LMFDB - Embedded newform 1344.3.d.f.449.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,3,Mod(449,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, 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("1344.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1344.d (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:	$36.6213475300$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.65856.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 14x^{2} + 21 $ x^4 + 14*x^2 + 21
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			449.3
Root			$1.30710i$ of defining polynomial
Character	$\chi$	$=$	1344.449
Dual form			1344.3.d.f.449.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.82288 - 2.38267i) q^{3} +7.37953i q^{5} -2.64575 q^{7} +(-2.35425 - 8.68663i) q^{9} +O(q^{10})$	\(q+(1.82288 - 2.38267i) q^{3} +7.37953i q^{5} -2.64575 q^{7} +(-2.35425 - 8.68663i) q^{9} -2.61419i q^{11} +6.35425 q^{13} +(17.5830 + 13.4520i) q^{15} +12.1449i q^{17} +10.2288 q^{19} +(-4.82288 + 6.30396i) q^{21} -4.30231i q^{23} -29.4575 q^{25} +(-24.9889 - 10.2252i) q^{27} +17.3733i q^{29} +39.2915 q^{31} +(-6.22876 - 4.76534i) q^{33} -19.5244i q^{35} -41.0405 q^{37} +(11.5830 - 15.1401i) q^{39} +30.2802i q^{41} +55.8745 q^{43} +(64.1033 - 17.3733i) q^{45} +39.9749i q^{47} +7.00000 q^{49} +(28.9373 + 22.1386i) q^{51} +105.002i q^{53} +19.2915 q^{55} +(18.6458 - 24.3718i) q^{57} +41.3640i q^{59} +20.4797 q^{61} +(6.22876 + 22.9827i) q^{63} +46.8914i q^{65} +27.1660 q^{67} +(-10.2510 - 7.84257i) q^{69} +67.8049i q^{71} +60.7895 q^{73} +(-53.6974 + 70.1876i) q^{75} +6.91650i q^{77} -63.2470 q^{79} +(-69.9150 + 40.9010i) q^{81} +89.9435i q^{83} -89.6235 q^{85} +(41.3948 + 31.6693i) q^{87} -63.1745i q^{89} -16.8118 q^{91} +(71.6235 - 93.6188i) q^{93} +75.4835i q^{95} +19.1660 q^{97} +(-22.7085 + 6.15445i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 20 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 20 * q^9	$ 4 q + 2 q^{3} - 20 q^{9} + 36 q^{13} + 28 q^{15} - 12 q^{19} - 14 q^{21} - 12 q^{25} - 10 q^{27} + 136 q^{31} + 28 q^{33} - 16 q^{37} + 4 q^{39} + 160 q^{43} + 140 q^{45} + 28 q^{49} + 84 q^{51} + 56 q^{55} + 64 q^{57} + 156 q^{61} - 28 q^{63} + 24 q^{67} - 168 q^{69} - 32 q^{73} - 146 q^{75} + 128 q^{79} - 68 q^{81} - 168 q^{85} + 28 q^{87} + 28 q^{91} + 96 q^{93} - 8 q^{97} - 112 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 20 * q^9 + 36 * q^13 + 28 * q^15 - 12 * q^19 - 14 * q^21 - 12 * q^25 - 10 * q^27 + 136 * q^31 + 28 * q^33 - 16 * q^37 + 4 * q^39 + 160 * q^43 + 140 * q^45 + 28 * q^49 + 84 * q^51 + 56 * q^55 + 64 * q^57 + 156 * q^61 - 28 * q^63 + 24 * q^67 - 168 * q^69 - 32 * q^73 - 146 * q^75 + 128 * q^79 - 68 * q^81 - 168 * q^85 + 28 * q^87 + 28 * q^91 + 96 * q^93 - 8 * q^97 - 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$1$	$-1$	$1$	$1$

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
$3$	1.82288	−	2.38267i	0.607625	−	0.794224i
$3$	1.82288	−	2.38267i	0.607625	−	0.794224i
$4$		0			0
$5$			7.37953i			1.47591i	0.674852	+	0.737953i	$0.264208\pi$
$5$			7.37953i			1.47591i	−0.674852	+	0.737953i	$0.735792\pi$
$6$		0			0
$7$	−2.64575			−0.377964
$7$	−2.64575			−0.377964
$8$		0			0
$9$	−2.35425	−	8.68663i	−0.261583	−	0.965181i
$10$		0			0
$11$		−	2.61419i		−	0.237654i	−0.992915	−	0.118827i	$-0.962087\pi$
$11$		−	2.61419i		−	0.237654i	0.992915	−	0.118827i	$-0.0379133\pi$
$12$		0			0
$13$	6.35425			0.488788			0.244394	−	0.969676i	$-0.421411\pi$
$13$	6.35425			0.488788			0.244394	+	0.969676i	$0.421411\pi$
$14$		0			0
$15$	17.5830	+	13.4520i	1.17220	+	0.896798i
$16$		0			0
$17$			12.1449i			0.714405i	0.934027	+	0.357202i	$0.116269\pi$
$17$			12.1449i			0.714405i	−0.934027	+	0.357202i	$0.883731\pi$
$18$		0			0
$19$	10.2288			0.538356			0.269178	−	0.963090i	$-0.413248\pi$
$19$	10.2288			0.538356			0.269178	+	0.963090i	$0.413248\pi$
$20$		0			0
$21$	−4.82288	+	6.30396i	−0.229661	+	0.300188i
$22$		0			0
$23$		−	4.30231i		−	0.187057i	−0.995617	−	0.0935284i	$-0.970185\pi$
$23$		−	4.30231i		−	0.187057i	0.995617	−	0.0935284i	$-0.0298146\pi$
$24$		0			0
$25$	−29.4575			−1.17830
$26$		0			0
$27$	−24.9889	−	10.2252i	−0.925514	−	0.378713i
$28$		0			0
$29$			17.3733i			0.599078i	0.954084	+	0.299539i	$0.0968328\pi$
$29$			17.3733i			0.599078i	−0.954084	+	0.299539i	$0.903167\pi$
$30$		0			0
$31$	39.2915			1.26747			0.633734	−	0.773551i	$-0.281521\pi$
$31$	39.2915			1.26747			0.633734	+	0.773551i	$0.281521\pi$
$32$		0			0
$33$	−6.22876	−	4.76534i	−0.188750	−	0.144404i
$34$		0			0
$35$		−	19.5244i		−	0.557840i
$36$		0			0
$37$	−41.0405			−1.10920			−0.554602	−	0.832116i	$-0.687129\pi$
$37$	−41.0405			−1.10920			−0.554602	+	0.832116i	$0.687129\pi$
$38$		0			0
$39$	11.5830	−	15.1401i	0.297000	−	0.388207i
$40$		0			0
$41$			30.2802i			0.738541i	0.929322	+	0.369270i	$0.120392\pi$
$41$			30.2802i			0.738541i	−0.929322	+	0.369270i	$0.879608\pi$
$42$		0			0
$43$	55.8745			1.29941			0.649704	−	0.760188i	$-0.274893\pi$
$43$	55.8745			1.29941			0.649704	+	0.760188i	$0.274893\pi$
$44$		0			0
$45$	64.1033	−	17.3733i	1.42452	−	0.386072i
$46$		0			0
$47$			39.9749i			0.850530i	0.905069	+	0.425265i	$0.139819\pi$
$47$			39.9749i			0.850530i	−0.905069	+	0.425265i	$0.860181\pi$
$48$		0			0
$49$	7.00000			0.142857
$50$		0			0
$51$	28.9373	+	22.1386i	0.567397	+	0.434090i
$52$		0			0
$53$			105.002i			1.98116i	0.136928	+	0.990581i	$0.456277\pi$
$53$			105.002i			1.98116i	−0.136928	+	0.990581i	$0.543723\pi$
$54$		0			0
$55$	19.2915			0.350755
$56$		0			0
$57$	18.6458	−	24.3718i	0.327118	−	0.427575i
$58$		0			0
$59$			41.3640i			0.701085i	0.936547	+	0.350542i	$0.114003\pi$
$59$			41.3640i			0.701085i	−0.936547	+	0.350542i	$0.885997\pi$
$60$		0			0
$61$	20.4797			0.335733			0.167867	−	0.985810i	$-0.446312\pi$
$61$	20.4797			0.335733			0.167867	+	0.985810i	$0.446312\pi$
$62$		0			0
$63$	6.22876	+	22.9827i	0.0988692	+	0.364804i
$64$		0			0
$65$			46.8914i			0.721406i
$66$		0			0
$67$	27.1660			0.405463			0.202731	−	0.979234i	$-0.435018\pi$
