LMFDB - Embedded newform 312.4.m.a.181.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("312.181");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			181.26
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.62508 + 2.31498i) q^{2} -3.00000i q^{3} +(-2.71825 - 7.52404i) q^{4} -20.0591 q^{5} +(6.94494 + 4.87523i) q^{6} +33.1512i q^{7} +(21.8353 + 5.93444i) q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+(-1.62508 + 2.31498i) q^{2} -3.00000i q^{3} +(-2.71825 - 7.52404i) q^{4} -20.0591 q^{5} +(6.94494 + 4.87523i) q^{6} +33.1512i q^{7} +(21.8353 + 5.93444i) q^{8} -9.00000 q^{9} +(32.5975 - 46.4363i) q^{10} +7.50344 q^{11} +(-22.5721 + 8.15476i) q^{12} +(-29.7031 + 36.2591i) q^{13} +(-76.7443 - 53.8732i) q^{14} +60.1772i q^{15} +(-49.2222 + 40.9045i) q^{16} +88.2549 q^{17} +(14.6257 - 20.8348i) q^{18} -43.0888 q^{19} +(54.5256 + 150.925i) q^{20} +99.4536 q^{21} +(-12.1937 + 17.3703i) q^{22} -192.337 q^{23} +(17.8033 - 65.5060i) q^{24} +277.366 q^{25} +(-35.6692 - 127.686i) q^{26} +27.0000i q^{27} +(249.431 - 90.1133i) q^{28} -133.095i q^{29} +(-139.309 - 97.7926i) q^{30} -114.640i q^{31} +(-14.7031 - 180.421i) q^{32} -22.5103i q^{33} +(-143.421 + 204.308i) q^{34} -664.982i q^{35} +(24.4643 + 67.7163i) q^{36} -59.6385 q^{37} +(70.0226 - 99.7496i) q^{38} +(108.777 + 89.1094i) q^{39} +(-437.997 - 119.039i) q^{40} -505.647i q^{41} +(-161.620 + 230.233i) q^{42} +142.605i q^{43} +(-20.3962 - 56.4562i) q^{44} +180.532 q^{45} +(312.563 - 445.257i) q^{46} +97.2263i q^{47} +(122.713 + 147.667i) q^{48} -756.001 q^{49} +(-450.742 + 642.097i) q^{50} -264.765i q^{51} +(353.556 + 124.926i) q^{52} -141.817i q^{53} +(-62.5044 - 43.8771i) q^{54} -150.512 q^{55} +(-196.734 + 723.868i) q^{56} +129.266i q^{57} +(308.112 + 216.289i) q^{58} +794.776 q^{59} +(452.775 - 163.577i) q^{60} -124.888i q^{61} +(265.390 + 186.299i) q^{62} -298.361i q^{63} +(441.565 + 259.161i) q^{64} +(595.817 - 727.324i) q^{65} +(52.1109 + 36.5810i) q^{66} +174.687 q^{67} +(-239.899 - 664.033i) q^{68} +577.012i q^{69} +(1539.42 + 1080.65i) q^{70} -519.031i q^{71} +(-196.518 - 53.4099i) q^{72} +616.082i q^{73} +(96.9171 - 138.062i) q^{74} -832.099i q^{75} +(117.126 + 324.202i) q^{76} +248.748i q^{77} +(-383.058 + 107.008i) q^{78} +937.405 q^{79} +(987.352 - 820.505i) q^{80} +81.0000 q^{81} +(1170.56 + 821.716i) q^{82} -1140.50 q^{83} +(-270.340 - 748.292i) q^{84} -1770.31 q^{85} +(-330.128 - 231.744i) q^{86} -399.285 q^{87} +(163.840 + 44.5287i) q^{88} -15.8988i q^{89} +(-293.378 + 417.927i) q^{90} +(-1202.03 - 984.694i) q^{91} +(522.821 + 1447.15i) q^{92} -343.921 q^{93} +(-225.077 - 158.000i) q^{94} +864.321 q^{95} +(-541.264 + 44.1093i) q^{96} +481.395i q^{97} +(1228.56 - 1750.13i) q^{98} -67.5310 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 756 q^{9}+O(q^{10}) $ 84 * q - 756 * q^9	$ 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52} - 1616 q^{55} + 608 q^{56} - 2120 q^{62} - 2856 q^{64} + 696 q^{65} - 396 q^{66} - 2536 q^{68} - 3936 q^{74} - 156 q^{78} + 3160 q^{79} + 6804 q^{81} + 4276 q^{82} - 2088 q^{87} + 1780 q^{88} + 324 q^{90} + 4792 q^{92} - 860 q^{94} + 2480 q^{95}+O(q^{100}) $ 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.62508	+	2.31498i	−0.574551	+	0.818469i
$2$	−1.62508	+	2.31498i	−0.574551	+	0.818469i
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	−2.71825	−	7.52404i	−0.339782	−	0.940504i
$5$	−20.0591			−1.79414			−0.897069	−	0.441891i	$-0.854308\pi$
$5$	−20.0591			−1.79414			−0.897069	+	0.441891i	$0.854308\pi$
$6$	6.94494	+	4.87523i	0.472543	+	0.331717i
$7$			33.1512i			1.79000i	0.446070	+	0.894998i	$0.352823\pi$
$7$			33.1512i			1.79000i	−0.446070	+	0.894998i	$0.647177\pi$
$8$	21.8353	+	5.93444i	0.964995	+	0.262267i
$9$	−9.00000			−0.333333
$10$	32.5975	−	46.4363i	1.03082	−	1.46845i
$11$	7.50344			0.205670			0.102835	−	0.994698i	$-0.467209\pi$
$11$	7.50344			0.205670			0.102835	+	0.994698i	$0.467209\pi$
$12$	−22.5721	+	8.15476i	−0.543000	+	0.196173i
$13$	−29.7031	+	36.2591i	−0.633705	+	0.773575i
$13$	−29.7031	+	36.2591i	−0.633705	+	0.773575i
$14$	−76.7443	−	53.8732i	−1.46506	−	1.02844i
$15$			60.1772i			1.03585i
$16$	−49.2222	+	40.9045i	−0.769097	+	0.639132i
$17$	88.2549			1.25912			0.629558	−	0.776954i	$-0.283236\pi$
$17$	88.2549			1.25912			0.629558	+	0.776954i	$0.283236\pi$
$18$	14.6257	−	20.8348i	0.191517	−	0.272823i
$19$	−43.0888			−0.520276			−0.260138	−	0.965571i	$-0.583768\pi$
$19$	−43.0888			−0.520276			−0.260138	+	0.965571i	$0.583768\pi$
$20$	54.5256	+	150.925i	0.609615	+	1.68739i
$21$	99.4536			1.03345
$22$	−12.1937	+	17.3703i	−0.118168	+	0.168335i
$23$	−192.337			−1.74370			−0.871850	−	0.489773i	$-0.837080\pi$
$23$	−192.337			−1.74370			−0.871850	+	0.489773i	$0.837080\pi$
$24$	17.8033	−	65.5060i	0.151420	−	0.557140i
$25$	277.366			2.21893
$26$	−35.6692	−	127.686i	−0.269050	−	0.963126i
$27$			27.0000i			0.192450i
$28$	249.431	−	90.1133i	1.68350	−	0.608208i
$29$		−	133.095i		−	0.852245i	−0.904665	−	0.426123i	$-0.859879\pi$
$29$		−	133.095i		−	0.852245i	0.904665	−	0.426123i	$-0.140121\pi$
$30$	−139.309	−	97.7926i	−0.847807	−	0.595147i
$31$		−	114.640i		−	0.664194i	−0.943245	−	0.332097i	$-0.892244\pi$
$31$		−	114.640i		−	0.664194i	0.943245	−	0.332097i	$-0.107756\pi$
$32$	−14.7031	−	180.421i	−0.0812239	−	0.996696i
$33$		−	22.5103i		−	0.118744i
$34$	−143.421	+	204.308i	−0.723426	+	1.03055i
$35$		−	664.982i		−	3.21150i
$36$	24.4643	+	67.7163i	0.113261	+	0.313501i
$37$	−59.6385			−0.264987			−0.132493	−	0.991184i	$-0.542298\pi$
$37$	−59.6385			−0.264987			−0.132493	+	0.991184i	$0.542298\pi$
$38$	70.0226	−	99.7496i	0.298925	−	0.425830i
$39$	108.777	+	89.1094i	0.446624	+	0.365870i
$40$	−437.997	−	119.039i	−1.73133	−	0.470544i
$41$		−	505.647i		−	1.92607i	−0.269377	−	0.963035i	$-0.586818\pi$
$41$		−	505.647i		−	1.92607i	0.269377	−	0.963035i	$-0.413182\pi$
$42$	−161.620	+	230.233i	−0.593773	+	0.845850i
$43$			142.605i			0.505746i	0.967499	+	0.252873i	$0.0813755\pi$
$43$			142.605i			0.505746i	−0.967499	+	0.252873i	$0.918624\pi$
$44$	−20.3962	−	56.4562i	−0.0698830	−	0.193434i
$45$	180.532			0.598046
$46$	312.563	−	445.257i	1.00184	−	1.42716i
$47$			97.2263i			0.301743i	0.988553	+	0.150871i	$0.0482079\pi$
