LMFDB - Embedded newform 60.7.g.a.41.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(41,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("60.41");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.g (of order $2$, degree $1$, 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:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 202x^{6} + 620x^{5} + 12167x^{4} - 25372x^{3} - 177926x^{2} + 190716x + 977814 $ x^8 - 4x^7 - 202x^6 + 620x^5 + 12167x^4 - 25372x^3 - 177926x^2 + 190716*x + 977814
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{7}\cdot 5^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			41.4
Root			$-9.26938 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	60.41
Dual form			60.7.g.a.41.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-22.1779 + 15.3993i) q^{3} -55.9017i q^{5} +437.053 q^{7} +(254.720 - 683.051i) q^{9} +O(q^{10})$	\(q+(-22.1779 + 15.3993i) q^{3} -55.9017i q^{5} +437.053 q^{7} +(254.720 - 683.051i) q^{9} +1898.54i q^{11} -2670.19 q^{13} +(860.849 + 1239.78i) q^{15} +4521.29i q^{17} -9502.28 q^{19} +(-9692.93 + 6730.33i) q^{21} +549.560i q^{23} -3125.00 q^{25} +(4869.36 + 19071.2i) q^{27} +43308.7i q^{29} +29588.2 q^{31} +(-29236.2 - 42105.6i) q^{33} -24432.0i q^{35} -45794.0 q^{37} +(59219.3 - 41119.2i) q^{39} +114611. i q^{41} -24917.0 q^{43} +(-38183.7 - 14239.3i) q^{45} -18258.6i q^{47} +73366.3 q^{49} +(-69624.9 - 100273. i) q^{51} -174021. i q^{53} +106131. q^{55} +(210741. - 146329. i) q^{57} +67872.4i q^{59} +175028. q^{61} +(111326. - 298529. i) q^{63} +149268. i q^{65} +16056.7 q^{67} +(-8462.86 - 12188.1i) q^{69} -222821. i q^{71} -620790. q^{73} +(69306.0 - 48122.9i) q^{75} +829761. i q^{77} +525417. q^{79} +(-401676. - 347974. i) q^{81} +790761. i q^{83} +252748. q^{85} +(-666925. - 960496. i) q^{87} +1.12565e6i q^{89} -1.16702e6 q^{91} +(-656204. + 455638. i) q^{93} +531194. i q^{95} -624200. q^{97} +(1.29680e6 + 483596. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 20 q^{3} - 560 q^{7} + 1492 q^{9}+O(q^{10}) $ 8 * q - 20 * q^3 - 560 * q^7 + 1492 * q^9	$ 8 q - 20 q^{3} - 560 q^{7} + 1492 q^{9} - 6440 q^{13} + 2000 q^{15} - 15272 q^{19} - 868 q^{21} - 25000 q^{25} - 18620 q^{27} + 35032 q^{31} - 111120 q^{33} + 99880 q^{37} + 39608 q^{39} - 161000 q^{43} - 5500 q^{45} + 202560 q^{49} + 429120 q^{51} - 33000 q^{55} - 27160 q^{57} - 135608 q^{61} + 377240 q^{63} + 404920 q^{67} - 254940 q^{69} - 356960 q^{73} + 62500 q^{75} + 707704 q^{79} - 1198112 q^{81} + 828000 q^{85} - 1528440 q^{87} - 2004112 q^{91} - 467920 q^{93} - 1326320 q^{97} + 2650080 q^{99}+O(q^{100}) $ 8 * q - 20 * q^3 - 560 * q^7 + 1492 * q^9 - 6440 * q^13 + 2000 * q^15 - 15272 * q^19 - 868 * q^21 - 25000 * q^25 - 18620 * q^27 + 35032 * q^31 - 111120 * q^33 + 99880 * q^37 + 39608 * q^39 - 161000 * q^43 - 5500 * q^45 + 202560 * q^49 + 429120 * q^51 - 33000 * q^55 - 27160 * q^57 - 135608 * q^61 + 377240 * q^63 + 404920 * q^67 - 254940 * q^69 - 356960 * q^73 + 62500 * q^75 + 707704 * q^79 - 1198112 * q^81 + 828000 * q^85 - 1528440 * q^87 - 2004112 * q^91 - 467920 * q^93 - 1326320 * q^97 + 2650080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−22.1779	+	15.3993i	−0.821405	+	0.570346i
$3$	−22.1779	+	15.3993i	−0.821405	+	0.570346i
$4$		0			0
$5$		−	55.9017i		−	0.447214i
$5$		−	55.9017i		−	0.447214i
$6$		0			0
$7$	437.053			1.27421			0.637103	−	0.770778i	$-0.280132\pi$
$7$	437.053			1.27421			0.637103	+	0.770778i	$0.280132\pi$
$8$		0			0
$9$	254.720	−	683.051i	0.349411	−	0.936970i
$10$		0			0
$11$			1898.54i			1.42640i	0.700962	+	0.713199i	$0.252754\pi$
$11$			1898.54i			1.42640i	−0.700962	+	0.713199i	$0.747246\pi$
$12$		0			0
$13$	−2670.19			−1.21538			−0.607691	−	0.794174i	$-0.707904\pi$
$13$	−2670.19			−1.21538			−0.607691	+	0.794174i	$0.707904\pi$
$14$		0			0
$15$	860.849	+	1239.78i	0.255067	+	0.367343i
$16$		0			0
$17$			4521.29i			0.920270i	0.887849	+	0.460135i	$0.152199\pi$
$17$			4521.29i			0.920270i	−0.887849	+	0.460135i	$0.847801\pi$
$18$		0			0
$19$	−9502.28			−1.38537			−0.692687	−	0.721238i	$-0.743573\pi$
$19$	−9502.28			−1.38537			−0.692687	+	0.721238i	$0.743573\pi$
$20$		0			0
$21$	−9692.93	+	6730.33i	−1.04664	+	0.726739i
$22$		0			0
$23$			549.560i			0.0451680i	0.999745	+	0.0225840i	$0.00718933\pi$
$23$			549.560i			0.0451680i	−0.999745	+	0.0225840i	$0.992811\pi$
$24$		0			0
$25$	−3125.00			−0.200000
$26$		0			0
$27$	4869.36	+	19071.2i	0.247389	+	0.968916i
$28$		0			0
$29$			43308.7i			1.77575i	0.460089	+	0.887873i	$0.347818\pi$
$29$			43308.7i			1.77575i	−0.460089	+	0.887873i	$0.652182\pi$
$30$		0			0
$31$	29588.2			0.993191			0.496596	−	0.867982i	$-0.334583\pi$
$31$	29588.2			0.993191			0.496596	+	0.867982i	$0.334583\pi$
$32$		0			0
$33$	−29236.2	−	42105.6i	−0.813540	−	1.17165i
$34$		0			0
$35$		−	24432.0i		−	0.569843i
$36$		0			0
$37$	−45794.0			−0.904074			−0.452037	−	0.891999i	$-0.649302\pi$
$37$	−45794.0			−0.904074			−0.452037	+	0.891999i	$0.649302\pi$
$38$		0			0
$39$	59219.3	−	41119.2i	0.998320	−	0.693188i
$40$		0			0
$41$			114611.i			1.66294i	0.555570	+	0.831470i	$0.312500\pi$
$41$			114611.i			1.66294i	−0.555570	+	0.831470i	$0.687500\pi$
$42$		0			0
$43$	−24917.0			−0.313394			−0.156697	−	0.987647i	$-0.550085\pi$
$43$	−24917.0			−0.313394			−0.156697	+	0.987647i	$0.550085\pi$
$44$		0			0
$45$	−38183.7	−	14239.3i	−0.419026	−	0.156261i
$46$		0			0
$47$		−	18258.6i		−	0.175863i	−0.996127	−	0.0879313i	$-0.971974\pi$
$47$		−	18258.6i		−	0.175863i	0.996127	−	0.0879313i	$-0.0280256\pi$
$48$		0			0
$49$	73366.3			0.623603
$50$		0			0
$51$	−69624.9	−	100273.i	−0.524873	−	0.755914i
$52$		0			0
$53$		−	174021.i		−	1.16889i	−0.811434	−	0.584444i	$-0.801313\pi$
$53$		−	174021.i		−	1.16889i	0.811434	−	0.584444i	$-0.198687\pi$
$54$		0			0
$55$	106131.			0.637905
$56$		0			0
$57$	210741.	−	146329.i	1.13795	−	0.790143i
$58$		0			0
$59$			67872.4i			0.330474i	0.986254	+	0.165237i	$0.0528389\pi$
$59$			67872.4i			0.330474i	−0.986254	+	0.165237i	$0.947161\pi$
$60$		0			0
$61$	175028.			0.771112			0.385556	−	0.922685i	$-0.374010\pi$
