LMFDB - Embedded newform 735.2.q.g.214.8

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			214.8
Root			$-0.281555 + 1.05078i$ of defining polynomial
Character	$\chi$	$=$	735.214
Dual form			735.2.q.g.79.8

$q$-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} +(1.11685 - 1.93717i) q^{5} +2.51658 q^{6} -5.87162i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.00343282 - 5.62724i) 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} +(-2.50528 - 4.32707i) q^{25} +(6.47990 + 11.2235i) q^{26} +1.00000i q^{27} -5.92664 q^{29} +(2.81065 - 4.87505i) 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} +(-11.3743 - 6.55773i) q^{40} -2.65505 q^{41} -0.344947i q^{43} +(2.11922 + 3.67059i) q^{44} +(2.23607 - 0.00136408i) 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} +(-0.00591081 - 9.68927i) q^{60} +(0.328128 + 0.568335i) q^{61} -1.59347i q^{62} +3.07689 q^{64} +(9.97599 + 5.75153i) 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} +(-0.00610036 - 5.00000i) q^{75} +9.96636 q^{76} +12.9598i q^{78} +(-5.44346 - 9.42835i) q^{79} +(-13.6625 + 0.00833461i) 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} +(5.14299 - 0.00313741i) 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	$-0.317549\pi$
$2$	2.17942	−	1.25829i	1.54108	−	0.889745i	0.998771	−	0.0495691i	$-0.0157848\pi$
$3$	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
$5$	1.11685	−	1.93717i	0.499472	−	0.866330i
$5$	1.11685	−	1.93717i	0.499472	−	0.866330i
$6$	2.51658			1.02739
$7$		0			0
$7$		0			0
$8$		−	5.87162i		−	2.07593i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.00343282	−	5.62724i	−0.00108555	−	1.77949i
$11$	−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	$0.253184\pi$
$13$			5.14977i			1.42829i	−0.699998	+	0.714144i	$0.746816\pi$
$14$		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	−0.00373753	−	0.999993i	$-0.501190\pi$
$17$	−3.59380	−	2.07488i	−0.871626	−	0.503233i	−0.867888	+	0.496760i	$0.834523\pi$
$18$	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	−0.882374	−	0.470548i	$-0.844056\pi$
$23$	−4.39324	+	2.53644i	−0.916054	+	0.528884i	−0.0336802	+	0.999433i	$0.510723\pi$
$24$	2.93581	−	5.08497i	0.599270	−	1.03797i
$25$	−2.50528	−	4.32707i	−0.501056	−	0.865415i
$26$	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	$0.685477\pi$
$30$	2.81065	−	4.87505i	0.513152	−	0.890059i
$31$	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	0.310686	−	0.950513i	$-0.399441\pi$
$37$	7.84188	−	4.52751i	1.28920	−	0.744318i	0.978511	+	0.206194i	$0.0661078\pi$
$38$	5.01270	+	2.89408i	0.813168	+	0.469483i
$39$	−2.57488	+	4.45983i	−0.412311	+	0.714144i
$40$	−11.3743	−	6.55773i	−1.79844	−	1.03687i
$41$	−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	$-0.991627\pi$
$43$		−	0.344947i		−	0.0526039i	0.999654	−	0.0263020i	$-0.00837314\pi$
$44$	2.11922	+	3.67059i	0.319484	+	0.553362i
$45$	2.23607	−	0.00136408i	0.333333	−	0.000203345i
$46$	−6.38315	+	11.0559i	−0.941144	+	1.63011i
$47$	3.67059	−	2.11922i	0.535410	−	0.309119i	−0.207806	−	0.978170i	$-0.566632\pi$
$47$	3.67059	−	2.11922i	0.535410	−	0.309119i	0.743217	+	0.669051i	$0.233299\pi$
$48$		−	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	0.879796	−	0.475352i	$-0.157679\pi$
$53$	6.61053	+	3.81659i	0.908027	+	0.524250i	0.0282311	+	0.999601i	$0.491013\pi$
$54$	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	$0.204395\pi$
$60$	−0.00591081	−	9.68927i	−0.000763082	−	1.25088i
$61$	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
$65$	9.97599	+	5.75153i	1.23737	+	0.713390i
$66$	−1.23078	+	2.13177i	−0.151498	+	0.262403i
$67$	8.01924	+	4.62991i	0.979706	+	0.565633i	0.902181	−	0.431357i	$-0.141965\pi$
$67$	8.01924	+	4.62991i	0.979706	+	0.565633i	0.0775244	+	0.996990i	$0.475298\pi$
$68$	−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	0.202027	−	0.979380i	$-0.435247\pi$
$73$	−4.65758	−	2.68905i	−0.545128	−	0.314730i	−0.747155	+	0.664650i	$0.768581\pi$
$74$	11.3938	−	19.7347i	1.32451	−	2.29411i
$75$	−0.00610036	−	5.00000i	−0.000704409	−	0.577350i
$76$	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	$-0.376477\pi$
$80$	−13.6625	+	0.00833461i	−1.52751	+	0.000931838i
$81$	−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	$0.118481\pi$
