LMFDB - Embedded newform 525.2.j.b.218.2

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			218.2
Character	$\chi$	$=$	525.218
Dual form			525.2.j.b.407.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54414 - 1.54414i) q^{2} +(1.73204 + 0.00622252i) q^{3} +2.76875i q^{4} +(-2.66491 - 2.68412i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(1.18705 - 1.18705i) q^{8} +(2.99992 + 0.0215553i) q^{9} +O(q^{10})$	\(q+(-1.54414 - 1.54414i) q^{2} +(1.73204 + 0.00622252i) 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} +(-0.0172286 + 4.79558i) q^{12} +(0.206632 + 0.206632i) q^{13} +2.18375 q^{14} +1.87154 q^{16} +(-0.167409 - 0.167409i) q^{17} +(-4.59902 - 4.66559i) 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} +(5.19585 + 0.0560017i) q^{27} +(-1.95780 - 1.95780i) q^{28} -2.84268 q^{29} +9.11776 q^{31} +(-5.26402 - 5.26402i) q^{32} +(0.0210636 - 5.86307i) 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} +(3.78233 + 0.0135884i) q^{42} +(3.76875 + 3.76875i) q^{43} +9.37239 q^{44} -15.6815 q^{46} +(3.56639 + 3.56639i) q^{47} +(3.24158 + 0.0116457i) 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} +(0.0330677 - 9.20439i) q^{57} +(4.38949 + 4.38949i) q^{58} -10.3168 q^{59} -6.80634 q^{61} +(-14.0791 - 14.0791i) q^{62} +(-2.13651 + 2.10602i) 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} +(3.58665 - 3.53548i) q^{72} +(-8.61099 - 8.61099i) q^{73} -16.2757 q^{74} +14.7136 q^{76} +(2.39360 + 2.39360i) q^{77} +(0.00397083 - 1.10528i) 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} +(-4.92363 - 0.0176886i) q^{87} +(-4.01825 - 4.01825i) q^{88} +2.00190 q^{89} -0.292222 q^{91} +(14.0589 + 14.0589i) q^{92} +(15.7923 + 0.0567354i) 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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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	−0.995329	−	0.0965442i	$-0.969221\pi$
$2$	−1.54414	−	1.54414i	−1.09187	−	1.09187i	−0.0965442	−	0.995329i	$-0.530779\pi$
$3$	1.73204	+	0.00622252i	0.999994	+	0.00359257i
$3$	1.73204	+	0.00622252i	0.999994	+	0.00359257i
$4$			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	$-0.170472\pi$
$12$	−0.0172286	+	4.79558i	−0.00497346	+	1.38436i
$13$	0.206632	+	0.206632i	0.0573094	+	0.0573094i	0.735181	−	0.677871i	$-0.237097\pi$
$13$	0.206632	+	0.206632i	0.0573094	+	0.0573094i	−0.677871	+	0.735181i	$0.737097\pi$
$14$	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	$-0.259140\pi$
$17$	−0.167409	−	0.167409i	−0.0406026	−	0.0406026i	−0.727117	+	0.686514i	$0.759140\pi$
$18$	−4.59902	−	4.66559i	−1.08400	−	1.09969i
$19$		−	5.31419i		−	1.21916i	−0.792725	−	0.609579i	$-0.791338\pi$
$19$		−	5.31419i		−	1.21916i	0.792725	−	0.609579i	$-0.208662\pi$
$20$		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	0.0606179	−	0.998161i	$-0.480693\pi$
$23$	5.07773	−	5.07773i	1.05878	−	1.05878i	0.998161	−	0.0606179i	$-0.0193071\pi$
$24$	2.06341	−	2.04864i	0.421191	−	0.418176i
$25$		0			0
$26$		−	0.638138i		−	0.125149i
$27$	5.19585	+	0.0560017i	0.999942	+	0.0107775i
$28$	−1.95780	−	1.95780i	−0.369989	−	0.369989i
$29$	−2.84268			−0.527872			−0.263936	−	0.964540i	$-0.585021\pi$
$29$	−2.84268			−0.527872			−0.263936	+	0.964540i	$0.585021\pi$
$30$		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
$33$	0.0210636	−	5.86307i	0.00366671	−	1.02063i
$34$			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	−0.125668	−	0.992072i	$-0.540107\pi$
$37$	5.27013	−	5.27013i	0.866404	−	0.866404i	0.992072	+	0.125668i	$0.0401075\pi$
$38$	−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	$-0.000782881\pi$
$42$	3.78233	+	0.0135884i	0.583627	+	0.00209674i
$43$	3.76875	+	3.76875i	0.574728	+	0.574728i	0.933446	−	0.358718i	$-0.116786\pi$
$43$	3.76875	+	3.76875i	0.574728	+	0.574728i	−0.358718	+	0.933446i	$0.616786\pi$
$44$	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	$-0.130096\pi$
$47$	3.56639	+	3.56639i	0.520211	+	0.520211i	−0.397424	+	0.917635i	$0.630096\pi$
$48$	3.24158	+	0.0116457i	0.467881	+	0.00168091i
$49$		−	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	$-0.862151\pi$
$53$	−3.55291	+	3.55291i	−0.488030	+	0.488030i	0.419654	+	0.907684i	$0.362151\pi$
$54$	−7.93665	−	8.10960i	−1.08004	−	1.10358i
$55$		0			0
$56$			1.67875i			0.224332i
$57$	0.0330677	−	9.20439i	0.00437992	−	1.21915i
$58$	4.38949	+	4.38949i	0.576369	+	0.576369i
$59$	−10.3168			−1.34313			−0.671565	−	0.740946i	$-0.734378\pi$
$59$	−10.3168			−1.34313			−0.671565	+	0.740946i	$0.734378\pi$
$60$		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
$63$	−2.13651	+	2.10602i	−0.269175	+	0.265334i
$64$			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	−0.979069	−	0.203530i	$-0.934759\pi$
$67$	−6.34806	+	6.34806i	−0.775539	+	0.775539i	0.203530	+	0.979069i	$0.434759\pi$
$68$	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	$-0.0753973\pi$
$72$	3.58665	−	3.53548i	0.422691	−	0.416660i
$73$	−8.61099	−	8.61099i	−1.00784	−	1.00784i	−0.999969	−	0.00787086i	$-0.997495\pi$
$73$	−8.61099	−	8.61099i	−1.00784	−	1.00784i	−0.00787086	−	0.999969i	$-0.502505\pi$
$74$	−16.2757			−1.89201
$75$		0			0
$76$	14.7136			1.68777
$77$	2.39360	+	2.39360i	0.272776	+	0.272776i
