LMFDB - Embedded newform 105.4.i.c.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(16,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("105.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.646154928.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 11x^{4} - 8x^{3} + 121x^{2} - 44x + 16 $ x^6 + 11x^4 - 8x^3 + 121x^2 - 44x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.2
Root			$0.184087 - 0.318847i$ of defining polynomial
Character	$\chi$	$=$	105.16
Dual form			105.4.i.c.46.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.684087 + 1.18487i) q^{2} +(1.50000 + 2.59808i) q^{3} +(3.06405 + 5.30709i) q^{4} +(-2.50000 + 4.33013i) q^{5} -4.10452 q^{6} +(17.2929 + 6.62978i) q^{7} -19.3297 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-0.684087 + 1.18487i) q^{2} +(1.50000 + 2.59808i) q^{3} +(3.06405 + 5.30709i) q^{4} +(-2.50000 + 4.33013i) q^{5} -4.10452 q^{6} +(17.2929 + 6.62978i) q^{7} -19.3297 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-3.42043 - 5.92436i) q^{10} +(-4.53674 - 7.85787i) q^{11} +(-9.19215 + 15.9213i) q^{12} -2.69663 q^{13} +(-19.6853 + 15.9546i) q^{14} -15.0000 q^{15} +(-11.2892 + 19.5535i) q^{16} +(-7.75248 - 13.4277i) q^{17} +(-6.15678 - 10.6639i) q^{18} +(-23.2214 + 40.2207i) q^{19} -30.6405 q^{20} +(8.71475 + 54.8731i) q^{21} +12.4141 q^{22} +(-23.7309 + 41.1031i) q^{23} +(-28.9945 - 50.2200i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(1.84473 - 3.19517i) q^{26} -27.0000 q^{27} +(17.8016 + 112.089i) q^{28} -8.21699 q^{29} +(10.2613 - 17.7731i) q^{30} +(114.174 + 197.755i) q^{31} +(-92.7644 - 160.673i) q^{32} +(13.6102 - 23.5736i) q^{33} +21.2135 q^{34} +(-71.9402 + 58.3062i) q^{35} -55.1529 q^{36} +(167.090 - 289.408i) q^{37} +(-31.7710 - 55.0289i) q^{38} +(-4.04495 - 7.00606i) q^{39} +(48.3242 - 83.7000i) q^{40} +35.3197 q^{41} +(-70.9792 - 27.2121i) q^{42} +510.201 q^{43} +(27.8016 - 48.1538i) q^{44} +(-22.5000 - 38.9711i) q^{45} +(-32.4680 - 56.2362i) q^{46} +(272.626 - 472.202i) q^{47} -67.7353 q^{48} +(255.092 + 229.297i) q^{49} +34.2043 q^{50} +(23.2574 - 40.2831i) q^{51} +(-8.26262 - 14.3113i) q^{52} +(2.16706 + 3.75346i) q^{53} +(18.4703 - 31.9916i) q^{54} +45.3674 q^{55} +(-334.267 - 128.152i) q^{56} -139.329 q^{57} +(5.62113 - 9.73609i) q^{58} +(395.945 + 685.797i) q^{59} +(-45.9608 - 79.6064i) q^{60} +(107.862 - 186.822i) q^{61} -312.420 q^{62} +(-129.492 + 104.951i) q^{63} +73.2079 q^{64} +(6.74158 - 11.6768i) q^{65} +(18.6212 + 32.2528i) q^{66} +(-201.111 - 348.334i) q^{67} +(47.5080 - 82.2862i) q^{68} -142.385 q^{69} +(-19.8722 - 125.126i) q^{70} -328.146 q^{71} +(86.9836 - 150.660i) q^{72} +(261.928 + 453.673i) q^{73} +(228.608 + 395.960i) q^{74} +(37.5000 - 64.9519i) q^{75} -284.607 q^{76} +(-26.3577 - 165.963i) q^{77} +11.0684 q^{78} +(65.3990 - 113.274i) q^{79} +(-56.4461 - 97.7675i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-24.1618 + 41.8494i) q^{82} -507.390 q^{83} +(-264.514 + 214.384i) q^{84} +77.5248 q^{85} +(-349.021 + 604.523i) q^{86} +(-12.3255 - 21.3484i) q^{87} +(87.6939 + 151.890i) q^{88} +(-282.946 + 490.076i) q^{89} +61.5678 q^{90} +(-46.6327 - 17.8781i) q^{91} -290.851 q^{92} +(-342.522 + 593.266i) q^{93} +(372.999 + 646.054i) q^{94} +(-116.107 - 201.104i) q^{95} +(278.293 - 482.018i) q^{96} -1439.25 q^{97} +(-446.193 + 145.393i) q^{98} +81.6614 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 9 q^{3} - q^{4} - 15 q^{5} - 18 q^{6} - 2 q^{7} + 18 q^{8} - 27 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + 9 * q^3 - q^4 - 15 * q^5 - 18 * q^6 - 2 * q^7 + 18 * q^8 - 27 * q^9	\( 6 q - 3 q^{2} + 9 q^{3} - q^{4} - 15 q^{5} - 18 q^{6} - 2 q^{7} + 18 q^{8} - 27 q^{9} - 15 q^{10} + q^{11} + 3 q^{12} - 158 q^{13} + 161 q^{14} - 90 q^{15} + 79 q^{16} + 72 q^{17} - 27 q^{18} + 29 q^{19} + 10 q^{20} - 39 q^{21} + 286 q^{22} + 63 q^{23} + 27 q^{24} - 75 q^{25} + 339 q^{26} - 162 q^{27} - 195 q^{28} + 440 q^{29} + 45 q^{30} - 136 q^{31} + 155 q^{32} - 3 q^{33} - 440 q^{34} - 55 q^{35} + 18 q^{36} - 43 q^{37} + 21 q^{38} - 237 q^{39} - 45 q^{40} - 1198 q^{41} - 42 q^{42} + 340 q^{43} - 135 q^{44} - 135 q^{45} - 265 q^{46} + 3 q^{47} + 474 q^{48} - 192 q^{49} + 150 q^{50} - 216 q^{51} + 701 q^{52} - 331 q^{53} + 81 q^{54} - 10 q^{55} - 1176 q^{56} + 174 q^{57} + 472 q^{58} + 1520 q^{59} + 15 q^{60} + 1160 q^{61} - 1496 q^{62} - 99 q^{63} + 34 q^{64} + 395 q^{65} + 429 q^{66} - 806 q^{67} + 684 q^{68} + 378 q^{69} - 875 q^{70} - 812 q^{71} - 81 q^{72} + 1192 q^{73} - 959 q^{74} + 225 q^{75} - 1182 q^{76} - 1309 q^{77} + 2034 q^{78} + 2590 q^{79} + 395 q^{80} - 243 q^{81} + 1191 q^{82} - 1016 q^{83} - 1629 q^{84} - 720 q^{85} + 742 q^{86} + 660 q^{87} + 749 q^{88} - 42 q^{89} + 270 q^{90} + 1346 q^{91} - 422 q^{92} + 408 q^{93} + 1167 q^{94} + 145 q^{95} - 465 q^{96} - 2040 q^{97} - 4053 q^{98} - 18 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 9 * q^3 - q^4 - 15 * q^5 - 18 * q^6 - 2 * q^7 + 18 * q^8 - 27 * q^9 - 15 * q^10 + q^11 + 3 * q^12 - 158 * q^13 + 161 * q^14 - 90 * q^15 + 79 * q^16 + 72 * q^17 - 27 * q^18 + 29 * q^19 + 10 * q^20 - 39 * q^21 + 286 * q^22 + 63 * q^23 + 27 * q^24 - 75 * q^25 + 339 * q^26 - 162 * q^27 - 195 * q^28 + 440 * q^29 + 45 * q^30 - 136 * q^31 + 155 * q^32 - 3 * q^33 - 440 * q^34 - 55 * q^35 + 18 * q^36 - 43 * q^37 + 21 * q^38 - 237 * q^39 - 45 * q^40 - 1198 * q^41 - 42 * q^42 + 340 * q^43 - 135 * q^44 - 135 * q^45 - 265 * q^46 + 3 * q^47 + 474 * q^48 - 192 * q^49 + 150 * q^50 - 216 * q^51 + 701 * q^52 - 331 * q^53 + 81 * q^54 - 10 * q^55 - 1176 * q^56 + 174 * q^57 + 472 * q^58 + 1520 * q^59 + 15 * q^60 + 1160 * q^61 - 1496 * q^62 - 99 * q^63 + 34 * q^64 + 395 * q^65 + 429 * q^66 - 806 * q^67 + 684 * q^68 + 378 * q^69 - 875 * q^70 - 812 * q^71 - 81 * q^72 + 1192 * q^73 - 959 * q^74 + 225 * q^75 - 1182 * q^76 - 1309 * q^77 + 2034 * q^78 + 2590 * q^79 + 395 * q^80 - 243 * q^81 + 1191 * q^82 - 1016 * q^83 - 1629 * q^84 - 720 * q^85 + 742 * q^86 + 660 * q^87 + 749 * q^88 - 42 * q^89 + 270 * q^90 + 1346 * q^91 - 422 * q^92 + 408 * q^93 + 1167 * q^94 + 145 * q^95 - 465 * q^96 - 2040 * q^97 - 4053 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.684087	+	1.18487i	−0.241861	+	0.418916i	−0.961244	−	0.275698i	$-0.911091\pi$
$2$	−0.684087	+	1.18487i	−0.241861	+	0.418916i	0.719383	+	0.694613i	$0.244425\pi$
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	3.06405	+	5.30709i	0.383006	+	0.663386i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$	−4.10452			−0.279277
$7$	17.2929	+	6.62978i	0.933731	+	0.357974i
$7$	17.2929	+	6.62978i	0.933731	+	0.357974i
$8$	−19.3297			−0.854260
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−3.42043	−	5.92436i	−0.108164	−	0.187345i
$11$	−4.53674	−	7.85787i	−0.124353	−	0.215385i	0.797127	−	0.603812i	$-0.206352\pi$
$11$	−4.53674	−	7.85787i	−0.124353	−	0.215385i	−0.921480	+	0.388426i	$0.873019\pi$
$12$	−9.19215	+	15.9213i	−0.221129	+	0.383006i
$13$	−2.69663			−0.0575316			−0.0287658	−	0.999586i	$-0.509158\pi$
$13$	−2.69663			−0.0575316			−0.0287658	+	0.999586i	$0.509158\pi$
$14$	−19.6853	+	15.9546i	−0.375794	+	0.304575i
$15$	−15.0000			−0.258199
$16$	−11.2892	+	19.5535i	−0.176394	+	0.305524i
$17$	−7.75248	−	13.4277i	−0.110603	−	0.191570i	0.805411	−	0.592717i	$-0.201945\pi$
$17$	−7.75248	−	13.4277i	−0.110603	−	0.191570i	−0.916014	+	0.401147i	$0.868612\pi$
$18$	−6.15678	−	10.6639i	−0.0806204	−	0.139639i
$19$	−23.2214	+	40.2207i	−0.280388	+	0.485646i	−0.971480	−	0.237121i	$-0.923796\pi$
$19$	−23.2214	+	40.2207i	−0.280388	+	0.485646i	0.691093	+	0.722766i	$0.257130\pi$
$20$	−30.6405			−0.342571
$21$	8.71475	+	54.8731i	0.0905579	+	0.570204i
$22$	12.4141			0.120304
$23$	−23.7309	+	41.1031i	−0.215140	+	0.372634i	−0.953316	−	0.301974i	$-0.902354\pi$
$23$	−23.7309	+	41.1031i	−0.215140	+	0.372634i	0.738176	+	0.674609i	$0.235688\pi$
$24$	−28.9945	−	50.2200i	−0.246604	−	0.427130i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	1.84473	−	3.19517i	0.0139147	−	0.0241009i
$27$	−27.0000			−0.192450
$28$	17.8016	+	112.089i	0.120150	+	0.756531i
$29$	−8.21699			−0.0526158			−0.0263079	−	0.999654i	$-0.508375\pi$
$29$	−8.21699			−0.0526158			−0.0263079	+	0.999654i	$0.508375\pi$
$30$	10.2613	−	17.7731i	0.0624483	−	0.108164i
$31$	114.174	+	197.755i	0.661492	+	1.14574i	0.980224	+	0.197893i	$0.0634099\pi$
$31$	114.174	+	197.755i	0.661492	+	1.14574i	−0.318731	+	0.947845i	$0.603257\pi$
$32$	−92.7644	−	160.673i	−0.512456	−	0.887599i
$33$	13.6102	−	23.5736i	0.0717951	−	0.124353i
$34$	21.2135			0.107002
$35$	−71.9402	+	58.3062i	−0.347432	+	0.281587i
$36$	−55.1529			−0.255338
$37$	167.090	−	289.408i	0.742415	−	1.28590i	−0.208978	−	0.977920i	$-0.567014\pi$
$37$	167.090	−	289.408i	0.742415	−	1.28590i	0.951393	−	0.307980i	$-0.0996531\pi$
$38$	−31.7710	−	55.0289i	−0.135630	−	0.234918i
$39$	−4.04495	−	7.00606i	−0.0166080	−	0.0287658i
$40$	48.3242	−	83.7000i	0.191018	−	0.330853i
$41$	35.3197			0.134537			0.0672685	−	0.997735i	$-0.478572\pi$
$41$	35.3197			0.134537			0.0672685	+	0.997735i	$0.478572\pi$
$42$	−70.9792	−	27.2121i	−0.260770	−	0.0999741i
$43$	510.201			1.80942			0.904708	−	0.426033i	$-0.140089\pi$
$43$	510.201			1.80942			0.904708	+	0.426033i	$0.140089\pi$
