LMFDB - Embedded newform 43.4.c.a.6.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,4,Mod(6,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, 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("43.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	43.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:	$2.53708213025$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 60 x^{18} - 25 x^{17} + 2336 x^{16} - 645 x^{15} + 52478 x^{14} - 2415 x^{13} + \cdots + 589824 $ x^20 - x^19 + 60x^18 - 25x^17 + 2336x^16 - 645x^15 + 52478x^14 - 2415x^13 + 850704x^12 - 4147x^11 + 8670544x^10 + 873865x^9 + 62344097x^8 + 3655316x^7 + 215661012x^6 + 43840208x^5 + 507687824x^4 - 3907840x^3 + 17517568x^2 + 245760x + 589824
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			6.7
Root			$-0.961392 + 1.66518i$ of defining polynomial
Character	$\chi$	$=$	43.6
Dual form			43.4.c.a.36.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.92278 q^{2} +(-4.18916 + 7.25584i) q^{3} -4.30290 q^{4} +(-0.0351129 + 0.0608173i) q^{5} +(-8.05486 + 13.9514i) q^{6} +(11.7213 + 20.3018i) q^{7} -23.6558 q^{8} +(-21.5982 - 37.4091i) q^{9} +O(q^{10})$	\(q+1.92278 q^{2} +(-4.18916 + 7.25584i) q^{3} -4.30290 q^{4} +(-0.0351129 + 0.0608173i) q^{5} +(-8.05486 + 13.9514i) q^{6} +(11.7213 + 20.3018i) q^{7} -23.6558 q^{8} +(-21.5982 - 37.4091i) q^{9} +(-0.0675145 + 0.116939i) q^{10} +55.0459 q^{11} +(18.0255 - 31.2212i) q^{12} +(13.8919 + 24.0615i) q^{13} +(22.5374 + 39.0360i) q^{14} +(-0.294187 - 0.509547i) q^{15} -11.0619 q^{16} +(-14.7103 - 25.4791i) q^{17} +(-41.5286 - 71.9296i) q^{18} +(22.9265 - 39.7099i) q^{19} +(0.151087 - 0.261691i) q^{20} -196.409 q^{21} +105.841 q^{22} +(-63.3970 + 109.807i) q^{23} +(99.0981 - 171.643i) q^{24} +(62.4975 + 108.249i) q^{25} +(26.7111 + 46.2650i) q^{26} +135.698 q^{27} +(-50.4354 - 87.3566i) q^{28} +(-67.6217 - 117.124i) q^{29} +(-0.565658 - 0.979749i) q^{30} +(109.025 - 188.838i) q^{31} +167.977 q^{32} +(-230.596 + 399.404i) q^{33} +(-28.2848 - 48.9907i) q^{34} -1.64627 q^{35} +(92.9347 + 160.968i) q^{36} +(-185.007 + 320.441i) q^{37} +(44.0827 - 76.3536i) q^{38} -232.781 q^{39} +(0.830624 - 1.43868i) q^{40} +357.357 q^{41} -377.652 q^{42} +(-256.869 - 116.299i) q^{43} -236.857 q^{44} +3.03349 q^{45} +(-121.899 + 211.135i) q^{46} +442.020 q^{47} +(46.3399 - 80.2631i) q^{48} +(-103.275 + 178.878i) q^{49} +(120.169 + 208.139i) q^{50} +246.496 q^{51} +(-59.7754 - 103.534i) q^{52} +(139.624 - 241.836i) q^{53} +260.918 q^{54} +(-1.93282 + 3.34774i) q^{55} +(-277.276 - 480.256i) q^{56} +(192.086 + 332.702i) q^{57} +(-130.022 - 225.205i) q^{58} +413.803 q^{59} +(1.26586 + 2.19253i) q^{60} +(-280.281 - 485.462i) q^{61} +(209.633 - 363.094i) q^{62} +(506.315 - 876.963i) q^{63} +411.478 q^{64} -1.95114 q^{65} +(-443.386 + 767.968i) q^{66} +(-89.6639 + 155.302i) q^{67} +(63.2971 + 109.634i) q^{68} +(-531.160 - 919.996i) q^{69} -3.16542 q^{70} +(-295.903 - 512.519i) q^{71} +(510.922 + 884.943i) q^{72} +(-352.364 - 610.312i) q^{73} +(-355.728 + 616.139i) q^{74} -1047.25 q^{75} +(-98.6505 + 170.868i) q^{76} +(645.206 + 1117.53i) q^{77} -447.589 q^{78} +(298.886 + 517.685i) q^{79} +(0.388413 - 0.672752i) q^{80} +(14.6898 - 25.4435i) q^{81} +687.120 q^{82} +(-18.9456 + 32.8147i) q^{83} +845.128 q^{84} +2.06609 q^{85} +(-493.903 - 223.617i) q^{86} +1133.11 q^{87} -1302.16 q^{88} +(188.195 - 325.963i) q^{89} +5.83275 q^{90} +(-325.661 + 564.061i) q^{91} +(272.791 - 472.487i) q^{92} +(913.451 + 1582.14i) q^{93} +849.909 q^{94} +(1.61003 + 2.78866i) q^{95} +(-703.683 + 1218.81i) q^{96} -1659.85 q^{97} +(-198.576 + 343.944i) q^{98} +(-1188.89 - 2059.22i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9	\( 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9} + 27 q^{10} + 54 q^{11} - 72 q^{12} - 15 q^{13} + 96 q^{14} + 65 q^{15} + 134 q^{16} - 82 q^{17} + 247 q^{18} + 78 q^{19} - 495 q^{20} - 18 q^{21} + 380 q^{22} - 61 q^{23} + 202 q^{24} - 151 q^{25} - 21 q^{26} - 194 q^{27} - 794 q^{28} - 53 q^{29} + 627 q^{30} + 253 q^{31} - 798 q^{32} - 424 q^{33} - 231 q^{34} + 710 q^{35} - 1092 q^{36} - 129 q^{37} - 854 q^{38} + 1382 q^{39} + 1345 q^{40} + 782 q^{41} + 62 q^{42} + 1025 q^{43} + 754 q^{44} + 1888 q^{45} - 40 q^{46} - 668 q^{47} - 2401 q^{48} - 115 q^{49} + 424 q^{50} + 1590 q^{51} - 564 q^{52} + 773 q^{53} + 364 q^{54} - 1242 q^{55} - 923 q^{56} - 765 q^{57} + 1328 q^{58} - 2966 q^{59} - 1075 q^{60} + 437 q^{61} + 1509 q^{62} - 2222 q^{63} - 1476 q^{64} - 2126 q^{65} + 1483 q^{66} - 642 q^{67} - 1052 q^{68} - 3503 q^{69} - 170 q^{70} - 1545 q^{71} + 3834 q^{72} + 1292 q^{73} - 2232 q^{74} + 164 q^{75} - 252 q^{76} + 1448 q^{77} + 5644 q^{78} - 1405 q^{79} - 3157 q^{80} + 974 q^{81} + 6608 q^{82} + 543 q^{83} + 7304 q^{84} + 1946 q^{85} + 2776 q^{86} + 2818 q^{87} - 5372 q^{88} - 2196 q^{89} - 1484 q^{90} - 3513 q^{91} + 2629 q^{92} - 983 q^{93} + 9878 q^{94} - 149 q^{95} + 3540 q^{96} - 850 q^{97} - 213 q^{98} - 3181 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9 + 27 * q^10 + 54 * q^11 - 72 * q^12 - 15 * q^13 + 96 * q^14 + 65 * q^15 + 134 * q^16 - 82 * q^17 + 247 * q^18 + 78 * q^19 - 495 * q^20 - 18 * q^21 + 380 * q^22 - 61 * q^23 + 202 * q^24 - 151 * q^25 - 21 * q^26 - 194 * q^27 - 794 * q^28 - 53 * q^29 + 627 * q^30 + 253 * q^31 - 798 * q^32 - 424 * q^33 - 231 * q^34 + 710 * q^35 - 1092 * q^36 - 129 * q^37 - 854 * q^38 + 1382 * q^39 + 1345 * q^40 + 782 * q^41 + 62 * q^42 + 1025 * q^43 + 754 * q^44 + 1888 * q^45 - 40 * q^46 - 668 * q^47 - 2401 * q^48 - 115 * q^49 + 424 * q^50 + 1590 * q^51 - 564 * q^52 + 773 * q^53 + 364 * q^54 - 1242 * q^55 - 923 * q^56 - 765 * q^57 + 1328 * q^58 - 2966 * q^59 - 1075 * q^60 + 437 * q^61 + 1509 * q^62 - 2222 * q^63 - 1476 * q^64 - 2126 * q^65 + 1483 * q^66 - 642 * q^67 - 1052 * q^68 - 3503 * q^69 - 170 * q^70 - 1545 * q^71 + 3834 * q^72 + 1292 * q^73 - 2232 * q^74 + 164 * q^75 - 252 * q^76 + 1448 * q^77 + 5644 * q^78 - 1405 * q^79 - 3157 * q^80 + 974 * q^81 + 6608 * q^82 + 543 * q^83 + 7304 * q^84 + 1946 * q^85 + 2776 * q^86 + 2818 * q^87 - 5372 * q^88 - 2196 * q^89 - 1484 * q^90 - 3513 * q^91 + 2629 * q^92 - 983 * q^93 + 9878 * q^94 - 149 * q^95 + 3540 * q^96 - 850 * q^97 - 213 * q^98 - 3181 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.92278			0.679807			0.339903	−	0.940460i	$-0.389606\pi$
$2$	1.92278			0.679807			0.339903	+	0.940460i	$0.389606\pi$
$3$	−4.18916	+	7.25584i	−0.806205	+	1.39639i	0.109270	+	0.994012i	$0.465149\pi$
$3$	−4.18916	+	7.25584i	−0.806205	+	1.39639i	−0.915475	+	0.402375i	$0.868185\pi$
$4$	−4.30290			−0.537862
$5$	−0.0351129	+	0.0608173i	−0.00314059	+	0.00543966i	−0.867591	−	0.497278i	$-0.834333\pi$
$5$	−0.0351129	+	0.0608173i	−0.00314059	+	0.00543966i	0.864451	+	0.502717i	$0.167666\pi$
$6$	−8.05486	+	13.9514i	−0.548063	+	0.949274i
$7$	11.7213	+	20.3018i	0.632888	+	1.09619i	0.986958	+	0.160975i	$0.0514640\pi$
$7$	11.7213	+	20.3018i	0.632888	+	1.09619i	−0.354070	+	0.935219i	$0.615203\pi$
$8$	−23.6558			−1.04545
$9$	−21.5982	−	37.4091i	−0.799932	−	1.38552i
$10$	−0.0675145	+	0.116939i	−0.00213500	+	0.00369792i
$11$	55.0459			1.50881			0.754407	−	0.656407i	$-0.227925\pi$
$11$	55.0459			1.50881			0.754407	+	0.656407i	$0.227925\pi$
$12$	18.0255	−	31.2212i	0.433627	−	0.751064i
$13$	13.8919	+	24.0615i	0.296378	+	0.513342i	0.975305	−	0.220864i	$-0.0708878\pi$
$13$	13.8919	+	24.0615i	0.296378	+	0.513342i	−0.678926	+	0.734206i	$0.737554\pi$
$14$	22.5374	+	39.0360i	0.430242	+	0.745200i
$15$	−0.294187	−	0.509547i	−0.00506392	−	0.00877096i
$16$	−11.0619			−0.172841
$17$	−14.7103	−	25.4791i	−0.209870	−	0.363505i	0.741804	−	0.670617i	$-0.233971\pi$
$17$	−14.7103	−	25.4791i	−0.209870	−	0.363505i	−0.951673	+	0.307112i	$0.900637\pi$
$18$	−41.5286	−	71.9296i	−0.543799	−	0.941888i
$19$	22.9265	−	39.7099i	0.276826	−	0.479478i	−0.693768	−	0.720199i	$-0.744051\pi$
$19$	22.9265	−	39.7099i	0.276826	−	0.479478i	0.970594	+	0.240721i	$0.0773839\pi$
$20$	0.151087	−	0.261691i	0.00168921	−	0.00292579i
$21$	−196.409			−2.04095
$22$	105.841			1.02570
$23$	−63.3970	+	109.807i	−0.574747	+	0.995491i	0.421322	+	0.906911i	$0.361566\pi$
$23$	−63.3970	+	109.807i	−0.574747	+	0.995491i	−0.996069	+	0.0885798i	$0.971767\pi$
$24$	99.0981	−	171.643i	0.842846	−	1.45985i
$25$	62.4975	+	108.249i	0.499980	+	0.865991i
$26$	26.7111	+	46.2650i	0.201480	+	0.348974i
$27$	135.698			0.967225
$28$	−50.4354	−	87.3566i	−0.340407	−	0.589602i
$29$	−67.6217	−	117.124i	−0.433001	−	0.749980i	0.564129	−	0.825687i	$-0.309212\pi$
$29$	−67.6217	−	117.124i	−0.433001	−	0.749980i	−0.997130	+	0.0757067i	$0.975879\pi$
$30$	−0.565658	−	0.979749i	−0.00344249	−	0.00596256i
$31$	109.025	−	188.838i	0.631663	−	1.09407i	−0.355549	−	0.934658i	$-0.615706\pi$
$31$	109.025	−	188.838i	0.631663	−	1.09407i	0.987212	−	0.159415i	$-0.0509607\pi$
$32$	167.977			0.927951
$33$	−230.596	+	399.404i	−1.21641	+	2.10689i
$34$	−28.2848	−	48.9907i	−0.142671	−	0.247113i
$35$	−1.64627			−0.00795057
$36$	92.9347	+	160.968i	0.430253	+	0.745220i
