LMFDB - Embedded newform 735.2.q.g.214.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [735,2,Mod(79,735)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("735.79"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,8,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.27814731656356152999936.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} - 4 x^{13} - 14 x^{12} + 38 x^{11} - 40 x^{10} + 64 x^{9} + 291 x^{8} + \cdots + 1 $ x^16 - 2x^15 + 2x^14 - 4x^13 - 14x^12 + 38x^11 - 40x^10 + 64x^9 + 291x^8 - 630x^7 + 584x^6 - 800x^5 + 734x^4 - 188x^3 + 32x^2 - 8*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			214.1
Root			$1.05078 + 0.281555i$ of defining polynomial
Character	$\chi$	$=$	735.214
Dual form			735.2.q.g.79.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.17942 + 1.25829i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(2.16659 - 3.75264i) q^{4} +(-2.23607 - 0.00136408i) q^{5} +2.51658 q^{6} +5.87162i q^{8} +(0.500000 + 0.866025i) q^{9} +(4.87505 - 2.81065i) q^{10} +(-0.489068 + 0.847090i) q^{11} +(-3.75264 + 2.16659i) q^{12} -5.14977i q^{13} +(1.93581 + 1.11922i) q^{15} +(-3.05502 - 5.29146i) q^{16} +(3.59380 + 2.07488i) q^{17} +(-2.17942 - 1.25829i) q^{18} +(1.15001 + 1.99187i) q^{19} +(-4.84975 + 8.38820i) q^{20} -2.46156i q^{22} +(4.39324 - 2.53644i) q^{23} +(2.93581 - 5.08497i) q^{24} +(5.00000 + 0.00610036i) q^{25} +(6.47990 + 11.2235i) q^{26} -1.00000i q^{27} -5.92664 q^{29} +(-5.62724 - 0.00343282i) q^{30} +(0.316594 - 0.548357i) q^{31} +(3.14643 + 1.81659i) q^{32} +(0.847090 - 0.489068i) q^{33} -10.4432 q^{34} +4.33317 q^{36} +(-7.84188 + 4.52751i) q^{37} +(-5.01270 - 2.89408i) q^{38} +(-2.57488 + 4.45983i) q^{39} +(0.00800937 - 13.1293i) q^{40} -2.65505 q^{41} +0.344947i q^{43} +(2.11922 + 3.67059i) q^{44} +(-1.11685 - 1.93717i) q^{45} +(-6.38315 + 11.0559i) q^{46} +(-3.67059 + 2.11922i) q^{47} +6.11005i q^{48} +(-10.9048 + 6.27815i) q^{50} +(-2.07488 - 3.59380i) q^{51} +(-19.3252 - 11.1574i) q^{52} +(-6.61053 - 3.81659i) q^{53} +(1.25829 + 2.17942i) q^{54} +(1.09474 - 1.89348i) q^{55} -2.30001i q^{57} +(12.9167 - 7.45743i) q^{58} +(-0.908297 + 1.57322i) q^{59} +(8.39411 - 4.83952i) q^{60} +(0.328128 + 0.568335i) q^{61} +1.59347i q^{62} +3.07689 q^{64} +(-0.00702471 + 11.5152i) q^{65} +(-1.23078 + 2.13177i) q^{66} +(-8.01924 - 4.62991i) q^{67} +(15.5726 - 8.99083i) q^{68} -5.07288 q^{69} -5.49351 q^{71} +(-5.08497 + 2.93581i) q^{72} +(4.65758 + 2.68905i) q^{73} +(11.3938 - 19.7347i) q^{74} +(-4.32707 - 2.50528i) q^{75} +9.96636 q^{76} -12.9598i q^{78} +(-5.44346 - 9.42835i) q^{79} +(6.82402 + 11.8362i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.78648 - 3.34083i) q^{82} -6.62663i q^{83} +(-8.03316 - 4.64448i) q^{85} +(-0.434043 - 0.751785i) q^{86} +(5.13262 + 2.96332i) q^{87} +(-4.97379 - 2.87162i) q^{88} +(-8.15542 - 14.1256i) q^{89} +(4.87162 + 2.81659i) q^{90} -21.9817i q^{92} +(-0.548357 + 0.316594i) q^{93} +(5.33317 - 9.23733i) q^{94} +(-2.56878 - 4.45553i) q^{95} +(-1.81659 - 3.14643i) q^{96} -1.53844i q^{97} -0.978135 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 2 q^{5} + 8 q^{6} + 8 q^{9} + 4 q^{10} - 4 q^{15} + 24 q^{19} + 8 q^{20} + 12 q^{24} - 4 q^{25} + 12 q^{26} + 24 q^{29} - 12 q^{30} - 16 q^{31} - 16 q^{34} + 16 q^{36} - 4 q^{39} - 32 q^{40}+ \cdots - 8 q^{96}+O(q^{100}) $ 16 * q + 8 * q^4 - 2 * q^5 + 8 * q^6 + 8 * q^9 + 4 * q^10 - 4 * q^15 + 24 * q^19 + 8 * q^20 + 12 * q^24 - 4 * q^25 + 12 * q^26 + 24 * q^29 - 12 * q^30 - 16 * q^31 - 16 * q^34 + 16 * q^36 - 4 * q^39 - 32 * q^40 - 16 * q^41 + 20 * q^44 + 2 * q^45 - 32 * q^46 - 40 * q^50 + 4 * q^51 + 4 * q^54 - 8 * q^55 - 4 * q^59 + 16 * q^60 - 16 * q^61 + 16 * q^64 + 30 * q^65 - 28 * q^66 - 40 * q^69 - 56 * q^71 + 40 * q^74 - 8 * q^75 + 64 * q^76 - 16 * q^79 - 52 * q^80 - 8 * q^81 - 64 * q^85 - 48 * q^86 - 16 * q^89 + 8 * q^90 + 32 * q^94 - 22 * q^95 - 8 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−2.17942	+	1.25829i	−1.54108	+	0.889745i	−0.542313	+	0.840176i	$0.682451\pi$
$2$	−2.17942	+	1.25829i	−1.54108	+	0.889745i	−0.998771	+	0.0495691i	$0.984215\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	2.16659	−	3.75264i	1.08329	−	1.87632i
$5$	−2.23607	−	0.00136408i	−1.00000	−	0.000610036i
$5$	−2.23607	−	0.00136408i	−1.00000	−	0.000610036i
$6$	2.51658			1.02739
$7$		0			0
$7$		0			0
$8$			5.87162i			2.07593i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	4.87505	−	2.81065i	1.54163	−	0.888805i
$11$	−0.489068	+	0.847090i	−0.147459	+	0.255407i	−0.930288	−	0.366830i	$-0.880443\pi$
$11$	−0.489068	+	0.847090i	−0.147459	+	0.255407i	0.782828	+	0.622238i	$0.213776\pi$
$12$	−3.75264	+	2.16659i	−1.08329	+	0.625440i
$13$		−	5.14977i		−	1.42829i	−0.699998	−	0.714144i	$-0.746816\pi$
$13$		−	5.14977i		−	1.42829i	0.699998	−	0.714144i	$-0.253184\pi$
$14$		0			0
$15$	1.93581	+	1.11922i	0.499824	+	0.288980i
$16$	−3.05502	−	5.29146i	−0.763756	−	1.32286i
$17$	3.59380	+	2.07488i	0.871626	+	0.503233i	0.867888	−	0.496760i	$-0.165477\pi$
$17$	3.59380	+	2.07488i	0.871626	+	0.503233i	0.00373753	+	0.999993i	$0.498810\pi$
$18$	−2.17942	−	1.25829i	−0.513695	−	0.296582i
$19$	1.15001	+	1.99187i	0.263830	+	0.456967i	0.967256	−	0.253801i	$-0.0816810\pi$
$19$	1.15001	+	1.99187i	0.263830	+	0.456967i	−0.703427	+	0.710768i	$0.748348\pi$
$20$	−4.84975	+	8.38820i	−1.08444	+	1.87566i
$21$		0			0
$22$		−	2.46156i		−	0.524805i
$23$	4.39324	−	2.53644i	0.916054	−	0.528884i	0.0336802	−	0.999433i	$-0.489277\pi$
$23$	4.39324	−	2.53644i	0.916054	−	0.528884i	0.882374	+	0.470548i	$0.155944\pi$
$24$	2.93581	−	5.08497i	0.599270	−	1.03797i
$25$	5.00000	+	0.00610036i	0.999999	+	0.00122007i
$26$	6.47990	+	11.2235i	1.27081	+	2.20111i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−5.92664			−1.10055			−0.550275	−	0.834983i	$-0.685477\pi$
$29$	−5.92664			−1.10055			−0.550275	+	0.834983i	$0.685477\pi$
$30$	−5.62724	−	0.00343282i	−1.02739	−	0.000626745i
$31$	0.316594	−	0.548357i	0.0568620	−	0.0984879i	−0.836193	−	0.548435i	$-0.815224\pi$
$31$	0.316594	−	0.548357i	0.0568620	−	0.0984879i	0.893055	+	0.449947i	$0.148557\pi$
$32$	3.14643	+	1.81659i	0.556216	+	0.321132i
$33$	0.847090	−	0.489068i	0.147459	−	0.0851357i
$34$	−10.4432			−1.79100
$35$		0			0
$36$	4.33317			0.722196
$37$	−7.84188	+	4.52751i	−1.28920	+	0.744318i	−0.978511	−	0.206194i	$-0.933892\pi$
$37$	−7.84188	+	4.52751i	−1.28920	+	0.744318i	−0.310686	+	0.950513i	$0.600559\pi$
$38$	−5.01270	−	2.89408i	−0.813168	−	0.469483i
$39$	−2.57488	+	4.45983i	−0.412311	+	0.714144i
$40$	0.00800937	−	13.1293i	0.00126639	−	2.07593i
$41$	−2.65505			−0.414650			−0.207325	−	0.978272i	$-0.566476\pi$
$41$	−2.65505			−0.414650			−0.207325	+	0.978272i	$0.566476\pi$
$42$		0			0
$43$			0.344947i			0.0526039i	0.999654	+	0.0263020i	$0.00837314\pi$
$43$			0.344947i			0.0526039i	−0.999654	+	0.0263020i	$0.991627\pi$
$44$	2.11922	+	3.67059i	0.319484	+	0.553362i
$45$	−1.11685	−	1.93717i	−0.166491	−	0.288777i
$46$	−6.38315	+	11.0559i	−0.941144	+	1.63011i
$47$	−3.67059	+	2.11922i	−0.535410	+	0.309119i	−0.743217	−	0.669051i	$-0.766701\pi$
$47$	−3.67059	+	2.11922i	−0.535410	+	0.309119i	0.207806	+	0.978170i	$0.433368\pi$
$48$			6.11005i			0.881910i
$49$		0			0
$50$	−10.9048	+	6.27815i	−1.54217	+	0.887864i
$51$	−2.07488	−	3.59380i	−0.290542	−	0.503233i
$52$	−19.3252	−	11.1574i	−2.67993	−	1.54726i
$53$	−6.61053	−	3.81659i	−0.908027	−	0.524250i	−0.0282311	−	0.999601i	$-0.508987\pi$
$53$	−6.61053	−	3.81659i	−0.908027	−	0.524250i	−0.879796	+	0.475352i	$0.842321\pi$
$54$	1.25829	+	2.17942i	0.171232	+	0.296582i
$55$	1.09474	−	1.89348i	0.147615	−	0.255317i
$56$		0			0
$57$		−	2.30001i		−	0.304644i
$58$	12.9167	−	7.45743i	1.69604	−	0.979209i
$59$	−0.908297	+	1.57322i	−0.118250	+	0.204815i	−0.919074	−	0.394084i	$-0.871062\pi$
$59$	−0.908297	+	1.57322i	−0.118250	+	0.204815i	0.800824	+	0.598900i	$0.204395\pi$
$60$	8.39411	−	4.83952i	1.08367	−	0.624779i
$61$	0.328128	+	0.568335i	0.0420125	+	0.0727678i	0.886267	−	0.463175i	$-0.153290\pi$
$61$	0.328128	+	0.568335i	0.0420125	+	0.0727678i	−0.844255	+	0.535942i	$0.819956\pi$
$62$			1.59347i			0.202371i
$63$		0			0
$64$	3.07689			0.384611
$65$	−0.00702471	+	11.5152i	−0.000871308	+	1.42829i
$66$	−1.23078	+	2.13177i	−0.151498	+	0.262403i
$67$	−8.01924	−	4.62991i	−0.979706	−	0.565633i	−0.0775244	−	0.996990i	$-0.524702\pi$
$67$	−8.01924	−	4.62991i	−0.979706	−	0.565633i	−0.902181	+	0.431357i	$0.858035\pi$
