LMFDB - Embedded newform 1150.3.c.c.1149.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,3,Mod(1149,1150)]

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([1, 1]))

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

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

chi := DirichletCharacter("1150.1149");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1150.c (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:	$31.3352304014$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 230)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1149.10
Character	$\chi$	$=$	1150.1149
Dual form			1150.3.c.c.1149.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +3.79379i q^{3} -2.00000 q^{4} -5.36524 q^{6} -7.10180 q^{7} -2.82843i q^{8} -5.39287 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +3.79379i q^{3} -2.00000 q^{4} -5.36524 q^{6} -7.10180 q^{7} -2.82843i q^{8} -5.39287 q^{9} +11.2644i q^{11} -7.58759i q^{12} -20.0597i q^{13} -10.0435i q^{14} +4.00000 q^{16} -1.63128 q^{17} -7.62667i q^{18} -29.4164i q^{19} -26.9428i q^{21} -15.9302 q^{22} +(11.3084 - 20.0280i) q^{23} +10.7305 q^{24} +28.3688 q^{26} +13.6847i q^{27} +14.2036 q^{28} +50.3233 q^{29} +11.1316 q^{31} +5.65685i q^{32} -42.7347 q^{33} -2.30698i q^{34} +10.7857 q^{36} -40.5429 q^{37} +41.6011 q^{38} +76.1025 q^{39} -7.24039 q^{41} +38.1028 q^{42} -71.7020 q^{43} -22.5287i q^{44} +(28.3239 + 15.9924i) q^{46} -6.40666i q^{47} +15.1752i q^{48} +1.43550 q^{49} -6.18873i q^{51} +40.1195i q^{52} -20.4148 q^{53} -19.3531 q^{54} +20.0869i q^{56} +111.600 q^{57} +71.1679i q^{58} +65.8889 q^{59} -37.7281i q^{61} +15.7425i q^{62} +38.2991 q^{63} -8.00000 q^{64} -60.4360i q^{66} +124.242 q^{67} +3.26256 q^{68} +(75.9821 + 42.9016i) q^{69} +43.5656 q^{71} +15.2533i q^{72} -48.1194i q^{73} -57.3363i q^{74} +58.8328i q^{76} -79.9972i q^{77} +107.625i q^{78} -101.026i q^{79} -100.453 q^{81} -10.2395i q^{82} +102.409 q^{83} +53.8855i q^{84} -101.402i q^{86} +190.916i q^{87} +31.8604 q^{88} +9.63875i q^{89} +142.460i q^{91} +(-22.6167 + 40.0560i) q^{92} +42.2310i q^{93} +9.06039 q^{94} -21.4609 q^{96} -143.631 q^{97} +2.03010i q^{98} -60.7473i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 64 q^{4} - 16 q^{6} - 128 q^{9}+O(q^{10}) $ 32 * q - 64 * q^4 - 16 * q^6 - 128 * q^9	$ 32 q - 64 q^{4} - 16 q^{6} - 128 q^{9} + 128 q^{16} + 32 q^{24} + 192 q^{26} + 216 q^{29} - 232 q^{31} + 256 q^{36} - 496 q^{39} - 312 q^{41} - 248 q^{46} + 56 q^{49} - 448 q^{54} - 408 q^{59} - 256 q^{64} + 536 q^{69} + 472 q^{71} - 272 q^{81} + 432 q^{94} - 64 q^{96}+O(q^{100}) $ 32 * q - 64 * q^4 - 16 * q^6 - 128 * q^9 + 128 * q^16 + 32 * q^24 + 192 * q^26 + 216 * q^29 - 232 * q^31 + 256 * q^36 - 496 * q^39 - 312 * q^41 - 248 * q^46 + 56 * q^49 - 448 * q^54 - 408 * q^59 - 256 * q^64 + 536 * q^69 + 472 * q^71 - 272 * q^81 + 432 * q^94 - 64 * q^96

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$			3.79379i			1.26460i	0.774724	+	0.632299i	$0.217889\pi$
$3$			3.79379i			1.26460i	−0.774724	+	0.632299i	$0.782111\pi$
$4$	−2.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	−5.36524			−0.894206
$7$	−7.10180			−1.01454			−0.507271	−	0.861787i	$-0.669346\pi$
$7$	−7.10180			−1.01454			−0.507271	+	0.861787i	$0.669346\pi$
$8$		−	2.82843i		−	0.353553i
$9$	−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	$0.828899\pi$
$12$		−	7.58759i		−	0.632299i
$13$		−	20.0597i		−	1.54306i	−0.636195	−	0.771528i	$-0.719493\pi$
$13$		−	20.0597i		−	1.54306i	0.636195	−	0.771528i	$-0.280507\pi$
$14$		−	10.0435i		−	0.717390i
$15$		0			0
$16$	4.00000			0.250000
$17$	−1.63128			−0.0959575			−0.0479788	−	0.998848i	$-0.515278\pi$
$17$	−1.63128			−0.0959575			−0.0479788	+	0.998848i	$0.515278\pi$
$18$		−	7.62667i		−	0.423704i
$19$		−	29.4164i		−	1.54823i	−0.633044	−	0.774116i	$-0.718195\pi$
$19$		−	29.4164i		−	1.54823i	0.633044	−	0.774116i	$-0.281805\pi$
$20$		0			0
$21$		−	26.9428i		−	1.28299i
$22$	−15.9302			−0.724101
$23$	11.3084	−	20.0280i	0.491668	−	0.870783i
$23$	11.3084	−	20.0280i	0.491668	−	0.870783i
$24$	10.7305			0.447103
$25$		0			0
$26$	28.3688			1.09111
$27$			13.6847i			0.506841i
$28$	14.2036			0.507271
$29$	50.3233			1.73529			0.867644	−	0.497187i	$-0.165634\pi$
$29$	50.3233			1.73529			0.867644	+	0.497187i	$0.165634\pi$
$30$		0			0
$31$	11.1316			0.359084			0.179542	−	0.983750i	$-0.442538\pi$
$31$	11.1316			0.359084			0.179542	+	0.983750i	$0.442538\pi$
$32$			5.65685i			0.176777i
$33$	−42.7347			−1.29499
$34$		−	2.30698i		−	0.0678522i
$35$		0			0
$36$	10.7857			0.299604
$37$	−40.5429			−1.09575			−0.547877	−	0.836559i	$-0.684564\pi$
$37$	−40.5429			−1.09575			−0.547877	+	0.836559i	$0.684564\pi$
$38$	41.6011			1.09477
$39$	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	$0.528143\pi$
$42$	38.1028			0.907210
$43$	−71.7020			−1.66749			−0.833745	−	0.552150i	$-0.813808\pi$
$43$	−71.7020			−1.66749			−0.833745	+	0.552150i	$0.813808\pi$
$44$		−	22.5287i		−	0.512017i
$45$		0			0
$46$	28.3239	+	15.9924i	0.615736	+	0.347662i
$47$		−	6.40666i		−	0.136312i	−0.997675	−	0.0681560i	$-0.978288\pi$
$47$		−	6.40666i		−	0.136312i	0.997675	−	0.0681560i	$-0.0217116\pi$
$48$			15.1752i			0.316150i
$49$	1.43550			0.0292959
$50$		0			0
$51$		−	6.18873i		−	0.121348i
$52$			40.1195i			0.771528i
$53$	−20.4148			−0.385184			−0.192592	−	0.981279i	$-0.561689\pi$
$53$	−20.4148			−0.385184			−0.192592	+	0.981279i	$0.561689\pi$
$54$	−19.3531			−0.358390
$55$		0			0
$56$			20.0869i			0.358695i
$57$	111.600			1.95789
$58$			71.1679i			1.22703i
$59$	65.8889			1.11676			0.558381	−	0.829585i	$-0.311423\pi$
$59$	65.8889			1.11676			0.558381	+	0.829585i	$0.311423\pi$
$60$		0			0
$61$		−	37.7281i		−	0.618493i	−0.950982	−	0.309247i	$-0.899923\pi$
