LMFDB - Embedded newform 115.4.e.a.22.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [115,4,Mod(22,115)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			22.5
Character	$\chi$	$=$	115.22
Dual form			115.4.e.a.68.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.78118 - 2.78118i) q^{2} +(1.69288 - 1.69288i) q^{3} +7.46996i q^{4} +(-9.46680 - 5.94809i) q^{5} -9.41642 q^{6} +(1.06728 - 1.06728i) q^{7} +(-1.47414 + 1.47414i) q^{8} +21.2683i q^{9} +(9.78619 + 42.8716i) q^{10} -55.8655i q^{11} +(12.6457 + 12.6457i) q^{12} +(-55.7428 + 55.7428i) q^{13} -5.93659 q^{14} +(-26.0956 + 5.95676i) q^{15} +67.9594 q^{16} +(-44.0172 + 44.0172i) q^{17} +(59.1511 - 59.1511i) q^{18} +15.1850 q^{19} +(44.4320 - 70.7166i) q^{20} -3.61355i q^{21} +(-155.372 + 155.372i) q^{22} +(105.533 + 32.0899i) q^{23} +4.99109i q^{24} +(54.2406 + 112.619i) q^{25} +310.062 q^{26} +(81.7125 + 81.7125i) q^{27} +(7.97253 + 7.97253i) q^{28} +43.6739i q^{29} +(89.1434 + 56.0097i) q^{30} +31.1324 q^{31} +(-177.214 - 177.214i) q^{32} +(-94.5737 - 94.5737i) q^{33} +244.840 q^{34} +(-16.4520 + 3.75545i) q^{35} -158.873 q^{36} +(-203.098 + 203.098i) q^{37} +(-42.2323 - 42.2323i) q^{38} +188.732i q^{39} +(22.7237 - 5.18708i) q^{40} -419.020 q^{41} +(-10.0499 + 10.0499i) q^{42} +(-390.269 - 390.269i) q^{43} +417.313 q^{44} +(126.506 - 201.343i) q^{45} +(-204.259 - 382.755i) q^{46} +(-329.500 - 329.500i) q^{47} +(115.047 - 115.047i) q^{48} +340.722i q^{49} +(162.360 - 464.066i) q^{50} +149.032i q^{51} +(-416.397 - 416.397i) q^{52} +(144.476 + 144.476i) q^{53} -454.515i q^{54} +(-332.293 + 528.868i) q^{55} +3.14664i q^{56} +(25.7064 - 25.7064i) q^{57} +(121.465 - 121.465i) q^{58} -274.910i q^{59} +(-44.4968 - 194.933i) q^{60} -300.181i q^{61} +(-86.5849 - 86.5849i) q^{62} +(22.6992 + 22.6992i) q^{63} +442.056i q^{64} +(859.269 - 196.143i) q^{65} +526.053i q^{66} +(-632.542 + 632.542i) q^{67} +(-328.807 - 328.807i) q^{68} +(232.979 - 124.331i) q^{69} +(56.2005 + 35.3114i) q^{70} +401.846 q^{71} +(-31.3525 - 31.3525i) q^{72} +(-308.059 + 308.059i) q^{73} +1129.70 q^{74} +(282.473 + 98.8272i) q^{75} +113.432i q^{76} +(-59.6241 - 59.6241i) q^{77} +(524.898 - 524.898i) q^{78} +8.07381 q^{79} +(-643.358 - 404.228i) q^{80} -297.585 q^{81} +(1165.37 + 1165.37i) q^{82} +(-806.388 - 806.388i) q^{83} +26.9931 q^{84} +(678.520 - 154.884i) q^{85} +2170.82i q^{86} +(73.9346 + 73.9346i) q^{87} +(82.3537 + 82.3537i) q^{88} -1253.12 q^{89} +(-911.807 + 208.136i) q^{90} +118.986i q^{91} +(-239.710 + 788.328i) q^{92} +(52.7034 - 52.7034i) q^{93} +1832.80i q^{94} +(-143.754 - 90.3219i) q^{95} -600.006 q^{96} +(461.250 - 461.250i) q^{97} +(947.610 - 947.610i) q^{98} +1188.17 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 $

$2$	−2.78118	−	2.78118i	−0.983297	−	0.983297i	0.0165661	−	0.999863i	$-0.494727\pi$
$2$	−2.78118	−	2.78118i	−0.983297	−	0.983297i	−0.999863	+	0.0165661i	$0.994727\pi$
$3$	1.69288	−	1.69288i	0.325795	−	0.325795i	−0.525190	−	0.850985i	$-0.676006\pi$
$3$	1.69288	−	1.69288i	0.325795	−	0.325795i	0.850985	+	0.525190i	$0.176006\pi$
$4$			7.46996i			0.933745i
$5$	−9.46680	−	5.94809i	−0.846736	−	0.532013i
$5$	−9.46680	−	5.94809i	−0.846736	−	0.532013i
$6$	−9.41642			−0.640706
$7$	1.06728	−	1.06728i	0.0576276	−	0.0576276i	−0.677706	−	0.735333i	$-0.737026\pi$
$7$	1.06728	−	1.06728i	0.0576276	−	0.0576276i	0.735333	+	0.677706i	$0.237026\pi$
$8$	−1.47414	+	1.47414i	−0.0651485	+	0.0651485i
$9$			21.2683i			0.787715i
$10$	9.78619	+	42.8716i	0.309466	+	1.35572i
$11$		−	55.8655i		−	1.53128i	−0.643269	−	0.765641i	$-0.722422\pi$
$11$		−	55.8655i		−	1.53128i	0.643269	−	0.765641i	$-0.277578\pi$
$12$	12.6457	+	12.6457i	0.304209	+	0.304209i
$13$	−55.7428	+	55.7428i	−1.18925	+	1.18925i	−0.211978	+	0.977275i	$0.567990\pi$
$13$	−55.7428	+	55.7428i	−1.18925	+	1.18925i	−0.977275	+	0.211978i	$0.932010\pi$
$14$	−5.93659			−0.113330
$15$	−26.0956	+	5.95676i	−0.449190	+	0.102535i
$16$	67.9594			1.06187
$17$	−44.0172	+	44.0172i	−0.627985	+	0.627985i	−0.947561	−	0.319576i	$-0.896460\pi$
$17$	−44.0172	+	44.0172i	−0.627985	+	0.627985i	0.319576	+	0.947561i	$0.396460\pi$
$18$	59.1511	−	59.1511i	0.774558	−	0.774558i
$19$	15.1850			0.183352			0.0916759	−	0.995789i	$-0.470778\pi$
$19$	15.1850			0.183352			0.0916759	+	0.995789i	$0.470778\pi$
$20$	44.4320	−	70.7166i	0.496764	−	0.790636i
$21$		−	3.61355i		−	0.0375496i
$22$	−155.372	+	155.372i	−1.50570	+	1.50570i
$23$	105.533	+	32.0899i	0.956747	+	0.290922i
$23$	105.533	+	32.0899i	0.956747	+	0.290922i
$24$			4.99109i			0.0424501i
$25$	54.2406	+	112.619i	0.433924	+	0.900949i
$26$	310.062			2.33878
$27$	81.7125	+	81.7125i	0.582429	+	0.582429i
$28$	7.97253	+	7.97253i	0.0538095	+	0.0538095i
$29$			43.6739i			0.279656i	0.990176	+	0.139828i	$0.0446550\pi$
$29$			43.6739i			0.279656i	−0.990176	+	0.139828i	$0.955345\pi$
$30$	89.1434	+	56.0097i	0.542509	+	0.340864i
$31$	31.1324			0.180372			0.0901862	−	0.995925i	$-0.471254\pi$
$31$	31.1324			0.180372			0.0901862	+	0.995925i	$0.471254\pi$
$32$	−177.214	−	177.214i	−0.978980	−	0.978980i
$33$	−94.5737	−	94.5737i	−0.498884	−	0.498884i
$34$	244.840			1.23499
$35$	−16.4520	+	3.75545i	−0.0794540	+	0.0181368i
$36$	−158.873			−0.735525
$37$	−203.098	+	203.098i	−0.902407	+	0.902407i	−0.995644	−	0.0932372i	$-0.970279\pi$
$37$	−203.098	+	203.098i	−0.902407	+	0.902407i	0.0932372	+	0.995644i	$0.470279\pi$
$38$	−42.2323	−	42.2323i	−0.180289	−	0.180289i
$39$			188.732i			0.774905i
$40$	22.7237	−	5.18708i	0.0898234	−	0.0205037i
$41$	−419.020			−1.59610			−0.798048	−	0.602594i	$-0.794134\pi$
$41$	−419.020			−1.59610			−0.798048	+	0.602594i	$0.794134\pi$
$42$	−10.0499	+	10.0499i	−0.0369224	+	0.0369224i
$43$	−390.269	−	390.269i	−1.38408	−	1.38408i	−0.837229	−	0.546852i	$-0.815826\pi$
$43$	−390.269	−	390.269i	−1.38408	−	1.38408i	−0.546852	−	0.837229i	$-0.684174\pi$
$44$	417.313			1.42983
$45$	126.506	−	201.343i	0.419075	−	0.666987i
$46$	−204.259	−	382.755i	−0.654703	−	1.22683i
$47$	−329.500	−	329.500i	−1.02261	−	1.02261i	−0.999738	−	0.0228692i	$-0.992720\pi$
$47$	−329.500	−	329.500i	−1.02261	−	1.02261i	−0.0228692	−	0.999738i	$-0.507280\pi$
$48$	115.047	−	115.047i	0.345950	−	0.345950i
$49$			340.722i			0.993358i
$50$	162.360	−	464.066i	0.459224	−	1.31258i
$51$			149.032i			0.409189i
$52$	−416.397	−	416.397i	−1.11046	−	1.11046i
$53$	144.476	+	144.476i	0.374440	+	0.374440i	0.869091	−	0.494652i	$-0.164704\pi$
$53$	144.476	+	144.476i	0.374440	+	0.374440i	−0.494652	+	0.869091i	$0.664704\pi$
$54$		−	454.515i		−	1.14540i
$55$	−332.293	+	528.868i	−0.814661	+	1.29659i
$56$			3.14664i			0.00750870i
$57$	25.7064	−	25.7064i	0.0597351	−	0.0597351i
$58$	121.465	−	121.465i	0.274985	−	0.274985i
$59$		−	274.910i		−	0.606614i	−0.952893	−	0.303307i	$-0.901909\pi$
$59$		−	274.910i		−	0.606614i	0.952893	−	0.303307i	$-0.0980907\pi$
$60$	−44.4968	−	194.933i	−0.0957418	−	0.419428i
$61$		−	300.181i		−	0.630069i	−0.949080	−	0.315034i	$-0.897984\pi$
$61$		−	300.181i		−	0.630069i	0.949080	−	0.315034i	$-0.102016\pi$
$62$	−86.5849	−	86.5849i	−0.177360	−	0.177360i
$63$	22.6992	+	22.6992i	0.0453941	+	0.0453941i
$64$			442.056i			0.863391i
$65$	859.269	−	196.143i	1.63968	−	0.374285i
$66$			526.053i			0.981102i
$67$	−632.542	+	632.542i	−1.15339	+	1.15339i	−0.167524	+	0.985868i	$0.553577\pi$
$67$	−632.542	+	632.542i	−1.15339	+	1.15339i	−0.985868	+	0.167524i	$0.946423\pi$
$68$	−328.807	−	328.807i	−0.586378	−	0.586378i
$69$	232.979	−	124.331i	0.406484	−	0.216922i
$70$	56.2005	+	35.3114i	0.0959607	+	0.0602931i
$71$	401.846			0.671695			0.335848	−	0.941916i	$-0.390977\pi$
$71$	401.846			0.671695			0.335848	+	0.941916i	$0.390977\pi$
$72$	−31.3525	−	31.3525i	−0.0513185	−	0.0513185i
$73$	−308.059	+	308.059i	−0.493912	+	0.493912i	−0.909536	−	0.415625i	$-0.863563\pi$
$73$	−308.059	+	308.059i	−0.493912	+	0.493912i	0.415625	+	0.909536i	$0.363563\pi$
$74$	1129.70			1.77467
$75$	282.473	+	98.8272i	0.434895	+	0.152154i
$76$			113.432i			0.171204i
$77$	−59.6241	−	59.6241i	−0.0882441	−	0.0882441i
$78$	524.898	−	524.898i	0.761961	−	0.761961i
$79$	8.07381			0.0114984			0.00574921	−	0.999983i	$-0.498170\pi$
