LMFDB - Embedded newform 525.2.j.b.407.12

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			407.12
Character	$\chi$	$=$	525.407
Dual form			525.2.j.b.218.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.79963 - 1.79963i) q^{2} +(1.66094 + 0.491204i) q^{3} -4.47734i q^{4} +(3.87306 - 2.10509i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-4.45829 - 4.45829i) q^{8} +(2.51744 + 1.63172i) q^{9} +O(q^{10})$	\(q+(1.79963 - 1.79963i) q^{2} +(1.66094 + 0.491204i) q^{3} -4.47734i q^{4} +(3.87306 - 2.10509i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-4.45829 - 4.45829i) q^{8} +(2.51744 + 1.63172i) q^{9} -1.56870i q^{11} +(2.19929 - 7.43658i) q^{12} +(-2.21881 + 2.21881i) q^{13} +2.54506 q^{14} -7.09187 q^{16} +(-3.60725 + 3.60725i) q^{17} +(7.46695 - 1.59396i) q^{18} -1.68040i q^{19} +(0.827127 + 1.52180i) q^{21} +(-2.82308 - 2.82308i) q^{22} +(-0.995850 - 0.995850i) q^{23} +(-5.21502 - 9.59488i) q^{24} +7.98606i q^{26} +(3.37980 + 3.94676i) q^{27} +(3.16595 - 3.16595i) q^{28} -8.91955 q^{29} +2.74834 q^{31} +(-3.84616 + 3.84616i) q^{32} +(0.770553 - 2.60552i) q^{33} +12.9834i q^{34} +(7.30576 - 11.2714i) q^{36} +(-0.440360 - 0.440360i) q^{37} +(-3.02410 - 3.02410i) q^{38} +(-4.77519 + 2.59542i) q^{39} +6.44292i q^{41} +(4.22719 + 1.25015i) q^{42} +(5.47734 - 5.47734i) q^{43} -7.02360 q^{44} -3.58432 q^{46} +(-3.69358 + 3.69358i) q^{47} +(-11.7792 - 3.48356i) q^{48} +1.00000i q^{49} +(-7.76331 + 4.21952i) q^{51} +(9.93435 + 9.93435i) q^{52} +(-2.83358 - 2.83358i) q^{53} +(13.1851 + 1.02033i) q^{54} -6.30497i q^{56} +(0.825420 - 2.79104i) q^{57} +(-16.0519 + 16.0519i) q^{58} +5.54871 q^{59} +7.40665 q^{61} +(4.94599 - 4.94599i) q^{62} +(0.626296 + 2.93390i) q^{63} -0.340400i q^{64} +(-3.30226 - 6.07568i) q^{66} +(3.75240 + 3.75240i) q^{67} +(16.1509 + 16.1509i) q^{68} +(-1.16488 - 2.14321i) q^{69} -3.61943i q^{71} +(-3.94878 - 18.4981i) q^{72} +(5.89737 - 5.89737i) q^{73} -1.58497 q^{74} -7.52372 q^{76} +(1.10924 - 1.10924i) q^{77} +(-3.92279 + 13.2644i) q^{78} +17.0572i q^{79} +(3.67497 + 8.21551i) q^{81} +(11.5949 + 11.5949i) q^{82} +(-3.21312 - 3.21312i) q^{83} +(6.81359 - 3.70333i) q^{84} -19.7144i q^{86} +(-14.8148 - 4.38132i) q^{87} +(-6.99372 + 6.99372i) q^{88} -9.40273 q^{89} -3.13787 q^{91} +(-4.45876 + 4.45876i) q^{92} +(4.56482 + 1.35000i) q^{93} +13.2941i q^{94} +(-8.27749 + 4.49899i) q^{96} +(-4.39640 - 4.39640i) q^{97} +(1.79963 + 1.79963i) q^{98} +(2.55968 - 3.94911i) 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 $

$2$	1.79963	−	1.79963i	1.27253	−	1.27253i	0.327775	−	0.944756i	$-0.393701\pi$
$2$	1.79963	−	1.79963i	1.27253	−	1.27253i	0.944756	−	0.327775i	$-0.106299\pi$
$3$	1.66094	+	0.491204i	0.958944	+	0.283597i
$3$	1.66094	+	0.491204i	0.958944	+	0.283597i
$4$		−	4.47734i		−	2.23867i
$5$		0			0
$5$		0			0
$6$	3.87306	−	2.10509i	1.58117	−	0.859399i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	−4.45829	−	4.45829i	−1.57624	−	1.57624i
$9$	2.51744	+	1.63172i	0.839146	+	0.543907i
$10$		0			0
$11$		−	1.56870i		−	0.472981i	−0.971634	−	0.236491i	$-0.924003\pi$
$11$		−	1.56870i		−	0.472981i	0.971634	−	0.236491i	$-0.0759973\pi$
$12$	2.19929	−	7.43658i	0.634880	−	2.14676i
$13$	−2.21881	+	2.21881i	−0.615386	+	0.615386i	−0.944345	−	0.328958i	$-0.893303\pi$
$13$	−2.21881	+	2.21881i	−0.615386	+	0.615386i	0.328958	+	0.944345i	$0.393303\pi$
$14$	2.54506			0.680196
$15$		0			0
$16$	−7.09187			−1.77297
$17$	−3.60725	+	3.60725i	−0.874886	+	0.874886i	−0.993000	−	0.118114i	$-0.962315\pi$
$17$	−3.60725	+	3.60725i	−0.874886	+	0.874886i	0.118114	+	0.993000i	$0.462315\pi$
$18$	7.46695	−	1.59396i	1.75998	−	0.375700i
$19$		−	1.68040i		−	0.385510i	−0.981247	−	0.192755i	$-0.938258\pi$
$19$		−	1.68040i		−	0.385510i	0.981247	−	0.192755i	$-0.0617423\pi$
$20$		0			0
$21$	0.827127	+	1.52180i	0.180494	+	0.332083i
$22$	−2.82308	−	2.82308i	−0.601883	−	0.601883i
$23$	−0.995850	−	0.995850i	−0.207649	−	0.207649i	0.595618	−	0.803268i	$-0.296907\pi$
$23$	−0.995850	−	0.995850i	−0.207649	−	0.207649i	−0.803268	+	0.595618i	$0.796907\pi$
$24$	−5.21502	−	9.59488i	−1.06451	−	1.95855i
$25$		0			0
$26$			7.98606i			1.56620i
$27$	3.37980	+	3.94676i	0.650443	+	0.759555i
$28$	3.16595	−	3.16595i	0.598309	−	0.598309i
$29$	−8.91955			−1.65632			−0.828159	−	0.560493i	$-0.810612\pi$
$29$	−8.91955			−1.65632			−0.828159	+	0.560493i	$0.810612\pi$
$30$		0			0
$31$	2.74834			0.493616			0.246808	−	0.969064i	$-0.420618\pi$
$31$	2.74834			0.493616			0.246808	+	0.969064i	$0.420618\pi$
$32$	−3.84616	+	3.84616i	−0.679912	+	0.679912i
$33$	0.770553	−	2.60552i	0.134136	−	0.453562i
$34$			12.9834i			2.22664i
$35$		0			0
$36$	7.30576	−	11.2714i	1.21763	−	1.87857i
$37$	−0.440360	−	0.440360i	−0.0723947	−	0.0723947i	0.669982	−	0.742377i	$-0.266302\pi$
$37$	−0.440360	−	0.440360i	−0.0723947	−	0.0723947i	−0.742377	+	0.669982i	$0.766302\pi$
$38$	−3.02410	−	3.02410i	−0.490574	−	0.490574i
$39$	−4.77519	+	2.59542i	−0.764643	+	0.415599i
$40$		0			0
$41$			6.44292i			1.00622i	0.864224	+	0.503108i	$0.167810\pi$
$41$			6.44292i			1.00622i	−0.864224	+	0.503108i	$0.832190\pi$
$42$	4.22719	+	1.25015i	0.652270	+	0.192902i
$43$	5.47734	−	5.47734i	0.835286	−	0.835286i	−0.152948	−	0.988234i	$-0.548877\pi$
$43$	5.47734	−	5.47734i	0.835286	−	0.835286i	0.988234	+	0.152948i	$0.0488768\pi$
$44$	−7.02360			−1.05885
$45$		0			0
$46$	−3.58432			−0.528480
$47$	−3.69358	+	3.69358i	−0.538763	+	0.538763i	−0.923166	−	0.384402i	$-0.874408\pi$
$47$	−3.69358	+	3.69358i	−0.538763	+	0.538763i	0.384402	+	0.923166i	$0.374408\pi$
$48$	−11.7792	−	3.48356i	−1.70018	−	0.502808i
$49$			1.00000i			0.142857i
$50$		0			0
$51$	−7.76331	+	4.21952i	−1.08708	+	0.590851i
$52$	9.93435	+	9.93435i	1.37765	+	1.37765i
$53$	−2.83358	−	2.83358i	−0.389222	−	0.389222i	0.485188	−	0.874410i	$-0.338751\pi$
$53$	−2.83358	−	2.83358i	−0.389222	−	0.389222i	−0.874410	+	0.485188i	$0.838751\pi$
$54$	13.1851	+	1.02033i	1.79427	+	0.138849i
$55$		0			0
$56$		−	6.30497i		−	0.842537i
$57$	0.825420	−	2.79104i	0.109330	−	0.369683i
$58$	−16.0519	+	16.0519i	−2.10772	+	2.10772i
$59$	5.54871			0.722381			0.361191	−	0.932492i	$-0.382370\pi$
$59$	5.54871			0.722381			0.361191	+	0.932492i	$0.382370\pi$
$60$		0			0
$61$	7.40665			0.948325			0.474162	−	0.880437i	$-0.342751\pi$
$61$	7.40665			0.948325			0.474162	+	0.880437i	$0.342751\pi$
$62$	4.94599	−	4.94599i	0.628141	−	0.628141i
$63$	0.626296	+	2.93390i	0.0789058	+	0.369636i
$64$		−	0.340400i		−	0.0425500i
$65$		0			0
$66$	−3.30226	−	6.07568i	−0.406480	−	0.747864i
$67$	3.75240	+	3.75240i	0.458429	+	0.458429i	0.898139	−	0.439711i	$-0.144919\pi$
$67$	3.75240	+	3.75240i	0.458429	+	0.458429i	−0.439711	+	0.898139i	$0.644919\pi$
$68$	16.1509	+	16.1509i	1.95858	+	1.95858i
$69$	−1.16488	−	2.14321i	−0.140235	−	0.258012i
$70$		0			0
$71$		−	3.61943i		−	0.429548i	−0.976664	−	0.214774i	$-0.931099\pi$
$71$		−	3.61943i		−	0.429548i	0.976664	−	0.214774i	$-0.0689015\pi$
$72$	−3.94878	−	18.4981i	−0.465368	−	2.18003i
$73$	5.89737	−	5.89737i	0.690235	−	0.690235i	−0.272049	−	0.962284i	$-0.587701\pi$
$73$	5.89737	−	5.89737i	0.690235	−	0.690235i	0.962284	+	0.272049i	$0.0877011\pi$
$74$	−1.58497			−0.184249
$75$		0			0
$76$	−7.52372			−0.863030
$77$	1.10924	−	1.10924i	0.126410	−	0.126410i
$78$	−3.92279	+	13.2644i	−0.444168	+	1.50189i
$79$			17.0572i			1.91909i	0.281558	+	0.959544i	$0.409149\pi$
$79$			17.0572i			1.91909i	−0.281558	+	0.959544i	$0.590851\pi$
$80$		0			0
$81$	3.67497	+	8.21551i	0.408330	+	0.912834i
$82$	11.5949	+	11.5949i	1.28044	+	1.28044i
$83$	−3.21312	−	3.21312i	−0.352686	−	0.352686i	0.508422	−	0.861108i	$-0.330229\pi$
