LMFDB - Embedded newform 900.3.f.f.199.16

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} + 5x^{14} + 12x^{12} + 25x^{10} + 53x^{8} + 100x^{6} + 192x^{4} + 320x^{2} + 256 $ x^16 + 5x^14 + 12x^12 + 25x^10 + 53x^8 + 100x^6 + 192x^4 + 320*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{28} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.16
Root			$-1.28061 - 0.600040i$ of defining polynomial
Character	$\chi$	$=$	900.199
Dual form			900.3.f.f.199.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.95141 + 0.438172i) q^{2} +(3.61601 + 1.71011i) q^{4} -6.33166 q^{7} +(6.30701 + 4.92155i) q^{8} +O(q^{10})$	\(q+(1.95141 + 0.438172i) q^{2} +(3.61601 + 1.71011i) q^{4} -6.33166 q^{7} +(6.30701 + 4.92155i) q^{8} -9.27963i q^{11} +18.5674i q^{13} +(-12.3557 - 2.77436i) q^{14} +(10.1511 + 12.3675i) q^{16} +13.9110i q^{17} +17.2468i q^{19} +(4.06607 - 18.1084i) q^{22} +33.7148 q^{23} +(-8.13571 + 36.2327i) q^{26} +(-22.8954 - 10.8278i) q^{28} -28.6177 q^{29} +23.4939i q^{31} +(14.3898 + 28.5820i) q^{32} +(-6.09542 + 27.1461i) q^{34} +67.3338i q^{37} +(-7.55706 + 33.6556i) q^{38} +44.0791 q^{41} +50.2937 q^{43} +(15.8691 - 33.5552i) q^{44} +(65.7915 + 14.7729i) q^{46} -31.1594 q^{47} -8.91003 q^{49} +(-31.7522 + 67.1400i) q^{52} -81.6070i q^{53} +(-39.9338 - 31.1616i) q^{56} +(-55.8449 - 12.5395i) q^{58} +19.2751i q^{59} -53.1563 q^{61} +(-10.2943 + 45.8462i) q^{62} +(15.5566 + 62.0805i) q^{64} +4.49911 q^{67} +(-23.7893 + 50.3025i) q^{68} -13.3360i q^{71} +40.8904i q^{73} +(-29.5037 + 131.396i) q^{74} +(-29.4939 + 62.3647i) q^{76} +58.7555i q^{77} -141.309i q^{79} +(86.0164 + 19.3142i) q^{82} -69.8503 q^{83} +(98.1438 + 22.0373i) q^{86} +(45.6702 - 58.5266i) q^{88} -46.3079 q^{89} -117.563i q^{91} +(121.913 + 57.6559i) q^{92} +(-60.8049 - 13.6532i) q^{94} -68.5543i q^{97} +(-17.3871 - 3.90412i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 20 q^{4}+O(q^{10}) $ 16 * q - 20 * q^4	$ 16 q - 20 q^{4} - 40 q^{14} + 68 q^{16} + 72 q^{26} + 128 q^{29} + 184 q^{34} + 32 q^{41} + 344 q^{44} + 304 q^{46} + 112 q^{49} - 232 q^{56} - 352 q^{61} + 220 q^{64} + 264 q^{74} - 48 q^{76} + 400 q^{86} + 160 q^{89} + 192 q^{94}+O(q^{100}) $ 16 * q - 20 * q^4 - 40 * q^14 + 68 * q^16 + 72 * q^26 + 128 * q^29 + 184 * q^34 + 32 * q^41 + 344 * q^44 + 304 * q^46 + 112 * q^49 - 232 * q^56 - 352 * q^61 + 220 * q^64 + 264 * q^74 - 48 * q^76 + 400 * q^86 + 160 * q^89 + 192 * 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 $

$2$	1.95141	+	0.438172i	0.975706	+	0.219086i
$2$	1.95141	+	0.438172i	0.975706	+	0.219086i
$3$		0			0
$3$		0			0
$4$	3.61601	+	1.71011i	0.904003	+	0.427526i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−6.33166			−0.904523			−0.452262	−	0.891885i	$-0.649383\pi$
$7$	−6.33166			−0.904523			−0.452262	+	0.891885i	$0.649383\pi$
$8$	6.30701	+	4.92155i	0.788376	+	0.615194i
$9$		0			0
$10$		0			0
$11$		−	9.27963i		−	0.843602i	−0.906688	−	0.421801i	$-0.861398\pi$
$11$		−	9.27963i		−	0.843602i	0.906688	−	0.421801i	$-0.138602\pi$
$12$		0			0
$13$			18.5674i			1.42826i	0.700012	+	0.714131i	$0.253178\pi$
$13$			18.5674i			1.42826i	−0.700012	+	0.714131i	$0.746822\pi$
$14$	−12.3557	−	2.77436i	−0.882549	−	0.198168i
$15$		0			0
$16$	10.1511	+	12.3675i	0.634442	+	0.772970i
$17$			13.9110i			0.818296i	0.912468	+	0.409148i	$0.134174\pi$
$17$			13.9110i			0.818296i	−0.912468	+	0.409148i	$0.865826\pi$
$18$		0			0
$19$			17.2468i			0.907727i	0.891071	+	0.453864i	$0.149955\pi$
$19$			17.2468i			0.907727i	−0.891071	+	0.453864i	$0.850045\pi$
$20$		0			0
$21$		0			0
$22$	4.06607	−	18.1084i	0.184821	−	0.823108i
$23$	33.7148			1.46586			0.732931	−	0.680303i	$-0.238152\pi$
$23$	33.7148			1.46586			0.732931	+	0.680303i	$0.238152\pi$
$24$		0			0
$25$		0			0
$26$	−8.13571	+	36.2327i	−0.312912	+	1.39356i
$27$		0			0
$28$	−22.8954	−	10.8278i	−0.817692	−	0.386708i
$29$	−28.6177			−0.986817			−0.493409	−	0.869798i	$-0.664249\pi$
$29$	−28.6177			−0.986817			−0.493409	+	0.869798i	$0.664249\pi$
$30$		0			0
$31$			23.4939i			0.757866i	0.925424	+	0.378933i	$0.123709\pi$
$31$			23.4939i			0.757866i	−0.925424	+	0.378933i	$0.876291\pi$
$32$	14.3898	+	28.5820i	0.449682	+	0.893189i
$33$		0			0
$34$	−6.09542	+	27.1461i	−0.179277	+	0.798416i
$35$		0			0
$36$		0			0
$37$			67.3338i			1.81983i	0.414793	+	0.909916i	$0.363854\pi$
$37$			67.3338i			1.81983i	−0.414793	+	0.909916i	$0.636146\pi$
$38$	−7.55706	+	33.6556i	−0.198870	+	0.885674i
$39$		0			0
$40$		0			0
$41$	44.0791			1.07510			0.537550	−	0.843232i	$-0.319350\pi$
$41$	44.0791			1.07510			0.537550	+	0.843232i	$0.319350\pi$
$42$		0			0
$43$	50.2937			1.16962			0.584811	−	0.811170i	$-0.301169\pi$
$43$	50.2937			1.16962			0.584811	+	0.811170i	$0.301169\pi$
$44$	15.8691	−	33.5552i	0.360662	−	0.762619i
$45$		0			0
$46$	65.7915	+	14.7729i	1.43025	+	0.321150i
$47$	−31.1594			−0.662967			−0.331483	−	0.943461i	$-0.607549\pi$
$47$	−31.1594			−0.662967			−0.331483	+	0.943461i	$0.607549\pi$
$48$		0			0
$49$	−8.91003			−0.181837
$50$		0			0
$51$		0			0
$52$	−31.7522	+	67.1400i	−0.610620	+	1.29115i
$53$		−	81.6070i		−	1.53975i	−0.638192	−	0.769877i	$-0.720318\pi$
$53$		−	81.6070i		−	1.53975i	0.638192	−	0.769877i	$-0.279682\pi$
$54$		0			0
$55$		0			0
$56$	−39.9338	−	31.1616i	−0.713104	−	0.556457i
$57$		0			0
$58$	−55.8449	−	12.5395i	−0.962843	−	0.216198i
$59$			19.2751i			0.326697i	0.986568	+	0.163349i	$0.0522296\pi$
$59$			19.2751i			0.326697i	−0.986568	+	0.163349i	$0.947770\pi$
$60$		0			0
$61$	−53.1563			−0.871415			−0.435707	−	0.900088i	$-0.643502\pi$
$61$	−53.1563			−0.871415			−0.435707	+	0.900088i	$0.643502\pi$
$62$	−10.2943	+	45.8462i	−0.166038	+	0.739455i
$63$		0			0
$64$	15.5566	+	62.0805i	0.243072	+	0.970008i
$65$		0			0
$66$		0			0
$67$	4.49911			0.0671509			0.0335754	−	0.999436i	$-0.489311\pi$
$67$	4.49911			0.0671509			0.0335754	+	0.999436i	$0.489311\pi$
$68$	−23.7893	+	50.3025i	−0.349843	+	0.739742i
$69$		0			0
$70$		0			0
$71$		−	13.3360i		−	0.187832i	−0.995580	−	0.0939158i	$-0.970062\pi$
$71$		−	13.3360i		−	0.187832i	0.995580	−	0.0939158i	$-0.0299385\pi$
$72$		0			0
$73$			40.8904i			0.560143i	0.959979	+	0.280071i	$0.0903581\pi$
