LMFDB - Embedded newform 312.4.m.a.181.79

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			181.79
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.80

$q$-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} +(-51.3028 + 122.246i) 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} +(-95.9376 + 362.497i) 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} +(-366.737 - 153.908i) 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	$-0.730063\pi$
$5$	−14.7907			−1.32292			−0.661461	+	0.749980i	$0.730063\pi$
$6$	1.17247	+	8.40389i	0.0797766	+	0.571812i
$7$		−	0.217747i		−	0.0117572i	−0.999983	−	0.00587861i	$-0.998129\pi$
$7$		−	0.217747i		−	0.0117572i	0.999983	−	0.00587861i	$-0.00187123\pi$
$8$	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	$-0.702995\pi$
$11$	−43.4416			−1.19074			−0.595370	+	0.803451i	$0.702995\pi$
$12$	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	$-0.644756\pi$
$19$	−72.7567			−0.878502			−0.439251	+	0.898364i	$0.644756\pi$
$20$	−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
$26$	−51.3028	+	122.246i	−0.386973	+	0.922091i
$27$		−	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	$0.346929\pi$
$31$			306.050i			1.77317i	−0.462566	+	0.886585i	$0.653071\pi$
$32$	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	$-0.772844\pi$
$37$	−340.290			−1.51198			−0.755990	+	0.654583i	$0.772844\pi$
$38$	−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	$-0.722895\pi$
$41$		−	401.502i		−	1.52937i	0.644405	−	0.764685i	$-0.277105\pi$
$42$	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	$-0.940884\pi$
$47$		−	118.996i		−	0.369305i	0.982804	−	0.184652i	$-0.0591159\pi$
$48$	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
$52$	−95.9376	+	362.497i	−0.255849	+	0.966717i
$53$			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	$-0.414216\pi$
$59$	241.321			0.532498			0.266249	+	0.963904i	$0.414216\pi$
$60$	−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	$-0.464578\pi$
$67$	121.806			0.222104			0.111052	+	0.993815i	$0.464578\pi$
$68$	−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	$-0.932468\pi$
$71$		−	251.950i		−	0.421140i	0.977579	−	0.210570i	$-0.0675319\pi$
$72$	−186.290	+	82.2689i	−0.304923	+	0.134660i
$73$		−	66.4276i		−	0.106504i	−0.998581	−	0.0532518i	$-0.983041\pi$
$73$		−	66.4276i		−	0.106504i	0.998581	−	0.0532518i	$-0.0169586\pi$
$74$	−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
$78$	−366.737	−	153.908i	−0.532369	−	0.223419i
$79$	−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	$-0.433968\pi$
$83$	311.484			0.411925			0.205962	+	0.978560i	$0.433968\pi$
$84$	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	$0.205187\pi$
$89$			1009.04i			1.20178i	−0.799333	+	0.600889i	$0.794813\pi$
$90$	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	$-0.927215\pi$
$97$		−	433.098i		−	0.453345i	0.973971	−	0.226673i	$-0.0727847\pi$
$98$	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	$0.248703\pi$
$104$	−127.077	+	1052.96i	−0.119817	+	0.992796i
$105$	−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	$-0.701837\pi$
$109$	−1348.39			−1.18489			−0.592444	+	0.805612i	$0.701837\pi$
$110$	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
$130$	758.804	−	1808.10i	0.511935	−	1.21985i
$131$		−	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	$-0.920191\pi$
$137$		−	795.708i		−	0.496219i	0.968732	−	0.248109i	$-0.0798092\pi$
$138$	−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	$-0.605688\pi$
$149$	−1185.70			−0.651924			−0.325962	+	0.945383i	$0.605688\pi$
$150$	109.937	+	787.991i	0.0598421	+	0.428928i
$151$			2242.51i			1.20856i	0.796772	+	0.604280i	$0.206539\pi$
$151$			2242.51i			1.20856i	−0.796772	+	0.604280i	$0.793461\pi$
$152$	−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
$156$	−1087.49	−	287.813i	−0.558134	−	0.147715i
$157$		−	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	$-0.223951\pi$
$163$	3173.77			1.52509			0.762543	+	0.646937i	$0.223951\pi$
$164$	−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	$0.0261340\pi$
$167$			353.974i			0.164020i	−0.996632	+	0.0820101i	$0.973866\pi$
$168$	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	$0.900069\pi$
$182$	26.6186	+	11.1710i	0.0108412	+	0.00454973i
$183$	−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	$0.0317311\pi$
$193$			533.681i			0.199043i	−0.995035	+	0.0995213i	$0.968269\pi$
$194$	−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	$-0.732977\pi$
$197$	−3695.72			−1.33659			−0.668297	+	0.743894i	$0.732977\pi$
$198$	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
$208$	55.5393	+	2999.30i	0.0185142	+	0.999829i
$209$	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	$0.154019\pi$
$223$			3098.36i			0.930409i	−0.885203	+	0.465205i	$0.845981\pi$
$224$	−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	$-0.408132\pi$
