LMFDB - Embedded newform 18.4.c.b.13.2

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			13.2
Root			$-2.31174 + 1.91203i$ of defining polynomial
Character	$\chi$	$=$	18.13
Dual form			18.4.c.b.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(3.31174 - 4.00405i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-5.43521 + 9.41407i) q^{5} +(10.2470 + 1.73205i) q^{6} +(-12.4352 - 21.5384i) q^{7} -8.00000 q^{8} +(-5.06479 - 26.5207i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 4 * q + 4 * q^2 + 3 * q^3 - 8 * q^4 + 9 * q^5 - 19 * q^7 - 32 * q^8 - 51 * q^9	\( 4 q + 4 q^{2} + 3 q^{3} - 8 q^{4} + 9 q^{5} - 19 q^{7} - 32 q^{8} - 51 q^{9} + 36 q^{10} + 24 q^{11} - 12 q^{12} - 61 q^{13} + 38 q^{14} + 171 q^{15} - 32 q^{16} + 6 q^{17} + 102 q^{18} + 266 q^{19} + 36 q^{20} - 315 q^{21} - 48 q^{22} - 69 q^{23} - 24 q^{24} - 263 q^{25} - 244 q^{26} + 152 q^{28} - 237 q^{29} - 288 q^{30} - 211 q^{31} + 64 q^{32} + 630 q^{33} + 6 q^{34} + 774 q^{35} + 408 q^{36} + 524 q^{37} + 266 q^{38} - 249 q^{39} - 72 q^{40} - 468 q^{41} - 258 q^{42} + 86 q^{43} - 192 q^{44} - 459 q^{45} - 276 q^{46} - 483 q^{47} + 33 q^{49} + 526 q^{50} - 153 q^{51} - 244 q^{52} + 300 q^{53} + 468 q^{54} - 1674 q^{55} + 152 q^{56} + 987 q^{57} + 474 q^{58} - 168 q^{59} - 1260 q^{60} + 1049 q^{61} - 844 q^{62} - 957 q^{63} + 256 q^{64} + 747 q^{65} + 558 q^{66} + 1166 q^{67} - 12 q^{68} - 261 q^{69} + 774 q^{70} - 624 q^{71} + 408 q^{72} - 622 q^{73} + 524 q^{74} + 2835 q^{75} - 532 q^{76} + 1173 q^{77} + 132 q^{78} - 349 q^{79} - 288 q^{80} - 1143 q^{81} - 1872 q^{82} - 1221 q^{83} + 744 q^{84} + 486 q^{85} - 172 q^{86} - 2205 q^{87} - 192 q^{88} - 984 q^{89} - 1404 q^{90} + 214 q^{91} - 276 q^{92} - 789 q^{93} + 966 q^{94} - 1764 q^{95} + 96 q^{96} + 128 q^{97} + 132 q^{98} + 1557 q^{99}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$11$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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	−0.999873	−	0.0159306i	$-0.994929\pi$
$5$	−5.43521	+	9.41407i	−0.486140	+	0.842020i	0.513733	+	0.857950i	$0.328262\pi$
$6$	10.2470	+	1.73205i	0.697217	+	0.117851i
$7$	−12.4352	−	21.5384i	−0.671438	−	1.16297i	−0.977496	−	0.210953i	$-0.932343\pi$
$7$	−12.4352	−	21.5384i	−0.671438	−	1.16297i	0.306058	−	0.952013i	$-0.400990\pi$
$8$	−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	0.994779	+	0.102048i	$0.0325396\pi$
$11$	21.3704	+	37.0147i	0.585766	+	1.01458i	−0.409013	+	0.912528i	$0.634127\pi$
$12$	7.24695	+	19.4803i	0.174335	+	0.468623i
$13$	−7.56479	+	13.1026i	−0.161392	+	0.279539i	−0.935368	−	0.353676i	$-0.884932\pi$
$13$	−7.56479	+	13.1026i	−0.161392	+	0.279539i	0.773976	+	0.633215i	$0.218265\pi$
$14$	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	−0.906120	−	0.423021i	$-0.860970\pi$
$23$	−9.56479	+	16.5667i	−0.0867129	+	0.150191i	0.819407	+	0.573212i	$0.194303\pi$
$24$	−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	−0.959438	−	0.281920i	$-0.909029\pi$
$29$	−113.046	−	195.802i	−0.723869	−	1.25378i	0.235569	−	0.971858i	$-0.424305\pi$
$30$	−72.0000	+	87.0514i	−0.438178	+	0.529778i
