LMFDB - Embedded newform 18.4.c.b.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,4,Mod(7,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("18.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	18.c (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:	$1.06203438010$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-35})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 8x^{2} - 9x + 81 $ x^4 - x^3 - 8x^2 - 9x + 81
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			7.2
Root			$-2.31174 - 1.91203i$ of defining polynomial
Character	$\chi$	$=$	18.7
Dual form			18.4.c.b.13.2

$q$-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} +(3.31174 + 4.00405i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-5.43521 - 9.41407i) q^{5} +(10.2470 - 1.73205i) q^{6} +(-12.4352 + 21.5384i) q^{7} -8.00000 q^{8} +(-5.06479 + 26.5207i) q^{9} -21.7409 q^{10} +(21.3704 - 37.0147i) q^{11} +(7.24695 - 19.4803i) q^{12} +(-7.56479 - 13.1026i) q^{13} +(24.8704 + 43.0768i) q^{14} +(19.6944 - 52.9398i) q^{15} +(-8.00000 + 13.8564i) q^{16} -13.8704 q^{17} +(40.8704 + 35.2932i) q^{18} +143.352 q^{19} +(-21.7409 + 37.6563i) q^{20} +(-127.423 + 21.5384i) q^{21} +(-42.7409 - 74.0293i) q^{22} +(-9.56479 - 16.5667i) q^{23} +(-26.4939 - 32.0324i) q^{24} +(3.41692 - 5.91828i) q^{25} -30.2591 q^{26} +(-122.963 + 67.5500i) q^{27} +99.4817 q^{28} +(-113.046 + 195.802i) q^{29} +(-72.0000 - 87.0514i) q^{30} +(-29.6944 - 51.4321i) q^{31} +(16.0000 + 27.7128i) q^{32} +(218.982 - 37.0147i) q^{33} +(-13.8704 + 24.0243i) q^{34} +270.352 q^{35} +(102.000 - 35.4965i) q^{36} -84.1860 q^{37} +(143.352 - 248.293i) q^{38} +(27.4108 - 73.6821i) q^{39} +(43.4817 + 75.3125i) q^{40} +(-101.630 - 176.028i) q^{41} +(-90.1174 + 242.242i) q^{42} +(-162.945 + 282.229i) q^{43} -170.963 q^{44} +(277.196 - 96.4655i) q^{45} -38.2591 q^{46} +(-5.47180 + 9.47744i) q^{47} +(-81.9756 + 13.8564i) q^{48} +(-137.769 - 238.623i) q^{49} +(-6.83384 - 11.8366i) q^{50} +(-45.9352 - 55.5378i) q^{51} +(-30.2591 + 52.4104i) q^{52} -140.186 q^{53} +(-5.96341 + 280.529i) q^{54} -464.611 q^{55} +(99.4817 - 172.307i) q^{56} +(474.745 + 573.989i) q^{57} +(226.093 + 391.605i) q^{58} +(-57.3704 - 99.3685i) q^{59} +(-222.777 + 37.6563i) q^{60} +(377.528 - 653.898i) q^{61} -118.777 q^{62} +(-508.232 - 438.878i) q^{63} +64.0000 q^{64} +(-82.2325 + 142.431i) q^{65} +(154.870 - 416.302i) q^{66} +(383.723 + 664.627i) q^{67} +(27.7409 + 48.0486i) q^{68} +(34.6578 - 93.1624i) q^{69} +(270.352 - 468.264i) q^{70} +335.854 q^{71} +(40.5183 - 212.166i) q^{72} +167.279 q^{73} +(-84.1860 + 145.814i) q^{74} +(35.0130 - 5.91828i) q^{75} +(-286.704 - 496.586i) q^{76} +(531.492 + 920.570i) q^{77} +(-100.210 - 121.159i) q^{78} +(12.6578 - 21.9239i) q^{79} +173.927 q^{80} +(-677.696 - 268.643i) q^{81} -406.518 q^{82} +(-143.861 + 249.174i) q^{83} +(329.457 + 398.329i) q^{84} +(75.3887 + 130.577i) q^{85} +(325.890 + 564.458i) q^{86} +(-1158.38 + 195.802i) q^{87} +(-170.963 + 296.117i) q^{88} -860.817 q^{89} +(110.113 - 576.583i) q^{90} +376.279 q^{91} +(-38.2591 + 66.2668i) q^{92} +(107.597 - 289.227i) q^{93} +(10.9436 + 18.9549i) q^{94} +(-779.149 - 1349.53i) q^{95} +(-57.9756 + 155.842i) q^{96} +(201.075 - 348.272i) q^{97} -551.076 q^{98} +(873.418 + 754.230i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 3 q^{3} - 8 q^{4} + 9 q^{5} - 19 q^{7} - 32 q^{8} - 51 q^{9} + 36 q^{10} + 24 q^{11} - 12 q^{12} - 61 q^{13} + 38 q^{14} + 171 q^{15} - 32 q^{16} + 6 q^{17} + 102 q^{18} + 266 q^{19} + 36 q^{20}+ \cdots + 1557 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 3 * q^3 - 8 * q^4 + 9 * q^5 - 19 * q^7 - 32 * q^8 - 51 * q^9 + 36 * q^10 + 24 * q^11 - 12 * q^12 - 61 * q^13 + 38 * q^14 + 171 * q^15 - 32 * q^16 + 6 * q^17 + 102 * q^18 + 266 * q^19 + 36 * q^20 - 315 * q^21 - 48 * q^22 - 69 * q^23 - 24 * q^24 - 263 * q^25 - 244 * q^26 + 152 * q^28 - 237 * q^29 - 288 * q^30 - 211 * q^31 + 64 * q^32 + 630 * q^33 + 6 * q^34 + 774 * q^35 + 408 * q^36 + 524 * q^37 + 266 * q^38 - 249 * q^39 - 72 * q^40 - 468 * q^41 - 258 * q^42 + 86 * q^43 - 192 * q^44 - 459 * q^45 - 276 * q^46 - 483 * q^47 + 33 * q^49 + 526 * q^50 - 153 * q^51 - 244 * q^52 + 300 * q^53 + 468 * q^54 - 1674 * q^55 + 152 * q^56 + 987 * q^57 + 474 * q^58 - 168 * q^59 - 1260 * q^60 + 1049 * q^61 - 844 * q^62 - 957 * q^63 + 256 * q^64 + 747 * q^65 + 558 * q^66 + 1166 * q^67 - 12 * q^68 - 261 * q^69 + 774 * q^70 - 624 * q^71 + 408 * q^72 - 622 * q^73 + 524 * q^74 + 2835 * q^75 - 532 * q^76 + 1173 * q^77 + 132 * q^78 - 349 * q^79 - 288 * q^80 - 1143 * q^81 - 1872 * q^82 - 1221 * q^83 + 744 * q^84 + 486 * q^85 - 172 * q^86 - 2205 * q^87 - 192 * q^88 - 984 * q^89 - 1404 * q^90 + 214 * q^91 - 276 * q^92 - 789 * q^93 + 966 * q^94 - 1764 * q^95 + 96 * q^96 + 128 * q^97 + 132 * q^98 + 1557 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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
$3$	3.31174	+	4.00405i	0.637344	+	0.770579i
$3$	3.31174	+	4.00405i	0.637344	+	0.770579i
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	−5.43521	−	9.41407i	−0.486140	−	0.842020i	0.513733	−	0.857950i	$-0.328262\pi$
$5$	−5.43521	−	9.41407i	−0.486140	−	0.842020i	−0.999873	+	0.0159306i	$0.994929\pi$
$6$	10.2470	−	1.73205i	0.697217	−	0.117851i
$7$	−12.4352	+	21.5384i	−0.671438	+	1.16297i	0.306058	+	0.952013i	$0.400990\pi$
$7$	−12.4352	+	21.5384i	−0.671438	+	1.16297i	−0.977496	+	0.210953i	$0.932343\pi$
$8$	−8.00000			−0.353553
$9$	−5.06479	+	26.5207i	−0.187585	+	0.982248i
$10$	−21.7409			−0.687506
$11$	21.3704	−	37.0147i	0.585766	−	1.01458i	−0.409013	−	0.912528i	$-0.634127\pi$
$11$	21.3704	−	37.0147i	0.585766	−	1.01458i	0.994779	−	0.102048i	$-0.0325396\pi$
$12$	7.24695	−	19.4803i	0.174335	−	0.468623i
$13$	−7.56479	−	13.1026i	−0.161392	−	0.279539i	0.773976	−	0.633215i	$-0.218265\pi$
$13$	−7.56479	−	13.1026i	−0.161392	−	0.279539i	−0.935368	+	0.353676i	$0.884932\pi$
$14$	24.8704	+	43.0768i	0.474779	+	0.822341i
$15$	19.6944	−	52.9398i	0.339004	−	0.911266i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−13.8704			−0.197887			−0.0989433	−	0.995093i	$-0.531546\pi$
$17$	−13.8704			−0.197887			−0.0989433	+	0.995093i	$0.531546\pi$
$18$	40.8704	+	35.2932i	0.535181	+	0.462149i
$19$	143.352			1.73091			0.865454	−	0.500989i	$-0.167030\pi$
$19$	143.352			1.73091			0.865454	+	0.500989i	$0.167030\pi$
$20$	−21.7409	+	37.6563i	−0.243070	+	0.421010i
$21$	−127.423	+	21.5384i	−1.32409	+	0.223813i
$22$	−42.7409	−	74.0293i	−0.414199	−	0.717414i
$23$	−9.56479	−	16.5667i	−0.0867129	−	0.150191i	0.819407	−	0.573212i	$-0.194303\pi$
$23$	−9.56479	−	16.5667i	−0.0867129	−	0.150191i	−0.906120	+	0.423021i	$0.860970\pi$
$24$	−26.4939	−	32.0324i	−0.225335	−	0.272441i
$25$	3.41692	−	5.91828i	0.0273353	−	0.0473462i
$26$	−30.2591			−0.228243
$27$	−122.963	+	67.5500i	−0.876456	+	0.481481i
$28$	99.4817			0.671438
$29$	−113.046	+	195.802i	−0.723869	+	1.25378i	0.235569	+	0.971858i	$0.424305\pi$
$29$	−113.046	+	195.802i	−0.723869	+	1.25378i	−0.959438	+	0.281920i	$0.909029\pi$
$30$	−72.0000	−	87.0514i	−0.438178	−	0.529778i
$31$	−29.6944	−	51.4321i	−0.172041	−	0.297983i	0.767092	−	0.641537i	$-0.221703\pi$
$31$	−29.6944	−	51.4321i	−0.172041	−	0.297983i	−0.939133	+	0.343553i	$0.888369\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$	218.982	−	37.0147i	1.15515	−	0.195255i
$34$	−13.8704	+	24.0243i	−0.0699635	+	0.121180i
$35$	270.352			1.30565
$36$	102.000	−	35.4965i	0.472222	−	0.164336i
$37$	−84.1860			−0.374056			−0.187028	−	0.982355i	$-0.559886\pi$
$37$	−84.1860			−0.374056			−0.187028	+	0.982355i	$0.559886\pi$
$38$	143.352	−	248.293i	0.611968	−	1.05996i
$39$	27.4108	−	73.6821i	0.112545	−	0.302528i
$40$	43.4817	+	75.3125i	0.171877	+	0.297699i
$41$	−101.630	−	176.028i	−0.387119	−	0.670510i	0.604942	−	0.796270i	$-0.293196\pi$
$41$	−101.630	−	176.028i	−0.387119	−	0.670510i	−0.992061	+	0.125760i	$0.959863\pi$
$42$	−90.1174	+	242.242i	−0.331081	+	0.889969i
$43$	−162.945	+	282.229i	−0.577881	+	1.00092i	0.417841	+	0.908520i	$0.362787\pi$
$43$	−162.945	+	282.229i	−0.577881	+	1.00092i	−0.995722	+	0.0923995i	$0.970546\pi$
$44$	−170.963			−0.585766
$45$	277.196	−	96.4655i	0.918265	−	0.319560i
$46$	−38.2591			−0.122631
$47$	−5.47180	+	9.47744i	−0.0169818	+	0.0294133i	−0.874391	−	0.485221i	$-0.838739\pi$
$47$	−5.47180	+	9.47744i	−0.0169818	+	0.0294133i	0.857410	+	0.514635i	$0.172072\pi$
$48$	−81.9756	+	13.8564i	−0.246503	+	0.0416667i
$49$	−137.769	−	238.623i	−0.401659	−	0.695694i
$50$	−6.83384	−	11.8366i	−0.0193290	−	0.0334788i
$51$	−45.9352	−	55.5378i	−0.126122	−	0.152487i
$52$	−30.2591	+	52.4104i	−0.0806959	+	0.139769i
$53$	−140.186			−0.363321			−0.181661	−	0.983361i	$-0.558147\pi$
$53$	−140.186			−0.363321			−0.181661	+	0.983361i	$0.558147\pi$
$54$	−5.96341	+	280.529i	−0.0150281	+	0.706947i
$55$	−464.611			−1.13906
$56$	99.4817	−	172.307i	0.237389	−	0.411170i
$57$	474.745	+	573.989i	1.10318	+	1.33380i
$58$	226.093	+	391.605i	0.511853	+	0.886555i
$59$	−57.3704	−	99.3685i	−0.126593	−	0.219266i	0.795761	−	0.605610i	$-0.207071\pi$