$44$	27.8016	−	48.1538i	0.0952558	−	0.164988i
$45$	−22.5000	−	38.9711i	−0.0745356	−	0.129099i
$46$	−32.4680	−	56.2362i	−0.104068	−	0.180252i
$47$	272.626	−	472.202i	0.846097	−	1.46548i	−0.0385678	−	0.999256i	$-0.512280\pi$
$47$	272.626	−	472.202i	0.846097	−	1.46548i	0.884665	−	0.466227i	$-0.154387\pi$
$48$	−67.7353			−0.203682
$49$	255.092	+	229.297i	0.743709	+	0.668504i
$50$	34.2043			0.0967445
$51$	23.2574	−	40.2831i	0.0638567	−	0.110603i
$52$	−8.26262	−	14.3113i	−0.0220350	−	0.0381657i
$53$	2.16706	+	3.75346i	0.00561639	+	0.00972787i	0.868820	−	0.495128i	$-0.164879\pi$
$53$	2.16706	+	3.75346i	0.00561639	+	0.00972787i	−0.863204	+	0.504856i	$0.831546\pi$
$54$	18.4703	−	31.9916i	0.0465462	−	0.0806204i
$55$	45.3674			0.111224
$56$	−334.267	−	128.152i	−0.797649	−	0.305803i
$57$	−139.329			−0.323764
$58$	5.62113	−	9.73609i	0.0127257	−	0.0220416i
$59$	395.945	+	685.797i	0.873689	+	1.51327i	0.858152	+	0.513395i	$0.171612\pi$
$59$	395.945	+	685.797i	0.873689	+	1.51327i	0.0155369	+	0.999879i	$0.495054\pi$
$60$	−45.9608	−	79.6064i	−0.0988918	−	0.171286i
$61$	107.862	−	186.822i	0.226399	−	0.392134i	−0.730340	−	0.683084i	$-0.760638\pi$
$61$	107.862	−	186.822i	0.226399	−	0.392134i	0.956738	+	0.290950i	$0.0939715\pi$
$62$	−312.420			−0.639957
$63$	−129.492	+	104.951i	−0.258960	+	0.209883i
$64$	73.2079			0.142984
$65$	6.74158	−	11.6768i	0.0128645	−	0.0222819i
$66$	18.6212	+	32.2528i	0.0347289	+	0.0601522i
$67$	−201.111	−	348.334i	−0.366710	−	0.635161i	0.622339	−	0.782748i	$-0.286183\pi$
$67$	−201.111	−	348.334i	−0.366710	−	0.635161i	−0.989049	+	0.147587i	$0.952849\pi$
$68$	47.5080	−	82.2862i	0.0847234	−	0.146745i
$69$	−142.385			−0.248423
$70$	−19.8722	−	125.126i	−0.0339311	−	0.213650i
$71$	−328.146			−0.548503			−0.274252	−	0.961658i	$-0.588430\pi$
$71$	−328.146			−0.548503			−0.274252	+	0.961658i	$0.588430\pi$
$72$	86.9836	−	150.660i	0.142377	−	0.246604i
$73$	261.928	+	453.673i	0.419950	+	0.727375i	0.995934	−	0.0900862i	$-0.0287143\pi$
$73$	261.928	+	453.673i	0.419950	+	0.727375i	−0.575984	+	0.817461i	$0.695381\pi$
$74$	228.608	+	395.960i	0.359123	+	0.622019i
$75$	37.5000	−	64.9519i	0.0577350	−	0.100000i
$76$	−284.607			−0.429561
$77$	−26.3577	−	165.963i	−0.0390096	−	0.245627i
$78$	11.0684			0.0160673
$79$	65.3990	−	113.274i	0.0931387	−	0.161321i	−0.815692	−	0.578487i	$-0.803643\pi$
$79$	65.3990	−	113.274i	0.0931387	−	0.161321i	0.908830	+	0.417166i	$0.136977\pi$
$80$	−56.4461	−	97.7675i	−0.0788858	−	0.136634i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	−24.1618	+	41.8494i	−0.0325393	+	0.0563596i
$83$	−507.390			−0.671003			−0.335502	−	0.942040i	$-0.608906\pi$
$83$	−507.390			−0.671003			−0.335502	+	0.942040i	$0.608906\pi$
$84$	−264.514	+	214.384i	−0.343581	+	0.278467i
$85$	77.5248			0.0989264
$86$	−349.021	+	604.523i	−0.437627	+	0.757993i
$87$	−12.3255	−	21.3484i	−0.0151889	−	0.0263079i
$88$	87.6939	+	151.890i	0.106230	+	0.183995i
$89$	−282.946	+	490.076i	−0.336991	+	0.583685i	−0.983865	−	0.178911i	$-0.942742\pi$
$89$	−282.946	+	490.076i	−0.336991	+	0.583685i	0.646874	+	0.762597i	$0.276076\pi$
$90$	61.5678			0.0721091
$91$	−46.6327	−	17.8781i	−0.0537191	−	0.0205949i
$92$	−290.851			−0.329601
$93$	−342.522	+	593.266i	−0.381913	+	0.661492i
$94$	372.999	+	646.054i	0.409276	+	0.708887i
$95$	−116.107	−	201.104i	−0.125393	−	0.217187i
$96$	278.293	−	482.018i	0.295866	−	0.512456i
$97$	−1439.25			−1.50654			−0.753269	−	0.657713i	$-0.771524\pi$
$97$	−1439.25			−1.50654			−0.753269	+	0.657713i	$0.771524\pi$
$98$	−446.193	+	145.393i	−0.459921	+	0.149866i
$99$	81.6614			0.0829018
$100$	76.6013	−	132.677i	0.0766013	−	0.132677i
$101$	932.614	+	1615.34i	0.918798	+	1.59140i	0.801243	+	0.598338i	$0.204172\pi$
$101$	932.614	+	1615.34i	0.918798	+	1.59140i	0.117555	+	0.993066i	$0.462494\pi$
$102$	31.8202	+	55.1142i	0.0308889	+	0.0535012i
$103$	−218.376	+	378.238i	−0.208905	+	0.361834i	−0.951370	−	0.308051i	$-0.900323\pi$
$103$	−218.376	+	378.238i	−0.208905	+	0.361834i	0.742465	+	0.669885i	$0.233657\pi$
$104$	52.1251			0.0491470
$105$	−259.394	−	99.4467i	−0.241088	−	0.0924286i
$106$	−5.92983			−0.00543355
$107$	1027.44	−	1779.57i	0.928279	−	1.60783i	0.142079	−	0.989855i	$-0.454621\pi$
$107$	1027.44	−	1779.57i	0.928279	−	1.60783i	0.786200	−	0.617972i	$-0.212045\pi$
$108$	−82.7294	−	143.291i	−0.0737096	−	0.127669i
$109$	−160.620	−	278.202i	−0.141143	−	0.244467i	0.786784	−	0.617228i	$-0.211744\pi$
$109$	−160.620	−	278.202i	−0.141143	−	0.244467i	−0.927927	+	0.372761i	$0.878411\pi$
$110$	−31.0353	+	53.7546i	−0.0269009	+	0.0465937i
$111$	1002.54			0.857267
$112$	−324.859	+	263.293i	−0.274074	+	0.222132i
$113$	762.909			0.635119			0.317559	−	0.948238i	$-0.397137\pi$
$113$	762.909			0.635119			0.317559	+	0.948238i	$0.397137\pi$
$114$	95.3129	−	165.087i	0.0783059	−	0.135630i
$115$	−118.654	−	205.515i	−0.0962138	−	0.166647i
$116$	−25.1773	−	43.6083i	−0.0201522	−	0.0349046i
$117$	12.1348	−	21.0182i	0.00958861	−	0.0166080i
$118$	−1083.44			−0.845246
$119$	−45.0406	−	283.602i	−0.0346964	−	0.218468i
$120$	289.945			0.220569
$121$	624.336	−	1081.38i	0.469073	−	0.812458i
$122$	147.574	+	255.605i	0.109514	+	0.189684i
$123$	52.9796	+	91.7633i	0.0388375	+	0.0672685i
$124$	−699.670	+	1211.86i	−0.506712	+	0.877650i
$125$	125.000			0.0894427
$126$	−35.7699	−	225.228i	−0.0252907	−	0.159245i
$127$	−696.163			−0.486413			−0.243207	−	0.969974i	$-0.578199\pi$
$127$	−696.163			−0.486413			−0.243207	+	0.969974i	$0.578199\pi$
$128$	692.034	−	1198.64i	0.477873	−	0.827701i
$129$	765.301	+	1325.54i	0.522333	+	0.904708i
$130$	9.22365	+	15.9758i	0.00622283	+	0.0107783i
$131$	341.367	−	591.265i	0.227675	−	0.394344i	−0.729444	−	0.684041i	$-0.760221\pi$
$131$	341.367	−	591.265i	0.227675	−	0.394344i	0.957119	+	0.289697i	$0.0935544\pi$
$132$	166.810			0.109992
$133$	−668.222	+	541.582i	−0.435655	+	0.353091i
$134$	550.309			0.354772
$135$	67.5000	−	116.913i	0.0430331	−	0.0745356i
$136$	149.853	+	259.553i	0.0944838	+	0.163651i
$137$	207.069	+	358.655i	0.129132	+	0.223664i	0.923341	−	0.383982i	$-0.125447\pi$
$137$	207.069	+	358.655i	0.129132	+	0.223664i	−0.794208	+	0.607646i	$0.792114\pi$
$138$	97.4039	−	168.708i	0.0600838	−	0.104068i
$139$	−1224.87			−0.747428			−0.373714	−	0.927544i	$-0.621916\pi$
$139$	−1224.87			−0.747428			−0.373714	+	0.927544i	$0.621916\pi$
$140$	−529.865	−	203.140i	−0.319870	−	0.122632i
$141$	1635.76			0.976989
$142$	224.480	−	388.811i	0.132662	−	0.229777i
$143$	12.2339	+	21.1898i	0.00715422	+	0.0123915i
$144$	−101.603	−	175.982i	−0.0587980	−	0.101841i
$145$	20.5425	−	35.5806i	0.0117652	−	0.0203780i
$146$	−716.726			−0.406278
$147$	−213.092	+	1006.69i	−0.119562	+	0.564835i
$148$	2047.88			1.13740
$149$	1187.97	−	2057.62i	0.653169	−	1.13132i	−0.329180	−	0.944267i	$-0.606772\pi$
$149$	1187.97	−	2057.62i	0.653169	−	1.13132i	0.982349	−	0.187055i	$-0.0598942\pi$
$150$	51.3065	+	88.8655i	0.0279277	+	0.0483722i
$151$	−1398.65	−	2422.53i	−0.753777	−	1.30558i	−0.945980	−	0.324225i	$-0.894897\pi$
$151$	−1398.65	−	2422.53i	−0.753777	−	1.30558i	0.192203	−	0.981355i	$-0.438437\pi$
$152$	448.863	−	777.454i	0.239524	−	0.414868i
$153$	139.545			0.0737354
$154$	214.676	+	82.3028i	0.112332	+	0.0430659i
$155$	−1141.74			−0.591657
$156$	24.7879	−	42.9338i	0.0127219	−	0.0220350i
$157$	−666.331	−	1154.12i	−0.338720	−	0.586680i	0.645473	−	0.763783i	$-0.276660\pi$
$157$	−666.331	−	1154.12i	−0.338720	−	0.586680i	−0.984192	+	0.177104i	$0.943327\pi$
$158$	89.4771	+	154.979i	0.0450533	+	0.0780346i
$159$	−6.50118	+	11.2604i	−0.00324262	+	0.00561639i
$160$	927.644			0.458354
$161$	−682.881	+	553.463i	−0.334277	+	0.270926i
$162$	110.822			0.0537469
$163$	1218.35	−	2110.24i	0.585451	−	1.01403i	−0.409368	−	0.912370i	$-0.634251\pi$
$163$	1218.35	−	2110.24i	0.585451	−	1.01403i	0.994819	−	0.101662i	$-0.0324160\pi$
$164$	108.221	+	187.445i	0.0515285	+	0.0892500i
$165$	68.0512	+	117.868i	0.0321077	+	0.0556122i
$166$	347.099	−	601.192i	0.162290	−	0.281094i
$167$	2395.37			1.10994			0.554968	−	0.831871i	$-0.312730\pi$
$167$	2395.37			1.10994			0.554968	+	0.831871i	$0.312730\pi$
$168$	−168.453	−	1060.68i	−0.0773599	−	0.487102i
$169$	−2189.73			−0.996690
$170$	−53.0337	+	91.8570i	−0.0239265	+	0.0414418i
$171$	−208.993	−	361.987i	−0.0934625	−	0.161882i
$172$	1563.28	+	2707.68i	0.693018	+	1.20034i
$173$	−1470.04	+	2546.18i	−0.646041	+	1.11898i	0.338019	+	0.941139i	$0.390243\pi$
$173$	−1470.04	+	2546.18i	−0.646041	+	1.11898i	−0.984060	+	0.177836i	$0.943090\pi$
$174$	33.7268			0.0146944
$175$	−72.6229	−	457.276i	−0.0313702	−	0.197524i
$176$	204.865			0.0877403
$177$	−1187.84	+	2057.39i	−0.504425	+	0.873689i
$178$	−387.119	−	670.509i	−0.163010	−	0.282342i
$179$	−1565.65	−	2711.78i	−0.653754	−	1.13234i	−0.982205	−	0.187814i	$-0.939860\pi$
$179$	−1565.65	−	2711.78i	−0.653754	−	1.13234i	0.328450	−	0.944521i	$-0.393474\pi$
$180$	137.882	−	238.819i	0.0570952	−	0.0988918i
$181$	−393.898			−0.161758			−0.0808791	−	0.996724i	$-0.525773\pi$
$181$	−393.898			−0.161758			−0.0808791	+	0.996724i	$0.525773\pi$
$182$	53.0841	−	43.0237i	0.0216201	−	0.0175227i
$183$	647.172			0.261423
$184$	458.711	−	794.510i	0.183786	−	0.318326i
$185$	835.448	+	1447.04i	0.332018	+	0.575072i
