LMFDB - Embedded newform 312.4.m.a.181.76

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			181.76
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.75

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.56970 + 1.18180i) q^{2} +3.00000i q^{3} +(5.20671 + 6.07373i) q^{4} +8.43796 q^{5} +(-3.54539 + 7.70910i) q^{6} +8.36709i q^{7} +(6.20176 + 21.7609i) q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+(2.56970 + 1.18180i) q^{2} +3.00000i q^{3} +(5.20671 + 6.07373i) q^{4} +8.43796 q^{5} +(-3.54539 + 7.70910i) q^{6} +8.36709i q^{7} +(6.20176 + 21.7609i) q^{8} -9.00000 q^{9} +(21.6830 + 9.97196i) q^{10} -57.7885 q^{11} +(-18.2212 + 15.6201i) q^{12} +(18.9697 + 42.8620i) q^{13} +(-9.88821 + 21.5009i) q^{14} +25.3139i q^{15} +(-9.78034 + 63.2483i) q^{16} -72.1970 q^{17} +(-23.1273 - 10.6362i) q^{18} +144.199 q^{19} +(43.9340 + 51.2499i) q^{20} -25.1013 q^{21} +(-148.499 - 68.2943i) q^{22} +168.461 q^{23} +(-65.2828 + 18.6053i) q^{24} -53.8009 q^{25} +(-1.90787 + 132.561i) q^{26} -27.0000i q^{27} +(-50.8194 + 43.5650i) q^{28} -96.0104i q^{29} +(-29.9159 + 65.0490i) q^{30} +59.3688i q^{31} +(-99.8792 + 150.971i) q^{32} -173.366i q^{33} +(-185.525 - 85.3222i) q^{34} +70.6012i q^{35} +(-46.8604 - 54.6636i) q^{36} -187.632 q^{37} +(370.547 + 170.413i) q^{38} +(-128.586 + 56.9090i) q^{39} +(52.3302 + 183.618i) q^{40} +211.432i q^{41} +(-64.5027 - 29.6646i) q^{42} -160.852i q^{43} +(-300.888 - 350.992i) q^{44} -75.9416 q^{45} +(432.893 + 199.086i) q^{46} +539.374i q^{47} +(-189.745 - 29.3410i) q^{48} +272.992 q^{49} +(-138.252 - 63.5817i) q^{50} -216.591i q^{51} +(-161.563 + 338.387i) q^{52} -583.906i q^{53} +(31.9085 - 69.3819i) q^{54} -487.617 q^{55} +(-182.076 + 51.8907i) q^{56} +432.596i q^{57} +(113.465 - 246.718i) q^{58} -236.128 q^{59} +(-153.750 + 131.802i) q^{60} -438.613i q^{61} +(-70.1619 + 152.560i) q^{62} -75.3038i q^{63} +(-435.076 + 269.912i) q^{64} +(160.065 + 361.668i) q^{65} +(204.883 - 445.497i) q^{66} +639.558 q^{67} +(-375.909 - 438.505i) q^{68} +505.382i q^{69} +(-83.4363 + 181.424i) q^{70} +79.3300i q^{71} +(-55.8159 - 195.848i) q^{72} -40.6482i q^{73} +(-482.158 - 221.743i) q^{74} -161.403i q^{75} +(750.800 + 875.822i) q^{76} -483.522i q^{77} +(-397.682 - 5.72361i) q^{78} +807.497 q^{79} +(-82.5261 + 533.686i) q^{80} +81.0000 q^{81} +(-249.870 + 543.317i) q^{82} +1390.02 q^{83} +(-130.695 - 152.458i) q^{84} -609.195 q^{85} +(190.094 - 413.340i) q^{86} +288.031 q^{87} +(-358.391 - 1257.53i) q^{88} -1051.90i q^{89} +(-195.147 - 89.7476i) q^{90} +(-358.630 + 158.721i) q^{91} +(877.125 + 1023.18i) q^{92} -178.106 q^{93} +(-637.431 + 1386.03i) q^{94} +1216.74 q^{95} +(-452.912 - 299.638i) q^{96} +1002.06i q^{97} +(701.507 + 322.621i) q^{98} +520.097 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 756 q^{9}+O(q^{10}) $ 84 * q - 756 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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 $

$2$	2.56970	+	1.18180i	0.908526	+	0.417828i
$2$	2.56970	+	1.18180i	0.908526	+	0.417828i
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	5.20671	+	6.07373i	0.650839	+	0.759216i
$5$	8.43796			0.754714			0.377357	−	0.926068i	$-0.376833\pi$
$5$	8.43796			0.754714			0.377357	+	0.926068i	$0.376833\pi$
$6$	−3.54539	+	7.70910i	−0.241233	+	0.524538i
$7$			8.36709i			0.451781i	0.974153	+	0.225890i	$0.0725291\pi$
$7$			8.36709i			0.451781i	−0.974153	+	0.225890i	$0.927471\pi$
$8$	6.20176	+	21.7609i	0.274082	+	0.961706i
$9$	−9.00000			−0.333333
$10$	21.6830	+	9.97196i	0.685677	+	0.315341i
$11$	−57.7885			−1.58399			−0.791995	−	0.610527i	$-0.790958\pi$
$11$	−57.7885			−1.58399			−0.791995	+	0.610527i	$0.790958\pi$
$12$	−18.2212	+	15.6201i	−0.438334	+	0.375762i
$13$	18.9697	+	42.8620i	0.404711	+	0.914445i
$13$	18.9697	+	42.8620i	0.404711	+	0.914445i
$14$	−9.88821	+	21.5009i	−0.188767	+	0.410454i
$15$			25.3139i			0.435734i
$16$	−9.78034	+	63.2483i	−0.152818	+	0.988254i
$17$	−72.1970			−1.03002			−0.515010	−	0.857184i	$-0.672212\pi$
$17$	−72.1970			−1.03002			−0.515010	+	0.857184i	$0.672212\pi$
$18$	−23.1273	−	10.6362i	−0.302842	−	0.139276i
$19$	144.199			1.74113			0.870563	−	0.492056i	$-0.163755\pi$
$19$	144.199			1.74113			0.870563	+	0.492056i	$0.163755\pi$
$20$	43.9340	+	51.2499i	0.491197	+	0.572991i
$21$	−25.1013			−0.260836
$22$	−148.499	−	68.2943i	−1.43910	−	0.661836i
$23$	168.461			1.52724			0.763619	−	0.645668i	$-0.223421\pi$
$23$	168.461			1.52724			0.763619	+	0.645668i	$0.223421\pi$
$24$	−65.2828	+	18.6053i	−0.555241	+	0.158241i
$25$	−53.8009			−0.430407
$26$	−1.90787	+	132.561i	−0.0143909	+	0.999896i
$27$		−	27.0000i		−	0.192450i
$28$	−50.8194	+	43.5650i	−0.342999	+	0.294036i
$29$		−	96.0104i		−	0.614782i	−0.951583	−	0.307391i	$-0.900544\pi$
$29$		−	96.0104i		−	0.614782i	0.951583	−	0.307391i	$-0.0994560\pi$
$30$	−29.9159	+	65.0490i	−0.182062	+	0.395876i
$31$			59.3688i			0.343966i	0.985100	+	0.171983i	$0.0550174\pi$
$31$			59.3688i			0.343966i	−0.985100	+	0.171983i	$0.944983\pi$
$32$	−99.8792	+	150.971i	−0.551760	+	0.834003i
$33$		−	173.366i		−	0.914517i
$34$	−185.525	−	85.3222i	−0.935800	−	0.430372i
$35$			70.6012i			0.340965i
$36$	−46.8604	−	54.6636i	−0.216946	−	0.253072i
$37$	−187.632			−0.833689			−0.416845	−	0.908978i	$-0.636864\pi$
$37$	−187.632			−0.833689			−0.416845	+	0.908978i	$0.636864\pi$
$38$	370.547	+	170.413i	1.58186	+	0.727492i
$39$	−128.586	+	56.9090i	−0.527955	+	0.233660i
$40$	52.3302	+	183.618i	0.206853	+	0.725813i
$41$			211.432i			0.805370i	0.915339	+	0.402685i	$0.131923\pi$
$41$			211.432i			0.805370i	−0.915339	+	0.402685i	$0.868077\pi$
$42$	−64.5027	−	29.6646i	−0.236976	−	0.108985i
$43$		−	160.852i		−	0.570456i	−0.958460	−	0.285228i	$-0.907931\pi$
$43$		−	160.852i		−	0.570456i	0.958460	−	0.285228i	$-0.0920694\pi$
$44$	−300.888	−	350.992i	−1.03092	−	1.20259i
$45$	−75.9416			−0.251571
$46$	432.893	+	199.086i	1.38753	+	0.638123i
$47$			539.374i			1.67395i	0.547239	+	0.836976i	$0.315679\pi$
$47$			539.374i			1.67395i	−0.547239	+	0.836976i	$0.684321\pi$
$48$	−189.745	−	29.3410i	−0.570569	−	0.0882294i
$49$	272.992			0.795894
$50$	−138.252	−	63.5817i	−0.391036	−	0.179836i
$51$		−	216.591i		−	0.594682i
$52$	−161.563	+	338.387i	−0.430860	+	0.902419i
