LMFDB - Embedded newform 900.3.f.h.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(199,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("900.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.f (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:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} - 14 x^{13} + 23 x^{12} - 26 x^{11} + 18 x^{10} - 10 x^{9} + 9 x^{8} + \cdots + 256 $ x^16 - 4x^15 + 8x^14 - 14x^13 + 23x^12 - 26x^11 + 18x^10 - 10x^9 + 9x^8 - 20x^7 + 72x^6 - 208x^5 + 368x^4 - 448x^3 + 512x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{20}\cdot 5^{4} $
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.2
Root			$-1.32811 - 0.485936i$ of defining polynomial
Character	$\chi$	$=$	900.199
Dual form			900.3.f.h.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99209 + 0.177680i) q^{2} +(3.93686 - 0.707911i) q^{4} +1.19501 q^{7} +(-7.71680 + 2.10973i) q^{8} +O(q^{10})$	\(q+(-1.99209 + 0.177680i) q^{2} +(3.93686 - 0.707911i) q^{4} +1.19501 q^{7} +(-7.71680 + 2.10973i) q^{8} +8.22072i q^{11} -11.1863i q^{13} +(-2.38058 + 0.212331i) q^{14} +(14.9977 - 5.57389i) q^{16} -20.9256i q^{17} +27.9657i q^{19} +(-1.46066 - 16.3764i) q^{22} -9.48564 q^{23} +(1.98759 + 22.2842i) q^{26} +(4.70460 - 0.845964i) q^{28} +40.4205 q^{29} -55.3130i q^{31} +(-28.8865 + 13.7685i) q^{32} +(3.71807 + 41.6858i) q^{34} +50.1890i q^{37} +(-4.96895 - 55.7102i) q^{38} +73.6361 q^{41} +19.0843 q^{43} +(5.81954 + 32.3638i) q^{44} +(18.8963 - 1.68541i) q^{46} -18.0598 q^{47} -47.5719 q^{49} +(-7.91894 - 44.0391i) q^{52} -57.2212i q^{53} +(-9.22169 + 2.52115i) q^{56} +(-80.5213 + 7.18193i) q^{58} +60.6645i q^{59} -21.3518 q^{61} +(9.82804 + 110.189i) q^{62} +(55.0981 - 32.5607i) q^{64} +9.68679 q^{67} +(-14.8135 - 82.3812i) q^{68} -68.6944i q^{71} -84.7825i q^{73} +(-8.91760 - 99.9811i) q^{74} +(19.7972 + 110.097i) q^{76} +9.82388i q^{77} +23.2903i q^{79} +(-146.690 + 13.0837i) q^{82} +93.2595 q^{83} +(-38.0177 + 3.39091i) q^{86} +(-17.3435 - 63.4377i) q^{88} +62.9898 q^{89} -13.3678i q^{91} +(-37.3436 + 6.71499i) q^{92} +(35.9767 - 3.20887i) q^{94} +91.3962i q^{97} +(94.7677 - 8.45260i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4}+O(q^{10}) $ 16 * q + 16 * q^4	$ 16 q + 16 q^{4} + 44 q^{14} + 80 q^{16} + 132 q^{26} - 64 q^{29} - 248 q^{34} + 32 q^{41} + 80 q^{44} - 152 q^{46} - 32 q^{49} + 344 q^{56} + 272 q^{61} - 32 q^{64} - 216 q^{74} + 240 q^{76} - 428 q^{86} + 256 q^{89} - 24 q^{94}+O(q^{100}) $ 16 * q + 16 * q^4 + 44 * q^14 + 80 * q^16 + 132 * q^26 - 64 * q^29 - 248 * q^34 + 32 * q^41 + 80 * q^44 - 152 * q^46 - 32 * q^49 + 344 * q^56 + 272 * q^61 - 32 * q^64 - 216 * q^74 + 240 * q^76 - 428 * q^86 + 256 * q^89 - 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.99209	+	0.177680i	−0.996046	+	0.0888402i
$2$	−1.99209	+	0.177680i	−0.996046	+	0.0888402i
$3$		0			0
$3$		0			0
$4$	3.93686	−	0.707911i	0.984215	−	0.176978i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.19501			0.170716			0.0853582	−	0.996350i	$-0.472797\pi$
$7$	1.19501			0.170716			0.0853582	+	0.996350i	$0.472797\pi$
$8$	−7.71680	+	2.10973i	−0.964600	+	0.263716i
$9$		0			0
$10$		0			0
$11$			8.22072i			0.747338i	0.927562	+	0.373669i	$0.121900\pi$
$11$			8.22072i			0.747338i	−0.927562	+	0.373669i	$0.878100\pi$
$12$		0			0
$13$		−	11.1863i		−	0.860488i	−0.902713	−	0.430244i	$-0.858428\pi$
$13$		−	11.1863i		−	0.860488i	0.902713	−	0.430244i	$-0.141572\pi$
$14$	−2.38058	+	0.212331i	−0.170041	+	0.0151665i
$15$		0			0
$16$	14.9977	−	5.57389i	0.937358	−	0.348368i
$17$		−	20.9256i		−	1.23092i	−0.788169	−	0.615459i	$-0.788970\pi$
$17$		−	20.9256i		−	1.23092i	0.788169	−	0.615459i	$-0.211030\pi$
$18$		0			0
$19$			27.9657i			1.47188i	0.677048	+	0.735939i	$0.263259\pi$
$19$			27.9657i			1.47188i	−0.677048	+	0.735939i	$0.736741\pi$
$20$		0			0
$21$		0			0
$22$	−1.46066	−	16.3764i	−0.0663937	−	0.744383i
$23$	−9.48564			−0.412419			−0.206209	−	0.978508i	$-0.566113\pi$
$23$	−9.48564			−0.412419			−0.206209	+	0.978508i	$0.566113\pi$
$24$		0			0
$25$		0			0
$26$	1.98759	+	22.2842i	0.0764459	+	0.857085i
$27$		0			0
$28$	4.70460	−	0.845964i	0.168022	−	0.0302130i
$29$	40.4205			1.39381			0.696905	−	0.717163i	$-0.254560\pi$
$29$	40.4205			1.39381			0.696905	+	0.717163i	$0.254560\pi$
$30$		0			0
$31$		−	55.3130i		−	1.78429i	−0.451748	−	0.892145i	$-0.649200\pi$
$31$		−	55.3130i		−	1.78429i	0.451748	−	0.892145i	$-0.350800\pi$
$32$	−28.8865	+	13.7685i	−0.902702	+	0.430266i
$33$		0			0
$34$	3.71807	+	41.6858i	0.109355	+	1.22605i
$35$		0			0
$36$		0			0
$37$			50.1890i			1.35646i	0.734850	+	0.678230i	$0.237253\pi$
$37$			50.1890i			1.35646i	−0.734850	+	0.678230i	$0.762747\pi$
$38$	−4.96895	−	55.7102i	−0.130762	−	1.46606i
$39$		0			0
$40$		0			0
$41$	73.6361			1.79600			0.898001	−	0.439994i	$-0.145019\pi$
$41$	73.6361			1.79600			0.898001	+	0.439994i	$0.145019\pi$
$42$		0			0
$43$	19.0843			0.443822			0.221911	−	0.975067i	$-0.428771\pi$
$43$	19.0843			0.443822			0.221911	+	0.975067i	$0.428771\pi$
$44$	5.81954	+	32.3638i	0.132262	+	0.735541i
$45$		0			0
$46$	18.8963	−	1.68541i	0.410788	−	0.0366394i
$47$	−18.0598			−0.384251			−0.192125	−	0.981370i	$-0.561538\pi$
$47$	−18.0598			−0.384251			−0.192125	+	0.981370i	$0.561538\pi$
$48$		0			0
$49$	−47.5719			−0.970856
$50$		0			0
$51$		0			0
$52$	−7.91894	−	44.0391i	−0.152287	−	0.846905i
$53$		−	57.2212i		−	1.07965i	−0.841779	−	0.539823i	$-0.818491\pi$
$53$		−	57.2212i		−	1.07965i	0.841779	−	0.539823i	$-0.181509\pi$
$54$		0			0
$55$		0			0
$56$	−9.22169	+	2.52115i	−0.164673	+	0.0450206i
$57$		0			0
$58$	−80.5213	+	7.18193i	−1.38830	+	0.123826i
$59$			60.6645i			1.02821i	0.857727	+	0.514106i	$0.171876\pi$
$59$			60.6645i			1.02821i	−0.857727	+	0.514106i	$0.828124\pi$
$60$		0			0
$61$	−21.3518			−0.350030			−0.175015	−	0.984566i	$-0.555997\pi$
$61$	−21.3518			−0.350030			−0.175015	+	0.984566i	$0.555997\pi$
$62$	9.82804	+	110.189i	0.158517	+	1.77724i
$63$		0			0
$64$	55.0981	−	32.5607i	0.860908	−	0.508761i
$65$		0			0
$66$		0			0
$67$	9.68679			0.144579			0.0722895	−	0.997384i	$-0.476969\pi$
$67$	9.68679			0.144579			0.0722895	+	0.997384i	$0.476969\pi$
$68$	−14.8135	−	82.3812i	−0.217845	−	1.21149i
