LMFDB - Embedded newform 245.4.e.b.226.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [245,4,Mod(116,245)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("245.116"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(245, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,-1,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$14.4554679514$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	245.226
Dual form			245.4.e.b.116.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-4.00000 - 6.92820i) q^{3} +(3.50000 + 6.06218i) q^{4} +(-2.50000 + 4.33013i) q^{5} +8.00000 q^{6} -15.0000 q^{8} +(-18.5000 + 32.0429i) q^{9} +(-2.50000 - 4.33013i) q^{10} +(-6.00000 - 10.3923i) q^{11} +(28.0000 - 48.4974i) q^{12} +78.0000 q^{13} +40.0000 q^{15} +(-20.5000 + 35.5070i) q^{16} +(-47.0000 - 81.4064i) q^{17} +(-18.5000 - 32.0429i) q^{18} +(20.0000 - 34.6410i) q^{19} -35.0000 q^{20} +12.0000 q^{22} +(-16.0000 + 27.7128i) q^{23} +(60.0000 + 103.923i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(-39.0000 + 67.5500i) q^{26} +80.0000 q^{27} -50.0000 q^{29} +(-20.0000 + 34.6410i) q^{30} +(-124.000 - 214.774i) q^{31} +(-80.5000 - 139.430i) q^{32} +(-48.0000 + 83.1384i) q^{33} +94.0000 q^{34} -259.000 q^{36} +(217.000 - 375.855i) q^{37} +(20.0000 + 34.6410i) q^{38} +(-312.000 - 540.400i) q^{39} +(37.5000 - 64.9519i) q^{40} -402.000 q^{41} -68.0000 q^{43} +(42.0000 - 72.7461i) q^{44} +(-92.5000 - 160.215i) q^{45} +(-16.0000 - 27.7128i) q^{46} +(268.000 - 464.190i) q^{47} +328.000 q^{48} +25.0000 q^{50} +(-376.000 + 651.251i) q^{51} +(273.000 + 472.850i) q^{52} +(-11.0000 - 19.0526i) q^{53} +(-40.0000 + 69.2820i) q^{54} +60.0000 q^{55} -320.000 q^{57} +(25.0000 - 43.3013i) q^{58} +(-280.000 - 484.974i) q^{59} +(140.000 + 242.487i) q^{60} +(-139.000 + 240.755i) q^{61} +248.000 q^{62} -167.000 q^{64} +(-195.000 + 337.750i) q^{65} +(-48.0000 - 83.1384i) q^{66} +(82.0000 + 142.028i) q^{67} +(329.000 - 569.845i) q^{68} +256.000 q^{69} +672.000 q^{71} +(277.500 - 480.644i) q^{72} +(41.0000 + 71.0141i) q^{73} +(217.000 + 375.855i) q^{74} +(-100.000 + 173.205i) q^{75} +280.000 q^{76} +624.000 q^{78} +(500.000 - 866.025i) q^{79} +(-102.500 - 177.535i) q^{80} +(179.500 + 310.903i) q^{81} +(201.000 - 348.142i) q^{82} +448.000 q^{83} +470.000 q^{85} +(34.0000 - 58.8897i) q^{86} +(200.000 + 346.410i) q^{87} +(90.0000 + 155.885i) q^{88} +(-435.000 + 753.442i) q^{89} +185.000 q^{90} -224.000 q^{92} +(-992.000 + 1718.19i) q^{93} +(268.000 + 464.190i) q^{94} +(100.000 + 173.205i) q^{95} +(-644.000 + 1115.44i) q^{96} -1026.00 q^{97} +444.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 8 q^{3} + 7 q^{4} - 5 q^{5} + 16 q^{6} - 30 q^{8} - 37 q^{9} - 5 q^{10} - 12 q^{11} + 56 q^{12} + 156 q^{13} + 80 q^{15} - 41 q^{16} - 94 q^{17} - 37 q^{18} + 40 q^{19} - 70 q^{20} + 24 q^{22}+ \cdots + 888 q^{99}+O(q^{100}) $ 2 * q - q^2 - 8 * q^3 + 7 * q^4 - 5 * q^5 + 16 * q^6 - 30 * q^8 - 37 * q^9 - 5 * q^10 - 12 * q^11 + 56 * q^12 + 156 * q^13 + 80 * q^15 - 41 * q^16 - 94 * q^17 - 37 * q^18 + 40 * q^19 - 70 * q^20 + 24 * q^22 - 32 * q^23 + 120 * q^24 - 25 * q^25 - 78 * q^26 + 160 * q^27 - 100 * q^29 - 40 * q^30 - 248 * q^31 - 161 * q^32 - 96 * q^33 + 188 * q^34 - 518 * q^36 + 434 * q^37 + 40 * q^38 - 624 * q^39 + 75 * q^40 - 804 * q^41 - 136 * q^43 + 84 * q^44 - 185 * q^45 - 32 * q^46 + 536 * q^47 + 656 * q^48 + 50 * q^50 - 752 * q^51 + 546 * q^52 - 22 * q^53 - 80 * q^54 + 120 * q^55 - 640 * q^57 + 50 * q^58 - 560 * q^59 + 280 * q^60 - 278 * q^61 + 496 * q^62 - 334 * q^64 - 390 * q^65 - 96 * q^66 + 164 * q^67 + 658 * q^68 + 512 * q^69 + 1344 * q^71 + 555 * q^72 + 82 * q^73 + 434 * q^74 - 200 * q^75 + 560 * q^76 + 1248 * q^78 + 1000 * q^79 - 205 * q^80 + 359 * q^81 + 402 * q^82 + 896 * q^83 + 940 * q^85 + 68 * q^86 + 400 * q^87 + 180 * q^88 - 870 * q^89 + 370 * q^90 - 448 * q^92 - 1984 * q^93 + 536 * q^94 + 200 * q^95 - 1288 * q^96 - 2052 * q^97 + 888 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.176777	+	0.306186i	−0.940775	−	0.339032i	$-0.889900\pi$
$2$	−0.500000	+	0.866025i	−0.176777	+	0.306186i	0.763998	+	0.645219i	$0.223234\pi$
$3$	−4.00000	−	6.92820i	−0.769800	−	1.33333i	−0.937671	−	0.347524i	$-0.887022\pi$
$3$	−4.00000	−	6.92820i	−0.769800	−	1.33333i	0.167871	−	0.985809i	$-0.446311\pi$
$4$	3.50000	+	6.06218i	0.437500	+	0.757772i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$	8.00000			0.544331
$7$		0			0
$7$		0			0
$8$	−15.0000			−0.662913
$9$	−18.5000	+	32.0429i	−0.685185	+	1.18678i
$10$	−2.50000	−	4.33013i	−0.0790569	−	0.136931i
$11$	−6.00000	−	10.3923i	−0.164461	−	0.284854i	0.772003	−	0.635619i	$-0.219255\pi$
$11$	−6.00000	−	10.3923i	−0.164461	−	0.284854i	−0.936464	+	0.350765i	$0.885922\pi$
$12$	28.0000	−	48.4974i	0.673575	−	1.16667i
$13$	78.0000			1.66410			0.832050	−	0.554700i	$-0.187167\pi$
$13$	78.0000			1.66410			0.832050	+	0.554700i	$0.187167\pi$
$14$		0			0
$15$	40.0000			0.688530
$16$	−20.5000	+	35.5070i	−0.320312	+	0.554798i
$17$	−47.0000	−	81.4064i	−0.670540	−	1.16141i	−0.977751	−	0.209768i	$-0.932729\pi$
$17$	−47.0000	−	81.4064i	−0.670540	−	1.16141i	0.307212	−	0.951641i	$-0.400604\pi$
$18$	−18.5000	−	32.0429i	−0.242250	−	0.419589i
$19$	20.0000	−	34.6410i	0.241490	−	0.418273i	−0.719649	−	0.694338i	$-0.755697\pi$
$19$	20.0000	−	34.6410i	0.241490	−	0.418273i	0.961139	+	0.276065i	$0.0890305\pi$
$20$	−35.0000			−0.391312
$21$		0			0
$22$	12.0000			0.116291
$23$	−16.0000	+	27.7128i	−0.145054	+	0.251240i	−0.929393	−	0.369092i	$-0.879669\pi$
$23$	−16.0000	+	27.7128i	−0.145054	+	0.251240i	0.784339	+	0.620332i	$0.213002\pi$
$24$	60.0000	+	103.923i	0.510310	+	0.883883i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	−39.0000	+	67.5500i	−0.294174	+	0.509525i
$27$	80.0000			0.570222
$28$		0			0
$29$	−50.0000			−0.320164			−0.160082	−	0.987104i	$-0.551176\pi$
$29$	−50.0000			−0.320164			−0.160082	+	0.987104i	$0.551176\pi$
$30$	−20.0000	+	34.6410i	−0.121716	+	0.210819i
$31$	−124.000	−	214.774i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−124.000	−	214.774i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$32$	−80.5000	−	139.430i	−0.444704	−	0.770250i
$33$	−48.0000	+	83.1384i	−0.253204	+	0.438562i
$34$	94.0000			0.474143
$35$		0			0
$36$	−259.000			−1.19907
$37$	217.000	−	375.855i	0.964178	−	1.67001i	0.252370	−	0.967631i	$-0.418790\pi$
$37$	217.000	−	375.855i	0.964178	−	1.67001i	0.711808	−	0.702374i	$-0.247877\pi$
$38$	20.0000	+	34.6410i	0.0853797	+	0.147882i
$39$	−312.000	−	540.400i	−1.28103	−	2.21880i
$40$	37.5000	−	64.9519i	0.148232	−	0.256745i
$41$	−402.000			−1.53126			−0.765632	−	0.643278i	$-0.777574\pi$
$41$	−402.000			−1.53126			−0.765632	+	0.643278i	$0.777574\pi$
$42$		0			0
$43$	−68.0000			−0.241161			−0.120580	−	0.992704i	$-0.538476\pi$
$43$	−68.0000			−0.241161			−0.120580	+	0.992704i	$0.538476\pi$
$44$	42.0000	−	72.7461i	0.143903	−	0.249248i
$45$	−92.5000	−	160.215i	−0.306424	−	0.530742i
$46$	−16.0000	−	27.7128i	−0.0512842	−	0.0888268i
$47$	268.000	−	464.190i	0.831741	−	1.44062i	−0.0649159	−	0.997891i	$-0.520678\pi$
$47$	268.000	−	464.190i	0.831741	−	1.44062i	0.896657	−	0.442727i	$-0.145989\pi$
$48$	328.000			0.986307
$49$		0			0
$50$	25.0000			0.0707107
$51$	−376.000	+	651.251i	−1.03236	+	1.78811i
$52$	273.000	+	472.850i	0.728044	+	1.26101i
$53$	−11.0000	−	19.0526i	−0.0285088	−	0.0493787i	0.851419	−	0.524486i	$-0.175743\pi$
$53$	−11.0000	−	19.0526i	−0.0285088	−	0.0493787i	−0.879928	+	0.475107i	$0.842409\pi$
$54$	−40.0000	+	69.2820i	−0.100802	+	0.174594i
$55$	60.0000			0.147098
$56$		0			0
$57$	−320.000			−0.743597
$58$	25.0000	−	43.3013i	0.0565976	−	0.0980299i
$59$	−280.000	−	484.974i	−0.617846	−	1.07014i	−0.989878	−	0.141920i	$-0.954672\pi$
$59$	−280.000	−	484.974i	−0.617846	−	1.07014i	0.372032	−	0.928220i	$-0.378661\pi$
$60$	140.000	+	242.487i	0.301232	+	0.521749i
$61$	−139.000	+	240.755i	−0.291756	+	0.505337i	−0.974225	−	0.225578i	$-0.927573\pi$
$61$	−139.000	+	240.755i	−0.291756	+	0.505337i	0.682469	+	0.730915i	$0.260906\pi$
$62$	248.000			0.508001
$63$		0			0
