LMFDB - Embedded newform 312.4.m.a.181.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,4,Mod(181,312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

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

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

chi := DirichletCharacter("312.181");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	312.m (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.4085959218$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.6
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.80130 + 0.390824i) q^{2} +3.00000i q^{3} +(7.69451 - 2.18963i) q^{4} +14.7907 q^{5} +(-1.17247 - 8.40389i) q^{6} +0.217747i q^{7} +(-20.6988 + 9.14099i) q^{8} -9.00000 q^{9} +(-41.4331 + 5.78056i) q^{10} +43.4416 q^{11} +(6.56888 + 23.0835i) q^{12} +(23.9363 + 40.2995i) q^{13} +(-0.0851006 - 0.609973i) q^{14} +44.3721i q^{15} +(54.4111 - 33.6962i) q^{16} -16.1502 q^{17} +(25.2117 - 3.51742i) q^{18} +72.7567 q^{19} +(113.807 - 32.3861i) q^{20} -0.653240 q^{21} +(-121.693 + 16.9780i) q^{22} -83.4483 q^{23} +(-27.4230 - 62.0965i) q^{24} +93.7650 q^{25} +(-82.8028 - 103.536i) q^{26} -27.0000i q^{27} +(0.476784 + 1.67545i) q^{28} -128.661i q^{29} +(-17.3417 - 124.299i) q^{30} -306.050i q^{31} +(-139.252 + 115.658i) q^{32} +130.325i q^{33} +(45.2414 - 6.31187i) q^{34} +3.22063i q^{35} +(-69.2506 + 19.7066i) q^{36} +340.290 q^{37} +(-203.813 + 28.4351i) q^{38} +(-120.899 + 71.8090i) q^{39} +(-306.151 + 135.202i) q^{40} +401.502i q^{41} +(1.82992 - 0.255302i) q^{42} +32.3051i q^{43} +(334.262 - 95.1210i) q^{44} -133.116 q^{45} +(233.763 - 32.6136i) q^{46} +118.996i q^{47} +(101.089 + 163.233i) q^{48} +342.953 q^{49} +(-262.664 + 36.6456i) q^{50} -48.4505i q^{51} +(272.419 + 257.674i) q^{52} +486.003i q^{53} +(10.5522 + 75.6350i) q^{54} +642.533 q^{55} +(-1.99042 - 4.50711i) q^{56} +218.270i q^{57} +(50.2839 + 360.418i) q^{58} -241.321 q^{59} +(97.1584 + 341.422i) q^{60} +457.486i q^{61} +(119.612 + 857.338i) q^{62} -1.95972i q^{63} +(344.885 - 378.416i) q^{64} +(354.036 + 596.058i) q^{65} +(-50.9341 - 365.079i) q^{66} -121.806 q^{67} +(-124.268 + 35.3628i) q^{68} -250.345i q^{69} +(-1.25870 - 9.02193i) q^{70} +251.950i q^{71} +(186.290 - 82.2689i) q^{72} +66.4276i q^{73} +(-953.252 + 132.993i) q^{74} +281.295i q^{75} +(559.828 - 159.310i) q^{76} +9.45927i q^{77} +(310.608 - 248.408i) q^{78} -164.272 q^{79} +(804.778 - 498.391i) q^{80} +81.0000 q^{81} +(-156.917 - 1124.73i) q^{82} -311.484 q^{83} +(-5.02636 + 1.43035i) q^{84} -238.872 q^{85} +(-12.6256 - 90.4962i) q^{86} +385.984 q^{87} +(-899.192 + 397.100i) q^{88} -1009.04i q^{89} +(372.898 - 52.0251i) q^{90} +(-8.77509 + 5.21206i) q^{91} +(-642.094 + 182.721i) q^{92} +918.151 q^{93} +(-46.5064 - 333.342i) q^{94} +1076.12 q^{95} +(-346.975 - 417.757i) q^{96} +433.098i q^{97} +(-960.712 + 134.034i) q^{98} -390.975 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) $ 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−2.80130	+	0.390824i	−0.990408	+	0.138177i
$2$	−2.80130	+	0.390824i	−0.990408	+	0.138177i
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	7.69451	−	2.18963i	0.961814	−	0.273703i
$5$	14.7907			1.32292			0.661461	−	0.749980i	$-0.269937\pi$
$5$	14.7907			1.32292			0.661461	+	0.749980i	$0.269937\pi$
$6$	−1.17247	−	8.40389i	−0.0797766	−	0.571812i
$7$			0.217747i			0.0117572i	0.999983	+	0.00587861i	$0.00187123\pi$
$7$			0.217747i			0.0117572i	−0.999983	+	0.00587861i	$0.998129\pi$
$8$	−20.6988	+	9.14099i	−0.914768	+	0.403979i
$9$	−9.00000			−0.333333
$10$	−41.4331	+	5.78056i	−1.31023	+	0.182797i
$11$	43.4416			1.19074			0.595370	−	0.803451i	$-0.297005\pi$
$11$	43.4416			1.19074			0.595370	+	0.803451i	$0.297005\pi$
$12$	6.56888	+	23.0835i	0.158023	+	0.555304i
$13$	23.9363	+	40.2995i	0.510673	+	0.859775i
$13$	23.9363	+	40.2995i	0.510673	+	0.859775i
$14$	−0.0851006	−	0.609973i	−0.00162458	−	0.0116444i
$15$			44.3721i			0.763789i
$16$	54.4111	−	33.6962i	0.850173	−	0.526504i
$17$	−16.1502			−0.230411			−0.115206	−	0.993342i	$-0.536753\pi$
$17$	−16.1502			−0.230411			−0.115206	+	0.993342i	$0.536753\pi$
$18$	25.2117	−	3.51742i	0.330136	−	0.0460590i
$19$	72.7567			0.878502			0.439251	−	0.898364i	$-0.355244\pi$
$19$	72.7567			0.878502			0.439251	+	0.898364i	$0.355244\pi$
$20$	113.807	−	32.3861i	1.27240	−	0.362088i
$21$	−0.653240			−0.00678803
$22$	−121.693	+	16.9780i	−1.17932	+	0.164533i
$23$	−83.4483			−0.756529			−0.378265	−	0.925698i	$-0.623479\pi$
$23$	−83.4483			−0.756529			−0.378265	+	0.925698i	$0.623479\pi$
$24$	−27.4230	−	62.0965i	−0.233237	−	0.528142i
$25$	93.7650			0.750120
$26$	−82.8028	−	103.536i	−0.624576	−	0.780964i
$27$		−	27.0000i		−	0.192450i
$28$	0.476784	+	1.67545i	0.00321799	+	0.0113083i
$29$		−	128.661i		−	0.823855i	−0.911217	−	0.411928i	$-0.864856\pi$
$29$		−	128.661i		−	0.823855i	0.911217	−	0.411928i	$-0.135144\pi$
$30$	−17.3417	−	124.299i	−0.105538	−	0.756462i
$31$		−	306.050i		−	1.77317i	−0.462566	−	0.886585i	$-0.653071\pi$
$31$		−	306.050i		−	1.77317i	0.462566	−	0.886585i	$-0.346929\pi$
$32$	−139.252	+	115.658i	−0.769267	+	0.638928i
$33$			130.325i			0.687474i
$34$	45.2414	−	6.31187i	0.228201	−	0.0318376i
$35$			3.22063i			0.0155539i
$36$	−69.2506	+	19.7066i	−0.320605	+	0.0912345i
$37$	340.290			1.51198			0.755990	−	0.654583i	$-0.227156\pi$
$37$	340.290			1.51198			0.755990	+	0.654583i	$0.227156\pi$
$38$	−203.813	+	28.4351i	−0.870075	+	0.121389i
$39$	−120.899	+	71.8090i	−0.496391	+	0.294837i
$40$	−306.151	+	135.202i	−1.21017	+	0.534432i
$41$			401.502i			1.52937i	0.644405	+	0.764685i	$0.277105\pi$
$41$			401.502i			1.52937i	−0.644405	+	0.764685i	$0.722895\pi$
$42$	1.82992	−	0.255302i	0.00672292	−	0.000937951i
$43$			32.3051i			0.114569i	0.998358	+	0.0572847i	$0.0182443\pi$
$43$			32.3051i			0.114569i	−0.998358	+	0.0572847i	$0.981756\pi$
$44$	334.262	−	95.1210i	1.14527	−	0.325910i
$45$	−133.116			−0.440974
$46$	233.763	−	32.6136i	0.749272	−	0.104535i
$47$			118.996i			0.369305i	0.982804	+	0.184652i	$0.0591159\pi$
$47$			118.996i			0.369305i	−0.982804	+	0.184652i	$0.940884\pi$
$48$	101.089	+	163.233i	0.303977	+	0.490848i
$49$	342.953			0.999862
$50$	−262.664	+	36.6456i	−0.742925	+	0.103649i
$51$		−	48.4505i		−	0.133028i
$52$	272.419	+	257.674i	0.726496	+	0.687171i
$53$			486.003i			1.25958i	0.776766	+	0.629789i	$0.216859\pi$
$53$			486.003i			1.25958i	−0.776766	+	0.629789i	$0.783141\pi$
$54$	10.5522	+	75.6350i	0.0265922	+	0.190604i
$55$	642.533			1.57526
$56$	−1.99042	−	4.50711i	−0.00474966	−	0.0107551i
$57$			218.270i			0.507203i
$58$	50.2839	+	360.418i	0.113838	+	0.815952i
$59$	−241.321			−0.532498			−0.266249	−	0.963904i	$-0.585784\pi$
$59$	−241.321			−0.532498			−0.266249	+	0.963904i	$0.585784\pi$
$60$	97.1584	+	341.422i	0.209052	+	0.734623i
$61$			457.486i			0.960247i	0.877201	+	0.480124i	$0.159408\pi$
$61$			457.486i			0.960247i	−0.877201	+	0.480124i	$0.840592\pi$
$62$	119.612	+	857.338i	0.245012	+	1.75616i
$63$		−	1.95972i		−	0.00391907i
$64$	344.885	−	378.416i	0.673603	−	0.739094i
$65$	354.036	+	596.058i	0.675580	+	1.13741i
$66$	−50.9341	−	365.079i	−0.0949932	−	0.680880i
$67$	−121.806			−0.222104			−0.111052	−	0.993815i	$-0.535422\pi$
$67$	−121.806			−0.222104			−0.111052	+	0.993815i	$0.535422\pi$
$68$	−124.268	+	35.3628i	−0.221613	+	0.0630643i
$69$		−	250.345i		−	0.436782i
$70$	−1.25870	−	9.02193i	−0.00214919	−	0.0154047i
$71$			251.950i			0.421140i	0.977579	+	0.210570i	$0.0675319\pi$
$71$			251.950i			0.421140i	−0.977579	+	0.210570i	$0.932468\pi$
$72$	186.290	−	82.2689i	0.304923	−	0.134660i
$73$			66.4276i			0.106504i	0.998581	+	0.0532518i	$0.0169586\pi$
$73$			66.4276i			0.106504i	−0.998581	+	0.0532518i	$0.983041\pi$
$74$	−953.252	+	132.993i	−1.49748	+	0.208921i
$75$			281.295i			0.433082i
$76$	559.828	−	159.310i	0.844956	−	0.240449i
$77$			9.45927i			0.0139998i