$69$		0			0
$70$		0			0
$71$		−	68.6944i		−	0.967527i	−0.875199	−	0.483763i	$-0.839270\pi$
$71$		−	68.6944i		−	0.967527i	0.875199	−	0.483763i	$-0.160730\pi$
$72$		0			0
$73$		−	84.7825i		−	1.16140i	−0.814116	−	0.580702i	$-0.802778\pi$
$73$		−	84.7825i		−	1.16140i	0.814116	−	0.580702i	$-0.197222\pi$
$74$	−8.91760	−	99.9811i	−0.120508	−	1.35110i
$75$		0			0
$76$	19.7972	+	110.097i	0.260490	+	1.44864i
$77$			9.82388i			0.127583i
$78$		0			0
$79$			23.2903i			0.294814i	0.989076	+	0.147407i	$0.0470928\pi$
$79$			23.2903i			0.294814i	−0.989076	+	0.147407i	$0.952907\pi$
$80$		0			0
$81$		0			0
$82$	−146.690	+	13.0837i	−1.78890	+	0.159557i
$83$	93.2595			1.12361			0.561804	−	0.827270i	$-0.310107\pi$
$83$	93.2595			1.12361			0.561804	+	0.827270i	$0.310107\pi$
$84$		0			0
$85$		0			0
$86$	−38.0177	+	3.39091i	−0.442067	+	0.0394292i
$87$		0			0
$88$	−17.3435	−	63.4377i	−0.197085	−	0.720883i
$89$	62.9898			0.707750			0.353875	−	0.935293i	$-0.384864\pi$
$89$	62.9898			0.707750			0.353875	+	0.935293i	$0.384864\pi$
$90$		0			0
$91$		−	13.3678i		−	0.146899i
$92$	−37.3436	+	6.71499i	−0.405909	+	0.0729890i
$93$		0			0
$94$	35.9767	−	3.20887i	0.382731	−	0.0341369i
$95$		0			0
$96$		0			0
$97$			91.3962i			0.942229i	0.882072	+	0.471115i	$0.156148\pi$
$97$			91.3962i			0.942229i	−0.882072	+	0.471115i	$0.843852\pi$
$98$	94.7677	−	8.45260i	0.967017	−	0.0862510i
$99$		0			0
$100$		0			0
$101$	29.9780			0.296811			0.148406	−	0.988927i	$-0.452586\pi$
$101$	29.9780			0.296811			0.148406	+	0.988927i	$0.452586\pi$
$102$		0			0
$103$	88.7485			0.861636			0.430818	−	0.902439i	$-0.358225\pi$
$103$	88.7485			0.861636			0.430818	+	0.902439i	$0.358225\pi$
$104$	23.6001	+	86.3228i	0.226924	+	0.830027i
$105$		0			0
$106$	10.1671	+	113.990i	0.0959159	+	1.07538i
$107$	162.922			1.52263			0.761316	−	0.648381i	$-0.224553\pi$
$107$	162.922			1.52263			0.761316	+	0.648381i	$0.224553\pi$
$108$		0			0
$109$	103.352			0.948182			0.474091	−	0.880476i	$-0.342777\pi$
$109$	103.352			0.948182			0.474091	+	0.880476i	$0.342777\pi$
$110$		0			0
$111$		0			0
$112$	17.9225	−	6.66088i	0.160022	−	0.0594722i
$113$		−	31.2691i		−	0.276717i	−0.990382	−	0.138359i	$-0.955817\pi$
$113$		−	31.2691i		−	0.276717i	0.990382	−	0.138359i	$-0.0441827\pi$
$114$		0			0
$115$		0			0
$116$	159.130	−	28.6141i	1.37181	−	0.246673i
$117$		0			0
$118$	−10.7789	−	120.849i	−0.0913465	−	1.02415i
$119$		−	25.0064i		−	0.210138i
$120$		0			0
$121$	53.4198			0.441486
$122$	42.5348	−	3.79380i	0.348646	−	0.0310967i
$123$		0			0
$124$	−39.1567	−	217.760i	−0.315780	−	1.75613i
$125$		0			0
$126$		0			0
$127$	178.474			1.40531			0.702655	−	0.711531i	$-0.251998\pi$
$127$	178.474			1.40531			0.702655	+	0.711531i	$0.251998\pi$
$128$	−103.975	+	74.6537i	−0.812305	+	0.583232i
$129$		0			0
$130$		0			0
$131$		−	153.743i		−	1.17361i	−0.809727	−	0.586806i	$-0.800385\pi$
$131$		−	153.743i		−	1.17361i	0.809727	−	0.586806i	$-0.199615\pi$
$132$		0			0
$133$			33.4194i			0.251274i
$134$	−19.2970	+	1.72115i	−0.144007	+	0.0128444i
$135$		0			0
$136$	44.1473	+	161.479i	0.324613	+	1.18734i
$137$			52.9928i			0.386809i	0.981119	+	0.193405i	$0.0619530\pi$
$137$			52.9928i			0.386809i	−0.981119	+	0.193405i	$0.938047\pi$
$138$		0			0
$139$		−	21.8420i		−	0.157137i	−0.996909	−	0.0785684i	$-0.974965\pi$
$139$		−	21.8420i		−	0.157137i	0.996909	−	0.0785684i	$-0.0250349\pi$
$140$		0			0
$141$		0			0
$142$	12.2056	+	136.846i	0.0859552	+	0.963701i
$143$	91.9598			0.643076
$144$		0			0
$145$		0			0
$146$	15.0642	+	168.895i	0.103179	+	1.15681i
$147$		0			0
$148$	35.5294	+	197.587i	0.240063	+	1.33505i
$149$	−3.12940			−0.0210027			−0.0105013	−	0.999945i	$-0.503343\pi$
$149$	−3.12940			−0.0210027			−0.0105013	+	0.999945i	$0.503343\pi$
$150$		0			0
$151$		−	296.461i		−	1.96332i	−0.190646	−	0.981659i	$-0.561058\pi$
$151$		−	296.461i		−	1.96332i	0.190646	−	0.981659i	$-0.438942\pi$
$152$	−58.9999	−	215.806i	−0.388157	−	1.41977i
$153$		0			0
$154$	−1.74551	−	19.5701i	−0.0113345	−	0.127078i
$155$		0			0
$156$		0			0
$157$		−	265.686i		−	1.69227i	−0.532972	−	0.846133i	$-0.678925\pi$
$157$		−	265.686i		−	1.69227i	0.532972	−	0.846133i	$-0.321075\pi$
$158$	−4.13824	−	46.3965i	−0.0261914	−	0.293649i
$159$		0			0
$160$		0			0
$161$	−11.3355			−0.0704067
$162$		0			0
$163$	205.531			1.26093			0.630465	−	0.776218i	$-0.282864\pi$
$163$	205.531			1.26093			0.630465	+	0.776218i	$0.282864\pi$
$164$	289.895	−	52.1278i	1.76765	−	0.317852i
$165$		0			0
$166$	−185.781	+	16.5704i	−1.11917	+	0.0998215i
$167$	−11.6359			−0.0696763			−0.0348381	−	0.999393i	$-0.511092\pi$
$167$	−11.6359			−0.0696763			−0.0348381	+	0.999393i	$0.511092\pi$
$168$		0			0
$169$	43.8657			0.259560
$170$		0			0
$171$		0			0
$172$	75.1323	−	13.5100i	0.436816	−	0.0785466i
$173$		−	106.062i		−	0.613077i	−0.951858	−	0.306538i	$-0.900829\pi$
$173$		−	106.062i		−	0.613077i	0.951858	−	0.306538i	$-0.0991708\pi$
$174$		0			0
$175$		0			0
$176$	45.8214	+	123.292i	0.260349	+	0.700523i
$177$		0			0
$178$	−125.481	+	11.1920i	−0.704951	+	0.0628766i
$179$		−	43.3304i		−	0.242069i	−0.992648	−	0.121035i	$-0.961379\pi$
$179$		−	43.3304i		−	0.242069i	0.992648	−	0.121035i	$-0.0386212\pi$
$180$		0			0
$181$	203.614			1.12494			0.562469	−	0.826819i	$-0.309852\pi$
$181$	203.614			1.12494			0.562469	+	0.826819i	$0.309852\pi$
$182$	2.37520	+	26.6300i	0.0130506	+	0.146319i
$183$		0			0
$184$	73.1988	−	20.0121i	0.397819	−	0.108761i
$185$		0			0
$186$		0			0
$187$	172.024			0.919913
$188$	−71.0988	+	12.7847i	−0.378185	+	0.0680038i
$189$		0			0
$190$		0			0
$191$			251.536i			1.31694i	0.752606	+	0.658471i	$0.228796\pi$
$191$			251.536i			1.31694i	−0.752606	+	0.658471i	$0.771204\pi$
$192$		0			0
$193$			281.811i			1.46016i	0.683360	+	0.730081i	$0.260518\pi$
$193$			281.811i			1.46016i	−0.683360	+	0.730081i	$0.739482\pi$
$194$	−16.2393	−	182.070i	−0.0837078	−	0.938503i
$195$		0			0
$196$	−187.284	+	33.6767i	−0.955531	+	0.171820i
$197$			243.485i			1.23596i	0.786193	+	0.617982i	$0.212049\pi$
$197$			243.485i			1.23596i	−0.786193	+	0.617982i	$0.787951\pi$
$198$		0			0
$199$			121.958i			0.612853i	0.951894	+	0.306427i	$0.0991335\pi$
