LMFDB - Embedded newform 1050.3.h.c.349.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(349,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1050.349");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.h (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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.2
Character	$\chi$	$=$	1050.349
Dual form			1050.3.h.c.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} -2.44949i q^{6} +(-4.78154 - 5.11242i) q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} -2.44949i q^{6} +(-4.78154 - 5.11242i) q^{7} -2.82843i q^{8} +3.00000 q^{9} +10.3587 q^{11} +3.46410 q^{12} +0.605169 q^{13} +(7.23005 - 6.76212i) q^{14} +4.00000 q^{16} +5.49382 q^{17} +4.24264i q^{18} +33.2186i q^{19} +(8.28188 + 8.85497i) q^{21} +14.6495i q^{22} -14.4299i q^{23} +4.89898i q^{24} +0.855838i q^{26} -5.19615 q^{27} +(9.56309 + 10.2248i) q^{28} -42.0972 q^{29} +0.540656i q^{31} +5.65685i q^{32} -17.9418 q^{33} +7.76943i q^{34} -6.00000 q^{36} +13.6996i q^{37} -46.9782 q^{38} -1.04818 q^{39} -13.7668i q^{41} +(-12.5228 + 11.7123i) q^{42} -82.3938i q^{43} -20.7175 q^{44} +20.4069 q^{46} -53.0228 q^{47} -6.92820 q^{48} +(-3.27369 + 48.8905i) q^{49} -9.51557 q^{51} -1.21034 q^{52} -19.4291i q^{53} -7.34847i q^{54} +(-14.4601 + 13.5242i) q^{56} -57.5364i q^{57} -59.5344i q^{58} +29.4240i q^{59} -74.7188i q^{61} -0.764604 q^{62} +(-14.3446 - 15.3373i) q^{63} -8.00000 q^{64} -25.3736i q^{66} -12.1937i q^{67} -10.9876 q^{68} +24.9933i q^{69} +42.3945 q^{71} -8.48528i q^{72} -66.9179 q^{73} -19.3742 q^{74} -66.4373i q^{76} +(-49.5307 - 52.9582i) q^{77} -1.48236i q^{78} +27.0962 q^{79} +9.00000 q^{81} +19.4693 q^{82} -126.850 q^{83} +(-16.5638 - 17.7099i) q^{84} +116.522 q^{86} +72.9145 q^{87} -29.2989i q^{88} -30.1856i q^{89} +(-2.89364 - 3.09388i) q^{91} +28.8597i q^{92} -0.936444i q^{93} -74.9856i q^{94} -9.79796i q^{96} -164.602 q^{97} +(-69.1416 - 4.62970i) q^{98} +31.0762 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 48 q^{4} + 72 q^{9}+O(q^{10}) $ 24 * q - 48 * q^4 + 72 * q^9	$ 24 q - 48 q^{4} + 72 q^{9} - 32 q^{11} - 16 q^{14} + 96 q^{16} - 12 q^{21} - 96 q^{29} - 144 q^{36} + 24 q^{39} + 64 q^{44} + 160 q^{46} - 236 q^{49} + 144 q^{51} + 32 q^{56} - 192 q^{64} + 496 q^{71} + 128 q^{74} + 416 q^{79} + 216 q^{81} + 24 q^{84} + 256 q^{86} - 316 q^{91} - 96 q^{99}+O(q^{100}) $ 24 * q - 48 * q^4 + 72 * q^9 - 32 * q^11 - 16 * q^14 + 96 * q^16 - 12 * q^21 - 96 * q^29 - 144 * q^36 + 24 * q^39 + 64 * q^44 + 160 * q^46 - 236 * q^49 + 144 * q^51 + 32 * q^56 - 192 * q^64 + 496 * q^71 + 128 * q^74 + 416 * q^79 + 216 * q^81 + 24 * q^84 + 256 * q^86 - 316 * q^91 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−2.00000			−0.500000
$5$		0			0
$5$		0			0
$6$		−	2.44949i		−	0.408248i
$7$	−4.78154	−	5.11242i	−0.683078	−	0.730346i
$7$	−4.78154	−	5.11242i	−0.683078	−	0.730346i
$8$		−	2.82843i		−	0.353553i
$9$	3.00000			0.333333
$10$		0			0
$11$	10.3587			0.941702			0.470851	−	0.882213i	$-0.343947\pi$
$11$	10.3587			0.941702			0.470851	+	0.882213i	$0.343947\pi$
$12$	3.46410			0.288675
$13$	0.605169			0.0465515			0.0232757	−	0.999729i	$-0.492590\pi$
$13$	0.605169			0.0465515			0.0232757	+	0.999729i	$0.492590\pi$
$14$	7.23005	−	6.76212i	0.516432	−	0.483009i
$15$		0			0
$16$	4.00000			0.250000
$17$	5.49382			0.323166			0.161583	−	0.986859i	$-0.448340\pi$
$17$	5.49382			0.323166			0.161583	+	0.986859i	$0.448340\pi$
$18$			4.24264i			0.235702i
$19$			33.2186i			1.74835i	0.485612	+	0.874175i	$0.338597\pi$
$19$			33.2186i			1.74835i	−0.485612	+	0.874175i	$0.661403\pi$
$20$		0			0
$21$	8.28188	+	8.85497i	0.394375	+	0.421665i
$22$			14.6495i			0.665884i
$23$		−	14.4299i		−	0.627385i	−0.949525	−	0.313693i	$-0.898434\pi$
$23$		−	14.4299i		−	0.627385i	0.949525	−	0.313693i	$-0.101566\pi$
$24$			4.89898i			0.204124i
$25$		0			0
$26$			0.855838i			0.0329169i
$27$	−5.19615			−0.192450
$28$	9.56309	+	10.2248i	0.341539	+	0.365173i
$29$	−42.0972			−1.45163			−0.725814	−	0.687891i	$-0.758536\pi$
$29$	−42.0972			−1.45163			−0.725814	+	0.687891i	$0.758536\pi$
$30$		0			0
$31$			0.540656i			0.0174405i	0.999962	+	0.00872026i	$0.00277578\pi$
$31$			0.540656i			0.0174405i	−0.999962	+	0.00872026i	$0.997224\pi$
$32$			5.65685i			0.176777i
$33$	−17.9418			−0.543692
$34$			7.76943i			0.228513i
$35$		0			0
$36$	−6.00000			−0.166667
$37$			13.6996i			0.370260i	0.982714	+	0.185130i	$0.0592706\pi$
$37$			13.6996i			0.370260i	−0.982714	+	0.185130i	$0.940729\pi$
$38$	−46.9782			−1.23627
$39$	−1.04818			−0.0268765
$40$		0			0
$41$		−	13.7668i		−	0.335777i	−0.985806	−	0.167888i	$-0.946305\pi$
$41$		−	13.7668i		−	0.335777i	0.985806	−	0.167888i	$-0.0536948\pi$
$42$	−12.5228	+	11.7123i	−0.298162	+	0.278865i
$43$		−	82.3938i		−	1.91614i	−0.286541	−	0.958068i	$-0.592506\pi$
$43$		−	82.3938i		−	1.91614i	0.286541	−	0.958068i	$-0.407494\pi$
$44$	−20.7175			−0.470851
$45$		0			0
$46$	20.4069			0.443628
$47$	−53.0228			−1.12814			−0.564072	−	0.825725i	$-0.690766\pi$
$47$	−53.0228			−1.12814			−0.564072	+	0.825725i	$0.690766\pi$
$48$	−6.92820			−0.144338
$49$	−3.27369	+	48.8905i	−0.0668101	+	0.997766i
$50$		0			0
$51$	−9.51557			−0.186580
$52$	−1.21034			−0.0232757
$53$		−	19.4291i		−	0.366587i	−0.983058	−	0.183294i	$-0.941324\pi$
$53$		−	19.4291i		−	0.366587i	0.983058	−	0.183294i	$-0.0586759\pi$
$54$		−	7.34847i		−	0.136083i
$55$		0			0
$56$	−14.4601	+	13.5242i	−0.258216	+	0.241504i
$57$		−	57.5364i		−	1.00941i
$58$		−	59.5344i		−	1.02646i
$59$			29.4240i			0.498713i	0.968412	+	0.249356i	$0.0802190\pi$
$59$			29.4240i			0.498713i	−0.968412	+	0.249356i	$0.919781\pi$
$60$		0			0
$61$		−	74.7188i		−	1.22490i	−0.790510	−	0.612449i	$-0.790185\pi$
$61$		−	74.7188i		−	1.22490i	0.790510	−	0.612449i	$-0.209815\pi$
$62$	−0.764604			−0.0123323
$63$	−14.3446	−	15.3373i	−0.227693	−	0.243449i
$64$	−8.00000			−0.125000
$65$		0			0
$66$		−	25.3736i		−	0.384448i
$67$		−	12.1937i		−	0.181996i	−0.995851	−	0.0909981i	$-0.970994\pi$
$67$		−	12.1937i		−	0.181996i	0.995851	−	0.0909981i	$-0.0290057\pi$
$68$	−10.9876			−0.161583
$69$			24.9933i			0.362221i
$70$		0			0
$71$	42.3945			0.597105			0.298553	−	0.954393i	$-0.403496\pi$
$71$	42.3945			0.597105			0.298553	+	0.954393i	$0.403496\pi$
$72$		−	8.48528i		−	0.117851i