$64$	−167.000			−0.326172
$65$	−195.000	+	337.750i	−0.372104	+	0.644503i
$66$	−48.0000	−	83.1384i	−0.0895211	−	0.155055i
$67$	82.0000	+	142.028i	0.149521	+	0.258978i	0.931050	−	0.364890i	$-0.118894\pi$
$67$	82.0000	+	142.028i	0.149521	+	0.258978i	−0.781530	+	0.623868i	$0.785560\pi$
$68$	329.000	−	569.845i	0.586722	−	1.01623i
$69$	256.000			0.446649
$70$		0			0
$71$	672.000			1.12326			0.561632	−	0.827387i	$-0.310174\pi$
$71$	672.000			1.12326			0.561632	+	0.827387i	$0.310174\pi$
$72$	277.500	−	480.644i	0.454218	−	0.786728i
$73$	41.0000	+	71.0141i	0.0657354	+	0.113857i	0.897020	−	0.441990i	$-0.145727\pi$
$73$	41.0000	+	71.0141i	0.0657354	+	0.113857i	−0.831285	+	0.555847i	$0.812394\pi$
$74$	217.000	+	375.855i	0.340888	+	0.590436i
$75$	−100.000	+	173.205i	−0.153960	+	0.266667i
$76$	280.000			0.422608
$77$		0			0
$78$	624.000			0.905822
$79$	500.000	−	866.025i	0.712081	−	1.23336i	−0.251994	−	0.967729i	$-0.581086\pi$
$79$	500.000	−	866.025i	0.712081	−	1.23336i	0.964075	−	0.265632i	$-0.0855804\pi$
$80$	−102.500	−	177.535i	−0.143248	−	0.248113i
$81$	179.500	+	310.903i	0.246228	+	0.426479i
$82$	201.000	−	348.142i	0.270692	−	0.468852i
$83$	448.000			0.592463			0.296231	−	0.955116i	$-0.404270\pi$
$83$	448.000			0.592463			0.296231	+	0.955116i	$0.404270\pi$
$84$		0			0
$85$	470.000			0.599749
$86$	34.0000	−	58.8897i	0.0426316	−	0.0738400i
$87$	200.000	+	346.410i	0.246463	+	0.426886i
$88$	90.0000	+	155.885i	0.109023	+	0.188834i
$89$	−435.000	+	753.442i	−0.518089	+	0.897356i	0.481690	+	0.876342i	$0.340023\pi$
$89$	−435.000	+	753.442i	−0.518089	+	0.897356i	−0.999779	+	0.0210147i	$0.993310\pi$
$90$	185.000			0.216675
$91$		0			0
$92$	−224.000			−0.253844
$93$	−992.000	+	1718.19i	−1.10608	+	1.91579i
$94$	268.000	+	464.190i	0.294065	+	0.509335i
$95$	100.000	+	173.205i	0.107998	+	0.187058i
$96$	−644.000	+	1115.44i	−0.684666	+	1.18588i
$97$	−1026.00			−1.07396			−0.536982	−	0.843594i	$-0.680436\pi$
$97$	−1026.00			−1.07396			−0.536982	+	0.843594i	$0.680436\pi$
$98$		0			0
$99$	444.000			0.450744
$100$	87.5000	−	151.554i	0.0875000	−	0.151554i
$101$	241.000	+	417.424i	0.237430	+	0.411240i	0.959976	−	0.280082i	$-0.0903617\pi$
$101$	241.000	+	417.424i	0.237430	+	0.411240i	−0.722546	+	0.691322i	$0.757028\pi$
$102$	−376.000	−	651.251i	−0.364996	−	0.632191i
$103$	136.000	−	235.559i	0.130102	−	0.225343i	−0.793614	−	0.608422i	$-0.791803\pi$
$103$	136.000	−	235.559i	0.130102	−	0.225343i	0.923716	+	0.383079i	$0.125136\pi$
$104$	−1170.00			−1.10315
$105$		0			0
$106$	22.0000			0.0201588
$107$	222.000	−	384.515i	0.200575	−	0.347406i	−0.748139	−	0.663542i	$-0.769052\pi$
$107$	222.000	−	384.515i	0.200575	−	0.347406i	0.948714	+	0.316136i	$0.102386\pi$
$108$	280.000	+	484.974i	0.249472	+	0.432099i
$109$	585.000	+	1013.25i	0.514063	+	0.890383i	0.999867	+	0.0163151i	$0.00519348\pi$
$109$	585.000	+	1013.25i	0.514063	+	0.890383i	−0.485804	+	0.874068i	$0.661473\pi$
$110$	−30.0000	+	51.9615i	−0.0260035	+	0.0450394i
$111$	−3472.00			−2.96890
$112$		0			0
$113$	−798.000			−0.664332			−0.332166	−	0.943221i	$-0.607779\pi$
$113$	−798.000			−0.664332			−0.332166	+	0.943221i	$0.607779\pi$
$114$	160.000	−	277.128i	0.131451	−	0.227679i
$115$	−80.0000	−	138.564i	−0.0648699	−	0.112358i
$116$	−175.000	−	303.109i	−0.140072	−	0.242612i
$117$	−1443.00	+	2499.35i	−1.14022	+	1.97491i
$118$	560.000			0.436883
$119$		0			0
$120$	−600.000			−0.456435
$121$	593.500	−	1027.97i	0.445905	−	0.772331i
$122$	−139.000	−	240.755i	−0.103151	−	0.178663i
$123$	1608.00	+	2785.14i	1.17877	+	2.04169i
$124$	868.000	−	1503.42i	0.628619	−	1.08880i
$125$	125.000			0.0894427
$126$		0			0
$127$	776.000			0.542196			0.271098	−	0.962552i	$-0.412613\pi$
$127$	776.000			0.542196			0.271098	+	0.962552i	$0.412613\pi$
$128$	727.500	−	1260.07i	0.502363	−	0.870119i
$129$	272.000	+	471.118i	0.185645	+	0.321547i
$130$	−195.000	−	337.750i	−0.131559	−	0.227866i
$131$	556.000	−	963.020i	0.370824	−	0.642286i	−0.618869	−	0.785495i	$-0.712409\pi$
$131$	556.000	−	963.020i	0.370824	−	0.642286i	0.989693	+	0.143209i	$0.0457420\pi$
$132$	−672.000			−0.443107
$133$		0			0
$134$	−164.000			−0.105727
$135$	−200.000	+	346.410i	−0.127506	+	0.220846i
$136$	705.000	+	1221.10i	0.444509	+	0.769913i
$137$	347.000	+	601.022i	0.216396	+	0.374808i	0.953703	−	0.300749i	$-0.0972365\pi$
$137$	347.000	+	601.022i	0.216396	+	0.374808i	−0.737308	+	0.675557i	$0.763903\pi$
$138$	−128.000	+	221.703i	−0.0789571	+	0.136758i
$139$	−360.000			−0.219675			−0.109837	−	0.993950i	$-0.535033\pi$
$139$	−360.000			−0.219675			−0.109837	+	0.993950i	$0.535033\pi$
$140$		0			0
$141$	−4288.00			−2.56110
$142$	−336.000	+	581.969i	−0.198567	+	0.343928i
$143$	−468.000	−	810.600i	−0.273679	−	0.474026i
$144$	−758.500	−	1313.76i	−0.438947	−	0.760278i
$145$	125.000	−	216.506i	0.0715909	−	0.123999i
$146$	−82.0000			−0.0464820
$147$		0			0
$148$	3038.00			1.68731
$149$	−1135.00	+	1965.88i	−0.624046	+	1.08088i	0.364679	+	0.931133i	$0.381179\pi$
$149$	−1135.00	+	1965.88i	−0.624046	+	1.08088i	−0.988725	+	0.149746i	$0.952155\pi$
$150$	−100.000	−	173.205i	−0.0544331	−	0.0942809i
$151$	−316.000	−	547.328i	−0.170303	−	0.294973i	0.768223	−	0.640182i	$-0.221141\pi$
$151$	−316.000	−	547.328i	−0.170303	−	0.294973i	−0.938526	+	0.345209i	$0.887808\pi$
$152$	−300.000	+	519.615i	−0.160087	+	0.277279i
$153$	3478.00			1.83778
$154$		0			0
$155$	1240.00			0.642575
$156$	2184.00	−	3782.80i	1.12090	−	1.94145i
$157$	−367.000	−	635.663i	−0.186559	−	0.323130i	0.757542	−	0.652787i	$-0.226400\pi$
$157$	−367.000	−	635.663i	−0.186559	−	0.323130i	−0.944101	+	0.329657i	$0.893067\pi$
$158$	500.000	+	866.025i	0.251759	+	0.436059i
$159$	−88.0000	+	152.420i	−0.0438922	+	0.0760235i
$160$	805.000			0.397755
$161$		0			0
$162$	−359.000			−0.174109
$163$	−1266.00	+	2192.78i	−0.608348	+	1.05369i	0.383164	+	0.923680i	$0.374834\pi$
$163$	−1266.00	+	2192.78i	−0.608348	+	1.05369i	−0.991513	+	0.130010i	$0.958499\pi$
$164$	−1407.00	−	2437.00i	−0.669928	−	1.16035i
$165$	−240.000	−	415.692i	−0.113236	−	0.196131i
$166$	−224.000	+	387.979i	−0.104734	+	0.181404i
$167$	−416.000			−0.192761			−0.0963804	−	0.995345i	$-0.530727\pi$
$167$	−416.000			−0.192761			−0.0963804	+	0.995345i	$0.530727\pi$
$168$		0			0
$169$	3887.00			1.76923
$170$	−235.000	+	407.032i	−0.106022	+	0.183635i
$171$	740.000	+	1281.72i	0.330931	+	0.573189i
$172$	−238.000	−	412.228i	−0.105508	−	0.182745i
$173$	1521.00	−	2634.45i	0.668436	−	1.15777i	−0.309905	−	0.950768i	$-0.600297\pi$
$173$	1521.00	−	2634.45i	0.668436	−	1.15777i	0.978341	−	0.206998i	$-0.0663694\pi$
$174$	−400.000			−0.174275
$175$		0			0
$176$	492.000			0.210715
$177$	−2240.00	+	3879.79i	−0.951236	+	1.64759i
$178$	−435.000	−	753.442i	−0.183172	−	0.317263i
$179$	90.0000	+	155.885i	0.0375805	+	0.0650914i	0.884204	−	0.467101i	$-0.154702\pi$
$179$	90.0000	+	155.885i	0.0375805	+	0.0650914i	−0.846623	+	0.532192i	$0.821368\pi$
$180$	647.500	−	1121.50i	0.268121	−	0.464399i
$181$	1958.00			0.804072			0.402036	−	0.915624i	$-0.368303\pi$
$181$	1958.00			0.804072			0.402036	+	0.915624i	$0.368303\pi$
$182$		0			0
$183$	2224.00			0.898376
$184$	240.000	−	415.692i	0.0961578	−	0.166550i
$185$	1085.00	+	1879.28i	0.431193	+	0.746849i
$186$	−992.000	−	1718.19i	−0.391059	−	0.677334i
$187$	−564.000	+	976.877i	−0.220555	+	0.382012i
$188$	3752.00			1.45555
$189$		0			0
$190$	−200.000			−0.0763659
$191$	1444.00	−	2501.08i	0.547038	−	0.947497i	−0.451438	−	0.892302i	$-0.649089\pi$
$191$	1444.00	−	2501.08i	0.547038	−	0.947497i	0.998476	−	0.0551944i	$-0.0175779\pi$
$192$	668.000	+	1157.01i	0.251087	+	0.434896i
$193$	−801.000	−	1387.37i	−0.298742	−	0.517437i	0.677106	−	0.735885i	$-0.263234\pi$
$193$	−801.000	−	1387.37i	−0.298742	−	0.517437i	−0.975848	+	0.218449i	$0.929900\pi$
$194$	513.000	−	888.542i	0.189852	−	0.328833i
$195$	3120.00			1.14578
$196$		0			0
$197$	−4794.00			−1.73380			−0.866899	−	0.498483i	$-0.833891\pi$
$197$	−4794.00			−1.73380			−0.866899	+	0.498483i	$0.833891\pi$
$198$	−222.000	+	384.515i	−0.0796811	+	0.138012i
$199$	640.000	+	1108.51i	0.227982	+	0.394876i	0.957210	−	0.289395i	$-0.0934540\pi$