$79$	8.07381			0.0114984			0.00574921	+	0.999983i	$0.498170\pi$
$80$	−643.358	−	404.228i	−0.899120	−	0.564926i
$81$	−297.585			−0.408210
$82$	1165.37	+	1165.37i	1.56944	+	1.56944i
$83$	−806.388	−	806.388i	−1.06642	−	1.06642i	−0.997632	−	0.0687846i	$-0.978088\pi$
$83$	−806.388	−	806.388i	−1.06642	−	1.06642i	−0.0687846	−	0.997632i	$-0.521912\pi$
$84$	26.9931			0.0350617
$85$	678.520	−	154.884i	0.865834	−	0.197641i
$86$			2170.82i			2.72193i
$87$	73.9346	+	73.9346i	0.0911106	+	0.0911106i
$88$	82.3537	+	82.3537i	0.0997607	+	0.0997607i
$89$	−1253.12			−1.49248			−0.746238	−	0.665679i	$-0.768142\pi$
$89$	−1253.12			−1.49248			−0.746238	+	0.665679i	$0.768142\pi$
$90$	−911.807	+	208.136i	−1.06792	+	0.243771i
$91$			118.986i			0.137068i
$92$	−239.710	+	788.328i	−0.271647	+	0.893357i
$93$	52.7034	−	52.7034i	0.0587644	−	0.0587644i
$94$			1832.80i			2.01105i
$95$	−143.754	−	90.3219i	−0.155251	−	0.0975455i
$96$	−600.006			−0.637894
$97$	461.250	−	461.250i	0.482813	−	0.482813i	−0.423216	−	0.906029i	$-0.639099\pi$
$97$	461.250	−	461.250i	0.482813	−	0.482813i	0.906029	+	0.423216i	$0.139099\pi$
$98$	947.610	−	947.610i	0.976766	−	0.976766i
$99$	1188.17			1.20621
$100$	−841.257	+	405.175i	−0.841257	+	0.405175i
$101$	1174.66			1.15725			0.578627	−	0.815593i	$-0.303589\pi$
$101$	1174.66			1.15725			0.578627	+	0.815593i	$0.303589\pi$
$102$	414.485	−	414.485i	0.402354	−	0.402354i
$103$	43.2418	+	43.2418i	0.0413664	+	0.0413664i	0.727487	−	0.686121i	$-0.240688\pi$
$103$	43.2418	+	43.2418i	0.0413664	+	0.0413664i	−0.686121	+	0.727487i	$0.740688\pi$
$104$		−	164.346i		−	0.154956i
$105$	−21.4937	+	34.2087i	−0.0199769	+	0.0317946i
$106$		−	803.628i		−	0.736370i
$107$	583.833	−	583.833i	0.527489	−	0.527489i	−0.392334	−	0.919823i	$-0.628332\pi$
$107$	583.833	−	583.833i	0.527489	−	0.527489i	0.919823	+	0.392334i	$0.128332\pi$
$108$	−610.389	+	610.389i	−0.543840	+	0.543840i
$109$	−149.681			−0.131531			−0.0657653	−	0.997835i	$-0.520949\pi$
$109$	−149.681			−0.131531			−0.0657653	+	0.997835i	$0.520949\pi$
$110$	2395.05	−	546.710i	2.07599	−	0.473880i
$111$			687.640i			0.587999i
$112$	72.5316	−	72.5316i	0.0611928	−	0.0611928i
$113$	1391.83	+	1391.83i	1.15869	+	1.15869i	0.984757	+	0.173933i	$0.0556476\pi$
$113$	1391.83	+	1391.83i	1.15869	+	1.15869i	0.173933	+	0.984757i	$0.444352\pi$
$114$	−142.989			−0.117475
$115$	−808.187	−	931.509i	−0.655338	−	0.755336i
$116$	−326.242			−0.261128
$117$	−1185.56	−	1185.56i	−0.936792	−	0.936792i
$118$	−764.574	+	764.574i	−0.596481	+	0.596481i
$119$			93.9573i			0.0723785i
$120$	29.6874	−	47.2497i	0.0225840	−	0.0359440i
$121$	−1789.96			−1.34482
$122$	−834.858	+	834.858i	−0.619545	+	0.619545i
$123$	−709.351	+	709.351i	−0.520000	+	0.520000i
$124$			232.558i			0.168422i
$125$	156.381	−	1388.77i	0.111897	−	0.993720i
$126$		−	126.261i		−	0.0892718i
$127$	586.535	+	586.535i	0.409816	+	0.409816i	0.881674	−	0.471859i	$-0.156417\pi$
$127$	586.535	+	586.535i	0.409816	+	0.409816i	−0.471859	+	0.881674i	$0.656417\pi$
$128$	−188.276	+	188.276i	−0.130011	+	0.130011i
$129$	−1321.36			−0.901854
$130$	−2935.29	−	1844.28i	−1.98033	−	1.24426i
$131$	−461.539			−0.307823			−0.153912	−	0.988085i	$-0.549187\pi$
$131$	−461.539			−0.307823			−0.153912	+	0.988085i	$0.549187\pi$
$132$	706.462	−	706.462i	0.465830	−	0.465830i
$133$	16.2067	−	16.2067i	0.0105661	−	0.0105661i
$134$	3518.43			2.26825
$135$	−287.523	−	1259.59i	−0.183304	−	0.803023i
$136$		−	129.775i		−	0.0818245i
$137$	−1134.30	+	1134.30i	−0.707369	+	0.707369i	−0.965981	−	0.258612i	$-0.916735\pi$
$137$	−1134.30	+	1134.30i	−0.707369	+	0.707369i	0.258612	+	0.965981i	$0.416735\pi$
$138$	−993.744	−	302.172i	−0.612994	−	0.186396i
$139$		−	827.765i		−	0.505109i	−0.967583	−	0.252554i	$-0.918729\pi$
$139$		−	827.765i		−	0.505109i	0.967583	−	0.252554i	$-0.0812707\pi$
$140$	−28.0530	−	122.896i	−0.0169351	−	0.0741898i
$141$	−1115.61			−0.666321
$142$	−1117.61	−	1117.61i	−0.660476	−	0.660476i
$143$	3114.10	+	3114.10i	1.82108	+	1.82108i
$144$			1445.38i			0.836448i
$145$	259.776	−	413.452i	0.148781	−	0.236795i
$146$	1713.54			0.971324
$147$	576.801	+	576.801i	0.323631	+	0.323631i
$148$	−1517.13	−	1517.13i	−0.842618	−	0.842618i
$149$	−1269.84			−0.698185			−0.349092	−	0.937088i	$-0.613510\pi$
$149$	−1269.84			−0.698185			−0.349092	+	0.937088i	$0.613510\pi$
$150$	−510.752	−	1060.46i	−0.278018	−	0.577244i
$151$	1708.16			0.920581			0.460291	−	0.887768i	$-0.347745\pi$
$151$	1708.16			0.920581			0.460291	+	0.887768i	$0.347745\pi$
$152$	−22.3849	+	22.3849i	−0.0119451	+	0.0119451i
$153$	−936.172	−	936.172i	−0.494673	−	0.494673i
$154$			331.651i			0.173540i
$155$	−294.724	−	185.178i	−0.152728	−	0.0959604i
$156$	−1409.82			−0.723563
$157$	938.008	−	938.008i	0.476823	−	0.476823i	−0.427291	−	0.904114i	$-0.640532\pi$
$157$	938.008	−	938.008i	0.476823	−	0.476823i	0.904114	+	0.427291i	$0.140532\pi$
$158$	−22.4547	−	22.4547i	−0.0113063	−	0.0113063i
$159$	489.161			0.243981
$160$	623.566	+	2731.74i	0.308108	+	1.34977i
$161$	146.882	−	78.3843i	0.0719002	−	0.0383699i
$162$	827.640	+	827.640i	0.401392	+	0.401392i
$163$	1076.56	−	1076.56i	0.517315	−	0.517315i	−0.399443	−	0.916758i	$-0.630796\pi$
$163$	1076.56	−	1076.56i	0.517315	−	0.517315i	0.916758	+	0.399443i	$0.130796\pi$
$164$		−	3130.06i		−	1.49035i
$165$	332.778	+	1457.84i	0.157010	+	0.687836i
$166$			4485.42i			2.09721i
$167$	173.874	+	173.874i	0.0805677	+	0.0805677i	0.746242	−	0.665675i	$-0.231856\pi$
$167$	173.874	+	173.874i	0.0805677	+	0.0805677i	−0.665675	+	0.746242i	$0.731856\pi$
$168$	5.32689	+	5.32689i	0.00244630	+	0.00244630i
$169$		−	4017.52i		−	1.82864i
$170$	−2317.85	−	1456.33i	−1.04571	−	0.657031i
$171$			322.960i			0.144429i
$172$	2915.30	−	2915.30i	1.29238	−	1.29238i
$173$	59.3069	−	59.3069i	0.0260637	−	0.0260637i	−0.693955	−	0.720019i	$-0.744133\pi$
$173$	59.3069	−	59.3069i	0.0260637	−	0.0260637i	0.720019	+	0.693955i	$0.244133\pi$
$174$		−	411.251i		−	0.179178i
$175$	178.085	+	62.3057i	0.0769256	+	0.0269135i
$176$		−	3796.59i		−	1.62601i
$177$	−465.389	−	465.389i	−0.197632	−	0.197632i
$178$	3485.15	+	3485.15i	1.46755	+	1.46755i
$179$			2017.71i			0.842518i	0.906940	+	0.421259i	$0.138412\pi$
$179$			2017.71i			0.842518i	−0.906940	+	0.421259i	$0.861588\pi$
$180$	1504.02	+	944.993i	0.622796	+	0.391309i
$181$		−	964.154i		−	0.395939i	−0.980208	−	0.197970i	$-0.936565\pi$
$181$		−	964.154i		−	0.395939i	0.980208	−	0.197970i	$-0.0634348\pi$
$182$	330.922	−	330.922i	0.134778	−	0.134778i
$183$	−508.170	−	508.170i	−0.205273	−	0.205273i
$184$	−202.876	+	108.266i	−0.0812837	+	0.0433775i
$185$	3130.73	−	714.642i	1.24419	−	0.284008i
$186$	−293.156			−0.115566
$187$	2459.05	+	2459.05i	0.961622	+	0.961622i
$188$	2461.35	−	2461.35i	0.954855	−	0.954855i
$189$	174.420			0.0671280
$190$	148.604	+	651.007i	0.0567412	+	0.248574i
$191$			284.307i			0.107705i	0.998549	+	0.0538527i	$0.0171501\pi$
$191$			284.307i			0.107705i	−0.998549	+	0.0538527i	$0.982850\pi$
$192$	748.348	+	748.348i	0.281288	+	0.281288i
$193$	−1594.75	+	1594.75i	−0.594782	+	0.594782i	−0.938919	−	0.344138i	$-0.888171\pi$
$193$	−1594.75	+	1594.75i	−0.594782	+	0.594782i	0.344138	+	0.938919i	$0.388171\pi$
$194$	−2565.64			−0.949496
$195$	1122.59	−	1786.69i	0.412259	−	0.656140i
$196$	−2545.18			−0.927543
$197$	−2755.55	−	2755.55i	−0.996572	−	0.996572i	0.00342214	−	0.999994i	$-0.498911\pi$
$197$	−2755.55	−	2755.55i	−0.996572	−	0.996572i	−0.999994	+	0.00342214i	$0.998911\pi$
$198$	−3304.51	−	3304.51i	−1.18607	−	1.18607i
$199$	−4380.57			−1.56046			−0.780228	−	0.625495i	$-0.784897\pi$
$199$	−4380.57			−1.56046			−0.780228	+	0.625495i	$0.784897\pi$
$200$	−245.974	−	86.0576i	−0.0869650	−	0.0304260i
$201$			2141.63i			0.751539i
$202$	−3266.93	−	3266.93i	−1.13792	−	1.13792i
$203$	46.6122	+	46.6122i	0.0161159	+	0.0161159i
$204$	−1113.26			−0.382078
$205$	3966.78	+	2492.37i	1.35147	+	0.849144i
$206$		−	240.527i		−	0.0813509i
$207$	−682.498	+	2244.51i	−0.229164	+	0.753644i
$208$	−3788.25	+	3788.25i	−1.26283	+	1.26283i
$209$		−	848.320i		−	0.280763i
$210$	154.919	−	35.3629i	0.0509067	−	0.0116203i
$211$	1826.57			0.595954			0.297977	−	0.954573i	$-0.403688\pi$
