LMFDB - Embedded newform 120.4.m.b.59.11

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			59.11
Character	$\chi$	$=$	120.59
Dual form			120.4.m.b.59.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.22835 + 1.74197i) q^{2} +(4.99538 - 1.43044i) q^{3} +(1.93108 - 7.76344i) q^{4} +(10.2117 - 4.55196i) q^{5} +(-8.63968 + 11.8893i) q^{6} -3.90466 q^{7} +(9.22055 + 20.6635i) q^{8} +(22.9077 - 14.2912i) q^{9} +O(q^{10})$	\(q+(-2.22835 + 1.74197i) q^{2} +(4.99538 - 1.43044i) q^{3} +(1.93108 - 7.76344i) q^{4} +(10.2117 - 4.55196i) q^{5} +(-8.63968 + 11.8893i) q^{6} -3.90466 q^{7} +(9.22055 + 20.6635i) q^{8} +(22.9077 - 14.2912i) q^{9} +(-14.8260 + 27.9319i) q^{10} -59.1208i q^{11} +(-1.45861 - 41.5436i) q^{12} -63.6374 q^{13} +(8.70094 - 6.80180i) q^{14} +(44.5003 - 37.3460i) q^{15} +(-56.5419 - 29.9836i) q^{16} +69.6213 q^{17} +(-26.1516 + 71.7502i) q^{18} +33.0635 q^{19} +(-15.6191 - 88.0684i) q^{20} +(-19.5053 + 5.58537i) q^{21} +(102.987 + 131.742i) q^{22} +90.6431i q^{23} +(75.6180 + 90.0328i) q^{24} +(83.5594 - 92.9668i) q^{25} +(141.806 - 110.854i) q^{26} +(93.9902 - 104.158i) q^{27} +(-7.54021 + 30.3136i) q^{28} +172.259 q^{29} +(-34.1065 + 160.738i) q^{30} +61.7877i q^{31} +(178.226 - 31.6802i) q^{32} +(-84.5685 - 295.331i) q^{33} +(-155.141 + 121.278i) q^{34} +(-39.8734 + 17.7738i) q^{35} +(-66.7118 - 205.440i) q^{36} -10.7673 q^{37} +(-73.6770 + 57.5956i) q^{38} +(-317.893 + 91.0292i) q^{39} +(188.217 + 169.039i) q^{40} +475.596i q^{41} +(33.7350 - 46.4237i) q^{42} -59.3761i q^{43} +(-458.980 - 114.167i) q^{44} +(168.875 - 250.212i) q^{45} +(-157.898 - 201.985i) q^{46} -500.434i q^{47} +(-325.338 - 68.9003i) q^{48} -327.754 q^{49} +(-24.2541 + 352.720i) q^{50} +(347.785 - 99.5888i) q^{51} +(-122.889 + 494.045i) q^{52} +407.866i q^{53} +(-28.0032 + 395.828i) q^{54} +(-269.115 - 603.726i) q^{55} +(-36.0031 - 80.6840i) q^{56} +(165.165 - 47.2952i) q^{57} +(-383.853 + 300.070i) q^{58} -17.5094i q^{59} +(-204.000 - 417.593i) q^{60} +245.109i q^{61} +(-107.632 - 137.685i) q^{62} +(-89.4468 + 55.8021i) q^{63} +(-341.963 + 381.058i) q^{64} +(-649.849 + 289.675i) q^{65} +(702.906 + 510.785i) q^{66} -35.7817i q^{67} +(134.444 - 540.500i) q^{68} +(129.659 + 452.797i) q^{69} +(57.8903 - 109.065i) q^{70} -889.439 q^{71} +(506.527 + 341.582i) q^{72} +617.595i q^{73} +(23.9933 - 18.7563i) q^{74} +(284.428 - 583.931i) q^{75} +(63.8483 - 256.686i) q^{76} +230.847i q^{77} +(549.807 - 756.605i) q^{78} +108.663i q^{79} +(-713.875 - 48.8092i) q^{80} +(320.526 - 654.755i) q^{81} +(-828.473 - 1059.79i) q^{82} +628.531 q^{83} +(5.69538 + 162.214i) q^{84} +(710.955 - 316.913i) q^{85} +(103.431 + 132.311i) q^{86} +(860.499 - 246.405i) q^{87} +(1221.64 - 545.126i) q^{88} +763.668i q^{89} +(59.5504 + 851.736i) q^{90} +248.482 q^{91} +(703.702 + 175.039i) q^{92} +(88.3834 + 308.653i) q^{93} +(871.741 + 1115.14i) q^{94} +(337.636 - 150.504i) q^{95} +(844.989 - 413.195i) q^{96} +866.259i q^{97} +(730.350 - 570.937i) q^{98} +(-844.904 - 1354.32i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9}+O(q^{10}) $ 64 * q - 32 * q^4 - 72 * q^6 - 112 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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 $

$2$	−2.22835	+	1.74197i	−0.787840	+	0.615879i
$2$	−2.22835	+	1.74197i	−0.787840	+	0.615879i
$3$	4.99538	−	1.43044i	0.961362	−	0.275288i
$3$	4.99538	−	1.43044i	0.961362	−	0.275288i
$4$	1.93108	−	7.76344i	0.241385	−	0.970429i
$5$	10.2117	−	4.55196i	0.913366	−	0.407139i
$5$	10.2117	−	4.55196i	0.913366	−	0.407139i
$6$	−8.63968	+	11.8893i	−0.587856	+	0.808966i
$7$	−3.90466			−0.210832			−0.105416	−	0.994428i	$-0.533617\pi$
$7$	−3.90466			−0.210832			−0.105416	+	0.994428i	$0.533617\pi$
$8$	9.22055	+	20.6635i	0.407495	+	0.913208i
$9$	22.9077	−	14.2912i	0.848433	−	0.529302i
$10$	−14.8260	+	27.9319i	−0.468838	+	0.883284i
$11$		−	59.1208i		−	1.62051i	−0.586079	−	0.810254i	$-0.699329\pi$
$11$		−	59.1208i		−	1.62051i	0.586079	−	0.810254i	$-0.300671\pi$
$12$	−1.45861	−	41.5436i	−0.0350887	−	0.999384i
$13$	−63.6374			−1.35768			−0.678840	−	0.734286i	$-0.737517\pi$
$13$	−63.6374			−1.35768			−0.678840	+	0.734286i	$0.737517\pi$
$14$	8.70094	−	6.80180i	0.166102	−	0.129847i
$15$	44.5003	−	37.3460i	0.765995	−	0.642847i
$16$	−56.5419	−	29.9836i	−0.883466	−	0.468494i
$17$	69.6213			0.993273			0.496636	−	0.867959i	$-0.334568\pi$
$17$	69.6213			0.993273			0.496636	+	0.867959i	$0.334568\pi$
$18$	−26.1516	+	71.7502i	−0.342444	+	0.939538i
$19$	33.0635			0.399226			0.199613	−	0.979875i	$-0.436032\pi$
$19$	33.0635			0.399226			0.199613	+	0.979875i	$0.436032\pi$
$20$	−15.6191	−	88.0684i	−0.174627	−	0.984635i
$21$	−19.5053	+	5.58537i	−0.202686	+	0.0580394i
$22$	102.987	+	131.742i	0.998038	+	1.27670i
$23$			90.6431i			0.821756i	0.911690	+	0.410878i	$0.134778\pi$
$23$			90.6431i			0.821756i	−0.911690	+	0.410878i	$0.865222\pi$
$24$	75.6180	+	90.0328i	0.643144	+	0.765745i
$25$	83.5594	−	92.9668i	0.668475	−	0.743734i
$26$	141.806	−	110.854i	1.06964	−	0.836167i
$27$	93.9902	−	104.158i	0.669941	−	0.742414i
$28$	−7.54021	+	30.3136i	−0.0508917	+	0.204597i
$29$	172.259			1.10302			0.551511	−	0.834167i	$-0.314051\pi$
$29$	172.259			1.10302			0.551511	+	0.834167i	$0.314051\pi$
$30$	−34.1065	+	160.738i	−0.207566	+	0.978221i
$31$			61.7877i			0.357981i	0.983851	+	0.178990i	$0.0572831\pi$
$31$			61.7877i			0.357981i	−0.983851	+	0.178990i	$0.942717\pi$
$32$	178.226	−	31.6802i	0.984567	−	0.175010i
$33$	−84.5685	−	295.331i	−0.446106	−	1.55789i
$34$	−155.141	+	121.278i	−0.782541	+	0.611736i
$35$	−39.8734	+	17.7738i	−0.192567	+	0.0858379i
$36$	−66.7118	−	205.440i	−0.308851	−	0.951110i
$37$	−10.7673			−0.0478414			−0.0239207	−	0.999714i	$-0.507615\pi$
$37$	−10.7673			−0.0478414			−0.0239207	+	0.999714i	$0.507615\pi$
$38$	−73.6770	+	57.5956i	−0.314526	+	0.245875i
$39$	−317.893	+	91.0292i	−1.30522	+	0.373752i
$40$	188.217	+	169.039i	0.743994	+	0.668186i
$41$			475.596i			1.81160i	0.423707	+	0.905799i	$0.360729\pi$
$41$			475.596i			1.81160i	−0.423707	+	0.905799i	$0.639271\pi$
$42$	33.7350	−	46.4237i	0.123939	−	0.170556i
$43$		−	59.3761i		−	0.210576i	−0.994442	−	0.105288i	$-0.966424\pi$
$43$		−	59.3761i		−	0.210576i	0.994442	−	0.105288i	$-0.0335764\pi$
$44$	−458.980	−	114.167i	−1.57259	−	0.391166i
$45$	168.875	−	250.212i	0.559431	−	0.828877i
$46$	−157.898	−	201.985i	−0.506103	−	0.647413i
$47$		−	500.434i		−	1.55310i	−0.630054	−	0.776551i	$-0.716967\pi$
$47$		−	500.434i		−	1.55310i	0.630054	−	0.776551i	$-0.283033\pi$
$48$	−325.338	−	68.9003i	−0.978302	−	0.207185i
$49$	−327.754			−0.955550
$50$	−24.2541	+	352.720i	−0.0686011	+	0.997644i
