LMFDB - Embedded newform 525.2.j.b.407.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(218,525)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("525.218");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			407.11
Character	$\chi$	$=$	525.407
Dual form			525.2.j.b.218.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.54414 - 1.54414i) q^{2} +(0.00622252 - 1.73204i) q^{3} -2.76875i q^{4} +(-2.66491 - 2.68412i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-1.18705 - 1.18705i) q^{8} +(-2.99992 - 0.0215553i) q^{9} +O(q^{10})$	\(q+(1.54414 - 1.54414i) q^{2} +(0.00622252 - 1.73204i) q^{3} -2.76875i q^{4} +(-2.66491 - 2.68412i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-1.18705 - 1.18705i) q^{8} +(-2.99992 - 0.0215553i) q^{9} -3.38507i q^{11} +(-4.79558 - 0.0172286i) q^{12} +(0.206632 - 0.206632i) q^{13} -2.18375 q^{14} +1.87154 q^{16} +(0.167409 - 0.167409i) q^{17} +(-4.66559 + 4.59902i) q^{18} +5.31419i q^{19} +(-1.22914 + 1.22034i) q^{21} +(-5.22702 - 5.22702i) q^{22} +(-5.07773 - 5.07773i) q^{23} +(-2.06341 + 2.04864i) q^{24} -0.638138i q^{26} +(-0.0560017 + 5.19585i) q^{27} +(-1.95780 + 1.95780i) q^{28} +2.84268 q^{29} +9.11776 q^{31} +(5.26402 - 5.26402i) q^{32} +(-5.86307 - 0.0210636i) q^{33} -0.517005i q^{34} +(-0.0596812 + 8.30602i) q^{36} +(5.27013 + 5.27013i) q^{37} +(8.20586 + 8.20586i) q^{38} +(-0.356609 - 0.359180i) q^{39} -0.0314968i q^{41} +(-0.0135884 + 3.78233i) q^{42} +(3.76875 - 3.76875i) q^{43} -9.37239 q^{44} -15.6815 q^{46} +(-3.56639 + 3.56639i) q^{47} +(0.0116457 - 3.24158i) q^{48} +1.00000i q^{49} +(-0.288917 - 0.291000i) q^{51} +(-0.572111 - 0.572111i) q^{52} +(3.55291 + 3.55291i) q^{53} +(7.93665 + 8.10960i) q^{54} +1.67875i q^{56} +(9.20439 + 0.0330677i) q^{57} +(4.38949 - 4.38949i) q^{58} +10.3168 q^{59} -6.80634 q^{61} +(14.0791 - 14.0791i) q^{62} +(2.10602 + 2.13651i) q^{63} -12.5137i q^{64} +(-9.08593 + 9.02088i) q^{66} +(-6.34806 - 6.34806i) q^{67} +(-0.463512 - 0.463512i) q^{68} +(-8.82642 + 8.76323i) q^{69} -3.95454i q^{71} +(3.53548 + 3.58665i) q^{72} +(-8.61099 + 8.61099i) q^{73} +16.2757 q^{74} +14.7136 q^{76} +(-2.39360 + 2.39360i) q^{77} +(-1.10528 - 0.00397083i) q^{78} -11.4449i q^{79} +(8.99907 + 0.129328i) q^{81} +(-0.0486356 - 0.0486356i) q^{82} +(3.88059 + 3.88059i) q^{83} +(3.37880 + 3.40317i) q^{84} -11.6390i q^{86} +(0.0176886 - 4.92363i) q^{87} +(-4.01825 + 4.01825i) q^{88} -2.00190 q^{89} -0.292222 q^{91} +(-14.0589 + 14.0589i) q^{92} +(0.0567354 - 15.7923i) q^{93} +11.0140i q^{94} +(-9.08474 - 9.15025i) q^{96} +(-2.26760 - 2.26760i) q^{97} +(1.54414 + 1.54414i) q^{98} +(-0.0729661 + 10.1549i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3}+O(q^{10}) $ 24 * q + 4 * q^3	$ 24 q + 4 q^{3} - 16 q^{12} + 8 q^{13} - 16 q^{16} + 20 q^{18} + 4 q^{21} - 8 q^{22} + 16 q^{27} - 28 q^{33} + 16 q^{36} + 16 q^{37} + 20 q^{42} + 40 q^{43} - 64 q^{46} - 16 q^{48} - 20 q^{51} - 4 q^{57} - 40 q^{58} + 32 q^{61} + 8 q^{63} - 16 q^{66} - 24 q^{67} + 8 q^{72} - 32 q^{73} + 32 q^{76} - 60 q^{78} + 52 q^{81} + 80 q^{82} - 4 q^{87} - 96 q^{88} - 24 q^{91} + 76 q^{93} - 96 q^{96} - 24 q^{97}+O(q^{100}) $ 24 * q + 4 * q^3 - 16 * q^12 + 8 * q^13 - 16 * q^16 + 20 * q^18 + 4 * q^21 - 8 * q^22 + 16 * q^27 - 28 * q^33 + 16 * q^36 + 16 * q^37 + 20 * q^42 + 40 * q^43 - 64 * q^46 - 16 * q^48 - 20 * q^51 - 4 * q^57 - 40 * q^58 + 32 * q^61 + 8 * q^63 - 16 * q^66 - 24 * q^67 + 8 * q^72 - 32 * q^73 + 32 * q^76 - 60 * q^78 + 52 * q^81 + 80 * q^82 - 4 * q^87 - 96 * q^88 - 24 * q^91 + 76 * q^93 - 96 * q^96 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	1.54414	−	1.54414i	1.09187	−	1.09187i	0.0965442	−	0.995329i	$-0.469221\pi$
$2$	1.54414	−	1.54414i	1.09187	−	1.09187i	0.995329	−	0.0965442i	$-0.0307789\pi$
$3$	0.00622252	−	1.73204i	0.00359257	−	0.999994i
$3$	0.00622252	−	1.73204i	0.00359257	−	0.999994i
$4$		−	2.76875i		−	1.38437i
$5$		0			0
$5$		0			0
$6$	−2.66491	−	2.68412i	−1.08794	−	1.09579i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	−1.18705	−	1.18705i	−0.419686	−	0.419686i
$9$	−2.99992	−	0.0215553i	−0.999974	−	0.00718510i
$10$		0			0
$11$		−	3.38507i		−	1.02064i	−0.859986	−	0.510318i	$-0.829528\pi$
$11$		−	3.38507i		−	1.02064i	0.859986	−	0.510318i	$-0.170472\pi$
$12$	−4.79558	−	0.0172286i	−1.38436	−	0.00497346i
$13$	0.206632	−	0.206632i	0.0573094	−	0.0573094i	−0.677871	−	0.735181i	$-0.737097\pi$
$13$	0.206632	−	0.206632i	0.0573094	−	0.0573094i	0.735181	+	0.677871i	$0.237097\pi$
$14$	−2.18375			−0.583631
$15$		0			0
$16$	1.87154			0.467884
$17$	0.167409	−	0.167409i	0.0406026	−	0.0406026i	−0.686514	−	0.727117i	$-0.740860\pi$
$17$	0.167409	−	0.167409i	0.0406026	−	0.0406026i	0.727117	+	0.686514i	$0.240860\pi$
$18$	−4.66559	+	4.59902i	−1.09969	+	1.08400i
$19$			5.31419i			1.21916i	0.792725	+	0.609579i	$0.208662\pi$
$19$			5.31419i			1.21916i	−0.792725	+	0.609579i	$0.791338\pi$
$20$		0			0
$21$	−1.22914	+	1.22034i	−0.268220	+	0.266299i
$22$	−5.22702	−	5.22702i	−1.11440	−	1.11440i
$23$	−5.07773	−	5.07773i	−1.05878	−	1.05878i	−0.998161	−	0.0606179i	$-0.980693\pi$
$23$	−5.07773	−	5.07773i	−1.05878	−	1.05878i	−0.0606179	−	0.998161i	$-0.519307\pi$
$24$	−2.06341	+	2.04864i	−0.421191	+	0.418176i
$25$		0			0
$26$		−	0.638138i		−	0.125149i
$27$	−0.0560017	+	5.19585i	−0.0107775	+	0.999942i
$28$	−1.95780	+	1.95780i	−0.369989	+	0.369989i
$29$	2.84268			0.527872			0.263936	−	0.964540i	$-0.414979\pi$
$29$	2.84268			0.527872			0.263936	+	0.964540i	$0.414979\pi$
$30$		0			0
$31$	9.11776			1.63760			0.818799	−	0.574081i	$-0.194640\pi$
$31$	9.11776			1.63760			0.818799	+	0.574081i	$0.194640\pi$
$32$	5.26402	−	5.26402i	0.930557	−	0.930557i
$33$	−5.86307	−	0.0210636i	−1.02063	−	0.00366671i
$34$		−	0.517005i		−	0.0886657i
$35$		0			0
$36$	−0.0596812	+	8.30602i	−0.00994686	+	1.38434i
$37$	5.27013	+	5.27013i	0.866404	+	0.866404i	0.992072	−	0.125668i	$-0.0401075\pi$
$37$	5.27013	+	5.27013i	0.866404	+	0.866404i	−0.125668	+	0.992072i	$0.540107\pi$
$38$	8.20586	+	8.20586i	1.33117	+	1.33117i
$39$	−0.356609	−	0.359180i	−0.0571031	−	0.0575149i
$40$		0			0
$41$		−	0.0314968i		−	0.00491898i	−0.999997	−	0.00245949i	$-0.999217\pi$
$41$		−	0.0314968i		−	0.00491898i	0.999997	−	0.00245949i	$-0.000782881\pi$
$42$	−0.0135884	+	3.78233i	−0.00209674	+	0.583627i
$43$	3.76875	−	3.76875i	0.574728	−	0.574728i	−0.358718	−	0.933446i	$-0.616786\pi$
$43$	3.76875	−	3.76875i	0.574728	−	0.574728i	0.933446	+	0.358718i	$0.116786\pi$
$44$	−9.37239			−1.41294
$45$		0			0
$46$	−15.6815			−2.31210
$47$	−3.56639	+	3.56639i	−0.520211	+	0.520211i	−0.917635	−	0.397424i	$-0.869904\pi$
$47$	−3.56639	+	3.56639i	−0.520211	+	0.520211i	0.397424	+	0.917635i	$0.369904\pi$
$48$	0.0116457	−	3.24158i	0.00168091	−	0.467881i
$49$			1.00000i			0.142857i
$50$		0			0
$51$	−0.288917	−	0.291000i	−0.0404564	−	0.0407482i
$52$	−0.572111	−	0.572111i	−0.0793376	−	0.0793376i
$53$	3.55291	+	3.55291i	0.488030	+	0.488030i	0.907684	−	0.419654i	$-0.137849\pi$
$53$	3.55291	+	3.55291i	0.488030	+	0.488030i	−0.419654	+	0.907684i	$0.637849\pi$
$54$	7.93665	+	8.10960i	1.08004	+	1.10358i
$55$		0			0
$56$			1.67875i			0.224332i
$57$	9.20439	+	0.0330677i	1.21915	+	0.00437992i
$58$	4.38949	−	4.38949i	0.576369	−	0.576369i
$59$	10.3168			1.34313			0.671565	−	0.740946i	$-0.265622\pi$
$59$	10.3168			1.34313			0.671565	+	0.740946i	$0.265622\pi$
$60$		0			0
$61$	−6.80634			−0.871462			−0.435731	−	0.900077i	$-0.643510\pi$
$61$	−6.80634			−0.871462			−0.435731	+	0.900077i	$0.643510\pi$
$62$	14.0791	−	14.0791i	1.78805	−	1.78805i
$63$	2.10602	+	2.13651i	0.265334	+	0.269175i
$64$		−	12.5137i		−	1.56422i
$65$		0			0
$66$	−9.08593	+	9.02088i	−1.11840	+	1.11039i
$67$	−6.34806	−	6.34806i	−0.775539	−	0.775539i	0.203530	−	0.979069i	$-0.434759\pi$
$67$	−6.34806	−	6.34806i	−0.775539	−	0.775539i	−0.979069	+	0.203530i	$0.934759\pi$
$68$	−0.463512	−	0.463512i	−0.0562091	−	0.0562091i
$69$	−8.82642	+	8.76323i	−1.06258	+	1.05497i
$70$		0			0
$71$		−	3.95454i		−	0.469318i	−0.972078	−	0.234659i	$-0.924603\pi$