$211$	1826.57			0.595954			0.297977	+	0.954573i	$0.403688\pi$
$212$	−1079.23	+	1079.23i	−0.349631	+	0.349631i
$213$	680.278	−	680.278i	0.218835	−	0.218835i
$214$	−3247.49			−1.03736
$215$	1373.25	+	6015.96i	0.435603	+	1.90830i
$216$	−240.912			−0.0758887
$217$	33.2269	−	33.2269i	0.0103944	−	0.0103944i
$218$	416.290	+	416.290i	0.129334	+	0.129334i
$219$			1043.01i			0.321828i
$220$	−3950.62	−	2482.21i	−1.21069	−	0.760686i
$221$		−	4907.29i		−	1.49366i
$222$	1912.45	−	1912.45i	0.578178	−	0.578178i
$223$	1398.92	−	1398.92i	0.420083	−	0.420083i	−0.465149	−	0.885232i	$-0.653999\pi$
$223$	1398.92	−	1398.92i	0.420083	−	0.420083i	0.885232	+	0.465149i	$0.153999\pi$
$224$	−378.274			−0.112833
$225$	−2395.21	+	1153.60i	−0.709691	+	0.341809i
$226$		−	7741.85i		−	2.27867i
$227$	−1385.38	+	1385.38i	−0.405069	+	0.405069i	−0.880015	−	0.474946i	$-0.842468\pi$
$227$	−1385.38	+	1385.38i	−0.405069	+	0.405069i	0.474946	+	0.880015i	$0.342468\pi$
$228$	192.026	+	192.026i	0.0557774	+	0.0557774i
$229$	3112.68			0.898216			0.449108	−	0.893477i	$-0.351742\pi$
$229$	3112.68			0.898216			0.449108	+	0.893477i	$0.351742\pi$
$230$	−342.980	+	4838.41i	−0.0983279	+	1.38711i
$231$	−201.873			−0.0574990
$232$	−64.3815	−	64.3815i	−0.0182192	−	0.0182192i
$233$	623.692	−	623.692i	0.175362	−	0.175362i	−0.613968	−	0.789331i	$-0.710428\pi$
$233$	623.692	−	623.692i	0.175362	−	0.175362i	0.789331	+	0.613968i	$0.210428\pi$
$234$			6594.49i			1.84229i
$235$	1159.42	+	5079.21i	0.321838	+	1.40992i
$236$	2053.56			0.566422
$237$	13.6680	−	13.6680i	0.00374612	−	0.00374612i
$238$	261.312	−	261.312i	0.0711696	−	0.0711696i
$239$		−	2723.56i		−	0.737122i	−0.929604	−	0.368561i	$-0.879851\pi$
$239$		−	2723.56i		−	0.737122i	0.929604	−	0.368561i	$-0.120149\pi$
$240$	−1773.44	+	404.818i	−0.476979	+	0.108879i
$241$			2073.21i			0.554139i	0.960850	+	0.277069i	$0.0893632\pi$
$241$			2073.21i			0.554139i	−0.960850	+	0.277069i	$0.910637\pi$
$242$	4978.20	+	4978.20i	1.32236	+	1.32236i
$243$	−2710.01	+	2710.01i	−0.715422	+	0.715422i
$244$	2242.34			0.588324
$245$	2026.64	−	3225.55i	0.528479	−	0.841112i
$246$	3945.67			1.02263
$247$	−846.456	+	846.456i	−0.218052	+	0.218052i
$248$	−45.8936	+	45.8936i	−0.0117510	+	0.0117510i
$249$	−2730.24			−0.694866
$250$	−4297.34	+	3427.49i	−1.08715	+	0.867093i
$251$			3142.79i			0.790324i	0.918612	+	0.395162i	$0.129311\pi$
$251$			3142.79i			0.790324i	−0.918612	+	0.395162i	$0.870689\pi$
$252$	−169.562	+	169.562i	−0.0423866	+	0.0423866i
$253$	1792.72	−	5895.66i	0.445484	−	1.46505i
$254$		−	3262.52i		−	0.805941i
$255$	886.454	−	1410.85i	0.217694	−	0.346475i
$256$	4583.71			1.11907
$257$	−448.441	−	448.441i	−0.108844	−	0.108844i	0.650587	−	0.759432i	$-0.274523\pi$
$257$	−448.441	−	448.441i	−0.108844	−	0.108844i	−0.759432	+	0.650587i	$0.774523\pi$
$258$	3674.94	+	3674.94i	0.886790	+	0.886790i
$259$			433.523i			0.104007i
$260$	1465.18	+	6418.71i	0.349487	+	1.53104i
$261$	−928.869			−0.220289
$262$	1283.63	+	1283.63i	0.302682	+	0.302682i
$263$	−2924.69	−	2924.69i	−0.685718	−	0.685718i	0.275564	−	0.961283i	$-0.411135\pi$
$263$	−2924.69	−	2924.69i	−0.685718	−	0.685718i	−0.961283	+	0.275564i	$0.911135\pi$
$264$	278.830			0.0650031
$265$	−508.369	−	2227.08i	−0.117845	−	0.516258i
$266$	−90.1473			−0.0207793
$267$	−2121.38	+	2121.38i	−0.486241	+	0.486241i
$268$	−4725.06	−	4725.06i	−1.07697	−	1.07697i
$269$		−	3493.00i		−	0.791717i	−0.918311	−	0.395859i	$-0.870447\pi$
$269$		−	3493.00i		−	0.791717i	0.918311	−	0.395859i	$-0.129553\pi$
$270$	−2703.49	+	4302.80i	−0.609368	+	0.969852i
$271$	5852.09			1.31177			0.655884	−	0.754862i	$-0.272296\pi$
$271$	5852.09			1.31177			0.655884	+	0.754862i	$0.272296\pi$
$272$	−2991.38	+	2991.38i	−0.666835	+	0.666835i
$273$	201.429	+	201.429i	0.0446559	+	0.0446559i
$274$	6309.38			1.39111
$275$	6291.50	−	3030.18i	1.37961	−	0.664460i
$276$	928.744	+	1740.35i	0.202550	+	0.379553i
$277$	2313.86	+	2313.86i	0.501900	+	0.501900i	0.912028	−	0.410128i	$-0.134516\pi$
$277$	2313.86	+	2313.86i	0.501900	+	0.501900i	−0.410128	+	0.912028i	$0.634516\pi$
$278$	−2302.17	+	2302.17i	−0.496672	+	0.496672i
$279$			662.133i			0.142082i
$280$	18.7165	−	29.7886i	0.00399473	−	0.00635789i
$281$			4058.84i			0.861673i	0.902430	+	0.430836i	$0.141781\pi$
$281$			4058.84i			0.861673i	−0.902430	+	0.430836i	$0.858219\pi$
$282$	3102.71	+	3102.71i	0.655191	+	0.655191i
$283$	−1249.60	−	1249.60i	−0.262477	−	0.262477i	0.563583	−	0.826060i	$-0.309423\pi$
$283$	−1249.60	−	1249.60i	−0.262477	−	0.262477i	−0.826060	+	0.563583i	$0.809423\pi$
$284$			3001.78i			0.627192i
$285$	−396.262	+	90.4536i	−0.0823597	+	0.0188000i
$286$		−	17321.8i		−	3.58132i
$287$	−447.211	+	447.211i	−0.0919792	+	0.0919792i
$288$	3769.05	−	3769.05i	0.771158	−	0.771158i
$289$			1037.97i			0.211270i
$290$	−1872.37	+	427.400i	−0.379135	+	0.0865442i
$291$		−	1561.68i		−	0.314596i
$292$	−2301.19	−	2301.19i	−0.461188	−	0.461188i
$293$	3999.83	+	3999.83i	0.797517	+	0.797517i	0.982703	−	0.185187i	$-0.0592889\pi$
$293$	3999.83	+	3999.83i	0.797517	+	0.797517i	−0.185187	+	0.982703i	$0.559289\pi$
$294$		−	3208.38i		−	0.636451i
$295$	−1635.19	+	2602.52i	−0.322726	+	0.513642i
$296$		−	598.790i		−	0.117581i
$297$	4564.91	−	4564.91i	0.891862	−	0.891862i
$298$	3531.66	+	3531.66i	0.686523	+	0.686523i
$299$	−7671.50	+	4093.93i	−1.48379	+	0.791833i
$300$	−738.235	+	2110.06i	−0.142073	+	0.406081i
$301$	−833.052			−0.159523
$302$	−4750.69	−	4750.69i	−0.905204	−	0.905204i
$303$	1988.55	−	1988.55i	0.377027	−	0.377027i
$304$	1031.97			0.194695
$305$	−1785.50	+	2841.75i	−0.335205	+	0.533502i
$306$			5207.33i			0.972821i
$307$	−3915.49	−	3915.49i	−0.727911	−	0.727911i	0.242292	−	0.970203i	$-0.422101\pi$
$307$	−3915.49	−	3915.49i	−0.727911	−	0.727911i	−0.970203	+	0.242292i	$0.922101\pi$
$308$	445.389	−	445.389i	0.0823975	−	0.0823975i
$309$	146.406			0.0269539
$310$	304.667	+	1334.70i	0.0558192	+	0.244534i
$311$	−4574.55			−0.834080			−0.417040	−	0.908888i	$-0.636933\pi$
$311$	−4574.55			−0.834080			−0.417040	+	0.908888i	$0.636933\pi$
$312$	−278.218	−	278.218i	−0.0504839	−	0.0504839i
$313$	5080.39	+	5080.39i	0.917446	+	0.917446i	0.996843	−	0.0793967i	$-0.0252994\pi$
$313$	5080.39	+	5080.39i	0.917446	+	0.917446i	−0.0793967	+	0.996843i	$0.525299\pi$
$314$	−5217.55			−0.937717
$315$	−79.8720	−	349.906i	−0.0142866	−	0.0625871i
$316$			60.3110i			0.0107366i
$317$	−2685.75	−	2685.75i	−0.475857	−	0.475857i	0.427947	−	0.903804i	$-0.359237\pi$
$317$	−2685.75	−	2685.75i	−0.475857	−	0.475857i	−0.903804	+	0.427947i	$0.859237\pi$
$318$	−1360.45	−	1360.45i	−0.239906	−	0.239906i
$319$	2439.86			0.428232
$320$	2629.39	−	4184.86i	0.459335	−	0.731064i
$321$		−	1976.72i		−	0.343706i
$322$	−626.507	−	190.505i	−0.108428	−	0.0329702i
$323$	−668.403	+	668.403i	−0.115142	+	0.115142i
$324$		−	2222.95i		−	0.381164i
$325$	−9301.20	−	3254.16i	−1.58750	−	0.555410i
$326$	−5988.20			−1.01735
$327$	−253.392	+	253.392i	−0.0428520	+	0.0428520i
$328$	617.695	−	617.695i	0.103983	−	0.103983i
$329$	−703.337			−0.117861
$330$	3129.01	−	4980.04i	0.521959	−	0.830734i
$331$	4017.20			0.667085			0.333543	−	0.942735i	$-0.391756\pi$
$331$	4017.20			0.667085			0.333543	+	0.942735i	$0.391756\pi$
$332$	6023.68	−	6023.68i	0.995761	−	0.995761i
$333$	−4319.54	−	4319.54i	−0.710839	−	0.710839i
$334$		−	967.153i		−	0.158444i
$335$	9750.56	−	2225.73i	1.59024	−	0.362999i
$336$		−	245.575i		−	0.0398726i
$337$	7559.60	−	7559.60i	1.22195	−	1.22195i	0.255015	−	0.966937i	$-0.417920\pi$
$337$	7559.60	−	7559.60i	1.22195	−	1.22195i	0.966937	−	0.255015i	$-0.0820803\pi$
$338$	−11173.5	+	11173.5i	−1.79810	+	1.79810i
$339$	4712.39			0.754991
$340$	1156.98	+	5068.52i	0.184547	+	0.808468i
$341$		−	1739.23i		−	0.276201i
$342$	898.211	−	898.211i	0.142017	−	0.142017i
$343$	729.722	+	729.722i	0.114872	+	0.114872i
$344$	1150.62			0.180342
$345$	−2945.10	−	208.769i	−0.459590	−	0.0325789i
$346$	−329.887			−0.0512567
$347$	2105.15	+	2105.15i	0.325679	+	0.325679i	0.850941	−	0.525262i	$-0.176033\pi$
$347$	2105.15	+	2105.15i	0.325679	+	0.325679i	−0.525262	+	0.850941i	$0.676033\pi$
$348$	−552.289	+	552.289i	−0.0850741	+	0.0850741i
