LMFDB - Embedded newform 287.4.e.a.165.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,4,Mod(165,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("287.165");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	287.e (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:	$16.9335481716$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.36
Character	$\chi$	$=$	287.165
Dual form			287.4.e.a.247.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.62102 + 4.53974i) q^{2} +(-0.734138 + 1.27156i) q^{3} +(-9.73948 + 16.8693i) q^{4} +(3.81699 + 6.61122i) q^{5} -7.69676 q^{6} +(17.9902 - 4.39897i) q^{7} -60.1731 q^{8} +(12.4221 + 21.5157i) q^{9} +O(q^{10})$	\(q+(2.62102 + 4.53974i) q^{2} +(-0.734138 + 1.27156i) q^{3} +(-9.73948 + 16.8693i) q^{4} +(3.81699 + 6.61122i) q^{5} -7.69676 q^{6} +(17.9902 - 4.39897i) q^{7} -60.1731 q^{8} +(12.4221 + 21.5157i) q^{9} +(-20.0088 + 34.6563i) q^{10} +(-17.6091 + 30.4999i) q^{11} +(-14.3002 - 24.7687i) q^{12} -18.1744 q^{13} +(67.1229 + 70.1412i) q^{14} -11.2088 q^{15} +(-79.7990 - 138.216i) q^{16} +(-1.78097 + 3.08474i) q^{17} +(-65.1170 + 112.786i) q^{18} +(-53.4589 - 92.5936i) q^{19} -148.702 q^{20} +(-7.61375 + 26.1052i) q^{21} -184.615 q^{22} +(49.0387 + 84.9376i) q^{23} +(44.1754 - 76.5140i) q^{24} +(33.3612 - 57.7833i) q^{25} +(-47.6354 - 82.5070i) q^{26} -76.1216 q^{27} +(-101.008 + 346.326i) q^{28} +138.042 q^{29} +(-29.3784 - 50.8850i) q^{30} +(111.593 - 193.285i) q^{31} +(177.617 - 307.642i) q^{32} +(-25.8551 - 44.7823i) q^{33} -18.6719 q^{34} +(97.7511 + 102.147i) q^{35} -483.938 q^{36} +(-19.8529 - 34.3862i) q^{37} +(280.234 - 485.379i) q^{38} +(13.3425 - 23.1099i) q^{39} +(-229.680 - 397.818i) q^{40} +41.0000 q^{41} +(-138.467 + 33.8578i) q^{42} +173.782 q^{43} +(-343.007 - 594.106i) q^{44} +(-94.8299 + 164.250i) q^{45} +(-257.063 + 445.246i) q^{46} +(-73.6977 - 127.648i) q^{47} +234.334 q^{48} +(304.298 - 158.277i) q^{49} +349.761 q^{50} +(-2.61496 - 4.52925i) q^{51} +(177.009 - 306.589i) q^{52} +(-265.697 + 460.200i) q^{53} +(-199.516 - 345.572i) q^{54} -268.855 q^{55} +(-1082.53 + 264.700i) q^{56} +156.985 q^{57} +(361.812 + 626.676i) q^{58} +(-274.506 + 475.459i) q^{59} +(109.168 - 189.084i) q^{60} +(321.641 + 557.099i) q^{61} +1169.95 q^{62} +(318.123 + 332.428i) q^{63} +585.366 q^{64} +(-69.3715 - 120.155i) q^{65} +(135.533 - 234.750i) q^{66} +(-21.2663 + 36.8343i) q^{67} +(-34.6915 - 60.0875i) q^{68} -144.005 q^{69} +(-207.511 + 711.493i) q^{70} -964.831 q^{71} +(-747.475 - 1294.67i) q^{72} +(41.1022 - 71.1911i) q^{73} +(104.070 - 180.254i) q^{74} +(48.9834 + 84.8418i) q^{75} +2082.65 q^{76} +(-182.624 + 626.163i) q^{77} +139.884 q^{78} +(104.995 + 181.857i) q^{79} +(609.184 - 1055.14i) q^{80} +(-279.512 + 484.130i) q^{81} +(107.462 + 186.129i) q^{82} +950.386 q^{83} +(-366.222 - 382.690i) q^{84} -27.1918 q^{85} +(455.486 + 788.925i) q^{86} +(-101.342 + 175.530i) q^{87} +(1059.60 - 1835.27i) q^{88} +(-248.129 - 429.772i) q^{89} -994.204 q^{90} +(-326.962 + 79.9486i) q^{91} -1910.45 q^{92} +(163.849 + 283.795i) q^{93} +(386.326 - 669.136i) q^{94} +(408.104 - 706.857i) q^{95} +(260.791 + 451.703i) q^{96} +482.621 q^{97} +(1516.11 + 966.586i) q^{98} -874.968 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 5 q^{2} + 6 q^{3} - 117 q^{4} - 4 q^{5} - 24 q^{6} - 30 q^{7} - 78 q^{8} - 236 q^{9}+O(q^{10}) $ 72 * q + 5 * q^2 + 6 * q^3 - 117 * q^4 - 4 * q^5 - 24 * q^6 - 30 * q^7 - 78 * q^8 - 236 * q^9	\( 72 q + 5 q^{2} + 6 q^{3} - 117 q^{4} - 4 q^{5} - 24 q^{6} - 30 q^{7} - 78 q^{8} - 236 q^{9} + 12 q^{10} + 140 q^{11} - 186 q^{12} - 144 q^{13} + 481 q^{14} - 732 q^{15} + 15 q^{16} + 2 q^{17} + 212 q^{18} - 30 q^{19} - 668 q^{20} + 368 q^{21} - 692 q^{22} + 314 q^{23} - 106 q^{24} - 570 q^{25} - 303 q^{26} - 408 q^{27} + 522 q^{28} - 712 q^{29} + 357 q^{30} + 4 q^{31} + 532 q^{32} + 30 q^{33} - 728 q^{34} + 462 q^{35} + 226 q^{36} + 1398 q^{37} + 264 q^{38} + 1348 q^{39} - 26 q^{40} + 2952 q^{41} - 1705 q^{42} - 2144 q^{43} + 1507 q^{44} + 1132 q^{45} + 1356 q^{46} + 622 q^{47} + 3448 q^{48} - 712 q^{49} - 2852 q^{50} + 668 q^{51} + 877 q^{52} + 412 q^{53} + 1814 q^{54} + 2228 q^{55} - 1321 q^{56} - 8164 q^{57} + 1309 q^{58} + 620 q^{59} + 3724 q^{60} - 774 q^{61} + 3330 q^{62} - 2550 q^{63} - 6570 q^{64} + 1036 q^{65} + 1056 q^{66} + 2972 q^{67} + 1525 q^{68} + 6608 q^{69} - 365 q^{70} - 7080 q^{71} + 821 q^{72} + 60 q^{73} + 2043 q^{74} - 450 q^{75} + 4342 q^{76} - 4846 q^{77} - 2272 q^{78} + 5190 q^{79} + 1564 q^{80} - 284 q^{81} + 205 q^{82} + 3312 q^{83} - 8326 q^{84} - 10128 q^{85} + 782 q^{86} + 1940 q^{87} + 4232 q^{88} + 1196 q^{89} + 16060 q^{90} - 4788 q^{91} - 9236 q^{92} - 698 q^{93} + 35 q^{94} + 1968 q^{95} + 7926 q^{96} + 7724 q^{97} - 11646 q^{98} - 11928 q^{99}+O(q^{100}) \) 72 * q + 5 * q^2 + 6 * q^3 - 117 * q^4 - 4 * q^5 - 24 * q^6 - 30 * q^7 - 78 * q^8 - 236 * q^9 + 12 * q^10 + 140 * q^11 - 186 * q^12 - 144 * q^13 + 481 * q^14 - 732 * q^15 + 15 * q^16 + 2 * q^17 + 212 * q^18 - 30 * q^19 - 668 * q^20 + 368 * q^21 - 692 * q^22 + 314 * q^23 - 106 * q^24 - 570 * q^25 - 303 * q^26 - 408 * q^27 + 522 * q^28 - 712 * q^29 + 357 * q^30 + 4 * q^31 + 532 * q^32 + 30 * q^33 - 728 * q^34 + 462 * q^35 + 226 * q^36 + 1398 * q^37 + 264 * q^38 + 1348 * q^39 - 26 * q^40 + 2952 * q^41 - 1705 * q^42 - 2144 * q^43 + 1507 * q^44 + 1132 * q^45 + 1356 * q^46 + 622 * q^47 + 3448 * q^48 - 712 * q^49 - 2852 * q^50 + 668 * q^51 + 877 * q^52 + 412 * q^53 + 1814 * q^54 + 2228 * q^55 - 1321 * q^56 - 8164 * q^57 + 1309 * q^58 + 620 * q^59 + 3724 * q^60 - 774 * q^61 + 3330 * q^62 - 2550 * q^63 - 6570 * q^64 + 1036 * q^65 + 1056 * q^66 + 2972 * q^67 + 1525 * q^68 + 6608 * q^69 - 365 * q^70 - 7080 * q^71 + 821 * q^72 + 60 * q^73 + 2043 * q^74 - 450 * q^75 + 4342 * q^76 - 4846 * q^77 - 2272 * q^78 + 5190 * q^79 + 1564 * q^80 - 284 * q^81 + 205 * q^82 + 3312 * q^83 - 8326 * q^84 - 10128 * q^85 + 782 * q^86 + 1940 * q^87 + 4232 * q^88 + 1196 * q^89 + 16060 * q^90 - 4788 * q^91 - 9236 * q^92 - 698 * q^93 + 35 * q^94 + 1968 * q^95 + 7926 * q^96 + 7724 * q^97 - 11646 * q^98 - 11928 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	2.62102	+	4.53974i	0.926670	+	1.60504i	0.788853	+	0.614582i	$0.210675\pi$
$2$	2.62102	+	4.53974i	0.926670	+	1.60504i	0.137817	+	0.990458i	$0.455991\pi$
$3$	−0.734138	+	1.27156i	−0.141285	+	0.244713i	−0.927981	−	0.372628i	$-0.878457\pi$
$3$	−0.734138	+	1.27156i	−0.141285	+	0.244713i	0.786696	+	0.617341i	$0.211790\pi$
$4$	−9.73948	+	16.8693i	−1.21743	+	2.10866i
$5$	3.81699	+	6.61122i	0.341402	+	0.591325i	0.984693	−	0.174296i	$-0.0557650\pi$
$5$	3.81699	+	6.61122i	0.341402	+	0.591325i	−0.643291	+	0.765621i	$0.722432\pi$
$6$	−7.69676			−0.523698
$7$	17.9902	−	4.39897i	0.971382	−	0.237522i
$7$	17.9902	−	4.39897i	0.971382	−	0.237522i
$8$	−60.1731			−2.65930
$9$	12.4221	+	21.5157i	0.460077	+	0.796877i
$10$	−20.0088	+	34.6563i	−0.632734	+	1.09593i
$11$	−17.6091	+	30.4999i	−0.482668	+	0.836006i	−0.999802	−	0.0198987i	$-0.993666\pi$
$11$	−17.6091	+	30.4999i	−0.482668	+	0.836006i	0.517134	+	0.855905i	$0.326999\pi$
$12$	−14.3002	−	24.7687i	−0.344010	−	0.595843i
$13$	−18.1744			−0.387744			−0.193872	−	0.981027i	$-0.562105\pi$
$13$	−18.1744			−0.387744			−0.193872	+	0.981027i	$0.562105\pi$
$14$	67.1229	+	70.1412i	1.28138	+	1.33900i
$15$	−11.2088			−0.192940
$16$	−79.7990	−	138.216i	−1.24686	−	2.15962i
$17$	−1.78097	+	3.08474i	−0.0254088	+	0.0440094i	−0.878450	−	0.477834i	$-0.841422\pi$
$17$	−1.78097	+	3.08474i	−0.0254088	+	0.0440094i	0.853041	+	0.521843i	$0.174755\pi$
$18$	−65.1170	+	112.786i	−0.852679	+	1.47688i
$19$	−53.4589	−	92.5936i	−0.645490	−	1.11802i	−0.984188	−	0.177127i	$-0.943320\pi$
$19$	−53.4589	−	92.5936i	−0.645490	−	1.11802i	0.338698	−	0.940895i	$-0.390014\pi$
$20$	−148.702			−1.66254
$21$	−7.61375	+	26.1052i	−0.0791170	+	0.271268i
$22$	−184.615			−1.78910
$23$	49.0387	+	84.9376i	0.444577	+	0.770031i	0.998023	−	0.0628549i	$-0.0200205\pi$
$23$	49.0387	+	84.9376i	0.444577	+	0.770031i	−0.553445	+	0.832886i	$0.686687\pi$
$24$	44.1754	−	76.5140i	0.375719	−	0.650765i
$25$	33.3612	−	57.7833i	0.266890	−	0.462266i
$26$	−47.6354	−	82.5070i	−0.359311	−	0.622344i
$27$	−76.1216			−0.542578
$28$	−101.008	+	346.326i	−0.681741	+	2.33748i
$29$	138.042			0.883925			0.441963	−	0.897034i	$-0.354282\pi$
$29$	138.042			0.883925			0.441963	+	0.897034i	$0.354282\pi$
$30$	−29.3784	−	50.8850i	−0.178791	−	0.309676i
$31$	111.593	−	193.285i	0.646538	−	1.11984i	−0.337405	−	0.941359i	$-0.609549\pi$
$31$	111.593	−	193.285i	0.646538	−	1.11984i	0.983944	−	0.178478i	$-0.0571173\pi$
$32$	177.617	−	307.642i	0.981205	−	1.69950i
$33$	−25.8551	−	44.7823i	−0.136388	−	0.236230i
$34$	−18.6719			−0.0941823
$35$	97.7511	+	102.147i	0.472084	+	0.493312i
$36$	−483.938			−2.24046
$37$	−19.8529	−	34.3862i	−0.0882107	−	0.152785i	0.818544	−	0.574444i	$-0.194782\pi$
$37$	−19.8529	−	34.3862i	−0.0882107	−	0.152785i	−0.906755	+	0.421658i	$0.861448\pi$
$38$	280.234	−	485.379i	1.19631	−	2.07208i