$199$			121.958i			0.612853i	−0.951894	+	0.306427i	$0.900867\pi$
$200$		0			0
$201$		0			0
$202$	−59.7188	+	5.32649i	−0.295638	+	0.0263688i
$203$	48.3031			0.237946
$204$		0			0
$205$		0			0
$206$	−176.795	+	15.7689i	−0.858229	+	0.0765479i
$207$		0			0
$208$	−62.3515	−	167.770i	−0.299767	−	0.806585i
$209$	−229.898			−1.09999
$210$		0			0
$211$		−	132.543i		−	0.628168i	−0.949395	−	0.314084i	$-0.898303\pi$
$211$		−	132.543i		−	0.628168i	0.949395	−	0.314084i	$-0.101697\pi$
$212$	−40.5076	−	225.272i	−0.191073	−	1.06260i
$213$		0			0
$214$	−324.555	+	28.9480i	−1.51661	+	0.135271i
$215$		0			0
$216$		0			0
$217$		−	66.0998i		−	0.304608i
$218$	−205.886	+	18.3636i	−0.944433	+	0.0842366i
$219$		0			0
$220$		0			0
$221$	−234.081			−1.05919
$222$		0			0
$223$	225.442			1.01095			0.505475	−	0.862841i	$-0.331317\pi$
$223$	225.442			1.01095			0.505475	+	0.862841i	$0.331317\pi$
$224$	−34.5198	+	16.4536i	−0.154106	+	0.0734534i
$225$		0			0
$226$	5.55590	+	62.2908i	0.0245836	+	0.275623i
$227$	−108.080			−0.476124			−0.238062	−	0.971250i	$-0.576512\pi$
$227$	−108.080			−0.476124			−0.238062	+	0.971250i	$0.576512\pi$
$228$		0			0
$229$	57.3495			0.250435			0.125217	−	0.992129i	$-0.460037\pi$
$229$	57.3495			0.250435			0.125217	+	0.992129i	$0.460037\pi$
$230$		0			0
$231$		0			0
$232$	−311.917	+	85.2762i	−1.34447	+	0.367570i
$233$			285.320i			1.22455i	0.790646	+	0.612274i	$0.209745\pi$
$233$			285.320i			1.22455i	−0.790646	+	0.612274i	$0.790255\pi$
$234$		0			0
$235$		0			0
$236$	42.9451	+	238.828i	0.181971	+	1.01198i
$237$		0			0
$238$	4.44315	+	49.8151i	0.0186687	+	0.209307i
$239$			77.2471i			0.323210i	0.986856	+	0.161605i	$0.0516670\pi$
$239$			77.2471i			0.323210i	−0.986856	+	0.161605i	$0.948333\pi$
$240$		0			0
$241$	−130.557			−0.541732			−0.270866	−	0.962617i	$-0.587310\pi$
$241$	−130.557			−0.541732			−0.270866	+	0.962617i	$0.587310\pi$
$242$	−106.417	+	9.49164i	−0.439740	+	0.0392217i
$243$		0			0
$244$	−84.0591	+	15.1152i	−0.344504	+	0.0619475i
$245$		0			0
$246$		0			0
$247$	312.834			1.26653
$248$	116.695	+	426.840i	0.470546	+	1.72113i
$249$		0			0
$250$		0			0
$251$		−	437.197i		−	1.74182i	−0.491441	−	0.870911i	$-0.663530\pi$
$251$		−	437.197i		−	1.74182i	0.491441	−	0.870911i	$-0.336470\pi$
$252$		0			0
$253$		−	77.9788i		−	0.308216i
$254$	−355.537	+	31.7114i	−1.39975	+	0.124848i
$255$		0			0
$256$	193.863	−	167.191i	0.757279	−	0.653091i
$257$		−	74.3682i		−	0.289370i	−0.989478	−	0.144685i	$-0.953783\pi$
$257$		−	74.3682i		−	0.289370i	0.989478	−	0.144685i	$-0.0462169\pi$
$258$		0			0
$259$			59.9766i			0.231570i
$260$		0			0
$261$		0			0
$262$	27.3172	+	306.271i	0.104264	+	1.16897i
$263$	−458.790			−1.74445			−0.872225	−	0.489105i	$-0.837324\pi$
$263$	−458.790			−1.74445			−0.872225	+	0.489105i	$0.837324\pi$
$264$		0			0
$265$		0			0
$266$	−5.93797	−	66.5745i	−0.0223232	−	0.250280i
$267$		0			0
$268$	38.1355	−	6.85739i	0.142297	−	0.0255873i
$269$	−320.405			−1.19110			−0.595549	−	0.803319i	$-0.703065\pi$
$269$	−320.405			−1.19110			−0.595549	+	0.803319i	$0.703065\pi$
$270$		0			0
$271$		−	359.059i		−	1.32494i	−0.749088	−	0.662470i	$-0.769508\pi$
$271$		−	359.059i		−	1.32494i	0.749088	−	0.662470i	$-0.230492\pi$
$272$	−116.637	−	313.837i	−0.428813	−	1.15381i
$273$		0			0
$274$	−9.41579	−	105.567i	−0.0343642	−	0.385280i
$275$		0			0
$276$		0			0
$277$			138.027i			0.498293i	0.968466	+	0.249147i	$0.0801501\pi$
$277$			138.027i			0.498293i	−0.968466	+	0.249147i	$0.919850\pi$
$278$	3.88090	+	43.5113i	0.0139601	+	0.156516i
$279$		0			0
$280$		0			0
$281$	−462.504			−1.64592			−0.822960	−	0.568099i	$-0.807679\pi$
$281$	−462.504			−1.64592			−0.822960	+	0.568099i	$0.807679\pi$
$282$		0			0
$283$	−323.973			−1.14478			−0.572391	−	0.819981i	$-0.693984\pi$
$283$	−323.973			−1.14478			−0.572391	+	0.819981i	$0.693984\pi$
$284$	−48.6295	−	270.440i	−0.171231	−	0.952254i
$285$		0			0
$286$	−183.192	+	16.3394i	−0.640533	+	0.0571309i
$287$	87.9962			0.306607
$288$		0			0
$289$	−148.882			−0.515161
$290$		0			0
$291$		0			0
$292$	−60.0185	−	333.777i	−0.205543	−	1.14307i
$293$			150.416i			0.513365i	0.966496	+	0.256683i	$0.0826295\pi$
$293$			150.416i			0.513365i	−0.966496	+	0.256683i	$0.917371\pi$
$294$		0			0
$295$		0			0
$296$	−105.885	−	387.299i	−0.357720	−	1.30844i
$297$		0			0
$298$	6.23406	−	0.556033i	0.0209196	−	0.00186588i
$299$			106.110i			0.354882i
$300$		0			0
$301$	22.8060			0.0757676
$302$	52.6753	+	590.577i	0.174421	+	1.95555i
$303$		0			0
$304$	155.878	+	419.421i	0.512755	+	1.37968i
$305$		0			0
$306$		0			0
$307$	−563.915			−1.83686			−0.918428	−	0.395587i	$-0.870541\pi$
$307$	−563.915			−1.83686			−0.918428	+	0.395587i	$0.870541\pi$
$308$	6.95443	+	38.6752i	0.0225793	+	0.125569i
$309$		0			0
$310$		0			0
$311$		−	40.0214i		−	0.128686i	−0.997928	−	0.0643431i	$-0.979505\pi$
$311$		−	40.0214i		−	0.128686i	0.997928	−	0.0643431i	$-0.0204952\pi$
$312$		0			0
$313$		−	1.82657i		−	0.00583568i	−0.999996	−	0.00291784i	$-0.999071\pi$
$313$		−	1.82657i		−	0.00583568i	0.999996	−	0.00291784i	$-0.000928778\pi$
$314$	47.2071	+	529.270i	0.150341	+	1.68557i
$315$		0			0
$316$	16.4875	+	91.6908i	0.0521756	+	0.290161i
$317$		−	246.416i		−	0.777338i	−0.921378	−	0.388669i	$-0.872935\pi$
$317$		−	246.416i		−	0.777338i	0.921378	−	0.388669i	$-0.127065\pi$
$318$		0			0
$319$			332.286i			1.04165i
$320$		0			0
$321$		0			0
$322$	22.5813	−	2.01409i	0.0701283	−	0.00625494i
$323$	585.199			1.81176
$324$		0			0
$325$		0			0
$326$	−409.438	+	36.5189i	−1.25594	+	0.112021i
$327$		0			0
$328$	−568.235	+	155.352i	−1.73242	+	0.473634i
$329$	−21.5817			−0.0655978
$330$		0			0
$331$			417.672i			1.26185i	0.775844	+	0.630925i	$0.217325\pi$
$331$			417.672i			1.26185i	−0.775844	+	0.630925i	$0.782675\pi$
$332$	367.149	−	66.0194i	1.10587	−	0.198854i
$333$		0			0
$334$	23.1798	−	2.06748i	0.0694007	−	0.00619005i
$335$		0			0
$336$		0			0
$337$		−	317.379i		−	0.941779i	−0.882192	−	0.470889i	$-0.843933\pi$
$337$		−	317.379i		−	0.941779i	0.882192	−	0.470889i	$-0.156067\pi$
$338$	−87.3845	+	7.79408i	−0.258534	+	0.0230594i
$339$		0			0
$340$		0			0
$341$	454.713			1.33347
$342$		0			0
$343$	−115.405			−0.336457
$344$	−147.270	+	40.2627i	−0.428110	+	0.117043i