$31$	−29.6944	+	51.4321i	−0.172041	+	0.297983i	−0.939133	−	0.343553i	$-0.888369\pi$
$31$	−29.6944	+	51.4321i	−0.172041	+	0.297983i	0.767092	+	0.641537i	$0.221703\pi$
$32$	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	−0.992061	−	0.125760i	$-0.959863\pi$
$41$	−101.630	+	176.028i	−0.387119	+	0.670510i	0.604942	+	0.796270i	$0.293196\pi$
$42$	−90.1174	−	242.242i	−0.331081	−	0.889969i
$43$	−162.945	−	282.229i	−0.577881	−	1.00092i	−0.995722	−	0.0923995i	$-0.970546\pi$
$43$	−162.945	−	282.229i	−0.577881	−	1.00092i	0.417841	−	0.908520i	$-0.362787\pi$
$44$	−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	0.857410	−	0.514635i	$-0.172072\pi$
$47$	−5.47180	−	9.47744i	−0.0169818	−	0.0294133i	−0.874391	+	0.485221i	$0.838739\pi$
$48$	−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	−0.922355	−	0.386345i	$-0.873738\pi$
$59$	−57.3704	+	99.3685i	−0.126593	+	0.219266i	0.795761	+	0.605610i	$0.207071\pi$
$60$	−222.777	−	37.6563i	−0.479341	−	0.0810234i
$61$	377.528	+	653.898i	0.792419	+	1.37251i	0.924465	+	0.381266i	$0.124512\pi$
$61$	377.528	+	653.898i	0.792419	+	1.37251i	−0.132047	+	0.991243i	$0.542155\pi$
$62$	−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	−0.268885	−	0.963172i	$-0.586655\pi$
$67$	383.723	−	664.627i	0.699689	−	1.21190i	0.968574	−	0.248725i	$-0.0800115\pi$
$68$	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	0.874898	−	0.484307i	$-0.160928\pi$
$79$	12.6578	+	21.9239i	0.0180267	+	0.0312232i	−0.856871	+	0.515530i	$0.827595\pi$
$80$	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	0.755083	−	0.655629i	$-0.227597\pi$
$83$	−143.861	−	249.174i	−0.190250	−	0.329523i	−0.945333	+	0.326107i	$0.894263\pi$
$84$	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	0.951863	−	0.306523i	$-0.0991657\pi$
$97$	201.075	+	348.272i	0.210475	+	0.364553i	−0.741389	+	0.671076i	$0.765832\pi$
$98$	−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	0.981680	+	0.190540i	$0.0610237\pi$
$101$	665.714	+	1153.05i	0.655852	+	1.13597i	−0.325828	+	0.945429i	$0.605643\pi$
$102$	−142.130	−	24.0243i	−0.137970	−	0.0233212i
$103$	259.252	−	449.038i	0.248009	−	0.429563i	−0.714965	−	0.699161i	$-0.753557\pi$
$103$	259.252	−	449.038i	0.248009	−	0.429563i	0.962973	+	0.269597i	$0.0868905\pi$
$104$	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	−0.996525	−	0.0832976i	$-0.973455\pi$
$113$	−511.864	+	886.574i	−0.426125	+	0.738069i	0.570400	+	0.821367i	$0.306788\pi$
$114$	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	−0.337997	−	0.941147i	$-0.609749\pi$
$131$	968.678	−	1677.80i	0.646059	−	1.11901i	0.984056	−	0.177860i	$-0.0569174\pi$
$132$	−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	0.626908	−	0.779093i	$-0.284320\pi$
$137$	−579.297	−	1003.37i	−0.361261	−	0.625722i	−0.988169	+	0.153372i	$0.950987\pi$
$138$	−126.704	+	153.191i	−0.0781578	+	0.0944965i
$139$	−1155.80	+	2001.90i	−0.705277	+	1.22158i	0.261314	+	0.965254i	$0.415844\pi$
$139$	−1155.80	+	2001.90i	−0.705277	+	1.22158i	−0.966591	+	0.256323i	$0.917489\pi$
$140$	−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	−0.101092	−	0.994877i	$-0.532234\pi$