$68$	15.5726	−	8.99083i	1.88845	−	1.09030i
$69$	−5.07288			−0.610703
$70$		0			0
$71$	−5.49351			−0.651960			−0.325980	−	0.945377i	$-0.605694\pi$
$71$	−5.49351			−0.651960			−0.325980	+	0.945377i	$0.605694\pi$
$72$	−5.08497	+	2.93581i	−0.599270	+	0.345988i
$73$	4.65758	+	2.68905i	0.545128	+	0.314730i	0.747155	−	0.664650i	$-0.231419\pi$
$73$	4.65758	+	2.68905i	0.545128	+	0.314730i	−0.202027	+	0.979380i	$0.564753\pi$
$74$	11.3938	−	19.7347i	1.32451	−	2.29411i
$75$	−4.32707	−	2.50528i	−0.499647	−	0.289285i
$76$	9.96636			1.14322
$77$		0			0
$78$		−	12.9598i		−	1.46741i
$79$	−5.44346	−	9.42835i	−0.612437	−	1.06077i	−0.990828	−	0.135127i	$-0.956856\pi$
$79$	−5.44346	−	9.42835i	−0.612437	−	1.06077i	0.378391	−	0.925646i	$-0.376477\pi$
$80$	6.82402	+	11.8362i	0.762949	+	1.32333i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	5.78648	−	3.34083i	0.639010	−	0.368933i
$83$		−	6.62663i		−	0.727367i	−0.931523	−	0.363683i	$-0.881519\pi$
$83$		−	6.62663i		−	0.727367i	0.931523	−	0.363683i	$-0.118481\pi$
$84$		0			0
$85$	−8.03316	−	4.64448i	−0.871318	−	0.503765i
$86$	−0.434043	−	0.751785i	−0.0468041	−	0.0810671i
$87$	5.13262	+	2.96332i	0.550275	+	0.317701i
$88$	−4.97379	−	2.87162i	−0.530208	−	0.306116i
$89$	−8.15542	−	14.1256i	−0.864472	−	1.49731i	−0.867570	−	0.497315i	$-0.834319\pi$
$89$	−8.15542	−	14.1256i	−0.864472	−	1.49731i	0.00309785	−	0.999995i	$-0.499014\pi$
$90$	4.87162	+	2.81659i	0.513514	+	0.296895i
$91$		0			0
$92$		−	21.9817i		−	2.29175i
$93$	−0.548357	+	0.316594i	−0.0568620	+	0.0328293i
$94$	5.33317	−	9.23733i	0.550075	−	0.952758i
$95$	−2.56878	−	4.45553i	−0.263551	−	0.457127i
$96$	−1.81659	−	3.14643i	−0.185405	−	0.321132i
$97$		−	1.53844i		−	0.156205i	−0.996945	−	0.0781027i	$-0.975114\pi$
$97$		−	1.53844i		−	0.156205i	0.996945	−	0.0781027i	$-0.0248862\pi$
$98$		0			0
$99$	−0.978135			−0.0983063
$100$	10.8558	−	18.7500i	1.08558	−	1.87500i
$101$	−2.75805	+	4.77708i	−0.274436	+	0.475338i	−0.969993	−	0.243134i	$-0.921825\pi$
$101$	−2.75805	+	4.77708i	−0.274436	+	0.475338i	0.695556	+	0.718471i	$0.255158\pi$
$102$	9.04410	+	5.22161i	0.895499	+	0.517017i
$103$	−14.3079	+	8.26066i	−1.40980	+	0.813947i	−0.995368	−	0.0961349i	$-0.969352\pi$
$103$	−14.3079	+	8.26066i	−1.40980	+	0.813947i	−0.414429	+	0.910082i	$0.636019\pi$
$104$	30.2375			2.96503
$105$		0			0
$106$	19.2095			1.86579
$107$	2.06824	−	1.19410i	0.199944	−	0.115438i	−0.396685	−	0.917955i	$-0.629840\pi$
$107$	2.06824	−	1.19410i	0.199944	−	0.115438i	0.596630	+	0.802517i	$0.296506\pi$
$108$	−3.75264	−	2.16659i	−0.361098	−	0.208480i
$109$	−9.05479	+	15.6833i	−0.867291	+	1.50219i	−0.00253705	+	0.999997i	$0.500808\pi$
$109$	−9.05479	+	15.6833i	−0.867291	+	1.50219i	−0.864754	+	0.502196i	$0.832526\pi$
$110$	−0.00335777	+	5.50420i	−0.000320150	+	0.524805i
$111$	9.05502			0.859465
$112$		0			0
$113$			4.04373i			0.380402i	0.981745	+	0.190201i	$0.0609140\pi$
$113$			4.04373i			0.380402i	−0.981745	+	0.190201i	$0.939086\pi$
$114$	2.89408	+	5.01270i	0.271056	+	0.469483i
$115$	−9.82705	+	5.66566i	−0.916377	+	0.528325i
$116$	−12.8406	+	22.2405i	−1.19222	+	2.06498i
$117$	4.45983	−	2.57488i	0.412311	−	0.238048i
$118$		−	4.57160i		−	0.420850i
$119$		0			0
$120$	−6.57160	+	11.3663i	−0.599903	+	1.03760i
$121$	5.02163	+	8.69771i	0.456511	+	0.790701i
$122$	−1.43026	−	0.825761i	−0.129490	−	0.0747608i
$123$	2.29934	+	1.32753i	0.207325	+	0.119699i
$124$	−1.37186	−	2.37613i	−0.123196	−	0.213383i
$125$	−11.1803	−	0.0204612i	−0.999998	−	0.00183011i
$126$		0			0
$127$		−	6.85023i		−	0.607860i	−0.952694	−	0.303930i	$-0.901701\pi$
$127$		−	6.85023i		−	0.607860i	0.952694	−	0.303930i	$-0.0982989\pi$
$128$	−12.9987	+	7.50481i	−1.14893	+	0.663337i
$129$	0.172473	−	0.298733i	0.0151854	−	0.0263020i
$130$	−14.4742	−	25.1054i	−1.26947	−	2.20189i
$131$	−2.01270	−	3.48610i	−0.175850	−	0.304582i	0.764605	−	0.644499i	$-0.222934\pi$
$131$	−2.01270	−	3.48610i	−0.175850	−	0.304582i	−0.940455	+	0.339918i	$0.889601\pi$
$132$		−	4.23843i		−	0.368908i
$133$		0			0
$134$	23.3031			2.01308
$135$	−0.00136408	+	2.23607i	−0.000117402	+	0.192450i
$136$	−12.1829	+	21.1014i	−1.04468	+	1.80943i
$137$	9.72709	+	5.61594i	0.831041	+	0.479802i	0.854209	−	0.519930i	$-0.174042\pi$
$137$	9.72709	+	5.61594i	0.831041	+	0.479802i	−0.0231680	+	0.999732i	$0.507375\pi$
$138$	11.0559	−	6.38315i	0.941144	−	0.543370i
$139$	−4.98991			−0.423238			−0.211619	−	0.977352i	$-0.567874\pi$
$139$	−4.98991			−0.423238			−0.211619	+	0.977352i	$0.567874\pi$
$140$		0			0
$141$	4.23843			0.356940
$142$	11.9727	−	6.91243i	1.00473	−	0.580078i
$143$	4.36232	+	2.51858i	0.364795	+	0.210615i
$144$	3.05502	−	5.29146i	0.254585	−	0.440955i
$145$	13.2524	+	0.00808443i	1.10055	+	0.000671376i
$146$	−13.5344			−1.12012
$147$		0			0
$148$			39.2370i			3.22526i
$149$	−7.24712	−	12.5524i	−0.593707	−	1.02833i	−0.993728	−	0.111825i	$-0.964330\pi$
$149$	−7.24712	−	12.5524i	−0.593707	−	1.02833i	0.400021	−	0.916506i	$-0.369003\pi$
$150$	12.5829	+	0.0153521i	1.02739	+	0.00125349i
$151$	−3.94346	+	6.83028i	−0.320914	+	0.555840i	−0.980677	−	0.195634i	$-0.937324\pi$
$151$	−3.94346	+	6.83028i	−0.320914	+	0.555840i	0.659763	+	0.751474i	$0.270657\pi$
$152$	−11.6955	+	6.75240i	−0.948631	+	0.547692i
$153$			4.14977i			0.335489i
$154$		0			0
$155$	−0.708674	+	1.22573i	−0.0569221	+	0.0984531i
$156$	11.1574	+	19.3252i	0.893309	+	1.54726i
$157$	−5.67792	−	3.27815i	−0.453147	−	0.261625i	0.256011	−	0.966674i	$-0.417592\pi$
$157$	−5.67792	−	3.27815i	−0.453147	−	0.261625i	−0.709159	+	0.705049i	$0.750925\pi$
$158$	23.7272	+	13.6989i	1.88763	+	1.08983i
$159$	3.81659	+	6.61053i	0.302676	+	0.524250i
$160$	−7.03316	−	4.06632i	−0.556020	−	0.321471i
$161$		0			0
$162$		−	2.51658i		−	0.197721i
$163$	−10.6138	+	6.12790i	−0.831340	+	0.479974i	−0.854311	−	0.519762i	$-0.826021\pi$
$163$	−10.6138	+	6.12790i	−0.831340	+	0.479974i	0.0229712	+	0.999736i	$0.492687\pi$
$164$	−5.75240	+	9.96346i	−0.449187	+	0.778015i
$165$	−1.89482	+	1.09243i	−0.147511	+	0.0850458i
$166$	8.33822	+	14.4422i	0.647171	+	1.12093i
$167$		−	2.13239i		−	0.165009i	−0.996591	−	0.0825047i	$-0.973708\pi$
$167$		−	2.13239i		−	0.165009i	0.996591	−	0.0825047i	$-0.0262920\pi$
$168$		0			0
$169$	−13.5201			−1.04001
$170$	23.3518	+	0.0142454i	1.79100	+	0.00109257i
$171$	−1.15001	+	1.99187i	−0.0879432	+	0.152322i
$172$	1.29446	+	0.747358i	0.0987017	+	0.0569855i
$173$	−10.0013	+	5.77427i	−0.760387	+	0.439009i	−0.829435	−	0.558604i	$-0.811337\pi$
$173$	−10.0013	+	5.77427i	−0.760387	+	0.439009i	0.0690479	+	0.997613i	$0.478004\pi$
$174$	−14.9149			−1.13069
$175$		0			0
$176$	5.97645			0.450492
$177$	1.57322	−	0.908297i	0.118250	−	0.0682718i
$178$	35.5482	+	20.5238i	2.66445	+	1.53832i
$179$	4.44978	−	7.70725i	0.332592	−	0.576067i	−0.650427	−	0.759569i	$-0.725410\pi$
$179$	4.44978	−	7.70725i	0.332592	−	0.576067i	0.983019	+	0.183502i	$0.0587434\pi$
$180$	−9.68927	−	0.00591081i	−0.722196	−	0.000440566i
$181$	3.17940			0.236323			0.118161	−	0.992994i	$-0.462300\pi$
$181$	3.17940			0.236323			0.118161	+	0.992994i	$0.462300\pi$
$182$		0			0
$183$		−	0.656256i		−	0.0485119i
$184$	14.8930	+	25.7954i	1.09793	+	1.90167i
$185$	17.5412	−	10.1131i	1.28965	−	0.743532i
$186$	0.796734	−	1.37998i	0.0584194	−	0.101185i
$187$	−3.51523	+	2.02952i	−0.257059	+	0.148413i
$188$			18.3659i			1.33947i
$189$		0			0
$190$	11.2048	+	6.47821i	0.812881	+	0.469979i
$191$	0.311309	+	0.539203i	0.0225255	+	0.0390154i	0.877068	−	0.480365i	$-0.159496\pi$
$191$	0.311309	+	0.539203i	0.0225255	+	0.0390154i	−0.854543	+	0.519381i	$0.826163\pi$
$192$	−2.66466	−	1.53844i	−0.192306	−	0.111028i
$193$	13.1529	+	7.59383i	0.946767	+	0.546616i	0.892075	−	0.451887i	$-0.149249\pi$
$193$	13.1529	+	7.59383i	0.946767	+	0.546616i	0.0546916	+	0.998503i	$0.482582\pi$
$194$	1.93581	+	3.35292i	0.138983	+	0.240726i
$195$	5.76370	−	9.96897i	0.412747	−	0.713893i
$196$		0			0
$197$			23.9410i			1.70573i	0.522136	+	0.852863i	$0.325136\pi$
$197$			23.9410i			1.70573i	−0.522136	+	0.852863i	$0.674864\pi$
$198$	2.13177	−	1.23078i	0.151498	−	0.0874676i
$199$	−6.97662	+	12.0839i	−0.494560	+	0.856602i	−0.999980	−	0.00627071i	$-0.998004\pi$
$199$	−6.97662	+	12.0839i	−0.494560	+	0.856602i	0.505421	+	0.862873i	$0.331337\pi$
$200$	−0.0358190	+	29.3581i	−0.00253279	+	2.07593i
$201$	4.62991	+	8.01924i	0.326569	+	0.565633i
$202$		−	13.8817i		−	0.976714i
$203$		0			0
