LMFDB - Embedded newform 1050.3.h.c.349.15

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			349.15
Character	$\chi$	$=$	1050.349
Dual form			1050.3.h.c.349.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +2.44949i q^{6} +(5.85173 - 3.84151i) q^{7} +2.82843i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +2.44949i q^{6} +(5.85173 - 3.84151i) q^{7} +2.82843i q^{8} +3.00000 q^{9} +20.2923 q^{11} +3.46410 q^{12} +11.5677 q^{13} +(-5.43272 - 8.27560i) q^{14} +4.00000 q^{16} -26.7353 q^{17} -4.24264i q^{18} +9.76295i q^{19} +(-10.1355 + 6.65370i) q^{21} -28.6976i q^{22} +34.8802i q^{23} -4.89898i q^{24} -16.3592i q^{26} -5.19615 q^{27} +(-11.7035 + 7.68303i) q^{28} +10.4554 q^{29} +39.3054i q^{31} -5.65685i q^{32} -35.1472 q^{33} +37.8094i q^{34} -6.00000 q^{36} +11.1970i q^{37} +13.8069 q^{38} -20.0358 q^{39} +49.9892i q^{41} +(9.40975 + 14.3338i) q^{42} -10.5469i q^{43} -40.5845 q^{44} +49.3281 q^{46} +34.8668 q^{47} -6.92820 q^{48} +(19.4856 - 44.9590i) q^{49} +46.3068 q^{51} -23.1354 q^{52} -68.9396i q^{53} +7.34847i q^{54} +(10.8654 + 16.5512i) q^{56} -16.9099i q^{57} -14.7861i q^{58} +49.7693i q^{59} +47.1666i q^{61} +55.5863 q^{62} +(17.5552 - 11.5245i) q^{63} -8.00000 q^{64} +49.7057i q^{66} -111.855i q^{67} +53.4705 q^{68} -60.4143i q^{69} +132.537 q^{71} +8.48528i q^{72} +130.413 q^{73} +15.8349 q^{74} -19.5259i q^{76} +(118.745 - 77.9530i) q^{77} +28.3350i q^{78} +3.57417 q^{79} +9.00000 q^{81} +70.6955 q^{82} -101.912 q^{83} +(20.2710 - 13.3074i) q^{84} -14.9155 q^{86} -18.1092 q^{87} +57.3952i q^{88} +7.58595i q^{89} +(67.6911 - 44.4375i) q^{91} -69.7605i q^{92} -68.0790i q^{93} -49.3090i q^{94} +9.79796i q^{96} -154.047 q^{97} +(-63.5816 - 27.5567i) q^{98} +60.8768 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	5.85173	−	3.84151i	0.835962	−	0.548788i
$7$	5.85173	−	3.84151i	0.835962	−	0.548788i
$8$			2.82843i			0.353553i
$9$	3.00000			0.333333
$10$		0			0
$11$	20.2923			1.84475			0.922376	−	0.386294i	$-0.126245\pi$
$11$	20.2923			1.84475			0.922376	+	0.386294i	$0.126245\pi$
$12$	3.46410			0.288675
$13$	11.5677			0.889823			0.444911	−	0.895575i	$-0.353235\pi$
$13$	11.5677			0.889823			0.444911	+	0.895575i	$0.353235\pi$
$14$	−5.43272	−	8.27560i	−0.388051	−	0.591114i
$15$		0			0
$16$	4.00000			0.250000
$17$	−26.7353			−1.57266			−0.786331	−	0.617805i	$-0.788022\pi$
$17$	−26.7353			−1.57266			−0.786331	+	0.617805i	$0.788022\pi$
$18$		−	4.24264i		−	0.235702i
$19$			9.76295i			0.513839i	0.966433	+	0.256920i	$0.0827076\pi$
$19$			9.76295i			0.513839i	−0.966433	+	0.256920i	$0.917292\pi$
$20$		0			0
$21$	−10.1355	+	6.65370i	−0.482643	+	0.316843i
$22$		−	28.6976i		−	1.30444i
$23$			34.8802i			1.51653i	0.651945	+	0.758266i	$0.273953\pi$
$23$			34.8802i			1.51653i	−0.651945	+	0.758266i	$0.726047\pi$
$24$		−	4.89898i		−	0.204124i
$25$		0			0
$26$		−	16.3592i		−	0.629200i
$27$	−5.19615			−0.192450
$28$	−11.7035	+	7.68303i	−0.417981	+	0.274394i
$29$	10.4554			0.360530			0.180265	−	0.983618i	$-0.442305\pi$
$29$	10.4554			0.360530			0.180265	+	0.983618i	$0.442305\pi$
$30$		0			0
$31$			39.3054i			1.26792i	0.773367	+	0.633958i	$0.218571\pi$
$31$			39.3054i			1.26792i	−0.773367	+	0.633958i	$0.781429\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−35.1472			−1.06507
$34$			37.8094i			1.11204i
$35$		0			0
$36$	−6.00000			−0.166667
$37$			11.1970i			0.302621i	0.988486	+	0.151310i	$0.0483493\pi$
$37$			11.1970i			0.302621i	−0.988486	+	0.151310i	$0.951651\pi$
$38$	13.8069			0.363339
$39$	−20.0358			−0.513739
$40$		0			0
$41$			49.9892i			1.21925i	0.792690	+	0.609625i	$0.208680\pi$
$41$			49.9892i			1.21925i	−0.792690	+	0.609625i	$0.791320\pi$
$42$	9.40975	+	14.3338i	0.224042	+	0.341280i
$43$		−	10.5469i		−	0.245276i	−0.992451	−	0.122638i	$-0.960865\pi$
$43$		−	10.5469i		−	0.245276i	0.992451	−	0.122638i	$-0.0391355\pi$
$44$	−40.5845			−0.922376
$45$		0			0
$46$	49.3281			1.07235
$47$	34.8668			0.741846			0.370923	−	0.928664i	$-0.379041\pi$
$47$	34.8668			0.741846			0.370923	+	0.928664i	$0.379041\pi$
$48$	−6.92820			−0.144338
$49$	19.4856	−	44.9590i	0.397664	−	0.917531i
$50$		0			0
$51$	46.3068			0.907977
$52$	−23.1354			−0.444911
$53$		−	68.9396i		−	1.30075i	−0.759615	−	0.650373i	$-0.774613\pi$
$53$		−	68.9396i		−	1.30075i	0.759615	−	0.650373i	$-0.225387\pi$
$54$			7.34847i			0.136083i
$55$		0			0
$56$	10.8654	+	16.5512i	0.194026	+	0.295557i
$57$		−	16.9099i		−	0.296665i
$58$		−	14.7861i		−	0.254933i
$59$			49.7693i			0.843548i	0.906701	+	0.421774i	$0.138592\pi$
$59$			49.7693i			0.843548i	−0.906701	+	0.421774i	$0.861408\pi$
$60$		0			0
$61$			47.1666i			0.773223i	0.922243	+	0.386611i	$0.126355\pi$
$61$			47.1666i			0.773223i	−0.922243	+	0.386611i	$0.873645\pi$
$62$	55.5863			0.896553
$63$	17.5552	−	11.5245i	0.278654	−	0.182929i
$64$	−8.00000			−0.125000
$65$		0			0
$66$			49.7057i			0.753117i
$67$		−	111.855i		−	1.66947i	−0.550651	−	0.834735i	$-0.685621\pi$
$67$		−	111.855i		−	1.66947i	0.550651	−	0.834735i	$-0.314379\pi$
$68$	53.4705			0.786331
$69$		−	60.4143i		−	0.875570i
$70$		0			0
$71$	132.537			1.86672			0.933361	−	0.358940i	$-0.116862\pi$
$71$	132.537			1.86672			0.933361	+	0.358940i	$0.116862\pi$
$72$			8.48528i			0.117851i
$73$	130.413			1.78648			0.893240	−	0.449580i	$-0.148427\pi$
$73$	130.413			1.78648			0.893240	+	0.449580i	$0.148427\pi$
$74$	15.8349			0.213985
$75$		0			0
$76$		−	19.5259i		−	0.256920i
$77$	118.745	−	77.9530i	1.54214	−	1.01238i
$78$			28.3350i			0.363269i
$79$	3.57417			0.0452427			0.0226213	−	0.999744i	$-0.492799\pi$
$79$	3.57417			0.0452427			0.0226213	+	0.999744i	$0.492799\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	70.6955			0.862140
$83$	−101.912			−1.22786			−0.613929	−	0.789361i	$-0.710412\pi$
$83$	−101.912			−1.22786			−0.613929	+	0.789361i	$0.710412\pi$
$84$	20.2710	−	13.3074i	0.241321	−	0.158421i
$85$		0			0
$86$	−14.9155			−0.173437
$87$	−18.1092			−0.208152
$88$			57.3952i			0.652218i
$89$			7.58595i			0.0852354i	0.999091	+	0.0426177i	$0.0135697\pi$
$89$			7.58595i			0.0852354i	−0.999091	+	0.0426177i	$0.986430\pi$