$71$		−	3.95454i		−	0.469318i	0.972078	−	0.234659i	$-0.0753973\pi$
$72$	3.53548	+	3.58665i	0.416660	+	0.422691i
$73$	−8.61099	+	8.61099i	−1.00784	+	1.00784i	−0.00787086	+	0.999969i	$0.502505\pi$
$73$	−8.61099	+	8.61099i	−1.00784	+	1.00784i	−0.999969	+	0.00787086i	$0.997495\pi$
$74$	16.2757			1.89201
$75$		0			0
$76$	14.7136			1.68777
$77$	−2.39360	+	2.39360i	−0.272776	+	0.272776i
$78$	−1.10528	−	0.00397083i	−0.125148	−	0.000449608i
$79$		−	11.4449i		−	1.28766i	−0.765170	−	0.643828i	$-0.777345\pi$
$79$		−	11.4449i		−	1.28766i	0.765170	−	0.643828i	$-0.222655\pi$
$80$		0			0
$81$	8.99907	+	0.129328i	0.999897	+	0.0143698i
$82$	−0.0486356	−	0.0486356i	−0.00537090	−	0.00537090i
$83$	3.88059	+	3.88059i	0.425951	+	0.425951i	0.887246	−	0.461296i	$-0.152615\pi$
$83$	3.88059	+	3.88059i	0.425951	+	0.425951i	−0.461296	+	0.887246i	$0.652615\pi$
$84$	3.37880	+	3.40317i	0.368658	+	0.371316i
$85$		0			0
$86$		−	11.6390i		−	1.25506i
$87$	0.0176886	−	4.92363i	0.00189642	−	0.527868i
$88$	−4.01825	+	4.01825i	−0.428347	+	0.428347i
$89$	−2.00190			−0.212201			−0.106100	−	0.994355i	$-0.533836\pi$
$89$	−2.00190			−0.212201			−0.106100	+	0.994355i	$0.533836\pi$
$90$		0			0
$91$	−0.292222			−0.0306332
$92$	−14.0589	+	14.0589i	−1.46574	+	1.46574i
$93$	0.0567354	−	15.7923i	0.00588319	−	1.63759i
$94$			11.0140i			1.13601i
$95$		0			0
$96$	−9.08474	−	9.15025i	−0.927208	−	0.933894i
$97$	−2.26760	−	2.26760i	−0.230240	−	0.230240i	0.582553	−	0.812793i	$-0.302054\pi$
$97$	−2.26760	−	2.26760i	−0.230240	−	0.230240i	−0.812793	+	0.582553i	$0.802054\pi$
$98$	1.54414	+	1.54414i	0.155982	+	0.155982i
$99$	−0.0729661	+	10.1549i	−0.00733337	+	1.02061i
$100$		0			0
$101$			8.63630i			0.859344i	0.902985	+	0.429672i	$0.141371\pi$
$101$			8.63630i			0.859344i	−0.902985	+	0.429672i	$0.858629\pi$
$102$	−0.895474	−	0.00321708i	−0.0886651	−	0.000318538i
$103$	−0.964332	+	0.964332i	−0.0950185	+	0.0950185i	−0.753018	−	0.658000i	$-0.771403\pi$
$103$	−0.964332	+	0.964332i	−0.0950185	+	0.0950185i	0.658000	+	0.753018i	$0.271403\pi$
$104$	−0.490566			−0.0481039
$105$		0			0
$106$	10.9724			1.06573
$107$	−2.95847	+	2.95847i	−0.286007	+	0.286007i	−0.835499	−	0.549492i	$-0.814821\pi$
$107$	−2.95847	+	2.95847i	−0.286007	+	0.286007i	0.549492	+	0.835499i	$0.314821\pi$
$108$	14.3860	+	0.155055i	1.38429	+	0.0149201i
$109$		−	2.82182i		−	0.270281i	−0.990826	−	0.135141i	$-0.956851\pi$
$109$		−	2.82182i		−	0.270281i	0.990826	−	0.135141i	$-0.0431486\pi$
$110$		0			0
$111$	9.16087	−	9.09528i	0.869511	−	0.863286i
$112$	−1.32338	−	1.32338i	−0.125047	−	0.125047i
$113$	2.01798	+	2.01798i	0.189835	+	0.189835i	0.795625	−	0.605790i	$-0.207143\pi$
$113$	2.01798	+	2.01798i	0.189835	+	0.189835i	−0.605790	+	0.795625i	$0.707143\pi$
$114$	14.2639	−	14.1618i	1.33594	−	1.32638i
$115$		0			0
$116$		−	7.87065i		−	0.730771i
$117$	−0.624334	+	0.615426i	−0.0577197	+	0.0568961i
$118$	15.9306	−	15.9306i	1.46653	−	1.46653i
$119$	−0.236752			−0.0217030
$120$		0			0
$121$	−0.458667			−0.0416970
$122$	−10.5099	+	10.5099i	−0.951526	+	0.951526i
$123$	−0.0545538		0.000195990i	−0.00491895		1.76718e-5i
$124$		−	25.2448i		−	2.26705i
$125$		0			0
$126$	6.55107	+	0.0470713i	0.583616	+	0.00419345i
$127$	11.6271	+	11.6271i	1.03174	+	1.03174i	0.999480	+	0.0322583i	$0.0102699\pi$
$127$	11.6271	+	11.6271i	1.03174	+	1.03174i	0.0322583	+	0.999480i	$0.489730\pi$
$128$	−8.79491	−	8.79491i	−0.777367	−	0.777367i
$129$	−6.50417	−	6.55107i	−0.572660	−	0.576789i
$130$		0			0
$131$			12.7013i			1.10972i	0.831943	+	0.554861i	$0.187228\pi$
$131$			12.7013i			1.10972i	−0.831943	+	0.554861i	$0.812772\pi$
$132$	−0.0583199	+	16.2333i	−0.00507609	+	1.41293i
$133$	3.75770	−	3.75770i	0.325834	−	0.325834i
$134$	−19.6046			−1.69358
$135$		0			0
$136$	−0.397446			−0.0340807
$137$	−5.19451	+	5.19451i	−0.443797	+	0.443797i	−0.893286	−	0.449489i	$-0.851606\pi$
$137$	−5.19451	+	5.19451i	−0.443797	+	0.443797i	0.449489	+	0.893286i	$0.351606\pi$
$138$	−0.0975782	+	27.1609i	−0.00830641	+	2.31209i
$139$		−	12.3138i		−	1.04444i	−0.852810	−	0.522221i	$-0.825103\pi$
$139$		−	12.3138i		−	1.04444i	0.852810	−	0.522221i	$-0.174897\pi$
$140$		0			0
$141$	6.15493	+	6.19932i	0.518339	+	0.522077i
$142$	−6.10637	−	6.10637i	−0.512435	−	0.512435i
$143$	−0.699463	−	0.699463i	−0.0584920	−	0.0584920i
$144$	−5.61447	−	0.0403416i	−0.467872	−	0.00336180i
$145$		0			0
$146$			26.5932i			2.20087i
$147$	1.73204	+	0.00622252i	0.142856	+	0.000513225i
$148$	14.5917	−	14.5917i	1.19943	−	1.19943i
$149$	−18.9350			−1.55121			−0.775607	−	0.631216i	$-0.782556\pi$
$149$	−18.9350			−1.55121			−0.775607	+	0.631216i	$0.782556\pi$
$150$		0			0
$151$	−1.90527			−0.155049			−0.0775243	−	0.996990i	$-0.524702\pi$
$151$	−1.90527			−0.155049			−0.0775243	+	0.996990i	$0.524702\pi$
$152$	6.30822	−	6.30822i	0.511665	−	0.511665i
$153$	−0.505822	+	0.498604i	−0.0408933	+	0.0403098i
$154$			7.39212i			0.595674i
$155$		0			0
$156$	−0.994479	+	0.987359i	−0.0796221	+	0.0790520i
$157$	4.31728	+	4.31728i	0.344557	+	0.344557i	0.858077	−	0.513521i	$-0.171659\pi$
$157$	4.31728	+	4.31728i	0.344557	+	0.344557i	−0.513521	+	0.858077i	$0.671659\pi$
$158$	−17.6726	−	17.6726i	−1.40596	−	1.40596i
$159$	6.17589	−	6.13167i	0.489780	−	0.486273i
$160$		0			0
$161$			7.18099i			0.565941i
$162$	14.0955	−	13.6961i	1.10745	−	1.07607i
$163$	−3.57655	+	3.57655i	−0.280137	+	0.280137i	−0.833164	−	0.553027i	$-0.813473\pi$
$163$	−3.57655	+	3.57655i	−0.280137	+	0.280137i	0.553027	+	0.833164i	$0.313473\pi$
$164$	−0.0872068			−0.00680970
$165$		0			0
$166$	11.9844			0.930168
$167$	−6.39241	+	6.39241i	−0.494659	+	0.494659i	−0.909771	−	0.415111i	$-0.863743\pi$
$167$	−6.39241	+	6.39241i	−0.494659	+	0.494659i	0.415111	+	0.909771i	$0.363743\pi$
$168$	2.90765	+	0.0104460i	0.224330	+	0.000805929i
$169$			12.9146i			0.993431i
$170$		0			0
$171$	0.114549	−	15.9422i	0.00875978	−	1.21913i
$172$	−10.4347	−	10.4347i	−0.795638	−	0.795638i
$173$	3.88791	+	3.88791i	0.295592	+	0.295592i	0.839285	−	0.543692i	$-0.182974\pi$
$173$	3.88791	+	3.88791i	0.295592	+	0.295592i	−0.543692	+	0.839285i	$0.682974\pi$
$174$	−7.57546	−	7.63009i	−0.574294	−	0.578436i
$175$		0			0
$176$		−	6.33528i		−	0.477540i
$177$	0.0641964	−	17.8691i	0.00482529	−	1.34312i
$178$	−3.09121	+	3.09121i	−0.231696	+	0.231696i
$179$	14.6322			1.09366			0.546832	−	0.837242i	$-0.315834\pi$
$179$	14.6322			1.09366			0.546832	+	0.837242i	$0.315834\pi$
$180$		0			0
$181$	−9.83718			−0.731192			−0.365596	−	0.930774i	$-0.619135\pi$
$181$	−9.83718			−0.731192			−0.365596	+	0.930774i	$0.619135\pi$
$182$	−0.451232	+	0.451232i	−0.0334475	+	0.0334475i
$183$	−0.0423526	+	11.7888i	−0.00313079	+	0.871456i
$184$			12.0551i			0.888710i
$185$		0			0
$186$	−24.2980	−	24.4732i	−1.78161	−	1.79446i
$187$	−0.566689	−	0.566689i	−0.0414404	−	0.0414404i
$188$	9.87442	+	9.87442i	0.720166	+	0.720166i
$189$	3.71362	−	3.63442i	0.270126	−	0.264365i
$190$		0			0
$191$			6.37886i			0.461558i	0.973006	+	0.230779i	$0.0741275\pi$
$191$			6.37886i			0.461558i	−0.973006	+	0.230779i	$0.925873\pi$
$192$	−21.6743	−	0.0778669i	−1.56421	−	0.00561956i
$193$	−7.56336	+	7.56336i	−0.544422	+	0.544422i	−0.924822	−	0.380400i	$-0.875786\pi$
$193$	−7.56336	+	7.56336i	−0.544422	+	0.544422i	0.380400	+	0.924822i	$0.375786\pi$
$194$	−7.00299			−0.502785
$195$		0			0
$196$	2.76875			0.197768
$197$	−1.01490	+	1.01490i	−0.0723090	+	0.0723090i	−0.742336	−	0.670027i	$-0.766282\pi$
$197$	−1.01490	+	1.01490i	−0.0723090	+	0.0723090i	0.670027	+	0.742336i	$0.266282\pi$
$198$	15.5680	+	15.7933i	1.10637	+	1.12238i
$199$			9.40041i			0.666378i	0.942860	+	0.333189i	$0.108125\pi$
$199$			9.40041i			0.666378i	−0.942860	+	0.333189i	$0.891875\pi$
$200$		0			0
$201$	−11.0346	+	10.9556i	−0.778320	+	0.772748i
$202$	13.3357	+	13.3357i	0.938295	+	0.938295i
$203$	−2.01007	−	2.01007i	−0.141080	−	0.141080i
$204$	−0.805705	+	0.799937i	−0.0564107	+	0.0560068i
$205$		0			0
$206$			2.97813i			0.207496i
$207$	15.1233	+	15.3422i	1.05114	+	1.06636i