$204$	−17.9817			−1.25897
$205$	5.93688	+	0.00362171i	0.414650	+	0.000252951i
$206$	20.7886	−	36.0069i	1.44841	−	2.50872i
$207$	4.39324	+	2.53644i	0.305351	+	0.176295i
$208$	−27.2498	+	15.7327i	−1.88943	+	1.09086i
$209$	−2.24973			−0.155617
$210$		0			0
$211$	4.82315			0.332040			0.166020	−	0.986122i	$-0.446908\pi$
$211$	4.82315			0.332040			0.166020	+	0.986122i	$0.446908\pi$
$212$	−28.6446	+	16.5380i	−1.96732	+	1.13583i
$213$	4.75752	+	2.74676i	0.325980	+	0.188205i
$214$	−3.00505	+	5.20489i	−0.205421	+	0.355799i
$215$	0.000470536	−	0.771325i	3.20903e−5	−	0.0526039i
$216$	5.87162			0.399513
$217$		0			0
$218$		−	45.5742i		−	3.08667i
$219$	−2.68905	−	4.65758i	−0.181709	−	0.314730i
$220$	−4.73370	−	8.21057i	−0.319146	−	0.553557i
$221$	10.6852	−	18.5073i	0.718762	−	1.24493i
$222$	−19.7347	+	11.3938i	−1.32451	+	0.764705i
$223$			15.8227i			1.05956i	0.848134	+	0.529782i	$0.177726\pi$
$223$			15.8227i			1.05956i	−0.848134	+	0.529782i	$0.822274\pi$
$224$		0			0
$225$	2.49472	+	4.33317i	0.166314	+	0.288878i
$226$	−5.08818	−	8.81299i	−0.338461	−	0.586232i
$227$	−18.7913	−	10.8492i	−1.24722	−	0.720084i	−0.276667	−	0.960966i	$-0.589230\pi$
$227$	−18.7913	−	10.8492i	−1.24722	−	0.720084i	−0.970554	+	0.240882i	$0.922563\pi$
$228$	−8.63112	−	4.98318i	−0.571610	−	0.330019i
$229$	1.03844	+	1.79864i	0.0686223	+	0.118857i	0.898295	−	0.439393i	$-0.144806\pi$
$229$	1.03844	+	1.79864i	0.0686223	+	0.118857i	−0.829673	+	0.558250i	$0.811473\pi$
$230$	14.2882	−	24.7131i	0.942139	−	1.62954i
$231$		0			0
$232$		−	34.7990i		−	2.28467i
$233$	5.85348	−	3.37951i	0.383474	−	0.221399i	−0.295854	−	0.955233i	$-0.595604\pi$
$233$	5.85348	−	3.37951i	0.383474	−	0.221399i	0.679329	+	0.733834i	$0.262271\pi$
$234$	−6.47990	+	11.2235i	−0.423604	+	0.733704i
$235$	8.21057	−	4.73370i	0.535599	−	0.308793i
$236$	3.93581	+	6.81702i	0.256199	+	0.443750i
$237$			10.8869i			0.707182i
$238$		0			0
$239$	2.90478			0.187894			0.0939472	−	0.995577i	$-0.470051\pi$
$239$	2.90478			0.187894			0.0939472	+	0.995577i	$0.470051\pi$
$240$	0.00833461	−	13.6625i	0.000537997	−	0.881909i
$241$	−4.44875	+	7.70546i	−0.286569	+	0.496352i	−0.972988	−	0.230854i	$-0.925848\pi$
$241$	−4.44875	+	7.70546i	−0.286569	+	0.496352i	0.686419	+	0.727206i	$0.259181\pi$
$242$	−21.8885	−	12.6373i	−1.40705	−	0.812358i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	2.84367			0.182047
$245$		0			0
$246$	−6.68165			−0.426007
$247$	10.2577	−	5.92227i	0.652680	−	0.376825i
$248$	3.21974	+	1.85892i	0.204454	+	0.118042i
$249$	−3.31331	+	5.73883i	−0.209973	+	0.363683i
$250$	24.3924	−	14.0235i	1.54271	−	0.886923i
$251$	21.1747			1.33653			0.668267	−	0.743921i	$-0.267036\pi$
$251$	21.1747			1.33653			0.668267	+	0.743921i	$0.267036\pi$
$252$		0			0
$253$			4.96196i			0.311956i
$254$	8.61958	+	14.9295i	0.540840	+	0.936763i
$255$	4.63468	+	8.03882i	0.290235	+	0.503410i
$256$	15.8096	−	27.3830i	0.988097	−	1.71143i
$257$	−5.39917	+	3.11721i	−0.336791	+	0.194446i	−0.658852	−	0.752273i	$-0.728958\pi$
$257$	−5.39917	+	3.11721i	−0.336791	+	0.194446i	0.322061	+	0.946719i	$0.395624\pi$
$258$			0.868086i			0.0540447i
$259$		0			0
$260$	43.1973	+	24.9751i	2.67898	+	1.54889i
$261$	−2.96332	−	5.13262i	−0.183425	−	0.317701i
$262$	8.77304	+	5.06512i	0.542000	+	0.312924i
$263$	−24.2903	−	14.0240i	−1.49780	−	0.864756i	−0.497805	−	0.867289i	$-0.665861\pi$
$263$	−24.2903	−	14.0240i	−1.49780	−	0.864756i	−0.999997	+	0.00253231i	$0.999194\pi$
$264$	2.87162	+	4.97379i	0.176736	+	0.306116i
$265$	14.7764	+	8.54318i	0.907707	+	0.524803i
$266$		0			0
$267$			16.3108i			0.998207i
$268$	−34.7487	+	20.0622i	−2.12262	+	1.22549i
$269$	−3.70915	+	6.42444i	−0.226151	+	0.391705i	−0.956664	−	0.291194i	$-0.905948\pi$
$269$	−3.70915	+	6.42444i	−0.226151	+	0.391705i	0.730513	+	0.682899i	$0.239281\pi$
$270$	−2.81065	−	4.87505i	−0.171051	−	0.296686i
$271$	−15.6058	−	27.0300i	−0.947985	−	1.64196i	−0.749662	−	0.661821i	$-0.769784\pi$
$271$	−15.6058	−	27.0300i	−0.947985	−	1.64196i	−0.198323	−	0.980137i	$-0.563550\pi$
$272$		−	25.3553i		−	1.53739i
$273$		0			0
$274$	−28.2659			−1.70761
$275$	−2.45050	+	4.23246i	−0.147771	+	0.255227i
$276$	−10.9908	+	19.0367i	−0.661570	+	1.14587i
$277$	10.7843	+	6.22629i	0.647963	+	0.374102i	0.787675	−	0.616090i	$-0.211284\pi$
$277$	10.7843	+	6.22629i	0.647963	+	0.374102i	−0.139712	+	0.990192i	$0.544618\pi$
$278$	10.8751	−	6.27875i	0.652246	−	0.376574i
$279$	0.633188			0.0379080
$280$		0			0
$281$	−0.0409225			−0.00244123			−0.00122061	−	0.999999i	$-0.500389\pi$
$281$	−0.0409225			−0.00244123			−0.00122061	+	0.999999i	$0.500389\pi$
$282$	−9.23733	+	5.33317i	−0.550075	+	0.317586i
$283$	−9.38944	−	5.42100i	−0.558144	−	0.322245i	0.194256	−	0.980951i	$-0.437771\pi$
$283$	−9.38944	−	5.42100i	−0.558144	−	0.322245i	−0.752400	+	0.658706i	$0.771104\pi$
$284$	−11.9022	+	20.6152i	−0.706264	+	1.22329i
$285$	−0.00313741	+	5.14299i	−0.000185844	+	0.304644i
$286$	−12.6764			−0.749574
$287$		0			0
$288$			3.63319i			0.214088i
$289$	0.110288	+	0.191024i	0.00648752	+	0.0112367i
$290$	−28.8927	+	16.6577i	−1.69664	+	0.978174i
$291$	−0.769222	+	1.33233i	−0.0450926	+	0.0781027i
$292$	20.1821	−	11.6521i	1.18107	−	0.681890i
$293$			29.6455i			1.73191i	0.500125	+	0.865953i	$0.333287\pi$
$293$			29.6455i			1.73191i	−0.500125	+	0.865953i	$0.666713\pi$
$294$		0			0
$295$	2.03316	−	3.51658i	0.118375	−	0.204743i
$296$	−26.5838	−	46.0445i	−1.54515	−	2.67628i
$297$	0.847090	+	0.489068i	0.0491531	+	0.0283786i
$298$	31.5891	+	18.2380i	1.82991	+	1.05650i
$299$	−13.0621	−	22.6242i	−0.755399	−	1.30839i
$300$	−18.7764	+	10.8100i	−1.08406	+	0.624118i
$301$		0			0
$302$		−	19.8481i		−	1.14213i
$303$	4.77708	−	2.75805i	0.274436	−	0.158446i
$304$	7.02660	−	12.1704i	0.403003	−	0.698022i
$305$	−0.732941	−	1.27128i	−0.0419681	−	0.0727934i
$306$	−5.22161	−	9.04410i	−0.298500	−	0.517017i
$307$		−	31.6055i		−	1.80382i	−0.431923	−	0.901910i	$-0.642165\pi$
$307$		−	31.6055i		−	1.80382i	0.431923	−	0.901910i	$-0.357835\pi$
$308$		0			0
$309$	16.5213			0.939865
$310$	0.00217362	−	3.56310i	0.000123454	−	0.202371i
$311$	11.0851	−	19.2000i	0.628581	−	1.08873i	−0.359256	−	0.933239i	$-0.616969\pi$
$311$	11.0851	−	19.2000i	0.628581	−	1.08873i	0.987837	−	0.155495i	$-0.0496972\pi$
$312$	−26.1864	−	15.1187i	−1.48251	−	0.855930i
$313$	5.96321	−	3.44286i	0.337060	−	0.194602i	−0.321911	−	0.946770i	$-0.604325\pi$
$313$	5.96321	−	3.44286i	0.337060	−	0.194602i	0.658971	+	0.752168i	$0.270992\pi$
$314$	16.4995			0.931118
$315$		0			0
$316$	−47.1749			−2.65380
$317$	11.1186	−	6.41935i	0.624485	−	0.360547i	−0.154128	−	0.988051i	$-0.549257\pi$
$317$	11.1186	−	6.41935i	0.624485	−	0.360547i	0.778613	+	0.627504i	$0.215923\pi$
$318$	−16.6359	−	9.60476i	−0.932897	−	0.538608i
$319$	2.89853	−	5.02040i	0.162286	−	0.281088i
$320$	−6.88013	−	0.00419713i	−0.384611	−	0.000234627i
$321$	−2.38820			−0.133296
$322$		0			0
$323$			9.54453i			0.531072i
$324$	2.16659	+	3.75264i	0.120366	+	0.208480i
$325$	0.0314155	−	25.7488i	0.00174262	−	1.42829i
$326$	15.4214	−	26.7106i	0.854110	−	1.47936i
$327$	15.6833	−	9.05479i	0.867291	−	0.500731i
$328$		−	15.5895i		−	0.860784i
$329$		0			0
$330$	2.75501	−	4.76510i	0.151658	−	0.262310i
$331$	4.26678	+	7.39028i	0.234524	+	0.406207i	0.959134	−	0.282952i	$-0.0913137\pi$
$331$	4.26678	+	7.39028i	0.234524	+	0.406207i	−0.724611	+	0.689159i	$0.757980\pi$
$332$	−24.8673	−	14.3572i	−1.36477	−	0.787952i
$333$	−7.84188	−	4.52751i	−0.429732	−	0.248106i
$334$	2.68317	+	4.64738i	0.146816	+	0.254293i
$335$	17.9252	+	10.3637i	0.979360	+	0.566231i
$336$		0			0
$337$		−	29.1131i		−	1.58589i	−0.609292	−	0.792946i	$-0.708546\pi$
$337$		−	29.1131i		−	1.58589i	0.609292	−	0.792946i	$-0.291454\pi$
$338$	29.4660	−	17.0122i	1.60274	−	0.925343i
$339$	2.02186	−	3.50197i	0.109813	−	0.190201i
$340$	−34.8336	+	20.0829i	−1.88912	+	1.08915i
$341$	0.309672	+	0.536367i	0.0167697	+	0.0290459i
$342$		−	5.78817i		−	0.312988i
$343$		0			0
$344$	−2.02540			−0.109202
$345$	11.3433	+	0.00691983i	0.610703	+	0.000372551i
$346$	14.5314	−	25.1691i	0.781213	−	1.35310i
$347$	11.6418	+	6.72137i	0.624962	+	0.360822i	0.778798	−	0.627274i	$-0.215829\pi$
$347$	11.6418	+	6.72137i	0.624962	+	0.360822i	−0.153836	+	0.988096i	$0.549163\pi$
$348$	22.2405	−	12.8406i	1.19222	−	0.688328i
$349$	−24.7397			−1.32429			−0.662144	−	0.749377i	$-0.730353\pi$
$349$	−24.7397			−1.32429			−0.662144	+	0.749377i	$0.730353\pi$
$350$		0			0