$90$		0			0
$91$	67.6911	−	44.4375i	0.743858	−	0.488324i
$92$		−	69.7605i		−	0.758266i
$93$		−	68.0790i		−	0.732032i
$94$		−	49.3090i		−	0.524564i
$95$		0			0
$96$			9.79796i			0.102062i
$97$	−154.047			−1.58811			−0.794055	−	0.607846i	$-0.792034\pi$
$97$	−154.047			−1.58811			−0.794055	+	0.607846i	$0.792034\pi$
$98$	−63.5816	−	27.5567i	−0.648792	−	0.281191i
$99$	60.8768			0.614917
$100$		0			0
$101$			50.7835i			0.502807i	0.967882	+	0.251404i	$0.0808921\pi$
$101$			50.7835i			0.502807i	−0.967882	+	0.251404i	$0.919108\pi$
$102$		−	65.4878i		−	0.642037i
$103$	5.35150			0.0519563			0.0259782	−	0.999663i	$-0.491730\pi$
$103$	5.35150			0.0519563			0.0259782	+	0.999663i	$0.491730\pi$
$104$			32.7184i			0.314600i
$105$		0			0
$106$	−97.4952			−0.919767
$107$			123.250i			1.15187i	0.817495	+	0.575935i	$0.195362\pi$
$107$			123.250i			1.15187i	−0.817495	+	0.575935i	$0.804638\pi$
$108$	10.3923			0.0962250
$109$	103.912			0.953320			0.476660	−	0.879088i	$-0.341847\pi$
$109$	103.912			0.953320			0.476660	+	0.879088i	$0.341847\pi$
$110$		0			0
$111$		−	19.3937i		−	0.174718i
$112$	23.4069	−	15.3661i	0.208990	−	0.137197i
$113$		−	124.546i		−	1.10218i	−0.834446	−	0.551089i	$-0.814212\pi$
$113$		−	124.546i		−	1.10218i	0.834446	−	0.551089i	$-0.185788\pi$
$114$	−23.9142			−0.209774
$115$		0			0
$116$	−20.9107			−0.180265
$117$	34.7031			0.296608
$118$	70.3844			0.596478
$119$	−156.448	+	102.704i	−1.31469	+	0.863058i
$120$		0			0
$121$	290.776			2.40311
$122$	66.7036			0.546751
$123$		−	86.5839i		−	0.703934i
$124$		−	78.6108i		−	0.633958i
$125$		0			0
$126$	−16.2982	−	24.8268i	−0.129350	−	0.197038i
$127$			41.3197i			0.325352i	0.986680	+	0.162676i	$0.0520125\pi$
$127$			41.3197i			0.325352i	−0.986680	+	0.162676i	$0.947987\pi$
$128$			11.3137i			0.0883883i
$129$			18.2677i			0.141610i
$130$		0			0
$131$			61.2476i			0.467539i	0.972292	+	0.233770i	$0.0751061\pi$
$131$			61.2476i			0.467539i	−0.972292	+	0.233770i	$0.924894\pi$
$132$	70.2945			0.532534
$133$	37.5045	+	57.1302i	0.281989	+	0.429550i
$134$	−158.186			−1.18049
$135$		0			0
$136$		−	75.6187i		−	0.556020i
$137$			202.074i			1.47499i	0.675351	+	0.737496i	$0.263992\pi$
$137$			202.074i			1.47499i	−0.675351	+	0.737496i	$0.736008\pi$
$138$	−85.4388			−0.619122
$139$		−	215.423i		−	1.54980i	−0.632082	−	0.774902i	$-0.717799\pi$
$139$		−	215.423i		−	1.54980i	0.632082	−	0.774902i	$-0.282201\pi$
$140$		0			0
$141$	−60.3910			−0.428305
$142$		−	187.436i		−	1.31997i
$143$	234.735			1.64150
$144$	12.0000			0.0833333
$145$		0			0
$146$		−	184.432i		−	1.26323i
$147$	−33.7500	+	77.8713i	−0.229592	+	0.529737i
$148$		−	22.3939i		−	0.151310i
$149$	30.5989			0.205362			0.102681	−	0.994714i	$-0.467258\pi$
$149$	30.5989			0.205362			0.102681	+	0.994714i	$0.467258\pi$
$150$		0			0
$151$	18.0694			0.119665			0.0598324	−	0.998208i	$-0.480943\pi$
$151$	18.0694			0.119665			0.0598324	+	0.998208i	$0.480943\pi$
$152$	−27.6138			−0.181670
$153$	−80.2058			−0.524221
$154$	−110.242	−	167.931i	−0.715858	−	1.09046i
$155$		0			0
$156$	40.0717			0.256870
$157$	108.203			0.689190			0.344595	−	0.938751i	$-0.388016\pi$
$157$	108.203			0.689190			0.344595	+	0.938751i	$0.388016\pi$
$158$		−	5.05464i		−	0.0319914i
$159$			119.407i			0.750986i
$160$		0			0
$161$	133.993	+	204.110i	0.832254	+	1.26776i
$162$		−	12.7279i		−	0.0785674i
$163$		−	188.783i		−	1.15818i	−0.815265	−	0.579089i	$-0.803409\pi$
$163$		−	188.783i		−	1.15818i	0.815265	−	0.579089i	$-0.196591\pi$
$164$		−	99.9785i		−	0.609625i
$165$		0			0
$166$			144.126i			0.868226i
$167$	151.221			0.905516			0.452758	−	0.891633i	$-0.350440\pi$
$167$	151.221			0.905516			0.452758	+	0.891633i	$0.350440\pi$
$168$	−18.8195	−	28.6675i	−0.112021	−	0.170640i
$169$	−35.1884			−0.208215
$170$		0			0
$171$			29.2888i			0.171280i
$172$			21.0938i			0.122638i
$173$	140.007			0.809290			0.404645	−	0.914474i	$-0.367395\pi$
$173$	140.007			0.809290			0.404645	+	0.914474i	$0.367395\pi$
$174$			25.6103i			0.147186i
$175$		0			0
$176$	81.1691			0.461188
$177$		−	86.2030i		−	0.487023i
$178$	10.7282			0.0602705
$179$	−5.92680			−0.0331106			−0.0165553	−	0.999863i	$-0.505270\pi$
$179$	−5.92680			−0.0331106			−0.0165553	+	0.999863i	$0.505270\pi$
$180$		0			0
$181$		−	155.966i		−	0.861689i	−0.902426	−	0.430844i	$-0.858216\pi$
$181$		−	155.966i		−	0.861689i	0.902426	−	0.430844i	$-0.141784\pi$
$182$	−62.8441	−	95.7296i	−0.345297	−	0.525987i
$183$		−	81.6949i		−	0.446420i
$184$	−98.6562			−0.536175
$185$		0			0
$186$	−96.2782			−0.517625
$187$	−542.519			−2.90117
$188$	−69.7335			−0.370923
$189$	−30.4065	+	19.9611i	−0.160881	+	0.105614i
$190$		0			0
$191$	−234.312			−1.22676			−0.613381	−	0.789787i	$-0.710191\pi$
$191$	−234.312			−1.22676			−0.613381	+	0.789787i	$0.710191\pi$
$192$	13.8564			0.0721688
$193$		−	142.787i		−	0.739829i	−0.929066	−	0.369915i	$-0.879387\pi$
$193$		−	142.787i		−	0.739829i	0.929066	−	0.369915i	$-0.120613\pi$
$194$			217.855i			1.12296i
$195$		0			0
$196$	−38.9711	+	89.9180i	−0.198832	+	0.458765i
$197$		−	2.22949i		−	0.0113172i	−0.999984	−	0.00565860i	$-0.998199\pi$
$197$		−	2.22949i		−	0.0113172i	0.999984	−	0.00565860i	$-0.00180120\pi$
$198$		−	86.0928i		−	0.434812i
$199$		−	304.732i		−	1.53132i	−0.643247	−	0.765659i	$-0.722413\pi$
$199$		−	304.732i		−	1.53132i	0.643247	−	0.765659i	$-0.277587\pi$
$200$		0			0
$201$			193.738i			0.963869i
$202$	71.8187			0.355538
$203$	61.1820	−	40.1644i	0.301389	−	0.197854i
$204$	−92.6137			−0.453989
$205$		0			0
$206$		−	7.56817i		−	0.0367387i
$207$			104.641i			0.505511i
$208$	46.2708			0.222456
$209$			198.112i			0.947906i
$210$		0			0
$211$	35.5075			0.168282			0.0841411	−	0.996454i	$-0.473185\pi$
$211$	35.5075			0.168282			0.0841411	+	0.996454i	$0.473185\pi$
$212$			137.879i			0.650373i
$213$	−229.561			−1.07775
$214$	174.302			0.814495
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	150.992	+	230.005i	0.695817	+	1.05993i
$218$		−	146.954i		−	0.674099i
$219$	−225.882			−1.03142
$220$		0			0
$221$	−309.265			−1.39939
$222$	−27.4269			−0.123544
