LMFDB - Embedded newform 240.3.c.e.209.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,3,Mod(209,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("240.209");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	240.c (of order $2$, degree $1$, not 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:	$6.53952634465$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 34x^{10} + 305x^{8} + 616x^{6} + 305x^{4} + 34x^{2} + 1 $ x^12 + 34x^10 + 305x^8 + 616x^6 + 305x^4 + 34*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{15}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			209.2
Root			$0.220185i$ of defining polynomial
Character	$\chi$	$=$	240.209
Dual form			240.3.c.e.209.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.72256 + 1.26002i) q^{3} +(-0.689011 - 4.95230i) q^{5} +0.735748i q^{7} +(5.82469 - 6.86097i) q^{9} +O(q^{10})$	\(q+(-2.72256 + 1.26002i) q^{3} +(-0.689011 - 4.95230i) q^{5} +0.735748i q^{7} +(5.82469 - 6.86097i) q^{9} +10.9451i q^{11} +21.1901i q^{13} +(8.11588 + 12.6148i) q^{15} -7.03488 q^{17} -23.1529 q^{19} +(-0.927058 - 2.00312i) q^{21} -24.7483 q^{23} +(-24.0505 + 6.82438i) q^{25} +(-7.21312 + 26.0187i) q^{27} +32.3284i q^{29} +34.9482 q^{31} +(-13.7911 - 29.7987i) q^{33} +(3.64364 - 0.506939i) q^{35} +37.7818i q^{37} +(-26.6999 - 57.6912i) q^{39} +39.0848i q^{41} -22.6804i q^{43} +(-37.9909 - 24.1183i) q^{45} +39.1076 q^{47} +48.4587 q^{49} +(19.1529 - 8.86409i) q^{51} -60.9179 q^{53} +(54.2034 - 7.54130i) q^{55} +(63.0352 - 29.1731i) q^{57} +7.79696i q^{59} -11.1529 q^{61} +(5.04795 + 4.28551i) q^{63} +(104.939 - 14.6002i) q^{65} -33.3485i q^{67} +(67.3787 - 31.1833i) q^{69} +96.9650i q^{71} -134.535i q^{73} +(56.8802 - 48.8840i) q^{75} -8.05284 q^{77} -121.049 q^{79} +(-13.1459 - 79.9261i) q^{81} -90.2345 q^{83} +(4.84711 + 34.8388i) q^{85} +(-40.7344 - 88.0160i) q^{87} +53.1846i q^{89} -15.5905 q^{91} +(-95.1486 + 44.0354i) q^{93} +(15.9526 + 114.660i) q^{95} -115.001i q^{97} +(75.0940 + 63.7519i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{9}+O(q^{10}) $ 12 * q + 8 * q^9	$ 12 q + 8 q^{9} - 16 q^{15} + 4 q^{21} + 36 q^{25} + 48 q^{31} + 128 q^{39} - 68 q^{45} - 252 q^{49} - 48 q^{51} + 48 q^{55} + 144 q^{61} + 268 q^{69} - 304 q^{75} - 432 q^{79} - 188 q^{81} + 336 q^{85} + 560 q^{99}+O(q^{100}) $ 12 * q + 8 * q^9 - 16 * q^15 + 4 * q^21 + 36 * q^25 + 48 * q^31 + 128 * q^39 - 68 * q^45 - 252 * q^49 - 48 * q^51 + 48 * q^55 + 144 * q^61 + 268 * q^69 - 304 * q^75 - 432 * q^79 - 188 * q^81 + 336 * q^85 + 560 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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
$3$	−2.72256	+	1.26002i	−0.907521	+	0.420007i
$3$	−2.72256	+	1.26002i	−0.907521	+	0.420007i
$4$		0			0
$5$	−0.689011	−	4.95230i	−0.137802	−	0.990460i
$5$	−0.689011	−	4.95230i	−0.137802	−	0.990460i
$6$		0			0
$7$			0.735748i			0.105107i	0.998618	+	0.0525534i	$0.0167360\pi$
$7$			0.735748i			0.105107i	−0.998618	+	0.0525534i	$0.983264\pi$
$8$		0			0
$9$	5.82469	−	6.86097i	0.647188	−	0.762330i
$10$		0			0
$11$			10.9451i			0.995009i	0.867461	+	0.497505i	$0.165750\pi$
$11$			10.9451i			0.995009i	−0.867461	+	0.497505i	$0.834250\pi$
$12$		0			0
$13$			21.1901i			1.63000i	0.579458	+	0.815002i	$0.303264\pi$
$13$			21.1901i			1.63000i	−0.579458	+	0.815002i	$0.696736\pi$
$14$		0			0
$15$	8.11588	+	12.6148i	0.541058	+	0.840985i
$16$		0			0
$17$	−7.03488			−0.413816			−0.206908	−	0.978360i	$-0.566340\pi$
$17$	−7.03488			−0.413816			−0.206908	+	0.978360i	$0.566340\pi$
$18$		0			0
$19$	−23.1529			−1.21857			−0.609287	−	0.792950i	$-0.708544\pi$
$19$	−23.1529			−1.21857			−0.609287	+	0.792950i	$0.708544\pi$
$20$		0			0
$21$	−0.927058	−	2.00312i	−0.0441456	−	0.0953867i
$22$		0			0
$23$	−24.7483			−1.07601			−0.538006	−	0.842941i	$-0.680822\pi$
$23$	−24.7483			−1.07601			−0.538006	+	0.842941i	$0.680822\pi$
$24$		0			0
$25$	−24.0505	+	6.82438i	−0.962021	+	0.272975i
$26$		0			0
$27$	−7.21312	+	26.0187i	−0.267153	+	0.963654i
$28$		0			0
$29$			32.3284i			1.11477i	0.830254	+	0.557386i	$0.188196\pi$
$29$			32.3284i			1.11477i	−0.830254	+	0.557386i	$0.811804\pi$
$30$		0			0
$31$	34.9482			1.12736			0.563680	−	0.825993i	$-0.309385\pi$
$31$	34.9482			1.12736			0.563680	+	0.825993i	$0.309385\pi$
$32$		0			0
$33$	−13.7911	−	29.7987i	−0.417911	−	0.902992i
$34$		0			0
$35$	3.64364	−	0.506939i	0.104104	−	0.0144840i
$36$		0			0
$37$			37.7818i			1.02113i	0.859839	+	0.510565i	$0.170564\pi$
$37$			37.7818i			1.02113i	−0.859839	+	0.510565i	$0.829436\pi$
$38$		0			0
$39$	−26.6999	−	57.6912i	−0.684613	−	1.47926i
$40$		0			0
$41$			39.0848i			0.953288i	0.879096	+	0.476644i	$0.158147\pi$
$41$			39.0848i			0.953288i	−0.879096	+	0.476644i	$0.841853\pi$
$42$		0			0
$43$		−	22.6804i		−	0.527451i	−0.964598	−	0.263725i	$-0.915049\pi$
$43$		−	22.6804i		−	0.527451i	0.964598	−	0.263725i	$-0.0849513\pi$
$44$		0			0
$45$	−37.9909	−	24.1183i	−0.844241	−	0.535963i
$46$		0			0
$47$	39.1076			0.832076			0.416038	−	0.909347i	$-0.363418\pi$
$47$	39.1076			0.832076			0.416038	+	0.909347i	$0.363418\pi$
$48$		0			0
$49$	48.4587			0.988953
$50$		0			0
$51$	19.1529	−	8.86409i	0.375547	−	0.173806i
$52$		0			0
$53$	−60.9179			−1.14939			−0.574697	−	0.818366i	$-0.694880\pi$
$53$	−60.9179			−1.14939			−0.574697	+	0.818366i	$0.694880\pi$
$54$		0			0
$55$	54.2034	−	7.54130i	0.985517	−	0.137115i
$56$		0			0
$57$	63.0352	−	29.1731i	1.10588	−	0.511809i
$58$		0			0
$59$			7.79696i			0.132152i	0.997815	+	0.0660759i	$0.0210480\pi$
$59$			7.79696i			0.132152i	−0.997815	+	0.0660759i	$0.978952\pi$
$60$		0			0
$61$	−11.1529			−0.182834			−0.0914171	−	0.995813i	$-0.529140\pi$
$61$	−11.1529			−0.182834			−0.0914171	+	0.995813i	$0.529140\pi$
$62$		0			0
$63$	5.04795	+	4.28551i	0.0801262	+	0.0680239i
$64$		0			0
$65$	104.939	−	14.6002i	1.61445	−	0.224618i
$66$		0			0
$67$		−	33.3485i		−	0.497739i	−0.968537	−	0.248869i	$-0.919941\pi$
$67$		−	33.3485i		−	0.497739i	0.968537	−	0.248869i	$-0.0800590\pi$
$68$		0			0
$69$	67.3787	−	31.1833i	0.976503	−	0.451933i
$70$		0			0
$71$			96.9650i			1.36570i	0.730557	+	0.682852i	$0.239261\pi$
