LMFDB - Embedded newform 143.4.e.a.133.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [143,4,Mod(100,143)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("143.100"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(143, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [34,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.15
Character	$\chi$	$=$	143.133
Dual form			143.4.e.a.100.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.09463 + 3.62801i) q^{2} +(4.10387 + 7.10811i) q^{3} +(-4.77499 + 8.27053i) q^{4} -18.8743 q^{5} +(-17.1922 + 29.7778i) q^{6} +(7.40609 - 12.8277i) q^{7} -6.49330 q^{8} +(-20.1835 + 34.9588i) q^{9} +(-39.5349 - 68.4764i) q^{10} +(5.50000 + 9.52628i) q^{11} -78.3838 q^{12} +(-18.0159 + 43.2716i) q^{13} +62.0522 q^{14} +(-77.4578 - 134.161i) q^{15} +(24.5988 + 42.6065i) q^{16} +(39.6422 - 68.6622i) q^{17} -169.108 q^{18} +(-54.9151 + 95.1157i) q^{19} +(90.1248 - 156.101i) q^{20} +121.574 q^{21} +(-23.0410 + 39.9082i) q^{22} +(56.2919 + 97.5004i) q^{23} +(-26.6476 - 46.1551i) q^{24} +231.241 q^{25} +(-194.727 + 25.2762i) q^{26} -109.713 q^{27} +(70.7280 + 122.505i) q^{28} +(-5.13248 - 8.88971i) q^{29} +(324.492 - 562.036i) q^{30} +250.224 q^{31} +(-129.024 + 223.477i) q^{32} +(-45.1426 + 78.1892i) q^{33} +332.143 q^{34} +(-139.785 + 242.115i) q^{35} +(-192.752 - 333.856i) q^{36} +(-168.252 - 291.422i) q^{37} -460.108 q^{38} +(-381.514 + 49.5219i) q^{39} +122.557 q^{40} +(-176.340 - 305.429i) q^{41} +(254.654 + 441.074i) q^{42} +(-141.861 + 245.710i) q^{43} -105.050 q^{44} +(380.950 - 659.825i) q^{45} +(-235.822 + 408.455i) q^{46} +75.5585 q^{47} +(-201.901 + 349.703i) q^{48} +(61.7997 + 107.040i) q^{49} +(484.365 + 838.946i) q^{50} +650.745 q^{51} +(-271.853 - 355.622i) q^{52} +195.259 q^{53} +(-229.808 - 398.039i) q^{54} +(-103.809 - 179.802i) q^{55} +(-48.0899 + 83.2942i) q^{56} -901.458 q^{57} +(21.5013 - 37.2414i) q^{58} +(9.09455 - 15.7522i) q^{59} +1479.44 q^{60} +(272.799 - 472.502i) q^{61} +(524.128 + 907.816i) q^{62} +(298.961 + 517.816i) q^{63} -687.454 q^{64} +(340.038 - 816.722i) q^{65} -378.229 q^{66} +(377.262 + 653.437i) q^{67} +(378.582 + 655.723i) q^{68} +(-462.029 + 800.257i) q^{69} -1171.20 q^{70} +(68.5416 - 118.718i) q^{71} +(131.057 - 226.998i) q^{72} +371.711 q^{73} +(704.854 - 1220.84i) q^{74} +(948.983 + 1643.69i) q^{75} +(-524.438 - 908.354i) q^{76} +162.934 q^{77} +(-978.798 - 1280.41i) q^{78} +1102.80 q^{79} +(-464.287 - 804.169i) q^{80} +(94.7082 + 164.039i) q^{81} +(738.734 - 1279.53i) q^{82} -753.357 q^{83} +(-580.517 + 1005.49i) q^{84} +(-748.220 + 1295.95i) q^{85} -1188.58 q^{86} +(42.1260 - 72.9644i) q^{87} +(-35.7131 - 61.8570i) q^{88} +(-431.528 - 747.429i) q^{89} +3191.80 q^{90} +(421.648 + 551.576i) q^{91} -1075.17 q^{92} +(1026.89 + 1778.62i) q^{93} +(158.267 + 274.127i) q^{94} +(1036.49 - 1795.25i) q^{95} -2118.00 q^{96} +(222.954 - 386.167i) q^{97} +(-258.895 + 448.420i) q^{98} -444.037 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 4 q^{2} + 6 q^{3} - 78 q^{4} + 32 q^{5} - 14 q^{6} + 6 q^{7} + 126 q^{8} - 135 q^{9} - 2 q^{10} + 187 q^{11} - 190 q^{12} - 60 q^{13} - 120 q^{14} + 28 q^{15} - 350 q^{16} - 118 q^{17} + 956 q^{18}+ \cdots - 2970 q^{99}+O(q^{100}) $ 34 * q - 4 * q^2 + 6 * q^3 - 78 * q^4 + 32 * q^5 - 14 * q^6 + 6 * q^7 + 126 * q^8 - 135 * q^9 - 2 * q^10 + 187 * q^11 - 190 * q^12 - 60 * q^13 - 120 * q^14 + 28 * q^15 - 350 * q^16 - 118 * q^17 + 956 * q^18 - 403 * q^19 - 98 * q^20 + 440 * q^21 + 44 * q^22 + 215 * q^23 - 26 * q^24 + 638 * q^25 - 989 * q^26 - 768 * q^27 + 396 * q^28 + 7 * q^29 + 1269 * q^30 + 1364 * q^31 - 813 * q^32 - 66 * q^33 + 1476 * q^34 - 10 * q^35 - 560 * q^36 - 1084 * q^37 + 820 * q^38 - 370 * q^39 + 190 * q^40 - 240 * q^41 - 393 * q^42 + 435 * q^43 - 1716 * q^44 - 1242 * q^45 - 1671 * q^46 + 1098 * q^47 - 894 * q^48 - 403 * q^49 + 651 * q^50 + 3104 * q^51 - 876 * q^52 - 1132 * q^53 - 311 * q^54 + 176 * q^55 + 1925 * q^56 - 1068 * q^57 - 618 * q^58 - 2010 * q^59 - 822 * q^60 - 460 * q^61 + 823 * q^62 - 820 * q^63 + 6342 * q^64 + 3070 * q^65 - 308 * q^66 + 232 * q^67 - 1795 * q^68 + 1608 * q^69 + 414 * q^70 - 489 * q^71 - 2556 * q^72 + 580 * q^73 - 2653 * q^74 + 2852 * q^75 - 2421 * q^76 + 132 * q^77 - 4760 * q^78 - 1464 * q^79 - 4915 * q^80 - 2393 * q^81 + 1772 * q^82 - 234 * q^83 - 4161 * q^84 - 4858 * q^85 + 2068 * q^86 - 3032 * q^87 + 693 * q^88 - 4113 * q^89 + 30290 * q^90 + 1096 * q^91 - 7108 * q^92 - 802 * q^93 - 2325 * q^94 + 3924 * q^95 + 5202 * q^96 - 2793 * q^97 - 533 * q^98 - 2970 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	2.09463	+	3.62801i	0.740565	+	1.28270i	0.952238	+	0.305356i	$0.0987755\pi$
$2$	2.09463	+	3.62801i	0.740565	+	1.28270i	−0.211673	+	0.977341i	$0.567891\pi$
$3$	4.10387	+	7.10811i	0.789790	+	1.36796i	0.926095	+	0.377289i	$0.123144\pi$
$3$	4.10387	+	7.10811i	0.789790	+	1.36796i	−0.136305	+	0.990667i	$0.543523\pi$
$4$	−4.77499	+	8.27053i	−0.596874	+	1.03382i
$5$	−18.8743			−1.68817			−0.844086	−	0.536207i	$-0.819857\pi$
$5$	−18.8743			−1.68817			−0.844086	+	0.536207i	$0.819857\pi$
$6$	−17.1922	+	29.7778i	−1.16978	+	2.02612i
$7$	7.40609	−	12.8277i	0.399891	−	0.692632i	−0.593821	−	0.804597i	$-0.702381\pi$
$7$	7.40609	−	12.8277i	0.399891	−	0.692632i	0.993712	+	0.111965i	$0.0357145\pi$
$8$	−6.49330			−0.286966
$9$	−20.1835	+	34.9588i	−0.747536	+	1.29477i
$10$	−39.5349	−	68.4764i	−1.25020	−	2.16541i
$11$	5.50000	+	9.52628i	0.150756	+	0.261116i
$11$	5.50000	+	9.52628i	0.150756	+	0.261116i
$12$	−78.3838			−1.88562
$13$	−18.0159	+	43.2716i	−0.384362	+	0.923182i
$13$	−18.0159	+	43.2716i	−0.384362	+	0.923182i
$14$	62.0522			1.18458
$15$	−77.4578	−	134.161i	−1.33330	−	2.30935i
$16$	24.5988	+	42.6065i	0.384357	+	0.665726i
$17$	39.6422	−	68.6622i	0.565567	−	0.979590i	−0.431430	−	0.902146i	$-0.641991\pi$
$17$	39.6422	−	68.6622i	0.565567	−	0.979590i	0.996997	−	0.0774439i	$-0.0246759\pi$
$18$	−169.108			−2.21440
$19$	−54.9151	+	95.1157i	−0.663073	+	1.14848i	0.316731	+	0.948515i	$0.397415\pi$
$19$	−54.9151	+	95.1157i	−0.663073	+	1.14848i	−0.979804	+	0.199961i	$0.935919\pi$
$20$	90.1248	−	156.101i	1.00763	−	1.74526i
$21$	121.574			1.26332
$22$	−23.0410	+	39.9082i	−0.223289	+	0.386748i
$23$	56.2919	+	97.5004i	0.510333	+	0.883923i	0.999928	+	0.0119732i	$0.00381127\pi$
$23$	56.2919	+	97.5004i	0.510333	+	0.883923i	−0.489595	+	0.871950i	$0.662855\pi$
$24$	−26.6476	−	46.1551i	−0.226643	−	0.392557i
$25$	231.241			1.84993
$26$	−194.727	+	25.2762i	−1.46881	+	0.190657i
$27$	−109.713			−0.782007
$28$	70.7280	+	122.505i	0.477369	+	0.826828i
$29$	−5.13248	−	8.88971i	−0.0328647	−	0.0569234i	0.849125	−	0.528192i	$-0.177130\pi$
$29$	−5.13248	−	8.88971i	−0.0328647	−	0.0569234i	−0.881990	+	0.471268i	$0.843796\pi$
$30$	324.492	−	562.036i	1.97479	−	3.42044i
$31$	250.224			1.44973			0.724863	−	0.688893i	$-0.241903\pi$
$31$	250.224			1.44973			0.724863	+	0.688893i	$0.241903\pi$
$32$	−129.024	+	223.477i	−0.712766	+	1.23455i
$33$	−45.1426	+	78.1892i	−0.238131	+	0.412454i
$34$	332.143			1.67536
$35$	−139.785	+	242.115i	−0.675086	+	1.16928i
$36$	−192.752	−	333.856i	−0.892370	−	1.54563i
$37$	−168.252	−	291.422i	−0.747581	−	1.29485i	−0.948979	−	0.315340i	$-0.897882\pi$
$37$	−168.252	−	291.422i	−0.747581	−	1.29485i	0.201397	−	0.979510i	$-0.435452\pi$
$38$	−460.108			−1.96420
$39$	−381.514	+	49.5219i	−1.56644	+	0.203329i
$40$	122.557			0.484448
$41$	−176.340	−	305.429i	−0.671698	−	1.16342i	−0.977422	−	0.211295i	$-0.932232\pi$
$41$	−176.340	−	305.429i	−0.671698	−	1.16342i	0.305724	−	0.952120i	$-0.401101\pi$
$42$	254.654	+	441.074i	0.935571	+	1.62046i
$43$	−141.861	+	245.710i	−0.503106	+	0.871405i	0.496888	+	0.867815i	$0.334476\pi$
$43$	−141.861	+	245.710i	−0.503106	+	0.871405i	−0.999994	+	0.00358984i	$0.998857\pi$
$44$	−105.050			−0.359929
$45$	380.950	−	659.825i	1.26197	−	2.18580i
$46$	−235.822	+	408.455i	−0.755870	+	1.30921i
$47$	75.5585			0.234497			0.117248	−	0.993103i	$-0.462593\pi$
$47$	75.5585			0.234497			0.117248	+	0.993103i	$0.462593\pi$
$48$	−201.901	+	349.703i	−0.607123	+	1.05157i
$49$	61.7997	+	107.040i	0.180174	+	0.312070i
$50$	484.365	+	838.946i	1.36999	+	2.37290i
$51$	650.745			1.78672
$52$	−271.853	−	355.622i	−0.724985	−	0.948383i
$53$	195.259			0.506055			0.253028	−	0.967459i	$-0.418574\pi$
$53$	195.259			0.506055			0.253028	+	0.967459i	$0.418574\pi$
$54$	−229.808	−	398.039i	−0.579127	−	1.00308i
$55$	−103.809	−	179.802i	−0.254502	−	0.440810i
$56$	−48.0899	+	83.2942i	−0.114755	+	0.198762i
$57$	−901.458			−2.09475
$58$	21.5013	−	37.2414i	0.0486770	−	0.0843110i
$59$	9.09455	−	15.7522i	0.0200680	−	0.0347587i	−0.855817	−	0.517279i	$-0.826945\pi$