$59$	−57.3704	−	99.3685i	−0.126593	−	0.219266i	−0.922355	+	0.386345i	$0.873738\pi$
$60$	−222.777	+	37.6563i	−0.479341	+	0.0810234i
$61$	377.528	−	653.898i	0.792419	−	1.37251i	−0.132047	−	0.991243i	$-0.542155\pi$
$61$	377.528	−	653.898i	0.792419	−	1.37251i	0.924465	−	0.381266i	$-0.124512\pi$
$62$	−118.777			−0.243302
$63$	−508.232	−	438.878i	−1.01637	−	0.877674i
$64$	64.0000			0.125000
$65$	−82.2325	+	142.431i	−0.156918	+	0.271790i
$66$	154.870	−	416.302i	0.288837	−	0.776413i
$67$	383.723	+	664.627i	0.699689	+	1.21190i	0.968574	+	0.248725i	$0.0800115\pi$
$67$	383.723	+	664.627i	0.699689	+	1.21190i	−0.268885	+	0.963172i	$0.586655\pi$
$68$	27.7409	+	48.0486i	0.0494717	+	0.0856874i
$69$	34.6578	−	93.1624i	0.0604682	−	0.162543i
$70$	270.352	−	468.264i	0.461618	−	0.799546i
$71$	335.854			0.561387			0.280694	−	0.959797i	$-0.409436\pi$
$71$	335.854			0.561387			0.280694	+	0.959797i	$0.409436\pi$
$72$	40.5183	−	212.166i	0.0663212	−	0.347277i
$73$	167.279			0.268199			0.134099	−	0.990968i	$-0.457186\pi$
$73$	167.279			0.268199			0.134099	+	0.990968i	$0.457186\pi$
$74$	−84.1860	+	145.814i	−0.132249	+	0.229062i
$75$	35.0130	−	5.91828i	0.0539060	−	0.00911178i
$76$	−286.704	−	496.586i	−0.432727	−	0.749505i
$77$	531.492	+	920.570i	0.786612	+	1.36245i
$78$	−100.210	−	121.159i	−0.145469	−	0.175879i
$79$	12.6578	−	21.9239i	0.0180267	−	0.0312232i	−0.856871	−	0.515530i	$-0.827595\pi$
$79$	12.6578	−	21.9239i	0.0180267	−	0.0312232i	0.874898	+	0.484307i	$0.160928\pi$
$80$	173.927			0.243070
$81$	−677.696	−	268.643i	−0.929624	−	0.368510i
$82$	−406.518			−0.547469
$83$	−143.861	+	249.174i	−0.190250	+	0.329523i	−0.945333	−	0.326107i	$-0.894263\pi$
$83$	−143.861	+	249.174i	−0.190250	+	0.329523i	0.755083	+	0.655629i	$0.227597\pi$
$84$	329.457	+	398.329i	0.427937	+	0.517396i
$85$	75.3887	+	130.577i	0.0962006	+	0.166624i
$86$	325.890	+	564.458i	0.408624	+	0.707757i
$87$	−1158.38	+	195.802i	−1.42749	+	0.241290i
$88$	−170.963	+	296.117i	−0.207100	+	0.358707i
$89$	−860.817			−1.02524			−0.512620	−	0.858615i	$-0.671325\pi$
$89$	−860.817			−1.02524			−0.512620	+	0.858615i	$0.671325\pi$
$90$	110.113	−	576.583i	0.128966	−	0.675302i
$91$	376.279			0.433459
$92$	−38.2591	+	66.2668i	−0.0433564	+	0.0750955i
$93$	107.597	−	289.227i	0.119971	−	0.322489i
$94$	10.9436	+	18.9549i	0.0120079	+	0.0207984i
$95$	−779.149	−	1349.53i	−0.841464	−	1.45746i
$96$	−57.9756	+	155.842i	−0.0616366	+	0.165683i
$97$	201.075	−	348.272i	0.210475	−	0.364553i	−0.741389	−	0.671076i	$-0.765832\pi$
$97$	201.075	−	348.272i	0.210475	−	0.364553i	0.951863	+	0.306523i	$0.0991657\pi$
$98$	−551.076			−0.568032
$99$	873.418	+	754.230i	0.886685	+	0.765687i
$100$	−27.3353			−0.0273353
$101$	665.714	−	1153.05i	0.655852	−	1.13597i	−0.325828	−	0.945429i	$-0.605643\pi$
$101$	665.714	−	1153.05i	0.655852	−	1.13597i	0.981680	−	0.190540i	$-0.0610237\pi$
$102$	−142.130	+	24.0243i	−0.137970	+	0.0233212i
$103$	259.252	+	449.038i	0.248009	+	0.429563i	0.962973	−	0.269597i	$-0.0868905\pi$
$103$	259.252	+	449.038i	0.248009	+	0.429563i	−0.714965	+	0.699161i	$0.753557\pi$
$104$	60.5183	+	104.821i	0.0570606	+	0.0988319i
$105$	895.335	+	1082.50i	0.832150	+	1.00611i
$106$	−140.186	+	242.809i	−0.128453	+	0.222488i
$107$	1471.87			1.32982			0.664912	−	0.746922i	$-0.268469\pi$
$107$	1471.87			1.32982			0.664912	+	0.746922i	$0.268469\pi$
$108$	479.927	+	290.858i	0.427602	+	0.259146i
$109$	−643.668			−0.565616			−0.282808	−	0.959176i	$-0.591266\pi$
$109$	−643.668			−0.565616			−0.282808	+	0.959176i	$0.591266\pi$
$110$	−464.611	+	804.730i	−0.402718	+	0.697528i
$111$	−278.802	−	337.085i	−0.238403	−	0.288240i
$112$	−198.963	−	344.615i	−0.167860	−	0.290741i
$113$	−511.864	−	886.574i	−0.426125	−	0.738069i	0.570400	−	0.821367i	$-0.306788\pi$
$113$	−511.864	−	886.574i	−0.426125	−	0.738069i	−0.996525	+	0.0832976i	$0.973455\pi$
$114$	1468.92	−	248.293i	1.20682	−	0.203989i
$115$	−103.973	+	180.087i	−0.0843092	+	0.146028i
$116$	904.372			0.723869
$117$	385.804	−	134.262i	0.304851	−	0.106090i
$118$	−229.482			−0.179030
$119$	172.482	−	298.747i	0.132869	−	0.230135i
$120$	−157.555	+	423.518i	−0.119856	+	0.322181i
$121$	−247.890	−	429.358i	−0.186244	−	0.322583i
$122$	−755.056	−	1307.80i	−0.560325	−	0.970511i
$123$	368.252	−	989.887i	0.269953	−	0.725651i
$124$	−118.777	+	205.729i	−0.0860204	+	0.148992i
$125$	−1433.09			−1.02544
$126$	−1268.39	+	441.406i	−0.896804	+	0.312092i
$127$	−31.4481			−0.0219730			−0.0109865	−	0.999940i	$-0.503497\pi$
$127$	−31.4481			−0.0219730			−0.0109865	+	0.999940i	$0.503497\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$	−1669.69	+	282.229i	−1.13960	+	0.192627i
$130$	164.465	+	284.862i	0.110958	+	0.192185i
$131$	968.678	+	1677.80i	0.646059	+	1.11901i	0.984056	+	0.177860i	$0.0569174\pi$
$131$	968.678	+	1677.80i	0.646059	+	1.11901i	−0.337997	+	0.941147i	$0.609749\pi$
$132$	−566.186	−	684.546i	−0.373335	−	0.451379i
$133$	−1782.61	+	3087.58i	−1.16220	+	2.01299i
$134$	1534.89			0.989510
$135$	1304.25	+	790.437i	0.831497	+	0.503926i
$136$	110.963			0.0699635
$137$	−579.297	+	1003.37i	−0.361261	+	0.625722i	−0.988169	−	0.153372i	$-0.950987\pi$
$137$	−579.297	+	1003.37i	−0.361261	+	0.625722i	0.626908	+	0.779093i	$0.284320\pi$
$138$	−126.704	−	153.191i	−0.0781578	−	0.0944965i
$139$	−1155.80	−	2001.90i	−0.705277	−	1.22158i	−0.966591	−	0.256323i	$-0.917489\pi$
$139$	−1155.80	−	2001.90i	−0.705277	−	1.22158i	0.261314	−	0.965254i	$-0.415844\pi$
$140$	−540.704	−	936.527i	−0.326413	−	0.565364i
$141$	−56.0693	+	9.47744i	−0.0334886	+	0.00566060i
$142$	335.854	−	581.716i	0.198480	−	0.343778i
$143$	−646.651			−0.378151
$144$	−326.963	−	282.345i	−0.189215	−	0.163394i
$145$	2457.73			1.40761
$146$	167.279	−	289.736i	0.0948226	−	0.164238i
$147$	499.203	−	1341.89i	0.280092	−	0.752907i
$148$	168.372	+	291.629i	0.0935141	+	0.161971i
$149$	1475.11	+	2554.96i	0.811043	+	1.40477i	0.912135	+	0.409890i	$0.134433\pi$
$149$	1475.11	+	2554.96i	0.811043	+	1.40477i	−0.101092	+	0.994877i	$0.532234\pi$
$150$	24.7622	−	66.5625i	0.0134789	−	0.0362321i
$151$	863.199	−	1495.10i	0.465206	−	0.805761i	−0.534005	−	0.845482i	$-0.679314\pi$
$151$	863.199	−	1495.10i	0.465206	−	0.805761i	0.999211	+	0.0397208i	$0.0126469\pi$
$152$	−1146.82			−0.611968
$153$	70.2508	−	367.854i	0.0371205	−	0.194374i
$154$	2125.97			1.11244
$155$	−322.790	+	559.089i	−0.167272	+	0.289723i
$156$	−310.064	+	52.4104i	−0.159135	+	0.0268986i
$157$	−641.694	−	1111.45i	−0.326196	−	0.564988i	0.655558	−	0.755145i	$-0.272434\pi$
$157$	−641.694	−	1111.45i	−0.326196	−	0.564988i	−0.981754	+	0.190157i	$0.939100\pi$
$158$	−25.3155	−	43.8478i	−0.0127468	−	0.0220781i
$159$	−464.259	−	561.311i	−0.231561	−	0.279968i
$160$	173.927	−	301.250i	0.0859383	−	0.148849i
$161$	475.761			0.232889
$162$	−1143.00	+	905.160i	−0.554337	+	0.438988i
$163$	1033.93			0.496831			0.248415	−	0.968654i	$-0.420090\pi$
$163$	1033.93			0.496831			0.248415	+	0.968654i	$0.420090\pi$
$164$	−406.518	+	704.110i	−0.193559	+	0.335255i
$165$	−1538.67	−	1860.33i	−0.725972	−	0.877734i
$166$	287.721	+	498.347i	0.134527	+	0.233008i
$167$	141.309	+	244.754i	0.0654778	+	0.113411i	0.896906	−	0.442222i	$-0.145810\pi$
$167$	141.309	+	244.754i	0.0654778	+	0.113411i	−0.831428	+	0.555632i	$0.812476\pi$
$168$	1019.38	−	172.307i	0.468138	−	0.0791298i
$169$	984.048	−	1704.42i	0.447905	−	0.775795i
$170$	301.555			0.136048
$171$	−726.048	+	3801.80i	−0.324692	+	1.70018i
$172$	1303.56			0.577881
$173$	1766.36	−	3059.43i	0.776266	−	1.34453i	−0.157814	−	0.987469i	$-0.550445\pi$
$173$	1766.36	−	3059.43i	0.776266	−	1.34453i	0.934080	−	0.357063i	$-0.116222\pi$
$174$	−819.242	+	2202.18i	−0.356934	+	0.959464i
$175$	84.9802	+	147.190i	0.0367080	+	0.0635801i
$176$	341.927	+	592.235i	0.146441	+	0.253644i
$177$	207.880	−	558.796i	0.0882782	−	0.237298i
$178$	−860.817	+	1490.98i	−0.362477	+	0.627829i
$179$	−4052.74			−1.69227			−0.846135	−	0.532969i	$-0.821076\pi$
$179$	−4052.74			−1.69227			−0.846135	+	0.532969i	$0.821076\pi$
$180$	−888.558	−	767.304i	−0.367940	−	0.317730i
$181$	−2830.97			−1.16257			−0.581283	−	0.813702i	$-0.697449\pi$
$181$	−2830.97			−1.16257			−0.581283	+	0.813702i	$0.697449\pi$
$182$	376.279	−	651.734i	0.153251	−	0.265438i
$183$	3868.51	−	653.898i	1.56267	−	0.264140i
$184$	76.5183	+	132.534i	0.0306576	+	0.0531006i
$185$	457.569	+	792.532i	0.181844	+	0.314963i
$186$	−393.360	−	475.590i	−0.155067	−	0.187484i
$187$	−296.417	+	513.409i	−0.115915	+	0.200771i
$188$	43.7744			0.0169818
$189$	74.1563	−	3488.44i	0.0285401	−	1.34257i
$190$	−3116.60			−1.19001
$191$	−2254.62	+	3905.12i	−0.854129	+	1.47940i	0.0233215	+	0.999728i	$0.492576\pi$
$191$	−2254.62	+	3905.12i	−0.854129	+	1.47940i	−0.877451	+	0.479667i	$0.840757\pi$
$192$	211.951	+	256.259i	0.0796680	+	0.0963224i
$193$	1610.56	+	2789.58i	0.600678	+	1.04040i	0.992719	+	0.120457i	$0.0384359\pi$
$193$	1610.56	+	2789.58i	0.600678	+	1.04040i	−0.392041	+	0.919948i	$0.628231\pi$
$194$	−402.149	−	696.543i	−0.148828	−	0.257778i
$195$	−842.632	+	142.431i	−0.309447	+	0.0523061i
$196$	−551.076	+	954.492i	−0.200830	+	0.347847i
