LMFDB - Embedded newform 1150.3.d.b.551.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,3,Mod(551,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1150.551");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1150.d (of order $2$, degree $1$, 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:	$31.3352304014$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 78x^{14} + 2165x^{12} + 28310x^{10} + 184804x^{8} + 569634x^{6} + 696037x^{4} + 285578x^{2} + 529 $ x^16 + 78x^14 + 2165x^12 + 28310x^10 + 184804x^8 + 569634x^6 + 696037x^4 + 285578*x^2 + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	no (minimal twist has level 230)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			551.7
Root			$-6.02373i$ of defining polynomial
Character	$\chi$	$=$	1150.551
Dual form			1150.3.d.b.551.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +3.79379 q^{3} +2.00000 q^{4} -5.36524 q^{6} -7.10180i q^{7} -2.82843 q^{8} +5.39287 q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +3.79379 q^{3} +2.00000 q^{4} -5.36524 q^{6} -7.10180i q^{7} -2.82843 q^{8} +5.39287 q^{9} +11.2644i q^{11} +7.58759 q^{12} -20.0597 q^{13} +10.0435i q^{14} +4.00000 q^{16} -1.63128i q^{17} -7.62667 q^{18} +29.4164i q^{19} -26.9428i q^{21} -15.9302i q^{22} +(-20.0280 - 11.3084i) q^{23} -10.7305 q^{24} +28.3688 q^{26} -13.6847 q^{27} -14.2036i q^{28} -50.3233 q^{29} +11.1316 q^{31} -5.65685 q^{32} +42.7347i q^{33} +2.30698i q^{34} +10.7857 q^{36} -40.5429i q^{37} -41.6011i q^{38} -76.1025 q^{39} -7.24039 q^{41} +38.1028i q^{42} +71.7020i q^{43} +22.5287i q^{44} +(28.3239 + 15.9924i) q^{46} +6.40666 q^{47} +15.1752 q^{48} -1.43550 q^{49} -6.18873i q^{51} -40.1195 q^{52} +20.4148i q^{53} +19.3531 q^{54} +20.0869i q^{56} +111.600i q^{57} +71.1679 q^{58} -65.8889 q^{59} -37.7281i q^{61} -15.7425 q^{62} -38.2991i q^{63} +8.00000 q^{64} -60.4360i q^{66} +124.242i q^{67} -3.26256i q^{68} +(-75.9821 - 42.9016i) q^{69} +43.5656 q^{71} -15.2533 q^{72} -48.1194 q^{73} +57.3363i q^{74} +58.8328i q^{76} +79.9972 q^{77} +107.625 q^{78} +101.026i q^{79} -100.453 q^{81} +10.2395 q^{82} -102.409i q^{83} -53.8855i q^{84} -101.402i q^{86} -190.916 q^{87} -31.8604i q^{88} -9.63875i q^{89} +142.460i q^{91} +(-40.0560 - 22.6167i) q^{92} +42.2310 q^{93} -9.06039 q^{94} -21.4609 q^{96} -143.631i q^{97} +2.03010 q^{98} +60.7473i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) $ 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9	$ 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9} - 24 q^{13} + 64 q^{16} + 32 q^{18} - 4 q^{23} - 16 q^{24} + 96 q^{26} + 96 q^{27} - 108 q^{29} - 116 q^{31} + 128 q^{36} + 248 q^{39} - 156 q^{41} - 124 q^{46} + 128 q^{47} - 28 q^{49} - 48 q^{52} + 224 q^{54} - 160 q^{58} + 204 q^{59} - 64 q^{62} + 128 q^{64} - 268 q^{69} + 236 q^{71} + 64 q^{72} + 112 q^{73} + 936 q^{77} + 432 q^{78} - 136 q^{81} + 64 q^{82} + 152 q^{87} - 8 q^{92} - 856 q^{93} - 216 q^{94} - 32 q^{96} - 256 q^{98}+O(q^{100}) $ 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9 - 24 * q^13 + 64 * q^16 + 32 * q^18 - 4 * q^23 - 16 * q^24 + 96 * q^26 + 96 * q^27 - 108 * q^29 - 116 * q^31 + 128 * q^36 + 248 * q^39 - 156 * q^41 - 124 * q^46 + 128 * q^47 - 28 * q^49 - 48 * q^52 + 224 * q^54 - 160 * q^58 + 204 * q^59 - 64 * q^62 + 128 * q^64 - 268 * q^69 + 236 * q^71 + 64 * q^72 + 112 * q^73 + 936 * q^77 + 432 * q^78 - 136 * q^81 + 64 * q^82 + 152 * q^87 - 8 * q^92 - 856 * q^93 - 216 * q^94 - 32 * q^96 - 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$	3.79379			1.26460			0.632299	−	0.774724i	$-0.282111\pi$
$3$	3.79379			1.26460			0.632299	+	0.774724i	$0.282111\pi$
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	−5.36524			−0.894206
$7$		−	7.10180i		−	1.01454i	−0.861787	−	0.507271i	$-0.830654\pi$
$7$		−	7.10180i		−	1.01454i	0.861787	−	0.507271i	$-0.169346\pi$
$8$	−2.82843			−0.353553
$9$	5.39287			0.599208
$10$		0			0
$11$			11.2644i			1.02403i	0.858975	+	0.512017i	$0.171101\pi$
$11$			11.2644i			1.02403i	−0.858975	+	0.512017i	$0.828899\pi$
$12$	7.58759			0.632299
$13$	−20.0597			−1.54306			−0.771528	−	0.636195i	$-0.780507\pi$
$13$	−20.0597			−1.54306			−0.771528	+	0.636195i	$0.780507\pi$
$14$			10.0435i			0.717390i
$15$		0			0
$16$	4.00000			0.250000
$17$		−	1.63128i		−	0.0959575i	−0.998848	−	0.0479788i	$-0.984722\pi$
$17$		−	1.63128i		−	0.0959575i	0.998848	−	0.0479788i	$-0.0152780\pi$
$18$	−7.62667			−0.423704
$19$			29.4164i			1.54823i	0.633044	+	0.774116i	$0.281805\pi$
$19$			29.4164i			1.54823i	−0.633044	+	0.774116i	$0.718195\pi$
$20$		0			0
$21$		−	26.9428i		−	1.28299i
$22$		−	15.9302i		−	0.724101i
$23$	−20.0280	−	11.3084i	−0.870783	−	0.491668i
$23$	−20.0280	−	11.3084i	−0.870783	−	0.491668i
$24$	−10.7305			−0.447103
$25$		0			0
$26$	28.3688			1.09111
$27$	−13.6847			−0.506841
$28$		−	14.2036i		−	0.507271i
$29$	−50.3233			−1.73529			−0.867644	−	0.497187i	$-0.834366\pi$
$29$	−50.3233			−1.73529			−0.867644	+	0.497187i	$0.834366\pi$
$30$		0			0
$31$	11.1316			0.359084			0.179542	−	0.983750i	$-0.442538\pi$
$31$	11.1316			0.359084			0.179542	+	0.983750i	$0.442538\pi$
$32$	−5.65685			−0.176777
$33$			42.7347i			1.29499i
$34$			2.30698i			0.0678522i
$35$		0			0
$36$	10.7857			0.299604
$37$		−	40.5429i		−	1.09575i	−0.836559	−	0.547877i	$-0.815436\pi$
$37$		−	40.5429i		−	1.09575i	0.836559	−	0.547877i	$-0.184564\pi$
$38$		−	41.6011i		−	1.09477i
$39$	−76.1025			−1.95135
$40$		0			0
$41$	−7.24039			−0.176595			−0.0882975	−	0.996094i	$-0.528143\pi$
$41$	−7.24039			−0.176595			−0.0882975	+	0.996094i	$0.528143\pi$
$42$			38.1028i			0.907210i
$43$			71.7020i			1.66749i	0.552150	+	0.833745i	$0.313808\pi$
$43$			71.7020i			1.66749i	−0.552150	+	0.833745i	$0.686192\pi$
$44$			22.5287i			0.512017i
$45$		0			0
$46$	28.3239	+	15.9924i	0.615736	+	0.347662i
$47$	6.40666			0.136312			0.0681560	−	0.997675i	$-0.478288\pi$
$47$	6.40666			0.136312			0.0681560	+	0.997675i	$0.478288\pi$
$48$	15.1752			0.316150
$49$	−1.43550			−0.0292959
$50$		0			0
$51$		−	6.18873i		−	0.121348i
$52$	−40.1195			−0.771528
$53$			20.4148i			0.385184i	0.981279	+	0.192592i	$0.0616894\pi$
$53$			20.4148i			0.385184i	−0.981279	+	0.192592i	$0.938311\pi$
$54$	19.3531			0.358390
$55$		0			0
$56$			20.0869i			0.358695i
$57$			111.600i			1.95789i