$71$			96.9650i			1.36570i	−0.730557	+	0.682852i	$0.760739\pi$
$72$		0			0
$73$		−	134.535i		−	1.84295i	−0.388436	−	0.921476i	$-0.626984\pi$
$73$		−	134.535i		−	1.84295i	0.388436	−	0.921476i	$-0.373016\pi$
$74$		0			0
$75$	56.8802	−	48.8840i	0.758403	−	0.651786i
$76$		0			0
$77$	−8.05284			−0.104582
$78$		0			0
$79$	−121.049			−1.53227			−0.766134	−	0.642681i	$-0.777822\pi$
$79$	−121.049			−1.53227			−0.766134	+	0.642681i	$0.777822\pi$
$80$		0			0
$81$	−13.1459	−	79.9261i	−0.162295	−	0.986742i
$82$		0			0
$83$	−90.2345			−1.08716			−0.543582	−	0.839356i	$-0.682932\pi$
$83$	−90.2345			−1.08716			−0.543582	+	0.839356i	$0.682932\pi$
$84$		0			0
$85$	4.84711	+	34.8388i	0.0570248	+	0.409868i
$86$		0			0
$87$	−40.7344	−	88.0160i	−0.468212	−	1.01168i
$88$		0			0
$89$			53.1846i			0.597579i	0.954319	+	0.298790i	$0.0965829\pi$
$89$			53.1846i			0.597579i	−0.954319	+	0.298790i	$0.903417\pi$
$90$		0			0
$91$	−15.5905			−0.171325
$92$		0			0
$93$	−95.1486	+	44.0354i	−1.02310	+	0.473499i
$94$		0			0
$95$	15.9526	+	114.660i	0.167922	+	1.20695i
$96$		0			0
$97$		−	115.001i		−	1.18557i	−0.805359	−	0.592787i	$-0.798028\pi$
$97$		−	115.001i		−	1.18557i	0.805359	−	0.592787i	$-0.201972\pi$
$98$		0			0
$99$	75.0940	+	63.7519i	0.758526	+	0.643958i
$100$		0			0
$101$		−	29.1802i		−	0.288913i	−0.989511	−	0.144457i	$-0.953857\pi$
$101$		−	29.1802i		−	0.288913i	0.989511	−	0.144457i	$-0.0461434\pi$
$102$		0			0
$103$		−	89.9481i		−	0.873283i	−0.899636	−	0.436641i	$-0.856168\pi$
$103$		−	89.9481i		−	0.873283i	0.899636	−	0.436641i	$-0.143832\pi$
$104$		0			0
$105$	−9.28130	+	5.97124i	−0.0883933	+	0.0568690i
$106$		0			0
$107$	153.586			1.43538			0.717689	−	0.696363i	$-0.245200\pi$
$107$	153.586			1.43538			0.717689	+	0.696363i	$0.245200\pi$
$108$		0			0
$109$	−59.5623			−0.546444			−0.273222	−	0.961951i	$-0.588089\pi$
$109$	−59.5623			−0.546444			−0.273222	+	0.961951i	$0.588089\pi$
$110$		0			0
$111$	−47.6059	−	102.863i	−0.428882	−	0.926697i
$112$		0			0
$113$	1.01796			0.00900851			0.00450426	−	0.999990i	$-0.498566\pi$
$113$	1.01796			0.00900851			0.00450426	+	0.999990i	$0.498566\pi$
$114$		0			0
$115$	17.0518	+	122.561i	0.148277	+	1.06575i
$116$		0			0
$117$	145.384	+	123.426i	1.24260	+	1.05492i
$118$		0			0
$119$		−	5.17590i		−	0.0434949i
$120$		0			0
$121$	1.20473			0.00995643
$122$		0			0
$123$	−49.2477	−	106.411i	−0.400388	−	0.865129i
$124$		0			0
$125$	50.3674	+	114.403i	0.402940	+	0.915227i
$126$		0			0
$127$			209.731i			1.65142i	0.564091	+	0.825712i	$0.309227\pi$
$127$			209.731i			1.65142i	−0.564091	+	0.825712i	$0.690773\pi$
$128$		0			0
$129$	28.5778	+	61.7488i	0.221533	+	0.478672i
$130$		0			0
$131$		−	210.051i		−	1.60344i	−0.597698	−	0.801721i	$-0.703918\pi$
$131$		−	210.051i		−	1.60344i	0.597698	−	0.801721i	$-0.296082\pi$
$132$		0			0
$133$		−	17.0347i		−	0.128080i
$134$		0			0
$135$	133.822	+	17.7944i	0.991275	+	0.131810i
$136$		0			0
$137$	−168.688			−1.23130			−0.615648	−	0.788021i	$-0.711106\pi$
$137$	−168.688			−1.23130			−0.615648	+	0.788021i	$0.711106\pi$
$138$		0			0
$139$	129.251			0.929866			0.464933	−	0.885346i	$-0.346078\pi$
$139$	129.251			0.929866			0.464933	+	0.885346i	$0.346078\pi$
$140$		0			0
$141$	−106.473	+	49.2763i	−0.755126	+	0.349478i
$142$		0			0
$143$	−231.927			−1.62187
$144$		0			0
$145$	160.100	−	22.2746i	1.10414	−	0.153618i
$146$		0			0
$147$	−131.932	+	61.0590i	−0.897495	+	0.415367i
$148$		0			0
$149$		−	83.9655i		−	0.563527i	−0.959484	−	0.281763i	$-0.909081\pi$
$149$		−	83.9655i		−	0.563527i	0.959484	−	0.281763i	$-0.0909193\pi$
$150$		0			0
$151$	−9.04922			−0.0599286			−0.0299643	−	0.999551i	$-0.509539\pi$
$151$	−9.04922			−0.0599286			−0.0299643	+	0.999551i	$0.509539\pi$
$152$		0			0
$153$	−40.9760	+	48.2661i	−0.267817	+	0.315465i
$154$		0			0
$155$	−24.0797	−	173.074i	−0.155353	−	1.11660i
$156$		0			0
$157$			162.054i			1.03219i	0.856530	+	0.516097i	$0.172616\pi$
$157$			162.054i			1.03219i	−0.856530	+	0.516097i	$0.827384\pi$
$158$		0			0
$159$	165.853	−	76.7578i	1.04310	−	0.482754i
$160$		0			0
$161$		−	18.2085i		−	0.113096i
$162$		0			0
$163$			136.172i			0.835411i	0.908583	+	0.417705i	$0.137166\pi$
$163$			136.172i			0.835411i	−0.908583	+	0.417705i	$0.862834\pi$
$164$		0			0
$165$	−138.070	+	88.8291i	−0.836788	+	0.538358i
$166$		0			0
$167$	140.931			0.843898			0.421949	−	0.906620i	$-0.361346\pi$
$167$	140.931			0.843898			0.421949	+	0.906620i	$0.361346\pi$
$168$		0			0
$169$	−280.018			−1.65691
$170$		0			0
$171$	−134.859	+	158.851i	−0.788646	+	0.928955i
$172$		0			0
$173$	−132.351			−0.765032			−0.382516	−	0.923949i	$-0.624942\pi$
$173$	−132.351			−0.765032			−0.382516	+	0.923949i	$0.624942\pi$
$174$		0			0
$175$	−5.02102	−	17.6951i	−0.0286916	−	0.101115i
$176$		0			0
$177$	−9.82433	−	21.2277i	−0.0555047	−	0.119931i
$178$		0			0
$179$			92.2499i			0.515363i	0.966230	+	0.257681i	$0.0829585\pi$
$179$			92.2499i			0.515363i	−0.966230	+	0.257681i	$0.917042\pi$
$180$		0			0
$181$	115.896			0.640311			0.320156	−	0.947365i	$-0.396265\pi$
$181$	115.896			0.640311			0.320156	+	0.947365i	$0.396265\pi$
$182$		0			0
$183$	30.3644	−	14.0529i	0.165926	−	0.0767917i
$184$		0			0
$185$	187.107	−	26.0321i	1.01139	−	0.140714i
$186$		0			0
$187$		−	76.9974i		−	0.411751i
$188$		0			0
$189$	−19.1432	−	5.30704i	−0.101287	−	0.0280796i
$190$		0			0
$191$			53.1183i			0.278106i	0.990285	+	0.139053i	$0.0444059\pi$
$191$			53.1183i			0.278106i	−0.990285	+	0.139053i	$0.955594\pi$
$192$		0			0
$193$			271.315i			1.40578i	0.711299	+	0.702890i	$0.248107\pi$
$193$			271.315i			1.40578i	−0.711299	+	0.702890i	$0.751893\pi$
$194$		0			0
$195$	−267.308	+	171.976i	−1.37081	+	0.881928i
$196$		0			0
$197$	64.3941			0.326873			0.163437	−	0.986554i	$-0.447742\pi$
$197$	64.3941			0.326873			0.163437	+	0.986554i	$0.447742\pi$
$198$		0			0
$199$	−72.0308			−0.361964			−0.180982	−	0.983486i	$-0.557928\pi$
$199$	−72.0308			−0.361964			−0.180982	+	0.983486i	$0.557928\pi$
$200$		0			0
$201$	42.0198	+	90.7933i	0.209054	+	0.451708i
$202$		0			0
$203$	−23.7855			−0.117170
$204$		0			0