$197$	3784.20			1.36859			0.684297	−	0.729204i	$-0.260109\pi$
$197$	3784.20			1.36859			0.684297	+	0.729204i	$0.260109\pi$
$198$	2179.78	−	758.575i	0.782376	−	0.272271i
$199$	−2926.27			−1.04240			−0.521200	−	0.853435i	$-0.674515\pi$
$199$	−2926.27			−1.04240			−0.521200	+	0.853435i	$0.674515\pi$
$200$	−27.3353	+	47.3462i	−0.00966450	+	0.0167394i
$201$	−1390.41	+	3737.51i	−0.487920	+	1.31156i
$202$	−1331.43	−	2306.10i	−0.463757	−	0.803251i
$203$	−2811.51	−	4869.69i	−0.972067	−	1.68367i
$204$	−100.518	+	270.200i	−0.0344985	+	0.0927342i
$205$	−1104.76	+	1913.49i	−0.376388	+	0.651923i
$206$	1037.01			0.350737
$207$	487.804	−	169.758i	0.163791	−	0.0570000i
$208$	242.073			0.0806959
$209$	3063.50	−	5306.13i	1.01391	−	1.75614i
$210$	2770.28	−	468.264i	0.910323	−	0.153873i
$211$	−156.737	−	271.476i	−0.0511385	−	0.0885744i	0.839323	−	0.543633i	$-0.182952\pi$
$211$	−156.737	−	271.476i	−0.0511385	−	0.0885744i	−0.890462	+	0.455059i	$0.849618\pi$
$212$	280.372	+	485.618i	0.0908303	+	0.157323i
$213$	1112.26	+	1344.77i	0.357797	+	0.432593i
$214$	1471.87	−	2549.35i	0.470164	−	0.814347i
$215$	3542.57			1.12373
$216$	983.707	−	540.400i	0.309874	−	0.170229i
$217$	1477.02			0.462059
$218$	−643.668	+	1114.87i	−0.199976	+	0.346368i
$219$	553.984	+	669.793i	0.170935	+	0.206669i
$220$	929.223	+	1609.46i	0.284764	+	0.493226i
$221$	104.927	+	181.739i	0.0319373	+	0.0553170i
$222$	−862.649	+	145.814i	−0.260798	+	0.0440830i
$223$	355.193	−	615.212i	0.106661	−	0.184743i	−0.807754	−	0.589519i	$-0.799317\pi$
$223$	355.193	−	615.212i	0.106661	−	0.184743i	0.914416	+	0.404776i	$0.132651\pi$
$224$	−795.854			−0.237389
$225$	139.651	+	120.594i	0.0413780	+	0.0357315i
$226$	−2047.45			−0.602631
$227$	−16.3308	+	28.2858i	−0.00477496	+	0.00827046i	−0.868403	−	0.495859i	$-0.834853\pi$
$227$	−16.3308	+	28.2858i	−0.00477496	+	0.00827046i	0.863628	+	0.504130i	$0.168187\pi$
$228$	1038.87	−	2792.54i	0.301757	−	0.811143i
$229$	2751.92	+	4766.47i	0.794114	+	1.37545i	0.923400	+	0.383839i	$0.125398\pi$
$229$	2751.92	+	4766.47i	0.794114	+	1.37545i	−0.129286	+	0.991607i	$0.541268\pi$
$230$	207.947	+	360.174i	0.0596156	+	0.103257i
$231$	−1925.85	+	5176.81i	−0.548534	+	1.47450i
$232$	904.372	−	1566.42i	0.255926	−	0.443278i
$233$	−6788.81			−1.90880			−0.954399	−	0.298534i	$-0.903502\pi$
$233$	−6788.81			−1.90880			−0.954399	+	0.298534i	$0.903502\pi$
$234$	153.256	−	802.494i	0.0428148	−	0.224191i
$235$	118.962			0.0330221
$236$	−229.482	+	397.474i	−0.0632966	+	0.109633i
$237$	129.704	−	21.9239i	0.0355492	−	0.00600890i
$238$	−344.963	−	597.494i	−0.0939523	−	0.162730i
$239$	214.694	+	371.862i	0.0581064	+	0.100643i	0.893615	−	0.448834i	$-0.148160\pi$
$239$	214.694	+	371.862i	0.0581064	+	0.100643i	−0.835509	+	0.549477i	$0.814827\pi$
$240$	576.000	+	696.411i	0.154919	+	0.187305i
$241$	2421.82	−	4194.72i	0.647317	−	1.12119i	−0.336444	−	0.941703i	$-0.609224\pi$
$241$	2421.82	−	4194.72i	0.647317	−	1.12119i	0.983761	−	0.179483i	$-0.0574424\pi$
$242$	−991.561			−0.263388
$243$	−1168.69	−	3603.20i	−0.308525	−	0.951216i
$244$	−3020.23			−0.792419
$245$	−1497.61	+	2593.93i	−0.390525	+	0.676410i
$246$	−1346.28	−	1627.72i	−0.348926	−	0.421868i
$247$	−1084.43	−	1878.28i	−0.279354	−	0.483856i
$248$	237.555	+	411.457i	0.0608256	+	0.105353i
$249$	−1474.13	+	249.174i	−0.375178	+	0.0634166i
$250$	−1433.09	+	2482.18i	−0.362546	+	0.627949i
$251$	2400.87			0.603752			0.301876	−	0.953347i	$-0.402387\pi$
$251$	2400.87			0.603752			0.301876	+	0.953347i	$0.402387\pi$
$252$	−503.854	+	2638.33i	−0.125952	+	0.659519i
$253$	−817.614			−0.203174
$254$	−31.4481	+	54.4698i	−0.00776863	+	0.0134557i
$255$	−273.169	+	734.297i	−0.0670844	+	0.180327i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−1490.50	−	2581.62i	−0.361769	−	0.626602i	0.626483	−	0.779435i	$-0.284494\pi$
$257$	−1490.50	−	2581.62i	−0.361769	−	0.626602i	−0.988252	+	0.152833i	$0.951160\pi$
$258$	−1180.86	+	3174.22i	−0.284949	+	0.765962i
$259$	1046.87	−	1813.23i	0.251156	−	0.435015i
$260$	657.860			0.156918
$261$	−4620.26	−	3989.77i	−1.09573	−	0.946209i
$262$	3874.71			0.913666
$263$	−2780.41	+	4815.81i	−0.651891	+	1.12911i	0.330773	+	0.943710i	$0.392691\pi$
$263$	−2780.41	+	4815.81i	−0.651891	+	1.12911i	−0.982664	+	0.185398i	$0.940643\pi$
$264$	−1751.85	+	296.117i	−0.408406	+	0.0690332i
$265$	761.941	+	1319.72i	0.176625	+	0.305924i
$266$	3565.23	+	6175.16i	0.821798	+	1.42340i
$267$	−2850.80	−	3446.75i	−0.653431	−	0.790029i
$268$	1534.89	−	2658.51i	0.349845	−	0.605949i
$269$	6288.50			1.42534			0.712671	−	0.701499i	$-0.247485\pi$
$269$	6288.50			1.42534			0.712671	+	0.701499i	$0.247485\pi$
$270$	2673.33	−	1468.59i	0.602569	−	0.331021i
$271$	6854.90			1.53655			0.768275	−	0.640119i	$-0.221115\pi$
$271$	6854.90			1.53655			0.768275	+	0.640119i	$0.221115\pi$
$272$	110.963	−	192.194i	0.0247358	−	0.0428437i
$273$	1246.14	+	1506.64i	0.276262	+	0.334014i
$274$	1158.59	+	2006.74i	0.255450	+	0.442452i
$275$	−146.042	−	252.952i	−0.0320242	−	0.0554676i
$276$	−392.040	+	66.2668i	−0.0855000	+	0.0144521i
$277$	−449.086	+	777.840i	−0.0974114	+	0.168722i	−0.910612	−	0.413261i	$-0.864390\pi$
$277$	−449.086	+	777.840i	−0.0974114	+	0.168722i	0.813201	+	0.581983i	$0.197723\pi$
$278$	−4623.20			−0.997413
$279$	1514.41	−	527.023i	0.324966	−	0.113090i
$280$	−2162.82			−0.461618
$281$	−119.385	+	206.781i	−0.0253448	+	0.0438986i	−0.878420	−	0.477890i	$-0.841402\pi$
$281$	−119.385	+	206.781i	−0.0253448	+	0.0438986i	0.853075	+	0.521789i	$0.174735\pi$
$282$	−39.6539	+	106.592i	−0.00837360	+	0.0225088i
$283$	−1035.58	−	1793.68i	−0.217523	−	0.376760i	0.736527	−	0.676408i	$-0.236464\pi$
$283$	−1035.58	−	1793.68i	−0.217523	−	0.376760i	−0.954050	+	0.299647i	$0.903131\pi$
$284$	−671.707	−	1163.43i	−0.140347	−	0.243088i
$285$	2823.23	−	7589.03i	0.586785	−	1.57732i
$286$	−646.651	+	1120.03i	−0.133697	+	0.231570i
$287$	5055.14			1.03971
$288$	−816.000	+	283.972i	−0.166956	+	0.0581014i
$289$	−4720.61			−0.960841
$290$	2457.73	−	4256.91i	0.497664	−	0.861980i
$291$	2060.40	−	348.272i	0.415062	−	0.0701582i
$292$	−334.558	−	579.471i	−0.0670497	−	0.116134i
$293$	3288.88	+	5696.51i	0.655763	+	1.13581i	0.981702	+	0.190423i	$0.0609861\pi$
$293$	3288.88	+	5696.51i	0.655763	+	1.13581i	−0.325939	+	0.945391i	$0.605681\pi$
$294$	−1825.02	−	2206.54i	−0.362032	−	0.437713i
$295$	−623.641	+	1080.18i	−0.123084	+	0.213188i
$296$	673.488			0.132249
$297$	−127.441	+	5995.02i	−0.0248985	+	1.17127i
$298$	5900.42			1.14699
$299$	−144.711	+	250.647i	−0.0279895	+	0.0484792i
$300$	−90.5275	−	109.452i	−0.0174220	−	0.0210640i
$301$	−4052.51	−	7019.16i	−0.776023	−	1.34411i
$302$	−1726.40	−	2990.21i	−0.328950	−	0.569759i
$303$	6821.54	−	1153.05i	1.29336	−	0.218617i
$304$	−1146.82	+	1986.35i	−0.216363	+	0.374752i
$305$	−8207.78			−1.54091
$306$	−566.890	−	489.531i	−0.105905	−	0.0914531i
$307$	−5237.30			−0.973644			−0.486822	−	0.873501i	$-0.661844\pi$
$307$	−5237.30			−0.973644			−0.486822	+	0.873501i	$0.661844\pi$
$308$	2125.97	−	3682.28i	0.393306	−	0.681226i
$309$	−939.394	+	2525.15i	−0.172946	+	0.464890i
$310$	645.581	+	1118.18i	0.118279	+	0.204865i
$311$	−2852.49	−	4940.67i	−0.520097	−	0.900834i	−0.999727	−	0.0233635i	$-0.992562\pi$
$311$	−2852.49	−	4940.67i	−0.520097	−	0.900834i	0.479630	−	0.877471i	$-0.340771\pi$
$312$	−219.287	+	589.457i	−0.0397906	+	0.106960i
$313$	−2538.74	+	4397.23i	−0.458460	+	0.794076i	−0.998880	−	0.0473193i	$-0.984932\pi$
$313$	−2538.74	+	4397.23i	−0.458460	+	0.794076i	0.540420	+	0.841396i	$0.318265\pi$
$314$	−2566.78			−0.461311
$315$	−1369.28	+	7169.93i	−0.244921	+	1.28248i
$316$	−101.262			−0.0180267
$317$	−1434.46	+	2484.55i	−0.254155	+	0.440209i	−0.964666	−	0.263477i	$-0.915131\pi$
$317$	−1434.46	+	2484.55i	−0.254155	+	0.440209i	0.710511	+	0.703686i	$0.248464\pi$
$318$	−1436.48	+	242.809i	−0.253314	+	0.0428178i
$319$	4831.70	+	8368.76i	0.848036	+	1.46884i
$320$	−347.854	−	602.500i	−0.0607675	−	0.105252i
$321$	4874.45	+	5893.44i	0.847555	+	1.02473i
$322$	475.761	−	824.042i	0.0823388	−	0.142615i
$323$	−1988.36			−0.342523
$324$	424.783	+	2884.89i	0.0728367	+	0.494666i
$325$	−103.393			−0.0176468
$326$	1033.93	−	1790.81i	0.175656	−	0.304245i
$327$	−2131.66	−	2577.28i	−0.360492	−	0.435852i
$328$	813.037	+	1408.22i	0.136867	+	0.237061i
$329$	−136.086	−	235.708i	−0.0228045	−	0.0394985i
$330$	−4760.85	+	804.730i	−0.794170	+	0.134239i
$331$	−1015.67	+	1759.20i	−0.168660	+	0.292128i	−0.937949	−	0.346773i	$-0.887277\pi$
$331$	−1015.67	+	1759.20i	−0.168660	+	0.292128i	0.769289	+	0.638901i	$0.220611\pi$
$332$	1150.88			0.190250
$333$	426.384	−	2232.67i	0.0701673	−	0.367416i
$334$	565.235			0.0925996
$335$	4171.23	−	7224.78i	0.680294	−	1.17830i
$336$	720.939	−	1937.93i	0.117055	−	0.314651i
$337$	−4899.14	−	8485.56i	−0.791909	−	1.37163i	−0.924784	−	0.380493i	$-0.875754\pi$
$337$	−4899.14	−	8485.56i	−0.791909	−	1.37163i	0.132875	−	0.991133i	$-0.457579\pi$
$338$	−1968.10	−	3408.84i	−0.316717	−	0.548570i
$339$	1854.72	−	4985.63i	0.297153	−	0.798767i
$340$	301.555	−	522.308i	0.0481003	−	0.0833122i
