LMFDB - Embedded newform 240.3.l.b.161.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,3,Mod(161,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("240.161");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.53952634465$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-5}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 5 $ x^2 + 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			161.2
Root			$2.23607i$ of defining polynomial
Character	$\chi$	$=$	240.161
Dual form			240.3.l.b.161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 2.23607i) q^{3} -2.23607i q^{5} +6.00000 q^{7} +(-1.00000 + 8.94427i) q^{9} +O(q^{10})$	\(q+(2.00000 + 2.23607i) q^{3} -2.23607i q^{5} +6.00000 q^{7} +(-1.00000 + 8.94427i) q^{9} +4.47214i q^{11} +16.0000 q^{13} +(5.00000 - 4.47214i) q^{15} -4.47214i q^{17} +2.00000 q^{19} +(12.0000 + 13.4164i) q^{21} +13.4164i q^{23} -5.00000 q^{25} +(-22.0000 + 15.6525i) q^{27} +31.3050i q^{29} +18.0000 q^{31} +(-10.0000 + 8.94427i) q^{33} -13.4164i q^{35} -16.0000 q^{37} +(32.0000 + 35.7771i) q^{39} -62.6099i q^{41} -16.0000 q^{43} +(20.0000 + 2.23607i) q^{45} -49.1935i q^{47} -13.0000 q^{49} +(10.0000 - 8.94427i) q^{51} -4.47214i q^{53} +10.0000 q^{55} +(4.00000 + 4.47214i) q^{57} +4.47214i q^{59} +82.0000 q^{61} +(-6.00000 + 53.6656i) q^{63} -35.7771i q^{65} -24.0000 q^{67} +(-30.0000 + 26.8328i) q^{69} -125.220i q^{71} -74.0000 q^{73} +(-10.0000 - 11.1803i) q^{75} +26.8328i q^{77} -138.000 q^{79} +(-79.0000 - 17.8885i) q^{81} -93.9149i q^{83} -10.0000 q^{85} +(-70.0000 + 62.6099i) q^{87} -107.331i q^{89} +96.0000 q^{91} +(36.0000 + 40.2492i) q^{93} -4.47214i q^{95} -166.000 q^{97} +(-40.0000 - 4.47214i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{3} + 12 q^{7} - 2 q^{9}+O(q^{10}) $ 2 * q + 4 * q^3 + 12 * q^7 - 2 * q^9	$ 2 q + 4 q^{3} + 12 q^{7} - 2 q^{9} + 32 q^{13} + 10 q^{15} + 4 q^{19} + 24 q^{21} - 10 q^{25} - 44 q^{27} + 36 q^{31} - 20 q^{33} - 32 q^{37} + 64 q^{39} - 32 q^{43} + 40 q^{45} - 26 q^{49} + 20 q^{51} + 20 q^{55} + 8 q^{57} + 164 q^{61} - 12 q^{63} - 48 q^{67} - 60 q^{69} - 148 q^{73} - 20 q^{75} - 276 q^{79} - 158 q^{81} - 20 q^{85} - 140 q^{87} + 192 q^{91} + 72 q^{93} - 332 q^{97} - 80 q^{99}+O(q^{100}) $ 2 * q + 4 * q^3 + 12 * q^7 - 2 * q^9 + 32 * q^13 + 10 * q^15 + 4 * q^19 + 24 * q^21 - 10 * q^25 - 44 * q^27 + 36 * q^31 - 20 * q^33 - 32 * q^37 + 64 * q^39 - 32 * q^43 + 40 * q^45 - 26 * q^49 + 20 * q^51 + 20 * q^55 + 8 * q^57 + 164 * q^61 - 12 * q^63 - 48 * q^67 - 60 * q^69 - 148 * q^73 - 20 * q^75 - 276 * q^79 - 158 * q^81 - 20 * q^85 - 140 * q^87 + 192 * q^91 + 72 * q^93 - 332 * q^97 - 80 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	2.00000	+	2.23607i	0.666667	+	0.745356i
$3$	2.00000	+	2.23607i	0.666667	+	0.745356i
$4$		0			0
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$		0			0
$7$	6.00000			0.857143			0.428571	−	0.903508i	$-0.359017\pi$
$7$	6.00000			0.857143			0.428571	+	0.903508i	$0.359017\pi$
$8$		0			0
$9$	−1.00000	+	8.94427i	−0.111111	+	0.993808i
$10$		0			0
$11$			4.47214i			0.406558i	0.979121	+	0.203279i	$0.0651598\pi$
$11$			4.47214i			0.406558i	−0.979121	+	0.203279i	$0.934840\pi$
$12$		0			0
$13$	16.0000			1.23077			0.615385	−	0.788227i	$-0.289001\pi$
$13$	16.0000			1.23077			0.615385	+	0.788227i	$0.289001\pi$
$14$		0			0
$15$	5.00000	−	4.47214i	0.333333	−	0.298142i
$16$		0			0
$17$		−	4.47214i		−	0.263067i	−0.991312	−	0.131533i	$-0.958010\pi$
$17$		−	4.47214i		−	0.263067i	0.991312	−	0.131533i	$-0.0419901\pi$
$18$		0			0
$19$	2.00000			0.105263			0.0526316	−	0.998614i	$-0.483239\pi$
$19$	2.00000			0.105263			0.0526316	+	0.998614i	$0.483239\pi$
$20$		0			0
$21$	12.0000	+	13.4164i	0.571429	+	0.638877i
$22$		0			0
$23$			13.4164i			0.583322i	0.956522	+	0.291661i	$0.0942079\pi$
$23$			13.4164i			0.583322i	−0.956522	+	0.291661i	$0.905792\pi$
$24$		0			0
$25$	−5.00000			−0.200000
$26$		0			0
$27$	−22.0000	+	15.6525i	−0.814815	+	0.579721i
$28$		0			0
$29$			31.3050i			1.07948i	0.841831	+	0.539741i	$0.181478\pi$
$29$			31.3050i			1.07948i	−0.841831	+	0.539741i	$0.818522\pi$
$30$		0			0
$31$	18.0000			0.580645			0.290323	−	0.956929i	$-0.406237\pi$
$31$	18.0000			0.580645			0.290323	+	0.956929i	$0.406237\pi$
$32$		0			0
$33$	−10.0000	+	8.94427i	−0.303030	+	0.271039i
$34$		0			0
$35$		−	13.4164i		−	0.383326i
$36$		0			0
$37$	−16.0000			−0.432432			−0.216216	−	0.976346i	$-0.569372\pi$
$37$	−16.0000			−0.432432			−0.216216	+	0.976346i	$0.569372\pi$
$38$		0			0
$39$	32.0000	+	35.7771i	0.820513	+	0.917361i
$40$		0			0
$41$		−	62.6099i		−	1.52707i	−0.645766	−	0.763535i	$-0.723462\pi$
$41$		−	62.6099i		−	1.52707i	0.645766	−	0.763535i	$-0.276538\pi$
$42$		0			0
$43$	−16.0000			−0.372093			−0.186047	−	0.982541i	$-0.559568\pi$
$43$	−16.0000			−0.372093			−0.186047	+	0.982541i	$0.559568\pi$
$44$		0			0
$45$	20.0000	+	2.23607i	0.444444	+	0.0496904i
$46$		0			0
$47$		−	49.1935i		−	1.04667i	−0.852127	−	0.523335i	$-0.824688\pi$
$47$		−	49.1935i		−	1.04667i	0.852127	−	0.523335i	$-0.175312\pi$
$48$		0			0
$49$	−13.0000			−0.265306
$50$		0			0
$51$	10.0000	−	8.94427i	0.196078	−	0.175378i
$52$		0			0
$53$		−	4.47214i		−	0.0843799i	−0.999110	−	0.0421900i	$-0.986567\pi$
$53$		−	4.47214i		−	0.0843799i	0.999110	−	0.0421900i	$-0.0134335\pi$
$54$		0			0
$55$	10.0000			0.181818
$56$		0			0
$57$	4.00000	+	4.47214i	0.0701754	+	0.0784585i
$58$		0			0
$59$			4.47214i			0.0757989i	0.999282	+	0.0378995i	$0.0120667\pi$
$59$			4.47214i			0.0757989i	−0.999282	+	0.0378995i	$0.987933\pi$
$60$		0			0
$61$	82.0000			1.34426			0.672131	−	0.740432i	$-0.265379\pi$
$61$	82.0000			1.34426			0.672131	+	0.740432i	$0.265379\pi$
$62$		0			0
$63$	−6.00000	+	53.6656i	−0.0952381	+	0.851835i
$64$		0			0
$65$		−	35.7771i		−	0.550417i
$66$		0			0
$67$	−24.0000			−0.358209			−0.179104	−	0.983830i	$-0.557320\pi$
$67$	−24.0000			−0.358209			−0.179104	+	0.983830i	$0.557320\pi$
$68$		0			0