$205$	193.560	−	26.9299i	0.944194	−	0.131365i
$206$		0			0
$207$	−144.151	+	169.797i	−0.696382	+	0.820276i
$208$		0			0
$209$		−	253.411i		−	1.21249i
$210$		0			0
$211$	−108.583			−0.514613			−0.257307	−	0.966330i	$-0.582835\pi$
$211$	−108.583			−0.514613			−0.257307	+	0.966330i	$0.582835\pi$
$212$		0			0
$213$	−122.178	−	263.993i	−0.573605	−	1.23940i
$214$		0			0
$215$	−112.320	+	15.6270i	−0.522419	+	0.0726839i
$216$		0			0
$217$			25.7130i			0.118493i
$218$		0			0
$219$	169.518	+	366.281i	0.774053	+	1.67252i
$220$		0			0
$221$		−	149.069i		−	0.674522i
$222$		0			0
$223$			83.6192i			0.374974i	0.982267	+	0.187487i	$0.0600342\pi$
$223$			83.6192i			0.374974i	−0.982267	+	0.187487i	$0.939966\pi$
$224$		0			0
$225$	−93.2651	+	204.760i	−0.414511	+	0.910044i
$226$		0			0
$227$	51.6591			0.227573			0.113787	−	0.993505i	$-0.463702\pi$
$227$	51.6591			0.227573			0.113787	+	0.993505i	$0.463702\pi$
$228$		0			0
$229$	−280.974			−1.22696			−0.613480	−	0.789710i	$-0.710231\pi$
$229$	−280.974			−1.22696			−0.613480	+	0.789710i	$0.710231\pi$
$230$		0			0
$231$	21.9244	−	10.1467i	0.0949106	−	0.0439253i
$232$		0			0
$233$	169.192			0.726148			0.363074	−	0.931760i	$-0.381727\pi$
$233$	169.192			0.726148			0.363074	+	0.931760i	$0.381727\pi$
$234$		0			0
$235$	−26.9455	−	193.672i	−0.114662	−	0.824137i
$236$		0			0
$237$	329.564	−	152.525i	1.39057	−	0.643564i
$238$		0			0
$239$			1.12039i			0.00468782i	0.999997	+	0.00234391i	$0.000746090\pi$
$239$			1.12039i			0.00468782i	−0.999997	+	0.00234391i	$0.999254\pi$
$240$		0			0
$241$	153.254			0.635908			0.317954	−	0.948106i	$-0.397004\pi$
$241$	153.254			0.635908			0.317954	+	0.948106i	$0.397004\pi$
$242$		0			0
$243$	136.499	+	201.040i	0.561725	+	0.827324i
$244$		0			0
$245$	−33.3886	−	239.982i	−0.136280	−	0.979518i
$246$		0			0
$247$		−	490.611i		−	1.98628i
$248$		0			0
$249$	245.669	−	113.697i	0.986623	−	0.456616i
$250$		0			0
$251$		−	126.692i		−	0.504751i	−0.967629	−	0.252375i	$-0.918788\pi$
$251$		−	126.692i		−	0.504751i	0.967629	−	0.252375i	$-0.0812118\pi$
$252$		0			0
$253$		−	270.872i		−	1.07064i
$254$		0			0
$255$	−57.0942	−	88.7434i	−0.223899	−	0.348013i
$256$		0			0
$257$	−396.692			−1.54355			−0.771774	−	0.635897i	$-0.780630\pi$
$257$	−396.692			−1.54355			−0.771774	+	0.635897i	$0.780630\pi$
$258$		0			0
$259$	−27.7979			−0.107328
$260$		0			0
$261$	221.804	+	188.303i	0.849824	+	0.721467i
$262$		0			0
$263$	394.431			1.49974			0.749868	−	0.661587i	$-0.230117\pi$
$263$	394.431			1.49974			0.749868	+	0.661587i	$0.230117\pi$
$264$		0			0
$265$	41.9731	+	301.684i	0.158389	+	1.13843i
$266$		0			0
$267$	−67.0137	−	144.798i	−0.250987	−	0.542316i
$268$		0			0
$269$			104.802i			0.389597i	0.980843	+	0.194798i	$0.0624053\pi$
$269$			104.802i			0.389597i	−0.980843	+	0.194798i	$0.937595\pi$
$270$		0			0
$271$	335.355			1.23747			0.618736	−	0.785599i	$-0.287645\pi$
$271$	335.355			1.23747			0.618736	+	0.785599i	$0.287645\pi$
$272$		0			0
$273$	42.4462	−	19.6444i	0.155481	−	0.0719576i
$274$		0			0
$275$	−74.6935	−	263.235i	−0.271613	−	0.957220i
$276$		0			0
$277$		−	167.790i		−	0.605739i	−0.953032	−	0.302870i	$-0.902055\pi$
$277$		−	167.790i		−	0.605739i	0.953032	−	0.302870i	$-0.0979447\pi$
$278$		0			0
$279$	203.562	−	239.778i	0.729614	−	0.859421i
$280$		0			0
$281$			99.4601i			0.353950i	0.984215	+	0.176975i	$0.0566312\pi$
$281$			99.4601i			0.353950i	−0.984215	+	0.176975i	$0.943369\pi$
$282$		0			0
$283$		−	487.022i		−	1.72093i	−0.509512	−	0.860464i	$-0.670174\pi$
$283$		−	487.022i		−	1.72093i	0.509512	−	0.860464i	$-0.329826\pi$
$284$		0			0
$285$	−187.906	−	292.069i	−0.659319	−	1.02480i
$286$		0			0
$287$	−28.7566			−0.100197
$288$		0			0
$289$	−239.511			−0.828756
$290$		0			0
$291$	144.903	+	313.097i	0.497950	+	1.07593i
$292$		0			0
$293$	343.107			1.17101			0.585507	−	0.810667i	$-0.300895\pi$
$293$	343.107			1.17101			0.585507	+	0.810667i	$0.300895\pi$
$294$		0			0
$295$	38.6129	−	5.37219i	0.130891	−	0.0182108i
$296$		0			0
$297$	−284.777	−	78.9484i	−0.958845	−	0.265819i
$298$		0			0
$299$		−	524.417i		−	1.75390i
$300$		0			0
$301$	16.6870			0.0554387
$302$		0			0
$303$	36.7677	+	79.4450i	0.121346	+	0.262195i
$304$		0			0
$305$	7.68447	+	55.2325i	0.0251950	+	0.181090i
$306$		0			0
$307$			364.627i			1.18771i	0.804573	+	0.593854i	$0.202394\pi$
$307$			364.627i			1.18771i	−0.804573	+	0.593854i	$0.797606\pi$
$308$		0			0
$309$	113.337	+	244.889i	0.366785	+	0.792522i
$310$		0			0
$311$			121.963i			0.392164i	0.980587	+	0.196082i	$0.0628219\pi$
$311$			121.963i			0.392164i	−0.980587	+	0.196082i	$0.937178\pi$
$312$		0			0
$313$			94.8060i			0.302895i	0.988465	+	0.151447i	$0.0483934\pi$
$313$			94.8060i			0.302895i	−0.988465	+	0.151447i	$0.951607\pi$
$314$		0			0
$315$	17.7450	−	27.9517i	0.0563334	−	0.0887356i
$316$		0			0
$317$	511.282			1.61288			0.806438	−	0.591318i	$-0.201392\pi$
$317$	511.282			1.61288			0.806438	+	0.591318i	$0.201392\pi$
$318$		0			0
$319$	−353.837			−1.10921
$320$		0			0
$321$	−418.146	+	193.521i	−1.30264	+	0.602869i
$322$		0			0
$323$	162.878			0.504265
$324$		0			0
$325$	−144.609	−	509.632i	−0.444951	−	1.56810i
$326$		0			0
$327$	162.162	−	75.0498i	0.495909	−	0.229510i
$328$		0			0
$329$			28.7733i			0.0874569i
$330$		0			0
$331$	182.682			0.551909			0.275954	−	0.961171i	$-0.411006\pi$
$331$	182.682			0.551909			0.275954	+	0.961171i	$0.411006\pi$
$332$		0			0
$333$	259.220	+	220.067i	0.778438	+	0.660863i
$334$		0			0
$335$	−165.152	+	22.9775i	−0.492990	+	0.0685895i
$336$		0			0
$337$			89.0617i			0.264278i	0.991231	+	0.132139i	$0.0421845\pi$
$337$			89.0617i			0.264278i	−0.991231	+	0.132139i	$0.957815\pi$
$338$		0			0
$339$	−2.77147	+	1.28265i	−0.00817541	+	0.00378364i
$340$		0			0
$341$			382.511i			1.12173i
$342$		0			0
$343$			71.7050i			0.209053i
$344$		0			0
$345$	−200.854	−	312.194i	−0.582185	−	0.904910i
$346$		0			0
$347$	17.7180			0.0510605			0.0255303	−	0.999674i	$-0.491873\pi$
$347$	17.7180			0.0510605			0.0255303	+	0.999674i	$0.491873\pi$
$348$		0			0
$349$	229.114			0.656488			0.328244	−	0.944593i	$-0.393543\pi$
