LMFDB - Embedded newform 120.4.m.b.59.9

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			59.9
Character	$\chi$	$=$	120.59
Dual form			120.4.m.b.59.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.22835 - 1.74197i) q^{2} +(4.99538 - 1.43044i) q^{3} +(1.93108 + 7.76344i) q^{4} +(-10.2117 + 4.55196i) q^{5} +(-13.6232 - 5.51430i) q^{6} +3.90466 q^{7} +(9.22055 - 20.6635i) q^{8} +(22.9077 - 14.2912i) q^{9} +O(q^{10})$	\(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} +(-13.6232 - 5.51430i) q^{6} +3.90466 q^{7} +(9.22055 - 20.6635i) q^{8} +(22.9077 - 14.2912i) q^{9} +(30.6847 + 7.64520i) q^{10} -59.1208i q^{11} +(20.7516 + 36.0190i) 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} +(-75.9411 - 8.05885i) q^{18} +33.0635 q^{19} +(-55.0585 - 70.4880i) q^{20} +(19.5053 - 5.58537i) q^{21} +(-102.987 + 131.742i) q^{22} -90.6431i q^{23} +(16.5023 - 116.412i) 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} +(164.218 - 5.70179i) 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} +(155.185 + 150.245i) q^{36} +10.7673 q^{37} +(-73.6770 - 57.5956i) q^{38} +(317.893 - 91.0292i) q^{39} +(-0.0984082 + 252.982i) q^{40} +475.596i q^{41} +(-53.1941 - 21.5314i) 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} +(-239.559 + 230.659i) q^{48} -327.754 q^{49} +(-348.145 + 61.6045i) q^{50} +(347.785 - 99.5888i) q^{51} +(122.889 + 494.045i) q^{52} -407.866i q^{53} +(-390.883 + 68.3719i) 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} +(-375.867 - 273.357i) 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} +(-326.010 + 805.416i) q^{66} -35.7817i q^{67} +(134.444 + 540.500i) q^{68} +(-129.659 - 452.797i) q^{69} +(119.813 + 29.8519i) q^{70} +889.439 q^{71} +(-84.0841 - 605.126i) 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} +(-866.947 - 350.915i) q^{78} -108.663i q^{79} +(440.907 - 563.561i) q^{80} +(320.526 - 654.755i) q^{81} +(828.473 - 1059.79i) q^{82} +628.531 q^{83} +(81.0279 + 140.642i) 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} +(812.175 - 263.386i) 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} +(935.622 - 96.6857i) 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
$6$	−13.6232	−	5.51430i	−0.926944	−	0.375200i
$7$	3.90466			0.210832			0.105416	−	0.994428i	$-0.466383\pi$
$7$	3.90466			0.210832			0.105416	+	0.994428i	$0.466383\pi$
$8$	9.22055	−	20.6635i	0.407495	−	0.913208i
$9$	22.9077	−	14.2912i	0.848433	−	0.529302i
$10$	30.6847	+	7.64520i	0.970335	+	0.241763i
$11$		−	59.1208i		−	1.62051i	−0.586079	−	0.810254i	$-0.699329\pi$
$11$		−	59.1208i		−	1.62051i	0.586079	−	0.810254i	$-0.300671\pi$
$12$	20.7516	+	36.0190i	0.499206	+	0.866484i
$13$	63.6374			1.35768			0.678840	−	0.734286i	$-0.262483\pi$
$13$	63.6374			1.35768			0.678840	+	0.734286i	$0.262483\pi$
$14$	−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	$0.334568\pi$
$18$	−75.9411	−	8.05885i	−0.994416	−	0.105527i
$19$	33.0635			0.399226			0.199613	−	0.979875i	$-0.436032\pi$
$19$	33.0635			0.399226			0.199613	+	0.979875i	$0.436032\pi$
$20$	−55.0585	−	70.4880i	−0.615573	−	0.788080i
$21$	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	$-0.865222\pi$
$23$		−	90.6431i		−	0.821756i	0.911690	−	0.410878i	$-0.134778\pi$
$24$	16.5023	−	116.412i	0.140355	−	0.990101i
$25$	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	$-0.685949\pi$
$29$	−172.259			−1.10302			−0.551511	+	0.834167i	$0.685949\pi$
$30$	164.218	−	5.70179i	0.999398	−	0.0347000i
$31$		−	61.7877i		−	0.357981i	−0.983851	−	0.178990i	$-0.942717\pi$
$31$		−	61.7877i		−	0.357981i	0.983851	−	0.178990i	$-0.0572831\pi$
$32$	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
$36$	155.185	+	150.245i	0.718449	+	0.695579i
$37$	10.7673			0.0478414			0.0239207	−	0.999714i	$-0.492385\pi$
$37$	10.7673			0.0478414			0.0239207	+	0.999714i	$0.492385\pi$
$38$	−73.6770	−	57.5956i	−0.314526	−	0.245875i
$39$	317.893	−	91.0292i	1.30522	−	0.373752i
$40$	−0.0984082	+	252.982i	−0.000388993	+	1.00000i
$41$			475.596i			1.81160i	0.423707	+	0.905799i	$0.360729\pi$
$41$			475.596i			1.81160i	−0.423707	+	0.905799i	$0.639271\pi$