$208$	0.386719	−	0.386719i	0.0268142	−	0.0268142i
$209$	17.9889			1.24432
$210$		0			0
$211$	−8.29157			−0.570815			−0.285407	−	0.958406i	$-0.592129\pi$
$211$	−8.29157			−0.570815			−0.285407	+	0.958406i	$0.592129\pi$
$212$	9.83710	−	9.83710i	0.675615	−	0.675615i
$213$	−6.84942	−	0.0246072i	−0.469315	−	0.00168606i
$214$			9.13661i			0.624566i
$215$		0			0
$216$	6.23422	−	6.10127i	0.424185	−	0.415139i
$217$	−6.44723	−	6.44723i	−0.437666	−	0.437666i
$218$	−4.35729	−	4.35729i	−0.295113	−	0.295113i
$219$	14.8610	+	14.9682i	1.00421	+	1.01145i
$220$		0			0
$221$		−	0.0691839i		−	0.00465382i
$222$	0.101276	−	28.1901i	0.00679717	−	1.89199i
$223$	−3.86020	+	3.86020i	−0.258498	+	0.258498i	−0.824443	−	0.565945i	$-0.808511\pi$
$223$	−3.86020	+	3.86020i	−0.258498	+	0.258498i	0.565945	+	0.824443i	$0.308511\pi$
$224$	−7.44445			−0.497404
$225$		0			0
$226$	6.23208			0.414552
$227$	1.50739	−	1.50739i	0.100049	−	0.100049i	−0.655310	−	0.755360i	$-0.727462\pi$
$227$	1.50739	−	1.50739i	0.100049	−	0.100049i	0.755360	+	0.655310i	$0.227462\pi$
$228$	0.0915560	−	25.4846i	0.00606344	−	1.68776i
$229$		−	6.26009i		−	0.413678i	−0.978375	−	0.206839i	$-0.933682\pi$
$229$		−	6.26009i		−	0.413678i	0.978375	−	0.206839i	$-0.0663177\pi$
$230$		0			0
$231$	4.13092	+	4.16071i	0.271795	+	0.273755i
$232$	−3.37440	−	3.37440i	−0.221541	−	0.221541i
$233$	−2.67422	−	2.67422i	−0.175194	−	0.175194i	0.614063	−	0.789257i	$-0.289534\pi$
$233$	−2.67422	−	2.67422i	−0.175194	−	0.175194i	−0.789257	+	0.614063i	$0.789534\pi$
$234$	−0.0137553	+	1.91436i	−0.000899209	+	0.125146i
$235$		0			0
$236$		−	28.5645i		−	1.85939i
$237$	−19.8231	−	0.0712164i	−1.28765	−	0.00462600i
$238$	−0.365578	+	0.365578i	−0.0236969	+	0.0236969i
$239$	−2.08521			−0.134881			−0.0674406	−	0.997723i	$-0.521483\pi$
$239$	−2.08521			−0.134881			−0.0674406	+	0.997723i	$0.521483\pi$
$240$		0			0
$241$	−5.43686			−0.350219			−0.175110	−	0.984549i	$-0.556028\pi$
$241$	−5.43686			−0.350219			−0.175110	+	0.984549i	$0.556028\pi$
$242$	−0.708247	+	0.708247i	−0.0455279	+	0.0455279i
$243$	0.279999	−	15.5859i	0.0179619	−	0.999839i
$244$			18.8450i			1.20643i
$245$		0			0
$246$	−0.0845414	+	0.0839361i	−0.00539016	+	0.00535157i
$247$	1.09808	+	1.09808i	0.0698692	+	0.0698692i
$248$	−10.8233	−	10.8233i	−0.687278	−	0.687278i
$249$	6.74549	−	6.69720i	0.427478	−	0.424418i
$250$		0			0
$251$			23.3428i			1.47339i	0.676227	+	0.736693i	$0.263614\pi$
$251$			23.3428i			1.47339i	−0.676227	+	0.736693i	$0.736386\pi$
$252$	5.91545	−	5.83104i	0.372638	−	0.367321i
$253$	−17.1884	+	17.1884i	−1.08063	+	1.08063i
$254$	35.9078			2.25305
$255$		0			0
$256$	−2.13372			−0.133358
$257$	10.9273	−	10.9273i	0.681627	−	0.681627i	−0.278740	−	0.960367i	$-0.589917\pi$
$257$	10.9273	−	10.9273i	0.681627	−	0.681627i	0.960367	+	0.278740i	$0.0899167\pi$
$258$	−20.1591	−	0.0724236i	−1.25505	−	0.00450890i
$259$		−	7.45309i		−	0.463112i
$260$		0			0
$261$	−8.52781	−	0.0612747i	−0.527858	−	0.00379281i
$262$	19.6127	+	19.6127i	1.21167	+	1.21167i
$263$	18.1808	+	18.1808i	1.12108	+	1.12108i	0.991580	+	0.129497i	$0.0413364\pi$
$263$	18.1808	+	18.1808i	1.12108	+	1.12108i	0.129497	+	0.991580i	$0.458664\pi$
$264$	6.93477	+	6.98477i	0.426805	+	0.429883i
$265$		0			0
$266$		−	11.6048i		−	0.711539i
$267$	−0.0124569	+	3.46737i	−0.000762347	+	0.212199i
$268$	−17.5762	+	17.5762i	−1.07364	+	1.07364i
$269$	−28.5125			−1.73844			−0.869219	−	0.494428i	$-0.835378\pi$
$269$	−28.5125			−1.73844			−0.869219	+	0.494428i	$0.835378\pi$
$270$		0			0
$271$	3.12214			0.189656			0.0948282	−	0.995494i	$-0.469770\pi$
$271$	3.12214			0.189656			0.0948282	+	0.995494i	$0.469770\pi$
$272$	0.313312	−	0.313312i	0.0189973	−	0.0189973i
$273$	−0.00181836	+	0.506139i	−0.000110052	+	0.0306330i
$274$			16.0421i			0.969139i
$275$		0			0
$276$	24.2631	+	24.4381i	1.46047	+	1.47100i
$277$	−12.2472	−	12.2472i	−0.735861	−	0.735861i	0.235913	−	0.971774i	$-0.424192\pi$
$277$	−12.2472	−	12.2472i	−0.735861	−	0.735861i	−0.971774	+	0.235913i	$0.924192\pi$
$278$	−19.0142	−	19.0142i	−1.14040	−	1.14040i
$279$	−27.3526	−	0.196536i	−1.63756	−	0.0117663i
$280$		0			0
$281$		−	12.7181i		−	0.758698i	−0.925254	−	0.379349i	$-0.876148\pi$
$281$		−	12.7181i		−	0.758698i	0.925254	−	0.379349i	$-0.123852\pi$
$282$	19.0767	+	0.0685349i	1.13600	+	0.00408120i
$283$	19.8271	−	19.8271i	1.17860	−	1.17860i	0.198495	−	0.980102i	$-0.436395\pi$
$283$	19.8271	−	19.8271i	1.17860	−	1.17860i	0.980102	−	0.198495i	$-0.0636053\pi$
$284$	−10.9491			−0.649711
$285$		0			0
$286$	−2.16014			−0.127732
$287$	−0.0222716	+	0.0222716i	−0.00131465	+	0.00131465i
$288$	−15.9051	+	15.6782i	−0.937219	+	0.923847i
$289$			16.9439i			0.996703i
$290$		0			0
$291$	−3.94168	+	3.91346i	−0.231066	+	0.229411i
$292$	23.8416	+	23.8416i	1.39523	+	1.39523i
$293$	−6.72836	−	6.72836i	−0.393075	−	0.393075i	0.482707	−	0.875782i	$-0.339654\pi$
$293$	−6.72836	−	6.72836i	−0.393075	−	0.393075i	−0.875782	+	0.482707i	$0.839654\pi$
$294$	2.68412	−	2.66491i	0.156541	−	0.155420i
$295$		0			0
$296$		−	12.5118i		−	0.727236i
$297$	17.5883	+	0.189570i	1.02058	+	0.0109999i
$298$	−29.2383	+	29.2383i	−1.69373	+	1.69373i
$299$	−2.09844			−0.121356
$300$		0			0
$301$	−5.32981			−0.307205
$302$	−2.94201	+	2.94201i	−0.169293	+	0.169293i
$303$	14.9584	+	0.0537396i	0.859339	+	0.00308726i
$304$			9.94571i			0.570426i
$305$		0			0
$306$	−0.0111442	+	1.55098i	−0.000637072	+	0.0886634i
$307$	−10.1105	−	10.1105i	−0.577034	−	0.577034i	0.357051	−	0.934085i	$-0.383782\pi$
$307$	−10.1105	−	10.1105i	−0.577034	−	0.577034i	−0.934085	+	0.357051i	$0.883782\pi$
$308$	6.62728	+	6.62728i	0.377624	+	0.377624i
$309$	1.66426	+	1.67626i	0.0946765	+	0.0953592i
$310$		0			0
$311$			0.394155i			0.0223505i	0.999938	+	0.0111752i	$0.00355726\pi$
$311$			0.394155i			0.0223505i	−0.999938	+	0.0111752i	$0.996443\pi$
$312$	−0.00305256	+	0.849680i	−0.000172817	+	0.0481036i
$313$	10.3810	−	10.3810i	0.586767	−	0.586767i	−0.349987	−	0.936754i	$-0.613814\pi$
$313$	10.3810	−	10.3810i	0.586767	−	0.586767i	0.936754	+	0.349987i	$0.113814\pi$
$314$	13.3330			0.752424
$315$		0			0
$316$	−31.6881			−1.78260
$317$	−19.8075	+	19.8075i	−1.11250	+	1.11250i	−0.119688	+	0.992812i	$0.538190\pi$
$317$	−19.8075	+	19.8075i	−1.11250	+	1.11250i	−0.992812	+	0.119688i	$0.961810\pi$
$318$	0.0682759	−	19.0046i	0.00382872	−	1.06573i
$319$		−	9.62264i		−	0.538764i
$320$		0			0
$321$	5.10579	+	5.14260i	0.284977	+	0.287032i
$322$	11.0885	+	11.0885i	0.617936	+	0.617936i
$323$	0.889642	+	0.889642i	0.0495010	+	0.0495010i
$324$	0.358078	−	24.9161i	0.0198932	−	1.38423i
$325$		0			0
$326$			11.0454i			0.611748i
$327$	−4.88750	−	0.0175588i	−0.270279	−	0.000971005i
$328$	−0.0373884	+	0.0373884i	−0.00206443	+	0.00206443i
$329$	5.04363			0.278065
$330$		0			0
$331$	−24.7348			−1.35955			−0.679774	−	0.733422i	$-0.737922\pi$
$331$	−24.7348			−1.35955			−0.679774	+	0.733422i	$0.737922\pi$
$332$	10.7444	−	10.7444i	0.589674	−	0.589674i
$333$	−15.6964	−	15.9236i	−0.860157	−	0.872607i
$334$			19.7416i			1.08021i
$335$		0			0
$336$	−2.30038	+	2.28391i	−0.125496	+	0.124597i
$337$	3.40139	+	3.40139i	0.185286	+	0.185286i	0.793655	−	0.608369i	$-0.208176\pi$
$337$	3.40139	+	3.40139i	0.185286	+	0.185286i	−0.608369	+	0.793655i	$0.708176\pi$
$338$	19.9420	+	19.9420i	1.08470	+	1.08470i
$339$	3.50777	−	3.48266i	0.190516	−	0.189152i
$340$		0			0
$341$		−	30.8642i		−	1.67139i
$342$	−24.4401	−	24.7938i	−1.32157	−	1.34070i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−8.94740			−0.482411
$345$		0			0
$346$	12.0070			0.645498
$347$	24.0324	−	24.0324i	1.29013	−	1.29013i	0.355421	−	0.934706i	$-0.384337\pi$
$347$	24.0324	−	24.0324i	1.29013	−	1.29013i	0.934706	−	0.355421i	$-0.115663\pi$
$348$	−13.6323	−	0.0489753i	−0.730766	−	0.00262535i
$349$			9.37078i			0.501607i	0.968038	+	0.250803i	$0.0806947\pi$
$349$			9.37078i			0.501607i	−0.968038	+	0.250803i	$0.919305\pi$
$350$		0			0
$351$	1.06206	+	1.08520i	0.0566884	+	0.0579237i
$352$	−17.8191	−	17.8191i	−0.949759	−	0.949759i