$73$	−66.9179			−0.916683			−0.458342	−	0.888776i	$-0.651556\pi$
$73$	−66.9179			−0.916683			−0.458342	+	0.888776i	$0.651556\pi$
$74$	−19.3742			−0.261813
$75$		0			0
$76$		−	66.4373i		−	0.874175i
$77$	−49.5307	−	52.9582i	−0.643256	−	0.687768i
$78$		−	1.48236i		−	0.0190046i
$79$	27.0962			0.342990			0.171495	−	0.985185i	$-0.445140\pi$
$79$	27.0962			0.342990			0.171495	+	0.985185i	$0.445140\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	19.4693			0.237430
$83$	−126.850			−1.52831			−0.764156	−	0.645031i	$-0.776844\pi$
$83$	−126.850			−1.52831			−0.764156	+	0.645031i	$0.776844\pi$
$84$	−16.5638	−	17.7099i	−0.197188	−	0.210833i
$85$		0			0
$86$	116.522			1.35491
$87$	72.9145			0.838097
$88$		−	29.2989i		−	0.332942i
$89$		−	30.1856i		−	0.339164i	−0.985516	−	0.169582i	$-0.945758\pi$
$89$		−	30.1856i		−	0.339164i	0.985516	−	0.169582i	$-0.0542417\pi$
$90$		0			0
$91$	−2.89364	−	3.09388i	−0.0317983	−	0.0339987i
$92$			28.8597i			0.313693i
$93$		−	0.936444i		−	0.0100693i
$94$		−	74.9856i		−	0.797719i
$95$		0			0
$96$		−	9.79796i		−	0.102062i
$97$	−164.602			−1.69693			−0.848465	−	0.529251i	$-0.822473\pi$
$97$	−164.602			−1.69693			−0.848465	+	0.529251i	$0.822473\pi$
$98$	−69.1416	−	4.62970i	−0.705527	−	0.0472419i
$99$	31.0762			0.313901
$100$		0			0
$101$		−	19.5033i		−	0.193102i	−0.995328	−	0.0965508i	$-0.969219\pi$
$101$		−	19.5033i		−	0.193102i	0.995328	−	0.0965508i	$-0.0307810\pi$
$102$		−	13.4570i		−	0.131932i
$103$	108.949			1.05775			0.528877	−	0.848699i	$-0.322613\pi$
$103$	108.949			1.05775			0.528877	+	0.848699i	$0.322613\pi$
$104$		−	1.71168i		−	0.0164584i
$105$		0			0
$106$	27.4769			0.259216
$107$		−	120.784i		−	1.12882i	−0.825495	−	0.564409i	$-0.809104\pi$
$107$		−	120.784i		−	1.12882i	0.825495	−	0.564409i	$-0.190896\pi$
$108$	10.3923			0.0962250
$109$	−123.855			−1.13628			−0.568141	−	0.822931i	$-0.692337\pi$
$109$	−123.855			−1.13628			−0.568141	+	0.822931i	$0.692337\pi$
$110$		0			0
$111$		−	23.7284i		−	0.213770i
$112$	−19.1262	−	20.4497i	−0.170769	−	0.182586i
$113$			201.420i			1.78248i	0.453534	+	0.891239i	$0.350163\pi$
$113$			201.420i			1.78248i	−0.453534	+	0.891239i	$0.649837\pi$
$114$	81.3687			0.713761
$115$		0			0
$116$	84.1944			0.725814
$117$	1.81551			0.0155172
$118$	−41.6119			−0.352643
$119$	−26.2689	−	28.0867i	−0.220747	−	0.236023i
$120$		0			0
$121$	−13.6968			−0.113196
$122$	105.668			0.866133
$123$			23.8449i			0.193861i
$124$		−	1.08131i		−	0.00872026i
$125$		0			0
$126$	21.6902	−	20.2864i	0.172144	−	0.161003i
$127$		−	213.378i		−	1.68014i	−0.542476	−	0.840071i	$-0.682513\pi$
$127$		−	213.378i		−	1.68014i	0.542476	−	0.840071i	$-0.317487\pi$
$128$		−	11.3137i		−	0.0883883i
$129$			142.710i			1.10628i
$130$		0			0
$131$		−	139.162i		−	1.06231i	−0.847276	−	0.531153i	$-0.821759\pi$
$131$		−	139.162i		−	1.06231i	0.847276	−	0.531153i	$-0.178241\pi$
$132$	35.8837			0.271846
$133$	169.828	−	158.836i	1.27690	−	1.19426i
$134$	17.2446			0.128691
$135$		0			0
$136$		−	15.5389i		−	0.114256i
$137$			18.2823i			0.133448i	0.997771	+	0.0667238i	$0.0212546\pi$
$137$			18.2823i			0.133448i	−0.997771	+	0.0667238i	$0.978745\pi$
$138$	−35.3458			−0.256129
$139$		−	38.7265i		−	0.278608i	−0.990250	−	0.139304i	$-0.955513\pi$
$139$		−	38.7265i		−	0.278608i	0.990250	−	0.139304i	$-0.0444865\pi$
$140$		0			0
$141$	91.8382			0.651335
$142$			59.9548i			0.422217i
$143$	6.26878			0.0438376
$144$	12.0000			0.0833333
$145$		0			0
$146$		−	94.6362i		−	0.648193i
$147$	5.67021	−	84.6809i	0.0385728	−	0.576060i
$148$		−	27.3992i		−	0.185130i
$149$	20.1135			0.134990			0.0674950	−	0.997720i	$-0.478499\pi$
$149$	20.1135			0.134990			0.0674950	+	0.997720i	$0.478499\pi$
$150$		0			0
$151$	11.3257			0.0750047			0.0375023	−	0.999297i	$-0.488060\pi$
$151$	11.3257			0.0750047			0.0375023	+	0.999297i	$0.488060\pi$
$152$	93.9565			0.618135
$153$	16.4814			0.107722
$154$	74.8942	−	70.0470i	0.486326	−	0.454851i
$155$		0			0
$156$	2.09637			0.0134382
$157$	−108.422			−0.690589			−0.345294	−	0.938494i	$-0.612221\pi$
$157$	−108.422			−0.690589			−0.345294	+	0.938494i	$0.612221\pi$
$158$			38.3198i			0.242531i
$159$			33.6522i			0.211649i
$160$		0			0
$161$	−73.7715	+	68.9970i	−0.458208	+	0.428553i
$162$			12.7279i			0.0785674i
$163$		−	82.1443i		−	0.503953i	−0.967733	−	0.251976i	$-0.918919\pi$
$163$		−	82.1443i		−	0.503953i	0.967733	−	0.251976i	$-0.0810806\pi$
$164$			27.5337i			0.167888i
$165$		0			0
$166$		−	179.393i		−	1.08068i
$167$	−314.645			−1.88410			−0.942050	−	0.335472i	$-0.891104\pi$
$167$	−314.645			−1.88410			−0.942050	+	0.335472i	$0.891104\pi$
$168$	25.0456	−	23.4247i	0.149081	−	0.139433i
$169$	−168.634			−0.997833
$170$		0			0
$171$			99.6559i			0.582783i
$172$			164.788i			0.958068i
$173$	−188.637			−1.09039			−0.545193	−	0.838311i	$-0.683544\pi$
$173$	−188.637			−1.09039			−0.545193	+	0.838311i	$0.683544\pi$
$174$			103.117i			0.592624i
$175$		0			0
$176$	41.4349			0.235426
$177$		−	50.9639i		−	0.287932i
$178$	42.6889			0.239825
$179$	−254.112			−1.41962			−0.709810	−	0.704393i	$-0.751219\pi$
$179$	−254.112			−1.41962			−0.709810	+	0.704393i	$0.751219\pi$
$180$		0			0
$181$		−	138.747i		−	0.766560i	−0.923632	−	0.383280i	$-0.874794\pi$
$181$		−	138.747i		−	0.766560i	0.923632	−	0.383280i	$-0.125206\pi$
$182$	4.37540	−	4.09223i	0.0240407	−	0.0224848i
$183$			129.417i			0.707195i
$184$	−40.8138			−0.221814
$185$		0			0
$186$	1.32433			0.00712007
$187$	56.9089			0.304326
$188$	106.046			0.564072
$189$	24.8456	+	26.5649i	0.131458	+	0.140555i
$190$		0			0
$191$	178.907			0.936685			0.468342	−	0.883547i	$-0.344851\pi$
$191$	178.907			0.936685			0.468342	+	0.883547i	$0.344851\pi$
$192$	13.8564			0.0721688
$193$			3.65902i			0.0189587i	0.999955	+	0.00947933i	$0.00301741\pi$
$193$			3.65902i			0.0189587i	−0.999955	+	0.00947933i	$0.996983\pi$
$194$		−	232.783i		−	1.19991i
$195$		0			0
$196$	6.54739	−	97.7810i	0.0334051	−	0.498883i
$197$			201.822i			1.02447i	0.858844	+	0.512237i	$0.171183\pi$
$197$			201.822i			1.02447i	−0.858844	+	0.512237i	$0.828817\pi$
$198$			43.9484i			0.221961i
$199$		−	97.5792i		−	0.490348i	−0.969479	−	0.245174i	$-0.921155\pi$
$199$		−	97.5792i		−	0.490348i	0.969479	−	0.245174i	$-0.0788451\pi$
$200$		0			0
$201$			21.1202i			0.105076i
$202$	27.5818			0.136543
$203$	201.290	+	215.219i	0.991574	+	1.06019i
