LMFDB - Embedded newform 546.4.i.a.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,4,Mod(79,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("546.79");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	546.i (of order $3$, degree $2$, 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:	$32.2150428631$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 25 $ x^4 - 5*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.2
Root			$-1.93649 + 1.11803i$ of defining polynomial
Character	$\chi$	$=$	546.79
Dual form			546.4.i.a.235.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(3.43649 - 5.95218i) q^{5} -6.00000 q^{6} +(0.809475 + 18.5026i) q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(6.87298 + 11.9044i) q^{10} +(-18.6825 - 32.3590i) q^{11} +(6.00000 - 10.3923i) q^{12} +13.0000 q^{13} +(-32.8569 - 17.1005i) q^{14} +20.6190 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-47.4284 - 82.1484i) q^{17} +(-9.00000 - 15.5885i) q^{18} +(-52.7379 + 91.3447i) q^{19} -27.4919 q^{20} +(-46.8569 + 29.8569i) q^{21} +74.7298 q^{22} +(-18.5474 + 32.1250i) q^{23} +(12.0000 + 20.7846i) q^{24} +(38.8810 + 67.3440i) q^{25} +(-13.0000 + 22.5167i) q^{26} -27.0000 q^{27} +(62.4758 - 39.8092i) q^{28} -57.9839 q^{29} +(-20.6190 + 35.7131i) q^{30} +(-111.571 - 193.246i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(56.0474 - 97.0769i) q^{33} +189.714 q^{34} +(112.912 + 58.7658i) q^{35} +36.0000 q^{36} +(13.7853 - 23.8768i) q^{37} +(-105.476 - 182.689i) q^{38} +(19.5000 + 33.7750i) q^{39} +(27.4919 - 47.6174i) q^{40} +137.446 q^{41} +(-4.85685 - 111.015i) q^{42} -495.044 q^{43} +(-74.7298 + 129.436i) q^{44} +(30.9284 + 53.5696i) q^{45} +(-37.0948 - 64.2500i) q^{46} +(-232.611 + 402.894i) q^{47} -48.0000 q^{48} +(-341.690 + 29.9547i) q^{49} -155.524 q^{50} +(142.285 - 246.445i) q^{51} +(-26.0000 - 45.0333i) q^{52} +(-136.292 - 236.065i) q^{53} +(27.0000 - 46.7654i) q^{54} -256.808 q^{55} +(6.47580 + 148.020i) q^{56} -316.427 q^{57} +(57.9839 - 100.431i) q^{58} +(-144.191 - 249.745i) q^{59} +(-41.2379 - 71.4261i) q^{60} +(-99.3800 + 172.131i) q^{61} +446.282 q^{62} +(-147.856 - 76.9523i) q^{63} +64.0000 q^{64} +(44.6744 - 77.3783i) q^{65} +(112.095 + 194.154i) q^{66} +(-103.690 - 179.595i) q^{67} +(-189.714 + 328.594i) q^{68} -111.284 q^{69} +(-214.698 + 136.804i) q^{70} -141.444 q^{71} +(-36.0000 + 62.3538i) q^{72} +(-162.737 - 281.869i) q^{73} +(27.5706 + 47.7536i) q^{74} +(-116.643 + 202.032i) q^{75} +421.903 q^{76} +(583.601 - 371.867i) q^{77} -78.0000 q^{78} +(529.855 - 917.735i) q^{79} +(54.9839 + 95.2349i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-137.446 + 238.063i) q^{82} -849.520 q^{83} +(197.141 + 102.603i) q^{84} -651.950 q^{85} +(495.044 - 857.442i) q^{86} +(-86.9758 - 150.647i) q^{87} +(-149.460 - 258.872i) q^{88} +(692.114 - 1198.78i) q^{89} -123.714 q^{90} +(10.5232 + 240.533i) q^{91} +148.379 q^{92} +(334.712 - 579.738i) q^{93} +(-465.222 - 805.788i) q^{94} +(362.467 + 627.811i) q^{95} +(48.0000 - 83.1384i) q^{96} +150.434 q^{97} +(289.806 - 621.778i) q^{98} +336.284 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 6 q^{5} - 24 q^{6} - 20 q^{7} + 32 q^{8} - 18 q^{9} + 12 q^{10} - 36 q^{11} + 24 q^{12} + 52 q^{13} + 8 q^{14} + 36 q^{15} - 32 q^{16} - 120 q^{17} - 36 q^{18} - 118 q^{19}+ \cdots + 648 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 + 6 * q^5 - 24 * q^6 - 20 * q^7 + 32 * q^8 - 18 * q^9 + 12 * q^10 - 36 * q^11 + 24 * q^12 + 52 * q^13 + 8 * q^14 + 36 * q^15 - 32 * q^16 - 120 * q^17 - 36 * q^18 - 118 * q^19 - 48 * q^20 - 48 * q^21 + 144 * q^22 + 42 * q^23 + 48 * q^24 + 202 * q^25 - 52 * q^26 - 108 * q^27 + 64 * q^28 - 108 * q^29 - 36 * q^30 - 28 * q^31 - 64 * q^32 + 108 * q^33 + 480 * q^34 + 258 * q^35 + 144 * q^36 - 154 * q^37 - 236 * q^38 + 78 * q^39 + 48 * q^40 + 1092 * q^41 + 120 * q^42 - 400 * q^43 - 144 * q^44 + 54 * q^45 + 84 * q^46 - 822 * q^47 - 192 * q^48 - 902 * q^49 - 808 * q^50 + 360 * q^51 - 104 * q^52 + 90 * q^53 + 108 * q^54 - 516 * q^55 - 160 * q^56 - 708 * q^57 + 108 * q^58 - 600 * q^59 - 72 * q^60 + 44 * q^61 + 112 * q^62 + 36 * q^63 + 256 * q^64 + 78 * q^65 + 216 * q^66 + 50 * q^67 - 480 * q^68 + 252 * q^69 - 456 * q^70 - 132 * q^71 - 144 * q^72 - 70 * q^73 - 308 * q^74 - 606 * q^75 + 944 * q^76 + 1188 * q^77 - 312 * q^78 + 1004 * q^79 + 96 * q^80 - 162 * q^81 - 1092 * q^82 - 1632 * q^83 - 48 * q^84 - 1260 * q^85 + 400 * q^86 - 162 * q^87 - 288 * q^88 + 282 * q^89 - 216 * q^90 - 260 * q^91 - 336 * q^92 + 84 * q^93 - 1644 * q^94 + 714 * q^95 + 192 * q^96 + 2972 * q^97 - 328 * q^98 + 648 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	3.43649	−	5.95218i	0.307369	−	0.532379i	−0.670417	−	0.741985i	$-0.733885\pi$
$5$	3.43649	−	5.95218i	0.307369	−	0.532379i	0.977786	+	0.209606i	$0.0672180\pi$
$6$	−6.00000			−0.408248
$7$	0.809475	+	18.5026i	0.0437075	+	0.999044i
$7$	0.809475	+	18.5026i	0.0437075	+	0.999044i
$8$	8.00000			0.353553
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	6.87298	+	11.9044i	0.217343	+	0.376449i
$11$	−18.6825	−	32.3590i	−0.512088	−	0.886963i	−0.999902	−	0.0140153i	$-0.995539\pi$
$11$	−18.6825	−	32.3590i	−0.512088	−	0.886963i	0.487813	−	0.872948i	$-0.337795\pi$
$12$	6.00000	−	10.3923i	0.144338	−	0.250000i
$13$	13.0000			0.277350
$13$	13.0000			0.277350
$14$	−32.8569	−	17.1005i	−0.627240	−	0.326450i
$15$	20.6190			0.354919
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−47.4284	−	82.1484i	−0.676652	−	1.17200i	−0.975983	−	0.217846i	$-0.930097\pi$
$17$	−47.4284	−	82.1484i	−0.676652	−	1.17200i	0.299331	−	0.954149i	$-0.403236\pi$
$18$	−9.00000	−	15.5885i	−0.117851	−	0.204124i
$19$	−52.7379	+	91.3447i	−0.636784	+	1.10294i	0.349350	+	0.936992i	$0.386403\pi$
$19$	−52.7379	+	91.3447i	−0.636784	+	1.10294i	−0.986134	+	0.165951i	$0.946931\pi$
$20$	−27.4919			−0.307369
$21$	−46.8569	+	29.8569i	−0.486905	+	0.310253i
$22$	74.7298			0.724202
$23$	−18.5474	+	32.1250i	−0.168148	+	0.291240i	−0.937769	−	0.347261i	$-0.887112\pi$
$23$	−18.5474	+	32.1250i	−0.168148	+	0.291240i	0.769621	+	0.638501i	$0.220445\pi$
$24$	12.0000	+	20.7846i	0.102062	+	0.176777i
$25$	38.8810	+	67.3440i	0.311048	+	0.538752i
$26$	−13.0000	+	22.5167i	−0.0980581	+	0.169842i
$27$	−27.0000			−0.192450
$28$	62.4758	−	39.8092i	0.421672	−	0.268687i
$29$	−57.9839			−0.371287			−0.185644	−	0.982617i	$-0.559437\pi$
$29$	−57.9839			−0.371287			−0.185644	+	0.982617i	$0.559437\pi$
$30$	−20.6190	+	35.7131i	−0.125483	+	0.217343i
$31$	−111.571	−	193.246i	−0.646408	−	1.11961i	−0.983974	−	0.178310i	$-0.942937\pi$
$31$	−111.571	−	193.246i	−0.646408	−	1.11961i	0.337566	−	0.941302i	$-0.390396\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$	56.0474	−	97.0769i	0.295654	−	0.512088i
$34$	189.714			0.956930
$35$	112.912	+	58.7658i	0.545305	+	0.283806i
$36$	36.0000			0.166667
$37$	13.7853	−	23.8768i	0.0612510	−	0.106090i	−0.833774	−	0.552106i	$-0.813824\pi$
$37$	13.7853	−	23.8768i	0.0612510	−	0.106090i	0.895025	+	0.446016i	$0.147158\pi$
$38$	−105.476	−	182.689i	−0.450275	−	0.779898i
$39$	19.5000	+	33.7750i	0.0800641	+	0.138675i
$40$	27.4919	−	47.6174i	0.108671	−	0.188224i
$41$	137.446			0.523546			0.261773	−	0.965129i	$-0.415693\pi$
$41$	137.446			0.523546			0.261773	+	0.965129i	$0.415693\pi$
$42$	−4.85685	−	111.015i	−0.0178435	−	0.407858i
$43$	−495.044			−1.75566			−0.877832	−	0.478969i	$-0.841011\pi$
$43$	−495.044			−1.75566			−0.877832	+	0.478969i	$0.841011\pi$
$44$	−74.7298	+	129.436i	−0.256044	+	0.443482i
$45$	30.9284	+	53.5696i	0.102456	+	0.177460i
$46$	−37.0948	−	64.2500i	−0.118898	−	0.205938i
$47$	−232.611	+	402.894i	−0.721910	+	1.25039i	0.238323	+	0.971186i	$0.423402\pi$
$47$	−232.611	+	402.894i	−0.721910	+	1.25039i	−0.960233	+	0.279199i	$0.909931\pi$
$48$	−48.0000			−0.144338
$49$	−341.690	+	29.9547i	−0.996179	+	0.0873315i
$50$	−155.524			−0.439889
$51$	142.285	−	246.445i	0.390665	−	0.676652i
$52$	−26.0000	−	45.0333i	−0.0693375	−	0.120096i
$53$	−136.292	−	236.065i	−0.353230	−	0.611812i	0.633583	−	0.773674i	$-0.281583\pi$
$53$	−136.292	−	236.065i	−0.353230	−	0.611812i	−0.986813	+	0.161862i	$0.948250\pi$
$54$	27.0000	−	46.7654i	0.0680414	−	0.117851i
$55$	−256.808			−0.629601
$56$	6.47580	+	148.020i	0.0154529	+	0.353216i
$57$	−316.427			−0.735295
$58$	57.9839	−	100.431i	0.131270	−	0.227366i
$59$	−144.191	−	249.745i	−0.318170	−	0.551086i	0.661937	−	0.749560i	$-0.269735\pi$
$59$	−144.191	−	249.745i	−0.318170	−	0.551086i	−0.980106	+	0.198474i	$0.936401\pi$
$60$	−41.2379	−	71.4261i	−0.0887298	−	0.153685i
$61$	−99.3800	+	172.131i	−0.208595	+	0.361298i	−0.951272	−	0.308352i	$-0.900222\pi$
$61$	−99.3800	+	172.131i	−0.208595	+	0.361298i	0.742677	+	0.669650i	$0.233556\pi$
$62$	446.282			0.914160
