0369042i	$0.988250\pi$
$830$	162.787	+	93.9851i	0.196129	+	0.113235i
$831$	14.7681	+	451.241i	0.0177715	+	0.543009i
$832$	−4.66404			−0.00560582
$833$		0			0
$834$	−292.915	+	547.994i	−0.351217	+	0.657067i
$835$	3.28363	+	5.68741i	0.00393249	+	0.00681127i
$836$	−403.343	−	232.870i	−0.482468	−	0.278553i
$837$	1437.65	+	651.435i	1.71762	+	0.778298i
$838$	63.4980	+	109.982i	0.0757733	+	0.131243i
$839$		−	1346.42i		−	1.60480i	−0.596789	−	0.802398i	$-0.703557\pi$
$839$		−	1346.42i		−	1.60480i	0.596789	−	0.802398i	$-0.296443\pi$
$840$		0			0
$841$	−438.320			−0.521189
$842$	344.337	−	198.803i	0.408952	−	0.236108i
$843$	−475.603	−	764.847i	−0.564179	−	0.907291i
$844$	−61.2549	+	106.097i	−0.0725769	+	0.125707i
$845$	−133.390	+	77.0128i	−0.157858	+	0.0911394i
$846$	−60.0000	−	89.7998i	−0.0709220	−	0.106146i
$847$		0			0
$848$		−	203.647i		−	0.240149i
$849$	−9.69866	−	296.343i	−0.0114236	−	0.349050i
$850$	368.018	−	637.426i	0.432963	−	0.749913i
$851$	−672.569	−	388.308i	−0.790328	−	0.456296i
$852$	−102.113	+	3.34192i	−0.119850	+	0.00392244i
$853$	966.235			1.13275			0.566375	−	0.824148i	$-0.308346\pi$
$853$	966.235			1.13275			0.566375	+	0.824148i	$0.308346\pi$
$854$		0			0
$855$	−109.344	+	73.0584i	−0.127888	+	0.0854484i
$856$	164.745	+	285.347i	0.192459	+	0.333349i
$857$	850.645	+	491.120i	0.992585	+	0.573069i	0.906046	−	0.423179i	$-0.139086\pi$
$857$	850.645	+	491.120i	0.992585	+	0.573069i	0.0865390	+	0.996248i	$0.472419\pi$
$858$	30.5714	−	19.0102i	0.0356311	−	0.0221564i
$859$	654.745	+	1134.05i	0.762218	+	1.32020i	0.941705	+	0.336440i	$0.109223\pi$
$859$	654.745	+	1134.05i	0.762218	+	1.32020i	−0.179487	+	0.983760i	$0.557444\pi$
$860$			21.4591i			0.0249525i
$861$		0			0
$862$	792.243			0.919076
$863$	−867.367	+	500.775i	−1.00506	+	0.580272i	−0.909742	−	0.415175i	$-0.863720\pi$
$863$	−867.367	+	500.775i	−1.00506	+	0.580272i	−0.0953191	+	0.995447i	$0.530387\pi$
$864$	−63.0385	+	139.119i	−0.0729612	+	0.161018i
$865$	87.9150	−	152.273i	0.101636	−	0.176038i
$866$	665.041	−	383.962i	0.767946	−	0.443374i
$867$	462.557	+	247.247i	0.533514	+	0.285175i
$868$		0			0
$869$		−	304.405i		−	0.350294i
$870$	138.508	−	4.53305i	0.159204	−	0.00521040i
$871$	−20.5751	+	35.6372i	−0.0236224	+	0.0409152i
$872$	215.139	+	124.210i	0.246719	+	0.142443i
$873$	442.523	−	897.308i	0.506899	−	1.02784i
$874$	−878.640			−1.00531
$875$		0			0
$876$	−382.745	−	204.586i	−0.436924	−	0.233545i
$877$	16.5712	+	28.7022i	0.0188953	+	0.0327277i	0.875318	−	0.483547i	$-0.160652\pi$
$877$	16.5712	+	28.7022i	0.0188953	+	0.0327277i	−0.856423	+	0.516275i	$0.827318\pi$
$878$	419.071	+	241.951i	0.477302	+	0.275570i
$879$	11.3336	+	18.2263i	0.0128937	+	0.0207352i
$880$	−26.5830	−	46.0431i	−0.0302080	−	0.0523217i
$881$		−	944.040i		−	1.07156i	−0.844359	−	0.535778i	$-0.820019\pi$