$204$	19.0311			0.0932899
$205$		0			0
$206$			154.077i			0.747945i
$207$		−	43.2896i		−	0.209128i
$208$	2.42068			0.0116379
$209$			344.103i			1.64642i
$210$		0			0
$211$	−104.122			−0.493469			−0.246734	−	0.969083i	$-0.579357\pi$
$211$	−104.122			−0.493469			−0.246734	+	0.969083i	$0.579357\pi$
$212$			38.8582i			0.183294i
$213$	−73.4294			−0.344739
$214$	170.814			0.798196
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	2.76406	−	2.58517i	0.0127376	−	0.0119132i
$218$		−	175.157i		−	0.803473i
$219$	115.905			0.529247
$220$		0			0
$221$	3.32469			0.0150438
$222$	33.5571			0.151158
$223$	255.861			1.14736			0.573679	−	0.819080i	$-0.305516\pi$
$223$	255.861			1.14736			0.573679	+	0.819080i	$0.305516\pi$
$224$	28.9202	−	27.0485i	0.129108	−	0.120752i
$225$		0			0
$226$	−284.851			−1.26040
$227$	−102.642			−0.452168			−0.226084	−	0.974108i	$-0.572592\pi$
$227$	−102.642			−0.452168			−0.226084	+	0.974108i	$0.572592\pi$
$228$			115.073i			0.504705i
$229$		−	254.063i		−	1.10945i	−0.832035	−	0.554723i	$-0.812824\pi$
$229$		−	254.063i		−	1.10945i	0.832035	−	0.554723i	$-0.187176\pi$
$230$		0			0
$231$	85.7897	+	91.7262i	0.371384	+	0.397083i
$232$			119.069i			0.513228i
$233$			87.3948i			0.375085i	0.982256	+	0.187543i	$0.0600523\pi$
$233$			87.3948i			0.375085i	−0.982256	+	0.187543i	$0.939948\pi$
$234$			2.56751i			0.0109723i
$235$		0			0
$236$		−	58.8481i		−	0.249356i
$237$	−46.9320			−0.198025
$238$	39.7206	−	37.1499i	0.166893	−	0.156092i
$239$	238.165			0.996505			0.498253	−	0.867032i	$-0.333975\pi$
$239$	238.165			0.996505			0.498253	+	0.867032i	$0.333975\pi$
$240$		0			0
$241$			235.615i			0.977655i	0.872381	+	0.488827i	$0.162575\pi$
$241$			235.615i			0.977655i	−0.872381	+	0.488827i	$0.837425\pi$
$242$		−	19.3702i		−	0.0800420i
$243$	−15.5885			−0.0641500
$244$			149.438i			0.612449i
$245$		0			0
$246$	−33.7217			−0.137080
$247$			20.1029i			0.0813882i
$248$	1.52921			0.00616616
$249$	219.710			0.882371
$250$		0			0
$251$			281.571i			1.12180i	0.827884	+	0.560899i	$0.189544\pi$
$251$			281.571i			1.12180i	−0.827884	+	0.560899i	$0.810456\pi$
$252$	28.6893	+	30.6745i	0.113846	+	0.121724i
$253$		−	149.475i		−	0.590810i
$254$	301.762			1.18804
$255$		0			0
$256$	16.0000			0.0625000
$257$	253.540			0.986539			0.493269	−	0.869877i	$-0.335802\pi$
$257$	253.540			0.986539			0.493269	+	0.869877i	$0.335802\pi$
$258$	−201.823			−0.782259
$259$	70.0382	−	65.5053i	0.270418	−	0.252916i
$260$		0			0
$261$	−126.292			−0.483876
$262$	196.805			0.751163
$263$			264.972i			1.00750i	0.863850	+	0.503749i	$0.168046\pi$
$263$			264.972i			1.00750i	−0.863850	+	0.503749i	$0.831954\pi$
$264$			50.7472i			0.192224i
$265$		0			0
$266$	224.628	+	240.173i	0.844468	+	0.902904i
$267$			52.2830i			0.195816i
$268$			24.3875i			0.0909981i
$269$		−	189.680i		−	0.705130i	−0.935787	−	0.352565i	$-0.885310\pi$
$269$		−	189.680i		−	0.705130i	0.935787	−	0.352565i	$-0.114690\pi$
$270$		0			0
$271$		−	286.595i		−	1.05755i	−0.848763	−	0.528773i	$-0.822652\pi$
$271$		−	286.595i		−	1.05755i	0.848763	−	0.528773i	$-0.177348\pi$
$272$	21.9753			0.0807914
$273$	5.01193	+	5.35875i	0.0183587	+	0.0196291i
$274$	−25.8551			−0.0943617
$275$		0			0
$276$		−	49.9865i		−	0.181111i
$277$			82.5341i			0.297957i	0.988840	+	0.148979i	$0.0475985\pi$
$277$			82.5341i			0.297957i	−0.988840	+	0.148979i	$0.952401\pi$
$278$	54.7676			0.197006
$279$			1.62197i			0.00581351i
$280$		0			0
$281$	−384.926			−1.36984			−0.684922	−	0.728617i	$-0.740164\pi$
$281$	−384.926			−1.36984			−0.684922	+	0.728617i	$0.740164\pi$
$282$			129.879i			0.460563i
$283$	514.332			1.81743			0.908714	−	0.417419i	$-0.137065\pi$
$283$	514.332			1.81743			0.908714	+	0.417419i	$0.137065\pi$
$284$	−84.7889			−0.298553
$285$		0			0
$286$			8.86539i			0.0309979i
$287$	−70.3819	+	65.8268i	−0.245233	+	0.229362i
$288$			16.9706i			0.0589256i
$289$	−258.818			−0.895564
$290$		0			0
$291$	285.099			0.979723
$292$	133.836			0.458342
$293$	−431.273			−1.47192			−0.735962	−	0.677023i	$-0.763270\pi$
$293$	−431.273			−1.47192			−0.735962	+	0.677023i	$0.763270\pi$
$294$	119.757	+	8.01888i	0.407336	+	0.0272751i
$295$		0			0
$296$	38.7484			0.130907
$297$	−53.8255			−0.181231
$298$			28.4448i			0.0954524i
$299$		−	8.73251i		−	0.0292057i
$300$		0			0
$301$	−421.232	+	393.970i	−1.39944	+	1.30887i
$302$			16.0170i			0.0530363i
$303$			33.7806i			0.111487i
$304$			132.875i			0.437087i
$305$		0			0
$306$			23.3083i			0.0761709i
$307$	−341.103			−1.11108			−0.555542	−	0.831489i	$-0.687489\pi$
$307$	−341.103			−1.11108			−0.555542	+	0.831489i	$0.687489\pi$
$308$	99.0614	+	105.916i	0.321628	+	0.343884i
$309$	−188.705			−0.610694
$310$		0			0
$311$			545.710i			1.75469i	0.479857	+	0.877347i	$0.340689\pi$
$311$			545.710i			1.75469i	−0.479857	+	0.877347i	$0.659311\pi$
$312$			2.96471i			0.00950228i
$313$	98.7397			0.315462			0.157731	−	0.987482i	$-0.449582\pi$
$313$	98.7397			0.315462			0.157731	+	0.987482i	$0.449582\pi$
$314$		−	153.332i		−	0.488320i
$315$		0			0
$316$	−54.1924			−0.171495
$317$		−	165.058i		−	0.520689i	−0.965516	−	0.260344i	$-0.916164\pi$
$317$		−	165.058i		−	0.520689i	0.965516	−	0.260344i	$-0.0838361\pi$
$318$	−47.5914			−0.149659
$319$	−436.073			−1.36700
$320$		0			0
$321$			209.203i			0.651724i
$322$	−97.5765	−	104.329i	−0.303033	−	0.324002i
$323$			182.497i			0.565006i
$324$	−18.0000			−0.0555556
$325$		0			0
$326$	116.170			0.356349
$327$	214.523			0.656033
$328$	−38.9385			−0.118715
$329$	253.531	+	271.075i	0.770610	+	0.823936i
$330$		0			0
$331$	−230.662			−0.696863			−0.348431	−	0.937334i	$-0.613286\pi$
$331$	−230.662			−0.696863			−0.348431	+	0.937334i	$0.613286\pi$
$332$	253.700			0.764156
$333$			41.0988i			0.123420i
$334$		−	444.975i		−	1.33226i
$335$		0			0
$336$	33.1275	+	35.4199i	0.0985938	+	0.105416i
$337$			144.633i			0.429179i	0.976704	+	0.214590i	$0.0688414\pi$
$337$			144.633i			0.429179i	−0.976704	+	0.214590i	$0.931159\pi$
$338$		−	238.484i		−	0.705574i
$339$		−	348.870i		−	1.02911i
$340$		0			0
$341$			5.60051i			0.0164238i
$342$	−140.935			−0.412090
$343$	265.602	−	217.036i	0.774351	−	0.632757i
$344$	−233.045			−0.677456
$345$		0			0
$346$		−	266.773i		−	0.771019i
$347$			162.310i			0.467751i	0.972267	+	0.233875i	$0.0751408\pi$
$347$			162.310i			0.467751i	−0.972267	+	0.233875i	$0.924859\pi$
