LMFDB - Embedded newform 115.4.e.a.22.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,4,Mod(22,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("115.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	115.e (of order $4$, degree $2$, 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:	$6.78521965066$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			22.12
Character	$\chi$	$=$	115.22
Dual form			115.4.e.a.68.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.84990 - 1.84990i) q^{2} +(-5.85544 + 5.85544i) q^{3} -1.15573i q^{4} +(10.6129 + 3.51653i) q^{5} +21.6640 q^{6} +(7.25929 - 7.25929i) q^{7} +(-16.9372 + 16.9372i) q^{8} -41.5723i q^{9} +(-13.1276 - 26.1381i) q^{10} -0.503049i q^{11} +(6.76730 + 6.76730i) q^{12} +(-4.59644 + 4.59644i) q^{13} -26.8579 q^{14} +(-82.7341 + 41.5524i) q^{15} +53.4185 q^{16} +(-74.8926 + 74.8926i) q^{17} +(-76.9047 + 76.9047i) q^{18} -133.354 q^{19} +(4.06416 - 12.2657i) q^{20} +85.0127i q^{21} +(-0.930591 + 0.930591i) q^{22} +(-84.1638 + 71.2984i) q^{23} -198.349i q^{24} +(100.268 + 74.6413i) q^{25} +17.0059 q^{26} +(85.3275 + 85.3275i) q^{27} +(-8.38978 - 8.38978i) q^{28} -150.499i q^{29} +(229.918 + 76.1821i) q^{30} -122.391 q^{31} +(36.6787 + 36.6787i) q^{32} +(2.94557 + 2.94557i) q^{33} +277.088 q^{34} +(102.570 - 51.5147i) q^{35} -48.0464 q^{36} +(-53.1409 + 53.1409i) q^{37} +(246.692 + 246.692i) q^{38} -53.8283i q^{39} +(-239.313 + 120.193i) q^{40} -134.778 q^{41} +(157.265 - 157.265i) q^{42} +(-300.444 - 300.444i) q^{43} -0.581389 q^{44} +(146.191 - 441.204i) q^{45} +(287.590 + 23.7997i) q^{46} +(31.8091 + 31.8091i) q^{47} +(-312.789 + 312.789i) q^{48} +237.605i q^{49} +(-47.4068 - 323.565i) q^{50} -877.058i q^{51} +(5.31224 + 5.31224i) q^{52} +(189.294 + 189.294i) q^{53} -315.695i q^{54} +(1.76899 - 5.33882i) q^{55} +245.904i q^{56} +(780.847 - 780.847i) q^{57} +(-278.409 + 278.409i) q^{58} +213.925i q^{59} +(48.0234 + 95.6183i) q^{60} +205.810i q^{61} +(226.412 + 226.412i) q^{62} +(-301.786 - 301.786i) q^{63} -563.052i q^{64} +(-64.9451 + 32.6181i) q^{65} -10.8980i q^{66} +(-710.343 + 710.343i) q^{67} +(86.5555 + 86.5555i) q^{68} +(75.3326 - 910.299i) q^{69} +(-285.041 - 94.4468i) q^{70} +449.783 q^{71} +(704.119 + 704.119i) q^{72} +(365.998 - 365.998i) q^{73} +196.611 q^{74} +(-1024.17 + 150.055i) q^{75} +154.121i q^{76} +(-3.65178 - 3.65178i) q^{77} +(-99.5771 + 99.5771i) q^{78} -625.818 q^{79} +(566.926 + 187.848i) q^{80} +123.193 q^{81} +(249.326 + 249.326i) q^{82} +(819.106 + 819.106i) q^{83} +98.2517 q^{84} +(-1058.19 + 531.466i) q^{85} +1111.58i q^{86} +(881.240 + 881.240i) q^{87} +(8.52024 + 8.52024i) q^{88} +397.018 q^{89} +(-1086.62 + 545.746i) q^{90} +66.7338i q^{91} +(82.4016 + 97.2706i) q^{92} +(716.655 - 716.655i) q^{93} -117.688i q^{94} +(-1415.28 - 468.944i) q^{95} -429.540 q^{96} +(1055.44 - 1055.44i) q^{97} +(439.547 - 439.547i) q^{98} -20.9129 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 4 q^{2} + 4 q^{3} + 32 q^{6} + 28 q^{8} + 200 q^{12} - 100 q^{13} - 832 q^{16} - 112 q^{18} - 46 q^{23} - 372 q^{25} - 312 q^{26} - 704 q^{27} - 1056 q^{31} + 560 q^{32} - 348 q^{35} + 2424 q^{36}+ \cdots - 3612 q^{98}+O(q^{100}) $ 68 * q - 4 * q^2 + 4 * q^3 + 32 * q^6 + 28 * q^8 + 200 * q^12 - 100 * q^13 - 832 * q^16 - 112 * q^18 - 46 * q^23 - 372 * q^25 - 312 * q^26 - 704 * q^27 - 1056 * q^31 + 560 * q^32 - 348 * q^35 + 2424 * q^36 + 2248 * q^41 - 96 * q^46 - 1412 * q^47 + 1532 * q^48 - 620 * q^50 + 112 * q^52 + 2688 * q^55 + 2044 * q^58 + 3948 * q^62 - 1836 * q^70 - 2272 * q^71 + 1128 * q^72 + 1100 * q^73 + 2828 * q^75 + 4216 * q^77 - 9180 * q^78 - 3580 * q^81 - 6516 * q^82 - 2684 * q^85 - 6304 * q^87 - 688 * q^92 - 1608 * q^93 - 8616 * q^95 - 544 * q^96 - 3612 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.84990	−	1.84990i	−0.654039	−	0.654039i	0.299924	−	0.953963i	$-0.403039\pi$
$2$	−1.84990	−	1.84990i	−0.654039	−	0.654039i	−0.953963	+	0.299924i	$0.903039\pi$
$3$	−5.85544	+	5.85544i	−1.12688	+	1.12688i	−0.136198	+	0.990682i	$0.543488\pi$
$3$	−5.85544	+	5.85544i	−1.12688	+	1.12688i	−0.990682	+	0.136198i	$0.956512\pi$
$4$		−	1.15573i		−	0.144466i
$5$	10.6129	+	3.51653i	0.949248	+	0.314528i
$5$	10.6129	+	3.51653i	0.949248	+	0.314528i
$6$	21.6640			1.47405
$7$	7.25929	−	7.25929i	0.391965	−	0.391965i	−0.483422	−	0.875387i	$-0.660606\pi$
$7$	7.25929	−	7.25929i	0.391965	−	0.391965i	0.875387	+	0.483422i	$0.160606\pi$
$8$	−16.9372	+	16.9372i	−0.748525	+	0.748525i
$9$		−	41.5723i		−	1.53972i
$10$	−13.1276	−	26.1381i	−0.415132	−	0.826559i
$11$		−	0.503049i		−	0.0137886i	−0.999976	−	0.00689432i	$-0.997805\pi$
$11$		−	0.503049i		−	0.0137886i	0.999976	−	0.00689432i	$-0.00219455\pi$
$12$	6.76730	+	6.76730i	0.162796	+	0.162796i
$13$	−4.59644	+	4.59644i	−0.0980633	+	0.0980633i	−0.754436	−	0.656373i	$-0.772090\pi$
$13$	−4.59644	+	4.59644i	−0.0980633	+	0.0980633i	0.656373	+	0.754436i	$0.272090\pi$
$14$	−26.8579			−0.512721
$15$	−82.7341	+	41.5524i	−1.42412	+	0.715253i
$16$	53.4185			0.834663
$17$	−74.8926	+	74.8926i	−1.06848	+	1.06848i	−0.0710011	+	0.997476i	$0.522619\pi$
$17$	−74.8926	+	74.8926i	−1.06848	+	1.06848i	−0.997476	+	0.0710011i	$0.977381\pi$
$18$	−76.9047	+	76.9047i	−1.00703	+	1.00703i
$19$	−133.354			−1.61019			−0.805093	−	0.593149i	$-0.797884\pi$
$19$	−133.354			−1.61019			−0.805093	+	0.593149i	$0.797884\pi$
$20$	4.06416	−	12.2657i	0.0454387	−	0.137134i
$21$			85.0127i			0.883395i
$22$	−0.930591	+	0.930591i	−0.00901831	+	0.00901831i
$23$	−84.1638	+	71.2984i	−0.763016	+	0.646380i
$23$	−84.1638	+	71.2984i	−0.763016	+	0.646380i
$24$		−	198.349i		−	1.68700i
$25$	100.268	+	74.6413i	0.802144	+	0.597131i
$26$	17.0059			0.128274
$27$	85.3275	+	85.3275i	0.608196	+	0.608196i
$28$	−8.38978	−	8.38978i	−0.0566257	−	0.0566257i
$29$		−	150.499i		−	0.963691i	−0.876256	−	0.481846i	$-0.839967\pi$
$29$		−	150.499i		−	0.963691i	0.876256	−	0.481846i	$-0.160033\pi$
$30$	229.918	+	76.1821i	1.39924	+	0.463629i
$31$	−122.391			−0.709101			−0.354550	−	0.935037i	$-0.615366\pi$
$31$	−122.391			−0.709101			−0.354550	+	0.935037i	$0.615366\pi$
$32$	36.6787	+	36.6787i	0.202623	+	0.202623i
$33$	2.94557	+	2.94557i	0.0155381	+	0.0155381i
$34$	277.088			1.39765
$35$	102.570	−	51.5147i	0.495356	−	0.248788i
$36$	−48.0464			−0.222437
$37$	−53.1409	+	53.1409i	−0.236117	+	0.236117i	−0.815240	−	0.579123i	$-0.803395\pi$
$37$	−53.1409	+	53.1409i	−0.236117	+	0.236117i	0.579123	+	0.815240i	$0.303395\pi$
$38$	246.692	+	246.692i	1.05312	+	1.05312i
$39$		−	53.8283i		−	0.221011i
$40$	−239.313	+	120.193i	−0.945969	+	0.475104i
$41$	−134.778			−0.513385			−0.256692	−	0.966493i	$-0.582633\pi$
$41$	−134.778			−0.513385			−0.256692	+	0.966493i	$0.582633\pi$
$42$	157.265	−	157.265i	0.577774	−	0.577774i
$43$	−300.444	−	300.444i	−1.06552	−	1.06552i	−0.997698	−	0.0678196i	$-0.978396\pi$
$43$	−300.444	−	300.444i	−1.06552	−	1.06552i	−0.0678196	−	0.997698i	$-0.521604\pi$
$44$	−0.581389			−0.00199199
$45$	146.191	−	441.204i	0.484284	−	1.46157i
$46$	287.590	+	23.7997i	0.921800	+	0.0762844i
$47$	31.8091	+	31.8091i	0.0987200	+	0.0987200i	0.754742	−	0.656022i	$-0.227762\pi$
$47$	31.8091	+	31.8091i	0.0987200	+	0.0987200i	−0.656022	+	0.754742i	$0.727762\pi$
$48$	−312.789	+	312.789i	−0.940565	+	0.940565i
$49$			237.605i			0.692727i
$50$	−47.4068	−	323.565i	−0.134087	−	0.915180i
$51$		−	877.058i		−	2.40809i
$52$	5.31224	+	5.31224i	0.0141668	+	0.0141668i
$53$	189.294	+	189.294i	0.490594	+	0.490594i	0.908493	−	0.417899i	$-0.137233\pi$
$53$	189.294	+	189.294i	0.490594	+	0.490594i	−0.417899	+	0.908493i	$0.637233\pi$
$54$		−	315.695i		−	0.795567i
$55$	1.76899	−	5.33882i	0.00433692	−	0.0130888i
$56$			245.904i			0.586791i
$57$	780.847	−	780.847i	1.81449	−	1.81449i
$58$	−278.409	+	278.409i	−0.630291	+	0.630291i
$59$			213.925i			0.472044i	0.971748	+	0.236022i	$0.0758438\pi$
$59$			213.925i			0.472044i	−0.971748	+	0.236022i	$0.924156\pi$
$60$	48.0234	+	95.6183i	0.103330	+	0.205738i
$61$			205.810i			0.431987i	0.976395	+	0.215994i	$0.0692990\pi$
$61$			205.810i			0.431987i	−0.976395	+	0.215994i	$0.930701\pi$
$62$	226.412	+	226.412i	0.463780	+	0.463780i
$63$	−301.786	−	301.786i	−0.603515	−	0.603515i
$64$		−	563.052i		−	1.09971i
$65$	−64.9451	+	32.6181i	−0.123930	+	0.0622427i
$66$		−	10.8980i		−	0.0203251i
$67$	−710.343	+	710.343i	−1.29526	+	1.29526i	−0.363767	+	0.931490i	$0.618510\pi$