$881$		−	944.040i		−	1.07156i	0.844359	−	0.535778i	$-0.179981\pi$
$882$		0			0
$883$	55.5138			0.0628695			0.0314348	−	0.999506i	$-0.489992\pi$
$883$	55.5138			0.0628695			0.0314348	+	0.999506i	$0.489992\pi$
$884$	−21.7477	+	12.5560i	−0.0246014	+	0.0142036i
$885$	135.447	−	84.2246i	0.153047	−	0.0951690i
$886$	282.712	−	489.672i	0.319089	−	0.552678i
$887$	−17.4345	+	10.0658i	−0.0196556	+	0.0113482i	−0.509796	−	0.860296i	$-0.670279\pi$
$887$	−17.4345	+	10.0658i	−0.0196556	+	0.0113482i	0.490140	+	0.871644i	$0.336946\pi$
$888$	−80.0000	+	149.666i	−0.0900901	+	0.168543i
$889$		0			0
$890$			69.2909i			0.0778549i
$891$	−153.837	−	1168.82i	−0.172656	−	1.31181i
$892$	−150.494	+	260.663i	−0.168715	+	0.292224i
$893$	−117.576	−	67.8823i	−0.131664	−	0.0760160i
$894$	−30.4690	−	930.984i	−0.0340817	−	1.04137i
$895$	39.8745			0.0445525
$896$		0			0
$897$	32.0157	−	59.8960i	0.0356920	−	0.0667737i
$898$	521.166	+	902.686i	0.580363	+	1.00522i
$899$	−1810.76	−	1045.44i	−2.01419	−	1.16289i
$900$	434.057	−	28.4419i	0.482286	−	0.0316021i
$901$	−548.235	−	949.571i	−0.608474	−	1.05391i
$902$			180.132i			0.199703i
$903$		0			0
$904$	195.660			0.216438
$905$	64.1285	−	37.0246i	0.0708603	−	0.0409112i
$906$	−474.197	−	762.586i	−0.523396	−	0.841706i
$907$	−109.822	+	190.218i	−0.121083	+	0.209722i	−0.920195	−	0.391460i	$-0.871970\pi$
$907$	−109.822	+	190.218i	−0.121083	+	0.209722i	0.799112	+	0.601182i	$0.205303\pi$
$908$	−330.057	+	190.558i	−0.363499	+	0.209866i
$909$	−432.810	+	289.184i	−0.476139	+	0.318134i
$910$		0			0
$911$		−	827.126i		−	0.907932i	−0.891019	−	0.453966i	$-0.850009\pi$
$911$		−	827.126i		−	0.907932i	0.891019	−	0.453966i	$-0.149991\pi$
$912$	6.28037	+	191.897i	0.00688637	+	0.210414i
$913$	−1059.15	+	1834.50i	−1.16008	+	2.00931i
$914$	−814.867	−	470.464i	−0.891539	−	0.514730i
$915$	106.558	−	3.48741i	0.116457	−	0.00381138i
$916$	−285.830			−0.312042
$917$		0			0
$918$	80.5830	+	818.395i	0.0877811	+	0.891498i
$919$	514.693	+	891.474i	0.560057	+	0.970048i	0.997491	+	0.0707970i	$0.0225543\pi$
$919$	514.693	+	891.474i	0.560057	+	0.970048i	−0.437433	+	0.899251i	$0.644112\pi$
$920$	−86.8625	−	50.1501i	−0.0944157	−	0.0545109i
$921$	−269.615	+	167.654i	−0.292741	+	0.182035i
$922$	−225.472	−	390.529i	−0.244546	−	0.423567i
$923$		−	9.92733i		−	0.0107555i
$924$		0			0
$925$	483.320			0.522508
$926$	492.754	−	284.492i	0.532132	−	0.307226i
$927$	−1072.05	+	70.2471i	−1.15648	+	0.0757790i
$928$	101.166	−	175.225i	0.109015	−	0.188820i
$929$	1247.92	−	720.489i	1.34330	−	0.775553i	0.356008	−	0.934483i	$-0.384138\pi$
$929$	1247.92	−	720.489i	1.34330	−	0.775553i	0.987290	+	0.158930i	$0.0508043\pi$
$930$	199.749	+	106.770i	0.214784	+	0.114807i
$931$		0			0
$932$			15.6765i			0.0168203i
$933$	795.782	−	26.0442i	0.852928	−	0.0279144i