$227$	1946.86			0.569241			0.284621	+	0.958640i	$0.408132\pi$
$228$	−477.930	−	1679.48i	−0.138823	−	0.487835i
$229$	−6878.01			−1.98477			−0.992384	−	0.123180i	$-0.960691\pi$
$229$	−6878.01			−1.98477			−0.992384	+	0.123180i	$0.960691\pi$
$230$	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	$0.574754\pi$
$234$	461.725	−	1100.21i	0.128991	−	0.307364i
$235$			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	$-0.915748\pi$
$239$		−	1933.18i		−	0.523208i	0.965175	−	0.261604i	$-0.0842515\pi$
$240$	−1495.17	−	2414.33i	−0.402138	−	0.649353i
$241$			1476.23i			0.394575i	0.980346	+	0.197288i	$0.0632133\pi$
$241$			1476.23i			0.394575i	−0.980346	+	0.197288i	$0.936787\pi$
$242$	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
$260$	1418.99	−	5361.59i	0.338468	−	1.27889i
$261$			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	$0.305186\pi$
$271$			7302.89i			1.63697i	−0.574527	+	0.818486i	$0.694814\pi$
$272$	−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	$0.247128\pi$
$281$			6601.16i			1.40140i	−0.713458	+	0.700698i	$0.752872\pi$
$282$	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
$286$	2228.68	−	5310.56i	0.460785	−	1.09797i
$287$	−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	$-0.680286\pi$
$293$	−5382.33			−1.07317			−0.536585	+	0.843846i	$0.680286\pi$
$294$	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	$-0.700611\pi$
$307$	−6340.17			−1.17867			−0.589336	+	0.807888i	$0.700611\pi$
$308$	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	$0.655270\pi$
$312$	−3158.87	−	381.232i	−0.573191	−	0.0691763i
$313$	−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	$-0.611284\pi$
$317$	−3866.52			−0.685064			−0.342532	+	0.939506i	$0.611284\pi$
$318$	−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	$-0.429862\pi$
$331$	2632.41			0.437132			0.218566	+	0.975822i	$0.429862\pi$
$332$	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	$0.553149\pi$
$338$	−3698.44	−	4993.59i	−0.595174	−	0.803597i
$339$		−	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	$-0.224878\pi$
$349$	9918.73			1.52131			0.760655	+	0.649156i	$0.224878\pi$
$350$	−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	$0.0924771\pi$
$353$			3799.70i			0.572911i	−0.958093	+	0.286456i	$0.907523\pi$
$354$	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	$0.239382\pi$
$359$			9293.42i			1.36626i	−0.730296	+	0.683131i	$0.760618\pi$
$360$	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
$364$	78.9325	+	20.8901i	0.0113659	+	0.00300807i
$365$			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	$-0.195972\pi$
$379$	12047.2			1.63278			0.816390	+	0.577501i	$0.195972\pi$
$380$	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	$-0.850404\pi$
$383$		−	6788.79i		−	0.905721i	0.891581	−	0.452860i	$-0.149596\pi$
$384$	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	$0.987000\pi$
$390$	5424.30	+	2276.41i	0.704283	+	0.295566i
$391$	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	$-0.354381\pi$
$397$	6987.59			0.883368			0.441684	+	0.897171i	$0.354381\pi$
$398$	−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	$-0.973607\pi$
$401$		−	1330.10i		−	0.165641i	0.996564	−	0.0828204i	$-0.0263928\pi$
$402$	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	$-0.920839\pi$
$409$		−	4071.81i		−	0.492270i	0.969236	−	0.246135i	$-0.0791606\pi$
$410$	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
$416$	1327.78	+	8380.23i	0.156490	+	0.987680i
$417$	−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	$-0.429806\pi$
$421$	3778.98			0.437474			0.218737	+	0.975784i	$0.429806\pi$
$422$	−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	$-0.900159\pi$
$431$		−	5521.55i		−	0.617085i	0.951211	−	0.308543i	$-0.0998412\pi$
$432$	−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
$442$	828.548	−	1974.29i	0.0891630	−	0.212460i
$443$		−	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	$0.241594\pi$
$449$			13095.1i			1.37638i	−0.725531	+	0.688190i	$0.758406\pi$
$450$	−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	$-0.804068\pi$
$457$		−	11281.8i		−	1.15480i	0.816462	−	0.577399i	$-0.195932\pi$
$458$	−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	$-0.470606\pi$
$461$	1825.45			0.184425			0.0922123	+	0.995739i	$0.470606\pi$
$462$	−79.4947	+	11.0907i	−0.00800525	+	0.00111686i
$463$			8151.83i			0.818246i	0.912479	+	0.409123i	$0.134165\pi$
$463$			8151.83i			0.818246i	−0.912479	+	0.409123i	$0.865835\pi$
$464$	−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	$0.781791\pi$
$468$	863.439	−	3262.47i	0.0852831	−	0.322239i
$469$		−	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	$-0.873416\pi$
$479$		−	8119.97i		−	0.774553i	0.921964	−	0.387277i	$-0.126584\pi$
$480$	−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	$-0.986230\pi$