$78$	310.608	−	248.408i	0.450890	−	0.360599i
$79$	−164.272			−0.233950			−0.116975	−	0.993135i	$-0.537320\pi$
$79$	−164.272			−0.233950			−0.116975	+	0.993135i	$0.537320\pi$
$80$	804.778	−	498.391i	1.12471	−	0.696523i
$81$	81.0000			0.111111
$82$	−156.917	−	1124.73i	−0.211324	−	1.51470i
$83$	−311.484			−0.411925			−0.205962	−	0.978560i	$-0.566032\pi$
$83$	−311.484			−0.411925			−0.205962	+	0.978560i	$0.566032\pi$
$84$	−5.02636	+	1.43035i	−0.00652883	+	0.00185791i
$85$	−238.872			−0.304816
$86$	−12.6256	−	90.4962i	−0.0158309	−	0.113470i
$87$	385.984			0.475653
$88$	−899.192	+	397.100i	−1.08925	+	0.481034i
$89$		−	1009.04i		−	1.20178i	−0.799333	−	0.600889i	$-0.794813\pi$
$89$		−	1009.04i		−	1.20178i	0.799333	−	0.600889i	$-0.205187\pi$
$90$	372.898	−	52.0251i	0.436744	−	0.0609325i
$91$	−8.77509	+	5.21206i	−0.0101086	+	0.00600409i
$92$	−642.094	+	182.721i	−0.727640	+	0.207065i
$93$	918.151			1.02374
$94$	−46.5064	−	333.342i	−0.0510295	−	0.365762i
$95$	1076.12			1.16219
$96$	−346.975	−	417.757i	−0.368885	−	0.444136i
$97$			433.098i			0.453345i	0.973971	+	0.226673i	$0.0727847\pi$
$97$			433.098i			0.453345i	−0.973971	+	0.226673i	$0.927215\pi$
$98$	−960.712	+	134.034i	−0.990271	+	0.138158i
$99$	−390.975			−0.396913
$100$	721.476	−	205.310i	0.721476	−	0.205310i
$101$			1615.63i			1.59169i	0.605499	+	0.795846i	$0.292974\pi$
$101$			1615.63i			1.59169i	−0.605499	+	0.795846i	$0.707026\pi$
$102$	18.9356	+	135.724i	0.0183814	+	0.131752i
$103$	1484.34			1.41996			0.709981	−	0.704221i	$-0.248703\pi$
$103$	1484.34			1.41996			0.709981	+	0.704221i	$0.248703\pi$
$104$	−863.832	−	615.352i	−0.814478	−	0.580194i
$105$	−9.66188			−0.00898003
$106$	−189.942	−	1361.44i	−0.174045	−	1.24750i
$107$			88.6747i			0.0801169i	0.999197	+	0.0400585i	$0.0127544\pi$
$107$			88.6747i			0.0801169i	−0.999197	+	0.0400585i	$0.987246\pi$
$108$	−59.1199	−	207.752i	−0.0526742	−	0.185101i
$109$	1348.39			1.18489			0.592444	−	0.805612i	$-0.298163\pi$
$109$	1348.39			1.18489			0.592444	+	0.805612i	$0.298163\pi$
$110$	−1799.92	+	251.117i	−1.56015	+	0.217664i
$111$			1020.87i			0.872942i
$112$	7.33724	+	11.8478i	0.00619022	+	0.00999567i
$113$	−1348.96			−1.12300			−0.561501	−	0.827476i	$-0.689776\pi$
$113$	−1348.96			−1.12300			−0.561501	+	0.827476i	$0.689776\pi$
$114$	−85.3052	−	611.439i	−0.0700839	−	0.502338i
$115$	−1234.26			−1.00083
$116$	−281.720	−	989.986i	−0.225492	−	0.792396i
$117$	−215.427	−	362.696i	−0.170224	−	0.286592i
$118$	676.012	−	94.3142i	0.527390	−	0.0735790i
$119$		−	3.51665i		−	0.00270900i
$120$	−405.605	−	918.452i	−0.308554	−	0.698690i
$121$	556.175			0.417863
$122$	−178.797	−	1281.55i	−0.132684	−	0.951036i
$123$	−1204.51			−0.882982
$124$	−670.136	−	2354.91i	−0.485323	−	1.70546i
$125$	−461.987			−0.330571
$126$	0.765906	+	5.48976i	0.000541526	+	0.00388148i
$127$	221.289			0.154616			0.0773080	−	0.997007i	$-0.475368\pi$
$127$	221.289			0.154616			0.0773080	+	0.997007i	$0.475368\pi$
$128$	−818.229	+	1194.84i	−0.565015	+	0.825080i
$129$	−96.9153			−0.0661467
$130$	−1224.71	−	1531.37i	−0.826264	−	1.03315i
$131$		−	2109.42i		−	1.40688i	−0.710756	−	0.703439i	$-0.751647\pi$
$131$		−	2109.42i		−	1.40688i	0.710756	−	0.703439i	$-0.248353\pi$
$132$	285.363	+	1002.79i	0.188164	+	0.661223i
$133$			15.8425i			0.0103287i
$134$	341.215	−	47.6047i	0.219974	−	0.0306897i
$135$		−	399.349i		−	0.254596i
$136$	334.290	−	147.629i	0.210773	−	0.0930812i
$137$			795.708i			0.496219i	0.968732	+	0.248109i	$0.0798092\pi$
$137$			795.708i			0.496219i	−0.968732	+	0.248109i	$0.920191\pi$
$138$	97.8408	+	701.290i	0.0603533	+	0.432592i
$139$			2231.81i			1.36187i	0.732344	+	0.680935i	$0.238426\pi$
$139$			2231.81i			1.36187i	−0.732344	+	0.680935i	$0.761574\pi$
$140$	7.05197	+	24.7812i	0.00425715	+	0.0149599i
$141$	−356.987			−0.213218
$142$	−98.4679	−	705.785i	−0.0581919	−	0.417100i
$143$	1039.83	+	1750.68i	0.608079	+	1.02377i
$144$	−489.700	+	303.266i	−0.283391	+	0.175501i
$145$		−	1902.99i		−	1.08990i
$146$	−25.9615	−	186.083i	−0.0147164	−	0.105482i
$147$			1028.86i			0.577270i
$148$	2618.36	−	745.107i	1.45424	−	0.413834i
$149$	1185.70			0.651924			0.325962	−	0.945383i	$-0.394312\pi$
$149$	1185.70			0.651924			0.325962	+	0.945383i	$0.394312\pi$
$150$	−109.937	−	787.991i	−0.0598421	−	0.428928i
$151$		−	2242.51i		−	1.20856i	−0.796772	−	0.604280i	$-0.793461\pi$
$151$		−	2242.51i		−	1.20856i	0.796772	−	0.604280i	$-0.206539\pi$
$152$	−1505.98	+	665.069i	−0.803626	+	0.354896i
$153$	145.352			0.0768038
$154$	−3.69691	−	26.4982i	−0.00193445	−	0.0138655i
$155$		−	4526.70i		−	2.34576i
$156$	−773.021	+	817.258i	−0.396738	+	0.419443i
$157$		−	2516.38i		−	1.27917i	−0.768721	−	0.639584i	$-0.779107\pi$
$157$		−	2516.38i		−	1.27917i	0.768721	−	0.639584i	$-0.220893\pi$
$158$	460.175	−	64.2015i	0.231706	−	0.0323265i
$159$	−1458.01			−0.727218
$160$	−2059.64	+	1710.67i	−1.01768	+	0.845251i
$161$		−	18.1706i		−	0.00889468i
$162$	−226.905	+	31.6567i	−0.110045	+	0.0153530i
$163$	−3173.77			−1.52509			−0.762543	−	0.646937i	$-0.776049\pi$
$163$	−3173.77			−1.52509			−0.762543	+	0.646937i	$0.776049\pi$
$164$	879.141	+	3089.37i	0.418594	+	1.47097i
$165$			1927.60i			0.909474i
$166$	872.558	−	121.735i	0.407974	−	0.0569186i
$167$		−	353.974i		−	0.164020i	−0.996632	−	0.0820101i	$-0.973866\pi$
$167$		−	353.974i		−	0.164020i	0.996632	−	0.0820101i	$-0.0261340\pi$
$168$	13.5213	−	5.97126i	0.00620948	−	0.00274222i
$169$	−1051.10	+	1929.25i	−0.478426	+	0.878128i
$170$	669.152	−	93.3571i	0.301892	−	0.0421186i
$171$	−654.811			−0.292834
$172$	70.7361	+	248.572i	0.0313580	+	0.110194i
$173$		−	1515.74i		−	0.666126i	−0.942905	−	0.333063i	$-0.891918\pi$
$173$		−	1515.74i		−	0.666126i	0.942905	−	0.333063i	$-0.108082\pi$
$174$	−1081.25	+	150.852i	−0.471090	+	0.0657244i
$175$			20.4170i			0.00881933i
$176$	2363.71	−	1463.82i	1.01234	−	0.626929i
$177$		−	723.964i		−	0.307438i
$178$	394.358	+	2826.62i	0.166058	+	1.19025i
$179$		−	4704.22i		−	1.96430i	−0.188094	−	0.982151i	$-0.560231\pi$
$179$		−	4704.22i		−	1.96430i	0.188094	−	0.982151i	$-0.439769\pi$
$180$	−1024.27	+	291.475i	−0.424135	+	0.120696i
$181$			1503.98i			0.617623i	0.951123	+	0.308812i	$0.0999313\pi$
$181$			1503.98i			0.617623i	−0.951123	+	0.308812i	$0.900069\pi$
$182$	22.5446	−	18.0300i	0.00918197	−	0.00734327i
$183$	−1372.46			−0.554399
$184$	1727.28	−	762.800i	0.692049	−	0.305622i
$185$	5033.12			2.00023
$186$	−2572.01	+	358.835i	−1.01392	+	0.141457i
$187$	−701.590			−0.274360
$188$	260.556	+	915.615i	0.101080	+	0.355202i
$189$	5.87916			0.00226268
$190$	−3014.54	+	420.575i	−1.15104	+	0.160588i
$191$	−1874.17			−0.710002			−0.355001	−	0.934866i	$-0.615519\pi$
$191$	−1874.17			−0.710002			−0.355001	+	0.934866i	$0.615519\pi$
$192$	1135.25	+	1034.65i	0.426716	+	0.388905i
$193$		−	533.681i		−	0.199043i	−0.995035	−	0.0995213i	$-0.968269\pi$
$193$		−	533.681i		−	0.199043i	0.995035	−	0.0995213i	$-0.0317311\pi$
$194$	−169.265	−	1213.24i	−0.0626419	−	0.448997i
$195$	−1788.18	+	1062.11i	−0.656687	+	0.390046i
$196$	2638.85	−	750.938i	0.961681	−	0.273666i
$197$	3695.72			1.33659			0.668297	−	0.743894i	$-0.267023\pi$
$197$	3695.72			1.33659			0.668297	+	0.743894i	$0.267023\pi$
$198$	1095.24	−	152.802i	0.393106	−	0.0548444i
$199$	−2806.99			−0.999909			−0.499955	−	0.866052i	$-0.666650\pi$
$199$	−2806.99			−0.999909			−0.499955	+	0.866052i	$0.666650\pi$
$200$	−1940.83	+	857.106i	−0.686186	+	0.303033i
$201$		−	365.418i		−	0.128232i
$202$	−631.426	−	4525.85i	−0.219935	−	1.57642i
$203$	28.0156			0.00968624
$204$	−106.089	−	372.803i	−0.0364102	−	0.127948i
$205$			5938.51i			2.02324i
$206$	−4158.07	+	580.115i	−1.40634	+	0.196206i
$207$	751.035			0.252176
$208$	2660.34	+	1386.18i	0.886835	+	0.462086i
$209$	3160.67			1.04607
$210$	27.0658	−	3.77610i	0.00889389	−	0.00124084i
$211$		−	2762.68i		−	0.901377i	−0.892681	−	0.450688i	$-0.851179\pi$