$83$			6.62663i			0.727367i	−0.931523	+	0.363683i	$0.881519\pi$
$84$		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
$95$	5.14299	−	0.00313741i	0.527659	−	0.000321892i
$96$	−1.81659	−	3.14643i	−0.185405	−	0.321132i
$97$			1.53844i			0.156205i	0.996945	+	0.0781027i	$0.0248862\pi$
$97$			1.53844i			0.156205i	−0.996945	+	0.0781027i	$0.975114\pi$
$98$		0			0
$99$	−0.978135			−0.0983063
$100$	−21.6659	+	0.0264339i	−2.16659	+	0.00264339i
$101$	−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	0.414429	−	0.910082i	$-0.363981\pi$
$103$	14.3079	−	8.26066i	1.40980	−	0.813947i	0.995368	+	0.0961349i	$0.0306480\pi$
$104$	30.2375			2.96503
$105$		0			0
$106$	19.2095			1.86579
$107$	−2.06824	+	1.19410i	−0.199944	+	0.115438i	−0.596630	−	0.802517i	$-0.703494\pi$
$107$	−2.06824	+	1.19410i	−0.199944	+	0.115438i	0.396685	+	0.917955i	$0.370160\pi$
$108$	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	$0.832526\pi$
$110$	4.76846	+	2.74919i	0.454655	+	0.262125i
$111$	9.05502			0.859465
$112$		0			0
$113$		−	4.04373i		−	0.380402i	−0.981745	−	0.190201i	$-0.939086\pi$
$113$		−	4.04373i		−	0.380402i	0.981745	−	0.190201i	$-0.0609140\pi$
$114$	2.89408	+	5.01270i	0.271056	+	0.469483i
$115$	0.00691983	+	11.3433i	0.000645277	+	1.05777i
$116$	−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	$0.0982989\pi$
$127$			6.85023i			0.607860i	−0.952694	+	0.303930i	$0.901701\pi$
$128$	12.9987	−	7.50481i	1.14893	−	0.663337i
$129$	0.172473	−	0.298733i	0.0151854	−	0.0263020i
$130$	28.9790	−	0.0176782i	2.54163	−	0.00155048i
$131$	−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
$135$	1.93717	+	1.11685i	0.166725	+	0.0961234i
$136$	−12.1829	+	21.1014i	−1.04468	+	1.80943i
$137$	−9.72709	−	5.61594i	−0.831041	−	0.479802i	0.0231680	−	0.999732i	$-0.492625\pi$
$137$	−9.72709	−	5.61594i	−0.831041	−	0.479802i	−0.854209	+	0.519930i	$0.825958\pi$
$138$	−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
$145$	−6.61919	+	11.4809i	−0.549693	+	0.953440i
$146$	−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	$-0.369003\pi$
$150$	−6.30474	−	10.8894i	−0.514780	−	0.889118i
$151$	−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	0.709159	−	0.705049i	$-0.249075\pi$
$157$	5.67792	+	3.27815i	0.453147	+	0.261625i	−0.256011	+	0.966674i	$0.582408\pi$
$158$	−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	−0.0229712	−	0.999736i	$-0.507313\pi$
$163$	10.6138	−	6.12790i	0.831340	−	0.479974i	0.854311	+	0.519762i	$0.173979\pi$
$164$	−5.75240	+	9.96346i	−0.449187	+	0.778015i
$165$	0.00133426	+	2.18718i	0.000103872	+	0.170271i
$166$	8.33822	+	14.4422i	0.647171	+	1.12093i
$167$			2.13239i			0.165009i	0.996591	+	0.0825047i	$0.0262920\pi$
$167$			2.13239i			0.165009i	−0.996591	+	0.0825047i	$0.973708\pi$
$168$		0			0
$169$	−13.5201			−1.04001
$170$	−11.6635	+	20.2303i	−0.894553	+	1.55160i
$171$	−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	−0.0690479	−	0.997613i	$-0.521996\pi$
$173$	10.0013	−	5.77427i	0.760387	−	0.439009i	0.829435	+	0.558604i	$0.188663\pi$
$174$	−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	$0.0587434\pi$
$180$	4.83952	−	8.39411i	0.360716	−	0.625660i
$181$	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
$185$	−0.0123518	−	20.2476i	−0.000908123	−	1.48864i
$186$	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	−0.0546916	−	0.998503i	$-0.517418\pi$
$193$	−13.1529	−	7.59383i	−0.946767	−	0.546616i	−0.892075	+	0.451887i	$0.850751\pi$
$194$	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	$-0.674864\pi$
$197$		−	23.9410i		−	1.70573i	0.522136	−	0.852863i	$-0.325136\pi$
$198$	−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	$0.331337\pi$
$200$	−25.4069	+	14.7101i	−1.79654	+	1.04016i
$201$	4.62991	+	8.01924i	0.326569	+	0.565633i
$202$			13.8817i			0.976714i
$203$		0			0
$204$	−17.9817			−1.25897
$205$	−2.96530	+	5.14330i	−0.207106	+	0.359224i
$206$	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
$215$	−0.668222	−	0.385255i	−0.0455724	−	0.0262742i
$216$	5.87162			0.399513
$217$		0			0
$218$			45.5742i			3.08667i
$219$	−2.68905	−	4.65758i	−0.181709	−	0.314730i
$220$	9.47742	−	0.00578157i	0.638967	−	0.000389793i
$221$	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	$-0.822274\pi$
$223$		−	15.8227i		−	1.05956i	0.848134	−	0.529782i	$-0.177726\pi$