$349$	229.114			0.656488			0.328244	+	0.944593i	$0.393543\pi$
$350$		0			0
$351$	−551.337	−	152.846i	−1.57076	−	0.435460i
$352$		0			0
$353$	183.760			0.520566			0.260283	−	0.965532i	$-0.416184\pi$
$353$	183.760			0.520566			0.260283	+	0.965532i	$0.416184\pi$
$354$		0			0
$355$	480.199	−	66.8099i	1.35267	−	0.188197i
$356$		0			0
$357$	6.52174	+	14.0917i	0.0182682	+	0.0394726i
$358$		0			0
$359$			537.837i			1.49815i	0.662484	+	0.749076i	$0.269502\pi$
$359$			537.837i			1.49815i	−0.662484	+	0.749076i	$0.730498\pi$
$360$		0			0
$361$	175.056			0.484921
$362$		0			0
$363$	−3.27995	+	1.51798i	−0.00903567	+	0.00418177i
$364$		0			0
$365$	−666.260	+	92.6964i	−1.82537	+	0.253963i
$366$		0			0
$367$			153.740i			0.418909i	0.977818	+	0.209455i	$0.0671689\pi$
$367$			153.740i			0.418909i	−0.977818	+	0.209455i	$0.932831\pi$
$368$		0			0
$369$	268.160	+	227.657i	0.726721	+	0.616957i
$370$		0			0
$371$		−	44.8202i		−	0.120809i
$372$		0			0
$373$			211.056i			0.565833i	0.959145	+	0.282917i	$0.0913020\pi$
$373$			211.056i			0.565833i	−0.959145	+	0.282917i	$0.908698\pi$
$374$		0			0
$375$	−281.279	−	248.006i	−0.750078	−	0.661350i
$376$		0			0
$377$	−685.040			−1.81708
$378$		0			0
$379$	−699.345			−1.84524			−0.922618	−	0.385715i	$-0.873955\pi$
$379$	−699.345			−1.84524			−0.922618	+	0.385715i	$0.873955\pi$
$380$		0			0
$381$	−264.265	−	571.006i	−0.693610	−	1.49870i
$382$		0			0
$383$	−186.008			−0.485662			−0.242831	−	0.970069i	$-0.578076\pi$
$383$	−186.008			−0.485662			−0.242831	+	0.970069i	$0.578076\pi$
$384$		0			0
$385$	5.54850	+	39.8801i	0.0144117	+	0.103585i
$386$		0			0
$387$	−155.609	−	132.106i	−0.402092	−	0.341360i
$388$		0			0
$389$		−	288.194i		−	0.740858i	−0.928861	−	0.370429i	$-0.879211\pi$
$389$		−	288.194i		−	0.740858i	0.928861	−	0.370429i	$-0.120789\pi$
$390$		0			0
$391$	174.101			0.445271
$392$		0			0
$393$	264.669	+	571.877i	0.673457	+	1.45516i
$394$		0			0
$395$	83.4043	+	599.472i	0.211150	+	1.51765i
$396$		0			0
$397$		−	64.3054i		−	0.161978i	−0.996715	−	0.0809892i	$-0.974192\pi$
$397$		−	64.3054i		−	0.161978i	0.996715	−	0.0809892i	$-0.0258079\pi$
$398$		0			0
$399$	21.4641	+	46.3780i	0.0537947	+	0.116236i
$400$		0			0
$401$		−	659.774i		−	1.64532i	−0.568533	−	0.822661i	$-0.692489\pi$
$401$		−	659.774i		−	1.64532i	0.568533	−	0.822661i	$-0.307511\pi$
$402$		0			0
$403$			740.553i			1.83760i
$404$		0			0
$405$	−386.760	+	120.172i	−0.954964	+	0.296722i
$406$		0			0
$407$	−413.526			−1.01603
$408$		0			0
$409$	217.863			0.532672			0.266336	−	0.963880i	$-0.414187\pi$
$409$	217.863			0.532672			0.266336	+	0.963880i	$0.414187\pi$
$410$		0			0
$411$	459.263	−	212.550i	1.11743	−	0.517153i
$412$		0			0
$413$	−5.73660			−0.0138901
$414$		0			0
$415$	62.1726	+	446.868i	0.149814	+	1.07679i
$416$		0			0
$417$	−351.895	+	162.859i	−0.843872	+	0.390550i
$418$		0			0
$419$		−	407.129i		−	0.971668i	−0.874051	−	0.485834i	$-0.838516\pi$
$419$		−	407.129i		−	0.971668i	0.874051	−	0.485834i	$-0.161484\pi$
$420$		0			0
$421$	−69.1949			−0.164359			−0.0821793	−	0.996618i	$-0.526188\pi$
$421$	−69.1949			−0.164359			−0.0821793	+	0.996618i	$0.526188\pi$
$422$		0			0
$423$	227.790	−	268.316i	0.538510	−	0.634316i
$424$		0			0
$425$	169.192	−	48.0087i	0.398100	−	0.112962i
$426$		0			0
$427$		−	8.20572i		−	0.0192171i
$428$		0			0
$429$	631.437	−	292.233i	1.47188	−	0.681197i
$430$		0			0
$431$			452.663i			1.05026i	0.851021	+	0.525132i	$0.175984\pi$
$431$			452.663i			1.05026i	−0.851021	+	0.525132i	$0.824016\pi$
$432$		0			0
$433$			226.323i			0.522686i	0.965246	+	0.261343i	$0.0841654\pi$
$433$			226.323i			0.522686i	−0.965246	+	0.261343i	$0.915835\pi$
$434$		0			0
$435$	−407.815	+	262.373i	−0.937506	+	0.603156i
$436$		0			0
$437$	572.994			1.31120
$438$		0			0
$439$	−188.642			−0.429709			−0.214855	−	0.976646i	$-0.568928\pi$
$439$	−188.642			−0.429709			−0.214855	+	0.976646i	$0.568928\pi$
$440$		0			0
$441$	282.257	−	332.474i	0.640038	−	0.753908i
$442$		0			0
$443$	499.705			1.12800			0.564001	−	0.825774i	$-0.309261\pi$
$443$	499.705			1.12800			0.564001	+	0.825774i	$0.309261\pi$
$444$		0			0
$445$	263.386	−	36.6448i	0.591878	−	0.0823478i
$446$		0			0
$447$	105.798	+	228.601i	0.236685	+	0.511412i
$448$		0			0
$449$			818.928i			1.82389i	0.410310	+	0.911946i	$0.365421\pi$
$449$			818.928i			1.82389i	−0.410310	+	0.911946i	$0.634579\pi$
$450$		0			0
$451$	−427.787			−0.948531
$452$		0			0
$453$	24.6371	−	11.4022i	0.0543864	−	0.0251704i
$454$		0			0
$455$	10.7421	+	77.2090i	0.0236089	+	0.169690i
$456$		0			0
$457$		−	311.602i		−	0.681842i	−0.940092	−	0.340921i	$-0.889261\pi$
$457$		−	311.602i		−	0.681842i	0.940092	−	0.340921i	$-0.110739\pi$
$458$		0			0
$459$	50.7434	−	183.038i	0.110552	−	0.398776i
$460$		0			0
$461$		−	7.18351i		−	0.0155825i	−0.999970	−	0.00779123i	$-0.997520\pi$
$461$		−	7.18351i		−	0.0155825i	0.999970	−	0.00779123i	$-0.00248005\pi$
$462$		0			0
$463$			557.563i			1.20424i	0.798406	+	0.602120i	$0.205677\pi$
$463$			557.563i			1.20424i	−0.798406	+	0.602120i	$0.794323\pi$
$464$		0			0
$465$	283.635	+	440.863i	0.609968	+	0.948093i
$466$		0			0
$467$	−659.257			−1.41168			−0.705842	−	0.708369i	$-0.749431\pi$
$467$	−659.257			−1.41168			−0.705842	+	0.708369i	$0.749431\pi$
$468$		0			0
$469$	24.5361			0.0523157
$470$		0			0
$471$	−204.192	−	441.203i	−0.433529	−	0.936738i
$472$		0			0
$473$	248.239			0.524818
$474$		0			0
$475$	556.839	−	158.004i	1.17229	−	0.332640i
$476$		0			0
$477$	−354.828	+	417.956i	−0.743875	+	0.876218i
$478$		0			0
$479$		−	30.3870i		−	0.0634384i	−0.999497	−	0.0317192i	$-0.989902\pi$
$479$		−	30.3870i		−	0.0634384i	0.999497	−	0.0317192i	$-0.0100982\pi$
$480$		0			0
$481$	−800.598			−1.66445
$482$		0			0
$483$	22.9431	+	49.5738i	0.0475012	+	0.102637i
$484$		0			0
$485$	−569.518	+	79.2368i	−1.17426	+	0.163375i
$486$		0			0
$487$			26.5618i			0.0545416i	0.999628	+	0.0272708i	$0.00868164\pi$
$487$			26.5618i			0.0545416i	−0.999628	+	0.0272708i	$0.991318\pi$
$488$		0			0
$489$	−171.580	−	370.737i	−0.350878	−	0.758153i
$490$		0			0
$491$		−	19.3354i		−	0.0393796i	−0.999806	−	0.0196898i	$-0.993732\pi$