$39$	13.3425	−	23.1099i	0.0547824	−	0.0948858i
$40$	−229.680	−	397.818i	−0.907890	−	1.57251i
$41$	41.0000			0.156174
$41$	41.0000			0.156174
$42$	−138.467	+	33.8578i	−0.508711	+	0.124390i
$43$	173.782			0.616314			0.308157	−	0.951335i	$-0.400288\pi$
$43$	173.782			0.616314			0.308157	+	0.951335i	$0.400288\pi$
$44$	−343.007	−	594.106i	−1.17523	−	2.03557i
$45$	−94.8299	+	164.250i	−0.314142	+	0.544111i
$46$	−257.063	+	445.246i	−0.823953	+	1.42713i
$47$	−73.6977	−	127.648i	−0.228721	−	0.396157i	0.728708	−	0.684825i	$-0.240121\pi$
$47$	−73.6977	−	127.648i	−0.228721	−	0.396157i	−0.957429	+	0.288667i	$0.906788\pi$
$48$	234.334			0.704650
$49$	304.298	−	158.277i	0.887167	−	0.461449i
$50$	349.761			0.989274
$51$	−2.61496	−	4.52925i	−0.00717977	−	0.0124357i
$52$	177.009	−	306.589i	0.472053	−	0.817620i
$53$	−265.697	+	460.200i	−0.688608	+	1.19270i	0.283680	+	0.958919i	$0.408445\pi$
$53$	−265.697	+	460.200i	−0.688608	+	1.19270i	−0.972288	+	0.233785i	$0.924889\pi$
$54$	−199.516	−	345.572i	−0.502791	−	0.870859i
$55$	−268.855			−0.659135
$56$	−1082.53	+	264.700i	−2.58320	+	0.631643i
$57$	156.985			0.364792
$58$	361.812	+	626.676i	0.819107	+	1.41873i
$59$	−274.506	+	475.459i	−0.605723	+	1.04914i	0.386214	+	0.922409i	$0.373783\pi$
$59$	−274.506	+	475.459i	−0.605723	+	1.04914i	−0.991937	+	0.126734i	$0.959551\pi$
$60$	109.168	−	189.084i	0.234892	−	0.406844i
$61$	321.641	+	557.099i	0.675114	+	1.16933i	0.976436	+	0.215809i	$0.0692387\pi$
$61$	321.641	+	557.099i	0.675114	+	1.16933i	−0.301322	+	0.953522i	$0.597428\pi$
$62$	1169.95			2.39651
$63$	318.123	+	332.428i	0.636187	+	0.664794i
$64$	585.366			1.14329
$65$	−69.3715	−	120.155i	−0.132376	−	0.229283i
$66$	135.533	−	234.750i	0.252772	−	0.437815i
$67$	−21.2663	+	36.8343i	−0.0387775	+	0.0671646i	−0.884763	−	0.466042i	$-0.845680\pi$
$67$	−21.2663	+	36.8343i	−0.0387775	+	0.0671646i	0.845985	+	0.533206i	$0.179013\pi$
$68$	−34.6915	−	60.0875i	−0.0618671	−	0.107157i
$69$	−144.005			−0.251248
$70$	−207.511	+	711.493i	−0.354319	+	1.21485i
$71$	−964.831			−1.61274			−0.806369	−	0.591413i	$-0.798570\pi$
$71$	−964.831			−1.61274			−0.806369	+	0.591413i	$0.798570\pi$
$72$	−747.475	−	1294.67i	−1.22348	−	2.11914i
$73$	41.1022	−	71.1911i	0.0658993	−	0.114141i	−0.831193	−	0.555984i	$-0.812342\pi$
$73$	41.1022	−	71.1911i	0.0658993	−	0.114141i	0.897093	+	0.441843i	$0.145675\pi$
$74$	104.070	−	180.254i	0.163484	−	0.283163i
$75$	48.9834	+	84.8418i	0.0754150	+	0.130623i
$76$	2082.65			3.14337
$77$	−182.624	+	626.163i	−0.270285	+	0.926726i
$78$	139.884			0.203061
$79$	104.995	+	181.857i	0.149530	+	0.258994i	0.931054	−	0.364882i	$-0.118891\pi$
$79$	104.995	+	181.857i	0.149530	+	0.258994i	−0.781524	+	0.623876i	$0.785557\pi$
$80$	609.184	−	1055.14i	0.851361	−	1.47460i
$81$	−279.512	+	484.130i	−0.383419	+	0.664101i
$82$	107.462	+	186.129i	0.144722	+	0.250665i
$83$	950.386			1.25685			0.628424	−	0.777871i	$-0.283700\pi$
$83$	950.386			1.25685			0.628424	+	0.777871i	$0.283700\pi$
$84$	−366.222	−	382.690i	−0.475691	−	0.497082i
$85$	−27.1918			−0.0346985
$86$	455.486	+	788.925i	0.571120	+	0.989209i
$87$	−101.342	+	175.530i	−0.124885	+	0.216308i
$88$	1059.60	−	1835.27i	1.28356	−	2.22319i
$89$	−248.129	−	429.772i	−0.295524	−	0.511862i	0.679583	−	0.733599i	$-0.262161\pi$
$89$	−248.129	−	429.772i	−0.295524	−	0.511862i	−0.975107	+	0.221736i	$0.928828\pi$
$90$	−994.204			−1.16443
$91$	−326.962	+	79.9486i	−0.376647	+	0.0920977i
$92$	−1910.45			−2.16498
$93$	163.849	+	283.795i	0.182692	+	0.316432i
$94$	386.326	−	669.136i	0.423899	−	0.734214i
$95$	408.104	−	706.857i	0.440743	−	0.763390i
$96$	260.791	+	451.703i	0.277259	+	0.480227i
$97$	482.621			0.505183			0.252592	−	0.967573i	$-0.418717\pi$
$97$	482.621			0.505183			0.252592	+	0.967573i	$0.418717\pi$
$98$	1516.11	+	966.586i	1.56276	+	0.996326i
$99$	−874.968			−0.888258
$100$	649.841	+	1125.56i	0.649841	+	1.12556i
$101$	156.657	−	271.338i	0.154336	−	0.267318i	−0.778481	−	0.627668i	$-0.784009\pi$
$101$	156.657	−	271.338i	0.154336	−	0.267318i	0.932817	+	0.360350i	$0.117343\pi$
$102$	13.7077	−	23.7425i	0.0133065	−	0.0230476i
$103$	27.1890	+	47.0927i	0.0260098	+	0.0450503i	0.878737	−	0.477306i	$-0.158387\pi$
$103$	27.1890	+	47.0927i	0.0260098	+	0.0450503i	−0.852728	+	0.522356i	$0.825053\pi$
$104$	1093.61			1.03113
$105$	−201.649	+	49.3071i	−0.187418	+	0.0458274i
$106$	−2785.58			−2.55245
$107$	−142.863	−	247.446i	−0.129076	−	0.223566i	0.794243	−	0.607600i	$-0.207868\pi$
$107$	−142.863	−	247.446i	−0.129076	−	0.223566i	−0.923319	+	0.384035i	$0.874534\pi$
$108$	741.384	−	1284.12i	0.660553	−	1.14411i
$109$	848.445	−	1469.55i	0.745563	−	1.29135i	−0.204369	−	0.978894i	$-0.565514\pi$
$109$	848.445	−	1469.55i	0.745563	−	1.29135i	0.949931	−	0.312458i	$-0.101153\pi$
$110$	−704.675	−	1220.53i	−0.610801	−	1.05794i
$111$	58.2991			0.0498514
$112$	−2043.61	−	2135.51i	−1.72414	−	1.80166i
$113$	989.589			0.823829			0.411915	−	0.911222i	$-0.364860\pi$
$113$	989.589			0.823829			0.411915	+	0.911222i	$0.364860\pi$
$114$	411.460	+	712.670i	0.338042	+	0.585506i
$115$	−374.360	+	648.411i	−0.303559	+	0.525780i
$116$	−1344.46	+	2328.67i	−1.07612	+	1.86390i
$117$	−225.764	−	391.034i	−0.178392	−	0.308984i
$118$	−2877.94			−2.24522
$119$	−18.4705	+	63.3297i	−0.0142285	+	0.0487851i
$120$	674.468			0.513085
$121$	45.3376	+	78.5270i	0.0340628	+	0.0589985i
$122$	−1686.05	+	2920.33i	−1.25121	+	2.16717i
$123$	−30.0997	+	52.1341i	−0.0220650	+	0.0382177i
$124$	2173.71	+	3764.98i	1.57424	+	2.72666i
$125$	1463.60			1.04727
$126$	−675.329	+	2315.50i	−0.477485	+	1.63715i
$127$	−892.111			−0.623323			−0.311662	−	0.950193i	$-0.600886\pi$
$127$	−892.111			−0.623323			−0.311662	+	0.950193i	$0.600886\pi$
$128$	113.319	+	196.274i	0.0782505	+	0.135534i
$129$	−127.580	+	220.975i	−0.0870759	+	0.150820i
$130$	363.648	−	629.856i	0.245339	−	0.424939i
$131$	1414.86	+	2450.61i	0.943643	+	1.63444i	0.758447	+	0.651735i	$0.225959\pi$
$131$	1414.86	+	2450.61i	0.943643	+	1.63444i	0.185196	+	0.982702i	$0.440708\pi$
$132$	1007.26			0.664172
$133$	−1369.06	−	1430.62i	−0.892573	−	0.932708i
$134$	−222.957			−0.143736
$135$	−290.555	−	503.256i	−0.185237	−	0.320840i
$136$	107.167	−	185.618i	0.0675697	−	0.117034i
$137$	−1379.09	+	2388.65i	−0.860025	+	1.48961i	0.0118791	+	0.999929i	$0.496219\pi$
$137$	−1379.09	+	2388.65i	−0.860025	+	1.48961i	−0.871904	+	0.489677i	$0.837115\pi$
$138$	−377.439	−	653.744i	−0.232824	−	0.403264i
$139$	2843.19			1.73494			0.867470	−	0.497490i	$-0.165745\pi$
$139$	2843.19			1.73494			0.867470	+	0.497490i	$0.165745\pi$
$140$	−2675.18	+	654.135i	−1.61496	+	0.394889i
$141$	216.417			0.129260
$142$	−2528.84	−	4380.08i	−1.49448	−	2.58851i
$143$	320.035	−	554.317i	0.187152	−	0.324156i
$144$	1982.54	−	3433.86i	1.14730	−	1.98719i
$145$	526.906	+	912.628i	0.301774	+	0.522687i
$146$	430.919			0.244268
$147$	−22.1373	+	503.132i	−0.0124208	+	0.282297i
$148$	773.427			0.429563
$149$	1728.59	+	2994.01i	0.950415	+	1.64617i	0.744527	+	0.667592i	$0.232675\pi$
$149$	1728.59	+	2994.01i	0.950415	+	1.64617i	0.205888	+	0.978575i	$0.433992\pi$
$150$	−256.773	+	444.744i	−0.139770	+	0.242088i
$151$	60.2082	−	104.284i	0.0324482	−	0.0562019i	−0.849345	−	0.527838i	$-0.823003\pi$
$151$	60.2082	−	104.284i	0.0324482	−	0.0562019i	0.881793	+	0.471636i	$0.156336\pi$
$152$	3216.79	+	5571.64i	1.71655	+	2.97316i
$153$	−88.4937			−0.0467601
$154$	−3321.28	+	812.117i	−1.73790	+	0.424950i
$155$	1703.80			0.882918
$156$	259.898	+	450.157i	0.133388	+	0.231035i
$157$	443.573	−	768.291i	0.225484	−	0.390550i	−0.730981	−	0.682398i	$-0.760937\pi$
$157$	443.573	−	768.291i	0.225484	−	0.390550i	0.956465	+	0.291849i	$0.0942703\pi$
$158$	−550.389	+	953.302i	−0.277130	+	0.480004i
$159$	−390.116	−	675.701i	−0.194580	−	0.337022i
$160$	2711.85			1.33994
$161$	1255.86	+	1312.33i	0.614754	+	0.642397i
$162$	−2930.43			−1.42121
$163$	−1027.60	−	1779.86i	−0.493791	−	0.855270i	0.506184	−	0.862426i	$-0.331056\pi$
$163$	−1027.60	−	1779.86i	−0.493791	−	0.855270i	−0.999974	+	0.00715519i	$0.997722\pi$
$164$	−399.319	+	691.640i	−0.190131	+	0.329317i
$165$	197.377	−	341.867i	0.0931259	−	0.161299i
$166$	2490.98	+	4314.50i	1.16468	+	2.01729i
$167$	−1792.73			−0.830691			−0.415346	−	0.909664i	$-0.636339\pi$
$167$	−1792.73			−0.830691			−0.415346	+	0.909664i	$0.636339\pi$
$168$	458.143	−	1570.83i	0.210396	−	0.721383i
$169$	−1866.69			−0.849655
$170$	−71.2703	−	123.444i	−0.0321540	−	0.0556924i
$171$	1328.14	−	2300.41i	0.593951	−	1.02875i
$172$	−1692.55	+	2931.58i	−0.750322	+	1.29960i
$173$	−316.309	−	547.863i	−0.139009	−	0.240770i	0.788113	−	0.615531i	$-0.211058\pi$
$173$	−316.309	−	547.863i	−0.139009	−	0.240770i	−0.927122	+	0.374761i	$0.877725\pi$
$174$	−1062.48			−0.462910
$175$	345.989	−	1186.29i	0.149453	−	0.512429i
$176$	5620.76			2.40728
$177$	−403.051	−	698.105i	−0.171159	−	0.296456i
$178$	1300.70	−	2252.88i	0.547706	−	0.948655i
$179$	−450.291	+	779.927i	−0.188024	+	0.325667i	−0.944591	−	0.328249i	$-0.893542\pi$
$179$	−450.291	+	779.927i	−0.188024	+	0.325667i	0.756567	+	0.653916i	$0.226875\pi$