$61$		−	37.7281i		−	0.618493i	0.950982	−	0.309247i	$-0.100077\pi$
$62$			15.7425i			0.253911i
$63$	38.2991			0.607922
$64$	−8.00000			−0.125000
$65$		0			0
$66$		−	60.4360i		−	0.915697i
$67$	124.242			1.85437			0.927183	−	0.374609i	$-0.122223\pi$
$67$	124.242			1.85437			0.927183	+	0.374609i	$0.122223\pi$
$68$	3.26256			0.0479788
$69$	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	$0.400742\pi$
$72$			15.2533i			0.211852i
$73$		−	48.1194i		−	0.659169i	−0.944126	−	0.329585i	$-0.893091\pi$
$73$		−	48.1194i		−	0.659169i	0.944126	−	0.329585i	$-0.106909\pi$
$74$		−	57.3363i		−	0.774815i
$75$		0			0
$76$			58.8328i			0.774116i
$77$		−	79.9972i		−	1.03893i
$78$			107.625i			1.37981i
$79$		−	101.026i		−	1.27882i	−0.768868	−	0.639408i	$-0.779179\pi$
$79$		−	101.026i		−	1.27882i	0.768868	−	0.639408i	$-0.220821\pi$
$80$		0			0
$81$	−100.453			−1.24016
$82$		−	10.2395i		−	0.124871i
$83$	102.409			1.23384			0.616921	−	0.787025i	$-0.288380\pi$
$83$	102.409			1.23384			0.616921	+	0.787025i	$0.288380\pi$
$84$			53.8855i			0.641494i
$85$		0			0
$86$		−	101.402i		−	1.17909i
$87$			190.916i			2.19444i
$88$	31.8604			0.362050
$89$			9.63875i			0.108301i	0.998533	+	0.0541503i	$0.0172450\pi$
$89$			9.63875i			0.108301i	−0.998533	+	0.0541503i	$0.982755\pi$
$90$		0			0
$91$			142.460i			1.56550i
$92$	−22.6167	+	40.0560i	−0.245834	+	0.435391i
$93$			42.2310i			0.454097i
$94$	9.06039			0.0963871
$95$		0			0
$96$	−21.4609			−0.223551
$97$	−143.631			−1.48074			−0.740368	−	0.672202i	$-0.765349\pi$
$97$	−143.631			−1.48074			−0.740368	+	0.672202i	$0.765349\pi$
$98$			2.03010i			0.0207154i
$99$		−	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	$0.329501\pi$
$102$	8.75219			0.0858058
$103$	98.8637			0.959841			0.479921	−	0.877312i	$-0.340665\pi$
$103$	98.8637			0.959841			0.479921	+	0.877312i	$0.340665\pi$
$104$	−56.7375			−0.545553
$105$		0			0
$106$		−	28.8708i		−	0.272366i
$107$	−22.5494			−0.210742			−0.105371	−	0.994433i	$-0.533603\pi$
$107$	−22.5494			−0.210742			−0.105371	+	0.994433i	$0.533603\pi$
$108$		−	27.3694i		−	0.253420i
$109$			30.2389i			0.277421i	0.990333	+	0.138711i	$0.0442958\pi$
$109$			30.2389i			0.277421i	−0.990333	+	0.138711i	$0.955704\pi$
$110$		0			0
$111$		−	153.811i		−	1.38569i
$112$	−28.4072			−0.253636
$113$	−213.437			−1.88882			−0.944410	−	0.328771i	$-0.893365\pi$
$113$	−213.437			−1.88882			−0.944410	+	0.328771i	$0.893365\pi$
$114$			157.826i			1.38444i
$115$		0			0
$116$	−100.647			−0.867644
$117$			108.180i			0.924612i
$118$			93.1810i			0.789670i
$119$	11.5850			0.0973530
$120$		0			0
$121$	−5.88598			−0.0486445
$122$	53.3556			0.437341
$123$		−	27.4686i		−	0.223322i
$124$	−22.2632			−0.179542
$125$		0			0
$126$			54.1631i			0.429866i
$127$		−	29.9509i		−	0.235834i	−0.993023	−	0.117917i	$-0.962378\pi$
$127$		−	29.9509i		−	0.235834i	0.993023	−	0.117917i	$-0.0376216\pi$
$128$		−	11.3137i		−	0.0883883i
$129$		−	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	$0.646656\pi$
$132$	85.4694			0.647495
$133$			208.909i			1.57075i
$134$			175.705i			1.31123i
$135$		0			0
$136$			4.61395i			0.0339261i
$137$	94.8211			0.692125			0.346062	−	0.938212i	$-0.387519\pi$
$137$	94.8211			0.692125			0.346062	+	0.938212i	$0.387519\pi$
$138$	−60.6720	+	107.455i	−0.439653	+	0.778659i
$139$	−89.2774			−0.642284			−0.321142	−	0.947031i	$-0.604067\pi$
$139$	−89.2774			−0.642284			−0.321142	+	0.947031i	$0.604067\pi$
$140$		0			0
$141$	24.3056			0.172380
$142$			61.6111i			0.433881i
$143$	225.960			1.58014
$144$	−21.5715			−0.149802
$145$		0			0
$146$	68.0510			0.466103
$147$			5.44599i			0.0370476i
$148$	81.0857			0.547877
$149$			182.441i			1.22443i	0.790690	+	0.612217i	$0.209722\pi$
$149$			182.441i			1.22443i	−0.790690	+	0.612217i	$0.790278\pi$
$150$		0			0
$151$	29.7608			0.197092			0.0985458	−	0.995133i	$-0.468581\pi$
$151$	29.7608			0.197092			0.0985458	+	0.995133i	$0.468581\pi$
$152$	−83.2022			−0.547383
$153$	8.79728			0.0574985
$154$	113.133			0.734631
$155$		0			0
$156$	−152.205			−0.975673
$157$	64.1093			0.408340			0.204170	−	0.978935i	$-0.434551\pi$
$157$	64.1093			0.408340			0.204170	+	0.978935i	$0.434551\pi$
$158$	142.873			0.904260
$159$		−	77.4494i		−	0.487103i
$160$		0			0
$161$	−80.3097	+	142.235i	−0.498818	+	0.883446i
$162$		−	142.062i		−	0.876924i
$163$			75.3328i			0.462164i	0.972934	+	0.231082i	$0.0742266\pi$
$163$			75.3328i			0.462164i	−0.972934	+	0.231082i	$0.925773\pi$
$164$	14.4808			0.0882975
$165$		0			0
$166$			144.828i			0.872458i
$167$			272.459i			1.63149i	0.578412	+	0.815745i	$0.303673\pi$
$167$			272.459i			1.63149i	−0.578412	+	0.815745i	$0.696327\pi$
$168$	−76.2056			−0.453605
$169$	−233.393			−1.38102
$170$		0			0
$171$			158.639i			0.927713i
$172$	143.404			0.833745
$173$		−	261.815i		−	1.51338i	−0.653773	−	0.756691i	$-0.726815\pi$
$173$		−	261.815i		−	1.51338i	0.653773	−	0.756691i	$-0.273185\pi$
$174$	−269.996			−1.55170
$175$		0			0
$176$			45.0575i			0.256008i
$177$			249.969i			1.41225i
$178$	−13.6312			−0.0765800
$179$	184.406			1.03020			0.515101	−	0.857130i	$-0.327754\pi$
$179$	184.406			1.03020			0.515101	+	0.857130i	$0.327754\pi$
$180$		0			0
$181$		−	191.867i		−	1.06004i	−0.847986	−	0.530019i	$-0.822185\pi$
$181$		−	191.867i		−	1.06004i	0.847986	−	0.530019i	$-0.177815\pi$
$182$	−201.469			−1.10697
$183$	143.133			0.782145
$184$	−56.6477	−	31.9849i	−0.307868	−	0.173831i
$185$		0			0
$186$	−59.7237			−0.321095
$187$		−	18.3753i		−	0.0982637i
$188$			12.8133i			0.0681560i
$189$		−	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	$0.972787\pi$
$192$		−	30.3504i		−	0.158075i
$193$		−	316.748i		−	1.64118i	−0.571515	−	0.820592i	$-0.693644\pi$
$193$		−	316.748i		−	1.64118i	0.571515	−	0.820592i	$-0.306356\pi$