$67$	−710.343	+	710.343i	−1.29526	+	1.29526i	−0.931490	+	0.363767i	$0.881490\pi$
$68$	86.5555	+	86.5555i	0.154359	+	0.154359i
$69$	75.3326	−	910.299i	0.131435	−	1.58822i
$70$	−285.041	−	94.4468i	−0.486699	−	0.161265i
$71$	449.783			0.751823			0.375912	−	0.926656i	$-0.377330\pi$
$71$	449.783			0.751823			0.375912	+	0.926656i	$0.377330\pi$
$72$	704.119	+	704.119i	1.15252	+	1.15252i
$73$	365.998	−	365.998i	0.586807	−	0.586807i	−0.349959	−	0.936765i	$-0.613804\pi$
$73$	365.998	−	365.998i	0.586807	−	0.586807i	0.936765	+	0.349959i	$0.113804\pi$
$74$	196.611			0.308859
$75$	−1024.17	+	150.055i	−1.57681	+	0.231025i
$76$			154.121i			0.232617i
$77$	−3.65178	−	3.65178i	−0.00540466	−	0.00540466i
$78$	−99.5771	+	99.5771i	−0.144550	+	0.144550i
$79$	−625.818			−0.891266			−0.445633	−	0.895216i	$-0.647021\pi$
$79$	−625.818			−0.891266			−0.445633	+	0.895216i	$0.647021\pi$
$80$	566.926	+	187.848i	0.792303	+	0.262525i
$81$	123.193			0.168990
$82$	249.326	+	249.326i	0.335774	+	0.335774i
$83$	819.106	+	819.106i	1.08324	+	1.08324i	0.996206	+	0.0870306i	$0.0277378\pi$
$83$	819.106	+	819.106i	1.08324	+	1.08324i	0.0870306	+	0.996206i	$0.472262\pi$
$84$	98.2517			0.127621
$85$	−1058.19	+	531.466i	−1.35032	+	0.678184i
$86$			1111.58i			1.39378i
$87$	881.240	+	881.240i	1.08596	+	1.08596i
$88$	8.52024	+	8.52024i	0.0103211	+	0.0103211i
$89$	397.018			0.472852			0.236426	−	0.971649i	$-0.424024\pi$
$89$	397.018			0.472852			0.236426	+	0.971649i	$0.424024\pi$
$90$	−1086.62	+	545.746i	−1.27267	+	0.639185i
$91$			66.7338i			0.0768747i
$92$	82.4016	+	97.2706i	0.0933800	+	0.110230i
$93$	716.655	−	716.655i	0.799072	−	0.799072i
$94$		−	117.688i		−	0.129133i
$95$	−1415.28	−	468.944i	−1.52847	−	0.506449i
$96$	−429.540			−0.456664
$97$	1055.44	−	1055.44i	1.10478	−	1.10478i	0.110951	−	0.993826i	$-0.464610\pi$
$97$	1055.44	−	1055.44i	1.10478	−	1.10478i	0.993826	−	0.110951i	$-0.0353898\pi$
$98$	439.547	−	439.547i	0.453070	−	0.453070i
$99$	−20.9129			−0.0212306
$100$	86.2652	−	115.883i	0.0862652	−	0.115883i
$101$	391.120			0.385326			0.192663	−	0.981265i	$-0.438288\pi$
$101$	391.120			0.385326			0.192663	+	0.981265i	$0.438288\pi$
$102$	−1622.47	+	1622.47i	−1.57499	+	1.57499i
$103$	−1072.57	−	1072.57i	−1.02605	−	1.02605i	−0.999652	−	0.0263981i	$-0.991596\pi$
$103$	−1072.57	−	1072.57i	−1.02605	−	1.02605i	−0.0263981	−	0.999652i	$-0.508404\pi$
$104$		−	155.702i		−	0.146806i
$105$	−298.950	+	902.232i	−0.277853	+	0.838561i
$106$		−	700.350i		−	0.641736i
$107$	−848.627	+	848.627i	−0.766728	+	0.766728i	−0.977529	−	0.210801i	$-0.932393\pi$
$107$	−848.627	+	848.627i	−0.766728	+	0.766728i	0.210801	+	0.977529i	$0.432393\pi$
$108$	98.6155	−	98.6155i	0.0878637	−	0.0878637i
$109$	−1503.89			−1.32152			−0.660762	−	0.750595i	$-0.729767\pi$
$109$	−1503.89			−1.32152			−0.660762	+	0.750595i	$0.729767\pi$
$110$	−13.1487	+	6.60383i	−0.0113971	+	0.00572410i
$111$		−	622.327i		−	0.532150i
$112$	387.780	−	387.780i	0.327159	−	0.327159i
$113$	−710.245	−	710.245i	−0.591277	−	0.591277i	0.346700	−	0.937976i	$-0.387302\pi$
$113$	−710.245	−	710.245i	−0.591277	−	0.591277i	−0.937976	+	0.346700i	$0.887302\pi$
$114$	−2888.98			−2.37349
$115$	−1143.95	+	460.719i	−0.927596	+	0.373585i
$116$	−173.937			−0.139221
$117$	191.085	+	191.085i	0.150990	+	0.150990i
$118$	395.739	−	395.739i	0.308735	−	0.308735i
$119$			1087.33i			0.837611i
$120$	697.502	−	2105.07i	0.530608	−	1.60138i
$121$	1330.75			0.999810
$122$	380.727	−	380.727i	0.282536	−	0.282536i
$123$	789.184	−	789.184i	0.578523	−	0.578523i
$124$			141.451i			0.102441i
$125$	801.657	+	1144.76i	0.573619	+	0.819122i
$126$			1116.55i			0.789444i
$127$	−1844.31	−	1844.31i	−1.28863	−	1.28863i	−0.935619	−	0.353012i	$-0.885158\pi$
$127$	−1844.31	−	1844.31i	−1.28863	−	1.28863i	−0.353012	−	0.935619i	$-0.614842\pi$
$128$	−748.160	+	748.160i	−0.516630	+	0.516630i
$129$	3518.46			2.40142
$130$	180.482	+	59.8018i	0.121764	+	0.0403459i
$131$	2266.15			1.51141			0.755704	−	0.654913i	$-0.227295\pi$
$131$	2266.15			1.51141			0.755704	+	0.654913i	$0.227295\pi$
$132$	3.40429	−	3.40429i	0.00224474	−	0.00224474i
$133$	−968.056	+	968.056i	−0.631136	+	0.631136i
$134$	2628.13			1.69430
$135$	605.517	+	1205.63i	0.386034	+	0.768623i
$136$		−	2536.94i		−	1.59956i
$137$	−592.705	+	592.705i	−0.369622	+	0.369622i	−0.867339	−	0.497717i	$-0.834172\pi$
$137$	−592.705	+	592.705i	−0.369622	+	0.369622i	0.497717	+	0.867339i	$0.334172\pi$
$138$	−1823.32	+	1544.61i	−1.12472	+	0.952794i
$139$			1031.29i			0.629299i	0.949208	+	0.314650i	$0.101887\pi$
$139$			1031.29i			0.629299i	−0.949208	+	0.314650i	$0.898113\pi$
$140$	−59.5371	−	118.543i	−0.0359414	−	0.0715622i
$141$	−372.513			−0.222491
$142$	−832.055	−	832.055i	−0.491722	−	0.491722i
$143$	2.31223	+	2.31223i	0.00135216	+	0.00135216i
$144$		−	2220.73i		−	1.28514i
$145$	529.236	−	1597.24i	0.303108	−	0.914782i
$146$	−1354.12			−0.767589
$147$	−1391.28	−	1391.28i	−0.780620	−	0.780620i
$148$	61.4165	+	61.4165i	0.0341109	+	0.0341109i
$149$	540.563			0.297213			0.148606	−	0.988896i	$-0.452521\pi$
$149$	540.563			0.297213			0.148606	+	0.988896i	$0.452521\pi$
$150$	2172.20	+	1617.03i	1.18240	+	0.880198i
$151$	2797.30			1.50756			0.753778	−	0.657129i	$-0.228229\pi$
$151$	2797.30			1.50756			0.753778	+	0.657129i	$0.228229\pi$
$152$	2258.64	−	2258.64i	1.20526	−	1.20526i
$153$	3113.46	+	3113.46i	1.64515	+	1.64515i
$154$			13.5109i			0.00706972i
$155$	−1298.93	−	430.393i	−0.673113	−	0.223032i
$156$	−62.2110			−0.0319286
$157$	491.173	−	491.173i	0.249681	−	0.249681i	−0.571159	−	0.820840i	$-0.693506\pi$
$157$	491.173	−	491.173i	0.249681	−	0.249681i	0.820840	+	0.571159i	$0.193506\pi$
$158$	1157.70	+	1157.70i	0.582923	+	0.582923i
$159$	−2216.80			−1.10568
$160$	260.286	+	518.250i	0.128609	+	0.256070i
$161$	−93.3938	+	1128.54i	−0.0457171	+	0.552434i
$162$	−227.896	−	227.896i	−0.110526	−	0.110526i
$163$	−439.096	+	439.096i	−0.210998	+	0.210998i	−0.804691	−	0.593693i	$-0.797669\pi$
$163$	−439.096	+	439.096i	−0.210998	+	0.210998i	0.593693	+	0.804691i	$0.297669\pi$
$164$			155.767i			0.0741667i
$165$	20.9029	+	41.6193i	0.00986237	+	0.0196367i
$166$		−	3030.53i		−	1.41696i
$167$	−468.862	−	468.862i	−0.217255	−	0.217255i	0.590085	−	0.807341i	$-0.299094\pi$
$167$	−468.862	−	468.862i	−0.217255	−	0.217255i	−0.807341	+	0.590085i	$0.799094\pi$
$168$	−1439.88	−	1439.88i	−0.661243	−	0.661243i
$169$			2154.75i			0.980767i
$170$	2940.71	+	974.388i	1.32672	+	0.439601i
$171$			5543.84i			2.47923i
$172$	−347.232	+	347.232i	−0.153931	+	0.153931i
$173$	1158.88	−	1158.88i	0.509293	−	0.509293i	−0.405016	−	0.914309i	$-0.632734\pi$
$173$	1158.88	−	1158.88i	0.509293	−	0.509293i	0.914309	+	0.405016i	$0.132734\pi$
$174$		−	3260.42i		−	1.42053i
$175$	1269.72	−	186.031i	0.548466	−	0.0803580i
$176$		−	26.8721i		−	0.0115089i
$177$	−1252.62	−	1252.62i	−0.531937	−	0.531937i
$178$	−734.445	−	734.445i	−0.309264	−	0.309264i
$179$		−	371.700i		−	0.155208i	−0.996984	−	0.0776039i	$-0.975273\pi$
$179$		−	371.700i		−	0.155208i	0.996984	−	0.0776039i	$-0.0247269\pi$
$180$	−509.912	−	168.957i	−0.211148	−	0.0699627i
$181$			2549.93i			1.04715i	0.851979	+	0.523576i	$0.175403\pi$
$181$			2549.93i			1.04715i	−0.851979	+	0.523576i	$0.824597\pi$
$182$	123.451	−	123.451i	0.0502790	−	0.0502790i
$183$	−1205.11	−	1205.11i	−0.486797	−	0.486797i
$184$	217.904	−	2633.09i	0.0873049	−	1.05497i
$185$	−750.852	+	377.108i	−0.298399	+	0.149868i
$186$	−2651.48			−1.04525
$187$	37.6746	+	37.6746i	0.0147328	+	0.0147328i
$188$	36.7628	−	36.7628i	0.0142617	−	0.0142617i
$189$	1238.83			0.476783
$190$	1750.62	+	3485.62i	0.668439	+	1.33091i
$191$		−	3346.43i		−	1.26774i	−0.773438	−	0.633872i	$-0.781465\pi$
$191$		−	3346.43i		−	1.26774i	0.773438	−	0.633872i	$-0.218535\pi$
$192$	3296.91	+	3296.91i	1.23924	+	1.23924i
$193$	−1459.17	+	1459.17i	−0.544215	+	0.544215i	−0.924762	−	0.380547i	$-0.875736\pi$
$193$	−1459.17	+	1459.17i	−0.544215	+	0.544215i	0.380547	+	0.924762i	$0.375736\pi$
$194$	−3904.91			−1.44513
$195$	189.289	−	571.276i	0.0695142	−	0.209794i
$196$	274.608			0.100076
$197$	−2542.11	−	2542.11i	−0.919380	−	0.919380i	0.0776046	−	0.996984i	$-0.475273\pi$
$197$	−2542.11	−	2542.11i	−0.919380	−	0.919380i	−0.996984	+	0.0776046i	$0.975273\pi$
$198$	38.6869	+	38.6869i	0.0138856	+	0.0138856i
$199$	1564.86			0.557436			0.278718	−	0.960373i	$-0.410091\pi$