$186$	−468.630	−	811.690i	−0.184740	−	0.319979i
$187$	−70.3420	+	121.836i	−0.0275076	+	0.0476445i
$188$	3341.36			1.29624
$189$	−466.910	−	179.004i	−0.179697	−	0.0688922i
$190$	317.710			0.121311
$191$	−2374.61	+	4112.95i	−0.899586	+	1.55813i	−0.0715622	+	0.997436i	$0.522798\pi$
$191$	−2374.61	+	4112.95i	−0.899586	+	1.55813i	−0.828024	+	0.560693i	$0.810535\pi$
$192$	109.812	+	190.200i	0.0412760	+	0.0714921i
$193$	185.971	+	322.112i	0.0693602	+	0.120135i	0.898620	−	0.438728i	$-0.144571\pi$
$193$	185.971	+	322.112i	0.0693602	+	0.120135i	−0.829260	+	0.558864i	$0.811238\pi$
$194$	984.574	−	1705.33i	0.364373	−	0.631112i
$195$	40.4495			0.0148546
$196$	−435.284	+	2056.37i	−0.158631	+	0.749408i
$197$	732.895			0.265059			0.132529	−	0.991179i	$-0.457690\pi$
$197$	732.895			0.265059			0.132529	+	0.991179i	$0.457690\pi$
$198$	−55.8635	+	96.7584i	−0.0200507	+	0.0347289i
$199$	−1558.55	−	2699.48i	−0.555188	−	0.961615i	−0.997889	−	0.0649450i	$-0.979313\pi$
$199$	−1558.55	−	2699.48i	−0.555188	−	0.961615i	0.442700	−	0.896670i	$-0.354021\pi$
$200$	241.621	+	418.500i	0.0854260	+	0.147962i
$201$	603.332	−	1045.00i	0.211720	−	0.366710i
$202$	−2551.96			−0.888886
$203$	−142.096	−	54.4768i	−0.0491290	−	0.0188351i
$204$	285.048			0.0978301
$205$	−88.2993	+	152.939i	−0.0300834	+	0.0521059i
$206$	−298.776	−	517.495i	−0.101052	−	0.175027i
$207$	−213.578	−	369.928i	−0.0717135	−	0.124211i
$208$	30.4429	−	52.7286i	0.0101482	−	0.0175773i
$209$	421.399			0.139468
$210$	295.280	−	239.319i	0.0970297	−	0.0786409i
$211$	1368.10			0.446369			0.223184	−	0.974776i	$-0.428355\pi$
$211$	1368.10			0.446369			0.223184	+	0.974776i	$0.428355\pi$
$212$	−13.2800	+	23.0016i	−0.00430223	+	0.00745167i
$213$	−492.218	−	852.547i	−0.158339	−	0.274252i
$214$	1405.71	+	2434.76i	0.449030	+	0.777742i
$215$	−1275.50	+	2209.23i	−0.404598	+	0.700783i
$216$	521.902			0.164402
$217$	663.332	+	4176.72i	0.207511	+	1.30661i
$218$	439.512			0.136548
$219$	−785.784	+	1361.02i	−0.242458	+	0.419950i
$220$	139.008	+	240.769i	0.0425997	+	0.0737848i
$221$	20.9056	+	36.2095i	0.00636318	+	0.0110213i
$222$	−685.823	+	1187.88i	−0.207340	+	0.359123i
$223$	−4161.15			−1.24956			−0.624779	−	0.780802i	$-0.714811\pi$
$223$	−4161.15			−1.24956			−0.624779	+	0.780802i	$0.714811\pi$
$224$	−538.946	−	3393.51i	−0.160758	−	1.01223i
$225$	225.000			0.0666667
$226$	−521.896	+	903.950i	−0.153611	+	0.266061i
$227$	917.493	+	1589.14i	0.268265	+	0.464649i	0.968414	−	0.249348i	$-0.0802164\pi$
$227$	917.493	+	1589.14i	0.268265	+	0.464649i	−0.700149	+	0.713997i	$0.746883\pi$
$228$	−426.910	−	739.430i	−0.124004	−	0.214781i
$229$	−922.278	+	1597.43i	−0.266139	+	0.460966i	−0.967861	−	0.251484i	$-0.919081\pi$
$229$	−922.278	+	1597.43i	−0.266139	+	0.460966i	0.701722	+	0.712451i	$0.252415\pi$
$230$	324.680			0.0930815
$231$	391.649	−	317.424i	0.111552	−	0.0904112i
$232$	158.832			0.0449475
$233$	−2673.29	+	4630.27i	−0.751644	+	1.30188i	0.195382	+	0.980727i	$0.437405\pi$
$233$	−2673.29	+	4630.27i	−0.751644	+	1.30188i	−0.947026	+	0.321158i	$0.895928\pi$
$234$	16.6026	+	28.7565i	0.00463822	+	0.00803364i
$235$	1363.13	+	2361.01i	0.378386	+	0.655384i
$236$	−2426.39	+	4202.63i	−0.669257	+	1.15919i
$237$	392.394			0.107547
$238$	366.843	+	140.641i	0.0999115	+	0.0383041i
$239$	−1406.13			−0.380564			−0.190282	−	0.981730i	$-0.560940\pi$
$239$	−1406.13			−0.380564			−0.190282	+	0.981730i	$0.560940\pi$
$240$	169.338	−	293.303i	0.0455448	−	0.0788858i
$241$	−900.135	−	1559.08i	−0.240593	−	0.416718i	0.720291	−	0.693672i	$-0.244008\pi$
$241$	−900.135	−	1559.08i	−0.240593	−	0.416718i	−0.960883	+	0.276954i	$0.910675\pi$
$242$	854.200	+	1479.52i	0.226901	+	0.393004i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	1321.98			0.346848
$245$	−1630.61	+	531.339i	−0.425209	+	0.138555i
$246$	−144.971			−0.0375731
$247$	62.6197	−	108.461i	0.0161312	−	0.0279400i
$248$	−2206.95	−	3822.55i	−0.565086	−	0.978758i
$249$	−761.085	−	1318.24i	−0.193702	−	0.335502i
$250$	−85.5108	+	148.109i	−0.0216327	+	0.0374690i
$251$	−2968.25			−0.746432			−0.373216	−	0.927744i	$-0.621745\pi$
$251$	−2968.25			−0.746432			−0.373216	+	0.927744i	$0.621745\pi$
$252$	−953.756	−	365.652i	−0.238417	−	0.0914043i
$253$	430.644			0.107013
$254$	476.236	−	824.865i	0.117644	−	0.203766i
$255$	116.287	+	201.415i	0.0285576	+	0.0494632i
$256$	1239.65	+	2147.15i	0.302650	+	0.524205i
$257$	3191.89	−	5528.52i	0.774726	−	1.34187i	−0.160222	−	0.987081i	$-0.551221\pi$
$257$	3191.89	−	5528.52i	0.774726	−	1.34187i	0.934948	−	0.354784i	$-0.115446\pi$
$258$	−2094.13			−0.505328
$259$	4808.18	−	3896.94i	1.15354	−	0.934920i
$260$	82.6262			0.0197087
$261$	36.9765	−	64.0451i	0.00876929	−	0.0151889i
$262$	467.049	+	808.953i	0.110131	+	0.190753i
$263$	−3513.84	−	6086.15i	−0.823850	−	1.42695i	−0.902795	−	0.430071i	$-0.858489\pi$
$263$	−3513.84	−	6086.15i	−0.823850	−	1.42695i	0.0789453	−	0.996879i	$-0.474845\pi$
$264$	−263.082	+	455.671i	−0.0613316	+	0.106230i
$265$	−21.6706			−0.00502345
$266$	−184.584	−	1162.25i	−0.0425473	−	0.267902i
$267$	−1697.67			−0.389124
$268$	1232.43	−	2134.63i	0.280905	−	0.486541i
$269$	2050.39	+	3551.38i	0.464738	+	0.804949i	0.999190	−	0.0402496i	$-0.0128153\pi$
$269$	2050.39	+	3551.38i	0.464738	+	0.804949i	−0.534452	+	0.845199i	$0.679482\pi$
$270$	92.3517	+	159.958i	0.0208161	+	0.0360545i
$271$	4150.49	−	7188.87i	0.930349	−	1.61141i	0.147624	−	0.989044i	$-0.452837\pi$
$271$	4150.49	−	7188.87i	0.930349	−	1.61141i	0.782725	−	0.622368i	$-0.213829\pi$
$272$	350.078			0.0780389
$273$	−23.5005	−	147.973i	−0.00520994	−	0.0328048i
$274$	−566.614			−0.124928
$275$	−113.419	+	196.447i	−0.0248705	+	0.0430770i
$276$	−436.276	−	755.652i	−0.0951475	−	0.164800i
$277$	3657.80	+	6335.50i	0.793416	+	1.37424i	0.923840	+	0.382778i	$0.125033\pi$
$277$	3657.80	+	6335.50i	0.793416	+	1.37424i	−0.130425	+	0.991458i	$0.541634\pi$
$278$	837.921	−	1451.32i	0.180774	−	0.313110i
$279$	−2055.13			−0.440995
$280$	1390.58	−	1127.04i	0.296797	−	0.240549i
$281$	−3004.11			−0.637759			−0.318880	−	0.947795i	$-0.603307\pi$
$281$	−3004.11			−0.637759			−0.318880	+	0.947795i	$0.603307\pi$
$282$	−1119.00	+	1938.16i	−0.236296	+	0.409276i
$283$	−1829.22	−	3168.31i	−0.384226	−	0.665500i	0.607435	−	0.794369i	$-0.292198\pi$
$283$	−1829.22	−	3168.31i	−0.384226	−	0.665500i	−0.991662	+	0.128870i	$0.958865\pi$
$284$	−1005.45	−	1741.50i	−0.210080	−	0.363870i
$285$	348.322	−	603.311i	0.0723958	−	0.125393i
$286$	−33.4763			−0.00692131
$287$	610.782	+	234.162i	0.125621	+	0.0481608i
$288$	1669.76			0.341637
$289$	2336.30	−	4046.59i	0.475534	−	0.823649i
$290$	28.1057	+	48.6804i	0.00569111	+	0.00985729i
$291$	−2158.88	−	3739.29i	−0.434900	−	0.753269i
$292$	−1605.12	+	2780.15i	−0.321687	+	0.557178i
$293$	4069.16			0.811342			0.405671	−	0.914019i	$-0.367038\pi$
$293$	4069.16			0.811342			0.405671	+	0.914019i	$0.367038\pi$
$294$	−1047.03	−	941.153i	−0.207701	−	0.186698i
$295$	−3959.45			−0.781451
$296$	−3229.79	+	5594.16i	−0.634215	+	1.09849i
$297$	122.492	+	212.163i	0.0239317	+	0.0414509i
$298$	1625.35	+	2815.18i	0.315952	+	0.547246i
$299$	63.9935	−	110.840i	0.0123774	−	0.0214383i
$300$	459.608			0.0884515
$301$	8822.87	+	3382.52i	1.68951	+	0.647724i
$302$	3827.18			0.729237
$303$	−2797.84	+	4846.01i	−0.530468	+	0.918798i
$304$	−524.304	−	908.121i	−0.0989175	−	0.171330i
$305$	539.310	+	934.112i	0.101249	+	0.175368i
$306$	−95.4606	+	165.343i	−0.0178337	+	0.0308889i
$307$	7902.82			1.46918			0.734589	−	0.678512i	$-0.237375\pi$
$307$	7902.82			1.46918			0.734589	+	0.678512i	$0.237375\pi$
$308$	800.021	−	648.403i	0.148005	−	0.119955i
$309$	−1310.26			−0.241223
$310$	781.049	−	1352.82i	0.143099	−	0.247854i
$311$	−1515.92	−	2625.65i	−0.276398	−	0.478735i	0.694089	−	0.719889i	$-0.255807\pi$
$311$	−1515.92	−	2625.65i	−0.276398	−	0.478735i	−0.970487	+	0.241154i	$0.922474\pi$
$312$	78.1876	+	135.425i	0.0141875	+	0.0245735i
$313$	164.463	−	284.858i	0.0296996	−	0.0514413i	−0.850794	−	0.525500i	$-0.823878\pi$
$313$	164.463	−	284.858i	0.0296996	−	0.0514413i	0.880493	+	0.474059i	$0.157212\pi$
$314$	1823.31			0.327692
$315$	−130.721	−	823.096i	−0.0233819	−	0.147226i
$316$	801.543			0.142691
$317$	−1435.63	+	2486.58i	−0.254362	+	0.440568i	−0.964722	−	0.263270i	$-0.915199\pi$
$317$	−1435.63	+	2486.58i	−0.254362	+	0.440568i	0.710360	+	0.703839i	$0.248532\pi$
$318$	−8.89474	−	15.4061i	−0.00156853	−	0.00271677i
$319$	37.2784	+	64.5681i	0.00654291	+	0.0113327i
$320$	−183.020	+	317.000i	−0.0319723	+	0.0553776i
$321$	6164.61			1.07188
$322$	−188.634	−	1187.74i	−0.0326464	−	0.205560i
$323$	720.095			0.124047
$324$	248.188	−	429.874i	0.0425563	−	0.0737096i
$325$	33.7079	+	58.3838i	0.00575316	+	0.00996477i
$326$	1666.91	+	2887.18i	0.283196	+	0.490510i
$327$	481.860	−	834.606i	0.0814890	−	0.141143i
$328$	−682.719			−0.114929
$329$	7845.10	−	6358.31i	1.31463	−	1.06549i
$330$	−186.212			−0.0310625
$331$	4579.30	−	7931.57i	0.760425	−	1.31710i	−0.182206	−	0.983260i	$-0.558324\pi$
$331$	4579.30	−	7931.57i	0.760425	−	1.31710i	0.942631	−	0.333835i	$-0.108343\pi$
$332$	−1554.67	−	2692.76i	−0.256998	−	0.445134i
$333$	1503.81	+	2604.67i	0.247472	+	0.428634i
$334$	−1638.64	+	2838.21i	−0.268451	+	0.464970i
$335$	2011.11			0.327996