$353$	14.5888	+	14.5888i	0.776481	+	0.776481i	0.979231	−	0.202750i	$-0.0649878\pi$
$353$	14.5888	+	14.5888i	0.776481	+	0.776481i	−0.202750	+	0.979231i	$0.564988\pi$
$354$	−27.4932	−	27.6915i	−1.46125	−	1.47179i
$355$		0			0
$356$			5.54275i			0.293765i
$357$	−0.00147319	+	0.410063i	−7.79696e−5	+	0.0217028i
$358$	22.5942	−	22.5942i	1.19414	−	1.19414i
$359$	−27.2654			−1.43901			−0.719506	−	0.694486i	$-0.755632\pi$
$359$	−27.2654			−1.43901			−0.719506	+	0.694486i	$0.755632\pi$
$360$		0			0
$361$	−9.24062			−0.486349
$362$	−15.1900	+	15.1900i	−0.798369	+	0.798369i
$363$	−0.00285407	+	0.794430i	−0.000149800	+	0.0416968i
$364$			0.809088i			0.0424077i
$365$		0			0
$366$	18.1382	+	18.2690i	0.948101	+	0.954938i
$367$	−15.9239	−	15.9239i	−0.831218	−	0.831218i	0.156465	−	0.987683i	$-0.449990\pi$
$367$	−15.9239	−	15.9239i	−0.831218	−	0.831218i	−0.987683	+	0.156465i	$0.949990\pi$
$368$	−9.50315	−	9.50315i	−0.495386	−	0.495386i
$369$	−0.000678924		0.0944881i	−3.53434e−5		0.00491885i
$370$		0			0
$371$		−	5.02457i		−	0.260863i
$372$	−43.7249	−	0.157086i	−2.26703	−	0.00814453i
$373$	−23.3283	+	23.3283i	−1.20790	+	1.20790i	−0.236189	+	0.971707i	$0.575898\pi$
$373$	−23.3283	+	23.3283i	−1.20790	+	1.20790i	−0.971707	+	0.236189i	$0.924102\pi$
$374$	−1.75010			−0.0904954
$375$		0			0
$376$	8.46698			0.436651
$377$	0.587387	−	0.587387i	0.0302520	−	0.0302520i
$378$	0.122294	−	11.3464i	0.00629010	−	0.583597i
$379$		−	37.4477i		−	1.92356i	−0.273828	−	0.961779i	$-0.588290\pi$
$379$		−	37.4477i		−	1.92356i	0.273828	−	0.961779i	$-0.411710\pi$
$380$		0			0
$381$	20.2109	−	20.0662i	1.03544	−	1.02802i
$382$	9.84986	+	9.84986i	0.503963	+	0.503963i
$383$	−4.95443	−	4.95443i	−0.253159	−	0.253159i	0.569105	−	0.822265i	$-0.307290\pi$
$383$	−4.95443	−	4.95443i	−0.253159	−	0.253159i	−0.822265	+	0.569105i	$0.807290\pi$
$384$	−15.2879	+	15.1784i	−0.780155	+	0.774570i
$385$		0			0
$386$			23.3578i			1.18888i
$387$	−11.3872	+	11.2247i	−0.578843	+	0.570584i
$388$	−6.27841	+	6.27841i	−0.318738	+	0.318738i
$389$	−9.20279			−0.466600			−0.233300	−	0.972405i	$-0.574952\pi$
$389$	−9.20279			−0.466600			−0.233300	+	0.972405i	$0.574952\pi$
$390$		0			0
$391$	−1.70011			−0.0859783
$392$	1.18705	−	1.18705i	0.0599552	−	0.0599552i
$393$	21.9992	+	0.0790344i	1.10971	+	0.00398676i
$394$			3.13431i			0.157904i
$395$		0			0
$396$	28.1164	+	0.202025i	1.41290	+	0.0101521i
$397$	−21.9242	−	21.9242i	−1.10034	−	1.10034i	−0.994369	−	0.105976i	$-0.966203\pi$
$397$	−21.9242	−	21.9242i	−1.10034	−	1.10034i	−0.105976	−	0.994369i	$-0.533797\pi$
$398$	14.5156	+	14.5156i	0.727600	+	0.727600i
$399$	−6.48510	−	6.53187i	−0.324661	−	0.327002i
$400$		0			0
$401$		−	25.7514i		−	1.28596i	−0.765882	−	0.642982i	$-0.777697\pi$
$401$		−	25.7514i		−	1.28596i	0.765882	−	0.642982i	$-0.222303\pi$
$402$	−0.121990	+	33.9560i	−0.00608431	+	1.69357i
$403$	1.88402	−	1.88402i	0.0938497	−	0.0938497i
$404$	23.9117			1.18965
$405$		0			0
$406$	−6.20768			−0.308082
$407$	17.8397	−	17.8397i	0.884283	−	0.884283i
$408$	−0.00247311	+	0.688392i	−0.000122437	+	0.0340805i
$409$		−	10.9496i		−	0.541425i	−0.962660	−	0.270712i	$-0.912741\pi$
$409$		−	10.9496i		−	0.541425i	0.962660	−	0.270712i	$-0.0872592\pi$
$410$		0			0
$411$	8.96477	+	9.02942i	0.442200	+	0.445388i
$412$	2.66999	+	2.66999i	0.131541	+	0.131541i
$413$	−7.29506	−	7.29506i	−0.358967	−	0.358967i
$414$	47.0431	+	0.338019i	2.31204	+	0.0166127i
$415$		0			0
$416$		−	2.17543i		−	0.106659i
$417$	−21.3280	−	0.0766229i	−1.04444	−	0.00375224i
$418$	27.7774	−	27.7774i	1.35864	−	1.35864i
$419$	5.86958			0.286748			0.143374	−	0.989669i	$-0.454205\pi$
$419$	5.86958			0.286748			0.143374	+	0.989669i	$0.454205\pi$
$420$		0			0
$421$	26.8842			1.31026			0.655129	−	0.755517i	$-0.272614\pi$
$421$	26.8842			1.31026			0.655129	+	0.755517i	$0.272614\pi$
$422$	−12.8034	+	12.8034i	−0.623257	+	0.623257i
$423$	10.7758	−	10.6220i	0.523936	−	0.516460i
$424$		−	8.43498i		−	0.409639i
$425$		0			0
$426$	−10.6145	+	10.5385i	−0.514273	+	0.510591i
$427$	4.81281	+	4.81281i	0.232908	+	0.232908i
$428$	8.19126	+	8.19126i	0.395940	+	0.395940i
$429$	−1.21585	+	1.20714i	−0.0587018	+	0.0582815i
$430$		0			0
$431$		−	4.18118i		−	0.201400i	−0.994917	−	0.100700i	$-0.967892\pi$
$431$		−	4.18118i		−	0.201400i	0.994917	−	0.100700i	$-0.0321083\pi$
$432$	−0.104809	+	9.72423i	−0.00504264	+	0.467857i
$433$	2.20877	−	2.20877i	0.106146	−	0.106146i	−0.652039	−	0.758185i	$-0.726086\pi$
$433$	2.20877	−	2.20877i	0.106146	−	0.106146i	0.758185	+	0.652039i	$0.226086\pi$
$434$	−19.9109			−0.955752
$435$		0			0
$436$	−7.81290			−0.374170
$437$	26.9840	−	26.9840i	1.29082	−	1.29082i
$438$	46.0604	+	0.165477i	2.20085	+	0.00790678i
$439$		−	27.6028i		−	1.31741i	−0.752401	−	0.658706i	$-0.771104\pi$
$439$		−	27.6028i		−	1.31741i	0.752401	−	0.658706i	$-0.228896\pi$
$440$		0			0
$441$	0.0215553	−	2.99992i	0.00102644	−	0.142853i
$442$	−0.106830	−	0.106830i	−0.00508138	−	0.00508138i
$443$	12.3040	+	12.3040i	0.584582	+	0.584582i	0.936159	−	0.351577i	$-0.114354\pi$
$443$	12.3040	+	12.3040i	0.584582	+	0.584582i	−0.351577	+	0.936159i	$0.614354\pi$
$444$	−25.1825	−	25.3641i	−1.19511	−	1.20373i
$445$		0			0
$446$			11.9214i			0.564494i
$447$	−0.117823	+	32.7961i	−0.00557285	+	1.55120i
$448$	−8.84854	+	8.84854i	−0.418054	+	0.418054i
$449$	34.1859			1.61333			0.806666	−	0.591008i	$-0.201270\pi$
$449$	34.1859			1.61333			0.806666	+	0.591008i	$0.201270\pi$
$450$		0			0
$451$	−0.106619			−0.00502049
$452$	5.58726	−	5.58726i	0.262803	−	0.262803i
$453$	−0.0118556	+	3.30000i	−0.000557024	+	0.155048i
$454$		−	4.65526i		−	0.218482i
$455$		0			0
$456$	−10.8868	−	10.9653i	−0.509823	−	0.513499i
$457$	9.31021	+	9.31021i	0.435513	+	0.435513i	0.890499	−	0.454986i	$-0.150356\pi$
$457$	9.31021	+	9.31021i	0.435513	+	0.435513i	−0.454986	+	0.890499i	$0.650356\pi$
$458$	−9.66646	−	9.66646i	−0.451684	−	0.451684i
$459$	0.860455	+	0.879206i	0.0401626	+	0.0410378i
$460$		0			0
$461$		−	25.6579i		−	1.19501i	−0.801865	−	0.597505i	$-0.796159\pi$
$461$		−	25.6579i		−	1.19501i	0.801865	−	0.597505i	$-0.203841\pi$
$462$	12.8034	+	0.0459976i	0.595670	+	0.00214000i
$463$	−13.2170	+	13.2170i	−0.614248	+	0.614248i	−0.944050	−	0.329802i	$-0.893018\pi$
$463$	−13.2170	+	13.2170i	−0.614248	+	0.614248i	0.329802	+	0.944050i	$0.393018\pi$
$464$	5.32017			0.246983
$465$		0			0
$466$	−8.25874			−0.382579
$467$	−19.6659	+	19.6659i	−0.910031	+	0.910031i	−0.996274	−	0.0862431i	$-0.972514\pi$
$467$	−19.6659	+	19.6659i	−0.910031	+	0.910031i	0.0862431	+	0.996274i	$0.472514\pi$
$468$	1.70396	+	1.72862i	0.0787655	+	0.0799056i
$469$			8.97752i			0.414543i
$470$		0			0
$471$	7.50457	−	7.45084i	0.345792	−	0.343317i
$472$	−12.2466	−	12.2466i	−0.563693	−	0.563693i
$473$	−12.7575	−	12.7575i	−0.586588	−	0.586588i
$474$	−30.7196	+	30.4997i	−1.41100	+	1.40090i
$475$		0			0
$476$			0.655505i			0.0300450i
$477$	−10.5819	−	10.7350i	−0.484510	−	0.491524i
$478$	−3.21986	+	3.21986i	−0.147273	+	0.147273i
$479$	26.9725			1.23240			0.616202	−	0.787588i	$-0.288670\pi$
$479$	26.9725			1.23240			0.616202	+	0.787588i	$0.288670\pi$
$480$		0			0
$481$	2.17795			0.0993062
$482$	−8.39528	+	8.39528i	−0.382395	+	0.382395i
$483$	12.4378	+	0.0446838i	0.565937	+	0.00203319i
$484$			1.26993i			0.0577242i
$485$		0			0
$486$	−23.6345	−	24.4993i	−1.07208	−	1.11131i
$487$	28.6505	+	28.6505i	1.29828	+	1.29828i	0.929529	+	0.368749i	$0.120214\pi$
$487$	28.6505	+	28.6505i	1.29828	+	1.29828i	0.368749	+	0.929529i	$0.379786\pi$
$488$	8.07948	+	8.07948i	0.365741	+	0.365741i
$489$	6.17247	+	6.21698i	0.279129	+	0.281141i
$490$		0			0
$491$		−	2.74522i		−	0.123890i	−0.998080	−	0.0619450i	$-0.980270\pi$
$491$		−	2.74522i		−	0.123890i	0.998080	−	0.0619450i	$-0.0197303\pi$
$492$	−0.000542646		0.151046i	−2.44644e−5		0.00680966i
$493$	0.475888	−	0.475888i	0.0214329	−	0.0214329i
$494$	3.39119			0.152577
$495$		0			0
$496$	17.0642			0.766206
$497$	−2.79628	+	2.79628i	−0.125430	+	0.125430i
$498$	0.0745730	−	20.7574i	0.00334170	−	0.930162i