$149$	1475.11	−	2554.96i	0.811043	−	1.40477i	0.912135	−	0.409890i	$-0.134433\pi$
$150$	24.7622	+	66.5625i	0.0134789	+	0.0362321i
$151$	863.199	+	1495.10i	0.465206	+	0.805761i	0.999211	−	0.0397208i	$-0.0126469\pi$
$151$	863.199	+	1495.10i	0.465206	+	0.805761i	−0.534005	+	0.845482i	$0.679314\pi$
$152$	−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	−0.981754	−	0.190157i	$-0.939100\pi$
$157$	−641.694	+	1111.45i	−0.326196	+	0.564988i	0.655558	+	0.755145i	$0.272434\pi$
$158$	−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	−0.831428	−	0.555632i	$-0.812476\pi$
$167$	141.309	−	244.754i	0.0654778	−	0.113411i	0.896906	+	0.442222i	$0.145810\pi$
$168$	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	0.934080	+	0.357063i	$0.116222\pi$
$173$	1766.36	+	3059.43i	0.776266	+	1.34453i	−0.157814	+	0.987469i	$0.550445\pi$
$174$	−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	−0.877451	−	0.479667i	$-0.840757\pi$
$191$	−2254.62	−	3905.12i	−0.854129	−	1.47940i	0.0233215	−	0.999728i	$-0.492576\pi$
$192$	211.951	−	256.259i	0.0796680	−	0.0963224i
$193$	1610.56	−	2789.58i	0.600678	−	1.04040i	−0.392041	−	0.919948i	$-0.628231\pi$
$193$	1610.56	−	2789.58i	0.600678	−	1.04040i	0.992719	−	0.120457i	$-0.0384359\pi$
$194$	−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	−0.890462	−	0.455059i	$-0.849618\pi$
$211$	−156.737	+	271.476i	−0.0511385	+	0.0885744i	0.839323	+	0.543633i	$0.182952\pi$
$212$	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	0.914416	−	0.404776i	$-0.132651\pi$
$223$	355.193	+	615.212i	0.106661	+	0.184743i	−0.807754	+	0.589519i	$0.799317\pi$
$224$	−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	0.863628	−	0.504130i	$-0.168187\pi$
$227$	−16.3308	−	28.2858i	−0.00477496	−	0.00827046i	−0.868403	+	0.495859i	$0.834853\pi$
$228$	1038.87	+	2792.54i	0.301757	+	0.811143i
$229$	2751.92	−	4766.47i	0.794114	−	1.37545i	−0.129286	−	0.991607i	$-0.541268\pi$
$229$	2751.92	−	4766.47i	0.794114	−	1.37545i	0.923400	−	0.383839i	$-0.125398\pi$
$230$	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	−0.835509	−	0.549477i	$-0.814827\pi$
$239$	214.694	−	371.862i	0.0581064	−	0.100643i	0.893615	+	0.448834i	$0.148160\pi$
$240$	576.000	−	696.411i	0.154919	−	0.187305i
$241$	2421.82	+	4194.72i	0.647317	+	1.12119i	0.983761	+	0.179483i	$0.0574424\pi$
$241$	2421.82	+	4194.72i	0.647317	+	1.12119i	−0.336444	+	0.941703i	$0.609224\pi$
$242$	−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	−0.988252	−	0.152833i	$-0.951160\pi$
$257$	−1490.50	+	2581.62i	−0.361769	+	0.626602i	0.626483	+	0.779435i	$0.284494\pi$
$258$	−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	−0.982664	−	0.185398i	$-0.940643\pi$
$263$	−2780.41	−	4815.81i	−0.651891	−	1.12911i	0.330773	−	0.943710i	$-0.392691\pi$
$264$	−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	0.813201	−	0.581983i	$-0.197723\pi$
$277$	−449.086	−	777.840i	−0.0974114	−	0.168722i	−0.910612	+	0.413261i	$0.864390\pi$
$278$	−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	0.853075	−	0.521789i	$-0.174735\pi$
$281$	−119.385	−	206.781i	−0.0253448	−	0.0438986i	−0.878420	+	0.477890i	$0.841402\pi$