$78$	0.00397083	−	1.10528i	0.000449608	−	0.125148i
$79$			11.4449i			1.28766i	0.765170	+	0.643828i	$0.222655\pi$
$79$			11.4449i			1.28766i	−0.765170	+	0.643828i	$0.777345\pi$
$80$		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	$-0.847385\pi$
$83$	−3.88059	+	3.88059i	−0.425951	+	0.425951i	0.461296	+	0.887246i	$0.347385\pi$
$84$	−3.37880	−	3.40317i	−0.368658	−	0.371316i
$85$		0			0
$86$		−	11.6390i		−	1.25506i
$87$	−4.92363	−	0.0176886i	−0.527868	−	0.00189642i
$88$	−4.01825	−	4.01825i	−0.428347	−	0.428347i
$89$	2.00190			0.212201			0.106100	−	0.994355i	$-0.466164\pi$
$89$	2.00190			0.212201			0.106100	+	0.994355i	$0.466164\pi$
$90$		0			0
$91$	−0.292222			−0.0306332
$92$	14.0589	+	14.0589i	1.46574	+	1.46574i
$93$	15.7923	+	0.0567354i	1.63759	+	0.00588319i
$94$		−	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	−0.812793	−	0.582553i	$-0.802054\pi$
$97$	−2.26760	+	2.26760i	−0.230240	+	0.230240i	0.582553	+	0.812793i	$0.302054\pi$
$98$	−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	$0.858629\pi$
$102$	−0.00321708	+	0.895474i	−0.000318538	+	0.0886651i
$103$	−0.964332	−	0.964332i	−0.0950185	−	0.0950185i	0.658000	−	0.753018i	$-0.271403\pi$
$103$	−0.964332	−	0.964332i	−0.0950185	−	0.0950185i	−0.753018	+	0.658000i	$0.771403\pi$
$104$	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	$-0.185179\pi$
$107$	2.95847	+	2.95847i	0.286007	+	0.286007i	−0.549492	+	0.835499i	$0.685179\pi$
$108$	−0.155055	+	14.3860i	−0.0149201	+	1.38429i
$109$			2.82182i			0.270281i	0.990826	+	0.135141i	$0.0431486\pi$
$109$			2.82182i			0.270281i	−0.990826	+	0.135141i	$0.956851\pi$
$110$		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	$-0.792857\pi$
$113$	−2.01798	+	2.01798i	−0.189835	+	0.189835i	0.605790	+	0.795625i	$0.292857\pi$
$114$	−14.2639	+	14.1618i	−1.33594	+	1.32638i
$115$		0			0
$116$		−	7.87065i		−	0.730771i
$117$	0.615426	+	0.624334i	0.0568961	+	0.0577197i
$118$	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
$123$	0.000195990	−	0.0545538i	1.76718e−5	−	0.00491895i
$124$			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	0.0322583	−	0.999480i	$-0.489730\pi$
$127$	11.6271	−	11.6271i	1.03174	−	1.03174i	0.999480	−	0.0322583i	$-0.0102699\pi$
$128$	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	$0.812772\pi$
$132$	16.2333	+	0.0583199i	1.41293	+	0.00507609i
$133$	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	$-0.148394\pi$
$137$	5.19451	+	5.19451i	0.443797	+	0.443797i	−0.449489	+	0.893286i	$0.648394\pi$
$138$	−27.1609	−	0.0975782i	−2.31209	−	0.00830641i
$139$			12.3138i			1.04444i	0.852810	+	0.522221i	$0.174897\pi$
$139$			12.3138i			1.04444i	−0.852810	+	0.522221i	$0.825103\pi$
$140$		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
$147$	0.00622252	−	1.73204i	0.000513225	−	0.142856i
$148$	14.5917	+	14.5917i	1.19943	+	1.19943i
$149$	18.9350			1.55121			0.775607	−	0.631216i	$-0.217444\pi$
$149$	18.9350			1.55121			0.775607	+	0.631216i	$0.217444\pi$
$150$		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
$153$	−0.498604	−	0.505822i	−0.0403098	−	0.0408933i
$154$		−	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	−0.513521	−	0.858077i	$-0.671659\pi$
$157$	4.31728	−	4.31728i	0.344557	−	0.344557i	0.858077	+	0.513521i	$0.171659\pi$
$158$	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
$162$	−13.6961	−	14.0955i	−1.07607	−	1.10745i
$163$	−3.57655	−	3.57655i	−0.280137	−	0.280137i	0.553027	−	0.833164i	$-0.313473\pi$
$163$	−3.57655	−	3.57655i	−0.280137	−	0.280137i	−0.833164	+	0.553027i	$0.813473\pi$
$164$	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	$-0.136257\pi$
$167$	6.39241	+	6.39241i	0.494659	+	0.494659i	−0.415111	+	0.909771i	$0.636257\pi$
$168$	−0.0104460	+	2.90765i	−0.000805929	+	0.224330i
$169$		−	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	$-0.817026\pi$
$173$	−3.88791	+	3.88791i	−0.295592	+	0.295592i	0.543692	+	0.839285i	$0.317026\pi$
$174$	7.57546	+	7.63009i	0.574294	+	0.578436i
$175$		0			0
$176$		−	6.33528i		−	0.477540i
$177$	−17.8691	−	0.0641964i	−1.34312	−	0.00482529i
$178$	−3.09121	−	3.09121i	−0.231696	−	0.231696i
$179$	−14.6322			−1.09366			−0.546832	−	0.837242i	$-0.684166\pi$
$179$	−14.6322			−1.09366			−0.546832	+	0.837242i	$0.684166\pi$
$180$		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
$183$	−11.7888	−	0.0423526i	−0.871456	−	0.00313079i
$184$		−	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	$0.925873\pi$
$192$	−0.0778669	+	21.6743i	−0.00561956	+	1.56421i
$193$	−7.56336	−	7.56336i	−0.544422	−	0.544422i	0.380400	−	0.924822i	$-0.375786\pi$
$193$	−7.56336	−	7.56336i	−0.544422	−	0.544422i	−0.924822	+	0.380400i	$0.875786\pi$
$194$	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	$-0.233718\pi$
$197$	1.01490	+	1.01490i	0.0723090	+	0.0723090i	−0.670027	+	0.742336i	$0.733718\pi$
$198$	−15.7933	+	15.5680i	−1.12238	+	1.10637i
$199$		−	9.40041i		−	0.666378i	−0.942860	−	0.333189i	$-0.891875\pi$
$199$		−	9.40041i		−	0.666378i	0.942860	−	0.333189i	$-0.108125\pi$
$200$		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
$207$	15.3422	−	15.1233i	1.06636	−	1.05114i
$208$	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