$499$			30.3151i			1.35709i	0.734558	+	0.678546i	$0.237389\pi$
$499$			30.3151i			1.35709i	−0.734558	+	0.678546i	$0.762611\pi$
$500$		0			0
$501$	11.0321	+	11.1117i	0.492879	+	0.496433i
$502$	36.0446	+	36.0446i	1.60875	+	1.60875i
$503$	−0.331820	−	0.331820i	−0.0147951	−	0.0147951i	0.699671	−	0.714466i	$-0.253330\pi$
$503$	−0.331820	−	0.331820i	−0.0147951	−	0.0147951i	−0.714466	+	0.699671i	$0.753330\pi$
$504$	0.0361859	−	5.03611i	0.00161185	−	0.224326i
$505$		0			0
$506$			53.0827i			2.35982i
$507$	22.3686	+	0.0803614i	0.993425	+	0.00356898i
$508$	32.1925	−	32.1925i	1.42831	−	1.42831i
$509$	−14.6491			−0.649311			−0.324656	−	0.945832i	$-0.605248\pi$
$509$	−14.6491			−0.649311			−0.324656	+	0.945832i	$0.605248\pi$
$510$		0			0
$511$	12.1778			0.538713
$512$	14.2950	−	14.2950i	0.631758	−	0.631758i
$513$	−27.6117	−	0.297604i	−1.21909	−	0.0131395i
$514$		−	33.7466i		−	1.48850i
$515$		0			0
$516$	−18.1382	+	18.0084i	−0.798492	+	0.792775i
$517$	12.0725	+	12.0725i	0.530946	+	0.530946i
$518$	−11.5086	−	11.5086i	−0.505660	−	0.505660i
$519$	6.75820	−	6.70982i	0.296652	−	0.294528i
$520$		0			0
$521$			24.6501i			1.07994i	0.841683	+	0.539971i	$0.181565\pi$
$521$			24.6501i			1.07994i	−0.841683	+	0.539971i	$0.818435\pi$
$522$	−13.2628	+	13.0735i	−0.580495	+	0.572212i
$523$	23.4069	−	23.4069i	1.02351	−	1.02351i	0.0237950	−	0.999717i	$-0.492425\pi$
$523$	23.4069	−	23.4069i	1.02351	−	1.02351i	0.999717	−	0.0237950i	$-0.00757491\pi$
$524$	35.1668			1.53627
$525$		0			0
$526$	56.1475			2.44815
$527$	1.52639	−	1.52639i	0.0664907	−	0.0664907i
$528$	−10.9730	−	0.0394214i	−0.477536	−	0.00171560i
$529$			28.5666i			1.24203i
$530$		0			0
$531$	−30.9495	−	0.222381i	−1.34310	−	0.00965053i
$532$	−10.4041	−	10.4041i	−0.451076	−	0.451076i
$533$	−0.00650825	−	0.00650825i	−0.000281904	−	0.000281904i
$534$	5.33487	+	5.37334i	0.230862	+	0.232527i
$535$		0			0
$536$			15.0710i			0.650967i
$537$	0.0910493	−	25.3436i	0.00392907	−	1.09366i
$538$	−44.0273	+	44.0273i	−1.89815	+	1.89815i
$539$	3.38507			0.145805
$540$		0			0
$541$	−27.2143			−1.17003			−0.585017	−	0.811021i	$-0.698912\pi$
$541$	−27.2143			−1.17003			−0.585017	+	0.811021i	$0.698912\pi$
$542$	4.82102	−	4.82102i	0.207081	−	0.207081i
$543$	−0.0612121	+	17.0384i	−0.00262686	+	0.731187i
$544$		−	1.76249i		−	0.0755660i
$545$		0			0
$546$	0.778743	+	0.784359i	0.0333271	+	0.0335675i
$547$	3.63475	+	3.63475i	0.155411	+	0.155411i	0.780530	−	0.625119i	$-0.214949\pi$
$547$	3.63475	+	3.63475i	0.155411	+	0.155411i	−0.625119	+	0.780530i	$0.714949\pi$
$548$	14.3823	+	14.3823i	0.614380	+	0.614380i
$549$	20.4185	+	0.146713i	0.871440	+	0.00626154i
$550$		0			0
$551$			15.1065i			0.643559i
$552$	20.8798	+	0.0750128i	0.888705	+	0.00319276i
$553$	−8.09279	+	8.09279i	−0.344141	+	0.344141i
$554$	−37.8227			−1.60693
$555$		0			0
$556$	−34.0938			−1.44590
$557$	5.91751	−	5.91751i	0.250733	−	0.250733i	−0.570538	−	0.821271i	$-0.693265\pi$
$557$	5.91751	−	5.91751i	0.250733	−	0.250733i	0.821271	+	0.570538i	$0.193265\pi$
$558$	−42.5397	+	41.9328i	−1.80085	+	1.77516i
$559$		−	1.55749i		−	0.0658747i
$560$		0			0
$561$	−0.985055	+	0.978002i	−0.0415890	+	0.0412913i
$562$	−19.6385	−	19.6385i	−0.828402	−	0.828402i
$563$	−13.8267	−	13.8267i	−0.582728	−	0.582728i	0.352924	−	0.935652i	$-0.385187\pi$
$563$	−13.8267	−	13.8267i	−0.582728	−	0.582728i	−0.935652	+	0.352924i	$0.885187\pi$
$564$	17.1643	−	17.0414i	0.722749	−	0.717574i
$565$		0			0
$566$		−	61.2316i		−	2.57376i
$567$	−6.27185	−	6.45475i	−0.263393	−	0.271074i
$568$	−4.69425	+	4.69425i	−0.196966	+	0.196966i
$569$	6.82232			0.286007			0.143003	−	0.989722i	$-0.454324\pi$
$569$	6.82232			0.286007			0.143003	+	0.989722i	$0.454324\pi$
$570$		0			0
$571$	19.7545			0.826701			0.413351	−	0.910572i	$-0.364358\pi$
$571$	19.7545			0.826701			0.413351	+	0.910572i	$0.364358\pi$
$572$	−1.93663	+	1.93663i	−0.0809747	+	0.0809747i
$573$	11.0484	+	0.0396926i	0.461555	+	0.00165818i
$574$			0.0687811i			0.00287087i
$575$		0			0
$576$	−0.269737	+	37.5402i	−0.0112390	+	1.56417i
$577$	−1.10727	−	1.10727i	−0.0460964	−	0.0460964i	0.683683	−	0.729779i	$-0.260377\pi$
$577$	−1.10727	−	1.10727i	−0.0460964	−	0.0460964i	−0.729779	+	0.683683i	$0.760377\pi$
$578$	26.1639	+	26.1639i	1.08827	+	1.08827i
$579$	13.0530	+	13.1471i	0.542463	+	0.546375i
$580$		0			0
$581$		−	5.48799i		−	0.227680i
$582$	−0.0435762	+	12.1295i	−0.00180629	+	0.502782i
$583$	12.0268	−	12.0268i	0.498100	−	0.498100i
$584$	20.4434			0.845953
$585$		0			0
$586$	−20.7791			−0.858376
$587$	7.76708	−	7.76708i	0.320582	−	0.320582i	−0.528408	−	0.848990i	$-0.677211\pi$
$587$	7.76708	−	7.76708i	0.320582	−	0.320582i	0.848990	+	0.528408i	$0.177211\pi$
$588$	0.0172286	−	4.79558i	0.000710495	−	0.197766i
$589$			48.4535i			1.99649i
$590$		0			0
$591$	1.75154	+	1.76417i	0.0720487	+	0.0725683i
$592$	9.86325	+	9.86325i	0.405377	+	0.405377i
$593$	−8.01301	−	8.01301i	−0.329055	−	0.329055i	0.523172	−	0.852227i	$-0.324748\pi$
$593$	−8.01301	−	8.01301i	−0.329055	−	0.329055i	−0.852227	+	0.523172i	$0.824748\pi$
$594$	27.4515	−	26.8661i	1.12635	−	1.10233i
$595$		0			0
$596$			52.4261i			2.14746i
$597$	16.2819	+	0.0584943i	0.666373	+	0.00239401i
$598$	−3.24029	+	3.24029i	−0.132505	+	0.132505i
$599$	20.3742			0.832467			0.416233	−	0.909258i	$-0.363350\pi$
$599$	20.3742			0.832467			0.416233	+	0.909258i	$0.363350\pi$
$600$		0			0
$601$	−32.4833			−1.32502			−0.662511	−	0.749052i	$-0.730509\pi$
$601$	−32.4833			−1.32502			−0.662511	+	0.749052i	$0.730509\pi$
$602$	−8.22998	+	8.22998i	−0.335429	+	0.335429i
$603$	18.9069	+	19.1805i	0.769947	+	0.781092i
$604$			5.27521i			0.214645i
$605$		0			0
$606$	23.1809	−	23.0149i	0.941660	−	0.934918i
$607$	0.0701607	+	0.0701607i	0.00284774	+	0.00284774i	0.708529	−	0.705681i	$-0.249359\pi$
$607$	0.0701607	+	0.0701607i	0.00284774	+	0.00284774i	−0.705681	+	0.708529i	$0.749359\pi$
$608$	27.9740	+	27.9740i	1.13450	+	1.13450i
$609$	−3.49404	+	3.46902i	−0.141586	+	0.140572i
$610$		0			0
$611$			1.47386i			0.0596260i
$612$	1.38051	+	1.40049i	0.0558038	+	0.0566115i
$613$	26.6840	−	26.6840i	1.07776	−	1.07776i	0.0810445	−	0.996710i	$-0.474174\pi$
$613$	26.6840	−	26.6840i	1.07776	−	1.07776i	0.996710	−	0.0810445i	$-0.0258256\pi$
$614$	−31.2239			−1.26010
$615$		0			0
$616$	5.68266			0.228961
$617$	6.37294	−	6.37294i	0.256565	−	0.256565i	−0.567090	−	0.823656i	$-0.691931\pi$
$617$	6.37294	−	6.37294i	0.256565	−	0.256565i	0.823656	+	0.567090i	$0.191931\pi$
$618$	5.15824	+	0.0185315i	0.207495	+	0.000745446i
$619$		−	17.7676i		−	0.714139i	−0.934078	−	0.357070i	$-0.883776\pi$
$619$		−	17.7676i		−	0.714139i	0.934078	−	0.357070i	$-0.116224\pi$
$620$		0			0
$621$	26.6675	−	26.0987i	1.07013	−	1.04731i
$622$	0.608631	+	0.608631i	0.0244039	+	0.0244039i
$623$	1.41556	+	1.41556i	0.0567130	+	0.0567130i
$624$	−0.667407	−	0.672220i	−0.0267177	−	0.0269103i
$625$		0			0
$626$		−	32.0594i		−	1.28135i
$627$	0.111936	−	31.1575i	0.00447030	−	1.24431i
$628$	11.9535	−	11.9535i	0.476995	−	0.476995i
$629$	1.76453			0.0703565
$630$		0			0
$631$	17.8248			0.709592			0.354796	−	0.934944i	$-0.384550\pi$
$631$	17.8248			0.709592			0.354796	+	0.934944i	$0.384550\pi$
$632$	−13.5857	+	13.5857i	−0.540412	+	0.540412i
$633$	−0.0515944	+	14.3613i	−0.00205070	+	0.570811i
$634$			61.1712i			2.42942i
$635$		0			0
$636$	−16.9770	−	17.0995i	−0.673183	−	0.678038i
$637$	0.206632	+	0.206632i	0.00818705	+	0.00818705i
$638$	−14.8587	−	14.8587i	−0.588262	−	0.588262i
$639$	−0.0852413	+	11.8633i	−0.00337210	+	0.469306i
$640$		0			0
$641$		−	14.8270i		−	0.585630i	−0.956169	−	0.292815i	$-0.905408\pi$
$641$		−	14.8270i		−	0.585630i	0.956169	−	0.292815i	$-0.0945920\pi$
$642$	15.8250	+	0.0568527i	0.624562	+	0.00224380i
$643$	32.7229	−	32.7229i	1.29047	−	1.29047i	0.355968	−	0.934498i	$-0.384151\pi$
$643$	32.7229	−	32.7229i	1.29047	−	1.29047i	0.934498	−	0.355968i	$-0.115849\pi$
$644$	19.8823			0.783474
$645$		0			0
$646$	2.74747			0.108098
$647$	−27.0564	+	27.0564i	−1.06370	+	1.06370i	−0.0658674	+	0.997828i	$0.520981\pi$