$336$	−1171.34	−	449.070i	−0.190185	−	0.0729131i
$337$	−6200.00			−1.00218			−0.501091	−	0.865394i	$-0.667068\pi$
$337$	−6200.00			−1.00218			−0.501091	+	0.865394i	$0.667068\pi$
$338$	1497.96	−	2594.55i	0.241061	−	0.417529i
$339$	1144.36	+	1982.09i	0.183343	+	0.317559i
$340$	237.540	+	411.431i	0.0378894	+	0.0656264i
$341$	1035.96	−	1794.33i	0.164517	−	0.284951i
$342$	571.877			0.0904198
$343$	2891.11	+	5656.42i	0.455117	+	0.890432i
$344$	−9862.02			−1.54571
$345$	355.963	−	616.546i	0.0555490	−	0.0962138i
$346$	−2011.27	−	3483.62i	−0.312504	−	0.541273i
$347$	−1856.03	−	3214.74i	−0.287138	−	0.497338i	0.685987	−	0.727614i	$-0.259371\pi$
$347$	−1856.03	−	3214.74i	−0.287138	−	0.497338i	−0.973125	+	0.230276i	$0.926037\pi$
$348$	75.5318	−	130.825i	0.0116349	−	0.0201522i
$349$	−619.951			−0.0950865			−0.0475433	−	0.998869i	$-0.515139\pi$
$349$	−619.951			−0.0950865			−0.0475433	+	0.998869i	$0.515139\pi$
$350$	591.494	+	226.767i	0.0903333	+	0.0346320i
$351$	72.8091			0.0110720
$352$	−841.697	+	1457.86i	−0.127450	+	0.220751i
$353$	−2087.78	−	3616.15i	−0.314792	−	0.545235i	0.664601	−	0.747198i	$-0.268601\pi$
$353$	−2087.78	−	3616.15i	−0.314792	−	0.545235i	−0.979393	+	0.201963i	$0.935268\pi$
$354$	−1625.16	−	2814.87i	−0.244002	−	0.422623i
$355$	820.364	−	1420.91i	0.122649	−	0.212434i
$356$	−3467.84			−0.516279
$357$	669.257	−	542.421i	0.0992181	−	0.0804145i
$358$	4284.16			0.632471
$359$	−3105.92	+	5379.61i	−0.456614	+	0.790878i	−0.998779	−	0.0493937i	$-0.984271\pi$
$359$	−3105.92	+	5379.61i	−0.456614	+	0.790878i	0.542166	+	0.840271i	$0.317604\pi$
$360$	434.918	+	753.300i	0.0636728	+	0.110284i
$361$	2351.03	+	4072.10i	0.342766	+	0.593687i
$362$	269.461	−	466.720i	0.0391230	−	0.0677631i
$363$	3746.02			0.541639
$364$	−48.0045	−	302.264i	−0.00691241	−	0.0435245i
$365$	−2619.28			−0.375615
$366$	−442.722	+	766.816i	−0.0632280	+	0.109514i
$367$	−2419.62	−	4190.91i	−0.344151	−	0.596087i	0.641048	−	0.767501i	$-0.278500\pi$
$367$	−2419.62	−	4190.91i	−0.344151	−	0.596087i	−0.985199	+	0.171414i	$0.945166\pi$
$368$	−535.806	−	928.044i	−0.0758990	−	0.131461i
$369$	−158.939	+	275.290i	−0.0224228	+	0.0388375i
$370$	−2286.08			−0.321209
$371$	12.5903	+	79.2755i	0.00176187	+	0.0110937i
$372$	−4198.02			−0.585100
$373$	−5978.69	+	10355.4i	−0.829933	+	1.43749i	0.0681568	+	0.997675i	$0.478288\pi$
$373$	−5978.69	+	10355.4i	−0.829933	+	1.43749i	−0.898090	+	0.439812i	$0.855045\pi$
$374$	−96.2401	−	166.693i	−0.0133060	−	0.0230467i
$375$	187.500	+	324.760i	0.0258199	+	0.0447214i
$376$	−5269.77	+	9127.52i	−0.722787	+	1.25190i
$377$	22.1582			0.00302707
$378$	531.504	−	430.774i	0.0723217	−	0.0586154i
$379$	−13037.0			−1.76692			−0.883462	−	0.468502i	$-0.844794\pi$
$379$	−13037.0			−1.76692			−0.883462	+	0.468502i	$0.844794\pi$
$380$	711.517	−	1232.38i	0.0960528	−	0.166368i
$381$	−1044.24	−	1808.69i	−0.140415	−	0.243207i
$382$	−3248.88	−	5627.23i	−0.435150	−	0.753702i
$383$	2156.50	−	3735.16i	0.287707	−	0.498323i	−0.685555	−	0.728021i	$-0.740440\pi$
$383$	2156.50	−	3735.16i	0.287707	−	0.498323i	0.973262	+	0.229698i	$0.0737737\pi$
$384$	4152.21			0.551801
$385$	784.537	+	300.776i	0.103854	+	0.0398155i
$386$	−508.882			−0.0671021
$387$	−2295.90	+	3976.62i	−0.301569	+	0.522333i
$388$	−4409.95	−	7638.25i	−0.577013	−	0.999416i
$389$	4080.02	+	7066.79i	0.531787	+	0.921081i	0.999312	+	0.0371015i	$0.0118125\pi$
$389$	4080.02	+	7066.79i	0.531787	+	0.921081i	−0.467525	+	0.883980i	$0.654854\pi$
$390$	−27.6710	+	47.9275i	−0.00359275	+	0.00622283i
$391$	735.893			0.0951808
$392$	−4930.85	−	4432.24i	−0.635320	−	0.571076i
$393$	2048.20			0.262896
$394$	−501.364	+	868.387i	−0.0641074	+	0.111037i
$395$	326.995	+	566.372i	0.0416529	+	0.0721450i
$396$	250.215	+	433.385i	0.0317519	+	0.0549959i
$397$	−1391.75	+	2410.59i	−0.175945	+	0.304745i	−0.940488	−	0.339827i	$-0.889631\pi$
$397$	−1391.75	+	2410.59i	−0.175945	+	0.304745i	0.764543	+	0.644573i	$0.222965\pi$
$398$	4264.73			0.537114
$399$	−2409.40	−	923.718i	−0.302308	−	0.115899i
$400$	564.461			0.0705576
$401$	882.119	−	1527.87i	0.109853	−	0.190270i	−0.805858	−	0.592109i	$-0.798295\pi$
$401$	882.119	−	1527.87i	0.109853	−	0.190270i	0.915710	+	0.401839i	$0.131629\pi$
$402$	825.463	+	1429.74i	0.102414	+	0.177386i
$403$	−307.885	−	533.273i	−0.0380567	−	0.0659162i
$404$	−5715.16	+	9898.94i	−0.703811	+	1.21904i
$405$	405.000			0.0496904
$406$	161.754	−	131.099i	0.0197727	−	0.0160254i
$407$	−3032.17			−0.369285
$408$	−449.559	+	778.659i	−0.0545502	+	0.0944838i
$409$	6785.38	+	11752.6i	0.820332	+	1.42086i	0.905435	+	0.424484i	$0.139544\pi$
$409$	6785.38	+	11752.6i	0.820332	+	1.42086i	−0.0851038	+	0.996372i	$0.527122\pi$
$410$	−120.809	−	209.247i	−0.0145520	−	0.0252048i
$411$	−621.208	+	1075.96i	−0.0745546	+	0.129132i
$412$	−2676.46			−0.320048
$413$	2300.38	+	14484.5i	0.274078	+	1.72575i
$414$	584.423			0.0693788
$415$	1268.47	−	2197.06i	0.150041	−	0.259878i
$416$	250.151	+	433.275i	0.0294824	+	0.0510650i
$417$	−1837.31	−	3182.32i	−0.215764	−	0.373714i
$418$	−288.273	+	499.304i	−0.0337319	+	0.0584253i
$419$	12093.9			1.41008			0.705042	−	0.709166i	$-0.250928\pi$
$419$	12093.9			1.41008			0.705042	+	0.709166i	$0.250928\pi$
$420$	−267.024	−	1681.34i	−0.0310225	−	0.195336i
$421$	−6544.53			−0.757627			−0.378813	−	0.925473i	$-0.623668\pi$
$421$	−6544.53			−0.757627			−0.378813	+	0.925473i	$0.623668\pi$
$422$	−935.898	+	1621.02i	−0.107959	+	0.186991i
$423$	2453.63	+	4249.82i	0.282032	+	0.488494i
$424$	−41.8886	−	72.5532i	−0.00479786	−	0.00831013i
$425$	−193.812	+	335.692i	−0.0221206	+	0.0383140i
$426$	1346.88			0.153184
$427$	3103.84	−	2515.61i	0.351769	−	0.285103i
$428$	12592.5			1.42215
$429$	−36.7018	+	63.5694i	−0.00413049	+	0.00715422i
$430$	−1745.11	−	3022.61i	−0.195713	−	0.338985i
$431$	1790.05	+	3100.46i	0.200055	+	0.346505i	0.948546	−	0.316640i	$-0.102555\pi$
$431$	1790.05	+	3100.46i	0.200055	+	0.346505i	−0.748491	+	0.663145i	$0.769221\pi$
$432$	304.809	−	527.945i	0.0339471	−	0.0587980i
$433$	−14612.4			−1.62178			−0.810888	−	0.585202i	$-0.801015\pi$
$433$	−14612.4			−1.62178			−0.810888	+	0.585202i	$0.801015\pi$
$434$	−5402.66	−	2071.27i	−0.597548	−	0.229088i
$435$	123.255			0.0135853
$436$	984.296	−	1704.85i	0.108117	−	0.187265i
$437$	−1102.13	−	1908.95i	−0.120645	−	0.208964i
$438$	−1075.09	−	1862.11i	−0.117282	−	0.203139i
$439$	−5786.75	+	10022.9i	−0.629126	+	1.08968i	0.358601	+	0.933491i	$0.383254\pi$
$439$	−5786.75	+	10022.9i	−0.629126	+	1.08968i	−0.987727	+	0.156188i	$0.950080\pi$
$440$	−876.939			−0.0950146
$441$	−2935.11	+	956.410i	−0.316932	+	0.103273i
$442$	−57.2049			−0.00615602
$443$	−8144.36	+	14106.5i	−0.873477	+	1.51291i	−0.0151012	+	0.999886i	$0.504807\pi$
$443$	−8144.36	+	14106.5i	−0.873477	+	1.51291i	−0.858376	+	0.513021i	$0.828526\pi$
$444$	3071.83	+	5320.56i	0.328339	+	0.568699i
$445$	−1414.73	−	2450.38i	−0.150707	−	0.261032i
$446$	2846.59	−	4930.44i	0.302219	−	0.523459i
$447$	7127.81			0.754215
$448$	1265.98	+	485.352i	0.133509	+	0.0511847i
$449$	4951.02			0.520385			0.260193	−	0.965557i	$-0.416214\pi$
$449$	4951.02			0.520385			0.260193	+	0.965557i	$0.416214\pi$
$450$	−153.919	+	266.596i	−0.0161241	+	0.0279277i
$451$	−160.237	−	277.538i	−0.0167300	−	0.0289773i
$452$	2337.59	+	4048.83i	0.243254	+	0.421329i
$453$	4195.94	−	7267.58i	0.435193	−	0.753777i
$454$	−2510.58			−0.259532
$455$	193.996	−	157.230i	0.0199883	−	0.0162002i
$456$	2693.18			0.276578
$457$	3219.14	−	5575.71i	0.329508	−	0.570724i	−0.652907	−	0.757438i	$-0.726451\pi$
$457$	3219.14	−	5575.71i	0.329508	−	0.570724i	0.982414	+	0.186714i	$0.0597839\pi$
$458$	−1261.84	−	2185.56i	−0.128737	−	0.222980i
$459$	209.317	+	362.548i	0.0212856	+	0.0368677i
$460$	727.126	−	1259.42i	0.0737010	−	0.127654i
$461$	−5615.41			−0.567323			−0.283661	−	0.958925i	$-0.591549\pi$
$461$	−5615.41			−0.567323			−0.283661	+	0.958925i	$0.591549\pi$
$462$	108.186	+	681.200i	0.0108945	+	0.0685980i
$463$	4355.36			0.437173			0.218586	−	0.975818i	$-0.429855\pi$
$463$	4355.36			0.437173			0.218586	+	0.975818i	$0.429855\pi$
$464$	92.7634	−	160.671i	0.00928111	−	0.0160754i
$465$	−1712.61	−	2966.33i	−0.170797	−	0.295828i
$466$	−3657.52	−	6335.01i	−0.363587	−	0.629751i
$467$	5275.42	−	9137.29i	0.522735	−	0.905403i	−0.476915	−	0.878949i	$-0.658245\pi$
$467$	5275.42	−	9137.29i	0.522735	−	0.905403i	0.999650	−	0.0264540i	$-0.00842156\pi$
$468$	148.727			0.0146900
$469$	−1168.42	−	7357.04i	−0.115038	−	0.724342i
$470$	−3729.99			−0.366068
$471$	1998.99	−	3462.36i	0.195560	−	0.338720i
$472$	−7653.50	−	13256.2i	−0.746358	−	1.29273i
$473$	−2314.65	−	4009.09i	−0.225006	−	0.389721i
$474$	−268.431	+	464.937i	−0.0260115	+	0.0450533i
$475$	1161.07			0.112155
$476$	1367.09	−	1108.00i	0.131640	−	0.106692i
$477$	−39.0071			−0.00374426
$478$	961.912	−	1666.08i	0.0920436	−	0.159424i
$479$	5348.72	+	9264.26i	0.510207	+	0.883705i	0.999930	+	0.0118270i	$0.00376472\pi$
$479$	5348.72	+	9264.26i	0.510207	+	0.883705i	−0.489723	+	0.871878i	$0.662902\pi$
$480$	1391.47	+	2410.09i	0.132315	+	0.229177i
$481$	−450.579	+	780.426i	−0.0427124	+	0.0739800i
$482$	2463.08			0.232760
$483$	−2462.26	−	943.983i	−0.231960	−	0.0889290i
$484$	7651.99			0.718631
$485$	3598.13	−	6232.15i	0.336872	−	0.583479i