$42$	−53.1941	−	21.5314i	−0.195429	−	0.0791042i
$43$		−	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	$0.283033\pi$
$47$			500.434i			1.55310i	−0.630054	+	0.776551i	$0.716967\pi$
$48$	−239.559	+	230.659i	−0.720360	+	0.693600i
$49$	−327.754			−0.955550
$50$	−348.145	+	61.6045i	−0.984703	+	0.174244i
$51$	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	$-0.822741\pi$
$53$		−	407.866i		−	1.05707i	0.848911	−	0.528535i	$-0.177259\pi$
$54$	−390.883	+	68.3719i	−0.985044	+	0.172301i
$55$	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	$-0.00614950\pi$
$60$	−375.867	−	273.357i	−0.808737	−	0.588170i
$61$		−	245.109i		−	0.514474i	−0.966348	−	0.257237i	$-0.917188\pi$
$61$		−	245.109i		−	0.514474i	0.966348	−	0.257237i	$-0.0828122\pi$
$62$	−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
$66$	−326.010	+	805.416i	−0.608015	+	1.50212i
$67$		−	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
$70$	119.813	+	29.8519i	0.204578	+	0.0509712i
$71$	889.439			1.48672			0.743359	−	0.668893i	$-0.233231\pi$
$71$	889.439			1.48672			0.743359	+	0.668893i	$0.233231\pi$
$72$	−84.0841	−	605.126i	−0.137631	−	0.990484i
$73$			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
$78$	−866.947	−	350.915i	−1.25849	−	0.509402i
$79$		−	108.663i		−	0.154753i	−0.997002	−	0.0773766i	$-0.975346\pi$
$79$		−	108.663i		−	0.154753i	0.997002	−	0.0773766i	$-0.0246544\pi$
$80$	440.907	−	563.561i	0.616186	−	0.787601i
$81$	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	$0.363570\pi$
$84$	81.0279	+	140.642i	0.105248	+	0.182682i
$85$	−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	$0.849722\pi$
$90$	812.175	−	263.386i	0.951230	−	0.308481i
$91$	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
$96$	935.622	−	96.6857i	0.994703	−	0.102791i
$97$			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
$100$	883.102	+	469.182i	0.883102	+	0.469182i
$101$	−1542.57			−1.51972			−0.759859	−	0.650088i	$-0.774732\pi$
$101$	−1542.57			−1.51972			−0.759859	+	0.650088i	$0.774732\pi$
$102$	−948.467	−	383.912i	−0.920708	−	0.372676i
$103$	360.822			0.345174			0.172587	−	0.984994i	$-0.444787\pi$
$103$	360.822			0.345174			0.172587	+	0.984994i	$0.444787\pi$
$104$	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	$0.708343\pi$
$108$	990.125	+	528.549i	0.882174	+	0.470923i
$109$		−	1187.79i		−	1.04376i	−0.853019	−	0.521880i	$-0.825231\pi$
$109$		−	1187.79i		−	1.04376i	0.853019	−	0.521880i	$-0.174769\pi$
$110$	451.990	−	1814.10i	0.391778	−	1.57244i
$111$	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	$0.589428\pi$
$114$	−450.432	−	182.322i	−0.370060	−	0.149790i
$115$	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
$120$	361.383	+	1263.88i	0.274914	+	0.961469i
$121$	−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
$126$	−296.524	−	31.4671i	−0.209655	−	0.0222485i
$127$	259.670			0.181433			0.0907163	−	0.995877i	$-0.471084\pi$
$127$	259.670			0.181433			0.0907163	+	0.995877i	$0.471084\pi$
$128$	98.2209	+	1444.82i	0.0678249	+	0.997697i
$129$	−84.9337	−	296.606i	−0.0579689	−	0.202440i
$130$	1952.69	+	486.521i	1.31740	+	0.328236i
$131$			930.506i			0.620601i	0.950639	+	0.310300i	$0.100430\pi$
$131$			930.506i			0.620601i	−0.950639	+	0.310300i	$0.899570\pi$
$132$	2129.47	−	1226.85i	1.40414	−	0.808967i
$133$	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	$0.464186\pi$
$138$	−499.833	+	1234.85i	−0.308323	+	0.761722i
$139$	−574.130			−0.350339			−0.175169	−	0.984538i	$-0.556047\pi$
$139$	−574.130			−0.350339			−0.175169	+	0.984538i	$0.556047\pi$
$140$	−214.985	−	275.232i	−0.129782	−	0.166152i
$141$	715.839	+	2499.86i	0.427550	+	1.49309i
$142$	−1981.98	−	1549.38i	−1.17130	−	0.915639i
$143$		−	3762.29i		−	2.20013i
$144$	−866.743	+	1494.90i	−0.501588	+	0.865107i
$145$	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	$-0.373991\pi$
$149$	1402.68			0.771223			0.385611	+	0.922661i	$0.373991\pi$
$150$	−1651.00	+	805.737i	−0.898688	+	0.438588i
$151$		−	713.088i		−	0.384306i	−0.981365	−	0.192153i	$-0.938453\pi$
$151$		−	713.088i		−	0.384306i	0.981365	−	0.192153i	$-0.0615471\pi$
$152$	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