$180$	−1847.19	−	3199.42i	−0.764896	−	1.32484i
$181$	−1006.29			−0.413243			−0.206621	−	0.978421i	$-0.566247\pi$
$181$	−1006.29			−0.413243			−0.206621	+	0.978421i	$0.566247\pi$
$182$	−1219.92	−	1274.77i	−0.496848	−	0.519190i
$183$	−944.516			−0.381534
$184$	−2950.81	−	5110.96i	−1.18227	−	2.04774i
$185$	151.557	−	262.504i	0.0602306	−	0.104322i
$186$	−858.904	+	1487.67i	−0.338591	+	0.586457i
$187$	−62.7228	−	108.639i	−0.0245281	−	0.0424838i
$188$	2871.11			1.11381
$189$	−1369.45	+	334.856i	−0.527050	+	0.128874i
$190$	4278.59			1.63369
$191$	−2334.15	−	4042.87i	−0.884259	−	1.53158i	−0.846561	−	0.532292i	$-0.821331\pi$
$191$	−2334.15	−	4042.87i	−0.884259	−	1.53158i	−0.0376975	−	0.999289i	$-0.512002\pi$
$192$	−429.740	+	744.331i	−0.161530	+	0.279778i
$193$	1427.97	−	2473.31i	0.532577	−	0.922450i	−0.466700	−	0.884416i	$-0.654557\pi$
$193$	1427.97	−	2473.31i	0.532577	−	0.922450i	0.999276	−	0.0380341i	$-0.0121096\pi$
$194$	1264.96	+	2190.97i	0.468138	+	0.810839i
$195$	203.713			0.0748112
$196$	−293.686	+	6674.82i	−0.107028	+	2.43252i
$197$	3932.30			1.42216			0.711078	−	0.703113i	$-0.248207\pi$
$197$	3932.30			1.42216			0.711078	+	0.703113i	$0.248207\pi$
$198$	−2293.31	−	3972.12i	−0.823122	−	1.42569i
$199$	683.424	−	1183.72i	0.243450	−	0.421668i	−0.718244	−	0.695791i	$-0.755054\pi$
$199$	683.424	−	1183.72i	0.243450	−	0.421668i	0.961695	+	0.274122i	$0.0883874\pi$
$200$	−2007.45	+	3477.00i	−0.709740	+	1.22931i
$201$	−31.2248	−	54.0829i	−0.0109573	−	0.0189787i
$202$	1642.41			0.572075
$203$	2483.42	−	607.244i	0.858629	−	0.209952i
$204$	101.873			0.0349636
$205$	156.497	+	271.060i	0.0533180	+	0.0923495i
$206$	−142.526	+	246.861i	−0.0482050	+	0.0834935i
$207$	−1218.33	+	2110.20i	−0.409080	+	0.708547i
$208$	1450.30	+	2511.99i	0.483462	+	0.837381i
$209$	3765.46			1.24623
$210$	−752.367	−	786.198i	−0.247230	−	0.258347i
$211$	1445.33			0.471568			0.235784	−	0.971806i	$-0.424234\pi$
$211$	1445.33			0.471568			0.235784	+	0.971806i	$0.424234\pi$
$212$	−5175.49	−	8964.21i	−1.67667	−	2.90408i
$213$	708.319	−	1226.84i	0.227856	−	0.394657i
$214$	748.893	−	1297.12i	0.239221	−	0.414343i
$215$	663.324	+	1148.91i	0.210411	+	0.364442i
$216$	4580.47			1.44288
$217$	1157.33	−	3968.13i	0.362050	−	1.24136i
$218$	8895.17			2.76356
$219$	60.3494	+	104.528i	0.0186212	+	0.0322528i
$220$	2618.51	−	4535.39i	0.802454	−	1.38989i
$221$	32.3681	−	56.0633i	0.00985211	−	0.0170644i
$222$	152.803	+	264.662i	0.0461958	+	0.0800134i
$223$	4820.99			1.44770			0.723851	−	0.689957i	$-0.242371\pi$
$223$	4820.99			1.44770			0.723851	+	0.689957i	$0.242371\pi$
$224$	1842.07	−	6315.88i	0.549457	−	1.88392i
$225$	1657.66			0.491159
$226$	2593.73	+	4492.48i	0.763418	+	1.32228i
$227$	978.219	−	1694.32i	0.286021	−	0.495402i	−0.686836	−	0.726813i	$-0.741001\pi$
$227$	978.219	−	1694.32i	0.286021	−	0.495402i	0.972856	+	0.231411i	$0.0743341\pi$
$228$	−1528.95	+	2648.22i	−0.444111	+	0.769222i
$229$	−103.506	−	179.277i	−0.0298684	−	0.0517336i	0.850705	−	0.525644i	$-0.176175\pi$
$229$	−103.506	−	179.277i	−0.0298684	−	0.0517336i	−0.880573	+	0.473910i	$0.842842\pi$
$230$	−3924.82			−1.12520
$231$	−662.135	−	691.909i	−0.188594	−	0.197075i
$232$	−8306.44			−2.35062
$233$	−1169.28	−	2025.25i	−0.328763	−	0.569435i	0.653503	−	0.756924i	$-0.273299\pi$
$233$	−1169.28	−	2025.25i	−0.328763	−	0.569435i	−0.982267	+	0.187489i	$0.939965\pi$
$234$	1183.46	−	2049.82i	0.330621	−	0.572653i
$235$	562.606	−	974.463i	0.156172	−	0.270498i
$236$	−5347.09	−	9261.44i	−1.47486	−	2.55453i
$237$	−308.324			−0.0845055
$238$	−335.912	+	82.1370i	−0.0914870	+	0.0223704i
$239$	10.0848			0.00272941			0.00136471	−	0.999999i	$-0.499566\pi$
$239$	10.0848			0.00272941			0.00136471	+	0.999999i	$0.499566\pi$
$240$	894.450	+	1549.23i	0.240569	+	0.416677i
$241$	−2720.17	+	4711.47i	−0.727060	+	1.25930i	0.231060	+	0.972939i	$0.425781\pi$
$241$	−2720.17	+	4711.47i	−0.727060	+	1.25930i	−0.958120	+	0.286366i	$0.907553\pi$
$242$	−237.661	+	411.641i	−0.0631299	+	0.109344i
$243$	−1438.04	−	2490.76i	−0.379632	−	0.657541i
$244$	−12530.5			−3.28763
$245$	2207.91	+	1407.64i	0.575747	+	0.367064i
$246$	−315.567			−0.0817879
$247$	971.583	+	1682.83i	0.250285	+	0.433506i
$248$	−6714.90	+	11630.5i	−1.71934	+	2.97798i
$249$	−697.715	+	1208.48i	−0.177574	+	0.307567i
$250$	3836.13	+	6644.38i	0.970474	+	1.68091i
$251$	−2680.51			−0.674072			−0.337036	−	0.941492i	$-0.609424\pi$
$251$	−2680.51			−0.674072			−0.337036	+	0.941492i	$0.609424\pi$
$252$	−8706.17	+	2128.83i	−2.17634	+	0.532158i
$253$	−3454.12			−0.858333
$254$	−2338.24	−	4049.95i	−0.577615	−	1.00046i
$255$	19.9626	−	34.5762i	0.00490237	−	0.00849115i
$256$	1747.44	−	3026.66i	0.426622	−	0.738931i
$257$	−2127.38	−	3684.73i	−0.516351	−	0.894346i	−0.999820	−	0.0189846i	$-0.993957\pi$
$257$	−2127.38	−	3684.73i	−0.516351	−	0.894346i	0.483469	−	0.875362i	$-0.339377\pi$
$258$	−1337.56			−0.322763
$259$	−508.422	−	531.284i	−0.121976	−	0.127461i
$260$	2702.57			0.644639
$261$	1714.77	+	2970.08i	0.406674	+	0.704380i
$262$	−7416.77	+	12846.2i	−1.74889	+	3.02917i
$263$	2546.21	−	4410.17i	0.596981	−	1.03400i	−0.396283	−	0.918128i	$-0.629700\pi$
$263$	2546.21	−	4410.17i	0.596981	−	1.03400i	0.993264	−	0.115873i	$-0.0369666\pi$
$264$	1555.78	+	2694.69i	0.362695	+	0.628207i
$265$	−4056.64			−0.940368
$266$	2906.31	−	9964.83i	0.669914	−	2.29693i
$267$	728.644			0.167012
$268$	−414.245	−	717.494i	−0.0944181	−	0.163537i
$269$	520.409	−	901.375i	0.117955	−	0.204304i	−0.801002	−	0.598662i	$-0.795699\pi$
$269$	520.409	−	901.375i	0.117955	−	0.204304i	0.918957	+	0.394357i	$0.129033\pi$
$270$	1523.10	−	2638.09i	0.343307	−	0.594626i
$271$	−2998.82	−	5194.12i	−0.672198	−	1.16428i	−0.977280	−	0.211954i	$-0.932017\pi$
$271$	−2998.82	−	5194.12i	−0.672198	−	1.16428i	0.305082	−	0.952326i	$-0.401316\pi$
$272$	568.480			0.126725
$273$	138.375	−	474.446i	0.0306771	−	0.105182i
$274$	−14458.5			−3.18784
$275$	1174.92	+	2035.03i	0.257638	+	0.446242i
$276$	1402.53	−	2429.26i	0.305878	−	0.529797i
$277$	1256.56	−	2176.42i	0.272560	−	0.472088i	−0.696957	−	0.717113i	$-0.745463\pi$
$277$	1256.56	−	2176.42i	0.272560	−	0.472088i	0.969517	+	0.245026i	$0.0787964\pi$
$278$	7452.07	+	12907.4i	1.60772	+	2.78465i
$279$	5544.87			1.18983
$280$	−5881.99	−	6146.48i	−1.25541	−	1.31187i
$281$	240.039			0.0509592			0.0254796	−	0.999675i	$-0.491889\pi$
$281$	240.039			0.0509592			0.0254796	+	0.999675i	$0.491889\pi$
$282$	567.233	+	982.476i	0.119781	+	0.207467i
$283$	−490.689	+	849.899i	−0.103069	+	0.178520i	−0.912948	−	0.408077i	$-0.866200\pi$
$283$	−490.689	+	849.899i	−0.103069	+	0.178520i	0.809879	+	0.586597i	$0.199533\pi$
$284$	9396.95	−	16276.0i	1.96340	−	3.40071i
$285$	599.210	+	1037.86i	0.124541	+	0.215711i
$286$	3355.27			0.693711
$287$	737.600	−	180.358i	0.151704	−	0.0370947i
$288$	8825.50			1.80572
$289$	2450.16	+	4243.80i	0.498709	+	0.863789i
$290$	−2762.06	+	4784.03i	−0.559289	+	0.968717i
$291$	−354.311	+	613.684i	−0.0713748	+	0.123625i
$292$	800.628	+	1386.73i	0.160456	+	0.277918i
$293$	−8089.43			−1.61293			−0.806467	−	0.591280i	$-0.798623\pi$
$293$	−8089.43			−1.61293			−0.806467	+	0.591280i	$0.798623\pi$
$294$	−2342.11	+	1218.22i	−0.464607	+	0.241660i
$295$	−4191.15			−0.827180
$296$	1194.61	+	2069.13i	0.234579	+	0.406302i
$297$	1340.43	−	2321.70i	0.261885	−	0.453598i
$298$	−9061.35	+	15694.7i	−1.76144	+	3.05091i
$299$	−891.249	−	1543.69i	−0.172382	−	0.298575i
$300$	−1908.29			−0.367251
$301$	3126.38	−	764.462i	0.598677	−	0.146388i
$302$	631.227			0.120275
$303$	230.016	+	398.399i	0.0436108	+	0.0755361i
$304$	−8531.94	+	14777.8i	−1.60967	+	2.78803i
$305$	−2455.40	+	4252.88i	−0.460970	+	0.798423i
$306$	−231.944	−	401.738i	−0.0433311	−	0.0750517i
$307$	4242.75			0.788750			0.394375	−	0.918950i	$-0.370961\pi$
$307$	4242.75			0.788750			0.394375	+	0.918950i	$0.370961\pi$
$308$	−8784.24	−	9179.24i	−1.62509	−	1.69817i
$309$	−79.8418			−0.0146992
$310$	4465.68	+	7734.79i	0.818173	+	1.41712i
$311$	4991.20	−	8645.01i	0.910048	−	1.57625i	0.0960537	−	0.995376i	$-0.469378\pi$
$311$	4991.20	−	8645.01i	0.910048	−	1.57625i	0.813994	−	0.580873i	$-0.197289\pi$
$312$	−802.861	+	1390.60i	−0.145683	+	0.252330i
$313$	−3108.15	−	5383.47i	−0.561287	−	0.972178i	−0.997385	−	0.0722782i	$-0.976973\pi$
$313$	−3108.15	−	5383.47i	−0.561287	−	0.972178i	0.436097	−	0.899899i	$-0.356360\pi$
$314$	4650.45			0.835797
$315$	−983.482	+	3372.06i	−0.175914	+	0.603155i
$316$	−4090.40			−0.728174
$317$	2651.21	+	4592.03i	0.469738	+	0.813609i	0.999401	−	0.0345983i	$-0.0110152\pi$
$317$	2651.21	+	4592.03i	0.469738	+	0.813609i	−0.529664	+	0.848208i	$0.677682\pi$
$318$	2045.00	−	3542.05i	0.360623	−	0.624617i
$319$	−2430.81	+	4210.28i	−0.426643	+	0.738967i
$320$	2234.34	+	3869.98i	0.390322	+	0.676058i
$321$	419.525			0.0729458
$322$	−2666.00	+	9140.89i	−0.461399	+	1.58199i
$323$	380.836			0.0656046
$324$	−5444.61	−	9430.34i	−0.933575	−	1.61700i
$325$	−606.320	+	1050.18i	−0.103485	+	0.179241i
$326$	5386.72	−	9330.07i	0.915162	−	1.58511i
$327$	1245.75	+	2157.71i	0.210674	+	0.364897i