$224$		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	0.970554	−	0.240882i	$-0.0774368\pi$
$227$	18.7913	+	10.8492i	1.24722	+	0.720084i	0.276667	+	0.960966i	$0.410770\pi$
$228$	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	−0.679329	−	0.733834i	$-0.737729\pi$
$233$	−5.85348	+	3.37951i	−0.383474	+	0.221399i	0.295854	+	0.955233i	$0.404396\pi$
$234$	−6.47990	+	11.2235i	−0.423604	+	0.733704i
$235$	−0.00578157	−	9.47742i	−0.000377148	−	0.618238i
$236$	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	$0.470051\pi$
$240$	−11.8362	−	6.82402i	−0.764025	−	0.440489i
$241$	−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
$250$	−24.3409	+	14.1127i	−1.53945	+	0.892564i
$251$	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
$255$	−9.27916	+	0.00566063i	−0.581084	+	0.000354482i
$256$	15.8096	−	27.3830i	0.988097	−	1.71143i
$257$	5.39917	−	3.11721i	0.336791	−	0.194446i	−0.322061	−	0.946719i	$-0.604376\pi$
$257$	5.39917	−	3.11721i	0.336791	−	0.194446i	0.658852	+	0.752273i	$0.271042\pi$
$258$		−	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	0.999997	−	0.00253231i	$-0.000806060\pi$
$263$	24.2903	+	14.0240i	1.49780	+	0.864756i	0.497805	+	0.867289i	$0.334139\pi$
$264$	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	$0.239281\pi$
$270$	5.62724	−	0.00343282i	0.342463	−	0.000208915i
$271$	−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
$275$	4.89067	−	0.00596698i	0.294919	−	0.000359822i
$276$	−10.9908	+	19.0367i	−0.661570	+	1.14587i
$277$	−10.7843	−	6.22629i	−0.647963	−	0.374102i	0.139712	−	0.990192i	$-0.455382\pi$
$277$	−10.7843	−	6.22629i	−0.647963	−	0.374102i	−0.787675	+	0.616090i	$0.788716\pi$
$278$	−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	0.752400	−	0.658706i	$-0.228896\pi$
$283$	9.38944	+	5.42100i	0.558144	+	0.322245i	−0.194256	+	0.980951i	$0.562229\pi$
$284$	−11.9022	+	20.6152i	−0.706264	+	1.22329i
$285$	4.45553	+	2.56878i	0.263923	+	0.152161i
$286$	−12.6764			−0.749574
$287$		0			0
$288$		−	3.63319i		−	0.214088i
$289$	0.110288	+	0.191024i	0.00648752	+	0.0112367i
$290$	0.0203451	+	33.3507i	0.00119471	+	1.95842i
$291$	−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	$-0.666713\pi$
$293$		−	29.6455i		−	1.73191i	0.500125	−	0.865953i	$-0.333287\pi$
$294$		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
$305$	1.46743		0.000895188i	0.0840250		5.12583e-5i
$306$	−5.22161	−	9.04410i	−0.298500	−	0.517017i
$307$			31.6055i			1.80382i	0.431923	+	0.901910i	$0.357835\pi$
$307$			31.6055i			1.80382i	−0.431923	+	0.901910i	$0.642165\pi$
$308$		0			0
$309$	16.5213			0.939865
$310$	−3.08683	−	1.77967i	−0.175320	−	0.101078i
$311$	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	−0.658971	−	0.752168i	$-0.729008\pi$
$313$	−5.96321	+	3.44286i	−0.337060	+	0.194602i	0.321911	+	0.946770i	$0.395675\pi$
$314$	16.4995			0.931118
$315$		0			0
$316$	−47.1749			−2.65380
$317$	−11.1186	+	6.41935i	−0.624485	+	0.360547i	−0.778613	−	0.627504i	$-0.784077\pi$
$317$	−11.1186	+	6.41935i	−0.624485	+	0.360547i	0.154128	+	0.988051i	$0.450743\pi$
$318$	16.6359	+	9.60476i	0.932897	+	0.538608i
$319$	2.89853	−	5.02040i	0.162286	−	0.281088i
$320$	3.43643	−	5.96047i	0.192102	−	0.333200i
$321$	−2.38820			−0.133296
$322$		0			0
$323$		−	9.54453i		−	0.531072i
$324$	2.16659	+	3.75264i	0.120366	+	0.208480i
$325$	22.2834	−	12.9016i	1.23606	−	0.715653i
$326$	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	$0.291454\pi$
$337$			29.1131i			1.58589i	−0.609292	+	0.792946i	$0.708546\pi$
$338$	−29.4660	+	17.0122i	−1.60274	+	0.925343i
$339$	2.02186	−	3.50197i	0.109813	−	0.190201i
$340$	0.0245285	+	40.2082i	0.00133024	+	2.18060i
$341$	0.309672	+	0.536367i	0.0167697	+	0.0290459i
$342$			5.78817i			0.312988i
$343$		0			0
$344$	−2.02540			−0.109202
$345$	−5.66566	+	9.82705i	−0.305029	+	0.529070i
$346$	14.5314	−	25.1691i	0.781213	−	1.35310i
$347$	−11.6418	−	6.72137i	−0.624962	−	0.360822i	0.153836	−	0.988096i	$-0.450837\pi$
$347$	−11.6418	−	6.72137i	−0.624962	−	0.360822i	−0.778798	+	0.627274i	$0.784171\pi$
$348$	−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	0.833696	−	0.552224i	$-0.186221\pi$
$353$	14.5103	+	8.37751i	0.772303	+	0.445890i	−0.0613923	+	0.998114i	$0.519554\pi$
$354$	−2.28580	+	3.95913i	−0.121489	+	0.210425i
$355$	−6.13544	+	10.6419i	−0.325635	+	0.564813i
