LMFDB - Embedded newform 1150.3.d.e.551.3

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:	$24$
Twist minimal:	no (minimal twist has level 230)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			551.3
Character	$\chi$	$=$	1150.551
Dual form			1150.3.d.e.551.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +2.29017 q^{3} +2.00000 q^{4} -3.23879 q^{6} -9.92340i q^{7} -2.82843 q^{8} -3.75511 q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +2.29017 q^{3} +2.00000 q^{4} -3.23879 q^{6} -9.92340i q^{7} -2.82843 q^{8} -3.75511 q^{9} -3.77166i q^{11} +4.58035 q^{12} -6.77647 q^{13} +14.0338i q^{14} +4.00000 q^{16} -8.36352i q^{17} +5.31052 q^{18} +3.59141i q^{19} -22.7263i q^{21} +5.33394i q^{22} +(22.9322 + 1.76487i) q^{23} -6.47759 q^{24} +9.58338 q^{26} -29.2114 q^{27} -19.8468i q^{28} -5.85684 q^{29} -42.7430 q^{31} -5.65685 q^{32} -8.63776i q^{33} +11.8278i q^{34} -7.51021 q^{36} +4.28977i q^{37} -5.07902i q^{38} -15.5193 q^{39} -25.3700 q^{41} +32.1399i q^{42} +65.1140i q^{43} -7.54332i q^{44} +(-32.4310 - 2.49590i) q^{46} -5.16843 q^{47} +9.16069 q^{48} -49.4739 q^{49} -19.1539i q^{51} -13.5529 q^{52} -8.63917i q^{53} +41.3112 q^{54} +28.0676i q^{56} +8.22495i q^{57} +8.28282 q^{58} -82.3317 q^{59} +108.297i q^{61} +60.4477 q^{62} +37.2634i q^{63} +8.00000 q^{64} +12.2156i q^{66} -30.7493i q^{67} -16.7270i q^{68} +(52.5187 + 4.04186i) q^{69} -117.687 q^{71} +10.6210 q^{72} +81.8929 q^{73} -6.06665i q^{74} +7.18282i q^{76} -37.4277 q^{77} +21.9476 q^{78} -138.608i q^{79} -33.1032 q^{81} +35.8787 q^{82} -33.5348i q^{83} -45.4526i q^{84} -92.0850i q^{86} -13.4132 q^{87} +10.6679i q^{88} +49.1683i q^{89} +67.2457i q^{91} +(45.8644 + 3.52974i) q^{92} -97.8888 q^{93} +7.30926 q^{94} -12.9552 q^{96} +138.450i q^{97} +69.9666 q^{98} +14.1630i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 48 q^{4} + 8 q^{6} + 96 q^{9}+O(q^{10}) $ 24 * q + 48 * q^4 + 8 * q^6 + 96 * q^9	$ 24 q + 48 q^{4} + 8 q^{6} + 96 q^{9} + 96 q^{16} + 16 q^{24} - 32 q^{26} - 100 q^{29} - 124 q^{31} + 192 q^{36} - 192 q^{39} - 116 q^{41} + 148 q^{46} + 76 q^{49} + 16 q^{54} - 84 q^{59} + 192 q^{64} + 340 q^{69} + 196 q^{71} + 1360 q^{81} + 376 q^{94} + 32 q^{96}+O(q^{100}) $ 24 * q + 48 * q^4 + 8 * q^6 + 96 * q^9 + 96 * q^16 + 16 * q^24 - 32 * q^26 - 100 * q^29 - 124 * q^31 + 192 * q^36 - 192 * q^39 - 116 * q^41 + 148 * q^46 + 76 * q^49 + 16 * q^54 - 84 * q^59 + 192 * q^64 + 340 * q^69 + 196 * q^71 + 1360 * q^81 + 376 * q^94 + 32 * 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 $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$	2.29017			0.763391			0.381696	−	0.924288i	$-0.375340\pi$
$3$	2.29017			0.763391			0.381696	+	0.924288i	$0.375340\pi$
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	−3.23879			−0.539799
$7$		−	9.92340i		−	1.41763i	−0.705395	−	0.708814i	$-0.749230\pi$
$7$		−	9.92340i		−	1.41763i	0.705395	−	0.708814i	$-0.250770\pi$
$8$	−2.82843			−0.353553
$9$	−3.75511			−0.417234
$10$		0			0
$11$		−	3.77166i		−	0.342878i	−0.985195	−	0.171439i	$-0.945158\pi$
$11$		−	3.77166i		−	0.342878i	0.985195	−	0.171439i	$-0.0548417\pi$
$12$	4.58035			0.381696
$13$	−6.77647			−0.521267			−0.260634	−	0.965438i	$-0.583931\pi$
$13$	−6.77647			−0.521267			−0.260634	+	0.965438i	$0.583931\pi$
$14$			14.0338i			1.00241i
$15$		0			0
$16$	4.00000			0.250000
$17$		−	8.36352i		−	0.491972i	−0.969273	−	0.245986i	$-0.920888\pi$
$17$		−	8.36352i		−	0.491972i	0.969273	−	0.245986i	$-0.0791117\pi$
$18$	5.31052			0.295029
$19$			3.59141i			0.189022i	0.995524	+	0.0945108i	$0.0301287\pi$
$19$			3.59141i			0.189022i	−0.995524	+	0.0945108i	$0.969871\pi$
$20$		0			0
$21$		−	22.7263i		−	1.08221i
$22$			5.33394i			0.242452i
$23$	22.9322	+	1.76487i	0.997052	+	0.0767335i
$23$	22.9322	+	1.76487i	0.997052	+	0.0767335i
$24$	−6.47759			−0.269900
$25$		0			0
$26$	9.58338			0.368592
$27$	−29.2114			−1.08190
$28$		−	19.8468i		−	0.708814i
$29$	−5.85684			−0.201960			−0.100980	−	0.994888i	$-0.532198\pi$
$29$	−5.85684			−0.201960			−0.100980	+	0.994888i	$0.532198\pi$
$30$		0			0
$31$	−42.7430			−1.37881			−0.689403	−	0.724378i	$-0.742127\pi$
$31$	−42.7430			−1.37881			−0.689403	+	0.724378i	$0.742127\pi$
$32$	−5.65685			−0.176777
$33$		−	8.63776i		−	0.261750i
$34$			11.8278i			0.347876i
$35$		0			0
$36$	−7.51021			−0.208617
$37$			4.28977i			0.115940i	0.998318	+	0.0579699i	$0.0184627\pi$
$37$			4.28977i			0.115940i	−0.998318	+	0.0579699i	$0.981537\pi$
$38$		−	5.07902i		−	0.133658i
$39$	−15.5193			−0.397931
$40$		0			0
$41$	−25.3700			−0.618781			−0.309391	−	0.950935i	$-0.600125\pi$
$41$	−25.3700			−0.618781			−0.309391	+	0.950935i	$0.600125\pi$
$42$			32.1399i			0.765235i
$43$			65.1140i			1.51428i	0.653254	+	0.757139i	$0.273404\pi$
$43$			65.1140i			1.51428i	−0.653254	+	0.757139i	$0.726596\pi$
$44$		−	7.54332i		−	0.171439i
$45$		0			0
$46$	−32.4310	−	2.49590i	−0.705022	−	0.0542587i
$47$	−5.16843			−0.109966			−0.0549832	−	0.998487i	$-0.517511\pi$
$47$	−5.16843			−0.109966			−0.0549832	+	0.998487i	$0.517511\pi$
$48$	9.16069			0.190848
$49$	−49.4739			−1.00967
$50$		0			0
$51$		−	19.1539i		−	0.375567i
$52$	−13.5529			−0.260634
$53$		−	8.63917i		−	0.163003i	−0.996673	−	0.0815016i	$-0.974028\pi$
$53$		−	8.63917i		−	0.163003i	0.996673	−	0.0815016i	$-0.0259716\pi$
$54$	41.3112			0.765022
$55$		0			0
$56$			28.0676i			0.501207i
$57$			8.22495i			0.144297i
$58$	8.28282			0.142807
$59$	−82.3317			−1.39545			−0.697726	−	0.716365i	$-0.745805\pi$
$59$	−82.3317			−1.39545			−0.697726	+	0.716365i	$0.745805\pi$
$60$		0			0
$61$			108.297i			1.77536i	0.460462	+	0.887680i	$0.347684\pi$
$61$			108.297i			1.77536i	−0.460462	+	0.887680i	$0.652316\pi$
$62$	60.4477			0.974963
$63$			37.2634i			0.591483i
$64$	8.00000			0.125000
$65$		0			0
$66$			12.2156i			0.185085i
$67$		−	30.7493i		−	0.458945i	−0.973315	−	0.229472i	$-0.926300\pi$
$67$		−	30.7493i		−	0.458945i	0.973315	−	0.229472i	$-0.0737001\pi$
$68$		−	16.7270i		−	0.245986i
$69$	52.5187	+	4.04186i	0.761140	+	0.0585776i
$70$		0			0
$71$	−117.687			−1.65756			−0.828779	−	0.559576i	$-0.810964\pi$