$83$	−3.21312	−	3.21312i	−0.352686	−	0.352686i	−0.861108	+	0.508422i	$0.830229\pi$
$84$	6.81359	−	3.70333i	0.743423	−	0.404066i
$85$		0			0
$86$		−	19.7144i		−	2.12585i
$87$	−14.8148	−	4.38132i	−1.58832	−	0.469727i
$88$	−6.99372	+	6.99372i	−0.745533	+	0.745533i
$89$	−9.40273			−0.996688			−0.498344	−	0.866979i	$-0.666058\pi$
$89$	−9.40273			−0.996688			−0.498344	+	0.866979i	$0.666058\pi$
$90$		0			0
$91$	−3.13787			−0.328938
$92$	−4.45876	+	4.45876i	−0.464858	+	0.464858i
$93$	4.56482	+	1.35000i	0.473350	+	0.139988i
$94$			13.2941i			1.37119i
$95$		0			0
$96$	−8.27749	+	4.49899i	−0.844818	+	0.459176i
$97$	−4.39640	−	4.39640i	−0.446386	−	0.446386i	0.447765	−	0.894151i	$-0.352220\pi$
$97$	−4.39640	−	4.39640i	−0.446386	−	0.446386i	−0.894151	+	0.447765i	$0.852220\pi$
$98$	1.79963	+	1.79963i	0.181790	+	0.181790i
$99$	2.55968	−	3.94911i	0.257258	−	0.396900i
$100$		0			0
$101$			1.01132i			0.100630i	0.998733	+	0.0503152i	$0.0160226\pi$
$101$			1.01132i			0.100630i	−0.998733	+	0.0503152i	$0.983977\pi$
$102$	−6.37751	+	21.5647i	−0.631468	+	2.13522i
$103$	4.03058	−	4.03058i	0.397145	−	0.397145i	−0.480080	−	0.877225i	$-0.659392\pi$
$103$	4.03058	−	4.03058i	0.397145	−	0.397145i	0.877225	+	0.480080i	$0.159392\pi$
$104$	19.7842			1.94000
$105$		0			0
$106$	−10.1988			−0.990593
$107$	−2.81760	+	2.81760i	−0.272388	+	0.272388i	−0.830061	−	0.557673i	$-0.811694\pi$
$107$	−2.81760	+	2.81760i	−0.272388	+	0.272388i	0.557673	+	0.830061i	$0.311694\pi$
$108$	17.6710	−	15.1325i	1.70039	−	1.45613i
$109$		−	6.42246i		−	0.615160i	−0.951522	−	0.307580i	$-0.900481\pi$
$109$		−	6.42246i		−	0.615160i	0.951522	−	0.307580i	$-0.0995192\pi$
$110$		0			0
$111$	−0.515104	−	0.947718i	−0.0488915	−	0.0899534i
$112$	−5.01471	−	5.01471i	−0.473845	−	0.473845i
$113$	−3.29246	−	3.29246i	−0.309729	−	0.309729i	0.535075	−	0.844804i	$-0.320283\pi$
$113$	−3.29246	−	3.29246i	−0.309729	−	0.309729i	−0.844804	+	0.535075i	$0.820283\pi$
$114$	−3.53739	−	6.50830i	−0.331307	−	0.609558i
$115$		0			0
$116$			39.9358i			3.70795i
$117$	−9.20618	+	1.96523i	−0.851112	+	0.181686i
$118$	9.98563	−	9.98563i	0.919252	−	0.919252i
$119$	−5.10142			−0.467646
$120$		0			0
$121$	8.53918			0.776289
$122$	13.3292	−	13.3292i	1.20677	−	1.20677i
$123$	−3.16479	+	10.7013i	−0.285360	+	0.964904i
$124$		−	12.3052i		−	1.10504i
$125$		0			0
$126$	6.40703	+	4.15283i	0.570784	+	0.369963i
$127$	−14.2818	−	14.2818i	−1.26730	−	1.26730i	−0.947476	−	0.319826i	$-0.896376\pi$
$127$	−14.2818	−	14.2818i	−1.26730	−	1.26730i	−0.319826	−	0.947476i	$-0.603624\pi$
$128$	−8.30492	−	8.30492i	−0.734058	−	0.734058i
$129$	11.7880	−	6.40703i	1.03788	−	0.564108i
$130$		0			0
$131$		−	4.89729i		−	0.427878i	−0.976847	−	0.213939i	$-0.931371\pi$
$131$		−	4.89729i		−	0.427878i	0.976847	−	0.213939i	$-0.0686294\pi$
$132$	−11.6658	−	3.45002i	−1.01538	−	0.300286i
$133$	1.18822	−	1.18822i	0.103032	−	0.103032i
$134$	13.5059			1.16673
$135$		0			0
$136$	32.1643			2.75807
$137$	4.55880	−	4.55880i	0.389485	−	0.389485i	−0.485019	−	0.874504i	$-0.661187\pi$
$137$	4.55880	−	4.55880i	0.389485	−	0.389485i	0.874504	+	0.485019i	$0.161187\pi$
$138$	−5.95334	−	1.76064i	−0.506782	−	0.149875i
$139$		−	10.2045i		−	0.865536i	−0.901505	−	0.432768i	$-0.857537\pi$
$139$		−	10.2045i		−	0.865536i	0.901505	−	0.432768i	$-0.142463\pi$
$140$		0			0
$141$	−7.94911	+	4.32050i	−0.669435	+	0.363852i
$142$	−6.51364	−	6.51364i	−0.546613	−	0.546613i
$143$	3.48065	+	3.48065i	0.291066	+	0.291066i
$144$	−17.8533	−	11.5720i	−1.48778	−	0.964329i
$145$		0			0
$146$		−	21.2262i		−	1.75669i
$147$	−0.491204	+	1.66094i	−0.0405139	+	0.136992i
$148$	−1.97164	+	1.97164i	−0.162068	+	0.162068i
$149$	−0.923124			−0.0756253			−0.0378126	−	0.999285i	$-0.512039\pi$
$149$	−0.923124			−0.0756253			−0.0378126	+	0.999285i	$0.512039\pi$
$150$		0			0
$151$	−13.7310			−1.11741			−0.558705	−	0.829366i	$-0.688702\pi$
$151$	−13.7310			−1.11741			−0.558705	+	0.829366i	$0.688702\pi$
$152$	−7.49171	+	7.49171i	−0.607658	+	0.607658i
$153$	−14.9670	+	3.19499i	−1.21001	+	0.258300i
$154$		−	3.99244i		−	0.321720i
$155$		0			0
$156$	11.6205	+	21.3801i	0.930389	+	1.71178i
$157$	13.7211	+	13.7211i	1.09506	+	1.09506i	0.994979	+	0.100086i	$0.0319118\pi$
$157$	13.7211	+	13.7211i	1.09506	+	1.09506i	0.100086	+	0.994979i	$0.468088\pi$
$158$	30.6967	+	30.6967i	2.44210	+	2.44210i
$159$	−3.31453	−	6.09826i	−0.262859	−	0.483624i
$160$		0			0
$161$		−	1.40834i		−	0.110993i
$162$	21.3985	+	8.17128i	1.68122	+	0.641997i
$163$	−6.60566	+	6.60566i	−0.517395	+	0.517395i	−0.916782	−	0.399387i	$-0.869223\pi$
$163$	−6.60566	+	6.60566i	−0.517395	+	0.517395i	0.399387	+	0.916782i	$0.369223\pi$
$164$	28.8471			2.25258
$165$		0			0
$166$	−11.5649			−0.897607
$167$	3.11442	−	3.11442i	0.241001	−	0.241001i	−0.576263	−	0.817264i	$-0.695490\pi$
$167$	3.11442	−	3.11442i	0.241001	−	0.241001i	0.817264	+	0.576263i	$0.195490\pi$
$168$	3.09703	−	10.4722i	0.238941	−	0.807946i
$169$			3.15379i			0.242599i
$170$		0			0
$171$	2.74195	−	4.23030i	0.209682	−	0.323499i
$172$	−24.5239	−	24.5239i	−1.86993	−	1.86993i
$173$	−8.12870	−	8.12870i	−0.618013	−	0.618013i	0.327008	−	0.945022i	$-0.393960\pi$
$173$	−8.12870	−	8.12870i	−0.618013	−	0.618013i	−0.945022	+	0.327008i	$0.893960\pi$
$174$	−34.5460	+	18.7764i	−2.61892	+	1.42344i
$175$		0			0
$176$			11.1250i			0.838580i
$177$	9.21608	+	2.72555i	0.692723	+	0.204865i
$178$	−16.9214	+	16.9214i	−1.26832	+	1.26832i
$179$	16.5980			1.24059			0.620297	−	0.784367i	$-0.287012\pi$
$179$	16.5980			1.24059			0.620297	+	0.784367i	$0.287012\pi$
$180$		0			0
$181$	11.6532			0.866174			0.433087	−	0.901352i	$-0.357424\pi$
$181$	11.6532			0.866174			0.433087	+	0.901352i	$0.357424\pi$
$182$	−5.64700	+	5.64700i	−0.418583	+	0.418583i
$183$	12.3020	+	3.63818i	0.909390	+	0.268942i
$184$			8.87958i			0.654611i
$185$		0			0
$186$	10.6445	−	5.78550i	0.780491	−	0.424213i
$187$	5.65869	+	5.65869i	0.413805	+	0.413805i
$188$	16.5374	+	16.5374i	1.20611	+	1.20611i
$189$	−0.400905	+	5.18066i	−0.0291615	+	0.376838i
$190$		0			0
$191$			12.8543i			0.930108i	0.885282	+	0.465054i	$0.153965\pi$
$191$			12.8543i			0.930108i	−0.885282	+	0.465054i	$0.846035\pi$
$192$	0.167206	−	0.565384i	0.0120671	−	0.0408031i
$193$	8.06158	−	8.06158i	0.580285	−	0.580285i	−0.354696	−	0.934982i	$-0.615416\pi$
$193$	8.06158	−	8.06158i	0.580285	−	0.580285i	0.934982	+	0.354696i	$0.115416\pi$
$194$	−15.8238			−1.13608
$195$		0			0
$196$	4.47734			0.319810
$197$	18.7512	−	18.7512i	1.33597	−	1.33597i	0.436036	−	0.899929i	$-0.356382\pi$
$197$	18.7512	−	18.7512i	1.33597	−	1.33597i	0.899929	−	0.436036i	$-0.143618\pi$
$198$	−2.50045	−	11.7134i	−0.177699	−	0.832436i
$199$		−	4.20728i		−	0.298246i	−0.988819	−	0.149123i	$-0.952355\pi$
$199$		−	4.20728i		−	0.298246i	0.988819	−	0.149123i	$-0.0476451\pi$
$200$		0			0
$201$	4.38931	+	8.07570i	0.309598	+	0.569616i
$202$	1.82001	+	1.82001i	0.128055	+	0.128055i
$203$	−6.30707	−	6.30707i	−0.442670	−	0.442670i
$204$	18.8922	+	34.7590i	1.32272	+	2.43361i
$205$		0			0
$206$		−	14.5071i		−	1.01076i
$207$	−0.882040	−	4.13194i	−0.0613060	−	0.287190i
$208$	15.7355	−	15.7355i	1.09106	−	1.09106i
$209$	−2.63605			−0.182339
$210$		0			0
$211$	−21.5211			−1.48158			−0.740788	−	0.671739i	$-0.765548\pi$
$211$	−21.5211			−1.48158			−0.740788	+	0.671739i	$0.765548\pi$
$212$	−12.6869	+	12.6869i	−0.871338	+	0.871338i
$213$	1.77788	−	6.01166i	0.121818	−	0.411912i
$214$			10.1413i			0.693244i
$215$		0			0
$216$	2.52769	−	32.6639i	0.171988	−	2.22250i
$217$	1.94337	+	1.94337i	0.131924	+	0.131924i
$218$	−11.5581	−	11.5581i	−0.782810	−	0.782810i
$219$	12.6920	−	6.89836i	0.857645	−	0.466148i
$220$		0			0
$221$		−	16.0076i		−	1.07679i