$223$	119.116			0.534152			0.267076	−	0.963675i	$-0.413943\pi$
$223$	119.116			0.534152			0.267076	+	0.963675i	$0.413943\pi$
$224$	−21.7309	−	33.1024i	−0.0970128	−	0.147779i
$225$		0			0
$226$	−176.135			−0.779357
$227$	31.0817			0.136924			0.0684619	−	0.997654i	$-0.478191\pi$
$227$	31.0817			0.136924			0.0684619	+	0.997654i	$0.478191\pi$
$228$			33.8198i			0.148333i
$229$			324.444i			1.41679i	0.705818	+	0.708393i	$0.250580\pi$
$229$			324.444i			1.41679i	−0.705818	+	0.708393i	$0.749420\pi$
$230$		0			0
$231$	−205.672	+	135.019i	−0.890356	+	0.584496i
$232$			29.5722i			0.127466i
$233$			357.680i			1.53511i	0.640985	+	0.767554i	$0.278526\pi$
$233$			357.680i			1.53511i	−0.640985	+	0.767554i	$0.721474\pi$
$234$		−	49.0776i		−	0.209733i
$235$		0			0
$236$		−	99.5386i		−	0.421774i
$237$	−6.19064			−0.0261209
$238$	145.245	+	221.250i	0.610274	+	0.929623i
$239$	50.5171			0.211369			0.105684	−	0.994400i	$-0.466297\pi$
$239$	50.5171			0.211369			0.105684	+	0.994400i	$0.466297\pi$
$240$		0			0
$241$		−	153.204i		−	0.635703i	−0.948140	−	0.317852i	$-0.897039\pi$
$241$		−	153.204i		−	0.635703i	0.948140	−	0.317852i	$-0.102961\pi$
$242$		−	411.219i		−	1.69925i
$243$	−15.5885			−0.0641500
$244$		−	94.3332i		−	0.386611i
$245$		0			0
$246$	−122.448			−0.497757
$247$			112.935i			0.457226i
$248$	−111.173			−0.448276
$249$	176.517			0.708904
$250$		0			0
$251$		−	324.765i		−	1.29389i	−0.762538	−	0.646943i	$-0.776047\pi$
$251$		−	324.765i		−	1.29389i	0.762538	−	0.646943i	$-0.223953\pi$
$252$	−35.1104	+	23.0491i	−0.139327	+	0.0914646i
$253$			707.799i			2.79762i
$254$	58.4349			0.230059
$255$		0			0
$256$	16.0000			0.0625000
$257$	−414.452			−1.61265			−0.806327	−	0.591470i	$-0.798548\pi$
$257$	−414.452			−1.61265			−0.806327	+	0.591470i	$0.798548\pi$
$258$	25.8345			0.100134
$259$	43.0133	+	65.5217i	0.166075	+	0.252980i
$260$		0			0
$261$	31.3661			0.120177
$262$	86.6172			0.330600
$263$		−	113.911i		−	0.433121i	−0.976269	−	0.216561i	$-0.930516\pi$
$263$		−	113.911i		−	0.433121i	0.976269	−	0.216561i	$-0.0694839\pi$
$264$		−	99.4114i		−	0.376558i
$265$		0			0
$266$	80.7943	−	53.0394i	0.303738	−	0.199396i
$267$		−	13.1393i		−	0.0492107i
$268$			223.709i			0.834735i
$269$		−	94.8435i		−	0.352578i	−0.984338	−	0.176289i	$-0.943591\pi$
$269$		−	94.8435i		−	0.352578i	0.984338	−	0.176289i	$-0.0564093\pi$
$270$		0			0
$271$		−	423.890i		−	1.56417i	−0.623173	−	0.782084i	$-0.714157\pi$
$271$		−	423.890i		−	1.56417i	0.623173	−	0.782084i	$-0.285843\pi$
$272$	−106.941			−0.393166
$273$	−117.244	+	76.9679i	−0.429467	+	0.281934i
$274$	285.776			1.04298
$275$		0			0
$276$			120.829i			0.437785i
$277$		−	229.314i		−	0.827848i	−0.910311	−	0.413924i	$-0.864158\pi$
$277$		−	229.314i		−	0.827848i	0.910311	−	0.413924i	$-0.135842\pi$
$278$	−304.654			−1.09588
$279$			117.916i			0.422639i
$280$		0			0
$281$	2.56112			0.00911432			0.00455716	−	0.999990i	$-0.498549\pi$
$281$	2.56112			0.00911432			0.00455716	+	0.999990i	$0.498549\pi$
$282$			85.4058i			0.302857i
$283$	296.124			1.04638			0.523188	−	0.852217i	$-0.324743\pi$
$283$	296.124			1.04638			0.523188	+	0.852217i	$0.324743\pi$
$284$	−265.074			−0.933361
$285$		0			0
$286$		−	331.965i		−	1.16072i
$287$	192.034	+	292.524i	0.669109	+	1.01925i
$288$		−	16.9706i		−	0.0589256i
$289$	425.774			1.47327
$290$		0			0
$291$	266.817			0.916896
$292$	−260.826			−0.893240
$293$	−201.781			−0.688672			−0.344336	−	0.938846i	$-0.611896\pi$
$293$	−201.781			−0.688672			−0.344336	+	0.938846i	$0.611896\pi$
$294$	110.127	+	47.7297i	0.374580	+	0.162346i
$295$		0			0
$296$	−31.6698			−0.106993
$297$	−105.442			−0.355023
$298$		−	43.2734i		−	0.145213i
$299$			403.484i			1.34944i
$300$		0			0
$301$	−40.5160	−	61.7175i	−0.134605	−	0.205042i
$302$		−	25.5540i		−	0.0846159i
$303$		−	87.9596i		−	0.290296i
$304$			39.0518i			0.128460i
$305$		0			0
$306$			113.428i			0.370680i
$307$	−62.9222			−0.204958			−0.102479	−	0.994735i	$-0.532677\pi$
$307$	−62.9222			−0.204958			−0.102479	+	0.994735i	$0.532677\pi$
$308$	−237.490	+	155.906i	−0.771071	+	0.506188i
$309$	−9.26907			−0.0299970
$310$		0			0
$311$			434.208i			1.39617i	0.716016	+	0.698084i	$0.245964\pi$
$311$			434.208i			1.39617i	−0.716016	+	0.698084i	$0.754036\pi$
$312$		−	56.6699i		−	0.181634i
$313$	349.023			1.11509			0.557545	−	0.830146i	$-0.311743\pi$
$313$	349.023			1.11509			0.557545	+	0.830146i	$0.311743\pi$
$314$		−	153.022i		−	0.487331i
$315$		0			0
$316$	−7.14834			−0.0226213
$317$			378.355i			1.19355i	0.802409	+	0.596775i	$0.203551\pi$
$317$			378.355i			1.19355i	−0.802409	+	0.596775i	$0.796449\pi$
$318$	168.867			0.531027
$319$	212.163			0.665088
$320$		0			0
$321$		−	213.476i		−	0.665033i
$322$	288.655	−	189.495i	0.896444	−	0.588492i
$323$		−	261.015i		−	0.808096i
$324$	−18.0000			−0.0555556
$325$		0			0
$326$	−266.979			−0.818955
$327$	−179.981			−0.550400
$328$	−141.391			−0.431070
$329$	204.031	−	133.941i	0.620155	−	0.407116i
$330$		0			0
$331$	−174.059			−0.525859			−0.262929	−	0.964815i	$-0.584689\pi$
$331$	−174.059			−0.525859			−0.262929	+	0.964815i	$0.584689\pi$
$332$	203.824			0.613929
$333$			33.5909i			0.100874i
$334$		−	213.859i		−	0.640297i
$335$		0			0
$336$	−40.5420	+	26.6148i	−0.120661	+	0.0792107i
$337$		−	15.8061i		−	0.0469024i	−0.999725	−	0.0234512i	$-0.992535\pi$
$337$		−	15.8061i		−	0.0469024i	0.999725	−	0.0234512i	$-0.00746544\pi$
$338$			49.7639i			0.147230i
$339$			215.720i			0.636343i
$340$		0			0
$341$			797.596i			2.33899i
$342$	41.4207			0.121113
$343$	−58.6863	−	337.942i	−0.171097	−	0.985254i
$344$	29.8311			0.0867183
$345$		0			0
$346$		−	198.000i		−	0.572254i
$347$			48.4741i			0.139695i	0.997558	+	0.0698474i	$0.0222512\pi$
$347$			48.4741i			0.139695i	−0.997558	+	0.0698474i	$0.977749\pi$
$348$	36.2184			0.104076
$349$			137.603i			0.394277i	0.980376	+	0.197138i	$0.0631648\pi$
$349$			137.603i			0.394277i	−0.980376	+	0.197138i	$0.936835\pi$
$350$		0			0
$351$	−60.1075			−0.171246
$352$		−	114.790i		−	0.326109i
$353$	−513.460			−1.45456			−0.727280	−	0.686341i	$-0.759216\pi$
$353$	−513.460			−1.45456			−0.727280	+	0.686341i	$0.759216\pi$
