LMFDB - Embedded newform 275.3.q.a.24.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(24,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.24"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.q (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-22,0,-50] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			24.2
Root			$0.951057 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	275.24
Dual form			275.3.q.a.149.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.951057 - 2.92705i) q^{2} +(-2.71441 - 3.73607i) q^{3} +(-4.42705 - 3.21644i) q^{4} +(-13.5172 + 4.39201i) q^{6} +(-8.78402 - 6.38197i) q^{7} +(-3.66547 + 2.66312i) q^{8} +(-3.80902 + 11.7229i) q^{9} +(10.3713 + 3.66547i) q^{11} +25.2705i q^{12} +(3.52671 - 10.8541i) q^{13} +(-27.0344 + 19.6417i) q^{14} +(-2.45492 - 7.55545i) q^{16} +(6.96767 + 21.4443i) q^{17} +(30.6911 + 22.2984i) q^{18} +(-4.96149 - 6.82891i) q^{19} +50.1410i q^{21} +(20.5927 - 26.8713i) q^{22} +0.472136i q^{23} +(19.8992 + 6.46564i) q^{24} +(-28.4164 - 20.6457i) q^{26} +(14.6089 - 4.74671i) q^{27} +(18.3601 + 56.5066i) q^{28} +(9.67376 - 13.3148i) q^{29} +(9.96556 - 30.6708i) q^{31} -42.5730 q^{32} +(-14.4576 - 48.6976i) q^{33} +69.3951 q^{34} +(54.5689 - 39.6466i) q^{36} +(-5.21682 + 7.18034i) q^{37} +(-24.7072 + 8.02786i) q^{38} +(-50.1246 + 16.2865i) q^{39} +(15.5902 + 21.4580i) q^{41} +(146.765 + 47.6869i) q^{42} -50.0350 q^{43} +(-34.1246 - 49.5860i) q^{44} +(1.38197 + 0.449028i) q^{46} +(20.6052 + 28.3607i) q^{47} +(-21.5640 + 29.6803i) q^{48} +(21.2877 + 65.5169i) q^{49} +(61.2041 - 84.2403i) q^{51} +(-50.5245 + 36.7082i) q^{52} +(31.9929 + 10.3951i) q^{53} -47.2753i q^{54} +49.1935 q^{56} +(-12.0457 + 37.0729i) q^{57} +(-29.7728 - 40.9787i) q^{58} +(-89.4681 - 65.0024i) q^{59} +(-71.4296 + 23.2089i) q^{61} +(-80.2973 - 58.3394i) q^{62} +(108.274 - 78.6656i) q^{63} +(-30.6697 + 94.3916i) q^{64} +(-156.290 - 3.99598i) q^{66} -44.4508i q^{67} +(38.1280 - 117.346i) q^{68} +(1.76393 - 1.28157i) q^{69} +(-16.2148 - 49.9040i) q^{71} +(-17.2578 - 53.1140i) q^{72} +(-63.7535 - 46.3197i) q^{73} +(16.0557 + 22.0988i) q^{74} +46.1903i q^{76} +(-67.7090 - 98.3870i) q^{77} +162.207i q^{78} +(121.151 + 39.3643i) q^{79} +(32.3607 + 23.5114i) q^{81} +(77.6359 - 25.2254i) q^{82} +(11.5765 + 35.6287i) q^{83} +(161.276 - 221.977i) q^{84} +(-47.5861 + 146.455i) q^{86} -76.0035 q^{87} +(-47.7773 + 14.1844i) q^{88} -108.326 q^{89} +(-100.249 + 72.8353i) q^{91} +(1.51860 - 2.09017i) q^{92} +(-141.639 + 46.0213i) q^{93} +(102.610 - 33.3400i) q^{94} +(115.561 + 159.056i) q^{96} +(-58.7863 - 19.1008i) q^{97} +212.017 q^{98} +(-82.4746 + 107.621i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 22 q^{4} - 50 q^{6} - 26 q^{9} - 2 q^{11} - 100 q^{14} - 42 q^{16} + 90 q^{19} + 110 q^{24} - 120 q^{26} + 140 q^{29} + 196 q^{31} + 260 q^{34} + 204 q^{36} - 240 q^{39} + 80 q^{41} - 112 q^{44} + 20 q^{46}+ \cdots - 226 q^{99}+O(q^{100}) $ 8 * q - 22 * q^4 - 50 * q^6 - 26 * q^9 - 2 * q^11 - 100 * q^14 - 42 * q^16 + 90 * q^19 + 110 * q^24 - 120 * q^26 + 140 * q^29 + 196 * q^31 + 260 * q^34 + 204 * q^36 - 240 * q^39 + 80 * q^41 - 112 * q^44 + 20 * q^46 - 22 * q^49 + 190 * q^51 - 434 * q^59 - 160 * q^61 - 62 * q^64 - 660 * q^66 + 32 * q^69 + 76 * q^71 + 200 * q^74 + 200 * q^79 + 80 * q^81 + 360 * q^84 - 90 * q^86 - 804 * q^89 - 480 * q^91 + 320 * q^94 + 200 * q^96 - 226 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.951057	−	2.92705i	0.475528	−	1.46353i	−0.369716	−	0.929145i	$-0.620545\pi$
$2$	0.951057	−	2.92705i	0.475528	−	1.46353i	0.845244	−	0.534381i	$-0.179455\pi$
$3$	−2.71441	−	3.73607i	−0.904804	−	1.24536i	−0.968910	−	0.247413i	$-0.920420\pi$
$3$	−2.71441	−	3.73607i	−0.904804	−	1.24536i	0.0641060	−	0.997943i	$-0.479580\pi$
$4$	−4.42705	−	3.21644i	−1.10676	−	0.804110i
$5$		0			0
$5$		0			0
$6$	−13.5172	+	4.39201i	−2.25287	+	0.732002i
$7$	−8.78402	−	6.38197i	−1.25486	−	0.911709i	−0.256367	−	0.966580i	$-0.582526\pi$
$7$	−8.78402	−	6.38197i	−1.25486	−	0.911709i	−0.998494	+	0.0548701i	$0.982526\pi$
$8$	−3.66547	+	2.66312i	−0.458184	+	0.332890i
$9$	−3.80902	+	11.7229i	−0.423224	+	1.30255i
$10$		0			0
$11$	10.3713	+	3.66547i	0.942848	+	0.333224i
$11$	10.3713	+	3.66547i	0.942848	+	0.333224i
$12$			25.2705i			2.10588i
$13$	3.52671	−	10.8541i	0.271286	−	0.834931i	−0.718893	−	0.695121i	$-0.755351\pi$
$13$	3.52671	−	10.8541i	0.271286	−	0.834931i	0.990178	−	0.139810i	$-0.0446492\pi$
$14$	−27.0344	+	19.6417i	−1.93103	+	1.40298i
$15$		0			0
$16$	−2.45492	−	7.55545i	−0.153432	−	0.472216i
$17$	6.96767	+	21.4443i	0.409863	+	1.26143i	0.916766	+	0.399425i	$0.130790\pi$
$17$	6.96767	+	21.4443i	0.409863	+	1.26143i	−0.506903	+	0.862003i	$0.669210\pi$
$18$	30.6911	+	22.2984i	1.70506	+	1.23880i
$19$	−4.96149	−	6.82891i	−0.261131	−	0.359416i	0.658239	−	0.752809i	$-0.271301\pi$
$19$	−4.96149	−	6.82891i	−0.261131	−	0.359416i	−0.919371	+	0.393392i	$0.871301\pi$
$20$		0			0
$21$			50.1410i			2.38767i
$22$	20.5927	−	26.8713i	0.936033	−	1.22142i
$23$			0.472136i			0.0205277i	0.999947	+	0.0102638i	$0.00326713\pi$
$23$			0.472136i			0.0205277i	−0.999947	+	0.0102638i	$0.996733\pi$
$24$	19.8992	+	6.46564i	0.829133	+	0.269402i
$25$		0			0
$26$	−28.4164	−	20.6457i	−1.09294	−	0.794066i
$27$	14.6089	−	4.74671i	0.541069	−	0.175804i
$28$	18.3601	+	56.5066i	0.655718	+	2.01809i
$29$	9.67376	−	13.3148i	0.333578	−	0.459131i	−0.608974	−	0.793190i	$-0.708419\pi$
$29$	9.67376	−	13.3148i	0.333578	−	0.459131i	0.942552	+	0.334059i	$0.108419\pi$
$30$		0			0
$31$	9.96556	−	30.6708i	0.321470	−	0.989382i	−0.651539	−	0.758615i	$-0.725876\pi$
$31$	9.96556	−	30.6708i	0.321470	−	0.989382i	0.973009	−	0.230767i	$-0.0741235\pi$
$32$	−42.5730			−1.33041
$33$	−14.4576	−	48.6976i	−0.438109	−	1.47568i
$34$	69.3951			2.04103
$35$		0			0
$36$	54.5689	−	39.6466i	1.51580	−	1.10129i
$37$	−5.21682	+	7.18034i	−0.140995	+	0.194063i	−0.873675	−	0.486511i	$-0.838269\pi$
$37$	−5.21682	+	7.18034i	−0.140995	+	0.194063i	0.732679	+	0.680574i	$0.238269\pi$
$38$	−24.7072	+	8.02786i	−0.650190	+	0.211260i
$39$	−50.1246	+	16.2865i	−1.28525	+	0.417602i
$40$		0			0
$41$	15.5902	+	21.4580i	0.380248	+	0.523367i	0.955650	−	0.294504i	$-0.0951545\pi$
$41$	15.5902	+	21.4580i	0.380248	+	0.523367i	−0.575402	+	0.817871i	$0.695154\pi$
$42$	146.765	+	47.6869i	3.49441	+	1.13540i
$43$	−50.0350			−1.16360			−0.581802	−	0.813330i	$-0.697652\pi$
$43$	−50.0350			−1.16360			−0.581802	+	0.813330i	$0.697652\pi$
$44$	−34.1246	−	49.5860i	−0.775559	−	1.12695i
$45$		0			0
$46$	1.38197	+	0.449028i	0.0300427	+	0.00976148i
$47$	20.6052	+	28.3607i	0.438409	+	0.603419i	0.969858	−	0.243672i	$-0.0783520\pi$
$47$	20.6052	+	28.3607i	0.438409	+	0.603419i	−0.531448	+	0.847091i	$0.678352\pi$
$48$	−21.5640	+	29.6803i	−0.449251	+	0.618340i
$49$	21.2877	+	65.5169i	0.434443	+	1.33708i
$50$		0			0
$51$	61.2041	−	84.2403i	1.20008	−	1.65177i
$52$	−50.5245	+	36.7082i	−0.971625	+	0.705927i
$53$	31.9929	+	10.3951i	0.603640	+	0.196134i	0.594863	−	0.803827i	$-0.297206\pi$
$53$	31.9929	+	10.3951i	0.603640	+	0.196134i	0.00877654	+	0.999961i	$0.497206\pi$
$54$		−	47.2753i		−	0.875469i
$55$		0			0
$56$	49.1935			0.878455
$57$	−12.0457	+	37.0729i	−0.211329	+	0.650403i
$58$	−29.7728	−	40.9787i	−0.513324	−	0.706530i
$59$	−89.4681	−	65.0024i	−1.51641	−	1.10173i	−0.963232	−	0.268670i	$-0.913416\pi$
$59$	−89.4681	−	65.0024i	−1.51641	−	1.10173i	−0.553176	−	0.833065i	$-0.686584\pi$
$60$		0			0
$61$	−71.4296	+	23.2089i	−1.17098	+	0.380473i	−0.829007	−	0.559238i	$-0.811094\pi$
$61$	−71.4296	+	23.2089i	−1.17098	+	0.380473i	−0.341969	+	0.939711i	$0.611094\pi$
$62$	−80.2973	−	58.3394i	−1.29512	−	0.940958i
$63$	108.274	−	78.6656i	1.71863	−	1.24866i
$64$	−30.6697	+	94.3916i	−0.479214	+	1.47487i
$65$		0			0
$66$	−156.290	−	3.99598i	−2.36803	−	0.0605452i
$67$		−	44.4508i		−	0.663446i	−0.943377	−	0.331723i	$-0.892370\pi$
$67$		−	44.4508i		−	0.663446i	0.943377	−	0.331723i	$-0.107630\pi$
$68$	38.1280	−	117.346i	0.560706	−	1.72568i
$69$	1.76393	−	1.28157i	0.0255642	−	0.0185735i
$70$		0			0