$351$	−5.14977			−0.274874
$352$	−3.07764	+	1.77687i	−0.164039	+	0.0947077i
$353$	−14.5103	−	8.37751i	−0.772303	−	0.445890i	0.0613923	−	0.998114i	$-0.480446\pi$
$353$	−14.5103	−	8.37751i	−0.772303	−	0.445890i	−0.833696	+	0.552224i	$0.813779\pi$
$354$	−2.28580	+	3.95913i	−0.121489	+	0.210425i
$355$	12.2839	+	0.00749361i	0.651960	+	0.000397719i
$356$	−70.6777			−3.74591
$357$		0			0
$358$			22.3965i			1.18369i
$359$	−16.2462	−	28.1393i	−0.857442	−	1.48513i	−0.874361	−	0.485276i	$-0.838719\pi$
$359$	−16.2462	−	28.1393i	−0.857442	−	1.48513i	0.0169190	−	0.999857i	$-0.494614\pi$
$360$	11.3743	−	6.55773i	0.599481	−	0.345623i
$361$	6.85497	−	11.8732i	0.360788	−	0.624903i
$362$	−6.92925	+	4.00060i	−0.364193	+	0.210267i
$363$		−	10.0433i		−	0.527134i
$364$		0			0
$365$	−10.4110	−	6.01926i	−0.544936	−	0.315062i
$366$	0.825761	+	1.43026i	0.0431632	+	0.0747608i
$367$	20.7516	+	11.9809i	1.08322	+	0.625400i	0.931764	−	0.363064i	$-0.118269\pi$
$367$	20.7516	+	11.9809i	1.08322	+	0.625400i	0.151460	+	0.988463i	$0.451603\pi$
$368$	−26.8429	−	15.4978i	−1.39928	−	0.807877i
$369$	−1.32753	−	2.29934i	−0.0691083	−	0.119699i
$370$	−25.5043	+	44.1126i	−1.32591	+	2.29331i
$371$		0			0
$372$			2.74372i			0.142255i
$373$	9.59160	−	5.53771i	0.496634	−	0.286732i	−0.230688	−	0.973028i	$-0.574098\pi$
$373$	9.59160	−	5.53771i	0.496634	−	0.286732i	0.727323	+	0.686296i	$0.240764\pi$
$374$	5.10744	−	8.84635i	0.264100	−	0.457434i
$375$	9.67221	+	5.60788i	0.499471	+	0.289590i
$376$	−12.4432	−	21.5523i	−0.641710	−	1.11147i
$377$			30.5208i			1.57190i
$378$		0			0
$379$	32.7423			1.68186			0.840929	−	0.541145i	$-0.182009\pi$
$379$	32.7423			1.68186			0.840929	+	0.541145i	$0.182009\pi$
$380$	−22.2855	−	0.0135949i	−1.14322	−	0.000697406i
$381$	−3.42512	+	5.93247i	−0.175474	+	0.303930i
$382$	−1.35695	−	0.783435i	−0.0694275	−	0.0400840i
$383$	20.1371	−	11.6262i	1.02896	−	0.594069i	0.112271	−	0.993678i	$-0.464187\pi$
$383$	20.1371	−	11.6262i	1.02896	−	0.594069i	0.916686	+	0.399609i	$0.130854\pi$
$384$	15.0096			0.765956
$385$		0			0
$386$	−38.2210			−1.94540
$387$	−0.298733	+	0.172473i	−0.0151854	+	0.00876732i
$388$	−5.77323	−	3.33317i	−0.293091	−	0.169216i
$389$	−18.8131	+	32.5852i	−0.953861	+	1.65214i	−0.216907	+	0.976192i	$0.569597\pi$
$389$	−18.8131	+	32.5852i	−0.953861	+	1.65214i	−0.736954	+	0.675943i	$0.763737\pi$
$390$	−0.0176782	+	28.9790i	−0.000895173	+	1.46741i
$391$	21.0513			1.06461
$392$		0			0
$393$			4.02540i			0.203054i
$394$	−30.1247	−	52.1775i	−1.51766	−	2.62867i
$395$	12.1591	+	21.0899i	0.611790	+	1.06115i
$396$	−2.11922	+	3.67059i	−0.106495	+	0.184454i
$397$	−0.0498605	+	0.0287870i	−0.00250243	+	0.00144478i	−0.501251	−	0.865302i	$-0.667127\pi$
$397$	−0.0498605	+	0.0287870i	−0.00250243	+	0.00144478i	0.498748	+	0.866747i	$0.333793\pi$
$398$		−	35.1144i		−	1.76013i
$399$		0			0
$400$	−15.2428	−	26.4759i	−0.762142	−	1.32380i
$401$	4.53797	+	7.85999i	0.226615	+	0.392509i	0.956803	−	0.290738i	$-0.0939007\pi$
$401$	4.53797	+	7.85999i	0.226615	+	0.392509i	−0.730188	+	0.683247i	$0.760567\pi$
$402$	−20.1810	−	11.6515i	−1.00654	−	0.581126i
$403$	−2.82391	−	1.63039i	−0.140669	−	0.0812153i
$404$	11.9511	+	20.6999i	0.594590	+	1.02986i
$405$	1.11922	−	1.93581i	0.0556142	−	0.0961911i
$406$		0			0
$407$		−	8.85704i		−	0.439027i
$408$	21.1014	−	12.1829i	1.04468	−	0.603145i
$409$	−8.30602	+	14.3865i	−0.410706	+	0.711364i	−0.994967	−	0.100202i	$-0.968051\pi$
$409$	−8.30602	+	14.3865i	−0.410706	+	0.711364i	0.584261	+	0.811566i	$0.301385\pi$
$410$	−12.9435	+	7.46242i	−0.639235	+	0.368543i
$411$	−5.61594	−	9.72709i	−0.277014	−	0.479802i
$412$			71.5897i			3.52697i
$413$		0			0
$414$	−12.7663			−0.627430
$415$	−0.00903927	+	14.8176i	−0.000443720	+	0.727367i
$416$	9.35504	−	16.2034i	0.458669	−	0.794437i
$417$	4.32139	+	2.49495i	0.211619	+	0.122178i
$418$	4.90310	−	2.83081i	0.239818	−	0.138459i
$419$	−29.8759			−1.45953			−0.729766	−	0.683697i	$-0.760371\pi$
$419$	−29.8759			−1.45953			−0.729766	+	0.683697i	$0.760371\pi$
$420$		0			0
$421$	−19.3201			−0.941602			−0.470801	−	0.882239i	$-0.656035\pi$
$421$	−19.3201			−0.941602			−0.470801	+	0.882239i	$0.656035\pi$
$422$	−10.5117	+	6.06893i	−0.511701	+	0.295431i
$423$	−3.67059	−	2.11922i	−0.178470	−	0.103040i
$424$	22.4096	−	38.8145i	1.08831	−	1.88500i
$425$	17.9564	+	10.3963i	0.871011	+	0.504296i
$426$	−13.8249			−0.669817
$427$		0			0
$428$		−	10.3485i		−	0.500213i
$429$	−2.51858	−	4.36232i	−0.121598	−	0.210615i
$430$	0.969525	+	1.68163i	0.0467546	+	0.0810956i
$431$	10.9981	−	19.0493i	0.529761	−	0.917572i	−0.469637	−	0.882860i	$-0.655615\pi$
$431$	10.9981	−	19.0493i	0.529761	−	0.917572i	0.999397	−	0.0347127i	$-0.0110516\pi$
$432$	−5.29146	+	3.05502i	−0.254585	+	0.146985i
$433$			2.72706i			0.131054i	0.997851	+	0.0655272i	$0.0208729\pi$
$433$			2.72706i			0.131054i	−0.997851	+	0.0655272i	$0.979127\pi$
$434$		0			0
$435$	−11.4729	−	6.63319i	−0.550081	−	0.318037i
$436$	39.2360	+	67.9587i	1.87906	+	3.25463i
$437$	10.1045	+	5.83385i	0.483365	+	0.279071i
$438$	11.7212	+	6.76722i	0.560059	+	0.323350i
$439$	3.77183	+	6.53300i	0.180020	+	0.311803i	0.941887	−	0.335930i	$-0.109051\pi$
$439$	3.77183	+	6.53300i	0.180020	+	0.311803i	−0.761867	+	0.647733i	$0.775717\pi$
$440$	11.1178	+	6.42792i	0.530021	+	0.306439i
$441$		0			0
$442$			53.7802i			2.55806i
$443$	−9.03987	+	5.21917i	−0.429497	+	0.247970i	−0.699132	−	0.714992i	$-0.746430\pi$
$443$	−9.03987	+	5.21917i	−0.429497	+	0.247970i	0.269635	+	0.962963i	$0.413097\pi$
$444$	19.6185	−	33.9802i	0.931053	−	1.61263i
$445$	18.2168	+	31.5969i	0.863559	+	1.49784i
$446$	−19.9095	−	34.4843i	−0.942743	−	1.63288i
$447$			14.4942i			0.685554i
$448$		0			0
$449$	1.73107			0.0816944			0.0408472	−	0.999165i	$-0.486994\pi$
$449$	1.73107			0.0816944			0.0408472	+	0.999165i	$0.486994\pi$
$450$	−10.8894	−	6.30474i	−0.513332	−	0.297208i
$451$	1.29850	−	2.24907i	0.0611440	−	0.105905i
$452$	15.1747	+	8.76109i	0.713756	+	0.412087i
$453$	6.83028	−	3.94346i	0.320914	−	0.185280i
$454$	54.6055			2.56276
$455$		0			0
$456$	13.5048			0.632421
$457$	−26.7268	+	15.4307i	−1.25023	+	0.721819i	−0.971154	−	0.238452i	$-0.923360\pi$
$457$	−26.7268	+	15.4307i	−1.25023	+	0.721819i	−0.279072	+	0.960270i	$0.590027\pi$
$458$	−4.52642	−	2.61333i	−0.211506	−	0.122113i
$459$	2.07488	−	3.59380i	0.0968473	−	0.167744i
$460$	−0.0299848	+	49.1525i	−0.00139805	+	2.29175i
$461$	−10.7294			−0.499718			−0.249859	−	0.968282i	$-0.580384\pi$
$461$	−10.7294			−0.499718			−0.249859	+	0.968282i	$0.580384\pi$
$462$		0			0
$463$			11.1060i			0.516141i	0.966126	+	0.258071i	$0.0830867\pi$
$463$			11.1060i			0.516141i	−0.966126	+	0.258071i	$0.916913\pi$
$464$	18.1060	+	31.3606i	0.840552	+	1.45588i
$465$	1.22660	−	0.707178i	0.0568820	−	0.0327946i
$466$	−8.50481	+	14.7308i	−0.393978	+	0.682389i
$467$	23.8932	−	13.7947i	1.10564	−	0.638344i	0.167946	−	0.985796i	$-0.446286\pi$
$467$	23.8932	−	13.7947i	1.10564	−	0.638344i	0.937698	+	0.347452i	$0.112953\pi$
$468$		−	22.3148i		−	1.03150i
$469$		0			0
$470$	−11.9379	+	20.6480i	−0.550656	+	0.952422i
$471$	3.27815	+	5.67792i	0.151049	+	0.261625i
$472$	−9.23733	−	5.33317i	−0.425182	−	0.245479i
$473$	−0.292201	−	0.168702i	−0.0134354	−	0.00775694i
$474$	−13.6989	−	23.7272i	−0.629212	−	1.08983i
$475$	5.73788	+	9.96636i	0.263272	+	0.457288i
$476$		0			0
$477$		−	7.63319i		−	0.349500i
$478$	−6.33074	+	3.65505i	−0.289561	+	0.167178i
$479$	5.00869	−	8.67530i	0.228853	−	0.396385i	−0.728616	−	0.684923i	$-0.759836\pi$
$479$	5.00869	−	8.67530i	0.228853	−	0.396385i	0.957468	+	0.288538i	$0.0931692\pi$
$480$	4.05774	+	7.03812i	0.185209	+	0.321245i
$481$	23.3156	+	40.3839i	1.06310	+	1.84135i
$482$		−	22.3913i		−	1.01989i
$483$		0			0
$484$	43.5192			1.97814
$485$	−0.00209857	+	3.44007i	−9.52910e−5	+	0.156205i
$486$	−1.25829	+	2.17942i	−0.0570772	+	0.0988606i
$487$	−26.6165	−	15.3671i	−1.20611	−	0.696348i	−0.244203	−	0.969724i	$-0.578526\pi$
$487$	−26.6165	−	15.3671i	−1.20611	−	0.696348i	−0.961907	+	0.273376i	$0.911860\pi$
$488$	−3.33704	+	1.92664i	−0.151061	+	0.0872150i
$489$	12.2558			0.554227
$490$		0			0
$491$	4.14054			0.186860			0.0934301	−	0.995626i	$-0.470217\pi$
$491$	4.14054			0.186860			0.0934301	+	0.995626i	$0.470217\pi$
$492$	9.96346	−	5.75240i	0.449187	−	0.259338i
$493$	−21.2992	−	12.2971i	−0.959268	−	0.553833i
$494$	−14.9039	+	25.8143i	−0.670557	+	1.16144i
$495$	2.18718	+	0.00133426i	0.0983063	+	5.99704e-5i