$341$	−2538.32			−0.403103
$342$	5858.86	+	5059.35i	0.926348	+	0.799937i
$343$	−1677.81			−0.264120
$344$	1303.56	−	2257.83i	0.204312	−	0.353879i
$345$	−1065.41	+	180.087i	−0.166260	+	0.0281031i
$346$	−3532.72	−	6118.86i	−0.548903	−	0.950728i
$347$	2278.28	+	3946.10i	0.352463	+	0.610483i	0.986680	−	0.162671i	$-0.0520111\pi$
$347$	2278.28	+	3946.10i	0.352463	+	0.610483i	−0.634218	+	0.773154i	$0.718678\pi$
$348$	2995.04	+	3621.15i	0.461354	+	0.557799i
$349$	−1674.44	+	2900.22i	−0.256822	+	0.444829i	−0.965389	−	0.260815i	$-0.916009\pi$
$349$	−1674.44	+	2900.22i	−0.256822	+	0.444829i	0.708567	+	0.705644i	$0.249342\pi$
$350$	339.921			0.0519129
$351$	1815.27	+	1100.14i	0.276046	+	0.167296i
$352$	1367.71			0.207100
$353$	−931.134	+	1612.77i	−0.140395	+	0.243170i	−0.927645	−	0.373463i	$-0.878170\pi$
$353$	−931.134	+	1612.77i	−0.140395	+	0.243170i	0.787251	+	0.616633i	$0.211504\pi$
$354$	−759.983	−	918.856i	−0.114104	−	0.137957i
$355$	−1825.44	−	3161.75i	−0.272913	−	0.472699i
$356$	1721.63	+	2981.96i	0.256310	+	0.443942i
$357$	1767.41	−	298.747i	0.262021	−	0.0442896i
$358$	−4052.74	+	7019.56i	−0.598308	+	1.03630i
$359$	6179.46			0.908466			0.454233	−	0.890883i	$-0.349913\pi$
$359$	6179.46			0.908466			0.454233	+	0.890883i	$0.349913\pi$
$360$	−2217.57	+	771.724i	−0.324656	+	0.112982i
$361$	13690.8			1.99604
$362$	−2830.97	+	4903.38i	−0.411029	+	0.711923i
$363$	898.224	−	2414.49i	0.129875	−	0.349112i
$364$	−752.558	−	1303.47i	−0.108365	−	0.187693i
$365$	−909.197	−	1574.77i	−0.130382	−	0.225829i
$366$	2735.93	−	7354.36i	0.390736	−	1.05032i
$367$	−3436.98	+	5953.02i	−0.488852	+	0.846717i	−0.999918	−	0.0128251i	$-0.995918\pi$
$367$	−3436.98	+	5953.02i	−0.488852	+	0.846717i	0.511066	+	0.859542i	$0.329251\pi$
$368$	306.073			0.0433564
$369$	5183.11	−	1803.75i	0.731224	−	0.254470i
$370$	1830.27			0.257166
$371$	1743.24	−	3019.38i	0.243948	−	0.422530i
$372$	−1217.11	+	205.729i	−0.169635	+	0.0286735i
$373$	−635.013	−	1099.87i	−0.0881494	−	0.152679i	0.818580	−	0.574393i	$-0.194762\pi$
$373$	−635.013	−	1099.87i	−0.0881494	−	0.152679i	−0.906729	+	0.421714i	$0.861429\pi$
$374$	592.834	+	1026.82i	0.0819645	+	0.141967i
$375$	−4746.02	−	5738.16i	−0.653556	−	0.790179i
$376$	43.7744	−	75.8195i	0.00600397	−	0.0103992i
$377$	3420.69			0.467306
$378$	−5967.99	−	3616.88i	−0.812065	−	0.492149i
$379$	2490.54			0.337548			0.168774	−	0.985655i	$-0.446019\pi$
$379$	2490.54			0.337548			0.168774	+	0.985655i	$0.446019\pi$
$380$	−3116.60	+	5398.11i	−0.420732	+	0.728729i
$381$	−104.148	−	125.920i	−0.0140044	−	0.0169319i
$382$	4509.24	+	7810.24i	0.603960	+	1.04609i
$383$	−156.213	−	270.568i	−0.0208410	−	0.0360976i	0.855417	−	0.517940i	$-0.173301\pi$
$383$	−156.213	−	270.568i	−0.0208410	−	0.0360976i	−0.876258	+	0.481843i	$0.839968\pi$
$384$	655.805	−	110.851i	0.0871521	−	0.0147314i
$385$	5777.54	−	10007.0i	0.764807	−	1.32468i
$386$	6442.25			0.849487
$387$	−6659.64	−	5750.85i	−0.874750	−	0.755380i
$388$	−1608.60			−0.210475
$389$	−4821.58	+	8351.23i	−0.628442	+	1.08849i	0.359422	+	0.933175i	$0.382974\pi$
$389$	−4821.58	+	8351.23i	−0.628442	+	1.08849i	−0.987864	+	0.155319i	$0.950360\pi$
$390$	−595.935	+	1601.91i	−0.0773752	+	0.207990i
$391$	132.668	+	229.787i	0.0171593	+	0.0297208i
$392$	1102.15	+	1908.98i	0.142008	+	0.245965i
$393$	−3509.98	+	9435.06i	−0.450522	+	1.21103i
$394$	3784.20	−	6554.42i	0.483871	−	0.838089i
$395$	−275.191			−0.0350540
$396$	865.893	−	4534.07i	0.109881	−	0.575368i
$397$	−2260.32			−0.285749			−0.142874	−	0.989741i	$-0.545634\pi$
$397$	−2260.32			−0.285749			−0.142874	+	0.989741i	$0.545634\pi$
$398$	−2926.27	+	5068.44i	−0.368544	+	0.638337i
$399$	−18266.4	+	3087.58i	−2.29188	+	0.387399i
$400$	54.6707	+	94.6924i	0.00683384	+	0.0118366i
$401$	−5084.64	−	8806.85i	−0.633204	−	1.09674i	−0.986893	−	0.161378i	$-0.948406\pi$
$401$	−5084.64	−	8806.85i	−0.633204	−	1.09674i	0.353689	−	0.935363i	$-0.384927\pi$
$402$	5083.15	+	6145.77i	0.630658	+	0.762496i
$403$	−449.263	+	778.146i	−0.0555320	+	0.0961842i
$404$	−5325.71			−0.655852
$405$	1154.39	+	7840.01i	0.141635	+	0.961909i
$406$	−11246.1			−1.37471
$407$	−1799.09	+	3116.12i	−0.219110	+	0.379509i
$408$	367.482	+	444.303i	0.0445908	+	0.0539124i
$409$	474.916	+	822.579i	0.0574159	+	0.0994472i	0.893305	−	0.449452i	$-0.148381\pi$
$409$	474.916	+	822.579i	0.0574159	+	0.0994472i	−0.835889	+	0.548899i	$0.815047\pi$
$410$	2209.51	+	3826.99i	0.266147	+	0.460979i
$411$	−5936.03	+	1003.37i	−0.712416	+	0.120420i
$412$	1037.01	−	1796.15i	0.124004	−	0.214782i
$413$	2853.65			0.339998
$414$	193.774	−	1014.66i	0.0230036	−	0.120454i
$415$	3127.65			0.369953
$416$	242.073	−	419.283i	0.0285303	−	0.0494160i
$417$	4188.01	−	11257.6i	0.491817	−	1.32204i
$418$	−6126.99	−	10612.3i	−0.716940	−	1.24178i
$419$	5899.63	+	10218.5i	0.687866	+	1.19142i	0.972527	+	0.232791i	$0.0747859\pi$
$419$	5899.63	+	10218.5i	0.687866	+	1.19142i	−0.284660	+	0.958628i	$0.591881\pi$
$420$	1959.23	−	5266.54i	0.227620	−	0.611859i
$421$	3206.46	−	5553.76i	0.371196	−	0.642930i	−0.618554	−	0.785742i	$-0.712281\pi$
$421$	3206.46	−	5553.76i	0.371196	−	0.642930i	0.989750	+	0.142812i	$0.0456145\pi$
$422$	−626.948			−0.0723207
$423$	−223.635	−	193.117i	−0.0257057	−	0.0221978i
$424$	1121.49			0.128453
$425$	−47.3941	+	82.0890i	−0.00540930	+	0.00936918i
$426$	3441.48	−	581.716i	0.391409	−	0.0661601i
$427$	9389.29	+	16262.7i	1.06412	+	1.84311i
$428$	−2943.74	−	5098.71i	−0.332456	−	0.575830i
$429$	−2141.54	−	2589.22i	−0.241013	−	0.291396i
$430$	3542.57	−	6135.90i	0.397297	−	0.688138i
$431$	−12042.7			−1.34589			−0.672945	−	0.739693i	$-0.734971\pi$
$431$	−12042.7			−1.34589			−0.672945	+	0.739693i	$0.734971\pi$
$432$	47.7073	−	2244.23i	0.00531323	−	0.249944i
$433$	7279.83			0.807959			0.403980	−	0.914768i	$-0.367627\pi$
$433$	7279.83			0.807959			0.403980	+	0.914768i	$0.367627\pi$
$434$	1477.02	−	2558.28i	0.163363	−	0.282952i
$435$	8139.35	+	9840.86i	0.897131	+	1.08467i
$436$	1287.34	+	2229.73i	0.141404	+	0.244919i
$437$	−1371.13	−	2374.87i	−0.150092	−	0.259967i
$438$	1714.10	−	289.736i	0.186993	−	0.0316075i
$439$	1799.35	−	3116.57i	0.195623	−	0.338828i	−0.751482	−	0.659754i	$-0.770661\pi$
$439$	1799.35	−	3116.57i	0.195623	−	0.338828i	0.947104	+	0.320926i	$0.103994\pi$
$440$	3716.89			0.402718
$441$	7026.22	−	2445.16i	0.758689	−	0.264027i
$442$	419.707			0.0451662
$443$	7393.18	−	12805.4i	0.792913	−	1.37337i	−0.131243	−	0.991350i	$-0.541897\pi$
$443$	7393.18	−	12805.4i	0.792913	−	1.37337i	0.924156	−	0.382016i	$-0.124770\pi$
$444$	−610.092	+	1639.97i	−0.0652110	+	0.175291i
$445$	4678.72	+	8103.79i	0.498411	+	0.863273i
$446$	−710.386	−	1230.42i	−0.0754209	−	0.130633i
$447$	−5345.01	+	14367.7i	−0.565571	+	1.52029i
$448$	−795.854	+	1378.46i	−0.0839298	+	0.145371i
$449$	114.489			0.0120336			0.00601681	−	0.999982i	$-0.498085\pi$
$449$	114.489			0.0120336			0.00601681	+	0.999982i	$0.498085\pi$
$450$	348.526	−	121.289i	0.0365103	−	0.0127058i
$451$	−8687.47			−0.907044
$452$	−2047.45	+	3546.29i	−0.213062	+	0.369035i
$453$	8845.16	−	1495.10i	0.917399	−	0.155069i
$454$	32.6616	+	56.5716i	0.00337640	+	0.00584810i
$455$	−2045.16	−	3542.31i	−0.210722	−	0.364981i
$456$	−3797.96	−	4591.91i	−0.390034	−	0.471570i
$457$	−3155.57	+	5465.60i	−0.323001	+	0.559453i	−0.981106	−	0.193473i	$-0.938025\pi$
$457$	−3155.57	+	5465.60i	−0.323001	+	0.559453i	0.658105	+	0.752926i	$0.271358\pi$
$458$	11007.7			1.12305
$459$	1705.55	−	936.947i	0.173439	−	0.0952787i
$460$	831.786			0.0843092
$461$	6872.41	−	11903.4i	0.694317	−	1.20259i	−0.276094	−	0.961131i	$-0.589040\pi$
$461$	6872.41	−	11903.4i	0.694317	−	1.20259i	0.970411	−	0.241461i	$-0.0776266\pi$
$462$	7040.64	+	8512.47i	0.709005	+	0.857221i
$463$	−7824.30	−	13552.1i	−0.785369	−	1.36030i	−0.928778	−	0.370636i	$-0.879140\pi$
$463$	−7824.30	−	13552.1i	−0.785369	−	1.36030i	0.143409	−	0.989664i	$-0.454194\pi$
$464$	−1808.74	−	3132.84i	−0.180967	−	0.313445i
$465$	−3307.62	+	559.089i	−0.329865	+	0.0557573i
$466$	−6788.81	+	11758.6i	−0.674862	+	1.16890i
$467$	−7395.79			−0.732840			−0.366420	−	0.930450i	$-0.619417\pi$
$467$	−7395.79			−0.732840			−0.366420	+	0.930450i	$0.619417\pi$
$468$	−1236.70	−	1067.94i	−0.122151	−	0.105482i
$469$	−19086.7			−1.87919
$470$	118.962	−	206.048i	0.0116751	−	0.0202219i
$471$	2325.16	−	6250.20i	0.227469	−	0.611452i
$472$	458.963	+	794.948i	0.0447574	+	0.0775221i
$473$	6964.41	+	12062.7i	0.677006	+	1.17261i
$474$	91.7302	−	246.577i	0.00888884	−	0.0238938i
$475$	489.822	−	848.397i	0.0473149	−	0.0819519i
$476$	−1379.85			−0.132869
$477$	710.012	−	3717.83i	0.0681535	−	0.356872i
$478$	858.777			0.0821748
$479$	3130.53	−	5422.24i	0.298617	−	0.517221i	−0.677202	−	0.735797i	$-0.736808\pi$
$479$	3130.53	−	5422.24i	0.298617	−	0.517221i	0.975820	+	0.218576i	$0.0701412\pi$
$480$	1782.22	−	301.250i	0.169473	−	0.0286461i
$481$	636.849	+	1103.05i	0.0603697	+	0.104563i
$482$	−4843.65	−	8389.45i	−0.457722	−	0.792798i
$483$	1575.59	+	1904.97i	0.148431	+	0.179460i
$484$	−991.561	+	1717.43i	−0.0931218	+	0.161292i
$485$	−4371.54			−0.409281