$199$	640.000	+	1108.51i	0.227982	+	0.394876i	−0.729228	+	0.684271i	$0.760121\pi$
$200$	187.500	+	324.760i	0.0662913	+	0.114820i
$201$	656.000	−	1136.23i	0.230202	−	0.398722i
$202$	−482.000			−0.167888
$203$		0			0
$204$	−5264.00			−1.80664
$205$	1005.00	−	1740.71i	0.342401	−	0.593056i
$206$	136.000	+	235.559i	0.0459979	+	0.0796707i
$207$	−592.000	−	1025.37i	−0.198777	−	0.344292i
$208$	−1599.00	+	2769.55i	−0.533032	+	0.923239i
$209$	−480.000			−0.158863
$210$		0			0
$211$	−68.0000			−0.0221863			−0.0110932	−	0.999938i	$-0.503531\pi$
$211$	−68.0000			−0.0221863			−0.0110932	+	0.999938i	$0.503531\pi$
$212$	77.0000	−	133.368i	0.0249452	−	0.0432063i
$213$	−2688.00	−	4655.75i	−0.864689	−	1.49769i
$214$	222.000	+	384.515i	0.0709141	+	0.122827i
$215$	170.000	−	294.449i	0.0539251	−	0.0934011i
$216$	−1200.00			−0.378008
$217$		0			0
$218$	−1170.00			−0.363497
$219$	328.000	−	568.113i	0.101206	−	0.175295i
$220$	210.000	+	363.731i	0.0643554	+	0.111467i
$221$	−3666.00	−	6349.70i	−1.11585	−	1.93270i
$222$	1736.00	−	3006.84i	0.524832	−	0.909036i
$223$	1728.00			0.518903			0.259452	−	0.965756i	$-0.416458\pi$
$223$	1728.00			0.518903			0.259452	+	0.965756i	$0.416458\pi$
$224$		0			0
$225$	925.000			0.274074
$226$	399.000	−	691.088i	0.117438	−	0.203409i
$227$	−2432.00	−	4212.35i	−0.711090	−	1.23164i	−0.964448	−	0.264272i	$-0.914868\pi$
$227$	−2432.00	−	4212.35i	−0.711090	−	1.23164i	0.253358	−	0.967373i	$-0.418465\pi$
$228$	−1120.00	−	1939.90i	−0.325324	−	0.563477i
$229$	−2755.00	+	4771.80i	−0.795002	+	1.37698i	0.127835	+	0.991795i	$0.459197\pi$
$229$	−2755.00	+	4771.80i	−0.795002	+	1.37698i	−0.922838	+	0.385189i	$0.874136\pi$
$230$	160.000			0.0458699
$231$		0			0
$232$	750.000			0.212241
$233$	−2661.00	+	4608.99i	−0.748188	+	1.29590i	0.200502	+	0.979693i	$0.435743\pi$
$233$	−2661.00	+	4608.99i	−0.748188	+	1.29590i	−0.948690	+	0.316207i	$0.897591\pi$
$234$	−1443.00	−	2499.35i	−0.403128	−	0.698238i
$235$	1340.00	+	2320.95i	0.371966	+	0.644264i
$236$	1960.00	−	3394.82i	0.540615	−	0.936373i
$237$	−8000.00			−2.19264
$238$		0			0
$239$	−1840.00			−0.497990			−0.248995	−	0.968505i	$-0.580100\pi$
$239$	−1840.00			−0.497990			−0.248995	+	0.968505i	$0.580100\pi$
$240$	−820.000	+	1420.28i	−0.220545	+	0.381995i
$241$	−219.000	−	379.319i	−0.0585354	−	0.101386i	0.835273	−	0.549836i	$-0.185310\pi$
$241$	−219.000	−	379.319i	−0.0585354	−	0.101386i	−0.893808	+	0.448450i	$0.851976\pi$
$242$	593.500	+	1027.97i	0.157651	+	0.273060i
$243$	2516.00	−	4357.84i	0.664204	−	1.15043i
$244$	−1946.00			−0.510573
$245$		0			0
$246$	−3216.00			−0.833515
$247$	1560.00	−	2702.00i	0.401864	−	0.696049i
$248$	1860.00	+	3221.61i	0.476250	+	0.824890i
$249$	−1792.00	−	3103.84i	−0.456078	−	0.789950i
$250$	−62.5000	+	108.253i	−0.0158114	+	0.0273861i
$251$	−5592.00			−1.40623			−0.703115	−	0.711076i	$-0.748208\pi$
$251$	−5592.00			−1.40623			−0.703115	+	0.711076i	$0.748208\pi$
$252$		0			0
$253$	384.000			0.0954224
$254$	−388.000	+	672.036i	−0.0958476	+	0.166013i
$255$	−1880.00	−	3256.26i	−0.461687	−	0.799665i
$256$	59.5000	+	103.057i	0.0145264	+	0.0251604i
$257$	−987.000	+	1709.53i	−0.239562	+	0.414933i	−0.960589	−	0.277974i	$-0.910337\pi$
$257$	−987.000	+	1709.53i	−0.239562	+	0.414933i	0.721027	+	0.692907i	$0.243670\pi$
$258$	−544.000			−0.131271
$259$		0			0
$260$	−2730.00			−0.651182
$261$	925.000	−	1602.15i	0.219372	−	0.379963i
$262$	556.000	+	963.020i	0.131106	+	0.227082i
$263$	364.000	+	630.466i	0.0853430	+	0.147818i	0.905537	−	0.424267i	$-0.139468\pi$
$263$	364.000	+	630.466i	0.0853430	+	0.147818i	−0.820194	+	0.572085i	$0.806135\pi$
$264$	720.000	−	1247.08i	0.167852	−	0.290728i
$265$	110.000			0.0254990
$266$		0			0
$267$	6960.00			1.59530
$268$	−574.000	+	994.197i	−0.130831	+	0.226605i
$269$	2905.00	+	5031.61i	0.658442	+	1.14046i	0.981019	+	0.193912i	$0.0621177\pi$
$269$	2905.00	+	5031.61i	0.658442	+	1.14046i	−0.322577	+	0.946543i	$0.604549\pi$
$270$	−200.000	−	346.410i	−0.0450800	−	0.0780809i
$271$	−3264.00	+	5653.41i	−0.731638	+	1.26723i	0.224545	+	0.974464i	$0.427910\pi$
$271$	−3264.00	+	5653.41i	−0.731638	+	1.26723i	−0.956183	+	0.292770i	$0.905423\pi$
$272$	3854.00			0.859129
$273$		0			0
$274$	−694.000			−0.153015
$275$	−150.000	+	259.808i	−0.0328921	+	0.0569709i
$276$	896.000	+	1551.92i	0.195409	+	0.338458i
$277$	−2563.00	−	4439.25i	−0.555941	−	0.962919i	−0.997830	−	0.0658485i	$-0.979025\pi$
$277$	−2563.00	−	4439.25i	−0.555941	−	0.962919i	0.441888	−	0.897070i	$-0.354309\pi$
$278$	180.000	−	311.769i	0.0388334	−	0.0672614i
$279$	9176.00			1.96901
$280$		0			0
$281$	−2358.00			−0.500592			−0.250296	−	0.968169i	$-0.580528\pi$
$281$	−2358.00			−0.500592			−0.250296	+	0.968169i	$0.580528\pi$
$282$	2144.00	−	3713.52i	0.452742	−	0.784173i
$283$	196.000	+	339.482i	0.0411696	+	0.0713078i	0.885876	−	0.463922i	$-0.153558\pi$
$283$	196.000	+	339.482i	0.0411696	+	0.0713078i	−0.844706	+	0.535230i	$0.820225\pi$
$284$	2352.00	+	4073.78i	0.491428	+	0.851178i
$285$	800.000	−	1385.64i	0.166273	−	0.287994i
$286$	936.000			0.193520
$287$		0			0
$288$	5957.00			1.21882
$289$	−1961.50	+	3397.42i	−0.399247	+	0.691516i
$290$	125.000	+	216.506i	0.0253112	+	0.0438403i
$291$	4104.00	+	7108.34i	0.826738	+	1.43195i
$292$	−287.000	+	497.099i	−0.0575185	+	0.0996250i
$293$	−1202.00			−0.239664			−0.119832	−	0.992794i	$-0.538236\pi$
$293$	−1202.00			−0.239664			−0.119832	+	0.992794i	$0.538236\pi$
$294$		0			0
$295$	2800.00			0.552618
$296$	−3255.00	+	5637.83i	−0.639166	+	1.10707i
$297$	−480.000	−	831.384i	−0.0937792	−	0.162430i
$298$	−1135.00	−	1965.88i	−0.220634	−	0.382148i
$299$	−1248.00	+	2161.60i	−0.241384	+	0.418089i
$300$	−1400.00			−0.269430
$301$		0			0
$302$	632.000			0.120422
$303$	1928.00	−	3339.39i	0.365547	−	0.633146i
$304$	820.000	+	1420.28i	0.154705	+	0.267956i
$305$	−695.000	−	1203.78i	−0.130477	−	0.225993i
$306$	−1739.00	+	3012.04i	−0.324876	+	0.562701i
$307$	6384.00			1.18682			0.593411	−	0.804900i	$-0.297781\pi$
$307$	6384.00			1.18682			0.593411	+	0.804900i	$0.297781\pi$
$308$		0			0
$309$	−2176.00			−0.400609
$310$	−620.000	+	1073.87i	−0.113592	+	0.196748i
$311$	−2484.00	−	4302.41i	−0.452909	−	0.784462i	0.545656	−	0.838009i	$-0.316280\pi$
$311$	−2484.00	−	4302.41i	−0.452909	−	0.784462i	−0.998565	+	0.0535476i	$0.982947\pi$
$312$	4680.00	+	8106.00i	0.849208	+	1.47087i
$313$	−1379.00	+	2388.50i	−0.249028	+	0.431329i	−0.963256	−	0.268584i	$-0.913444\pi$
$313$	−1379.00	+	2388.50i	−0.249028	+	0.431329i	0.714229	+	0.699913i	$0.246778\pi$
$314$	734.000			0.131917
$315$		0			0
$316$	7000.00			1.24614
$317$	3137.00	−	5433.44i	0.555809	−	0.962690i	−0.442031	−	0.897000i	$-0.645742\pi$
$317$	3137.00	−	5433.44i	0.555809	−	0.962690i	0.997840	−	0.0656898i	$-0.0209248\pi$
$318$	−88.0000	−	152.420i	−0.0155182	−	0.0268784i
$319$	300.000	+	519.615i	0.0526545	+	0.0912002i
$320$	417.500	−	723.131i	0.0729342	−	0.126326i
$321$	−3552.00			−0.617612
$322$		0			0
$323$	−3760.00			−0.647715
$324$	−1256.50	+	2176.32i	−0.215449	+	0.373169i
$325$	−975.000	−	1688.75i	−0.166410	−	0.288231i
$326$	−1266.00	−	2192.78i	−0.215084	−	0.372536i
$327$	4680.00	−	8106.00i	0.791451	−	1.37083i
$328$	6030.00			1.01509
$329$		0			0
$330$	480.000			0.0800701
$331$	−966.000	+	1673.16i	−0.160411	+	0.277841i	−0.935016	−	0.354605i	$-0.884615\pi$
$331$	−966.000	+	1673.16i	−0.160411	+	0.277841i	0.774605	+	0.632445i	$0.217949\pi$
$332$	1568.00	+	2715.86i	0.259202	+	0.448952i
$333$	8029.00	+	13906.6i	1.32128	+	2.28853i
$334$	208.000	−	360.267i	0.0340756	−	0.0590207i
$335$	−820.000			−0.133735
$336$		0			0
$337$	2386.00			0.385679			0.192839	−	0.981230i	$-0.438230\pi$
$337$	2386.00			0.385679			0.192839	+	0.981230i	$0.438230\pi$
$338$	−1943.50	+	3366.24i	−0.312759	+	0.541714i
$339$	3192.00	+	5528.71i	0.511403	+	0.885776i
$340$	1645.00	+	2849.22i	0.262390	+	0.454473i
$341$	−1488.00	+	2577.29i	−0.236304	+	0.409291i
$342$	−1480.00			−0.234004
$343$		0			0
$344$	1020.00			0.159868
$345$	−640.000	+	1108.51i	−0.0998737	+	0.172986i
$346$	1521.00	+	2634.45i	0.236328	+	0.409332i