$222$	−2.63254	−	0.778544i	−0.176684	−	0.0522525i
$223$	−12.4001	+	12.4001i	−0.830375	+	0.830375i	−0.987568	−	0.157193i	$-0.949756\pi$
$223$	−12.4001	+	12.4001i	−0.830375	+	0.830375i	0.157193	+	0.987568i	$0.449756\pi$
$224$	−5.43929			−0.363428
$225$		0			0
$226$	−11.8504			−0.788279
$227$	8.70556	−	8.70556i	0.577809	−	0.577809i	−0.356490	−	0.934299i	$-0.616027\pi$
$227$	8.70556	−	8.70556i	0.577809	−	0.577809i	0.934299	+	0.356490i	$0.116027\pi$
$228$	−12.4964	−	3.69568i	−0.827597	−	0.244753i
$229$		−	4.46342i		−	0.294951i	−0.989066	−	0.147476i	$-0.952885\pi$
$229$		−	4.46342i		−	0.294951i	0.989066	−	0.147476i	$-0.0471148\pi$
$230$		0			0
$231$	2.38724	−	1.29752i	0.157069	−	0.0853703i
$232$	39.7659	+	39.7659i	2.61076	+	2.61076i
$233$	5.64161	+	5.64161i	0.369594	+	0.369594i	0.867329	−	0.497735i	$-0.165835\pi$
$233$	5.64161	+	5.64161i	0.369594	+	0.369594i	−0.497735	+	0.867329i	$0.665835\pi$
$234$	−13.0310	+	20.1044i	−0.851865	+	1.31427i
$235$		0			0
$236$		−	24.8435i		−	1.61717i
$237$	−8.37859	+	28.3310i	−0.544248	+	1.84030i
$238$	−9.18066	+	9.18066i	−0.595094	+	0.595094i
$239$	11.8594			0.767124			0.383562	−	0.923515i	$-0.374697\pi$
$239$	11.8594			0.767124			0.383562	+	0.923515i	$0.374697\pi$
$240$		0			0
$241$	−18.0723			−1.16414			−0.582071	−	0.813138i	$-0.697757\pi$
$241$	−18.0723			−1.16414			−0.582071	+	0.813138i	$0.697757\pi$
$242$	15.3674	−	15.3674i	0.987851	−	0.987851i
$243$	2.06841	+	15.4506i	0.132689	+	0.991158i
$244$		−	33.1621i		−	2.12298i
$245$		0			0
$246$	13.5629	+	24.9538i	0.864741	+	1.59100i
$247$	3.72849	+	3.72849i	0.237238	+	0.237238i
$248$	−12.2529	−	12.2529i	−0.778059	−	0.778059i
$249$	−3.75850	−	6.91510i	−0.238185	−	0.438226i
$250$		0			0
$251$		−	3.19253i		−	0.201511i	−0.994911	−	0.100755i	$-0.967874\pi$
$251$		−	3.19253i		−	0.201511i	0.994911	−	0.100755i	$-0.0321259\pi$
$252$	13.1360	−	2.80414i	0.827493	−	0.176644i
$253$	−1.56219	+	1.56219i	−0.0982141	+	0.0982141i
$254$	−51.4038			−3.22536
$255$		0			0
$256$	−29.2108			−1.82567
$257$	−11.8118	+	11.8118i	−0.736799	+	0.736799i	−0.971957	−	0.235158i	$-0.924439\pi$
$257$	−11.8118	+	11.8118i	−0.736799	+	0.736799i	0.235158	+	0.971957i	$0.424439\pi$
$258$	9.68378	−	32.7443i	0.602886	−	2.03857i
$259$		−	0.622763i		−	0.0386966i
$260$		0			0
$261$	−22.4544	−	14.5542i	−1.38989	−	0.900883i
$262$	−8.81331	−	8.81331i	−0.544488	−	0.544488i
$263$	−13.1502	−	13.1502i	−0.810874	−	0.810874i	0.173891	−	0.984765i	$-0.444366\pi$
$263$	−13.1502	−	13.1502i	−0.810874	−	0.810874i	−0.984765	+	0.173891i	$0.944366\pi$
$264$	−15.0515	+	8.18080i	−0.926356	+	0.503493i
$265$		0			0
$266$		−	4.27672i		−	0.262223i
$267$	−15.6174	−	4.61866i	−0.955767	−	0.282658i
$268$	16.8008	−	16.8008i	1.02627	−	1.02627i
$269$	−29.3405			−1.78892			−0.894461	−	0.447146i	$-0.852441\pi$
$269$	−29.3405			−1.78892			−0.894461	+	0.447146i	$0.852441\pi$
$270$		0			0
$271$	3.18366			0.193394			0.0966968	−	0.995314i	$-0.469172\pi$
$271$	3.18366			0.193394			0.0966968	+	0.995314i	$0.469172\pi$
$272$	25.5821	−	25.5821i	1.55114	−	1.55114i
$273$	−5.21181	−	1.54133i	−0.315433	−	0.0932858i
$274$		−	16.4083i		−	0.991263i
$275$		0			0
$276$	−9.59588	+	5.21556i	−0.577604	+	0.313940i
$277$	−16.8636	−	16.8636i	−1.01324	−	1.01324i	−0.999911	−	0.0133247i	$-0.995758\pi$
$277$	−16.8636	−	16.8636i	−1.01324	−	1.01324i	−0.0133247	−	0.999911i	$-0.504242\pi$
$278$	−18.3644	−	18.3644i	−1.10142	−	1.10142i
$279$	6.91877	+	4.48452i	0.414216	+	0.268481i
$280$		0			0
$281$		−	24.8052i		−	1.47975i	−0.672742	−	0.739877i	$-0.734884\pi$
$281$		−	24.8052i		−	1.47975i	0.672742	−	0.739877i	$-0.265116\pi$
$282$	−6.53014	+	22.0808i	−0.388864	+	1.31489i
$283$	−5.41918	+	5.41918i	−0.322137	+	0.322137i	−0.849586	−	0.527449i	$-0.823148\pi$
$283$	−5.41918	+	5.41918i	−0.322137	+	0.322137i	0.527449	+	0.849586i	$0.323148\pi$
$284$	−16.2054			−0.961615
$285$		0			0
$286$	12.5277			0.740781
$287$	−4.55583	+	4.55583i	−0.268922	+	0.268922i
$288$	−15.9583	+	3.40661i	−0.940354	+	0.200736i
$289$		−	9.02446i		−	0.530850i
$290$		0			0
$291$	−5.14262	−	9.46168i	−0.301466	−	0.554653i
$292$	−26.4045	−	26.4045i	−1.54521	−	1.54521i
$293$	−8.60739	−	8.60739i	−0.502849	−	0.502849i	0.409473	−	0.912322i	$-0.365712\pi$
$293$	−8.60739	−	8.60739i	−0.502849	−	0.502849i	−0.912322	+	0.409473i	$0.865712\pi$
$294$	2.10509	+	3.87306i	0.122771	+	0.225882i
$295$		0			0
$296$			3.92650i			0.228223i
$297$	6.19129	−	5.30190i	0.359255	−	0.307647i
$298$	−1.66128	+	1.66128i	−0.0962355	+	0.0962355i
$299$	4.41920			0.255569
$300$		0			0
$301$	7.74612			0.446479
$302$	−24.7107	+	24.7107i	−1.42194	+	1.42194i
$303$	−0.496766	+	1.67975i	−0.0285385	+	0.0964989i
$304$			11.9172i			0.683497i
$305$		0			0
$306$	−21.1853	+	32.6849i	−1.21108	+	1.86847i
$307$	11.8525	+	11.8525i	0.676457	+	0.676457i	0.959197	−	0.282740i	$-0.0912434\pi$
$307$	11.8525	+	11.8525i	0.676457	+	0.676457i	−0.282740	+	0.959197i	$0.591243\pi$
$308$	−4.96644	−	4.96644i	−0.282989	−	0.282989i
$309$	8.67440	−	4.71471i	0.493469	−	0.268211i
$310$		0			0
$311$			29.2800i			1.66032i	0.557528	+	0.830158i	$0.311750\pi$
$311$			29.2800i			1.66032i	−0.557528	+	0.830158i	$0.688250\pi$
$312$	32.8603	+	9.71807i	1.86035	+	0.550177i
$313$	−1.22577	+	1.22577i	−0.0692848	+	0.0692848i	−0.740900	−	0.671615i	$-0.765601\pi$
$313$	−1.22577	+	1.22577i	−0.0692848	+	0.0692848i	0.671615	+	0.740900i	$0.265601\pi$
$314$	49.3859			2.78701
$315$		0			0
$316$	76.3710			4.29620
$317$	4.30159	−	4.30159i	0.241601	−	0.241601i	−0.575911	−	0.817512i	$-0.695353\pi$
$317$	4.30159	−	4.30159i	0.241601	−	0.241601i	0.817512	+	0.575911i	$0.195353\pi$
$318$	−16.9395	−	5.00968i	−0.949922	−	0.280929i
$319$			13.9921i			0.783408i
$320$		0			0
$321$	−6.06388	+	3.29585i	−0.338453	+	0.183956i
$322$	−2.53450	−	2.53450i	−0.141242	−	0.141242i
$323$	6.06162	+	6.06162i	0.337278	+	0.337278i
$324$	36.7836	−	16.4541i	2.04353	−	0.914116i
$325$		0			0
$326$			23.7755i			1.31680i
$327$	3.15474	−	10.6673i	0.174458	−	0.589904i
$328$	28.7244	−	28.7244i	1.58604	−	1.58604i
$329$	−5.22351			−0.287981
$330$		0			0
$331$	33.2602			1.82815			0.914074	−	0.405548i	$-0.132919\pi$
$331$	33.2602			1.82815			0.914074	+	0.405548i	$0.132919\pi$
$332$	−14.3862	+	14.3862i	−0.789547	+	0.789547i
$333$	−0.390034	−	1.82712i	−0.0213737	−	0.100126i
$334$		−	11.2096i		−	0.613363i
$335$		0			0
$336$	−5.86588	−	10.7924i	−0.320010	−	0.588772i
$337$	−10.3056	−	10.3056i	−0.561383	−	0.561383i	0.368317	−	0.929700i	$-0.379934\pi$
$337$	−10.3056	−	10.3056i	−0.561383	−	0.561383i	−0.929700	+	0.368317i	$0.879934\pi$
$338$	5.67565	+	5.67565i	0.308715	+	0.308715i
$339$	−3.85131	−	7.08585i	−0.209174	−	0.384851i
$340$		0			0
$341$		−	4.31132i		−	0.233471i
$342$	−2.67849	−	12.5475i	−0.144836	−	0.678489i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−48.8391			−2.63323
$345$		0			0
$346$	−29.2573			−1.57288
$347$	−19.2241	+	19.2241i	−1.03200	+	1.03200i	−0.0325323	+	0.999471i	$0.510357\pi$
$347$	−19.2241	+	19.2241i	−1.03200	+	1.03200i	−0.999471	+	0.0325323i	$0.989643\pi$
$348$	−19.6166	+	66.3310i	−1.05156	+	3.55571i
$349$			30.1301i			1.61283i	0.591353	+	0.806413i	$0.298594\pi$
$349$			30.1301i			1.61283i	−0.591353	+	0.806413i	$0.701406\pi$
$350$		0			0
$351$	−16.2562	−	1.25799i	−0.867694	−	0.0671463i
$352$	6.03348	+	6.03348i	0.321586	+	0.321586i
$353$	17.0339	+	17.0339i	0.906625	+	0.906625i	0.995998	−	0.0893729i	$-0.0284863\pi$
$353$	17.0339	+	17.0339i	0.906625	+	0.906625i	−0.0893729	+	0.995998i	$0.528486\pi$
$354$	21.4905	−	11.6805i	1.14221	−	0.620814i
$355$		0			0
$356$			42.0992i			2.23125i
$357$	−8.47314	−	2.50584i	−0.448446	−	0.132623i
$358$	29.8703	−	29.8703i	1.57869	−	1.57869i