$199$	1564.86			0.557436			0.278718	+	0.960373i	$0.410091\pi$
$200$	−2962.47	+	434.044i	−1.04739	+	0.153458i
$201$		−	8318.74i		−	2.91920i
$202$	−723.534	−	723.534i	−0.252018	−	0.252018i
$203$	−1092.52	−	1092.52i	−0.377733	−	0.377733i
$204$	−1013.64			−0.347888
$205$	−1430.39	−	473.951i	−0.487329	−	0.161474i
$206$			3968.28i			1.34215i
$207$	2964.04	+	3498.89i	0.995242	+	1.17483i
$208$	−245.535	+	245.535i	−0.0818498	+	0.0818498i
$209$			67.0836i			0.0222023i
$210$	2222.07	−	1116.01i	0.730178	−	0.366725i
$211$	−137.567			−0.0448840			−0.0224420	−	0.999748i	$-0.507144\pi$
$211$	−137.567			−0.0448840			−0.0224420	+	0.999748i	$0.507144\pi$
$212$	218.772	−	218.772i	0.0708743	−	0.0708743i
$213$	−2633.68	+	2633.68i	−0.847215	+	0.847215i
$214$	3139.75			1.00294
$215$	−2132.06	−	4245.10i	−0.676305	−	1.34658i
$216$	−2890.42			−0.910500
$217$	−888.474	+	888.474i	−0.277943	+	0.277943i
$218$	2782.04	+	2782.04i	0.864329	+	0.864329i
$219$			4286.16i			1.32252i
$220$	−6.17023	−	2.04447i	−0.00189089	−	0.000626538i
$221$		−	688.478i		−	0.209557i
$222$	−1151.24	+	1151.24i	−0.348047	+	0.348047i
$223$	3435.79	−	3435.79i	1.03174	−	1.03174i	0.0322582	−	0.999480i	$-0.489730\pi$
$223$	3435.79	−	3435.79i	1.03174	−	1.03174i	0.999480	−	0.0322582i	$-0.0102699\pi$
$224$	532.523			0.158842
$225$	3103.02	−	4168.38i	0.919412	−	1.23507i
$226$			2627.77i			0.773436i
$227$	−2524.56	+	2524.56i	−0.738153	+	0.738153i	−0.972220	−	0.234067i	$-0.924796\pi$
$227$	−2524.56	+	2524.56i	−0.738153	+	0.738153i	0.234067	+	0.972220i	$0.424796\pi$
$228$	−902.447	−	902.447i	−0.262132	−	0.262132i
$229$	1964.53			0.566900			0.283450	−	0.958987i	$-0.408521\pi$
$229$	1964.53			0.566900			0.283450	+	0.958987i	$0.408521\pi$
$230$	2968.47	+	1263.90i	0.851023	+	0.362345i
$231$	42.7656			0.0121808
$232$	2549.04	+	2549.04i	0.721347	+	0.721347i
$233$	2236.36	−	2236.36i	0.628793	−	0.628793i	−0.318971	−	0.947764i	$-0.603337\pi$
$233$	2236.36	−	2236.36i	0.628793	−	0.628793i	0.947764	+	0.318971i	$0.103337\pi$
$234$		−	706.976i		−	0.197506i
$235$	225.730	+	449.446i	0.0626596	+	0.124760i
$236$	247.239			0.0681944
$237$	3664.44	−	3664.44i	1.00435	−	1.00435i
$238$	2011.46	−	2011.46i	0.547830	−	0.547830i
$239$			3196.23i			0.865050i	0.901622	+	0.432525i	$0.142377\pi$
$239$			3196.23i			0.865050i	−0.901622	+	0.432525i	$0.857623\pi$
$240$	−4419.53	+	2219.67i	−1.18866	+	0.596996i
$241$			1965.34i			0.525305i	0.964891	+	0.262652i	$0.0845972\pi$
$241$			1965.34i			0.525305i	−0.964891	+	0.262652i	$0.915403\pi$
$242$	−2461.75	−	2461.75i	−0.653915	−	0.653915i
$243$	−3025.19	+	3025.19i	−0.798627	+	0.798627i
$244$	237.860			0.0624075
$245$	−835.547	+	2521.69i	−0.217882	+	0.657570i
$246$	−2919.82			−0.756753
$247$	612.954	−	612.954i	0.157900	−	0.157900i
$248$	2072.97	−	2072.97i	0.530780	−	0.530780i
$249$	−9592.46			−2.44135
$250$	634.703	−	3600.68i	0.160568	−	0.910907i
$251$			1985.68i			0.499343i	0.968331	+	0.249671i	$0.0803226\pi$
$251$			1985.68i			0.499343i	−0.968331	+	0.249671i	$0.919677\pi$
$252$	−348.783	+	348.783i	−0.0871875	+	0.0871875i
$253$	35.8666	+	42.3385i	0.00891270	+	0.0105209i
$254$			6823.59i			1.68563i
$255$	3084.20	−	9308.14i	0.757413	−	2.28588i
$256$	−1736.37			−0.423918
$257$	4227.41	+	4227.41i	1.02607	+	1.02607i	0.999651	+	0.0264141i	$0.00840885\pi$
$257$	4227.41	+	4227.41i	1.02607	+	1.02607i	0.0264141	+	0.999651i	$0.491591\pi$
$258$	−6508.80	−	6508.80i	−1.57062	−	1.57062i
$259$			771.531i			0.185099i
$260$	37.6977	+	75.0590i	0.00899197	+	0.0179037i
$261$	−6256.61			−1.48381
$262$	−4192.15	−	4192.15i	−0.988520	−	0.988520i
$263$	3980.50	+	3980.50i	0.933263	+	0.933263i	0.997908	−	0.0646449i	$-0.0205915\pi$
$263$	3980.50	+	3980.50i	0.933263	+	0.933263i	−0.0646449	+	0.997908i	$0.520591\pi$
$264$	−99.7795			−0.0232614
$265$	1343.30	+	2674.62i	0.311390	+	0.620002i
$266$	3581.62			0.825575
$267$	−2324.72	+	2324.72i	−0.532848	+	0.532848i
$268$	820.964	+	820.964i	0.187121	+	0.187121i
$269$			7753.02i			1.75729i	0.477479	+	0.878643i	$0.341551\pi$
$269$			7753.02i			1.75729i	−0.477479	+	0.878643i	$0.658449\pi$
$270$	1110.15	−	3350.44i	0.250228	−	0.755191i
$271$	−5540.81			−1.24199			−0.620997	−	0.783813i	$-0.713272\pi$
$271$	−5540.81			−1.24199			−0.620997	+	0.783813i	$0.713272\pi$
$272$	−4000.64	+	4000.64i	−0.891819	+	0.891819i
$273$	−390.755	−	390.755i	−0.0866286	−	0.0866286i
$274$	2192.89			0.483494
$275$	37.5483	−	50.4397i	0.00823362	−	0.0110605i
$276$	−1052.06	−	87.0641i	−0.229444	−	0.0189878i
$277$	−2648.85	−	2648.85i	−0.574563	−	0.574563i	0.358837	−	0.933400i	$-0.383173\pi$
$277$	−2648.85	−	2648.85i	−0.574563	−	0.574563i	−0.933400	+	0.358837i	$0.883173\pi$
$278$	1907.78	−	1907.78i	0.411586	−	0.411586i
$279$			5088.09i			1.09181i
$280$	−864.730	+	2609.76i	−0.184562	+	0.557011i
$281$			485.195i			0.103005i	0.998673	+	0.0515023i	$0.0164009\pi$
$281$			485.195i			0.103005i	−0.998673	+	0.0515023i	$0.983599\pi$
$282$	689.112	+	689.112i	0.145518	+	0.145518i
$283$	3114.36	+	3114.36i	0.654167	+	0.654167i	0.953994	−	0.299827i	$-0.0969289\pi$
$283$	3114.36	+	3114.36i	0.654167	+	0.654167i	−0.299827	+	0.953994i	$0.596929\pi$
$284$		−	519.828i		−	0.108613i
$285$	11032.9	−	5541.19i	2.29310	−	1.15169i
$286$		−	8.55481i		−	0.00176873i
$287$	−978.392	+	978.392i	−0.201229	+	0.201229i
$288$	1524.82	−	1524.82i	0.311982	−	0.311982i
$289$		−	6304.79i		−	1.28329i
$290$	−3933.77	+	1975.70i	−0.796547	+	0.400059i
$291$			12360.1i			2.48990i
$292$	−422.995	−	422.995i	−0.0847737	−	0.0847737i
$293$	−5460.39	−	5460.39i	−1.08874	−	1.08874i	−0.995659	−	0.0930762i	$-0.970330\pi$
$293$	−5460.39	−	5460.39i	−1.08874	−	1.08874i	−0.0930762	−	0.995659i	$-0.529670\pi$
$294$			5147.48i			1.02111i
$295$	−752.273	+	2270.36i	−0.148471	+	0.448087i
$296$		−	1800.12i		−	0.353478i
$297$	42.9239	−	42.9239i	0.00838619	−	0.00838619i
$298$	−999.989	−	999.989i	−0.194389	−	0.194389i
$299$	59.1351	−	714.572i	0.0114377	−	0.138210i
$300$	173.423	+	1183.66i	0.0333753	+	0.227796i
$301$	−4362.02			−0.835291
$302$	−5174.73	−	5174.73i	−0.986001	−	0.986001i
$303$	−2290.18	+	2290.18i	−0.434216	+	0.434216i
$304$	−7123.57			−1.34396
$305$	−723.736	+	2184.24i	−0.135872	+	0.410063i
$306$		−	11519.2i		−	2.15199i
$307$	7130.23	+	7130.23i	1.32555	+	1.32555i	0.909209	+	0.416340i	$0.136687\pi$
$307$	7130.23	+	7130.23i	1.32555	+	1.32555i	0.416340	+	0.909209i	$0.363313\pi$
$308$	−4.22047	+	4.22047i	−0.000780791	+	0.000780791i
$309$	12560.7			2.31247
$310$	1606.71	+	3199.07i	0.294370	+	0.586114i
$311$	−1853.34			−0.337921			−0.168961	−	0.985623i	$-0.554041\pi$
$311$	−1853.34			−0.337921			−0.168961	+	0.985623i	$0.554041\pi$
$312$	911.701	+	911.701i	0.165432	+	0.165432i
$313$	1356.77	+	1356.77i	0.245013	+	0.245013i	0.818920	−	0.573907i	$-0.194573\pi$
$313$	1356.77	+	1356.77i	0.245013	+	0.245013i	−0.573907	+	0.818920i	$0.694573\pi$
$314$	−1817.24			−0.326602
$315$	−2141.59	−	4264.07i	−0.383063	−	0.762708i
$316$			723.276i			0.128758i
$317$	309.563	+	309.563i	0.0548480	+	0.0548480i	0.733999	−	0.679151i	$-0.237652\pi$
$317$	309.563	+	309.563i	0.0548480	+	0.0548480i	−0.679151	+	0.733999i	$0.737652\pi$
$318$	4100.85	+	4100.85i	0.723159	+	0.723159i
$319$	−75.7086			−0.0132880
$320$	1979.99	−	5975.62i	0.345890	−	1.04390i
$321$		−	9938.17i		−	1.72802i
$322$	2260.47	−	1914.93i	0.391214	−	0.331412i
$323$	9987.23	−	9987.23i	1.72045	−	1.72045i
$324$		−	142.378i		−	0.0244133i
$325$	−803.960	+	117.791i	−0.137217	+	0.0201043i
$326$	1624.57			0.276002
$327$	8805.92	−	8805.92i	1.48920	−	1.48920i
$328$	2282.76	−	2282.76i	0.384282	−	0.384282i
$329$	461.824			0.0773896
$330$	38.3233	−	115.660i	0.00639282	−	0.0192936i
$331$	−3448.22			−0.572602			−0.286301	−	0.958140i	$-0.592426\pi$
$331$	−3448.22			−0.572602			−0.286301	+	0.958140i	$0.592426\pi$
$332$	946.665	−	946.665i	0.156491	−	0.156491i
$333$	2209.19	+	2209.19i	0.363553	+	0.363553i
$334$			1734.70i			0.284187i
$335$	−10036.8	+	5040.87i	−1.63692	+	0.822125i
$336$			4541.25i			0.737337i
$337$	−3720.80	+	3720.80i	−0.601438	+	0.601438i	−0.940694	−	0.339256i	$-0.889825\pi$
$337$	−3720.80	+	3720.80i	−0.601438	+	0.601438i	0.339256	+	0.940694i	$0.389825\pi$
$338$	3986.07	−	3986.07i	0.641460	−	0.641460i
$339$	8317.60			1.33260
$340$	614.231	+	1222.98i	0.0979746	+	0.195075i
$341$			61.5688i			0.00977754i
$342$	10255.6	−	10255.6i	1.62151	−	1.62151i
