LMFDB - Embedded newform 925.2.e.c.26.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(26,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.26"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 11 x^{12} - 2 x^{11} + 86 x^{10} - 18 x^{9} + 332 x^{8} - 110 x^{7} + 935 x^{6} - 290 x^{5} + \cdots + 81 $ x^14 + 11x^12 - 2x^11 + 86x^10 - 18x^9 + 332x^8 - 110x^7 + 935x^6 - 290x^5 + 985x^4 - 441x^3 + 792x^2 - 243x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			26.5
Root			$-0.560420 + 0.970676i$ of defining polynomial
Character	$\chi$	$=$	925.26
Dual form			925.2.e.c.676.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.560420 + 0.970676i) q^{2} +(1.67000 - 2.89252i) q^{3} +(0.371859 - 0.644078i) q^{4} +3.74360 q^{6} +(0.612087 - 1.06017i) q^{7} +3.07527 q^{8} +(-4.07778 - 7.06292i) q^{9} -3.59983 q^{11} +(-1.24201 - 2.15122i) q^{12} +(0.349805 - 0.605879i) q^{13} +1.37210 q^{14} +(0.979724 + 1.69693i) q^{16} +(0.289385 + 0.501229i) q^{17} +(4.57054 - 7.91640i) q^{18} +(-3.87804 + 6.71697i) q^{19} +(-2.04437 - 3.54094i) q^{21} +(-2.01742 - 3.49427i) q^{22} +4.47887 q^{23} +(5.13569 - 8.89527i) q^{24} +0.784150 q^{26} -17.2195 q^{27} +(-0.455220 - 0.788464i) q^{28} +3.04867 q^{29} +7.98457 q^{31} +(1.97715 - 3.42453i) q^{32} +(-6.01171 + 10.4126i) q^{33} +(-0.324354 + 0.561797i) q^{34} -6.06543 q^{36} +(1.32431 + 5.93685i) q^{37} -8.69333 q^{38} +(-1.16835 - 2.02363i) q^{39} +(-2.79335 + 4.83822i) q^{41} +(2.29141 - 3.96883i) q^{42} -4.02235 q^{43} +(-1.33863 + 2.31857i) q^{44} +(2.51005 + 4.34753i) q^{46} +8.09571 q^{47} +6.54454 q^{48} +(2.75070 + 4.76435i) q^{49} +1.93309 q^{51} +(-0.260156 - 0.450603i) q^{52} +(-4.96979 - 8.60794i) q^{53} +(-9.65017 - 16.7146i) q^{54} +(1.88233 - 3.26029i) q^{56} +(12.9526 + 22.4346i) q^{57} +(1.70853 + 2.95927i) q^{58} +(-0.242678 - 0.420330i) q^{59} +(0.459736 - 0.796287i) q^{61} +(4.47471 + 7.75043i) q^{62} -9.98382 q^{63} +8.35104 q^{64} -13.4763 q^{66} +(5.62845 - 9.74876i) q^{67} +0.430441 q^{68} +(7.47970 - 12.9552i) q^{69} +(0.253677 - 0.439381i) q^{71} +(-12.5403 - 21.7204i) q^{72} +3.55519 q^{73} +(-5.02059 + 4.61261i) q^{74} +(2.88417 + 4.99553i) q^{76} +(-2.20341 + 3.81642i) q^{77} +(1.30953 - 2.26817i) q^{78} +(1.90707 - 3.30314i) q^{79} +(-16.5232 + 28.6191i) q^{81} -6.26179 q^{82} +(-5.80544 - 10.0553i) q^{83} -3.04086 q^{84} +(-2.25421 - 3.90440i) q^{86} +(5.09126 - 8.81833i) q^{87} -11.0705 q^{88} +(-7.19183 - 12.4566i) q^{89} +(-0.428221 - 0.741701i) q^{91} +(1.66551 - 2.88475i) q^{92} +(13.3342 - 23.0955i) q^{93} +(4.53700 + 7.85831i) q^{94} +(-6.60368 - 11.4379i) q^{96} +10.2579 q^{97} +(-3.08309 + 5.34008i) q^{98} +(14.6793 + 25.4253i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{3} - 8 q^{4} - 4 q^{6} - 6 q^{8} - 13 q^{9} - 2 q^{11} - 6 q^{12} - 4 q^{13} + 20 q^{14} + 2 q^{16} + 3 q^{17} + 6 q^{18} - 14 q^{19} + q^{21} - 7 q^{22} + 15 q^{24} - 22 q^{26} + 14 q^{27}+ \cdots + 56 q^{99}+O(q^{100}) $ 14 * q + 2 * q^3 - 8 * q^4 - 4 * q^6 - 6 * q^8 - 13 * q^9 - 2 * q^11 - 6 * q^12 - 4 * q^13 + 20 * q^14 + 2 * q^16 + 3 * q^17 + 6 * q^18 - 14 * q^19 + q^21 - 7 * q^22 + 15 * q^24 - 22 * q^26 + 14 * q^27 - 9 * q^28 - 12 * q^29 - 4 * q^32 + 11 * q^33 + 33 * q^34 + 40 * q^36 - 18 * q^37 + 4 * q^38 - 25 * q^39 - 7 * q^41 + 29 * q^42 - 38 * q^43 - 19 * q^44 - 14 * q^46 - 8 * q^47 - 36 * q^48 + 5 * q^49 + 58 * q^51 + 8 * q^52 + 6 * q^53 - 9 * q^54 - 25 * q^56 + 44 * q^57 + 12 * q^58 + 2 * q^59 - 4 * q^61 + 25 * q^62 - 10 * q^63 - 62 * q^64 - 2 * q^66 + 8 * q^67 - 26 * q^68 - 11 * q^69 + 33 * q^71 - 43 * q^72 + 18 * q^74 - 12 * q^76 + 5 * q^77 + 22 * q^78 - 9 * q^79 - 35 * q^81 - 152 * q^82 + 11 * q^83 - 80 * q^84 + 17 * q^86 + 29 * q^87 - 40 * q^88 - 12 * q^89 - 24 * q^91 + 7 * q^92 + 47 * q^93 + 10 * q^94 - 15 * q^96 - 30 * q^97 - 54 * q^98 + 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.560420	+	0.970676i	0.396277	+	0.686372i	0.993263	−	0.115880i	$-0.0369687\pi$
$2$	0.560420	+	0.970676i	0.396277	+	0.686372i	−0.596986	+	0.802251i	$0.703635\pi$
$3$	1.67000	−	2.89252i	0.964173	−	1.67000i	0.252353	−	0.967635i	$-0.418796\pi$
$3$	1.67000	−	2.89252i	0.964173	−	1.67000i	0.711821	−	0.702361i	$-0.247871\pi$
$4$	0.371859	−	0.644078i	0.185929	−	0.322039i
$5$		0			0
$5$		0			0
$6$	3.74360			1.52832
$7$	0.612087	−	1.06017i	0.231347	−	0.400705i	−0.726858	−	0.686788i	$-0.759020\pi$
$7$	0.612087	−	1.06017i	0.231347	−	0.400705i	0.958205	+	0.286083i	$0.0923534\pi$
$8$	3.07527			1.08727
$9$	−4.07778	−	7.06292i	−1.35926	−	2.35431i
$10$		0			0
$11$	−3.59983			−1.08539			−0.542695	−	0.839930i	$-0.682596\pi$
$11$	−3.59983			−1.08539			−0.542695	+	0.839930i	$0.682596\pi$
$12$	−1.24201	−	2.15122i	−0.358536	−	0.621003i
$13$	0.349805	−	0.605879i	0.0970183	−	0.168041i	−0.813431	−	0.581662i	$-0.802403\pi$
$13$	0.349805	−	0.605879i	0.0970183	−	0.168041i	0.910449	+	0.413621i	$0.135736\pi$
$14$	1.37210			0.366710
$15$		0			0
$16$	0.979724	+	1.69693i	0.244931	+	0.424233i
$17$	0.289385	+	0.501229i	0.0701861	+	0.121566i	0.898983	−	0.437984i	$-0.144307\pi$
$17$	0.289385	+	0.501229i	0.0701861	+	0.121566i	−0.828797	+	0.559550i	$0.810974\pi$
$18$	4.57054	−	7.91640i	1.07729	−	1.86591i
$19$	−3.87804	+	6.71697i	−0.889684	+	1.54098i	−0.0494348	+	0.998777i	$0.515742\pi$
$19$	−3.87804	+	6.71697i	−0.889684	+	1.54098i	−0.840249	+	0.542200i	$0.817591\pi$
$20$		0			0
$21$	−2.04437	−	3.54094i	−0.446117	−	0.772698i
$22$	−2.01742	−	3.49427i	−0.430115	−	0.744981i
$23$	4.47887			0.933910			0.466955	−	0.884281i	$-0.345351\pi$
$23$	4.47887			0.933910			0.466955	+	0.884281i	$0.345351\pi$
$24$	5.13569	−	8.89527i	1.04832	−	1.81574i
$25$		0			0
$26$	0.784150			0.153784
$27$	−17.2195			−3.31390
$28$	−0.455220	−	0.788464i	−0.0860284	−	0.149006i
$29$	3.04867			0.566123			0.283062	−	0.959102i	$-0.408650\pi$
$29$	3.04867			0.566123			0.283062	+	0.959102i	$0.408650\pi$
$30$		0			0
$31$	7.98457			1.43407			0.717035	−	0.697037i	$-0.245499\pi$
$31$	7.98457			1.43407			0.717035	+	0.697037i	$0.245499\pi$
$32$	1.97715	−	3.42453i	0.349515	−	0.605377i
$33$	−6.01171	+	10.4126i	−1.04650	+	1.81260i
$34$	−0.324354	+	0.561797i	−0.0556262	+	0.0963474i
$35$		0			0
$36$	−6.06543			−1.01091
$37$	1.32431	+	5.93685i	0.217715	+	0.976012i
$37$	1.32431	+	5.93685i	0.217715	+	0.976012i
$38$	−8.69333			−1.41024
$39$	−1.16835	−	2.02363i	−0.187085	−	0.324041i
$40$		0			0
$41$	−2.79335	+	4.83822i	−0.436247	+	0.755603i	−0.997397	−	0.0721120i	$-0.977026\pi$
$41$	−2.79335	+	4.83822i	−0.436247	+	0.755603i	0.561149	+	0.827715i	$0.310359\pi$
$42$	2.29141	−	3.96883i	0.353572	−	0.612404i
$43$	−4.02235			−0.613403			−0.306701	−	0.951806i	$-0.599225\pi$
$43$	−4.02235			−0.613403			−0.306701	+	0.951806i	$0.599225\pi$
$44$	−1.33863	+	2.31857i	−0.201806	+	0.349538i
$45$		0			0
$46$	2.51005	+	4.34753i	0.370087	+	0.641009i
$47$	8.09571			1.18088			0.590440	−	0.807081i	$-0.298954\pi$
$47$	8.09571			1.18088			0.590440	+	0.807081i	$0.298954\pi$
$48$	6.54454			0.944624
$49$	2.75070	+	4.76435i	0.392957	+	0.680622i
$50$		0			0
$51$	1.93309			0.270686
$52$	−0.260156	−	0.450603i	−0.0360771	−	0.0624874i
$53$	−4.96979	−	8.60794i	−0.682654	−	1.18239i	−0.974168	−	0.225824i	$-0.927492\pi$
$53$	−4.96979	−	8.60794i	−0.682654	−	1.18239i	0.291514	−	0.956566i	$-0.405841\pi$
$54$	−9.65017	−	16.7146i	−1.31322	−	2.27457i
$55$		0			0
$56$	1.88233	−	3.26029i	0.251537	−	0.435675i
$57$	12.9526	+	22.4346i	1.71562	+	2.97154i
$58$	1.70853	+	2.95927i	0.224341	+	0.388571i
$59$	−0.242678	−	0.420330i	−0.0315940	−	0.0547224i	0.849796	−	0.527112i	$-0.176725\pi$
$59$	−0.242678	−	0.420330i	−0.0315940	−	0.0547224i	−0.881390	+	0.472389i	$0.843392\pi$
$60$		0			0
$61$	0.459736	−	0.796287i	0.0588632	−	0.101954i	−0.835092	−	0.550110i	$-0.814586\pi$
$61$	0.459736	−	0.796287i	0.0588632	−	0.101954i	0.893955	+	0.448156i	$0.147919\pi$