$491$		−	19.3354i		−	0.0393796i	0.999806	−	0.0196898i	$-0.00626786\pi$
$492$		0			0
$493$		−	227.426i		−	0.461311i
$494$		0			0
$495$	263.978	−	415.814i	0.533288	−	0.840028i
$496$		0			0
$497$	−71.3418			−0.143545
$498$		0			0
$499$	−313.190			−0.627635			−0.313817	−	0.949483i	$-0.601608\pi$
$499$	−313.190			−0.627635			−0.313817	+	0.949483i	$0.601608\pi$
$500$		0			0
$501$	−383.693	+	177.576i	−0.765855	+	0.354443i
$502$		0			0
$503$	551.684			1.09679			0.548394	−	0.836220i	$-0.315240\pi$
$503$	551.684			1.09679			0.548394	+	0.836220i	$0.315240\pi$
$504$		0			0
$505$	−144.509	+	20.1055i	−0.286157	+	0.0398129i
$506$		0			0
$507$	762.368	−	352.829i	1.50368	−	0.695915i
$508$		0			0
$509$			567.057i			1.11406i	0.830492	+	0.557031i	$0.188059\pi$
$509$			567.057i			1.11406i	−0.830492	+	0.557031i	$0.811941\pi$
$510$		0			0
$511$	98.9842			0.193707
$512$		0			0
$513$	167.005	−	602.407i	0.325545	−	1.17428i
$514$		0			0
$515$	−445.450	+	61.9753i	−0.864951	+	0.120340i
$516$		0			0
$517$			428.036i			0.827923i
$518$		0			0
$519$	360.333	−	166.764i	0.694283	−	0.321319i
$520$		0			0
$521$			740.223i			1.42077i	0.703811	+	0.710387i	$0.251480\pi$
$521$			740.223i			1.42077i	−0.703811	+	0.710387i	$0.748520\pi$
$522$		0			0
$523$		−	2.11805i		−	0.00404981i	−0.999998	−	0.00202491i	$-0.999355\pi$
$523$		−	2.11805i		−	0.00404981i	0.999998	−	0.00202491i	$-0.000644548\pi$
$524$		0			0
$525$	35.9663	+	41.8495i	0.0685072	+	0.0797133i
$526$		0			0
$527$	−245.856			−0.466520
$528$		0			0
$529$	83.4771			0.157802
$530$		0			0
$531$	53.4947	+	45.4149i	0.100743	+	0.0855271i
$532$		0			0
$533$	−828.210			−1.55386
$534$		0			0
$535$	−105.822	−	760.602i	−0.197798	−	1.42169i
$536$		0			0
$537$	−116.237	−	251.156i	−0.216456	−	0.467702i
$538$		0			0
$539$			530.385i			0.984017i
$540$		0			0
$541$	6.61681			0.0122307			0.00611535	−	0.999981i	$-0.498053\pi$
$541$	6.61681			0.0122307			0.00611535	+	0.999981i	$0.498053\pi$
$542$		0			0
$543$	−315.535	+	146.032i	−0.581096	+	0.268935i
$544$		0			0
$545$	41.0391	+	294.971i	0.0753011	+	0.541230i
$546$		0			0
$547$		−	230.092i		−	0.420644i	−0.977632	−	0.210322i	$-0.932549\pi$
$547$		−	230.092i		−	0.420644i	0.977632	−	0.210322i	$-0.0674512\pi$
$548$		0			0
$549$	−64.9622	+	76.5197i	−0.118328	+	0.139380i
$550$		0			0
$551$		−	748.495i		−	1.35843i
$552$		0			0
$553$		−	89.0617i		−	0.161052i
$554$		0			0
$555$	−476.609	+	306.632i	−0.858755	+	0.552491i
$556$		0			0
$557$	529.620			0.950844			0.475422	−	0.879758i	$-0.342295\pi$
$557$	529.620			0.950844			0.475422	+	0.879758i	$0.342295\pi$
$558$		0			0
$559$	480.598			0.859747
$560$		0			0
$561$	97.0184	+	209.630i	0.172938	+	0.373673i
$562$		0			0
$563$	131.530			0.233623			0.116812	−	0.993154i	$-0.462733\pi$
$563$	131.530			0.233623			0.116812	+	0.993154i	$0.462733\pi$
$564$		0			0
$565$	−0.701387	−	5.04125i	−0.00124139	−	0.00892257i
$566$		0			0
$567$	58.8055	−	9.67206i	0.103713	−	0.0170583i
$568$		0			0
$569$		−	172.534i		−	0.303224i	−0.988440	−	0.151612i	$-0.951554\pi$
$569$		−	172.534i		−	0.303224i	0.988440	−	0.151612i	$-0.0484464\pi$
$570$		0			0
$571$	−197.935			−0.346646			−0.173323	−	0.984865i	$-0.555450\pi$
$571$	−197.935			−0.346646			−0.173323	+	0.984865i	$0.555450\pi$
$572$		0			0
$573$	−66.9302	−	144.618i	−0.116807	−	0.252387i
$574$		0			0
$575$	595.209	−	168.892i	1.03515	−	0.293724i
$576$		0			0
$577$		−	865.374i		−	1.49978i	−0.661562	−	0.749891i	$-0.730106\pi$
$577$		−	865.374i		−	1.49978i	0.661562	−	0.749891i	$-0.269894\pi$
$578$		0			0
$579$	−341.863	−	738.673i	−0.590437	−	1.27577i
$580$		0			0
$581$		−	66.3899i		−	0.114268i
$582$		0			0
$583$		−	666.753i		−	1.14366i
$584$		0			0
$585$	511.069	−	805.028i	0.873622	−	1.37612i
$586$		0			0
$587$	−30.8886			−0.0526211			−0.0263105	−	0.999654i	$-0.508376\pi$
$587$	−30.8886			−0.0526211			−0.0263105	+	0.999654i	$0.508376\pi$
$588$		0			0
$589$	−809.151			−1.37377
$590$		0			0
$591$	−175.317	+	81.1379i	−0.296644	+	0.137289i
$592$		0			0
$593$	511.286			0.862202			0.431101	−	0.902304i	$-0.358125\pi$
$593$	511.286			0.862202			0.431101	+	0.902304i	$0.358125\pi$
$594$		0			0
$595$	−25.6326	+	3.56625i	−0.0430800	+	0.00599370i
$596$		0			0
$597$	196.108	−	90.7603i	0.328490	−	0.152027i
$598$		0			0
$599$			514.866i			0.859543i	0.902938	+	0.429772i	$0.141406\pi$
$599$			514.866i			0.859543i	−0.902938	+	0.429772i	$0.858594\pi$
$600$		0			0
$601$	853.532			1.42019			0.710093	−	0.704107i	$-0.248653\pi$
$601$	853.532			1.42019			0.710093	+	0.704107i	$0.248653\pi$
$602$		0			0
$603$	−228.803	−	194.245i	−0.379441	−	0.322131i
$604$		0			0
$605$	−0.830071	−	5.96618i	−0.00137202	−	0.00986145i
$606$		0			0
$607$		−	88.0713i		−	0.145093i	−0.997365	−	0.0725464i	$-0.976887\pi$
$607$		−	88.0713i		−	0.145093i	0.997365	−	0.0725464i	$-0.0231125\pi$
$608$		0			0
$609$	64.7576	−	29.9703i	0.106334	−	0.0492123i
$610$		0			0
$611$			828.691i			1.35629i
$612$		0			0
$613$			403.346i			0.657987i	0.944332	+	0.328994i	$0.106709\pi$
$613$			403.346i			0.657987i	−0.944332	+	0.328994i	$0.893291\pi$
$614$		0			0
$615$	−493.046	+	317.208i	−0.801701	+	0.515785i
$616$		0			0
$617$	365.738			0.592769			0.296384	−	0.955069i	$-0.404219\pi$
$617$	365.738			0.592769			0.296384	+	0.955069i	$0.404219\pi$
$618$		0			0
$619$	399.495			0.645389			0.322694	−	0.946503i	$-0.395411\pi$
$619$	399.495			0.645389			0.322694	+	0.946503i	$0.395411\pi$
$620$		0			0
$621$	178.512	−	643.917i	0.287460	−	1.03690i
$622$		0			0
$623$	−39.1304			−0.0628097
$624$		0			0
$625$	531.856	−	328.260i	0.850969	−	0.525216i
$626$		0			0
$627$	319.303	+	689.927i	0.509255	+	1.10036i
$628$		0			0
$629$		−	265.790i		−	0.422560i
$630$		0			0
$631$	715.762			1.13433			0.567165	−	0.823604i	$-0.308040\pi$
$631$	715.762			1.13433			0.567165	+	0.823604i	$0.308040\pi$
$632$		0			0
$633$	295.625	−	136.817i	0.467022	−	0.216141i
$634$		0			0
$635$	1038.65	−	144.507i	1.63567	−	0.227570i
$636$		0			0
$637$			1026.84i			1.61200i
$638$		0			0
$639$	665.274	+	564.791i	1.04112	+	0.883867i
$640$		0			0
$641$		−	627.158i		−	0.978406i	−0.872170	−	0.489203i	$-0.837288\pi$