$343$	4214.78	+	4214.78i	0.663490	+	0.663490i
$344$	10177.3			1.59513
$345$	4000.60	−	9396.02i	0.624304	−	1.46627i
$346$	−4287.61			−0.666195
$347$	2049.87	+	2049.87i	0.317126	+	0.317126i	0.847662	−	0.530536i	$-0.178009\pi$
$347$	2049.87	+	2049.87i	0.317126	+	0.317126i	−0.530536	+	0.847662i	$0.678009\pi$
$348$	1018.48	−	1018.48i	0.156885	−	0.156885i
$349$		−	11825.7i		−	1.81379i	−0.421352	−	0.906897i	$-0.638444\pi$
$349$		−	11825.7i		−	1.81379i	0.421352	−	0.906897i	$-0.361556\pi$
$350$	−2692.99	−	2004.71i	−0.411276	−	0.306161i
$351$	−784.405			−0.119283
$352$	18.4512	−	18.4512i	0.00279390	−	0.00279390i
$353$	−5463.27	+	5463.27i	−0.823740	+	0.823740i	−0.986642	−	0.162902i	$-0.947915\pi$
$353$	−5463.27	+	5463.27i	−0.823740	+	0.823740i	0.162902	+	0.986642i	$0.447915\pi$
$354$			4634.46i			0.695815i
$355$	4773.51	+	1581.68i	0.713667	+	0.236470i
$356$		−	458.846i		−	0.0683112i
$357$	−6366.82	−	6366.82i	−0.943887	−	0.943887i
$358$	−687.609	+	687.609i	−0.101512	+	0.101512i
$359$	−5814.63			−0.854831			−0.427416	−	0.904055i	$-0.640576\pi$
$359$	−5814.63			−0.854831			−0.427416	+	0.904055i	$0.640576\pi$
$360$	4996.70	+	9948.81i	0.731525	+	1.45652i
$361$	10924.3			1.59270
$362$	4717.11	−	4717.11i	0.684879	−	0.684879i
$363$	−7792.11	+	7792.11i	−1.12667	+	1.12667i
$364$	77.1262			0.0111058
$365$	5171.36	−	2597.27i	0.741592	−	0.372458i
$366$			4458.65i			0.636769i
$367$	4200.09	−	4200.09i	0.597392	−	0.597392i	−0.342226	−	0.939618i	$-0.611181\pi$
$367$	4200.09	−	4200.09i	0.597392	−	0.597392i	0.939618	+	0.342226i	$0.111181\pi$
$368$	−4495.90	+	3808.65i	−0.636861	+	0.539510i
$369$			5603.03i			0.790467i
$370$	2086.62	+	691.389i	0.293184	+	0.0971448i
$371$	2748.28			0.384591
$372$	−828.259	−	828.259i	−0.115439	−	0.115439i
$373$	−4490.67	−	4490.67i	−0.623373	−	0.623373i	0.323019	−	0.946392i	$-0.395302\pi$
$373$	−4490.67	−	4490.67i	−0.623373	−	0.623373i	−0.946392	+	0.323019i	$0.895302\pi$
$374$		−	139.389i		−	0.0192717i
$375$	−11397.1	−	2009.01i	−1.56945	−	0.276652i
$376$	−1077.52			−0.147789
$377$	691.761	+	691.761i	0.0945027	+	0.0945027i
$378$	−2291.72	−	2291.72i	−0.311834	−	0.311834i
$379$	−11193.1			−1.51702			−0.758511	−	0.651660i	$-0.774073\pi$
$379$	−11193.1			−1.51702			−0.758511	+	0.651660i	$0.774073\pi$
$380$	−541.972	+	1635.68i	−0.0731647	+	0.220812i
$381$	21598.5			2.90426
$382$	−6190.56	+	6190.56i	−0.829153	+	0.829153i
$383$	−10128.5	−	10128.5i	−1.35128	−	1.35128i	−0.884231	−	0.467050i	$-0.845317\pi$
$383$	−10128.5	−	10128.5i	−1.35128	−	1.35128i	−0.467050	−	0.884231i	$-0.654683\pi$
$384$		−	8761.62i		−	1.16436i
$385$	−25.9144	−	51.5976i	−0.00343045	−	0.00683028i
$386$	5398.65			0.711875
$387$	−12490.2	+	12490.2i	−1.64059	+	1.64059i
$388$	−1219.80	−	1219.80i	−0.159603	−	0.159603i
$389$	−5091.74			−0.663654			−0.331827	−	0.943340i	$-0.607665\pi$
$389$	−5091.74			−0.663654			−0.331827	+	0.943340i	$0.607665\pi$
$390$	−1406.97	+	706.637i	−0.182679	+	0.0917486i
$391$	963.524	−	11643.0i	0.124623	−	1.50591i
$392$	−4024.37	−	4024.37i	−0.518524	−	0.518524i
$393$	−13269.3	+	13269.3i	−1.70318	+	1.70318i
$394$			9405.30i			1.20262i
$395$	−6641.75	−	2200.71i	−0.846032	−	0.280328i
$396$			24.1697i			0.00306710i
$397$	−7017.86	−	7017.86i	−0.887195	−	0.887195i	0.107058	−	0.994253i	$-0.465857\pi$
$397$	−7017.86	−	7017.86i	−0.887195	−	0.887195i	−0.994253	+	0.107058i	$0.965857\pi$
$398$	−2894.83	−	2894.83i	−0.364585	−	0.364585i
$399$		−	11336.8i		−	1.42243i
$400$	5356.16	+	3987.22i	0.669520	+	0.498403i
$401$			4694.52i			0.584621i	0.956323	+	0.292310i	$0.0944240\pi$
$401$			4694.52i			0.584621i	−0.956323	+	0.292310i	$0.905576\pi$
$402$	−15388.9	+	15388.9i	−1.90927	+	1.90927i
$403$	562.564	−	562.564i	0.0695368	−	0.0695368i
$404$		−	452.029i		−	0.0556665i
$405$	1307.44	+	433.214i	0.160413	+	0.0531520i
$406$			4042.11i			0.494104i
$407$	26.7325	+	26.7325i	0.00325573	+	0.00325573i
$408$	14854.9	+	14854.9i	1.80252	+	1.80252i
$409$		−	9665.07i		−	1.16848i	−0.811582	−	0.584238i	$-0.801393\pi$
$409$		−	9665.07i		−	1.16848i	0.811582	−	0.584238i	$-0.198607\pi$
$410$	1769.31	+	3522.84i	0.213122	+	0.424343i
$411$		−	6941.10i		−	0.833039i
$412$	−1239.60	+	1239.60i	−0.148229	+	0.148229i
$413$	1552.94	+	1552.94i	0.185025	+	0.185025i
$414$	989.411	−	11955.8i	0.117456	−	1.41931i
$415$	5812.69	+	11573.5i	0.687552	+	1.36897i
$416$	−337.183			−0.0397398
$417$	−6038.64	−	6038.64i	−0.709145	−	0.709145i
$418$	124.098	−	124.098i	0.0145211	−	0.0145211i
$419$	2184.46			0.254697			0.127348	−	0.991858i	$-0.459353\pi$
$419$	2184.46			0.254697			0.127348	+	0.991858i	$0.459353\pi$
$420$	1042.74	+	345.505i	0.121144	+	0.0401403i
$421$			9809.98i			1.13565i	0.823149	+	0.567825i	$0.192215\pi$
$421$			9809.98i			1.13565i	−0.823149	+	0.567825i	$0.807785\pi$
$422$	254.486	+	254.486i	0.0293559	+	0.0293559i
$423$	1322.38	−	1322.38i	0.152001	−	0.152001i
$424$	−6412.21			−0.734445
$425$	−13099.4	+	1919.25i	−1.49509	+	0.219052i
$426$	9744.09			1.10822
$427$	1494.03	+	1494.03i	0.169324	+	0.169324i
$428$	980.783	+	980.783i	0.110766	+	0.110766i
$429$	−27.0783			−0.00304744
$430$	−3908.92	+	11797.1i	−0.438383	+	1.32304i
$431$		−	14369.3i		−	1.60591i	−0.596041	−	0.802954i	$-0.703260\pi$
$431$		−	14369.3i		−	1.60591i	0.596041	−	0.802954i	$-0.296740\pi$
$432$	4558.06	+	4558.06i	0.507639	+	0.507639i
$433$	3589.57	+	3589.57i	0.398392	+	0.398392i	0.877666	−	0.479273i	$-0.159100\pi$
$433$	3589.57	+	3589.57i	0.398392	+	0.398392i	−0.479273	+	0.877666i	$0.659100\pi$
$434$	3287.18			0.363571
$435$	6253.62	+	12451.4i	0.689283	+	1.37242i
$436$			1738.09i			0.190916i
$437$	11223.6	−	9507.93i	1.22860	−	1.04079i
$438$	7928.98	−	7928.98i	0.864980	−	0.864980i
$439$			3913.40i			0.425459i	0.977111	+	0.212730i	$0.0682354\pi$
$439$			3913.40i			0.425459i	−0.977111	+	0.212730i	$0.931765\pi$
$440$	60.4629	+	120.386i	0.00655104	+	0.0130436i
$441$	9877.81			1.06660
$442$	−1273.62	+	1273.62i	−0.137058	+	0.137058i
$443$	6616.32	−	6616.32i	0.709596	−	0.709596i	−0.256854	−	0.966450i	$-0.582686\pi$
$443$	6616.32	−	6616.32i	0.709596	−	0.709596i	0.966450	+	0.256854i	$0.0826861\pi$
$444$	−719.241			−0.0768777
$445$	4213.52	+	1396.13i	0.448854	+	0.148725i
$446$	−12711.7			−1.34959
$447$	−3165.24	+	3165.24i	−0.334923	+	0.334923i
$448$	−4087.36	−	4087.36i	−0.431048	−	0.431048i
$449$			2465.92i			0.259185i	0.991567	+	0.129592i	$0.0413669\pi$
$449$			2465.92i			0.259185i	−0.991567	+	0.129592i	$0.958633\pi$
$450$	−13451.4	+	1970.81i	−1.40912	+	0.206455i
$451$			67.7999i			0.00707888i
$452$	−820.851	+	820.851i	−0.0854195	+	0.0854195i
$453$	−16379.4	+	16379.4i	−1.69884	+	1.69884i
$454$	9340.37			0.965562
$455$	−234.671	+	708.240i	−0.0241793	+	0.0729732i
$456$			26450.7i			2.71638i
$457$	−116.177	+	116.177i	−0.0118917	+	0.0118917i	−0.713028	−	0.701136i	$-0.752677\pi$
$457$	−116.177	+	116.177i	−0.0118917	+	0.0118917i	0.701136	+	0.713028i	$0.252677\pi$
$458$	−3634.20	−	3634.20i	−0.370775	−	0.370775i
$459$	−12780.8			−1.29969
$460$	532.466	+	1322.09i	0.0539704	+	0.134006i
$461$	−3362.71			−0.339734			−0.169867	−	0.985467i	$-0.554334\pi$
$461$	−3362.71			−0.339734			−0.169867	+	0.985467i	$0.554334\pi$
$462$	−79.1121	−	79.1121i	−0.00796672	−	0.00796672i
$463$	1782.49	−	1782.49i	0.178919	−	0.178919i	−0.611966	−	0.790884i	$-0.709621\pi$
$463$	1782.49	−	1782.49i	0.178919	−	0.178919i	0.790884	+	0.611966i	$0.209621\pi$
$464$		−	8039.45i		−	0.804358i
$465$	10125.9	−	5085.66i	1.00985	−	0.507187i
$466$	−8274.09			−0.822511
$467$	−7735.30	+	7735.30i	−0.766482	+	0.766482i	−0.977485	−	0.211004i	$-0.932327\pi$
$467$	−7735.30	+	7735.30i	−0.766482	+	0.766482i	0.211004	+	0.977485i	$0.432327\pi$
$468$	220.842	−	220.842i	0.0218129	−	0.0218129i
$469$			10313.2i			1.01539i
$470$	413.852	−	1249.01i	0.0406161	−	0.122580i
$471$			5752.07i			0.562720i
$472$	−3623.28	−	3623.28i	−0.353337	−	0.353337i
$473$	−151.138	+	151.138i	−0.0146920	+	0.0146920i
$474$	−13557.7			−1.31377
$475$	−13371.1	−	9953.73i	−1.29160	−	0.961491i
$476$	1256.66			0.121006
$477$	7869.39	−	7869.39i	0.755376	−	0.755376i
$478$	5912.71	−	5912.71i	0.565777	−	0.565777i
$479$	5001.62			0.477098			0.238549	−	0.971130i	$-0.423328\pi$
$479$	5001.62			0.477098			0.238549	+	0.971130i	$0.423328\pi$
$480$	−4558.67	−	1510.49i	−0.433487	−	0.143634i
$481$		−	488.518i		−	0.0463087i
$482$	3635.68	−	3635.68i	0.343570	−	0.343570i
$483$	−6061.27	−	7154.99i	−0.571009	−	0.674044i