$69$	−30.0000	+	26.8328i	−0.434783	+	0.388881i
$70$		0			0
$71$		−	125.220i		−	1.76366i	−0.471568	−	0.881830i	$-0.656312\pi$
$71$		−	125.220i		−	1.76366i	0.471568	−	0.881830i	$-0.343688\pi$
$72$		0			0
$73$	−74.0000			−1.01370			−0.506849	−	0.862035i	$-0.669190\pi$
$73$	−74.0000			−1.01370			−0.506849	+	0.862035i	$0.669190\pi$
$74$		0			0
$75$	−10.0000	−	11.1803i	−0.133333	−	0.149071i
$76$		0			0
$77$			26.8328i			0.348478i
$78$		0			0
$79$	−138.000			−1.74684			−0.873418	−	0.486972i	$-0.838101\pi$
$79$	−138.000			−1.74684			−0.873418	+	0.486972i	$0.838101\pi$
$80$		0			0
$81$	−79.0000	−	17.8885i	−0.975309	−	0.220846i
$82$		0			0
$83$		−	93.9149i		−	1.13150i	−0.824575	−	0.565752i	$-0.808586\pi$
$83$		−	93.9149i		−	1.13150i	0.824575	−	0.565752i	$-0.191414\pi$
$84$		0			0
$85$	−10.0000			−0.117647
$86$		0			0
$87$	−70.0000	+	62.6099i	−0.804598	+	0.719654i
$88$		0			0
$89$		−	107.331i		−	1.20597i	−0.797753	−	0.602985i	$-0.793978\pi$
$89$		−	107.331i		−	1.20597i	0.797753	−	0.602985i	$-0.206022\pi$
$90$		0			0
$91$	96.0000			1.05495
$92$		0			0
$93$	36.0000	+	40.2492i	0.387097	+	0.432787i
$94$		0			0
$95$		−	4.47214i		−	0.0470751i
$96$		0			0
$97$	−166.000			−1.71134			−0.855670	−	0.517522i	$-0.826855\pi$
$97$	−166.000			−1.71134			−0.855670	+	0.517522i	$0.826855\pi$
$98$		0			0
$99$	−40.0000	−	4.47214i	−0.404040	−	0.0451731i
$100$		0			0
$101$		−	67.0820i		−	0.664179i	−0.943248	−	0.332089i	$-0.892246\pi$
$101$		−	67.0820i		−	0.664179i	0.943248	−	0.332089i	$-0.107754\pi$
$102$		0			0
$103$	−26.0000			−0.252427			−0.126214	−	0.992003i	$-0.540282\pi$
$103$	−26.0000			−0.252427			−0.126214	+	0.992003i	$0.540282\pi$
$104$		0			0
$105$	30.0000	−	26.8328i	0.285714	−	0.255551i
$106$		0			0
$107$			201.246i			1.88080i	0.340064	+	0.940402i	$0.389551\pi$
$107$			201.246i			1.88080i	−0.340064	+	0.940402i	$0.610449\pi$
$108$		0			0
$109$	38.0000			0.348624			0.174312	−	0.984690i	$-0.444230\pi$
$109$	38.0000			0.348624			0.174312	+	0.984690i	$0.444230\pi$
$110$		0			0
$111$	−32.0000	−	35.7771i	−0.288288	−	0.322316i
$112$		0			0
$113$		−	31.3050i		−	0.277035i	−0.990360	−	0.138517i	$-0.955766\pi$
$113$		−	31.3050i		−	0.277035i	0.990360	−	0.138517i	$-0.0442337\pi$
$114$		0			0
$115$	30.0000			0.260870
$116$		0			0
$117$	−16.0000	+	143.108i	−0.136752	+	1.22315i
$118$		0			0
$119$		−	26.8328i		−	0.225486i
$120$		0			0
$121$	101.000			0.834711
$122$		0			0
$123$	140.000	−	125.220i	1.13821	−	1.01805i
$124$		0			0
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	26.0000			0.204724			0.102362	−	0.994747i	$-0.467360\pi$
$127$	26.0000			0.204724			0.102362	+	0.994747i	$0.467360\pi$
$128$		0			0
$129$	−32.0000	−	35.7771i	−0.248062	−	0.277342i
$130$		0			0
$131$			13.4164i			0.102415i	0.998688	+	0.0512077i	$0.0163070\pi$
$131$			13.4164i			0.102415i	−0.998688	+	0.0512077i	$0.983693\pi$
$132$		0			0
$133$	12.0000			0.0902256
$134$		0			0
$135$	35.0000	+	49.1935i	0.259259	+	0.364396i
$136$		0			0
$137$			120.748i			0.881370i	0.897662	+	0.440685i	$0.145264\pi$
$137$			120.748i			0.881370i	−0.897662	+	0.440685i	$0.854736\pi$
$138$		0			0
$139$	82.0000			0.589928			0.294964	−	0.955508i	$-0.404692\pi$
$139$	82.0000			0.589928			0.294964	+	0.955508i	$0.404692\pi$
$140$		0			0
$141$	110.000	−	98.3870i	0.780142	−	0.697780i
$142$		0			0
$143$			71.5542i			0.500379i
$144$		0			0
$145$	70.0000			0.482759
$146$		0			0
$147$	−26.0000	−	29.0689i	−0.176871	−	0.197748i
$148$		0			0
$149$			111.803i			0.750358i	0.926952	+	0.375179i	$0.122419\pi$
$149$			111.803i			0.750358i	−0.926952	+	0.375179i	$0.877581\pi$
$150$		0			0
$151$	158.000			1.04636			0.523179	−	0.852223i	$-0.324746\pi$
$151$	158.000			1.04636			0.523179	+	0.852223i	$0.324746\pi$
$152$		0			0
$153$	40.0000	+	4.47214i	0.261438	+	0.0292296i
$154$		0			0
$155$		−	40.2492i		−	0.259672i
$156$		0			0
$157$	164.000			1.04459			0.522293	−	0.852766i	$-0.325077\pi$
$157$	164.000			1.04459			0.522293	+	0.852766i	$0.325077\pi$
$158$		0			0
$159$	10.0000	−	8.94427i	0.0628931	−	0.0562533i
$160$		0			0
$161$			80.4984i			0.499990i
$162$		0			0
$163$	−236.000			−1.44785			−0.723926	−	0.689877i	$-0.757664\pi$
$163$	−236.000			−1.44785			−0.723926	+	0.689877i	$0.757664\pi$
$164$		0			0
$165$	20.0000	+	22.3607i	0.121212	+	0.135519i
$166$		0			0
$167$			93.9149i			0.562364i	0.959654	+	0.281182i	$0.0907265\pi$
$167$			93.9149i			0.562364i	−0.959654	+	0.281182i	$0.909273\pi$
$168$		0			0
$169$	87.0000			0.514793
$170$		0			0
$171$	−2.00000	+	17.8885i	−0.0116959	+	0.104611i
$172$		0			0
$173$		−	13.4164i		−	0.0775515i	−0.999248	−	0.0387757i	$-0.987654\pi$
$173$		−	13.4164i		−	0.0775515i	0.999248	−	0.0387757i	$-0.0123458\pi$
$174$		0			0
$175$	−30.0000			−0.171429
$176$		0			0
$177$	−10.0000	+	8.94427i	−0.0564972	+	0.0505326i
$178$		0			0
$179$			192.302i			1.07431i	0.843483	+	0.537156i	$0.180501\pi$
$179$			192.302i			1.07431i	−0.843483	+	0.537156i	$0.819499\pi$
$180$		0			0
$181$	2.00000			0.0110497			0.00552486	−	0.999985i	$-0.498241\pi$
$181$	2.00000			0.0110497			0.00552486	+	0.999985i	$0.498241\pi$
$182$		0			0
$183$	164.000	+	183.358i	0.896175	+	1.00195i
$184$		0			0
$185$			35.7771i			0.193390i
$186$		0			0
$187$	20.0000			0.106952
$188$		0			0
$189$	−132.000	+	93.9149i	−0.698413	+	0.496904i
$190$		0			0
$191$		−	205.718i		−	1.07706i	−0.842607	−	0.538529i	$-0.818980\pi$
$191$		−	205.718i		−	1.07706i	0.842607	−	0.538529i	$-0.181020\pi$
$192$		0			0
$193$	−214.000			−1.10881			−0.554404	−	0.832248i	$-0.687054\pi$
$193$	−214.000			−1.10881			−0.554404	+	0.832248i	$0.687054\pi$
$194$		0			0
$195$	80.0000	−	71.5542i	0.410256	−	0.366944i
$196$		0			0
$197$			93.9149i			0.476725i	0.971176	+	0.238363i	$0.0766107\pi$
$197$			93.9149i			0.476725i	−0.971176	+	0.238363i	$0.923389\pi$
$198$		0			0
$199$	242.000			1.21608			0.608040	−	0.793906i	$-0.291956\pi$
$199$	242.000			1.21608			0.608040	+	0.793906i	$0.291956\pi$
$200$		0			0
$201$	−48.0000	−	53.6656i	−0.238806	−	0.266993i