$67$	27.1660			0.405463			0.202731	+	0.979234i	$0.435018\pi$
$68$		0			0
$69$	−10.2510	−	7.84257i	−0.148565	−	0.113660i
$70$		0			0
$71$			67.8049i			0.954999i	0.878632	+	0.477499i	$0.158457\pi$
$71$			67.8049i			0.954999i	−0.878632	+	0.477499i	$0.841543\pi$
$72$		0			0
$73$	60.7895			0.832733			0.416367	−	0.909197i	$-0.363303\pi$
$73$	60.7895			0.832733			0.416367	+	0.909197i	$0.363303\pi$
$74$		0			0
$75$	−53.6974	+	70.1876i	−0.715965	+	0.935834i
$76$		0			0
$77$			6.91650i			0.0898246i
$78$		0			0
$79$	−63.2470			−0.800596			−0.400298	−	0.916385i	$-0.631093\pi$
$79$	−63.2470			−0.800596			−0.400298	+	0.916385i	$0.631093\pi$
$80$		0			0
$81$	−69.9150	+	40.9010i	−0.863148	+	0.504950i
$82$		0			0
$83$			89.9435i			1.08366i	0.840489	+	0.541828i	$0.182268\pi$
$83$			89.9435i			1.08366i	−0.840489	+	0.541828i	$0.817732\pi$
$84$		0			0
$85$	−89.6235			−1.05439
$86$		0			0
$87$	41.3948	+	31.6693i	0.475802	+	0.364015i
$88$		0			0
$89$		−	63.1745i		−	0.709826i	−0.934899	−	0.354913i	$-0.884510\pi$
$89$		−	63.1745i		−	0.709826i	0.934899	−	0.354913i	$-0.115490\pi$
$90$		0			0
$91$	−16.8118			−0.184745
$92$		0			0
$93$	71.6235	−	93.6188i	0.770145	−	1.00665i
$94$		0			0
$95$			75.4835i			0.794563i
$96$		0			0
$97$	19.1660			0.197588			0.0987939	−	0.995108i	$-0.468502\pi$
$97$	19.1660			0.197588			0.0987939	+	0.995108i	$0.468502\pi$
$98$		0			0
$99$	−22.7085	+	6.15445i	−0.229379	+	0.0621662i
$100$		0			0
$101$		−	98.7122i		−	0.977348i	−0.872466	−	0.488674i	$-0.837481\pi$
$101$		−	98.7122i		−	0.977348i	0.872466	−	0.488674i	$-0.162519\pi$
$102$		0			0
$103$	−56.2510			−0.546126			−0.273063	−	0.961996i	$-0.588037\pi$
$103$	−56.2510			−0.546126			−0.273063	+	0.961996i	$0.588037\pi$
$104$		0			0
$105$	−46.5203	−	35.5906i	−0.443050	−	0.338958i
$106$		0			0
$107$			123.137i			1.15081i	0.817868	+	0.575406i	$0.195156\pi$
$107$			123.137i			1.15081i	−0.817868	+	0.575406i	$0.804844\pi$
$108$		0			0
$109$	−164.539			−1.50953			−0.754764	−	0.655996i	$-0.772249\pi$
$109$	−164.539			−1.50953			−0.754764	+	0.655996i	$0.772249\pi$
$110$		0			0
$111$	−74.8118	+	97.7861i	−0.673980	+	0.880956i
$112$		0			0
$113$			144.050i			1.27478i	0.770540	+	0.637391i	$0.219986\pi$
$113$			144.050i			1.27478i	−0.770540	+	0.637391i	$0.780014\pi$
$114$		0			0
$115$	31.7490			0.276078
$116$		0			0
$117$	−14.9595	−	55.1970i	−0.127859	−	0.471769i
$118$		0			0
$119$		−	32.1323i		−	0.270020i
$120$		0			0
$121$	114.166			0.943521
$122$		0			0
$123$	72.1477	+	55.1970i	0.586567	+	0.448756i
$124$		0			0
$125$		−	32.8944i		−	0.263155i
$126$		0			0
$127$	−36.5830			−0.288055			−0.144028	−	0.989574i	$-0.546005\pi$
$127$	−36.5830			−0.288055			−0.144028	+	0.989574i	$0.546005\pi$
$128$		0			0
$129$	101.852	−	133.131i	0.789553	−	1.03202i
$130$		0			0
$131$			33.6855i			0.257141i	0.991700	+	0.128570i	$0.0410389\pi$
$131$			33.6855i			0.257141i	−0.991700	+	0.128570i	$0.958961\pi$
$132$		0			0
$133$	−27.0627			−0.203479
$134$		0			0
$135$	75.4575	−	184.406i	0.558945	−	1.36597i
$136$		0			0
$137$		−	39.9749i		−	0.291788i	−0.989300	−	0.145894i	$-0.953394\pi$
$137$		−	39.9749i		−	0.291788i	0.989300	−	0.145894i	$-0.0466058\pi$
$138$		0			0
$139$	194.642			1.40030			0.700150	−	0.713995i	$-0.253116\pi$
$139$	194.642			1.40030			0.700150	+	0.713995i	$0.253116\pi$
$140$		0			0
$141$	95.2470	+	72.8693i	0.675511	+	0.516803i
$142$		0			0
$143$		−	16.6112i		−	0.116162i
$144$		0			0
$145$	−128.207			−0.884183
$146$		0			0
$147$	12.7601	−	16.6787i	0.0868036	−	0.113461i
$148$		0			0
$149$		−	203.685i		−	1.36701i	−0.729945	−	0.683506i	$-0.760454\pi$
$149$		−	203.685i		−	1.36701i	0.729945	−	0.683506i	$-0.239546\pi$
$150$		0			0
$151$	165.749			1.09768			0.548838	−	0.835929i	$-0.315070\pi$
$151$	165.749			1.09768			0.548838	+	0.835929i	$0.315070\pi$
$152$		0			0
$153$	105.498	−	28.5921i	0.689530	−	0.186876i
$154$		0			0
$155$			289.953i			1.87066i
$156$		0			0
$157$	302.723			1.92817			0.964086	−	0.265592i	$-0.0855674\pi$
$157$	302.723			1.92817			0.964086	+	0.265592i	$0.0855674\pi$
$158$		0			0
$159$	250.184	+	191.405i	1.57349	+	1.20380i
$160$		0			0
$161$			11.3828i			0.0707008i
$162$		0			0
$163$	145.041			0.889819			0.444910	−	0.895576i	$-0.353236\pi$
$163$	145.041			0.889819			0.444910	+	0.895576i	$0.353236\pi$
$164$		0			0
$165$	35.1660	−	45.9653i	0.213127	−	0.278578i
$166$		0			0
$167$		−	19.6594i		−	0.117721i	−0.998266	−	0.0588604i	$-0.981253\pi$
$167$		−	19.6594i		−	0.117721i	0.998266	−	0.0588604i	$-0.0187467\pi$
$168$		0			0
$169$	−128.624			−0.761086
$170$		0			0
$171$	−24.0810	−	88.8534i	−0.140825	−	0.519611i
$172$		0			0
$173$			19.6884i			0.113806i	0.998380	+	0.0569030i	$0.0181226\pi$
$173$			19.6884i			0.113806i	−0.998380	+	0.0569030i	$0.981877\pi$
$174$		0			0
$175$	77.9373			0.445356
$176$		0			0
$177$	98.5568	+	75.4014i	0.556818	+	0.425997i
$178$		0			0
$179$		−	341.745i		−	1.90919i	−0.297910	−	0.954594i	$-0.596289\pi$
$179$		−	341.745i		−	1.90919i	0.297910	−	0.954594i	$-0.403711\pi$
$180$		0			0
$181$	−215.889			−1.19276			−0.596378	−	0.802704i	$-0.703394\pi$
$181$	−215.889			−1.19276			−0.596378	+	0.802704i	$0.703394\pi$
$182$		0			0
$183$	37.3320	−	48.7965i	0.204000	−	0.266648i
$184$		0			0
$185$		−	302.860i		−	1.63708i
$186$		0			0
$187$	31.7490			0.169781
$188$		0			0
$189$	66.1144	+	27.0534i	0.349812	+	0.143140i
$190$		0			0
$191$		−	44.7112i		−	0.234090i	−0.993127	−	0.117045i	$-0.962658\pi$
$191$		−	44.7112i		−	0.234090i	0.993127	−	0.117045i	$-0.0373422\pi$
$192$		0			0
$193$	−145.122			−0.751925			−0.375963	−	0.926635i	$-0.622688\pi$
$193$	−145.122			−0.751925			−0.375963	+	0.926635i	$0.622688\pi$
$194$		0			0
$195$	111.727	+	85.4772i	0.572958	+	0.438344i
$196$		0			0
$197$			87.4643i			0.443981i	0.975049	+	0.221991i	$0.0712554\pi$
$197$			87.4643i			0.443981i	−0.975049	+	0.221991i	$0.928745\pi$
$198$		0			0
$199$	65.4170			0.328729			0.164364	−	0.986400i	$-0.447443\pi$
$199$	65.4170			0.328729			0.164364	+	0.986400i	$0.447443\pi$
$200$		0			0