$156$	1320.58	+	2292.16i	0.677761	+	1.17641i
$157$	−1894.80			−0.963192			−0.481596	−	0.876393i	$-0.659943\pi$
$157$	−1894.80			−0.963192			−0.481596	+	0.876393i	$0.659943\pi$
$158$	−189.287	+	242.138i	−0.0953093	+	0.121921i
$159$	−583.427	−	2037.45i	−0.290998	−	1.01623i
$160$	−1964.20	+	487.765i	−0.970523	+	0.241008i
$161$		−	353.930i		−	0.173252i
$162$	−1854.81	+	900.677i	−0.899552	+	0.436814i
$163$		−	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	$0.256348\pi$
$167$			3112.29i			1.44213i	−0.692865	+	0.721067i	$0.743652\pi$
$168$	64.4359	−	454.548i	0.0295913	−	0.208745i
$169$	1852.72			0.843294
$170$	2136.31	+	532.269i	0.963808	+	0.240136i
$171$	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	$-0.761438\pi$
$173$		−	3100.30i		−	1.36250i	0.732053	−	0.681248i	$-0.238562\pi$
$174$	2346.72	+	949.886i	1.02244	+	0.413855i
$175$	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	$0.861538\pi$
$180$	−2268.62	−	827.869i	−0.939405	−	0.342809i
$181$			1943.41i			0.798079i	0.916934	+	0.399039i	$0.130656\pi$
$181$			1943.41i			0.798079i	−0.916934	+	0.399039i	$0.869344\pi$
$182$	−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
$186$	−340.716	+	841.749i	−0.134315	+	0.331828i
$187$		−	4116.06i		−	1.60961i
$188$	−3885.09	+	966.379i	−1.50718	+	0.374896i
$189$	367.000	−	406.701i	0.141245	−	0.156524i
$190$	1014.54	+	252.777i	0.387383	+	0.0965178i
$191$	−3928.20			−1.48814			−0.744070	−	0.668101i	$-0.767107\pi$
$191$	−3928.20			−1.48814			−0.744070	+	0.668101i	$0.767107\pi$
$192$	−2253.32	−	1414.38i	−0.846974	−	0.531634i
$193$			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	$0.268171\pi$
$197$			4127.07i			1.49260i	−0.665611	+	0.746299i	$0.731829\pi$
$198$	−476.446	+	4489.70i	−0.171008	+	1.61146i
$199$			4395.85i			1.56590i	0.622087	+	0.782948i	$0.286285\pi$
$199$			4395.85i			1.56590i	−0.622087	+	0.782948i	$0.713715\pi$
$200$	−1150.56	−	2583.84i	−0.406784	−	0.913524i
$201$	−51.1834	−	178.743i	−0.0179612	−	0.0627242i
$202$	3437.39	+	2687.11i	1.19730	+	0.935963i
$203$	−672.612			−0.232552
$204$	1444.75	+	2507.69i	0.495847	+	0.860655i
$205$	−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
$210$	641.215	−	22.2635i	0.210705	−	0.00731586i
$211$	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
$216$	−1285.63	−	2902.56i	−0.404981	−	0.914325i
$217$		−	241.260i		−	0.0754737i
$218$	−2069.10	+	2646.81i	−0.642830	+	0.822316i
$219$	883.431	+	3085.13i	0.272588	+	0.951934i
$220$	−4167.31	+	3255.10i	−1.27709	+	0.997541i
$221$	4430.52			1.34855
$222$	−146.685	−	59.3741i	−0.0443463	−	0.0179501i
$223$	5589.89			1.67859			0.839297	−	0.543673i	$-0.182967\pi$
$223$	5589.89			1.67859			0.839297	+	0.543673i	$0.182967\pi$
$224$	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	$0.399727\pi$
$228$	686.120	+	1190.92i	0.199296	+	0.345922i
$229$			3484.25i			1.00544i	0.864449	+	0.502721i	$0.167668\pi$
$229$			3484.25i			1.00544i	−0.864449	+	0.502721i	$0.832332\pi$
$230$	692.985	−	2781.36i	0.198670	−	0.797379i
$231$	−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	$0.471525\pi$
$234$	−4832.70	−	512.844i	−1.35010	−	0.143272i
$235$	−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	$-0.649700\pi$
$239$	−3348.65			−0.906302			−0.453151	+	0.891434i	$0.649700\pi$
$240$	1396.36	−	3445.89i	0.375561	−	0.926798i
$241$	−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
$246$	2622.57	−	6479.15i	0.679712	−	1.67925i
$247$	2104.07			0.542020
$248$	−1276.75	−	569.717i	−0.326911	−	0.145875i
$249$	3139.75	−	899.074i	0.799092	−	0.228821i
$250$	3274.75	−	2213.83i	0.828452	−	0.560060i
$251$			2194.08i			0.551750i	0.961194	+	0.275875i	$0.0889676\pi$
$251$			2194.08i			0.551750i	−0.961194	+	0.275875i	$0.911032\pi$
$252$	605.945	+	586.656i	0.151472	+	0.146650i
$253$	−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	$0.267511\pi$
$258$	−327.417	+	808.894i	−0.0790082	+	0.195192i
$259$	42.0426			0.0100865
$260$	−3503.78	−	4485.67i	−0.835751	−	1.06996i
$261$	−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	$-0.865588\pi$
$263$		−	3495.97i		−	0.819660i	0.912162	−	0.409830i	$-0.134412\pi$