$37$	−185.007	+	320.441i	−0.822025	+	1.42379i	0.0821464	+	0.996620i	$0.473822\pi$
$37$	−185.007	+	320.441i	−0.822025	+	1.42379i	−0.904172	+	0.427169i	$0.859511\pi$
$38$	44.0827	−	76.3536i	0.188189	−	0.325952i
$39$	−232.781			−0.955766
$40$	0.830624	−	1.43868i	0.00328333	−	0.00568689i
$41$	357.357			1.36121			0.680606	−	0.732649i	$-0.261716\pi$
$41$	357.357			1.36121			0.680606	+	0.732649i	$0.261716\pi$
$42$	−377.652			−1.38745
$43$	−256.869	−	116.299i	−0.910980	−	0.412451i
$43$	−256.869	−	116.299i	−0.910980	−	0.412451i
$44$	−236.857			−0.811534
$45$	3.03349			0.0100490
$46$	−121.899	+	211.135i	−0.390717	+	0.676742i
$47$	442.020			1.37181			0.685907	−	0.727689i	$-0.259406\pi$
$47$	442.020			1.37181			0.685907	+	0.727689i	$0.259406\pi$
$48$	46.3399	−	80.2631i	0.139346	−	0.241354i
$49$	−103.275	+	178.878i	−0.301094	+	0.521511i
$50$	120.169	+	208.139i	0.339890	+	0.588707i
$51$	246.496			0.676791
$52$	−59.7754	−	103.534i	−0.159411	−	0.276107i
$53$	139.624	−	241.836i	0.361865	−	0.626769i	−0.626403	−	0.779500i	$-0.715473\pi$
$53$	139.624	−	241.836i	0.361865	−	0.626769i	0.988268	+	0.152731i	$0.0488067\pi$
$54$	260.918			0.657526
$55$	−1.93282	+	3.34774i	−0.00473857	+	0.00820744i
$56$	−277.276	−	480.256i	−0.661653	−	1.14602i
$57$	192.086	+	332.702i	0.446358	+	0.773114i
$58$	−130.022	−	225.205i	−0.294357	−	0.509842i
$59$	413.803			0.913095			0.456547	−	0.889699i	$-0.349086\pi$
$59$	413.803			0.913095			0.456547	+	0.889699i	$0.349086\pi$
$60$	1.26586	+	2.19253i	0.00272369	+	0.00471757i
$61$	−280.281	−	485.462i	−0.588301	−	1.01897i	−0.994455	−	0.105163i	$-0.966464\pi$
$61$	−280.281	−	485.462i	−0.588301	−	1.01897i	0.406154	−	0.913805i	$-0.366870\pi$
$62$	209.633	−	363.094i	0.429409	−	0.743758i
$63$	506.315	−	876.963i	1.01253	−	1.75376i
$64$	411.478			0.803669
$65$	−1.95114			−0.00372321
$66$	−443.386	+	767.968i	−0.826926	+	1.43228i
$67$	−89.6639	+	155.302i	−0.163495	+	0.283182i	−0.936120	−	0.351681i	$-0.885610\pi$
$67$	−89.6639	+	155.302i	−0.163495	+	0.283182i	0.772625	+	0.634863i	$0.218944\pi$
$68$	63.2971	+	109.634i	0.112881	+	0.195516i
$69$	−531.160	−	919.996i	−0.926727	−	1.60514i
$70$	−3.16542			−0.00540485
$71$	−295.903	−	512.519i	−0.494608	−	0.856687i	0.505372	−	0.862901i	$-0.331355\pi$
$71$	−295.903	−	512.519i	−0.494608	−	0.856687i	−0.999981	+	0.00621447i	$0.998022\pi$
$72$	510.922	+	884.943i	0.836288	+	1.44849i
$73$	−352.364	−	610.312i	−0.564946	−	0.978515i	−0.997055	−	0.0766932i	$-0.975564\pi$
$73$	−352.364	−	610.312i	−0.564946	−	0.978515i	0.432109	−	0.901821i	$-0.357770\pi$
$74$	−355.728	+	616.139i	−0.558819	+	0.967902i
$75$	−1047.25			−1.61235
$76$	−98.6505	+	170.868i	−0.148895	+	0.257893i
$77$	645.206	+	1117.53i	0.954910	+	1.65395i
$78$	−447.589			−0.649736
$79$	298.886	+	517.685i	0.425661	+	0.737267i	0.996482	−	0.0838076i	$-0.0267081\pi$
$79$	298.886	+	517.685i	0.425661	+	0.737267i	−0.570820	+	0.821075i	$0.693375\pi$
$80$	0.388413	−	0.672752i	0.000542824	−	0.000940199i
$81$	14.6898	−	25.4435i	0.0201507	−	0.0349020i
$82$	687.120			0.925362
$83$	−18.9456	+	32.8147i	−0.0250548	+	0.0433962i	−0.878281	−	0.478145i	$-0.841309\pi$
$83$	−18.9456	+	32.8147i	−0.0250548	+	0.0433962i	0.853226	+	0.521541i	$0.174643\pi$
$84$	845.128			1.09775
$85$	2.06609			0.00263646
$86$	−493.903	−	223.617i	−0.619290	−	0.280387i
$87$	1133.11			1.39635
$88$	−1302.16			−1.57739
$89$	188.195	−	325.963i	0.224142	−	0.388225i	−0.731920	−	0.681391i	$-0.761375\pi$
$89$	188.195	−	325.963i	0.224142	−	0.388225i	0.956062	+	0.293166i	$0.0947088\pi$
$90$	5.83275			0.00683140
$91$	−325.661	+	564.061i	−0.375148	+	0.649776i
$92$	272.791	−	472.487i	0.309135	−	0.535437i
$93$	913.451	+	1582.14i	1.01850	+	1.76409i
$94$	849.909			0.932569
$95$	1.61003	+	2.78866i	0.00173880	+	0.00301169i
$96$	−703.683	+	1218.81i	−0.748118	+	1.29578i
$97$	−1659.85			−1.73745			−0.868723	−	0.495298i	$-0.835059\pi$
$97$	−1659.85			−1.73745			−0.868723	+	0.495298i	$0.835059\pi$
$98$	−198.576	+	343.944i	−0.204686	+	0.354527i
$99$	−1188.89	−	2059.22i	−1.20695	−	2.09049i
$100$	−268.921	−	465.784i	−0.268921	−	0.465784i
$101$	511.226	+	885.469i	0.503652	+	0.872351i	0.999991	+	0.00422218i	$0.00134396\pi$
$101$	511.226	+	885.469i	0.503652	+	0.872351i	−0.496339	+	0.868129i	$0.665323\pi$
$102$	473.959			0.460087
$103$	33.3182	+	57.7087i	0.0318732	+	0.0552059i	0.881522	−	0.472143i	$-0.156519\pi$
$103$	33.3182	+	57.7087i	0.0318732	+	0.0552059i	−0.849649	+	0.527349i	$0.823186\pi$
$104$	−328.624	−	569.194i	−0.309848	−	0.536673i
$105$	6.89648	−	11.9450i	0.00640978	−	0.0111021i
$106$	268.467	−	464.999i	0.245998	−	0.426082i
$107$	1282.02			1.15830			0.579148	−	0.815222i	$-0.303385\pi$
$107$	1282.02			1.15830			0.579148	+	0.815222i	$0.303385\pi$
$108$	−583.894			−0.520234
$109$	−793.527	+	1374.43i	−0.697303	+	1.20776i	0.272095	+	0.962271i	$0.412284\pi$
$109$	−793.527	+	1374.43i	−0.697303	+	1.20776i	−0.969398	+	0.245494i	$0.921050\pi$
$110$	−3.71639	+	6.43698i	−0.00322131	+	0.00557947i
$111$	−1550.05	−	2684.76i	−1.32544	−	2.29573i
$112$	−129.659	−	224.576i	−0.109389	−	0.189468i
$113$	999.212			0.831840			0.415920	−	0.909401i	$-0.363460\pi$
$113$	999.212			0.831840			0.415920	+	0.909401i	$0.363460\pi$
$114$	369.340	+	639.715i	0.303437	+	0.525568i
$115$	−4.45210	−	7.71126i	−0.00361009	−	0.00625286i
$116$	290.969	+	503.974i	0.232895	+	0.403386i
$117$	600.078	−	1039.37i	0.474165	−	0.821277i
$118$	795.654			0.620728
$119$	344.847	−	597.293i	0.265648	−	0.460115i
$120$	6.95924	+	12.0537i	0.00529407	+	0.00916960i
$121$	1699.05			1.27652
$122$	−538.921	−	933.438i	−0.399931	−	0.692701i
$123$	−1497.02	+	2592.92i	−1.09742	+	1.90078i
$124$	−469.126	+	812.550i	−0.339748	+	0.588461i
$125$	−17.5561			−0.0125621
$126$	973.534	−	1686.21i	0.688328	−	1.19222i
$127$	1275.21			0.890994			0.445497	−	0.895284i	$-0.353027\pi$
$127$	1275.21			0.890994			0.445497	+	0.895284i	$0.353027\pi$
$128$	−552.632			−0.381611
$129$	1919.91	−	1376.61i	1.31038	−	0.939561i
$130$	−3.75161			−0.00253106
$131$	−1567.29			−1.04530			−0.522651	−	0.852547i	$-0.675057\pi$
$131$	−1567.29			−1.04530			−0.522651	+	0.852547i	$0.675057\pi$
$132$	992.232	−	1718.60i	0.654263	−	1.13322i
$133$	1074.91			0.700801
$134$	−172.404	+	298.613i	−0.111145	+	0.192509i
$135$	−4.76474	+	8.25277i	−0.00303766	+	0.00526137i
$136$	347.985	+	602.728i	0.219408	+	0.380026i
$137$	−630.037			−0.392903			−0.196452	−	0.980514i	$-0.562942\pi$
$137$	−630.037			−0.392903			−0.196452	+	0.980514i	$0.562942\pi$
$138$	−1021.31	−	1768.95i	−0.629996	−	1.09118i
$139$	−299.762	+	519.203i	−0.182917	+	0.316822i	−0.942873	−	0.333153i	$-0.891887\pi$
$139$	−299.762	+	519.203i	−0.182917	+	0.316822i	0.759956	+	0.649975i	$0.225221\pi$
$140$	7.08372			0.00427631
$141$	−1851.69	+	3207.23i	−1.10596	+	1.91558i
$142$	−568.957	−	985.463i	−0.336238	−	0.582382i
$143$	764.691	+	1324.48i	0.447180	+	0.774538i
$144$	238.916	+	413.814i	0.138261	+	0.239476i
$145$	9.49757			0.00543952
$146$	−677.519	−	1173.50i	−0.384054	−	0.665201i
$147$	−865.275	−	1498.70i	−0.485487	−	0.840889i
$148$	796.066	−	1378.83i	0.442137	−	0.765803i
$149$	−1237.33	+	2143.12i	−0.680309	+	1.17833i	0.294578	+	0.955628i	$0.404821\pi$
$149$	−1237.33	+	2143.12i	−0.680309	+	1.17833i	−0.974887	+	0.222702i	$0.928512\pi$
$150$	−2013.63			−1.09608
$151$	2083.60			1.12292			0.561459	−	0.827504i	$-0.310240\pi$
$151$	2083.60			1.12292			0.561459	+	0.827504i	$0.310240\pi$
$152$	−542.346	+	939.370i	−0.289408	+	0.501270i
$153$	−635.432	+	1100.60i	−0.335762	+	0.581558i
$154$	1240.59	+	2148.77i	0.649155	+	1.12437i
$155$	7.65640	+	13.2613i	0.00396759	+	0.00687207i
$156$	1001.64			0.514071
$157$	−1327.94	−	2300.07i	−0.675042	−	1.16921i	−0.976457	−	0.215713i	$-0.930792\pi$
$157$	−1327.94	−	2300.07i	−0.675042	−	1.16921i	0.301415	−	0.953493i	$-0.402541\pi$
$158$	574.693	+	995.397i	0.289368	+	0.501199i
$159$	1169.82	+	2026.18i	0.583475	+	1.01061i
$160$	−5.89816	+	10.2159i	−0.00291431	+	0.00504774i
$161$	−2972.37			−1.45500
$162$	28.2454	−	48.9224i	0.0136986	−	0.0237266i
$163$	−590.172	−	1022.21i	−0.283594	−	0.491199i	0.688673	−	0.725072i	$-0.258193\pi$
$163$	−590.172	−	1022.21i	−0.283594	−	0.491199i	−0.972267	+	0.233873i	$0.924860\pi$
$164$	−1537.67			−0.732145
$165$	−16.1938	−	28.0484i	−0.00764051	−	0.0132337i
$166$	−36.4283	+	63.0956i	−0.0170324	+	0.0295010i
$167$	1430.44	−	2477.59i	0.662819	−	1.14804i	−0.317053	−	0.948408i	$-0.602693\pi$
$167$	1430.44	−	2477.59i	0.662819	−	1.14804i	0.979872	−	0.199628i	$-0.0639734\pi$
$168$	4646.21			2.13371
$169$	712.531	−	1234.14i	0.324320	−	0.561739i
$170$	3.97264			0.00179228
$171$	−1980.68			−0.885769
$172$	1105.28	+	500.422i	0.489982	+	0.221842i
$173$	−315.057			−0.138459			−0.0692293	−	0.997601i	$-0.522054\pi$
$173$	−315.057			−0.138459			−0.0692293	+	0.997601i	$0.522054\pi$
$174$	2178.73			0.949248
$175$	−1465.10	+	2537.62i	−0.632863	+	1.09615i
$176$	−608.909			−0.260786
$177$	−1733.49	+	3002.49i	−0.736141	+	1.27503i
$178$	361.858	−	626.757i	0.152373	−	0.263918i
$179$	−118.762	−	205.703i	−0.0495906	−	0.0858935i	0.840165	−	0.542332i	$-0.182458\pi$