$347$	−3038.00	−	5261.97i	−0.469995	−	0.814056i	0.529416	−	0.848362i	$-0.322411\pi$
$347$	−3038.00	−	5261.97i	−0.469995	−	0.814056i	−0.999411	+	0.0343065i	$0.989078\pi$
$348$	−1400.00	+	2424.87i	−0.215655	+	0.373525i
$349$	−2210.00			−0.338964			−0.169482	−	0.985533i	$-0.554210\pi$
$349$	−2210.00			−0.338964			−0.169482	+	0.985533i	$0.554210\pi$
$350$		0			0
$351$	6240.00			0.948908
$352$	−966.000	+	1673.16i	−0.146273	+	0.253352i
$353$	−1299.00	−	2249.93i	−0.195861	−	0.339241i	0.751322	−	0.659936i	$-0.229417\pi$
$353$	−1299.00	−	2249.93i	−0.195861	−	0.339241i	−0.947182	+	0.320696i	$0.896083\pi$
$354$	−2240.00	−	3879.79i	−0.336313	−	0.582510i
$355$	−1680.00	+	2909.85i	−0.251169	+	0.435038i
$356$	−6090.00			−0.906655
$357$		0			0
$358$	−180.000			−0.0265735
$359$	6660.00	−	11535.5i	0.979112	−	1.69587i	0.313476	−	0.949596i	$-0.398506\pi$
$359$	6660.00	−	11535.5i	0.979112	−	1.69587i	0.665636	−	0.746276i	$-0.268160\pi$
$360$	1387.50	+	2403.22i	0.203132	+	0.351836i
$361$	2629.50	+	4554.43i	0.383365	+	0.664008i
$362$	−979.000	+	1695.68i	−0.142141	+	0.246196i
$363$	−9496.00			−1.37303
$364$		0			0
$365$	−410.000			−0.0587956
$366$	−1112.00	+	1926.04i	−0.158812	+	0.275070i
$367$	5408.00	+	9366.93i	0.769197	+	1.33229i	0.937999	+	0.346638i	$0.112677\pi$
$367$	5408.00	+	9366.93i	0.769197	+	1.33229i	−0.168802	+	0.985650i	$0.553990\pi$
$368$	−656.000	−	1136.23i	−0.0929249	−	0.160951i
$369$	7437.00	−	12881.3i	1.04920	−	1.81727i
$370$	−2170.00			−0.304900
$371$		0			0
$372$	−13888.0			−1.93564
$373$	5549.00	−	9611.15i	0.770285	−	1.33417i	−0.167122	−	0.985936i	$-0.553447\pi$
$373$	5549.00	−	9611.15i	0.770285	−	1.33417i	0.937407	−	0.348237i	$-0.113219\pi$
$374$	−564.000	−	976.877i	−0.0779779	−	0.135062i
$375$	−500.000	−	866.025i	−0.0688530	−	0.119257i
$376$	−4020.00	+	6962.84i	−0.551371	+	0.955003i
$377$	−3900.00			−0.532786
$378$		0			0
$379$	7100.00			0.962276			0.481138	−	0.876645i	$-0.340224\pi$
$379$	7100.00			0.962276			0.481138	+	0.876645i	$0.340224\pi$
$380$	−700.000	+	1212.44i	−0.0944980	+	0.163675i
$381$	−3104.00	−	5376.29i	−0.417383	−	0.722928i
$382$	1444.00	+	2501.08i	0.193407	+	0.334991i
$383$	−364.000	+	630.466i	−0.0485627	+	0.0841131i	−0.889285	−	0.457353i	$-0.848797\pi$
$383$	−364.000	+	630.466i	−0.0485627	+	0.0841131i	0.840722	+	0.541467i	$0.182131\pi$
$384$	−11640.0			−1.54688
$385$		0			0
$386$	1602.00			0.211243
$387$	1258.00	−	2178.92i	0.165240	−	0.286203i
$388$	−3591.00	−	6219.79i	−0.469859	−	0.813820i
$389$	3405.00	+	5897.63i	0.443806	+	0.768694i	0.997968	−	0.0637147i	$-0.0202948\pi$
$389$	3405.00	+	5897.63i	0.443806	+	0.768694i	−0.554163	+	0.832408i	$0.686961\pi$
$390$	−1560.00	+	2702.00i	−0.202548	+	0.350823i
$391$	3008.00			0.389057
$392$		0			0
$393$	−8896.00			−1.14184
$394$	2397.00	−	4151.73i	0.306495	−	0.530865i
$395$	2500.00	+	4330.13i	0.318452	+	0.551576i
$396$	1554.00	+	2691.61i	0.197201	+	0.341561i
$397$	−287.000	+	497.099i	−0.0362824	+	0.0628430i	−0.883596	−	0.468249i	$-0.844885\pi$
$397$	−287.000	+	497.099i	−0.0362824	+	0.0628430i	0.847314	+	0.531092i	$0.178218\pi$
$398$	−1280.00			−0.161208
$399$		0			0
$400$	1025.00			0.128125
$401$	−3081.00	+	5336.45i	−0.383685	+	0.664562i	−0.991586	−	0.129451i	$-0.958679\pi$
$401$	−3081.00	+	5336.45i	−0.383685	+	0.664562i	0.607901	+	0.794013i	$0.292012\pi$
$402$	656.000	+	1136.23i	0.0813888	+	0.140970i
$403$	−9672.00	−	16752.4i	−1.19553	−	2.07071i
$404$	−1687.00	+	2921.97i	−0.207751	+	0.359835i
$405$	−1795.00			−0.220233
$406$		0			0
$407$	−5208.00			−0.634278
$408$	5640.00	−	9768.77i	0.684367	−	1.18536i
$409$	4105.00	+	7110.07i	0.496282	+	0.859585i	0.999991	−	0.00428830i	$-0.00136501\pi$
$409$	4105.00	+	7110.07i	0.496282	+	0.859585i	−0.503709	+	0.863873i	$0.668032\pi$
$410$	1005.00	+	1740.71i	0.121057	+	0.209677i
$411$	2776.00	−	4808.17i	0.333163	−	0.577055i
$412$	1904.00			0.227678
$413$		0			0
$414$	1184.00			0.140557
$415$	−1120.00	+	1939.90i	−0.132479	+	0.229460i
$416$	−6279.00	−	10875.5i	−0.740032	−	1.28177i
$417$	1440.00	+	2494.15i	0.169106	+	0.292900i
$418$	240.000	−	415.692i	0.0280832	−	0.0486416i
$419$	−4800.00			−0.559655			−0.279827	−	0.960050i	$-0.590277\pi$
$419$	−4800.00			−0.559655			−0.279827	+	0.960050i	$0.590277\pi$
$420$		0			0
$421$	−9938.00			−1.15047			−0.575236	−	0.817988i	$-0.695090\pi$
$421$	−9938.00			−1.15047			−0.575236	+	0.817988i	$0.695090\pi$
$422$	34.0000	−	58.8897i	0.00392202	−	0.00679314i
$423$	9916.00	+	17175.0i	1.13979	+	1.97418i
$424$	165.000	+	285.788i	0.0188988	+	0.0327338i
$425$	−1175.00	+	2035.16i	−0.134108	+	0.232282i
$426$	5376.00			0.611427
$427$		0			0
$428$	3108.00			0.351007
$429$	−3744.00	+	6484.80i	−0.421357	+	0.729811i
$430$	170.000	+	294.449i	0.0190654	+	0.0330223i
$431$	4624.00	+	8009.00i	0.516776	+	0.895081i	0.999810	+	0.0194802i	$0.00620115\pi$
$431$	4624.00	+	8009.00i	0.516776	+	0.895081i	−0.483035	+	0.875601i	$0.660466\pi$
$432$	−1640.00	+	2840.56i	−0.182649	+	0.316358i
$433$	1118.00			0.124082			0.0620412	−	0.998074i	$-0.480239\pi$
$433$	1118.00			0.124082			0.0620412	+	0.998074i	$0.480239\pi$
$434$		0			0
$435$	−2000.00			−0.220443
$436$	−4095.00	+	7092.75i	−0.449805	+	0.779085i
$437$	640.000	+	1108.51i	0.0700580	+	0.121344i
$438$	328.000	+	568.113i	0.0357818	+	0.0619760i
$439$	−5980.00	+	10357.7i	−0.650136	+	1.12607i	0.332953	+	0.942943i	$0.391955\pi$
$439$	−5980.00	+	10357.7i	−0.650136	+	1.12607i	−0.983090	+	0.183126i	$0.941378\pi$
$440$	−900.000			−0.0975132
$441$		0			0
$442$	7332.00			0.789022
$443$	−3666.00	+	6349.70i	−0.393176	+	0.681001i	−0.992867	−	0.119231i	$-0.961957\pi$
$443$	−3666.00	+	6349.70i	−0.393176	+	0.681001i	0.599691	+	0.800232i	$0.295290\pi$
$444$	−12152.0	−	21047.9i	−1.29889	−	2.24975i
$445$	−2175.00	−	3767.21i	−0.231696	−	0.401310i
$446$	−864.000	+	1496.49i	−0.0917300	+	0.158881i
$447$	18160.0			1.92156
$448$		0			0
$449$	1890.00			0.198652			0.0993259	−	0.995055i	$-0.468331\pi$
$449$	1890.00			0.198652			0.0993259	+	0.995055i	$0.468331\pi$
$450$	−462.500	+	801.073i	−0.0484499	+	0.0839177i
$451$	2412.00	+	4177.71i	0.251833	+	0.436187i
$452$	−2793.00	−	4837.62i	−0.290645	−	0.503412i
$453$	−2528.00	+	4378.62i	−0.262198	+	0.454141i
$454$	4864.00			0.502817
$455$		0			0
$456$	4800.00			0.492940
$457$	3507.00	−	6074.30i	0.358973	−	0.621759i	−0.628817	−	0.777554i	$-0.716460\pi$
$457$	3507.00	−	6074.30i	0.358973	−	0.621759i	0.987789	+	0.155795i	$0.0497938\pi$
$458$	−2755.00	−	4771.80i	−0.281076	−	0.486837i
$459$	−3760.00	−	6512.51i	−0.382357	−	0.662261i
$460$	560.000	−	969.948i	0.0567612	−	0.0983132i
$461$	8318.00			0.840364			0.420182	−	0.907440i	$-0.361966\pi$
$461$	8318.00			0.840364			0.420182	+	0.907440i	$0.361966\pi$
$462$		0			0
$463$	6432.00			0.645616			0.322808	−	0.946464i	$-0.395373\pi$
$463$	6432.00			0.645616			0.322808	+	0.946464i	$0.395373\pi$
$464$	1025.00	−	1775.35i	0.102553	−	0.177626i
$465$	−4960.00	−	8590.97i	−0.494655	−	0.856767i
$466$	−2661.00	−	4608.99i	−0.264525	−	0.458170i
$467$	−5032.00	+	8715.68i	−0.498615	+	0.863626i	−0.999999	−	0.00159856i	$-0.999491\pi$
$467$	−5032.00	+	8715.68i	−0.498615	+	0.863626i	0.501384	+	0.865225i	$0.332824\pi$
$468$	−20202.0			−1.99538
$469$		0			0
$470$	−2680.00			−0.263020
$471$	−2936.00	+	5085.30i	−0.287227	+	0.497491i
$472$	4200.00	+	7274.61i	0.409578	+	0.709409i
$473$	408.000	+	706.677i	0.0396614	+	0.0686956i
$474$	4000.00	−	6928.20i	0.387608	−	0.671356i
$475$	−1000.00			−0.0965961
$476$		0			0
$477$	814.000			0.0781352
$478$	920.000	−	1593.49i	0.0880331	−	0.152478i
$479$	700.000	+	1212.44i	0.0667721	+	0.115653i	0.897479	−	0.441058i	$-0.145397\pi$
$479$	700.000	+	1212.44i	0.0667721	+	0.115653i	−0.830707	+	0.556710i	$0.812063\pi$
$480$	−3220.00	−	5577.20i	−0.306192	−	0.530340i
$481$	16926.0	−	29316.7i	1.60449	−	2.77906i
$482$	438.000			0.0413908
$483$		0			0
$484$	8309.00			0.780334
$485$	2565.00	−	4442.71i	0.240146	−	0.415945i
$486$	2516.00	+	4357.84i	0.234831	+	0.406740i
$487$	−6688.00	−	11584.0i	−0.622304	−	1.07786i	−0.989056	−	0.147544i	$-0.952863\pi$
$487$	−6688.00	−	11584.0i	−0.622304	−	1.07786i	0.366751	−	0.930319i	$-0.380470\pi$