$201$	49.5203	−	64.7277i	0.246369	−	0.322028i
$202$		0			0
$203$		−	45.9653i		−	0.226430i
$204$		0			0
$205$	−223.454			−1.09002
$206$		0			0
$207$	−37.3725	+	10.1287i	−0.180544	+	0.0489309i
$208$		0			0
$209$		−	26.7399i		−	0.127942i
$210$		0			0
$211$	−40.5830			−0.192337			−0.0961683	−	0.995365i	$-0.530659\pi$
$211$	−40.5830			−0.192337			−0.0961683	+	0.995365i	$0.530659\pi$
$212$		0			0
$213$	161.557	+	123.600i	0.758483	+	0.580281i
$214$		0			0
$215$			412.328i			1.91780i
$216$		0			0
$217$	−103.956			−0.479058
$218$		0			0
$219$	110.812	−	144.842i	0.505990	−	0.661377i
$220$		0			0
$221$			77.1716i			0.349193i
$222$		0			0
$223$	100.959			0.452733			0.226367	−	0.974042i	$-0.427315\pi$
$223$	100.959			0.452733			0.226367	+	0.974042i	$0.427315\pi$
$224$		0			0
$225$	69.3503	+	255.886i	0.308224	+	1.13727i
$226$		0			0
$227$		−	391.279i		−	1.72370i	−0.507166	−	0.861849i	$-0.669307\pi$
$227$		−	391.279i		−	1.72370i	0.507166	−	0.861849i	$-0.330693\pi$
$228$		0			0
$229$	6.81176			0.0297457			0.0148728	−	0.999889i	$-0.495266\pi$
$229$	6.81176			0.0297457			0.0148728	+	0.999889i	$0.495266\pi$
$230$		0			0
$231$	16.4797	+	12.6079i	0.0713409	+	0.0545797i
$232$		0			0
$233$		−	116.877i		−	0.501616i	−0.968037	−	0.250808i	$-0.919304\pi$
$233$		−	116.877i		−	0.501616i	0.968037	−	0.250808i	$-0.0806963\pi$
$234$		0			0
$235$	−294.996			−1.25530
$236$		0			0
$237$	−115.292	+	150.697i	−0.486462	+	0.635852i
$238$		0			0
$239$			59.9623i			0.250888i	0.992101	+	0.125444i	$0.0400356\pi$
$239$			59.9623i			0.250888i	−0.992101	+	0.125444i	$0.959964\pi$
$240$		0			0
$241$	134.753			0.559141			0.279570	−	0.960125i	$-0.409808\pi$
$241$	134.753			0.559141			0.279570	+	0.960125i	$0.409808\pi$
$242$		0			0
$243$	−29.9928	+	241.142i	−0.123427	+	0.992354i
$244$		0			0
$245$			51.6567i			0.210844i
$246$		0			0
$247$	64.9961			0.263142
$248$		0			0
$249$	214.306	+	163.956i	0.860666	+	0.658457i
$250$		0			0
$251$			268.248i			1.06872i	0.845257	+	0.534359i	$0.179447\pi$
$251$			268.248i			1.06872i	−0.845257	+	0.534359i	$0.820553\pi$
$252$		0			0
$253$	−11.2470			−0.0444547
$254$		0			0
$255$	−163.373	+	213.543i	−0.640677	+	0.837425i
$256$		0			0
$257$		−	234.129i		−	0.911007i	−0.890234	−	0.455504i	$-0.849459\pi$
$257$		−	234.129i		−	0.911007i	0.890234	−	0.455504i	$-0.150541\pi$
$258$		0			0
$259$	108.583			0.419239
$260$		0			0
$261$	150.915	−	40.9010i	0.578218	−	0.156709i
$262$		0			0
$263$		−	250.142i		−	0.951111i	−0.879686	−	0.475555i	$-0.842247\pi$
$263$		−	250.142i		−	0.951111i	0.879686	−	0.475555i	$-0.157753\pi$
$264$		0			0
$265$	−774.863			−2.92401
$266$		0			0
$267$	−150.524	−	115.159i	−0.563761	−	0.431308i
$268$		0			0
$269$			340.684i			1.26648i	0.773955	+	0.633241i	$0.218276\pi$
$269$			340.684i			1.26648i	−0.773955	+	0.633241i	$0.781724\pi$
$270$		0			0
$271$	−21.2994			−0.0785955			−0.0392977	−	0.999228i	$-0.512512\pi$
$271$	−21.2994			−0.0785955			−0.0392977	+	0.999228i	$0.512512\pi$
$272$		0			0
$273$	−30.6458	+	40.0569i	−0.112255	+	0.146729i
$274$		0			0
$275$			77.0075i			0.280027i
$276$		0			0
$277$	226.915			0.819188			0.409594	−	0.912268i	$-0.365670\pi$
$277$	226.915			0.819188			0.409594	+	0.912268i	$0.365670\pi$
$278$		0			0
$279$	−92.5020	−	341.311i	−0.331548	−	1.22334i
$280$		0			0
$281$			235.489i			0.838039i	0.907977	+	0.419019i	$0.137626\pi$
$281$			235.489i			0.838039i	−0.907977	+	0.419019i	$0.862374\pi$
$282$		0			0
$283$	−368.634			−1.30259			−0.651297	−	0.758823i	$-0.725775\pi$
$283$	−368.634			−1.30259			−0.651297	+	0.758823i	$0.725775\pi$
$284$		0			0
$285$	179.852	+	137.597i	0.631061	+	0.482796i
$286$		0			0
$287$		−	80.1138i		−	0.279142i
$288$		0			0
$289$	141.502			0.489626
$290$		0			0
$291$	34.9373	−	45.6663i	0.120059	−	0.156929i
$292$		0			0
$293$		−	531.625i		−	1.81442i	−0.420677	−	0.907211i	$-0.638207\pi$
$293$		−	531.625i		−	1.81442i	0.420677	−	0.907211i	$-0.361793\pi$
$294$		0			0
$295$	−305.247			−1.03474
$296$		0			0
$297$	−26.7307	+	65.3257i	−0.0900024	+	0.219952i
$298$		0			0
$299$		−	27.3379i		−	0.0914312i
$300$		0			0
$301$	−147.830			−0.491130
$302$		0			0
$303$	−235.199	−	179.940i	−0.776233	−	0.593861i
$304$		0			0
$305$			151.131i			0.495511i
$306$		0			0
$307$	−567.763			−1.84939			−0.924696	−	0.380706i	$-0.875681\pi$
$307$	−567.763			−1.84939			−0.924696	+	0.380706i	$0.875681\pi$
$308$		0			0
$309$	−102.539	+	134.028i	−0.331840	+	0.433746i
$310$		0			0
$311$		−	42.7531i		−	0.137470i	−0.997635	−	0.0687349i	$-0.978104\pi$
$311$		−	42.7531i		−	0.137470i	0.997635	−	0.0687349i	$-0.0218963\pi$
$312$		0			0
$313$	−158.118			−0.505168			−0.252584	−	0.967575i	$-0.581280\pi$
$313$	−158.118			−0.505168			−0.252584	+	0.967575i	$0.581280\pi$
$314$		0			0
$315$	−169.601	+	45.9653i	−0.538417	+	0.145922i
$316$		0			0
$317$		−	140.944i		−	0.444619i	−0.974976	−	0.222309i	$-0.928641\pi$
$317$		−	140.944i		−	0.444619i	0.974976	−	0.222309i	$-0.0713595\pi$
$318$		0			0
$319$	45.4170			0.142373
$320$		0			0
$321$	293.395	+	224.463i	0.914002	+	0.699262i
$322$		0			0
$323$			124.227i			0.384604i
$324$		0			0
$325$	−187.180			−0.575940
$326$		0			0
$327$	−299.933	+	392.041i	−0.917227	+	1.19890i
$328$		0			0
$329$		−	105.764i		−	0.321470i
$330$		0			0
$331$	258.369			0.780570			0.390285	−	0.920694i	$-0.372377\pi$
$331$	258.369			0.780570			0.390285	+	0.920694i	$0.372377\pi$
$332$		0			0
$333$	96.6196	+	356.504i	0.290149	+	1.07058i
$334$		0			0
$335$			200.472i			0.598425i
$336$		0			0
$337$	328.959			0.976141			0.488070	−	0.872804i	$-0.337701\pi$
$337$	328.959			0.976141			0.488070	+	0.872804i	$0.337701\pi$
$338$		0			0
$339$	343.225	+	262.586i	1.01246	+	0.774590i
$340$		0			0
$341$		−	102.715i		−	0.301218i
$342$		0			0
$343$	−18.5203			−0.0539949
$344$		0			0
$345$	57.8745	−	75.6475i	0.167752	−	0.219268i
$346$		0			0
$347$			128.635i			0.370707i	0.982672	+	0.185353i	$0.0593430\pi$
$347$			128.635i			0.370707i	−0.982672	+	0.185353i	$0.940657\pi$
$348$		0			0
$349$	73.4837			0.210555			0.105277	−	0.994443i	$-0.466427\pi$