$61$	175028.			0.771112			0.385556	+	0.922685i	$0.374010\pi$
$62$		0			0
$63$	111326.	−	298529.i	0.445222	−	1.19389i
$64$		0			0
$65$			149268.i			0.543535i
$66$		0			0
$67$	16056.7			0.0533865			0.0266932	−	0.999644i	$-0.491502\pi$
$67$	16056.7			0.0533865			0.0266932	+	0.999644i	$0.491502\pi$
$68$		0			0
$69$	−8462.86	−	12188.1i	−0.0257614	−	0.0371012i
$70$		0			0
$71$		−	222821.i		−	0.622561i	−0.950318	−	0.311281i	$-0.899242\pi$
$71$		−	222821.i		−	0.622561i	0.950318	−	0.311281i	$-0.100758\pi$
$72$		0			0
$73$	−620790.			−1.59579			−0.797896	−	0.602796i	$-0.794053\pi$
$73$	−620790.			−1.59579			−0.797896	+	0.602796i	$0.794053\pi$
$74$		0			0
$75$	69306.0	−	48122.9i	0.164281	−	0.114069i
$76$		0			0
$77$			829761.i			1.81753i
$78$		0			0
$79$	525417.			1.06567			0.532835	−	0.846219i	$-0.321127\pi$
$79$	525417.			1.06567			0.532835	+	0.846219i	$0.321127\pi$
$80$		0			0
$81$	−401676.	−	347974.i	−0.755824	−	0.654775i
$82$		0			0
$83$			790761.i			1.38296i	0.722394	+	0.691482i	$0.243042\pi$
$83$			790761.i			1.38296i	−0.722394	+	0.691482i	$0.756958\pi$
$84$		0			0
$85$	252748.			0.411557
$86$		0			0
$87$	−666925.	−	960496.i	−1.01279	−	1.45861i
$88$		0			0
$89$			1.12565e6i			1.59673i	0.602172	+	0.798366i	$0.294302\pi$
$89$			1.12565e6i			1.59673i	−0.602172	+	0.798366i	$0.705698\pi$
$90$		0			0
$91$	−1.16702e6			−1.54865
$92$		0			0
$93$	−656204.	+	455638.i	−0.815812	+	0.566463i
$94$		0			0
$95$			531194.i			0.619558i
$96$		0			0
$97$	−624200.			−0.683925			−0.341963	−	0.939714i	$-0.611092\pi$
$97$	−624200.			−0.683925			−0.341963	+	0.939714i	$0.611092\pi$
$98$		0			0
$99$	1.29680e6	+	483596.i	1.33649	+	0.498399i
$100$		0			0
$101$			136558.i			0.132542i	0.997802	+	0.0662709i	$0.0211101\pi$
$101$			136558.i			0.132542i	−0.997802	+	0.0662709i	$0.978890\pi$
$102$		0			0
$103$	244469.			0.223724			0.111862	−	0.993724i	$-0.464319\pi$
$103$	244469.			0.223724			0.111862	+	0.993724i	$0.464319\pi$
$104$		0			0
$105$	376237.	+	541851.i	0.325007	+	0.468071i
$106$		0			0
$107$		−	1.66094e6i		−	1.35582i	−0.735143	−	0.677912i	$-0.762885\pi$
$107$		−	1.66094e6i		−	1.35582i	0.735143	−	0.677912i	$-0.237115\pi$
$108$		0			0
$109$	1.14498e6			0.884138			0.442069	−	0.896981i	$-0.354245\pi$
$109$	1.14498e6			0.884138			0.442069	+	0.896981i	$0.354245\pi$
$110$		0			0
$111$	1.01562e6	−	705198.i	0.742610	−	0.515635i
$112$		0			0
$113$		−	1.03300e6i		−	0.715924i	−0.933736	−	0.357962i	$-0.883472\pi$
$113$		−	1.03300e6i		−	0.715924i	0.933736	−	0.357962i	$-0.116528\pi$
$114$		0			0
$115$	30721.3			0.0201998
$116$		0			0
$117$	−680153.	+	1.82388e6i	−0.424667	+	1.13878i
$118$		0			0
$119$			1.97604e6i			1.17261i
$120$		0			0
$121$	−1.83288e6			−1.03461
$122$		0			0
$123$	−1.76494e6	−	2.54184e6i	−0.948451	−	1.36595i
$124$		0			0
$125$			174693.i			0.0894427i
$126$		0			0
$127$	3.16679e6			1.54600			0.772998	−	0.634408i	$-0.218756\pi$
$127$	3.16679e6			1.54600			0.772998	+	0.634408i	$0.218756\pi$
$128$		0			0
$129$	552608.	−	383706.i	0.257423	−	0.178743i
$130$		0			0
$131$		−	2.06944e6i		−	0.920533i	−0.887781	−	0.460266i	$-0.847754\pi$
$131$		−	2.06944e6i		−	0.920533i	0.887781	−	0.460266i	$-0.152246\pi$
$132$		0			0
$133$	−4.15300e6			−1.76525
$134$		0			0
$135$	1.06611e6	−	272206.i	0.433312	−	0.110636i
$136$		0			0
$137$		−	520796.i		−	0.202538i	−0.994859	−	0.101269i	$-0.967710\pi$
$137$		−	520796.i		−	0.202538i	0.994859	−	0.101269i	$-0.0322902\pi$
$138$		0			0
$139$	3.89209e6			1.44923			0.724616	−	0.689153i	$-0.242017\pi$
$139$	3.89209e6			1.44923			0.724616	+	0.689153i	$0.242017\pi$
$140$		0			0
$141$	281170.	+	404937.i	0.100303	+	0.144454i
$142$		0			0
$143$		−	5.06946e6i		−	1.73362i
$144$		0			0
$145$	2.42103e6			0.794138
$146$		0			0
$147$	−1.62711e6	+	1.12979e6i	−0.512230	+	0.355670i
$148$		0			0
$149$		−	2.27030e6i		−	0.686318i	−0.939277	−	0.343159i	$-0.888503\pi$
$149$		−	2.27030e6i		−	0.686318i	0.939277	−	0.343159i	$-0.111497\pi$
$150$		0			0
$151$	1.27718e6			0.370954			0.185477	−	0.982649i	$-0.440617\pi$
$151$	1.27718e6			0.370954			0.185477	+	0.982649i	$0.440617\pi$
$152$		0			0
$153$	3.08827e6	+	1.15166e6i	0.862265	+	0.321552i
$154$		0			0
$155$		−	1.65403e6i		−	0.444169i
$156$		0			0
$157$	1.40437e6			0.362897			0.181448	−	0.983400i	$-0.441921\pi$
$157$	1.40437e6			0.362897			0.181448	+	0.983400i	$0.441921\pi$
$158$		0			0
$159$	2.67980e6	+	3.85942e6i	0.666671	+	0.960130i
$160$		0			0
$161$			240187.i			0.0575534i
$162$		0			0
$163$	−4.84510e6			−1.11877			−0.559384	−	0.828909i	$-0.688962\pi$
$163$	−4.84510e6			−1.11877			−0.559384	+	0.828909i	$0.688962\pi$
$164$		0			0
$165$	−2.35377e6	+	1.63435e6i	−0.523978	+	0.363826i
$166$		0			0
$167$		−	823298.i		−	0.176770i	−0.996086	−	0.0883848i	$-0.971829\pi$
$167$		−	823298.i		−	0.176770i	0.996086	−	0.0883848i	$-0.0281705\pi$
$168$		0			0
$169$	2.30312e6			0.477152
$170$		0			0
$171$	−2.42043e6	+	6.49054e6i	−0.484065	+	1.29805i
$172$		0			0
$173$		−	9.06349e6i		−	1.75048i	−0.483689	−	0.875240i	$-0.660703\pi$
$173$		−	9.06349e6i		−	1.75048i	0.483689	−	0.875240i	$-0.339297\pi$
$174$		0			0
$175$	−1.36579e6			−0.254841
$176$		0			0
$177$	−1.04519e6	−	1.50527e6i	−0.188485	−	0.271453i
$178$		0			0
$179$			6.68808e6i			1.16612i	0.812430	+	0.583059i	$0.198144\pi$
$179$			6.68808e6i			1.16612i	−0.812430	+	0.583059i	$0.801856\pi$
$180$		0			0
$181$	−963367.			−0.162464			−0.0812318	−	0.996695i	$-0.525885\pi$
$181$	−963367.			−0.162464			−0.0812318	+	0.996695i	$0.525885\pi$
$182$		0			0
$183$	−3.88175e6	+	2.69531e6i	−0.633395	+	0.439800i
$184$		0			0
$185$			2.55996e6i			0.404314i
$186$		0			0
$187$	−8.58383e6			−1.31267
$188$		0			0
$189$	2.12817e6	+	8.33511e6i	0.315225	+	1.23460i
$190$		0			0
$191$			1.37892e6i			0.197896i	0.995093	+	0.0989482i	$0.0315478\pi$
$191$			1.37892e6i			0.197896i	−0.995093	+	0.0989482i	$0.968452\pi$
$192$		0			0
$193$	549967.			0.0765006			0.0382503	−	0.999268i	$-0.487822\pi$
$193$	549967.			0.0765006			0.0382503	+	0.999268i	$0.487822\pi$
$194$		0			0
$195$	−2.29863e6	−	3.31046e6i	−0.310003	−	0.446462i
$196$		0			0
$197$			4.23680e6i			0.554166i	0.960846	+	0.277083i	$0.0893677\pi$