$58$	71.1679			1.22703
$59$	−65.8889			−1.11676			−0.558381	−	0.829585i	$-0.688577\pi$
$59$	−65.8889			−1.11676			−0.558381	+	0.829585i	$0.688577\pi$
$60$		0			0
$61$		−	37.7281i		−	0.618493i	−0.950982	−	0.309247i	$-0.899923\pi$
$61$		−	37.7281i		−	0.618493i	0.950982	−	0.309247i	$-0.100077\pi$
$62$	−15.7425			−0.253911
$63$		−	38.2991i		−	0.607922i
$64$	8.00000			0.125000
$65$		0			0
$66$		−	60.4360i		−	0.915697i
$67$			124.242i			1.85437i	0.374609	+	0.927183i	$0.377777\pi$
$67$			124.242i			1.85437i	−0.374609	+	0.927183i	$0.622223\pi$
$68$		−	3.26256i		−	0.0479788i
$69$	−75.9821	−	42.9016i	−1.10119	−	0.621763i
$70$		0			0
$71$	43.5656			0.613600			0.306800	−	0.951774i	$-0.400742\pi$
$71$	43.5656			0.613600			0.306800	+	0.951774i	$0.400742\pi$
$72$	−15.2533			−0.211852
$73$	−48.1194			−0.659169			−0.329585	−	0.944126i	$-0.606909\pi$
$73$	−48.1194			−0.659169			−0.329585	+	0.944126i	$0.606909\pi$
$74$			57.3363i			0.774815i
$75$		0			0
$76$			58.8328i			0.774116i
$77$	79.9972			1.03893
$78$	107.625			1.37981
$79$			101.026i			1.27882i	0.768868	+	0.639408i	$0.220821\pi$
$79$			101.026i			1.27882i	−0.768868	+	0.639408i	$0.779179\pi$
$80$		0			0
$81$	−100.453			−1.24016
$82$	10.2395			0.124871
$83$		−	102.409i		−	1.23384i	−0.787025	−	0.616921i	$-0.788380\pi$
$83$		−	102.409i		−	1.23384i	0.787025	−	0.616921i	$-0.211620\pi$
$84$		−	53.8855i		−	0.641494i
$85$		0			0
$86$		−	101.402i		−	1.17909i
$87$	−190.916			−2.19444
$88$		−	31.8604i		−	0.362050i
$89$		−	9.63875i		−	0.108301i	−0.998533	−	0.0541503i	$-0.982755\pi$
$89$		−	9.63875i		−	0.108301i	0.998533	−	0.0541503i	$-0.0172450\pi$
$90$		0			0
$91$			142.460i			1.56550i
$92$	−40.0560	−	22.6167i	−0.435391	−	0.245834i
$93$	42.2310			0.454097
$94$	−9.06039			−0.0963871
$95$		0			0
$96$	−21.4609			−0.223551
$97$		−	143.631i		−	1.48074i	−0.672202	−	0.740368i	$-0.734651\pi$
$97$		−	143.631i		−	1.48074i	0.672202	−	0.740368i	$-0.265349\pi$
$98$	2.03010			0.0207154
$99$			60.7473i			0.613609i
$100$		0			0
$101$	103.099			1.02078			0.510391	−	0.859943i	$-0.329501\pi$
$101$	103.099			1.02078			0.510391	+	0.859943i	$0.329501\pi$
$102$			8.75219i			0.0858058i
$103$		−	98.8637i		−	0.959841i	−0.877312	−	0.479921i	$-0.840665\pi$
$103$		−	98.8637i		−	0.959841i	0.877312	−	0.479921i	$-0.159335\pi$
$104$	56.7375			0.545553
$105$		0			0
$106$		−	28.8708i		−	0.272366i
$107$		−	22.5494i		−	0.210742i	−0.994433	−	0.105371i	$-0.966397\pi$
$107$		−	22.5494i		−	0.210742i	0.994433	−	0.105371i	$-0.0336029\pi$
$108$	−27.3694			−0.253420
$109$		−	30.2389i		−	0.277421i	−0.990333	−	0.138711i	$-0.955704\pi$
$109$		−	30.2389i		−	0.277421i	0.990333	−	0.138711i	$-0.0442958\pi$
$110$		0			0
$111$		−	153.811i		−	1.38569i
$112$		−	28.4072i		−	0.253636i
$113$			213.437i			1.88882i	0.328771	+	0.944410i	$0.393365\pi$
$113$			213.437i			1.88882i	−0.328771	+	0.944410i	$0.606635\pi$
$114$		−	157.826i		−	1.38444i
$115$		0			0
$116$	−100.647			−0.867644
$117$	−108.180			−0.924612
$118$	93.1810			0.789670
$119$	−11.5850			−0.0973530
$120$		0			0
$121$	−5.88598			−0.0486445
$122$			53.3556i			0.437341i
$123$	−27.4686			−0.223322
$124$	22.2632			0.179542
$125$		0			0
$126$			54.1631i			0.429866i
$127$	29.9509			0.235834			0.117917	−	0.993023i	$-0.462378\pi$
$127$	29.9509			0.235834			0.117917	+	0.993023i	$0.462378\pi$
$128$	−11.3137			−0.0883883
$129$			272.023i			2.10870i
$130$		0			0
$131$	−116.486			−0.889208			−0.444604	−	0.895727i	$-0.646656\pi$
$131$	−116.486			−0.889208			−0.444604	+	0.895727i	$0.646656\pi$
$132$			85.4694i			0.647495i
$133$	208.909			1.57075
$134$		−	175.705i		−	1.31123i
$135$		0			0
$136$			4.61395i			0.0339261i
$137$			94.8211i			0.692125i	0.938212	+	0.346062i	$0.112481\pi$
$137$			94.8211i			0.692125i	−0.938212	+	0.346062i	$0.887519\pi$
$138$	107.455	+	60.6720i	0.778659	+	0.439653i
$139$	89.2774			0.642284			0.321142	−	0.947031i	$-0.395933\pi$
$139$	89.2774			0.642284			0.321142	+	0.947031i	$0.395933\pi$
$140$		0			0
$141$	24.3056			0.172380
$142$	−61.6111			−0.433881
$143$		−	225.960i		−	1.58014i
$144$	21.5715			0.149802
$145$		0			0
$146$	68.0510			0.466103
$147$	−5.44599			−0.0370476
$148$		−	81.0857i		−	0.547877i
$149$		−	182.441i		−	1.22443i	−0.790690	−	0.612217i	$-0.790278\pi$
$149$		−	182.441i		−	1.22443i	0.790690	−	0.612217i	$-0.209722\pi$
$150$		0			0
$151$	29.7608			0.197092			0.0985458	−	0.995133i	$-0.468581\pi$
$151$	29.7608			0.197092			0.0985458	+	0.995133i	$0.468581\pi$
$152$		−	83.2022i		−	0.547383i
$153$		−	8.79728i		−	0.0574985i
$154$	−113.133			−0.734631
$155$		0			0
$156$	−152.205			−0.975673
$157$			64.1093i			0.408340i	0.978935	+	0.204170i	$0.0654495\pi$
$157$			64.1093i			0.408340i	−0.978935	+	0.204170i	$0.934551\pi$
$158$		−	142.873i		−	0.904260i
$159$			77.4494i			0.487103i
$160$		0			0
$161$	−80.3097	+	142.235i	−0.498818	+	0.883446i
$162$	142.062			0.876924
$163$	75.3328			0.462164			0.231082	−	0.972934i	$-0.425773\pi$
$163$	75.3328			0.462164			0.231082	+	0.972934i	$0.425773\pi$
$164$	−14.4808			−0.0882975
$165$		0			0
$166$			144.828i			0.872458i
$167$	−272.459			−1.63149			−0.815745	−	0.578412i	$-0.803673\pi$
$167$	−272.459			−1.63149			−0.815745	+	0.578412i	$0.803673\pi$
$168$			76.2056i			0.453605i
$169$	233.393			1.38102
$170$		0			0
$171$			158.639i			0.927713i
$172$			143.404i			0.833745i
$173$	−261.815			−1.51338			−0.756691	−	0.653773i	$-0.773185\pi$
$173$	−261.815			−1.51338			−0.756691	+	0.653773i	$0.773185\pi$
$174$	269.996			1.55170
$175$		0			0
$176$			45.0575i			0.256008i
$177$	−249.969			−1.41225
$178$			13.6312i			0.0765800i
$179$	−184.406			−1.03020			−0.515101	−	0.857130i	$-0.672246\pi$
$179$	−184.406			−1.03020			−0.515101	+	0.857130i	$0.672246\pi$
$180$		0			0
$181$		−	191.867i		−	1.06004i	−0.847986	−	0.530019i	$-0.822185\pi$
$181$		−	191.867i		−	1.06004i	0.847986	−	0.530019i	$-0.177815\pi$
$182$		−	201.469i		−	1.10697i
$183$		−	143.133i		−	0.782145i
$184$	56.6477	+	31.9849i	0.307868	+	0.173831i
$185$		0			0
$186$	−59.7237			−0.321095
$187$	18.3753			0.0982637
$188$	12.8133			0.0681560
$189$			97.1859i			0.514211i
$190$		0			0
$191$			32.6185i			0.170778i	0.996348	+	0.0853888i	$0.0272132\pi$
$191$			32.6185i			0.170778i	−0.996348	+	0.0853888i	$0.972787\pi$
$192$	30.3504			0.158075