$73$			40.8904i			0.560143i	−0.959979	+	0.280071i	$0.909642\pi$
$74$	−29.5037	+	131.396i	−0.398699	+	1.77562i
$75$		0			0
$76$	−29.4939	+	62.3647i	−0.388077	+	0.820588i
$77$			58.7555i			0.763058i
$78$		0			0
$79$		−	141.309i		−	1.78872i	−0.447352	−	0.894358i	$-0.647633\pi$
$79$		−	141.309i		−	1.78872i	0.447352	−	0.894358i	$-0.352367\pi$
$80$		0			0
$81$		0			0
$82$	86.0164	+	19.3142i	1.04898	+	0.235539i
$83$	−69.8503			−0.841570			−0.420785	−	0.907160i	$-0.638245\pi$
$83$	−69.8503			−0.841570			−0.420785	+	0.907160i	$0.638245\pi$
$84$		0			0
$85$		0			0
$86$	98.1438	+	22.0373i	1.14121	+	0.256248i
$87$		0			0
$88$	45.6702	−	58.5266i	0.518979	−	0.665076i
$89$	−46.3079			−0.520313			−0.260157	−	0.965566i	$-0.583774\pi$
$89$	−46.3079			−0.520313			−0.260157	+	0.965566i	$0.583774\pi$
$90$		0			0
$91$		−	117.563i		−	1.29190i
$92$	121.913	+	57.6559i	1.32514	+	0.626695i
$93$		0			0
$94$	−60.8049	−	13.6532i	−0.646860	−	0.145247i
$95$		0			0
$96$		0			0
$97$		−	68.5543i		−	0.706745i	−0.935483	−	0.353373i	$-0.885035\pi$
$97$		−	68.5543i		−	0.706745i	0.935483	−	0.353373i	$-0.114965\pi$
$98$	−17.3871	−	3.90412i	−0.177420	−	0.0398380i
$99$		0			0
$100$		0			0
$101$	43.3949			0.429653			0.214826	−	0.976652i	$-0.431081\pi$
$101$	43.3949			0.429653			0.214826	+	0.976652i	$0.431081\pi$
$102$		0			0
$103$	85.7919			0.832931			0.416465	−	0.909152i	$-0.363269\pi$
$103$	85.7919			0.832931			0.416465	+	0.909152i	$0.363269\pi$
$104$	−91.3805	+	117.105i	−0.878659	+	1.12601i
$105$		0			0
$106$	35.7579	−	159.249i	0.337338	−	1.50235i
$107$	183.075			1.71098			0.855491	−	0.517818i	$-0.173255\pi$
$107$	183.075			1.71098			0.855491	+	0.517818i	$0.173255\pi$
$108$		0			0
$109$	−81.4798			−0.747521			−0.373761	−	0.927525i	$-0.621932\pi$
$109$	−81.4798			−0.747521			−0.373761	+	0.927525i	$0.621932\pi$
$110$		0			0
$111$		0			0
$112$	−64.2732	−	78.3070i	−0.573868	−	0.699170i
$113$			172.814i			1.52933i	0.644429	+	0.764664i	$0.277095\pi$
$113$			172.814i			1.52933i	−0.644429	+	0.764664i	$0.722905\pi$
$114$		0			0
$115$		0			0
$116$	−103.482	−	48.9393i	−0.892086	−	0.421891i
$117$		0			0
$118$	−8.44582	+	37.6137i	−0.0715748	+	0.318760i
$119$		−	88.0800i		−	0.740168i
$120$		0			0
$121$	34.8885			0.288335
$122$	−103.730	−	23.2916i	−0.850244	−	0.190915i
$123$		0			0
$124$	−40.1770	+	84.9541i	−0.324008	+	0.685113i
$125$		0			0
$126$		0			0
$127$	22.3785			0.176208			0.0881041	−	0.996111i	$-0.471919\pi$
$127$	22.3785			0.176208			0.0881041	+	0.996111i	$0.471919\pi$
$128$	3.15546	+	127.961i	0.0246520	+	0.999696i
$129$		0			0
$130$		0			0
$131$			1.75315i			0.0133828i	0.999978	+	0.00669141i	$0.00212996\pi$
$131$			1.75315i			0.0133828i	−0.999978	+	0.00669141i	$0.997870\pi$
$132$		0			0
$133$		−	109.201i		−	0.821060i
$134$	8.77961	+	1.97138i	0.0655195	+	0.0147118i
$135$		0			0
$136$	−68.4639	+	87.7370i	−0.503411	+	0.645125i
$137$		−	19.5084i		−	0.142397i	−0.997462	−	0.0711987i	$-0.977318\pi$
$137$		−	19.5084i		−	0.142397i	0.997462	−	0.0711987i	$-0.0226824\pi$
$138$		0			0
$139$		−	257.370i		−	1.85158i	−0.378038	−	0.925790i	$-0.623401\pi$
$139$		−	257.370i		−	1.85158i	0.378038	−	0.925790i	$-0.376599\pi$
$140$		0			0
$141$		0			0
$142$	5.84348	−	26.0241i	0.0411512	−	0.183268i
$143$	172.299			1.20489
$144$		0			0
$145$		0			0
$146$	−17.9170	+	79.7940i	−0.122719	+	0.546534i
$147$		0			0
$148$	−115.148	+	243.480i	−0.778026	+	1.64513i
$149$	−111.673			−0.749486			−0.374743	−	0.927129i	$-0.622269\pi$
$149$	−111.673			−0.749486			−0.374743	+	0.927129i	$0.622269\pi$
$150$		0			0
$151$			6.45275i			0.0427335i	0.999772	+	0.0213667i	$0.00680176\pi$
$151$			6.45275i			0.0427335i	−0.999772	+	0.0213667i	$0.993198\pi$
$152$	−84.8811	+	108.776i	−0.558428	+	0.715630i
$153$		0			0
$154$	−25.7450	+	114.656i	−0.167175	+	0.744520i
$155$		0			0
$156$		0			0
$157$			75.9075i			0.483488i	0.970340	+	0.241744i	$0.0777193\pi$
$157$			75.9075i			0.483488i	−0.970340	+	0.241744i	$0.922281\pi$
$158$	61.9174	−	275.751i	0.391882	−	1.74526i
$159$		0			0
$160$		0			0
$161$	−213.471			−1.32591
$162$		0			0
$163$	249.298			1.52944			0.764719	−	0.644364i	$-0.222878\pi$
$163$	249.298			1.52944			0.764719	+	0.644364i	$0.222878\pi$
$164$	159.391	+	75.3799i	0.971893	+	0.459634i
$165$		0			0
$166$	−136.307	−	30.6064i	−0.821124	−	0.184376i
$167$	−79.1883			−0.474182			−0.237091	−	0.971487i	$-0.576194\pi$
$167$	−79.1883			−0.474182			−0.237091	+	0.971487i	$0.576194\pi$
$168$		0			0
$169$	−175.749			−1.03993
$170$		0			0
$171$		0			0
$172$	181.863	+	86.0076i	1.05734	+	0.500044i
$173$			27.7204i			0.160234i	0.996785	+	0.0801168i	$0.0255293\pi$
$173$			27.7204i			0.160234i	−0.996785	+	0.0801168i	$0.974471\pi$
$174$		0			0
$175$		0			0
$176$	114.766	−	94.1982i	0.652080	−	0.535217i
$177$		0			0
$178$	−90.3657	−	20.2908i	−0.507673	−	0.113993i
$179$		−	204.324i		−	1.14147i	−0.821133	−	0.570737i	$-0.806658\pi$
$179$		−	204.324i		−	1.14147i	0.821133	−	0.570737i	$-0.193342\pi$
$180$		0			0
$181$	−49.8262			−0.275283			−0.137641	−	0.990482i	$-0.543952\pi$
$181$	−49.8262			−0.275283			−0.137641	+	0.990482i	$0.543952\pi$
$182$	51.5126	−	229.413i	0.283036	−	1.26051i
$183$		0			0
$184$	212.640	+	165.929i	1.15565	+	0.901790i
$185$		0			0
$186$		0			0
$187$	129.089			0.690317
$188$	−112.673	−	53.2859i	−0.599324	−	0.283436i
$189$		0			0
$190$		0			0
$191$		−	1.13703i		−	0.00595301i	−0.999996	−	0.00297651i	$-0.999053\pi$
$191$		−	1.13703i		−	0.00595301i	0.999996	−	0.00297651i	$-0.000947453\pi$
$192$		0			0
$193$		−	76.6452i		−	0.397126i	−0.980088	−	0.198563i	$-0.936373\pi$
$193$		−	76.6452i		−	0.397126i	0.980088	−	0.198563i	$-0.0636274\pi$
$194$	30.0385	−	133.778i	0.154838	−	0.689575i
$195$		0			0
$196$	−32.2188	−	15.2371i	−0.164382	−	0.0777403i
$197$			134.496i			0.682719i	0.939933	+	0.341359i	$0.110887\pi$
$197$			134.496i			0.682719i	−0.939933	+	0.341359i	$0.889113\pi$
$198$		0			0
$199$			176.014i			0.884491i	0.896894	+	0.442245i	$0.145818\pi$
$199$			176.014i			0.884491i	−0.896894	+	0.442245i	$0.854182\pi$
$200$		0			0
$201$		0			0
$202$	84.6813	+	19.0144i	0.419214	+	0.0941308i
$203$	181.198			0.892599
$204$		0			0
$205$		0			0
$206$	167.415	+	37.5916i	0.812695	+	0.182483i