$486$	−7409.62	−	1578.97i	−0.691579	−	0.147374i
$487$	−10314.7			−0.959763			−0.479881	−	0.877333i	$-0.659320\pi$
$487$	−10314.7			−0.959763			−0.479881	+	0.877333i	$0.659320\pi$
$488$	−3020.23	+	5231.18i	−0.280162	+	0.485255i
$489$	3424.09	+	4139.89i	0.316652	+	0.382847i
$490$	2995.22	+	5187.87i	0.276143	+	0.478294i
$491$	1380.45	+	2391.01i	0.126881	+	0.219765i	0.922467	−	0.386076i	$-0.126170\pi$
$491$	1380.45	+	2391.01i	0.126881	+	0.219765i	−0.795585	+	0.605841i	$0.792837\pi$
$492$	−4165.57	+	704.110i	−0.381704	+	0.0645198i
$493$	1568.00	−	2715.86i	0.143244	−	0.248106i
$494$	−4337.71			−0.395067
$495$	2353.16	−	12321.8i	0.213670	−	1.11884i
$496$	950.220			0.0860204
$497$	−4176.41	+	7233.76i	−0.376937	+	0.652874i
$498$	−1042.55	+	2802.44i	−0.0938108	+	0.252170i
$499$	4793.00	+	8301.71i	0.429988	+	0.744761i	0.996872	−	0.0790369i	$-0.0251845\pi$
$499$	4793.00	+	8301.71i	0.429988	+	0.744761i	−0.566884	+	0.823798i	$0.691851\pi$
$500$	2866.18	+	4964.37i	0.256359	+	0.444027i
$501$	−512.028	+	1376.37i	−0.0456602	+	0.122738i
$502$	2400.87	−	4158.43i	0.213459	−	0.369721i
$503$	8829.60			0.782689			0.391344	−	0.920244i	$-0.372010\pi$
$503$	8829.60			0.782689			0.391344	+	0.920244i	$0.372010\pi$
$504$	4065.86	+	3511.03i	0.359341	+	0.310305i
$505$	−14473.2			−1.27534
$506$	−817.614	+	1416.15i	−0.0718328	+	0.124418i
$507$	10083.5	−	1704.42i	0.883281	−	0.149302i
$508$	62.8963	+	108.940i	0.00549325	+	0.00951458i
$509$	−2370.87	−	4106.47i	−0.206458	−	0.357595i	0.744138	−	0.668025i	$-0.232860\pi$
$509$	−2370.87	−	4106.47i	−0.206458	−	0.357595i	−0.950596	+	0.310430i	$0.899527\pi$
$510$	998.671	+	1207.44i	0.0867096	+	0.104836i
$511$	−2080.15	+	3602.92i	−0.180079	+	0.311906i
$512$	−512.000			−0.0441942
$513$	−17627.1	+	9683.43i	−1.51706	+	0.833400i
$514$	−5961.99			−0.511619
$515$	2818.18	−	4881.24i	0.241134	−	0.417656i
$516$	4317.05	+	5219.52i	0.368309	+	0.445303i
$517$	233.870	+	405.074i	0.0198947	+	0.0344587i
$518$	−2093.74	−	3626.47i	−0.177594	−	0.307602i
$519$	18099.8	−	3059.43i	1.53082	−	0.258755i
$520$	657.860	−	1139.45i	0.0554790	−	0.0960924i
$521$	−2753.22			−0.231518			−0.115759	−	0.993277i	$-0.536930\pi$
$521$	−2753.22			−0.231518			−0.115759	+	0.993277i	$0.536930\pi$
$522$	−11530.7	+	4012.75i	−0.966833	+	0.336462i
$523$	17115.3			1.43098			0.715489	−	0.698624i	$-0.246204\pi$
$523$	17115.3			1.43098			0.715489	+	0.698624i	$0.246204\pi$
$524$	3874.71	−	6711.20i	0.323030	−	0.559504i
$525$	−307.924	+	827.719i	−0.0255979	+	0.0688088i
$526$	5560.82	+	9631.61i	0.460956	+	0.798400i
$527$	411.873	+	713.386i	0.0340446	+	0.0589669i
$528$	−1238.96	+	3330.42i	−0.102119	+	0.274503i
$529$	5900.53	−	10220.0i	0.484962	−	0.839978i
$530$	3047.76			0.249786
$531$	2925.89	−	1018.22i	0.239120	−	0.0832150i
$532$	14260.9			1.16220
$533$	−1537.61	+	2663.22i	−0.124956	+	0.216430i
$534$	−8820.75	+	1490.98i	−0.714815	+	0.120826i
$535$	−7999.93	−	13856.3i	−0.646481	−	1.11974i
$536$	−3069.78	−	5317.02i	−0.247377	−	0.428470i
$537$	−13421.6	−	16227.4i	−1.07856	−	1.30403i
$538$	6288.50	−	10892.0i	0.503934	−	0.872840i
$539$	−11776.7			−0.941113
$540$	129.650	−	6098.94i	0.0103319	−	0.486030i
$541$	17880.1			1.42093			0.710467	−	0.703731i	$-0.248484\pi$
$541$	17880.1			1.42093			0.710467	+	0.703731i	$0.248484\pi$
$542$	6854.90	−	11873.0i	0.543253	−	0.940941i
$543$	−9375.43	−	11335.3i	−0.740954	−	0.895849i
$544$	−221.927	−	384.389i	−0.0174909	−	0.0302951i
$545$	3498.47	+	6059.53i	0.274969	+	0.476260i
$546$	3855.71	−	651.734i	0.302215	−	0.0510836i
$547$	6534.73	−	11318.5i	0.510795	−	0.884723i	−0.489127	−	0.872213i	$-0.662684\pi$
$547$	6534.73	−	11318.5i	0.510795	−	0.884723i	0.999922	−	0.0125101i	$-0.00398218\pi$
$548$	4634.38			0.361261
$549$	15429.7	+	13324.2i	1.19950	+	1.03581i
$550$	−584.168			−0.0452891
$551$	−16205.5	+	28068.7i	−1.25295	+	2.17017i
$552$	−277.262	+	745.299i	−0.0213787	+	0.0574675i
$553$	314.804	+	545.257i	0.0242077	+	0.0419289i
$554$	898.172	+	1555.68i	0.0688803	+	0.119304i
$555$	−1657.99	+	4456.79i	−0.126807	+	0.340865i
$556$	−4623.20	+	8007.61i	−0.352639	+	0.610788i
$557$	9507.62			0.723251			0.361626	−	0.932323i	$-0.382222\pi$
$557$	9507.62			0.723251			0.361626	+	0.932323i	$0.382222\pi$
$558$	601.582	−	3150.06i	0.0456398	−	0.238983i
$559$	4930.58			0.373061
$560$	−2162.82	+	3746.11i	−0.163207	+	0.282682i
$561$	−3037.37	+	513.409i	−0.228588	+	0.0386384i
$562$	238.770	+	413.561i	0.0179215	+	0.0310410i
$563$	10222.3	+	17705.6i	0.765221	+	1.32540i	0.940130	+	0.340817i	$0.110704\pi$
$563$	10222.3	+	17705.6i	0.765221	+	1.32540i	−0.174909	+	0.984585i	$0.555963\pi$
$564$	144.969	+	175.275i	0.0108233	+	0.0130858i
$565$	−5564.17	+	9637.43i	−0.414313	+	0.717610i
$566$	−4142.33			−0.307624
$567$	14213.4	−	11255.9i	1.05275	−	0.833689i
$568$	−2686.83			−0.198480
$569$	−1323.03	+	2291.56i	−0.0974770	+	0.168835i	−0.910640	−	0.413201i	$-0.864411\pi$
$569$	−1323.03	+	2291.56i	−0.0974770	+	0.168835i	0.813163	+	0.582036i	$0.197744\pi$
$570$	−10321.4	−	12479.0i	−0.758445	−	0.916996i
$571$	−878.514	−	1521.63i	−0.0643864	−	0.111521i	0.832035	−	0.554723i	$-0.187176\pi$
$571$	−878.514	−	1521.63i	−0.0643864	−	0.111521i	−0.896422	+	0.443202i	$0.853842\pi$
$572$	1293.30	+	2240.06i	0.0945379	+	0.163744i
$573$	−23103.0	+	3905.12i	−1.68437	+	0.284710i
$574$	5055.14	−	8755.76i	0.367592	−	0.636687i
$575$	−130.728			−0.00948130
$576$	−324.146	+	1697.33i	−0.0234481	+	0.122781i
$577$	−7515.43			−0.542238			−0.271119	−	0.962546i	$-0.587394\pi$
$577$	−7515.43			−0.542238			−0.271119	+	0.962546i	$0.587394\pi$
$578$	−4720.61	+	8176.34i	−0.339709	+	0.588392i
$579$	−5835.83	+	15687.1i	−0.418876	+	1.12597i
$580$	−4915.45	−	8513.82i	−0.351902	−	0.609512i
$581$	−3577.87	−	6197.06i	−0.255482	−	0.442508i
$582$	1457.18	−	3916.99i	0.103783	−	0.278977i
$583$	−2995.83	+	5188.94i	−0.212821	+	0.368617i
$584$	−1338.23			−0.0948226
$585$	−3360.88	−	2902.24i	−0.237530	−	0.205116i
$586$	13155.5			0.927388
$587$	2476.24	−	4288.98i	0.174115	−	0.301576i	−0.765740	−	0.643151i	$-0.777627\pi$
$587$	2476.24	−	4288.98i	0.174115	−	0.301576i	0.939855	+	0.341575i	$0.110960\pi$
$588$	−5646.85	+	954.492i	−0.396041	+	0.0669432i
$589$	−4256.75	−	7372.91i	−0.297787	−	0.515782i
$590$	1247.28	+	2160.36i	0.0870335	+	0.150747i
$591$	12532.3	+	15152.1i	0.872265	+	1.05461i
$592$	673.488	−	1166.51i	0.0467571	−	0.0809856i
$593$	17115.3			1.18523			0.592613	−	0.805487i	$-0.298096\pi$
$593$	17115.3			1.18523			0.592613	+	0.805487i	$0.298096\pi$
$594$	10256.2	+	6215.75i	0.708449	+	0.429353i
$595$	−3749.90			−0.258371
$596$	5900.42	−	10219.8i	0.405521	−	0.702384i
$597$	−9691.02	−	11716.9i	−0.664367	−	0.803251i
$598$	289.422	+	501.294i	0.0197916	+	0.0342800i
$599$	−4207.06	−	7286.85i	−0.286972	−	0.497049i	0.686114	−	0.727494i	$-0.259315\pi$
$599$	−4207.06	−	7286.85i	−0.286972	−	0.497049i	−0.973085	+	0.230445i	$0.925982\pi$
$600$	−280.104	+	47.3462i	−0.0190587	+	0.00322150i
$601$	−14047.1	+	24330.3i	−0.953399	+	1.65134i	−0.215409	+	0.976524i	$0.569108\pi$
$601$	−14047.1	+	24330.3i	−0.953399	+	1.65134i	−0.737990	+	0.674812i	$0.764225\pi$
$602$	−16210.1			−1.09746
$603$	−19569.9	+	6810.40i	−1.32164	+	0.459935i
$604$	−6905.59			−0.465206
$605$	−2694.67	+	4667.31i	−0.181081	+	0.313642i
$606$	4824.40	−	12968.3i	0.323396	−	0.869309i
$607$	−715.423	−	1239.15i	−0.0478388	−	0.0828592i	0.841114	−	0.540857i	$-0.181900\pi$
$607$	−715.423	−	1239.15i	−0.0478388	−	0.0828592i	−0.888953	+	0.457998i	$0.848567\pi$
$608$	2293.63	+	3972.69i	0.152992	+	0.264990i
$609$	10187.5	−	27384.6i	0.677860	−	1.82213i
$610$	−8207.78	+	14216.3i	−0.544793	+	0.943608i
$611$	165.572			0.0109629
$612$	−1414.78	+	492.351i	−0.0934465	+	0.0325198i
$613$	14438.1			0.951306			0.475653	−	0.879633i	$-0.342212\pi$
$613$	14438.1			0.951306			0.475653	+	0.879633i	$0.342212\pi$
$614$	−5237.30	+	9071.27i	−0.344235	+	0.596233i
$615$	−11320.4	+	1913.49i	−0.742247	+	0.125463i
$616$	−4251.93	−	7364.56i	−0.278109	−	0.481699i
$617$	−12722.5	−	22036.0i	−0.830125	−	1.43782i	−0.897938	−	0.440121i	$-0.854935\pi$
$617$	−12722.5	−	22036.0i	−0.830125	−	1.43782i	0.0678130	−	0.997698i	$-0.478398\pi$
$618$	3434.30	+	4152.23i	0.223540	+	0.270271i
$619$	1739.73	−	3013.30i	0.112966	−	0.195662i	−0.803999	−	0.594631i	$-0.797298\pi$
$619$	1739.73	−	3013.30i	0.112966	−	0.195662i	0.916965	+	0.398968i	$0.130632\pi$
$620$	2582.32			0.167272
$621$	2295.20	+	1391.00i	0.148314	+	0.0898853i
$622$	−11410.0			−0.735528
$623$	10704.4	−	18540.6i	0.688386	−	1.19232i
$624$	801.683	+	969.272i	0.0514311	+	0.0621826i
$625$	7362.03	+	12751.4i	0.471170	+	0.816091i
$626$	5077.48	+	8794.45i	0.324180	+	0.561497i
$627$	31391.5	−	5306.13i	1.99945	−	0.337969i
$628$	−2566.78	+	4445.79i	−0.163098	+	0.282494i
$629$	1167.70			0.0740208
$630$	11049.4	+	9541.59i	0.698760	+	0.603406i
$631$	11151.7			0.703552			0.351776	−	0.936084i	$-0.385578\pi$
$631$	11151.7			0.703552			0.351776	+	0.936084i	$0.385578\pi$
$632$	−101.262	+	175.391i	−0.00637341	+	0.0110391i
$633$	567.933	−	1526.64i	0.0356608	−	0.0958587i
$634$	2868.91	+	4969.10i	0.179714	+	0.311275i