$484$		−	1537.98i		−	0.144439i
$485$	14912.7	−	7489.79i	1.39619	−	0.701224i
$486$	11192.6			1.04467
$487$	9743.25	+	9743.25i	0.906589	+	0.906589i	0.995995	−	0.0894065i	$-0.0284970\pi$
$487$	9743.25	+	9743.25i	0.906589	+	0.906589i	−0.0894065	+	0.995995i	$0.528497\pi$
$488$	−3485.84	−	3485.84i	−0.323353	−	0.323353i
$489$		−	5142.21i		−	0.475539i
$490$	6210.55	−	3119.19i	0.572580	−	0.287573i
$491$	−5576.92			−0.512593			−0.256296	−	0.966598i	$-0.582502\pi$
$491$	−5576.92			−0.512593			−0.256296	+	0.966598i	$0.582502\pi$
$492$	−912.083	−	912.083i	−0.0835770	−	0.0835770i
$493$	11271.3	+	11271.3i	1.02968	+	1.02968i
$494$	−2267.81			−0.206546
$495$	−221.947	−	73.5410i	−0.0201531	−	0.00667762i
$496$	−6537.95			−0.591861
$497$	3265.11	−	3265.11i	0.294688	−	0.294688i
$498$	17745.1	+	17745.1i	1.59674	+	1.59674i
$499$		−	9649.45i		−	0.865669i	−0.901473	−	0.432834i	$-0.857513\pi$
$499$		−	9649.45i		−	0.865669i	0.901473	−	0.432834i	$-0.142487\pi$
$500$	1323.03	−	926.499i	0.118335	−	0.0828686i
$501$	5490.79			0.489641
$502$	3673.31	−	3673.31i	0.326590	−	0.326590i
$503$	−3329.89	−	3329.89i	−0.295174	−	0.295174i	0.543946	−	0.839120i	$-0.316930\pi$
$503$	−3329.89	−	3329.89i	−0.295174	−	0.295174i	−0.839120	+	0.543946i	$0.816930\pi$
$504$	10222.8			0.903492
$505$	4150.92	+	1375.39i	0.365770	+	0.121196i
$506$	11.9724	−	144.672i	0.00105186	−	0.0127104i
$507$	−12617.0	−	12617.0i	−1.10521	−	1.10521i
$508$	−2131.52	+	2131.52i	−0.186164	+	0.186164i
$509$			14272.2i			1.24284i	0.783478	+	0.621419i	$0.213443\pi$
$509$			14272.2i			1.24284i	−0.783478	+	0.621419i	$0.786557\pi$
$510$	−22924.6	+	11513.7i	−1.99043	+	0.999675i
$511$		−	5313.78i		−	0.460015i
$512$	9197.39	+	9197.39i	0.793889	+	0.793889i
$513$	−11378.8	−	11378.8i	−0.979308	−	0.979308i
$514$		−	15640.6i		−	1.34217i
$515$	−7611.34	−	15154.8i	−0.651254	−	1.29670i
$516$		−	4066.39i		−	0.346924i
$517$	16.0016	−	16.0016i	0.00136121	−	0.00136121i
$518$	1427.26	−	1427.26i	0.121062	−	0.121062i
$519$			13571.5i			1.14782i
$520$	547.530	−	1652.45i	0.0461745	−	0.139355i
$521$		−	9927.43i		−	0.834796i	−0.908724	−	0.417398i	$-0.862942\pi$
$521$		−	9927.43i		−	0.834796i	0.908724	−	0.417398i	$-0.137058\pi$
$522$	11574.1	+	11574.1i	0.970470	+	0.970470i
$523$	−10057.5	−	10057.5i	−0.840887	−	0.840887i	0.148088	−	0.988974i	$-0.452688\pi$
$523$	−10057.5	−	10057.5i	−0.840887	−	0.840887i	−0.988974	+	0.148088i	$0.952688\pi$
$524$		−	2619.06i		−	0.218347i
$525$	−6345.46	+	8524.05i	−0.527502	+	0.708610i
$526$		−	14727.1i		−	1.22078i
$527$	9166.20	−	9166.20i	0.757658	−	0.757658i
$528$	157.348	+	157.348i	0.0129691	+	0.0129691i
$529$	2000.08	−	12001.5i	0.164386	−	0.986396i
$530$	2462.80	−	7432.75i	0.201844	−	0.609166i
$531$	8893.35			0.726814
$532$	1118.81	+	1118.81i	0.0911778	+	0.0911778i
$533$	619.498	−	619.498i	0.0503442	−	0.0503442i
$534$	8600.99			0.697006
$535$	−11990.6	+	6022.18i	−0.968972	+	0.486657i
$536$		−	24062.4i		−	1.93907i
$537$	2176.47	+	2176.47i	0.174900	+	0.174900i
$538$	14342.3	−	14342.3i	1.14933	−	1.14933i
$539$	119.527			0.00955176
$540$	1393.38	−	699.813i	0.111040	−	0.0557688i
$541$	−8573.49			−0.681337			−0.340668	−	0.940184i	$-0.610653\pi$
$541$	−8573.49			−0.681337			−0.340668	+	0.940184i	$0.610653\pi$
$542$	10250.0	+	10250.0i	0.812312	+	0.812312i
$543$	−14930.9	−	14930.9i	−1.18002	−	1.18002i
$544$	−5493.92			−0.432996
$545$	−15960.6	−	5288.47i	−1.25445	−	0.415657i
$546$			1445.72i			0.113317i
$547$	10840.7	+	10840.7i	0.847378	+	0.847378i	0.989805	−	0.142427i	$-0.0454906\pi$
$547$	10840.7	+	10840.7i	0.847378	+	0.847378i	−0.142427	+	0.989805i	$0.545491\pi$
$548$	685.007	+	685.007i	0.0533979	+	0.0533979i
$549$	8555.98			0.665138
$550$	−162.769	+	23.8479i	−0.0126191	+	0.00184887i
$551$			20069.7i			1.55172i
$552$	14142.0	+	16693.8i	1.09044	+	1.28720i
$553$	−4542.99	+	4542.99i	−0.349345	+	0.349345i
$554$			9800.23i			0.751574i
$555$	2188.43	−	6604.70i	0.167376	−	0.505142i
$556$	1191.89			0.0909125
$557$	−11350.7	+	11350.7i	−0.863455	+	0.863455i	−0.991738	−	0.128282i	$-0.959054\pi$
$557$	−11350.7	+	11350.7i	−0.863455	+	0.863455i	0.128282	+	0.991738i	$0.459054\pi$
$558$	9412.47	−	9412.47i	0.714089	−	0.714089i
$559$	2761.94			0.208976
$560$	5479.12	−	2751.84i	0.413455	−	0.207654i
$561$	−441.203			−0.0332043
$562$	897.562	−	897.562i	0.0673690	−	0.0673690i
$563$	11657.3	+	11657.3i	0.872637	+	0.872637i	0.992759	−	0.120122i	$-0.0383285\pi$
$563$	11657.3	+	11657.3i	0.872637	+	0.872637i	−0.120122	+	0.992759i	$0.538329\pi$
$564$			430.524i			0.0321425i
$565$	−5040.17	−	10035.4i	−0.375295	−	0.747241i
$566$		−	11522.5i		−	0.855701i
$567$	894.297	−	894.297i	0.0662380	−	0.0662380i
$568$	−7618.07	+	7618.07i	−0.562759	+	0.562759i
$569$	−20010.6			−1.47432			−0.737162	−	0.675716i	$-0.763834\pi$
$569$	−20010.6			−1.47432			−0.737162	+	0.675716i	$0.763834\pi$
$570$	−30660.5	−	10159.2i	−2.25303	−	0.746529i
$571$			9517.11i			0.697511i	0.937214	+	0.348756i	$0.113396\pi$
$571$			9517.11i			0.697511i	−0.937214	+	0.348756i	$0.886604\pi$
$572$	2.67232	−	2.67232i	0.000195341	−	0.000195341i
$573$	19594.8	+	19594.8i	1.42859	+	1.42859i
$574$	3619.86			0.263223
$575$	−13760.7	+	866.848i	−0.998022	+	0.0628697i
$576$	−23407.4			−1.69324
$577$	−9261.46	−	9261.46i	−0.668214	−	0.668214i	0.289088	−	0.957302i	$-0.406648\pi$
$577$	−9261.46	−	9261.46i	−0.668214	−	0.668214i	−0.957302	+	0.289088i	$0.906648\pi$
$578$	−11663.2	+	11663.2i	−0.839320	+	0.839320i
$579$		−	17088.2i		−	1.22653i
$580$	−1845.97	−	611.654i	−0.132155	−	0.0437889i
$581$	11892.3			0.849181
$582$	22865.0	−	22865.0i	1.62849	−	1.62849i
$583$	95.2241	−	95.2241i	0.00676463	−	0.00676463i
$584$			12398.0i			0.878479i
$585$	1356.01	+	2699.92i	0.0958361	+	0.190817i
$586$			20202.4i			1.42415i
$587$	14419.3	+	14419.3i	1.01388	+	1.01388i	0.999902	+	0.0139823i	$0.00445086\pi$
$587$	14419.3	+	14419.3i	1.01388	+	1.01388i	0.0139823	+	0.999902i	$0.495549\pi$
$588$	−1607.95	+	1607.95i	−0.112773	+	0.112773i
$589$	16321.4			1.14178
$590$	5591.58	−	2808.32i	0.390172	−	0.195960i
$591$	29770.3			2.07206
$592$	−2838.71	+	2838.71i	−0.197078	+	0.197078i
$593$	−10401.8	+	10401.8i	−0.720319	+	0.720319i	−0.968670	−	0.248351i	$-0.920111\pi$
$593$	−10401.8	+	10401.8i	−0.720319	+	0.720319i	0.248351	+	0.968670i	$0.420111\pi$
$594$	−158.810			−0.0109698
$595$	−3823.64	+	11539.8i	−0.263452	+	0.795101i
$596$		−	624.745i		−	0.0429372i
$597$	−9162.92	+	9162.92i	−0.628163	+	0.628163i
$598$	−1431.28	+	1212.49i	−0.0978754	+	0.0829140i
$599$			2357.32i			0.160797i	0.996763	+	0.0803987i	$0.0256193\pi$
$599$			2357.32i			0.160797i	−0.996763	+	0.0803987i	$0.974381\pi$
$600$	14805.1	−	19888.1i	1.00736	−	1.35321i
$601$	2597.15			0.176273			0.0881363	−	0.996108i	$-0.471909\pi$
$601$	2597.15			0.176273			0.0881363	+	0.996108i	$0.471909\pi$
$602$	8069.30	+	8069.30i	0.546313	+	0.546313i
$603$	29530.6	+	29530.6i	1.99433	+	1.99433i
$604$		−	3232.92i		−	0.217791i
$605$	14123.1	+	4679.62i	0.949068	+	0.314468i
$606$	8473.21			0.567988
$607$	956.512	+	956.512i	0.0639599	+	0.0639599i	0.738363	−	0.674403i	$-0.235599\pi$
$607$	956.512	+	956.512i	0.0639599	+	0.0639599i	−0.674403	+	0.738363i	$0.735599\pi$
$608$	−4891.25	−	4891.25i	−0.326261	−	0.326261i
$609$	12794.4			0.851319
$610$	5379.47	−	2701.79i	0.357063	−	0.179331i
$611$	−292.418			−0.0193616
$612$	3598.32	−	3598.32i	0.237669	−	0.237669i
$613$	−10533.3	−	10533.3i	−0.694025	−	0.694025i	0.269090	−	0.963115i	$-0.413277\pi$
$613$	−10533.3	−	10533.3i	−0.694025	−	0.694025i	−0.963115	+	0.269090i	$0.913277\pi$
$614$		−	26380.4i		−	1.73392i
$615$	11150.7	−	5600.35i	0.731124	−	0.367200i
$616$	123.702			0.00809105
$617$	4250.50	−	4250.50i	0.277340	−	0.277340i	−0.554706	−	0.832046i	$-0.687169\pi$
$617$	4250.50	−	4250.50i	0.277340	−	0.277340i	0.832046	+	0.554706i	$0.187169\pi$
$618$	−23236.0	−	23236.0i	−1.51244	−	1.51244i
$619$	19672.0			1.27736			0.638679	−	0.769473i	$-0.279481\pi$
$619$	19672.0			1.27736			0.638679	+	0.769473i	$0.279481\pi$
$620$	−497.418	+	1501.21i	−0.0322206	+	0.0972420i
$621$	−13265.2	−	1097.77i	−0.857188	−	0.0709374i
$622$	3428.50	+	3428.50i	0.221014	+	0.221014i
$623$	2882.07	−	2882.07i	0.185342	−	0.185342i
$624$		−	2875.43i		−	0.184470i
$625$	4482.34	+	14968.3i	0.286870	+	0.957970i
$626$		−	5019.78i		−	0.320496i
$627$	−392.804	−	392.804i	−0.0250193	−	0.0250193i
$628$	−567.663	−	567.663i	−0.0360704	−	0.0360704i