$194$		−	203.125i		−	1.04704i
$195$		0			0
$196$	−2.87100			−0.0146480
$197$		−	194.946i		−	0.989573i	−0.869015	−	0.494787i	$-0.835246\pi$
$197$		−	194.946i		−	0.989573i	0.869015	−	0.494787i	$-0.164754\pi$
$198$	85.9097			0.433887
$199$		−	74.0815i		−	0.372269i	−0.982524	−	0.186134i	$-0.940404\pi$
$199$		−	74.0815i		−	0.372269i	0.982524	−	0.186134i	$-0.0595960\pi$
$200$		0			0
$201$			471.350i			2.34503i
$202$			145.804i			0.721802i
$203$	−357.386			−1.76052
$204$			12.3775i			0.0606739i
$205$		0			0
$206$			139.814i			0.678710i
$207$	−60.9846	+	108.008i	−0.294612	+	0.521780i
$208$		−	80.2390i		−	0.385764i
$209$	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	$0.503583\pi$
$212$	40.8295			0.192592
$213$			165.279i			0.775958i
$214$		−	31.8896i		−	0.149017i
$215$		0			0
$216$	38.7062			0.179195
$217$	−79.0544			−0.364306
$218$	−42.7643			−0.196167
$219$	182.555			0.833584
$220$		0			0
$221$			32.7230i			0.148068i
$222$	217.522			0.979829
$223$		−	211.977i		−	0.950571i	−0.879832	−	0.475286i	$-0.842345\pi$
$223$		−	211.977i		−	0.950571i	0.879832	−	0.475286i	$-0.157655\pi$
$224$		−	40.1738i		−	0.179347i
$225$		0			0
$226$		−	301.845i		−	1.33560i
$227$	389.941			1.71780			0.858901	−	0.512141i	$-0.171148\pi$
$227$	389.941			1.71780			0.858901	+	0.512141i	$0.171148\pi$
$228$	−223.200			−0.978945
$229$		−	156.000i		−	0.681224i	−0.940204	−	0.340612i	$-0.889366\pi$
$229$		−	156.000i		−	0.681224i	0.940204	−	0.340612i	$-0.110634\pi$
$230$		0			0
$231$	303.493			1.31382
$232$		−	142.336i		−	0.613517i
$233$			46.4968i			0.199557i	0.995010	+	0.0997785i	$0.0318134\pi$
$233$			46.4968i			0.199557i	−0.995010	+	0.0997785i	$0.968187\pi$
$234$	−152.989			−0.653800
$235$		0			0
$236$	−131.778			−0.558381
$237$	383.274			1.61719
$238$			16.3837i			0.0688389i
$239$	454.735			1.90266			0.951328	−	0.308181i	$-0.0997201\pi$
$239$	454.735			1.90266			0.951328	+	0.308181i	$0.0997201\pi$
$240$		0			0
$241$		−	149.357i		−	0.619739i	−0.950779	−	0.309870i	$-0.899715\pi$
$241$		−	149.357i		−	0.619739i	0.950779	−	0.309870i	$-0.100285\pi$
$242$		−	8.32404i		−	0.0343968i
$243$		−	257.935i		−	1.06146i
$244$			75.4562i			0.309247i
$245$		0			0
$246$	38.8464			0.157912
$247$	−590.085			−2.38901
$248$		−	31.4849i		−	0.126955i
$249$			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	$-0.258679\pi$
$252$	−76.5982			−0.303961
$253$	225.603	+	127.382i	0.891711	+	0.503485i
$254$	42.3570			0.166760
$255$		0			0
$256$	16.0000			0.0625000
$257$			59.7088i			0.232330i	0.993230	+	0.116165i	$0.0370601\pi$
$257$			59.7088i			0.232330i	−0.993230	+	0.116165i	$0.962940\pi$
$258$	384.698			1.49108
$259$	287.927			1.11169
$260$		0			0
$261$	−271.387			−1.03980
$262$		−	164.736i		−	0.628765i
$263$	−282.085			−1.07257			−0.536284	−	0.844038i	$-0.680172\pi$
$263$	−282.085			−1.07257			−0.536284	+	0.844038i	$0.680172\pi$
$264$			120.872i			0.457848i
$265$		0			0
$266$	−295.442			−1.11069
$267$	−36.5674			−0.136957
$268$	−248.485			−0.927183
$269$	−14.7823			−0.0549529			−0.0274764	−	0.999622i	$-0.508747\pi$
$269$	−14.7823			−0.0549529			−0.0274764	+	0.999622i	$0.508747\pi$
$270$		0			0
$271$	−34.7150			−0.128100			−0.0640499	−	0.997947i	$-0.520402\pi$
$271$	−34.7150			−0.128100			−0.0640499	+	0.997947i	$0.520402\pi$
$272$	−6.52511			−0.0239894
$273$	−540.465			−1.97972
$274$			134.097i			0.489406i
$275$		0			0
$276$	−151.964	−	85.8032i	−0.550595	−	0.310881i
$277$		−	191.042i		−	0.689682i	−0.938661	−	0.344841i	$-0.887933\pi$
$277$		−	191.042i		−	0.689682i	0.938661	−	0.344841i	$-0.112067\pi$
$278$		−	126.257i		−	0.454163i
$279$	−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	$-0.316683\pi$
$282$			34.3733i			0.121891i
$283$	−23.4603			−0.0828984			−0.0414492	−	0.999141i	$-0.513197\pi$
$283$	−23.4603			−0.0828984			−0.0414492	+	0.999141i	$0.513197\pi$
$284$	−87.1312			−0.306800
$285$		0			0
$286$			319.556i			1.11733i
$287$	51.4198			0.179163
$288$		−	30.5067i		−	0.105926i
$289$	−286.339			−0.990792
$290$		0			0
$291$		−	544.908i		−	1.87254i
$292$			96.2387i			0.329585i
$293$	−289.288			−0.987331			−0.493666	−	0.869652i	$-0.664343\pi$
$293$	−289.288			−0.987331			−0.493666	+	0.869652i	$0.664343\pi$
$294$	−7.70180			−0.0261966
$295$		0			0
$296$			114.673i			0.387407i
$297$	−154.149			−0.519022
$298$	−258.010			−0.865805
$299$	−401.756	−	226.843i	−1.34367	−	0.758672i
$300$		0			0
$301$	509.213			1.69174
$302$			42.0882i			0.139365i
$303$			391.136i			1.29088i
$304$		−	117.666i		−	0.387058i
$305$		0			0
$306$			12.4412i			0.0406576i
$307$		−	563.775i		−	1.83640i	−0.396117	−	0.918200i	$-0.629642\pi$
$307$		−	563.775i		−	1.83640i	0.396117	−	0.918200i	$-0.370358\pi$
$308$			159.994i			0.519463i
$309$			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	$0.460523\pi$
$312$		−	215.250i		−	0.689905i
$313$	436.773			1.39544			0.697721	−	0.716370i	$-0.254198\pi$
$313$	436.773			1.39544			0.697721	+	0.716370i	$0.254198\pi$
$314$			90.6643i			0.288740i
$315$		0			0
$316$			202.053i			0.639408i
$317$			95.6774i			0.301822i	0.988547	+	0.150911i	$0.0482206\pi$
$317$			95.6774i			0.301822i	−0.988547	+	0.150911i	$0.951779\pi$
$318$	109.530			0.344434
$319$			566.860i			1.77699i
$320$		0			0
$321$		−	85.5476i		−	0.266503i
$322$	−201.150	−	113.575i	−0.624691	−	0.352718i
$323$			47.9863i			0.148565i
$324$	200.906			0.620079
$325$		0			0
$326$	−106.537			−0.326799
$327$	−114.720			−0.350827
$328$			20.4789i			0.0624357i
$329$			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	$0.216157\pi$
$332$	−204.818			−0.616921
$333$	218.643			0.656584
$334$	−385.315			−1.15364
$335$		0			0
$336$		−	107.771i		−	0.320747i
$337$	−251.793			−0.747161			−0.373580	−	0.927598i	$-0.621870\pi$