$47$			97.2263i			0.301743i	−0.988553	+	0.150871i	$0.951792\pi$
$48$	122.713	+	147.667i	0.369003	+	0.444038i
$49$	−756.001			−2.20409
$50$	−450.742	+	642.097i	−1.27489	+	1.81613i
$51$		−	264.765i		−	0.726951i
$52$	353.556	+	124.926i	0.942872	+	0.333156i
$53$		−	141.817i		−	0.367548i	−0.982968	−	0.183774i	$-0.941168\pi$
$53$		−	141.817i		−	0.367548i	0.982968	−	0.183774i	$-0.0588315\pi$
$54$	−62.5044	−	43.8771i	−0.157514	−	0.110572i
$55$	−150.512			−0.369001
$56$	−196.734	+	723.868i	−0.469458	+	1.72734i
$57$			129.266i			0.300382i
$58$	308.112	+	216.289i	0.697536	+	0.489659i
$59$	794.776			1.75375			0.876873	−	0.480722i	$-0.159625\pi$
$59$	794.776			1.75375			0.876873	+	0.480722i	$0.159625\pi$
$60$	452.775	−	163.577i	0.974218	−	0.351961i
$61$		−	124.888i		−	0.262137i	−0.991373	−	0.131068i	$-0.958159\pi$
$61$		−	124.888i		−	0.262137i	0.991373	−	0.131068i	$-0.0418407\pi$
$62$	265.390	+	186.299i	0.543622	+	0.381613i
$63$		−	298.361i		−	0.596665i
$64$	441.565	+	259.161i	0.862432	+	0.506174i
$65$	595.817	−	727.324i	1.13695	−	1.38790i
$66$	52.1109	+	36.5810i	0.0971880	+	0.0682244i
$67$	174.687			0.318528			0.159264	−	0.987236i	$-0.449088\pi$
$67$	174.687			0.318528			0.159264	+	0.987236i	$0.449088\pi$
$68$	−239.899	−	664.033i	−0.427824	−	1.18420i
$69$			577.012i			1.00673i
$70$	1539.42	+	1080.65i	2.62851	+	1.84517i
$71$		−	519.031i		−	0.867573i	−0.901016	−	0.433786i	$-0.857177\pi$
$71$		−	519.031i		−	0.867573i	0.901016	−	0.433786i	$-0.142823\pi$
$72$	−196.518	−	53.4099i	−0.321665	−	0.0874225i
$73$			616.082i			0.987766i	0.869528	+	0.493883i	$0.164423\pi$
$73$			616.082i			0.987766i	−0.869528	+	0.493883i	$0.835577\pi$
$74$	96.9171	−	138.062i	0.152248	−	0.216883i
$75$		−	832.099i		−	1.28110i
$76$	117.126	+	324.202i	0.176780	+	0.489322i
$77$			248.748i			0.368149i
$78$	−383.058	+	107.008i	−0.556061	+	0.155336i
$79$	937.405			1.33502			0.667508	−	0.744602i	$-0.267361\pi$
$79$	937.405			1.33502			0.667508	+	0.744602i	$0.267361\pi$
$80$	987.352	−	820.505i	1.37987	−	1.14669i
$81$	81.0000			0.111111
$82$	1170.56	+	821.716i	1.57643	+	1.10663i
$83$	−1140.50			−1.50826			−0.754132	−	0.656723i	$-0.771942\pi$
$83$	−1140.50			−1.50826			−0.754132	+	0.656723i	$0.771942\pi$
$84$	−270.340	−	748.292i	−0.351149	−	0.971969i
$85$	−1770.31			−2.25903
$86$	−330.128	−	231.744i	−0.413937	−	0.290577i
$87$	−399.285			−0.492044
$88$	163.840	+	44.5287i	0.198471	+	0.0539406i
$89$		−	15.8988i		−	0.0189356i	−0.999955	−	0.00946780i	$-0.996986\pi$
$89$		−	15.8988i		−	0.0189356i	0.999955	−	0.00946780i	$-0.00301374\pi$
$90$	−293.378	+	417.927i	−0.343608	+	0.489482i
$91$	−1202.03	−	984.694i	−1.38470	−	1.13433i
$92$	522.821	+	1447.15i	0.592477	+	1.63996i
$93$	−343.921			−0.383472
$94$	−225.077	−	158.000i	−0.246967	−	0.173367i
$95$	864.321			0.933447
$96$	−541.264	+	44.1093i	−0.575443	+	0.0468946i
$97$			481.395i			0.503899i	0.967740	+	0.251950i	$0.0810717\pi$
$97$			481.395i			0.503899i	−0.967740	+	0.251950i	$0.918928\pi$
$98$	1228.56	−	1750.13i	1.26636	−	1.80397i
$99$	−67.5310			−0.0685567
$100$	−753.952	−	2086.91i	−0.753952	−	2.08691i
$101$		−	1081.34i		−	1.06532i	−0.846330	−	0.532659i	$-0.821193\pi$
$101$		−	1081.34i		−	1.06532i	0.846330	−	0.532659i	$-0.178807\pi$
$102$	612.925	+	430.263i	0.594986	+	0.417670i
$103$	1371.79			1.31230			0.656150	−	0.754631i	$-0.272184\pi$
$103$	1371.79			1.31230			0.656150	+	0.754631i	$0.272184\pi$
$104$	−863.756	+	615.459i	−0.814406	+	0.580296i
$105$	−1994.95			−1.85416
$106$	328.303	+	230.464i	0.300827	+	0.211175i
$107$			983.266i			0.888373i	0.895934	+	0.444187i	$0.146507\pi$
$107$			983.266i			0.888373i	−0.895934	+	0.444187i	$0.853493\pi$
$108$	203.149	−	73.3928i	0.181000	−	0.0653910i
$109$	22.1146			0.0194330			0.00971651	−	0.999953i	$-0.496907\pi$
$109$	22.1146			0.0194330			0.00971651	+	0.999953i	$0.496907\pi$
$110$	244.594	−	348.432i	0.212010	−	0.302016i
$111$			178.915i			0.152990i
$112$	−1356.03	−	1631.77i	−1.14404	−	1.37668i
$113$	815.087			0.678557			0.339279	−	0.940686i	$-0.389817\pi$
$113$	815.087			0.678557			0.339279	+	0.940686i	$0.389817\pi$
$114$	−299.249	−	210.068i	−0.245853	−	0.172585i
$115$	3858.11			3.12844
$116$	−1001.41	+	361.786i	−0.801540	+	0.289577i
$117$	267.328	−	326.332i	0.211235	−	0.257858i
$118$	−1291.57	+	1839.89i	−1.00762	+	1.43539i
$119$			2925.76i			2.25381i
$120$	−357.118	+	1313.99i	−0.271669	+	0.999586i
$121$	−1274.70			−0.957700
$122$	289.114	+	202.953i	0.214551	+	0.150611i
$123$	−1516.94			−1.11202
$124$	−862.557	+	311.621i	−0.624677	+	0.225681i
$125$	−3056.33			−2.18693
$126$	690.699	+	484.859i	0.488352	+	0.342815i
$127$	781.793			0.546244			0.273122	−	0.961979i	$-0.411944\pi$
$127$	781.793			0.546244			0.273122	+	0.961979i	$0.411944\pi$
$128$	−1317.53	+	601.057i	−0.909798	+	0.415050i
$129$	427.816			0.291993
$130$	715.492	+	2561.26i	0.482714	+	1.72798i
$131$		−	105.610i		−	0.0704369i	−0.999380	−	0.0352184i	$-0.988787\pi$
$131$		−	105.610i		−	0.0704369i	0.999380	−	0.0352184i	$-0.0112127\pi$
$132$	−169.368	+	61.1887i	−0.111679	+	0.0403469i
$133$		−	1428.44i		−	0.931292i
$134$	−283.879	+	404.396i	−0.183011	+	0.260705i
$135$		−	541.595i		−	0.345282i
$136$	1927.08	+	523.743i	1.21504	+	0.330225i
$137$		−	276.985i		−	0.172733i	−0.996263	−	0.0863666i	$-0.972474\pi$
$137$		−	276.985i		−	0.172733i	0.996263	−	0.0863666i	$-0.0275256\pi$
$138$	−1335.77	−	937.688i	−0.823973	−	0.578415i
$139$		−	1775.32i		−	1.08332i	−0.840599	−	0.541658i	$-0.817797\pi$
$139$		−	1775.32i		−	1.08332i	0.840599	−	0.541658i	$-0.182203\pi$
$140$	−5003.35	+	1807.59i	−3.02043	+	1.09121i
$141$	291.679			0.174211
$142$	1201.55	+	843.465i	0.710081	+	0.498465i
$143$	−222.876	+	272.068i	−0.130334	+	0.159101i
$144$	443.000	−	368.140i	0.256366	−	0.213044i
$145$			2669.76i			1.52905i
$146$	−1426.22	−	1001.18i	−0.808455	−	0.567522i
$147$			2268.00i			1.27253i
$148$	162.112	+	448.722i	0.0900375	+	0.249221i
$149$	−2088.89			−1.14852			−0.574258	−	0.818674i	$-0.694709\pi$
$149$	−2088.89			−1.14852			−0.574258	+	0.818674i	$0.694709\pi$
$150$	1926.29	+	1352.22i	1.04854	+	0.736058i
$151$		−	1583.70i		−	0.853506i	−0.904368	−	0.426753i	$-0.859657\pi$
$151$		−	1583.70i		−	0.853506i	0.904368	−	0.426753i	$-0.140343\pi$
$152$	−940.859	−	255.708i	−0.502064	−	0.136452i
$153$	−794.294			−0.419705