$51$	347.785	−	99.5888i	0.954895	−	0.273436i
$52$	−122.889	+	494.045i	−0.327724	+	1.31753i
$53$			407.866i			1.05707i	0.848911	+	0.528535i	$0.177259\pi$
$53$			407.866i			1.05707i	−0.848911	+	0.528535i	$0.822741\pi$
$54$	−28.0032	+	395.828i	−0.0705694	+	0.997507i
$55$	−269.115	−	603.726i	−0.659772	−	1.48012i
$56$	−36.0031	−	80.6840i	−0.0859128	−	0.192533i
$57$	165.165	−	47.2952i	0.383800	−	0.109902i
$58$	−383.853	+	300.070i	−0.869006	+	0.679329i
$59$		−	17.5094i		−	0.0386360i	−0.999813	−	0.0193180i	$-0.993851\pi$
$59$		−	17.5094i		−	0.0386360i	0.999813	−	0.0193180i	$-0.00614950\pi$
$60$	−204.000	−	417.593i	−0.438937	−	0.898518i
$61$			245.109i			0.514474i	0.966348	+	0.257237i	$0.0828122\pi$
$61$			245.109i			0.514474i	−0.966348	+	0.257237i	$0.917188\pi$
$62$	−107.632	−	137.685i	−0.220473	−	0.282032i
$63$	−89.4468	+	55.8021i	−0.178877	+	0.111594i
$64$	−341.963	+	381.058i	−0.667896	+	0.744254i
$65$	−649.849	+	289.675i	−1.24006	+	0.552765i
$66$	702.906	+	510.785i	1.31094	+	0.952625i
$67$		−	35.7817i		−	0.0652452i	−0.999468	−	0.0326226i	$-0.989614\pi$
$67$		−	35.7817i		−	0.0652452i	0.999468	−	0.0326226i	$-0.0103859\pi$
$68$	134.444	−	540.500i	0.239761	−	0.963901i
$69$	129.659	+	452.797i	0.226219	+	0.790005i
$70$	57.8903	−	109.065i	0.0988460	−	0.186224i
$71$	−889.439			−1.48672			−0.743359	−	0.668893i	$-0.766769\pi$
$71$	−889.439			−1.48672			−0.743359	+	0.668893i	$0.766769\pi$
$72$	506.527	+	341.582i	0.829095	+	0.559108i
$73$			617.595i			0.990193i	0.868838	+	0.495096i	$0.164867\pi$
$73$			617.595i			0.990193i	−0.868838	+	0.495096i	$0.835133\pi$
$74$	23.9933	−	18.7563i	0.0376914	−	0.0294646i
$75$	284.428	−	583.931i	0.437906	−	0.899021i
$76$	63.8483	−	256.686i	0.0963671	−	0.387420i
$77$			230.847i			0.341655i
$78$	549.807	−	756.605i	0.798120	−	1.09832i
$79$			108.663i			0.154753i	0.997002	+	0.0773766i	$0.0246544\pi$
$79$			108.663i			0.154753i	−0.997002	+	0.0773766i	$0.975346\pi$
$80$	−713.875	−	48.8092i	−0.997671	−	0.0682130i
$81$	320.526	−	654.755i	0.439679	−	0.898155i
$82$	−828.473	−	1059.79i	−1.11573	−	1.42725i
$83$	628.531			0.831208			0.415604	−	0.909546i	$-0.363570\pi$
$83$	628.531			0.831208			0.415604	+	0.909546i	$0.363570\pi$
$84$	5.69538	+	162.214i	0.00739782	+	0.210702i
$85$	710.955	−	316.913i	0.907222	−	0.404400i
$86$	103.431	+	132.311i	0.129689	+	0.165900i
$87$	860.499	−	246.405i	1.06040	−	0.303649i
$88$	1221.64	−	545.126i	1.47986	−	0.660348i
$89$			763.668i			0.909535i	0.890610	+	0.454768i	$0.150278\pi$
$89$			763.668i			0.909535i	−0.890610	+	0.454768i	$0.849722\pi$
$90$	59.5504	+	851.736i	0.0697462	+	0.997565i
$91$	248.482			0.286242
$92$	703.702	+	175.039i	0.797457	+	0.198360i
$93$	88.3834	+	308.653i	0.0985477	+	0.344149i
$94$	871.741	+	1115.14i	0.956524	+	1.22360i
$95$	337.636	−	150.504i	0.364639	−	0.162540i
$96$	844.989	−	413.195i	0.898347	−	0.439287i
$97$			866.259i			0.906755i	0.891319	+	0.453378i	$0.149781\pi$
$97$			866.259i			0.906755i	−0.891319	+	0.453378i	$0.850219\pi$
$98$	730.350	−	570.937i	0.752821	−	0.588504i
$99$	−844.904	−	1354.32i	−0.857738	−	1.37489i
$100$	−560.382	−	828.234i	−0.560382	−	0.828234i
$101$	1542.57			1.51972			0.759859	−	0.650088i	$-0.225268\pi$
$101$	1542.57			1.51972			0.759859	+	0.650088i	$0.225268\pi$
$102$	−601.506	+	827.750i	−0.583901	+	0.803524i
$103$	−360.822			−0.345174			−0.172587	−	0.984994i	$-0.555213\pi$
$103$	−360.822			−0.345174			−0.172587	+	0.984994i	$0.555213\pi$
$104$	−586.772	−	1314.97i	−0.553247	−	1.23984i
$105$	−173.758	+	145.823i	−0.161496	+	0.135532i
$106$	−710.491	−	908.868i	−0.651028	−	0.832803i
$107$	−1347.63			−1.21757			−0.608785	−	0.793336i	$-0.708343\pi$
$107$	−1347.63			−1.21757			−0.608785	+	0.793336i	$0.708343\pi$
$108$	−627.120	−	930.824i	−0.558747	−	0.829338i
$109$			1187.79i			1.04376i	0.853019	+	0.521880i	$0.174769\pi$
$109$			1187.79i			1.04376i	−0.853019	+	0.521880i	$0.825231\pi$
$110$	1651.36	+	876.522i	1.43137	+	0.759756i
$111$	−53.7868	+	15.4019i	−0.0459929	+	0.0131702i
$112$	220.777	+	117.076i	0.186263	+	0.0987735i
$113$	−666.104			−0.554529			−0.277265	−	0.960794i	$-0.589428\pi$
$113$	−666.104			−0.554529			−0.277265	+	0.960794i	$0.589428\pi$
$114$	−285.658	+	393.102i	−0.234687	+	0.322960i
$115$	412.603	+	925.624i	0.334569	+	0.750564i
$116$	332.646	−	1337.32i	0.266253	−	1.07041i
$117$	−1457.79	+	909.452i	−1.15190	+	0.718623i
$118$	30.5008	+	39.0170i	0.0237951	+	0.0304390i
$119$	−271.847			−0.209413
$120$	1182.02	+	575.182i	0.899191	+	0.437556i
$121$	−2164.27			−1.62605
$122$	−426.972	−	546.187i	−0.316854	−	0.405324i
$123$	680.309	+	2375.78i	0.498711	+	1.74160i
$124$	479.685	+	119.317i	0.347395	+	0.0864112i
$125$	430.106	−	1329.71i	0.307759	−	0.951464i
$126$	102.113	−	280.160i	0.0721981	−	0.198085i
$127$	−259.670			−0.181433			−0.0907163	−	0.995877i	$-0.528916\pi$
$127$	−259.670			−0.181433			−0.0907163	+	0.995877i	$0.528916\pi$
$128$	98.2209	−	1444.82i	0.0678249	−	0.997697i
$129$	−84.9337	−	296.606i	−0.0579689	−	0.202440i
$130$	943.485	−	1777.51i	0.636532	−	1.19922i
$131$			930.506i			0.620601i	0.950639	+	0.310300i	$0.100430\pi$
$131$			930.506i			0.620601i	−0.950639	+	0.310300i	$0.899570\pi$
$132$	−2456.09	+	86.2343i	−1.61951	+	0.0568616i
$133$	−129.102			−0.0841694
$134$	62.3306	+	79.7340i	0.0401831	+	0.0514028i
$135$	485.682	−	1491.47i	0.309636	−	0.950855i
$136$	641.946	+	1438.62i	0.404753	+	0.907064i
$137$	360.083			0.224554			0.112277	−	0.993677i	$-0.464186\pi$
$137$	360.083			0.224554			0.112277	+	0.993677i	$0.464186\pi$
$138$	−1077.68	−	783.128i	−0.664773	−	0.483074i
$139$	−574.130			−0.350339			−0.175169	−	0.984538i	$-0.556047\pi$
$139$	−574.130			−0.350339			−0.175169	+	0.984538i	$0.556047\pi$
$140$	60.9873	+	343.877i	0.0368169	+	0.207592i
$141$	−715.839	−	2499.86i	−0.427550	−	1.49309i
$142$	1981.98	−	1549.38i	1.17130	−	0.915639i
$143$			3762.29i			2.20013i
$144$	−1723.74	+	121.192i	−0.997538	+	0.0701343i
$145$	1759.06	−	784.115i	1.00746	−	0.449084i
$146$	−1075.83	−	1376.22i	−0.609839	−	0.780114i
$147$	−1637.25	+	468.831i	−0.918629	+	0.263051i
$148$	−20.7925	+	83.5913i	−0.0115482	+	0.0464267i
$149$	−1402.68			−0.771223			−0.385611	−	0.922661i	$-0.626009\pi$
$149$	−1402.68			−0.771223			−0.385611	+	0.922661i	$0.626009\pi$
$150$	383.385	+	1796.67i	0.208689	+	0.977982i
$151$			713.088i			0.384306i	0.981365	+	0.192153i	$0.0615471\pi$
$151$			713.088i			0.384306i	−0.981365	+	0.192153i	$0.938453\pi$
$152$	304.864	+	683.208i	0.162682	+	0.364576i
$153$	1594.86	−	994.968i	0.842726	−	0.525741i
$154$	−402.128	−	514.407i	−0.210418	−	0.269169i
$155$	281.255	+	630.961i	0.145748	+	0.326968i
$156$	92.8222	+	2643.73i	0.0476393	+	1.35684i
$157$	1894.80			0.963192			0.481596	−	0.876393i	$-0.340057\pi$