$71$	−117.687			−1.65756			−0.828779	+	0.559576i	$0.810964\pi$
$72$	10.6210			0.147514
$73$	81.8929			1.12182			0.560910	−	0.827877i	$-0.310451\pi$
$73$	81.8929			1.12182			0.560910	+	0.827877i	$0.310451\pi$
$74$		−	6.06665i		−	0.0819818i
$75$		0			0
$76$			7.18282i			0.0945108i
$77$	−37.4277			−0.486074
$78$	21.9476			0.281380
$79$		−	138.608i		−	1.75453i	−0.480007	−	0.877265i	$-0.659366\pi$
$79$		−	138.608i		−	1.75453i	0.480007	−	0.877265i	$-0.340634\pi$
$80$		0			0
$81$	−33.1032			−0.408682
$82$	35.8787			0.437545
$83$		−	33.5348i		−	0.404034i	−0.979382	−	0.202017i	$-0.935250\pi$
$83$		−	33.5348i		−	0.404034i	0.979382	−	0.202017i	$-0.0647496\pi$
$84$		−	45.4526i		−	0.541103i
$85$		0			0
$86$		−	92.0850i		−	1.07076i
$87$	−13.4132			−0.154174
$88$			10.6679i			0.121226i
$89$			49.1683i			0.552453i	0.961093	+	0.276226i	$0.0890839\pi$
$89$			49.1683i			0.552453i	−0.961093	+	0.276226i	$0.910916\pi$
$90$		0			0
$91$			67.2457i			0.738963i
$92$	45.8644	+	3.52974i	0.498526	+	0.0383667i
$93$	−97.8888			−1.05257
$94$	7.30926			0.0777581
$95$		0			0
$96$	−12.9552			−0.134950
$97$			138.450i			1.42732i	0.700495	+	0.713658i	$0.252963\pi$
$97$			138.450i			1.42732i	−0.700495	+	0.713658i	$0.747037\pi$
$98$	69.9666			0.713945
$99$			14.1630i			0.143060i
$100$		0			0
$101$	−118.002			−1.16834			−0.584168	−	0.811633i	$-0.698579\pi$
$101$	−118.002			−1.16834			−0.584168	+	0.811633i	$0.698579\pi$
$102$			27.0877i			0.265566i
$103$		−	93.5481i		−	0.908234i	−0.890942	−	0.454117i	$-0.849955\pi$
$103$		−	93.5481i		−	0.908234i	0.890942	−	0.454117i	$-0.150045\pi$
$104$	19.1668			0.184296
$105$		0			0
$106$			12.2176i			0.115261i
$107$		−	94.3250i		−	0.881542i	−0.897620	−	0.440771i	$-0.854705\pi$
$107$		−	94.3250i		−	0.881542i	0.897620	−	0.440771i	$-0.145295\pi$
$108$	−58.4228			−0.540952
$109$		−	39.6045i		−	0.363344i	−0.983359	−	0.181672i	$-0.941849\pi$
$109$		−	39.6045i		−	0.363344i	0.983359	−	0.181672i	$-0.0581509\pi$
$110$		0			0
$111$			9.82432i			0.0885074i
$112$		−	39.6936i		−	0.354407i
$113$		−	139.567i		−	1.23511i	−0.786528	−	0.617555i	$-0.788123\pi$
$113$		−	139.567i		−	1.23511i	0.786528	−	0.617555i	$-0.211877\pi$
$114$		−	11.6318i		−	0.102034i
$115$		0			0
$116$	−11.7137			−0.100980
$117$	25.4464			0.217490
$118$	116.435			0.986733
$119$	−82.9945			−0.697433
$120$		0			0
$121$	106.775			0.882434
$122$		−	153.155i		−	1.25537i
$123$	−58.1018			−0.472372
$124$	−85.4860			−0.689403
$125$		0			0
$126$		−	52.6984i		−	0.418241i
$127$	97.7645			0.769799			0.384900	−	0.922958i	$-0.374236\pi$
$127$	97.7645			0.769799			0.384900	+	0.922958i	$0.374236\pi$
$128$	−11.3137			−0.0883883
$129$			149.122i			1.15599i
$130$		0			0
$131$	−39.3002			−0.300002			−0.150001	−	0.988686i	$-0.547928\pi$
$131$	−39.3002			−0.300002			−0.150001	+	0.988686i	$0.547928\pi$
$132$		−	17.2755i		−	0.130875i
$133$	35.6390			0.267962
$134$			43.4861i			0.324523i
$135$		0			0
$136$			23.6556i			0.173938i
$137$			65.5953i			0.478798i	0.970921	+	0.239399i	$0.0769503\pi$
$137$			65.5953i			0.478798i	−0.970921	+	0.239399i	$0.923050\pi$
$138$	−74.2726	−	5.71605i	−0.538208	−	0.0414206i
$139$	109.952			0.791022			0.395511	−	0.918461i	$-0.370568\pi$
$139$	109.952			0.791022			0.395511	+	0.918461i	$0.370568\pi$
$140$		0			0
$141$	−11.8366			−0.0839475
$142$	166.434			1.17207
$143$			25.5586i			0.178731i
$144$	−15.0204			−0.104308
$145$		0			0
$146$	−115.814			−0.793247
$147$	−113.304			−0.770774
$148$			8.57955i			0.0579699i
$149$			241.014i			1.61754i	0.588124	+	0.808771i	$0.299867\pi$
$149$			241.014i			1.61754i	−0.588124	+	0.808771i	$0.700133\pi$
$150$		0			0
$151$	−215.991			−1.43041			−0.715203	−	0.698917i	$-0.753666\pi$
$151$	−215.991			−1.43041			−0.715203	+	0.698917i	$0.753666\pi$
$152$		−	10.1580i		−	0.0668292i
$153$			31.4059i			0.205267i
$154$	52.9308			0.343706
$155$		0			0
$156$	−31.0386			−0.198965
$157$		−	29.1218i		−	0.185489i	−0.995690	−	0.0927445i	$-0.970436\pi$
$157$		−	29.1218i		−	0.185489i	0.995690	−	0.0927445i	$-0.0295640\pi$
$158$			196.021i			1.24064i
$159$		−	19.7852i		−	0.124435i
$160$		0			0
$161$	17.5135	−	227.565i	0.108780	−	1.41345i
$162$	46.8150			0.288982
$163$	−80.6418			−0.494735			−0.247367	−	0.968922i	$-0.579565\pi$
$163$	−80.6418			−0.494735			−0.247367	+	0.968922i	$0.579565\pi$
$164$	−50.7401			−0.309391
$165$		0			0
$166$			47.4254i			0.285695i
$167$	−150.797			−0.902975			−0.451487	−	0.892277i	$-0.649106\pi$
$167$	−150.797			−0.902975			−0.451487	+	0.892277i	$0.649106\pi$
$168$			64.2797i			0.382617i
$169$	−123.079			−0.728280
$170$		0			0
$171$		−	13.4861i		−	0.0788662i
$172$			130.228i			0.757139i
$173$	−19.4076			−0.112182			−0.0560912	−	0.998426i	$-0.517864\pi$
$173$	−19.4076			−0.112182			−0.0560912	+	0.998426i	$0.517864\pi$
$174$	18.9691			0.109018
$175$		0			0
$176$		−	15.0866i		−	0.0857196i
$177$	−188.554			−1.06528
$178$		−	69.5345i		−	0.390643i
$179$	−131.190			−0.732906			−0.366453	−	0.930437i	$-0.619428\pi$
$179$	−131.190			−0.732906			−0.366453	+	0.930437i	$0.619428\pi$
$180$		0			0
$181$		−	119.940i		−	0.662652i	−0.943516	−	0.331326i	$-0.892504\pi$
$181$		−	119.940i		−	0.662652i	0.943516	−	0.331326i	$-0.107496\pi$
$182$		−	95.0997i		−	0.522526i
$183$			248.019i			1.35529i
$184$	−64.8620	−	4.99180i	−0.352511	−	0.0271294i
$185$		0			0
$186$	138.436			0.744278
$187$	−31.5444			−0.168686
$188$	−10.3369			−0.0549832
$189$			289.876i			1.53374i
$190$		0			0
$191$		−	40.1019i		−	0.209957i	−0.994474	−	0.104979i	$-0.966523\pi$
$191$		−	40.1019i		−	0.209957i	0.994474	−	0.104979i	$-0.0334774\pi$
$192$	18.3214			0.0954239
$193$	−214.452			−1.11115			−0.555575	−	0.831466i	$-0.687502\pi$
$193$	−214.452			−1.11115			−0.555575	+	0.831466i	$0.687502\pi$
$194$		−	195.797i		−	1.00926i
$195$		0			0
$196$	−98.9477			−0.504835
$197$	−38.6221			−0.196051			−0.0980257	−	0.995184i	$-0.531253\pi$
$197$	−38.6221			−0.196051			−0.0980257	+	0.995184i	$0.531253\pi$
$198$		−	20.0295i		−	0.101159i
$199$		−	334.055i		−	1.67867i	−0.543617	−	0.839333i	$-0.682946\pi$
$199$		−	334.055i		−	1.67867i	0.543617	−	0.839333i	$-0.317054\pi$