$349$	73.4837			0.210555			0.105277	+	0.994443i	$0.466427\pi$
$350$		0			0
$351$	−158.786	−	64.9737i	−0.452381	−	0.185110i
$352$		0			0
$353$			239.685i			0.678995i	0.940607	+	0.339498i	$0.110257\pi$
$353$			239.685i			0.678995i	−0.940607	+	0.339498i	$0.889743\pi$
$354$		0			0
$355$	−500.369			−1.40949
$356$		0			0
$357$	−76.5608	−	58.5732i	−0.214456	−	0.164071i
$358$		0			0
$359$		−	180.215i		−	0.501992i	−0.967988	−	0.250996i	$-0.919242\pi$
$359$		−	180.215i		−	0.501992i	0.967988	−	0.250996i	$-0.0807581\pi$
$360$		0			0
$361$	−256.373			−0.710173
$362$		0			0
$363$	208.110	−	272.020i	0.573307	−	0.749367i
$364$		0			0
$365$			448.598i			1.22904i
$366$		0			0
$367$	229.786			0.626119			0.313059	−	0.949734i	$-0.398646\pi$
$367$	229.786			0.626119			0.313059	+	0.949734i	$0.398646\pi$
$368$		0			0
$369$	263.033	−	71.2871i	0.712826	−	0.193190i
$370$		0			0
$371$		−	277.808i		−	0.748809i
$372$		0			0
$373$	−441.749			−1.18431			−0.592157	−	0.805823i	$-0.701723\pi$
$373$	−441.749			−1.18431			−0.592157	+	0.805823i	$0.701723\pi$
$374$		0			0
$375$	−78.3765	−	59.9623i	−0.209004	−	0.159900i
$376$		0			0
$377$			110.394i			0.292822i
$378$		0			0
$379$	421.203			1.11135			0.555676	−	0.831399i	$-0.312459\pi$
$379$	421.203			1.11135			0.555676	+	0.831399i	$0.312459\pi$
$380$		0			0
$381$	−66.6863	+	87.1653i	−0.175030	+	0.228780i
$382$		0			0
$383$		−	595.591i		−	1.55507i	−0.628841	−	0.777534i	$-0.716470\pi$
$383$		−	595.591i		−	1.55507i	0.628841	−	0.777534i	$-0.283530\pi$
$384$		0			0
$385$	−51.0405			−0.132573
$386$		0			0
$387$	−131.542	−	485.361i	−0.339903	−	1.25416i
$388$		0			0
$389$		−	367.347i		−	0.944336i	−0.881509	−	0.472168i	$-0.843472\pi$
$389$		−	367.347i		−	0.944336i	0.881509	−	0.472168i	$-0.156528\pi$
$390$		0			0
$391$	52.2510			0.133634
$392$		0			0
$393$	80.2614	+	61.4044i	0.204227	+	0.156245i
$394$		0			0
$395$		−	466.734i		−	1.18160i
$396$		0			0
$397$	−408.346			−1.02858			−0.514290	−	0.857616i	$-0.671945\pi$
$397$	−408.346			−1.02858			−0.514290	+	0.857616i	$0.671945\pi$
$398$		0			0
$399$	−49.3320	+	64.4816i	−0.123639	+	0.161608i
$400$		0			0
$401$			238.817i			0.595555i	0.954635	+	0.297777i	$0.0962453\pi$
$401$			238.817i			0.595555i	−0.954635	+	0.297777i	$0.903755\pi$
$402$		0			0
$403$	249.668			0.619524
$404$		0			0
$405$	−301.830	−	515.940i	−0.745259	−	1.27393i
$406$		0			0
$407$			107.288i			0.263606i
$408$		0			0
$409$	−649.365			−1.58769			−0.793844	−	0.608121i	$-0.791924\pi$
$409$	−649.365			−1.58769			−0.793844	+	0.608121i	$0.791924\pi$
$410$		0			0
$411$	−95.2470	−	72.8693i	−0.231745	−	0.177297i
$412$		0			0
$413$		−	109.439i		−	0.264985i
$414$		0			0
$415$	−663.741			−1.59938
$416$		0			0
$417$	354.808	−	463.768i	0.850858	−	1.11215i
$418$		0			0
$419$		−	11.5178i		−	0.0274888i	−0.999906	−	0.0137444i	$-0.995625\pi$
$419$		−	11.5178i		−	0.0274888i	0.999906	−	0.0137444i	$-0.00437512\pi$
$420$		0			0
$421$	83.9921			0.199506			0.0997531	−	0.995012i	$-0.468195\pi$
$421$	83.9921			0.199506			0.0997531	+	0.995012i	$0.468195\pi$
$422$		0			0
$423$	347.247	−	94.1108i	0.820915	−	0.222484i
$424$		0			0
$425$		−	357.758i		−	0.841783i
$426$		0			0
$427$	−54.1843			−0.126895
$428$		0			0
$429$	−39.5791	−	30.2802i	−0.0922589	−	0.0705832i
$430$		0			0
$431$		−	694.004i		−	1.61022i	−0.593127	−	0.805109i	$-0.702107\pi$
$431$		−	694.004i		−	1.61022i	0.593127	−	0.805109i	$-0.297893\pi$
$432$		0			0
$433$	116.834			0.269824			0.134912	−	0.990858i	$-0.456925\pi$
$433$	116.834			0.269824			0.134912	+	0.990858i	$0.456925\pi$
$434$		0			0
$435$	−233.705	+	305.474i	−0.537252	+	0.702239i
$436$		0			0
$437$		−	44.0072i		−	0.100703i
$438$		0			0
$439$	−528.073			−1.20290			−0.601450	−	0.798910i	$-0.705410\pi$
$439$	−528.073			−1.20290			−0.601450	+	0.798910i	$0.705410\pi$
$440$		0			0
$441$	−16.4797	−	60.8064i	−0.0373690	−	0.137883i
$442$		0			0
$443$			272.252i			0.614564i	0.951619	+	0.307282i	$0.0994194\pi$
$443$			272.252i			0.614564i	−0.951619	+	0.307282i	$0.900581\pi$
$444$		0			0
$445$	466.199			1.04764
$446$		0			0
$447$	−485.314	−	371.292i	−1.08571	−	0.830631i
$448$		0			0
$449$			525.770i			1.17098i	0.810680	+	0.585490i	$0.199098\pi$
$449$			525.770i			1.17098i	−0.810680	+	0.585490i	$0.800902\pi$
$450$		0			0
$451$	79.1581			0.175517
$452$		0			0
$453$	302.140	−	394.925i	0.666975	−	0.871800i
$454$		0			0
$455$		−	124.063i		−	0.272666i
$456$		0			0
$457$	−513.786			−1.12426			−0.562129	−	0.827050i	$-0.690017\pi$
$457$	−513.786			−1.12426			−0.562129	+	0.827050i	$0.690017\pi$
$458$		0			0
$459$	124.184	−	303.487i	0.270554	−	0.661192i
$460$		0			0
$461$			687.879i			1.49214i	0.665865	+	0.746072i	$0.268063\pi$
$461$			687.879i			1.49214i	−0.665865	+	0.746072i	$0.731937\pi$
$462$		0			0
$463$	781.061			1.68696			0.843479	−	0.537162i	$-0.180504\pi$
$463$	781.061			1.68696			0.843479	+	0.537162i	$0.180504\pi$
$464$		0			0
$465$	690.863	+	528.548i	1.48573	+	1.13666i
$466$		0			0
$467$			163.353i			0.349792i	0.984587	+	0.174896i	$0.0559589\pi$
$467$			163.353i			0.349792i	−0.984587	+	0.174896i	$0.944041\pi$
$468$		0			0
$469$	−71.8745			−0.153251
$470$		0			0
$471$	551.826	−	721.289i	1.17161	−	1.53140i
$472$		0			0
$473$		−	146.067i		−	0.308809i
$474$		0			0
$475$	−301.314			−0.634345
$476$		0			0
$477$	912.110	−	247.200i	1.91218	−	0.518239i
$478$		0			0
$479$		−	700.159i		−	1.46171i	−0.682533	−	0.730855i	$-0.739122\pi$
$479$		−	700.159i		−	1.46171i	0.682533	−	0.730855i	$-0.260878\pi$
$480$		0			0
$481$	−260.782			−0.542166
$482$		0			0
$483$	27.1216	+	20.7495i	0.0561523	+	0.0429596i
$484$		0			0
$485$			141.436i			0.291621i
$486$		0			0
$487$	86.5909			0.177805			0.0889023	−	0.996040i	$-0.471664\pi$
$487$	86.5909			0.177805			0.0889023	+	0.996040i	$0.471664\pi$
$488$		0			0
$489$	264.391	−	345.584i	0.540677	−	0.706716i
$490$		0			0
$491$		−	741.494i		−	1.51017i	−0.655627	−	0.755085i	$-0.727596\pi$
$491$		−	741.494i		−	1.51017i	0.655627	−	0.755085i	$-0.272404\pi$
$492$		0			0
$493$	−210.996			−0.427984