$488$	2085.00	−	3611.33i	0.193409	−	0.334994i
$489$	20256.0			1.87323
$490$		0			0
$491$	7092.00			0.651848			0.325924	−	0.945396i	$-0.394325\pi$
$491$	7092.00			0.651848			0.325924	+	0.945396i	$0.394325\pi$
$492$	−11256.0	+	19496.0i	−1.03142	+	1.78648i
$493$	2350.00	+	4070.32i	0.214683	+	0.371842i
$494$	1560.00	+	2702.00i	0.142080	+	0.246090i
$495$	−1110.00	+	1922.58i	−0.100789	+	0.174572i
$496$	10168.0			0.920477
$497$		0			0
$498$	3584.00			0.322496
$499$	410.000	−	710.141i	0.0367818	−	0.0637080i	−0.847048	−	0.531516i	$-0.821623\pi$
$499$	410.000	−	710.141i	0.0367818	−	0.0637080i	0.883830	+	0.467808i	$0.154956\pi$
$500$	437.500	+	757.772i	0.0391312	+	0.0677772i
$501$	1664.00	+	2882.13i	0.148387	+	0.257014i
$502$	2796.00	−	4842.81i	0.248589	−	0.430568i
$503$	4568.00			0.404925			0.202462	−	0.979290i	$-0.435106\pi$
$503$	4568.00			0.404925			0.202462	+	0.979290i	$0.435106\pi$
$504$		0			0
$505$	−2410.00			−0.212364
$506$	−192.000	+	332.554i	−0.0168685	+	0.0292170i
$507$	−15548.0	−	26929.9i	−1.36195	−	2.35897i
$508$	2716.00	+	4704.25i	0.237211	+	0.410861i
$509$	9905.00	−	17156.0i	0.862537	−	1.49396i	−0.00693487	−	0.999976i	$-0.502207\pi$
$509$	9905.00	−	17156.0i	0.862537	−	1.49396i	0.869472	−	0.493982i	$-0.164459\pi$
$510$	3760.00			0.326462
$511$		0			0
$512$	11521.0			0.994455
$513$	1600.00	−	2771.28i	0.137703	−	0.238509i
$514$	−987.000	−	1709.53i	−0.0846979	−	0.146701i
$515$	680.000	+	1177.79i	0.0581833	+	0.100776i
$516$	−1904.00	+	3297.82i	−0.162440	+	0.281354i
$517$	−6432.00			−0.547155
$518$		0			0
$519$	−24336.0			−2.05825
$520$	2925.00	−	5066.25i	0.246673	−	0.427249i
$521$	−919.000	−	1591.75i	−0.0772785	−	0.133850i	0.824796	−	0.565430i	$-0.191290\pi$
$521$	−919.000	−	1591.75i	−0.0772785	−	0.133850i	−0.902075	+	0.431580i	$0.857956\pi$
$522$	925.000	+	1602.15i	0.0775597	+	0.134337i
$523$	1036.00	−	1794.40i	0.0866178	−	0.150026i	−0.819462	−	0.573134i	$-0.805727\pi$
$523$	1036.00	−	1794.40i	0.0866178	−	0.150026i	0.906079	+	0.423108i	$0.139061\pi$
$524$	7784.00			0.648942
$525$		0			0
$526$	−728.000			−0.0603466
$527$	−11656.0	+	20188.8i	−0.963460	+	1.66876i
$528$	−1968.00	−	3408.68i	−0.162209	−	0.280954i
$529$	5571.50	+	9650.12i	0.457919	+	0.793139i
$530$	−55.0000	+	95.2628i	−0.00450764	+	0.00780746i
$531$	20720.0			1.69335
$532$		0			0
$533$	−31356.0			−2.54818
$534$	−3480.00	+	6027.54i	−0.282012	+	0.488459i
$535$	1110.00	+	1922.58i	0.0897000	+	0.155365i
$536$	−1230.00	−	2130.42i	−0.0991192	−	0.171680i
$537$	720.000	−	1247.08i	0.0578590	−	0.100215i
$538$	−5810.00			−0.465589
$539$		0			0
$540$	−2800.00			−0.223135
$541$	1749.00	−	3029.36i	0.138993	−	0.240743i	−0.788123	−	0.615518i	$-0.788947\pi$
$541$	1749.00	−	3029.36i	0.138993	−	0.240743i	0.927116	+	0.374775i	$0.122280\pi$
$542$	−3264.00	−	5653.41i	−0.258673	−	0.448035i
$543$	−7832.00	−	13565.4i	−0.618975	−	1.07210i
$544$	−7567.00	+	13106.4i	−0.596383	+	1.03297i
$545$	−5850.00			−0.459792
$546$		0			0
$547$	5076.00			0.396772			0.198386	−	0.980124i	$-0.436430\pi$
$547$	5076.00			0.396772			0.198386	+	0.980124i	$0.436430\pi$
$548$	−2429.00	+	4207.15i	−0.189346	+	0.327957i
$549$	−5143.00	−	8907.94i	−0.399814	−	0.692498i
$550$	−150.000	−	259.808i	−0.0116291	−	0.0201422i
$551$	−1000.00	+	1732.05i	−0.0773166	+	0.133916i
$552$	−3840.00			−0.296089
$553$		0			0
$554$	5126.00			0.393110
$555$	8680.00	−	15034.2i	0.663866	−	1.14985i
$556$	−1260.00	−	2182.38i	−0.0961077	−	0.166463i
$557$	4337.00	+	7511.90i	0.329918	+	0.571436i	0.982495	−	0.186287i	$-0.0596454\pi$
$557$	4337.00	+	7511.90i	0.329918	+	0.571436i	−0.652577	+	0.757722i	$0.726312\pi$
$558$	−4588.00	+	7946.65i	−0.348074	+	0.602883i
$559$	−5304.00			−0.401315
$560$		0			0
$561$	9024.00			0.679133
$562$	1179.00	−	2042.09i	0.0884931	−	0.153275i
$563$	8036.00	+	13918.8i	0.601558	+	1.04193i	0.992585	+	0.121550i	$0.0387864\pi$
$563$	8036.00	+	13918.8i	0.601558	+	1.04193i	−0.391028	+	0.920379i	$0.627880\pi$
$564$	−15008.0	−	25994.6i	−1.12048	−	1.94073i
$565$	1995.00	−	3455.44i	0.148549	−	0.257295i
$566$	−392.000			−0.0291113
$567$		0			0
$568$	−10080.0			−0.744626
$569$	−1365.00	+	2364.25i	−0.100569	+	0.174191i	−0.911919	−	0.410370i	$-0.865400\pi$
$569$	−1365.00	+	2364.25i	−0.100569	+	0.174191i	0.811350	+	0.584560i	$0.198733\pi$
$570$	800.000	+	1385.64i	0.0587865	+	0.101821i
$571$	−9966.00	−	17261.6i	−0.730410	−	1.26511i	−0.956708	−	0.291049i	$-0.905996\pi$
$571$	−9966.00	−	17261.6i	−0.730410	−	1.26511i	0.226298	−	0.974058i	$-0.427338\pi$
$572$	3276.00	−	5674.20i	0.239469	−	0.414773i
$573$	−23104.0			−1.68444
$574$		0			0
$575$	800.000			0.0580214
$576$	3089.50	−	5351.17i	0.223488	−	0.387093i
$577$	−10027.0	−	17367.3i	−0.723448	−	1.25305i	−0.959610	−	0.281335i	$-0.909223\pi$
$577$	−10027.0	−	17367.3i	−0.723448	−	1.25305i	0.236162	−	0.971714i	$-0.424110\pi$
$578$	−1961.50	−	3397.42i	−0.141155	−	0.244488i
$579$	−6408.00	+	11099.0i	−0.459944	+	0.796646i
$580$	1750.00			0.125284
$581$		0			0
$582$	−8208.00			−0.584592
$583$	−132.000	+	228.631i	−0.00937716	+	0.0162417i
$584$	−615.000	−	1065.21i	−0.0435769	−	0.0754773i
$585$	−7215.00	−	12496.7i	−0.509921	−	0.883208i
$586$	601.000	−	1040.96i	0.0423670	−	0.0733819i
$587$	2544.00			0.178879			0.0894396	−	0.995992i	$-0.471492\pi$
$587$	2544.00			0.178879			0.0894396	+	0.995992i	$0.471492\pi$
$588$		0			0
$589$	−9920.00			−0.693967
$590$	−1400.00	+	2424.87i	−0.0976900	+	0.169204i
$591$	19176.0	+	33213.8i	1.33468	+	2.31173i
$592$	8897.00	+	15410.1i	0.617676	+	1.06985i
$593$	7101.00	−	12299.3i	0.491742	−	0.851722i	−0.508213	−	0.861232i	$-0.669694\pi$
$593$	7101.00	−	12299.3i	0.491742	−	0.851722i	0.999955	+	0.00950919i	$0.00302692\pi$
$594$	960.000			0.0663119
$595$		0			0
$596$	−15890.0			−1.09208
$597$	5120.00	−	8868.10i	0.351001	−	0.607952i
$598$	−1248.00	−	2161.60i	−0.0853420	−	0.147817i
$599$	9800.00	+	16974.1i	0.668476	+	1.15783i	0.978330	+	0.207050i	$0.0663864\pi$
$599$	9800.00	+	16974.1i	0.668476	+	1.15783i	−0.309854	+	0.950784i	$0.600280\pi$
$600$	1500.00	−	2598.08i	0.102062	−	0.176777i
$601$	27078.0			1.83783			0.918914	−	0.394458i	$-0.129068\pi$
$601$	27078.0			1.83783			0.918914	+	0.394458i	$0.129068\pi$
$602$		0			0
$603$	−6068.00			−0.409798
$604$	2212.00	−	3831.30i	0.149015	−	0.258101i
$605$	2967.50	+	5139.86i	0.199415	+	0.345397i
$606$	1928.00	+	3339.39i	0.129240	+	0.223851i
$607$	−1352.00	+	2341.73i	−0.0904053	+	0.156586i	−0.907682	−	0.419659i	$-0.862150\pi$
$607$	−1352.00	+	2341.73i	−0.0904053	+	0.156586i	0.817276	+	0.576246i	$0.195483\pi$
$608$	−6440.00			−0.429567
$609$		0			0
$610$	1390.00			0.0922614
$611$	20904.0	−	36206.8i	1.38410	−	2.39733i
$612$	12173.0	+	21084.3i	0.804027	+	1.39262i
$613$	−6351.00	−	11000.3i	−0.418458	−	0.724790i	0.577327	−	0.816513i	$-0.304096\pi$
$613$	−6351.00	−	11000.3i	−0.418458	−	0.724790i	−0.995785	+	0.0917233i	$0.970762\pi$
$614$	−3192.00	+	5528.71i	−0.209802	+	0.363388i
$615$	−16080.0			−1.05432
$616$		0			0
$617$	12666.0			0.826441			0.413220	−	0.910631i	$-0.364404\pi$
$617$	12666.0			0.826441			0.413220	+	0.910631i	$0.364404\pi$
$618$	1088.00	−	1884.47i	0.0708184	−	0.122661i
$619$	480.000	+	831.384i	0.0311677	+	0.0539841i	0.881189	−	0.472765i	$-0.156744\pi$
$619$	480.000	+	831.384i	0.0311677	+	0.0539841i	−0.850021	+	0.526749i	$0.823411\pi$
$620$	4340.00	+	7517.10i	0.281127	+	0.486926i
$621$	−1280.00	+	2217.03i	−0.0827128	+	0.143263i
$622$	4968.00			0.320255
$623$		0			0
$624$	25584.0			1.64131
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−1379.00	−	2388.50i	−0.0880446	−	0.152498i
$627$	1920.00	+	3325.54i	0.122293	+	0.211817i
$628$	2569.00	−	4449.64i	0.163239	−	0.282739i
$629$	−40796.0			−2.58608
$630$		0			0
$631$	23232.0			1.46569			0.732846	−	0.680395i	$-0.238192\pi$
$631$	23232.0			1.46569			0.732846	+	0.680395i	$0.238192\pi$
$632$	−7500.00	+	12990.4i	−0.472047	+	0.817610i
$633$	272.000	+	471.118i	0.0170790	+	0.0295818i
$634$	3137.00	+	5433.44i	0.196508	+	0.340362i
$635$	−1940.00	+	3360.18i	−0.121239	+	0.209992i
$636$	−1232.00			−0.0768113
$637$		0			0
$638$	−600.000			−0.0372323