$207$		0			0
$208$	−229.633	+	188.479i	−1.10400	+	0.906150i
$209$	160.044			0.765761
$210$		0			0
$211$		−	218.087i		−	1.03359i	−0.856110	−	0.516793i	$-0.827126\pi$
$211$		−	218.087i		−	1.03359i	0.856110	−	0.516793i	$-0.172874\pi$
$212$	139.557	−	295.092i	0.658286	−	1.39194i
$213$		0			0
$214$	357.255	+	80.2183i	1.66941	+	0.374852i
$215$		0			0
$216$		0			0
$217$		−	148.755i		−	0.685508i
$218$	−159.001	−	35.7021i	−0.729361	−	0.163771i
$219$		0			0
$220$		0			0
$221$	−258.292			−1.16874
$222$		0			0
$223$	−328.579			−1.47345			−0.736724	−	0.676193i	$-0.763628\pi$
$223$	−328.579			−1.47345			−0.736724	+	0.676193i	$0.763628\pi$
$224$	−91.1115	−	180.972i	−0.406748	−	0.807910i
$225$		0			0
$226$	−75.7222	+	337.231i	−0.335054	+	1.49217i
$227$	−157.649			−0.694491			−0.347245	−	0.937774i	$-0.612883\pi$
$227$	−157.649			−0.694491			−0.347245	+	0.937774i	$0.612883\pi$
$228$		0			0
$229$	273.148			1.19279			0.596393	−	0.802692i	$-0.296600\pi$
$229$	273.148			1.19279			0.596393	+	0.802692i	$0.296600\pi$
$230$		0			0
$231$		0			0
$232$	−180.492	−	140.844i	−0.777983	−	0.607084i
$233$		−	108.746i		−	0.466720i	−0.972390	−	0.233360i	$-0.925028\pi$
$233$		−	108.746i		−	0.466720i	0.972390	−	0.233360i	$-0.0749721\pi$
$234$		0			0
$235$		0			0
$236$	−32.9625	+	69.6992i	−0.139672	+	0.295335i
$237$		0			0
$238$	38.5942	−	171.880i	0.162160	−	0.722186i
$239$		−	178.994i		−	0.748927i	−0.927242	−	0.374464i	$-0.877827\pi$
$239$		−	178.994i		−	0.748927i	0.927242	−	0.374464i	$-0.122173\pi$
$240$		0			0
$241$	358.623			1.48806			0.744032	−	0.668144i	$-0.232911\pi$
$241$	358.623			1.48806			0.744032	+	0.668144i	$0.232911\pi$
$242$	68.0819	+	15.2872i	0.281330	+	0.0631701i
$243$		0			0
$244$	−192.214	−	90.9029i	−0.787762	−	0.372553i
$245$		0			0
$246$		0			0
$247$	−320.229			−1.29647
$248$	−115.626	+	148.176i	−0.466235	+	0.597483i
$249$		0			0
$250$		0			0
$251$		−	306.220i		−	1.22000i	−0.792401	−	0.610000i	$-0.791169\pi$
$251$		−	306.220i		−	1.22000i	0.792401	−	0.610000i	$-0.208831\pi$
$252$		0			0
$253$		−	312.861i		−	1.23660i
$254$	43.6696	+	9.80560i	0.171927	+	0.0386047i
$255$		0			0
$256$	−49.9113	+	251.087i	−0.194966	+	0.980810i
$257$		−	251.062i		−	0.976895i	−0.872593	−	0.488447i	$-0.837563\pi$
$257$		−	251.062i		−	0.976895i	0.872593	−	0.488447i	$-0.162437\pi$
$258$		0			0
$259$		−	426.335i		−	1.64608i
$260$		0			0
$261$		0			0
$262$	−0.768181	+	3.42112i	−0.00293199	+	0.0130577i
$263$	48.7645			0.185416			0.0927082	−	0.995693i	$-0.470448\pi$
$263$	48.7645			0.185416			0.0927082	+	0.995693i	$0.470448\pi$
$264$		0			0
$265$		0			0
$266$	47.8488	−	213.096i	0.179883	−	0.801113i
$267$		0			0
$268$	16.2688	+	7.69395i	0.0607046	+	0.0287088i
$269$	148.696			0.552772			0.276386	−	0.961047i	$-0.410863\pi$
$269$	148.696			0.552772			0.276386	+	0.961047i	$0.410863\pi$
$270$		0			0
$271$		−	83.3415i		−	0.307533i	−0.988107	−	0.153767i	$-0.950860\pi$
$271$		−	83.3415i		−	0.307533i	0.988107	−	0.153767i	$-0.0491404\pi$
$272$	−172.045	+	141.212i	−0.632519	+	0.519162i
$273$		0			0
$274$	8.54805	−	38.0690i	0.0311972	−	0.138938i
$275$		0			0
$276$		0			0
$277$		−	144.080i		−	0.520146i	−0.965589	−	0.260073i	$-0.916253\pi$
$277$		−	144.080i		−	0.520146i	0.965589	−	0.260073i	$-0.0837466\pi$
$278$	112.772	−	502.234i	0.405655	−	1.80660i
$279$		0			0
$280$		0			0
$281$	343.671			1.22303			0.611514	−	0.791233i	$-0.290561\pi$
$281$	343.671			1.22303			0.611514	+	0.791233i	$0.290561\pi$
$282$		0			0
$283$	314.955			1.11292			0.556458	−	0.830876i	$-0.312160\pi$
$283$	314.955			1.11292			0.556458	+	0.830876i	$0.312160\pi$
$284$	22.8061	−	48.2233i	0.0803030	−	0.169800i
$285$		0			0
$286$	336.225	+	75.4964i	1.17561	+	0.263973i
$287$	−279.094			−0.972453
$288$		0			0
$289$	95.4831			0.330391
$290$		0			0
$291$		0			0
$292$	−69.9269	+	147.860i	−0.239476	+	0.506371i
$293$			6.55421i			0.0223693i	0.999937	+	0.0111847i	$0.00356026\pi$
$293$			6.55421i			0.0223693i	−0.999937	+	0.0111847i	$0.996440\pi$
$294$		0			0
$295$		0			0
$296$	−331.387	+	424.674i	−1.11955	+	1.43471i
$297$		0			0
$298$	−217.921	−	48.9321i	−0.731278	−	0.164202i
$299$			625.997i			2.09364i
$300$		0			0
$301$	−318.443			−1.05795
$302$	−2.82741	+	12.5920i	−0.00936229	+	0.0416953i
$303$		0			0
$304$	−213.300	+	175.074i	−0.701646	+	0.575900i
$305$		0			0
$306$		0			0
$307$	−354.559			−1.15492			−0.577458	−	0.816420i	$-0.695955\pi$
$307$	−354.559			−1.15492			−0.577458	+	0.816420i	$0.695955\pi$
$308$	−100.478	+	212.460i	−0.326228	+	0.689807i
$309$		0			0
$310$		0			0
$311$			193.387i			0.621823i	0.950439	+	0.310912i	$0.100634\pi$
$311$			193.387i			0.621823i	−0.950439	+	0.310912i	$0.899366\pi$
$312$		0			0
$313$		−	23.5224i		−	0.0751514i	−0.999294	−	0.0375757i	$-0.988036\pi$
$313$		−	23.5224i		−	0.0751514i	0.999294	−	0.0375757i	$-0.0119635\pi$
$314$	−33.2605	+	148.127i	−0.105925	+	0.471742i
$315$		0			0
$316$	241.653	−	510.973i	0.764724	−	1.61700i
$317$		−	214.004i		−	0.675092i	−0.941309	−	0.337546i	$-0.890403\pi$
$317$		−	214.004i		−	0.675092i	0.941309	−	0.337546i	$-0.109597\pi$
$318$		0			0
$319$			265.562i			0.832481i
$320$		0			0
$321$		0			0
$322$	−416.570	−	93.5369i	−1.29369	−	0.290487i
$323$	−239.921			−0.742790
$324$		0			0
$325$		0			0
$326$	486.483	+	109.235i	1.49228	+	0.335078i
$327$		0			0
$328$	278.007	+	216.938i	0.847583	+	0.661395i
$329$	197.291			0.599669
$330$		0			0
$331$			412.454i			1.24609i	0.782188	+	0.623043i	$0.214104\pi$
$331$			412.454i			1.24609i	−0.782188	+	0.623043i	$0.785896\pi$
$332$	−252.579	−	119.451i	−0.760782	−	0.359793i
$333$		0			0
$334$	−154.529	−	34.6981i	−0.462662	−	0.103886i
$335$		0			0
$336$		0			0
$337$		−	103.268i		−	0.306433i	−0.988193	−	0.153216i	$-0.951037\pi$
$337$		−	103.268i		−	0.306433i	0.988193	−	0.153216i	$-0.0489631\pi$
$338$	−342.958	−	77.0081i	−1.01467	−	0.227835i
$339$		0			0
$340$		0			0
$341$	218.014			0.639338
$342$		0			0
$343$	366.667			1.06900
$344$	317.203	+	247.523i	0.922102	+	0.719545i
$345$		0			0
$346$	−12.1463	+	54.0939i	−0.0351049	+	0.156341i
$347$	−153.211			−0.441531			−0.220766	−	0.975327i	$-0.570856\pi$
$347$	−153.211			−0.441531			−0.220766	+	0.975327i	$0.570856\pi$
$348$		0			0