$154$	−575.846	−	404.235i	−0.301318	−	0.211520i
$155$			2299.58i			1.19165i
$156$	374.778	−	1060.67i	0.192348	−	0.544367i
$157$		−	209.534i		−	0.106514i	−0.998581	−	0.0532569i	$-0.983040\pi$
$157$		−	209.534i		−	0.106514i	0.998581	−	0.0532569i	$-0.0169602\pi$
$158$	−1523.35	+	2170.07i	−0.767035	+	1.09267i
$159$	−425.451			−0.212204
$160$	294.930	+	3619.08i	0.145727	+	1.78821i
$161$		−	6376.21i		−	3.12122i
$162$	−131.631	+	187.513i	−0.0638390	+	0.0909410i
$163$	−1946.15			−0.935182			−0.467591	−	0.883945i	$-0.654878\pi$
$163$	−1946.15			−0.935182			−0.467591	+	0.883945i	$0.654878\pi$
$164$	−3804.51	+	1374.48i	−1.81148	+	0.654443i
$165$			451.536i			0.213043i
$166$	1853.40	−	2640.23i	0.866575	−	1.23447i
$167$		−	1358.13i		−	0.629311i	−0.949206	−	0.314656i	$-0.898111\pi$
$167$		−	1358.13i		−	0.629311i	0.949206	−	0.314656i	$-0.101889\pi$
$168$	2171.60	+	590.201i	0.997279	+	0.271042i
$169$	−432.448	−	2154.02i	−0.196836	−	0.980437i
$170$	2876.89	−	4098.23i	1.29793	−	1.84894i
$171$	387.799			0.173425
$172$	1072.97	−	387.637i	0.475656	−	0.171843i
$173$			1327.81i			0.583534i	0.956489	+	0.291767i	$0.0942431\pi$
$173$			1327.81i			0.583534i	−0.956489	+	0.291767i	$0.905757\pi$
$174$	648.868	−	924.336i	0.282705	−	0.402723i
$175$			9195.02i			3.97188i
$176$	−369.336	+	306.924i	−0.158180	+	0.131450i
$177$		−	2384.33i		−	1.01253i
$178$	36.8053	+	25.8367i	0.0154982	+	0.0108795i
$179$		−	1483.95i		−	0.619641i	−0.950795	−	0.309820i	$-0.899731\pi$
$179$		−	1483.95i		−	0.619641i	0.950795	−	0.309820i	$-0.100269\pi$
$180$	−490.731	−	1358.33i	−0.203205	−	0.562465i
$181$		−	1399.61i		−	0.574763i	−0.957816	−	0.287381i	$-0.907215\pi$
$181$		−	1399.61i		−	0.574763i	0.957816	−	0.287381i	$-0.0927847\pi$
$182$	4232.94	−	1182.48i	1.72399	−	0.481599i
$183$	−374.665			−0.151345
$184$	−4199.75	−	1141.41i	−1.68266	−	0.457316i
$185$	1196.29			0.475422
$186$	558.898	−	796.169i	0.220325	−	0.313860i
$187$	662.216			0.258963
$188$	731.534	−	264.286i	0.283790	−	0.102527i
$189$	−895.082			−0.344485
$190$	−1404.59	+	2000.89i	−0.536313	+	0.763997i
$191$	876.182			0.331928			0.165964	−	0.986132i	$-0.446926\pi$
$191$	876.182			0.331928			0.165964	+	0.986132i	$0.446926\pi$
$192$	777.483	−	1324.69i	0.292240	−	0.497925i
$193$		−	2926.75i		−	1.09156i	−0.837927	−	0.545782i	$-0.816233\pi$
$193$		−	2926.75i		−	1.09156i	0.837927	−	0.545782i	$-0.183767\pi$
$194$	−1114.42	−	782.303i	−0.412426	−	0.289516i
$195$	−2181.97	−	1787.45i	−0.801304	−	0.656421i
$196$	2055.00	+	5688.18i	0.748908	+	2.07295i
$197$	2802.49			1.01355			0.506775	−	0.862079i	$-0.330838\pi$
$197$	2802.49			1.01355			0.506775	+	0.862079i	$0.330838\pi$
$198$	109.743	−	156.333i	0.0393894	−	0.0561115i
$199$	−411.646			−0.146637			−0.0733187	−	0.997309i	$-0.523359\pi$
$199$	−411.646			−0.146637			−0.0733187	+	0.997309i	$0.523359\pi$
$200$	6056.39	+	1646.01i	2.14126	+	0.581953i
$201$		−	524.060i		−	0.183902i
$202$	2503.28	+	1757.26i	0.871930	+	0.612080i
$203$	4412.26			1.52552
$204$	−1992.10	+	719.697i	−0.683700	+	0.247004i
$205$			10142.8i			3.45563i
$206$	−2229.27	+	3175.67i	−0.753984	+	1.07408i
$207$	1731.04			0.581233
$208$	−21.1058	−	2999.74i	−0.00703569	−	0.999975i
$209$	−323.314			−0.107005
$210$	3241.94	−	4618.26i	1.06531	−	1.51757i
$211$		−	3033.68i		−	0.989798i	−0.868950	−	0.494899i	$-0.835205\pi$
$211$		−	3033.68i		−	0.989798i	0.868950	−	0.494899i	$-0.164795\pi$
$212$	−1067.04	+	385.495i	−0.345681	+	0.124886i
$213$	−1557.09			−0.500893
$214$	−2276.24	−	1597.88i	−0.727106	−	0.510416i
$215$		−	2860.53i		−	0.907378i
$216$	−160.230	+	589.554i	−0.0504734	+	0.185713i
$217$	3800.46			1.18890
$218$	−35.9380	+	51.1949i	−0.0111653	+	0.0159053i
$219$	1848.25			0.570287
$220$	409.130	+	1132.46i	0.125380	+	0.347047i
$221$	−2621.45	+	3200.05i	−0.797908	+	0.974020i
$222$	−414.185	−	290.751i	−0.125218	−	0.0879006i
$223$		−	2017.39i		−	0.605805i	−0.953022	−	0.302903i	$-0.902044\pi$
$223$		−	2017.39i		−	0.605805i	0.953022	−	0.302903i	$-0.0979557\pi$
$224$	5981.18	−	487.425i	1.78408	−	0.145390i
$225$	−2496.30			−0.739644
$226$	−1324.58	+	1886.91i	−0.389866	+	0.555378i
$227$	−979.522			−0.286401			−0.143201	−	0.989694i	$-0.545739\pi$
$227$	−979.522			−0.286401			−0.143201	+	0.989694i	$0.545739\pi$
$228$	972.605	−	351.379i	0.282510	−	0.102064i
$229$	4660.51			1.34487			0.672435	−	0.740156i	$-0.265248\pi$
$229$	4660.51			1.34487			0.672435	+	0.740156i	$0.265248\pi$
$230$	−6269.72	+	8931.44i	−1.79745	+	2.56053i
$231$	746.244			0.212551
$232$	789.843	−	2906.17i	0.223516	−	0.822413i
$233$	−4665.89			−1.31190			−0.655950	−	0.754804i	$-0.727732\pi$
$233$	−4665.89			−1.31190			−0.655950	+	0.754804i	$0.727732\pi$
$234$	321.023	+	1149.17i	0.0896835	+	0.321042i
$235$		−	1950.27i		−	0.541368i
$236$	−2160.40	−	5979.92i	−0.595891	−	1.64941i
$237$		−	2812.21i		−	0.770772i
$238$	−6773.06	−	4754.58i	−1.84467	−	1.29493i
$239$			1143.81i			0.309569i	0.987948	+	0.154784i	$0.0494683\pi$
$239$			1143.81i			0.309569i	−0.987948	+	0.154784i	$0.950532\pi$
$240$	−2461.52	−	2962.06i	−0.662042	−	0.796666i
$241$			1212.01i			0.323952i	0.986795	+	0.161976i	$0.0517867\pi$
$241$			1212.01i			0.323952i	−0.986795	+	0.161976i	$0.948213\pi$
$242$	2071.48	−	2950.90i	0.550248	−	0.783847i
$243$		−	243.000i		−	0.0641500i
$244$	−939.665	+	339.478i	−0.246541	+	0.0890692i
$245$	15164.7			3.95443
$246$	2465.15	−	3511.69i	0.638911	−	0.910151i
$247$	1279.87	−	1562.36i	0.329702	−	0.402472i
$248$	680.325	−	2503.21i	0.174196	−	0.640944i
$249$			3421.49i			0.870796i
$250$	4966.77	−	7075.33i	1.25650	−	1.78993i
$251$			5722.02i			1.43893i	0.694530	+	0.719464i	$0.255612\pi$
$251$			5722.02i			1.43893i	−0.694530	+	0.719464i	$0.744388\pi$
$252$	−2244.88	+	811.020i	−0.561166	+	0.202736i
$253$	−1443.19			−0.358627
$254$	−1270.47	+	1809.84i	−0.313845	+	0.447083i
$255$			5310.93i			1.30425i
$256$	749.651	−	4026.82i	0.183020	−	0.983109i
$257$	−3403.03			−0.825974			−0.412987	−	0.910737i	$-0.635515\pi$
$257$	−3403.03			−0.825974			−0.412987	+	0.910737i	$0.635515\pi$
$258$	−695.233	+	990.384i	−0.167765	+	0.238987i
$259$		−	1977.09i		−	0.474325i
$260$	−7092.00	−	2505.90i	−1.69164	−	0.597728i
$261$			1197.85i			0.284082i
$262$	244.486	+	171.625i	0.0576504	+	0.0404696i
$263$	1648.64			0.386538			0.193269	−	0.981146i	$-0.438091\pi$