$629$		−	7959.72i		−	0.504570i
$630$	−3926.38	+	11849.8i	−0.248303	+	0.749379i
$631$			3946.36i			0.248973i	0.992221	+	0.124487i	$0.0397284\pi$
$631$			3946.36i			0.248973i	−0.992221	+	0.124487i	$0.960272\pi$
$632$	10599.6	−	10599.6i	0.667135	−	0.667135i
$633$	805.516	−	805.516i	0.0505788	−	0.0505788i
$634$		−	1145.32i		−	0.0717455i
$635$	−13087.9	−	26059.1i	−0.817920	−	1.62854i
$636$			2562.02i			0.159734i
$637$	−1092.14	−	1092.14i	−0.0679311	−	0.0679311i
$638$	140.053	+	140.053i	0.00869086	+	0.00869086i
$639$		−	18698.5i		−	1.15759i
$640$	−10571.1	+	5309.23i	−0.652905	+	0.327915i
$641$			17277.0i			1.06459i	0.846559	+	0.532295i	$0.178670\pi$
$641$			17277.0i			1.06459i	−0.846559	+	0.532295i	$0.821330\pi$
$642$	−18384.6	+	18384.6i	−1.13019	+	1.13019i
$643$	6563.82	+	6563.82i	0.402569	+	0.402569i	0.879137	−	0.476569i	$-0.158120\pi$
$643$	6563.82	+	6563.82i	0.402569	+	0.402569i	−0.476569	+	0.879137i	$0.658120\pi$
$644$	1304.29	+	107.938i	0.0798080	+	0.00660458i
$645$	37341.1	+	12372.8i	2.27954	+	0.755314i
$646$	−36950.8			−2.25048
$647$	−15122.2	−	15122.2i	−0.918881	−	0.918881i	0.0780670	−	0.996948i	$-0.475125\pi$
$647$	−15122.2	−	15122.2i	−0.918881	−	0.918881i	−0.996948	+	0.0780670i	$0.975125\pi$
$648$	−2086.55	+	2086.55i	−0.126493	+	0.126493i
$649$	107.615			0.00650885
$650$	1705.15	+	1269.34i	0.102895	+	0.0765966i
$651$		−	10404.8i		−	0.626416i
$652$	507.477	+	507.477i	0.0304821	+	0.0304821i
$653$	5336.67	−	5336.67i	0.319816	−	0.319816i	−0.528880	−	0.848697i	$-0.677388\pi$
$653$	5336.67	−	5336.67i	0.319816	−	0.319816i	0.848697	+	0.528880i	$0.177388\pi$
$654$	−32580.2			−1.94799
$655$	24050.5	+	7968.99i	1.43470	+	0.475380i
$656$	−7199.63			−0.428503
$657$	−15215.4	−	15215.4i	−0.903516	−	0.903516i
$658$	−854.328	−	854.328i	−0.0506158	−	0.0506158i
$659$	−25483.4			−1.50636			−0.753180	−	0.657815i	$-0.771481\pi$
$659$	−25483.4			−1.50636			−0.753180	+	0.657815i	$0.771481\pi$
$660$	48.1007	−	24.1581i	0.00283684	−	0.00142478i
$661$			11464.6i			0.674618i	0.941394	+	0.337309i	$0.109517\pi$
$661$			11464.6i			0.674618i	−0.941394	+	0.337309i	$0.890483\pi$
$662$	6378.87	+	6378.87i	0.374504	+	0.374504i
$663$	4031.34	+	4031.34i	0.236145	+	0.236145i
$664$	−27746.7			−1.62166
$665$	−13678.1	+	6869.70i	−0.797615	+	0.400595i
$666$		−	8173.58i		−	0.475555i
$667$	10730.4	+	12666.6i	0.622911	+	0.735311i
$668$	−541.878	+	541.878i	−0.0313860	+	0.0313860i
$669$			40236.1i			2.32529i
$670$	27892.1	+	9241.90i	1.60831	+	0.532904i
$671$	103.532			0.00595651
$672$	−3118.15	+	3118.15i	−0.178996	+	0.178996i
$673$	8366.16	−	8366.16i	0.479186	−	0.479186i	−0.425686	−	0.904871i	$-0.639967\pi$
$673$	8366.16	−	8366.16i	0.479186	−	0.479186i	0.904871	+	0.425686i	$0.139967\pi$
$674$	13766.2			0.786728
$675$	2186.66	+	14924.6i	0.124688	+	0.851033i
$676$	2490.30			0.141688
$677$	−23927.8	+	23927.8i	−1.35838	+	1.35838i	−0.482454	+	0.875921i	$0.660255\pi$
$677$	−23927.8	+	23927.8i	−1.35838	+	1.35838i	−0.875921	+	0.482454i	$0.839745\pi$
$678$	−15386.7	−	15386.7i	−0.871569	−	0.871569i
$679$		−	15323.4i		−	0.866068i
$680$	8921.23	−	26924.3i	0.503108	−	1.51838i
$681$		−	29564.8i		−	1.66362i
$682$	113.896	−	113.896i	0.00639489	−	0.00639489i
$683$	−13609.0	+	13609.0i	−0.762420	+	0.762420i	−0.976759	−	0.214339i	$-0.931240\pi$
$683$	−13609.0	+	13609.0i	−0.762420	+	0.762420i	0.214339	+	0.976759i	$0.431240\pi$
$684$	6407.18			0.358165
$685$	−8374.60	+	4206.06i	−0.467120	+	0.234606i
$686$		−	15593.9i		−	0.867896i
$687$	−11503.2	+	11503.2i	−0.638828	+	0.638828i
$688$	−16049.2	−	16049.2i	−0.889348	−	0.889348i
$689$	−1740.15			−0.0962186
$690$	−24782.4	+	9981.00i	−1.36732	+	0.550682i
$691$	−23724.8			−1.30613			−0.653063	−	0.757303i	$-0.726516\pi$
$691$	−23724.8			−1.30613			−0.653063	+	0.757303i	$0.726516\pi$
$692$	−1339.35	−	1339.35i	−0.0735756	−	0.0735756i
$693$	−151.813	+	151.813i	−0.00832165	+	0.00832165i
$694$		−	7584.12i		−	0.414826i
$695$	−3626.55	+	10945.0i	−0.197932	+	0.597361i
$696$	−29851.5			−1.62574
$697$	10093.9	−	10093.9i	0.548540	−	0.548540i
$698$	−21876.3	+	21876.3i	−1.18629	+	1.18629i
$699$			26189.8i			1.41715i
$700$	−215.002	−	1467.45i	−0.0116090	−	0.0792349i
$701$			5842.52i			0.314792i	0.987536	+	0.157396i	$0.0503099\pi$
$701$			5842.52i			0.314792i	−0.987536	+	0.157396i	$0.949690\pi$
$702$	1451.07	+	1451.07i	0.0780159	+	0.0780159i
$703$	7086.56	−	7086.56i	0.380191	−	0.380191i
$704$	−283.243			−0.0151635
$705$	−3953.45	−	1309.95i	−0.211199	−	0.0699798i
$706$	20213.0			1.07752
$707$	2839.25	−	2839.25i	0.151034	−	0.151034i
$708$	−1447.69	+	1447.69i	−0.0768469	+	0.0768469i
$709$	555.625			0.0294315			0.0147157	−	0.999892i	$-0.495316\pi$
$709$	555.625			0.0294315			0.0147157	+	0.999892i	$0.495316\pi$
$710$	−5904.58	−	11756.5i	−0.312106	−	0.621426i
$711$			26016.7i			1.37230i
$712$	−6724.38	+	6724.38i	−0.353942	+	0.353942i
$713$	10300.9	−	8726.30i	0.541055	−	0.458349i
$714$			23556.0i			1.23468i
$715$	16.4085	+	32.6706i	0.000858242	+	0.00170883i
$716$	−429.585			−0.0224223
$717$	−18715.3	−	18715.3i	−0.974808	−	0.974808i
$718$	10756.5	+	10756.5i	0.559093	+	0.559093i
$719$			16315.0i			0.846239i	0.906074	+	0.423120i	$0.139065\pi$
$719$			16315.0i			0.846239i	−0.906074	+	0.423120i	$0.860935\pi$
$720$	7809.27	−	23568.4i	0.404214	−	1.21992i
$721$	−15572.1			−0.804351
$722$	−20208.9	−	20208.9i	−1.04169	−	1.04169i
$723$	−11507.9	−	11507.9i	−0.591955	−	0.591955i
$724$	2947.03			0.151278
$725$	11233.5	−	15090.3i	0.575449	−	0.773019i
$726$	28829.3			1.47377
$727$	10929.0	−	10929.0i	0.557544	−	0.557544i	−0.371064	−	0.928607i	$-0.621007\pi$
$727$	10929.0	−	10929.0i	0.557544	−	0.557544i	0.928607	+	0.371064i	$0.121007\pi$
$728$	−1130.28	−	1130.28i	−0.0575427	−	0.0575427i
$729$		−	32101.5i		−	1.63092i
$730$	−14371.2	−	4761.81i	−0.728632	−	0.241428i
$731$	45002.0			2.27696
$732$	−1392.78	+	1392.78i	−0.0703258	+	0.0703258i
$733$	14665.6	+	14665.6i	0.739001	+	0.739001i	0.972385	−	0.233383i	$-0.0749797\pi$
$733$	14665.6	+	14665.6i	0.739001	+	0.739001i	−0.233383	+	0.972385i	$0.574980\pi$
$734$	−15539.5			−0.781435
$735$	−9873.09	−	19658.1i	−0.495475	−	0.986529i
$736$	−5702.15	−	471.887i	−0.285576	−	0.0236331i
$737$	357.337	+	357.337i	0.0178598	+	0.0178598i
$738$	10365.1	−	10365.1i	0.516996	−	0.516996i
$739$		−	5318.71i		−	0.264752i	−0.991200	−	0.132376i	$-0.957739\pi$
$739$		−	5318.71i		−	0.264752i	0.991200	−	0.132376i	$-0.0422607\pi$
$740$	435.835	+	867.782i	0.0216508	+	0.0431085i
$741$			7178.23i			0.355869i
$742$	−5084.04	−	5084.04i	−0.251538	−	0.251538i
$743$	2074.70	+	2074.70i	0.102441	+	0.102441i	0.756470	−	0.654029i	$-0.226923\pi$
$743$	2074.70	+	2074.70i	0.102441	+	0.102441i	−0.654029	+	0.756470i	$0.726923\pi$
$744$			24276.3i			1.19625i
$745$	5736.95	+	1900.91i	0.282128	+	0.0934817i
$746$			16614.6i			0.815421i
$747$	34052.2	−	34052.2i	1.66788	−	1.66788i
$748$	43.5417	−	43.5417i	0.00212840	−	0.00212840i
$749$			12320.9i			0.601061i
$750$	17367.1	+	24800.0i	0.845541	+	1.20742i
$751$		−	27699.5i		−	1.34590i	−0.739689	−	0.672949i	$-0.765027\pi$
$751$		−	27699.5i		−	1.34590i	0.739689	−	0.672949i	$-0.234973\pi$
$752$	1699.20	+	1699.20i	0.0823980	+	0.0823980i
$753$	−11627.0	−	11627.0i	−0.562699	−	0.562699i
$754$		−	2559.38i		−	0.123617i
$755$	29687.5	+	9836.80i	1.43105	+	0.474169i
$756$		−	1431.76i		−	0.0688790i
$757$	−20005.6	+	20005.6i	−0.960523	+	0.960523i	−0.999250	−	0.0387265i	$-0.987670\pi$
$757$	−20005.6	+	20005.6i	−0.960523	+	0.960523i	0.0387265	+	0.999250i	$0.487670\pi$
$758$	20706.2	+	20706.2i	0.992192	+	0.992192i
$759$	−457.925	−	37.8960i	−0.0218994	−	0.00181230i
$760$	31913.4	−	16028.2i	1.52318	−	0.765005i
$761$	19931.3			0.949420			0.474710	−	0.880142i	$-0.342553\pi$
$761$	19931.3			0.949420			0.474710	+	0.880142i	$0.342553\pi$
$762$	−39955.1	−	39955.1i	−1.89950	−	1.89950i
$763$	−10917.1	+	10917.1i	−0.517991	+	0.517991i
$764$	−3867.56			−0.183146
$765$	22094.3	+	43991.5i	1.04421	+	2.07910i
$766$			37473.3i			1.76758i
$767$	−983.291	−	983.291i	−0.0462902	−	0.0462902i
$768$	10167.2	−	10167.2i	0.477704	−	0.477704i
$769$	17879.5			0.838429			0.419214	−	0.907887i	$-0.362306\pi$
$769$	17879.5			0.838429			0.419214	+	0.907887i	$0.362306\pi$
$770$	−47.5114	+	143.390i	−0.00222363	+	0.00671092i
$771$	−49506.7			−2.31250
$772$	1686.41	+	1686.41i	0.0786206	+	0.0786206i