$53$		−	583.906i		−	1.51332i	−0.653811	−	0.756658i	$-0.726831\pi$
$53$		−	583.906i		−	1.51332i	0.653811	−	0.756658i	$-0.273169\pi$
$54$	31.9085	−	69.3819i	0.0804111	−	0.174846i
$55$	−487.617			−1.19546
$56$	−182.076	+	51.8907i	−0.434480	+	0.123825i
$57$			432.596i			1.00524i
$58$	113.465	−	246.718i	0.256874	−	0.558546i
$59$	−236.128			−0.521038			−0.260519	−	0.965469i	$-0.583894\pi$
$59$	−236.128			−0.521038			−0.260519	+	0.965469i	$0.583894\pi$
$60$	−153.750	+	131.802i	−0.330816	+	0.283593i
$61$		−	438.613i		−	0.920634i	−0.887755	−	0.460317i	$-0.847736\pi$
$61$		−	438.613i		−	0.920634i	0.887755	−	0.460317i	$-0.152264\pi$
$62$	−70.1619	+	152.560i	−0.143719	+	0.312502i
$63$		−	75.3038i		−	0.150594i
$64$	−435.076	+	269.912i	−0.849758	+	0.527172i
$65$	160.065	+	361.668i	0.305441	+	0.690144i
$66$	204.883	−	445.497i	0.382111	−	0.830863i
$67$	639.558			1.16619			0.583093	−	0.812405i	$-0.301842\pi$
$67$	639.558			1.16619			0.583093	+	0.812405i	$0.301842\pi$
$68$	−375.909	−	438.505i	−0.670377	−	0.782008i
$69$			505.382i			0.881751i
$70$	−83.4363	+	181.424i	−0.142465	+	0.309776i
$71$			79.3300i			0.132602i	0.997800	+	0.0663009i	$0.0211197\pi$
$71$			79.3300i			0.132602i	−0.997800	+	0.0663009i	$0.978880\pi$
$72$	−55.8159	−	195.848i	−0.0913606	−	0.320569i
$73$		−	40.6482i		−	0.0651713i	−0.999469	−	0.0325857i	$-0.989626\pi$
$73$		−	40.6482i		−	0.0651713i	0.999469	−	0.0325857i	$-0.0103742\pi$
$74$	−482.158	−	221.743i	−0.757429	−	0.348339i
$75$		−	161.403i		−	0.248496i
$76$	750.800	+	875.822i	1.13319	+	1.32189i
$77$		−	483.522i		−	0.715616i
$78$	−397.682	−	5.72361i	−0.577290	−	0.00830860i
$79$	807.497			1.15001			0.575004	−	0.818151i	$-0.305001\pi$
$79$	807.497			1.15001			0.575004	+	0.818151i	$0.305001\pi$
$80$	−82.5261	+	533.686i	−0.115334	+	0.745849i
$81$	81.0000			0.111111
$82$	−249.870	+	543.317i	−0.336506	+	0.731699i
$83$	1390.02			1.83825			0.919124	−	0.393969i	$-0.128898\pi$
$83$	1390.02			1.83825			0.919124	+	0.393969i	$0.128898\pi$
$84$	−130.695	−	152.458i	−0.169762	−	0.198031i
$85$	−609.195			−0.777370
$86$	190.094	−	413.340i	0.238353	−	0.518275i
$87$	288.031			0.354945
$88$	−358.391	−	1257.53i	−0.434143	−	1.52333i
$89$		−	1051.90i		−	1.25282i	−0.779494	−	0.626409i	$-0.784524\pi$
$89$		−	1051.90i		−	1.25282i	0.779494	−	0.626409i	$-0.215476\pi$
$90$	−195.147	−	89.7476i	−0.228559	−	0.105114i
$91$	−358.630	+	158.721i	−0.413128	+	0.182840i
$92$	877.125	+	1023.18i	0.993985	+	1.15950i
$93$	−178.106			−0.198589
$94$	−637.431	+	1386.03i	−0.699425	+	1.52083i
$95$	1216.74			1.31405
$96$	−452.912	−	299.638i	−0.481512	−	0.318559i
$97$			1002.06i			1.04890i	0.851441	+	0.524450i	$0.175729\pi$
$97$			1002.06i			1.04890i	−0.851441	+	0.524450i	$0.824271\pi$
$98$	701.507	+	322.621i	0.723091	+	0.332547i
$99$	520.097			0.527997
$100$	−280.126	−	326.772i	−0.280126	−	0.326772i
$101$		−	709.387i		−	0.698878i	−0.936959	−	0.349439i	$-0.886372\pi$
$101$		−	709.387i		−	0.698878i	0.936959	−	0.349439i	$-0.113628\pi$
$102$	255.967	−	556.574i	0.248475	−	0.540284i
$103$	535.679			0.512446			0.256223	−	0.966618i	$-0.417522\pi$
$103$	535.679			0.512446			0.256223	+	0.966618i	$0.417522\pi$
$104$	−815.072	+	678.618i	−0.768504	+	0.639846i
$105$	−211.804			−0.196856
$106$	690.059	−	1500.46i	0.632306	−	1.37489i
$107$		−	1877.42i		−	1.69623i	−0.529810	−	0.848116i	$-0.677737\pi$
$107$		−	1877.42i		−	1.69623i	0.529810	−	0.848116i	$-0.322263\pi$
$108$	163.991	−	140.581i	0.146111	−	0.125254i
$109$	1084.63			0.953110			0.476555	−	0.879145i	$-0.341885\pi$
$109$	1084.63			0.953110			0.476555	+	0.879145i	$0.341885\pi$
$110$	−1253.03	−	576.265i	−1.08611	−	0.499497i
$111$		−	562.896i		−	0.481331i
$112$	−529.204	−	81.8330i	−0.446474	−	0.0690401i
$113$	393.209			0.327345			0.163672	−	0.986515i	$-0.447666\pi$
$113$	393.209			0.327345			0.163672	+	0.986515i	$0.447666\pi$
$114$	−511.240	+	1111.64i	−0.420018	+	0.913287i
$115$	1421.46			1.15263
$116$	583.141	−	499.898i	0.466752	−	0.400124i
$117$	−170.727	−	385.758i	−0.134904	−	0.304815i
$118$	−606.778	−	279.055i	−0.473377	−	0.217705i
$119$		−	604.079i		−	0.465343i
$120$	−550.853	+	156.991i	−0.419048	+	0.119427i
$121$	2008.51			1.50903
$122$	518.352	−	1127.10i	0.384667	−	0.836419i
$123$	−634.297			−0.464980
$124$	−360.590	+	309.116i	−0.261144	+	0.223866i
$125$	−1508.71			−1.07955
$126$	88.9939	−	193.508i	0.0629223	−	0.136818i
$127$	−1119.16			−0.781966			−0.390983	−	0.920398i	$-0.627865\pi$
$127$	−1119.16			−0.781966			−0.390983	+	0.920398i	$0.627865\pi$
$128$	−1437.00	+	179.421i	−0.992295	+	0.123897i
$129$	482.555			0.329353
$130$	−16.0985	+	1118.54i	−0.0108610	+	0.754636i
$131$			2927.91i			1.95277i	0.216041	+	0.976384i	$0.430686\pi$
$131$			2927.91i			1.95277i	−0.216041	+	0.976384i	$0.569314\pi$
$132$	1052.98	−	902.664i	0.694316	−	0.595203i
$133$			1206.52i			0.786607i
$134$	1643.47	+	755.828i	1.05951	+	0.487266i
$135$		−	227.825i		−	0.145245i
$136$	−447.749	−	1571.07i	−0.282310	−	0.990577i
$137$			366.021i			0.228257i	0.993466	+	0.114129i	$0.0364076\pi$
$137$			366.021i			0.228257i	−0.993466	+	0.114129i	$0.963592\pi$
$138$	−597.259	+	1298.68i	−0.368421	+	0.801093i
$139$			1679.55i			1.02488i	0.858724	+	0.512439i	$0.171258\pi$
$139$			1679.55i			1.02488i	−0.858724	+	0.512439i	$0.828742\pi$
$140$	−428.812	+	367.600i	−0.258866	+	0.221913i
$141$	−1618.12			−0.966457
$142$	−93.7519	+	203.854i	−0.0554048	+	0.120472i
$143$	−1096.23	−	2476.93i	−0.641058	−	1.44847i
$144$	88.0231	−	569.235i	0.0509393	−	0.329418i
$145$		−	810.132i		−	0.463985i
$146$	48.0379	−	104.454i	0.0272304	−	0.0592099i
$147$			818.975i			0.459510i
$148$	−976.945	−	1139.63i	−0.542597	−	0.632950i
$149$	693.976			0.381562			0.190781	−	0.981633i	$-0.438898\pi$
$149$	693.976			0.381562			0.190781	+	0.981633i	$0.438898\pi$
$150$	190.745	−	414.756i	0.103829	−	0.225765i
$151$			1464.84i			0.789448i	0.918800	+	0.394724i	$0.129160\pi$
$151$			1464.84i			0.789448i	−0.918800	+	0.394724i	$0.870840\pi$
$152$	894.285	+	3137.89i	0.477211	+	1.67445i
$153$	649.773			0.343340
$154$	571.425	−	1242.51i	0.299005	−	0.650156i
$155$			500.951i			0.259596i
$156$	−1015.16	−	484.688i	−0.521012	−	0.248757i
$157$		−	3120.49i		−	1.58625i	−0.609056	−	0.793127i	$-0.708451\pi$