$641$		−	627.158i		−	0.978406i	0.872170	−	0.489203i	$-0.162712\pi$
$642$		0			0
$643$		−	802.039i		−	1.24734i	−0.781688	−	0.623669i	$-0.785641\pi$
$643$		−	802.039i		−	1.24734i	0.781688	−	0.623669i	$-0.214359\pi$
$644$		0			0
$645$	286.108	−	184.071i	0.443578	−	0.285382i
$646$		0			0
$647$	19.9275			0.0307998			0.0153999	−	0.999881i	$-0.495098\pi$
$647$	19.9275			0.0307998			0.0153999	+	0.999881i	$0.495098\pi$
$648$		0			0
$649$	−85.3385			−0.131492
$650$		0			0
$651$	−32.3990	−	70.0054i	−0.0497680	−	0.107535i
$652$		0			0
$653$	−78.4638			−0.120159			−0.0600795	−	0.998194i	$-0.519135\pi$
$653$	−78.4638			−0.120159			−0.0600795	+	0.998194i	$0.519135\pi$
$654$		0			0
$655$	−1040.23	+	144.727i	−1.58815	+	0.220958i
$656$		0			0
$657$	−923.044	−	783.628i	−1.40494	−	1.19274i
$658$		0			0
$659$			371.793i			0.564178i	0.959388	+	0.282089i	$0.0910274\pi$
$659$			371.793i			0.564178i	−0.959388	+	0.282089i	$0.908973\pi$
$660$		0			0
$661$	782.868			1.18437			0.592185	−	0.805802i	$-0.298266\pi$
$661$	782.868			1.18437			0.592185	+	0.805802i	$0.298266\pi$
$662$		0			0
$663$	187.831	+	405.851i	0.283304	+	0.612143i
$664$		0			0
$665$	−84.3609	+	11.7371i	−0.126859	+	0.0176498i
$666$		0			0
$667$		−	800.071i		−	1.19951i
$668$		0			0
$669$	−105.362	−	227.658i	−0.157492	−	0.340297i
$670$		0			0
$671$		−	122.070i		−	0.181922i
$672$		0			0
$673$		−	221.323i		−	0.328860i	−0.986389	−	0.164430i	$-0.947421\pi$
$673$		−	221.323i		−	0.328860i	0.986389	−	0.164430i	$-0.0525785\pi$
$674$		0			0
$675$	−4.08178	−	674.988i	−0.00604707	−	0.999982i
$676$		0			0
$677$	576.855			0.852076			0.426038	−	0.904705i	$-0.359909\pi$
$677$	576.855			0.852076			0.426038	+	0.904705i	$0.359909\pi$
$678$		0			0
$679$	84.6116			0.124612
$680$		0			0
$681$	−140.645	+	65.0916i	−0.206527	+	0.0955824i
$682$		0			0
$683$	−1272.02			−1.86239			−0.931197	−	0.364516i	$-0.881234\pi$
$683$	−1272.02			−1.86239			−0.931197	+	0.364516i	$0.881234\pi$
$684$		0			0
$685$	116.228	+	835.392i	0.169675	+	1.21955i
$686$		0			0
$687$	764.969	−	354.033i	1.11349	−	0.515332i
$688$		0			0
$689$		−	1290.85i		−	1.87352i
$690$		0			0
$691$	−1.61487			−0.00233701			−0.00116851	−	0.999999i	$-0.500372\pi$
$691$	−1.61487			−0.00233701			−0.00116851	+	0.999999i	$0.500372\pi$
$692$		0			0
$693$	−46.9053	+	55.2503i	−0.0676844	+	0.0797263i
$694$		0			0
$695$	−89.0556	−	640.091i	−0.128138	−	0.920995i
$696$		0			0
$697$		−	274.957i		−	0.394486i
$698$		0			0
$699$	−460.637	+	213.186i	−0.658994	+	0.304987i
$700$		0			0
$701$			550.235i			0.784929i	0.919767	+	0.392465i	$0.128377\pi$
$701$			550.235i			0.784929i	−0.919767	+	0.392465i	$0.871623\pi$
$702$		0			0
$703$		−	874.758i		−	1.24432i
$704$		0			0
$705$	317.392	+	493.333i	0.450202	+	0.699763i
$706$		0			0
$707$	21.4693			0.0303668
$708$		0			0
$709$	−430.539			−0.607249			−0.303624	−	0.952792i	$-0.598197\pi$
$709$	−430.539			−0.607249			−0.303624	+	0.952792i	$0.598197\pi$
$710$		0			0
$711$	−705.075	+	830.515i	−0.991666	+	1.16809i
$712$		0			0
$713$	−864.907			−1.21305
$714$		0			0
$715$	159.801	+	1148.57i	0.223497	+	1.60640i
$716$		0			0
$717$	−1.41171	−	3.05033i	−0.00196892	−	0.00425429i
$718$		0			0
$719$		−	460.561i		−	0.640558i	−0.947323	−	0.320279i	$-0.896223\pi$
$719$		−	460.561i		−	0.640558i	0.947323	−	0.320279i	$-0.103777\pi$
$720$		0			0
$721$	66.1792			0.0917880
$722$		0			0
$723$	−417.243	+	193.103i	−0.577100	+	0.267086i
$724$		0			0
$725$	−220.621	−	777.514i	−0.304305	−	1.07243i
$726$		0			0
$727$			413.275i			0.568467i	0.958755	+	0.284233i	$0.0917390\pi$
$727$			413.275i			0.568467i	−0.958755	+	0.284233i	$0.908261\pi$
$728$		0			0
$729$	−624.942	−	375.352i	−0.857259	−	0.514886i
$730$		0			0
$731$			159.554i			0.218268i
$732$		0			0
$733$		−	307.003i		−	0.418831i	−0.977827	−	0.209416i	$-0.932844\pi$
$733$		−	307.003i		−	0.418831i	0.977827	−	0.209416i	$-0.0671562\pi$
$734$		0			0
$735$	393.285	+	611.295i	0.535081	+	0.831694i
$736$		0			0
$737$	365.003			0.495255
$738$		0			0
$739$	988.511			1.33763			0.668817	−	0.743427i	$-0.266801\pi$
$739$	988.511			1.33763			0.668817	+	0.743427i	$0.266801\pi$
$740$		0			0
$741$	618.180	+	1335.72i	0.834251	+	1.80259i
$742$		0			0
$743$	−652.187			−0.877775			−0.438887	−	0.898542i	$-0.644627\pi$
$743$	−652.187			−0.877775			−0.438887	+	0.898542i	$0.644627\pi$
$744$		0			0
$745$	−415.822	+	57.8532i	−0.558151	+	0.0776552i
$746$		0			0
$747$	−525.589	+	619.097i	−0.703599	+	0.828777i
$748$		0			0
$749$			113.000i			0.150868i
$750$		0			0
$751$	−554.876			−0.738850			−0.369425	−	0.929261i	$-0.620445\pi$
$751$	−554.876			−0.738850			−0.369425	+	0.929261i	$0.620445\pi$
$752$		0			0
$753$	159.635	+	344.928i	0.211999	+	0.458072i
$754$		0			0
$755$	6.23501	+	44.8144i	0.00825829	+	0.0593569i
$756$		0			0
$757$			547.156i			0.722795i	0.932412	+	0.361397i	$0.117700\pi$
$757$			547.156i			0.722795i	−0.932412	+	0.361397i	$0.882300\pi$
$758$		0			0
$759$	341.305	+	737.467i	0.449677	+	0.971630i
$760$		0			0
$761$			1361.34i			1.78888i	0.447184	+	0.894442i	$0.352427\pi$
$761$			1361.34i			1.78888i	−0.447184	+	0.894442i	$0.647573\pi$
$762$		0			0
$763$		−	43.8229i		−	0.0574350i
$764$		0			0
$765$	267.261	+	169.670i	0.349361	+	0.221790i
$766$		0			0
$767$	−165.218			−0.215408
$768$		0			0
$769$	−396.180			−0.515188			−0.257594	−	0.966253i	$-0.582930\pi$
$769$	−396.180			−0.515188			−0.257594	+	0.966253i	$0.582930\pi$
$770$		0			0
$771$	1080.02	−	499.840i	1.40080	−	0.648301i
$772$		0			0
$773$	−664.286			−0.859361			−0.429681	−	0.902981i	$-0.641374\pi$
$773$	−664.286			−0.859361			−0.429681	+	0.902981i	$0.641374\pi$
$774$		0			0
$775$	−840.522	+	238.499i	−1.08454	+	0.307741i
$776$		0			0
$777$	75.6815	−	35.0259i	0.0974022	−	0.0450784i
$778$		0			0
$779$		−	904.927i		−	1.16165i
$780$		0			0
$781$	−1061.29			−1.35889
$782$		0			0
$783$	−841.141	−	233.189i	−1.07425	−	0.297814i
$784$		0			0
$785$	802.542	−	111.657i	1.02235	−	0.142239i
$786$		0			0
$787$			957.551i			1.21671i	0.793665	+	0.608355i	$0.208170\pi$
$787$			957.551i			1.21671i	−0.793665	+	0.608355i	$0.791830\pi$