$496$	−3.86881			−0.173715
$497$		0			0
$498$		−	16.6764i		−	0.747289i
$499$	−0.774139	−	1.34085i	−0.0346552	−	0.0600246i	0.848178	−	0.529712i	$-0.177700\pi$
$499$	−0.774139	−	1.34085i	−0.0346552	−	0.0600246i	−0.882833	+	0.469687i	$0.844367\pi$
$500$	−24.2999	+	41.9114i	−1.08673	+	1.87433i
$501$	−1.06620	+	1.84671i	−0.0476341	+	0.0825047i
$502$	−46.1486	+	26.6439i	−2.05971	+	1.18918i
$503$		−	15.1658i		−	0.676210i	−0.941108	−	0.338105i	$-0.890214\pi$
$503$		−	15.1658i		−	0.676210i	0.941108	−	0.338105i	$-0.109786\pi$
$504$		0			0
$505$	6.17370	−	10.6781i	0.274726	−	0.475170i
$506$	−6.24359	−	10.8142i	−0.277561	−	0.480750i
$507$	11.7088	+	6.76006i	0.520004	+	0.300225i
$508$	−25.7064	−	14.8416i	−1.14054	−	0.658491i
$509$	10.2327	+	17.7236i	0.453558	+	0.785586i	0.998604	−	0.0528204i	$-0.0168211\pi$
$509$	10.2327	+	17.7236i	0.453558	+	0.785586i	−0.545046	+	0.838406i	$0.683488\pi$
$510$	−20.2161	−	11.6882i	−0.895183	−	0.517563i
$511$		0			0
$512$			49.5528i			2.18994i
$513$	1.99187	−	1.15001i	0.0879432	−	0.0507741i
$514$	7.84471	−	13.5874i	0.346015	−	0.599316i
$515$	32.0047	−	18.4519i	1.41029	−	0.813087i
$516$	−0.747358	−	1.29446i	−0.0329006	−	0.0569855i
$517$		−	4.14576i		−	0.182330i
$518$		0			0
$519$	11.5485			0.506924
$520$	−67.6130	−	0.0412464i	−2.96503	−	0.00180878i
$521$	1.37337	−	2.37875i	0.0601685	−	0.104215i	−0.834372	−	0.551202i	$-0.814170\pi$
$521$	1.37337	−	2.37875i	0.0601685	−	0.104215i	0.894541	+	0.446987i	$0.147503\pi$
$522$	12.9167	+	7.45743i	0.565347	+	0.326403i
$523$	−34.5258	+	19.9335i	−1.50971	+	0.871629i	−0.509770	+	0.860311i	$0.670269\pi$
$523$	−34.5258	+	19.9335i	−1.50971	+	0.871629i	−0.999936	+	0.0113184i	$0.996397\pi$
$524$	−17.4427			−0.761990
$525$		0			0
$526$	70.5850			3.07765
$527$	2.27556	−	1.31379i	0.0991247	−	0.0572297i
$528$	−5.17576	−	2.98823i	−0.225246	−	0.130046i
$529$	1.36705	−	2.36780i	0.0594370	−	0.102948i
$530$	−42.9538	−	0.0262034i	−1.86579	−	0.00113820i
$531$	−1.81659			−0.0788335
$532$		0			0
$533$			13.6729i			0.592239i
$534$	−20.5238	−	35.5482i	−0.888150	−	1.53832i
$535$	−4.62635	+	2.66727i	−0.200015	+	0.115316i
$536$	27.1851	−	47.0859i	1.17422	−	2.03380i
$537$	−7.70725	+	4.44978i	−0.332592	+	0.192022i
$538$		−	18.6688i		−	0.804867i
$539$		0			0
$540$	8.38820	+	4.84975i	0.360971	+	0.208700i
$541$	−13.2493	−	22.9485i	−0.569633	−	0.986633i	−0.996602	−	0.0823667i	$-0.973752\pi$
$541$	−13.2493	−	22.9485i	−0.569633	−	0.986633i	0.426969	−	0.904266i	$-0.359581\pi$
$542$	68.0232	+	39.2732i	2.92185	+	1.68693i
$543$	−2.75344	−	1.58970i	−0.118161	−	0.0682205i
$544$	7.53844	+	13.0570i	0.323208	+	0.559813i
$545$	20.2685	−	35.0567i	0.868207	−	1.50166i
$546$		0			0
$547$		−	12.9090i		−	0.551950i	−0.961165	−	0.275975i	$-0.910999\pi$
$547$		−	12.9090i		−	0.551950i	0.961165	−	0.275975i	$-0.0890008\pi$
$548$	42.1492	−	24.3348i	1.80052	−	1.03953i
$549$	−0.328128	+	0.568335i	−0.0140042	+	0.0242559i
$550$	0.0150164	−	12.3078i	0.000640301	−	0.524805i
$551$	−6.81568	−	11.8051i	−0.290358	−	0.502914i
$552$		−	29.7860i		−	1.26778i
$553$		0			0
$554$	−31.3379			−1.33142
$555$	−20.2476	−	0.0123518i	−0.859465	−	0.000524305i
$556$	−10.8111	+	18.7253i	−0.458492	+	0.794131i
$557$	6.22247	+	3.59254i	0.263654	+	0.152221i	0.626000	−	0.779823i	$-0.284691\pi$
$557$	6.22247	+	3.59254i	0.263654	+	0.152221i	−0.362346	+	0.932044i	$0.618024\pi$
$558$	−1.37998	+	0.796734i	−0.0584194	+	0.0337285i
$559$	1.77640			0.0751336
$560$		0			0
$561$	4.05903			0.171373
$562$	0.0891873	−	0.0514923i	0.00376214	−	0.00217207i
$563$	2.06720	+	1.19350i	0.0871220	+	0.0502999i	0.542928	−	0.839779i	$-0.317316\pi$
$563$	2.06720	+	1.19350i	0.0871220	+	0.0502999i	−0.455806	+	0.890079i	$0.650649\pi$
$564$	9.18293	−	15.9053i	0.386671	−	0.669734i
$565$	0.00551598	−	9.04205i	0.000232059	−	0.380402i
$566$	27.2847			1.14686
$567$		0			0
$568$		−	32.2558i		−	1.35342i
$569$	14.9271	+	25.8545i	0.625776	+	1.08388i	0.988390	+	0.151936i	$0.0485508\pi$
$569$	14.9271	+	25.8545i	0.625776	+	1.08388i	−0.362615	+	0.931939i	$0.618116\pi$
$570$	−6.46453	−	11.2127i	−0.270769	−	0.469648i
$571$	9.73170	−	16.8558i	0.407259	−	0.705393i	−0.587322	−	0.809353i	$-0.699818\pi$
$571$	9.73170	−	16.8558i	0.407259	−	0.705393i	0.994582	+	0.103960i	$0.0331513\pi$
$572$	18.9027	−	10.9135i	0.790361	−	0.456315i
$573$		−	0.622618i		−	0.0260103i
$574$		0			0
$575$	21.9817	−	12.6554i	0.916699	−	0.527766i
$576$	1.53844	+	2.66466i	0.0641019	+	0.111028i
$577$	−3.43108	−	1.98094i	−0.142838	−	0.0824675i	0.426878	−	0.904309i	$-0.359613\pi$
$577$	−3.43108	−	1.98094i	−0.142838	−	0.0824675i	−0.569716	+	0.821842i	$0.692947\pi$
$578$	−0.480727	−	0.277548i	−0.0199956	−	0.0115445i
$579$	−7.59383	−	13.1529i	−0.315589	−	0.546616i
$580$	28.7428	−	49.7139i	1.19348	−	2.06426i
$581$		0			0
$582$		−	3.87162i		−	0.160484i
$583$	6.46600	−	3.73315i	0.267794	−	0.154611i
$584$	−15.7891	+	27.3475i	−0.653357	+	1.13165i
$585$	−9.97599	+	5.75153i	−0.412457	+	0.237797i
$586$	−37.3026	−	64.6100i	−1.54096	−	2.66901i
$587$		−	13.9419i		−	0.575446i	−0.957714	−	0.287723i	$-0.907102\pi$
$587$		−	13.9419i		−	0.575446i	0.957714	−	0.287723i	$-0.0928982\pi$
$588$		0			0
$589$	1.45634			0.0600075
$590$	−0.00623605	+	10.2224i	−0.000256734	+	0.420850i
$591$	11.9705	−	20.7335i	0.492400	−	0.852863i
$592$	47.9143	+	27.6633i	1.96926	+	1.13696i
$593$	−33.3396	+	19.2486i	−1.36909	+	0.790447i	−0.990812	−	0.135243i	$-0.956818\pi$
$593$	−33.3396	+	19.2486i	−1.36909	+	0.790447i	−0.378282	+	0.925690i	$0.623485\pi$
$594$	−2.46156			−0.100999
$595$		0			0
$596$	−62.8061			−2.57264
$597$	12.0839	−	6.97662i	0.494560	−	0.285534i
$598$	56.9356	+	32.8718i	2.32827	+	1.34423i
$599$	8.74985	−	15.1552i	0.357509	−	0.619224i	−0.630035	−	0.776567i	$-0.716959\pi$
$599$	8.74985	−	15.1552i	0.357509	−	0.619224i	0.987544	+	0.157343i	$0.0502927\pi$
$600$	14.7101	−	25.4069i	0.600536	−	1.03723i
$601$	−34.5192			−1.40807			−0.704033	−	0.710167i	$-0.748619\pi$
$601$	−34.5192			−1.40807			−0.704033	+	0.710167i	$0.748619\pi$
$602$		0			0
$603$		−	9.25982i		−	0.377089i
$604$	17.0877	+	29.5968i	0.695289	+	1.20428i
$605$	−11.2168	−	19.4555i	−0.456029	−	0.790979i
$606$	−6.94086	+	12.0219i	−0.281953	+	0.488357i
$607$	−9.45318	+	5.45780i	−0.383693	+	0.221525i	−0.679424	−	0.733746i	$-0.737770\pi$
$607$	−9.45318	+	5.45780i	−0.383693	+	0.221525i	0.295731	+	0.955271i	$0.404437\pi$
$608$			8.35639i			0.338896i
$609$		0			0
$610$	3.19703	+	1.84841i	0.129444	+	0.0748398i
$611$	10.9135	+	18.9027i	0.441512	+	0.764721i
$612$	15.5726	+	8.99083i	0.629484	+	0.363433i
$613$	−22.6183	−	13.0587i	−0.913543	−	0.527435i	−0.0319739	−	0.999489i	$-0.510179\pi$
$613$	−22.6183	−	13.0587i	−0.913543	−	0.527435i	−0.881570	+	0.472054i	$0.843513\pi$
$614$	39.7689	+	68.8817i	1.60494	+	2.77984i
$615$	−5.13968	−	2.97158i	−0.207252	−	0.119825i
$616$		0			0
$617$			11.6689i			0.469772i	0.972023	+	0.234886i	$0.0754717\pi$
$617$			11.6689i			0.469772i	−0.972023	+	0.234886i	$0.924528\pi$
$618$	−36.0069	+	20.7886i	−1.44841	+	0.836240i
$619$	0.411816	−	0.713286i	0.0165523	−	0.0286694i	−0.857631	−	0.514266i	$-0.828064\pi$
$619$	0.411816	−	0.713286i	0.0165523	−	0.0286694i	0.874183	+	0.485597i	$0.161398\pi$
$620$	3.06432	+	5.31505i	0.123066	+	0.213458i
$621$	−2.53644	−	4.39324i	−0.101784	−	0.176295i
$622$			55.7933i			2.23711i
$623$		0			0
$624$	31.4653			1.25962
$625$	24.9999	+	0.0610036i	0.999997	+	0.00244014i
$626$	−8.66423	+	15.0069i	−0.346292	+	0.599796i
$627$	1.94832	+	1.12486i	0.0778084	+	0.0449227i
$628$	−24.6034	+	14.2048i	−0.981783	+	0.566833i
$629$	−37.5763			−1.49826
$630$		0			0
$631$	−20.5920			−0.819755			−0.409877	−	0.912141i	$-0.634429\pi$
$631$	−20.5920			−0.819755			−0.409877	+	0.912141i	$0.634429\pi$
$632$	55.3597	−	31.9619i	2.20209	−	1.27138i
$633$	−4.17697	−	2.41158i	−0.166020	−	0.0958516i
$634$	−16.1548	+	27.9810i	−0.641590	+	1.11127i
$635$	−0.00934428	+	15.3176i	−0.000370817	+	0.607860i
$636$	33.0759			1.31155
$637$		0			0
$638$			14.5888i			0.577575i
$639$	−2.74676	−	4.75752i	−0.108660	−	0.188205i
$640$	29.0762	−	16.7635i	1.14934	−	0.662636i
$641$	−14.8371	+	25.6986i	−0.586029	+	1.01503i	0.408717	+	0.912661i	$0.365976\pi$
$641$	−14.8371	+	25.6986i	−0.586029	+	1.01503i	−0.994746	+	0.102371i	$0.967357\pi$
$642$	5.20489	−	3.00505i	0.205421	−	0.118600i
$643$			11.1286i			0.438870i	0.975627	+	0.219435i	$0.0704214\pi$
$643$			11.1286i			0.438870i	−0.975627	+	0.219435i	$0.929579\pi$