$211$		−	2762.68i		−	0.901377i	0.892681	−	0.450688i	$-0.148821\pi$
$212$	1064.17	+	3739.56i	0.344751	+	1.21148i
$213$	−755.849			−0.243145
$214$	−34.6562	−	248.404i	−0.0110703	−	0.0793484i
$215$			477.816i			0.151566i
$216$	246.807	+	558.869i	0.0777457	+	0.176047i
$217$	66.6415			0.0208475
$218$	−3777.25	+	526.985i	−1.17352	+	0.163724i
$219$	−199.283			−0.0614899
$220$	4943.97	−	1406.91i	1.51510	−	0.431153i
$221$	−386.576	−	650.844i	−0.117665	−	0.198102i
$222$	−398.980	−	2859.76i	−0.120621	−	0.864569i
$223$		−	3098.36i		−	0.930409i	−0.885203	−	0.465205i	$-0.845981\pi$
$223$		−	3098.36i		−	0.930409i	0.885203	−	0.465205i	$-0.154019\pi$
$224$	−25.1842	−	30.3217i	−0.00751201	−	0.00904444i
$225$	−843.885			−0.250040
$226$	3778.83	−	527.205i	1.11223	−	0.155173i
$227$	−1946.86			−0.569241			−0.284621	−	0.958640i	$-0.591868\pi$
$227$	−1946.86			−0.569241			−0.284621	+	0.958640i	$0.591868\pi$
$228$	477.930	+	1679.48i	0.138823	+	0.487835i
$229$	6878.01			1.98477			0.992384	−	0.123180i	$-0.0393094\pi$
$229$	6878.01			1.98477			0.992384	+	0.123180i	$0.0393094\pi$
$230$	3457.52	−	482.378i	0.991228	−	0.138292i
$231$	−28.3778			−0.00808278
$232$	1176.09	+	2663.14i	0.332820	+	0.753637i
$233$	−1655.20			−0.465388			−0.232694	−	0.972550i	$-0.574754\pi$
$233$	−1655.20			−0.465388			−0.232694	+	0.972550i	$0.574754\pi$
$234$	745.225	+	931.824i	0.208192	+	0.260321i
$235$			1760.03i			0.488561i
$236$	−1856.85	+	528.404i	−0.512164	+	0.145746i
$237$		−	492.816i		−	0.135071i
$238$	1.37439	+	9.85117i	0.000374321	+	0.00268301i
$239$			1933.18i			0.523208i	0.965175	+	0.261604i	$0.0842515\pi$
$239$			1933.18i			0.523208i	−0.965175	+	0.261604i	$0.915748\pi$
$240$	1495.17	+	2414.33i	0.402138	+	0.649353i
$241$		−	1476.23i		−	0.394575i	−0.980346	−	0.197288i	$-0.936787\pi$
$241$		−	1476.23i		−	0.394575i	0.980346	−	0.197288i	$-0.0632133\pi$
$242$	−1558.01	+	217.367i	−0.413855	+	0.0577391i
$243$			243.000i			0.0641500i
$244$	1001.72	+	3520.13i	0.262823	+	0.923580i
$245$	5072.51			1.32274
$246$	3374.18	−	470.750i	0.874512	−	0.122008i
$247$	1741.53	+	2932.06i	0.448627	+	0.755314i
$248$	2797.60	+	6334.89i	0.716323	+	1.62204i
$249$		−	934.451i		−	0.237825i
$250$	1294.16	−	180.556i	0.327400	−	0.0456774i
$251$			6677.27i			1.67915i	0.543247	+	0.839573i	$0.317195\pi$
$251$			6677.27i			1.67915i	−0.543247	+	0.839573i	$0.682805\pi$
$252$	−4.29106	−	15.0791i	−0.00107266	−	0.00376942i
$253$	−3625.13			−0.900830
$254$	−619.896	+	86.4850i	−0.153133	+	0.0213644i
$255$		−	716.617i		−	0.175986i
$256$	1825.13	−	3666.90i	0.445588	−	0.895238i
$257$	−6716.94			−1.63032			−0.815158	−	0.579238i	$-0.803350\pi$
$257$	−6716.94			−1.63032			−0.815158	+	0.579238i	$0.803350\pi$
$258$	271.489	−	37.8768i	0.0655122	−	0.00913996i
$259$			74.0969i			0.0177767i
$260$	4029.28	+	3811.17i	0.961097	+	0.909073i
$261$			1157.95i			0.274618i
$262$	824.412	+	5909.11i	0.194398	+	1.39338i
$263$	−1746.72			−0.409534			−0.204767	−	0.978811i	$-0.565644\pi$
$263$	−1746.72			−0.409534			−0.204767	+	0.978811i	$0.565644\pi$
$264$	−1191.30	−	2697.58i	−0.277725	−	0.628880i
$265$			7188.33i			1.66632i
$266$	−6.19164	−	44.3796i	−0.00142720	−	0.0102297i
$267$	3027.12			0.693846
$268$	−937.238	+	266.710i	−0.213623	+	0.0607906i
$269$		−	6634.71i		−	1.50381i	−0.659270	−	0.751906i	$-0.729135\pi$
$269$		−	6634.71i		−	1.50381i	0.659270	−	0.751906i	$-0.270865\pi$
$270$	156.075	+	1118.69i	0.0351794	+	0.252154i
$271$		−	7302.89i		−	1.63697i	−0.574527	−	0.818486i	$-0.694814\pi$
$271$		−	7302.89i		−	1.63697i	0.574527	−	0.818486i	$-0.305186\pi$
$272$	−878.748	+	544.200i	−0.195889	+	0.121312i
$273$	−15.6362	−	26.3253i	−0.00346646	−	0.00583618i
$274$	−310.982	−	2229.01i	−0.0685661	−	0.491459i
$275$	4073.31			0.893199
$276$	−548.162	−	1926.28i	−0.119549	−	0.420103i
$277$			6130.45i			1.32976i	0.746951	+	0.664879i	$0.231517\pi$
$277$			6130.45i			1.32976i	−0.746951	+	0.664879i	$0.768483\pi$
$278$	−872.246	−	6251.97i	−0.188179	−	1.34881i
$279$			2754.45i			0.591057i
$280$	−29.4397	−	66.6633i	−0.00628343	−	0.0142282i
$281$		−	6601.16i		−	1.40140i	−0.713458	−	0.700698i	$-0.752872\pi$
$281$		−	6601.16i		−	1.40140i	0.713458	−	0.700698i	$-0.247128\pi$
$282$	1000.03	−	139.519i	0.211173	−	0.0294619i
$283$		−	4058.19i		−	0.852417i	−0.904625	−	0.426209i	$-0.859849\pi$
$283$		−	4058.19i		−	0.852417i	0.904625	−	0.426209i	$-0.140151\pi$
$284$	551.675	+	1938.63i	0.115267	+	0.405058i
$285$			3228.37i			0.670990i
$286$	−3597.09	−	4497.77i	−0.743707	−	0.929926i
$287$	−87.4258			−0.0179811
$288$	1253.27	−	1040.92i	0.256422	−	0.212976i
$289$	−4652.17			−0.946911
$290$	743.735	+	5330.84i	0.150599	+	1.07944i
$291$	−1299.30			−0.261739
$292$	145.452	+	511.128i	0.0291504	+	0.102437i
$293$	5382.33			1.07317			0.536585	−	0.843846i	$-0.319714\pi$
$293$	5382.33			1.07317			0.536585	+	0.843846i	$0.319714\pi$
$294$	−402.102	−	2882.13i	−0.0797656	−	0.571733i
$295$	−3569.31			−0.704452
$296$	−7043.60	+	3110.58i	−1.38311	+	0.610808i
$297$		−	1172.92i		−	0.229158i
$298$	−3321.51	+	463.402i	−0.645670	+	0.0900810i
$299$	−1997.45	−	3362.93i	−0.386339	−	0.650445i
$300$	615.931	+	2164.43i	0.118536	+	0.416545i
$301$	−7.03433			−0.00134702
$302$	876.426	+	6281.93i	0.166995	+	1.19697i
$303$	−4846.88			−0.918964
$304$	3958.77	−	2451.63i	0.746879	−	0.462534i
$305$			6766.54i			1.27033i
$306$	−407.173	+	56.8069i	−0.0760670	+	0.0106125i
$307$	6340.17			1.17867			0.589336	−	0.807888i	$-0.299389\pi$
$307$	6340.17			1.17867			0.589336	+	0.807888i	$0.299389\pi$
$308$	20.7123	+	72.7845i	0.00383179	+	0.0134652i
$309$			4453.01i			0.819816i
$310$	1769.14	+	12680.6i	0.324131	+	2.32326i
$311$	−5140.97			−0.937356			−0.468678	−	0.883369i	$-0.655270\pi$
$311$	−5140.97			−0.937356			−0.468678	+	0.883369i	$0.655270\pi$
$312$	1846.05	−	2591.50i	0.334975	−	0.470239i
$313$	−10059.6			−1.81662			−0.908309	−	0.418300i	$-0.862626\pi$
$313$	−10059.6			−1.81662			−0.908309	+	0.418300i	$0.862626\pi$
$314$	983.463	+	7049.14i	0.176752	+	1.26690i
$315$		−	28.9857i		−	0.00518462i
$316$	−1263.99	+	359.695i	−0.225016	+	0.0640329i
$317$	3866.52			0.685064			0.342532	−	0.939506i	$-0.388716\pi$
$317$	3866.52			0.685064			0.342532	+	0.939506i	$0.388716\pi$
$318$	4084.31	−	569.825i	0.720242	−	0.100485i
$319$		−	5589.26i		−	0.980998i
$320$	5101.09	−	5597.04i	0.891123	−	0.977763i
$321$	−266.024			−0.0462555
$322$	7.10150	+	50.9012i	0.00122904	+	0.00880936i
$323$	−1175.03			−0.202417
$324$	623.256	−	177.360i	0.106868	−	0.0304115i
$325$	2244.39	+	3778.69i	0.383066	+	0.644935i
$326$	8890.67	−	1240.39i	1.51046	−	0.210732i
$327$			4045.18i			0.684095i
$328$	−3670.13	−	8310.64i	−0.617833	−	1.39902i
$329$	−25.9109			−0.00434199
$330$	−753.351	−	5399.77i	−0.125669	−	0.900750i
$331$	−2632.41			−0.437132			−0.218566	−	0.975822i	$-0.570138\pi$
$331$	−2632.41			−0.437132			−0.218566	+	0.975822i	$0.570138\pi$
$332$	−2396.71	+	682.033i	−0.396195	+	0.112745i
$333$	−3062.61			−0.503993
$334$	138.342	+	991.587i	0.0226638	+	0.162447i
$335$	−1801.60			−0.293826
$336$	−35.5435	+	22.0117i	−0.00577100	+	0.00357392i
$337$	−2056.36			−0.332394			−0.166197	−	0.986093i	$-0.553149\pi$
$337$	−2056.36			−0.332394			−0.166197	+	0.986093i	$0.553149\pi$
$338$	2190.45	−	5815.19i	0.352500	−	0.935812i
$339$		−	4046.87i		−	0.648365i
$340$	−1838.01	+	523.042i	−0.293176	+	0.0834291i
$341$		−	13295.3i		−	2.11139i
$342$	1834.32	−	255.916i	0.290025	−	0.0404630i
$343$			149.364i			0.0235128i
$344$	−295.301	−	668.679i	−0.0462836	−	0.104804i
$345$		−	3702.78i		−	0.577829i
$346$	592.389	+	4246.04i	0.0920434	+	0.659736i
$347$			3256.42i			0.503787i	0.967755	+	0.251893i	$0.0810532\pi$
$347$			3256.42i			0.503787i	−0.967755	+	0.251893i	$0.918947\pi$
$348$	2969.96	−	845.161i	0.457490	−	0.130188i
$349$	−9918.73			−1.52131			−0.760655	−	0.649156i	$-0.775122\pi$