$179$	−118.762	−	205.703i	−0.0495906	−	0.0858935i	−0.889755	+	0.456438i	$0.849125\pi$
$180$	−13.0528			−0.00540500
$181$	106.932	+	185.212i	0.0439127	+	0.0760591i	0.887146	−	0.461488i	$-0.152684\pi$
$181$	106.932	+	185.212i	0.0439127	+	0.0760591i	−0.843234	+	0.537547i	$0.819351\pi$
$182$	−626.175	+	1084.57i	−0.255029	+	0.441722i
$183$	4696.58			1.89716
$184$	1499.71	−	2597.57i	0.600869	−	1.04074i
$185$	−12.9922	−	22.5032i	−0.00516329	−	0.00894308i
$186$	1756.37	+	3042.12i	0.692383	+	1.19924i
$187$	−809.743	−	1402.52i	−0.316654	−	0.548461i
$188$	−1901.97			−0.737847
$189$	1590.55	+	2754.91i	0.612145	+	1.06027i
$190$	3.09574	+	5.36198i	0.00118205	+	0.00204736i
$191$	−816.795	+	1414.73i	−0.309430	+	0.535949i	−0.978238	−	0.207487i	$-0.933472\pi$
$191$	−816.795	+	1414.73i	−0.309430	+	0.535949i	0.668808	+	0.743436i	$0.266805\pi$
$192$	−1723.75	+	2985.62i	−0.647922	+	1.12223i
$193$	−4902.71			−1.82852			−0.914261	−	0.405126i	$-0.867228\pi$
$193$	−4902.71			−1.82852			−0.914261	+	0.405126i	$0.867228\pi$
$194$	−3191.53			−1.18113
$195$	8.17362	−	14.1571i	0.00300167	−	0.00519904i
$196$	444.384	−	769.695i	0.161947	−	0.280501i
$197$	−2215.52	−	3837.39i	−0.801265	−	1.38783i	−0.918784	−	0.394761i	$-0.870827\pi$
$197$	−2215.52	−	3837.39i	−0.801265	−	1.38783i	0.117518	−	0.993071i	$-0.462506\pi$
$198$	−2285.98	−	3959.43i	−0.820492	−	1.42113i
$199$	961.504			0.342508			0.171254	−	0.985227i	$-0.445218\pi$
$199$	961.504			0.342508			0.171254	+	0.985227i	$0.445218\pi$
$200$	−1478.43	−	2560.72i	−0.522704	−	0.905350i
$201$	−751.233	−	1301.17i	−0.263621	−	0.456605i
$202$	982.977	+	1702.57i	0.342386	+	0.593030i
$203$	1585.22	−	2745.68i	0.548082	−	0.949307i
$204$	−1060.65			−0.364020
$205$	−12.5478	+	21.7335i	−0.00427501	+	0.00740454i
$206$	64.0636	+	110.961i	0.0216676	+	0.0375294i
$207$	5477.03			1.83903
$208$	−153.670	−	266.164i	−0.0512264	−	0.0887268i
$209$	1262.01	−	2185.87i	0.417680	−	0.723442i
$210$	13.2604	−	22.9678i	0.00435742	−	0.00754727i
$211$	−3416.62			−1.11474			−0.557370	−	0.830264i	$-0.688189\pi$
$211$	−3416.62			−1.11474			−0.557370	+	0.830264i	$0.688189\pi$
$212$	−600.789	+	1040.60i	−0.194634	+	0.337115i
$213$	4958.34			1.59502
$214$	2465.05			0.787418
$215$	16.0924	−	11.5385i	0.00510461	−	0.00366008i
$216$	−3210.04			−1.01118
$217$	5111.66			1.59909
$218$	−1525.78	+	2642.73i	−0.474032	+	0.821047i
$219$	5904.43			1.82185
$220$	8.31672	−	14.4050i	0.00254870	−	0.00441447i
$221$	408.709	−	707.904i	0.124401	−	0.215470i
$222$	−2980.41	−	5162.22i	−0.901044	−	1.56065i
$223$	4025.40			1.20879			0.604396	−	0.796684i	$-0.293415\pi$
$223$	4025.40			1.20879			0.604396	+	0.796684i	$0.293415\pi$
$224$	1968.90	+	3410.24i	0.587289	+	1.01721i
$225$	2699.66	−	4675.95i	0.799900	−	1.38547i
$226$	1921.27			0.565491
$227$	1351.97	−	2341.69i	0.395303	−	0.684684i	−0.597837	−	0.801618i	$-0.703973\pi$
$227$	1351.97	−	2341.69i	0.395303	−	0.684684i	0.993140	+	0.116933i	$0.0373064\pi$
$228$	−826.526	−	1431.58i	−0.240079	−	0.415829i
$229$	−1438.15	−	2490.95i	−0.415004	−	0.718807i	0.580425	−	0.814314i	$-0.302886\pi$
$229$	−1438.15	−	2490.95i	−0.415004	−	0.718807i	−0.995429	+	0.0955062i	$0.969553\pi$
$230$	−8.56042	−	14.8271i	−0.00245416	−	0.00425074i
$231$	−10811.5			−3.07941
$232$	1599.65	+	2770.67i	0.452681	+	0.784066i
$233$	668.312	+	1157.55i	0.187908	+	0.325466i	0.944553	−	0.328360i	$-0.106496\pi$
$233$	668.312	+	1157.55i	0.187908	+	0.325466i	−0.756645	+	0.653826i	$0.773163\pi$
$234$	1153.82	−	1998.48i	0.322340	−	0.558310i
$235$	−15.5206	+	26.8825i	−0.00430831	+	0.00746221i
$236$	−1780.55			−0.491119
$237$	−5008.32			−1.37268
$238$	663.067	−	1148.47i	0.180589	−	0.312790i
$239$	−1722.37	+	2983.23i	−0.466154	+	0.807402i	−0.999253	−	0.0386508i	$-0.987694\pi$
$239$	−1722.37	+	2983.23i	−0.466154	+	0.807402i	0.533099	+	0.846053i	$0.321027\pi$
$240$	3.25425	+	5.63653i	0.000875255	+	0.00151599i
$241$	−370.298	−	641.375i	−0.0989750	−	0.171430i	0.812286	−	0.583260i	$-0.198223\pi$
$241$	−370.298	−	641.375i	−0.0989750	−	0.171430i	−0.911261	+	0.411830i	$0.864890\pi$
$242$	3266.90			0.867787
$243$	1955.00	+	3386.15i	0.516103	+	0.893917i
$244$	1206.02	+	2088.89i	0.316425	+	0.548064i
$245$	−7.25259	−	12.5619i	−0.00189123	−	0.00327570i
$246$	−2878.46	+	4985.63i	−0.746031	+	1.29216i
$247$	1273.97			0.328181
$248$	−2579.09	+	4467.11i	−0.660372	+	1.14380i
$249$	−158.732	−	274.932i	−0.0403986	−	0.0699724i
$250$	−33.7566			−0.00853981
$251$	−656.541	−	1137.16i	−0.165102	−	0.285964i	0.771590	−	0.636121i	$-0.219462\pi$
$251$	−656.541	−	1137.16i	−0.165102	−	0.285964i	−0.936691	+	0.350156i	$0.886129\pi$
$252$	−2178.62	+	3773.48i	−0.544604	+	0.943282i
$253$	−3489.74	+	6044.41i	−0.867186	+	1.50201i
$254$	2451.95			0.605704
$255$	−8.65518	+	14.9912i	−0.00212552	+	0.00368151i
$256$	−4354.42			−1.06309
$257$	4405.40			1.06927			0.534633	−	0.845084i	$-0.320450\pi$
$257$	4405.40			1.06927			0.534633	+	0.845084i	$0.320450\pi$
$258$	3691.57	−	2646.92i	0.890804	−	0.638720i
$259$	−8674.05			−2.08100
$260$	8.39554			0.00200258
$261$	−2921.01	+	5059.33i	−0.692743	+	1.19987i
$262$	−3013.56			−0.710604
$263$	150.475	−	260.630i	0.0352802	−	0.0611070i	−0.847846	−	0.530242i	$-0.822101\pi$
$263$	150.475	−	260.630i	0.0352802	−	0.0611070i	0.883126	+	0.469135i	$0.155434\pi$
$264$	5454.94	−	9448.23i	1.27170	−	2.20265i
$265$	9.80521	+	16.9831i	0.00227294	+	0.00393685i
$266$	2066.82			0.476409
$267$	1576.76	+	2731.02i	0.361408	+	0.625977i
$268$	385.815	−	668.250i	0.0879380	−	0.152313i
$269$	−2216.51			−0.502389			−0.251195	−	0.967937i	$-0.580823\pi$
$269$	−2216.51			−0.502389			−0.251195	+	0.967937i	$0.580823\pi$
$270$	−9.16157	+	15.8683i	−0.00206502	+	0.00357672i
$271$	−64.6236	−	111.931i	−0.0144856	−	0.0250898i	0.858692	−	0.512492i	$-0.171278\pi$
$271$	−64.6236	−	111.931i	−0.0144856	−	0.0250898i	−0.873177	+	0.487403i	$0.837944\pi$
$272$	162.724	+	281.846i	0.0362742	+	0.0628287i
$273$	−2728.49	−	4725.88i	−0.604893	−	1.04770i
$274$	−1211.43			−0.267098
$275$	3440.23	+	5958.65i	0.754377	+	1.30662i
$276$	2285.53	+	3958.65i	0.498452	+	0.863344i
$277$	603.242	−	1044.85i	0.130849	−	0.226638i	−0.793155	−	0.609020i	$-0.791563\pi$
$277$	603.242	−	1044.85i	0.130849	−	0.226638i	0.924004	+	0.382382i	$0.124896\pi$
$278$	−576.377	+	998.315i	−0.124348	+	0.215378i
$279$	−9419.00			−2.02115
$280$	38.9438			0.00831192
$281$	3971.04	−	6878.05i	0.843034	−	1.46018i	−0.0442833	−	0.999019i	$-0.514100\pi$
$281$	3971.04	−	6878.05i	0.843034	−	1.46018i	0.887318	−	0.461159i	$-0.152566\pi$
$282$	−3560.41	+	6166.81i	−0.751841	+	1.30223i
$283$	1753.25	+	3036.71i	0.368267	+	0.637858i	0.989295	−	0.145931i	$-0.0466178\pi$
$283$	1753.25	+	3036.71i	0.368267	+	0.637858i	−0.621027	+	0.783789i	$0.713284\pi$
$284$	1273.24	+	2205.32i	0.266031	+	0.460780i
$285$	−26.9787			−0.00560730
$286$	1470.34	+	2546.70i	0.303996	+	0.526536i
$287$	4188.67	+	7254.98i	0.861495	+	1.49215i
$288$	−3627.99	−	6283.87i	−0.742297	−	1.28570i
$289$	2023.71	−	3505.17i	0.411910	−	0.713448i
$290$	18.2618			0.00369782
$291$	6953.38	−	12043.6i	1.40074	−	2.42615i
$292$	1516.18	+	2626.11i	0.303863	+	0.526306i
$293$	5419.92			1.08067			0.540333	−	0.841451i	$-0.318298\pi$
$293$	5419.92			1.08067			0.540333	+	0.841451i	$0.318298\pi$
$294$	−1663.74	−	2881.68i	−0.330038	−	0.571642i
$295$	−14.5298	+	25.1664i	−0.00286766	+	0.00496693i
$296$	4376.49	−	7580.30i	0.859386	−	1.48850i
$297$	7469.61			1.45936
$298$	−2379.12	+	4120.75i	−0.462479	+	0.801037i
$299$	−3522.81			−0.681370
$300$	4506.21			0.867220
$301$	−649.750	−	6578.07i	−0.124422	−	1.25965i
$302$	4006.31			0.763368
$303$	−8566.43			−1.62419
$304$	−253.610	+	439.265i	−0.0478471	+	0.0828736i
$305$	39.3659			0.00739045
$306$	−1221.80	+	2116.22i	−0.228254	+	0.395347i
$307$	−2878.08	+	4984.98i	−0.535051	+	0.926735i	0.464110	+	0.885778i	$0.346374\pi$
$307$	−2878.08	+	4984.98i	−0.535051	+	0.926735i	−0.999161	+	0.0409579i	$0.986959\pi$
$308$	−2776.26	−	4808.62i	−0.513610	−	0.889599i
$309$	−558.301			−0.102785
$310$	14.7216	+	25.4986i	0.00269720	+	0.00467168i
$311$	244.854	−	424.100i	0.0446444	−	0.0773264i	−0.842840	−	0.538165i	$-0.819118\pi$
$311$	244.854	−	424.100i	0.0446444	−	0.0773264i	0.887484	+	0.460838i	$0.152451\pi$
$312$	5506.64			0.999205
$313$	4038.86	−	6995.51i	0.729361	−	1.26329i	−0.227793	−	0.973710i	$-0.573151\pi$
$313$	4038.86	−	6995.51i	0.729361	−	1.26329i	0.957154	−	0.289580i	$-0.0935156\pi$
$314$	−2553.35	−	4422.53i	−0.458898	−	0.794835i
$315$	35.5563	+	61.5854i	0.00635991	+	0.0110157i
$316$	−1286.07	−	2227.55i	−0.228947	−	0.396548i
$317$	−4400.14			−0.779610			−0.389805	−	0.920897i	$-0.627458\pi$
$317$	−4400.14			−0.779610			−0.389805	+	0.920897i	$0.627458\pi$
$318$	2249.30	+	3895.91i	0.396650	+	0.687018i
$319$	−3722.29	−	6447.20i	−0.653318	−	1.13158i
$320$	−14.4482	+	25.0250i	−0.00252399	+	0.00437169i
$321$	−5370.60	+	9302.15i	−0.933824	+	1.61743i
$322$	−5715.22			−0.989120
$323$	−1349.03			−0.232390
$324$	−63.2089	+	109.481i	−0.0108383	+	0.0187725i
$325$	−1736.42	+	3007.56i	−0.296367	+	0.513322i
$326$	−1134.77	−	1965.48i	−0.192789	−	0.333921i