$934$	−492.915	+	853.754i	−0.527746	+	0.914083i
$935$	−247.904	−	143.128i	−0.265138	−	0.153078i
$936$	−13.3103	−	6.56419i	−0.0142204	−	0.00701303i
$937$	−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
$939$	686.118	+	366.745i	0.730690	+	0.390570i
$940$	−7.74902	−	13.4217i	−0.00824363	−	0.0142784i
$941$	166.082	+	95.8874i	0.176495	+	0.101899i	0.585645	−	0.810568i	$-0.300841\pi$
$941$	166.082	+	95.8874i	0.176495	+	0.101899i	−0.409150	+	0.912467i	$0.634175\pi$
$942$	−467.666	−	752.083i	−0.496461	−	0.798390i
$943$	169.914	+	294.299i	0.180184	+	0.312088i
$944$		−	232.870i		−	0.246684i
$945$		0			0
$946$	−241.830			−0.255634
$947$	773.454	−	446.554i	0.816742	−	0.471546i	−0.0325499	−	0.999470i	$-0.510363\pi$
$947$	773.454	−	446.554i	0.816742	−	0.471546i	0.849292	+	0.527924i	$0.177029\pi$
$948$	−106.567	+	66.2664i	−0.112413	+	0.0699012i
$949$	21.0850	−	36.5202i	0.0222181	−	0.0384829i
$950$	473.555	−	273.407i	0.498479	−	0.287797i
$951$	−53.4902	+	100.071i	−0.0562462	+	0.105227i
$952$		0			0
$953$			1300.12i			1.36423i	0.731243	+	0.682117i	$0.238941\pi$
$953$			1300.12i			1.36423i	−0.731243	+	0.682117i	$0.761059\pi$
$954$	286.613	−	581.168i	0.300433	−	0.609191i
$955$	24.4550	−	42.3573i	0.0256073	−	0.0443531i
$956$	−369.566	−	213.369i	−0.386575	−	0.223189i
$957$	51.0844	+	1560.89i	0.0533798	+	1.63102i
$958$	231.660			0.241816
$959$		0			0
$960$	−10.3320	+	19.3294i	−0.0107625	+	0.0201348i
$961$	−1228.14	−	2127.20i	−1.27798	−	2.21353i
$962$	−14.2807	−	8.24494i	−0.0148448	−	0.00857062i
$963$	68.5522	+	1046.19i	0.0711861	+	1.08638i
$964$	130.000	+	225.167i	0.134855	+	0.233575i
$965$		−	100.907i		−	0.104566i
$966$		0			0
$967$	−375.247			−0.388053			−0.194026	−	0.980996i	$-0.562155\pi$
$967$	−375.247			−0.388053			−0.194026	+	0.980996i	$0.562155\pi$
$968$	222.487	−	128.453i	0.229842	−	0.132699i
$969$	545.889	+	877.878i	0.563353	+	0.905963i
$970$	71.7856	−	124.336i	0.0740058	−	0.128182i
$971$	905.053	−	522.532i	0.932083	−	0.538138i	0.0446133	−	0.999004i	$-0.485794\pi$
$971$	905.053	−	522.532i	0.932083	−	0.538138i	0.887470	+	0.460866i	$0.152461\pi$
$972$	−375.697	+	308.299i	−0.386519	+	0.317180i
$973$		0			0
$974$		−	146.368i		−	0.150275i
$975$	1.38256	+	42.2441i	0.00141801	+	0.0433273i
$976$	77.8301	−	134.806i	0.0797439	−	0.138120i
$977$	397.874	+	229.713i	0.407240	+	0.235120i	0.689603	−	0.724187i	$-0.257785\pi$
$977$	397.874	+	229.713i	0.407240	+	0.235120i	−0.282363	+	0.959308i	$0.591118\pi$
$978$	−1132.16	+	37.0531i	−1.15763	+	0.0378867i
$979$	−780.863			−0.797613
$980$		0			0
$981$	439.150	+	657.260i	0.447656	+	0.669990i
$982$	−403.118	−	698.220i	−0.410507	−	0.711019i
$983$	89.4305	+	51.6327i	0.0909771	+	0.0525257i	0.544798	−	0.838567i	$-0.316606\pi$
$983$	89.4305	+	51.6327i	0.0909771	+	0.0525257i	−0.453821	+	0.891093i	$0.649940\pi$