$202$		0			0
$203$			187.830i			0.925270i
$204$		0			0
$205$	−140.000			−0.682927
$206$		0			0
$207$	−120.000	−	13.4164i	−0.579710	−	0.0648136i
$208$		0			0
$209$			8.94427i			0.0427956i
$210$		0			0
$211$	−2.00000			−0.00947867			−0.00473934	−	0.999989i	$-0.501509\pi$
$211$	−2.00000			−0.00947867			−0.00473934	+	0.999989i	$0.501509\pi$
$212$		0			0
$213$	280.000	−	250.440i	1.31455	−	1.17577i
$214$		0			0
$215$			35.7771i			0.166405i
$216$		0			0
$217$	108.000			0.497696
$218$		0			0
$219$	−148.000	−	165.469i	−0.675799	−	0.755566i
$220$		0			0
$221$		−	71.5542i		−	0.323775i
$222$		0			0
$223$	−86.0000			−0.385650			−0.192825	−	0.981233i	$-0.561765\pi$
$223$	−86.0000			−0.385650			−0.192825	+	0.981233i	$0.561765\pi$
$224$		0			0
$225$	5.00000	−	44.7214i	0.0222222	−	0.198762i
$226$		0			0
$227$		−	58.1378i		−	0.256114i	−0.991767	−	0.128057i	$-0.959126\pi$
$227$		−	58.1378i		−	0.256114i	0.991767	−	0.128057i	$-0.0408740\pi$
$228$		0			0
$229$	−282.000			−1.23144			−0.615721	−	0.787965i	$-0.711135\pi$
$229$	−282.000			−1.23144			−0.615721	+	0.787965i	$0.711135\pi$
$230$		0			0
$231$	−60.0000	+	53.6656i	−0.259740	+	0.232319i
$232$		0			0
$233$			362.243i			1.55469i	0.629074	+	0.777346i	$0.283434\pi$
$233$			362.243i			1.55469i	−0.629074	+	0.777346i	$0.716566\pi$
$234$		0			0
$235$	−110.000			−0.468085
$236$		0			0
$237$	−276.000	−	308.577i	−1.16456	−	1.30201i
$238$		0			0
$239$		−	250.440i		−	1.04786i	−0.851760	−	0.523932i	$-0.824464\pi$
$239$		−	250.440i		−	1.04786i	0.851760	−	0.523932i	$-0.175536\pi$
$240$		0			0
$241$	262.000			1.08714			0.543568	−	0.839365i	$-0.317073\pi$
$241$	262.000			1.08714			0.543568	+	0.839365i	$0.317073\pi$
$242$		0			0
$243$	−118.000	−	212.426i	−0.485597	−	0.874183i
$244$		0			0
$245$			29.0689i			0.118649i
$246$		0			0
$247$	32.0000			0.129555
$248$		0			0
$249$	210.000	−	187.830i	0.843373	−	0.754336i
$250$		0			0
$251$			469.574i			1.87081i	0.353573	+	0.935407i	$0.384967\pi$
$251$			469.574i			1.87081i	−0.353573	+	0.935407i	$0.615033\pi$
$252$		0			0
$253$	−60.0000			−0.237154
$254$		0			0
$255$	−20.0000	−	22.3607i	−0.0784314	−	0.0876889i
$256$		0			0
$257$		−	201.246i		−	0.783059i	−0.920166	−	0.391529i	$-0.871946\pi$
$257$		−	201.246i		−	0.783059i	0.920166	−	0.391529i	$-0.128054\pi$
$258$		0			0
$259$	−96.0000			−0.370656
$260$		0			0
$261$	−280.000	−	31.3050i	−1.07280	−	0.119942i
$262$		0			0
$263$		−	58.1378i		−	0.221056i	−0.993873	−	0.110528i	$-0.964746\pi$
$263$		−	58.1378i		−	0.221056i	0.993873	−	0.110528i	$-0.0352542\pi$
$264$		0			0
$265$	−10.0000			−0.0377358
$266$		0			0
$267$	240.000	−	214.663i	0.898876	−	0.803979i
$268$		0			0
$269$			371.187i			1.37988i	0.723867	+	0.689939i	$0.242363\pi$
$269$			371.187i			1.37988i	−0.723867	+	0.689939i	$0.757637\pi$
$270$		0			0
$271$	−82.0000			−0.302583			−0.151292	−	0.988489i	$-0.548343\pi$
$271$	−82.0000			−0.302583			−0.151292	+	0.988489i	$0.548343\pi$
$272$		0			0
$273$	192.000	+	214.663i	0.703297	+	0.786310i
$274$		0			0
$275$		−	22.3607i		−	0.0813116i
$276$		0			0
$277$	24.0000			0.0866426			0.0433213	−	0.999061i	$-0.486206\pi$
$277$	24.0000			0.0866426			0.0433213	+	0.999061i	$0.486206\pi$
$278$		0			0
$279$	−18.0000	+	160.997i	−0.0645161	+	0.577050i
$280$		0			0
$281$			187.830i			0.668433i	0.942496	+	0.334217i	$0.108472\pi$
$281$			187.830i			0.668433i	−0.942496	+	0.334217i	$0.891528\pi$
$282$		0			0
$283$	144.000			0.508834			0.254417	−	0.967095i	$-0.418116\pi$
$283$	144.000			0.508834			0.254417	+	0.967095i	$0.418116\pi$
$284$		0			0
$285$	10.0000	−	8.94427i	0.0350877	−	0.0313834i
$286$		0			0
$287$		−	375.659i		−	1.30892i
$288$		0			0
$289$	269.000			0.930796
$290$		0			0
$291$	−332.000	−	371.187i	−1.14089	−	1.27556i
$292$		0			0
$293$		−	469.574i		−	1.60264i	−0.598234	−	0.801321i	$-0.704131\pi$
$293$		−	469.574i		−	1.60264i	0.598234	−	0.801321i	$-0.295869\pi$
$294$		0			0
$295$	10.0000			0.0338983
$296$		0			0
$297$	−70.0000	−	98.3870i	−0.235690	−	0.331269i
$298$		0			0
$299$			214.663i			0.717935i
$300$		0			0
$301$	−96.0000			−0.318937
$302$		0			0
$303$	150.000	−	134.164i	0.495050	−	0.442786i
$304$		0			0
$305$		−	183.358i		−	0.601172i
$306$		0			0
$307$	−184.000			−0.599349			−0.299674	−	0.954042i	$-0.596878\pi$
$307$	−184.000			−0.599349			−0.299674	+	0.954042i	$0.596878\pi$
$308$		0			0
$309$	−52.0000	−	58.1378i	−0.168285	−	0.188148i
$310$		0			0
$311$			160.997i			0.517675i	0.965921	+	0.258837i	$0.0833394\pi$
$311$			160.997i			0.517675i	−0.965921	+	0.258837i	$0.916661\pi$
$312$		0			0
$313$	−394.000			−1.25879			−0.629393	−	0.777087i	$-0.716696\pi$
$313$	−394.000			−1.25879			−0.629393	+	0.777087i	$0.716696\pi$
$314$		0			0
$315$	120.000	+	13.4164i	0.380952	+	0.0425918i
$316$		0			0
$317$		−	451.686i		−	1.42488i	−0.701735	−	0.712438i	$-0.747591\pi$
$317$		−	451.686i		−	1.42488i	0.701735	−	0.712438i	$-0.252409\pi$
$318$		0			0
$319$	−140.000			−0.438871
$320$		0			0
$321$	−450.000	+	402.492i	−1.40187	+	1.25387i
$322$		0			0
$323$		−	8.94427i		−	0.0276912i
$324$		0			0
$325$	−80.0000			−0.246154
$326$		0			0
$327$	76.0000	+	84.9706i	0.232416	+	0.259849i
$328$		0			0
$329$		−	295.161i		−	0.897146i
$330$		0			0
$331$	198.000			0.598187			0.299094	−	0.954224i	$-0.403316\pi$
$331$	198.000			0.598187			0.299094	+	0.954224i	$0.403316\pi$
$332$		0			0
$333$	16.0000	−	143.108i	0.0480480	−	0.429755i
$334$		0			0
$335$			53.6656i			0.160196i
$336$		0			0
$337$	394.000			1.16914			0.584570	−	0.811343i	$-0.301263\pi$
$337$	394.000			1.16914			0.584570	+	0.811343i	$0.301263\pi$
$338$		0			0
$339$	70.0000	−	62.6099i	0.206490	−	0.184690i
$340$		0			0
$341$			80.4984i			0.236066i
$342$		0			0
$343$	−372.000			−1.08455
$344$		0			0
$345$	60.0000	+	67.0820i	0.173913	+	0.194441i
$346$		0			0
$347$		−	183.358i		−	0.528408i	−0.964467	−	0.264204i	$-0.914891\pi$
$347$		−	183.358i		−	0.528408i	0.964467	−	0.264204i	$-0.0851092\pi$
$348$		0			0