$327$	−6648.42	−	11515.4i	−1.12434	−	1.94741i
$328$	−8453.57			−1.42308
$329$	5181.03	+	8973.80i	0.868205	+	1.50377i
$330$	−31.1371	−	53.9311i	−0.00519407	−	0.00899639i
$331$	4491.19	+	7778.97i	0.745795	+	1.29175i	0.949822	+	0.312789i	$0.101263\pi$
$331$	4491.19	+	7778.97i	0.745795	+	1.29175i	−0.204028	+	0.978965i	$0.565403\pi$
$332$	81.5210	−	141.198i	0.0134760	−	0.0233412i
$333$	15983.2			2.63026
$334$	2750.43	−	4763.88i	0.450589	−	0.780443i
$335$	−6.29671	−	10.9062i	−0.00102694	−	0.00177872i
$336$	2172.65			0.352761
$337$	−1756.82	−	3042.90i	−0.283976	−	0.491861i	0.688384	−	0.725346i	$-0.258320\pi$
$337$	−1756.82	−	3042.90i	−0.283976	−	0.491861i	−0.972360	+	0.233485i	$0.924987\pi$
$338$	1370.04	−	2372.98i	0.220475	−	0.381874i
$339$	−4185.86	+	7250.12i	−0.670633	+	1.16157i
$340$	−8.89017			−0.00141805
$341$	6001.40	−	10394.7i	0.953062	−	1.65075i
$342$	−3808.42			−0.602152
$343$	3198.71			0.503540
$344$	6076.44	+	2751.14i	0.952384	+	0.431197i
$345$	74.6022			0.0116419
$346$	−605.787			−0.0941251
$347$	1504.62	−	2606.08i	0.232773	−	0.403175i	−0.725850	−	0.687853i	$-0.758553\pi$
$347$	1504.62	−	2606.08i	0.232773	−	0.403175i	0.958623	+	0.284678i	$0.0918867\pi$
$348$	−4875.67			−0.751044
$349$	−2916.80	+	5052.04i	−0.447371	+	0.774869i	−0.998214	−	0.0597396i	$-0.980973\pi$
$349$	−2916.80	+	5052.04i	−0.447371	+	0.774869i	0.550843	+	0.834609i	$0.314306\pi$
$350$	−2817.07	+	4879.31i	−0.430225	+	0.745171i
$351$	1885.10	+	3265.09i	0.286664	+	0.496517i
$352$	9246.44			1.40011
$353$	−3091.77	−	5355.11i	−0.466171	−	0.807432i	0.533082	−	0.846063i	$-0.321034\pi$
$353$	−3091.77	−	5355.11i	−0.466171	−	0.807432i	−0.999254	+	0.0386313i	$0.987700\pi$
$354$	−3333.13	+	5773.14i	−0.500434	+	0.866777i
$355$	41.5600			0.00621345
$356$	−809.784	+	1402.59i	−0.120557	+	0.208812i
$357$	2889.24	+	5004.31i	0.428333	+	0.741894i
$358$	−228.355	−	395.522i	−0.0337121	−	0.0583910i
$359$	2154.46	+	3731.64i	0.316736	+	0.548603i	0.979805	−	0.199955i	$-0.0640797\pi$
$359$	2154.46	+	3731.64i	0.316736	+	0.548603i	−0.663069	+	0.748558i	$0.730746\pi$
$360$	−71.7598			−0.0105058
$361$	2378.25	+	4119.25i	0.346734	+	0.600561i
$362$	205.607	+	356.122i	0.0298522	+	0.0517055i
$363$	−7117.58	+	12328.0i	−1.02914	+	1.78252i
$364$	1401.28	−	2427.10i	0.201778	−	0.349490i
$365$	49.4900			0.00709705
$366$	9030.51			1.28971
$367$	347.868	−	602.524i	0.0494783	−	0.0856990i	−0.840226	−	0.542237i	$-0.817577\pi$
$367$	347.868	−	602.524i	0.0494783	−	0.0856990i	0.889704	+	0.456538i	$0.150911\pi$
$368$	701.288	−	1214.67i	0.0993401	−	0.172062i
$369$	−7718.24	−	13368.4i	−1.08888	−	1.88599i
$370$	−24.9813	−	43.2688i	−0.00351004	−	0.00607957i
$371$	6546.28			0.916081
$372$	−3930.49	−	6807.80i	−0.547813	−	0.948839i
$373$	−539.937	−	935.198i	−0.0749514	−	0.129820i	0.826114	−	0.563503i	$-0.190547\pi$
$373$	−539.937	−	935.198i	−0.0749514	−	0.129820i	−0.901065	+	0.433684i	$0.857213\pi$
$374$	−1556.96	−	2696.74i	−0.215264	−	0.372848i
$375$	73.5453	−	127.384i	0.0101276	−	0.0175416i
$376$	−10456.4			−1.43416
$377$	1878.79	−	3254.15i	0.256664	−	0.444555i
$378$	3058.28	+	5297.10i	0.416140	+	0.720776i
$379$	−5259.67			−0.712853			−0.356426	−	0.934323i	$-0.616005\pi$
$379$	−5259.67			−0.712853			−0.356426	+	0.934323i	$0.616005\pi$
$380$	−6.92780	−	11.9993i	−0.000935234	−	0.00161987i
$381$	−5342.04	+	9252.69i	−0.718323	+	1.24417i
$382$	−1570.52	+	2720.22i	−0.210353	+	0.364342i
$383$	−9371.54			−1.25030			−0.625148	−	0.780506i	$-0.714961\pi$
$383$	−9371.54			−1.25030			−0.625148	+	0.780506i	$0.714961\pi$
$384$	2315.06	−	4009.81i	0.307657	−	0.532877i
$385$	−90.6202			−0.0119959
$386$	−9426.85			−1.24304
$387$	1197.26	+	12121.1i	0.157262	+	1.59212i
$388$	7142.17			0.934507
$389$	−3732.64			−0.486510			−0.243255	−	0.969962i	$-0.578215\pi$
$389$	−3732.64			−0.486510			−0.243255	+	0.969962i	$0.578215\pi$
$390$	15.7161	−	27.2211i	0.00204056	−	0.00353435i
$391$	3730.36			0.482487
$392$	2443.07	−	4231.51i	0.314779	−	0.545213i
$393$	6565.62	−	11372.0i	0.842727	−	1.45965i
$394$	−4259.97	−	7378.48i	−0.544706	−	0.943458i
$395$	−41.9789			−0.00534731
$396$	5115.67	+	8860.60i	0.649172	+	1.12440i
$397$	−2453.43	+	4249.47i	−0.310161	+	0.537215i	−0.978397	−	0.206734i	$-0.933716\pi$
$397$	−2453.43	+	4249.47i	−0.310161	+	0.537215i	0.668236	+	0.743950i	$0.267050\pi$
$398$	1848.76			0.232840
$399$	−4502.97	+	7799.37i	−0.564989	+	0.978589i
$400$	−691.339	−	1197.43i	−0.0864173	−	0.149679i
$401$	935.972	+	1621.15i	0.116559	+	0.201886i	0.918402	−	0.395649i	$-0.129480\pi$
$401$	935.972	+	1621.15i	0.116559	+	0.201886i	−0.801843	+	0.597535i	$0.796147\pi$
$402$	−1444.46	−	2501.88i	−0.179212	−	0.310404i
$403$	6058.28			0.748845
$404$	−2199.75	−	3810.08i	−0.270896	−	0.469205i
$405$	1.03160	+	1.78679i	0.000126570	+	0.000219226i
$406$	3048.04	−	5279.36i	0.372590	−	0.645345i
$407$	−10183.9	+	17639.0i	−1.24028	+	2.14823i
$408$	−5831.07			−0.707551
$409$	1917.96			0.231875			0.115937	−	0.993257i	$-0.463013\pi$
$409$	1917.96			0.231875			0.115937	+	0.993257i	$0.463013\pi$
$410$	−24.1267	+	41.7887i	−0.00290618	+	0.00503366i
$411$	2639.33	−	4571.45i	0.316760	−	0.548645i
$412$	−143.365	−	248.315i	−0.0171434	−	0.0296932i
$413$	4850.29	+	8400.95i	0.577887	+	1.00093i
$414$	10531.1			1.25019
$415$	−1.33047	−	2.30444i	−0.000157374	−	0.000272579i
$416$	2333.52	+	4041.77i	0.275024	+	0.476356i
$417$	−2511.50	−	4350.05i	−0.294937	−	0.510846i
$418$	2426.57	−	4202.95i	0.283942	−	0.491801i
$419$	9353.24			1.09054			0.545269	−	0.838261i	$-0.316427\pi$
$419$	9353.24			1.09054			0.545269	+	0.838261i	$0.316427\pi$
$420$	−29.6749	+	51.3984i	−0.00344758	+	0.00597139i
$421$	−1738.45	−	3011.08i	−0.201251	−	0.348577i	0.747681	−	0.664058i	$-0.231167\pi$
$421$	−1738.45	−	3011.08i	−0.201251	−	0.348577i	−0.948932	+	0.315481i	$0.897834\pi$
$422$	−6569.43			−0.757808
$423$	−9546.82	−	16535.6i	−1.09736	−	1.90068i
$424$	−3302.92	+	5720.83i	−0.378312	+	0.655255i
$425$	1838.72	−	3184.76i	0.209861	−	0.363490i
$426$	9533.82			1.08431
$427$	6570.50	−	11380.4i	0.744657	−	1.28978i
$428$	−5516.41			−0.623004
$429$	−12813.7			−1.44207
$430$	30.9422	−	22.1860i	0.00347015	−	0.00248815i
$431$	−4840.83			−0.541008			−0.270504	−	0.962719i	$-0.587190\pi$
$431$	−4840.83			−0.541008			−0.270504	+	0.962719i	$0.587190\pi$
$432$	−1501.07			−0.167177
$433$	−5795.79	+	10038.6i	−0.643251	+	1.11414i	0.341451	+	0.939899i	$0.389082\pi$
$433$	−5795.79	+	10038.6i	−0.643251	+	1.11414i	−0.984702	+	0.174244i	$0.944252\pi$
$434$	9828.62			1.08707
$435$	−39.7868	+	68.9128i	−0.00438536	+	0.00759567i
$436$	3414.47	−	5914.03i	0.375053	−	0.649611i
$437$	2906.94	+	5034.97i	0.318210	+	0.551156i
$438$	11352.9			1.23850
$439$	2238.86	+	3877.82i	0.243405	+	0.421591i	0.961682	−	0.274167i	$-0.0884021\pi$
$439$	2238.86	+	3877.82i	0.243405	+	0.421591i	−0.718277	+	0.695758i	$0.755069\pi$
$440$	45.7224	−	79.1935i	0.00495393	−	0.00858046i
$441$	8922.23			0.963420
$442$	785.859	−	1361.15i	0.0845690	−	0.146478i
$443$	−2209.22	−	3826.47i	−0.236937	−	0.410387i	0.722897	−	0.690956i	$-0.242810\pi$
$443$	−2209.22	−	3826.47i	−0.236937	−	0.410387i	−0.959834	+	0.280569i	$0.909477\pi$
$444$	6669.70	+	11552.3i	0.712905	+	1.23479i
$445$	13.2161	+	22.8910i	0.00140787	+	0.00243851i
$446$	7739.97			0.821745
$447$	−10366.7	−	17955.7i	−1.09694	−	1.89995i
$448$	4823.04	+	8353.75i	0.508632	+	0.880977i
$449$	5519.82	−	9560.61i	0.580170	−	1.00488i	−0.415288	−	0.909690i	$-0.636319\pi$
$449$	5519.82	−	9560.61i	0.580170	−	1.00488i	0.995459	−	0.0951945i	$-0.0303473\pi$
$450$	5190.87	−	8990.85i	0.543778	−	0.941850i
$451$	19671.0			2.05382
$452$	−4299.51			−0.447416
$453$	−8728.53	+	15118.3i	−0.905302	+	1.56803i
$454$	2599.56	−	4502.56i	0.268729	−	0.465453i
$455$	−22.8698	−	39.6116i	−0.00235638	−	0.00408136i
$456$	−4543.95	−	7870.35i	−0.466644	−	0.808252i
$457$	−12619.7			−1.29174			−0.645870	−	0.763447i	$-0.723505\pi$
$457$	−12619.7			−1.29174			−0.645870	+	0.763447i	$0.723505\pi$
$458$	−2765.26	−	4789.57i	−0.282122	−	0.488650i
$459$	−1996.16	−	3457.45i	−0.202991	−	0.351591i
$460$	19.1569	+	33.1808i	0.00194173	+	0.00336318i
$461$	3432.48	−	5945.23i	0.346782	−	0.600644i	−0.638894	−	0.769295i	$-0.720608\pi$
$461$	3432.48	−	5945.23i	0.346782	−	0.600644i	0.985676	+	0.168651i	$0.0539410\pi$
$462$	−20788.2			−2.09341
$463$	147.484	−	255.449i	0.0148038	−	0.0256409i	−0.858529	−	0.512766i	$-0.828621\pi$
$463$	147.484	−	255.449i	0.0148038	−	0.0256409i	0.873332	+	0.487125i	$0.161954\pi$
$464$	748.021	+	1295.61i	0.0748406	+	0.129628i
$465$	−128.296			−0.0127948
$466$	1285.02	+	2225.72i	0.127741	+	0.221254i
$467$	2799.34	−	4848.59i	0.277383	−	0.480441i	−0.693351	−	0.720600i	$-0.743866\pi$
$467$	2799.34	−	4848.59i	0.277383	−	0.480441i	0.970734	+	0.240159i	$0.0771996\pi$
$468$	−2582.08	+	4472.29i	−0.255035	+	0.441734i
$469$	−4203.89			−0.413897
$470$	−29.8428	+	51.6892i	−0.00292882	+	0.00507286i
$471$	22251.9			2.17689
$472$	−9788.86			−0.954595
$473$	−14139.6	−	6401.76i	−1.37450	−	0.622312i
$474$	−9629.92			−0.933158
$475$	5731.40			0.553631
$476$	−1483.84	+	2570.09i	−0.142882	+	0.247479i