$71$	−16.2148	−	49.9040i	−0.228377	−	0.702873i	−0.997931	−	0.0642910i	$-0.979521\pi$
$71$	−16.2148	−	49.9040i	−0.228377	−	0.702873i	0.769554	−	0.638582i	$-0.220479\pi$
$72$	−17.2578	−	53.1140i	−0.239691	−	0.737694i
$73$	−63.7535	−	46.3197i	−0.873336	−	0.634516i	0.0581439	−	0.998308i	$-0.481482\pi$
$73$	−63.7535	−	46.3197i	−0.873336	−	0.634516i	−0.931480	+	0.363792i	$0.881482\pi$
$74$	16.0557	+	22.0988i	0.216969	+	0.298633i
$75$		0			0
$76$			46.1903i			0.607767i
$77$	−67.7090	−	98.3870i	−0.879338	−	1.27775i
$78$			162.207i			2.07957i
$79$	121.151	+	39.3643i	1.53356	+	0.498283i	0.949590	−	0.313495i	$-0.101500\pi$
$79$	121.151	+	39.3643i	1.53356	+	0.498283i	0.583966	+	0.811778i	$0.301500\pi$
$80$		0			0
$81$	32.3607	+	23.5114i	0.399515	+	0.290264i
$82$	77.6359	−	25.2254i	0.946779	−	0.307627i
$83$	11.5765	+	35.6287i	0.139475	+	0.429261i	0.996259	−	0.0864145i	$-0.0275409\pi$
$83$	11.5765	+	35.6287i	0.139475	+	0.429261i	−0.856784	+	0.515676i	$0.827541\pi$
$84$	161.276	−	221.977i	1.91995	−	2.64258i
$85$		0			0
$86$	−47.5861	+	146.455i	−0.553327	+	1.70296i
$87$	−76.0035			−0.873604
$88$	−47.7773	+	14.1844i	−0.542924	+	0.161186i
$89$	−108.326			−1.21715			−0.608574	−	0.793497i	$-0.708258\pi$
$89$	−108.326			−1.21715			−0.608574	+	0.793497i	$0.708258\pi$
$90$		0			0
$91$	−100.249	+	72.8353i	−1.10164	+	0.800388i
$92$	1.51860	−	2.09017i	0.0165065	−	0.0227192i
$93$	−141.639	+	46.0213i	−1.52300	+	0.494853i
$94$	102.610	−	33.3400i	1.09159	−	0.354681i
$95$		0			0
$96$	115.561	+	159.056i	1.20376	+	1.65683i
$97$	−58.7863	−	19.1008i	−0.606044	−	0.196916i	−0.0101097	−	0.999949i	$-0.503218\pi$
$97$	−58.7863	−	19.1008i	−0.606044	−	0.196916i	−0.595934	+	0.803033i	$0.703218\pi$
$98$	212.017			2.16344
$99$	−82.4746	+	107.621i	−0.833077	+	1.08708i
$100$		0			0
$101$	54.8460	+	17.8205i	0.543029	+	0.176441i	0.567671	−	0.823255i	$-0.307845\pi$
$101$	54.8460	+	17.8205i	0.543029	+	0.176441i	−0.0246418	+	0.999696i	$0.507845\pi$
$102$	−188.367	−	259.265i	−1.84673	−	2.54181i
$103$	64.6063	−	88.9230i	0.627246	−	0.863330i	−0.370609	−	0.928789i	$-0.620851\pi$
$103$	64.6063	−	88.9230i	0.627246	−	0.863330i	0.997855	+	0.0654589i	$0.0208511\pi$
$104$	15.9787	+	49.1774i	0.153641	+	0.472860i
$105$		0			0
$106$	60.8541	−	83.7585i	0.574095	−	0.790174i
$107$	45.3934	−	32.9803i	0.424238	−	0.308227i	−0.355103	−	0.934827i	$-0.615554\pi$
$107$	45.3934	−	32.9803i	0.424238	−	0.308227i	0.779341	+	0.626600i	$0.215554\pi$
$108$	−79.9417	−	25.9746i	−0.740201	−	0.240506i
$109$		−	64.2478i		−	0.589430i	−0.955585	−	0.294715i	$-0.904775\pi$
$109$		−	64.2478i		−	0.589430i	0.955585	−	0.294715i	$-0.0952247\pi$
$110$		0			0
$111$	40.9868			0.369251
$112$	−26.6546	+	82.0344i	−0.237988	+	0.732450i
$113$	−5.26982	−	7.25329i	−0.0466356	−	0.0641884i	0.785062	−	0.619417i	$-0.212631\pi$
$113$	−5.26982	−	7.25329i	−0.0466356	−	0.0641884i	−0.831698	+	0.555228i	$0.812631\pi$
$114$	97.0582	+	70.5169i	0.851388	+	0.618570i
$115$		0			0
$116$	−85.6525	+	27.8302i	−0.738383	+	0.239915i
$117$	113.809	+	82.6869i	0.972725	+	0.706726i
$118$	−275.354	+	200.057i	−2.33351	+	1.69540i
$119$	75.6525	−	232.834i	0.635735	−	1.95659i
$120$		0			0
$121$	94.1287	+	76.0315i	0.777923	+	0.628360i
$122$			231.151i			1.89468i
$123$	37.8505	−	116.492i	0.307728	−	0.947088i
$124$	−142.769	+	103.728i	−1.15136	+	0.836514i
$125$		0			0
$126$	−127.284	−	391.739i	−1.01019	−	3.10904i
$127$	−46.5893	−	143.387i	−0.366845	−	1.12903i	−0.948818	−	0.315824i	$-0.897719\pi$
$127$	−46.5893	−	143.387i	−0.366845	−	1.12903i	0.581973	−	0.813208i	$-0.302281\pi$
$128$	109.351	+	79.4483i	0.854307	+	0.620690i
$129$	135.816	+	186.934i	1.05283	+	1.44910i
$130$		0			0
$131$		−	97.0983i		−	0.741208i	−0.928791	−	0.370604i	$-0.879151\pi$
$131$		−	97.0983i		−	0.741208i	0.928791	−	0.370604i	$-0.120849\pi$
$132$	−92.6283	+	262.089i	−0.701729	+	1.98552i
$133$			91.6494i			0.689093i
$134$	−130.110	−	42.2753i	−0.970969	−	0.315487i
$135$		0			0
$136$	−82.6484	−	60.0476i	−0.607709	−	0.441526i
$137$	199.200	−	64.7239i	1.45401	−	0.472437i	0.527777	−	0.849383i	$-0.323026\pi$
$137$	199.200	−	64.7239i	1.45401	−	0.472437i	0.926235	+	0.376946i	$0.123026\pi$
$138$	−2.07363	−	6.38197i	−0.0150263	−	0.0462461i
$139$	4.72136	−	6.49839i	0.0339666	−	0.0467510i	−0.791696	−	0.610915i	$-0.790802\pi$
$139$	4.72136	−	6.49839i	0.0339666	−	0.0467510i	0.825663	+	0.564164i	$0.190802\pi$
$140$		0			0
$141$	50.0263	−	153.965i	0.354797	−	1.09195i
$142$	−161.493			−1.13727
$143$	76.3620	−	99.6443i	0.534000	−	0.696814i
$144$	97.9230			0.680021
$145$		0			0
$146$	−196.213	+	142.557i	−1.34393	+	0.976420i
$147$	186.992	−	257.372i	1.27205	−	1.75083i
$148$	46.1903	−	15.0081i	0.312096	−	0.101406i
$149$	44.3951	−	14.4248i	0.297954	−	0.0968111i	−0.156225	−	0.987721i	$-0.549933\pi$
$149$	44.3951	−	14.4248i	0.297954	−	0.0968111i	0.454179	+	0.890910i	$0.349933\pi$
$150$		0			0
$151$	44.1459	+	60.7616i	0.292357	+	0.402395i	0.929778	−	0.368121i	$-0.119999\pi$
$151$	44.1459	+	60.7616i	0.292357	+	0.402395i	−0.637421	+	0.770516i	$0.719999\pi$
$152$	36.3724	+	11.8181i	0.239292	+	0.0777507i
$153$	−277.930			−1.81654
$154$	−352.379	+	104.616i	−2.28817	+	0.679326i
$155$		0			0
$156$	274.289	+	89.1218i	1.75826	+	0.571294i
$157$	−21.7462	−	29.9311i	−0.138511	−	0.190644i	0.734126	−	0.679013i	$-0.237592\pi$
$157$	−21.7462	−	29.9311i	−0.138511	−	0.190644i	−0.872637	+	0.488369i	$0.837592\pi$
$158$	230.443	−	317.177i	1.45850	−	2.00745i
$159$	−48.0050	−	147.744i	−0.301918	−	0.929209i
$160$		0			0
$161$	3.01316	−	4.14725i	0.0187153	−	0.0257593i
$162$	99.5959	−	72.3607i	0.614790	−	0.446671i
$163$	44.7074	+	14.5263i	0.274278	+	0.0891185i	0.442927	−	0.896558i	$-0.353940\pi$
$163$	44.7074	+	14.5263i	0.274278	+	0.0891185i	−0.168648	+	0.985676i	$0.553940\pi$
$164$		−	145.141i		−	0.885004i
$165$		0			0
$166$	115.297			0.694559
$167$	14.7119	−	45.2786i	0.0880953	−	0.271130i	−0.897297	−	0.441426i	$-0.854473\pi$
$167$	14.7119	−	45.2786i	0.0880953	−	0.271130i	0.985393	+	0.170297i	$0.0544726\pi$
$168$	−133.531	−	183.790i	−0.794830	−	1.09399i
$169$	31.3500	+	22.7771i	0.185503	+	0.134776i
$170$		0			0
$171$	98.9534	−	32.1519i	0.578675	−	0.188023i
$172$	221.507	+	160.935i	1.28783	+	0.935666i
$173$	154.439	−	112.207i	0.892712	−	0.648593i	−0.0438716	−	0.999037i	$-0.513969\pi$
$173$	154.439	−	112.207i	0.892712	−	0.648593i	0.936584	+	0.350444i	$0.113969\pi$
$174$	−72.2837	+	222.466i	−0.415423	+	1.27854i
$175$		0			0
$176$	2.23356	−	87.3584i	0.0126907	−	0.496355i
$177$			510.702i			2.88532i
$178$	−103.024	+	317.076i	−0.578789	+	1.78133i
$179$	208.919	−	151.788i	1.16714	−	0.847980i	0.176480	−	0.984304i	$-0.443529\pi$
$179$	208.919	−	151.788i	1.16714	−	0.847980i	0.990664	+	0.136324i	$0.0435288\pi$
$180$		0			0
$181$	−50.8115	−	156.382i	−0.280727	−	0.863988i	−0.987647	−	0.156695i	$-0.949916\pi$
$181$	−50.8115	−	156.382i	−0.280727	−	0.863988i	0.706920	−	0.707293i	$-0.250084\pi$
$182$	117.850	+	362.705i	0.647528	+	1.99289i
$183$	280.599	+	203.867i	1.53333	+	1.11403i
$184$	−1.25735	−	1.73060i	−0.00683345	−	0.00940543i
$185$		0			0
$186$			458.353i			2.46426i
$187$	−6.33939	+	247.945i	−0.0339005	+	1.32591i
$188$		−	191.830i		−	1.02037i
$189$	−158.618	−	51.5381i	−0.839249	−	0.272688i
$190$		0			0
$191$	30.7426	+	22.3358i	0.160956	+	0.116942i	0.665348	−	0.746533i	$-0.268283\pi$
$191$	30.7426	+	22.3358i	0.160956	+	0.116942i	−0.504392	+	0.863475i	$0.668283\pi$
$192$	435.904	−	141.634i	2.27033	−	0.737676i
$193$	1.45309	+	4.47214i	0.00752894	+	0.0231717i	0.954750	−	0.297408i	$-0.0961222\pi$
$193$	1.45309	+	4.47214i	0.00752894	+	0.0231717i	−0.947221	+	0.320580i	$0.896122\pi$
$194$	−111.818	+	153.904i	−0.576382	+	0.793322i
$195$		0			0
$196$	116.489	−	358.517i	0.594333	−	1.82917i
$197$	−107.254			−0.544439			−0.272219	−	0.962235i	$-0.587758\pi$
$197$	−107.254			−0.544439			−0.272219	+	0.962235i	$0.587758\pi$
$198$	236.573	+	343.761i	1.19481	+	1.73617i
$199$	−18.5936			−0.0934354			−0.0467177	−	0.998908i	$-0.514876\pi$
$199$	−18.5936			−0.0934354			−0.0467177	+	0.998908i	$0.514876\pi$
$200$		0			0
$201$	−166.071	+	120.658i	−0.826226	+	0.600288i