$193$	−316.748			−1.64118			−0.820592	−	0.571515i	$-0.806356\pi$
$193$	−316.748			−1.64118			−0.820592	+	0.571515i	$0.806356\pi$
$194$			203.125i			1.04704i
$195$		0			0
$196$	−2.87100			−0.0146480
$197$	194.946			0.989573			0.494787	−	0.869015i	$-0.335246\pi$
$197$	194.946			0.989573			0.494787	+	0.869015i	$0.335246\pi$
$198$		−	85.9097i		−	0.433887i
$199$			74.0815i			0.372269i	0.982524	+	0.186134i	$0.0595960\pi$
$199$			74.0815i			0.372269i	−0.982524	+	0.186134i	$0.940404\pi$
$200$		0			0
$201$			471.350i			2.34503i
$202$	−145.804			−0.721802
$203$			357.386i			1.76052i
$204$		−	12.3775i		−	0.0606739i
$205$		0			0
$206$			139.814i			0.678710i
$207$	−108.008	−	60.9846i	−0.521780	−	0.294612i
$208$	−80.2390			−0.385764
$209$	−331.357			−1.58544
$210$		0			0
$211$	−4.75017			−0.0225126			−0.0112563	−	0.999937i	$-0.503583\pi$
$211$	−4.75017			−0.0225126			−0.0112563	+	0.999937i	$0.503583\pi$
$212$			40.8295i			0.192592i
$213$	165.279			0.775958
$214$			31.8896i			0.149017i
$215$		0			0
$216$	38.7062			0.179195
$217$		−	79.0544i		−	0.364306i
$218$			42.7643i			0.196167i
$219$	−182.555			−0.833584
$220$		0			0
$221$			32.7230i			0.148068i
$222$			217.522i			0.979829i
$223$	−211.977			−0.950571			−0.475286	−	0.879832i	$-0.657655\pi$
$223$	−211.977			−0.950571			−0.475286	+	0.879832i	$0.657655\pi$
$224$			40.1738i			0.179347i
$225$		0			0
$226$		−	301.845i		−	1.33560i
$227$			389.941i			1.71780i	0.512141	+	0.858901i	$0.328852\pi$
$227$			389.941i			1.71780i	−0.512141	+	0.858901i	$0.671148\pi$
$228$			223.200i			0.978945i
$229$			156.000i			0.681224i	0.940204	+	0.340612i	$0.110634\pi$
$229$			156.000i			0.681224i	−0.940204	+	0.340612i	$0.889366\pi$
$230$		0			0
$231$	303.493			1.31382
$232$	142.336			0.613517
$233$	46.4968			0.199557			0.0997785	−	0.995010i	$-0.468187\pi$
$233$	46.4968			0.199557			0.0997785	+	0.995010i	$0.468187\pi$
$234$	152.989			0.653800
$235$		0			0
$236$	−131.778			−0.558381
$237$			383.274i			1.61719i
$238$	16.3837			0.0688389
$239$	−454.735			−1.90266			−0.951328	−	0.308181i	$-0.900280\pi$
$239$	−454.735			−1.90266			−0.951328	+	0.308181i	$0.900280\pi$
$240$		0			0
$241$		−	149.357i		−	0.619739i	−0.950779	−	0.309870i	$-0.899715\pi$
$241$		−	149.357i		−	0.619739i	0.950779	−	0.309870i	$-0.100285\pi$
$242$	8.32404			0.0343968
$243$	−257.935			−1.06146
$244$		−	75.4562i		−	0.309247i
$245$		0			0
$246$	38.8464			0.157912
$247$		−	590.085i		−	2.38901i
$248$	−31.4849			−0.126955
$249$		−	388.518i		−	1.56031i
$250$		0			0
$251$		−	364.513i		−	1.45224i	−0.687567	−	0.726121i	$-0.741321\pi$
$251$		−	364.513i		−	1.45224i	0.687567	−	0.726121i	$-0.258679\pi$
$252$		−	76.5982i		−	0.303961i
$253$	127.382	−	225.603i	0.503485	−	0.891711i
$254$	−42.3570			−0.166760
$255$		0			0
$256$	16.0000			0.0625000
$257$	−59.7088			−0.232330			−0.116165	−	0.993230i	$-0.537060\pi$
$257$	−59.7088			−0.232330			−0.116165	+	0.993230i	$0.537060\pi$
$258$		−	384.698i		−	1.49108i
$259$	−287.927			−1.11169
$260$		0			0
$261$	−271.387			−1.03980
$262$	164.736			0.628765
$263$			282.085i			1.07257i	0.844038	+	0.536284i	$0.180172\pi$
$263$			282.085i			1.07257i	−0.844038	+	0.536284i	$0.819828\pi$
$264$		−	120.872i		−	0.457848i
$265$		0			0
$266$	−295.442			−1.11069
$267$		−	36.5674i		−	0.136957i
$268$			248.485i			0.927183i
$269$	14.7823			0.0549529			0.0274764	−	0.999622i	$-0.491253\pi$
$269$	14.7823			0.0549529			0.0274764	+	0.999622i	$0.491253\pi$
$270$		0			0
$271$	−34.7150			−0.128100			−0.0640499	−	0.997947i	$-0.520402\pi$
$271$	−34.7150			−0.128100			−0.0640499	+	0.997947i	$0.520402\pi$
$272$		−	6.52511i		−	0.0239894i
$273$			540.465i			1.97972i
$274$		−	134.097i		−	0.489406i
$275$		0			0
$276$	−151.964	−	85.8032i	−0.550595	−	0.310881i
$277$	191.042			0.689682			0.344841	−	0.938661i	$-0.387933\pi$
$277$	191.042			0.689682			0.344841	+	0.938661i	$0.387933\pi$
$278$	−126.257			−0.454163
$279$	60.0314			0.215166
$280$		0			0
$281$		−	471.349i		−	1.67740i	−0.544596	−	0.838698i	$-0.683317\pi$
$281$		−	471.349i		−	1.67740i	0.544596	−	0.838698i	$-0.316683\pi$
$282$	−34.3733			−0.121891
$283$			23.4603i			0.0828984i	0.999141	+	0.0414492i	$0.0131975\pi$
$283$			23.4603i			0.0828984i	−0.999141	+	0.0414492i	$0.986803\pi$
$284$	87.1312			0.306800
$285$		0			0
$286$			319.556i			1.11733i
$287$			51.4198i			0.179163i
$288$	−30.5067			−0.105926
$289$	286.339			0.990792
$290$		0			0
$291$		−	544.908i		−	1.87254i
$292$	−96.2387			−0.329585
$293$			289.288i			0.987331i	0.869652	+	0.493666i	$0.164343\pi$
$293$			289.288i			0.987331i	−0.869652	+	0.493666i	$0.835657\pi$
$294$	7.70180			0.0261966
$295$		0			0
$296$			114.673i			0.387407i
$297$		−	154.149i		−	0.519022i
$298$			258.010i			0.865805i
$299$	401.756	+	226.843i	1.34367	+	0.758672i
$300$		0			0
$301$	509.213			1.69174
$302$	−42.0882			−0.139365
$303$	391.136			1.29088
$304$			117.666i			0.387058i
$305$		0			0
$306$			12.4412i			0.0406576i
$307$	563.775			1.83640			0.918200	−	0.396117i	$-0.129642\pi$
$307$	563.775			1.83640			0.918200	+	0.396117i	$0.129642\pi$
$308$	159.994			0.519463
$309$		−	375.068i		−	1.21381i
$310$		0			0
$311$	76.9428			0.247404			0.123702	−	0.992319i	$-0.460523\pi$
$311$	76.9428			0.247404			0.123702	+	0.992319i	$0.460523\pi$
$312$	215.250			0.689905
$313$		−	436.773i		−	1.39544i	−0.716370	−	0.697721i	$-0.754198\pi$
$313$		−	436.773i		−	1.39544i	0.716370	−	0.697721i	$-0.245802\pi$
$314$		−	90.6643i		−	0.288740i
$315$		0			0
$316$			202.053i			0.639408i
$317$	−95.6774			−0.301822			−0.150911	−	0.988547i	$-0.548221\pi$
$317$	−95.6774			−0.301822			−0.150911	+	0.988547i	$0.548221\pi$
$318$		−	109.530i		−	0.344434i
$319$		−	566.860i		−	1.77699i
$320$		0			0
$321$		−	85.5476i		−	0.266503i
$322$	113.575	−	201.150i	0.352718	−	0.624691i
$323$	47.9863			0.148565
$324$	−200.906			−0.620079
$325$		0			0
$326$	−106.537			−0.326799
$327$		−	114.720i		−	0.350827i
$328$	20.4789			0.0624357
$329$		−	45.4988i		−	0.138294i
$330$		0			0
$331$	515.137			1.55631			0.778153	−	0.628074i	$-0.216157\pi$
$331$	515.137			1.55631			0.778153	+	0.628074i	$0.216157\pi$
$332$		−	204.818i		−	0.616921i
$333$		−	218.643i		−	0.656584i
$334$	385.315			1.15364
$335$		0			0
$336$		−	107.771i		−	0.320747i
$337$		−	251.793i		−	0.747161i	−0.927598	−	0.373580i	$-0.878130\pi$