$349$		−	5497.97i		−	0.843265i	−0.906767	−	0.421632i	$-0.861457\pi$
$349$		−	5497.97i		−	0.843265i	0.906767	−	0.421632i	$-0.138543\pi$
$350$	−322.004	−	668.571i	−0.0491767	−	0.102105i
$351$	−9109.77			−1.38531
$352$	−9900.18	+	9900.18i	−1.49909	+	1.49909i
$353$	−3337.40	+	3337.40i	−0.503207	+	0.503207i	−0.912433	−	0.409226i	$-0.865799\pi$
$353$	−3337.40	+	3337.40i	−0.503207	+	0.503207i	0.409226	+	0.912433i	$0.365799\pi$
$354$			2588.67i			0.388661i
$355$	−3804.20	−	2390.22i	−0.568749	−	0.357351i
$356$		−	9360.75i		−	1.39359i
$357$	159.058	+	159.058i	0.0235806	+	0.0235806i
$358$	5611.62	−	5611.62i	0.828445	−	0.828445i
$359$	−4077.39			−0.599433			−0.299717	−	0.954028i	$-0.596892\pi$
$359$	−4077.39			−0.599433			−0.299717	+	0.954028i	$0.596892\pi$
$360$	110.320	+	483.295i	0.0161511	+	0.0707553i
$361$	−6628.41			−0.966382
$362$	−2681.49	+	2681.49i	−0.389326	+	0.389326i
$363$	−3030.19	+	3030.19i	−0.438136	+	0.438136i
$364$	−888.822			−0.127986
$365$	4748.69	−	1083.97i	0.680980	−	0.155446i
$366$			2826.63i			0.403689i
$367$	3299.02	−	3299.02i	0.469230	−	0.469230i	−0.432435	−	0.901665i	$-0.642345\pi$
$367$	3299.02	−	3299.02i	0.469230	−	0.469230i	0.901665	+	0.432435i	$0.142345\pi$
$368$	7171.97	+	2180.81i	1.01594	+	0.308920i
$369$		−	8911.85i		−	1.25727i
$370$	−10694.7	−	6719.57i	−1.50267	−	0.944146i
$371$	308.392			0.0431561
$372$	393.692	+	393.692i	0.0548710	+	0.0548710i
$373$	−2478.22	−	2478.22i	−0.344014	−	0.344014i	0.513860	−	0.857874i	$-0.328215\pi$
$373$	−2478.22	−	2478.22i	−0.344014	−	0.344014i	−0.857874	+	0.513860i	$0.828215\pi$
$374$		−	13678.1i		−	1.89112i
$375$	−2086.28	−	2615.75i	−0.287293	−	0.360204i
$376$	971.461			0.133243
$377$	−2434.50	−	2434.50i	−0.332582	−	0.332582i
$378$	−485.094	−	485.094i	−0.0660067	−	0.0660067i
$379$	−290.087			−0.0393161			−0.0196580	−	0.999807i	$-0.506258\pi$
$379$	−290.087			−0.0393161			−0.0196580	+	0.999807i	$0.506258\pi$
$380$	674.701	−	1073.83i	0.0910826	−	0.144964i
$381$	1985.87			0.267032
$382$	790.709	−	790.709i	0.105906	−	0.105906i
$383$	−5194.83	−	5194.83i	−0.693064	−	0.693064i	0.269841	−	0.962905i	$-0.413029\pi$
$383$	−5194.83	−	5194.83i	−0.693064	−	0.693064i	−0.962905	+	0.269841i	$0.913029\pi$
$384$			637.458i			0.0847139i
$385$	209.800	+	919.098i	0.0277725	+	0.121666i
$386$	8870.60			1.16969
$387$	8300.37	−	8300.37i	1.09026	−	1.09026i
$388$	3445.52	+	3445.52i	0.450824	+	0.450824i
$389$	−9641.89			−1.25672			−0.628359	−	0.777924i	$-0.716273\pi$
$389$	−9641.89			−1.25672			−0.628359	+	0.777924i	$0.716273\pi$
$390$	−8091.24	+	1846.97i	−1.05055	+	0.239807i
$391$	−6057.78	+	3232.77i	−0.783517	+	0.418128i
$392$	−502.272	−	502.272i	−0.0647158	−	0.0647158i
$393$	−781.331	+	781.331i	−0.100287	+	0.100287i
$394$			15327.4i			1.95985i
$395$	−76.4331	−	48.0237i	−0.00973612	−	0.00611730i
$396$			8875.55i			1.12630i
$397$	8236.95	+	8236.95i	1.04131	+	1.04131i	0.999109	+	0.0422024i	$0.0134374\pi$
$397$	8236.95	+	8236.95i	1.04131	+	1.04131i	0.0422024	+	0.999109i	$0.486563\pi$
$398$	12183.2	+	12183.2i	1.53439	+	1.53439i
$399$		−	54.8719i		−	0.00688478i
$400$	3686.15	+	7653.50i	0.460769	+	0.956687i
$401$			8063.16i			1.00413i	0.864831	+	0.502063i	$0.167426\pi$
$401$			8063.16i			1.00413i	−0.864831	+	0.502063i	$0.832574\pi$
$402$	5956.28	−	5956.28i	0.738985	−	0.738985i
$403$	−1735.41	+	1735.41i	−0.214508	+	0.214508i
$404$			8774.63i			1.08058i
$405$	2817.18	+	1770.06i	0.345647	+	0.217173i
$406$		−	259.274i		−	0.0316935i
$407$	11346.2	+	11346.2i	1.38184	+	1.38184i
$408$	−219.694	−	219.694i	−0.0266580	−	0.0266580i
$409$		−	4934.18i		−	0.596527i	−0.954484	−	0.298264i	$-0.903593\pi$
$409$		−	4934.18i		−	0.596527i	0.954484	−	0.298264i	$-0.0964075\pi$
$410$	−4100.61	−	17964.1i	−0.493938	−	2.16386i
$411$			3840.46i			0.460915i
$412$	−323.014	+	323.014i	−0.0386257	+	0.0386257i
$413$	−293.405	−	293.405i	−0.0349577	−	0.0349577i
$414$	8140.55	−	4344.24i	0.966392	−	0.515720i
$415$	2837.45	+	12430.4i	0.335626	+	1.47032i
$416$	19756.9			2.32851
$417$	−1401.31	−	1401.31i	−0.164562	−	0.164562i
$418$	−2359.33	+	2359.33i	−0.276074	+	0.276074i
$419$	−9132.74			−1.06483			−0.532415	−	0.846483i	$-0.678715\pi$
$419$	−9132.74			−1.06483			−0.532415	+	0.846483i	$0.678715\pi$
$420$	−255.538	−	160.557i	−0.0296880	−	0.0186533i
$421$			13814.9i			1.59928i	0.600478	+	0.799642i	$0.294977\pi$
$421$			13814.9i			1.59928i	−0.600478	+	0.799642i	$0.705023\pi$
$422$	−5080.03	−	5080.03i	−0.586000	−	0.586000i
$423$	7007.91	−	7007.91i	0.805524	−	0.805524i
$424$	−425.956			−0.0487883
$425$	−7344.68	−	2569.64i	−0.838281	−	0.293285i
$426$	−3783.95			−0.430360
$427$	−320.376	−	320.376i	−0.0363094	−	0.0363094i
$428$	4361.21	+	4361.21i	0.492540	+	0.492540i
$429$	10543.6			1.18660
$430$	12912.2	−	20550.7i	1.44810	−	2.30475i
$431$			7808.71i			0.872697i	0.899778	+	0.436349i	$0.143729\pi$
$431$			7808.71i			0.872697i	−0.899778	+	0.436349i	$0.856271\pi$
$432$	5553.13	+	5553.13i	0.618461	+	0.618461i
$433$	−7463.44	−	7463.44i	−0.828337	−	0.828337i	0.158949	−	0.987287i	$-0.449189\pi$
$433$	−7463.44	−	7463.44i	−0.828337	−	0.828337i	−0.987287	+	0.158949i	$0.949189\pi$
$434$	−184.820			−0.0204416
$435$	−260.155	−	1139.69i	−0.0286746	−	0.125619i
$436$		−	1118.11i		−	0.122816i
$437$	1602.52	+	487.286i	0.175421	+	0.0533411i
$438$	2900.81	−	2900.81i	0.316452	−	0.316452i
$439$			14368.5i			1.56213i	0.624453	+	0.781063i	$0.285322\pi$
$439$			14368.5i			1.56213i	−0.624453	+	0.781063i	$0.714678\pi$
$440$	−289.779	−	1269.47i	−0.0313970	−	0.137545i
$441$	−7246.58			−0.782483
$442$	−13648.1	+	13648.1i	−1.46872	+	1.46872i
$443$	3022.02	−	3022.02i	0.324109	−	0.324109i	−0.526232	−	0.850341i	$-0.676396\pi$
$443$	3022.02	−	3022.02i	0.324109	−	0.324109i	0.850341	+	0.526232i	$0.176396\pi$
$444$	−5136.64			−0.549041
$445$	11863.0	+	7453.66i	1.26373	+	0.794016i
$446$	−7781.29			−0.826132
$447$	−2149.69	+	2149.69i	−0.227465	+	0.227465i
$448$	471.797	+	471.797i	0.0497551	+	0.0497551i
$449$			6140.06i			0.645362i	0.946508	+	0.322681i	$0.104584\pi$
$449$			6140.06i			0.645362i	−0.946508	+	0.322681i	$0.895416\pi$
$450$	9869.90	+	3453.13i	1.03394	+	0.361738i
$451$			23408.8i			2.44407i
$452$	−10396.9	+	10396.9i	−1.08192	+	1.08192i
$453$	2891.70	−	2891.70i	0.299921	−	0.299921i
$454$	7705.97			0.796606
$455$	707.740	−	1126.42i	0.0729217	−	0.116060i
$456$			75.7899i			0.00778330i
$457$	3490.79	−	3490.79i	0.357314	−	0.357314i	−0.505508	−	0.862822i	$-0.668695\pi$
$457$	3490.79	−	3490.79i	0.357314	−	0.357314i	0.862822	+	0.505508i	$0.168695\pi$
$458$	−8656.93	−	8656.93i	−0.883213	−	0.883213i
$459$	−7193.51			−0.731513
$460$	6958.33	−	6037.12i	0.705291	−	0.611918i
$461$	−1500.76			−0.151621			−0.0758103	−	0.997122i	$-0.524154\pi$
$461$	−1500.76			−0.151621			−0.0758103	+	0.997122i	$0.524154\pi$
$462$	561.445	+	561.445i	0.0565385	+	0.0565385i
$463$	7235.48	−	7235.48i	0.726266	−	0.726266i	−0.243608	−	0.969874i	$-0.578331\pi$
$463$	7235.48	−	7235.48i	0.726266	−	0.726266i	0.969874	+	0.243608i	$0.0783309\pi$
$464$			2968.05i			0.296957i
$465$	−812.417	+	185.448i	−0.0810214	+	0.0184945i
$466$	−3469.20			−0.344866
$467$	3378.86	−	3378.86i	0.334807	−	0.334807i	−0.519601	−	0.854409i	$-0.673920\pi$
$467$	3378.86	−	3378.86i	0.334807	−	0.334807i	0.854409	+	0.519601i	$0.173920\pi$
$468$	8856.05	−	8856.05i	0.874725	−	0.874725i
$469$			1350.20i			0.132934i
$470$	10901.7	−	17350.8i	1.06991	−	1.70283i
$471$		−	3175.87i		−	0.310693i
$472$	405.256	+	405.256i	0.0395200	+	0.0395200i
$473$	−21802.6	+	21802.6i	−2.11942	+	2.11942i
$474$	−76.0264			−0.00736710
$475$	823.644	+	1710.12i	0.0795608	+	0.165191i
$476$	−701.857			−0.0675831
$477$	−3072.76	+	3072.76i	−0.294952	+	0.294952i
$478$	−7574.71	+	7574.71i	−0.724810	+	0.724810i
$479$	3085.56			0.294327			0.147164	−	0.989112i	$-0.452986\pi$
$479$	3085.56			0.294327			0.147164	+	0.989112i	$0.452986\pi$
$480$	5680.13	+	3568.88i	0.540128	+	0.339368i
$481$		−	22642.5i		−	2.14638i
$482$	5765.99	−	5765.99i	0.544883	−	0.544883i
$483$	115.958	−	381.349i	0.0109240	−	0.0359254i
$484$		−	13370.9i		−	1.25572i
$485$	−7110.11	+	1623.01i	−0.665678	+	0.151952i
$486$	15074.1			1.40694