$773$	9474.61	+	9474.61i	0.440851	+	0.440851i	0.892298	−	0.451447i	$-0.149092\pi$
$773$	9474.61	+	9474.61i	0.440851	+	0.440851i	−0.451447	+	0.892298i	$0.649092\pi$
$774$	46211.1			2.14603
$775$	−12271.9	−	9135.45i	−0.568801	−	0.423426i
$776$			35752.3i			1.65391i
$777$	−4517.65	−	4517.65i	−0.208584	−	0.208584i
$778$	9419.22	+	9419.22i	0.434056	+	0.434056i
$779$	17973.2			0.826645
$780$	−660.240	−	218.767i	−0.0303082	−	0.0100425i
$781$		−	226.263i		−	0.0103666i
$782$	−23320.8	+	19755.9i	−1.06643	+	0.903414i
$783$	12841.7	−	12841.7i	0.586113	−	0.586113i
$784$			12692.5i			0.578194i
$785$	6940.00	−	3485.55i	0.315541	−	0.158477i
$786$	49093.8			2.22789
$787$	30098.0	−	30098.0i	1.36325	−	1.36325i	0.493512	−	0.869739i	$-0.335713\pi$
$787$	30098.0	−	30098.0i	1.36325	−	1.36325i	0.869739	−	0.493512i	$-0.164287\pi$
$788$	−2937.99	+	2937.99i	−0.132819	+	0.132819i
$789$	−46615.2			−2.10335
$790$	8215.49	+	16357.7i	0.369993	+	0.736684i
$791$	−10311.8			−0.463519
$792$	354.206	−	354.206i	0.0158916	−	0.0158916i
$793$	−945.991	−	945.991i	−0.0423621	−	0.0423621i
$794$			25964.7i			1.16052i
$795$	−23526.7	−	7795.44i	−1.04957	−	0.347768i
$796$		−	1808.55i		−	0.0805306i
$797$	−23590.4	+	23590.4i	−1.04845	+	1.04845i	−0.0496874	+	0.998765i	$0.515823\pi$
$797$	−23590.4	+	23590.4i	−1.04845	+	1.04845i	−0.998765	+	0.0496874i	$0.984177\pi$
$798$	−20971.9	+	20971.9i	−0.930324	+	0.930324i
$799$	−4764.54			−0.210960
$800$	939.953	+	6415.45i	0.0415404	+	0.283525i
$801$		−	16505.0i		−	0.728059i
$802$	8684.39	−	8684.39i	0.382365	−	0.382365i
$803$	−184.115	−	184.115i	−0.00809126	−	0.00809126i
$804$	−9614.22			−0.421725
$805$	−4959.75	+	11648.7i	−0.217153	+	0.510017i
$806$	−2081.38			−0.0909595
$807$	−45397.4	−	45397.4i	−1.98025	−	1.98025i
$808$	−6624.48	+	6624.48i	−0.288426	+	0.288426i
$809$		−	29931.4i		−	1.30078i	−0.759599	−	0.650391i	$-0.774605\pi$
$809$		−	29931.4i		−	1.30078i	0.759599	−	0.650391i	$-0.225395\pi$
$810$	−1617.23	−	3220.04i	−0.0701529	−	0.139680i
$811$	−12895.4			−0.558345			−0.279172	−	0.960241i	$-0.590060\pi$
$811$	−12895.4			−0.558345			−0.279172	+	0.960241i	$0.590060\pi$
$812$	−1262.66	+	1262.66i	−0.0545696	+	0.0545696i
$813$	32443.9	−	32443.9i	1.39958	−	1.39958i
$814$		−	98.9049i		−	0.00425874i
$815$	−6204.19	+	3116.00i	−0.266654	+	0.133925i
$816$		−	46851.1i		−	2.00995i
$817$	40065.4	+	40065.4i	1.71568	+	1.71568i
$818$	−17879.4	+	17879.4i	−0.764229	+	0.764229i
$819$	2774.28			0.118365
$820$	−547.759	+	1653.14i	−0.0233275	+	0.0704026i
$821$	−14897.5			−0.633285			−0.316642	−	0.948545i	$-0.602555\pi$
$821$	−14897.5			−0.633285			−0.316642	+	0.948545i	$0.602555\pi$
$822$	−12840.3	+	12840.3i	−0.544840	+	0.544840i
$823$	−10519.6	+	10519.6i	−0.445555	+	0.445555i	−0.893874	−	0.448319i	$-0.852023\pi$
$823$	−10519.6	+	10519.6i	−0.445555	+	0.445555i	0.448319	+	0.893874i	$0.352023\pi$
$824$	36332.5			1.53605
$825$	75.4852	+	515.208i	0.00318552	+	0.0217421i
$826$		−	5745.57i		−	0.242027i
$827$	−9669.65	+	9669.65i	−0.406586	+	0.406586i	−0.880546	−	0.473960i	$-0.842824\pi$
$827$	−9669.65	+	9669.65i	−0.406586	+	0.406586i	0.473960	+	0.880546i	$0.342824\pi$
$828$	4043.77	−	3425.63i	0.169723	−	0.143779i
$829$			19455.4i			0.815094i	0.913184	+	0.407547i	$0.133616\pi$
$829$			19455.4i			0.815094i	−0.913184	+	0.407547i	$0.866384\pi$
$830$	10657.0	−	32162.8i	0.445673	−	1.34504i
$831$	31020.4			1.29493
$832$	2588.03	+	2588.03i	0.107841	+	0.107841i
$833$	−17794.9	−	17794.9i	−0.740163	−	0.740163i
$834$			22341.8i			0.927616i
$835$	−3327.23	−	6624.76i	−0.137896	−	0.274562i
$836$	77.5305			0.00320748
$837$	−10443.3	−	10443.3i	−0.431272	−	0.431272i
$838$	−4041.04	−	4041.04i	−0.166581	−	0.166581i
$839$	31057.9			1.27799			0.638997	−	0.769209i	$-0.279350\pi$
$839$	31057.9			1.27799			0.638997	+	0.769209i	$0.279350\pi$
$840$	−10217.9	−	20344.7i	−0.419704	−	0.835664i
$841$	1738.92			0.0712996
$842$	18147.5	−	18147.5i	0.742760	−	0.742760i
$843$	−2841.03	−	2841.03i	−0.116074	−	0.116074i
$844$			158.990i			0.00648422i
$845$	−7577.23	+	22868.1i	−0.308479	+	0.930991i
$846$	−4892.55			−0.198829
$847$	9660.28	−	9660.28i	0.391890	−	0.391890i
$848$	10111.8	+	10111.8i	0.409481	+	0.409481i
$849$	−36471.8			−1.47434
$850$	27783.0	+	20682.2i	1.12112	+	0.834581i
$851$	683.680	−	8261.40i	0.0275396	−	0.332782i
$852$	3043.82	+	3043.82i	0.122394	+	0.122394i
$853$	22537.1	−	22537.1i	0.904638	−	0.904638i	−0.0911950	−	0.995833i	$-0.529069\pi$
$853$	22537.1	−	22537.1i	0.904638	−	0.904638i	0.995833	+	0.0911950i	$0.0290686\pi$
$854$		−	5527.62i		−	0.221489i
$855$	−19495.1	+	58836.3i	−0.779788	+	2.35340i
$856$		−	28746.7i		−	1.14783i
$857$	−24473.8	−	24473.8i	−0.975505	−	0.975505i	0.0242021	−	0.999707i	$-0.492295\pi$
$857$	−24473.8	−	24473.8i	−0.975505	−	0.975505i	−0.999707	+	0.0242021i	$0.992295\pi$
$858$	50.0922	+	50.0922i	0.00199315	+	0.00199315i
$859$		−	8319.52i		−	0.330452i	−0.986256	−	0.165226i	$-0.947165\pi$
$859$		−	8319.52i		−	0.330452i	0.986256	−	0.165226i	$-0.0528354\pi$
$860$	−4906.19	+	2464.09i	−0.194535	+	0.0977032i
$861$		−	11457.8i		−	0.453521i
$862$	−26581.8	+	26581.8i	−1.05033	+	1.05033i
$863$	−2982.85	+	2982.85i	−0.117656	+	0.117656i	−0.763484	−	0.645827i	$-0.776513\pi$
$863$	−2982.85	+	2982.85i	−0.117656	+	0.117656i	0.645827	+	0.763484i	$0.276513\pi$
$864$			6259.40i			0.246469i
$865$	16374.3	−	8223.83i	0.643633	−	0.323258i
$866$		−	13280.7i		−	0.521128i
$867$	36917.3	+	36917.3i	1.44611	+	1.44611i
$868$	1026.84	+	1026.84i	0.0401533	+	0.0401533i
$869$			314.817i			0.0122893i
$870$	11465.4	−	34602.5i	0.446795	−	1.34843i
$871$		−	6530.10i		−	0.254034i
$872$	25471.6	−	25471.6i	0.989195	−	0.989195i
$873$	−43877.0	−	43877.0i	−1.70104	−	1.70104i
$874$	−38351.3	−	3173.79i	−1.48427	−	0.122832i
$875$	14129.6	+	2490.67i	0.545906	+	0.0962285i
$876$	4953.65			0.191060
$877$	−8243.53	−	8243.53i	−0.317405	−	0.317405i	0.530365	−	0.847770i	$-0.322055\pi$
$877$	−8243.53	−	8243.53i	−0.317405	−	0.317405i	−0.847770	+	0.530365i	$0.822055\pi$
$878$	7239.41	−	7239.41i	0.278267	−	0.278267i
$879$	63946.0			2.45375
$880$	94.4966	−	285.191i	0.00361986	−	0.0109248i
$881$			26007.6i			0.994574i	0.867586	+	0.497287i	$0.165670\pi$
$881$			26007.6i			0.994574i	−0.867586	+	0.497287i	$0.834330\pi$
$882$	−18273.0	−	18273.0i	−0.697600	−	0.697600i
$883$	23966.1	−	23966.1i	0.913390	−	0.913390i	−0.0831477	−	0.996537i	$-0.526497\pi$
$883$	23966.1	−	23966.1i	0.913390	−	0.913390i	0.996537	+	0.0831477i	$0.0264973\pi$
$884$	−795.694			−0.0302739
$885$	−8889.09	−	17698.9i	−0.337631	−	0.672250i
$886$	−24479.1			−0.928207
$887$	3525.09	+	3525.09i	0.133440	+	0.133440i	0.770672	−	0.637232i	$-0.219921\pi$
$887$	3525.09	+	3525.09i	0.133440	+	0.133440i	−0.637232	+	0.770672i	$0.719921\pi$
$888$	10540.5	+	10540.5i	0.398328	+	0.398328i
$889$	−26776.8			−1.01020
$890$	−5211.90	−	10377.3i	−0.196296	−	0.390840i
$891$		−	61.9723i		−	0.00233014i
$892$	−3970.84	−	3970.84i	−0.149051	−	0.149051i
$893$	−4241.88	−	4241.88i	−0.158958	−	0.158958i
$894$	11710.7			0.438105
$895$	1307.10	−	3944.82i	0.0488172	−	0.147331i
$896$			10862.2i			0.405002i
$897$	3837.87	+	4530.40i	0.142857	+	0.168635i
$898$	4561.71	−	4561.71i	0.169517	−	0.169517i
$899$			18419.8i			0.683354i
$900$	−4817.51	−	3586.25i	−0.178426	−	0.132824i
$901$	−28353.4			−1.04838
$902$	125.423	−	125.423i	0.00462986	−	0.00462986i
$903$	25541.5	−	25541.5i	0.941272	−	0.941272i
$904$	24059.1			0.885171
$905$	−8966.90	+	27062.2i	−0.329359	+	0.994008i
$906$	60600.6			2.22221
$907$	32118.4	−	32118.4i	1.17583	−	1.17583i	0.195027	−	0.980798i	$-0.437520\pi$
$907$	32118.4	−	32118.4i	1.17583	−	1.17583i	0.980798	−	0.195027i	$-0.0624795\pi$
$908$	2917.71	+	2917.71i	0.106638	+	0.106638i
$909$		−	16259.8i		−	0.593292i
$910$	1744.29	−	876.055i	0.0635415	−	0.0319131i
$911$			47142.5i			1.71449i	0.514907	+	0.857246i	$0.327826\pi$
$911$			47142.5i			1.71449i	−0.514907	+	0.857246i	$0.672174\pi$
$912$	41711.6	−	41711.6i	1.51448	−	1.51448i
$913$	412.051	−	412.051i	0.0149364	−	0.0149364i
$914$	429.830			0.0155553
$915$	−8551.89	−	17027.5i	−0.308980	−	0.615203i
$916$		−	2270.47i		−	0.0818979i
$917$	16450.6	−	16450.6i	0.592419	−	0.592419i
$918$	23643.2	+	23643.2i	0.850046	+	0.850046i
$919$	−10157.7			−0.364604			−0.182302	−	0.983243i	$-0.558355\pi$
$919$	−10157.7			−0.364604			−0.182302	+	0.983243i	$0.558355\pi$
$920$	11572.0	−	27178.5i	0.414691	−	0.973967i