$328$	−2467.10			−0.415313
$329$	−1887.36	−	1972.23i	−0.316272	−	0.330494i
$330$	2069.31			0.345188
$331$	1050.90	+	1820.22i	0.174510	+	0.302260i	0.939992	−	0.341198i	$-0.110833\pi$
$331$	1050.90	+	1820.22i	0.174510	+	0.302260i	−0.765482	+	0.643458i	$0.777499\pi$
$332$	−9256.27	+	16032.3i	−1.53013	+	2.65027i
$333$	493.229	−	854.297i	0.0811675	−	0.140586i
$334$	−4698.77	−	8138.52i	−0.769777	−	1.33329i
$335$	−324.693			−0.0529548
$336$	4215.73	−	1030.83i	0.684485	−	0.167370i
$337$	−6384.39			−1.03199			−0.515994	−	0.856592i	$-0.672577\pi$
$337$	−6384.39			−1.03199			−0.515994	+	0.856592i	$0.672577\pi$
$338$	−4892.63	−	8474.29i	−0.787350	−	1.36373i
$339$	−726.495	+	1258.33i	−0.116395	+	0.201602i
$340$	264.834	−	458.707i	0.0422431	−	0.0731672i
$341$	3930.11	+	6807.15i	0.624127	+	1.08102i
$342$	13924.3			2.20159
$343$	4778.14	−	4186.04i	0.752173	−	0.658965i
$344$	−10457.0			−1.63896
$345$	−549.665	−	952.047i	−0.0857766	−	0.148570i
$346$	1658.10	−	2871.92i	0.257630	−	0.446229i
$347$	3546.66	−	6142.99i	0.548688	−	0.950355i	−0.449677	−	0.893191i	$-0.648461\pi$
$347$	3546.66	−	6142.99i	0.548688	−	0.950355i	0.998365	−	0.0571638i	$-0.0182057\pi$
$348$	−1974.04	−	3419.14i	−0.304079	−	0.526681i
$349$	−6799.57			−1.04290			−0.521451	−	0.853281i	$-0.674609\pi$
$349$	−6799.57			−1.04290			−0.521451	+	0.853281i	$0.674609\pi$
$350$	6292.29	−	1538.59i	0.960963	−	0.234974i
$351$	1383.46			0.210381
$352$	6255.36	+	10834.6i	0.947193	+	1.64059i
$353$	−1212.91	+	2100.83i	−0.182881	+	0.316759i	−0.942860	−	0.333188i	$-0.891876\pi$
$353$	−1212.91	+	2100.83i	−0.182881	+	0.316759i	0.759980	+	0.649947i	$0.225209\pi$
$354$	2112.81	−	3659.49i	0.317216	−	0.549434i
$355$	−3682.75	−	6378.71i	−0.550592	−	0.953653i
$356$	9666.59			1.43912
$357$	−66.9679	−	69.9792i	−0.00992805	−	0.0103745i
$358$	−4720.88			−0.696945
$359$	−5821.07	−	10082.4i	−0.855779	−	1.48225i	−0.875921	−	0.482455i	$-0.839745\pi$
$359$	−5821.07	−	10082.4i	−0.855779	−	1.48225i	0.0201419	−	0.999797i	$-0.493588\pi$
$360$	5706.21	−	9883.45i	0.835399	−	1.44695i
$361$	−2286.21	+	3959.83i	−0.333315	+	0.577319i
$362$	−2637.51	−	4568.29i	−0.382940	−	0.663271i
$363$	−133.136			−0.0192502
$364$	1835.76	−	6294.27i	0.264341	−	0.906344i
$365$	627.547			0.0899926
$366$	−2475.59	−	4287.85i	−0.353556	−	0.612376i
$367$	6398.00	−	11081.7i	0.910008	−	1.57618i	0.0959570	−	0.995385i	$-0.469409\pi$
$367$	6398.00	−	11081.7i	0.910008	−	1.57618i	0.814051	−	0.580794i	$-0.197258\pi$
$368$	7826.48	−	13555.9i	1.10865	−	1.92024i
$369$	509.305	+	882.143i	0.0718520	+	0.124451i
$370$	1588.93			0.223256
$371$	−2755.54	+	9447.90i	−0.385608	+	1.32213i
$372$	−6383.23			−0.889664
$373$	668.172	+	1157.31i	0.0927523	+	0.160652i	0.908668	−	0.417519i	$-0.137100\pi$
$373$	668.172	+	1157.31i	0.0927523	+	0.160652i	−0.815916	+	0.578170i	$0.803767\pi$
$374$	328.795	−	569.490i	0.0454588	−	0.0787370i
$375$	−1074.49	+	1861.07i	−0.147963	+	0.256280i
$376$	4434.62	+	7680.98i	0.608239	+	1.05350i
$377$	−2508.84			−0.342737
$378$	−5109.50	−	5339.26i	−0.695250	−	0.726513i
$379$	−4334.88			−0.587514			−0.293757	−	0.955880i	$-0.594906\pi$
$379$	−4334.88			−0.587514			−0.293757	+	0.955880i	$0.594906\pi$
$380$	7949.44	+	13768.8i	1.07315	+	1.85875i
$381$	654.933	−	1134.38i	0.0880662	−	0.152535i
$382$	12235.7	−	21192.9i	1.63883	−	2.83854i
$383$	793.545	+	1374.46i	0.105870	+	0.183372i	0.914093	−	0.405504i	$-0.132904\pi$
$383$	793.545	+	1374.46i	0.105870	+	0.183372i	−0.808223	+	0.588876i	$0.799571\pi$
$384$	−332.767			−0.0442225
$385$	−4836.77	+	1182.69i	−0.640272	+	0.156559i
$386$	14970.9			1.97409
$387$	2158.73	+	3739.04i	0.283552	+	0.491127i
$388$	−4700.48	+	8141.47i	−0.615027	+	1.06526i
$389$	2939.83	−	5091.93i	0.383175	−	0.663678i	−0.608339	−	0.793677i	$-0.708164\pi$
$389$	2939.83	−	5091.93i	0.383175	−	0.663678i	0.991514	+	0.129999i	$0.0414973\pi$
$390$	533.935	+	924.803i	0.0693253	+	0.120075i
$391$	−349.347			−0.0451847
$392$	−18310.6	+	9524.03i	−2.35924	+	1.22713i
$393$	−4154.82			−0.533290
$394$	10306.6	+	17851.6i	1.31787	+	2.28262i
$395$	−801.532	+	1388.29i	−0.102100	+	0.176842i
$396$	8521.73	−	14760.1i	1.08140	−	1.87303i
$397$	4985.16	+	8634.55i	0.630221	+	1.09158i	0.987506	+	0.157580i	$0.0503692\pi$
$397$	4985.16	+	8634.55i	0.630221	+	1.09158i	−0.357285	+	0.933996i	$0.616297\pi$
$398$	7165.07			0.902393
$399$	2824.20	−	690.572i	0.354353	−	0.0866462i
$400$	−10648.8			−1.33110
$401$	4573.22	+	7921.05i	0.569516	+	0.986430i	0.996614	+	0.0822246i	$0.0262025\pi$
$401$	4573.22	+	7921.05i	0.569516	+	0.986430i	−0.427098	+	0.904205i	$0.640464\pi$
$402$	163.681	−	283.505i	0.0203077	−	0.0351739i
$403$	−2028.13	+	3512.83i	−0.250691	+	0.434210i
$404$	3051.52	+	5285.38i	0.375789	+	0.650885i
$405$	−4267.58			−0.523600
$406$	9265.81	+	9682.46i	1.13265	+	1.18358i
$407$	1398.37			0.170306
$408$	157.350	+	272.539i	0.0190932	+	0.0330703i
$409$	6893.95	−	11940.7i	0.833457	−	1.44359i	−0.0618229	−	0.998087i	$-0.519691\pi$
$409$	6893.95	−	11940.7i	0.833457	−	1.44359i	0.895280	−	0.445503i	$-0.146975\pi$
$410$	−820.361	+	1420.91i	−0.0988164	+	0.171155i
$411$	−2024.88	−	3507.20i	−0.243017	−	0.420918i
$412$	−1059.23			−0.126661
$413$	−2846.91	+	9761.16i	−0.339194	+	1.16299i
$414$	−12773.0			−1.51633
$415$	3627.61	+	6283.21i	0.429090	+	0.743206i
$416$	−3228.08	+	5591.20i	−0.380456	+	0.658970i
$417$	−2087.30	+	3615.31i	−0.245121	+	0.424562i
$418$	9869.34	+	17094.2i	1.15484	+	2.00025i
$419$	8640.54			1.00744			0.503721	−	0.863867i	$-0.331964\pi$
$419$	8640.54			1.00744			0.503721	+	0.863867i	$0.331964\pi$
$420$	1132.18	−	3881.89i	0.131535	−	0.450993i
$421$	−14901.0			−1.72502			−0.862508	−	0.506044i	$-0.831107\pi$
$421$	−14901.0			−1.72502			−0.862508	+	0.506044i	$0.831107\pi$
$422$	3788.24	+	6561.43i	0.436988	+	0.756885i
$423$	1830.96	−	3171.31i	0.210459	−	0.364526i
$424$	15987.8	−	27691.7i	1.83122	−	3.17176i
$425$	118.831	+	205.821i	0.0135627	+	0.0234913i
$426$	7426.07			0.844588
$427$	8237.06	+	8607.46i	0.933535	+	0.975513i
$428$	5565.65			0.628565
$429$	469.900	+	813.891i	0.0528834	+	0.0915968i
$430$	−3477.17	+	6022.63i	−0.389963	+	0.675435i
$431$	3470.00	−	6010.21i	0.387805	−	0.671698i	−0.604349	−	0.796720i	$-0.706567\pi$
$431$	3470.00	−	6010.21i	0.387805	−	0.671698i	0.992154	+	0.125022i	$0.0399001\pi$
$432$	6074.43	+	10521.2i	0.676518	+	1.17176i
$433$	−13346.5			−1.48127			−0.740637	−	0.671905i	$-0.765476\pi$
$433$	−13346.5			−1.48127			−0.740637	+	0.671905i	$0.765476\pi$
$434$	21047.7	−	5146.57i	2.32793	−	0.569224i
$435$	−1547.29			−0.170544
$436$	16526.8	+	28625.3i	1.81535	+	3.14427i
$437$	5243.11	−	9081.34i	0.573941	−	0.994095i
$438$	−316.354	+	547.941i	−0.0345113	+	0.0597754i
$439$	−4950.28	−	8574.13i	−0.538186	−	0.932166i	−0.999002	−	0.0446702i	$-0.985776\pi$
$439$	−4950.28	−	8574.13i	−0.538186	−	0.932166i	0.460815	−	0.887496i	$-0.347557\pi$
$440$	16177.9			1.75284
$441$	7185.46	+	4581.05i	0.775883	+	0.494660i
$442$	339.350			0.0365186
$443$	5037.72	+	8725.59i	0.540292	+	0.935814i	0.998887	+	0.0471681i	$0.0150197\pi$
$443$	5037.72	+	8725.59i	0.540292	+	0.935814i	−0.458595	+	0.888646i	$0.651647\pi$
$444$	−567.802	+	983.463i	−0.0606908	+	0.105120i
$445$	1894.21	−	3280.87i	0.201785	−	0.349502i
$446$	12635.9	+	21886.0i	1.34154	+	2.32362i
$447$	−5076.11			−0.537118
$448$	10530.9	−	2575.01i	1.11057	−	0.271557i
$449$	3733.61			0.392428			0.196214	−	0.980561i	$-0.437135\pi$
$449$	3733.61			0.392428			0.196214	+	0.980561i	$0.437135\pi$
$450$	4344.76	+	7525.35i	0.455142	+	0.788330i
$451$	−721.974	+	1250.50i	−0.0753801	+	0.130562i
$452$	−9638.08	+	16693.6i	−1.00296	+	1.73718i
$453$	88.4023	+	153.117i	0.00916888	+	0.0158810i
$454$	10255.7			1.06019
$455$	−1776.57	−	1856.45i	−0.183048	−	0.191279i
$456$	−9446.27			−0.970092
$457$	8323.07	+	14416.0i	0.851940	+	1.47560i	0.879455	+	0.475982i	$0.157907\pi$
$457$	8323.07	+	14416.0i	0.851940	+	1.47560i	−0.0275148	+	0.999621i	$0.508759\pi$
$458$	542.582	−	939.779i	0.0553563	−	0.0958799i
$459$	135.571	−	234.815i	0.0137863	−	0.0238785i
$460$	−7292.15	−	12630.4i	−0.739127	−	1.28021i
$461$	−2065.33			−0.208660			−0.104330	−	0.994543i	$-0.533270\pi$
$461$	−2065.33			−0.208660			−0.104330	+	0.994543i	$0.533270\pi$
$462$	1405.62	−	4819.42i	0.141548	−	0.485324i
$463$	8816.23			0.884935			0.442468	−	0.896784i	$-0.354103\pi$
$463$	8816.23			0.884935			0.442468	+	0.896784i	$0.354103\pi$
$464$	−11015.6	−	19079.7i	−1.10213	−	1.90895i
$465$	−1250.82	+	2166.49i	−0.124743	+	0.216061i
$466$	6129.39	−	10616.4i	0.609310	−	1.05536i
$467$	−9128.13	−	15810.4i	−0.904496	−	1.56663i	−0.821593	−	0.570075i	$-0.806914\pi$
$467$	−9128.13	−	15810.4i	−0.904496	−	1.56663i	−0.0829026	−	0.996558i	$-0.526419\pi$
$468$	8795.29			0.868723
$469$	−220.553	+	756.208i	−0.0217147	+	0.0744530i
$470$	5898.41			0.578879
$471$	651.288	+	1128.06i	0.0637150	+	0.110358i
$472$	16517.9	−	28609.8i	1.61080	−	2.78999i
$473$	−3060.15	+	5300.33i	−0.297475	+	0.515242i
$474$	−808.123	−	1399.71i	−0.0783087	−	0.135635i
$475$	−7133.81			−0.689099