$157$		−	3120.49i		−	1.58625i	0.609056	−	0.793127i	$-0.291549\pi$
$158$	2075.03	+	954.298i	1.04481	+	0.480506i
$159$	1751.72			0.873713
$160$	−842.776	+	1273.88i	−0.416421	+	0.629434i
$161$			1409.53i			0.689976i
$162$	208.146	+	95.7256i	0.100947	+	0.0464254i
$163$	2488.19			1.19565			0.597824	−	0.801628i	$-0.296032\pi$
$163$	2488.19			1.19565			0.597824	+	0.801628i	$0.296032\pi$
$164$	−1284.18	+	1100.87i	−0.611450	+	0.524166i
$165$		−	1462.85i		−	0.690199i
$166$	3571.93	+	1642.72i	1.67010	+	0.768072i
$167$		−	2905.66i		−	1.34639i	−0.739466	−	0.673194i	$-0.764922\pi$
$167$		−	2905.66i		−	1.34639i	0.739466	−	0.673194i	$-0.235078\pi$
$168$	−155.672	−	546.227i	−0.0714903	−	0.250847i
$169$	−1477.30	+	1626.16i	−0.672419	+	0.740171i
$170$	−1565.45	−	719.945i	−0.706261	−	0.324808i
$171$	−1297.79			−0.580376
$172$	976.968	−	837.507i	0.433100	−	0.371275i
$173$		−	2339.59i		−	1.02818i	−0.857735	−	0.514092i	$-0.828129\pi$
$173$		−	2339.59i		−	1.02818i	0.857735	−	0.514092i	$-0.171871\pi$
$174$	740.154	+	340.395i	0.322476	+	0.148306i
$175$		−	450.157i		−	0.194449i
$176$	565.192	−	3655.02i	0.242062	−	1.56539i
$177$		−	708.384i		−	0.300822i
$178$	1243.13	−	2703.06i	0.523463	−	1.13822i
$179$		−	4222.06i		−	1.76297i	−0.472214	−	0.881484i	$-0.656545\pi$
$179$		−	4222.06i		−	1.76297i	0.472214	−	0.881484i	$-0.343455\pi$
$180$	−395.406	−	461.249i	−0.163732	−	0.190997i
$181$			3070.52i			1.26094i	0.776215	+	0.630469i	$0.217137\pi$
$181$			3070.52i			1.26094i	−0.776215	+	0.630469i	$0.782863\pi$
$182$	−1109.15	−	15.9633i	−0.451734	−	0.00650154i
$183$	1315.84			0.531528
$184$	1044.75	+	3665.86i	0.418588	+	1.46875i
$185$	−1583.23			−0.629197
$186$	−457.680	−	210.486i	−0.180423	−	0.0829761i
$187$	4172.16			1.63154
$188$	−3276.01	+	2808.36i	−1.27089	+	1.08947i
$189$	225.911			0.0869452
$190$	3126.66	+	1437.94i	1.19385	+	0.549049i
$191$	−623.978			−0.236385			−0.118192	−	0.992991i	$-0.537710\pi$
$191$	−623.978			−0.236385			−0.118192	+	0.992991i	$0.537710\pi$
$192$	−809.737	−	1305.23i	−0.304363	−	0.490608i
$193$		−	197.490i		−	0.0736560i	−0.999322	−	0.0368280i	$-0.988275\pi$
$193$		−	197.490i		−	0.0736560i	0.999322	−	0.0368280i	$-0.0117254\pi$
$194$	−1184.23	+	2574.98i	−0.438260	+	0.952953i
$195$	−1085.00	+	480.196i	−0.398455	+	0.176346i
$196$	1421.39	+	1658.08i	0.517999	+	0.604256i
$197$	−3571.39			−1.29163			−0.645815	−	0.763494i	$-0.723482\pi$
$197$	−3571.39			−1.29163			−0.645815	+	0.763494i	$0.723482\pi$
$198$	1336.49	+	614.649i	0.479699	+	0.220612i
$199$	2395.86			0.853458			0.426729	−	0.904379i	$-0.359666\pi$
$199$	2395.86			0.853458			0.426729	+	0.904379i	$0.359666\pi$
$200$	−333.660	−	1170.76i	−0.117967	−	0.413925i
$201$			1918.67i			0.673298i
$202$	838.352	−	1822.91i	0.292011	−	0.634949i
$203$	803.328			0.277747
$204$	1315.51	−	1127.73i	0.451492	−	0.387042i
$205$			1784.06i			0.607824i
$206$	1376.53	+	633.064i	0.465571	+	0.214115i
$207$	−1516.14			−0.509079
$208$	−2896.48	+	780.594i	−0.965551	+	0.260214i
$209$	−8333.02			−2.75793
$210$	−544.271	−	250.309i	−0.178849	−	0.0822521i
$211$			197.614i			0.0644754i	0.999480	+	0.0322377i	$0.0102633\pi$
$211$			197.614i			0.0644754i	−0.999480	+	0.0322377i	$0.989737\pi$
$212$	3546.49	−	3040.23i	1.14893	−	0.984924i
$213$	−237.990			−0.0765577
$214$	2218.73	−	4824.40i	0.708734	−	1.54107i
$215$		−	1357.26i		−	0.430531i
$216$	587.545	−	167.448i	0.185080	−	0.0527471i
$217$	−496.744			−0.155397
$218$	2787.18	+	1281.82i	0.865925	+	0.398236i
$219$	121.945			0.0376267
$220$	−2538.88	−	2961.65i	−0.778051	−	0.907612i
$221$	−1369.55	−	3094.51i	−0.416860	−	0.941897i
$222$	665.229	−	1446.47i	0.201114	−	0.437302i
$223$		−	2694.89i		−	0.809252i	−0.914482	−	0.404626i	$-0.867402\pi$
$223$		−	2694.89i		−	0.809252i	0.914482	−	0.404626i	$-0.132598\pi$
$224$	−1263.19	−	835.698i	−0.376786	−	0.249274i
$225$	484.208			0.143469
$226$	1010.43	+	464.693i	0.297401	+	0.136774i
$227$	825.056			0.241237			0.120619	−	0.992699i	$-0.461512\pi$
$227$	825.056			0.241237			0.120619	+	0.992699i	$0.461512\pi$
$228$	−2627.47	+	2252.40i	−0.763194	+	0.654249i
$229$	−838.916			−0.242084			−0.121042	−	0.992647i	$-0.538624\pi$
$229$	−838.916			−0.242084			−0.121042	+	0.992647i	$0.538624\pi$
$230$	3652.73	+	1679.88i	1.04719	+	0.481600i
$231$	1450.57			0.413161
$232$	2089.28	−	595.434i	0.591240	−	0.168501i
$233$	486.416			0.136765			0.0683824	−	0.997659i	$-0.478216\pi$
$233$	486.416			0.136765			0.0683824	+	0.997659i	$0.478216\pi$
$234$	17.1708	−	1193.05i	0.00479697	−	0.333299i
$235$			4551.21i			1.26336i
$236$	−1229.45	−	1434.18i	−0.339112	−	0.395581i
$237$			2422.49i			0.663957i
$238$	713.899	−	1552.30i	0.194434	−	0.422776i
$239$			690.902i			0.186990i	0.995620	+	0.0934952i	$0.0298040\pi$
$239$			690.902i			0.186990i	−0.995620	+	0.0934952i	$0.970196\pi$
$240$	−1601.06	−	247.578i	−0.430616	−	0.0665880i
$241$			1005.08i			0.268643i	0.990938	+	0.134322i	$0.0428855\pi$
$241$			1005.08i			0.268643i	−0.990938	+	0.134322i	$0.957114\pi$
$242$	5161.28	+	2373.66i	1.37099	+	0.630514i
$243$			243.000i			0.0641500i
$244$	2664.02	−	2283.73i	0.698960	−	0.599184i
$245$	2303.49			0.600673
$246$	−1629.95	−	749.610i	−0.422447	−	0.194282i
$247$	2735.40	+	6180.64i	0.704653	+	1.59216i
$248$	−1291.92	+	368.191i	−0.330794	+	0.0942748i
$249$			4170.06i			1.06131i
$250$	−3876.94	−	1782.99i	−0.980797	−	0.451066i
$251$		−	2502.31i		−	0.629262i	−0.949214	−	0.314631i	$-0.898119\pi$
$251$		−	2502.31i		−	0.629262i	0.949214	−	0.314631i	$-0.101881\pi$
$252$	457.375	−	392.085i	0.114333	−	0.0980121i
$253$	−9735.09			−2.41913
$254$	−2875.91	−	1322.62i	−0.710437	−	0.326728i
$255$		−	1827.59i		−	0.448815i
$256$	−3904.69	−	1237.18i	−0.953293	−	0.302046i
$257$	−1805.64			−0.438259			−0.219130	−	0.975696i	$-0.570322\pi$
$257$	−1805.64			−0.438259			−0.219130	+	0.975696i	$0.570322\pi$
$258$	1240.02	+	570.282i	0.299226	+	0.137613i
$259$		−	1569.93i		−	0.376645i
$260$	−1363.26	+	2855.29i	−0.325176	+	0.681068i
$261$			864.094i			0.204927i
$262$	−3460.20	+	7523.85i	−0.815922	+	1.77414i
$263$	−7806.91			−1.83040			−0.915199	−	0.403002i	$-0.867967\pi$
$263$	−7806.91			−1.83040			−0.915199	+	0.403002i	$0.867967\pi$
$264$	3772.60	−	1075.17i	0.879497	−	0.250653i
$265$		−	4926.98i		−	1.14212i
$266$	−1425.86	+	3100.40i	−0.328667	+	0.714653i