$921$	−83501.2			−2.98747
$922$	6220.69	+	6220.69i	0.222199	+	0.222199i
$923$	−2067.40	+	2067.40i	−0.0737262	+	0.0737262i
$924$		−	49.4254i		−	0.00175971i
$925$	−9294.84	+	1361.82i	−0.330392	+	0.0484070i
$926$	−6594.86			−0.234040
$927$	−44589.1	+	44589.1i	−1.57983	+	1.57983i
$928$	5520.12	−	5520.12i	0.195266	−	0.195266i
$929$			33639.2i			1.18802i	0.804459	+	0.594008i	$0.202455\pi$
$929$			33639.2i			1.18802i	−0.804459	+	0.594008i	$0.797545\pi$
$930$	−28140.0	−	9324.02i	−0.992200	−	0.328760i
$931$		−	31685.6i		−	1.11542i
$932$	−2584.63	−	2584.63i	−0.0908394	−	0.0908394i
$933$	10852.1	−	10852.1i	0.380797	−	0.380797i
$934$	28619.1			1.00262
$935$	267.354	+	532.322i	0.00935123	+	0.0186190i
$936$	−6472.88			−0.226039
$937$	−39501.7	+	39501.7i	−1.37723	+	1.37723i	−0.527962	+	0.849268i	$0.677044\pi$
$937$	−39501.7	+	39501.7i	−1.37723	+	1.37723i	−0.849268	+	0.527962i	$0.822956\pi$
$938$	19078.4	−	19078.4i	0.664105	−	0.664105i
$939$	−15889.0			−0.552201
$940$	519.438	−	260.883i	0.0180236	−	0.00905219i
$941$		−	15101.0i		−	0.523143i	−0.965184	−	0.261572i	$-0.915759\pi$
$941$		−	15101.0i		−	0.523143i	0.965184	−	0.261572i	$-0.0842407\pi$
$942$	10640.8	−	10640.8i	0.368041	−	0.368041i
$943$	11343.4	−	9609.45i	0.391721	−	0.331842i
$944$			11427.5i			0.393998i
$945$	13147.6	+	4356.40i	0.452585	+	0.149962i
$946$	559.181			0.0192183
$947$	15792.7	+	15792.7i	0.541917	+	0.541917i	0.924090	−	0.382174i	$-0.124824\pi$
$947$	15792.7	+	15792.7i	0.541917	+	0.541917i	−0.382174	+	0.924090i	$0.624824\pi$
$948$	−4235.10	−	4235.10i	−0.145095	−	0.145095i
$949$			3364.58i			0.115088i
$950$	6321.89	+	43148.7i	0.215904	+	1.47361i
$951$	−3625.26			−0.123614
$952$	−18416.4	−	18416.4i	−0.626973	−	0.626973i
$953$	−9363.98	−	9363.98i	−0.318289	−	0.318289i	0.529821	−	0.848110i	$-0.322259\pi$
$953$	−9363.98	−	9363.98i	−0.318289	−	0.318289i	−0.848110	+	0.529821i	$0.822259\pi$
$954$	−29115.2			−0.988091
$955$	11767.8	−	35515.3i	0.398741	−	1.20340i
$956$	3693.98			0.124971
$957$	443.307	−	443.307i	0.0149740	−	0.0149740i
$958$	−9252.50	−	9252.50i	−0.312040	−	0.312040i
$959$			8605.24i			0.289758i
$960$	23396.2	+	46583.6i	0.786571	+	1.56612i
$961$	−14811.4			−0.497176
$962$	−903.710	+	903.710i	−0.0302877	+	0.0302877i
$963$	35279.4	+	35279.4i	1.18054	+	1.18054i
$964$	2271.40			0.0758888
$965$	−20617.3	+	10354.8i	−0.687766	+	0.345424i
$966$	−2023.28	+	24448.8i	−0.0673892	+	0.814313i
$967$	892.555	+	892.555i	0.0296821	+	0.0296821i	0.721792	−	0.692110i	$-0.243319\pi$
$967$	892.555	+	892.555i	0.0296821	+	0.0296821i	−0.692110	+	0.721792i	$0.743319\pi$
$968$	−22539.1	+	22539.1i	−0.748383	+	0.748383i
$969$			116959.i			3.87747i
$970$	−41442.5	−	13731.7i	−1.37179	−	0.454536i
$971$			2873.06i			0.0949545i	0.998872	+	0.0474772i	$0.0151182\pi$
$971$			2873.06i			0.0949545i	−0.998872	+	0.0474772i	$0.984882\pi$
$972$	3496.31	+	3496.31i	0.115375	+	0.115375i
$973$	7486.41	+	7486.41i	0.246663	+	0.246663i
$974$		−	36048.1i		−	1.18589i
$975$	4017.82	−	5397.26i	0.131972	−	0.177283i
$976$			10994.0i			0.360564i
$977$	9875.66	−	9875.66i	0.323388	−	0.323388i	−0.526677	−	0.850065i	$-0.676562\pi$
$977$	9875.66	−	9875.66i	0.323388	−	0.323388i	0.850065	+	0.526677i	$0.176562\pi$
$978$	−9512.57	+	9512.57i	−0.311021	+	0.311021i
$979$		−	199.720i		−	0.00651999i
$980$	2914.39	+	965.666i	0.0949966	+	0.0314766i
$981$			62520.1i			2.03477i
$982$	10316.8	+	10316.8i	0.335256	+	0.335256i
$983$	21643.9	+	21643.9i	0.702271	+	0.702271i	0.964898	−	0.262627i	$-0.0845888\pi$
$983$	21643.9	+	21643.9i	0.702271	+	0.702271i	−0.262627	+	0.964898i	$0.584589\pi$
$984$			26733.1i			0.866078i
$985$	−18039.8	−	35918.6i	−0.583549	−	1.16189i
$986$		−	41701.5i		−	1.34690i
$987$	−2704.18	+	2704.18i	−0.0872087	+	0.0872087i
$988$	−708.409	−	708.409i	−0.0228112	−	0.0228112i
$989$	46707.6	+	3865.33i	1.50174	+	0.124277i
$990$	274.537	+	546.624i	0.00881349	+	0.0175483i
$991$	24688.6			0.791382			0.395691	−	0.918384i	$-0.370505\pi$
$991$	24688.6			0.791382			0.395691	+	0.918384i	$0.370505\pi$
$992$	−4489.15	−	4489.15i	−0.143680	−	0.143680i
$993$	20190.8	−	20190.8i	0.645254	−	0.645254i
$994$	−12080.3			−0.385475
$995$	16607.7	+	5502.87i	0.529145	+	0.175329i
$996$			11086.3i			0.352693i
$997$	34626.7	+	34626.7i	1.09994	+	1.09994i	0.994417	+	0.105522i	$0.0336514\pi$
$997$	34626.7	+	34626.7i	1.09994	+	1.09994i	0.105522	+	0.994417i	$0.466349\pi$
$998$	−17850.5	+	17850.5i	−0.566181	+	0.566181i
$999$	−9068.76			−0.287210

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.4.e.a.22.12	yes	68
5.3	odd	4	inner	115.4.e.a.68.11	yes	68
23.22	odd	2	inner	115.4.e.a.22.11	✓	68
115.68	even	4	inner	115.4.e.a.68.12	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.4.e.a.22.11	✓	68	23.22	odd	2	inner
115.4.e.a.22.12	yes	68	1.1	even	1	trivial
115.4.e.a.68.11	yes	68	5.3	odd	4	inner
115.4.e.a.68.12	yes	68	115.68	even	4	inner

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	115.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.84990 - 1.84990i) q^{2} +(-5.85544 + 5.85544i) q^{3} -1.15573i q^{4} +(10.6129 + 3.51653i) q^{5} +21.6640 q^{6} +(7.25929 - 7.25929i) q^{7} +(-16.9372 + 16.9372i) q^{8} -41.5723i q^{9} +(-13.1276 - 26.1381i) q^{10} -0.503049i q^{11} +(6.76730 + 6.76730i) q^{12} +(-4.59644 + 4.59644i) q^{13} -26.8579 q^{14} +(-82.7341 + 41.5524i) q^{15} +53.4185 q^{16} +(-74.8926 + 74.8926i) q^{17} +(-76.9047 + 76.9047i) q^{18} -133.354 q^{19} +(4.06416 - 12.2657i) q^{20} +85.0127i q^{21} +(-0.930591 + 0.930591i) q^{22} +(-84.1638 + 71.2984i) q^{23} -198.349i q^{24} +(100.268 + 74.6413i) q^{25} +17.0059 q^{26} +(85.3275 + 85.3275i) q^{27} +(-8.38978 - 8.38978i) q^{28} -150.499i q^{29} +(229.918 + 76.1821i) q^{30} -122.391 q^{31} +(36.6787 + 36.6787i) q^{32} +(2.94557 + 2.94557i) q^{33} +277.088 q^{34} +(102.570 - 51.5147i) q^{35} -48.0464 q^{36} +(-53.1409 + 53.1409i) q^{37} +(246.692 + 246.692i) q^{38} -53.8283i q^{39} +(-239.313 + 120.193i) q^{40} -134.778 q^{41} +(157.265 - 157.265i) q^{42} +(-300.444 - 300.444i) q^{43} -0.581389 q^{44} +(146.191 - 441.204i) q^{45} +(287.590 + 23.7997i) q^{46} +(31.8091 + 31.8091i) q^{47} +(-312.789 + 312.789i) q^{48} +237.605i q^{49} +(-47.4068 - 323.565i) q^{50} -877.058i q^{51} +(5.31224 + 5.31224i) q^{52} +(189.294 + 189.294i) q^{53} -315.695i q^{54} +(1.76899 - 5.33882i) q^{55} +245.904i q^{56} +(780.847 - 780.847i) q^{57} +(-278.409 + 278.409i) q^{58} +213.925i q^{59} +(48.0234 + 95.6183i) q^{60} +205.810i q^{61} +(226.412 + 226.412i) q^{62} +(-301.786 - 301.786i) q^{63} -563.052i q^{64} +(-64.9451 + 32.6181i) q^{65} -10.8980i q^{66} +(-710.343 + 710.343i) q^{67} +(86.5555 + 86.5555i) q^{68} +(75.3326 - 910.299i) q^{69} +(-285.041 - 94.4468i) q^{70} +449.783 q^{71} +(704.119 + 704.119i) q^{72} +(365.998 - 365.998i) q^{73} +196.611 q^{74} +(-1024.17 + 150.055i) q^{75} +154.121i q^{76} +(-3.65178 - 3.65178i) q^{77} +(-99.5771 + 99.5771i) q^{78} -625.818 q^{79} +(566.926 + 187.848i) q^{80} +123.193 q^{81} +(249.326 + 249.326i) q^{82} +(819.106 + 819.106i) q^{83} +98.2517 q^{84} +(-1058.19 + 531.466i) q^{85} +1111.58i q^{86} +(881.240 + 881.240i) q^{87} +(8.52024 + 8.52024i) q^{88} +397.018 q^{89} +(-1086.62 + 545.746i) q^{90} +66.7338i q^{91} +(82.4016 + 97.2706i) q^{92} +(716.655 - 716.655i) q^{93} -117.688i q^{94} +(-1415.28 - 468.944i) q^{95} -429.540 q^{96} +(1055.44 - 1055.44i) q^{97} +(439.547 - 439.547i) q^{98} -20.9129 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 4 q^{2} + 4 q^{3} + 32 q^{6} + 28 q^{8} + 200 q^{12} - 100 q^{13} - 832 q^{16} - 112 q^{18} - 46 q^{23} - 372 q^{25} - 312 q^{26} - 704 q^{27} - 1056 q^{31} + 560 q^{32} - 348 q^{35} + 2424 q^{36}+ \cdots - 3612 q^{98}+O(q^{100}) \) 68 * q - 4 * q^2 + 4 * q^3 + 32 * q^6 + 28 * q^8 + 200 * q^12 - 100 * q^13 - 832 * q^16 - 112 * q^18 - 46 * q^23 - 372 * q^25 - 312 * q^26 - 704 * q^27 - 1056 * q^31 + 560 * q^32 - 348 * q^35 + 2424 * q^36 + 2248 * q^41 - 96 * q^46 - 1412 * q^47 + 1532 * q^48 - 620 * q^50 + 112 * q^52 + 2688 * q^55 + 2044 * q^58 + 3948 * q^62 - 1836 * q^70 - 2272 * q^71 + 1128 * q^72 + 1100 * q^73 + 2828 * q^75 + 4216 * q^77 - 9180 * q^78 - 3580 * q^81 - 6516 * q^82 - 2684 * q^85 - 6304 * q^87 - 688 * q^92 - 1608 * q^93 - 8616 * q^95 - 544 * q^96 - 3612 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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