$345$		0			0
$346$	18.8452	+	211.286i	0.0544659	+	0.610653i
$347$	222.581			0.641443			0.320721	−	0.947174i	$-0.396075\pi$
$347$	222.581			0.641443			0.320721	+	0.947174i	$0.396075\pi$
$348$		0			0
$349$	−560.812			−1.60691			−0.803455	−	0.595366i	$-0.797007\pi$
$349$	−560.812			−1.60691			−0.803455	+	0.595366i	$0.797007\pi$
$350$		0			0
$351$		0			0
$352$	−113.187	−	237.468i	−0.321554	−	0.674624i
$353$			304.856i			0.863616i	0.901966	+	0.431808i	$0.142124\pi$
$353$			304.856i			0.863616i	−0.901966	+	0.431808i	$0.857876\pi$
$354$		0			0
$355$		0			0
$356$	247.982	−	44.5911i	0.696578	−	0.125256i
$357$		0			0
$358$	7.69896	+	86.3181i	0.0215055	+	0.241112i
$359$		−	105.860i		−	0.294874i	−0.989071	−	0.147437i	$-0.952898\pi$
$359$		−	105.860i		−	0.294874i	0.989071	−	0.147437i	$-0.0471023\pi$
$360$		0			0
$361$	−421.079			−1.16642
$362$	−405.617	+	36.1782i	−1.12049	+	0.0999396i
$363$		0			0
$364$	−9.46324	−	52.6273i	−0.0259979	−	0.144581i
$365$		0			0
$366$		0			0
$367$	−360.200			−0.981470			−0.490735	−	0.871309i	$-0.663272\pi$
$367$	−360.200			−0.981470			−0.490735	+	0.871309i	$0.663272\pi$
$368$	−142.263	+	52.8719i	−0.386584	+	0.143674i
$369$		0			0
$370$		0			0
$371$		−	68.3802i		−	0.184313i
$372$		0			0
$373$			135.489i			0.363242i	0.983369	+	0.181621i	$0.0581344\pi$
$373$			135.489i			0.363242i	−0.983369	+	0.181621i	$0.941866\pi$
$374$	−342.687	+	30.5652i	−0.916275	+	0.0817252i
$375$		0			0
$376$	139.364	−	38.1012i	0.370648	−	0.101333i
$377$		−	452.158i		−	1.19936i
$378$		0			0
$379$		−	310.686i		−	0.819753i	−0.912141	−	0.409876i	$-0.865572\pi$
$379$		−	310.686i		−	0.819753i	0.912141	−	0.409876i	$-0.134428\pi$
$380$		0			0
$381$		0			0
$382$	−44.6930	−	501.083i	−0.116997	−	1.31173i
$383$	−121.981			−0.318487			−0.159244	−	0.987239i	$-0.550906\pi$
$383$	−121.981			−0.318487			−0.159244	+	0.987239i	$0.550906\pi$
$384$		0			0
$385$		0			0
$386$	−50.0723	−	561.394i	−0.129721	−	1.45439i
$387$		0			0
$388$	64.7004	+	359.814i	0.166754	+	0.927356i
$389$	544.266			1.39914			0.699570	−	0.714564i	$-0.253375\pi$
$389$	544.266			1.39914			0.699570	+	0.714564i	$0.253375\pi$
$390$		0			0
$391$			198.493i			0.507654i
$392$	367.103	−	100.364i	0.936488	−	0.256030i
$393$		0			0
$394$	−43.2625	−	485.044i	−0.109803	−	1.23108i
$395$		0			0
$396$		0			0
$397$			504.528i			1.27085i	0.772162	+	0.635425i	$0.219175\pi$
$397$			504.528i			1.27085i	−0.772162	+	0.635425i	$0.780825\pi$
$398$	−21.6695	−	242.951i	−0.0544460	−	0.610430i
$399$		0			0
$400$		0			0
$401$	278.018			0.693312			0.346656	−	0.937992i	$-0.387317\pi$
$401$	278.018			0.693312			0.346656	+	0.937992i	$0.387317\pi$
$402$		0			0
$403$	−618.750			−1.53536
$404$	118.019	−	21.2217i	0.292126	−	0.0525290i
$405$		0			0
$406$	−96.2242	+	8.58251i	−0.237005	+	0.0211392i
$407$	−412.590			−1.01373
$408$		0			0
$409$	296.549			0.725059			0.362530	−	0.931972i	$-0.381913\pi$
$409$	296.549			0.725059			0.362530	+	0.931972i	$0.381913\pi$
$410$		0			0
$411$		0			0
$412$	349.390	−	62.8261i	0.848035	−	0.152490i
$413$			72.4950i			0.175533i
$414$		0			0
$415$		0			0
$416$	154.019	+	323.134i	0.370239	+	0.776764i
$417$		0			0
$418$	457.978	−	40.8483i	1.09564	−	0.0977233i
$419$			315.615i			0.753258i	0.926364	+	0.376629i	$0.122917\pi$
$419$			315.615i			0.753258i	−0.926364	+	0.376629i	$0.877083\pi$
$420$		0			0
$421$	−360.355			−0.855951			−0.427975	−	0.903790i	$-0.640773\pi$
$421$	−360.355			−0.855951			−0.427975	+	0.903790i	$0.640773\pi$
$422$	23.5504	+	264.039i	0.0558066	+	0.625684i
$423$		0			0
$424$	120.721	+	441.565i	0.284720	+	1.04143i
$425$		0			0
$426$		0			0
$427$	−25.5157			−0.0597558
$428$	641.400	−	115.334i	1.49860	−	0.269472i
$429$		0			0
$430$		0			0
$431$			523.617i			1.21489i	0.794362	+	0.607445i	$0.207805\pi$
$431$			523.617i			1.21489i	−0.794362	+	0.607445i	$0.792195\pi$
$432$		0			0
$433$			21.5381i			0.0497415i	0.999691	+	0.0248707i	$0.00791742\pi$
$433$			21.5381i			0.0497415i	−0.999691	+	0.0248707i	$0.992083\pi$
$434$	11.7446	+	131.677i	0.0270614	+	0.303403i
$435$		0			0
$436$	406.882	−	73.1639i	0.933215	−	0.167807i
$437$		−	265.272i		−	0.607030i
$438$		0			0
$439$		−	247.777i		−	0.564412i	−0.959354	−	0.282206i	$-0.908934\pi$
$439$		−	247.777i		−	0.564412i	0.959354	−	0.282206i	$-0.0910662\pi$
$440$		0			0
$441$		0			0
$442$	466.311	−	41.5916i	1.05500	−	0.0940987i
$443$	−584.775			−1.32003			−0.660017	−	0.751251i	$-0.729451\pi$
$443$	−584.775			−1.32003			−0.660017	+	0.751251i	$0.729451\pi$
$444$		0			0
$445$		0			0
$446$	−449.101	+	40.0566i	−1.00695	+	0.0898130i
$447$		0			0
$448$	65.8430	−	38.9105i	0.146971	−	0.0868538i
$449$	152.093			0.338738			0.169369	−	0.985553i	$-0.445827\pi$
$449$	152.093			0.338738			0.169369	+	0.985553i	$0.445827\pi$
$450$		0			0
$451$			605.342i			1.34222i
$452$	−22.1357	−	123.102i	−0.0489728	−	0.272349i
$453$		0			0
$454$	215.306	−	19.2037i	0.474242	−	0.0422990i
$455$		0			0
$456$		0			0
$457$			602.441i			1.31825i	0.752033	+	0.659126i	$0.229074\pi$
$457$			602.441i			1.31825i	−0.752033	+	0.659126i	$0.770926\pi$
$458$	−114.246	+	10.1899i	−0.249444	+	0.0222487i
$459$		0			0
$460$		0			0
$461$	504.912			1.09525			0.547626	−	0.836723i	$-0.315532\pi$
$461$	504.912			1.09525			0.547626	+	0.836723i	$0.315532\pi$
$462$		0			0
$463$	504.560			1.08976			0.544881	−	0.838513i	$-0.316575\pi$
$463$	504.560			1.08976			0.544881	+	0.838513i	$0.316575\pi$
$464$	606.215	−	225.300i	1.30650	−	0.485559i
$465$		0			0
$466$	−50.6957	−	568.383i	−0.108789	−	1.21971i
$467$	751.418			1.60903			0.804516	−	0.593931i	$-0.202425\pi$
$467$	751.418			1.60903			0.804516	+	0.593931i	$0.202425\pi$
$468$		0			0
$469$	11.5759			0.0246820
$470$		0			0
$471$		0			0
$472$	−127.986	−	468.136i	−0.271156	−	0.991814i
$473$			156.887i			0.331685i
$474$		0			0
$475$		0			0
$476$	−17.7023	−	98.4468i	−0.0371898	−	0.206821i
$477$		0			0
$478$	−13.7253	−	153.883i	−0.0287140	−	0.321932i
$479$		−	581.401i		−	1.21378i	−0.794786	−	0.606890i	$-0.792417\pi$
$479$		−	581.401i		−	1.21378i	0.794786	−	0.606890i	$-0.207583\pi$
$480$		0			0
$481$	561.431			1.16722
$482$	260.082	−	23.1975i	0.539590	−	0.0481276i
$483$		0			0
$484$	210.306	−	37.8164i	0.434517	−	0.0781331i