$788$		0			0
$789$	−1073.86	+	496.991i	−1.36104	+	0.629900i
$790$		0			0
$791$			0.748964i			0.000946857i
$792$		0			0
$793$		−	236.330i		−	0.298021i
$794$		0			0
$795$	−494.402	−	768.466i	−0.621890	−	0.966623i
$796$		0			0
$797$	−643.860			−0.807854			−0.403927	−	0.914791i	$-0.632355\pi$
$797$	−643.860			−0.807854			−0.403927	+	0.914791i	$0.632355\pi$
$798$		0			0
$799$	−275.117			−0.344326
$800$		0			0
$801$	364.898	+	309.784i	0.455553	+	0.386746i
$802$		0			0
$803$	1472.50			1.83375
$804$		0			0
$805$	−90.1739	+	12.5459i	−0.112017	+	0.0155849i
$806$		0			0
$807$	−132.052	−	285.329i	−0.163633	−	0.353567i
$808$		0			0
$809$			675.342i			0.834786i	0.908726	+	0.417393i	$0.137056\pi$
$809$			675.342i			0.834786i	−0.908726	+	0.417393i	$0.862944\pi$
$810$		0			0
$811$	−808.662			−0.997117			−0.498559	−	0.866856i	$-0.666137\pi$
$811$	−808.662			−0.997117			−0.498559	+	0.866856i	$0.666137\pi$
$812$		0			0
$813$	−913.025	+	422.554i	−1.12303	+	0.519747i
$814$		0			0
$815$	674.364	−	93.8240i	0.827441	−	0.115121i
$816$		0			0
$817$			525.116i			0.642737i
$818$		0			0
$819$	−90.8101	+	106.966i	−0.110879	+	0.130606i
$820$		0			0
$821$		−	1348.63i		−	1.64267i	−0.570445	−	0.821336i	$-0.693229\pi$
$821$		−	1348.63i		−	1.64267i	0.570445	−	0.821336i	$-0.306771\pi$
$822$		0			0
$823$			1433.75i			1.74211i	0.491188	+	0.871053i	$0.336563\pi$
$823$			1433.75i			1.74211i	−0.491188	+	0.871053i	$0.663437\pi$
$824$		0			0
$825$	535.040	+	622.560i	0.648533	+	0.754618i
$826$		0			0
$827$	27.5276			0.0332861			0.0166431	−	0.999861i	$-0.494702\pi$
$827$	27.5276			0.0332861			0.0166431	+	0.999861i	$0.494702\pi$
$828$		0			0
$829$	374.884			0.452212			0.226106	−	0.974103i	$-0.427400\pi$
$829$	374.884			0.452212			0.226106	+	0.974103i	$0.427400\pi$
$830$		0			0
$831$	211.419	+	456.818i	0.254415	+	0.549721i
$832$		0			0
$833$	−340.901			−0.409245
$834$		0			0
$835$	−97.1030	−	697.932i	−0.116291	−	0.835847i
$836$		0			0
$837$	−252.085	+	909.304i	−0.301177	+	1.08639i
$838$		0			0
$839$		−	1173.68i		−	1.39890i	−0.714681	−	0.699451i	$-0.753428\pi$
$839$		−	1173.68i		−	1.39890i	0.714681	−	0.699451i	$-0.246572\pi$
$840$		0			0
$841$	−204.123			−0.242715
$842$		0			0
$843$	−125.322	−	270.786i	−0.148662	−	0.321217i
$844$		0			0
$845$	192.936	+	1386.73i	0.228326	+	1.64111i
$846$		0			0
$847$			0.886377i			0.00104649i
$848$		0			0
$849$	613.659	+	1325.95i	0.722802	+	1.56178i
$850$		0			0
$851$		−	935.034i		−	1.09875i
$852$		0			0
$853$			112.279i			0.131629i	0.997832	+	0.0658143i	$0.0209645\pi$
$853$			112.279i			0.131629i	−0.997832	+	0.0658143i	$0.979036\pi$
$854$		0			0
$855$	879.598	+	558.409i	1.02877	+	0.653110i
$856$		0			0
$857$	619.631			0.723023			0.361511	−	0.932368i	$-0.382261\pi$
$857$	619.631			0.723023			0.361511	+	0.932368i	$0.382261\pi$
$858$		0			0
$859$	1227.29			1.42875			0.714373	−	0.699765i	$-0.246712\pi$
$859$	1227.29			1.42875			0.714373	+	0.699765i	$0.246712\pi$
$860$		0			0
$861$	78.2916	−	36.2339i	0.0909310	−	0.0420835i
$862$		0			0
$863$	−975.318			−1.13015			−0.565074	−	0.825040i	$-0.691152\pi$
$863$	−975.318			−1.13015			−0.565074	+	0.825040i	$0.691152\pi$
$864$		0			0
$865$	91.1910	+	655.439i	0.105423	+	0.757734i
$866$		0			0
$867$	652.082	−	301.788i	0.752113	−	0.348083i
$868$		0			0
$869$		−	1324.90i		−	1.52462i
$870$		0			0
$871$	706.656			0.811316
$872$		0			0
$873$	−789.017	−	669.844i	−0.903799	−	0.767290i
$874$		0			0
$875$	−84.1720	+	37.0578i	−0.0961966	+	0.0423517i
$876$		0			0
$877$		−	991.857i		−	1.13097i	−0.824760	−	0.565483i	$-0.808690\pi$
$877$		−	991.857i		−	1.13097i	0.824760	−	0.565483i	$-0.191310\pi$
$878$		0			0
$879$	−934.131	+	432.322i	−1.06272	+	0.491834i
$880$		0			0
$881$		−	1024.25i		−	1.16260i	−0.813690	−	0.581299i	$-0.802545\pi$
$881$		−	1024.25i		−	1.16260i	0.813690	−	0.581299i	$-0.197455\pi$
$882$		0			0
$883$			1170.22i			1.32527i	0.748941	+	0.662637i	$0.230563\pi$
$883$			1170.22i			1.32527i	−0.748941	+	0.662637i	$0.769437\pi$
$884$		0			0
$885$	−98.3569	+	63.2792i	−0.111138	+	0.0715019i
$886$		0			0
$887$	540.358			0.609197			0.304599	−	0.952481i	$-0.401478\pi$
$887$	540.358			0.609197			0.304599	+	0.952481i	$0.401478\pi$
$888$		0			0
$889$	−154.309			−0.173576
$890$		0			0
$891$	874.800	−	143.883i	0.981818	−	0.161485i
$892$		0			0
$893$	−905.453			−1.01395
$894$		0			0
$895$	456.849	−	63.5612i	0.510446	−	0.0710181i
$896$		0			0
$897$	660.777	+	1427.76i	0.736652	+	1.59170i
$898$		0			0
$899$			1129.82i			1.25675i
$900$		0			0
$901$	428.550			0.475638
$902$		0			0
$903$	−45.4315	+	21.0260i	−0.0503118	+	0.0232846i
$904$		0			0
$905$	−79.8539	−	573.953i	−0.0882363	−	0.634202i
$906$		0			0
$907$			682.738i			0.752744i	0.926469	+	0.376372i	$0.122828\pi$
$907$			682.738i			0.752744i	−0.926469	+	0.376372i	$0.877172\pi$
$908$		0			0
$909$	−200.205	−	169.966i	−0.220247	−	0.186981i
$910$		0			0
$911$		−	1326.30i		−	1.45587i	−0.685647	−	0.727934i	$-0.740481\pi$
$911$		−	1326.30i		−	1.45587i	0.685647	−	0.727934i	$-0.259519\pi$
$912$		0			0
$913$		−	987.626i		−	1.08174i
$914$		0			0
$915$	−90.5155	−	140.691i	−0.0989240	−	0.153761i
$916$		0			0
$917$	154.545			0.168533
$918$		0			0
$919$	−688.107			−0.748756			−0.374378	−	0.927276i	$-0.622144\pi$
$919$	−688.107			−0.748756			−0.374378	+	0.927276i	$0.622144\pi$
$920$		0			0
$921$	−459.437	−	992.719i	−0.498846	−	1.07787i
$922$		0			0
$923$	−2054.69			−2.22610
$924$		0			0
$925$	−257.837	−	908.672i	−0.278743	−	0.982348i
$926$		0			0
$927$	−617.132	−	523.920i	−0.665730	−	0.565178i
$928$		0			0
$929$		−	637.084i		−	0.685774i	−0.939377	−	0.342887i	$-0.888595\pi$
$929$		−	637.084i		−	0.685774i	0.939377	−	0.342887i	$-0.111405\pi$
$930$		0			0
$931$	−1121.96			−1.20511
$932$		0			0
$933$	−153.676	−	332.052i	−0.164712	−	0.355897i
$934$		0			0
$935$	−381.314	+	53.0521i	−0.407823	+	0.0567402i
$936$		0			0
$937$			358.254i			0.382341i	0.981557	+	0.191171i	$0.0612284\pi$
$937$			358.254i			0.382341i	−0.981557	+	0.191171i	$0.938772\pi$
$938$		0			0
$939$	−119.458	−	258.115i	−0.127218	−	0.274883i
$940$		0			0
$941$		−	124.973i		−	0.132809i	−0.997793	−	0.0664043i	$-0.978847\pi$