$282$	−39.6539	−	106.592i	−0.00837360	−	0.0225088i
$283$	−1035.58	+	1793.68i	−0.217523	+	0.376760i	−0.954050	−	0.299647i	$-0.903131\pi$
$283$	−1035.58	+	1793.68i	−0.217523	+	0.376760i	0.736527	+	0.676408i	$0.236464\pi$
$284$	−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	−0.325939	−	0.945391i	$-0.605681\pi$
$293$	3288.88	−	5696.51i	0.655763	−	1.13581i	0.981702	−	0.190423i	$-0.0609861\pi$
$294$	−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	0.479630	+	0.877471i	$0.340771\pi$
$311$	−2852.49	+	4940.67i	−0.520097	+	0.900834i	−0.999727	+	0.0233635i	$0.992562\pi$
$312$	−219.287	−	589.457i	−0.0397906	−	0.106960i
$313$	−2538.74	−	4397.23i	−0.458460	−	0.794076i	0.540420	−	0.841396i	$-0.318265\pi$
$313$	−2538.74	−	4397.23i	−0.458460	−	0.794076i	−0.998880	+	0.0473193i	$0.984932\pi$
$314$	−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	0.710511	−	0.703686i	$-0.248464\pi$
$317$	−1434.46	−	2484.55i	−0.254155	−	0.440209i	−0.964666	+	0.263477i	$0.915131\pi$
$318$	−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	0.769289	−	0.638901i	$-0.220611\pi$
$331$	−1015.67	−	1759.20i	−0.168660	−	0.292128i	−0.937949	+	0.346773i	$0.887277\pi$
$332$	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	0.132875	+	0.991133i	$0.457579\pi$
$337$	−4899.14	+	8485.56i	−0.791909	+	1.37163i	−0.924784	+	0.380493i	$0.875754\pi$
$338$	−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	−0.634218	−	0.773154i	$-0.718678\pi$
$347$	2278.28	−	3946.10i	0.352463	−	0.610483i	0.986680	+	0.162671i	$0.0520111\pi$
$348$	2995.04	−	3621.15i	0.461354	−	0.557799i
$349$	−1674.44	−	2900.22i	−0.256822	−	0.444829i	0.708567	−	0.705644i	$-0.249342\pi$
$349$	−1674.44	−	2900.22i	−0.256822	−	0.444829i	−0.965389	+	0.260815i	$0.916009\pi$
$350$	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	0.787251	−	0.616633i	$-0.211504\pi$
$353$	−931.134	−	1612.77i	−0.140395	−	0.243170i	−0.927645	+	0.373463i	$0.878170\pi$
$354$	−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	0.511066	−	0.859542i	$-0.329251\pi$
$367$	−3436.98	−	5953.02i	−0.488852	−	0.846717i	−0.999918	+	0.0128251i	$0.995918\pi$
$368$	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	−0.906729	−	0.421714i	$-0.861429\pi$
$373$	−635.013	+	1099.87i	−0.0881494	+	0.152679i	0.818580	+	0.574393i	$0.194762\pi$
$374$	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	−0.876258	−	0.481843i	$-0.839968\pi$
$383$	−156.213	+	270.568i	−0.0208410	+	0.0360976i	0.855417	+	0.517940i	$0.173301\pi$
$384$	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	−0.987864	−	0.155319i	$-0.950360\pi$
$389$	−4821.58	−	8351.23i	−0.628442	−	1.08849i	0.359422	−	0.933175i	$-0.382974\pi$
$390$	−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	0.353689	+	0.935363i	$0.384927\pi$
$401$	−5084.64	+	8806.85i	−0.633204	+	1.09674i	−0.986893	+	0.161378i	$0.948406\pi$
$402$	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	−0.835889	−	0.548899i	$-0.815047\pi$
$409$	474.916	−	822.579i	0.0574159	−	0.0994472i	0.893305	+	0.449452i	$0.148381\pi$
$410$	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	−0.284660	−	0.958628i	$-0.591881\pi$