$356$	−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	$-0.494614\pi$
$360$	−0.00800937	−	13.1293i	−0.000422131	−	0.691977i
$361$	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	−0.151460	−	0.988463i	$-0.548397\pi$
$367$	−20.7516	−	11.9809i	−1.08322	−	0.625400i	−0.931764	+	0.363064i	$0.881731\pi$
$368$	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	−0.727323	−	0.686296i	$-0.759236\pi$
$373$	−9.59160	+	5.53771i	−0.496634	+	0.286732i	0.230688	+	0.973028i	$0.425902\pi$
$374$	5.10744	−	8.84635i	0.264100	−	0.457434i
$375$	−9.69267	−	5.57244i	−0.500527	−	0.287760i
$376$	−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	$0.182009\pi$
$380$	11.1310	−	19.3066i	0.571006	−	0.990406i
$381$	−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	−0.916686	−	0.399609i	$-0.869146\pi$
$383$	−20.1371	+	11.6262i	−1.02896	+	0.594069i	−0.112271	+	0.993678i	$0.535813\pi$
$384$	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	$0.763737\pi$
$390$	25.1054	+	14.4742i	1.27126	+	0.732929i
$391$	21.0513			1.06461
$392$		0			0
$393$		−	4.02540i		−	0.203054i
$394$	−30.1247	−	52.1775i	−1.51766	−	2.62867i
$395$	−24.3439	+	0.0148507i	−1.22487	+	0.000747218i
$396$	−2.11922	+	3.67059i	−0.106495	+	0.184454i
$397$	0.0498605	−	0.0287870i	0.00250243	−	0.00144478i	−0.498748	−	0.866747i	$-0.666207\pi$
$397$	0.0498605	−	0.0287870i	0.00250243	−	0.00144478i	0.501251	+	0.865302i	$0.332873\pi$
$398$			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	$0.301385\pi$
$410$	0.00911433	+	14.9406i	0.000450125	+	0.737865i
$411$	−5.61594	−	9.72709i	−0.277014	−	0.479802i
$412$		−	71.5897i		−	3.52697i
$413$		0			0
$414$	−12.7663			−0.627430
$415$	12.8369	+	7.40097i	0.630140	+	0.363299i
$416$	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
$425$	0.0253151	+	20.7488i	0.00122796	+	1.00647i
$426$	−13.8249			−0.669817
$427$		0			0
$428$			10.3485i			0.500213i
$429$	−2.51858	−	4.36232i	−0.121598	−	0.210615i
$430$	−1.94110	+	0.00118414i	−0.0936082	+	5.71044e-5i
$431$	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	$-0.979127\pi$
$433$		−	2.72706i		−	0.131054i	0.997851	−	0.0655272i	$-0.0208729\pi$
$434$		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	−0.269635	−	0.962963i	$-0.586903\pi$
$443$	9.03987	−	5.21917i	0.429497	−	0.247970i	0.699132	+	0.714992i	$0.253570\pi$
$444$	19.6185	−	33.9802i	0.931053	−	1.61263i
$445$	−36.4721	+	0.0222493i	−1.72894	+	0.00105472i
$446$	−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	$0.486994\pi$
$450$	−0.0153521	−	12.5829i	−0.000723703	−	0.593163i
$451$	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	0.279072	−	0.960270i	$-0.409973\pi$
$457$	26.7268	−	15.4307i	1.25023	−	0.721819i	0.971154	+	0.238452i	$0.0766398\pi$
$458$	4.52642	+	2.61333i	0.211506	+	0.122113i
$459$	2.07488	−	3.59380i	0.0968473	−	0.167744i
$460$	42.5823	+	24.5503i	1.98541	+	1.14466i
$461$	−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	$-0.916913\pi$
$463$		−	11.1060i		−	0.516141i	0.966126	−	0.258071i	$-0.0830867\pi$
$464$	18.1060	+	31.3606i	0.840552	+	1.45588i
$465$	−0.000863721	−	1.41585i	−4.00541e−5	−	0.0656586i
$466$	−8.50481	+	14.7308i	−0.393978	+	0.682389i
$467$	−23.8932	+	13.7947i	−1.10564	+	0.638344i	−0.937698	−	0.347452i	$-0.887047\pi$
$467$	−23.8932	+	13.7947i	−1.10564	+	0.638344i	−0.167946	+	0.985796i	$0.553714\pi$
$468$			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	$0.0931692\pi$
$480$	−8.12405	+	0.00495597i	−0.370811	+	0.000226208i
$481$	23.3156	+	40.3839i	1.06310	+	1.84135i
$482$			22.3913i			1.01989i
$483$		0			0
$484$	43.5192			1.97814
$485$	2.98023	+	1.71822i	0.135325	+	0.0780202i
$486$	−1.25829	+	2.17942i	−0.0570772	+	0.0988606i
$487$	26.6165	+	15.3671i	1.20611	+	0.696348i	0.961907	−	0.273376i	$-0.0881403\pi$
$487$	26.6165	+	15.3671i	1.20611	+	0.696348i	0.244203	+	0.969724i	$0.421474\pi$
$488$	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
$495$	−1.09243	+	1.89482i	−0.0491012	+	0.0851657i
$496$	−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	$0.844367\pi$
$500$	−24.1464	+	42.0000i	−1.07986	+	1.87830i
$501$	−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	$0.109786\pi$
$503$			15.1658i			0.676210i	−0.941108	+	0.338105i	$0.890214\pi$
$504$		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