$486$	166.233	+	287.924i	0.0155154	+	0.0268735i
$487$	−1205.77	−	2088.45i	−0.112194	−	0.194326i	0.804461	−	0.594006i	$-0.202454\pi$
$487$	−1205.77	−	2088.45i	−0.112194	−	0.194326i	−0.916655	+	0.399680i	$0.869121\pi$
$488$	−2084.94	+	3611.22i	−0.193403	+	0.334984i
$489$	7310.10			0.676021
$490$	485.912	−	2295.55i	0.0447985	−	0.211638i
$491$	20725.7			1.90496			0.952480	−	0.304601i	$-0.0985230\pi$
$491$	20725.7			1.90496			0.952480	+	0.304601i	$0.0985230\pi$
$492$	−324.664	+	562.335i	−0.0297500	+	0.0515285i
$493$	63.7020	+	110.335i	0.00581946	+	0.0100796i
$494$	85.6746	+	148.393i	0.00780300	+	0.0135152i
$495$	−204.153	+	353.604i	−0.0185374	+	0.0321077i
$496$	−5155.74			−0.466733
$497$	−5674.60	−	2175.53i	−0.512155	−	0.196350i
$498$	2082.59			0.187396
$499$	8253.57	−	14295.6i	0.740442	−	1.28248i	−0.211853	−	0.977302i	$-0.567950\pi$
$499$	8253.57	−	14295.6i	0.740442	−	1.28248i	0.952294	−	0.305181i	$-0.0987170\pi$
$500$	383.006	+	663.386i	0.0342571	+	0.0593351i
$501$	3593.06	+	6223.36i	0.320411	+	0.554968i
$502$	2030.54	−	3517.00i	0.180533	−	0.312692i
$503$	−7943.62			−0.704152			−0.352076	−	0.935971i	$-0.614524\pi$
$503$	−7943.62			−0.704152			−0.352076	+	0.935971i	$0.614524\pi$
$504$	2503.05	−	2028.67i	0.221219	−	0.179294i
$505$	−9326.14			−0.821798
$506$	−294.598	+	510.258i	−0.0258823	+	0.0448295i
$507$	−3284.59	−	5689.08i	−0.287720	−	0.498345i
$508$	−2133.08	−	3694.60i	−0.186299	−	0.322680i
$509$	4067.28	−	7044.73i	0.354183	−	0.613462i	−0.632795	−	0.774319i	$-0.718092\pi$
$509$	4067.28	−	7044.73i	0.354183	−	0.613462i	0.986978	+	0.160857i	$0.0514258\pi$
$510$	−318.202			−0.0276279
$511$	1521.76	+	9581.86i	0.131739	+	0.829504i
$512$	7680.43			0.662949
$513$	626.979	−	1085.96i	0.0539606	−	0.0934625i
$514$	4367.06	+	7563.97i	0.374752	+	0.649090i
$515$	−1091.88	−	1891.19i	−0.0934252	−	0.161817i
$516$	−4689.84	+	8123.04i	−0.400114	+	0.693018i
$517$	−4947.34			−0.420858
$518$	1328.17	+	8362.93i	0.112657	+	0.709355i
$519$	−8820.24			−0.745984
$520$	−130.313	+	225.708i	−0.0109896	+	0.0190345i
$521$	−6419.15	−	11118.3i	−0.539785	−	0.934936i	−0.998915	−	0.0465664i	$-0.985172\pi$
$521$	−6419.15	−	11118.3i	−0.539785	−	0.934936i	0.459130	−	0.888369i	$-0.348161\pi$
$522$	50.5902	+	87.6248i	0.00424190	+	0.00734719i
$523$	4063.53	−	7038.25i	0.339744	−	0.588453i	−0.644641	−	0.764486i	$-0.722993\pi$
$523$	4063.53	−	7038.25i	0.339744	−	0.588453i	0.984384	+	0.176032i	$0.0563264\pi$
$524$	4183.86			0.348803
$525$	1079.10	−	874.593i	0.0897064	−	0.0727055i
$526$	9615.08			0.797029
$527$	1770.26	−	3066.19i	0.146326	−	0.253444i
$528$	307.298	+	532.256i	0.0253285	+	0.0438702i
$529$	4957.19	+	8586.11i	0.407429	+	0.705688i
$530$	14.8246	−	25.6769i	0.00121498	−	0.00210440i
$531$	−7127.01			−0.582460
$532$	−4921.69	−	1886.88i	−0.401095	−	0.153772i
$533$	−95.2443			−0.00774013
$534$	1161.36	−	2011.53i	0.0941139	−	0.163010i
$535$	5137.18	+	8897.85i	0.415139	+	0.719042i
$536$	3887.41	+	6733.19i	0.313266	+	0.542592i
$537$	4696.94	−	8135.34i	0.377445	−	0.653754i
$538$	−5610.57			−0.449608
$539$	644.497	−	3044.74i	0.0515037	−	0.243314i
$540$	827.294			0.0659279
$541$	−4201.72	+	7277.60i	−0.333912	+	0.578352i	−0.983275	−	0.182126i	$-0.941702\pi$
$541$	−4201.72	+	7277.60i	−0.333912	+	0.578352i	0.649364	+	0.760478i	$0.275035\pi$
$542$	5678.59	+	9835.61i	0.450031	+	0.779476i
$543$	−590.848	−	1023.38i	−0.0466956	−	0.0808791i
$544$	−1438.31	+	2491.22i	−0.113358	+	0.196342i
$545$	1606.20			0.126242
$546$	191.405	+	73.3809i	0.0150025	+	0.00575167i
$547$	15317.1			1.19728			0.598639	−	0.801019i	$-0.295709\pi$
$547$	15317.1			1.19728			0.598639	+	0.801019i	$0.295709\pi$
$548$	−1268.94	+	2197.87i	−0.0989170	+	0.171329i
$549$	970.758	+	1681.40i	0.0754662	+	0.130711i
$550$	−155.176	−	268.773i	−0.0120304	−	0.0208373i
$551$	190.810	−	330.493i	0.0147528	−	0.0255526i
$552$	2752.26			0.212218
$553$	1881.93	−	1525.27i	0.144715	−	0.117289i
$554$	−10009.0			−0.767586
$555$	−2506.34	+	4341.11i	−0.191691	+	0.332018i
$556$	−3753.08	−	6500.52i	−0.286270	−	0.495834i
$557$	−9911.16	−	17166.6i	−0.753948	−	1.30588i	−0.945896	−	0.324471i	$-0.894814\pi$
$557$	−9911.16	−	17166.6i	−0.753948	−	1.30588i	0.191947	−	0.981405i	$-0.438520\pi$
$558$	1405.89	−	2435.07i	0.106660	−	0.184740i
$559$	−1375.82			−0.104099
$560$	−327.943	−	2064.91i	−0.0247466	−	0.155819i
$561$	−422.052			−0.0317630
$562$	2055.07	−	3559.49i	0.154249	−	0.267167i
$563$	−5495.57	−	9518.60i	−0.411386	−	0.712542i	0.583655	−	0.812002i	$-0.301622\pi$
$563$	−5495.57	−	9518.60i	−0.411386	−	0.712542i	−0.995042	+	0.0994594i	$0.968289\pi$
$564$	5012.04	+	8681.10i	0.374193	+	0.648121i
$565$	−1907.27	+	3303.49i	−0.142017	+	0.245980i
$566$	5005.39			0.371718
$567$	−235.298	−	1481.57i	−0.0174279	−	0.109736i
$568$	6342.95			0.468564
$569$	−807.265	+	1398.22i	−0.0594768	+	0.103017i	−0.894231	−	0.447606i	$-0.852277\pi$
$569$	−807.265	+	1398.22i	−0.0594768	+	0.103017i	0.834754	+	0.550623i	$0.185610\pi$
$570$	476.564	+	825.434i	0.0350195	+	0.0606555i
$571$	2132.08	+	3692.88i	0.156261	+	0.270652i	0.933517	−	0.358532i	$-0.116723\pi$
$571$	2132.08	+	3692.88i	0.156261	+	0.270652i	−0.777257	+	0.629184i	$0.783389\pi$
$572$	−74.9708	+	129.853i	−0.00548022	+	0.00949202i
$573$	−14247.7			−1.03875
$574$	−695.280	+	563.512i	−0.0505582	+	0.0409766i
$575$	1186.54			0.0860562
$576$	−329.436	+	570.599i	−0.0238307	+	0.0412760i
$577$	−1270.09	−	2199.86i	−0.0916371	−	0.158720i	0.816563	−	0.577256i	$-0.195877\pi$
$577$	−1270.09	−	2199.86i	−0.0916371	−	0.158720i	−0.908200	+	0.418536i	$0.862543\pi$
$578$	3196.46	+	5536.43i	0.230026	+	0.398417i
$579$	−557.914	+	966.336i	−0.0400451	+	0.0693602i
$580$	251.773			0.0180246
$581$	−8774.26	−	3363.88i	−0.626537	−	0.240202i
$582$	5907.45			0.420741
$583$	19.6628	−	34.0570i	0.00139683	−	0.00241937i
$584$	−5062.99	−	8769.35i	−0.358746	−	0.621367i
$585$	60.6742	+	105.091i	0.00428816	+	0.00742730i
$586$	−2783.66	+	4821.44i	−0.196232	+	0.339884i
$587$	−21188.9			−1.48988			−0.744940	−	0.667131i	$-0.767522\pi$
$587$	−21188.9			−1.48988			−0.744940	+	0.667131i	$0.767522\pi$
$588$	−5995.54	+	1953.66i	−0.420497	+	0.137020i
$589$	−10605.1			−0.741897
$590$	2708.61	−	4691.45i	0.189003	−	0.327362i
$591$	1099.34	+	1904.12i	0.0765159	+	0.132529i
$592$	3772.62	+	6534.38i	0.261915	+	0.453651i
$593$	5049.33	−	8745.69i	0.349665	−	0.605637i	−0.636525	−	0.771256i	$-0.719629\pi$
$593$	5049.33	−	8745.69i	0.349665	−	0.605637i	0.986190	+	0.165619i	$0.0529622\pi$
$594$	−335.181			−0.0231526
$595$	1340.63	+	513.972i	0.0923707	+	0.0354131i
$596$	14560.0			1.00067
$597$	4675.64	−	8098.45i	0.320538	−	0.555188i
$598$	87.5542	+	151.648i	0.00598722	+	0.0103702i
$599$	−1040.24	−	1801.74i	−0.0709564	−	0.122900i	0.828364	−	0.560190i	$-0.189272\pi$
$599$	−1040.24	−	1801.74i	−0.0709564	−	0.122900i	−0.899321	+	0.437290i	$0.855938\pi$
$600$	−724.863	+	1255.50i	−0.0493207	+	0.0854260i
$601$	−15577.1			−1.05724			−0.528621	−	0.848858i	$-0.677291\pi$
$601$	−15577.1			−1.05724			−0.528621	+	0.848858i	$0.677291\pi$
$602$	−10043.5	+	8140.05i	−0.679968	+	0.551102i
$603$	3619.99			0.244473
$604$	8571.05	−	14845.5i	0.577403	−	1.00009i
$605$	3121.68	+	5406.91i	0.209776	+	0.363342i
$606$	−3827.93	−	6630.18i	−0.256599	−	0.444443i
$607$	−9266.80	+	16050.6i	−0.619650	+	1.07327i	0.369899	+	0.929072i	$0.379392\pi$
$607$	−9266.80	+	16050.6i	−0.619650	+	1.07327i	−0.989549	+	0.144194i	$0.953941\pi$
$608$	8616.49			0.574745
$609$	−71.6090	−	450.891i	−0.00476477	−	0.0300017i
$610$	−1475.74			−0.0979523
$611$	−735.172	+	1273.35i	−0.0486774	+	0.0843117i
$612$	427.572	+	740.576i	0.0282411	+	0.0489151i
$613$	6325.37	+	10955.9i	0.416769	+	0.721865i	0.995612	−	0.0935737i	$-0.0298291\pi$
$613$	6325.37	+	10955.9i	0.416769	+	0.721865i	−0.578843	+	0.815439i	$0.696496\pi$
$614$	−5406.21	+	9363.84i	−0.355337	+	0.615462i
$615$	−529.796			−0.0347373
$616$	509.487	+	3208.02i	0.0333244	+	0.209829i
$617$	−795.348			−0.0518955			−0.0259477	−	0.999663i	$-0.508260\pi$
$617$	−795.348			−0.0518955			−0.0259477	+	0.999663i	$0.508260\pi$
$618$	896.328	−	1552.49i	0.0583424	−	0.101052i
$619$	12327.9	+	21352.5i	0.800483	+	1.38648i	0.919299	+	0.393561i	$0.128757\pi$
$619$	12327.9	+	21352.5i	0.800483	+	1.38648i	−0.118816	+	0.992916i	$0.537910\pi$
$620$	−3498.35	−	6059.32i	−0.226608	−	0.392497i
$621$	640.734	−	1109.78i	0.0414038	−	0.0717135i
$622$	4148.07			0.267400
$623$	−8142.06	+	6599.00i	−0.523603	+	0.424371i
$624$	182.657			0.0117182
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	225.014	+	389.735i	0.0143664	+	0.0248833i
$627$	632.099	+	1094.83i	0.0402609	+	0.0697339i
$628$	4083.34	−	7072.56i	0.259464	−	0.449404i
$629$	−5181.43			−0.328454
$630$	1064.69	+	408.181i	0.0673305	+	0.0258132i
$631$	−12153.3			−0.766743			−0.383371	−	0.923594i	$-0.625237\pi$
$631$	−12153.3			−0.766743			−0.383371	+	0.923594i	$0.625237\pi$
$632$	−1264.14	+	2189.56i	−0.0795647	+	0.137810i
$633$	2052.15	+	3554.43i	0.128856	+	0.223184i
$634$	−1964.19	−	3402.07i	−0.123041	−	0.213113i
$635$	1740.41	−	3014.48i	0.108765	−	0.188387i
$636$	−79.6798			−0.00496778
$637$	−687.890	−	618.329i	−0.0427868	−	0.0384601i
$638$	−102.007			−0.00632990
$639$	1476.66	−	2557.64i	0.0914172	−	0.158339i