$354$	−121.909			−0.344377
$355$		0			0
$356$		−	15.1719i		−	0.0426177i
$357$	270.975	−	177.888i	0.759034	−	0.498287i
$358$			8.38177i			0.0234128i
$359$	−249.088			−0.693839			−0.346919	−	0.937895i	$-0.612772\pi$
$359$	−249.088			−0.693839			−0.346919	+	0.937895i	$0.612772\pi$
$360$		0			0
$361$	265.685			0.735969
$362$	−220.569			−0.609306
$363$	−503.639			−1.38743
$364$	−135.382	+	88.8749i	−0.371929	+	0.244162i
$365$		0			0
$366$	−115.534			−0.315667
$367$	−480.602			−1.30954			−0.654771	−	0.755827i	$-0.727235\pi$
$367$	−480.602			−1.30954			−0.654771	+	0.755827i	$0.727235\pi$
$368$			139.521i			0.379133i
$369$			149.968i			0.406417i
$370$		0			0
$371$	−264.832	−	403.416i	−0.713833	−	1.08737i
$372$			136.158i			0.366016i
$373$			632.408i			1.69546i	0.530425	+	0.847732i	$0.322032\pi$
$373$			632.408i			1.69546i	−0.530425	+	0.847732i	$0.677968\pi$
$374$			767.238i			2.05144i
$375$		0			0
$376$			98.6181i			0.262282i
$377$	120.944			0.320808
$378$	28.2292	+	43.0013i	0.0746805	+	0.113760i
$379$	460.572			1.21523			0.607614	−	0.794232i	$-0.292127\pi$
$379$	460.572			1.21523			0.607614	+	0.794232i	$0.292127\pi$
$380$		0			0
$381$		−	71.5678i		−	0.187842i
$382$			331.367i			0.867452i
$383$	−445.151			−1.16227			−0.581137	−	0.813805i	$-0.697392\pi$
$383$	−445.151			−1.16227			−0.581137	+	0.813805i	$0.697392\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	−201.931			−0.523138
$387$		−	31.6406i		−	0.0817588i
$388$	308.093			0.794055
$389$	232.158			0.596807			0.298404	−	0.954440i	$-0.403546\pi$
$389$	232.158			0.596807			0.298404	+	0.954440i	$0.403546\pi$
$390$		0			0
$391$		−	932.532i		−	2.38499i
$392$	127.163	+	55.1135i	0.324396	+	0.140596i
$393$		−	106.084i		−	0.269934i
$394$	−3.15297			−0.00800247
$395$		0			0
$396$	−121.754			−0.307459
$397$	212.888			0.536241			0.268120	−	0.963385i	$-0.413598\pi$
$397$	212.888			0.536241			0.268120	+	0.963385i	$0.413598\pi$
$398$	−430.956			−1.08280
$399$	−64.9597	−	98.9524i	−0.162806	−	0.248001i
$400$		0			0
$401$	11.3396			0.0282782			0.0141391	−	0.999900i	$-0.495499\pi$
$401$	11.3396			0.0282782			0.0141391	+	0.999900i	$0.495499\pi$
$402$	273.987			0.681559
$403$			454.673i			1.12822i
$404$		−	101.567i		−	0.251404i
$405$		0			0
$406$	−56.8010	−	86.5244i	−0.139904	−	0.213114i
$407$			227.212i			0.558260i
$408$			130.976i			0.321018i
$409$		−	71.7286i		−	0.175376i	−0.996148	−	0.0876878i	$-0.972052\pi$
$409$		−	71.7286i		−	0.175376i	0.996148	−	0.0876878i	$-0.0279478\pi$
$410$		0			0
$411$		−	350.002i		−	0.851587i
$412$	−10.7030			−0.0259782
$413$	191.189	+	291.237i	0.462928	+	0.705174i
$414$	147.984			0.357450
$415$		0			0
$416$		−	65.4368i		−	0.157300i
$417$			373.123i			0.894779i
$418$	280.173			0.670271
$419$		−	397.678i		−	0.949113i	−0.880225	−	0.474556i	$-0.842608\pi$
$419$		−	397.678i		−	0.949113i	0.880225	−	0.474556i	$-0.157392\pi$
$420$		0			0
$421$	−101.170			−0.240309			−0.120155	−	0.992755i	$-0.538339\pi$
$421$	−101.170			−0.240309			−0.120155	+	0.992755i	$0.538339\pi$
$422$		−	50.2152i		−	0.118993i
$423$	104.600			0.247282
$424$	194.990			0.459883
$425$		0			0
$426$			324.649i			0.762086i
$427$	181.191	+	276.006i	0.424335	+	0.646385i
$428$		−	246.500i		−	0.575935i
$429$	−406.573			−0.947722
$430$		0			0
$431$	−557.096			−1.29257			−0.646283	−	0.763098i	$-0.723678\pi$
$431$	−557.096			−1.29257			−0.646283	+	0.763098i	$0.723678\pi$
$432$	−20.7846			−0.0481125
$433$	−480.559			−1.10984			−0.554918	−	0.831905i	$-0.687250\pi$
$433$	−480.559			−1.10984			−0.554918	+	0.831905i	$0.687250\pi$
$434$	325.276	−	213.535i	0.749484	−	0.492017i
$435$		0			0
$436$	−207.824			−0.476660
$437$	−340.534			−0.779254
$438$			319.445i			0.729327i
$439$			82.2468i			0.187350i	0.995603	+	0.0936752i	$0.0298615\pi$
$439$			82.2468i			0.187350i	−0.995603	+	0.0936752i	$0.970138\pi$
$440$		0			0
$441$	58.4567	−	134.877i	0.132555	−	0.305844i
$442$			437.367i			0.989519i
$443$			90.6359i			0.204596i	0.994754	+	0.102298i	$0.0326195\pi$
$443$			90.6359i			0.204596i	−0.994754	+	0.102298i	$0.967381\pi$
$444$			38.7875i			0.0873591i
$445$		0			0
$446$		−	168.455i		−	0.377703i
$447$	−52.9989			−0.118566
$448$	−46.8139	+	30.7321i	−0.104495	+	0.0685984i
$449$	540.602			1.20401			0.602007	−	0.798491i	$-0.294368\pi$
$449$	540.602			1.20401			0.602007	+	0.798491i	$0.294368\pi$
$450$		0			0
$451$			1014.40i			2.24921i
$452$			249.092i			0.551089i
$453$	−31.2971			−0.0690886
$454$		−	43.9561i		−	0.0968197i
$455$		0			0
$456$	47.8285			0.104887
$457$		−	92.5484i		−	0.202513i	−0.994860	−	0.101256i	$-0.967714\pi$
$457$		−	92.5484i		−	0.202513i	0.994860	−	0.101256i	$-0.0322863\pi$
$458$	458.833			1.00182
$459$	138.921			0.302659
$460$		0			0
$461$		−	440.112i		−	0.954690i	−0.878716	−	0.477345i	$-0.841599\pi$
$461$		−	440.112i		−	0.954690i	0.878716	−	0.477345i	$-0.158401\pi$
$462$	190.945	+	290.864i	0.413301	+	0.629577i
$463$			393.775i			0.850487i	0.905079	+	0.425243i	$0.139811\pi$
$463$			393.775i			0.850487i	−0.905079	+	0.425243i	$0.860189\pi$
$464$	41.8214			0.0901324
$465$		0			0
$466$	505.836			1.08548
$467$	−182.217			−0.390187			−0.195094	−	0.980785i	$-0.562501\pi$
$467$	−182.217			−0.390187			−0.195094	+	0.980785i	$0.562501\pi$
$468$	−69.4062			−0.148304
$469$	−429.691	−	654.543i	−0.916185	−	1.39561i
$470$		0			0
$471$	−187.413			−0.397904
$472$	−140.769			−0.298239
$473$		−	214.020i		−	0.452474i
$474$			8.75489i			0.0184702i
$475$		0			0
$476$	312.895	−	205.408i	0.657343	−	0.431529i
$477$		−	206.819i		−	0.433582i
$478$		−	71.4420i		−	0.149460i
$479$		−	501.169i		−	1.04628i	−0.852246	−	0.523141i	$-0.824760\pi$
$479$		−	501.169i		−	1.04628i	0.852246	−	0.523141i	$-0.175240\pi$
$480$		0			0
$481$			129.523i			0.269279i
$482$	−216.664			−0.449510
$483$	−232.082	−	353.529i	−0.480502	−	0.731943i
$484$	−581.552			−1.20155
$485$		0			0
$486$			22.0454i			0.0453609i
$487$		−	483.296i		−	0.992393i	−0.868210	−	0.496197i	$-0.834729\pi$
$487$		−	483.296i		−	0.992393i	0.868210	−	0.496197i	$-0.165271\pi$
$488$	−133.407			−0.273375
$489$			326.981i			0.668674i
$490$		0			0