$267$	3155.69			0.723315
$268$	3329.99	+	3884.50i	0.758999	+	0.885387i
$269$			5945.63i			1.34763i	0.738902	+	0.673813i	$0.235345\pi$
$269$			5945.63i			1.34763i	−0.738902	+	0.673813i	$0.764655\pi$
$270$	269.243	−	585.441i	0.0606874	−	0.131959i
$271$		−	1898.73i		−	0.425608i	−0.977095	−	0.212804i	$-0.931740\pi$
$271$		−	1898.73i		−	0.425608i	0.977095	−	0.212804i	$-0.0682596\pi$
$272$	706.111	−	4566.34i	0.157405	−	1.01792i
$273$	−476.163	−	1075.89i	−0.105563	−	0.238520i
$274$	−432.562	+	940.563i	−0.0953724	+	0.207378i
$275$	3109.07			0.681761
$276$	−3069.55	+	2631.38i	−0.669439	+	0.573878i
$277$		−	2881.71i		−	0.625073i	−0.949906	−	0.312536i	$-0.898821\pi$
$277$		−	2881.71i		−	0.625073i	0.949906	−	0.312536i	$-0.101179\pi$
$278$	−1984.89	+	4315.95i	−0.428223	+	0.931128i
$279$		−	534.319i		−	0.114655i
$280$	−1536.35	+	437.852i	−0.327908	+	0.0934523i
$281$			2630.79i			0.558505i	0.960218	+	0.279252i	$0.0900866\pi$
$281$			2630.79i			0.558505i	−0.960218	+	0.279252i	$0.909913\pi$
$282$	−4158.09	−	1912.29i	−0.878051	−	0.403813i
$283$			6320.15i			1.32754i	0.747937	+	0.663770i	$0.231045\pi$
$283$			6320.15i			1.32754i	−0.747937	+	0.663770i	$0.768955\pi$
$284$	−481.829	+	413.048i	−0.100673	+	0.0863024i
$285$			3650.22i			0.758669i
$286$	110.253	−	7660.49i	0.0227951	−	1.58383i
$287$	−1769.07			−0.363850
$288$	898.913	−	1358.74i	0.183920	−	0.278001i
$289$	299.405			0.0609414
$290$	957.411	−	2081.79i	0.193866	−	0.421542i
$291$	−3006.17			−0.605583
$292$	246.886	−	211.643i	0.0494791	−	0.0424160i
$293$	4914.81			0.979953			0.489976	−	0.871736i	$-0.337005\pi$
$293$	4914.81			0.979953			0.489976	+	0.871736i	$0.337005\pi$
$294$	−967.863	+	2104.52i	−0.191996	+	0.417477i
$295$	−1992.44			−0.393235
$296$	−1163.65	−	4083.05i	−0.228499	−	0.801764i
$297$			1560.29i			0.304839i
$298$	1783.31	+	820.139i	0.346659	+	0.159427i
$299$	3195.64	+	7220.56i	0.618089	+	1.39657i
$300$	980.316	−	840.377i	0.188662	−	0.161731i
$301$	1345.86			0.257721
$302$	−1731.14	+	3764.19i	−0.329854	+	0.717234i
$303$	2128.16			0.403497
$304$	−1410.31	+	9120.31i	−0.266075	+	1.72068i
$305$		−	3701.00i		−	0.694815i
$306$	1669.72	+	767.900i	0.311933	+	0.143457i
$307$	−34.9320			−0.00649405			−0.00324702	−	0.999995i	$-0.501034\pi$
$307$	−34.9320			−0.00649405			−0.00324702	+	0.999995i	$0.501034\pi$
$308$	2936.78	−	2517.56i	0.543307	−	0.465751i
$309$			1607.04i			0.295861i
$310$	−592.023	+	1287.29i	−0.108467	+	0.235850i
$311$	−6754.52			−1.23155			−0.615777	−	0.787920i	$-0.711158\pi$
$311$	−6754.52			−1.23155			−0.615777	+	0.787920i	$0.711158\pi$
$312$	−2035.85	−	2445.22i	−0.369415	−	0.443696i
$313$	3933.85			0.710397			0.355199	−	0.934791i	$-0.384413\pi$
$313$	3933.85			0.710397			0.355199	+	0.934791i	$0.384413\pi$
$314$	3687.78	−	8018.71i	0.662782	−	1.44115i
$315$		−	635.411i		−	0.113655i
$316$	4204.40	+	4904.52i	0.748469	+	0.873104i
$317$	−4978.06			−0.882005			−0.441003	−	0.897506i	$-0.645377\pi$
$317$	−4978.06			−0.882005			−0.441003	+	0.897506i	$0.645377\pi$
$318$	4501.39	+	2070.18i	0.793791	+	0.365062i
$319$			5548.30i			0.973809i
$320$	−3671.16	+	2277.51i	−0.641324	+	0.397864i
$321$	5632.25			0.979320
$322$	−1665.77	+	3622.06i	−0.288292	+	0.626861i
$323$	−10410.7			−1.79340
$324$	421.744	+	491.972i	0.0723154	+	0.0843573i
$325$	−1020.58	−	2306.01i	−0.174190	−	0.393583i
$326$	6393.91	+	2940.54i	1.08628	+	0.499575i
$327$			3253.90i			0.550278i
$328$	−4600.96	+	1311.25i	−0.774529	+	0.220737i
$329$	−4512.99			−0.756259
$330$	1728.79	−	3759.09i	0.288385	−	0.627064i
$331$	−9305.29			−1.54521			−0.772606	−	0.634886i	$-0.781047\pi$
$331$	−9305.29			−1.54521			−0.772606	+	0.634886i	$0.781047\pi$
$332$	7237.43	+	8442.60i	1.19640	+	1.39563i
$333$	1688.69			0.277896
$334$	3433.90	−	7466.68i	0.562560	−	1.22323i
$335$	5396.57			0.880137
$336$	245.499	−	1587.61i	0.0398603	−	0.257772i
$337$	−9088.98			−1.46916			−0.734582	−	0.678520i	$-0.762622\pi$
$337$	−9088.98			−1.46916			−0.734582	+	0.678520i	$0.762622\pi$
$338$	−5718.01	+	2432.86i	−0.920174	+	0.391509i
$339$			1179.63i			0.188993i
$340$	−3171.90	−	3700.09i	−0.505943	−	0.590192i
$341$		−	3430.83i		−	0.544839i
$342$	−3334.92	−	1533.72i	−0.527286	−	0.242497i
$343$			5154.06i			0.811350i
$344$	3500.28	−	997.563i	0.548612	−	0.156352i
$345$			4264.39i			0.665470i
$346$	2764.92	−	6012.05i	0.429605	−	0.934132i
$347$		−	3.22515i		−	0.000498948i	−1.00000		0.000249474i	$-0.999921\pi$
$347$		−	3.22515i		−	0.000498948i	1.00000		0.000249474i	$-7.94101e-5\pi$
$348$	1499.69	+	1749.42i	0.231012	+	0.269480i
$349$	−12260.0			−1.88041			−0.940207	−	0.340604i	$-0.889368\pi$
$349$	−12260.0			−1.88041			−0.940207	+	0.340604i	$0.889368\pi$
$350$	531.994	−	1156.77i	0.0812465	−	0.176662i
$351$	1157.27	−	512.181i	0.175985	−	0.0778866i
$352$	5771.87	−	8724.37i	0.873982	−	1.32105i
$353$			8026.84i			1.21027i	0.796123	+	0.605135i	$0.206881\pi$
$353$			8026.84i			1.21027i	−0.796123	+	0.605135i	$0.793119\pi$
$354$	837.166	−	1820.33i	0.125692	−	0.273304i
$355$			669.383i			0.100076i
$356$	6388.94	−	5476.92i	0.951160	−	0.815383i
$357$	1812.24			0.268666
$358$	4989.61	−	10849.4i	0.736618	−	1.60170i
$359$		−	5963.70i		−	0.876747i	−0.898793	−	0.438374i	$-0.855555\pi$
$359$		−	5963.70i		−	0.876747i	0.898793	−	0.438374i	$-0.144445\pi$
$360$	−470.972	−	1652.56i	−0.0689511	−	0.241938i
$361$	13934.2			2.03152
$362$	−3628.73	+	7890.30i	−0.526855	+	1.14559i
$363$			6025.54i			0.871236i
$364$	−2831.31	−	1351.81i	−0.407695	−	0.194654i
$365$		−	342.988i		−	0.0491857i
$366$	3381.31	+	1555.06i	0.482907	+	0.222088i
$367$	−9542.35			−1.35724			−0.678619	−	0.734490i	$-0.737421\pi$
$367$	−9542.35			−1.35724			−0.678619	+	0.734490i	$0.737421\pi$
$368$	−1647.60	+	10654.8i	−0.233389	+	1.50930i
$369$		−	1902.89i		−	0.268457i
$370$	−4068.43	−	1871.06i	−0.571642	−	0.262896i
$371$	4885.60			0.683686
$372$	−927.348	−	1081.77i	−0.129249	−	0.150772i
$373$			7120.07i			0.988373i	0.869356	+	0.494186i	$0.164534\pi$
$373$			7120.07i			0.988373i	−0.869356	+	0.494186i	$0.835466\pi$
$374$	10721.2	+	4930.64i	1.48230	+	0.681705i
$375$		−	4526.14i		−	0.623277i
$376$	−11737.3	+	3345.07i	−1.60985	+	0.458800i
$377$	4115.20	−	1821.29i	0.562184	−	0.248809i
$378$	580.525	+	266.982i	0.0789920	+	0.0363282i
