LMFDB - Embedded newform 120.4.m.b.59.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(59,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("120.59");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	120.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:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			59.3
Character	$\chi$	$=$	120.59
Dual form			120.4.m.b.59.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.80496 + 0.363625i) q^{2} +(3.73183 - 3.61572i) q^{3} +(7.73555 - 2.03990i) q^{4} +(-2.66357 + 10.8584i) q^{5} +(-9.15285 + 11.4989i) q^{6} -26.3409 q^{7} +(-20.9561 + 8.53468i) q^{8} +(0.853113 - 26.9865i) q^{9} +(3.52280 - 31.4259i) q^{10} +37.4262i q^{11} +(21.4921 - 35.5822i) q^{12} -30.8736 q^{13} +(73.8850 - 9.57820i) q^{14} +(29.3211 + 50.1525i) q^{15} +(55.6776 - 31.5596i) q^{16} -54.0168 q^{17} +(7.42002 + 76.0062i) q^{18} -4.70847 q^{19} +(1.54596 + 89.4294i) q^{20} +(-98.2997 + 95.2413i) q^{21} +(-13.6091 - 104.979i) q^{22} +129.048i q^{23} +(-47.3457 + 107.621i) q^{24} +(-110.811 - 57.8443i) q^{25} +(86.5990 - 11.2264i) q^{26} +(-94.3921 - 103.794i) q^{27} +(-203.761 + 53.7329i) q^{28} -230.566 q^{29} +(-100.481 - 130.014i) q^{30} +123.860i q^{31} +(-144.697 + 108.769i) q^{32} +(135.323 + 139.668i) q^{33} +(151.515 - 19.6419i) q^{34} +(70.1608 - 286.021i) q^{35} +(-48.4506 - 210.496i) q^{36} +349.557 q^{37} +(13.2070 - 1.71212i) q^{38} +(-115.215 + 111.630i) q^{39} +(-36.8551 - 250.283i) q^{40} +74.8414i q^{41} +(241.094 - 302.892i) q^{42} +364.853i q^{43} +(76.3458 + 289.512i) q^{44} +(290.759 + 81.1439i) q^{45} +(-46.9252 - 361.975i) q^{46} -45.7642i q^{47} +(93.6687 - 319.090i) q^{48} +350.842 q^{49} +(331.853 + 121.957i) q^{50} +(-201.582 + 195.310i) q^{51} +(-238.824 + 62.9791i) q^{52} -682.936i q^{53} +(302.508 + 256.814i) q^{54} +(-406.390 - 99.6872i) q^{55} +(552.003 - 224.811i) q^{56} +(-17.5712 + 17.0245i) q^{57} +(646.728 - 83.8397i) q^{58} +256.129i q^{59} +(329.121 + 328.145i) q^{60} -435.099i q^{61} +(-45.0386 - 347.422i) q^{62} +(-22.4718 + 710.849i) q^{63} +(366.318 - 357.708i) q^{64} +(82.2339 - 335.238i) q^{65} +(-430.361 - 342.556i) q^{66} -862.064i q^{67} +(-417.850 + 110.189i) q^{68} +(466.603 + 481.586i) q^{69} +(-92.7936 + 827.787i) q^{70} -366.537 q^{71} +(212.443 + 572.814i) q^{72} -215.240i q^{73} +(-980.492 + 127.108i) q^{74} +(-622.676 + 184.796i) q^{75} +(-36.4226 + 9.60482i) q^{76} -985.839i q^{77} +(282.581 - 355.013i) q^{78} +340.273i q^{79} +(194.386 + 688.632i) q^{80} +(-727.544 - 46.0451i) q^{81} +(-27.2142 - 209.927i) q^{82} +605.094 q^{83} +(-566.120 + 937.266i) q^{84} +(143.878 - 586.538i) q^{85} +(-132.670 - 1023.40i) q^{86} +(-860.434 + 833.664i) q^{87} +(-319.421 - 784.308i) q^{88} +517.431i q^{89} +(-845.071 - 121.878i) q^{90} +813.237 q^{91} +(263.246 + 998.260i) q^{92} +(447.843 + 462.225i) q^{93} +(16.6410 + 128.367i) q^{94} +(12.5413 - 51.1265i) q^{95} +(-146.708 + 929.093i) q^{96} +1441.60i q^{97} +(-984.097 + 127.575i) q^{98} +(1010.00 + 31.9288i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9} - 72 q^{10} - 128 q^{16} + 672 q^{19} - 416 q^{24} + 496 q^{25} - 248 q^{30} + 240 q^{34} - 608 q^{36} - 1344 q^{40} + 336 q^{46} + 3520 q^{49} - 544 q^{51} - 952 q^{54}+ \cdots + 256 q^{99}+O(q^{100}) $ 64 * q - 32 * q^4 - 72 * q^6 - 112 * q^9 - 72 * q^10 - 128 * q^16 + 672 * q^19 - 416 * q^24 + 496 * q^25 - 248 * q^30 + 240 * q^34 - 608 * q^36 - 1344 * q^40 + 336 * q^46 + 3520 * q^49 - 544 * q^51 - 952 * q^54 - 2064 * q^60 + 2176 * q^64 - 176 * q^66 + 672 * q^70 - 1600 * q^75 + 2304 * q^76 - 2304 * q^81 - 736 * q^84 - 1432 * q^90 - 2752 * q^91 + 4496 * q^94 + 640 * q^96 + 256 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−2.80496	+	0.363625i	−0.991702	+	0.128561i
$2$	−2.80496	+	0.363625i	−0.991702	+	0.128561i
$3$	3.73183	−	3.61572i	0.718191	−	0.695846i
$3$	3.73183	−	3.61572i	0.718191	−	0.695846i
$4$	7.73555	−	2.03990i	0.966944	−	0.254988i
$5$	−2.66357	+	10.8584i	−0.238237	+	0.971207i
$5$	−2.66357	+	10.8584i	−0.238237	+	0.971207i
$6$	−9.15285	+	11.4989i	−0.622773	+	0.782403i
$7$	−26.3409			−1.42227			−0.711137	−	0.703053i	$-0.751819\pi$
$7$	−26.3409			−1.42227			−0.711137	+	0.703053i	$0.751819\pi$
$8$	−20.9561	+	8.53468i	−0.926139	+	0.377183i
$9$	0.853113	−	26.9865i	0.0315968	−	0.999501i
$10$	3.52280	−	31.4259i	0.111401	−	0.993776i
$11$			37.4262i			1.02586i	0.858431	+	0.512928i	$0.171439\pi$
$11$			37.4262i			1.02586i	−0.858431	+	0.512928i	$0.828561\pi$
$12$	21.4921	−	35.5822i	0.517018	−	0.855974i
$13$	−30.8736			−0.658676			−0.329338	−	0.944212i	$-0.606826\pi$
$13$	−30.8736			−0.658676			−0.329338	+	0.944212i	$0.606826\pi$
$14$	73.8850	−	9.57820i	1.41047	−	0.182849i
$15$	29.3211	+	50.1525i	0.504711	+	0.863288i
$16$	55.6776	−	31.5596i	0.869962	−	0.493118i
$17$	−54.0168			−0.770648			−0.385324	−	0.922781i	$-0.625910\pi$
$17$	−54.0168			−0.770648			−0.385324	+	0.922781i	$0.625910\pi$
$18$	7.42002	+	76.0062i	0.0971620	+	0.995269i
$19$	−4.70847			−0.0568524			−0.0284262	−	0.999596i	$-0.509050\pi$
$19$	−4.70847			−0.0568524			−0.0284262	+	0.999596i	$0.509050\pi$
$20$	1.54596	+	89.4294i	0.0172844	+	0.999851i
$21$	−98.2997	+	95.2413i	−1.02146	+	0.989684i
$22$	−13.6091	−	104.979i	−0.131885	−	1.01734i
$23$			129.048i			1.16993i	0.811058	+	0.584966i	$0.198892\pi$
$23$			129.048i			1.16993i	−0.811058	+	0.584966i	$0.801108\pi$
$24$	−47.3457	+	107.621i	−0.402683	+	0.915339i
$25$	−110.811	−	57.8443i	−0.886486	−	0.462755i
$26$	86.5990	−	11.2264i	0.653210	−	0.0846799i
$27$	−94.3921	−	103.794i	−0.672806	−	0.739819i
$28$	−203.761	+	53.7329i	−1.37526	+	0.362663i
$29$	−230.566			−1.47638			−0.738191	−	0.674591i	$-0.764320\pi$
$29$	−230.566			−1.47638			−0.738191	+	0.674591i	$0.764320\pi$
$30$	−100.481	−	130.014i	−0.611508	−	0.791238i
$31$			123.860i			0.717610i	0.933413	+	0.358805i	$0.116816\pi$
$31$			123.860i			0.717610i	−0.933413	+	0.358805i	$0.883184\pi$
$32$	−144.697	+	108.769i	−0.799347	+	0.600869i
$33$	135.323	+	139.668i	0.713838	+	0.736761i
$34$	151.515	−	19.6419i	0.764253	−	0.0990751i
$35$	70.1608	−	286.021i	0.338838	−	1.38132i
$36$	−48.4506	−	210.496i	−0.224308	−	0.974518i
$37$	349.557			1.55316			0.776579	−	0.630020i	$-0.216953\pi$
$37$	349.557			1.55316			0.776579	+	0.630020i	$0.216953\pi$
$38$	13.2070	−	1.71212i	0.0563807	−	0.00730900i
$39$	−115.215	+	111.630i	−0.473055	+	0.458337i
$40$	−36.8551	−	250.283i	−0.145683	−	0.989331i
$41$			74.8414i			0.285080i	0.989789	+	0.142540i	$0.0455269\pi$
$41$			74.8414i			0.285080i	−0.989789	+	0.142540i	$0.954473\pi$
$42$	241.094	−	302.892i	0.885754	−	1.11279i
$43$			364.853i			1.29394i	0.762515	+	0.646971i	$0.223965\pi$
$43$			364.853i			1.29394i	−0.762515	+	0.646971i	$0.776035\pi$