$202$	104.323	−	143.589i	0.516452	−	0.710835i
$203$	−169.949	+	55.2198i	−0.837188	+	0.272019i
$204$	−541.908	+	176.076i	−2.65641	+	0.863120i
$205$		0			0
$206$	−198.838	−	273.677i	−0.965232	−	1.32853i
$207$	−5.53483	−	1.79837i	−0.0267383	−	0.00868780i
$208$	−90.6654			−0.435891
$209$	−26.4261	−	89.0110i	−0.126441	−	0.425890i
$210$		0			0
$211$	−92.8829	−	30.1795i	−0.440203	−	0.143031i	0.0805260	−	0.996753i	$-0.474340\pi$
$211$	−92.8829	−	30.1795i	−0.440203	−	0.143031i	−0.520729	+	0.853722i	$0.674340\pi$
$212$	−108.199	−	148.923i	−0.510372	−	0.702467i
$213$	−142.431	+	196.039i	−0.668690	+	0.920373i
$214$	−53.3632	−	164.235i	−0.249361	−	0.767453i
$215$		0			0
$216$	−40.9073	+	56.3041i	−0.189386	+	0.260667i
$217$	−283.278	+	205.813i	−1.30543	+	0.948449i
$218$	−188.057	−	61.1033i	−0.862645	−	0.280290i
$219$			363.918i			1.66173i
$220$		0			0
$221$	257.331			1.16439
$222$	38.9808	−	119.971i	0.175589	−	0.540408i
$223$	222.990	+	306.920i	0.999957	+	1.37632i	0.925352	+	0.379109i	$0.123770\pi$
$223$	222.990	+	306.920i	0.999957	+	1.37632i	0.0746047	+	0.997213i	$0.476230\pi$
$224$	373.962	+	271.700i	1.66948	+	1.21294i
$225$		0			0
$226$	−26.2426	+	8.52675i	−0.116118	+	0.0377290i
$227$	−168.624	−	122.513i	−0.742837	−	0.539703i	0.150761	−	0.988570i	$-0.451828\pi$
$227$	−168.624	−	122.513i	−0.742837	−	0.539703i	−0.893598	+	0.448867i	$0.851828\pi$
$228$	172.570	−	125.379i	0.756886	−	0.549910i
$229$	19.2179	−	59.1466i	0.0839209	−	0.258282i	−0.900287	−	0.435296i	$-0.856644\pi$
$229$	19.2179	−	59.1466i	0.0839209	−	0.258282i	0.984208	+	0.177014i	$0.0566438\pi$
$230$		0			0
$231$	−183.790	+	520.028i	−0.795629	+	2.25121i
$232$			74.5673i			0.321411i
$233$	−85.6124	+	263.488i	−0.367435	+	1.13085i	0.581007	+	0.813899i	$0.302659\pi$
$233$	−85.6124	+	263.488i	−0.367435	+	1.13085i	−0.948442	+	0.316950i	$0.897341\pi$
$234$	350.267	−	254.484i	1.49687	−	1.08754i
$235$		0			0
$236$	187.003	+	575.538i	0.792388	+	2.43872i
$237$	−181.786	−	559.479i	−0.767029	−	2.36067i
$238$	−609.568	−	442.877i	−2.56121	−	1.86083i
$239$	87.2179	+	120.045i	0.364928	+	0.502281i	0.951514	−	0.307607i	$-0.0995281\pi$
$239$	87.2179	+	120.045i	0.364928	+	0.502281i	−0.586585	+	0.809888i	$0.699528\pi$
$240$		0			0
$241$		−	413.928i		−	1.71754i	−0.512358	−	0.858772i	$-0.671228\pi$
$241$		−	413.928i		−	1.71754i	0.512358	−	0.858772i	$-0.328772\pi$
$242$	312.070	−	203.209i	1.28954	−	0.839707i
$243$		−	322.967i		−	1.32908i
$244$	390.872	+	127.002i	1.60194	+	0.520500i
$245$		0			0
$246$	−304.980	−	221.581i	−1.23975	−	0.900735i
$247$	−91.6194	+	29.7690i	−0.370929	+	0.120522i
$248$	45.1516	+	138.962i	0.182063	+	0.560332i
$249$	101.688	−	139.961i	0.408385	−	0.562094i
$250$		0			0
$251$	115.281	−	354.797i	0.459285	−	1.41353i	−0.406745	−	0.913542i	$-0.633336\pi$
$251$	115.281	−	354.797i	0.459285	−	1.41353i	0.866030	−	0.499992i	$-0.166664\pi$
$252$	−732.358			−2.90618
$253$	−1.73060	+	4.89667i	−0.00684031	+	0.0193544i
$254$	−464.010			−1.82681
$255$		0			0
$256$	15.3713	−	11.1679i	0.0600442	−	0.0436247i
$257$	−119.953	+	165.102i	−0.466745	+	0.642419i	−0.975890	−	0.218261i	$-0.929962\pi$
$257$	−119.953	+	165.102i	−0.466745	+	0.642419i	0.509145	+	0.860681i	$0.329962\pi$
$258$	676.334	−	219.754i	2.62145	−	0.851761i
$259$	91.6494	−	29.7787i	0.353859	−	0.114976i
$260$		0			0
$261$	119.241	+	164.121i	0.456862	+	0.628817i
$262$	−284.212	−	92.3460i	−1.08478	−	0.352466i
$263$	−64.2788			−0.244406			−0.122203	−	0.992505i	$-0.538996\pi$
$263$	−64.2788			−0.244406			−0.122203	+	0.992505i	$0.538996\pi$
$264$	182.681	+	139.997i	0.691975	+	0.530292i
$265$		0			0
$266$	268.262	+	87.1637i	1.00851	+	0.327683i
$267$	294.042	+	404.714i	1.10128	+	1.51578i
$268$	−142.974	+	196.786i	−0.533483	+	0.734277i
$269$	69.0050	+	212.376i	0.256524	+	0.789500i	0.993526	+	0.113609i	$0.0362412\pi$
$269$	69.0050	+	212.376i	0.256524	+	0.789500i	−0.737001	+	0.675891i	$0.763759\pi$
$270$		0			0
$271$	−165.220	+	227.406i	−0.609667	+	0.839135i	−0.996550	−	0.0829940i	$-0.973552\pi$
$271$	−165.220	+	227.406i	−0.609667	+	0.839135i	0.386883	+	0.922129i	$0.373552\pi$
$272$	144.916	−	105.288i	0.532780	−	0.387087i
$273$	544.235	+	176.833i	1.99354	+	0.647739i
$274$		−	644.623i		−	2.35264i
$275$		0			0
$276$	−11.9311			−0.0432287
$277$	37.2156	−	114.538i	0.134352	−	0.413494i	−0.861136	−	0.508374i	$-0.830247\pi$
$277$	37.2156	−	114.538i	0.134352	−	0.413494i	0.995489	+	0.0948799i	$0.0302467\pi$
$278$	−14.5309	−	20.0000i	−0.0522692	−	0.0719424i
$279$	321.594	+	233.651i	1.15267	+	0.837460i
$280$		0			0
$281$	−385.665	+	125.310i	−1.37247	+	0.445944i	−0.900188	−	0.435502i	$-0.856571\pi$
$281$	−385.665	+	125.310i	−1.37247	+	0.445944i	−0.472286	+	0.881446i	$0.656571\pi$
$282$	−403.086	−	292.859i	−1.42938	−	1.03851i
$283$	−446.305	+	324.259i	−1.57705	+	1.14579i	−0.657065	+	0.753834i	$0.728202\pi$
$283$	−446.305	+	324.259i	−1.57705	+	1.14579i	−0.919983	+	0.391959i	$0.871798\pi$
$284$	−88.7295	+	273.081i	−0.312428	+	0.961554i
$285$		0			0
$286$	−219.039	−	318.283i	−0.765872	−	1.11288i
$287$		−	287.984i		−	1.00343i
$288$	162.161	−	499.081i	0.563060	−	1.73292i
$289$	−177.503	+	128.963i	−0.614196	+	0.446239i
$290$		0			0
$291$	88.2082	+	271.477i	0.303121	+	0.932910i
$292$	133.256	+	410.119i	0.456355	+	1.40452i
$293$	−260.493	−	189.259i	−0.889055	−	0.645936i	0.0465766	−	0.998915i	$-0.485169\pi$
$293$	−260.493	−	189.259i	−0.889055	−	0.645936i	−0.935631	+	0.352979i	$0.885169\pi$
$294$	−575.502	−	792.110i	−1.95749	−	2.69425i
$295$		0			0
$296$		−	40.2123i		−	0.135852i
$297$	168.912	+	4.31870i	0.568728	+	0.0145411i
$298$		−	143.666i		−	0.482099i
$299$	5.12461	+	1.66509i	0.0171392	+	0.00556885i
$300$		0			0
$301$	439.508	+	319.322i	1.46016	+	1.06087i
$302$	219.838	−	71.4296i	0.727939	−	0.236522i
$303$	−82.2958	−	253.281i	−0.271603	−	0.835909i
$304$	−39.4154	+	54.2507i	−0.129656	+	0.178456i
$305$		0			0
$306$	−264.327	+	813.515i	−0.863814	+	2.65855i
$307$	100.126			0.326143			0.163072	−	0.986614i	$-0.447860\pi$
$307$	100.126			0.326143			0.163072	+	0.986614i	$0.447860\pi$
$308$	−16.7046	+	653.346i	−0.0542356	+	2.12125i
$309$	−507.591			−1.64269
$310$		0			0
$311$	159.456	−	115.851i	0.512720	−	0.372513i	−0.301135	−	0.953582i	$-0.597365\pi$
$311$	159.456	−	115.851i	0.512720	−	0.372513i	0.813854	+	0.581069i	$0.197365\pi$
$312$	140.357	−	193.185i	0.449863	−	0.619184i
$313$	231.099	−	75.0886i	0.738335	−	0.239900i	0.0843809	−	0.996434i	$-0.473109\pi$
$313$	231.099	−	75.0886i	0.738335	−	0.239900i	0.653955	+	0.756534i	$0.273109\pi$
$314$	−108.292	+	35.1861i	−0.344878	+	0.112058i
$315$		0			0
$316$	−409.728	−	563.943i	−1.29661	−	1.78463i
$317$	537.949	+	174.790i	1.69700	+	0.551389i	0.988086	−	0.153906i	$-0.0491851\pi$
$317$	537.949	+	174.790i	1.69700	+	0.551389i	0.708915	+	0.705294i	$0.249185\pi$
$318$	−478.111			−1.50349
$319$	149.135	−	102.633i	0.467507	−	0.321734i
$320$		0			0
$321$	−246.433	−	80.0709i	−0.767704	−	0.249442i
$322$	−9.27354	−	12.7639i	−0.0287998	−	0.0396395i
$323$	111.871	−	153.977i	0.346350	−	0.476709i
$324$	−67.6393	−	208.172i	−0.208763	−	0.642507i
$325$		0			0
$326$	85.0385	−	117.045i	0.260854	−	0.359035i
$327$	−240.034	+	174.395i	−0.734050	+	0.533318i
$328$	−114.291	−	37.1353i	−0.348447	−	0.113217i
$329$		−	380.623i		−	1.15691i
$330$		0			0
$331$	−144.353			−0.436110			−0.218055	−	0.975936i	$-0.569971\pi$
$331$	−144.353			−0.436110			−0.218055	+	0.975936i	$0.569971\pi$
$332$	63.3480	−	194.965i	0.190807	−	0.587244i
$333$	−64.3038	−	88.5066i	−0.193104	−	0.265786i
$334$	−118.541	−	86.1251i	−0.354913	−	0.257860i
$335$		0			0
$336$	378.838	−	123.092i	1.12749	−	0.366345i
$337$	156.516	+	113.715i	0.464439	+	0.337434i	0.795270	−	0.606256i	$-0.207329\pi$
$337$	156.516	+	113.715i	0.464439	+	0.337434i	−0.330831	+	0.943690i	$0.607329\pi$
$338$	96.4855	−	70.1008i	0.285460	−	0.207399i
$339$	−12.7943	+	39.3768i	−0.0377413	+	0.116156i
$340$		0			0
$341$	215.779	−	281.569i	0.632783	−	0.825715i
$342$		−	320.220i		−	0.936315i
$343$	66.7300	−	205.374i	0.194548	−	0.598758i
$344$	183.402	−	133.249i	0.533144	−	0.387352i