$348$	−145.829			−0.419049
$349$			313.404i			0.898006i	0.893530	+	0.449003i	$0.148221\pi$
$349$			313.404i			0.898006i	−0.893530	+	0.449003i	$0.851779\pi$
$350$		0			0
$351$	−3.14455			−0.00895883
$352$			58.5978i			0.166471i
$353$	−343.028			−0.971752			−0.485876	−	0.874028i	$-0.661499\pi$
$353$	−343.028			−0.971752			−0.485876	+	0.874028i	$0.661499\pi$
$354$	72.0739			0.203599
$355$		0			0
$356$			60.3712i			0.169582i
$357$	45.4991	+	48.6476i	0.127448	+	0.136268i
$358$		−	359.369i		−	1.00382i
$359$	357.293			0.995244			0.497622	−	0.867394i	$-0.334207\pi$
$359$	357.293			0.995244			0.497622	+	0.867394i	$0.334207\pi$
$360$		0			0
$361$	−742.478			−2.05672
$362$	196.218			0.542040
$363$	23.7235			0.0653540
$364$	5.78728	+	6.18776i	0.0158991	+	0.0169993i
$365$		0			0
$366$	−183.023			−0.500062
$367$	617.139			1.68158			0.840789	−	0.541363i	$-0.182091\pi$
$367$	617.139			1.68158			0.840789	+	0.541363i	$0.182091\pi$
$368$		−	57.7195i		−	0.156846i
$369$		−	41.3005i		−	0.111926i
$370$		0			0
$371$	−99.3298	+	92.9011i	−0.267735	+	0.250407i
$372$			1.87289i			0.00503465i
$373$		−	338.873i		−	0.908506i	−0.890873	−	0.454253i	$-0.849906\pi$
$373$		−	338.873i		−	0.908506i	0.890873	−	0.454253i	$-0.150094\pi$
$374$			80.4814i			0.215191i
$375$		0			0
$376$			149.971i			0.398859i
$377$	−25.4759			−0.0675754
$378$	−37.5685	+	35.1370i	−0.0993875	+	0.0929551i
$379$	211.631			0.558392			0.279196	−	0.960234i	$-0.409932\pi$
$379$	211.631			0.558392			0.279196	+	0.960234i	$0.409932\pi$
$380$		0			0
$381$			369.582i			0.970031i
$382$			253.012i			0.662336i
$383$	−238.751			−0.623370			−0.311685	−	0.950185i	$-0.600893\pi$
$383$	−238.751			−0.623370			−0.311685	+	0.950185i	$0.600893\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−5.17464			−0.0134058
$387$		−	247.182i		−	0.638712i
$388$	329.204			0.848465
$389$	21.7723			0.0559700			0.0279850	−	0.999608i	$-0.491091\pi$
$389$	21.7723			0.0559700			0.0279850	+	0.999608i	$0.491091\pi$
$390$		0			0
$391$		−	79.2750i		−	0.202749i
$392$	138.283	+	9.25941i	0.352763	+	0.0236209i
$393$			241.036i			0.613322i
$394$	−285.419			−0.724413
$395$		0			0
$396$	−62.1524			−0.156950
$397$	552.917			1.39274			0.696369	−	0.717684i	$-0.254798\pi$
$397$	552.917			1.39274			0.696369	+	0.717684i	$0.254798\pi$
$398$	137.998			0.346728
$399$	−294.150	+	275.113i	−0.737218	+	0.689505i
$400$		0			0
$401$	−636.205			−1.58655			−0.793273	−	0.608866i	$-0.791625\pi$
$401$	−636.205			−1.58655			−0.793273	+	0.608866i	$0.791625\pi$
$402$	−29.8685			−0.0742997
$403$			0.327188i			0.000811882i
$404$			39.0065i			0.0965508i
$405$		0			0
$406$	−304.365	+	284.666i	−0.749667	+	0.701149i
$407$			141.911i			0.348675i
$408$			26.9141i			0.0659659i
$409$		−	358.386i		−	0.876249i	−0.898914	−	0.438124i	$-0.855643\pi$
$409$		−	358.386i		−	0.876249i	0.898914	−	0.438124i	$-0.144357\pi$
$410$		0			0
$411$		−	31.6659i		−	0.0770460i
$412$	−217.897			−0.528877
$413$	150.428	−	140.692i	0.364233	−	0.340659i
$414$	61.2207			0.147876
$415$		0			0
$416$			3.42335i			0.00822921i
$417$			67.0763i			0.160854i
$418$	−486.635			−1.16420
$419$			391.544i			0.934472i	0.884133	+	0.467236i	$0.154750\pi$
$419$			391.544i			0.934472i	−0.884133	+	0.467236i	$0.845250\pi$
$420$		0			0
$421$	472.677			1.12275			0.561374	−	0.827563i	$-0.310273\pi$
$421$	472.677			1.12275			0.561374	+	0.827563i	$0.310273\pi$
$422$		−	147.251i		−	0.348935i
$423$	−159.068			−0.376048
$424$	−54.9538			−0.129608
$425$		0			0
$426$		−	103.845i		−	0.243767i
$427$	−381.994	+	357.271i	−0.894599	+	0.836700i
$428$			241.567i			0.564409i
$429$	−10.8578			−0.0253097
$430$		0			0
$431$	−671.160			−1.55721			−0.778607	−	0.627511i	$-0.784074\pi$
$431$	−671.160			−1.55721			−0.778607	+	0.627511i	$0.784074\pi$
$432$	−20.7846			−0.0481125
$433$	113.211			0.261456			0.130728	−	0.991418i	$-0.458268\pi$
$433$	113.211			0.261456			0.130728	+	0.991418i	$0.458268\pi$
$434$	3.65599	+	3.90898i	0.00842393	+	0.00900686i
$435$		0			0
$436$	247.710			0.568141
$437$	479.340			1.09689
$438$			163.915i			0.374234i
$439$		−	603.089i		−	1.37378i	−0.726762	−	0.686890i	$-0.758976\pi$
$439$		−	603.089i		−	1.37378i	0.726762	−	0.686890i	$-0.241024\pi$
$440$		0			0
$441$	−9.82108	+	146.672i	−0.0222700	+	0.332589i
$442$			4.70182i			0.0106376i
$443$			853.722i			1.92714i	0.267459	+	0.963569i	$0.413816\pi$
$443$			853.722i			1.92714i	−0.267459	+	0.963569i	$0.586184\pi$
$444$			47.4569i			0.106885i
$445$		0			0
$446$			361.842i			0.811305i
$447$	−34.8376			−0.0779366
$448$	38.2523	+	40.8994i	0.0853847	+	0.0912932i
$449$	232.558			0.517946			0.258973	−	0.965885i	$-0.416616\pi$
$449$	232.558			0.517946			0.258973	+	0.965885i	$0.416616\pi$
$450$		0			0
$451$		−	142.607i		−	0.316202i
$452$		−	402.840i		−	0.891239i
$453$	−19.6167			−0.0433040
$454$		−	145.158i		−	0.319731i
$455$		0			0
$456$	−162.737			−0.356880
$457$			389.899i			0.853170i	0.904448	+	0.426585i	$0.140283\pi$
$457$			389.899i			0.853170i	−0.904448	+	0.426585i	$0.859717\pi$
$458$	359.299			0.784496
$459$	−28.5467			−0.0621932
$460$		0			0
$461$		−	599.713i		−	1.30090i	−0.759551	−	0.650448i	$-0.774581\pi$
$461$		−	599.713i		−	1.30090i	0.759551	−	0.650448i	$-0.225419\pi$
$462$	−129.721	+	121.325i	−0.280780	+	0.262608i
$463$			211.263i			0.456292i	0.973627	+	0.228146i	$0.0732664\pi$
$463$			211.263i			0.456292i	−0.973627	+	0.228146i	$0.926734\pi$
$464$	−168.389			−0.362907
$465$		0			0
$466$	−123.595			−0.265225
$467$	796.828			1.70627			0.853135	−	0.521690i	$-0.174698\pi$
$467$	796.828			1.70627			0.853135	+	0.521690i	$0.174698\pi$
$468$	−3.63101			−0.00775858
$469$	−62.3396	+	58.3049i	−0.132920	+	0.124318i
$470$		0			0
$471$	187.793			0.398712
$472$	83.2238			0.176322
$473$		−	853.495i		−	1.80443i
$474$		−	66.3719i		−	0.140025i
$475$		0			0
$476$	52.5378	+	56.1734i	0.110374	+	0.118011i
$477$		−	58.2873i		−	0.122196i
$478$			336.816i			0.704636i
$479$		−	522.525i		−	1.09087i	−0.838154	−	0.545433i	$-0.816365\pi$
$479$		−	522.525i		−	1.09087i	0.838154	−	0.545433i	$-0.183635\pi$
$480$		0			0
$481$			8.29058i			0.0172361i
$482$	−333.210			−0.691306
$483$	127.776	−	119.506i	0.264547	−	0.247425i
$484$	27.3935			0.0565982
$485$		0			0
$486$		−	22.0454i		−	0.0453609i
$487$			216.781i			0.445135i	0.974917	+	0.222568i	$0.0714438\pi$