$62$	4.47471	+	7.75043i	0.568289	+	0.984305i
$63$	−9.98382			−1.25784
$64$	8.35104			1.04388
$65$		0			0
$66$	−13.4763			−1.65882
$67$	5.62845	−	9.74876i	0.687624	−	1.19100i	−0.284980	−	0.958533i	$-0.591987\pi$
$67$	5.62845	−	9.74876i	0.687624	−	1.19100i	0.972604	−	0.232467i	$-0.0746797\pi$
$68$	0.430441			0.0521986
$69$	7.47970	−	12.9552i	0.900451	−	1.55963i
$70$		0			0
$71$	0.253677	−	0.439381i	0.0301059	−	0.0521450i	−0.850580	−	0.525846i	$-0.823749\pi$
$71$	0.253677	−	0.439381i	0.0301059	−	0.0521450i	0.880686	+	0.473701i	$0.157082\pi$
$72$	−12.5403	−	21.7204i	−1.47788	−	2.55977i
$73$	3.55519			0.416104			0.208052	−	0.978118i	$-0.433288\pi$
$73$	3.55519			0.416104			0.208052	+	0.978118i	$0.433288\pi$
$74$	−5.02059	+	4.61261i	−0.583632	+	0.536204i
$75$		0			0
$76$	2.88417	+	4.99553i	0.330837	+	0.573026i
$77$	−2.20341	+	3.81642i	−0.251102	+	0.434921i
$78$	1.30953	−	2.26817i	0.148275	−	0.256820i
$79$	1.90707	−	3.30314i	0.214562	−	0.371633i	−0.738575	−	0.674172i	$-0.764501\pi$
$79$	1.90707	−	3.30314i	0.214562	−	0.371633i	0.953137	+	0.302539i	$0.0978342\pi$
$80$		0			0
$81$	−16.5232	+	28.6191i	−1.83591	+	3.17989i
$82$	−6.26179			−0.691499
$83$	−5.80544	−	10.0553i	−0.637230	−	1.10371i	−0.986038	−	0.166521i	$-0.946747\pi$
$83$	−5.80544	−	10.0553i	−0.637230	−	1.10371i	0.348808	−	0.937194i	$-0.386587\pi$
$84$	−3.04086			−0.331785
$85$		0			0
$86$	−2.25421	−	3.90440i	−0.243077	−	0.421022i
$87$	5.09126	−	8.81833i	0.545841	−	0.945424i
$88$	−11.0705			−1.18011
$89$	−7.19183	−	12.4566i	−0.762333	−	1.32040i	−0.941645	−	0.336607i	$-0.890721\pi$
$89$	−7.19183	−	12.4566i	−0.762333	−	1.32040i	0.179312	−	0.983792i	$-0.442613\pi$
$90$		0			0
$91$	−0.428221	−	0.741701i	−0.0448898	−	0.0777514i
$92$	1.66551	−	2.88475i	0.173641	−	0.300756i
$93$	13.3342	−	23.0955i	1.38269	−	2.39489i
$94$	4.53700	+	7.85831i	0.467956	+	0.810523i
$95$		0			0
$96$	−6.60368	−	11.4379i	−0.673986	−	1.16738i
$97$	10.2579			1.04154			0.520768	−	0.853698i	$-0.325646\pi$
$97$	10.2579			1.04154			0.520768	+	0.853698i	$0.325646\pi$
$98$	−3.08309	+	5.34008i	−0.311440	+	0.539429i
$99$	14.6793	+	25.4253i	1.47533	+	2.55534i
$100$		0			0
$101$	−5.50183			−0.547452			−0.273726	−	0.961808i	$-0.588256\pi$
$101$	−5.50183			−0.547452			−0.273726	+	0.961808i	$0.588256\pi$
$102$	1.08334	+	1.87640i	0.107267	+	0.185791i
$103$	−6.24169			−0.615012			−0.307506	−	0.951546i	$-0.599494\pi$
$103$	−6.24169			−0.615012			−0.307506	+	0.951546i	$0.599494\pi$
$104$	1.07574	−	1.86324i	0.105485	−	0.182706i
$105$		0			0
$106$	5.57034	−	9.64812i	0.541040	−	0.937108i
$107$	−0.185069	+	0.320549i	−0.0178913	+	0.0309886i	−0.874832	−	0.484426i	$-0.839029\pi$
$107$	−0.185069	+	0.320549i	−0.0178913	+	0.0309886i	0.856941	+	0.515414i	$0.172362\pi$
$108$	−6.40323	+	11.0907i	−0.616151	+	1.06721i
$109$	−1.55541	−	2.69404i	−0.148981	−	0.258043i	0.781870	−	0.623441i	$-0.214266\pi$
$109$	−1.55541	−	2.69404i	−0.148981	−	0.258043i	−0.930851	+	0.365399i	$0.880933\pi$
$110$		0			0
$111$	19.3840	+	6.08393i	1.83985	+	0.577461i
$112$	2.39870			0.226656
$113$	5.84618	+	10.1259i	0.549962	+	0.952562i	0.998276	+	0.0586863i	$0.0186912\pi$
$113$	5.84618	+	10.1259i	0.549962	+	0.952562i	−0.448314	+	0.893876i	$0.647975\pi$
$114$	−14.5178	+	25.1456i	−1.35972	+	2.35510i
$115$		0			0
$116$	1.13367	−	1.96358i	0.105259	−	0.182314i
$117$	−5.70570			−0.527492
$118$	0.272003	−	0.471123i	0.0250399	−	0.0433704i
$119$	0.708514			0.0649494
$120$		0			0
$121$	1.95880			0.178072
$122$	1.03058			0.0933045
$123$	9.32976	+	16.1596i	0.841236	+	1.45706i
$124$	2.96913	−	5.14269i	0.266636	−	0.461827i
$125$		0			0
$126$	−5.59513	−	9.69105i	−0.498454	−	0.863347i
$127$	8.87482	+	15.3716i	0.787513	+	1.36401i	0.927486	+	0.373857i	$0.121965\pi$
$127$	8.87482	+	15.3716i	0.787513	+	1.36401i	−0.139973	+	0.990155i	$0.544702\pi$
$128$	0.725783	+	1.25709i	0.0641508	+	0.111112i
$129$	−6.71731	+	11.6347i	−0.591426	+	1.02438i
$130$		0			0
$131$	0.575328	+	0.996498i	0.0502667	+	0.0870644i	0.890064	−	0.455836i	$-0.150660\pi$
$131$	0.575328	+	0.996498i	0.0502667	+	0.0870644i	−0.839797	+	0.542900i	$0.817326\pi$
$132$	4.47101	+	7.74402i	0.389152	+	0.674031i
$133$	4.74740	+	8.22273i	0.411651	+	0.713001i
$134$	12.6172			1.08996
$135$		0			0
$136$	0.889935	+	1.54141i	0.0763113	+	0.132175i
$137$	−1.91138			−0.163301			−0.0816503	−	0.996661i	$-0.526019\pi$
$137$	−1.91138			−0.163301			−0.0816503	+	0.996661i	$0.526019\pi$
$138$	16.7671			1.42731
$139$	1.89002	+	3.27360i	0.160309	+	0.277663i	0.934980	−	0.354702i	$-0.115418\pi$
$139$	1.89002	+	3.27360i	0.160309	+	0.277663i	−0.774670	+	0.632365i	$0.782084\pi$
$140$		0			0
$141$	13.5198	−	23.4170i	1.13857	−	1.97207i
$142$	0.568663			0.0477211
$143$	−1.25924	+	2.18106i	−0.105303	+	0.182390i
$144$	7.99020	−	13.8394i	0.665850	−	1.15329i
$145$		0			0
$146$	1.99240	+	3.45094i	0.164892	+	0.285602i
$147$	18.3746			1.51551
$148$	4.31625	+	1.35471i	0.354794	+	0.111357i
$149$	−0.552510			−0.0452633			−0.0226317	−	0.999744i	$-0.507205\pi$
$149$	−0.552510			−0.0452633			−0.0226317	+	0.999744i	$0.507205\pi$
$150$		0			0
$151$	−4.57907	+	7.93118i	−0.372639	+	0.645430i	−0.989971	−	0.141273i	$-0.954880\pi$
$151$	−4.57907	+	7.93118i	−0.372639	+	0.645430i	0.617331	+	0.786703i	$0.288214\pi$
$152$	−11.9260	+	20.6565i	−0.967328	+	1.67546i
$153$	2.36009	−	4.08780i	0.190802	−	0.330479i
$154$	−4.93934			−0.398023
$155$		0			0
$156$	−1.73784			−0.139138
$157$	−1.37082	−	2.37433i	−0.109403	−	0.189492i	0.806125	−	0.591745i	$-0.201561\pi$
$157$	−1.37082	−	2.37433i	−0.109403	−	0.189492i	−0.915529	+	0.402253i	$0.868227\pi$
$158$	4.27504			0.340104
$159$	−33.1982			−2.63279
$160$		0			0
$161$	2.74146	−	4.74835i	0.216057	−	0.374222i
$162$	−37.0398			−2.91012
$163$	10.5345	+	18.2462i	0.825123	+	1.42915i	0.901826	+	0.432100i	$0.142227\pi$
$163$	10.5345	+	18.2462i	0.825123	+	1.42915i	−0.0767030	+	0.997054i	$0.524439\pi$
$164$	2.07746	+	3.59827i	0.162222	+	0.280978i
$165$		0			0
$166$	6.50697	−	11.2704i	0.505039	−	0.874753i
$167$	−5.01447	+	8.68532i	−0.388031	+	0.672090i	−0.992185	−	0.124778i	$-0.960178\pi$
$167$	−5.01447	+	8.68532i	−0.388031	+	0.672090i	0.604153	+	0.796868i	$0.293511\pi$
$168$	−6.28697	−	10.8894i	−0.485050	−	0.840132i
$169$	6.25527	+	10.8345i	0.481175	+	0.833419i
$170$		0			0
$171$	63.2552			4.83725
$172$	−1.49575	+	2.59071i	−0.114050	+	0.197540i
$173$	−6.65162	−	11.5209i	−0.505714	−	0.875922i	−0.999978	−	0.00661007i	$-0.997896\pi$
$173$	−6.65162	−	11.5209i	−0.505714	−	0.875922i	0.494265	−	0.869312i	$-0.335437\pi$
$174$	11.4130			0.865216
$175$		0			0
$176$	−3.52684	−	6.10867i	−0.265846	−	0.460458i
$177$	−1.62109			−0.121848
$178$	8.06089	−	13.9619i	0.604190	−	1.04649i
$179$	9.15637			0.684379			0.342190	−	0.939631i	$-0.388832\pi$
$179$	9.15637			0.684379			0.342190	+	0.939631i	$0.388832\pi$
$180$		0			0
$181$	−10.5528	+	18.2780i	−0.784382	+	1.35859i	0.144986	+	0.989434i	$0.453686\pi$
$181$	−10.5528	+	18.2780i	−0.784382	+	1.35859i	−0.929368	+	0.369156i	$0.879647\pi$
$182$	0.479968	−	0.831328i	0.0355776	−	0.0616222i
$183$	−1.53552	−	2.65959i	−0.113509	−	0.196603i
$184$	13.7737			1.01541
$185$		0			0
$186$	29.8910			2.19172
$187$	−1.04174	−	1.80434i	−0.0761793	−	0.131946i
$188$	3.01046	−	5.21427i	0.219561	−	0.380290i
$189$	−10.5398	+	18.2555i	−0.766661	+	1.32790i
$190$		0			0
$191$	−7.51240			−0.543578			−0.271789	−	0.962357i	$-0.587615\pi$
$191$	−7.51240			−0.543578			−0.271789	+	0.962357i	$0.587615\pi$
$192$	13.9462	−	24.1556i	1.00648	−	1.74328i
$193$	−16.5435			−1.19083			−0.595415	−	0.803418i	$-0.703012\pi$
$193$	−16.5435			−1.19083			−0.595415	+	0.803418i	$0.703012\pi$
$194$	5.74876	+	9.95714i	0.412737	+	0.714881i
$195$		0			0
$196$	4.09149			0.292249
$197$	0.873381	+	1.51274i	0.0622259	+	0.107778i	0.895460	−	0.445142i	$-0.146847\pi$