$337$		−	251.793i		−	0.747161i	0.927598	−	0.373580i	$-0.121870\pi$
$338$	−330.068			−0.976532
$339$			809.734i			2.38860i
$340$		0			0
$341$			125.391i			0.367714i
$342$		−	224.349i		−	0.655992i
$343$		−	337.793i		−	0.984820i
$344$		−	202.804i		−	0.589547i
$345$		0			0
$346$	370.262			1.07012
$347$	167.899			0.483858			0.241929	−	0.970294i	$-0.422220\pi$
$347$	167.899			0.483858			0.241929	+	0.970294i	$0.422220\pi$
$348$	−381.833			−1.09722
$349$	131.699			0.377360			0.188680	−	0.982039i	$-0.439579\pi$
$349$	131.699			0.377360			0.188680	+	0.982039i	$0.439579\pi$
$350$		0			0
$351$	274.511			0.782084
$352$		−	63.7209i		−	0.181025i
$353$	−232.683			−0.659159			−0.329580	−	0.944128i	$-0.606907\pi$
$353$	−232.683			−0.659159			−0.329580	+	0.944128i	$0.606907\pi$
$354$	353.510			0.998615
$355$		0			0
$356$		−	19.2775i		−	0.0541503i
$357$	−43.9511			−0.123112
$358$	260.790			0.728463
$359$			205.862i			0.573432i	0.958016	+	0.286716i	$0.0925636\pi$
$359$			205.862i			0.573432i	−0.958016	+	0.286716i	$0.907436\pi$
$360$		0			0
$361$	−504.325			−1.39702
$362$			271.341i			0.749560i
$363$	−22.3302			−0.0615157
$364$			284.920i			0.782748i
$365$		0			0
$366$			202.420i			0.553060i
$367$			158.406i			0.431623i	0.976435	+	0.215811i	$0.0692396\pi$
$367$			158.406i			0.431623i	−0.976435	+	0.215811i	$0.930760\pi$
$368$	−80.1120	−	45.2335i	−0.217696	−	0.122917i
$369$	−39.0465			−0.105817
$370$		0			0
$371$	144.981			0.390786
$372$	84.4621			0.227049
$373$			67.1037i			0.179903i	0.995946	+	0.0899513i	$0.0286712\pi$
$373$			67.1037i			0.179903i	−0.995946	+	0.0899513i	$0.971329\pi$
$374$	−25.9866			−0.0694829
$375$		0			0
$376$	−18.1208			−0.0481936
$377$	1009.47			2.67765
$378$		−	137.442i		−	0.363602i
$379$			10.5032i			0.0277128i	0.999904	+	0.0138564i	$0.00441078\pi$
$379$			10.5032i			0.0277128i	−0.999904	+	0.0138564i	$0.995589\pi$
$380$		0			0
$381$	113.628			0.298235
$382$		−	46.1296i		−	0.120758i
$383$			360.978i			0.942501i	0.882000	+	0.471250i	$0.156197\pi$
$383$			360.978i			0.942501i	−0.882000	+	0.471250i	$0.843803\pi$
$384$	−42.9219			−0.111776
$385$		0			0
$386$	447.950			1.16049
$387$			386.680i			0.999173i
$388$		−	287.263i		−	0.740368i
$389$			47.2280i			0.121409i	0.998156	+	0.0607044i	$0.0193347\pi$
$389$			47.2280i			0.121409i	−0.998156	+	0.0607044i	$0.980665\pi$
$390$		0			0
$391$	−18.4471	+	32.6712i	−0.0471793	+	0.0835582i
$392$	4.06021			0.0103577
$393$	−441.925			−1.12449
$394$	−275.695			−0.699734
$395$		0			0
$396$			121.495i			0.306805i
$397$	−4.85826			−0.0122374			−0.00611872	−	0.999981i	$-0.501948\pi$
$397$	−4.85826			−0.0122374			−0.00611872	+	0.999981i	$0.501948\pi$
$398$		−	104.767i		−	0.263234i
$399$	792.559			1.98636
$400$		0			0
$401$			297.502i			0.741900i	0.928653	+	0.370950i	$0.120968\pi$
$401$			297.502i			0.741900i	−0.928653	+	0.370950i	$0.879032\pi$
$402$		−	666.590i		−	1.65818i
$403$	−223.297			−0.554087
$404$	206.198			0.510391
$405$		0			0
$406$		−	505.420i		−	1.24488i
$407$	456.690			1.12209
$408$			17.5044i			0.0429029i
$409$	238.943			0.584213			0.292106	−	0.956386i	$-0.405644\pi$
$409$	238.943			0.584213			0.292106	+	0.956386i	$0.405644\pi$
$410$		0			0
$411$			359.732i			0.875259i
$412$		−	197.727i		−	0.479921i
$413$			467.930i			1.13300i
$414$	152.747	+	86.2452i	0.368954	+	0.208322i
$415$		0			0
$416$	113.475			0.272776
$417$	338.700			0.812231
$418$	468.610			1.12108
$419$		−	197.316i		−	0.470920i	−0.971884	−	0.235460i	$-0.924340\pi$
$419$		−	197.316i		−	0.470920i	0.971884	−	0.235460i	$-0.0756597\pi$
$420$		0			0
$421$		−	459.256i		−	1.09087i	−0.838153	−	0.545435i	$-0.816365\pi$
$421$		−	459.256i		−	1.09087i	0.838153	−	0.545435i	$-0.183635\pi$
$422$	6.71775			0.0159188
$423$	34.5503			0.0816793
$424$		−	57.7417i		−	0.136183i
$425$		0			0
$426$	−233.740			−0.548685
$427$	−267.937			−0.627487
$428$		−	45.0987i		−	0.105371i
$429$		−	857.247i		−	1.99824i
$430$		0			0
$431$			475.283i			1.10275i	0.834259	+	0.551373i	$0.185896\pi$
$431$			475.283i			1.10275i	−0.834259	+	0.551373i	$0.814104\pi$
$432$	−54.7388			−0.126710
$433$		−	694.309i		−	1.60349i	−0.597669	−	0.801743i	$-0.703906\pi$
$433$		−	694.309i		−	1.60349i	0.597669	−	0.801743i	$-0.296094\pi$
$434$			111.800i			0.257603i
$435$		0			0
$436$		−	60.4779i		−	0.138711i
$437$	332.651	−	589.152i	0.761216	−	1.34817i
$438$	258.172			0.589433
$439$	−692.132			−1.57661			−0.788305	−	0.615284i	$-0.789041\pi$
$439$	−692.132			−1.57661			−0.788305	+	0.615284i	$0.789041\pi$
$440$		0			0
$441$	−7.74147			−0.0175544
$442$		−	46.2773i		−	0.104700i
$443$	282.065			0.636716			0.318358	−	0.947971i	$-0.396869\pi$
$443$	282.065			0.636716			0.318358	+	0.947971i	$0.396869\pi$
$444$		−	307.623i		−	0.692844i
$445$		0			0
$446$	299.781			0.672155
$447$		−	692.142i		−	1.54842i
$448$		−	56.8144i		−	0.126818i
$449$	−4.51574			−0.0100573			−0.00502866	−	0.999987i	$-0.501601\pi$
$449$	−4.51574			−0.0100573			−0.00502866	+	0.999987i	$0.501601\pi$
$450$		0			0
$451$		−	81.5584i		−	0.180839i
$452$			426.873i			0.944410i
$453$	112.907			0.249242
$454$		−	551.460i		−	1.21467i
$455$		0			0
$456$		−	315.652i		−	0.692219i
$457$			399.040i			0.873174i	0.899662	+	0.436587i	$0.143813\pi$
$457$			399.040i			0.873174i	−0.899662	+	0.436587i	$0.856187\pi$
$458$		−	220.618i		−	0.481698i
$459$			22.3235i			0.0486352i
$460$		0			0
$461$	44.2537			0.0959950			0.0479975	−	0.998847i	$-0.484716\pi$
$461$	44.2537			0.0959950			0.0479975	+	0.998847i	$0.484716\pi$
$462$	−429.204			−0.929013
$463$	668.258			1.44332			0.721661	−	0.692247i	$-0.243379\pi$
$463$	668.258			1.44332			0.721661	+	0.692247i	$0.243379\pi$
$464$	−201.293			−0.433822
$465$		0			0
$466$	−65.7564			−0.141108
$467$		−	670.150i		−	1.43501i	−0.696554	−	0.717505i	$-0.745284\pi$
$467$		−	670.150i		−	1.43501i	0.696554	−	0.717505i	$-0.254716\pi$
$468$	−216.359			−0.462306
$469$	882.345			1.88133
$470$		0			0
$471$			243.218i			0.516385i
$472$	186.362			0.394835
$473$	−807.678			−1.70756
$474$		−	542.031i		−	1.14352i
$475$		0			0
$476$	−23.1700			−0.0486765
$477$			110.094i			0.230805i
$478$	643.092			1.34538
$479$			310.492i			0.648209i	0.946021	+	0.324105i	$0.105063\pi$
$479$			310.492i			0.648209i	−0.946021	+	0.324105i	$0.894937\pi$
$480$		0			0
$481$			813.279i			1.69081i