$59$	9.09455	−	15.7522i	0.0200680	−	0.0347587i	0.875885	+	0.482520i	$0.160278\pi$
$60$	1479.44			3.18325
$61$	272.799	−	472.502i	0.572596	−	0.991766i	−0.423702	−	0.905802i	$-0.639270\pi$
$61$	272.799	−	472.502i	0.572596	−	0.991766i	0.996298	−	0.0859643i	$-0.0273971\pi$
$62$	524.128	+	907.816i	1.07362	+	1.85956i
$63$	298.961	+	517.816i	0.597866	+	1.03554i
$64$	−687.454			−1.34268
$65$	340.038	−	816.722i	0.648870	−	1.55849i
$66$	−378.229			−0.705405
$67$	377.262	+	653.437i	0.687909	+	1.19149i	0.972513	+	0.232848i	$0.0748045\pi$
$67$	377.262	+	653.437i	0.687909	+	1.19149i	−0.284604	+	0.958645i	$0.591862\pi$
$68$	378.582	+	655.723i	0.675144	+	1.16938i
$69$	−462.029	+	800.257i	−0.806112	+	1.39623i
$70$	−1171.20			−1.99978
$71$	68.5416	−	118.718i	0.114569	−	0.198439i	−0.803038	−	0.595927i	$-0.796785\pi$
$71$	68.5416	−	118.718i	0.114569	−	0.198439i	0.917607	+	0.397488i	$0.130118\pi$
$72$	131.057	−	226.998i	0.214517	−	0.371555i
$73$	371.711			0.595965			0.297983	−	0.954571i	$-0.403686\pi$
$73$	371.711			0.595965			0.297983	+	0.954571i	$0.403686\pi$
$74$	704.854	−	1220.84i	1.10727	−	1.91784i
$75$	948.983	+	1643.69i	1.46105	+	2.53062i
$76$	−524.438	−	908.354i	−0.791542	−	1.37099i
$77$	162.934			0.241144
$78$	−978.798	−	1280.41i	−1.42086	−	1.85869i
$79$	1102.80			1.57056			0.785281	−	0.619140i	$-0.212519\pi$
$79$	1102.80			1.57056			0.785281	+	0.619140i	$0.212519\pi$
$80$	−464.287	−	804.169i	−0.648861	−	1.12386i
$81$	94.7082	+	164.039i	0.129915	+	0.225020i
$82$	738.734	−	1279.53i	0.994873	−	1.72317i
$83$	−753.357			−0.996286			−0.498143	−	0.867095i	$-0.665984\pi$
$83$	−753.357			−0.996286			−0.498143	+	0.867095i	$0.665984\pi$
$84$	−580.517	+	1005.49i	−0.754043	+	1.30604i
$85$	−748.220	+	1295.95i	−0.954774	+	1.65372i
$86$	−1188.58			−1.49033
$87$	42.1260	−	72.9644i	0.0519125	−	0.0899150i
$88$	−35.7131	−	61.8570i	−0.0432617	−	0.0749315i
$89$	−431.528	−	747.429i	−0.513954	−	0.890194i	−0.999869	−	0.0161883i	$-0.994847\pi$
$89$	−431.528	−	747.429i	−0.513954	−	0.890194i	0.485915	−	0.874006i	$-0.338486\pi$
$90$	3191.80			3.73829
$91$	421.648	+	551.576i	0.485723	+	0.635394i
$92$	−1075.17			−1.21842
$93$	1026.89	+	1778.62i	1.14498	+	1.98316i
$94$	158.267	+	274.127i	0.173660	+	0.300788i
$95$	1036.49	−	1795.25i	1.11938	−	1.93883i
$96$	−2118.00			−2.25174
$97$	222.954	−	386.167i	0.233377	−	0.404220i	−0.725423	−	0.688303i	$-0.758356\pi$
$97$	222.954	−	386.167i	0.233377	−	0.404220i	0.958800	+	0.284083i	$0.0916892\pi$
$98$	−258.895	+	448.420i	−0.266861	+	0.462217i
$99$	−444.037			−0.450781
$100$	−1104.17	+	1912.49i	−1.10417	+	1.91249i
$101$	−458.420	−	794.006i	−0.451628	−	0.782244i	0.546859	−	0.837225i	$-0.315823\pi$
$101$	−458.420	−	794.006i	−0.451628	−	0.782244i	−0.998487	+	0.0549813i	$0.982490\pi$
$102$	1363.07	+	2360.91i	1.32318	+	2.29181i
$103$	487.817			0.466660			0.233330	−	0.972398i	$-0.425038\pi$
$103$	487.817			0.466660			0.233330	+	0.972398i	$0.425038\pi$
$104$	116.983	−	280.975i	0.110299	−	0.264922i
$105$	−2294.64			−2.13270
$106$	408.997	+	708.404i	0.374767	+	0.649116i
$107$	383.719	+	664.620i	0.346687	+	0.600479i	0.985659	−	0.168751i	$-0.0539734\pi$
$107$	383.719	+	664.620i	0.346687	+	0.600479i	−0.638972	+	0.769230i	$0.720640\pi$
$108$	523.876	−	907.380i	0.466759	−	0.808451i
$109$	244.701			0.215029			0.107514	−	0.994204i	$-0.465711\pi$
$109$	244.701			0.215029			0.107514	+	0.994204i	$0.465711\pi$
$110$	434.884	−	753.240i	0.376950	−	0.652897i
$111$	1380.97	−	2391.91i	1.18086	−	2.04532i
$112$	728.725			0.614804
$113$	476.982	−	826.156i	0.397085	−	0.687772i	−0.596280	−	0.802777i	$-0.703355\pi$
$113$	476.982	−	826.156i	0.397085	−	0.687772i	0.993365	+	0.115005i	$0.0366883\pi$
$114$	−1888.22	−	3270.50i	−1.55130	−	2.68693i
$115$	−1062.47	−	1840.26i	−0.861531	−	1.49222i
$116$	98.0301			0.0784644
$117$	−1149.10	−	1503.18i	−0.907985	−	1.18777i
$118$	76.1991			0.0594466
$119$	−587.187	−	1017.04i	−0.452330	−	0.783459i
$120$	502.957	+	871.147i	0.382612	+	0.662704i
$121$	−60.5000	+	104.789i	−0.0454545	+	0.0787296i
$122$	2285.66			1.69618
$123$	1447.35	−	2506.88i	1.06100	−	1.83771i
$124$	−1194.82	+	2069.48i	−0.865304	+	1.49875i
$125$	−2005.23			−1.43483
$126$	−1252.43	+	2169.27i	−0.885518	+	1.53376i
$127$	469.118	+	812.536i	0.327775	+	0.567724i	0.982070	−	0.188516i	$-0.0603678\pi$
$127$	469.118	+	812.536i	0.327775	+	0.567724i	−0.654295	+	0.756240i	$0.727034\pi$
$128$	−407.771	−	706.280i	−0.281580	−	0.487710i
$129$	−2328.71			−1.58939
$130$	3675.34	−	477.072i	2.47960	−	0.321861i
$131$	−679.049			−0.452892			−0.226446	−	0.974024i	$-0.572711\pi$
$131$	−679.049			−0.452892			−0.226446	+	0.974024i	$0.572711\pi$
$132$	−431.111	−	746.706i	−0.284268	−	0.492366i
$133$	813.412	+	1408.87i	0.530314	+	0.918531i
$134$	−1580.45	+	2737.42i	−1.01888	+	1.76476i
$135$	2070.75			1.32016
$136$	−257.408	+	445.844i	−0.162298	+	0.281109i
$137$	104.714	−	181.370i	0.0653015	−	0.113105i	−0.831526	−	0.555486i	$-0.812532\pi$
$137$	104.714	−	181.370i	0.0653015	−	0.113105i	0.896828	+	0.442380i	$0.145866\pi$
$138$	−3871.13			−2.38791
$139$	−595.384	+	1031.23i	−0.363308	+	0.629267i	−0.988503	−	0.151201i	$-0.951686\pi$
$139$	−595.384	+	1031.23i	−0.363308	+	0.629267i	0.625195	+	0.780468i	$0.285019\pi$
$140$	−1334.95	−	2312.19i	−0.805882	−	1.39583i
$141$	310.082	+	537.078i	0.185203	+	0.320781i
$142$	574.279			0.339383
$143$	−511.304	+	66.3692i	−0.299003	+	0.0388117i
$144$	−1985.96			−1.14928
$145$	96.8722	+	167.788i	0.0554813	+	0.0960965i
$146$	778.599	+	1348.57i	0.441351	+	0.764443i
$147$	−507.235	+	878.558i	−0.284599	+	0.492940i
$148$	3213.61			1.78485
$149$	1512.48	−	2619.68i	0.831589	−	1.44035i	−0.0651884	−	0.997873i	$-0.520765\pi$
$149$	1512.48	−	2619.68i	0.831589	−	1.44035i	0.896778	−	0.442482i	$-0.145902\pi$
$150$	−3975.54	+	6885.85i	−2.16401	+	3.74818i
$151$	−213.087			−0.114840			−0.0574198	−	0.998350i	$-0.518287\pi$
$151$	−213.087			−0.114840			−0.0574198	+	0.998350i	$0.518287\pi$
$152$	356.580	−	617.615i	0.190279	−	0.329573i
$153$	1600.23	+	2771.69i	0.845563	+	1.46456i
$154$	341.287	+	591.127i	0.178583	+	0.309314i
$155$	−4722.81			−2.44739
$156$	1412.15	−	3391.79i	0.724761	−	1.74077i
$157$	−2688.92			−1.36687			−0.683437	−	0.730009i	$-0.739516\pi$
$157$	−2688.92			−1.36687			−0.683437	+	0.730009i	$0.739516\pi$
$158$	2309.96	+	4000.96i	1.16310	+	2.01455i
$159$	801.319	+	1387.93i	0.399678	+	0.692262i
$160$	2435.25	−	4217.98i	1.20327	−	2.08413i
$161$	1667.61			0.816311
$162$	−396.758	+	687.205i	−0.192421	+	0.333284i
$163$	−1268.74	+	2197.52i	−0.609663	+	1.05597i	0.381632	+	0.924314i	$0.375362\pi$
$163$	−1268.74	+	2197.52i	−0.609663	+	1.05597i	−0.991296	+	0.131654i	$0.957971\pi$
$164$	3368.08			1.60368
$165$	852.036	−	1475.77i	0.402006	−	0.696294i
$166$	−1578.01	−	2733.19i	−0.737815	−	1.27793i
$167$	−884.914	−	1532.72i	−0.410040	−	0.710210i	0.584854	−	0.811139i	$-0.301152\pi$
$167$	−884.914	−	1532.72i	−0.410040	−	0.710210i	−0.994894	+	0.100929i	$0.967819\pi$
$168$	−789.419			−0.362530
$169$	−1547.86	−	1559.15i	−0.704531	−	0.709673i
$170$	−6268.99			−2.82829
$171$	−2216.76	−	3839.53i	−0.991342	−	1.71706i
$172$	−1354.77	−	2346.52i	−0.600581	−	1.04024i
$173$	1786.84	−	3094.89i	0.785264	−	1.36012i	−0.143578	−	0.989639i	$-0.545861\pi$
$173$	1786.84	−	3094.89i	0.785264	−	1.36012i	0.928841	−	0.370478i	$-0.120806\pi$
$174$	352.955			0.153778
$175$	1712.59	−	2966.30i	0.739770	−	1.28132i
$176$	−270.587	+	468.671i	−0.115888	+	0.200724i
$177$	149.291			0.0633979
$178$	1807.79	−	3131.18i	0.761233	−	1.31849i
$179$	−800.528	−	1386.56i	−0.334270	−	0.578972i	0.649075	−	0.760725i	$-0.275156\pi$
$179$	−800.528	−	1386.56i	−0.334270	−	0.578972i	−0.983344	+	0.181753i	$0.941823\pi$
$180$	3638.07	+	6301.32i	1.50647	+	2.60929i
$181$	2558.21			1.05055			0.525277	−	0.850931i	$-0.323962\pi$
$181$	2558.21			1.05055			0.525277	+	0.850931i	$0.323962\pi$
$182$	−1117.93	+	2685.10i	−0.455309	+	1.09359i
$183$	4478.13			1.80892
$184$	−365.520	−	633.099i	−0.146448	−	0.253656i
$185$	3175.65	+	5500.39i	1.26205	+	2.18593i
$186$	−4301.90	+	7451.11i	−1.69586	+	2.93732i
$187$	872.127			0.341050
$188$	−360.791	+	624.909i	−0.139965	+	0.242426i
$189$	−812.541	+	1407.36i	−0.312718	+	0.541643i
$190$	8684.25			3.31590
$191$	−2059.26	+	3566.75i	−0.780121	+	1.35121i	0.151750	+	0.988419i	$0.451509\pi$
$191$	−2059.26	+	3566.75i	−0.780121	+	1.35121i	−0.931871	+	0.362790i	$0.881824\pi$
$192$	−2821.22	−	4886.50i	−1.06044	−	1.83673i
$193$	−667.399	−	1155.97i	−0.248914	−	0.431132i	0.714311	−	0.699829i	$-0.246740\pi$
$193$	−667.399	−	1155.97i	−0.248914	−	0.431132i	−0.963225	+	0.268697i	$0.913407\pi$