$640$	3460.17	+	5993.19i	0.213711	+	0.370159i
$641$	−5218.85	−	9039.32i	−0.321579	−	0.556991i	0.659235	−	0.751937i	$-0.270880\pi$
$641$	−5218.85	−	9039.32i	−0.321579	−	0.556991i	−0.980814	+	0.194946i	$0.937547\pi$
$642$	−4217.13	+	7304.28i	−0.259247	+	0.449030i
$643$	16184.5			0.992621			0.496311	−	0.868145i	$-0.334688\pi$
$643$	16184.5			0.992621			0.496311	+	0.868145i	$0.334688\pi$
$644$	−5029.66	−	1928.27i	−0.307759	−	0.117989i
$645$	−7653.01			−0.467189
$646$	−492.607	+	853.221i	−0.0300021	+	0.0519652i
$647$	13445.5	+	23288.3i	0.816997	+	1.41508i	0.907885	+	0.419219i	$0.137696\pi$
$647$	13445.5	+	23288.3i	0.816997	+	1.41508i	−0.0908880	+	0.995861i	$0.528971\pi$
$648$	782.853	+	1355.94i	0.0474589	+	0.0822012i
$649$	3592.60	−	6222.57i	0.217291	−	0.376360i
$650$	−92.2365			−0.00556587
$651$	−9856.44	+	7988.47i	−0.593401	+	0.480941i
$652$	14932.4			0.896926
$653$	2592.17	−	4489.76i	0.155343	−	0.269063i	−0.777841	−	0.628462i	$-0.783685\pi$
$653$	2592.17	−	4489.76i	0.155343	−	0.269063i	0.933184	+	0.359399i	$0.117018\pi$
$654$	659.268	+	1141.89i	0.0394181	+	0.0682741i
$655$	1706.83	+	2956.32i	0.101819	+	0.176356i
$656$	−398.732	+	690.624i	−0.0237315	+	0.0411042i
$657$	−4714.70			−0.279967
$658$	2167.07	+	13645.1i	0.128391	+	0.808420i
$659$	−30149.8			−1.78220			−0.891099	−	0.453809i	$-0.850065\pi$
$659$	−30149.8			−1.78220			−0.891099	+	0.453809i	$0.850065\pi$
$660$	−417.024	+	722.308i	−0.0245949	+	0.0425997i
$661$	7591.20	+	13148.3i	0.446692	+	0.773694i	0.998168	−	0.0604970i	$-0.0192686\pi$
$661$	7591.20	+	13148.3i	0.446692	+	0.773694i	−0.551476	+	0.834191i	$0.685935\pi$
$662$	6265.27	+	10851.8i	0.367835	+	0.637108i
$663$	−62.7168	+	108.629i	−0.00367378	+	0.00636318i
$664$	9807.69			0.573211
$665$	−674.564	−	4247.44i	−0.0393360	−	0.247682i
$666$	−4114.94			−0.239415
$667$	194.996	−	337.744i	0.0113198	−	0.0196064i
$668$	7339.54	+	12712.5i	0.425113	+	0.736317i
$669$	−6241.73	−	10811.0i	−0.360716	−	0.624779i
$670$	−1375.77	+	2382.91i	−0.0793294	+	0.137403i
$671$	−1957.37			−0.112613
$672$	8008.18	−	6490.49i	0.459706	−	0.372583i
$673$	12549.6			0.718799			0.359399	−	0.933184i	$-0.382982\pi$
$673$	12549.6			0.718799			0.359399	+	0.933184i	$0.382982\pi$
$674$	4241.34	−	7346.21i	0.242389	−	0.419830i
$675$	337.500	+	584.567i	0.0192450	+	0.0333333i
$676$	−6709.44	−	11621.1i	−0.381739	−	0.661191i
$677$	−9371.64	+	16232.2i	−0.532026	+	0.921496i	0.467275	+	0.884112i	$0.345236\pi$
$677$	−9371.64	+	16232.2i	−0.532026	+	0.921496i	−0.999301	+	0.0373837i	$0.988098\pi$
$678$	−3131.37			−0.177374
$679$	−24888.9	−	9541.93i	−1.40670	−	0.539302i
$680$	−1498.53			−0.0845088
$681$	−2752.48	+	4767.43i	−0.154883	+	0.268265i
$682$	1417.37	+	2454.95i	0.0795804	+	0.137837i
$683$	−12613.0	−	21846.3i	−0.706622	−	1.22390i	−0.966103	−	0.258157i	$-0.916885\pi$
$683$	−12613.0	−	21846.3i	−0.706622	−	1.22390i	0.259481	−	0.965748i	$-0.416448\pi$
$684$	1280.73	−	2218.29i	0.0715935	−	0.124004i
$685$	−2070.69			−0.115499
$686$	−8679.91	−	443.889i	−0.483091	−	0.0247052i
$687$	−5533.67			−0.307311
$688$	−5759.77	+	9976.21i	−0.319170	+	0.552819i
$689$	−5.84377	−	10.1217i	−0.000323120	−	0.000559660i
$690$	487.019	+	843.542i	0.0268703	+	0.0465407i
$691$	9936.24	−	17210.1i	0.547022	−	0.947470i	−0.451455	−	0.892294i	$-0.649095\pi$
$691$	9936.24	−	17210.1i	0.547022	−	0.947470i	0.998477	−	0.0551758i	$-0.0175719\pi$
$692$	−18017.1			−0.989751
$693$	1412.17	+	541.397i	0.0774080	+	0.0296767i
$694$	5078.75			0.277790
$695$	3062.19	−	5303.86i	0.167130	−	0.289478i
$696$	238.248	+	412.657i	0.0129752	+	0.0224738i
$697$	−273.815	−	474.262i	−0.0148802	−	0.0257733i
$698$	424.100	−	734.563i	0.0229977	−	0.0398332i
$699$	−16039.7			−0.867923
$700$	2204.28	−	1786.53i	0.119020	−	0.0964637i
$701$	25586.8			1.37860			0.689301	−	0.724475i	$-0.257918\pi$
$701$	25586.8			1.37860			0.689301	+	0.724475i	$0.257918\pi$
$702$	−49.8077	+	86.2695i	−0.00267788	+	0.00463822i
$703$	7760.12	+	13440.9i	0.416328	+	0.721101i
$704$	−332.126	−	575.259i	−0.0177805	−	0.0307967i
$705$	−4089.39	+	7083.03i	−0.218461	+	0.378386i
$706$	5712.90			0.304544
$707$	5418.34	+	34116.9i	0.288228	+	1.81485i
$708$	−14558.4			−0.772792
$709$	11747.1	−	20346.5i	0.622244	−	1.07776i	−0.366823	−	0.930291i	$-0.619555\pi$
$709$	11747.1	−	20346.5i	0.622244	−	1.07776i	0.989067	−	0.147467i	$-0.0471120\pi$
$710$	1122.40	+	1944.05i	0.0593281	+	0.102759i
$711$	588.591	+	1019.47i	0.0310462	+	0.0537737i
$712$	5469.25	−	9473.02i	0.287878	−	0.498619i
$713$	−10837.8			−0.569255
$714$	184.870	+	1164.05i	0.00968990	+	0.0610132i
$715$	−122.339			−0.00639893
$716$	9594.45	−	16618.1i	0.500784	−	0.867383i
$717$	−2109.19	−	3653.22i	−0.109859	−	0.190282i
$718$	−4249.44	−	7360.24i	−0.220874	−	0.382565i
$719$	−7048.12	+	12207.7i	−0.365578	+	0.633200i	−0.988869	−	0.148790i	$-0.952462\pi$
$719$	−7048.12	+	12207.7i	−0.365578	+	0.633200i	0.623291	+	0.781990i	$0.285795\pi$
$720$	1016.03			0.0525906
$721$	−6284.00	+	5093.07i	−0.324589	+	0.263073i
$722$	−6433.23			−0.331607
$723$	2700.41	−	4677.24i	0.138906	−	0.240593i
$724$	−1206.92	−	2090.46i	−0.0619544	−	0.107308i
$725$	102.712	+	177.903i	0.00526158	+	0.00911332i
$726$	−2562.60	+	4438.55i	−0.131001	+	0.226901i
$727$	25807.9			1.31659			0.658296	−	0.752759i	$-0.271278\pi$
$727$	25807.9			1.31659			0.658296	+	0.752759i	$0.271278\pi$
$728$	901.396	+	345.578i	0.0458901	+	0.0175934i
$729$	729.000			0.0370370
$730$	1791.81	−	3103.51i	0.0908466	−	0.157351i
$731$	−3955.32	−	6850.81i	−0.200127	−	0.346630i
$732$	1982.97	+	3434.60i	0.100126	+	0.173424i
$733$	12842.4	−	22243.7i	0.647127	−	1.12086i	−0.336679	−	0.941620i	$-0.609304\pi$
$733$	12842.4	−	22243.7i	0.647127	−	1.12086i	0.983806	−	0.179237i	$-0.0573630\pi$
$734$	6620.93			0.332947
$735$	−3826.38	−	3439.45i	−0.192025	−	0.172607i
$736$	8805.52			0.441000
$737$	−1824.78	+	3160.60i	−0.0912028	+	0.157968i
$738$	−217.456	−	376.644i	−0.0108464	−	0.0187865i
$739$	−7964.29	−	13794.5i	−0.396443	−	0.686659i	0.596842	−	0.802359i	$-0.296422\pi$
$739$	−7964.29	−	13794.5i	−0.396443	−	0.686659i	−0.993284	+	0.115700i	$0.963089\pi$
$740$	−5119.71	+	8867.60i	−0.254330	+	0.440513i
$741$	375.718			0.0186267
$742$	−102.544	−	39.3134i	−0.00507347	−	0.00194507i
$743$	−9733.51			−0.480603			−0.240301	−	0.970698i	$-0.577246\pi$
$743$	−9733.51			−0.480603			−0.240301	+	0.970698i	$0.577246\pi$
$744$	6620.85	−	11467.6i	0.326253	−	0.565086i
$745$	5939.84	+	10288.1i	0.292106	+	0.505943i
$746$	−8179.89	−	14168.0i	−0.401457	−	0.695344i
$747$	2283.25	−	3954.71i	0.111834	−	0.193702i
$748$	−862.126			−0.0421423
$749$	29565.5	−	23962.3i	1.44232	−	1.16898i
$750$	−513.065			−0.0249793
$751$	−10902.8	+	18884.1i	−0.529756	+	0.917565i	0.469641	+	0.882857i	$0.344383\pi$
$751$	−10902.8	+	18884.1i	−0.529756	+	0.917565i	−0.999398	+	0.0347077i	$0.988950\pi$
$752$	6155.47	+	10661.6i	0.298493	+	0.517005i
$753$	−4452.38	−	7711.75i	−0.215476	−	0.373216i
$754$	−15.1581	+	26.2547i	−0.000732131	+	0.00126809i
$755$	13986.5			0.674198
$756$	−480.644	−	3026.41i	−0.0231228	−	0.145595i
$757$	−5231.20			−0.251164			−0.125582	−	0.992083i	$-0.540080\pi$
$757$	−5231.20			−0.251164			−0.125582	+	0.992083i	$0.540080\pi$
$758$	8918.42	−	15447.2i	0.427350	−	0.740193i
$759$	645.966	+	1118.85i	0.0308921	+	0.0535066i
$760$	2244.32	+	3887.27i	0.107118	+	0.185534i
$761$	11778.6	−	20401.1i	0.561069	−	0.971800i	−0.436334	−	0.899785i	$-0.643723\pi$
$761$	11778.6	−	20401.1i	0.561069	−	0.971800i	0.997403	−	0.0720157i	$-0.0229432\pi$
$762$	2857.42			0.135844
$763$	−933.176	−	5875.81i	−0.0442768	−	0.278792i
$764$	−29103.7			−1.37819
$765$	−348.862	+	604.246i	−0.0164877	+	0.0285576i
$766$	2950.46	+	5110.35i	0.139170	+	0.241050i
$767$	−1067.72	−	1849.34i	−0.0502648	−	0.0870612i
$768$	−3718.96	+	6441.44i	−0.174735	+	0.302650i
$769$	−7441.48			−0.348955			−0.174478	−	0.984661i	$-0.555824\pi$
$769$	−7441.48			−0.348955			−0.174478	+	0.984661i	$0.555824\pi$
$770$	−893.073	+	723.819i	−0.0417975	+	0.0338762i
$771$	19151.3			0.894577
$772$	−1139.65	+	1973.93i	−0.0531308	+	0.0920252i
$773$	−8451.83	−	14639.0i	−0.393262	−	0.681149i	0.599616	−	0.800288i	$-0.295320\pi$
$773$	−8451.83	−	14639.0i	−0.393262	−	0.681149i	−0.992878	+	0.119139i	$0.961987\pi$
$774$	−3141.19	−	5440.70i	−0.145876	−	0.252664i
$775$	2854.35	−	4943.88i	0.132298	−	0.229148i
$776$	27820.3			1.28697
$777$	17336.8	+	6646.60i	0.800457	+	0.306880i
$778$	−11164.3			−0.514474
$779$	−820.175	+	1420.58i	−0.0377225	+	0.0653373i
$780$	123.939	+	214.669i	0.00568941	+	0.00985435i
$781$	1488.71	+	2578.53i	0.0682078	+	0.118139i
$782$	−503.414	+	871.939i	−0.0230205	+	0.0398727i
$783$	221.859			0.0101259
$784$	−7363.35	+	2399.36i	−0.335429	+	0.109300i
$785$	6663.31			0.302960
$786$	−1401.15	+	2426.86i	−0.0635843	+	0.110131i
$787$	6822.17	+	11816.3i	0.309001	+	0.535206i	0.978144	−	0.207928i	$-0.0666719\pi$
$787$	6822.17	+	11816.3i	0.309001	+	0.535206i	−0.669143	+	0.743134i	$0.733339\pi$
$788$	2245.63	+	3889.54i	0.101519	+	0.175836i
$789$	10541.5	−	18258.4i	0.475650	−	0.823850i
$790$	−894.771			−0.0402969
$791$	13192.9	+	5057.91i	0.593030	+	0.227356i
$792$	−1578.49			−0.0708197
$793$	−290.864	+	503.792i	−0.0130251	+	0.0225601i
$794$	−1904.16	−	3298.10i	−0.0851084	−	0.147412i