$349$	84.7317			0.242784			0.121392	−	0.992605i	$-0.461264\pi$
$349$	84.7317			0.242784			0.121392	+	0.992605i	$0.461264\pi$
$350$		0			0
$351$		0			0
$352$	265.231	−	133.532i	0.753496	−	0.379353i
$353$		−	256.065i		−	0.725396i	−0.931907	−	0.362698i	$-0.881856\pi$
$353$		−	256.065i		−	0.725396i	0.931907	−	0.362698i	$-0.118144\pi$
$354$		0			0
$355$		0			0
$356$	−167.450	−	79.1914i	−0.470365	−	0.222448i
$357$		0			0
$358$	89.5289	−	398.720i	0.250081	−	1.11374i
$359$		−	667.258i		−	1.85866i	−0.369253	−	0.929329i	$-0.620386\pi$
$359$		−	667.258i		−	1.85866i	0.369253	−	0.929329i	$-0.379614\pi$
$360$		0			0
$361$	63.5473			0.176031
$362$	−97.2314	−	21.8324i	−0.268595	−	0.0603106i
$363$		0			0
$364$	201.044	−	425.108i	0.552320	−	1.16788i
$365$		0			0
$366$		0			0
$367$	245.301			0.668396			0.334198	−	0.942503i	$-0.391535\pi$
$367$	245.301			0.668396			0.334198	+	0.942503i	$0.391535\pi$
$368$	342.242	+	416.969i	0.930005	+	1.13307i
$369$		0			0
$370$		0			0
$371$			516.708i			1.39274i
$372$		0			0
$373$			698.787i			1.87342i	0.350101	+	0.936712i	$0.386147\pi$
$373$			698.787i			1.87342i	−0.350101	+	0.936712i	$0.613853\pi$
$374$	251.906	+	56.5632i	0.673546	+	0.151239i
$375$		0			0
$376$	−196.523	−	153.353i	−0.522667	−	0.407853i
$377$		−	531.357i		−	1.40943i
$378$		0			0
$379$		−	208.691i		−	0.550636i	−0.961353	−	0.275318i	$-0.911217\pi$
$379$		−	208.691i		−	0.550636i	0.961353	−	0.275318i	$-0.0887831\pi$
$380$		0			0
$381$		0			0
$382$	0.498212	−	2.21880i	0.00130422	−	0.00580839i
$383$	−156.524			−0.408680			−0.204340	−	0.978900i	$-0.565505\pi$
$383$	−156.524			−0.408680			−0.204340	+	0.978900i	$0.565505\pi$
$384$		0			0
$385$		0			0
$386$	33.5838	−	149.566i	0.0870046	−	0.387478i
$387$		0			0
$388$	117.235	−	247.893i	0.302152	−	0.638900i
$389$	386.588			0.993801			0.496900	−	0.867808i	$-0.334471\pi$
$389$	386.588			0.993801			0.496900	+	0.867808i	$0.334471\pi$
$390$		0			0
$391$			469.008i			1.19951i
$392$	−56.1956	−	43.8512i	−0.143356	−	0.111865i
$393$		0			0
$394$	−58.9322	+	262.456i	−0.149574	+	0.666133i
$395$		0			0
$396$		0			0
$397$			561.155i			1.41349i	0.707470	+	0.706744i	$0.249837\pi$
$397$			561.155i			1.41349i	−0.707470	+	0.706744i	$0.750163\pi$
$398$	−77.1242	+	343.475i	−0.193779	+	0.863002i
$399$		0			0
$400$		0			0
$401$	−16.9333			−0.0422276			−0.0211138	−	0.999777i	$-0.506721\pi$
$401$	−16.9333			−0.0422276			−0.0211138	+	0.999777i	$0.506721\pi$
$402$		0			0
$403$	−436.220			−1.08243
$404$	156.917	+	74.2099i	0.388407	+	0.183688i
$405$		0			0
$406$	353.591	+	79.3957i	0.870914	+	0.195556i
$407$	624.832			1.53521
$408$		0			0
$409$	−258.490			−0.632006			−0.316003	−	0.948758i	$-0.602341\pi$
$409$	−258.490			−0.632006			−0.316003	+	0.948758i	$0.602341\pi$
$410$		0			0
$411$		0			0
$412$	310.224	+	146.713i	0.752972	+	0.356100i
$413$		−	122.044i		−	0.295505i
$414$		0			0
$415$		0			0
$416$	−530.694	+	267.182i	−1.27571	+	0.642264i
$417$		0			0
$418$	312.312	+	70.1267i	0.747157	+	0.167767i
$419$			258.917i			0.617941i	0.951072	+	0.308970i	$0.0999844\pi$
$419$			258.917i			0.617941i	−0.951072	+	0.308970i	$0.900016\pi$
$420$		0			0
$421$	97.4654			0.231509			0.115755	−	0.993278i	$-0.463071\pi$
$421$	97.4654			0.231509			0.115755	+	0.993278i	$0.463071\pi$
$422$	95.5594	−	425.577i	0.226444	−	1.00848i
$423$		0			0
$424$	401.633	−	514.696i	0.947248	−	1.21390i
$425$		0			0
$426$		0			0
$427$	336.568			0.788215
$428$	662.002	+	313.078i	1.54673	+	0.731490i
$429$		0			0
$430$		0			0
$431$		−	389.968i		−	0.904799i	−0.891815	−	0.452399i	$-0.850568\pi$
$431$		−	389.968i		−	0.904799i	0.891815	−	0.452399i	$-0.149432\pi$
$432$		0			0
$433$			275.893i			0.637166i	0.947895	+	0.318583i	$0.103207\pi$
$433$			275.893i			0.637166i	−0.947895	+	0.318583i	$0.896793\pi$
$434$	65.1803	−	290.283i	0.150185	−	0.668854i
$435$		0			0
$436$	−294.632	−	139.339i	−0.675761	−	0.319585i
$437$			581.473i			1.33060i
$438$		0			0
$439$			446.143i			1.01627i	0.861277	+	0.508136i	$0.169665\pi$
$439$			446.143i			1.01627i	−0.861277	+	0.508136i	$0.830335\pi$
$440$		0			0
$441$		0			0
$442$	−504.034	−	113.176i	−1.14035	−	0.256055i
$443$	−794.679			−1.79386			−0.896929	−	0.442174i	$-0.854207\pi$
$443$	−794.679			−1.79386			−0.896929	+	0.442174i	$0.854207\pi$
$444$		0			0
$445$		0			0
$446$	−641.193	−	143.974i	−1.43765	−	0.322812i
$447$		0			0
$448$	−98.4993	−	393.073i	−0.219865	−	0.877395i
$449$	−750.226			−1.67088			−0.835441	−	0.549581i	$-0.814788\pi$
$449$	−750.226			−1.67088			−0.835441	+	0.549581i	$0.814788\pi$
$450$		0			0
$451$		−	409.037i		−	0.906957i
$452$	−295.530	+	624.898i	−0.653828	+	1.38252i
$453$		0			0
$454$	−307.639	−	69.0775i	−0.677619	−	0.152153i
$455$		0			0
$456$		0			0
$457$		−	101.092i		−	0.221209i	−0.993865	−	0.110604i	$-0.964721\pi$
$457$		−	101.092i		−	0.221209i	0.993865	−	0.110604i	$-0.0352787\pi$
$458$	533.024	+	119.686i	1.16381	+	0.261323i
$459$		0			0
$460$		0			0
$461$	4.48690			0.00973297			0.00486648	−	0.999988i	$-0.498451\pi$
$461$	4.48690			0.00973297			0.00486648	+	0.999988i	$0.498451\pi$
$462$		0			0
$463$	−515.108			−1.11254			−0.556272	−	0.831000i	$-0.687769\pi$
$463$	−515.108			−1.11254			−0.556272	+	0.831000i	$0.687769\pi$
$464$	−290.500	−	353.930i	−0.626079	−	0.762780i
$465$		0			0
$466$	47.6493	−	212.208i	0.102252	−	0.455382i
$467$	295.498			0.632758			0.316379	−	0.948633i	$-0.397533\pi$
$467$	295.498			0.632758			0.316379	+	0.948633i	$0.397533\pi$
$468$		0			0
$469$	−28.4869			−0.0607396
$470$		0			0
$471$		0			0
$472$	−94.8637	+	121.568i	−0.200982	+	0.257560i
$473$		−	466.707i		−	0.986696i
$474$		0			0
$475$		0			0
$476$	150.626	−	318.498i	0.316441	−	0.669114i
$477$		0			0
$478$	78.4299	−	349.290i	0.164079	−	0.730732i
$479$			273.155i			0.570260i	0.958489	+	0.285130i	$0.0920368\pi$
$479$			273.155i			0.570260i	−0.958489	+	0.285130i	$0.907963\pi$
$480$		0			0
$481$	−1250.21			−2.59920
$482$	699.822	+	157.139i	1.45191	+	0.326014i
$483$		0			0
$484$	126.157	+	59.6631i	0.260656	+	0.123271i
$485$		0			0
$486$		0			0
$487$	357.751			0.734601			0.367301	−	0.930102i	$-0.380282\pi$
$487$	357.751			0.734601			0.367301	+	0.930102i	$0.380282\pi$
$488$	−335.257	−	261.612i	−0.687002	−	0.536089i
