LMFDB - Embedded newform 196.4.e.f.165.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,4,Mod(165,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("196.165");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	196.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.5643743611$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	196.165
Dual form			196.4.e.f.177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.00000 - 8.66025i) q^{3} +(4.00000 + 6.92820i) q^{5} +(-36.5000 - 63.2199i) q^{9} +O(q^{10})$	\(q+(5.00000 - 8.66025i) q^{3} +(4.00000 + 6.92820i) q^{5} +(-36.5000 - 63.2199i) q^{9} +(20.0000 - 34.6410i) q^{11} -12.0000 q^{13} +80.0000 q^{15} +(29.0000 - 50.2295i) q^{17} +(-13.0000 - 22.5167i) q^{19} +(32.0000 + 55.4256i) q^{23} +(30.5000 - 52.8275i) q^{25} -460.000 q^{27} -62.0000 q^{29} +(-126.000 + 218.238i) q^{31} +(-200.000 - 346.410i) q^{33} +(-13.0000 - 22.5167i) q^{37} +(-60.0000 + 103.923i) q^{39} +6.00000 q^{41} +416.000 q^{43} +(292.000 - 505.759i) q^{45} +(198.000 + 342.946i) q^{47} +(-290.000 - 502.295i) q^{51} +(225.000 - 389.711i) q^{53} +320.000 q^{55} -260.000 q^{57} +(-137.000 + 237.291i) q^{59} +(288.000 + 498.831i) q^{61} +(-48.0000 - 83.1384i) q^{65} +(238.000 - 412.228i) q^{67} +640.000 q^{69} -448.000 q^{71} +(79.0000 - 136.832i) q^{73} +(-305.000 - 528.275i) q^{75} +(468.000 + 810.600i) q^{79} +(-1314.50 + 2276.78i) q^{81} +530.000 q^{83} +464.000 q^{85} +(-310.000 + 536.936i) q^{87} +(195.000 + 337.750i) q^{89} +(1260.00 + 2182.38i) q^{93} +(104.000 - 180.133i) q^{95} +214.000 q^{97} -2920.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 10 q^{3} + 8 q^{5} - 73 q^{9}+O(q^{10}) $ 2 * q + 10 * q^3 + 8 * q^5 - 73 * q^9	$ 2 q + 10 q^{3} + 8 q^{5} - 73 q^{9} + 40 q^{11} - 24 q^{13} + 160 q^{15} + 58 q^{17} - 26 q^{19} + 64 q^{23} + 61 q^{25} - 920 q^{27} - 124 q^{29} - 252 q^{31} - 400 q^{33} - 26 q^{37} - 120 q^{39} + 12 q^{41} + 832 q^{43} + 584 q^{45} + 396 q^{47} - 580 q^{51} + 450 q^{53} + 640 q^{55} - 520 q^{57} - 274 q^{59} + 576 q^{61} - 96 q^{65} + 476 q^{67} + 1280 q^{69} - 896 q^{71} + 158 q^{73} - 610 q^{75} + 936 q^{79} - 2629 q^{81} + 1060 q^{83} + 928 q^{85} - 620 q^{87} + 390 q^{89} + 2520 q^{93} + 208 q^{95} + 428 q^{97} - 5840 q^{99}+O(q^{100}) $ 2 * q + 10 * q^3 + 8 * q^5 - 73 * q^9 + 40 * q^11 - 24 * q^13 + 160 * q^15 + 58 * q^17 - 26 * q^19 + 64 * q^23 + 61 * q^25 - 920 * q^27 - 124 * q^29 - 252 * q^31 - 400 * q^33 - 26 * q^37 - 120 * q^39 + 12 * q^41 + 832 * q^43 + 584 * q^45 + 396 * q^47 - 580 * q^51 + 450 * q^53 + 640 * q^55 - 520 * q^57 - 274 * q^59 + 576 * q^61 - 96 * q^65 + 476 * q^67 + 1280 * q^69 - 896 * q^71 + 158 * q^73 - 610 * q^75 + 936 * q^79 - 2629 * q^81 + 1060 * q^83 + 928 * q^85 - 620 * q^87 + 390 * q^89 + 2520 * q^93 + 208 * q^95 + 428 * q^97 - 5840 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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			0
$2$		0			0
$3$	5.00000	−	8.66025i	0.962250	−	1.66667i	0.245423	−	0.969416i	$-0.421073\pi$
$3$	5.00000	−	8.66025i	0.962250	−	1.66667i	0.716827	−	0.697251i	$-0.245594\pi$
$4$		0			0
$5$	4.00000	+	6.92820i	0.357771	+	0.619677i	0.987588	−	0.157066i	$-0.0502036\pi$
$5$	4.00000	+	6.92820i	0.357771	+	0.619677i	−0.629817	+	0.776743i	$0.716870\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−36.5000	−	63.2199i	−1.35185	−	2.34148i
$10$		0			0
$11$	20.0000	−	34.6410i	0.548202	−	0.949514i	−0.450195	−	0.892930i	$-0.648646\pi$
$11$	20.0000	−	34.6410i	0.548202	−	0.949514i	0.998398	−	0.0565844i	$-0.0180210\pi$
$12$		0			0
$13$	−12.0000			−0.256015			−0.128008	−	0.991773i	$-0.540858\pi$
$13$	−12.0000			−0.256015			−0.128008	+	0.991773i	$0.540858\pi$
$14$		0			0
$15$	80.0000			1.37706
$16$		0			0
$17$	29.0000	−	50.2295i	0.413737	−	0.716614i	−0.581558	−	0.813505i	$-0.697557\pi$
$17$	29.0000	−	50.2295i	0.413737	−	0.716614i	0.995295	+	0.0968912i	$0.0308899\pi$
$18$		0			0
$19$	−13.0000	−	22.5167i	−0.156969	−	0.271878i	0.776805	−	0.629741i	$-0.216839\pi$
$19$	−13.0000	−	22.5167i	−0.156969	−	0.271878i	−0.933774	+	0.357863i	$0.883505\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	32.0000	+	55.4256i	0.290107	+	0.502480i	0.973835	−	0.227257i	$-0.0729758\pi$
$23$	32.0000	+	55.4256i	0.290107	+	0.502480i	−0.683728	+	0.729737i	$0.739642\pi$
$24$		0			0
$25$	30.5000	−	52.8275i	0.244000	−	0.422620i
$26$		0			0
$27$	−460.000			−3.27878
$28$		0			0
$29$	−62.0000			−0.397004			−0.198502	−	0.980101i	$-0.563608\pi$
$29$	−62.0000			−0.397004			−0.198502	+	0.980101i	$0.563608\pi$
$30$		0			0
$31$	−126.000	+	218.238i	−0.730009	+	1.26441i	0.226870	+	0.973925i	$0.427151\pi$
$31$	−126.000	+	218.238i	−0.730009	+	1.26441i	−0.956879	+	0.290487i	$0.906183\pi$
$32$		0			0
$33$	−200.000	−	346.410i	−1.05502	−	1.82734i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−13.0000	−	22.5167i	−0.0577618	−	0.100046i	0.835699	−	0.549188i	$-0.185063\pi$
$37$	−13.0000	−	22.5167i	−0.0577618	−	0.100046i	−0.893460	+	0.449142i	$0.851730\pi$
$38$		0			0
$39$	−60.0000	+	103.923i	−0.246351	+	0.426692i
$40$		0			0
$41$	6.00000			0.0228547			0.0114273	−	0.999935i	$-0.496362\pi$
$41$	6.00000			0.0228547			0.0114273	+	0.999935i	$0.496362\pi$
$42$		0			0
$43$	416.000			1.47534			0.737668	−	0.675164i	$-0.235927\pi$
$43$	416.000			1.47534			0.737668	+	0.675164i	$0.235927\pi$
$44$		0			0
$45$	292.000	−	505.759i	0.967306	−	1.67542i
$46$		0			0
$47$	198.000	+	342.946i	0.614495	+	1.06434i	0.990473	+	0.137708i	$0.0439736\pi$
$47$	198.000	+	342.946i	0.614495	+	1.06434i	−0.375978	+	0.926629i	$0.622693\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−290.000	−	502.295i	−0.796238	−	1.37912i
$52$		0			0
$53$	225.000	−	389.711i	0.583134	−	1.01002i	−0.411971	−	0.911197i	$-0.635159\pi$
$53$	225.000	−	389.711i	0.583134	−	1.01002i	0.995105	−	0.0988214i	$-0.0315073\pi$
$54$		0			0
$55$	320.000			0.784523
$56$		0			0
$57$	−260.000			−0.604173
$58$		0			0
$59$	−137.000	+	237.291i	−0.302303	+	0.523604i	−0.976657	−	0.214804i	$-0.931089\pi$
$59$	−137.000	+	237.291i	−0.302303	+	0.523604i	0.674354	+	0.738408i	$0.264422\pi$
$60$		0			0
$61$	288.000	+	498.831i	0.604502	+	1.04703i	0.992130	+	0.125212i	$0.0399612\pi$
$61$	288.000	+	498.831i	0.604502	+	1.04703i	−0.387628	+	0.921816i	$0.626705\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−48.0000	−	83.1384i	−0.0915949	−	0.158647i
$66$		0			0