$44$	76.3458	+	289.512i	0.261581	+	0.991946i
$45$	290.759	+	81.1439i	0.963195	+	0.268805i
$46$	−46.9252	−	361.975i	−0.150407	−	1.16022i
$47$		−	45.7642i		−	0.142030i	−0.997475	−	0.0710148i	$-0.977376\pi$
$47$		−	45.7642i		−	0.142030i	0.997475	−	0.0710148i	$-0.0226238\pi$
$48$	93.6687	−	319.090i	0.281665	−	0.959513i
$49$	350.842			1.02286
$50$	331.853	+	121.957i	0.938622	+	0.344947i
$51$	−201.582	+	195.310i	−0.553472	+	0.536252i
$52$	−238.824	+	62.9791i	−0.636903	+	0.167954i
$53$		−	682.936i		−	1.76997i	−0.465619	−	0.884985i	$-0.654168\pi$
$53$		−	682.936i		−	1.76997i	0.465619	−	0.884985i	$-0.345832\pi$
$54$	302.508	+	256.814i	0.762335	+	0.647183i
$55$	−406.390	−	99.6872i	−0.996319	−	0.244397i
$56$	552.003	−	224.811i	1.31722	−	0.536458i
$57$	−17.5712	+	17.0245i	−0.0408309	+	0.0395605i
$58$	646.728	−	83.8397i	1.46413	−	0.189805i
$59$			256.129i			0.565172i	0.959242	+	0.282586i	$0.0911923\pi$
$59$			256.129i			0.565172i	−0.959242	+	0.282586i	$0.908808\pi$
$60$	329.121	+	328.145i	0.708156	+	0.706056i
$61$		−	435.099i		−	0.913259i	−0.889657	−	0.456629i	$-0.849057\pi$
$61$		−	435.099i		−	0.913259i	0.889657	−	0.456629i	$-0.150943\pi$
$62$	−45.0386	−	347.422i	−0.0922566	−	0.711655i
$63$	−22.4718	+	710.849i	−0.0449393	+	1.42156i
$64$	366.318	−	357.708i	0.715466	−	0.698648i
$65$	82.2339	−	335.238i	0.156921	−	0.639711i
$66$	−430.361	−	342.556i	−0.802633	−	0.638876i
$67$		−	862.064i		−	1.57191i	−0.618285	−	0.785954i	$-0.712172\pi$
$67$		−	862.064i		−	1.57191i	0.618285	−	0.785954i	$-0.287828\pi$
$68$	−417.850	+	110.189i	−0.745173	+	0.196506i
$69$	466.603	+	481.586i	0.814092	+	0.840235i
$70$	−92.7936	+	827.787i	−0.158442	+	1.41342i
$71$	−366.537			−0.612675			−0.306338	−	0.951923i	$-0.599104\pi$
$71$	−366.537			−0.612675			−0.306338	+	0.951923i	$0.599104\pi$
$72$	212.443	+	572.814i	0.347732	+	0.937594i
$73$		−	215.240i		−	0.345095i	−0.985001	−	0.172547i	$-0.944800\pi$
$73$		−	215.240i		−	0.345095i	0.985001	−	0.172547i	$-0.0551998\pi$
$74$	−980.492	+	127.108i	−1.54027	+	0.199675i
$75$	−622.676	+	184.796i	−0.958673	+	0.284512i
$76$	−36.4226	+	9.60482i	−0.0549731	+	0.0144967i
$77$		−	985.839i		−	1.45905i
$78$	282.581	−	355.013i	0.410205	−	0.515350i
$79$			340.273i			0.484604i	0.970201	+	0.242302i	$0.0779026\pi$
$79$			340.273i			0.484604i	−0.970201	+	0.242302i	$0.922097\pi$
$80$	194.386	+	688.632i	0.271663	+	0.962392i
$81$	−727.544	−	46.0451i	−0.998003	−	0.0631620i
$82$	−27.2142	−	209.927i	−0.0366501	−	0.282714i
$83$	605.094			0.800214			0.400107	−	0.916469i	$-0.368973\pi$
$83$	605.094			0.800214			0.400107	+	0.916469i	$0.368973\pi$
$84$	−566.120	+	937.266i	−0.735342	+	1.21743i
$85$	143.878	−	586.538i	0.183597	−	0.748458i
$86$	−132.670	−	1023.40i	−0.166350	−	1.28320i
$87$	−860.434	+	833.664i	−1.06032	+	1.02733i
$88$	−319.421	−	784.308i	−0.386936	−	0.950086i
$89$			517.431i			0.616265i	0.951343	+	0.308132i	$0.0997040\pi$
$89$			517.431i			0.616265i	−0.951343	+	0.308132i	$0.900296\pi$
$90$	−845.071	−	121.878i	−0.989759	−	0.142745i
$91$	813.237			0.936818
$92$	263.246	+	998.260i	0.298319	+	1.13126i
$93$	447.843	+	462.225i	0.499346	+	0.515381i
$94$	16.6410	+	128.367i	0.0182595	+	0.140851i
$95$	12.5413	−	51.1265i	0.0135443	−	0.0552155i
$96$	−146.708	+	929.093i	−0.155972	+	0.987762i
$97$			1441.60i			1.50900i	0.656302	+	0.754498i	$0.272120\pi$
$97$			1441.60i			1.50900i	−0.656302	+	0.754498i	$0.727880\pi$
$98$	−984.097	+	127.575i	−1.01438	+	0.131500i
$99$	1010.00	+	31.9288i	1.02534	+	0.0324138i
$100$	−975.180	−	221.414i	−0.975180	−	0.221414i
$101$	422.189			0.415934			0.207967	−	0.978136i	$-0.433315\pi$
$101$	422.189			0.415934			0.207967	+	0.978136i	$0.433315\pi$
$102$	494.408	−	621.136i	0.479938	−	0.602957i
$103$	−1058.99			−1.01307			−0.506533	−	0.862221i	$-0.669073\pi$
$103$	−1058.99			−1.01307			−0.506533	+	0.862221i	$0.669073\pi$
$104$	646.990	−	263.496i	0.610025	−	0.248441i
$105$	−772.343	−	1321.06i	−0.717837	−	1.22783i
$106$	248.332	+	1915.60i	0.227549	+	1.75528i
$107$	−819.034			−0.739991			−0.369995	−	0.929034i	$-0.620641\pi$
$107$	−819.034			−0.739991			−0.369995	+	0.929034i	$0.620641\pi$
$108$	−941.904	−	610.351i	−0.839211	−	0.543806i
$109$		−	1139.42i		−	1.00125i	−0.865663	−	0.500627i	$-0.833103\pi$
$109$		−	1139.42i		−	1.00125i	0.865663	−	0.500627i	$-0.166897\pi$
$110$	1176.15	+	131.845i	1.01947	+	0.114281i
$111$	1304.49	−	1263.90i	1.11546	−	1.08076i
$112$	−1466.60	+	831.307i	−1.23732	+	0.701349i
$113$	1448.12			1.20555			0.602776	−	0.797911i	$-0.294061\pi$
$113$	1448.12			1.20555			0.602776	+	0.797911i	$0.294061\pi$
$114$	43.0959	−	54.1423i	0.0354062	−	0.0444815i
$115$	−1401.26	−	343.729i	−1.13625	−	0.278721i
$116$	−1783.56	+	470.333i	−1.42758	+	0.376460i
$117$	−26.3387	+	833.170i	−0.0208120	+	0.658347i
$118$	−93.1349	−	718.430i	−0.0726590	−	0.560482i
$119$	1422.85			1.09607
$120$	−1042.49	−	800.757i	−0.793050	−	0.609156i
$121$	−69.7203			−0.0523819
$122$	158.213	+	1220.43i	0.117409	+	0.905680i
$123$	270.606	+	279.295i	0.198372	+	0.204742i
$124$	252.662	+	958.126i	0.182982	+	0.693889i
$125$	923.250	−	1049.16i	0.660624	−	0.750717i
$126$	−195.450	−	2002.07i	−0.138191	−	1.41554i
$127$	1075.20			0.751245			0.375623	−	0.926773i	$-0.377429\pi$
$127$	1075.20			0.751245			0.375623	+	0.926773i	$0.377429\pi$
$128$	−897.436	+	1136.56i	−0.619710	+	0.784831i
$129$	1319.21	+	1361.57i	0.900384	+	0.929298i
$130$	−108.761	+	970.231i	−0.0733769	+	0.654576i
$131$			729.865i			0.486784i	0.969928	+	0.243392i	$0.0782601\pi$
$131$			729.865i			0.486784i	−0.969928	+	0.243392i	$0.921740\pi$
$132$	1331.71	+	804.366i	0.878107	+	0.530387i
$133$	124.025			0.0808598
$134$	313.468	+	2418.05i	0.202086	+	1.55886i
$135$	1378.46	−	748.488i	0.878805	−	0.477182i
$136$	1131.98	−	461.016i	0.713727	−	0.290675i
$137$	−505.557			−0.315275			−0.157637	−	0.987497i	$-0.550388\pi$
$137$	−505.557			−0.315275			−0.157637	+	0.987497i	$0.550388\pi$
$138$	−1483.92	−	1181.16i	−0.915358	−	0.728602i
$139$	−677.815			−0.413608			−0.206804	−	0.978382i	$-0.566306\pi$
$139$	−677.815			−0.413608			−0.206804	+	0.978382i	$0.566306\pi$
$140$	−40.7221	−	2355.65i	−0.0245832	−	1.42206i
$141$	−165.471	−	170.784i	−0.0988308	−	0.102004i
$142$	1028.12	−	133.282i	0.607591	−	0.0787660i
$143$		−	1155.48i		−	0.675707i
$144$	−804.184	−	1529.47i	−0.465384	−	0.885109i
$145$	614.129	−	2503.59i	0.351729	−	1.43387i
$146$	78.2666	+	603.739i	0.0443657	+	0.342231i
$147$	1309.28	−	1268.55i	0.734612	−	0.711756i
$148$	2704.02	−	713.063i	1.50182	−	0.396037i
$149$	−2640.39			−1.45174			−0.725869	−	0.687833i	$-0.758562\pi$
$149$	−2640.39			−1.45174			−0.725869	+	0.687833i	$0.758562\pi$
$150$	1679.38	−	744.765i	0.914140	−	0.405399i
$151$			2466.32i			1.32918i	0.747207	+	0.664591i	$0.231394\pi$