$635$	170.927	+	296.055i	0.0106820	+	0.0185017i
$636$	−1015.92	+	2730.86i	−0.0633394	+	0.170261i
$637$	−2084.39	+	3610.26i	−0.129649	+	0.224559i
$638$	19326.8			1.19930
$639$	−1701.03	+	8907.08i	−0.105308	+	0.551422i
$640$	−1391.41			−0.0859383
$641$	546.388	−	946.373i	0.0336678	−	0.0583143i	−0.848701	−	0.528874i	$-0.822615\pi$
$641$	546.388	−	946.373i	0.0336678	−	0.0583143i	0.882368	+	0.470559i	$0.155948\pi$
$642$	15082.2	−	2549.35i	0.927175	−	0.156721i
$643$	−15847.0	−	27447.8i	−0.971922	−	1.68342i	−0.689741	−	0.724056i	$-0.742276\pi$
$643$	−15847.0	−	27447.8i	−0.971922	−	1.68342i	−0.282181	−	0.959361i	$-0.591058\pi$
$644$	−951.521	−	1648.08i	−0.0582223	−	0.100844i
$645$	11732.0	+	14184.6i	0.716200	+	0.865919i
$646$	−1988.36	+	3443.93i	−0.121100	+	0.209752i
$647$	−13719.9			−0.833672			−0.416836	−	0.908982i	$-0.636861\pi$
$647$	−13719.9			−0.833672			−0.416836	+	0.908982i	$0.636861\pi$
$648$	5421.57	+	2149.15i	0.328672	+	0.130288i
$649$	−4904.12			−0.296616
$650$	−103.393	+	179.082i	−0.00623909	+	0.0108064i
$651$	4891.51	+	5914.07i	0.294491	+	0.356053i
$652$	−2067.85	−	3581.63i	−0.124208	−	0.215134i
$653$	−6642.59	−	11505.3i	−0.398078	−	0.689491i	0.595411	−	0.803421i	$-0.296989\pi$
$653$	−6642.59	−	11505.3i	−0.398078	−	0.689491i	−0.993489	+	0.113930i	$0.963656\pi$
$654$	−6595.63	+	1114.87i	−0.394357	+	0.0666585i
$655$	10529.9	−	18238.4i	0.628151	−	1.08799i
$656$	3252.15			0.193559
$657$	−847.232	+	4436.36i	−0.0503100	+	0.263438i
$658$	−544.344			−0.0322504
$659$	1296.99	−	2246.45i	0.0766670	−	0.132791i	−0.825143	−	0.564924i	$-0.808905\pi$
$659$	1296.99	−	2246.45i	0.0766670	−	0.132791i	0.901810	+	0.432133i	$0.142239\pi$
$660$	−3367.02	+	9050.76i	−0.198577	+	0.533789i
$661$	7937.67	+	13748.4i	0.467079	+	0.809005i	0.999293	−	0.0376052i	$-0.0119729\pi$
$661$	7937.67	+	13748.4i	0.467079	+	0.809005i	−0.532213	+	0.846610i	$0.678640\pi$
$662$	2031.35	+	3518.40i	0.119261	+	0.206566i
$663$	−380.200	+	1022.00i	−0.0222711	+	0.0598662i
$664$	1150.88	−	1993.39i	0.0672635	−	0.116504i
$665$	38755.6			2.25996
$666$	−3440.72	−	2971.19i	−0.200188	−	0.172870i
$667$	4325.06			0.251075
$668$	565.235	−	979.015i	0.0327389	−	0.0567054i
$669$	3639.64	−	615.212i	0.210339	−	0.0355538i
$670$	−8342.46	−	14449.6i	−0.481041	−	0.833187i
$671$	−16135.9	−	27948.2i	−0.928344	−	1.60794i
$672$	−2635.66	−	3186.64i	−0.151299	−	0.182927i
$673$	−10717.3	+	18563.0i	−0.613853	+	1.06323i	0.376731	+	0.926323i	$0.377048\pi$
$673$	−10717.3	+	18563.0i	−0.613853	+	1.06323i	−0.990585	+	0.136903i	$0.956285\pi$
$674$	−19596.6			−1.11993
$675$	−20.3765	+	958.544i	−0.00116191	+	0.0546583i
$676$	−7872.38			−0.447905
$677$	10166.5	−	17608.9i	0.577150	−	0.999653i	−0.418655	−	0.908146i	$-0.637498\pi$
$677$	10166.5	−	17608.9i	0.577150	−	0.999653i	0.995804	−	0.0915074i	$-0.0291685\pi$
$678$	−6780.63	−	8198.10i	−0.384083	−	0.464375i
$679$	5000.81	+	8661.66i	0.282642	+	0.489549i
$680$	−603.110	−	1044.62i	−0.0340121	−	0.0589106i
$681$	−167.341	+	28.2858i	−0.00941634	+	0.00159165i
$682$	−2538.32	+	4396.51i	−0.142518	+	0.246849i
$683$	−27149.0			−1.52097			−0.760487	−	0.649353i	$-0.775040\pi$
$683$	−27149.0			−1.52097			−0.760487	+	0.649353i	$0.775040\pi$
$684$	14621.9	−	5088.50i	0.817373	−	0.284450i
$685$	12594.4			0.702493
$686$	−1677.81	+	2906.05i	−0.0933804	+	0.161740i
$687$	−9971.53	+	26804.1i	−0.553766	+	1.48856i
$688$	−2607.12	−	4515.67i	−0.144470	−	0.250230i
$689$	1060.48	+	1836.80i	0.0586371	+	0.101562i
$690$	−753.489	+	2025.43i	−0.0415723	+	0.111749i
$691$	−11355.1	+	19667.6i	−0.625134	+	1.08276i	0.363381	+	0.931641i	$0.381622\pi$
$691$	−11355.1	+	19667.6i	−0.625134	+	1.08276i	−0.988515	+	0.151123i	$0.951711\pi$
$692$	−14130.9			−0.776266
$693$	−27106.1	+	9433.04i	−1.48582	+	0.517073i
$694$	9113.12			0.498457
$695$	−12564.0	+	21761.5i	−0.685728	+	1.18771i
$696$	9267.05	−	1566.42i	0.504694	−	0.0853088i
$697$	1409.65	+	2441.58i	0.0766056	+	0.132685i
$698$	3348.89	+	5800.45i	0.181601	+	0.314542i
$699$	−22482.8	−	27182.7i	−1.21656	−	1.47088i
$700$	339.921	−	588.760i	0.0183540	−	0.0317901i
$701$	−20079.5			−1.08187			−0.540936	−	0.841064i	$-0.681930\pi$
$701$	−20079.5			−1.08187			−0.540936	+	0.841064i	$0.681930\pi$
$702$	3720.77	−	2044.00i	0.200045	−	0.109895i
$703$	−12068.2			−0.647457
$704$	1367.71	−	2368.94i	0.0732207	−	0.126822i
$705$	393.970	+	476.328i	0.0210465	+	0.0254462i
$706$	1862.27	+	3225.54i	0.0992739	+	0.171947i
$707$	16556.6	+	28676.9i	0.880728	+	1.52547i
$708$	−2351.49	+	397.474i	−0.124822	+	0.0210989i
$709$	14491.8	−	25100.6i	0.767634	−	1.32958i	−0.171209	−	0.985235i	$-0.554767\pi$
$709$	14491.8	−	25100.6i	0.767634	−	1.32958i	0.938843	−	0.344346i	$-0.111899\pi$
$710$	−7301.74			−0.385957
$711$	517.328	+	446.733i	0.0272874	+	0.0235637i
$712$	6886.54			0.362477
$713$	−568.040	+	983.875i	−0.0298363	+	0.0516780i
$714$	1249.97	−	3359.99i	0.0655166	−	0.176113i
$715$	3514.69	+	6087.61i	0.183835	+	0.318411i
$716$	8105.49	+	14039.1i	0.423067	+	0.732774i
$717$	−777.940	+	2091.15i	−0.0405198	+	0.108920i
$718$	6179.46	−	10703.1i	0.321191	−	0.556320i
$719$	14496.2			0.751901			0.375951	−	0.926640i	$-0.377316\pi$
$719$	14496.2			0.751901			0.375951	+	0.926640i	$0.377316\pi$
$720$	−880.902	+	4612.66i	−0.0455962	+	0.238755i
$721$	−12895.4			−0.666090
$722$	13690.8	−	23713.2i	0.705706	−	1.22232i
$723$	24816.3	−	4194.72i	1.27653	−	0.215772i
$724$	5661.94	+	9806.77i	0.290641	+	0.503405i
$725$	772.541	+	1338.08i	0.0395744	+	0.0685449i
$726$	−3283.79	−	3970.26i	−0.167869	−	0.202961i
$727$	−2500.25	+	4330.56i	−0.127550	+	0.220924i	−0.922727	−	0.385454i	$-0.874045\pi$
$727$	−2500.25	+	4330.56i	−0.127550	+	0.220924i	0.795177	+	0.606378i	$0.207378\pi$
$728$	−3010.23			−0.153251
$729$	10557.0	−	16612.4i	0.536351	−	0.843995i
$730$	−3636.79			−0.184388
$731$	2260.12	−	3914.64i	0.114355	−	0.198069i
$732$	−10002.2	−	12093.1i	−0.505043	−	0.610621i
$733$	−8757.79	−	15168.9i	−0.441305	−	0.764362i	0.556482	−	0.830860i	$-0.312151\pi$
$733$	−8757.79	−	15168.9i	−0.441305	−	0.764362i	−0.997787	+	0.0664977i	$0.978817\pi$
$734$	6873.95	+	11906.0i	0.345671	+	0.598719i
$735$	−15345.9	+	2593.93i	−0.770126	+	0.130175i
$736$	306.073	−	530.134i	0.0153288	−	0.0265503i
$737$	32801.3			1.63942
$738$	2058.93	−	10781.2i	0.102697	−	0.537750i
$739$	−20169.2			−1.00397			−0.501985	−	0.864876i	$-0.667397\pi$
$739$	−20169.2			−1.00397			−0.501985	+	0.864876i	$0.667397\pi$
$740$	1830.27	−	3170.13i	0.0909219	−	0.157481i
$741$	3929.40	−	10562.5i	0.194804	−	0.523647i
$742$	−3486.48	−	6038.77i	−0.172497	−	0.298774i
$743$	18351.3	+	31785.4i	0.906116	+	1.56944i	0.819412	+	0.573205i	$0.194300\pi$
$743$	18351.3	+	31785.4i	0.906116	+	1.56944i	0.0867044	+	0.996234i	$0.472366\pi$
$744$	−860.774	+	2313.82i	−0.0424160	+	0.114017i
$745$	16035.0	−	27773.5i	0.788561	−	1.36583i
$746$	−2540.05			−0.124662
$747$	−5879.64	−	5077.29i	−0.287985	−	0.248686i
$748$	2371.34			0.115915
$749$	−18303.0	+	31701.8i	−0.892894	+	1.54654i
$750$	−14684.8	+	2482.18i	−0.714951	+	0.120849i
$751$	16660.0	+	28856.0i	0.809499	+	1.40209i	0.913212	+	0.407485i	$0.133594\pi$
$751$	16660.0	+	28856.0i	0.809499	+	1.40209i	−0.103713	+	0.994607i	$0.533072\pi$
$752$	−87.5489	−	151.639i	−0.00424545	−	0.00735334i
$753$	7951.06	+	9613.21i	0.384798	+	0.465239i
$754$	3420.69	−	5924.81i	0.165218	−	0.286166i
$755$	−18766.7			−0.904622
$756$	−12232.6	+	6719.99i	−0.588486	+	0.323285i
$757$	26515.6			1.27309			0.636543	−	0.771241i	$-0.280364\pi$
$757$	26515.6			1.27309			0.636543	+	0.771241i	$0.280364\pi$
$758$	2490.54	−	4313.74i	0.119341	−	0.206705i
$759$	−2707.72	−	3273.77i	−0.129492	−	0.156562i
$760$	6233.20	+	10796.2i	0.297502	+	0.515289i
$761$	2842.17	+	4922.79i	0.135386	+	0.234495i	0.925745	−	0.378149i	$-0.123439\pi$
$761$	2842.17	+	4922.79i	0.135386	+	0.234495i	−0.790359	+	0.612644i	$0.790106\pi$
$762$	−322.247	+	54.4698i	−0.0153199	+	0.00258954i
$763$	8004.14	−	13863.6i	0.379777	−	0.657792i
$764$	18037.0			0.854129
$765$	−3844.82	+	1338.02i	−0.181712	+	0.0632367i
$766$	−624.851			−0.0294736
$767$	−867.990	+	1503.40i	−0.0408622	+	0.0707754i
$768$	463.805	−	1246.74i	0.0217918	−	0.0585779i
$769$	199.189	+	345.005i	0.00934060	+	0.0161784i	0.870658	−	0.491889i	$-0.163693\pi$
$769$	199.189	+	345.005i	0.00934060	+	0.0161784i	−0.861317	+	0.508067i	$0.830360\pi$
$770$	−11555.1	−	20014.0i	−0.540800	−	0.936694i
$771$	5400.78	−	14517.7i	0.252275	−	0.678133i
$772$	6442.25	−	11158.3i	0.300339	−	0.520202i
$773$	−8437.17			−0.392579			−0.196290	−	0.980546i	$-0.562889\pi$
$773$	−8437.17			−0.392579			−0.196290	+	0.980546i	$0.562889\pi$
$774$	−16620.4	+	5783.98i	−0.771845	+	0.268606i
$775$	−405.853			−0.0188112
$776$	−1608.60	+	2786.17i	−0.0744140	+	0.128889i
$777$	10727.2	−	1813.23i	0.495286	−	0.0837186i
$778$	9643.17	+	16702.5i	0.444376	+	0.769681i
$779$	−14568.8	−	25233.9i	−0.670067	−	1.16059i
$780$	2178.66	+	2634.10i	0.100011	+	0.120918i
$781$	7177.34	−	12431.5i	0.328842	−	0.569570i
$782$	530.671			0.0242669
$783$	674.142	−	31712.8i	0.0307687	−	1.44741i
$784$	4408.61			0.200830
$785$	−6975.49	+	12081.9i	−0.317154	+	0.549327i