$197$			4.23680e6i			0.554166i	−0.960846	+	0.277083i	$0.910632\pi$
$198$		0			0
$199$	−1.42388e7			−1.80682			−0.903411	−	0.428775i	$-0.858945\pi$
$199$	−1.42388e7			−1.80682			−0.903411	+	0.428775i	$0.858945\pi$
$200$		0			0
$201$	−356104.	+	247262.i	−0.0438519	+	0.0304488i
$202$		0			0
$203$			1.89282e7i			2.26267i
$204$		0			0
$205$	6.40697e6			0.743689
$206$		0			0
$207$	375377.	+	139984.i	0.0423211	+	0.0157822i
$208$		0			0
$209$		−	1.80404e7i		−	1.97610i
$210$		0			0
$211$	920077.			0.0979437			0.0489719	−	0.998800i	$-0.484406\pi$
$211$	920077.			0.0979437			0.0489719	+	0.998800i	$0.484406\pi$
$212$		0			0
$213$	3.43130e6	+	4.94172e6i	0.355075	+	0.511374i
$214$		0			0
$215$			1.39290e6i			0.140154i
$216$		0			0
$217$	1.29316e7			1.26553
$218$		0			0
$219$	1.37678e7	−	9.55976e6i	1.31079	−	0.910153i
$220$		0			0
$221$		−	1.20727e7i		−	1.11848i
$222$		0			0
$223$	1.23626e7			1.11479			0.557397	−	0.830246i	$-0.311800\pi$
$223$	1.23626e7			1.11479			0.557397	+	0.830246i	$0.311800\pi$
$224$		0			0
$225$	−796001.	+	2.13453e6i	−0.0698822	+	0.187394i
$226$		0			0
$227$		−	447256.i		−	0.0382365i	−0.999817	−	0.0191183i	$-0.993914\pi$
$227$		−	447256.i		−	0.0382365i	0.999817	−	0.0191183i	$-0.00608590\pi$
$228$		0			0
$229$	−1.85551e7			−1.54510			−0.772550	−	0.634954i	$-0.781019\pi$
$229$	−1.85551e7			−1.54510			−0.772550	+	0.634954i	$0.781019\pi$
$230$		0			0
$231$	−1.27778e7	−	1.84024e7i	−1.03662	−	1.49292i
$232$		0			0
$233$		−	1.33318e6i		−	0.105395i	−0.998611	−	0.0526976i	$-0.983218\pi$
$233$		−	1.33318e6i		−	0.105395i	0.998611	−	0.0526976i	$-0.0167819\pi$
$234$		0			0
$235$	−1.02069e6			−0.0786481
$236$		0			0
$237$	−1.16526e7	+	8.09107e6i	−0.875346	+	0.607800i
$238$		0			0
$239$			4.84514e6i			0.354905i	0.984129	+	0.177453i	$0.0567857\pi$
$239$			4.84514e6i			0.354905i	−0.984129	+	0.177453i	$0.943214\pi$
$240$		0			0
$241$	1.84505e7			1.31813			0.659063	−	0.752088i	$-0.270953\pi$
$241$	1.84505e7			1.31813			0.659063	+	0.752088i	$0.270953\pi$
$242$		0			0
$243$	1.42669e7	+	1.53180e6i	0.994286	+	0.106754i
$244$		0			0
$245$		−	4.10130e6i		−	0.278884i
$246$		0			0
$247$	2.53729e7			1.68376
$248$		0			0
$249$	−1.21772e7	−	1.75374e7i	−0.788768	−	1.13597i
$250$		0			0
$251$			1.38133e7i			0.873526i	0.899577	+	0.436763i	$0.143875\pi$
$251$			1.38133e7i			0.873526i	−0.899577	+	0.436763i	$0.856125\pi$
$252$		0			0
$253$	−1.04336e6			−0.0644276
$254$		0			0
$255$	−5.60542e6	+	3.89215e6i	−0.338055	+	0.234730i
$256$		0			0
$257$		−	2.89697e7i		−	1.70665i	−0.521381	−	0.853324i	$-0.674583\pi$
$257$		−	2.89697e7i		−	1.70665i	0.521381	−	0.853324i	$-0.325417\pi$
$258$		0			0
$259$	−2.00144e7			−1.15198
$260$		0			0
$261$	2.95820e7	+	1.10316e7i	1.66382	+	0.620465i
$262$		0			0
$263$			1.65865e7i			0.911776i	0.890037	+	0.455888i	$0.150678\pi$
$263$			1.65865e7i			0.911776i	−0.890037	+	0.455888i	$0.849322\pi$
$264$		0			0
$265$	−9.72805e6			−0.522743
$266$		0			0
$267$	−1.73342e7	−	2.49645e7i	−0.910690	−	1.31156i
$268$		0			0
$269$			230441.i			0.0118387i	0.999982	+	0.00591934i	$0.00188420\pi$
$269$			230441.i			0.0118387i	−0.999982	+	0.00591934i	$0.998116\pi$
$270$		0			0
$271$	−1.94774e7			−0.978638			−0.489319	−	0.872105i	$-0.662755\pi$
$271$	−1.94774e7			−0.978638			−0.489319	+	0.872105i	$0.662755\pi$
$272$		0			0
$273$	2.58820e7	−	1.79713e7i	1.27207	−	0.883265i
$274$		0			0
$275$		−	5.93292e6i		−	0.285280i
$276$		0			0
$277$	140418.			0.00660667			0.00330334	−	0.999995i	$-0.498949\pi$
$277$	140418.			0.00660667			0.00330334	+	0.999995i	$0.498949\pi$
$278$		0			0
$279$	7.53671e6	−	2.02102e7i	0.347032	−	0.930590i
$280$		0			0
$281$			1.34994e7i			0.608407i	0.952607	+	0.304203i	$0.0983902\pi$
$281$			1.34994e7i			0.608407i	−0.952607	+	0.304203i	$0.901610\pi$
$282$		0			0
$283$	2.01080e7			0.887174			0.443587	−	0.896231i	$-0.353706\pi$
$283$	2.01080e7			0.887174			0.443587	+	0.896231i	$0.353706\pi$
$284$		0			0
$285$	−8.18004e6	−	1.17808e7i	−0.353363	−	0.508908i
$286$		0			0
$287$			5.00913e7i			2.11893i
$288$		0			0
$289$	3.69552e6			0.153102
$290$		0			0
$291$	1.38435e7	−	9.61227e6i	0.561779	−	0.390074i
$292$		0			0
$293$			4.37099e7i			1.73771i	0.495068	+	0.868854i	$0.335143\pi$
$293$			4.37099e7i			1.73771i	−0.495068	+	0.868854i	$0.664857\pi$
$294$		0			0
$295$	3.79418e6			0.147793
$296$		0			0
$297$	−3.62073e7	+	9.24466e6i	−1.38206	+	0.352876i
$298$		0			0
$299$		−	1.46743e6i		−	0.0548964i
$300$		0			0
$301$	−1.08901e7			−0.399329
$302$		0			0
$303$	−2.10290e6	−	3.02857e6i	−0.0755947	−	0.108870i
$304$		0			0
$305$		−	9.78434e6i		−	0.344852i
$306$		0			0
$307$	4.79809e7			1.65826			0.829131	−	0.559055i	$-0.188836\pi$
$307$	4.79809e7			1.65826			0.829131	+	0.559055i	$0.188836\pi$
$308$		0			0
$309$	−5.42181e6	+	3.76466e6i	−0.183768	+	0.127600i
$310$		0			0
$311$			2.28475e7i			0.759553i	0.925078	+	0.379777i	$0.123999\pi$
$311$			2.28475e7i			0.759553i	−0.925078	+	0.379777i	$0.876001\pi$
$312$		0			0
$313$	−2.38707e7			−0.778451			−0.389226	−	0.921142i	$-0.627257\pi$
$313$	−2.38707e7			−0.778451			−0.389226	+	0.921142i	$0.627257\pi$
$314$		0			0
$315$	−1.66883e7	−	6.22333e6i	−0.533925	−	0.199109i
$316$		0			0
$317$			1.21703e7i			0.382054i	0.981585	+	0.191027i	$0.0611818\pi$
$317$			1.21703e7i			0.382054i	−0.981585	+	0.191027i	$0.938818\pi$
$318$		0			0
$319$	−8.22230e7			−2.53292
$320$		0			0
$321$	2.55774e7	+	3.68363e7i	0.773289	+	1.11368i
$322$		0			0
$323$		−	4.29626e7i		−	1.27492i
$324$		0			0
$325$	8.34435e6			0.243076
$326$		0			0
$327$	−2.53934e7	+	1.76320e7i	−0.726235	+	0.504265i
$328$		0			0
$329$		−	7.97997e6i		−	0.224085i
$330$		0			0
$331$	−3.94247e6			−0.108714			−0.0543569	−	0.998522i	$-0.517311\pi$
$331$	−3.94247e6			−0.108714			−0.0543569	+	0.998522i	$0.517311\pi$
$332$		0			0
$333$	−1.16647e7	+	3.12797e7i	−0.315893	+	0.847090i
$334$		0			0
$335$		−	897595.i		−	0.0238752i
$336$		0			0
$337$	3.45006e7			0.901439			0.450720	−	0.892666i	$-0.351167\pi$
$337$	3.45006e7			0.901439			0.450720	+	0.892666i	$0.351167\pi$
$338$		0			0
$339$	1.59076e7	+	2.29099e7i	0.408324	+	0.588063i