$63$	−147.856	−	76.9523i	−0.295684	−	0.153890i
$64$	64.0000			0.125000
$65$	44.6744	−	77.3783i	0.0852489	−	0.147655i
$66$	112.095	+	194.154i	0.209059	+	0.362101i
$67$	−103.690	−	179.595i	−0.189070	−	0.327479i	0.755870	−	0.654721i	$-0.227214\pi$
$67$	−103.690	−	179.595i	−0.189070	−	0.327479i	−0.944940	+	0.327242i	$0.893881\pi$
$68$	−189.714	+	328.594i	−0.338326	+	0.585998i
$69$	−111.284			−0.194160
$70$	−214.698	+	136.804i	−0.366590	+	0.233589i
$71$	−141.444			−0.236426			−0.118213	−	0.992988i	$-0.537717\pi$
$71$	−141.444			−0.236426			−0.118213	+	0.992988i	$0.537717\pi$
$72$	−36.0000	+	62.3538i	−0.0589256	+	0.102062i
$73$	−162.737	−	281.869i	−0.260917	−	0.451921i	0.705569	−	0.708641i	$-0.250691\pi$
$73$	−162.737	−	281.869i	−0.260917	−	0.451921i	−0.966486	+	0.256720i	$0.917358\pi$
$74$	27.5706	+	47.7536i	0.0433110	+	0.0750168i
$75$	−116.643	+	202.032i	−0.179584	+	0.311048i
$76$	421.903			0.636784
$77$	583.601	−	371.867i	0.863734	−	0.550366i
$78$	−78.0000			−0.113228
$79$	529.855	−	917.735i	0.754599	−	1.30700i	−0.190974	−	0.981595i	$-0.561165\pi$
$79$	529.855	−	917.735i	0.754599	−	1.30700i	0.945573	−	0.325409i	$-0.105502\pi$
$80$	54.9839	+	95.2349i	0.0768423	+	0.133095i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	−137.446	+	238.063i	−0.185102	+	0.320605i
$83$	−849.520			−1.12346			−0.561729	−	0.827322i	$-0.689863\pi$
$83$	−849.520			−1.12346			−0.561729	+	0.827322i	$0.689863\pi$
$84$	197.141	+	102.603i	0.256070	+	0.133273i
$85$	−651.950			−0.831928
$86$	495.044	−	857.442i	0.620721	−	1.07512i
$87$	−86.9758	−	150.647i	−0.107181	−	0.185644i
$88$	−149.460	−	258.872i	−0.181051	−	0.313589i
$89$	692.114	−	1198.78i	0.824314	−	1.42775i	−0.0781290	−	0.996943i	$-0.524895\pi$
$89$	692.114	−	1198.78i	0.824314	−	1.42775i	0.902443	−	0.430810i	$-0.141772\pi$
$90$	−123.714			−0.144895
$91$	10.5232	+	240.533i	0.0121223	+	0.277085i
$92$	148.379			0.168148
$93$	334.712	−	579.738i	0.373204	−	0.646408i
$94$	−465.222	−	805.788i	−0.510468	−	0.884156i
$95$	362.467	+	627.811i	0.391456	+	0.678021i
$96$	48.0000	−	83.1384i	0.0510310	−	0.0883883i
$97$	150.434			0.157466			0.0787331	−	0.996896i	$-0.474913\pi$
$97$	150.434			0.157466			0.0787331	+	0.996896i	$0.474913\pi$
$98$	289.806	−	621.778i	0.298723	−	0.640909i
$99$	336.284			0.341392
$100$	155.524	−	269.376i	0.155524	−	0.269376i
$101$	−1.96773	−	3.40821i	−0.00193858	−	0.00335772i	0.865054	−	0.501678i	$-0.167284\pi$
$101$	−1.96773	−	3.40821i	−0.00193858	−	0.00335772i	−0.866993	+	0.498320i	$0.833950\pi$
$102$	284.571	+	492.891i	0.276242	+	0.478465i
$103$	−385.429	+	667.583i	−0.368714	+	0.638631i	−0.989365	−	0.145456i	$-0.953535\pi$
$103$	−385.429	+	667.583i	−0.368714	+	0.638631i	0.620651	+	0.784087i	$0.286868\pi$
$104$	104.000			0.0980581
$105$	16.6905	+	381.503i	0.0155127	+	0.354580i
$106$	545.169			0.499543
$107$	310.379	−	537.592i	0.280425	−	0.485710i	−0.691064	−	0.722793i	$-0.742858\pi$
$107$	310.379	−	537.592i	0.280425	−	0.485710i	0.971489	+	0.237083i	$0.0761913\pi$
$108$	54.0000	+	93.5307i	0.0481125	+	0.0833333i
$109$	−368.282	−	637.883i	−0.323624	−	0.560534i	0.657609	−	0.753360i	$-0.271568\pi$
$109$	−368.282	−	637.883i	−0.323624	−	0.560534i	−0.981233	+	0.192826i	$0.938235\pi$
$110$	256.808	−	444.805i	0.222598	−	0.385550i
$111$	82.7117			0.0707265
$112$	−262.855	−	136.804i	−0.221763	−	0.115418i
$113$	710.877			0.591802			0.295901	−	0.955219i	$-0.404380\pi$
$113$	710.877			0.591802			0.295901	+	0.955219i	$0.404380\pi$
$114$	316.427	−	548.068i	0.259966	−	0.450275i
$115$	127.476	+	220.795i	0.103367	+	0.179037i
$116$	115.968	+	200.862i	0.0928218	+	0.160772i
$117$	−58.5000	+	101.325i	−0.0462250	+	0.0800641i
$118$	576.762			0.449960
$119$	1481.56	−	944.044i	1.14130	−	0.727230i
$120$	164.952			0.125483
$121$	−32.5685	+	56.4103i	−0.0244692	+	0.0423819i
$122$	−198.760	−	344.263i	−0.147499	−	0.255476i
$123$	206.168	+	357.094i	0.151135	+	0.261773i
$124$	−446.282	+	772.983i	−0.323204	+	0.559806i
$125$	1393.58			0.997165
$126$	281.141	−	179.142i	0.198778	−	0.126660i
$127$	−2120.99			−1.48195			−0.740974	−	0.671534i	$-0.765636\pi$
$127$	−2120.99			−1.48195			−0.740974	+	0.671534i	$0.765636\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$	−742.566	−	1286.16i	−0.506817	−	0.877832i
$130$	89.3488	+	154.757i	0.0602801	+	0.104408i
$131$	454.531	−	787.271i	0.303149	−	0.525070i	−0.673698	−	0.739007i	$-0.735295\pi$
$131$	454.531	−	787.271i	0.303149	−	0.525070i	0.976848	+	0.213936i	$0.0686285\pi$
$132$	−448.379			−0.295654
$133$	−1732.80	−	901.845i	−1.12972	−	0.587969i
$134$	414.758			0.267385
$135$	−92.7853	+	160.709i	−0.0591532	+	0.102456i
$136$	−379.427	−	657.188i	−0.239233	−	0.414363i
$137$	−49.6421	−	85.9827i	−0.0309578	−	0.0536204i	0.850131	−	0.526571i	$-0.176522\pi$
$137$	−49.6421	−	85.9827i	−0.0309578	−	0.0536204i	−0.881089	+	0.472950i	$0.843189\pi$
$138$	111.284	−	192.750i	0.0686460	−	0.118898i
$139$	−1056.43			−0.644639			−0.322320	−	0.946631i	$-0.604463\pi$
$139$	−1056.43			−0.644639			−0.322320	+	0.946631i	$0.604463\pi$
$140$	−22.2540	−	508.671i	−0.0134344	−	0.307075i
$141$	−1395.67			−0.833590
$142$	141.444	−	244.987i	0.0835893	−	0.144781i
$143$	−242.872	−	420.667i	−0.142028	−	0.245999i
$144$	−72.0000	−	124.708i	−0.0416667	−	0.0721688i
$145$	−199.261	+	345.130i	−0.114122	+	0.197666i
$146$	650.948			0.368992
$147$	−590.359	−	842.803i	−0.331238	−	0.472879i
$148$	−110.282			−0.0612510
$149$	−282.297	+	488.954i	−0.155213	+	0.268836i	−0.933136	−	0.359522i	$-0.882940\pi$
$149$	−282.297	+	488.954i	−0.155213	+	0.268836i	0.777924	+	0.628359i	$0.216273\pi$
$150$	−233.286	−	404.064i	−0.126985	−	0.219944i
$151$	187.525	+	324.803i	0.101063	+	0.175047i	0.912123	−	0.409916i	$-0.134442\pi$
$151$	187.525	+	324.803i	0.101063	+	0.175047i	−0.811060	+	0.584964i	$0.801109\pi$
$152$	−421.903	+	730.758i	−0.225137	+	0.389949i
$153$	853.712			0.451101
$154$	60.4919	+	1382.69i	0.0316531	+	0.723510i
$155$	−1533.65			−0.794744
$156$	78.0000	−	135.100i	0.0400320	−	0.0693375i
$157$	865.858	+	1499.71i	0.440146	+	0.762356i	0.997700	−	0.0677851i	$-0.0215932\pi$
$157$	865.858	+	1499.71i	0.440146	+	0.762356i	−0.557554	+	0.830141i	$0.688260\pi$
$158$	1059.71	+	1835.47i	0.533582	+	0.924191i
$159$	408.877	−	708.196i	0.203937	−	0.353230i
$160$	−219.935			−0.108671
$161$	−609.408	−	317.170i	−0.298311	−	0.155258i
$162$	162.000			0.0785674
$163$	−1469.97	+	2546.07i	−0.706362	+	1.22346i	0.259835	+	0.965653i	$0.416332\pi$
$163$	−1469.97	+	2546.07i	−0.706362	+	1.22346i	−0.966198	+	0.257803i	$0.917002\pi$
$164$	−274.891	−	476.125i	−0.130887	−	0.226702i
$165$	−385.213	−	667.208i	−0.181750	−	0.314800i
$166$	849.520	−	1471.41i	0.397202	−	0.687974i
$167$	−737.024			−0.341513			−0.170756	−	0.985313i	$-0.554621\pi$
$167$	−737.024			−0.341513			−0.170756	+	0.985313i	$0.554621\pi$
$168$	−374.855	+	238.855i	−0.172147	+	0.109691i
$169$	169.000			0.0769231
$170$	651.950	−	1129.21i	0.294131	−	0.509450i
$171$	−474.641	−	822.103i	−0.212261	−	0.367648i
$172$	990.089	+	1714.88i	0.438916	+	0.760225i
$173$	−767.097	+	1328.65i	−0.337117	+	0.583904i	−0.983889	−	0.178779i	$-0.942785\pi$
$173$	−767.097	+	1328.65i	−0.337117	+	0.583904i	0.646772	+	0.762683i	$0.276119\pi$
$174$	347.903			0.151577
$175$	−1214.56	+	773.912i	−0.524642	+	0.334299i
$176$	597.839			0.256044
$177$	432.572	−	749.236i	0.183695	−	0.318170i
$178$	1384.23	+	2397.55i	0.582878	+	1.00957i
$179$	−1207.16	−	2090.86i	−0.504062	−	0.873062i	−0.999989	−	0.00469721i	$-0.998505\pi$
$179$	−1207.16	−	2090.86i	−0.504062	−	0.873062i	0.495927	−	0.868364i	$-0.334829\pi$
$180$	123.714	−	214.278i	0.0512282	−	0.0887298i
$181$	−260.651			−0.107039			−0.0535194	−	0.998567i	$-0.517044\pi$
$181$	−260.651			−0.107039			−0.0535194	+	0.998567i	$0.517044\pi$
$182$	−427.139	−	222.307i	−0.173965	−	0.0905410i
$183$	−596.280			−0.240865
$184$	−148.379	+	257.000i	−0.0594492	+	0.102969i
$185$	−94.7460	−	164.105i	−0.0376533	−	0.0652174i
$186$	669.423	+	1159.48i	0.263895	+	0.457080i
$187$	−1772.16	+	3069.47i	−0.693011	+	1.20033i
$188$	1860.89			0.721910
$189$	−21.8558	−	499.569i	−0.00841152	−	0.192266i
$190$	−1449.87			−0.553602
$191$	−1903.73	+	3297.36i	−0.721201	+	1.24916i	0.239318	+	0.970941i	$0.423076\pi$
$191$	−1903.73	+	3297.36i	−0.721201	+	1.24916i	−0.960519	+	0.278215i	$0.910257\pi$
$192$	96.0000	+	166.277i	0.0360844	+	0.0625000i
$193$	−463.644	−	803.055i	−0.172921	−	0.299509i	0.766519	−	0.642222i	$-0.221987\pi$
$193$	−463.644	−	803.055i	−0.172921	−	0.299509i	−0.939440	+	0.342713i	$0.888654\pi$
$194$	−150.434	+	260.559i	−0.0556727	+	0.0964279i
$195$	268.046			0.0984369
$196$	787.145	+	1123.74i	0.286860	+	0.409525i
$197$	4272.57			1.54522			0.772609	−	0.634882i	$-0.218951\pi$
$197$	4272.57			1.54522			0.772609	+	0.634882i	$0.218951\pi$