$213$	0.0246072	−	6.84942i	0.00168606	−	0.469315i
$214$		−	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
$222$	−28.1901	−	0.101276i	−1.89199	−	0.00679717i
$223$	−3.86020	−	3.86020i	−0.258498	−	0.258498i	0.565945	−	0.824443i	$-0.308511\pi$
$223$	−3.86020	−	3.86020i	−0.258498	−	0.258498i	−0.824443	+	0.565945i	$0.808511\pi$
$224$	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	$-0.272538\pi$
$227$	−1.50739	−	1.50739i	−0.100049	−	0.100049i	−0.755360	+	0.655310i	$0.772538\pi$
$228$	25.4846	+	0.0915560i	1.68776	+	0.00606344i
$229$			6.26009i			0.413678i	0.978375	+	0.206839i	$0.0663177\pi$
$229$			6.26009i			0.413678i	−0.978375	+	0.206839i	$0.933682\pi$
$230$		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	$-0.710466\pi$
$233$	2.67422	−	2.67422i	0.175194	−	0.175194i	0.789257	+	0.614063i	$0.210466\pi$
$234$	0.0137553	−	1.91436i	0.000899209	−	0.125146i
$235$		0			0
$236$		−	28.5645i		−	1.85939i
$237$	−0.0712164	+	19.8231i	−0.00462600	+	1.28765i
$238$	−0.365578	−	0.365578i	−0.0236969	−	0.0236969i
$239$	2.08521			0.134881			0.0674406	−	0.997723i	$-0.478517\pi$
$239$	2.08521			0.134881			0.0674406	+	0.997723i	$0.478517\pi$
$240$		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
$243$	15.5859	+	0.279999i	0.999839	+	0.0179619i
$244$		−	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	$0.736386\pi$
$252$	−5.83104	−	5.91545i	−0.367321	−	0.372638i
$253$	−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	$-0.410083\pi$
$257$	−10.9273	−	10.9273i	−0.681627	−	0.681627i	−0.960367	+	0.278740i	$0.910083\pi$
$258$	0.0724236	−	20.1591i	0.00450890	−	1.25505i
$259$			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	−0.129497	+	0.991580i	$0.541336\pi$
$263$	−18.1808	+	18.1808i	−1.12108	+	1.12108i	−0.991580	+	0.129497i	$0.958664\pi$
$264$	−6.93477	−	6.98477i	−0.426805	−	0.429883i
$265$		0			0
$266$		−	11.6048i		−	0.711539i
$267$	3.46737	+	0.0124569i	0.212199	+	0.000762347i
$268$	−17.5762	−	17.5762i	−1.07364	−	1.07364i
$269$	28.5125			1.73844			0.869219	−	0.494428i	$-0.164622\pi$
$269$	28.5125			1.73844			0.869219	+	0.494428i	$0.164622\pi$
$270$		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
$273$	−0.506139	−	0.00181836i	−0.0306330	−	0.000110052i
$274$		−	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	−0.971774	−	0.235913i	$-0.924192\pi$
$277$	−12.2472	+	12.2472i	−0.735861	+	0.735861i	0.235913	+	0.971774i	$0.424192\pi$
$278$	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	$-0.123852\pi$
$282$	0.0685349	−	19.0767i	0.00408120	−	1.13600i
$283$	19.8271	+	19.8271i	1.17860	+	1.17860i	0.980102	+	0.198495i	$0.0636053\pi$
$283$	19.8271	+	19.8271i	1.17860	+	1.17860i	0.198495	+	0.980102i	$0.436395\pi$
$284$	10.9491			0.649711
$285$		0			0
$286$	−2.16014			−0.127732
$287$	0.0222716	+	0.0222716i	0.00131465	+	0.00131465i
$288$	−15.6782	−	15.9051i	−0.923847	−	0.937219i
$289$		−	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	$-0.660346\pi$
$293$	6.72836	−	6.72836i	0.393075	−	0.393075i	0.875782	+	0.482707i	$0.160346\pi$
$294$	−2.68412	+	2.66491i	−0.156541	+	0.155420i
$295$		0			0
$296$		−	12.5118i		−	0.727236i
$297$	0.189570	−	17.5883i	0.0109999	−	1.02058i
$298$	−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
$303$	−0.0537396	+	14.9584i	−0.00308726	+	0.859339i
$304$		−	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	−0.934085	−	0.357051i	$-0.883782\pi$
$307$	−10.1105	+	10.1105i	−0.577034	+	0.577034i	0.357051	+	0.934085i	$0.383782\pi$
$308$	−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	$0.996443\pi$
$312$	0.849680	+	0.00305256i	0.0481036	+	0.000172817i
$313$	10.3810	+	10.3810i	0.586767	+	0.586767i	0.936754	−	0.349987i	$-0.113814\pi$
$313$	10.3810	+	10.3810i	0.586767	+	0.586767i	−0.349987	+	0.936754i	$0.613814\pi$
$314$	−13.3330			−0.752424
$315$		0			0
$316$	−31.6881			−1.78260
$317$	19.8075	+	19.8075i	1.11250	+	1.11250i	0.992812	+	0.119688i	$0.0381896\pi$
$317$	19.8075	+	19.8075i	1.11250	+	1.11250i	0.119688	+	0.992812i	$0.461810\pi$
$318$	19.0046	+	0.0682759i	1.06573	+	0.00382872i
$319$			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
$327$	−0.0175588	+	4.88750i	−0.000971005	+	0.270279i
$328$	−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
$333$	15.9236	−	15.6964i	0.872607	−	0.860157i
$334$		−	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	−0.608369	−	0.793655i	$-0.708176\pi$
$337$	3.40139	−	3.40139i	0.185286	−	0.185286i	0.793655	+	0.608369i	$0.208176\pi$
$338$	−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
$342$	−24.7938	+	24.4401i	−1.34070	+	1.32157i
$343$	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	−0.934706	−	0.355421i	$-0.884337\pi$
$347$	−24.0324	−	24.0324i	−1.29013	−	1.29013i	−0.355421	−	0.934706i	$-0.615663\pi$
$348$	0.0489753	−	13.6323i	0.00262535	−	0.730766i
$349$		−	9.37078i		−	0.501607i	−0.968038	−	0.250803i	$-0.919305\pi$
$349$		−	9.37078i		−	0.501607i	0.968038	−	0.250803i	$-0.0806947\pi$
$350$		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	$-0.935012\pi$
$353$	−14.5888	+	14.5888i	−0.776481	+	0.776481i	0.202750	+	0.979231i	$0.435012\pi$
$354$	27.4932	+	27.6915i	1.46125	+	1.47179i
$355$		0			0
$356$			5.54275i			0.293765i