$359$	0.737982			0.0389492			0.0194746	−	0.999810i	$-0.493801\pi$
$359$	0.737982			0.0389492			0.0194746	+	0.999810i	$0.493801\pi$
$360$		0			0
$361$	16.1763			0.851382
$362$	20.9714	−	20.9714i	1.10223	−	1.10223i
$363$	14.1831	+	4.19448i	0.744417	+	0.220153i
$364$			14.0493i			0.736383i
$365$		0			0
$366$	28.6864	−	15.5917i	1.49946	−	0.814990i
$367$	−23.2923	−	23.2923i	−1.21585	−	1.21585i	−0.969073	−	0.246776i	$-0.920629\pi$
$367$	−23.2923	−	23.2923i	−1.21585	−	1.21585i	−0.246776	−	0.969073i	$-0.579371\pi$
$368$	7.06244	+	7.06244i	0.368155	+	0.368155i
$369$	−10.5131	+	16.2196i	−0.547288	+	0.844361i
$370$		0			0
$371$		−	4.00728i		−	0.208048i
$372$	6.04438	−	20.4382i	0.313387	−	1.05967i
$373$	5.28110	−	5.28110i	0.273445	−	0.273445i	−0.557040	−	0.830485i	$-0.688063\pi$
$373$	5.28110	−	5.28110i	0.273445	−	0.273445i	0.830485	+	0.557040i	$0.188063\pi$
$374$	20.3671			1.05316
$375$		0			0
$376$	32.9341			1.69844
$377$	19.7908	−	19.7908i	1.01928	−	1.01928i
$378$	8.60180	+	10.0448i	0.442429	+	0.516647i
$379$			3.38353i			0.173800i	0.996217	+	0.0869000i	$0.0276961\pi$
$379$			3.38353i			0.173800i	−0.996217	+	0.0869000i	$0.972304\pi$
$380$		0			0
$381$	−16.7059	−	30.7364i	−0.855868	−	1.57467i
$382$	23.1331	+	23.1331i	1.18359	+	1.18359i
$383$	−2.86741	−	2.86741i	−0.146518	−	0.146518i	0.630043	−	0.776561i	$-0.283037\pi$
$383$	−2.86741	−	2.86741i	−0.146518	−	0.146518i	−0.776561	+	0.630043i	$0.783037\pi$
$384$	−9.71455	−	17.8734i	−0.495744	−	0.912097i
$385$		0			0
$386$		−	29.0157i		−	1.47686i
$387$	22.7263	−	4.85136i	1.15524	−	0.246609i
$388$	−19.6841	+	19.6841i	−0.999311	+	0.999311i
$389$	−10.2102			−0.517675			−0.258838	−	0.965921i	$-0.583339\pi$
$389$	−10.2102			−0.517675			−0.258838	+	0.965921i	$0.583339\pi$
$390$		0			0
$391$	7.18455			0.363339
$392$	4.45829	−	4.45829i	0.225178	−	0.225178i
$393$	2.40557	−	8.13410i	0.121345	−	0.410311i
$394$		−	67.4903i		−	3.40011i
$395$		0			0
$396$	−17.6815	−	11.4606i	−0.888528	−	0.575915i
$397$	24.0534	+	24.0534i	1.20721	+	1.20721i	0.971928	+	0.235280i	$0.0756009\pi$
$397$	24.0534	+	24.0534i	1.20721	+	1.20721i	0.235280	+	0.971928i	$0.424399\pi$
$398$	−7.57156	−	7.57156i	−0.379528	−	0.379528i
$399$	2.55723	−	1.38991i	0.128021	−	0.0695823i
$400$		0			0
$401$			20.0912i			1.00331i	0.865068	+	0.501654i	$0.167275\pi$
$401$			20.0912i			1.00331i	−0.865068	+	0.501654i	$0.832725\pi$
$402$	22.4324	+	6.63414i	1.11883	+	0.330881i
$403$	−6.09803	+	6.09803i	−0.303765	+	0.303765i
$404$	4.52803			0.225278
$405$		0			0
$406$	−22.7008			−1.12662
$407$	−0.690793	+	0.690793i	−0.0342413	+	0.0342413i
$408$	53.4229	+	15.7992i	2.64483	+	0.782179i
$409$		−	33.5102i		−	1.65697i	−0.560008	−	0.828487i	$-0.689202\pi$
$409$		−	33.5102i		−	1.65697i	0.560008	−	0.828487i	$-0.310798\pi$
$410$		0			0
$411$	9.81120	−	5.33259i	0.483951	−	0.263037i
$412$	−18.0463	−	18.0463i	−0.889077	−	0.889077i
$413$	3.92353	+	3.92353i	0.193064	+	0.193064i
$414$	−9.02331	−	5.84862i	−0.443471	−	0.287444i
$415$		0			0
$416$		−	17.0678i		−	0.836817i
$417$	5.01251	−	16.9491i	0.245463	−	0.830000i
$418$	−4.74391	+	4.74391i	−0.232032	+	0.232032i
$419$	25.8773			1.26419			0.632093	−	0.774892i	$-0.282196\pi$
$419$	25.8773			1.26419			0.632093	+	0.774892i	$0.282196\pi$
$420$		0			0
$421$	10.4030			0.507013			0.253507	−	0.967334i	$-0.418416\pi$
$421$	10.4030			0.507013			0.253507	+	0.967334i	$0.418416\pi$
$422$	−38.7301	+	38.7301i	−1.88535	+	1.88535i
$423$	−15.3252	+	3.27146i	−0.745138	+	0.159064i
$424$			25.2658i			1.22702i
$425$		0			0
$426$	−7.61923	−	14.0183i	−0.369153	−	0.679188i
$427$	5.23730	+	5.23730i	0.253450	+	0.253450i
$428$	12.6154	+	12.6154i	0.609786	+	0.609786i
$429$	4.07143	+	7.49085i	0.196571	+	0.361662i
$430$		0			0
$431$		−	0.449005i		−	0.0216278i	−0.999942	−	0.0108139i	$-0.996558\pi$
$431$		−	0.449005i		−	0.0216278i	0.999942	−	0.0108139i	$-0.00344224\pi$
$432$	−23.9691	−	27.9899i	−1.15321	−	1.34667i
$433$	17.7813	−	17.7813i	0.854517	−	0.854517i	−0.136169	−	0.990686i	$-0.543479\pi$
$433$	17.7813	−	17.7813i	0.854517	−	0.854517i	0.990686	+	0.136169i	$0.0434790\pi$
$434$	6.99469			0.335756
$435$		0			0
$436$	−28.7555			−1.37714
$437$	−1.67343	+	1.67343i	−0.0800509	+	0.0800509i
$438$	10.4264	−	35.2554i	0.498192	−	1.68457i
$439$			29.5293i			1.40936i	0.709526	+	0.704679i	$0.248909\pi$
$439$			29.5293i			1.40936i	−0.709526	+	0.704679i	$0.751091\pi$
$440$		0			0
$441$	−1.63172	+	2.51744i	−0.0777010	+	0.119878i
$442$	−28.8077	−	28.8077i	−1.37024	−	1.37024i
$443$	15.5643	+	15.5643i	0.739483	+	0.739483i	0.972478	−	0.232995i	$-0.0748525\pi$
$443$	15.5643	+	15.5643i	0.739483	+	0.739483i	−0.232995	+	0.972478i	$0.574853\pi$
$444$	−4.24325	+	2.30630i	−0.201376	+	0.109452i
$445$		0			0
$446$			44.6313i			2.11336i
$447$	−1.53325	−	0.453443i	−0.0725204	−	0.0214471i
$448$	0.240699	−	0.240699i	0.0113720	−	0.0113720i
$449$	16.3214			0.770252			0.385126	−	0.922864i	$-0.374158\pi$
$449$	16.3214			0.770252			0.385126	+	0.922864i	$0.374158\pi$
$450$		0			0
$451$	10.1070			0.475921
$452$	−14.7415	+	14.7415i	−0.693380	+	0.693380i
$453$	−22.8063	−	6.74471i	−1.07153	−	0.316894i
$454$		−	31.3336i		−	1.47056i
$455$		0			0
$456$	−16.1232	+	8.76332i	−0.755040	+	0.410380i
$457$	20.6299	+	20.6299i	0.965028	+	0.965028i	0.999409	−	0.0343811i	$-0.0109460\pi$
$457$	20.6299	+	20.6299i	0.965028	+	0.965028i	−0.0343811	+	0.999409i	$0.510946\pi$
$458$	−8.03251	−	8.03251i	−0.375335	−	0.375335i
$459$	−26.4287	−	2.04518i	−1.23359	−	0.0954609i
$460$		0			0
$461$			15.2893i			0.712094i	0.934468	+	0.356047i	$0.115876\pi$
$461$			15.2893i			0.712094i	−0.934468	+	0.356047i	$0.884124\pi$
$462$	1.96110	−	6.63120i	0.0912388	−	0.308511i
$463$	−0.492195	+	0.492195i	−0.0228743	+	0.0228743i	−0.718451	−	0.695577i	$-0.755149\pi$
$463$	−0.492195	+	0.492195i	−0.0228743	+	0.0228743i	0.695577	+	0.718451i	$0.255149\pi$
$464$	63.2563			2.93660
$465$		0			0
$466$	20.3056			0.940640
$467$	9.00044	−	9.00044i	0.416491	−	0.416491i	−0.467501	−	0.883992i	$-0.654846\pi$
$467$	9.00044	−	9.00044i	0.416491	−	0.416491i	0.883992	+	0.467501i	$0.154846\pi$
$468$	8.79901	+	41.2192i	0.406734	+	1.90536i
$469$			5.30669i			0.245040i
$470$		0			0
$471$	16.0501	+	29.5298i	0.739548	+	1.36066i
$472$	−24.7378	−	24.7378i	−1.13865	−	1.13865i
$473$	−8.59230	−	8.59230i	−0.395075	−	0.395075i
$474$	35.9070	+	66.0637i	1.64926	+	3.03441i
$475$		0			0
$476$			22.8408i			1.04690i
$477$	−2.50974	−	11.7570i	−0.114913	−	0.538314i
$478$	21.3426	−	21.3426i	0.976188	−	0.976188i
$479$	−22.7572			−1.03980			−0.519901	−	0.854226i	$-0.674031\pi$
$479$	−22.7572			−1.03980			−0.519901	+	0.854226i	$0.674031\pi$
$480$		0			0
$481$	1.95415			0.0891015
$482$	−32.5235	+	32.5235i	−1.48141	+	1.48141i
$483$	0.691785	−	2.33917i	0.0314773	−	0.106436i
$484$		−	38.2328i		−	1.73785i
$485$		0			0
$486$	31.5278	+	24.0830i	1.43013	+	1.09243i
$487$	11.4919	+	11.4919i	0.520746	+	0.520746i	0.917797	−	0.397051i	$-0.129966\pi$
$487$	11.4919	+	11.4919i	0.520746	+	0.520746i	−0.397051	+	0.917797i	$0.629966\pi$
$488$	−33.0210	−	33.0210i	−1.49479	−	1.49479i
$489$	−14.2163	+	7.72687i	−0.642884	+	0.349421i
$490$		0			0
$491$			0.301729i			0.0136168i	0.999977	+	0.00680841i	$0.00216720\pi$
$491$			0.301729i			0.0136168i	−0.999977	+	0.00680841i	$0.997833\pi$
$492$	47.9133	+	14.1698i	2.16010	+	0.638826i
$493$	32.1750	−	32.1750i	1.44909	−	1.44909i
$494$	13.4198			0.603785
$495$		0			0
$496$	−19.4909			−0.875165
$497$	2.55933	−	2.55933i	0.114801	−	0.114801i
$498$	−19.2085	−	5.68071i	−0.860754	−	0.254559i
$499$			20.2207i			0.905202i	0.891713	+	0.452601i	$0.149504\pi$
$499$			20.2207i			0.905202i	−0.891713	+	0.452601i	$0.850496\pi$