$786$	12832.0	+	15514.5i	0.582320	+	0.704052i
$787$	−8138.94	−	14097.1i	−0.368643	−	0.638508i	0.620711	−	0.784040i	$-0.286844\pi$
$787$	−8138.94	−	14097.1i	−0.368643	−	0.638508i	−0.989354	+	0.145531i	$0.953511\pi$
$788$	−7568.40	−	13108.8i	−0.342148	−	0.592618i
$789$	−28490.7	+	4815.81i	−1.28555	+	0.217297i
$790$	−275.191	+	476.644i	−0.0123935	+	0.0214661i
$791$	25460.5			1.14447
$792$	−6987.35	−	6033.84i	−0.313491	−	0.270711i
$793$	−11423.7			−0.511560
$794$	−2260.32	+	3914.99i	−0.101027	+	0.174985i
$795$	−2760.87	+	7421.41i	−0.123167	+	0.331082i
$796$	5852.53	+	10136.9i	0.260600	+	0.451372i
$797$	−2556.06	−	4427.22i	−0.113601	−	0.196763i	0.803619	−	0.595145i	$-0.202905\pi$
$797$	−2556.06	−	4427.22i	−0.113601	−	0.196763i	−0.917220	+	0.398382i	$0.869572\pi$
$798$	−12918.5	+	34725.8i	−0.573071	+	1.54045i
$799$	75.8963	−	131.456i	0.00336047	−	0.00582051i
$800$	218.683			0.00966450
$801$	4359.85	−	22829.5i	0.192319	−	1.00704i
$802$	−20338.6			−0.895485
$803$	3574.82	−	6191.77i	0.157102	−	0.272108i
$804$	15727.9	−	2658.51i	0.689903	−	0.116615i
$805$	−2585.86	−	4478.84i	−0.113217	−	0.196097i
$806$	898.526	+	1556.29i	0.0392670	+	0.0680125i
$807$	20825.9	+	25179.5i	0.908433	+	1.09834i
$808$	−5325.71	+	9224.41i	−0.231879	+	0.401626i
$809$	−13141.2			−0.571100			−0.285550	−	0.958364i	$-0.592176\pi$
$809$	−13141.2			−0.571100			−0.285550	+	0.958364i	$0.592176\pi$
$810$	14733.7	+	5840.54i	0.639122	+	0.253353i
$811$	−18614.2			−0.805957			−0.402979	−	0.915209i	$-0.632025\pi$
$811$	−18614.2			−0.805957			−0.402979	+	0.915209i	$0.632025\pi$
$812$	−11246.1	+	19478.7i	−0.486034	+	0.841835i
$813$	22701.6	+	27447.3i	0.979312	+	1.18403i
$814$	3598.18	+	6232.23i	0.154934	+	0.268353i
$815$	−5619.61	−	9733.45i	−0.241529	−	0.418341i
$816$	1137.04	−	192.194i	0.0487797	−	0.00824528i
$817$	−23358.5	+	40458.2i	−1.00026	+	1.73250i
$818$	1899.67			0.0811983
$819$	−1905.77	+	9979.18i	−0.0813102	+	0.425764i
$820$	8838.05			0.376388
$821$	5660.01	−	9803.43i	0.240604	−	0.416738i	−0.720283	−	0.693681i	$-0.755988\pi$
$821$	5660.01	−	9803.43i	0.240604	−	0.416738i	0.960886	+	0.276943i	$0.0893212\pi$
$822$	−4198.14	+	11284.9i	−0.178135	+	0.478839i
$823$	−5433.29	−	9410.73i	−0.230125	−	0.398587i	0.727720	−	0.685874i	$-0.240580\pi$
$823$	−5433.29	−	9410.73i	−0.230125	−	0.398587i	−0.957845	+	0.287287i	$0.907247\pi$
$824$	−2074.02	−	3592.30i	−0.0876843	−	0.151874i
$825$	529.179	−	1422.47i	0.0223317	−	0.0600292i
$826$	2853.65	−	4942.67i	0.120207	−	0.208205i
$827$	−13059.3			−0.549114			−0.274557	−	0.961571i	$-0.588531\pi$
$827$	−13059.3			−0.549114			−0.274557	+	0.961571i	$0.588531\pi$
$828$	−1563.67	−	1350.29i	−0.0656295	−	0.0566736i
$829$	−21203.7			−0.888341			−0.444171	−	0.895942i	$-0.646502\pi$
$829$	−21203.7			−0.888341			−0.444171	+	0.895942i	$0.646502\pi$
$830$	3127.65	−	5417.25i	0.130798	−	0.226549i
$831$	−4601.76	+	777.840i	−0.192098	+	0.0324705i
$832$	−484.146	−	838.566i	−0.0201740	−	0.0349424i
$833$	1910.92	+	3309.80i	0.0794829	+	0.137669i
$834$	−15310.8	−	18511.5i	−0.635695	−	0.768586i
$835$	1536.09	−	2660.58i	0.0636628	−	0.110267i
$836$	−24508.0			−1.01391
$837$	7125.56	+	4318.42i	0.294260	+	0.178335i
$838$	23598.5			0.972790
$839$	7240.28	−	12540.5i	0.297929	−	0.516028i	−0.677733	−	0.735308i	$-0.737038\pi$
$839$	7240.28	−	12540.5i	0.297929	−	0.516028i	0.975662	+	0.219280i	$0.0703708\pi$
$840$	−7162.68	−	8660.02i	−0.294210	−	0.355713i
$841$	−13364.5	−	23148.0i	−0.547973	−	0.949117i
$842$	−6412.93	−	11107.5i	−0.262475	−	0.454620i
$843$	−1223.33	+	206.781i	−0.0499807	+	0.00844828i
$844$	−626.948	+	1085.91i	−0.0255692	+	0.0442872i
$845$	−21394.0			−0.870979
$846$	−558.124	+	194.230i	−0.0226817	+	0.00789333i
$847$	12330.3			0.500204
$848$	1121.49	−	1942.47i	0.0454151	−	0.0786613i
$849$	3752.40	−	10086.7i	0.151687	−	0.407745i
$850$	94.7882	+	164.178i	0.00382495	+	0.00662501i
$851$	805.221	+	1394.68i	0.0324355	+	0.0561799i
$852$	2433.91	−	6542.53i	0.0978692	−	0.263079i
$853$	3233.61	−	5600.78i	0.129797	−	0.224815i	−0.793801	−	0.608178i	$-0.791901\pi$
$853$	3233.61	−	5600.78i	0.129797	−	0.224815i	0.923598	+	0.383363i	$0.125234\pi$
$854$	37557.1			1.50489
$855$	39736.6	−	13828.5i	1.58943	−	0.553130i
$856$	−11775.0			−0.470164
$857$	−1947.32	+	3372.85i	−0.0776186	+	0.134439i	−0.902222	−	0.431272i	$-0.858065\pi$
$857$	−1947.32	+	3372.85i	−0.0776186	+	0.134439i	0.824603	+	0.565711i	$0.191398\pi$
$858$	−6626.20	+	1120.03i	−0.263654	+	0.0445656i
$859$	18826.9	+	32609.1i	0.747805	+	1.29524i	0.948873	+	0.315659i	$0.102226\pi$
$859$	18826.9	+	32609.1i	0.747805	+	1.29524i	−0.201067	+	0.979577i	$0.564441\pi$
$860$	−7085.13	−	12271.8i	−0.280931	−	0.486587i
$861$	16741.3	+	20241.0i	0.662651	+	0.801176i
$862$	−12042.7	+	20858.6i	−0.475844	+	0.824186i
$863$	47067.5			1.85654			0.928271	−	0.371905i	$-0.121295\pi$
$863$	47067.5			1.85654			0.928271	+	0.371905i	$0.121295\pi$
$864$	−3839.41	−	2326.86i	−0.151180	−	0.0916221i
$865$	−38402.2			−1.50950
$866$	7279.83	−	12609.0i	0.285657	−	0.494772i
$867$	−15633.4	−	18901.6i	−0.612386	−	0.740404i
$868$	−2954.05	−	5116.56i	−0.115515	−	0.200077i
$869$	−541.004	−	937.046i	−0.0211189	−	0.0365790i
$870$	25184.2	−	4256.91i	0.981408	−	0.165888i
$871$	5805.56	−	10055.5i	0.225848	−	0.391181i
$872$	5149.34			0.199976
$873$	8218.01	+	7096.56i	0.318600	+	0.275123i
$874$	−5484.53			−0.212262
$875$	17820.8	−	30866.5i	0.688517	−	1.19255i
$876$	1212.26	−	3258.64i	0.0467563	−	0.125684i
$877$	3721.77	+	6446.29i	0.143301	+	0.248205i	0.928738	−	0.370737i	$-0.120895\pi$
$877$	3721.77	+	6446.29i	0.143301	+	0.248205i	−0.785437	+	0.618942i	$0.787562\pi$
$878$	−3598.70	−	6233.13i	−0.138326	−	0.239588i
$879$	−11917.2	+	32034.2i	−0.457288	+	1.22922i
$880$	3716.89	−	6437.84i	0.142382	−	0.246613i
$881$	−13781.9			−0.527040			−0.263520	−	0.964654i	$-0.584884\pi$
$881$	−13781.9			−0.527040			−0.263520	+	0.964654i	$0.584884\pi$
$882$	2791.08	−	14614.9i	0.106554	−	0.557948i
$883$	12230.3			0.466119			0.233060	−	0.972462i	$-0.425126\pi$
$883$	12230.3			0.466119			0.233060	+	0.972462i	$0.425126\pi$
$884$	419.707	−	726.954i	0.0159686	−	0.0276585i
$885$	−6390.42	+	1080.18i	−0.242725	+	0.0410280i
$886$	−14786.4	−	25610.7i	−0.560674	−	0.971116i
$887$	837.437	+	1450.48i	0.0317005	+	0.0549069i	0.881440	−	0.472295i	$-0.156574\pi$
$887$	837.437	+	1450.48i	0.0317005	+	0.0549069i	−0.849740	+	0.527202i	$0.823241\pi$
$888$	2230.41	+	2696.68i	0.0842881	+	0.101908i
$889$	391.064	−	677.343i	0.0147535	−	0.0255538i
$890$	18714.9			0.704859
$891$	−24426.4	+	19343.7i	−0.918423	+	0.727314i
$892$	−2841.54			−0.106661
$893$	−784.395	+	1358.61i	−0.0293939	+	0.0509118i
$894$	19540.7	+	23625.6i	0.731026	+	0.883845i
$895$	22027.5	+	38152.8i	0.822680	+	1.42492i
$896$	1591.71	+	2756.92i	0.0593473	+	0.102793i
$897$	−1482.85	+	250.647i	−0.0551960	+	0.00932983i
$898$	114.489	−	198.302i	0.00425452	−	0.00736905i
$899$	13427.4			0.498140
$900$	138.448	−	724.953i	0.00512769	−	0.0268501i
$901$	1944.44			0.0718964
$902$	−8687.47	+	15047.1i	−0.320689	+	0.555449i
$903$	14684.2	−	39472.1i	0.541151	−	1.45465i
$904$	4094.91	+	7092.59i	0.150658	+	0.260947i
$905$	15386.9	+	26650.9i	0.565170	+	0.978903i
$906$	6255.56	−	16815.4i	0.229390	−	0.616615i
$907$	−8544.04	+	14798.7i	−0.312790	+	0.541768i	−0.978965	−	0.204027i	$-0.934597\pi$
$907$	−8544.04	+	14798.7i	−0.312790	+	0.541768i	0.666175	+	0.745795i	$0.267930\pi$
$908$	130.647			0.00477496
$909$	27208.0	+	23495.2i	0.992776	+	0.857300i
$910$	−8180.63			−0.298006
$911$	−10644.2	+	18436.3i	−0.387111	+	0.670496i	−0.992060	−	0.125769i	$-0.959860\pi$
$911$	−10644.2	+	18436.3i	−0.387111	+	0.670496i	0.604949	+	0.796264i	$0.293194\pi$
$912$	−11751.4	+	1986.35i	−0.426674	+	0.0721211i
$913$	6148.72	+	10649.9i	0.222884	+	0.386046i
$914$	6311.14	+	10931.2i	0.228396	+	0.395593i
$915$	−27182.0	−	32864.4i	−0.982088	−	1.18739i
$916$	11007.7	−	19065.9i	0.397057	−	0.687723i
$917$	−48182.8			−1.73516
$918$	82.7150	−	3891.05i	0.00297386	−	0.139895i
$919$	−10413.4			−0.373784			−0.186892	−	0.982380i	$-0.559841\pi$
$919$	−10413.4			−0.373784			−0.186892	+	0.982380i	$0.559841\pi$
$920$	831.786	−	1440.70i	0.0298078	−	0.0516286i
$921$	−17344.6	−	20970.4i	−0.620546	−	0.750270i
$922$	−13744.8	−	23806.7i	−0.490956	−	0.850361i
$923$	−2540.66	−	4400.55i	−0.0906033	−	0.156930i
$924$	21784.7	−	3682.28i	0.775609	−	0.131102i
$925$	−287.657	+	498.236i	−0.0102250	+	0.0177102i
$926$	−31297.2			−1.11068
$927$	−13221.9	+	4601.27i	−0.468461	+	0.163027i
$928$	−7234.98			−0.255926
$929$	3411.72	−	5909.26i	0.120490	−	0.208694i	−0.799471	−	0.600704i	$-0.794887\pi$
$929$	3411.72	−	5909.26i	0.120490	−	0.208694i	0.919961	+	0.392010i	$0.128220\pi$
$930$	−2339.25	+	6288.05i	−0.0824805	+	0.221713i
$931$	−19749.5	−	34207.1i	−0.695234	−	1.20418i
$932$	13577.6	+	23517.1i	0.477199	+	0.826534i
$933$	10335.9	−	27783.7i	0.362683	−	0.974917i
$934$	−7395.79	+	12809.9i	−0.259098	+	0.448771i
$935$	6444.36			0.225404
$936$	−3086.43	+	1074.09i	−0.107781	+	0.0375084i
$937$	41049.8			1.43120			0.715602	−	0.698508i	$-0.246152\pi$