$197$	0.873381	+	1.51274i	0.0622259	+	0.107778i	−0.833234	+	0.552920i	$0.813513\pi$
$198$	−16.4532	+	28.4977i	−1.16928	+	2.02525i
$199$	−14.8223			−1.05073			−0.525364	−	0.850878i	$-0.676071\pi$
$199$	−14.8223			−1.05073			−0.525364	+	0.850878i	$0.676071\pi$
$200$		0			0
$201$	−18.7990	−	32.5608i	−1.32598	−	2.29666i
$202$	−3.08334	−	5.34049i	−0.216943	−	0.375756i
$203$	1.86605	−	3.23209i	0.130971	−	0.226848i
$204$	0.718835	−	1.24506i	0.0503285	−	0.0871715i
$205$		0			0
$206$	−3.49797	−	6.05866i	−0.243715	−	0.422127i
$207$	−18.2639	−	31.6339i	−1.26943	−	2.19871i
$208$	1.37085			0.0950512
$209$	13.9603	−	24.1800i	0.965654	−	1.67256i
$210$		0			0
$211$	−18.1359			−1.24853			−0.624264	−	0.781214i	$-0.714601\pi$
$211$	−18.1359			−1.24853			−0.624264	+	0.781214i	$0.714601\pi$
$212$	−7.39225			−0.507702
$213$	−0.847279	−	1.46753i	−0.0580546	−	0.100554i
$214$	−0.414866			−0.0283596
$215$		0			0
$216$	−52.9547			−3.60311
$217$	4.88725	−	8.46496i	0.331768	−	0.574639i
$218$	1.74336	−	3.01959i	0.118075	−	0.204513i
$219$	5.93716	−	10.2835i	0.401196	−	0.694892i
$220$		0			0
$221$	0.404912			0.0272373
$222$	4.95768	+	22.2252i	0.332738	+	1.49166i
$223$	3.84578			0.257532			0.128766	−	0.991675i	$-0.458898\pi$
$223$	3.84578			0.257532			0.128766	+	0.991675i	$0.458898\pi$
$224$	−2.42038	−	4.19222i	−0.161718	−	0.280105i
$225$		0			0
$226$	−6.55263	+	11.3495i	−0.435874	+	0.754957i
$227$	−6.90676	+	11.9629i	−0.458418	+	0.794003i	−0.998878	−	0.0473671i	$-0.984917\pi$
$227$	−6.90676	+	11.9629i	−0.458418	+	0.794003i	0.540460	+	0.841370i	$0.318250\pi$
$228$	19.2662			1.27594
$229$	−0.301499	+	0.522211i	−0.0199236	+	0.0345087i	−0.875815	−	0.482646i	$-0.839676\pi$
$229$	−0.301499	+	0.522211i	−0.0199236	+	0.0345087i	0.855892	+	0.517155i	$0.173009\pi$
$230$		0			0
$231$	7.35937	+	12.7468i	0.484211	+	0.838679i
$232$	9.37547			0.615530
$233$	−23.3424			−1.52921			−0.764605	−	0.644499i	$-0.777066\pi$
$233$	−23.3424			−1.52921			−0.764605	+	0.644499i	$0.777066\pi$
$234$	−3.19759	−	5.53839i	−0.209033	−	0.362056i
$235$		0			0
$236$	−0.360968			−0.0234970
$237$	−6.36961	−	11.0325i	−0.413750	−	0.716637i
$238$	0.397065	+	0.687737i	0.0257379	+	0.0445794i
$239$	14.0468	+	24.3297i	0.908610	+	1.57376i	0.815997	+	0.578057i	$0.196189\pi$
$239$	14.0468	+	24.3297i	0.908610	+	1.57376i	0.0926135	+	0.995702i	$0.470478\pi$
$240$		0			0
$241$	−0.0182021	+	0.0315270i	−0.00117250	+	0.00203084i	−0.866611	−	0.498984i	$-0.833707\pi$
$241$	−0.0182021	+	0.0315270i	−0.00117250	+	0.00203084i	0.865439	+	0.501015i	$0.167040\pi$
$242$	1.09775	+	1.90136i	0.0705659	+	0.122224i
$243$	29.3582	+	50.8498i	1.88333	+	3.26202i
$244$	−0.341914	−	0.592213i	−0.0218888	−	0.0379125i
$245$		0			0
$246$	−10.4572	+	18.1123i	−0.666725	+	1.15480i
$247$	2.71311	+	4.69925i	0.172631	+	0.299006i
$248$	24.5547			1.55922
$249$	−38.7803			−2.45760
$250$		0			0
$251$	−21.4173			−1.35185			−0.675924	−	0.736971i	$-0.736255\pi$
$251$	−21.4173			−1.35185			−0.675924	+	0.736971i	$0.736255\pi$
$252$	−3.71257	+	6.43036i	−0.233870	+	0.405075i
$253$	−16.1232			−1.01366
$254$	−9.94726	+	17.2292i	−0.624146	+	1.08105i
$255$		0			0
$256$	7.53756	−	13.0554i	0.471097	−	0.815965i
$257$	−0.403879	−	0.699538i	−0.0251933	−	0.0436360i	0.853154	−	0.521659i	$-0.174687\pi$
$257$	−0.403879	−	0.699538i	−0.0251933	−	0.0436360i	−0.878347	+	0.478023i	$0.841353\pi$
$258$	−15.0581			−0.937474
$259$	7.10464	+	2.22988i	0.441461	+	0.138558i
$260$		0			0
$261$	−12.4318	−	21.5325i	−0.769508	−	1.33283i
$262$	−0.644851	+	1.11691i	−0.0398390	+	0.0690032i
$263$	1.21933	−	2.11194i	0.0751871	−	0.130228i	−0.825981	−	0.563699i	$-0.809378\pi$
$263$	1.21933	−	2.11194i	0.0751871	−	0.130228i	0.901168	+	0.433471i	$0.142711\pi$
$264$	−18.4876	+	32.0215i	−1.13783	+	1.97079i
$265$		0			0
$266$	−5.32107	+	9.21637i	−0.326256	+	0.565092i
$267$	−48.0414			−2.94008
$268$	−4.18598	−	7.25032i	−0.255699	−	0.442884i
$269$	12.1567			0.741208			0.370604	−	0.928791i	$-0.379151\pi$
$269$	12.1567			0.741208			0.370604	+	0.928791i	$0.379151\pi$
$270$		0			0
$271$	15.6514	+	27.1090i	0.950755	+	1.64676i	0.743797	+	0.668405i	$0.233023\pi$
$271$	15.6514	+	27.1090i	0.950755	+	1.64676i	0.206957	+	0.978350i	$0.433644\pi$
$272$	−0.567034	+	0.982132i	−0.0343815	+	0.0595505i
$273$	−2.86051			−0.173126
$274$	−1.07118	−	1.85533i	−0.0647122	−	0.112085i
$275$		0			0
$276$	−5.56279	−	9.63503i	−0.334841	−	0.579961i
$277$	11.5959	−	20.0847i	0.696732	−	1.20678i	−0.272861	−	0.962053i	$-0.587970\pi$
$277$	11.5959	−	20.0847i	0.696732	−	1.20678i	0.969593	−	0.244722i	$-0.0786967\pi$
$278$	−2.11841	+	3.66919i	−0.127053	+	0.220063i
$279$	−32.5593	−	56.3944i	−1.94927	−	3.37624i
$280$		0			0
$281$	10.7114	+	18.5527i	0.638988	+	1.10676i	0.985655	+	0.168771i	$0.0539799\pi$
$281$	10.7114	+	18.5527i	0.638988	+	1.10676i	−0.346668	+	0.937988i	$0.612687\pi$
$282$	30.3071			1.80476
$283$	−6.90784	+	11.9647i	−0.410628	+	0.711229i	−0.994959	−	0.100287i	$-0.968024\pi$
$283$	−6.90784	+	11.9647i	−0.410628	+	0.711229i	0.584330	+	0.811516i	$0.301357\pi$
$284$	−0.188664	−	0.326776i	−0.0111952	−	0.0193906i
$285$		0			0
$286$	−2.82281			−0.166916
$287$	3.41954	+	5.92282i	0.201849	+	0.349613i
$288$	−32.2496			−1.90033
$289$	8.33251	−	14.4323i	0.490148	−	0.848961i
$290$		0			0
$291$	17.1307	−	29.6713i	1.00422	−	1.73936i
$292$	1.32203	−	2.28982i	0.0773659	−	0.134002i
$293$	−3.55370	+	6.15518i	−0.207609	+	0.359589i	−0.950961	−	0.309311i	$-0.899902\pi$
$293$	−3.55370	+	6.15518i	−0.207609	+	0.359589i	0.743352	+	0.668901i	$0.233235\pi$
$294$	10.2975	+	17.8358i	0.600563	+	1.04021i
$295$		0			0
$296$	4.07261	+	18.2574i	0.236715	+	1.06119i
$297$	61.9874			3.59687
$298$	−0.309637	−	0.536308i	−0.0179368	−	0.0310675i
$299$	1.56673	−	2.71366i	0.0906064	−	0.156935i
$300$		0			0
$301$	−2.46203	+	4.26436i	−0.141909	+	0.245793i
$302$	−10.2648			−0.590673
$303$	−9.18804	+	15.9141i	−0.527839	+	0.914244i
$304$	−15.1976			−0.871645
$305$		0			0
$306$	5.29057			0.302442
$307$	23.6385			1.34912			0.674560	−	0.738220i	$-0.264333\pi$
$307$	23.6385			1.34912			0.674560	+	0.738220i	$0.264333\pi$
$308$	1.63871	+	2.83834i	0.0933744	+	0.161729i
$309$	−10.4236	+	18.0542i	−0.592978	+	1.02707i
$310$		0			0
$311$	9.68043	+	16.7670i	0.548927	+	0.950769i	0.998348	+	0.0574494i	$0.0182968\pi$
$311$	9.68043	+	16.7670i	0.548927	+	0.950769i	−0.449422	+	0.893320i	$0.648370\pi$
$312$	−3.59297	−	6.22321i	−0.203412	−	0.352320i
$313$	3.05523	+	5.29181i	0.172692	+	0.299111i	0.939360	−	0.342932i	$-0.111420\pi$
$313$	3.05523	+	5.29181i	0.172692	+	0.299111i	−0.766668	+	0.642043i	$0.778087\pi$
$314$	1.53647	−	2.66124i	0.0867079	−	0.150183i
$315$		0			0
$316$	−1.41832	−	2.45661i	−0.0797869	−	0.138195i
$317$	−16.6203	−	28.7872i	−0.933490	−	1.61685i	−0.777304	−	0.629125i	$-0.783414\pi$
$317$	−16.6203	−	28.7872i	−0.933490	−	1.61685i	−0.156186	−	0.987728i	$-0.549920\pi$
$318$	−18.6049	−	32.2247i	−1.04331	−	1.80707i
$319$	−10.9747			−0.614465
$320$		0			0
$321$	0.618129	+	1.07063i	0.0345006	+	0.0597568i
$322$	6.14547			0.342474
$323$	−4.48898			−0.249774
$324$	12.2886	+	21.2845i	0.682701	+	1.18247i
$325$		0			0
$326$	−11.8074	+	20.4511i	−0.653954	+	1.13268i
$327$	−10.3901			−0.574574
$328$	−8.59029	+	14.8788i	−0.474319	+	0.821545i
$329$	4.95528	−	8.58279i	0.273193	−	0.473185i
$330$		0			0
$331$	−0.693675	−	1.20148i	−0.0381278	−	0.0660394i	0.846332	−	0.532656i	$-0.178806\pi$
$331$	−0.693675	−	1.20148i	−0.0381278	−	0.0660394i	−0.884460	+	0.466617i	$0.845473\pi$
$332$	−8.63522			−0.473919
$333$	36.5313	−	33.5627i	2.00190	−	1.83922i
$334$	−11.2408			−0.615071
$335$		0			0
$336$	4.00583	−	6.93830i	0.218536	−	0.378515i
$337$	7.65489	−	13.2587i	0.416989	−	0.722245i	−0.578646	−	0.815579i	$-0.696419\pi$
$337$	7.65489	−	13.2587i	0.416989	−	0.722245i	0.995635	+	0.0933332i	$0.0297522\pi$
$338$	−7.01116	+	12.1437i	−0.381357	+	0.660529i