$337$	−251.793			−0.747161			−0.373580	+	0.927598i	$0.621870\pi$
$338$		−	330.068i		−	0.976532i
$339$		−	809.734i		−	2.38860i
$340$		0			0
$341$			125.391i			0.367714i
$342$	−224.349			−0.655992
$343$	337.793			0.984820
$344$			202.804i			0.589547i
$345$		0			0
$346$	370.262			1.07012
$347$		−	167.899i		−	0.483858i	−0.970294	−	0.241929i	$-0.922220\pi$
$347$		−	167.899i		−	0.483858i	0.970294	−	0.241929i	$-0.0777801\pi$
$348$		−	381.833i		−	1.09722i
$349$	−131.699			−0.377360			−0.188680	−	0.982039i	$-0.560421\pi$
$349$	−131.699			−0.377360			−0.188680	+	0.982039i	$0.560421\pi$
$350$		0			0
$351$	274.511			0.782084
$352$	−63.7209			−0.181025
$353$		−	232.683i		−	0.659159i	−0.944128	−	0.329580i	$-0.893093\pi$
$353$		−	232.683i		−	0.659159i	0.944128	−	0.329580i	$-0.106907\pi$
$354$	−353.510			−0.998615
$355$		0			0
$356$		−	19.2775i		−	0.0541503i
$357$			43.9511i			0.123112i
$358$			260.790i			0.728463i
$359$		−	205.862i		−	0.573432i	−0.958016	−	0.286716i	$-0.907436\pi$
$359$		−	205.862i		−	0.573432i	0.958016	−	0.286716i	$-0.0925636\pi$
$360$		0			0
$361$	−504.325			−1.39702
$362$	271.341			0.749560
$363$		−	22.3302i		−	0.0615157i
$364$		−	284.920i		−	0.782748i
$365$		0			0
$366$			202.420i			0.553060i
$367$	158.406			0.431623			0.215811	−	0.976435i	$-0.430760\pi$
$367$	158.406			0.431623			0.215811	+	0.976435i	$0.430760\pi$
$368$	45.2335	−	80.1120i	0.122917	−	0.217696i
$369$	39.0465			0.105817
$370$		0			0
$371$	144.981			0.390786
$372$		−	84.4621i		−	0.227049i
$373$	−67.1037			−0.179903			−0.0899513	−	0.995946i	$-0.528671\pi$
$373$	−67.1037			−0.179903			−0.0899513	+	0.995946i	$0.528671\pi$
$374$	25.9866			0.0694829
$375$		0			0
$376$	−18.1208			−0.0481936
$377$		−	1009.47i		−	2.67765i
$378$	137.442			0.363602
$379$		−	10.5032i		−	0.0277128i	−0.999904	−	0.0138564i	$-0.995589\pi$
$379$		−	10.5032i		−	0.0277128i	0.999904	−	0.0138564i	$-0.00441078\pi$
$380$		0			0
$381$	113.628			0.298235
$382$	−46.1296			−0.120758
$383$	−360.978			−0.942501			−0.471250	−	0.882000i	$-0.656197\pi$
$383$	−360.978			−0.942501			−0.471250	+	0.882000i	$0.656197\pi$
$384$	42.9219			0.111776
$385$		0			0
$386$	447.950			1.16049
$387$	386.680			0.999173
$388$	287.263			0.740368
$389$		−	47.2280i		−	0.121409i	−0.998156	−	0.0607044i	$-0.980665\pi$
$389$		−	47.2280i		−	0.121409i	0.998156	−	0.0607044i	$-0.0193347\pi$
$390$		0			0
$391$	−18.4471	+	32.6712i	−0.0471793	+	0.0835582i
$392$		−	4.06021i		−	0.0103577i
$393$		−	441.925i		−	1.12449i
$394$	275.695			0.699734
$395$		0			0
$396$			121.495i			0.306805i
$397$			4.85826i			0.0122374i	0.999981	+	0.00611872i	$0.00194766\pi$
$397$			4.85826i			0.0122374i	−0.999981	+	0.00611872i	$0.998052\pi$
$398$	104.767			0.263234
$399$	−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	$0.879032\pi$
$402$	−666.590			−1.65818
$403$		−	223.297i		−	0.554087i
$404$	−206.198			−0.510391
$405$		0			0
$406$		−	505.420i		−	1.24488i
$407$		−	456.690i		−	1.12209i
$408$	−17.5044			−0.0429029
$409$	−238.943			−0.584213			−0.292106	−	0.956386i	$-0.594356\pi$
$409$	−238.943			−0.584213			−0.292106	+	0.956386i	$0.594356\pi$
$410$		0			0
$411$			359.732i			0.875259i
$412$	−197.727			−0.479921
$413$	−467.930			−1.13300
$414$	−152.747	−	86.2452i	−0.368954	−	0.208322i
$415$		0			0
$416$	113.475			0.272776
$417$		−	338.700i		−	0.812231i
$418$			468.610i			1.12108i
$419$			197.316i			0.470920i	0.971884	+	0.235460i	$0.0756597\pi$
$419$			197.316i			0.470920i	−0.971884	+	0.235460i	$0.924340\pi$
$420$		0			0
$421$		−	459.256i		−	1.09087i	−0.838153	−	0.545435i	$-0.816365\pi$
$421$		−	459.256i		−	1.09087i	0.838153	−	0.545435i	$-0.183635\pi$
$422$		−	6.71775i		−	0.0159188i
$423$			34.5503i			0.0816793i
$424$			57.7417i			0.136183i
$425$		0			0
$426$	−233.740			−0.548685
$427$			267.937i			0.627487i
$428$	45.0987			0.105371
$429$			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	$0.814104\pi$
$432$			54.7388i			0.126710i
$433$	694.309			1.60349			0.801743	−	0.597669i	$-0.203906\pi$
$433$	694.309			1.60349			0.801743	+	0.597669i	$0.203906\pi$
$434$		−	111.800i		−	0.257603i
$435$		0			0
$436$		−	60.4779i		−	0.138711i
$437$	−589.152	−	332.651i	−1.34817	−	0.761216i
$438$			258.172i			0.589433i
$439$	692.132			1.57661			0.788305	−	0.615284i	$-0.210959\pi$
$439$	692.132			1.57661			0.788305	+	0.615284i	$0.210959\pi$
$440$		0			0
$441$	−7.74147			−0.0175544
$442$	−46.2773			−0.104700
$443$			282.065i			0.636716i	0.947971	+	0.318358i	$0.103131\pi$
$443$			282.065i			0.636716i	−0.947971	+	0.318358i	$0.896869\pi$
$444$			307.623i			0.692844i
$445$		0			0
$446$	299.781			0.672155
$447$	−692.142			−1.54842
$448$	56.8144			0.126818
$449$	4.51574			0.0100573			0.00502866	−	0.999987i	$-0.498399\pi$
$449$	4.51574			0.0100573			0.00502866	+	0.999987i	$0.498399\pi$
$450$		0			0
$451$		−	81.5584i		−	0.180839i
$452$	426.873			0.944410
$453$			112.907i			0.249242i
$454$			551.460i			1.21467i
$455$		0			0
$456$		−	315.652i		−	0.692219i
$457$	399.040			0.873174			0.436587	−	0.899662i	$-0.356187\pi$
$457$	399.040			0.873174			0.436587	+	0.899662i	$0.356187\pi$
$458$	220.618			0.481698
$459$		−	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	$0.484716\pi$
$462$			429.204i			0.929013i
$463$			668.258i			1.44332i	0.692247	+	0.721661i	$0.256621\pi$
$463$			668.258i			1.44332i	−0.692247	+	0.721661i	$0.743379\pi$
$464$	201.293			0.433822
$465$		0			0
$466$	−65.7564			−0.141108
$467$	−670.150			−1.43501			−0.717505	−	0.696554i	$-0.754716\pi$
$467$	−670.150			−1.43501			−0.717505	+	0.696554i	$0.754716\pi$
$468$		−	216.359i		−	0.462306i
$469$	−882.345			−1.88133
$470$		0			0
$471$			243.218i			0.516385i
$472$		−	186.362i		−	0.394835i
$473$		−	807.678i		−	1.70756i
$474$			542.031i			1.14352i