$194$	1868.03			0.691322
$195$	7200.82	−	934.693i	2.64442	−	0.343255i
$196$	−1180.37			−0.430165
$197$	−2058.54	−	3565.49i	−0.744491	−	1.28950i	−0.950432	−	0.310932i	$-0.899359\pi$
$197$	−2058.54	−	3565.49i	−0.744491	−	1.28950i	0.205941	−	0.978564i	$-0.433975\pi$
$198$	−930.095	−	1610.97i	−0.333833	−	0.578216i
$199$	2300.37	−	3984.35i	0.819441	−	1.41931i	−0.0866542	−	0.996238i	$-0.527618\pi$
$199$	2300.37	−	3984.35i	0.819441	−	1.41931i	0.906095	−	0.423075i	$-0.139049\pi$
$200$	−1501.52			−0.530866
$201$	−3096.47	+	5363.24i	−1.08661	+	1.88206i
$202$	1920.44	−	3326.31i	0.668921	−	1.15860i
$203$	−152.046			−0.0525693
$204$	−3107.30	+	5382.00i	−1.06644	+	1.84714i
$205$	3328.30	+	5764.78i	1.13394	+	1.96405i
$206$	1021.80	+	1769.81i	0.345592	+	0.598584i
$207$	−4544.66			−1.52597
$208$	−2286.82	+	296.837i	−0.762319	+	0.0989517i
$209$	−1208.13			−0.399848
$210$	−4806.43	−	8324.98i	−1.57941	−	2.73561i
$211$	984.172	+	1704.64i	0.321105	+	0.556171i	0.980716	−	0.195436i	$-0.0626123\pi$
$211$	984.172	+	1704.64i	0.321105	+	0.556171i	−0.659611	+	0.751607i	$0.729279\pi$
$212$	−932.362	+	1614.90i	−0.302051	+	0.523168i
$213$	1125.14			0.361942
$214$	−1607.50	+	2784.27i	−0.513488	+	0.889388i
$215$	2677.53	−	4637.61i	0.849329	−	1.47108i
$216$	712.396			0.224409
$217$	1853.18	−	3209.80i	0.579733	−	1.00413i
$218$	512.559	+	887.779i	0.159243	+	0.275816i
$219$	1525.45	+	2642.16i	0.470687	+	0.815255i
$220$	1982.75			0.607622
$221$	2256.93	+	2952.39i	0.686958	+	0.898639i
$222$	11570.5			3.49803
$223$	−1172.41	−	2030.67i	−0.352064	−	0.609793i	0.634547	−	0.772885i	$-0.281187\pi$
$223$	−1172.41	−	2030.67i	−0.352064	−	0.609793i	−0.986611	+	0.163091i	$0.947854\pi$
$224$	1911.13	+	3310.18i	0.570058	+	0.987369i
$225$	−4667.25	+	8083.91i	−1.38289	+	2.39523i
$226$	3996.41			1.17627
$227$	487.678	−	844.684i	0.142592	−	0.246976i	−0.785880	−	0.618379i	$-0.787790\pi$
$227$	487.678	−	844.684i	0.142592	−	0.246976i	0.928472	+	0.371403i	$0.121123\pi$
$228$	4304.45	−	7455.53i	1.25030	−	2.16559i
$229$	−1963.85			−0.566703			−0.283352	−	0.959016i	$-0.591446\pi$
$229$	−1963.85			−0.566703			−0.283352	+	0.959016i	$0.591446\pi$
$230$	4450.98	−	7709.33i	1.27604	−	2.21017i
$231$	668.660	+	1158.15i	0.190453	+	0.329874i
$232$	33.3267	+	57.7235i	0.00943106	+	0.0163351i
$233$	−5091.60			−1.43160			−0.715798	−	0.698308i	$-0.753937\pi$
$233$	−5091.60			−1.43160			−0.715798	+	0.698308i	$0.753937\pi$
$234$	3046.63	−	7317.57i	0.851131	−	2.04429i
$235$	−1426.12			−0.395871
$236$	86.8528	+	150.434i	0.0239561	+	0.0414932i
$237$	4525.74	+	7838.80i	1.24041	+	2.14846i
$238$	2459.88	−	4260.64i	0.669960	−	1.16041i
$239$	2244.17			0.607378			0.303689	−	0.952771i	$-0.401782\pi$
$239$	2244.17			0.607378			0.303689	+	0.952771i	$0.401782\pi$
$240$	3810.75	−	6600.41i	1.02493	−	1.77523i
$241$	−130.652	+	226.296i	−0.0349212	+	0.0604854i	−0.882958	−	0.469452i	$-0.844451\pi$
$241$	−130.652	+	226.296i	−0.0349212	+	0.0604854i	0.848037	+	0.529938i	$0.177785\pi$
$242$	−506.902			−0.134648
$243$	−2258.46	+	3911.77i	−0.596215	+	1.03267i
$244$	2605.23	+	4512.39i	0.683536	+	1.18392i
$245$	−1166.43	−	2020.31i	−0.304165	−	0.526829i
$246$	12126.7			3.14296
$247$	−3126.46	−	4089.86i	−0.805393	−	1.05357i
$248$	−1624.78			−0.416022
$249$	−3091.68	−	5354.95i	−0.786856	−	1.36288i
$250$	−4200.22	−	7275.00i	−1.06258	−	1.84045i
$251$	−3024.38	+	5238.38i	−0.760546	+	1.31730i	0.182023	+	0.983294i	$0.441735\pi$
$251$	−3024.38	+	5238.38i	−0.760546	+	1.31730i	−0.942569	+	0.334011i	$0.891598\pi$
$252$	−5710.15			−1.42740
$253$	−619.210	+	1072.50i	−0.153871	+	0.266513i
$254$	−1965.26	+	3403.93i	−0.485478	+	0.840873i
$255$	−12282.4			−3.01628
$256$	−1041.55	+	1804.03i	−0.254286	+	0.440436i
$257$	279.016	+	483.270i	0.0677220	+	0.117298i	0.897898	−	0.440203i	$-0.145094\pi$
$257$	279.016	+	483.270i	0.0677220	+	0.117298i	−0.830176	+	0.557501i	$0.811760\pi$
$258$	−4877.80	−	8448.59i	−1.17705	−	2.03871i
$259$	−4984.37			−1.19581
$260$	5131.05	+	6712.14i	1.22390	+	1.60103i
$261$	414.365			0.0982703
$262$	−1422.36	−	2463.60i	−0.335396	−	0.580923i
$263$	638.009	+	1105.06i	0.149587	+	0.259092i	0.931075	−	0.364828i	$-0.118872\pi$
$263$	638.009	+	1105.06i	0.149587	+	0.259092i	−0.781488	+	0.623920i	$0.785539\pi$
$264$	293.124	−	507.706i	0.0683354	−	0.118360i
$265$	−3685.39			−0.854309
$266$	−3407.60	+	5902.14i	−0.785465	+	1.36046i
$267$	3541.87	−	6134.70i	0.811831	−	1.40613i
$268$	−7205.69			−1.64238
$269$	−2147.81	+	3720.11i	−0.486818	+	0.843194i	−0.999885	−	0.0151544i	$-0.995176\pi$
$269$	−2147.81	+	3720.11i	−0.486818	+	0.843194i	0.513067	+	0.858349i	$0.328509\pi$
$270$	4337.47	+	7512.72i	0.977667	+	1.69337i
$271$	3082.61	+	5339.24i	0.690980	+	1.19681i	0.971517	+	0.236969i	$0.0761539\pi$
$271$	3082.61	+	5339.24i	0.690980	+	1.19681i	−0.280538	+	0.959843i	$0.590513\pi$
$272$	3900.60			0.869518
$273$	−2190.27	+	5260.72i	−0.485573	+	1.16628i
$274$	877.349			0.193440
$275$	1271.83	+	2202.87i	0.278887	+	0.483047i
$276$	−4412.37	−	7642.44i	−0.962295	−	1.66674i
$277$	−1672.31	+	2896.52i	−0.362740	+	0.628285i	−0.988411	−	0.151803i	$-0.951492\pi$
$277$	−1672.31	+	2896.52i	−0.362740	+	0.628285i	0.625670	+	0.780088i	$0.284826\pi$
$278$	−4988.44			−1.07621
$279$	−5050.39	+	8747.53i	−1.08372	+	1.87706i
$280$	907.666	−	1572.12i	0.193727	−	0.335544i
$281$	1266.76			0.268928			0.134464	−	0.990918i	$-0.457069\pi$
$281$	1266.76			0.268928			0.134464	+	0.990918i	$0.457069\pi$
$282$	−1299.02	+	2249.96i	−0.274310	+	0.475119i
$283$	−2883.73	−	4994.77i	−0.605724	−	1.04915i	−0.991937	−	0.126736i	$-0.959550\pi$
$283$	−2883.73	−	4994.77i	−0.605724	−	1.04915i	0.386212	−	0.922410i	$-0.373783\pi$
$284$	654.572	+	1133.75i	0.136766	+	0.236886i
$285$	17014.4			3.53631
$286$	−1311.78	−	1716.00i	−0.271215	−	0.354787i
$287$	−5223.95			−1.07442
$288$	−5208.32	−	9021.08i	−1.06564	−	1.84574i
$289$	−686.500	−	1189.05i	−0.139731	−	0.242022i
$290$	−405.824	+	702.907i	−0.0821751	+	0.142331i
$291$	3659.89			0.737274
$292$	−1774.92	+	3074.25i	−0.355716	+	0.616119i
$293$	1773.54	−	3071.86i	0.353622	−	0.612492i	−0.633259	−	0.773940i	$-0.718283\pi$
$293$	1773.54	−	3071.86i	0.353622	−	0.612492i	0.986881	+	0.161448i	$0.0516164\pi$
$294$	−4249.89			−0.843057
$295$	−171.654	+	297.313i	−0.0338782	+	0.0586788i
$296$	1092.51	+	1892.29i	0.214530	+	0.371577i
$297$	−603.419	−	1045.15i	−0.117892	−	0.204195i
$298$	12672.3			2.46338
$299$	−5233.14	+	679.281i	−1.01218	+	0.131384i
$300$	−18125.5			−3.48826
$301$	2101.27	+	3639.50i	0.402375	+	0.696934i
$302$	−446.339	−	773.082i	−0.0850462	−	0.147304i
$303$	3762.59	−	6517.00i	0.713383	−	1.23562i
$304$	−5403.39			−1.01943
$305$	−5148.91	+	8918.17i	−0.966642	+	1.67427i
$306$	−6703.81	+	11611.3i	−1.25239	+	2.16920i
$307$	−2194.62			−0.407991			−0.203996	−	0.978972i	$-0.565393\pi$
$307$	−2194.62			−0.407991			−0.203996	+	0.978972i	$0.565393\pi$
$308$	−778.008	+	1347.55i	−0.143932	+	0.249298i
$309$	2001.94	+	3467.45i	0.368564	+	0.638371i
$310$	−9892.57	−	17134.4i	−1.81245	−	3.13926i
$311$	−6523.92			−1.18951			−0.594755	−	0.803907i	$-0.702751\pi$
$311$	−6523.92			−1.18951			−0.594755	+	0.803907i	$0.702751\pi$
$312$	2477.28	−	321.560i	0.449514	−	0.0583486i
$313$	8801.52			1.58943			0.794715	−	0.606983i	$-0.207620\pi$
$313$	8801.52			1.58943			0.794715	+	0.606983i	$0.207620\pi$
$314$	−5632.31	−	9755.45i	−1.01226	−	1.75329i
$315$	−5642.70	−	9773.44i	−1.00930	−	1.74816i
$316$	−5265.85	+	9120.71i	−0.937427	+	1.62367i
$317$	1309.05			0.231935			0.115967	−	0.993253i	$-0.463003\pi$
$317$	1309.05			0.231935			0.115967	+	0.993253i	$0.463003\pi$
$318$	−3356.94	+	5814.39i	−0.591975	+	1.02533i
$319$	56.4573	−	97.7868i	0.00990909	−	0.0171630i
$320$	12975.3			2.26668
$321$	−3149.46	+	5455.03i	−0.547619	+	0.948505i
$322$	3493.04	+	6050.11i	0.604532	+	1.04708i
$323$	4353.91	+	7541.19i	0.750024	+	1.29908i
$324$	−1808.92			−0.310172
$325$	−4166.01	+	10006.2i	−0.711042	+	1.70782i
$326$	−10630.2			−1.80598
$327$	1004.22	+	1739.36i	0.169827	+	0.294150i
$328$	1145.03	+	1983.24i	0.192754	+	0.333860i
$329$	559.593	−	969.243i	0.0937731	−	0.162420i
$330$	7138.82			1.19085
$331$	4250.63	−	7362.30i	0.705848	−	1.22256i	−0.260537	−	0.965464i	$-0.583900\pi$
$331$	4250.63	−	7362.30i	0.705848	−	1.22256i	0.966385	−	0.257101i	$-0.0827671\pi$
$332$	3597.27	−	6230.66i	0.594657	−	1.02998i
$333$	13583.7			2.23538
$334$	3707.14	−	6420.96i	0.607323	−	1.05191i
$335$	−7120.57	−	12333.2i	−1.16131	−	2.01145i
$336$	2990.59	+	5179.86i	0.485566	+	0.841025i
$337$	−2532.52			−0.409362			−0.204681	−	0.978829i	$-0.565616\pi$
$337$	−2532.52			−0.409362			−0.204681	+	0.978829i	$0.565616\pi$
$338$	2414.43	−	8881.49i	0.388544	−	1.42926i