$263$	1648.64			0.386538			0.193269	+	0.981146i	$0.438091\pi$
$264$	133.586	−	491.521i	0.0311426	−	0.114587i
$265$			2844.72i			0.659433i
$266$	3306.82	+	2321.33i	0.762233	+	0.535075i
$267$	−47.6964			−0.0109325
$268$	−474.842	−	1314.35i	−0.108230	−	0.299577i
$269$			5618.78i			1.27354i	0.771052	+	0.636772i	$0.219731\pi$
$269$			5618.78i			1.27354i	−0.771052	+	0.636772i	$0.780269\pi$
$270$	1253.78	+	880.133i	0.282602	+	0.198382i
$271$			7307.37i			1.63797i	0.573812	+	0.818987i	$0.305464\pi$
$271$			7307.37i			1.63797i	−0.573812	+	0.818987i	$0.694536\pi$
$272$	−4344.10	+	3610.02i	−0.968382	+	0.804741i
$273$	−2954.08	+	3606.10i	−0.654906	+	0.799454i
$274$	641.215	+	450.122i	0.141377	+	0.0992441i
$275$	2081.20			0.456368
$276$	4341.46	−	1568.46i	0.946830	−	0.342067i
$277$		−	3317.53i		−	0.719607i	−0.933028	−	0.359804i	$-0.882844\pi$
$277$		−	3317.53i		−	0.719607i	0.933028	−	0.359804i	$-0.117156\pi$
$278$	4109.83	+	2885.04i	0.886660	+	0.622421i
$279$			1031.76i			0.221398i
$280$	3946.29	−	14520.1i	0.842272	−	3.09908i
$281$		−	4753.70i		−	1.00919i	−0.863357	−	0.504594i	$-0.831642\pi$
$281$		−	4753.70i		−	1.00919i	0.863357	−	0.504594i	$-0.168358\pi$
$282$	−474.000	+	675.230i	−0.100093	+	0.142586i
$283$		−	1741.89i		−	0.365882i	−0.983124	−	0.182941i	$-0.941438\pi$
$283$		−	1741.89i		−	0.365882i	0.983124	−	0.182941i	$-0.0585617\pi$
$284$	−3905.21	+	1410.86i	−0.815956	+	0.294785i
$285$		−	2592.96i		−	0.538926i
$286$	−267.642	−	958.084i	−0.0553357	−	0.198086i
$287$	16762.8			3.44766
$288$	132.328	+	1623.79i	0.0270746	+	0.332232i
$289$	2875.93			0.585371
$290$	−6180.44	−	4338.57i	−1.25148	−	0.878515i
$291$	1444.18			0.290926
$292$	4635.42	−	1674.67i	0.928998	−	0.335625i
$293$	2160.37			0.430752			0.215376	−	0.976531i	$-0.430902\pi$
$293$	2160.37			0.430752			0.215376	+	0.976531i	$0.430902\pi$
$294$	−5250.38	−	3685.68i	−1.04153	−	0.731133i
$295$	−15942.5			−3.14646
$296$	−1302.23	−	353.921i	−0.255711	−	0.0694974i
$297$			202.593i			0.0395813i
$298$	3394.61	−	4835.75i	0.659881	−	0.940024i
$299$	5713.02	−	6973.98i	1.10499	−	1.34888i
$300$	−6260.74	+	2261.86i	−1.20488	+	0.435294i
$301$	−4727.53			−0.905284
$302$	3666.23	+	2573.63i	0.698568	+	0.490383i
$303$	−3244.01			−0.615062
$304$	2120.93	−	1762.52i	0.400143	−	0.332525i
$305$			2505.15i			0.470309i
$306$	1290.79	−	1838.77i	0.241142	−	0.343515i
$307$	2315.83			0.430525			0.215263	−	0.976556i	$-0.430939\pi$
$307$	2315.83			0.430525			0.215263	+	0.976556i	$0.430939\pi$
$308$	1871.59	−	676.160i	0.346246	−	0.125090i
$309$		−	4115.38i		−	0.757657i
$310$	−5323.47	−	3736.99i	−0.975332	−	0.684667i
$311$	1524.32			0.277929			0.138965	−	0.990297i	$-0.455623\pi$
$311$	1524.32			0.277929			0.138965	+	0.990297i	$0.455623\pi$
$312$	1846.38	+	2591.27i	0.335034	+	0.470197i
$313$	−4983.63			−0.899973			−0.449987	−	0.893035i	$-0.648571\pi$
$313$	−4983.63			−0.899973			−0.449987	+	0.893035i	$0.648571\pi$
$314$	485.068	+	340.509i	0.0871782	+	0.0611976i
$315$			5984.84i			1.07050i
$316$	−2548.10	−	7053.07i	−0.453614	−	1.25559i
$317$	−7295.94			−1.29268			−0.646342	−	0.763048i	$-0.723702\pi$
$317$	−7295.94			−1.29268			−0.646342	+	0.763048i	$0.723702\pi$
$318$	691.391	−	984.910i	0.121922	−	0.173682i
$319$		−	998.670i		−	0.175281i
$320$	−8857.38	−	5198.53i	−1.54732	−	0.908145i
$321$	2949.80			0.512903
$322$	14760.8	+	10361.8i	2.55462	+	1.79330i
$323$	−3802.80			−0.655088
$324$	−220.178	−	609.447i	−0.0377535	−	0.104500i
$325$	−8238.65	+	10057.1i	−1.40615	+	1.71651i
$326$	3162.65	−	4505.31i	0.537310	−	0.765417i
$327$		−	66.3439i		−	0.0112197i
$328$	3000.73	−	11041.0i	0.505145	−	1.85865i
$329$	−3223.17			−0.540118
$330$	−1045.30	−	733.781i	−0.174369	−	0.122404i
$331$	8489.50			1.40974			0.704872	−	0.709335i	$-0.251004\pi$
$331$	8489.50			1.40974			0.704872	+	0.709335i	$0.251004\pi$
$332$	3100.16	+	8581.15i	0.512480	+	1.41853i
$333$	536.746			0.0883288
$334$	3144.03	+	2207.06i	0.515072	+	0.361572i
$335$	−3504.05			−0.571483
$336$	−4895.32	+	4068.09i	−0.794827	+	0.660514i
$337$	−1188.31			−0.192082			−0.0960408	−	0.995377i	$-0.530618\pi$
$337$	−1188.31			−0.192082			−0.0960408	+	0.995377i	$0.530618\pi$
$338$	5689.27	+	2499.34i	0.915549	+	0.402207i
$339$		−	2445.26i		−	0.391765i
$340$	4812.15	+	13319.9i	0.767576	+	2.12462i
$341$		−	860.197i		−	0.136605i
$342$	−630.203	+	897.747i	−0.0996418	+	0.141943i
$343$		−	13691.5i		−	2.15531i
$344$	−846.281	+	3113.83i	−0.132641	+	0.488043i
$345$		−	11574.3i		−	1.80620i
$346$	−3073.85	−	2157.79i	−0.477604	−	0.335270i
$347$			8002.52i			1.23803i	0.785378	+	0.619017i	$0.212469\pi$
$347$			8002.52i			1.23803i	−0.785378	+	0.619017i	$0.787531\pi$
$348$	1085.36	+	3004.23i	0.167187	+	0.462770i
$349$	−3387.46			−0.519561			−0.259781	−	0.965668i	$-0.583650\pi$
$349$	−3387.46			−0.519561			−0.259781	+	0.965668i	$0.583650\pi$
$350$	−21286.3	−	14942.6i	−3.25086	−	2.28205i
$351$	−978.996	−	801.985i	−0.148875	−	0.121957i
$352$	−110.324	−	1353.78i	−0.0167053	−	0.204991i
$353$			2594.71i			0.391226i	0.980681	+	0.195613i	$0.0626696\pi$
$353$			2594.71i			0.391226i	−0.980681	+	0.195613i	$0.937330\pi$
$354$	5519.67	+	3874.72i	0.828721	+	0.581748i
$355$			10411.3i			1.55655i
$356$	−119.623	+	43.2169i	−0.0178090	+	0.00643397i
$357$	8777.27			1.30124
$358$	3435.31	+	2411.53i	0.507156	+	0.356015i
$359$		−	513.024i		−	0.0754217i	−0.999289	−	0.0377108i	$-0.987993\pi$
$359$		−	513.024i		−	0.0754217i	0.999289	−	0.0377108i	$-0.0120066\pi$
$360$	3941.97	+	1071.35i	0.577112	+	0.156848i
$361$	−5002.36			−0.729313
$362$	3240.06	+	2274.47i	0.470425	+	0.330231i
$363$			3824.10i			0.552928i
$364$	−4141.44	+	11720.8i	−0.596348	+	1.68774i
$365$		−	12358.0i		−	1.77219i
$366$	608.860	−	867.343i	0.0869553	−	0.123871i
$367$	−10393.3			−1.47828			−0.739138	−	0.673554i	$-0.764767\pi$
$367$	−10393.3			−1.47828			−0.739138	+	0.673554i	$0.764767\pi$
$368$	9467.26	−	7867.45i	1.34107	−	1.11445i
$369$			4550.83i			0.642023i
$370$	−1944.07	+	2769.39i	−0.273155	+	0.389118i
$371$	4701.40			0.657910
$372$	934.864	+	2587.67i	0.130297	+	0.360657i
$373$		−	2096.99i		−	0.291094i	−0.989351	−	0.145547i	$-0.953506\pi$
$373$		−	2096.99i		−	0.291094i	0.989351	−	0.145547i	$-0.0464942\pi$
$374$	−1076.15	+	1533.01i	−0.148787	+	0.211953i