$515$	−0.0225364	−	36.9428i	−0.000993074	−	1.62789i
$516$	−0.747358	−	1.29446i	−0.0329006	−	0.0569855i
$517$			4.14576i			0.182330i
$518$		0			0
$519$	11.5485			0.506924
$520$	33.7708	−	58.5752i	1.48095	−	2.56869i
$521$	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	$-0.329731\pi$
$523$	34.5258	−	19.9335i	1.50971	−	0.871629i	0.999936	−	0.0113184i	$-0.00360283\pi$
$524$	−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
$530$	21.4542	−	37.2122i	0.931911	−	1.61639i
$531$	−1.81659			−0.0788335
$532$		0			0
$533$		−	13.6729i		−	0.592239i
$534$	−20.5238	−	35.5482i	−0.888150	−	1.53832i
$535$	0.00325770	+	5.34017i	0.000140843	+	0.230876i
$536$	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	$0.0890008\pi$
$547$			12.9090i			0.551950i	−0.961165	+	0.275975i	$0.910999\pi$
$548$	−42.1492	+	24.3348i	−1.80052	+	1.03953i
$549$	−0.328128	+	0.568335i	−0.0140042	+	0.0242559i
$550$	10.6513	−	6.16689i	0.454174	−	0.262957i
$551$	−6.81568	−	11.8051i	−0.290358	−	0.502914i
$552$			29.7860i			1.26778i
$553$		0			0
$554$	−31.3379			−1.33142
$555$	10.1131	−	17.5412i	0.429278	−	0.744580i
$556$	−10.8111	+	18.7253i	−0.458492	+	0.794131i
$557$	−6.22247	−	3.59254i	−0.263654	−	0.152221i	0.362346	−	0.932044i	$-0.381976\pi$
$557$	−6.22247	−	3.59254i	−0.263654	−	0.152221i	−0.626000	+	0.779823i	$0.715309\pi$
$558$	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	0.455806	−	0.890079i	$-0.349351\pi$
$563$	−2.06720	−	1.19350i	−0.0871220	−	0.0502999i	−0.542928	+	0.839779i	$0.682684\pi$
$564$	9.18293	−	15.9053i	0.386671	−	0.669734i
$565$	−7.83341	−	4.51625i	−0.329554	−	0.190000i
$566$	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	$0.618116\pi$
$570$	12.9427	−	0.00789554i	0.542112	−	0.000330708i
$571$	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	0.569716	−	0.821842i	$-0.307053\pi$
$577$	3.43108	+	1.98094i	0.142838	+	0.0824675i	−0.426878	+	0.904309i	$0.640387\pi$
$578$	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
$585$	0.00702471	+	11.5152i	0.000290436	+	0.476096i
$586$	−37.3026	−	64.6100i	−1.54096	−	2.66901i
$587$			13.9419i			0.575446i	0.957714	+	0.287723i	$0.0928982\pi$
$587$			13.9419i			0.575446i	−0.957714	+	0.287723i	$0.907102\pi$
$588$		0			0
$589$	1.45634			0.0600075
$590$	8.85599	+	5.10581i	0.364595	+	0.210203i
$591$	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	0.378282	−	0.925690i	$-0.376515\pi$
$593$	33.3396	−	19.2486i	1.36909	−	0.790447i	0.990812	+	0.135243i	$0.0431816\pi$
$594$	−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	$0.0502927\pi$
$600$	−29.3581	+	0.0358190i	−1.19854	+	0.00146230i
$601$	−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
$605$	22.4574	−	0.0136998i	0.913023	−	0.000556977i
$606$	−6.94086	+	12.0219i	−0.281953	+	0.488357i
$607$	9.45318	−	5.45780i	0.383693	−	0.221525i	−0.295731	−	0.955271i	$-0.595563\pi$
$607$	9.45318	−	5.45780i	0.383693	−	0.221525i	0.679424	+	0.733746i	$0.262230\pi$
$608$		−	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	0.881570	−	0.472054i	$-0.156487\pi$
$613$	22.6183	+	13.0587i	0.913543	+	0.527435i	0.0319739	+	0.999489i	$0.489821\pi$
$614$	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	$-0.924528\pi$
$617$		−	11.6689i		−	0.469772i	0.972023	−	0.234886i	$-0.0754717\pi$
$618$	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	$0.161398\pi$
$620$	−6.13513	+	0.00374265i	−0.246393	+	0.000150309i
$621$	−2.53644	−	4.39324i	−0.101784	−	0.176295i
$622$		−	55.7933i		−	2.23711i
$623$		0			0
$624$	31.4653			1.25962
$625$	−12.4471	+	21.6811i	−0.497885	+	0.867243i
$626$	−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
$635$	13.2701	+	7.65070i	0.526607	+	0.303609i
$636$	33.0759			1.31155
$637$		0			0
$638$		−	14.5888i		−	0.577575i
$639$	−2.74676	−	4.75752i	−0.108660	−	0.188205i
$640$	−0.0204744	−	33.5625i	−0.000809320	−	1.32667i
$641$	−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	$-0.929579\pi$
$643$		−	11.1286i		−	0.438870i	0.975627	−	0.219435i	$-0.0704214\pi$
$644$		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	0.674291	−	0.738465i	$-0.264449\pi$
$647$	9.45991	+	5.46168i	0.371907	+	0.214721i	−0.302384	+	0.953186i	$0.597783\pi$
$648$	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	−0.616563	−	0.787305i	$-0.711476\pi$