$339$	39.0524			2.12103
$340$		0			0
$341$	−28.7431			−1.55653
$342$	35.4495	+	61.4003i	1.91689	+	3.32015i
$343$	15.3039			0.826332
$344$	−12.3698			−0.666935
$345$		0			0
$346$	7.45541	−	12.9131i	0.400805	−	0.694215i
$347$	−27.0099			−1.44997			−0.724983	−	0.688767i	$-0.758152\pi$
$347$	−27.0099			−1.44997			−0.724983	+	0.688767i	$0.758152\pi$
$348$	−3.78646	−	6.55835i	−0.202976	−	0.351564i
$349$	10.1591	+	17.5961i	0.543806	+	0.941900i	0.998681	+	0.0513447i	$0.0163507\pi$
$349$	10.1591	+	17.5961i	0.543806	+	0.941900i	−0.454875	+	0.890555i	$0.650316\pi$
$350$		0			0
$351$	−6.02347	+	10.4330i	−0.321509	+	0.556870i
$352$	−7.11743	+	12.3277i	−0.379360	+	0.657071i
$353$	−2.23510	−	3.87131i	−0.118962	−	0.206049i	0.800394	−	0.599474i	$-0.204623\pi$
$353$	−2.23510	−	3.87131i	−0.118962	−	0.206049i	−0.919357	+	0.393425i	$0.871290\pi$
$354$	−0.908489	−	1.57355i	−0.0482856	−	0.0836332i
$355$		0			0
$356$	−10.6974			−0.566960
$357$	1.18322	−	2.04939i	0.0626224	−	0.108465i
$358$	5.13141	+	8.88786i	0.271204	+	0.469738i
$359$	−31.2742			−1.65059			−0.825295	−	0.564702i	$-0.808991\pi$
$359$	−31.2742			−1.65059			−0.825295	+	0.564702i	$0.808991\pi$
$360$		0			0
$361$	−20.5784	−	35.6429i	−1.08308	−	1.87594i
$362$	−23.6560			−1.24333
$363$	3.27118	−	5.66585i	0.171693	−	0.297380i
$364$	−0.636952			−0.0333853
$365$		0			0
$366$	1.72107	−	2.98098i	0.0899617	−	0.155818i
$367$	−8.06325	+	13.9660i	−0.420898	+	0.729017i	−0.996028	−	0.0890456i	$-0.971618\pi$
$367$	−8.06325	+	13.9660i	−0.420898	+	0.729017i	0.575130	+	0.818062i	$0.304952\pi$
$368$	4.38806	+	7.60034i	0.228743	+	0.396195i
$369$	45.5626			2.37189
$370$		0			0
$371$	−12.1678			−0.631720
$372$	−9.91688	−	17.1765i	−0.514166	−	0.890562i
$373$	−5.12016	+	8.86838i	−0.265112	+	0.459187i	−0.967593	−	0.252515i	$-0.918742\pi$
$373$	−5.12016	+	8.86838i	−0.265112	+	0.459187i	0.702481	+	0.711703i	$0.252076\pi$
$374$	1.16762	−	2.02238i	0.0603762	−	0.104575i
$375$		0			0
$376$	24.8965			1.28394
$377$	1.06644	−	1.84712i	0.0549243	−	0.0951317i
$378$	−23.6270			−1.21524
$379$	−8.28107	−	14.3432i	−0.425370	−	0.736763i	0.571085	−	0.820891i	$-0.306523\pi$
$379$	−8.28107	−	14.3432i	−0.425370	−	0.736763i	−0.996455	+	0.0841283i	$0.973189\pi$
$380$		0			0
$381$	59.2837			3.03720
$382$	−4.21010	−	7.29211i	−0.215408	−	0.373097i
$383$	9.15069	−	15.8495i	0.467578	−	0.809869i	−0.531735	−	0.846911i	$-0.678460\pi$
$383$	9.15069	−	15.8495i	0.467578	−	0.809869i	0.999314	+	0.0370411i	$0.0117933\pi$
$384$	4.84822			0.247410
$385$		0			0
$386$	−9.27133	−	16.0584i	−0.471898	−	0.817352i
$387$	16.4023	+	28.4095i	0.833773	+	1.44414i
$388$	3.81451	−	6.60692i	0.193652	−	0.335416i
$389$	7.33608	−	12.7065i	0.371954	−	0.644243i	−0.617912	−	0.786247i	$-0.712021\pi$
$389$	7.33608	−	12.7065i	0.371954	−	0.644243i	0.989866	+	0.142004i	$0.0453546\pi$
$390$		0			0
$391$	1.29612	+	2.24494i	0.0655474	+	0.113532i
$392$	8.45914	+	14.6517i	0.427251	+	0.740021i
$393$	3.84319			0.193863
$394$	−0.978921	+	1.69554i	−0.0493173	+	0.0854201i
$395$		0			0
$396$	21.8345			1.09723
$397$	2.00229			0.100492			0.0502460	−	0.998737i	$-0.483999\pi$
$397$	2.00229			0.100492			0.0502460	+	0.998737i	$0.483999\pi$
$398$	−8.30673	−	14.3877i	−0.416379	−	0.721189i
$399$	31.7125			1.58761
$400$		0			0
$401$	−22.8854			−1.14284			−0.571422	−	0.820656i	$-0.693608\pi$
$401$	−22.8854			−1.14284			−0.571422	+	0.820656i	$0.693608\pi$
$402$	21.0706	−	36.4954i	1.05091	−	1.82023i
$403$	2.79304	−	4.83768i	0.139131	−	0.240982i
$404$	−2.04590	+	3.54361i	−0.101788	+	0.176301i
$405$		0			0
$406$	4.18308			0.207603
$407$	−4.76729	−	21.3717i	−0.236306	−	1.05935i
$408$	5.94476			0.294309
$409$	−4.55814	−	7.89494i	−0.225386	−	0.390380i	0.731049	−	0.682325i	$-0.239031\pi$
$409$	−4.55814	−	7.89494i	−0.225386	−	0.390380i	−0.956435	+	0.291945i	$0.905698\pi$
$410$		0			0
$411$	−3.19200	+	5.52871i	−0.157450	+	0.272711i
$412$	−2.32103	+	4.02014i	−0.114349	+	0.198058i
$413$	−0.594160			−0.0292367
$414$	20.4709	−	35.4566i	1.00609	−	1.74259i
$415$		0			0
$416$	−1.38324	−	2.39583i	−0.0678187	−	0.117465i
$417$	12.6253			0.618263
$418$	31.2945			1.53067
$419$	4.25529	+	7.37039i	0.207885	+	0.360067i	0.951048	−	0.309043i	$-0.100009\pi$
$419$	4.25529	+	7.37039i	0.207885	+	0.360067i	−0.743163	+	0.669110i	$0.766675\pi$
$420$		0			0
$421$	−8.83588			−0.430635			−0.215317	−	0.976544i	$-0.569079\pi$
$421$	−8.83588			−0.430635			−0.215317	+	0.976544i	$0.569079\pi$
$422$	−10.1637	−	17.6041i	−0.494762	−	0.856953i
$423$	−33.0125	−	57.1794i	−1.60512	−	2.78016i
$424$	−15.2834	−	26.4717i	−0.742230	−	1.28558i
$425$		0			0
$426$	0.949665	−	1.64487i	0.0460114	−	0.0796941i
$427$	−0.562797	−	0.974793i	−0.0272357	−	0.0471735i
$428$	0.137639	+	0.238398i	0.00665304	+	0.0115234i
$429$	4.20585	+	7.28474i	0.203060	+	0.351711i
$430$		0			0
$431$	−0.755326	+	1.30826i	−0.0363828	+	0.0630168i	−0.883643	−	0.468161i	$-0.844917\pi$
$431$	−0.755326	+	1.30826i	−0.0363828	+	0.0630168i	0.847261	+	0.531177i	$0.178250\pi$
$432$	−16.8704	−	29.2204i	−0.811677	−	1.40587i
$433$	−6.85824			−0.329586			−0.164793	−	0.986328i	$-0.552696\pi$
$433$	−6.85824			−0.329586			−0.164793	+	0.986328i	$0.552696\pi$
$434$	10.9556			0.525888
$435$		0			0
$436$	−2.31357			−0.110800
$437$	−17.3693	+	30.0844i	−0.830884	+	1.43913i
$438$	13.3092			0.635938
$439$	−9.56891	+	16.5738i	−0.456699	+	0.791026i	−0.998784	−	0.0492976i	$-0.984302\pi$
$439$	−9.56891	+	16.5738i	−0.456699	+	0.791026i	0.542085	+	0.840324i	$0.317635\pi$
$440$		0			0
$441$	22.4335	−	38.8559i	1.06826	−	1.85028i
$442$	0.226921	+	0.393039i	0.0107935	+	0.0186949i
$443$	2.25690			0.107229			0.0536144	−	0.998562i	$-0.482926\pi$
$443$	2.25690			0.107229			0.0536144	+	0.998562i	$0.482926\pi$
$444$	11.1267	−	10.2225i	0.528048	−	0.485138i
$445$		0			0
$446$	2.15525	+	3.73300i	0.102054	+	0.176763i
$447$	−0.922689	+	1.59814i	−0.0436417	+	0.0755896i
$448$	5.11156	−	8.85349i	0.241499	−	0.418288i
$449$	12.1889	−	21.1119i	0.575232	−	0.996330i	−0.420785	−	0.907160i	$-0.638245\pi$
$449$	12.1889	−	21.1119i	0.575232	−	0.996330i	0.996016	−	0.0891698i	$-0.0284214\pi$
$450$		0			0
$451$	10.0556	−	17.4168i	0.473499	−	0.820124i
$452$	8.69581			0.409017
$453$	15.2941	+	26.4901i	0.718578	+	1.24461i
$454$	−15.4827			−0.726641
$455$		0			0
$456$	39.8328	+	68.9925i	1.86534	+	3.23087i
$457$	−7.02629	+	12.1699i	−0.328676	+	0.569283i	−0.982249	−	0.187580i	$-0.939936\pi$
$457$	−7.02629	+	12.1699i	−0.328676	+	0.569283i	0.653574	+	0.756863i	$0.273269\pi$
$458$	−0.675864			−0.0315810
$459$	−4.98307	−	8.63092i	−0.232590	−	0.402857i
$460$		0			0
$461$	13.2088	+	22.8783i	0.615195	+	1.06555i	0.990350	+	0.138587i	$0.0442559\pi$
$461$	13.2088	+	22.8783i	0.615195	+	1.06555i	−0.375156	+	0.926962i	$0.622411\pi$
$462$	−8.24868	+	14.2871i	−0.383763	+	0.664698i
$463$	12.5712	−	21.7739i	0.584233	−	1.01192i	−0.410738	−	0.911753i	$-0.634729\pi$
$463$	12.5712	−	21.7739i	0.584233	−	1.01192i	0.994971	−	0.100167i	$-0.0319378\pi$
$464$	2.98685	+	5.17338i	0.138661	+	0.240168i
$465$		0			0
$466$	−13.0815	−	22.6579i	−0.605991	−	1.04961i
$467$	14.0309			0.649271			0.324635	−	0.945839i	$-0.394758\pi$
$467$	14.0309			0.649271			0.324635	+	0.945839i	$0.394758\pi$
$468$	−2.12172	+	3.67492i	−0.0980764	+	0.169873i
$469$	−6.89019	−	11.9342i	−0.318160	−	0.551069i
$470$		0			0
$471$	−9.15705			−0.421935
$472$	−0.746300	−	1.29263i	−0.0343512	−	0.0594981i
$473$	14.4798			0.665781
$474$	7.13931	−	12.3656i	0.327919	−	0.567973i
$475$		0			0
$476$	0.263467	−	0.456339i	0.0120760	−	0.0209162i
$477$	−40.5314	+	70.2025i	−1.85581	+	3.21435i
$478$	−15.7442	+	27.2697i	−0.720122	+	1.24729i
$479$	3.34106	+	5.78689i	0.152657	+	0.264410i	0.932203	−	0.361935i	$-0.117884\pi$
$479$	3.34106	+	5.78689i	0.152657	+	0.264410i	−0.779546	+	0.626344i	$0.784550\pi$
$480$		0			0