$264$	−6882.35	−	975.630i	−1.60447	−	0.227446i
$265$	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	$-0.521140\pi$
$269$	−585.602			−0.132732			−0.0663658	+	0.997795i	$0.521140\pi$
$270$	3680.37	−	2477.48i	0.829556	−	0.558424i
$271$		−	7517.66i		−	1.68511i	−0.538609	−	0.842556i	$-0.681050\pi$
$271$		−	7517.66i		−	1.68511i	0.538609	−	0.842556i	$-0.318950\pi$
$272$	−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
$276$	3264.88	−	1880.99i	0.712038	−	0.410225i
$277$	504.031			0.109330			0.0546648	−	0.998505i	$-0.482591\pi$
$277$	504.031			0.109330			0.0546648	+	0.998505i	$0.482591\pi$
$278$	1279.36	+	1000.12i	0.276011	+	0.215767i
$279$	−883.018	−	1415.42i	−0.189480	−	0.303723i
$280$	−0.384251	+	987.809i	−8.20120e−5	+	0.210832i
$281$		−	7892.83i		−	1.67561i	−0.545969	−	0.837805i	$-0.683839\pi$
$281$		−	7892.83i		−	1.67561i	0.545969	−	0.837805i	$-0.316161\pi$
$282$	2759.54	−	6817.53i	0.582725	−	1.43964i
$283$			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
$288$	4535.49	−	1821.33i	0.927972	−	0.372649i
$289$	−65.8786			−0.0134090
$290$	−5285.71	−	1316.95i	−1.07030	−	0.266670i
$291$	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	$0.0218615\pi$
$293$			688.366i			0.137252i	−0.997642	+	0.0686259i	$0.978139\pi$
$294$	4465.06	+	1807.33i	0.885741	+	0.358523i
$295$	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
$300$	5082.57	+	1080.52i	0.978140	+	0.207946i
$301$		−	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
$306$	−5287.12	−	561.067i	−0.987727	−	0.104817i
$307$			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
$310$	472.380	−	1895.94i	0.0865464	−	0.347361i
$311$	7832.47			1.42810			0.714049	−	0.700096i	$-0.246859\pi$
$311$	7832.47			1.42810			0.714049	+	0.700096i	$0.246859\pi$
$312$	1050.16	−	7408.13i	0.190557	−	1.34424i
$313$			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	$0.118528\pi$
$317$			4106.84i			0.727643i	−0.931469	+	0.363822i	$0.881472\pi$
$318$	−2249.09	+	5556.46i	−0.396613	+	0.979845i
$319$			10184.1i			1.78746i
$320$	5226.60	+	2334.67i	0.913049	+	0.407850i
$321$	−6731.91	+	1927.69i	−1.17052	+	0.335182i
$322$	−616.536	+	788.681i	−0.106703	+	0.136495i
$323$	2301.92			0.396540
$324$	5702.11	+	1224.00i	0.977728	+	0.209876i
$325$	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
$330$	−337.094	−	9708.69i	−0.0562316	−	1.61953i
$331$	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
$336$	−935.394	+	900.646i	−0.151875	+	0.146233i
$337$			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
$340$	−3833.24	−	4907.47i	−0.611432	−	0.782778i
$341$	−3652.94			−0.580111
$342$	−2510.88	−	266.454i	−0.396996	−	0.0421291i
$343$	−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	$0.379186\pi$
$348$	−3574.64	−	6204.60i	−0.550635	−	0.955751i
$349$			3221.38i			0.494087i	0.969004	+	0.247043i	$0.0794590\pi$
$349$			3221.38i			0.494087i	−0.969004	+	0.247043i	$0.920541\pi$
$350$	−1359.39	+	240.545i	−0.207607	+	0.0367362i
$351$	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	$0.542815\pi$
$354$	−96.5518	+	238.534i	−0.0144962	+	0.0358134i
$355$	−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	$-0.479192\pi$
$359$	888.661			0.130645			0.0653227	+	0.997864i	$0.479192\pi$
$360$	3613.15	+	5796.65i	0.528972	+	0.848639i
$361$	−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
$366$	−1351.60	+	3339.17i	−0.193031	+	0.476889i
$367$	2399.81			0.341333			0.170666	−	0.985329i	$-0.445408\pi$
$367$	2399.81			0.341333			0.170666	+	0.985329i	$0.445408\pi$
$368$	2717.81	+	5125.13i	0.384988	+	0.725994i
$369$	6796.81	+	10894.8i	0.958883	+	1.53702i
$370$	330.391	+	82.3182i	0.0464223	+	0.0115663i
$371$		−	1592.58i		−	0.222864i
$372$	2225.54	−	1282.19i	0.310185	−	0.178706i
$373$	7562.31			1.04976			0.524881	−	0.851175i	$-0.324110\pi$
$373$	7562.31			1.04976			0.524881	+	0.851175i	$0.324110\pi$
$374$	−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
$378$	−1526.26	+	266.969i	−0.207679	+	0.0363265i
$379$	−7024.75			−0.952077			−0.476038	−	0.879424i	$-0.657928\pi$
$379$	−7024.75			−0.952077			−0.476038	+	0.879424i	$0.657928\pi$