$482$			211.223i			0.438222i
$483$	−304.679	+	539.609i	−0.630804	+	1.11720i
$484$	−11.7720			−0.0243222
$485$		0			0
$486$	364.775			0.750566
$487$	−829.644			−1.70358			−0.851790	−	0.523883i	$-0.824483\pi$
$487$	−829.644			−1.70358			−0.851790	+	0.523883i	$0.824483\pi$
$488$			106.711i			0.218670i
$489$	285.797			0.584452
$490$		0			0
$491$	−123.794			−0.252126			−0.126063	−	0.992022i	$-0.540234\pi$
$491$	−123.794			−0.252126			−0.126063	+	0.992022i	$0.540234\pi$
$492$	−54.9371			−0.111661
$493$			82.0913i			0.166514i
$494$			834.507i			1.68928i
$495$		0			0
$496$	44.5264			0.0897710
$497$		−	309.394i		−	0.622523i
$498$			549.448i			1.10331i
$499$	757.919			1.51887			0.759437	−	0.650580i	$-0.225474\pi$
$499$	757.919			1.51887			0.759437	+	0.650580i	$0.225474\pi$
$500$		0			0
$501$	−1033.65			−2.06318
$502$			515.499i			1.02689i
$503$			242.915i			0.482933i	0.970409	+	0.241467i	$0.0776284\pi$
$503$			242.915i			0.482933i	−0.970409	+	0.241467i	$0.922372\pi$
$504$			108.326i			0.214933i
$505$		0			0
$506$	−180.145	+	319.050i	−0.356017	+	0.630535i
$507$	885.445			1.74644
$508$	59.9018			0.117917
$509$	822.585			1.61608			0.808040	−	0.589127i	$-0.200528\pi$
$509$	822.585			1.61608			0.808040	+	0.589127i	$0.200528\pi$
$510$		0			0
$511$			341.734i			0.668755i
$512$	−22.6274			−0.0441942
$513$		−	402.555i		−	0.784707i
$514$	84.4409			0.164282
$515$		0			0
$516$			544.046i			1.05435i
$517$			72.1670i			0.139588i
$518$	407.191			0.786082
$519$	−993.273			−1.91382
$520$		0			0
$521$		−	95.3538i		−	0.183021i	−0.995804	−	0.0915103i	$-0.970831\pi$
$521$		−	95.3538i		−	0.183021i	0.995804	−	0.0915103i	$-0.0291694\pi$
$522$	383.800			0.735248
$523$		−	277.463i		−	0.530522i	−0.964177	−	0.265261i	$-0.914542\pi$
$523$		−	277.463i		−	0.530522i	0.964177	−	0.265261i	$-0.0854581\pi$
$524$	−232.972			−0.444604
$525$		0			0
$526$		−	398.929i		−	0.758420i
$527$		−	18.1588i		−	0.0344568i
$528$			170.939i			0.323748i
$529$	273.242	+	452.968i	0.516525	+	0.856272i
$530$		0			0
$531$	−355.331			−0.669173
$532$	417.819			0.785373
$533$	145.240			0.272496
$534$			51.7141i			0.0968430i
$535$		0			0
$536$		−	351.411i		−	0.655617i
$537$	−699.599			−1.30279
$538$	−20.9054			−0.0388575
$539$		−	16.1700i		−	0.0300000i
$540$		0			0
$541$	−666.108			−1.23125			−0.615627	−	0.788038i	$-0.711097\pi$
$541$	−666.108			−1.23125			−0.615627	+	0.788038i	$0.711097\pi$
$542$	49.0945			0.0905802
$543$		−	727.903i		−	1.34052i
$544$			9.22790i			0.0169631i
$545$		0			0
$546$		−	764.332i		−	1.39988i
$547$	−349.611			−0.639143			−0.319571	−	0.947562i	$-0.603539\pi$
$547$	−349.611			−0.639143			−0.319571	+	0.947562i	$0.603539\pi$
$548$			189.642i			0.346062i
$549$		−	203.463i		−	0.370606i
$550$		0			0
$551$		−	1480.33i		−	2.68663i
$552$	214.910	+	121.344i	0.389329	+	0.219826i
$553$	717.469			1.29741
$554$	−270.174			−0.487679
$555$		0			0
$556$	178.555			0.321142
$557$			8.96150i			0.0160889i	0.999968	+	0.00804443i	$0.00256065\pi$
$557$			8.96150i			0.0160889i	−0.999968	+	0.00804443i	$0.997439\pi$
$558$	−84.8972			−0.152145
$559$		−	1438.32i		−	2.57303i
$560$		0			0
$561$	69.7122			0.124264
$562$			666.587i			1.18610i
$563$		−	732.683i		−	1.30139i	−0.759339	−	0.650696i	$-0.774477\pi$
$563$		−	732.683i		−	1.30139i	0.759339	−	0.650696i	$-0.225523\pi$
$564$	48.6111			0.0861900
$565$		0			0
$566$		−	33.1778i		−	0.0586181i
$567$			713.395i			1.25819i
$568$	−123.222			−0.216940
$569$		−	42.5363i		−	0.0747563i	−0.999301	−	0.0373781i	$-0.988099\pi$
$569$		−	42.5363i		−	0.0747563i	0.999301	−	0.0373781i	$-0.0119006\pi$
$570$		0			0
$571$			459.356i			0.804476i	0.915535	+	0.402238i	$0.131768\pi$
$571$			459.356i			0.804476i	−0.915535	+	0.402238i	$0.868232\pi$
$572$		−	451.921i		−	0.790071i
$573$			123.748i			0.215965i
$574$		−	72.7186i		−	0.126687i
$575$		0			0
$576$	43.1430			0.0749010
$577$	−831.608			−1.44126			−0.720630	−	0.693319i	$-0.756148\pi$
$577$	−831.608			−1.44126			−0.720630	+	0.693319i	$0.756148\pi$
$578$	−404.944			−0.700596
$579$	−1201.68			−2.07544
$580$		0			0
$581$	−727.287			−1.25179
$582$			770.616i			1.32408i
$583$	−229.959			−0.394441
$584$	136.102			0.233052
$585$		0			0
$586$		−	409.115i		−	0.698149i
$587$	166.970			0.284447			0.142223	−	0.989835i	$-0.454575\pi$
$587$	166.970			0.284447			0.142223	+	0.989835i	$0.454575\pi$
$588$	−10.8920			−0.0185238
$589$			327.452i			0.555945i
$590$		0			0
$591$	739.585			1.25141
$592$		−	162.171i		−	0.273938i
$593$	−900.895			−1.51922			−0.759608	−	0.650381i	$-0.774609\pi$
$593$	−900.895			−1.51922			−0.759608	+	0.650381i	$0.774609\pi$
$594$			218.000i			0.367004i
$595$		0			0
$596$		−	364.881i		−	0.612217i
$597$			281.050i			0.470771i
$598$	−568.169	−	320.804i	−0.950116	−	0.536462i
$599$	−129.221			−0.215727			−0.107864	−	0.994166i	$-0.534401\pi$
$599$	−129.221			−0.215727			−0.107864	+	0.994166i	$0.534401\pi$
$600$		0			0
$601$	580.916			0.966582			0.483291	−	0.875460i	$-0.339441\pi$
$601$	580.916			0.966582			0.483291	+	0.875460i	$0.339441\pi$
$602$	−720.136			−1.19624
$603$			670.024i			1.11115i
$604$	59.5217			0.0985458
$605$		0			0
$606$	−553.150			−0.912789
$607$	1063.36			1.75183			0.875915	−	0.482466i	$-0.160259\pi$
$607$	1063.36			1.75183			0.875915	+	0.482466i	$0.160259\pi$
$608$		−	166.404i		−	0.273691i
$609$			1355.85i			2.22635i
$610$		0			0
$611$	−128.516			−0.210337
$612$		−	17.5946i		−	0.0287493i
$613$			442.412i			0.721715i	0.932621	+	0.360858i	$0.117516\pi$
$613$			442.412i			0.721715i	−0.932621	+	0.360858i	$0.882484\pi$
$614$	−797.298			−1.29853
$615$		0			0
$616$	−226.266			−0.367316
$617$		−	936.724i		−	1.51819i	−0.650979	−	0.759095i	$-0.725642\pi$
$617$		−	936.724i		−	1.51819i	0.650979	−	0.759095i	$-0.274358\pi$
$618$			530.427i			0.858296i
$619$		−	401.856i		−	0.649202i	−0.945851	−	0.324601i	$-0.894770\pi$
$619$		−	401.856i		−	0.649202i	0.945851	−	0.324601i	$-0.105230\pi$
$620$		0			0
$621$	274.077	+	154.752i	0.441348	+	0.249197i
$622$	−108.814			−0.174941
$623$	−68.4524			−0.109875
$624$	−304.410			−0.487837
$625$		0			0
$626$			617.691i			0.986726i
$627$	−1257.10			−2.00495
$628$			128.219i			0.204170i
$629$	−66.1367			−0.105146
$630$		0			0
$631$		−	1033.92i		−	1.63854i	−0.573411	−	0.819268i	$-0.694380\pi$
$631$		−	1033.92i		−	1.63854i	0.573411	−	0.819268i	$-0.305620\pi$