$157$	1894.80			0.963192			0.481596	+	0.876393i	$0.340057\pi$
$158$	−189.287	−	242.138i	−0.0953093	−	0.121921i
$159$	583.427	+	2037.45i	0.290998	+	1.01623i
$160$	1675.79	−	1134.79i	0.828016	−	0.560704i
$161$		−	353.930i		−	0.173252i
$162$	426.320	+	2017.37i	0.206759	+	0.978392i
$163$		−	2482.58i		−	1.19295i	−0.802633	−	0.596473i	$-0.796568\pi$
$163$		−	2482.58i		−	1.19295i	0.802633	−	0.596473i	$-0.203432\pi$
$164$	3692.26	+	918.414i	1.75803	+	0.437293i
$165$	−2207.93	−	2630.89i	−1.04174	−	1.24130i
$166$	−1400.59	+	1094.88i	−0.654859	+	0.511924i
$167$		−	3112.29i		−	1.44213i	−0.692865	−	0.721067i	$-0.743652\pi$
$167$		−	3112.29i		−	1.44213i	0.692865	−	0.721067i	$-0.256348\pi$
$168$	−295.263	−	351.548i	−0.135595	−	0.161443i
$169$	1852.72			0.843294
$170$	−1032.20	+	1944.65i	−0.465684	+	0.877342i
$171$	757.409	−	472.515i	0.338716	−	0.211311i
$172$	−460.962	−	114.660i	−0.204349	−	0.0508299i
$173$			3100.30i			1.36250i	0.732053	+	0.681248i	$0.238562\pi$
$173$			3100.30i			1.36250i	−0.732053	+	0.681248i	$0.761438\pi$
$174$	−1488.26	+	2048.04i	−0.648418	+	0.892308i
$175$	−326.271	+	363.004i	−0.140936	+	0.156803i
$176$	−1772.66	+	3342.80i	−0.759199	+	1.43166i
$177$	−25.0460	−	87.4660i	−0.0106360	−	0.0371432i
$178$	−1330.29	−	1701.72i	−0.560164	−	0.716569i
$179$			2018.40i			0.842805i	0.906874	+	0.421402i	$0.138462\pi$
$179$			2018.40i			0.842805i	−0.906874	+	0.421402i	$0.861538\pi$
$180$	−1616.40	−	1794.23i	−0.669328	−	0.742967i
$181$		−	1943.41i		−	0.798079i	−0.916934	−	0.399039i	$-0.869344\pi$
$181$		−	1943.41i		−	0.798079i	0.916934	−	0.399039i	$-0.130656\pi$
$182$	−553.705	+	432.849i	−0.225513	+	0.176291i
$183$	350.612	+	1224.41i	0.141628	+	0.494596i
$184$	−1873.01	+	835.779i	−0.750434	+	0.334861i
$185$	−109.953	+	49.0123i	−0.0436968	+	0.0194781i
$186$	−734.614	−	533.826i	−0.289594	−	0.210441i
$187$		−	4116.06i		−	1.60961i
$188$	−3885.09	−	966.379i	−1.50718	−	0.374896i
$189$	−367.000	+	406.701i	−0.141245	+	0.156524i
$190$	−490.198	+	923.526i	−0.187172	+	0.352630i
$191$	3928.20			1.48814			0.744070	−	0.668101i	$-0.232893\pi$
$191$	3928.20			1.48814			0.744070	+	0.668101i	$0.232893\pi$
$192$	−1163.16	+	2392.69i	−0.437206	+	0.899361i
$193$			456.350i			0.170201i	0.996372	+	0.0851005i	$0.0271211\pi$
$193$			456.350i			0.170201i	−0.996372	+	0.0851005i	$0.972879\pi$
$194$	−1509.00	−	1930.33i	−0.558452	−	0.714379i
$195$	−2831.88	+	2376.60i	−1.03998	+	0.872780i
$196$	−632.919	+	2544.49i	−0.230656	+	0.927294i
$197$		−	4127.07i		−	1.49260i	−0.665611	−	0.746299i	$-0.731829\pi$
$197$		−	4127.07i		−	1.49260i	0.665611	−	0.746299i	$-0.268171\pi$
$198$	4241.93	+	1546.10i	1.52253	+	0.554933i
$199$		−	4395.85i		−	1.56590i	−0.622087	−	0.782948i	$-0.713715\pi$
$199$		−	4395.85i		−	1.56590i	0.622087	−	0.782948i	$-0.286285\pi$
$200$	2691.49	+	869.427i	0.951584	+	0.307389i
$201$	−51.1834	−	178.743i	−0.0179612	−	0.0627242i
$202$	−3437.39	+	2687.11i	−1.19730	+	0.935963i
$203$	−672.612			−0.232552
$204$	−101.550	−	2892.32i	−0.0348527	−	0.992661i
$205$	2164.89	+	4856.66i	0.737573	+	1.65465i
$206$	804.038	−	628.542i	0.271942	−	0.212585i
$207$	1295.39	+	2076.43i	0.434957	+	0.697206i
$208$	3598.18	+	1908.08i	1.19946	+	0.636065i
$209$		−	1954.74i		−	0.646948i
$210$	133.174	−	627.628i	0.0437615	−	0.206240i
$211$	4297.34			1.40209			0.701045	−	0.713117i	$-0.252717\pi$
$211$	4297.34			1.40209			0.701045	+	0.713117i	$0.252717\pi$
$212$	3166.44	+	787.623i	1.02581	+	0.255161i
$213$	−4443.09	+	1272.29i	−1.42927	+	0.409275i
$214$	3002.98	−	2347.52i	0.959250	−	0.749876i
$215$	−270.277	−	606.333i	−0.0857337	−	0.192333i
$216$	3018.91	+	981.777i	0.950976	+	0.309266i
$217$		−	241.260i		−	0.0754737i
$218$	−2069.10	−	2646.81i	−0.642830	−	0.822316i
$219$	883.431	+	3085.13i	0.272588	+	0.951934i
$220$	−5206.67	+	923.414i	−1.59561	+	0.282984i
$221$	−4430.52			−1.34855
$222$	93.0261	−	128.016i	0.0281239	−	0.0387021i
$223$	−5589.89			−1.67859			−0.839297	−	0.543673i	$-0.817033\pi$
$223$	−5589.89			−1.67859			−0.839297	+	0.543673i	$0.817033\pi$
$224$	−695.910	+	123.700i	−0.207578	+	0.0368977i
$225$	585.551	−	3323.82i	0.173497	−	0.984834i
$226$	1484.31	−	1160.33i	0.436881	−	0.341523i
$227$	2119.31			0.619662			0.309831	−	0.950792i	$-0.399727\pi$
$227$	2119.31			0.619662			0.309831	+	0.950792i	$0.399727\pi$
$228$	−48.2268	−	1373.58i	−0.0140083	−	0.398980i
$229$		−	3484.25i		−	1.00544i	−0.864449	−	0.502721i	$-0.832332\pi$
$229$		−	3484.25i		−	1.00544i	0.864449	−	0.502721i	$-0.167668\pi$
$230$	−2531.83	−	1343.87i	−0.725844	−	0.385271i
$231$	330.211	+	1153.17i	0.0940533	+	0.328454i
$232$	1588.32	+	3559.48i	0.449476	+	1.00729i
$233$	635.469			0.178674			0.0893368	−	0.996001i	$-0.471525\pi$
$233$	635.469			0.178674			0.0893368	+	0.996001i	$0.471525\pi$
$234$	1664.22	−	4566.00i	0.464929	−	1.27559i
$235$	−2277.95	−	5110.31i	−0.632329	−	1.41855i
$236$	−135.933	−	33.8120i	−0.0374935	−	0.00932616i
$237$	155.435	+	542.812i	0.0426016	+	0.148774i
$238$	605.771	−	473.550i	0.164984	−	0.128973i
$239$	3348.65			0.906302			0.453151	−	0.891434i	$-0.350300\pi$
$239$	3348.65			0.906302			0.453151	+	0.891434i	$0.350300\pi$
$240$	−3635.90	+	777.332i	−0.977901	+	0.209069i
$241$	−4429.34			−1.18390			−0.591948	−	0.805976i	$-0.701641\pi$
$241$	−4429.34			−1.18390			−0.591948	+	0.805976i	$0.701641\pi$
$242$	4822.74	−	3770.09i	1.28106	−	1.00145i
$243$	664.564	−	3729.24i	0.175439	−	0.984490i
$244$	1902.88	+	473.324i	0.499261	+	0.124186i
$245$	−3346.94	+	1491.92i	−0.872767	+	0.389042i
$246$	−5654.51	−	4108.99i	−1.46552	−	1.06496i
$247$	−2104.07			−0.542020
$248$	−1276.75	+	569.717i	−0.326911	+	0.145875i
$249$	3139.75	−	899.074i	0.799092	−	0.228821i
$250$	1357.89	+	3712.29i	0.343522	+	0.939145i
$251$			2194.08i			0.551750i	0.961194	+	0.275875i	$0.0889676\pi$
$251$			2194.08i			0.551750i	−0.961194	+	0.275875i	$0.911032\pi$
$252$	260.487	+	802.173i	0.0651156	+	0.200524i
$253$	5358.89			1.33166
$254$	578.634	−	452.337i	0.142940	−	0.111741i
$255$	3098.17	−	2600.08i	0.760842	−	0.638522i
$256$	2297.96	+	3390.66i	0.561026	+	0.827798i
$257$	5497.40			1.33431			0.667156	−	0.744918i	$-0.267511\pi$
$257$	5497.40			1.33431			0.667156	+	0.744918i	$0.267511\pi$
$258$	705.941	+	512.990i	0.170349	+	0.123788i
$259$	42.0426			0.0100865
$260$	993.960	+	5604.44i	0.237088	+	1.33682i
$261$	3946.05	−	2461.78i	0.935842	−	0.583832i
$262$	−1620.91	−	2073.49i	−0.382215	−	0.488934i
$263$			3495.97i			0.819660i	0.912162	+	0.409830i	$0.134412\pi$
$263$			3495.97i			0.819660i	−0.912162	+	0.409830i	$0.865588\pi$
$264$	5322.81	−	4470.60i	1.24090	−	1.04222i
$265$	1856.59	+	4165.02i	0.430375	+	0.965492i
$266$	287.684	−	224.891i	0.0663121	−	0.0518382i