$477$	−12062.5			−1.15787
$478$	−3311.74	+	5736.11i	−0.316895	+	0.548878i
$479$	−3186.39	+	5518.99i	−0.303946	+	0.526449i	−0.977026	−	0.213120i	$-0.931637\pi$
$479$	−3186.39	+	5518.99i	−0.303946	+	0.526449i	0.673080	+	0.739569i	$0.264971\pi$
$480$	−49.4167	−	85.5922i	−0.00469907	−	0.00813902i
$481$	−10280.4			−0.974522
$482$	−712.003	−	1233.23i	−0.0672839	−	0.116539i
$483$	12451.7	−	21567.0i	1.17303	−	2.03175i
$484$	−7310.83			−0.686592
$485$	58.2821	−	100.948i	0.00545661	−	0.00945112i
$486$	3759.04	+	6510.85i	0.350851	+	0.607691i
$487$	7983.31	+	13827.5i	0.742830	+	1.28662i	0.951202	+	0.308570i	$0.0998503\pi$
$487$	7983.31	+	13827.5i	0.742830	+	1.28662i	−0.208372	+	0.978050i	$0.566816\pi$
$488$	6630.29	+	11484.0i	0.615039	+	1.06528i
$489$	9889.30			0.914539
$490$	−13.9452	−	24.1537i	−0.00128567	−	0.00222685i
$491$	−5722.04	−	9910.86i	−0.525931	−	0.910939i	−0.999544	−	0.0302059i	$-0.990384\pi$
$491$	−5722.04	−	9910.86i	−0.525931	−	0.910939i	0.473613	−	0.880733i	$-0.342950\pi$
$492$	6441.55	−	11157.1i	0.590259	−	1.02236i
$493$	−1989.48	+	3445.87i	−0.181747	+	0.314796i
$494$	2449.57			0.223100
$495$	166.981			0.0151621
$496$	−1206.02	+	2088.90i	−0.109178	+	0.189101i
$497$	6936.70	−	12014.7i	0.626064	−	1.08437i
$498$	−305.208	−	528.636i	−0.0274632	−	0.0475677i
$499$	−690.385	−	1195.78i	−0.0619356	−	0.107276i	0.833395	−	0.552678i	$-0.186394\pi$
$499$	−690.385	−	1195.78i	−0.0619356	−	0.107276i	−0.895331	+	0.445402i	$0.853061\pi$
$500$	75.5421			0.00675669
$501$	11984.7	+	20758.1i	1.06874	+	1.85110i
$502$	−1262.39	−	2186.52i	−0.112237	−	0.194401i
$503$	4831.72	+	8368.79i	0.428302	+	0.741840i	0.996722	−	0.0808977i	$-0.0257787\pi$
$503$	4831.72	+	8368.79i	0.428302	+	0.741840i	−0.568421	+	0.822738i	$0.692445\pi$
$504$	−11977.3	+	20745.3i	−1.05855	+	1.83347i
$505$	−71.8024			−0.00632706
$506$	−6710.02	+	11622.1i	−0.589519	+	1.02108i
$507$	5969.81	+	10340.0i	0.522936	+	0.905752i
$508$	−5487.08			−0.479232
$509$	3783.15	+	6552.61i	0.329441	+	0.570608i	0.982401	−	0.186784i	$-0.0598066\pi$
$509$	3783.15	+	6552.61i	0.329441	+	0.570608i	−0.652960	+	0.757392i	$0.726473\pi$
$510$	−16.6420	+	28.8249i	−0.00144495	+	0.00250272i
$511$	8260.28	−	14307.2i	0.715095	−	1.23858i
$512$	−3951.56			−0.341085
$513$	3111.08	−	5388.55i	0.267753	−	0.463762i
$514$	8470.64			0.726894
$515$	−4.67958			−0.000400402
$516$	−8261.18	+	5923.39i	−0.704803	+	0.505354i
$517$	24331.4			2.06981
$518$	−16678.3			−1.41468
$519$	1319.82	−	2286.00i	0.111626	−	0.193342i
$520$	46.1557			0.00389243
$521$	−2358.61	+	4085.23i	−0.198335	+	0.343526i	−0.947989	−	0.318304i	$-0.896887\pi$
$521$	−2358.61	+	4085.23i	−0.198335	+	0.343526i	0.749654	+	0.661830i	$0.230220\pi$
$522$	−5616.47	+	9728.01i	−0.470931	+	0.815677i
$523$	3443.03	+	5963.51i	0.287865	+	0.498597i	0.973300	−	0.229537i	$-0.0737213\pi$
$523$	3443.03	+	5963.51i	0.287865	+	0.498597i	−0.685435	+	0.728134i	$0.740388\pi$
$524$	6743.88			0.562229
$525$	−12275.1	−	21261.0i	−1.02043	−	1.76744i
$526$	289.331	−	501.136i	0.0239837	−	0.0415410i
$527$	−6415.21			−0.530267
$528$	2550.82	−	4418.15i	0.210247	−	0.364158i
$529$	−1954.85	−	3385.89i	−0.160668	−	0.278285i
$530$	18.8533	+	32.6549i	0.00154516	+	0.00267630i
$531$	−8937.38	−	15480.0i	−0.730413	−	1.26511i
$532$	−4625.23			−0.376934
$533$	4964.36	+	8598.52i	0.403434	+	0.698768i
$534$	3031.76	+	5251.17i	0.245688	+	0.425544i
$535$	−45.0155	+	77.9691i	−0.00363774	+	0.00630074i
$536$	2121.07	−	3673.81i	0.170926	−	0.296053i
$537$	1990.06			0.159921
$538$	−4261.86			−0.341528
$539$	−5684.88	+	9846.51i	−0.454296	+	0.786863i
$540$	20.5022	−	35.5109i	0.00163384	−	0.00282990i
$541$	−530.306	−	918.518i	−0.0421435	−	0.0729947i	0.844184	−	0.536053i	$-0.180085\pi$
$541$	−530.306	−	918.518i	−0.0421435	−	0.0729947i	−0.886328	+	0.463058i	$0.846752\pi$
$542$	−124.257	−	215.220i	−0.00984743	−	0.0170562i
$543$	−1791.82			−0.141611
$544$	−2471.00	−	4279.90i	−0.194749	−	0.337314i
$545$	−55.7260	−	96.5203i	−0.00437989	−	0.00758619i
$546$	−5246.30	−	9086.85i	−0.411210	−	0.712237i
$547$	−6561.53	+	11364.9i	−0.512890	+	0.888351i	0.486998	+	0.873403i	$0.338092\pi$
$547$	−6561.53	+	11364.9i	−0.512890	+	0.888351i	−0.999888	+	0.0149486i	$0.995242\pi$
$548$	2710.99			0.211328
$549$	−12107.1	+	20970.2i	−0.941201	+	1.63021i
$550$	6614.82	+	11457.2i	0.512831	+	0.888249i
$551$	−6201.32			−0.479465
$552$	12565.0	+	21763.3i	0.968847	+	1.67809i
$553$	−7006.63	+	12135.8i	−0.538792	+	0.933215i
$554$	1159.90	−	2009.01i	0.0889524	−	0.154070i
$555$	217.706			0.0166507
$556$	1289.85	−	2234.08i	0.0983842	−	0.170406i
$557$	−10395.9			−0.790826			−0.395413	−	0.918504i	$-0.629398\pi$
$557$	−10395.9			−0.790826			−0.395413	+	0.918504i	$0.629398\pi$
$558$	−18110.7			−1.37399
$559$	−770.076	−	7796.25i	−0.0582661	−	0.589886i
$560$	18.2108			0.00137419
$561$	13568.6			1.02115
$562$	7635.46	−	13225.0i	0.573101	−	0.992639i
$563$	−10043.6			−0.751844			−0.375922	−	0.926651i	$-0.622674\pi$
$563$	−10043.6			−0.751844			−0.375922	+	0.926651i	$0.622674\pi$
$564$	7967.65	−	13800.4i	0.594856	−	1.03032i
$565$	−35.0852	+	60.7693i	−0.00261247	+	0.00452493i
$566$	3371.11	+	5838.94i	0.250351	+	0.433620i
$567$	688.733			0.0510124
$568$	6999.82	+	12124.1i	0.517088	+	0.895623i
$569$	−3187.79	+	5521.41i	−0.234867	+	0.406801i	−0.959234	−	0.282613i	$-0.908799\pi$
$569$	−3187.79	+	5521.41i	−0.234867	+	0.406801i	0.724367	+	0.689414i	$0.242132\pi$
$570$	−51.8743			−0.00381188
$571$	1520.80	−	2634.10i	0.111459	−	0.193053i	−0.804899	−	0.593411i	$-0.797781\pi$
$571$	1520.80	−	2634.10i	0.111459	−	0.193053i	0.916359	+	0.400358i	$0.131114\pi$
$572$	−3290.39	−	5699.12i	−0.240521	−	0.416595i
$573$	−6843.37	−	11853.1i	−0.498928	−	0.864169i
$574$	8053.90	+	13949.8i	0.585651	+	1.01438i
$575$	−15848.6			−1.14945
$576$	−8887.17	−	15393.0i	−0.642880	−	1.11350i
$577$	−11217.2	−	19428.7i	−0.809319	−	1.40178i	−0.913336	−	0.407207i	$-0.866503\pi$
$577$	−11217.2	−	19428.7i	−0.809319	−	1.40178i	0.104017	−	0.994576i	$-0.466831\pi$
$578$	3891.16	−	6739.69i	0.280019	−	0.485007i
$579$	20538.2	−	35573.3i	1.47416	−	2.55332i
$580$	−40.8671			−0.00292571
$581$	−888.264			−0.0634275
$582$	13369.9	−	23157.3i	0.952231	−	1.64931i
$583$	7685.73	−	13312.1i	0.545987	−	0.945678i
$584$	8335.45	+	14437.4i	0.590622	+	1.02299i
$585$	42.1409	+	72.9902i	0.00297831	+	0.00515859i
$586$	10421.3			0.734644
$587$	−13562.7	−	23491.3i	−0.953650	−	1.65177i	−0.737428	−	0.675426i	$-0.763960\pi$
$587$	−13562.7	−	23491.3i	−0.953650	−	1.65177i	−0.216222	−	0.976344i	$-0.569374\pi$
$588$	3723.19	+	6448.76i	0.261126	+	0.452283i
$589$	−4999.15	−	8658.78i	−0.349722	−	0.605737i
$590$	−27.9377	+	48.3895i	−0.00194945	+	0.00337655i
$591$	37124.7			2.58393
$592$	2046.52	−	3544.67i	0.142080	−	0.246090i
$593$	5824.98	+	10089.2i	0.403378	+	0.698671i	0.994131	−	0.108181i	$-0.0345026\pi$
$593$	5824.98	+	10089.2i	0.403378	+	0.698671i	−0.590753	+	0.806852i	$0.701169\pi$
$594$	14362.4			0.992084
$595$	24.2171	+	41.9453i	0.00166858	+	0.00289007i
$596$	5324.11	−	9221.62i	0.365913	−	0.633779i
$597$	−4027.89	+	6976.52i	−0.276132	+	0.478274i
$598$	−6773.61			−0.463200
$599$	−10171.0	+	17616.8i	−0.693786	+	1.20167i	0.276803	+	0.960927i	$0.410725\pi$
$599$	−10171.0	+	17616.8i	−0.693786	+	1.20167i	−0.970588	+	0.240745i	$0.922608\pi$
$600$	24773.5			1.68563
$601$	14226.2			0.965553			0.482777	−	0.875744i	$-0.339628\pi$
$601$	14226.2			0.965553			0.482777	+	0.875744i	$0.339628\pi$
$602$	−1249.33	−	12648.2i	−0.0845828	−	0.856316i
$603$	7746.29			0.523140
$604$	−8965.51			−0.603976
$605$	−59.6584	+	103.331i	−0.00400902	+	0.00694383i
$606$	−16471.4			−1.10413
$607$	−9265.16	+	16047.7i	−0.619541	+	1.07308i	0.370028	+	0.929020i	$0.379348\pi$
$607$	−9265.16	+	16047.7i	−0.619541	+	1.07308i	−0.989570	+	0.144056i	$0.953985\pi$
$608$	3851.13	−	6670.35i	0.256881	−	0.444932i
$609$	13281.5	+	23004.2i	0.883733	+	1.53067i
$610$	75.6922			0.00502408
$611$	6140.49	+	10635.6i	0.406576	+	0.704210i
$612$	2734.20	−	4735.78i	0.180594	−	0.312798i
$613$	−10295.0			−0.678321			−0.339160	−	0.940729i	$-0.610143\pi$
$613$	−10295.0			−0.678321			−0.339160	+	0.940729i	$0.610143\pi$
$614$	−5533.93	+	9585.04i	−0.363731	+	0.630001i
$615$	−105.130	−	182.090i	−0.00689307	−	0.0119391i
$616$	−15262.9	−	26436.1i	−0.998311	−	1.72912i
$617$	−3394.51	−	5879.46i	−0.221487	−	0.383628i	0.733772	−	0.679395i	$-0.237758\pi$
$617$	−3394.51	−	5879.46i	−0.221487	−	0.383628i	−0.955260	+	0.295768i	$0.904425\pi$
$618$	−1073.49			−0.0698741
$619$	−14423.5	−	24982.2i	−0.936557	−	1.62216i	−0.771833	−	0.635825i	$-0.780660\pi$
$619$	−14423.5	−	24982.2i	−0.936557	−	1.62216i	−0.164724	−	0.986340i	$-0.552673\pi$
$620$	−32.9447	−	57.0619i	−0.00213402	−	0.00369623i
$621$	−8602.83	+	14900.5i	−0.555909	+	0.962863i
$622$	470.802	−	815.453i	0.0303496	−	0.0525670i
$623$	8823.52			0.567426
$624$	2574.99			0.165196
$625$	−7811.58	+	13530.0i	−0.499941	+	0.865923i
$626$	7765.86	−	13450.9i	0.495824	−	0.858793i
$627$	10573.5	+	18313.9i	0.673470	+	1.16649i
$628$	5714.01	+	9896.96i	0.363080	+	0.628872i
$629$	10886.1			0.690072