$491$	−444.474			−0.905242			−0.452621	−	0.891703i	$-0.649511\pi$
$491$	−444.474			−0.905242			−0.452621	+	0.891703i	$0.649511\pi$
$492$			173.168i			0.351967i
$493$	−279.527			−0.566991
$494$	159.714			0.323308
$495$		0			0
$496$			157.222i			0.316979i
$497$	775.572	−	509.143i	1.56051	−	1.02443i
$498$		−	249.633i		−	0.501271i
$499$	−197.610			−0.396011			−0.198006	−	0.980201i	$-0.563446\pi$
$499$	−197.610			−0.396011			−0.198006	+	0.980201i	$0.563446\pi$
$500$		0			0
$501$	−261.923			−0.522800
$502$	−459.288			−0.914915
$503$	395.369			0.786022			0.393011	−	0.919534i	$-0.371433\pi$
$503$	395.369			0.786022			0.393011	+	0.919534i	$0.371433\pi$
$504$	32.5963	+	49.6536i	0.0646752	+	0.0985191i
$505$		0			0
$506$	1000.98			1.97822
$507$	60.9480			0.120213
$508$		−	82.6394i		−	0.162676i
$509$			229.224i			0.450341i	0.974319	+	0.225171i	$0.0722940\pi$
$509$			229.224i			0.450341i	−0.974319	+	0.225171i	$0.927706\pi$
$510$		0			0
$511$	763.142	−	500.983i	1.49343	−	0.980398i
$512$		−	22.6274i		−	0.0441942i
$513$		−	50.7298i		−	0.0988884i
$514$			586.124i			1.14032i
$515$		0			0
$516$		−	36.5355i		−	0.0708052i
$517$	707.525			1.36852
$518$	92.6617	−	60.8300i	0.178884	−	0.117432i
$519$	−242.499			−0.467244
$520$		0			0
$521$			679.550i			1.30432i	0.758082	+	0.652159i	$0.226136\pi$
$521$			679.550i			1.30432i	−0.758082	+	0.652159i	$0.773864\pi$
$522$		−	44.3583i		−	0.0849776i
$523$	696.333			1.33142			0.665710	−	0.746210i	$-0.268129\pi$
$523$	696.333			1.33142			0.665710	+	0.746210i	$0.268129\pi$
$524$		−	122.495i		−	0.233770i
$525$		0			0
$526$	−161.094			−0.306263
$527$		−	1050.84i		−	1.99401i
$528$	−140.589			−0.266267
$529$	−687.631			−1.29987
$530$		0			0
$531$			149.308i			0.281183i
$532$	−75.0090	−	114.260i	−0.140994	−	0.214775i
$533$			578.260i			1.08492i
$534$	−18.5817			−0.0347972
$535$		0			0
$536$	316.372			0.590247
$537$	10.2655			0.0191164
$538$	−134.129			−0.249310
$539$	395.406	−	912.320i	0.733592	−	1.69262i
$540$		0			0
$541$	−280.172			−0.517877			−0.258939	−	0.965894i	$-0.583373\pi$
$541$	−280.172			−0.517877			−0.258939	+	0.965894i	$0.583373\pi$
$542$	−599.470			−1.10603
$543$			270.140i			0.497496i
$544$			151.237i			0.278010i
$545$		0			0
$546$	108.849	+	165.809i	0.199357	+	0.303679i
$547$			36.4362i			0.0666109i	0.999445	+	0.0333055i	$0.0106034\pi$
$547$			36.4362i			0.0666109i	−0.999445	+	0.0333055i	$0.989397\pi$
$548$		−	404.148i		−	0.737496i
$549$			141.500i			0.257741i
$550$		0			0
$551$			102.075i			0.185254i
$552$	170.878			0.309561
$553$	20.9151	−	13.7302i	0.0378211	−	0.0248286i
$554$	−324.299			−0.585377
$555$		0			0
$556$			430.845i			0.774902i
$557$			514.266i			0.923278i	0.887068	+	0.461639i	$0.152739\pi$
$557$			514.266i			0.923278i	−0.887068	+	0.461639i	$0.847261\pi$
$558$	166.759			0.298851
$559$		−	122.003i		−	0.218252i
$560$		0			0
$561$	939.671			1.67499
$562$		−	3.62198i		−	0.00644480i
$563$	36.7295			0.0652389			0.0326194	−	0.999468i	$-0.489615\pi$
$563$	36.7295			0.0652389			0.0326194	+	0.999468i	$0.489615\pi$
$564$	120.782			0.214152
$565$		0			0
$566$		−	418.783i		−	0.739899i
$567$	52.6656	−	34.5736i	0.0928847	−	0.0609764i
$568$			374.872i			0.659986i
$569$	210.857			0.370574			0.185287	−	0.982684i	$-0.440678\pi$
$569$	210.857			0.370574			0.185287	+	0.982684i	$0.440678\pi$
$570$		0			0
$571$	−528.624			−0.925786			−0.462893	−	0.886414i	$-0.653189\pi$
$571$	−528.624			−0.925786			−0.462893	+	0.886414i	$0.653189\pi$
$572$	−469.470			−0.820751
$573$	405.840			0.708272
$574$	413.691	−	271.578i	0.720716	−	0.473132i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$	−1097.09			−1.90137			−0.950684	−	0.310160i	$-0.899617\pi$
$577$	−1097.09			−1.90137			−0.950684	+	0.310160i	$0.899617\pi$
$578$		−	602.136i		−	1.04176i
$579$			247.314i			0.427141i
$580$		0			0
$581$	−596.363	+	391.497i	−1.02644	+	0.673833i
$582$		−	377.336i		−	0.648343i
$583$		−	1398.94i		−	2.39955i
$584$			368.864i			0.631616i
$585$		0			0
$586$			285.361i			0.486965i
$587$	607.968			1.03572			0.517860	−	0.855465i	$-0.326729\pi$
$587$	607.968			1.03572			0.517860	+	0.855465i	$0.326729\pi$
$588$	67.5000	−	155.743i	0.114796	−	0.264868i
$589$	−383.737			−0.651506
$590$		0			0
$591$			3.86159i			0.00653399i
$592$			44.7879i			0.0756552i
$593$	638.076			1.07601			0.538007	−	0.842941i	$-0.319177\pi$
$593$	638.076			1.07601			0.538007	+	0.842941i	$0.319177\pi$
$594$			149.117i			0.251039i
$595$		0			0
$596$	−61.1979			−0.102681
$597$			527.812i			0.884106i
$598$	570.613			0.954202
$599$	−875.423			−1.46147			−0.730737	−	0.682659i	$-0.760823\pi$
$599$	−875.423			−1.46147			−0.730737	+	0.682659i	$0.760823\pi$
$600$		0			0
$601$		−	529.211i		−	0.880551i	−0.897863	−	0.440276i	$-0.854881\pi$
$601$		−	529.211i		−	0.880551i	0.897863	−	0.440276i	$-0.145119\pi$
$602$	−87.2818	+	57.2982i	−0.144986	+	0.0951798i
$603$		−	335.564i		−	0.556490i
$604$	−36.1388			−0.0598324
$605$		0			0
$606$	−124.394			−0.205270
$607$	−1177.00			−1.93904			−0.969518	−	0.245019i	$-0.921206\pi$
$607$	−1177.00			−1.93904			−0.969518	+	0.245019i	$0.921206\pi$
$608$	55.2276			0.0908348
$609$	−105.970	+	69.5668i	−0.174007	+	0.114231i
$610$		0			0
$611$	403.328			0.660111
$612$	160.412			0.262110
$613$			122.839i			0.200390i	0.994968	+	0.100195i	$0.0319467\pi$
$613$			122.839i			0.200390i	−0.994968	+	0.100195i	$0.968053\pi$
$614$			88.9854i			0.144927i
$615$		0			0
$616$	220.484	+	335.861i	0.357929	+	0.545229i
$617$			9.30421i			0.0150798i	0.999972	+	0.00753988i	$0.00240004\pi$
$617$			9.30421i			0.0150798i	−0.999972	+	0.00753988i	$0.997600\pi$
$618$			13.1084i			0.0212111i
$619$		−	147.314i		−	0.237988i	−0.992895	−	0.118994i	$-0.962033\pi$
$619$		−	147.314i		−	0.237988i	0.992895	−	0.118994i	$-0.0379669\pi$
$620$		0			0
$621$		−	181.243i		−	0.291857i
$622$	614.063			0.987240
$623$	29.1415	+	44.3910i	0.0467761	+	0.0712536i
$624$	−80.1434			−0.128435
$625$		0			0
$626$		−	493.594i		−	0.788488i
$627$		−	343.141i		−	0.547274i
$628$	−216.406			−0.344595
$629$		−	299.354i		−	0.475921i
$630$		0			0