$349$	−362.000			−1.03725			−0.518625	−	0.855002i	$-0.673556\pi$
$349$	−362.000			−1.03725			−0.518625	+	0.855002i	$0.673556\pi$
$350$		0			0
$351$	−352.000	+	250.440i	−1.00285	+	0.713503i
$352$		0			0
$353$			308.577i			0.874157i	0.899423	+	0.437078i	$0.143987\pi$
$353$			308.577i			0.874157i	−0.899423	+	0.437078i	$0.856013\pi$
$354$		0			0
$355$	−280.000			−0.788732
$356$		0			0
$357$	60.0000	−	53.6656i	0.168067	−	0.150324i
$358$		0			0
$359$			295.161i			0.822175i	0.911596	+	0.411088i	$0.134851\pi$
$359$			295.161i			0.822175i	−0.911596	+	0.411088i	$0.865149\pi$
$360$		0			0
$361$	−357.000			−0.988920
$362$		0			0
$363$	202.000	+	225.843i	0.556474	+	0.622157i
$364$		0			0
$365$			165.469i			0.453340i
$366$		0			0
$367$	186.000			0.506812			0.253406	−	0.967360i	$-0.418449\pi$
$367$	186.000			0.506812			0.253406	+	0.967360i	$0.418449\pi$
$368$		0			0
$369$	560.000	+	62.6099i	1.51762	+	0.169675i
$370$		0			0
$371$		−	26.8328i		−	0.0723256i
$372$		0			0
$373$	−44.0000			−0.117962			−0.0589812	−	0.998259i	$-0.518785\pi$
$373$	−44.0000			−0.117962			−0.0589812	+	0.998259i	$0.518785\pi$
$374$		0			0
$375$	−25.0000	+	22.3607i	−0.0666667	+	0.0596285i
$376$		0			0
$377$			500.879i			1.32859i
$378$		0			0
$379$	362.000			0.955145			0.477573	−	0.878592i	$-0.341517\pi$
$379$	362.000			0.955145			0.477573	+	0.878592i	$0.341517\pi$
$380$		0			0
$381$	52.0000	+	58.1378i	0.136483	+	0.152593i
$382$		0			0
$383$		−	362.243i		−	0.945804i	−0.881115	−	0.472902i	$-0.843206\pi$
$383$		−	362.243i		−	0.945804i	0.881115	−	0.472902i	$-0.156794\pi$
$384$		0			0
$385$	60.0000			0.155844
$386$		0			0
$387$	16.0000	−	143.108i	0.0413437	−	0.369789i
$388$		0			0
$389$		−	442.741i		−	1.13815i	−0.822285	−	0.569076i	$-0.807301\pi$
$389$		−	442.741i		−	1.13815i	0.822285	−	0.569076i	$-0.192699\pi$
$390$		0			0
$391$	60.0000			0.153453
$392$		0			0
$393$	−30.0000	+	26.8328i	−0.0763359	+	0.0682769i
$394$		0			0
$395$			308.577i			0.781209i
$396$		0			0
$397$	124.000			0.312343			0.156171	−	0.987730i	$-0.450085\pi$
$397$	124.000			0.312343			0.156171	+	0.987730i	$0.450085\pi$
$398$		0			0
$399$	24.0000	+	26.8328i	0.0601504	+	0.0672502i
$400$		0			0
$401$			268.328i			0.669148i	0.942370	+	0.334574i	$0.108592\pi$
$401$			268.328i			0.669148i	−0.942370	+	0.334574i	$0.891408\pi$
$402$		0			0
$403$	288.000			0.714640
$404$		0			0
$405$	−40.0000	+	176.649i	−0.0987654	+	0.436171i
$406$		0			0
$407$		−	71.5542i		−	0.175809i
$408$		0			0
$409$	458.000			1.11980			0.559902	−	0.828559i	$-0.310839\pi$
$409$	458.000			1.11980			0.559902	+	0.828559i	$0.310839\pi$
$410$		0			0
$411$	−270.000	+	241.495i	−0.656934	+	0.587580i
$412$		0			0
$413$			26.8328i			0.0649705i
$414$		0			0
$415$	−210.000			−0.506024
$416$		0			0
$417$	164.000	+	183.358i	0.393285	+	0.439706i
$418$		0			0
$419$		−	594.794i		−	1.41956i	−0.704425	−	0.709778i	$-0.748795\pi$
$419$		−	594.794i		−	1.41956i	0.704425	−	0.709778i	$-0.251205\pi$
$420$		0			0
$421$	562.000			1.33492			0.667458	−	0.744647i	$-0.267382\pi$
$421$	562.000			1.33492			0.667458	+	0.744647i	$0.267382\pi$
$422$		0			0
$423$	440.000	+	49.1935i	1.04019	+	0.116297i
$424$		0			0
$425$			22.3607i			0.0526134i
$426$		0			0
$427$	492.000			1.15222
$428$		0			0
$429$	−160.000	+	143.108i	−0.372960	+	0.333586i
$430$		0			0
$431$			348.827i			0.809342i	0.914462	+	0.404671i	$0.132614\pi$
$431$			348.827i			0.809342i	−0.914462	+	0.404671i	$0.867386\pi$
$432$		0			0
$433$	226.000			0.521940			0.260970	−	0.965347i	$-0.415958\pi$
$433$	226.000			0.521940			0.260970	+	0.965347i	$0.415958\pi$
$434$		0			0
$435$	140.000	+	156.525i	0.321839	+	0.359827i
$436$		0			0
$437$			26.8328i			0.0614023i
$438$		0			0
$439$	2.00000			0.00455581			0.00227790	−	0.999997i	$-0.499275\pi$
$439$	2.00000			0.00455581			0.00227790	+	0.999997i	$0.499275\pi$
$440$		0			0
$441$	13.0000	−	116.276i	0.0294785	−	0.263663i
$442$		0			0
$443$			201.246i			0.454280i	0.973862	+	0.227140i	$0.0729375\pi$
$443$			201.246i			0.454280i	−0.973862	+	0.227140i	$0.927062\pi$
$444$		0			0
$445$	−240.000			−0.539326
$446$		0			0
$447$	−250.000	+	223.607i	−0.559284	+	0.500239i
$448$		0			0
$449$		−	313.050i		−	0.697215i	−0.937269	−	0.348607i	$-0.886655\pi$
$449$		−	313.050i		−	0.697215i	0.937269	−	0.348607i	$-0.113345\pi$
$450$		0			0
$451$	280.000			0.620843
$452$		0			0
$453$	316.000	+	353.299i	0.697572	+	0.779909i
$454$		0			0
$455$		−	214.663i		−	0.471786i
$456$		0			0
$457$	334.000			0.730853			0.365427	−	0.930840i	$-0.380923\pi$
$457$	334.000			0.730853			0.365427	+	0.930840i	$0.380923\pi$
$458$		0			0
$459$	70.0000	+	98.3870i	0.152505	+	0.214351i
$460$		0			0
$461$		−	93.9149i		−	0.203720i	−0.994799	−	0.101860i	$-0.967521\pi$
$461$		−	93.9149i		−	0.203720i	0.994799	−	0.101860i	$-0.0324794\pi$
$462$		0			0
$463$	−366.000			−0.790497			−0.395248	−	0.918574i	$-0.629341\pi$
$463$	−366.000			−0.790497			−0.395248	+	0.918574i	$0.629341\pi$
$464$		0			0
$465$	90.0000	−	80.4984i	0.193548	−	0.173115i
$466$		0			0
$467$			451.686i			0.967207i	0.875287	+	0.483604i	$0.160672\pi$
$467$			451.686i			0.967207i	−0.875287	+	0.483604i	$0.839328\pi$
$468$		0			0
$469$	−144.000			−0.307036
$470$		0			0
$471$	328.000	+	366.715i	0.696391	+	0.778588i
$472$		0			0
$473$		−	71.5542i		−	0.151277i
$474$		0			0
$475$	−10.0000			−0.0210526
$476$		0			0
$477$	40.0000	+	4.47214i	0.0838574	+	0.00937555i
$478$		0			0
$479$		−	590.322i		−	1.23240i	−0.787588	−	0.616202i	$-0.788670\pi$
$479$		−	590.322i		−	1.23240i	0.787588	−	0.616202i	$-0.211330\pi$
$480$		0			0
$481$	−256.000			−0.532225
$482$		0			0
$483$	−180.000	+	160.997i	−0.372671	+	0.333327i
$484$		0			0
$485$			371.187i			0.765335i
$486$		0			0
$487$	886.000			1.81930			0.909651	−	0.415374i	$-0.136349\pi$
$487$	886.000			1.81930			0.909651	+	0.415374i	$0.136349\pi$
$488$		0			0
$489$	−472.000	−	527.712i	−0.965235	−	1.07917i
$490$		0			0
$491$		−	406.964i		−	0.828848i	−0.910084	−	0.414424i	$-0.863983\pi$