$941$		−	124.973i		−	0.132809i	0.997793	−	0.0664043i	$-0.0211527\pi$
$942$		0			0
$943$		−	967.282i		−	1.02575i
$944$		0			0
$945$	−13.0922	+	98.4594i	−0.0138542	+	0.104190i
$946$		0			0
$947$	−378.826			−0.400027			−0.200014	−	0.979793i	$-0.564099\pi$
$947$	−378.826			−0.400027			−0.200014	+	0.979793i	$0.564099\pi$
$948$		0			0
$949$	2850.81			3.00402
$950$		0			0
$951$	−1392.00	+	644.226i	−1.46372	+	0.677419i
$952$		0			0
$953$	−6.82139			−0.00715780			−0.00357890	−	0.999994i	$-0.501139\pi$
$953$	−6.82139			−0.00715780			−0.00357890	+	0.999994i	$0.501139\pi$
$954$		0			0
$955$	263.058	−	36.5991i	0.275453	−	0.0383237i
$956$		0			0
$957$	963.344	−	445.842i	1.00663	−	0.465875i
$958$		0			0
$959$		−	124.112i		−	0.129418i
$960$		0			0
$961$	260.374			0.270941
$962$		0			0
$963$	894.589	−	1053.75i	0.928960	−	1.09423i
$964$		0			0
$965$	1343.63	−	186.939i	1.39237	−	0.193719i
$966$		0			0
$967$			1193.53i			1.23426i	0.786861	+	0.617130i	$0.211705\pi$
$967$			1193.53i			1.23426i	−0.786861	+	0.617130i	$0.788295\pi$
$968$		0			0
$969$	−443.445	+	205.229i	−0.457631	+	0.211795i
$970$		0			0
$971$			1256.06i			1.29357i	0.762672	+	0.646785i	$0.223887\pi$
$971$			1256.06i			1.29357i	−0.762672	+	0.646785i	$0.776113\pi$
$972$		0			0
$973$			95.0964i			0.0977353i
$974$		0			0
$975$	1035.85	+	1205.29i	1.06241	+	1.23620i
$976$		0			0
$977$	−551.251			−0.564228			−0.282114	−	0.959381i	$-0.591036\pi$
$977$	−551.251			−0.564228			−0.282114	+	0.959381i	$0.591036\pi$
$978$		0			0
$979$	−582.110			−0.594597
$980$		0			0
$981$	−346.932	+	408.656i	−0.353652	+	0.416570i
$982$		0			0
$983$	1598.65			1.62630			0.813151	−	0.582053i	$-0.197750\pi$
$983$	1598.65			1.62630			0.813151	+	0.582053i	$0.197750\pi$
$984$		0			0
$985$	−44.3682	−	318.899i	−0.0450439	−	0.323755i
$986$		0			0
$987$	−36.2550	−	78.3371i	−0.0367325	−	0.0793689i
$988$		0			0
$989$			561.300i			0.567543i
$990$		0			0
$991$	1734.40			1.75015			0.875077	−	0.483984i	$-0.160811\pi$
$991$	1734.40			1.75015			0.875077	+	0.483984i	$0.160811\pi$
$992$		0			0
$993$	−497.363	+	230.183i	−0.500869	+	0.231806i
$994$		0			0
$995$	49.6300	+	356.718i	0.0498794	+	0.358511i
$996$		0			0
$997$		−	1118.15i		−	1.12151i	−0.827980	−	0.560757i	$-0.810510\pi$
$997$		−	1118.15i		−	1.12151i	0.827980	−	0.560757i	$-0.189490\pi$
$998$		0			0
$999$	−983.032	−	272.525i	−0.984016	−	0.272798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.3.c.e.209.2		12
3.2	odd	2	inner	240.3.c.e.209.12		12
4.3	odd	2		120.3.c.a.89.11	yes	12
5.2	odd	4		1200.3.l.y.401.8		12
5.3	odd	4		1200.3.l.y.401.5		12
5.4	even	2	inner	240.3.c.e.209.11		12
8.3	odd	2		960.3.c.k.449.2		12
8.5	even	2		960.3.c.j.449.11		12
12.11	even	2		120.3.c.a.89.1	✓	12
15.2	even	4		1200.3.l.y.401.7		12
15.8	even	4		1200.3.l.y.401.6		12
15.14	odd	2	inner	240.3.c.e.209.1		12
20.3	even	4		600.3.l.g.401.8		12
20.7	even	4		600.3.l.g.401.5		12
20.19	odd	2		120.3.c.a.89.2	yes	12
24.5	odd	2		960.3.c.j.449.1		12
24.11	even	2		960.3.c.k.449.12		12
40.19	odd	2		960.3.c.k.449.11		12
40.29	even	2		960.3.c.j.449.2		12
60.23	odd	4		600.3.l.g.401.7		12
60.47	odd	4		600.3.l.g.401.6		12
60.59	even	2		120.3.c.a.89.12	yes	12
120.29	odd	2		960.3.c.j.449.12		12
120.59	even	2		960.3.c.k.449.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.3.c.a.89.1	✓	12	12.11	even	2
120.3.c.a.89.2	yes	12	20.19	odd	2
120.3.c.a.89.11	yes	12	4.3	odd	2
120.3.c.a.89.12	yes	12	60.59	even	2
240.3.c.e.209.1		12	15.14	odd	2	inner
240.3.c.e.209.2		12	1.1	even	1	trivial
240.3.c.e.209.11		12	5.4	even	2	inner
240.3.c.e.209.12		12	3.2	odd	2	inner
600.3.l.g.401.5		12	20.7	even	4
600.3.l.g.401.6		12	60.47	odd	4
600.3.l.g.401.7		12	60.23	odd	4
600.3.l.g.401.8		12	20.3	even	4
960.3.c.j.449.1		12	24.5	odd	2
960.3.c.j.449.2		12	40.29	even	2
960.3.c.j.449.11		12	8.5	even	2
960.3.c.j.449.12		12	120.29	odd	2
960.3.c.k.449.1		12	120.59	even	2
960.3.c.k.449.2		12	8.3	odd	2
960.3.c.k.449.11		12	40.19	odd	2
960.3.c.k.449.12		12	24.11	even	2
1200.3.l.y.401.5		12	5.3	odd	4
1200.3.l.y.401.6		12	15.8	even	4
1200.3.l.y.401.7		12	15.2	even	4
1200.3.l.y.401.8		12	5.2	odd	4

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	240.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.72256 + 1.26002i) q^{3} +(-0.689011 - 4.95230i) q^{5} +0.735748i q^{7} +(5.82469 - 6.86097i) q^{9} +O(q^{10})\)	\(q+(-2.72256 + 1.26002i) q^{3} +(-0.689011 - 4.95230i) q^{5} +0.735748i q^{7} +(5.82469 - 6.86097i) q^{9} +10.9451i q^{11} +21.1901i q^{13} +(8.11588 + 12.6148i) q^{15} -7.03488 q^{17} -23.1529 q^{19} +(-0.927058 - 2.00312i) q^{21} -24.7483 q^{23} +(-24.0505 + 6.82438i) q^{25} +(-7.21312 + 26.0187i) q^{27} +32.3284i q^{29} +34.9482 q^{31} +(-13.7911 - 29.7987i) q^{33} +(3.64364 - 0.506939i) q^{35} +37.7818i q^{37} +(-26.6999 - 57.6912i) q^{39} +39.0848i q^{41} -22.6804i q^{43} +(-37.9909 - 24.1183i) q^{45} +39.1076 q^{47} +48.4587 q^{49} +(19.1529 - 8.86409i) q^{51} -60.9179 q^{53} +(54.2034 - 7.54130i) q^{55} +(63.0352 - 29.1731i) q^{57} +7.79696i q^{59} -11.1529 q^{61} +(5.04795 + 4.28551i) q^{63} +(104.939 - 14.6002i) q^{65} -33.3485i q^{67} +(67.3787 - 31.1833i) q^{69} +96.9650i q^{71} -134.535i q^{73} +(56.8802 - 48.8840i) q^{75} -8.05284 q^{77} -121.049 q^{79} +(-13.1459 - 79.9261i) q^{81} -90.2345 q^{83} +(4.84711 + 34.8388i) q^{85} +(-40.7344 - 88.0160i) q^{87} +53.1846i q^{89} -15.5905 q^{91} +(-95.1486 + 44.0354i) q^{93} +(15.9526 + 114.660i) q^{95} -115.001i q^{97} +(75.0940 + 63.7519i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{9}+O(q^{10}) \) 12 * q + 8 * q^9	\( 12 q + 8 q^{9} - 16 q^{15} + 4 q^{21} + 36 q^{25} + 48 q^{31} + 128 q^{39} - 68 q^{45} - 252 q^{49} - 48 q^{51} + 48 q^{55} + 144 q^{61} + 268 q^{69} - 304 q^{75} - 432 q^{79} - 188 q^{81} + 336 q^{85} + 560 q^{99}+O(q^{100}) \) 12 * q + 8 * q^9 - 16 * q^15 + 4 * q^21 + 36 * q^25 + 48 * q^31 + 128 * q^39 - 68 * q^45 - 252 * q^49 - 48 * q^51 + 48 * q^55 + 144 * q^61 + 268 * q^69 - 304 * q^75 - 432 * q^79 - 188 * q^81 + 336 * q^85 + 560 * q^99

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