$476$	−888.432	−	928.382i	−0.0855488	−	0.0893956i
$477$	−13202.0			−1.26725
$478$	26.4324	+	45.7822i	0.00252926	+	0.00438081i
$479$	−8006.96	+	13868.5i	−0.763773	+	1.32289i	0.177120	+	0.984189i	$0.443322\pi$
$479$	−8006.96	+	13868.5i	−0.763773	+	1.32289i	−0.940893	+	0.338705i	$0.890011\pi$
$480$	−1990.87	+	3448.29i	−0.189313	+	0.327901i
$481$	360.814	+	624.949i	0.0342032	+	0.0592416i
$482$	−28518.5			−2.69498
$483$	−2590.68	+	633.473i	−0.244058	+	0.0596770i
$484$	−1766.26			−0.165877
$485$	1842.16	+	3190.71i	0.172470	+	0.298728i
$486$	7538.27	−	13056.7i	0.703586	−	1.21865i
$487$	−5477.52	+	9487.34i	−0.509672	+	0.882777i	0.490266	+	0.871573i	$0.336900\pi$
$487$	−5477.52	+	9487.34i	−0.509672	+	0.882777i	−0.999937	+	0.0112040i	$0.996434\pi$
$488$	−19354.1	−	33522.4i	−1.79533	−	3.10960i
$489$	3017.60			0.279061
$490$	−603.348	+	13712.8i	−0.0556255	+	1.26424i
$491$	−17514.3			−1.60980			−0.804898	−	0.593413i	$-0.797780\pi$
$491$	−17514.3			−1.60980			−0.804898	+	0.593413i	$0.797780\pi$
$492$	−586.310	−	1015.52i	−0.0537254	−	0.0930551i
$493$	−245.850	+	425.825i	−0.0224595	+	0.0389010i
$494$	−5093.08	+	8821.47i	−0.463863	+	0.803434i
$495$	−3339.74	−	5784.60i	−0.303253	−	0.525250i
$496$	−35620.0			−3.22457
$497$	−17357.6	+	4244.26i	−1.56658	+	0.383061i
$498$	−7314.89			−0.658209
$499$	4497.06	+	7789.14i	0.403439	+	0.698777i	0.994138	−	0.108115i	$-0.0344813\pi$
$499$	4497.06	+	7789.14i	0.403439	+	0.698777i	−0.590699	+	0.806892i	$0.701148\pi$
$500$	−14254.7	+	24689.9i	−1.27498	+	2.20834i
$501$	1316.11	−	2279.57i	0.117364	−	0.203281i
$502$	−7025.66	−	12168.8i	−0.624642	−	1.08191i
$503$	−41.3189			−0.00366267			−0.00183133	−	0.999998i	$-0.500583\pi$
$503$	−41.3189			−0.00366267			−0.00183133	+	0.999998i	$0.500583\pi$
$504$	−19142.5	−	20003.2i	−1.69181	−	1.76789i
$505$	2391.83			0.210763
$506$	−9053.30	−	15680.8i	−0.795392	−	1.37766i
$507$	1370.41	−	2373.62i	0.120043	−	0.207921i
$508$	8688.70	−	15049.3i	0.758856	−	1.31438i
$509$	−3539.47	−	6130.55i	−0.308221	−	0.533854i	0.669752	−	0.742585i	$-0.266400\pi$
$509$	−3539.47	−	6130.55i	−0.308221	−	0.533854i	−0.977973	+	0.208730i	$0.933067\pi$
$510$	209.289			0.0181715
$511$	426.271	−	1461.55i	0.0369024	−	0.126527i
$512$	20133.4			1.73785
$513$	4069.38	+	7048.37i	0.350229	+	0.606614i
$514$	11151.8	−	19315.5i	0.956974	−	1.65753i
$515$	−207.560	+	359.504i	−0.0177596	+	0.0307605i
$516$	−2485.12	−	4304.36i	−0.212018	−	0.367227i
$517$	5191.00			0.441586
$518$	1079.31	−	3700.61i	0.0915483	−	0.313891i
$519$	928.857			0.0785593
$520$	4174.30	+	7230.09i	0.352029	+	0.609732i
$521$	7009.03	−	12140.0i	0.589388	−	1.02085i	−0.404925	−	0.914350i	$-0.632702\pi$
$521$	7009.03	−	12140.0i	0.589388	−	1.02085i	0.994313	−	0.106500i	$-0.0339645\pi$
$522$	−8988.91	+	15569.2i	−0.753705	+	1.30545i
$523$	2320.96	+	4020.02i	0.194051	+	0.336106i	0.946589	−	0.322443i	$-0.104504\pi$
$523$	2320.96	+	4020.02i	0.194051	+	0.336106i	−0.752538	+	0.658549i	$0.771171\pi$
$524$	−55120.1			−4.59529
$525$	1254.44	+	1310.85i	0.104282	+	0.108972i
$526$	26694.7			2.21282
$527$	397.489	+	688.470i	0.0328555	+	0.0569075i
$528$	−4126.42	+	7147.16i	−0.340112	+	0.589092i
$529$	1273.91	−	2206.47i	0.104702	−	0.181349i
$530$	−10632.5	−	18416.1i	−0.871411	−	1.50933i
$531$	−13639.8			−1.11472
$532$	37467.4	−	9161.50i	3.05341	−	0.746619i
$533$	−745.150			−0.0605554
$534$	1909.79	+	3307.85i	0.154765	+	0.268061i
$535$	1090.61	−	1889.00i	0.0881333	−	0.152651i
$536$	1279.66	−	2216.43i	0.103121	−	0.178611i
$537$	−661.151	−	1145.15i	−0.0531300	−	0.0920238i
$538$	5456.01			0.437222
$539$	−530.988	+	12068.2i	−0.0424328	+	0.964403i
$540$	11319.4			0.902056
$541$	4609.87	+	7984.53i	0.366347	+	0.634532i	0.988991	−	0.147973i	$-0.0472749\pi$
$541$	4609.87	+	7984.53i	0.366347	+	0.634532i	−0.622644	+	0.782505i	$0.713942\pi$
$542$	15719.9	−	27227.7i	1.24581	−	2.15781i
$543$	738.756	−	1279.56i	0.0583850	−	0.101126i
$544$	632.663	+	1095.80i	0.0498625	+	0.0863644i
$545$	12954.0			1.01815
$546$	2516.55	−	615.345i	0.197250	−	0.0482314i
$547$	−23869.8			−1.86581			−0.932904	−	0.360125i	$-0.882734\pi$
$547$	−23869.8			−1.86581			−0.932904	+	0.360125i	$0.882734\pi$
$548$	−26863.2	−	46528.4i	−2.09405	−	3.62700i
$549$	−7990.91	+	13840.7i	−0.621209	+	1.07596i
$550$	−6158.99	+	10667.7i	−0.477491	+	0.827039i
$551$	−7379.60	−	12781.8i	−0.570565	−	0.988248i
$552$	8665.22			0.668145
$553$	2688.88	+	2809.79i	0.206768	+	0.216065i
$554$	13173.8			1.01029
$555$	222.527	+	385.428i	0.0170194	+	0.0294784i
$556$	−27691.2	+	47962.6i	−2.11218	+	3.65840i
$557$	−9093.16	+	15749.8i	−0.691723	+	1.19810i	0.279550	+	0.960131i	$0.409815\pi$
$557$	−9093.16	+	15749.8i	−0.691723	+	1.19810i	−0.971273	+	0.237968i	$0.923519\pi$
$558$	14533.2	+	25172.2i	1.10258	+	1.90972i
$559$	−3158.38			−0.238972
$560$	6317.85	−	21662.0i	0.476747	−	1.63462i
$561$	184.189			0.0138618
$562$	629.147	+	1089.71i	0.0472224	+	0.0817915i
$563$	−121.683	+	210.762i	−0.00910895	+	0.0157772i	−0.870544	−	0.492091i	$-0.836233\pi$
$563$	−121.683	+	210.762i	−0.00910895	+	0.0157772i	0.861435	+	0.507868i	$0.169566\pi$
$564$	−2107.79	+	3650.80i	−0.157365	+	0.272564i
$565$	3777.25	+	6542.39i	0.281257	+	0.487151i
$566$	−5144.42			−0.382043
$567$	−2898.83	+	9939.18i	−0.214708	+	0.736167i
$568$	58056.9			4.28876
$569$	2669.75	+	4624.14i	0.196699	+	0.340693i	0.947456	−	0.319886i	$-0.103645\pi$
$569$	2669.75	+	4624.14i	0.196699	+	0.340693i	−0.750757	+	0.660578i	$0.770311\pi$
$570$	−3141.08	+	5440.51i	−0.230816	+	0.399786i
$571$	3478.18	−	6024.39i	0.254917	−	0.441528i	−0.709956	−	0.704246i	$-0.751285\pi$
$571$	3478.18	−	6024.39i	0.254917	−	0.441528i	0.964873	+	0.262717i	$0.0846186\pi$
$572$	6233.95	+	10797.5i	0.455690	+	0.789278i
$573$	6854.36			0.499730
$574$	2752.04	+	2875.79i	0.200118	+	0.209117i
$575$	6543.96			0.474612
$576$	7271.47	+	12594.5i	0.526003	+	0.911064i
$577$	−10680.2	+	18498.6i	−0.770575	+	1.33467i	0.166673	+	0.986012i	$0.446697\pi$
$577$	−10680.2	+	18498.6i	−0.770575	+	1.33467i	−0.937248	+	0.348663i	$0.886636\pi$
$578$	−12843.8	+	22246.1i	−0.924277	+	1.60089i
$579$	2096.65	+	3631.50i	0.150490	+	0.260657i
$580$	−20527.2			−1.46956
$581$	17097.7	−	4180.72i	1.22088	−	0.298529i
$582$	−3714.62			−0.264563
$583$	−9357.37	−	16207.4i	−0.664738	−	1.15136i
$584$	−2473.25	+	4283.79i	−0.175246	+	0.303535i
$585$	1723.48	−	2985.15i	0.121807	−	0.210976i
$586$	−21202.5	−	36723.9i	−1.49466	−	2.58882i
$587$	9725.11			0.683813			0.341907	−	0.939734i	$-0.388927\pi$
$587$	9725.11			0.683813			0.341907	+	0.939734i	$0.388927\pi$
$588$	−8271.86	−	5273.68i	−0.580146	−	0.369869i
$589$	−23862.6			−1.66934
$590$	−10985.1	−	19026.7i	−0.766523	−	1.32766i
$591$	−2886.85	+	5000.17i	−0.200929	+	0.348020i
$592$	−3168.48	+	5487.98i	−0.219973	+	0.381004i
$593$	12472.2	+	21602.5i	0.863698	+	1.49597i	0.868334	+	0.495980i	$0.165191\pi$
$593$	12472.2	+	21602.5i	0.863698	+	1.49597i	−0.00463622	+	0.999989i	$0.501476\pi$
$594$	14053.2			0.970724
$595$	−489.188	+	119.616i	−0.0337055	+	0.00824165i
$596$	−67342.4			−4.62827
$597$	1003.45	+	1738.03i	0.0687917	+	0.119151i
$598$	4671.96	−	8092.07i	0.319483	−	0.553360i
$599$	3327.67	−	5763.69i	0.226987	−	0.393152i	−0.729927	−	0.683525i	$-0.760446\pi$
$599$	3327.67	−	5763.69i	0.226987	−	0.393152i	0.956914	+	0.290373i	$0.0937793\pi$
$600$	−2947.49	−	5105.20i	−0.200551	−	0.347365i
$601$	4860.95			0.329921			0.164960	−	0.986300i	$-0.447250\pi$
$601$	4860.95			0.329921			0.164960	+	0.986300i	$0.447250\pi$
$602$	11664.8	+	12189.3i	0.789734	+	0.825246i
$603$	−1056.69			−0.0713625
$604$	1172.79	+	2031.34i	0.0790071	+	0.136844i
$605$	−346.106	+	599.473i	−0.0232582	+	0.0402844i
$606$	−1205.75	+	2088.42i	−0.0808256	+	0.139994i
$607$	1020.14	+	1766.94i	0.0682148	+	0.118151i	0.898116	−	0.439760i	$-0.144936\pi$
$607$	1020.14	+	1766.94i	0.0682148	+	0.118151i	−0.829901	+	0.557911i	$0.811603\pi$
$608$	−37980.9			−2.53343
$609$	−1051.02	+	3603.63i	−0.0699335	+	0.239780i
$610$	−25742.6			−1.70867
$611$	1339.41	+	2319.93i	0.0886853	+	0.153608i
$612$	861.882	−	1492.82i	0.0569273	−	0.0986010i
$613$	10989.2	−	19033.9i	0.724063	−	1.25411i	−0.235295	−	0.971924i	$-0.575606\pi$
$613$	10989.2	−	19033.9i	0.724063	−	1.25411i	0.959358	−	0.282191i	$-0.0910610\pi$
$614$	11120.3	+	19261.0i	0.730911	+	1.26598i
$615$	−459.560			−0.0301321
$616$	10989.1	−	37678.2i	0.718771	−	2.46444i
$617$	−3997.68			−0.260843			−0.130422	−	0.991459i	$-0.541633\pi$
$617$	−3997.68			−0.260843			−0.130422	+	0.991459i	$0.541633\pi$
$618$	−209.267	−	362.461i	−0.0136213	−	0.0235927i
$619$	1006.51	−	1743.32i	0.0653552	−	0.113199i	−0.831496	−	0.555530i	$-0.812515\pi$
$619$	1006.51	−	1743.32i	0.0653552	−	0.113199i	0.896851	+	0.442332i	$0.145849\pi$
$620$	−16594.1	+	28741.8i	−1.07489	+	1.86177i
$621$	−3732.90	−	6465.58i	−0.241218	−	0.417801i
$622$	52328.1			3.37326
$623$	−6354.46	−	6640.20i	−0.408645	−	0.427021i
$624$	−4258.88			−0.273224
$625$	1416.41	+	2453.30i	0.0906504	+	0.157011i
$626$	16293.0	−	28220.3i	1.04026	−	1.80178i
$627$	−2764.37	+	4788.02i	−0.176074	+	0.304968i