$357$	0.410063	+	0.00147319i	0.0217028	+	7.79696e-5i
$358$	22.5942	+	22.5942i	1.19414	+	1.19414i
$359$	27.2654			1.43901			0.719506	−	0.694486i	$-0.244368\pi$
$359$	27.2654			1.43901			0.719506	+	0.694486i	$0.244368\pi$
$360$		0			0
$361$	−9.24062			−0.486349
$362$	15.1900	+	15.1900i	0.798369	+	0.798369i
$363$	−0.794430	−	0.00285407i	−0.0416968	−	0.000149800i
$364$		−	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	−0.987683	−	0.156465i	$-0.949990\pi$
$367$	−15.9239	+	15.9239i	−0.831218	+	0.831218i	0.156465	+	0.987683i	$0.449990\pi$
$368$	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
$372$	−0.157086	+	43.7249i	−0.00814453	+	2.26703i
$373$	−23.3283	−	23.3283i	−1.20790	−	1.20790i	−0.971707	−	0.236189i	$-0.924102\pi$
$373$	−23.3283	−	23.3283i	−1.20790	−	1.20790i	−0.236189	−	0.971707i	$-0.575898\pi$
$374$	1.75010			0.0904954
$375$		0			0
$376$	8.46698			0.436651
$377$	−0.587387	−	0.587387i	−0.0302520	−	0.0302520i
$378$	11.3464	+	0.122294i	0.583597	+	0.00629010i
$379$			37.4477i			1.92356i	0.273828	+	0.961779i	$0.411710\pi$
$379$			37.4477i			1.92356i	−0.273828	+	0.961779i	$0.588290\pi$
$380$		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	$-0.692710\pi$
$383$	4.95443	−	4.95443i	0.253159	−	0.253159i	0.822265	+	0.569105i	$0.192710\pi$
$384$	15.2879	−	15.1784i	0.780155	−	0.774570i
$385$		0			0
$386$			23.3578i			1.18888i
$387$	11.2247	+	11.3872i	0.570584	+	0.578843i
$388$	−6.27841	−	6.27841i	−0.318738	−	0.318738i
$389$	9.20279			0.466600			0.233300	−	0.972405i	$-0.425048\pi$
$389$	9.20279			0.466600			0.233300	+	0.972405i	$0.425048\pi$
$390$		0			0
$391$	−1.70011			−0.0859783
$392$	−1.18705	−	1.18705i	−0.0599552	−	0.0599552i
$393$	−0.0790344	+	21.9992i	−0.00398676	+	1.10971i
$394$		−	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	−0.105976	+	0.994369i	$0.533797\pi$
$397$	−21.9242	+	21.9242i	−1.10034	+	1.10034i	−0.994369	+	0.105976i	$0.966203\pi$
$398$	−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	$-0.222303\pi$
$402$	33.9560	+	0.121990i	1.69357	+	0.00608431i
$403$	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
$408$	−0.688392	−	0.00247311i	−0.0340805	−	0.000122437i
$409$			10.9496i			0.541425i	0.962660	+	0.270712i	$0.0872592\pi$
$409$			10.9496i			0.541425i	−0.962660	+	0.270712i	$0.912741\pi$
$410$		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
$417$	−0.0766229	+	21.3280i	−0.00375224	+	1.04444i
$418$	27.7774	+	27.7774i	1.35864	+	1.35864i
$419$	−5.86958			−0.286748			−0.143374	−	0.989669i	$-0.545795\pi$
$419$	−5.86958			−0.286748			−0.143374	+	0.989669i	$0.545795\pi$
$420$		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
$423$	10.6220	+	10.7758i	0.516460	+	0.523936i
$424$			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	$-0.0321083\pi$
$432$	9.72423	+	0.104809i	0.467857	+	0.00504264i
$433$	2.20877	+	2.20877i	0.106146	+	0.106146i	0.758185	−	0.652039i	$-0.226086\pi$
$433$	2.20877	+	2.20877i	0.106146	+	0.106146i	−0.652039	+	0.758185i	$0.726086\pi$
$434$	19.9109			0.955752
$435$		0			0
$436$	−7.81290			−0.374170
$437$	−26.9840	−	26.9840i	−1.29082	−	1.29082i
$438$	−0.165477	+	46.0604i	−0.00790678	+	2.20085i
$439$			27.6028i			1.31741i	0.752401	+	0.658706i	$0.228896\pi$
$439$			27.6028i			1.31741i	−0.752401	+	0.658706i	$0.771104\pi$
$440$		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	$-0.885646\pi$
$443$	−12.3040	+	12.3040i	−0.584582	+	0.584582i	0.351577	+	0.936159i	$0.385646\pi$
$444$	25.1825	+	25.3641i	1.19511	+	1.20373i
$445$		0			0
$446$			11.9214i			0.564494i
$447$	32.7961	+	0.117823i	1.55120	+	0.00557285i
$448$	−8.84854	−	8.84854i	−0.418054	−	0.418054i
$449$	−34.1859			−1.61333			−0.806666	−	0.591008i	$-0.798730\pi$
$449$	−34.1859			−1.61333			−0.806666	+	0.591008i	$0.798730\pi$
$450$		0			0
$451$	−0.106619			−0.00502049
$452$	−5.58726	−	5.58726i	−0.262803	−	0.262803i
$453$	−3.30000	−	0.0118556i	−0.155048	−	0.000557024i
$454$			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	−0.454986	−	0.890499i	$-0.650356\pi$
$457$	9.31021	−	9.31021i	0.435513	−	0.435513i	0.890499	+	0.454986i	$0.150356\pi$
$458$	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	$-0.203841\pi$
$462$	0.0459976	−	12.8034i	0.00214000	−	0.595670i
$463$	−13.2170	−	13.2170i	−0.614248	−	0.614248i	0.329802	−	0.944050i	$-0.393018\pi$
$463$	−13.2170	−	13.2170i	−0.614248	−	0.614248i	−0.944050	+	0.329802i	$0.893018\pi$
$464$	−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	$-0.0274862\pi$
$467$	19.6659	+	19.6659i	0.910031	+	0.910031i	−0.0862431	+	0.996274i	$0.527486\pi$
$468$	−1.72862	+	1.70396i	−0.0799056	+	0.0787655i
$469$		−	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
$477$	−10.7350	+	10.5819i	−0.491524	+	0.484510i
$478$	−3.21986	−	3.21986i	−0.147273	−	0.147273i
$479$	−26.9725			−1.23240			−0.616202	−	0.787588i	$-0.711330\pi$
$479$	−26.9725			−1.23240			−0.616202	+	0.787588i	$0.711330\pi$
$480$		0			0
$481$	2.17795			0.0993062
$482$	8.39528	+	8.39528i	0.382395	+	0.382395i
$483$	−0.0446838	+	12.4378i	−0.00203319	+	0.565937i
$484$		−	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	0.368749	−	0.929529i	$-0.379786\pi$
$487$	28.6505	−	28.6505i	1.29828	−	1.29828i	0.929529	−	0.368749i	$-0.120214\pi$