$200$		0			0
$201$		−	70.4213i		−	0.350355i
$202$	166.880			0.826138
$203$			58.1197i			0.286304i
$204$		−	38.3078i		−	0.187783i
$205$		0			0
$206$			132.297i			0.642219i
$207$	−86.1128	−	6.62727i	−0.416004	−	0.0320158i
$208$	−27.1059			−0.130317
$209$	13.5456			0.0648114
$210$		0			0
$211$	17.2731			0.0818630			0.0409315	−	0.999162i	$-0.486967\pi$
$211$	17.2731			0.0818630			0.0409315	+	0.999162i	$0.486967\pi$
$212$		−	17.2783i		−	0.0815016i
$213$	−269.523			−1.26536
$214$			133.396i			0.623344i
$215$		0			0
$216$	82.6223			0.382511
$217$			424.156i			1.95463i
$218$			56.0092i			0.256923i
$219$	187.549			0.856388
$220$		0			0
$221$			56.6752i			0.256449i
$222$		−	13.8937i		−	0.0625842i
$223$	218.370			0.979239			0.489620	−	0.871936i	$-0.337136\pi$
$223$	218.370			0.979239			0.489620	+	0.871936i	$0.337136\pi$
$224$			56.1352i			0.250604i
$225$		0			0
$226$			197.378i			0.873355i
$227$		−	170.495i		−	0.751078i	−0.926807	−	0.375539i	$-0.877458\pi$
$227$		−	170.495i		−	0.751078i	0.926807	−	0.375539i	$-0.122542\pi$
$228$			16.4499i			0.0721487i
$229$		−	373.215i		−	1.62976i	−0.579629	−	0.814881i	$-0.696802\pi$
$229$		−	373.215i		−	1.62976i	0.579629	−	0.814881i	$-0.303198\pi$
$230$		0			0
$231$	−85.7160			−0.371065
$232$	16.5656			0.0714036
$233$	−308.084			−1.32225			−0.661124	−	0.750276i	$-0.729920\pi$
$233$	−308.084			−1.32225			−0.661124	+	0.750276i	$0.729920\pi$
$234$	−35.9866			−0.153789
$235$		0			0
$236$	−164.663			−0.697726
$237$		−	317.436i		−	1.33939i
$238$	117.372			0.493160
$239$	−141.838			−0.593463			−0.296732	−	0.954961i	$-0.595897\pi$
$239$	−141.838			−0.593463			−0.296732	+	0.954961i	$0.595897\pi$
$240$		0			0
$241$			171.606i			0.712060i	0.934475	+	0.356030i	$0.115870\pi$
$241$			171.606i			0.712060i	−0.934475	+	0.356030i	$0.884130\pi$
$242$	−151.002			−0.623975
$243$	187.090			0.769920
$244$			216.594i			0.887680i
$245$		0			0
$246$	82.1683			0.334018
$247$		−	24.3371i		−	0.0985307i
$248$	120.895			0.487481
$249$		−	76.8005i		−	0.308436i
$250$		0			0
$251$			48.8673i			0.194691i	0.995251	+	0.0973453i	$0.0310351\pi$
$251$			48.8673i			0.194691i	−0.995251	+	0.0973453i	$0.968965\pi$
$252$			74.5268i			0.295741i
$253$	6.65649	−	86.4925i	0.0263102	−	0.341867i
$254$	−138.260			−0.544330
$255$		0			0
$256$	16.0000			0.0625000
$257$	−319.787			−1.24431			−0.622155	−	0.782894i	$-0.713742\pi$
$257$	−319.787			−1.24431			−0.622155	+	0.782894i	$0.713742\pi$
$258$		−	210.891i		−	0.817406i
$259$	42.5691			0.164360
$260$		0			0
$261$	21.9930			0.0842645
$262$	55.5789			0.212133
$263$		−	390.798i		−	1.48593i	−0.669333	−	0.742963i	$-0.733420\pi$
$263$		−	390.798i		−	1.48593i	0.669333	−	0.742963i	$-0.266580\pi$
$264$			24.4313i			0.0925427i
$265$		0			0
$266$	−50.4011			−0.189478
$267$			112.604i			0.421738i
$268$		−	61.4986i		−	0.229472i
$269$	364.221			1.35398			0.676992	−	0.735991i	$-0.263283\pi$
$269$	364.221			1.35398			0.676992	+	0.735991i	$0.263283\pi$
$270$		0			0
$271$	301.823			1.11374			0.556869	−	0.830601i	$-0.312003\pi$
$271$	301.823			1.11374			0.556869	+	0.830601i	$0.312003\pi$
$272$		−	33.4541i		−	0.122993i
$273$			154.004i			0.564118i
$274$		−	92.7657i		−	0.338561i
$275$		0			0
$276$	105.037	+	8.08371i	0.380570	+	0.0292888i
$277$	−362.800			−1.30975			−0.654873	−	0.755739i	$-0.727278\pi$
$277$	−362.800			−1.30975			−0.654873	+	0.755739i	$0.727278\pi$
$278$	−155.496			−0.559337
$279$	160.504			0.575285
$280$		0			0
$281$			86.2564i			0.306962i	0.988152	+	0.153481i	$0.0490484\pi$
$281$			86.2564i			0.306962i	−0.988152	+	0.153481i	$0.950952\pi$
$282$	16.7395			0.0593598
$283$			371.739i			1.31357i	0.754079	+	0.656783i	$0.228083\pi$
$283$			371.739i			1.31357i	−0.754079	+	0.656783i	$0.771917\pi$
$284$	−235.373			−0.828779
$285$		0			0
$286$		−	36.1453i		−	0.126382i
$287$			251.757i			0.877202i
$288$	21.2421			0.0737572
$289$	219.052			0.757964
$290$		0			0
$291$			317.074i			1.08960i
$292$	163.786			0.560910
$293$		−	159.208i		−	0.543371i	−0.962386	−	0.271685i	$-0.912419\pi$
$293$		−	159.208i		−	0.543371i	0.962386	−	0.271685i	$-0.0875810\pi$
$294$	160.236			0.545019
$295$		0			0
$296$		−	12.1333i		−	0.0409909i
$297$			110.176i			0.370961i
$298$		−	340.845i		−	1.14377i
$299$	−155.399	−	11.9596i	−0.519730	−	0.0399986i
$300$		0			0
$301$	646.152			2.14668
$302$	305.458			1.01145
$303$	−270.245			−0.891897
$304$			14.3656i			0.0472554i
$305$		0			0
$306$		−	44.4146i		−	0.145146i
$307$	10.1864			0.0331804			0.0165902	−	0.999862i	$-0.494719\pi$
$307$	10.1864			0.0331804			0.0165902	+	0.999862i	$0.494719\pi$
$308$	−74.8554			−0.243037
$309$		−	214.241i		−	0.693338i
$310$		0			0
$311$	390.702			1.25628			0.628138	−	0.778102i	$-0.283817\pi$
$311$	390.702			1.25628			0.628138	+	0.778102i	$0.283817\pi$
$312$	43.8952			0.140690
$313$		−	536.465i		−	1.71395i	−0.515361	−	0.856973i	$-0.672342\pi$
$313$		−	536.465i		−	1.71395i	0.515361	−	0.856973i	$-0.327658\pi$
$314$			41.1844i			0.131160i
$315$		0			0
$316$		−	277.216i		−	0.877265i
$317$	295.497			0.932167			0.466083	−	0.884741i	$-0.345665\pi$
$317$	295.497			0.932167			0.466083	+	0.884741i	$0.345665\pi$
$318$			27.9805i			0.0879890i
$319$			22.0900i			0.0692477i
$320$		0			0
$321$		−	216.021i		−	0.672961i
$322$	−24.7678	+	321.826i	−0.0769187	+	0.999459i
$323$	30.0368			0.0929932
$324$	−66.2065			−0.204341
$325$		0			0
$326$	114.045			0.349830
$327$		−	90.7011i		−	0.277373i
$328$	71.7573			0.218772
$329$			51.2884i			0.155892i
$330$		0			0
$331$	−199.717			−0.603374			−0.301687	−	0.953407i	$-0.597550\pi$
$331$	−199.717			−0.603374			−0.301687	+	0.953407i	$0.597550\pi$
$332$		−	67.0696i		−	0.202017i
$333$		−	16.1085i		−	0.0483740i
$334$	213.259			0.638500
$335$		0			0
$336$		−	90.9052i		−	0.270551i
$337$		−	367.909i		−	1.09172i	−0.837877	−	0.545860i	$-0.816203\pi$
$337$		−	367.909i		−	1.09172i	0.837877	−	0.545860i	$-0.183797\pi$
$338$	174.061			0.514972
$339$		−	319.634i		−	0.942872i
$340$		0			0
$341$			161.212i			0.472763i
$342$			19.0723i			0.0557668i
$343$			4.70237i			0.0137095i
$344$		−	184.170i		−	0.535378i
$345$		0			0