$151$			2466.32i			1.32918i	−0.747207	+	0.664591i	$0.768606\pi$
$152$	98.6712	−	40.1853i	0.0526532	−	0.0214438i
$153$	−46.0825	+	1457.73i	−0.0243500	+	0.770263i
$154$	358.476	+	2765.24i	0.187577	+	1.44694i
$155$	−1344.92	−	329.910i	−0.696948	−	0.170961i
$156$	−663.536	+	1098.55i	−0.340548	+	0.563810i
$157$	−1553.13			−0.789512			−0.394756	−	0.918786i	$-0.629171\pi$
$157$	−1553.13			−0.789512			−0.394756	+	0.918786i	$0.629171\pi$
$158$	−123.732	−	954.452i	−0.0623011	−	0.480583i
$159$	−2469.31	−	2548.60i	−1.23163	−	1.27118i
$160$	−795.648	−	1860.90i	−0.393135	−	0.919481i
$161$		−	3399.25i		−	1.66396i
$162$	2057.47	−	135.399i	0.997842	−	0.0656662i
$163$			3936.58i			1.89164i	0.324694	+	0.945819i	$0.394739\pi$
$163$			3936.58i			1.89164i	−0.324694	+	0.945819i	$0.605261\pi$
$164$	152.669	+	578.940i	0.0726919	+	0.275656i
$165$	−1877.02	+	1097.38i	−0.885610	+	0.517761i
$166$	−1697.26	+	220.027i	−0.793573	+	0.102876i
$167$		−	1998.86i		−	0.926208i	−0.886304	−	0.463104i	$-0.846736\pi$
$167$		−	1998.86i		−	0.926208i	0.886304	−	0.463104i	$-0.153264\pi$
$168$	1247.13	−	2834.85i	0.572726	−	1.30186i
$169$	−1243.82			−0.566146
$170$	−190.290	+	1697.53i	−0.0858506	+	0.765851i
$171$	−4.01686	+	127.065i	−0.00179635	+	0.0568241i
$172$	744.264	+	2822.34i	0.329940	+	1.25117i
$173$			2816.75i			1.23788i	0.785438	+	0.618940i	$0.212438\pi$
$173$			2816.75i			1.23788i	−0.785438	+	0.618940i	$0.787562\pi$
$174$	2110.34	−	2651.27i	0.919451	−	1.15513i
$175$	2918.85	+	1523.67i	1.26083	+	0.658164i
$176$	1181.15	+	2083.80i	0.505869	+	0.892457i
$177$	926.091	+	955.830i	0.393273	+	0.405901i
$178$	−188.151	−	1451.37i	−0.0792275	−	0.611151i
$179$		−	905.857i		−	0.378251i	−0.981953	−	0.189125i	$-0.939435\pi$
$179$		−	905.857i		−	0.378251i	0.981953	−	0.189125i	$-0.0605653\pi$
$180$	2414.71	+	34.5732i	0.999898	+	0.0143163i
$181$			174.804i			0.0717851i	0.999356	+	0.0358925i	$0.0114274\pi$
$181$			174.804i			0.0717851i	−0.999356	+	0.0358925i	$0.988573\pi$
$182$	−2281.09	+	295.713i	−0.929044	+	0.120438i
$183$	−1573.20	−	1623.72i	−0.635487	−	0.655894i
$184$	−1101.39	−	2704.35i	−0.441279	−	1.08352i
$185$	−931.069	+	3795.64i	−0.370019	+	1.50844i
$186$	−1424.26	−	1133.67i	−0.561460	−	0.446908i
$187$		−	2021.65i		−	0.790574i
$188$	−93.3546	−	354.011i	−0.0362159	−	0.137335i
$189$	2486.37	+	2734.02i	0.956915	+	1.05223i
$190$	−16.5870	+	147.968i	−0.00633340	+	0.0564986i
$191$	−1267.32			−0.480107			−0.240053	−	0.970760i	$-0.577165\pi$
$191$	−1267.32			−0.480107			−0.240053	+	0.970760i	$0.577165\pi$
$192$	73.6672	−	2659.41i	0.0276899	−	0.999617i
$193$			2265.21i			0.844838i	0.906401	+	0.422419i	$0.138819\pi$
$193$			2265.21i			0.844838i	−0.906401	+	0.422419i	$0.861181\pi$
$194$	−524.203	−	4043.63i	−0.193998	−	1.49647i
$195$	−905.246	−	1548.39i	−0.332441	−	0.568627i
$196$	2713.96	−	715.684i	0.989052	−	0.260818i
$197$			630.779i			0.228128i	0.993473	+	0.114064i	$0.0363868\pi$
$197$			630.779i			0.228128i	−0.993473	+	0.114064i	$0.963613\pi$
$198$	−2844.62	+	277.703i	−1.02100	+	0.0996743i
$199$			3357.04i			1.19585i	0.801551	+	0.597926i	$0.204008\pi$
$199$			3357.04i			1.19585i	−0.801551	+	0.597926i	$0.795992\pi$
$200$	2815.85	+	266.458i	0.995553	+	0.0942072i
$201$	−3116.98	−	3217.08i	−1.09381	−	1.12893i
$202$	−1184.22	+	153.518i	−0.412482	+	0.0534728i
$203$	6073.32			2.09982
$204$	−1160.93	+	1922.04i	−0.398439	+	0.659655i
$205$	−812.660	−	199.345i	−0.276871	−	0.0679165i
$206$	2970.43	−	385.077i	1.00466	−	0.130241i
$207$	3482.56	+	110.093i	1.16935	+	0.0369661i
$208$	−1718.97	+	974.356i	−0.573023	+	0.324805i
$209$		−	176.220i		−	0.0583225i
$210$	2646.76	+	3424.68i	0.869732	+	1.12536i
$211$	3809.37			1.24288			0.621440	−	0.783462i	$-0.286548\pi$
$211$	3809.37			1.24288			0.621440	+	0.783462i	$0.286548\pi$
$212$	−1393.12	−	5282.89i	−0.451321	−	1.71146i
$213$	−1367.85	+	1325.30i	−0.440018	+	0.426327i
$214$	2297.35	−	297.821i	0.733850	−	0.0951338i
$215$	−3961.73	−	971.810i	−1.25669	−	0.308265i
$216$	2863.94	+	1369.51i	0.902159	+	0.431404i
$217$		−	3262.58i		−	1.02064i
$218$	414.322	+	3196.03i	0.128722	+	0.992946i
$219$	−778.248	−	803.239i	−0.240133	−	0.247844i
$220$	−3347.00	+	57.8596i	−1.02570	+	0.0177313i
$221$	1667.69			0.507607
$222$	−3199.44	+	4019.53i	−0.967264	+	1.21519i
$223$	4261.82			1.27979			0.639894	−	0.768463i	$-0.278978\pi$
$223$	4261.82			1.27979			0.639894	+	0.768463i	$0.278978\pi$
$224$	3811.46	−	2865.07i	1.13689	−	0.854601i
$225$	−1655.55	+	2941.05i	−0.490534	+	0.871422i
$226$	−4061.90	+	526.571i	−1.19555	+	0.154987i
$227$	−4481.95			−1.31047			−0.655236	−	0.755424i	$-0.727431\pi$
$227$	−4481.95			−1.31047			−0.655236	+	0.755424i	$0.727431\pi$
$228$	−101.195	+	167.538i	−0.0293938	+	0.0486642i
$229$		−	1157.74i		−	0.334085i	−0.985950	−	0.167042i	$-0.946578\pi$
$229$		−	1157.74i		−	0.334085i	0.985950	−	0.167042i	$-0.0534216\pi$
$230$	4055.47	+	454.611i	1.16265	+	0.130331i
$231$	−3564.52	−	3678.98i	−1.01527	−	1.04788i
$232$	4831.78	−	1967.81i	1.36733	−	0.556867i
$233$	2549.55			0.716852			0.358426	−	0.933558i	$-0.383314\pi$
$233$	2549.55			0.716852			0.358426	+	0.933558i	$0.383314\pi$
$234$	−229.083	−	2346.58i	−0.0639983	−	0.655559i
$235$	496.927	+	121.896i	0.137940	+	0.0338367i
$236$	522.478	+	1981.30i	0.144112	+	0.546490i
$237$	1230.33	+	1269.84i	0.337210	+	0.348039i
$238$	−3991.04	+	517.384i	−1.08698	+	0.140912i
$239$	−714.592			−0.193402			−0.0967010	−	0.995313i	$-0.530829\pi$
$239$	−714.592			−0.193402			−0.0967010	+	0.995313i	$0.530829\pi$
$240$	3215.32	+	1867.01i	0.864783	+	0.502146i
$241$	−2330.00			−0.622774			−0.311387	−	0.950283i	$-0.600794\pi$
$241$	−2330.00			−0.622774			−0.311387	+	0.950283i	$0.600794\pi$
$242$	195.562	−	25.3520i	0.0519472	−	0.00673426i
$243$	−2881.56	+	2458.77i	−0.760708	+	0.649094i
$244$	−887.561	−	3365.74i	−0.232870	−	0.883070i
$245$	−934.492	+	3809.60i	−0.243684	+	0.993413i
$246$	−860.596	−	685.012i	−0.223047	−	0.177540i
$247$	145.367			0.0374473
$248$	−1057.11	−	2595.63i	−0.270670	−	0.664607i
$249$	2258.11	−	2187.85i	0.574706	−	0.556825i
$250$	−2208.18	+	3278.56i	−0.558629	+	0.829417i
$251$			3006.17i			0.755966i	0.925812	+	0.377983i	$0.123382\pi$
$251$			3006.17i			0.755966i	−0.925812	+	0.377983i	$0.876618\pi$
$252$	1276.23	+	5544.65i	0.319028	+	1.38603i
$253$	−4829.79			−1.20018
$254$	−3015.88	+	390.968i	−0.745011	+	0.0965807i
$255$	−1583.83	−	2709.08i	−0.388954	−	0.665291i
$256$	2103.99	−	3514.32i	0.513669	−	0.857989i
$257$	−7814.60			−1.89674			−0.948369	−	0.317170i	$-0.897267\pi$
$257$	−7814.60			−1.89674			−0.948369	+	0.317170i	$0.897267\pi$
$258$	−4195.41	−	3339.44i	−1.01238	−	0.805832i
$259$	−9207.64			−2.20902
$260$	−47.7294	−	2761.00i	−0.0113848	−	0.658578i
$261$	−196.699	+	6222.18i	−0.0466490	+	1.47565i