$379$	1748.05			0.236917			0.118458	−	0.992959i	$-0.462205\pi$
$379$	1748.05			0.236917			0.118458	+	0.992959i	$0.462205\pi$
$380$	6335.22	+	7390.15i	0.855236	+	0.997650i
$381$		−	3357.49i		−	0.451468i
$382$	−1603.44	−	737.416i	−0.214762	−	0.0987682i
$383$		−	5565.09i		−	0.742462i	−0.928541	−	0.371231i	$-0.878936\pi$
$383$		−	5565.09i		−	0.742462i	0.928541	−	0.371231i	$-0.121064\pi$
$384$	−538.264	−	4310.99i	−0.0715317	−	0.572902i
$385$		−	4079.94i		−	0.540085i
$386$	233.393	−	507.489i	0.0307756	−	0.0669184i
$387$			1447.66i			0.190152i
$388$	−6086.21	+	5217.41i	−0.796342	+	0.682665i
$389$			561.404i			0.0731731i	0.999330	+	0.0365865i	$0.0116485\pi$
$389$			561.404i			0.0731731i	−0.999330	+	0.0365865i	$0.988352\pi$
$390$	−3355.63	−	48.2956i	−0.435689	−	0.00627062i
$391$	−12162.3			−1.57308
$392$	1693.03	+	5940.56i	0.218140	+	0.765417i
$393$	−8783.73			−1.12743
$394$	−9177.40	−	4220.66i	−1.17348	−	0.539680i
$395$	6813.63			0.867926
$396$	2707.99	+	3158.93i	0.343641	+	0.400864i
$397$	5649.99			0.714269			0.357134	−	0.934053i	$-0.383754\pi$
$397$	5649.99			0.714269			0.357134	+	0.934053i	$0.383754\pi$
$398$	6156.65	+	2831.42i	0.775389	+	0.356599i
$399$	−3619.57			−0.454148
$400$	526.191	−	3402.81i	0.0657739	−	0.425352i
$401$		−	5458.35i		−	0.679743i	−0.940472	−	0.339871i	$-0.889616\pi$
$401$		−	5458.35i		−	0.679743i	0.940472	−	0.339871i	$-0.110384\pi$
$402$	−2267.48	+	4930.42i	−0.281323	+	0.611709i
$403$	−2544.66	+	1126.21i	−0.314538	+	0.139207i
$404$	4308.62	−	3693.57i	0.530599	−	0.454857i
$405$	683.475			0.0838571
$406$	2064.31	+	949.371i	0.252340	+	0.116050i
$407$	10843.0			1.32056
$408$	4713.22	−	1343.25i	0.571910	−	0.162992i
$409$		−	12750.8i		−	1.54154i	−0.637116	−	0.770768i	$-0.719873\pi$
$409$		−	12750.8i		−	1.54154i	0.637116	−	0.770768i	$-0.280127\pi$
$410$	−2108.39	+	4584.49i	−0.253966	+	0.552224i
$411$	−1098.06			−0.131784
$412$	2789.12	+	3253.57i	0.333520	+	0.389058i
$413$		−	1975.71i		−	0.235395i
$414$	−3896.04	−	1791.78i	−0.462512	−	0.212708i
$415$	11728.9			1.38735
$416$	−8365.58	−	1417.16i	−0.985953	−	0.167024i
$417$	−5038.66			−0.591713
$418$	−21413.4	−	9847.94i	−2.50565	−	1.15234i
$419$		−	4624.93i		−	0.539242i	−0.962966	−	0.269621i	$-0.913102\pi$
$419$		−	4624.93i		−	0.539242i	0.962966	−	0.269621i	$-0.0868985\pi$
$420$	−1102.80	−	1286.44i	−0.128122	−	0.149456i
$421$	−1108.40			−0.128314			−0.0641568	−	0.997940i	$-0.520436\pi$
$421$	−1108.40			−0.128314			−0.0641568	+	0.997940i	$0.520436\pi$
$422$	−233.540	+	507.808i	−0.0269396	+	0.0585775i
$423$		−	4854.37i		−	0.557984i
$424$	12706.3	−	3621.25i	1.45536	−	0.414772i
$425$	3884.26			0.443328
$426$	−611.562	−	281.256i	−0.0695547	−	0.0319880i
$427$	3669.92			0.415924
$428$	11402.9	−	9775.17i	1.28781	−	1.10397i
$429$	7430.80	−	3288.69i	0.836276	−	0.370115i
$430$	1604.00	−	3487.75i	0.179888	−	0.391149i
$431$			2059.16i			0.230130i	0.993358	+	0.115065i	$0.0367077\pi$
$431$			2059.16i			0.230130i	−0.993358	+	0.115065i	$0.963292\pi$
$432$	1707.70	+	264.069i	0.190190	+	0.0294098i
$433$	8396.61			0.931906			0.465953	−	0.884809i	$-0.345712\pi$
$433$	8396.61			0.931906			0.465953	+	0.884809i	$0.345712\pi$
$434$	−1276.48	−	587.051i	−0.141182	−	0.0649293i
$435$	2430.40			0.267882
$436$	5647.37	+	6587.76i	0.620321	+	0.723616i
$437$	24291.8			2.65911
$438$	313.361	+	144.114i	0.0341848	+	0.0157215i
$439$	−827.173			−0.0899290			−0.0449645	−	0.998989i	$-0.514317\pi$
$439$	−827.173			−0.0899290			−0.0449645	+	0.998989i	$0.514317\pi$
$440$	−3024.09	−	10611.0i	−0.327654	−	1.14968i
$441$	−2456.93			−0.265298
$442$	137.742	−	9570.49i	0.0148229	−	1.02991i
$443$		−	14728.4i		−	1.57961i	−0.613358	−	0.789805i	$-0.710182\pi$
$443$		−	14728.4i		−	1.57961i	0.613358	−	0.789805i	$-0.289818\pi$
$444$	3418.88	−	2930.84i	0.365434	−	0.313269i
$445$		−	8875.86i		−	0.945520i
$446$	3184.81	−	6925.06i	0.338129	−	0.735227i
$447$			2081.93i			0.220295i
$448$	−2258.38	−	3640.32i	−0.238166	−	0.383904i
$449$		−	1124.15i		−	0.118156i	−0.998253	−	0.0590781i	$-0.981184\pi$
$449$		−	1124.15i		−	0.118156i	0.998253	−	0.0590781i	$-0.0188161\pi$
$450$	1244.27	+	572.236i	0.130345	+	0.0599454i
$451$		−	12218.4i		−	1.27570i
$452$	2047.32	+	2388.24i	0.213049	+	0.248525i
$453$	−4394.51			−0.455788
$454$	2120.15	+	975.049i	0.219170	+	0.100796i
$455$	−3026.11	+	1339.28i	−0.311794	+	0.137992i
$456$	−9413.68	+	2682.86i	−0.966746	+	0.275518i
$457$		−	17029.0i		−	1.74307i	−0.490334	−	0.871535i	$-0.663125\pi$
$457$		−	17029.0i		−	1.74307i	0.490334	−	0.871535i	$-0.336875\pi$
$458$	−2155.76	−	991.429i	−0.219939	−	0.101149i
$459$			1949.32i			0.198227i
$460$	7401.15	+	8633.58i	0.750174	+	0.875093i
$461$	7086.48			0.715944			0.357972	−	0.933732i	$-0.383468\pi$
$461$	7086.48			0.715944			0.357972	+	0.933732i	$0.383468\pi$
$462$	3727.52	+	1714.27i	0.375368	+	0.172630i
$463$			9841.61i			0.987859i	0.869502	+	0.493929i	$0.164440\pi$
$463$			9841.61i			0.987859i	−0.869502	+	0.493929i	$0.835560\pi$
$464$	6072.49	+	939.015i	0.607561	+	0.0939497i
$465$	−1502.85			−0.149878
$466$	1249.94	+	574.845i	0.124254	+	0.0571442i
$467$		−	13523.9i		−	1.34007i	−0.742331	−	0.670034i	$-0.766280\pi$
$467$		−	13523.9i		−	1.34007i	0.742331	−	0.670034i	$-0.233720\pi$
$468$	1454.06	−	3045.48i	0.143620	−	0.300806i
$469$			5351.24i			0.526860i
$470$	−5378.61	+	11695.3i	−0.527866	+	1.14779i
$471$	9361.46			0.915825
$472$	−1464.41	−	5138.37i	−0.142807	−	0.501086i
$473$			9295.37i			0.903598i
$474$	−2862.89	+	6225.08i	−0.277420	+	0.603222i
$475$	−7758.01			−0.749393
$476$	3669.01	−	3145.26i	0.353296	−	0.302863i
$477$			5255.16i			0.504438i
$478$	−816.506	+	1775.41i	−0.0781299	+	0.169886i
$479$			8823.16i			0.841630i	0.907147	+	0.420815i	$0.138256\pi$
$479$			8823.16i			0.841630i	−0.907147	+	0.420815i	$0.861744\pi$
$480$	−3821.65	−	2528.33i	−0.363404	−	0.240421i
$481$	−3559.32	−	8042.28i	−0.337403	−	0.762363i
$482$	−1187.80	+	2582.76i	−0.112247	+	0.244069i
$483$	−4228.58			−0.398358
$484$	10457.7	+	12199.2i	0.982132	+	1.14568i
$485$			8455.30i			0.791619i
$486$	−287.177	+	624.437i	−0.0268037	+	0.0582820i
$487$			8482.21i			0.789252i	0.918842	+	0.394626i	$0.129126\pi$
$487$			8482.21i			0.789252i	−0.918842	+	0.394626i	$0.870874\pi$