$198$	−336.284	+	582.461i	−0.120700	+	0.209059i
$199$	309.358	+	535.824i	0.110200	+	0.190872i	0.915851	−	0.401519i	$-0.131518\pi$
$199$	309.358	+	535.824i	0.110200	+	0.190872i	−0.805651	+	0.592391i	$0.798184\pi$
$200$	311.048	+	538.752i	0.109972	+	0.190477i
$201$	311.069	−	538.786i	0.109160	−	0.189070i
$202$	7.87093			0.00274157
$203$	−46.9365	−	1072.85i	−0.0162281	−	0.370933i
$204$	−1138.28			−0.390665
$205$	472.331	−	818.101i	0.160922	−	0.278725i
$206$	−770.859	−	1335.17i	−0.260720	−	0.451580i
$207$	−166.926	−	289.125i	−0.0560492	−	0.0970801i
$208$	−104.000	+	180.133i	−0.0346688	+	0.0600481i
$209$	3941.09			1.30436
$210$	−677.474	−	352.595i	−0.222620	−	0.115863i
$211$	3483.58			1.13659			0.568293	−	0.822827i	$-0.307604\pi$
$211$	3483.58			1.13659			0.568293	+	0.822827i	$0.307604\pi$
$212$	−545.169	+	944.261i	−0.176615	+	0.305906i
$213$	−212.165	−	367.481i	−0.0682504	−	0.118213i
$214$	620.758	+	1075.18i	0.198290	+	0.343449i
$215$	−1701.22	+	2946.59i	−0.539637	+	0.934679i
$216$	−216.000			−0.0680414
$217$	3485.23	−	2220.77i	1.09029	−	0.694726i
$218$	1473.13			0.457674
$219$	488.211	−	845.606i	0.150640	−	0.260917i
$220$	513.617	+	889.611i	0.157400	+	0.272625i
$221$	−616.570	−	1067.93i	−0.187669	−	0.325053i
$222$	−82.7117	+	143.261i	−0.0250056	+	0.0433110i
$223$	−3301.86			−0.991521			−0.495761	−	0.868459i	$-0.665111\pi$
$223$	−3301.86			−0.991521			−0.495761	+	0.868459i	$0.665111\pi$
$224$	499.806	−	318.474i	0.149084	−	0.0949952i
$225$	−699.859			−0.207366
$226$	−710.877	+	1231.27i	−0.209234	+	0.362403i
$227$	−144.817	−	250.830i	−0.0423428	−	0.0733399i	0.844077	−	0.536222i	$-0.180149\pi$
$227$	−144.817	−	250.830i	−0.0423428	−	0.0733399i	−0.886420	+	0.462882i	$0.846815\pi$
$228$	632.855	+	1096.14i	0.183824	+	0.318392i
$229$	−3001.04	+	5197.96i	−0.866002	+	1.49996i	4.68398e−5		1.00000i	$0.499985\pi$
$229$	−3001.04	+	5197.96i	−0.866002	+	1.49996i	−0.866049	+	0.499959i	$0.833348\pi$
$230$	−509.903			−0.146183
$231$	1841.54	+	958.439i	0.524521	+	0.272990i
$232$	−463.871			−0.131270
$233$	−1348.67	+	2335.96i	−0.379203	+	0.656798i	−0.990946	−	0.134258i	$-0.957135\pi$
$233$	−1348.67	+	2335.96i	−0.379203	+	0.656798i	0.611744	+	0.791056i	$0.290468\pi$
$234$	−117.000	−	202.650i	−0.0326860	−	0.0566139i
$235$	1598.73	+	2769.08i	0.443786	+	0.768660i
$236$	−576.762	+	998.981i	−0.159085	+	0.275543i
$237$	3179.13			0.871336
$238$	153.569	+	3510.19i	0.0418251	+	0.956016i
$239$	1851.40			0.501076			0.250538	−	0.968107i	$-0.419393\pi$
$239$	1851.40			0.501076			0.250538	+	0.968107i	$0.419393\pi$
$240$	−164.952	+	285.705i	−0.0443649	+	0.0768423i
$241$	−1847.95	−	3200.75i	−0.493930	−	0.855512i	0.506045	−	0.862507i	$-0.331107\pi$
$241$	−1847.95	−	3200.75i	−0.493930	−	0.855512i	−0.999976	+	0.00699477i	$0.997773\pi$
$242$	−65.1370	−	112.821i	−0.0173023	−	0.0299685i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	795.040			0.208595
$245$	−995.917	+	2136.74i	−0.259701	+	0.557188i
$246$	−824.673			−0.213737
$247$	−685.593	+	1187.48i	−0.176612	+	0.305901i
$248$	−892.564	−	1545.97i	−0.228540	−	0.395843i
$249$	−1274.28	−	2207.12i	−0.324314	−	0.561729i
$250$	−1393.58	+	2413.75i	−0.352551	+	0.610636i
$251$	−4141.18			−1.04139			−0.520695	−	0.853743i	$-0.674327\pi$
$251$	−4141.18			−1.04139			−0.520695	+	0.853743i	$0.674327\pi$
$252$	29.1411	+	666.092i	0.00728459	+	0.166507i
$253$	1386.04			0.344426
$254$	2120.99	−	3673.66i	0.523948	−	0.907504i
$255$	−977.924	−	1693.81i	−0.240157	−	0.415964i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	1246.94	−	2159.77i	0.302654	−	0.524212i	−0.674082	−	0.738656i	$-0.735461\pi$
$257$	1246.94	−	2159.77i	0.302654	−	0.524212i	0.976736	+	0.214444i	$0.0687940\pi$
$258$	2970.27			0.716747
$259$	452.941	+	235.735i	0.108666	+	0.0565555i
$260$	−357.395			−0.0852489
$261$	260.927	−	451.940i	0.0618812	−	0.107181i
$262$	909.062	+	1574.54i	0.214359	+	0.371281i
$263$	1440.14	+	2494.40i	0.337653	+	0.584833i	0.983991	−	0.178219i	$-0.0570335\pi$
$263$	1440.14	+	2494.40i	0.337653	+	0.584833i	−0.646338	+	0.763052i	$0.723700\pi$
$264$	448.379	−	776.615i	0.104530	−	0.181051i
$265$	−1873.47			−0.434288
$266$	3294.84	−	2099.45i	0.759473	−	0.483932i
$267$	4152.68			0.951835
$268$	−414.758	+	718.382i	−0.0945350	+	0.163739i
$269$	3021.86	+	5234.01i	0.684929	+	1.18633i	0.973459	+	0.228861i	$0.0735002\pi$
$269$	3021.86	+	5234.01i	0.684929	+	1.18633i	−0.288530	+	0.957471i	$0.593166\pi$
$270$	−185.571	−	321.418i	−0.0418276	−	0.0724476i
$271$	−2211.94	+	3831.19i	−0.495814	+	0.858775i	−0.999988	−	0.00482701i	$-0.998464\pi$
$271$	−2211.94	+	3831.19i	−0.495814	+	0.858775i	0.504174	+	0.863602i	$0.331797\pi$
$272$	1517.71			0.338326
$273$	−609.139	+	388.140i	−0.135043	+	0.0860487i
$274$	198.569			0.0437809
$275$	1452.79	−	2516.30i	0.318569	−	0.551777i
$276$	222.569	+	385.500i	0.0485400	+	0.0840738i
$277$	3058.51	+	5297.50i	0.663423	+	1.14908i	0.979710	+	0.200419i	$0.0642304\pi$
$277$	3058.51	+	5297.50i	0.663423	+	1.14908i	−0.316287	+	0.948664i	$0.602436\pi$
$278$	1056.43	−	1829.78i	0.227914	−	0.394759i
$279$	2008.27			0.430939
$280$	903.298	+	470.126i	0.192794	+	0.100341i
$281$	−6771.02			−1.43746			−0.718728	−	0.695291i	$-0.755276\pi$
$281$	−6771.02			−1.43746			−0.718728	+	0.695291i	$0.755276\pi$
$282$	1395.67	−	2417.36i	0.294719	−	0.510468i
$283$	442.446	+	766.340i	0.0929354	+	0.160969i	0.908745	−	0.417352i	$-0.137042\pi$
$283$	442.446	+	766.340i	0.0929354	+	0.160969i	−0.815810	+	0.578320i	$0.803708\pi$
$284$	282.887	+	489.975i	0.0591065	+	0.102376i
$285$	−1087.40	+	1883.43i	−0.226007	+	0.391456i
$286$	971.488			0.200858
$287$	111.259	+	2543.10i	0.0228829	+	0.523046i
$288$	288.000			0.0589256
$289$	−2042.41	+	3537.56i	−0.415716	+	0.720041i
$290$	−398.522	−	690.261i	−0.0806966	−	0.139771i
$291$	225.650	+	390.838i	0.0454566	+	0.0787331i
$292$	−650.948	+	1127.47i	−0.130458	+	0.225960i
$293$	5971.86			1.19072			0.595358	−	0.803461i	$-0.297010\pi$
$293$	5971.86			1.19072			0.595358	+	0.803461i	$0.297010\pi$
$294$	2050.14	−	179.728i	0.406688	−	0.0356530i
$295$	−1982.04			−0.391182
$296$	110.282	−	191.014i	0.0216555	−	0.0375084i
$297$	504.426	+	873.692i	0.0985515	+	0.170696i
$298$	−564.595	−	977.907i	−0.109752	−	0.190096i
$299$	−241.116	+	417.625i	−0.0466358	+	0.0807755i
$300$	933.145			0.179584
$301$	−400.726	−	9159.59i	−0.0767358	−	1.75399i
$302$	−750.101			−0.142925
$303$	5.90320	−	10.2246i	0.00111924	−	0.00193858i
$304$	−843.806	−	1461.52i	−0.159196	−	0.275736i
$305$	683.037	+	1183.06i	0.128231	+	0.222103i
$306$	−853.712	+	1478.67i	−0.159488	+	0.276242i
$307$	6395.36			1.18893			0.594467	−	0.804120i	$-0.297363\pi$
$307$	6395.36			1.18893			0.594467	+	0.804120i	$0.297363\pi$
$308$	−2455.39	−	1277.92i	−0.454249	−	0.236416i
$309$	−2312.58			−0.425754
$310$	1533.65	−	2656.35i	0.280984	−	0.486679i
$311$	320.273	+	554.729i	0.0583956	+	0.101144i	0.893745	−	0.448575i	$-0.148068\pi$
$311$	320.273	+	554.729i	0.0583956	+	0.101144i	−0.835350	+	0.549719i	$0.814735\pi$
$312$	156.000	+	270.200i	0.0283069	+	0.0490290i
$313$	−5005.59	+	8669.94i	−0.903939	+	1.56567i	−0.0816031	+	0.996665i	$0.526004\pi$
$313$	−5005.59	+	8669.94i	−0.903939	+	1.56567i	−0.822336	+	0.569003i	$0.807329\pi$
$314$	−3463.43			−0.622461
$315$	−966.139	+	615.618i	−0.172812	+	0.110115i
$316$	−4238.84			−0.754599
$317$	−2933.78	+	5081.46i	−0.519804	+	0.900326i	0.479931	+	0.877306i	$0.340662\pi$
$317$	−2933.78	+	5081.46i	−0.519804	+	0.900326i	−0.999735	+	0.0230202i	$0.992672\pi$
$318$	817.754	+	1416.39i	0.144206	+	0.249771i
$319$	1083.28	+	1876.30i	0.190132	+	0.329318i
$320$	219.935	−	380.939i	0.0384211	−	0.0665474i
$321$	1862.27			0.323807
$322$	1158.76	−	738.357i	0.200544	−	0.127786i
$323$	10005.1			1.72353
$324$	−162.000	+	280.592i	−0.0277778	+	0.0481125i
$325$	505.454	+	875.471i	0.0862693	+	0.149423i
$326$	−2939.94	−	5092.13i	−0.499474	−	0.865114i
$327$	1104.85	−	1913.65i	0.186845	−	0.323624i
$328$	1099.56			0.185102
$329$	−7642.86	−	3977.76i	−1.28074	−	0.666569i
$330$	1540.85			0.257033
$331$	−2570.04	+	4451.44i	−0.426774	+	0.739194i	−0.996584	−	0.0825821i	$-0.973683\pi$
$331$	−2570.04	+	4451.44i	−0.426774	+	0.739194i	0.569810	+	0.821776i	$0.307017\pi$
$332$	1699.04	+	2942.82i	0.280864	+	0.486471i
$333$	124.067	+	214.891i	0.0204170	+	0.0353633i
$334$	737.024	−	1276.56i	0.120743	−	0.209133i
$335$	−1425.31			−0.232457
$336$	−38.8548	−	888.123i	−0.00630864	−	0.144200i
$337$	−8309.33			−1.34314			−0.671570	−	0.740941i	$-0.734380\pi$
$337$	−8309.33			−1.34314			−0.671570	+	0.740941i	$0.734380\pi$
$338$	−169.000	+	292.717i	−0.0271964	+	0.0471056i
$339$	1066.32	+	1846.91i	0.170839	+	0.295901i
$340$	1303.90	+	2258.42i	0.207982	+	0.360235i
$341$	−4168.82	+	7220.62i	−0.662037	+	1.14668i
$342$	1898.56			0.300183