$67$	238.000	−	412.228i	0.433975	−	0.751667i	−0.563236	−	0.826296i	$-0.690444\pi$
$67$	238.000	−	412.228i	0.433975	−	0.751667i	0.997211	+	0.0746290i	$0.0237773\pi$
$68$		0			0
$69$	640.000			1.11662
$70$		0			0
$71$	−448.000			−0.748843			−0.374421	−	0.927259i	$-0.622159\pi$
$71$	−448.000			−0.748843			−0.374421	+	0.927259i	$0.622159\pi$
$72$		0			0
$73$	79.0000	−	136.832i	0.126661	−	0.219383i	−0.795720	−	0.605665i	$-0.792907\pi$
$73$	79.0000	−	136.832i	0.126661	−	0.219383i	0.922381	+	0.386281i	$0.126241\pi$
$74$		0			0
$75$	−305.000	−	528.275i	−0.469578	−	0.813333i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	468.000	+	810.600i	0.666508	+	1.15443i	0.978874	+	0.204464i	$0.0655450\pi$
$79$	468.000	+	810.600i	0.666508	+	1.15443i	−0.312366	+	0.949962i	$0.601122\pi$
$80$		0			0
$81$	−1314.50	+	2276.78i	−1.80316	+	3.12316i
$82$		0			0
$83$	530.000			0.700904			0.350452	−	0.936581i	$-0.386028\pi$
$83$	530.000			0.700904			0.350452	+	0.936581i	$0.386028\pi$
$84$		0			0
$85$	464.000			0.592093
$86$		0			0
$87$	−310.000	+	536.936i	−0.382017	+	0.661673i
$88$		0			0
$89$	195.000	+	337.750i	0.232247	+	0.402263i	0.958469	−	0.285197i	$-0.0920590\pi$
$89$	195.000	+	337.750i	0.232247	+	0.402263i	−0.726222	+	0.687460i	$0.758726\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1260.00	+	2182.38i	1.40490	+	2.43336i
$94$		0			0
$95$	104.000	−	180.133i	0.112318	−	0.194540i
$96$		0			0
$97$	214.000			0.224004			0.112002	−	0.993708i	$-0.464274\pi$
$97$	214.000			0.224004			0.112002	+	0.993708i	$0.464274\pi$
$98$		0			0
$99$	−2920.00			−2.96435
$100$		0			0
$101$	−716.000	+	1240.15i	−0.705393	+	1.22178i	0.261157	+	0.965296i	$0.415896\pi$
$101$	−716.000	+	1240.15i	−0.705393	+	1.22178i	−0.966550	+	0.256480i	$0.917437\pi$
$102$		0			0
$103$	−382.000	−	661.643i	−0.365433	−	0.632948i	0.623413	−	0.781893i	$-0.285746\pi$
$103$	−382.000	−	661.643i	−0.365433	−	0.632948i	−0.988846	+	0.148945i	$0.952412\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−162.000	−	280.592i	−0.146366	−	0.253513i	0.783516	−	0.621372i	$-0.213424\pi$
$107$	−162.000	−	280.592i	−0.146366	−	0.253513i	−0.929882	+	0.367859i	$0.880091\pi$
$108$		0			0
$109$	667.000	−	1155.28i	0.586119	−	1.01519i	−0.408615	−	0.912707i	$-0.633988\pi$
$109$	667.000	−	1155.28i	0.586119	−	1.01519i	0.994735	−	0.102482i	$-0.0326784\pi$
$110$		0			0
$111$	−260.000			−0.222325
$112$		0			0
$113$	1798.00			1.49683			0.748414	−	0.663232i	$-0.230816\pi$
$113$	1798.00			1.49683			0.748414	+	0.663232i	$0.230816\pi$
$114$		0			0
$115$	−256.000	+	443.405i	−0.207584	+	0.359545i
$116$		0			0
$117$	438.000	+	758.638i	0.346095	+	0.599454i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−134.500	−	232.961i	−0.101052	−	0.175027i
$122$		0			0
$123$	30.0000	−	51.9615i	0.0219919	−	0.0380912i
$124$		0			0
$125$	1488.00			1.06473
$126$		0			0
$127$	−384.000			−0.268303			−0.134152	−	0.990961i	$-0.542831\pi$
$127$	−384.000			−0.268303			−0.134152	+	0.990961i	$0.542831\pi$
$128$		0			0
$129$	2080.00	−	3602.67i	1.41964	−	2.45889i
$130$		0			0
$131$	907.000	+	1570.97i	0.604923	+	1.04776i	0.992064	+	0.125737i	$0.0401296\pi$
$131$	907.000	+	1570.97i	0.604923	+	1.04776i	−0.387140	+	0.922021i	$0.626537\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−1840.00	−	3186.97i	−1.17305	−	2.03179i
$136$		0			0
$137$	−833.000	+	1442.80i	−0.519474	+	0.899756i	0.480269	+	0.877121i	$0.340539\pi$
$137$	−833.000	+	1442.80i	−0.519474	+	0.899756i	−0.999744	+	0.0226350i	$0.992794\pi$
$138$		0			0
$139$	1126.00			0.687094			0.343547	−	0.939135i	$-0.388372\pi$
$139$	1126.00			0.687094			0.343547	+	0.939135i	$0.388372\pi$
$140$		0			0
$141$	3960.00			2.36519
$142$		0			0
$143$	−240.000	+	415.692i	−0.140348	+	0.243090i
$144$		0			0
$145$	−248.000	−	429.549i	−0.142036	−	0.246014i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1347.00	−	2333.07i	−0.740608	−	1.28277i	−0.952219	−	0.305416i	$-0.901204\pi$
$149$	−1347.00	−	2333.07i	−0.740608	−	1.28277i	0.211611	−	0.977354i	$-0.432129\pi$
$150$		0			0
$151$	1324.00	−	2293.24i	0.713547	−	1.23590i	−0.249970	−	0.968253i	$-0.580421\pi$
$151$	1324.00	−	2293.24i	0.713547	−	1.23590i	0.963517	−	0.267646i	$-0.0862458\pi$
$152$		0			0
$153$	−4234.00			−2.23725
$154$		0			0
$155$	−2016.00			−1.04470
$156$		0			0
$157$	278.000	−	481.510i	0.141317	−	0.244769i	−0.786676	−	0.617367i	$-0.788200\pi$
$157$	278.000	−	481.510i	0.141317	−	0.244769i	0.927993	+	0.372598i	$0.121533\pi$
$158$		0			0
$159$	−2250.00	−	3897.11i	−1.12224	−	1.94378i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	164.000	+	284.056i	0.0788066	+	0.136497i	0.902735	−	0.430196i	$-0.141556\pi$
$163$	164.000	+	284.056i	0.0788066	+	0.136497i	−0.823929	+	0.566693i	$0.808222\pi$
$164$		0			0
$165$	1600.00	−	2771.28i	0.754908	−	1.30754i
$166$		0			0
$167$	−4268.00			−1.97765			−0.988826	−	0.149077i	$-0.952370\pi$
$167$	−4268.00			−1.97765			−0.988826	+	0.149077i	$0.952370\pi$
$168$		0			0
$169$	−2053.00			−0.934456
$170$		0			0
$171$	−949.000	+	1643.72i	−0.424397	+	0.735077i
$172$		0			0
$173$	1738.00	+	3010.30i	0.763802	+	1.32294i	0.940878	+	0.338746i	$0.110003\pi$
$173$	1738.00	+	3010.30i	0.763802	+	1.32294i	−0.177076	+	0.984197i	$0.556664\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1370.00	+	2372.91i	0.581783	+	1.00768i
$178$		0			0
$179$	−1134.00	+	1964.15i	−0.473515	+	0.820152i	−0.999540	−	0.0303171i	$-0.990348\pi$
$179$	−1134.00	+	1964.15i	−0.473515	+	0.820152i	0.526026	+	0.850469i	$0.323682\pi$
$180$		0			0
$181$	−276.000			−0.113342			−0.0566710	−	0.998393i	$-0.518049\pi$
$181$	−276.000			−0.113342			−0.0566710	+	0.998393i	$0.518049\pi$
$182$		0			0
$183$	5760.00			2.32673
$184$		0			0
$185$	104.000	−	180.133i	0.0413310	−	0.0715874i
$186$		0			0
$187$	−1160.00	−	2009.18i	−0.453624	−	0.785699i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1500.00	+	2598.08i	0.568252	+	0.984242i	0.996739	+	0.0806937i	$0.0257136\pi$
$191$	1500.00	+	2598.08i	0.568252	+	0.984242i	−0.428487	+	0.903548i	$0.640953\pi$
$192$		0			0
$193$	−1639.00	+	2838.83i	−0.611284	+	1.05877i	0.379740	+	0.925093i	$0.376013\pi$
$193$	−1639.00	+	2838.83i	−0.611284	+	1.05877i	−0.991024	+	0.133682i	$0.957320\pi$
$194$		0			0
$195$	−960.000			−0.352549
$196$		0			0
$197$	−2362.00			−0.854241			−0.427121	−	0.904195i	$-0.640472\pi$
$197$	−2362.00			−0.854241			−0.427121	+	0.904195i	$0.640472\pi$
$198$		0			0