$487$	3690.56	+	3690.56i	0.343399	+	0.343399i	0.857644	−	0.514245i	$-0.171928\pi$
$487$	3690.56	+	3690.56i	0.343399	+	0.343399i	−0.514245	+	0.857644i	$0.671928\pi$
$488$	442.509	+	442.509i	0.0410480	+	0.0410480i
$489$		−	3644.96i		−	0.337077i
$490$	−14607.3	+	3334.37i	−1.34671	+	0.307411i
$491$	−19160.4			−1.76109			−0.880546	−	0.473961i	$-0.842824\pi$
$491$	−19160.4			−1.76109			−0.880546	+	0.473961i	$0.842824\pi$
$492$	−5298.82	−	5298.82i	−0.485547	−	0.485547i
$493$	−1922.40	−	1922.40i	−0.175620	−	0.175620i
$494$	4708.30			0.428819
$495$	−11248.1	−	7067.31i	−1.02134	−	0.641721i
$496$	2115.74			0.191531
$497$	428.882	−	428.882i	0.0387082	−	0.0387082i
$498$	7593.29	+	7593.29i	0.683260	+	0.683260i
$499$			8432.30i			0.756476i	0.925708	+	0.378238i	$0.123470\pi$
$499$			8432.30i			0.756476i	−0.925708	+	0.378238i	$0.876530\pi$
$500$	10374.0	+	1168.16i	0.927881	+	0.104483i
$501$	588.697			0.0524971
$502$	8740.68	−	8740.68i	0.777123	−	0.777123i
$503$	1153.57	+	1153.57i	0.102256	+	0.102256i	0.756384	−	0.654128i	$-0.226964\pi$
$503$	1153.57	+	1153.57i	0.102256	+	0.102256i	−0.654128	+	0.756384i	$0.726964\pi$
$504$	−66.9237			−0.00591472
$505$	−11120.2	−	6986.95i	−0.979888	−	0.615674i
$506$	−21382.8	+	11411.0i	−1.87862	+	1.00253i
$507$	−6801.19	−	6801.19i	−0.595762	−	0.595762i
$508$	−4381.39	+	4381.39i	−0.382663	+	0.382663i
$509$			14551.4i			1.26715i	0.773682	+	0.633575i	$0.218413\pi$
$509$			14551.4i			1.26715i	−0.773682	+	0.633575i	$0.781587\pi$
$510$	−6389.23	+	1458.45i	−0.554745	+	0.126630i
$511$			657.569i			0.0569259i
$512$	−11241.9	−	11241.9i	−0.970366	−	0.970366i
$513$	1240.81	+	1240.81i	0.106789	+	0.106789i
$514$			2494.40i			0.214053i
$515$	−152.155	−	666.567i	−0.0130190	−	0.0570339i
$516$		−	9870.49i		−	0.842101i
$517$	−18407.7	+	18407.7i	−1.56590	+	1.56590i
$518$	1205.71	−	1205.71i	0.102270	−	0.102270i
$519$		−	200.799i		−	0.0169828i
$520$	−977.542	+	1555.83i	−0.0824386	+	0.131207i
$521$		−	16272.7i		−	1.36837i	−0.729310	−	0.684184i	$-0.760159\pi$
$521$		−	16272.7i		−	1.36837i	0.729310	−	0.684184i	$-0.239841\pi$
$522$	2583.35	+	2583.35i	0.216610	+	0.216610i
$523$	−12124.5	−	12124.5i	−1.01371	−	1.01371i	−0.999905	−	0.0138021i	$-0.995607\pi$
$523$	−12124.5	−	12124.5i	−1.01371	−	1.01371i	−0.0138021	−	0.999905i	$-0.504393\pi$
$524$		−	3447.68i		−	0.287429i
$525$	406.953	−	196.001i	0.0338303	−	0.0162937i
$526$			16268.2i			1.34853i
$527$	−1370.36	+	1370.36i	−0.113271	+	0.113271i
$528$	−6427.17	−	6427.17i	−0.529747	−	0.529747i
$529$	10107.5	+	6773.10i	0.830729	+	0.556678i
$530$	−4780.05	+	7607.78i	−0.391759	+	0.623511i
$531$	5846.87			0.477839
$532$	121.063	+	121.063i	0.00986607	+	0.00986607i
$533$	23357.4	−	23357.4i	1.89816	−	1.89816i
$534$	11799.9			0.956239
$535$	−8999.72	+	2054.34i	−0.727275	+	0.166013i
$536$		−	1864.91i		−	0.150283i
$537$	3415.74	+	3415.74i	0.274488	+	0.274488i
$538$	−9714.67	+	9714.67i	−0.778493	+	0.778493i
$539$	19034.6			1.52111
$540$	9409.07	−	2147.78i	0.749819	−	0.171159i
$541$	10496.2			0.834137			0.417068	−	0.908875i	$-0.363058\pi$
$541$	10496.2			0.834137			0.417068	+	0.908875i	$0.363058\pi$
$542$	−16275.7	−	16275.7i	−1.28986	−	1.28986i
$543$	−1632.20	−	1632.20i	−0.128995	−	0.128995i
$544$	15601.0			1.22957
$545$	1417.00	+	890.315i	0.111372	+	0.0699760i
$546$		−	1120.42i		−	0.0878200i
$547$	−12797.8	−	12797.8i	−1.00036	−	1.00036i	−1.00000		0.000357937i	$-0.999886\pi$
$547$	−12797.8	−	12797.8i	−1.00036	−	1.00036i	−0.000357937	−	1.00000i	$-0.500114\pi$
$548$	−8473.16	−	8473.16i	−0.660502	−	0.660502i
$549$	6384.34			0.496315
$550$	−25925.3	−	9070.34i	−2.00992	−	0.703201i
$551$			663.189i			0.0512755i
$552$	−160.164	+	526.726i	−0.0123497	+	0.0406140i
$553$	8.61700	−	8.61700i	0.000662626	−	0.000662626i
$554$		−	12870.5i		−	0.987033i
$555$	4090.14	−	6509.75i	0.312823	−	0.497880i
$556$	6183.37			0.471643
$557$	3834.37	−	3834.37i	0.291683	−	0.291683i	−0.546062	−	0.837745i	$-0.683874\pi$
$557$	3834.37	−	3834.37i	0.291683	−	0.291683i	0.837745	+	0.546062i	$0.183874\pi$
$558$	1841.51	−	1841.51i	0.139709	−	0.139709i
$559$	43509.4			3.29204
$560$	−1118.07	+	255.218i	−0.0843695	+	0.0192588i
$561$	8325.74			0.626583
$562$	11288.4	−	11288.4i	0.847280	−	0.847280i
$563$	−2578.60	−	2578.60i	−0.193029	−	0.193029i	0.603975	−	0.797003i	$-0.293583\pi$
$563$	−2578.60	−	2578.60i	−0.193029	−	0.193029i	−0.797003	+	0.603975i	$0.793583\pi$
$564$		−	8333.56i		−	0.622174i
$565$	−4897.44	−	21454.8i	−0.364667	−	1.59754i
$566$			6950.74i			0.516186i
$567$	−317.606	+	317.606i	−0.0235242	+	0.0235242i
$568$	−592.378	+	592.378i	−0.0437599	+	0.0437599i
$569$	−27117.7			−1.99795			−0.998974	−	0.0452860i	$-0.985580\pi$
$569$	−27117.7			−1.99795			−0.998974	+	0.0452860i	$0.985580\pi$
$570$	1353.64	+	850.509i	0.0994701	+	0.0624980i
$571$		−	8880.25i		−	0.650835i	−0.945570	−	0.325417i	$-0.894495\pi$
$571$		−	8880.25i		−	0.650835i	0.945570	−	0.325417i	$-0.105505\pi$
$572$	−23262.2	+	23262.2i	−1.70042	+	1.70042i
$573$	481.297	+	481.297i	0.0350899	+	0.0350899i
$574$	2487.55			0.180886
$575$	2110.25	+	13625.6i	0.153050	+	0.988218i
$576$	−9401.79			−0.680106
$577$	8211.41	+	8211.41i	0.592453	+	0.592453i	0.938293	−	0.345840i	$-0.112406\pi$
$577$	8211.41	+	8211.41i	0.592453	+	0.592453i	−0.345840	+	0.938293i	$0.612406\pi$
$578$	2886.78	−	2886.78i	0.207741	−	0.207741i
$579$			5399.45i			0.387554i
$580$	3088.47	+	1940.51i	0.221106	+	0.138923i
$581$	−1721.28			−0.122910
$582$	−4343.32	+	4343.32i	−0.309341	+	0.309341i
$583$	8071.23	−	8071.23i	0.573372	−	0.573372i
$584$		−	908.245i		−	0.0643552i
$585$	4171.63	+	18275.2i	0.294830	+	1.29160i
$586$		−	22248.5i		−	1.56839i
$587$	9371.65	+	9371.65i	0.658960	+	0.658960i	0.955134	−	0.296174i	$-0.0957109\pi$
$587$	9371.65	+	9371.65i	0.658960	+	0.658960i	−0.296174	+	0.955134i	$0.595711\pi$
$588$	−4308.68	+	4308.68i	−0.302189	+	0.302189i
$589$	472.746			0.0330716
$590$	11785.8	−	2690.32i	0.822398	−	0.187726i
$591$	−9329.63			−0.649356
$592$	−13802.4	+	13802.4i	−0.958234	+	0.958234i
$593$	−8845.92	+	8845.92i	−0.612577	+	0.612577i	−0.943617	−	0.331040i	$-0.892601\pi$
$593$	−8845.92	+	8845.92i	−0.612577	+	0.612577i	0.331040	+	0.943617i	$0.392601\pi$
$594$	−25391.7			−1.75393
$595$	558.866	−	889.474i	0.0385063	−	0.0612855i
$596$		−	9485.67i		−	0.651926i
$597$	−7415.79	+	7415.79i	−0.508389	+	0.508389i
$598$	32721.8	+	9949.86i	2.23762	+	0.680402i
$599$		−	19547.1i		−	1.33334i	−0.745352	−	0.666671i	$-0.767719\pi$
$599$		−	19547.1i		−	1.33334i	0.745352	−	0.666671i	$-0.232281\pi$
$600$	−562.090	+	270.720i	−0.0382454	+	0.0184201i
$601$	6473.70			0.439381			0.219690	−	0.975570i	$-0.429495\pi$
$601$	6473.70			0.439381			0.219690	+	0.975570i	$0.429495\pi$
$602$	2316.87	+	2316.87i	0.156858	+	0.156858i
$603$	−13453.1	−	13453.1i	−0.908544	−	0.908544i
$604$			12759.9i			0.859588i
$605$	16945.2	+	10646.8i	1.13871	+	0.715463i
$606$	−11061.1			−0.741460
$607$	−15087.9	−	15087.9i	−1.00889	−	1.00889i	−0.999960	−	0.00893393i	$-0.997156\pi$
$607$	−15087.9	−	15087.9i	−1.00889	−	1.00889i	−0.00893393	−	0.999960i	$-0.502844\pi$
$608$	−2691.01	−	2691.01i	−0.179498	−	0.179498i
$609$	157.818			0.0105010
$610$	12869.2	−	2937.62i	0.854197	−	0.194985i
$611$	36734.6			2.43228
$612$	6993.17	−	6993.17i	0.461899	−	0.461899i
$613$	7465.03	+	7465.03i	0.491859	+	0.491859i	0.908892	−	0.417032i	$-0.136930\pi$
$613$	7465.03	+	7465.03i	0.491859	+	0.491859i	−0.417032	+	0.908892i	$0.636930\pi$
$614$			21779.4i			1.43151i
$615$	10934.6	−	2496.00i	0.716950	−	0.163656i
$616$	175.789			0.0114979
$617$	5029.07	−	5029.07i	0.328140	−	0.328140i	−0.523739	−	0.851879i	$-0.675463\pi$
$617$	5029.07	−	5029.07i	0.328140	−	0.328140i	0.851879	+	0.523739i	$0.175463\pi$
$618$	−407.183	−	407.183i	−0.0265037	−	0.0265037i
$619$	−2258.07			−0.146623			−0.0733115	−	0.997309i	$-0.523357\pi$
$619$	−2258.07			−0.146623			−0.0733115	+	0.997309i	$0.523357\pi$
$620$	1383.27	−	2201.58i	0.0896025	−	0.142609i
$621$	6001.23	+	11245.5i	0.387795	+	0.726678i
$622$	12722.7	+	12722.7i	0.820148	+	0.820148i
$623$	−1337.43	+	1337.43i	−0.0860078	+	0.0860078i
$624$			12826.1i			0.822845i
$625$	−9740.92	+	12217.0i	−0.623419	+	0.781888i