$481$	4.06026	+	1.27437i	0.185132	+	0.0581061i
$482$	−0.0408034			−0.00185854
$483$	−9.15645	−	15.8594i	−0.416633	−	0.721630i
$484$	0.728396	−	1.26162i	0.0331089	−	0.0573463i
$485$		0			0
$486$	−32.9058	+	56.9945i	−1.49264	+	2.58532i
$487$	7.26544			0.329229			0.164614	−	0.986358i	$-0.447362\pi$
$487$	7.26544			0.329229			0.164614	+	0.986358i	$0.447362\pi$
$488$	1.41381	−	2.44880i	0.0640003	−	0.110852i
$489$	70.3701			3.18224
$490$		0			0
$491$	0.446623			0.0201558			0.0100779	−	0.999949i	$-0.496792\pi$
$491$	0.446623			0.0201558			0.0100779	+	0.999949i	$0.496792\pi$
$492$	13.8774			0.625642
$493$	0.882237	+	1.52808i	0.0397340	+	0.0688212i
$494$	−3.04097	+	5.26711i	−0.136820	+	0.236978i
$495$		0			0
$496$	7.82267	+	13.5493i	0.351248	+	0.608380i
$497$	−0.310545	−	0.537879i	−0.0139298	−	0.0241272i
$498$	−21.7332	−	37.6431i	−0.973890	−	1.68683i
$499$	5.30225	−	9.18376i	0.237361	−	0.411122i	−0.722595	−	0.691272i	$-0.757051\pi$
$499$	5.30225	−	9.18376i	0.237361	−	0.411122i	0.959956	+	0.280150i	$0.0903842\pi$
$500$		0			0
$501$	16.7483	+	29.0089i	0.748259	+	1.29602i
$502$	−12.0027	−	20.7893i	−0.535706	−	0.927870i
$503$	6.98478	+	12.0980i	0.311436	+	0.539423i	0.978673	−	0.205422i	$-0.0658567\pi$
$503$	6.98478	+	12.0980i	0.311436	+	0.539423i	−0.667237	+	0.744845i	$0.732523\pi$
$504$	−30.7029			−1.36762
$505$		0			0
$506$	−9.03576	−	15.6504i	−0.401689	−	0.695745i
$507$	41.7851			1.85574
$508$	13.2007			0.585687
$509$	−19.8167	−	34.3235i	−0.878360	−	1.52136i	−0.853140	−	0.521682i	$-0.825305\pi$
$509$	−19.8167	−	34.3235i	−0.878360	−	1.52136i	−0.0252198	−	0.999682i	$-0.508029\pi$
$510$		0			0
$511$	2.17609	−	3.76909i	0.0962643	−	0.166735i
$512$	19.7999			0.875041
$513$	66.7781	−	115.663i	2.94832	−	5.10665i
$514$	0.452683	−	0.784070i	0.0199670	−	0.0345839i
$515$		0			0
$516$	4.99578	+	8.65295i	0.219927	+	0.380925i
$517$	−29.1432			−1.28172
$518$	1.81709	+	8.14597i	0.0798383	+	0.357913i
$519$	−44.4328			−1.95038
$520$		0			0
$521$	15.7148	−	27.2188i	0.688477	−	1.19248i	−0.283854	−	0.958868i	$-0.591613\pi$
$521$	15.7148	−	27.2188i	0.688477	−	1.19248i	0.972331	−	0.233609i	$-0.0750537\pi$
$522$	13.9340	−	24.1345i	0.609877	−	1.05634i
$523$	7.17472	−	12.4270i	0.313729	−	0.543394i	−0.665438	−	0.746453i	$-0.731755\pi$
$523$	7.17472	−	12.4270i	0.313729	−	0.543394i	0.979166	+	0.203059i	$0.0650884\pi$
$524$	0.855764			0.0373842
$525$		0			0
$526$	2.73335			0.119180
$527$	2.31061	+	4.00210i	0.100652	+	0.174334i
$528$	−23.5593			−1.02529
$529$	−2.93969			−0.127813
$530$		0			0
$531$	−1.97917	+	3.42803i	−0.0858888	+	0.148764i
$532$	7.06145			0.306153
$533$	1.95425	+	3.38486i	0.0846480	+	0.146615i
$534$	−26.9233	−	46.6326i	−1.16509	−	2.01799i
$535$		0			0
$536$	17.3090	−	29.9800i	0.747634	−	1.29494i
$537$	15.2911	−	26.4850i	0.659860	−	1.14291i
$538$	6.81287	+	11.8002i	0.293723	+	0.508744i
$539$	−9.90206	−	17.1509i	−0.426512	−	0.738740i
$540$		0			0
$541$	14.4219			0.620046			0.310023	−	0.950729i	$-0.399663\pi$
$541$	14.4219			0.620046			0.310023	+	0.950729i	$0.399663\pi$
$542$	−17.5427	+	30.3849i	−0.753524	+	1.30514i
$543$	35.2462	+	61.0482i	1.51256	+	2.61983i
$544$	2.28863			0.0981243
$545$		0			0
$546$	−1.60309	−	2.77663i	−0.0686059	−	0.118829i
$547$	−4.85582			−0.207620			−0.103810	−	0.994597i	$-0.533103\pi$
$547$	−4.85582			−0.207620			−0.103810	+	0.994597i	$0.533103\pi$
$548$	−0.710765	+	1.23108i	−0.0303624	+	0.0525892i
$549$	−7.49881			−0.320041
$550$		0			0
$551$	−11.8229	+	20.4778i	−0.503671	+	0.872383i
$552$	23.0021	−	39.8408i	0.979034	−	1.69574i
$553$	−2.33459	−	4.04362i	−0.0992767	−	0.171952i
$554$	25.9944			1.10439
$555$		0			0
$556$	2.81128			0.119225
$557$	−2.37410	−	4.11206i	−0.100594	−	0.174233i	0.811336	−	0.584581i	$-0.198741\pi$
$557$	−2.37410	−	4.11206i	−0.100594	−	0.174233i	−0.911929	+	0.410347i	$0.865408\pi$
$558$	36.4938	−	63.2091i	1.54490	−	2.67585i
$559$	−1.40704	+	2.43706i	−0.0595113	+	0.103077i
$560$		0			0
$561$	−6.95878			−0.293800
$562$	−12.0057	+	20.7946i	−0.506432	+	0.877166i
$563$	−12.4349			−0.524069			−0.262035	−	0.965058i	$-0.584393\pi$
$563$	−12.4349			−0.524069			−0.262035	+	0.965058i	$0.584393\pi$
$564$	−10.0549	−	17.4156i	−0.423389	−	0.733331i
$565$		0			0
$566$	−15.4852			−0.650890
$567$	20.2273	+	35.0347i	0.849466	+	1.47132i
$568$	0.780125	−	1.35122i	0.0327333	−	0.0566958i
$569$	11.9189			0.499666			0.249833	−	0.968289i	$-0.419624\pi$
$569$	11.9189			0.499666			0.249833	+	0.968289i	$0.419624\pi$
$570$		0			0
$571$	13.7047	+	23.7372i	0.573522	+	0.993369i	0.996201	+	0.0870894i	$0.0277566\pi$
$571$	13.7047	+	23.7372i	0.573522	+	0.993369i	−0.422679	+	0.906280i	$0.638910\pi$
$572$	0.936518	+	1.62210i	0.0391578	+	0.0678232i
$573$	−12.5457	+	21.7298i	−0.524104	+	0.907774i
$574$	−3.83276	+	6.63853i	−0.159976	+	0.277087i
$575$		0			0
$576$	−34.0537	−	58.9828i	−1.41890	−	2.45761i
$577$	−3.23957	−	5.61111i	−0.134865	−	0.233593i	0.790681	−	0.612229i	$-0.209727\pi$
$577$	−3.23957	−	5.61111i	−0.134865	−	0.233593i	−0.925546	+	0.378635i	$0.876393\pi$
$578$	18.6788			0.776937
$579$	−27.6277	+	47.8525i	−1.14817	+	1.98868i
$580$		0			0
$581$	−14.2137			−0.589685
$582$	38.4016			1.59180
$583$	17.8904	+	30.9871i	0.740946	+	1.28336i
$584$	10.9332			0.452418
$585$		0			0
$586$	−7.96625			−0.329083
$587$	19.4315	−	33.6563i	0.802022	−	1.38914i	−0.116261	−	0.993219i	$-0.537091\pi$
$587$	19.4315	−	33.6563i	0.802022	−	1.38914i	0.918283	−	0.395924i	$-0.129576\pi$
$588$	6.83277	−	11.8347i	0.281779	−	0.488055i
$589$	−30.9645	+	53.6321i	−1.27587	+	2.20987i
$590$		0			0
$591$	5.83418			0.239986
$592$	−8.77698	+	8.06374i	−0.360731	+	0.331418i
$593$	−35.6076			−1.46223			−0.731115	−	0.682254i	$-0.761000\pi$
$593$	−35.6076			−1.46223			−0.731115	+	0.682254i	$0.761000\pi$
$594$	34.7390	+	60.1697i	1.42536	+	2.46879i
$595$		0			0
$596$	−0.205456	+	0.355859i	−0.00841579	+	0.0145766i
$597$	−24.7532	+	42.8739i	−1.01308	+	1.75471i
$598$	3.51211			0.143621
$599$	−8.46167	+	14.6560i	−0.345735	+	0.598830i	−0.985487	−	0.169751i	$-0.945704\pi$
$599$	−8.46167	+	14.6560i	−0.345735	+	0.598830i	0.639752	+	0.768581i	$0.279037\pi$
$600$		0			0
$601$	6.62845	+	11.4808i	0.270380	+	0.468312i	0.968959	−	0.247221i	$-0.0795173\pi$
$601$	6.62845	+	11.4808i	0.270380	+	0.468312i	−0.698579	+	0.715533i	$0.746184\pi$
$602$	−5.51908			−0.224941
$603$	−91.8062			−3.73864
$604$	3.40553	+	5.89856i	0.138569	+	0.240009i
$605$		0			0
$606$	−20.5966			−0.836681
$607$	−2.88086	−	4.98980i	−0.116931	−	0.202530i	0.801619	−	0.597835i	$-0.203972\pi$
$607$	−2.88086	−	4.98980i	−0.116931	−	0.202530i	−0.918550	+	0.395305i	$0.870639\pi$
$608$	15.3350	+	26.5610i	0.621916	+	1.07719i
$609$	−6.23259	−	10.7952i	−0.252557	−	0.437442i
$610$		0			0
$611$	2.83192	−	4.90502i	0.114567	−	0.198436i
$612$	−1.75524	−	3.04017i	−0.0709515	−	0.122892i
$613$	−16.6927	−	28.9125i	−0.674210	−	1.16777i	−0.976699	−	0.214613i	$-0.931151\pi$
$613$	−16.6927	−	28.9125i	−0.674210	−	1.16777i	0.302489	−	0.953153i	$-0.402182\pi$
$614$	13.2475	+	22.9453i	0.534625	+	0.925998i
$615$		0			0
$616$	−6.77608	+	11.7365i	−0.273016	+	0.472877i
$617$	−16.8377	−	29.1637i	−0.677860	−	1.17409i	−0.975624	−	0.219448i	$-0.929574\pi$
$617$	−16.8377	−	29.1637i	−0.677860	−	1.17409i	0.297765	−	0.954639i	$-0.403759\pi$
$618$	−23.3664			−0.939934
$619$	28.0530			1.12755			0.563774	−	0.825929i	$-0.309349\pi$
$619$	28.0530			1.12755			0.563774	+	0.825929i	$0.309349\pi$
$620$		0			0
$621$	−77.1241			−3.09488
$622$	−10.8502	+	18.7931i	−0.435054	+	0.753535i
$623$	−17.6081			−0.705454
$624$	2.28931	−	3.96520i	0.0916458	−	0.158735i
$625$		0			0
$626$	−3.42442	+	5.93127i	−0.136867	+	0.237061i
$627$	−46.6273	−	80.7609i	−1.86212	−	3.22528i
$628$	−2.03900			−0.0813652
$629$	−2.59249	+	2.38182i	−0.103369	+	0.0949692i
$630$		0			0
$631$	−15.8300	−	27.4183i	−0.630181	−	1.09151i	−0.987514	−	0.157528i	$-0.949647\pi$