$628$	8640.34	+	14965.5i	0.549024	+	0.950938i
$629$	141.430			0.00896532
$630$	−17886.0	+	4373.47i	−1.13110	+	0.276577i
$631$	−10583.9			−0.667731			−0.333866	−	0.942621i	$-0.608353\pi$
$631$	−10583.9			−0.667731			−0.333866	+	0.942621i	$0.608353\pi$
$632$	−6317.89	−	10942.9i	−0.397646	−	0.688743i
$633$	−1061.07	+	1837.83i	−0.0666254	+	0.115399i
$634$	−13897.7	+	24071.6i	−0.870584	+	1.50790i
$635$	−3405.18	−	5897.94i	−0.212804	−	0.368587i
$636$	15198.1			0.947553
$637$	−5530.43	+	2876.59i	−0.343993	+	0.178924i
$638$	−25484.7			−1.58143
$639$	−11985.2	−	20759.0i	−0.741984	−	1.28515i
$640$	−865.074	+	1498.35i	−0.0534297	+	0.0925430i
$641$	10032.6	−	17377.0i	0.618196	−	1.07075i	−0.371619	−	0.928385i	$-0.621197\pi$
$641$	10032.6	−	17377.0i	0.618196	−	1.07075i	0.989815	−	0.142361i	$-0.0454694\pi$
$642$	1099.58	+	1904.53i	0.0675966	+	0.117081i
$643$	24092.2			1.47761			0.738805	−	0.673919i	$-0.235390\pi$
$643$	24092.2			1.47761			0.738805	+	0.673919i	$0.235390\pi$
$644$	−34369.4	+	8403.99i	−2.10302	+	0.514229i
$645$	−1947.89			−0.118911
$646$	998.178	+	1728.90i	0.0607938	+	0.105298i
$647$	675.540	−	1170.07i	0.0410483	−	0.0710977i	−0.844771	−	0.535127i	$-0.820264\pi$
$647$	675.540	−	1170.07i	0.0410483	−	0.0710977i	0.885820	+	0.464030i	$0.153597\pi$
$648$	16819.1	−	29131.6i	1.01963	−	1.76605i
$649$	−9667.63	−	16744.8i	−0.584727	−	1.01278i
$650$	−6356.70			−0.383585
$651$	4196.10	+	4384.78i	0.252624	+	0.263983i
$652$	40033.2			2.40463
$653$	−1477.23	−	2558.64i	−0.0885275	−	0.153334i	0.818361	−	0.574704i	$-0.194883\pi$
$653$	−1477.23	−	2558.64i	−0.0885275	−	0.153334i	−0.906889	+	0.421370i	$0.861549\pi$
$654$	−6530.28	+	11310.8i	−0.390450	+	0.676279i
$655$	−10801.0	+	18707.9i	−0.644323	+	1.11600i
$656$	−3271.76	−	5666.86i	−0.194727	−	0.337277i
$657$	2042.30			0.121275
$658$	4006.59	−	13737.4i	0.237376	−	0.813888i
$659$	25668.7			1.51732			0.758659	−	0.651488i	$-0.225855\pi$
$659$	25668.7			1.51732			0.758659	+	0.651488i	$0.225855\pi$
$660$	3844.70	+	6659.21i	0.226749	+	0.392741i
$661$	−10071.1	+	17443.6i	−0.592617	+	1.02644i	0.401261	+	0.915964i	$0.368572\pi$
$661$	−10071.1	+	17443.6i	−0.592617	+	1.02644i	−0.993878	+	0.110480i	$0.964761\pi$
$662$	−5508.87	+	9541.64i	−0.323426	+	0.560191i
$663$	47.5254	+	82.3164i	0.00278391	+	0.00482187i
$664$	−57187.7			−3.34234
$665$	4232.45	−	14511.8i	0.246808	−	0.846229i
$666$	5171.05			0.300862
$667$	6769.42	+	11725.0i	0.392973	+	0.680649i
$668$	17460.2	−	30242.0i	1.01131	−	1.75164i
$669$	−3539.27	+	6130.20i	−0.204538	+	0.354271i
$670$	−851.026	−	1474.02i	−0.0490716	−	0.0849946i
$671$	−22655.3			−1.30342
$672$	6678.72	+	6979.04i	0.383389	+	0.400628i
$673$	3934.29			0.225343			0.112671	−	0.993632i	$-0.464059\pi$
$673$	3934.29			0.225343			0.112671	+	0.993632i	$0.464059\pi$
$674$	−16733.6	−	28983.4i	−0.956312	−	1.65638i
$675$	−2539.51	+	4398.55i	−0.144808	+	0.250815i
$676$	18180.6	−	31489.7i	1.03440	−	1.79163i
$677$	6864.01	+	11888.8i	0.389668	+	0.674925i	0.992405	−	0.123015i	$-0.0392564\pi$
$677$	6864.01	+	11888.8i	0.389668	+	0.674925i	−0.602737	+	0.797940i	$0.705923\pi$
$678$	−7616.63			−0.431438
$679$	8682.48	−	2123.04i	0.490726	−	0.119992i
$680$	1636.22			0.0922737
$681$	1436.30	+	2487.74i	0.0808208	+	0.139986i
$682$	−20601.8	+	35683.3i	−1.15672	+	2.00350i
$683$	9859.13	−	17076.5i	0.552341	−	0.956683i	−0.445764	−	0.895151i	$-0.647068\pi$
$683$	9859.13	−	17076.5i	0.552341	−	0.956683i	0.998105	−	0.0615324i	$-0.0195987\pi$
$684$	25870.8	+	44809.6i	1.44619	+	2.50488i
$685$	−21055.8			−1.17446
$686$	31527.1	+	10719.8i	1.75468	+	0.596625i
$687$	303.950			0.0168798
$688$	−13867.6	−	24019.5i	−0.768457	−	1.33101i
$689$	4828.87	−	8363.86i	0.267004	−	0.462464i
$690$	2881.36	−	4990.67i	0.158973	−	0.275350i
$691$	3806.89	+	6593.73i	0.209582	+	0.363006i	0.951583	−	0.307392i	$-0.0994564\pi$
$691$	3806.89	+	6593.73i	0.209582	+	0.363006i	−0.742001	+	0.670399i	$0.766123\pi$
$692$	12322.7			0.676936
$693$	−15740.9	+	3848.96i	−0.862838	+	0.210981i
$694$	37183.4			2.03381
$695$	10852.4	+	18797.0i	0.592312	+	1.02591i
$696$	6098.07	−	10562.2i	0.332108	−	0.575227i
$697$	−73.0200	+	126.474i	−0.00396819	+	0.00687311i
$698$	−17821.8	−	30868.3i	−0.966426	−	1.67390i
$699$	3433.64			0.185797
$700$	16642.1	+	17390.4i	0.898589	+	0.938995i
$701$	425.724			0.0229378			0.0114689	−	0.999934i	$-0.496349\pi$
$701$	425.724			0.0229378			0.0114689	+	0.999934i	$0.496349\pi$
$702$	3626.08	+	6280.56i	0.194954	+	0.337670i
$703$	−2122.63	+	3676.50i	−0.113878	+	0.197243i
$704$	−10307.8	+	17853.6i	−0.551831	+	0.955800i
$705$	826.061	+	1430.78i	0.0441295	+	0.0764345i
$706$	−12716.3			−0.677880
$707$	1624.69	−	5570.57i	0.0864256	−	0.296327i
$708$	15702.0			0.833500
$709$	9869.42	+	17094.3i	0.522784	+	0.905489i	0.999649	+	0.0265117i	$0.00843992\pi$
$709$	9869.42	+	17094.3i	0.522784	+	0.905489i	−0.476864	+	0.878977i	$0.658227\pi$
$710$	19305.1	−	33437.4i	1.02043	−	1.76744i
$711$	−2608.52	+	4518.09i	−0.137591	+	0.238315i
$712$	14930.7	+	25860.7i	0.785887	+	1.36120i
$713$	21889.5			1.14975
$714$	142.163	−	487.433i	0.00745143	−	0.0255486i
$715$	4886.28			0.255576
$716$	−8771.20	−	15192.2i	−0.457814	−	0.792957i
$717$	−7.40361	+	12.8234i	−0.000385625	+	0.000667922i
$718$	30514.3	−	52852.3i	1.58605	−	2.74712i
$719$	−6391.04	−	11069.6i	−0.331496	−	0.574168i	0.651309	−	0.758812i	$-0.274220\pi$
$719$	−6391.04	−	11069.6i	−0.331496	−	0.574168i	−0.982805	+	0.184644i	$0.940887\pi$
$720$	30269.3			1.56677
$721$	696.295	+	727.605i	0.0359659	+	0.0375831i
$722$	−23968.8			−1.23549
$723$	−3993.96	−	6917.74i	−0.205445	−	0.355842i
$724$	9800.74	−	16975.4i	0.503096	−	0.871388i
$725$	4605.26	−	7976.54i	0.235910	−	0.408609i
$726$	−348.952	−	604.403i	−0.0178386	−	0.0308974i
$727$	1612.28			0.0822508			0.0411254	−	0.999154i	$-0.486906\pi$
$727$	1612.28			0.0822508			0.0411254	+	0.999154i	$0.486906\pi$
$728$	19674.3	−	4810.76i	1.00162	−	0.244916i
$729$	−10870.8			−0.552293
$730$	1644.81	+	2848.90i	0.0833934	+	0.144442i
$731$	−309.501	+	536.072i	−0.0156598	+	0.0271236i
$732$	9199.09	−	15933.3i	0.464492	−	0.804524i
$733$	15861.2	+	27472.4i	0.799245	+	1.38433i	0.920108	+	0.391664i	$0.128100\pi$
$733$	15861.2	+	27472.4i	0.799245	+	1.38433i	−0.120864	+	0.992669i	$0.538566\pi$
$734$	67077.1			3.37311
$735$	−3410.81	+	1774.09i	−0.171170	+	0.0890319i
$736$	34840.5			1.74489
$737$	−748.961	−	1297.24i	−0.0374333	−	0.0648364i
$738$	−2669.80	+	4624.23i	−0.133166	+	0.230651i
$739$	17461.9	−	30244.9i	0.869209	−	1.50551i	0.00640338	−	0.999979i	$-0.497962\pi$
$739$	17461.9	−	30244.9i	0.869209	−	1.50551i	0.862806	−	0.505535i	$-0.168705\pi$
$740$	2952.16	+	5113.30i	0.146654	+	0.254012i
$741$	−2853.11			−0.141446
$742$	−50113.3	+	12253.7i	−2.47940	+	0.606263i
$743$	6981.82			0.344735			0.172367	−	0.985033i	$-0.444858\pi$
$743$	6981.82			0.344735			0.172367	+	0.985033i	$0.444858\pi$
$744$	−9859.32	−	17076.8i	−0.485834	−	0.841489i
$745$	−13196.0	+	22856.2i	−0.648947	+	1.12401i
$746$	−3502.58	+	6066.65i	−0.171902	+	0.297742i
$747$	11805.8	+	20448.2i	0.578247	+	1.00155i
$748$	2443.55			0.119445
$749$	−3658.65	−	3823.17i	−0.178483	−	0.186509i
$750$	−11265.0			−0.548453
$751$	−1376.25	−	2383.74i	−0.0668710	−	0.115824i	0.830651	−	0.556793i	$-0.187968\pi$
$751$	−1376.25	−	2383.74i	−0.0668710	−	0.115824i	−0.897522	+	0.440969i	$0.854635\pi$
$752$	−11762.0	+	20372.4i	−0.570367	+	0.987905i
$753$	1967.86	−	3408.44i	0.0952362	−	0.164954i
$754$	−6575.71	−	11389.5i	−0.317604	−	0.550106i
$755$	919.256			0.0443115
$756$	7688.90	−	26362.9i	0.369898	−	1.26827i
$757$	−13352.0			−0.641066			−0.320533	−	0.947237i	$-0.603862\pi$
$757$	−13352.0			−0.641066			−0.320533	+	0.947237i	$0.603862\pi$
$758$	−11361.8	−	19679.2i	−0.544432	−	0.942983i
$759$	2535.80	−	4392.13i	0.121270	−	0.210045i
$760$	−24556.9	+	42533.8i	−1.17207	+	2.03008i
$761$	−17492.8	−	30298.4i	−0.833264	−	1.44326i	−0.895436	−	0.445191i	$-0.853136\pi$
$761$	−17492.8	−	30298.4i	−0.833264	−	1.44326i	0.0621715	−	0.998065i	$-0.480197\pi$
$762$	6866.37			0.326433
$763$	8799.24	−	30169.9i	0.417502	−	1.43148i
$764$	90933.7			4.30611
$765$	−337.779	−	585.051i	−0.0159640	−	0.0276504i
$766$	−4159.79	+	7204.97i	−0.196213	+	0.339851i
$767$	4988.98	−	8641.17i	0.234865	−	0.406799i
$768$	2565.73	+	4443.97i	0.120550	+	0.208800i
$769$	−7824.38			−0.366911			−0.183455	−	0.983028i	$-0.558728\pi$
$769$	−7824.38			−0.366911			−0.183455	+	0.983028i	$0.558728\pi$
$770$	−18046.4	−	18857.8i	−0.844605	−	0.882584i
$771$	6247.16			0.291811
$772$	27815.3	+	48177.5i	1.29675	+	2.24605i
$773$	4190.36	−	7257.91i	0.194976	−	0.337709i	−0.751916	−	0.659258i	$-0.770870\pi$
$773$	4190.36	−	7257.91i	0.194976	−	0.337709i	0.946893	+	0.321550i	$0.104204\pi$
$774$	−11316.2	+	19600.2i	−0.525518	+	0.910224i
$775$	−7445.75	−	12896.4i	−0.345109	−	0.597746i
$776$	−29040.8			−1.34343
$777$	1048.81	−	256.456i	0.0484247	−	0.0118408i
$778$	30821.3			1.42031
$779$	−2191.82	−	3796.34i	−0.100809	−	0.174606i
$780$	−1984.06	+	3436.49i	−0.0910778	+	0.157751i
$781$	16989.8	−	29427.2i	0.778417	−	1.34826i