$199$	518.000	−	897.202i	0.184523	−	0.319603i	−0.758893	−	0.651216i	$-0.774259\pi$
$199$	518.000	−	897.202i	0.184523	−	0.319603i	0.943416	+	0.331613i	$0.107593\pi$
$200$		0			0
$201$	−2380.00	−	4122.28i	−0.835185	−	1.44658i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	24.0000	+	41.5692i	0.00817674	+	0.0141625i
$206$		0			0
$207$	2336.00	−	4046.07i	0.784363	−	1.35856i
$208$		0			0
$209$	−1040.00			−0.344202
$210$		0			0
$211$	3524.00			1.14977			0.574887	−	0.818233i	$-0.305046\pi$
$211$	3524.00			1.14977			0.574887	+	0.818233i	$0.305046\pi$
$212$		0			0
$213$	−2240.00	+	3879.79i	−0.720574	+	1.24807i
$214$		0			0
$215$	1664.00	+	2882.13i	0.527832	+	0.914232i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−790.000	−	1368.32i	−0.243759	−	0.422203i
$220$		0			0
$221$	−348.000	+	602.754i	−0.105923	+	0.183464i
$222$		0			0
$223$	−1336.00			−0.401189			−0.200595	−	0.979674i	$-0.564287\pi$
$223$	−1336.00			−0.401189			−0.200595	+	0.979674i	$0.564287\pi$
$224$		0			0
$225$	−4453.00			−1.31941
$226$		0			0
$227$	−645.000	+	1117.17i	−0.188591	+	0.326649i	−0.944781	−	0.327703i	$-0.893725\pi$
$227$	−645.000	+	1117.17i	−0.188591	+	0.326649i	0.756190	+	0.654352i	$0.227059\pi$
$228$		0			0
$229$	−2762.00	−	4783.92i	−0.797022	−	1.38048i	−0.921547	−	0.388267i	$-0.873074\pi$
$229$	−2762.00	−	4783.92i	−0.797022	−	1.38048i	0.124525	−	0.992216i	$-0.460259\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3157.00	−	5468.08i	−0.887648	−	1.53745i	−0.842648	−	0.538464i	$-0.819005\pi$
$233$	−3157.00	−	5468.08i	−0.887648	−	1.53745i	−0.0449994	−	0.998987i	$-0.514329\pi$
$234$		0			0
$235$	−1584.00	+	2743.57i	−0.439697	+	0.761577i
$236$		0			0
$237$	9360.00			2.56539
$238$		0			0
$239$	−3960.00			−1.07176			−0.535881	−	0.844294i	$-0.680020\pi$
$239$	−3960.00			−1.07176			−0.535881	+	0.844294i	$0.680020\pi$
$240$		0			0
$241$	3509.00	−	6077.77i	0.937903	−	1.62450i	0.168529	−	0.985697i	$-0.446098\pi$
$241$	3509.00	−	6077.77i	0.937903	−	1.62450i	0.769374	−	0.638798i	$-0.220568\pi$
$242$		0			0
$243$	6935.00	+	12011.8i	1.83078	+	3.17101i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	156.000	+	270.200i	0.0401864	+	0.0696049i
$248$		0			0
$249$	2650.00	−	4589.93i	0.674445	−	1.16817i
$250$		0			0
$251$	−2394.00			−0.602024			−0.301012	−	0.953620i	$-0.597324\pi$
$251$	−2394.00			−0.602024			−0.301012	+	0.953620i	$0.597324\pi$
$252$		0			0
$253$	2560.00			0.636149
$254$		0			0
$255$	2320.00	−	4018.36i	0.569741	−	0.986821i
$256$		0			0
$257$	1383.00	+	2395.43i	0.335678	+	0.581411i	0.983615	−	0.180283i	$-0.0577014\pi$
$257$	1383.00	+	2395.43i	0.335678	+	0.581411i	−0.647937	+	0.761694i	$0.724368\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	2263.00	+	3919.63i	0.536690	+	0.929575i
$262$		0			0
$263$	−3984.00	+	6900.49i	−0.934084	+	1.61788i	−0.157823	+	0.987467i	$0.550448\pi$
$263$	−3984.00	+	6900.49i	−0.934084	+	1.61788i	−0.776260	+	0.630413i	$0.782886\pi$
$264$		0			0
$265$	3600.00			0.834514
$266$		0			0
$267$	3900.00			0.893918
$268$		0			0
$269$	1450.00	−	2511.47i	0.328654	−	0.569246i	−0.653591	−	0.756848i	$-0.726738\pi$
$269$	1450.00	−	2511.47i	0.328654	−	0.569246i	0.982245	+	0.187602i	$0.0600715\pi$
$270$		0			0
$271$	−1320.00	−	2286.31i	−0.295883	−	0.512484i	0.679307	−	0.733854i	$-0.262281\pi$
$271$	−1320.00	−	2286.31i	−0.295883	−	0.512484i	−0.975190	+	0.221370i	$0.928947\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1220.00	−	2113.10i	−0.267523	−	0.463363i
$276$		0			0
$277$	761.000	−	1318.09i	0.165069	−	0.285908i	−0.771611	−	0.636095i	$-0.780549\pi$
$277$	761.000	−	1318.09i	0.165069	−	0.285908i	0.936680	+	0.350187i	$0.113882\pi$
$278$		0			0
$279$	18396.0			3.94745
$280$		0			0
$281$	−4534.00			−0.962547			−0.481274	−	0.876570i	$-0.659826\pi$
$281$	−4534.00			−0.962547			−0.481274	+	0.876570i	$0.659826\pi$
$282$		0			0
$283$	−2417.00	+	4186.37i	−0.507688	+	0.879342i	0.492272	+	0.870441i	$0.336166\pi$
$283$	−2417.00	+	4186.37i	−0.507688	+	0.879342i	−0.999960	+	0.00890034i	$0.997167\pi$
$284$		0			0
$285$	−1040.00	−	1801.33i	−0.216155	−	0.374392i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	774.500	+	1341.47i	0.157643	+	0.273046i
$290$		0			0
$291$	1070.00	−	1853.29i	0.215548	−	0.373340i
$292$		0			0
$293$	−4656.00			−0.928350			−0.464175	−	0.885744i	$-0.653649\pi$
$293$	−4656.00			−0.928350			−0.464175	+	0.885744i	$0.653649\pi$
$294$		0			0
$295$	−2192.00			−0.432621
$296$		0			0
$297$	−9200.00	+	15934.9i	−1.79743	+	3.11325i
$298$		0			0
$299$	−384.000	−	665.108i	−0.0742719	−	0.128643i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	7160.00	+	12401.5i	1.35753	+	2.35131i
$304$		0			0
$305$	−2304.00	+	3990.65i	−0.432546	+	0.749192i
$306$		0			0
$307$	−7238.00			−1.34558			−0.672792	−	0.739831i	$-0.734905\pi$
$307$	−7238.00			−1.34558			−0.672792	+	0.739831i	$0.734905\pi$
$308$		0			0
$309$	−7640.00			−1.40655
$310$		0			0
$311$	−548.000	+	949.164i	−0.0999171	+	0.173062i	−0.911650	−	0.410967i	$-0.865191\pi$
$311$	−548.000	+	949.164i	−0.0999171	+	0.173062i	0.811733	+	0.584029i	$0.198524\pi$
$312$		0			0
$313$	1909.00	+	3306.48i	0.344738	+	0.597104i	0.985306	−	0.170797i	$-0.0546344\pi$
$313$	1909.00	+	3306.48i	0.344738	+	0.597104i	−0.640568	+	0.767901i	$0.721301\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−999.000	−	1730.32i	−0.177001	−	0.306575i	0.763851	−	0.645393i	$-0.223306\pi$
$317$	−999.000	−	1730.32i	−0.177001	−	0.306575i	−0.940852	+	0.338818i	$0.889973\pi$
$318$		0			0
$319$	−1240.00	+	2147.74i	−0.217638	+	0.376961i
$320$		0			0
$321$	−3240.00			−0.563362
$322$		0			0
$323$	−1508.00			−0.259775
$324$		0			0
$325$	−366.000	+	633.931i	−0.0624678	+	0.108197i
$326$		0			0
$327$	−6670.00	−	11552.8i	−1.12799	−	1.95373i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	3968.00	+	6872.78i	0.658915	+	1.14127i	0.980897	+	0.194529i	$0.0623178\pi$
$331$	3968.00	+	6872.78i	0.658915	+	1.14127i	−0.321981	+	0.946746i	$0.604349\pi$
$332$		0			0
$333$	−949.000	+	1643.72i	−0.156171	+	0.270496i
$334$		0			0
$335$	3808.00			0.621055
$336$		0			0
$337$	2766.00			0.447103			0.223551	−	0.974692i	$-0.428235\pi$
$337$	2766.00			0.447103			0.223551	+	0.974692i	$0.428235\pi$
$338$		0			0
$339$	8990.00	−	15571.1i	1.44032	−	2.49471i
$340$		0			0
$341$	5040.00	+	8729.54i	0.800385	+	1.38631i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	2560.00	+	4434.05i	0.399495	+	0.691946i
$346$		0			0