$380$	−1820.43	−	2330.58i	−0.245752	−	0.314622i
$381$	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	$0.0707822\pi$
$383$			3306.11i			0.441081i	−0.975378	+	0.220541i	$0.929218\pi$
$384$	2557.37	+	7076.93i	0.339858	+	0.940477i
$385$	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	$-0.593248\pi$
$389$	−4431.14			−0.577551			−0.288776	+	0.957397i	$0.593248\pi$
$390$	10450.4	−	362.847i	1.35686	−	0.0471115i
$391$		−	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
$396$	8882.61	−	9174.66i	1.12719	−	1.16425i
$397$	−10715.8			−1.35469			−0.677343	−	0.735668i	$-0.736869\pi$
$397$	−10715.8			−1.35469			−0.677343	+	0.735668i	$0.736869\pi$
$398$	7657.44	−	9795.49i	0.964403	−	1.23368i
$399$	644.912	−	184.672i	0.0809173	−	0.0231708i
$400$	−1937.12	+	7761.93i	−0.242140	+	0.970241i
$401$			3245.09i			0.404120i	0.979373	+	0.202060i	$0.0647635\pi$
$401$			3245.09i			0.404120i	−0.979373	+	0.202060i	$0.935236\pi$
$402$	−197.311	+	487.462i	−0.0244800	+	0.0604786i
$403$		−	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
$408$	1148.91	−	8104.73i	0.139411	−	0.983441i
$409$	−3135.87			−0.379117			−0.189558	−	0.981869i	$-0.560706\pi$
$409$	−3135.87			−0.379117			−0.189558	+	0.981869i	$0.560706\pi$
$410$	−3636.03	+	14593.5i	−0.437977	+	1.75786i
$411$	1798.75	−	515.076i	0.215878	−	0.0618171i
$412$	696.777	+	2801.22i	0.0833198	+	0.334967i
$413$		−	68.3681i		−	0.00814570i
$414$	−730.479	+	6883.54i	−0.0867176	+	0.817168i
$415$	−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	$-0.141249\pi$
$420$	−1467.63	−	1067.37i	−0.170507	−	0.124005i
$421$			4582.24i			0.530463i	0.964185	+	0.265231i	$0.0854483\pi$
$421$			4582.24i			0.530463i	−0.964185	+	0.265231i	$0.914552\pi$
$422$	−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
$426$	−12117.0	−	4904.63i	−1.37810	−	0.557817i
$427$		−	957.065i		−	0.108468i
$428$	−2602.37	−	10462.2i	−0.293903	−	1.18157i
$429$	−5381.72	−	18794.1i	−0.605669	−	2.11512i
$430$	453.942	−	1821.94i	0.0509094	−	0.204329i
$431$	5956.76			0.665724			0.332862	−	0.942976i	$-0.391986\pi$
$431$	5956.76			0.665724			0.332862	+	0.942976i	$0.391986\pi$
$432$	−2191.35	+	8707.44i	−0.244054	+	0.969762i
$433$		−	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
$438$	3405.60	−	8413.65i	0.371521	−	0.917853i
$439$			3323.14i			0.361287i	0.983549	+	0.180644i	$0.0578180\pi$
$439$			3323.14i			0.361287i	−0.983549	+	0.180644i	$0.942182\pi$
$440$	14956.5	+	5.81797i	1.62051	+	0.000630366i
$441$	−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	$0.310876\pi$
$444$	223.439	+	387.828i	0.0238827	+	0.0414538i
$445$	−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	$-0.0253371\pi$
$450$	−7094.80	+	6386.61i	−0.743227	+	0.669039i
$451$	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
$456$	545.624	−	3848.98i	0.0560333	−	0.395274i
$457$		−	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
$460$	−6389.25	+	4990.68i	−0.647610	+	0.505851i
$461$	−12494.6			−1.26233			−0.631164	−	0.775649i	$-0.717423\pi$
$461$	−12494.6			−1.26233			−0.631164	+	0.775649i	$0.717423\pi$
$462$	−1272.96	+	3144.88i	−0.128189	+	0.316695i
$463$	−1991.33			−0.199881			−0.0999406	−	0.994993i	$-0.531865\pi$
$463$	−1991.33			−0.199881			−0.0999406	+	0.994993i	$0.531865\pi$
$464$	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	$0.468772\pi$
$468$	9875.57	+	9561.21i	0.975424	+	0.944374i
$469$		−	139.715i		−	0.0137558i
$470$	−3825.92	+	15355.7i	−0.375482	+	1.50703i
$471$	−9465.23	+	2710.39i	−0.925976	+	0.265155i
$472$	−361.805	−	161.446i	−0.0352827	−	0.0157440i
$473$	−3510.36			−0.341240
$474$	−599.198	+	1480.34i	−0.0580634	+	0.143448i
$475$	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	$-0.236767\pi$
$479$	15429.2			1.47177			0.735884	+	0.677108i	$0.236767\pi$
$480$	−9114.22	+	5246.24i	−0.866678	+	0.498869i
$481$	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
$486$	−7977.11	+	7152.41i	−0.744546	+	0.667572i
$487$	−323.435			−0.0300949			−0.0150475	−	0.999887i	$-0.504790\pi$
$487$	−323.435			−0.0300949			−0.0150475	+	0.999887i	$0.504790\pi$
$488$	−5064.81	−	2260.04i	−0.469822	−	0.209645i