$349$	−9918.73			−1.52131			−0.760655	+	0.649156i	$0.775122\pi$
$350$	−7.97946	−	57.1941i	−0.00121863	−	0.00873473i
$351$	1088.09	−	646.281i	0.165464	−	0.0982791i
$352$	−6049.34	+	5024.38i	−0.915997	+	0.760797i
$353$		−	3799.70i		−	0.572911i	−0.958093	−	0.286456i	$-0.907523\pi$
$353$		−	3799.70i		−	0.572911i	0.958093	−	0.286456i	$-0.0924771\pi$
$354$	282.943	+	2028.04i	0.0424809	+	0.304489i
$355$			3726.51i			0.557134i
$356$	−2209.42	−	7764.08i	−0.328930	−	1.15589i
$357$	10.5499			0.00156404
$358$	1838.52	+	13177.9i	0.271422	+	1.94546i
$359$		−	9293.42i		−	1.36626i	−0.730296	−	0.683131i	$-0.760618\pi$
$359$		−	9293.42i		−	1.36626i	0.730296	−	0.683131i	$-0.239382\pi$
$360$	2755.36	−	1216.82i	0.403389	−	0.178144i
$361$	−1565.46			−0.228234
$362$	−587.791	−	4213.09i	−0.0853414	−	0.611699i
$363$			1668.53i			0.241253i
$364$	−56.1076	+	59.3184i	−0.00807922	+	0.00854157i
$365$			982.511i			0.140896i
$366$	3844.66	−	536.390i	0.549081	−	0.0766053i
$367$	13669.3			1.94423			0.972116	−	0.234502i	$-0.0753461\pi$
$367$	13669.3			1.94423			0.972116	+	0.234502i	$0.0753461\pi$
$368$	−4540.51	+	2811.89i	−0.643181	+	0.398315i
$369$		−	3613.52i		−	0.509790i
$370$	−14099.3	+	1967.07i	−1.98104	+	0.276386i
$371$	−105.826			−0.0148091
$372$	7064.73	−	2010.41i	0.984648	−	0.280201i
$373$		−	9533.65i		−	1.32341i	−0.749762	−	0.661707i	$-0.769832\pi$
$373$		−	9533.65i		−	1.32341i	0.749762	−	0.661707i	$-0.230168\pi$
$374$	1965.36	−	274.198i	0.271728	−	0.0379103i
$375$		−	1385.96i		−	0.190855i
$376$	−1087.74	−	2463.08i	−0.149191	−	0.337828i
$377$	5184.99	−	3079.68i	0.708330	−	0.420721i
$378$	−16.4693	+	2.29772i	−0.00224097	+	0.000312650i
$379$	−12047.2			−1.63278			−0.816390	−	0.577501i	$-0.804028\pi$
$379$	−12047.2			−1.63278			−0.816390	+	0.577501i	$0.804028\pi$
$380$	8280.25	−	2356.31i	1.11781	−	0.318095i
$381$			663.867i			0.0892675i
$382$	5250.11	−	732.471i	0.703191	−	0.0981060i
$383$			6788.79i			0.905721i	0.891581	+	0.452860i	$0.149596\pi$
$383$			6788.79i			0.905721i	−0.891581	+	0.452860i	$0.850404\pi$
$384$	−3584.53	−	2454.69i	−0.476360	−	0.326212i
$385$			139.909i			0.0185206i
$386$	208.575	+	1495.00i	0.0275031	+	0.197133i
$387$		−	290.746i		−	0.0381898i
$388$	948.324	+	3332.48i	0.124082	+	0.436034i
$389$			626.526i			0.0816610i	0.999166	+	0.0408305i	$0.0130004\pi$
$389$			626.526i			0.0816610i	−0.999166	+	0.0408305i	$0.987000\pi$
$390$	4594.11	−	3674.14i	0.596492	−	0.477044i
$391$	1347.70			0.174313
$392$	−7098.72	+	3134.93i	−0.914642	+	0.403923i
$393$	6328.26			0.812261
$394$	−10352.8	+	1444.38i	−1.32377	+	0.184687i
$395$	−2429.70			−0.309497
$396$	−3008.36	+	856.089i	−0.381757	+	0.108637i
$397$	−6987.59			−0.883368			−0.441684	−	0.897171i	$-0.645619\pi$
$397$	−6987.59			−0.883368			−0.441684	+	0.897171i	$0.645619\pi$
$398$	7863.20	−	1097.04i	0.990318	−	0.138165i
$399$	−47.5276			−0.00596330
$400$	5101.86	−	3159.53i	0.637732	−	0.394941i
$401$			1330.10i			0.165641i	0.996564	+	0.0828204i	$0.0263928\pi$
$401$			1330.10i			0.165641i	−0.996564	+	0.0828204i	$0.973607\pi$
$402$	142.814	+	1023.64i	0.0177187	+	0.127002i
$403$	12333.7	−	7325.73i	1.52453	−	0.905510i
$404$	3537.62	+	12431.5i	0.435652	+	1.53091i
$405$	1198.05			0.146991
$406$	−78.4799	+	10.9492i	−0.00959333	+	0.00133842i
$407$	14782.7			1.80038
$408$	442.886	+	1002.87i	0.0537405	+	0.121690i
$409$			4071.81i			0.492270i	0.969236	+	0.246135i	$0.0791606\pi$
$409$			4071.81i			0.492270i	−0.969236	+	0.246135i	$0.920839\pi$
$410$	−2320.91	−	16635.5i	−0.279565	−	2.00383i
$411$	−2387.12			−0.286492
$412$	11421.3	−	3250.14i	1.36574	−	0.388648i
$413$		−	52.5469i		−	0.00626069i
$414$	−2103.87	+	293.522i	−0.249757	+	0.0348450i
$415$	−4607.06			−0.544944
$416$	−7994.16	−	2843.36i	−0.942178	−	0.335113i
$417$	−6695.44			−0.786276
$418$	−8853.98	+	1235.27i	−1.03603	+	0.144543i
$419$		−	6626.33i		−	0.772596i	−0.922374	−	0.386298i	$-0.873754\pi$
$419$		−	6626.33i		−	0.772596i	0.922374	−	0.386298i	$-0.126246\pi$
$420$	−74.3435	+	21.1559i	−0.00863712	+	0.00245786i
$421$	−3778.98			−0.437474			−0.218737	−	0.975784i	$-0.570194\pi$
$421$	−3778.98			−0.437474			−0.218737	+	0.975784i	$0.570194\pi$
$422$	1079.72	+	7739.07i	0.124550	+	0.892730i
$423$		−	1070.96i		−	0.123102i
$424$	−4442.55	−	10059.7i	−0.508843	−	1.15222i
$425$	−1514.32			−0.172836
$426$	2117.36	−	295.404i	0.240813	−	0.0335971i
$427$	−99.6161			−0.0112898
$428$	194.165	+	682.309i	0.0219283	+	0.0770576i
$429$	−5252.03	+	3119.50i	−0.591073	+	0.351075i
$430$	−186.742	−	1338.50i	−0.0209430	−	0.150112i
$431$			5521.55i			0.617085i	0.951211	+	0.308543i	$0.0998412\pi$
$431$			5521.55i			0.617085i	−0.951211	+	0.308543i	$0.900159\pi$
$432$	−909.798	−	1469.10i	−0.101326	−	0.163616i
$433$	−2290.27			−0.254188			−0.127094	−	0.991891i	$-0.540565\pi$
$433$	−2290.27			−0.254188			−0.127094	+	0.991891i	$0.540565\pi$
$434$	−186.682	+	26.0451i	−0.0206476	+	0.00288065i
$435$	5708.97			0.629251
$436$	10375.2	−	2952.48i	1.13964	−	0.324308i
$437$	−6071.42			−0.664612
$438$	558.250	−	77.8845i	0.0609000	−	0.00849649i
$439$	3708.61			0.403194			0.201597	−	0.979469i	$-0.435387\pi$
$439$	3708.61			0.403194			0.201597	+	0.979469i	$0.435387\pi$
$440$	−13299.7	+	5873.38i	−1.44099	+	0.636370i
$441$	−3086.57			−0.333287
$442$	1337.28	+	1672.12i	0.143909	+	0.179943i
$443$		−	1552.41i		−	0.166495i	−0.996529	−	0.0832476i	$-0.973471\pi$
$443$		−	1552.41i		−	0.166495i	0.996529	−	0.0832476i	$-0.0265292\pi$
$444$	2235.32	+	7855.09i	0.238927	+	0.839608i
$445$		−	14924.4i		−	1.58986i
$446$	1210.91	+	8679.41i	0.128561	+	0.921484i
$447$			3557.11i			0.376388i
$448$	82.3988	+	75.0975i	0.00868969	+	0.00791969i
$449$		−	13095.1i		−	1.37638i	−0.725531	−	0.688190i	$-0.758406\pi$
$449$		−	13095.1i		−	1.37638i	0.725531	−	0.688190i	$-0.241594\pi$
$450$	2363.97	−	329.811i	0.247642	−	0.0345498i
$451$			17441.9i			1.82108i
$452$	−10379.6	+	2953.71i	−1.08012	+	0.307369i
$453$	6727.52			0.697763
$454$	5453.73	−	760.880i	0.563781	−	0.0786561i
$455$	−129.790	+	77.0901i	−0.0133728	+	0.00794294i
$456$	−1995.21	−	4517.94i	−0.204899	−	0.463974i
$457$			11281.8i			1.15480i	0.816462	+	0.577399i	$0.195932\pi$
$457$			11281.8i			1.15480i	−0.816462	+	0.577399i	$0.804068\pi$
$458$	−19267.4	+	2688.09i	−1.96573	+	0.274250i
$459$			436.055i			0.0443427i
$460$	−9497.02	+	2702.57i	−0.962611	+	0.273930i
$461$	−1825.45			−0.184425			−0.0922123	−	0.995739i	$-0.529394\pi$
$461$	−1825.45			−0.184425			−0.0922123	+	0.995739i	$0.529394\pi$
$462$	79.4947	−	11.0907i	0.00800525	−	0.00111686i
$463$		−	8151.83i		−	0.818246i	−0.912479	−	0.409123i	$-0.865835\pi$
$463$		−	8151.83i		−	0.818246i	0.912479	−	0.409123i	$-0.134165\pi$
$464$	−4335.40	−	7000.60i	−0.433763	−	0.700419i
$465$	13580.1			1.35433
$466$	4636.69	−	646.890i	0.460924	−	0.0643060i
$467$			12778.0i			1.26616i	0.774088	+	0.633078i	$0.218209\pi$
$467$			12778.0i			1.26616i	−0.774088	+	0.633078i	$0.781791\pi$
$468$	−2451.78	−	2319.06i	−0.242165	−	0.229057i
$469$		−	26.5229i		−	0.00261133i
$470$	−687.863	−	4930.37i	−0.0675079	−	0.483874i
$471$	7549.15			0.738528
$472$	4995.07	−	2205.92i	0.487112	−	0.215118i
$473$			1403.39i			0.136422i
$474$	192.604	+	1380.52i	0.0186637	+	0.133775i
$475$	6822.04			0.658982
$476$	−7.70014	−	27.0589i	−0.000741461	−	0.00260555i
$477$		−	4374.03i		−	0.419859i
$478$	−755.532	−	5415.40i	−0.0722954	−	0.518190i
$479$			8119.97i			0.774553i	0.921964	+	0.387277i	$0.126584\pi$
$479$			8119.97i			0.774553i	−0.921964	+	0.387277i	$0.873416\pi$
$480$	−5132.00	−	6178.92i	−0.488006	−	0.587558i
$481$	8145.29	+	13713.5i	0.772127	+	1.29996i
$482$	576.948	+	4135.37i	0.0545213	+	0.390790i
$483$	54.5118			0.00513534
$484$	4279.50	−	1217.82i	0.401906	−	0.114370i
$485$			6405.83i			0.599740i
$486$	−94.9702	−	680.715i	−0.00886407	−	0.0635347i
$487$			929.534i			0.0864912i	0.999064	+	0.0432456i	$0.0137698\pi$