$488$	9544.63	−	2720.17i	0.885379	−	0.252329i
$489$			7464.58i			0.690307i
$490$	5919.28	+	2722.26i	0.545727	+	0.250978i
$491$			6293.37i			0.578444i	0.957262	+	0.289222i	$0.0933965\pi$
$491$			6293.37i			0.578444i	−0.957262	+	0.289222i	$0.906603\pi$
$492$	−3302.60	−	3852.54i	−0.302627	−	0.353021i
$493$			6931.66i			0.633238i
$494$	−275.112	+	19115.1i	−0.0250564	+	1.74095i
$495$	4388.55			0.398487
$496$	−3754.97	−	580.647i	−0.339926	−	0.0525642i
$497$	−663.761			−0.0599069
$498$	−4928.17	+	10715.8i	−0.443447	+	0.964230i
$499$	−503.304			−0.0451523			−0.0225761	−	0.999745i	$-0.507187\pi$
$499$	−503.304			−0.0451523			−0.0225761	+	0.999745i	$0.507187\pi$
$500$	−7855.44	−	9163.52i	−0.702612	−	0.819610i
$501$	8716.99			0.777338
$502$	2957.23	−	6430.20i	0.262923	−	0.571701i
$503$	4401.21			0.390139			0.195070	−	0.980789i	$-0.437507\pi$
$503$	4401.21			0.390139			0.195070	+	0.980789i	$0.437507\pi$
$504$	1638.68	−	467.017i	0.144827	−	0.0412749i
$505$		−	5985.78i		−	0.527453i
$506$	−25016.2	−	11504.9i	−2.19784	−	1.01078i
$507$	−4878.47	−	4431.91i	−0.427338	−	0.388221i
$508$	−5827.16	−	6797.49i	−0.508934	−	0.593681i
$509$	−4188.23			−0.364715			−0.182358	−	0.983232i	$-0.558373\pi$
$509$	−4188.23			−0.364715			−0.182358	+	0.983232i	$0.558373\pi$
$510$	2159.84	−	4696.35i	0.187528	−	0.407760i
$511$	340.107			0.0294431
$512$	−8571.78	−	7793.73i	−0.739888	−	0.672730i
$513$		−	3893.36i		−	0.335080i
$514$	−4639.95	−	2133.90i	−0.398170	−	0.183117i
$515$	4520.03			0.386750
$516$	2512.52	+	2930.91i	0.214356	+	0.250050i
$517$		−	31169.6i		−	2.65153i
$518$	1855.34	−	4034.26i	0.157373	−	0.342191i
$519$	7018.77			0.593622
$520$	−6877.54	+	5726.15i	−0.580000	+	0.482900i
$521$	280.072			0.0235512			0.0117756	−	0.999931i	$-0.496252\pi$
$521$	280.072			0.0235512			0.0117756	+	0.999931i	$0.496252\pi$
$522$	−1021.18	+	2220.46i	−0.0856245	+	0.186182i
$523$		−	10351.8i		−	0.865493i	−0.901516	−	0.432747i	$-0.857544\pi$
$523$		−	10351.8i		−	0.865493i	0.901516	−	0.432747i	$-0.142456\pi$
$524$	−17783.3	+	15244.8i	−1.48257	+	1.27094i
$525$	1350.47			0.112265
$526$	−20061.4	−	9226.19i	−1.66296	−	0.764793i
$527$		−	4286.25i		−	0.354292i
$528$	10965.1	+	1695.57i	0.903776	+	0.139755i
$529$	16212.0			1.33245
$530$	5822.69	−	12660.8i	0.477210	−	1.03765i
$531$	2125.15			0.173679
$532$	−7328.09	+	6282.01i	−0.597205	+	0.511954i
$533$	−9062.41	+	4010.80i	−0.736466	+	0.325942i
$534$	8109.18	+	3729.39i	0.657151	+	0.302222i
$535$		−	15841.6i		−	1.28017i
$536$	3966.39	+	13917.4i	0.319630	+	1.12153i
$537$	12666.2			1.01785
$538$	−7026.53	+	15278.5i	−0.563076	+	1.22435i
$539$	−15775.8			−1.26069
$540$	1383.75	−	1186.22i	0.110272	−	0.0945309i
$541$	16992.5			1.35040			0.675199	−	0.737635i	$-0.264058\pi$
$541$	16992.5			1.35040			0.675199	+	0.737635i	$0.264058\pi$
$542$	2243.92	−	4879.17i	0.177831	−	0.386676i
$543$	−9211.55			−0.728002
$544$	7210.98	−	10899.6i	0.568324	−	0.859040i
$545$	9152.09			0.719325
$546$	47.8900	−	3327.44i	0.00375366	−	0.260809i
$547$		−	162.426i		−	0.0126963i	−0.999980	−	0.00634813i	$-0.997979\pi$
$547$		−	162.426i		−	0.0126963i	0.999980	−	0.00634813i	$-0.00202069\pi$
$548$	−2223.11	+	1905.76i	−0.173297	+	0.148559i
$549$			3947.52i			0.306878i
$550$	7989.38	+	3674.29i	0.619397	+	0.284859i
$551$		−	13844.6i		−	1.07041i
$552$	−10997.6	+	3134.26i	−0.847985	+	0.241672i
$553$			6756.41i			0.519551i
$554$	3405.60	−	7405.13i	0.261173	−	0.567895i
$555$		−	4749.69i		−	0.363267i
$556$	−10201.2	+	8744.95i	−0.778103	+	0.667030i
$557$	−135.037			−0.0102723			−0.00513617	−	0.999987i	$-0.501635\pi$
$557$	−135.037			−0.0102723			−0.00513617	+	0.999987i	$0.501635\pi$
$558$	631.457	−	1373.04i	0.0479063	−	0.104167i
$559$	6894.42	−	3051.30i	0.521651	−	0.230870i
$560$	−4465.40	−	690.504i	−0.336960	−	0.0521056i
$561$			12516.5i			0.941971i
$562$	−3109.06	+	6760.34i	−0.233359	+	0.507416i
$563$		−	15659.2i		−	1.17221i	−0.810234	−	0.586106i	$-0.800660\pi$
$563$		−	15659.2i		−	1.17221i	0.810234	−	0.586106i	$-0.199340\pi$
$564$	−8425.09	−	9828.03i	−0.629008	−	0.733750i
$565$	3317.88			0.247052
$566$	−7469.14	+	16240.9i	−0.554684	+	1.20610i
$567$			677.734i			0.0501978i
$568$	−1726.29	+	491.986i	−0.127524	+	0.0363438i
$569$	−13692.7			−1.00884			−0.504418	−	0.863460i	$-0.668293\pi$
$569$	−13692.7			−1.00884			−0.504418	+	0.863460i	$0.668293\pi$
$570$	−4313.82	+	9379.97i	−0.316993	+	0.689270i
$571$			23805.8i			1.74473i	0.488856	+	0.872365i	$0.337414\pi$
$571$			23805.8i			1.74473i	−0.488856	+	0.872365i	$0.662586\pi$
$572$	9336.47	−	19554.9i	0.682478	−	1.42942i
$573$		−	1871.93i		−	0.136477i
$574$	−4545.98	−	2090.69i	−0.330567	−	0.152027i
$575$	−9063.32			−0.657333
$576$	3915.69	−	2429.21i	0.283253	−	0.175724i
$577$			10653.4i			0.768642i	0.923200	+	0.384321i	$0.125564\pi$
$577$			10653.4i			0.768642i	−0.923200	+	0.384321i	$0.874436\pi$
$578$	769.381	+	353.836i	0.0553669	+	0.0254631i
$579$	592.469			0.0425253
$580$	4920.52	−	4218.12i	0.352265	−	0.301979i
$581$			11630.4i			0.830484i
$582$	−7724.94	−	3552.68i	−0.550188	−	0.253030i
$583$			33743.1i			2.39708i
$584$	884.542	−	252.090i	0.0626757	−	0.0178623i
$585$	−1440.59	−	3255.01i	−0.101814	−	0.230048i
$586$	12629.6	+	5808.31i	0.890313	+	0.409452i
$587$	−15680.9			−1.10259			−0.551294	−	0.834311i	$-0.685866\pi$
$587$	−15680.9			−1.10259			−0.551294	+	0.834311i	$0.685866\pi$
$588$	−4974.23	+	4264.17i	−0.348867	+	0.299067i
$589$			8560.89i			0.598888i
$590$	−5119.97	−	2354.66i	−0.357264	−	0.164305i
$591$		−	10714.2i		−	0.745723i
$592$	1835.11	−	11867.4i	0.127403	−	0.823897i
$593$		−	7750.92i		−	0.536749i	−0.963315	−	0.268375i	$-0.913514\pi$
$593$		−	7750.92i		−	0.536749i	0.963315	−	0.268375i	$-0.0864865\pi$
$594$	−1843.95	+	4009.48i	−0.127370	+	0.276954i
$595$		−	5097.19i		−	0.351201i
$596$	3613.33	+	4215.02i	0.248335	+	0.289688i
$597$			7187.59i			0.492744i
$598$	−321.401	+	22331.3i	−0.0219783	+	1.52708i
$599$	5641.89			0.384844			0.192422	−	0.981312i	$-0.438366\pi$
$599$	5641.89			0.384844			0.192422	+	0.981312i	$0.438366\pi$
$600$	3512.27	−	1000.98i	0.238980	−	0.0681081i
$601$	10995.2			0.746264			0.373132	−	0.927778i	$-0.378284\pi$
$601$	10995.2			0.746264			0.373132	+	0.927778i	$0.378284\pi$
$602$	3458.45	+	1590.53i	0.234146	+	0.107683i