$639$	−12432.0	+	21532.9i	−0.769644	+	1.33306i
$640$	3637.50	+	6300.33i	0.224664	+	0.389129i
$641$	−6081.00	−	10532.6i	−0.374704	−	0.649006i	0.615579	−	0.788075i	$-0.288922\pi$
$641$	−6081.00	−	10532.6i	−0.374704	−	0.649006i	−0.990283	+	0.139069i	$0.955589\pi$
$642$	1776.00	−	3076.12i	0.109179	−	0.189104i
$643$	488.000			0.0299298			0.0149649	−	0.999888i	$-0.495236\pi$
$643$	488.000			0.0299298			0.0149649	+	0.999888i	$0.495236\pi$
$644$		0			0
$645$	−2720.00			−0.166046
$646$	1880.00	−	3256.26i	0.114501	−	0.198321i
$647$	−1992.00	−	3450.25i	−0.121041	−	0.209649i	0.799137	−	0.601148i	$-0.205290\pi$
$647$	−1992.00	−	3450.25i	−0.121041	−	0.209649i	−0.920179	+	0.391499i	$0.871957\pi$
$648$	−2692.50	−	4663.55i	−0.163227	−	0.282718i
$649$	−3360.00	+	5819.69i	−0.203223	+	0.351992i
$650$	1950.00			0.117670
$651$		0			0
$652$	−17724.0			−1.06461
$653$	15269.0	−	26446.7i	0.915042	−	1.58490i	0.108201	−	0.994129i	$-0.465491\pi$
$653$	15269.0	−	26446.7i	0.915042	−	1.58490i	0.806840	−	0.590769i	$-0.201176\pi$
$654$	4680.00	+	8106.00i	0.279820	+	0.484663i
$655$	2780.00	+	4815.10i	0.165838	+	0.287239i
$656$	8241.00	−	14273.8i	0.490483	−	0.849542i
$657$	−3034.00			−0.180164
$658$		0			0
$659$	22740.0			1.34420			0.672098	−	0.740463i	$-0.265394\pi$
$659$	22740.0			1.34420			0.672098	+	0.740463i	$0.265394\pi$
$660$	1680.00	−	2909.85i	0.0990817	−	0.171615i
$661$	−9359.00	−	16210.3i	−0.550715	−	0.953867i	−0.998223	−	0.0595870i	$-0.981022\pi$
$661$	−9359.00	−	16210.3i	−0.550715	−	0.953867i	0.447508	−	0.894280i	$-0.352312\pi$
$662$	−966.000	−	1673.16i	−0.0567140	−	0.0982315i
$663$	−29328.0	+	50797.6i	−1.71796	+	2.97559i
$664$	−6720.00			−0.392751
$665$		0			0
$666$	−16058.0			−0.934287
$667$	800.000	−	1385.64i	0.0464410	−	0.0804381i
$668$	−1456.00	−	2521.87i	−0.0843328	−	0.146069i
$669$	−6912.00	−	11971.9i	−0.399452	−	0.691871i
$670$	410.000	−	710.141i	0.0236413	−	0.0409480i
$671$	3336.00			0.191930
$672$		0			0
$673$	10802.0			0.618702			0.309351	−	0.950948i	$-0.399888\pi$
$673$	10802.0			0.618702			0.309351	+	0.950948i	$0.399888\pi$
$674$	−1193.00	+	2066.34i	−0.0681790	+	0.118089i
$675$	−1000.00	−	1732.05i	−0.0570222	−	0.0987654i
$676$	13604.5	+	23563.7i	0.774038	+	1.34067i
$677$	173.000	−	299.645i	0.00982117	−	0.0170108i	−0.861073	−	0.508481i	$-0.830207\pi$
$677$	173.000	−	299.645i	0.00982117	−	0.0170108i	0.870894	+	0.491471i	$0.163540\pi$
$678$	−6384.00			−0.361617
$679$		0			0
$680$	−7050.00			−0.397581
$681$	−19456.0	+	33698.8i	−1.09480	+	1.89624i
$682$	−1488.00	−	2577.29i	−0.0835461	−	0.144706i
$683$	5814.00	+	10070.1i	0.325720	+	0.564163i	0.981658	−	0.190652i	$-0.0610601\pi$
$683$	5814.00	+	10070.1i	0.325720	+	0.564163i	−0.655938	+	0.754815i	$0.727727\pi$
$684$	−5180.00	+	8972.02i	−0.289565	+	0.501541i
$685$	−3470.00			−0.193550
$686$		0			0
$687$	44080.0			2.44797
$688$	1394.00	−	2414.48i	0.0772467	−	0.133795i
$689$	−858.000	−	1486.10i	−0.0474415	−	0.0821711i
$690$	−640.000	−	1108.51i	−0.0353107	−	0.0611599i
$691$	1236.00	−	2140.81i	0.0680458	−	0.117859i	−0.829995	−	0.557771i	$-0.811657\pi$
$691$	1236.00	−	2140.81i	0.0680458	−	0.117859i	0.898041	+	0.439912i	$0.144990\pi$
$692$	21294.0			1.16976
$693$		0			0
$694$	6076.00			0.332337
$695$	900.000	−	1558.85i	0.0491208	−	0.0850797i
$696$	−3000.00	−	5196.15i	−0.163383	−	0.282988i
$697$	18894.0	+	32725.4i	1.02677	+	1.77842i
$698$	1105.00	−	1913.92i	0.0599210	−	0.103786i
$699$	42576.0			2.30382
$700$		0			0
$701$	−2018.00			−0.108729			−0.0543643	−	0.998521i	$-0.517313\pi$
$701$	−2018.00			−0.108729			−0.0543643	+	0.998521i	$0.517313\pi$
$702$	−3120.00	+	5404.00i	−0.167745	+	0.290542i
$703$	−8680.00	−	15034.2i	−0.465679	−	0.806580i
$704$	1002.00	+	1735.51i	0.0536425	+	0.0929115i
$705$	10720.0	−	18567.6i	0.572679	−	0.991909i
$706$	2598.00			0.138494
$707$		0			0
$708$	−31360.0			−1.66466
$709$	−395.000	+	684.160i	−0.0209232	+	0.0362400i	−0.876297	−	0.481771i	$-0.839994\pi$
$709$	−395.000	+	684.160i	−0.0209232	+	0.0362400i	0.855374	+	0.518011i	$0.173327\pi$
$710$	−1680.00	−	2909.85i	−0.0888018	−	0.153809i
$711$	18500.0	+	32042.9i	0.975815	+	1.69016i
$712$	6525.00	−	11301.6i	0.343448	−	0.594869i
$713$	7936.00			0.416838
$714$		0			0
$715$	4680.00			0.244786
$716$	−630.000	+	1091.19i	−0.0328830	+	0.0569550i
$717$	7360.00	+	12747.9i	0.383353	+	0.663987i
$718$	6660.00	+	11535.5i	0.346169	+	0.599581i
$719$	9100.00	−	15761.7i	0.472007	−	0.817539i	−0.527480	−	0.849567i	$-0.676863\pi$
$719$	9100.00	−	15761.7i	0.472007	−	0.817539i	0.999487	+	0.0320278i	$0.0101965\pi$
$720$	7585.00			0.392606
$721$		0			0
$722$	−5259.00			−0.271080
$723$	−1752.00	+	3034.55i	−0.0901211	+	0.156094i
$724$	6853.00	+	11869.7i	0.351781	+	0.609303i
$725$	625.000	+	1082.53i	0.0320164	+	0.0554541i
$726$	4748.00	−	8223.78i	0.242720	−	0.420404i
$727$	−29056.0			−1.48229			−0.741147	−	0.671343i	$-0.765718\pi$
$727$	−29056.0			−1.48229			−0.741147	+	0.671343i	$0.765718\pi$
$728$		0			0
$729$	−30563.0			−1.55276
$730$	205.000	−	355.070i	0.0103937	−	0.0180024i
$731$	3196.00	+	5535.63i	0.161708	+	0.280086i
$732$	7784.00	+	13482.3i	0.393040	+	0.680764i
$733$	3541.00	−	6133.19i	0.178431	−	0.309051i	−0.762912	−	0.646502i	$-0.776231\pi$
$733$	3541.00	−	6133.19i	0.178431	−	0.309051i	0.941343	+	0.337451i	$0.109565\pi$
$734$	−10816.0			−0.543904
$735$		0			0
$736$	5152.00			0.258023
$737$	984.000	−	1704.34i	0.0491806	−	0.0851833i
$738$	7437.00	+	12881.3i	0.370948	+	0.642501i
$739$	−5530.00	−	9578.24i	−0.275270	−	0.476781i	0.694933	−	0.719074i	$-0.255434\pi$
$739$	−5530.00	−	9578.24i	−0.275270	−	0.476781i	−0.970203	+	0.242293i	$0.922100\pi$
$740$	−7595.00	+	13154.9i	−0.377294	+	0.653493i
$741$	−24960.0			−1.23742
$742$		0			0
$743$	33072.0			1.63297			0.816483	−	0.577369i	$-0.195921\pi$
$743$	33072.0			1.63297			0.816483	+	0.577369i	$0.195921\pi$
$744$	14880.0	−	25772.9i	0.733236	−	1.27000i
$745$	−5675.00	−	9829.39i	−0.279082	−	0.483384i
$746$	5549.00	+	9611.15i	0.272337	+	0.471701i
$747$	−8288.00	+	14355.2i	−0.405947	+	0.703120i
$748$	−7896.00			−0.385971
$749$		0			0
$750$	1000.00			0.0486864
$751$	−14536.0	+	25177.1i	−0.706293	+	1.22334i	0.259930	+	0.965628i	$0.416301\pi$
$751$	−14536.0	+	25177.1i	−0.706293	+	1.22334i	−0.966223	+	0.257708i	$0.917033\pi$
$752$	10988.0	+	19031.8i	0.532834	+	0.922895i
$753$	22368.0	+	38742.5i	1.08252	+	1.87497i
$754$	1950.00	−	3377.50i	0.0941841	−	0.163132i
$755$	3160.00			0.152323
$756$		0			0
$757$	−13234.0			−0.635400			−0.317700	−	0.948191i	$-0.602911\pi$
$757$	−13234.0			−0.635400			−0.317700	+	0.948191i	$0.602911\pi$
$758$	−3550.00	+	6148.78i	−0.170108	+	0.294636i
$759$	−1536.00	−	2660.43i	−0.0734562	−	0.127230i
$760$	−1500.00	−	2598.08i	−0.0715931	−	0.124003i
$761$	−11199.0	+	19397.2i	−0.533460	+	0.923981i	0.465776	+	0.884903i	$0.345775\pi$
$761$	−11199.0	+	19397.2i	−0.533460	+	0.923981i	−0.999236	+	0.0390778i	$0.987558\pi$
$762$	6208.00			0.295134
$763$		0			0
$764$	20216.0			0.957316
$765$	−8695.00	+	15060.2i	−0.410939	+	0.711767i
$766$	−364.000	−	630.466i	−0.0171695	−	0.0297385i
$767$	−21840.0	−	37828.0i	−1.02816	−	1.78082i
$768$	476.000	−	824.456i	0.0223648	−	0.0387370i
$769$	−6890.00			−0.323095			−0.161547	−	0.986865i	$-0.551648\pi$
$769$	−6890.00			−0.323095			−0.161547	+	0.986865i	$0.551648\pi$
$770$		0			0
$771$	15792.0			0.737659
$772$	5607.00	−	9711.61i	0.261399	−	0.452757i
$773$	8361.00	+	14481.7i	0.389035	+	0.673829i	0.992320	−	0.123697i	$-0.0394751\pi$
$773$	8361.00	+	14481.7i	0.389035	+	0.673829i	−0.603285	+	0.797526i	$0.706142\pi$
$774$	1258.00	+	2178.92i	0.0584210	+	0.101188i
$775$	−3100.00	+	5369.36i	−0.143684	+	0.248868i
$776$	15390.0			0.711944
$777$		0			0
$778$	−6810.00			−0.313818
$779$	−8040.00	+	13925.7i	−0.369785	+	0.640487i
$780$	10920.0	+	18914.0i	0.501280	+	0.868243i
$781$	−4032.00	−	6983.63i	−0.184733	−	0.319967i
$782$	−1504.00	+	2605.00i	−0.0687761	+	0.119124i
$783$	−4000.00			−0.182565
$784$		0			0
$785$	3670.00			0.166864
$786$	4448.00	−	7704.16i	0.201851	−	0.349616i
$787$	−16312.0	−	28253.2i	−0.738831	−	1.27969i	−0.953022	−	0.302901i	$-0.902045\pi$