$375$			9168.98i			1.26262i
$376$	−576.983	+	2122.97i	−0.0791373	+	0.291180i
$377$	4825.91	+	3953.34i	0.659275	+	0.540072i
$378$	1454.58	−	2072.10i	0.197924	−	0.281950i
$379$	6475.00			0.877569			0.438784	−	0.898592i	$-0.355409\pi$
$379$	6475.00			0.877569			0.438784	+	0.898592i	$0.355409\pi$
$380$	−2349.44	−	6503.18i	−0.317168	−	0.877911i
$381$		−	2345.38i		−	0.315374i
$382$	−1423.86	+	2028.34i	−0.190710	+	0.271673i
$383$		−	10028.3i		−	1.33791i	−0.743302	−	0.668956i	$-0.766742\pi$
$383$		−	10028.3i		−	1.33791i	0.743302	−	0.668956i	$-0.233258\pi$
$384$	1803.17	+	3952.59i	0.239629	+	0.525272i
$385$		−	4989.65i		−	0.660510i
$386$	6775.36	+	4756.19i	0.893412	+	0.627160i
$387$		−	1283.45i		−	0.168582i
$388$	3622.03	−	1308.55i	0.473920	−	0.171216i
$389$		−	13407.8i		−	1.74757i	−0.486315	−	0.873784i	$-0.661659\pi$
$389$		−	13407.8i		−	1.74757i	0.486315	−	0.873784i	$-0.338341\pi$
$390$	7683.79	−	2146.47i	0.997650	−	0.278695i
$391$	−16974.7			−2.19552
$392$	−16507.6	−	4486.44i	−2.12693	−	0.578060i
$393$	−316.831			−0.0406667
$394$	−4554.26	+	6487.71i	−0.582336	+	0.829558i
$395$	−18803.5			−2.39520
$396$	183.566	+	508.105i	0.0232943	+	0.0644779i
$397$	−9324.59			−1.17881			−0.589405	−	0.807838i	$-0.700638\pi$
$397$	−9324.59			−1.17881			−0.589405	+	0.807838i	$0.700638\pi$
$398$	668.957	−	952.952i	0.0842507	−	0.120018i
$399$	−4285.33			−0.537682
$400$	−13652.6	+	11345.5i	−1.70657	+	1.41819i
$401$			11606.9i			1.44544i	0.691139	+	0.722722i	$0.257109\pi$
$401$			11606.9i			1.44544i	−0.691139	+	0.722722i	$0.742891\pi$
$402$	1213.19	+	851.637i	0.150518	+	0.105661i
$403$	4156.76	+	3405.18i	0.513803	+	0.420903i
$404$	−8136.03	+	2939.35i	−1.00194	+	0.361976i
$405$	−1624.78			−0.199349
$406$	−7170.25	+	10214.3i	−0.876487	+	1.24859i
$407$	−447.494			−0.0544998
$408$	1571.23	−	5781.23i	0.190655	−	0.701504i
$409$			10381.2i			1.25505i	0.778596	+	0.627525i	$0.215932\pi$
$409$			10381.2i			1.25505i	−0.778596	+	0.627525i	$0.784068\pi$
$410$	−23480.4	−	16482.9i	−2.82833	−	1.98544i
$411$	−830.956			−0.0997276
$412$	−3728.88	−	10321.4i	−0.445895	−	1.23422i
$413$			26347.8i			3.13920i
$414$	−2813.06	+	4007.31i	−0.333948	+	0.475721i
$415$	22877.3			2.70603
$416$	6978.64	+	4825.95i	0.822491	+	0.568779i
$417$	−5325.97			−0.625453
$418$	525.410	−	748.466i	0.0614800	−	0.0875805i
$419$		−	2309.14i		−	0.269234i	−0.990898	−	0.134617i	$-0.957020\pi$
$419$		−	2309.14i		−	0.269234i	0.990898	−	0.134617i	$-0.0429804\pi$
$420$	5422.77	+	15010.0i	0.630009	+	1.74385i
$421$	−264.567			−0.0306276			−0.0153138	−	0.999883i	$-0.504875\pi$
$421$	−264.567			−0.0306276			−0.0153138	+	0.999883i	$0.504875\pi$
$422$	7022.91	+	4929.97i	0.810119	+	0.568690i
$423$		−	875.036i		−	0.100581i
$424$	841.604	−	3096.62i	0.0963960	−	0.354682i
$425$	24478.9			2.79389
$426$	2530.40	−	3604.64i	0.287789	−	0.409965i
$427$	4140.20			0.469223
$428$	7398.13	−	2672.77i	0.835519	−	0.301853i
$429$	816.205	+	668.627i	0.0918572	+	0.0752485i
$430$	6622.06	+	4648.58i	0.742661	+	0.521335i
$431$		−	5169.06i		−	0.577691i	−0.957376	−	0.288846i	$-0.906729\pi$
$431$		−	5169.06i		−	0.577691i	0.957376	−	0.288846i	$-0.0932714\pi$
$432$	−1104.42	−	1329.00i	−0.123001	−	0.148013i
$433$	−1101.65			−0.122267			−0.0611336	−	0.998130i	$-0.519472\pi$
$433$	−1101.65			−0.122267			−0.0611336	+	0.998130i	$0.519472\pi$
$434$	−6176.04	+	8797.99i	−0.683086	+	0.973080i
$435$	8009.28			0.882795
$436$	−60.1132	−	166.391i	−0.00660298	−	0.0182768i
$437$	8287.58			0.907205
$438$	−3003.54	+	4278.65i	−0.327659	+	0.466762i
$439$	8435.37			0.917080			0.458540	−	0.888674i	$-0.348373\pi$
$439$	8435.37			0.917080			0.458540	+	0.888674i	$0.348373\pi$
$440$	−3286.48	−	893.204i	−0.356084	−	0.0967769i
$441$	6804.01			0.734695
$442$	−3147.98	−	11268.9i	−0.338765	−	1.21269i
$443$		−	10547.0i		−	1.13116i	−0.824695	−	0.565578i	$-0.808653\pi$
$443$		−	10547.0i		−	1.13116i	0.824695	−	0.565578i	$-0.191347\pi$
$444$	1346.17	−	486.337i	0.143888	−	0.0519832i
$445$			318.915i			0.0339731i
$446$	4670.22	+	3278.42i	0.495833	+	0.348066i
$447$			6266.68i			0.663096i
$448$	−8591.49	+	14638.4i	−0.906049	+	1.54375i
$449$		−	15026.4i		−	1.57937i	−0.613510	−	0.789687i	$-0.710243\pi$
$449$		−	15026.4i		−	1.57937i	0.613510	−	0.789687i	$-0.289757\pi$
$450$	4056.67	−	5778.87i	0.424963	−	0.605375i
$451$		−	3794.09i		−	0.396135i
$452$	−2215.61	−	6132.75i	−0.230561	−	0.638186i
$453$	−4751.09			−0.492772
$454$	1591.80	−	2267.57i	0.164552	−	0.234411i
$455$	24111.7	+	19752.1i	2.48433	+	2.03514i
$456$	−767.123	+	2822.58i	−0.0787803	+	0.289867i
$457$		−	9353.93i		−	0.957458i	−0.877963	−	0.478729i	$-0.841098\pi$
$457$		−	9353.93i		−	0.957458i	0.877963	−	0.478729i	$-0.158902\pi$
$458$	−7573.69	+	10789.0i	−0.772697	+	1.10073i
$459$			2382.88i			0.242317i
$460$	−10487.3	−	29028.5i	−1.06299	−	2.94231i
$461$	682.098			0.0689121			0.0344560	−	0.999406i	$-0.489030\pi$
$461$	682.098			0.0689121			0.0344560	+	0.999406i	$0.489030\pi$
$462$	−1212.70	+	1727.54i	−0.122121	+	0.173966i
$463$		−	14480.9i		−	1.45353i	−0.686885	−	0.726766i	$-0.741022\pi$
$463$		−	14480.9i		−	1.45353i	0.686885	−	0.726766i	$-0.258978\pi$
$464$	5444.18	+	6551.23i	0.544697	+	0.655459i
$465$	6898.73			0.688002
$466$	7582.43	−	10801.4i	0.753754	−	1.07375i
$467$			2055.97i			0.203724i	0.994799	+	0.101862i	$0.0324800\pi$
$467$			2055.97i			0.203724i	−0.994799	+	0.101862i	$0.967520\pi$
$468$	−3182.00	−	1124.33i	−0.314291	−	0.111052i
$469$			5791.07i			0.570164i
$470$	4514.83	+	3169.34i	0.443093	+	0.311044i
$471$	−628.603			−0.0614958
$472$	17354.2	+	4716.55i	1.69236	+	0.459951i
$473$			1070.03i			0.104017i
$474$	6510.22	+	4570.06i	0.630853	+	0.442848i
$475$	−11951.4			−1.15446
$476$	22013.5	−	7952.94i	2.11972	−	0.765804i
$477$			1276.35i			0.122516i
$478$	−2647.90	−	1858.78i	−0.253372	−	0.177863i
$479$		−	6724.22i		−	0.641414i	−0.947178	−	0.320707i	$-0.896080\pi$
$479$		−	6724.22i		−	0.641414i	0.947178	−	0.320707i	$-0.103920\pi$
$480$	10857.2	−	884.791i	1.03242	−	0.0841354i
$481$	1771.45	−	2162.44i	0.167923	−	0.204987i
$482$	−2805.78	−	1969.61i	−0.265144	−	0.186127i
$483$	−19128.6			−1.80203
$484$	3464.95	+	9590.88i	0.325409	+	0.900721i
$485$		−	9656.33i		−	0.904065i
$486$	562.540	+	394.894i	0.0525048	+	0.0368575i