$419$	5899.63	−	10218.5i	0.687866	−	1.19142i	0.972527	−	0.232791i	$-0.0747859\pi$
$420$	1959.23	+	5266.54i	0.227620	+	0.611859i
$421$	3206.46	+	5553.76i	0.371196	+	0.642930i	0.989750	−	0.142812i	$-0.0456145\pi$
$421$	3206.46	+	5553.76i	0.371196	+	0.642930i	−0.618554	+	0.785742i	$0.712281\pi$
$422$	−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	0.947104	−	0.320926i	$-0.103994\pi$
$439$	1799.35	+	3116.57i	0.195623	+	0.338828i	−0.751482	+	0.659754i	$0.770661\pi$
$440$	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	0.924156	+	0.382016i	$0.124770\pi$
$443$	7393.18	+	12805.4i	0.792913	+	1.37337i	−0.131243	+	0.991350i	$0.541897\pi$
$444$	−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	0.658105	−	0.752926i	$-0.271358\pi$
$457$	−3155.57	−	5465.60i	−0.323001	−	0.559453i	−0.981106	+	0.193473i	$0.938025\pi$
$458$	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	0.970411	+	0.241461i	$0.0776266\pi$
$461$	6872.41	+	11903.4i	0.694317	+	1.20259i	−0.276094	+	0.961131i	$0.589040\pi$
$462$	7040.64	−	8512.47i	0.709005	−	0.857221i
$463$	−7824.30	+	13552.1i	−0.785369	+	1.36030i	0.143409	+	0.989664i	$0.454194\pi$
$463$	−7824.30	+	13552.1i	−0.785369	+	1.36030i	−0.928778	+	0.370636i	$0.879140\pi$
$464$	−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	0.975820	−	0.218576i	$-0.0701412\pi$
$479$	3130.53	+	5422.24i	0.298617	+	0.517221i	−0.677202	+	0.735797i	$0.736808\pi$
$480$	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	−0.795585	−	0.605841i	$-0.792837\pi$
$491$	1380.45	−	2391.01i	0.126881	−	0.219765i	0.922467	+	0.386076i	$0.126170\pi$
$492$	−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	−0.566884	−	0.823798i	$-0.691851\pi$
$499$	4793.00	−	8301.71i	0.429988	−	0.744761i	0.996872	+	0.0790369i	$0.0251845\pi$
$500$	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	−0.950596	−	0.310430i	$-0.899527\pi$
$509$	−2370.87	+	4106.47i	−0.206458	+	0.357595i	0.744138	+	0.668025i	$0.232860\pi$
$510$	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	0.999922	+	0.0125101i	$0.00398218\pi$
$547$	6534.73	+	11318.5i	0.510795	+	0.884723i	−0.489127	+	0.872213i	$0.662684\pi$
$548$	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	−0.174909	−	0.984585i	$-0.555963\pi$
$563$	10222.3	−	17705.6i	0.765221	−	1.32540i	0.940130	−	0.340817i	$-0.110704\pi$
$564$	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	0.813163	−	0.582036i	$-0.197744\pi$
$569$	−1323.03	−	2291.56i	−0.0974770	−	0.168835i	−0.910640	+	0.413201i	$0.864411\pi$
$570$	−10321.4	+	12479.0i	−0.758445	+	0.916996i
$571$	−878.514	+	1521.63i	−0.0643864	+	0.111521i	−0.896422	−	0.443202i	$-0.853842\pi$
$571$	−878.514	+	1521.63i	−0.0643864	+	0.111521i	0.832035	+	0.554723i	$0.187176\pi$
$572$	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	0.939855	−	0.341575i	$-0.110960\pi$
$587$	2476.24	+	4288.98i	0.174115	+	0.301576i	−0.765740	+	0.643151i	$0.777627\pi$
$588$	−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	−0.973085	−	0.230445i	$-0.925982\pi$
$599$	−4207.06	+	7286.85i	−0.286972	+	0.497049i	0.686114	+	0.727494i	$0.259315\pi$
$600$	−280.104	−	47.3462i	−0.0190587	−	0.00322150i