$488$	−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	$-0.0197303\pi$
$492$	0.151046		0.000542646i	0.00680966		2.44644e-5i
$493$	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
$498$	20.7574	+	0.0745730i	0.930162	+	0.00334170i
$499$		−	30.3151i		−	1.35709i	−0.734558	−	0.678546i	$-0.762611\pi$
$499$		−	30.3151i		−	1.35709i	0.734558	−	0.678546i	$-0.237389\pi$
$500$		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	$-0.746670\pi$
$503$	0.331820	−	0.331820i	0.0147951	−	0.0147951i	0.714466	+	0.699671i	$0.246670\pi$
$504$	−0.0361859	+	5.03611i	−0.00161185	+	0.224326i
$505$		0			0
$506$			53.0827i			2.35982i
$507$	0.0803614	−	22.3686i	0.00356898	−	0.993425i
$508$	32.1925	+	32.1925i	1.42831	+	1.42831i
$509$	14.6491			0.649311			0.324656	−	0.945832i	$-0.394752\pi$
$509$	14.6491			0.649311			0.324656	+	0.945832i	$0.394752\pi$
$510$		0			0
$511$	12.1778			0.538713
$512$	−14.2950	−	14.2950i	−0.631758	−	0.631758i
$513$	0.297604	−	27.6117i	0.0131395	−	1.21909i
$514$			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	$0.818435\pi$
$522$	13.0735	+	13.2628i	0.572212	+	0.580495i
$523$	23.4069	+	23.4069i	1.02351	+	1.02351i	0.999717	+	0.0237950i	$0.00757491\pi$
$523$	23.4069	+	23.4069i	1.02351	+	1.02351i	0.0237950	+	0.999717i	$0.492425\pi$
$524$	−35.1668			−1.53627
$525$		0			0
$526$	56.1475			2.44815
$527$	−1.52639	−	1.52639i	−0.0664907	−	0.0664907i
$528$	0.0394214	−	10.9730i	0.00171560	−	0.477536i
$529$		−	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
$537$	−25.3436	−	0.0910493i	−1.09366	−	0.00392907i
$538$	−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
$543$	−17.0384	−	0.0612121i	−0.731187	−	0.00262686i
$544$			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	−0.625119	−	0.780530i	$-0.714949\pi$
$547$	3.63475	−	3.63475i	0.155411	−	0.155411i	0.780530	+	0.625119i	$0.214949\pi$
$548$	−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
$552$	0.0750128	−	20.8798i	0.00319276	−	0.888705i
$553$	−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	$-0.306735\pi$
$557$	−5.91751	−	5.91751i	−0.250733	−	0.250733i	−0.821271	+	0.570538i	$0.806735\pi$
$558$	−41.9328	−	42.5397i	−1.77516	−	1.80085i
$559$			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	$-0.614813\pi$
$563$	13.8267	−	13.8267i	0.582728	−	0.582728i	0.935652	+	0.352924i	$0.114813\pi$
$564$	−17.1643	+	17.0414i	−0.722749	+	0.717574i
$565$		0			0
$566$		−	61.2316i		−	2.57376i
$567$	−6.45475	+	6.27185i	−0.271074	+	0.263393i
$568$	−4.69425	−	4.69425i	−0.196966	−	0.196966i
$569$	−6.82232			−0.286007			−0.143003	−	0.989722i	$-0.545676\pi$
$569$	−6.82232			−0.286007			−0.143003	+	0.989722i	$0.545676\pi$
$570$		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
$573$	−0.0396926	+	11.0484i	−0.00165818	+	0.461555i
$574$		−	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	−0.729779	−	0.683683i	$-0.760377\pi$
$577$	−1.10727	+	1.10727i	−0.0460964	+	0.0460964i	0.683683	+	0.729779i	$0.260377\pi$
$578$	−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
$582$	12.1295	+	0.0435762i	0.502782	+	0.00180629i
$583$	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	$-0.322789\pi$
$587$	−7.76708	−	7.76708i	−0.320582	−	0.320582i	−0.848990	+	0.528408i	$0.822789\pi$
$588$	4.79558	+	0.0172286i	0.197766	+	0.000710495i
$589$		−	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	$-0.675252\pi$
$593$	8.01301	−	8.01301i	0.329055	−	0.329055i	0.852227	+	0.523172i	$0.175252\pi$
$594$	−27.4515	+	26.8661i	−1.12635	+	1.10233i
$595$		0			0
$596$			52.4261i			2.14746i
$597$	0.0584943	−	16.2819i	0.00239401	−	0.666373i
$598$	−3.24029	−	3.24029i	−0.132505	−	0.132505i
$599$	−20.3742			−0.832467			−0.416233	−	0.909258i	$-0.636650\pi$
$599$	−20.3742			−0.832467			−0.416233	+	0.909258i	$0.636650\pi$
$600$		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
$603$	−19.1805	+	18.9069i	−0.781092	+	0.769947i
$604$		−	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	−0.705681	−	0.708529i	$-0.749359\pi$
$607$	0.0701607	−	0.0701607i	0.00284774	−	0.00284774i	0.708529	+	0.705681i	$0.249359\pi$
$608$	−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
$612$	1.40049	−	1.38051i	0.0566115	−	0.0558038i
$613$	26.6840	+	26.6840i	1.07776	+	1.07776i	0.996710	+	0.0810445i	$0.0258256\pi$
$613$	26.6840	+	26.6840i	1.07776	+	1.07776i	0.0810445	+	0.996710i	$0.474174\pi$
$614$	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	$-0.308069\pi$
$617$	−6.37294	−	6.37294i	−0.256565	−	0.256565i	−0.823656	+	0.567090i	$0.808069\pi$
$618$	−0.0185315	+	5.15824i	−0.000745446	+	0.207495i
$619$			17.7676i			0.714139i	0.934078	+	0.357070i	$0.116224\pi$
$619$			17.7676i			0.714139i	−0.934078	+	0.357070i	$0.883776\pi$
$620$		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
$627$	−31.1575	−	0.111936i	−1.24431	−	0.00447030i
$628$	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
$633$	−14.3613	−	0.0515944i	−0.570811	−	0.00205070i
$634$		−	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	$-0.0945920\pi$
$642$	0.0568527	−	15.8250i	0.00224380	−	0.624562i
$643$	32.7229	+	32.7229i	1.29047	+	1.29047i	0.934498	+	0.355968i	$0.115849\pi$