$267$	1092.38	+	3814.81i	0.250384	+	0.874392i
$268$	−277.789	−	69.0973i	−0.0633158	−	0.0157492i
$269$	585.602			0.132732			0.0663658	−	0.997795i	$-0.478860\pi$
$269$	585.602			0.132732			0.0663658	+	0.997795i	$0.478860\pi$
$270$	1515.83	+	4169.56i	0.341669	+	0.939821i
$271$			7517.66i			1.68511i	0.538609	+	0.842556i	$0.318950\pi$
$271$			7517.66i			1.68511i	−0.538609	+	0.842556i	$0.681050\pi$
$272$	−3936.52	−	2087.50i	−0.877523	−	0.465343i
$273$	1241.26	−	355.438i	0.275182	−	0.0787989i
$274$	−802.391	+	627.254i	−0.176913	+	0.138298i
$275$	−5496.27	−	4940.10i	−1.20523	−	1.08327i
$276$	3765.64	−	132.213i	0.821250	−	0.0288344i
$277$	−504.031			−0.109330			−0.0546648	−	0.998505i	$-0.517409\pi$
$277$	−504.031			−0.109330			−0.0546648	+	0.998505i	$0.517409\pi$
$278$	1279.36	−	1000.12i	0.276011	−	0.215767i
$279$	883.018	+	1415.42i	0.189480	+	0.303723i
$280$	−734.925	−	660.040i	−0.156858	−	0.140875i
$281$		−	7892.83i		−	1.67561i	−0.545969	−	0.837805i	$-0.683839\pi$
$281$		−	7892.83i		−	1.67561i	0.545969	−	0.837805i	$-0.316161\pi$
$282$	5949.82	+	4323.59i	1.25641	+	0.913001i
$283$			5494.85i			1.15419i	0.816678	+	0.577094i	$0.195813\pi$
$283$			5494.85i			1.15419i	−0.816678	+	0.577094i	$0.804187\pi$
$284$	−1717.58	+	6905.10i	−0.358872	+	1.44275i
$285$	1471.33	−	1234.79i	0.305805	−	0.256641i
$286$	−6553.80	−	8383.70i	−1.35502	−	1.73335i
$287$		−	1857.04i		−	0.381943i
$288$	3629.99	−	3272.77i	0.742706	−	0.669617i
$289$	−65.8786			−0.0134090
$290$	−2553.90	+	4811.52i	−0.517139	+	0.974283i
$291$	1239.13	+	4327.30i	0.249619	+	0.871720i
$292$	4794.66	+	1192.63i	0.960912	+	0.239018i
$293$		−	688.366i		−	0.137252i	−0.997642	−	0.0686259i	$-0.978139\pi$
$293$		−	688.366i		−	0.137252i	0.997642	−	0.0686259i	$-0.0218615\pi$
$294$	2831.69	−	3896.77i	0.561726	−	0.773007i
$295$	−79.7019	−	178.801i	−0.0157302	−	0.0352888i
$296$	−99.2804	−	222.490i	−0.0194951	−	0.0436892i
$297$	−6157.89	−	5556.77i	−1.20309	−	1.08565i
$298$	3125.67	−	2443.43i	0.607601	−	0.474980i
$299$		−	5768.29i		−	1.11568i
$300$	−3984.06	−	3335.76i	−0.766732	−	0.641967i
$301$			231.843i			0.0443961i
$302$	−1242.18	−	1589.01i	−0.236686	−	0.302772i
$303$	7705.73	−	2206.55i	1.46100	−	0.418360i
$304$	−1869.47	−	991.364i	−0.352702	−	0.187035i
$305$	1115.72	+	2502.99i	0.209463	+	0.469903i
$306$	−1820.71	+	4995.34i	−0.340140	+	0.933218i
$307$			5319.52i			0.988929i	0.869198	+	0.494464i	$0.164636\pi$
$307$			5319.52i			0.988929i	−0.869198	+	0.494464i	$0.835364\pi$
$308$	1792.16	+	445.783i	0.331552	+	0.0824703i
$309$	−1802.45	+	516.134i	−0.331837	+	0.0950220i
$310$	−1725.85	−	916.063i	−0.316199	−	0.167835i
$311$	−7832.47			−1.42810			−0.714049	−	0.700096i	$-0.753141\pi$
$311$	−7832.47			−1.42810			−0.714049	+	0.700096i	$0.753141\pi$
$312$	−4812.13	−	5729.46i	−0.873184	−	1.03964i
$313$			2374.67i			0.428831i	0.976743	+	0.214416i	$0.0687847\pi$
$313$			2374.67i			0.428831i	−0.976743	+	0.214416i	$0.931215\pi$
$314$	−4222.27	+	3300.68i	−0.758842	+	0.593210i
$315$	−659.399	+	976.994i	−0.117946	+	0.174754i
$316$	843.595	+	209.836i	0.150177	+	0.0373551i
$317$		−	4106.84i		−	0.727643i	−0.931469	−	0.363822i	$-0.881472\pi$
$317$		−	4106.84i		−	0.727643i	0.931469	−	0.363822i	$-0.118528\pi$
$318$	−4849.25	−	3523.83i	−0.855134	−	0.621405i
$319$		−	10184.1i		−	1.78746i
$320$	−1757.48	+	5447.87i	−0.307019	+	0.951703i
$321$	−6731.91	+	1927.69i	−1.17052	+	0.335182i
$322$	616.536	+	788.681i	0.106703	+	0.136495i
$323$	2301.92			0.396540
$324$	−4464.19	−	3752.77i	−0.765464	−	0.643478i
$325$	−5317.50	+	5916.17i	−0.907575	+	1.00975i
$326$	4324.57	+	5532.05i	0.734711	+	0.939852i
$327$	1699.06	+	5933.47i	0.287334	+	1.00343i
$328$	−9827.48	+	4385.25i	−1.65437	+	0.738217i
$329$			1954.03i			0.327443i
$330$	9502.96	+	2016.41i	1.58522	+	0.336362i
$331$	4379.02			0.727168			0.363584	−	0.931562i	$-0.381553\pi$
$331$	4379.02			0.727168			0.363584	+	0.931562i	$0.381553\pi$
$332$	1213.74	−	4879.56i	0.200641	−	0.806629i
$333$	−246.654	+	153.877i	−0.0405903	+	0.0253226i
$334$	5421.52	+	6935.28i	0.888181	+	1.13617i
$335$	−162.877	−	365.393i	−0.0265639	−	0.0595927i
$336$	1270.33	+	269.032i	0.206257	+	0.0436812i
$337$			6774.53i			1.09505i	0.836789	+	0.547525i	$0.184430\pi$
$337$			6774.53i			1.09505i	−0.836789	+	0.547525i	$0.815570\pi$
$338$	−4128.50	+	3227.38i	−0.664381	+	0.519368i
$339$	−3327.45	+	952.820i	−0.533104	+	0.152655i
$340$	−1087.42	−	6131.43i	−0.173452	−	0.978011i
$341$	3652.94			0.580111
$342$	−864.663	+	2372.31i	−0.136712	+	0.375088i
$343$	2619.06			0.412292
$344$	1226.92	−	547.480i	0.192300	−	0.0858085i
$345$	3385.16	+	4033.64i	0.528263	+	0.629461i
$346$	−5400.63	−	6908.56i	−0.839133	−	1.07343i
$347$	4789.77			0.741004			0.370502	−	0.928832i	$-0.379186\pi$
$347$	4789.77			0.741004			0.370502	+	0.928832i	$0.379186\pi$
$348$	−251.259	−	7156.26i	−0.0387037	−	1.10234i
$349$		−	3221.38i		−	0.494087i	−0.969004	−	0.247043i	$-0.920541\pi$
$349$		−	3221.38i		−	0.494087i	0.969004	−	0.247043i	$-0.0794590\pi$
$350$	94.7041	−	1377.25i	0.0144633	−	0.210335i
$351$	−5981.29	+	6628.33i	−0.909566	+	1.00796i
$352$	−1872.96	−	10536.8i	−0.283605	−	1.59550i
$353$	−1778.82			−0.268207			−0.134104	−	0.990967i	$-0.542815\pi$
$353$	−1778.82			−0.268207			−0.134104	+	0.990967i	$0.542815\pi$
$354$	208.174	+	151.275i	0.0312552	+	0.0227124i
$355$	−9082.72	+	4048.69i	−1.35792	+	0.605301i
$356$	5928.69	+	1474.70i	0.882640	+	0.219548i
$357$	−1357.98	+	388.860i	−0.201322	+	0.0576489i
$358$	−3515.99	−	4497.69i	−0.519066	−	0.663996i
$359$	−888.661			−0.130645			−0.0653227	−	0.997864i	$-0.520808\pi$
$359$	−888.661			−0.130645			−0.0653227	+	0.997864i	$0.520808\pi$
$360$	6727.39	+	1182.46i	0.984902	+	0.173113i
$361$	−5765.81			−0.840619
$362$	3385.36	+	4330.59i	0.491520	+	0.628759i
$363$	−10811.3	+	3095.85i	−1.56322	+	0.447630i
$364$	479.839	−	1929.08i	0.0690946	−	0.277778i
$365$	2811.27	+	6306.73i	0.403146	+	0.904409i
$366$	−2914.17	−	2117.66i	−0.416192	−	0.302437i
$367$	−2399.81			−0.341333			−0.170666	−	0.985329i	$-0.554592\pi$
$367$	−2399.81			−0.341333			−0.170666	+	0.985329i	$0.554592\pi$
$368$	2717.81	−	5125.13i	0.384988	−	0.725994i
$369$	6796.81	+	10894.8i	0.958883	+	1.53702i
$370$	159.636	−	300.751i	0.0224299	−	0.0422576i
$371$		−	1592.58i		−	0.222864i
$372$	2566.89	−	90.1243i	0.357760	−	0.0125611i
$373$	−7562.31			−1.04976			−0.524881	−	0.851175i	$-0.675890\pi$
$373$	−7562.31			−1.04976			−0.524881	+	0.851175i	$0.675890\pi$
$374$	7170.06	+	9172.03i	0.991324	+	1.26811i
$375$	246.478	−	7257.66i	0.0339415	−	0.999424i
$376$	10340.7	−	4614.28i	1.41831	−	0.632881i
$377$	−10962.1			−1.49755
$378$	109.343	−	1545.57i	0.0148783	−	0.210306i