$632$		−	285.746i		−	0.452130i
$633$	−18.0212			−0.0284694
$634$	135.308			0.213420
$635$		0			0
$636$			154.899i			0.243552i
$637$	28.7958			0.0452053
$638$			801.662i			1.25652i
$639$	234.944			0.367674
$640$		0			0
$641$			188.175i			0.293564i	0.989169	+	0.146782i	$0.0468916\pi$
$641$			188.175i			0.293564i	−0.989169	+	0.146782i	$0.953108\pi$
$642$			120.983i			0.188446i
$643$			1055.82i			1.64203i	0.570909	+	0.821013i	$0.306591\pi$
$643$			1055.82i			1.64203i	−0.570909	+	0.821013i	$0.693409\pi$
$644$	−160.619	+	284.470i	−0.249409	+	0.441723i
$645$		0			0
$646$	−67.8629			−0.105051
$647$	443.636			0.685681			0.342841	−	0.939394i	$-0.388611\pi$
$647$	443.636			0.685681			0.342841	+	0.939394i	$0.388611\pi$
$648$	284.123			0.438462
$649$		−	742.197i		−	1.14360i
$650$		0			0
$651$		−	299.916i		−	0.460701i
$652$	150.666			0.231082
$653$	−117.465			−0.179886			−0.0899429	−	0.995947i	$-0.528668\pi$
$653$	−117.465			−0.179886			−0.0899429	+	0.995947i	$0.528668\pi$
$654$			162.239i			0.248072i
$655$		0			0
$656$	−28.9616			−0.0441487
$657$	−259.502			−0.394980
$658$			64.3451i			0.0977888i
$659$			664.743i			1.00871i	0.863495	+	0.504357i	$0.168270\pi$
$659$			664.743i			1.00871i	−0.863495	+	0.504357i	$0.831730\pi$
$660$		0			0
$661$			426.231i			0.644828i	0.946599	+	0.322414i	$0.104494\pi$
$661$			426.231i			0.644828i	−0.946599	+	0.322414i	$0.895506\pi$
$662$	−728.514			−1.10047
$663$			124.144i			0.187246i
$664$			289.656i			0.436229i
$665$		0			0
$666$			309.207i			0.464275i
$667$	1007.88	+	569.075i	1.51106	+	0.853185i
$668$	−544.918			−0.815745
$669$	−804.198			−1.20209
$670$		0			0
$671$	424.983			0.633358
$672$			152.411i			0.226802i
$673$	824.444			1.22503			0.612514	−	0.790460i	$-0.290158\pi$
$673$	824.444			1.22503			0.612514	+	0.790460i	$0.290158\pi$
$674$			356.089i			0.528322i
$675$		0			0
$676$	466.786			0.690512
$677$			530.039i			0.782924i	0.920194	+	0.391462i	$0.128031\pi$
$677$			530.039i			0.782924i	−0.920194	+	0.391462i	$0.871969\pi$
$678$		−	1145.14i		−	1.68899i
$679$	−1020.04			−1.50227
$680$		0			0
$681$			1479.36i			2.17233i
$682$		−	177.329i		−	0.260013i
$683$	−414.954			−0.607546			−0.303773	−	0.952744i	$-0.598246\pi$
$683$	−414.954			−0.607546			−0.303773	+	0.952744i	$0.598246\pi$
$684$			317.278i			0.463857i
$685$		0			0
$686$			477.712i			0.696373i
$687$			591.833i			0.861475i
$688$			286.808i			0.416872i
$689$		−	409.515i		−	0.594361i
$690$		0			0
$691$	−363.154			−0.525548			−0.262774	−	0.964857i	$-0.584637\pi$
$691$	−363.154			−0.525548			−0.262774	+	0.964857i	$0.584637\pi$
$692$	−523.630			−0.756691
$693$	431.415			0.622532
$694$	−237.445			−0.342139
$695$		0			0
$696$	539.993			0.775852
$697$			11.8111i			0.0169456i
$698$	−186.250			−0.266834
$699$	176.399			0.252360
$700$		0			0
$701$			928.839i			1.32502i	0.749053	+	0.662510i	$0.230509\pi$
$701$			928.839i			1.32502i	−0.749053	+	0.662510i	$0.769491\pi$
$702$	−388.218			−0.553017
$703$	1192.63			1.69648
$704$			90.1149i			0.128004i
$705$		0			0
$706$	329.064			0.466096
$707$		−	732.188i		−	1.03563i
$708$	−499.938			−0.706127
$709$		−	44.8088i		−	0.0632000i	−0.999501	−	0.0316000i	$-0.989940\pi$
$709$		−	44.8088i		−	0.0632000i	0.999501	−	0.0316000i	$-0.0100603\pi$
$710$		0			0
$711$			544.823i			0.766277i
$712$			27.2625i			0.0382900i
$713$	−222.944	−	125.880i	−0.312684	−	0.176550i
$714$	62.1563			0.0870536
$715$		0			0
$716$	−368.812			−0.515101
$717$	−1725.17			−2.40609
$718$		−	291.133i		−	0.405478i
$719$	1308.36			1.81969			0.909844	−	0.414950i	$-0.136201\pi$
$719$	1308.36			1.81969			0.909844	+	0.414950i	$0.136201\pi$
$720$		0			0
$721$	−702.110			−0.973800
$722$	713.223			0.987843
$723$		−	566.630i		−	0.783721i
$724$		−	383.734i		−	0.530019i
$725$		0			0
$726$	31.5797			0.0434982
$727$			515.858i			0.709570i	0.934948	+	0.354785i	$0.115446\pi$
$727$			515.858i			0.709570i	−0.934948	+	0.354785i	$0.884554\pi$
$728$		−	402.938i		−	0.553487i
$729$	−74.4769			−0.102163
$730$		0			0
$731$	116.966			0.160008
$732$		−	286.265i		−	0.391073i
$733$		−	405.638i		−	0.553394i	−0.960957	−	0.276697i	$-0.910760\pi$
$733$		−	405.638i		−	0.553394i	0.960957	−	0.276697i	$-0.0892398\pi$
$734$		−	224.019i		−	0.305203i
$735$		0			0
$736$	113.295	+	63.9698i	0.153934	+	0.0869155i
$737$	−1399.51			−1.89893
$738$	55.2201			0.0748240
$739$	601.397			0.813798			0.406899	−	0.913473i	$-0.366610\pi$
$739$	601.397			0.813798			0.406899	+	0.913473i	$0.366610\pi$
$740$		0			0
$741$		−	2238.66i		−	3.02114i
$742$	−205.035			−0.276327
$743$			775.124i			1.04324i	0.853179	+	0.521618i	$0.174671\pi$
$743$			775.124i			1.04324i	−0.853179	+	0.521618i	$0.825329\pi$
$744$	−119.447			−0.160548
$745$		0			0
$746$		−	94.8990i		−	0.127210i
$747$		−	552.278i		−	0.739328i
$748$	36.7506			0.0491319
$749$	−160.141			−0.213806
$750$		0			0
$751$			533.250i			0.710054i	0.934856	+	0.355027i	$0.115528\pi$
$751$			533.250i			0.710054i	−0.934856	+	0.355027i	$0.884472\pi$
$752$	25.6267			0.0340780
$753$		−	1382.89i		−	1.83650i
$754$	−1427.61			−1.89338
$755$		0			0
$756$			194.372i			0.257106i
$757$			794.660i			1.04975i	0.851180	+	0.524875i	$0.175888\pi$
$757$			794.660i			1.04975i	−0.851180	+	0.524875i	$0.824112\pi$
$758$		−	14.8537i		−	0.0195959i
$759$	483.260	−	855.890i	0.636706	−	1.12766i
$760$		0			0
$761$	−1322.01			−1.73720			−0.868599	−	0.495515i	$-0.834979\pi$
$761$	−1322.01			−1.73720			−0.868599	+	0.495515i	$0.834979\pi$
$762$	−160.694			−0.210884
$763$	−214.751			−0.281456
$764$			65.2371i			0.0853888i
$765$		0			0
$766$		−	510.500i		−	0.666449i
$767$	1321.71			1.72323
$768$	60.7007			0.0790374
$769$			1443.85i			1.87757i	0.344500	+	0.938786i	$0.388048\pi$
$769$			1443.85i			1.87757i	−0.344500	+	0.938786i	$0.611952\pi$
$770$		0			0
$771$	−226.523			−0.293804
$772$	−633.497			−0.820592
$773$		−	64.8298i		−	0.0838678i	−0.999120	−	0.0419339i	$-0.986648\pi$
$773$		−	64.8298i		−	0.0838678i	0.999120	−	0.0419339i	$-0.0133519\pi$
$774$		−	546.848i		−	0.706522i
$775$		0			0
$776$			406.251i			0.523519i
$777$	−1092.34			−1.40584
$778$		−	66.7905i		−	0.0858490i
$779$		−	212.986i		−	0.273410i
$780$		0			0
$781$			490.739i			0.628347i
$782$	26.0881	−	46.2041i	0.0333608	−	0.0590845i
$783$	688.659			0.879514
$784$	−5.74200			−0.00732398