$339$	7829.88			1.25446
$340$	−7145.49	−	12376.3i	−1.13976	−	1.97412i
$341$	1376.23	+	2383.70i	0.218555	+	0.378548i
$342$	9286.59	−	16084.8i	1.46831	−	2.54318i
$343$	6911.35			1.08798
$344$	921.143	−	1595.47i	0.144374	−	0.250063i
$345$	8720.49	−	15104.3i	1.36086	−	2.35707i
$346$	14971.1			2.32616
$347$	−1197.68	+	2074.44i	−0.185287	+	0.320927i	−0.943673	−	0.330879i	$-0.892655\pi$
$347$	−1197.68	+	2074.44i	−0.185287	+	0.320927i	0.758386	+	0.651806i	$0.225988\pi$
$348$	402.303	+	696.809i	0.0619704	+	0.107336i
$349$	−5198.58	−	9004.21i	−0.797346	−	1.38104i	−0.921339	−	0.388760i	$-0.872903\pi$
$349$	−5198.58	−	9004.21i	−0.797346	−	1.38104i	0.123993	−	0.992283i	$-0.460430\pi$
$350$	14349.0			2.19139
$351$	1976.57	−	4747.43i	0.300574	−	0.721935i
$352$	−2838.54			−0.429814
$353$	4995.17	+	8651.89i	0.753162	+	1.30451i	0.946283	+	0.323340i	$0.104806\pi$
$353$	4995.17	+	8651.89i	0.753162	+	1.30451i	−0.193121	+	0.981175i	$0.561861\pi$
$354$	312.711	+	541.631i	0.0469503	+	0.0813203i
$355$	−1293.68	+	2240.72i	−0.193412	+	0.335000i
$356$	8242.17			1.22706
$357$	4819.47	−	8347.57i	0.714492	−	1.23754i
$358$	3353.63	−	5808.66i	0.495097	−	0.857533i
$359$	−3557.96			−0.523070			−0.261535	−	0.965194i	$-0.584229\pi$
$359$	−3557.96			−0.523070			−0.261535	+	0.965194i	$0.584229\pi$
$360$	−2473.62	+	4284.44i	−0.362142	+	0.627249i
$361$	−2601.84	−	4506.51i	−0.379332	−	0.657022i
$362$	5358.52	+	9281.23i	0.778004	+	1.34754i
$363$	−993.136			−0.143598
$364$	−6575.19	+	853.484i	−0.946796	+	0.122898i
$365$	−7015.80			−1.00609
$366$	9380.05	+	16246.7i	1.33963	+	2.32030i
$367$	2050.09	+	3550.86i	0.291591	+	0.505050i	0.974186	−	0.225746i	$-0.0724821\pi$
$367$	2050.09	+	3550.86i	0.291591	+	0.505050i	−0.682595	+	0.730797i	$0.739149\pi$
$368$	−2769.43	+	4796.79i	−0.392300	+	0.679484i
$369$	14236.6			2.00848
$370$	−13303.7	+	23042.6i	−1.86926	+	3.23765i
$371$	1446.11	−	2504.73i	0.202367	−	0.350510i
$372$	−19613.5			−2.73363
$373$	4178.33	−	7237.09i	0.580016	−	1.00462i	−0.415461	−	0.909611i	$-0.636380\pi$
$373$	4178.33	−	7237.09i	0.580016	−	1.00462i	0.995477	−	0.0950061i	$-0.0302870\pi$
$374$	1826.79	+	3164.09i	0.252569	+	0.437463i
$375$	−8229.20	−	14253.4i	−1.13321	−	1.96278i
$376$	−490.624			−0.0672925
$377$	477.138	−	61.9342i	0.0651826	−	0.00846094i
$378$	−6807.90			−0.926351
$379$	−1983.22	−	3435.04i	−0.268789	−	0.465557i	0.699760	−	0.714378i	$-0.253290\pi$
$379$	−1983.22	−	3435.04i	−0.268789	−	0.465557i	−0.968549	+	0.248821i	$0.919957\pi$
$380$	9898.43	+	17144.6i	1.33626	+	2.31447i
$381$	−3850.40	+	6669.08i	−0.517747	+	0.896765i
$382$	−17253.6			−2.31092
$383$	4474.79	−	7750.56i	0.597000	−	1.03403i	−0.396261	−	0.918138i	$-0.629692\pi$
$383$	4474.79	−	7750.56i	0.597000	−	1.03403i	0.993261	−	0.115897i	$-0.0369742\pi$
$384$	3346.88	−	5796.96i	0.444778	−	0.770378i
$385$	−3075.27			−0.407092
$386$	2795.91	−	4842.67i	0.368674	−	0.638563i
$387$	−5726.48	−	9918.56i	−0.752180	−	1.30281i
$388$	2129.21	+	3687.89i	0.278593	+	0.482537i
$389$	10120.9			1.31915			0.659574	−	0.751640i	$-0.270737\pi$
$389$	10120.9			1.31915			0.659574	+	0.751640i	$0.270737\pi$
$390$	18474.2	+	24166.9i	2.39866	+	3.13778i
$391$	8926.12			1.15451
$392$	−401.284	−	695.043i	−0.0517038	−	0.0895536i
$393$	−2786.73	−	4826.76i	−0.357689	−	0.619536i
$394$	8623.77	−	14936.8i	1.10269	−	1.90991i
$395$	−20814.6			−2.65138
$396$	2120.27	−	3672.42i	0.269060	−	0.466025i
$397$	−7070.22	+	12246.0i	−0.893814	+	1.54813i	−0.0585483	+	0.998285i	$0.518647\pi$
$397$	−7070.22	+	12246.0i	−0.893814	+	1.54813i	−0.835266	+	0.549847i	$0.814686\pi$
$398$	19273.7			2.42740
$399$	−6676.28	+	11563.6i	−0.837674	+	1.45089i
$400$	5688.26	+	9852.36i	0.711033	+	1.23154i
$401$	−6321.56	−	10949.3i	−0.787241	−	1.36354i	−0.927651	−	0.373447i	$-0.878176\pi$
$401$	−6321.56	−	10949.3i	−0.787241	−	1.36354i	0.140411	−	0.990093i	$-0.455158\pi$
$402$	−25943.9			−3.21881
$403$	−4508.01	+	10827.6i	−0.557220	+	1.33836i
$404$	8755.80			1.07826
$405$	−1787.56	−	3096.14i	−0.219319	−	0.379872i
$406$	−318.482	−	551.626i	−0.0389310	−	0.0674304i
$407$	1850.78	−	3205.64i	0.225404	−	0.390412i
$408$	−4225.48			−0.512726
$409$	−2013.10	+	3486.80i	−0.243378	+	0.421543i	−0.961674	−	0.274194i	$-0.911589\pi$
$409$	−2013.10	+	3486.80i	−0.243378	+	0.421543i	0.718296	+	0.695737i	$0.244922\pi$
$410$	−13943.1	+	24150.2i	−1.67952	+	2.90901i
$411$	1718.93			0.206298
$412$	−2329.32	+	4034.50i	−0.278537	+	0.482441i
$413$	−134.710	−	233.325i	−0.0160500	−	0.0277994i
$414$	−9519.41	−	16488.1i	−1.13008	−	1.95736i
$415$	14219.1			1.68190
$416$	−7345.70	−	9609.22i	−0.865751	−	1.13253i
$417$	−9773.50			−1.14775
$418$	−2530.60	−	4383.12i	−0.296114	−	0.512884i
$419$	2896.61	+	5017.07i	0.337729	+	0.584964i	0.984005	−	0.178140i	$-0.0570079\pi$
$419$	2896.61	+	5017.07i	0.337729	+	0.584964i	−0.646276	+	0.763104i	$0.723675\pi$
$420$	10956.9	−	18977.9i	1.27296	−	2.20482i
$421$	3667.48			0.424566			0.212283	−	0.977208i	$-0.431910\pi$
$421$	3667.48			0.424566			0.212283	+	0.977208i	$0.431910\pi$
$422$	−4122.96	+	7141.18i	−0.475599	+	0.823761i
$423$	−1525.03	+	2641.44i	−0.175295	+	0.303619i
$424$	−1267.88			−0.145221
$425$	9166.89	−	15877.5i	1.04626	−	1.81217i
$426$	2356.77	+	4082.04i	0.268041	+	0.464261i
$427$	−4040.75	−	6998.79i	−0.457953	−	0.793197i
$428$	−7329.01			−0.827713
$429$	−2570.09	−	3362.04i	−0.289242	−	0.378370i
$430$	22433.8			2.51594
$431$	7501.06	+	12992.2i	0.838314	+	1.45200i	0.891303	+	0.453407i	$0.149792\pi$
$431$	7501.06	+	12992.2i	0.838314	+	1.45200i	−0.0529896	+	0.998595i	$0.516875\pi$
$432$	−2698.80	−	4674.46i	−0.300570	−	0.520602i
$433$	−4080.78	+	7068.13i	−0.452910	+	0.784463i	−0.998565	−	0.0535466i	$-0.982947\pi$
$433$	−4080.78	+	7068.13i	−0.452910	+	0.784463i	0.545655	+	0.838010i	$0.316281\pi$
$434$	15526.9			1.71732
$435$	−795.101	+	1377.16i	−0.0876372	+	0.151792i
$436$	−1168.45	+	2023.81i	−0.128345	+	0.222300i
$437$	−12365.1			−1.35355
$438$	−6390.53	+	11068.7i	−0.697150	+	1.20750i
$439$	−497.423	−	861.562i	−0.0540791	−	0.0936677i	0.837719	−	0.546102i	$-0.183889\pi$
$439$	−497.423	−	861.562i	−0.0540791	−	0.0936677i	−0.891798	+	0.452434i	$0.850556\pi$
$440$	674.062	+	1167.51i	0.0730333	+	0.126497i
$441$	−4989.33			−0.538746
$442$	−5983.86	+	14372.4i	−0.643944	+	1.54666i
$443$	11863.5			1.27235			0.636175	−	0.771545i	$-0.280516\pi$
$443$	11863.5			1.27235			0.636175	+	0.771545i	$0.280516\pi$
$444$	13188.3	+	22842.7i	1.40965	+	2.44159i
$445$	8144.81	+	14107.2i	0.867643	+	1.50280i
$446$	4911.54	−	8507.04i	0.521453	−	0.903184i
$447$	24828.0			2.62712
$448$	−5091.35	+	8818.48i	−0.536928	+	0.929986i
$449$	−6928.33	+	12000.2i	−0.728214	+	1.26130i	0.229423	+	0.973327i	$0.426316\pi$
$449$	−6928.33	+	12000.2i	−0.728214	+	1.26130i	−0.957637	+	0.287978i	$0.907017\pi$
$450$	−39104.7			−4.09648
$451$	1939.74	−	3359.72i	0.202525	−	0.350783i
$452$	4555.17	+	7889.78i	0.474020	+	0.821026i
$453$	−874.481	−	1514.65i	−0.0906991	−	0.157095i
$454$	4086.03			0.422394
$455$	−7958.34	−	10410.6i	−0.819984	−	1.07266i
$456$	5853.43			0.601123
$457$	3824.45	+	6624.14i	0.391467	+	0.678040i	0.992643	−	0.121076i	$-0.0386345\pi$
$457$	3824.45	+	6624.14i	0.391467	+	0.678040i	−0.601177	+	0.799116i	$0.705301\pi$
$458$	−4113.56	−	7124.89i	−0.419681	−	0.726909i
$459$	−4349.24	+	7533.10i	−0.442277	+	0.766046i
$460$	20293.2			2.05690
$461$	−2328.53	+	4033.14i	−0.235251	+	0.407467i	−0.959346	−	0.282234i	$-0.908925\pi$
$461$	−2328.53	+	4033.14i	−0.235251	+	0.407467i	0.724095	+	0.689701i	$0.242258\pi$
$462$	−2801.20	+	4851.81i	−0.282085	+	0.488586i
$463$	15545.9			1.56043			0.780214	−	0.625513i	$-0.215110\pi$
$463$	15545.9			1.56043			0.780214	+	0.625513i	$0.215110\pi$
$464$	252.506	−	437.353i	0.0252636	−	0.0437578i
$465$	−19381.8	−	33570.3i	−1.93292	−	3.34792i
$466$	−10665.0	−	18472.4i	−1.06019	−	1.83630i
$467$	−6249.15			−0.619221			−0.309610	−	0.950864i	$-0.600199\pi$
$467$	−6249.15			−0.619221			−0.309610	+	0.950864i	$0.600199\pi$
$468$	17919.1	−	2325.96i	1.76989	−	0.229738i
$469$	11176.1			1.10035
$470$	−2987.19	−	5173.97i	−0.293168	−	0.507782i
$471$	−11035.0	−	19113.2i	−1.07954	−	1.86982i
$472$	−59.0536	+	102.284i	−0.00575882	+	0.00997457i
$473$	−3120.93			−0.303384
$474$	−18959.5	+	32838.9i	−1.83721	+	3.18215i
$475$	−12698.6	+	21994.7i	−1.22664	+	2.12460i
$476$	11215.2			1.07994
$477$	−3941.01	+	6826.04i	−0.378295	+	0.655226i
$478$	4700.72	+	8141.88i	0.449803	+	0.779081i
$479$	−5371.73	−	9304.12i	−0.512403	−	0.887507i	−0.999897	−	0.0143809i	$-0.995422\pi$
$479$	−5371.73	−	9304.12i	−0.512403	−	0.887507i	0.487494	−	0.873126i	$-0.337911\pi$
$480$	39975.8			3.80133