$340$		0			0
$341$			5.61742e7i			1.41669i
$342$		0			0
$343$	−1.93539e7			−0.479607
$344$		0			0
$345$	−681335.	+	473088.i	−0.0165922	+	0.0115209i
$346$		0			0
$347$			5.55712e7i			1.33003i	0.746830	+	0.665015i	$0.231575\pi$
$347$			5.55712e7i			1.33003i	−0.746830	+	0.665015i	$0.768425\pi$
$348$		0			0
$349$	−7.36309e7			−1.73214			−0.866071	−	0.499921i	$-0.833362\pi$
$349$	−7.36309e7			−1.73214			−0.866071	+	0.499921i	$0.833362\pi$
$350$		0			0
$351$	−1.30021e7	−	5.09237e7i	−0.300672	−	1.17760i
$352$		0			0
$353$		−	5.13378e7i		−	1.16711i	−0.812072	−	0.583557i	$-0.801660\pi$
$353$		−	5.13378e7i		−	1.16711i	0.812072	−	0.583557i	$-0.198340\pi$
$354$		0			0
$355$	−1.24561e7			−0.278418
$356$		0			0
$357$	−3.04298e7	−	4.38245e7i	−0.668796	−	0.963191i
$358$		0			0
$359$		−	4.77258e7i		−	1.03150i	−0.856739	−	0.515751i	$-0.827513\pi$
$359$		−	4.77258e7i		−	1.03150i	0.856739	−	0.515751i	$-0.172487\pi$
$360$		0			0
$361$	4.32475e7			0.919263
$362$		0			0
$363$	4.06494e7	−	2.82251e7i	0.849834	−	0.590086i
$364$		0			0
$365$			3.47032e7i			0.713659i
$366$		0			0
$367$	8.29285e7			1.67767			0.838834	−	0.544388i	$-0.183238\pi$
$367$	8.29285e7			1.67767			0.838834	+	0.544388i	$0.183238\pi$
$368$		0			0
$369$	7.82854e7	+	2.91939e7i	1.55812	+	0.581049i
$370$		0			0
$371$		−	7.60562e7i		−	1.48941i
$372$		0			0
$373$	4.09826e7			0.789719			0.394860	−	0.918741i	$-0.370793\pi$
$373$	4.09826e7			0.789719			0.394860	+	0.918741i	$0.370793\pi$
$374$		0			0
$375$	−2.69015e6	−	3.87432e6i	−0.0510133	−	0.0734687i
$376$		0			0
$377$		−	1.15642e8i		−	2.15821i
$378$		0			0
$379$	9.54504e7			1.75332			0.876658	−	0.481114i	$-0.159768\pi$
$379$	9.54504e7			1.75332			0.876658	+	0.481114i	$0.159768\pi$
$380$		0			0
$381$	−7.02329e7	+	4.87665e7i	−1.26989	+	0.881753i
$382$		0			0
$383$			4.90198e7i			0.872520i	0.899821	+	0.436260i	$0.143697\pi$
$383$			4.90198e7i			0.872520i	−0.899821	+	0.436260i	$0.856303\pi$
$384$		0			0
$385$	4.63850e7			0.812822
$386$		0			0
$387$	−6.34688e6	+	1.70196e7i	−0.109503	+	0.293641i
$388$		0			0
$389$		−	6.92192e6i		−	0.117592i	−0.998270	−	0.0587960i	$-0.981274\pi$
$389$		−	6.92192e6i		−	0.117592i	0.998270	−	0.0587960i	$-0.0187262\pi$
$390$		0			0
$391$	−2.48472e6			−0.0415668
$392$		0			0
$393$	3.18680e7	+	4.58959e7i	0.525022	+	0.756130i
$394$		0			0
$395$		−	2.93717e7i		−	0.476582i
$396$		0			0
$397$	−1.04166e8			−1.66478			−0.832389	−	0.554191i	$-0.813028\pi$
$397$	−1.04166e8			−1.66478			−0.832389	+	0.554191i	$0.813028\pi$
$398$		0			0
$399$	9.21049e7	−	6.39535e7i	1.44999	−	1.00681i
$400$		0			0
$401$		−	1.09926e8i		−	1.70477i	−0.522911	−	0.852387i	$-0.675154\pi$
$401$		−	1.09926e8i		−	1.70477i	0.522911	−	0.852387i	$-0.324846\pi$
$402$		0			0
$403$	−7.90061e7			−1.20711
$404$		0			0
$405$	−1.94523e7	+	2.24544e7i	−0.292824	+	0.338015i
$406$		0			0
$407$		−	8.69416e7i		−	1.28957i
$408$		0			0
$409$	−9.73956e7			−1.42354			−0.711770	−	0.702413i	$-0.752106\pi$
$409$	−9.73956e7			−1.42354			−0.711770	+	0.702413i	$0.752106\pi$
$410$		0			0
$411$	8.01992e6	+	1.15502e7i	0.115517	+	0.166365i
$412$		0			0
$413$			2.96639e7i			0.421092i
$414$		0			0
$415$	4.42049e7			0.618480
$416$		0			0
$417$	−8.63184e7	+	5.99356e7i	−1.19041	+	0.826564i
$418$		0			0
$419$			6.80064e7i			0.924501i	0.886749	+	0.462251i	$0.152958\pi$
$419$			6.80064e7i			0.924501i	−0.886749	+	0.462251i	$0.847042\pi$
$420$		0			0
$421$	3.17666e7			0.425720			0.212860	−	0.977083i	$-0.431722\pi$
$421$	3.17666e7			0.425720			0.212860	+	0.977083i	$0.431722\pi$
$422$		0			0
$423$	−1.24715e7	−	4.65083e6i	−0.164778	−	0.0614483i
$424$		0			0
$425$		−	1.41290e7i		−	0.184054i
$426$		0			0
$427$	7.64964e7			0.982556
$428$		0			0
$429$	7.80663e7	+	1.12430e8i	0.988762	+	1.42400i
$430$		0			0
$431$		−	8.40240e7i		−	1.04947i	−0.851264	−	0.524737i	$-0.824164\pi$
$431$		−	8.40240e7i		−	1.04947i	0.851264	−	0.524737i	$-0.175836\pi$
$432$		0			0
$433$	−8.82768e7			−1.08738			−0.543692	−	0.839285i	$-0.682974\pi$
$433$	−8.82768e7			−1.08738			−0.543692	+	0.839285i	$0.682974\pi$
$434$		0			0
$435$	−5.36934e7	+	3.72822e7i	−0.652308	+	0.452933i
$436$		0			0
$437$		−	5.22207e6i		−	0.0625747i
$438$		0			0
$439$	1.03991e8			1.22914			0.614569	−	0.788863i	$-0.289330\pi$
$439$	1.03991e8			1.22914			0.614569	+	0.788863i	$0.289330\pi$
$440$		0			0
$441$	1.86879e7	−	5.01129e7i	0.217894	−	0.584297i
$442$		0			0
$443$		−	1.29638e8i		−	1.49115i	−0.666422	−	0.745575i	$-0.732175\pi$
$443$		−	1.29638e8i		−	1.49115i	0.666422	−	0.745575i	$-0.267825\pi$
$444$		0			0
$445$	6.29256e7			0.714080
$446$		0			0
$447$	3.49612e7	+	5.03506e7i	0.391439	+	0.563745i
$448$		0			0
$449$			9.46554e7i			1.04570i	0.852425	+	0.522849i	$0.175131\pi$
$449$			9.46554e7i			1.04570i	−0.852425	+	0.522849i	$0.824869\pi$
$450$		0			0
$451$	−2.17594e8			−2.37201
$452$		0			0
$453$	−2.83251e7	+	1.96677e7i	−0.304703	+	0.211572i
$454$		0			0
$455$			6.52382e7i			0.692576i
$456$		0			0
$457$	5.45336e7			0.571367			0.285684	−	0.958324i	$-0.407779\pi$
$457$	5.45336e7			0.571367			0.285684	+	0.958324i	$0.407779\pi$
$458$		0			0
$459$	−8.62263e7	+	2.20158e7i	−0.891665	+	0.227665i
$460$		0			0
$461$			7.37094e7i			0.752350i	0.926549	+	0.376175i	$0.122761\pi$
$461$			7.37094e7i			0.752350i	−0.926549	+	0.376175i	$0.877239\pi$
$462$		0			0
$463$	−1.87082e7			−0.188490			−0.0942452	−	0.995549i	$-0.530044\pi$
$463$	−1.87082e7			−0.188490			−0.0942452	+	0.995549i	$0.530044\pi$
$464$		0			0
$465$	2.54710e7	+	3.66829e7i	0.253330	+	0.364842i
$466$		0			0
$467$			1.19481e8i			1.17313i	0.809901	+	0.586567i	$0.199521\pi$
$467$			1.19481e8i			1.17313i	−0.809901	+	0.586567i	$0.800479\pi$
$468$		0			0
$469$	7.01762e6			0.0680254
$470$		0			0
$471$	−3.11461e7	+	2.16264e7i	−0.298085	+	0.206977i
$472$		0			0
$473$		−	4.73059e7i		−	0.447025i
$474$		0			0
$475$	2.96946e7			0.277075
$476$		0			0
$477$	−1.18865e8	−	4.43266e7i	−1.09521	−	0.408422i
$478$		0			0
$479$			1.84244e7i			0.167644i	0.996481	+	0.0838220i	$0.0267127\pi$
$479$			1.84244e7i			0.167644i	−0.996481	+	0.0838220i	$0.973287\pi$
$480$		0			0