$487$			216.781i			0.445135i	−0.974917	+	0.222568i	$0.928556\pi$
$488$	−211.337			−0.433067
$489$			142.278i			0.290957i
$490$		0			0
$491$	451.246			0.919035			0.459517	−	0.888169i	$-0.348022\pi$
$491$	451.246			0.919035			0.459517	+	0.888169i	$0.348022\pi$
$492$		−	47.6897i		−	0.0969304i
$493$	−231.274			−0.469116
$494$	−28.4298			−0.0575501
$495$		0			0
$496$			2.16263i			0.00436013i
$497$	−202.711	−	216.738i	−0.407869	−	0.436093i
$498$			310.718i			0.623931i
$499$	−347.296			−0.695984			−0.347992	−	0.937498i	$-0.613136\pi$
$499$	−347.296			−0.695984			−0.347992	+	0.937498i	$0.613136\pi$
$500$		0			0
$501$	544.981			1.08779
$502$	−398.202			−0.793231
$503$	684.193			1.36022			0.680112	−	0.733108i	$-0.261931\pi$
$503$	684.193			1.36022			0.680112	+	0.733108i	$0.261931\pi$
$504$	−43.3803	+	40.5727i	−0.0860721	+	0.0805015i
$505$		0			0
$506$	211.390			0.417766
$507$	292.082			0.576099
$508$			426.756i			0.840071i
$509$			577.464i			1.13451i	0.823543	+	0.567253i	$0.191994\pi$
$509$			577.464i			1.13451i	−0.823543	+	0.567253i	$0.808006\pi$
$510$		0			0
$511$	319.971	+	342.112i	0.626166	+	0.669496i
$512$			22.6274i			0.0441942i
$513$		−	172.609i		−	0.336470i
$514$			358.560i			0.697588i
$515$		0			0
$516$		−	285.421i		−	0.553141i
$517$	−549.249			−1.06238
$518$	92.6385	+	99.0490i	0.178839	+	0.191214i
$519$	326.728			0.629534
$520$		0			0
$521$		−	871.106i		−	1.67199i	−0.548738	−	0.835994i	$-0.684891\pi$
$521$		−	871.106i		−	1.67199i	0.548738	−	0.835994i	$-0.315109\pi$
$522$		−	178.603i		−	0.342152i
$523$	−108.067			−0.206629			−0.103315	−	0.994649i	$-0.532945\pi$
$523$	−108.067			−0.206629			−0.103315	+	0.994649i	$0.532945\pi$
$524$			278.324i			0.531153i
$525$		0			0
$526$	−374.727			−0.712408
$527$			2.97027i			0.00563618i
$528$	−71.7674			−0.135923
$529$	320.779			0.606388
$530$		0			0
$531$			88.2721i			0.166238i
$532$	−339.655	+	317.673i	−0.638450	+	0.597129i
$533$		−	8.33127i		−	0.0156309i
$534$	−73.9393			−0.138463
$535$		0			0
$536$	−34.4891			−0.0643454
$537$	440.135			0.819618
$538$	268.248			0.498602
$539$	−33.9113	+	506.444i	−0.0629152	+	0.939598i
$540$		0			0
$541$	608.803			1.12533			0.562664	−	0.826685i	$-0.309776\pi$
$541$	608.803			1.12533			0.562664	+	0.826685i	$0.309776\pi$
$542$	405.306			0.747797
$543$			240.318i			0.442574i
$544$			31.0777i			0.0571281i
$545$		0			0
$546$	−7.57842	+	7.08794i	−0.0138799	+	0.0129816i
$547$		−	1020.16i		−	1.86502i	−0.361150	−	0.932508i	$-0.617616\pi$
$547$		−	1020.16i		−	1.86502i	0.361150	−	0.932508i	$-0.382384\pi$
$548$		−	36.5646i		−	0.0667238i
$549$		−	224.156i		−	0.408299i
$550$		0			0
$551$		−	1398.41i		−	2.53795i
$552$	70.6916			0.128065
$553$	−129.562	−	138.527i	−0.234289	−	0.250501i
$554$	−116.721			−0.210687
$555$		0			0
$556$			77.4531i			0.139304i
$557$			162.089i			0.291003i	0.989358	+	0.145502i	$0.0464796\pi$
$557$			162.089i			0.291003i	−0.989358	+	0.145502i	$0.953520\pi$
$558$	−2.29381			−0.00411077
$559$		−	49.8622i		−	0.0891989i
$560$		0			0
$561$	−98.5692			−0.175703
$562$		−	544.368i		−	0.968626i
$563$	273.813			0.486347			0.243173	−	0.969983i	$-0.421812\pi$
$563$	273.813			0.486347			0.243173	+	0.969983i	$0.421812\pi$
$564$	−183.676			−0.325667
$565$		0			0
$566$			727.375i			1.28512i
$567$	−43.0339	−	46.0118i	−0.0758975	−	0.0811495i
$568$		−	119.910i		−	0.211109i
$569$	618.238			1.08653			0.543267	−	0.839560i	$-0.317187\pi$
$569$	618.238			1.08653			0.543267	+	0.839560i	$0.317187\pi$
$570$		0			0
$571$	602.897			1.05586			0.527931	−	0.849287i	$-0.322968\pi$
$571$	602.897			1.05586			0.527931	+	0.849287i	$0.322968\pi$
$572$	−12.5376			−0.0219188
$573$	−309.876			−0.540795
$574$	−93.0931	−	99.5350i	−0.162183	−	0.173406i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$	−491.145			−0.851204			−0.425602	−	0.904911i	$-0.639938\pi$
$577$	−491.145			−0.851204			−0.425602	+	0.904911i	$0.639938\pi$
$578$		−	366.024i		−	0.633259i
$579$		−	6.33761i		−	0.0109458i
$580$		0			0
$581$	606.538	+	648.510i	1.04396	+	1.11620i
$582$			403.192i			0.692769i
$583$		−	201.261i		−	0.345216i
$584$			189.272i			0.324096i
$585$		0			0
$586$		−	609.913i		−	1.04081i
$587$	−990.289			−1.68703			−0.843517	−	0.537102i	$-0.819519\pi$
$587$	−990.289			−1.68703			−0.843517	+	0.537102i	$0.819519\pi$
$588$	−11.3404	+	169.362i	−0.0192864	+	0.288030i
$589$	−17.9599			−0.0304921
$590$		0			0
$591$		−	349.565i		−	0.591481i
$592$			54.7985i			0.0925650i
$593$	−10.4613			−0.0176414			−0.00882070	−	0.999961i	$-0.502808\pi$
$593$	−10.4613			−0.0176414			−0.00882070	+	0.999961i	$0.502808\pi$
$594$		−	76.1208i		−	0.128149i
$595$		0			0
$596$	−40.2270			−0.0674950
$597$			169.012i			0.283102i
$598$	12.3496			0.0206516
$599$	592.559			0.989248			0.494624	−	0.869107i	$-0.335306\pi$
$599$	592.559			0.989248			0.494624	+	0.869107i	$0.335306\pi$
$600$		0			0
$601$			595.499i			0.990846i	0.868652	+	0.495423i	$0.164987\pi$
$601$			595.499i			0.990846i	−0.868652	+	0.495423i	$0.835013\pi$
$602$	−557.157	−	595.712i	−0.925510	−	0.989555i
$603$		−	36.5812i		−	0.0606654i
$604$	−22.6514			−0.0375023
$605$		0			0
$606$	−47.7730			−0.0788334
$607$	621.260			1.02349			0.511747	−	0.859136i	$-0.328999\pi$
$607$	621.260			1.02349			0.511747	+	0.859136i	$0.328999\pi$
$608$	−187.913			−0.309067
$609$	−348.644	−	372.769i	−0.572485	−	0.612101i
$610$		0			0
$611$	−32.0878			−0.0525168
$612$	−32.9629			−0.0538609
$613$			332.564i			0.542519i	0.962506	+	0.271259i	$0.0874401\pi$
$613$			332.564i			0.542519i	−0.962506	+	0.271259i	$0.912560\pi$
$614$		−	482.392i		−	0.785654i
$615$		0			0
$616$	−149.788	+	140.094i	−0.243163	+	0.227425i
$617$			366.977i			0.594776i	0.954757	+	0.297388i	$0.0961156\pi$
$617$			366.977i			0.594776i	−0.954757	+	0.297388i	$0.903884\pi$
$618$		−	266.869i		−	0.431826i
$619$		−	1123.84i		−	1.81557i	−0.419439	−	0.907783i	$-0.637773\pi$
$619$		−	1123.84i		−	1.81557i	0.419439	−	0.907783i	$-0.362227\pi$
$620$		0			0
$621$			74.9798i			0.120740i
$622$	−771.750			−1.24076
$623$	−154.321	+	144.334i	−0.247707	+	0.231675i
$624$	−4.19273			−0.00671912
$625$		0			0
$626$			139.639i			0.223066i
$627$		−	596.003i		−	0.950564i
$628$	216.845			0.345294
$629$			75.2632i			0.119655i
$630$		0			0
$631$	782.201			1.23962			0.619810	−	0.784752i	$-0.287210\pi$
$631$	782.201			1.23962			0.619810	+	0.784752i	$0.287210\pi$