$782$	−915.645	−	1585.94i	−0.0418713	−	0.0725233i
$783$	−10508.0			−0.479598
$784$	−46159.1	−	29428.5i	−2.10273	−	1.34058i
$785$	6772.46			0.307923
$786$	−10889.9	−	18861.8i	−0.494184	−	0.855951i
$787$	16059.8	−	27816.4i	0.727408	−	1.25991i	−0.230568	−	0.973056i	$-0.574058\pi$
$787$	16059.8	−	27816.4i	0.727408	−	1.25991i	0.957975	−	0.286851i	$-0.0926084\pi$
$788$	−38298.5	+	66335.0i	−1.73138	+	2.99884i
$789$	3738.54	+	6475.34i	0.168689	+	0.292178i
$790$	−8403.32			−0.378451
$791$	17803.0	−	4353.17i	0.800253	−	0.195678i
$792$	52649.5			2.36215
$793$	−5845.63	−	10124.9i	−0.261771	−	0.453401i
$794$	−26132.4	+	45262.6i	−1.16801	+	2.02306i
$795$	2978.14	−	5158.28i	0.132860	−	0.230120i
$796$	13312.4	+	23057.7i	0.592770	+	1.02671i
$797$	−23594.9			−1.04865			−0.524324	−	0.851519i	$-0.675682\pi$
$797$	−23594.9			−1.04865			−0.524324	+	0.851519i	$0.675682\pi$
$798$	10537.3	+	11011.1i	0.467439	+	0.488458i
$799$	525.015			0.0232462
$800$	−11851.0	−	20526.6i	−0.523747	−	0.907156i
$801$	6164.56	−	10677.3i	0.271928	−	0.470992i
$802$	−23973.0	+	41522.4i	−1.05551	+	1.82819i
$803$	1447.55	+	2507.23i	0.0636150	+	0.110184i
$804$	1216.45			0.0533594
$805$	−3882.50	+	13311.9i	−0.169988	+	0.582835i
$806$	−21263.1			−0.929233
$807$	764.104	+	1323.47i	0.0333305	+	0.0577302i
$808$	−9426.55	+	16327.3i	−0.410427	+	0.710880i
$809$	12645.5	−	21902.6i	0.549557	−	0.951861i	−0.448748	−	0.893658i	$-0.648130\pi$
$809$	12645.5	−	21902.6i	0.549557	−	0.951861i	0.998305	−	0.0582023i	$-0.0185368\pi$
$810$	−11185.4	−	19373.7i	−0.485204	−	0.840399i
$811$	−41992.3			−1.81819			−0.909093	−	0.416594i	$-0.863224\pi$
$811$	−41992.3			−1.81819			−0.909093	+	0.416594i	$0.863224\pi$
$812$	−13943.4	+	47807.7i	−0.602608	+	2.06616i
$813$	8806.20			0.379886
$814$	3665.15	+	6348.23i	0.157817	+	0.273348i
$815$	7844.68	−	13587.4i	0.337162	−	0.583982i
$816$	−417.343	+	722.859i	−0.0179043	+	0.0310112i
$817$	−9290.20	−	16091.1i	−0.397825	−	0.689053i
$818$	72276.7			3.08936
$819$	−5781.70	−	6041.68i	−0.246677	−	0.257770i
$820$	−6096.78			−0.259645
$821$	8812.81	+	15264.2i	0.374628	+	0.648874i	0.990271	−	0.139151i	$-0.0444372\pi$
$821$	8812.81	+	15264.2i	0.374628	+	0.648874i	−0.615644	+	0.788025i	$0.711104\pi$
$822$	10614.5	−	18384.9i	0.450393	−	0.780104i
$823$	−1062.86	+	1840.94i	−0.0450172	+	0.0779720i	−0.887656	−	0.460507i	$-0.847668\pi$
$823$	−1062.86	+	1840.94i	−0.0450172	+	0.0779720i	0.842639	+	0.538479i	$0.181001\pi$
$824$	−1636.04	−	2833.71i	−0.0691678	−	0.119802i
$825$	−3450.22			−0.145602
$826$	−51774.9	+	12660.0i	−2.18097	+	0.533290i
$827$	−24450.9			−1.02810			−0.514051	−	0.857760i	$-0.671856\pi$
$827$	−24450.9			−1.02810			−0.514051	+	0.857760i	$0.671856\pi$
$828$	−23731.7	−	41104.5i	−0.996056	−	1.72522i
$829$	−568.128	+	984.027i	−0.0238021	+	0.0412264i	−0.877681	−	0.479245i	$-0.840910\pi$
$829$	−568.128	+	984.027i	−0.0238021	+	0.0412264i	0.853879	+	0.520472i	$0.174244\pi$
$830$	−19016.1	+	32936.8i	−0.795251	+	1.37741i
$831$	1844.97	+	3195.58i	0.0770172	+	0.133398i
$832$	−10638.7			−0.443305
$833$	−53.7038	+	1220.57i	−0.00223376	+	0.0507685i
$834$	−21883.4			−0.908585
$835$	−6842.82	−	11852.1i	−0.283600	−	0.491209i
$836$	−36673.6	+	63520.5i	−1.51720	+	2.62788i
$837$	−8494.63	+	14713.1i	−0.350797	+	0.607599i
$838$	22647.0	+	39225.8i	0.933566	+	1.61698i
$839$	18014.1			0.741259			0.370629	−	0.928781i	$-0.379142\pi$
$839$	18014.1			0.741259			0.370629	+	0.928781i	$0.379142\pi$
$840$	12133.8	−	2966.96i	0.498402	−	0.121869i
$841$	−5333.30			−0.218677
$842$	−39055.9	−	67646.7i	−1.59852	−	2.76872i
$843$	−176.222	+	305.225i	−0.00719977	+	0.0124704i
$844$	−14076.8	+	24381.7i	−0.574103	+	0.994375i
$845$	−7125.14	−	12341.1i	−0.290074	−	0.502422i
$846$	19195.9			0.780104
$847$	1161.07	+	1213.28i	0.0471014	+	0.0492194i
$848$	84809.3			3.43439
$849$	−720.468	−	1247.89i	−0.0291241	−	0.0504445i
$850$	−622.916	+	1078.92i	−0.0251363	+	0.0435373i
$851$	1947.12	−	3372.51i	0.0784330	−	0.135850i
$852$	13797.3	+	23897.7i	0.554799	+	0.960939i
$853$	6002.06			0.240922			0.120461	−	0.992718i	$-0.461563\pi$
$853$	6002.06			0.240922			0.120461	+	0.992718i	$0.461563\pi$
$854$	−17486.1	+	59954.4i	−0.700658	+	2.40234i
$855$	20278.0			0.811103
$856$	8596.51	+	14889.6i	0.343251	+	0.594528i
$857$	11069.8	−	19173.5i	0.441234	−	0.764240i	−0.556547	−	0.830816i	$-0.687874\pi$
$857$	11069.8	−	19173.5i	0.441234	−	0.764240i	0.997781	+	0.0665759i	$0.0212075\pi$
$858$	−2463.23	+	4266.45i	−0.0980110	+	0.169760i
$859$	−17092.5	−	29605.0i	−0.678915	−	1.17591i	−0.975308	−	0.220849i	$-0.929117\pi$
$859$	−17092.5	−	29605.0i	−0.678915	−	1.17591i	0.296393	−	0.955066i	$-0.404216\pi$
$860$	−25841.7			−1.02465
$861$	−312.164	+	1070.31i	−0.0123560	+	0.0423649i
$862$	36379.7			1.43747
$863$	22463.0	+	38907.0i	0.886036	+	1.53466i	0.844522	+	0.535521i	$0.179885\pi$
$863$	22463.0	+	38907.0i	0.886036	+	1.53466i	0.0415134	+	0.999138i	$0.486782\pi$
$864$	−13520.5	+	23418.2i	−0.532380	+	0.922109i
$865$	2414.69	−	4182.37i	0.0949156	−	0.164399i
$866$	−34981.4	−	60589.6i	−1.37265	−	2.37750i
$867$	−7195.01			−0.281840
$868$	55667.7	+	58170.9i	2.17683	+	2.27471i
$869$	−7395.50			−0.288694
$870$	−4055.47	−	7024.28i	−0.158038	−	0.273730i
$871$	386.502	−	669.441i	0.0150357	−	0.0260426i
$872$	−51053.6	+	88427.4i	−1.98268	+	3.43410i
$873$	5995.16	+	10383.9i	0.232423	+	0.402569i
$874$	54969.2			2.12741
$875$	26330.6	−	6438.35i	1.01730	−	0.248750i
$876$	−2351.09			−0.0906802
$877$	−12598.9	−	21822.0i	−0.485103	−	0.840222i	0.514751	−	0.857340i	$-0.327884\pi$
$877$	−12598.9	−	21822.0i	−0.485103	−	0.840222i	−0.999853	+	0.0171174i	$0.994551\pi$
$878$	25949.5	−	44945.9i	0.997442	−	1.72762i
$879$	5938.76	−	10286.2i	0.227883	−	0.394705i
$880$	21454.4	+	37160.1i	0.821849	+	1.42348i
$881$	10356.6			0.396052			0.198026	−	0.980197i	$-0.436547\pi$
$881$	10356.6			0.396052			0.198026	+	0.980197i	$0.436547\pi$
$882$	−1963.55	+	44627.1i	−0.0749616	+	1.70371i
$883$	−23262.0			−0.886555			−0.443278	−	0.896384i	$-0.646184\pi$
$883$	−23262.0			−0.886555			−0.443278	+	0.896384i	$0.646184\pi$
$884$	630.498	+	1092.05i	0.0239886	+	0.0415495i
$885$	3076.88	−	5329.32i	0.116868	−	0.202421i
$886$	−26407.9	+	45739.9i	−1.00135	+	1.73438i
$887$	−6431.10	−	11139.0i	−0.243444	−	0.421658i	0.718249	−	0.695786i	$-0.244944\pi$
$887$	−6431.10	−	11139.0i	−0.243444	−	0.421658i	−0.961693	+	0.274128i	$0.911611\pi$
$888$	−3508.04			−0.132570
$889$	−16049.3	+	3924.37i	−0.605485	+	0.148053i
$890$	19859.1			0.747952
$891$	−9843.94	−	17050.2i	−0.370128	−	0.641081i
$892$	−46953.9	+	81326.6i	−1.76248	+	3.05271i
$893$	−7879.59	+	13647.9i	−0.295275	+	0.511431i
$894$	−13304.6	−	23044.2i	−0.497731	−	0.862095i
$895$	−6875.02			−0.256767
$896$	2902.04	+	3032.53i	0.108203	+	0.113069i
$897$	2617.20			0.0974200
$898$	9785.87	+	16949.6i	0.363651	+	0.629862i
$899$	15404.6	−	26681.5i	0.571492	−	0.989852i
$900$	−16144.8	+	27963.6i	−0.597954	+	1.03569i
$901$	−946.398	−	1639.21i	−0.0349934	−	0.0606104i
$902$	−7569.23			−0.279410
$903$	−1323.13	+	4536.62i	−0.0487609	+	0.167186i
$904$	−59546.7			−2.19081
$905$	−3841.00	−	6652.81i	−0.141082	−	0.244361i
$906$	−463.408	+	802.646i	−0.0169930	+	0.0294328i
$907$	5857.83	−	10146.1i	0.214450	−	0.371438i	−0.738652	−	0.674086i	$-0.764538\pi$
$907$	5857.83	−	10146.1i	0.214450	−	0.371438i	0.953102	+	0.302649i	$0.0978708\pi$
$908$	19054.7	+	33003.7i	0.696423	+	1.20624i
$909$	7784.03			0.284026
$910$	3771.40	−	12931.0i	0.137385	−	0.471051i
$911$	−51454.2			−1.87130			−0.935650	−	0.352930i	$-0.885185\pi$
$911$	−51454.2			−1.87130			−0.935650	+	0.352930i	$0.885185\pi$
$912$	−12527.2	−	21697.8i	−0.454845	−	0.787814i
$913$	−16735.5	+	28986.7i	−0.606641	+	1.05073i
$914$	−43629.8	+	75569.1i	−1.57893	+	2.73480i
$915$	−3605.21	−	6244.40i	−0.130256	−	0.225610i
$916$	4032.37			0.145451
$917$	36233.9	+	37863.2i	1.30485	+	1.36353i
$918$	1421.33			0.0511012
$919$	−12792.0	−	22156.5i	−0.459163	−	0.795293i	0.539754	−	0.841823i	$-0.318517\pi$
$919$	−12792.0	−	22156.5i	−0.459163	−	0.795293i	−0.998917	+	0.0465294i	$0.985184\pi$
$920$	22526.4	−	39016.9i	0.807255	−	1.39821i
$921$	−3114.76	+	5394.92i	−0.111439	+	0.193017i
$922$	−5413.27	−	9376.07i	−0.193359	−	0.334907i
$923$	17535.2			0.625329
$924$	18120.8	−	4430.90i	0.645164	−	0.157755i
$925$	−2649.27			−0.0941701
$926$	23107.5	+	40023.4i	0.820043	+	1.42036i
$927$	−675.487	+	1169.98i	−0.0239330	+	0.0414532i
$928$	24518.7	−	42467.6i	0.867312	−	1.50223i
$929$	24973.3	+	43255.0i	0.881967	+	1.52761i	0.849151	+	0.528151i	$0.177114\pi$
$929$	24973.3	+	43255.0i	0.881967	+	1.52761i	0.0328168	+	0.999461i	$0.489552\pi$
$930$	−13113.7			−0.462382
$931$	−30922.9	−	19714.7i	−1.08857	−	0.694011i
$932$	45552.6			1.60099
$933$	7328.46	+	12693.3i	0.257152	+	0.445401i
$934$	47850.0	−	82878.6i	1.67634	−	2.90350i
$935$	478.824	−	829.348i	0.0167478	−	0.0290081i
$936$	13584.9	+	23529.8i	0.474398	+	0.821682i
$937$	−10887.8			−0.379603			−0.189802	−	0.981822i	$-0.560785\pi$
$937$	−10887.8			−0.379603			−0.189802	+	0.981822i	$0.560785\pi$