$345$		0			0
$346$	−181.554	−	558.766i	−0.524723	−	1.61493i
$347$	81.0382	+	249.410i	0.233539	+	0.718760i	0.997312	+	0.0732747i	$0.0233450\pi$
$347$	81.0382	+	249.410i	0.233539	+	0.718760i	−0.763772	+	0.645486i	$0.776655\pi$
$348$	336.472	+	244.461i	0.966872	+	0.702474i
$349$	−70.2310	−	96.6647i	−0.201235	−	0.276976i	0.696458	−	0.717597i	$-0.254758\pi$
$349$	−70.2310	−	96.6647i	−0.201235	−	0.276976i	−0.897693	+	0.440621i	$0.854758\pi$
$350$		0			0
$351$		−	175.306i		−	0.499449i
$352$	−441.539	−	156.050i	−1.25437	−	0.443324i
$353$			150.674i			0.426838i	0.976961	+	0.213419i	$0.0684599\pi$
$353$			150.674i			0.426838i	−0.976961	+	0.213419i	$0.931540\pi$
$354$	1494.85	+	485.706i	4.22274	+	1.37205i
$355$		0			0
$356$	479.566	+	348.425i	1.34709	+	0.978722i
$357$	−1075.24	+	349.366i	−3.01187	+	0.978615i
$358$	−245.599	−	755.876i	−0.686031	−	2.11138i
$359$	−160.143	+	220.418i	−0.446080	+	0.613977i	−0.971550	−	0.236836i	$-0.923890\pi$
$359$	−160.143	+	220.418i	−0.446080	+	0.613977i	0.525470	+	0.850812i	$0.323890\pi$
$360$		0			0
$361$	89.5375	−	275.568i	0.248026	−	0.763347i
$362$	−506.062			−1.39796
$363$	28.5549	−	558.052i	0.0786636	−	1.53733i
$364$	678.079			1.86285
$365$		0			0
$366$	863.596	−	627.439i	2.35955	−	1.71431i
$367$	380.644	−	523.912i	1.03718	−	1.42755i	0.137758	−	0.990466i	$-0.456010\pi$
$367$	380.644	−	523.912i	1.03718	−	1.42755i	0.899419	−	0.437087i	$-0.143990\pi$
$368$	3.56720	−	1.15905i	0.00969348	−	0.00314960i
$369$	−310.935	+	101.029i	−0.842641	+	0.273791i
$370$		0			0
$371$	−214.685	−	295.489i	−0.578666	−	0.796465i
$372$	775.068	+	251.835i	2.08352	+	0.676975i
$373$	402.936			1.08026			0.540129	−	0.841583i	$-0.318376\pi$
$373$	402.936			1.08026			0.540129	+	0.841583i	$0.318376\pi$
$374$	719.719	+	254.366i	1.92438	+	0.680122i
$375$		0			0
$376$	−151.056	−	49.0810i	−0.401744	−	0.130535i
$377$	−110.404	−	151.957i	−0.292848	−	0.403070i
$378$	−301.709	+	415.267i	−0.798173	+	1.09859i
$379$	−41.9023	−	128.962i	−0.110560	−	0.340269i	0.880435	−	0.474167i	$-0.157251\pi$
$379$	−41.9023	−	128.962i	−0.110560	−	0.340269i	−0.990995	+	0.133898i	$0.957251\pi$
$380$		0			0
$381$	−409.241	+	563.272i	−1.07412	+	1.47840i
$382$	94.6161	−	68.7426i	0.247686	−	0.179955i
$383$	−525.769	−	170.833i	−1.37277	−	0.446039i	−0.472481	−	0.881341i	$-0.656642\pi$
$383$	−525.769	−	170.833i	−1.37277	−	0.446039i	−0.900285	+	0.435302i	$0.856642\pi$
$384$		−	624.199i		−	1.62552i
$385$		0			0
$386$	14.4721			0.0374926
$387$	190.584	−	586.558i	0.492465	−	1.51565i
$388$	198.813	+	273.643i	0.512405	+	0.705265i
$389$	−107.164	−	77.8593i	−0.275486	−	0.200152i	0.441460	−	0.897281i	$-0.354461\pi$
$389$	−107.164	−	77.8593i	−0.275486	−	0.200152i	−0.716946	+	0.697129i	$0.754461\pi$
$390$		0			0
$391$	−10.1246	+	3.28969i	−0.0258941	+	0.00841352i
$392$	−252.509	−	183.458i	−0.644155	−	0.468006i
$393$	−362.766	+	263.565i	−0.923068	+	0.670648i
$394$	−102.005	+	313.939i	−0.258896	+	0.796800i
$395$		0			0
$396$	711.275	−	211.167i	1.79615	−	0.533251i
$397$			110.721i			0.278895i	0.990229	+	0.139448i	$0.0445327\pi$
$397$			110.721i			0.278895i	−0.990229	+	0.139448i	$0.955467\pi$
$398$	−17.6836	+	54.4245i	−0.0444312	+	0.136745i
$399$	342.408	−	248.774i	0.858166	−	0.623494i
$400$		0			0
$401$	9.64494	+	29.6841i	0.0240522	+	0.0740251i	0.962362	−	0.271770i	$-0.0876091\pi$
$401$	9.64494	+	29.6841i	0.0240522	+	0.0740251i	−0.938310	+	0.345795i	$0.887609\pi$
$402$	195.229	+	600.852i	0.485643	+	1.49466i
$403$	−297.759	−	216.334i	−0.738855	−	0.536810i
$404$	−185.487	−	255.301i	−0.459127	−	0.631934i
$405$		0			0
$406$			549.967i			1.35460i
$407$	−80.4247	+	55.3475i	−0.197604	+	0.135989i
$408$			471.774i			1.15631i
$409$	−436.217	−	141.735i	−1.06654	−	0.346541i	−0.277404	−	0.960753i	$-0.589474\pi$
$409$	−436.217	−	141.735i	−1.06654	−	0.346541i	−0.789141	+	0.614212i	$0.789474\pi$
$410$		0			0
$411$	−782.523	−	568.536i	−1.90395	−	1.38330i
$412$	−572.031	+	185.864i	−1.38842	+	0.451127i
$413$	371.047	+	1141.96i	0.898418	+	2.76505i
$414$	−10.5279	+	14.4904i	−0.0254296	+	0.0350009i
$415$		0			0
$416$	−150.143	+	462.092i	−0.360920	+	1.11080i
$417$	−37.0942			−0.0889548
$418$	−285.672	−	7.30399i	−0.683427	−	0.0174737i
$419$	47.0476			0.112285			0.0561427	−	0.998423i	$-0.482120\pi$
$419$	47.0476			0.112285			0.0561427	+	0.998423i	$0.482120\pi$
$420$		0			0
$421$	122.931	−	89.3147i	0.291998	−	0.212149i	−0.432136	−	0.901809i	$-0.642240\pi$
$421$	122.931	−	89.3147i	0.291998	−	0.212149i	0.724134	+	0.689660i	$0.242240\pi$
$422$	−176.674	+	243.171i	−0.418658	+	0.576234i
$423$	−410.957	+	133.528i	−0.971528	+	0.315669i
$424$	−144.952	+	47.0979i	−0.341869	+	0.111080i
$425$		0			0
$426$	438.358	+	603.347i	1.02901	+	1.41631i
$427$	775.557	+	251.994i	1.81629	+	0.590149i
$428$	−307.038			−0.717379
$429$	−579.556	−	14.8179i	−1.35095	−	0.0345406i
$430$		0			0
$431$	−492.254	−	159.943i	−1.14212	−	0.371098i	−0.323951	−	0.946074i	$-0.605011\pi$
$431$	−492.254	−	159.943i	−1.14212	−	0.371098i	−0.818170	+	0.574976i	$0.805011\pi$
$432$	−71.7271	−	98.7239i	−0.166035	−	0.228527i
$433$	244.693	−	336.791i	0.565111	−	0.777809i	−0.426854	−	0.904321i	$-0.640378\pi$
$433$	244.693	−	336.791i	0.565111	−	0.777809i	0.991965	+	0.126512i	$0.0403782\pi$
$434$	333.013	+	1024.91i	0.767311	+	2.36154i
$435$		0			0
$436$	−206.649	+	284.428i	−0.473966	+	0.652359i
$437$	3.22417	−	2.34250i	0.00737797	−	0.00536041i
$438$	1065.21	+	346.107i	2.43198	+	0.790198i
$439$			685.921i			1.56246i	0.624242	+	0.781231i	$0.285408\pi$
$439$			685.921i			1.56246i	−0.624242	+	0.781231i	$0.714592\pi$
$440$		0			0
$441$	−849.137			−1.92548
$442$	244.737	−	753.222i	0.553703	−	1.70412i
$443$	340.140	+	468.163i	0.767810	+	1.05680i	0.996524	+	0.0833065i	$0.0265481\pi$
$443$	340.140	+	468.163i	0.767810	+	1.05680i	−0.228714	+	0.973494i	$0.573452\pi$
$444$	−181.451	−	131.832i	−0.408673	−	0.296918i
$445$		0			0
$446$	1110.45	−	360.806i	2.48979	−	0.808982i
$447$	−174.399	−	126.708i	−0.390154	−	0.283464i
$448$	871.807	−	633.405i	1.94600	−	1.41385i
$449$	262.733	−	808.609i	0.585151	−	1.80091i	−0.0135103	−	0.999909i	$-0.504301\pi$
$449$	262.733	−	808.609i	0.585151	−	1.80091i	0.598662	−	0.801002i	$-0.295699\pi$
$450$		0			0
$451$	83.0370	+	279.693i	0.184117	+	0.620163i
$452$			49.0608i			0.108541i
$453$	107.179	−	329.864i	0.236599	−	0.728177i
$454$	−518.972	+	377.055i	−1.14311	+	0.830517i
$455$		0			0
$456$	−54.5764	−	167.969i	−0.119685	−	0.368353i
$457$	125.987	+	387.747i	0.275682	+	0.848462i	0.989038	+	0.147660i	$0.0471742\pi$
$457$	125.987	+	387.747i	0.275682	+	0.848462i	−0.713356	+	0.700802i	$0.752826\pi$
$458$	−154.848	−	112.503i	−0.338096	−	0.245641i
$459$	203.580	+	280.203i	0.443528	+	0.610464i
$460$		0			0
$461$			721.774i			1.56567i	0.622229	+	0.782835i	$0.286227\pi$
$461$			721.774i			1.56567i	−0.622229	+	0.782835i	$0.713773\pi$
$462$	1347.35	+	1032.54i	2.91635	+	2.23493i
$463$			775.669i			1.67531i	0.546198	+	0.837656i	$0.316075\pi$
$463$			775.669i			1.67531i	−0.546198	+	0.837656i	$0.683925\pi$
$464$	−124.348	−	40.4030i	−0.267990	−	0.0870753i
$465$		0			0
$466$	689.820	+	501.184i	1.48030	+	1.07550i
$467$	444.372	−	144.385i	0.951545	−	0.309176i	0.208202	−	0.978086i	$-0.433239\pi$
$467$	444.372	−	144.385i	0.951545	−	0.309176i	0.743343	+	0.668910i	$0.233239\pi$
$468$	−237.880	−	732.118i	−0.508290	−	1.56436i
$469$	−283.684	+	390.457i	−0.604870	+	0.832531i
$470$		0			0
$471$	−52.7965	+	162.491i	−0.112094	+	0.344991i
$472$	501.051			1.06155
$473$	−518.929	−	183.402i	−1.09710	−	0.387741i
$474$	−1810.51			−3.81965
$475$		0			0
$476$	−1083.82	+	787.438i	−2.27692	+	1.65428i
$477$	−243.723	+	335.456i	−0.510950	+	0.703262i
$478$	434.327	−	141.122i	0.908635	−	0.295233i
$479$	8.26238	−	2.68461i	0.0172492	−	0.00560461i	−0.300380	−	0.953820i	$-0.597113\pi$
$479$	8.26238	−	2.68461i	0.0172492	−	0.00560461i	0.317629	+	0.948215i	$0.397113\pi$
$480$		0			0
$481$	59.5379	+	81.9469i	0.123779	+	0.170368i
$482$	−1211.59	−	393.669i	−2.51367	−	0.816741i
$483$	−23.6734			−0.0490132
$484$	−172.162	−	639.355i	−0.355706	−	1.32098i
$485$		0			0