$653$	−6.21006	+	3.58538i	−0.243019	+	0.140307i	0.373545	+	0.927612i	$0.378142\pi$
$654$	−22.7871	+	39.4684i	−0.891046	+	1.54334i
$655$	−9.00106	+	0.00549097i	−0.351700	+	0.000214550i
$656$	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	$0.588704\pi$
$660$	8.21057	+	4.73370i	0.319596	+	0.184259i
$661$	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
$670$	26.0261	−	45.1421i	1.00548	−	1.74399i
$671$	−0.641907			−0.0247806
$672$		0			0
$673$		−	14.4081i		−	0.555392i	−0.960669	−	0.277696i	$-0.910429\pi$
$673$		−	14.4081i		−	0.555392i	0.960669	−	0.277696i	$-0.0895709\pi$
$674$	36.6327	+	63.4497i	1.41104	+	2.44399i
$675$	4.32707	−	2.50528i	0.166549	−	0.0964283i
$676$	−29.2925	+	50.7361i	−1.12663	+	1.95139i
$677$	−26.0991	+	15.0683i	−1.00307	+	0.579123i	−0.909155	−	0.416457i	$-0.863271\pi$
$677$	−26.0991	+	15.0683i	−1.00307	+	0.579123i	−0.0939148	+	0.995580i	$0.529938\pi$
$678$		−	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	0.734554	−	0.678550i	$-0.237391\pi$
$683$	13.4380	+	7.75842i	0.514190	+	0.296868i	−0.220364	+	0.975418i	$0.570725\pi$
$684$	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
$690$	0.0174143	+	28.5463i	0.000662951	+	1.08674i
$691$	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
$695$	−5.57299	+	9.66632i	−0.211396	+	0.366664i
$696$	−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
$705$	4.73370	−	8.21057i	0.178282	−	0.309228i
$706$	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	$0.721057\pi$
$710$	0.0188583	+	30.9133i	0.000707738	+	1.16016i
$711$	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
$725$	14.8479	+	25.6450i	0.551437	+	0.952432i
$726$	12.6373	+	21.8885i	0.469015	+	0.812358i
$727$			42.6977i			1.58357i	0.610800	+	0.791785i	$0.290848\pi$
$727$			42.6977i			1.58357i	−0.610800	+	0.791785i	$0.709152\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−15.1160	+	26.2185i	−0.559467	+	0.970392i
$731$	−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	−0.999978	−	0.00666408i	$-0.997879\pi$
$733$	−40.4538	+	23.3560i	−1.49420	+	0.862674i	−0.494218	+	0.869338i	$0.664545\pi$
$734$	−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	$0.125286\pi$
$740$	−76.0089	−	43.8219i	−2.79414	−	1.61093i
$741$	−11.8445			−0.435120
$742$		0			0
$743$			8.55510i			0.313856i	0.987610	+	0.156928i	$0.0501591\pi$
$743$			8.55510i			0.313856i	−0.987610	+	0.156928i	$0.949841\pi$
$744$	−1.85892	−	3.21974i	−0.0681513	−	0.118042i
$745$	−32.4101	+	0.0197713i	−1.18741	+	0.000724366i
$746$	−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	$0.291847\pi$
$757$			43.6750i			1.58740i	−0.608313	+	0.793698i	$0.708153\pi$
$758$	71.3592	−	41.1993i	2.59188	−	1.49643i
$759$	2.48098	−	4.29718i	0.0900539	−	0.155978i
$760$	−0.0184217	−	30.1977i	−0.000668224	−	1.09538i
$761$	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
$765$	−8.03882	−	4.63468i	−0.290644	−	0.167567i
$766$	−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	0.398478	−	0.917178i	$-0.369538\pi$
$773$	−5.46553	−	3.15553i	−0.196581	−	0.113496i	−0.595060	+	0.803681i	$0.702872\pi$
$774$	0.434043	−	0.751785i	0.0156014	−	0.0270224i
$775$	−3.16594	+	0.00386268i	−0.113724	+	0.000138752i
$776$	9.03316			0.324272
$777$		0			0
$778$			94.6892i			3.39477i
$779$	−3.05333	−	5.28852i	−0.109397	−	0.189481i
$780$	49.8975	−	0.0304393i	1.78662	−	0.00108990i
$781$	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	0.885340	−	0.464943i	$-0.153925\pi$
$787$	25.9595	+	14.9877i	0.925358	+	0.534256i	0.0400174	+	0.999199i	$0.487259\pi$
$788$	−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
$795$	17.0683	−	0.0104123i	0.605351	−	0.000369286i
$796$	30.2309	+	52.3615i	1.07151	+	1.85590i
$797$		−	0.676527i		−	0.0239638i	−0.999928	−	0.0119819i	$-0.996186\pi$
$797$		−	0.676527i		−	0.0239638i	0.999928	−	0.0119819i	$-0.00381405\pi$
$798$		0			0
$799$	−17.5885			−0.622236
$800$	0.0221638	+	18.1659i	0.000783608	+	0.642263i
$801$	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	$0.823468\pi$
$810$	4.87505	+	2.81065i	0.171292	+	0.0987561i
$811$	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
$815$	−0.0167179	−	27.4048i	−0.000585604	−	0.959949i
$816$	−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	0.782058	−	0.623206i	$-0.214170\pi$
$823$	18.1702	+	10.4906i	0.633375	+	0.365679i	−0.148683	+	0.988885i	$0.547503\pi$