$481$	1.22279e8			1.09879
$482$		0			0
$483$	−3.69872e6	−	5.32684e6i	−0.0328254	−	0.0472747i
$484$		0			0
$485$			3.48939e7i			0.305861i
$486$		0			0
$487$	6.48625e7			0.561574			0.280787	−	0.959770i	$-0.409405\pi$
$487$	6.48625e7			0.561574			0.280787	+	0.959770i	$0.409405\pi$
$488$		0			0
$489$	1.07454e8	−	7.46113e7i	0.918961	−	0.638085i
$490$		0			0
$491$			1.01202e8i			0.854961i	0.904025	+	0.427480i	$0.140599\pi$
$491$			1.01202e8i			0.854961i	−0.904025	+	0.427480i	$0.859401\pi$
$492$		0			0
$493$	−1.95811e8			−1.63417
$494$		0			0
$495$	2.70338e7	−	7.24931e7i	0.222891	−	0.597697i
$496$		0			0
$497$		−	9.73848e7i		−	0.793272i
$498$		0			0
$499$	−3.08259e7			−0.248092			−0.124046	−	0.992276i	$-0.539587\pi$
$499$	−3.08259e7			−0.248092			−0.124046	+	0.992276i	$0.539587\pi$
$500$		0			0
$501$	1.26782e7	+	1.82590e7i	0.100820	+	0.145199i
$502$		0			0
$503$			1.31110e8i			1.03022i	0.857123	+	0.515111i	$0.172249\pi$
$503$			1.31110e8i			1.03022i	−0.857123	+	0.515111i	$0.827751\pi$
$504$		0			0
$505$	7.63382e6			0.0592745
$506$		0			0
$507$	−5.10784e7	+	3.54665e7i	−0.391935	+	0.272142i
$508$		0			0
$509$		−	1.77883e7i		−	0.134890i	−0.997723	−	0.0674452i	$-0.978515\pi$
$509$		−	1.77883e7i		−	0.134890i	0.997723	−	0.0674452i	$-0.0214848\pi$
$510$		0			0
$511$	−2.71318e8			−2.03337
$512$		0			0
$513$	−4.62701e7	−	1.81220e8i	−0.342727	−	1.34231i
$514$		0			0
$515$		−	1.36662e7i		−	0.100052i
$516$		0			0
$517$	3.46646e7			0.250850
$518$		0			0
$519$	1.39572e8	+	2.01009e8i	0.998379	+	1.43785i
$520$		0			0
$521$			1.90916e8i			1.34999i	0.737823	+	0.674994i	$0.235854\pi$
$521$			1.90916e8i			1.34999i	−0.737823	+	0.674994i	$0.764146\pi$
$522$		0			0
$523$	−1.68384e8			−1.17705			−0.588527	−	0.808478i	$-0.700292\pi$
$523$	−1.68384e8			−1.17705			−0.588527	+	0.808478i	$0.700292\pi$
$524$		0			0
$525$	3.02904e7	−	2.10323e7i	0.209328	−	0.145348i
$526$		0			0
$527$			1.33777e8i			0.914005i
$528$		0			0
$529$	1.47734e8			0.997960
$530$		0			0
$531$	4.63603e7	+	1.72885e7i	0.309644	+	0.115471i
$532$		0			0
$533$		−	3.06035e8i		−	2.02111i
$534$		0			0
$535$	−9.28496e7			−0.606343
$536$		0			0
$537$	−1.02992e8	−	1.48328e8i	−0.665091	−	0.957855i
$538$		0			0
$539$			1.39289e8i			0.889506i
$540$		0			0
$541$	2.49423e8			1.57523			0.787616	−	0.616167i	$-0.211315\pi$
$541$	2.49423e8			1.57523			0.787616	+	0.616167i	$0.211315\pi$
$542$		0			0
$543$	2.13655e7	−	1.48352e7i	0.133448	−	0.0926605i
$544$		0			0
$545$		−	6.40066e7i		−	0.395399i
$546$		0			0
$547$	1.16411e8			0.711268			0.355634	−	0.934625i	$-0.384265\pi$
$547$	1.16411e8			0.711268			0.355634	+	0.934625i	$0.384265\pi$
$548$		0			0
$549$	4.45831e7	−	1.19553e8i	0.269435	−	0.722508i
$550$		0			0
$551$		−	4.11531e8i		−	2.46007i
$552$		0			0
$553$	2.29635e8			1.35788
$554$		0			0
$555$	−3.94218e7	−	5.67747e7i	−0.230599	−	0.332105i
$556$		0			0
$557$			2.07511e8i			1.20082i	0.799694	+	0.600408i	$0.204995\pi$
$557$			2.07511e8i			1.20082i	−0.799694	+	0.600408i	$0.795005\pi$
$558$		0			0
$559$	6.65333e7			0.380894
$560$		0			0
$561$	1.90371e8	−	1.32185e8i	1.07823	−	0.748677i
$562$		0			0
$563$		−	8.47557e7i		−	0.474945i	−0.971394	−	0.237473i	$-0.923681\pi$
$563$		−	8.47557e7i		−	0.474945i	0.971394	−	0.237473i	$-0.0763190\pi$
$564$		0			0
$565$	−5.77467e7			−0.320171
$566$		0			0
$567$	−1.75554e8	−	1.52083e8i	−0.963076	−	0.834318i
$568$		0			0
$569$		−	1.84731e8i		−	1.00278i	−0.865223	−	0.501388i	$-0.832823\pi$
$569$		−	1.84731e8i		−	1.00278i	0.865223	−	0.501388i	$-0.167177\pi$
$570$		0			0
$571$	6.60597e7			0.354837			0.177418	−	0.984136i	$-0.443225\pi$
$571$	6.60597e7			0.354837			0.177418	+	0.984136i	$0.443225\pi$
$572$		0			0
$573$	−2.12344e7	−	3.05815e7i	−0.112869	−	0.162553i
$574$		0			0
$575$		−	1.71737e6i		−	0.00903361i
$576$		0			0
$577$	9.03538e7			0.470348			0.235174	−	0.971953i	$-0.424434\pi$
$577$	9.03538e7			0.470348			0.235174	+	0.971953i	$0.424434\pi$
$578$		0			0
$579$	−1.21971e7	+	8.46913e6i	−0.0628379	+	0.0436318i
$580$		0			0
$581$			3.45604e8i			1.76218i
$582$		0			0
$583$	3.30384e8			1.66730
$584$		0			0
$585$	1.01958e8	+	3.80217e7i	0.509276	+	0.189917i
$586$		0			0
$587$		−	1.74492e8i		−	0.862704i	−0.902184	−	0.431352i	$-0.858037\pi$
$587$		−	1.74492e8i		−	0.862704i	0.902184	−	0.431352i	$-0.141963\pi$
$588$		0			0
$589$	−2.81155e8			−1.37594
$590$		0			0
$591$	−6.52440e7	−	9.39635e7i	−0.316066	−	0.455194i
$592$		0			0
$593$			2.18826e8i			1.04938i	0.851292	+	0.524692i	$0.175820\pi$
$593$			2.18826e8i			1.04938i	−0.851292	+	0.524692i	$0.824180\pi$
$594$		0			0
$595$	1.10464e8			0.524409
$596$		0			0
$597$	3.15788e8	−	2.19269e8i	1.48413	−	1.03051i
$598$		0			0
$599$			3.01081e8i			1.40088i	0.713709	+	0.700442i	$0.247014\pi$
$599$			3.01081e8i			1.40088i	−0.713709	+	0.700442i	$0.752986\pi$
$600$		0			0
$601$	−2.54238e8			−1.17116			−0.585582	−	0.810614i	$-0.699134\pi$
$601$	−2.54238e8			−1.17116			−0.585582	+	0.810614i	$0.699134\pi$
$602$		0			0
$603$	4.08996e6	−	1.09675e7i	0.0186538	−	0.0500215i
$604$		0			0
$605$			1.02461e8i			0.462692i
$606$		0			0
$607$	−1.76940e8			−0.791153			−0.395576	−	0.918433i	$-0.629455\pi$
$607$	−1.76940e8			−0.791153			−0.395576	+	0.918433i	$0.629455\pi$
$608$		0			0
$609$	−2.91482e8	−	4.19788e8i	−1.29050	−	1.85857i
$610$		0			0
$611$			4.87539e7i			0.213740i
$612$		0			0
$613$	−1.16816e8			−0.507132			−0.253566	−	0.967318i	$-0.581603\pi$
$613$	−1.16816e8			−0.507132			−0.253566	+	0.967318i	$0.581603\pi$
$614$		0			0
$615$	−1.42093e8	+	9.86632e7i	−0.610870	+	0.424160i
$616$		0			0
$617$			1.32683e8i			0.564886i	0.959284	+	0.282443i	$0.0911448\pi$
$617$			1.32683e8i			0.564886i	−0.959284	+	0.282443i	$0.908855\pi$
$618$		0			0
$619$	1.63767e7			0.0690484			0.0345242	−	0.999404i	$-0.489008\pi$
$619$	1.63767e7			0.0690484			0.0345242	+	0.999404i	$0.489008\pi$
$620$		0			0
$621$	−1.04807e7	+	2.67601e6i	−0.0437641	+	0.0111741i
$622$		0			0
$623$			4.91967e8i			2.03457i
$624$		0			0
$625$	9.76562e6			0.0400000
$626$		0			0
$627$	2.77811e8	+	4.00099e8i	1.12706	+	1.62317i
$628$		0			0
$629$		−	2.07048e8i		−	0.831992i
$630$		0			0