$644$		0			0
$645$	−0.386070	+	0.667751i	−0.0152015	+	0.0262927i
$646$	−12.0098	−	20.8016i	−0.472519	−	0.818426i
$647$	−9.45991	−	5.46168i	−0.371907	−	0.214721i	0.302384	−	0.953186i	$-0.402217\pi$
$647$	−9.45991	−	5.46168i	−0.371907	−	0.214721i	−0.674291	+	0.738465i	$0.735551\pi$
$648$	−5.08497	−	2.93581i	−0.199757	−	0.115329i
$649$	−0.888437	−	1.53882i	−0.0348742	−	0.0604039i
$650$	32.3310	+	56.1571i	1.26813	+	2.20266i
$651$		0			0
$652$			53.1065i			2.07981i
$653$	6.21006	−	3.58538i	0.243019	−	0.140307i	−0.373545	−	0.927612i	$-0.621858\pi$
$653$	6.21006	−	3.58538i	0.243019	−	0.140307i	0.616563	+	0.787305i	$0.288524\pi$
$654$	−22.7871	+	39.4684i	−0.891046	+	1.54334i
$655$	4.49577	+	7.79789i	0.175664	+	0.304689i
$656$	8.11125	+	14.0491i	0.316691	+	0.548525i
$657$			5.37811i			0.209820i
$658$		0			0
$659$	−14.1232			−0.550161			−0.275080	−	0.961421i	$-0.588704\pi$
$659$	−14.1232			−0.550161			−0.275080	+	0.961421i	$0.588704\pi$
$660$	−0.00578157	+	9.47742i	−0.000225047	+	0.368908i
$661$	14.4608	−	25.0469i	0.562461	−	0.974212i	−0.434819	−	0.900518i	$-0.643188\pi$
$661$	14.4608	−	25.0469i	0.562461	−	0.974212i	0.997281	−	0.0736941i	$-0.0234789\pi$
$662$	−18.5982	−	10.7377i	−0.722841	−	0.417333i
$663$	−18.5073	+	10.6852i	−0.718762	+	0.414978i
$664$	38.9090			1.50996
$665$		0			0
$666$	22.7877			0.883005
$667$	−26.0372	+	15.0326i	−1.00816	+	0.582063i
$668$	−8.00210	−	4.62001i	−0.309610	−	0.178754i
$669$	7.91134	−	13.7028i	0.305870	−	0.529782i
$670$	−52.1072	−	0.0317873i	−2.01308	−	0.00122805i
$671$	−0.641907			−0.0247806
$672$		0			0
$673$			14.4081i			0.555392i	0.960669	+	0.277696i	$0.0895709\pi$
$673$			14.4081i			0.555392i	−0.960669	+	0.277696i	$0.910429\pi$
$674$	36.6327	+	63.4497i	1.41104	+	2.44399i
$675$	0.00610036	−	5.00000i	0.000234803	−	0.192450i
$676$	−29.2925	+	50.7361i	−1.12663	+	1.95139i
$677$	26.0991	−	15.0683i	1.00307	−	0.579123i	0.0939148	−	0.995580i	$-0.470062\pi$
$677$	26.0991	−	15.0683i	1.00307	−	0.579123i	0.909155	+	0.416457i	$0.136729\pi$
$678$			10.1764i			0.390821i
$679$		0			0
$680$	27.2706	−	47.1676i	1.04578	−	1.80880i
$681$	10.8492	+	18.7913i	0.415740	+	0.720084i
$682$	−1.34981	−	0.779314i	−0.0516870	−	0.0298415i
$683$	−13.4380	−	7.75842i	−0.514190	−	0.296868i	0.220364	−	0.975418i	$-0.429275\pi$
$683$	−13.4380	−	7.75842i	−0.514190	−	0.296868i	−0.734554	+	0.678550i	$0.762609\pi$
$684$	4.98318	+	8.63112i	0.190537	+	0.330019i
$685$	−21.7428	−	12.5709i	−0.830748	−	0.480309i
$686$		0			0
$687$		−	2.07689i		−	0.0792383i
$688$	1.82527	−	1.05382i	0.0695878	−	0.0401766i
$689$	−19.6546	+	34.0427i	−0.748780	+	1.29692i
$690$	−24.7305	+	14.2581i	−0.941476	+	0.542796i
$691$	22.8917	+	39.6496i	0.870842	+	1.50834i	0.861127	+	0.508391i	$0.169759\pi$
$691$	22.8917	+	39.6496i	0.870842	+	1.50834i	0.00971588	+	0.999953i	$0.496907\pi$
$692$			50.0418i			1.90230i
$693$		0			0
$694$	−33.8297			−1.28416
$695$	11.1578	+	0.00680665i	0.423238	+	0.000258191i
$696$	−17.3995	+	30.1368i	−0.659526	+	1.14233i
$697$	−9.54174	−	5.50893i	−0.361419	−	0.208666i
$698$	53.9183	−	31.1298i	2.04084	−	1.17828i
$699$	−6.75902			−0.255650
$700$		0			0
$701$	24.0419			0.908050			0.454025	−	0.890989i	$-0.349988\pi$
$701$	24.0419			0.908050			0.454025	+	0.890989i	$0.349988\pi$
$702$	11.2235	−	6.47990i	0.423604	−	0.244568i
$703$	−18.0364	−	10.4133i	−0.680257	−	0.392747i
$704$	−1.50481	+	2.60640i	−0.0567145	+	0.0982325i
$705$	−9.47742	−	0.00578157i	−0.356940	−	0.000217747i
$706$	42.1653			1.58691
$707$		0			0
$708$		−	7.87162i		−	0.295834i
$709$	9.19854	+	15.9323i	0.345459	+	0.598352i	0.985437	−	0.170041i	$-0.0543901\pi$
$709$	9.19854	+	15.9323i	0.345459	+	0.598352i	−0.639978	+	0.768393i	$0.721057\pi$
$710$	−26.7812	+	15.4403i	−1.00508	+	0.579465i
$711$	5.44346	−	9.42835i	0.204146	−	0.353591i
$712$	82.9401	−	47.8855i	3.10831	−	1.79458i
$713$		−	3.21209i		−	0.120294i
$714$		0			0
$715$	−9.75100	−	5.63768i	−0.364667	−	0.210837i
$716$	−19.2817	−	33.3969i	−0.720590	−	1.24810i
$717$	−2.51561	−	1.45239i	−0.0939472	−	0.0542405i
$718$	70.8147	+	40.8849i	2.64278	+	1.52581i
$719$	8.12275	+	14.0690i	0.302927	+	0.524686i	0.976798	−	0.214164i	$-0.0687027\pi$
$719$	8.12275	+	14.0690i	0.302927	+	0.524686i	−0.673870	+	0.738850i	$0.735369\pi$
$720$	−6.83846	+	11.8279i	−0.254854	+	0.440799i
$721$		0			0
$722$			34.5021i			1.28404i
$723$	7.70546	−	4.44875i	0.286569	−	0.165451i
$724$	6.88844	−	11.9311i	0.256007	−	0.443417i
$725$	−29.6332	−	0.0361547i	−1.10055	−	0.00134275i
$726$	12.6373	+	21.8885i	0.469015	+	0.812358i
$727$		−	42.6977i		−	1.58357i	−0.610800	−	0.791785i	$-0.709152\pi$
$727$		−	42.6977i		−	1.58357i	0.610800	−	0.791785i	$-0.290848\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	30.2639	+	0.0184621i	1.12012	+	0.000683313i
$731$	−0.715725	+	1.23967i	−0.0264720	+	0.0458509i
$732$	−2.46269	−	1.42184i	−0.0910237	−	0.0525526i
$733$	40.4538	−	23.3560i	1.49420	−	0.862674i	0.494218	−	0.869338i	$-0.335455\pi$
$733$	40.4538	−	23.3560i	1.49420	−	0.862674i	0.999978	+	0.00666408i	$0.00212126\pi$
$734$	−60.3020			−2.22579
$735$		0			0
$736$	18.4307			0.679366
$737$	7.84390	−	4.52868i	0.288934	−	0.166816i
$738$	5.78648	+	3.34083i	0.213003	+	0.122978i
$739$	3.52410	−	6.10393i	0.129636	−	0.224537i	−0.793899	−	0.608049i	$-0.791952\pi$
$739$	3.52410	−	6.10393i	0.129636	−	0.224537i	0.923536	+	0.383513i	$0.125286\pi$
$740$	0.0535225	−	87.7366i	0.00196753	−	3.22526i
$741$	−11.8445			−0.435120
$742$		0			0
$743$		−	8.55510i		−	0.313856i	−0.987610	−	0.156928i	$-0.949841\pi$
$743$		−	8.55510i		−	0.313856i	0.987610	−	0.156928i	$-0.0501591\pi$
$744$	−1.85892	−	3.21974i	−0.0681513	−	0.118042i
$745$	16.1879	+	28.0778i	0.593080	+	1.02869i
$746$	−13.9361	+	24.1380i	−0.510237	+	0.883756i
$747$	5.73883	−	3.31331i	0.209973	−	0.121228i
$748$			17.5885i			0.643099i
$749$		0			0
$750$	−28.1362	−	0.0514923i	−1.02739	−	0.00188023i
$751$	1.48823	+	2.57768i	0.0543062	+	0.0940611i	0.891901	−	0.452232i	$-0.149372\pi$
$751$	1.48823	+	2.57768i	0.0543062	+	0.0940611i	−0.837594	+	0.546293i	$0.816039\pi$
$752$	22.4275	+	12.9485i	0.817846	+	0.472183i
$753$	−18.3378	−	10.5873i	−0.668267	−	0.385824i
$754$	−38.4041	−	66.5178i	−1.39859	−	2.42243i
$755$	8.82716	−	15.2676i	0.321253	−	0.555644i
$756$		0			0
$757$		−	43.6750i		−	1.58740i	−0.608313	−	0.793698i	$-0.708153\pi$
$757$		−	43.6750i		−	1.58740i	0.608313	−	0.793698i	$-0.291847\pi$
$758$	−71.3592	+	41.1993i	−2.59188	+	1.49643i
$759$	2.48098	−	4.29718i	0.0900539	−	0.155978i
$760$	26.1612	−	15.0829i	0.948965	−	0.547113i
$761$	13.3628	+	23.1451i	0.484402	+	0.839008i	0.999839	−	0.0179187i	$-0.00570401\pi$
$761$	13.3628	+	23.1451i	0.484402	+	0.839008i	−0.515438	+	0.856927i	$0.672371\pi$
$762$		−	17.2392i		−	0.624509i
$763$		0			0
$764$	2.69791			0.0976071
$765$	0.00566063	−	9.27916i	0.000204660	−	0.335489i
$766$	−29.2581	+	50.6766i	−1.05714	+	1.83102i
$767$	8.10170	+	4.67752i	0.292535	+	0.168895i
$768$	−27.3830	+	15.8096i	−0.988097	+	0.570478i
$769$	−4.04661			−0.145925			−0.0729623	−	0.997335i	$-0.523245\pi$
$769$	−4.04661			−0.145925			−0.0729623	+	0.997335i	$0.523245\pi$
$770$		0			0
$771$	6.23442			0.224527
$772$	56.9938	−	32.9054i	2.05125	−	1.18429i
$773$	5.46553	+	3.15553i	0.196581	+	0.113496i	0.595060	−	0.803681i	$-0.297128\pi$
$773$	5.46553	+	3.15553i	0.196581	+	0.113496i	−0.398478	+	0.917178i	$0.630462\pi$
$774$	0.434043	−	0.751785i	0.0156014	−	0.0270224i
$775$	1.58631	−	2.73985i	0.0569821	−	0.0984184i
$776$	9.03316			0.324272
$777$		0			0
$778$		−	94.6892i		−	3.39477i
$779$	−3.05333	−	5.28852i	−0.109397	−	0.189481i
$780$	−24.9224	−	43.2277i	−0.892365	−	1.54780i
$781$	2.68670	−	4.65350i	0.0961376	−	0.166515i
$782$	−45.8796	+	26.4886i	−1.64065	+	0.947230i
$783$			5.92664i			0.211801i
$784$		0			0
$785$	12.6917	+	7.33791i	0.452988	+	0.261901i
$786$	−5.06512	−	8.77304i	−0.180667	−	0.312924i
$787$	−25.9595	−	14.9877i	−0.925358	−	0.534256i	−0.0400174	−	0.999199i	$-0.512741\pi$
$787$	−25.9595	−	14.9877i	−0.925358	−	0.534256i	−0.885340	+	0.464943i	$0.846075\pi$
$788$	89.8419	+	51.8702i	3.20048	+	1.84780i
$789$	14.0240	+	24.2903i	0.499267	+	0.864756i
$790$	−53.0369	−	30.6640i	−1.88697	−	1.09098i
$791$		0			0
$792$		−	5.74324i		−	0.204077i
$793$	2.92679	−	1.68978i	0.103933	−	0.0600060i
$794$	0.0724448	−	0.125478i	0.00257097	−	0.00445305i
$795$	−8.52515	−	14.7868i	−0.302356	−	0.524434i
$796$	30.2309	+	52.3615i	1.07151	+	1.85590i