$491$		−	406.964i		−	0.828848i	0.910084	−	0.414424i	$-0.136017\pi$
$492$		0			0
$493$	140.000			0.283976
$494$		0			0
$495$	−10.0000	+	89.4427i	−0.0202020	+	0.180692i
$496$		0			0
$497$		−	751.319i		−	1.51171i
$498$		0			0
$499$	2.00000			0.00400802			0.00200401	−	0.999998i	$-0.499362\pi$
$499$	2.00000			0.00400802			0.00200401	+	0.999998i	$0.499362\pi$
$500$		0			0
$501$	−210.000	+	187.830i	−0.419162	+	0.374910i
$502$		0			0
$503$		−	219.135i		−	0.435655i	−0.975987	−	0.217828i	$-0.930103\pi$
$503$		−	219.135i		−	0.435655i	0.975987	−	0.217828i	$-0.0698971\pi$
$504$		0			0
$505$	−150.000			−0.297030
$506$		0			0
$507$	174.000	+	194.538i	0.343195	+	0.383704i
$508$		0			0
$509$			800.512i			1.57272i	0.617771	+	0.786358i	$0.288036\pi$
$509$			800.512i			1.57272i	−0.617771	+	0.786358i	$0.711964\pi$
$510$		0			0
$511$	−444.000			−0.868885
$512$		0			0
$513$	−44.0000	+	31.3050i	−0.0857700	+	0.0610233i
$514$		0			0
$515$			58.1378i			0.112889i
$516$		0			0
$517$	220.000			0.425532
$518$		0			0
$519$	30.0000	−	26.8328i	0.0578035	−	0.0517010i
$520$		0			0
$521$			527.712i			1.01288i	0.862274	+	0.506441i	$0.169039\pi$
$521$			527.712i			1.01288i	−0.862274	+	0.506441i	$0.830961\pi$
$522$		0			0
$523$	−376.000			−0.718929			−0.359465	−	0.933159i	$-0.617041\pi$
$523$	−376.000			−0.718929			−0.359465	+	0.933159i	$0.617041\pi$
$524$		0			0
$525$	−60.0000	−	67.0820i	−0.114286	−	0.127775i
$526$		0			0
$527$		−	80.4984i		−	0.152748i
$528$		0			0
$529$	349.000			0.659735
$530$		0			0
$531$	−40.0000	−	4.47214i	−0.0753296	−	0.00842210i
$532$		0			0
$533$		−	1001.76i		−	1.87947i
$534$		0			0
$535$	450.000			0.841121
$536$		0			0
$537$	−430.000	+	384.604i	−0.800745	+	0.716208i
$538$		0			0
$539$		−	58.1378i		−	0.107862i
$540$		0			0
$541$	−198.000			−0.365989			−0.182994	−	0.983114i	$-0.558579\pi$
$541$	−198.000			−0.365989			−0.182994	+	0.983114i	$0.558579\pi$
$542$		0			0
$543$	4.00000	+	4.47214i	0.00736648	+	0.00823598i
$544$		0			0
$545$		−	84.9706i		−	0.155909i
$546$		0			0
$547$	−1024.00			−1.87203			−0.936015	−	0.351961i	$-0.885515\pi$
$547$	−1024.00			−1.87203			−0.936015	+	0.351961i	$0.885515\pi$
$548$		0			0
$549$	−82.0000	+	733.430i	−0.149362	+	1.33594i
$550$		0			0
$551$			62.6099i			0.113630i
$552$		0			0
$553$	−828.000			−1.49729
$554$		0			0
$555$	−80.0000	+	71.5542i	−0.144144	+	0.128926i
$556$		0			0
$557$		−	67.0820i		−	0.120435i	−0.998185	−	0.0602173i	$-0.980821\pi$
$557$		−	67.0820i		−	0.120435i	0.998185	−	0.0602173i	$-0.0191794\pi$
$558$		0			0
$559$	−256.000			−0.457961
$560$		0			0
$561$	40.0000	+	44.7214i	0.0713012	+	0.0797172i
$562$		0			0
$563$			254.912i			0.452774i	0.974037	+	0.226387i	$0.0726914\pi$
$563$			254.912i			0.452774i	−0.974037	+	0.226387i	$0.927309\pi$
$564$		0			0
$565$	−70.0000			−0.123894
$566$		0			0
$567$	−474.000	−	107.331i	−0.835979	−	0.189297i
$568$		0			0
$569$		−	858.650i		−	1.50905i	−0.656271	−	0.754526i	$-0.727867\pi$
$569$		−	858.650i		−	1.50905i	0.656271	−	0.754526i	$-0.272133\pi$
$570$		0			0
$571$	−962.000			−1.68476			−0.842382	−	0.538881i	$-0.818847\pi$
$571$	−962.000			−1.68476			−0.842382	+	0.538881i	$0.818847\pi$
$572$		0			0
$573$	460.000	−	411.437i	0.802792	−	0.718039i
$574$		0			0
$575$		−	67.0820i		−	0.116664i
$576$		0			0
$577$	−886.000			−1.53553			−0.767764	−	0.640732i	$-0.778631\pi$
$577$	−886.000			−1.53553			−0.767764	+	0.640732i	$0.778631\pi$
$578$		0			0
$579$	−428.000	−	478.519i	−0.739206	−	0.826457i
$580$		0			0
$581$		−	563.489i		−	0.969861i
$582$		0			0
$583$	20.0000			0.0343053
$584$		0			0
$585$	320.000	+	35.7771i	0.547009	+	0.0611574i
$586$		0			0
$587$		−	657.404i		−	1.11994i	−0.828513	−	0.559969i	$-0.810813\pi$
$587$		−	657.404i		−	1.11994i	0.828513	−	0.559969i	$-0.189187\pi$
$588$		0			0
$589$	36.0000			0.0611205
$590$		0			0
$591$	−210.000	+	187.830i	−0.355330	+	0.317817i
$592$		0			0
$593$			111.803i			0.188539i	0.995547	+	0.0942693i	$0.0300515\pi$
$593$			111.803i			0.188539i	−0.995547	+	0.0942693i	$0.969949\pi$
$594$		0			0
$595$	−60.0000			−0.100840
$596$		0			0
$597$	484.000	+	541.128i	0.810720	+	0.906413i
$598$		0			0
$599$			223.607i			0.373300i	0.982426	+	0.186650i	$0.0597631\pi$
$599$			223.607i			0.373300i	−0.982426	+	0.186650i	$0.940237\pi$
$600$		0			0
$601$	2.00000			0.00332779			0.00166389	−	0.999999i	$-0.499470\pi$
$601$	2.00000			0.00332779			0.00166389	+	0.999999i	$0.499470\pi$
$602$		0			0
$603$	24.0000	−	214.663i	0.0398010	−	0.355991i
$604$		0			0
$605$		−	225.843i		−	0.373294i
$606$		0			0
$607$	506.000			0.833608			0.416804	−	0.908996i	$-0.363150\pi$
$607$	506.000			0.833608			0.416804	+	0.908996i	$0.363150\pi$
$608$		0			0
$609$	−420.000	+	375.659i	−0.689655	+	0.616846i
$610$		0			0
$611$		−	787.096i		−	1.28821i
$612$		0			0
$613$	556.000			0.907015			0.453507	−	0.891253i	$-0.350173\pi$
$613$	556.000			0.907015			0.453507	+	0.891253i	$0.350173\pi$
$614$		0			0
$615$	−280.000	−	313.050i	−0.455285	−	0.509024i
$616$		0			0
$617$		−	93.9149i		−	0.152212i	−0.997100	−	0.0761060i	$-0.975751\pi$
$617$		−	93.9149i		−	0.152212i	0.997100	−	0.0761060i	$-0.0242488\pi$
$618$		0			0
$619$	802.000			1.29564			0.647819	−	0.761794i	$-0.275681\pi$
$619$	802.000			1.29564			0.647819	+	0.761794i	$0.275681\pi$
$620$		0			0
$621$	−210.000	−	295.161i	−0.338164	−	0.475299i
$622$		0			0
$623$		−	643.988i		−	1.03369i
$624$		0			0
$625$	25.0000			0.0400000
$626$		0			0
$627$	−20.0000	+	17.8885i	−0.0318979	+	0.0285304i
$628$		0			0
$629$			71.5542i			0.113759i
$630$		0			0
$631$	698.000			1.10618			0.553090	−	0.833121i	$-0.313448\pi$
$631$	698.000			1.10618			0.553090	+	0.833121i	$0.313448\pi$
$632$		0			0
$633$	−4.00000	−	4.47214i	−0.00631912	−	0.00706499i
$634$		0			0
$635$		−	58.1378i		−	0.0915555i
$636$		0			0
$637$	−208.000			−0.326531
$638$		0			0
$639$	1120.00	+	125.220i	1.75274	+	0.195962i
$640$		0			0
$641$		−	912.316i		−	1.42327i	−0.702550	−	0.711635i	$-0.747955\pi$
$641$		−	912.316i		−	1.42327i	0.702550	−	0.711635i	$-0.252045\pi$