$343$	−830.828	−	6297.88i	−0.130789	−	0.991410i
$344$	−3960.35			−0.620721
$345$	−382.427	+	662.384i	−0.0596788	+	0.103367i
$346$	−1534.19	−	2657.30i	−0.238378	−	0.412883i
$347$	5218.01	+	9037.86i	0.807255	+	1.39821i	0.914758	+	0.404002i	$0.132381\pi$
$347$	5218.01	+	9037.86i	0.807255	+	1.39821i	−0.107503	+	0.994205i	$0.534285\pi$
$348$	−347.903	+	602.586i	−0.0535907	+	0.0928218i
$349$	7035.05			1.07902			0.539509	−	0.841980i	$-0.318610\pi$
$349$	7035.05			1.07902			0.539509	+	0.841980i	$0.318610\pi$
$350$	−125.893	−	2877.60i	−0.0192265	−	0.439468i
$351$	−351.000			−0.0533761
$352$	−597.839	+	1035.49i	−0.0905253	+	0.156794i
$353$	−5042.57	−	8733.99i	−0.760309	−	1.31689i	−0.942691	−	0.333666i	$-0.891714\pi$
$353$	−5042.57	−	8733.99i	−0.760309	−	1.31689i	0.182382	−	0.983228i	$-0.441619\pi$
$354$	865.143	+	1498.47i	0.129892	+	0.224980i
$355$	−486.070	+	841.897i	−0.0726701	+	0.125868i
$356$	−5536.91			−0.824314
$357$	4675.05	+	2433.15i	0.693080	+	0.360717i
$358$	4828.63			0.712852
$359$	−183.359	+	317.587i	−0.0269563	+	0.0466897i	−0.879189	−	0.476473i	$-0.841915\pi$
$359$	−183.359	+	317.587i	−0.0269563	+	0.0466897i	0.852233	+	0.523163i	$0.175248\pi$
$360$	247.427	+	428.557i	0.0362238	+	0.0627415i
$361$	−2133.07	−	3694.59i	−0.310989	−	0.538648i
$362$	260.651	−	451.461i	0.0378440	−	0.0655476i
$363$	−195.411			−0.0282546
$364$	812.185	−	517.520i	0.116951	−	0.0745204i
$365$	−2236.98			−0.320791
$366$	596.280	−	1032.79i	0.0851586	−	0.147499i
$367$	815.834	+	1413.07i	0.116039	+	0.200985i	0.918194	−	0.396130i	$-0.129647\pi$
$367$	815.834	+	1413.07i	0.116039	+	0.200985i	−0.802156	+	0.597115i	$0.796314\pi$
$368$	−296.758	−	514.000i	−0.0420369	−	0.0728101i
$369$	−618.505	+	1071.28i	−0.0872577	+	0.151135i
$370$	378.984			0.0532498
$371$	4257.49	−	2712.85i	0.595789	−	0.379633i
$372$	−2677.69			−0.373204
$373$	−926.727	+	1605.14i	−0.128644	+	0.222817i	−0.923151	−	0.384437i	$-0.874396\pi$
$373$	−926.727	+	1605.14i	−0.128644	+	0.222817i	0.794508	+	0.607254i	$0.207729\pi$
$374$	−3544.32	−	6138.94i	−0.490033	−	0.848762i
$375$	2090.37	+	3620.63i	0.287857	+	0.498583i
$376$	−1860.89	+	3223.15i	−0.255234	+	0.442078i
$377$	−753.790			−0.102977
$378$	887.135	+	461.714i	0.120712	+	0.0628254i
$379$	8143.37			1.10369			0.551843	−	0.833948i	$-0.313925\pi$
$379$	8143.37			1.10369			0.551843	+	0.833948i	$0.313925\pi$
$380$	1449.87	−	2511.24i	0.195728	−	0.339011i
$381$	−3181.48	−	5510.49i	−0.427802	−	0.740974i
$382$	−3807.47	−	6594.73i	−0.509966	−	0.883287i
$383$	3664.00	−	6346.23i	0.488829	−	0.846677i	−0.511088	−	0.859528i	$-0.670757\pi$
$383$	3664.00	−	6346.23i	0.488829	−	0.846677i	0.999917	+	0.0128511i	$0.00409074\pi$
$384$	−384.000			−0.0510310
$385$	−207.880	−	4751.61i	−0.0275183	−	0.628999i
$386$	1854.58			0.244548
$387$	2227.70	−	3858.49i	0.292611	−	0.506817i
$388$	−300.867	−	521.117i	−0.0393665	−	0.0681848i
$389$	−1801.60	−	3120.46i	−0.234819	−	0.406719i	0.724401	−	0.689379i	$-0.242117\pi$
$389$	−1801.60	−	3120.46i	−0.234819	−	0.406719i	−0.959220	+	0.282660i	$0.908783\pi$
$390$	−268.046	+	464.270i	−0.0348027	+	0.0602801i
$391$	3518.69			0.455110
$392$	−2733.52	+	239.638i	−0.352203	+	0.0308764i
$393$	2727.19			0.350047
$394$	−4272.57	+	7400.31i	−0.546317	+	0.946249i
$395$	−3641.68	−	6307.58i	−0.463881	−	0.803465i
$396$	−672.569	−	1164.92i	−0.0853481	−	0.147827i
$397$	6937.60	−	12016.3i	0.877049	−	1.51909i	0.0224844	−	0.999747i	$-0.492842\pi$
$397$	6937.60	−	12016.3i	0.877049	−	1.51909i	0.854564	−	0.519346i	$-0.173824\pi$
$398$	−1237.43			−0.155846
$399$	−256.140	−	5854.72i	−0.0321380	−	0.734593i
$400$	−1244.19			−0.155524
$401$	3480.14	−	6027.78i	0.433391	−	0.750656i	−0.563771	−	0.825931i	$-0.690650\pi$
$401$	3480.14	−	6027.78i	0.433391	−	0.750656i	0.997163	+	0.0752748i	$0.0239834\pi$
$402$	622.137	+	1077.57i	0.0771875	+	0.133693i
$403$	−1450.42	−	2512.20i	−0.179281	−	0.310525i
$404$	−7.87093	+	13.6329i	−0.000969291	+	0.00167886i
$405$	−556.712			−0.0683043
$406$	1905.17	+	991.554i	0.232886	+	0.121207i
$407$	−1030.17			−0.125464
$408$	1138.28	−	1971.56i	0.138121	−	0.239233i
$409$	−5816.90	−	10075.2i	−0.703244	−	1.21806i	−0.967321	−	0.253553i	$-0.918401\pi$
$409$	−5816.90	−	10075.2i	−0.703244	−	1.21806i	0.264077	−	0.964502i	$-0.414933\pi$
$410$	944.661	+	1636.20i	0.113789	+	0.197088i
$411$	148.926	−	257.948i	0.0178735	−	0.0309578i
$412$	3083.44			0.368714
$413$	4504.21	−	2870.06i	0.536653	−	0.341952i
$414$	667.706			0.0792655
$415$	−2919.37	+	5056.50i	−0.345316	+	0.598105i
$416$	−208.000	−	360.267i	−0.0245145	−	0.0424604i
$417$	−1584.64	−	2744.67i	−0.186091	−	0.322320i
$418$	−3941.09	+	6826.18i	−0.461161	+	0.798754i
$419$	9044.25			1.05451			0.527256	−	0.849707i	$-0.323221\pi$
$419$	9044.25			1.05451			0.527256	+	0.849707i	$0.323221\pi$
$420$	1288.19	−	820.824i	0.149660	−	0.0953622i
$421$	−14419.0			−1.66921			−0.834607	−	0.550846i	$-0.814305\pi$
$421$	−14419.0			−1.66921			−0.834607	+	0.550846i	$0.814305\pi$
$422$	−3483.58	+	6033.74i	−0.401844	+	0.696013i
$423$	−2093.50	−	3626.04i	−0.240637	−	0.416795i
$424$	−1090.34	−	1888.52i	−0.124886	−	0.216308i
$425$	3688.13	−	6388.04i	0.420943	−	0.729095i
$426$	848.661			0.0965206
$427$	−3265.31	−	1699.45i	−0.370069	−	0.192604i
$428$	−2483.03			−0.280425
$429$	728.616	−	1262.00i	0.0819998	−	0.142028i
$430$	−3402.43	−	5893.18i	−0.381581	−	0.660918i
$431$	3517.98	+	6093.31i	0.393167	+	0.680985i	0.992865	−	0.119241i	$-0.0380461\pi$
$431$	3517.98	+	6093.31i	0.393167	+	0.680985i	−0.599698	+	0.800226i	$0.704713\pi$
$432$	216.000	−	374.123i	0.0240563	−	0.0416667i
$433$	8976.40			0.996255			0.498127	−	0.867104i	$-0.334021\pi$
$433$	8976.40			0.996255			0.498127	+	0.867104i	$0.334021\pi$
$434$	361.254	+	8257.36i	0.0399557	+	0.913286i
$435$	−1195.57			−0.131777
$436$	−1473.13	+	2551.53i	−0.161812	+	0.280267i
$437$	−1956.30	−	3388.41i	−0.214148	−	0.370914i
$438$	976.421	+	1691.21i	0.106519	+	0.184496i
$439$	7485.73	−	12965.7i	0.813836	−	1.40961i	−0.0963239	−	0.995350i	$-0.530708\pi$
$439$	7485.73	−	12965.7i	0.813836	−	1.40961i	0.910160	−	0.414256i	$-0.135958\pi$
$440$	−2054.47			−0.222598
$441$	1304.13	−	2798.00i	0.140819	−	0.302127i
$442$	2466.28			0.265405
$443$	−7071.91	+	12248.9i	−0.758457	+	1.31369i	0.185181	+	0.982705i	$0.440713\pi$
$443$	−7071.91	+	12248.9i	−0.758457	+	1.31369i	−0.943637	+	0.330981i	$0.892620\pi$
$444$	−165.423	−	286.522i	−0.0176816	−	0.0306255i
$445$	−4756.89	−	8239.17i	−0.506737	−	0.877695i
$446$	3301.86	−	5719.00i	0.350556	−	0.607180i
$447$	−1693.78			−0.179224
$448$	51.8064	+	1184.16i	0.00546344	+	0.124881i
$449$	12278.7			1.29058			0.645288	−	0.763939i	$-0.276737\pi$
$449$	12278.7			1.29058			0.645288	+	0.763939i	$0.276737\pi$
$450$	699.859	−	1212.19i	0.0733148	−	0.126985i
$451$	−2567.82	−	4447.60i	−0.268102	−	0.464366i
$452$	−1421.75	−	2462.55i	−0.147951	−	0.256258i
$453$	−562.576	+	974.410i	−0.0583490	+	0.101063i
$454$	579.267			0.0598818
$455$	1467.86	+	763.955i	0.151240	+	0.0787137i
$456$	−2531.42			−0.259966
$457$	−6195.94	+	10731.7i	−0.634209	+	1.09848i	0.352473	+	0.935822i	$0.385341\pi$
$457$	−6195.94	+	10731.7i	−0.634209	+	1.09848i	−0.986682	+	0.162661i	$0.947992\pi$
$458$	−6002.08	−	10395.9i	−0.612356	−	1.06063i
$459$	1280.57	+	2218.01i	0.130222	+	0.225551i
$460$	509.903	−	883.178i	0.0516834	−	0.0895183i
$461$	−12194.8			−1.23203			−0.616017	−	0.787733i	$-0.711255\pi$
$461$	−12194.8			−1.23203			−0.616017	+	0.787733i	$0.711255\pi$
$462$	−3501.60	+	2231.20i	−0.352618	+	0.224686i
$463$	12130.0			1.21756			0.608778	−	0.793341i	$-0.291660\pi$
$463$	12130.0			1.21756			0.608778	+	0.793341i	$0.291660\pi$
$464$	463.871	−	803.448i	0.0464109	−	0.0803861i
$465$	−2300.47	−	3984.53i	−0.229423	−	0.397372i
$466$	−2697.34	−	4671.92i	−0.268137	−	0.464426i
$467$	−3187.95	+	5521.68i	−0.315890	+	0.547137i	−0.979626	−	0.200829i	$-0.935636\pi$
$467$	−3187.95	+	5521.68i	−0.315890	+	0.547137i	0.663736	+	0.747967i	$0.268970\pi$
$468$	468.000			0.0462250
$469$	3239.04	−	2063.90i	0.318902	−	0.203203i
$470$	−6394.92			−0.627608
$471$	−2597.57	+	4499.13i	−0.254119	+	0.440146i
$472$	−1153.52	−	1997.96i	−0.112490	−	0.194838i
$473$	9248.64	+	16019.1i	0.899055	+	1.55721i
$474$	−3179.13	+	5506.41i	−0.308064	+	0.533582i
$475$	−8202.02			−0.792283
$476$	−6233.39	−	3244.20i	−0.600225	−	0.312390i
$477$	2453.26			0.235487
$478$	−1851.40	+	3206.72i	−0.177157	+	0.306845i
$479$	−8595.69	−	14888.2i	−0.819931	−	1.42016i	−0.905732	−	0.423851i	$-0.860678\pi$
$479$	−8595.69	−	14888.2i	−0.819931	−	1.42016i	0.0858007	−	0.996312i	$-0.472655\pi$
$480$	−329.903	−	571.409i	−0.0313707	−	0.0543357i
$481$	179.209	−	310.398i	0.0169880	−	0.0294240i
$482$	7391.81			0.698523
$483$	−90.0818	−	2059.04i	−0.00848626	−	0.193975i
$484$	260.548			0.0244692