$797$			0.676527i			0.0239638i	0.999928	+	0.0119819i	$0.00381405\pi$
$797$			0.676527i			0.0239638i	−0.999928	+	0.0119819i	$0.996186\pi$
$798$		0			0
$799$	−17.5885			−0.622236
$800$	15.7211	+	9.10216i	0.555824	+	0.321810i
$801$	8.15542	−	14.1256i	0.288157	−	0.499103i
$802$	−19.7803	−	11.4202i	−0.698466	−	0.403260i
$803$	−4.55574	+	2.63026i	−0.160769	+	0.0928198i
$804$	40.1244			1.41508
$805$		0			0
$806$	8.20600			0.289044
$807$	6.42444	−	3.70915i	0.226151	−	0.130568i
$808$	−28.0492	−	16.1942i	−0.986768	−	0.569711i
$809$	−25.0612	+	43.4072i	−0.881104	+	1.52612i	−0.0309881	+	0.999520i	$0.509865\pi$
$809$	−25.0612	+	43.4072i	−0.881104	+	1.52612i	−0.850115	+	0.526596i	$0.823468\pi$
$810$	−0.00343282	+	5.62724i	−0.000120617	+	0.197721i
$811$	36.4884			1.28128			0.640641	−	0.767841i	$-0.278669\pi$
$811$	36.4884			1.28128			0.640641	+	0.767841i	$0.278669\pi$
$812$		0			0
$813$			31.2116i			1.09464i
$814$	11.1447	+	19.3032i	0.390622	+	0.676578i
$815$	23.7416	−	13.6879i	0.831633	−	0.479467i
$816$	−12.6776	+	21.9583i	−0.443806	+	0.768695i
$817$	−0.687090	+	0.396691i	−0.0240382	+	0.0138785i
$818$		−	41.8055i		−	1.46170i
$819$		0			0
$820$	12.8764	−	22.2711i	0.449662	−	0.777741i
$821$	−19.3654	−	33.5419i	−0.675858	−	1.17062i	−0.976217	−	0.216794i	$-0.930440\pi$
$821$	−19.3654	−	33.5419i	−0.675858	−	1.17062i	0.300359	−	0.953826i	$-0.402893\pi$
$822$	24.4790	+	14.1329i	0.853803	+	0.492943i
$823$	−18.1702	−	10.4906i	−0.633375	−	0.365679i	0.148683	−	0.988885i	$-0.452497\pi$
$823$	−18.1702	−	10.4906i	−0.633375	−	0.365679i	−0.782058	+	0.623206i	$0.785830\pi$
$824$	−48.5034	−	84.0104i	−1.68970	−	2.92664i
$825$	4.23843	−	2.44017i	0.147563	−	0.0849558i
$826$		0			0
$827$		−	37.8114i		−	1.31483i	−0.753528	−	0.657416i	$-0.771650\pi$
$827$		−	37.8114i		−	1.31483i	0.753528	−	0.657416i	$-0.228350\pi$
$828$	19.0367	−	10.9908i	0.661570	−	0.381958i
$829$	26.6591	−	46.1749i	0.925908	−	1.60372i	0.135813	−	0.990734i	$-0.456635\pi$
$829$	26.6591	−	46.1749i	0.925908	−	1.60372i	0.790095	−	0.612985i	$-0.210031\pi$
$830$	−18.6251	−	32.3052i	−0.646487	−	1.12133i
$831$	−6.22629	−	10.7843i	−0.215988	−	0.374102i
$832$		−	15.8453i		−	0.549336i
$833$		0			0
$834$	−12.5575			−0.434831
$835$	−0.00290876	+	4.76817i	−0.000100662	+	0.165009i
$836$	−4.87423	+	8.44241i	−0.168579	+	0.291987i
$837$	−0.548357	−	0.316594i	−0.0189540	−	0.0109431i
$838$	65.1121	−	37.5925i	2.24926	−	1.29861i
$839$	52.6452			1.81752			0.908758	−	0.417324i	$-0.137032\pi$
$839$	52.6452			1.81752			0.908758	+	0.417324i	$0.137032\pi$
$840$		0			0
$841$	6.12510			0.211210
$842$	42.1066	−	24.3102i	1.45109	−	0.837786i
$843$	0.0354399	+	0.0204612i	0.00122061	+	0.000704722i
$844$	10.4498	−	18.0996i	0.359696	−	0.623012i
$845$	30.2319	+	0.0184426i	1.04001	+	0.000634443i
$846$	10.6663			0.366717
$847$		0			0
$848$			46.6392i			1.60160i
$849$	5.42100	+	9.38944i	0.186048	+	0.322245i
$850$	−52.2161	−	0.0637075i	−1.79100	−	0.00218515i
$851$	−22.9675	+	39.7809i	−0.787316	+	1.36367i
$852$	20.6152	−	11.9022i	0.706264	−	0.407762i
$853$			5.01225i			0.171616i	0.996312	+	0.0858081i	$0.0273472\pi$
$853$			5.01225i			0.171616i	−0.996312	+	0.0858081i	$0.972653\pi$
$854$		0			0
$855$	2.57421	−	4.45239i	0.0880362	−	0.152268i
$856$	7.01129	+	12.1439i	0.239641	+	0.415071i
$857$	33.2737	+	19.2106i	1.13661	+	0.656222i	0.945589	−	0.325364i	$-0.105487\pi$
$857$	33.2737	+	19.2106i	1.13661	+	0.656222i	0.191021	+	0.981586i	$0.438820\pi$
$858$	10.9781	+	6.33822i	0.374787	+	0.216383i
$859$	−11.6709	−	20.2146i	−0.398207	−	0.689714i	0.595298	−	0.803505i	$-0.297034\pi$
$859$	−11.6709	−	20.2146i	−0.398207	−	0.689714i	−0.993505	+	0.113791i	$0.963701\pi$
$860$	−2.89348	−	1.67291i	−0.0986670	−	0.0570457i
$861$		0			0
$862$			55.3553i			1.88541i
$863$	−47.0908	+	27.1879i	−1.60299	+	0.925486i	−0.612103	+	0.790778i	$0.709676\pi$
$863$	−47.0908	+	27.1879i	−1.60299	+	0.925486i	−0.990885	+	0.134707i	$0.956991\pi$
$864$	1.81659	−	3.14643i	0.0618018	−	0.107044i
$865$	22.3715	−	12.8980i	0.760654	−	0.438546i
$866$	−3.43144	−	5.94342i	−0.116605	−	0.201966i
$867$		−	0.220576i		−	0.00749114i
$868$		0			0
$869$	10.6489			0.361239
$870$	33.3507	+	0.0203451i	1.13069	+	0.000689764i
$871$	−23.8430	+	41.2972i	−0.807888	+	1.39930i
$872$	−92.0866	−	53.1662i	−3.11845	−	1.80044i
$873$	1.33233	−	0.769222i	0.0450926	−	0.0260342i
$874$	−29.3627			−0.993208
$875$		0			0
$876$	−23.3043			−0.787378
$877$	−24.6434	+	14.2279i	−0.832148	+	0.480441i	−0.854587	−	0.519307i	$-0.826190\pi$
$877$	−24.6434	+	14.2279i	−0.832148	+	0.480441i	0.0224397	+	0.999748i	$0.492857\pi$
$878$	−16.4408	−	9.49211i	−0.554851	−	0.320343i
$879$	14.8227	−	25.6737i	0.499958	−	0.865953i
$880$	−13.3638	−	0.00815238i	−0.450492	−	0.000274817i
$881$	6.50466			0.219148			0.109574	−	0.993979i	$-0.465051\pi$
$881$	6.50466			0.219148			0.109574	+	0.993979i	$0.465051\pi$
$882$		0			0
$883$		−	34.7640i		−	1.16990i	−0.811069	−	0.584951i	$-0.801114\pi$
$883$		−	34.7640i		−	1.16990i	0.811069	−	0.584951i	$-0.198886\pi$
$884$	−46.3007	−	80.1952i	−1.55726	−	2.69726i
$885$	−3.51906	+	2.02887i	−0.118292	+	0.0681996i
$886$	13.1345	−	22.7496i	0.441261	−	0.764286i
$887$	−25.4214	+	14.6770i	−0.853566	+	0.492807i	−0.861853	−	0.507159i	$-0.830696\pi$
$887$	−25.4214	+	14.6770i	−0.853566	+	0.492807i	0.00828615	+	0.999966i	$0.497362\pi$
$888$			53.1676i			1.78419i
$889$		0			0
$890$	−79.4601	−	45.9410i	−2.66351	−	1.53995i
$891$	−0.489068	−	0.847090i	−0.0163844	−	0.0283786i
$892$	59.3768	+	34.2812i	1.98808	+	1.14782i
$893$	−8.44241	−	4.87423i	−0.282514	−	0.163110i
$894$	−18.2380	−	31.5891i	−0.609968	−	1.05650i
$895$	−9.96053	+	17.2279i	−0.332944	+	0.575864i
$896$		0			0
$897$			26.1242i			0.872260i
$898$	−3.77274	+	2.17819i	−0.125898	+	0.0726872i
$899$	−1.87634	+	3.24992i	−0.0625795	+	0.108391i
$900$	21.6659	+	0.0264339i	0.722195	+	0.000881131i
$901$	−15.8380	−	27.4322i	−0.527640	−	0.913899i
$902$			6.53556i			0.217610i
$903$		0			0
$904$	−23.7432			−0.789688
$905$	−7.10934	−	0.00433696i	−0.236323	−	0.000144165i
$906$	−9.92404	+	17.1889i	−0.329704	+	0.571064i
$907$	−31.4256	−	18.1436i	−1.04347	−	0.602447i	−0.122655	−	0.992449i	$-0.539141\pi$
$907$	−31.4256	−	18.1436i	−1.04347	−	0.602447i	−0.920814	+	0.390002i	$0.872474\pi$
$908$	−81.4259	+	47.0113i	−2.70221	+	1.56012i
$909$	−5.51610			−0.182958
$910$		0			0
$911$	51.6732			1.71201			0.856004	−	0.516968i	$-0.172940\pi$
$911$	51.6732			1.71201			0.856004	+	0.516968i	$0.172940\pi$
$912$	−12.1704	+	7.02660i	−0.403003	+	0.232674i
$913$	5.61335	+	3.24087i	0.185775	+	0.107257i
$914$	38.8326	−	67.2601i	1.28447	−	2.22477i
$915$	−0.000895188		1.46743i	−2.95940e−5		0.0485118i
$916$	8.99952			0.297353
$917$		0			0
$918$			10.4432i			0.344678i
$919$	−20.5188	−	35.5397i	−0.676854	−	1.17235i	−0.975923	−	0.218114i	$-0.930010\pi$
$919$	−20.5188	−	35.5397i	−0.676854	−	1.17235i	0.299069	−	0.954231i	$-0.403324\pi$
$920$	−33.2666	−	57.7007i	−1.09677	−	1.90233i
$921$	−15.8027	+	27.3712i	−0.520718	+	0.901910i
$922$	23.3839	−	13.5007i	0.770107	−	0.444621i
$923$			28.2903i			0.931187i
$924$		0			0
$925$	−39.2370	+	22.5897i	−1.29010	+	0.742745i
$926$	−13.9746	−	24.2047i	−0.459234	−	0.795417i
$927$	−14.3079	−	8.26066i	−0.469932	−	0.271316i
$928$	−18.6478	−	10.7663i	−0.612144	−	0.353421i
$929$	1.49260	+	2.58526i	0.0489706	+	0.0848196i	0.889472	−	0.456990i	$-0.151073\pi$
$929$	1.49260	+	2.58526i	0.0489706	+	0.0848196i	−0.840501	+	0.541810i	$0.817739\pi$
$930$	−1.78343	+	3.08465i	−0.0584811	+	0.101150i
$931$		0			0
$932$		−	29.2880i		−	0.959361i
$933$	−19.2000	+	11.0851i	−0.628581	+	0.362911i
$934$	−34.7155	+	60.1291i	−1.13593	+	1.96748i
$935$	7.86305	−	4.53334i	0.257149	−	0.148256i
$936$	15.1187	+	26.1864i	0.494171	+	0.855930i
$937$		−	26.1169i		−	0.853201i	−0.904440	−	0.426601i	$-0.859711\pi$
$937$		−	26.1169i		−	0.853201i	0.904440	−	0.426601i	$-0.140289\pi$
$938$		0			0
$939$	−6.88572			−0.224707
$940$	0.0250525	−	41.0673i	0.000817124	−	1.33947i
$941$	5.10580	−	8.84351i	0.166444	−	0.288290i	−0.770723	−	0.637171i	$-0.780105\pi$
$941$	5.10580	−	8.84351i	0.166444	−	0.288290i	0.937167	+	0.348880i	$0.113438\pi$
$942$	−14.2889	−	8.24973i	−0.465559	−	0.268791i
$943$	−11.6643	+	6.73438i	−0.379842	+	0.219302i
$944$	11.0995			0.361257
$945$		0			0
$946$	0.849106			0.0276068
$947$	40.3086	−	23.2722i	1.30985	−	0.756245i	0.327783	−	0.944753i	$-0.393699\pi$
$947$	40.3086	−	23.2722i	1.30985	−	0.756245i	0.982072	+	0.188509i	$0.0603653\pi$