$487$			929.534i			0.0864912i	−0.999064	+	0.0432456i	$0.986230\pi$
$488$	−4181.88	−	9469.43i	−0.387919	−	0.878404i
$489$		−	9521.32i		−	0.880509i
$490$	−14209.6	+	1982.46i	−1.31005	+	0.182772i
$491$		−	5954.02i		−	0.547253i	−0.961836	−	0.273627i	$-0.911777\pi$
$491$		−	5954.02i		−	0.547253i	0.961836	−	0.273627i	$-0.0882232\pi$
$492$	−9268.10	+	2637.42i	−0.849264	+	0.241675i
$493$			2077.90i			0.189825i
$494$	−6024.46	−	7532.94i	−0.548691	−	0.686079i
$495$	−5782.79			−0.525085
$496$	−10312.7	−	16652.5i	−0.933580	−	1.50750i
$497$	−54.8612			−0.00495143
$498$	365.206	+	2617.67i	0.0328620	+	0.235544i
$499$	−997.844			−0.0895183			−0.0447591	−	0.998998i	$-0.514252\pi$
$499$	−997.844			−0.0895183			−0.0447591	+	0.998998i	$0.514252\pi$
$500$	−3554.77	+	1011.58i	−0.317948	+	0.0904784i
$501$	1061.92			0.0946971
$502$	−2609.64	−	18705.0i	−0.232020	−	1.66304i
$503$	−10659.5			−0.944893			−0.472447	−	0.881359i	$-0.656629\pi$
$503$	−10659.5			−0.944893			−0.472447	+	0.881359i	$0.656629\pi$
$504$	17.9138	+	40.5640i	0.00158322	+	0.00358504i
$505$			23896.3i			2.10568i
$506$	10155.1	−	1416.79i	0.892189	−	0.124474i
$507$	−5787.74	−	3153.31i	−0.506987	−	0.276220i
$508$	1702.71	−	484.540i	0.148712	−	0.0423189i
$509$	−9446.08			−0.822574			−0.411287	−	0.911506i	$-0.634921\pi$
$509$	−9446.08			−0.822574			−0.411287	+	0.911506i	$0.634921\pi$
$510$	280.071	+	2007.46i	0.0243172	+	0.174297i
$511$	−14.4644			−0.00125219
$512$	−3679.61	+	10985.4i	−0.317612	+	0.948221i
$513$		−	1964.43i		−	0.169068i
$514$	18816.1	−	2625.14i	1.61468	−	0.225272i
$515$	21954.4			1.87850
$516$	−745.716	+	212.208i	−0.0636208	+	0.0181046i
$517$			5169.37i			0.439746i
$518$	−28.9589	−	207.567i	−0.00245633	−	0.0176062i
$519$	4547.23			0.384588
$520$	−12776.7	−	9101.49i	−1.07749	−	0.767551i
$521$	22602.3			1.90063			0.950313	−	0.311296i	$-0.100763\pi$
$521$	22602.3			1.90063			0.950313	+	0.311296i	$0.100763\pi$
$522$	−452.555	−	3243.76i	−0.0379460	−	0.271984i
$523$			15055.5i			1.25876i	0.777099	+	0.629379i	$0.216691\pi$
$523$			15055.5i			1.25876i	−0.777099	+	0.629379i	$0.783309\pi$
$524$	−4618.84	−	16231.0i	−0.385067	−	1.35315i
$525$	−61.2511			−0.00509184
$526$	4893.09	−	682.661i	0.405606	−	0.0565883i
$527$			4942.77i			0.408558i
$528$	4391.46	+	7091.12i	0.361958	+	0.584472i
$529$	−5203.38			−0.427664
$530$	−2809.37	−	20136.6i	−0.230248	−	1.65034i
$531$	2171.89			0.177499
$532$	34.6893	+	121.901i	0.00282701	+	0.00993433i
$533$	−16180.4	+	9610.50i	−1.31491	+	0.781008i
$534$	−8479.87	+	1183.07i	−0.687191	+	0.0958737i
$535$			1311.56i			0.105988i
$536$	2521.24	−	1113.43i	0.203174	−	0.0897253i
$537$	14112.7			1.13409
$538$	2593.00	+	18585.8i	0.207792	+	1.48939i
$539$	14898.4			1.19058
$540$	−874.426	−	3072.80i	−0.0696839	−	0.244874i
$541$	−7560.93			−0.600869			−0.300434	−	0.953802i	$-0.597132\pi$
$541$	−7560.93			−0.600869			−0.300434	+	0.953802i	$0.597132\pi$
$542$	2854.15	+	20457.6i	0.226192	+	1.62127i
$543$	−4511.93			−0.356585
$544$	2248.95	−	1867.90i	0.177248	−	0.147216i
$545$	19943.7			1.56751
$546$	54.0901	+	67.6338i	0.00423964	+	0.00530121i
$547$		−	23434.6i		−	1.83179i	−0.401415	−	0.915896i	$-0.631481\pi$
$547$		−	23434.6i		−	1.83179i	0.401415	−	0.915896i	$-0.368519\pi$
$548$	1742.30	+	6122.59i	0.135817	+	0.477270i
$549$		−	4117.37i		−	0.320082i
$550$	−11410.5	+	1591.95i	−0.884631	+	0.123420i
$551$		−	9360.97i		−	0.723759i
$552$	2288.40	+	5181.85i	0.176451	+	0.399555i
$553$		−	35.7697i		−	0.00275060i
$554$	−2395.93	−	17173.2i	−0.183742	−	1.31700i
$555$			15099.4i			1.15483i
$556$	4886.84	+	17172.7i	0.372748	+	1.30987i
$557$	−5076.81			−0.386196			−0.193098	−	0.981179i	$-0.561854\pi$
$557$	−5076.81			−0.386196			−0.193098	+	0.981179i	$0.561854\pi$
$558$	−1076.51	−	7716.04i	−0.0816705	−	0.585387i
$559$	−1301.88	+	773.266i	−0.0985039	+	0.0585075i
$560$	108.523	+	175.238i	0.00818917	+	0.0132235i
$561$		−	2104.77i		−	0.158402i
$562$	2579.89	+	18491.8i	0.193641	+	1.38795i
$563$			3458.50i			0.258896i	0.991586	+	0.129448i	$0.0413206\pi$
$563$			3458.50i			0.258896i	−0.991586	+	0.129448i	$0.958679\pi$
$564$	−2746.84	+	781.669i	−0.205076	+	0.0583585i
$565$	−19952.0			−1.48564
$566$	1586.04	+	11368.2i	0.117785	+	0.844241i
$567$			17.6375i			0.00130636i
$568$	−2303.07	−	5215.06i	−0.170131	−	0.385245i
$569$	262.599			0.0193475			0.00967376	−	0.999953i	$-0.496921\pi$
$569$	262.599			0.0193475			0.00967376	+	0.999953i	$0.496921\pi$
$570$	−1261.72	−	9043.62i	−0.0927155	−	0.664554i
$571$			6517.21i			0.477647i	0.971063	+	0.238824i	$0.0767618\pi$
$571$			6517.21i			0.477647i	−0.971063	+	0.238824i	$0.923238\pi$
$572$	11834.3	+	11193.8i	0.865068	+	0.818242i
$573$		−	5622.52i		−	0.409920i
$574$	244.906	−	34.1681i	0.0178086	−	0.00248458i
$575$	−7824.53			−0.567488
$576$	−3103.96	+	3405.74i	−0.224534	+	0.246365i
$577$		−	468.070i		−	0.0337712i	−0.999857	−	0.0168856i	$-0.994625\pi$
$577$		−	468.070i		−	0.0337712i	0.999857	−	0.0168856i	$-0.00537512\pi$
$578$	13032.1	−	1818.18i	0.937827	−	0.130841i
$579$	1601.04			0.114917
$580$	−4166.84	−	14642.6i	−0.298308	−	1.04828i
$581$		−	67.8245i		−	0.00484309i
$582$	3639.71	−	507.796i	0.259228	−	0.0361663i
$583$			21112.8i			1.49983i
$584$	−607.214	−	1374.97i	−0.0430252	−	0.0974261i
$585$	−3186.32	−	5364.53i	−0.225193	−	0.379138i
$586$	−15077.5	+	2103.54i	−1.06288	+	0.148288i
$587$	−18079.3			−1.27123			−0.635614	−	0.772007i	$-0.719253\pi$
$587$	−18079.3			−1.27123			−0.635614	+	0.772007i	$0.719253\pi$
$588$	2252.81	+	7916.56i	0.158001	+	0.555227i
$589$		−	22267.2i		−	1.55773i
$590$	9998.70	−	1394.97i	0.697695	−	0.0973392i
$591$			11087.2i			0.771683i
$592$	18515.5	−	11466.5i	1.28544	−	0.796063i
$593$		−	12109.1i		−	0.838552i	−0.907859	−	0.419276i	$-0.862284\pi$
$593$		−	12109.1i		−	0.838552i	0.907859	−	0.419276i	$-0.137716\pi$
$594$	458.407	+	3285.71i	0.0316644	+	0.226960i
$595$		−	52.0137i		−	0.00358379i
$596$	9123.41	−	2596.25i	0.627030	−	0.178434i
$597$		−	8420.96i		−	0.577298i
$598$	6909.75	+	8639.90i	0.472510	+	0.590822i
$599$	−3624.13			−0.247209			−0.123604	−	0.992332i	$-0.539445\pi$
$599$	−3624.13			−0.247209			−0.123604	+	0.992332i	$0.539445\pi$
$600$	−2571.32	−	5822.49i	−0.174956	−	0.396170i
$601$	15755.1			1.06933			0.534664	−	0.845065i	$-0.320438\pi$
$601$	15755.1			1.06933			0.534664	+	0.845065i	$0.320438\pi$
$602$	19.7052	−	2.74919i	0.00133410	−	0.000186127i
$603$	1096.25			0.0740347
$604$	−4910.26	−	17255.0i	−0.330787	−	1.16241i
$605$	8226.23			0.552800
$606$	13577.5	−	1894.28i	0.910149	−	0.126980i
$607$	9240.47			0.617890			0.308945	−	0.951080i	$-0.400024\pi$
$607$	9240.47			0.617890			0.308945	+	0.951080i	$0.400024\pi$
$608$	−10131.5	+	8414.92i	−0.675803	+	0.561299i
$609$			84.0467i			0.00559236i
$610$	−2644.53	−	18955.1i	−0.175531	−	1.25815i
$611$	−4795.47	+	2848.32i	−0.317519	+	0.188594i
$612$	1118.41	−	318.266i	0.0738709	−	0.0210214i
$613$	8042.08			0.529880			0.264940	−	0.964265i	$-0.414648\pi$
$613$	8042.08			0.529880			0.264940	+	0.964265i	$0.414648\pi$
$614$	−17760.7	+	2477.89i	−1.16737	+	0.162866i
$615$	−17815.5			−1.16812
$616$	−86.4671	−	195.796i	−0.00565562	−	0.0128066i
$617$		−	14180.1i		−	0.925236i	−0.886558	−	0.462618i	$-0.846910\pi$
$617$		−	14180.1i		−	0.925236i	0.886558	−	0.462618i	$-0.153090\pi$
$618$	−1740.34	−	12474.2i	−0.113280	−	0.811951i
$619$	8596.09			0.558168			0.279084	−	0.960267i	$-0.409969\pi$
$619$	8596.09			0.558168			0.279084	+	0.960267i	$0.409969\pi$
$620$	−9911.79	−	34830.8i	−0.642044	−	2.25619i
$621$			2253.10i			0.145594i
$622$	14401.4	−	2009.22i	0.928365	−	0.129521i
$623$	219.715			0.0141296
$624$	−4158.53	+	7981.03i	−0.266786	+	0.512014i
$625$	−18553.7			−1.18744
$626$	28179.9	−	3931.53i	1.79919	−	0.251015i
$627$			9482.01i			0.603948i
$628$	−5509.94	−	19362.4i	−0.350113	−	1.23032i
$629$	−5495.73			−0.348377
$630$	11.3283	+	81.1974i	0.000716396	+	0.00513489i