$824$	−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	$0.228350\pi$
$827$			37.8114i			1.31483i	−0.753528	+	0.657416i	$0.771650\pi$
$828$	−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	$-0.210031\pi$
$830$	37.2896	−	0.0227480i	1.29434	−	0.000789596i
$831$	−6.22629	−	10.7843i	−0.215988	−	0.374102i
$832$			15.8453i			0.549336i
$833$		0			0
$834$	−12.5575			−0.434831
$835$	4.13081	+	2.38157i	0.142953	+	0.0824175i
$836$	−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
$845$	−15.1000	+	26.1908i	−0.519455	+	0.900991i
$846$	10.6663			0.366717
$847$		0			0
$848$		−	46.6392i		−	1.60160i
$849$	5.42100	+	9.38944i	0.186048	+	0.322245i
$850$	26.1632	+	45.1886i	0.897391	+	1.54996i
$851$	−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	$-0.972653\pi$
$853$		−	5.01225i		−	0.171616i	0.996312	−	0.0858081i	$-0.0273472\pi$
$854$		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	−0.191021	−	0.981586i	$-0.561180\pi$
$857$	−33.2737	−	19.2106i	−1.13661	−	0.656222i	−0.945589	+	0.325364i	$0.894513\pi$
$858$	−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	$-0.290324\pi$
$863$	47.0908	−	27.1879i	1.60299	−	0.925486i	0.990885	−	0.134707i	$-0.0430094\pi$
$864$	1.81659	−	3.14643i	0.0618018	−	0.107044i
$865$	−0.0157532	−	25.8233i	−0.000535624	−	0.878019i
$866$	−3.43144	−	5.94342i	−0.116605	−	0.201966i
$867$			0.220576i			0.00749114i
$868$		0			0
$869$	10.6489			0.361239
$870$	−16.6577	+	28.8927i	−0.564749	+	0.979554i
$871$	−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	−0.0224397	−	0.999748i	$-0.507143\pi$
$877$	24.6434	−	14.2279i	0.832148	−	0.480441i	0.854587	+	0.519307i	$0.173810\pi$
$878$	16.4408	+	9.49211i	0.554851	+	0.320343i
$879$	14.8227	−	25.6737i	0.499958	−	0.865953i
$880$	6.67482	−	11.5774i	0.225008	−	0.390275i
$881$	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	$0.198886\pi$
$883$			34.7640i			1.16990i	−0.811069	+	0.584951i	$0.801114\pi$
$884$	−46.3007	−	80.1952i	−1.55726	−	2.69726i
$885$	0.00247799	+	4.06203i	8.32966e−5	+	0.136544i
$886$	13.1345	−	22.7496i	0.441261	−	0.764286i
$887$	25.4214	−	14.6770i	0.853566	−	0.492807i	−0.00828615	−	0.999966i	$-0.502638\pi$
$887$	25.4214	−	14.6770i	0.853566	−	0.492807i	0.861853	+	0.507159i	$0.169304\pi$
$888$		−	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
$900$	−10.8558	−	18.7500i	−0.361861	−	0.624999i
$901$	−15.8380	−	27.4322i	−0.527640	−	0.913899i
$902$		−	6.53556i		−	0.217610i
$903$		0			0
$904$	−23.7432			−0.789688
$905$	3.55092	−	6.15904i	0.118036	−	0.204733i
$906$	−9.92404	+	17.1889i	−0.329704	+	0.571064i
$907$	31.4256	+	18.1436i	1.04347	+	0.602447i	0.920814	−	0.390002i	$-0.127526\pi$
$907$	31.4256	+	18.1436i	1.04347	+	0.602447i	0.122655	+	0.992449i	$0.460859\pi$
$908$	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
$915$	1.27128	+	0.732941i	0.0420273	+	0.0242303i
$916$	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	$-0.403324\pi$
$920$	66.6035	−	0.0406306i	2.19585	−	0.00133955i
$921$	−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
$935$	−0.00553686	−	9.07628i	−0.000181075	−	0.296826i
$936$	15.1187	+	26.1864i	0.494171	+	0.855930i
$937$			26.1169i			0.853201i	0.904440	+	0.426601i	$0.140289\pi$
$937$			26.1169i			0.853201i	−0.904440	+	0.426601i	$0.859711\pi$
$938$		0			0
$939$	−6.88572			−0.224707
$940$	−35.5778	−	20.5120i	−1.16042	−	0.669026i
$941$	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	−0.982072	−	0.188509i	$-0.939635\pi$
$947$	−40.3086	+	23.2722i	−1.30985	+	0.756245i	−0.327783	+	0.944753i	$0.606301\pi$
$948$	−40.8547	−	23.5875i	−1.32690	−	0.766085i
$949$	13.8480	−	23.9854i	0.449525	−	0.778600i
$950$	−0.0353099	−	28.9408i	−0.00114561	−	0.938964i
$951$	−12.8387			−0.416324
$952$		0			0
$953$			30.6348i			0.992358i	0.868220	+	0.496179i	$0.165264\pi$
$953$			30.6348i			0.992358i	−0.868220	+	0.496179i	$0.834736\pi$
$954$	9.60476	+	16.6359i	0.310966	+	0.538608i
$955$	1.39222		0.000849303i	0.0450511		2.74828e-5i
$956$	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	$-0.625253\pi$
$967$		−	57.4401i		−	1.84715i	0.383419	−	0.923575i	$-0.374747\pi$
$968$	51.0696	−	29.4851i	1.64144	−	0.947686i
$969$	4.77226	−	8.26580i	0.153307	−	0.265536i
$970$	8.65720	−	0.00528121i	0.277966	−	0.000169569i