$631$	−186.419			−0.295434			−0.147717	−	0.989030i	$-0.547193\pi$
$631$	−186.419			−0.295434			−0.147717	+	0.989030i	$0.547193\pi$
$632$			10.1093i			0.0159957i
$633$	−61.5009			−0.0971578
$634$	535.075			0.843967
$635$		0			0
$636$		−	238.814i		−	0.375493i
$637$	225.403	−	520.072i	0.353851	−	0.816440i
$638$		−	300.044i		−	0.470288i
$639$	397.612			0.622240
$640$		0			0
$641$	−103.262			−0.161096			−0.0805479	−	0.996751i	$-0.525667\pi$
$641$	−103.262			−0.161096			−0.0805479	+	0.996751i	$0.525667\pi$
$642$	−301.900			−0.470249
$643$	−389.717			−0.606091			−0.303046	−	0.952976i	$-0.598003\pi$
$643$	−389.717			−0.606091			−0.303046	+	0.952976i	$0.598003\pi$
$644$	−267.986	−	408.220i	−0.416127	−	0.633881i
$645$		0			0
$646$	−369.131			−0.571410
$647$	636.001			0.982999			0.491500	−	0.870878i	$-0.336449\pi$
$647$	636.001			0.982999			0.491500	+	0.870878i	$0.336449\pi$
$648$			25.4558i			0.0392837i
$649$			1009.93i			1.55614i
$650$		0			0
$651$	−261.526	−	398.380i	−0.401730	−	0.611951i
$652$			377.566i			0.579089i
$653$		−	200.929i		−	0.307701i	−0.988094	−	0.153851i	$-0.950833\pi$
$653$		−	200.929i		−	0.307701i	0.988094	−	0.153851i	$-0.0491674\pi$
$654$			254.531i			0.389191i
$655$		0			0
$656$			199.957i			0.304812i
$657$	391.239			0.595493
$658$	−189.421	−	288.543i	−0.287874	−	0.438516i
$659$	−527.053			−0.799776			−0.399888	−	0.916564i	$-0.630951\pi$
$659$	−527.053			−0.799776			−0.399888	+	0.916564i	$0.630951\pi$
$660$		0			0
$661$		−	409.713i		−	0.619839i	−0.950763	−	0.309919i	$-0.899698\pi$
$661$		−	409.713i		−	0.619839i	0.950763	−	0.309919i	$-0.100302\pi$
$662$			246.157i			0.371838i
$663$	535.664			0.807939
$664$		−	288.251i		−	0.434113i
$665$		0			0
$666$	47.5047			0.0713284
$667$			364.685i			0.546755i
$668$	−302.442			−0.452758
$669$	−206.315			−0.308393
$670$		0			0
$671$			957.117i			1.42640i
$672$	37.6390	+	57.3350i	0.0560104	+	0.0853200i
$673$		−	1026.56i		−	1.52535i	−0.646779	−	0.762677i	$-0.723884\pi$
$673$		−	1026.56i		−	1.52535i	0.646779	−	0.762677i	$-0.276116\pi$
$674$	−22.3532			−0.0331650
$675$		0			0
$676$	70.3767			0.104108
$677$	−267.679			−0.395390			−0.197695	−	0.980264i	$-0.563345\pi$
$677$	−267.679			−0.395390			−0.197695	+	0.980264i	$0.563345\pi$
$678$	305.074			0.449962
$679$	−901.440	+	591.772i	−1.32760	+	0.871535i
$680$		0			0
$681$	−53.8351			−0.0790529
$682$	1127.97			1.65392
$683$		−	1070.54i		−	1.56741i	−0.621136	−	0.783703i	$-0.713329\pi$
$683$		−	1070.54i		−	1.56741i	0.621136	−	0.783703i	$-0.286671\pi$
$684$		−	58.5777i		−	0.0856399i
$685$		0			0
$686$	−477.922	+	82.9950i	−0.696680	+	0.120984i
$687$		−	561.953i		−	0.817982i
$688$		−	42.1875i		−	0.0613191i
$689$		−	797.472i		−	1.15743i
$690$		0			0
$691$			351.566i			0.508779i	0.967102	+	0.254390i	$0.0818745\pi$
$691$			351.566i			0.508779i	−0.967102	+	0.254390i	$0.918125\pi$
$692$	−280.014			−0.404645
$693$	356.235	−	233.859i	0.514047	−	0.337459i
$694$	68.5527			0.0987792
$695$		0			0
$696$		−	51.2206i		−	0.0735928i
$697$		−	1336.48i		−	1.91747i
$698$	194.599			0.278796
$699$		−	619.520i		−	0.886294i
$700$		0			0
$701$	764.715			1.09089			0.545446	−	0.838146i	$-0.316360\pi$
$701$	764.715			1.09089			0.545446	+	0.838146i	$0.316360\pi$
$702$			85.0049i			0.121090i
$703$	−109.315			−0.155499
$704$	−162.338			−0.230594
$705$		0			0
$706$			726.142i			1.02853i
$707$	195.085	+	297.172i	0.275934	+	0.420327i
$708$			172.406i			0.243511i
$709$	1297.85			1.83054			0.915271	−	0.402840i	$-0.131977\pi$
$709$	1297.85			1.83054			0.915271	+	0.402840i	$0.131977\pi$
$710$		0			0
$711$	10.7225			0.0150809
$712$	−21.4563			−0.0301353
$713$	−1370.98			−1.92284
$714$	−251.572	−	383.217i	−0.352342	−	0.536718i
$715$		0			0
$716$	11.8536			0.0165553
$717$	−87.4982			−0.122034
$718$			352.264i			0.490618i
$719$			734.309i			1.02129i	0.859791	+	0.510646i	$0.170594\pi$
$719$			734.309i			1.02129i	−0.859791	+	0.510646i	$0.829406\pi$
$720$		0			0
$721$	31.3156	−	20.5579i	0.0434335	−	0.0285130i
$722$		−	375.735i		−	0.520409i
$723$			265.358i			0.367023i
$724$			311.931i			0.430844i
$725$		0			0
$726$			712.253i			0.981065i
$727$	878.842			1.20886			0.604430	−	0.796658i	$-0.293401\pi$
$727$	878.842			1.20886			0.604430	+	0.796658i	$0.293401\pi$
$728$	125.688	+	191.459i	0.172649	+	0.262994i
$729$	27.0000			0.0370370
$730$		0			0
$731$			281.974i			0.385737i
$732$			163.390i			0.223210i
$733$	547.305			0.746665			0.373333	−	0.927698i	$-0.378215\pi$
$733$	547.305			0.746665			0.373333	+	0.927698i	$0.378215\pi$
$734$			679.674i			0.925986i
$735$		0			0
$736$	197.312			0.268088
$737$		−	2269.78i		−	3.07976i
$738$	212.086			0.287380
$739$	−1366.72			−1.84942			−0.924708	−	0.380678i	$-0.875691\pi$
$739$	−1366.72			−1.84942			−0.924708	+	0.380678i	$0.875691\pi$
$740$		0			0
$741$		−	195.609i		−	0.263980i
$742$	−570.516	+	374.529i	−0.768890	+	0.504756i
$743$		−	312.379i		−	0.420430i	−0.977655	−	0.210215i	$-0.932584\pi$
$743$		−	312.379i		−	0.420430i	0.977655	−	0.210215i	$-0.0674163\pi$
$744$	192.556			0.258812
$745$		0			0
$746$	894.360			1.19887
$747$	−305.737			−0.409286
$748$	1085.04			1.45059
$749$	473.467	+	721.227i	0.632132	+	0.962920i
$750$		0			0
$751$	−399.099			−0.531423			−0.265711	−	0.964053i	$-0.585607\pi$
$751$	−399.099			−0.531423			−0.265711	+	0.964053i	$0.585607\pi$
$752$	139.467			0.185461
$753$			562.510i			0.747025i
$754$		−	171.041i		−	0.226845i
$755$		0			0
$756$	60.8130	−	39.9222i	0.0804405	−	0.0528071i
$757$		−	379.405i		−	0.501195i	−0.968091	−	0.250598i	$-0.919373\pi$
$757$		−	379.405i		−	0.501195i	0.968091	−	0.250598i	$-0.0806271\pi$
$758$		−	651.347i		−	0.859296i
$759$		−	1225.94i		−	1.61521i
$760$		0			0
$761$			997.303i			1.31052i	0.755405	+	0.655258i	$0.227440\pi$
$761$			997.303i			1.31052i	−0.755405	+	0.655258i	$0.772560\pi$
$762$	−101.212			−0.132824
$763$	608.065	−	399.179i	0.796939	−	0.523170i
$764$	468.623			0.613381
$765$		0			0
$766$			629.539i			0.821852i
$767$			575.716i			0.750608i
$768$	−27.7128			−0.0360844
$769$		−	1425.18i		−	1.85329i	−0.375936	−	0.926645i	$-0.622679\pi$
$769$		−	1425.18i		−	1.85329i	0.375936	−	0.926645i	$-0.377321\pi$