$642$		0			0
$643$	−156.000			−0.242613			−0.121306	−	0.992615i	$-0.538708\pi$
$643$	−156.000			−0.242613			−0.121306	+	0.992615i	$0.538708\pi$
$644$		0			0
$645$	−80.0000	+	71.5542i	−0.124031	+	0.110937i
$646$		0			0
$647$			755.791i			1.16815i	0.811701	+	0.584073i	$0.198542\pi$
$647$			755.791i			1.16815i	−0.811701	+	0.584073i	$0.801458\pi$
$648$		0			0
$649$	−20.0000			−0.0308166
$650$		0			0
$651$	216.000	+	241.495i	0.331797	+	0.370961i
$652$		0			0
$653$			487.463i			0.746497i	0.927731	+	0.373249i	$0.121756\pi$
$653$			487.463i			0.746497i	−0.927731	+	0.373249i	$0.878244\pi$
$654$		0			0
$655$	30.0000			0.0458015
$656$		0			0
$657$	74.0000	−	661.876i	0.112633	−	1.00742i
$658$		0			0
$659$			406.964i			0.617548i	0.951135	+	0.308774i	$0.0999187\pi$
$659$			406.964i			0.617548i	−0.951135	+	0.308774i	$0.900081\pi$
$660$		0			0
$661$	682.000			1.03177			0.515885	−	0.856658i	$-0.327463\pi$
$661$	682.000			1.03177			0.515885	+	0.856658i	$0.327463\pi$
$662$		0			0
$663$	160.000	−	143.108i	0.241327	−	0.215850i
$664$		0			0
$665$		−	26.8328i		−	0.0403501i
$666$		0			0
$667$	−420.000			−0.629685
$668$		0			0
$669$	−172.000	−	192.302i	−0.257100	−	0.287447i
$670$		0			0
$671$			366.715i			0.546520i
$672$		0			0
$673$	−894.000			−1.32838			−0.664190	−	0.747564i	$-0.731223\pi$
$673$	−894.000			−1.32838			−0.664190	+	0.747564i	$0.731223\pi$
$674$		0			0
$675$	110.000	−	78.2624i	0.162963	−	0.115944i
$676$		0			0
$677$			550.073i			0.812515i	0.913759	+	0.406258i	$0.133166\pi$
$677$			550.073i			0.812515i	−0.913759	+	0.406258i	$0.866834\pi$
$678$		0			0
$679$	−996.000			−1.46686
$680$		0			0
$681$	130.000	−	116.276i	0.190896	−	0.170742i
$682$		0			0
$683$			442.741i			0.648231i	0.946018	+	0.324115i	$0.105067\pi$
$683$			442.741i			0.648231i	−0.946018	+	0.324115i	$0.894933\pi$
$684$		0			0
$685$	270.000			0.394161
$686$		0			0
$687$	−564.000	−	630.571i	−0.820961	−	0.917862i
$688$		0			0
$689$		−	71.5542i		−	0.103852i
$690$		0			0
$691$	758.000			1.09696			0.548480	−	0.836163i	$-0.315207\pi$
$691$	758.000			1.09696			0.548480	+	0.836163i	$0.315207\pi$
$692$		0			0
$693$	−240.000	−	26.8328i	−0.346320	−	0.0387198i
$694$		0			0
$695$		−	183.358i		−	0.263824i
$696$		0			0
$697$	−280.000			−0.401722
$698$		0			0
$699$	−810.000	+	724.486i	−1.15880	+	1.03646i
$700$		0			0
$701$			782.624i			1.11644i	0.829693	+	0.558220i	$0.188515\pi$
$701$			782.624i			1.11644i	−0.829693	+	0.558220i	$0.811485\pi$
$702$		0			0
$703$	−32.0000			−0.0455192
$704$		0			0
$705$	−220.000	−	245.967i	−0.312057	−	0.348890i
$706$		0			0
$707$		−	402.492i		−	0.569296i
$708$		0			0
$709$	−2.00000			−0.00282087			−0.00141044	−	0.999999i	$-0.500449\pi$
$709$	−2.00000			−0.00282087			−0.00141044	+	0.999999i	$0.500449\pi$
$710$		0			0
$711$	138.000	−	1234.31i	0.194093	−	1.73602i
$712$		0			0
$713$			241.495i			0.338703i
$714$		0			0
$715$	160.000			0.223776
$716$		0			0
$717$	560.000	−	500.879i	0.781032	−	0.698576i
$718$		0			0
$719$			858.650i			1.19423i	0.802156	+	0.597114i	$0.203686\pi$
$719$			858.650i			1.19423i	−0.802156	+	0.597114i	$0.796314\pi$
$720$		0			0
$721$	−156.000			−0.216366
$722$		0			0
$723$	524.000	+	585.850i	0.724758	+	0.810304i
$724$		0			0
$725$		−	156.525i		−	0.215896i
$726$		0			0
$727$	−674.000			−0.927098			−0.463549	−	0.886071i	$-0.653424\pi$
$727$	−674.000			−0.927098			−0.463549	+	0.886071i	$0.653424\pi$
$728$		0			0
$729$	239.000	−	688.709i	0.327846	−	0.944731i
$730$		0			0
$731$			71.5542i			0.0978853i
$732$		0			0
$733$	656.000			0.894952			0.447476	−	0.894296i	$-0.352323\pi$
$733$	656.000			0.894952			0.447476	+	0.894296i	$0.352323\pi$
$734$		0			0
$735$	−65.0000	+	58.1378i	−0.0884354	+	0.0790990i
$736$		0			0
$737$		−	107.331i		−	0.145633i
$738$		0			0
$739$	−598.000			−0.809202			−0.404601	−	0.914493i	$-0.632590\pi$
$739$	−598.000			−0.809202			−0.404601	+	0.914493i	$0.632590\pi$
$740$		0			0
$741$	64.0000	+	71.5542i	0.0863698	+	0.0965643i
$742$		0			0
$743$			782.624i			1.05333i	0.850073	+	0.526665i	$0.176558\pi$
$743$			782.624i			1.05333i	−0.850073	+	0.526665i	$0.823442\pi$
$744$		0			0
$745$	250.000			0.335570
$746$		0			0
$747$	840.000	+	93.9149i	1.12450	+	0.125723i
$748$		0			0
$749$			1207.48i			1.61212i
$750$		0			0
$751$	338.000			0.450067			0.225033	−	0.974351i	$-0.427751\pi$
$751$	338.000			0.450067			0.225033	+	0.974351i	$0.427751\pi$
$752$		0			0
$753$	−1050.00	+	939.149i	−1.39442	+	1.24721i
$754$		0			0
$755$		−	353.299i		−	0.467945i
$756$		0			0
$757$	−656.000			−0.866579			−0.433289	−	0.901255i	$-0.642647\pi$
$757$	−656.000			−0.866579			−0.433289	+	0.901255i	$0.642647\pi$
$758$		0			0
$759$	−120.000	−	134.164i	−0.158103	−	0.176764i
$760$		0			0
$761$		−	295.161i		−	0.387859i	−0.981015	−	0.193930i	$-0.937877\pi$
$761$		−	295.161i		−	0.387859i	0.981015	−	0.193930i	$-0.0621234\pi$
$762$		0			0
$763$	228.000			0.298820
$764$		0			0
$765$	10.0000	−	89.4427i	0.0130719	−	0.116919i
$766$		0			0
$767$			71.5542i			0.0932910i
$768$		0			0
$769$	−82.0000			−0.106632			−0.0533160	−	0.998578i	$-0.516979\pi$
$769$	−82.0000			−0.106632			−0.0533160	+	0.998578i	$0.516979\pi$
$770$		0			0
$771$	450.000	−	402.492i	0.583658	−	0.522039i
$772$		0			0
$773$			1059.90i			1.37115i	0.728004	+	0.685573i	$0.240448\pi$
$773$			1059.90i			1.37115i	−0.728004	+	0.685573i	$0.759552\pi$
$774$		0			0
$775$	−90.0000			−0.116129
$776$		0			0
$777$	−192.000	−	214.663i	−0.247104	−	0.276271i
$778$		0			0
$779$		−	125.220i		−	0.160744i
$780$		0			0
$781$	560.000			0.717029
$782$		0			0
$783$	−490.000	−	688.709i	−0.625798	−	0.879577i
$784$		0			0
$785$		−	366.715i		−	0.467153i
$786$		0			0
$787$	536.000			0.681067			0.340534	−	0.940232i	$-0.389392\pi$
$787$	536.000			0.681067			0.340534	+	0.940232i	$0.389392\pi$
$788$		0			0
$789$	130.000	−	116.276i	0.164766	−	0.147371i
$790$		0			0
$791$		−	187.830i		−	0.237459i
$792$		0			0
$793$	1312.00			1.65448
$794$		0			0