$601$	−14047.1	−	24330.3i	−0.953399	−	1.65134i	−0.737990	−	0.674812i	$-0.764225\pi$
$601$	−14047.1	−	24330.3i	−0.953399	−	1.65134i	−0.215409	−	0.976524i	$-0.569108\pi$
$602$	−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	−0.888953	−	0.457998i	$-0.848567\pi$
$607$	−715.423	+	1239.15i	−0.0478388	+	0.0828592i	0.841114	+	0.540857i	$0.181900\pi$
$608$	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	0.0678130	+	0.997698i	$0.478398\pi$
$617$	−12722.5	+	22036.0i	−0.830125	+	1.43782i	−0.897938	+	0.440121i	$0.854935\pi$
$618$	3434.30	−	4152.23i	0.223540	−	0.270271i
$619$	1739.73	+	3013.30i	0.112966	+	0.195662i	0.916965	−	0.398968i	$-0.130632\pi$
$619$	1739.73	+	3013.30i	0.112966	+	0.195662i	−0.803999	+	0.594631i	$0.797298\pi$
$620$	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	0.882368	−	0.470559i	$-0.155948\pi$
$641$	546.388	+	946.373i	0.0336678	+	0.0583143i	−0.848701	+	0.528874i	$0.822615\pi$
$642$	15082.2	+	2549.35i	0.927175	+	0.156721i
$643$	−15847.0	+	27447.8i	−0.971922	+	1.68342i	−0.282181	+	0.959361i	$0.591058\pi$
$643$	−15847.0	+	27447.8i	−0.971922	+	1.68342i	−0.689741	+	0.724056i	$0.742276\pi$
$644$	−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	−0.993489	−	0.113930i	$-0.963656\pi$
$653$	−6642.59	+	11505.3i	−0.398078	+	0.689491i	0.595411	+	0.803421i	$0.296989\pi$
$654$	−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	0.901810	−	0.432133i	$-0.142239\pi$
$659$	1296.99	+	2246.45i	0.0766670	+	0.132791i	−0.825143	+	0.564924i	$0.808905\pi$
$660$	−3367.02	−	9050.76i	−0.198577	−	0.533789i
$661$	7937.67	−	13748.4i	0.467079	−	0.809005i	−0.532213	−	0.846610i	$-0.678640\pi$
$661$	7937.67	−	13748.4i	0.467079	−	0.809005i	0.999293	+	0.0376052i	$0.0119729\pi$
$662$	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	−0.990585	−	0.136903i	$-0.956285\pi$
$673$	−10717.3	−	18563.0i	−0.613853	−	1.06323i	0.376731	−	0.926323i	$-0.377048\pi$
$674$	−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	0.995804	+	0.0915074i	$0.0291685\pi$
$677$	10166.5	+	17608.9i	0.577150	+	0.999653i	−0.418655	+	0.908146i	$0.637498\pi$
$678$	−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	−0.988515	−	0.151123i	$-0.951711\pi$
$691$	−11355.1	−	19667.6i	−0.625134	−	1.08276i	0.363381	−	0.931641i	$-0.381622\pi$
$692$	−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	0.938843	+	0.344346i	$0.111899\pi$
$709$	14491.8	+	25100.6i	0.767634	+	1.32958i	−0.171209	+	0.985235i	$0.554767\pi$
$710$	−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	0.795177	−	0.606378i	$-0.207378\pi$
$727$	−2500.25	−	4330.56i	−0.127550	−	0.220924i	−0.922727	+	0.385454i	$0.874045\pi$
$728$	−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	−0.997787	−	0.0664977i	$-0.978817\pi$
$733$	−8757.79	+	15168.9i	−0.441305	+	0.764362i	0.556482	+	0.830860i	$0.312151\pi$
$734$	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	0.0867044	−	0.996234i	$-0.472366\pi$
$743$	18351.3	−	31785.4i	0.906116	−	1.56944i	0.819412	−	0.573205i	$-0.194300\pi$
$744$	−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	−0.103713	−	0.994607i	$-0.533072\pi$