$770$		0			0
$771$	717.852			0.931066
$772$			285.574i			0.369915i
$773$	−258.654			−0.334610			−0.167305	−	0.985905i	$-0.553506\pi$
$773$	−258.654			−0.334610			−0.167305	+	0.985905i	$0.553506\pi$
$774$	−44.7466			−0.0578122
$775$		0			0
$776$		−	435.710i		−	0.561482i
$777$	−74.5013	−	113.487i	−0.0958832	−	0.146058i
$778$		−	328.321i		−	0.422007i
$779$	−488.042			−0.626499
$780$		0			0
$781$	2689.48			3.44364
$782$	−1318.80			−1.68645
$783$	−54.3276			−0.0693840
$784$	77.9422	−	179.836i	0.0994161	−	0.229383i
$785$		0			0
$786$	−150.025			−0.190872
$787$	1523.79			1.93620			0.968101	−	0.250562i	$-0.0806153\pi$
$787$	1523.79			1.93620			0.968101	+	0.250562i	$0.0806153\pi$
$788$			4.45898i			0.00565860i
$789$			197.299i			0.250063i
$790$		0			0
$791$	−478.445	−	728.811i	−0.604862	−	0.921379i
$792$			172.186i			0.217406i
$793$			545.609i			0.688031i
$794$		−	301.068i		−	0.379179i
$795$		0			0
$796$			609.464i			0.765659i
$797$	636.982			0.799225			0.399612	−	0.916684i	$-0.369145\pi$
$797$	636.982			0.799225			0.399612	+	0.916684i	$0.369145\pi$
$798$	−139.940	+	91.8669i	−0.175363	+	0.115121i
$799$	−932.172			−1.16667
$800$		0			0
$801$			22.7579i			0.0284118i
$802$		−	16.0366i		−	0.0199957i
$803$	2646.38			3.29561
$804$		−	387.475i		−	0.481935i
$805$		0			0
$806$	643.005			0.797773
$807$			164.274i			0.203561i
$808$	−143.637			−0.177769
$809$	−230.833			−0.285331			−0.142666	−	0.989771i	$-0.545567\pi$
$809$	−230.833			−0.285331			−0.142666	+	0.989771i	$0.545567\pi$
$810$		0			0
$811$			552.305i			0.681017i	0.940241	+	0.340508i	$0.110599\pi$
$811$			552.305i			0.681017i	−0.940241	+	0.340508i	$0.889401\pi$
$812$	−122.364	+	80.3288i	−0.150695	+	0.0989271i
$813$			734.198i			0.903073i
$814$	321.326			0.394750
$815$		0			0
$816$	185.227			0.226994
$817$	102.969			0.126033
$818$	−101.440			−0.124009
$819$	203.073	−	133.312i	0.247953	−	0.162775i
$820$		0			0
$821$	1344.79			1.63799			0.818996	−	0.573799i	$-0.194531\pi$
$821$	1344.79			1.63799			0.818996	+	0.573799i	$0.194531\pi$
$822$	−494.978			−0.602163
$823$		−	1047.30i		−	1.27254i	−0.771467	−	0.636270i	$-0.780477\pi$
$823$		−	1047.30i		−	1.27254i	0.771467	−	0.636270i	$-0.219523\pi$
$824$			15.1363i			0.0183693i
$825$		0			0
$826$	411.871	−	270.383i	0.498633	−	0.327340i
$827$		−	6.27860i		−	0.00759202i	−0.999993	−	0.00379601i	$-0.998792\pi$
$827$		−	6.27860i		−	0.00759202i	0.999993	−	0.00379601i	$-0.00120831\pi$
$828$		−	209.281i		−	0.252755i
$829$			1057.67i			1.27584i	0.770102	+	0.637921i	$0.220205\pi$
$829$			1057.67i			1.27584i	−0.770102	+	0.637921i	$0.779795\pi$
$830$		0			0
$831$			397.183i			0.477958i
$832$	−92.5416			−0.111228
$833$	−520.952	+	1201.99i	−0.625392	+	1.44297i
$834$	527.676			0.632705
$835$		0			0
$836$		−	396.225i		−	0.473953i
$837$		−	204.237i		−	0.244011i
$838$	−562.402			−0.671124
$839$		−	1597.12i		−	1.90360i	−0.306718	−	0.951801i	$-0.599231\pi$
$839$		−	1597.12i		−	1.90360i	0.306718	−	0.951801i	$-0.400769\pi$
$840$		0			0
$841$	−731.685			−0.870018
$842$			143.076i			0.169924i
$843$	−4.43600			−0.00526216
$844$	−71.0151			−0.0841411
$845$		0			0
$846$		−	147.927i		−	0.174855i
$847$	1701.54	−	1117.02i	2.00891	−	1.31880i
$848$		−	275.758i		−	0.325187i
$849$	−512.902			−0.604125
$850$		0			0
$851$	−390.553			−0.458934
$852$	459.122			0.538876
$853$	−1383.40			−1.62180			−0.810901	−	0.585183i	$-0.801022\pi$
$853$	−1383.40			−1.62180			−0.810901	+	0.585183i	$0.801022\pi$
$854$	390.332	−	256.243i	0.457063	−	0.300050i
$855$		0			0
$856$	−348.604			−0.407248
$857$	371.114			0.433038			0.216519	−	0.976278i	$-0.430530\pi$
$857$	371.114			0.433038			0.216519	+	0.976278i	$0.430530\pi$
$858$			574.980i			0.670140i
$859$			614.383i			0.715230i	0.933869	+	0.357615i	$0.116410\pi$
$859$			614.383i			0.715230i	−0.933869	+	0.357615i	$0.883590\pi$
$860$		0			0
$861$	−332.613	−	506.666i	−0.386310	−	0.588462i
$862$			787.853i			0.913982i
$863$			1385.63i			1.60560i	0.596250	+	0.802799i	$0.296657\pi$
$863$			1385.63i			1.60560i	−0.596250	+	0.802799i	$0.703343\pi$
$864$			29.3939i			0.0340207i
$865$		0			0
$866$			679.613i			0.784773i
$867$	−737.463			−0.850592
$868$	−301.985	−	460.010i	−0.347908	−	0.529965i
$869$	72.5280			0.0834615
$870$		0			0
$871$		−	1293.90i		−	1.48553i
$872$			293.907i			0.337049i
$873$	−462.140			−0.529370
$874$			481.588i			0.551016i
$875$		0			0
$876$	451.764			0.515712
$877$			154.155i			0.175775i	0.996130	+	0.0878874i	$0.0280116\pi$
$877$			154.155i			0.175775i	−0.996130	+	0.0878874i	$0.971988\pi$
$878$	116.315			0.132477
$879$	349.495			0.397605
$880$		0			0
$881$		−	612.561i		−	0.695302i	−0.937624	−	0.347651i	$-0.886979\pi$
$881$		−	612.561i		−	0.695302i	0.937624	−	0.347651i	$-0.113021\pi$
$882$	−190.745	−	82.6702i	−0.216264	−	0.0937304i
$883$			1193.81i			1.35199i	0.736906	+	0.675995i	$0.236286\pi$
$883$			1193.81i			1.35199i	−0.736906	+	0.675995i	$0.763714\pi$
$884$	618.531			0.699696
$885$		0			0
$886$	128.179			0.144671
$887$	−701.565			−0.790942			−0.395471	−	0.918479i	$-0.629419\pi$
$887$	−701.565			−0.790942			−0.395471	+	0.918479i	$0.629419\pi$
$888$	54.8537			0.0617722
$889$	158.730	+	241.792i	0.178549	+	0.271982i
$890$		0			0
$891$	182.630			0.204972
$892$	−238.232			−0.267076
$893$			340.402i			0.381190i
$894$			74.9518i			0.0838387i
$895$		0			0
$896$	43.4618	+	66.2048i	0.0485064	+	0.0738893i
$897$		−	698.855i		−	0.779102i
$898$		−	764.527i		−	0.851366i
$899$			410.952i			0.457122i
$900$		0			0
$901$			1843.12i			2.04564i
$902$	1434.57			1.59043
$903$	70.1757	+	106.898i	0.0777140	+	0.118381i
$904$	352.270			0.389679
$905$		0			0
$906$			44.2608i			0.0488530i
$907$			1260.16i			1.38937i	0.719315	+	0.694684i	$0.244456\pi$
$907$			1260.16i			1.38937i	−0.719315	+	0.694684i	$0.755544\pi$
$908$	−62.1634			−0.0684619
$909$			152.351i			0.167602i
$910$		0			0
$911$	−482.589			−0.529736			−0.264868	−	0.964285i	$-0.585328\pi$
$911$	−482.589			−0.529736			−0.264868	+	0.964285i	$0.585328\pi$
$912$		−	67.6397i		−	0.0741663i
$913$	−2068.03			−2.26509
$914$	−130.883			−0.143198