$795$	−32.5059	−	56.3019i	−0.00145015	−	0.00251173i
$796$	9550.94	−	16542.7i	0.425281	−	0.736609i
$797$	−35027.5			−1.55676			−0.778379	−	0.627795i	$-0.783958\pi$
$797$	−35027.5			−1.55676			−0.778379	+	0.627795i	$0.783958\pi$
$798$	2742.73	−	2222.93i	0.121669	−	0.0986103i
$799$	−8454.10			−0.374324
$800$	−2319.11	+	4016.82i	−0.102491	+	0.177520i
$801$	−2546.51	−	4410.69i	−0.112330	−	0.194562i
$802$	1206.89	+	2090.40i	0.0531382	+	0.0920380i
$803$	2376.60	−	4116.39i	0.104444	−	0.180902i
$804$	7394.56			0.324361
$805$	−689.363	−	4340.62i	−0.0301824	−	0.190046i
$806$	842.481			0.0368178
$807$	−6151.17	+	10654.1i	−0.268316	+	0.464738i
$808$	−18027.1	−	31223.9i	−0.784892	−	1.35947i
$809$	20113.0	+	34836.8i	0.874087	+	1.51396i	0.857733	+	0.514096i	$0.171873\pi$
$809$	20113.0	+	34836.8i	0.874087	+	1.51396i	0.0163539	+	0.999866i	$0.494794\pi$
$810$	−277.055	+	479.874i	−0.0120182	+	0.0208161i
$811$	16374.0			0.708963			0.354482	−	0.935063i	$-0.384657\pi$
$811$	16374.0			0.708963			0.354482	+	0.935063i	$0.384657\pi$
$812$	−146.276	−	921.036i	−0.00632177	−	0.0398055i
$813$	24903.0			1.07427
$814$	2074.27	−	3592.74i	0.0893158	−	0.154699i
$815$	6091.75	+	10551.2i	0.261822	+	0.453489i
$816$	525.117	+	909.529i	0.0225279	+	0.0390195i
$817$	−11847.6	+	20520.6i	−0.507338	+	0.878735i
$818$	−18567.2			−0.793625
$819$	349.193	−	283.015i	0.0148984	−	0.0120749i
$820$	−1082.21			−0.0460885
$821$	13801.8	−	23905.3i	0.586705	−	1.01620i	−0.407956	−	0.913002i	$-0.633758\pi$
$821$	13801.8	−	23905.3i	0.586705	−	1.01620i	0.994661	−	0.103201i	$-0.0329084\pi$
$822$	−849.920	−	1472.11i	−0.0360637	−	0.0624642i
$823$	−4470.74	−	7743.55i	−0.189356	−	0.327975i	0.755680	−	0.654942i	$-0.227307\pi$
$823$	−4470.74	−	7743.55i	−0.189356	−	0.327975i	−0.945036	+	0.326967i	$0.893973\pi$
$824$	4221.14	−	7311.23i	0.178459	−	0.309100i
$825$	−680.512			−0.0287180
$826$	−18735.9	−	7182.99i	−0.789233	−	0.302576i
$827$	36920.4			1.55242			0.776208	−	0.630476i	$-0.217140\pi$
$827$	36920.4			1.55242			0.776208	+	0.630476i	$0.217140\pi$
$828$	1308.83	−	2266.96i	0.0549335	−	0.0951475i
$829$	−1611.11	−	2790.52i	−0.0674983	−	0.116910i	0.830301	−	0.557315i	$-0.188168\pi$
$829$	−1611.11	−	2790.52i	−0.0674983	−	0.116910i	−0.897799	+	0.440404i	$0.854835\pi$
$830$	1735.49	+	3005.96i	0.0725781	+	0.125709i
$831$	−10973.4	+	19006.5i	−0.458079	+	0.793416i
$832$	−197.415			−0.00822612
$833$	1101.33	−	5202.92i	0.0458089	−	0.216411i
$834$	5027.52			0.208740
$835$	−5988.43	+	10372.3i	−0.248189	+	0.429877i
$836$	1291.19	+	2236.40i	0.0534171	+	0.0925211i
$837$	−3082.70	−	5339.39i	−0.127304	−	0.220497i
$838$	−8273.27	+	14329.7i	−0.341044	+	0.590706i
$839$	8534.92			0.351201			0.175601	−	0.984461i	$-0.443813\pi$
$839$	8534.92			0.351201			0.175601	+	0.984461i	$0.443813\pi$
$840$	5014.01	+	1922.27i	0.205952	+	0.0789580i
$841$	−24321.5			−0.997232
$842$	4477.03	−	7754.44i	0.183240	−	0.317382i
$843$	−4506.17	−	7804.92i	−0.184105	−	0.318880i
$844$	4191.92	+	7260.63i	0.170962	+	0.296115i
$845$	5474.32	−	9481.80i	0.222867	−	0.386016i
$846$	−6713.99			−0.272851
$847$	17965.9	−	14561.1i	0.728827	−	0.590701i
$848$	−97.8577			−0.00396279
$849$	5487.67	−	9504.93i	0.221833	−	0.384226i
$850$	−265.168	−	459.285i	−0.0107002	−	0.0185334i
$851$	7930.37	+	13735.8i	0.319447	+	0.553299i
$852$	3016.36	−	5224.50i	0.121290	−	0.210080i
$853$	12096.5			0.485553			0.242776	−	0.970082i	$-0.421942\pi$
$853$	12096.5			0.485553			0.242776	+	0.970082i	$0.421942\pi$
$854$	857.380	+	5398.55i	0.0343547	+	0.216317i
$855$	2089.93			0.0835954
$856$	−19860.0	+	34398.5i	−0.792992	+	1.37350i
$857$	8936.79	+	15479.0i	0.356213	+	0.616980i	0.987325	−	0.158713i	$-0.0507343\pi$
$857$	8936.79	+	15479.0i	0.356213	+	0.616980i	−0.631112	+	0.775692i	$0.717401\pi$
$858$	−50.2144	−	86.9739i	−0.00199801	−	0.00346065i
$859$	11869.0	−	20557.7i	0.471438	−	0.816554i	−0.528028	−	0.849227i	$-0.677069\pi$
$859$	11869.0	−	20557.7i	0.471438	−	0.816554i	0.999466	+	0.0326728i	$0.0104019\pi$
$860$	−15632.8			−0.619854
$861$	307.803	+	1938.10i	0.0121834	+	0.0767135i
$862$	−4898.20			−0.193542
$863$	−15135.8	+	26215.9i	−0.597019	+	1.03407i	0.396240	+	0.918147i	$0.370315\pi$
$863$	−15135.8	+	26215.9i	−0.597019	+	1.03407i	−0.993259	+	0.115920i	$0.963018\pi$
$864$	2504.64	+	4338.16i	0.0986221	+	0.170819i
$865$	−7350.20	−	12730.9i	−0.288918	−	0.500421i
$866$	9996.17	−	17313.9i	0.392244	−	0.679387i
$867$	14017.8			0.549099
$868$	−20133.7	+	16318.0i	−0.787309	+	0.638100i
$869$	−1186.79			−0.0463282
$870$	−84.3170	+	146.041i	−0.00328576	+	0.00569111i
$871$	542.322	+	939.329i	0.0210974	+	0.0365418i
$872$	3104.73	+	5377.56i	0.120573	+	0.208838i
$873$	6476.64	−	11217.9i	0.251090	−	0.434900i
$874$	3015.81			0.116718
$875$	2161.62	+	828.722i	0.0835155	+	0.0320182i
$876$	−9630.73			−0.371452
$877$	−14222.4	+	24633.8i	−0.547611	+	0.948490i	0.450827	+	0.892612i	$0.351129\pi$
$877$	−14222.4	+	24633.8i	−0.547611	+	0.948490i	−0.998438	+	0.0558784i	$0.982204\pi$
$878$	−7917.27	−	13713.1i	−0.304322	−	0.527102i
$879$	6103.75	+	10572.0i	0.234214	+	0.405671i
$880$	−512.163	+	887.093i	−0.0196193	+	0.0339817i
$881$	−6712.92			−0.256713			−0.128356	−	0.991728i	$-0.540970\pi$
$881$	−6712.92			−0.256713			−0.128356	+	0.991728i	$0.540970\pi$
$882$	874.642	−	4132.00i	0.0333909	−	0.157745i
$883$	21771.1			0.829735			0.414867	−	0.909882i	$-0.363828\pi$
$883$	21771.1			0.829735			0.414867	+	0.909882i	$0.363828\pi$
$884$	−128.112	+	221.896i	−0.00487427	+	0.00844249i
$885$	−5939.18	−	10287.0i	−0.225586	−	0.390726i
$886$	−11142.9	−	19300.1i	−0.422520	−	0.731827i
$887$	−22594.8	+	39135.3i	−0.855307	+	1.48144i	0.0210523	+	0.999778i	$0.493298\pi$
$887$	−22594.8	+	39135.3i	−0.855307	+	1.48144i	−0.876360	+	0.481657i	$0.840035\pi$
$888$	−19378.7			−0.732329
$889$	−12038.7	−	4615.41i	−0.454179	−	0.174124i
$890$	3871.19			0.145801
$891$	−367.476	+	636.488i	−0.0138170	+	0.0239317i
$892$	−12750.0	−	22083.6i	−0.478589	−	0.828940i
$893$	12661.5	+	21930.4i	0.474470	+	0.821807i
$894$	−4876.04	+	8445.55i	−0.182415	+	0.315952i
$895$	15656.5			0.584736
$896$	19914.0	−	16140.0i	0.742501	−	0.601784i
$897$	383.961			0.0142922
$898$	−3386.92	+	5866.33i	−0.125861	+	0.217998i
$899$	−938.167	−	1624.95i	−0.0348049	−	0.0602839i
$900$	689.411	+	1194.10i	0.0255338	+	0.0442258i
$901$	33.6002	−	58.1972i	0.00124238	−	0.00215187i
$902$	438.463			0.0161854
$903$	4446.27	+	27996.3i	0.163857	+	1.03174i
$904$	−14746.8			−0.542556
$905$	984.746	−	1705.63i	0.0361702	−	0.0626487i
$906$	5740.78	+	9943.31i	0.210513	+	0.364619i
$907$	−1838.72	−	3184.75i	−0.0673139	−	0.116591i	0.830404	−	0.557161i	$-0.188110\pi$
$907$	−1838.72	−	3184.75i	−0.0673139	−	0.116591i	−0.897718	+	0.440570i	$0.854776\pi$
$908$	−5622.49	+	9738.44i	−0.205494	+	0.355927i
$909$	−16787.1			−0.612532
$910$	53.5879	+	337.420i	0.00195211	+	0.0122916i
$911$	−45601.1			−1.65843			−0.829217	−	0.558927i	$-0.811213\pi$
$911$	−45601.1			−1.65843			−0.829217	+	0.558927i	$0.811213\pi$
$912$	1572.91	−	2724.36i	0.0571100	−	0.0989175i
$913$	2301.90	+	3987.00i	0.0834411	+	0.144524i
$914$	4404.34	+	7628.54i	0.159390	+	0.276072i
$915$	−1617.93	+	2802.34i	−0.0584559	+	0.101249i
$916$	−11303.6			−0.407732
$917$	9823.20	−	7961.53i	0.353752	−	0.286710i
$918$	−572.764			−0.0205926
$919$	−2709.26	+	4692.57i	−0.0972471	+	0.168437i	−0.910544	−	0.413412i	$-0.864337\pi$
$919$	−2709.26	+	4692.57i	−0.0972471	+	0.168437i	0.813297	+	0.581849i	$0.197670\pi$
$920$	2293.55	+	3972.55i	0.0821915	+	0.142360i
$921$	11854.2	+	20532.1i	0.424115	+	0.734589i
$922$	3841.43	−	6653.55i	0.137213	−	0.237660i
$923$	884.888			0.0315563
$924$	2884.63	+	1105.91i	0.102703	+	0.0393743i
$925$	−8354.48			−0.296966
$926$	−2979.45	+	5160.55i	−0.105735	+	0.183139i
$927$	−1965.38	−	3404.14i	−0.0696350	−	0.120611i
$928$	762.244	+	1320.25i	0.0269632	+	0.0467017i
$929$	−5011.32	+	8679.87i	−0.176982	+	0.306542i	−0.940845	−	0.338836i	$-0.889967\pi$
$929$	−5011.32	+	8679.87i	−0.176982	+	0.306542i	0.763863	+	0.645378i	$0.223300\pi$
$930$	4686.30			0.165236
$931$	−15146.1	+	4935.38i	−0.533183	+	0.173739i
$932$	−32764.4			−1.15154
$933$	4547.75	−	7876.94i	0.159578	−	0.276398i
$934$	7217.68	+	12501.4i	0.252859	+	0.437964i
$935$	−351.710	−	609.180i	−0.0123018	−	0.0213073i
$936$	−234.563	+	406.275i	−0.00819116	+	0.0141875i
$937$	−25723.9			−0.896865			−0.448432	−	0.893817i	$-0.648018\pi$
$937$	−25723.9			−0.896865			−0.448432	+	0.893817i	$0.648018\pi$
$938$	9516.46	+	3648.42i	0.331262	+	0.126999i
$939$	986.777			0.0342942
$940$	−8353.39	+	14468.5i	−0.289849	+	0.502033i
$941$	−9649.99	−	16714.3i	−0.334305	−	0.579033i	0.649046	−	0.760749i	$-0.275168\pi$
$941$	−9649.99	−	16714.3i	−0.334305	−	0.579033i	−0.983351	+	0.181716i	$0.941835\pi$
$942$	2734.97	+	4737.10i	0.0945967	+	0.163846i
$943$	−838.168	+	1451.75i	−0.0289443	+	0.0501331i
$944$	−17879.7			−0.616455
$945$	1942.38	−	1574.27i	0.0668632	−	0.0541915i
$946$	6333.68			0.217681
$947$	19126.6	−	33128.3i	0.656317	−	1.13677i	−0.325245	−	0.945630i	$-0.605447\pi$
$947$	19126.6	−	33128.3i	0.656317	−	1.13677i	0.981562	−	0.191144i	$-0.0612198\pi$
$948$	1202.31	+	2082.47i	0.0411913	+	0.0713455i
$949$	−706.324	−	1223.39i	−0.0241604	−	0.0418471i
$950$	−794.274	+	1375.72i	−0.0271260	+	0.0469835i