$630$	68.3671	+	118.415i	0.00432351	+	0.00748854i
$631$	7108.11	+	12311.6i	0.448446	+	0.776731i	0.998285	−	0.0585392i	$-0.0186443\pi$
$631$	7108.11	+	12311.6i	0.448446	+	0.776731i	−0.549839	+	0.835271i	$0.685311\pi$
$632$	−7070.38	−	12246.3i	−0.445008	−	0.770776i
$633$	14312.8	−	24790.5i	0.898708	−	1.55661i
$634$	−8460.51			−0.529984
$635$	−44.7761	+	77.5545i	−0.00279825	+	0.00484670i
$636$	−5033.60	−	8718.46i	−0.313829	−	0.543568i
$637$	−5738.76			−0.356951
$638$	−7157.17	−	12396.6i	−0.444130	−	0.769256i
$639$	−12781.9	+	22138.9i	−0.791306	+	1.37058i
$640$	19.4045	−	33.6096i	0.00119848	−	0.00207584i
$641$	−21448.7			−1.32164			−0.660821	−	0.750543i	$-0.729792\pi$
$641$	−21448.7			−1.32164			−0.660821	+	0.750543i	$0.729792\pi$
$642$	−10326.5	+	17886.0i	−0.634820	+	1.09954i
$643$	−26733.7			−1.63961			−0.819807	−	0.572639i	$-0.805920\pi$
$643$	−26733.7			−1.63961			−0.819807	+	0.572639i	$0.805920\pi$
$644$	12789.8			0.782591
$645$	16.3078	+	165.100i	0.000995534	+	0.0100788i
$646$	−2593.89			−0.157980
$647$	−535.525			−0.0325404			−0.0162702	−	0.999868i	$-0.505179\pi$
$647$	−535.525			−0.0325404			−0.0162702	+	0.999868i	$0.505179\pi$
$648$	−347.500	+	601.888i	−0.0210665	+	0.0364882i
$649$	22778.2			1.37769
$650$	−3338.76	+	5782.90i	−0.201472	+	0.348960i
$651$	−21413.6	+	37089.4i	−1.28919	+	2.23295i
$652$	2539.45	+	4398.45i	0.152535	+	0.264198i
$653$	130.350			0.00781159			0.00390580	−	0.999992i	$-0.498757\pi$
$653$	130.350			0.00781159			0.00390580	+	0.999992i	$0.498757\pi$
$654$	−12783.5	−	22141.6i	−0.764333	−	1.32386i
$655$	55.0320	−	95.3182i	0.00328287	−	0.00568609i
$656$	−3953.03			−0.235274
$657$	−15220.8	+	26363.2i	−0.903836	+	1.56549i
$658$	9962.00	+	17254.7i	0.590212	+	1.02228i
$659$	−13894.5	−	24065.9i	−0.821323	−	1.42257i	−0.904698	−	0.426054i	$-0.859903\pi$
$659$	−13894.5	−	24065.9i	−0.821323	−	1.42257i	0.0833751	−	0.996518i	$-0.473430\pi$
$660$	69.6802	+	120.690i	0.00410954	+	0.00711794i
$661$	21026.7			1.23729			0.618643	−	0.785673i	$-0.287683\pi$
$661$	21026.7			1.23729			0.618643	+	0.785673i	$0.287683\pi$
$662$	8635.59	+	14957.3i	0.506997	+	0.878144i
$663$	3424.29	+	5931.05i	0.200586	+	0.347425i
$664$	448.174	−	776.259i	0.0261935	−	0.0453685i
$665$	−37.7432	+	65.3731i	−0.00220093	+	0.00381212i
$666$	30732.3			1.78807
$667$	17148.0			0.995464
$668$	−6155.04	+	10660.8i	−0.356505	+	0.617485i
$669$	−16863.0	+	29207.6i	−0.974533	+	1.68794i
$670$	−12.1072	−	20.9703i	−0.000698123	−	0.00120918i
$671$	−15428.3	−	26722.7i	−0.887637	−	1.53743i
$672$	−32992.2			−1.89390
$673$	5338.07	+	9245.81i	0.305747	+	0.529569i	0.977427	−	0.211272i	$-0.0677606\pi$
$673$	5338.07	+	9245.81i	0.305747	+	0.529569i	−0.671681	+	0.740841i	$0.734427\pi$
$674$	−3377.98	−	5850.84i	−0.193049	−	0.334371i
$675$	8480.78	+	14689.1i	0.483593	+	0.837608i
$676$	−3065.95	+	5310.38i	−0.174440	+	0.302138i
$677$	−6422.42			−0.364599			−0.182300	−	0.983243i	$-0.558354\pi$
$677$	−6422.42			−0.364599			−0.182300	+	0.983243i	$0.558354\pi$
$678$	−8048.50	+	13940.4i	−0.455901	+	0.789644i
$679$	−19455.5	−	33697.9i	−1.09961	−	1.90458i
$680$	−48.8750			−0.00275628
$681$	11327.3	+	19619.4i	0.637390	+	1.10399i
$682$	11539.4	−	19986.8i	0.647898	−	1.12219i
$683$	1347.81	−	2334.47i	0.0755087	−	0.130785i	−0.825799	−	0.563965i	$-0.809275\pi$
$683$	1347.81	−	2334.47i	0.0755087	−	0.130785i	0.901307	+	0.433180i	$0.142609\pi$
$684$	8522.67			0.476422
$685$	22.1224	−	38.3171i	0.00123395	−	0.00213726i
$686$	6150.43			0.342310
$687$	24098.6			1.33831
$688$	2841.45	+	1286.48i	0.157455	+	0.0712886i
$689$	7758.57			0.428996
$690$	143.444			0.00791423
$691$	−4323.87	+	7489.17i	−0.238043	+	0.412303i	−0.960153	−	0.279476i	$-0.909839\pi$
$691$	−4323.87	+	7489.17i	−0.238043	+	0.412303i	0.722109	+	0.691779i	$0.243173\pi$
$692$	1355.66			0.0744717
$693$	27870.5	−	48273.2i	1.52773	−	2.64610i
$694$	2893.06	−	5010.93i	0.158241	−	0.274081i
$695$	−21.0510	−	36.4614i	−0.00114893	−	0.00199001i
$696$	−26804.7			−1.45981
$697$	−5256.84	−	9105.11i	−0.285677	−	0.494807i
$698$	−5608.37	+	9713.98i	−0.304126	+	0.526762i
$699$	−11198.7			−0.605969
$700$	6304.17	−	10919.1i	0.340393	−	0.589578i
$701$	6754.48	+	11699.1i	0.363927	+	0.630341i	0.988603	−	0.150543i	$-0.0481023\pi$
$701$	6754.48	+	11699.1i	0.363927	+	0.630341i	−0.624676	+	0.780884i	$0.714769\pi$
$702$	3624.64	+	6278.06i	0.194876	+	0.337536i
$703$	8483.12	+	14693.2i	0.455117	+	0.788285i
$704$	22650.2			1.21259
$705$	−130.037	−	225.230i	−0.00694675	−	0.0120321i
$706$	−5944.81	−	10296.7i	−0.316906	−	0.548898i
$707$	−11984.4	+	20757.6i	−0.637511	+	1.10420i
$708$	7459.03	−	12919.4i	0.395943	−	0.685793i
$709$	−5130.31			−0.271753			−0.135877	−	0.990726i	$-0.543385\pi$
$709$	−5130.31			−0.271753			−0.135877	+	0.990726i	$0.543385\pi$
$710$	79.9109			0.00422395
$711$	12910.8	−	22362.1i	0.681000	−	1.17953i
$712$	−4451.90	+	7710.92i	−0.234329	+	0.405870i
$713$	13823.8	+	23943.5i	0.726093	+	1.25763i
$714$	5555.39	+	9622.21i	0.291184	+	0.504345i
$715$	−107.402			−0.00561763
$716$	511.023	+	885.118i	0.0266729	+	0.0461989i
$717$	−14430.6	−	24994.5i	−0.751631	−	1.30186i
$718$	4142.57	+	7175.14i	0.215319	+	0.372944i
$719$	13293.6	−	23025.1i	0.689521	−	1.19429i	−0.282472	−	0.959276i	$-0.591154\pi$
$719$	13293.6	−	23025.1i	0.689521	−	1.19429i	0.971993	−	0.235010i	$-0.0755124\pi$
$720$	−33.5560			−0.00173689
$721$	−781.061	+	1352.84i	−0.0403443	+	0.0698784i
$722$	4572.86	+	7920.43i	0.235712	+	0.408266i
$723$	6204.95			0.319176
$724$	−460.118	−	796.948i	−0.0236190	−	0.0409093i
$725$	8452.38	−	14639.9i	0.432984	−	0.749950i
$726$	−13685.6	+	23704.1i	−0.699614	+	1.21177i
$727$	23833.0			1.21584			0.607920	−	0.793999i	$-0.292004\pi$
$727$	23833.0			1.21584			0.607920	+	0.793999i	$0.292004\pi$
$728$	7703.77	−	13343.3i	0.392199	−	0.679308i
$729$	−31965.9			−1.62404
$730$	95.1586			0.00482462
$731$	815.446	+	8255.57i	0.0412590	+	0.417706i
$732$	−20208.9			−1.02041
$733$	1707.21			0.0860261			0.0430130	−	0.999075i	$-0.486304\pi$
$733$	1707.21			0.0860261			0.0430130	+	0.999075i	$0.486304\pi$
$734$	668.875	−	1158.52i	0.0336357	−	0.0582588i
$735$	121.529			0.00609887
$736$	−10649.2	+	18445.0i	−0.533337	+	0.923767i
$737$	−4935.62	+	8548.75i	−0.246684	+	0.427269i
$738$	−14840.5	−	25704.5i	−0.740226	−	1.28211i
$739$	−17540.3			−0.873111			−0.436556	−	0.899677i	$-0.643802\pi$
$739$	−17540.3			−0.873111			−0.436556	+	0.899677i	$0.643802\pi$
$740$	55.9043	+	96.8291i	0.00277714	+	0.00481015i
$741$	−5336.87	+	9243.73i	−0.264581	+	0.458268i
$742$	12587.1			0.622758
$743$	4355.47	−	7543.89i	0.215056	−	0.372488i	−0.738234	−	0.674545i	$-0.764340\pi$
$743$	4355.47	−	7543.89i	0.215056	−	0.372488i	0.953290	+	0.302057i	$0.0976733\pi$
$744$	−21608.4	−	37426.9i	−1.06479	−	1.84427i
$745$	−86.8924	−	150.502i	−0.00427314	−	0.00740130i
$746$	−1038.18	−	1798.18i	−0.0509525	−	0.0882522i
$747$	1636.76			0.0801685
$748$	3484.24	+	6034.89i	0.170316	+	0.294997i
$749$	15026.9	+	26027.4i	0.733072	+	1.26972i
$750$	141.412	−	244.932i	0.00688484	−	0.0119249i
$751$	−12765.5	+	22110.4i	−0.620264	+	1.07433i	0.369172	+	0.929361i	$0.379641\pi$
$751$	−12765.5	+	22110.4i	−0.620264	+	1.07433i	−0.989436	+	0.144968i	$0.953692\pi$
$752$	−4889.56			−0.237106
$753$	11001.4			0.532423
$754$	3612.50	−	6257.03i	0.174482	−	0.302212i
$755$	−73.1611	+	126.719i	−0.00352663	+	0.00610830i
$756$	−6843.97	−	11854.1i	−0.329250	−	0.570277i
$757$	18328.4	+	31745.8i	0.879998	+	1.52420i	0.851342	+	0.524612i	$0.175790\pi$
$757$	18328.4	+	31745.8i	0.879998	+	1.52420i	0.0286563	+	0.999589i	$0.490877\pi$
$758$	−10113.2			−0.484602
$759$	−29238.2	−	50642.0i	−1.39826	−	2.42186i
$760$	−38.0866	−	65.9680i	−0.00181782	−	0.00314857i
$761$	−7587.33	−	13141.6i	−0.361420	−	0.625998i	0.626775	−	0.779200i	$-0.284375\pi$
$761$	−7587.33	−	13141.6i	−0.361420	−	0.625998i	−0.988195	+	0.153203i	$0.951041\pi$
$762$	−10271.6	+	17790.9i	−0.488321	+	0.845797i
$763$	−37204.5			−1.76526
$764$	3514.59	−	6087.44i	0.166431	−	0.288267i
$765$	−44.6237	−	77.2905i	−0.00210898	−	0.00365287i
$766$	−18019.4			−0.849959
$767$	5748.51	+	9956.71i	0.270621	+	0.468730i
$768$	18241.4	−	31595.0i	0.857069	−	1.48449i
$769$	5637.67	−	9764.72i	0.264369	−	0.457900i	−0.703029	−	0.711161i	$-0.748170\pi$
$769$	5637.67	−	9764.72i	0.264369	−	0.457900i	0.967398	+	0.253261i	$0.0815031\pi$
$770$	−174.243			−0.00815492
$771$	−18454.9	+	31964.9i	−0.862047	+	1.49311i
$772$	21095.9			0.983493
$773$	7328.29			0.340983			0.170492	−	0.985359i	$-0.445464\pi$
$773$	7328.29			0.340983			0.170492	+	0.985359i	$0.445464\pi$
$774$	2302.08	+	23306.2i	0.106908	+	1.08233i
$775$	27255.3			1.26328
$776$	39265.1			1.81641
$777$	36337.0	−	62937.5i	1.67771	−	2.90588i
$778$	−7177.06			−0.330733
$779$	8192.94	−	14190.6i	0.376820	−	0.652671i
$780$	−35.1703	+	60.9167i	−0.00161449	+	0.00279637i
$781$	−16288.2	−	28212.0i	−0.746272	−	1.29258i
$782$	7172.68			0.327998
$783$	−9176.12	−	15893.5i	−0.418809	−	0.725399i
$784$	1142.42	−	1978.73i	0.0520416	−	0.0901387i
$785$	186.512			0.00848012
$786$	12624.3	−	21865.9i	0.572892	−	0.992278i