$347$	−4176.00	+	7233.04i	−0.646050	+	1.11899i	0.338008	+	0.941143i	$0.390247\pi$
$347$	−4176.00	+	7233.04i	−0.646050	+	1.11899i	−0.984058	+	0.177848i	$0.943086\pi$
$348$		0			0
$349$	−5924.00			−0.908609			−0.454304	−	0.890847i	$-0.650112\pi$
$349$	−5924.00			−0.908609			−0.454304	+	0.890847i	$0.650112\pi$
$350$		0			0
$351$	5520.00			0.839418
$352$		0			0
$353$	−1113.00	+	1927.77i	−0.167816	+	0.290666i	−0.937652	−	0.347576i	$-0.887005\pi$
$353$	−1113.00	+	1927.77i	−0.167816	+	0.290666i	0.769836	+	0.638242i	$0.220338\pi$
$354$		0			0
$355$	−1792.00	−	3103.84i	−0.267914	−	0.464041i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1940.00	−	3360.18i	−0.285207	−	0.493993i	0.687452	−	0.726229i	$-0.258729\pi$
$359$	−1940.00	−	3360.18i	−0.285207	−	0.493993i	−0.972659	+	0.232237i	$0.925396\pi$
$360$		0			0
$361$	3091.50	−	5354.64i	0.450722	−	0.780673i
$362$		0			0
$363$	−2690.00			−0.388949
$364$		0			0
$365$	1264.00			0.181262
$366$		0			0
$367$	1292.00	−	2237.81i	0.183765	−	0.318291i	−0.759394	−	0.650630i	$-0.774505\pi$
$367$	1292.00	−	2237.81i	0.183765	−	0.318291i	0.943160	+	0.332340i	$0.107838\pi$
$368$		0			0
$369$	−219.000	−	379.319i	−0.0308962	−	0.0535137i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−5267.00	−	9122.71i	−0.731139	−	1.26637i	−0.956397	−	0.292071i	$-0.905656\pi$
$373$	−5267.00	−	9122.71i	−0.731139	−	1.26637i	0.225257	−	0.974299i	$-0.427678\pi$
$374$		0			0
$375$	7440.00	−	12886.5i	1.02453	−	1.77454i
$376$		0			0
$377$	744.000			0.101639
$378$		0			0
$379$	−4472.00			−0.606098			−0.303049	−	0.952975i	$-0.598005\pi$
$379$	−4472.00			−0.606098			−0.303049	+	0.952975i	$0.598005\pi$
$380$		0			0
$381$	−1920.00	+	3325.54i	−0.258175	+	0.447172i
$382$		0			0
$383$	−1234.00	−	2137.35i	−0.164633	−	0.285153i	0.771892	−	0.635754i	$-0.219311\pi$
$383$	−1234.00	−	2137.35i	−0.164633	−	0.285153i	−0.936525	+	0.350601i	$0.885977\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−15184.0	−	26299.5i	−1.99443	−	3.45446i
$388$		0			0
$389$	523.000	−	905.863i	0.0681675	−	0.118070i	−0.829927	−	0.557872i	$-0.811618\pi$
$389$	523.000	−	905.863i	0.0681675	−	0.118070i	0.898095	+	0.439802i	$0.144951\pi$
$390$		0			0
$391$	3712.00			0.480112
$392$		0			0
$393$	18140.0			2.32835
$394$		0			0
$395$	−3744.00	+	6484.80i	−0.476914	+	0.826040i
$396$		0			0
$397$	−1062.00	−	1839.44i	−0.134258	−	0.232541i	0.791056	−	0.611744i	$-0.209532\pi$
$397$	−1062.00	−	1839.44i	−0.134258	−	0.232541i	−0.925314	+	0.379203i	$0.876198\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5799.00	−	10044.2i	−0.722165	−	1.25083i	−0.960130	−	0.279553i	$-0.909814\pi$
$401$	−5799.00	−	10044.2i	−0.722165	−	1.25083i	0.237965	−	0.971274i	$-0.423520\pi$
$402$		0			0
$403$	1512.00	−	2618.86i	0.186894	−	0.323709i
$404$		0			0
$405$	−21032.0			−2.58047
$406$		0			0
$407$	−1040.00			−0.126661
$408$		0			0
$409$	1385.00	−	2398.89i	0.167442	−	0.290018i	−0.770078	−	0.637950i	$-0.779783\pi$
$409$	1385.00	−	2398.89i	0.167442	−	0.290018i	0.937520	+	0.347932i	$0.113116\pi$
$410$		0			0
$411$	8330.00	+	14428.0i	0.999729	+	1.73158i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	2120.00	+	3671.95i	0.250763	+	0.434335i
$416$		0			0
$417$	5630.00	−	9751.45i	0.661157	−	1.14516i
$418$		0			0
$419$	9438.00			1.10042			0.550211	−	0.835026i	$-0.314547\pi$
$419$	9438.00			1.10042			0.550211	+	0.835026i	$0.314547\pi$
$420$		0			0
$421$	5550.00			0.642495			0.321248	−	0.946995i	$-0.395898\pi$
$421$	5550.00			0.642495			0.321248	+	0.946995i	$0.395898\pi$
$422$		0			0
$423$	14454.0	−	25035.1i	1.66141	−	2.87765i
$424$		0			0
$425$	−1769.00	−	3064.00i	−0.201904	−	0.349708i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	2400.00	+	4156.92i	0.270100	+	0.467828i
$430$		0			0
$431$	1500.00	−	2598.08i	0.167639	−	0.290359i	−0.769950	−	0.638104i	$-0.779719\pi$
$431$	1500.00	−	2598.08i	0.167639	−	0.290359i	0.937589	+	0.347744i	$0.113052\pi$
$432$		0			0
$433$	12926.0			1.43460			0.717302	−	0.696762i	$-0.245377\pi$
$433$	12926.0			1.43460			0.717302	+	0.696762i	$0.245377\pi$
$434$		0			0
$435$	−4960.00			−0.546698
$436$		0			0
$437$	832.000	−	1441.07i	0.0910754	−	0.157747i
$438$		0			0
$439$	204.000	+	353.338i	0.0221786	+	0.0384144i	0.876902	−	0.480670i	$-0.159606\pi$
$439$	204.000	+	353.338i	0.0221786	+	0.0384144i	−0.854723	+	0.519084i	$0.826273\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	7226.00	+	12515.8i	0.774983	+	1.34231i	0.934804	+	0.355164i	$0.115575\pi$
$443$	7226.00	+	12515.8i	0.774983	+	1.34231i	−0.159821	+	0.987146i	$0.551092\pi$
$444$		0			0
$445$	−1560.00	+	2702.00i	−0.166182	+	0.287836i
$446$		0			0
$447$	−26940.0			−2.85060
$448$		0			0
$449$	10258.0			1.07818			0.539092	−	0.842247i	$-0.318767\pi$
$449$	10258.0			1.07818			0.539092	+	0.842247i	$0.318767\pi$
$450$		0			0
$451$	120.000	−	207.846i	0.0125290	−	0.0217009i
$452$		0			0
$453$	−13240.0	−	22932.4i	−1.37322	−	2.37849i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	2749.00	+	4761.41i	0.281385	+	0.487373i	0.971726	−	0.236111i	$-0.0758730\pi$
$457$	2749.00	+	4761.41i	0.281385	+	0.487373i	−0.690341	+	0.723484i	$0.742540\pi$
$458$		0			0
$459$	−13340.0	+	23105.6i	−1.35655	+	2.34962i
$460$		0			0
$461$	−16316.0			−1.64840			−0.824199	−	0.566300i	$-0.808375\pi$
$461$	−16316.0			−1.64840			−0.824199	+	0.566300i	$0.808375\pi$
$462$		0			0
$463$	8944.00			0.897760			0.448880	−	0.893592i	$-0.351823\pi$
$463$	8944.00			0.897760			0.448880	+	0.893592i	$0.351823\pi$
$464$		0			0
$465$	−10080.0	+	17459.1i	−1.00527	+	1.74117i
$466$		0			0
$467$	4711.00	+	8159.69i	0.466807	+	0.808534i	0.999281	−	0.0379124i	$-0.0120708\pi$
$467$	4711.00	+	8159.69i	0.466807	+	0.808534i	−0.532474	+	0.846447i	$0.678737\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−2780.00	−	4815.10i	−0.271965	−	0.471058i
$472$		0			0
$473$	8320.00	−	14410.7i	0.808782	−	1.40085i
$474$		0			0
$475$	−1586.00			−0.153201
$476$		0			0
$477$	−32850.0			−3.15325
$478$		0			0
$479$	−6910.00	+	11968.5i	−0.659136	+	1.14166i	0.321704	+	0.946840i	$0.395744\pi$
$479$	−6910.00	+	11968.5i	−0.659136	+	1.14166i	−0.980840	+	0.194816i	$0.937589\pi$
$480$		0			0
$481$	156.000	+	270.200i	0.0147879	+	0.0256134i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	856.000	+	1482.64i	0.0801422	+	0.138810i
$486$		0			0
$487$	6632.00	−	11487.0i	0.617094	−	1.06884i	−0.372920	−	0.927864i	$-0.621643\pi$