$647$	−27.0564	+	27.0564i	−1.06370	+	1.06370i	−0.997828	+	0.0658674i	$0.979019\pi$
$648$	−10.5289	−	10.8359i	−0.413612	−	0.425674i
$649$		−	34.9230i		−	1.37085i
$650$		0			0
$651$	−11.2070	+	11.1267i	−0.439236	+	0.436091i
$652$	9.90255	+	9.90255i	0.387814	+	0.387814i
$653$	−4.04918	−	4.04918i	−0.158457	−	0.158457i	0.623426	−	0.781883i	$-0.285740\pi$
$653$	−4.04918	−	4.04918i	−0.158457	−	0.158457i	−0.781883	+	0.623426i	$0.785740\pi$
$654$	−7.57410	+	7.51988i	−0.296171	+	0.294050i
$655$		0			0
$656$		−	0.0589475i		−	0.00230151i
$657$	26.0179	−	25.6467i	1.01506	−	1.00057i
$658$	7.78809	−	7.78809i	0.303611	−	0.303611i
$659$	−11.5870			−0.451366			−0.225683	−	0.974201i	$-0.572461\pi$
$659$	−11.5870			−0.451366			−0.225683	+	0.974201i	$0.572461\pi$
$660$		0			0
$661$	−15.1550			−0.589462			−0.294731	−	0.955580i	$-0.595230\pi$
$661$	−15.1550			−0.589462			−0.294731	+	0.955580i	$0.595230\pi$
$662$	−38.1940	+	38.1940i	−1.48445	+	1.48445i
$663$	−0.119829		0.000430499i	−0.00465379		1.67192e-5i
$664$		−	9.21294i		−	0.357531i
$665$		0			0
$666$	−48.8257	−	0.350827i	−1.89196	−	0.0135943i
$667$	−14.4343	−	14.4343i	−0.558899	−	0.558899i
$668$	17.6990	+	17.6990i	0.684793	+	0.684793i
$669$	6.66199	+	6.71003i	0.257568	+	0.259425i
$670$		0			0
$671$			23.0399i			0.889445i
$672$	−0.0463233	+	12.8941i	−0.00178696	+	0.497400i
$673$	13.7667	−	13.7667i	0.530666	−	0.530666i	−0.390105	−	0.920770i	$-0.627561\pi$
$673$	13.7667	−	13.7667i	0.530666	−	0.530666i	0.920770	+	0.390105i	$0.127561\pi$
$674$	10.5045			0.404617
$675$		0			0
$676$	35.7573			1.37528
$677$	16.3594	−	16.3594i	0.628742	−	0.628742i	−0.319009	−	0.947752i	$-0.603350\pi$
$677$	16.3594	−	16.3594i	0.628742	−	0.628742i	0.947752	+	0.319009i	$0.103350\pi$
$678$	0.0387793	−	10.7942i	0.00148931	−	0.414549i
$679$			3.20687i			0.123068i
$680$		0			0
$681$	−2.60148	−	2.62024i	−0.0996891	−	0.100408i
$682$	−47.6587	−	47.6587i	−1.82495	−	1.82495i
$683$	5.85622	+	5.85622i	0.224082	+	0.224082i	0.810215	−	0.586133i	$-0.199350\pi$
$683$	5.85622	+	5.85622i	0.224082	+	0.224082i	−0.586133	+	0.810215i	$0.699350\pi$
$684$	−44.1398	−	0.317157i	−1.68773	−	0.0121268i
$685$		0			0
$686$		−	2.18375i		−	0.0833758i
$687$	−10.8427	−	0.0389535i	−0.413676	−	0.00148617i
$688$	7.05335	−	7.05335i	0.268906	−	0.268906i
$689$	1.46829			0.0559373
$690$		0			0
$691$	25.9095			0.985642			0.492821	−	0.870131i	$-0.335966\pi$
$691$	25.9095			0.985642			0.492821	+	0.870131i	$0.335966\pi$
$692$	10.7646	−	10.7646i	0.409210	−	0.409210i
$693$	7.23222	−	7.12903i	0.274729	−	0.270809i
$694$		−	74.2189i		−	2.81731i
$695$		0			0
$696$	−5.86560	+	5.82361i	−0.222335	+	0.220743i
$697$	−0.00527284	−	0.00527284i	−0.000199723	−	0.000199723i
$698$	14.4698	+	14.4698i	0.547691	+	0.547691i
$699$	−4.64849	+	4.61521i	−0.175822	+	0.174563i
$700$		0			0
$701$		−	37.9089i		−	1.43180i	−0.698204	−	0.715899i	$-0.746017\pi$
$701$		−	37.9089i		−	1.43180i	0.698204	−	0.715899i	$-0.253983\pi$
$702$	3.31567	+	0.0357368i	0.125142	+	0.00134880i
$703$	−28.0065	+	28.0065i	−1.05628	+	1.05628i
$704$	−42.3598			−1.59649
$705$		0			0
$706$	45.0542			1.69564
$707$	6.10679	−	6.10679i	0.229669	−	0.229669i
$708$	−49.4749	−	0.177743i	−1.85938	−	0.00668001i
$709$		−	16.6841i		−	0.626586i	−0.949656	−	0.313293i	$-0.898568\pi$
$709$		−	16.6841i		−	0.626586i	0.949656	−	0.313293i	$-0.101432\pi$
$710$		0			0
$711$	−0.246699	+	34.3339i	−0.00925194	+	1.28762i
$712$	2.37636	+	2.37636i	0.0890578	+	0.0890578i
$713$	−46.2975	−	46.2975i	−1.73385	−	1.73385i
$714$	0.630921	+	0.635470i	0.0236116	+	0.0237819i
$715$		0			0
$716$		−	40.5129i		−	1.51404i
$717$	−0.0129753	+	3.61167i	−0.000484570	+	0.134880i
$718$	−42.1016	+	42.1016i	−1.57122	+	1.57122i
$719$	−13.0709			−0.487464			−0.243732	−	0.969843i	$-0.578372\pi$
$719$	−13.0709			−0.487464			−0.243732	+	0.969843i	$0.578372\pi$
$720$		0			0
$721$	1.36377			0.0507895
$722$	−14.2688	+	14.2688i	−0.531031	+	0.531031i
$723$	−0.0338310	+	9.41686i	−0.00125819	+	0.350217i
$724$			27.2367i			1.01224i
$725$		0			0
$726$	1.22231	+	1.23112i	0.0453640	+	0.0456911i
$727$	−19.4878	−	19.4878i	−0.722761	−	0.722761i	0.246406	−	0.969167i	$-0.420750\pi$
$727$	−19.4878	−	19.4878i	−0.722761	−	0.722761i	−0.969167	+	0.246406i	$0.920750\pi$
$728$	0.346882	+	0.346882i	0.0128563	+	0.0128563i
$729$	−26.9937	−	0.581953i	−0.999768	−	0.0215538i
$730$		0			0
$731$		−	1.26184i		−	0.0466709i
$732$	32.6403	+	0.117264i	1.20642	+	0.00433418i
$733$	−24.5624	+	24.5624i	−0.907232	+	0.907232i	−0.996048	−	0.0888162i	$-0.971692\pi$
$733$	−24.5624	+	24.5624i	−0.907232	+	0.907232i	0.0888162	+	0.996048i	$0.471692\pi$
$734$	−49.1774			−1.81517
$735$		0			0
$736$	−53.4585			−1.97051
$737$	−21.4886	+	21.4886i	−0.791543	+	0.791543i
$738$	0.144855	+	0.146951i	0.00533217	+	0.00540935i
$739$		−	25.3925i		−	0.934079i	−0.884236	−	0.467040i	$-0.845321\pi$
$739$		−	25.3925i		−	0.934079i	0.884236	−	0.467040i	$-0.154679\pi$
$740$		0			0
$741$	1.90875	−	1.89509i	0.0701198	−	0.0696178i
$742$	−7.75865	−	7.75865i	−0.284829	−	0.284829i
$743$	−14.4447	−	14.4447i	−0.529923	−	0.529923i	0.390626	−	0.920549i	$-0.372258\pi$
$743$	−14.4447	−	14.4447i	−0.529923	−	0.529923i	−0.920549	+	0.390626i	$0.872258\pi$
$744$	−18.8137	+	18.6790i	−0.689742	+	0.684804i
$745$		0			0
$746$			72.0445i			2.63774i
$747$	−11.5578	−	11.7251i	−0.422879	−	0.429000i
$748$	−1.56902	+	1.56902i	−0.0573690	+	0.0573690i
$749$	4.18391			0.152877
$750$		0			0
$751$	27.4358			1.00115			0.500573	−	0.865694i	$-0.333123\pi$
$751$	27.4358			1.00115			0.500573	+	0.865694i	$0.333123\pi$
$752$	−6.67463	+	6.67463i	−0.243399	+	0.243399i
$753$	40.4307	+	0.145251i	1.47338	+	0.00529325i
$754$		−	1.81402i		−	0.0660627i
$755$		0			0
$756$	−10.0628	−	10.2821i	−0.365980	−	0.373955i
$757$	11.9760	+	11.9760i	0.435274	+	0.435274i	0.890418	−	0.455144i	$-0.150412\pi$
$757$	11.9760	+	11.9760i	0.435274	+	0.435274i	−0.455144	+	0.890418i	$0.650412\pi$
$758$	−57.8245	−	57.8245i	−2.10028	−	2.10028i
$759$	29.6641	+	29.8780i	1.07674	+	1.08450i
$760$		0			0
$761$			41.1635i			1.49217i	0.665848	+	0.746087i	$0.268070\pi$
$761$			41.1635i			1.49217i	−0.665848	+	0.746087i	$0.731930\pi$
$762$	0.223437	−	62.1937i	0.00809426	−	2.25304i
$763$	−1.99533	+	1.99533i	−0.0722357	+	0.0722357i
$764$	17.6614			0.638969
$765$		0			0
$766$	−15.3007			−0.552836
$767$	2.13178	−	2.13178i	0.0769740	−	0.0769740i
$768$	−0.0132771	+	3.69569i	−0.000479097	+	0.133357i
$769$			3.96520i			0.142989i	0.997441	+	0.0714944i	$0.0227768\pi$
$769$			3.96520i			0.142989i	−0.997441	+	0.0714944i	$0.977223\pi$
$770$		0			0
$771$	−18.8585	−	18.9945i	−0.679174	−	0.684071i
$772$	20.9410	+	20.9410i	0.753684	+	0.753684i
$773$	−5.99943	−	5.99943i	−0.215785	−	0.215785i	0.590935	−	0.806719i	$-0.298759\pi$
$773$	−5.99943	−	5.99943i	−0.215785	−	0.215785i	−0.806719	+	0.590935i	$0.798759\pi$
$774$	−0.250881	+	34.9160i	−0.00901774	+	1.25503i
$775$		0			0
$776$			5.38352i			0.193257i
$777$	−12.9090	−	0.0463770i	−0.463109	−	0.00166377i
$778$	−14.2104	+	14.2104i	−0.509468	+	0.509468i
$779$	0.167380			0.00599702
$780$		0			0
$781$	−13.3864			−0.479002
$782$	−2.62521	+	2.62521i	−0.0938774	+	0.0938774i
$783$	−0.159195	+	14.7701i	−0.00568916	+	0.527841i
$784$			1.87154i			0.0668406i
$785$		0			0
$786$	34.0920	−	33.8479i	1.21602	−	1.20731i
$787$	−15.8108	−	15.8108i	−0.563593	−	0.563593i	0.366733	−	0.930326i	$-0.380476\pi$
$787$	−15.8108	−	15.8108i	−0.563593	−	0.563593i	−0.930326	+	0.366733i	$0.880476\pi$
$788$	2.81001	+	2.81001i	0.100103	+	0.100103i
$789$	31.6030	−	31.3768i	1.12510	−	1.11704i
$790$		0			0
$791$		−	2.85385i		−	0.101471i
$792$	12.1411	−	11.9678i	0.431414	−	0.425258i
$793$	−1.40641	+	1.40641i	−0.0499429	+	0.0499429i
$794$	−67.7082			−2.40287
$795$		0			0
$796$	26.0274			0.922515
$797$	8.46554	−	8.46554i	0.299865	−	0.299865i	−0.541096	−	0.840961i	$-0.681990\pi$
$797$	8.46554	−	8.46554i	0.299865	−	0.299865i	0.840961	+	0.541096i	$0.181990\pi$
$798$	−20.1000	−	0.0722114i	−0.711534	−	0.00255625i