$500$		0			0
$501$	6.70268	−	3.64305i	0.299454	−	0.162759i
$502$	−5.74537	−	5.74537i	−0.256428	−	0.256428i
$503$	23.8859	+	23.8859i	1.06502	+	1.06502i	0.997734	+	0.0672882i	$0.0214347\pi$
$503$	23.8859	+	23.8859i	1.06502	+	1.06502i	0.0672882	+	0.997734i	$0.478565\pi$
$504$	10.2880	−	15.8724i	0.458262	−	0.707012i
$505$		0			0
$506$			5.62273i			0.249961i
$507$	−1.54915	+	5.23825i	−0.0688004	+	0.232639i
$508$	−63.9443	+	63.9443i	−2.83707	+	2.83707i
$509$	−11.7721			−0.521788			−0.260894	−	0.965368i	$-0.584017\pi$
$509$	−11.7721			−0.521788			−0.260894	+	0.965368i	$0.584017\pi$
$510$		0			0
$511$	8.34014			0.368946
$512$	−35.9587	+	35.9587i	−1.58917	+	1.58917i
$513$	6.63215	−	5.67942i	0.292816	−	0.250752i
$514$			42.5137i			1.87520i
$515$		0			0
$516$	−28.6864	−	52.7789i	−1.26285	−	2.32346i
$517$	5.79412	+	5.79412i	0.254825	+	0.254825i
$518$	−1.12074	−	1.12074i	−0.0492426	−	0.0492426i
$519$	−9.50842	−	17.4941i	−0.417373	−	0.767907i
$520$		0			0
$521$		−	29.7872i		−	1.30500i	−0.757789	−	0.652500i	$-0.773720\pi$
$521$		−	29.7872i		−	1.30500i	0.757789	−	0.652500i	$-0.226280\pi$
$522$	−66.6018	+	14.2174i	−2.91508	+	0.622279i
$523$	−17.4673	+	17.4673i	−0.763792	+	0.763792i	−0.977006	−	0.213214i	$-0.931607\pi$
$523$	−17.4673	+	17.4673i	−0.763792	+	0.763792i	0.213214	+	0.977006i	$0.431607\pi$
$524$	−21.9268			−0.957877
$525$		0			0
$526$	−47.3309			−2.06373
$527$	−9.91393	+	9.91393i	−0.431858	+	0.431858i
$528$	−5.46466	+	18.4780i	−0.237819	+	0.804151i
$529$		−	21.0166i		−	0.913764i
$530$		0			0
$531$	13.9685	+	9.05395i	0.606183	+	0.392908i
$532$	−5.32007	−	5.32007i	−0.230654	−	0.230654i
$533$	−14.2956	−	14.2956i	−0.619211	−	0.619211i
$534$	−36.4174	+	19.7936i	−1.57593	+	0.856553i
$535$		0			0
$536$		−	33.4586i		−	1.44519i
$537$	27.5683	+	8.15302i	1.18966	+	0.351829i
$538$	−52.8021	+	52.8021i	−2.27646	+	2.27646i
$539$	1.56870			0.0675687
$540$		0			0
$541$	−23.1117			−0.993650			−0.496825	−	0.867851i	$-0.665501\pi$
$541$	−23.1117			−0.993650			−0.496825	+	0.867851i	$0.665501\pi$
$542$	5.72941	−	5.72941i	0.246099	−	0.246099i
$543$	19.3552	+	5.72409i	0.830612	+	0.245644i
$544$		−	27.7481i		−	1.18969i
$545$		0			0
$546$	−12.1532	+	6.60549i	−0.520107	+	0.282689i
$547$	25.6689	+	25.6689i	1.09752	+	1.09752i	0.994700	+	0.102823i	$0.0327874\pi$
$547$	25.6689	+	25.6689i	1.09752	+	1.09752i	0.102823	+	0.994700i	$0.467213\pi$
$548$	−20.4113	−	20.4113i	−0.871928	−	0.871928i
$549$	18.6458	+	12.0856i	0.795783	+	0.515801i
$550$		0			0
$551$			14.9884i			0.638528i
$552$	−4.36169	+	14.7484i	−0.185646	+	0.627735i
$553$	−12.0613	+	12.0613i	−0.512898	+	0.512898i
$554$	−60.6965			−2.57875
$555$		0			0
$556$	−45.6891			−1.93765
$557$	10.5779	−	10.5779i	0.448199	−	0.448199i	−0.446556	−	0.894756i	$-0.647350\pi$
$557$	10.5779	−	10.5779i	0.448199	−	0.448199i	0.894756	+	0.446556i	$0.147350\pi$
$558$	20.5217	−	4.38074i	0.868753	−	0.185452i
$559$			24.3063i			1.02805i
$560$		0			0
$561$	6.61917	+	12.1783i	0.279462	+	0.514169i
$562$	−44.6402	−	44.6402i	−1.88303	−	1.88303i
$563$	10.9216	+	10.9216i	0.460291	+	0.460291i	0.898751	−	0.438460i	$-0.144476\pi$
$563$	10.9216	+	10.9216i	0.460291	+	0.460291i	−0.438460	+	0.898751i	$0.644476\pi$
$564$	19.3444	+	35.5908i	0.814544	+	1.49864i
$565$		0			0
$566$			19.5050i			0.819858i
$567$	−3.21064	+	8.40784i	−0.134834	+	0.353096i
$568$	−16.1365	+	16.1365i	−0.677072	+	0.677072i
$569$	42.0710			1.76371			0.881854	−	0.471523i	$-0.156295\pi$
$569$	42.0710			1.76371			0.881854	+	0.471523i	$0.156295\pi$
$570$		0			0
$571$	10.8342			0.453399			0.226699	−	0.973965i	$-0.427207\pi$
$571$	10.8342			0.453399			0.226699	+	0.973965i	$0.427207\pi$
$572$	15.5840	−	15.5840i	0.651601	−	0.651601i
$573$	−6.31411	+	21.3503i	−0.263776	+	0.891921i
$574$			16.3976i			0.684424i
$575$		0			0
$576$	0.555438	−	0.856936i	0.0231433	−	0.0357057i
$577$	−14.6975	−	14.6975i	−0.611865	−	0.611865i	0.331567	−	0.943432i	$-0.392423\pi$
$577$	−14.6975	−	14.6975i	−0.611865	−	0.611865i	−0.943432	+	0.331567i	$0.892423\pi$
$578$	−16.2407	−	16.2407i	−0.675523	−	0.675523i
$579$	17.3497	−	9.42991i	0.721028	−	0.391894i
$580$		0			0
$581$		−	4.54404i		−	0.188519i
$582$	−26.2823	−	7.77271i	−1.08944	−	0.322189i
$583$	−4.44503	+	4.44503i	−0.184094	+	0.184094i
$584$	−52.5844			−2.17596
$585$		0			0
$586$	−30.9802			−1.27978
$587$	−4.89737	+	4.89737i	−0.202136	+	0.202136i	−0.800915	−	0.598779i	$-0.795653\pi$
$587$	−4.89737	+	4.89737i	−0.202136	+	0.202136i	0.598779	+	0.800915i	$0.295653\pi$
$588$	7.43658	+	2.19929i	0.306680	+	0.0906971i
$589$		−	4.61831i		−	0.190294i
$590$		0			0
$591$	40.3552	−	21.9339i	1.65999	−	0.902240i
$592$	3.12297	+	3.12297i	0.128353	+	0.128353i
$593$	22.5635	+	22.5635i	0.926573	+	0.926573i	0.997483	−	0.0709102i	$-0.0225904\pi$
$593$	22.5635	+	22.5635i	0.926573	+	0.926573i	−0.0709102	+	0.997483i	$0.522590\pi$
$594$	1.60059	−	20.6835i	0.0656729	−	0.848654i
$595$		0			0
$596$			4.13314i			0.169300i
$597$	2.06664	−	6.98804i	0.0845818	−	0.286002i
$598$	7.95292	−	7.95292i	0.325219	−	0.325219i
$599$	6.81971			0.278646			0.139323	−	0.990247i	$-0.455507\pi$
$599$	6.81971			0.278646			0.139323	+	0.990247i	$0.455507\pi$
$600$		0			0
$601$	−8.46733			−0.345390			−0.172695	−	0.984975i	$-0.555247\pi$
$601$	−8.46733			−0.345390			−0.172695	+	0.984975i	$0.555247\pi$
$602$	13.9402	−	13.9402i	0.568158	−	0.568158i
$603$	3.32356	+	15.5693i	0.135346	+	0.634031i
$604$			61.4782i			2.50151i
$605$		0			0
$606$	2.12893	+	3.91692i	0.0864817	+	0.159114i
$607$	−6.30295	−	6.30295i	−0.255829	−	0.255829i	0.567526	−	0.823355i	$-0.307900\pi$
$607$	−6.30295	−	6.30295i	−0.255829	−	0.255829i	−0.823355	+	0.567526i	$0.807900\pi$
$608$	6.46309	+	6.46309i	0.262113	+	0.262113i
$609$	−7.37760	−	13.5737i	−0.298956	−	0.550035i
$610$		0			0
$611$		−	16.3907i		−	0.663095i
$612$	14.3051	+	67.0125i	0.578248	+	2.70882i
$613$	5.24728	−	5.24728i	0.211935	−	0.211935i	−0.593154	−	0.805089i	$-0.702117\pi$
$613$	5.24728	−	5.24728i	0.211935	−	0.211935i	0.805089	+	0.593154i	$0.202117\pi$
$614$	42.6601			1.72162
$615$		0			0
$616$	−9.89062			−0.398504
$617$	2.10719	−	2.10719i	0.0848323	−	0.0848323i	−0.663417	−	0.748250i	$-0.730895\pi$
$617$	2.10719	−	2.10719i	0.0848323	−	0.0848323i	0.748250	+	0.663417i	$0.230895\pi$
$618$	7.12596	−	24.0954i	0.286648	−	0.969261i
$619$			21.0734i			0.847012i	0.905893	+	0.423506i	$0.139201\pi$
$619$			21.0734i			0.847012i	−0.905893	+	0.423506i	$0.860799\pi$
$620$		0			0
$621$	0.564612	−	7.29616i	0.0226571	−	0.292785i
$622$	52.6932	+	52.6932i	2.11280	+	2.11280i
$623$	−6.64874	−	6.64874i	−0.266376	−	0.266376i
$624$	33.8650	−	18.4063i	1.35569	−	0.736844i
$625$		0			0
$626$			4.41188i			0.176334i
$627$	−4.37831	−	1.29484i	−0.174853	−	0.0517108i
$628$	61.4341	−	61.4341i	2.45149	−	2.45149i
$629$	3.17697			0.126674
$630$		0			0
$631$	−11.6376			−0.463287			−0.231643	−	0.972801i	$-0.574410\pi$
$631$	−11.6376			−0.463287			−0.231643	+	0.972801i	$0.574410\pi$
$632$	76.0461	−	76.0461i	3.02495	−	3.02495i
$633$	−35.7453	−	10.5713i	−1.42075	−	0.420170i
$634$		−	15.4825i		−	0.614890i
$635$		0			0
$636$	−27.3040	+	14.8403i	−1.08267	+	0.588455i
$637$	−2.21881	−	2.21881i	−0.0879123	−	0.0879123i
$638$	25.1806	+	25.1806i	0.996910	+	0.996910i
$639$	5.90591	−	9.11170i	0.233634	−	0.360453i
$640$		0			0
$641$		−	36.1036i		−	1.42601i	−0.701161	−	0.713003i	$-0.747335\pi$
$641$		−	36.1036i		−	1.42601i	0.701161	−	0.713003i	$-0.252665\pi$
$642$	−4.98144	+	16.8441i	−0.196602	+	0.664782i
$643$	21.0115	−	21.0115i	0.828614	−	0.828614i	−0.158711	−	0.987325i	$-0.550734\pi$
$643$	21.0115	−	21.0115i	0.828614	−	0.828614i	0.987325	+	0.158711i	$0.0507337\pi$