$603$	−5756.02			−0.388729
$604$	−8897.01	+	7626.97i	−0.599361	+	0.513803i
$605$	16947.8			1.13888
$606$	5468.73	+	2515.06i	0.366588	+	0.168593i
$607$	−1343.46			−0.0898344			−0.0449172	−	0.998991i	$-0.514302\pi$
$607$	−1343.46			−0.0898344			−0.0449172	+	0.998991i	$0.514302\pi$
$608$	−14402.4	+	21769.7i	−0.960684	+	1.45210i
$609$			2409.98i			0.160357i
$610$	4373.83	−	9510.45i	0.290313	−	0.631257i
$611$	−23118.7	+	10231.7i	−1.53074	+	0.677467i
$612$	3383.18	+	3946.54i	0.223459	+	0.260669i
$613$	−9486.08			−0.625023			−0.312511	−	0.949914i	$-0.601170\pi$
$613$	−9486.08			−0.625023			−0.312511	+	0.949914i	$0.601170\pi$
$614$	−89.7647	−	41.2825i	−0.00590001	−	0.00271340i
$615$	−5352.17			−0.350927
$616$	10521.9	−	2998.69i	0.688213	−	0.196137i
$617$			23208.1i			1.51430i	0.653242	+	0.757149i	$0.273408\pi$
$617$			23208.1i			1.51430i	−0.653242	+	0.757149i	$0.726592\pi$
$618$	−1899.19	+	4129.60i	−0.123619	+	0.268797i
$619$	15457.5			1.00370			0.501849	−	0.864955i	$-0.332653\pi$
$619$	15457.5			1.00370			0.501849	+	0.864955i	$0.332653\pi$
$620$	−3042.64	+	2608.31i	−0.197089	+	0.168955i
$621$		−	4548.43i		−	0.293917i
$622$	−17357.1	−	7982.47i	−1.11890	−	0.514579i
$623$	8801.32			0.565999
$624$	−2341.78	−	8689.43i	−0.150234	−	0.557461i
$625$	−6005.36			−0.384343
$626$	10108.8	+	4649.01i	0.645415	+	0.296824i
$627$		−	24999.1i		−	1.59229i
$628$	18953.0	−	16247.5i	1.20431	−	1.03240i
$629$	13546.5			0.858717
$630$	750.927	−	1632.81i	0.0474883	−	0.103259i
$631$			16138.7i			1.01818i	0.860713	+	0.509091i	$0.170018\pi$
$631$			16138.7i			1.01818i	−0.860713	+	0.509091i	$0.829982\pi$
$632$	5007.91	+	17571.9i	0.315196	+	1.10597i
$633$	−592.842			−0.0372249
$634$	−12792.1	−	5883.06i	−0.801325	−	0.368527i
$635$	−9443.45			−0.590161
$636$	9120.69	+	10639.5i	0.568646	+	0.663337i
$637$	5178.56	+	11701.0i	0.322107	+	0.727801i
$638$	−6556.97	+	14257.5i	−0.406885	+	0.884731i
$639$		−	713.970i		−	0.0442006i
$640$	−12125.3	+	1513.95i	−0.748899	+	0.0935065i
$641$	−4067.71			−0.250647			−0.125324	−	0.992116i	$-0.539997\pi$
$641$	−4067.71			−0.250647			−0.125324	+	0.992116i	$0.539997\pi$
$642$	14473.2	+	6656.18i	0.889738	+	0.409188i
$643$	−14570.0			−0.893603			−0.446801	−	0.894633i	$-0.647437\pi$
$643$	−14570.0			−0.893603			−0.446801	+	0.894633i	$0.647437\pi$
$644$	−8561.07	+	7338.99i	−0.523841	+	0.449063i
$645$	4071.78			0.248567
$646$	−26752.4	−	12303.3i	−1.62935	−	0.749332i
$647$	19304.6			1.17302			0.586509	−	0.809943i	$-0.300502\pi$
$647$	19304.6			1.17302			0.586509	+	0.809943i	$0.300502\pi$
$648$	502.343	+	1762.64i	0.0304535	+	0.106856i
$649$	13645.5			0.825319
$650$	102.645	−	7131.89i	0.00619395	−	0.430362i
$651$		−	1490.23i		−	0.0897186i
$652$	12955.3	+	15112.6i	0.778173	+	0.907754i
$653$		−	1649.08i		−	0.0988260i	−0.998778	−	0.0494130i	$-0.984265\pi$
$653$		−	1649.08i		−	0.0988260i	0.998778	−	0.0494130i	$-0.0157351\pi$
$654$	−3845.45	+	8361.54i	−0.229922	+	0.499942i
$655$			24705.6i			1.47378i
$656$	−13372.7	−	2067.88i	−0.795910	−	0.123075i
$657$			365.834i			0.0217238i
$658$	−11597.0	−	5333.44i	−0.687081	−	0.315987i
$659$			16643.2i			0.983803i	0.870651	+	0.491902i	$0.163698\pi$
$659$			16643.2i			0.983803i	−0.870651	+	0.491902i	$0.836302\pi$
$660$	8884.96	−	7616.64i	0.524010	−	0.449208i
$661$	5394.04			0.317403			0.158702	−	0.987327i	$-0.449269\pi$
$661$	5394.04			0.317403			0.158702	+	0.987327i	$0.449269\pi$
$662$	−23911.8	−	10997.0i	−1.40387	−	0.645634i
$663$	9283.52	−	4108.66i	0.543804	−	0.240674i
$664$	8620.58	+	30248.1i	0.503830	+	1.76785i
$665$			10180.6i			0.593663i
$666$	4339.42	+	1995.69i	0.252476	+	0.116113i
$667$		−	16174.0i		−	0.938918i
$668$	17648.2	−	15128.9i	1.02220	−	0.876282i
$669$	8084.67			0.467222
$670$	13867.6	+	6377.65i	0.799627	+	0.367746i
$671$			25346.8i			1.45827i
$672$	2507.10	−	3789.56i	0.143919	−	0.217538i
$673$	−29896.5			−1.71237			−0.856186	−	0.516668i	$-0.827172\pi$
$673$	−29896.5			−1.71237			−0.856186	+	0.516668i	$0.827172\pi$
$674$	−23356.0	−	10741.3i	−1.33477	−	0.613859i
$675$			1452.62i			0.0828319i
$676$	−17568.7	−	505.817i	−0.999586	−	0.0287789i
$677$		−	5527.06i		−	0.313770i	−0.987617	−	0.156885i	$-0.949855\pi$
$677$		−	5527.06i		−	0.313770i	0.987617	−	0.156885i	$-0.0501452\pi$
$678$	−1394.08	+	3031.28i	−0.0789665	+	0.171705i
$679$	−8384.29			−0.473873
$680$	−3778.08	−	13256.7i	−0.213063	−	0.747602i
$681$			2475.17i			0.139278i
$682$	4054.55	−	8816.21i	0.227649	−	0.495000i
$683$	1482.94			0.0830790			0.0415395	−	0.999137i	$-0.486774\pi$
$683$	1482.94			0.0830790			0.0415395	+	0.999137i	$0.486774\pi$
$684$	−6757.20	−	7882.40i	−0.377731	−	0.440630i
$685$			3088.47i			0.172269i
$686$	−6091.05	+	13244.4i	−0.339005	+	0.737133i
$687$		−	2516.75i		−	0.139767i
$688$	10173.6	+	1573.18i	0.563756	+	0.0871759i
$689$	25027.4	−	11076.5i	1.38384	−	0.612455i
$690$	−5039.64	+	10958.2i	−0.278052	+	0.604596i
$691$	18752.3			1.03237			0.516187	−	0.856476i	$-0.327351\pi$
$691$	18752.3			1.03237			0.516187	+	0.856476i	$0.327351\pi$
$692$	14210.0	−	12181.6i	0.780614	−	0.669182i
$693$			4351.70i			0.238539i
$694$	3.81147	−	8.28766i	0.000208475	−	0.000453307i
$695$			14172.0i			0.773489i
$696$	1786.30	+	6267.83i	0.0972839	+	0.341353i
$697$		−	15264.8i		−	0.829547i
$698$	−31504.6	−	14488.9i	−1.70840	−	0.785690i
$699$			1459.25i			0.0789612i
$700$	2734.13	−	2343.84i	0.147629	−	0.126555i
$701$		−	30930.9i		−	1.66654i	−0.552867	−	0.833269i	$-0.686466\pi$
$701$		−	30930.9i		−	1.66654i	0.552867	−	0.833269i	$-0.313534\pi$
$702$	3579.14	+	51.5125i	0.192430	+	0.00276953i
$703$	−27056.3			−1.45156
$704$	25142.4	−	15597.8i	1.34601	−	0.835036i
$705$	−13653.6			−0.729399
$706$	−9486.10	+	20626.6i	−0.505686	+	1.09956i
$707$	5935.51			0.315739
$708$	4302.53	−	3688.35i	0.228389	−	0.195786i
$709$	−15172.9			−0.803711			−0.401855	−	0.915703i	$-0.631635\pi$
$709$	−15172.9			−0.803711			−0.401855	+	0.915703i	$0.631635\pi$
$710$	−791.075	+	1720.11i	−0.0418148	+	0.0909221i
$711$	−7267.48			−0.383336
$712$	22890.3	−	6523.62i	1.20484	−	0.343375i
$713$			10001.3i			0.525318i
$714$	4656.90	+	2141.70i	0.244090	+	0.112256i
$715$	−9249.93	−	20900.2i	−0.483815	−	1.09318i
$716$	25643.6	−	21983.0i	1.33847	−	1.14741i
$717$	−2072.71			−0.107959
$718$	7047.89	−	15324.9i	0.366330	−	0.796547i