$631$	−3.22391e7			−0.128320			−0.0641600	−	0.997940i	$-0.520437\pi$
$631$	−3.22391e7			−0.128320			−0.0641600	+	0.997940i	$0.520437\pi$
$632$		0			0
$633$	−2.04054e7	+	1.41686e7i	−0.0804514	+	0.0558618i
$634$		0			0
$635$		−	1.77029e8i		−	0.691391i
$636$		0			0
$637$	−1.95902e8			−0.757916
$638$		0			0
$639$	−1.52198e8	−	5.67572e7i	−0.583321	−	0.217530i
$640$		0			0
$641$		−	1.81122e8i		−	0.687698i	−0.939025	−	0.343849i	$-0.888269\pi$
$641$		−	1.81122e8i		−	0.687698i	0.939025	−	0.343849i	$-0.111731\pi$
$642$		0			0
$643$	−7.65331e6			−0.0287883			−0.0143942	−	0.999896i	$-0.504582\pi$
$643$	−7.65331e6			−0.0287883			−0.0143942	+	0.999896i	$0.504582\pi$
$644$		0			0
$645$	−2.14498e7	−	3.08917e7i	−0.0799364	−	0.115123i
$646$		0			0
$647$		−	2.31805e8i		−	0.855875i	−0.903808	−	0.427937i	$-0.859240\pi$
$647$		−	2.31805e8i		−	0.855875i	0.903808	−	0.427937i	$-0.140760\pi$
$648$		0			0
$649$	−1.28858e8			−0.471388
$650$		0			0
$651$	−2.86796e8	+	1.99138e8i	−1.03951	+	0.721791i
$652$		0			0
$653$			3.95202e8i			1.41932i	0.704545	+	0.709660i	$0.251151\pi$
$653$			3.95202e8i			1.41932i	−0.704545	+	0.709660i	$0.748849\pi$
$654$		0			0
$655$	−1.15685e8			−0.411675
$656$		0			0
$657$	−1.58128e8	+	4.24031e8i	−0.557587	+	1.49521i
$658$		0			0
$659$		−	5.10657e8i		−	1.78432i	−0.451719	−	0.892160i	$-0.649189\pi$
$659$		−	5.10657e8i		−	1.78432i	0.451719	−	0.892160i	$-0.350811\pi$
$660$		0			0
$661$	4.10564e8			1.42160			0.710799	−	0.703395i	$-0.248333\pi$
$661$	4.10564e8			1.42160			0.710799	+	0.703395i	$0.248333\pi$
$662$		0			0
$663$	1.85912e8	+	2.67748e8i	0.637920	+	0.918724i
$664$		0			0
$665$			2.32160e8i			0.789446i
$666$		0			0
$667$	−2.38007e7			−0.0802070
$668$		0			0
$669$	−2.74176e8	+	1.90376e8i	−0.915696	+	0.635818i
$670$		0			0
$671$			3.32296e8i			1.09991i
$672$		0			0
$673$	9.19215e7			0.301559			0.150779	−	0.988567i	$-0.451822\pi$
$673$	9.19215e7			0.301559			0.150779	+	0.988567i	$0.451822\pi$
$674$		0			0
$675$	−1.52168e7	−	5.95974e7i	−0.0494779	−	0.193783i
$676$		0			0
$677$		−	1.47302e8i		−	0.474726i	−0.971421	−	0.237363i	$-0.923717\pi$
$677$		−	1.47302e8i		−	0.474726i	0.971421	−	0.237363i	$-0.0762830\pi$
$678$		0			0
$679$	−2.72809e8			−0.871462
$680$		0			0
$681$	6.88744e6	+	9.91920e6i	0.0218080	+	0.0314076i
$682$		0			0
$683$		−	1.01111e8i		−	0.317347i	−0.987331	−	0.158673i	$-0.949278\pi$
$683$		−	1.01111e8i		−	0.317347i	0.987331	−	0.158673i	$-0.0507217\pi$
$684$		0			0
$685$	−2.91134e7			−0.0905776
$686$		0			0
$687$	4.11513e8	−	2.85736e8i	1.26915	−	0.881241i
$688$		0			0
$689$			4.64669e8i			1.42065i
$690$		0			0
$691$	2.65597e8			0.804987			0.402493	−	0.915423i	$-0.368144\pi$
$691$	2.65597e8			0.804987			0.402493	+	0.915423i	$0.368144\pi$
$692$		0			0
$693$	5.66769e8	+	2.11357e8i	1.70297	+	0.635063i
$694$		0			0
$695$		−	2.17574e8i		−	0.648116i
$696$		0			0
$697$	−5.18191e8			−1.53035
$698$		0			0
$699$	2.05301e7	+	2.95671e7i	0.0601117	+	0.0865721i
$700$		0			0
$701$		−	4.56699e8i		−	1.32579i	−0.748711	−	0.662897i	$-0.769327\pi$
$701$		−	4.56699e8i		−	1.32579i	0.748711	−	0.662897i	$-0.230673\pi$
$702$		0			0
$703$	4.35148e8			1.25248
$704$		0			0
$705$	2.26367e7	−	1.57179e7i	0.0646019	−	0.0448566i
$706$		0			0
$707$			5.96830e7i			0.168886i
$708$		0			0
$709$	−2.21150e7			−0.0620509			−0.0310255	−	0.999519i	$-0.509877\pi$
$709$	−2.21150e7			−0.0620509			−0.0310255	+	0.999519i	$0.509877\pi$
$710$		0			0
$711$	1.33834e8	−	3.58886e8i	0.372356	−	0.998500i
$712$		0			0
$713$			1.62605e7i			0.0448605i
$714$		0			0
$715$	−2.83391e8			−0.775297
$716$		0			0
$717$	−7.46119e7	−	1.07455e8i	−0.202419	−	0.291521i
$718$		0			0
$719$		−	1.60221e8i		−	0.431054i	−0.976498	−	0.215527i	$-0.930853\pi$
$719$		−	1.60221e8i		−	0.431054i	0.976498	−	0.215527i	$-0.0691469\pi$
$720$		0			0
$721$	1.06846e8			0.285070
$722$		0			0
$723$	−4.09194e8	+	2.84126e8i	−1.08271	+	0.751788i
$724$		0			0
$725$		−	1.35340e8i		−	0.355149i
$726$		0			0
$727$	−3.41495e8			−0.888753			−0.444376	−	0.895840i	$-0.646575\pi$
$727$	−3.41495e8			−0.888753			−0.444376	+	0.895840i	$0.646575\pi$
$728$		0			0
$729$	−3.39999e8	+	1.85729e8i	−0.877597	+	0.479399i
$730$		0			0
$731$		−	1.12657e8i		−	0.288407i
$732$		0			0
$733$	4.06271e8			1.03158			0.515791	−	0.856714i	$-0.327498\pi$
$733$	4.06271e8			1.03158			0.515791	+	0.856714i	$0.327498\pi$
$734$		0			0
$735$	6.31573e7	+	9.09583e7i	0.159060	+	0.229076i
$736$		0			0
$737$			3.04842e7i			0.0761503i
$738$		0			0
$739$	1.06192e7			0.0263123			0.0131562	−	0.999913i	$-0.495812\pi$
$739$	1.06192e7			0.0263123			0.0131562	+	0.999913i	$0.495812\pi$
$740$		0			0
$741$	−5.62719e8	+	3.90726e8i	−1.38305	+	0.960325i
$742$		0			0
$743$		−	5.86011e8i		−	1.42869i	−0.699791	−	0.714347i	$-0.746724\pi$
$743$		−	5.86011e8i		−	1.42869i	0.699791	−	0.714347i	$-0.253276\pi$
$744$		0			0
$745$	−1.26914e8			−0.306931
$746$		0			0
$747$	5.40130e8	+	2.01423e8i	1.29579	+	0.483222i
$748$		0			0
$749$		−	7.25920e8i		−	1.72760i
$750$		0			0
$751$	4.96057e7			0.117115			0.0585574	−	0.998284i	$-0.481350\pi$
$751$	4.96057e7			0.117115			0.0585574	+	0.998284i	$0.481350\pi$
$752$		0			0
$753$	−2.12715e8	−	3.06350e8i	−0.498212	−	0.717518i
$754$		0			0
$755$		−	7.13963e7i		−	0.165896i
$756$		0			0
$757$	4.58919e7			0.105791			0.0528955	−	0.998600i	$-0.483155\pi$
$757$	4.58919e7			0.105791			0.0528955	+	0.998600i	$0.483155\pi$
$758$		0			0
$759$	2.31395e7	−	1.60670e7i	0.0529211	−	0.0367460i
$760$		0			0
$761$			6.06778e8i			1.37682i	0.725323	+	0.688408i	$0.241690\pi$
$761$			6.06778e8i			1.37682i	−0.725323	+	0.688408i	$0.758310\pi$
$762$		0			0
$763$	5.00419e8			1.12658
$764$		0			0
$765$	6.43800e7	−	1.72640e8i	0.143803	−	0.385617i
$766$		0			0
$767$		−	1.81233e8i		−	0.401652i
$768$		0			0
$769$	4.78906e8			1.05310			0.526552	−	0.850143i	$-0.323484\pi$
$769$	4.78906e8			1.05310			0.526552	+	0.850143i	$0.323484\pi$
$770$		0			0
$771$	4.46114e8	+	6.42487e8i	0.973380	+	1.40185i
$772$		0			0
$773$			3.49686e7i			0.0757076i	0.999283	+	0.0378538i	$0.0120521\pi$
$773$			3.49686e7i			0.0757076i	−0.999283	+	0.0378538i	$0.987948\pi$