$643$	32.7229	+	32.7229i	1.29047	+	1.29047i	0.355968	+	0.934498i	$0.384151\pi$
$644$	−19.8823			−0.783474
$645$		0			0
$646$	2.74747			0.108098
$647$	27.0564	+	27.0564i	1.06370	+	1.06370i	0.997828	+	0.0658674i	$0.0209814\pi$
$647$	27.0564	+	27.0564i	1.06370	+	1.06370i	0.0658674	+	0.997828i	$0.479019\pi$
$648$	10.8359	−	10.5289i	0.425674	−	0.413612i
$649$			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	$-0.714260\pi$
$653$	4.04918	−	4.04918i	0.158457	−	0.158457i	0.781883	+	0.623426i	$0.214260\pi$
$654$	7.57410	−	7.51988i	0.296171	−	0.294050i
$655$		0			0
$656$		−	0.0589475i		−	0.00230151i
$657$	−25.6467	−	26.0179i	−1.00057	−	1.01506i
$658$	7.78809	+	7.78809i	0.303611	+	0.303611i
$659$	11.5870			0.451366			0.225683	−	0.974201i	$-0.427539\pi$
$659$	11.5870			0.451366			0.225683	+	0.974201i	$0.427539\pi$
$660$		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
$663$	0.000430499	−	0.119829i	1.67192e−5	−	0.00465379i
$664$			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
$672$	12.8941	+	0.0463233i	0.497400	+	0.00178696i
$673$	13.7667	+	13.7667i	0.530666	+	0.530666i	0.920770	−	0.390105i	$-0.127561\pi$
$673$	13.7667	+	13.7667i	0.530666	+	0.530666i	−0.390105	+	0.920770i	$0.627561\pi$
$674$	−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	$-0.396650\pi$
$677$	−16.3594	−	16.3594i	−0.628742	−	0.628742i	−0.947752	+	0.319009i	$0.896650\pi$
$678$	10.7942	+	0.0387793i	0.414549	+	0.00148931i
$679$		−	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	$-0.800650\pi$
$683$	−5.85622	+	5.85622i	−0.224082	+	0.224082i	0.586133	+	0.810215i	$0.300650\pi$
$684$	44.1398	+	0.317157i	1.68773	+	0.0121268i
$685$		0			0
$686$		−	2.18375i		−	0.0833758i
$687$	−0.0389535	+	10.8427i	−0.00148617	+	0.413676i
$688$	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
$693$	7.12903	+	7.23222i	0.270809	+	0.274729i
$694$			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	$-0.253983\pi$
$702$	0.0357368	−	3.31567i	0.00134880	−	0.125142i
$703$	−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
$708$	0.177743	−	49.4749i	0.00668001	−	1.85938i
$709$			16.6841i			0.626586i	0.949656	+	0.313293i	$0.101432\pi$
$709$			16.6841i			0.626586i	−0.949656	+	0.313293i	$0.898568\pi$
$710$		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
$717$	3.61167	+	0.0129753i	0.134880	+	0.000484570i
$718$	−42.1016	−	42.1016i	−1.57122	−	1.57122i
$719$	13.0709			0.487464			0.243732	−	0.969843i	$-0.421628\pi$
$719$	13.0709			0.487464			0.243732	+	0.969843i	$0.421628\pi$
$720$		0			0
$721$	1.36377			0.0507895
$722$	14.2688	+	14.2688i	0.531031	+	0.531031i
$723$	−9.41686	−	0.0338310i	−0.350217	−	0.00125819i
$724$		−	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	−0.969167	−	0.246406i	$-0.920750\pi$
$727$	−19.4878	+	19.4878i	−0.722761	+	0.722761i	0.246406	+	0.969167i	$0.420750\pi$
$728$	−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
$732$	0.117264	−	32.6403i	0.00433418	−	1.20642i
$733$	−24.5624	−	24.5624i	−0.907232	−	0.907232i	0.0888162	−	0.996048i	$-0.471692\pi$
$733$	−24.5624	−	24.5624i	−0.907232	−	0.907232i	−0.996048	+	0.0888162i	$0.971692\pi$
$734$	49.1774			1.81517
$735$		0			0
$736$	−53.4585			−1.97051
$737$	21.4886	+	21.4886i	0.791543	+	0.791543i
$738$	−0.146951	+	0.144855i	−0.00540935	+	0.00533217i
$739$			25.3925i			0.934079i	0.884236	+	0.467040i	$0.154679\pi$
$739$			25.3925i			0.934079i	−0.884236	+	0.467040i	$0.845321\pi$
$740$		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	$-0.627742\pi$
$743$	14.4447	−	14.4447i	0.529923	−	0.529923i	0.920549	+	0.390626i	$0.127742\pi$
$744$	18.8137	−	18.6790i	0.689742	−	0.684804i
$745$		0			0
$746$			72.0445i			2.63774i
$747$	−11.7251	+	11.5578i	−0.429000	+	0.422879i
$748$	−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
$753$	−0.145251	+	40.4307i	−0.00529325	+	1.47338i
$754$			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	−0.455144	−	0.890418i	$-0.650412\pi$
$757$	11.9760	−	11.9760i	0.435274	−	0.435274i	0.890418	+	0.455144i	$0.150412\pi$
$758$	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	$0.731930\pi$
$762$	−62.1937	−	0.223437i	−2.25304	−	0.00809426i
$763$	−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
$768$	−3.69569	−	0.0132771i	−0.133357	−	0.000479097i
$769$		−	3.96520i		−	0.142989i	−0.997441	−	0.0714944i	$-0.977223\pi$
$769$		−	3.96520i		−	0.142989i	0.997441	−	0.0714944i	$-0.0227768\pi$
$770$		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	$-0.701241\pi$
$773$	5.99943	−	5.99943i	0.215785	−	0.215785i	0.806719	+	0.590935i	$0.201241\pi$
$774$	0.250881	−	34.9160i	0.00901774	−	1.25503i
$775$		0			0
$776$			5.38352i			0.193257i
$777$	−0.0463770	+	12.9090i	−0.00166377	+	0.463109i
$778$	−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
$783$	−14.7701	−	0.159195i	−0.527841	−	0.00568916i
$784$		−	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	−0.930326	−	0.366733i	$-0.880476\pi$
$787$	−15.8108	+	15.8108i	−0.563593	+	0.563593i	0.366733	+	0.930326i	$0.380476\pi$
$788$	−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
$792$	−11.9678	−	12.1411i	−0.425258	−	0.431414i
$793$	−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	$-0.318010\pi$
$797$	−8.46554	−	8.46554i	−0.299865	−	0.299865i	−0.840961	+	0.541096i	$0.818010\pi$