$631$		−	12694.0i		−	0.800858i	−0.916328	−	0.400429i	$-0.868861\pi$
$631$		−	12694.0i		−	0.800858i	0.916328	−	0.400429i	$-0.131139\pi$
$632$	3400.24	−	1501.61i	0.214010	−	0.0945108i
$633$	8288.03			0.520410
$634$	−10831.3	+	1511.13i	−0.678492	+	0.0946602i
$635$	3273.02			0.204545
$636$	−11218.7	+	3192.50i	−0.699448	+	0.199042i
$637$	8209.03	+	13820.8i	0.510602	+	0.859656i
$638$	2184.42	+	15657.2i	0.135551	+	0.971587i
$639$		−	2267.55i		−	0.140380i
$640$	−12102.2	+	17672.6i	−0.747471	+	1.09152i
$641$	−9877.43			−0.608635			−0.304318	−	0.952571i	$-0.598428\pi$
$641$	−9877.43			−0.608635			−0.304318	+	0.952571i	$0.598428\pi$
$642$	745.212	−	103.969i	0.0458118	−	0.00639146i
$643$	−1673.36			−0.102630			−0.0513148	−	0.998683i	$-0.516341\pi$
$643$	−1673.36			−0.102630			−0.0513148	+	0.998683i	$0.516341\pi$
$644$	−39.7868	−	139.814i	−0.00243450	−	0.00855503i
$645$	−1433.45			−0.0875068
$646$	3291.62	−	459.231i	0.200475	−	0.0279694i
$647$	9339.92			0.567527			0.283764	−	0.958894i	$-0.408417\pi$
$647$	9339.92			0.567527			0.283764	+	0.958894i	$0.408417\pi$
$648$	−1676.61	+	740.420i	−0.101641	+	0.0448865i
$649$	−10483.4			−0.634067
$650$	−7764.01	−	9708.05i	−0.468507	−	0.585817i
$651$			199.924i			0.0120363i
$652$	−24420.6	+	6949.38i	−1.46685	+	0.417421i
$653$		−	7410.32i		−	0.444086i	−0.975037	−	0.222043i	$-0.928727\pi$
$653$		−	7410.32i		−	0.444086i	0.975037	−	0.222043i	$-0.0712725\pi$
$654$	−1580.95	−	11331.8i	−0.0945263	−	0.677533i
$655$		−	31199.8i		−	1.86119i
$656$	13529.1	+	21846.2i	0.805218	+	1.30023i
$657$		−	597.848i		−	0.0355012i
$658$	72.5842	−	10.1266i	0.00430034	−	0.000599964i
$659$			13144.9i			0.777013i	0.921446	+	0.388507i	$0.127009\pi$
$659$			13144.9i			0.777013i	−0.921446	+	0.388507i	$0.872991\pi$
$660$	4220.72	+	14831.9i	0.248926	+	0.874745i
$661$	−8190.36			−0.481949			−0.240974	−	0.970531i	$-0.577467\pi$
$661$	−8190.36			−0.481949			−0.240974	+	0.970531i	$0.577467\pi$
$662$	7374.17	−	1028.81i	0.432938	−	0.0604016i
$663$	1952.53	−	1159.73i	0.114374	−	0.0679338i
$664$	6447.35	−	2847.27i	0.376816	−	0.166409i
$665$			234.322i			0.0136641i
$666$	8579.27	−	1196.94i	0.499159	−	0.0696404i
$667$			10736.6i			0.623270i
$668$	−775.072	−	2723.66i	−0.0448929	−	0.157757i
$669$	9295.07			0.537172
$670$	5046.81	−	704.107i	0.291008	−	0.0406001i
$671$			19873.9i			1.14341i
$672$	90.9651	−	75.5526i	0.00522181	−	0.00433706i
$673$	−4991.19			−0.285879			−0.142939	−	0.989731i	$-0.545655\pi$
$673$	−4991.19			−0.285879			−0.142939	+	0.989731i	$0.545655\pi$
$674$	5760.46	−	803.673i	0.329206	−	0.0459293i
$675$		−	2531.66i		−	0.144361i
$676$	−3863.39	+	17146.1i	−0.219811	+	0.975543i
$677$			2640.52i			0.149902i	0.997187	+	0.0749508i	$0.0238800\pi$
$677$			2640.52i			0.149902i	−0.997187	+	0.0749508i	$0.976120\pi$
$678$	1581.61	+	11336.5i	0.0895893	+	0.642146i
$679$	−94.3058			−0.00533008
$680$	4944.38	−	2183.53i	0.278836	−	0.123139i
$681$		−	5840.58i		−	0.328651i
$682$	5196.13	+	37244.1i	0.291745	+	2.09113i
$683$	32008.8			1.79324			0.896621	−	0.442799i	$-0.146015\pi$
$683$	32008.8			1.79324			0.896621	+	0.442799i	$0.146015\pi$
$684$	−5038.45	+	1433.79i	−0.281652	+	0.0801497i
$685$			11769.1i			0.656458i
$686$	−58.3750	−	418.412i	−0.00324893	−	0.0232873i
$687$			20634.0i			1.14591i
$688$	1088.56	+	1757.76i	0.0603212	+	0.0974038i
$689$	−19585.7	+	11633.1i	−1.08295	+	0.643232i
$690$	1447.13	+	10372.6i	0.0798427	+	0.572286i
$691$	28514.4			1.56981			0.784904	−	0.619618i	$-0.212712\pi$
$691$	28514.4			1.56981			0.784904	+	0.619618i	$0.212712\pi$
$692$	−3318.91	−	11662.9i	−0.182321	−	0.640690i
$693$		−	85.1335i		−	0.00466660i
$694$	−1272.69	−	9122.21i	−0.0696118	−	0.498954i
$695$			33010.1i			1.80165i
$696$	−7989.42	+	3528.27i	−0.435112	+	0.192154i
$697$		−	6484.33i		−	0.352384i
$698$	27785.3	−	3876.48i	1.50672	−	0.210210i
$699$		−	4965.59i		−	0.268692i
$700$	44.7057	+	157.099i	0.00241388	+	0.00848255i
$701$			25877.8i			1.39428i	0.716935	+	0.697140i	$0.245545\pi$
$701$			25877.8i			1.39428i	−0.716935	+	0.697140i	$0.754455\pi$
$702$	−2795.47	+	2235.68i	−0.150297	+	0.120200i
$703$	24758.4			1.32828
$704$	14982.3	−	16439.0i	0.802086	−	0.880069i
$705$	−5280.10			−0.282071
$706$	1485.01	+	10644.1i	0.0791632	+	0.567416i
$707$	−351.798			−0.0187139
$708$	−1585.21	−	5570.55i	−0.0841467	−	0.295698i
$709$	−9601.34			−0.508584			−0.254292	−	0.967127i	$-0.581842\pi$
$709$	−9601.34			−0.508584			−0.254292	+	0.967127i	$0.581842\pi$
$710$	−1456.41	−	10439.1i	−0.0769832	−	0.551790i
$711$	1478.45			0.0779833
$712$	9223.64	+	20886.0i	0.485492	+	1.09935i
$713$			25539.4i			1.34145i
$714$	−29.5535	+	4.12317i	−0.00154904	+	0.000216114i
$715$	15379.9	+	25893.8i	0.804441	+	1.35437i
$716$	−10300.5	−	36196.7i	−0.537636	−	1.88929i
$717$	−5799.53			−0.302074
$718$	3632.09	+	26033.6i	0.188786	+	1.35316i
$719$	24296.8			1.26025			0.630124	−	0.776494i	$-0.283004\pi$
$719$	24296.8			1.26025			0.630124	+	0.776494i	$0.283004\pi$
$720$	−7243.00	+	4485.52i	−0.374904	+	0.232174i
$721$			323.210i			0.0166948i
$722$	4385.31	−	611.818i	0.226045	−	0.0315367i
$723$	4428.70			0.227808
$724$	3293.15	+	11572.4i	0.169046	+	0.594039i
$725$		−	12063.9i		−	0.617991i
$726$	−652.100	−	4674.04i	−0.0333357	−	0.238939i
$727$	−2605.14			−0.132901			−0.0664507	−	0.997790i	$-0.521168\pi$
$727$	−2605.14			−0.132901			−0.0664507	+	0.997790i	$0.521168\pi$
$728$	133.991	−	188.097i	0.00682147	−	0.00957600i
$729$	−729.000			−0.0370370
$730$	−383.989	−	2752.30i	−0.0194686	−	0.139544i
$731$		−	521.733i		−	0.0263981i
$732$	−10560.4	+	3005.17i	−0.533229	+	0.151741i
$733$	38944.7			1.96242			0.981210	−	0.192943i	$-0.0618032\pi$
$733$	38944.7			1.96242			0.981210	+	0.192943i	$0.0618032\pi$
$734$	−38291.8	+	5342.30i	−1.92558	+	0.268648i
$735$			15217.5i			0.763683i
$736$	11620.4	−	9651.48i	0.581973	−	0.483367i
$737$	−5291.45			−0.264468
$738$	1412.25	+	10122.5i	0.0704413	+	0.504900i
$739$	−31475.0			−1.56675			−0.783373	−	0.621551i	$-0.786503\pi$
$739$	−31475.0			−1.56675			−0.783373	+	0.621551i	$0.786503\pi$
$740$	38727.4	−	11020.7i	1.92385	−	0.547470i
$741$	−8796.18	+	5224.59i	−0.436081	+	0.259015i
$742$	296.449	−	41.3592i	0.0146671	−	0.00204628i
$743$			23967.1i			1.18340i	0.806157	+	0.591701i	$0.201543\pi$
$743$			23967.1i			1.18340i	−0.806157	+	0.591701i	$0.798457\pi$
$744$	−19004.7	+	8392.81i	−0.936485	+	0.413569i
$745$	17537.4			0.862444
$746$	3725.98	+	26706.6i	0.182866	+	1.31072i
$747$	2803.35			0.137308
$748$	−5398.39	+	1536.22i	−0.263883	+	0.0750933i
$749$	−19.3086			−0.000941952
$750$	541.667	+	3882.49i	0.0263718	+	0.189024i
$751$	21751.2			1.05687			0.528436	−	0.848973i	$-0.322779\pi$
$751$	21751.2			1.05687			0.528436	+	0.848973i	$0.322779\pi$
$752$	4009.71	+	6474.69i	0.194440	+	0.313973i
$753$	−20031.8			−0.969456
$754$	−13321.1	+	10653.5i	−0.643401	+	0.514560i
$755$		−	33168.3i		−	1.59883i
$756$	45.2373	−	12.8732i	0.00217628	−	0.000619302i
$757$		−	34563.4i		−	1.65948i	−0.558150	−	0.829740i	$-0.688489\pi$
$757$		−	34563.4i		−	1.65948i	0.558150	−	0.829740i	$-0.311511\pi$
$758$	33747.8	−	4708.34i	1.61712	−	0.225613i
$759$		−	10875.4i		−	0.520094i
$760$	−22274.5	+	9836.84i	−1.06313	+	0.469500i
$761$		−	1383.22i		−	0.0658893i	−0.999457	−	0.0329446i	$-0.989511\pi$
$761$		−	1383.22i		−	0.0658893i	0.999457	−	0.0329446i	$-0.0104885\pi$
$762$	−259.455	−	1859.69i	−0.0123347	−	0.0884112i
$763$			293.608i			0.0139310i
$764$	−14420.8	+	4103.74i	−0.682890	+	0.194330i
$765$	2149.85			0.101605
$766$	−2653.22	−	19017.4i	−0.125150	−	0.897032i
$767$	−5776.35	−	9725.13i	−0.271932	−	0.457828i
$768$	11000.7	+	5475.39i	0.516866	+	0.257260i
$769$		−	7417.38i		−	0.347825i	−0.984761	−	0.173913i	$-0.944359\pi$
$769$		−	7417.38i		−	0.347825i	0.984761	−	0.173913i	$-0.0556411\pi$
$770$	−54.6799	−	391.927i	−0.00255913	−	0.0183430i
$771$		−	20150.8i		−	0.941264i