$379$	−7024.75			−0.952077			−0.476038	−	0.879424i	$-0.657928\pi$
$379$	−7024.75			−0.952077			−0.476038	+	0.879424i	$0.657928\pi$
$380$	−516.422	−	2911.85i	−0.0697155	−	0.393091i
$381$	−1297.15	+	371.441i	−0.174422	+	0.0499462i
$382$	−8753.41	+	6842.81i	−1.17242	+	0.916515i
$383$		−	3306.11i		−	0.441081i	−0.975378	−	0.220541i	$-0.929218\pi$
$383$		−	3306.11i		−	0.441081i	0.975378	−	0.220541i	$-0.0707822\pi$
$384$	−1576.07	−	7357.93i	−0.209449	−	0.977819i
$385$	1050.80	+	2357.35i	0.139101	+	0.312056i
$386$	−794.948	−	1016.91i	−0.104823	−	0.134091i
$387$	−848.553	−	1360.17i	−0.111458	−	0.178660i
$388$	6725.15	+	1672.82i	0.879942	+	0.218877i
$389$	4431.14			0.577551			0.288776	−	0.957397i	$-0.406752\pi$
$389$	4431.14			0.577551			0.288776	+	0.957397i	$0.406752\pi$
$390$	2170.45	−	10229.0i	0.281808	−	1.32811i
$391$			6310.69i			0.816228i
$392$	−3022.07	−	6772.55i	−0.389381	−	0.872616i
$393$	1331.03	+	4648.23i	0.170844	+	0.596622i
$394$	7189.24	+	9196.56i	0.919261	+	1.17593i
$395$	494.628	+	1109.63i	0.0630061	+	0.141346i
$396$	−12145.8	+	3944.06i	−1.54128	+	0.500496i
$397$	10715.8			1.35469			0.677343	−	0.735668i	$-0.263131\pi$
$397$	10715.8			1.35469			0.677343	+	0.735668i	$0.263131\pi$
$398$	7657.44	+	9795.49i	0.964403	+	1.23368i
$399$	−644.912	+	184.672i	−0.0809173	+	0.0231708i
$400$	−7512.09	+	2751.10i	−0.939011	+	0.343888i
$401$			3245.09i			0.404120i	0.979373	+	0.202060i	$0.0647635\pi$
$401$			3245.09i			0.404120i	−0.979373	+	0.202060i	$0.935236\pi$
$402$	425.420	+	309.142i	0.0527811	+	0.0383547i
$403$		−	3932.01i		−	0.486023i
$404$	2978.83	−	11975.6i	0.366837	−	1.47478i
$405$	292.711	−	8145.21i	0.0359134	−	0.999355i
$406$	1498.81	−	1171.67i	0.183214	−	0.143224i
$407$			636.571i			0.0775274i
$408$	5264.62	+	6268.20i	0.638818	+	0.760594i
$409$	−3135.87			−0.379117			−0.189558	−	0.981869i	$-0.560706\pi$
$409$	−3135.87			−0.379117			−0.189558	+	0.981869i	$0.560706\pi$
$410$	−13284.3	−	7051.16i	−1.60016	−	0.849346i
$411$	1798.75	−	515.076i	0.215878	−	0.0618171i
$412$	−696.777	+	2801.22i	−0.0833198	+	0.334967i
$413$			68.3681i			0.00814570i
$414$	−6503.66	−	2370.46i	−0.772071	−	0.281406i
$415$	6418.40	−	2861.05i	0.759197	−	0.338418i
$416$	−11341.8	+	2016.04i	−1.33673	+	0.237608i
$417$	−2868.00	+	821.257i	−0.336803	+	0.0964440i
$418$	3405.10	+	4355.84i	0.398442	+	0.509692i
$419$		−	7364.44i		−	0.858655i	−0.903149	−	0.429327i	$-0.858751\pi$
$419$		−	7364.44i		−	0.858655i	0.903149	−	0.429327i	$-0.141249\pi$
$420$	796.549	+	1630.56i	0.0925420	+	0.189436i
$421$		−	4582.24i		−	0.530463i	−0.964185	−	0.265231i	$-0.914552\pi$
$421$		−	4582.24i		−	0.530463i	0.964185	−	0.265231i	$-0.0854483\pi$
$422$	−9575.97	+	7485.83i	−1.10462	+	0.863518i
$423$	−7151.78	−	11463.8i	−0.822060	−	1.31770i
$424$	−8427.96	+	3760.75i	−0.965325	+	0.430750i
$425$	5817.51	−	6472.47i	0.663978	−	0.738731i
$426$	7684.47	−	10574.8i	0.873976	−	1.20270i
$427$		−	957.065i		−	0.108468i
$428$	−2602.37	+	10462.2i	−0.293903	+	1.18157i
$429$	5381.72	+	18794.1i	0.605669	+	2.11512i
$430$	1658.49	+	880.307i	0.185998	+	0.0987260i
$431$	−5956.76			−0.665724			−0.332862	−	0.942976i	$-0.608014\pi$
$431$	−5956.76			−0.665724			−0.332862	+	0.942976i	$0.608014\pi$
$432$	−8437.41	+	3071.11i	−0.939688	+	0.342034i
$433$		−	5990.82i		−	0.664897i	−0.943121	−	0.332449i	$-0.892125\pi$
$433$		−	5990.82i		−	0.664897i	0.943121	−	0.332449i	$-0.107875\pi$
$434$	420.268	+	537.612i	0.0464827	+	0.0594613i
$435$	7665.57	−	6433.18i	0.844910	−	0.709075i
$436$	9221.34	+	2293.72i	1.01289	+	0.251948i
$437$			2996.98i			0.328066i
$438$	−7342.79	−	5335.83i	−0.801032	−	0.582091i
$439$		−	3323.14i		−	0.361287i	−0.983549	−	0.180644i	$-0.942182\pi$
$439$		−	3323.14i		−	0.361287i	0.983549	−	0.180644i	$-0.0578180\pi$
$440$	9993.73	−	11127.6i	1.08280	−	1.20565i
$441$	−7508.08	+	4683.98i	−0.810721	+	0.505775i
$442$	9872.74	−	7717.83i	1.06244	−	0.830542i
$443$	10439.3			1.11961			0.559805	−	0.828624i	$-0.310876\pi$
$443$	10439.3			1.11961			0.559805	+	0.828624i	$0.310876\pi$
$444$	15.7053	+	447.313i	0.00167870	+	0.0478120i
$445$	3476.18	+	7798.38i	0.370307	+	0.830739i
$446$	12456.2	−	9737.41i	1.32246	−	1.03381i
$447$	−7006.93	+	2006.45i	−0.741424	+	0.212308i
$448$	1335.25	−	1487.90i	0.140814	−	0.156912i
$449$		−	1513.03i		−	0.159029i	−0.996834	−	0.0795147i	$-0.974663\pi$
$449$		−	1513.03i		−	0.159029i	0.996834	−	0.0795147i	$-0.0253371\pi$
$450$	4485.18	+	8426.64i	0.469852	+	0.882745i
$451$	28117.6			2.93571
$452$	−1286.30	+	5171.26i	−0.133855	+	0.538132i
$453$	1020.03	+	3562.15i	0.105795	+	0.369458i
$454$	−4722.56	+	3691.77i	−0.488195	+	0.381637i
$455$	2537.44	−	1131.08i	0.261444	−	0.116540i
$456$	2500.20	+	2976.80i	0.256760	+	0.305705i
$457$		−	14449.0i		−	1.47898i	−0.673165	−	0.739492i	$-0.735066\pi$
$457$		−	14449.0i		−	1.47898i	0.673165	−	0.739492i	$-0.264934\pi$
$458$	6069.47	+	7764.14i	0.619230	+	0.792127i
$459$	6543.72	−	7251.60i	0.665435	−	0.737420i
$460$	7982.79	−	1415.76i	0.809130	−	0.143501i
$461$	12494.6			1.26233			0.631164	−	0.775649i	$-0.282577\pi$
$461$	12494.6			1.26233			0.631164	+	0.775649i	$0.282577\pi$
$462$	−2744.61	−	1994.44i	−0.276387	−	0.200844i
$463$	1991.33			0.199881			0.0999406	−	0.994993i	$-0.468135\pi$
$463$	1991.33			0.199881			0.0999406	+	0.994993i	$0.468135\pi$
$464$	−9739.83	−	5164.95i	−0.974484	−	0.516760i
$465$	2307.53	+	2749.57i	0.230127	+	0.274212i
$466$	−1416.05	+	1106.97i	−0.140766	+	0.110041i
$467$	1976.98			0.195897			0.0979485	−	0.995191i	$-0.468772\pi$
$467$	1976.98			0.195897			0.0979485	+	0.995191i	$0.468772\pi$
$468$	4245.37	+	13073.7i	0.419321	+	1.29130i
$469$			139.715i			0.0137558i
$470$	13978.1	+	7419.42i	1.37183	+	0.728154i
$471$	9465.23	−	2710.39i	0.925976	−	0.265155i
$472$	361.805	−	161.446i	0.0352827	−	0.0157440i
$473$	−3510.36			−0.341240
$474$	−1291.92	−	938.811i	−0.125190	−	0.0909726i
$475$	2762.77	−	3073.81i	0.266872	−	0.296918i
$476$	−524.959	+	2110.47i	−0.0505493	+	0.203221i
$477$	5828.88	+	9343.28i	0.559509	+	0.896854i
$478$	−7461.97	+	5833.25i	−0.714022	+	0.558173i
$479$	−15429.2			−1.47177			−0.735884	−	0.677108i	$-0.763233\pi$
$479$	−15429.2			−1.47177			−0.735884	+	0.677108i	$0.763233\pi$
$480$	6747.96	−	8065.79i	0.641669	−	0.766982i
$481$	685.203			0.0649534
$482$	9870.12	−	7715.78i	0.932721	−	0.729137i
$483$	−506.275	−	1768.02i	−0.0476942	−	0.166558i
$484$	−4179.38	+	16802.1i	−0.392503	+	1.57796i
$485$	3943.17	+	8846.01i	0.369176	+	0.828200i
$486$	5015.35	+	9467.71i	0.468109	+	0.883671i
$487$	323.435			0.0300949			0.0150475	−	0.999887i	$-0.495210\pi$
$487$	323.435			0.0300949			0.0150475	+	0.999887i	$0.495210\pi$
$488$	−5064.81	+	2260.04i	−0.469822	+	0.209645i