$795$	−20.0000	−	22.3607i	−0.0251572	−	0.0281266i
$796$		0			0
$797$			406.964i			0.510620i	0.966859	+	0.255310i	$0.0821776\pi$
$797$			406.964i			0.510620i	−0.966859	+	0.255310i	$0.917822\pi$
$798$		0			0
$799$	−220.000			−0.275344
$800$		0			0
$801$	960.000	+	107.331i	1.19850	+	0.133997i
$802$		0			0
$803$		−	330.938i		−	0.412127i
$804$		0			0
$805$	180.000			0.223602
$806$		0			0
$807$	−830.000	+	742.375i	−1.02850	+	0.919919i
$808$		0			0
$809$			1091.20i			1.34883i	0.738354	+	0.674414i	$0.235603\pi$
$809$			1091.20i			1.34883i	−0.738354	+	0.674414i	$0.764397\pi$
$810$		0			0
$811$	558.000			0.688039			0.344020	−	0.938962i	$-0.388211\pi$
$811$	558.000			0.688039			0.344020	+	0.938962i	$0.388211\pi$
$812$		0			0
$813$	−164.000	−	183.358i	−0.201722	−	0.225532i
$814$		0			0
$815$			527.712i			0.647499i
$816$		0			0
$817$	−32.0000			−0.0391677
$818$		0			0
$819$	−96.0000	+	858.650i	−0.117216	+	1.04841i
$820$		0			0
$821$		−	389.076i		−	0.473905i	−0.971521	−	0.236952i	$-0.923851\pi$
$821$		−	389.076i		−	0.473905i	0.971521	−	0.236952i	$-0.0761485\pi$
$822$		0			0
$823$	214.000			0.260024			0.130012	−	0.991512i	$-0.458498\pi$
$823$	214.000			0.260024			0.130012	+	0.991512i	$0.458498\pi$
$824$		0			0
$825$	50.0000	−	44.7214i	0.0606061	−	0.0542077i
$826$		0			0
$827$			31.3050i			0.0378536i	0.999821	+	0.0189268i	$0.00602495\pi$
$827$			31.3050i			0.0378536i	−0.999821	+	0.0189268i	$0.993975\pi$
$828$		0			0
$829$	318.000			0.383595			0.191797	−	0.981435i	$-0.438568\pi$
$829$	318.000			0.383595			0.191797	+	0.981435i	$0.438568\pi$
$830$		0			0
$831$	48.0000	+	53.6656i	0.0577617	+	0.0645796i
$832$		0			0
$833$			58.1378i			0.0697932i
$834$		0			0
$835$	210.000			0.251497
$836$		0			0
$837$	−396.000	+	281.745i	−0.473118	+	0.336612i
$838$		0			0
$839$			62.6099i			0.0746244i	0.999304	+	0.0373122i	$0.0118796\pi$
$839$			62.6099i			0.0746244i	−0.999304	+	0.0373122i	$0.988120\pi$
$840$		0			0
$841$	−139.000			−0.165279
$842$		0			0
$843$	−420.000	+	375.659i	−0.498221	+	0.445622i
$844$		0			0
$845$		−	194.538i		−	0.230222i
$846$		0			0
$847$	606.000			0.715466
$848$		0			0
$849$	288.000	+	321.994i	0.339223	+	0.379262i
$850$		0			0
$851$		−	214.663i		−	0.252247i
$852$		0			0
$853$	−684.000			−0.801876			−0.400938	−	0.916105i	$-0.631316\pi$
$853$	−684.000			−0.801876			−0.400938	+	0.916105i	$0.631316\pi$
$854$		0			0
$855$	40.0000	+	4.47214i	0.0467836	+	0.00523057i
$856$		0			0
$857$			1498.17i			1.74815i	0.485790	+	0.874076i	$0.338532\pi$
$857$			1498.17i			1.74815i	−0.485790	+	0.874076i	$0.661468\pi$
$858$		0			0
$859$	842.000			0.980210			0.490105	−	0.871664i	$-0.336959\pi$
$859$	842.000			0.980210			0.490105	+	0.871664i	$0.336959\pi$
$860$		0			0
$861$	840.000	−	751.319i	0.975610	−	0.872612i
$862$		0			0
$863$			1015.17i			1.17633i	0.808740	+	0.588166i	$0.200150\pi$
$863$			1015.17i			1.17633i	−0.808740	+	0.588166i	$0.799850\pi$
$864$		0			0
$865$	−30.0000			−0.0346821
$866$		0			0
$867$	538.000	+	601.502i	0.620531	+	0.693774i
$868$		0			0
$869$		−	617.155i		−	0.710190i
$870$		0			0
$871$	−384.000			−0.440873
$872$		0			0
$873$	166.000	−	1484.75i	0.190149	−	1.70074i
$874$		0			0
$875$			67.0820i			0.0766652i
$876$		0			0
$877$	−156.000			−0.177879			−0.0889396	−	0.996037i	$-0.528348\pi$
$877$	−156.000			−0.177879			−0.0889396	+	0.996037i	$0.528348\pi$
$878$		0			0
$879$	1050.00	−	939.149i	1.19454	−	1.06843i
$880$		0			0
$881$		−	125.220i		−	0.142134i	−0.997472	−	0.0710669i	$-0.977360\pi$
$881$		−	125.220i		−	0.142134i	0.997472	−	0.0710669i	$-0.0226404\pi$
$882$		0			0
$883$	964.000			1.09173			0.545866	−	0.837872i	$-0.316201\pi$
$883$	964.000			1.09173			0.545866	+	0.837872i	$0.316201\pi$
$884$		0			0
$885$	20.0000	+	22.3607i	0.0225989	+	0.0252663i
$886$		0			0
$887$			952.565i			1.07392i	0.843608	+	0.536959i	$0.180427\pi$
$887$			952.565i			1.07392i	−0.843608	+	0.536959i	$0.819573\pi$
$888$		0			0
$889$	156.000			0.175478
$890$		0			0
$891$	80.0000	−	353.299i	0.0897868	−	0.396519i
$892$		0			0
$893$		−	98.3870i		−	0.110176i
$894$		0			0
$895$	430.000			0.480447
$896$		0			0
$897$	−480.000	+	429.325i	−0.535117	+	0.478623i
$898$		0			0
$899$			563.489i			0.626795i
$900$		0			0
$901$	−20.0000			−0.0221976
$902$		0			0
$903$	−192.000	−	214.663i	−0.212625	−	0.237722i
$904$		0			0
$905$		−	4.47214i		−	0.00494159i
$906$		0			0
$907$	−1284.00			−1.41566			−0.707828	−	0.706385i	$-0.750325\pi$
$907$	−1284.00			−1.41566			−0.707828	+	0.706385i	$0.750325\pi$
$908$		0			0
$909$	600.000	+	67.0820i	0.660066	+	0.0737976i
$910$		0			0
$911$		−	62.6099i		−	0.0687266i	−0.999409	−	0.0343633i	$-0.989060\pi$
$911$		−	62.6099i		−	0.0687266i	0.999409	−	0.0343633i	$-0.0109403\pi$
$912$		0			0
$913$	420.000			0.460022
$914$		0			0
$915$	410.000	−	366.715i	0.448087	−	0.400782i
$916$		0			0
$917$			80.4984i			0.0877846i
$918$		0			0
$919$	−418.000			−0.454842			−0.227421	−	0.973797i	$-0.573029\pi$
$919$	−418.000			−0.454842			−0.227421	+	0.973797i	$0.573029\pi$
$920$		0			0
$921$	−368.000	−	411.437i	−0.399566	−	0.446728i
$922$		0			0
$923$		−	2003.52i		−	2.17066i
$924$		0			0
$925$	80.0000			0.0864865
$926$		0			0
$927$	26.0000	−	232.551i	0.0280475	−	0.250864i
$928$		0			0
$929$		−	169.941i		−	0.182929i	−0.995808	−	0.0914646i	$-0.970845\pi$
$929$		−	169.941i		−	0.182929i	0.995808	−	0.0914646i	$-0.0291548\pi$
$930$		0			0
$931$	−26.0000			−0.0279270
$932$		0			0
$933$	−360.000	+	321.994i	−0.385852	+	0.345117i
$934$		0			0
$935$		−	44.7214i		−	0.0478303i
$936$		0			0
$937$	534.000			0.569904			0.284952	−	0.958542i	$-0.408022\pi$
$937$	534.000			0.569904			0.284952	+	0.958542i	$0.408022\pi$
$938$		0			0
$939$	−788.000	−	881.011i	−0.839191	−	0.938244i
$940$		0			0
$941$		−	129.692i		−	0.137824i	−0.997623	−	0.0689118i	$-0.978047\pi$
$941$		−	129.692i		−	0.137824i	0.997623	−	0.0689118i	$-0.0219527\pi$
$942$		0			0
$943$	840.000			0.890774
$944$		0			0
$945$	210.000	+	295.161i	0.222222	+	0.312340i