$626$		−	28259.0i		−	1.80424i
$627$	−1436.10	−	1436.10i	−0.0914713	−	0.0914713i
$628$	7006.88	+	7006.88i	0.445231	+	0.445231i
$629$		−	17879.6i		−	1.13340i
$630$	−751.013	+	1195.29i	−0.0474938	+	0.0755897i
$631$			7288.79i			0.459845i	0.973209	+	0.229922i	$0.0738472\pi$
$631$			7288.79i			0.459845i	−0.973209	+	0.229922i	$0.926153\pi$
$632$	−11.9019	+	11.9019i	−0.000749104	+	0.000749104i
$633$	3092.17	−	3092.17i	0.194159	−	0.194159i
$634$			14939.1i			0.935818i
$635$	−2063.85	−	9041.37i	−0.128979	−	0.565033i
$636$			3654.01i			0.227816i
$637$	−18992.8	−	18992.8i	−1.18135	−	1.18135i
$638$	−6785.71	−	6785.71i	−0.421079	−	0.421079i
$639$			8546.59i			0.529105i
$640$	2902.25	−	662.489i	0.179253	−	0.0409175i
$641$			13007.3i			0.801493i	0.916189	+	0.400747i	$0.131249\pi$
$641$			13007.3i			0.801493i	−0.916189	+	0.400747i	$0.868751\pi$
$642$	−5497.62	+	5497.62i	−0.337965	+	0.337965i
$643$	−2348.81	−	2348.81i	−0.144056	−	0.144056i	0.631401	−	0.775457i	$-0.282480\pi$
$643$	−2348.81	−	2348.81i	−0.144056	−	0.144056i	−0.775457	+	0.631401i	$0.782480\pi$
$644$	585.528	+	1097.20i	0.0358277	+	0.0671364i
$645$	12509.0	+	7859.55i	0.763632	+	0.479798i
$646$	3717.90			0.226438
$647$	1079.02	+	1079.02i	0.0655651	+	0.0655651i	0.739129	−	0.673564i	$-0.235237\pi$
$647$	1079.02	+	1079.02i	0.0655651	+	0.0655651i	−0.673564	+	0.739129i	$0.735237\pi$
$648$	438.683	−	438.683i	0.0265943	−	0.0265943i
$649$	−15358.0			−0.928896
$650$	16817.9	+	34918.8i	1.01485	+	2.10712i
$651$		−	112.498i		−	0.00677290i
$652$	8041.83	+	8041.83i	0.483040	+	0.483040i
$653$	−10600.2	+	10600.2i	−0.635249	+	0.635249i	−0.949380	−	0.314131i	$-0.898287\pi$
$653$	−10600.2	+	10600.2i	−0.635249	+	0.635249i	0.314131	+	0.949380i	$0.398287\pi$
$654$	1409.46			0.0842725
$655$	4369.30	+	2745.28i	0.260645	+	0.163766i
$656$	−28476.3			−1.69484
$657$	−6551.89	−	6551.89i	−0.389062	−	0.389062i
$658$	1956.11	+	1956.11i	0.115892	+	0.115892i
$659$	28717.5			1.69754			0.848768	−	0.528765i	$-0.177345\pi$
$659$	28717.5			1.69754			0.848768	+	0.528765i	$0.177345\pi$
$660$	−10890.0	+	2485.84i	−0.642263	+	0.146608i
$661$		−	20493.0i		−	1.20588i	−0.797787	−	0.602940i	$-0.793996\pi$
$661$		−	20493.0i		−	1.20588i	0.797787	−	0.602940i	$-0.206004\pi$
$662$	−11172.6	−	11172.6i	−0.655943	−	0.655943i
$663$	−8307.45	−	8307.45i	−0.486629	−	0.486629i
$664$	2377.46			0.138951
$665$	−249.824	+	57.0266i	−0.0145680	+	0.00332541i
$666$			24026.9i			1.39793i
$667$	−1401.49	+	4609.04i	−0.0813582	+	0.267560i
$668$	−1298.84	+	1298.84i	−0.0752297	+	0.0752297i
$669$		−	4736.40i		−	0.273722i
$670$	−33308.2	−	20927.9i	−1.92061	−	1.20674i
$671$	−16769.8			−0.964813
$672$	−640.373	+	640.373i	−0.0367603	+	0.0367603i
$673$	18282.5	−	18282.5i	1.04716	−	1.04716i	0.0483273	−	0.998832i	$-0.484611\pi$
$673$	18282.5	−	18282.5i	1.04716	−	1.04716i	0.998832	−	0.0483273i	$-0.0153890\pi$
$674$	−42049.3			−2.40308
$675$	−4770.22	+	13634.5i	−0.272009	+	0.777469i
$676$	30010.7			1.70748
$677$	−4075.44	+	4075.44i	−0.231362	+	0.231362i	−0.813261	−	0.581899i	$-0.802310\pi$
$677$	−4075.44	+	4075.44i	−0.231362	+	0.231362i	0.581899	+	0.813261i	$0.302310\pi$
$678$	−13106.0	−	13106.0i	−0.742380	−	0.742380i
$679$		−	984.564i		−	0.0556467i
$680$	−771.914	+	1228.56i	−0.0435317	+	0.0692838i
$681$			4690.55i			0.263939i
$682$	−4837.11	+	4837.11i	−0.271587	+	0.271587i
$683$	11380.6	−	11380.6i	0.637578	−	0.637578i	−0.312379	−	0.949957i	$-0.601126\pi$
$683$	11380.6	−	11380.6i	0.637578	−	0.637578i	0.949957	+	0.312379i	$0.101126\pi$
$684$	−2412.50			−0.134860
$685$	17485.1	−	3991.27i	0.975285	−	0.222626i
$686$		−	4058.98i		−	0.225907i
$687$	5269.39	−	5269.39i	0.292634	−	0.292634i
$688$	−26522.5	−	26522.5i	−1.46971	−	1.46971i
$689$	−16107.0			−0.890606
$690$	7610.23	+	8771.48i	0.419879	+	0.483949i
$691$	−30731.6			−1.69187			−0.845936	−	0.533284i	$-0.820958\pi$
$691$	−30731.6			−1.69187			−0.845936	+	0.533284i	$0.820958\pi$
$692$	443.020	+	443.020i	0.0243368	+	0.0243368i
$693$	1268.10	−	1268.10i	0.0695112	−	0.0695112i
$694$		−	11709.6i		−	0.640478i
$695$	−4923.62	+	7836.29i	−0.268724	+	0.427694i
$696$	−217.980			−0.0118714
$697$	18444.1	−	18444.1i	1.00232	−	1.00232i
$698$	−15290.9	+	15290.9i	−0.829180	+	0.829180i
$699$		−	2111.67i		−	0.114264i
$700$	−465.421	+	1330.29i	−0.0251304	+	0.0718289i
$701$			18984.7i			1.02289i	0.859317	+	0.511443i	$0.170889\pi$
$701$			18984.7i			1.02289i	−0.859317	+	0.511443i	$0.829111\pi$
$702$	25335.9	+	25335.9i	1.36217	+	1.36217i
$703$	−3084.04	+	3084.04i	−0.165458	+	0.165458i
$704$	24695.7			1.32209
$705$	10561.2	+	6635.74i	0.564198	+	0.354491i
$706$	18563.9			0.989604
$707$	1253.68	−	1253.68i	0.0666898	−	0.0666898i
$708$	3476.44	−	3476.44i	0.184538	−	0.184538i
$709$	11238.0			0.595275			0.297638	−	0.954679i	$-0.403801\pi$
$709$	11238.0			0.595275			0.297638	+	0.954679i	$0.403801\pi$
$710$	3932.54	+	17227.8i	0.207867	+	0.910631i
$711$			171.716i			0.00905747i
$712$	1847.28	−	1847.28i	0.0972325	−	0.0972325i
$713$	3285.50	+	999.036i	0.172571	+	0.0524743i
$714$		−	884.741i		−	0.0463734i
$715$	−10957.6	−	48003.5i	−0.573136	−	2.51081i
$716$	−15072.2			−0.786697
$717$	−4610.66	−	4610.66i	−0.240151	−	0.240151i
$718$	11340.0	+	11340.0i	0.589421	+	0.589421i
$719$		−	11223.6i		−	0.582158i	−0.956699	−	0.291079i	$-0.905986\pi$
$719$		−	11223.6i		−	0.582158i	0.956699	−	0.291079i	$-0.0940142\pi$
$720$	8597.25	−	13683.1i	0.445001	−	0.708250i
$721$	92.3020			0.00476769
$722$	18434.8	+	18434.8i	0.950240	+	0.950240i
$723$	3509.70	+	3509.70i	0.180536	+	0.180536i
$724$	7202.19			0.369706
$725$	−4918.49	+	2368.89i	−0.251956	+	0.121350i
$726$	16855.0			0.861636
$727$	−21942.3	+	21942.3i	−1.11939	+	1.11939i	−0.127555	+	0.991832i	$0.540713\pi$
$727$	−21942.3	+	21942.3i	−1.11939	+	1.11939i	−0.991832	+	0.127555i	$0.959287\pi$
$728$	−175.403	−	175.403i	−0.00892974	−	0.00892974i
$729$			1140.65i			0.0579512i
$730$	−16221.7	−	10192.3i	−0.822455	−	0.516757i
$731$	34357.1			1.73836
$732$	3796.01	−	3796.01i	0.191673	−	0.191673i
$733$	8102.69	+	8102.69i	0.408294	+	0.408294i	0.881143	−	0.472849i	$-0.156774\pi$
$733$	8102.69	+	8102.69i	0.408294	+	0.408294i	−0.472849	+	0.881143i	$0.656774\pi$
$734$	−18350.4			−0.922785
$735$	−2029.60	−	8891.33i	−0.101854	−	0.446206i
$736$	−13015.2	−	24388.8i	−0.651829	−	1.22144i
$737$	35337.3	+	35337.3i	1.76617	+	1.76617i
$738$	−24785.5	+	24785.5i	−1.23627	+	1.23627i
$739$		−	7554.88i		−	0.376063i	−0.982163	−	0.188032i	$-0.939789\pi$
$739$		−	7554.88i		−	0.376063i	0.982163	−	0.188032i	$-0.0602107\pi$
$740$	5338.35	+	23386.4i	0.265191	+	1.16176i
$741$			2865.90i			0.142080i
$742$	−857.695	−	857.695i	−0.0424353	−	0.0424353i
$743$	39.8165	+	39.8165i	0.00196598	+	0.00196598i	0.708089	−	0.706123i	$-0.249557\pi$
$743$	39.8165	+	39.8165i	0.00196598	+	0.00196598i	−0.706123	+	0.708089i	$0.749557\pi$
$744$			155.385i			0.00765682i
$745$	12021.3	+	7553.13i	0.591178	+	0.371443i
$746$			13784.8i			0.676536i
$747$	17150.5	−	17150.5i	0.840032	−	0.840032i
$748$	−18369.0	+	18369.0i	−0.897909	+	0.897909i
$749$		−	1246.23i		−	0.0607958i
$750$	−1472.55	+	13077.2i	−0.0716932	+	0.636683i
$751$			3501.49i			0.170135i	0.996375	+	0.0850673i	$0.0271105\pi$
$751$			3501.49i			0.170135i	−0.996375	+	0.0850673i	$0.972889\pi$
$752$	−22392.6	−	22392.6i	−1.08587	−	1.08587i
$753$	5320.37	+	5320.37i	0.257483	+	0.257483i
$754$			13541.6i			0.654053i
$755$	−16170.8	−	10160.3i	−0.779489	−	0.489761i
$756$			1302.91i			0.0626804i
$757$	6113.41	−	6113.41i	0.293521	−	0.293521i	−0.544948	−	0.838470i	$-0.683451\pi$
$757$	6113.41	−	6113.41i	0.293521	−	0.293521i	0.838470	+	0.544948i	$0.183451\pi$
$758$	806.786	+	806.786i	0.0386594	+	0.0386594i
$759$	−6945.79	−	13015.5i	−0.332169	−	0.622442i
$760$	345.061	−	78.7660i	0.0164693	−	0.00375940i
$761$	−1162.97			−0.0553976			−0.0276988	−	0.999616i	$-0.508818\pi$
$761$	−1162.97			−0.0553976			−0.0276988	+	0.999616i	$0.508818\pi$
$762$	−5523.06	−	5523.06i	−0.262572	−	0.262572i
$763$	−159.751	+	159.751i	−0.00757979	+	0.00757979i
$764$	−2123.76			−0.100569
$765$	3294.12	+	14431.0i	0.155685	+	0.682030i
$766$			28895.6i			1.36297i