$346$	27.4464			0.0793250
$347$	−206.127			−0.594025			−0.297012	−	0.954874i	$-0.595990\pi$
$347$	−206.127			−0.594025			−0.297012	+	0.954874i	$0.595990\pi$
$348$	−26.8263			−0.0770872
$349$	195.800			0.561032			0.280516	−	0.959849i	$-0.409494\pi$
$349$	195.800			0.561032			0.280516	+	0.959849i	$0.409494\pi$
$350$		0			0
$351$	197.950			0.563961
$352$			21.3357i			0.0606129i
$353$	335.246			0.949706			0.474853	−	0.880065i	$-0.342501\pi$
$353$	335.246			0.949706			0.474853	+	0.880065i	$0.342501\pi$
$354$	266.655			0.753264
$355$		0			0
$356$			98.3366i			0.276226i
$357$	−190.072			−0.532414
$358$	185.531			0.518243
$359$			562.219i			1.56607i	0.621978	+	0.783035i	$0.286329\pi$
$359$			562.219i			1.56607i	−0.621978	+	0.783035i	$0.713671\pi$
$360$		0			0
$361$	348.102			0.964271
$362$			169.621i			0.468565i
$363$	244.532			0.673643
$364$			134.491i			0.369482i
$365$		0			0
$366$		−	350.751i		−	0.958337i
$367$		−	402.041i		−	1.09548i	−0.836649	−	0.547740i	$-0.815488\pi$
$367$		−	402.041i		−	1.09548i	0.836649	−	0.547740i	$-0.184512\pi$
$368$	91.7288	+	7.05948i	0.249263	+	0.0191834i
$369$	95.2672			0.258177
$370$		0			0
$371$	−85.7299			−0.231078
$372$	−195.778			−0.526284
$373$			476.171i			1.27660i	0.769789	+	0.638299i	$0.220362\pi$
$373$			476.171i			1.27660i	−0.769789	+	0.638299i	$0.779638\pi$
$374$	44.6105			0.119279
$375$		0			0
$376$	14.6185			0.0388790
$377$	39.6887			0.105275
$378$		−	409.947i		−	1.08452i
$379$			522.262i			1.37800i	0.724762	+	0.688999i	$0.241950\pi$
$379$			522.262i			1.37800i	−0.724762	+	0.688999i	$0.758050\pi$
$380$		0			0
$381$	223.898			0.587658
$382$			56.7126i			0.148462i
$383$			562.573i			1.46886i	0.678685	+	0.734429i	$0.262550\pi$
$383$			562.573i			1.46886i	−0.678685	+	0.734429i	$0.737450\pi$
$384$	−25.9104			−0.0674749
$385$		0			0
$386$	303.281			0.785702
$387$		−	244.510i		−	0.631808i
$388$			276.899i			0.713658i
$389$		−	700.851i		−	1.80167i	−0.434158	−	0.900837i	$-0.642954\pi$
$389$		−	700.851i		−	1.80167i	0.434158	−	0.900837i	$-0.357046\pi$
$390$		0			0
$391$	14.7605	−	191.794i	0.0377507	−	0.490521i
$392$	139.933			0.356973
$393$	−90.0043			−0.229019
$394$	54.6200			0.138629
$395$		0			0
$396$			28.3260i			0.0715302i
$397$	−87.9617			−0.221566			−0.110783	−	0.993845i	$-0.535336\pi$
$397$	−87.9617			−0.221566			−0.110783	+	0.993845i	$0.535336\pi$
$398$			472.425i			1.18700i
$399$	81.6195			0.204560
$400$		0			0
$401$		−	422.433i		−	1.05345i	−0.850036	−	0.526725i	$-0.823420\pi$
$401$		−	422.433i		−	1.05345i	0.850036	−	0.526725i	$-0.176580\pi$
$402$			99.5907i			0.247738i
$403$	289.647			0.718726
$404$	−236.004			−0.584168
$405$		0			0
$406$		−	82.1937i		−	0.202448i
$407$	16.1796			0.0397532
$408$			54.1754i			0.132783i
$409$	153.708			0.375814			0.187907	−	0.982187i	$-0.439830\pi$
$409$	153.708			0.375814			0.187907	+	0.982187i	$0.439830\pi$
$410$		0			0
$411$			150.225i			0.365510i
$412$		−	187.096i		−	0.454117i
$413$			817.010i			1.97823i
$414$	121.782	+	9.37238i	0.294159	+	0.0226386i
$415$		0			0
$416$	38.3335			0.0921479
$417$	251.809			0.603859
$418$	−19.1563			−0.0458286
$419$			715.672i			1.70805i	0.520233	+	0.854024i	$0.325845\pi$
$419$			715.672i			1.70805i	−0.520233	+	0.854024i	$0.674155\pi$
$420$		0			0
$421$			201.138i			0.477762i	0.971049	+	0.238881i	$0.0767806\pi$
$421$			201.138i			0.477762i	−0.971049	+	0.238881i	$0.923219\pi$
$422$	−24.4279			−0.0578859
$423$	19.4080			0.0458818
$424$			24.4353i			0.0576303i
$425$		0			0
$426$	381.163			0.894748
$427$	1074.67			2.51680
$428$		−	188.650i		−	0.440771i
$429$			58.5336i			0.136442i
$430$		0			0
$431$		−	81.1508i		−	0.188285i	−0.995559	−	0.0941425i	$-0.969989\pi$
$431$		−	81.1508i		−	0.188285i	0.995559	−	0.0941425i	$-0.0300109\pi$
$432$	−116.846			−0.270476
$433$		−	260.642i		−	0.601944i	−0.953633	−	0.300972i	$-0.902689\pi$
$433$		−	260.642i		−	0.601944i	0.953633	−	0.300972i	$-0.0973111\pi$
$434$		−	599.847i		−	1.38214i
$435$		0			0
$436$		−	79.2089i		−	0.181672i
$437$	−6.33837	+	82.3589i	−0.0145043	+	0.188464i
$438$	−265.234			−0.605558
$439$	668.702			1.52324			0.761620	−	0.648024i	$-0.224404\pi$
$439$	668.702			1.52324			0.761620	+	0.648024i	$0.224404\pi$
$440$		0			0
$441$	185.780			0.421269
$442$		−	80.1508i		−	0.181337i
$443$	592.784			1.33811			0.669056	−	0.743212i	$-0.266698\pi$
$443$	592.784			1.33811			0.669056	+	0.743212i	$0.266698\pi$
$444$			19.6486i			0.0442537i
$445$		0			0
$446$	−308.822			−0.692427
$447$			551.963i			1.23482i
$448$		−	79.3872i		−	0.177204i
$449$	−326.176			−0.726449			−0.363225	−	0.931702i	$-0.618324\pi$
$449$	−326.176			−0.726449			−0.363225	+	0.931702i	$0.618324\pi$
$450$		0			0
$451$			95.6872i			0.212167i
$452$		−	279.135i		−	0.617555i
$453$	−494.658			−1.09196
$454$			241.116i			0.531092i
$455$		0			0
$456$		−	23.2637i		−	0.0510168i
$457$		−	724.352i		−	1.58501i	−0.609862	−	0.792507i	$-0.708775\pi$
$457$		−	724.352i		−	1.58501i	0.609862	−	0.792507i	$-0.291225\pi$
$458$			527.806i			1.15242i
$459$			244.310i			0.532266i
$460$		0			0
$461$	509.925			1.10613			0.553064	−	0.833138i	$-0.313458\pi$
$461$	509.925			1.10613			0.553064	+	0.833138i	$0.313458\pi$
$462$	121.221			0.262382
$463$	639.749			1.38175			0.690874	−	0.722975i	$-0.257226\pi$
$463$	639.749			1.38175			0.690874	+	0.722975i	$0.257226\pi$
$464$	−23.4273			−0.0504900
$465$		0			0
$466$	435.696			0.934971
$467$			163.138i			0.349332i	0.984628	+	0.174666i	$0.0558846\pi$
$467$			163.138i			0.349332i	−0.984628	+	0.174666i	$0.944115\pi$
$468$	50.8928			0.108745
$469$	−305.138			−0.650613
$470$		0			0
$471$		−	66.6939i		−	0.141601i
$472$	232.869			0.493367
$473$	245.588			0.519213
$474$			448.922i			0.947093i
$475$		0			0
$476$	−165.989			−0.348716
$477$			32.4410i			0.0680104i
$478$	200.589			0.419642
$479$		−	141.599i		−	0.295613i	−0.989016	−	0.147807i	$-0.952779\pi$
$479$		−	141.599i		−	0.295613i	0.989016	−	0.147807i	$-0.0472213\pi$
$480$		0			0
$481$		−	29.0695i		−	0.0604356i
$482$		−	242.688i		−	0.503502i
$483$	40.1090	−	521.164i	0.0830413	−	1.07901i
$484$	213.549			0.441217
$485$		0			0