$489$	−3551.17	−	12401.4i	−0.328403	−	1.14685i
$490$	−10057.0	−	2505.74i	−0.927204	−	0.231016i
$491$		−	10843.0i		−	0.996617i	−0.867000	−	0.498308i	$-0.833955\pi$
$491$		−	10843.0i		−	0.996617i	0.867000	−	0.498308i	$-0.166045\pi$
$492$	−17130.5	+	9869.36i	−1.56972	+	0.904360i
$493$	−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
$498$	−8562.63	−	3465.91i	−0.770483	−	0.311870i
$499$	−8534.00			−0.765599			−0.382800	−	0.923831i	$-0.625040\pi$
$499$	−8534.00			−0.765599			−0.382800	+	0.923831i	$0.625040\pi$
$500$	−11153.7	−	771.322i	−0.997617	−	0.0689891i
$501$	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	$0.118359\pi$
$503$			8197.47i			0.726654i	−0.931662	+	0.363327i	$0.881641\pi$
$504$	−328.320	−	2362.81i	−0.0290169	−	0.208825i
$505$	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	$-0.369762\pi$
$509$	9137.11			0.795669			0.397834	+	0.917457i	$0.369762\pi$
$510$	11433.1	−	396.966i	0.992675	−	0.0344665i
$511$			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
$516$	2138.67	−	1232.15i	0.182461	−	0.105121i
$517$	29586.1			2.51682
$518$	−93.6857	−	73.2370i	−0.00794655	−	0.00621207i
$519$	−4434.79	−	15487.2i	−0.375078	−	1.30985i
$520$	−6.26244	+	16099.1i	−0.000528127	+	1.35768i
$521$			9974.29i			0.838736i	0.907816	+	0.419368i	$0.137748\pi$
$521$			9974.29i			0.838736i	−0.907816	+	0.419368i	$0.862252\pi$
$522$	13081.5	+	1388.21i	1.09686	+	0.116399i
$523$		−	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
$528$	13636.8	+	14162.9i	1.12398	+	1.16735i
$529$	3950.83			0.324717
$530$	3118.22	−	12515.3i	0.255560	−	1.02571i
$531$	−250.229	−	401.099i	−0.0204501	−	0.0327801i
$532$	249.306	+	1002.27i	0.0203172	+	0.0816805i
$533$			30265.7i			2.45957i
$534$	4211.09	−	10403.6i	0.341258	−	0.843088i
$535$	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
$540$	−12516.8	−	890.407i	−0.997479	−	0.0709574i
$541$			8972.66i			0.713059i	0.934284	+	0.356530i	$0.116040\pi$
$541$			8972.66i			0.713059i	−0.934284	+	0.356530i	$0.883960\pi$
$542$	−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
$546$	−3385.13	−	1370.21i	−0.265330	−	0.107398i
$547$			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
$550$	3642.11	+	20582.6i	0.282364	+	1.59572i
$551$	−5695.48			−0.440355
$552$	−10551.9	−	1495.82i	−0.813622	−	0.115338i
$553$		−	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	$-0.831824\pi$
$557$		−	13253.5i		−	1.00820i	0.863644	−	0.504102i	$-0.168176\pi$
$558$	−497.938	+	4692.23i	−0.0377767	+	0.355982i
$559$		−	3778.54i		−	0.285895i
$560$	1721.59	−	2200.51i	0.129912	−	0.166051i
$561$	−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	$0.584737\pi$
$564$	−18025.2	+	10384.8i	−1.34574	+	0.775318i
$565$	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	$0.811058\pi$
$570$	5429.61	−	188.521i	0.398985	−	0.0138531i
$571$	−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
$576$	−13279.3	−	3842.12i	−0.960601	−	0.277931i
$577$		−	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
$580$	9484.32	+	12142.2i	0.678991	+	0.869270i
$581$	2454.20			0.175245
$582$	4776.81	−	11801.2i	0.340215	−	0.840511i
$583$	−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	$0.723795\pi$
$588$	−6801.41	−	11805.4i	−0.477016	−	0.827968i
$589$		−	2042.92i		−	0.142915i
$590$	133.863	−	537.270i	0.00934074	−	0.0374899i
$591$	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	$0.873396\pi$
$594$	4042.20	+	23109.3i	0.279215	+	1.59627i
$595$	−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	$-0.653394\pi$
$599$	−13589.0			−0.926929			−0.463465	+	0.886115i	$0.653394\pi$
$600$	−9443.50	−	11261.5i	−0.642549	−	0.766245i
$601$	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
$606$	21014.8	+	8506.19i	1.40869	+	0.570199i
$607$	−21346.6			−1.42740			−0.713701	−	0.700451i	$-0.752982\pi$
$607$	−21346.6			−1.42740			−0.713701	+	0.700451i	$0.752982\pi$
$608$	5892.76	+	1047.46i	0.393064	+	0.0698684i
$609$	−3359.96	+	962.129i	−0.223567	+	0.0640188i
$610$	1873.90	−	7521.08i	0.124381	−	0.499213i
$611$			31846.3i			2.10862i
$612$	10804.2	+	10460.3i	0.713616	+	0.690900i