$486$	−945.342	−	307.160i	−1.94515	−	0.632017i
$487$	−469.217	−	645.822i	−0.963484	−	1.32612i	−0.945270	−	0.326288i	$-0.894202\pi$
$487$	−469.217	−	645.822i	−0.963484	−	1.32612i	−0.0182139	−	0.999834i	$-0.505798\pi$
$488$	200.015	−	275.297i	0.409866	−	0.564133i
$489$	−67.0830	−	206.460i	−0.137184	−	0.422209i
$490$		0			0
$491$	−87.5364	+	120.483i	−0.178282	+	0.245384i	−0.888800	−	0.458295i	$-0.848460\pi$
$491$	−87.5364	+	120.483i	−0.178282	+	0.245384i	0.710519	+	0.703678i	$0.248460\pi$
$492$	−542.255	+	393.972i	−1.10214	+	0.800755i
$493$	352.930	+	114.674i	0.715881	+	0.232604i
$494$			296.487i			0.600176i
$495$		0			0
$496$	−256.197			−0.516525
$497$	−176.054	+	541.840i	−0.354234	+	1.09022i
$498$	−312.963	−	430.757i	−0.628440	−	0.864973i
$499$	493.030	+	358.207i	0.988036	+	0.717850i	0.959490	−	0.281743i	$-0.0909124\pi$
$499$	493.030	+	358.207i	0.988036	+	0.717850i	0.0285456	+	0.999592i	$0.490912\pi$
$500$		0			0
$501$	−209.098	+	67.9402i	−0.417362	+	0.135609i
$502$	−928.871	−	674.864i	−1.85034	−	1.34435i
$503$	121.221	−	88.0720i	0.240995	−	0.175093i	−0.460731	−	0.887540i	$-0.652413\pi$
$503$	121.221	−	88.0720i	0.240995	−	0.175093i	0.701727	+	0.712446i	$0.252413\pi$
$504$	−187.379	+	576.693i	−0.371783	+	1.14423i
$505$		0			0
$506$	12.6869	+	9.72257i	0.0250730	+	0.0192146i
$507$		−	178.952i		−	0.352963i
$508$	−254.943	+	784.633i	−0.501856	+	1.54455i
$509$	256.395	−	186.282i	0.503723	−	0.365976i	−0.306714	−	0.951802i	$-0.599230\pi$
$509$	256.395	−	186.282i	0.503723	−	0.365976i	0.810437	+	0.585825i	$0.199230\pi$
$510$		0			0
$511$	264.402	+	813.746i	0.517421	+	1.59246i
$512$	149.004	+	458.586i	0.291023	+	0.895677i
$513$	−104.897	−	76.2119i	−0.204477	−	0.148561i
$514$	369.179	+	508.131i	0.718247	+	0.988582i
$515$		0			0
$516$		−	1264.41i		−	2.45041i
$517$	109.748	+	369.666i	0.212279	+	0.715021i
$518$		−	296.584i		−	0.572555i
$519$	−838.423	−	272.420i	−1.61546	−	0.524895i
$520$		0			0
$521$	−298.555	−	216.913i	−0.573042	−	0.416340i	0.263167	−	0.964750i	$-0.415233\pi$
$521$	−298.555	−	216.913i	−0.573042	−	0.416340i	−0.836209	+	0.548411i	$0.815233\pi$
$522$	593.796	−	192.936i	1.13754	−	0.369609i
$523$	151.734	+	466.990i	0.290123	+	0.892907i	0.984816	+	0.173601i	$0.0555402\pi$
$523$	151.734	+	466.990i	0.290123	+	0.892907i	−0.694693	+	0.719306i	$0.744460\pi$
$524$	−312.311	+	429.859i	−0.596013	+	0.820342i
$525$		0			0
$526$	−61.1327	+	188.147i	−0.116222	+	0.357694i
$527$	727.150			1.37979
$528$	−332.440	+	228.782i	−0.629621	+	0.433299i
$529$	528.777			0.999579
$530$		0			0
$531$	1102.80	−	801.235i	2.07685	−	1.50892i
$532$	294.785	−	405.736i	0.554107	−	0.762662i
$533$	287.890	−	93.5410i	0.540131	−	0.175499i
$534$	1464.27	−	475.770i	2.74208	−	0.890955i
$535$		0			0
$536$	118.378	+	162.933i	0.220854	+	0.303980i
$537$	−1134.18	−	368.519i	−2.11207	−	0.686255i
$538$	687.262			1.27744
$539$	−19.3682	+	757.526i	−0.0359336	+	1.40543i
$540$		0			0
$541$	−418.618	−	136.017i	−0.773786	−	0.251418i	−0.104601	−	0.994514i	$-0.533357\pi$
$541$	−418.618	−	136.017i	−0.773786	−	0.251418i	−0.669185	+	0.743096i	$0.733357\pi$
$542$	508.494	+	699.882i	0.938181	+	1.29130i
$543$	−446.330	+	614.320i	−0.821970	+	1.13134i
$544$	−296.635	−	912.948i	−0.545284	−	1.67821i
$545$		0			0
$546$	1035.20	−	1424.83i	1.89597	−	2.60957i
$547$	482.392	−	350.478i	0.881886	−	0.640728i	−0.0518636	−	0.998654i	$-0.516516\pi$
$547$	482.392	−	350.478i	0.881886	−	0.640728i	0.933750	+	0.357926i	$0.116516\pi$
$548$	−1090.05	−	354.178i	−1.98914	−	0.646310i
$549$		−	925.768i		−	1.68628i
$550$		0			0
$551$	−138.922			−0.252127
$552$	−3.05266	+	9.39512i	−0.00553018	+	0.0170201i
$553$	−812.971	−	1118.96i	−1.47011	−	2.02343i
$554$	−299.864	−	217.864i	−0.541271	−	0.393256i
$555$		0			0
$556$	−41.8034	+	13.5827i	−0.0751860	+	0.0244294i
$557$	485.709	+	352.889i	0.872010	+	0.633552i	0.931125	−	0.364699i	$-0.118828\pi$
$557$	485.709	+	352.889i	0.872010	+	0.633552i	−0.0591158	+	0.998251i	$0.518828\pi$
$558$	989.763	−	719.105i	1.77377	−	1.28872i
$559$	−176.459	+	543.085i	−0.315669	+	0.971529i
$560$		0			0
$561$	943.548	−	649.341i	1.68190	−	1.15747i
$562$			1248.04i			2.22071i
$563$	205.365	−	632.047i	0.364768	−	1.12264i	−0.585358	−	0.810775i	$-0.699046\pi$
$563$	205.365	−	632.047i	0.364768	−	1.12264i	0.950126	−	0.311866i	$-0.100954\pi$
$564$	−716.689	+	520.705i	−1.27072	+	0.923236i
$565$		0			0
$566$	524.663	+	1614.75i	0.926966	+	2.85291i
$567$	−134.208	−	413.050i	−0.236698	−	0.728482i
$568$	192.335	+	139.740i	0.338618	+	0.246020i
$569$	255.449	+	351.595i	0.448943	+	0.617917i	0.972170	−	0.234276i	$-0.0752720\pi$
$569$	255.449	+	351.595i	0.448943	+	0.617917i	−0.523227	+	0.852193i	$0.675272\pi$
$570$		0			0
$571$		−	807.082i		−	1.41345i	−0.707487	−	0.706727i	$-0.750171\pi$
$571$		−	807.082i		−	1.41345i	0.707487	−	0.706727i	$-0.249829\pi$
$572$	−658.559	+	195.517i	−1.15133	+	0.341812i
$573$		−	175.485i		−	0.306257i
$574$	−842.943	−	273.889i	−1.46854	−	0.477158i
$575$		0			0
$576$	−989.727	−	719.079i	−1.71828	−	1.24840i
$577$	−690.288	+	224.288i	−1.19634	+	0.388715i	−0.838413	−	0.545035i	$-0.816516\pi$
$577$	−690.288	+	224.288i	−1.19634	+	0.388715i	−0.357927	+	0.933750i	$0.616516\pi$
$578$	208.667	+	642.210i	0.361015	+	1.11109i
$579$	12.7639	−	17.5680i	0.0220448	−	0.0303420i
$580$		0			0
$581$	125.693	−	386.844i	0.216339	−	0.665824i
$582$	878.518			1.50948
$583$	293.706	+	225.080i	0.503783	+	0.386072i
$584$	357.041			0.611372
$585$		0			0
$586$	−801.715	+	582.480i	−1.36811	+	0.993993i
$587$	111.330	−	153.232i	0.189659	−	0.261043i	−0.703590	−	0.710607i	$-0.748421\pi$
$587$	111.330	−	153.232i	0.189659	−	0.261043i	0.893248	+	0.449564i	$0.148421\pi$
$588$	−1655.65	+	537.952i	−2.81572	+	0.914884i
$589$	−258.892	+	84.1192i	−0.439546	+	0.142817i
$590$		0			0
$591$	291.133	+	400.710i	0.492610	+	0.678020i
$592$	67.0576	+	21.7883i	0.113273	+	0.0368046i
$593$	−216.058			−0.364348			−0.182174	−	0.983266i	$-0.558313\pi$
$593$	−216.058			−0.364348			−0.182174	+	0.983266i	$0.558313\pi$
$594$	173.286	−	490.308i	0.291728	−	0.825434i
$595$		0			0
$596$	−242.936	−	78.9347i	−0.407611	−	0.132441i
$597$	50.4708	+	69.4671i	0.0845407	+	0.116360i
$598$	9.74759	−	13.4164i	0.0163003	−	0.0224355i
$599$	309.617	+	952.903i	0.516890	+	1.59082i	0.779817	+	0.626007i	$0.215312\pi$
$599$	309.617	+	952.903i	0.516890	+	1.59082i	−0.262928	+	0.964815i	$0.584688\pi$
$600$		0			0
$601$	230.744	−	317.592i	0.383934	−	0.528440i	−0.572688	−	0.819774i	$-0.694099\pi$
$601$	230.744	−	317.592i	0.383934	−	0.528440i	0.956621	+	0.291334i	$0.0940992\pi$
$602$	1352.67	−	982.771i	2.24696	−	1.63251i
$603$	521.095	+	169.314i	0.864171	+	0.280786i
$604$		−	410.987i		−	0.680443i
$605$		0			0
$606$	−819.633			−1.35253
$607$	−162.986	+	501.620i	−0.268511	+	0.826392i	0.722353	+	0.691525i	$0.243061\pi$
$607$	−162.986	+	501.620i	−0.268511	+	0.826392i	−0.990864	+	0.134867i	$0.956939\pi$
$608$	211.226	+	290.727i	0.347411	+	0.478170i
$609$	667.617	+	485.052i	1.09625	+	0.796473i
$610$		0			0
$611$	380.498	−	123.631i	0.622747	−	0.202343i
$612$	1230.41	+	893.946i	2.01047	+	1.46070i
$613$	−217.265	+	157.852i	−0.354429	+	0.257508i	−0.750725	−	0.660615i	$-0.770295\pi$
$613$	−217.265	+	157.852i	−0.354429	+	0.257508i	0.396296	+	0.918123i	$0.370295\pi$
$614$	95.2254	−	293.074i	0.155090	−	0.477319i
$615$		0			0
$616$	510.202	+	180.317i	0.828249	+	0.292723i
$617$		−	623.989i		−	1.01133i	−0.862731	−	0.505664i	$-0.831248\pi$
$617$		−	623.989i		−	1.01133i	0.862731	−	0.505664i	$-0.168752\pi$
$618$	−482.747	+	1485.74i	−0.781144	+	2.40412i
$619$	727.247	−	528.376i	1.17487	−	0.853596i	0.183290	−	0.983059i	$-0.441325\pi$
$619$	727.247	−	528.376i	1.17487	−	0.853596i	0.991584	+	0.129463i	$0.0413253\pi$
$620$		0			0
$621$	2.24109	+	6.89737i	0.00360885	+	0.0111069i
$622$	−187.452	−	576.917i	−0.301369	−	0.927519i
$623$	951.540	+	691.334i	1.52735	+	1.10969i
$624$	246.103	+	338.732i	0.394396	+	0.542840i
$625$		0			0
$626$		−	747.852i		−	1.19465i
$627$	−260.820	+	340.342i	−0.415981	+	0.542811i
$628$			202.452i			0.322376i
$629$	−190.326	−	61.8407i	−0.302585	−	0.0983160i