$751$	16660.0	−	28856.0i	0.809499	−	1.40209i	0.913212	−	0.407485i	$-0.133594\pi$
$752$	−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	−0.790359	−	0.612644i	$-0.790106\pi$
$761$	2842.17	−	4922.79i	0.135386	−	0.234495i	0.925745	+	0.378149i	$0.123439\pi$
$762$	−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	−0.861317	−	0.508067i	$-0.830360\pi$
$769$	199.189	−	345.005i	0.00934060	−	0.0161784i	0.870658	+	0.491889i	$0.163693\pi$
$770$	−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	−0.989354	−	0.145531i	$-0.953511\pi$
$787$	−8138.94	+	14097.1i	−0.368643	+	0.638508i	0.620711	+	0.784040i	$0.286844\pi$
$788$	−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	−0.917220	−	0.398382i	$-0.869572\pi$
$797$	−2556.06	+	4427.22i	−0.113601	+	0.196763i	0.803619	+	0.595145i	$0.202905\pi$
$798$	−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	0.960886	−	0.276943i	$-0.0893212\pi$
$821$	5660.01	+	9803.43i	0.240604	+	0.416738i	−0.720283	+	0.693681i	$0.755988\pi$
$822$	−4198.14	−	11284.9i	−0.178135	−	0.478839i
$823$	−5433.29	+	9410.73i	−0.230125	+	0.398587i	−0.957845	−	0.287287i	$-0.907247\pi$
$823$	−5433.29	+	9410.73i	−0.230125	+	0.398587i	0.727720	+	0.685874i	$0.240580\pi$
$824$	−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	0.975662	−	0.219280i	$-0.0703708\pi$
$839$	7240.28	+	12540.5i	0.297929	+	0.516028i	−0.677733	+	0.735308i	$0.737038\pi$
$840$	−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	0.923598	−	0.383363i	$-0.125234\pi$
$853$	3233.61	+	5600.78i	0.129797	+	0.224815i	−0.793801	+	0.608178i	$0.791901\pi$
$854$	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	0.824603	−	0.565711i	$-0.191398\pi$
$857$	−1947.32	−	3372.85i	−0.0776186	−	0.134439i	−0.902222	+	0.431272i	$0.858065\pi$
$858$	−6626.20	−	1120.03i	−0.263654	−	0.0445656i
$859$	18826.9	−	32609.1i	0.747805	−	1.29524i	−0.201067	−	0.979577i	$-0.564441\pi$
$859$	18826.9	−	32609.1i	0.747805	−	1.29524i	0.948873	−	0.315659i	$-0.102226\pi$
$860$	−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	−0.785437	−	0.618942i	$-0.787562\pi$
$877$	3721.77	−	6446.29i	0.143301	−	0.248205i	0.928738	+	0.370737i	$0.120895\pi$
$878$	−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	−0.849740	−	0.527202i	$-0.823241\pi$
$887$	837.437	−	1450.48i	0.0317005	−	0.0549069i	0.881440	+	0.472295i	$0.156574\pi$
$888$	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	0.666175	−	0.745795i	$-0.267930\pi$
$907$	−8544.04	−	14798.7i	−0.312790	−	0.541768i	−0.978965	+	0.204027i	$0.934597\pi$
$908$	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	0.604949	−	0.796264i	$-0.293194\pi$
$911$	−10644.2	−	18436.3i	−0.387111	−	0.670496i	−0.992060	+	0.125769i	$0.959860\pi$
$912$	−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	0.919961	−	0.392010i	$-0.128220\pi$
$929$	3411.72	+	5909.26i	0.120490	+	0.208694i	−0.799471	+	0.600704i	$0.794887\pi$
$930$	−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	−0.886192	−	0.463318i	$-0.846659\pi$
$941$	−1208.06	+	2092.42i	−0.0418508	+	0.0724878i	0.844341	+	0.535806i	$0.179992\pi$
$942$	−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	0.885832	−	0.464006i	$-0.153588\pi$