$787$	−16312.0	−	28253.2i	−0.738831	−	1.27969i	0.214191	−	0.976792i	$-0.431289\pi$
$788$	−16779.0	−	29062.1i	−0.758537	−	1.31382i
$789$	2912.00	−	5043.73i	0.131394	−	0.227581i
$790$	−5000.00			−0.225180
$791$		0			0
$792$	−6660.00			−0.298804
$793$	−10842.0	+	18778.9i	−0.485512	+	0.840931i
$794$	−287.000	−	497.099i	−0.0128278	−	0.0222183i
$795$	−440.000	−	762.102i	−0.0196292	−	0.0339987i
$796$	−4480.00	+	7759.59i	−0.199484	+	0.345517i
$797$	−11346.0			−0.504261			−0.252130	−	0.967693i	$-0.581131\pi$
$797$	−11346.0			−0.504261			−0.252130	+	0.967693i	$0.581131\pi$
$798$		0			0
$799$	−50384.0			−2.23086
$800$	−2012.50	+	3485.75i	−0.0889408	+	0.154050i
$801$	−16095.0	−	27877.4i	−0.709974	−	1.22971i
$802$	−3081.00	−	5336.45i	−0.135653	−	0.234958i
$803$	492.000	−	852.169i	0.0216218	−	0.0374501i
$804$	9184.00			0.402854
$805$		0			0
$806$	19344.0			0.845364
$807$	23240.0	−	40252.9i	1.01374	−	1.75585i
$808$	−3615.00	−	6261.36i	−0.157395	−	0.272616i
$809$	17595.0	+	30475.4i	0.764657	+	1.32442i	0.940428	+	0.339993i	$0.110425\pi$
$809$	17595.0	+	30475.4i	0.764657	+	1.32442i	−0.175771	+	0.984431i	$0.556242\pi$
$810$	897.500	−	1554.52i	0.0389320	−	0.0674322i
$811$	−30432.0			−1.31765			−0.658824	−	0.752297i	$-0.728946\pi$
$811$	−30432.0			−1.31765			−0.658824	+	0.752297i	$0.728946\pi$
$812$		0			0
$813$	52224.0			2.25286
$814$	2604.00	−	4510.26i	0.112125	−	0.194207i
$815$	−6330.00	−	10963.9i	−0.272062	−	0.471225i
$816$	−15416.0	−	26701.3i	−0.661358	−	1.14551i
$817$	−1360.00	+	2355.59i	−0.0582379	+	0.100871i
$818$	−8210.00			−0.350924
$819$		0			0
$820$	14070.0			0.599202
$821$	−6351.00	+	11000.3i	−0.269977	+	0.467615i	−0.968856	−	0.247626i	$-0.920350\pi$
$821$	−6351.00	+	11000.3i	−0.269977	+	0.467615i	0.698878	+	0.715241i	$0.253683\pi$
$822$	2776.00	+	4808.17i	0.117791	+	0.204020i
$823$	−8476.00	−	14680.9i	−0.358997	−	0.621802i	0.628796	−	0.777570i	$-0.283548\pi$
$823$	−8476.00	−	14680.9i	−0.358997	−	0.621802i	−0.987794	+	0.155769i	$0.950215\pi$
$824$	−2040.00	+	3533.38i	−0.0862461	+	0.149383i
$825$	2400.00			0.101282
$826$		0			0
$827$	−25404.0			−1.06818			−0.534089	−	0.845428i	$-0.679345\pi$
$827$	−25404.0			−1.06818			−0.534089	+	0.845428i	$0.679345\pi$
$828$	4144.00	−	7177.62i	0.173930	−	0.301255i
$829$	13125.0	+	22733.2i	0.549879	+	0.952419i	0.998282	+	0.0585876i	$0.0186597\pi$
$829$	13125.0	+	22733.2i	0.549879	+	0.952419i	−0.448403	+	0.893832i	$0.648007\pi$
$830$	−1120.00	−	1939.90i	−0.0468383	−	0.0811263i
$831$	−20504.0	+	35514.0i	−0.855928	+	1.48251i
$832$	−13026.0			−0.542783
$833$		0			0
$834$	−2880.00			−0.119576
$835$	1040.00	−	1801.33i	0.0431026	−	0.0746559i
$836$	−1680.00	−	2909.85i	−0.0695024	−	0.120382i
$837$	−9920.00	−	17181.9i	−0.409660	−	0.709552i
$838$	2400.00	−	4156.92i	0.0989339	−	0.171359i
$839$	15360.0			0.632045			0.316023	−	0.948752i	$-0.397652\pi$
$839$	15360.0			0.632045			0.316023	+	0.948752i	$0.397652\pi$
$840$		0			0
$841$	−21889.0			−0.897495
$842$	4969.00	−	8606.56i	0.203377	−	0.352259i
$843$	9432.00	+	16336.7i	0.385356	+	0.667457i
$844$	−238.000	−	412.228i	−0.00970651	−	0.0168122i
$845$	−9717.50	+	16831.2i	−0.395612	+	0.685220i
$846$	−19832.0			−0.805955
$847$		0			0
$848$	902.000			0.0365269
$849$	1568.00	−	2715.86i	0.0633847	−	0.109786i
$850$	−1175.00	−	2035.16i	−0.0474143	−	0.0821240i
$851$	6944.00	+	12027.4i	0.279715	+	0.484480i
$852$	18816.0	−	32590.3i	0.756603	−	1.31047i
$853$	−10362.0			−0.415930			−0.207965	−	0.978136i	$-0.566684\pi$
$853$	−10362.0			−0.415930			−0.207965	+	0.978136i	$0.566684\pi$
$854$		0			0
$855$	−7400.00			−0.295994
$856$	−3330.00	+	5767.73i	−0.132964	+	0.230300i
$857$	2253.00	+	3902.31i	0.0898028	+	0.155543i	0.907428	−	0.420208i	$-0.138043\pi$
$857$	2253.00	+	3902.31i	0.0898028	+	0.155543i	−0.817625	+	0.575751i	$0.804710\pi$
$858$	−3744.00	−	6484.80i	−0.148972	−	0.258027i
$859$	12100.0	−	20957.8i	0.480613	−	0.832446i	−0.519139	−	0.854690i	$-0.673747\pi$
$859$	12100.0	−	20957.8i	0.480613	−	0.832446i	0.999753	+	0.0222432i	$0.00708081\pi$
$860$	2380.00			0.0943690
$861$		0			0
$862$	−9248.00			−0.365415
$863$	18504.0	−	32049.9i	0.729877	−	1.26418i	−0.227058	−	0.973881i	$-0.572911\pi$
$863$	18504.0	−	32049.9i	0.729877	−	1.26418i	0.956935	−	0.290302i	$-0.0937558\pi$
$864$	−6440.00	−	11154.4i	−0.253580	−	0.439214i
$865$	7605.00	+	13172.2i	0.298934	+	0.517769i
$866$	−559.000	+	968.216i	−0.0219349	+	0.0379923i
$867$	31384.0			1.22936
$868$		0			0
$869$	−12000.0			−0.468437
$870$	1000.00	−	1732.05i	0.0389692	−	0.0674966i
$871$	6396.00	+	11078.2i	0.248818	+	0.430965i
$872$	−8775.00	−	15198.7i	−0.340779	−	0.590246i
$873$	18981.0	−	32876.1i	0.735864	−	1.27455i
$874$	−1280.00			−0.0495385
$875$		0			0
$876$	4592.00			0.177111
$877$	−1723.00	+	2984.32i	−0.0663416	+	0.114907i	−0.897288	−	0.441445i	$-0.854466\pi$
$877$	−1723.00	+	2984.32i	−0.0663416	+	0.114907i	0.830947	+	0.556352i	$0.187799\pi$
$878$	−5980.00	−	10357.7i	−0.229858	−	0.398126i
$879$	4808.00	+	8327.70i	0.184494	+	0.319552i
$880$	−1230.00	+	2130.42i	−0.0471174	+	0.0816097i
$881$	16158.0			0.617908			0.308954	−	0.951077i	$-0.400021\pi$
$881$	16158.0			0.617908			0.308954	+	0.951077i	$0.400021\pi$
$882$		0			0
$883$	−44708.0			−1.70390			−0.851950	−	0.523623i	$-0.824580\pi$
$883$	−44708.0			−1.70390			−0.851950	+	0.523623i	$0.824580\pi$
$884$	25662.0	−	44447.9i	0.976365	−	1.69111i
$885$	−11200.0	−	19399.0i	−0.425406	−	0.736824i
$886$	−3666.00	−	6349.70i	−0.139009	−	0.240770i
$887$	−11752.0	+	20355.1i	−0.444863	+	0.770525i	−0.998043	−	0.0625366i	$-0.980081\pi$
$887$	−11752.0	+	20355.1i	−0.444863	+	0.770525i	0.553180	+	0.833062i	$0.313414\pi$
$888$	52080.0			1.96812
$889$		0			0
$890$	4350.00			0.163834
$891$	2154.00	−	3730.84i	0.0809896	−	0.140278i
$892$	6048.00	+	10475.4i	0.227020	+	0.393211i
$893$	−10720.0	−	18567.6i	−0.401715	−	0.695790i
$894$	−9080.00	+	15727.0i	−0.339688	+	0.588356i
$895$	−900.000			−0.0336131
$896$		0			0
$897$	19968.0			0.743269
$898$	−945.000	+	1636.79i	−0.0351170	+	0.0608244i
$899$	6200.00	+	10738.7i	0.230013	+	0.398394i
$900$	3237.50	+	5607.51i	0.119907	+	0.207686i
$901$	−1034.00	+	1790.94i	−0.0382326	+	0.0662207i
$902$	−4824.00			−0.178073
$903$		0			0
$904$	11970.0			0.440394
$905$	−4895.00	+	8478.39i	−0.179796	+	0.311416i
$906$	−2528.00	−	4378.62i	−0.0927011	−	0.160563i
$907$	−21218.0	−	36750.7i	−0.776772	−	1.34541i	−0.933793	−	0.357813i	$-0.883522\pi$
$907$	−21218.0	−	36750.7i	−0.776772	−	1.34541i	0.157021	−	0.987595i	$-0.449811\pi$
$908$	17024.0	−	29486.4i	0.622204	−	1.07769i
$909$	−17834.0			−0.650733
$910$		0			0
$911$	−7968.00			−0.289782			−0.144891	−	0.989448i	$-0.546283\pi$
$911$	−7968.00			−0.289782			−0.144891	+	0.989448i	$0.546283\pi$
$912$	6560.00	−	11362.3i	0.238183	−	0.412546i
$913$	−2688.00	−	4655.75i	−0.0974368	−	0.168766i
$914$	3507.00	+	6074.30i	0.126916	+	0.219825i
$915$	−5560.00	+	9630.20i	−0.200883	+	0.347940i
$916$	−38570.0			−1.39125
$917$		0			0
$918$	7520.00			0.270367
$919$	−7440.00	+	12886.5i	−0.267054	+	0.462552i	−0.968100	−	0.250565i	$-0.919384\pi$
$919$	−7440.00	+	12886.5i	−0.267054	+	0.462552i	0.701045	+	0.713117i	$0.252717\pi$
$920$	1200.00	+	2078.46i	0.0430031	+	0.0744835i
$921$	−25536.0	−	44229.6i	−0.913615	−	1.58243i
$922$	−4159.00	+	7203.60i	−0.148557	+	0.257308i
$923$	52416.0			1.86922
$924$		0			0
$925$	−10850.0			−0.385671
$926$	−3216.00	+	5570.28i	−0.114130	+	0.197679i
$927$	5032.00	+	8715.68i	0.178288	+	0.308803i
$928$	4025.00	+	6971.50i	0.142378	+	0.246607i
$929$	13805.0	−	23911.0i	0.487543	−	0.844449i	−0.512354	−	0.858774i	$-0.671227\pi$
$929$	13805.0	−	23911.0i	0.487543	−	0.844449i	0.999897	+	0.0143250i	$0.00455994\pi$
$930$	9920.00			0.349774
$931$		0			0
$932$	−37254.0			−1.30933
$933$	−19872.0	+	34419.3i	−0.697299	+	1.20776i
$934$	−5032.00	−	8715.68i	−0.176287	−	0.305338i
$935$	−2820.00	−	4884.38i	−0.0986351	−	0.170841i
$936$	21645.0	−	37490.2i	0.755864	−	1.30920i
$937$	28094.0			0.979499			0.489750	−	0.871863i	$-0.337088\pi$
$937$	28094.0			0.979499			0.489750	+	0.871863i	$0.337088\pi$
$938$		0			0
$939$	22064.0			0.766807