$767$	15324.2	+	15324.2i	0.721417	+	0.721417i
$768$	7759.67	−	7759.67i	0.364587	−	0.364587i
$769$	−38945.9			−1.82630			−0.913151	−	0.407621i	$-0.866358\pi$
$769$	−38945.9			−1.82630			−0.913151	+	0.407621i	$0.866358\pi$
$770$	1972.69	−	3139.67i	0.0923257	−	0.146943i
$771$	−1518.32			−0.0709219
$772$	−11912.7	−	11912.7i	−0.555374	−	0.555374i
$773$	21868.1	+	21868.1i	1.01752	+	1.01752i	0.999844	+	0.0176751i	$0.00562646\pi$
$773$	21868.1	+	21868.1i	1.01752	+	1.01752i	0.0176751	+	0.999844i	$0.494374\pi$
$774$	−46169.7			−2.14410
$775$	1688.64	+	3506.09i	0.0782680	+	0.162506i
$776$			1359.90i			0.0629090i
$777$	733.903	+	733.903i	0.0338850	+	0.0338850i
$778$	26815.9	+	26815.9i	1.23573	+	1.23573i
$779$	−6362.83			−0.292647
$780$	13346.5	+	8385.73i	0.612667	+	0.384945i
$781$		−	22449.4i		−	1.02855i
$782$	25838.7	+	7856.89i	1.18157	+	0.359286i
$783$	−3568.70	+	3568.70i	−0.162880	+	0.162880i
$784$			23155.2i			1.05481i
$785$	−14459.3	+	3300.58i	−0.657419	+	0.150067i
$786$	4346.05			0.197224
$787$	−16354.5	+	16354.5i	−0.740755	+	0.740755i	−0.972723	−	0.231969i	$-0.925483\pi$
$787$	−16354.5	+	16354.5i	−0.740755	+	0.740755i	0.231969	+	0.972723i	$0.425483\pi$
$788$	20583.8	−	20583.8i	0.930544	−	0.930544i
$789$	−9902.29			−0.446807
$790$	79.0118	+	346.137i	0.00355837	+	0.0155886i
$791$	2970.93			0.133545
$792$	−1751.52	+	1751.52i	−0.0785830	+	0.0785830i
$793$	16732.9	+	16732.9i	0.749311	+	0.749311i
$794$		−	45816.9i		−	2.04784i
$795$	−4630.79	−	2909.57i	−0.206588	−	0.129801i
$796$		−	32722.7i		−	1.45707i
$797$	15363.0	−	15363.0i	0.682794	−	0.682794i	−0.277835	−	0.960629i	$-0.589617\pi$
$797$	15363.0	−	15363.0i	0.682794	−	0.682794i	0.960629	+	0.277835i	$0.0896167\pi$
$798$	−152.609	+	152.609i	−0.00676979	+	0.00676979i
$799$	29007.4			1.28436
$800$	10345.4	−	29569.8i	0.457208	−	1.30682i
$801$		−	26651.7i		−	1.17565i
$802$	22425.1	−	22425.1i	0.987355	−	0.987355i
$803$	17209.9	+	17209.9i	0.756318	+	0.756318i
$804$	−15997.9			−0.701745
$805$	−1856.74	−	131.618i	−0.0812938	−	0.00576266i
$806$	9652.97			0.421850
$807$	−5913.23	−	5913.23i	−0.257938	−	0.257938i
$808$	−1731.61	+	1731.61i	−0.0753933	+	0.0753933i
$809$			38761.6i			1.68453i	0.539064	+	0.842264i	$0.318778\pi$
$809$			38761.6i			1.68453i	−0.539064	+	0.842264i	$0.681222\pi$
$810$	−2912.23	−	12758.0i	−0.126327	−	0.553419i
$811$	−24102.8			−1.04360			−0.521802	−	0.853067i	$-0.674740\pi$
$811$	−24102.8			−1.04360			−0.521802	+	0.853067i	$0.674740\pi$
$812$	−348.191	+	348.191i	−0.0150482	+	0.0150482i
$813$	9906.89	−	9906.89i	0.427367	−	0.427367i
$814$		−	63111.5i		−	2.71751i
$815$	−16595.0	+	3788.09i	−0.713248	+	0.162811i
$816$			10128.1i			0.434503i
$817$	−5926.25	−	5926.25i	−0.253774	−	0.253774i
$818$	−13722.9	+	13722.9i	−0.586563	+	0.586563i
$819$	−2530.64			−0.107970
$820$	−18617.9	+	29631.7i	−0.792884	+	1.26193i
$821$	27404.4			1.16494			0.582472	−	0.812851i	$-0.302086\pi$
$821$	27404.4			1.16494			0.582472	+	0.812851i	$0.302086\pi$
$822$	10681.0	−	10681.0i	0.453216	−	0.453216i
$823$	−13909.0	+	13909.0i	−0.589111	+	0.589111i	−0.937391	−	0.348279i	$-0.886766\pi$
$823$	−13909.0	+	13909.0i	−0.589111	+	0.589111i	0.348279	+	0.937391i	$0.386766\pi$
$824$	−127.489			−0.00538992
$825$	5521.03	−	15780.5i	0.232991	−	0.665947i
$826$			1632.03i			0.0687476i
$827$	9355.73	−	9355.73i	0.393387	−	0.393387i	−0.482506	−	0.875893i	$-0.660273\pi$
$827$	9355.73	−	9355.73i	0.393387	−	0.393387i	0.875893	+	0.482506i	$0.160273\pi$
$828$	−16766.4	−	5098.23i	−0.703711	−	0.213981i
$829$		−	7475.70i		−	0.313199i	−0.987662	−	0.156599i	$-0.949947\pi$
$829$		−	7475.70i		−	0.313199i	0.987662	−	0.156599i	$-0.0500531\pi$
$830$	26679.7	−	42462.6i	1.11574	−	1.77578i
$831$	7834.17			0.327033
$832$	−24641.5	−	24641.5i	−1.02679	−	1.02679i
$833$	−14997.6	−	14997.6i	−0.623814	−	0.623814i
$834$			7794.59i			0.323626i
$835$	−611.814	−	2680.25i	−0.0253565	−	0.111083i
$836$	6336.91			0.262161
$837$	2543.90	+	2543.90i	0.105054	+	0.105054i
$838$	25399.8	+	25399.8i	1.04704	+	1.04704i
$839$	−31566.1			−1.29891			−0.649453	−	0.760402i	$-0.725002\pi$
$839$	−31566.1			−1.29891			−0.649453	+	0.760402i	$0.725002\pi$
$840$	−18.7438	−	82.1133i	−0.000769907	−	0.00337283i
$841$	22481.6			0.921792
$842$	38421.8	−	38421.8i	1.57257	−	1.57257i
$843$	6871.13	+	6871.13i	0.280729	+	0.280729i
$844$			13644.4i			0.556469i
$845$	−23896.6	+	38033.1i	−0.972861	+	1.54838i
$846$	−38980.6			−1.58414
$847$	−1910.38	+	1910.38i	−0.0774989	+	0.0774989i
$848$	9818.50	+	9818.50i	0.397604	+	0.397604i
$849$	−4230.85			−0.171027
$850$	13280.3	+	27573.5i	0.535893	+	1.11266i
$851$	−27950.9	+	14916.1i	−1.12590	+	0.600845i
$852$	5081.65	+	5081.65i	0.204336	+	0.204336i
$853$	−16338.4	+	16338.4i	−0.655823	+	0.655823i	−0.954389	−	0.298566i	$-0.903492\pi$
$853$	−16338.4	+	16338.4i	−0.655823	+	0.655823i	0.298566	+	0.954389i	$0.403492\pi$
$854$			1782.05i			0.0714058i
$855$	1920.99	−	3057.40i	0.0768381	−	0.122293i
$856$			1721.31i			0.0687302i
$857$	14209.0	+	14209.0i	0.566358	+	0.566358i	0.931106	−	0.364748i	$-0.118845\pi$
$857$	14209.0	+	14209.0i	0.566358	+	0.566358i	−0.364748	+	0.931106i	$0.618845\pi$
$858$	−29323.7	−	29323.7i	−1.16678	−	1.16678i
$859$		−	29633.0i		−	1.17702i	−0.808489	−	0.588512i	$-0.799714\pi$
$859$		−	29633.0i		−	1.17702i	0.808489	−	0.588512i	$-0.200286\pi$
$860$	−44938.9	+	10258.1i	−1.78187	+	0.406742i
$861$			1514.15i			0.0599327i
$862$	21717.5	−	21717.5i	0.858120	−	0.858120i
$863$	18299.5	−	18299.5i	0.721810	−	0.721810i	−0.247164	−	0.968974i	$-0.579499\pi$
$863$	18299.5	−	18299.5i	0.721810	−	0.721810i	0.968974	+	0.247164i	$0.0794986\pi$
$864$		−	28961.3i		−	1.14037i
$865$	−914.209	+	208.684i	−0.0359353	+	0.00820285i
$866$			41514.4i			1.62900i
$867$	1757.16	+	1757.16i	0.0688307	+	0.0688307i
$868$	248.204	+	248.204i	0.00970574	+	0.00970574i
$869$		−	451.048i		−	0.0176073i
$870$	−2446.16	+	3893.23i	−0.0953248	+	0.151716i
$871$		−	70519.3i		−	2.74335i
$872$	220.651	−	220.651i	0.00856902	−	0.00856902i
$873$	9810.00	+	9810.00i	0.380319	+	0.380319i
$874$	−3101.68	−	5812.14i	−0.120041	−	0.224941i
$875$	−1315.30	−	1649.10i	−0.0508173	−	0.0637141i
$876$	−7791.27			−0.300505
$877$	−6459.04	−	6459.04i	−0.248696	−	0.248696i	0.571739	−	0.820435i	$-0.306269\pi$
$877$	−6459.04	−	6459.04i	−0.248696	−	0.248696i	−0.820435	+	0.571739i	$0.806269\pi$
$878$	39961.5	−	39961.5i	1.53603	−	1.53603i
$879$	13542.5			0.519654
$880$	−22582.4	+	35941.5i	−0.865061	+	1.37681i
$881$		−	30076.3i		−	1.15017i	−0.818095	−	0.575083i	$-0.804970\pi$
$881$		−	30076.3i		−	1.15017i	0.818095	−	0.575083i	$-0.195030\pi$
$882$	20154.1	+	20154.1i	0.769413	+	0.769413i
$883$	−21612.4	+	21612.4i	−0.823687	+	0.823687i	−0.986635	−	0.162948i	$-0.947900\pi$
$883$	−21612.4	+	21612.4i	−0.823687	+	0.823687i	0.162948	+	0.986635i	$0.447900\pi$
$884$	36657.2			1.39470
$885$	1637.57	+	7173.92i	0.0621993	+	0.272485i
$886$	−16809.6			−0.637391
$887$	−26291.7	−	26291.7i	−0.995254	−	0.995254i	0.00473466	−	0.999989i	$-0.498493\pi$
$887$	−26291.7	−	26291.7i	−0.995254	−	0.995254i	−0.999989	+	0.00473466i	$0.998493\pi$
$888$	−1013.68	−	1013.68i	−0.0383073	−	0.0383073i
$889$	1251.99			0.0472334
$890$	−12263.3	−	53723.2i	−0.461871	−	2.02338i
$891$			16624.8i			0.625085i
$892$	10449.9	+	10449.9i	0.392250	+	0.392250i
$893$	−5003.47	−	5003.47i	−0.187497	−	0.187497i
$894$	11957.4			0.447331
$895$	12001.5	−	19101.3i	0.448231	−	0.713391i
$896$			401.886i			0.0149844i
$897$	−6056.39	+	19917.5i	−0.225437	+	0.741388i
$898$	17076.6	−	17076.6i	0.634582	−	0.634582i
$899$			1359.67i			0.0504422i
$900$	−8617.38	−	17892.1i	−0.319162	−	0.662671i
$901$	−12718.9			−0.470285
$902$	65104.1	−	65104.1i	2.40325	−	2.40325i
$903$	−1410.26	+	1410.26i	−0.0519717	+	0.0519717i
$904$	−4103.50			−0.150974
$905$	−5734.87	+	9127.46i	−0.210645	+	0.335256i
$906$	−16084.7			−0.589822
$907$	−26223.8	+	26223.8i	−0.960032	+	0.960032i	−0.999231	−	0.0391999i	$-0.987519\pi$
$907$	−26223.8	+	26223.8i	−0.960032	+	0.960032i	0.0391999	+	0.999231i	$0.487519\pi$
$908$	−10348.7	−	10348.7i	−0.378231	−	0.378231i
$909$			24982.9i			0.911586i
$910$	−5101.13	+	1164.42i	−0.185825	+	0.0424178i