$644$	−6.30563			−0.248477
$645$		0			0
$646$	21.8173			0.858392
$647$	−18.9025	+	18.9025i	−0.743133	+	0.743133i	−0.973180	−	0.230046i	$-0.926112\pi$
$647$	−18.9025	+	18.9025i	−0.743133	+	0.743133i	0.230046	+	0.973180i	$0.426112\pi$
$648$	20.2430	−	53.0112i	0.795221	−	2.08248i
$649$		−	8.70428i		−	0.341673i
$650$		0			0
$651$	2.27322	+	4.18241i	0.0890947	+	0.163921i
$652$	29.5757	+	29.5757i	1.15828	+	1.15828i
$653$	−12.2864	−	12.2864i	−0.480803	−	0.480803i	0.424585	−	0.905388i	$-0.360420\pi$
$653$	−12.2864	−	12.2864i	−0.480803	−	0.480803i	−0.905388	+	0.424585i	$0.860420\pi$
$654$	−13.5199	−	24.8746i	−0.528668	−	0.972674i
$655$		0			0
$656$		−	45.6924i		−	1.78399i
$657$	24.4691	−	5.22339i	0.954631	−	0.203784i
$658$	−9.40038	+	9.40038i	−0.366465	+	0.366465i
$659$	0.708622			0.0276040			0.0138020	−	0.999905i	$-0.495607\pi$
$659$	0.708622			0.0276040			0.0138020	+	0.999905i	$0.495607\pi$
$660$		0			0
$661$	17.4206			0.677582			0.338791	−	0.940862i	$-0.389982\pi$
$661$	17.4206			0.677582			0.338791	+	0.940862i	$0.389982\pi$
$662$	59.8561	−	59.8561i	2.32637	−	2.32637i
$663$	7.86299	−	26.5876i	0.305373	−	1.03258i
$664$			28.6500i			1.11184i
$665$		0			0
$666$	−3.99006	−	2.58623i	−0.154612	−	0.100214i
$667$	8.88253	+	8.88253i	0.343933	+	0.343933i
$668$	−13.9443	−	13.9443i	−0.539522	−	0.539522i
$669$	−26.6869	+	14.5049i	−1.03177	+	0.560791i
$670$		0			0
$671$		−	11.6188i		−	0.448540i
$672$	−9.03434	−	2.67181i	−0.348507	−	0.103067i
$673$	8.20389	−	8.20389i	0.316237	−	0.316237i	−0.531083	−	0.847320i	$-0.678215\pi$
$673$	8.20389	−	8.20389i	0.316237	−	0.316237i	0.847320	+	0.531083i	$0.178215\pi$
$674$	−37.0926			−1.42875
$675$		0			0
$676$	14.1206			0.543099
$677$	−32.8605	+	32.8605i	−1.26293	+	1.26293i	−0.313264	+	0.949666i	$0.601422\pi$
$677$	−32.8605	+	32.8605i	−1.26293	+	1.26293i	−0.949666	+	0.313264i	$0.898578\pi$
$678$	−19.6828	−	5.82098i	−0.755915	−	0.223554i
$679$		−	6.21744i		−	0.238604i
$680$		0			0
$681$	18.7356	−	10.1832i	0.717951	−	0.390221i
$682$	−7.75878	−	7.75878i	−0.297099	−	0.297099i
$683$	28.4978	+	28.4978i	1.09044	+	1.09044i	0.995481	+	0.0949562i	$0.0302711\pi$
$683$	28.4978	+	28.4978i	1.09044	+	1.09044i	0.0949562	+	0.995481i	$0.469729\pi$
$684$	−18.9405	−	12.2766i	−0.724208	−	0.469408i
$685$		0			0
$686$			2.54506i			0.0971709i
$687$	2.19245	−	7.41347i	0.0836473	−	0.282842i
$688$	−38.8446	+	38.8446i	−1.48093	+	1.48093i
$689$	12.5743			0.479043
$690$		0			0
$691$	5.79939			0.220619			0.110310	−	0.993897i	$-0.464816\pi$
$691$	5.79939			0.220619			0.110310	+	0.993897i	$0.464816\pi$
$692$	−36.3949	+	36.3949i	−1.38353	+	1.38353i
$693$	4.60241	−	0.982471i	0.174831	−	0.0373210i
$694$			69.1925i			2.62651i
$695$		0			0
$696$	46.5156	+	85.5820i	1.76317	+	3.24398i
$697$	−23.2412	−	23.2412i	−0.880324	−	0.880324i
$698$	54.2230	+	54.2230i	2.05237	+	2.05237i
$699$	6.59919	+	12.1416i	0.249604	+	0.459236i
$700$		0			0
$701$			4.92775i			0.186118i	0.995661	+	0.0930592i	$0.0296646\pi$
$701$			4.92775i			0.186118i	−0.995661	+	0.0930592i	$0.970335\pi$
$702$	−31.5191	+	26.9913i	−1.18961	+	1.01872i
$703$	−0.739981	+	0.739981i	−0.0279089	+	0.0279089i
$704$	−0.533986			−0.0201254
$705$		0			0
$706$	61.3096			2.30742
$707$	−0.715113	+	0.715113i	−0.0268946	+	0.0268946i
$708$	12.2032	−	41.2635i	0.458625	−	1.55078i
$709$		−	17.1922i		−	0.645666i	−0.946456	−	0.322833i	$-0.895365\pi$
$709$		−	17.1922i		−	0.645666i	0.946456	−	0.322833i	$-0.104635\pi$
$710$		0			0
$711$	−27.8326	+	42.9405i	−1.04381	+	1.61039i
$712$	41.9201	+	41.9201i	1.57102	+	1.57102i
$713$	−2.73693	−	2.73693i	−0.102499	−	0.102499i
$714$	−19.7581	+	10.7389i	−0.739428	+	0.401895i
$715$		0			0
$716$		−	74.3149i		−	2.77728i
$717$	19.6978	+	5.82541i	0.735628	+	0.217554i
$718$	1.32809	−	1.32809i	0.0495640	−	0.0495640i
$719$	12.2556			0.457059			0.228529	−	0.973537i	$-0.426608\pi$
$719$	12.2556			0.457059			0.228529	+	0.973537i	$0.426608\pi$
$720$		0			0
$721$	5.70011			0.212283
$722$	29.1113	−	29.1113i	1.08341	−	1.08341i
$723$	−30.0170	−	8.87721i	−1.11635	−	0.330147i
$724$		−	52.1752i		−	1.93908i
$725$		0			0
$726$	33.0728	−	17.9757i	1.22745	−	0.667142i
$727$	−5.83842	−	5.83842i	−0.216535	−	0.216535i	0.590501	−	0.807037i	$-0.298930\pi$
$727$	−5.83842	−	5.83842i	−0.216535	−	0.216535i	−0.807037	+	0.590501i	$0.798930\pi$
$728$	13.9895	+	13.9895i	0.518486	+	0.518486i
$729$	−4.15390	+	26.6786i	−0.153848	+	0.988094i
$730$		0			0
$731$			39.5162i			1.46156i
$732$	16.2894	−	55.0802i	0.602072	−	2.03582i
$733$	−13.5940	+	13.5940i	−0.502105	+	0.502105i	−0.912091	−	0.409987i	$-0.865533\pi$
$733$	−13.5940	+	13.5940i	−0.502105	+	0.502105i	0.409987	+	0.912091i	$0.365533\pi$
$734$	−83.8351			−3.09441
$735$		0			0
$736$	7.66040			0.282366
$737$	5.88639	−	5.88639i	0.216828	−	0.216828i
$738$	10.2698	+	48.1090i	0.378035	+	1.77092i
$739$		−	15.1801i		−	0.558411i	−0.960231	−	0.279205i	$-0.909929\pi$
$739$		−	15.1801i		−	0.558411i	0.960231	−	0.279205i	$-0.0900710\pi$
$740$		0			0
$741$	4.36134	+	8.02424i	0.160218	+	0.294778i
$742$	−7.21162	−	7.21162i	−0.264747	−	0.264747i
$743$	34.4215	+	34.4215i	1.26280	+	1.26280i	0.949729	+	0.313073i	$0.101358\pi$
$743$	34.4215	+	34.4215i	1.26280	+	1.26280i	0.313073	+	0.949729i	$0.398642\pi$
$744$	−14.3326	−	26.3700i	−0.525459	−	0.966770i
$745$		0			0
$746$		−	19.0080i		−	0.695934i
$747$	−2.84591	−	13.3317i	−0.104126	−	0.487783i
$748$	25.3359	−	25.3359i	0.926371	−	0.926371i
$749$	−3.98469			−0.145597
$750$		0			0
$751$	−22.2515			−0.811970			−0.405985	−	0.913880i	$-0.633071\pi$
$751$	−22.2515			−0.811970			−0.405985	+	0.913880i	$0.633071\pi$
$752$	26.1944	−	26.1944i	0.955210	−	0.955210i
$753$	1.56818	−	5.30260i	0.0571478	−	0.193237i
$754$		−	71.2321i		−	2.59412i
$755$		0			0
$756$	23.1956	+	1.79498i	0.843615	+	0.0652830i
$757$	1.88407	+	1.88407i	0.0684777	+	0.0684777i	0.740516	−	0.672038i	$-0.234581\pi$
$757$	1.88407	+	1.88407i	0.0684777	+	0.0684777i	−0.672038	+	0.740516i	$0.734581\pi$
$758$	6.08909	+	6.08909i	0.221166	+	0.221166i
$759$	−3.36206	+	1.82735i	−0.122035	+	0.0663286i
$760$		0			0
$761$			35.6674i			1.29294i	0.762938	+	0.646472i	$0.223756\pi$
$761$			35.6674i			1.29294i	−0.762938	+	0.646472i	$0.776244\pi$
$762$	−85.3786	−	25.2498i	−3.09294	−	0.914703i
$763$	4.54137	−	4.54137i	0.164409	−	0.164409i
$764$	57.5532			2.08220
$765$		0			0
$766$	−10.3206			−0.372897
$767$	−12.3115	+	12.3115i	−0.444543	+	0.444543i
$768$	−48.5173	−	14.3485i	−1.75072	−	0.517755i
$769$		−	31.7331i		−	1.14432i	−0.820141	−	0.572162i	$-0.806105\pi$
$769$		−	31.7331i		−	1.14432i	0.820141	−	0.572162i	$-0.193895\pi$
$770$		0			0
$771$	−25.4207	+	13.8167i	−0.915503	+	0.497595i
$772$	−36.0944	−	36.0944i	−1.29907	−	1.29907i
$773$	−4.97844	−	4.97844i	−0.179062	−	0.179062i	0.611885	−	0.790947i	$-0.290412\pi$
$773$	−4.97844	−	4.97844i	−0.179062	−	0.179062i	−0.790947	+	0.611885i	$0.790412\pi$
$774$	32.1683	−	49.6296i	1.15627	−	1.78390i
$775$		0			0
$776$			39.2008i			1.40723i
$777$	0.305904	−	1.03437i	0.0109742	−	0.0371079i
$778$	−18.3745	+	18.3745i	−0.658758	+	0.658758i
$779$	10.8267			0.387907
$780$		0			0
$781$	−5.67781			−0.203168
$782$	12.9295	−	12.9295i	0.462359	−	0.462359i
$783$	−30.1463	−	35.2034i	−1.07734	−	1.25807i
$784$		−	7.09187i		−	0.253281i
$785$		0			0
$786$	−10.3092	−	18.9675i	−0.367718	−	0.676548i
$787$	−18.7554	−	18.7554i	−0.668557	−	0.668557i	0.288825	−	0.957382i	$-0.406735\pi$
$787$	−18.7554	−	18.7554i	−0.668557	−	0.668557i	−0.957382	+	0.288825i	$0.906735\pi$
$788$	−83.9553	−	83.9553i	−2.99078	−	2.99078i
$789$	−15.3822	−	28.3011i	−0.547621	−	1.00754i
$790$		0			0
$791$		−	4.65625i		−	0.165557i
$792$	−29.0181	+	6.19445i	−1.03111	+	0.220110i