$631$	−15.8300	−	27.4183i	−0.630181	−	1.09151i	0.357334	−	0.933977i	$-0.383686\pi$
$632$	5.86476	−	10.1581i	0.233288	−	0.404066i
$633$	−30.2869	+	52.4585i	−1.20380	+	2.08504i
$634$	18.6287	−	32.2659i	0.739841	−	1.28144i
$635$		0			0
$636$	−12.3450	+	21.3822i	−0.489512	+	0.847860i
$637$	3.84883			0.152496
$638$	−6.15044	−	10.6529i	−0.243498	−	0.421751i
$639$	−4.13775			−0.163687
$640$		0			0
$641$	1.04348	+	1.80736i	0.0412149	+	0.0713864i	0.885897	−	0.463882i	$-0.153544\pi$
$641$	1.04348	+	1.80736i	0.0412149	+	0.0713864i	−0.844682	+	0.535268i	$0.820210\pi$
$642$	−0.692824	+	1.20001i	−0.0273436	+	0.0473605i
$643$	−1.07099			−0.0422359			−0.0211179	−	0.999777i	$-0.506723\pi$
$643$	−1.07099			−0.0422359			−0.0211179	+	0.999777i	$0.506723\pi$
$644$	−2.03887	−	3.53143i	−0.0803428	−	0.139158i
$645$		0			0
$646$	−2.51572	−	4.35735i	−0.0989795	−	0.171438i
$647$	−17.4463	+	30.2179i	−0.685886	+	1.18799i	0.287271	+	0.957849i	$0.407252\pi$
$647$	−17.4463	+	30.2179i	−0.685886	+	1.18799i	−0.973157	+	0.230141i	$0.926081\pi$
$648$	−50.8133	+	88.0113i	−1.99614	+	3.45741i
$649$	0.873600	+	1.51312i	0.0342918	+	0.0593951i
$650$		0			0
$651$	−16.3234	−	28.2729i	−0.639764	−	1.10810i
$652$	15.6693			0.613658
$653$	−0.981744	+	1.70043i	−0.0384186	+	0.0665430i	−0.884595	−	0.466359i	$-0.845565\pi$
$653$	−0.981744	+	1.70043i	−0.0384186	+	0.0665430i	0.846177	+	0.532902i	$0.178899\pi$
$654$	−5.82282	−	10.0854i	−0.227690	−	0.394371i
$655$		0			0
$656$	−10.9468			−0.427402
$657$	−14.4973	−	25.1100i	−0.565593	−	0.979635i
$658$	11.1081			0.433041
$659$	−9.77811	+	16.9362i	−0.380901	+	0.659740i	−0.991191	−	0.132438i	$-0.957720\pi$
$659$	−9.77811	+	16.9362i	−0.380901	+	0.659740i	0.610290	+	0.792178i	$0.291053\pi$
$660$		0			0
$661$	−0.987098	+	1.70970i	−0.0383937	+	0.0664998i	−0.884584	−	0.466381i	$-0.845557\pi$
$661$	−0.987098	+	1.70970i	−0.0383937	+	0.0664998i	0.846190	+	0.532881i	$0.178891\pi$
$662$	0.777499	−	1.34667i	0.0302184	−	0.0523397i
$663$	0.676202	−	1.17122i	0.0262615	−	0.0454863i
$664$	−17.8533	−	30.9228i	−0.692842	−	1.20004i
$665$		0			0
$666$	53.0513	+	16.6508i	2.05570	+	0.645207i
$667$	13.6546			0.528708
$668$	3.72935	+	6.45942i	0.144293	+	0.249923i
$669$	6.42244	−	11.1240i	0.248306	−	0.430078i
$670$		0			0
$671$	−1.65497	+	2.86650i	−0.0638896	+	0.110660i
$672$	−16.1681			−0.623698
$673$	10.3326	−	17.8966i	0.398292	−	0.689861i	−0.595224	−	0.803560i	$-0.702937\pi$
$673$	10.3326	−	17.8966i	0.398292	−	0.689861i	0.993515	+	0.113699i	$0.0362698\pi$
$674$	17.1598			0.660971
$675$		0			0
$676$	9.30432			0.357858
$677$	10.7458			0.412994			0.206497	−	0.978447i	$-0.433794\pi$
$677$	10.7458			0.412994			0.206497	+	0.978447i	$0.433794\pi$
$678$	21.8857	+	37.9072i	0.840517	+	1.45582i
$679$	6.27875	−	10.8751i	0.240956	−	0.417349i
$680$		0			0
$681$	23.0685	+	39.9559i	0.883988	+	1.53111i
$682$	−16.1082	−	27.9002i	−0.616815	−	1.06836i
$683$	6.02617	+	10.4376i	0.230585	+	0.399385i	0.957980	−	0.286834i	$-0.0926027\pi$
$683$	6.02617	+	10.4376i	0.230585	+	0.399385i	−0.727396	+	0.686218i	$0.759269\pi$
$684$	23.5220	−	40.7413i	0.899386	−	1.55778i
$685$		0			0
$686$	8.57660	+	14.8551i	0.327456	+	0.567171i
$687$	1.00700	+	1.74418i	0.0384196	+	0.0665447i
$688$	−3.94079	−	6.82565i	−0.150241	−	0.260226i
$689$	−6.95383			−0.264920
$690$		0			0
$691$	−5.15674	−	8.93174i	−0.196172	−	0.339779i	0.751112	−	0.660175i	$-0.229518\pi$
$691$	−5.15674	−	8.93174i	−0.196172	−	0.339779i	−0.947284	+	0.320395i	$0.896184\pi$
$692$	−9.89386			−0.376108
$693$	35.9401			1.36525
$694$	−15.1369	−	26.2178i	−0.574587	−	0.995215i
$695$		0			0
$696$	15.6570	−	27.1187i	0.593477	−	1.02793i
$697$	−3.23341			−0.122474
$698$	−11.3868	+	19.7225i	−0.430996	+	0.746506i
$699$	−38.9817	+	67.5183i	−1.47442	+	2.55378i
$700$		0			0
$701$	−17.7577	−	30.7573i	−0.670699	−	1.16169i	−0.977706	−	0.209978i	$-0.932661\pi$
$701$	−17.7577	−	30.7573i	−0.670699	−	1.16169i	0.307007	−	0.951707i	$-0.400673\pi$
$702$	−13.5027			−0.509626
$703$	−45.0134	−	14.1280i	−1.69771	−	0.532848i
$704$	−30.0624			−1.13302
$705$		0			0
$706$	2.50519	−	4.33912i	0.0942841	−	0.163305i
$707$	−3.36760	+	5.83285i	−0.126652	+	0.219367i
$708$	−0.602815	+	1.04411i	−0.0226552	+	0.0392399i
$709$	−32.6695			−1.22693			−0.613465	−	0.789722i	$-0.710225\pi$
$709$	−32.6695			−1.22693			−0.613465	+	0.789722i	$0.710225\pi$
$710$		0			0
$711$	−31.1065			−1.16658
$712$	−22.1168	−	38.3075i	−0.828863	−	1.43563i
$713$	35.7619			1.33929
$714$	2.65239			0.0992632
$715$		0			0
$716$	3.40488	−	5.89742i	0.127246	−	0.220397i
$717$	93.8323			3.50423
$718$	−17.5267	−	30.3571i	−0.654090	−	1.13292i
$719$	−16.3243	−	28.2746i	−0.608794	−	1.05446i	−0.991439	−	0.130567i	$-0.958320\pi$
$719$	−16.3243	−	28.2746i	−0.608794	−	1.05446i	0.382645	−	0.923895i	$-0.375013\pi$
$720$		0			0
$721$	−3.82046	+	6.61723i	−0.142281	+	0.246438i
$722$	23.0651	−	39.9500i	0.858395	−	1.48678i
$723$	0.0607951	+	0.105300i	0.00226099	+	0.00391615i
$724$	7.84829	+	13.5936i	0.291679	+	0.505204i
$725$		0			0
$726$	7.33294			0.272151
$727$	−7.09098	+	12.2819i	−0.262990	+	0.455512i	−0.967035	−	0.254643i	$-0.918042\pi$
$727$	−7.09098	+	12.2819i	−0.262990	+	0.455512i	0.704045	+	0.710155i	$0.251375\pi$
$728$	−1.31690	−	2.28093i	−0.0488074	−	0.0845369i
$729$	96.9728			3.59158
$730$		0			0
$731$	−1.16401	−	2.01612i	−0.0430523	−	0.0745688i
$732$	−2.28398			−0.0844184
$733$	9.72667	−	16.8471i	0.359263	−	0.622261i	−0.628575	−	0.777749i	$-0.716362\pi$
$733$	9.72667	−	16.8471i	0.359263	−	0.622261i	0.987838	+	0.155488i	$0.0496948\pi$
$734$	−18.0752			−0.667168
$735$		0			0
$736$	8.85542	−	15.3380i	0.326415	−	0.565368i
$737$	−20.2615	+	35.0939i	−0.746341	+	1.29270i
$738$	25.5342	+	44.2265i	0.939926	+	1.62800i
$739$	−52.1774			−1.91938			−0.959689	−	0.281063i	$-0.909313\pi$
$739$	−52.1774			−1.91938			−0.959689	+	0.281063i	$0.909313\pi$
$740$		0			0
$741$	18.1236			0.665786
$742$	−6.81907	−	11.8110i	−0.250336	−	0.433594i
$743$	6.68363	−	11.5764i	0.245198	−	0.424696i	−0.716989	−	0.697085i	$-0.754480\pi$
$743$	6.68363	−	11.5764i	0.245198	−	0.424696i	0.962187	+	0.272388i	$0.0878135\pi$
$744$	41.0063	−	71.0249i	1.50336	−	2.60390i
$745$		0			0
$746$	−11.4778			−0.420231
$747$	−47.3466	+	82.0067i	−1.73232	+	3.00047i
$748$	−1.54952			−0.0566559
$749$	0.226557	+	0.392408i	0.00827820	+	0.0143383i
$750$		0			0
$751$	16.7410			0.610887			0.305443	−	0.952210i	$-0.401195\pi$
$751$	16.7410			0.610887			0.305443	+	0.952210i	$0.401195\pi$
$752$	7.93156	+	13.7379i	0.289234	+	0.500969i
$753$	−35.7668	+	61.9500i	−1.30342	+	2.25758i
$754$	2.39061			0.0870609
$755$		0			0
$756$	7.83867	+	13.5770i	0.285090	+	0.493790i
$757$	−5.63936	−	9.76765i	−0.204966	−	0.355011i	0.745156	−	0.666890i	$-0.232375\pi$
$757$	−5.63936	−	9.76765i	−0.204966	−	0.355011i	−0.950122	+	0.311879i	$0.899042\pi$
$758$	9.28176	−	16.0765i	0.337129	−	0.583924i
$759$	−26.9257	+	46.6367i	−0.977340	+	1.69280i
$760$		0			0
$761$	23.3731	+	40.4834i	0.847275	+	1.46752i	0.883631	+	0.468184i	$0.155092\pi$
$761$	23.3731	+	40.4834i	0.847275	+	1.46752i	−0.0363559	+	0.999339i	$0.511575\pi$
$762$	33.2238	+	57.5453i	1.20357	+	2.08464i
$763$	−3.80818			−0.137865
$764$	−2.79355	+	4.83858i	−0.101067	+	0.175054i
$765$		0			0
$766$	20.5129			0.741162
$767$	−0.339559			−0.0122608
$768$	−25.1754	−	43.6051i	−0.908439	−	1.57346i
$769$	37.8487			1.36486			0.682430	−	0.730951i	$-0.260923\pi$
$769$	37.8487			1.36486			0.682430	+	0.730951i	$0.260923\pi$
$770$		0			0
$771$	−2.69790			−0.0971626
$772$	−6.15186	+	10.6553i	−0.221410	+	0.383494i
$773$	−2.07440	+	3.59297i	−0.0746110	+	0.129230i	−0.900917	−	0.433991i	$-0.857105\pi$
$773$	−2.07440	+	3.59297i	−0.0746110	+	0.129230i	0.826306	+	0.563221i	$0.190438\pi$
$774$	−18.3843	+	31.8425i	−0.660810	+	1.14456i
$775$		0			0
$776$	31.5459			1.13243