$489$		0			0
$490$		0			0
$491$			422.379i			0.860242i	0.902771	+	0.430121i	$0.141529\pi$
$491$			422.379i			0.860242i	−0.902771	+	0.430121i	$0.858471\pi$
$492$		0			0
$493$		−	398.102i		−	0.807509i
$494$	−624.898	−	140.315i	−1.26498	−	0.284039i
$495$		0			0
$496$	−290.561	+	238.488i	−0.585808	+	0.480822i
$497$			84.4394i			0.169898i
$498$		0			0
$499$			207.096i			0.415021i	0.978233	+	0.207511i	$0.0665362\pi$
$499$			207.096i			0.415021i	−0.978233	+	0.207511i	$0.933464\pi$
$500$		0			0
$501$		0			0
$502$	134.177	−	597.562i	0.267285	−	1.19036i
$503$	702.853			1.39732			0.698661	−	0.715452i	$-0.253779\pi$
$503$	702.853			1.39732			0.698661	+	0.715452i	$0.253779\pi$
$504$		0			0
$505$		0			0
$506$	137.087	−	610.520i	0.270923	−	1.20656i
$507$		0			0
$508$	80.9207	+	38.2695i	0.159293	+	0.0753337i
$509$	−389.029			−0.764300			−0.382150	−	0.924100i	$-0.624816\pi$
$509$	−389.029			−0.764300			−0.382150	+	0.924100i	$0.624816\pi$
$510$		0			0
$511$		−	258.904i		−	0.506662i
$512$	−207.417	+	468.105i	−0.405111	+	0.914267i
$513$		0			0
$514$	110.008	−	489.925i	0.214024	−	0.953162i
$515$		0			0
$516$		0			0
$517$			289.148i			0.559280i
$518$	186.808	−	831.954i	0.360633	−	1.60609i
$519$		0			0
$520$		0			0
$521$	151.753			0.291273			0.145637	−	0.989338i	$-0.453477\pi$
$521$	151.753			0.291273			0.145637	+	0.989338i	$0.453477\pi$
$522$		0			0
$523$	−557.762			−1.06647			−0.533234	−	0.845968i	$-0.679023\pi$
$523$	−557.762			−1.06647			−0.533234	+	0.845968i	$0.679023\pi$
$524$	−2.99807	+	6.33941i	−0.00572151	+	0.0120981i
$525$		0			0
$526$	95.1596	+	21.3672i	0.180912	+	0.0406221i
$527$	−326.824			−0.620159
$528$		0			0
$529$	607.689			1.14875
$530$		0			0
$531$		0			0
$532$	186.745	−	394.872i	0.351025	−	0.742241i
$533$			818.435i			1.53552i
$534$		0			0
$535$		0			0
$536$	28.3759	+	22.1426i	0.0529401	+	0.0413108i
$537$		0			0
$538$	290.166	+	65.1542i	0.539342	+	0.121104i
$539$			82.6818i			0.153398i
$540$		0			0
$541$	340.979			0.630275			0.315137	−	0.949046i	$-0.397949\pi$
$541$	340.979			0.630275			0.315137	+	0.949046i	$0.397949\pi$
$542$	36.5179	−	162.633i	0.0673761	−	0.300062i
$543$		0			0
$544$	−397.606	+	200.177i	−0.730893	+	0.367973i
$545$		0			0
$546$		0			0
$547$	−113.651			−0.207771			−0.103885	−	0.994589i	$-0.533128\pi$
$547$	−113.651			−0.207771			−0.103885	+	0.994589i	$0.533128\pi$
$548$	33.3615	−	70.5428i	0.0608787	−	0.128728i
$549$		0			0
$550$		0			0
$551$		−	493.564i		−	0.895761i
$552$		0			0
$553$			894.718i			1.61794i
$554$	63.1319	−	281.160i	0.113957	−	0.507509i
$555$		0			0
$556$	440.129	−	930.651i	0.791599	−	1.67383i
$557$			233.232i			0.418728i	0.977838	+	0.209364i	$0.0671394\pi$
$557$			233.232i			0.418728i	−0.977838	+	0.209364i	$0.932861\pi$
$558$		0			0
$559$			933.825i			1.67053i
$560$		0			0
$561$		0			0
$562$	670.644	+	150.587i	1.19332	+	0.267948i
$563$	−167.786			−0.298021			−0.149011	−	0.988836i	$-0.547609\pi$
$563$	−167.786			−0.298021			−0.149011	+	0.988836i	$0.547609\pi$
$564$		0			0
$565$		0			0
$566$	614.607	+	138.004i	1.08588	+	0.243824i
$567$		0			0
$568$	65.6341	−	84.1105i	0.115553	−	0.148082i
$569$	381.089			0.669752			0.334876	−	0.942262i	$-0.391306\pi$
$569$	381.089			0.669752			0.334876	+	0.942262i	$0.391306\pi$
$570$		0			0
$571$			453.871i			0.794870i	0.917630	+	0.397435i	$0.130100\pi$
$571$			453.871i			0.794870i	−0.917630	+	0.397435i	$0.869900\pi$
$572$	623.034	+	294.649i	1.08922	+	0.515120i
$573$		0			0
$574$	−544.627	−	122.291i	−0.948828	−	0.213051i
$575$		0			0
$576$		0			0
$577$		−	688.294i		−	1.19288i	−0.802656	−	0.596442i	$-0.796581\pi$
$577$		−	688.294i		−	1.19288i	0.802656	−	0.596442i	$-0.203419\pi$
$578$	186.327	+	41.8380i	0.322365	+	0.0723841i
$579$		0			0
$580$		0			0
$581$	442.269			0.761220
$582$		0			0
$583$	−757.282			−1.29894
$584$	−201.244	+	257.896i	−0.344597	+	0.441603i
$585$		0			0
$586$	−2.87187	+	12.7900i	−0.00490080	+	0.0218259i
$587$	−249.163			−0.424468			−0.212234	−	0.977219i	$-0.568074\pi$
$587$	−249.163			−0.424468			−0.212234	+	0.977219i	$0.568074\pi$
$588$		0			0
$589$	−405.194			−0.687936
$590$		0			0
$591$		0			0
$592$	−832.752	+	683.510i	−1.40668	+	1.15458i
$593$			163.937i			0.276454i	0.990401	+	0.138227i	$0.0441404\pi$
$593$			163.937i			0.276454i	−0.990401	+	0.138227i	$0.955860\pi$
$594$		0			0
$595$		0			0
$596$	−403.812	−	190.973i	−0.677538	−	0.320425i
$597$		0			0
$598$	−274.294	+	1221.58i	−0.458686	+	2.04277i
$599$			170.412i			0.284494i	0.989831	+	0.142247i	$0.0454327\pi$
$599$			170.412i			0.284494i	−0.989831	+	0.142247i	$0.954567\pi$
$600$		0			0
$601$	1119.87			1.86335			0.931674	−	0.363295i	$-0.118348\pi$
$601$	1119.87			1.86335			0.931674	+	0.363295i	$0.118348\pi$
$602$	−621.413	−	139.533i	−1.03225	−	0.231782i
$603$		0			0
$604$	−11.0349	+	23.3332i	−0.0182697	+	0.0386312i
$605$		0			0
$606$		0			0
$607$	660.957			1.08889			0.544445	−	0.838796i	$-0.316740\pi$
$607$	660.957			1.08889			0.544445	+	0.838796i	$0.316740\pi$
$608$	−492.949	+	248.179i	−0.810772	+	0.408189i
$609$		0			0
$610$		0			0
$611$		−	578.550i		−	0.946890i
$612$		0			0
$613$		−	179.315i		−	0.292520i	−0.989246	−	0.146260i	$-0.953276\pi$
$613$		−	179.315i		−	0.292520i	0.989246	−	0.146260i	$-0.0467236\pi$
$614$	−691.891	−	155.358i	−1.12686	−	0.253026i
$615$		0			0
$616$	−289.168	+	370.571i	−0.469429	+	0.601576i
$617$		−	63.6752i		−	0.103201i	−0.998668	−	0.0516007i	$-0.983568\pi$
$617$		−	63.6752i		−	0.103201i	0.998668	−	0.0516007i	$-0.0164323\pi$
$618$		0			0
$619$			872.350i			1.40929i	0.709561	+	0.704644i	$0.248893\pi$
$619$			872.350i			1.40929i	−0.709561	+	0.704644i	$0.751107\pi$
$620$		0			0
$621$		0			0
$622$	−84.7367	+	377.378i	−0.136233	+	0.606716i
$623$	293.206			0.470636
$624$		0			0
$625$		0			0
$626$	10.3068	−	45.9019i	0.0164646	−	0.0733257i
$627$		0			0
$628$	−129.810	+	274.483i	−0.206704	+	0.437074i
$629$	−936.682			−1.48916
$630$		0			0
$631$			340.783i			0.540068i	0.962851	+	0.270034i	$0.0870349\pi$
$631$			340.783i			0.540068i	−0.962851	+	0.270034i	$0.912965\pi$
$632$	695.458	−	891.234i	1.10041	−	1.41018i
$633$		0			0
$634$	93.7705	−	417.610i	0.147903	−	0.658691i
$635$		0			0