$487$	6632.00	−	11487.0i	0.617094	−	1.06884i	0.990013	−	0.140974i	$-0.0450234\pi$
$488$		0			0
$489$	3280.00			0.303327
$490$		0			0
$491$	−5940.00			−0.545964			−0.272982	−	0.962019i	$-0.588010\pi$
$491$	−5940.00			−0.545964			−0.272982	+	0.962019i	$0.588010\pi$
$492$		0			0
$493$	−1798.00	+	3114.23i	−0.164255	+	0.284498i
$494$		0			0
$495$	−11680.0	−	20230.4i	−1.06056	−	1.83694i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	4126.00	+	7146.44i	0.370151	+	0.641120i	0.989588	−	0.143926i	$-0.0459728\pi$
$499$	4126.00	+	7146.44i	0.370151	+	0.641120i	−0.619438	+	0.785046i	$0.712639\pi$
$500$		0			0
$501$	−21340.0	+	36962.0i	−1.90300	+	3.29609i
$502$		0			0
$503$	4704.00			0.416980			0.208490	−	0.978024i	$-0.433145\pi$
$503$	4704.00			0.416980			0.208490	+	0.978024i	$0.433145\pi$
$504$		0			0
$505$	−11456.0			−1.00948
$506$		0			0
$507$	−10265.0	+	17779.5i	−0.899181	+	1.55743i
$508$		0			0
$509$	5394.00	+	9342.68i	0.469715	+	0.813570i	0.999400	−	0.0346241i	$-0.0110234\pi$
$509$	5394.00	+	9342.68i	0.469715	+	0.813570i	−0.529686	+	0.848194i	$0.677690\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	5980.00	+	10357.7i	0.514666	+	0.891427i
$514$		0			0
$515$	3056.00	−	5293.15i	0.261482	−	0.452901i
$516$		0			0
$517$	15840.0			1.34747
$518$		0			0
$519$	34760.0			2.93987
$520$		0			0
$521$	7293.00	−	12631.8i	0.613267	−	1.06221i	−0.377419	−	0.926043i	$-0.623188\pi$
$521$	7293.00	−	12631.8i	0.613267	−	1.06221i	0.990686	−	0.136167i	$-0.0434784\pi$
$522$		0			0
$523$	−13.0000	−	22.5167i	−0.00108690	−	0.00188257i	0.865481	−	0.500941i	$-0.167013\pi$
$523$	−13.0000	−	22.5167i	−0.00108690	−	0.00188257i	−0.866568	+	0.499058i	$0.833679\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	7308.00	+	12657.8i	0.604064	+	1.04627i
$528$		0			0
$529$	4035.50	−	6989.69i	0.331676	−	0.574479i
$530$		0			0
$531$	20002.0			1.63468
$532$		0			0
$533$	−72.0000			−0.00585116
$534$		0			0
$535$	1296.00	−	2244.74i	0.104731	−	0.181399i
$536$		0			0
$537$	11340.0	+	19641.5i	0.911280	+	1.57838i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−5607.00	−	9711.61i	−0.445589	−	0.771783i	0.552504	−	0.833510i	$-0.313672\pi$
$541$	−5607.00	−	9711.61i	−0.445589	−	0.771783i	−0.998093	+	0.0617272i	$0.980339\pi$
$542$		0			0
$543$	−1380.00	+	2390.23i	−0.109063	+	0.188903i
$544$		0			0
$545$	10672.0			0.838786
$546$		0			0
$547$	−5424.00			−0.423973			−0.211987	−	0.977273i	$-0.567993\pi$
$547$	−5424.00			−0.423973			−0.211987	+	0.977273i	$0.567993\pi$
$548$		0			0
$549$	21024.0	−	36414.6i	1.63439	−	2.83085i
$550$		0			0
$551$	806.000	+	1396.03i	0.0623172	+	0.107936i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−1040.00	−	1801.33i	−0.0795415	−	0.137770i
$556$		0			0
$557$	8809.00	−	15257.6i	0.670106	−	1.16066i	−0.307767	−	0.951462i	$-0.599582\pi$
$557$	8809.00	−	15257.6i	0.670106	−	1.16066i	0.977874	−	0.209197i	$-0.0670849\pi$
$558$		0			0
$559$	−4992.00			−0.377709
$560$		0			0
$561$	−23200.0			−1.74600
$562$		0			0
$563$	1781.00	−	3084.78i	0.133322	−	0.230920i	−0.791633	−	0.610997i	$-0.790769\pi$
$563$	1781.00	−	3084.78i	0.133322	−	0.230920i	0.924955	+	0.380076i	$0.124102\pi$
$564$		0			0
$565$	7192.00	+	12456.9i	0.535522	+	0.927551i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1419.00	−	2457.78i	−0.104548	−	0.181082i	0.809006	−	0.587801i	$-0.200006\pi$
$569$	−1419.00	−	2457.78i	−0.104548	−	0.181082i	−0.913553	+	0.406719i	$0.866673\pi$
$570$		0			0
$571$	180.000	−	311.769i	0.0131922	−	0.0228496i	−0.859354	−	0.511381i	$-0.829134\pi$
$571$	180.000	−	311.769i	0.0131922	−	0.0228496i	0.872546	+	0.488532i	$0.162467\pi$
$572$		0			0
$573$	30000.0			2.18720
$574$		0			0
$575$	3904.00			0.283144
$576$		0			0
$577$	−11009.0	+	19068.1i	−0.794299	+	1.37577i	0.128984	+	0.991647i	$0.458828\pi$
$577$	−11009.0	+	19068.1i	−0.794299	+	1.37577i	−0.923283	+	0.384120i	$0.874505\pi$
$578$		0			0
$579$	16390.0	+	28388.3i	1.17642	+	2.03761i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−9000.00	−	15588.5i	−0.639351	−	1.10739i
$584$		0			0
$585$	−3504.00	+	6069.11i	−0.247645	+	0.428934i
$586$		0			0
$587$	1454.00			0.102237			0.0511184	−	0.998693i	$-0.483721\pi$
$587$	1454.00			0.102237			0.0511184	+	0.998693i	$0.483721\pi$
$588$		0			0
$589$	6552.00			0.458354
$590$		0			0
$591$	−11810.0	+	20455.5i	−0.821994	+	1.42374i
$592$		0			0
$593$	−6909.00	−	11966.7i	−0.478446	−	0.828693i	0.521248	−	0.853405i	$-0.325467\pi$
$593$	−6909.00	−	11966.7i	−0.478446	−	0.828693i	−0.999695	+	0.0247118i	$0.992133\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−5180.00	−	8972.02i	−0.355114	−	0.615076i
$598$		0			0
$599$	−3348.00	+	5798.91i	−0.228373	+	0.395554i	−0.957326	−	0.289010i	$-0.906674\pi$
$599$	−3348.00	+	5798.91i	−0.228373	+	0.395554i	0.728953	+	0.684564i	$0.240007\pi$
$600$		0			0
$601$	10010.0			0.679395			0.339698	−	0.940535i	$-0.389675\pi$
$601$	10010.0			0.679395			0.339698	+	0.940535i	$0.389675\pi$
$602$		0			0
$603$	−34748.0			−2.34668
$604$		0			0
$605$	1076.00	−	1863.69i	0.0723068	−	0.125239i
$606$		0			0
$607$	−1440.00	−	2494.15i	−0.0962896	−	0.166779i	0.813856	−	0.581066i	$-0.197364\pi$
$607$	−1440.00	−	2494.15i	−0.0962896	−	0.166779i	−0.910146	+	0.414287i	$0.864031\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2376.00	−	4115.35i	−0.157320	−	0.272487i
$612$		0			0
$613$	−3261.00	+	5648.22i	−0.214862	+	0.372152i	−0.953230	−	0.302246i	$-0.902264\pi$
$613$	−3261.00	+	5648.22i	−0.214862	+	0.372152i	0.738368	+	0.674398i	$0.235597\pi$
$614$		0			0
$615$	480.000			0.0314723
$616$		0			0
$617$	6614.00			0.431555			0.215778	−	0.976443i	$-0.430771\pi$
$617$	6614.00			0.431555			0.215778	+	0.976443i	$0.430771\pi$
$618$		0			0
$619$	−2633.00	+	4560.49i	−0.170968	+	0.296125i	−0.938759	−	0.344576i	$-0.888023\pi$
$619$	−2633.00	+	4560.49i	−0.170968	+	0.296125i	0.767791	+	0.640701i	$0.221356\pi$
$620$		0			0
$621$	−14720.0	−	25495.8i	−0.951197	−	1.64752i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	2139.50	+	3705.72i	0.136928	+	0.237166i
$626$		0			0
$627$	−5200.00	+	9006.66i	−0.331209	+	0.573671i
$628$		0			0
$629$	−1508.00			−0.0955928
$630$		0			0
$631$	3344.00			0.210971			0.105485	−	0.994421i	$-0.466360\pi$
$631$	3344.00			0.210971			0.105485	+	0.994421i	$0.466360\pi$
$632$		0			0
$633$	17620.0	−	30518.7i	1.10637	−	1.91629i
$634$		0			0
$635$	−1536.00	−	2660.43i	−0.0959910	−	0.166261i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	16352.0	+	28322.5i	1.01232	+	1.75340i