$485$	516.964	−	895.407i	0.0484002	−	0.0838316i
$486$	243.000	+	420.888i	0.0226805	+	0.0392837i
$487$	−6014.43	−	10417.3i	−0.559630	−	0.969308i	−0.997527	−	0.0702826i	$-0.977610\pi$
$487$	−6014.43	−	10417.3i	−0.559630	−	0.969308i	0.437897	−	0.899025i	$-0.355723\pi$
$488$	−795.040	+	1377.05i	−0.0737495	+	0.127738i
$489$	−8819.83			−0.815637
$490$	−2705.02	−	3861.72i	−0.249388	−	0.356030i
$491$	10398.6			0.955767			0.477884	−	0.878423i	$-0.341404\pi$
$491$	10398.6			0.955767			0.477884	+	0.878423i	$0.341404\pi$
$492$	824.673	−	1428.38i	0.0755674	−	0.130887i
$493$	2750.08	+	4763.28i	0.251232	+	0.435147i
$494$	−1371.19	−	2374.96i	−0.124884	−	0.216305i
$495$	1155.64	−	2001.62i	0.104933	−	0.181750i
$496$	3570.26			0.323204
$497$	−114.495	−	2617.07i	−0.0103336	−	0.236200i
$498$	5097.12			0.458649
$499$	422.453	−	731.711i	0.0378990	−	0.0656430i	−0.846454	−	0.532462i	$-0.821267\pi$
$499$	422.453	−	731.711i	0.0378990	−	0.0656430i	0.884353	+	0.466819i	$0.154600\pi$
$500$	−2787.16	−	4827.50i	−0.249291	−	0.431785i
$501$	−1105.54	−	1914.84i	−0.0985862	−	0.170756i
$502$	4141.18	−	7172.74i	0.368187	−	0.637719i
$503$	−5808.89			−0.514922			−0.257461	−	0.966289i	$-0.582886\pi$
$503$	−5808.89			−0.514922			−0.257461	+	0.966289i	$0.582886\pi$
$504$	−1182.85	−	615.618i	−0.104540	−	0.0544084i
$505$	−27.0484			−0.00238344
$506$	−1386.04	+	2400.70i	−0.121773	+	0.210917i
$507$	253.500	+	439.075i	0.0222058	+	0.0384615i
$508$	4241.98	+	7347.32i	0.370487	+	0.641702i
$509$	10024.7	−	17363.3i	0.872960	−	1.51201i	0.0140401	−	0.999901i	$-0.495531\pi$
$509$	10024.7	−	17363.3i	0.872960	−	1.51201i	0.858920	−	0.512110i	$-0.171136\pi$
$510$	3911.70			0.339633
$511$	5083.56	−	3239.21i	0.440085	−	0.280420i
$512$	512.000			0.0441942
$513$	1423.92	−	2466.31i	0.122549	−	0.212261i
$514$	2493.88	+	4319.53i	0.214009	+	0.370674i
$515$	2649.05	+	4588.29i	0.226662	+	0.392591i
$516$	−2970.27	+	5144.65i	−0.253408	+	0.438916i
$517$	17383.0			1.47873
$518$	−861.246	+	548.781i	−0.0730521	+	0.0465484i
$519$	−4602.58			−0.389269
$520$	357.395	−	619.027i	0.0301400	−	0.0522041i
$521$	3947.57	+	6837.39i	0.331951	+	0.574955i	0.982894	−	0.184171i	$-0.0589599\pi$
$521$	3947.57	+	6837.39i	0.331951	+	0.574955i	−0.650944	+	0.759126i	$0.725627\pi$
$522$	521.855	+	903.879i	0.0437566	+	0.0757887i
$523$	−10172.0	+	17618.5i	−0.850462	+	1.47304i	0.0303307	+	0.999540i	$0.490344\pi$
$523$	−10172.0	+	17618.5i	−0.850462	+	1.47304i	−0.880792	+	0.473503i	$0.842989\pi$
$524$	−3636.25			−0.303149
$525$	−3832.53	−	1994.66i	−0.318600	−	0.165817i
$526$	−5760.56			−0.477514
$527$	−10583.2	+	18330.7i	−0.874787	+	1.51518i
$528$	896.758	+	1553.23i	0.0739136	+	0.128022i
$529$	5395.49	+	9345.26i	0.443453	+	0.768083i
$530$	1873.47	−	3244.94i	0.153544	−	0.265946i
$531$	2595.43			0.212113
$532$	341.520	+	7806.29i	0.0278323	+	0.636176i
$533$	1786.79			0.145206
$534$	−4152.68	+	7192.66i	−0.336525	+	0.582878i
$535$	−2133.23	−	3694.86i	−0.172388	−	0.298585i
$536$	−829.516	−	1436.76i	−0.0668463	−	0.115781i
$537$	3621.47	−	6272.57i	0.291021	−	0.504062i
$538$	−12087.4			−0.968636
$539$	7352.90	+	10497.1i	0.587592	+	0.838853i
$540$	742.282			0.0591532
$541$	7186.18	−	12446.8i	0.571087	−	0.989151i	−0.425368	−	0.905021i	$-0.639855\pi$
$541$	7186.18	−	12446.8i	0.571087	−	0.989151i	0.996455	−	0.0841309i	$-0.0268114\pi$
$542$	−4423.87	−	7662.37i	−0.350593	−	0.607245i
$543$	−390.976	−	677.191i	−0.0308995	−	0.0535194i
$544$	−1517.71	+	2628.75i	−0.119616	+	0.207181i
$545$	−5062.39			−0.397888
$546$	−63.1391	−	1443.20i	−0.00494890	−	0.113119i
$547$	2625.07			0.205192			0.102596	−	0.994723i	$-0.467285\pi$
$547$	2625.07			0.205192			0.102596	+	0.994723i	$0.467285\pi$
$548$	−198.569	+	343.931i	−0.0154789	+	0.0268102i
$549$	−894.420	−	1549.18i	−0.0695317	−	0.120433i
$550$	2905.57	+	5032.60i	0.225262	+	0.390165i
$551$	3057.95	−	5296.52i	0.236430	−	0.409509i
$552$	−890.274			−0.0686460
$553$	17409.4	+	9060.79i	1.33874	+	0.696752i
$554$	−12234.1			−0.938222
$555$	284.238	−	492.314i	0.0217391	−	0.0376533i
$556$	2112.85	+	3659.56i	0.161160	+	0.279137i
$557$	−457.229	−	791.945i	−0.0347817	−	0.0602438i	0.848111	−	0.529819i	$-0.177740\pi$
$557$	−457.229	−	791.945i	−0.0347817	−	0.0602438i	−0.882892	+	0.469576i	$0.844407\pi$
$558$	−2008.27	+	3478.43i	−0.152360	+	0.263895i
$559$	−6435.58			−0.486934
$560$	−1717.58	+	1094.43i	−0.129609	+	0.0825861i
$561$	−10633.0			−0.800221
$562$	6771.02	−	11727.8i	0.508218	−	0.880259i
$563$	−6355.48	−	11008.0i	−0.475758	−	0.824037i	0.523857	−	0.851806i	$-0.324493\pi$
$563$	−6355.48	−	11008.0i	−0.475758	−	0.824037i	−0.999614	+	0.0277698i	$0.991159\pi$
$564$	2791.33	+	4834.73i	0.208398	+	0.360955i
$565$	2442.92	−	4231.27i	0.181902	−	0.315063i
$566$	−1769.79			−0.131430
$567$	1265.13	−	806.137i	0.0937049	−	0.0597082i
$568$	−1131.55			−0.0835893
$569$	−4136.78	+	7165.11i	−0.304785	+	0.527904i	−0.977213	−	0.212259i	$-0.931918\pi$
$569$	−4136.78	+	7165.11i	−0.304785	+	0.527904i	0.672428	+	0.740162i	$0.265251\pi$
$570$	−2174.80	−	3766.86i	−0.159811	−	0.276801i
$571$	5612.73	+	9721.53i	0.411358	+	0.712492i	0.995038	−	0.0994908i	$-0.0317214\pi$
$571$	5612.73	+	9721.53i	0.411358	+	0.712492i	−0.583681	+	0.811983i	$0.698388\pi$
$572$	−971.488	+	1682.67i	−0.0710139	+	0.123000i
$573$	−11422.4			−0.832771
$574$	−4516.03	−	2350.39i	−0.328389	−	0.170912i
$575$	−2884.57			−0.209208
$576$	−288.000	+	498.831i	−0.0208333	+	0.0360844i
$577$	−5632.71	−	9756.15i	−0.406400	−	0.703906i	0.588083	−	0.808801i	$-0.299883\pi$
$577$	−5632.71	−	9756.15i	−0.406400	−	0.703906i	−0.994483	+	0.104895i	$0.966549\pi$
$578$	−4084.82	−	7075.12i	−0.293955	−	0.509146i
$579$	1390.93	−	2409.17i	0.0998362	−	0.172921i
$580$	1594.09			0.114122
$581$	−687.665	−	15718.3i	−0.0491036	−	1.12238i
$582$	−902.601			−0.0642853
$583$	−5092.55	+	8820.56i	−0.361770	+	0.626604i
$584$	−1301.90	−	2254.95i	−0.0922479	−	0.159778i
$585$	402.070	+	696.405i	0.0284163	+	0.0492185i
$586$	−5971.86	+	10343.6i	−0.420982	+	0.729162i
$587$	7643.94			0.537477			0.268739	−	0.963213i	$-0.413393\pi$
$587$	7643.94			0.537477			0.268739	+	0.963213i	$0.413393\pi$
$588$	−1738.84	+	3730.67i	−0.121953	+	0.261650i
$589$	23536.0			1.64649
$590$	1982.04	−	3432.99i	0.138304	−	0.239549i
$591$	6408.86	+	11100.5i	0.446066	+	0.772609i
$592$	220.564	+	382.029i	0.0153127	+	0.0265224i
$593$	7379.09	−	12781.0i	0.511000	−	0.885078i	−0.488919	−	0.872329i	$-0.662609\pi$
$593$	7379.09	−	12781.0i	0.511000	−	0.885078i	0.999919	−	0.0127487i	$-0.00405816\pi$
$594$	−2017.71			−0.139373
$595$	−527.737	−	12062.7i	−0.0363615	−	0.831133i
$596$	2258.38			0.155213
$597$	−928.074	+	1607.47i	−0.0636240	+	0.110200i
$598$	−482.232	−	835.250i	−0.0329765	−	0.0571169i
$599$	14582.5	+	25257.6i	0.994698	+	1.72287i	0.586413	+	0.810012i	$0.300539\pi$
$599$	14582.5	+	25257.6i	0.994698	+	1.72287i	0.408284	+	0.912855i	$0.366127\pi$
$600$	−933.145	+	1616.25i	−0.0634925	+	0.109972i
$601$	1815.00			0.123187			0.0615936	−	0.998101i	$-0.480382\pi$
$601$	1815.00			0.123187			0.0615936	+	0.998101i	$0.480382\pi$
$602$	16265.6	+	8465.51i	1.10122	+	0.573137i
$603$	1866.41			0.126047
$604$	750.101	−	1299.21i	0.0505317	−	0.0875235i
$605$	223.843	+	387.707i	0.0150422	+	0.0260538i
$606$	11.8064	+	20.4493i	0.000791423	+	0.00137078i
$607$	8552.88	−	14814.0i	0.571912	−	0.990581i	−0.424457	−	0.905448i	$-0.639535\pi$
$607$	8552.88	−	14814.0i	0.571912	−	0.990581i	0.996370	−	0.0851330i	$-0.0271315\pi$
$608$	3375.23			0.225137
$609$	2716.94	−	1731.22i	0.180782	−	0.115193i
$610$	−2732.15			−0.181347
$611$	−3023.94	+	5237.62i	−0.200222	+	0.346794i
$612$	−1707.42	−	2957.34i	−0.112775	−	0.195333i
$613$	−7034.97	−	12184.9i	−0.463523	−	0.802845i	0.535611	−	0.844465i	$-0.320082\pi$
$613$	−7034.97	−	12184.9i	−0.463523	−	0.802845i	−0.999134	+	0.0416198i	$0.986748\pi$
$614$	−6395.36	+	11077.1i	−0.420352	+	0.728070i
$615$	2833.98			0.185817
$616$	4668.81	−	2974.94i	0.305376	−	0.194584i
$617$	−6621.60			−0.432051			−0.216026	−	0.976388i	$-0.569309\pi$
$617$	−6621.60			−0.432051			−0.216026	+	0.976388i	$0.569309\pi$
$618$	2312.58	−	4005.50i	0.150527	−	0.260720i
$619$	7603.83	+	13170.2i	0.493738	+	0.855179i	0.999974	−	0.00721586i	$-0.00229690\pi$
$619$	7603.83	+	13170.2i	0.493738	+	0.855179i	−0.506236	+	0.862395i	$0.668964\pi$
$620$	3067.29	+	5312.70i	0.198686	+	0.344134i
$621$	500.779	−	867.375i	0.0323600	−	0.0560492i
$622$	−1281.09			−0.0825838
$623$	22740.7	+	11835.5i	1.46242	+	0.761122i
$624$	−624.000			−0.0400320
$625$	−71.1033	+	123.155i	−0.00455061	+	0.00788189i
$626$	−10011.2	−	17339.9i	−0.639181	−	1.10709i
$627$	5911.64	+	10239.3i	0.376536	+	0.652180i
$628$	3463.43	−	5998.84i	0.220073	−	0.381178i
$629$	−2615.26			−0.165782
$630$	−100.143	−	2289.02i	−0.00633301	−	0.144757i