$785$		0			0
$786$	624.976			0.795135
$787$			1247.04i			1.58455i	0.610163	+	0.792276i	$0.291104\pi$
$787$			1247.04i			1.58455i	−0.610163	+	0.792276i	$0.708896\pi$
$788$	389.892			0.494787
$789$			1070.17i			1.35637i
$790$		0			0
$791$	1515.78			1.91629
$792$		−	171.819i		−	0.216944i
$793$			756.815i			0.954370i
$794$	6.87062			0.00865317
$795$		0			0
$796$			148.163i			0.186134i
$797$			965.218i			1.21106i	0.795821	+	0.605532i	$0.207040\pi$
$797$			965.218i			1.21106i	−0.795821	+	0.605532i	$0.792960\pi$
$798$	−1120.85			−1.40457
$799$		−	10.4511i		−	0.0130802i
$800$		0			0
$801$		−	51.9805i		−	0.0648946i
$802$		−	420.731i		−	0.524602i
$803$		−	542.034i		−	0.675011i
$804$			942.701i			1.17251i
$805$		0			0
$806$	315.790			0.391799
$807$	56.0811			0.0694933
$808$	−291.608			−0.360901
$809$	−1310.48			−1.61988			−0.809939	−	0.586514i	$-0.800500\pi$
$809$	−1310.48			−1.61988			−0.809939	+	0.586514i	$0.800500\pi$
$810$		0			0
$811$	−1174.00			−1.44760			−0.723799	−	0.690010i	$-0.757606\pi$
$811$	−1174.00			−1.44760			−0.723799	+	0.690010i	$0.757606\pi$
$812$			714.772i			0.880261i
$813$	−131.702			−0.161995
$814$	−645.857			−0.793436
$815$		0			0
$816$		−	24.7549i		−	0.0303369i
$817$	−2109.22			−2.58166
$818$	−337.917			−0.413101
$819$			768.270i			0.938058i
$820$		0			0
$821$	−1238.00			−1.50791			−0.753956	−	0.656925i	$-0.771857\pi$
$821$	−1238.00			−1.50791			−0.753956	+	0.656925i	$0.771857\pi$
$822$		−	508.737i		−	0.618902i
$823$	937.653			1.13931			0.569656	−	0.821883i	$-0.307077\pi$
$823$	937.653			1.13931			0.569656	+	0.821883i	$0.307077\pi$
$824$			279.629i			0.339355i
$825$		0			0
$826$		−	661.753i		−	0.801153i
$827$		−	199.863i		−	0.241672i	−0.992672	−	0.120836i	$-0.961443\pi$
$827$		−	199.863i		−	0.241672i	0.992672	−	0.120836i	$-0.0385575\pi$
$828$	−216.017	−	121.969i	−0.260890	−	0.147306i
$829$	−892.787			−1.07695			−0.538473	−	0.842643i	$-0.680998\pi$
$829$	−892.787			−1.07695			−0.538473	+	0.842643i	$0.680998\pi$
$830$		0			0
$831$	724.774			0.872171
$832$	−160.478			−0.192882
$833$			2.34170i			0.00281117i
$834$	−478.994			−0.574334
$835$		0			0
$836$	−662.714			−0.792721
$837$	−152.333			−0.181998
$838$			279.046i			0.332991i
$839$		−	515.108i		−	0.613955i	−0.951717	−	0.306977i	$-0.900682\pi$
$839$		−	515.108i		−	0.613955i	0.951717	−	0.306977i	$-0.0993176\pi$
$840$		0			0
$841$	1691.44			2.01122
$842$			649.486i			0.771361i
$843$		−	1788.20i		−	2.12123i
$844$	−9.50033			−0.0112563
$845$		0			0
$846$	−48.8615			−0.0577560
$847$			41.8010i			0.0493519i
$848$			81.6590i			0.0962960i
$849$			89.0034i			0.104833i
$850$		0			0
$851$	−458.474	+	811.993i	−0.538747	+	0.954163i
$852$	330.558			0.387979
$853$	483.197			0.566467			0.283234	−	0.959051i	$-0.408593\pi$
$853$	483.197			0.566467			0.283234	+	0.959051i	$0.408593\pi$
$854$	378.920			0.443701
$855$		0			0
$856$			63.7792i			0.0745084i
$857$	−920.413			−1.07399			−0.536997	−	0.843584i	$-0.680441\pi$
$857$	−920.413			−1.07399			−0.536997	+	0.843584i	$0.680441\pi$
$858$			1212.33i			1.41297i
$859$	1173.30			1.36589			0.682947	−	0.730468i	$-0.260698\pi$
$859$	1173.30			1.36589			0.682947	+	0.730468i	$0.260698\pi$
$860$		0			0
$861$			195.076i			0.226569i
$862$		−	672.152i		−	0.779759i
$863$	−866.353			−1.00388			−0.501942	−	0.864901i	$-0.667381\pi$
$863$	−866.353			−1.00388			−0.501942	+	0.864901i	$0.667381\pi$
$864$	77.4123			0.0895976
$865$		0			0
$866$			981.901i			1.13384i
$867$	1086.31			1.25295
$868$		−	158.109i		−	0.182153i
$869$	−1138.00			−1.30955
$870$		0			0
$871$		−	2492.27i		−	2.86139i
$872$			85.5286i			0.0980833i
$873$		−	774.586i		−	0.887269i
$874$	−470.440	+	833.186i	−0.538261	+	0.953303i
$875$		0			0
$876$	−365.110			−0.416792
$877$	−281.590			−0.321084			−0.160542	−	0.987029i	$-0.551324\pi$
$877$	−281.590			−0.321084			−0.160542	+	0.987029i	$0.551324\pi$
$878$	978.823			1.11483
$879$			1097.50i			1.24858i
$880$		0			0
$881$			919.123i			1.04327i	0.853168	+	0.521636i	$0.174678\pi$
$881$			919.123i			1.04327i	−0.853168	+	0.521636i	$0.825322\pi$
$882$	10.9481			0.0124128
$883$	821.800			0.930691			0.465346	−	0.885129i	$-0.345930\pi$
$883$	821.800			0.930691			0.465346	+	0.885129i	$0.345930\pi$
$884$			65.4460i			0.0740340i
$885$		0			0
$886$	−398.901			−0.450226
$887$	−1280.91			−1.44409			−0.722047	−	0.691844i	$-0.756799\pi$
$887$	−1280.91			−1.44409			−0.722047	+	0.691844i	$0.756799\pi$
$888$			435.044i			0.489915i
$889$		−	212.705i		−	0.239263i
$890$		0			0
$891$		−	1131.54i		−	1.26996i
$892$	−423.955			−0.475286
$893$			188.461i			0.211043i
$894$			978.837i			1.09490i
$895$		0			0
$896$			80.3476i			0.0896737i
$897$	1524.18	+	860.595i	1.69920	+	0.959415i
$898$	6.38621			0.00711160
$899$	−560.180			−0.623114
$900$		0			0
$901$	33.3022			0.0369613
$902$			115.341i			0.127873i
$903$	1931.85			2.13937
$904$		−	603.690i		−	0.667798i
$905$		0			0
$906$	−159.674			−0.176241
$907$		−	1726.39i		−	1.90341i	−0.307021	−	0.951703i	$-0.599332\pi$
$907$		−	1726.39i		−	1.90341i	0.307021	−	0.951703i	$-0.400668\pi$
$908$			779.882i			0.858901i
$909$	556.000			0.611661
$910$		0			0
$911$		−	791.171i		−	0.868464i	−0.900801	−	0.434232i	$-0.857020\pi$
$911$		−	791.171i		−	0.868464i	0.900801	−	0.434232i	$-0.142980\pi$
$912$			446.399i			0.489473i
$913$	1153.57			1.26350
$914$		−	564.328i		−	0.617427i
$915$		0			0
$916$			312.001i			0.340612i
$917$			827.262i			0.902139i
$918$		−	31.5703i		−	0.0343903i
$919$		−	1272.36i		−	1.38451i	−0.721655	−	0.692253i	$-0.756618\pi$
$919$		−	1272.36i		−	1.38451i	0.721655	−	0.692253i	$-0.243382\pi$
$920$		0			0
$921$	2138.85			2.32231
$922$	−62.5842			−0.0678787
$923$	−873.915			−0.946820
$924$	606.986			0.656911
$925$		0			0
$926$	−945.060			−1.02058
$927$		−	533.159i		−	0.575145i
$928$	284.672			0.306758
$929$	672.653			0.724062			0.362031	−	0.932166i	$-0.382083\pi$
$929$	672.653			0.724062			0.362031	+	0.932166i	$0.382083\pi$
$930$		0			0
$931$		−	42.2273i		−	0.0453569i
$932$	92.9936			0.0997785
$933$	291.905			0.312867
$934$			947.735i			1.01471i
$935$		0			0
$936$	305.978			0.326900
$937$			1599.57i			1.70711i	0.520999	+	0.853557i	$0.325560\pi$
$937$			1599.57i			1.70711i	−0.520999	+	0.853557i	$0.674440\pi$
$938$	−1247.82			−1.33030
$939$		−	1657.03i		−	1.76467i