$640$		0			0
$641$	2441.00	−	4227.94i	0.150411	−	0.260520i	−0.780967	−	0.624572i	$-0.785274\pi$
$641$	2441.00	−	4227.94i	0.150411	−	0.260520i	0.931379	+	0.364052i	$0.118607\pi$
$642$		0			0
$643$	−15898.0			−0.975048			−0.487524	−	0.873110i	$-0.662100\pi$
$643$	−15898.0			−0.975048			−0.487524	+	0.873110i	$0.662100\pi$
$644$		0			0
$645$	33280.0			2.03163
$646$		0			0
$647$	−3066.00	+	5310.47i	−0.186301	+	0.322683i	−0.944014	−	0.329905i	$-0.892983\pi$
$647$	−3066.00	+	5310.47i	−0.186301	+	0.322683i	0.757713	+	0.652588i	$0.226317\pi$
$648$		0			0
$649$	5480.00	+	9491.64i	0.331447	+	0.574082i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	12099.0	+	20956.1i	0.725070	+	1.25586i	0.958945	+	0.283591i	$0.0915258\pi$
$653$	12099.0	+	20956.1i	0.725070	+	1.25586i	−0.233876	+	0.972266i	$0.575141\pi$
$654$		0			0
$655$	−7256.00	+	12567.8i	−0.432848	+	0.749715i
$656$		0			0
$657$	−11534.0			−0.684907
$658$		0			0
$659$	17456.0			1.03185			0.515925	−	0.856634i	$-0.327448\pi$
$659$	17456.0			1.03185			0.515925	+	0.856634i	$0.327448\pi$
$660$		0			0
$661$	328.000	−	568.113i	0.0193006	−	0.0334297i	−0.856214	−	0.516622i	$-0.827189\pi$
$661$	328.000	−	568.113i	0.0193006	−	0.0334297i	0.875514	+	0.483192i	$0.160523\pi$
$662$		0			0
$663$	3480.00	+	6027.54i	0.203849	+	0.353077i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1984.00	−	3436.39i	−0.115174	−	0.199487i
$668$		0			0
$669$	−6680.00	+	11570.1i	−0.386044	+	0.668649i
$670$		0			0
$671$	23040.0			1.32556
$672$		0			0
$673$	−18214.0			−1.04324			−0.521618	−	0.853179i	$-0.674671\pi$
$673$	−18214.0			−1.04324			−0.521618	+	0.853179i	$0.674671\pi$
$674$		0			0
$675$	−14030.0	+	24300.7i	−0.800022	+	1.38568i
$676$		0			0
$677$	−15126.0	−	26199.0i	−0.858699	−	1.48731i	−0.873170	−	0.487415i	$-0.837940\pi$
$677$	−15126.0	−	26199.0i	−0.858699	−	1.48731i	0.0144709	−	0.999895i	$-0.495394\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	6450.00	+	11171.7i	0.362944	+	0.628637i
$682$		0			0
$683$	5418.00	−	9384.25i	0.303534	−	0.525737i	−0.673400	−	0.739279i	$-0.735167\pi$
$683$	5418.00	−	9384.25i	0.303534	−	0.525737i	0.976934	+	0.213542i	$0.0684999\pi$
$684$		0			0
$685$	−13328.0			−0.743411
$686$		0			0
$687$	−55240.0			−3.06774
$688$		0			0
$689$	−2700.00	+	4676.54i	−0.149291	+	0.258580i
$690$		0			0
$691$	−4789.00	−	8294.79i	−0.263650	−	0.456655i	0.703559	−	0.710637i	$-0.251593\pi$
$691$	−4789.00	−	8294.79i	−0.263650	−	0.456655i	−0.967209	+	0.253982i	$0.918260\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4504.00	+	7801.16i	0.245822	+	0.425777i
$696$		0			0
$697$	174.000	−	301.377i	0.00945584	−	0.0163780i
$698$		0			0
$699$	−63140.0			−3.41656
$700$		0			0
$701$	12442.0			0.670368			0.335184	−	0.942153i	$-0.391202\pi$
$701$	12442.0			0.670368			0.335184	+	0.942153i	$0.391202\pi$
$702$		0			0
$703$	−338.000	+	585.433i	−0.0181336	+	0.0314083i
$704$		0			0
$705$	15840.0	+	27435.7i	0.846197	+	1.46566i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	12587.0	+	21801.3i	0.666734	+	1.15482i	0.978812	+	0.204761i	$0.0656418\pi$
$709$	12587.0	+	21801.3i	0.666734	+	1.15482i	−0.312078	+	0.950057i	$0.601025\pi$
$710$		0			0
$711$	34164.0	−	59173.8i	1.80204	−	3.12122i
$712$		0			0
$713$	−16128.0			−0.847123
$714$		0			0
$715$	−3840.00			−0.200850
$716$		0			0
$717$	−19800.0	+	34294.6i	−1.03130	+	1.78627i
$718$		0			0
$719$	−17094.0	−	29607.7i	−0.886646	−	1.53572i	−0.843815	−	0.536634i	$-0.819696\pi$
$719$	−17094.0	−	29607.7i	−0.886646	−	1.53572i	−0.0428311	−	0.999082i	$-0.513638\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−35090.0	−	60777.7i	−1.80499	−	3.12634i
$724$		0			0
$725$	−1891.00	+	3275.31i	−0.0968689	+	0.167782i
$726$		0			0
$727$	−5204.00			−0.265482			−0.132741	−	0.991151i	$-0.542378\pi$
$727$	−5204.00			−0.265482			−0.132741	+	0.991151i	$0.542378\pi$
$728$		0			0
$729$	67717.0			3.44038
$730$		0			0
$731$	12064.0	−	20895.5i	0.610401	−	1.05725i
$732$		0			0
$733$	16440.0	+	28474.9i	0.828411	+	1.43485i	0.899284	+	0.437365i	$0.144088\pi$
$733$	16440.0	+	28474.9i	0.828411	+	1.43485i	−0.0708733	+	0.997485i	$0.522579\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−9520.00	−	16489.1i	−0.475812	−	0.824131i
$738$		0			0
$739$	1956.00	−	3387.89i	0.0973648	−	0.168641i	−0.813228	−	0.581945i	$-0.802292\pi$
$739$	1956.00	−	3387.89i	0.0973648	−	0.168641i	0.910593	+	0.413304i	$0.135625\pi$
$740$		0			0
$741$	3120.00			0.154678
$742$		0			0
$743$	−16008.0			−0.790413			−0.395206	−	0.918592i	$-0.629327\pi$
$743$	−16008.0			−0.790413			−0.395206	+	0.918592i	$0.629327\pi$
$744$		0			0
$745$	10776.0	−	18664.6i	0.529936	−	0.917876i
$746$		0			0
$747$	−19345.0	−	33506.5i	−0.947519	−	1.64115i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−4980.00	−	8625.61i	−0.241974	−	0.419112i	0.719302	−	0.694697i	$-0.244462\pi$
$751$	−4980.00	−	8625.61i	−0.241974	−	0.419112i	−0.961277	+	0.275585i	$0.911128\pi$
$752$		0			0
$753$	−11970.0	+	20732.6i	−0.579298	+	1.00337i
$754$		0			0
$755$	21184.0			1.02115
$756$		0			0
$757$	12378.0			0.594301			0.297151	−	0.954831i	$-0.403964\pi$
$757$	12378.0			0.594301			0.297151	+	0.954831i	$0.403964\pi$
$758$		0			0
$759$	12800.0	−	22170.3i	0.612135	−	1.06025i
$760$		0			0
$761$	−17335.0	−	30025.1i	−0.825747	−	1.43024i	−0.901347	−	0.433097i	$-0.857421\pi$
$761$	−17335.0	−	30025.1i	−0.825747	−	1.43024i	0.0756005	−	0.997138i	$-0.475913\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−16936.0	−	29334.0i	−0.800421	−	1.38637i
$766$		0			0
$767$	1644.00	−	2847.49i	0.0773943	−	0.134051i
$768$		0			0
$769$	−10898.0			−0.511043			−0.255521	−	0.966803i	$-0.582247\pi$
$769$	−10898.0			−0.511043			−0.255521	+	0.966803i	$0.582247\pi$
$770$		0			0
$771$	27660.0			1.29202
$772$		0			0
$773$	12904.0	−	22350.4i	0.600420	−	1.03996i	−0.392337	−	0.919821i	$-0.628333\pi$
$773$	12904.0	−	22350.4i	0.600420	−	1.03996i	0.992757	−	0.120136i	$-0.0383332\pi$
$774$		0			0
$775$	7686.00	+	13312.5i	0.356244	+	0.617033i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−78.0000	−	135.100i	−0.00358747	−	0.00621368i
$780$		0			0
$781$	−8960.00	+	15519.2i	−0.410517	+	0.711037i
$782$		0			0
$783$	28520.0			1.30169
$784$		0			0
$785$	4448.00			0.202237
$786$		0			0
$787$	10527.0	−	18233.3i	0.476807	−	0.825854i	−0.522840	−	0.852431i	$-0.675127\pi$
$787$	10527.0	−	18233.3i	0.476807	−	0.825854i	0.999647	+	0.0265772i	$0.00846077\pi$