$940$	−9380.00	+	16246.6i	−0.325470	+	0.563731i
$941$	−6099.00	−	10563.8i	−0.211288	−	0.365961i	0.740830	−	0.671692i	$-0.234432\pi$
$941$	−6099.00	−	10563.8i	−0.211288	−	0.365961i	−0.952118	+	0.305731i	$0.901099\pi$
$942$	−2936.00	−	5085.30i	−0.101550	−	0.175890i
$943$	6432.00	−	11140.6i	0.222115	−	0.384715i
$944$	22960.0			0.791615
$945$		0			0
$946$	−816.000			−0.0280449
$947$	−15658.0	+	27120.5i	−0.537293	+	0.930619i	0.461755	+	0.887007i	$0.347220\pi$
$947$	−15658.0	+	27120.5i	−0.537293	+	0.930619i	−0.999049	+	0.0436118i	$0.986114\pi$
$948$	−28000.0	−	48497.4i	−0.959280	−	1.66152i
$949$	3198.00	+	5539.10i	0.109390	+	0.189470i
$950$	500.000	−	866.025i	0.0170759	−	0.0295764i
$951$	−50192.0			−1.71145
$952$		0			0
$953$	27322.0			0.928695			0.464348	−	0.885653i	$-0.346289\pi$
$953$	27322.0			0.928695			0.464348	+	0.885653i	$0.346289\pi$
$954$	−407.000	+	704.945i	−0.0138125	+	0.0239239i
$955$	7220.00	+	12505.4i	0.244643	+	0.423733i
$956$	−6440.00	−	11154.4i	−0.217871	−	0.377363i
$957$	2400.00	−	4156.92i	0.0810669	−	0.140412i
$958$	−1400.00			−0.0472150
$959$		0			0
$960$	−6680.00			−0.224579
$961$	−15856.5	+	27464.3i	−0.532258	+	0.921898i
$962$	16926.0	+	29316.7i	0.567272	+	0.982545i
$963$	8214.00	+	14227.1i	0.274862	+	0.476076i
$964$	1533.00	−	2655.23i	0.0512185	−	0.0887130i
$965$	8010.00			0.267203
$966$		0			0
$967$	5296.00			0.176120			0.0880599	−	0.996115i	$-0.471933\pi$
$967$	5296.00			0.176120			0.0880599	+	0.996115i	$0.471933\pi$
$968$	−8902.50	+	15419.6i	−0.295596	+	0.511988i
$969$	15040.0	+	26050.0i	0.498611	+	0.863620i
$970$	2565.00	+	4442.71i	0.0849043	+	0.147059i
$971$	256.000	−	443.405i	0.00846079	−	0.0146545i	−0.861764	−	0.507309i	$-0.830640\pi$
$971$	256.000	−	443.405i	0.00846079	−	0.0146545i	0.870225	+	0.492655i	$0.163973\pi$
$972$	35224.0			1.16236
$973$		0			0
$974$	13376.0			0.440036
$975$	−7800.00	+	13510.0i	−0.256205	+	0.443760i
$976$	−5699.00	−	9870.96i	−0.186906	−	0.323731i
$977$	10367.0	+	17956.2i	0.339478	+	0.587993i	0.984335	−	0.176311i	$-0.0564164\pi$
$977$	10367.0	+	17956.2i	0.339478	+	0.587993i	−0.644857	+	0.764303i	$0.723083\pi$
$978$	−10128.0	+	17542.2i	−0.331143	+	0.573556i
$979$	10440.0			0.340821
$980$		0			0
$981$	−43290.0			−1.40891
$982$	−3546.00	+	6141.85i	−0.115232	+	0.199587i
$983$	−30584.0	−	52973.0i	−0.992348	−	1.71880i	−0.603104	−	0.797662i	$-0.706070\pi$
$983$	−30584.0	−	52973.0i	−0.992348	−	1.71880i	−0.389244	−	0.921135i	$-0.627264\pi$
$984$	−24120.0	−	41777.1i	−0.781420	−	1.35346i
$985$	11985.0	−	20758.6i	0.387689	−	0.671497i
$986$	−4700.00			−0.151804
$987$		0			0
$988$	21840.0			0.703262
$989$	1088.00	−	1884.47i	0.0349812	−	0.0605892i
$990$	−1110.00	−	1922.58i	−0.0356345	−	0.0617207i
$991$	23964.0	+	41506.9i	0.768155	+	1.33048i	0.938562	+	0.345110i	$0.112158\pi$
$991$	23964.0	+	41506.9i	0.768155	+	1.33048i	−0.170407	+	0.985374i	$0.554508\pi$
$992$	−19964.0	+	34578.7i	−0.638969	+	1.10673i
$993$	15456.0			0.493939
$994$		0			0
$995$	−6400.00			−0.203913
$996$	12544.0	−	21726.8i	0.399068	−	0.691206i
$997$	−4727.00	−	8187.40i	−0.150156	−	0.260078i	0.781129	−	0.624370i	$-0.214644\pi$
$997$	−4727.00	−	8187.40i	−0.150156	−	0.260078i	−0.931285	+	0.364292i	$0.881311\pi$
$998$	410.000	+	710.141i	0.0130043	+	0.0225242i
$999$	17360.0	−	30068.4i	0.549796	−	0.952274i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.e.b.226.1		2
7.2	even	3		245.4.a.d.1.1		1
7.3	odd	6		245.4.e.e.116.1		2
7.4	even	3	inner	245.4.e.b.116.1		2
7.5	odd	6		35.4.a.a.1.1	✓	1
7.6	odd	2		245.4.e.e.226.1		2
21.2	odd	6		2205.4.a.i.1.1		1
21.5	even	6		315.4.a.c.1.1		1
28.19	even	6		560.4.a.p.1.1		1
35.9	even	6		1225.4.a.e.1.1		1
35.12	even	12		175.4.b.a.99.2		2
35.19	odd	6		175.4.a.a.1.1		1
35.33	even	12		175.4.b.a.99.1		2
56.5	odd	6		2240.4.a.bk.1.1		1
56.19	even	6		2240.4.a.b.1.1		1
105.89	even	6		1575.4.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.a.a.1.1	✓	1	7.5	odd	6
175.4.a.a.1.1		1	35.19	odd	6
175.4.b.a.99.1		2	35.33	even	12
175.4.b.a.99.2		2	35.12	even	12
245.4.a.d.1.1		1	7.2	even	3
245.4.e.b.116.1		2	7.4	even	3	inner
245.4.e.b.226.1		2	1.1	even	1	trivial
245.4.e.e.116.1		2	7.3	odd	6
245.4.e.e.226.1		2	7.6	odd	2
315.4.a.c.1.1		1	21.5	even	6
560.4.a.p.1.1		1	28.19	even	6
1225.4.a.e.1.1		1	35.9	even	6
1575.4.a.g.1.1		1	105.89	even	6
2205.4.a.i.1.1		1	21.2	odd	6
2240.4.a.b.1.1		1	56.19	even	6
2240.4.a.bk.1.1		1	56.5	odd	6

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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-4.00000 - 6.92820i) q^{3} +(3.50000 + 6.06218i) q^{4} +(-2.50000 + 4.33013i) q^{5} +8.00000 q^{6} -15.0000 q^{8} +(-18.5000 + 32.0429i) q^{9} +(-2.50000 - 4.33013i) q^{10} +(-6.00000 - 10.3923i) q^{11} +(28.0000 - 48.4974i) q^{12} +78.0000 q^{13} +40.0000 q^{15} +(-20.5000 + 35.5070i) q^{16} +(-47.0000 - 81.4064i) q^{17} +(-18.5000 - 32.0429i) q^{18} +(20.0000 - 34.6410i) q^{19} -35.0000 q^{20} +12.0000 q^{22} +(-16.0000 + 27.7128i) q^{23} +(60.0000 + 103.923i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(-39.0000 + 67.5500i) q^{26} +80.0000 q^{27} -50.0000 q^{29} +(-20.0000 + 34.6410i) q^{30} +(-124.000 - 214.774i) q^{31} +(-80.5000 - 139.430i) q^{32} +(-48.0000 + 83.1384i) q^{33} +94.0000 q^{34} -259.000 q^{36} +(217.000 - 375.855i) q^{37} +(20.0000 + 34.6410i) q^{38} +(-312.000 - 540.400i) q^{39} +(37.5000 - 64.9519i) q^{40} -402.000 q^{41} -68.0000 q^{43} +(42.0000 - 72.7461i) q^{44} +(-92.5000 - 160.215i) q^{45} +(-16.0000 - 27.7128i) q^{46} +(268.000 - 464.190i) q^{47} +328.000 q^{48} +25.0000 q^{50} +(-376.000 + 651.251i) q^{51} +(273.000 + 472.850i) q^{52} +(-11.0000 - 19.0526i) q^{53} +(-40.0000 + 69.2820i) q^{54} +60.0000 q^{55} -320.000 q^{57} +(25.0000 - 43.3013i) q^{58} +(-280.000 - 484.974i) q^{59} +(140.000 + 242.487i) q^{60} +(-139.000 + 240.755i) q^{61} +248.000 q^{62} -167.000 q^{64} +(-195.000 + 337.750i) q^{65} +(-48.0000 - 83.1384i) q^{66} +(82.0000 + 142.028i) q^{67} +(329.000 - 569.845i) q^{68} +256.000 q^{69} +672.000 q^{71} +(277.500 - 480.644i) q^{72} +(41.0000 + 71.0141i) q^{73} +(217.000 + 375.855i) q^{74} +(-100.000 + 173.205i) q^{75} +280.000 q^{76} +624.000 q^{78} +(500.000 - 866.025i) q^{79} +(-102.500 - 177.535i) q^{80} +(179.500 + 310.903i) q^{81} +(201.000 - 348.142i) q^{82} +448.000 q^{83} +470.000 q^{85} +(34.0000 - 58.8897i) q^{86} +(200.000 + 346.410i) q^{87} +(90.0000 + 155.885i) q^{88} +(-435.000 + 753.442i) q^{89} +185.000 q^{90} -224.000 q^{92} +(-992.000 + 1718.19i) q^{93} +(268.000 + 464.190i) q^{94} +(100.000 + 173.205i) q^{95} +(-644.000 + 1115.44i) q^{96} -1026.00 q^{97} +444.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 8 q^{3} + 7 q^{4} - 5 q^{5} + 16 q^{6} - 30 q^{8} - 37 q^{9} - 5 q^{10} - 12 q^{11} + 56 q^{12} + 156 q^{13} + 80 q^{15} - 41 q^{16} - 94 q^{17} - 37 q^{18} + 40 q^{19} - 70 q^{20} + 24 q^{22}+ \cdots + 888 q^{99}+O(q^{100}) \) 2 * q - q^2 - 8 * q^3 + 7 * q^4 - 5 * q^5 + 16 * q^6 - 30 * q^8 - 37 * q^9 - 5 * q^10 - 12 * q^11 + 56 * q^12 + 156 * q^13 + 80 * q^15 - 41 * q^16 - 94 * q^17 - 37 * q^18 + 40 * q^19 - 70 * q^20 + 24 * q^22 - 32 * q^23 + 120 * q^24 - 25 * q^25 - 78 * q^26 + 160 * q^27 - 100 * q^29 - 40 * q^30 - 248 * q^31 - 161 * q^32 - 96 * q^33 + 188 * q^34 - 518 * q^36 + 434 * q^37 + 40 * q^38 - 624 * q^39 + 75 * q^40 - 804 * q^41 - 136 * q^43 + 84 * q^44 - 185 * q^45 - 32 * q^46 + 536 * q^47 + 656 * q^48 + 50 * q^50 - 752 * q^51 + 546 * q^52 - 22 * q^53 - 80 * q^54 + 120 * q^55 - 640 * q^57 + 50 * q^58 - 560 * q^59 + 280 * q^60 - 278 * q^61 + 496 * q^62 - 334 * q^64 - 390 * q^65 - 96 * q^66 + 164 * q^67 + 658 * q^68 + 512 * q^69 + 1344 * q^71 + 555 * q^72 + 82 * q^73 + 434 * q^74 - 200 * q^75 + 560 * q^76 + 1248 * q^78 + 1000 * q^79 - 205 * q^80 + 359 * q^81 + 402 * q^82 + 896 * q^83 + 940 * q^85 + 68 * q^86 + 400 * q^87 + 180 * q^88 - 870 * q^89 + 370 * q^90 - 448 * q^92 - 1984 * q^93 + 536 * q^94 + 200 * q^95 - 1288 * q^96 - 2052 * q^97 + 888 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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