$494$		0			0
$495$	−45.4170	−	167.578i	−0.0917515	−	0.338542i
$496$		0			0
$497$		−	179.395i		−	0.360956i
$498$		0			0
$499$	−379.814			−0.761151			−0.380575	−	0.924750i	$-0.624274\pi$
$499$	−379.814			−0.761151			−0.380575	+	0.924750i	$0.624274\pi$
$500$		0			0
$501$	−46.8419	−	35.8366i	−0.0934967	−	0.0715302i
$502$		0			0
$503$			465.808i			0.926059i	0.886343	+	0.463029i	$0.153238\pi$
$503$			465.808i			0.926059i	−0.886343	+	0.463029i	$0.846762\pi$
$504$		0			0
$505$	728.450			1.44247
$506$		0			0
$507$	−234.465	+	306.468i	−0.462455	+	0.604473i
$508$		0			0
$509$		−	750.503i		−	1.47447i	−0.675639	−	0.737233i	$-0.736132\pi$
$509$		−	750.503i		−	1.47447i	0.675639	−	0.737233i	$-0.263868\pi$
$510$		0			0
$511$	−160.834			−0.314744
$512$		0			0
$513$	−255.605	−	104.592i	−0.498256	−	0.203882i
$514$		0			0
$515$		−	415.106i		−	0.806031i
$516$		0			0
$517$	104.502			0.202131
$518$		0			0
$519$	46.9111	+	35.8896i	0.0903875	+	0.0691514i
$520$		0			0
$521$			726.946i			1.39529i	0.716443	+	0.697645i	$0.245769\pi$
$521$			726.946i			1.39529i	−0.716443	+	0.697645i	$0.754231\pi$
$522$		0			0
$523$	624.707			1.19447			0.597234	−	0.802067i	$-0.296266\pi$
$523$	624.707			1.19447			0.597234	+	0.802067i	$0.296266\pi$
$524$		0			0
$525$	142.070	−	185.699i	0.270609	−	0.353712i
$526$		0			0
$527$			477.190i			0.905485i
$528$		0			0
$529$	510.490			0.965010
$530$		0			0
$531$	359.314	−	97.3812i	0.676674	−	0.183392i
$532$		0			0
$533$			192.408i			0.360990i
$534$		0			0
$535$	−908.693			−1.69849
$536$		0			0
$537$	−814.265	−	622.958i	−1.51632	−	1.16007i
$538$		0			0
$539$		−	18.2993i		−	0.0339505i
$540$		0			0
$541$	291.757			0.539292			0.269646	−	0.962960i	$-0.413093\pi$
$541$	291.757			0.539292			0.269646	+	0.962960i	$0.413093\pi$
$542$		0			0
$543$	−393.539	+	514.392i	−0.724749	+	0.947315i
$544$		0			0
$545$		−	1214.22i		−	2.22792i
$546$		0			0
$547$	−204.952			−0.374683			−0.187342	−	0.982295i	$-0.559987\pi$
$547$	−204.952			−0.374683			−0.187342	+	0.982295i	$0.559987\pi$
$548$		0			0
$549$	−48.2144	−	177.900i	−0.0878222	−	0.324044i
$550$		0			0
$551$			177.707i			0.322517i
$552$		0			0
$553$	167.336			0.302597
$554$		0			0
$555$	−721.616	−	552.076i	−1.30021	−	0.994731i
$556$		0			0
$557$			503.883i			0.904637i	0.891857	+	0.452318i	$0.149403\pi$
$557$			503.883i			0.904637i	−0.891857	+	0.452318i	$0.850597\pi$
$558$		0			0
$559$	355.041			0.635135
$560$		0			0
$561$	57.8745	−	75.6475i	0.103163	−	0.134844i
$562$		0			0
$563$		−	108.735i		−	0.193135i	−0.995326	−	0.0965674i	$-0.969214\pi$
$563$		−	108.735i		−	0.193135i	0.995326	−	0.0965674i	$-0.0307863\pi$
$564$		0			0
$565$	−1063.02			−1.88146
$566$		0			0
$567$	184.978	−	108.214i	0.326239	−	0.190853i
$568$		0			0
$569$		−	434.871i		−	0.764273i	−0.924106	−	0.382136i	$-0.875188\pi$
$569$		−	434.871i		−	0.764273i	0.924106	−	0.382136i	$-0.124812\pi$
$570$		0			0
$571$	−119.122			−0.208619			−0.104310	−	0.994545i	$-0.533263\pi$
$571$	−119.122			−0.208619			−0.104310	+	0.994545i	$0.533263\pi$
$572$		0			0
$573$	−106.532	−	81.5029i	−0.185920	−	0.142239i
$574$		0			0
$575$			126.735i			0.220409i
$576$		0			0
$577$	−655.417			−1.13590			−0.567952	−	0.823061i	$-0.692264\pi$
$577$	−655.417			−1.13590			−0.567952	+	0.823061i	$0.692264\pi$
$578$		0			0
$579$	−264.539	+	345.777i	−0.456889	+	0.597197i
$580$		0			0
$581$		−	237.968i		−	0.409584i
$582$		0			0
$583$	274.494			0.470830
$584$		0			0
$585$	407.328	−	110.394i	0.696287	−	0.188708i
$586$		0			0
$587$		−	736.236i		−	1.25424i	−0.778925	−	0.627118i	$-0.784235\pi$
$587$		−	736.236i		−	1.25424i	0.778925	−	0.627118i	$-0.215765\pi$
$588$		0			0
$589$	401.903			0.682348
$590$		0			0
$591$	208.399	+	159.437i	0.352620	+	0.269774i
$592$		0			0
$593$			832.884i			1.40453i	0.711917	+	0.702263i	$0.247827\pi$
$593$			832.884i			1.40453i	−0.711917	+	0.702263i	$0.752173\pi$
$594$		0			0
$595$	237.122			0.398524
$596$		0			0
$597$	119.247	−	155.867i	0.199744	−	0.261084i
$598$		0			0
$599$			69.3290i			0.115741i	0.998324	+	0.0578706i	$0.0184311\pi$
$599$			69.3290i			0.115741i	−0.998324	+	0.0578706i	$0.981569\pi$
$600$		0			0
$601$	−161.720			−0.269085			−0.134543	−	0.990908i	$-0.542957\pi$
$601$	−161.720			−0.269085			−0.134543	+	0.990908i	$0.542957\pi$
$602$		0			0
$603$	−63.9555	−	235.981i	−0.106062	−	0.391345i
$604$		0			0
$605$			842.492i			1.39255i
$606$		0			0
$607$	929.608			1.53148			0.765740	−	0.643151i	$-0.222373\pi$
$607$	929.608			1.53148			0.765740	+	0.643151i	$0.222373\pi$
$608$		0			0
$609$	−109.520	−	83.7891i	−0.179836	−	0.137585i
$610$		0			0
$611$			254.010i			0.415729i
$612$		0			0
$613$	−297.940			−0.486036			−0.243018	−	0.970022i	$-0.578137\pi$
$613$	−297.940			−0.486036			−0.243018	+	0.970022i	$0.578137\pi$
$614$		0			0
$615$	−407.328	+	532.417i	−0.662322	+	0.865718i
$616$		0			0
$617$		−	975.575i		−	1.58116i	−0.612360	−	0.790579i	$-0.709780\pi$
$617$		−	975.575i		−	1.58116i	0.612360	−	0.790579i	$-0.290220\pi$
$618$		0			0
$619$	−357.034			−0.576792			−0.288396	−	0.957511i	$-0.593122\pi$
$619$	−357.034			−0.576792			−0.288396	+	0.957511i	$0.593122\pi$
$620$		0			0
$621$	−43.9921	+	107.510i	−0.0708408	+	0.173124i
$622$		0			0
$623$			167.144i			0.268289i
$624$		0			0
$625$	−493.693			−0.789908
$626$		0			0
$627$	−63.7124	−	48.7435i	−0.101615	−	0.0777409i
$628$		0			0
$629$		−	498.432i		−	0.792420i
$630$		0			0
$631$	−813.223			−1.28879			−0.644393	−	0.764695i	$-0.722890\pi$
$631$	−813.223			−1.28879			−0.644393	+	0.764695i	$0.722890\pi$
$632$		0			0
$633$	−73.9778	+	96.6960i	−0.116869	+	0.152758i
$634$		0			0
$635$		−	269.966i		−	0.425143i
$636$		0			0
$637$	44.4797			0.0698269
$638$		0			0
$639$	588.996	−	159.630i	0.921747	−	0.249812i
$640$		0			0
$641$			646.727i			1.00893i	0.863431	+	0.504467i	$0.168311\pi$
$641$			646.727i			1.00893i	−0.863431	+	0.504467i	$0.831689\pi$
$642$		0			0
$643$	−144.561			−0.224822			−0.112411	−	0.993662i	$-0.535857\pi$
$643$	−144.561			−0.224822			−0.112411	+	0.993662i	$0.535857\pi$
$644$		0			0