$915$		0			0
$916$		−	648.888i		−	0.708393i
$917$	235.283	+	358.405i	0.256580	+	0.390845i
$918$		−	196.463i		−	0.214012i
$919$	−542.327			−0.590127			−0.295064	−	0.955478i	$-0.595341\pi$
$919$	−542.327			−0.590127			−0.295064	+	0.955478i	$0.595341\pi$
$920$		0			0
$921$	108.984			0.118333
$922$	−622.413			−0.675068
$923$	1533.15			1.66105
$924$	411.344	−	270.037i	0.445178	−	0.292248i
$925$		0			0
$926$	556.882			0.601385
$927$	16.0545			0.0173188
$928$		−	59.1444i		−	0.0637332i
$929$		−	975.056i		−	1.04958i	−0.851233	−	0.524788i	$-0.824145\pi$
$929$		−	975.056i		−	1.04958i	0.851233	−	0.524788i	$-0.175855\pi$
$930$		0			0
$931$	438.933	+	190.237i	0.471464	+	0.204336i
$932$		−	715.360i		−	0.767554i
$933$		−	752.071i		−	0.806078i
$934$			257.694i			0.275904i
$935$		0			0
$936$			98.1552i			0.104867i
$937$	463.813			0.494997			0.247499	−	0.968888i	$-0.420391\pi$
$937$	463.813			0.494997			0.247499	+	0.968888i	$0.420391\pi$
$938$	−925.663	+	607.674i	−0.986848	+	0.647840i
$939$	−604.526			−0.643798
$940$		0			0
$941$			348.155i			0.369985i	0.982740	+	0.184992i	$0.0592260\pi$
$941$			348.155i			0.369985i	−0.982740	+	0.184992i	$0.940774\pi$
$942$			265.042i			0.281361i
$943$	−1743.64			−1.84903
$944$			199.077i			0.210887i
$945$		0			0
$946$	−302.670			−0.319947
$947$			1790.81i			1.89104i	0.325565	+	0.945520i	$0.394445\pi$
$947$			1790.81i			1.89104i	−0.325565	+	0.945520i	$0.605555\pi$
$948$	12.3813			0.0130604
$949$	1508.58			1.58965
$950$		0			0
$951$		−	655.330i		−	0.689096i
$952$	−290.490	−	442.501i	−0.305137	−	0.464812i
$953$			706.749i			0.741604i	0.928712	+	0.370802i	$0.120917\pi$
$953$			706.749i			0.741604i	−0.928712	+	0.370802i	$0.879083\pi$
$954$	−292.486			−0.306589
$955$		0			0
$956$	−101.034			−0.105684
$957$	−367.477			−0.383988
$958$	−708.760			−0.739833
$959$	776.270	+	1182.48i	0.809457	+	1.23304i
$960$		0			0
$961$	−583.916			−0.607613
$962$	183.173			0.190409
$963$			369.750i			0.383957i
$964$			306.409i			0.317852i
$965$		0			0
$966$	−499.965	+	328.214i	−0.517562	+	0.339766i
$967$			854.298i			0.883452i	0.897150	+	0.441726i	$0.145634\pi$
$967$			854.298i			0.883452i	−0.897150	+	0.441726i	$0.854366\pi$
$968$			822.439i			0.849627i
$969$			452.091i			0.466554i
$970$		0			0
$971$		−	1637.54i		−	1.68645i	−0.537563	−	0.843224i	$-0.680655\pi$
$971$		−	1637.54i		−	1.68645i	0.537563	−	0.843224i	$-0.319345\pi$
$972$	31.1769			0.0320750
$973$	−827.549	−	1260.60i	−0.850513	−	1.29558i
$974$	−683.483			−0.701728
$975$		0			0
$976$			188.666i			0.193306i
$977$		−	242.601i		−	0.248312i	−0.992263	−	0.124156i	$-0.960378\pi$
$977$		−	242.601i		−	0.248312i	0.992263	−	0.124156i	$-0.0396224\pi$
$978$	462.422			0.472824
$979$			153.936i			0.157238i
$980$		0			0
$981$	311.736			0.317773
$982$			628.581i			0.640103i
$983$	1037.28			1.05522			0.527611	−	0.849486i	$-0.323088\pi$
$983$	1037.28			1.05522			0.527611	+	0.849486i	$0.323088\pi$
$984$	244.896			0.248878
$985$		0			0
$986$			395.311i			0.400924i
$987$	−353.392	+	231.993i	−0.358047	+	0.235048i
$988$		−	225.870i		−	0.228613i
$989$	367.878			0.371969
$990$		0			0
$991$	−842.370			−0.850020			−0.425010	−	0.905189i	$-0.639729\pi$
$991$	−842.370			−0.850020			−0.425010	+	0.905189i	$0.639729\pi$
$992$	222.345			0.224138
$993$	301.479			0.303605
$994$	−720.038	−	1096.83i	−0.724384	−	1.10345i
$995$		0			0
$996$	−353.034			−0.354452
$997$	−731.640			−0.733842			−0.366921	−	0.930252i	$-0.619588\pi$
$997$	−731.640			−0.733842			−0.366921	+	0.930252i	$0.619588\pi$
$998$			279.462i			0.280022i
$999$		−	58.1812i		−	0.0582394i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.h.c.349.15		24
5.2	odd	4		1050.3.f.d.601.11	yes	12
5.3	odd	4		1050.3.f.c.601.2	✓	12
5.4	even	2	inner	1050.3.h.c.349.4		24
7.6	odd	2	inner	1050.3.h.c.349.3		24
35.13	even	4		1050.3.f.c.601.5	yes	12
35.27	even	4		1050.3.f.d.601.8	yes	12
35.34	odd	2	inner	1050.3.h.c.349.16		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.f.c.601.2	✓	12	5.3	odd	4
1050.3.f.c.601.5	yes	12	35.13	even	4
1050.3.f.d.601.8	yes	12	35.27	even	4
1050.3.f.d.601.11	yes	12	5.2	odd	4
1050.3.h.c.349.3		24	7.6	odd	2	inner
1050.3.h.c.349.4		24	5.4	even	2	inner
1050.3.h.c.349.15		24	1.1	even	1	trivial
1050.3.h.c.349.16		24	35.34	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)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +2.44949i q^{6} +(5.85173 - 3.84151i) q^{7} +2.82843i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +2.44949i q^{6} +(5.85173 - 3.84151i) q^{7} +2.82843i q^{8} +3.00000 q^{9} +20.2923 q^{11} +3.46410 q^{12} +11.5677 q^{13} +(-5.43272 - 8.27560i) q^{14} +4.00000 q^{16} -26.7353 q^{17} -4.24264i q^{18} +9.76295i q^{19} +(-10.1355 + 6.65370i) q^{21} -28.6976i q^{22} +34.8802i q^{23} -4.89898i q^{24} -16.3592i q^{26} -5.19615 q^{27} +(-11.7035 + 7.68303i) q^{28} +10.4554 q^{29} +39.3054i q^{31} -5.65685i q^{32} -35.1472 q^{33} +37.8094i q^{34} -6.00000 q^{36} +11.1970i q^{37} +13.8069 q^{38} -20.0358 q^{39} +49.9892i q^{41} +(9.40975 + 14.3338i) q^{42} -10.5469i q^{43} -40.5845 q^{44} +49.3281 q^{46} +34.8668 q^{47} -6.92820 q^{48} +(19.4856 - 44.9590i) q^{49} +46.3068 q^{51} -23.1354 q^{52} -68.9396i q^{53} +7.34847i q^{54} +(10.8654 + 16.5512i) q^{56} -16.9099i q^{57} -14.7861i q^{58} +49.7693i q^{59} +47.1666i q^{61} +55.5863 q^{62} +(17.5552 - 11.5245i) q^{63} -8.00000 q^{64} +49.7057i q^{66} -111.855i q^{67} +53.4705 q^{68} -60.4143i q^{69} +132.537 q^{71} +8.48528i q^{72} +130.413 q^{73} +15.8349 q^{74} -19.5259i q^{76} +(118.745 - 77.9530i) q^{77} +28.3350i q^{78} +3.57417 q^{79} +9.00000 q^{81} +70.6955 q^{82} -101.912 q^{83} +(20.2710 - 13.3074i) q^{84} -14.9155 q^{86} -18.1092 q^{87} +57.3952i q^{88} +7.58595i q^{89} +(67.6911 - 44.4375i) q^{91} -69.7605i q^{92} -68.0790i q^{93} -49.3090i q^{94} +9.79796i q^{96} -154.047 q^{97} +(-63.5816 - 27.5567i) q^{98} +60.8768 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 48 q^{4} + 72 q^{9}+O(q^{10}) \) 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

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