$630$		0			0
$631$	861.325	+	625.789i	1.36502	+	0.991742i	0.998108	+	0.0614849i	$0.0195836\pi$
$631$	861.325	+	625.789i	1.36502	+	0.991742i	0.366908	+	0.930257i	$0.380416\pi$
$632$	−548.907	+	178.351i	−0.868523	+	0.282200i
$633$	139.370	+	428.937i	0.220174	+	0.677625i
$634$	1023.24	−	1408.37i	1.61394	−	2.22140i
$635$		0			0
$636$	−262.690	+	808.477i	−0.413035	+	1.27119i
$637$	786.203			1.23423
$638$	−158.577	−	534.135i	−0.248553	−	0.837202i
$639$	646.784			1.01218
$640$		0			0
$641$	717.550	−	521.330i	1.11942	−	0.813308i	0.135301	−	0.990805i	$-0.456800\pi$
$641$	717.550	−	521.330i	1.11942	−	0.813308i	0.984121	+	0.177497i	$0.0568000\pi$
$642$	−468.743	+	645.170i	−0.730130	+	1.00494i
$643$	996.713	−	323.852i	1.55010	−	0.503657i	0.595957	−	0.803016i	$-0.296773\pi$
$643$	996.713	−	323.852i	1.55010	−	0.503657i	0.954141	+	0.299359i	$0.0967729\pi$
$644$	−26.6788	+	8.66846i	−0.0414267	+	0.0134603i
$645$		0			0
$646$	−344.303	−	473.893i	−0.532977	−	0.733580i
$647$	−1195.56	−	388.461i	−1.84785	−	0.600403i	−0.997209	−	0.0746578i	$-0.976214\pi$
$647$	−1195.56	−	388.461i	−1.84785	−	0.600403i	−0.850642	−	0.525745i	$-0.823786\pi$
$648$	−181.231			−0.279677
$649$	−689.638	−	1002.10i	−1.06262	−	1.54407i
$650$		0			0
$651$	1537.87	+	499.683i	2.36231	+	0.767562i
$652$	−151.199	−	208.107i	−0.231900	−	0.319183i
$653$	−101.012	+	139.031i	−0.154689	+	0.212912i	−0.879327	−	0.476218i	$-0.842007\pi$
$653$	−101.012	+	139.031i	−0.154689	+	0.212912i	0.724638	+	0.689130i	$0.242007\pi$
$654$	282.177	+	868.452i	0.431464	+	1.32791i
$655$		0			0
$656$	123.853	−	170.468i	0.188800	−	0.259860i
$657$	785.841	−	570.947i	1.19611	−	0.869022i
$658$	−1114.10	−	361.994i	−1.69316	−	0.550143i
$659$		−	719.550i		−	1.09188i	−0.837824	−	0.545941i	$-0.816172\pi$
$659$		−	719.550i		−	1.09188i	0.837824	−	0.545941i	$-0.183828\pi$
$660$		0			0
$661$	655.240			0.991286			0.495643	−	0.868526i	$-0.334932\pi$
$661$	655.240			0.991286			0.495643	+	0.868526i	$0.334932\pi$
$662$	−137.287	+	422.527i	−0.207383	+	0.638259i
$663$	−698.503	−	961.407i	−1.05355	−	1.45009i
$664$	−137.317	−	99.7663i	−0.206802	−	0.150250i
$665$		0			0
$666$	−320.220	+	104.046i	−0.480811	+	0.156225i
$667$	6.28639	+	4.56733i	0.00942488	+	0.00684757i
$668$	−210.766	+	153.131i	−0.315519	+	0.229238i
$669$	541.386	−	1666.21i	0.809246	−	2.49060i
$670$		0			0
$671$	−825.890	−	21.1161i	−1.23084	−	0.0314696i
$672$		−	2134.65i		−	3.17657i
$673$	211.274	−	650.235i	0.313929	−	0.966173i	−0.662264	−	0.749270i	$-0.730404\pi$
$673$	211.274	−	650.235i	0.313929	−	0.966173i	0.976193	−	0.216903i	$-0.0695955\pi$
$674$	481.706	−	349.980i	0.714697	−	0.519258i
$675$		0			0
$676$	−65.5269	−	201.671i	−0.0969333	−	0.298330i
$677$	233.777	+	719.490i	0.345313	+	1.06276i	0.961416	+	0.275098i	$0.0887102\pi$
$677$	233.777	+	719.490i	0.345313	+	1.06276i	−0.616104	+	0.787665i	$0.711290\pi$
$678$	103.090	+	74.8992i	0.152050	+	0.110471i
$679$	394.479	+	542.954i	0.580971	+	0.799638i
$680$		0			0
$681$			962.541i			1.41342i
$682$	−618.948	−	899.384i	−0.907548	−	1.31874i
$683$		−	781.639i		−	1.14442i	−0.820107	−	0.572210i	$-0.806086\pi$
$683$		−	781.639i		−	1.14442i	0.820107	−	0.572210i	$-0.193914\pi$
$684$	−541.486	−	175.940i	−0.791647	−	0.257222i
$685$		0			0
$686$	−537.676	−	390.644i	−0.783784	−	0.569452i
$687$	−273.141	+	88.7489i	−0.397585	+	0.129183i
$688$	122.832	+	378.037i	0.178534	+	0.549472i
$689$	225.659	−	310.594i	0.327517	−	0.450789i
$690$		0			0
$691$	−290.643	+	894.507i	−0.420612	+	1.29451i	0.486522	+	0.873668i	$0.338265\pi$
$691$	−290.643	+	894.507i	−0.420612	+	1.29451i	−0.907134	+	0.420842i	$0.861735\pi$
$692$	−1044.62			−1.50956
$693$	1411.29	−	418.992i	2.03649	−	0.604606i
$694$	807.107			1.16298
$695$		0			0
$696$	278.589	−	202.406i	0.400271	−	0.290814i
$697$	−351.525	+	483.832i	−0.504340	+	0.694164i
$698$	−349.736	+	113.636i	−0.501055	+	0.162803i
$699$	1216.80	−	395.361i	1.74077	−	0.565609i
$700$		0			0
$701$	−3.94427	−	5.42882i	−0.00562664	−	0.00774440i	0.806194	−	0.591651i	$-0.201524\pi$
$701$	−3.94427	−	5.42882i	−0.00562664	−	0.00774440i	−0.811821	+	0.583906i	$0.801524\pi$
$702$	−513.131	−	166.726i	−0.730956	−	0.237502i
$703$	74.9171			0.106568
$704$	−664.075	+	866.547i	−0.943288	+	1.23089i
$705$		0			0
$706$	441.030	+	143.299i	0.624688	+	0.202973i
$707$	−368.038	−	506.561i	−0.520563	−	0.716494i
$708$	1642.64	−	2260.90i	2.32012	−	3.19337i
$709$	307.854	+	947.478i	0.434209	+	1.33636i	0.893895	+	0.448276i	$0.147962\pi$
$709$	307.854	+	947.478i	0.434209	+	1.33636i	−0.459686	+	0.888081i	$0.652038\pi$
$710$		0			0
$711$	−922.932	+	1270.31i	−1.29808	+	1.78665i
$712$	397.066	−	288.486i	0.557678	−	0.405176i
$713$	14.4808	+	4.70510i	0.0203097	+	0.00659902i
$714$			3479.54i			4.87331i
$715$		0			0
$716$	−1413.11			−1.97362
$717$	211.751	−	651.704i	0.295330	−	0.908932i
$718$	492.869	+	678.376i	0.686447	+	0.944813i
$719$	−478.315	−	347.516i	−0.665250	−	0.483333i	0.203182	−	0.979141i	$-0.434872\pi$
$719$	−478.315	−	347.516i	−0.665250	−	0.483333i	−0.868432	+	0.495808i	$0.834872\pi$
$720$		0			0
$721$	−1135.01	+	368.786i	−1.57421	+	0.511493i
$722$	−721.447	−	524.162i	−0.999234	−	0.725986i
$723$	−1546.46	+	1123.57i	−2.13895	+	1.55404i
$724$	−278.048	+	855.743i	−0.384044	+	1.18196i
$725$		0			0
$726$	−1606.29	−	614.321i	−2.21252	−	0.846172i
$727$			1276.13i			1.75534i	0.479266	+	0.877670i	$0.340903\pi$
$727$			1276.13i			1.75534i	−0.479266	+	0.877670i	$0.659097\pi$
$728$	173.491	−	533.951i	0.238312	−	0.733449i
$729$	−915.382	+	665.064i	−1.25567	+	0.912297i
$730$		0			0
$731$	−348.627	−	1072.96i	−0.476918	−	1.46780i
$732$	−586.500	−	1805.06i	−0.801230	−	2.46593i
$733$	27.2811	+	19.8208i	0.0372184	+	0.0270407i	0.606239	−	0.795283i	$-0.292678\pi$
$733$	27.2811	+	19.8208i	0.0372184	+	0.0270407i	−0.569021	+	0.822323i	$0.692678\pi$
$734$	−1171.50	−	1612.43i	−1.59605	−	2.19678i
$735$		0			0
$736$		−	20.1003i		−	0.0273101i
$737$	162.933	−	461.014i	0.221076	−	0.625528i
$738$			1006.21i			1.36342i
$739$	−1127.54	−	366.361i	−1.52577	−	0.495752i	−0.578361	−	0.815781i	$-0.696308\pi$
$739$	−1127.54	−	366.361i	−1.52577	−	0.495752i	−0.947408	+	0.320028i	$0.896308\pi$
$740$		0			0
$741$	359.912	+	261.491i	0.485711	+	0.352890i
$742$	−1069.09	+	347.368i	−1.44082	+	0.468150i
$743$	−423.321	−	1302.85i	−0.569746	−	1.75350i	−0.653412	−	0.757003i	$-0.726663\pi$
$743$	−423.321	−	1302.85i	−0.569746	−	1.75350i	0.0836663	−	0.996494i	$-0.473337\pi$
$744$	396.613	−	545.891i	0.533082	−	0.733724i
$745$		0			0
$746$	383.215	−	1179.41i	0.513693	−	1.58098i
$747$	−461.768			−0.618163
$748$	825.566	−	1077.28i	1.10370	−	1.44021i
$749$	−609.216			−0.813372
$750$		0			0
$751$	316.835	−	230.194i	0.421884	−	0.306517i	−0.356512	−	0.934291i	$-0.616034\pi$
$751$	316.835	−	230.194i	0.421884	−	0.306517i	0.778395	+	0.627774i	$0.216034\pi$
$752$	163.694	−	225.305i	0.217678	−	0.299608i
$753$	−1638.46	+	532.370i	−2.17592	+	0.706998i
$754$	−549.787	+	178.637i	−0.729161	+	0.236919i
$755$		0			0
$756$	536.441	+	738.347i	0.709578	+	0.976650i
$757$	227.712	+	73.9880i	0.300808	+	0.0977385i	0.455532	−	0.890219i	$-0.349449\pi$
$757$	227.712	+	73.9880i	0.300808	+	0.0977385i	−0.154724	+	0.987958i	$0.549449\pi$
$758$	−417.330			−0.550567
$759$	22.9919	−	6.82596i	0.0302923	−	0.00899335i
$760$		0			0
$761$	31.0228	+	10.0799i	0.0407659	+	0.0132456i	0.329329	−	0.944215i	$-0.393177\pi$
$761$	31.0228	+	10.0799i	0.0407659	+	0.0132456i	−0.288563	+	0.957461i	$0.593177\pi$
$762$	1259.51	+	1733.57i	1.65291	+	2.27503i
$763$	−410.028	+	564.354i	−0.537389	+	0.739652i
$764$	−64.2574	−	197.764i	−0.0841065	−	0.258853i
$765$		0			0
$766$	−1000.07	+	1376.48i	−1.30558	+	1.79697i
$767$	−1021.07	+	741.851i	−1.33125	+	0.967211i
$768$	−83.4482	−	27.1140i	−0.108657	−	0.0353046i
$769$			80.9870i			0.105315i	0.998613	+	0.0526573i	$0.0167691\pi$
$769$			80.9870i			0.105315i	−0.998613	+	0.0526573i	$0.983231\pi$
$770$		0			0
$771$	942.435			1.22235
$772$	7.95148	−	24.4721i	0.0102998	−	0.0316997i
$773$	−169.033	−	232.654i	−0.218672	−	0.300976i	0.685561	−	0.728015i	$-0.259557\pi$