$487$		−	821.946i		−	0.0764803i	−0.999269	−	0.0382402i	$-0.987825\pi$
$487$		−	821.946i		−	0.0764803i	0.999269	−	0.0382402i	$-0.0121752\pi$
$488$	741.143	−	2726.98i	0.0687499	−	0.252961i
$489$			5838.46i			0.539927i
$490$	−24643.8	+	35105.9i	−2.27203	+	3.23658i
$491$			7804.46i			0.717332i	0.933466	+	0.358666i	$0.116768\pi$
$491$			7804.46i			0.717332i	−0.933466	+	0.358666i	$0.883232\pi$
$492$	4123.43	+	11413.5i	0.377843	+	1.04586i
$493$		−	11746.3i		−	1.07307i
$494$	1536.94	+	5501.83i	0.139981	+	0.501092i
$495$	1354.61			0.123000
$496$	4689.30	+	5642.85i	0.424507	+	0.510829i
$497$	17206.5			1.55295
$498$	−7920.68	−	5560.19i	−0.712720	−	0.500317i
$499$	−9817.67			−0.880760			−0.440380	−	0.897812i	$-0.645156\pi$
$499$	−9817.67			−0.880760			−0.440380	+	0.897812i	$0.645156\pi$
$500$	8307.87	+	22995.9i	0.743079	+	2.05682i
$501$	−4074.38			−0.363333
$502$	−13246.4	−	9298.72i	−1.17772	−	0.826737i
$503$	−6789.90			−0.601882			−0.300941	−	0.953643i	$-0.597301\pi$
$503$	−6789.90			−0.601882			−0.300941	+	0.953643i	$0.597301\pi$
$504$	1770.60	−	6514.81i	0.156486	−	0.575779i
$505$			21690.6i			1.91133i
$506$	2345.30	−	3340.96i	0.206050	−	0.293525i
$507$	−6462.06	+	1297.34i	−0.566055	+	0.113643i
$508$	−2125.11	−	5882.24i	−0.185604	−	0.513745i
$509$	2193.34			0.190998			0.0954990	−	0.995430i	$-0.469555\pi$
$509$	2193.34			0.190998			0.0954990	+	0.995430i	$0.469555\pi$
$510$	−12294.7	−	8630.68i	−1.06749	−	0.749358i
$511$	−20423.8			−1.76810
$512$	8103.75	+	8279.31i	0.699489	+	0.714643i
$513$		−	1163.40i		−	0.100127i
$514$	5530.19	−	7877.95i	0.474565	−	0.676034i
$515$	−27516.9			−2.35445
$516$	−1162.91	−	3218.90i	−0.0992137	−	0.274620i
$517$			729.531i			0.0620595i
$518$	4576.91	+	3212.92i	0.388220	+	0.272524i
$519$	3983.42			0.336903
$520$	17326.1	−	12345.5i	1.46116	−	1.04113i
$521$	−20816.7			−1.75047			−0.875237	−	0.483694i	$-0.839295\pi$
$521$	−20816.7			−1.75047			−0.875237	+	0.483694i	$0.839295\pi$
$522$	−2773.01	−	1946.61i	−0.232512	−	0.163220i
$523$		−	3282.67i		−	0.274457i	−0.990539	−	0.137229i	$-0.956180\pi$
$523$		−	3282.67i		−	0.274457i	0.990539	−	0.137229i	$-0.0438195\pi$
$524$	−794.617	+	287.076i	−0.0662462	+	0.0239332i
$525$	27585.1			2.29316
$526$	−2679.17	+	3816.57i	−0.222086	+	0.316370i
$527$		−	10117.6i		−	0.836296i
$528$	920.773	+	1108.01i	0.0758930	+	0.0913255i
$529$	24826.6			2.04049
$530$	−6585.46	−	4622.88i	−0.539725	−	0.378878i
$531$	−7152.98			−0.584582
$532$	−10747.7	+	3882.87i	−0.875884	+	0.316436i
$533$	18334.3	+	15019.3i	1.48996	+	1.22056i
$534$	77.5102	−	110.416i	0.00628126	−	0.00894788i
$535$		−	19723.4i		−	1.59386i
$536$	3814.34	+	1036.67i	0.307378	+	0.0835395i
$537$	−4451.85			−0.357750
$538$	−13007.4	−	9130.95i	−1.04236	−	0.731716i
$539$	−5672.61			−0.453315
$540$	−4074.98	+	1472.19i	−0.324739	+	0.117320i
$541$	−6655.14			−0.528885			−0.264443	−	0.964401i	$-0.585188\pi$
$541$	−6655.14			−0.528885			−0.264443	+	0.964401i	$0.585188\pi$
$542$	−16916.4	−	11875.0i	−1.34063	−	0.941100i
$543$	−4198.82			−0.331839
$544$	−1297.62	−	15923.1i	−0.102270	−	1.25496i
$545$	−443.599			−0.0348655
$546$	−3547.43	−	12698.8i	−0.278051	−	0.995347i
$547$		−	5361.51i		−	0.419089i	−0.977799	−	0.209545i	$-0.932802\pi$
$547$		−	5361.51i		−	0.419089i	0.977799	−	0.209545i	$-0.0671981\pi$
$548$	−2084.05	+	752.916i	−0.162456	+	0.0586916i
$549$			1124.00i			0.0873789i
$550$	−3382.11	+	4817.94i	−0.262207	+	0.373523i
$551$			5734.90i			0.443403i
$552$	−3424.24	+	12599.3i	−0.264031	+	0.971485i
$553$			31076.1i			2.38967i
$554$	7680.01	+	5391.24i	0.588976	+	0.413451i
$555$		−	3588.88i		−	0.274485i
$556$	−13357.6	+	4825.78i	−1.01886	+	0.368091i
$557$	−20610.0			−1.56781			−0.783907	−	0.620878i	$-0.786776\pi$
$557$	−20610.0			−1.56781			−0.783907	+	0.620878i	$0.786776\pi$
$558$	−2388.51	−	1676.69i	−0.181207	−	0.127204i
$559$	−5170.74	−	4235.82i	−0.391232	−	0.320494i
$560$	27200.7	+	32731.9i	2.05257	+	2.46995i
$561$		−	1986.65i		−	0.149512i
$562$	11004.7	+	7725.12i	0.825989	+	0.579830i
$563$			1875.47i			0.140394i	0.997533	+	0.0701969i	$0.0223628\pi$
$563$			1875.47i			0.140394i	−0.997533	+	0.0701969i	$0.977637\pi$
$564$	−792.857	−	2194.60i	−0.0591938	−	0.163846i
$565$	−16349.9			−1.21743
$566$	4032.43	+	2830.70i	0.299463	+	0.210218i
$567$			2685.25i			0.198888i
$568$	3080.16	−	11333.2i	0.227536	−	0.837204i
$569$	−22280.0			−1.64152			−0.820761	−	0.571271i	$-0.806450\pi$
$569$	−22280.0			−1.64152			−0.820761	+	0.571271i	$0.806450\pi$
$570$	6002.66	+	4213.76i	0.441094	+	0.309641i
$571$			10159.6i			0.744602i	0.928112	+	0.372301i	$0.121431\pi$
$571$			10159.6i			0.744602i	−0.928112	+	0.372301i	$0.878569\pi$
$572$	2652.88	+	937.375i	0.193921	+	0.0685203i
$573$		−	2628.55i		−	0.191639i
$574$	−27240.8	+	38805.5i	−1.98086	+	2.82180i
$575$	−53347.9			−3.86915
$576$	−3974.08	−	2332.45i	−0.287477	−	0.168725i
$577$		−	3444.22i		−	0.248501i	−0.992251	−	0.124250i	$-0.960347\pi$
$577$		−	3444.22i		−	0.248501i	0.992251	−	0.124250i	$-0.0396526\pi$
$578$	−4673.61	+	6657.72i	−0.336326	+	0.479108i
$579$	−8780.25			−0.630215
$580$	20087.4	−	7257.09i	1.43807	−	0.519541i
$581$		−	37808.9i		−	2.69979i
$582$	−2346.91	+	3343.26i	−0.167152	+	0.238114i
$583$		−	1064.12i		−	0.0755938i
$584$	−3656.10	+	13452.4i	−0.259059	+	0.953189i
$585$	−5362.36	+	6545.92i	−0.378985	+	0.462633i
$586$	−3510.77	+	5001.21i	−0.247489	+	0.352557i
$587$	4097.27			0.288096			0.144048	−	0.989571i	$-0.453988\pi$
$587$	4097.27			0.288096			0.144048	+	0.989571i	$0.453988\pi$
$588$	17064.5	−	6165.01i	1.19682	−	0.432382i
$589$			4939.71i			0.345564i
$590$	25907.7	−	36906.5i	1.80780	−	2.57528i
$591$		−	8407.47i		−	0.585173i
$592$	2935.54	−	2439.48i	0.203800	−	0.169361i
$593$		−	17564.2i		−	1.21632i	−0.793815	−	0.608159i	$-0.791908\pi$
$593$		−	17564.2i		−	1.21632i	0.793815	−	0.608159i	$-0.208092\pi$
$594$	−468.998	−	329.229i	−0.0323960	−	0.0227415i
$595$		−	58687.9i		−	4.04365i
$596$	5678.14	+	15716.9i	0.390245	+	1.08018i
$597$			1234.94i			0.0846611i
$598$	6860.52	+	24558.8i	0.469143	+	1.67940i
$599$	−3134.23			−0.213791			−0.106896	−	0.994270i	$-0.534091\pi$
$599$	−3134.23			−0.213791			−0.106896	+	0.994270i	$0.534091\pi$
$600$	4938.04	−	18169.2i	0.335991	−	1.23626i
$601$	−6865.54			−0.465976			−0.232988	−	0.972480i	$-0.574850\pi$