$262$	−265.397	−	2047.24i	−0.0625813	−	0.482744i
$263$			4366.70i			1.02381i	0.859042	+	0.511905i	$0.171060\pi$
$263$			4366.70i			1.02381i	−0.859042	+	0.511905i	$0.828940\pi$
$264$	−4027.86	−	1771.97i	−0.939007	−	0.413095i
$265$	7415.61	+	1819.05i	1.71901	+	0.421672i
$266$	−347.885	+	45.0987i	−0.0801888	+	0.0103954i
$267$	1870.89	+	1930.96i	0.428825	+	0.442596i
$268$	−1758.53	−	6668.54i	−0.400818	−	1.51995i
$269$	4336.63			0.982933			0.491467	−	0.870896i	$-0.336461\pi$
$269$	4336.63			0.982933			0.491467	+	0.870896i	$0.336461\pi$
$270$	−3594.34	+	2600.72i	−0.810165	+	0.586202i
$271$			4429.78i			0.992952i	0.868050	+	0.496476i	$0.165373\pi$
$271$			4429.78i			0.992952i	−0.868050	+	0.496476i	$0.834627\pi$
$272$	−3007.53	+	1704.75i	−0.670434	+	0.380020i
$273$	3034.86	−	2940.44i	0.672814	−	0.651881i
$274$	1418.07	−	183.833i	0.312659	−	0.0405320i
$275$	2164.89	−	4147.23i	0.474720	−	0.909408i
$276$	4591.82	+	2773.51i	1.00143	+	0.604876i
$277$	−3024.43			−0.656030			−0.328015	−	0.944673i	$-0.606380\pi$
$277$	−3024.43			−0.656030			−0.328015	+	0.944673i	$0.606380\pi$
$278$	1901.24	−	246.470i	0.410176	−	0.0531738i
$279$	3342.55	+	105.667i	0.717252	+	0.0226742i
$280$	970.796	+	6592.68i	0.207201	+	1.40710i
$281$		−	330.776i		−	0.0702223i	−0.999383	−	0.0351112i	$-0.988821\pi$
$281$		−	330.776i		−	0.0702223i	0.999383	−	0.0351112i	$-0.0111785\pi$
$282$	526.239	+	418.873i	0.111124	+	0.0884522i
$283$		−	5051.97i		−	1.06116i	−0.847635	−	0.530580i	$-0.821974\pi$
$283$		−	5051.97i		−	1.06116i	0.847635	−	0.530580i	$-0.178026\pi$
$284$	−2835.37	+	747.700i	−0.592423	+	0.156225i
$285$	−138.057	−	236.141i	−0.0286941	−	0.0490801i
$286$	420.161	+	3241.07i	0.0868695	+	0.670100i
$287$		−	1971.39i		−	0.405461i
$288$	2811.85	+	3997.67i	0.575312	+	0.817934i
$289$	−1995.18			−0.406102
$290$	−812.238	+	7245.76i	−0.164470	+	1.46719i
$291$	5212.44	+	5379.82i	1.05003	+	1.08375i
$292$	−439.069	−	1665.00i	−0.0879950	−	0.333688i
$293$			1269.80i			0.253182i	0.991955	+	0.126591i	$0.0404036\pi$
$293$			1269.80i			0.253182i	−0.991955	+	0.126591i	$0.959596\pi$
$294$	−3211.21	+	4034.31i	−0.637012	+	0.800292i
$295$	−2781.16	−	682.217i	−0.548899	−	0.134645i
$296$	−7325.36	+	2983.36i	−1.43844	+	0.585825i
$297$	3884.60	−	3532.74i	0.758948	−	0.690203i
$298$	7406.17	−	960.111i	1.43969	−	0.186637i
$299$		−	3984.18i		−	0.770606i
$300$	−4439.78	+	2699.70i	−0.854436	+	0.519557i
$301$		−	9610.54i		−	1.84034i
$302$	−896.817	−	6917.93i	−0.170881	−	1.31815i
$303$	1575.54	−	1526.52i	0.298720	−	0.289426i
$304$	−262.156	+	148.597i	−0.0494595	+	0.0280350i
$305$	4724.50	+	1158.92i	0.886963	+	0.217572i
$306$	−400.806	−	4105.62i	−0.0748777	−	0.767001i
$307$			5056.64i			0.940057i	0.882651	+	0.470029i	$0.155756\pi$
$307$			5056.64i			0.940057i	−0.882651	+	0.470029i	$0.844244\pi$
$308$	−2011.02	−	7626.01i	−0.372040	−	1.41082i
$309$	−3951.99	+	3829.03i	−0.727575	+	0.704938i
$310$	3892.42	+	436.334i	0.713143	+	0.0799422i
$311$	2886.68			0.526329			0.263165	−	0.964751i	$-0.415234\pi$
$311$	2886.68			0.526329			0.263165	+	0.964751i	$0.415234\pi$
$312$	1461.73	−	3322.66i	0.265238	−	0.602912i
$313$			5771.03i			1.04217i	0.853506	+	0.521083i	$0.174472\pi$
$313$			5771.03i			1.04217i	−0.853506	+	0.521083i	$0.825528\pi$
$314$	4356.47	−	564.758i	0.782961	−	0.101500i
$315$	−7658.84	−	2137.40i	−1.36993	−	0.382314i
$316$	694.125	+	2632.20i	0.123568	+	0.468585i
$317$			1124.02i			0.199153i	0.995030	+	0.0995765i	$0.0317488\pi$
$317$			1124.02i			0.199153i	−0.995030	+	0.0995765i	$0.968251\pi$
$318$	7853.03	+	6250.81i	1.38483	+	1.10229i
$319$		−	8629.22i		−	1.51456i
$320$	2908.43	+	4930.42i	0.508081	+	0.861309i
$321$	−3056.50	+	2961.40i	−0.531455	+	0.514920i
$322$	1236.05	+	9534.74i	0.213921	+	1.65016i
$323$	254.337			0.0438132
$324$	−5721.89	+	1127.94i	−0.981119	+	0.193405i
$325$	3421.12	+	1785.86i	0.583907	+	0.304805i
$326$	−1431.44	−	11041.9i	−0.243191	−	1.87594i
$327$	−4119.83	−	4252.13i	−0.696719	−	0.719092i
$328$	−638.747	−	1568.39i	−0.107527	−	0.264023i
$329$			1205.47i			0.202005i
$330$	4865.92	−	3760.62i	0.811697	−	0.627319i
$331$	10427.1			1.73150			0.865752	−	0.500474i	$-0.166841\pi$
$331$	10427.1			1.73150			0.865752	+	0.500474i	$0.166841\pi$
$332$	4680.74	−	1234.33i	0.773762	−	0.204045i
$333$	298.212	−	9433.33i	0.0490748	−	1.55238i
$334$	726.836	+	5606.72i	0.119074	+	0.918522i
$335$	9360.65	+	2296.17i	1.52665	+	0.374486i
$336$	−2467.32	+	8405.10i	−0.400605	+	1.36469i
$337$		−	4932.89i		−	0.797364i	−0.917089	−	0.398682i	$-0.869468\pi$
$337$		−	4932.89i		−	0.797364i	0.917089	−	0.398682i	$-0.130532\pi$
$338$	3488.87	−	452.285i	0.561448	−	0.0727842i
$339$	5404.12	−	5235.99i	0.865816	−	0.838878i
$340$	−83.5081	−	4830.69i	−0.0133202	−	0.770533i
$341$	−4635.61			−0.736165
$342$	−34.9369	−	357.873i	−0.00552390	−	0.0565835i
$343$	−206.574			−0.0325187
$344$	−3113.90	−	7645.90i	−0.488053	−	1.19837i
$345$	−6472.10	+	3783.83i	−1.00999	+	0.590478i
$346$	−1024.24	−	7900.85i	−0.159143	−	1.22761i
$347$	−3247.36			−0.502385			−0.251192	−	0.967937i	$-0.580823\pi$
$347$	−3247.36			−0.502385			−0.251192	+	0.967937i	$0.580823\pi$
$348$	−4955.34	+	8204.05i	−0.763317	+	1.26375i
$349$		−	11995.6i		−	1.83986i	−0.392086	−	0.919929i	$-0.628246\pi$
$349$		−	11995.6i		−	1.83986i	0.392086	−	0.919929i	$-0.371754\pi$
$350$	−8741.30	−	3212.46i	−1.33498	−	0.490609i
$351$	2914.22	+	3204.48i	0.443161	+	0.487301i
$352$	−4070.81	−	5415.47i	−0.616406	−	0.820016i
$353$	−6654.12			−1.00330			−0.501648	−	0.865072i	$-0.667273\pi$
$353$	−6654.12			−1.00330			−0.501648	+	0.865072i	$0.667273\pi$
$354$	−2945.21	−	2344.31i	−0.442192	−	0.351974i
$355$	976.296	−	3980.01i	0.145962	−	0.595034i
$356$	1055.51	+	4002.61i	0.157140	+	0.595894i
$357$	5309.84	−	5144.64i	0.787189	−	0.762697i
$358$	329.392	+	2540.89i	0.0486283	+	0.375112i
$359$	5238.10			0.770073			0.385037	−	0.922901i	$-0.374189\pi$
$359$	5238.10			0.770073			0.385037	+	0.922901i	$0.374189\pi$
$360$	−6785.72	+	781.071i	−0.993441	+	0.114350i
$361$	−6836.83			−0.996768
$362$	−63.5632	−	490.318i	−0.00922875	−	0.0711894i
$363$	−260.184	+	252.089i	−0.0376202	+	0.0364497i
$364$	6290.84	−	1658.93i	0.905851	−	0.238877i
$365$	2337.17	+	573.306i	0.335159	+	0.0822143i
$366$	5003.18	+	3982.40i	0.714536	+	0.568753i
$367$	−3524.68			−0.501326			−0.250663	−	0.968074i	$-0.580649\pi$
$367$	−3524.68			−0.501326			−0.250663	+	0.968074i	$0.580649\pi$
$368$	4072.71	+	7185.10i	0.576915	+	1.01780i
$369$	2019.71	+	63.8482i	0.284937	+	0.00900760i
$370$	1231.42	−	10985.2i	0.173023	−	1.54349i
$371$			17989.1i			2.51738i
$372$	4407.21	+	2662.01i	0.614256	+	0.371018i
$373$	3078.40			0.427328			0.213664	−	0.976907i	$-0.431460\pi$
$373$	3078.40			0.427328			0.213664	+	0.976907i	$0.431460\pi$