$486$	−264.586			−0.544415
$487$	861.286			1.76855			0.884277	−	0.466963i	$-0.154652\pi$
$487$	861.286			1.76855			0.884277	+	0.466963i	$0.154652\pi$
$488$		−	306.310i		−	0.627684i
$489$	−184.684			−0.377676
$490$		0			0
$491$	−714.739			−1.45568			−0.727840	−	0.685747i	$-0.759476\pi$
$491$	−714.739			−1.45568			−0.727840	+	0.685747i	$0.759476\pi$
$492$	−116.204			−0.236186
$493$			48.9838i			0.0993585i
$494$			34.4178i			0.0696718i
$495$		0			0
$496$	−170.972			−0.344701
$497$			1167.85i			2.34980i
$498$			108.612i			0.218097i
$499$	−531.913			−1.06596			−0.532979	−	0.846128i	$-0.678928\pi$
$499$	−531.913			−1.06596			−0.532979	+	0.846128i	$0.678928\pi$
$500$		0			0
$501$	−345.351			−0.689323
$502$		−	69.1089i		−	0.137667i
$503$		−	721.625i		−	1.43464i	−0.696743	−	0.717321i	$-0.745368\pi$
$503$		−	721.625i		−	1.43464i	0.696743	−	0.717321i	$-0.254632\pi$
$504$		−	105.397i		−	0.209121i
$505$		0			0
$506$	−9.41370	+	122.319i	−0.0186041	+	0.241737i
$507$	−281.873			−0.555963
$508$	195.529			0.384900
$509$	−829.610			−1.62988			−0.814941	−	0.579544i	$-0.803231\pi$
$509$	−829.610			−1.62988			−0.814941	+	0.579544i	$0.803231\pi$
$510$		0			0
$511$		−	812.656i		−	1.59033i
$512$	−22.6274			−0.0441942
$513$		−	104.910i		−	0.204503i
$514$	452.248			0.879859
$515$		0			0
$516$			298.245i			0.577993i
$517$			19.4936i			0.0377051i
$518$	−60.2018			−0.116220
$519$	−44.4467			−0.0856391
$520$		0			0
$521$			431.800i			0.828790i	0.910097	+	0.414395i	$0.136007\pi$
$521$			431.800i			0.828790i	−0.910097	+	0.414395i	$0.863993\pi$
$522$	−31.1029			−0.0595840
$523$		−	419.527i		−	0.802155i	−0.916044	−	0.401078i	$-0.868636\pi$
$523$		−	419.527i		−	0.802155i	0.916044	−	0.401078i	$-0.131364\pi$
$524$	−78.6004			−0.150001
$525$		0			0
$526$			552.672i			1.05071i
$527$			357.482i			0.678333i
$528$		−	34.5510i		−	0.0654376i
$529$	522.770	+	80.9446i	0.988224	+	0.153014i
$530$		0			0
$531$	309.164			0.582230
$532$	71.2780			0.133981
$533$	171.919			0.322551
$534$		−	159.246i		−	0.298213i
$535$		0			0
$536$			86.9722i			0.162262i
$537$	−300.448			−0.559494
$538$	−515.087			−0.957411
$539$			186.599i			0.346194i
$540$		0			0
$541$	311.858			0.576448			0.288224	−	0.957563i	$-0.406935\pi$
$541$	311.858			0.576448			0.288224	+	0.957563i	$0.406935\pi$
$542$	−426.842			−0.787531
$543$		−	274.683i		−	0.505862i
$544$			47.3112i			0.0869691i
$545$		0			0
$546$		−	217.795i		−	0.398892i
$547$	−248.962			−0.455141			−0.227570	−	0.973762i	$-0.573078\pi$
$547$	−248.962			−0.455141			−0.227570	+	0.973762i	$0.573078\pi$
$548$			131.191i			0.239399i
$549$		−	406.666i		−	0.740740i
$550$		0			0
$551$		−	21.0343i		−	0.0381748i
$552$	−148.545	−	11.4321i	−0.269104	−	0.0207103i
$553$	−1375.46			−2.48727
$554$	513.076			0.926131
$555$		0			0
$556$	219.904			0.395511
$557$		−	309.966i		−	0.556492i	−0.960510	−	0.278246i	$-0.910247\pi$
$557$		−	309.966i		−	0.556492i	0.960510	−	0.278246i	$-0.0897530\pi$
$558$	−226.987			−0.406788
$559$		−	441.243i		−	0.789344i
$560$		0			0
$561$	−72.2421			−0.128774
$562$		−	121.985i		−	0.217055i
$563$		−	1076.21i		−	1.91156i	−0.294075	−	0.955782i	$-0.595011\pi$
$563$		−	1076.21i		−	1.91156i	0.294075	−	0.955782i	$-0.404989\pi$
$564$	−23.6732			−0.0419737
$565$		0			0
$566$		−	525.719i		−	0.928832i
$567$			328.497i			0.579359i
$568$	332.868			0.586035
$569$		−	670.488i		−	1.17836i	−0.808001	−	0.589181i	$-0.799450\pi$
$569$		−	670.488i		−	1.17836i	0.808001	−	0.589181i	$-0.200550\pi$
$570$		0			0
$571$			487.987i			0.854618i	0.904106	+	0.427309i	$0.140538\pi$
$571$			487.987i			0.854618i	−0.904106	+	0.427309i	$0.859462\pi$
$572$			51.1171i			0.0893656i
$573$		−	91.8402i		−	0.160280i
$574$		−	356.038i		−	0.620276i
$575$		0			0
$576$	−30.0408			−0.0521542
$577$	435.218			0.754278			0.377139	−	0.926157i	$-0.376908\pi$
$577$	435.218			0.754278			0.377139	+	0.926157i	$0.376908\pi$
$578$	−309.786			−0.535961
$579$	−491.132			−0.848242
$580$		0			0
$581$	−332.779			−0.572770
$582$		−	448.410i		−	0.770463i
$583$	−32.5840			−0.0558903
$584$	−231.628			−0.396624
$585$		0			0
$586$			225.154i			0.384221i
$587$	634.204			1.08042			0.540208	−	0.841532i	$-0.318346\pi$
$587$	634.204			1.08042			0.540208	+	0.841532i	$0.318346\pi$
$588$	−226.607			−0.385387
$589$		−	153.508i		−	0.260624i
$590$		0			0
$591$	−88.4514			−0.149664
$592$			17.1591i			0.0289850i
$593$	−201.595			−0.339957			−0.169979	−	0.985448i	$-0.554370\pi$
$593$	−201.595			−0.339957			−0.169979	+	0.985448i	$0.554370\pi$
$594$		−	155.812i		−	0.262309i
$595$		0			0
$596$			482.027i			0.808771i
$597$		−	765.043i		−	1.28148i
$598$	219.768	+	16.9134i	0.367505	+	0.0282833i
$599$	−522.791			−0.872773			−0.436387	−	0.899759i	$-0.643742\pi$
$599$	−522.791			−0.872773			−0.436387	+	0.899759i	$0.643742\pi$
$600$		0			0
$601$	−568.503			−0.945929			−0.472965	−	0.881081i	$-0.656816\pi$
$601$	−568.503			−0.945929			−0.472965	+	0.881081i	$0.656816\pi$
$602$	−913.797			−1.51793
$603$			115.467i			0.191487i
$604$	−431.983			−0.715203
$605$		0			0
$606$	382.184			0.630666
$607$	−686.871			−1.13158			−0.565791	−	0.824549i	$-0.691429\pi$
$607$	−686.871			−1.13158			−0.565791	+	0.824549i	$0.691429\pi$
$608$		−	20.3161i		−	0.0334146i
$609$			133.104i			0.218562i
$610$		0			0
$611$	35.0237			0.0573219
$612$			62.8118i			0.102634i
$613$			900.475i			1.46896i	0.678628	+	0.734482i	$0.262575\pi$
$613$			900.475i			1.46896i	−0.678628	+	0.734482i	$0.737425\pi$
$614$	−14.4057			−0.0234621
$615$		0			0
$616$	105.862			0.171853
$617$			18.4606i			0.0299199i	0.999888	+	0.0149599i	$0.00476207\pi$
$617$			18.4606i			0.0299199i	−0.999888	+	0.0149599i	$0.995238\pi$
$618$			302.983i			0.490264i
$619$		−	228.644i		−	0.369377i	−0.982797	−	0.184689i	$-0.940872\pi$
$619$		−	228.644i		−	0.369377i	0.982797	−	0.184689i	$-0.0591276\pi$
$620$		0			0
$621$	−669.881	−	51.5543i	−1.07871	−	0.0830182i
$622$	−552.536			−0.888321
$623$	487.917			0.783173
$624$	−62.0772			−0.0994827
$625$		0			0
$626$			758.676i			1.21194i
$627$	31.0217			0.0494764
$628$		−	58.2435i		−	0.0927445i
$629$	35.8776			0.0570391
$630$		0			0