$475$		0			0
$476$	−23.1700			−0.0486765
$477$	110.094			0.230805
$478$			643.092i			1.34538i
$479$		−	310.492i		−	0.648209i	−0.946021	−	0.324105i	$-0.894937\pi$
$479$		−	310.492i		−	0.648209i	0.946021	−	0.324105i	$-0.105063\pi$
$480$		0			0
$481$			813.279i			1.69081i
$482$	211.223			0.438222
$483$	−539.609	−	304.679i	−1.11720	−	0.630804i
$484$	11.7720			0.0243222
$485$		0			0
$486$	364.775			0.750566
$487$			829.644i			1.70358i	0.523883	+	0.851790i	$0.324483\pi$
$487$			829.644i			1.70358i	−0.523883	+	0.851790i	$0.675517\pi$
$488$	−106.711			−0.218670
$489$	−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	$0.540234\pi$
$492$			54.9371i			0.111661i
$493$	−82.0913			−0.166514
$494$		−	834.507i		−	1.68928i
$495$		0			0
$496$	44.5264			0.0897710
$497$	−309.394			−0.622523
$498$	−549.448			−1.10331
$499$	−757.919			−1.51887			−0.759437	−	0.650580i	$-0.774526\pi$
$499$	−757.919			−1.51887			−0.759437	+	0.650580i	$0.774526\pi$
$500$		0			0
$501$	−1033.65			−2.06318
$502$	515.499			1.02689
$503$	−242.915			−0.482933			−0.241467	−	0.970409i	$-0.577628\pi$
$503$	−242.915			−0.482933			−0.241467	+	0.970409i	$0.577628\pi$
$504$		−	108.326i		−	0.214933i
$505$		0			0
$506$	−180.145	+	319.050i	−0.356017	+	0.630535i
$507$		−	885.445i		−	1.74644i
$508$			59.9018i			0.117917i
$509$	−822.585			−1.61608			−0.808040	−	0.589127i	$-0.799472\pi$
$509$	−822.585			−1.61608			−0.808040	+	0.589127i	$0.799472\pi$
$510$		0			0
$511$			341.734i			0.668755i
$512$			22.6274i			0.0441942i
$513$	402.555			0.784707
$514$	−84.4409			−0.164282
$515$		0			0
$516$			544.046i			1.05435i
$517$	72.1670			0.139588
$518$			407.191i			0.786082i
$519$	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	$-0.0291694\pi$
$522$		−	383.800i		−	0.735248i
$523$	277.463			0.530522			0.265261	−	0.964177i	$-0.414542\pi$
$523$	277.463			0.530522			0.265261	+	0.964177i	$0.414542\pi$
$524$	232.972			0.444604
$525$		0			0
$526$		−	398.929i		−	0.758420i
$527$	−18.1588			−0.0344568
$528$	−170.939			−0.323748
$529$	−273.242	−	452.968i	−0.516525	−	0.856272i
$530$		0			0
$531$	−355.331			−0.669173
$532$		−	417.819i		−	0.785373i
$533$			145.240i			0.272496i
$534$		−	51.7141i		−	0.0968430i
$535$		0			0
$536$		−	351.411i		−	0.655617i
$537$			699.599i			1.30279i
$538$		−	20.9054i		−	0.0388575i
$539$			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	$0.711097\pi$
$542$		−	49.0945i		−	0.0905802i
$543$	727.903			1.34052
$544$		−	9.22790i		−	0.0169631i
$545$		0			0
$546$		−	764.332i		−	1.39988i
$547$			349.611i			0.639143i	0.947562	+	0.319571i	$0.103539\pi$
$547$			349.611i			0.639143i	−0.947562	+	0.319571i	$0.896461\pi$
$548$	−189.642			−0.346062
$549$			203.463i			0.370606i
$550$		0			0
$551$		−	1480.33i		−	2.68663i
$552$	121.344	−	214.910i	0.219826	−	0.389329i
$553$			717.469i			1.29741i
$554$	270.174			0.487679
$555$		0			0
$556$	178.555			0.321142
$557$	8.96150			0.0160889			0.00804443	−	0.999968i	$-0.497439\pi$
$557$	8.96150			0.0160889			0.00804443	+	0.999968i	$0.497439\pi$
$558$		−	84.8972i		−	0.152145i
$559$			1438.32i			2.57303i
$560$		0			0
$561$	69.7122			0.124264
$562$	666.587			1.18610
$563$	732.683			1.30139			0.650696	−	0.759339i	$-0.274477\pi$
$563$	732.683			1.30139			0.650696	+	0.759339i	$0.274477\pi$
$564$	−48.6111			−0.0861900
$565$		0			0
$566$		−	33.1778i		−	0.0586181i
$567$	713.395			1.25819
$568$		−	123.222i		−	0.216940i
$569$			42.5363i			0.0747563i	0.999301	+	0.0373781i	$0.0119006\pi$
$569$			42.5363i			0.0747563i	−0.999301	+	0.0373781i	$0.988099\pi$
$570$		0			0
$571$			459.356i			0.804476i	0.915535	+	0.402238i	$0.131768\pi$
$571$			459.356i			0.804476i	−0.915535	+	0.402238i	$0.868232\pi$
$572$	−451.921			−0.790071
$573$	−123.748			−0.215965
$574$			72.7186i			0.126687i
$575$		0			0
$576$	43.1430			0.0749010
$577$			831.608i			1.44126i	0.693319	+	0.720630i	$0.256148\pi$
$577$			831.608i			1.44126i	−0.693319	+	0.720630i	$0.743852\pi$
$578$		−	404.944i		−	0.700596i
$579$	1201.68			2.07544
$580$		0			0
$581$	−727.287			−1.25179
$582$	770.616			1.32408
$583$		−	229.959i		−	0.394441i
$584$	−136.102			−0.233052
$585$		0			0
$586$		−	409.115i		−	0.698149i
$587$		−	166.970i		−	0.284447i	−0.989835	−	0.142223i	$-0.954575\pi$
$587$		−	166.970i		−	0.284447i	0.989835	−	0.142223i	$-0.0454252\pi$
$588$		−	10.8920i		−	0.0185238i
$589$		−	327.452i		−	0.555945i
$590$		0			0
$591$	739.585			1.25141
$592$	−162.171			−0.273938
$593$		−	900.895i		−	1.51922i	−0.650381	−	0.759608i	$-0.725391\pi$
$593$		−	900.895i		−	1.51922i	0.650381	−	0.759608i	$-0.274609\pi$
$594$		−	218.000i		−	0.367004i
$595$		0			0
$596$		−	364.881i		−	0.612217i
$597$	281.050			0.470771
$598$	320.804	−	568.169i	0.536462	−	0.950116i
$599$	129.221			0.215727			0.107864	−	0.994166i	$-0.465599\pi$
$599$	129.221			0.215727			0.107864	+	0.994166i	$0.465599\pi$
$600$		0			0
$601$	580.916			0.966582			0.483291	−	0.875460i	$-0.339441\pi$
$601$	580.916			0.966582			0.483291	+	0.875460i	$0.339441\pi$
$602$			720.136i			1.19624i
$603$	−670.024			−1.11115
$604$	−59.5217			−0.0985458
$605$		0			0
$606$	−553.150			−0.912789
$607$		−	1063.36i		−	1.75183i	−0.482466	−	0.875915i	$-0.660259\pi$
$607$		−	1063.36i		−	1.75183i	0.482466	−	0.875915i	$-0.339741\pi$
$608$	166.404			0.273691
$609$		−	1355.85i		−	2.22635i
$610$		0			0
$611$	−128.516			−0.210337
$612$	−17.5946			−0.0287493
$613$	−442.412			−0.721715			−0.360858	−	0.932621i	$-0.617516\pi$
$613$	−442.412			−0.721715			−0.360858	+	0.932621i	$0.617516\pi$
$614$	797.298			1.29853
$615$		0			0
$616$	−226.266			−0.367316
$617$	−936.724			−1.51819			−0.759095	−	0.650979i	$-0.774358\pi$
$617$	−936.724			−1.51819			−0.759095	+	0.650979i	$0.774358\pi$
$618$	−530.427			−0.858296