$485$		0			0
$486$		0			0
$487$	557.489			1.14474			0.572371	−	0.819995i	$-0.306024\pi$
$487$	557.489			1.14474			0.572371	+	0.819995i	$0.306024\pi$
$488$	164.768	−	45.0465i	0.337639	−	0.0923084i
$489$		0			0
$490$		0			0
$491$		−	26.2032i		−	0.0533670i	−0.999644	−	0.0266835i	$-0.991505\pi$
$491$		−	26.2032i		−	0.0533670i	0.999644	−	0.0266835i	$-0.00849463\pi$
$492$		0			0
$493$		−	845.824i		−	1.71567i
$494$	−623.193	+	55.5844i	−1.26152	+	0.112519i
$495$		0			0
$496$	−308.309	−	829.569i	−0.621590	−	1.67252i
$497$		−	82.0908i		−	0.165173i
$498$		0			0
$499$		−	444.615i		−	0.891011i	−0.895279	−	0.445506i	$-0.853024\pi$
$499$		−	444.615i		−	0.891011i	0.895279	−	0.445506i	$-0.146976\pi$
$500$		0			0
$501$		0			0
$502$	77.6814	+	870.937i	0.154744	+	1.73493i
$503$	216.819			0.431052			0.215526	−	0.976498i	$-0.430853\pi$
$503$	216.819			0.431052			0.215526	+	0.976498i	$0.430853\pi$
$504$		0			0
$505$		0			0
$506$	13.8553	+	155.341i	0.0273820	+	0.306998i
$507$		0			0
$508$	702.628	−	126.344i	1.38313	−	0.248708i
$509$	202.830			0.398488			0.199244	−	0.979950i	$-0.436151\pi$
$509$	202.830			0.398488			0.199244	+	0.979950i	$0.436151\pi$
$510$		0			0
$511$		−	101.316i		−	0.198271i
$512$	−356.487	+	367.506i	−0.696264	+	0.717786i
$513$		0			0
$514$	13.2138	+	148.148i	0.0257077	+	0.288226i
$515$		0			0
$516$		0			0
$517$		−	148.464i		−	0.287165i
$518$	−10.6567	−	119.479i	−0.0205727	−	0.230654i
$519$		0			0
$520$		0			0
$521$	−769.410			−1.47679			−0.738397	−	0.674366i	$-0.764417\pi$
$521$	−769.410			−1.47679			−0.738397	+	0.674366i	$0.764417\pi$
$522$		0			0
$523$	−38.9898			−0.0745502			−0.0372751	−	0.999305i	$-0.511868\pi$
$523$	−38.9898			−0.0745502			−0.0372751	+	0.999305i	$0.511868\pi$
$524$	−108.837	−	605.266i	−0.207703	−	1.15509i
$525$		0			0
$526$	913.953	−	81.5180i	1.73755	−	0.154977i
$527$	−1157.46			−2.19632
$528$		0			0
$529$	−439.023			−0.829911
$530$		0			0
$531$		0			0
$532$	23.6579	+	131.567i	0.0444698	+	0.247307i
$533$		−	823.718i		−	1.54544i
$534$		0			0
$535$		0			0
$536$	−74.7510	+	20.4365i	−0.139461	+	0.0381277i
$537$		0			0
$538$	638.277	−	56.9297i	1.18639	−	0.105817i
$539$		−	391.076i		−	0.725558i
$540$		0			0
$541$	−32.0904			−0.0593168			−0.0296584	−	0.999560i	$-0.509442\pi$
$541$	−32.0904			−0.0593168			−0.0296584	+	0.999560i	$0.509442\pi$
$542$	63.7977	+	715.278i	0.117708	+	1.31970i
$543$		0			0
$544$	288.115	+	604.467i	0.529622	+	1.11115i
$545$		0			0
$546$		0			0
$547$	−254.839			−0.465885			−0.232942	−	0.972491i	$-0.574835\pi$
$547$	−254.839			−0.465885			−0.232942	+	0.972491i	$0.574835\pi$
$548$	37.5142	+	208.625i	0.0684566	+	0.380703i
$549$		0			0
$550$		0			0
$551$			1130.39i			2.05152i
$552$		0			0
$553$			27.8323i			0.0503296i
$554$	−24.5247	−	274.963i	−0.0442685	−	0.496323i
$555$		0			0
$556$	−15.4622	−	85.9890i	−0.0278097	−	0.154656i
$557$			577.439i			1.03670i	0.855170	+	0.518348i	$0.173453\pi$
$557$			577.439i			1.03670i	−0.855170	+	0.518348i	$0.826547\pi$
$558$		0			0
$559$		−	213.484i		−	0.381903i
$560$		0			0
$561$		0			0
$562$	921.350	−	82.1778i	1.63941	−	0.146224i
$563$	−367.058			−0.651967			−0.325984	−	0.945375i	$-0.605695\pi$
$563$	−367.058			−0.651967			−0.325984	+	0.945375i	$0.605695\pi$
$564$		0			0
$565$		0			0
$566$	645.384	−	57.5636i	1.14025	−	0.101703i
$567$		0			0
$568$	144.926	+	530.101i	0.255152	+	0.933277i
$569$	−522.006			−0.917410			−0.458705	−	0.888589i	$-0.651687\pi$
$569$	−522.006			−0.917410			−0.458705	+	0.888589i	$0.651687\pi$
$570$		0			0
$571$			832.421i			1.45783i	0.684604	+	0.728915i	$0.259975\pi$
$571$			832.421i			1.45783i	−0.684604	+	0.728915i	$0.740025\pi$
$572$	362.033	−	65.0994i	0.632925	−	0.113810i
$573$		0			0
$574$	−175.296	+	15.6352i	−0.305394	+	0.0272390i
$575$		0			0
$576$		0			0
$577$		−	427.659i		−	0.741177i	−0.928797	−	0.370588i	$-0.879156\pi$
$577$		−	427.659i		−	0.741177i	0.928797	−	0.370588i	$-0.120844\pi$
$578$	296.586	−	26.4533i	0.513124	−	0.0457670i
$579$		0			0
$580$		0			0
$581$	111.446			0.191818
$582$		0			0
$583$	470.400			0.806861
$584$	178.868	+	654.250i	0.306281	+	1.12029i
$585$		0			0
$586$	−26.7260	−	299.642i	−0.0456074	−	0.511335i
$587$	−586.262			−0.998743			−0.499372	−	0.866388i	$-0.666436\pi$
$587$	−586.262			−0.998743			−0.499372	+	0.866388i	$0.666436\pi$
$588$		0			0
$589$	1546.87			2.62626
$590$		0			0
$591$		0			0
$592$	279.748	+	752.721i	0.472548	+	1.27149i
$593$		−	518.375i		−	0.874156i	−0.899424	−	0.437078i	$-0.856013\pi$
$593$		−	518.375i		−	0.874156i	0.899424	−	0.437078i	$-0.143987\pi$
$594$		0			0
$595$		0			0
$596$	−12.3200	+	2.21534i	−0.0206712	+	0.00371701i
$597$		0			0
$598$	−18.8536	−	211.380i	−0.0315277	−	0.353478i
$599$			405.480i			0.676928i	0.940979	+	0.338464i	$0.109907\pi$
$599$			405.480i			0.676928i	−0.940979	+	0.338464i	$0.890093\pi$
$600$		0			0
$601$	−350.551			−0.583279			−0.291640	−	0.956528i	$-0.594201\pi$
$601$	−350.551			−0.583279			−0.291640	+	0.956528i	$0.594201\pi$
$602$	−45.4317	+	4.05219i	−0.0754680	+	0.00673121i
$603$		0			0
$604$	−209.868	−	1167.13i	−0.347464	−	1.93233i
$605$		0			0
$606$		0			0
$607$	−737.786			−1.21546			−0.607731	−	0.794143i	$-0.707920\pi$
$607$	−737.786			−1.21546			−0.607731	+	0.794143i	$0.707920\pi$
$608$	−385.046	−	807.829i	−0.633299	−	1.32867i
$609$		0			0
$610$		0			0
$611$			202.023i			0.330643i
$612$		0			0
$613$			345.495i			0.563614i	0.959471	+	0.281807i	$0.0909338\pi$
$613$			345.495i			0.563614i	−0.959471	+	0.281807i	$0.909066\pi$
$614$	1123.37	−	100.197i	1.82959	−	0.163187i
$615$		0			0
$616$	−20.7257	−	75.8090i	−0.0336456	−	0.123066i
$617$			862.171i			1.39736i	0.715434	+	0.698680i	$0.246229\pi$
$617$			862.171i			1.39736i	−0.715434	+	0.698680i	$0.753771\pi$
$618$		0			0
$619$		−	469.363i		−	0.758260i	−0.925343	−	0.379130i	$-0.876223\pi$
$619$		−	469.363i		−	0.758260i	0.925343	−	0.379130i	$-0.123777\pi$
$620$		0			0
$621$		0			0
$622$	7.11102	+	79.7264i	0.0114325	+	0.128177i
$623$	75.2737			0.120824
$624$		0			0
$625$		0			0
$626$	0.324545	+	3.63869i	0.000518443	+	0.00581260i
$627$		0			0
$628$	−188.082	−	1045.97i	−0.299494	−	1.66555i
$629$	1050.24			1.66969
$630$		0			0
$631$			323.243i			0.512271i	0.966641	+	0.256136i	$0.0824494\pi$