$984$	63.0611	−	39.2132i	0.0640865	−	0.0398508i
$985$	−39.3360	−	68.1319i	−0.0399350	−	0.0691694i
$986$		−	1089.39i		−	1.10486i
$987$		0			0
$988$	−18.6562			−0.0188828
$989$	−395.101	+	228.112i	−0.399496	+	0.230649i
$990$	−11.0615	−	168.811i	−0.0111732	−	0.170516i
$991$	−664.863	+	1151.58i	−0.670901	+	1.16203i	0.306748	+	0.951791i	$0.400759\pi$
$991$	−664.863	+	1151.58i	−0.670901	+	1.16203i	−0.977649	+	0.210244i	$0.932574\pi$
$992$	286.382	−	165.343i	0.288692	−	0.166676i
$993$	−384.931	−	205.754i	−0.387644	−	0.207205i
$994$		0			0
$995$			80.3643i			0.0807681i
$996$	872.796	−	28.5647i	0.876301	−	0.0286794i
$997$	332.129	−	575.265i	0.333129	−	0.576996i	−0.649995	−	0.759939i	$-0.725229\pi$
$997$	332.129	−	575.265i	0.333129	−	0.576996i	0.983124	+	0.182943i	$0.0585623\pi$
$998$	597.259	+	344.828i	0.598456	+	0.345519i
$999$	−438.946	+	314.526i	−0.439385	+	0.314841i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.3.h.g.263.4		8
3.2	odd	2	inner	294.3.h.g.263.2		8
7.2	even	3	inner	294.3.h.g.275.2		8
7.3	odd	6		42.3.b.a.29.4	yes	4
7.4	even	3		294.3.b.h.197.3		4
7.5	odd	6		294.3.h.d.275.1		8
7.6	odd	2		294.3.h.d.263.3		8
21.2	odd	6	inner	294.3.h.g.275.4		8
21.5	even	6		294.3.h.d.275.3		8
21.11	odd	6		294.3.b.h.197.1		4
21.17	even	6		42.3.b.a.29.2	✓	4
21.20	even	2		294.3.h.d.263.1		8
28.3	even	6		336.3.d.b.113.1		4
35.3	even	12		1050.3.c.a.449.7		8
35.17	even	12		1050.3.c.a.449.1		8
35.24	odd	6		1050.3.e.a.701.1		4
56.3	even	6		1344.3.d.e.449.4		4
56.45	odd	6		1344.3.d.c.449.1		4
63.31	odd	6		1134.3.q.a.1079.1		8
63.38	even	6		1134.3.q.a.701.1		8
63.52	odd	6		1134.3.q.a.701.4		8
63.59	even	6		1134.3.q.a.1079.4		8
84.59	odd	6		336.3.d.b.113.2		4
105.17	odd	12		1050.3.c.a.449.6		8
105.38	odd	12		1050.3.c.a.449.4		8
105.59	even	6		1050.3.e.a.701.3		4
168.59	odd	6		1344.3.d.e.449.3		4
168.101	even	6		1344.3.d.c.449.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.b.a.29.2	✓	4	21.17	even	6
42.3.b.a.29.4	yes	4	7.3	odd	6
294.3.b.h.197.1		4	21.11	odd	6
294.3.b.h.197.3		4	7.4	even	3
294.3.h.d.263.1		8	21.20	even	2
294.3.h.d.263.3		8	7.6	odd	2
294.3.h.d.275.1		8	7.5	odd	6
294.3.h.d.275.3		8	21.5	even	6
294.3.h.g.263.2		8	3.2	odd	2	inner
294.3.h.g.263.4		8	1.1	even	1	trivial
294.3.h.g.275.2		8	7.2	even	3	inner
294.3.h.g.275.4		8	21.2	odd	6	inner
336.3.d.b.113.1		4	28.3	even	6
336.3.d.b.113.2		4	84.59	odd	6
1050.3.c.a.449.1		8	35.17	even	12
1050.3.c.a.449.4		8	105.38	odd	12
1050.3.c.a.449.6		8	105.17	odd	12
1050.3.c.a.449.7		8	35.3	even	12
1050.3.e.a.701.1		4	35.24	odd	6
1050.3.e.a.701.3		4	105.59	even	6
1134.3.q.a.701.1		8	63.38	even	6
1134.3.q.a.701.4		8	63.52	odd	6
1134.3.q.a.1079.1		8	63.31	odd	6
1134.3.q.a.1079.4		8	63.59	even	6
1344.3.d.c.449.1		4	56.45	odd	6
1344.3.d.c.449.2		4	168.101	even	6