$487$		−	929.534i		−	0.0864912i	0.999064	−	0.0432456i	$-0.0137698\pi$
$488$	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
$494$	3732.62	−	8894.20i	0.339957	−	0.810059i
$495$	−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	$-0.485748\pi$
$499$	997.844			0.0895183			0.0447591	+	0.998998i	$0.485748\pi$
$500$	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	$-0.365079\pi$
$509$	9446.08			0.822574			0.411287	+	0.911506i	$0.365079\pi$
$510$	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
$520$	1879.56	−	15574.0i	0.158508	−	1.31339i
$521$	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	$-0.402868\pi$
$541$	7560.93			0.600869			0.300434	+	0.953802i	$0.402868\pi$
$542$	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
$546$	−33.5130	+	79.8558i	−0.00262679	+	0.00625918i
$547$		−	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	$-0.438146\pi$
$557$	5076.81			0.386196			0.193098	+	0.981179i	$0.438146\pi$
$558$	−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	$0.923238\pi$
$572$	4167.69	−	15747.5i	0.304650	−	1.15111i
$573$		−	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	$0.00537512\pi$
$577$			468.070i			0.0337712i	−0.999857	+	0.0168856i	$0.994625\pi$
$578$	−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	$-0.280747\pi$
$587$	18079.3			1.27123			0.635614	+	0.772007i	$0.280747\pi$
$588$	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	$0.137716\pi$
$593$			12109.1i			0.838552i	−0.907859	+	0.419276i	$0.862284\pi$
$594$	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
$598$	4281.13	−	10201.2i	0.292756	−	0.697589i
$599$	−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	$-0.585352\pi$
$613$	−8042.08			−0.529880			−0.264940	+	0.964265i	$0.585352\pi$
$614$	−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	$0.153090\pi$
$617$			14180.1i			0.925236i	−0.886558	+	0.462618i	$0.846910\pi$
$618$	1740.34	+	12474.2i	0.113280	+	0.811951i
$619$	−8596.09			−0.558168			−0.279084	−	0.960267i	$-0.590031\pi$
$619$	−8596.09			−0.558168			−0.279084	+	0.960267i	$0.590031\pi$
$620$	−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
$624$	−8997.91	+	166.618i	−0.577251	+	0.0106892i
$625$	−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	$0.131139\pi$
$631$			12694.0i			0.800858i	−0.916328	+	0.400429i	$0.868861\pi$
$632$	−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	$-0.483659\pi$
$643$	1673.36			0.102630			0.0513148	+	0.998683i	$0.483659\pi$
$644$	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
$650$	−4810.41	+	11462.4i	−0.290276	+	0.691679i
$651$			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	$-0.422533\pi$
$661$	8190.36			0.481949			0.240974	+	0.970531i	$0.422533\pi$
$662$	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
$676$	−12312.1	−	12543.1i	−0.700504	−	0.713649i
$677$			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	$-0.853985\pi$
$683$	−32008.8			−1.79324			−0.896621	+	0.442799i	$0.853985\pi$
$684$	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	$-0.787288\pi$
$691$	−28514.4			−1.56981			−0.784904	+	0.619618i	$0.787288\pi$
$692$	−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	$0.754455\pi$
$702$	3300.64	+	1385.17i	0.177456	+	0.0744730i
$703$	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	$-0.418158\pi$
$709$	9601.34			0.508584			0.254292	+	0.967127i	$0.418158\pi$
$710$	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	$0.521168\pi$
$728$	229.278	+	27.6707i	0.0116725	+	0.00140871i
$729$	−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	$-0.938197\pi$
$733$	−38944.7			−1.96242			−0.981210	+	0.192943i	$0.938197\pi$
$734$	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	$-0.213497\pi$
$739$	31475.0			1.56675			0.783373	+	0.621551i	$0.213497\pi$
$740$	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	$-0.798457\pi$
$743$		−	23967.1i		−	1.18340i	0.806157	−	0.591701i	$-0.201543\pi$
$744$	−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
$754$	15728.3	+	6600.68i	0.759669	+	0.318810i
$755$		−	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	$0.0104885\pi$
$761$			1383.22i			0.0658893i	−0.999457	+	0.0329446i	$0.989511\pi$
$762$	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	$0.0556411\pi$
$769$			7417.38i			0.347825i	−0.984761	+	0.173913i	$0.944359\pi$
$770$	−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	$-0.384296\pi$
$773$	15282.4			0.711085			0.355542	+	0.934660i	$0.384296\pi$
$774$	−113.631	−	814.466i	−0.00527696	−	0.0378235i

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} +(-51.3028 + 122.246i) 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} +(-95.9376 + 362.497i) 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} +(-366.737 - 153.908i) 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

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