$636$		0			0
$637$		−	165.436i		−	0.259712i
$638$	−116.362	+	518.220i	−0.182385	+	0.812257i
$639$		0			0
$640$		0			0
$641$	−766.210			−1.19534			−0.597668	−	0.801744i	$-0.703906\pi$
$641$	−766.210			−1.19534			−0.597668	+	0.801744i	$0.703906\pi$
$642$		0			0
$643$	1163.47			1.80943			0.904717	−	0.426014i	$-0.140083\pi$
$643$	1163.47			1.80943			0.904717	+	0.426014i	$0.140083\pi$
$644$	−771.913	−	365.058i	−1.19862	−	0.566860i
$645$		0			0
$646$	−468.185	−	105.127i	−0.724744	−	0.162735i
$647$	740.530			1.14456			0.572279	−	0.820059i	$-0.306059\pi$
$647$	740.530			1.14456			0.572279	+	0.820059i	$0.306059\pi$
$648$		0			0
$649$	178.866			0.275603
$650$		0			0
$651$		0			0
$652$	901.465	+	426.326i	1.38262	+	0.653875i
$653$		−	109.569i		−	0.167793i	−0.996474	−	0.0838967i	$-0.973263\pi$
$653$		−	109.569i		−	0.167793i	0.996474	−	0.0838967i	$-0.0267366\pi$
$654$		0			0
$655$		0			0
$656$	447.450	+	545.149i	0.682089	+	0.831020i
$657$		0			0
$658$	384.996	+	86.4473i	0.585100	+	0.131379i
$659$			723.214i			1.09744i	0.836006	+	0.548721i	$0.184885\pi$
$659$			723.214i			1.09744i	−0.836006	+	0.548721i	$0.815115\pi$
$660$		0			0
$661$	700.333			1.05951			0.529753	−	0.848152i	$-0.322285\pi$
$661$	700.333			1.05951			0.529753	+	0.848152i	$0.322285\pi$
$662$	−180.726	+	804.868i	−0.273000	+	1.21581i
$663$		0			0
$664$	−440.546	−	343.772i	−0.663473	−	0.517729i
$665$		0			0
$666$		0			0
$667$	−964.841			−1.44654
$668$	−286.346	−	135.420i	−0.428662	−	0.202725i
$669$		0			0
$670$		0			0
$671$			493.271i			0.735128i
$672$		0			0
$673$		−	1221.18i		−	1.81454i	−0.420552	−	0.907269i	$-0.638163\pi$
$673$		−	1221.18i		−	1.81454i	0.420552	−	0.907269i	$-0.361837\pi$
$674$	45.2490	−	201.518i	0.0671350	−	0.298988i
$675$		0			0
$676$	−635.509	−	300.549i	−0.940103	−	0.444599i
$677$			989.373i			1.46141i	0.682695	+	0.730704i	$0.260808\pi$
$677$			989.373i			1.46141i	−0.682695	+	0.730704i	$0.739192\pi$
$678$		0			0
$679$			434.063i			0.639268i
$680$		0			0
$681$		0			0
$682$	425.435	+	95.5276i	0.623806	+	0.140070i
$683$	−307.312			−0.449945			−0.224972	−	0.974365i	$-0.572229\pi$
$683$	−307.312			−0.449945			−0.224972	+	0.974365i	$0.572229\pi$
$684$		0			0
$685$		0			0
$686$	715.518	+	160.663i	1.04303	+	0.234203i
$687$		0			0
$688$	510.536	+	622.009i	0.742058	+	0.904083i
$689$	1515.23			2.19917
$690$		0			0
$691$		−	893.378i		−	1.29288i	−0.762966	−	0.646438i	$-0.776258\pi$
$691$		−	893.378i		−	1.29288i	0.762966	−	0.646438i	$-0.223742\pi$
$692$	−47.4048	+	100.237i	−0.0685041	+	0.144852i
$693$		0			0
$694$	−298.978	−	67.1329i	−0.430805	−	0.0967332i
$695$		0			0
$696$		0			0
$697$			613.186i			0.879750i
$698$	165.346	+	37.1270i	0.236886	+	0.0531906i
$699$		0			0
$700$		0			0
$701$	−1127.42			−1.60830			−0.804149	−	0.594428i	$-0.797378\pi$
$701$	−1127.42			−1.60830			−0.804149	+	0.594428i	$0.797378\pi$
$702$		0			0
$703$	−1161.29			−1.65191
$704$	576.084	−	144.360i	0.818301	−	0.205056i
$705$		0			0
$706$	112.200	−	499.688i	0.158924	−	0.707773i
$707$	−274.762			−0.388631
$708$		0			0
$709$	−1093.27			−1.54199			−0.770997	−	0.636839i	$-0.780242\pi$
$709$	−1093.27			−1.54199			−0.770997	+	0.636839i	$0.780242\pi$
$710$		0			0
$711$		0			0
$712$	−292.064	−	227.907i	−0.410202	−	0.320094i
$713$			792.091i			1.11093i
$714$		0			0
$715$		0			0
$716$	349.415	−	738.837i	0.488010	−	1.03190i
$717$		0			0
$718$	292.374	−	1302.10i	0.407206	−	1.81350i
$719$			769.690i			1.07050i	0.844693	+	0.535251i	$0.179783\pi$
$719$			769.690i			1.07050i	−0.844693	+	0.535251i	$0.820217\pi$
$720$		0			0
$721$	−543.205			−0.753405
$722$	124.007	+	27.8446i	0.171755	+	0.0385660i
$723$		0			0
$724$	−180.172	−	85.2081i	−0.248857	−	0.117691i
$725$		0			0
$726$		0			0
$727$	−295.050			−0.405846			−0.202923	−	0.979195i	$-0.565044\pi$
$727$	−295.050			−0.405846			−0.202923	+	0.979195i	$0.565044\pi$
$728$	578.591	−	741.468i	0.794767	−	1.01850i
$729$		0			0
$730$		0			0
$731$			699.638i			0.957097i
$732$		0			0
$733$			261.200i			0.356344i	0.983999	+	0.178172i	$0.0570184\pi$
$733$			261.200i			0.356344i	−0.983999	+	0.178172i	$0.942982\pi$
$734$	478.684	+	107.484i	0.652158	+	0.146436i
$735$		0			0
$736$	485.150	+	963.638i	0.659172	+	1.30929i
$737$		−	41.7501i		−	0.0566487i
$738$		0			0
$739$		−	482.679i		−	0.653151i	−0.945171	−	0.326576i	$-0.894105\pi$
$739$		−	482.679i		−	0.653151i	0.945171	−	0.326576i	$-0.105895\pi$
$740$		0			0
$741$		0			0
$742$	−226.407	+	1008.31i	−0.305130	+	1.35891i
$743$	23.7067			0.0319067			0.0159534	−	0.999873i	$-0.494922\pi$
$743$	23.7067			0.0319067			0.0159534	+	0.999873i	$0.494922\pi$
$744$		0			0
$745$		0			0
$746$	−306.189	+	1363.62i	−0.410441	+	1.82791i
$747$		0			0
$748$	466.788	+	220.756i	0.624048	+	0.295129i
$749$	−1159.17			−1.54762
$750$		0			0
$751$			395.508i			0.526642i	0.964708	+	0.263321i	$0.0848179\pi$
$751$			395.508i			0.526642i	−0.964708	+	0.263321i	$0.915182\pi$
$752$	−316.302	−	385.365i	−0.420614	−	0.512453i
$753$		0			0
$754$	232.825	−	1036.90i	0.308787	−	1.37519i
$755$		0			0
$756$		0			0
$757$		−	393.940i		−	0.520396i	−0.965555	−	0.260198i	$-0.916212\pi$
$757$		−	393.940i		−	0.520396i	0.965555	−	0.260198i	$-0.0837879\pi$
$758$	91.4425	−	407.242i	0.120637	−	0.537259i
$759$		0			0
$760$		0			0
$761$	369.354			0.485354			0.242677	−	0.970107i	$-0.421975\pi$
$761$	369.354			0.485354			0.242677	+	0.970107i	$0.421975\pi$
$762$		0			0
$763$	515.903			0.676150
$764$	1.94443	−	4.11150i	0.00254507	−	0.00538154i
$765$		0			0
$766$	−305.444	−	68.5846i	−0.398751	−	0.0895360i
$767$	−357.890			−0.466610
$768$		0			0
$769$	873.491			1.13588			0.567940	−	0.823070i	$-0.307741\pi$
$769$	873.491			1.13588			0.567940	+	0.823070i	$0.307741\pi$
$770$		0			0
$771$		0			0
$772$	131.071	−	277.150i	0.169782	−	0.359003i
$773$			1176.93i			1.52254i	0.648432	+	0.761272i	$0.275425\pi$
$773$			1176.93i			1.52254i	−0.648432	+	0.761272i	$0.724575\pi$
$774$		0			0
$775$		0			0
$776$	337.394	−	432.372i	0.434786	−	0.557181i
$777$		0			0
$778$	754.393	+	169.392i	0.969657	+	0.217728i
$779$			760.224i			0.975897i
$780$		0			0
$781$	−123.754			−0.158455
$782$	−205.506	+	915.228i	−0.262795	+	1.17037i
$783$		0			0