$773$	−169.033	−	232.654i	−0.218672	−	0.300976i	−0.904233	+	0.427039i	$0.859557\pi$
$774$	−1535.63	−	1115.70i	−1.98402	−	1.44147i
$775$		0			0
$776$	266.347	−	86.5414i	0.343231	−	0.111522i
$777$	−360.029	−	261.577i	−0.463358	−	0.336649i
$778$	−329.817	+	239.626i	−0.423929	+	0.308003i
$779$	69.1844	−	212.928i	0.0888118	−	0.273335i
$780$		0			0
$781$	14.7527	−	577.005i	0.0188895	−	0.738803i
$782$			32.7639i			0.0418976i
$783$	78.1213	−	240.433i	0.0997718	−	0.307066i
$784$	442.750	−	321.677i	0.564732	−	0.410302i
$785$		0			0
$786$	426.457	+	1312.50i	0.542566	+	1.66985i
$787$	24.6845	+	75.9709i	0.0313653	+	0.0965323i	0.965514	−	0.260353i	$-0.0838388\pi$
$787$	24.6845	+	75.9709i	0.0313653	+	0.0965323i	−0.934148	+	0.356885i	$0.883839\pi$
$788$	474.821	+	344.978i	0.602565	+	0.437789i
$789$	174.479	+	240.150i	0.221140	+	0.304372i
$790$		0			0
$791$			97.3449i			0.123066i
$792$	15.7016	−	614.120i	0.0198253	−	0.775404i
$793$			857.155i			1.08090i
$794$	324.087	+	105.302i	0.408170	+	0.132623i
$795$		0			0
$796$	82.3150	+	59.8053i	0.103411	+	0.0751323i
$797$	823.002	−	267.409i	1.03262	−	0.335520i	0.256797	−	0.966465i	$-0.417333\pi$
$797$	823.002	−	267.409i	1.03262	−	0.335520i	0.775827	+	0.630945i	$0.217333\pi$
$798$	−402.525	−	1238.84i	−0.504417	−	1.55244i
$799$	−464.604	+	639.472i	−0.581481	+	0.800341i
$800$		0			0
$801$	412.616	−	1269.90i	0.515127	−	1.58540i
$802$	96.0597			0.119775
$803$	−491.425	−	714.083i	−0.611987	−	0.889269i
$804$	1123.30			1.39713
$805$		0			0
$806$	−916.407	+	665.809i	−1.13698	+	0.826065i
$807$	606.142	−	834.282i	0.751105	−	1.03381i
$808$	−248.494	+	80.7407i	−0.307543	+	0.0999266i
$809$	164.498	−	53.4487i	0.203335	−	0.0660676i	−0.205579	−	0.978641i	$-0.565908\pi$
$809$	164.498	−	53.4487i	0.203335	−	0.0660676i	0.408914	+	0.912573i	$0.365908\pi$
$810$		0			0
$811$	−508.782	−	700.279i	−0.627352	−	0.863476i	0.370510	−	0.928828i	$-0.379183\pi$
$811$	−508.782	−	700.279i	−0.627352	−	0.863476i	−0.997862	+	0.0653524i	$0.979183\pi$
$812$	929.985	+	302.170i	1.14530	+	0.372131i
$813$	1298.08			1.59665
$814$	85.5166	+	288.046i	0.105057	+	0.353865i
$815$		0			0
$816$	−786.724	−	255.622i	−0.964123	−	0.313263i
$817$	248.248	+	341.684i	0.303853	+	0.418218i
$818$	−829.733	+	1142.03i	−1.01434	+	1.39612i
$819$	−471.994	−	1452.65i	−0.576305	−	1.77368i
$820$		0			0
$821$	−66.2686	+	91.2109i	−0.0807169	+	0.111097i	−0.847466	−	0.530849i	$-0.821873\pi$
$821$	−66.2686	+	91.2109i	−0.0807169	+	0.111097i	0.766749	+	0.641947i	$0.221873\pi$
$822$	−2408.36	+	1749.77i	−2.92987	+	2.12868i
$823$	−380.030	−	123.479i	−0.461761	−	0.150035i	0.0688924	−	0.997624i	$-0.478053\pi$
$823$	−380.030	−	123.479i	−0.461761	−	0.150035i	−0.530654	+	0.847589i	$0.678053\pi$
$824$			497.999i			0.604367i
$825$		0			0
$826$	3695.47			4.47394
$827$	226.990	−	698.603i	0.274474	−	0.844744i	−0.714884	−	0.699243i	$-0.753521\pi$
$827$	226.990	−	698.603i	0.274474	−	0.844744i	0.989358	−	0.145501i	$-0.0464794\pi$
$828$	18.7186	+	25.7639i	0.0226070	+	0.0311159i
$829$	−251.233	−	182.531i	−0.303055	−	0.220183i	0.425856	−	0.904791i	$-0.359973\pi$
$829$	−251.233	−	182.531i	−0.303055	−	0.220183i	−0.728911	+	0.684609i	$0.759973\pi$
$830$		0			0
$831$	−528.940	+	171.863i	−0.636510	+	0.206815i
$832$	916.373	+	665.784i	1.10141	+	0.800221i
$833$	−1256.64	+	913.000i	−1.50857	+	1.09604i
$834$	−35.2786	+	108.576i	−0.0423005	+	0.130188i
$835$		0			0
$836$	−169.309	+	479.054i	−0.202523	+	0.573031i
$837$		−	495.370i		−	0.591840i
$838$	44.7449	−	137.711i	0.0533949	−	0.164333i
$839$	−534.323	+	388.208i	−0.636857	+	0.462704i	−0.858769	−	0.512363i	$-0.828770\pi$
$839$	−534.323	+	388.208i	−0.636857	+	0.462704i	0.221912	+	0.975067i	$0.428770\pi$
$840$		0			0
$841$	176.181	+	542.230i	0.209490	+	0.644745i
$842$	−144.514	−	444.769i	−0.171632	−	0.528229i
$843$	1515.02	+	1100.73i	1.79718	+	1.30573i
$844$	314.127	+	432.359i	0.372188	+	0.512273i
$845$		0			0
$846$			1329.88i			1.57197i
$847$	−341.598	−	1268.59i	−0.403303	−	1.49774i
$848$		−	267.240i		−	0.315141i
$849$	2422.91	+	787.251i	2.85384	+	0.927269i
$850$		0			0
$851$	−3.39010	−	2.46305i	−0.00398366	−	0.00289430i
$852$	1261.10	−	409.756i	1.48016	−	0.480934i
$853$	−151.061	−	464.919i	−0.177094	−	0.545040i	0.822629	−	0.568579i	$-0.192507\pi$
$853$	−151.061	−	464.919i	−0.177094	−	0.545040i	−0.999723	+	0.0235392i	$0.992507\pi$
$854$	1475.20	−	2030.43i	1.72740	−	2.37756i
$855$		0			0
$856$	−78.5579	+	241.776i	−0.0917732	+	0.282449i
$857$	−433.345			−0.505653			−0.252827	−	0.967512i	$-0.581360\pi$
$857$	−433.345			−0.505653			−0.252827	+	0.967512i	$0.581360\pi$
$858$	−594.563	+	1682.30i	−0.692964	+	1.96072i
$859$	199.533			0.232285			0.116143	−	0.993233i	$-0.462947\pi$
$859$	199.533			0.232285			0.116143	+	0.993233i	$0.462947\pi$
$860$		0			0
$861$	−1075.93	+	781.707i	−1.24962	+	0.907905i
$862$	−936.323	+	1288.74i	−1.08622	+	1.49506i
$863$	909.036	−	295.364i	1.05334	−	0.342252i	0.269364	−	0.963038i	$-0.413186\pi$
$863$	909.036	−	295.364i	1.05334	−	0.342252i	0.783980	+	0.620786i	$0.213186\pi$
$864$	−621.944	+	202.082i	−0.719843	+	0.233891i
$865$		0			0
$866$	−753.088	−	1036.54i	−0.869617	−	1.19692i
$867$	963.630	+	313.102i	1.11145	+	0.361133i
$868$	1916.07			2.20746
$869$	1112.21	+	852.335i	1.27987	+	0.980823i
$870$		0			0
$871$	−482.474	−	156.765i	−0.553931	−	0.179983i
$872$	171.100	+	235.498i	0.196215	+	0.270067i
$873$	447.836	−	616.393i	0.512985	−	0.706063i
$874$	−3.79024	−	11.6652i	−0.00433666	−	0.0133469i
$875$		0			0
$876$	1170.52	−	1611.08i	1.33621	−	1.83914i
$877$	254.363	−	184.805i	0.290037	−	0.210724i	−0.433246	−	0.901276i	$-0.642632\pi$
$877$	254.363	−	184.805i	0.290037	−	0.210724i	0.723284	+	0.690551i	$0.242632\pi$
$878$	2007.73	+	652.349i	2.28670	+	0.742995i
$879$			1486.95i			1.69164i
$880$		0			0
$881$	330.178			0.374777			0.187388	−	0.982286i	$-0.439998\pi$
$881$	330.178			0.374777			0.187388	+	0.982286i	$0.439998\pi$
$882$	−807.577	+	2485.47i	−0.915620	+	2.81799i
$883$	594.275	+	817.950i	0.673018	+	0.926330i	0.999824	−	0.0187613i	$-0.00597225\pi$
$883$	594.275	+	817.950i	0.673018	+	0.926330i	−0.326806	+	0.945092i	$0.605972\pi$
$884$	−1139.22	−	827.691i	−1.28871	−	0.936302i
$885$		0			0
$886$	1693.83	−	550.358i	1.91177	−	0.621172i
$887$	186.442	+	135.458i	0.210194	+	0.152715i	0.687901	−	0.725804i	$-0.258532\pi$
$887$	186.442	+	135.458i	0.210194	+	0.152715i	−0.477708	+	0.878519i	$0.658532\pi$
$888$	−150.236	+	109.153i	−0.169185	+	0.122920i
$889$	−505.850	+	1556.85i	−0.569010	+	1.75123i
$890$		0			0
$891$	249.443	+	362.461i	0.279958	+	0.406803i
$892$		−	2075.99i		−	2.32734i
$893$	91.4398	−	281.423i	0.102396	−	0.315143i
$894$	−536.745	+	389.968i	−0.600385	+	0.436206i
$895$		0			0
$896$	−453.507	−	1395.75i	−0.506147	−	1.55776i
$897$	−7.68943	−	23.6656i	−0.00857239	−	0.0263831i
$898$	−2116.97	−	1538.07i	−2.35742	−	1.71277i
$899$	−311.971	−	429.392i	−0.347020	−	0.477633i
$900$		0			0
$901$			758.494i			0.841836i
$902$	897.650	+	22.9508i	0.995177	+	0.0254444i
$903$		−	2508.80i		−	2.77830i
$904$	38.6327	+	12.5525i	0.0427353	+	0.0138856i
$905$		0			0
$906$	−863.596	−	627.439i	−0.953196	−	0.692537i
$907$	1097.69	−	356.661i	1.21024	−	0.393232i	0.366723	−	0.930330i	$-0.380480\pi$
$907$	1097.69	−	356.661i	1.21024	−	0.393232i	0.843519	+	0.537099i	$0.180480\pi$
$908$	352.453	+	1084.74i	0.388164	+	1.19465i
$909$	−417.818	+	575.078i	−0.459646	+	0.632649i
$910$		0			0
$911$	187.421	−	576.824i	0.205732	−	0.633177i	−0.793951	−	0.607982i	$-0.791979\pi$
$911$	187.421	−	576.824i	0.205732	−	0.633177i	0.999683	−	0.0251948i	$-0.00802062\pi$
$912$	309.674			0.339555
$913$	−10.5326	+	411.950i	−0.0115363	+	0.451204i
$914$	1254.78			1.37284
$915$		0			0
$916$	−275.320	+	200.032i	−0.300568	+	0.218375i
$917$	−619.678	+	852.914i	−0.675767	+	0.930113i
$918$	1013.78	−	329.399i	1.10434	−	0.358822i
$919$	1094.16	−	355.514i	1.19060	−	0.386849i	0.354304	−	0.935130i	$-0.384718\pi$
$919$	1094.16	−	355.514i	1.19060	−	0.386849i	0.836294	+	0.548281i	$0.184718\pi$
$920$		0			0
$921$	−271.783	−	374.077i	−0.295096	−	0.406164i
$922$	2112.67	+	686.448i	2.29140	+	0.744520i