$631$		−	1089.20i		−	1.72615i	−0.505075	−	0.863075i	$-0.668535\pi$
$631$		−	1089.20i		−	1.72615i	0.505075	−	0.863075i	$-0.331465\pi$
$632$			392.042i			0.620320i
$633$	39.5584			0.0624935
$634$	−417.896			−0.659141
$635$		0			0
$636$		−	39.5704i		−	0.0622176i
$637$	335.258			0.526308
$638$		−	31.2400i		−	0.0489655i
$639$	441.925			0.691589
$640$		0			0
$641$			16.8364i			0.0262659i	0.999914	+	0.0131329i	$0.00418046\pi$
$641$			16.8364i			0.0262659i	−0.999914	+	0.0131329i	$0.995820\pi$
$642$			305.499i			0.475856i
$643$			472.059i			0.734150i	0.930191	+	0.367075i	$0.119641\pi$
$643$			472.059i			0.734150i	−0.930191	+	0.367075i	$0.880359\pi$
$644$	35.0270	−	455.131i	0.0543898	−	0.706724i
$645$		0			0
$646$	−42.4785			−0.0657561
$647$	−175.941			−0.271933			−0.135967	−	0.990713i	$-0.543414\pi$
$647$	−175.941			−0.271933			−0.135967	+	0.990713i	$0.543414\pi$
$648$	93.6301			0.144491
$649$			310.527i			0.478470i
$650$		0			0
$651$			971.390i			1.49215i
$652$	−161.284			−0.247367
$653$	−698.137			−1.06912			−0.534561	−	0.845130i	$-0.679523\pi$
$653$	−698.137			−1.06912			−0.534561	+	0.845130i	$0.679523\pi$
$654$			128.271i			0.196133i
$655$		0			0
$656$	−101.480			−0.154695
$657$	−307.517			−0.468062
$658$		−	72.5327i		−	0.110232i
$659$			30.4888i			0.0462652i	0.999732	+	0.0231326i	$0.00736399\pi$
$659$			30.4888i			0.0462652i	−0.999732	+	0.0231326i	$0.992636\pi$
$660$		0			0
$661$			749.974i			1.13461i	0.823509	+	0.567303i	$0.192013\pi$
$661$			749.974i			1.13461i	−0.823509	+	0.567303i	$0.807987\pi$
$662$	282.442			0.426650
$663$			129.796i			0.195771i
$664$			94.8508i			0.142848i
$665$		0			0
$666$			22.7809i			0.0342056i
$667$	−134.310	−	10.3366i	−0.201364	−	0.0154971i
$668$	−301.594			−0.451487
$669$	500.106			0.747543
$670$		0			0
$671$	408.459			0.608732
$672$			128.559i			0.191309i
$673$	375.227			0.557543			0.278772	−	0.960357i	$-0.410073\pi$
$673$	375.227			0.557543			0.278772	+	0.960357i	$0.410073\pi$
$674$			520.303i			0.771962i
$675$		0			0
$676$	−246.159			−0.364140
$677$		−	119.598i		−	0.176659i	−0.996091	−	0.0883296i	$-0.971847\pi$
$677$		−	119.598i		−	0.176659i	0.996091	−	0.0883296i	$-0.0281529\pi$
$678$			452.030i			0.666711i
$679$	1373.89			2.02340
$680$		0			0
$681$		−	390.462i		−	0.573366i
$682$		−	227.988i		−	0.334294i
$683$	−149.185			−0.218427			−0.109213	−	0.994018i	$-0.534833\pi$
$683$	−149.185			−0.218427			−0.109213	+	0.994018i	$0.534833\pi$
$684$		−	26.9722i		−	0.0394331i
$685$		0			0
$686$		−	6.65016i		−	0.00969411i
$687$		−	854.728i		−	1.24415i
$688$			260.456i			0.378570i
$689$			58.5431i			0.0849682i
$690$		0			0
$691$	45.1261			0.0653055			0.0326528	−	0.999467i	$-0.489604\pi$
$691$	45.1261			0.0653055			0.0326528	+	0.999467i	$0.489604\pi$
$692$	−38.8151			−0.0560912
$693$	140.545			0.202807
$694$	291.507			0.420039
$695$		0			0
$696$	37.9382			0.0545089
$697$			212.183i			0.304423i
$698$	−276.903			−0.396709
$699$	−705.566			−1.00939
$700$		0			0
$701$		−	775.256i		−	1.10593i	−0.833205	−	0.552964i	$-0.813497\pi$
$701$		−	775.256i		−	1.10593i	0.833205	−	0.552964i	$-0.186503\pi$
$702$	−279.944			−0.398781
$703$	−15.4063			−0.0219151
$704$		−	30.1733i		−	0.0428598i
$705$		0			0
$706$	−474.110			−0.671544
$707$			1170.98i			1.65627i
$708$	−377.108			−0.532638
$709$			959.884i			1.35386i	0.736049	+	0.676928i	$0.236689\pi$
$709$			959.884i			1.35386i	−0.736049	+	0.676928i	$0.763311\pi$
$710$		0			0
$711$			520.487i			0.732049i
$712$		−	139.069i		−	0.195322i
$713$	−980.190	−	75.4358i	−1.37474	−	0.105801i
$714$	268.802			0.376474
$715$		0			0
$716$	−262.380			−0.366453
$717$	−324.833			−0.453045
$718$		−	795.098i		−	1.10738i
$719$	−50.3372			−0.0700101			−0.0350050	−	0.999387i	$-0.511145\pi$
$719$	−50.3372			−0.0700101			−0.0350050	+	0.999387i	$0.511145\pi$
$720$		0			0
$721$	−928.316			−1.28754
$722$	−492.290			−0.681842
$723$			393.009i			0.543580i
$724$		−	239.880i		−	0.331326i
$725$		0			0
$726$	−345.821			−0.476337
$727$			313.655i			0.431438i	0.976456	+	0.215719i	$0.0692095\pi$
$727$			313.655i			0.431438i	−0.976456	+	0.215719i	$0.930791\pi$
$728$		−	190.199i		−	0.261263i
$729$	726.399			0.996432
$730$		0			0
$731$	544.582			0.744982
$732$			496.037i			0.677647i
$733$			1032.82i			1.40903i	0.709688	+	0.704516i	$0.248836\pi$
$733$			1032.82i			1.40903i	−0.709688	+	0.704516i	$0.751164\pi$
$734$			568.572i			0.774621i
$735$		0			0
$736$	−129.724	−	9.98361i	−0.176255	−	0.0135647i
$737$	−115.976			−0.157362
$738$	−134.728			−0.182558
$739$	−1033.23			−1.39815			−0.699075	−	0.715049i	$-0.746405\pi$
$739$	−1033.23			−1.39815			−0.699075	+	0.715049i	$0.746405\pi$
$740$		0			0
$741$		−	55.7362i		−	0.0752175i
$742$	121.240			0.163397
$743$			378.634i			0.509602i	0.966994	+	0.254801i	$0.0820099\pi$
$743$			378.634i			0.509602i	−0.966994	+	0.254801i	$0.917990\pi$
$744$	276.871			0.372139
$745$		0			0
$746$		−	673.407i		−	0.902691i
$747$			125.927i			0.168577i
$748$	−63.0887			−0.0843432
$749$	−936.025			−1.24970
$750$		0			0
$751$		−	1031.32i		−	1.37327i	−0.727004	−	0.686633i	$-0.759088\pi$
$751$		−	1031.32i		−	1.37327i	0.727004	−	0.686633i	$-0.240912\pi$
$752$	−20.6737			−0.0274916
$753$			111.915i			0.148625i
$754$	−56.1283			−0.0744407
$755$		0			0
$756$			579.753i			0.766869i
$757$		−	456.485i		−	0.603018i	−0.953463	−	0.301509i	$-0.902510\pi$
$757$		−	456.485i		−	0.603018i	0.953463	−	0.301509i	$-0.0974903\pi$
$758$		−	738.589i		−	0.974392i
$759$	15.2445	−	198.083i	0.0200850	−	0.260979i
$760$		0			0
$761$	363.034			0.477049			0.238525	−	0.971136i	$-0.423336\pi$
$761$	363.034			0.477049			0.238525	+	0.971136i	$0.423336\pi$
$762$	−316.639			−0.415537
$763$	−393.011			−0.515086
$764$		−	80.2037i		−	0.104979i
$765$		0			0
$766$		−	795.598i		−	1.03864i
$767$	557.918			0.727403
$768$	36.6428			0.0477119
$769$			1390.41i			1.80807i	0.427455	+	0.904037i	$0.359410\pi$
$769$			1390.41i			1.80807i	−0.427455	+	0.904037i	$0.640590\pi$
$770$		0			0
$771$	−732.369			−0.949895
$772$	−428.904			−0.555575
$773$			197.113i			0.254998i	0.991839	+	0.127499i	$0.0406949\pi$