$787$	5754.50	+	9967.08i	0.260642	+	0.451446i	0.966413	−	0.256995i	$-0.0827323\pi$
$787$	5754.50	+	9967.08i	0.260642	+	0.451446i	−0.705770	+	0.708441i	$0.749399\pi$
$788$	9533.16	+	16511.9i	0.430971	+	0.746463i
$789$	1260.73	+	2183.65i	0.0568861	+	0.0985296i
$790$	−80.7164			−0.00363514
$791$	11712.0	+	20285.8i	0.526462	+	0.911858i
$792$	28124.1	+	48712.5i	1.26180	+	2.18551i
$793$	7787.28	−	13488.0i	0.348719	−	0.603999i
$794$	−4717.42	+	8170.81i	−0.210850	+	0.365203i
$795$	−164.302			−0.00732982
$796$	−4137.25			−0.184222
$797$	−3815.51	+	6608.66i	−0.169576	+	0.293715i	−0.938271	−	0.345901i	$-0.887573\pi$
$797$	−3815.51	+	6608.66i	−0.169576	+	0.293715i	0.768695	+	0.639616i	$0.220907\pi$
$798$	−8658.24	+	14996.5i	−0.384083	+	0.665252i
$799$	−6502.27	−	11262.3i	−0.287902	−	0.498661i
$800$	10498.2	+	18183.3i	0.463957	+	0.803597i
$801$	−16258.6			−0.717192
$802$	1799.67	+	3117.12i	0.0792377	+	0.137244i
$803$	−19396.2	−	33595.1i	−0.852398	−	1.47640i
$804$	3232.48	+	5598.82i	0.141792	+	0.245591i
$805$	104.368	−	180.771i	0.00456956	−	0.00791472i
$806$	11648.8			0.509070
$807$	9285.30	−	16082.6i	0.405028	−	0.701530i
$808$	−12093.5	−	20946.5i	−0.526543	−	0.911999i
$809$	7806.54			0.339262			0.169631	−	0.985508i	$-0.445742\pi$
$809$	7806.54			0.339262			0.169631	+	0.985508i	$0.445742\pi$
$810$	1.98355	+	3.43561i	8.60431e−5	+	0.000149031i
$811$	10102.7	−	17498.3i	0.437426	−	0.757644i	−0.560064	−	0.828449i	$-0.689224\pi$
$811$	10102.7	−	17498.3i	0.437426	−	0.757644i	0.997490	+	0.0708052i	$0.0225569\pi$
$812$	−6821.05	+	11814.4i	−0.294793	+	0.510596i
$813$	1082.87			0.0467135
$814$	−19581.4	+	33915.9i	−0.843153	+	1.46038i
$815$	82.8905			0.00356261
$816$	−2726.70			−0.116978
$817$	−10507.3	+	7533.91i	−0.449944	+	0.322617i
$818$	3687.82			0.157630
$819$	28134.7			1.20037
$820$	53.9920	−	93.5169i	0.00229937	−	0.00398262i
$821$	9050.07			0.384713			0.192357	−	0.981325i	$-0.438387\pi$
$821$	9050.07			0.384713			0.192357	+	0.981325i	$0.438387\pi$
$822$	5074.86	−	8789.91i	0.215336	−	0.372973i
$823$	15775.7	−	27324.2i	0.668171	−	1.15731i	−0.310244	−	0.950657i	$-0.600411\pi$
$823$	15775.7	−	27324.2i	0.668171	−	1.15731i	0.978415	−	0.206649i	$-0.0662559\pi$
$824$	−788.169	−	1365.15i	−0.0333218	−	0.0577150i
$825$	−57646.7			−2.43273
$826$	9326.06	+	16153.2i	0.392851	+	0.680439i
$827$	−12709.6	+	22013.7i	−0.534410	+	0.925625i	0.464782	+	0.885425i	$0.346133\pi$
$827$	−12709.6	+	22013.7i	−0.534410	+	0.925625i	−0.999192	+	0.0401997i	$0.987201\pi$
$828$	−23567.1			−0.989147
$829$	−18258.4	+	31624.5i	−0.764947	+	1.32493i	0.175327	+	0.984510i	$0.443902\pi$
$829$	−18258.4	+	31624.5i	−0.764947	+	1.32493i	−0.940274	+	0.340417i	$0.889432\pi$
$830$	−2.55820	−	4.43094i	−0.000106984	−	0.000185301i
$831$	5054.16	+	8754.05i	0.210983	+	0.365433i
$832$	5716.21	+	9900.77i	0.238190	+	0.412557i
$833$	6076.87			0.252762
$834$	−4829.08	−	8364.21i	−0.200500	−	0.347277i
$835$	100.454	+	173.991i	0.00416328	+	0.00721102i
$836$	−5430.30	+	9405.56i	−0.224654	+	0.389113i
$837$	14794.5	−	25624.9i	0.610960	−	1.05821i
$838$	17984.3			0.741355
$839$	−9085.26			−0.373847			−0.186924	−	0.982374i	$-0.559852\pi$
$839$	−9085.26			−0.373847			−0.186924	+	0.982374i	$0.559852\pi$
$840$	−163.142	+	282.570i	−0.00670111	+	0.0116067i
$841$	3049.11	−	5281.22i	0.125020	−	0.216541i
$842$	−3342.66	−	5789.65i	−0.136812	−	0.236965i
$843$	33270.7	+	57626.5i	1.35932	+	2.35440i
$844$	14701.4			0.599577
$845$	50.0380	+	86.6684i	0.00203711	+	0.00352838i
$846$	−18356.5	−	31794.3i	−0.745991	−	1.29209i
$847$	19915.0	+	34493.7i	0.807894	+	1.39931i
$848$	−1544.50	+	2675.16i	−0.0625453	+	0.108332i
$849$	−29378.5			−1.18760
$850$	3535.46	−	6123.60i	0.142665	−	0.247103i
$851$	−23457.7	−	40630.0i	−0.944913	−	1.63664i
$852$	−21335.2			−0.857903
$853$	−11268.4	−	19517.4i	−0.452313	−	0.783429i	0.546217	−	0.837644i	$-0.316068\pi$
$853$	−11268.4	−	19517.4i	−0.452313	−	0.783429i	−0.998529	+	0.0542154i	$0.982734\pi$
$854$	12633.7	−	21882.1i	0.506223	−	0.876804i
$855$	69.5474	−	120.460i	0.00278184	−	0.00481828i
$856$	−30327.3			−1.21094
$857$	13650.0	−	23642.6i	0.544080	−	0.942375i	−0.454584	−	0.890704i	$-0.650212\pi$
$857$	13650.0	−	23642.6i	0.544080	−	0.942375i	0.998664	−	0.0516708i	$-0.0164547\pi$
$858$	−24637.9			−0.980331
$859$	2423.33			0.0962549			0.0481275	−	0.998841i	$-0.484675\pi$
$859$	2423.33			0.0962549			0.0481275	+	0.998841i	$0.484675\pi$
$860$	−69.2439	+	49.6489i	−0.00274558	+	0.00196862i
$861$	−70188.0			−2.77817
$862$	−9307.86			−0.367781
$863$	−429.835	+	744.497i	−0.0169545	+	0.0293661i	−0.874378	−	0.485245i	$-0.838730\pi$
$863$	−429.835	+	744.497i	−0.0169545	+	0.0293661i	0.857424	+	0.514611i	$0.172064\pi$
$864$	22794.1			0.897537
$865$	11.0626	−	19.1609i	0.000434842	−	0.000753168i
$866$	−11144.0	+	19302.1i	−0.437287	+	0.757403i
$867$	16955.3	+	29367.5i	0.664167	+	1.15037i
$868$	−21995.0			−0.860089
$869$	16452.4	+	28496.4i	0.642244	+	1.11240i
$870$	−76.5015	+	132.505i	−0.00298120	+	0.00516359i
$871$	−4982.40			−0.193826
$872$	18771.5	−	32513.2i	0.728996	−	1.26266i
$873$	35849.7	+	62093.5i	1.38984	+	2.40727i
$874$	5589.42	+	9681.17i	0.216322	+	0.374680i
$875$	−205.779	−	356.420i	−0.00795041	−	0.0137705i
$876$	−25406.2			−0.979903
$877$	8783.41	+	15213.3i	0.338192	+	0.585766i	0.984093	−	0.177655i	$-0.0568512\pi$
$877$	8783.41	+	15213.3i	0.338192	+	0.585766i	−0.645900	+	0.763422i	$0.723518\pi$
$878$	4304.85	+	7456.21i	0.165469	+	0.286600i
$879$	−22704.9	+	39326.1i	−0.871238	+	1.50903i
$880$	21.3806	−	37.0322i	0.000819021	−	0.00141859i
$881$	−25664.9			−0.981469			−0.490734	−	0.871309i	$-0.663271\pi$
$881$	−25664.9			−0.981469			−0.490734	+	0.871309i	$0.663271\pi$
$882$	17155.5			0.654940
$883$	19408.6	−	33616.7i	0.739695	−	1.28119i	−0.212937	−	0.977066i	$-0.568303\pi$
$883$	19408.6	−	33616.7i	0.739695	−	1.28119i	0.952632	−	0.304124i	$-0.0983637\pi$
$884$	−1758.63	+	3046.04i	−0.0669109	+	0.115893i
$885$	−121.736	−	210.852i	−0.00462384	−	0.00800872i
$886$	−4247.85	−	7357.48i	−0.161071	−	0.278984i
$887$	19118.6			0.723721			0.361861	−	0.932232i	$-0.382142\pi$
$887$	19118.6			0.723721			0.361861	+	0.932232i	$0.382142\pi$
$888$	36667.6	+	63510.2i	1.38568	+	2.40007i
$889$	14947.0	+	25889.0i	0.563899	+	0.976702i
$890$	25.4118	+	44.0144i	0.000957083	+	0.00165772i
$891$	808.614	−	1400.56i	0.0304036	−	0.0526606i
$892$	−17320.9			−0.650164
$893$	10134.0	−	17552.6i	0.379754	−	0.657754i
$894$	−19933.0	−	34525.0i	−0.745705	−	1.29160i
$895$	16.6804			0.000622975
$896$	−6477.54	−	11219.4i	−0.241517	−	0.418320i
$897$	14757.6	−	25561.0i	0.549323	−	0.951456i
$898$	10613.4	−	18383.0i	0.394404	−	0.683127i
$899$	−29490.0			−1.09404
$900$	−11616.4	+	20120.2i	−0.430236	+	0.745191i
$901$	−8215.68			−0.303778
$902$	37823.1			1.39620
$903$	50451.3	+	22842.1i	1.85926	+	0.841791i
$904$	−23637.2			−0.869647
$905$	−15.0188			−0.000551647
$906$	−16783.1	+	29069.1i	−0.615431	+	1.06596i
$907$	−9172.98			−0.335814			−0.167907	−	0.985803i	$-0.553701\pi$
$907$	−9172.98			−0.335814			−0.167907	+	0.985803i	$0.553701\pi$
$908$	−5817.41	+	10076.1i	−0.212618	+	0.368266i
$909$	22083.1	−	38249.0i	0.805774	−	1.39564i
$910$	−43.9736	−	76.1645i	−0.00160188	−	0.00277454i
$911$	18316.9			0.666154			0.333077	−	0.942900i	$-0.391913\pi$
$911$	18316.9			0.666154			0.333077	+	0.942900i	$0.391913\pi$
$912$	−2124.82	−	3680.30i	−0.0771491	−	0.133626i
$913$	−1042.88	+	1806.31i	−0.0378030	+	0.0654768i
$914$	−24265.0			−0.878134
$915$	−164.910	+	285.633i	−0.00595821	+	0.0103199i
$916$	6188.23	+	10718.3i	0.223215	+	0.386620i
$917$	−18370.6	−	31818.8i	−0.661559	−	1.14585i
$918$	−3838.19	−	6647.94i	−0.137995	−	0.239014i
$919$	23462.4			0.842168			0.421084	−	0.907022i	$-0.361650\pi$
$919$	23462.4			0.842168			0.421084	+	0.907022i	$0.361650\pi$
$920$	105.318	+	182.416i	0.00377417	+	0.00653705i
$921$	−24113.5	−	41765.8i	−0.862721	−	1.49428i
$922$	6599.92	−	11431.4i	0.235745	−	0.408322i
$923$	8221.30	−	14239.7i	0.293182	−	0.507807i
$924$	46520.8			1.65630
$925$	−46249.9			−1.64399
$926$	283.580	−	491.174i	0.0100637	−	0.0174309i
$927$	1439.22	−	2492.80i	0.0509927	−	0.0883219i
$928$	−11358.9	−	19674.2i	−0.401804	−	0.695945i
$929$	19668.8	+	34067.4i	0.694631	+	1.20314i	0.970305	+	0.241885i	$0.0777657\pi$
$929$	19668.8	+	34067.4i	0.694631	+	1.20314i	−0.275674	+	0.961251i	$0.588901\pi$
$930$	−246.685			−0.00869796
$931$	4735.49	+	8202.11i	0.166702	+	0.288736i
$932$	−2875.68	−	4980.82i	−0.101069	−	0.175056i
$933$	2051.47	+	3553.25i	0.0719851	+	0.124682i
$934$	5382.52	−	9322.80i	0.188567	−	0.326607i
$935$	113.730			0.00397792
$936$	−14195.3	+	24587.1i	−0.495715	+	0.858604i
$937$	−20538.7	−	35574.0i	−0.716082	−	1.24029i	−0.962541	−	0.271137i	$-0.912600\pi$
$937$	−20538.7	−	35574.0i	−0.716082	−	1.24029i	0.246459	−	0.969153i	$-0.420733\pi$
$938$	−8083.17			−0.281370
$939$	33838.9	+	58610.6i	1.17603	+	2.03694i
$940$	66.7836	−	115.673i	0.00231728	−	0.00401364i
$941$	19244.2	−	33331.9i	0.666675	−	1.15472i	−0.312153	−	0.950032i	$-0.601050\pi$
$941$	19244.2	−	33331.9i	0.666675	−	1.15472i	0.978828	−	0.204684i	$-0.0656166\pi$