$923$	−598.848			−0.648806
$924$	2486.29	−	1711.04i	2.69079	−	1.85178i
$925$		0			0
$926$	2270.42	+	737.706i	2.45186	+	0.796658i
$927$	796.353	+	1096.09i	0.859065	+	1.18240i
$928$	−411.841	+	566.851i	−0.443795	+	0.610831i
$929$	−444.730	−	1368.74i	−0.478719	−	1.47335i	−0.840876	−	0.541228i	$-0.817960\pi$
$929$	−444.730	−	1368.74i	−0.478719	−	1.47335i	0.362157	−	0.932117i	$-0.382040\pi$
$930$		0			0
$931$	341.790	−	470.434i	0.367121	−	0.505299i
$932$	1226.50	−	891.107i	1.31599	−	0.956123i
$933$	−865.658	−	281.269i	−0.927822	−	0.301468i
$934$		−	1438.02i		−	1.53963i
$935$		0			0
$936$	−637.368			−0.680948
$937$	151.919	−	467.559i	0.162133	−	0.498996i	−0.836680	−	0.547692i	$-0.815507\pi$
$937$	151.919	−	467.559i	0.162133	−	0.498996i	0.998814	+	0.0486963i	$0.0155066\pi$
$938$	873.089	+	1201.70i	0.930799	+	1.28113i
$939$	−907.834	−	659.580i	−0.966810	−	0.702428i
$940$		0			0
$941$	1702.39	−	553.141i	1.80913	−	0.587822i	0.809132	−	0.587628i	$-0.199938\pi$
$941$	1702.39	−	553.141i	1.80913	−	0.587822i	1.00000		0.000194881i	$-6.20325e-5\pi$
$942$	425.406	+	309.076i	0.451599	+	0.328106i
$943$	−10.1311	+	7.36068i	−0.0107435	+	0.00780560i
$944$	−271.486	+	835.547i	−0.287591	+	0.885113i
$945$		0			0
$946$	−1030.36	+	1344.51i	−1.08917	+	1.42125i
$947$			1111.85i			1.17407i	0.809560	+	0.587037i	$0.199706\pi$
$947$			1111.85i			1.17407i	−0.809560	+	0.587037i	$0.800294\pi$
$948$	−994.756	+	3061.55i	−1.04932	+	3.22948i
$949$	−727.599	+	528.631i	−0.766700	+	0.557040i
$950$		0			0
$951$	−807.187	−	2484.27i	−0.848777	−	2.61227i
$952$	342.764	+	1054.92i	0.360046	+	1.10811i
$953$	241.935	+	175.776i	0.253867	+	0.184445i	0.707439	−	0.706775i	$-0.249850\pi$
$953$	241.935	+	175.776i	0.253867	+	0.184445i	−0.453572	+	0.891220i	$0.649850\pi$
$954$	750.102	+	1032.43i	0.786271	+	1.08221i
$955$		0			0
$956$		−	811.977i		−	0.849348i
$957$	−788.257	−	278.589i	−0.823675	−	0.291106i
$958$		−	26.7376i		−	0.0279098i
$959$	−2162.84	−	702.749i	−2.25531	−	0.732794i
$960$		0			0
$961$	−63.9224	−	46.4423i	−0.0665165	−	0.0483271i
$962$	296.487	−	96.3344i	0.308198	−	0.100140i
$963$	213.722	+	657.767i	0.221933	+	0.683040i
$964$	−1331.38	+	1832.48i	−1.38109	+	1.90091i
$965$		0			0
$966$	−22.5147	+	69.2931i	−0.0233072	+	0.0717320i
$967$	−246.770			−0.255191			−0.127596	−	0.991826i	$-0.540726\pi$
$967$	−246.770			−0.255191			−0.127596	+	0.991826i	$0.540726\pi$
$968$	−547.507	−	28.0153i	−0.565606	−	0.0289414i
$969$	−878.933			−0.907052
$970$		0			0
$971$	−161.120	+	117.060i	−0.165932	+	0.120556i	−0.667652	−	0.744473i	$-0.732701\pi$
$971$	−161.120	+	117.060i	−0.165932	+	0.120556i	0.501720	+	0.865030i	$0.332701\pi$
$972$	−1038.81	+	1429.79i	−1.06873	+	1.47098i
$973$	−82.9451	+	26.9505i	−0.0852467	+	0.0276983i
$974$	−2336.60	+	759.209i	−2.39898	+	0.779475i
$975$		0			0
$976$	350.707	+	482.707i	0.359331	+	0.494577i
$977$	224.505	+	72.9462i	0.229790	+	0.0746635i	0.421649	−	0.906759i	$-0.361451\pi$
$977$	224.505	+	72.9462i	0.229790	+	0.0746635i	−0.191858	+	0.981423i	$0.561451\pi$
$978$	−668.119			−0.683149
$979$	−1123.49	−	397.066i	−1.14759	−	0.405584i
$980$		0			0
$981$	753.174	+	244.721i	0.767762	+	0.249461i
$982$	269.409	+	370.810i	0.274347	+	0.377607i
$983$	218.714	−	301.034i	0.222497	−	0.306241i	−0.683146	−	0.730282i	$-0.739389\pi$
$983$	218.714	−	301.034i	0.222497	−	0.306241i	0.905643	+	0.424041i	$0.139389\pi$
$984$	171.492	+	527.798i	0.174280	+	0.536380i
$985$		0			0
$986$	671.312	−	923.982i	0.680844	−	0.937101i
$987$	−1422.03	+	1033.17i	−1.44076	+	1.04678i
$988$	501.354	+	162.900i	0.507443	+	0.164878i
$989$		−	23.6233i		−	0.0238861i
$990$		0			0
$991$	−759.033			−0.765927			−0.382963	−	0.923764i	$-0.625096\pi$
$991$	−759.033			−0.765927			−0.382963	+	0.923764i	$0.625096\pi$
$992$	−424.264	+	1305.75i	−0.427685	+	1.31628i
$993$	391.832	+	539.311i	0.394594	+	0.543113i
$994$	1418.55	+	1030.64i	1.42712	+	1.03686i
$995$		0			0
$996$	−900.355	+	292.543i	−0.903971	+	0.293718i
$997$	572.222	+	415.743i	0.573944	+	0.416994i	0.836536	−	0.547913i	$-0.184577\pi$
$997$	572.222	+	415.743i	0.573944	+	0.416994i	−0.262592	+	0.964907i	$0.584577\pi$
$998$	1517.39	−	1102.45i	1.52043	−	1.10466i
$999$	−42.1289	+	129.659i	−0.0421711	+	0.129789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.q.a.24.2		8
5.2	odd	4		55.3.i.b.46.1	yes	4
5.3	odd	4		275.3.x.a.101.1		4
5.4	even	2	inner	275.3.q.a.24.1		8
11.6	odd	10	inner	275.3.q.a.149.1		8
55.7	even	20		605.3.c.b.241.1		4
55.17	even	20		55.3.i.b.6.1	✓	4
55.28	even	20		275.3.x.a.226.1		4
55.37	odd	20		605.3.c.b.241.4		4
55.39	odd	10	inner	275.3.q.a.149.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.i.b.6.1	✓	4	55.17	even	20
55.3.i.b.46.1	yes	4	5.2	odd	4
275.3.q.a.24.1		8	5.4	even	2	inner
275.3.q.a.24.2		8	1.1	even	1	trivial
275.3.q.a.149.1		8	11.6	odd	10	inner
275.3.q.a.149.2		8	55.39	odd	10	inner
275.3.x.a.101.1		4	5.3	odd	4
275.3.x.a.226.1		4	55.28	even	20
605.3.c.b.241.1		4	55.7	even	20
605.3.c.b.241.4		4	55.37	odd	20

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.q (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 2.92705i) q^{2} +(-2.71441 - 3.73607i) q^{3} +(-4.42705 - 3.21644i) q^{4} +(-13.5172 + 4.39201i) q^{6} +(-8.78402 - 6.38197i) q^{7} +(-3.66547 + 2.66312i) q^{8} +(-3.80902 + 11.7229i) q^{9} +(10.3713 + 3.66547i) q^{11} +25.2705i q^{12} +(3.52671 - 10.8541i) q^{13} +(-27.0344 + 19.6417i) q^{14} +(-2.45492 - 7.55545i) q^{16} +(6.96767 + 21.4443i) q^{17} +(30.6911 + 22.2984i) q^{18} +(-4.96149 - 6.82891i) q^{19} +50.1410i q^{21} +(20.5927 - 26.8713i) q^{22} +0.472136i q^{23} +(19.8992 + 6.46564i) q^{24} +(-28.4164 - 20.6457i) q^{26} +(14.6089 - 4.74671i) q^{27} +(18.3601 + 56.5066i) q^{28} +(9.67376 - 13.3148i) q^{29} +(9.96556 - 30.6708i) q^{31} -42.5730 q^{32} +(-14.4576 - 48.6976i) q^{33} +69.3951 q^{34} +(54.5689 - 39.6466i) q^{36} +(-5.21682 + 7.18034i) q^{37} +(-24.7072 + 8.02786i) q^{38} +(-50.1246 + 16.2865i) q^{39} +(15.5902 + 21.4580i) q^{41} +(146.765 + 47.6869i) q^{42} -50.0350 q^{43} +(-34.1246 - 49.5860i) q^{44} +(1.38197 + 0.449028i) q^{46} +(20.6052 + 28.3607i) q^{47} +(-21.5640 + 29.6803i) q^{48} +(21.2877 + 65.5169i) q^{49} +(61.2041 - 84.2403i) q^{51} +(-50.5245 + 36.7082i) q^{52} +(31.9929 + 10.3951i) q^{53} -47.2753i q^{54} +49.1935 q^{56} +(-12.0457 + 37.0729i) q^{57} +(-29.7728 - 40.9787i) q^{58} +(-89.4681 - 65.0024i) q^{59} +(-71.4296 + 23.2089i) q^{61} +(-80.2973 - 58.3394i) q^{62} +(108.274 - 78.6656i) q^{63} +(-30.6697 + 94.3916i) q^{64} +(-156.290 - 3.99598i) q^{66} -44.4508i q^{67} +(38.1280 - 117.346i) q^{68} +(1.76393 - 1.28157i) q^{69} +(-16.2148 - 49.9040i) q^{71} +(-17.2578 - 53.1140i) q^{72} +(-63.7535 - 46.3197i) q^{73} +(16.0557 + 22.0988i) q^{74} +46.1903i q^{76} +(-67.7090 - 98.3870i) q^{77} +162.207i q^{78} +(121.151 + 39.3643i) q^{79} +(32.3607 + 23.5114i) q^{81} +(77.6359 - 25.2254i) q^{82} +(11.5765 + 35.6287i) q^{83} +(161.276 - 221.977i) q^{84} +(-47.5861 + 146.455i) q^{86} -76.0035 q^{87} +(-47.7773 + 14.1844i) q^{88} -108.326 q^{89} +(-100.249 + 72.8353i) q^{91} +(1.51860 - 2.09017i) q^{92} +(-141.639 + 46.0213i) q^{93} +(102.610 - 33.3400i) q^{94} +(115.561 + 159.056i) q^{96} +(-58.7863 - 19.1008i) q^{97} +212.017 q^{98} +(-82.4746 + 107.621i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 22 q^{4} - 50 q^{6} - 26 q^{9} - 2 q^{11} - 100 q^{14} - 42 q^{16} + 90 q^{19} + 110 q^{24} - 120 q^{26} + 140 q^{29} + 196 q^{31} + 260 q^{34} + 204 q^{36} - 240 q^{39} + 80 q^{41} - 112 q^{44} + 20 q^{46}+ \cdots - 226 q^{99}+O(q^{100}) \) 8 * q - 22 * q^4 - 50 * q^6 - 26 * q^9 - 2 * q^11 - 100 * q^14 - 42 * q^16 + 90 * q^19 + 110 * q^24 - 120 * q^26 + 140 * q^29 + 196 * q^31 + 260 * q^34 + 204 * q^36 - 240 * q^39 + 80 * q^41 - 112 * q^44 + 20 * q^46 - 22 * q^49 + 190 * q^51 - 434 * q^59 - 160 * q^61 - 62 * q^64 - 660 * q^66 + 32 * q^69 + 76 * q^71 + 200 * q^74 + 200 * q^79 + 80 * q^81 + 360 * q^84 - 90 * q^86 - 804 * q^89 - 480 * q^91 + 320 * q^94 + 200 * q^96 - 226 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more