$481$	15641.5	−	2030.32i	1.48272	−	0.192463i
$482$	−1094.67			−0.103446
$483$	6843.65	+	11853.6i	0.644714	+	1.11668i
$484$	−577.774	−	1000.73i	−0.0542613	−	0.0939833i
$485$	−4208.11	+	7288.66i	−0.393980	+	0.682393i
$486$	−18922.6			−1.76614
$487$	1713.09	−	2967.16i	0.159400	−	0.276088i	−0.775253	−	0.631651i	$-0.782377\pi$
$487$	1713.09	−	2967.16i	0.159400	−	0.276088i	0.934652	+	0.355563i	$0.115711\pi$
$488$	−1771.37	+	3068.10i	−0.164316	+	0.284603i
$489$	−20826.9			−1.92602
$490$	4886.48	−	8463.64i	0.450508	−	0.780302i
$491$	−5435.05	−	9413.79i	−0.499553	−	0.865251i	0.500447	−	0.865767i	$-0.333169\pi$
$491$	−5435.05	−	9413.79i	−0.499553	−	0.865251i	−1.00000		0.000516083i	$0.999836\pi$
$492$	13822.2	+	23940.7i	1.26657	+	2.19376i
$493$	−813.850			−0.0743488
$494$	8289.26	−	19909.6i	0.754963	−	1.81331i
$495$	8380.90			0.760997
$496$	6155.22	+	10661.2i	0.557213	+	0.965121i
$497$	−1015.25	−	1758.47i	−0.0916303	−	0.158708i
$498$	12951.9	−	22433.3i	1.16544	−	2.01860i
$499$	−7870.01			−0.706032			−0.353016	−	0.935617i	$-0.614844\pi$
$499$	−7870.01			−0.706032			−0.353016	+	0.935617i	$0.614844\pi$
$500$	9574.95	−	16584.3i	0.856410	−	1.48335i
$501$	7263.14	−	12580.1i	0.647691	−	1.12183i
$502$	−25339.9			−2.25294
$503$	3617.09	−	6264.99i	0.320632	−	0.555352i	−0.659986	−	0.751278i	$-0.729438\pi$
$503$	3617.09	−	6264.99i	0.320632	−	0.555352i	0.980619	+	0.195926i	$0.0627712\pi$
$504$	−1941.24	−	3362.33i	−0.171567	−	0.297163i
$505$	8652.38	+	14986.4i	0.762427	+	1.32056i
$506$	−5188.08			−0.455807
$507$	4730.42	−	17400.9i	0.414370	−	1.52426i
$508$	−8960.13			−0.782562
$509$	−3648.26	−	6318.97i	−0.317694	−	0.550263i	0.662312	−	0.749228i	$-0.269575\pi$
$509$	−3648.26	−	6318.97i	−0.317694	−	0.550263i	−0.980007	+	0.198965i	$0.936242\pi$
$510$	−25727.1	−	44560.7i	−2.23376	−	3.86898i
$511$	2752.92	−	4768.21i	0.238321	−	0.412785i
$512$	−15251.0			−1.31642
$513$	6024.87	−	10435.4i	0.518528	−	0.898116i
$514$	−1168.87	+	2024.55i	−0.100305	+	0.173733i
$515$	−9207.22			−0.787803
$516$	11119.6	−	19259.7i	0.948666	−	1.64314i
$517$	415.572	+	719.791i	0.0353517	+	0.0612309i
$518$	−10440.4	−	18083.4i	−0.885572	−	1.53386i
$519$	29331.8			2.48077
$520$	−2207.97	+	5303.22i	−0.186204	+	0.447234i
$521$	2117.88			0.178092			0.0890462	−	0.996027i	$-0.471618\pi$
$521$	2117.88			0.178092			0.0890462	+	0.996027i	$0.471618\pi$
$522$	867.944	+	1503.32i	0.0727756	+	0.126051i
$523$	−3989.60	−	6910.19i	−0.333562	−	0.577747i	0.649645	−	0.760237i	$-0.274917\pi$
$523$	−3989.60	−	6910.19i	−0.333562	−	0.577747i	−0.983208	+	0.182491i	$0.941584\pi$
$524$	3242.45	−	5616.09i	0.270319	−	0.468207i
$525$	28113.0			2.33705
$526$	−2672.79	+	4629.41i	−0.221558	+	0.383749i
$527$	9919.41	−	17180.9i	0.819917	−	1.42014i
$528$	−4441.82			−0.366109
$529$	−254.047	+	440.023i	−0.0208800	+	0.0361653i
$530$	−7719.55	−	13370.7i	−0.632672	−	1.09582i
$531$	367.120	+	635.870i	0.0300031	+	0.0519668i
$532$	−15536.1			−1.26612
$533$	16393.3	−	2127.91i	1.33222	−	0.172927i
$534$	29675.7			2.40486
$535$	−7242.44	−	12544.3i	−0.585267	−	1.01371i
$536$	−2449.67	−	4242.96i	−0.197406	−	0.341918i
$537$	6570.53	−	11380.5i	0.528006	−	0.914533i
$538$	−17995.5			−1.44208
$539$	−679.796	+	1177.44i	−0.0543245	+	0.0940928i
$540$	−9887.82	+	17126.2i	−0.787971	+	1.36481i
$541$	−13841.4			−1.09998			−0.549990	−	0.835171i	$-0.685368\pi$
$541$	−13841.4			−1.09998			−0.549990	+	0.835171i	$0.685368\pi$
$542$	−12913.9	+	22367.5i	−1.02343	+	1.77263i
$543$	10498.6	+	18184.0i	0.829717	+	1.43711i
$544$	10229.6	+	17718.2i	0.806233	+	1.39644i
$545$	−4618.57			−0.363005
$546$	−23673.8	+	3072.94i	−1.85558	+	0.240860i
$547$	5590.64			0.436999			0.218500	−	0.975837i	$-0.429884\pi$
$547$	5590.64			0.436999			0.218500	+	0.975837i	$0.429884\pi$
$548$	1000.01	+	1732.08i	0.0779535	+	0.135019i
$549$	11012.1	+	19073.5i	0.856073	+	1.48276i
$550$	−5328.02	+	9228.40i	−0.413068	+	0.715455i
$551$	1127.40			0.0871669
$552$	3000.09	−	5196.31i	0.231327	−	0.400670i
$553$	8167.42	−	14146.4i	0.628054	−	1.08782i
$554$	−14011.5			−1.07453
$555$	−26064.9	+	45145.8i	−1.99350	+	3.45285i
$556$	−5685.90	−	9848.27i	−0.433698	−	0.751187i
$557$	9484.56	+	16427.7i	0.721496	+	1.24967i	0.960400	+	0.278625i	$0.0898787\pi$
$557$	9484.56	+	16427.7i	0.721496	+	1.24967i	−0.238904	+	0.971043i	$0.576788\pi$
$558$	−42314.9			−3.21027
$559$	−8076.50	−	10565.2i	−0.611091	−	0.799393i
$560$	−13754.2			−1.03790
$561$	3579.10	+	6199.18i	0.269358	+	0.466541i
$562$	2653.40	+	4595.83i	0.199159	+	0.344953i
$563$	6549.85	−	11344.7i	0.490308	−	0.849238i	−0.509630	−	0.860394i	$-0.670218\pi$
$563$	6549.85	−	11344.7i	0.490308	−	0.849238i	0.999938	+	0.0111555i	$0.00355099\pi$
$564$	−5922.56			−0.442171
$565$	−9002.72	+	15593.2i	−0.670349	+	1.16108i
$566$	12080.7	−	20924.4i	0.897157	−	1.55392i
$567$	2805.67			0.207808
$568$	−445.061	+	770.869i	−0.0328774	+	0.0569453i
$569$	5657.82	+	9799.63i	0.416851	+	0.722007i	0.995621	−	0.0934839i	$-0.0298004\pi$
$569$	5657.82	+	9799.63i	0.416851	+	0.722007i	−0.578770	+	0.815491i	$0.696467\pi$
$570$	35639.0	+	61728.6i	2.61887	+	4.53601i
$571$	−3798.54			−0.278395			−0.139198	−	0.990265i	$-0.544452\pi$
$571$	−3798.54			−0.278395			−0.139198	+	0.990265i	$0.544452\pi$
$572$	1892.57	−	4545.67i	0.138343	−	0.332280i
$573$	−33803.8			−2.46453
$574$	−10942.3	−	18952.6i	−0.795682	−	1.37816i
$575$	13017.0	+	22546.1i	0.944080	+	1.63519i
$576$	13875.2	−	24032.6i	1.00371	−	1.73847i
$577$	−16362.1			−1.18053			−0.590263	−	0.807211i	$-0.700976\pi$
$577$	−16362.1			−1.18053			−0.590263	+	0.807211i	$0.700976\pi$
$578$	2875.94	−	4981.27i	0.206960	−	0.358466i
$579$	5477.84	−	9487.89i	0.393180	−	0.681007i
$580$	−1850.26			−0.132461
$581$	−5579.43	+	9663.86i	−0.398406	+	0.690059i
$582$	7666.14	+	13278.1i	0.545999	+	0.945699i
$583$	1073.93	+	1860.10i	0.0762907	+	0.132139i
$584$	−2413.63			−0.171022
$585$	21688.5	+	28371.6i	1.53284	+	2.00517i
$586$	14859.7			1.04752
$587$	2358.01	+	4084.19i	0.165801	+	0.287176i	0.936940	−	0.349492i	$-0.113646\pi$
$587$	2358.01	+	4084.19i	0.165801	+	0.287176i	−0.771138	+	0.636668i	$0.780312\pi$
$588$	−4844.09	−	8390.21i	−0.339740	−	0.588446i
$589$	−13741.1	+	23800.2i	−0.961275	+	1.66498i
$590$	−1438.21			−0.100356
$591$	16895.9	−	29264.6i	1.17598	−	2.03686i
$592$	8277.63	−	14337.3i	0.574676	−	0.995369i
$593$	1492.38			0.103347			0.0516733	−	0.998664i	$-0.483545\pi$
$593$	1492.38			0.103347			0.0516733	+	0.998664i	$0.483545\pi$
$594$	2527.88	−	4378.42i	0.174613	−	0.302439i
$595$	11082.8	+	19195.9i	0.763612	+	1.32261i
$596$	14444.1	+	25017.9i	0.992708	+	1.71942i
$597$	37761.6			2.58874
$598$	−13426.0	−	17563.1i	−0.918108	−	1.20102i
$599$	−14436.5			−0.984740			−0.492370	−	0.870386i	$-0.663869\pi$
$599$	−14436.5			−0.984740			−0.492370	+	0.870386i	$0.663869\pi$
$600$	−6162.03	−	10672.9i	−0.419273	−	0.726202i
$601$	−3091.61	−	5354.82i	−0.209832	−	0.363440i	0.741829	−	0.670589i	$-0.233959\pi$
$601$	−3091.61	−	5354.82i	−0.209832	−	0.363440i	−0.951662	+	0.307149i	$0.900625\pi$
$602$	−8802.77	+	15246.8i	−0.595970	+	1.03225i
$603$	−30457.8			−2.05695
$604$	1017.49	−	1762.34i	0.0685447	−	0.118723i
$605$	1141.90	−	1977.83i	0.0767351	−	0.132909i
$606$	31525.0			2.11323
$607$	3111.86	−	5389.90i	0.208083	−	0.360411i	−0.743027	−	0.669261i	$-0.766611\pi$
$607$	3111.86	−	5389.90i	0.208083	−	0.360411i	0.951111	+	0.308850i	$0.0999441\pi$
$608$	−14170.8	−	24544.5i	−0.945232	−	1.63719i
$609$	−623.978	−	1080.76i	−0.0415187	−	0.0719125i
$610$	−43140.3			−2.86345
$611$	−1361.25	+	3269.53i	−0.0901316	+	0.216483i
$612$	−30564.4			−2.01878
$613$	−1679.14	−	2908.36i	−0.110636	−	0.191627i	0.805391	−	0.592744i	$-0.201955\pi$
$613$	−1679.14	−	2908.36i	−0.110636	−	0.191627i	−0.916027	+	0.401117i	$0.868622\pi$
$614$	−4596.92	−	7962.10i	−0.302144	−	0.523329i
$615$	−27317.8	+	47315.8i	−1.79115	+	3.10237i
$616$	−1057.98			−0.0692000
$617$	9223.27	−	15975.2i	0.601807	−	1.04236i	−0.390741	−	0.920501i	$-0.627781\pi$
$617$	9223.27	−	15975.2i	0.601807	−	1.04236i	0.992547	−	0.121859i	$-0.0388856\pi$
$618$	−8386.65	+	14526.1i	−0.545891	+	0.945510i
$619$	19732.0			1.28125			0.640627	−	0.767852i	$-0.278674\pi$
$619$	19732.0			1.28125			0.640627	+	0.767852i	$0.278674\pi$
$620$	22551.4	−	39060.2i	1.46078	−	2.53015i
$621$	−6175.92	−	10697.0i	−0.399084	−	0.691234i
$622$	−13665.2	−	23668.9i	−0.880910	−	1.52578i
$623$	−12783.7			−0.822103
$624$	−11494.8	−	15036.8i	−0.737433	−	0.964667i
$625$	8942.27			0.572305
$626$	18436.0	+	31932.1i	1.17708	+	2.03876i
$627$	−4958.02	−	8587.54i	−0.315796	−	0.546975i
$628$	12839.6	−	22238.8i	0.815852	−	1.41310i
$629$	−26679.5			−1.69123
$630$	23638.8	−	40943.6i	1.49491	−	2.58926i