$788$		0			0
$789$	39840.0	+	69004.9i	1.79764	+	3.11361i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−3456.00	−	5985.97i	−0.154762	−	0.268055i
$794$		0			0
$795$	18000.0	−	31176.9i	0.803012	−	1.39086i
$796$		0			0
$797$	−24276.0			−1.07892			−0.539461	−	0.842011i	$-0.681372\pi$
$797$	−24276.0			−1.07892			−0.539461	+	0.842011i	$0.681372\pi$
$798$		0			0
$799$	22968.0			1.01696
$800$		0			0
$801$	14235.0	−	24655.7i	0.627926	−	1.08760i
$802$		0			0
$803$	−3160.00	−	5473.28i	−0.138872	−	0.240533i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−14500.0	−	25114.7i	−0.632496	−	1.09551i
$808$		0			0
$809$	−10763.0	+	18642.1i	−0.467747	+	0.810161i	−0.999321	−	0.0368510i	$-0.988267\pi$
$809$	−10763.0	+	18642.1i	−0.467747	+	0.810161i	0.531574	+	0.847012i	$0.321601\pi$
$810$		0			0
$811$	−12806.0			−0.554475			−0.277238	−	0.960801i	$-0.589419\pi$
$811$	−12806.0			−0.554475			−0.277238	+	0.960801i	$0.589419\pi$
$812$		0			0
$813$	−26400.0			−1.13885
$814$		0			0
$815$	−1312.00	+	2272.45i	−0.0563894	+	0.0976693i
$816$		0			0
$817$	−5408.00	−	9366.93i	−0.231581	−	0.401111i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−6607.00	−	11443.7i	−0.280860	−	0.486463i	0.690737	−	0.723106i	$-0.257286\pi$
$821$	−6607.00	−	11443.7i	−0.280860	−	0.486463i	−0.971597	+	0.236643i	$0.923953\pi$
$822$		0			0
$823$	−16124.0	+	27927.6i	−0.682925	+	1.18286i	0.291159	+	0.956675i	$0.405959\pi$
$823$	−16124.0	+	27927.6i	−0.682925	+	1.18286i	−0.974084	+	0.226186i	$0.927374\pi$
$824$		0			0
$825$	−24400.0			−1.02970
$826$		0			0
$827$	−14316.0			−0.601954			−0.300977	−	0.953631i	$-0.597313\pi$
$827$	−14316.0			−0.601954			−0.300977	+	0.953631i	$0.597313\pi$
$828$		0			0
$829$	−12584.0	+	21796.1i	−0.527214	+	0.913161i	0.472283	+	0.881447i	$0.343430\pi$
$829$	−12584.0	+	21796.1i	−0.527214	+	0.913161i	−0.999497	+	0.0317144i	$0.989903\pi$
$830$		0			0
$831$	−7610.00	−	13180.9i	−0.317675	−	0.550229i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−17072.0	−	29569.6i	−0.707546	−	1.22551i
$836$		0			0
$837$	57960.0	−	100390.i	2.39354	−	4.14573i
$838$		0			0
$839$	9356.00			0.384988			0.192494	−	0.981298i	$-0.438342\pi$
$839$	9356.00			0.384988			0.192494	+	0.981298i	$0.438342\pi$
$840$		0			0
$841$	−20545.0			−0.842388
$842$		0			0
$843$	−22670.0	+	39265.6i	−0.926211	+	1.60425i
$844$		0			0
$845$	−8212.00	−	14223.6i	−0.334321	−	0.579061i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	24170.0	+	41863.7i	0.977046	+	1.69229i
$850$		0			0
$851$	832.000	−	1441.07i	0.0335142	−	0.0580483i
$852$		0			0
$853$	2372.00			0.0952119			0.0476059	−	0.998866i	$-0.484841\pi$
$853$	2372.00			0.0952119			0.0476059	+	0.998866i	$0.484841\pi$
$854$		0			0
$855$	−15184.0			−0.607347
$856$		0			0
$857$	−5847.00	+	10127.3i	−0.233057	+	0.403666i	−0.958706	−	0.284398i	$-0.908206\pi$
$857$	−5847.00	+	10127.3i	−0.233057	+	0.403666i	0.725649	+	0.688065i	$0.241539\pi$
$858$		0			0
$859$	10253.0	+	17758.7i	0.407250	+	0.705378i	0.994580	−	0.103969i	$-0.0331544\pi$
$859$	10253.0	+	17758.7i	0.407250	+	0.705378i	−0.587330	+	0.809347i	$0.699821\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	14068.0	+	24366.5i	0.554902	+	0.961118i	0.997911	+	0.0646012i	$0.0205775\pi$
$863$	14068.0	+	24366.5i	0.554902	+	0.961118i	−0.443009	+	0.896517i	$0.646089\pi$
$864$		0			0
$865$	−13904.0	+	24082.4i	−0.546532	+	0.946621i
$866$		0			0
$867$	15490.0			0.606768
$868$		0			0
$869$	37440.0			1.46152
$870$		0			0
$871$	−2856.00	+	4946.74i	−0.111104	+	0.192438i
$872$		0			0
$873$	−7811.00	−	13529.0i	−0.302821	−	0.524500i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	18535.0	+	32103.6i	0.713663	+	1.23610i	0.963473	+	0.267806i	$0.0862985\pi$
$877$	18535.0	+	32103.6i	0.713663	+	1.23610i	−0.249810	+	0.968295i	$0.580368\pi$
$878$		0			0
$879$	−23280.0	+	40322.1i	−0.893305	+	1.54725i
$880$		0			0
$881$	−6198.00			−0.237021			−0.118511	−	0.992953i	$-0.537812\pi$
$881$	−6198.00			−0.237021			−0.118511	+	0.992953i	$0.537812\pi$
$882$		0			0
$883$	−31876.0			−1.21485			−0.607425	−	0.794377i	$-0.707798\pi$
$883$	−31876.0			−1.21485			−0.607425	+	0.794377i	$0.707798\pi$
$884$		0			0
$885$	−10960.0	+	18983.3i	−0.416290	+	0.721035i
$886$		0			0
$887$	66.0000	+	114.315i	0.00249838	+	0.00432732i	0.867272	−	0.497835i	$-0.165871\pi$
$887$	66.0000	+	114.315i	0.00249838	+	0.00432732i	−0.864774	+	0.502162i	$0.832538\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	52580.0	+	91071.2i	1.97699	+	3.42424i
$892$		0			0
$893$	5148.00	−	8916.60i	0.192913	−	0.334135i
$894$		0			0
$895$	−18144.0			−0.677639
$896$		0			0
$897$	−7680.00			−0.285873
$898$		0			0
$899$	7812.00	−	13530.8i	0.289816	−	0.501976i
$900$		0			0
$901$	−13050.0	−	22603.3i	−0.482529	−	0.835765i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1104.00	−	1912.18i	−0.0405505	−	0.0702355i
$906$		0			0
$907$	−19122.0	+	33120.3i	−0.700039	+	1.21250i	0.268413	+	0.963304i	$0.413501\pi$
$907$	−19122.0	+	33120.3i	−0.700039	+	1.21250i	−0.968452	+	0.249200i	$0.919832\pi$
$908$		0			0
$909$	104536.			3.81435
$910$		0			0
$911$	−7008.00			−0.254869			−0.127434	−	0.991847i	$-0.540674\pi$
$911$	−7008.00			−0.254869			−0.127434	+	0.991847i	$0.540674\pi$
$912$		0			0
$913$	10600.0	−	18359.7i	0.384237	−	0.665519i
$914$		0			0
$915$	23040.0	+	39906.5i	0.832436	+	1.44182i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−18332.0	−	31752.0i	−0.658016	−	1.13972i	−0.981128	−	0.193357i	$-0.938062\pi$
$919$	−18332.0	−	31752.0i	−0.658016	−	1.13972i	0.323112	−	0.946361i	$-0.395271\pi$
$920$		0			0
$921$	−36190.0	+	62682.9i	−1.29479	+	2.24264i
$922$		0			0
$923$	5376.00			0.191715
$924$		0			0
$925$	−1586.00			−0.0563755
$926$		0			0
$927$	−27886.0	+	48300.0i	−0.988022	+	1.71130i
$928$		0			0
$929$	−22755.0	−	39412.8i	−0.803625	−	1.39192i	−0.917216	−	0.398391i	$-0.869569\pi$
$929$	−22755.0	−	39412.8i	−0.803625	−	1.39192i	0.113591	−	0.993528i	$-0.463765\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	5480.00	+	9491.64i	0.192291	+	0.333057i
$934$		0			0
$935$	9280.00	−	16073.4i	0.324587	−	0.562200i
$936$		0			0
$937$	−3838.00			−0.133812			−0.0669061	−	0.997759i	$-0.521313\pi$
$937$	−3838.00			−0.133812			−0.0669061	+	0.997759i	$0.521313\pi$
$938$		0			0
$939$	38180.0			1.32690
$940$		0			0
$941$	8416.00	−	14576.9i	0.291556	−	0.504989i	−0.682622	−	0.730771i	$-0.739161\pi$