$619$			401.856i			0.649202i	0.945851	+	0.324601i	$0.105230\pi$
$619$			401.856i			0.649202i	−0.945851	+	0.324601i	$0.894770\pi$
$620$		0			0
$621$	274.077	+	154.752i	0.441348	+	0.249197i
$622$			108.814i			0.174941i
$623$		−	68.4524i		−	0.109875i
$624$	304.410			0.487837
$625$		0			0
$626$			617.691i			0.986726i
$627$			1257.10i			2.00495i
$628$	−128.219			−0.204170
$629$	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	$-0.305620\pi$
$632$	−285.746			−0.452130
$633$		−	18.0212i		−	0.0284694i
$634$	−135.308			−0.213420
$635$		0			0
$636$			154.899i			0.243552i
$637$		−	28.7958i		−	0.0452053i
$638$	−801.662			−1.25652
$639$	−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	$0.953108\pi$
$642$	120.983			0.188446
$643$	−1055.82			−1.64203			−0.821013	−	0.570909i	$-0.806591\pi$
$643$	−1055.82			−1.64203			−0.821013	+	0.570909i	$0.806591\pi$
$644$	160.619	−	284.470i	0.249409	−	0.441723i
$645$		0			0
$646$	−67.8629			−0.105051
$647$		−	443.636i		−	0.685681i	−0.939394	−	0.342841i	$-0.888611\pi$
$647$		−	443.636i		−	0.685681i	0.939394	−	0.342841i	$-0.111389\pi$
$648$			284.123i			0.438462i
$649$			742.197i			1.14360i
$650$		0			0
$651$		−	299.916i		−	0.460701i
$652$		−	150.666i		−	0.231082i
$653$		−	117.465i		−	0.179886i	−0.995947	−	0.0899429i	$-0.971332\pi$
$653$		−	117.465i		−	0.179886i	0.995947	−	0.0899429i	$-0.0286685\pi$
$654$		−	162.239i		−	0.248072i
$655$		0			0
$656$	−28.9616			−0.0441487
$657$			259.502i			0.394980i
$658$	−64.3451			−0.0977888
$659$		−	664.743i		−	1.00871i	−0.863495	−	0.504357i	$-0.831730\pi$
$659$		−	664.743i		−	1.00871i	0.863495	−	0.504357i	$-0.168270\pi$
$660$		0			0
$661$			426.231i			0.644828i	0.946599	+	0.322414i	$0.104494\pi$
$661$			426.231i			0.644828i	−0.946599	+	0.322414i	$0.895506\pi$
$662$			728.514i			1.10047i
$663$	−124.144			−0.187246
$664$		−	289.656i		−	0.436229i
$665$		0			0
$666$			309.207i			0.464275i
$667$	569.075	−	1007.88i	0.853185	−	1.51106i
$668$		−	544.918i		−	0.815745i
$669$	804.198			1.20209
$670$		0			0
$671$	424.983			0.633358
$672$	152.411			0.226802
$673$			824.444i			1.22503i	0.790460	+	0.612514i	$0.209842\pi$
$673$			824.444i			1.22503i	−0.790460	+	0.612514i	$0.790158\pi$
$674$		−	356.089i		−	0.528322i
$675$		0			0
$676$	466.786			0.690512
$677$	530.039			0.782924			0.391462	−	0.920194i	$-0.371969\pi$
$677$	530.039			0.782924			0.391462	+	0.920194i	$0.371969\pi$
$678$	1145.14			1.68899
$679$	1020.04			1.50227
$680$		0			0
$681$			1479.36i			2.17233i
$682$	−177.329			−0.260013
$683$		−	414.954i		−	0.607546i	−0.952744	−	0.303773i	$-0.901754\pi$
$683$		−	414.954i		−	0.607546i	0.952744	−	0.303773i	$-0.0982464\pi$
$684$		−	317.278i		−	0.463857i
$685$		0			0
$686$			477.712i			0.696373i
$687$	591.833			0.861475
$688$	−286.808			−0.416872
$689$			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	$0.584637\pi$
$692$			523.630i			0.756691i
$693$			431.415i			0.622532i
$694$	237.445			0.342139
$695$		0			0
$696$	539.993			0.775852
$697$	11.8111			0.0169456
$698$		−	186.250i		−	0.266834i
$699$	−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	$0.769491\pi$
$702$			388.218i			0.553017i
$703$			1192.63i			1.69648i
$704$		−	90.1149i		−	0.128004i
$705$		0			0
$706$	329.064			0.466096
$707$	−732.188			−1.03563
$708$		−	499.938i		−	0.706127i
$709$			44.8088i			0.0632000i	0.999501	+	0.0316000i	$0.0100603\pi$
$709$			44.8088i			0.0632000i	−0.999501	+	0.0316000i	$0.989940\pi$
$710$		0			0
$711$			544.823i			0.766277i
$712$	27.2625			0.0382900
$713$	125.880	−	222.944i	0.176550	−	0.312684i
$714$	−62.1563			−0.0870536
$715$		0			0
$716$	−368.812			−0.515101
$717$			1725.17i			2.40609i
$718$	291.133			0.405478
$719$	−1308.36			−1.81969			−0.909844	−	0.414950i	$-0.863799\pi$
$719$	−1308.36			−1.81969			−0.909844	+	0.414950i	$0.863799\pi$
$720$		0			0
$721$	−702.110			−0.973800
$722$		−	713.223i		−	0.987843i
$723$	566.630			0.783721
$724$			383.734i			0.530019i
$725$		0			0
$726$	31.5797			0.0434982
$727$	515.858			0.709570			0.354785	−	0.934948i	$-0.384554\pi$
$727$	515.858			0.709570			0.354785	+	0.934948i	$0.384554\pi$
$728$	402.938			0.553487
$729$	74.4769			0.102163
$730$		0			0
$731$	116.966			0.160008
$732$	−286.265			−0.391073
$733$	405.638			0.553394			0.276697	−	0.960957i	$-0.410760\pi$
$733$	405.638			0.553394			0.276697	+	0.960957i	$0.410760\pi$
$734$			224.019i			0.305203i
$735$		0			0
$736$	113.295	+	63.9698i	0.153934	+	0.0869155i
$737$			1399.51i			1.89893i
$738$			55.2201i			0.0748240i
$739$	−601.397			−0.813798			−0.406899	−	0.913473i	$-0.633390\pi$
$739$	−601.397			−0.813798			−0.406899	+	0.913473i	$0.633390\pi$
$740$		0			0
$741$		−	2238.66i		−	3.02114i
$742$			205.035i			0.276327i
$743$	−775.124			−1.04324			−0.521618	−	0.853179i	$-0.674671\pi$
$743$	−775.124			−1.04324			−0.521618	+	0.853179i	$0.674671\pi$
$744$	119.447			0.160548
$745$		0			0
$746$		−	94.8990i		−	0.127210i
$747$	−552.278			−0.739328
$748$			36.7506i			0.0491319i
$749$	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	$0.884472\pi$
$752$		−	25.6267i		−	0.0340780i
$753$	1382.89			1.83650
$754$	1427.61			1.89338
$755$		0			0
$756$			194.372i			0.257106i
$757$	794.660			1.04975			0.524875	−	0.851180i	$-0.324112\pi$
$757$	794.660			1.04975			0.524875	+	0.851180i	$0.324112\pi$
$758$	14.8537			0.0195959
$759$	−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	$0.834979\pi$
$762$			160.694i			0.210884i
$763$		−	214.751i		−	0.281456i
$764$		−	65.2371i		−	0.0853888i
$765$		0			0
$766$		−	510.500i		−	0.666449i
$767$		−	1321.71i		−	1.72323i
$768$			60.7007i			0.0790374i
$769$		−	1443.85i		−	1.87757i	−0.344500	−	0.938786i	$-0.611952\pi$
$769$		−	1443.85i		−	1.87757i	0.344500	−	0.938786i	$-0.388048\pi$
$770$		0			0
$771$	−226.523			−0.293804