$374$	735.121	+	5670.63i	0.101637	+	0.784014i
$375$	−348.052	−	7253.50i	−0.0479289	−	0.998851i
$376$	390.583	+	959.040i	0.0535712	+	0.131539i
$377$	7118.41			0.972458
$378$	−7968.32	−	6764.70i	−1.08425	−	0.920472i
$379$	−3244.44			−0.439725			−0.219863	−	0.975531i	$-0.570561\pi$
$379$	−3244.44			−0.439725			−0.219863	+	0.975531i	$0.570561\pi$
$380$	−7.27912	−	421.075i	−0.000982661	−	0.0568440i
$381$	4012.45	−	3887.61i	0.539538	−	0.522751i
$382$	3554.79	−	460.831i	0.476123	−	0.0617229i
$383$			5023.39i			0.670191i	0.942184	+	0.335096i	$0.108769\pi$
$383$			5023.39i			0.670191i	−0.942184	+	0.335096i	$0.891231\pi$
$384$	760.395	+	7486.31i	0.101051	+	0.994881i
$385$	10704.7	+	2625.85i	1.41704	+	0.347599i
$386$	−823.688	−	6353.83i	−0.108613	−	0.837827i
$387$	9846.10	+	311.261i	1.29330	+	0.0408844i
$388$	2940.73	+	11151.6i	0.384776	+	1.45912i
$389$	−289.283			−0.0377049			−0.0188525	−	0.999822i	$-0.506001\pi$
$389$	−289.283			−0.0377049			−0.0188525	+	0.999822i	$0.506001\pi$
$390$	3102.21	+	4013.99i	0.402785	+	0.521170i
$391$		−	6970.78i		−	0.901605i
$392$	−7352.30	+	2994.33i	−0.947314	+	0.385807i
$393$	2638.99	+	2723.73i	0.338726	+	0.349604i
$394$	−229.367	−	1769.31i	−0.0293283	−	0.226235i
$395$	−3694.83	−	906.342i	−0.470651	−	0.115451i
$396$	7878.06	−	1813.32i	0.999716	−	0.230108i
$397$	10915.5			1.37993			0.689964	−	0.723843i	$-0.257626\pi$
$397$	10915.5			1.37993			0.689964	+	0.723843i	$0.257626\pi$
$398$	−1220.71	−	9416.36i	−0.153740	−	1.18593i
$399$	462.841	−	448.441i	0.0580728	−	0.0562659i
$400$	−7995.22	+	276.509i	−0.999402	+	0.0345636i
$401$		−	9711.60i		−	1.20941i	−0.796449	−	0.604706i	$-0.793291\pi$
$401$		−	9711.60i		−	1.20941i	0.796449	−	0.604706i	$-0.206709\pi$
$402$	9912.81	+	7890.34i	1.22987	+	0.978941i
$403$		−	3824.00i		−	0.472673i
$404$	3265.86	−	861.224i	0.402185	−	0.106058i
$405$	2437.84	−	7777.34i	0.299105	−	0.954220i
$406$	−17035.4	+	2208.41i	−2.08240	+	0.269955i
$407$			13082.6i			1.59332i
$408$	2557.46	−	5813.37i	0.310327	−	0.705404i
$409$	611.519			0.0739307			0.0369653	−	0.999317i	$-0.488231\pi$
$409$	611.519			0.0739307			0.0369653	+	0.999317i	$0.488231\pi$
$410$	2351.96	+	263.651i	0.283305	+	0.0317581i
$411$	−1886.65	+	1827.95i	−0.226428	+	0.219383i
$412$	−8191.91	+	2160.25i	−0.979578	+	0.258320i
$413$		−	6746.66i		−	0.803830i
$414$	−9808.47	+	957.542i	−1.16440	+	0.113673i
$415$	−1611.71	+	6570.37i	−0.190640	+	0.777173i
$416$	4467.32	−	3358.09i	0.526511	−	0.395778i
$417$	−2529.49	+	2450.79i	−0.297050	+	0.287807i
$418$	64.0780	+	494.289i	0.00749798	+	0.0578385i
$419$		−	5936.35i		−	0.692147i	−0.938207	−	0.346073i	$-0.887515\pi$
$419$		−	5936.35i		−	0.692147i	0.938207	−	0.346073i	$-0.112485\pi$
$420$	−8669.34	−	8643.64i	−1.00719	−	1.00421i
$421$			7758.48i			0.898159i	0.893492	+	0.449080i	$0.148248\pi$
$421$			7758.48i			0.898159i	−0.893492	+	0.449080i	$0.851752\pi$
$422$	−10685.1	+	1385.18i	−1.23257	+	0.159786i
$423$	−1235.02	−	39.0421i	−0.141959	−	0.00448768i
$424$	5828.64	+	14311.7i	0.667603	+	1.63924i
$425$	5985.65	+	3124.57i	0.683169	+	0.356621i
$426$	3354.86	−	4214.78i	0.381557	−	0.479359i
$427$			11460.9i			1.29890i
$428$	−6335.68	+	1670.75i	−0.715530	+	0.188689i
$429$	−4177.89	−	4312.06i	−0.470188	−	0.485287i
$430$	11465.8	+	1285.30i	1.28589	+	0.144146i
$431$	−3682.13			−0.411513			−0.205756	−	0.978603i	$-0.565965\pi$
$431$	−3682.13			−0.411513			−0.205756	+	0.978603i	$0.565965\pi$
$432$	−8531.21	−	2800.01i	−0.950134	−	0.311842i
$433$		−	9874.56i		−	1.09594i	−0.836499	−	0.547969i	$-0.815401\pi$
$433$		−	9874.56i		−	1.09594i	0.836499	−	0.547969i	$-0.184599\pi$
$434$	1186.36	+	9151.40i	0.131214	+	1.01217i
$435$	−6760.45	−	11563.5i	−0.745146	−	1.27454i
$436$	−2324.31	−	8814.06i	−0.255308	−	0.968158i
$437$		−	607.620i		−	0.0665135i
$438$	2475.03	+	1970.06i	0.270003	+	0.214916i
$439$			12519.6i			1.36111i	0.732698	+	0.680554i	$0.238261\pi$
$439$			12519.6i			1.36111i	−0.732698	+	0.680554i	$0.761739\pi$
$440$	9367.15	−	1379.35i	1.01491	−	0.149449i
$441$	299.308	−	9468.01i	0.0323192	−	1.02235i
$442$	−4677.80	+	606.415i	−0.503395	+	0.0652584i
$443$	−7308.73			−0.783856			−0.391928	−	0.919996i	$-0.628192\pi$
$443$	−7308.73			−0.783856			−0.391928	+	0.919996i	$0.628192\pi$
$444$	7512.70	−	12438.0i	0.803011	−	1.32946i
$445$	−5618.48	−	1378.21i	−0.598521	−	0.146817i
$446$	−11954.2	+	1549.71i	−1.26917	+	0.164531i
$447$	−9853.48	+	9546.91i	−1.04263	+	1.01019i
$448$	−9649.15	+	9422.34i	−1.01759	+	0.993669i
$449$			7884.95i			0.828761i	0.910104	+	0.414380i	$0.136002\pi$
$449$			7884.95i			0.828761i	−0.910104	+	0.414380i	$0.863998\pi$
$450$	3574.31	−	8851.52i	0.374432	−	0.927254i
$451$	−2801.03			−0.292451
$452$	11202.0	−	2954.02i	1.16570	−	0.307401i
$453$	8917.54	+	9203.90i	0.924906	+	0.954607i
$454$	12571.7	−	1629.75i	1.29960	−	0.168475i
$455$	−2166.11	+	8830.47i	−0.223184	+	0.909844i
$456$	222.926	−	506.732i	0.0228935	−	0.0520393i
$457$			197.196i			0.0201847i	0.999949	+	0.0100924i	$0.00321256\pi$
$457$			197.196i			0.0201847i	−0.999949	+	0.0100924i	$0.996787\pi$
$458$	420.982	+	3247.40i	0.0429502	+	0.331312i
$459$	5098.76	+	5606.61i	0.518496	+	0.570140i
$460$	−11540.7	+	199.504i	−1.16976	+	0.0202216i
$461$	8936.49			0.902850			0.451425	−	0.892309i	$-0.350916\pi$
$461$	8936.49			0.902850			0.451425	+	0.892309i	$0.350916\pi$
$462$	11336.1	+	9023.24i	1.14156	+	0.908656i
$463$	−18183.1			−1.82514			−0.912571	−	0.408919i	$-0.865906\pi$
$463$	−18183.1			−1.82514			−0.912571	+	0.408919i	$0.865906\pi$
$464$	−12837.4	+	7276.57i	−1.28440	+	0.728031i
$465$	−6211.89	+	3631.71i	−0.619505	+	0.362186i
$466$	−7151.37	+	927.079i	−0.710903	+	0.0921590i
$467$	81.4817			0.00807393			0.00403696	−	0.999992i	$-0.498715\pi$
$467$	81.4817			0.00807393			0.00403696	+	0.999992i	$0.498715\pi$
$468$	1495.84	+	6498.76i	0.147746	+	0.641892i
$469$			22707.5i			2.23568i
$470$	−1438.18	−	161.218i	−0.141146	−	0.0158222i
$471$	−5796.03	+	5615.69i	−0.567021	+	0.549379i
$472$	−2185.98	−	5367.47i	−0.213173	−	0.523428i
$473$	−13655.0			−1.32740
$474$	−3912.78	−	3114.47i	−0.379156	−	0.301798i
$475$	521.749	+	272.358i	0.0503989	+	0.0263087i
$476$	11006.5	−	2902.48i	1.05984	−	0.279485i
$477$	−18430.1	−	582.622i	−1.76909	−	0.0559254i
$478$	2004.40	−	259.843i	0.191797	−	0.0248639i
$479$	−19196.4			−1.83112			−0.915559	−	0.402183i	$-0.868252\pi$
$479$	−19196.4			−1.83112			−0.915559	+	0.402183i	$0.868252\pi$
$480$	−9697.72	−	4067.71i	−0.922163	−	0.386802i
$481$	−10792.1			−1.02303
$482$	6535.55	−	847.246i	0.617606	−	0.0800643i
$483$	−12290.7	−	12685.4i	−1.15786	−	1.19504i
$484$	−539.325	+	142.223i	−0.0506504	+	0.0133567i
$485$	−15653.5	−	3839.81i	−1.46555	−	0.359498i
$486$	7188.58	−	7944.53i	0.670947	−	0.741505i