$773$			197.113i			0.254998i	−0.991839	+	0.127499i	$0.959305\pi$
$774$			345.789i			0.446756i
$775$		0			0
$776$		−	391.595i		−	0.504632i
$777$	97.4907			0.125471
$778$			991.153i			1.27398i
$779$		−	91.1142i		−	0.116963i
$780$		0			0
$781$			443.874i			0.568341i
$782$	−20.8745	+	271.237i	−0.0266938	+	0.346851i
$783$	171.086			0.218501
$784$	−197.895			−0.252418
$785$		0			0
$786$	127.285			0.161941
$787$			326.291i			0.414601i	0.978277	+	0.207300i	$0.0664677\pi$
$787$			326.291i			0.414601i	−0.978277	+	0.207300i	$0.933532\pi$
$788$	−77.2443			−0.0980257
$789$		−	894.996i		−	1.13434i
$790$		0			0
$791$	−1384.98			−1.75093
$792$		−	40.0590i		−	0.0505795i
$793$		−	733.871i		−	0.925437i
$794$	124.397			0.156671
$795$		0			0
$796$		−	668.109i		−	0.839333i
$797$		−	1370.61i		−	1.71971i	−0.510542	−	0.859853i	$-0.670555\pi$
$797$		−	1370.61i		−	1.71971i	0.510542	−	0.859853i	$-0.329445\pi$
$798$	−115.427			−0.144646
$799$			43.2262i			0.0541004i
$800$		0			0
$801$		−	184.632i		−	0.230502i
$802$			597.411i			0.744902i
$803$		−	308.872i		−	0.384648i
$804$		−	140.843i		−	0.175177i
$805$		0			0
$806$	−409.622			−0.508216
$807$	834.130			1.03362
$808$	333.760			0.413069
$809$	−1063.74			−1.31488			−0.657439	−	0.753508i	$-0.728360\pi$
$809$	−1063.74			−1.31488			−0.657439	+	0.753508i	$0.728360\pi$
$810$		0			0
$811$	414.464			0.511053			0.255527	−	0.966802i	$-0.417751\pi$
$811$	414.464			0.511053			0.255527	+	0.966802i	$0.417751\pi$
$812$			116.239i			0.143152i
$813$	691.227			0.850217
$814$	−22.8814			−0.0281098
$815$		0			0
$816$		−	76.6156i		−	0.0938917i
$817$	−233.851			−0.286231
$818$	−217.376			−0.265740
$819$		−	252.515i		−	0.308321i
$820$		0			0
$821$	−1214.92			−1.47980			−0.739900	−	0.672717i	$-0.765127\pi$
$821$	−1214.92			−1.47980			−0.739900	+	0.672717i	$0.765127\pi$
$822$		−	212.450i		−	0.258454i
$823$	1234.78			1.50033			0.750167	−	0.661248i	$-0.229973\pi$
$823$	1234.78			1.50033			0.750167	+	0.661248i	$0.229973\pi$
$824$			264.594i			0.321109i
$825$		0			0
$826$		−	1155.43i		−	1.39882i
$827$		−	108.207i		−	0.130843i	−0.997858	−	0.0654213i	$-0.979161\pi$
$827$		−	108.207i		−	0.130843i	0.997858	−	0.0654213i	$-0.0208391\pi$
$828$	−172.226	−	13.2545i	−0.208002	−	0.0160079i
$829$	1028.48			1.24062			0.620311	−	0.784356i	$-0.287006\pi$
$829$	1028.48			1.24062			0.620311	+	0.784356i	$0.287006\pi$
$830$		0			0
$831$	−830.874			−0.999849
$832$	−54.2118			−0.0651584
$833$			413.776i			0.496729i
$834$	−356.112			−0.426993
$835$		0			0
$836$	27.0912			0.0324057
$837$	1248.58			1.49174
$838$		−	1012.11i		−	1.20777i
$839$		−	225.069i		−	0.268258i	−0.990964	−	0.134129i	$-0.957176\pi$
$839$		−	225.069i		−	0.268258i	0.990964	−	0.134129i	$-0.0428237\pi$
$840$		0			0
$841$	−806.697			−0.959212
$842$		−	284.452i		−	0.337829i
$843$			197.542i			0.234332i
$844$	34.5462			0.0409315
$845$		0			0
$846$	−27.4470			−0.0324433
$847$		−	1059.57i		−	1.25096i
$848$		−	34.5567i		−	0.0407508i
$849$			851.348i			1.00277i
$850$		0			0
$851$	−7.57089	+	98.3739i	−0.00889646	+	0.115598i
$852$	−539.045			−0.632682
$853$	−1303.75			−1.52843			−0.764214	−	0.644963i	$-0.776873\pi$
$853$	−1303.75			−1.52843			−0.764214	+	0.644963i	$0.776873\pi$
$854$	−1519.82			−1.77965
$855$		0			0
$856$			266.791i			0.311672i
$857$	−590.095			−0.688559			−0.344279	−	0.938867i	$-0.611877\pi$
$857$	−590.095			−0.688559			−0.344279	+	0.938867i	$0.611877\pi$
$858$		−	82.7790i		−	0.0964790i
$859$	518.499			0.603607			0.301804	−	0.953370i	$-0.402411\pi$
$859$	518.499			0.603607			0.301804	+	0.953370i	$0.402411\pi$
$860$		0			0
$861$			576.567i			0.669648i
$862$			114.765i			0.133138i
$863$	718.122			0.832123			0.416061	−	0.909337i	$-0.363410\pi$
$863$	718.122			0.832123			0.416061	+	0.909337i	$0.363410\pi$
$864$	165.245			0.191255
$865$		0			0
$866$			368.603i			0.425639i
$867$	501.666			0.578623
$868$			848.311i			0.977317i
$869$	−522.782			−0.601590
$870$		0			0
$871$			208.372i			0.239233i
$872$			112.018i			0.128461i
$873$		−	519.893i		−	0.595524i
$874$	8.96381	−	116.473i	0.0102561	−	0.133264i
$875$		0			0
$876$	375.098			0.428194
$877$	97.4101			0.111072			0.0555360	−	0.998457i	$-0.482313\pi$
$877$	97.4101			0.111072			0.0555360	+	0.998457i	$0.482313\pi$
$878$	−945.688			−1.07709
$879$		−	364.613i		−	0.414804i
$880$		0			0
$881$			903.406i			1.02543i	0.858558	+	0.512716i	$0.171361\pi$
$881$			903.406i			1.02543i	−0.858558	+	0.512716i	$0.828639\pi$
$882$	−262.732			−0.297882
$883$	−261.231			−0.295844			−0.147922	−	0.988999i	$-0.547259\pi$
$883$	−261.231			−0.295844			−0.147922	+	0.988999i	$0.547259\pi$
$884$			113.350i			0.128224i
$885$		0			0
$886$	−838.323			−0.946189
$887$	1163.44			1.31166			0.655828	−	0.754911i	$-0.272320\pi$
$887$	1163.44			1.31166			0.655828	+	0.754911i	$0.272320\pi$
$888$		−	27.7874i		−	0.0312921i
$889$		−	970.156i		−	1.09129i
$890$		0			0
$891$			124.854i			0.140128i
$892$	436.741			0.489620
$893$		−	18.5619i		−	0.0207860i
$894$		−	780.594i		−	0.873147i
$895$		0			0
$896$			112.270i			0.125302i
$897$	−355.892	−	27.3895i	−0.396758	−	0.0305346i
$898$	461.282			0.513677
$899$	250.339			0.278463
$900$		0			0
$901$	−72.2538			−0.0801929
$902$		−	135.322i		−	0.150025i
$903$	1479.80			1.63876
$904$			394.756i			0.436677i
$905$		0			0
$906$	699.552			0.772132
$907$		−	1170.12i		−	1.29009i	−0.764143	−	0.645047i	$-0.776838\pi$
$907$		−	1170.12i		−	1.29009i	0.764143	−	0.645047i	$-0.223162\pi$
$908$		−	340.989i		−	0.375539i
$909$	443.110			0.487469
$910$		0			0
$911$			1409.98i			1.54773i	0.633352	+	0.773864i	$0.281678\pi$
$911$			1409.98i			1.54773i	−0.633352	+	0.773864i	$0.718322\pi$
$912$			32.8998i			0.0360743i
$913$	−126.482			−0.138534
$914$			1024.39i			1.12077i
$915$		0			0
$916$		−	746.431i		−	0.814881i
$917$			389.992i			0.425291i
$918$		−	345.507i		−	0.376369i
$919$			898.968i			0.978202i	0.872227	+	0.489101i	$0.162675\pi$
$919$			898.968i			0.978202i	−0.872227	+	0.489101i	$0.837325\pi$
$920$		0			0
$921$	23.3286			0.0253296
$922$	−721.143			−0.782151
$923$	797.500			0.864030
$924$	−171.432			−0.185532
$925$		0			0
$926$	−904.742			−0.977043