$631$			323.243i			0.512271i	−0.966641	+	0.256136i	$0.917551\pi$
$632$	−49.1362	−	179.727i	−0.0777472	−	0.284378i
$633$		0			0
$634$	43.7833	+	490.883i	0.0690588	+	0.774264i
$635$		0			0
$636$		0			0
$637$			532.156i			0.835410i
$638$	−59.0406	−	661.943i	−0.0925402	−	1.03753i
$639$		0			0
$640$		0			0
$641$	44.1100			0.0688144			0.0344072	−	0.999408i	$-0.489046\pi$
$641$	44.1100			0.0688144			0.0344072	+	0.999408i	$0.489046\pi$
$642$		0			0
$643$	−934.204			−1.45288			−0.726442	−	0.687228i	$-0.758827\pi$
$643$	−934.204			−1.45288			−0.726442	+	0.687228i	$0.758827\pi$
$644$	−44.6262	+	8.02451i	−0.0692953	+	0.0124604i
$645$		0			0
$646$	−1165.77	+	103.978i	−1.80460	+	0.160957i
$647$	481.023			0.743467			0.371734	−	0.928339i	$-0.378763\pi$
$647$	481.023			0.743467			0.371734	+	0.928339i	$0.378763\pi$
$648$		0			0
$649$	−498.706			−0.768422
$650$		0			0
$651$		0			0
$652$	809.148	−	145.498i	1.24103	−	0.223156i
$653$		−	1131.38i		−	1.73259i	−0.499536	−	0.866293i	$-0.666496\pi$
$653$		−	1131.38i		−	1.73259i	0.499536	−	0.866293i	$-0.333504\pi$
$654$		0			0
$655$		0			0
$656$	1104.37	−	410.440i	1.68350	−	0.625670i
$657$		0			0
$658$	42.9927	−	3.83464i	0.0653385	−	0.00582772i
$659$		−	154.348i		−	0.234215i	−0.993119	−	0.117107i	$-0.962638\pi$
$659$		−	154.348i		−	0.234215i	0.993119	−	0.117107i	$-0.0373622\pi$
$660$		0			0
$661$	795.115			1.20290			0.601448	−	0.798912i	$-0.294591\pi$
$661$	795.115			1.20290			0.601448	+	0.798912i	$0.294591\pi$
$662$	−74.2122	−	832.042i	−0.112103	−	1.25686i
$663$		0			0
$664$	−719.665	+	196.752i	−1.08383	+	0.296313i
$665$		0			0
$666$		0			0
$667$	−383.414			−0.574834
$668$	−45.8090	+	8.23721i	−0.0685764	+	0.0123311i
$669$		0			0
$670$		0			0
$671$		−	175.527i		−	0.261591i
$672$		0			0
$673$			197.215i			0.293039i	0.989208	+	0.146520i	$0.0468071\pi$
$673$			197.215i			0.293039i	−0.989208	+	0.146520i	$0.953193\pi$
$674$	56.3921	+	632.249i	0.0836678	+	0.938055i
$675$		0			0
$676$	172.693	−	31.0530i	0.255463	−	0.0459364i
$677$			530.367i			0.783408i	0.920091	+	0.391704i	$0.128114\pi$
$677$			530.367i			0.783408i	−0.920091	+	0.391704i	$0.871886\pi$
$678$		0			0
$679$			109.220i			0.160854i
$680$		0			0
$681$		0			0
$682$	−905.830	+	80.7935i	−1.32820	+	0.118466i
$683$	797.231			1.16725			0.583625	−	0.812024i	$-0.301634\pi$
$683$	797.231			1.16725			0.583625	+	0.812024i	$0.301634\pi$
$684$		0			0
$685$		0			0
$686$	229.897	−	20.5052i	0.335127	−	0.0298909i
$687$		0			0
$688$	286.221	−	106.374i	0.416020	−	0.154613i
$689$	−640.096			−0.929022
$690$		0			0
$691$			498.569i			0.721518i	0.932659	+	0.360759i	$0.117482\pi$
$691$			498.569i			0.721518i	−0.932659	+	0.360759i	$0.882518\pi$
$692$	−75.0827	−	417.552i	−0.108501	−	0.603399i
$693$		0			0
$694$	−443.401	+	39.5482i	−0.638906	+	0.0569859i
$695$		0			0
$696$		0			0
$697$		−	1540.88i		−	2.21073i
$698$	1117.19	−	99.6452i	1.60056	−	0.142758i
$699$		0			0
$700$		0			0
$701$	455.939			0.650412			0.325206	−	0.945643i	$-0.394566\pi$
$701$	455.939			0.650412			0.325206	+	0.945643i	$0.394566\pi$
$702$		0			0
$703$	−1403.57			−1.99654
$704$	267.672	+	452.946i	0.380216	+	0.643389i
$705$		0			0
$706$	−54.1670	−	607.302i	−0.0767238	−	0.860201i
$707$	35.8241			0.0506706
$708$		0			0
$709$	44.4190			0.0626502			0.0313251	−	0.999509i	$-0.490027\pi$
$709$	44.4190			0.0626502			0.0313251	+	0.999509i	$0.490027\pi$
$710$		0			0
$711$		0			0
$712$	−486.080	+	132.891i	−0.682696	+	0.186645i
$713$			524.679i			0.735875i
$714$		0			0
$715$		0			0
$716$	−30.6741	−	170.586i	−0.0428409	−	0.238248i
$717$		0			0
$718$	18.8092	+	210.882i	0.0261966	+	0.293708i
$719$		−	1349.94i		−	1.87752i	−0.344566	−	0.938762i	$-0.611974\pi$
$719$		−	1349.94i		−	1.87752i	0.344566	−	0.938762i	$-0.388026\pi$
$720$		0			0
$721$	106.056			0.147095
$722$	838.827	−	74.8174i	1.16181	−	0.103625i
$723$		0			0
$724$	801.599	−	144.140i	1.10718	−	0.199089i
$725$		0			0
$726$		0			0
$727$	−191.470			−0.263370			−0.131685	−	0.991292i	$-0.542039\pi$
$727$	−191.470			−0.263370			−0.131685	+	0.991292i	$0.542039\pi$
$728$	28.2025	+	103.157i	0.0387397	+	0.141699i
$729$		0			0
$730$		0			0
$731$		−	399.351i		−	0.546308i
$732$		0			0
$733$		−	358.832i		−	0.489539i	−0.969581	−	0.244769i	$-0.921288\pi$
$733$		−	358.832i		−	0.489539i	0.969581	−	0.244769i	$-0.0787122\pi$
$734$	717.551	−	64.0004i	0.977589	−	0.0871940i
$735$		0			0
$736$	274.007	−	130.603i	0.372291	−	0.177450i
$737$			79.6324i			0.108049i
$738$		0			0
$739$			756.311i			1.02342i	0.859157	+	0.511712i	$0.170989\pi$
$739$			756.311i			1.02342i	−0.859157	+	0.511712i	$0.829011\pi$
$740$		0			0
$741$		0			0
$742$	12.1498	+	136.220i	0.0163744	+	0.183584i
$743$	−1148.65			−1.54596			−0.772979	−	0.634432i	$-0.781234\pi$
$743$	−1148.65			−1.54596			−0.772979	+	0.634432i	$0.781234\pi$
$744$		0			0
$745$		0			0
$746$	−24.0738	−	269.907i	−0.0322705	−	0.361805i
$747$		0			0
$748$	677.233	−	121.777i	0.905392	−	0.162804i
$749$	194.694			0.259938
$750$		0			0
$751$			431.186i			0.574149i	0.957908	+	0.287074i	$0.0926827\pi$
$751$			431.186i			0.574149i	−0.957908	+	0.287074i	$0.907317\pi$
$752$	−270.856	+	100.663i	−0.360180	+	0.133861i
$753$		0			0
$754$	80.3395	+	900.739i	0.106551	+	1.19461i
$755$		0			0
$756$		0			0
$757$		−	645.657i		−	0.852916i	−0.904507	−	0.426458i	$-0.859761\pi$
$757$		−	645.657i		−	0.852916i	0.904507	−	0.426458i	$-0.140239\pi$
$758$	55.2029	+	618.916i	0.0728270	+	0.816511i
$759$		0			0
$760$		0			0
$761$	291.287			0.382768			0.191384	−	0.981515i	$-0.438702\pi$
$761$	291.287			0.382768			0.191384	+	0.981515i	$0.438702\pi$
$762$		0			0
$763$	123.507			0.161870
$764$	178.065	+	990.261i	0.233069	+	1.29615i
$765$		0			0
$766$	242.997	−	21.6736i	0.317228	−	0.0282945i
$767$	678.614			0.884764
$768$		0			0
$769$	724.076			0.941582			0.470791	−	0.882245i	$-0.343969\pi$
$769$	724.076			0.941582			0.470791	+	0.882245i	$0.343969\pi$
$770$		0			0
$771$		0			0
$772$	199.497	+	1109.45i	0.258416	+	1.43711i
$773$		−	399.686i		−	0.517058i	−0.966003	−	0.258529i	$-0.916762\pi$
$773$		−	399.686i		−	0.517058i	0.966003	−	0.258529i	$-0.0832378\pi$
$774$		0			0
$775$		0			0
$776$	−192.821	−	705.287i	−0.248481	−	0.908875i