$798$	0.0722114	−	20.1000i	0.00255625	−	0.711534i
$799$		−	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
$807$	49.3848	+	0.177420i	1.73843	+	0.00624547i
$808$	10.2517	+	10.2517i	0.360655	+	0.360655i
$809$	25.5350			0.897764			0.448882	−	0.893591i	$-0.351822\pi$
$809$	25.5350			0.897764			0.448882	+	0.893591i	$0.351822\pi$
$810$		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
$813$	5.40767	+	0.0194276i	0.189655	+	0.000681355i
$814$			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	$0.876537\pi$
$822$	0.0998224	−	27.7856i	0.00348171	−	0.969133i
$823$	−8.35207	−	8.35207i	−0.291135	−	0.291135i	0.546394	−	0.837528i	$-0.316000\pi$
$823$	−8.35207	−	8.35207i	−0.291135	−	0.291135i	−0.837528	+	0.546394i	$0.816000\pi$
$824$	−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	$-0.136680\pi$
$827$	14.1747	+	14.1747i	0.492902	+	0.492902i	−0.416318	+	0.909219i	$0.636680\pi$
$828$	41.8727	+	42.4788i	1.45518	+	1.47624i
$829$			19.3836i			0.673219i	0.941644	+	0.336610i	$0.109280\pi$
$829$			19.3836i			0.673219i	−0.941644	+	0.336610i	$0.890720\pi$
$830$		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
$837$	47.3745	+	0.510610i	1.63750	+	0.0176493i
$838$	9.06346	+	9.06346i	0.313092	+	0.313092i
$839$	26.2528			0.906346			0.453173	−	0.891423i	$-0.350292\pi$
$839$	26.2528			0.906346			0.453173	+	0.891423i	$0.350292\pi$
$840$		0			0
$841$	−20.9192			−0.721352
$842$	−41.5131	−	41.5131i	−1.43063	−	1.43063i
$843$	0.0791386	−	22.0282i	0.00272568	−	0.758693i
$844$		−	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
$852$	18.9643	+	0.0681311i	0.649707	+	0.00233413i
$853$	−29.8920	−	29.8920i	−1.02348	−	1.02348i	−0.999718	−	0.0237636i	$-0.992435\pi$
$853$	−29.8920	−	29.8920i	−1.02348	−	1.02348i	−0.0237636	−	0.999718i	$-0.507565\pi$
$854$	−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	$-0.295701\pi$
$857$	−5.92367	−	5.92367i	−0.202349	−	0.202349i	−0.801006	+	0.598657i	$0.795701\pi$
$858$	−3.74145	−	0.0134415i	−0.127731	−	0.000458885i
$859$		−	10.3620i		−	0.353548i	−0.984252	−	0.176774i	$-0.943434\pi$
$859$		−	10.3620i		−	0.353548i	0.984252	−	0.176774i	$-0.0565661\pi$
$860$		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	$-0.646419\pi$
$863$	13.2818	−	13.2818i	0.452118	−	0.452118i	0.896057	+	0.443939i	$0.146419\pi$
$864$	−27.0563	−	27.6459i	−0.920474	−	0.940532i
$865$		0			0
$866$		−	6.82129i		−	0.231797i
$867$	0.105434	−	29.3476i	0.00358073	−	0.996696i
$868$	−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
$873$	−6.85150	+	6.75374i	−0.231888	+	0.228580i
$874$			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	−0.784116	−	0.620614i	$-0.786883\pi$
$877$	−4.84197	+	4.84197i	−0.163502	+	0.163502i	0.620614	+	0.784116i	$0.286883\pi$
$878$	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	$-0.0926701\pi$
$882$	−4.66559	+	4.59902i	−0.157099	+	0.154857i
$883$	−12.2389	−	12.2389i	−0.411871	−	0.411871i	0.470519	−	0.882390i	$-0.344067\pi$
$883$	−12.2389	−	12.2389i	−0.411871	−	0.411871i	−0.882390	+	0.470519i	$0.844067\pi$
$884$	0.191553			0.00644262
$885$		0			0
$886$	37.9983			1.27658
$887$	41.0767	+	41.0767i	1.37922	+	1.37922i	0.845934	+	0.533287i	$0.179043\pi$
$887$	41.0767	+	41.0767i	1.37922	+	1.37922i	0.533287	+	0.845934i	$0.320957\pi$
$888$	0.0778552	−	21.6710i	0.00261265	−	0.727231i
$889$			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
$897$	3.63458	+	0.0130576i	0.121355	+	0.000435980i
$898$	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
$903$	−9.23144	−	0.0331649i	−0.307203	−	0.00110366i
$904$			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	−0.987068	−	0.160303i	$-0.948753\pi$
$907$	−24.8992	+	24.8992i	−0.826765	+	0.826765i	0.160303	+	0.987068i	$0.448753\pi$
$908$	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	$-0.126893\pi$
$912$	0.0618874	−	17.2264i	0.00204930	−	0.570422i
$913$	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
$918$	−0.0289532	+	2.68628i	−0.000955598	+	0.0886605i
$919$		−	31.9950i		−	1.05542i	−0.849425	−	0.527710i	$-0.823051\pi$
$919$		−	31.9950i		−	1.05542i	0.849425	−	0.527710i	$-0.176949\pi$
$920$		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
$927$	−2.87214	−	2.91371i	−0.0943333	−	0.0956987i
$928$	14.9639	+	14.9639i	0.491214	+	0.491214i
$929$	−49.7858			−1.63342			−0.816709	−	0.577050i	$-0.804204\pi$
$929$	−49.7858			−1.63342			−0.816709	+	0.577050i	$0.804204\pi$
$930$		0			0
$931$	−5.31419			−0.174166
$932$	7.40423	+	7.40423i	0.242534	+	0.242534i
$933$	−0.00245264	+	0.682692i	−8.02958e−5	+	0.0223503i
$934$		−	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	−0.937911	−	0.346876i	$-0.887243\pi$
$937$	−18.0919	+	18.0919i	−0.591035	+	0.591035i	0.346876	+	0.937911i	$0.387243\pi$
$938$	−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	$0.531557\pi$
$942$	−23.0933	−	0.0829648i	−0.752419	−	0.00270314i
$943$	−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	$-0.473710\pi$
$947$	−28.1297	−	28.1297i	−0.914093	−	0.914093i	−0.996591	+	0.0824986i	$0.973710\pi$
$948$	−54.8851	−	0.197180i	−1.78259	−	0.00640411i
$949$		−	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	$-0.627100\pi$