$940$		0			0
$941$			1628.06i			1.73014i	0.501651	+	0.865070i	$0.332726\pi$
$941$			1628.06i			1.73014i	−0.501651	+	0.865070i	$0.667274\pi$
$942$		−	343.961i		−	0.365140i
$943$	145.011	+	81.8770i	0.153776	+	0.0868261i
$944$	−263.556			−0.279190
$945$		0			0
$946$	1142.23			1.20743
$947$	1829.88			1.93229			0.966147	−	0.257992i	$-0.0830608\pi$
$947$	1829.88			1.93229			0.966147	+	0.257992i	$0.0830608\pi$
$948$			766.547i			0.808594i
$949$	965.262			1.01714
$950$		0			0
$951$	−362.980			−0.381683
$952$	32.7673			0.0344195
$953$		−	655.714i		−	0.688053i	−0.938960	−	0.344026i	$-0.888209\pi$
$953$		−	655.714i		−	0.688053i	0.938960	−	0.344026i	$-0.111791\pi$
$954$		−	155.697i		−	0.163204i
$955$		0			0
$956$	−909.469			−0.951328
$957$		−	2150.55i		−	2.24718i
$958$		−	439.102i		−	0.458353i
$959$	673.400			0.702190
$960$		0			0
$961$	−837.087			−0.871059
$962$		−	1150.15i		−	1.19558i
$963$		−	121.606i		−	0.126278i
$964$		−	298.714i		−	0.309870i
$965$		0			0
$966$	430.880	−	763.123i	0.446046	−	0.789982i
$967$	−143.641			−0.148543			−0.0742716	−	0.997238i	$-0.523663\pi$
$967$	−143.641			−0.148543			−0.0742716	+	0.997238i	$0.523663\pi$
$968$	16.6481			0.0171984
$969$	182.050			0.187874
$970$		0			0
$971$			1107.60i			1.14068i	0.821408	+	0.570341i	$0.193189\pi$
$971$			1107.60i			1.14068i	−0.821408	+	0.570341i	$0.806811\pi$
$972$	−515.870			−0.530730
$973$		−	634.030i		−	0.651624i
$974$	1173.29			1.20461
$975$		0			0
$976$		−	150.912i		−	0.154623i
$977$			626.322i			0.641066i	0.947237	+	0.320533i	$0.103862\pi$
$977$			626.322i			0.641066i	−0.947237	+	0.320533i	$0.896138\pi$
$978$	−404.178			−0.413270
$979$	108.574			0.110903
$980$		0			0
$981$		−	163.075i		−	0.166233i
$982$	175.071			0.178280
$983$		−	202.538i		−	0.206041i	−0.994679	−	0.103020i	$-0.967149\pi$
$983$		−	202.538i		−	0.206041i	0.994679	−	0.103020i	$-0.0328507\pi$
$984$	77.6928			0.0789561
$985$		0			0
$986$		−	116.095i		−	0.117743i
$987$		−	172.613i		−	0.174887i
$988$		−	1180.17i		−	1.19450i
$989$	810.833	−	1436.05i	0.819851	−	1.45202i
$990$		0			0
$991$	354.302			0.357520			0.178760	−	0.983893i	$-0.442791\pi$
$991$	354.302			0.357520			0.178760	+	0.983893i	$0.442791\pi$
$992$	−62.9699			−0.0634777
$993$	1954.33			1.96810
$994$			437.549i			0.440190i
$995$		0			0
$996$		−	777.037i		−	0.780157i
$997$	−184.596			−0.185152			−0.0925758	−	0.995706i	$-0.529510\pi$
$997$	−184.596			−0.185152			−0.0925758	+	0.995706i	$0.529510\pi$
$998$	−1071.86			−1.07401
$999$			554.817i			0.555372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.3.d.b.551.7		16
5.2	odd	4		1150.3.c.c.1149.23		32
5.3	odd	4		1150.3.c.c.1149.10		32
5.4	even	2		230.3.d.a.91.9	✓	16
15.14	odd	2		2070.3.c.a.91.8		16
20.19	odd	2		1840.3.k.d.321.13		16
23.22	odd	2	inner	1150.3.d.b.551.8		16
115.22	even	4		1150.3.c.c.1149.9		32
115.68	even	4		1150.3.c.c.1149.24		32
115.114	odd	2		230.3.d.a.91.10	yes	16
345.344	even	2		2070.3.c.a.91.1		16
460.459	even	2		1840.3.k.d.321.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.d.a.91.9	✓	16	5.4	even	2
230.3.d.a.91.10	yes	16	115.114	odd	2
1150.3.c.c.1149.9		32	115.22	even	4
1150.3.c.c.1149.10		32	5.3	odd	4
1150.3.c.c.1149.23		32	5.2	odd	4
1150.3.c.c.1149.24		32	115.68	even	4
1150.3.d.b.551.7		16	1.1	even	1	trivial
1150.3.d.b.551.8		16	23.22	odd	2	inner
1840.3.k.d.321.13		16	20.19	odd	2
1840.3.k.d.321.14		16	460.459	even	2
2070.3.c.a.91.1		16	345.344	even	2
2070.3.c.a.91.8		16	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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1150.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +3.79379 q^{3} +2.00000 q^{4} -5.36524 q^{6} -7.10180i q^{7} -2.82843 q^{8} +5.39287 q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +3.79379 q^{3} +2.00000 q^{4} -5.36524 q^{6} -7.10180i q^{7} -2.82843 q^{8} +5.39287 q^{9} +11.2644i q^{11} +7.58759 q^{12} -20.0597 q^{13} +10.0435i q^{14} +4.00000 q^{16} -1.63128i q^{17} -7.62667 q^{18} +29.4164i q^{19} -26.9428i q^{21} -15.9302i q^{22} +(-20.0280 - 11.3084i) q^{23} -10.7305 q^{24} +28.3688 q^{26} -13.6847 q^{27} -14.2036i q^{28} -50.3233 q^{29} +11.1316 q^{31} -5.65685 q^{32} +42.7347i q^{33} +2.30698i q^{34} +10.7857 q^{36} -40.5429i q^{37} -41.6011i q^{38} -76.1025 q^{39} -7.24039 q^{41} +38.1028i q^{42} +71.7020i q^{43} +22.5287i q^{44} +(28.3239 + 15.9924i) q^{46} +6.40666 q^{47} +15.1752 q^{48} -1.43550 q^{49} -6.18873i q^{51} -40.1195 q^{52} +20.4148i q^{53} +19.3531 q^{54} +20.0869i q^{56} +111.600i q^{57} +71.1679 q^{58} -65.8889 q^{59} -37.7281i q^{61} -15.7425 q^{62} -38.2991i q^{63} +8.00000 q^{64} -60.4360i q^{66} +124.242i q^{67} -3.26256i q^{68} +(-75.9821 - 42.9016i) q^{69} +43.5656 q^{71} -15.2533 q^{72} -48.1194 q^{73} +57.3363i q^{74} +58.8328i q^{76} +79.9972 q^{77} +107.625 q^{78} +101.026i q^{79} -100.453 q^{81} +10.2395 q^{82} -102.409i q^{83} -53.8855i q^{84} -101.402i q^{86} -190.916 q^{87} -31.8604i q^{88} -9.63875i q^{89} +142.460i q^{91} +(-40.0560 - 22.6167i) q^{92} +42.2310 q^{93} -9.06039 q^{94} -21.4609 q^{96} -143.631i q^{97} +2.03010 q^{98} +60.7473i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) \) 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9	\( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9} - 24 q^{13} + 64 q^{16} + 32 q^{18} - 4 q^{23} - 16 q^{24} + 96 q^{26} + 96 q^{27} - 108 q^{29} - 116 q^{31} + 128 q^{36} + 248 q^{39} - 156 q^{41} - 124 q^{46} + 128 q^{47} - 28 q^{49} - 48 q^{52} + 224 q^{54} - 160 q^{58} + 204 q^{59} - 64 q^{62} + 128 q^{64} - 268 q^{69} + 236 q^{71} + 64 q^{72} + 112 q^{73} + 936 q^{77} + 432 q^{78} - 136 q^{81} + 64 q^{82} + 152 q^{87} - 8 q^{92} - 856 q^{93} - 216 q^{94} - 32 q^{96} - 256 q^{98}+O(q^{100}) \) 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9 - 24 * q^13 + 64 * q^16 + 32 * q^18 - 4 * q^23 - 16 * q^24 + 96 * q^26 + 96 * q^27 - 108 * q^29 - 116 * q^31 + 128 * q^36 + 248 * q^39 - 156 * q^41 - 124 * q^46 + 128 * q^47 - 28 * q^49 - 48 * q^52 + 224 * q^54 - 160 * q^58 + 204 * q^59 - 64 * q^62 + 128 * q^64 - 268 * q^69 + 236 * q^71 + 64 * q^72 + 112 * q^73 + 936 * q^77 + 432 * q^78 - 136 * q^81 + 64 * q^82 + 152 * q^87 - 8 * q^92 - 856 * q^93 - 216 * q^94 - 32 * q^96 - 256 * q^98

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