$613$	25625.9			1.68845			0.844227	−	0.535986i	$-0.180060\pi$
$613$	25625.9			1.68845			0.844227	+	0.535986i	$0.180060\pi$
$614$	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	$0.193888\pi$
$618$	−4915.57	−	1989.68i	−0.319957	−	0.129509i
$619$	2383.46			0.154765			0.0773824	−	0.997001i	$-0.475344\pi$
$619$	2383.46			0.154765			0.0773824	+	0.997001i	$0.475344\pi$
$620$	−4355.30	+	3401.94i	−0.282118	+	0.220363i
$621$	−9441.19	−	8519.56i	−0.610083	−	0.550529i
$622$	−17453.5	−	13643.9i	−1.12511	−	0.879536i
$623$			2981.86i			0.191759i
$624$	−15244.9	+	14678.6i	−0.978019	+	0.941687i
$625$	−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
$630$	3171.27	−	1028.43i	0.200550	−	0.0650376i
$631$		−	13751.7i		−	0.867585i	−0.901013	−	0.433793i	$-0.857175\pi$
$631$		−	13751.7i		−	0.867585i	0.901013	−	0.433793i	$-0.142825\pi$
$632$	−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
$636$	14691.0	−	8463.87i	0.915934	−	0.527695i
$637$	−20857.4			−1.29733
$638$	17740.4	−	22693.7i	1.10086	−	1.40823i
$639$	20375.0	−	12711.1i	1.26138	−	0.786923i
$640$	−7579.76	−	14307.0i	−0.468151	−	0.883649i
$641$		−	7866.10i		−	0.484699i	−0.970189	−	0.242350i	$-0.922082\pi$
$641$		−	7866.10i		−	0.484699i	0.970189	−	0.242350i	$-0.0779181\pi$
$642$	18359.0	+	7431.21i	1.12862	+	0.456832i
$643$			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	$-0.977913\pi$
$647$		−	2282.05i		−	0.138666i	0.997594	−	0.0693328i	$-0.0220870\pi$
$648$	−10574.1	−	12660.4i	−0.641035	−	0.767511i
$649$	−1035.17			−0.0626100
$650$	−22155.0	+	3920.35i	−1.33691	+	0.236567i
$651$	−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	$0.124776\pi$
$653$			12749.7i			0.764065i	−0.924149	+	0.382032i	$0.875224\pi$
$654$	−6549.83	+	16181.6i	−0.391619	+	0.967506i
$655$	−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	$-0.107610\pi$
$660$	−16161.1	+	22221.6i	−0.953135	+	1.31056i
$661$			16408.1i			0.965506i	0.875756	+	0.482753i	$0.160363\pi$
$661$			16408.1i			0.965506i	−0.875756	+	0.482753i	$0.839637\pi$
$662$	−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
$666$	−817.681	−	86.7721i	−0.0475743	−	0.00504857i
$667$			15614.1i			0.906416i
$668$	−24162.1	+	6010.09i	−1.39949	+	0.348110i
$669$	27923.6	−	7995.98i	1.61374	−	0.462096i
$670$	273.558	−	1097.95i	0.0157738	−	0.0633097i
$671$	−14491.0			−0.833710
$672$	3653.28	−	377.525i	0.209715	−	0.0216716i
$673$			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	$-0.831257\pi$
$677$		−	17813.6i		−	1.01128i	0.862746	−	0.505638i	$-0.168743\pi$
$678$	9074.50	+	3673.10i	0.514018	+	0.208060i
$679$			3382.45i			0.191173i
$680$	−6.85131	+	17612.9i	−0.000386376	+	0.993273i
$681$	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	$0.511391\pi$
$684$	5130.96	+	4967.63i	0.286823	+	0.277693i
$685$	−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
$690$	−516.828	−	14885.2i	−0.0285149	−	0.821261i
$691$	−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
$696$	−2842.67	+	20052.9i	−0.154815	+	1.09210i
$697$			33111.6i			1.79941i
$698$	5611.54	−	7178.35i	0.304298	−	0.389262i
$699$	3174.41	−	908.998i	0.171770	−	0.0491866i
$700$	3448.21	+	1831.99i	0.186186	+	0.0989184i
$701$	8649.55			0.466033			0.233016	−	0.972473i	$-0.425140\pi$
$701$	8649.55			0.466033			0.233016	+	0.972473i	$0.425140\pi$
$702$	−24874.8	+	4351.01i	−1.33737	+	0.233929i
$703$	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
$708$	630.671	−	363.347i	0.0334775	−	0.0192873i
$709$			32669.4i			1.73050i	0.501339	+	0.865251i	$0.332841\pi$
$709$			32669.4i			1.73050i	−0.501339	+	0.865251i	$0.667159\pi$
$710$	27292.2	+	6799.94i	1.44262	+	0.359433i
$711$	−1552.91	−	2489.21i	−0.0819112	−	0.131298i
$712$	15780.1	+	7041.44i	0.830594	+	0.370631i
$713$	−5600.63			−0.294173
$714$	−3703.44	−	1499.05i	−0.194115	−	0.0785720i
$715$	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	$-0.879521\pi$
$719$	−35829.6			−1.85844			−0.929221	+	0.369524i	$0.879521\pi$
$720$	2046.22	−	19211.0i	0.105914	−	0.994375i
$721$	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
$726$	29484.3	+	11934.4i	1.50725	+	0.610093i
$727$	15633.8			0.797561			0.398781	−	0.917046i	$-0.369434\pi$