$719$	−7513.99			−0.389742			−0.194871	−	0.980829i	$-0.562429\pi$
$719$	−7513.99			−0.389742			−0.194871	+	0.980829i	$0.562429\pi$
$720$	742.735	−	4803.18i	0.0384446	−	0.248616i
$721$			4482.07i			0.231513i
$722$	35806.7	+	16467.4i	1.84569	+	0.848828i
$723$	−3015.25			−0.155101
$724$	−18649.5	+	15987.3i	−0.957324	+	0.820667i
$725$			5165.44i			0.264607i
$726$	−7120.97	+	15483.8i	−0.364027	+	0.791541i
$727$	9581.83			0.488818			0.244409	−	0.969672i	$-0.421406\pi$
$727$	9581.83			0.488818			0.244409	+	0.969672i	$0.421406\pi$
$728$	−5678.06	−	6819.78i	−0.289070	−	0.347195i
$729$	−729.000			−0.0370370
$730$	405.342	−	881.375i	0.0205512	−	0.0446865i
$731$			11613.0i			0.587582i
$732$	6851.19	+	7992.05i	0.345939	+	0.403545i
$733$	−1242.65			−0.0626170			−0.0313085	−	0.999510i	$-0.509967\pi$
$733$	−1242.65			−0.0626170			−0.0313085	+	0.999510i	$0.509967\pi$
$734$	−24521.0	−	11277.1i	−1.23309	−	0.567093i
$735$			6910.48i			0.346798i
$736$	−16825.7	+	25432.6i	−0.842668	+	1.27372i
$737$	−36959.1			−1.84723
$738$	2248.83	−	4889.85i	0.112169	−	0.243900i
$739$	7607.91			0.378703			0.189351	−	0.981909i	$-0.439361\pi$
$739$	7607.91			0.378703			0.189351	+	0.981909i	$0.439361\pi$
$740$	−8243.42	−	9616.11i	−0.409506	−	0.477696i
$741$	−18541.9	+	8206.19i	−0.919236	+	0.406831i
$742$	12554.5	+	5773.79i	0.621147	+	0.285664i
$743$		−	23962.7i		−	1.18318i	−0.806238	−	0.591591i	$-0.798500\pi$
$743$		−	23962.7i		−	1.18318i	0.806238	−	0.591591i	$-0.201500\pi$
$744$	−1104.57	−	3875.76i	−0.0544296	−	0.190984i
$745$	5855.74			0.287970
$746$	−8414.48	+	18296.4i	−0.412970	+	0.897962i
$747$	−12510.2			−0.612749
$748$	21723.2	+	25340.5i	1.06187	+	1.23869i
$749$	15708.5			0.766325
$750$	5348.98	−	11630.8i	0.260423	−	0.566264i
$751$	−14661.3			−0.712383			−0.356192	−	0.934413i	$-0.615925\pi$
$751$	−14661.3			−0.712383			−0.356192	+	0.934413i	$0.615925\pi$
$752$	−34114.5	−	5275.26i	−1.65429	−	0.255810i
$753$	7506.94			0.363304
$754$	12727.2	+	183.175i	0.614719	+	0.00884728i
$755$			12360.2i			0.595807i
$756$	1176.26	+	1372.12i	0.0565873	+	0.0660102i
$757$		−	6391.51i		−	0.306874i	−0.988158	−	0.153437i	$-0.950966\pi$
$757$		−	6391.51i		−	0.306874i	0.988158	−	0.153437i	$-0.0490342\pi$
$758$	4491.97	+	2065.84i	0.215245	+	0.0989906i
$759$		−	29205.3i		−	1.39668i
$760$	7545.94	+	26477.4i	0.360158	+	1.26373i
$761$			3654.75i			0.174093i	0.996204	+	0.0870464i	$0.0277428\pi$
$761$			3654.75i			0.174093i	−0.996204	+	0.0870464i	$0.972257\pi$
$762$	3967.87	−	8627.74i	0.188636	−	0.410171i
$763$			9075.22i			0.430597i
$764$	−3248.87	−	3789.87i	−0.153848	−	0.179467i
$765$	5482.76			0.259123
$766$	6576.81	−	14300.6i	0.310222	−	0.674546i
$767$	−4479.27	−	10120.9i	−0.210870	−	0.476461i
$768$	3711.54	−	11714.1i	0.174386	−	0.550384i
$769$		−	13844.0i		−	0.649188i	−0.945853	−	0.324594i	$-0.894772\pi$
$769$		−	13844.0i		−	0.649188i	0.945853	−	0.324594i	$-0.105228\pi$
$770$	4821.66	−	10484.2i	0.225663	−	0.490682i
$771$		−	5416.91i		−	0.253029i
$772$	1199.50	−	1028.27i	0.0559208	−	0.0479382i
$773$	−9330.55			−0.434148

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)

\(f(q)\)	\(=\)	\(q+(2.56970 + 1.18180i) q^{2} +3.00000i q^{3} +(5.20671 + 6.07373i) q^{4} +8.43796 q^{5} +(-3.54539 + 7.70910i) q^{6} +8.36709i q^{7} +(6.20176 + 21.7609i) q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+(2.56970 + 1.18180i) q^{2} +3.00000i q^{3} +(5.20671 + 6.07373i) q^{4} +8.43796 q^{5} +(-3.54539 + 7.70910i) q^{6} +8.36709i q^{7} +(6.20176 + 21.7609i) q^{8} -9.00000 q^{9} +(21.6830 + 9.97196i) q^{10} -57.7885 q^{11} +(-18.2212 + 15.6201i) q^{12} +(18.9697 + 42.8620i) q^{13} +(-9.88821 + 21.5009i) q^{14} +25.3139i q^{15} +(-9.78034 + 63.2483i) q^{16} -72.1970 q^{17} +(-23.1273 - 10.6362i) q^{18} +144.199 q^{19} +(43.9340 + 51.2499i) q^{20} -25.1013 q^{21} +(-148.499 - 68.2943i) q^{22} +168.461 q^{23} +(-65.2828 + 18.6053i) q^{24} -53.8009 q^{25} +(-1.90787 + 132.561i) q^{26} -27.0000i q^{27} +(-50.8194 + 43.5650i) q^{28} -96.0104i q^{29} +(-29.9159 + 65.0490i) q^{30} +59.3688i q^{31} +(-99.8792 + 150.971i) q^{32} -173.366i q^{33} +(-185.525 - 85.3222i) q^{34} +70.6012i q^{35} +(-46.8604 - 54.6636i) q^{36} -187.632 q^{37} +(370.547 + 170.413i) q^{38} +(-128.586 + 56.9090i) q^{39} +(52.3302 + 183.618i) q^{40} +211.432i q^{41} +(-64.5027 - 29.6646i) q^{42} -160.852i q^{43} +(-300.888 - 350.992i) q^{44} -75.9416 q^{45} +(432.893 + 199.086i) q^{46} +539.374i q^{47} +(-189.745 - 29.3410i) q^{48} +272.992 q^{49} +(-138.252 - 63.5817i) q^{50} -216.591i q^{51} +(-161.563 + 338.387i) q^{52} -583.906i q^{53} +(31.9085 - 69.3819i) q^{54} -487.617 q^{55} +(-182.076 + 51.8907i) q^{56} +432.596i q^{57} +(113.465 - 246.718i) q^{58} -236.128 q^{59} +(-153.750 + 131.802i) q^{60} -438.613i q^{61} +(-70.1619 + 152.560i) q^{62} -75.3038i q^{63} +(-435.076 + 269.912i) q^{64} +(160.065 + 361.668i) q^{65} +(204.883 - 445.497i) q^{66} +639.558 q^{67} +(-375.909 - 438.505i) q^{68} +505.382i q^{69} +(-83.4363 + 181.424i) q^{70} +79.3300i q^{71} +(-55.8159 - 195.848i) q^{72} -40.6482i q^{73} +(-482.158 - 221.743i) q^{74} -161.403i q^{75} +(750.800 + 875.822i) q^{76} -483.522i q^{77} +(-397.682 - 5.72361i) q^{78} +807.497 q^{79} +(-82.5261 + 533.686i) q^{80} +81.0000 q^{81} +(-249.870 + 543.317i) q^{82} +1390.02 q^{83} +(-130.695 - 152.458i) q^{84} -609.195 q^{85} +(190.094 - 413.340i) q^{86} +288.031 q^{87} +(-358.391 - 1257.53i) q^{88} -1051.90i q^{89} +(-195.147 - 89.7476i) q^{90} +(-358.630 + 158.721i) q^{91} +(877.125 + 1023.18i) q^{92} -178.106 q^{93} +(-637.431 + 1386.03i) q^{94} +1216.74 q^{95} +(-452.912 - 299.638i) q^{96} +1002.06i q^{97} +(701.507 + 322.621i) q^{98} +520.097 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 756 q^{9}+O(q^{10}) \) 84 * q - 756 * q^9	\( 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52} - 1616 q^{55} + 608 q^{56} - 2120 q^{62} - 2856 q^{64} + 696 q^{65} - 396 q^{66} - 2536 q^{68} - 3936 q^{74} - 156 q^{78} + 3160 q^{79} + 6804 q^{81} + 4276 q^{82} - 2088 q^{87} + 1780 q^{88} + 324 q^{90} + 4792 q^{92} - 860 q^{94} + 2480 q^{95}+O(q^{100}) \) 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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