$631$	3289.70	−	5697.93i	0.207545	−	0.359479i	−0.743395	−	0.668852i	$-0.766786\pi$
$631$	3289.70	−	5697.93i	0.207545	−	0.359479i	0.950941	+	0.309373i	$0.100119\pi$
$632$	−7160.79			−0.450698
$633$	−8077.83	+	13991.2i	−0.507211	+	0.878516i
$634$	2741.97	+	4749.24i	0.171763	+	0.297502i
$635$	−8854.29	−	15336.1i	−0.553341	−	0.958416i
$636$	−15305.2			−0.954228
$637$	−5745.17	+	745.744i	−0.357350	+	0.0463853i
$638$	473.029			0.0293533
$639$	2766.82	+	4792.27i	0.171289	+	0.296681i
$640$	7696.41	+	13330.6i	0.475355	+	0.823340i
$641$	6691.22	−	11589.5i	0.412304	−	0.714132i	−0.582837	−	0.812589i	$-0.698057\pi$
$641$	6691.22	−	11589.5i	0.412304	−	0.714132i	0.995141	+	0.0984570i	$0.0313907\pi$
$642$	−26387.9			−1.62219
$643$	−12324.7	+	21347.1i	−0.755894	+	1.30925i	0.189034	+	0.981971i	$0.439464\pi$
$643$	−12324.7	+	21347.1i	−0.755894	+	1.30925i	−0.944928	+	0.327277i	$0.893869\pi$
$644$	−7962.83	+	13792.0i	−0.487235	+	0.843916i
$645$	43952.9			2.68317
$646$	−18239.7	+	31592.1i	−1.11088	+	1.92411i
$647$	841.601	+	1457.70i	0.0511387	+	0.0885749i	0.890462	−	0.455058i	$-0.150382\pi$
$647$	841.601	+	1457.70i	0.0511387	+	0.0885749i	−0.839323	+	0.543633i	$0.817048\pi$
$648$	−614.968	−	1065.16i	−0.0372812	−	0.0645730i
$649$	200.080			0.0121014
$650$	−45028.8	+	5844.90i	−2.71719	+	0.352701i
$651$	30420.8			1.83147
$652$	−12116.4	−	20986.2i	−0.727784	−	1.26056i
$653$	1627.40	+	2818.73i	0.0975266	+	0.168921i	0.910660	−	0.413156i	$-0.135574\pi$
$653$	1627.40	+	2818.73i	0.0975266	+	0.168921i	−0.813134	+	0.582077i	$0.802240\pi$
$654$	−4206.95	+	7286.66i	−0.251536	+	0.435674i
$655$	12816.6			0.764559
$656$	8675.50	−	15026.4i	0.516344	−	0.894334i
$657$	−7502.42	+	12994.6i	−0.445506	+	0.771639i
$658$	4688.57			0.277781
$659$	15446.3	−	26753.8i	0.913054	−	1.58146i	0.103327	−	0.994647i	$-0.467051\pi$
$659$	15446.3	−	26753.8i	0.913054	−	1.58146i	0.809726	−	0.586808i	$-0.199616\pi$
$660$	8136.93	+	14093.6i	0.479893	+	0.831200i
$661$	−15710.5	−	27211.4i	−0.924458	−	1.60121i	−0.792430	−	0.609963i	$-0.791184\pi$
$661$	−15710.5	−	27211.4i	−0.924458	−	1.60121i	−0.132029	−	0.991246i	$-0.542149\pi$
$662$	35614.1			2.09091
$663$	−11723.7	+	28158.7i	−0.686746	+	1.64946i
$664$	4891.77			0.285900
$665$	−15352.6	−	26591.5i	−0.895262	−	1.55064i
$666$	28452.8	+	49281.8i	1.65544	+	2.86731i
$667$	577.833	−	1000.84i	0.0335439	−	0.0580998i
$668$	16901.8			0.978969
$669$	9622.83	−	16667.2i	0.556114	−	0.963217i
$670$	29830.0	−	51667.1i	1.72005	−	2.97921i
$671$	6001.59			0.345289
$672$	−15686.1	+	27169.1i	−0.900452	+	1.55963i
$673$	−6136.12	−	10628.1i	−0.351456	−	0.608740i	0.635049	−	0.772472i	$-0.280980\pi$
$673$	−6136.12	−	10628.1i	−0.351456	−	0.608740i	−0.986505	+	0.163732i	$0.947647\pi$
$674$	−5304.70	−	9188.02i	−0.303160	−	0.525088i
$675$	−25370.0			−1.44666
$676$	20286.0	−	5356.65i	1.15419	−	0.304771i
$677$	−7951.18			−0.451387			−0.225693	−	0.974198i	$-0.572465\pi$
$677$	−7951.18			−0.451387			−0.225693	+	0.974198i	$0.572465\pi$
$678$	16400.7	+	28406.9i	0.929007	+	1.60909i
$679$	−3302.43	−	5719.98i	−0.186651	−	0.323288i
$680$	4858.41	−	8415.02i	0.273988	−	0.474561i
$681$	8005.47			0.450470
$682$	−5765.40	+	9985.97i	−0.323708	+	0.560678i
$683$	−3012.28	+	5217.42i	−0.168758	+	0.292297i	−0.937983	−	0.346680i	$-0.887309\pi$
$683$	−3012.28	+	5217.42i	−0.168758	+	0.292297i	0.769226	+	0.638977i	$0.220642\pi$
$684$	42340.0			2.36683
$685$	−1976.40	+	3423.23i	−0.110240	+	0.190942i
$686$	14476.8	+	25074.5i	0.805722	+	1.39555i
$687$	−8059.40	−	13959.3i	−0.447577	−	0.775226i
$688$	−13958.4			−0.773489
$689$	−3517.77	+	8449.18i	−0.194509	+	0.467181i
$690$	73065.0			4.03121
$691$	11405.1	+	19754.1i	0.627885	+	1.08753i	0.987975	+	0.154612i	$0.0494127\pi$
$691$	11405.1	+	19754.1i	0.627885	+	1.08753i	−0.360090	+	0.932918i	$0.617254\pi$
$692$	17064.3	+	29556.2i	0.937407	+	1.62364i
$693$	−3288.57	+	5695.98i	−0.180264	+	0.312226i
$694$	−10034.8			−0.548870
$695$	11237.5	−	19463.9i	0.613326	−	1.06231i
$696$	−273.537	+	473.780i	−0.0148971	+	0.0258025i
$697$	−27961.9			−1.51956
$698$	21778.3	−	37721.1i	1.18097	−	2.04551i
$699$	−20895.3	−	36191.6i	−1.13066	−	1.95836i
$700$	16355.2	+	28328.1i	0.883099	+	1.52957i
$701$	4150.51			0.223627			0.111814	−	0.993729i	$-0.464334\pi$
$701$	4150.51			0.223627			0.111814	+	0.993729i	$0.464334\pi$
$702$	21363.9	−	2773.12i	1.14862	−	0.149095i
$703$	36958.4			1.98280
$704$	−3781.00	−	6548.88i	−0.202417	−	0.350597i
$705$	−5852.60	−	10137.0i	−0.312655	−	0.541534i
$706$	−20926.1	+	36245.1i	−1.11553	+	1.93216i
$707$	−13580.4			−0.722409
$708$	−712.865	+	1234.72i	−0.0378406	+	0.0655418i
$709$	−5582.46	+	9669.10i	−0.295703	+	0.512173i	−0.975148	−	0.221554i	$-0.928887\pi$
$709$	−5582.46	+	9669.10i	−0.295703	+	0.512173i	0.679445	+	0.733726i	$0.262221\pi$
$710$	−10839.1			−0.572938
$711$	−22258.3	+	38552.5i	−1.17405	+	2.03352i
$712$	2802.04	+	4853.28i	0.147487	+	0.255455i
$713$	14085.6	+	24396.9i	0.739844	+	1.28145i
$714$	40380.2			2.11651
$715$	9650.54	−	1252.67i	0.504769	−	0.0655208i
$716$	15290.1			0.798068
$717$	9209.78	+	15951.8i	0.479701	+	0.830866i
$718$	−7452.63	−	12908.3i	−0.387367	−	0.670940i
$719$	15065.6	−	26094.4i	0.781434	−	1.35348i	−0.149672	−	0.988736i	$-0.547822\pi$
$719$	15065.6	−	26094.4i	0.781434	−	1.35348i	0.931106	−	0.364748i	$-0.118845\pi$
$720$	37483.7			1.94019
$721$	3612.81	−	6257.58i	0.186613	−	0.323224i
$722$	10899.8	−	18879.0i	0.561840	−	0.973135i
$723$	−2144.71			−0.110322
$724$	−12215.4	+	21157.8i	−0.627049	+	1.08608i
$725$	−1186.84	−	2055.67i	−0.0607974	−	0.105304i
$726$	−2080.26	−	3603.11i	−0.106344	−	0.184193i
$727$	−28376.9			−1.44765			−0.723824	−	0.689985i	$-0.757617\pi$
$727$	−28376.9			−1.44765			−0.723824	+	0.689985i	$0.757617\pi$
$728$	−2737.89	−	3581.55i	−0.139386	−	0.182336i
$729$	−31959.4			−1.62371
$730$	−14695.5	−	25453.4i	−0.745077	−	1.29051i
$731$	11247.3	+	19480.9i	0.569080	+	0.985675i
$732$	−21383.0	+	37036.5i	−1.07970	+	1.87009i
$733$	−18937.3			−0.954248			−0.477124	−	0.878836i	$-0.658321\pi$
$733$	−18937.3			−0.954248			−0.477124	+	0.878836i	$0.658321\pi$
$734$	−8588.39	+	14875.5i	−0.431884	+	0.748046i
$735$	9573.74	−	16582.2i	0.480453	−	0.832168i
$736$	−29052.1			−1.45499
$737$	−4149.88	+	7187.81i	−0.207412	+	0.359249i
$738$	29820.5	+	51650.6i	1.48741	+	2.57626i
$739$	11740.0	+	20334.2i	0.584386	+	1.01219i	0.994952	+	0.100355i	$0.0319979\pi$
$739$	11740.0	+	20334.2i	0.584386	+	1.01219i	−0.410566	+	0.911831i	$0.634669\pi$
$740$	−60654.9			−3.01313
$741$	16240.6	−	39007.5i	0.805144	−	1.93384i
$742$	12116.3			0.599464
$743$	2246.12	+	3890.39i	0.110905	+	0.192092i	0.916135	−	0.400869i	$-0.131292\pi$
$743$	2246.12	+	3890.39i	0.110905	+	0.192092i	−0.805231	+	0.592962i	$0.797959\pi$
$744$	−6667.88	−	11549.1i	−0.328570	−	0.569100i
$745$	−28547.0	+	49444.8i	−1.40387	+	2.43157i
$746$	35008.3			1.71816
$747$	15205.4	−	26336.5i	0.744760	−	1.28996i
$748$	−4164.40	+	7212.95i	−0.203564	+	0.352582i
$749$	11367.4			0.554548
$750$	34474.3	−	59711.3i	1.67843	−	2.90713i
$751$	12230.7	+	21184.2i	0.594279	+	1.02932i	0.993648	+	0.112532i	$0.0358960\pi$
$751$	12230.7	+	21184.2i	0.594279	+	1.02932i	−0.399369	+	0.916790i	$0.630771\pi$
$752$	1858.65	+	3219.28i	0.0901304	+	0.156110i
$753$	−49646.6			−2.40269
$754$	1224.13	+	1601.33i	0.0591248	+	0.0773437i
$755$	4021.88			0.193869
$756$	−7759.75	−	13440.3i	−0.373306	−	0.646585i
$757$	−4578.68	−	7930.50i	−0.219835	−	0.380765i	0.734923	−	0.678151i	$-0.237218\pi$
$757$	−4578.68	−	7930.50i	−0.219835	−	0.380765i	−0.954757	+	0.297386i	$0.903885\pi$
$758$	8308.24	−	14390.3i	0.398112	−	0.689550i
$759$	−10164.6			−0.486104
$760$	−6730.22	+	11657.1i	−0.321224	+	0.556377i
$761$	−6909.57	+	11967.7i	−0.329135	+	0.570078i	−0.982340	−	0.187102i	$-0.940090\pi$
$761$	−6909.57	+	11967.7i	−0.329135	+	0.570078i	0.653206	+	0.757181i	$0.273424\pi$
$762$	−32260.7			−1.53370
$763$	1812.28	−	3138.96i	0.0859880	−	0.148936i
$764$	−19665.9	−	34062.4i	−0.931267	−	1.61300i
$765$	−30203.4	−	52313.7i	−1.42746	−	2.47243i
$766$	37492.2			1.76847
$767$	517.777	+	677.326i	0.0243753	+	0.0318863i
$768$	−17097.6			−0.803330
$769$	−3717.94	−	6439.65i	−0.174346	−	0.301976i	0.765589	−	0.643330i	$-0.222448\pi$
$769$	−3717.94	−	6439.65i	−0.174346	−	0.301976i	−0.939935	+	0.341354i	$0.889114\pi$
$770$	−6441.57	−	11157.1i	−0.301478	−	0.522176i
$771$	−2290.09	+	3966.55i	−0.106972	+	0.185281i
$772$	12747.3			0.594281
$773$	−9482.17	+	16423.6i	−0.441203	+	0.764186i	−0.997779	−	0.0666105i	$-0.978782\pi$
$773$	−9482.17	+	16423.6i	−0.441203	+	0.764186i	0.556576	+	0.830797i	$0.312115\pi$
$774$	23989.8	−	41551.5i	1.11408	−	1.92964i
$775$	57862.0			2.68189