$631$	−10712.5			−0.675845			−0.337923	−	0.941174i	$-0.609724\pi$
$631$	−10712.5			−0.675845			−0.337923	+	0.941174i	$0.609724\pi$
$632$	4238.84	−	7341.88i	0.266791	−	0.462096i
$633$	5225.37	+	9050.60i	0.328104	+	0.568293i
$634$	−5867.57	−	10162.9i	−0.367557	−	0.636627i
$635$	−7288.76	+	12624.5i	−0.455505	+	0.788958i
$636$	−3271.02			−0.203937
$637$	−4441.96	+	389.411i	−0.276290	+	0.0242214i
$638$	−4333.12			−0.268887
$639$	636.496	−	1102.44i	0.0394044	−	0.0682504i
$640$	439.871	+	761.879i	0.0271679	+	0.0470561i
$641$	457.392	+	792.226i	0.0281839	+	0.0488160i	0.879773	−	0.475393i	$-0.157694\pi$
$641$	457.392	+	792.226i	0.0281839	+	0.0488160i	−0.851589	+	0.524209i	$0.824361\pi$
$642$	−1862.27	+	3225.55i	−0.114483	+	0.198290i
$643$	6292.65			0.385938			0.192969	−	0.981205i	$-0.438188\pi$
$643$	6292.65			0.385938			0.192969	+	0.981205i	$0.438188\pi$
$644$	120.109	+	2745.39i	0.00734932	+	0.167987i
$645$	−10207.3			−0.623119
$646$	−10005.1	+	17329.3i	−0.609358	+	1.05544i
$647$	−13589.6	−	23538.0i	−0.825756	−	1.43025i	−0.901340	−	0.433112i	$-0.857416\pi$
$647$	−13589.6	−	23538.0i	−0.825756	−	1.43025i	0.0755843	−	0.997139i	$-0.475918\pi$
$648$	−324.000	−	561.184i	−0.0196419	−	0.0340207i
$649$	−5387.67	+	9331.71i	−0.325862	+	0.564410i
$650$	−2021.81			−0.122003
$651$	10997.6	+	5723.74i	0.662103	+	0.344595i
$652$	11759.8			0.706362
$653$	−8091.10	+	14014.2i	−0.484884	+	0.839843i	−0.999849	−	0.0173677i	$-0.994471\pi$
$653$	−8091.10	+	14014.2i	−0.484884	+	0.839843i	0.514965	+	0.857211i	$0.327805\pi$
$654$	2209.69	+	3827.30i	0.132119	+	0.228837i
$655$	−3123.99	−	5410.90i	−0.186358	−	0.322781i
$656$	−1099.56	+	1904.50i	−0.0654433	+	0.113351i
$657$	2929.26			0.173944
$658$	14532.6	−	9260.06i	0.861000	−	0.548624i
$659$	−27804.3			−1.64355			−0.821777	−	0.569809i	$-0.807017\pi$
$659$	−27804.3			−1.64355			−0.821777	+	0.569809i	$0.807017\pi$
$660$	−1540.85	+	2668.83i	−0.0908750	+	0.157400i
$661$	−10254.5	−	17761.3i	−0.603408	−	1.04513i	−0.992301	−	0.123850i	$-0.960476\pi$
$661$	−10254.5	−	17761.3i	−0.603408	−	1.04513i	0.388893	−	0.921283i	$-0.372858\pi$
$662$	−5140.08	−	8902.88i	−0.301775	−	0.522689i
$663$	1849.71	−	3203.79i	0.108351	−	0.187669i
$664$	−6796.16			−0.397202
$665$	−11322.7	+	7214.76i	−0.660264	+	0.420716i
$666$	−496.270			−0.0288740
$667$	1075.45	−	1862.73i	0.0624311	−	0.108134i
$668$	1474.05	+	2553.13i	0.0853782	+	0.147879i
$669$	−4952.80	−	8578.50i	−0.286227	−	0.495761i
$670$	1425.31	−	2468.71i	0.0821860	−	0.142350i
$671$	7426.65			0.427277
$672$	1577.13	+	820.824i	0.0905343	+	0.0471190i
$673$	−28966.8			−1.65912			−0.829559	−	0.558418i	$-0.811408\pi$
$673$	−28966.8			−1.65912			−0.829559	+	0.558418i	$0.811408\pi$
$674$	8309.33	−	14392.2i	0.474872	−	0.822502i
$675$	−1049.79	−	1818.29i	−0.0598613	−	0.103683i
$676$	−338.000	−	585.433i	−0.0192308	−	0.0333087i
$677$	6725.08	−	11648.2i	0.381781	−	0.661264i	−0.609536	−	0.792758i	$-0.708644\pi$
$677$	6725.08	−	11648.2i	0.381781	−	0.661264i	0.991317	+	0.131494i	$0.0419775\pi$
$678$	−4265.26			−0.241602
$679$	121.772	+	2783.41i	0.00688246	+	0.157316i
$680$	−5215.60			−0.294131
$681$	434.450	−	752.489i	0.0244466	−	0.0423428i
$682$	−8337.65	−	14441.2i	−0.468131	−	0.810826i
$683$	16299.8	+	28232.1i	0.913171	+	1.58166i	0.809558	+	0.587040i	$0.199707\pi$
$683$	16299.8	+	28232.1i	0.913171	+	1.58166i	0.103613	+	0.994618i	$0.466960\pi$
$684$	−1898.56	+	3288.41i	−0.106131	+	0.183824i
$685$	−682.379			−0.0380618
$686$	11739.1	+	4858.85i	0.653353	+	0.270425i
$687$	−18006.3			−0.999973
$688$	3960.35	−	6859.54i	0.219458	−	0.380112i
$689$	−1771.80	−	3068.85i	−0.0979684	−	0.169686i
$690$	−764.855	−	1324.77i	−0.0421993	−	0.0730914i
$691$	−10146.9	+	17575.0i	−0.558622	+	0.967561i	0.438990	+	0.898492i	$0.355336\pi$
$691$	−10146.9	+	17575.0i	−0.558622	+	0.967561i	−0.997612	+	0.0690691i	$0.977997\pi$
$692$	6136.77			0.337117
$693$	272.214	+	6222.12i	0.0149214	+	0.341066i
$694$	−20872.1			−1.14163
$695$	−3630.40	+	6288.03i	−0.198142	+	0.343192i
$696$	−695.806	−	1205.17i	−0.0378944	−	0.0656350i
$697$	−6518.83	−	11290.9i	−0.354259	−	0.613594i
$698$	−7035.05	+	12185.1i	−0.381491	+	0.660761i
$699$	−8092.01			−0.437865
$700$	5110.04	+	2659.54i	0.275916	+	0.143602i
$701$	9724.69			0.523961			0.261980	−	0.965073i	$-0.415624\pi$
$701$	9724.69			0.523961			0.261980	+	0.965073i	$0.415624\pi$
$702$	351.000	−	607.950i	0.0188713	−	0.0326860i
$703$	1454.01	+	2518.42i	0.0780073	+	0.135113i
$704$	−1195.68	−	2070.97i	−0.0640111	−	0.110870i
$705$	−4796.19	+	8307.25i	−0.256220	+	0.443786i
$706$	20170.3			1.07524
$707$	61.4679	−	39.1670i	0.00326978	−	0.00208349i
$708$	−3460.57			−0.183695
$709$	−10742.9	+	18607.2i	−0.569050	+	0.985624i	0.427610	+	0.903963i	$0.359356\pi$
$709$	−10742.9	+	18607.2i	−0.569050	+	0.985624i	−0.996660	+	0.0816604i	$0.973978\pi$
$710$	−972.139	−	1683.79i	−0.0513855	−	0.0890024i
$711$	4768.69	+	8259.62i	0.251533	+	0.435668i
$712$	5536.91	−	9590.21i	0.291439	−	0.504787i
$713$	8277.36			0.434768
$714$	−8889.39	+	5664.27i	−0.465934	+	0.296891i
$715$	−3338.51			−0.174620
$716$	−4828.63	+	8363.43i	−0.252031	+	0.436531i
$717$	2777.10	+	4810.08i	0.144648	+	0.250538i
$718$	−366.718	−	635.174i	−0.0190610	−	0.0330146i
$719$	−9038.75	+	15655.6i	−0.468830	+	0.812037i	−0.999365	−	0.0356260i	$-0.988657\pi$
$719$	−9038.75	+	15655.6i	−0.468830	+	0.812037i	0.530536	+	0.847663i	$0.321991\pi$
$720$	−989.710			−0.0512282
$721$	−12664.0	−	6591.04i	−0.654136	−	0.340448i
$722$	8532.29			0.439805
$723$	5543.86	−	9602.25i	0.285171	−	0.493930i
$724$	521.302	+	902.921i	0.0267597	+	0.0463492i
$725$	−2254.47	−	3904.86i	−0.115488	−	0.200032i
$726$	195.411	−	338.462i	0.00998951	−	0.0173023i
$727$	18754.7			0.956772			0.478386	−	0.878150i	$-0.341222\pi$
$727$	18754.7			0.956772			0.478386	+	0.878150i	$0.341222\pi$
$728$	84.1854	+	1924.27i	0.00428588	+	0.0979644i
$729$	729.000			0.0370370
$730$	2236.98	−	3874.56i	0.113417	−	0.196443i
$731$	23479.2	+	40667.1i	1.18797	+	2.05763i
$732$	1192.56	+	2065.58i	0.0602163	+	0.104298i
$733$	1762.14	−	3052.12i	0.0887943	−	0.153796i	−0.818207	−	0.574923i	$-0.805032\pi$
$733$	1762.14	−	3052.12i	0.0887943	−	0.153796i	0.907002	+	0.421127i	$0.138365\pi$
$734$	−3263.34			−0.164104
$735$	−7045.28	+	617.635i	−0.353563	+	0.0309957i
$736$	1187.03			0.0594492
$737$	−3874.35	+	6710.57i	−0.193641	+	0.335396i
$738$	−1237.01	−	2142.56i	−0.0617005	−	0.106868i
$739$	−17227.2	−	29838.5i	−0.857530	−	1.48529i	−0.874278	−	0.485425i	$-0.838665\pi$
$739$	−17227.2	−	29838.5i	−0.857530	−	1.48529i	0.0167483	−	0.999860i	$-0.494669\pi$
$740$	−378.984	+	656.419i	−0.0188267	+	0.0326087i
$741$	−4113.56			−0.203934
$742$	441.301	+	10087.0i	0.0218338	+	0.499065i
$743$	6510.61			0.321469			0.160734	−	0.986998i	$-0.448614\pi$
$743$	6510.61			0.321469			0.160734	+	0.986998i	$0.448614\pi$
$744$	2677.69	−	4637.90i	0.131948	−	0.228540i
$745$	1940.23	+	3360.57i	0.0954153	+	0.165264i
$746$	−1853.45	−	3210.28i	−0.0909648	−	0.157556i
$747$	3822.84	−	6621.35i	0.187243	−	0.324314i
$748$	14177.3			0.693011
$749$	10198.1	+	5307.64i	0.497503	+	0.258928i
$750$	−8361.48			−0.407091
$751$	5831.63	−	10100.7i	0.283354	−	0.490784i	−0.688854	−	0.724900i	$-0.741886\pi$
$751$	5831.63	−	10100.7i	0.283354	−	0.490784i	0.972209	+	0.234116i	$0.0752194\pi$
$752$	−3721.77	−	6446.30i	−0.180478	−	0.312596i
$753$	−6211.77	−	10759.1i	−0.300624	−	0.520695i
$754$	753.790	−	1305.60i	0.0364077	−	0.0630600i
$755$	2577.72			0.124255
$756$	−1686.85	+	1074.85i	−0.0811508	+	0.0517088i
$757$	11268.4			0.541027			0.270514	−	0.962716i	$-0.412806\pi$
$757$	11268.4			0.541027			0.270514	+	0.962716i	$0.412806\pi$
$758$	−8143.37	+	14104.7i	−0.390212	+	0.675867i
$759$	2079.06	+	3601.04i	0.0994272	+	0.172213i
$760$	2899.73	+	5022.49i	0.138401	+	0.239717i
$761$	4241.85	−	7347.09i	0.202059	−	0.349976i	−0.747133	−	0.664675i	$-0.768570\pi$
$761$	4241.85	−	7347.09i	0.202059	−	0.349976i	0.949192	+	0.314699i	$0.101903\pi$
$762$	12725.9			0.605003
$763$	11504.4	−	7330.51i	0.545853	−	0.347814i
$764$	15229.9			0.721201
$765$	2933.77	−	5081.44i	0.138655	−	0.240157i
$766$	7328.00	+	12692.5i	0.345655	+	0.598691i
$767$	−1874.48	−	3246.69i	−0.0882444	−	0.152844i
$768$	384.000	−	665.108i	0.0180422	−	0.0312500i
$769$	21134.3			0.991056			0.495528	−	0.868592i	$-0.334975\pi$
$769$	21134.3			0.991056			0.495528	+	0.868592i	$0.334975\pi$
$770$	8437.92	+	4391.56i	0.394911	+	0.205533i
$771$	7481.65			0.349475
$772$	−1854.58	+	3212.22i	−0.0864607	+	0.149754i
$773$	−2673.23	−	4630.17i	−0.124385	−	0.215441i	0.797108	−	0.603837i	$-0.206362\pi$
$773$	−2673.23	−	4630.17i	−0.124385	−	0.215441i	−0.921492	+	0.388397i	$0.873029\pi$
$774$	4455.40	+	7716.98i	0.206907	+	0.358373i
$775$	8675.96	−	15027.2i	0.402129	−	0.696507i