$948$	40.8547	+	23.5875i	1.32690	+	0.766085i
$949$	13.8480	−	23.9854i	0.449525	−	0.778600i
$950$	−25.0458	−	14.5010i	−0.812594	−	0.470474i
$951$	−12.8387			−0.416324
$952$		0			0
$953$		−	30.6348i		−	0.992358i	−0.868220	−	0.496179i	$-0.834736\pi$
$953$		−	30.6348i		−	0.992358i	0.868220	−	0.496179i	$-0.165264\pi$
$954$	9.60476	+	16.6359i	0.310966	+	0.538608i
$955$	−0.695373	−	1.20612i	−0.0225017	−	0.0390291i
$956$	6.29345	−	10.9006i	0.203545	−	0.352550i
$957$	−5.02040	+	2.89853i	−0.162286	+	0.0936961i
$958$			25.2095i			0.814483i
$959$		0			0
$960$	5.95627	+	3.44370i	0.192238	+	0.111145i
$961$	15.2995	+	26.4996i	0.493533	+	0.854825i
$962$	−101.629	−	58.6757i	−3.27666	−	1.89178i
$963$	2.06824	+	1.19410i	0.0666481	+	0.0384793i
$964$	19.2772	+	33.3891i	0.620877	+	1.07539i
$965$	−29.4004	−	16.9983i	−0.946433	−	0.547193i
$966$		0			0
$967$			57.4401i			1.84715i	0.383419	+	0.923575i	$0.374747\pi$
$967$			57.4401i			1.84715i	−0.383419	+	0.923575i	$0.625253\pi$
$968$	−51.0696	+	29.4851i	−1.64144	+	0.947686i
$969$	4.77226	−	8.26580i	0.153307	−	0.265536i
$970$	−4.32403	−	7.50000i	−0.138836	−	0.240810i
$971$	24.0908	+	41.7265i	0.773110	+	1.33907i	0.935850	+	0.352397i	$0.114633\pi$
$971$	24.0908	+	41.7265i	0.773110	+	1.33907i	−0.162740	+	0.986669i	$0.552033\pi$
$972$		−	4.33317i		−	0.138987i
$973$		0			0
$974$	77.3449			2.47829
$975$	−12.9016	+	22.2834i	−0.413182	+	0.713641i
$976$	2.00488	−	3.47255i	0.0641746	−	0.111154i
$977$	11.9099	+	6.87617i	0.381031	+	0.219988i	0.678267	−	0.734816i	$-0.262731\pi$
$977$	11.9099	+	6.87617i	0.381031	+	0.219988i	−0.297236	+	0.954804i	$0.596065\pi$
$978$	−26.7106	+	15.4214i	−0.854110	+	0.493121i
$979$	15.9542			0.509898
$980$		0			0
$981$	−18.1096			−0.578194
$982$	−9.02399	+	5.21001i	−0.287967	+	0.166258i
$983$	33.0773	+	19.0972i	1.05500	+	0.609106i	0.924046	−	0.382282i	$-0.124862\pi$
$983$	33.0773	+	19.0972i	1.05500	+	0.609106i	0.130957	+	0.991388i	$0.458195\pi$
$984$	−7.79473	+	13.5009i	−0.248487	+	0.430392i
$985$	0.0326575	−	53.5337i	0.00104055	−	1.70572i
$986$	61.8933			1.97108
$987$		0			0
$988$		−	51.3245i		−	1.63285i
$989$	0.874937	+	1.51544i	0.0278214	+	0.0481880i
$990$	−4.76846	+	2.74919i	−0.151552	+	0.0873751i
$991$	−19.7600	+	34.2253i	−0.627697	+	1.08720i	0.360316	+	0.932830i	$0.382669\pi$
$991$	−19.7600	+	34.2253i	−0.627697	+	1.08720i	−0.988013	+	0.154372i	$0.950665\pi$
$992$	1.99228	−	1.15025i	0.0632551	−	0.0365204i
$993$		−	8.53357i		−	0.270805i
$994$		0			0
$995$	15.6167	−	27.0108i	0.495082	−	0.856300i
$996$	14.3572	+	24.8673i	0.454924	+	0.787952i
$997$	9.98438	+	5.76448i	0.316208	+	0.182563i	0.649701	−	0.760190i	$-0.274894\pi$
$997$	9.98438	+	5.76448i	0.316208	+	0.182563i	−0.333493	+	0.942753i	$0.608227\pi$
$998$	3.37435	+	1.94818i	0.106813	+	0.0616687i
$999$	4.52751	+	7.84188i	0.143244	+	0.248106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.q.g.214.1		16
5.4	even	2	inner	735.2.q.g.214.8		16
7.2	even	3	inner	735.2.q.g.79.8		16
7.3	odd	6		735.2.d.d.589.1		8
7.4	even	3		735.2.d.e.589.1		8
7.5	odd	6		105.2.q.a.79.8	yes	16
7.6	odd	2		105.2.q.a.4.1	✓	16
21.5	even	6		315.2.bf.b.289.1		16
21.11	odd	6		2205.2.d.o.1324.8		8
21.17	even	6		2205.2.d.s.1324.8		8
21.20	even	2		315.2.bf.b.109.8		16
28.19	even	6		1680.2.di.d.289.5		16
28.27	even	2		1680.2.di.d.529.4		16
35.3	even	12		3675.2.a.bp.1.1		4
35.4	even	6		735.2.d.e.589.8		8
35.9	even	6	inner	735.2.q.g.79.1		16
35.12	even	12		525.2.i.h.226.1		8
35.13	even	4		525.2.i.k.151.4		8
35.17	even	12		3675.2.a.bz.1.4		4
35.18	odd	12		3675.2.a.bn.1.1		4
35.19	odd	6		105.2.q.a.79.1	yes	16
35.24	odd	6		735.2.d.d.589.8		8
35.27	even	4		525.2.i.h.151.1		8
35.32	odd	12		3675.2.a.cb.1.4		4
35.33	even	12		525.2.i.k.226.4		8
35.34	odd	2		105.2.q.a.4.8	yes	16
105.59	even	6		2205.2.d.s.1324.1		8
105.74	odd	6		2205.2.d.o.1324.1		8
105.89	even	6		315.2.bf.b.289.8		16
105.104	even	2		315.2.bf.b.109.1		16
140.19	even	6		1680.2.di.d.289.4		16
140.139	even	2		1680.2.di.d.529.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.1	✓	16	7.6	odd	2
105.2.q.a.4.8	yes	16	35.34	odd	2
105.2.q.a.79.1	yes	16	35.19	odd	6
105.2.q.a.79.8	yes	16	7.5	odd	6
315.2.bf.b.109.1		16	105.104	even	2
315.2.bf.b.109.8		16	21.20	even	2
315.2.bf.b.289.1		16	21.5	even	6
315.2.bf.b.289.8		16	105.89	even	6
525.2.i.h.151.1		8	35.27	even	4
525.2.i.h.226.1		8	35.12	even	12
525.2.i.k.151.4		8	35.13	even	4
525.2.i.k.226.4		8	35.33	even	12
735.2.d.d.589.1		8	7.3	odd	6
735.2.d.d.589.8		8	35.24	odd	6
735.2.d.e.589.1		8	7.4	even	3
735.2.d.e.589.8		8	35.4	even	6
735.2.q.g.79.1		16	35.9	even	6	inner
735.2.q.g.79.8		16	7.2	even	3	inner
735.2.q.g.214.1		16	1.1	even	1	trivial
735.2.q.g.214.8		16	5.4	even	2	inner
1680.2.di.d.289.4		16	140.19	even	6
1680.2.di.d.289.5		16	28.19	even	6
1680.2.di.d.529.4		16	28.27	even	2
1680.2.di.d.529.5		16	140.139	even	2
2205.2.d.o.1324.1		8	105.74	odd	6
2205.2.d.o.1324.8		8	21.11	odd	6
2205.2.d.s.1324.1		8	105.59	even	6
2205.2.d.s.1324.8		8	21.17	even	6
3675.2.a.bn.1.1		4	35.18	odd	12
3675.2.a.bp.1.1		4	35.3	even	12
3675.2.a.bz.1.4		4	35.17	even	12
3675.2.a.cb.1.4		4	35.32	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.17942 + 1.25829i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(2.16659 - 3.75264i) q^{4} +(-2.23607 - 0.00136408i) q^{5} +2.51658 q^{6} +5.87162i q^{8} +(0.500000 + 0.866025i) q^{9} +(4.87505 - 2.81065i) q^{10} +(-0.489068 + 0.847090i) q^{11} +(-3.75264 + 2.16659i) q^{12} -5.14977i q^{13} +(1.93581 + 1.11922i) q^{15} +(-3.05502 - 5.29146i) q^{16} +(3.59380 + 2.07488i) q^{17} +(-2.17942 - 1.25829i) q^{18} +(1.15001 + 1.99187i) q^{19} +(-4.84975 + 8.38820i) q^{20} -2.46156i q^{22} +(4.39324 - 2.53644i) q^{23} +(2.93581 - 5.08497i) q^{24} +(5.00000 + 0.00610036i) q^{25} +(6.47990 + 11.2235i) q^{26} -1.00000i q^{27} -5.92664 q^{29} +(-5.62724 - 0.00343282i) q^{30} +(0.316594 - 0.548357i) q^{31} +(3.14643 + 1.81659i) q^{32} +(0.847090 - 0.489068i) q^{33} -10.4432 q^{34} +4.33317 q^{36} +(-7.84188 + 4.52751i) q^{37} +(-5.01270 - 2.89408i) q^{38} +(-2.57488 + 4.45983i) q^{39} +(0.00800937 - 13.1293i) q^{40} -2.65505 q^{41} +0.344947i q^{43} +(2.11922 + 3.67059i) q^{44} +(-1.11685 - 1.93717i) q^{45} +(-6.38315 + 11.0559i) q^{46} +(-3.67059 + 2.11922i) q^{47} +6.11005i q^{48} +(-10.9048 + 6.27815i) q^{50} +(-2.07488 - 3.59380i) q^{51} +(-19.3252 - 11.1574i) q^{52} +(-6.61053 - 3.81659i) q^{53} +(1.25829 + 2.17942i) q^{54} +(1.09474 - 1.89348i) q^{55} -2.30001i q^{57} +(12.9167 - 7.45743i) q^{58} +(-0.908297 + 1.57322i) q^{59} +(8.39411 - 4.83952i) q^{60} +(0.328128 + 0.568335i) q^{61} +1.59347i q^{62} +3.07689 q^{64} +(-0.00702471 + 11.5152i) q^{65} +(-1.23078 + 2.13177i) q^{66} +(-8.01924 - 4.62991i) q^{67} +(15.5726 - 8.99083i) q^{68} -5.07288 q^{69} -5.49351 q^{71} +(-5.08497 + 2.93581i) q^{72} +(4.65758 + 2.68905i) q^{73} +(11.3938 - 19.7347i) q^{74} +(-4.32707 - 2.50528i) q^{75} +9.96636 q^{76} -12.9598i q^{78} +(-5.44346 - 9.42835i) q^{79} +(6.82402 + 11.8362i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.78648 - 3.34083i) q^{82} -6.62663i q^{83} +(-8.03316 - 4.64448i) q^{85} +(-0.434043 - 0.751785i) q^{86} +(5.13262 + 2.96332i) q^{87} +(-4.97379 - 2.87162i) q^{88} +(-8.15542 - 14.1256i) q^{89} +(4.87162 + 2.81659i) q^{90} -21.9817i q^{92} +(-0.548357 + 0.316594i) q^{93} +(5.33317 - 9.23733i) q^{94} +(-2.56878 - 4.45553i) q^{95} +(-1.81659 - 3.14643i) q^{96} -1.53844i q^{97} -0.978135 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 2 q^{5} + 8 q^{6} + 8 q^{9} + 4 q^{10} - 4 q^{15} + 24 q^{19} + 8 q^{20} + 12 q^{24} - 4 q^{25} + 12 q^{26} + 24 q^{29} - 12 q^{30} - 16 q^{31} - 16 q^{34} + 16 q^{36} - 4 q^{39} - 32 q^{40}+ \cdots - 8 q^{96}+O(q^{100}) \) 16 * q + 8 * q^4 - 2 * q^5 + 8 * q^6 + 8 * q^9 + 4 * q^10 - 4 * q^15 + 24 * q^19 + 8 * q^20 + 12 * q^24 - 4 * q^25 + 12 * q^26 + 24 * q^29 - 12 * q^30 - 16 * q^31 - 16 * q^34 + 16 * q^36 - 4 * q^39 - 32 * q^40 - 16 * q^41 + 20 * q^44 + 2 * q^45 - 32 * q^46 - 40 * q^50 + 4 * q^51 + 4 * q^54 - 8 * q^55 - 4 * q^59 + 16 * q^60 - 16 * q^61 + 16 * q^64 + 30 * q^65 - 28 * q^66 - 40 * q^69 - 56 * q^71 + 40 * q^74 - 8 * q^75 + 64 * q^76 - 16 * q^79 - 52 * q^80 - 8 * q^81 - 64 * q^85 - 48 * q^86 - 16 * q^89 + 8 * q^90 + 32 * q^94 - 22 * q^95 - 8 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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