$774$		0			0
$775$	−9.24630e7			−0.198638
$776$		0			0
$777$	4.43878e8	−	3.08209e8i	0.946239	−	0.657025i
$778$		0			0
$779$		−	1.08907e9i		−	2.30379i
$780$		0			0
$781$	4.23034e8			0.888020
$782$		0			0
$783$	−8.25947e8	+	2.10886e8i	−1.72055	+	0.439301i
$784$		0			0
$785$		−	7.85068e7i		−	0.162292i
$786$		0			0
$787$	3.11411e8			0.638866			0.319433	−	0.947609i	$-0.396508\pi$
$787$	3.11411e8			0.638866			0.319433	+	0.947609i	$0.396508\pi$
$788$		0			0
$789$	−2.55422e8	−	3.67855e8i	−0.520028	−	0.748937i
$790$		0			0
$791$		−	4.51478e8i		−	0.912235i
$792$		0			0
$793$	−4.67358e8			−0.937195
$794$		0			0
$795$	2.15748e8	−	1.49806e8i	0.429383	−	0.298144i
$796$		0			0
$797$			4.48813e8i			0.886525i	0.896392	+	0.443262i	$0.146179\pi$
$797$			4.48813e8i			0.886525i	−0.896392	+	0.443262i	$0.853821\pi$
$798$		0			0
$799$	8.25523e7			0.161841
$800$		0			0
$801$	7.68874e8	+	2.86725e8i	1.49609	+	0.557915i
$802$		0			0
$803$		−	1.17859e9i		−	2.27623i
$804$		0			0
$805$	1.34268e7			0.0257387
$806$		0			0
$807$	−3.54864e6	−	5.11071e6i	−0.00675215	−	0.00972435i
$808$		0			0
$809$			4.94261e8i			0.933493i	0.884391	+	0.466746i	$0.154574\pi$
$809$			4.94261e8i			0.933493i	−0.884391	+	0.466746i	$0.845426\pi$
$810$		0			0
$811$	−2.89935e8			−0.543549			−0.271774	−	0.962361i	$-0.587610\pi$
$811$	−2.89935e8			−0.543549			−0.271774	+	0.962361i	$0.587610\pi$
$812$		0			0
$813$	4.31967e8	−	2.99939e8i	0.803858	−	0.558162i
$814$		0			0
$815$			2.70849e8i			0.500328i
$816$		0			0
$817$	2.36769e8			0.434168
$818$		0			0
$819$	−2.97263e8	+	7.97131e8i	−0.541114	+	1.45104i
$820$		0			0
$821$		−	1.20406e8i		−	0.217579i	−0.994065	−	0.108789i	$-0.965303\pi$
$821$		−	1.20406e8i		−	0.217579i	0.994065	−	0.108789i	$-0.0346974\pi$
$822$		0			0
$823$	2.61929e8			0.469878			0.234939	−	0.972010i	$-0.424511\pi$
$823$	2.61929e8			0.469878			0.234939	+	0.972010i	$0.424511\pi$
$824$		0			0
$825$	9.13631e7	+	1.31580e8i	0.162708	+	0.234330i
$826$		0			0
$827$			1.59768e8i			0.282471i	0.989976	+	0.141236i	$0.0451075\pi$
$827$			1.59768e8i			0.282471i	−0.989976	+	0.141236i	$0.954893\pi$
$828$		0			0
$829$	7.51308e7			0.131873			0.0659363	−	0.997824i	$-0.478997\pi$
$829$	7.51308e7			0.131873			0.0659363	+	0.997824i	$0.478997\pi$
$830$		0			0
$831$	−3.11417e6	+	2.16234e6i	−0.00542675	+	0.00376809i
$832$		0			0
$833$			3.31710e8i			0.573884i
$834$		0			0
$835$	−4.60237e7			−0.0790537
$836$		0			0
$837$	1.44076e8	+	5.64281e8i	0.245705	+	0.962319i
$838$		0			0
$839$			7.46323e8i			1.26369i	0.775094	+	0.631846i	$0.217702\pi$
$839$			7.46323e8i			1.26369i	−0.775094	+	0.631846i	$0.782298\pi$
$840$		0			0
$841$	−1.28082e9			−2.15327
$842$		0			0
$843$	−2.07881e8	−	2.99388e8i	−0.347002	−	0.499748i
$844$		0			0
$845$		−	1.28748e8i		−	0.213389i
$846$		0			0
$847$	−8.01064e8			−1.31831
$848$		0			0
$849$	−4.45953e8	+	3.09649e8i	−0.728729	+	0.505996i
$850$		0			0
$851$		−	2.51666e7i		−	0.0408352i
$852$		0			0
$853$	−7.32618e8			−1.18040			−0.590201	−	0.807256i	$-0.700952\pi$
$853$	−7.32618e8			−1.18040			−0.590201	+	0.807256i	$0.700952\pi$
$854$		0			0
$855$	3.62832e8	+	1.35306e8i	0.580507	+	0.216480i
$856$		0			0
$857$		−	4.41490e8i		−	0.701420i	−0.936484	−	0.350710i	$-0.885940\pi$
$857$		−	4.41490e8i		−	0.701420i	0.936484	−	0.350710i	$-0.114060\pi$
$858$		0			0
$859$	8.02777e8			1.26653			0.633265	−	0.773935i	$-0.281714\pi$
$859$	8.02777e8			1.26653			0.633265	+	0.773935i	$0.281714\pi$
$860$		0			0
$861$	−7.71373e8	−	1.11092e9i	−1.20852	−	1.74050i
$862$		0			0
$863$			8.01287e8i			1.24668i	0.781950	+	0.623341i	$0.214225\pi$
$863$			8.01287e8i			1.24668i	−0.781950	+	0.623341i	$0.785775\pi$
$864$		0			0
$865$	−5.06664e8			−0.782838
$866$		0			0
$867$	−8.19589e7	+	5.69085e7i	−0.125759	+	0.0873213i
$868$		0			0
$869$			9.97522e8i			1.52007i
$870$		0			0
$871$	−4.28744e7			−0.0648849
$872$		0			0
$873$	−1.58997e8	+	4.26360e8i	−0.238971	+	0.640817i
$874$		0			0
$875$			7.63500e7i			0.113969i
$876$		0			0
$877$	−7.69001e8			−1.14006			−0.570031	−	0.821623i	$-0.693069\pi$
$877$	−7.69001e8			−1.14006			−0.570031	+	0.821623i	$0.693069\pi$
$878$		0			0
$879$	−6.73104e8	−	9.69394e8i	−0.991095	−	1.42736i
$880$		0			0
$881$			9.64066e8i			1.40987i	0.709272	+	0.704935i	$0.249024\pi$
$881$			9.64066e8i			1.40987i	−0.709272	+	0.704935i	$0.750976\pi$
$882$		0			0
$883$	4.12143e8			0.598639			0.299320	−	0.954153i	$-0.403240\pi$
$883$	4.12143e8			0.598639			0.299320	+	0.954153i	$0.403240\pi$
$884$		0			0
$885$	−8.41471e7	+	5.84280e7i	−0.121397	+	0.0842929i
$886$		0			0
$887$			5.16317e8i			0.739854i	0.929061	+	0.369927i	$0.120617\pi$
$887$			5.16317e8i			0.739854i	−0.929061	+	0.369927i	$0.879383\pi$
$888$		0			0
$889$	1.38406e9			1.96992
$890$		0			0
$891$	6.60641e8	−	7.62596e8i	0.933969	−	1.07811i
$892$		0			0
$893$			1.73498e8i			0.243636i
$894$		0			0
$895$	3.73875e8			0.521504
$896$		0			0
$897$	2.25975e7	+	3.25446e7i	0.0313099	+	0.0450922i
$898$		0			0
$899$			1.28142e9i			1.76366i
$900$		0			0
$901$	7.86798e8			1.07569
$902$		0			0
$903$	2.41519e8	−	1.67700e8i	0.328011	−	0.227756i
$904$		0			0
$905$			5.38539e7i			0.0726559i
$906$		0			0
$907$	−1.20289e9			−1.61214			−0.806072	−	0.591817i	$-0.798411\pi$
$907$	−1.20289e9			−1.61214			−0.806072	+	0.591817i	$0.798411\pi$
$908$		0			0
$909$	9.32760e7	+	3.47841e7i	0.124188	+	0.0463115i
$910$		0			0
$911$			2.04819e8i			0.270903i	0.990784	+	0.135452i	$0.0432485\pi$
$911$			2.04819e8i			0.270903i	−0.990784	+	0.135452i	$0.956751\pi$
$912$		0			0
$913$	−1.50129e9			−1.97266
$914$		0			0
$915$	1.50672e8	+	2.16996e8i	0.196685	+	0.283263i
$916$		0			0
$917$		−	9.04456e8i		−	1.17295i
$918$		0			0
$919$	1.07525e9			1.38536			0.692682	−	0.721243i	$-0.256429\pi$
$919$	1.07525e9			1.38536			0.692682	+	0.721243i	$0.256429\pi$
$920$		0			0
$921$	−1.06412e9	+	7.38874e8i	−1.36210	+	0.945783i
$922$		0			0
$923$			5.94976e8i			0.756649i
$924$		0			0
$925$	1.43106e8			0.180815
$926$		0			0
$927$	6.22712e7	−	1.66985e8i	0.0781714	−	0.209622i
$928$		0			0
$929$		−	3.27972e8i		−	0.409063i	−0.978860	−	0.204532i	$-0.934433\pi$