$645$	982.442	+	751.622i	1.52317	+	1.16531i
$646$		0			0
$647$		−	716.654i		−	1.10766i	−0.832631	−	0.553828i	$-0.813166\pi$
$647$		−	716.654i		−	1.10766i	0.832631	−	0.553828i	$-0.186834\pi$
$648$		0			0
$649$	108.133			0.166615
$650$		0			0
$651$	−189.498	+	247.692i	−0.291088	+	0.380479i
$652$		0			0
$653$		−	378.999i		−	0.580397i	−0.956966	−	0.290199i	$-0.906279\pi$
$653$		−	378.999i		−	0.580397i	0.956966	−	0.290199i	$-0.0937214\pi$
$654$		0			0
$655$	−248.583			−0.379516
$656$		0			0
$657$	−143.114	−	528.056i	−0.217829	−	0.803738i
$658$		0			0
$659$			710.721i			1.07848i	0.842151	+	0.539242i	$0.181289\pi$
$659$			710.721i			1.07848i	−0.842151	+	0.539242i	$0.818711\pi$
$660$		0			0
$661$	−91.5045			−0.138433			−0.0692167	−	0.997602i	$-0.522050\pi$
$661$	−91.5045			−0.138433			−0.0692167	+	0.997602i	$0.522050\pi$
$662$		0			0
$663$	183.875	+	140.674i	0.277337	+	0.212178i
$664$		0			0
$665$		−	199.710i		−	0.300316i
$666$		0			0
$667$	74.7451			0.112062
$668$		0			0
$669$	184.037	−	240.553i	0.275092	−	0.359571i
$670$		0			0
$671$		−	53.5379i		−	0.0797883i
$672$		0			0
$673$	645.806			0.959594			0.479797	−	0.877380i	$-0.340710\pi$
$673$	645.806			0.959594			0.479797	+	0.877380i	$0.340710\pi$
$674$		0			0
$675$	736.110	+	301.210i	1.09053	+	0.446237i
$676$		0			0
$677$			335.571i			0.495674i	0.968802	+	0.247837i	$0.0797198\pi$
$677$			335.571i			0.495674i	−0.968802	+	0.247837i	$0.920280\pi$
$678$		0			0
$679$	−50.7085			−0.0746811
$680$		0			0
$681$	−932.290	−	713.254i	−1.36900	−	1.04736i
$682$		0			0
$683$			113.336i			0.165939i	0.996552	+	0.0829694i	$0.0264404\pi$
$683$			113.336i			0.165939i	−0.996552	+	0.0829694i	$0.973560\pi$
$684$		0			0
$685$	294.996			0.430651
$686$		0			0
$687$	12.4170	−	16.2302i	0.0180742	−	0.0236247i
$688$		0			0
$689$			667.206i			0.968369i
$690$		0			0
$691$	−565.667			−0.818620			−0.409310	−	0.912395i	$-0.634231\pi$
$691$	−565.667			−0.818620			−0.409310	+	0.912395i	$0.634231\pi$
$692$		0			0
$693$	60.0810	−	16.2832i	0.0866970	−	0.0234966i
$694$		0			0
$695$			1436.37i			2.06671i
$696$		0			0
$697$	−367.749			−0.527617
$698$		0			0
$699$	−278.478	−	213.051i	−0.398395	−	0.304794i
$700$		0			0
$701$			872.955i			1.24530i	0.782501	+	0.622650i	$0.213944\pi$
$701$			872.955i			1.24530i	−0.782501	+	0.622650i	$0.786056\pi$
$702$		0			0
$703$	−419.793			−0.597146
$704$		0			0
$705$	−537.741	+	702.879i	−0.762753	+	0.996991i
$706$		0			0
$707$			261.168i			0.369403i
$708$		0			0
$709$	−1092.04			−1.54025			−0.770125	−	0.637894i	$-0.779806\pi$
$709$	−1092.04			−1.54025			−0.770125	+	0.637894i	$0.779806\pi$
$710$		0			0
$711$	148.899	+	549.404i	0.209422	+	0.772720i
$712$		0			0
$713$		−	169.044i		−	0.237088i
$714$		0			0
$715$	122.583			0.171445
$716$		0			0
$717$	142.871	+	109.304i	0.199262	+	0.152446i
$718$		0			0
$719$		−	901.769i		−	1.25420i	−0.778939	−	0.627099i	$-0.784242\pi$
$719$		−	901.769i		−	1.25420i	0.778939	−	0.627099i	$-0.215758\pi$
$720$		0			0
$721$	148.826			0.206416
$722$		0			0
$723$	245.638	−	321.072i	0.339748	−	0.444083i
$724$		0			0
$725$		−	511.773i		−	0.705894i
$726$		0			0
$727$	297.506			0.409224			0.204612	−	0.978843i	$-0.434407\pi$
$727$	297.506			0.409224			0.204612	+	0.978843i	$0.434407\pi$
$728$		0			0
$729$	519.889	+	511.035i	0.713153	+	0.701008i
$730$		0			0
$731$			678.589i			0.928302i
$732$		0			0
$733$	−456.966			−0.623419			−0.311709	−	0.950177i	$-0.600902\pi$
$733$	−456.966			−0.623419			−0.311709	+	0.950177i	$0.600902\pi$
$734$		0			0
$735$	123.081	+	94.1638i	0.167457	+	0.128114i
$736$		0			0
$737$		−	71.0171i		−	0.0963597i
$738$		0			0
$739$	332.199			0.449525			0.224762	−	0.974414i	$-0.427839\pi$
$739$	332.199			0.449525			0.224762	+	0.974414i	$0.427839\pi$
$740$		0			0
$741$	118.480	−	154.864i	0.159892	−	0.208994i
$742$		0			0
$743$			64.5346i			0.0868568i	0.999057	+	0.0434284i	$0.0138280\pi$
$743$			64.5346i			0.0868568i	−0.999057	+	0.0434284i	$0.986172\pi$
$744$		0			0
$745$	1503.10			2.01758
$746$		0			0
$747$	781.306	−	211.749i	1.04592	−	0.283466i
$748$		0			0
$749$		−	325.790i		−	0.434966i
$750$		0			0
$751$	−611.668			−0.814471			−0.407236	−	0.913323i	$-0.633507\pi$
$751$	−611.668			−0.814471			−0.407236	+	0.913323i	$0.633507\pi$
$752$		0			0
$753$	639.148	+	488.983i	0.848802	+	0.649380i
$754$		0			0
$755$			1223.15i			1.62007i
$756$		0			0
$757$	207.357			0.273919			0.136960	−	0.990577i	$-0.456267\pi$
$757$	207.357			0.273919			0.136960	+	0.990577i	$0.456267\pi$
$758$		0			0
$759$	−20.5020	+	26.7980i	−0.0270118	+	0.0353070i
$760$		0			0
$761$		−	337.770i		−	0.443851i	−0.975064	−	0.221925i	$-0.928766\pi$
$761$		−	337.770i		−	0.443851i	0.975064	−	0.221925i	$-0.0712341\pi$
$762$		0			0
$763$	435.328			0.570548
$764$		0			0
$765$	210.996	+	778.526i	0.275812	+	1.01768i
$766$		0			0
$767$			262.837i			0.342682i
$768$		0			0
$769$	−1042.22			−1.35529			−0.677646	−	0.735388i	$-0.737000\pi$
$769$	−1042.22			−1.35529			−0.677646	+	0.735388i	$0.737000\pi$
$770$		0			0
$771$	−557.852	−	426.788i	−0.723544	−	0.553551i
$772$		0			0
$773$			291.448i			0.377035i	0.982070	+	0.188517i	$0.0603682\pi$
$773$			291.448i			0.377035i	−0.982070	+	0.188517i	$0.939632\pi$
$774$		0			0
$775$	−1157.43			−1.49346
$776$		0			0
$777$	197.933	−	258.718i	0.254740	−	0.332970i
$778$		0			0
$779$			309.729i			0.397598i
$780$		0			0
$781$	177.255			0.226959
$782$		0			0
$783$	177.646	−	434.138i	0.226878	−	0.554455i
$784$		0			0
$785$			2233.95i			2.84580i
$786$		0			0
$787$	−293.889			−0.373429			−0.186715	−	0.982414i	$-0.559784\pi$
$787$	−293.889			−0.373429			−0.186715	+	0.982414i	$0.559784\pi$
$788$		0			0
$789$	−596.006	−	455.978i	−0.755395	−	0.577919i
$790$		0			0
$791$		−	381.122i		−	0.481822i
$792$		0			0
$793$	130.133			0.164103
$794$		0			0
$795$	−1412.48	+	1846.24i	−1.77670	+	2.32232i
$796$		0			0
$797$		−	568.764i		−	0.713631i	−0.934175	−	0.356816i	$-0.883862\pi$
$797$		−	568.764i		−	0.713631i	0.934175	−	0.356816i	$-0.116138\pi$
$798$		0			0
$799$	−485.490			−0.607622