$953$	16.4406	−	16.4406i	0.532564	−	0.532564i	0.921335	+	0.388771i	$0.127100\pi$
$954$	32.9163	+	0.236513i	1.06571	+	0.00765740i
$955$		0			0
$956$			5.77342i			0.186726i
$957$	−0.0598771	+	16.6668i	−0.00193555	+	0.538761i
$958$	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
$963$	8.81142	+	8.93897i	0.283944	+	0.288054i
$964$		−	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	−0.652158	−	0.758083i	$-0.726136\pi$
$967$	3.29391	−	3.29391i	0.105925	−	0.105925i	0.758083	+	0.652158i	$0.226136\pi$
$968$	−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	$0.826477\pi$
$972$	−0.775246	+	43.1535i	−0.0248660	+	1.38415i
$973$	−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	$-0.188941\pi$
$977$	8.42742	+	8.42742i	0.269617	+	0.269617i	−0.559329	+	0.828946i	$0.688941\pi$
$978$	−0.0687302	+	19.1311i	−0.00219775	+	0.611744i
$979$		−	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	−0.532042	+	0.846718i	$0.678575\pi$
$983$	−43.2280	+	43.2280i	−1.37876	+	1.37876i	−0.846718	+	0.532042i	$0.821425\pi$
$984$	−0.0645255	−	0.0649908i	−0.00205700	−	0.00207183i
$985$		0			0
$986$		−	1.46968i		−	0.0468041i
$987$	−8.73578	−	0.0313841i	−0.278063	−	0.000998968i
$988$	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
$993$	−42.8417	−	0.153913i	−1.35954	−	0.00488428i
$994$		−	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	−0.233543	−	0.972346i	$-0.575032\pi$
$997$	23.3279	−	23.3279i	0.738803	−	0.738803i	0.972346	+	0.233543i	$0.0750321\pi$
$998$	−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.218.2		24
3.2	odd	2	inner	525.2.j.b.218.11		24
5.2	odd	4	inner	525.2.j.b.407.11		24
5.3	odd	4		105.2.j.a.92.2	yes	24
5.4	even	2		105.2.j.a.8.11	yes	24
15.2	even	4	inner	525.2.j.b.407.2		24
15.8	even	4		105.2.j.a.92.11	yes	24
15.14	odd	2		105.2.j.a.8.2	✓	24
35.3	even	12		735.2.y.g.422.2		48
35.4	even	6		735.2.y.j.128.2		48
35.9	even	6		735.2.y.j.263.11		48
35.13	even	4		735.2.j.h.197.2		24
35.18	odd	12		735.2.y.j.422.2		48
35.19	odd	6		735.2.y.g.263.11		48
35.23	odd	12		735.2.y.j.557.11		48
35.24	odd	6		735.2.y.g.128.2		48
35.33	even	12		735.2.y.g.557.11		48
35.34	odd	2		735.2.j.h.638.11		24
105.23	even	12		735.2.y.j.557.2		48
105.38	odd	12		735.2.y.g.422.11		48
105.44	odd	6		735.2.y.j.263.2		48
105.53	even	12		735.2.y.j.422.11		48
105.59	even	6		735.2.y.g.128.11		48
105.68	odd	12		735.2.y.g.557.2		48
105.74	odd	6		735.2.y.j.128.11		48
105.83	odd	4		735.2.j.h.197.11		24
105.89	even	6		735.2.y.g.263.2		48
105.104	even	2		735.2.j.h.638.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.2	✓	24	15.14	odd	2
105.2.j.a.8.11	yes	24	5.4	even	2
105.2.j.a.92.2	yes	24	5.3	odd	4
105.2.j.a.92.11	yes	24	15.8	even	4
525.2.j.b.218.2		24	1.1	even	1	trivial
525.2.j.b.218.11		24	3.2	odd	2	inner
525.2.j.b.407.2		24	15.2	even	4	inner
525.2.j.b.407.11		24	5.2	odd	4	inner
735.2.j.h.197.2		24	35.13	even	4
735.2.j.h.197.11		24	105.83	odd	4
735.2.j.h.638.2		24	105.104	even	2
735.2.j.h.638.11		24	35.34	odd	2
735.2.y.g.128.2		48	35.24	odd	6
735.2.y.g.128.11		48	105.59	even	6
735.2.y.g.263.2		48	105.89	even	6
735.2.y.g.263.11		48	35.19	odd	6
735.2.y.g.422.2		48	35.3	even	12
735.2.y.g.422.11		48	105.38	odd	12
735.2.y.g.557.2		48	105.68	odd	12
735.2.y.g.557.11		48	35.33	even	12
735.2.y.j.128.2		48	35.4	even	6
735.2.y.j.128.11		48	105.74	odd	6
735.2.y.j.263.2		48	105.44	odd	6
735.2.y.j.263.11		48	35.9	even	6
735.2.y.j.422.2		48	35.18	odd	12
735.2.y.j.422.11		48	105.53	even	12
735.2.y.j.557.2		48	105.23	even	12
735.2.y.j.557.11		48	35.23	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.54414 - 1.54414i) q^{2} +(1.73204 + 0.00622252i) q^{3} +2.76875i q^{4} +(-2.66491 - 2.68412i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(1.18705 - 1.18705i) q^{8} +(2.99992 + 0.0215553i) q^{9} +O(q^{10})\)	\(q+(-1.54414 - 1.54414i) q^{2} +(1.73204 + 0.00622252i) 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} +(-0.0172286 + 4.79558i) q^{12} +(0.206632 + 0.206632i) q^{13} +2.18375 q^{14} +1.87154 q^{16} +(-0.167409 - 0.167409i) q^{17} +(-4.59902 - 4.66559i) 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} +(5.19585 + 0.0560017i) q^{27} +(-1.95780 - 1.95780i) q^{28} -2.84268 q^{29} +9.11776 q^{31} +(-5.26402 - 5.26402i) q^{32} +(0.0210636 - 5.86307i) 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} +(3.78233 + 0.0135884i) q^{42} +(3.76875 + 3.76875i) q^{43} +9.37239 q^{44} -15.6815 q^{46} +(3.56639 + 3.56639i) q^{47} +(3.24158 + 0.0116457i) 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} +(0.0330677 - 9.20439i) q^{57} +(4.38949 + 4.38949i) q^{58} -10.3168 q^{59} -6.80634 q^{61} +(-14.0791 - 14.0791i) q^{62} +(-2.13651 + 2.10602i) 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} +(3.58665 - 3.53548i) q^{72} +(-8.61099 - 8.61099i) q^{73} -16.2757 q^{74} +14.7136 q^{76} +(2.39360 + 2.39360i) q^{77} +(0.00397083 - 1.10528i) 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} +(-4.92363 - 0.0176886i) q^{87} +(-4.01825 - 4.01825i) q^{88} +2.00190 q^{89} -0.292222 q^{91} +(14.0589 + 14.0589i) q^{92} +(15.7923 + 0.0567354i) 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

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