$487$	2061.46			0.191814			0.0959072	−	0.995390i	$-0.469425\pi$
$487$	2061.46			0.191814			0.0959072	+	0.995390i	$0.469425\pi$
$488$	3713.43	+	9118.00i	0.344466	+	0.845804i
$489$	14233.6	+	14690.7i	1.31629	+	1.35856i
$490$	1235.95	−	11025.6i	0.113948	−	1.01650i
$491$		−	10688.0i		−	0.982371i	−0.871055	−	0.491186i	$-0.836564\pi$
$491$		−	10688.0i		−	0.982371i	0.871055	−	0.491186i	$-0.163436\pi$
$492$	2663.02	+	1608.50i	0.244021	+	0.147391i
$493$	12454.5			1.13777
$494$	−407.748	+	52.8591i	−0.0371366	+	0.00481426i
$495$	−3036.91	+	10882.0i	−0.275755	+	0.988100i
$496$	3908.97	+	6896.23i	0.353867	+	0.624294i
$497$	9654.91			0.871392
$498$	−5538.34	+	6957.93i	−0.498351	+	0.626089i
$499$	−5962.49			−0.534906			−0.267453	−	0.963571i	$-0.586182\pi$
$499$	−5962.49			−0.534906			−0.267453	+	0.963571i	$0.586182\pi$
$500$	5001.67	−	9999.16i	0.447363	−	0.894352i
$501$	−7227.33	−	7459.42i	−0.644498	−	0.665194i
$502$	−1093.12	−	8432.16i	−0.0971876	−	0.749693i
$503$		−	9237.66i		−	0.818861i	−0.912341	−	0.409430i	$-0.865727\pi$
$503$		−	9237.66i		−	0.818861i	0.912341	−	0.409430i	$-0.134273\pi$
$504$	−5595.95	−	15088.4i	−0.494570	−	1.33352i
$505$	−1124.53	+	4584.30i	−0.0990908	+	0.403958i
$506$	13547.3	−	1756.23i	1.19022	−	0.154296i
$507$	−4641.74	+	4497.32i	−0.406601	+	0.393950i
$508$	8317.23	−	2193.29i	0.726412	−	0.191559i
$509$	9365.55			0.815561			0.407781	−	0.913080i	$-0.366303\pi$
$509$	9365.55			0.815561			0.407781	+	0.913080i	$0.366303\pi$
$510$	5427.67	+	7022.93i	0.471257	+	0.609766i
$511$			5669.61i			0.490820i
$512$	−4623.70	+	10622.6i	−0.399102	+	0.916906i
$513$	444.442	+	488.709i	0.0382507	+	0.0420605i
$514$	21919.6	−	2841.58i	1.88100	−	0.243846i
$515$	2820.70	−	11499.0i	0.241350	−	0.983897i
$516$	12982.3	+	7841.43i	1.10758	+	0.668992i
$517$	1712.78			0.145702
$518$	25827.0	−	3348.13i	2.19068	−	0.283993i
$519$	10184.6	+	10511.6i	0.861374	+	0.889035i
$520$	1137.85	+	7727.14i	0.0959576	+	0.651649i
$521$		−	10927.3i		−	0.918874i	−0.888210	−	0.459437i	$-0.848051\pi$
$521$		−	10927.3i		−	0.918874i	0.888210	−	0.459437i	$-0.151949\pi$
$522$	−1710.81	−	17524.5i	−0.143448	−	1.46940i
$523$		−	5024.90i		−	0.420122i	−0.977688	−	0.210061i	$-0.932634\pi$
$523$		−	5024.90i		−	0.420122i	0.977688	−	0.210061i	$-0.0673662\pi$
$524$	1488.86	+	5645.91i	0.124124	+	0.470693i
$525$	16401.8	−	4867.69i	1.36350	−	0.404654i
$526$	−1587.84	−	12248.4i	−0.131622	−	1.01531i
$527$		−	6690.53i		−	0.553025i
$528$	11942.3	+	3505.66i	0.984323	+	0.288948i
$529$	−4486.47			−0.368741
$530$	−21461.9	−	2405.84i	−1.75895	−	0.197176i
$531$	6912.03	+	218.507i	0.564890	+	0.0178576i
$532$	959.404	−	252.999i	0.0781869	−	0.0206183i
$533$		−	2310.62i		−	0.187775i
$534$	−5949.90	−	4735.97i	−0.482167	−	0.383793i
$535$	2181.55	−	8893.42i	0.176293	−	0.718684i
$536$	7357.44	+	18065.5i	0.592897	+	1.45580i
$537$	−3275.33	−	3380.50i	−0.263204	−	0.271656i
$538$	−12164.1	+	1576.91i	−0.974776	+	0.126367i
$539$			13130.7i			1.04931i
$540$	9136.28	−	8601.88i	0.728079	−	0.685493i
$541$			4558.22i			0.362243i	0.983461	+	0.181121i	$0.0579727\pi$
$541$			4558.22i			0.362243i	−0.983461	+	0.181121i	$0.942027\pi$
$542$	−1610.78	−	12425.3i	−0.127655	−	0.984712i
$543$	632.044	+	652.340i	0.0499514	+	0.0515554i
$544$	7816.09	−	5875.36i	0.616015	−	0.463058i
$545$	12372.3	+	3034.93i	0.972426	+	0.238536i
$546$	−7443.44	+	9351.35i	−0.583425	+	0.732969i
$547$		−	6925.96i		−	0.541376i	−0.962667	−	0.270688i	$-0.912749\pi$
$547$		−	6925.96i		−	0.541376i	0.962667	−	0.270688i	$-0.0872512\pi$
$548$	−3910.76	+	1031.29i	−0.304853	+	0.0803913i
$549$	−11741.8	−	371.189i	−0.912803	−	0.0288560i
$550$	−4564.39	+	12420.0i	−0.353866	+	0.962892i
$551$	1085.61			0.0839360
$552$	−13888.4	−	6109.88i	−1.07088	−	0.471112i
$553$		−	8963.10i		−	0.689240i
$554$	8483.38	−	1099.76i	0.650586	−	0.0843397i
$555$	10249.4	+	17531.2i	0.783896	+	1.34082i
$556$	−5243.27	+	1382.68i	−0.399936	+	0.105465i
$557$		−	13278.5i		−	1.01010i	−0.863089	−	0.505052i	$-0.831473\pi$
$557$		−	13278.5i		−	1.01010i	0.863089	−	0.505052i	$-0.168527\pi$
$558$	−9414.13	+	919.044i	−0.714215	+	0.0697245i
$559$		−	11264.3i		−	0.852288i
$560$	−5120.30	−	18139.2i	−0.386379	−	1.36879i
$561$	−7309.71	−	7544.44i	−0.550118	−	0.567783i
$562$	120.279	+	927.813i	0.00902784	+	0.0696396i
$563$	14521.4			1.08704			0.543520	−	0.839396i	$-0.317091\pi$
$563$	14521.4			1.08704			0.543520	+	0.839396i	$0.317091\pi$
$564$	−1628.39	−	983.566i	−0.121574	−	0.0734319i
$565$	−3857.16	+	15724.3i	−0.287207	+	1.17084i
$566$	1837.02	+	14170.5i	0.136424	+	1.05235i
$567$	19164.2	+	1212.87i	1.41943	+	0.0898337i
$568$	7681.19	−	3128.28i	0.567422	−	0.231091i
$569$		−	1852.91i		−	0.136517i	−0.997668	−	0.0682583i	$-0.978256\pi$
$569$		−	1852.91i		−	0.136517i	0.997668	−	0.0682583i	$-0.0217442\pi$
$570$	473.111	+	612.165i	0.0347657	+	0.0449838i
$571$	10888.0			0.797980			0.398990	−	0.916955i	$-0.369361\pi$
$571$	10888.0			0.797980			0.398990	+	0.916955i	$0.369361\pi$
$572$	−2357.07	−	8938.28i	−0.172297	−	0.653371i
$573$	−4729.44	+	4582.29i	−0.344808	+	0.334080i
$574$	716.846	+	5529.66i	0.0521265	+	0.402097i
$575$	7464.71	−	14299.9i	0.541391	−	1.03713i
$576$	−9340.77	−	10190.8i	−0.675692	−	0.737184i
$577$			23942.9i			1.72748i	0.503941	+	0.863738i	$0.331883\pi$
$577$			23942.9i			1.72748i	−0.503941	+	0.863738i	$0.668117\pi$
$578$	5596.39	−	725.497i	0.402732	−	0.0522088i
$579$	8190.38	+	8453.39i	0.587877	+	0.606755i
$580$	−356.447	−	20619.4i	−0.0255184	−	1.47616i
$581$	−15938.7			−1.13812
$582$	−16576.9	−	13194.8i	−1.18064	−	0.939762i
$583$	25559.7			1.81574
$584$	1837.00	+	4510.60i	0.130164	+	0.319606i
$585$	−8976.76	−	2505.20i	−0.634433	−	0.177055i
$586$	−461.730	−	3561.72i	−0.0325493	−	0.251081i
$587$	10172.0			0.715239			0.357620	−	0.933867i	$-0.383588\pi$
$587$	10172.0			0.715239			0.357620	+	0.933867i	$0.383588\pi$
$588$	7540.32	−	12483.7i	0.528839	−	0.875545i
$589$		−	583.191i		−	0.0407979i
$590$	8049.09	+	902.290i	0.561654	+	0.0629605i
$591$	2280.72	+	2353.96i	0.158742	+	0.163839i
$592$	19462.5	−	11031.9i	1.35119	−	0.765890i
$593$	−17454.1			−1.20869			−0.604346	−	0.796722i	$-0.706565\pi$
$593$	−17454.1			−1.20869			−0.604346	+	0.796722i	$0.706565\pi$
$594$	−9611.55	+	11321.7i	−0.663917	+	0.782046i
$595$	−3789.86	+	15449.9i	−0.261125	+	1.06451i
$596$	−20424.9	+	5386.14i	−1.40375	+	0.370176i
$597$	12138.1	+	12527.9i	0.832129	+	0.858850i
$598$	1448.75	+	11175.5i	0.0990697	+	0.764211i
$599$	239.830			0.0163592			0.00817961	−	0.999967i	$-0.497396\pi$
$599$	239.830			0.0163592			0.00817961	+	0.999967i	$0.497396\pi$
$600$	11471.7	−	9186.95i	0.780551	−	0.625093i
$601$	387.340			0.0262894			0.0131447	−	0.999914i	$-0.495816\pi$
$601$	387.340			0.0262894			0.0131447	+	0.999914i	$0.495816\pi$