$937$	41049.8			1.43120			0.715602	+	0.698508i	$0.246152\pi$
$938$	−19086.7	+	33059.1i	−0.664395	+	1.15077i
$939$	−26014.3	+	4397.23i	−0.904096	+	0.152820i
$940$	−237.923	−	412.095i	−0.00825554	−	0.0142990i
$941$	−1208.06	−	2092.42i	−0.0418508	−	0.0724878i	0.844341	−	0.535806i	$-0.179992\pi$
$941$	−1208.06	−	2092.42i	−0.0418508	−	0.0724878i	−0.886192	+	0.463318i	$0.846659\pi$
$942$	−8500.49	−	10277.5i	−0.294014	−	0.355477i
$943$	−1944.13	+	3367.33i	−0.0671364	+	0.116284i
$944$	1835.85			0.0632966
$945$	−33243.4	+	18262.3i	−1.14435	+	0.628648i
$946$	27857.7			0.957432
$947$	1197.04	−	2073.33i	0.0410755	−	0.0711448i	−0.844757	−	0.535150i	$-0.820255\pi$
$947$	1197.04	−	2073.33i	0.0410755	−	0.0711448i	0.885832	+	0.464006i	$0.153588\pi$
$948$	−335.354	−	405.458i	−0.0114892	−	0.0138910i
$949$	−1265.43	−	2191.79i	−0.0432851	−	0.0749720i
$950$	−979.645	−	1696.79i	−0.0334567	−	0.0579487i
$951$	−14698.8	+	2484.55i	−0.501200	+	0.0847182i
$952$	−1379.85	+	2389.98i	−0.0469762	+	0.0813651i
$953$	−50651.3			−1.72168			−0.860838	−	0.508879i	$-0.830060\pi$
$953$	−50651.3			−1.72168			−0.860838	+	0.508879i	$0.830060\pi$
$954$	−5729.46	−	4947.61i	−0.194442	−	0.167909i
$955$	49017.4			1.66091
$956$	858.777	−	1487.45i	0.0290532	−	0.0503216i
$957$	−17507.6	+	47061.5i	−0.591368	+	1.58964i
$958$	−6261.07	−	10844.5i	−0.211154	−	0.365730i
$959$	−14407.4	−	24954.3i	−0.485128	−	0.840267i
$960$	1260.44	−	3388.14i	0.0423755	−	0.113908i
$961$	13132.0	−	22745.3i	0.440804	−	0.763495i
$962$	2547.40			0.0853756
$963$	−7454.71	+	39035.0i	−0.249454	+	1.30622i
$964$	−19374.6			−0.647317
$965$	17507.5	−	30323.9i	0.584027	−	1.01156i
$966$	4875.10	−	824.042i	0.162374	−	0.0274463i
$967$	−12517.5	−	21680.9i	−0.416271	−	0.721003i	0.579290	−	0.815122i	$-0.303330\pi$
$967$	−12517.5	−	21680.9i	−0.416271	−	0.721003i	−0.995561	+	0.0941189i	$0.969997\pi$
$968$	1983.12	+	3434.87i	0.0658471	+	0.114050i
$969$	−6584.91	−	7961.47i	−0.218305	−	0.263941i
$970$	−4371.54	+	7571.72i	−0.144703	+	0.250632i
$971$	49553.7			1.63775			0.818875	−	0.573972i	$-0.194598\pi$
$971$	49553.7			1.63775			0.818875	+	0.573972i	$0.194598\pi$
$972$	−10144.5	+	11254.9i	−0.334758	+	0.371399i
$973$	57490.4			1.89420
$974$	−10314.7	+	17865.6i	−0.339327	+	0.587732i
$975$	−342.411	−	413.991i	−0.0112471	−	0.0135983i
$976$	6040.45	+	10462.4i	0.198105	+	0.343127i
$977$	17588.1	+	30463.5i	0.575939	+	0.997556i	0.995939	+	0.0900320i	$0.0286969\pi$
$977$	17588.1	+	30463.5i	0.575939	+	0.997556i	−0.419999	+	0.907524i	$0.637970\pi$
$978$	10594.6	−	1790.81i	0.346399	−	0.0585521i
$979$	−18396.0	+	31862.9i	−0.600551	+	1.04019i
$980$	11980.9			0.390525
$981$	3260.04	−	17070.5i	0.106101	−	0.555576i
$982$	5521.79			0.179437
$983$	−16674.6	+	28881.3i	−0.541036	+	0.937102i	0.457809	+	0.889051i	$0.348634\pi$
$983$	−16674.6	+	28881.3i	−0.541036	+	0.937102i	−0.998845	+	0.0480511i	$0.984699\pi$
$984$	−2946.02	+	7919.09i	−0.0954427	+	0.256556i
$985$	−20567.9	−	35624.7i	−0.665328	−	1.15238i
$986$	−3136.01	−	5431.72i	−0.101289	−	0.175437i
$987$	493.105	−	1325.50i	0.0159024	−	0.0427468i
$988$	−4337.71	+	7513.14i	−0.139677	+	0.241928i
$989$	6234.14			0.200439
$990$	−18988.9	−	16397.6i	−0.609602	−	0.526414i
$991$	23066.3			0.739378			0.369689	−	0.929156i	$-0.379464\pi$
$991$	23066.3			0.739378			0.369689	+	0.929156i	$0.379464\pi$
$992$	950.220	−	1645.83i	0.0304128	−	0.0526765i
$993$	−10407.6	+	1759.20i	−0.332602	+	0.0562201i
$994$	8352.82	+	14467.5i	0.266535	+	0.461652i
$995$	15904.9	+	27548.1i	0.506752	+	0.877721i
$996$	3811.43	+	4608.19i	0.121255	+	0.146603i
$997$	27884.9	−	48298.1i	0.885782	−	1.53422i	0.0409671	−	0.999160i	$-0.486956\pi$
$997$	27884.9	−	48298.1i	0.885782	−	1.53422i	0.844815	−	0.535059i	$-0.179711\pi$
$998$	19172.0			0.608095
$999$	10351.8	−	5686.76i	0.327844	−	0.180101i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.4.c.b.7.2	✓	4
3.2	odd	2		54.4.c.b.19.2		4
4.3	odd	2		144.4.i.b.97.1		4
9.2	odd	6		162.4.a.g.1.1		2
9.4	even	3	inner	18.4.c.b.13.2	yes	4
9.5	odd	6		54.4.c.b.37.2		4
9.7	even	3		162.4.a.f.1.2		2
12.11	even	2		432.4.i.b.289.2		4
36.7	odd	6		1296.4.a.l.1.2		2
36.11	even	6		1296.4.a.r.1.1		2
36.23	even	6		432.4.i.b.145.2		4
36.31	odd	6		144.4.i.b.49.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.4.c.b.7.2	✓	4	1.1	even	1	trivial
18.4.c.b.13.2	yes	4	9.4	even	3	inner
54.4.c.b.19.2		4	3.2	odd	2
54.4.c.b.37.2		4	9.5	odd	6
144.4.i.b.49.1		4	36.31	odd	6
144.4.i.b.97.1		4	4.3	odd	2
162.4.a.f.1.2		2	9.7	even	3
162.4.a.g.1.1		2	9.2	odd	6
432.4.i.b.145.2		4	36.23	even	6
432.4.i.b.289.2		4	12.11	even	2
1296.4.a.l.1.2		2	36.7	odd	6
1296.4.a.r.1.1		2	36.11	even	6

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:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	18.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(3.31174 + 4.00405i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-5.43521 - 9.41407i) q^{5} +(10.2470 - 1.73205i) q^{6} +(-12.4352 + 21.5384i) q^{7} -8.00000 q^{8} +(-5.06479 + 26.5207i) q^{9} -21.7409 q^{10} +(21.3704 - 37.0147i) q^{11} +(7.24695 - 19.4803i) q^{12} +(-7.56479 - 13.1026i) q^{13} +(24.8704 + 43.0768i) q^{14} +(19.6944 - 52.9398i) q^{15} +(-8.00000 + 13.8564i) q^{16} -13.8704 q^{17} +(40.8704 + 35.2932i) q^{18} +143.352 q^{19} +(-21.7409 + 37.6563i) q^{20} +(-127.423 + 21.5384i) q^{21} +(-42.7409 - 74.0293i) q^{22} +(-9.56479 - 16.5667i) q^{23} +(-26.4939 - 32.0324i) q^{24} +(3.41692 - 5.91828i) q^{25} -30.2591 q^{26} +(-122.963 + 67.5500i) q^{27} +99.4817 q^{28} +(-113.046 + 195.802i) q^{29} +(-72.0000 - 87.0514i) q^{30} +(-29.6944 - 51.4321i) q^{31} +(16.0000 + 27.7128i) q^{32} +(218.982 - 37.0147i) q^{33} +(-13.8704 + 24.0243i) q^{34} +270.352 q^{35} +(102.000 - 35.4965i) q^{36} -84.1860 q^{37} +(143.352 - 248.293i) q^{38} +(27.4108 - 73.6821i) q^{39} +(43.4817 + 75.3125i) q^{40} +(-101.630 - 176.028i) q^{41} +(-90.1174 + 242.242i) q^{42} +(-162.945 + 282.229i) q^{43} -170.963 q^{44} +(277.196 - 96.4655i) q^{45} -38.2591 q^{46} +(-5.47180 + 9.47744i) q^{47} +(-81.9756 + 13.8564i) q^{48} +(-137.769 - 238.623i) q^{49} +(-6.83384 - 11.8366i) q^{50} +(-45.9352 - 55.5378i) q^{51} +(-30.2591 + 52.4104i) q^{52} -140.186 q^{53} +(-5.96341 + 280.529i) q^{54} -464.611 q^{55} +(99.4817 - 172.307i) q^{56} +(474.745 + 573.989i) q^{57} +(226.093 + 391.605i) q^{58} +(-57.3704 - 99.3685i) q^{59} +(-222.777 + 37.6563i) q^{60} +(377.528 - 653.898i) q^{61} -118.777 q^{62} +(-508.232 - 438.878i) q^{63} +64.0000 q^{64} +(-82.2325 + 142.431i) q^{65} +(154.870 - 416.302i) q^{66} +(383.723 + 664.627i) q^{67} +(27.7409 + 48.0486i) q^{68} +(34.6578 - 93.1624i) q^{69} +(270.352 - 468.264i) q^{70} +335.854 q^{71} +(40.5183 - 212.166i) q^{72} +167.279 q^{73} +(-84.1860 + 145.814i) q^{74} +(35.0130 - 5.91828i) q^{75} +(-286.704 - 496.586i) q^{76} +(531.492 + 920.570i) q^{77} +(-100.210 - 121.159i) q^{78} +(12.6578 - 21.9239i) q^{79} +173.927 q^{80} +(-677.696 - 268.643i) q^{81} -406.518 q^{82} +(-143.861 + 249.174i) q^{83} +(329.457 + 398.329i) q^{84} +(75.3887 + 130.577i) q^{85} +(325.890 + 564.458i) q^{86} +(-1158.38 + 195.802i) q^{87} +(-170.963 + 296.117i) q^{88} -860.817 q^{89} +(110.113 - 576.583i) q^{90} +376.279 q^{91} +(-38.2591 + 66.2668i) q^{92} +(107.597 - 289.227i) q^{93} +(10.9436 + 18.9549i) q^{94} +(-779.149 - 1349.53i) q^{95} +(-57.9756 + 155.842i) q^{96} +(201.075 - 348.272i) q^{97} -551.076 q^{98} +(873.418 + 754.230i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 3 q^{3} - 8 q^{4} + 9 q^{5} - 19 q^{7} - 32 q^{8} - 51 q^{9} + 36 q^{10} + 24 q^{11} - 12 q^{12} - 61 q^{13} + 38 q^{14} + 171 q^{15} - 32 q^{16} + 6 q^{17} + 102 q^{18} + 266 q^{19} + 36 q^{20}+ \cdots + 1557 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 3 * q^3 - 8 * q^4 + 9 * q^5 - 19 * q^7 - 32 * q^8 - 51 * q^9 + 36 * q^10 + 24 * q^11 - 12 * q^12 - 61 * q^13 + 38 * q^14 + 171 * q^15 - 32 * q^16 + 6 * q^17 + 102 * q^18 + 266 * q^19 + 36 * q^20 - 315 * q^21 - 48 * q^22 - 69 * q^23 - 24 * q^24 - 263 * q^25 - 244 * q^26 + 152 * q^28 - 237 * q^29 - 288 * q^30 - 211 * q^31 + 64 * q^32 + 630 * q^33 + 6 * q^34 + 774 * q^35 + 408 * q^36 + 524 * q^37 + 266 * q^38 - 249 * q^39 - 72 * q^40 - 468 * q^41 - 258 * q^42 + 86 * q^43 - 192 * q^44 - 459 * q^45 - 276 * q^46 - 483 * q^47 + 33 * q^49 + 526 * q^50 - 153 * q^51 - 244 * q^52 + 300 * q^53 + 468 * q^54 - 1674 * q^55 + 152 * q^56 + 987 * q^57 + 474 * q^58 - 168 * q^59 - 1260 * q^60 + 1049 * q^61 - 844 * q^62 - 957 * q^63 + 256 * q^64 + 747 * q^65 + 558 * q^66 + 1166 * q^67 - 12 * q^68 - 261 * q^69 + 774 * q^70 - 624 * q^71 + 408 * q^72 - 622 * q^73 + 524 * q^74 + 2835 * q^75 - 532 * q^76 + 1173 * q^77 + 132 * q^78 - 349 * q^79 - 288 * q^80 - 1143 * q^81 - 1872 * q^82 - 1221 * q^83 + 744 * q^84 + 486 * q^85 - 172 * q^86 - 2205 * q^87 - 192 * q^88 - 984 * q^89 - 1404 * q^90 + 214 * q^91 - 276 * q^92 - 789 * q^93 + 966 * q^94 - 1764 * q^95 + 96 * q^96 + 128 * q^97 + 132 * q^98 + 1557 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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