$947$	1197.04	+	2073.33i	0.0410755	+	0.0711448i	−0.844757	+	0.535150i	$0.820255\pi$
$948$	−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	−0.995561	−	0.0941189i	$-0.969997\pi$
$967$	−12517.5	+	21680.9i	−0.416271	+	0.721003i	0.579290	+	0.815122i	$0.303330\pi$
$968$	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	−0.419999	−	0.907524i	$-0.637970\pi$
$977$	17588.1	−	30463.5i	0.575939	−	0.997556i	0.995939	−	0.0900320i	$-0.0286969\pi$
$978$	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	−0.998845	−	0.0480511i	$-0.984699\pi$
$983$	−16674.6	−	28881.3i	−0.541036	−	0.937102i	0.457809	−	0.889051i	$-0.348634\pi$
$984$	−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	0.844815	+	0.535059i	$0.179711\pi$
$997$	27884.9	+	48298.1i	0.885782	+	1.53422i	0.0409671	+	0.999160i	$0.486956\pi$
$998$	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.13.2	yes	4
3.2	odd	2		54.4.c.b.37.2		4
4.3	odd	2		144.4.i.b.49.1		4
9.2	odd	6		54.4.c.b.19.2		4
9.4	even	3		162.4.a.f.1.2		2
9.5	odd	6		162.4.a.g.1.1		2
9.7	even	3	inner	18.4.c.b.7.2	✓	4
12.11	even	2		432.4.i.b.145.2		4
36.7	odd	6		144.4.i.b.97.1		4
36.11	even	6		432.4.i.b.289.2		4
36.23	even	6		1296.4.a.r.1.1		2
36.31	odd	6		1296.4.a.l.1.2		2

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

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(3.31174 - 4.00405i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-5.43521 + 9.41407i) q^{5} +(10.2470 + 1.73205i) q^{6} +(-12.4352 - 21.5384i) q^{7} -8.00000 q^{8} +(-5.06479 - 26.5207i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 3 q^{3} - 8 q^{4} + 9 q^{5} - 19 q^{7} - 32 q^{8} - 51 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 3 * q^3 - 8 * q^4 + 9 * q^5 - 19 * q^7 - 32 * q^8 - 51 * q^9	\( 4 q + 4 q^{2} + 3 q^{3} - 8 q^{4} + 9 q^{5} - 19 q^{7} - 32 q^{8} - 51 q^{9} + 36 q^{10} + 24 q^{11} - 12 q^{12} - 61 q^{13} + 38 q^{14} + 171 q^{15} - 32 q^{16} + 6 q^{17} + 102 q^{18} + 266 q^{19} + 36 q^{20} - 315 q^{21} - 48 q^{22} - 69 q^{23} - 24 q^{24} - 263 q^{25} - 244 q^{26} + 152 q^{28} - 237 q^{29} - 288 q^{30} - 211 q^{31} + 64 q^{32} + 630 q^{33} + 6 q^{34} + 774 q^{35} + 408 q^{36} + 524 q^{37} + 266 q^{38} - 249 q^{39} - 72 q^{40} - 468 q^{41} - 258 q^{42} + 86 q^{43} - 192 q^{44} - 459 q^{45} - 276 q^{46} - 483 q^{47} + 33 q^{49} + 526 q^{50} - 153 q^{51} - 244 q^{52} + 300 q^{53} + 468 q^{54} - 1674 q^{55} + 152 q^{56} + 987 q^{57} + 474 q^{58} - 168 q^{59} - 1260 q^{60} + 1049 q^{61} - 844 q^{62} - 957 q^{63} + 256 q^{64} + 747 q^{65} + 558 q^{66} + 1166 q^{67} - 12 q^{68} - 261 q^{69} + 774 q^{70} - 624 q^{71} + 408 q^{72} - 622 q^{73} + 524 q^{74} + 2835 q^{75} - 532 q^{76} + 1173 q^{77} + 132 q^{78} - 349 q^{79} - 288 q^{80} - 1143 q^{81} - 1872 q^{82} - 1221 q^{83} + 744 q^{84} + 486 q^{85} - 172 q^{86} - 2205 q^{87} - 192 q^{88} - 984 q^{89} - 1404 q^{90} + 214 q^{91} - 276 q^{92} - 789 q^{93} + 966 q^{94} - 1764 q^{95} + 96 q^{96} + 128 q^{97} + 132 q^{98} + 1557 q^{99}+O(q^{100}) \) 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

Related objects

Downloads

Learn more