$927$			351.283i			0.378946i
$928$	33.1313			0.0357018
$929$	−878.502			−0.945643			−0.472822	−	0.881158i	$-0.656764\pi$
$929$	−878.502			−0.945643			−0.472822	+	0.881158i	$0.656764\pi$
$930$		0			0
$931$		−	177.681i		−	0.190850i
$932$	−616.168			−0.661124
$933$	894.775			0.959030
$934$		−	230.712i		−	0.247015i
$935$		0			0
$936$	−71.9732			−0.0768945
$937$			1074.33i			1.14656i	0.819358	+	0.573282i	$0.194330\pi$
$937$			1074.33i			1.14656i	−0.819358	+	0.573282i	$0.805670\pi$
$938$	431.530			0.460053
$939$		−	1228.60i		−	1.30841i
$940$		0			0
$941$			586.745i			0.623533i	0.950159	+	0.311767i	$0.100921\pi$
$941$			586.745i			0.623533i	−0.950159	+	0.311767i	$0.899079\pi$
$942$			94.3194i			0.100127i
$943$	−581.791	−	44.7748i	−0.616957	−	0.0474812i
$944$	−329.327			−0.348863
$945$		0			0
$946$	−347.314			−0.367139
$947$	−70.3459			−0.0742829			−0.0371414	−	0.999310i	$-0.511825\pi$
$947$	−70.3459			−0.0742829			−0.0371414	+	0.999310i	$0.511825\pi$
$948$		−	634.872i		−	0.669696i
$949$	−554.945			−0.584768
$950$		0			0
$951$	676.739			0.711608
$952$	234.744			0.246580
$953$			446.648i			0.468675i	0.972155	+	0.234338i	$0.0752921\pi$
$953$			446.648i			0.468675i	−0.972155	+	0.234338i	$0.924708\pi$
$954$		−	45.8785i		−	0.0480906i
$955$		0			0
$956$	−283.676			−0.296732
$957$			50.5900i			0.0528631i
$958$			200.251i			0.209030i
$959$	650.928			0.678757
$960$		0			0
$961$	865.962			0.901105
$962$			41.1105i			0.0427344i
$963$			354.200i			0.367809i
$964$			343.213i			0.356030i
$965$		0			0
$966$	−56.7226	+	737.037i	−0.0587191	+	0.762978i
$967$	24.8727			0.0257215			0.0128608	−	0.999917i	$-0.495906\pi$
$967$	24.8727			0.0257215			0.0128608	+	0.999917i	$0.495906\pi$
$968$	−302.004			−0.311988
$969$	68.7895			0.0709902
$970$		0			0
$971$		−	272.102i		−	0.280229i	−0.990135	−	0.140114i	$-0.955253\pi$
$971$		−	272.102i		−	0.280229i	0.990135	−	0.140114i	$-0.0447470\pi$
$972$	374.181			0.384960
$973$		−	1091.10i		−	1.12137i
$974$	−1218.04			−1.25056
$975$		0			0
$976$			433.188i			0.443840i
$977$		−	1948.04i		−	1.99390i	−0.0780340	−	0.996951i	$-0.524864\pi$
$977$		−	1948.04i		−	1.99390i	0.0780340	−	0.996951i	$-0.475136\pi$
$978$	261.182			0.267057
$979$	185.446			0.189424
$980$		0			0
$981$			148.719i			0.151599i
$982$	1010.79			1.02932
$983$		−	1755.62i		−	1.78598i	−0.450079	−	0.892989i	$-0.648604\pi$
$983$		−	1755.62i		−	1.78598i	0.450079	−	0.892989i	$-0.351396\pi$
$984$	164.337			0.167009
$985$		0			0
$986$		−	69.2735i		−	0.0702571i
$987$			117.459i			0.119006i
$988$		−	48.6742i		−	0.0492654i
$989$	−114.918	+	1493.21i	−0.116196	+	1.50981i
$990$		0			0
$991$	249.984			0.252254			0.126127	−	0.992014i	$-0.459745\pi$
$991$	249.984			0.252254			0.126127	+	0.992014i	$0.459745\pi$
$992$	241.791			0.243741
$993$	−457.386			−0.460610
$994$		−	1651.59i		−	1.66156i
$995$		0			0
$996$		−	153.601i		−	0.154218i
$997$	1422.36			1.42664			0.713321	−	0.700838i	$-0.247190\pi$
$997$	1422.36			1.42664			0.713321	+	0.700838i	$0.247190\pi$
$998$	752.239			0.753746
$999$		−	125.310i		−	0.125436i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.3.d.e.551.3		24
5.2	odd	4		230.3.c.a.229.4	yes	24
5.3	odd	4		230.3.c.a.229.21	yes	24
5.4	even	2	inner	1150.3.d.e.551.22		24
23.22	odd	2	inner	1150.3.d.e.551.10		24
115.22	even	4		230.3.c.a.229.3	✓	24
115.68	even	4		230.3.c.a.229.22	yes	24
115.114	odd	2	inner	1150.3.d.e.551.15		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.c.a.229.3	✓	24	115.22	even	4
230.3.c.a.229.4	yes	24	5.2	odd	4
230.3.c.a.229.21	yes	24	5.3	odd	4
230.3.c.a.229.22	yes	24	115.68	even	4
1150.3.d.e.551.3		24	1.1	even	1	trivial
1150.3.d.e.551.10		24	23.22	odd	2	inner
1150.3.d.e.551.15		24	115.114	odd	2	inner
1150.3.d.e.551.22		24	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1150.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +2.29017 q^{3} +2.00000 q^{4} -3.23879 q^{6} -9.92340i q^{7} -2.82843 q^{8} -3.75511 q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +2.29017 q^{3} +2.00000 q^{4} -3.23879 q^{6} -9.92340i q^{7} -2.82843 q^{8} -3.75511 q^{9} -3.77166i q^{11} +4.58035 q^{12} -6.77647 q^{13} +14.0338i q^{14} +4.00000 q^{16} -8.36352i q^{17} +5.31052 q^{18} +3.59141i q^{19} -22.7263i q^{21} +5.33394i q^{22} +(22.9322 + 1.76487i) q^{23} -6.47759 q^{24} +9.58338 q^{26} -29.2114 q^{27} -19.8468i q^{28} -5.85684 q^{29} -42.7430 q^{31} -5.65685 q^{32} -8.63776i q^{33} +11.8278i q^{34} -7.51021 q^{36} +4.28977i q^{37} -5.07902i q^{38} -15.5193 q^{39} -25.3700 q^{41} +32.1399i q^{42} +65.1140i q^{43} -7.54332i q^{44} +(-32.4310 - 2.49590i) q^{46} -5.16843 q^{47} +9.16069 q^{48} -49.4739 q^{49} -19.1539i q^{51} -13.5529 q^{52} -8.63917i q^{53} +41.3112 q^{54} +28.0676i q^{56} +8.22495i q^{57} +8.28282 q^{58} -82.3317 q^{59} +108.297i q^{61} +60.4477 q^{62} +37.2634i q^{63} +8.00000 q^{64} +12.2156i q^{66} -30.7493i q^{67} -16.7270i q^{68} +(52.5187 + 4.04186i) q^{69} -117.687 q^{71} +10.6210 q^{72} +81.8929 q^{73} -6.06665i q^{74} +7.18282i q^{76} -37.4277 q^{77} +21.9476 q^{78} -138.608i q^{79} -33.1032 q^{81} +35.8787 q^{82} -33.5348i q^{83} -45.4526i q^{84} -92.0850i q^{86} -13.4132 q^{87} +10.6679i q^{88} +49.1683i q^{89} +67.2457i q^{91} +(45.8644 + 3.52974i) q^{92} -97.8888 q^{93} +7.30926 q^{94} -12.9552 q^{96} +138.450i q^{97} +69.9666 q^{98} +14.1630i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 48 q^{4} + 8 q^{6} + 96 q^{9}+O(q^{10}) \) 24 * q + 48 * q^4 + 8 * q^6 + 96 * q^9	\( 24 q + 48 q^{4} + 8 q^{6} + 96 q^{9} + 96 q^{16} + 16 q^{24} - 32 q^{26} - 100 q^{29} - 124 q^{31} + 192 q^{36} - 192 q^{39} - 116 q^{41} + 148 q^{46} + 76 q^{49} + 16 q^{54} - 84 q^{59} + 192 q^{64} + 340 q^{69} + 196 q^{71} + 1360 q^{81} + 376 q^{94} + 32 q^{96}+O(q^{100}) \) 24 * q + 48 * q^4 + 8 * q^6 + 96 * q^9 + 96 * q^16 + 16 * q^24 - 32 * q^26 - 100 * q^29 - 124 * q^31 + 192 * q^36 - 192 * q^39 - 116 * q^41 + 148 * q^46 + 76 * q^49 + 16 * q^54 - 84 * q^59 + 192 * q^64 + 340 * q^69 + 196 * q^71 + 1360 * q^81 + 376 * q^94 + 32 * q^96

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