$601$	−6865.54			−0.465976			−0.232988	+	0.972480i	$0.574850\pi$
$602$	7682.60	−	10944.1i	0.520132	−	0.740946i
$603$	−1572.18			−0.106176
$604$	−11915.8	+	4304.89i	−0.802727	+	0.290006i
$605$	25569.3			1.71825
$606$	5271.77	−	7509.83i	0.353385	−	0.503409i
$607$	5911.47			0.395287			0.197643	−	0.980274i	$-0.436671\pi$
$607$	5911.47			0.395287			0.197643	+	0.980274i	$0.436671\pi$
$608$	633.538	+	7774.13i	0.0422588	+	0.518557i
$609$		−	13236.8i		−	0.880757i
$610$	−5799.36	−	4071.06i	−0.384933	−	0.270217i
$611$	−3525.34	−	2887.92i	−0.233420	−	0.191216i
$612$	2159.09	+	5976.30i	0.142608	+	0.394734i
$613$	18065.3			1.19029			0.595146	−	0.803617i	$-0.297094\pi$
$613$	18065.3			1.19029			0.595146	+	0.803617i	$0.297094\pi$
$614$	−3763.40	+	5361.09i	−0.247359	+	0.352371i
$615$	30428.4			1.99511
$616$	−1476.18	+	5431.50i	−0.0965535	+	0.355262i
$617$		−	18244.1i		−	1.19040i	−0.803577	−	0.595201i	$-0.797072\pi$
$617$		−	18244.1i		−	1.19040i	0.803577	−	0.595201i	$-0.202928\pi$
$618$	9527.02	+	6687.81i	0.620118	+	0.435313i
$619$	20042.8			1.30143			0.650717	−	0.759321i	$-0.274469\pi$
$619$	20042.8			1.30143			0.650717	+	0.759321i	$0.274469\pi$
$620$	17302.1	−	6250.83i	1.12076	−	0.404902i
$621$		−	5193.11i		−	0.335575i
$622$	−2477.13	+	3528.76i	−0.159685	+	0.227476i
$623$	527.064			0.0338946
$624$	−8999.23	+	63.3174i	−0.577336	+	0.00406206i
$625$	26636.3			1.70472
$626$	8098.79	−	11537.0i	0.517081	−	0.736600i
$627$			969.943i			0.0617796i
$628$	−1576.54	+	569.567i	−0.100177	+	0.0361914i
$629$	−5263.39			−0.333649
$630$	−13854.8	−	9725.82i	−0.876171	−	0.615057i
$631$		−	4394.10i		−	0.277221i	−0.990347	−	0.138610i	$-0.955736\pi$
$631$		−	4394.10i		−	0.277221i	0.990347	−	0.138610i	$-0.0442636\pi$
$632$	20468.6	+	5562.97i	1.28828	+	0.350131i
$633$	−9101.05			−0.571460
$634$	11856.5	−	16889.9i	0.742713	−	1.05802i
$635$	−15682.0			−0.980036
$636$	1156.48	+	3201.11i	0.0721031	+	0.199579i
$637$	22455.6	−	27411.9i	1.39674	−	1.70502i
$638$	2311.90	+	1622.92i	0.143462	+	0.100708i
$639$			4671.28i			0.289191i
$640$	26428.4	−	12056.6i	1.63230	−	0.744657i
$641$	20234.0			1.24679			0.623397	−	0.781906i	$-0.285752\pi$
$641$	20234.0			1.24679			0.623397	+	0.781906i	$0.285752\pi$
$642$	−4793.65	+	6828.72i	−0.294689	+	0.419795i
$643$	17695.6			1.08530			0.542648	−	0.839960i	$-0.317422\pi$
$643$	17695.6			1.08530			0.542648	+	0.839960i	$0.317422\pi$
$644$	−47974.8	+	17332.1i	−2.93552	+	1.06053i
$645$	−8581.58			−0.523875
$646$	6179.84	−	8803.40i	0.376381	−	0.536169i
$647$	3886.43			0.236154			0.118077	−	0.993004i	$-0.462327\pi$
$647$	3886.43			0.236154			0.118077	+	0.993004i	$0.462327\pi$
$648$	1768.66	+	480.689i	0.107222	+	0.0291408i
$649$	5963.55			0.360693
$650$	−9893.44	−	35415.8i	−0.597004	−	2.13711i
$651$		−	11401.4i		−	0.686414i
$652$	5290.14	+	14642.9i	0.317758	+	0.879542i
$653$		−	23468.4i		−	1.40642i	−0.710984	−	0.703208i	$-0.751750\pi$
$653$		−	23468.4i		−	1.40642i	0.710984	−	0.703208i	$-0.248250\pi$
$654$	153.585	+	107.814i	0.00918294	+	0.00644627i
$655$			2118.45i			0.126373i
$656$	20683.2	+	24889.1i	1.23101	+	1.48133i
$657$		−	5544.74i		−	0.329255i
$658$	5237.89	−	7461.56i	0.310326	−	0.442070i
$659$			22637.2i			1.33812i	0.743208	+	0.669061i	$0.233303\pi$
$659$			22637.2i			1.33812i	−0.743208	+	0.669061i	$0.766697\pi$
$660$	3397.37	−	1227.39i	0.200368	−	0.0723880i
$661$	−3387.82			−0.199351			−0.0996754	−	0.995020i	$-0.531780\pi$
$661$	−3387.82			−0.199351			−0.0996754	+	0.995020i	$0.531780\pi$
$662$	−13796.1	+	19653.0i	−0.809970	+	1.15383i
$663$	9600.14	+	7864.34i	0.562351	+	0.460672i
$664$	−24903.2	−	6768.21i	−1.45547	−	0.395569i
$665$			28653.3i			1.67087i
$666$	−872.254	+	1242.56i	−0.0507495	+	0.0722944i
$667$			25599.1i			1.48606i
$668$	−10218.6	+	3691.73i	−0.591870	+	0.213828i
$669$	−6052.18			−0.349762
$670$	5694.35	−	8111.80i	0.328346	−	0.467741i
$671$		−	937.093i		−	0.0539137i
$672$	−1462.28	−	17943.5i	−0.0839412	−	1.03004i
$673$	−25563.1			−1.46417			−0.732083	−	0.681215i	$-0.761452\pi$
$673$	−25563.1			−1.46417			−0.732083	+	0.681215i	$0.761452\pi$
$674$	1931.10	−	2750.92i	0.110361	−	0.157213i
$675$			7488.89i			0.427033i
$676$	−15031.4	+	9108.92i	−0.855224	+	0.518259i
$677$			5125.96i			0.290999i	0.989358	+	0.145500i	$0.0464790\pi$
$677$			5125.96i			0.290999i	−0.989358	+	0.145500i	$0.953521\pi$
$678$	5660.73	+	3973.74i	0.320648	+	0.225089i
$679$	−15958.8			−0.901978
$680$	−38655.4	−	10505.8i	−2.17995	−	0.592469i
$681$			2938.56i			0.165354i
$682$	1991.34	+	1397.89i	0.111807	+	0.0784865i
$683$	19348.8			1.08398			0.541992	−	0.840383i	$-0.317670\pi$
$683$	19348.8			1.08398			0.541992	+	0.840383i	$0.317670\pi$
$684$	−1054.14	−	2917.81i	−0.0589268	−	0.163107i
$685$			5556.07i			0.309907i
$686$	31695.5	+	22249.7i	1.76405	+	1.23834i
$687$		−	13981.5i		−	0.776461i
$688$	−5833.19	−	7019.34i	−0.323239	−	0.388968i
$689$	5142.16	+	4212.41i	0.284326	+	0.232917i
$690$	26794.3	+	18809.2i	1.47832	+	1.03776i
$691$	−6848.71			−0.377044			−0.188522	−	0.982069i	$-0.560370\pi$
$691$	−6848.71			−0.377044			−0.188522	+	0.982069i	$0.560370\pi$
$692$	9990.47	−	3609.32i	0.548816	−	0.198274i
$693$		−	2238.73i		−	0.122716i
$694$	−18525.7	−	13004.7i	−1.01329	−	0.711314i
$695$			35611.3i			1.94362i
$696$	−8718.52	−	2369.53i	−0.474820	−	0.129047i
$697$		−	44625.9i		−	2.42514i
$698$	5504.89	−	7841.91i	0.298515	−	0.425244i
$699$			13997.7i			0.757426i
$700$	69183.7	−	24994.4i	3.73557	−	1.34957i
$701$		−	15306.7i		−	0.824715i	−0.911022	−	0.412358i	$-0.864705\pi$
$701$		−	15306.7i		−	0.824715i	0.911022	−	0.412358i	$-0.135295\pi$
$702$	3447.52	−	963.069i	0.185354	−	0.0517788i
$703$	2569.75			0.137866
$704$	3313.26	+	1944.60i	0.177376	+	0.104105i
$705$	−5850.81			−0.312559
$706$	−6006.71	−	4216.61i	−0.320206	−	0.224779i
$707$	35847.7			1.90692
$708$	−17939.8	+	6481.21i	−0.952285	+	0.344038i
$709$	−24287.6			−1.28651			−0.643257	−	0.765650i	$-0.722417\pi$
$709$	−24287.6			−1.28651			−0.643257	+	0.765650i	$0.722417\pi$
$710$	−24101.9	−	16919.1i	−1.27398	−	0.894315i
$711$	−8436.64			−0.445005
$712$	94.3503	−	347.156i	0.00496619	−	0.0182728i
$713$			22049.6i			1.15815i
$714$	−14263.7	+	20319.2i	−0.747628	+	1.06502i
$715$	4470.68	−	5457.43i	0.233838	−	0.285450i
$716$	−11165.3	+	4033.75i	−0.582775	+	0.210542i