$772$	−1168.56	−	4106.42i	−0.0544786	−	0.191442i
$773$	−15282.4			−0.711085			−0.355542	−	0.934660i	$-0.615704\pi$
$773$	−15282.4			−0.711085			−0.355542	+	0.934660i	$0.615704\pi$
$774$	113.631	+	814.466i	0.00527696	+	0.0378235i
$775$		−	28696.8i		−	1.33009i
$776$	−3958.95	−	8964.64i	−0.183142	−	0.414706i
$777$	−222.291			−0.0102634
$778$	−244.861	−	1755.08i	−0.0112837	−	0.0808776i
$779$			29212.0i			1.34355i
$780$	−11433.5	+	12087.8i	−0.524853	+	0.554889i
$781$			10945.1i			0.501468i
$782$	−3775.32	+	526.715i	−0.172641	+	0.0240860i
$783$	−3473.85			−0.158551
$784$	18660.4	−	11556.2i	0.850055	−	0.526431i
$785$		−	37219.1i		−	1.69224i
$786$	−17727.3	+	2473.24i	−0.804469	+	0.112236i
$787$	−8134.80			−0.368455			−0.184228	−	0.982884i	$-0.558978\pi$
$787$	−8134.80			−0.368455			−0.184228	+	0.982884i	$0.558978\pi$
$788$	28436.8	−	8092.25i	1.28556	−	0.365830i
$789$		−	5240.17i		−	0.236445i
$790$	6806.31	−	949.585i	0.306529	−	0.0427655i
$791$		−	293.731i		−	0.0132034i
$792$	8092.73	−	3573.90i	0.363084	−	0.160345i
$793$	−18436.5	+	10950.5i	−0.825597	+	0.490372i
$794$	19574.3	−	2730.92i	0.874894	−	0.122061i
$795$	−21565.0			−0.962052
$796$	−21598.4	+	6146.25i	−0.961727	+	0.273678i
$797$		−	2510.82i		−	0.111591i	−0.998442	−	0.0557953i	$-0.982231\pi$
$797$		−	2510.82i		−	0.111591i	0.998442	−	0.0557953i	$-0.0177694\pi$
$798$	133.139	−	18.5749i	0.00590610	−	0.000823992i
$799$		−	1921.80i		−	0.0850919i
$800$	−13057.0	+	10844.7i	−0.577043	+	0.479273i
$801$			9081.37i			0.400592i
$802$	−519.835	−	3726.00i	−0.0228878	−	0.164052i
$803$			2885.72i			0.126818i
$804$	−800.129	−	2811.71i	−0.0350975	−	0.123335i
$805$		−	268.756i		−	0.0117670i
$806$	−31687.2	+	25341.8i	−1.38478	+	1.10748i
$807$	19904.1			0.868227
$808$	−14768.4	−	33441.6i	−0.643010	−	1.45603i
$809$	−1963.25			−0.0853203			−0.0426601	−	0.999090i	$-0.513583\pi$
$809$	−1963.25			−0.0853203			−0.0426601	+	0.999090i	$0.513583\pi$
$810$	−3356.08	+	468.226i	−0.145581	+	0.0203108i
$811$	34566.9			1.49668			0.748341	−	0.663314i	$-0.230851\pi$
$811$	34566.9			1.49668			0.748341	+	0.663314i	$0.230851\pi$
$812$	215.566	−	61.3436i	0.00931637	−	0.00265116i
$813$	21908.7			0.945106
$814$	−41410.8	+	5777.45i	−1.78311	+	0.248771i
$815$	−46942.3			−2.01757
$816$	−1632.60	−	2636.24i	−0.0700397	−	0.113097i
$817$			2350.41i			0.100649i
$818$	−1591.36	−	11406.4i	−0.0680204	−	0.487547i
$819$	78.9758	−	46.9086i	0.00336952	−	0.00200136i
$820$	13003.1	+	45693.9i	0.553766	+	1.94598i
$821$	8804.25			0.374264			0.187132	−	0.982335i	$-0.440081\pi$
$821$	8804.25			0.374264			0.187132	+	0.982335i	$0.440081\pi$
$822$	6687.04	−	932.945i	0.283744	−	0.0395866i
$823$	−13852.8			−0.586728			−0.293364	−	0.956001i	$-0.594775\pi$
$823$	−13852.8			−0.586728			−0.293364	+	0.956001i	$0.594775\pi$
$824$	−30724.1	+	13568.3i	−1.29894	+	0.573634i
$825$			12219.9i			0.515689i
$826$	20.5366	+	147.199i	0.000865084	+	0.00620064i
$827$	−25803.5			−1.08498			−0.542489	−	0.840063i	$-0.682518\pi$
$827$	−25803.5			−1.08498			−0.542489	+	0.840063i	$0.682518\pi$
$828$	5778.85	−	1644.49i	0.242547	−	0.0690215i
$829$		−	31998.7i		−	1.34060i	−0.742089	−	0.670302i	$-0.766165\pi$
$829$		−	31998.7i		−	1.34060i	0.742089	−	0.670302i	$-0.233835\pi$
$830$	12905.7	−	1800.55i	0.539717	−	0.0752988i
$831$	−18391.4			−0.767737
$832$	23505.3	+	4840.78i	0.979445	+	0.201711i
$833$	−5538.74			−0.230379
$834$	18755.9	−	2616.74i	0.778734	−	0.108645i
$835$		−	5235.53i		−	0.216986i
$836$	24319.8	−	6920.69i	1.00612	−	0.286312i
$837$	−8263.36			−0.341247
$838$	2589.73	+	18562.3i	0.106755	+	0.765185i
$839$		−	33051.9i		−	1.36005i	−0.733191	−	0.680023i	$-0.761970\pi$
$839$		−	33051.9i		−	1.36005i	0.733191	−	0.680023i	$-0.238030\pi$
$840$	199.990	−	88.3192i	0.00821465	−	0.00362774i
$841$	7835.28			0.321263
$842$	10586.0	−	1476.92i	0.433277	−	0.0604488i
$843$	19803.5			0.809096
$844$	−6049.23	−	21257.4i	−0.246710	−	0.866957i
$845$	−15546.5	+	28534.9i	−0.632920	+	1.16169i
$846$	418.558	+	3000.08i	0.0170098	+	0.121921i
$847$			121.105i			0.00491290i
$848$	16376.5	+	26443.9i	0.663172	+	1.07086i
$849$	12174.6			0.492143
$850$	4242.06	−	591.833i	0.171178	−	0.0238820i
$851$	−28396.6			−1.14386
$852$	−5815.89	+	1655.03i	−0.233860	+	0.0665496i
$853$	−18913.6			−0.759191			−0.379596	−	0.925153i	$-0.623937\pi$
$853$	−18913.6			−0.759191			−0.379596	+	0.925153i	$0.623937\pi$
$854$	279.054	−	38.9324i	0.0111815	−	0.00156000i
$855$	−9685.11			−0.387396
$856$	−810.575	−	1835.46i	−0.0323655	−	0.0732884i
$857$	29160.7			1.16232			0.581162	−	0.813788i	$-0.302598\pi$
$857$	29160.7			1.16232			0.581162	+	0.813788i	$0.302598\pi$
$858$	13493.3	−	10791.3i	0.536893	−	0.429380i
$859$		−	41899.6i		−	1.66426i	−0.554583	−	0.832128i	$-0.687122\pi$
$859$		−	41899.6i		−	1.66426i	0.554583	−	0.832128i	$-0.312878\pi$
$860$	1046.24	+	3676.56i	0.0414842	+	0.145779i
$861$		−	262.278i		−	0.0103814i
$862$	−2157.95	−	15467.5i	−0.0852671	−	0.611166i
$863$		−	27896.1i		−	1.10034i	−0.835053	−	0.550170i	$-0.814563\pi$
$863$		−	27896.1i		−	1.10034i	0.835053	−	0.550170i	$-0.185437\pi$
$864$	3122.77	+	3759.81i	0.122962	+	0.148045i
$865$		−	22418.9i		−	0.881232i
$866$	6415.72	−	895.092i	0.251750	−	0.0351229i
$867$		−	13956.5i		−	0.546699i
$868$	512.774	−	145.920i	0.0200515	−	0.00570604i
$869$	−7136.25			−0.278574
$870$	−15992.5	+	2231.20i	−0.623215	+	0.0869482i
$871$	−2915.59	−	4908.72i	−0.113423	−	0.190960i
$872$	−27910.2	+	12325.7i	−1.08390	+	0.478669i
$873$		−	3897.89i		−	0.151115i
$874$	17007.9	−	2372.86i	0.658237	−	0.0918342i
$875$		−	100.596i		−	0.00388660i
$876$	−1533.38	+	436.355i	−0.0591418	+	0.0168300i
$877$	3379.82			0.130135			0.0650676	−	0.997881i	$-0.479274\pi$
$877$	3379.82			0.130135			0.0650676	+	0.997881i	$0.479274\pi$
$878$	−10388.9	+	1449.41i	−0.399326	+	0.0557122i
$879$			16147.0i			0.619595i
$880$	34960.9	−	21650.9i	1.33924	−	0.829378i
$881$	−33026.3			−1.26298			−0.631489	−	0.775385i	$-0.717556\pi$
$881$	−33026.3			−1.26298			−0.631489	+	0.775385i	$0.717556\pi$
$882$	8646.40	−	1206.31i	0.330090	−	0.0460527i
$883$			12869.3i			0.490471i	0.969464	+	0.245235i	$0.0788652\pi$
$883$			12869.3i			0.490471i	−0.969464	+	0.245235i	$0.921135\pi$
$884$	−4399.62	−	4161.47i	−0.167393	−	0.158332i
$885$		−	10707.9i		−	0.406716i
$886$	606.720	+	4348.77i	0.0230058	+	0.164898i
$887$	−19272.8			−0.729556			−0.364778	−	0.931095i	$-0.618855\pi$
$887$	−19272.8			−0.729556			−0.364778	+	0.931095i	$0.618855\pi$
$888$	−9331.75	−	21130.8i	−0.352650	−	0.798540i
$889$			48.1849i			0.00181785i
$890$	5832.83	+	41807.8i	0.219682	+	1.57461i
$891$	3518.77			0.132304
$892$	−6784.24	−	23840.3i	−0.254656	−	0.894881i
$893$			8657.74i			0.324435i
$894$	−1390.20	−	9964.52i	−0.0520083	−	0.372778i
$895$		−	69578.8i		−	2.59862i
$896$	−260.173	−	178.167i	−0.00970065	−	0.00664301i
$897$	10088.8	−	5992.34i	0.375535	−	0.223053i
$898$	5117.87	+	36683.2i	0.190184	+	1.36318i
$899$	−39376.8			−1.46084
$900$	−6493.29	+	1847.79i	−0.240492	+	0.0684368i
$901$		−	7849.03i		−	0.290221i
$902$	−6816.72	−	48860.0i	−0.251632	−	1.80361i
$903$		−	21.1030i		−	0.000777701i
$904$	27921.9	−	12330.8i	1.02729	−	0.453669i
$905$			22244.9i			0.817067i
$906$	−18845.8	+	2629.28i	−0.691070	+	0.0964149i
$907$		−	18934.1i		−	0.693161i	−0.938020	−	0.346581i	$-0.887343\pi$
$907$		−	18934.1i		−	0.693161i	0.938020	−	0.346581i	$-0.112657\pi$
$908$	−14980.2	+	4262.90i	−0.547504	+	0.155803i
$909$		−	14540.6i		−	0.530564i
$910$	333.451	−	266.677i	0.0121470	−	0.00971457i
$911$	−35785.6			−1.30146			−0.650731	−	0.759309i	$-0.725537\pi$
$911$	−35785.6			−1.30146			−0.650731	+	0.759309i	$0.725537\pi$
$912$	7354.88	+	11876.3i	0.267044	+	0.431211i
$913$	−13531.4			−0.490496
$914$	−4409.21	−	31603.8i	−0.159567	−	1.14372i
$915$	−20299.6			−0.733426
$916$	52923.0	−	15060.3i	1.90898	−	0.543238i
$917$	459.319			0.0165410