$784$	−90.4464	−	110.195i	−0.115365	−	0.140555i
$785$		0			0
$786$		0			0
$787$	603.482			0.766814			0.383407	−	0.923580i	$-0.374751\pi$
$787$	603.482			0.766814			0.383407	+	0.923580i	$0.374751\pi$
$788$	−230.002	+	486.338i	−0.291880	+	0.617180i
$789$		0			0
$790$		0			0
$791$		−	1094.20i		−	1.38331i
$792$		0			0
$793$		−	986.975i		−	1.24461i
$794$	−245.882	+	1095.04i	−0.309675	+	1.37915i
$795$		0			0
$796$	−301.002	+	636.467i	−0.378143	+	0.799582i
$797$			860.121i			1.07920i	0.841922	+	0.539599i	$0.181424\pi$
$797$			860.121i			1.07920i	−0.841922	+	0.539599i	$0.818576\pi$
$798$		0			0
$799$		−	433.460i		−	0.542503i
$800$		0			0
$801$		0			0
$802$	−33.0437	−	7.41967i	−0.0412017	−	0.00925146i
$803$	379.448			0.472538
$804$		0			0
$805$		0			0
$806$	−851.245	−	191.139i	−1.05614	−	0.237145i
$807$		0			0
$808$	273.692	+	213.570i	0.338728	+	0.264320i
$809$	941.012			1.16318			0.581589	−	0.813483i	$-0.302431\pi$
$809$	941.012			1.16318			0.581589	+	0.813483i	$0.302431\pi$
$810$		0			0
$811$			1105.29i			1.36287i	0.731878	+	0.681436i	$0.238644\pi$
$811$			1105.29i			1.36287i	−0.731878	+	0.681436i	$0.761356\pi$
$812$	655.213	+	309.867i	0.806912	+	0.381610i
$813$		0			0
$814$	1219.30	+	273.784i	1.49792	+	0.336344i
$815$		0			0
$816$		0			0
$817$			867.407i			1.06170i
$818$	−504.421	−	113.263i	−0.616652	−	0.138463i
$819$		0			0
$820$		0			0
$821$	193.170			0.235286			0.117643	−	0.993056i	$-0.462466\pi$
$821$	193.170			0.235286			0.117643	+	0.993056i	$0.462466\pi$
$822$		0			0
$823$	−178.778			−0.217227			−0.108614	−	0.994084i	$-0.534641\pi$
$823$	−178.778			−0.217227			−0.108614	+	0.994084i	$0.534641\pi$
$824$	541.090	+	422.229i	0.656662	+	0.512414i
$825$		0			0
$826$	53.4761	−	238.158i	0.0647410	−	0.288326i
$827$	1558.61			1.88465			0.942326	−	0.334697i	$-0.108634\pi$
$827$	1558.61			1.88465			0.942326	+	0.334697i	$0.108634\pi$
$828$		0			0
$829$	565.477			0.682119			0.341059	−	0.940042i	$-0.389214\pi$
$829$	565.477			0.682119			0.341059	+	0.940042i	$0.389214\pi$
$830$		0			0
$831$		0			0
$832$	−1152.67	+	288.846i	−1.38543	+	0.347171i
$833$		−	123.948i		−	0.148797i
$834$		0			0
$835$		0			0
$836$	578.721	+	273.692i	0.692250	+	0.327383i
$837$		0			0
$838$	−113.450	+	505.254i	−0.135382	+	0.602928i
$839$		−	1280.25i		−	1.52592i	−0.646443	−	0.762962i	$-0.723744\pi$
$839$		−	1280.25i		−	1.52592i	0.646443	−	0.762962i	$-0.276256\pi$
$840$		0			0
$841$	−22.0271			−0.0261915
$842$	190.195	+	42.7066i	0.225885	+	0.0507204i
$843$		0			0
$844$	372.952	−	788.604i	0.441886	−	0.934365i
$845$		0			0
$846$		0			0
$847$	−220.903			−0.260806
$848$	1009.28	−	828.398i	1.19018	−	0.976885i
$849$		0			0
$850$		0			0
$851$			2270.15i			2.66762i
$852$		0			0
$853$			120.366i			0.141109i	0.997508	+	0.0705546i	$0.0224769\pi$
$853$			120.366i			0.141109i	−0.997508	+	0.0705546i	$0.977523\pi$
$854$	656.782	+	147.474i	0.769066	+	0.172687i
$855$		0			0
$856$	1154.66	+	901.014i	1.34890	+	1.05259i
$857$		−	717.784i		−	0.837554i	−0.908089	−	0.418777i	$-0.862459\pi$
$857$		−	717.784i		−	0.837554i	0.908089	−	0.418777i	$-0.137541\pi$
$858$		0			0
$859$			252.894i			0.294405i	0.989106	+	0.147203i	$0.0470269\pi$
$859$			252.894i			0.294405i	−0.989106	+	0.147203i	$0.952973\pi$
$860$		0			0
$861$		0			0
$862$	170.873	−	760.989i	0.198229	−	0.882817i
$863$	−1234.73			−1.43075			−0.715373	−	0.698743i	$-0.753743\pi$
$863$	−1234.73			−1.43075			−0.715373	+	0.698743i	$0.753743\pi$
$864$		0			0
$865$		0			0
$866$	−120.888	+	538.381i	−0.139594	+	0.621687i
$867$		0			0
$868$	254.387	−	537.901i	0.293073	−	0.619701i
$869$	−1311.29			−1.50897
$870$		0			0
$871$			83.5368i			0.0959091i
$872$	−513.894	−	401.007i	−0.589327	−	0.459871i
$873$		0			0
$874$	−254.785	+	1134.69i	−0.291516	+	1.29828i
$875$		0			0
$876$		0			0
$877$			685.723i			0.781896i	0.920413	+	0.390948i	$0.127853\pi$
$877$			685.723i			0.781896i	−0.920413	+	0.390948i	$0.872147\pi$
$878$	−195.487	+	870.609i	−0.222651	+	0.991582i
$879$		0			0
$880$		0			0
$881$	458.454			0.520379			0.260189	−	0.965558i	$-0.416215\pi$
$881$	458.454			0.520379			0.260189	+	0.965558i	$0.416215\pi$
$882$		0			0
$883$	−771.505			−0.873732			−0.436866	−	0.899527i	$-0.643912\pi$
$883$	−771.505			−0.873732			−0.436866	+	0.899527i	$0.643912\pi$
$884$	−933.986	−	441.707i	−1.05655	−	0.499668i
$885$		0			0
$886$	−1550.75	−	348.206i	−1.75028	−	0.393009i
$887$	−1161.05			−1.30896			−0.654480	−	0.756080i	$-0.727112\pi$
$887$	−1161.05			−1.30896			−0.654480	+	0.756080i	$0.727112\pi$
$888$		0			0
$889$	−141.693			−0.159385
$890$		0			0
$891$		0			0
$892$	−1188.15	−	561.905i	−1.33200	−	0.629938i
$893$		−	537.401i		−	0.601793i
$894$		0			0
$895$		0			0
$896$	−19.9793	−	810.207i	−0.0222983	−	0.904248i
$897$		0			0
$898$	−1464.00	−	328.728i	−1.63029	−	0.366066i
$899$		−	672.340i		−	0.747876i
$900$		0			0
$901$	1135.24			1.25997
$902$	179.229	−	798.200i	0.198701	−	0.884923i
$903$		0			0
$904$	−850.514	+	1089.94i	−0.940834	+	1.20569i
$905$		0			0
$906$		0			0
$907$	−392.544			−0.432793			−0.216397	−	0.976306i	$-0.569430\pi$
$907$	−392.544			−0.432793			−0.216397	+	0.976306i	$0.569430\pi$
$908$	−570.062	−	269.597i	−0.627822	−	0.296913i
$909$		0			0
$910$		0			0
$911$			1013.40i			1.11240i	0.831048	+	0.556201i	$0.187741\pi$
$911$			1013.40i			1.11240i	−0.831048	+	0.556201i	$0.812259\pi$
$912$		0			0
$913$			648.185i			0.709950i
$914$	44.2958	−	197.273i	0.0484637	−	0.215835i
$915$		0			0
$916$	987.707	+	467.112i	1.07828	+	0.509948i
$917$		−	11.1004i		−	0.0121051i
$918$		0			0
$919$		−	970.018i		−	1.05551i	−0.849395	−	0.527757i	$-0.823033\pi$
$919$		−	970.018i		−	1.05551i	0.849395	−	0.527757i	$-0.176967\pi$
$920$		0			0
$921$		0			0
$922$	8.75578	+	1.96603i	0.00949651	+	0.00213236i
$923$	247.616			0.268273
$924$		0			0
$925$		0			0
$926$	−1005.19	−	225.706i	−1.08552	−	0.243743i
$927$		0			0
$928$	−411.804	−	817.952i	−0.443754	−	0.881414i
$929$	980.857			1.05582			0.527910	−	0.849300i	$-0.322976\pi$
$929$	980.857			1.05582			0.527910	+	0.849300i	$0.322976\pi$
$930$		0			0
$931$		−	153.670i		−	0.165059i
$932$	185.967	−	393.226i	0.199535	−	0.421917i
$933$		0			0
$934$	576.638	+	129.479i	0.617386	+	0.138628i
$935$		0			0
$936$		0			0