$793$	−16.4339	+	16.4339i	−0.583586	+	0.583586i
$794$	86.5746			3.07242
$795$		0			0
$796$	−18.8374			−0.667675
$797$	7.92792	−	7.92792i	0.280821	−	0.280821i	−0.552615	−	0.833437i	$-0.686370\pi$
$797$	7.92792	−	7.92792i	0.280821	−	0.280821i	0.833437	+	0.552615i	$0.186370\pi$
$798$	2.10075	−	7.10338i	0.0743656	−	0.251457i
$799$		−	26.6473i		−	0.942713i
$800$		0			0
$801$	−23.6708	−	15.3426i	−0.836366	−	0.542105i
$802$	36.1568	+	36.1568i	1.27674	+	1.27674i
$803$	−9.25121	−	9.25121i	−0.326468	−	0.326468i
$804$	36.1576	−	19.6524i	1.27518	−	0.693088i
$805$		0			0
$806$			21.9484i			0.773099i
$807$	−48.7328	−	14.4122i	−1.71548	−	0.507333i
$808$	4.50877	−	4.50877i	0.158618	−	0.158618i
$809$	33.2281			1.16824			0.584119	−	0.811668i	$-0.301440\pi$
$809$	33.2281			1.16824			0.584119	+	0.811668i	$0.301440\pi$
$810$		0			0
$811$	−49.8680			−1.75110			−0.875550	−	0.483127i	$-0.839501\pi$
$811$	−49.8680			−1.75110			−0.875550	+	0.483127i	$0.839501\pi$
$812$	−28.2389	+	28.2389i	−0.990991	+	0.990991i
$813$	5.28787	+	1.56383i	0.185454	+	0.0548458i
$814$			2.48634i			0.0871463i
$815$		0			0
$816$	55.0564	−	29.9243i	1.92736	−	1.04756i
$817$	−9.20412	−	9.20412i	−0.322011	−	0.322011i
$818$	−60.3060	−	60.3060i	−2.10855	−	2.10855i
$819$	−7.89938	−	5.12012i	−0.276027	−	0.178912i
$820$		0			0
$821$			32.4420i			1.13223i	0.824325	+	0.566116i	$0.191555\pi$
$821$			32.4420i			1.13223i	−0.824325	+	0.566116i	$0.808445\pi$
$822$	8.05984	−	27.2532i	0.281119	−	0.950565i
$823$	32.7235	−	32.7235i	1.14067	−	1.14067i	0.152341	−	0.988328i	$-0.451319\pi$
$823$	32.7235	−	32.7235i	1.14067	−	1.14067i	0.988328	−	0.152341i	$-0.0486813\pi$
$824$	−35.9390			−1.25200
$825$		0			0
$826$	14.1218			0.491361
$827$	36.7198	−	36.7198i	1.27687	−	1.27687i	0.334465	−	0.942408i	$-0.391444\pi$
$827$	36.7198	−	36.7198i	1.27687	−	1.27687i	0.942408	−	0.334465i	$-0.108556\pi$
$828$	−18.5001	+	3.94919i	−0.642922	+	0.137244i
$829$			14.2972i			0.496562i	0.968688	+	0.248281i	$0.0798657\pi$
$829$			14.2972i			0.496562i	−0.968688	+	0.248281i	$0.920134\pi$
$830$		0			0
$831$	−19.7259	−	36.2929i	−0.684285	−	1.25899i
$832$	0.755282	+	0.755282i	0.0261847	+	0.0261847i
$833$	−3.60725	−	3.60725i	−0.124984	−	0.124984i
$834$	−21.4814	−	39.5227i	−0.743841	−	1.36856i
$835$		0			0
$836$			11.8025i			0.408197i
$837$	9.28883	+	10.8470i	0.321069	+	0.374929i
$838$	46.5695	−	46.5695i	1.60872	−	1.60872i
$839$	−33.6309			−1.16107			−0.580534	−	0.814236i	$-0.697156\pi$
$839$	−33.6309			−1.16107			−0.580534	+	0.814236i	$0.697156\pi$
$840$		0			0
$841$	50.5583			1.74339
$842$	18.7216	−	18.7216i	0.645190	−	0.645190i
$843$	12.1844	−	41.1999i	0.419654	−	1.41900i
$844$			96.3574i			3.31676i
$845$		0			0
$846$	−21.6923	+	33.4672i	−0.745798	+	1.15062i
$847$	6.03811	+	6.03811i	0.207472	+	0.207472i
$848$	20.0953	+	20.0953i	0.690077	+	0.690077i
$849$	−11.6629	+	6.33901i	−0.400268	+	0.217554i
$850$		0			0
$851$			0.877065i			0.0300654i
$852$	−26.9162	−	7.96017i	−0.922134	−	0.272711i
$853$	−26.5544	+	26.5544i	−0.909206	+	0.909206i	−0.996208	−	0.0870025i	$-0.972271\pi$
$853$	−26.5544	+	26.5544i	−0.909206	+	0.909206i	0.0870025	+	0.996208i	$0.472271\pi$
$854$	18.8504			0.645047
$855$		0			0
$856$	25.1234			0.858699
$857$	−23.0711	+	23.0711i	−0.788092	+	0.788092i	−0.981181	−	0.193089i	$-0.938149\pi$
$857$	−23.0711	+	23.0711i	−0.788092	+	0.788092i	0.193089	+	0.981181i	$0.438149\pi$
$858$	20.8078	+	6.15368i	0.710367	+	0.210083i
$859$			17.3242i			0.591095i	0.955328	+	0.295548i	$0.0955021\pi$
$859$			17.3242i			0.591095i	−0.955328	+	0.295548i	$0.904498\pi$
$860$		0			0
$861$	−9.80481	+	5.32912i	−0.334147	+	0.181616i
$862$	−0.808044	−	0.808044i	−0.0275221	−	0.0275221i
$863$	9.05228	+	9.05228i	0.308143	+	0.308143i	0.844189	−	0.536046i	$-0.180083\pi$
$863$	9.05228	+	9.05228i	0.308143	+	0.308143i	−0.536046	+	0.844189i	$0.680083\pi$
$864$	−28.1792	−	2.18064i	−0.958674	−	0.0741868i
$865$		0			0
$866$		−	63.9997i		−	2.17480i
$867$	4.43285	−	14.9891i	0.150548	−	0.509056i
$868$	8.70111	−	8.70111i	0.295335	−	0.295335i
$869$	26.7577			0.907693
$870$		0			0
$871$	−16.6517			−0.564221
$872$	−28.6332	+	28.6332i	−0.969642	+	0.969642i
$873$	−3.89396	−	18.2413i	−0.131790	−	0.617376i
$874$			6.02310i			0.203734i
$875$		0			0
$876$	−30.8863	−	56.8263i	−1.04355	−	1.91998i
$877$	−15.4630	−	15.4630i	−0.522148	−	0.522148i	0.396072	−	0.918220i	$-0.370373\pi$
$877$	−15.4630	−	15.4630i	−0.522148	−	0.522148i	−0.918220	+	0.396072i	$0.870373\pi$
$878$	53.1419	+	53.1419i	1.79345	+	1.79345i
$879$	−10.0684	−	18.5243i	−0.339597	−	0.624810i
$880$		0			0
$881$		−	3.93409i		−	0.132543i	−0.997802	−	0.0662714i	$-0.978890\pi$
$881$		−	3.93409i		−	0.132543i	0.997802	−	0.0662714i	$-0.0211103\pi$
$882$	1.59396	+	7.46695i	0.0536714	+	0.251425i
$883$	−13.5688	+	13.5688i	−0.456625	+	0.456625i	−0.897546	−	0.440921i	$-0.854652\pi$
$883$	−13.5688	+	13.5688i	−0.456625	+	0.456625i	0.440921	+	0.897546i	$0.354652\pi$
$884$	−71.6713			−2.41057
$885$		0			0
$886$	56.0200			1.88203
$887$	−4.92491	+	4.92491i	−0.165362	+	0.165362i	−0.784937	−	0.619575i	$-0.787305\pi$
$887$	−4.92491	+	4.92491i	−0.165362	+	0.165362i	0.619575	+	0.784937i	$0.287305\pi$
$888$	−1.92872	+	6.52168i	−0.0647235	+	0.218853i
$889$		−	20.1975i		−	0.677401i
$890$		0			0
$891$	12.8877	−	5.76494i	0.431753	−	0.193133i
$892$	55.5196	+	55.5196i	1.85893	+	1.85893i
$893$	6.20669	+	6.20669i	0.207699	+	0.207699i
$894$	−3.57532	+	1.94326i	−0.119577	+	0.0649923i
$895$		0			0
$896$		−	11.7449i		−	0.392371i
$897$	7.34002	+	2.17073i	0.245076	+	0.0724786i
$898$	29.3724	−	29.3724i	0.980170	−	0.980170i
$899$	−24.5139			−0.817585
$900$		0			0
$901$	20.4428			0.681049
$902$	18.1889	−	18.1889i	0.605624	−	0.605624i
$903$	12.8658	+	3.80493i	0.428148	+	0.126620i
$904$			29.3575i			0.976416i
$905$		0			0
$906$	−53.1809	+	28.9049i	−1.76682	+	0.960302i
$907$	19.0317	+	19.0317i	0.631938	+	0.631938i	0.948554	−	0.316616i	$-0.102547\pi$
$907$	19.0317	+	19.0317i	0.631938	+	0.631938i	−0.316616	+	0.948554i	$0.602547\pi$
$908$	−38.9777	−	38.9777i	−1.29352	−	1.29352i
$909$	−1.65020	+	2.54594i	−0.0547336	+	0.0844436i
$910$		0			0
$911$			17.7669i			0.588644i	0.955706	+	0.294322i	$0.0950938\pi$
$911$			17.7669i			0.588644i	−0.955706	+	0.294322i	$0.904906\pi$
$912$	−5.85377	+	19.7937i	−0.193838	+	0.655435i
$913$	−5.04043	+	5.04043i	−0.166814	+	0.166814i
$914$	74.2525			2.45605
$915$		0			0
$916$	−19.9842			−0.660298
$917$	3.46291	−	3.46291i	0.114355	−	0.114355i
$918$	−51.2425	+	43.8814i	−1.69125	+	1.44830i
$919$			8.50470i			0.280544i	0.990113	+	0.140272i	$0.0447977\pi$
$919$			8.50470i			0.280544i	−0.990113	+	0.140272i	$0.955202\pi$
$920$		0			0
$921$	13.8643	+	25.5082i	0.456843	+	0.840525i
$922$	27.5151	+	27.5151i	0.906162	+	0.906162i
$923$	8.03083	+	8.03083i	0.264338	+	0.264338i
$924$	−5.80941	−	10.6885i	−0.191116	−	0.351625i
$925$		0			0
$926$			1.77154i			0.0582164i
$927$	16.7235	−	3.56995i	0.549273	−	0.117253i
$928$	34.3060	−	34.3060i	1.12615	−	1.12615i
$929$	−14.1589			−0.464538			−0.232269	−	0.972652i	$-0.574615\pi$
$929$	−14.1589			−0.464538			−0.232269	+	0.972652i	$0.574615\pi$
$930$		0			0
$931$	1.68040			0.0550729
$932$	25.2594	−	25.2594i	0.827399	−	0.827399i
$933$	−14.3825	+	48.6323i	−0.470861	+	1.59215i
$934$		−	32.3949i		−	1.05999i
$935$		0			0
$936$	49.8054	+	32.2822i	1.62794	+	1.05518i
$937$	−28.7165	−	28.7165i	−0.938127	−	0.938127i	0.0600678	−	0.998194i	$-0.480868\pi$
$937$	−28.7165	−	28.7165i	−0.938127	−	0.938127i	−0.998194	+	0.0600678i	$0.980868\pi$
$938$	9.55009	+	9.55009i	0.311821	+	0.311821i
$939$	−2.63804	+	1.43383i	−0.0860891	+	0.0467912i
$940$		0			0