$632$		−	76.6397i		−	0.121265i
$633$	180.344			0.284904
$634$	233.428			0.368183
$635$		0			0
$636$		−	67.3044i		−	0.105825i
$637$	−1.98114	+	29.5870i	−0.00311011	+	0.0464474i
$638$		−	616.701i		−	0.966616i
$639$	127.183			0.199035
$640$		0			0
$641$	6.16909			0.00962416			0.00481208	−	0.999988i	$-0.498468\pi$
$641$	6.16909			0.00962416			0.00481208	+	0.999988i	$0.498468\pi$
$642$	−295.858			−0.460838
$643$	−82.5062			−0.128315			−0.0641573	−	0.997940i	$-0.520436\pi$
$643$	−82.5062			−0.128315			−0.0641573	+	0.997940i	$0.520436\pi$
$644$	147.543	−	137.994i	0.229104	−	0.214276i
$645$		0			0
$646$	−258.090			−0.399520
$647$	−863.567			−1.33472			−0.667362	−	0.744733i	$-0.732577\pi$
$647$	−863.567			−1.33472			−0.667362	+	0.744733i	$0.732577\pi$
$648$		−	25.4558i		−	0.0392837i
$649$			304.796i			0.469639i
$650$		0			0
$651$	−4.78750	+	4.47765i	−0.00735407	+	0.00687811i
$652$			164.289i			0.251976i
$653$			172.088i			0.263535i	0.991281	+	0.131767i	$0.0420652\pi$
$653$			172.088i			0.263535i	−0.991281	+	0.131767i	$0.957935\pi$
$654$			303.381i			0.463885i
$655$		0			0
$656$		−	55.0674i		−	0.0839442i
$657$	−200.754			−0.305561
$658$	−383.358	+	358.547i	−0.582611	+	0.544904i
$659$	−170.542			−0.258789			−0.129394	−	0.991593i	$-0.541303\pi$
$659$	−170.542			−0.258789			−0.129394	+	0.991593i	$0.541303\pi$
$660$		0			0
$661$			53.4631i			0.0808822i	0.999182	+	0.0404411i	$0.0128763\pi$
$661$			53.4631i			0.0808822i	−0.999182	+	0.0404411i	$0.987124\pi$
$662$		−	326.205i		−	0.492756i
$663$	−5.75853			−0.00868556
$664$			358.786i			0.540340i
$665$		0			0
$666$	−58.1225			−0.0872711
$667$			607.457i			0.910730i
$668$	629.290			0.942050
$669$	−443.164			−0.662427
$670$		0			0
$671$		−	773.991i		−	1.15349i
$672$	−50.0913	+	46.8494i	−0.0745406	+	0.0697163i
$673$		−	1215.31i		−	1.80581i	−0.429836	−	0.902907i	$-0.641429\pi$
$673$		−	1215.31i		−	1.80581i	0.429836	−	0.902907i	$-0.358571\pi$
$674$	−204.542			−0.303475
$675$		0			0
$676$	337.268			0.498916
$677$	1161.52			1.71569			0.857846	−	0.513907i	$-0.171802\pi$
$677$	1161.52			1.71569			0.857846	+	0.513907i	$0.171802\pi$
$678$	493.376			0.727694
$679$	787.053	+	841.516i	1.15914	+	1.23935i
$680$		0			0
$681$	177.781			0.261059
$682$	−7.92032			−0.0116134
$683$		−	724.141i		−	1.06024i	−0.847924	−	0.530118i	$-0.822148\pi$
$683$		−	724.141i		−	1.06024i	0.847924	−	0.530118i	$-0.177852\pi$
$684$		−	199.312i		−	0.291392i
$685$		0			0
$686$	306.935	+	375.618i	0.447427	+	0.547549i
$687$			440.050i			0.640539i
$688$		−	329.575i		−	0.479034i
$689$		−	11.7579i		−	0.0170652i
$690$		0			0
$691$		−	1084.92i		−	1.57007i	−0.619450	−	0.785036i	$-0.712644\pi$
$691$		−	1084.92i		−	1.57007i	0.619450	−	0.785036i	$-0.287356\pi$
$692$	377.273			0.545193
$693$	−148.592	−	158.875i	−0.214419	−	0.229256i
$694$	−229.540			−0.330750
$695$		0			0
$696$		−	206.233i		−	0.296312i
$697$		−	75.6325i		−	0.108511i
$698$	−443.220			−0.634986
$699$		−	151.372i		−	0.216556i
$700$		0			0
$701$	−405.283			−0.578150			−0.289075	−	0.957307i	$-0.593348\pi$
$701$	−405.283			−0.578150			−0.289075	+	0.957307i	$0.593348\pi$
$702$		−	4.44707i		−	0.00633485i
$703$	−455.083			−0.647344
$704$	−82.8698			−0.117713
$705$		0			0
$706$		−	485.115i		−	0.687132i
$707$	−99.7089	+	93.2557i	−0.141031	+	0.131903i
$708$			101.928i			0.143966i
$709$	−906.179			−1.27811			−0.639055	−	0.769161i	$-0.720674\pi$
$709$	−906.179			−1.27811			−0.639055	+	0.769161i	$0.720674\pi$
$710$		0			0
$711$	81.2886			0.114330
$712$	−85.3777			−0.119913
$713$	7.80160			0.0109419
$714$	−68.7981	+	64.3454i	−0.0963558	+	0.0901197i
$715$		0			0
$716$	508.224			0.709810
$717$	−412.514			−0.575333
$718$			505.288i			0.703744i
$719$		−	1374.58i		−	1.91180i	−0.293693	−	0.955900i	$-0.594884\pi$
$719$		−	1374.58i		−	1.91180i	0.293693	−	0.955900i	$-0.405116\pi$
$720$		0			0
$721$	−520.943	−	556.991i	−0.722528	−	0.772526i
$722$		−	1050.02i		−	1.45432i
$723$		−	408.097i		−	0.564449i
$724$			277.495i			0.383280i
$725$		0			0
$726$			33.5501i			0.0462122i
$727$	−203.600			−0.280055			−0.140028	−	0.990148i	$-0.544719\pi$
$727$	−203.600			−0.280055			−0.140028	+	0.990148i	$0.544719\pi$
$728$	−8.75081	+	8.18445i	−0.0120203	+	0.0112424i
$729$	27.0000			0.0370370
$730$		0			0
$731$		−	452.657i		−	0.619229i
$732$		−	258.833i		−	0.353597i
$733$	−841.642			−1.14822			−0.574108	−	0.818780i	$-0.694651\pi$
$733$	−841.642			−1.14822			−0.574108	+	0.818780i	$0.694651\pi$
$734$			872.767i			1.18906i
$735$		0			0
$736$	81.6276			0.110907
$737$		−	126.312i		−	0.171386i
$738$	58.4078			0.0791433
$739$	1251.55			1.69358			0.846788	−	0.531930i	$-0.178533\pi$
$739$	1251.55			1.69358			0.846788	+	0.531930i	$0.178533\pi$
$740$		0			0
$741$		−	34.8192i		−	0.0469895i
$742$	−131.382	−	140.474i	−0.177065	−	0.189317i
$743$			83.5814i			0.112492i	0.998417	+	0.0562459i	$0.0179131\pi$
$743$			83.5814i			0.112492i	−0.998417	+	0.0562459i	$0.982087\pi$
$744$	−2.64866			−0.00356003
$745$		0			0
$746$	479.239			0.642411
$747$	−380.550			−0.509437
$748$	−113.818			−0.152163
$749$	−617.497	+	577.532i	−0.824428	+	0.771071i
$750$		0			0
$751$	1364.04			1.81630			0.908152	−	0.418641i	$-0.137493\pi$
$751$	1364.04			1.81630			0.908152	+	0.418641i	$0.137493\pi$
$752$	−212.091			−0.282036
$753$		−	487.696i		−	0.647670i
$754$		−	36.0284i		−	0.0477830i
$755$		0			0
$756$	−49.6913	−	53.1298i	−0.0657292	−	0.0702776i
$757$		−	193.941i		−	0.256196i	−0.991761	−	0.128098i	$-0.959113\pi$
$757$		−	193.941i		−	0.256196i	0.991761	−	0.128098i	$-0.0408873\pi$
$758$			299.291i			0.394843i
$759$			258.898i			0.341105i
$760$		0			0
$761$		−	698.879i		−	0.918369i	−0.888341	−	0.459185i	$-0.848142\pi$
$761$		−	698.879i		−	0.918369i	0.888341	−	0.459185i	$-0.151858\pi$
$762$	−522.667			−0.685915
$763$	592.217	+	633.198i	0.776169	+	0.829879i
$764$	−357.814			−0.468342
$765$		0			0
$766$		−	337.645i		−	0.440789i
$767$			17.8065i			0.0232158i
$768$	−27.7128			−0.0360844
$769$			335.359i			0.436097i	0.975938	+	0.218049i	$0.0699691\pi$
$769$			335.359i			0.436097i	−0.975938	+	0.218049i	$0.930031\pi$
$770$		0			0
$771$	−439.145			−0.569578
$772$		−	7.31805i		−	0.00947933i
$773$	−1276.11			−1.65085			−0.825426	−	0.564511i	$-0.809065\pi$
$773$	−1276.11			−1.65085			−0.825426	+	0.564511i	$0.809065\pi$