$776$	−1447.71	+	2507.50i	−0.0669711	+	0.115997i
$777$	−20455.2	−	35429.4i	−0.944435	−	1.63581i
$778$	21199.5	+	36718.6i	0.976915	+	1.69207i
$779$	38734.8			1.78154
$780$	−26653.5	+	64017.8i	−1.22352	+	2.93872i
$781$	1507.92			0.0690877
$782$	18697.0	+	32384.1i	0.854990	+	1.48089i
$783$	563.097	+	975.313i	0.0257004	+	0.0445145i
$784$	−3040.40	+	5266.13i	−0.138502	+	0.239893i
$785$	50751.6			2.30752
$786$	11674.4	−	20220.6i	0.529784	−	0.917614i
$787$	13611.0	−	23575.0i	0.616495	−	1.06780i	−0.373626	−	0.927580i	$-0.621886\pi$
$787$	13611.0	−	23575.0i	0.616495	−	1.06780i	0.990120	−	0.140221i	$-0.0447812\pi$
$788$	39318.0			1.77747
$789$	−5236.61	+	9070.07i	−0.236284	+	0.409256i
$790$	−43598.9	−	75515.6i	−1.96352	−	3.40092i
$791$	−7065.14	−	12237.2i	−0.317582	−	0.550068i
$792$	2883.26			0.129359
$793$	15531.2	+	20317.0i	0.695496	+	0.909808i
$794$	−59238.1			−2.64771
$795$	−15124.4	−	26196.2i	−0.674725	−	1.16866i
$796$	21968.5	+	38050.5i	0.978206	+	1.69430i
$797$	16957.3	−	29371.0i	0.753650	−	1.30536i	−0.192392	−	0.981318i	$-0.561624\pi$
$797$	16957.3	−	29371.0i	0.753650	−	1.30536i	0.946042	−	0.324043i	$-0.105042\pi$
$798$	−55937.4			−2.48141
$799$	2995.30	−	5188.01i	0.132623	−	0.229711i
$800$	−29835.7	+	51677.0i	−1.31857	+	2.28382i
$801$	34839.0			1.53680
$802$	26482.7	−	45869.4i	1.16601	−	2.01958i
$803$	2044.41	+	3541.02i	0.0898452	+	0.155616i
$804$	−29571.2	−	51218.8i	−1.29713	−	2.24670i
$805$	−31475.1			−1.37807
$806$	−48725.2	+	6324.71i	−2.12937	+	0.276400i
$807$	−35257.3			−1.53794
$808$	2976.66	+	5155.72i	0.129602	+	0.224477i
$809$	−2624.86	−	4546.39i	−0.114073	−	0.197580i	0.803336	−	0.595526i	$-0.203056\pi$
$809$	−2624.86	−	4546.39i	−0.114073	−	0.197580i	−0.917409	+	0.397946i	$0.869723\pi$
$810$	7488.55	−	12970.6i	0.324841	−	0.562641i
$811$	−2127.83			−0.0921308			−0.0460654	−	0.998938i	$-0.514668\pi$
$811$	−2127.83			−0.0921308			−0.0460654	+	0.998938i	$0.514668\pi$
$812$	726.020	−	1257.50i	0.0313772	−	0.0543470i
$813$	−25301.3	+	43823.1i	−1.09146	+	1.89046i
$814$	15506.8			0.667706
$815$	23946.6	−	41476.7i	1.02922	−	1.78266i
$816$	16007.6	+	27725.9i	0.686737	+	1.18946i
$817$	−15580.6	−	26986.4i	−0.667192	−	1.15561i
$818$	−16866.9			−0.720949
$819$	−27792.8	+	3607.60i	−1.18579	+	0.153919i
$820$	−63570.3			−2.70728
$821$	−3942.97	−	6829.42i	−0.167613	−	0.290315i	0.769967	−	0.638084i	$-0.220273\pi$
$821$	−3942.97	−	6829.42i	−0.167613	−	0.290315i	−0.937580	+	0.347769i	$0.886939\pi$
$822$	3600.52	+	6236.29i	0.152777	+	0.264618i
$823$	−22976.1	+	39795.7i	−0.973142	+	1.68553i	−0.287206	+	0.957869i	$0.592726\pi$
$823$	−22976.1	+	39795.7i	−0.973142	+	1.68553i	−0.685936	+	0.727662i	$0.740607\pi$
$824$	−3167.54			−0.133916
$825$	−10438.8	+	18080.5i	−0.440524	+	0.763011i
$826$	564.337	−	977.461i	0.0237722	−	0.0411746i
$827$	10754.8			0.452213			0.226107	−	0.974103i	$-0.427400\pi$
$827$	10754.8			0.452213			0.226107	+	0.974103i	$0.427400\pi$
$828$	21700.7	−	37586.8i	0.910812	−	1.57757i
$829$	−11503.7	−	19924.9i	−0.481953	−	0.834767i	0.517832	−	0.855482i	$-0.326739\pi$
$829$	−11503.7	−	19924.9i	−0.481953	−	0.834767i	−0.999785	+	0.0207150i	$0.993406\pi$
$830$	29783.9	+	51587.2i	1.24556	+	2.15737i
$831$	−27451.7			−1.14596
$832$	12385.1	−	29747.2i	0.516077	−	1.23954i
$833$	9799.49			0.407602
$834$	−20471.9	−	35458.4i	−0.849982	−	1.47221i
$835$	16702.2	+	28929.0i	0.692219	+	1.19896i
$836$	5768.82	−	9991.89i	0.238659	−	0.413369i
$837$	−27452.7			−1.13370
$838$	−12134.7	+	21017.9i	−0.500221	+	0.866408i
$839$	−13073.3	+	22643.6i	−0.537949	+	0.931755i	0.461065	+	0.887366i	$0.347467\pi$
$839$	−13073.3	+	22643.6i	−0.537949	+	0.931755i	−0.999014	+	0.0443888i	$0.985866\pi$
$840$	14899.8			0.612013
$841$	12141.8	−	21030.2i	0.497840	−	0.862284i
$842$	7682.04	+	13305.7i	0.314419	+	0.544589i
$843$	5198.63	+	9004.28i	0.212396	+	0.367881i
$844$	−18797.7			−0.766637
$845$	29214.8	+	29428.0i	1.18937	+	1.19805i
$846$	−12777.6			−0.519269
$847$	896.137	+	1552.15i	0.0363538	+	0.0629665i
$848$	4803.16	+	8319.31i	0.194506	+	0.336894i
$849$	23668.9	−	40995.8i	0.956790	−	1.65721i
$850$	76805.2			3.09929
$851$	18942.5	−	32809.3i	0.763031	−	1.32161i
$852$	−5372.55	+	9305.53i	−0.216034	+	0.374181i
$853$	19146.9			0.768553			0.384277	−	0.923218i	$-0.374451\pi$
$853$	19146.9			0.768553			0.384277	+	0.923218i	$0.374451\pi$
$854$	16927.8	−	29319.8i	0.678288	−	1.17483i
$855$	41839.8	+	72468.7i	1.67356	+	2.89869i
$856$	−2491.60	−	4315.58i	−0.0994873	−	0.172317i
$857$	30715.8			1.22431			0.612154	−	0.790739i	$-0.290303\pi$
$857$	30715.8			1.22431			0.612154	+	0.790739i	$0.290303\pi$
$858$	6814.13	−	16366.5i	0.271131	−	0.651218i
$859$	−1618.21			−0.0642755			−0.0321377	−	0.999483i	$-0.510232\pi$
$859$	−1618.21			−0.0642755			−0.0321377	+	0.999483i	$0.510232\pi$
$860$	25570.3	+	44289.1i	1.01389	+	1.75610i
$861$	−21438.4	−	37132.4i	−0.848570	−	1.46977i
$862$	−31424.0	+	54427.9i	−1.24165	+	2.15060i
$863$	−16781.8			−0.661946			−0.330973	−	0.943640i	$-0.607377\pi$
$863$	−16781.8			−0.661946			−0.330973	+	0.943640i	$0.607377\pi$
$864$	14155.6	−	24518.2i	0.557388	−	0.965424i
$865$	−33725.4	+	58414.0i	−1.32566	+	2.29611i
$866$	−34191.0			−1.34164
$867$	5634.62	−	9759.44i	0.220717	−	0.382293i
$868$	17697.8	+	30653.6i	0.692055	+	1.19867i
$869$	6065.38	+	10505.6i	0.236771	+	0.410100i
$870$	−6661.79			−0.259604
$871$	−35071.9	+	4552.47i	−1.36437	+	0.177100i
$872$	−1588.92			−0.0617058
$873$	8999.97	+	15588.4i	0.348915	+	0.604338i
$874$	−25900.4	−	44860.7i	−1.00239	−	1.73620i
$875$	−14850.9	+	25722.5i	−0.573774	+	0.993806i
$876$	−29136.1			−1.12376
$877$	14773.4	−	25588.3i	0.568828	−	0.985240i	−0.427854	−	0.903848i	$-0.640730\pi$
$877$	14773.4	−	25588.3i	0.568828	−	0.985240i	0.996682	−	0.0813918i	$-0.0259365\pi$
$878$	2083.84	−	3609.32i	0.0800982	−	0.138734i
$879$	29113.5			1.11715
$880$	5107.16	−	8845.86i	0.195639	−	0.338857i
$881$	−5309.13	−	9195.68i	−0.203030	−	0.351658i	0.746474	−	0.665415i	$-0.231745\pi$
$881$	−5309.13	−	9195.68i	−0.203030	−	0.351658i	−0.949503	+	0.313758i	$0.898412\pi$
$882$	−10450.8	−	18101.4i	−0.398977	−	0.691048i
$883$	28816.4			1.09824			0.549121	−	0.835743i	$-0.314962\pi$
$883$	28816.4			1.09824			0.549121	+	0.835743i	$0.314962\pi$
$884$	−35194.6	+	4568.39i	−1.33905	+	0.173814i
$885$	−2817.78			−0.107027
$886$	24849.7	+	43040.9i	0.942258	+	1.63204i
$887$	−7821.36	−	13547.0i	−0.296072	−	0.512811i	0.679162	−	0.733988i	$-0.262343\pi$
$887$	−7821.36	−	13547.0i	−0.296072	−	0.512811i	−0.975234	+	0.221177i	$0.929010\pi$
$888$	−8967.05	+	15531.4i	−0.338868	+	0.586936i
$889$	13897.3			0.524298
$890$	−34120.8	+	59099.0i	−1.28509	+	2.22585i
$891$	−1041.79	+	1804.43i	−0.0391709	+	0.0678460i
$892$	22393.0			0.840552
$893$	−4149.30	+	7186.80i	−0.155488	+	0.269314i
$894$	52005.6	+	90076.3i	1.94556	+	3.36980i
$895$	15109.4	+	26170.3i	0.564305	+	0.977405i
$896$	−12080.0			−0.450405
$897$	−26304.5	−	34410.1i	−0.979133	−	1.28085i
$898$	−58049.3			−2.15716
$899$	−1284.27	−	2224.42i	−0.0476449	−	0.0825234i
$900$	−44572.1	−	77201.2i	−1.65082	−	2.85930i
$901$	7740.50	−	13406.9i	0.286208	−	0.495727i
$902$	16252.2			0.599931
$903$	−17246.6	+	29872.0i	−0.635584	+	1.10086i
$904$	−3097.18	+	5364.48i	−0.113950	+	0.197367i
$905$	−48284.6			−1.77352
$906$	3663.44	−	6345.26i	0.134337	−	0.232679i
$907$	−1367.69	−	2368.91i	−0.0500699	−	0.0867236i	0.839904	−	0.542735i	$-0.182611\pi$
$907$	−1367.69	−	2368.91i	−0.0500699	−	0.0867236i	−0.889974	+	0.456011i	$0.849278\pi$
$908$	4657.32	+	8066.71i	0.170219	+	0.294827i
$909$	37010.0			1.35043
$910$	21100.1	−	50679.4i	0.768640	−	1.84616i
$911$	−45895.4			−1.66914			−0.834568	−	0.550905i	$-0.814283\pi$
$911$	−45895.4			−1.66914			−0.834568	+	0.550905i	$0.814283\pi$
$912$	−22174.8	−	38407.9i	−0.805133	−	1.39453i
$913$	−4143.46	−	7176.69i	−0.150196	−	0.260147i
$914$	−16021.7	+	27750.3i	−0.579813	+	1.00427i
$915$	−84521.8			−3.05378
$916$	9377.38	−	16242.1i	0.338251	−	0.585867i
$917$	−5029.10	+	8710.65i	−0.181107	+	0.313687i
$918$	−36440.3			−1.31014
$919$	−5959.10	+	10321.5i	−0.213898	+	0.370483i	−0.952931	−	0.303186i	$-0.901949\pi$
$919$	−5959.10	+	10321.5i	−0.213898	+	0.370483i	0.739033	+	0.673669i	$0.235283\pi$
$920$	6898.95	+	11949.3i	0.247230	+	0.428215i
$921$	−9006.42	−	15599.6i	−0.322227	−	0.558114i
$922$	−19509.7			−0.696875
$923$	3902.26	+	5104.71i	0.139160	+	0.182041i
$924$	−12771.4			−0.454705
$925$	−38906.8	−	67388.6i	−1.38297	−	2.39538i
$926$	32562.9	+	56400.6i	1.15560	+	2.00155i
$927$	−9845.84	+	17053.5i	−0.348845	+	0.604218i
$928$	2648.86			0.0936994
$929$	5523.00	−	9566.11i	0.195052	−	0.337841i	−0.751865	−	0.659317i	$-0.770846\pi$