$929$		−	3.27972e8i		−	0.409063i	0.978860	−	0.204532i	$-0.0655671\pi$
$930$		0			0
$931$	−6.97147e8			−0.863924
$932$		0			0
$933$	−3.51837e8	−	5.06711e8i	−0.433208	−	0.623900i
$934$		0			0
$935$			4.79851e8i			0.587045i
$936$		0			0
$937$	1.00558e8			0.122235			0.0611177	−	0.998131i	$-0.480533\pi$
$937$	1.00558e8			0.122235			0.0611177	+	0.998131i	$0.480533\pi$
$938$		0			0
$939$	5.29402e8	−	3.67592e8i	0.639423	−	0.443987i
$940$		0			0
$941$		−	1.31841e9i		−	1.58227i	−0.611642	−	0.791134i	$-0.709491\pi$
$941$		−	1.31841e9i		−	1.58227i	0.611642	−	0.791134i	$-0.290509\pi$
$942$		0			0
$943$	−6.29858e7			−0.0751117
$944$		0			0
$945$	4.65947e8	−	1.18968e8i	0.552130	−	0.140973i
$946$		0			0
$947$		−	7.08841e8i		−	0.834640i	−0.908760	−	0.417320i	$-0.862969\pi$
$947$		−	7.08841e8i		−	0.834640i	0.908760	−	0.417320i	$-0.137031\pi$
$948$		0			0
$949$	1.65763e9			1.93949
$950$		0			0
$951$	−1.87415e8	−	2.69913e8i	−0.217903	−	0.313821i
$952$		0			0
$953$		−	4.08239e8i		−	0.471668i	−0.971793	−	0.235834i	$-0.924218\pi$
$953$		−	4.08239e8i		−	0.471668i	0.971793	−	0.235834i	$-0.0757821\pi$
$954$		0			0
$955$	7.70838e7			0.0885019
$956$		0			0
$957$	1.82354e9	−	1.26618e9i	2.08055	−	1.44464i
$958$		0			0
$959$		−	2.27615e8i		−	0.258075i
$960$		0			0
$961$	−1.20442e7			−0.0135709
$962$		0			0
$963$	−1.13451e9	−	4.23076e8i	−1.27037	−	0.473740i
$964$		0			0
$965$		−	3.07441e7i		−	0.0342121i
$966$		0			0
$967$	6.53392e8			0.722594			0.361297	−	0.932451i	$-0.382334\pi$
$967$	6.53392e8			0.722594			0.361297	+	0.932451i	$0.382334\pi$
$968$		0			0
$969$	6.61595e8	+	9.52821e8i	0.727145	+	1.04722i
$970$		0			0
$971$			2.53885e8i			0.277319i	0.990340	+	0.138659i	$0.0442793\pi$
$971$			2.53885e8i			0.277319i	−0.990340	+	0.138659i	$0.955721\pi$
$972$		0			0
$973$	1.70105e9			1.84662
$974$		0			0
$975$	−1.85060e8	+	1.28498e8i	−0.199664	+	0.138638i
$976$		0			0
$977$			4.70410e8i			0.504420i	0.967672	+	0.252210i	$0.0811574\pi$
$977$			4.70410e8i			0.504420i	−0.967672	+	0.252210i	$0.918843\pi$
$978$		0			0
$979$	−2.13708e9			−2.27758
$980$		0			0
$981$	2.91651e8	−	7.82083e8i	0.308928	−	0.828411i
$982$		0			0
$983$			5.68355e8i			0.598355i	0.954197	+	0.299178i	$0.0967124\pi$
$983$			5.68355e8i			0.598355i	−0.954197	+	0.299178i	$0.903288\pi$
$984$		0			0
$985$	2.36845e8			0.247830
$986$		0			0
$987$	1.22886e8	+	1.76979e8i	0.127806	+	0.184065i
$988$		0			0
$989$		−	1.36934e7i		−	0.0141554i
$990$		0			0
$991$	−3.44684e8			−0.354161			−0.177080	−	0.984196i	$-0.556665\pi$
$991$	−3.44684e8			−0.354161			−0.177080	+	0.984196i	$0.556665\pi$
$992$		0			0
$993$	8.74358e7	−	6.07115e7i	0.0892980	−	0.0620045i
$994$		0			0
$995$			7.95976e8i			0.808036i
$996$		0			0
$997$	−4.23493e8			−0.427327			−0.213664	−	0.976907i	$-0.568540\pi$
$997$	−4.23493e8			−0.427327			−0.213664	+	0.976907i	$0.568540\pi$
$998$		0			0
$999$	−2.22988e8	−	8.73346e8i	−0.223658	−	0.875972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.g.a.41.4	yes	8
3.2	odd	2	inner	60.7.g.a.41.3	✓	8
4.3	odd	2		240.7.l.c.161.5		8
5.2	odd	4		300.7.b.e.149.14		16
5.3	odd	4		300.7.b.e.149.3		16
5.4	even	2		300.7.g.h.101.5		8
12.11	even	2		240.7.l.c.161.6		8
15.2	even	4		300.7.b.e.149.4		16
15.8	even	4		300.7.b.e.149.13		16
15.14	odd	2		300.7.g.h.101.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.g.a.41.3	✓	8	3.2	odd	2	inner
60.7.g.a.41.4	yes	8	1.1	even	1	trivial
240.7.l.c.161.5		8	4.3	odd	2
240.7.l.c.161.6		8	12.11	even	2
300.7.b.e.149.3		16	5.3	odd	4
300.7.b.e.149.4		16	15.2	even	4
300.7.b.e.149.13		16	15.8	even	4
300.7.b.e.149.14		16	5.2	odd	4
300.7.g.h.101.5		8	5.4	even	2
300.7.g.h.101.6		8	15.14	odd	2

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-22.1779 + 15.3993i) q^{3} -55.9017i q^{5} +437.053 q^{7} +(254.720 - 683.051i) q^{9} +O(q^{10})\)	\(q+(-22.1779 + 15.3993i) q^{3} -55.9017i q^{5} +437.053 q^{7} +(254.720 - 683.051i) q^{9} +1898.54i q^{11} -2670.19 q^{13} +(860.849 + 1239.78i) q^{15} +4521.29i q^{17} -9502.28 q^{19} +(-9692.93 + 6730.33i) q^{21} +549.560i q^{23} -3125.00 q^{25} +(4869.36 + 19071.2i) q^{27} +43308.7i q^{29} +29588.2 q^{31} +(-29236.2 - 42105.6i) q^{33} -24432.0i q^{35} -45794.0 q^{37} +(59219.3 - 41119.2i) q^{39} +114611. i q^{41} -24917.0 q^{43} +(-38183.7 - 14239.3i) q^{45} -18258.6i q^{47} +73366.3 q^{49} +(-69624.9 - 100273. i) q^{51} -174021. i q^{53} +106131. q^{55} +(210741. - 146329. i) q^{57} +67872.4i q^{59} +175028. q^{61} +(111326. - 298529. i) q^{63} +149268. i q^{65} +16056.7 q^{67} +(-8462.86 - 12188.1i) q^{69} -222821. i q^{71} -620790. q^{73} +(69306.0 - 48122.9i) q^{75} +829761. i q^{77} +525417. q^{79} +(-401676. - 347974. i) q^{81} +790761. i q^{83} +252748. q^{85} +(-666925. - 960496. i) q^{87} +1.12565e6i q^{89} -1.16702e6 q^{91} +(-656204. + 455638. i) q^{93} +531194. i q^{95} -624200. q^{97} +(1.29680e6 + 483596. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 20 q^{3} - 560 q^{7} + 1492 q^{9}+O(q^{10}) \) 8 * q - 20 * q^3 - 560 * q^7 + 1492 * q^9	\( 8 q - 20 q^{3} - 560 q^{7} + 1492 q^{9} - 6440 q^{13} + 2000 q^{15} - 15272 q^{19} - 868 q^{21} - 25000 q^{25} - 18620 q^{27} + 35032 q^{31} - 111120 q^{33} + 99880 q^{37} + 39608 q^{39} - 161000 q^{43} - 5500 q^{45} + 202560 q^{49} + 429120 q^{51} - 33000 q^{55} - 27160 q^{57} - 135608 q^{61} + 377240 q^{63} + 404920 q^{67} - 254940 q^{69} - 356960 q^{73} + 62500 q^{75} + 707704 q^{79} - 1198112 q^{81} + 828000 q^{85} - 1528440 q^{87} - 2004112 q^{91} - 467920 q^{93} - 1326320 q^{97} + 2650080 q^{99}+O(q^{100}) \) 8 * q - 20 * q^3 - 560 * q^7 + 1492 * q^9 - 6440 * q^13 + 2000 * q^15 - 15272 * q^19 - 868 * q^21 - 25000 * q^25 - 18620 * q^27 + 35032 * q^31 - 111120 * q^33 + 99880 * q^37 + 39608 * q^39 - 161000 * q^43 - 5500 * q^45 + 202560 * q^49 + 429120 * q^51 - 33000 * q^55 - 27160 * q^57 - 135608 * q^61 + 377240 * q^63 + 404920 * q^67 - 254940 * q^69 - 356960 * q^73 + 62500 * q^75 + 707704 * q^79 - 1198112 * q^81 + 828000 * q^85 - 1528440 * q^87 - 2004112 * q^91 - 467920 * q^93 - 1326320 * q^97 + 2650080 * q^99

Introduction

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