$774$	349.567			0.451638
$775$		0			0
$776$			465.565i			0.599955i
$777$	−121.310	+	113.459i	−0.156126	+	0.146021i
$778$			30.7907i			0.0395767i
$779$	457.316			0.587055
$780$		0			0
$781$	439.153			0.562295
$782$	112.112			0.143365
$783$	218.743			0.279366
$784$	−13.0948	+	195.562i	−0.0167025	+	0.249441i
$785$		0			0
$786$	−340.876			−0.433684
$787$	−415.510			−0.527967			−0.263983	−	0.964527i	$-0.585036\pi$
$787$	−415.510			−0.527967			−0.263983	+	0.964527i	$0.585036\pi$
$788$		−	403.643i		−	0.512237i
$789$		−	458.945i		−	0.581679i
$790$		0			0
$791$	1029.74	−	963.098i	1.30183	−	1.21757i
$792$		−	87.8967i		−	0.110981i
$793$		−	45.2175i		−	0.0570208i
$794$			781.943i			0.984814i
$795$		0			0
$796$			195.158i			0.245174i
$797$	−1337.78			−1.67852			−0.839259	−	0.543731i	$-0.817011\pi$
$797$	−1337.78			−1.67852			−0.839259	+	0.543731i	$0.817011\pi$
$798$	−389.068	−	415.991i	−0.487554	−	0.521292i
$799$	−291.297			−0.364578
$800$		0			0
$801$		−	90.5568i		−	0.113055i
$802$		−	899.730i		−	1.12186i
$803$	−693.184			−0.863243
$804$		−	42.2404i		−	0.0525378i
$805$		0			0
$806$	−0.462714			−0.000574087
$807$			328.535i			0.407107i
$808$	−55.1635			−0.0682717
$809$	−754.137			−0.932184			−0.466092	−	0.884736i	$-0.654338\pi$
$809$	−754.137			−0.932184			−0.466092	+	0.884736i	$0.654338\pi$
$810$		0			0
$811$			509.569i			0.628321i	0.949370	+	0.314161i	$0.101723\pi$
$811$			509.569i			0.628321i	−0.949370	+	0.314161i	$0.898277\pi$
$812$	−402.579	−	430.437i	−0.495787	−	0.530095i
$813$			496.397i			0.610574i
$814$	−200.692			−0.246550
$815$		0			0
$816$	−38.0623			−0.0466449
$817$	2737.01			3.35007
$818$	506.834			0.619602
$819$	−8.68092	−	9.28163i	−0.0105994	−	0.0113329i
$820$		0			0
$821$	−508.671			−0.619575			−0.309787	−	0.950806i	$-0.600258\pi$
$821$	−508.671			−0.619575			−0.309787	+	0.950806i	$0.600258\pi$
$822$	44.7824			0.0544797
$823$			717.806i			0.872182i	0.899903	+	0.436091i	$0.143637\pi$
$823$			717.806i			0.872182i	−0.899903	+	0.436091i	$0.856363\pi$
$824$		−	308.153i		−	0.373972i
$825$		0			0
$826$	198.969	+	212.737i	0.240883	+	0.257551i
$827$			444.662i			0.537681i	0.963185	+	0.268841i	$0.0866405\pi$
$827$			444.662i			0.537681i	−0.963185	+	0.268841i	$0.913360\pi$
$828$			86.5792i			0.104564i
$829$		−	250.314i		−	0.301947i	−0.988538	−	0.150973i	$-0.951759\pi$
$829$		−	250.314i		−	0.301947i	0.988538	−	0.150973i	$-0.0482407\pi$
$830$		0			0
$831$		−	142.953i		−	0.172026i
$832$	−4.84135			−0.00581893
$833$	−17.9851	+	268.595i	−0.0215907	+	0.322444i
$834$	−94.8602			−0.113741
$835$		0			0
$836$		−	688.206i		−	0.823212i
$837$		−	2.80933i		−	0.00335643i
$838$	−553.726			−0.660771
$839$		−	1026.45i		−	1.22343i	−0.791080	−	0.611713i	$-0.790481\pi$
$839$		−	1026.45i		−	1.22343i	0.791080	−	0.611713i	$-0.209519\pi$
$840$		0			0
$841$	931.173			1.10722
$842$			668.466i			0.793902i
$843$	666.711			0.790880
$844$	208.244			0.246734
$845$		0			0
$846$		−	224.957i		−	0.265906i
$847$	65.4917	+	70.0236i	0.0773219	+	0.0826725i
$848$		−	77.7165i		−	0.0916468i
$849$	−890.849			−1.04929
$850$		0			0
$851$	197.684			0.232296
$852$	146.859			0.172369
$853$	−840.837			−0.985740			−0.492870	−	0.870103i	$-0.664052\pi$
$853$	−840.837			−0.985740			−0.492870	+	0.870103i	$0.664052\pi$
$854$	−505.257	−	540.221i	−0.591636	−	0.632577i
$855$		0			0
$856$	−341.628			−0.399098
$857$	860.502			1.00409			0.502043	−	0.864843i	$-0.332582\pi$
$857$	860.502			1.00409			0.502043	+	0.864843i	$0.332582\pi$
$858$		−	15.3553i		−	0.0178966i
$859$			1163.93i			1.35498i	0.735532	+	0.677490i	$0.236932\pi$
$859$			1163.93i			1.35498i	−0.735532	+	0.677490i	$0.763068\pi$
$860$		0			0
$861$	121.905	−	114.015i	0.141585	−	0.132422i
$862$		−	949.163i		−	1.10112i
$863$			704.504i			0.816343i	0.912905	+	0.408172i	$0.133833\pi$
$863$			704.504i			0.816343i	−0.912905	+	0.408172i	$0.866167\pi$
$864$		−	29.3939i		−	0.0340207i
$865$		0			0
$866$			160.104i			0.184878i
$867$	448.286			0.517054
$868$	−5.52813	+	5.17034i	−0.00636881	+	0.00595662i
$869$	280.682			0.322995
$870$		0			0
$871$		−	7.37928i		−	0.00847219i
$872$			350.314i			0.401736i
$873$	−493.807			−0.565643
$874$			677.890i			0.775618i
$875$		0			0
$876$	−231.810			−0.264624
$877$		−	570.744i		−	0.650792i	−0.945578	−	0.325396i	$-0.894502\pi$
$877$		−	570.744i		−	0.650792i	0.945578	−	0.325396i	$-0.105498\pi$
$878$	852.897			0.971409
$879$	746.988			0.849815
$880$		0			0
$881$			1241.29i			1.40895i	0.709728	+	0.704476i	$0.248818\pi$
$881$			1241.29i			1.40895i	−0.709728	+	0.704476i	$0.751182\pi$
$882$	−207.425	−	13.8891i	−0.235176	−	0.0157473i
$883$			907.346i			1.02757i	0.857918	+	0.513786i	$0.171758\pi$
$883$			907.346i			1.02757i	−0.857918	+	0.513786i	$0.828242\pi$
$884$	−6.64937			−0.00752191
$885$		0			0
$886$	−1207.35			−1.36269
$887$	−132.595			−0.149487			−0.0747437	−	0.997203i	$-0.523814\pi$
$887$	−132.595			−0.149487			−0.0747437	+	0.997203i	$0.523814\pi$
$888$	−67.1141			−0.0755790
$889$	−1090.88	+	1020.28i	−1.22708	+	1.14767i
$890$		0			0
$891$	93.2285			0.104634
$892$	−511.722			−0.573679
$893$		−	1761.35i		−	1.97239i
$894$		−	49.2679i		−	0.0551095i
$895$		0			0
$896$	−57.8404	+	54.0970i	−0.0645541	+	0.0603761i
$897$			15.1251i			0.0168619i
$898$			328.887i			0.366243i
$899$		−	22.7601i		−	0.0253171i
$900$		0			0
$901$		−	106.740i		−	0.118468i
$902$	201.677			0.223588
$903$	729.595	−	682.375i	0.807968	−	0.755676i
$904$	569.702			0.630201
$905$		0			0
$906$		−	27.7422i		−	0.0306205i
$907$		−	1309.04i		−	1.44326i	−0.692277	−	0.721632i	$-0.743392\pi$
$907$		−	1309.04i		−	1.44326i	0.692277	−	0.721632i	$-0.256608\pi$
$908$	205.284			0.226084
$909$		−	58.5098i		−	0.0643672i
$910$		0			0
$911$	−1252.86			−1.37525			−0.687627	−	0.726064i	$-0.741348\pi$
$911$	−1252.86			−1.37525			−0.687627	+	0.726064i	$0.741348\pi$
$912$		−	230.145i		−	0.252352i
$913$	−1314.00			−1.43922
$914$	−551.400			−0.603282
$915$		0			0
$916$			508.126i			0.554723i
$917$	−711.455	+	665.409i	−0.775850	+	0.725637i
$918$		−	40.3711i		−	0.0439773i
$919$	329.889			0.358966			0.179483	−	0.983761i	$-0.442558\pi$
$919$	329.889			0.358966			0.179483	+	0.983761i	$0.442558\pi$
$920$		0			0
$921$	590.807			0.641484
$922$	848.122			0.919872
$923$	25.6558			0.0277961
$924$	−171.579	−	183.452i	−0.185692	−	0.198542i
$925$		0			0