$941$	8416.00	−	14576.9i	0.291556	−	0.504989i	0.974178	+	0.225782i	$0.0724939\pi$
$942$		0			0
$943$	192.000	+	332.554i	0.00663031	+	0.0114840i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	20464.0	+	35444.7i	0.702208	+	1.21626i	0.967690	+	0.252144i	$0.0811355\pi$
$947$	20464.0	+	35444.7i	0.702208	+	1.21626i	−0.265482	+	0.964116i	$0.585531\pi$
$948$		0			0
$949$	−948.000	+	1641.98i	−0.0324272	+	0.0561655i
$950$		0			0
$951$	−19980.0			−0.681279
$952$		0			0
$953$	−24070.0			−0.818157			−0.409079	−	0.912499i	$-0.634150\pi$
$953$	−24070.0			−0.818157			−0.409079	+	0.912499i	$0.634150\pi$
$954$		0			0
$955$	−12000.0	+	20784.6i	−0.406608	+	0.704266i
$956$		0			0
$957$	12400.0	+	21477.4i	0.418845	+	0.725462i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−16856.5	−	29196.3i	−0.565825	−	0.980038i
$962$		0			0
$963$	−11826.0	+	20483.2i	−0.395730	+	0.685424i
$964$		0			0
$965$	−26224.0			−0.874798
$966$		0			0
$967$	−17152.0			−0.570394			−0.285197	−	0.958469i	$-0.592059\pi$
$967$	−17152.0			−0.570394			−0.285197	+	0.958469i	$0.592059\pi$
$968$		0			0
$969$	−7540.00	+	13059.7i	−0.249969	+	0.432959i
$970$		0			0
$971$	16455.0	+	28500.9i	0.543837	+	0.941954i	0.998679	+	0.0513817i	$0.0163625\pi$
$971$	16455.0	+	28500.9i	0.543837	+	0.941954i	−0.454842	+	0.890572i	$0.650304\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	3660.00	+	6339.31i	0.120219	+	0.208226i
$976$		0			0
$977$	3411.00	−	5908.03i	0.111697	−	0.193464i	−0.804758	−	0.593603i	$-0.797705\pi$
$977$	3411.00	−	5908.03i	0.111697	−	0.193464i	0.916454	+	0.400139i	$0.131038\pi$
$978$		0			0
$979$	15600.0			0.509273
$980$		0			0
$981$	−97382.0			−3.16939
$982$		0			0
$983$	24210.0	−	41933.0i	0.785533	−	1.36058i	−0.143147	−	0.989701i	$-0.545722\pi$
$983$	24210.0	−	41933.0i	0.785533	−	1.36058i	0.928680	−	0.370882i	$-0.120945\pi$
$984$		0			0
$985$	−9448.00	−	16364.4i	−0.305623	−	0.529354i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	13312.0	+	23057.1i	0.428005	+	0.741326i
$990$		0			0
$991$	24608.0	−	42622.3i	0.788798	−	1.36624i	−0.137906	−	0.990445i	$-0.544037\pi$
$991$	24608.0	−	42622.3i	0.788798	−	1.36624i	0.926704	−	0.375793i	$-0.122630\pi$
$992$		0			0
$993$	79360.0			2.53617
$994$		0			0
$995$	8288.00			0.264068
$996$		0			0
$997$	−17632.0	+	30539.5i	−0.560091	+	0.970107i	0.437397	+	0.899269i	$0.355901\pi$
$997$	−17632.0	+	30539.5i	−0.560091	+	0.970107i	−0.997488	+	0.0708379i	$0.977433\pi$
$998$		0			0
$999$	5980.00	+	10357.7i	0.189388	+	0.328030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.4.e.f.165.1		2
3.2	odd	2		1764.4.k.d.361.1		2
7.2	even	3	inner	196.4.e.f.177.1		2
7.3	odd	6		196.4.a.d.1.1		1
7.4	even	3		28.4.a.a.1.1	✓	1
7.5	odd	6		196.4.e.a.177.1		2
7.6	odd	2		196.4.e.a.165.1		2
21.2	odd	6		1764.4.k.d.1549.1		2
21.5	even	6		1764.4.k.m.1549.1		2
21.11	odd	6		252.4.a.d.1.1		1
21.17	even	6		1764.4.a.c.1.1		1
21.20	even	2		1764.4.k.m.361.1		2
28.3	even	6		784.4.a.a.1.1		1
28.11	odd	6		112.4.a.g.1.1		1
35.4	even	6		700.4.a.n.1.1		1
35.18	odd	12		700.4.e.a.449.1		2
35.32	odd	12		700.4.e.a.449.2		2
56.11	odd	6		448.4.a.a.1.1		1
56.53	even	6		448.4.a.p.1.1		1
84.11	even	6		1008.4.a.o.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.4.a.a.1.1	✓	1	7.4	even	3
112.4.a.g.1.1		1	28.11	odd	6
196.4.a.d.1.1		1	7.3	odd	6
196.4.e.a.165.1		2	7.6	odd	2
196.4.e.a.177.1		2	7.5	odd	6
196.4.e.f.165.1		2	1.1	even	1	trivial
196.4.e.f.177.1		2	7.2	even	3	inner
252.4.a.d.1.1		1	21.11	odd	6
448.4.a.a.1.1		1	56.11	odd	6
448.4.a.p.1.1		1	56.53	even	6
700.4.a.n.1.1		1	35.4	even	6
700.4.e.a.449.1		2	35.18	odd	12
700.4.e.a.449.2		2	35.32	odd	12
784.4.a.a.1.1		1	28.3	even	6
1008.4.a.o.1.1		1	84.11	even	6
1764.4.a.c.1.1		1	21.17	even	6
1764.4.k.d.361.1		2	3.2	odd	2
1764.4.k.d.1549.1		2	21.2	odd	6
1764.4.k.m.361.1		2	21.20	even	2
1764.4.k.m.1549.1		2	21.5	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	196.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(5.00000 - 8.66025i) q^{3} +(4.00000 + 6.92820i) q^{5} +(-36.5000 - 63.2199i) q^{9} +O(q^{10})\)	\(q+(5.00000 - 8.66025i) q^{3} +(4.00000 + 6.92820i) q^{5} +(-36.5000 - 63.2199i) q^{9} +(20.0000 - 34.6410i) q^{11} -12.0000 q^{13} +80.0000 q^{15} +(29.0000 - 50.2295i) q^{17} +(-13.0000 - 22.5167i) q^{19} +(32.0000 + 55.4256i) q^{23} +(30.5000 - 52.8275i) q^{25} -460.000 q^{27} -62.0000 q^{29} +(-126.000 + 218.238i) q^{31} +(-200.000 - 346.410i) q^{33} +(-13.0000 - 22.5167i) q^{37} +(-60.0000 + 103.923i) q^{39} +6.00000 q^{41} +416.000 q^{43} +(292.000 - 505.759i) q^{45} +(198.000 + 342.946i) q^{47} +(-290.000 - 502.295i) q^{51} +(225.000 - 389.711i) q^{53} +320.000 q^{55} -260.000 q^{57} +(-137.000 + 237.291i) q^{59} +(288.000 + 498.831i) q^{61} +(-48.0000 - 83.1384i) q^{65} +(238.000 - 412.228i) q^{67} +640.000 q^{69} -448.000 q^{71} +(79.0000 - 136.832i) q^{73} +(-305.000 - 528.275i) q^{75} +(468.000 + 810.600i) q^{79} +(-1314.50 + 2276.78i) q^{81} +530.000 q^{83} +464.000 q^{85} +(-310.000 + 536.936i) q^{87} +(195.000 + 337.750i) q^{89} +(1260.00 + 2182.38i) q^{93} +(104.000 - 180.133i) q^{95} +214.000 q^{97} -2920.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 10 q^{3} + 8 q^{5} - 73 q^{9}+O(q^{10}) \) 2 * q + 10 * q^3 + 8 * q^5 - 73 * q^9	\( 2 q + 10 q^{3} + 8 q^{5} - 73 q^{9} + 40 q^{11} - 24 q^{13} + 160 q^{15} + 58 q^{17} - 26 q^{19} + 64 q^{23} + 61 q^{25} - 920 q^{27} - 124 q^{29} - 252 q^{31} - 400 q^{33} - 26 q^{37} - 120 q^{39} + 12 q^{41} + 832 q^{43} + 584 q^{45} + 396 q^{47} - 580 q^{51} + 450 q^{53} + 640 q^{55} - 520 q^{57} - 274 q^{59} + 576 q^{61} - 96 q^{65} + 476 q^{67} + 1280 q^{69} - 896 q^{71} + 158 q^{73} - 610 q^{75} + 936 q^{79} - 2629 q^{81} + 1060 q^{83} + 928 q^{85} - 620 q^{87} + 390 q^{89} + 2520 q^{93} + 208 q^{95} + 428 q^{97} - 5840 q^{99}+O(q^{100}) \) 2 * q + 10 * q^3 + 8 * q^5 - 73 * q^9 + 40 * q^11 - 24 * q^13 + 160 * q^15 + 58 * q^17 - 26 * q^19 + 64 * q^23 + 61 * q^25 - 920 * q^27 - 124 * q^29 - 252 * q^31 - 400 * q^33 - 26 * q^37 - 120 * q^39 + 12 * q^41 + 832 * q^43 + 584 * q^45 + 396 * q^47 - 580 * q^51 + 450 * q^53 + 640 * q^55 - 520 * q^57 - 274 * q^59 + 576 * q^61 - 96 * q^65 + 476 * q^67 + 1280 * q^69 - 896 * q^71 + 158 * q^73 - 610 * q^75 + 936 * q^79 - 2629 * q^81 + 1060 * q^83 + 928 * q^85 - 620 * q^87 + 390 * q^89 + 2520 * q^93 + 208 * q^95 + 428 * q^97 - 5840 * q^99

Introduction

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