$941$		−	17.4001i		−	0.567228i	−0.958939	−	0.283614i	$-0.908467\pi$
$941$		−	17.4001i		−	0.567228i	0.958939	−	0.283614i	$-0.0915335\pi$
$942$	82.0269	+	24.2586i	2.67258	+	0.790387i
$943$	6.41619	−	6.41619i	0.208940	−	0.208940i
$944$	−39.3508			−1.28076
$945$		0			0
$946$	−30.9259			−1.00549
$947$	8.15693	−	8.15693i	0.265065	−	0.265065i	−0.562043	−	0.827108i	$-0.689985\pi$
$947$	8.15693	−	8.15693i	0.265065	−	0.265065i	0.827108	+	0.562043i	$0.189985\pi$
$948$	126.848	+	37.5138i	4.11982	+	1.21839i
$949$			26.1703i			0.849522i
$950$		0			0
$951$	9.25764	−	5.03172i	0.300199	−	0.163165i
$952$	22.7436	+	22.7436i	0.737124	+	0.737124i
$953$	−38.6159	−	38.6159i	−1.25089	−	1.25089i	−0.955321	−	0.295569i	$-0.904491\pi$
$953$	−38.6159	−	38.6159i	−1.25089	−	1.25089i	−0.295569	−	0.955321i	$-0.595509\pi$
$954$	−25.6748	−	16.6416i	−0.831251	−	0.538790i
$955$		0			0
$956$		−	53.0987i		−	1.71734i
$957$	−6.87298	+	23.2400i	−0.222172	+	0.751244i
$958$	−40.9545	+	40.9545i	−1.32318	+	1.32318i
$959$	6.44712			0.208188
$960$		0			0
$961$	−23.4466			−0.756343
$962$	3.51674	−	3.51674i	0.113384	−	0.113384i
$963$	−11.6907	+	2.49559i	−0.376727	+	0.0804194i
$964$			80.9159i			2.60613i
$965$		0			0
$966$	−2.96469	−	5.45461i	−0.0953874	−	0.175499i
$967$	18.6836	+	18.6836i	0.600824	+	0.600824i	0.940531	−	0.339707i	$-0.110328\pi$
$967$	18.6836	+	18.6836i	0.600824	+	0.600824i	−0.339707	+	0.940531i	$0.610328\pi$
$968$	−38.0701	−	38.0701i	−1.22362	−	1.22362i
$969$	7.09049	+	13.0455i	0.227779	+	0.419081i
$970$		0			0
$971$		−	57.4980i		−	1.84520i	−0.385761	−	0.922599i	$-0.626061\pi$
$971$		−	57.4980i		−	1.84520i	0.385761	−	0.922599i	$-0.373939\pi$
$972$	69.1776	−	9.26098i	2.21887	−	0.297046i
$973$	7.21569	−	7.21569i	0.231324	−	0.231324i
$974$	41.3622			1.32533
$975$		0			0
$976$	−52.5270			−1.68135
$977$	2.08515	−	2.08515i	0.0667100	−	0.0667100i	−0.672965	−	0.739675i	$-0.734979\pi$
$977$	2.08515	−	2.08515i	0.0667100	−	0.0667100i	0.739675	+	0.672965i	$0.234979\pi$
$978$	−11.6786	+	39.4896i	−0.373441	+	1.26274i
$979$			14.7501i			0.471415i
$980$		0			0
$981$	10.4797	−	16.1681i	0.334590	−	0.516209i
$982$	0.543000	+	0.543000i	0.0173278	+	0.0173278i
$983$	−11.6041	−	11.6041i	−0.370114	−	0.370114i	0.497405	−	0.867519i	$-0.334286\pi$
$983$	−11.6041	−	11.6041i	−0.370114	−	0.370114i	−0.867519	+	0.497405i	$0.834286\pi$
$984$	61.8191	−	33.5999i	1.97072	−	1.07113i
$985$		0			0
$986$		−	115.806i		−	3.68802i
$987$	−8.67592	−	2.56581i	−0.276158	−	0.0816706i
$988$	16.6937	−	16.6937i	0.531097	−	0.531097i
$989$	−10.9092			−0.346893
$990$		0			0
$991$	−6.34125			−0.201436			−0.100718	−	0.994915i	$-0.532114\pi$
$991$	−6.34125			−0.201436			−0.100718	+	0.994915i	$0.532114\pi$
$992$	−10.5706	+	10.5706i	−0.335615	+	0.335615i
$993$	55.2432	+	16.3376i	1.75309	+	0.518457i
$994$		−	9.21168i		−	0.292177i
$995$		0			0
$996$	−30.9612	+	16.8281i	−0.981044	+	0.533218i
$997$	−1.89647	−	1.89647i	−0.0600618	−	0.0600618i	0.676438	−	0.736500i	$-0.263523\pi$
$997$	−1.89647	−	1.89647i	−0.0600618	−	0.0600618i	−0.736500	+	0.676438i	$0.763523\pi$
$998$	36.3897	+	36.3897i	1.15190	+	1.15190i
$999$	0.249668	−	3.22633i	0.00789916	−	0.102076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.j.b.407.12		24
3.2	odd	2	inner	525.2.j.b.407.1		24
5.2	odd	4		105.2.j.a.8.12	yes	24
5.3	odd	4	inner	525.2.j.b.218.1		24
5.4	even	2		105.2.j.a.92.1	yes	24
15.2	even	4		105.2.j.a.8.1	✓	24
15.8	even	4	inner	525.2.j.b.218.12		24
15.14	odd	2		105.2.j.a.92.12	yes	24
35.2	odd	12		735.2.y.j.263.12		48
35.4	even	6		735.2.y.j.422.1		48
35.9	even	6		735.2.y.j.557.12		48
35.12	even	12		735.2.y.g.263.12		48
35.17	even	12		735.2.y.g.128.1		48
35.19	odd	6		735.2.y.g.557.12		48
35.24	odd	6		735.2.y.g.422.1		48
35.27	even	4		735.2.j.h.638.12		24
35.32	odd	12		735.2.y.j.128.1		48
35.34	odd	2		735.2.j.h.197.1		24
105.2	even	12		735.2.y.j.263.1		48
105.17	odd	12		735.2.y.g.128.12		48
105.32	even	12		735.2.y.j.128.12		48
105.44	odd	6		735.2.y.j.557.1		48
105.47	odd	12		735.2.y.g.263.1		48
105.59	even	6		735.2.y.g.422.12		48
105.62	odd	4		735.2.j.h.638.1		24
105.74	odd	6		735.2.y.j.422.12		48
105.89	even	6		735.2.y.g.557.1		48
105.104	even	2		735.2.j.h.197.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.1	✓	24	15.2	even	4
105.2.j.a.8.12	yes	24	5.2	odd	4
105.2.j.a.92.1	yes	24	5.4	even	2
105.2.j.a.92.12	yes	24	15.14	odd	2
525.2.j.b.218.1		24	5.3	odd	4	inner
525.2.j.b.218.12		24	15.8	even	4	inner
525.2.j.b.407.1		24	3.2	odd	2	inner
525.2.j.b.407.12		24	1.1	even	1	trivial
735.2.j.h.197.1		24	35.34	odd	2
735.2.j.h.197.12		24	105.104	even	2
735.2.j.h.638.1		24	105.62	odd	4
735.2.j.h.638.12		24	35.27	even	4
735.2.y.g.128.1		48	35.17	even	12
735.2.y.g.128.12		48	105.17	odd	12
735.2.y.g.263.1		48	105.47	odd	12
735.2.y.g.263.12		48	35.12	even	12
735.2.y.g.422.1		48	35.24	odd	6
735.2.y.g.422.12		48	105.59	even	6
735.2.y.g.557.1		48	105.89	even	6
735.2.y.g.557.12		48	35.19	odd	6
735.2.y.j.128.1		48	35.32	odd	12
735.2.y.j.128.12		48	105.32	even	12
735.2.y.j.263.1		48	105.2	even	12
735.2.y.j.263.12		48	35.2	odd	12
735.2.y.j.422.1		48	35.4	even	6
735.2.y.j.422.12		48	105.74	odd	6
735.2.y.j.557.1		48	105.44	odd	6
735.2.y.j.557.12		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)

\(f(q)\)	\(=\)	\(q+(1.79963 - 1.79963i) q^{2} +(1.66094 + 0.491204i) q^{3} -4.47734i q^{4} +(3.87306 - 2.10509i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-4.45829 - 4.45829i) q^{8} +(2.51744 + 1.63172i) q^{9} +O(q^{10})\)	\(q+(1.79963 - 1.79963i) q^{2} +(1.66094 + 0.491204i) q^{3} -4.47734i q^{4} +(3.87306 - 2.10509i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-4.45829 - 4.45829i) q^{8} +(2.51744 + 1.63172i) q^{9} -1.56870i q^{11} +(2.19929 - 7.43658i) q^{12} +(-2.21881 + 2.21881i) q^{13} +2.54506 q^{14} -7.09187 q^{16} +(-3.60725 + 3.60725i) q^{17} +(7.46695 - 1.59396i) q^{18} -1.68040i q^{19} +(0.827127 + 1.52180i) q^{21} +(-2.82308 - 2.82308i) q^{22} +(-0.995850 - 0.995850i) q^{23} +(-5.21502 - 9.59488i) q^{24} +7.98606i q^{26} +(3.37980 + 3.94676i) q^{27} +(3.16595 - 3.16595i) q^{28} -8.91955 q^{29} +2.74834 q^{31} +(-3.84616 + 3.84616i) q^{32} +(0.770553 - 2.60552i) q^{33} +12.9834i q^{34} +(7.30576 - 11.2714i) q^{36} +(-0.440360 - 0.440360i) q^{37} +(-3.02410 - 3.02410i) q^{38} +(-4.77519 + 2.59542i) q^{39} +6.44292i q^{41} +(4.22719 + 1.25015i) q^{42} +(5.47734 - 5.47734i) q^{43} -7.02360 q^{44} -3.58432 q^{46} +(-3.69358 + 3.69358i) q^{47} +(-11.7792 - 3.48356i) q^{48} +1.00000i q^{49} +(-7.76331 + 4.21952i) q^{51} +(9.93435 + 9.93435i) q^{52} +(-2.83358 - 2.83358i) q^{53} +(13.1851 + 1.02033i) q^{54} -6.30497i q^{56} +(0.825420 - 2.79104i) q^{57} +(-16.0519 + 16.0519i) q^{58} +5.54871 q^{59} +7.40665 q^{61} +(4.94599 - 4.94599i) q^{62} +(0.626296 + 2.93390i) q^{63} -0.340400i q^{64} +(-3.30226 - 6.07568i) q^{66} +(3.75240 + 3.75240i) q^{67} +(16.1509 + 16.1509i) q^{68} +(-1.16488 - 2.14321i) q^{69} -3.61943i q^{71} +(-3.94878 - 18.4981i) q^{72} +(5.89737 - 5.89737i) q^{73} -1.58497 q^{74} -7.52372 q^{76} +(1.10924 - 1.10924i) q^{77} +(-3.92279 + 13.2644i) q^{78} +17.0572i q^{79} +(3.67497 + 8.21551i) q^{81} +(11.5949 + 11.5949i) q^{82} +(-3.21312 - 3.21312i) q^{83} +(6.81359 - 3.70333i) q^{84} -19.7144i q^{86} +(-14.8148 - 4.38132i) q^{87} +(-6.99372 + 6.99372i) q^{88} -9.40273 q^{89} -3.13787 q^{91} +(-4.45876 + 4.45876i) q^{92} +(4.56482 + 1.35000i) q^{93} +13.2941i q^{94} +(-8.27749 + 4.49899i) q^{96} +(-4.39640 - 4.39640i) q^{97} +(1.79963 + 1.79963i) q^{98} +(2.55968 - 3.94911i) 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

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