1344.3.d.e.449.3		4	168.59	odd	6
1344.3.d.e.449.4		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)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(2.54762 - 1.58418i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.790881 - 0.456615i) q^{5} +(2.00000 - 3.74166i) q^{6} -2.82843i q^{8} +(3.98074 - 8.07178i) q^{9} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(2.54762 - 1.58418i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.790881 - 0.456615i) q^{5} +(2.00000 - 3.74166i) q^{6} -2.82843i q^{8} +(3.98074 - 8.07178i) q^{9} +(0.645751 - 1.11847i) q^{10} +(12.6045 + 7.27719i) q^{11} +(-0.196262 - 5.99679i) q^{12} +0.583005 q^{13} +(1.29150 - 2.41618i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(-18.6513 - 10.7684i) q^{17} +(-0.832222 - 12.7007i) q^{18} +(-8.00000 - 13.8564i) q^{19} -1.82646i q^{20} +20.5830 q^{22} +(33.6284 - 19.4154i) q^{23} +(-4.48074 - 7.20576i) q^{24} +(-12.0830 + 20.9284i) q^{25} +(0.714033 - 0.412247i) q^{26} +(-2.64575 - 26.8701i) q^{27} +35.7676i q^{29} +(-0.126736 - 3.87243i) q^{30} +(-29.2288 + 50.6257i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(43.6398 - 1.42823i) q^{33} -30.4575 q^{34} +(-10.0000 - 14.9666i) q^{36} +(-10.0000 - 17.3205i) q^{37} +(-19.5959 - 11.3137i) q^{38} +(1.48528 - 0.923586i) q^{39} +(-1.29150 - 2.23695i) q^{40} +8.75149i q^{41} -11.7490 q^{43} +(25.2089 - 14.5544i) q^{44} +(-0.537408 - 8.20148i) q^{45} +(27.4575 - 47.5578i) q^{46} +(7.34847 - 4.24264i) q^{47} +(-10.5830 - 5.65685i) q^{48} +34.1759i q^{50} +(-64.5756 + 2.11341i) q^{51} +(0.583005 - 1.00979i) q^{52} +(44.0908 + 25.4558i) q^{53} +(-22.2404 - 31.0381i) q^{54} +13.2915 q^{55} +(-42.3320 - 22.6274i) q^{57} +(25.2915 + 43.8062i) q^{58} +(50.4179 + 29.1088i) q^{59} +(-2.89344 - 4.65313i) q^{60} +(19.4575 + 33.7014i) q^{61} +82.6714i q^{62} -8.00000 q^{64} +(0.461088 - 0.266209i) q^{65} +(52.4377 - 32.6072i) q^{66} +(-35.2915 + 61.1267i) q^{67} +(-37.3027 + 21.5367i) q^{68} +(54.9150 - 102.737i) q^{69} -17.0279i q^{71} +(-22.8305 - 11.2592i) q^{72} +(36.1660 - 62.6414i) q^{73} +(-24.4949 - 14.1421i) q^{74} +(2.37143 + 72.4592i) q^{75} -32.0000 q^{76} +(1.16601 - 2.18141i) q^{78} +(-10.4575 - 18.1129i) q^{79} +(-3.16352 - 1.82646i) q^{80} +(-49.3074 - 64.2634i) q^{81} +(6.18824 + 10.7183i) q^{82} +145.544i q^{83} -19.6680 q^{85} +(-14.3895 + 8.30781i) q^{86} +(56.6623 + 91.1222i) q^{87} +(20.5830 - 35.6508i) q^{88} +(-46.4635 + 26.8257i) q^{89} +(-6.45751 - 9.66472i) q^{90} -77.6616i q^{92} +(5.73648 + 175.279i) q^{93} +(6.00000 - 10.3923i) q^{94} +(-12.6541 - 7.30584i) q^{95} +(-16.9615 + 0.555112i) q^{96} +111.166 q^{97} +(108.915 - 72.7719i) 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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