$971$	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
$975$	25.7488	−	0.0314155i	0.824622	−	0.00100610i
$976$	2.00488	−	3.47255i	0.0641746	−	0.111154i
$977$	−11.9099	−	6.87617i	−0.381031	−	0.219988i	0.297236	−	0.954804i	$-0.403935\pi$
$977$	−11.9099	−	6.87617i	−0.381031	−	0.219988i	−0.678267	+	0.734816i	$0.737269\pi$
$978$	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	−0.130957	−	0.991388i	$-0.541805\pi$
$983$	−33.0773	−	19.0972i	−1.05500	−	0.609106i	−0.924046	+	0.382282i	$0.875138\pi$
$984$	−7.79473	+	13.5009i	−0.248487	+	0.430392i
$985$	−46.3779	−	26.7386i	−1.47772	−	0.851961i
$986$	61.8933			1.97108
$987$		0			0
$988$			51.3245i			1.63285i
$989$	0.874937	+	1.51544i	0.0278214	+	0.0481880i
$990$	0.00335777	+	5.50420i	0.000106717	+	0.174935i
$991$	−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	0.333493	−	0.942753i	$-0.391773\pi$
$997$	−9.98438	−	5.76448i	−0.316208	−	0.182563i	−0.649701	+	0.760190i	$0.725106\pi$
$998$	−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.214.8		16
5.4	even	2	inner	735.2.q.g.214.1		16
7.2	even	3	inner	735.2.q.g.79.1		16
7.3	odd	6		735.2.d.d.589.8		8
7.4	even	3		735.2.d.e.589.8		8
7.5	odd	6		105.2.q.a.79.1	yes	16
7.6	odd	2		105.2.q.a.4.8	yes	16
21.5	even	6		315.2.bf.b.289.8		16
21.11	odd	6		2205.2.d.o.1324.1		8
21.17	even	6		2205.2.d.s.1324.1		8
21.20	even	2		315.2.bf.b.109.1		16
28.19	even	6		1680.2.di.d.289.4		16
28.27	even	2		1680.2.di.d.529.5		16
35.3	even	12		3675.2.a.bz.1.4		4
35.4	even	6		735.2.d.e.589.1		8
35.9	even	6	inner	735.2.q.g.79.8		16
35.12	even	12		525.2.i.k.226.4		8
35.13	even	4		525.2.i.h.151.1		8
35.17	even	12		3675.2.a.bp.1.1		4
35.18	odd	12		3675.2.a.cb.1.4		4
35.19	odd	6		105.2.q.a.79.8	yes	16
35.24	odd	6		735.2.d.d.589.1		8
35.27	even	4		525.2.i.k.151.4		8
35.32	odd	12		3675.2.a.bn.1.1		4
35.33	even	12		525.2.i.h.226.1		8
35.34	odd	2		105.2.q.a.4.1	✓	16
105.59	even	6		2205.2.d.s.1324.8		8
105.74	odd	6		2205.2.d.o.1324.8		8
105.89	even	6		315.2.bf.b.289.1		16
105.104	even	2		315.2.bf.b.109.8		16
140.19	even	6		1680.2.di.d.289.5		16
140.139	even	2		1680.2.di.d.529.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.1	✓	16	35.34	odd	2
105.2.q.a.4.8	yes	16	7.6	odd	2
105.2.q.a.79.1	yes	16	7.5	odd	6
105.2.q.a.79.8	yes	16	35.19	odd	6
315.2.bf.b.109.1		16	21.20	even	2
315.2.bf.b.109.8		16	105.104	even	2
315.2.bf.b.289.1		16	105.89	even	6
315.2.bf.b.289.8		16	21.5	even	6
525.2.i.h.151.1		8	35.13	even	4
525.2.i.h.226.1		8	35.33	even	12
525.2.i.k.151.4		8	35.27	even	4
525.2.i.k.226.4		8	35.12	even	12
735.2.d.d.589.1		8	35.24	odd	6
735.2.d.d.589.8		8	7.3	odd	6
735.2.d.e.589.1		8	35.4	even	6
735.2.d.e.589.8		8	7.4	even	3
735.2.q.g.79.1		16	7.2	even	3	inner
735.2.q.g.79.8		16	35.9	even	6	inner
735.2.q.g.214.1		16	5.4	even	2	inner
735.2.q.g.214.8		16	1.1	even	1	trivial
1680.2.di.d.289.4		16	28.19	even	6
1680.2.di.d.289.5		16	140.19	even	6
1680.2.di.d.529.4		16	140.139	even	2
1680.2.di.d.529.5		16	28.27	even	2
2205.2.d.o.1324.1		8	21.11	odd	6
2205.2.d.o.1324.8		8	105.74	odd	6
2205.2.d.s.1324.1		8	21.17	even	6
2205.2.d.s.1324.8		8	105.59	even	6
3675.2.a.bn.1.1		4	35.32	odd	12
3675.2.a.bp.1.1		4	35.17	even	12
3675.2.a.bz.1.4		4	35.3	even	12
3675.2.a.cb.1.4		4	35.18	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} +(1.11685 - 1.93717i) q^{5} +2.51658 q^{6} -5.87162i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.00343282 - 5.62724i) 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} +(-2.50528 - 4.32707i) q^{25} +(6.47990 + 11.2235i) q^{26} +1.00000i q^{27} -5.92664 q^{29} +(2.81065 - 4.87505i) 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} +(-11.3743 - 6.55773i) q^{40} -2.65505 q^{41} -0.344947i q^{43} +(2.11922 + 3.67059i) q^{44} +(2.23607 - 0.00136408i) 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} +(-0.00591081 - 9.68927i) q^{60} +(0.328128 + 0.568335i) q^{61} -1.59347i q^{62} +3.07689 q^{64} +(9.97599 + 5.75153i) 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} +(-0.00610036 - 5.00000i) q^{75} +9.96636 q^{76} +12.9598i q^{78} +(-5.44346 - 9.42835i) q^{79} +(-13.6625 + 0.00833461i) 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} +(5.14299 - 0.00313741i) 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

Properties

Related objects

Downloads

Learn more