$777$	18.3147	−	16.8264i	0.657036	−	0.603644i
$778$	16.4451			0.589587
$779$	−21.6654	−	37.5256i	−0.776245	−	1.34450i
$780$		0			0
$781$	−0.913195	+	1.58170i	−0.0326767	+	0.0565977i
$782$	−1.45274	+	2.51622i	−0.0519499	+	0.0899798i
$783$	−52.4966			−1.87608
$784$	−5.38985	+	9.33550i	−0.192495	+	0.333411i
$785$		0			0
$786$	2.15380	+	3.73049i	0.0768234	+	0.133062i
$787$	42.8205			1.52639			0.763193	−	0.646170i	$-0.223630\pi$
$787$	42.8205			1.52639			0.763193	+	0.646170i	$0.223630\pi$
$788$	1.29910			0.0462785
$789$	−4.07256	−	7.05387i	−0.144987	−	0.251125i
$790$		0			0
$791$	14.3135			0.508928
$792$	45.1429	+	78.1897i	1.60408	+	2.77835i
$793$	−0.321636	−	0.557089i	−0.0114216	−	0.0197828i
$794$	1.12212	+	1.94357i	0.0398226	+	0.0689748i
$795$		0			0
$796$	−5.51182	+	9.54674i	−0.195361	+	0.338375i
$797$	−18.8156	−	32.5896i	−0.666482	−	1.15438i	−0.978881	−	0.204430i	$-0.934466\pi$
$797$	−18.8156	−	32.5896i	−0.666482	−	1.15438i	0.312399	−	0.949951i	$-0.398867\pi$
$798$	17.7723	+	30.7826i	0.629134	+	1.08969i
$799$	2.34277	+	4.05780i	0.0828814	+	0.143555i
$800$		0			0
$801$	−58.6534	+	101.591i	−2.07242	+	3.58953i
$802$	−12.8255	−	22.2143i	−0.452883	−	0.784416i
$803$	−12.7981			−0.451635
$804$	−27.9623			−0.986153
$805$		0			0
$806$	6.26110			0.220538
$807$	20.3017	−	35.1635i	0.714653	−	1.23781i
$808$	−16.9196			−0.595230
$809$	11.7837	−	20.4099i	0.414292	−	0.717576i	−0.581061	−	0.813860i	$-0.697362\pi$
$809$	11.7837	−	20.4099i	0.414292	−	0.717576i	0.995354	+	0.0962841i	$0.0306957\pi$
$810$		0			0
$811$	24.7159	−	42.8093i	0.867894	−	1.50324i	0.00374948	−	0.999993i	$-0.498807\pi$
$811$	24.7159	−	42.8093i	0.867894	−	1.50324i	0.864145	−	0.503244i	$-0.167860\pi$
$812$	−1.38781	−	2.40376i	−0.0487027	−	0.0843555i
$813$	104.551			3.66677
$814$	18.0733	−	16.6046i	0.633468	−	0.581991i
$815$		0			0
$816$	1.89389	+	3.28031i	0.0662994	+	0.114834i
$817$	15.5988	−	27.0180i	0.545734	−	0.945240i
$818$	5.10895	−	8.84896i	0.178630	−	0.309397i
$819$	−3.49238	+	6.04899i	−0.122034	+	0.211369i
$820$		0			0
$821$	−12.6853	+	21.9716i	−0.442721	+	0.766815i	−0.997890	−	0.0649222i	$-0.979320\pi$
$821$	−12.6853	+	21.9716i	−0.442721	+	0.766815i	0.555169	+	0.831737i	$0.312653\pi$
$822$	−7.15545			−0.249575
$823$	−4.08512	−	7.07564i	−0.142398	−	0.246641i	0.786001	−	0.618225i	$-0.212148\pi$
$823$	−4.08512	−	7.07564i	−0.142398	−	0.246641i	−0.928399	+	0.371584i	$0.878815\pi$
$824$	−19.1949			−0.668686
$825$		0			0
$826$	−0.332979	−	0.576736i	−0.0115858	−	0.0200672i
$827$	−0.495060	+	0.857468i	−0.0172149	+	0.0298171i	−0.874505	−	0.485017i	$-0.838813\pi$
$827$	−0.495060	+	0.857468i	−0.0172149	+	0.0298171i	0.857290	+	0.514834i	$0.172147\pi$
$828$	−27.1663			−0.944094
$829$	13.0618	+	22.6237i	0.453654	+	0.785752i	0.998610	−	0.0527126i	$-0.0167867\pi$
$829$	13.0618	+	22.6237i	0.453654	+	0.785752i	−0.544955	+	0.838465i	$0.683453\pi$
$830$		0			0
$831$	−38.7303	−	67.0829i	−1.34354	−	2.32708i
$832$	2.92123	−	5.05972i	0.101276	−	0.175414i
$833$	−1.59202	+	2.75746i	−0.0551602	+	0.0955403i
$834$	7.07546	+	12.2551i	0.245003	+	0.424358i
$835$		0			0
$836$	−10.3825	−	17.9831i	−0.359087	−	0.621957i
$837$	−137.490			−4.75237
$838$	−4.76950	+	8.26102i	−0.164760	+	0.285372i
$839$	20.0623	+	34.7490i	0.692629	+	1.19967i	0.970973	+	0.239187i	$0.0768810\pi$
$839$	20.0623	+	34.7490i	0.692629	+	1.19967i	−0.278344	+	0.960481i	$0.589786\pi$
$840$		0			0
$841$	−19.7056			−0.679505
$842$	−4.95181	−	8.57678i	−0.170650	−	0.295575i
$843$	71.5519			2.46438
$844$	−6.74400	+	11.6809i	−0.232138	+	0.402075i
$845$		0			0
$846$	37.0017	−	64.0889i	1.27215	−	2.20342i
$847$	1.19895	−	2.07665i	0.0411965	−	0.0713544i
$848$	9.73805	−	16.8668i	0.334406	−	0.579208i
$849$	23.0721	+	39.9621i	0.791833	+	1.37150i
$850$		0			0
$851$	5.93141	+	26.5904i	0.203326	+	0.911507i
$852$	−1.26027			−0.0431763
$853$	−16.3382	−	28.2985i	−0.559408	−	0.968923i	−0.997546	−	0.0700154i	$-0.977695\pi$
$853$	−16.3382	−	28.2985i	−0.559408	−	0.968923i	0.438138	−	0.898908i	$-0.355638\pi$
$854$	0.630805	−	1.09259i	0.0215857	−	0.0373876i
$855$		0			0
$856$	−0.569137	+	0.985774i	−0.0194527	+	0.0336931i
$857$	9.95029			0.339896			0.169948	−	0.985453i	$-0.445640\pi$
$857$	9.95029			0.339896			0.169948	+	0.985453i	$0.445640\pi$
$858$	−4.71408	+	8.16503i	−0.160936	+	0.278749i
$859$	4.53739			0.154814			0.0774068	−	0.997000i	$-0.475336\pi$
$859$	4.53739			0.154814			0.0774068	+	0.997000i	$0.475336\pi$
$860$		0			0
$861$	22.8425			0.778470
$862$	−1.69320			−0.0576706
$863$	1.72742	+	2.99198i	0.0588020	+	0.101848i	0.893928	−	0.448211i	$-0.147939\pi$
$863$	1.72742	+	2.99198i	0.0588020	+	0.101848i	−0.835126	+	0.550059i	$0.814605\pi$
$864$	−34.0457	+	58.9688i	−1.15826	+	2.00616i
$865$		0			0
$866$	−3.84349	−	6.65712i	−0.130607	−	0.226218i
$867$	−27.8305	−	48.2039i	−0.945175	−	1.63709i
$868$	−3.63473	−	6.29554i	−0.123371	−	0.213685i
$869$	−6.86514	+	11.8908i	−0.232884	+	0.403367i
$870$		0			0
$871$	−3.93771	−	6.82032i	−0.133424	−	0.231098i
$872$	−4.78330	−	8.28491i	−0.161983	−	0.280562i
$873$	−41.8296	−	72.4510i	−1.41572	−	2.45210i
$874$	−38.9363			−1.31704
$875$		0			0
$876$	−4.41557	−	7.64799i	−0.149188	−	0.258402i
$877$	23.2726			0.785861			0.392931	−	0.919568i	$-0.371461\pi$
$877$	23.2726			0.785861			0.392931	+	0.919568i	$0.371461\pi$
$878$	−21.4504			−0.723917
$879$	11.8693	+	20.5583i	0.400342	+	0.693413i
$880$		0			0
$881$	−6.16226	+	10.6733i	−0.207612	+	0.359594i	−0.950962	−	0.309309i	$-0.899902\pi$
$881$	−6.16226	+	10.6733i	−0.207612	+	0.359594i	0.743350	+	0.668903i	$0.233236\pi$
$882$	50.2887			1.69331
$883$	8.82778	−	15.2902i	0.297078	−	0.514555i	−0.678388	−	0.734704i	$-0.737321\pi$
$883$	8.82778	−	15.2902i	0.297078	−	0.514555i	0.975466	+	0.220149i	$0.0706544\pi$
$884$	0.150570	−	0.260795i	0.00506422	−	0.00877149i
$885$		0			0
$886$	1.26481	+	2.19072i	0.0424922	+	0.0735987i
$887$	−40.8268			−1.37083			−0.685415	−	0.728153i	$-0.740379\pi$
$887$	−40.8268			−1.37083			−0.685415	+	0.728153i	$0.740379\pi$
$888$	59.6112	+	18.7097i	2.00042	+	0.627857i
$889$	21.7286			0.728755
$890$		0			0
$891$	59.4808	−	103.024i	1.99268	−	3.45143i
$892$	1.43009	−	2.47698i	0.0478828	−	0.0829355i
$893$	−31.3955	+	54.3786i	−1.05061	+	1.81971i
$894$	−2.06837			−0.0691768
$895$		0			0
$896$	1.77697			0.0593644
$897$	−5.23287	−	9.06360i	−0.174720	−	0.302625i
$898$	27.3237			0.911804
$899$	24.3423			0.811861
$900$		0			0
$901$	2.87636	−	4.98201i	0.0958256	−	0.165975i
$902$	22.5414			0.750546
$903$	8.22315	+	14.2429i	0.273649	+	0.473975i
$904$	17.9786	+	31.1398i	0.597958	+	1.03569i
$905$		0			0
$906$	−17.1422	+	29.6912i	−0.569511	+	0.986422i
$907$	−28.6551	+	49.6320i	−0.951475	+	1.64800i	−0.209240	+	0.977864i	$0.567099\pi$
$907$	−28.6551	+	49.6320i	−0.951475	+	1.64800i	−0.742235	+	0.670139i	$0.766234\pi$
$908$	5.13668	+	8.89699i	0.170467	+	0.295257i
$909$	22.4352	+	38.8590i	0.744130	+	1.28887i
$910$		0			0
$911$	−21.6237			−0.716426			−0.358213	−	0.933640i	$-0.616614\pi$
$911$	−21.6237			−0.716426			−0.358213	+	0.933640i	$0.616614\pi$
$912$	−25.3800	+	43.9595i	−0.840417	+	1.45564i
$913$	20.8986	+	36.1975i	0.691643	+	1.19796i
$914$	−15.7507			−0.520986
$915$		0			0
$916$	0.224230	+	0.388378i	0.00740877	+	0.0128324i
$917$	1.40860			0.0465162
$918$	5.58522	−	9.67388i	0.184340	−	0.319286i
$919$	30.6901			1.01237			0.506186	−	0.862424i	$-0.331055\pi$
$919$	30.6901			1.01237			0.506186	+	0.862424i	$0.331055\pi$
$920$		0			0
$921$	39.4762	−	68.3748i	1.30079	−	2.25303i
$922$	−14.8049	+	25.6429i	−0.487575	+	0.844504i
$923$	−0.177475	−	0.307395i	−0.00584165	−	0.0101180i
$924$	10.9466			0.360117
$925$		0			0
$926$	28.1806			0.926071
$927$	25.4522	+	44.0846i	0.835961	+	1.44793i
$928$	6.02768	−	10.4403i	0.197868	−	0.342718i
$929$	4.44146	−	7.69284i	0.145720	−	0.252394i	−0.783922	−	0.620860i	$-0.786784\pi$