$489$	−3551.17	−	12401.4i	−0.328403	−	1.14685i
$490$	4859.26	−	9154.78i	0.447998	−	0.844022i
$491$		−	10843.0i		−	0.996617i	−0.867000	−	0.498308i	$-0.833955\pi$
$491$		−	10843.0i		−	0.996617i	0.867000	−	0.498308i	$-0.166045\pi$
$492$	19758.0	−	693.709i	1.81048	−	0.0635667i
$493$	11992.9			1.09560
$494$	4688.61	−	3665.23i	0.427026	−	0.333819i
$495$	−14792.8	−	9984.02i	−1.34320	−	0.906562i
$496$	1852.62	−	3493.59i	0.167712	−	0.316264i
$497$	3472.96			0.313447
$498$	−5430.31	+	7472.81i	−0.488631	+	0.672419i
$499$	−8534.00			−0.765599			−0.382800	−	0.923831i	$-0.625040\pi$
$499$	−8534.00			−0.765599			−0.382800	+	0.923831i	$0.625040\pi$
$500$	−9492.56	−	5906.88i	−0.849041	−	0.528328i
$501$	−4451.94	−	15547.1i	−0.397002	−	1.38641i
$502$	−3822.02	−	4889.18i	−0.339811	−	0.434691i
$503$		−	8197.47i		−	0.726654i	−0.931662	−	0.363327i	$-0.881641\pi$
$503$		−	8197.47i		−	0.726654i	0.931662	−	0.363327i	$-0.118359\pi$
$504$	−1977.82	−	1333.76i	−0.174800	−	0.117878i
$505$	15752.3	−	7021.71i	1.38806	−	0.618737i
$506$	−11941.5	+	9335.03i	−1.04914	+	0.820144i
$507$	9255.04	−	2650.20i	0.810711	−	0.232149i
$508$	−501.443	+	2015.93i	−0.0437951	+	0.176068i
$509$	−9137.11			−0.795669			−0.397834	−	0.917457i	$-0.630238\pi$
$509$	−9137.11			−0.795669			−0.397834	+	0.917457i	$0.630238\pi$
$510$	−2374.54	+	11190.8i	−0.206170	+	0.971640i
$511$		−	2411.50i		−	0.208764i
$512$	−11027.1	−	3552.60i	−0.951823	−	0.306649i
$513$	3107.64	−	3443.82i	0.267458	−	0.296391i
$514$	−12250.1	+	9576.30i	−1.05123	+	0.821775i
$515$	−3684.63	+	1642.45i	−0.315270	+	0.140534i
$516$	−2466.70	+	86.6066i	−0.210446	+	0.00738884i
$517$	−29586.1			−2.51682
$518$	−93.6857	+	73.2370i	−0.00794655	+	0.00621207i
$519$	4434.79	+	15487.2i	0.375078	+	1.30985i
$520$	−11977.7	−	10757.2i	−1.01011	−	0.907182i
$521$			9974.29i			0.838736i	0.907816	+	0.419368i	$0.137748\pi$
$521$			9974.29i			0.838736i	−0.907816	+	0.419368i	$0.862252\pi$
$522$	−4504.84	+	12359.6i	−0.377724	+	1.03633i
$523$		−	13425.7i		−	1.12250i	−0.827647	−	0.561248i	$-0.810321\pi$
$523$		−	13425.7i		−	1.12250i	0.827647	−	0.561248i	$-0.189679\pi$
$524$	7223.92	+	1796.88i	0.602249	+	0.149804i
$525$	−1110.59	+	2280.05i	−0.0923244	+	0.189542i
$526$	−6089.87	−	7790.23i	−0.504812	−	0.645761i
$527$			4301.74i			0.355573i
$528$	−4073.44	+	19234.2i	−0.335745	+	1.58535i
$529$	3950.83			0.324717
$530$	−11392.5	−	6047.01i	−0.933694	−	0.495595i
$531$	−250.229	−	401.099i	−0.0204501	−	0.0327801i
$532$	−249.306	+	1002.27i	−0.0203172	+	0.0816805i
$533$		−	30265.7i		−	2.45957i
$534$	−9079.49	−	6597.85i	−0.735783	−	0.534676i
$535$	−13761.6	+	6134.33i	−1.11209	+	0.495720i
$536$	739.375	−	329.927i	0.0595824	−	0.0265870i
$537$	2887.19	+	10082.7i	0.232014	+	0.810241i
$538$	−1304.93	+	1020.10i	−0.104571	+	0.0817466i
$539$			19377.1i			1.54848i
$540$	−10641.1	−	6650.71i	−0.847996	−	0.530002i
$541$		−	8972.66i		−	0.713059i	−0.934284	−	0.356530i	$-0.883960\pi$
$541$		−	8972.66i		−	0.713059i	0.934284	−	0.356530i	$-0.116040\pi$
$542$	−13095.5	−	16752.0i	−1.03783	−	1.32760i
$543$	−2779.92	−	9708.06i	−0.219701	−	0.767243i
$544$	12408.3	−	2205.62i	0.977943	−	0.173833i
$545$	5406.77	+	12129.4i	0.424955	+	0.953334i
$546$	−2146.81	+	2954.29i	−0.168269	+	0.231560i
$547$			1210.47i			0.0946175i	0.998880	+	0.0473087i	$0.0150645\pi$
$547$			1210.47i			0.0946175i	−0.998880	+	0.0473087i	$0.984936\pi$
$548$	695.349	−	2795.48i	0.0542041	−	0.217914i
$549$	3502.88	+	5614.87i	0.272312	+	0.436497i
$550$	20853.1	+	1433.92i	1.61669	+	0.111169i
$551$	5695.48			0.440355
$552$	−8160.86	+	6854.25i	−0.629256	+	0.528508i
$553$		−	424.291i		−	0.0326269i
$554$	1123.16	−	878.008i	0.0861343	−	0.0673339i
$555$	−479.148	+	402.116i	−0.0366463	+	0.0307547i
$556$	−1108.69	+	4457.22i	−0.0845666	+	0.339979i
$557$			13253.5i			1.00820i	0.863644	+	0.504102i	$0.168176\pi$
$557$			13253.5i			1.00820i	−0.863644	+	0.504102i	$0.831824\pi$
$558$	−4433.28	−	1615.85i	−0.336337	−	0.122588i
$559$			3778.54i			0.285895i
$560$	2787.44	+	190.583i	0.210341	+	0.0143815i
$561$	−5887.77	−	20561.3i	−0.443105	−	1.54741i
$562$	13749.1	+	17588.0i	1.03197	+	1.32011i
$563$	−7028.69			−0.526152			−0.263076	−	0.964775i	$-0.584737\pi$
$563$	−7028.69			−0.526152			−0.263076	+	0.964775i	$0.584737\pi$
$564$	−20789.8	+	729.939i	−1.55215	+	0.0544964i
$565$	−6802.09	+	3032.08i	−0.506488	+	0.225771i
$566$	−9571.87	−	12244.5i	−0.710840	−	0.909316i
$567$	−1251.54	+	2556.60i	−0.0926983	+	0.189360i
$568$	−8201.11	−	18378.9i	−0.605829	−	1.35768i
$569$			15183.3i			1.11866i	0.828945	+	0.559330i	$0.188942\pi$
$569$			15183.3i			1.11866i	−0.828945	+	0.559330i	$0.811058\pi$
$570$	−1127.68	+	5314.56i	−0.0828656	+	0.390531i
$571$	−20286.3			−1.48679			−0.743395	−	0.668853i	$-0.766786\pi$
$571$	−20286.3			−1.48679			−0.743395	+	0.668853i	$0.766786\pi$
$572$	29208.3	+	7265.29i	2.13507	+	0.531079i
$573$	19622.9	−	5619.05i	1.43064	−	0.409667i
$574$	3234.91	+	4138.13i	0.235231	+	0.300910i
$575$	8426.80	+	7574.08i	0.611168	+	0.549324i
$576$	−2387.82	+	13616.2i	−0.172730	+	0.984969i
$577$		−	11832.9i		−	0.853744i	−0.904312	−	0.426872i	$-0.859615\pi$
$577$		−	11832.9i		−	0.853744i	0.904312	−	0.426872i	$-0.140385\pi$
$578$	146.801	−	114.759i	0.0105642	−	0.00825836i
$579$	652.780	+	2279.64i	0.0468542	+	0.163625i
$580$	−2690.53	−	15170.6i	−0.192618	−	1.08607i
$581$	−2454.20			−0.175245
$582$	−10299.2	−	7484.20i	−0.733534	−	0.533041i
$583$	24113.4			1.71299
$584$	−12761.7	+	5694.57i	−0.904252	+	0.403498i
$585$	−10746.8	+	15922.9i	−0.759528	+	1.12535i
$586$	1199.11	+	1533.92i	0.0845306	+	0.108133i
$587$	−18390.7			−1.29313			−0.646565	−	0.762859i	$-0.723795\pi$
$587$	−18390.7			−1.29313			−0.646565	+	0.762859i	$0.723795\pi$
$588$	478.065	+	13616.1i	0.0335290	+	0.954962i
$589$			2042.92i			0.142915i
$590$	489.070	+	259.593i	0.0341266	+	0.0181140i
$591$	−5903.52	−	20616.3i	−0.410894	−	1.43493i
$592$	608.803	+	322.843i	0.0422663	+	0.0224134i
$593$	−26626.5			−1.84388			−0.921939	−	0.387335i	$-0.873396\pi$
$593$	−26626.5			−1.84388			−0.921939	+	0.387335i	$0.873396\pi$
$594$	23401.7	+	1655.57i	1.61647	+	0.114358i
$595$	−2776.04	+	1237.44i	−0.191271	+	0.0852605i
$596$	−2708.69	+	10889.6i	−0.186162	+	0.748417i
$597$	−6287.98	−	21958.9i	−0.431072	−	1.50539i
$598$	10048.2	+	12853.8i	0.687126	+	0.878979i
$599$	13589.0			0.926929			0.463465	−	0.886115i	$-0.346606\pi$
$599$	13589.0			0.926929			0.463465	+	0.886115i	$0.346606\pi$
$600$	14688.7	+	493.123i	0.999437	+	0.0335527i
$601$	271.371			0.0184184			0.00920920	−	0.999958i	$-0.497069\pi$
$601$	271.371			0.0184184			0.00920920	+	0.999958i	$0.497069\pi$
$602$	−403.864	−	516.628i	−0.0273426	−	0.0349770i