$800$		0			0
$801$	−548.774	+	148.729i	−0.685111	+	0.185679i
$802$		0			0
$803$		−	158.915i		−	0.197902i
$804$		0			0
$805$	−84.0000			−0.104348
$806$		0			0
$807$	811.737	+	621.024i	1.00587	+	0.769546i
$808$		0			0
$809$			183.697i			0.227067i	0.993534	+	0.113534i	$0.0362169\pi$
$809$			183.697i			0.227067i	−0.993534	+	0.113534i	$0.963783\pi$
$810$		0			0
$811$	544.663			0.671594			0.335797	−	0.941934i	$-0.390994\pi$
$811$	544.663			0.671594			0.335797	+	0.941934i	$0.390994\pi$
$812$		0			0
$813$	−38.8261	+	50.7494i	−0.0477566	+	0.0624224i
$814$		0			0
$815$			1070.33i			1.31329i
$816$		0			0
$817$	571.527			0.699543
$818$		0			0
$819$	39.5791	+	146.038i	0.0483261	+	0.178312i
$820$		0			0
$821$			1188.78i			1.44797i	0.689818	+	0.723983i	$0.257691\pi$
$821$			1188.78i			1.44797i	−0.689818	+	0.723983i	$0.742309\pi$
$822$		0			0
$823$	1265.15			1.53724			0.768621	−	0.639704i	$-0.220943\pi$
$823$	1265.15			1.53724			0.768621	+	0.639704i	$0.220943\pi$
$824$		0			0
$825$	183.484	+	140.375i	0.222404	+	0.170152i
$826$		0			0
$827$		−	790.941i		−	0.956398i	−0.878252	−	0.478199i	$-0.841290\pi$
$827$		−	790.941i		−	0.956398i	0.878252	−	0.478199i	$-0.158710\pi$
$828$		0			0
$829$	−99.1961			−0.119658			−0.0598288	−	0.998209i	$-0.519055\pi$
$829$	−99.1961			−0.119658			−0.0598288	+	0.998209i	$0.519055\pi$
$830$		0			0
$831$	413.638	−	540.664i	0.497759	−	0.650619i
$832$		0			0
$833$			85.0141i			0.102058i
$834$		0			0
$835$	145.077			0.173745
$836$		0			0
$837$	−981.851	−	401.765i	−1.17306	−	0.480006i
$838$		0			0
$839$		−	243.824i		−	0.290612i	−0.989387	−	0.145306i	$-0.953583\pi$
$839$		−	243.824i		−	0.290612i	0.989387	−	0.145306i	$-0.0464167\pi$
$840$		0			0
$841$	539.170			0.641106
$842$		0			0
$843$	561.093	+	429.267i	0.665591	+	0.509214i
$844$		0			0
$845$		−	949.182i		−	1.12329i
$846$		0			0
$847$	−302.055			−0.356617
$848$		0			0
$849$	−671.974	+	878.334i	−0.791489	+	1.03455i
$850$		0			0
$851$			176.569i			0.207484i
$852$		0			0
$853$	1122.06			1.31543			0.657713	−	0.753268i	$-0.271524\pi$
$853$	1122.06			1.31543			0.657713	+	0.753268i	$0.271524\pi$
$854$		0			0
$855$	655.697	−	177.707i	0.766897	−	0.207844i
$856$		0			0
$857$			871.489i			1.01691i	0.861090	+	0.508453i	$0.169783\pi$
$857$			871.489i			1.01691i	−0.861090	+	0.508453i	$0.830217\pi$
$858$		0			0
$859$	1674.92			1.94985			0.974925	−	0.222533i	$-0.0714324\pi$
$859$	1674.92			1.94985			0.974925	+	0.222533i	$0.0714324\pi$
$860$		0			0
$861$	−190.885	−	146.038i	−0.221701	−	0.169614i
$862$		0			0
$863$			1320.74i			1.53041i	0.643787	+	0.765205i	$0.277362\pi$
$863$			1320.74i			1.53041i	−0.643787	+	0.765205i	$0.722638\pi$
$864$		0			0
$865$	−145.292			−0.167967
$866$		0			0
$867$	257.940	−	337.153i	0.297509	−	0.388873i
$868$		0			0
$869$			165.340i			0.190264i
$870$		0			0
$871$	172.620			0.198186
$872$		0			0
$873$	−45.1216	−	166.488i	−0.0516856	−	0.190708i
$874$		0			0
$875$			87.0303i			0.0994632i
$876$		0			0
$877$	344.790			0.393147			0.196573	−	0.980489i	$-0.437019\pi$
$877$	344.790			0.393147			0.196573	+	0.980489i	$0.437019\pi$
$878$		0			0
$879$	−1266.69	−	969.087i	−1.44106	−	1.10249i
$880$		0			0
$881$		−	518.737i		−	0.588805i	−0.955682	−	0.294403i	$-0.904879\pi$
$881$		−	518.737i		−	0.588805i	0.955682	−	0.294403i	$-0.0951206\pi$
$882$		0			0
$883$	584.008			0.661391			0.330695	−	0.943738i	$-0.392717\pi$
$883$	584.008			0.661391			0.330695	+	0.943738i	$0.392717\pi$
$884$		0			0
$885$	−556.427	+	727.303i	−0.628732	+	0.821812i
$886$		0			0
$887$		−	263.213i		−	0.296745i	−0.988932	−	0.148373i	$-0.952597\pi$
$887$		−	263.213i		−	0.296745i	0.988932	−	0.148373i	$-0.0474035\pi$
$888$		0			0
$889$	96.7895			0.108875
$890$		0			0
$891$	106.923	+	182.771i	0.120003	+	0.205130i
$892$		0			0
$893$			408.893i			0.457887i
$894$		0			0
$895$	2521.92			2.81778
$896$		0			0
$897$	−65.1373	−	49.8336i	−0.0726168	−	0.0555559i
$898$		0			0
$899$			682.621i			0.759312i
$900$		0			0
$901$	−1275.23			−1.41535
$902$		0			0
$903$	−269.476	+	352.230i	−0.298423	+	0.390067i
$904$		0			0
$905$		−	1593.16i		−	1.76040i
$906$		0			0
$907$	1501.72			1.65570			0.827849	−	0.560951i	$-0.189565\pi$
$907$	1501.72			1.65570			0.827849	+	0.560951i	$0.189565\pi$
$908$		0			0
$909$	−857.476	+	232.393i	−0.943318	+	0.255658i
$910$		0			0
$911$		−	879.178i		−	0.965069i	−0.875877	−	0.482534i	$-0.839716\pi$
$911$		−	879.178i		−	0.965069i	0.875877	−	0.482534i	$-0.160284\pi$
$912$		0			0
$913$	235.129			0.257535
$914$		0			0
$915$	360.095	+	275.493i	0.393547	+	0.301085i
$916$		0			0
$917$		−	89.1234i		−	0.0971901i
$918$		0			0
$919$	76.9882			0.0837739			0.0418869	−	0.999122i	$-0.486663\pi$
$919$	76.9882			0.0837739			0.0418869	+	0.999122i	$0.486663\pi$
$920$		0			0
$921$	−1034.96	+	1352.79i	−1.12374	+	1.46883i
$922$		0			0
$923$			430.849i			0.466792i
$924$		0			0
$925$	1208.95			1.30697
$926$		0			0
$927$	132.429	+	488.631i	0.142857	+	0.527110i
$928$		0			0
$929$		−	1629.76i		−	1.75431i	−0.480204	−	0.877157i	$-0.659437\pi$
$929$		−	1629.76i		−	1.75431i	0.480204	−	0.877157i	$-0.340563\pi$
$930$		0			0
$931$	71.6013			0.0769079
$932$		0			0
$933$	−101.867	−	77.9336i	−0.109182	−	0.0835301i
$934$		0			0
$935$			234.293i			0.250581i
$936$		0			0
$937$	−497.720			−0.531185			−0.265592	−	0.964085i	$-0.585568\pi$
$937$	−497.720			−0.531185			−0.265592	+	0.964085i	$0.585568\pi$
$938$		0			0
$939$	−288.229	+	376.742i	−0.306953	+	0.401217i
$940$		0			0
$941$		−	238.894i		−	0.253873i	−0.991911	−	0.126936i	$-0.959486\pi$
$941$		−	238.894i		−	0.253873i	0.991911	−	0.126936i	$-0.0405144\pi$
$942$		0			0
$943$	130.275			0.138149
$944$		0			0
$945$	−199.642	+	487.893i	−0.211261	+	0.516289i
$946$		0			0
$947$		−	667.910i		−	0.705291i	−0.935757	−	0.352645i	$-0.885282\pi$
$947$		−	667.910i		−	0.705291i	0.935757	−	0.352645i	$-0.114718\pi$
$948$		0			0
$949$	386.272			0.407030
$950$		0			0
$951$	−335.824	−	256.924i	−0.353127	−	0.270162i
$952$		0			0
$953$			11.3247i			0.0118832i	0.999982	+	0.00594162i	$0.00189129\pi$