$777$		0			0
$778$	−1084.23	+	96.7053i	−1.39361	+	0.124300i
$779$			2059.28i			2.64349i
$780$		0			0
$781$	564.717			0.723070
$782$	−35.2683	−	395.416i	−0.0451001	−	0.505647i
$783$		0			0
$784$	−713.471	+	265.161i	−0.910039	+	0.338215i
$785$		0			0
$786$		0			0
$787$	−381.830			−0.485172			−0.242586	−	0.970130i	$-0.577996\pi$
$787$	−381.830			−0.485172			−0.242586	+	0.970130i	$0.577996\pi$
$788$	172.366	+	958.565i	0.218738	+	1.21645i
$789$		0			0
$790$		0			0
$791$		−	37.3670i		−	0.0472402i
$792$		0			0
$793$			238.849i			0.301196i
$794$	−89.6446	−	1005.07i	−0.112903	−	1.26583i
$795$		0			0
$796$	86.3353	+	480.131i	0.108461	+	0.603180i
$797$			18.3955i			0.0230810i	0.999933	+	0.0115405i	$0.00367353\pi$
$797$			18.3955i			0.0230810i	−0.999933	+	0.0115405i	$0.996326\pi$
$798$		0			0
$799$			377.912i			0.472981i
$800$		0			0
$801$		0			0
$802$	−553.837	+	49.3983i	−0.690570	+	0.0615939i
$803$	696.974			0.867962
$804$		0			0
$805$		0			0
$806$	1232.61	−	109.940i	1.52929	−	0.136402i
$807$		0			0
$808$	−231.334	+	63.2453i	−0.286304	+	0.0782739i
$809$	−992.161			−1.22640			−0.613202	−	0.789926i	$-0.710119\pi$
$809$	−992.161			−1.22640			−0.613202	+	0.789926i	$0.710119\pi$
$810$		0			0
$811$			482.957i			0.595509i	0.954643	+	0.297754i	$0.0962376\pi$
$811$			482.957i			0.595509i	−0.954643	+	0.297754i	$0.903762\pi$
$812$	190.162	−	34.1943i	0.234190	−	0.0421112i
$813$		0			0
$814$	821.917	−	73.3091i	1.00973	−	0.0900603i
$815$		0			0
$816$		0			0
$817$			533.706i			0.653251i
$818$	−590.753	+	52.6910i	−0.722192	+	0.0644144i
$819$		0			0
$820$		0			0
$821$	−614.955			−0.749031			−0.374516	−	0.927221i	$-0.622191\pi$
$821$	−614.955			−0.749031			−0.374516	+	0.927221i	$0.622191\pi$
$822$		0			0
$823$	−11.2878			−0.0137154			−0.00685772	−	0.999976i	$-0.502183\pi$
$823$	−11.2878			−0.0137154			−0.00685772	+	0.999976i	$0.502183\pi$
$824$	−684.855	+	187.235i	−0.831135	+	0.227227i
$825$		0			0
$826$	−12.8809	−	144.417i	−0.0155943	−	0.174839i
$827$	−449.125			−0.543078			−0.271539	−	0.962427i	$-0.587533\pi$
$827$	−449.125			−0.543078			−0.271539	+	0.962427i	$0.587533\pi$
$828$		0			0
$829$	−135.766			−0.163771			−0.0818855	−	0.996642i	$-0.526094\pi$
$829$	−135.766			−0.163771			−0.0818855	+	0.996642i	$0.526094\pi$
$830$		0			0
$831$		0			0
$832$	−364.235	−	616.346i	−0.437782	−	0.740801i
$833$			995.472i			1.19504i
$834$		0			0
$835$		0			0
$836$	−905.076	+	162.747i	−1.08263	+	0.194674i
$837$		0			0
$838$	−56.0786	−	628.734i	−0.0669196	−	0.750280i
$839$			1509.47i			1.79913i	0.436789	+	0.899564i	$0.356116\pi$
$839$			1509.47i			1.79913i	−0.436789	+	0.899564i	$0.643884\pi$
$840$		0			0
$841$	792.817			0.942707
$842$	717.861	−	64.0280i	0.852566	−	0.0760428i
$843$		0			0
$844$	−93.8290	−	521.805i	−0.111172	−	0.618252i
$845$		0			0
$846$		0			0
$847$	63.8374			0.0753688
$848$	−318.945	−	858.188i	−0.376114	−	1.01201i
$849$		0			0
$850$		0			0
$851$		−	476.075i		−	0.559430i
$852$		0			0
$853$		−	909.826i		−	1.06662i	−0.845920	−	0.533310i	$-0.820948\pi$
$853$		−	909.826i		−	1.06662i	0.845920	−	0.533310i	$-0.179052\pi$
$854$	50.8297	−	4.53364i	0.0595195	−	0.00530872i
$855$		0			0
$856$	−1257.23	+	343.720i	−1.46873	+	0.401542i
$857$		−	505.304i		−	0.589620i	−0.955556	−	0.294810i	$-0.904744\pi$
$857$		−	505.304i		−	0.589620i	0.955556	−	0.294810i	$-0.0952563\pi$
$858$		0			0
$859$			45.9728i			0.0535189i	0.999642	+	0.0267595i	$0.00851882\pi$
$859$			45.9728i			0.0535189i	−0.999642	+	0.0267595i	$0.991481\pi$
$860$		0			0
$861$		0			0
$862$	−93.0365	−	1043.09i	−0.107931	−	1.21009i
$863$	−142.006			−0.164549			−0.0822746	−	0.996610i	$-0.526218\pi$
$863$	−142.006			−0.164549			−0.0822746	+	0.996610i	$0.526218\pi$
$864$		0			0
$865$		0			0
$866$	−3.82689	−	42.9058i	−0.00441904	−	0.0495448i
$867$		0			0
$868$	−46.7928	−	260.226i	−0.0539088	−	0.299799i
$869$	−191.463			−0.220326
$870$		0			0
$871$		−	108.360i		−	0.124408i
$872$	−797.546	+	218.044i	−0.914617	+	0.250051i
$873$		0			0
$874$	47.1336	+	528.446i	0.0539287	+	0.604630i
$875$		0			0
$876$		0			0
$877$		−	549.975i		−	0.627109i	−0.949570	−	0.313555i	$-0.898480\pi$
$877$		−	549.975i		−	0.627109i	0.949570	−	0.313555i	$-0.101520\pi$
$878$	44.0251	+	493.594i	0.0501425	+	0.562180i
$879$		0			0
$880$		0			0
$881$	−636.072			−0.721989			−0.360995	−	0.932568i	$-0.617563\pi$
$881$	−636.072			−0.721989			−0.360995	+	0.932568i	$0.617563\pi$
$882$		0			0
$883$	689.661			0.781043			0.390521	−	0.920594i	$-0.372295\pi$
$883$	689.661			0.781043			0.390521	+	0.920594i	$0.372295\pi$
$884$	−921.545	+	165.709i	−1.04247	+	0.187453i
$885$		0			0
$886$	1164.93	−	103.903i	1.31481	−	0.117272i
$887$	−1053.94			−1.18821			−0.594103	−	0.804389i	$-0.702493\pi$
$887$	−1053.94			−1.18821			−0.594103	+	0.804389i	$0.702493\pi$
$888$		0			0
$889$	213.279			0.239909
$890$		0			0
$891$		0			0
$892$	887.533	−	159.593i	0.994992	−	0.178916i
$893$		−	505.054i		−	0.565570i
$894$		0			0
$895$		0			0
$896$	−124.252	+	89.2123i	−0.138674	+	0.0995673i
$897$		0			0
$898$	−302.984	+	27.0240i	−0.337399	+	0.0300936i
$899$		−	2235.78i		−	2.48696i
$900$		0			0
$901$	−1197.39			−1.32896
$902$	−107.557	−	1205.90i	−0.119243	−	1.33691i
$903$		0			0
$904$	65.9691	+	241.297i	0.0729747	+	0.266922i
$905$		0			0
$906$		0			0
$907$	−496.037			−0.546899			−0.273449	−	0.961886i	$-0.588165\pi$
$907$	−496.037			−0.546899			−0.273449	+	0.961886i	$0.588165\pi$
$908$	−425.497	+	76.5112i	−0.468609	+	0.0842635i
$909$		0			0
$910$		0			0
$911$		−	336.684i		−	0.369577i	−0.982778	−	0.184788i	$-0.940840\pi$
$911$		−	336.684i		−	0.369577i	0.982778	−	0.184788i	$-0.0591599\pi$
$912$		0			0
$913$			766.660i			0.839715i
$914$	−107.042	−	1200.12i	−0.117114	−	1.31304i
$915$		0			0
$916$	225.777	−	40.5984i	0.246481	−	0.0443214i
$917$		−	183.725i		−	0.200355i
$918$		0			0
$919$		−	937.464i		−	1.02009i	−0.860147	−	0.510046i	$-0.829629\pi$
$919$		−	937.464i		−	1.02009i	0.860147	−	0.510046i	$-0.170371\pi$
$920$		0			0
$921$		0			0
$922$	−1005.83	+	89.7129i	−1.09092	+	0.0973025i
$923$	−768.439			−0.832545
$924$		0			0
$925$		0			0
$926$	−1005.13	+	89.6504i	−1.08545	+	0.0968147i
$927$		0			0
$928$	−1167.61	+	556.530i	−1.25820	+	0.599709i