$942$	42785.6			1.47986
$943$	−22655.3	+	39240.2i	−0.782353	+	1.35507i
$944$	−4577.43			−0.157821
$945$	−223.395			−0.00768998
$946$	−27187.3	−	12309.2i	−0.934394	−	0.423052i
$947$	24162.6			0.829122			0.414561	−	0.910022i	$-0.363935\pi$
$947$	24162.6			0.829122			0.414561	+	0.910022i	$0.363935\pi$
$948$	21550.3			0.738313
$949$	9789.99	−	16956.8i	0.334875	−	0.580021i
$950$	11020.3			0.376362
$951$	18432.9	−	31926.7i	0.628525	−	1.08864i
$952$	−8157.64	+	14129.5i	−0.277721	+	0.481028i
$953$	−12928.6	−	22393.0i	−0.439453	−	0.761155i	0.558194	−	0.829710i	$-0.311494\pi$
$953$	−12928.6	−	22393.0i	−0.439453	−	0.761155i	−0.997647	+	0.0685550i	$0.978161\pi$
$954$	−23193.6			−0.787128
$955$	−57.3600	−	99.3504i	−0.00194359	−	0.00336639i
$956$	7411.18	−	12836.5i	0.250727	−	0.434271i
$957$	62373.2			2.10683
$958$	−6126.74	+	10611.8i	−0.206624	+	0.357884i
$959$	−7384.82	−	12790.9i	−0.248664	−	0.430698i
$960$	−121.052	−	209.668i	−0.00406971	−	0.00704895i
$961$	−8877.62	−	15376.5i	−0.297997	−	0.516145i
$962$	−19766.9			−0.662487
$963$	−27689.3	−	47959.3i	−0.926558	−	1.60485i
$964$	1593.35	+	2759.77i	0.0532350	+	0.0922057i
$965$	172.148	−	298.169i	0.00574264	−	0.00994654i
$966$	23942.0	−	41468.7i	0.797433	−	1.38119i
$967$	−42638.6			−1.41796			−0.708979	−	0.705230i	$-0.750844\pi$
$967$	−42638.6			−1.41796			−0.708979	+	0.705230i	$0.750844\pi$
$968$	−40192.4			−1.33454
$969$	5651.29	−	9788.33i	0.187354	−	0.324506i
$970$	112.064	−	194.100i	0.00370944	−	0.00642494i
$971$	24599.3	+	42607.3i	0.813007	+	1.40817i	0.910750	+	0.412958i	$0.135504\pi$
$971$	24599.3	+	42607.3i	0.813007	+	1.40817i	−0.0977432	+	0.995212i	$0.531162\pi$
$972$	−8412.16	−	14570.3i	−0.277593	−	0.480805i
$973$	−14054.3			−0.463064
$974$	15350.2	+	26587.3i	0.504981	+	0.874653i
$975$	−14548.3	−	25198.3i	−0.477864	−	0.827685i
$976$	3100.43	+	5370.11i	0.101683	+	0.176120i
$977$	−21000.7	+	36374.3i	−0.687688	+	1.19111i	0.284895	+	0.958559i	$0.408041\pi$
$977$	−21000.7	+	36374.3i	−0.687688	+	1.19111i	−0.972584	+	0.232553i	$0.925292\pi$
$978$	19015.0			0.621710
$979$	10359.3	−	17942.9i	0.338188	−	0.585759i
$980$	31.2072	+	54.0524i	0.00101722	+	0.00176188i
$981$	68554.8			2.23118
$982$	−11002.3	−	19056.5i	−0.357531	−	0.619263i
$983$	−11537.6	+	19983.7i	−0.374356	+	0.648403i	−0.990230	−	0.139441i	$-0.955469\pi$
$983$	−11537.6	+	19983.7i	−0.374356	+	0.648403i	0.615875	+	0.787844i	$0.288803\pi$
$984$	35413.4	−	61337.7i	1.14729	−	1.98717i
$985$	311.173			0.0100658
$986$	−3825.33	+	6625.67i	−0.123553	+	0.214000i
$987$	−86816.7			−2.79980
$988$	−5481.77			−0.176516
$989$	29055.1	−	20832.9i	0.934174	−	0.669817i
$990$	321.069			0.0103073
$991$	−23753.3			−0.761401			−0.380701	−	0.924698i	$-0.624317\pi$
$991$	−23753.3			−0.761401			−0.380701	+	0.924698i	$0.624317\pi$
$992$	18313.8	−	31720.4i	0.586152	−	1.01525i
$993$	−75257.3			−2.40505
$994$	13337.8	−	23101.7i	0.425602	−	0.737165i
$995$	−33.7611	+	58.4760i	−0.00107568	+	0.00186313i
$996$	683.009	+	1183.01i	0.0217289	+	0.0376355i
$997$	−881.578			−0.0280039			−0.0140019	−	0.999902i	$-0.504457\pi$
$997$	−881.578			−0.0280039			−0.0140019	+	0.999902i	$0.504457\pi$
$998$	−1327.46	−	2299.23i	−0.0421043	−	0.0729267i
$999$	−25105.0	+	43483.2i	−0.795083	+	1.37712i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.4.c.a.6.7	✓	20
43.6	even	3		1849.4.a.d.1.7		10
43.36	even	3	inner	43.4.c.a.36.7	yes	20
43.37	odd	6		1849.4.a.f.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.c.a.6.7	✓	20	1.1	even	1	trivial
43.4.c.a.36.7	yes	20	43.36	even	3	inner
1849.4.a.d.1.7		10	43.6	even	3
1849.4.a.f.1.4		10	43.37	odd	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.92278 q^{2} +(-4.18916 + 7.25584i) q^{3} -4.30290 q^{4} +(-0.0351129 + 0.0608173i) q^{5} +(-8.05486 + 13.9514i) q^{6} +(11.7213 + 20.3018i) q^{7} -23.6558 q^{8} +(-21.5982 - 37.4091i) q^{9} +O(q^{10})\)	\(q+1.92278 q^{2} +(-4.18916 + 7.25584i) q^{3} -4.30290 q^{4} +(-0.0351129 + 0.0608173i) q^{5} +(-8.05486 + 13.9514i) q^{6} +(11.7213 + 20.3018i) q^{7} -23.6558 q^{8} +(-21.5982 - 37.4091i) q^{9} +(-0.0675145 + 0.116939i) q^{10} +55.0459 q^{11} +(18.0255 - 31.2212i) q^{12} +(13.8919 + 24.0615i) q^{13} +(22.5374 + 39.0360i) q^{14} +(-0.294187 - 0.509547i) q^{15} -11.0619 q^{16} +(-14.7103 - 25.4791i) q^{17} +(-41.5286 - 71.9296i) q^{18} +(22.9265 - 39.7099i) q^{19} +(0.151087 - 0.261691i) q^{20} -196.409 q^{21} +105.841 q^{22} +(-63.3970 + 109.807i) q^{23} +(99.0981 - 171.643i) q^{24} +(62.4975 + 108.249i) q^{25} +(26.7111 + 46.2650i) q^{26} +135.698 q^{27} +(-50.4354 - 87.3566i) q^{28} +(-67.6217 - 117.124i) q^{29} +(-0.565658 - 0.979749i) q^{30} +(109.025 - 188.838i) q^{31} +167.977 q^{32} +(-230.596 + 399.404i) q^{33} +(-28.2848 - 48.9907i) q^{34} -1.64627 q^{35} +(92.9347 + 160.968i) q^{36} +(-185.007 + 320.441i) q^{37} +(44.0827 - 76.3536i) q^{38} -232.781 q^{39} +(0.830624 - 1.43868i) q^{40} +357.357 q^{41} -377.652 q^{42} +(-256.869 - 116.299i) q^{43} -236.857 q^{44} +3.03349 q^{45} +(-121.899 + 211.135i) q^{46} +442.020 q^{47} +(46.3399 - 80.2631i) q^{48} +(-103.275 + 178.878i) q^{49} +(120.169 + 208.139i) q^{50} +246.496 q^{51} +(-59.7754 - 103.534i) q^{52} +(139.624 - 241.836i) q^{53} +260.918 q^{54} +(-1.93282 + 3.34774i) q^{55} +(-277.276 - 480.256i) q^{56} +(192.086 + 332.702i) q^{57} +(-130.022 - 225.205i) q^{58} +413.803 q^{59} +(1.26586 + 2.19253i) q^{60} +(-280.281 - 485.462i) q^{61} +(209.633 - 363.094i) q^{62} +(506.315 - 876.963i) q^{63} +411.478 q^{64} -1.95114 q^{65} +(-443.386 + 767.968i) q^{66} +(-89.6639 + 155.302i) q^{67} +(63.2971 + 109.634i) q^{68} +(-531.160 - 919.996i) q^{69} -3.16542 q^{70} +(-295.903 - 512.519i) q^{71} +(510.922 + 884.943i) q^{72} +(-352.364 - 610.312i) q^{73} +(-355.728 + 616.139i) q^{74} -1047.25 q^{75} +(-98.6505 + 170.868i) q^{76} +(645.206 + 1117.53i) q^{77} -447.589 q^{78} +(298.886 + 517.685i) q^{79} +(0.388413 - 0.672752i) q^{80} +(14.6898 - 25.4435i) q^{81} +687.120 q^{82} +(-18.9456 + 32.8147i) q^{83} +845.128 q^{84} +2.06609 q^{85} +(-493.903 - 223.617i) q^{86} +1133.11 q^{87} -1302.16 q^{88} +(188.195 - 325.963i) q^{89} +5.83275 q^{90} +(-325.661 + 564.061i) q^{91} +(272.791 - 472.487i) q^{92} +(913.451 + 1582.14i) q^{93} +849.909 q^{94} +(1.61003 + 2.78866i) q^{95} +(-703.683 + 1218.81i) q^{96} -1659.85 q^{97} +(-198.576 + 343.944i) q^{98} +(-1188.89 - 2059.22i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9	\( 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9} + 27 q^{10} + 54 q^{11} - 72 q^{12} - 15 q^{13} + 96 q^{14} + 65 q^{15} + 134 q^{16} - 82 q^{17} + 247 q^{18} + 78 q^{19} - 495 q^{20} - 18 q^{21} + 380 q^{22} - 61 q^{23} + 202 q^{24} - 151 q^{25} - 21 q^{26} - 194 q^{27} - 794 q^{28} - 53 q^{29} + 627 q^{30} + 253 q^{31} - 798 q^{32} - 424 q^{33} - 231 q^{34} + 710 q^{35} - 1092 q^{36} - 129 q^{37} - 854 q^{38} + 1382 q^{39} + 1345 q^{40} + 782 q^{41} + 62 q^{42} + 1025 q^{43} + 754 q^{44} + 1888 q^{45} - 40 q^{46} - 668 q^{47} - 2401 q^{48} - 115 q^{49} + 424 q^{50} + 1590 q^{51} - 564 q^{52} + 773 q^{53} + 364 q^{54} - 1242 q^{55} - 923 q^{56} - 765 q^{57} + 1328 q^{58} - 2966 q^{59} - 1075 q^{60} + 437 q^{61} + 1509 q^{62} - 2222 q^{63} - 1476 q^{64} - 2126 q^{65} + 1483 q^{66} - 642 q^{67} - 1052 q^{68} - 3503 q^{69} - 170 q^{70} - 1545 q^{71} + 3834 q^{72} + 1292 q^{73} - 2232 q^{74} + 164 q^{75} - 252 q^{76} + 1448 q^{77} + 5644 q^{78} - 1405 q^{79} - 3157 q^{80} + 974 q^{81} + 6608 q^{82} + 543 q^{83} + 7304 q^{84} + 1946 q^{85} + 2776 q^{86} + 2818 q^{87} - 5372 q^{88} - 2196 q^{89} - 1484 q^{90} - 3513 q^{91} + 2629 q^{92} - 983 q^{93} + 9878 q^{94} - 149 q^{95} + 3540 q^{96} - 850 q^{97} - 213 q^{98} - 3181 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9 + 27 * q^10 + 54 * q^11 - 72 * q^12 - 15 * q^13 + 96 * q^14 + 65 * q^15 + 134 * q^16 - 82 * q^17 + 247 * q^18 + 78 * q^19 - 495 * q^20 - 18 * q^21 + 380 * q^22 - 61 * q^23 + 202 * q^24 - 151 * q^25 - 21 * q^26 - 194 * q^27 - 794 * q^28 - 53 * q^29 + 627 * q^30 + 253 * q^31 - 798 * q^32 - 424 * q^33 - 231 * q^34 + 710 * q^35 - 1092 * q^36 - 129 * q^37 - 854 * q^38 + 1382 * q^39 + 1345 * q^40 + 782 * q^41 + 62 * q^42 + 1025 * q^43 + 754 * q^44 + 1888 * q^45 - 40 * q^46 - 668 * q^47 - 2401 * q^48 - 115 * q^49 + 424 * q^50 + 1590 * q^51 - 564 * q^52 + 773 * q^53 + 364 * q^54 - 1242 * q^55 - 923 * q^56 - 765 * q^57 + 1328 * q^58 - 2966 * q^59 - 1075 * q^60 + 437 * q^61 + 1509 * q^62 - 2222 * q^63 - 1476 * q^64 - 2126 * q^65 + 1483 * q^66 - 642 * q^67 - 1052 * q^68 - 3503 * q^69 - 170 * q^70 - 1545 * q^71 + 3834 * q^72 + 1292 * q^73 - 2232 * q^74 + 164 * q^75 - 252 * q^76 + 1448 * q^77 + 5644 * q^78 - 1405 * q^79 - 3157 * q^80 + 974 * q^81 + 6608 * q^82 + 543 * q^83 + 7304 * q^84 + 1946 * q^85 + 2776 * q^86 + 2818 * q^87 - 5372 * q^88 - 2196 * q^89 - 1484 * q^90 - 3513 * q^91 + 2629 * q^92 - 983 * q^93 + 9878 * q^94 - 149 * q^95 + 3540 * q^96 - 850 * q^97 - 213 * q^98 - 3181 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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