$953$			11.3247i			0.0118832i	−0.999982	+	0.00594162i	$0.998109\pi$
$954$		0			0
$955$	329.948			0.345495
$956$		0			0
$957$	82.7895	−	108.214i	0.0865094	−	0.113076i
$958$		0			0
$959$			105.764i			0.110285i
$960$		0			0
$961$	582.822			0.606475
$962$		0			0
$963$	1069.64	−	289.895i	1.11074	−	0.301033i
$964$		0			0
$965$		−	1070.93i		−	1.10977i
$966$		0			0
$967$	830.324			0.858660			0.429330	−	0.903148i	$-0.358750\pi$
$967$	830.324			0.858660			0.429330	+	0.903148i	$0.358750\pi$
$968$		0			0
$969$	295.992	+	226.450i	0.305461	+	0.233695i
$970$		0			0
$971$		−	1217.58i		−	1.25394i	−0.779044	−	0.626970i	$-0.784295\pi$
$971$		−	1217.58i		−	1.25394i	0.779044	−	0.626970i	$-0.215705\pi$
$972$		0			0
$973$	−514.974			−0.529264
$974$		0			0
$975$	−341.207	+	445.989i	−0.349955	+	0.457425i
$976$		0			0
$977$		−	424.579i		−	0.434574i	−0.976108	−	0.217287i	$-0.930279\pi$
$977$		−	424.579i		−	0.434574i	0.976108	−	0.217287i	$-0.0697207\pi$
$978$		0			0
$979$	−165.150			−0.168693
$980$		0			0
$981$	387.365	+	1429.29i	0.394867	+	1.45697i
$982$		0			0
$983$		−	76.7273i		−	0.0780542i	−0.999238	−	0.0390271i	$-0.987574\pi$
$983$		−	76.7273i		−	0.0780542i	0.999238	−	0.0390271i	$-0.0124259\pi$
$984$		0			0
$985$	−645.446			−0.655275
$986$		0			0
$987$	−252.000	−	192.794i	−0.255319	−	0.195333i
$988$		0			0
$989$		−	240.389i		−	0.243063i
$990$		0			0
$991$	181.271			0.182917			0.0914585	−	0.995809i	$-0.470847\pi$
$991$	181.271			0.182917			0.0914585	+	0.995809i	$0.470847\pi$
$992$		0			0
$993$	470.974	−	615.608i	0.474294	−	0.619947i
$994$		0			0
$995$			482.747i			0.485173i
$996$		0			0
$997$	1184.43			1.18800			0.593998	−	0.804466i	$-0.297549\pi$
$997$	1184.43			1.18800			0.593998	+	0.804466i	$0.297549\pi$
$998$		0			0
$999$	1025.56	+	419.649i	1.02658	+	0.420069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.3.d.f.449.3		4
3.2	odd	2	inner	1344.3.d.f.449.4		4
4.3	odd	2		1344.3.d.b.449.2		4
8.3	odd	2		336.3.d.c.113.3		4
8.5	even	2		21.3.b.a.8.3	yes	4
12.11	even	2		1344.3.d.b.449.1		4
24.5	odd	2		21.3.b.a.8.2	✓	4
24.11	even	2		336.3.d.c.113.4		4
40.13	odd	4		525.3.f.a.449.5		8
40.29	even	2		525.3.c.a.176.2		4
40.37	odd	4		525.3.f.a.449.4		8
56.5	odd	6		147.3.h.c.116.3		8
56.13	odd	2		147.3.b.f.50.3		4
56.37	even	6		147.3.h.e.116.3		8
56.45	odd	6		147.3.h.c.128.2		8
56.53	even	6		147.3.h.e.128.2		8
72.5	odd	6		567.3.r.c.512.3		8
72.13	even	6		567.3.r.c.512.2		8
72.29	odd	6		567.3.r.c.134.2		8
72.61	even	6		567.3.r.c.134.3		8
120.29	odd	2		525.3.c.a.176.3		4
120.53	even	4		525.3.f.a.449.3		8
120.77	even	4		525.3.f.a.449.6		8
168.5	even	6		147.3.h.c.116.2		8
168.53	odd	6		147.3.h.e.128.3		8
168.101	even	6		147.3.h.c.128.3		8
168.125	even	2		147.3.b.f.50.2		4
168.149	odd	6		147.3.h.e.116.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.b.a.8.2	✓	4	24.5	odd	2
21.3.b.a.8.3	yes	4	8.5	even	2
147.3.b.f.50.2		4	168.125	even	2
147.3.b.f.50.3		4	56.13	odd	2
147.3.h.c.116.2		8	168.5	even	6
147.3.h.c.116.3		8	56.5	odd	6
147.3.h.c.128.2		8	56.45	odd	6
147.3.h.c.128.3		8	168.101	even	6
147.3.h.e.116.2		8	168.149	odd	6
147.3.h.e.116.3		8	56.37	even	6
147.3.h.e.128.2		8	56.53	even	6
147.3.h.e.128.3		8	168.53	odd	6
336.3.d.c.113.3		4	8.3	odd	2
336.3.d.c.113.4		4	24.11	even	2
525.3.c.a.176.2		4	40.29	even	2
525.3.c.a.176.3		4	120.29	odd	2
525.3.f.a.449.3		8	120.53	even	4
525.3.f.a.449.4		8	40.37	odd	4
525.3.f.a.449.5		8	40.13	odd	4
525.3.f.a.449.6		8	120.77	even	4
567.3.r.c.134.2		8	72.29	odd	6
567.3.r.c.134.3		8	72.61	even	6
567.3.r.c.512.2		8	72.13	even	6
567.3.r.c.512.3		8	72.5	odd	6
1344.3.d.b.449.1		4	12.11	even	2
1344.3.d.b.449.2		4	4.3	odd	2
1344.3.d.f.449.3		4	1.1	even	1	trivial
1344.3.d.f.449.4		4	3.2	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:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1344.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.82288 - 2.38267i) q^{3} +7.37953i q^{5} -2.64575 q^{7} +(-2.35425 - 8.68663i) q^{9} +O(q^{10})\)	\(q+(1.82288 - 2.38267i) q^{3} +7.37953i q^{5} -2.64575 q^{7} +(-2.35425 - 8.68663i) q^{9} -2.61419i q^{11} +6.35425 q^{13} +(17.5830 + 13.4520i) q^{15} +12.1449i q^{17} +10.2288 q^{19} +(-4.82288 + 6.30396i) q^{21} -4.30231i q^{23} -29.4575 q^{25} +(-24.9889 - 10.2252i) q^{27} +17.3733i q^{29} +39.2915 q^{31} +(-6.22876 - 4.76534i) q^{33} -19.5244i q^{35} -41.0405 q^{37} +(11.5830 - 15.1401i) q^{39} +30.2802i q^{41} +55.8745 q^{43} +(64.1033 - 17.3733i) q^{45} +39.9749i q^{47} +7.00000 q^{49} +(28.9373 + 22.1386i) q^{51} +105.002i q^{53} +19.2915 q^{55} +(18.6458 - 24.3718i) q^{57} +41.3640i q^{59} +20.4797 q^{61} +(6.22876 + 22.9827i) q^{63} +46.8914i q^{65} +27.1660 q^{67} +(-10.2510 - 7.84257i) q^{69} +67.8049i q^{71} +60.7895 q^{73} +(-53.6974 + 70.1876i) q^{75} +6.91650i q^{77} -63.2470 q^{79} +(-69.9150 + 40.9010i) q^{81} +89.9435i q^{83} -89.6235 q^{85} +(41.3948 + 31.6693i) q^{87} -63.1745i q^{89} -16.8118 q^{91} +(71.6235 - 93.6188i) q^{93} +75.4835i q^{95} +19.1660 q^{97} +(-22.7085 + 6.15445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 20 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 20 * q^9	\( 4 q + 2 q^{3} - 20 q^{9} + 36 q^{13} + 28 q^{15} - 12 q^{19} - 14 q^{21} - 12 q^{25} - 10 q^{27} + 136 q^{31} + 28 q^{33} - 16 q^{37} + 4 q^{39} + 160 q^{43} + 140 q^{45} + 28 q^{49} + 84 q^{51} + 56 q^{55} + 64 q^{57} + 156 q^{61} - 28 q^{63} + 24 q^{67} - 168 q^{69} - 32 q^{73} - 146 q^{75} + 128 q^{79} - 68 q^{81} - 168 q^{85} + 28 q^{87} + 28 q^{91} + 96 q^{93} - 8 q^{97} - 112 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 20 * q^9 + 36 * q^13 + 28 * q^15 - 12 * q^19 - 14 * q^21 - 12 * q^25 - 10 * q^27 + 136 * q^31 + 28 * q^33 - 16 * q^37 + 4 * q^39 + 160 * q^43 + 140 * q^45 + 28 * q^49 + 84 * q^51 + 56 * q^55 + 64 * q^57 + 156 * q^61 - 28 * q^63 + 24 * q^67 - 168 * q^69 - 32 * q^73 - 146 * q^75 + 128 * q^79 - 68 * q^81 - 168 * q^85 + 28 * q^87 + 28 * q^91 + 96 * q^93 - 8 * q^97 - 112 * q^99

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