$937$		−	964.666i		−	1.02953i	−0.857333	−	0.514763i	$-0.827880\pi$
$937$		−	964.666i		−	1.02953i	0.857333	−	0.514763i	$-0.172120\pi$
$938$	−55.5896	−	12.4821i	−0.0592639	−	0.0133072i
$939$		0			0
$940$		0			0
$941$	1581.10			1.68023			0.840117	−	0.542405i	$-0.182486\pi$
$941$	1581.10			1.68023			0.840117	+	0.542405i	$0.182486\pi$
$942$		0			0
$943$	1486.12			1.57595
$944$	−238.386	+	195.663i	−0.252527	+	0.207271i
$945$		0			0
$946$	204.498	−	910.738i	0.216171	−	0.962725i
$947$	−1245.27			−1.31497			−0.657483	−	0.753469i	$-0.728379\pi$
$947$	−1245.27			−1.31497			−0.657483	+	0.753469i	$0.728379\pi$
$948$		0			0
$949$	−759.229			−0.800031
$950$		0			0
$951$		0			0
$952$	433.490	−	555.521i	0.455347	−	0.583530i
$953$		−	1106.52i		−	1.16109i	−0.814228	−	0.580546i	$-0.802839\pi$
$953$		−	1106.52i		−	1.16109i	0.814228	−	0.580546i	$-0.197161\pi$
$954$		0			0
$955$		0			0
$956$	306.098	−	647.243i	0.320186	−	0.677032i
$957$		0			0
$958$	−119.689	+	533.037i	−0.124936	+	0.556406i
$959$			123.521i			0.128802i
$960$		0			0
$961$	409.039			0.425638
$962$	−2439.68	−	547.808i	−2.53605	−	0.569447i
$963$		0			0
$964$	1296.79	+	613.284i	1.34521	+	0.636187i
$965$		0			0
$966$		0			0
$967$	−406.453			−0.420324			−0.210162	−	0.977667i	$-0.567399\pi$
$967$	−406.453			−0.420324			−0.210162	+	0.977667i	$0.567399\pi$
$968$	220.042	+	171.706i	0.227316	+	0.177382i
$969$		0			0
$970$		0			0
$971$		−	1815.22i		−	1.86943i	−0.355393	−	0.934717i	$-0.615653\pi$
$971$		−	1815.22i		−	1.86943i	0.355393	−	0.934717i	$-0.384347\pi$
$972$		0			0
$973$			1629.58i			1.67480i
$974$	698.119	+	156.756i	0.716754	+	0.160941i
$975$		0			0
$976$	−539.594	−	657.412i	−0.552862	−	0.673578i
$977$		−	1457.74i		−	1.49205i	−0.665916	−	0.746027i	$-0.731959\pi$
$977$		−	1457.74i		−	1.49205i	0.665916	−	0.746027i	$-0.268041\pi$
$978$		0			0
$979$			429.720i			0.438938i
$980$		0			0
$981$		0			0
$982$	−185.074	+	824.235i	−0.188467	+	0.839343i
$983$	−19.9496			−0.0202946			−0.0101473	−	0.999949i	$-0.503230\pi$
$983$	−19.9496			−0.0202946			−0.0101473	+	0.999949i	$0.503230\pi$
$984$		0			0
$985$		0			0
$986$	174.437	−	776.860i	0.176914	−	0.787891i
$987$		0			0
$988$	−1157.95	−	547.625i	−1.17201	−	0.554276i
$989$	1695.65			1.71450
$990$		0			0
$991$		−	605.720i		−	0.611221i	−0.952157	−	0.305611i	$-0.901139\pi$
$991$		−	605.720i		−	0.611221i	0.952157	−	0.305611i	$-0.0988605\pi$
$992$	−671.502	+	338.073i	−0.676918	+	0.340799i
$993$		0			0
$994$	−36.9989	+	164.776i	−0.0372223	+	0.165771i
$995$		0			0
$996$		0			0
$997$		−	1238.47i		−	1.24220i	−0.783732	−	0.621099i	$-0.786686\pi$
$997$		−	1238.47i		−	1.24220i	0.783732	−	0.621099i	$-0.213314\pi$
$998$	−90.7434	+	404.129i	−0.0909253	+	0.404939i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.f.f.199.16		16
3.2	odd	2		300.3.f.b.199.1		16
4.3	odd	2	inner	900.3.f.f.199.2		16
5.2	odd	4		180.3.c.b.91.6		8
5.3	odd	4		900.3.c.u.451.3		8
5.4	even	2	inner	900.3.f.f.199.1		16
12.11	even	2		300.3.f.b.199.15		16
15.2	even	4		60.3.c.a.31.3	✓	8
15.8	even	4		300.3.c.d.151.6		8
15.14	odd	2		300.3.f.b.199.16		16
20.3	even	4		900.3.c.u.451.4		8
20.7	even	4		180.3.c.b.91.5		8
20.19	odd	2	inner	900.3.f.f.199.15		16
40.27	even	4		2880.3.e.j.2431.8		8
40.37	odd	4		2880.3.e.j.2431.5		8
60.23	odd	4		300.3.c.d.151.5		8
60.47	odd	4		60.3.c.a.31.4	yes	8
60.59	even	2		300.3.f.b.199.2		16
120.77	even	4		960.3.e.c.511.5		8
120.107	odd	4		960.3.e.c.511.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.c.a.31.3	✓	8	15.2	even	4
60.3.c.a.31.4	yes	8	60.47	odd	4
180.3.c.b.91.5		8	20.7	even	4
180.3.c.b.91.6		8	5.2	odd	4
300.3.c.d.151.5		8	60.23	odd	4
300.3.c.d.151.6		8	15.8	even	4
300.3.f.b.199.1		16	3.2	odd	2
300.3.f.b.199.2		16	60.59	even	2
300.3.f.b.199.15		16	12.11	even	2
300.3.f.b.199.16		16	15.14	odd	2
900.3.c.u.451.3		8	5.3	odd	4
900.3.c.u.451.4		8	20.3	even	4
900.3.f.f.199.1		16	5.4	even	2	inner
900.3.f.f.199.2		16	4.3	odd	2	inner
900.3.f.f.199.15		16	20.19	odd	2	inner
900.3.f.f.199.16		16	1.1	even	1	trivial
960.3.e.c.511.2		8	120.107	odd	4
960.3.e.c.511.5		8	120.77	even	4
2880.3.e.j.2431.5		8	40.37	odd	4
2880.3.e.j.2431.8		8	40.27	even	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.95141 + 0.438172i) q^{2} +(3.61601 + 1.71011i) q^{4} -6.33166 q^{7} +(6.30701 + 4.92155i) q^{8} +O(q^{10})\)	\(q+(1.95141 + 0.438172i) q^{2} +(3.61601 + 1.71011i) q^{4} -6.33166 q^{7} +(6.30701 + 4.92155i) q^{8} -9.27963i q^{11} +18.5674i q^{13} +(-12.3557 - 2.77436i) q^{14} +(10.1511 + 12.3675i) q^{16} +13.9110i q^{17} +17.2468i q^{19} +(4.06607 - 18.1084i) q^{22} +33.7148 q^{23} +(-8.13571 + 36.2327i) q^{26} +(-22.8954 - 10.8278i) q^{28} -28.6177 q^{29} +23.4939i q^{31} +(14.3898 + 28.5820i) q^{32} +(-6.09542 + 27.1461i) q^{34} +67.3338i q^{37} +(-7.55706 + 33.6556i) q^{38} +44.0791 q^{41} +50.2937 q^{43} +(15.8691 - 33.5552i) q^{44} +(65.7915 + 14.7729i) q^{46} -31.1594 q^{47} -8.91003 q^{49} +(-31.7522 + 67.1400i) q^{52} -81.6070i q^{53} +(-39.9338 - 31.1616i) q^{56} +(-55.8449 - 12.5395i) q^{58} +19.2751i q^{59} -53.1563 q^{61} +(-10.2943 + 45.8462i) q^{62} +(15.5566 + 62.0805i) q^{64} +4.49911 q^{67} +(-23.7893 + 50.3025i) q^{68} -13.3360i q^{71} +40.8904i q^{73} +(-29.5037 + 131.396i) q^{74} +(-29.4939 + 62.3647i) q^{76} +58.7555i q^{77} -141.309i q^{79} +(86.0164 + 19.3142i) q^{82} -69.8503 q^{83} +(98.1438 + 22.0373i) q^{86} +(45.6702 - 58.5266i) q^{88} -46.3079 q^{89} -117.563i q^{91} +(121.913 + 57.6559i) q^{92} +(-60.8049 - 13.6532i) q^{94} -68.5543i q^{97} +(-17.3871 - 3.90412i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 20 q^{4}+O(q^{10}) \) 16 * q - 20 * q^4	\( 16 q - 20 q^{4} - 40 q^{14} + 68 q^{16} + 72 q^{26} + 128 q^{29} + 184 q^{34} + 32 q^{41} + 344 q^{44} + 304 q^{46} + 112 q^{49} - 232 q^{56} - 352 q^{61} + 220 q^{64} + 264 q^{74} - 48 q^{76} + 400 q^{86} + 160 q^{89} + 192 q^{94}+O(q^{100}) \) 16 * q - 20 * q^4 - 40 * q^14 + 68 * q^16 + 72 * q^26 + 128 * q^29 + 184 * q^34 + 32 * q^41 + 344 * q^44 + 304 * q^46 + 112 * q^49 - 232 * q^56 - 352 * q^61 + 220 * q^64 + 264 * q^74 - 48 * q^76 + 400 * q^86 + 160 * q^89 + 192 * q^94

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