$799$			1.19409i			0.0422438i
$800$		0			0
$801$	6.00554	+	0.0431515i	0.212195	+	0.00152468i
$802$	−39.7638	−	39.7638i	−1.40411	−	1.40411i
$803$	29.1488	+	29.1488i	1.02864	+	1.02864i
$804$	30.3333	+	30.5520i	1.06977	+	1.07749i
$805$		0			0
$806$		−	5.81839i		−	0.204944i
$807$	−0.177420	+	49.3848i	−0.00624547	+	1.73843i
$808$	10.2517	−	10.2517i	0.360655	−	0.360655i
$809$	−25.5350			−0.897764			−0.448882	−	0.893591i	$-0.648178\pi$
$809$	−25.5350			−0.897764			−0.448882	+	0.893591i	$0.648178\pi$
$810$		0			0
$811$	−1.94760			−0.0683895			−0.0341947	−	0.999415i	$-0.510887\pi$
$811$	−1.94760			−0.0683895			−0.0341947	+	0.999415i	$0.510887\pi$
$812$	−5.56539	+	5.56539i	−0.195307	+	0.195307i
$813$	0.0194276	−	5.40767i	0.000681355	−	0.189655i
$814$		−	55.0942i		−	1.93105i
$815$		0			0
$816$	−0.540719	−	0.544618i	−0.0189289	−	0.0190654i
$817$	20.0278	+	20.0278i	0.700685	+	0.700685i
$818$	−16.9078	−	16.9078i	−0.591167	−	0.591167i
$819$	0.876642	+	0.00629893i	0.0306324	+	0.000220102i
$820$		0			0
$821$			21.6742i			0.756434i	0.925717	+	0.378217i	$0.123463\pi$
$821$			21.6742i			0.756434i	−0.925717	+	0.378217i	$0.876537\pi$
$822$	27.7856	+	0.0998224i	0.969133	+	0.00348171i
$823$	−8.35207	+	8.35207i	−0.291135	+	0.291135i	−0.837528	−	0.546394i	$-0.816000\pi$
$823$	−8.35207	+	8.35207i	−0.291135	+	0.291135i	0.546394	+	0.837528i	$0.316000\pi$
$824$	2.28943			0.0797559
$825$		0			0
$826$	−22.5292			−0.783892
$827$	−14.1747	+	14.1747i	−0.492902	+	0.492902i	−0.909219	−	0.416318i	$-0.863320\pi$
$827$	−14.1747	+	14.1747i	−0.492902	+	0.492902i	0.416318	+	0.909219i	$0.363320\pi$
$828$	42.4788	−	41.8727i	1.47624	−	1.45518i
$829$		−	19.3836i		−	0.673219i	−0.941644	−	0.336610i	$-0.890720\pi$
$829$		−	19.3836i		−	0.673219i	0.941644	−	0.336610i	$-0.109280\pi$
$830$		0			0
$831$	−21.2888	+	21.1364i	−0.738500	+	0.733213i
$832$	−2.58573	−	2.58573i	−0.0896442	−	0.0896442i
$833$	0.167409	+	0.167409i	0.00580037	+	0.00580037i
$834$	−33.0517	+	32.8151i	−1.14449	+	1.13629i
$835$		0			0
$836$		−	49.8066i		−	1.72260i
$837$	−0.510610	+	47.3745i	−0.0176493	+	1.63750i
$838$	9.06346	−	9.06346i	0.313092	−	0.313092i
$839$	−26.2528			−0.906346			−0.453173	−	0.891423i	$-0.649708\pi$
$839$	−26.2528			−0.906346			−0.453173	+	0.891423i	$0.649708\pi$
$840$		0			0
$841$	−20.9192			−0.721352
$842$	41.5131	−	41.5131i	1.43063	−	1.43063i
$843$	−22.0282	−	0.0791386i	−0.758693	−	0.00272568i
$844$			22.9572i			0.790221i
$845$		0			0
$846$	0.237410	−	33.0412i	0.00816234	−	1.13598i
$847$	0.324327	+	0.324327i	0.0111440	+	0.0111440i
$848$	6.64940	+	6.64940i	0.228341	+	0.228341i
$849$	−34.2179	−	34.4646i	−1.17435	−	1.18282i
$850$		0			0
$851$		−	53.5206i		−	1.83466i
$852$	−0.0681311	+	18.9643i	−0.00233413	+	0.649707i
$853$	−29.8920	+	29.8920i	−1.02348	+	1.02348i	−0.0237636	+	0.999718i	$0.507565\pi$
$853$	−29.8920	+	29.8920i	−1.02348	+	1.02348i	−0.999718	+	0.0237636i	$0.992435\pi$
$854$	14.8633			0.508612
$855$		0			0
$856$	7.02373			0.240066
$857$	5.92367	−	5.92367i	0.202349	−	0.202349i	−0.598657	−	0.801006i	$-0.704299\pi$
$857$	5.92367	−	5.92367i	0.202349	−	0.202349i	0.801006	+	0.598657i	$0.204299\pi$
$858$	−0.0134415	+	3.74145i	−0.000458885	+	0.127731i
$859$			10.3620i			0.353548i	0.984252	+	0.176774i	$0.0565661\pi$
$859$			10.3620i			0.353548i	−0.984252	+	0.176774i	$0.943434\pi$
$860$		0			0
$861$	0.0384368	+	0.0387139i	0.00130992	+	0.00131937i
$862$	−6.45633	−	6.45633i	−0.219904	−	0.219904i
$863$	−13.2818	−	13.2818i	−0.452118	−	0.452118i	0.443939	−	0.896057i	$-0.353581\pi$
$863$	−13.2818	−	13.2818i	−0.452118	−	0.452118i	−0.896057	+	0.443939i	$0.853581\pi$
$864$	27.0563	+	27.6459i	0.920474	+	0.940532i
$865$		0			0
$866$		−	6.82129i		−	0.231797i
$867$	29.3476	+	0.105434i	0.996696	+	0.00358073i
$868$	−17.8507	+	17.8507i	−0.605894	+	0.605894i
$869$	−38.7419			−1.31423
$870$		0			0
$871$	−2.62342			−0.0888913
$872$	−3.34965	+	3.34965i	−0.113433	+	0.113433i
$873$	6.75374	+	6.85150i	0.228580	+	0.231888i
$874$		−	83.3342i		−	2.81882i
$875$		0			0
$876$	41.4430	−	41.1463i	1.40023	−	1.39020i
$877$	−4.84197	−	4.84197i	−0.163502	−	0.163502i	0.620614	−	0.784116i	$-0.286883\pi$
$877$	−4.84197	−	4.84197i	−0.163502	−	0.163502i	−0.784116	+	0.620614i	$0.786883\pi$
$878$	−42.6227	−	42.6227i	−1.43845	−	1.43845i
$879$	−11.6957	+	11.6119i	−0.394485	+	0.391660i
$880$		0			0
$881$		−	17.0394i		−	0.574073i	−0.957920	−	0.287036i	$-0.907330\pi$
$881$		−	17.0394i		−	0.574073i	0.957920	−	0.287036i	$-0.0926701\pi$
$882$	−4.59902	−	4.66559i	−0.154857	−	0.157099i
$883$	−12.2389	+	12.2389i	−0.411871	+	0.411871i	−0.882390	−	0.470519i	$-0.844067\pi$
$883$	−12.2389	+	12.2389i	−0.411871	+	0.411871i	0.470519	+	0.882390i	$0.344067\pi$
$884$	−0.191553			−0.00644262
$885$		0			0
$886$	37.9983			1.27658
$887$	−41.0767	+	41.0767i	−1.37922	+	1.37922i	−0.533287	+	0.845934i	$0.679043\pi$
$887$	−41.0767	+	41.0767i	−1.37922	+	1.37922i	−0.845934	+	0.533287i	$0.820957\pi$
$888$	−21.6710	−	0.0778552i	−0.727231	−	0.00261265i
$889$		−	16.4432i		−	0.551487i
$890$		0			0
$891$	0.437785	−	30.4624i	0.0146664	−	1.02053i
$892$	10.6879	+	10.6879i	0.357858	+	0.357858i
$893$	−18.9525	−	18.9525i	−0.634220	−	0.634220i
$894$	50.4599	+	50.8238i	1.68763	+	1.69980i
$895$		0			0
$896$			12.4379i			0.415520i
$897$	−0.0130576	+	3.63458i	−0.000435980	+	0.121355i
$898$	52.7879	−	52.7879i	1.76155	−	1.76155i
$899$	25.9188			0.864441
$900$		0			0
$901$	1.18958			0.0396305
$902$	−0.164635	+	0.164635i	−0.00548173	+	0.00548173i
$903$	−0.0331649	+	9.23144i	−0.00110366	+	0.307203i
$904$		−	4.79089i		−	0.159343i
$905$		0			0
$906$	5.07736	+	5.11398i	0.168684	+	0.169901i
$907$	−24.8992	−	24.8992i	−0.826765	−	0.826765i	0.160303	−	0.987068i	$-0.448753\pi$
$907$	−24.8992	−	24.8992i	−0.826765	−	0.826765i	−0.987068	+	0.160303i	$0.948753\pi$
$908$	−4.17359	−	4.17359i	−0.138505	−	0.138505i
$909$	0.186158	−	25.9082i	0.00617448	−	0.859322i
$910$		0			0
$911$		−	23.4322i		−	0.776342i	−0.921587	−	0.388171i	$-0.873107\pi$
$911$		−	23.4322i		−	0.776342i	0.921587	−	0.388171i	$-0.126893\pi$
$912$	17.2264	+	0.0618874i	0.570422	+	0.00204930i
$913$	13.1361	−	13.1361i	0.434740	−	0.434740i
$914$	28.7526			0.951050
$915$		0			0
$916$	−17.3326			−0.572685
$917$	8.98121	−	8.98121i	0.296586	−	0.296586i
$918$	2.68628	+	0.0289532i	0.0886605	+	0.000955598i
$919$			31.9950i			1.05542i	0.849425	+	0.527710i	$0.176949\pi$
$919$			31.9950i			1.05542i	−0.849425	+	0.527710i	$0.823051\pi$
$920$		0			0
$921$	−17.5746	+	17.4488i	−0.579103	+	0.574957i
$922$	−39.6195	−	39.6195i	−1.30480	−	1.30480i
$923$	−0.817134	−	0.817134i	−0.0268963	−	0.0268963i
$924$	11.5199	−	11.4375i	0.378978	−	0.376265i
$925$		0			0
$926$			40.8180i			1.34136i
$927$	2.91371	−	2.87214i	0.0956987	−	0.0943333i
$928$	14.9639	−	14.9639i	0.491214	−	0.491214i
$929$	49.7858			1.63342			0.816709	−	0.577050i	$-0.195796\pi$
$929$	49.7858			1.63342			0.816709	+	0.577050i	$0.195796\pi$
$930$		0			0
$931$	−5.31419			−0.174166
$932$	−7.40423	+	7.40423i	−0.242534	+	0.242534i
$933$	0.682692	+	0.00245264i	0.0223503	+	8.02958e-5i
$934$			60.7340i			1.98728i
$935$		0			0
$936$	1.47166	+	0.0105743i	0.0481027	+	0.000345632i
$937$	−18.0919	−	18.0919i	−0.591035	−	0.591035i	0.346876	−	0.937911i	$-0.387243\pi$
$937$	−18.0919	−	18.0919i	−0.591035	−	0.591035i	−0.937911	+	0.346876i	$0.887243\pi$
$938$	13.8626	+	13.8626i	0.452628	+	0.452628i
$939$	−17.9157	−	18.0449i	−0.584656	−	0.588872i
$940$		0			0
$941$			61.0502i			1.99018i	0.0989766	+	0.995090i	$0.468443\pi$
$941$			61.0502i			1.99018i	−0.0989766	+	0.995090i	$0.531557\pi$
$942$	0.0829648	−	23.0933i	0.00270314	−	0.752419i
$943$	−0.159932	+	0.159932i	−0.00520811	+	0.00520811i
$944$	19.3082			0.628430
$945$		0			0
$946$	−39.3986			−1.28096
$947$	28.1297	−	28.1297i	0.914093	−	0.914093i	−0.0824986	−	0.996591i	$-0.526290\pi$
$947$	28.1297	−	28.1297i	0.914093	−	0.914093i	0.996591	+	0.0824986i	$0.0262900\pi$
$948$	−0.197180	+	54.8851i	−0.00640411	+	1.78259i
$949$			3.55861i			0.115517i
$950$		0			0