$772$			633.497i			0.820592i
$773$	64.8298			0.0838678			0.0419339	−	0.999120i	$-0.486648\pi$
$773$	64.8298			0.0838678			0.0419339	+	0.999120i	$0.486648\pi$
$774$			546.848i			0.706522i
$775$		0			0
$776$			406.251i			0.523519i
$777$			1092.34i			1.40584i
$778$	66.7905			0.0858490
$779$			212.986i			0.273410i
$780$		0			0
$781$			490.739i			0.628347i
$782$	−46.2041	−	26.0881i	−0.0590845	−	0.0333608i
$783$			688.659i			0.879514i
$784$	5.74200			0.00732398
$785$		0			0
$786$	624.976			0.795135
$787$	1247.04			1.58455			0.792276	−	0.610163i	$-0.208896\pi$
$787$	1247.04			1.58455			0.792276	+	0.610163i	$0.208896\pi$
$788$			389.892i			0.494787i
$789$		−	1070.17i		−	1.35637i
$790$		0			0
$791$	1515.78			1.91629
$792$	−171.819			−0.216944
$793$	−756.815			−0.954370
$794$	−6.87062			−0.00865317
$795$		0			0
$796$			148.163i			0.186134i
$797$	965.218			1.21106			0.605532	−	0.795821i	$-0.292960\pi$
$797$	965.218			1.21106			0.605532	+	0.795821i	$0.292960\pi$
$798$		−	1120.85i		−	1.40457i
$799$			10.4511i			0.0130802i
$800$		0			0
$801$		−	51.9805i		−	0.0648946i
$802$	−420.731			−0.524602
$803$	542.034			0.675011
$804$		−	942.701i		−	1.17251i
$805$		0			0
$806$	315.790			0.391799
$807$		−	56.0811i		−	0.0694933i
$808$		−	291.608i		−	0.360901i
$809$	1310.48			1.61988			0.809939	−	0.586514i	$-0.199500\pi$
$809$	1310.48			1.61988			0.809939	+	0.586514i	$0.199500\pi$
$810$		0			0
$811$	−1174.00			−1.44760			−0.723799	−	0.690010i	$-0.757606\pi$
$811$	−1174.00			−1.44760			−0.723799	+	0.690010i	$0.757606\pi$
$812$	714.772			0.880261
$813$		−	131.702i		−	0.161995i
$814$	645.857			0.793436
$815$		0			0
$816$		−	24.7549i		−	0.0303369i
$817$			2109.22i			2.58166i
$818$		−	337.917i		−	0.413101i
$819$		−	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	$0.771857\pi$
$822$	−508.737			−0.618902
$823$			937.653i			1.13931i	0.821883	+	0.569656i	$0.192923\pi$
$823$			937.653i			1.13931i	−0.821883	+	0.569656i	$0.807077\pi$
$824$		−	279.629i		−	0.339355i
$825$		0			0
$826$		−	661.753i		−	0.801153i
$827$	−199.863			−0.241672			−0.120836	−	0.992672i	$-0.538557\pi$
$827$	−199.863			−0.241672			−0.120836	+	0.992672i	$0.538557\pi$
$828$	121.969	−	216.017i	0.147306	−	0.260890i
$829$	892.787			1.07695			0.538473	−	0.842643i	$-0.319002\pi$
$829$	892.787			1.07695			0.538473	+	0.842643i	$0.319002\pi$
$830$		0			0
$831$	724.774			0.872171
$832$			160.478i			0.192882i
$833$	−2.34170			−0.00281117
$834$	478.994			0.574334
$835$		0			0
$836$	−662.714			−0.792721
$837$			152.333i			0.181998i
$838$	−279.046			−0.332991
$839$			515.108i			0.613955i	0.951717	+	0.306977i	$0.0993176\pi$
$839$			515.108i			0.613955i	−0.951717	+	0.306977i	$0.900682\pi$
$840$		0			0
$841$	1691.44			2.01122
$842$	649.486			0.771361
$843$	1788.20			2.12123
$844$	9.50033			0.0112563
$845$		0			0
$846$	−48.8615			−0.0577560
$847$	41.8010			0.0493519
$848$	−81.6590			−0.0962960
$849$		−	89.0034i		−	0.104833i
$850$		0			0
$851$	−458.474	+	811.993i	−0.538747	+	0.954163i
$852$		−	330.558i		−	0.387979i
$853$			483.197i			0.566467i	0.959051	+	0.283234i	$0.0914072\pi$
$853$			483.197i			0.566467i	−0.959051	+	0.283234i	$0.908593\pi$
$854$	−378.920			−0.443701
$855$		0			0
$856$			63.7792i			0.0745084i
$857$			920.413i			1.07399i	0.843584	+	0.536997i	$0.180441\pi$
$857$			920.413i			1.07399i	−0.843584	+	0.536997i	$0.819559\pi$
$858$	−1212.33			−1.41297
$859$	−1173.30			−1.36589			−0.682947	−	0.730468i	$-0.739302\pi$
$859$	−1173.30			−1.36589			−0.682947	+	0.730468i	$0.739302\pi$
$860$		0			0
$861$			195.076i			0.226569i
$862$	−672.152			−0.779759
$863$		−	866.353i		−	1.00388i	−0.864901	−	0.501942i	$-0.832619\pi$
$863$		−	866.353i		−	1.00388i	0.864901	−	0.501942i	$-0.167381\pi$
$864$	−77.4123			−0.0895976
$865$		0			0
$866$			981.901i			1.13384i
$867$		−	1086.31i		−	1.25295i
$868$	158.109			0.182153
$869$	1138.00			1.30955
$870$		0			0
$871$		−	2492.27i		−	2.86139i
$872$	85.5286			0.0980833
$873$	774.586			0.887269
$874$	470.440	−	833.186i	0.538261	−	0.953303i
$875$		0			0
$876$	−365.110			−0.416792
$877$			281.590i			0.321084i	0.987029	+	0.160542i	$0.0513242\pi$
$877$			281.590i			0.321084i	−0.987029	+	0.160542i	$0.948676\pi$
$878$			978.823i			1.11483i
$879$		−	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	$0.825322\pi$
$882$		−	10.9481i		−	0.0124128i
$883$			821.800i			0.930691i	0.885129	+	0.465346i	$0.154070\pi$
$883$			821.800i			0.930691i	−0.885129	+	0.465346i	$0.845930\pi$
$884$		−	65.4460i		−	0.0740340i
$885$		0			0
$886$	−398.901			−0.450226
$887$			1280.91i			1.44409i	0.691844	+	0.722047i	$0.256799\pi$
$887$			1280.91i			1.44409i	−0.691844	+	0.722047i	$0.743201\pi$
$888$	−435.044			−0.489915
$889$			212.705i			0.239263i
$890$		0			0
$891$		−	1131.54i		−	1.26996i
$892$			423.955i			0.475286i
$893$	−188.461			−0.211043
$894$		−	978.837i		−	1.09490i
$895$		0			0
$896$			80.3476i			0.0896737i
$897$	860.595	−	1524.18i	0.959415	−	1.69920i
$898$			6.38621i			0.00711160i
$899$	560.180			0.623114
$900$		0			0
$901$	33.3022			0.0369613
$902$	115.341			0.127873
$903$			1931.85i			2.13937i
$904$			603.690i			0.667798i
$905$		0			0
$906$	−159.674			−0.176241
$907$	−1726.39			−1.90341			−0.951703	−	0.307021i	$-0.900668\pi$
$907$	−1726.39			−1.90341			−0.951703	+	0.307021i	$0.900668\pi$
$908$	−779.882			−0.858901
$909$	−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	$-0.142980\pi$
$912$	446.399			0.489473
$913$			1153.57i			1.26350i
$914$			564.328i			0.617427i
$915$		0			0
$916$			312.001i			0.340612i
$917$	827.262			0.902139
$918$	31.5703			0.0343903
$919$			1272.36i			1.38451i	0.721655	+	0.692253i	$0.243382\pi$
$919$			1272.36i			1.38451i	−0.721655	+	0.692253i	$0.756618\pi$
$920$		0			0
$921$	2138.85			2.32231