$926$	−298.771			−0.322647
$927$	326.846			0.352585
$928$		−	238.138i		−	0.256614i
$929$		−	12.0040i		−	0.0129214i	−0.999979	−	0.00646072i	$-0.997943\pi$
$929$		−	12.0040i		−	0.0129214i	0.999979	−	0.00646072i	$-0.00205653\pi$
$930$		0			0
$931$	−1624.08	−	108.748i	−1.74444	−	0.116807i
$932$		−	174.790i		−	0.187543i
$933$		−	945.197i		−	1.01307i
$934$			1126.89i			1.20652i
$935$		0			0
$936$		−	5.13503i		−	0.00548614i
$937$	300.461			0.320663			0.160331	−	0.987063i	$-0.448744\pi$
$937$	300.461			0.320663			0.160331	+	0.987063i	$0.448744\pi$
$938$	−82.4556	−	88.1615i	−0.0879058	−	0.0939888i
$939$	−171.022			−0.182132
$940$		0			0
$941$			494.625i			0.525637i	0.964845	+	0.262819i	$0.0846521\pi$
$941$			494.625i			0.525637i	−0.964845	+	0.262819i	$0.915348\pi$
$942$			265.580i			0.281932i
$943$	−198.654			−0.210661
$944$			117.696i			0.124678i
$945$		0			0
$946$	1207.02			1.27592
$947$			337.631i			0.356527i	0.983983	+	0.178263i	$0.0570479\pi$
$947$			337.631i			0.356527i	−0.983983	+	0.178263i	$0.942952\pi$
$948$	93.8640			0.0990127
$949$	−40.4966			−0.0426729
$950$		0			0
$951$			285.889i			0.300620i
$952$	−79.4412	+	74.2997i	−0.0834466	+	0.0780459i
$953$		−	635.279i		−	0.666610i	−0.942819	−	0.333305i	$-0.891836\pi$
$953$		−	635.279i		−	0.666610i	0.942819	−	0.333305i	$-0.108164\pi$
$954$	82.4308			0.0864054
$955$		0			0
$956$	−476.330			−0.498253
$957$	755.301			0.789238
$958$	738.962			0.771359
$959$	93.4669	−	87.4177i	0.0974629	−	0.0911551i
$960$		0			0
$961$	960.708			0.999696
$962$	−11.7247			−0.0121878
$963$		−	362.351i		−	0.376273i
$964$		−	471.230i		−	0.488827i
$965$		0			0
$966$	169.007	+	180.703i	0.174956	+	0.187063i
$967$		−	489.313i		−	0.506011i	−0.967465	−	0.253006i	$-0.918581\pi$
$967$		−	489.313i		−	0.506011i	0.967465	−	0.253006i	$-0.0814191\pi$
$968$			38.7403i			0.0400210i
$969$		−	316.094i		−	0.326207i
$970$		0			0
$971$		−	621.040i		−	0.639588i	−0.947487	−	0.319794i	$-0.896386\pi$
$971$		−	621.040i		−	0.639588i	0.947487	−	0.319794i	$-0.103614\pi$
$972$	31.1769			0.0320750
$973$	−197.986	+	185.173i	−0.203480	+	0.190311i
$974$	−306.574			−0.314758
$975$		0			0
$976$		−	298.875i		−	0.306224i
$977$			1475.20i			1.50993i	0.655768	+	0.754963i	$0.272345\pi$
$977$			1475.20i			1.50993i	−0.655768	+	0.754963i	$0.727655\pi$
$978$	−201.212			−0.205738
$979$		−	312.684i		−	0.319392i
$980$		0			0
$981$	−371.564			−0.378761
$982$			638.158i			0.649856i
$983$	−343.366			−0.349304			−0.174652	−	0.984630i	$-0.555880\pi$
$983$	−343.366			−0.349304			−0.174652	+	0.984630i	$0.555880\pi$
$984$	67.4435			0.0685401
$985$		0			0
$986$		−	327.071i		−	0.331715i
$987$	−439.128	−	469.515i	−0.444912	−	0.475700i
$988$		−	40.2058i		−	0.0406941i
$989$	−1188.93			−1.20216
$990$		0			0
$991$	−1389.23			−1.40184			−0.700921	−	0.713239i	$-0.747228\pi$
$991$	−1389.23			−1.40184			−0.700921	+	0.713239i	$0.747228\pi$
$992$	−3.05841			−0.00308308
$993$	399.518			0.402334
$994$	306.514	−	286.677i	0.308364	−	0.288407i
$995$		0			0
$996$	−439.421			−0.441186
$997$	347.412			0.348458			0.174229	−	0.984705i	$-0.444257\pi$
$997$	347.412			0.348458			0.174229	+	0.984705i	$0.444257\pi$
$998$		−	491.151i		−	0.492135i
$999$		−	71.1853i		−	0.0712565i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.h.c.349.2		24
5.2	odd	4		1050.3.f.d.601.6	yes	12
5.3	odd	4		1050.3.f.c.601.7	✓	12
5.4	even	2	inner	1050.3.h.c.349.23		24
7.6	odd	2	inner	1050.3.h.c.349.24		24
35.13	even	4		1050.3.f.c.601.10	yes	12
35.27	even	4		1050.3.f.d.601.3	yes	12
35.34	odd	2	inner	1050.3.h.c.349.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.f.c.601.7	✓	12	5.3	odd	4
1050.3.f.c.601.10	yes	12	35.13	even	4
1050.3.f.d.601.3	yes	12	35.27	even	4
1050.3.f.d.601.6	yes	12	5.2	odd	4
1050.3.h.c.349.1		24	35.34	odd	2	inner
1050.3.h.c.349.2		24	1.1	even	1	trivial
1050.3.h.c.349.23		24	5.4	even	2	inner
1050.3.h.c.349.24		24	7.6	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.h (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} -2.44949i q^{6} +(-4.78154 - 5.11242i) q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} -2.44949i q^{6} +(-4.78154 - 5.11242i) q^{7} -2.82843i q^{8} +3.00000 q^{9} +10.3587 q^{11} +3.46410 q^{12} +0.605169 q^{13} +(7.23005 - 6.76212i) q^{14} +4.00000 q^{16} +5.49382 q^{17} +4.24264i q^{18} +33.2186i q^{19} +(8.28188 + 8.85497i) q^{21} +14.6495i q^{22} -14.4299i q^{23} +4.89898i q^{24} +0.855838i q^{26} -5.19615 q^{27} +(9.56309 + 10.2248i) q^{28} -42.0972 q^{29} +0.540656i q^{31} +5.65685i q^{32} -17.9418 q^{33} +7.76943i q^{34} -6.00000 q^{36} +13.6996i q^{37} -46.9782 q^{38} -1.04818 q^{39} -13.7668i q^{41} +(-12.5228 + 11.7123i) q^{42} -82.3938i q^{43} -20.7175 q^{44} +20.4069 q^{46} -53.0228 q^{47} -6.92820 q^{48} +(-3.27369 + 48.8905i) q^{49} -9.51557 q^{51} -1.21034 q^{52} -19.4291i q^{53} -7.34847i q^{54} +(-14.4601 + 13.5242i) q^{56} -57.5364i q^{57} -59.5344i q^{58} +29.4240i q^{59} -74.7188i q^{61} -0.764604 q^{62} +(-14.3446 - 15.3373i) q^{63} -8.00000 q^{64} -25.3736i q^{66} -12.1937i q^{67} -10.9876 q^{68} +24.9933i q^{69} +42.3945 q^{71} -8.48528i q^{72} -66.9179 q^{73} -19.3742 q^{74} -66.4373i q^{76} +(-49.5307 - 52.9582i) q^{77} -1.48236i q^{78} +27.0962 q^{79} +9.00000 q^{81} +19.4693 q^{82} -126.850 q^{83} +(-16.5638 - 17.7099i) q^{84} +116.522 q^{86} +72.9145 q^{87} -29.2989i q^{88} -30.1856i q^{89} +(-2.89364 - 3.09388i) q^{91} +28.8597i q^{92} -0.936444i q^{93} -74.9856i q^{94} -9.79796i q^{96} -164.602 q^{97} +(-69.1416 - 4.62970i) q^{98} +31.0762 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 48 q^{4} + 72 q^{9}+O(q^{10}) \) 24 * q - 48 * q^4 + 72 * q^9	\( 24 q - 48 q^{4} + 72 q^{9} - 32 q^{11} - 16 q^{14} + 96 q^{16} - 12 q^{21} - 96 q^{29} - 144 q^{36} + 24 q^{39} + 64 q^{44} + 160 q^{46} - 236 q^{49} + 144 q^{51} + 32 q^{56} - 192 q^{64} + 496 q^{71} + 128 q^{74} + 416 q^{79} + 216 q^{81} + 24 q^{84} + 256 q^{86} - 316 q^{91} - 96 q^{99}+O(q^{100}) \) 24 * q - 48 * q^4 + 72 * q^9 - 32 * q^11 - 16 * q^14 + 96 * q^16 - 12 * q^21 - 96 * q^29 - 144 * q^36 + 24 * q^39 + 64 * q^44 + 160 * q^46 - 236 * q^49 + 144 * q^51 + 32 * q^56 - 192 * q^64 + 496 * q^71 + 128 * q^74 + 416 * q^79 + 216 * q^81 + 24 * q^84 + 256 * q^86 - 316 * q^91 - 96 * q^99

Introduction

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