$603$	−511.361	−	819.676i	−0.0345344	−	0.0553562i
$604$	5536.01	+	1377.03i	0.372942	+	0.0927659i
$605$	−22100.9	+	9851.65i	−1.48518	+	0.662027i
$606$	−13327.3	+	18340.1i	−0.893375	+	1.22940i
$607$	21346.6			1.42740			0.713701	−	0.700451i	$-0.247018\pi$
$607$	21346.6			1.42740			0.713701	+	0.700451i	$0.247018\pi$
$608$	5892.76	−	1047.46i	0.393064	−	0.0698684i
$609$	−3359.96	+	962.129i	−0.223567	+	0.0640188i
$610$	−6846.35	−	3633.97i	−0.454427	−	0.241205i
$611$			31846.3i			2.10862i
$612$	−4644.56	−	14303.0i	−0.306773	−	0.944712i
$613$	−25625.9			−1.68845			−0.844227	−	0.535986i	$-0.819940\pi$
$613$	−25625.9			−1.68845			−0.844227	+	0.535986i	$0.819940\pi$
$614$	−9266.45	−	11853.8i	−0.609061	−	0.779118i
$615$	17761.6	+	21164.1i	1.16458	+	1.38768i
$616$	−4770.10	+	2128.53i	−0.312002	+	0.139222i
$617$	25139.3			1.64031			0.820154	−	0.572142i	$-0.193888\pi$
$617$	25139.3			1.64031			0.820154	+	0.572142i	$0.193888\pi$
$618$	3117.39	−	4289.93i	0.202912	−	0.279234i
$619$	2383.46			0.154765			0.0773824	−	0.997001i	$-0.475344\pi$
$619$	2383.46			0.154765			0.0773824	+	0.997001i	$0.475344\pi$
$620$	5441.55	−	965.070i	0.352480	−	0.0625131i
$621$	9441.19	+	8519.56i	0.610083	+	0.550529i
$622$	17453.5	−	13643.9i	1.12511	−	0.879536i
$623$		−	2981.86i		−	0.191759i
$624$	20703.7	+	4384.63i	1.32822	+	0.281291i
$625$	−1660.65	−	15536.5i	−0.106282	−	0.994336i
$626$	−4136.60	−	5291.59i	−0.264108	−	0.337851i
$627$	−2796.13	−	9764.67i	−0.178097	−	0.621951i
$628$	3659.00	−	14710.1i	0.232500	−	0.934710i
$629$	−749.633			−0.0475196
$630$	−232.524	−	3325.74i	−0.0147047	−	0.210318i
$631$			13751.7i			0.867585i	0.901013	+	0.433793i	$0.142825\pi$
$631$			13751.7i			0.867585i	−0.901013	+	0.433793i	$0.857175\pi$
$632$	−2245.35	+	1001.93i	−0.141322	+	0.0630611i
$633$	21466.9	−	6147.07i	1.34792	−	0.385978i
$634$	7153.99	+	9151.47i	0.448140	+	0.573267i
$635$	−2651.68	+	1182.00i	−0.165714	+	0.0738684i
$636$	16944.2	−	594.918i	1.05642	−	0.0370913i
$637$	20857.4			1.29733
$638$	17740.4	+	22693.7i	1.10086	+	1.40823i
$639$	−20375.0	+	12711.1i	−1.26138	+	0.786923i
$640$	−5573.75	−	15201.2i	−0.344253	−	0.938877i
$641$		−	7866.10i		−	0.484699i	−0.970189	−	0.242350i	$-0.922082\pi$
$641$		−	7866.10i		−	0.484699i	0.970189	−	0.242350i	$-0.0779181\pi$
$642$	11643.1	−	16022.4i	0.715755	−	0.984972i
$643$			27498.6i			1.68653i	0.537498	+	0.843265i	$0.319370\pi$
$643$			27498.6i			1.68653i	−0.537498	+	0.843265i	$0.680630\pi$
$644$	−2747.72	−	683.468i	−0.168129	−	0.0418205i
$645$	−2217.46	−	2642.25i	−0.135368	−	0.161300i
$646$	−5129.49	+	4009.88i	−0.312410	+	0.244221i
$647$			2282.05i			0.138666i	0.997594	+	0.0693328i	$0.0220870\pi$
$647$			2282.05i			0.138666i	−0.997594	+	0.0693328i	$0.977913\pi$
$648$	16485.0	+	585.993i	0.999369	+	0.0355247i
$649$	−1035.17			−0.0626100
$650$	1543.47	−	22446.2i	0.0931383	−	1.35448i
$651$	−345.107	−	1205.19i	−0.0207770	−	0.0725576i
$652$	−19273.3	−	4794.05i	−1.15767	−	0.287960i
$653$		−	12749.7i		−	0.764065i	−0.924149	−	0.382032i	$-0.875224\pi$
$653$		−	12749.7i		−	0.764065i	0.924149	−	0.382032i	$-0.124776\pi$
$654$	−14122.0	−	10262.1i	−0.844365	−	0.613580i
$655$	4235.62	+	9502.09i	0.252671	+	0.566836i
$656$	14260.1	−	26891.1i	0.848724	−	1.60049i
$657$	8826.15	+	14147.7i	0.524111	+	0.840113i
$658$	−3403.85	−	4354.25i	−0.201666	−	0.257973i
$659$		−	11221.7i		−	0.663329i	−0.943397	−	0.331664i	$-0.892390\pi$
$659$		−	11221.7i		−	0.663329i	0.943397	−	0.331664i	$-0.107610\pi$
$660$	−24688.4	+	12060.6i	−1.45605	+	0.711302i
$661$		−	16408.1i		−	0.965506i	−0.875756	−	0.482753i	$-0.839637\pi$
$661$		−	16408.1i		−	0.965506i	0.875756	−	0.482753i	$-0.160363\pi$
$662$	−9757.98	+	7628.11i	−0.572892	+	0.447848i
$663$	−22132.1	+	6337.57i	−1.29644	+	0.371238i
$664$	5795.40	+	12987.7i	0.338713	+	0.759066i
$665$	−1318.35	+	587.665i	−0.0768775	+	0.0342687i
$666$	281.582	−	772.556i	0.0163830	−	0.0449489i
$667$			15614.1i			0.906416i
$668$	−24162.1	−	6010.09i	−1.39949	−	0.348110i
$669$	−27923.6	+	7995.98i	−1.61374	+	0.462096i
$670$	999.450	+	530.497i	0.0576300	+	0.0305894i
$671$	14491.0			0.833710
$672$	−3299.39	+	1613.39i	−0.189400	+	0.0926156i
$673$			9153.75i			0.524296i	0.965028	+	0.262148i	$0.0844309\pi$
$673$			9153.75i			0.524296i	−0.965028	+	0.262148i	$0.915569\pi$
$674$	−11801.0	−	15096.0i	−0.674419	−	0.862725i
$675$	−1829.46	−	17441.3i	−0.104320	−	0.994544i
$676$	3577.75	−	14383.5i	0.203559	−	0.818358i
$677$			17813.6i			1.01128i	0.862746	+	0.505638i	$0.168743\pi$
$677$			17813.6i			1.01128i	−0.862746	+	0.505638i	$0.831257\pi$
$678$	5754.93	−	7919.53i	0.325983	−	0.448595i
$679$		−	3382.45i		−	0.191173i
$680$	13103.9	+	11768.7i	0.738989	+	0.663691i
$681$	10586.8	−	3031.53i	0.595720	−	0.170585i
$682$	−8140.03	+	6363.31i	−0.457035	+	0.357278i
$683$	−1277.22			−0.0715540			−0.0357770	−	0.999360i	$-0.511391\pi$
$683$	−1277.22			−0.0715540			−0.0357770	+	0.999360i	$0.511391\pi$
$684$	−2205.73	−	6792.56i	−0.123301	−	0.379708i
$685$	3677.07	−	1639.08i	0.205100	−	0.0914250i
$686$	−5836.19	+	4562.33i	−0.324820	+	0.253922i
$687$	−4984.00	−	17405.2i	−0.276785	−	0.966593i
$688$	−1780.31	+	3357.23i	−0.0986536	+	0.186037i
$689$		−	25955.5i		−	1.43516i
$690$	−14569.8	−	3091.52i	−0.803859	−	0.170569i
$691$	−6041.97			−0.332630			−0.166315	−	0.986073i	$-0.553187\pi$
$691$	−6041.97			−0.332630			−0.166315	+	0.986073i	$0.553187\pi$
$692$	24069.0	+	5986.94i	1.32221	+	0.328886i
$693$	3299.06	+	5288.16i	0.180838	+	0.289871i
$694$	−10673.3	+	8343.64i	−0.583793	+	0.456369i
$695$	−5862.87	+	2613.42i	−0.319988	+	0.142637i
$696$	13025.9	+	15509.0i	0.709403	+	0.844634i
$697$			33111.6i			1.79941i
$698$	5611.54	+	7178.35i	0.304298	+	0.389262i
$699$	3174.41	−	908.998i	0.171770	−	0.0491866i
$700$	2188.10	+	3233.97i	0.118146	+	0.174618i
$701$	−8649.55			−0.466033			−0.233016	−	0.972473i	$-0.574860\pi$
$701$	−8649.55			−0.466033			−0.233016	+	0.972473i	$0.574860\pi$
$702$	1782.05	−	25189.5i	0.0958106	−	1.35429i
$703$	−356.005			−0.0190995
$704$	22528.5	+	20217.1i	1.20607	+	1.08233i
$705$	−18689.2	−	22269.5i	−0.998407	−	1.18967i
$706$	3963.83	−	3098.65i	0.211304	−	0.165183i
$707$	−6023.21			−0.320405
$708$	−727.402	+	25.5394i	−0.0386122	+	0.00135569i
$709$		−	32669.4i		−	1.73050i	−0.501339	−	0.865251i	$-0.667159\pi$
$709$		−	32669.4i		−	1.73050i	0.501339	−	0.865251i	$-0.332841\pi$
$710$	13186.8	−	24843.7i	0.697030	−	1.31319i
$711$	1552.91	+	2489.21i	0.0819112	+	0.131298i
$712$	−15780.1	+	7041.44i	−0.830594	+	0.370631i
$713$	−5600.63			−0.294173
$714$	2348.67	−	3232.08i	0.123105	−	0.169408i
$715$	17125.8	+	38419.6i	0.895760	+	2.00952i
$716$	15669.7	+	3897.69i	0.817883	+	0.203441i