$929$	858.647			0.924270			0.462135	−	0.886810i	$-0.347084\pi$
$929$	858.647			0.924270			0.462135	+	0.886810i	$0.347084\pi$
$930$		0			0
$931$		−	1330.38i		−	1.42898i
$932$	201.981	+	1123.26i	0.216718	+	1.20522i
$933$		0			0
$934$	−1496.89	+	133.512i	−1.60267	+	0.142947i
$935$		0			0
$936$		0			0
$937$			1276.09i			1.36189i	0.732336	+	0.680943i	$0.238430\pi$
$937$			1276.09i			1.36189i	−0.732336	+	0.680943i	$0.761570\pi$
$938$	−23.0602	+	2.05680i	−0.0245844	+	0.00219275i
$939$		0			0
$940$		0			0
$941$	−536.218			−0.569838			−0.284919	−	0.958552i	$-0.591967\pi$
$941$	−536.218			−0.569838			−0.284919	+	0.958552i	$0.591967\pi$
$942$		0			0
$943$	−698.485			−0.740705
$944$	338.138	+	909.830i	0.358197	+	0.963803i
$945$		0			0
$946$	−27.8757	−	312.533i	−0.0294669	−	0.330373i
$947$	−48.1723			−0.0508683			−0.0254341	−	0.999677i	$-0.508097\pi$
$947$	−48.1723			−0.0508683			−0.0254341	+	0.999677i	$0.508097\pi$
$948$		0			0
$949$	−948.407			−0.999375
$950$		0			0
$951$		0			0
$952$	52.7567	+	192.970i	0.0554167	+	0.202699i
$953$			1449.85i			1.52136i	0.649129	+	0.760679i	$0.275134\pi$
$953$			1449.85i			1.52136i	−0.649129	+	0.760679i	$0.724866\pi$
$954$		0			0
$955$		0			0
$956$	54.6841	+	304.111i	0.0572009	+	0.318108i
$957$		0			0
$958$	103.303	+	1158.20i	0.107832	+	1.20898i
$959$			63.3272i			0.0660346i
$960$		0			0
$961$	−2098.53			−2.18369
$962$	−1118.42	+	99.7553i	−1.16260	+	0.103696i
$963$		0			0
$964$	−513.986	+	92.4231i	−0.533181	+	0.0958746i
$965$		0			0
$966$		0			0
$967$	1320.06			1.36510			0.682552	−	0.730837i	$-0.260870\pi$
$967$	1320.06			1.36510			0.682552	+	0.730837i	$0.260870\pi$
$968$	−412.230	+	112.701i	−0.425857	+	0.116427i
$969$		0			0
$970$		0			0
$971$			1269.58i			1.30749i	0.756713	+	0.653747i	$0.226804\pi$
$971$			1269.58i			1.30749i	−0.756713	+	0.653747i	$0.773196\pi$
$972$		0			0
$973$		−	26.1015i		−	0.0268258i
$974$	−1110.57	+	99.0548i	−1.14021	+	0.101699i
$975$		0			0
$976$	−320.229	+	119.013i	−0.328103	+	0.121939i
$977$		−	1262.18i		−	1.29190i	−0.763382	−	0.645948i	$-0.776462\pi$
$977$		−	1262.18i		−	1.29190i	0.763382	−	0.645948i	$-0.223538\pi$
$978$		0			0
$979$			517.821i			0.528929i
$980$		0			0
$981$		0			0
$982$	4.65580	+	52.1992i	0.00474114	+	0.0531560i
$983$	235.722			0.239798			0.119899	−	0.992786i	$-0.461743\pi$
$983$	235.722			0.239798			0.119899	+	0.992786i	$0.461743\pi$
$984$		0			0
$985$		0			0
$986$	150.286	+	1684.96i	0.152420	+	1.70888i
$987$		0			0
$988$	1231.58	−	221.458i	1.24654	−	0.224148i
$989$	−181.027			−0.183040
$990$		0			0
$991$		−	1601.53i		−	1.61607i	−0.589135	−	0.808035i	$-0.700531\pi$
$991$		−	1601.53i		−	1.61607i	0.589135	−	0.808035i	$-0.299469\pi$
$992$	761.578	+	1597.80i	0.767719	+	1.61068i
$993$		0			0
$994$	14.5859	+	163.532i	0.0146740	+	0.164520i
$995$		0			0
$996$		0			0
$997$			984.298i			0.987260i	0.869672	+	0.493630i	$0.164330\pi$
$997$			984.298i			0.987260i	−0.869672	+	0.493630i	$0.835670\pi$
$998$	78.9993	+	885.713i	0.0791576	+	0.887488i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.f.h.199.2		16
3.2	odd	2		300.3.f.c.199.15		16
4.3	odd	2	inner	900.3.f.h.199.16		16
5.2	odd	4		900.3.c.t.451.3		8
5.3	odd	4		900.3.c.n.451.6		8
5.4	even	2	inner	900.3.f.h.199.15		16
12.11	even	2		300.3.f.c.199.1		16
15.2	even	4		300.3.c.e.151.6	yes	8
15.8	even	4		300.3.c.g.151.3	yes	8
15.14	odd	2		300.3.f.c.199.2		16
20.3	even	4		900.3.c.n.451.5		8
20.7	even	4		900.3.c.t.451.4		8
20.19	odd	2	inner	900.3.f.h.199.1		16
60.23	odd	4		300.3.c.g.151.4	yes	8
60.47	odd	4		300.3.c.e.151.5	✓	8
60.59	even	2		300.3.f.c.199.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.3.c.e.151.5	✓	8	60.47	odd	4
300.3.c.e.151.6	yes	8	15.2	even	4
300.3.c.g.151.3	yes	8	15.8	even	4
300.3.c.g.151.4	yes	8	60.23	odd	4
300.3.f.c.199.1		16	12.11	even	2
300.3.f.c.199.2		16	15.14	odd	2
300.3.f.c.199.15		16	3.2	odd	2
300.3.f.c.199.16		16	60.59	even	2
900.3.c.n.451.5		8	20.3	even	4
900.3.c.n.451.6		8	5.3	odd	4
900.3.c.t.451.3		8	5.2	odd	4
900.3.c.t.451.4		8	20.7	even	4
900.3.f.h.199.1		16	20.19	odd	2	inner
900.3.f.h.199.2		16	1.1	even	1	trivial
900.3.f.h.199.15		16	5.4	even	2	inner
900.3.f.h.199.16		16	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.99209 + 0.177680i) q^{2} +(3.93686 - 0.707911i) q^{4} +1.19501 q^{7} +(-7.71680 + 2.10973i) q^{8} +O(q^{10})\)	\(q+(-1.99209 + 0.177680i) q^{2} +(3.93686 - 0.707911i) q^{4} +1.19501 q^{7} +(-7.71680 + 2.10973i) q^{8} +8.22072i q^{11} -11.1863i q^{13} +(-2.38058 + 0.212331i) q^{14} +(14.9977 - 5.57389i) q^{16} -20.9256i q^{17} +27.9657i q^{19} +(-1.46066 - 16.3764i) q^{22} -9.48564 q^{23} +(1.98759 + 22.2842i) q^{26} +(4.70460 - 0.845964i) q^{28} +40.4205 q^{29} -55.3130i q^{31} +(-28.8865 + 13.7685i) q^{32} +(3.71807 + 41.6858i) q^{34} +50.1890i q^{37} +(-4.96895 - 55.7102i) q^{38} +73.6361 q^{41} +19.0843 q^{43} +(5.81954 + 32.3638i) q^{44} +(18.8963 - 1.68541i) q^{46} -18.0598 q^{47} -47.5719 q^{49} +(-7.91894 - 44.0391i) q^{52} -57.2212i q^{53} +(-9.22169 + 2.52115i) q^{56} +(-80.5213 + 7.18193i) q^{58} +60.6645i q^{59} -21.3518 q^{61} +(9.82804 + 110.189i) q^{62} +(55.0981 - 32.5607i) q^{64} +9.68679 q^{67} +(-14.8135 - 82.3812i) q^{68} -68.6944i q^{71} -84.7825i q^{73} +(-8.91760 - 99.9811i) q^{74} +(19.7972 + 110.097i) q^{76} +9.82388i q^{77} +23.2903i q^{79} +(-146.690 + 13.0837i) q^{82} +93.2595 q^{83} +(-38.0177 + 3.39091i) q^{86} +(-17.3435 - 63.4377i) q^{88} +62.9898 q^{89} -13.3678i q^{91} +(-37.3436 + 6.71499i) q^{92} +(35.9767 - 3.20887i) q^{94} +91.3962i q^{97} +(94.7677 - 8.45260i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4}+O(q^{10}) \) 16 * q + 16 * q^4	\( 16 q + 16 q^{4} + 44 q^{14} + 80 q^{16} + 132 q^{26} - 64 q^{29} - 248 q^{34} + 32 q^{41} + 80 q^{44} - 152 q^{46} - 32 q^{49} + 344 q^{56} + 272 q^{61} - 32 q^{64} - 216 q^{74} + 240 q^{76} - 428 q^{86} + 256 q^{89} - 24 q^{94}+O(q^{100}) \) 16 * q + 16 * q^4 + 44 * q^14 + 80 * q^16 + 132 * q^26 - 64 * q^29 - 248 * q^34 + 32 * q^41 + 80 * q^44 - 152 * q^46 - 32 * q^49 + 344 * q^56 + 272 * q^61 - 32 * q^64 - 216 * q^74 + 240 * q^76 - 428 * q^86 + 256 * q^89 - 24 * q^94

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