$929$	4.44146	−	7.69284i	0.145720	−	0.252394i	0.929641	+	0.368466i	$0.120117\pi$
$930$		0			0
$931$	−42.6693			−1.39843
$932$	−8.68007	+	15.0343i	−0.284325	+	0.492466i
$933$	64.6652			2.11704
$934$	7.86317	+	13.6194i	0.257291	+	0.445641i
$935$		0			0
$936$	−17.5466			−0.573527
$937$	0.306294	+	0.530517i	0.0100062	+	0.0173312i	0.870985	−	0.491309i	$-0.163482\pi$
$937$	0.306294	+	0.530517i	0.0100062	+	0.0173312i	−0.860979	+	0.508641i	$0.830148\pi$
$938$	7.72281	−	13.3763i	0.252159	−	0.436751i
$939$	20.4089			0.666019
$940$		0			0
$941$	−16.6946	−	28.9159i	−0.544229	−	0.942632i	−0.998655	−	0.0518474i	$-0.983489\pi$
$941$	−16.6946	−	28.9159i	−0.544229	−	0.942632i	0.454426	−	0.890784i	$-0.349844\pi$
$942$	−5.13180	−	8.88853i	−0.167203	−	0.289604i
$943$	−12.5110	+	21.6698i	−0.407416	+	0.705665i
$944$	0.475515	−	0.823616i	0.0154767	−	0.0268064i
$945$		0			0
$946$	8.11476	+	14.0552i	0.263834	+	0.456973i
$947$	−5.18210	−	8.97566i	−0.168396	−	0.291670i	0.769460	−	0.638695i	$-0.220525\pi$
$947$	−5.18210	−	8.97566i	−0.168396	−	0.291670i	−0.937856	+	0.347025i	$0.887192\pi$
$948$	−9.47438			−0.307714
$949$	1.24362	−	2.15402i	0.0403697	−	0.0699223i
$950$		0			0
$951$	−111.024			−3.60018
$952$	2.17887			0.0706176
$953$	7.44472	+	12.8946i	0.241158	+	0.417698i	0.961044	−	0.276394i	$-0.0891394\pi$
$953$	7.44472	+	12.8946i	0.241158	+	0.417698i	−0.719886	+	0.694092i	$0.755806\pi$
$954$	−90.8585			−2.94165
$955$		0			0
$956$	20.8937			0.675749
$957$	−18.3277	+	31.7445i	−0.592450	+	1.02615i
$958$	−3.74479	+	6.48617i	−0.120989	+	0.209559i
$959$	−1.16993	+	2.02638i	−0.0377791	+	0.0654353i
$960$		0			0
$961$	32.7533			1.05656
$962$	1.03846	+	4.65538i	0.0334812	+	0.150096i
$963$	3.01868			0.0972757
$964$	0.0135373	+	0.0234472i	0.000436006	+	0.000755184i
$965$		0			0
$966$	10.2629	−	17.7759i	0.330204	−	0.571930i
$967$	21.6538	−	37.5055i	0.696339	−	1.20609i	−0.273389	−	0.961904i	$-0.588145\pi$
$967$	21.6538	−	37.5055i	0.696339	−	1.20609i	0.969727	−	0.244190i	$-0.0785222\pi$
$968$	6.02382			0.193613
$969$	−7.49659	+	12.9845i	−0.240825	+	0.417121i
$970$		0			0
$971$	−4.45691	−	7.71960i	−0.143029	−	0.247734i	0.785607	−	0.618726i	$-0.212351\pi$
$971$	−4.45691	−	7.71960i	−0.143029	−	0.247734i	−0.928636	+	0.370992i	$0.879018\pi$
$972$	43.6684			1.40066
$973$	4.62741			0.148348
$974$	4.07170	+	7.05239i	0.130466	+	0.225973i
$975$		0			0
$976$	1.80166			0.0576697
$977$	6.68632	+	11.5810i	0.213914	+	0.370511i	0.952936	−	0.303171i	$-0.0980453\pi$
$977$	6.68632	+	11.5810i	0.213914	+	0.370511i	−0.739022	+	0.673681i	$0.764712\pi$
$978$	39.4368	+	68.3065i	1.26105	+	2.18420i
$979$	25.8894	+	44.8418i	0.827429	+	1.43315i
$980$		0			0
$981$	−12.6852	+	21.9714i	−0.405008	+	0.701494i
$982$	0.250296	+	0.433526i	0.00798728	+	0.0138344i
$983$	−11.5659	−	20.0327i	−0.368894	−	0.638944i	0.620499	−	0.784208i	$-0.286930\pi$
$983$	−11.5659	−	20.0327i	−0.368894	−	0.638944i	−0.989393	+	0.145264i	$0.953597\pi$
$984$	28.6915	+	49.6952i	0.914652	+	1.58422i
$985$		0			0
$986$	−0.988847	+	1.71273i	−0.0314913	+	0.0545445i
$987$	−16.5506	−	28.6665i	−0.526811	−	0.912464i
$988$	4.03558			0.128389
$989$	−18.0156			−0.572863
$990$		0			0
$991$	14.4144			0.457887			0.228944	−	0.973440i	$-0.426473\pi$
$991$	14.4144			0.457887			0.228944	+	0.973440i	$0.426473\pi$
$992$	15.7867	−	27.3434i	0.501229	−	0.868154i
$993$	−4.63374			−0.147047
$994$	0.348071	−	0.602876i	0.0110401	−	0.0191221i
$995$		0			0
$996$	−14.4208	+	24.9775i	−0.456940	+	0.791444i
$997$	−0.509477	−	0.882439i	−0.0161353	−	0.0279471i	0.857845	−	0.513908i	$-0.171803\pi$
$997$	−0.509477	−	0.882439i	−0.0161353	−	0.0279471i	−0.873980	+	0.485961i	$0.838470\pi$
$998$	11.8859			0.376243
$999$	−22.8040	−	102.230i	−0.721486	−	3.23441i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.e.c.26.5		14
5.2	odd	4		925.2.o.b.174.5		28
5.3	odd	4		925.2.o.b.174.10		28
5.4	even	2		185.2.e.a.26.3	✓	14
37.10	even	3	inner	925.2.e.c.676.5		14
185.47	odd	12		925.2.o.b.824.10		28
185.84	even	6		185.2.e.a.121.3	yes	14
185.158	odd	12		925.2.o.b.824.5		28
185.159	even	6		6845.2.a.k.1.3		7
185.174	even	6		6845.2.a.l.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.e.a.26.3	✓	14	5.4	even	2
185.2.e.a.121.3	yes	14	185.84	even	6
925.2.e.c.26.5		14	1.1	even	1	trivial
925.2.e.c.676.5		14	37.10	even	3	inner
925.2.o.b.174.5		28	5.2	odd	4
925.2.o.b.174.10		28	5.3	odd	4
925.2.o.b.824.5		28	185.158	odd	12
925.2.o.b.824.10		28	185.47	odd	12
6845.2.a.k.1.3		7	185.159	even	6
6845.2.a.l.1.5		7	185.174	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.560420 + 0.970676i) q^{2} +(1.67000 - 2.89252i) q^{3} +(0.371859 - 0.644078i) q^{4} +3.74360 q^{6} +(0.612087 - 1.06017i) q^{7} +3.07527 q^{8} +(-4.07778 - 7.06292i) q^{9} -3.59983 q^{11} +(-1.24201 - 2.15122i) q^{12} +(0.349805 - 0.605879i) q^{13} +1.37210 q^{14} +(0.979724 + 1.69693i) q^{16} +(0.289385 + 0.501229i) q^{17} +(4.57054 - 7.91640i) q^{18} +(-3.87804 + 6.71697i) q^{19} +(-2.04437 - 3.54094i) q^{21} +(-2.01742 - 3.49427i) q^{22} +4.47887 q^{23} +(5.13569 - 8.89527i) q^{24} +0.784150 q^{26} -17.2195 q^{27} +(-0.455220 - 0.788464i) q^{28} +3.04867 q^{29} +7.98457 q^{31} +(1.97715 - 3.42453i) q^{32} +(-6.01171 + 10.4126i) q^{33} +(-0.324354 + 0.561797i) q^{34} -6.06543 q^{36} +(1.32431 + 5.93685i) q^{37} -8.69333 q^{38} +(-1.16835 - 2.02363i) q^{39} +(-2.79335 + 4.83822i) q^{41} +(2.29141 - 3.96883i) q^{42} -4.02235 q^{43} +(-1.33863 + 2.31857i) q^{44} +(2.51005 + 4.34753i) q^{46} +8.09571 q^{47} +6.54454 q^{48} +(2.75070 + 4.76435i) q^{49} +1.93309 q^{51} +(-0.260156 - 0.450603i) q^{52} +(-4.96979 - 8.60794i) q^{53} +(-9.65017 - 16.7146i) q^{54} +(1.88233 - 3.26029i) q^{56} +(12.9526 + 22.4346i) q^{57} +(1.70853 + 2.95927i) q^{58} +(-0.242678 - 0.420330i) q^{59} +(0.459736 - 0.796287i) q^{61} +(4.47471 + 7.75043i) q^{62} -9.98382 q^{63} +8.35104 q^{64} -13.4763 q^{66} +(5.62845 - 9.74876i) q^{67} +0.430441 q^{68} +(7.47970 - 12.9552i) q^{69} +(0.253677 - 0.439381i) q^{71} +(-12.5403 - 21.7204i) q^{72} +3.55519 q^{73} +(-5.02059 + 4.61261i) q^{74} +(2.88417 + 4.99553i) q^{76} +(-2.20341 + 3.81642i) q^{77} +(1.30953 - 2.26817i) q^{78} +(1.90707 - 3.30314i) q^{79} +(-16.5232 + 28.6191i) q^{81} -6.26179 q^{82} +(-5.80544 - 10.0553i) q^{83} -3.04086 q^{84} +(-2.25421 - 3.90440i) q^{86} +(5.09126 - 8.81833i) q^{87} -11.0705 q^{88} +(-7.19183 - 12.4566i) q^{89} +(-0.428221 - 0.741701i) q^{91} +(1.66551 - 2.88475i) q^{92} +(13.3342 - 23.0955i) q^{93} +(4.53700 + 7.85831i) q^{94} +(-6.60368 - 11.4379i) q^{96} +10.2579 q^{97} +(-3.08309 + 5.34008i) q^{98} +(14.6793 + 25.4253i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{3} - 8 q^{4} - 4 q^{6} - 6 q^{8} - 13 q^{9} - 2 q^{11} - 6 q^{12} - 4 q^{13} + 20 q^{14} + 2 q^{16} + 3 q^{17} + 6 q^{18} - 14 q^{19} + q^{21} - 7 q^{22} + 15 q^{24} - 22 q^{26} + 14 q^{27}+ \cdots + 56 q^{99}+O(q^{100}) \) 14 * q + 2 * q^3 - 8 * q^4 - 4 * q^6 - 6 * q^8 - 13 * q^9 - 2 * q^11 - 6 * q^12 - 4 * q^13 + 20 * q^14 + 2 * q^16 + 3 * q^17 + 6 * q^18 - 14 * q^19 + q^21 - 7 * q^22 + 15 * q^24 - 22 * q^26 + 14 * q^27 - 9 * q^28 - 12 * q^29 - 4 * q^32 + 11 * q^33 + 33 * q^34 + 40 * q^36 - 18 * q^37 + 4 * q^38 - 25 * q^39 - 7 * q^41 + 29 * q^42 - 38 * q^43 - 19 * q^44 - 14 * q^46 - 8 * q^47 - 36 * q^48 + 5 * q^49 + 58 * q^51 + 8 * q^52 + 6 * q^53 - 9 * q^54 - 25 * q^56 + 44 * q^57 + 12 * q^58 + 2 * q^59 - 4 * q^61 + 25 * q^62 - 10 * q^63 - 62 * q^64 - 2 * q^66 + 8 * q^67 - 26 * q^68 - 11 * q^69 + 33 * q^71 - 43 * q^72 + 18 * q^74 - 12 * q^76 + 5 * q^77 + 22 * q^78 - 9 * q^79 - 35 * q^81 - 152 * q^82 + 11 * q^83 - 80 * q^84 + 17 * q^86 + 29 * q^87 - 40 * q^88 - 12 * q^89 - 24 * q^91 + 7 * q^92 + 47 * q^93 + 10 * q^94 - 15 * q^96 - 30 * q^97 - 54 * q^98 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more