$727$	15633.8			0.797561			0.398781	+	0.917046i	$0.369434\pi$
$728$	2291.14	−	5134.52i	0.116642	−	0.261398i
$729$	−2014.70	−	19579.6i	−0.102357	−	0.994748i
$730$	−4721.64	+	18950.7i	−0.239392	+	0.960819i
$731$		−	4133.84i		−	0.209159i
$732$	8828.58	−	5086.39i	0.445784	−	0.256828i
$733$	−6139.39			−0.309364			−0.154682	−	0.987964i	$-0.549435\pi$
$733$	−6139.39			−0.309364			−0.154682	+	0.987964i	$0.549435\pi$
$734$	−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
$738$	3832.75	−	36117.3i	0.191173	−	1.80148i
$739$	−23289.0			−1.15927			−0.579634	−	0.814877i	$-0.696804\pi$
$739$	−23289.0			−1.15927			−0.579634	+	0.814877i	$0.696804\pi$
$740$	−592.832	−	758.966i	−0.0294499	−	0.0377029i
$741$	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	$-0.808453\pi$
$743$		−	22930.0i		−	1.13219i	0.824339	−	0.566096i	$-0.191547\pi$
$744$	−7192.81	−	1019.64i	−0.354437	−	0.0502444i
$745$	−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
$750$	13191.9	−	15743.2i	0.642265	−	0.766483i
$751$		−	10373.1i		−	0.504023i	−0.967724	−	0.252011i	$-0.918908\pi$
$751$		−	10373.1i		−	0.504023i	0.967724	−	0.252011i	$-0.0810920\pi$
$752$	−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
$756$	3866.10	+	2063.81i	0.185990	+	0.0992856i
$757$	19427.2			0.932753			0.466377	−	0.884586i	$-0.345559\pi$
$757$	19427.2			0.932753			0.466377	+	0.884586i	$0.345559\pi$
$758$	15653.6	+	12236.9i	0.750085	+	0.586364i
$759$	−26769.7	+	7665.55i	−1.28021	+	0.366590i
$760$	−3.25372	+	8364.47i	−0.000155296	+	0.399225i
$761$		−	17770.0i		−	0.846467i	−0.906021	−	0.423233i	$-0.860895\pi$
$761$		−	17770.0i		−	0.846467i	0.906021	−	0.423233i	$-0.139105\pi$
$762$	−3537.54	−	1431.89i	−0.168178	−	0.0680736i
$763$		−	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
$768$	6629.08	−	20224.7i	0.311466	−	0.950257i
$769$	6380.37			0.299196			0.149598	−	0.988747i	$-0.452202\pi$
$769$	6380.37			0.299196			0.149598	+	0.988747i	$0.452202\pi$
$770$	1764.87	−	7083.46i	0.0825993	−	0.3

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)

\(f(q)\)	\(=\)	\(q+(-2.22835 - 1.74197i) q^{2} +(4.99538 - 1.43044i) q^{3} +(1.93108 + 7.76344i) q^{4} +(-10.2117 + 4.55196i) q^{5} +(-13.6232 - 5.51430i) q^{6} +3.90466 q^{7} +(9.22055 - 20.6635i) q^{8} +(22.9077 - 14.2912i) q^{9} +O(q^{10})\)	\(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} +(-13.6232 - 5.51430i) q^{6} +3.90466 q^{7} +(9.22055 - 20.6635i) q^{8} +(22.9077 - 14.2912i) q^{9} +(30.6847 + 7.64520i) q^{10} -59.1208i q^{11} +(20.7516 + 36.0190i) 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} +(-75.9411 - 8.05885i) q^{18} +33.0635 q^{19} +(-55.0585 - 70.4880i) q^{20} +(19.5053 - 5.58537i) q^{21} +(-102.987 + 131.742i) q^{22} -90.6431i q^{23} +(16.5023 - 116.412i) 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} +(164.218 - 5.70179i) 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} +(155.185 + 150.245i) q^{36} +10.7673 q^{37} +(-73.6770 - 57.5956i) q^{38} +(317.893 - 91.0292i) q^{39} +(-0.0984082 + 252.982i) q^{40} +475.596i q^{41} +(-53.1941 - 21.5314i) 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} +(-239.559 + 230.659i) q^{48} -327.754 q^{49} +(-348.145 + 61.6045i) q^{50} +(347.785 - 99.5888i) q^{51} +(122.889 + 494.045i) q^{52} -407.866i q^{53} +(-390.883 + 68.3719i) 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} +(-375.867 - 273.357i) 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} +(-326.010 + 805.416i) q^{66} -35.7817i q^{67} +(134.444 + 540.500i) q^{68} +(-129.659 - 452.797i) q^{69} +(119.813 + 29.8519i) q^{70} +889.439 q^{71} +(-84.0841 - 605.126i) 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} +(-866.947 - 350.915i) q^{78} -108.663i q^{79} +(440.907 - 563.561i) q^{80} +(320.526 - 654.755i) q^{81} +(828.473 - 1059.79i) q^{82} +628.531 q^{83} +(81.0279 + 140.642i) 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} +(812.175 - 263.386i) 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} +(935.622 - 96.6857i) 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

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