$951$	−8613.76			−0.293712
$952$	870.621	+	5481.93i	0.0296397	+	0.186629i
$953$	29645.9			1.00769			0.503843	−	0.863795i	$-0.331919\pi$
$953$	29645.9			1.00769			0.503843	+	0.863795i	$0.331919\pi$
$954$	26.6842	−	46.2184i	0.000905591	−	0.00156853i
$955$	−11873.1	−	20564.7i	−0.402307	−	0.696816i
$956$	−4308.44	−	7462.44i	−0.145758	−	0.252461i
$957$	−111.835	+	193.704i	−0.00377755	+	0.00654291i
$958$	−14636.0			−0.493597
$959$	1203.04	+	7575.02i	0.0405090	+	0.255068i
$960$	−1098.12			−0.0369184
$961$	−11175.9	+	19357.3i	−0.375144	+	0.649769i
$962$	−616.471	−	1067.76i	−0.0206609	−	0.0357858i
$963$	9246.92	+	16016.1i	0.309426	+	0.535942i
$964$	5516.12	−	9554.20i	0.184297	−	0.319212i
$965$	−1859.71			−0.0620376
$966$	2802.90	−	2271.70i	0.0933559	−	0.0756633i
$967$	13170.0			0.437970			0.218985	−	0.975728i	$-0.429725\pi$
$967$	13170.0			0.437970			0.218985	+	0.975728i	$0.429725\pi$
$968$	−12068.2	+	20902.8i	−0.400710	+	0.694050i
$969$	1080.14	+	1870.86i	0.0358093	+	0.0620235i
$970$	4922.87	+	8526.66i	0.162952	+	0.282242i
$971$	−16992.3	+	29431.5i	−0.561595	+	0.972710i	0.435763	+	0.900061i	$0.356479\pi$
$971$	−16992.3	+	29431.5i	−0.561595	+	0.972710i	−0.997358	+	0.0726489i	$0.976855\pi$
$972$	1489.13			0.0491397
$973$	−21181.7	−	8120.65i	−0.697897	−	0.267560i
$974$	3299.40			0.108542
$975$	−101.124	+	175.151i	−0.00332159	+	0.00575316i
$976$	2435.36	+	4218.16i	0.0798707	+	0.138340i
$977$	−14126.6	−	24468.0i	−0.462589	−	0.801227i	0.536500	−	0.843900i	$-0.319746\pi$
$977$	−14126.6	−	24468.0i	−0.462589	−	0.801227i	−0.999089	+	0.0426728i	$0.986413\pi$
$978$	−5000.74	+	8661.54i	−0.163503	+	0.283196i
$979$	5134.61			0.167623
$980$	−7816.15	−	7025.77i	−0.254773	−	0.229010i
$981$	2891.16			0.0940954
$982$	−14178.1	+	24557.3i	−0.460736	+	0.798018i
$983$	−19444.3	−	33678.5i	−0.630902	−	1.09275i	−0.987368	−	0.158446i	$-0.949352\pi$
$983$	−19444.3	−	33678.5i	−0.630902	−	1.09275i	0.356466	−	0.934308i	$-0.383982\pi$
$984$	−1024.08	−	1773.76i	−0.0331773	−	0.0574647i
$985$	−1832.24	+	3173.53i	−0.0592690	+	0.102657i
$986$	−174.311			−0.00563001
$987$	28287.0	+	10844.7i	0.912245	+	0.349737i
$988$	767.480			0.0247134
$989$	−12107.5	+	20970.8i	−0.389278	+	0.674250i
$990$	−279.317	−	483.792i	−0.00896696	−	0.0155312i
$991$	−5046.75	−	8741.23i	−0.161771	−	0.280196i	0.773733	−	0.633512i	$-0.218387\pi$
$991$	−5046.75	−	8741.23i	−0.161771	−	0.280196i	−0.935504	+	0.353316i	$0.885054\pi$
$992$	21182.6	−	36689.3i	0.677971	−	1.17428i
$993$	27475.8			0.878064
$994$	6459.65	−	5235.43i	0.206124	−	0.167060i
$995$	15585.5			0.496576
$996$	4664.00	−	8078.29i	0.148378	−	0.256998i
$997$	−22123.6	−	38319.3i	−0.702771	−	1.21723i	−0.967490	−	0.252909i	$-0.918613\pi$
$997$	−22123.6	−	38319.3i	−0.702771	−	1.21723i	0.264719	−	0.964326i	$-0.414721\pi$
$998$	11292.3	+	19558.9i	0.358168	+	0.620366i
$999$	−4511.42	+	7814.01i	−0.142878	+	0.247472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.i.c.16.2	✓	6
3.2	odd	2		315.4.j.e.226.2		6
7.2	even	3		735.4.a.r.1.2		3
7.4	even	3	inner	105.4.i.c.46.2	yes	6
7.5	odd	6		735.4.a.s.1.2		3
21.2	odd	6		2205.4.a.bi.1.2		3
21.5	even	6		2205.4.a.bj.1.2		3
21.11	odd	6		315.4.j.e.46.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.i.c.16.2	✓	6	1.1	even	1	trivial
105.4.i.c.46.2	yes	6	7.4	even	3	inner
315.4.j.e.46.2		6	21.11	odd	6
315.4.j.e.226.2		6	3.2	odd	2
735.4.a.r.1.2		3	7.2	even	3
735.4.a.s.1.2		3	7.5	odd	6
2205.4.a.bi.1.2		3	21.2	odd	6
2205.4.a.bj.1.2		3	21.5	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.684087 + 1.18487i) q^{2} +(1.50000 + 2.59808i) q^{3} +(3.06405 + 5.30709i) q^{4} +(-2.50000 + 4.33013i) q^{5} -4.10452 q^{6} +(17.2929 + 6.62978i) q^{7} -19.3297 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-0.684087 + 1.18487i) q^{2} +(1.50000 + 2.59808i) q^{3} +(3.06405 + 5.30709i) q^{4} +(-2.50000 + 4.33013i) q^{5} -4.10452 q^{6} +(17.2929 + 6.62978i) q^{7} -19.3297 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-3.42043 - 5.92436i) q^{10} +(-4.53674 - 7.85787i) q^{11} +(-9.19215 + 15.9213i) q^{12} -2.69663 q^{13} +(-19.6853 + 15.9546i) q^{14} -15.0000 q^{15} +(-11.2892 + 19.5535i) q^{16} +(-7.75248 - 13.4277i) q^{17} +(-6.15678 - 10.6639i) q^{18} +(-23.2214 + 40.2207i) q^{19} -30.6405 q^{20} +(8.71475 + 54.8731i) q^{21} +12.4141 q^{22} +(-23.7309 + 41.1031i) q^{23} +(-28.9945 - 50.2200i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(1.84473 - 3.19517i) q^{26} -27.0000 q^{27} +(17.8016 + 112.089i) q^{28} -8.21699 q^{29} +(10.2613 - 17.7731i) q^{30} +(114.174 + 197.755i) q^{31} +(-92.7644 - 160.673i) q^{32} +(13.6102 - 23.5736i) q^{33} +21.2135 q^{34} +(-71.9402 + 58.3062i) q^{35} -55.1529 q^{36} +(167.090 - 289.408i) q^{37} +(-31.7710 - 55.0289i) q^{38} +(-4.04495 - 7.00606i) q^{39} +(48.3242 - 83.7000i) q^{40} +35.3197 q^{41} +(-70.9792 - 27.2121i) q^{42} +510.201 q^{43} +(27.8016 - 48.1538i) q^{44} +(-22.5000 - 38.9711i) q^{45} +(-32.4680 - 56.2362i) q^{46} +(272.626 - 472.202i) q^{47} -67.7353 q^{48} +(255.092 + 229.297i) q^{49} +34.2043 q^{50} +(23.2574 - 40.2831i) q^{51} +(-8.26262 - 14.3113i) q^{52} +(2.16706 + 3.75346i) q^{53} +(18.4703 - 31.9916i) q^{54} +45.3674 q^{55} +(-334.267 - 128.152i) q^{56} -139.329 q^{57} +(5.62113 - 9.73609i) q^{58} +(395.945 + 685.797i) q^{59} +(-45.9608 - 79.6064i) q^{60} +(107.862 - 186.822i) q^{61} -312.420 q^{62} +(-129.492 + 104.951i) q^{63} +73.2079 q^{64} +(6.74158 - 11.6768i) q^{65} +(18.6212 + 32.2528i) q^{66} +(-201.111 - 348.334i) q^{67} +(47.5080 - 82.2862i) q^{68} -142.385 q^{69} +(-19.8722 - 125.126i) q^{70} -328.146 q^{71} +(86.9836 - 150.660i) q^{72} +(261.928 + 453.673i) q^{73} +(228.608 + 395.960i) q^{74} +(37.5000 - 64.9519i) q^{75} -284.607 q^{76} +(-26.3577 - 165.963i) q^{77} +11.0684 q^{78} +(65.3990 - 113.274i) q^{79} +(-56.4461 - 97.7675i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-24.1618 + 41.8494i) q^{82} -507.390 q^{83} +(-264.514 + 214.384i) q^{84} +77.5248 q^{85} +(-349.021 + 604.523i) q^{86} +(-12.3255 - 21.3484i) q^{87} +(87.6939 + 151.890i) q^{88} +(-282.946 + 490.076i) q^{89} +61.5678 q^{90} +(-46.6327 - 17.8781i) q^{91} -290.851 q^{92} +(-342.522 + 593.266i) q^{93} +(372.999 + 646.054i) q^{94} +(-116.107 - 201.104i) q^{95} +(278.293 - 482.018i) q^{96} -1439.25 q^{97} +(-446.193 + 145.393i) q^{98} +81.6614 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 9 q^{3} - q^{4} - 15 q^{5} - 18 q^{6} - 2 q^{7} + 18 q^{8} - 27 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + 9 * q^3 - q^4 - 15 * q^5 - 18 * q^6 - 2 * q^7 + 18 * q^8 - 27 * q^9	\( 6 q - 3 q^{2} + 9 q^{3} - q^{4} - 15 q^{5} - 18 q^{6} - 2 q^{7} + 18 q^{8} - 27 q^{9} - 15 q^{10} + q^{11} + 3 q^{12} - 158 q^{13} + 161 q^{14} - 90 q^{15} + 79 q^{16} + 72 q^{17} - 27 q^{18} + 29 q^{19} + 10 q^{20} - 39 q^{21} + 286 q^{22} + 63 q^{23} + 27 q^{24} - 75 q^{25} + 339 q^{26} - 162 q^{27} - 195 q^{28} + 440 q^{29} + 45 q^{30} - 136 q^{31} + 155 q^{32} - 3 q^{33} - 440 q^{34} - 55 q^{35} + 18 q^{36} - 43 q^{37} + 21 q^{38} - 237 q^{39} - 45 q^{40} - 1198 q^{41} - 42 q^{42} + 340 q^{43} - 135 q^{44} - 135 q^{45} - 265 q^{46} + 3 q^{47} + 474 q^{48} - 192 q^{49} + 150 q^{50} - 216 q^{51} + 701 q^{52} - 331 q^{53} + 81 q^{54} - 10 q^{55} - 1176 q^{56} + 174 q^{57} + 472 q^{58} + 1520 q^{59} + 15 q^{60} + 1160 q^{61} - 1496 q^{62} - 99 q^{63} + 34 q^{64} + 395 q^{65} + 429 q^{66} - 806 q^{67} + 684 q^{68} + 378 q^{69} - 875 q^{70} - 812 q^{71} - 81 q^{72} + 1192 q^{73} - 959 q^{74} + 225 q^{75} - 1182 q^{76} - 1309 q^{77} + 2034 q^{78} + 2590 q^{79} + 395 q^{80} - 243 q^{81} + 1191 q^{82} - 1016 q^{83} - 1629 q^{84} - 720 q^{85} + 742 q^{86} + 660 q^{87} + 749 q^{88} - 42 q^{89} + 270 q^{90} + 1346 q^{91} - 422 q^{92} + 408 q^{93} + 1167 q^{94} + 145 q^{95} - 465 q^{96} - 2040 q^{97} - 4053 q^{98} - 18 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 9 * q^3 - q^4 - 15 * q^5 - 18 * q^6 - 2 * q^7 + 18 * q^8 - 27 * q^9 - 15 * q^10 + q^11 + 3 * q^12 - 158 * q^13 + 161 * q^14 - 90 * q^15 + 79 * q^16 + 72 * q^17 - 27 * q^18 + 29 * q^19 + 10 * q^20 - 39 * q^21 + 286 * q^22 + 63 * q^23 + 27 * q^24 - 75 * q^25 + 339 * q^26 - 162 * q^27 - 195 * q^28 + 440 * q^29 + 45 * q^30 - 136 * q^31 + 155 * q^32 - 3 * q^33 - 440 * q^34 - 55 * q^35 + 18 * q^36 - 43 * q^37 + 21 * q^38 - 237 * q^39 - 45 * q^40 - 1198 * q^41 - 42 * q^42 + 340 * q^43 - 135 * q^44 - 135 * q^45 - 265 * q^46 + 3 * q^47 + 474 * q^48 - 192 * q^49 + 150 * q^50 - 216 * q^51 + 701 * q^52 - 331 * q^53 + 81 * q^54 - 10 * q^55 - 1176 * q^56 + 174 * q^57 + 472 * q^58 + 1520 * q^59 + 15 * q^60 + 1160 * q^61 - 1496 * q^62 - 99 * q^63 + 34 * q^64 + 395 * q^65 + 429 * q^66 - 806 * q^67 + 684 * q^68 + 378 * q^69 - 875 * q^70 - 812 * q^71 - 81 * q^72 + 1192 * q^73 - 959 * q^74 + 225 * q^75 - 1182 * q^76 - 1309 * q^77 + 2034 * q^78 + 2590 * q^79 + 395 * q^80 - 243 * q^81 + 1191 * q^82 - 1016 * q^83 - 1629 * q^84 - 720 * q^85 + 742 * q^86 + 660 * q^87 + 749 * q^88 - 42 * q^89 + 270 * q^90 + 1346 * q^91 - 422 * q^92 + 408 * q^93 + 1167 * q^94 + 145 * q^95 - 465 * q^96 - 2040 * q^97 - 4053 * q^98 - 18 * q^99

Introduction

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