$946$		0			0
$947$			1516.05i			1.60090i	0.599398	+	0.800451i	$0.295407\pi$
$947$			1516.05i			1.60090i	−0.599398	+	0.800451i	$0.704593\pi$
$948$		0			0
$949$	−1184.00			−1.24763
$950$		0			0
$951$	1010.00	−	903.371i	1.06204	−	0.949917i
$952$		0			0
$953$		−	406.964i		−	0.427035i	−0.976939	−	0.213518i	$-0.931508\pi$
$953$		−	406.964i		−	0.427035i	0.976939	−	0.213518i	$-0.0684920\pi$
$954$		0			0
$955$	−460.000			−0.481675
$956$		0			0
$957$	−280.000	−	313.050i	−0.292581	−	0.327115i
$958$		0			0
$959$			724.486i			0.755460i
$960$		0			0
$961$	−637.000			−0.662851
$962$		0			0
$963$	−1800.00	−	201.246i	−1.86916	−	0.208978i
$964$		0			0
$965$			478.519i			0.495874i
$966$		0			0
$967$	−674.000			−0.697001			−0.348501	−	0.937309i	$-0.613309\pi$
$967$	−674.000			−0.697001			−0.348501	+	0.937309i	$0.613309\pi$
$968$		0			0
$969$	20.0000	−	17.8885i	0.0206398	−	0.0184608i
$970$		0			0
$971$			1328.22i			1.36789i	0.729532	+	0.683947i	$0.239738\pi$
$971$			1328.22i			1.36789i	−0.729532	+	0.683947i	$0.760262\pi$
$972$		0			0
$973$	492.000			0.505653
$974$		0			0
$975$	−160.000	−	178.885i	−0.164103	−	0.183472i
$976$		0			0
$977$			371.187i			0.379926i	0.981791	+	0.189963i	$0.0608367\pi$
$977$			371.187i			0.379926i	−0.981791	+	0.189963i	$0.939163\pi$
$978$		0			0
$979$	480.000			0.490296
$980$		0			0
$981$	−38.0000	+	339.882i	−0.0387360	+	0.346465i
$982$		0			0
$983$			442.741i			0.450398i	0.974313	+	0.225199i	$0.0723033\pi$
$983$			442.741i			0.450398i	−0.974313	+	0.225199i	$0.927697\pi$
$984$		0			0
$985$	210.000			0.213198
$986$		0			0
$987$	660.000	−	590.322i	0.668693	−	0.598097i
$988$		0			0
$989$		−	214.663i		−	0.217050i
$990$		0			0
$991$	−962.000			−0.970737			−0.485368	−	0.874310i	$-0.661314\pi$
$991$	−962.000			−0.970737			−0.485368	+	0.874310i	$0.661314\pi$
$992$		0			0
$993$	396.000	+	442.741i	0.398792	+	0.445862i
$994$		0			0
$995$		−	541.128i		−	0.543848i
$996$		0			0
$997$	24.0000			0.0240722			0.0120361	−	0.999928i	$-0.496169\pi$
$997$	24.0000			0.0240722			0.0120361	+	0.999928i	$0.496169\pi$
$998$		0			0
$999$	352.000	−	250.440i	0.352352	−	0.250690i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.3.l.b.161.2		2
3.2	odd	2	inner	240.3.l.b.161.1		2
4.3	odd	2		15.3.c.a.11.2	yes	2
5.2	odd	4		1200.3.c.f.449.3		4
5.3	odd	4		1200.3.c.f.449.2		4
5.4	even	2		1200.3.l.g.401.1		2
8.3	odd	2		960.3.l.c.641.2		2
8.5	even	2		960.3.l.b.641.1		2
12.11	even	2		15.3.c.a.11.1	✓	2
15.2	even	4		1200.3.c.f.449.1		4
15.8	even	4		1200.3.c.f.449.4		4
15.14	odd	2		1200.3.l.g.401.2		2
20.3	even	4		75.3.d.b.74.3		4
20.7	even	4		75.3.d.b.74.2		4
20.19	odd	2		75.3.c.e.26.1		2
24.5	odd	2		960.3.l.b.641.2		2
24.11	even	2		960.3.l.c.641.1		2
36.7	odd	6		405.3.i.b.296.2		4
36.11	even	6		405.3.i.b.296.1		4
36.23	even	6		405.3.i.b.26.2		4
36.31	odd	6		405.3.i.b.26.1		4
60.23	odd	4		75.3.d.b.74.1		4
60.47	odd	4		75.3.d.b.74.4		4
60.59	even	2		75.3.c.e.26.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.3.c.a.11.1	✓	2	12.11	even	2
15.3.c.a.11.2	yes	2	4.3	odd	2
75.3.c.e.26.1		2	20.19	odd	2
75.3.c.e.26.2		2	60.59	even	2
75.3.d.b.74.1		4	60.23	odd	4
75.3.d.b.74.2		4	20.7	even	4
75.3.d.b.74.3		4	20.3	even	4
75.3.d.b.74.4		4	60.47	odd	4
240.3.l.b.161.1		2	3.2	odd	2	inner
240.3.l.b.161.2		2	1.1	even	1	trivial
405.3.i.b.26.1		4	36.31	odd	6
405.3.i.b.26.2		4	36.23	even	6
405.3.i.b.296.1		4	36.11	even	6
405.3.i.b.296.2		4	36.7	odd	6
960.3.l.b.641.1		2	8.5	even	2
960.3.l.b.641.2		2	24.5	odd	2
960.3.l.c.641.1		2	24.11	even	2
960.3.l.c.641.2		2	8.3	odd	2
1200.3.c.f.449.1		4	15.2	even	4
1200.3.c.f.449.2		4	5.3	odd	4
1200.3.c.f.449.3		4	5.2	odd	4
1200.3.c.f.449.4		4	15.8	even	4
1200.3.l.g.401.1		2	5.4	even	2
1200.3.l.g.401.2		2	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(2.00000 + 2.23607i) q^{3} -2.23607i q^{5} +6.00000 q^{7} +(-1.00000 + 8.94427i) q^{9} +O(q^{10})\)	\(q+(2.00000 + 2.23607i) q^{3} -2.23607i q^{5} +6.00000 q^{7} +(-1.00000 + 8.94427i) q^{9} +4.47214i q^{11} +16.0000 q^{13} +(5.00000 - 4.47214i) q^{15} -4.47214i q^{17} +2.00000 q^{19} +(12.0000 + 13.4164i) q^{21} +13.4164i q^{23} -5.00000 q^{25} +(-22.0000 + 15.6525i) q^{27} +31.3050i q^{29} +18.0000 q^{31} +(-10.0000 + 8.94427i) q^{33} -13.4164i q^{35} -16.0000 q^{37} +(32.0000 + 35.7771i) q^{39} -62.6099i q^{41} -16.0000 q^{43} +(20.0000 + 2.23607i) q^{45} -49.1935i q^{47} -13.0000 q^{49} +(10.0000 - 8.94427i) q^{51} -4.47214i q^{53} +10.0000 q^{55} +(4.00000 + 4.47214i) q^{57} +4.47214i q^{59} +82.0000 q^{61} +(-6.00000 + 53.6656i) q^{63} -35.7771i q^{65} -24.0000 q^{67} +(-30.0000 + 26.8328i) q^{69} -125.220i q^{71} -74.0000 q^{73} +(-10.0000 - 11.1803i) q^{75} +26.8328i q^{77} -138.000 q^{79} +(-79.0000 - 17.8885i) q^{81} -93.9149i q^{83} -10.0000 q^{85} +(-70.0000 + 62.6099i) q^{87} -107.331i q^{89} +96.0000 q^{91} +(36.0000 + 40.2492i) q^{93} -4.47214i q^{95} -166.000 q^{97} +(-40.0000 - 4.47214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{3} + 12 q^{7} - 2 q^{9}+O(q^{10}) \) 2 * q + 4 * q^3 + 12 * q^7 - 2 * q^9	\( 2 q + 4 q^{3} + 12 q^{7} - 2 q^{9} + 32 q^{13} + 10 q^{15} + 4 q^{19} + 24 q^{21} - 10 q^{25} - 44 q^{27} + 36 q^{31} - 20 q^{33} - 32 q^{37} + 64 q^{39} - 32 q^{43} + 40 q^{45} - 26 q^{49} + 20 q^{51} + 20 q^{55} + 8 q^{57} + 164 q^{61} - 12 q^{63} - 48 q^{67} - 60 q^{69} - 148 q^{73} - 20 q^{75} - 276 q^{79} - 158 q^{81} - 20 q^{85} - 140 q^{87} + 192 q^{91} + 72 q^{93} - 332 q^{97} - 80 q^{99}+O(q^{100}) \) 2 * q + 4 * q^3 + 12 * q^7 - 2 * q^9 + 32 * q^13 + 10 * q^15 + 4 * q^19 + 24 * q^21 - 10 * q^25 - 44 * q^27 + 36 * q^31 - 20 * q^33 - 32 * q^37 + 64 * q^39 - 32 * q^43 + 40 * q^45 - 26 * q^49 + 20 * q^51 + 20 * q^55 + 8 * q^57 + 164 * q^61 - 12 * q^63 - 48 * q^67 - 60 * q^69 - 148 * q^73 - 20 * q^75 - 276 * q^79 - 158 * q^81 - 20 * q^85 - 140 * q^87 + 192 * q^91 + 72 * q^93 - 332 * q^97 - 80 * q^99

Introduction

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