$918$	−170.421	−	1221.52i	−0.00612714	−	0.0439173i
$919$	29849.4			1.07143			0.535713	−	0.844400i	$-0.320043\pi$
$919$	29849.4			1.07143			0.535713	+	0.844400i	$0.320043\pi$
$920$	25547.7	−	11282.4i	0.915526	−	0.404313i
$921$			19020.5i			0.680507i
$922$	5113.63	−	713.430i	0.182655	−	0.0254833i
$923$	−10153.4	+	6030.75i	−0.362085	+	0.215065i
$924$	−218.353	+	62.1368i	−0.00777414	+	0.00221229i
$925$	31907.3			1.13417
$926$	3185.93	+	22835.7i	0.113063	+	0.810397i
$927$	−13359.0			−0.473321
$928$	14880.7	+	17916.4i	0.526384	+	0.633765i
$929$		−	18336.2i		−	0.647568i	−0.946131	−	0.323784i	$-0.895045\pi$
$929$		−	18336.2i		−	0.647568i	0.946131	−	0.323784i	$-0.104955\pi$
$930$	−38041.9	+	5307.43i	−1.34134	+	0.187137i
$931$	24952.1			0.878381
$932$	−12735.9	+	3624.26i	−0.447617	+	0.127378i
$933$		−	15422.9i		−	0.541183i
$934$	−4993.95	−	35794.9i	−0.174954	−	1.25401i
$935$	−10377.0			−0.362957
$936$	7774.49	+	5538.16i	0.271493	+	0.193398i
$937$	25276.9			0.881281			0.440641	−	0.897684i	$-0.354751\pi$
$937$	25276.9			0.881281			0.440641	+	0.897684i	$0.354751\pi$
$938$	10.3658	+	74.2984i	0.000360826	+	0.00258628i
$939$		−	30178.8i		−	1.04882i
$940$	3853.81	+	13542.6i	0.133721	+	0.469905i
$941$	1836.34			0.0636162			0.0318081	−	0.999494i	$-0.489873\pi$
$941$	1836.34			0.0636162			0.0318081	+	0.999494i	$0.489873\pi$
$942$	−21147.4	+	2950.39i	−0.731444	+	0.102048i
$943$		−	33504.7i		−	1.15701i
$944$	−13130.6	+	8131.62i	−0.452715	+	0.280362i
$945$	86.9570			0.00299334
$946$	−548.477	−	3931.30i	−0.0188505	−	0.135114i
$947$	28339.5			0.972451			0.486225	−	0.873833i	$-0.338373\pi$
$947$	28339.5			0.972451			0.486225	+	0.873833i	$0.338373\pi$
$948$	−1079.08	−	3791.98i	−0.0369694	−	0.129913i
$949$	−2677.00	+	1590.03i	−0.0915691	+	0.0543885i
$950$	−19110.5	+	2666.22i	−0.652661	+	0.0910563i
$951$			11599.6i			0.395522i
$952$	32.1456	+	72.7905i	0.00109438	+	0.00247810i
$953$	−41198.6			−1.40037			−0.700186	−	0.713960i	$-0.746900\pi$
$953$	−41198.6			−1.40037			−0.700186	+	0.713960i	$0.746900\pi$
$954$	1709.47	+	12252.9i	0.0580150	+	0.415832i
$955$	−27720.3			−0.939276
$956$	4232.94	+	14874.9i	0.143204	+	0.503229i
$957$	16767.8			0.566379
$958$	−3173.48	−	22746.4i	−0.107026	−	0.767124i
$959$	−173.263			−0.00583415
$960$	16791.1	+	15303.3i	0.564512	+	0.514490i
$961$	−63875.8			−2.14413
$962$	−28176.9	−	35232.2i	−0.944346	−	1.18080i
$963$		−	798.073i		−	0.0267056i
$964$	−3232.40	−	11358.9i	−0.107997	−	0.379508i
$965$		−	7893.52i		−	0.263318i
$966$	−152.704	+	21.3045i	−0.00508608	+	0.000709587i
$967$			18131.0i			0.602951i	0.953474	+	0.301475i	$0.0974791\pi$
$967$			18131.0i			0.602951i	−0.953474	+	0.301475i	$0.902521\pi$
$968$	−11512.2	+	5084.00i	−0.382248	+	0.168808i
$969$		−	3525.10i		−	0.116865i
$970$	−2503.55	−	17944.6i	−0.0828704	−	0.593987i
$971$			13259.5i			0.438225i	0.975700	+	0.219112i	$0.0703161\pi$
$971$			13259.5i			0.438225i	−0.975700	+	0.219112i	$0.929684\pi$
$972$	532.079	+	1869.77i	0.0175581	+	0.0617004i
$973$	−485.970			−0.0160118
$974$	−363.284	−	2603.90i	−0.0119511	−	0.0856615i
$975$	−11336.1	+	6733.18i	−0.372353	+	0.221163i
$976$	15415.6	+	24892.3i	0.505574	+	0.816376i
$977$		−	20780.3i		−	0.680471i	−0.940340	−	0.340236i	$-0.889493\pi$
$977$		−	20780.3i		−	0.680471i	0.940340	−	0.340236i	$-0.110507\pi$
$978$	3721.16	+	26672.0i	0.121666	+	0.872063i
$979$		−	43834.4i		−	1.43100i
$980$	39030.5	−	11106.9i	1.27223	−	0.362038i
$981$	−12135.6			−0.394963
$982$	2326.97	+	16679.0i	0.0756179	+	0.542004i
$983$		−	29090.8i		−	0.943897i	−0.881626	−	0.471949i	$-0.843551\pi$
$983$		−	29090.8i		−	0.943897i	0.881626	−	0.471949i	$-0.156449\pi$
$984$	24931.9	−	11010.4i	0.807724	−	0.356706i
$985$	54662.3			1.76821
$986$	−812.094	−	5820.82i	−0.0262295	−	0.188005i
$987$		−	77.7328i		−	0.00250685i
$988$	19820.4	+	18747.5i	0.638228	+	0.603681i
$989$		−	2695.81i		−	0.0866751i
$990$	16199.3	−	2260.05i	0.520048	−	0.0725548i
$991$	−14302.6			−0.458464			−0.229232	−	0.973372i	$-0.573621\pi$
$991$	−14302.6			−0.458464			−0.229232	+	0.973372i	$0.573621\pi$
$992$	35397.2	+	42618.2i	1.13293	+	1.36404i
$993$		−	7897.24i		−	0.252378i
$994$	153.682	−	21.4411i	0.00490393	−	0.000684174i
$995$	−41517.3			−1.32280
$996$	−2046.10	−	7190.14i	−0.0650935	−	0.228743i
$997$			39926.6i			1.26829i	0.773213	+	0.634146i	$0.218648\pi$
$997$			39926.6i			1.26829i	−0.773213	+	0.634146i	$0.781352\pi$
$998$	2795.26	−	389.981i	0.0886596	−	0.0123694i
$999$		−	9187.82i		−	0.290981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.4.m.a.181.6	yes	84
4.3	odd	2		1248.4.m.a.337.50		84
8.3	odd	2		1248.4.m.a.337.51		84
8.5	even	2	inner	312.4.m.a.181.80	yes	84
13.12	even	2	inner	312.4.m.a.181.79	yes	84
52.51	odd	2		1248.4.m.a.337.49		84
104.51	odd	2		1248.4.m.a.337.52		84
104.77	even	2	inner	312.4.m.a.181.5	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.4.m.a.181.5	✓	84	104.77	even	2	inner
312.4.m.a.181.6	yes	84	1.1	even	1	trivial
312.4.m.a.181.79	yes	84	13.12	even	2	inner
312.4.m.a.181.80	yes	84	8.5	even	2	inner
1248.4.m.a.337.49		84	52.51	odd	2
1248.4.m.a.337.50		84	4.3	odd	2
1248.4.m.a.337.51		84	8.3	odd	2
1248.4.m.a.337.52		84	104.51	odd	2

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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	312.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.80130 + 0.390824i) q^{2} +3.00000i q^{3} +(7.69451 - 2.18963i) q^{4} +14.7907 q^{5} +(-1.17247 - 8.40389i) q^{6} +0.217747i q^{7} +(-20.6988 + 9.14099i) q^{8} -9.00000 q^{9} +(-41.4331 + 5.78056i) q^{10} +43.4416 q^{11} +(6.56888 + 23.0835i) q^{12} +(23.9363 + 40.2995i) q^{13} +(-0.0851006 - 0.609973i) q^{14} +44.3721i q^{15} +(54.4111 - 33.6962i) q^{16} -16.1502 q^{17} +(25.2117 - 3.51742i) q^{18} +72.7567 q^{19} +(113.807 - 32.3861i) q^{20} -0.653240 q^{21} +(-121.693 + 16.9780i) q^{22} -83.4483 q^{23} +(-27.4230 - 62.0965i) q^{24} +93.7650 q^{25} +(-82.8028 - 103.536i) q^{26} -27.0000i q^{27} +(0.476784 + 1.67545i) q^{28} -128.661i q^{29} +(-17.3417 - 124.299i) q^{30} -306.050i q^{31} +(-139.252 + 115.658i) q^{32} +130.325i q^{33} +(45.2414 - 6.31187i) q^{34} +3.22063i q^{35} +(-69.2506 + 19.7066i) q^{36} +340.290 q^{37} +(-203.813 + 28.4351i) q^{38} +(-120.899 + 71.8090i) q^{39} +(-306.151 + 135.202i) q^{40} +401.502i q^{41} +(1.82992 - 0.255302i) q^{42} +32.3051i q^{43} +(334.262 - 95.1210i) q^{44} -133.116 q^{45} +(233.763 - 32.6136i) q^{46} +118.996i q^{47} +(101.089 + 163.233i) q^{48} +342.953 q^{49} +(-262.664 + 36.6456i) q^{50} -48.4505i q^{51} +(272.419 + 257.674i) q^{52} +486.003i q^{53} +(10.5522 + 75.6350i) q^{54} +642.533 q^{55} +(-1.99042 - 4.50711i) q^{56} +218.270i q^{57} +(50.2839 + 360.418i) q^{58} -241.321 q^{59} +(97.1584 + 341.422i) q^{60} +457.486i q^{61} +(119.612 + 857.338i) q^{62} -1.95972i q^{63} +(344.885 - 378.416i) q^{64} +(354.036 + 596.058i) q^{65} +(-50.9341 - 365.079i) q^{66} -121.806 q^{67} +(-124.268 + 35.3628i) q^{68} -250.345i q^{69} +(-1.25870 - 9.02193i) q^{70} +251.950i q^{71} +(186.290 - 82.2689i) q^{72} +66.4276i q^{73} +(-953.252 + 132.993i) q^{74} +281.295i q^{75} +(559.828 - 159.310i) q^{76} +9.45927i q^{77} +(310.608 - 248.408i) q^{78} -164.272 q^{79} +(804.778 - 498.391i) q^{80} +81.0000 q^{81} +(-156.917 - 1124.73i) q^{82} -311.484 q^{83} +(-5.02636 + 1.43035i) q^{84} -238.872 q^{85} +(-12.6256 - 90.4962i) q^{86} +385.984 q^{87} +(-899.192 + 397.100i) q^{88} -1009.04i q^{89} +(372.898 - 52.0251i) q^{90} +(-8.77509 + 5.21206i) q^{91} +(-642.094 + 182.721i) q^{92} +918.151 q^{93} +(-46.5064 - 333.342i) q^{94} +1076.12 q^{95} +(-346.975 - 417.757i) q^{96} +433.098i q^{97} +(-960.712 + 134.034i) q^{98} -390.975 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) \) 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

Introduction

L-functions

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