$602$	3494.63	+	26957.1i	0.236596	+	1.82507i
$603$	−23264.1	−	735.438i	−1.57112	−	0.0496673i
$604$	5031.06	+	19078.4i	0.338926	+	1.28525i
$605$	185.705	−	757.053i	0.0124793	−	0.0508737i
$606$	−3864.23	+	4854.72i	−0.259032	+	0.325428i
$607$	3054.14			0.204223			0.102112	−	0.994773i	$-0.467440\pi$
$607$	3054.14			0.204223			0.102112	+	0.994773i	$0.467440\pi$
$608$	681.303	−	512.135i	0.0454448	−	0.0341609i
$609$	22664.6	−	21959.4i	1.50807	−	1.46115i
$610$	−13673.4	−	1532.77i	−0.907574	−	0.101738i
$611$			1412.90i			0.0935515i
$612$	2617.15	+	11370.3i	0.172863	+	0.751010i
$613$	1899.37			0.125146			0.0625732	−	0.998040i	$-0.480069\pi$
$613$	1899.37			0.125146			0.0625732	+	0.998040i	$0.480069\pi$
$614$	−1838.72	−	14183.6i	−0.120855	−	0.932256i
$615$	−3753.49	+	2194.43i	−0.246106	+	0.143883i
$616$	8413.82	+	20659.4i	0.550329	+	1.35128i
$617$	−5098.97			−0.332701			−0.166351	−	0.986067i	$-0.553198\pi$
$617$	−5098.97			−0.332701			−0.166351	+	0.986067i	$0.553198\pi$
$618$	9692.82	−	12177.3i	0.630910	−	0.792626i
$619$	−11519.4			−0.747988			−0.373994	−	0.927431i	$-0.622012\pi$
$619$	−11519.4			−0.747988			−0.373994	+	0.927431i	$0.622012\pi$
$620$	−11076.7	+	191.483i	−0.717503	+	0.0124035i
$621$	13394.4	−	12181.1i	0.865538	−	0.787137i
$622$	−8097.00	+	1049.67i	−0.521962	+	0.0676653i
$623$		−	13629.6i		−	0.876498i
$624$	−2891.89	+	9851.43i	−0.185526	+	0.632008i
$625$	8933.07	+	12819.6i	0.571716	+	0.820451i
$626$	−2098.49	−	16187.5i	−0.133982	−	1.03352i
$627$	−637.163	−	657.623i	−0.0405834	−	0.0418867i
$628$	−12014.3	+	3168.24i	−0.763414	+	0.201316i
$629$	−18882.0			−1.19694
$630$	22259.9	+	3210.37i	1.40771	+	0.203023i
$631$		−	11392.7i		−	0.718757i	−0.933192	−	0.359379i	$-0.882989\pi$
$631$		−	11392.7i		−	0.718757i	0.933192	−	0.359379i	$-0.117011\pi$
$632$	−2904.12	−	7130.81i	−0.182785	−	0.448811i
$633$	14215.9	−	13773.6i	0.892625	−	0.864853i
$634$	−408.723	−	3152.84i	−0.0256033	−	0.197500i
$635$	−2863.86	+	11674.9i	−0.178974	+	0.729615i
$636$	−24300.3	−	14677.7i	−1.51505	−	0.915107i
$637$	−10831.8			−0.673736
$638$	3137.80	+	24204.6i	0.194713	+	1.50199i
$639$	−312.698	+	9891.56i	−0.0193586	+	0.612369i
$640$	−9950.83	−	12772.0i	−0.614596	−	0.788842i
$641$			2495.47i			0.153768i	0.997040	+	0.0768838i	$0.0244970\pi$
$641$			2495.47i			0.153768i	−0.997040	+	0.0768838i	$0.975503\pi$
$642$	7496.50	−	9418.01i	0.460846	−	0.578971i
$643$		−	1618.30i		−	0.0992527i	−0.998768	−	0.0496263i	$-0.984197\pi$
$643$		−	1618.30i		−	0.0992527i	0.998768	−	0.0496263i	$-0.0158030\pi$
$644$	−6934.14	−	26295.1i	−0.424291	−	1.60896i
$645$	−18298.3	+	10697.9i	−1.11705	+	0.653067i
$646$	−713.403	+	92.4831i	−0.0434496	+	0.00563266i
$647$		−	21039.5i		−	1.27844i	−0.769025	−	0.639219i	$-0.779258\pi$
$647$		−	21039.5i		−	1.27844i	0.769025	−	0.639219i	$-0.220742\pi$
$648$	15639.5	−	5244.43i	0.948113	−	0.317933i
$649$	−9585.93			−0.579785
$650$	−10245.5	−	3765.25i	−0.618248	−	0.227208i
$651$	−11796.6	−	12175.4i	−0.710207	−	0.733013i
$652$	8030.25	+	30451.7i	0.482345	+	1.82911i
$653$			3169.58i			0.189947i	0.995480	+	0.0949735i	$0.0302766\pi$
$653$			3169.58i			0.189947i	−0.995480	+	0.0949735i	$0.969723\pi$
$654$	13102.1	+	10429.0i	0.783385	+	0.623554i
$655$	−7925.19	−	1944.05i	−0.472768	−	0.115970i
$656$	2361.96	+	4166.99i	0.140578	+	0.248009i
$657$	−5808.58	−	183.624i	−0.344923	−	0.0109039i
$658$	−438.339	−	3381.29i	−0.0259699	−	0.200329i
$659$		−	3243.75i		−	0.191743i	−0.995394	−	0.0958714i	$-0.969436\pi$
$659$		−	3243.75i		−	0.191743i	0.995394	−	0.0958714i	$-0.0305638\pi$
$660$	−12281.2	+	12317.7i	−0.724313	+	0.726466i
$661$			18084.9i			1.06418i	0.846689	+	0.532088i	$0.178592\pi$
$661$			18084.9i			1.06418i	−0.846689	+	0.532088i	$0.821408\pi$
$662$	−29247.7	+	3791.57i	−1.71713	+	0.222603i
$663$	6223.55	−	6029.91i	0.364559	−	0.353216i
$664$	−12680.4	+	5164.29i	−0.741109	+	0.301827i
$665$	−330.350	+	1346.72i	−0.0192638	+	0.0785316i
$666$	2593.72	+	26568.5i	0.150908	+	1.54581i
$667$		−	29754.2i		−	1.72727i
$668$	−4077.49	−	15462.3i	−0.236172	−	0.895591i
$669$	15904.4	−	15409.6i	0.919133	−	0.890536i
$670$	−27091.2	−	3036.88i	−1.56212	−	0.175112i
$671$	16284.1			0.936873
$672$	3864.41	−	24473.1i	0.221835	−	1.40487i
$673$		−	19706.8i		−	1.12874i	−0.825523	−	0.564368i	$-0.809120\pi$
$673$		−	19706.8i		−	1.12874i	0.825523	−	0.564368i	$-0.190880\pi$
$674$	1793.72	+	13836.5i	0.102510	+	0.790747i
$675$	4455.78	+	16961.5i	0.254079	+	0.967184i
$676$	−9621.66	+	2537.28i	−0.547432	+	0.144360i
$677$			22320.7i			1.26714i	0.773686	+	0.633569i	$0.218411\pi$
$677$			22320.7i			1.26714i	−0.773686	+	0.633569i	$0.781589\pi$
$678$	−13254.4	+	16651.8i	−0.750785	+	0.943227i
$679$		−	37973.1i		−	2.14621i
$680$	1990.80	+	13519.5i	0.112270	+	0.762426i
$681$	−16725.9	+	16205.5i	−0.941170	+	0.911887i
$682$	13002.7	−	1685.62i	0.730056	−	0.0946420i
$683$	12949.2			0.725458			0.362729	−	0.931895i	$-0.381845\pi$
$683$	12949.2			0.725458			0.362729	+	0.931895i	$0.381845\pi$
$684$	228.128	+	991.113i	0.0127525	+	0.0554037i
$685$	1346.59	−	5489.55i	0.0751101	−	0.306197i
$686$	579.430	−	75.1153i	0.0322489	−	0.00418063i
$687$	−4186.05	−	4320.48i	−0.232471	−	0.239937i
$688$	11514.6	+	20314.1i	0.638066	+	1.12568i
$689$			21084.7i			1.16584i
$690$	16778.1	−	12966.9i	0.925695	−	0.715422i
$691$	14104.3			0.776489			0.388244	−	0.921556i	$-0.373082\pi$
$691$	14104.3			0.776489			0.388244	+	0.921556i	$0.373082\pi$
$692$	5745.89	+	21789.1i	0.315645	+	1.19696i
$693$	−26604.4	−	841.033i	−1.45832	−	0.0461013i
$694$	9108.70	−	1180.82i	0.498216	−	0.0645870i
$695$	1805.41	−	7360.00i	0.0985366	−	0.401699i
$696$	10916.3	−	24813.9i	0.594514	−	1.35139i
$697$		−	4042.70i		−	0.219696i
$698$	4361.90	+	33647.2i	0.236534	+	1.82459i
$699$	9514.48	−	9218.46i	0.514836	−	0.498818i
$700$	25687.1	+	5832.25i	1.38697	+	0.314912i
$701$	26508.0			1.42823			0.714117	−	0.700026i	$-0.246828\pi$
$701$	26508.0			1.42823			0.714117	+	0.700026i	$0.246828\pi$
$702$	−9339.49	−	7928.75i	−0.502131	−	0.426284i
$703$	−1645.88			−0.0883008
$704$	13387.6	+	13709.9i	0.716712	+	0.733965i
$705$	2295.19	−	1341.85i	0.122613	−	0.0716839i
$706$	18664.5	−	2419.60i	0.994970	−	0.128984i
$707$	−11120.8			−0.591572
$708$	9113.63	+	5504.74i	0.483773	+	0.292204i
$709$		−	5707.61i		−	0.302333i	−0.988508	−	0.151166i	$-0.951697\pi$
$709$		−	5707.61i		−	0.302333i	0.988508	−	0.151166i	$-0.0483029\pi$
$710$	−1291.24	+	11518.8i	−0.0682524	+	0.608862i
$711$	9182.80	+	290.292i	0.484362	+	0.0153119i
$712$	−4416.11	−	10843.3i	−0.232445	−	0.570747i
$713$	−15983.9			−0.839555
$714$	−13023.2	+	16361.3i	−0.682604	+	0.857570i
$715$	12546.7	+	3077.70i	0.656252	+	0.160978i
$716$	−1847.86	−	7007.30i	−0.0964494	−	0.365748i