$922$			62.5842i			0.0678787i
$923$		−	873.915i		−	0.946820i
$924$	−606.986			−0.656911
$925$		0			0
$926$	−945.060			−1.02058
$927$	−533.159			−0.575145
$928$			284.672i			0.306758i
$929$	−672.653			−0.724062			−0.362031	−	0.932166i	$-0.617917\pi$
$929$	−672.653			−0.724062			−0.362031	+	0.932166i	$0.617917\pi$
$930$		0			0
$931$		−	42.2273i		−	0.0453569i
$932$		−	92.9936i		−	0.0997785i
$933$			291.905i			0.312867i
$934$		−	947.735i		−	1.01471i
$935$		0			0
$936$	305.978			0.326900
$937$	1599.57			1.70711			0.853557	−	0.520999i	$-0.174440\pi$
$937$	1599.57			1.70711			0.853557	+	0.520999i	$0.174440\pi$
$938$		−	1247.82i		−	1.33030i
$939$			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	$0.667274\pi$
$942$	−343.961			−0.365140
$943$	−81.8770	+	145.011i	−0.0868261	+	0.153776i
$944$	263.556			0.279190
$945$		0			0
$946$	1142.23			1.20743
$947$		−	1829.88i		−	1.93229i	−0.257992	−	0.966147i	$-0.583061\pi$
$947$		−	1829.88i		−	1.93229i	0.257992	−	0.966147i	$-0.416939\pi$
$948$	−766.547			−0.808594
$949$	−965.262			−1.01714
$950$		0			0
$951$	−362.980			−0.381683
$952$		−	32.7673i		−	0.0344195i
$953$	655.714			0.688053			0.344026	−	0.938960i	$-0.388209\pi$
$953$	655.714			0.688053			0.344026	+	0.938960i	$0.388209\pi$
$954$			155.697i			0.163204i
$955$		0			0
$956$	−909.469			−0.951328
$957$	−2150.55			−2.24718
$958$	439.102			0.458353
$959$	−673.400			−0.702190
$960$		0			0
$961$	−837.087			−0.871059
$962$	−1150.15			−1.19558
$963$	121.606			0.126278
$964$			298.714i			0.309870i
$965$		0			0
$966$	430.880	−	763.123i	0.446046	−	0.789982i
$967$			143.641i			0.148543i	0.997238	+	0.0742716i	$0.0236632\pi$
$967$			143.641i			0.148543i	−0.997238	+	0.0742716i	$0.976337\pi$
$968$			16.6481i			0.0171984i
$969$	−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	$0.806811\pi$
$972$			515.870i			0.530730i
$973$	634.030			0.651624
$974$	−1173.29			−1.20461
$975$		0			0
$976$		−	150.912i		−	0.154623i
$977$	626.322			0.641066			0.320533	−	0.947237i	$-0.396138\pi$
$977$	626.322			0.641066			0.320533	+	0.947237i	$0.396138\pi$
$978$		−	404.178i		−	0.413270i
$979$	−108.574			−0.110903
$980$		0			0
$981$		−	163.075i		−	0.166233i
$982$		−	175.071i		−	0.178280i
$983$	202.538			0.206041			0.103020	−	0.994679i	$-0.467149\pi$
$983$	202.538			0.206041			0.103020	+	0.994679i	$0.467149\pi$
$984$	−77.6928			−0.0789561
$985$		0			0
$986$		−	116.095i		−	0.117743i
$987$	−172.613			−0.174887
$988$	1180.17			1.19450
$989$	−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	$0.442791\pi$
$992$			62.9699i			0.0634777i
$993$			1954.33i			1.96810i
$994$		−	437.549i		−	0.440190i
$995$		0			0
$996$		−	777.037i		−	0.780157i
$997$			184.596i			0.185152i	0.995706	+	0.0925758i	$0.0295100\pi$
$997$			184.596i			0.185152i	−0.995706	+	0.0925758i	$0.970490\pi$
$998$		−	1071.86i		−	1.07401i
$999$		−	554.817i		−	0.555372i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.d.a.91.9	✓	16	5.3	odd	4
230.3.d.a.91.10	yes	16	115.68	even	4
1150.3.c.c.1149.9		32	115.114	odd	2	inner
1150.3.c.c.1149.10		32	1.1	even	1	trivial
1150.3.c.c.1149.23		32	5.4	even	2	inner
1150.3.c.c.1149.24		32	23.22	odd	2	inner
1150.3.d.b.551.7		16	5.2	odd	4
1150.3.d.b.551.8		16	115.22	even	4
1840.3.k.d.321.13		16	20.3	even	4
1840.3.k.d.321.14		16	460.183	odd	4
2070.3.c.a.91.1		16	345.68	odd	4
2070.3.c.a.91.8		16	15.8	even	4

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.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +3.79379i q^{3} -2.00000 q^{4} -5.36524 q^{6} -7.10180 q^{7} -2.82843i q^{8} -5.39287 q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +3.79379i q^{3} -2.00000 q^{4} -5.36524 q^{6} -7.10180 q^{7} -2.82843i q^{8} -5.39287 q^{9} +11.2644i q^{11} -7.58759i q^{12} -20.0597i q^{13} -10.0435i q^{14} +4.00000 q^{16} -1.63128 q^{17} -7.62667i q^{18} -29.4164i q^{19} -26.9428i q^{21} -15.9302 q^{22} +(11.3084 - 20.0280i) q^{23} +10.7305 q^{24} +28.3688 q^{26} +13.6847i q^{27} +14.2036 q^{28} +50.3233 q^{29} +11.1316 q^{31} +5.65685i q^{32} -42.7347 q^{33} -2.30698i q^{34} +10.7857 q^{36} -40.5429 q^{37} +41.6011 q^{38} +76.1025 q^{39} -7.24039 q^{41} +38.1028 q^{42} -71.7020 q^{43} -22.5287i q^{44} +(28.3239 + 15.9924i) q^{46} -6.40666i q^{47} +15.1752i q^{48} +1.43550 q^{49} -6.18873i q^{51} +40.1195i q^{52} -20.4148 q^{53} -19.3531 q^{54} +20.0869i q^{56} +111.600 q^{57} +71.1679i q^{58} +65.8889 q^{59} -37.7281i q^{61} +15.7425i q^{62} +38.2991 q^{63} -8.00000 q^{64} -60.4360i q^{66} +124.242 q^{67} +3.26256 q^{68} +(75.9821 + 42.9016i) q^{69} +43.5656 q^{71} +15.2533i q^{72} -48.1194i q^{73} -57.3363i q^{74} +58.8328i q^{76} -79.9972i q^{77} +107.625i q^{78} -101.026i q^{79} -100.453 q^{81} -10.2395i q^{82} +102.409 q^{83} +53.8855i q^{84} -101.402i q^{86} +190.916i q^{87} +31.8604 q^{88} +9.63875i q^{89} +142.460i q^{91} +(-22.6167 + 40.0560i) q^{92} +42.2310i q^{93} +9.06039 q^{94} -21.4609 q^{96} -143.631 q^{97} +2.03010i q^{98} -60.7473i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 64 q^{4} - 16 q^{6} - 128 q^{9}+O(q^{10}) \) 32 * q - 64 * q^4 - 16 * q^6 - 128 * q^9	\( 32 q - 64 q^{4} - 16 q^{6} - 128 q^{9} + 128 q^{16} + 32 q^{24} + 192 q^{26} + 216 q^{29} - 232 q^{31} + 256 q^{36} - 496 q^{39} - 312 q^{41} - 248 q^{46} + 56 q^{49} - 448 q^{54} - 408 q^{59} - 256 q^{64} + 536 q^{69} + 472 q^{71} - 272 q^{81} + 432 q^{94} - 64 q^{96}+O(q^{100}) \) 32 * q - 64 * q^4 - 16 * q^6 - 128 * q^9 + 128 * q^16 + 32 * q^24 + 192 * q^26 + 216 * q^29 - 232 * q^31 + 256 * q^36 - 496 * q^39 - 312 * q^41 - 248 * q^46 + 56 * q^49 - 448 * q^54 - 408 * q^59 - 256 * q^64 + 536 * q^69 + 472 * q^71 - 272 * q^81 + 432 * q^94 - 64 * q^96

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