$929$	5523.00	−	9566.11i	0.195052	−	0.337841i	0.946918	+	0.321476i	$0.104179\pi$
$930$	81195.6	−	140635.i	2.86291	−	4.95871i
$931$	−13574.9			−0.477874
$932$	24312.3	−	42110.2i	0.854482	−	1.48001i
$933$	−26773.3	−	46372.8i	−0.939463	−	1.62720i
$934$	−13089.7	−	22672.0i	−0.458573	−	0.794272i
$935$	−16460.8			−0.575751
$936$	7461.44	+	9760.62i	0.260561	+	0.340850i
$937$	43996.1			1.53393			0.766964	−	0.641691i	$-0.221767\pi$
$937$	43996.1			1.53393			0.766964	+	0.641691i	$0.221767\pi$
$938$	23409.9	+	40547.2i	0.814885	+	1.41142i
$939$	36120.3	+	62562.2i	1.25532	+	2.17427i
$940$	6809.70	−	11794.7i	0.236285	−	0.409258i
$941$	54071.6			1.87320			0.936601	−	0.350397i	$-0.113953\pi$
$941$	54071.6			1.87320			0.936601	+	0.350397i	$0.113953\pi$
$942$	46228.5	−	80070.1i	1.59895	−	2.76945i
$943$	19853.0	−	34386.4i	0.685580	−	1.18746i
$944$	894.862			0.0308531
$945$	15336.2	−	26563.0i	0.527922	−	0.914387i
$946$	−6537.22	−	11322.8i	−0.224676	−	0.389150i
$947$	6728.19	+	11653.6i	0.230873	+	0.399884i	0.958065	−	0.286550i	$-0.0925084\pi$
$947$	6728.19	+	11653.6i	0.230873	+	0.399884i	−0.727192	+	0.686434i	$0.759175\pi$
$948$	−86441.4			−2.96148
$949$	−6696.70	+	16084.5i	−0.229067	+	0.550185i
$950$	−106396.			−3.63362
$951$	5372.15	+	9304.85i	0.183180	+	0.317277i
$952$	3812.78	+	6603.92i	0.129803	+	0.224826i
$953$	8157.73	−	14129.6i	0.277287	−	0.480276i	−0.693422	−	0.720531i	$-0.743898\pi$
$953$	8157.73	−	14129.6i	0.277287	−	0.480276i	0.970710	+	0.240256i	$0.0772313\pi$
$954$	−33019.9			−1.12061
$955$	38867.2	−	67320.1i	1.31698	−	2.28107i
$956$	−10715.9	+	18560.5i	−0.362528	+	0.627917i
$957$	926.773			0.0313044
$958$	22503.6	−	38977.5i	0.758935	−	1.31451i
$959$	−1551.04	−	2686.48i	−0.0522270	−	0.0904598i
$960$	53248.7	+	92229.5i	1.79020	+	3.10072i
$961$	32821.0			1.10171
$962$	40129.2	+	52494.7i	1.34493	+	1.75935i
$963$	−30979.1			−1.03664
$964$	−1247.72	−	2161.12i	−0.0416872	−	0.0722043i
$965$	12596.7	+	21818.2i	0.420210	+	0.727825i
$966$	−28669.9	+	49657.8i	−0.954906	+	1.65395i
$967$	9095.06			0.302458			0.151229	−	0.988499i	$-0.451677\pi$
$967$	9095.06			0.302458			0.151229	+	0.988499i	$0.451677\pi$
$968$	392.844	−	680.426i	0.0130439	−	0.0225927i
$969$	−35735.7	+	61896.1i	−1.18472	+	2.05200i
$970$	−35257.8			−1.16707
$971$	4095.33	−	7093.31i	0.135350	−	0.234434i	−0.790381	−	0.612616i	$-0.790117\pi$
$971$	4095.33	−	7093.31i	0.135350	−	0.234434i	0.925731	+	0.378182i	$0.123451\pi$
$972$	−21568.2	−	37357.3i	−0.711730	−	1.23275i
$973$	8818.93	+	15274.8i	0.290567	+	0.503277i
$974$	14353.2			0.472183
$975$	−88221.6	+	11451.5i	−2.89780	+	0.376145i
$976$	26842.2			0.880326
$977$	30348.3	+	52564.8i	0.993786	+	1.72129i	0.593291	+	0.804988i	$0.297829\pi$
$977$	30348.3	+	52564.8i	0.993786	+	1.72129i	0.400495	+	0.916299i	$0.368838\pi$
$978$	−43624.8	−	75560.4i	−1.42635	−	2.47050i
$979$	4746.81	−	8221.72i	0.154963	−	0.268404i
$980$	22278.7			0.726192
$981$	−4938.92	+	8554.46i	−0.160742	+	0.278413i
$982$	22768.9	−	39436.9i	0.739903	−	1.28155i
$983$	−42736.7			−1.38666			−0.693331	−	0.720619i	$-0.743858\pi$
$983$	−42736.7			−1.38666			−0.693331	+	0.720619i	$0.743858\pi$
$984$	−9398.07	+	16277.9i	−0.304471	+	0.527359i
$985$	38853.6	+	67296.3i	1.25683	+	2.17689i
$986$	−1704.72	−	2952.66i	−0.0550601	−	0.0953670i
$987$	9185.98			0.296244
$988$	48754.1	−	6328.46i	1.56991	−	0.203781i
$989$	−31942.4			−1.02701
$990$	17554.9	+	30406.0i	0.563568	+	0.976128i
$991$	8479.97	+	14687.7i	0.271821	+	0.470808i	0.969328	−	0.245770i	$-0.0790407\pi$
$991$	8479.97	+	14687.7i	0.271821	+	0.470808i	−0.697507	+	0.716578i	$0.745707\pi$
$992$	−32285.0	+	55919.2i	−1.03332	+	1.78976i
$993$	69776.1			2.22989
$994$	4253.16	−	7366.69i	0.135716	−	0.235068i
$995$	−43417.9	+	75202.1i	−1.38336	+	2.39605i
$996$	59051.0			1.87862
$997$	22129.0	−	38328.6i	0.702942	−	1.21753i	−0.264488	−	0.964389i	$-0.585203\pi$
$997$	22129.0	−	38328.6i	0.702942	−	1.21753i	0.967429	−	0.253142i	$-0.0814639\pi$
$998$	−16484.8	−	28552.5i	−0.522863	−	0.905625i
$999$	18459.4	+	31972.6i	0.584614	+	1.01258i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.e.a.133.15	yes	34
13.3	even	3		1859.4.a.i.1.3		17
13.9	even	3	inner	143.4.e.a.100.15	✓	34
13.10	even	6		1859.4.a.f.1.15		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.a.100.15	✓	34	13.9	even	3	inner
143.4.e.a.133.15	yes	34	1.1	even	1	trivial
1859.4.a.f.1.15		17	13.10	even	6
1859.4.a.i.1.3		17	13.3	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.09463 + 3.62801i) q^{2} +(4.10387 + 7.10811i) q^{3} +(-4.77499 + 8.27053i) q^{4} -18.8743 q^{5} +(-17.1922 + 29.7778i) q^{6} +(7.40609 - 12.8277i) q^{7} -6.49330 q^{8} +(-20.1835 + 34.9588i) q^{9} +(-39.5349 - 68.4764i) q^{10} +(5.50000 + 9.52628i) q^{11} -78.3838 q^{12} +(-18.0159 + 43.2716i) q^{13} +62.0522 q^{14} +(-77.4578 - 134.161i) q^{15} +(24.5988 + 42.6065i) q^{16} +(39.6422 - 68.6622i) q^{17} -169.108 q^{18} +(-54.9151 + 95.1157i) q^{19} +(90.1248 - 156.101i) q^{20} +121.574 q^{21} +(-23.0410 + 39.9082i) q^{22} +(56.2919 + 97.5004i) q^{23} +(-26.6476 - 46.1551i) q^{24} +231.241 q^{25} +(-194.727 + 25.2762i) q^{26} -109.713 q^{27} +(70.7280 + 122.505i) q^{28} +(-5.13248 - 8.88971i) q^{29} +(324.492 - 562.036i) q^{30} +250.224 q^{31} +(-129.024 + 223.477i) q^{32} +(-45.1426 + 78.1892i) q^{33} +332.143 q^{34} +(-139.785 + 242.115i) q^{35} +(-192.752 - 333.856i) q^{36} +(-168.252 - 291.422i) q^{37} -460.108 q^{38} +(-381.514 + 49.5219i) q^{39} +122.557 q^{40} +(-176.340 - 305.429i) q^{41} +(254.654 + 441.074i) q^{42} +(-141.861 + 245.710i) q^{43} -105.050 q^{44} +(380.950 - 659.825i) q^{45} +(-235.822 + 408.455i) q^{46} +75.5585 q^{47} +(-201.901 + 349.703i) q^{48} +(61.7997 + 107.040i) q^{49} +(484.365 + 838.946i) q^{50} +650.745 q^{51} +(-271.853 - 355.622i) q^{52} +195.259 q^{53} +(-229.808 - 398.039i) q^{54} +(-103.809 - 179.802i) q^{55} +(-48.0899 + 83.2942i) q^{56} -901.458 q^{57} +(21.5013 - 37.2414i) q^{58} +(9.09455 - 15.7522i) q^{59} +1479.44 q^{60} +(272.799 - 472.502i) q^{61} +(524.128 + 907.816i) q^{62} +(298.961 + 517.816i) q^{63} -687.454 q^{64} +(340.038 - 816.722i) q^{65} -378.229 q^{66} +(377.262 + 653.437i) q^{67} +(378.582 + 655.723i) q^{68} +(-462.029 + 800.257i) q^{69} -1171.20 q^{70} +(68.5416 - 118.718i) q^{71} +(131.057 - 226.998i) q^{72} +371.711 q^{73} +(704.854 - 1220.84i) q^{74} +(948.983 + 1643.69i) q^{75} +(-524.438 - 908.354i) q^{76} +162.934 q^{77} +(-978.798 - 1280.41i) q^{78} +1102.80 q^{79} +(-464.287 - 804.169i) q^{80} +(94.7082 + 164.039i) q^{81} +(738.734 - 1279.53i) q^{82} -753.357 q^{83} +(-580.517 + 1005.49i) q^{84} +(-748.220 + 1295.95i) q^{85} -1188.58 q^{86} +(42.1260 - 72.9644i) q^{87} +(-35.7131 - 61.8570i) q^{88} +(-431.528 - 747.429i) q^{89} +3191.80 q^{90} +(421.648 + 551.576i) q^{91} -1075.17 q^{92} +(1026.89 + 1778.62i) q^{93} +(158.267 + 274.127i) q^{94} +(1036.49 - 1795.25i) q^{95} -2118.00 q^{96} +(222.954 - 386.167i) q^{97} +(-258.895 + 448.420i) q^{98} -444.037 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 4 q^{2} + 6 q^{3} - 78 q^{4} + 32 q^{5} - 14 q^{6} + 6 q^{7} + 126 q^{8} - 135 q^{9} - 2 q^{10} + 187 q^{11} - 190 q^{12} - 60 q^{13} - 120 q^{14} + 28 q^{15} - 350 q^{16} - 118 q^{17} + 956 q^{18}+ \cdots - 2970 q^{99}+O(q^{100}) \) 34 * q - 4 * q^2 + 6 * q^3 - 78 * q^4 + 32 * q^5 - 14 * q^6 + 6 * q^7 + 126 * q^8 - 135 * q^9 - 2 * q^10 + 187 * q^11 - 190 * q^12 - 60 * q^13 - 120 * q^14 + 28 * q^15 - 350 * q^16 - 118 * q^17 + 956 * q^18 - 403 * q^19 - 98 * q^20 + 440 * q^21 + 44 * q^22 + 215 * q^23 - 26 * q^24 + 638 * q^25 - 989 * q^26 - 768 * q^27 + 396 * q^28 + 7 * q^29 + 1269 * q^30 + 1364 * q^31 - 813 * q^32 - 66 * q^33 + 1476 * q^34 - 10 * q^35 - 560 * q^36 - 1084 * q^37 + 820 * q^38 - 370 * q^39 + 190 * q^40 - 240 * q^41 - 393 * q^42 + 435 * q^43 - 1716 * q^44 - 1242 * q^45 - 1671 * q^46 + 1098 * q^47 - 894 * q^48 - 403 * q^49 + 651 * q^50 + 3104 * q^51 - 876 * q^52 - 1132 * q^53 - 311 * q^54 + 176 * q^55 + 1925 * q^56 - 1068 * q^57 - 618 * q^58 - 2010 * q^59 - 822 * q^60 - 460 * q^61 + 823 * q^62 - 820 * q^63 + 6342 * q^64 + 3070 * q^65 - 308 * q^66 + 232 * q^67 - 1795 * q^68 + 1608 * q^69 + 414 * q^70 - 489 * q^71 - 2556 * q^72 + 580 * q^73 - 2653 * q^74 + 2852 * q^75 - 2421 * q^76 + 132 * q^77 - 4760 * q^78 - 1464 * q^79 - 4915 * q^80 - 2393 * q^81 + 1772 * q^82 - 234 * q^83 - 4161 * q^84 - 4858 * q^85 + 2068 * q^86 - 3032 * q^87 + 693 * q^88 - 4113 * q^89 + 30290 * q^90 + 1096 * q^91 - 7108 * q^92 - 802 * q^93 - 2325 * q^94 + 3924 * q^95 + 5202 * q^96 - 2793 * q^97 - 533 * q^98 - 2970 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more