$717$	−2666.73	+	2583.76i	−0.138900	+	0.134578i
$718$	−14692.6	+	1904.70i	−0.763683	+	0.0990012i
$719$	6320.76			0.327851			0.163925	−	0.986473i	$-0.447584\pi$
$719$	6320.76			0.327851			0.163925	+	0.986473i	$0.447584\pi$
$720$	18749.6	−	4658.32i	0.970496	−	0.241119i
$721$	27894.8			1.44086
$722$	19177.0	−	2486.04i	0.988496	−	0.128145i
$723$	−8695.17	+	8424.63i	−0.447271	+	0.433355i
$724$	356.584	+	1352.21i	0.0183043	+	0.0694122i
$725$	25549.2	+	13337.0i	1.30879	+	0.683203i
$726$	638.139	−	801.708i	0.0326220	−	0.0409837i
$727$	−7788.82			−0.397347			−0.198674	−	0.980066i	$-0.563663\pi$
$727$	−7788.82			−0.397347			−0.198674	+	0.980066i	$0.563663\pi$
$728$	−17042.3	+	6940.72i	−0.867623	+	0.353352i
$729$	−1863.28	+	19594.6i	−0.0946642	+	0.995509i
$730$	−6764.12	−	758.247i	−0.342947	−	0.0384438i
$731$		−	19708.2i		−	0.997173i
$732$	−15481.8	−	9351.18i	−0.781726	−	0.472172i
$733$	−37009.1			−1.86489			−0.932443	−	0.361317i	$-0.882327\pi$
$733$	−37009.1			−1.86489			−0.932443	+	0.361317i	$0.882327\pi$
$734$	9886.57	−	1281.66i	0.497166	−	0.0644509i
$735$	10287.1	+	17595.6i	0.516251	+	0.883027i
$736$	−14036.4	−	18672.9i	−0.702976	−	0.935182i
$737$	32263.8			1.61255
$738$	−5688.41	+	555.325i	−0.283731	+	0.0276989i
$739$	8679.66			0.432052			0.216026	−	0.976388i	$-0.430690\pi$
$739$	8679.66			0.432052			0.216026	+	0.976388i	$0.430690\pi$
$740$	540.403	+	31260.7i	0.0268454	+	1.55293i
$741$	542.486	−	525.607i	0.0268943	−	0.0260576i
$742$	−6541.30	−	50458.7i	−0.323637	−	2.49649i
$743$			18604.8i			0.918634i	0.888272	+	0.459317i	$0.151906\pi$
$743$			18604.8i			0.918634i	−0.888272	+	0.459317i	$0.848094\pi$
$744$	−13330.0	−	5864.24i	−0.656857	−	0.288970i
$745$	7032.85	−	28670.5i	0.345857	−	1.40994i
$746$	−8634.77	+	1119.38i	−0.423782	+	0.0549377i
$747$	516.214	−	16329.4i	0.0252842	−	0.799814i
$748$	−4123.96	−	15638.5i	−0.201587	−	0.764441i
$749$	21574.1			1.05247
$750$	3613.82	+	20219.2i	0.175944	+	0.984400i
$751$		−	23589.9i		−	1.14621i	−0.819481	−	0.573107i	$-0.805738\pi$
$751$		−	23589.9i		−	1.14621i	0.819481	−	0.573107i	$-0.194262\pi$
$752$	−1444.30	−	2548.04i	−0.0700374	−	0.123560i
$753$	10869.5	+	11218.5i	0.526036	+	0.542928i
$754$	−19966.8	+	2588.43i	−0.964388	+	0.125020i
$755$	−26780.4	−	6569.22i	−1.29091	−	0.316660i
$756$	24810.6	+	16077.2i	1.19359	+	0.773442i
$757$	−28338.1			−1.36059			−0.680294	−	0.732939i	$-0.738148\pi$
$757$	−28338.1			−1.36059			−0.680294	+	0.732939i	$0.738148\pi$
$758$	9100.52	−	1179.76i	0.436076	−	0.0565314i
$759$	−18023.9	+	17463.2i	−0.861960	+	0.835142i
$760$	173.531	+	1178.45i	0.00828241	+	0.0562459i
$761$			9122.56i			0.434550i	0.976110	+	0.217275i	$0.0697168\pi$
$761$			9122.56i			0.434550i	−0.976110	+	0.217275i	$0.930283\pi$
$762$	−9841.10	+	12363.6i	−0.467855	+	0.587777i
$763$			30013.4i			1.42406i
$764$	−9803.46	+	2585.22i	−0.464236	+	0.122421i
$765$	−15705.9	−	4383.14i	−0.742284	−	0.207154i
$766$	−1826.63	−	14090.4i	−0.0861603	−	0.664630i
$767$		−	7907.61i		−	0.372265i
$768$	−4855.08	−	20722.3i	−0.228116	−	0.973634i
$769$	−28401.1			−1.33182			−0.665910	−	0.746032i	$-0.731956\pi$
$769$	−28401.1			−1.33182			−0.665910	+	0.746032i	$0.731956\pi$
$770$	−30980.9	−	3472.91i	−1.44997	−	0.162539i
$771$	−29162.8	+	28255.4i	−1.36222	+	1.31984i
$772$	4620.82	+

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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.80496 + 0.363625i) q^{2} +(3.73183 - 3.61572i) q^{3} +(7.73555 - 2.03990i) q^{4} +(-2.66357 + 10.8584i) q^{5} +(-9.15285 + 11.4989i) q^{6} -26.3409 q^{7} +(-20.9561 + 8.53468i) q^{8} +(0.853113 - 26.9865i) q^{9} +(3.52280 - 31.4259i) q^{10} +37.4262i q^{11} +(21.4921 - 35.5822i) q^{12} -30.8736 q^{13} +(73.8850 - 9.57820i) q^{14} +(29.3211 + 50.1525i) q^{15} +(55.6776 - 31.5596i) q^{16} -54.0168 q^{17} +(7.42002 + 76.0062i) q^{18} -4.70847 q^{19} +(1.54596 + 89.4294i) q^{20} +(-98.2997 + 95.2413i) q^{21} +(-13.6091 - 104.979i) q^{22} +129.048i q^{23} +(-47.3457 + 107.621i) q^{24} +(-110.811 - 57.8443i) q^{25} +(86.5990 - 11.2264i) q^{26} +(-94.3921 - 103.794i) q^{27} +(-203.761 + 53.7329i) q^{28} -230.566 q^{29} +(-100.481 - 130.014i) q^{30} +123.860i q^{31} +(-144.697 + 108.769i) q^{32} +(135.323 + 139.668i) q^{33} +(151.515 - 19.6419i) q^{34} +(70.1608 - 286.021i) q^{35} +(-48.4506 - 210.496i) q^{36} +349.557 q^{37} +(13.2070 - 1.71212i) q^{38} +(-115.215 + 111.630i) q^{39} +(-36.8551 - 250.283i) q^{40} +74.8414i q^{41} +(241.094 - 302.892i) q^{42} +364.853i q^{43} +(76.3458 + 289.512i) q^{44} +(290.759 + 81.1439i) q^{45} +(-46.9252 - 361.975i) q^{46} -45.7642i q^{47} +(93.6687 - 319.090i) q^{48} +350.842 q^{49} +(331.853 + 121.957i) q^{50} +(-201.582 + 195.310i) q^{51} +(-238.824 + 62.9791i) q^{52} -682.936i q^{53} +(302.508 + 256.814i) q^{54} +(-406.390 - 99.6872i) q^{55} +(552.003 - 224.811i) q^{56} +(-17.5712 + 17.0245i) q^{57} +(646.728 - 83.8397i) q^{58} +256.129i q^{59} +(329.121 + 328.145i) q^{60} -435.099i q^{61} +(-45.0386 - 347.422i) q^{62} +(-22.4718 + 710.849i) q^{63} +(366.318 - 357.708i) q^{64} +(82.2339 - 335.238i) q^{65} +(-430.361 - 342.556i) q^{66} -862.064i q^{67} +(-417.850 + 110.189i) q^{68} +(466.603 + 481.586i) q^{69} +(-92.7936 + 827.787i) q^{70} -366.537 q^{71} +(212.443 + 572.814i) q^{72} -215.240i q^{73} +(-980.492 + 127.108i) q^{74} +(-622.676 + 184.796i) q^{75} +(-36.4226 + 9.60482i) q^{76} -985.839i q^{77} +(282.581 - 355.013i) q^{78} +340.273i q^{79} +(194.386 + 688.632i) q^{80} +(-727.544 - 46.0451i) q^{81} +(-27.2142 - 209.927i) q^{82} +605.094 q^{83} +(-566.120 + 937.266i) q^{84} +(143.878 - 586.538i) q^{85} +(-132.670 - 1023.40i) q^{86} +(-860.434 + 833.664i) q^{87} +(-319.421 - 784.308i) q^{88} +517.431i q^{89} +(-845.071 - 121.878i) q^{90} +813.237 q^{91} +(263.246 + 998.260i) q^{92} +(447.843 + 462.225i) q^{93} +(16.6410 + 128.367i) q^{94} +(12.5413 - 51.1265i) q^{95} +(-146.708 + 929.093i) q^{96} +1441.60i q^{97} +(-984.097 + 127.575i) q^{98} +(1010.00 + 31.9288i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9} - 72 q^{10} - 128 q^{16} + 672 q^{19} - 416 q^{24} + 496 q^{25} - 248 q^{30} + 240 q^{34} - 608 q^{36} - 1344 q^{40} + 336 q^{46} + 3520 q^{49} - 544 q^{51} - 952 q^{54}+ \cdots + 256 q^{99}+O(q^{100}) \) 64 * q - 32 * q^4 - 72 * q^6 - 112 * q^9 - 72 * q^10 - 128 * q^16 + 672 * q^19 - 416 * q^24 + 496 * q^25 - 248 * q^30 + 240 * q^34 - 608 * q^36 - 1344 * q^40 + 336 * q^46 + 3520 * q^49 - 544 * q^51 - 952 * q^54 - 2064 * q^60 + 2176 * q^64 - 176 * q^66 + 672 * q^70 - 1600 * q^75 + 2304 * q^76 - 2304 * q^81 - 736 * q^84 - 1432 * q^90 - 2752 * q^91 + 4496 * q^94 + 640 * q^96 + 256 * q^99

Introduction

L-functions

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