$776$	1203.47			0.0556727
$777$	66.9530	+	1530.38i	0.00309128	+	0.0706589i
$778$	7206.40			0.332085
$779$	−7248.59	+	12554.9i	−0.333386	+	0.577442i
$780$	−536.093	−	928.540i	−0.0246092	−	0.0426244i
$781$	2642.51	+	4576.97i	0.121071	+	0.209701i
$782$	−3518.69	+	6094.55i	−0.160906	+	0.278697i
$783$	1565.56			0.0714543
$784$	2318.45	−	4974.23i	0.105615	−	0.226596i
$785$	11902.1			0.541150
$786$	−2727.19	+	4723.63i	−0.123760	+	0.214359i
$787$	−1063.64	−	1842.27i	−0.0481760	−	0.0834433i	0.840932	−	0.541141i	$-0.182008\pi$
$787$	−1063.64	−	1842.27i	−0.0481760	−	0.0834433i	−0.889108	+	0.457698i	$0.848674\pi$
$788$	−8545.14	−	14800.6i	−0.386305	−	0.669099i
$789$	−4320.42	+	7483.19i	−0.194944	+	0.337653i
$790$	14566.7			0.656027
$791$	575.437	+	13153.0i	0.0258662	+	0.591237i
$792$	2690.27			0.120700
$793$	−1291.94	+	2237.71i	−0.0578539	+	0.100206i
$794$	13875.2	+	24032.6i	0.620167	+	1.07416i
$795$	−2810.20	−	4867.42i	−0.125368	−	0.217144i
$796$	1237.43	−	2143.29i	0.0551000	−	0.0954360i
$797$	−37823.6			−1.68103			−0.840514	−	0.541790i	$-0.817747\pi$
$797$	−37823.6			−1.68103			−0.840514	+	0.541790i	$0.817747\pi$
$798$	10396.8	+	5411.07i	0.461207	+	0.240037i
$799$	44129.5			1.95393
$800$	1244.19	−	2155.01i	0.0549861	−	0.0952387i
$801$	6229.02	+	10789.0i	0.274771	+	0.475918i
$802$	6960.28	+	12055.6i	0.306454	+	0.530794i
$803$	−6080.65	+	10532.0i	−0.267225	+	0.462847i
$804$	−2488.55			−0.109160
$805$	−3982.08	+	2537.36i	−0.174348	+	0.111093i
$806$	5801.67			0.253542
$807$	−9065.58	+	15702.0i	−0.395444	+	0.684929i
$808$	−15.7419	−	27.2657i	−0.000685392	−	0.00118713i
$809$	11917.4	+	20641.5i	0.517914	+	0.897053i	0.999783	+	0.0208101i	$0.00662455\pi$
$809$	11917.4	+	20641.5i	0.517914	+	0.897053i	−0.481870	+	0.876243i	$0.660042\pi$
$810$	556.712	−	964.253i	0.0241492	−	0.0418276i
$811$	24263.1			1.05055			0.525273	−	0.850934i	$-0.323963\pi$
$811$	24263.1			1.05055			0.525273	+	0.850934i	$0.323963\pi$
$812$	−3622.59	+	2308.29i	−0.156561	+	0.0997601i
$813$	−13271.6			−0.572517
$814$	1030.17	−	1784.31i	0.0443581	−	0.0768305i
$815$	10103.1	+	17499.1i	0.434228	+	0.752105i
$816$	2276.56	+	3943.13i	0.0976663	+	0.169163i
$817$	26107.6	−	45219.7i	1.11798	−	1.93640i
$818$	23267.6			0.994538
$819$	−1922.13	−	1000.38i	−0.0820079	−	0.0426814i
$820$	−3778.64			−0.160922
$821$	19343.7	−	33504.3i	0.822291	−	1.42425i	−0.0816810	−	0.996659i	$-0.526029\pi$
$821$	19343.7	−	33504.3i	0.822291	−	1.42425i	0.903972	−	0.427591i	$-0.140638\pi$
$822$	297.853	+	515.896i	0.0126385	+	0.0218904i
$823$	18711.7	+	32409.5i	0.792524	+	1.37269i	0.924399	+	0.381426i	$0.124567\pi$
$823$	18711.7	+	32409.5i	0.792524	+	1.37269i	−0.131875	+	0.991266i	$0.542100\pi$
$824$	−3083.44	+	5340.67i	−0.130360	+	0.225790i
$825$	8716.72			0.367851
$826$	466.875	+	10671.6i	0.0196666	+	0.449530i
$827$	8358.27			0.351446			0.175723	−	0.984440i	$-0.443774\pi$
$827$	8358.27			0.351446			0.175723	+	0.984440i	$0.443774\pi$
$828$	−667.706	+	1156.50i	−0.0280246	+	0.0485400i
$829$	−16695.8	−	28918.1i	−0.699482	−	1.21154i	−0.968646	−	0.248444i	$-0.920081\pi$
$829$	−16695.8	−	28918.1i	−0.699482	−	1.21154i	0.269164	−	0.963094i	$-0.413253\pi$
$830$	−5838.74	−	10113.0i	−0.244175	−	0.422924i
$831$	−9175.54	+	15892.5i	−0.383028	+	0.663423i
$832$	832.000			0.0346688
$833$	18666.5	+	26648.6i	0.776419	+	1.10842i
$834$	6338.55			0.263173
$835$	−2532.78	+	4386.90i	−0.104970	+	0.181814i
$836$	−7882.19	−	13652.4i	−0.326090	−	0.564804i
$837$	3012.40	+	5217.64i	0.124401	+	0.215469i
$838$	−9044.25	+	15665.1i	−0.372826	+	0.645754i
$839$	15014.7			0.617835			0.308918	−	0.951089i	$-0.400033\pi$
$839$	15014.7			0.617835			0.308918	+	0.951089i	$0.400033\pi$
$840$	133.524	+	3052.03i	0.00548455	+	0.125363i
$841$	−21026.9			−0.862146
$842$	14419.0	−	24974.4i	0.590156	−	1.02218i
$843$	−10156.5	−	17591.6i	−0.414958	−	0.718728i
$844$	−6967.16	−	12067.5i	−0.284146	−	0.492156i
$845$	580.767	−	1005.92i	0.0236438	−	0.0409522i
$846$	8373.99			0.340312
$847$	−1070.10	−	556.938i	−0.0434109	−	0.0225934i
$848$	4361.35			0.176615
$849$	−1327.34	+	2299.02i	−0.0536563	+	0.0929354i
$850$	7376.27	+	12776.1i	0.297652	+	0.515548i
$851$	511.361	+	885.704i	0.0205984	+	0.0356775i
$852$	−848.661	+	1469.92i	−0.0341252	+	0.0591065i
$853$	−31433.8			−1.26175			−0.630874	−	0.775885i	$-0.717304\pi$
$853$	−31433.8			−1.26175			−0.630874	+	0.775885i	$0.717304\pi$
$854$	6208.85	−	3956.24i	0.248785	−	0.158524i
$855$	−6524.40			−0.260971
$856$	2483.03	−	4300.74i	0.0991452	−	0.171725i
$857$	−19425.5	−	33645.9i	−0.774285	−	1.34110i	−0.935195	−	0.354132i	$-0.884776\pi$
$857$	−19425.5	−	33645.9i	−0.774285	−	1.34110i	0.160910	−	0.986969i	$-0.448557\pi$
$858$	1457.23	+	2524.00i	0.0579826	+	0.100429i
$859$	14189.6	−	24577.2i	0.563614	−	0.976208i	−0.433563	−	0.901123i	$-0.642744\pi$
$859$	14189.6	−	24577.2i	0.563614	−	0.976208i	0.997177	−	0.0750850i	$-0.0239228\pi$
$860$	13609.7			0.539637
$861$	−6440.27	+	4103.70i	−0.254917	+	0.162432i
$862$	−14071.9			−0.556022
$863$	−4032.08	+	6983.77i	−0.159042	+	0.275469i	−0.934524	−	0.355901i	$-0.884174\pi$
$863$	−4032.08	+	6983.77i	−0.159042	+	0.275469i	0.775481	+	0.631371i	$0.217507\pi$
$864$	432.000	+	748.246i	0.0170103	+	0.0294628i
$865$	5272.24	+	9131.79i	0.207239	+	0.358948i
$866$	−8976.40	+	15547.6i	−0.352229	+	0.610079i
$867$	−12254.5			−0.480027
$868$	−14663.4	−	7631.65i	−0.573398	−	0.298428i
$869$	−39596.0			−1.54569
$870$	1195.57	−	2070.78i	0.0465902	−	0.0806966i
$871$	−1347.96	−	2334.74i	−0.0524386	−	0.0908263i
$872$	−2946.26	−	5103.07i	−0.114418	−	0.198179i
$873$	−676.951	+	1172.51i	−0.0262444	+	0.0454566i
$874$	7825.20			0.302850
$875$	1128.07	+	25784.8i	0.0435836	+	0.996212i
$876$	−3905.69			−0.150640
$877$	−12007.0	+	20796.8i	−0.462313	+	0.800750i	−0.999076	−	0.0429836i	$-0.986314\pi$
$877$	−12007.0	+	20796.8i	−0.462313	+	0.800750i	0.536763	+	0.843733i	$0.319647\pi$
$878$	14971.5	+	25931.3i	0.575469	+	0.996742i
$879$	8957.79	+	15515.3i	0.343730	+	0.595358i
$880$	2054.47	−	3558.44i	0.0787001	−	0.136313i
$881$	−30327.2			−1.15976			−0.579880	−	0.814702i	$-0.696901\pi$
$881$	−30327.2			−1.15976			−0.579880	+	0.814702i	$0.696901\pi$
$882$	3542.15	+	5056.82i	0.135227	+	0.193052i
$883$	−7991.80			−0.304581			−0.152291	−	0.988336i	$-0.548665\pi$
$883$	−7991.80			−0.304581			−0.152291	+	0.988336i	$0.548665\pi$
$884$	−2466.28	+	4271.72i	−0.0938347	+	0.162527i
$885$	−2973.06	−	5149.49i	−0.112925	−	0.195591i
$886$	−14143.8	−	24497.8i	−0.536310	−	0.928916i
$887$	13820.7	−	23938.2i	0.523173	−	0.906161i	−0.476464	−	0.879194i	$-0.658082\pi$
$887$	13820.7	−	23938.2i	0.523173	−	0.906161i	0.999636	−	0.0269673i	$-0.00858499\pi$
$888$	661.693			0.0250056
$889$	−1716.89	−	39243.7i	−0.0647723	−	1.48053i
$890$	19027.5			0.716635
$891$	−1513.28	+	2621.08i	−0.0568987	+	0.0985515i
$892$	6603.73	+	11438.0i	0.247880	+	0.429341i
$893$	−24534.8	−	42495.6i	−0.919402	−	1.59245i
$894$	1693.78	−	2933.72i	0.0633654	−	0.109752i
$895$	−16593.5			−0.619733
$896$	−2102.84	−	1094.43i	−0.0784050	−	0.0408063i
$897$	−1446.70			−0.0538503
$898$	−12278.7	+	21267.4i	−0.456288	+	0.790313i
$899$	6469.29	+	11205.1i	0.240003	+	0.415698i
$900$	1399.72	+	2424.38i	0.0518414	+	0.0897919i
$901$	−12928.3	+	22392.4i	−0.478028	+	0.827968i
$902$	10271.3			0.379153
$903$	23196.2	−	14780.5i	0.854841	−	0.544700i
$904$	5687.01			0.209234
$905$	−895.725	+	1551.44i	−0.0329004	+	0.0569852i
$906$	−1125.15	−	1948.82i	−0.0412590	−	0.0714627i
$907$	13383.9	+	23181.7i	0.489974	+	0.848659i	0.999933	−	0.0115389i	$-0.00367302\pi$
$907$	13383.9	+	23181.7i	0.489974	+	0.848659i	−0.509960	+	0.860198i	$0.670340\pi$
$908$	−579.267	+	1003.32i	−0.0211714	+	0.0366700i
$909$	35.4192			0.00129239
$910$	−2791.07	+	1778.45i	−0.101674	+	0.0647859i
$911$	−18868.4			−0.686209			−0.343105	−	0.939297i	$-0.611479\pi$
$911$	−18868.4			−0.686209			−0.343105	+	0.939297i	$0.611479\pi$
$912$	2531.42	−	4384.55i	0.0919119	−	0.159196i
$913$	15871.1	+	27489.6i	0.575309	+	0.996465i
$914$	−12391.9	−	21463.4i	−0.448454	−	0.776745i
$915$	−2049.11	+	3549.17i	−0.0740345	+	0.128231i
$916$	24008.3			0.866002
$917$	14934.5	+	7772.72i	0.537818	+	0.279910i
$918$	−5122.27			−0.184161
$919$	−1356.75	+	2349.97i	−0.0486999	+	0.0843506i	−0.889348	−	0.457231i	$-0.848841\pi$
$919$	−1356.75	+	2349.97i	−0.0486999	+	0.0843506i	0.840648	+	0.541582i	$0.182174\pi$
$920$	1019.81	+	1766.36i	0.0365457	+	0.0632990i
$921$	9593.04	+	16615.6i	0.343216	+	0.594467i
$922$	12194.8	−	21122.0i	0.435590	−	0.754463i
$923$	−1838.77			−0.0655728
$924$	−362.952	−	8296.16i	−0.0129223	−	0.295372i
$925$	2143.94			0.0762080
$926$	−12130.0	+	21009.7i	−0.430471	+	0.745597i
$927$	−3468.87	−	6008.25i	−0.122905	−	0.212877i
$928$	927.742	+	1606.90i	0.0328175	+	0.0568415i