$717$	3431.43			0.178730
$718$	1187.64	+	833.704i	0.0617303	+	0.0433336i
$719$	−11711.7			−0.607474			−0.303737	−	0.952756i	$-0.598234\pi$
$719$	−11711.7			−0.607474			−0.303737	+	0.952756i	$0.598234\pi$
$720$	−8886.17	+	7384.55i	−0.459955	+	0.382230i
$721$			45476.6i			2.34901i
$722$	8129.21	−	11580.3i	0.419028	−	0.596920i
$723$	3636.03			0.187034
$724$	−10530.7	+	3804.49i	−0.540567	+	0.195294i
$725$		−	36916.1i		−	1.89107i
$726$	−8852.70	−	6214.45i	−0.452554	−	0.317686i
$727$	3053.44			0.155772			0.0778858	−	0.996962i	$-0.475183\pi$
$727$	3053.44			0.155772			0.0778858	+	0.996962i	$0.475183\pi$
$728$	−20403.2	−	28634.5i	−1.03873	−	1.45778i
$729$	−729.000			−0.0370370
$730$	28608.6	+	20082.7i	1.45048	+	1.01821i
$731$			12585.6i			0.636793i
$732$	1018.44	+	2819.00i	0.0514241	+	0.142340i
$733$	18182.2			0.916201			0.458100	−	0.888900i	$-0.348530\pi$
$733$	18182.2			0.916201			0.458100	+	0.888900i	$0.348530\pi$
$734$	16890.0	−	24060.3i	0.849346	−	1.20992i
$735$		−	45494.1i		−	2.28309i
$736$	2827.95	+	34701.7i	0.141630	+	1.73794i
$737$	1310.75			0.0655117
$738$	−10535.1	−	7395.44i	−0.525476	−	0.368875i
$739$	−33748.8			−1.67993			−0.839967	−	0.542638i	$-0.817426\pi$
$739$	−33748.8			−1.67993			−0.839967	+	0.542638i	$0.817426\pi$
$740$	−3251.82	−	9000.94i	−0.161540	−	0.447137i
$741$	−4687.09	−	3839.62i	−0.232368	−	0.190353i
$742$	−7640.14	+	10883.6i	−0.378003	+	0.538479i
$743$		−	14765.5i		−	0.729065i	−0.931191	−	0.364533i	$-0.881229\pi$
$743$		−	14765.5i		−	0.729065i	0.931191	−	0.364533i	$-0.118771\pi$
$744$	−7509.63	−	2040.98i	−0.370049	−	0.100572i
$745$	41901.3			2.06060
$746$	4854.48	+	3407.77i	0.238251	+	0.167248i
$747$	10264.5			0.502755
$748$	−1800.07	−	4982.53i	−0.0879907	−	0.243555i
$749$	−32596.4			−1.59018
$750$	−21226.0	−	14900.3i	−1.03342	−	0.725443i
$751$	20722.4			1.00689			0.503443	−	0.864028i	$-0.332066\pi$
$751$	20722.4			1.00689			0.503443	+	0.864028i	$0.332066\pi$
$752$	−3976.99	−	4785.69i	−0.192853	−	0.232069i
$753$	17166.1			0.830765
$754$	−16994.4	+	4747.39i	−0.820820	+	0.229297i
$755$			31767.5i			1.53131i
$756$	2433.06	+	6734.63i	0.117050	+	0.323990i
$757$		−	3918.30i		−	0.188128i	−0.995566	−	0.0940640i	$-0.970014\pi$
$757$		−	3918.30i		−	0.188128i	0.995566	−	0.0940640i	$-0.0299858\pi$
$758$	−10522.4	+	14989.5i	−0.504208	+	0.718263i
$759$			4329.57i			0.207053i
$760$	18872.8	+	5129.26i	0.900772	+	0.244813i
$761$		−	14201.0i		−	0.676458i	−0.941064	−	0.338229i	$-0.890172\pi$
$761$		−	14201.0i		−	0.676458i	0.941064	−	0.338229i	$-0.109828\pi$
$762$	5429.51	+	3811.42i	0.258124	+	0.181199i
$763$			733.127i			0.0347850i
$764$	−2381.68	−	6592.42i	−0.112783	−	0.312180i
$765$	15932.8			0.753009
$766$	23215.2	+	16296.7i	1.09504	+	0.768699i
$767$	−23607.3	+	28817.9i	−1.11136	+	1.35665i
$768$	−12080.4	−	2248.95i	−0.567598	−	0.105667i
$769$			9610.01i			0.450645i	0.974284	+	0.225322i	$0.0723435\pi$
$769$			9610.01i			0.450645i	−0.974284	+	0.225322i	$0.927656\pi$
$770$	11550.9	+	8108.57i	0.540607	+	0.379497i
$771$			10209.1i			0.476877i
$772$	−22021.0	+	7955.64i	−1.02662	+	0.370894i
$773$	−4076.62			−0.189684			−0.0948420 </

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.62508 + 2.31498i) q^{2} -3.00000i q^{3} +(-2.71825 - 7.52404i) q^{4} -20.0591 q^{5} +(6.94494 + 4.87523i) q^{6} +33.1512i q^{7} +(21.8353 + 5.93444i) q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+(-1.62508 + 2.31498i) q^{2} -3.00000i q^{3} +(-2.71825 - 7.52404i) q^{4} -20.0591 q^{5} +(6.94494 + 4.87523i) q^{6} +33.1512i q^{7} +(21.8353 + 5.93444i) q^{8} -9.00000 q^{9} +(32.5975 - 46.4363i) q^{10} +7.50344 q^{11} +(-22.5721 + 8.15476i) q^{12} +(-29.7031 + 36.2591i) q^{13} +(-76.7443 - 53.8732i) q^{14} +60.1772i q^{15} +(-49.2222 + 40.9045i) q^{16} +88.2549 q^{17} +(14.6257 - 20.8348i) q^{18} -43.0888 q^{19} +(54.5256 + 150.925i) q^{20} +99.4536 q^{21} +(-12.1937 + 17.3703i) q^{22} -192.337 q^{23} +(17.8033 - 65.5060i) q^{24} +277.366 q^{25} +(-35.6692 - 127.686i) q^{26} +27.0000i q^{27} +(249.431 - 90.1133i) q^{28} -133.095i q^{29} +(-139.309 - 97.7926i) q^{30} -114.640i q^{31} +(-14.7031 - 180.421i) q^{32} -22.5103i q^{33} +(-143.421 + 204.308i) q^{34} -664.982i q^{35} +(24.4643 + 67.7163i) q^{36} -59.6385 q^{37} +(70.0226 - 99.7496i) q^{38} +(108.777 + 89.1094i) q^{39} +(-437.997 - 119.039i) q^{40} -505.647i q^{41} +(-161.620 + 230.233i) q^{42} +142.605i q^{43} +(-20.3962 - 56.4562i) q^{44} +180.532 q^{45} +(312.563 - 445.257i) q^{46} +97.2263i q^{47} +(122.713 + 147.667i) q^{48} -756.001 q^{49} +(-450.742 + 642.097i) q^{50} -264.765i q^{51} +(353.556 + 124.926i) q^{52} -141.817i q^{53} +(-62.5044 - 43.8771i) q^{54} -150.512 q^{55} +(-196.734 + 723.868i) q^{56} +129.266i q^{57} +(308.112 + 216.289i) q^{58} +794.776 q^{59} +(452.775 - 163.577i) q^{60} -124.888i q^{61} +(265.390 + 186.299i) q^{62} -298.361i q^{63} +(441.565 + 259.161i) q^{64} +(595.817 - 727.324i) q^{65} +(52.1109 + 36.5810i) q^{66} +174.687 q^{67} +(-239.899 - 664.033i) q^{68} +577.012i q^{69} +(1539.42 + 1080.65i) q^{70} -519.031i q^{71} +(-196.518 - 53.4099i) q^{72} +616.082i q^{73} +(96.9171 - 138.062i) q^{74} -832.099i q^{75} +(117.126 + 324.202i) q^{76} +248.748i q^{77} +(-383.058 + 107.008i) q^{78} +937.405 q^{79} +(987.352 - 820.505i) q^{80} +81.0000 q^{81} +(1170.56 + 821.716i) q^{82} -1140.50 q^{83} +(-270.340 - 748.292i) q^{84} -1770.31 q^{85} +(-330.128 - 231.744i) q^{86} -399.285 q^{87} +(163.840 + 44.5287i) q^{88} -15.8988i q^{89} +(-293.378 + 417.927i) q^{90} +(-1202.03 - 984.694i) q^{91} +(522.821 + 1447.15i) q^{92} -343.921 q^{93} +(-225.077 - 158.000i) q^{94} +864.321 q^{95} +(-541.264 + 44.1093i) q^{96} +481.395i q^{97} +(1228.56 - 1750.13i) q^{98} -67.5310 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 756 q^{9}+O(q^{10}) \) 84 * q - 756 * q^9	\( 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52} - 1616 q^{55} + 608 q^{56} - 2120 q^{62} - 2856 q^{64} + 696 q^{65} - 396 q^{66} - 2536 q^{68} - 3936 q^{74} - 156 q^{78} + 3160 q^{79} + 6804 q^{81} + 4276 q^{82} - 2088 q^{87} + 1780 q^{88} + 324 q^{90} + 4792 q^{92} - 860 q^{94} + 2480 q^{95}+O(q^{100}) \) 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

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