$911$		−	14276.4i		−	0.519206i	−0.965715	−	0.259603i	$-0.916408\pi$
$911$		−	14276.4i		−	0.519206i	0.965715	−	0.259603i	$-0.0835917\pi$
$912$	1746.99	−	1746.99i	0.0634306	−	0.0634306i
$913$	−45049.3	+	45049.3i	−1.63298	+	1.63298i
$914$	−19417.1			−0.702690
$915$	1788.10	+	7833.38i	0.0646043	+	0.283020i
$916$			23251.6i			0.838705i
$917$	−492.591	+	492.591i	−0.0177391	+	0.0177391i
$918$	20006.5	+	20006.5i	0.719294	+	0.719294i
$919$	544.315			0.0195379			0.00976894	−	0.999952i	$-0.496890\pi$
$919$	544.315			0.0195379			0.00976894	+	0.999952i	$0.496890\pi$
$920$	2564.56	+	181.794i	0.0919033	+	0.00651473i
$921$	−13256.9			−0.474300
$922$	4173.87	+	4173.87i	0.149088	+	0.149088i
$923$	−22400.0	+	22400.0i	−0.798815	+	0.798815i
$924$		−	1507.98i		−	0.0536894i
$925$	−33888.7	−	11856.5i	−1.20460	−	0.421446i
$926$	−40246.4			−1.42827
$927$	−919.680	+	919.680i	−0.0325849	+	0.0325849i
$928$	7739.63	−	7739.63i	0.273778	−	0.273778i
$929$			44573.3i			1.57417i	0.616845	+	0.787084i	$0.288410\pi$
$929$			44573.3i			1.57417i	−0.616845	+	0.787084i	$0.711590\pi$
$930$	2775.25	+	1743.72i	0.0978537	+	0.0614824i
$931$			5173.87i			0.182134i
$932$	4658.95	+	4658.95i	0.163744	+	0.163744i
$933$	−7744.17	+	7744.17i	−0.271739	+	0.271739i
$934$	−18794.5			−0.658430
$935$	−8652.68	−	37905.9i	−0.302645	−	1.32583i
$936$	3495.36			0.122061
$937$	16214.1	−	16214.1i	0.565305	−	0.565305i	−0.365504	−	0.930810i	$-0.619103\pi$
$937$	16214.1	−	16214.1i	0.565305	−	0.565305i	0.930810	+	0.365504i	$0.119103\pi$
$938$	3755.14	−	3755.14i	0.130714	−	0.130714i
$939$	17201.0			0.597799
$940$	−37941.5	+	8660.80i	−1.31650	+	0.300515i
$941$			44627.3i			1.54602i	0.634391	+	0.773012i	$0.281251\pi$
$941$			44627.3i			1.54602i	−0.634391	+	0.773012i	$0.718749\pi$
$942$	−8832.68	+	8832.68i	−0.305504	+	0.305504i
$943$	−44220.5	−	13446.3i	−1.52706	−	0.464340i
$944$		−	18682.7i		−	0.644142i
$945$	−1651.20	−	1037.46i	−0.0568397	−	0.0357129i
$946$	121274.			4.16803
$947$	2707.13	+	2707.13i	0.0928932	+	0.0928932i	0.752026	−	0.659133i	$-0.229077\pi$
$947$	2707.13	+	2707.13i	0.0928932	+	0.0928932i	−0.659133	+	0.752026i	$0.729077\pi$
$948$	102.099	+	102.099i	0.00349792	+	0.00349792i
$949$		−	34344.1i		−	1.17477i
$950$	2465.44	−	7046.86i	0.0841996	−	0.240663i
$951$	−9093.31			−0.310064
$952$	−138.506	−	138.506i	−0.00471535	−	0.00471535i
$953$	−11789.9	−	11789.9i	−0.400746	−	0.400746i	0.477750	−	0.878496i	$-0.341453\pi$
$953$	−11789.9	−	11789.9i	−0.400746	−	0.400746i	−0.878496	+	0.477750i	$0.841453\pi$
$954$	17091.8			0.580050
$955$	1691.08	−	2691.47i	0.0573006	−	0.0911980i
$956$	20344.9			0.688284
$957$	4130.40	−	4130.40i	0.139516	−	0.139516i
$958$	−8581.51	−	8581.51i	−0.289411	−	0.289411i
$959$			2421.22i			0.0815280i
$960$	−2633.22	−	11535.7i	−0.0885280	−	0.387826i
$961$	−28821.8			−0.967466
$962$	−62972.9	+	62972.9i	−2.11053	+	2.11053i
$963$	12417.1	+	12417.1i	0.415511	+	0.415511i
$964$	−15486.8			−0.517424
$965$	24582.9	−	5611.48i	0.820055	−	0.187192i
$966$	−1383.10	+	738.100i	−0.0460669	+	0.0245838i
$967$	−31065.7	−	31065.7i	−1.03310	−	1.03310i	−0.999433	−	0.0336657i	$-0.989282\pi$
$967$	−31065.7	−	31065.7i	−1.03310	−	1.03310i	−0.0336657	−	0.999433i	$-0.510718\pi$
$968$	2638.65	−	2638.65i	0.0876131	−	0.0876131i
$969$			2263.05i			0.0750255i
$970$	24288.4	+	15260.6i	0.803973	+	0.505144i
$971$		−	23784.3i		−	0.786070i	−0.919524	−	0.393035i	$-0.871425\pi$
$971$		−	23784.3i		−	0.786070i	0.919524	−	0.393035i	$-0.128575\pi$
$972$	−20243.7	−	20243.7i	−0.668021	−	0.668021i
$973$	−883.456	−	883.456i	−0.0291082	−	0.0291082i
$974$		−	20528.3i		−	0.675326i
$975$	−21254.7	+	10236.9i	−0.698150	+	0.336250i
$976$		−	20400.1i		−	0.669048i
$977$	−17164.3	+	17164.3i	−0.562061	+	0.562061i	−0.929892	−	0.367831i	$-0.880100\pi$
$977$	−17164.3	+	17164.3i	−0.562061	+	0.562061i	0.367831	+	0.929892i	$0.380100\pi$
$978$	−10137.3	+	10137.3i	−0.331447	+	0.331447i
$979$			70006.2i			2.28540i
$980$	24094.7	+	15138.9i	0.785384	+	0.493465i
$981$		−	3183.46i		−	0.103609i
$982$	53288.5	+	53288.5i	1.73168	+	1.73168i
$983$	23401.0	+	23401.0i	0.759284	+	0.759284i	0.976192	−	0.216908i	$-0.0695972\pi$
$983$	23401.0	+	23401.0i	0.759284	+	0.759284i	−0.216908	+	0.976192i	$0.569597\pi$
$984$		−	2091.37i		−	0.0677544i
$985$	9695.98	+	42476.5i	0.313644	+	1.37402i
$986$			10693.1i			0.345373i
$987$	−1190.67	+	1190.67i	−0.0383985	+	0.0383985i
$988$	−6322.99	−	6322.99i	−0.203605	−	0.203605i
$989$	−28662.6	−	53710.0i	−0.921555	−	1.72688i
$990$	11627.6	+	50938.6i	0.373282	+	1.63529i
$991$	33712.7			1.08064			0.540322	−	0.841458i	$-0.318302\pi$
$991$	33712.7			1.08064			0.540322	+	0.841458i	$0.318302\pi$
$992$	−5517.11	−	5517.11i	−0.176581	−	0.176581i
$993$	6800.64	−	6800.64i	0.217333	−	0.217333i
$994$	−2385.60			−0.0761233
$995$	41470.0	+	26056.0i	1.32129	+	0.830183i
$996$		−	20394.7i		−	0.648828i
$997$	24114.0	+	24114.0i	0.765996	+	0.765996i	0.977399	−	0.211403i	$-0.0678032\pi$
$997$	24114.0	+	24114.0i	0.765996	+	0.765996i	−0.211403	+	0.977399i	$0.567803\pi$
$998$	23451.8	−	23451.8i	0.743841	−	0.743841i
$999$	−33191.2			−1.05118

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.4.e.a.22.5	✓	68
5.3	odd	4	inner	115.4.e.a.68.6	yes	68
23.22	odd	2	inner	115.4.e.a.22.6	yes	68
115.68	even	4	inner	115.4.e.a.68.5	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.4.e.a.22.5	✓	68	1.1	even	1	trivial
115.4.e.a.22.6	yes	68	23.22	odd	2	inner
115.4.e.a.68.5	yes	68	115.68	even	4	inner
115.4.e.a.68.6	yes	68	5.3	odd	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-2.78118 - 2.78118i) q^{2} +(1.69288 - 1.69288i) q^{3} +7.46996i q^{4} +(-9.46680 - 5.94809i) q^{5} -9.41642 q^{6} +(1.06728 - 1.06728i) q^{7} +(-1.47414 + 1.47414i) q^{8} +21.2683i q^{9} +(9.78619 + 42.8716i) q^{10} -55.8655i q^{11} +(12.6457 + 12.6457i) q^{12} +(-55.7428 + 55.7428i) q^{13} -5.93659 q^{14} +(-26.0956 + 5.95676i) q^{15} +67.9594 q^{16} +(-44.0172 + 44.0172i) q^{17} +(59.1511 - 59.1511i) q^{18} +15.1850 q^{19} +(44.4320 - 70.7166i) q^{20} -3.61355i q^{21} +(-155.372 + 155.372i) q^{22} +(105.533 + 32.0899i) q^{23} +4.99109i q^{24} +(54.2406 + 112.619i) q^{25} +310.062 q^{26} +(81.7125 + 81.7125i) q^{27} +(7.97253 + 7.97253i) q^{28} +43.6739i q^{29} +(89.1434 + 56.0097i) q^{30} +31.1324 q^{31} +(-177.214 - 177.214i) q^{32} +(-94.5737 - 94.5737i) q^{33} +244.840 q^{34} +(-16.4520 + 3.75545i) q^{35} -158.873 q^{36} +(-203.098 + 203.098i) q^{37} +(-42.2323 - 42.2323i) q^{38} +188.732i q^{39} +(22.7237 - 5.18708i) q^{40} -419.020 q^{41} +(-10.0499 + 10.0499i) q^{42} +(-390.269 - 390.269i) q^{43} +417.313 q^{44} +(126.506 - 201.343i) q^{45} +(-204.259 - 382.755i) q^{46} +(-329.500 - 329.500i) q^{47} +(115.047 - 115.047i) q^{48} +340.722i q^{49} +(162.360 - 464.066i) q^{50} +149.032i q^{51} +(-416.397 - 416.397i) q^{52} +(144.476 + 144.476i) q^{53} -454.515i q^{54} +(-332.293 + 528.868i) q^{55} +3.14664i q^{56} +(25.7064 - 25.7064i) q^{57} +(121.465 - 121.465i) q^{58} -274.910i q^{59} +(-44.4968 - 194.933i) q^{60} -300.181i q^{61} +(-86.5849 - 86.5849i) q^{62} +(22.6992 + 22.6992i) q^{63} +442.056i q^{64} +(859.269 - 196.143i) q^{65} +526.053i q^{66} +(-632.542 + 632.542i) q^{67} +(-328.807 - 328.807i) q^{68} +(232.979 - 124.331i) q^{69} +(56.2005 + 35.3114i) q^{70} +401.846 q^{71} +(-31.3525 - 31.3525i) q^{72} +(-308.059 + 308.059i) q^{73} +1129.70 q^{74} +(282.473 + 98.8272i) q^{75} +113.432i q^{76} +(-59.6241 - 59.6241i) q^{77} +(524.898 - 524.898i) q^{78} +8.07381 q^{79} +(-643.358 - 404.228i) q^{80} -297.585 q^{81} +(1165.37 + 1165.37i) q^{82} +(-806.388 - 806.388i) q^{83} +26.9931 q^{84} +(678.520 - 154.884i) q^{85} +2170.82i q^{86} +(73.9346 + 73.9346i) q^{87} +(82.3537 + 82.3537i) q^{88} -1253.12 q^{89} +(-911.807 + 208.136i) q^{90} +118.986i q^{91} +(-239.710 + 788.328i) q^{92} +(52.7034 - 52.7034i) q^{93} +1832.80i q^{94} +(-143.754 - 90.3219i) q^{95} -600.006 q^{96} +(461.250 - 461.250i) q^{97} +(947.610 - 947.610i) q^{98} +1188.17 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

Fields

Representations

Groups

Database

Properties

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