$717$	16727.8	−	4790.03i	0.871285	−	0.249494i
$718$	1980.25	−	1548.02i	0.102928	−	0.0804618i
$719$	35829.6			1.85844			0.929221	−	0.369524i	$-0.120479\pi$
$719$	35829.6			1.85844			0.929221	+	0.369524i	$0.120479\pi$
$720$	−17050.8	+	9083.99i	−0.882563	+	0.470195i
$721$	1408.89			0.0727736
$722$	12848.2	−	10043.9i	0.662274	−	0.517720i
$723$	−22126.3	+	6335.89i	−1.13815	+	0.325912i
$724$	−15087.5	−	3752.87i	−0.774479	−	0.192644i
$725$	14393.8	−	16014.4i	0.737343	−	0.820356i
$726$	18698.6	−	25731.7i	0.955881	−	1.31542i
$727$	−15633.8			−0.797561			−0.398781	−	0.917046i	$-0.630566\pi$
$727$	−15633.8			−0.797561			−0.398781	+	0.917046i	$0.630566\pi$
$728$	2291.14	+	5134.52i	0.116642	+	0.261398i
$729$	−2014.70	−	19579.6i	−0.102357	−	0.994748i
$730$	−17250.6	−	9156.45i	−0.874622	−	0.464240i
$731$		−	4133.84i		−	0.209159i
$732$	10182.7	−	357.518i	0.514158	−	0.0180523i
$733$	6139.39			0.309364			0.154682	−	0.987964i	$-0.450565\pi$
$733$	6139.39			0.309364			0.154682	+	0.987964i	$0.450565\pi$
$734$	5347.62	−	4180.40i	0.268916	−	0.210220i
$735$	−14585.1	+	12240.3i	−0.731946	+	0.614272i
$736$	2871.59	+	16154.9i	0.143816	+	0.809074i
$737$	−2115.44			−0.105730
$738$	−34124.1	−	12437.6i	−1.70207	−	0.620371i
$739$	−23289.0			−1.15927			−0.579634	−	0.814877i	$-0.696804\pi$
$739$	−23289.0			−1.15927			−0.579634	+	0.814877i	$0.696804\pi$
$740$	168.176	+	948.259i	0.00835441	+	0.0471063i
$741$	−10510.7	+	3009.74i	−0.521078	+	0.149211i
$742$	2774.22	+	3548.82i	0.137257	+	0.175581i
$743$			22930.0i			1.13219i	0.824339	+	0.566096i	$0.191547\pi$
$743$			22930.0i			1.13219i	−0.824339	+	0.566096i	$0.808453\pi$
$744$	−5562.93	+	4672.27i	−0.274122	+	0.230233i
$745$	−14323.8	+	6384.95i	−0.704409	+	0.313995i
$746$	16851.5	−	13173.3i	0.827045	−	0.646527i
$747$	14398.2	−	8982.44i	0.705225	−	0.439960i
$748$	−31954.8	−	7948.45i	−1.56201	−	0.388535i
$749$	5262.02			0.256702
$750$	12093.4	+	16602.0i	0.588784	+	0.808290i
$751$			10373.1i			0.504023i	0.967724	+	0.252011i	$0.0810920\pi$
$751$			10373.1i			0.504023i	−0.967724	+	0.252011i	$0.918908\pi$
$752$	−15004.8	+	28295.5i	−0.727620	+	1.37211i
$753$	3138.49	+	10960.3i	0.151890	+	0.530431i
$754$	24427.4	−	19095.7i	1.17983	−	0.922311i
$755$	3245.95	+	7281.87i	0.156466	+	0.351013i
$756$	2448.69	+	3634.55i	0.117802	+	0.174851i
$757$	−19427.2			−0.932753			−0.466377	−	0.884586i	$-0.654441\pi$
$757$	−19427.2			−0.932753			−0.466377	+	0.884586i	$0.654441\pi$
$758$	15653.6	−	12236.9i	0.750085	−	0.586364i
$759$	26769.7	−	7665.55i	1.28021	−	0.366590i
$760$	6223.12	+	5589.02i	0.297022	+	0.266757i
$761$		−	17770.0i		−	0.846467i	−0.906021	−	0.423233i	$-0.860895\pi$
$761$		−	17770.0i		−	0.846467i	0.906021	−	0.423233i	$-0.139105\pi$
$762$	2243.46	−	3087.29i	0.106656	−	0.146773i
$763$		−	4637.92i		−	0.220058i
$764$	7585.68	−	30496.4i	0.359215	−	1.44414i
$765$	11757.3	−	17420.1i	0.555667	−	0.823301i
$766$	5759.14	+	7367.16i	0.271653	+	0.347502i
$767$			1114.25i			0.0524553i
$768$	16329.3	+	13650.6i	0.767232	+	0.641370i
$769$	6380.37			0.299196			0.149598	−	0.988747i	$-0.452202\pi$
$769$	6380.37			0.299196			0.149598	+	0.988747i	$0.452202\pi$
$770$	−6447.98	−	3422.52i	−0.301778	−	0.160181i

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)

\(f(q)\)	\(=\)	\(q+(-2.22835 + 1.74197i) q^{2} +(4.99538 - 1.43044i) q^{3} +(1.93108 - 7.76344i) q^{4} +(10.2117 - 4.55196i) q^{5} +(-8.63968 + 11.8893i) q^{6} -3.90466 q^{7} +(9.22055 + 20.6635i) q^{8} +(22.9077 - 14.2912i) q^{9} +O(q^{10})\)	\(q+(-2.22835 + 1.74197i) q^{2} +(4.99538 - 1.43044i) q^{3} +(1.93108 - 7.76344i) q^{4} +(10.2117 - 4.55196i) q^{5} +(-8.63968 + 11.8893i) q^{6} -3.90466 q^{7} +(9.22055 + 20.6635i) q^{8} +(22.9077 - 14.2912i) q^{9} +(-14.8260 + 27.9319i) q^{10} -59.1208i q^{11} +(-1.45861 - 41.5436i) q^{12} -63.6374 q^{13} +(8.70094 - 6.80180i) q^{14} +(44.5003 - 37.3460i) q^{15} +(-56.5419 - 29.9836i) q^{16} +69.6213 q^{17} +(-26.1516 + 71.7502i) q^{18} +33.0635 q^{19} +(-15.6191 - 88.0684i) q^{20} +(-19.5053 + 5.58537i) q^{21} +(102.987 + 131.742i) q^{22} +90.6431i q^{23} +(75.6180 + 90.0328i) q^{24} +(83.5594 - 92.9668i) q^{25} +(141.806 - 110.854i) q^{26} +(93.9902 - 104.158i) q^{27} +(-7.54021 + 30.3136i) q^{28} +172.259 q^{29} +(-34.1065 + 160.738i) q^{30} +61.7877i q^{31} +(178.226 - 31.6802i) q^{32} +(-84.5685 - 295.331i) q^{33} +(-155.141 + 121.278i) q^{34} +(-39.8734 + 17.7738i) q^{35} +(-66.7118 - 205.440i) q^{36} -10.7673 q^{37} +(-73.6770 + 57.5956i) q^{38} +(-317.893 + 91.0292i) q^{39} +(188.217 + 169.039i) q^{40} +475.596i q^{41} +(33.7350 - 46.4237i) q^{42} -59.3761i q^{43} +(-458.980 - 114.167i) q^{44} +(168.875 - 250.212i) q^{45} +(-157.898 - 201.985i) q^{46} -500.434i q^{47} +(-325.338 - 68.9003i) q^{48} -327.754 q^{49} +(-24.2541 + 352.720i) q^{50} +(347.785 - 99.5888i) q^{51} +(-122.889 + 494.045i) q^{52} +407.866i q^{53} +(-28.0032 + 395.828i) q^{54} +(-269.115 - 603.726i) q^{55} +(-36.0031 - 80.6840i) q^{56} +(165.165 - 47.2952i) q^{57} +(-383.853 + 300.070i) q^{58} -17.5094i q^{59} +(-204.000 - 417.593i) q^{60} +245.109i q^{61} +(-107.632 - 137.685i) q^{62} +(-89.4468 + 55.8021i) q^{63} +(-341.963 + 381.058i) q^{64} +(-649.849 + 289.675i) q^{65} +(702.906 + 510.785i) q^{66} -35.7817i q^{67} +(134.444 - 540.500i) q^{68} +(129.659 + 452.797i) q^{69} +(57.8903 - 109.065i) q^{70} -889.439 q^{71} +(506.527 + 341.582i) q^{72} +617.595i q^{73} +(23.9933 - 18.7563i) q^{74} +(284.428 - 583.931i) q^{75} +(63.8483 - 256.686i) q^{76} +230.847i q^{77} +(549.807 - 756.605i) q^{78} +108.663i q^{79} +(-713.875 - 48.8092i) q^{80} +(320.526 - 654.755i) q^{81} +(-828.473 - 1059.79i) q^{82} +628.531 q^{83} +(5.69538 + 162.214i) q^{84} +(710.955 - 316.913i) q^{85} +(103.431 + 132.311i) q^{86} +(860.499 - 246.405i) q^{87} +(1221.64 - 545.126i) q^{88} +763.668i q^{89} +(59.5504 + 851.736i) q^{90} +248.482 q^{91} +(703.702 + 175.039i) q^{92} +(88.3834 + 308.653i) q^{93} +(871.741 + 1115.14i) q^{94} +(337.636 - 150.504i) q^{95} +(844.989 - 413.195i) q^{96} +866.259i q^{97} +(730.350 - 570.937i) q^{98} +(-844.904 - 1354.32i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9}+O(q^{10}) \) 64 * q - 32 * q^4 - 72 * q^6 - 112 * q^9	\( 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9} - 72 q^{10} - 128 q^{16} + 672 q^{19} - 416 q^{24} + 496 q^{25} - 248 q^{30} + 240 q^{34} - 608 q^{36} - 1344 q^{40} + 336 q^{46} + 3520 q^{49} - 544 q^{51} - 952 q^{54} - 2064 q^{60} + 2176 q^{64} - 176 q^{66} + 672 q^{70} - 1600 q^{75} + 2304 q^{76} - 2304 q^{81} - 736 q^{84} - 1432 q^{90} - 2752 q^{91} + 4496 q^{94} + 640 q^{96} + 256 q^{99}+O(q^{100}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more