$929$	2235.73	−	3872.40i	0.0789581	−	0.136759i	−0.823843	−	0.566819i	$-0.808174\pi$
$929$	2235.73	−	3872.40i	0.0789581	−	0.136759i	0.902801	+	0.430059i	$0.141507\pi$
$930$	9201.87			0.324453
$931$	15283.8	−	32791.3i	0.538030	−	1.15434i
$932$	10789.3			0.379203
$933$	−960.819	+	1664.19i	−0.0337147	+	0.0583956i
$934$	−6375.89	−	11043.4i	−0.223368	−	0.386884i
$935$	12180.0	+	21096.4i	0.426021	+	0.737889i
$936$	−468.000	+	810.600i	−0.0163430	+	0.0283069i
$937$	46869.4			1.63410			0.817052	−	0.576564i	$-0.195607\pi$
$937$	46869.4			1.63410			0.817052	+	0.576564i	$0.195607\pi$
$938$	335.736	+	7674.09i	0.0116868	+	0.267130i
$939$	−30033.6			−1.04378
$940$	6394.92	−	11076.3i	0.221893	−	0.384330i
$941$	−13870.6	−	24024.6i	−0.480519	−	0.832283i	0.519231	−	0.854634i	$-0.326218\pi$
$941$	−13870.6	−	24024.6i	−0.480519	−	0.832283i	−0.999750	+	0.0223507i	$0.992885\pi$
$942$	−5195.15	−	8998.26i	−0.179689	−	0.311230i
$943$	−2549.25	+	4415.44i	−0.0880330	+	0.152478i
$944$	4614.10			0.159085
$945$	−3048.63	−	1586.68i	−0.104944	−	0.0546186i
$946$	−36994.6			−1.27146
$947$	−6989.74	+	12106.6i	−0.239848	+	0.415429i	−0.960671	−	0.277691i	$-0.910431\pi$
$947$	−6989.74	+	12106.6i	−0.239848	+	0.415429i	0.720822	+	0.693120i	$0.243764\pi$
$948$	−6358.26	−	11012.8i	−0.217834	−	0.377300i
$949$	−2115.58	−	3664.29i	−0.0723652	−	0.125340i
$950$	8202.02	−	14206.3i	0.280114	−	0.485172i
$951$	−17602.7			−0.600218
$952$	11852.5	−	7552.36i	0.403511	−	0.257115i
$953$	24513.3			0.833224			0.416612	−	0.909084i	$-0.363217\pi$
$953$	24513.3			0.833224			0.416612	+	0.909084i	$0.363217\pi$
$954$	−2453.26	+	4249.17i	−0.0832571	+	0.144206i
$955$	13084.3	+	22662.7i	0.443350	+	0.767904i
$956$	−3702.80	−	6413.44i	−0.125269	−	0.216972i
$957$	−3249.84	+	5628.89i	−0.109773	+	0.190132i
$958$	34382.8			1.15956
$959$	1550.72	−	988.107i	0.0522161	−	0.0332718i
$960$	1319.61			0.0443649
$961$	−10000.5	+	17321.3i	−0.335688	+	0.581428i
$962$	358.417	+	620.797i	0.0120123	+	0.0208059i
$963$	2793.41	+	4838.33i	0.0934750	+	0.161903i
$964$	−7391.81	+	12803.0i	−0.246965	+	0.427756i
$965$	−6373.24			−0.212603
$966$	3656.45	+	1903.02i	0.121785	+	0.0633836i
$967$	11102.1			0.369204			0.184602	−	0.982813i	$-0.440900\pi$
$967$	11102.1			0.369204			0.184602	+	0.982813i	$0.440900\pi$
$968$	−260.548	+	451.282i	−0.00865117	+	0.0149843i
$969$	15007.7	+	25994.0i	0.497539	+	0.861763i
$970$	1033.93	+	1790.81i	0.0342241	+	0.0592779i
$971$	−16268.1	+	28177.1i	−0.537659	+	0.931253i	0.461370	+	0.887208i	$0.347358\pi$
$971$	−16268.1	+	28177.1i	−0.537659	+	0.931253i	−0.999030	+	0.0440455i	$0.985975\pi$
$972$	−972.000			−0.0320750
$973$	−855.150	−	19546.6i	−0.0281756	−	0.644023i
$974$	24057.7			0.791436
$975$	−1516.36	+	2626.41i	−0.0498076	+	0.0862693i
$976$	−1590.08	−	2754.10i	−0.0521488	−	0.0903244i
$977$	−1668.84	−	2890.51i	−0.0546477	−	0.0946525i	0.837407	−	0.546579i	$-0.184070\pi$
$977$	−1668.84	−	2890.51i	−0.0546477	−	0.0946525i	−0.892055	+	0.451927i	$0.850737\pi$
$978$	8819.83	−	15276.4i	0.288371	−	0.499474i
$979$	−51721.6			−1.68849
$980$	9393.70	−	823.513i	0.306195	−	0.0268430i
$981$	6629.08			0.215749
$982$	−10398.6	+	18010.9i	−0.337915	+	0.585286i
$983$	−12735.5	−	22058.6i	−0.413226	−	0.715728i	0.582015	−	0.813178i	$-0.302265\pi$
$983$	−12735.5	−	22058.6i	−0.413226	−	0.715728i	−0.995240	+	0.0974504i	$0.968931\pi$
$984$	1649.35	+	2856.75i	0.0534342	+	0.0925508i
$985$	14682.7	−	25431.1i	0.474952	−	0.822642i
$986$	−11000.3			−0.355296
$987$	−1129.76	−	25823.4i	−0.0364342	−	0.832794i
$988$	5484.74			0.176612
$989$	9181.77	−	15903.3i	0.295211	−	0.511320i
$990$	2311.28	+	4003.25i	0.0741992	+	0.128517i
$991$	14421.8	+	24979.4i	0.462286	+	0.800702i	0.999074	−	0.0430143i	$-0.0136961\pi$
$991$	14421.8	+	24979.4i	0.462286	+	0.800702i	−0.536789	+	0.843717i	$0.680363\pi$
$992$	−3570.26	+	6183.87i	−0.114270	+	0.197921i
$993$	−15420.2			−0.492796
$994$	4647.39	+	2418.76i	0.148296	+	0.0771814i
$995$	4252.42			0.135488
$996$	−5097.12	+	8828.47i	−0.162157	+	0.280864i
$997$	−2714.30	−	4701.30i	−0.0862213	−	0.149340i	0.819690	−	0.572808i	$-0.194146\pi$
$997$	−2714.30	−	4701.30i	−0.0862213	−	0.149340i	−0.905911	+	0.423468i	$0.860813\pi$
$998$	844.907	+	1463.42i	0.0267986	+	0.0464166i
$999$	−372.202	+	644.674i	−0.0117878	+	0.0204170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.4.i.a.79.2	✓	4
7.4	even	3	inner	546.4.i.a.235.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.4.i.a.79.2	✓	4	1.1	even	1	trivial
546.4.i.a.235.2	yes	4	7.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	546.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(3.43649 - 5.95218i) q^{5} -6.00000 q^{6} +(0.809475 + 18.5026i) q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(6.87298 + 11.9044i) q^{10} +(-18.6825 - 32.3590i) q^{11} +(6.00000 - 10.3923i) q^{12} +13.0000 q^{13} +(-32.8569 - 17.1005i) q^{14} +20.6190 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-47.4284 - 82.1484i) q^{17} +(-9.00000 - 15.5885i) q^{18} +(-52.7379 + 91.3447i) q^{19} -27.4919 q^{20} +(-46.8569 + 29.8569i) q^{21} +74.7298 q^{22} +(-18.5474 + 32.1250i) q^{23} +(12.0000 + 20.7846i) q^{24} +(38.8810 + 67.3440i) q^{25} +(-13.0000 + 22.5167i) q^{26} -27.0000 q^{27} +(62.4758 - 39.8092i) q^{28} -57.9839 q^{29} +(-20.6190 + 35.7131i) q^{30} +(-111.571 - 193.246i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(56.0474 - 97.0769i) q^{33} +189.714 q^{34} +(112.912 + 58.7658i) q^{35} +36.0000 q^{36} +(13.7853 - 23.8768i) q^{37} +(-105.476 - 182.689i) q^{38} +(19.5000 + 33.7750i) q^{39} +(27.4919 - 47.6174i) q^{40} +137.446 q^{41} +(-4.85685 - 111.015i) q^{42} -495.044 q^{43} +(-74.7298 + 129.436i) q^{44} +(30.9284 + 53.5696i) q^{45} +(-37.0948 - 64.2500i) q^{46} +(-232.611 + 402.894i) q^{47} -48.0000 q^{48} +(-341.690 + 29.9547i) q^{49} -155.524 q^{50} +(142.285 - 246.445i) q^{51} +(-26.0000 - 45.0333i) q^{52} +(-136.292 - 236.065i) q^{53} +(27.0000 - 46.7654i) q^{54} -256.808 q^{55} +(6.47580 + 148.020i) q^{56} -316.427 q^{57} +(57.9839 - 100.431i) q^{58} +(-144.191 - 249.745i) q^{59} +(-41.2379 - 71.4261i) q^{60} +(-99.3800 + 172.131i) q^{61} +446.282 q^{62} +(-147.856 - 76.9523i) q^{63} +64.0000 q^{64} +(44.6744 - 77.3783i) q^{65} +(112.095 + 194.154i) q^{66} +(-103.690 - 179.595i) q^{67} +(-189.714 + 328.594i) q^{68} -111.284 q^{69} +(-214.698 + 136.804i) q^{70} -141.444 q^{71} +(-36.0000 + 62.3538i) q^{72} +(-162.737 - 281.869i) q^{73} +(27.5706 + 47.7536i) q^{74} +(-116.643 + 202.032i) q^{75} +421.903 q^{76} +(583.601 - 371.867i) q^{77} -78.0000 q^{78} +(529.855 - 917.735i) q^{79} +(54.9839 + 95.2349i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-137.446 + 238.063i) q^{82} -849.520 q^{83} +(197.141 + 102.603i) q^{84} -651.950 q^{85} +(495.044 - 857.442i) q^{86} +(-86.9758 - 150.647i) q^{87} +(-149.460 - 258.872i) q^{88} +(692.114 - 1198.78i) q^{89} -123.714 q^{90} +(10.5232 + 240.533i) q^{91} +148.379 q^{92} +(334.712 - 579.738i) q^{93} +(-465.222 - 805.788i) q^{94} +(362.467 + 627.811i) q^{95} +(48.0000 - 83.1384i) q^{96} +150.434 q^{97} +(289.806 - 621.778i) q^{98} +336.284 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 6 q^{5} - 24 q^{6} - 20 q^{7} + 32 q^{8} - 18 q^{9} + 12 q^{10} - 36 q^{11} + 24 q^{12} + 52 q^{13} + 8 q^{14} + 36 q^{15} - 32 q^{16} - 120 q^{17} - 36 q^{18} - 118 q^{19}+ \cdots + 648 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 + 6 * q^5 - 24 * q^6 - 20 * q^7 + 32 * q^8 - 18 * q^9 + 12 * q^10 - 36 * q^11 + 24 * q^12 + 52 * q^13 + 8 * q^14 + 36 * q^15 - 32 * q^16 - 120 * q^17 - 36 * q^18 - 118 * q^19 - 48 * q^20 - 48 * q^21 + 144 * q^22 + 42 * q^23 + 48 * q^24 + 202 * q^25 - 52 * q^26 - 108 * q^27 + 64 * q^28 - 108 * q^29 - 36 * q^30 - 28 * q^31 - 64 * q^32 + 108 * q^33 + 480 * q^34 + 258 * q^35 + 144 * q^36 - 154 * q^37 - 236 * q^38 + 78 * q^39 + 48 * q^40 + 1092 * q^41 + 120 * q^42 - 400 * q^43 - 144 * q^44 + 54 * q^45 + 84 * q^46 - 822 * q^47 - 192 * q^48 - 902 * q^49 - 808 * q^50 + 360 * q^51 - 104 * q^52 + 90 * q^53 + 108 * q^54 - 516 * q^55 - 160 * q^56 - 708 * q^57 + 108 * q^58 - 600 * q^59 - 72 * q^60 + 44 * q^61 + 112 * q^62 + 36 * q^63 + 256 * q^64 + 78 * q^65 + 216 * q^66 + 50 * q^67 - 480 * q^68 + 252 * q^69 - 456 * q^70 - 132 * q^71 - 144 * q^72 - 70 * q^73 - 308 * q^74 - 606 * q^75 + 944 * q^76 + 1188 * q^77 - 312 * q^78 + 1004 * q^79 + 96 * q^80 - 162 * q^81 - 1092 * q^82 - 1632 * q^83 - 48 * q^84 - 1260 * q^85 + 400 * q^86 - 162 * q^87 - 288 * q^88 + 282 * q^89 - 216 * q^90 - 260 * q^91 - 336 * q^92 + 84 * q^93 - 1644 * q^94 + 714 * q^95 + 192 * q^96 + 2972 * q^97 - 328 * q^98 + 648 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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