$951$	34.1841	+	34.4306i	1.10850	+	1.11649i
$952$	0.281037	+	0.281037i	0.00910845	+	0.00910845i
$953$	−16.4406	−	16.4406i	−0.532564	−	0.532564i	0.388771	−	0.921335i	$-0.372900\pi$
$953$	−16.4406	−	16.4406i	−0.532564	−	0.532564i	−0.921335	+	0.388771i	$0.872900\pi$
$954$	−32.9163	−	0.236513i	−1.06571	−	0.00765740i
$955$		0			0
$956$			5.77342i			0.186726i
$957$	−16.6668	−	0.0598771i	−0.538761	−	0.00193555i
$958$	41.6493	−	41.6493i	1.34563	−	1.34563i
$959$	7.34614			0.237219
$960$		0			0
$961$	52.1335			1.68173
$962$	3.36307	−	3.36307i	0.108430	−	0.108430i
$963$	8.93897	−	8.81142i	0.288054	−	0.283944i
$964$			15.0533i			0.484834i
$965$		0			0
$966$	19.2747	−	19.1367i	0.620152	−	0.615712i
$967$	3.29391	+	3.29391i	0.105925	+	0.105925i	0.758083	−	0.652158i	$-0.226136\pi$
$967$	3.29391	+	3.29391i	0.105925	+	0.105925i	−0.652158	+	0.758083i	$0.726136\pi$
$968$	0.544462	+	0.544462i	0.0174997	+	0.0174997i
$969$	1.54643	−	1.53536i	0.0496785	−	0.0493228i
$970$		0			0
$971$			32.3161i			1.03707i	0.855056	+	0.518536i	$0.173523\pi$
$971$			32.3161i			1.03707i	−0.855056	+	0.518536i	$0.826477\pi$
$972$	−43.1535	−	0.775246i	−1.38415	−	0.0248660i
$973$	−8.70717	+	8.70717i	−0.279139	+	0.279139i
$974$	88.4809			2.83511
$975$		0			0
$976$	−12.7383			−0.407744
$977$	−8.42742	+	8.42742i	−0.269617	+	0.269617i	−0.828946	−	0.559329i	$-0.811059\pi$
$977$	−8.42742	+	8.42742i	−0.269617	+	0.269617i	0.559329	+	0.828946i	$0.311059\pi$
$978$	19.1311	+	0.0687302i	0.611744	+	0.00219775i
$979$			6.77655i			0.216580i
$980$		0			0
$981$	−0.0608251	+	8.46523i	−0.00194200	+	0.270274i
$982$	−4.23900	−	4.23900i	−0.135272	−	0.135272i
$983$	43.2280	+	43.2280i	1.37876	+	1.37876i	0.846718	+	0.532042i	$0.178575\pi$
$983$	43.2280	+	43.2280i	1.37876	+	1.37876i	0.532042	+	0.846718i	$0.321425\pi$
$984$	0.0645255	+	0.0649908i	0.00205700	+	0.00207183i
$985$		0			0
$986$		−	1.46968i		−	0.0468041i
$987$	0.0313841	−	8.73578i	0.000998968	−	0.278063i
$988$	3.04031	−	3.04031i	0.0967251	−	0.0967251i
$989$	−38.2733			−1.21702
$990$		0			0
$991$	−25.2971			−0.803590			−0.401795	−	0.915730i	$-0.631614\pi$
$991$	−25.2971			−0.803590			−0.401795	+	0.915730i	$0.631614\pi$
$992$	47.9961	−	47.9961i	1.52388	−	1.52388i
$993$	−0.153913	+	42.8417i	−0.00488428	+	1.35954i
$994$			8.63571i			0.273908i
$995$		0			0
$996$	−18.5428	−	18.6765i	−0.587552	−	0.591789i
$997$	23.3279	+	23.3279i	0.738803	+	0.738803i	0.972346	−	0.233543i	$-0.0750321\pi$
$997$	23.3279	+	23.3279i	0.738803	+	0.738803i	−0.233543	+	0.972346i	$0.575032\pi$
$998$	46.8108	+	46.8108i	1.48177	+	1.48177i
$999$	−27.6779	+	27.0877i	−0.875691	+	0.857016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.j.b.407.11		24
3.2	odd	2	inner	525.2.j.b.407.2		24
5.2	odd	4		105.2.j.a.8.11	yes	24
5.3	odd	4	inner	525.2.j.b.218.2		24
5.4	even	2		105.2.j.a.92.2	yes	24
15.2	even	4		105.2.j.a.8.2	✓	24
15.8	even	4	inner	525.2.j.b.218.11		24
15.14	odd	2		105.2.j.a.92.11	yes	24
35.2	odd	12		735.2.y.j.263.11		48
35.4	even	6		735.2.y.j.422.2		48
35.9	even	6		735.2.y.j.557.11		48
35.12	even	12		735.2.y.g.263.11		48
35.17	even	12		735.2.y.g.128.2		48
35.19	odd	6		735.2.y.g.557.11		48
35.24	odd	6		735.2.y.g.422.2		48
35.27	even	4		735.2.j.h.638.11		24
35.32	odd	12		735.2.y.j.128.2		48
35.34	odd	2		735.2.j.h.197.2		24
105.2	even	12		735.2.y.j.263.2		48
105.17	odd	12		735.2.y.g.128.11		48
105.32	even	12		735.2.y.j.128.11		48
105.44	odd	6		735.2.y.j.557.2		48
105.47	odd	12		735.2.y.g.263.2		48
105.59	even	6		735.2.y.g.422.11		48
105.62	odd	4		735.2.j.h.638.2		24
105.74	odd	6		735.2.y.j.422.11		48
105.89	even	6		735.2.y.g.557.2		48
105.104	even	2		735.2.j.h.197.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.2	✓	24	15.2	even	4
105.2.j.a.8.11	yes	24	5.2	odd	4
105.2.j.a.92.2	yes	24	5.4	even	2
105.2.j.a.92.11	yes	24	15.14	odd	2
525.2.j.b.218.2		24	5.3	odd	4	inner
525.2.j.b.218.11		24	15.8	even	4	inner
525.2.j.b.407.2		24	3.2	odd	2	inner
525.2.j.b.407.11		24	1.1	even	1	trivial
735.2.j.h.197.2		24	35.34	odd	2
735.2.j.h.197.11		24	105.104	even	2
735.2.j.h.638.2		24	105.62	odd	4
735.2.j.h.638.11		24	35.27	even	4
735.2.y.g.128.2		48	35.17	even	12
735.2.y.g.128.11		48	105.17	odd	12
735.2.y.g.263.2		48	105.47	odd	12
735.2.y.g.263.11		48	35.12	even	12
735.2.y.g.422.2		48	35.24	odd	6
735.2.y.g.422.11		48	105.59	even	6
735.2.y.g.557.2		48	105.89	even	6
735.2.y.g.557.11		48	35.19	odd	6
735.2.y.j.128.2		48	35.32	odd	12
735.2.y.j.128.11		48	105.32	even	12
735.2.y.j.263.2		48	105.2	even	12
735.2.y.j.263.11		48	35.2	odd	12
735.2.y.j.422.2		48	35.4	even	6
735.2.y.j.422.11		48	105.74	odd	6
735.2.y.j.557.2		48	105.44	odd	6
735.2.y.j.557.11		48	35.9	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.54414 - 1.54414i) q^{2} +(0.00622252 - 1.73204i) q^{3} -2.76875i q^{4} +(-2.66491 - 2.68412i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-1.18705 - 1.18705i) q^{8} +(-2.99992 - 0.0215553i) q^{9} +O(q^{10})\)	\(q+(1.54414 - 1.54414i) q^{2} +(0.00622252 - 1.73204i) q^{3} -2.76875i q^{4} +(-2.66491 - 2.68412i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-1.18705 - 1.18705i) q^{8} +(-2.99992 - 0.0215553i) q^{9} -3.38507i q^{11} +(-4.79558 - 0.0172286i) q^{12} +(0.206632 - 0.206632i) q^{13} -2.18375 q^{14} +1.87154 q^{16} +(0.167409 - 0.167409i) q^{17} +(-4.66559 + 4.59902i) q^{18} +5.31419i q^{19} +(-1.22914 + 1.22034i) q^{21} +(-5.22702 - 5.22702i) q^{22} +(-5.07773 - 5.07773i) q^{23} +(-2.06341 + 2.04864i) q^{24} -0.638138i q^{26} +(-0.0560017 + 5.19585i) q^{27} +(-1.95780 + 1.95780i) q^{28} +2.84268 q^{29} +9.11776 q^{31} +(5.26402 - 5.26402i) q^{32} +(-5.86307 - 0.0210636i) q^{33} -0.517005i q^{34} +(-0.0596812 + 8.30602i) q^{36} +(5.27013 + 5.27013i) q^{37} +(8.20586 + 8.20586i) q^{38} +(-0.356609 - 0.359180i) q^{39} -0.0314968i q^{41} +(-0.0135884 + 3.78233i) q^{42} +(3.76875 - 3.76875i) q^{43} -9.37239 q^{44} -15.6815 q^{46} +(-3.56639 + 3.56639i) q^{47} +(0.0116457 - 3.24158i) q^{48} +1.00000i q^{49} +(-0.288917 - 0.291000i) q^{51} +(-0.572111 - 0.572111i) q^{52} +(3.55291 + 3.55291i) q^{53} +(7.93665 + 8.10960i) q^{54} +1.67875i q^{56} +(9.20439 + 0.0330677i) q^{57} +(4.38949 - 4.38949i) q^{58} +10.3168 q^{59} -6.80634 q^{61} +(14.0791 - 14.0791i) q^{62} +(2.10602 + 2.13651i) q^{63} -12.5137i q^{64} +(-9.08593 + 9.02088i) q^{66} +(-6.34806 - 6.34806i) q^{67} +(-0.463512 - 0.463512i) q^{68} +(-8.82642 + 8.76323i) q^{69} -3.95454i q^{71} +(3.53548 + 3.58665i) q^{72} +(-8.61099 + 8.61099i) q^{73} +16.2757 q^{74} +14.7136 q^{76} +(-2.39360 + 2.39360i) q^{77} +(-1.10528 - 0.00397083i) q^{78} -11.4449i q^{79} +(8.99907 + 0.129328i) q^{81} +(-0.0486356 - 0.0486356i) q^{82} +(3.88059 + 3.88059i) q^{83} +(3.37880 + 3.40317i) q^{84} -11.6390i q^{86} +(0.0176886 - 4.92363i) q^{87} +(-4.01825 + 4.01825i) q^{88} -2.00190 q^{89} -0.292222 q^{91} +(-14.0589 + 14.0589i) q^{92} +(0.0567354 - 15.7923i) q^{93} +11.0140i q^{94} +(-9.08474 - 9.15025i) q^{96} +(-2.26760 - 2.26760i) q^{97} +(1.54414 + 1.54414i) q^{98} +(-0.0729661 + 10.1549i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3}+O(q^{10}) \) 24 * q + 4 * q^3	\( 24 q + 4 q^{3} - 16 q^{12} + 8 q^{13} - 16 q^{16} + 20 q^{18} + 4 q^{21} - 8 q^{22} + 16 q^{27} - 28 q^{33} + 16 q^{36} + 16 q^{37} + 20 q^{42} + 40 q^{43} - 64 q^{46} - 16 q^{48} - 20 q^{51} - 4 q^{57} - 40 q^{58} + 32 q^{61} + 8 q^{63} - 16 q^{66} - 24 q^{67} + 8 q^{72} - 32 q^{73} + 32 q^{76} - 60 q^{78} + 52 q^{81} + 80 q^{82} - 4 q^{87} - 96 q^{88} - 24 q^{91} + 76 q^{93} - 96 q^{96} - 24 q^{97}+O(q^{100}) \) 24 * q + 4 * q^3 - 16 * q^12 + 8 * q^13 - 16 * q^16 + 20 * q^18 + 4 * q^21 - 8 * q^22 + 16 * q^27 - 28 * q^33 + 16 * q^36 + 16 * q^37 + 20 * q^42 + 40 * q^43 - 64 * q^46 - 16 * q^48 - 20 * q^51 - 4 * q^57 - 40 * q^58 + 32 * q^61 + 8 * q^63 - 16 * q^66 - 24 * q^67 + 8 * q^72 - 32 * q^73 + 32 * q^76 - 60 * q^78 + 52 * q^81 + 80 * q^82 - 4 * q^87 - 96 * q^88 - 24 * q^91 + 76 * q^93 - 96 * q^96 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more