$938$	−4011.06	+	980.783i	−0.139622	+	0.0341404i
$939$	9127.24			0.317206
$940$	10959.0	+	18981.5i	0.380258	+	0.658626i
$941$	−9496.07	+	16447.7i	−0.328973	+	0.569797i	−0.982308	−	0.187271i	$-0.940036\pi$
$941$	−9496.07	+	16447.7i	−0.328973	+	0.569797i	0.653336	+	0.757068i	$0.273369\pi$
$942$	−3414.08	+	5913.35i	−0.118086	+	0.204530i
$943$	2010.59	+	3482.44i	0.0694313	+	0.120259i
$944$	87621.3			3.02101
$945$	−7440.97	−	7775.56i	−0.256143	−	0.267660i
$946$	−32082.8			−1.10265
$947$	−6753.02	−	11696.6i	−0.231725	−	0.401359i	0.726591	−	0.687070i	$-0.241104\pi$
$947$	−6753.02	−	11696.6i	−0.231725	−	0.401359i	−0.958316	+	0.285711i	$0.907770\pi$
$948$	3002.92	−	5201.20i	0.102880	−	0.178193i
$949$	−747.008	+	1293.86i	−0.0255520	+	0.0442574i
$950$	−18697.9	−	32385.6i	−0.638567	−	1.10603i
$951$	−7785.42			−0.265467
$952$	1111.43	−	3810.74i	0.0378378	−	0.129734i
$953$	41338.8			1.40514			0.702568	−	0.711616i	$-0.252037\pi$
$953$	41338.8			1.40514			0.702568	+	0.711616i	$0.252037\pi$
$954$	−34602.7	−	59933.7i	−1.17432	−	2.03399i
$955$	17818.9	−	30863.2i	0.603775	−	1.04577i
$956$	−98.2204	+	170.123i	−0.00332288	+	0.00575540i
$957$	−3569.09	−	6181.85i	−0.120556	−	0.208810i
$958$	−83945.6			−2.83106
$959$	−14302.5	+	49039.0i	−0.481598	+	1.65125i
$960$	−6561.24			−0.220587
$961$	−10010.5	−	17338.7i	−0.336024	−	0.582010i
$962$	−1891.40	+	3276.01i	−0.0633901	+	0.109795i
$963$	3549.31	−	6147.59i	0.118769	−	0.205715i
$964$	−52986.0	−	91774.5i	−1.77030	−	3.06624i
$965$	21802.1			0.727291
$966$	−9666.02	−	10100.7i	−0.321945	−	0.336422i
$967$	−2718.28			−0.0903972			−0.0451986	−	0.998978i	$-0.514392\pi$
$967$	−2718.28			−0.0903972			−0.0451986	+	0.998978i	$0.514392\pi$
$968$	−2728.10	−	4725.21i	−0.0905832	−	0.156895i
$969$	−279.586	+	484.257i	−0.00926894	+	0.0160543i
$970$	−9656.67	+	16725.8i	−0.319646	+	0.553644i
$971$	−21981.0	−	38072.2i	−0.726471	−	1.25829i	−0.958366	−	0.285544i	$-0.907826\pi$
$971$	−21981.0	−	38072.2i	−0.726471	−	1.25829i	0.231894	−	0.972741i	$-0.425508\pi$
$972$	56023.1			1.84871
$973$	51149.8	−	12507.1i	1.68529	−	0.412086i
$974$	−57426.7			−1.88919
$975$	−890.245	−	1541.95i	−0.0292417	−	0.0506481i
$976$	51333.3	−	88911.9i	1.68354	−	2.91598i
$977$	−13239.5	+	22931.6i	−0.433542	+	0.750917i	−0.997175	−	0.0751081i	$-0.976070\pi$
$977$	−13239.5	+	22931.6i	−0.433542	+	0.750917i	0.563633	+	0.826025i	$0.309403\pi$
$978$	7909.19	+	13699.1i	0.258597	+	0.447903i
$979$	17477.3			0.570560
$980$	−45249.7	+	23536.1i	−1.47495	+	0.767177i
$981$	42157.8			1.37207
$982$	−45905.3	−	79510.4i	−1.49175	−	2.58379i
$983$	21197.2	−	36714.5i	0.687776	−	1.19126i	−0.284779	−	0.958593i	$-0.591920\pi$
$983$	21197.2	−	36714.5i	0.687776	−	1.19126i	0.972556	−	0.232670i	$-0.0747464\pi$
$984$	1811.19	−	3137.07i	0.0586775	−	0.101632i
$985$	15009.5	+	25997.3i	0.485527	+	0.840957i
$986$	−2577.51			−0.0832501
$987$	3893.40	−	952.012i	0.125560	−	0.0307020i
$988$	−37850.9			−1.21882
$989$	8522.05	+	14760.6i	0.273999	+	0.474581i
$990$	17507.1	−	30323.1i	0.562031	−	0.973466i
$991$	9998.86	−	17318.5i	0.320509	−	0.555138i	−0.660084	−	0.751192i	$-0.729479\pi$
$991$	9998.86	−	17318.5i	0.320509	−	0.555138i	0.980593	+	0.196054i	$0.0628127\pi$
$992$	−39641.6	−	68661.3i	−1.26877	−	2.19758i
$993$	−3086.03			−0.0986225
$994$	−64762.3	−	67674.4i	−2.06653	−	2.15946i
$995$	10434.5			0.332458
$996$	−13590.8	−	23539.9i	−0.432369	−	0.748885i
$997$	−15155.3	+	26249.7i	−0.481416	+	0.833837i	−0.999773	−	0.0213276i	$-0.993211\pi$
$997$	−15155.3	+	26249.7i	−0.481416	+	0.833837i	0.518357	+	0.855165i	$0.326544\pi$
$998$	−23573.8	+	40831.0i	−0.747710	+	1.29507i
$999$	1511.23	+	2617.53i	0.0478612	+	0.0828980i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.4.e.a.165.36	✓	72
7.2	even	3	inner	287.4.e.a.247.36	yes	72
7.3	odd	6		2009.4.a.k.1.1		36
7.4	even	3		2009.4.a.j.1.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.4.e.a.165.36	✓	72	1.1	even	1	trivial
287.4.e.a.247.36	yes	72	7.2	even	3	inner
2009.4.a.j.1.1		36	7.4	even	3
2009.4.a.k.1.1		36	7.3	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	287.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.62102 + 4.53974i) q^{2} +(-0.734138 + 1.27156i) q^{3} +(-9.73948 + 16.8693i) q^{4} +(3.81699 + 6.61122i) q^{5} -7.69676 q^{6} +(17.9902 - 4.39897i) q^{7} -60.1731 q^{8} +(12.4221 + 21.5157i) q^{9} +O(q^{10})\)	\(q+(2.62102 + 4.53974i) q^{2} +(-0.734138 + 1.27156i) q^{3} +(-9.73948 + 16.8693i) q^{4} +(3.81699 + 6.61122i) q^{5} -7.69676 q^{6} +(17.9902 - 4.39897i) q^{7} -60.1731 q^{8} +(12.4221 + 21.5157i) q^{9} +(-20.0088 + 34.6563i) q^{10} +(-17.6091 + 30.4999i) q^{11} +(-14.3002 - 24.7687i) q^{12} -18.1744 q^{13} +(67.1229 + 70.1412i) q^{14} -11.2088 q^{15} +(-79.7990 - 138.216i) q^{16} +(-1.78097 + 3.08474i) q^{17} +(-65.1170 + 112.786i) q^{18} +(-53.4589 - 92.5936i) q^{19} -148.702 q^{20} +(-7.61375 + 26.1052i) q^{21} -184.615 q^{22} +(49.0387 + 84.9376i) q^{23} +(44.1754 - 76.5140i) q^{24} +(33.3612 - 57.7833i) q^{25} +(-47.6354 - 82.5070i) q^{26} -76.1216 q^{27} +(-101.008 + 346.326i) q^{28} +138.042 q^{29} +(-29.3784 - 50.8850i) q^{30} +(111.593 - 193.285i) q^{31} +(177.617 - 307.642i) q^{32} +(-25.8551 - 44.7823i) q^{33} -18.6719 q^{34} +(97.7511 + 102.147i) q^{35} -483.938 q^{36} +(-19.8529 - 34.3862i) q^{37} +(280.234 - 485.379i) q^{38} +(13.3425 - 23.1099i) q^{39} +(-229.680 - 397.818i) q^{40} +41.0000 q^{41} +(-138.467 + 33.8578i) q^{42} +173.782 q^{43} +(-343.007 - 594.106i) q^{44} +(-94.8299 + 164.250i) q^{45} +(-257.063 + 445.246i) q^{46} +(-73.6977 - 127.648i) q^{47} +234.334 q^{48} +(304.298 - 158.277i) q^{49} +349.761 q^{50} +(-2.61496 - 4.52925i) q^{51} +(177.009 - 306.589i) q^{52} +(-265.697 + 460.200i) q^{53} +(-199.516 - 345.572i) q^{54} -268.855 q^{55} +(-1082.53 + 264.700i) q^{56} +156.985 q^{57} +(361.812 + 626.676i) q^{58} +(-274.506 + 475.459i) q^{59} +(109.168 - 189.084i) q^{60} +(321.641 + 557.099i) q^{61} +1169.95 q^{62} +(318.123 + 332.428i) q^{63} +585.366 q^{64} +(-69.3715 - 120.155i) q^{65} +(135.533 - 234.750i) q^{66} +(-21.2663 + 36.8343i) q^{67} +(-34.6915 - 60.0875i) q^{68} -144.005 q^{69} +(-207.511 + 711.493i) q^{70} -964.831 q^{71} +(-747.475 - 1294.67i) q^{72} +(41.1022 - 71.1911i) q^{73} +(104.070 - 180.254i) q^{74} +(48.9834 + 84.8418i) q^{75} +2082.65 q^{76} +(-182.624 + 626.163i) q^{77} +139.884 q^{78} +(104.995 + 181.857i) q^{79} +(609.184 - 1055.14i) q^{80} +(-279.512 + 484.130i) q^{81} +(107.462 + 186.129i) q^{82} +950.386 q^{83} +(-366.222 - 382.690i) q^{84} -27.1918 q^{85} +(455.486 + 788.925i) q^{86} +(-101.342 + 175.530i) q^{87} +(1059.60 - 1835.27i) q^{88} +(-248.129 - 429.772i) q^{89} -994.204 q^{90} +(-326.962 + 79.9486i) q^{91} -1910.45 q^{92} +(163.849 + 283.795i) q^{93} +(386.326 - 669.136i) q^{94} +(408.104 - 706.857i) q^{95} +(260.791 + 451.703i) q^{96} +482.621 q^{97} +(1516.11 + 966.586i) q^{98} -874.968 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 5 q^{2} + 6 q^{3} - 117 q^{4} - 4 q^{5} - 24 q^{6} - 30 q^{7} - 78 q^{8} - 236 q^{9}+O(q^{10}) \) 72 * q + 5 * q^2 + 6 * q^3 - 117 * q^4 - 4 * q^5 - 24 * q^6 - 30 * q^7 - 78 * q^8 - 236 * q^9	\( 72 q + 5 q^{2} + 6 q^{3} - 117 q^{4} - 4 q^{5} - 24 q^{6} - 30 q^{7} - 78 q^{8} - 236 q^{9} + 12 q^{10} + 140 q^{11} - 186 q^{12} - 144 q^{13} + 481 q^{14} - 732 q^{15} + 15 q^{16} + 2 q^{17} + 212 q^{18} - 30 q^{19} - 668 q^{20} + 368 q^{21} - 692 q^{22} + 314 q^{23} - 106 q^{24} - 570 q^{25} - 303 q^{26} - 408 q^{27} + 522 q^{28} - 712 q^{29} + 357 q^{30} + 4 q^{31} + 532 q^{32} + 30 q^{33} - 728 q^{34} + 462 q^{35} + 226 q^{36} + 1398 q^{37} + 264 q^{38} + 1348 q^{39} - 26 q^{40} + 2952 q^{41} - 1705 q^{42} - 2144 q^{43} + 1507 q^{44} + 1132 q^{45} + 1356 q^{46} + 622 q^{47} + 3448 q^{48} - 712 q^{49} - 2852 q^{50} + 668 q^{51} + 877 q^{52} + 412 q^{53} + 1814 q^{54} + 2228 q^{55} - 1321 q^{56} - 8164 q^{57} + 1309 q^{58} + 620 q^{59} + 3724 q^{60} - 774 q^{61} + 3330 q^{62} - 2550 q^{63} - 6570 q^{64} + 1036 q^{65} + 1056 q^{66} + 2972 q^{67} + 1525 q^{68} + 6608 q^{69} - 365 q^{70} - 7080 q^{71} + 821 q^{72} + 60 q^{73} + 2043 q^{74} - 450 q^{75} + 4342 q^{76} - 4846 q^{77} - 2272 q^{78} + 5190 q^{79} + 1564 q^{80} - 284 q^{81} + 205 q^{82} + 3312 q^{83} - 8326 q^{84} - 10128 q^{85} + 782 q^{86} + 1940 q^{87} + 4232 q^{88} + 1196 q^{89} + 16060 q^{90} - 4788 q^{91} - 9236 q^{92} - 698 q^{93} + 35 q^{94} + 1968 q^{95} + 7926 q^{96} + 7724 q^{97} - 11646 q^{98} - 11928 q^{99}+O(q^{100}) \) 72 * q + 5 * q^2 + 6 * q^3 - 117 * q^4 - 4 * q^5 - 24 * q^6 - 30 * q^7 - 78 * q^8 - 236 * q^9 + 12 * q^10 + 140 * q^11 - 186 * q^12 - 144 * q^13 + 481 * q^14 - 732 * q^15 + 15 * q^16 + 2 * q^17 + 212 * q^18 - 30 * q^19 - 668 * q^20 + 368 * q^21 - 692 * q^22 + 314 * q^23 - 106 * q^24 - 570 * q^25 - 303 * q^26 - 408 * q^27 + 522 * q^28 - 712 * q^29 + 357 * q^30 + 4 * q^31 + 532 * q^32 + 30 * q^33 - 728 * q^34 + 462 * q^35 + 226 * q^36 + 1398 * q^37 + 264 * q^38 + 1348 * q^39 - 26 * q^40 + 2952 * q^41 - 1705 * q^42 - 2144 * q^43 + 1507 * q^44 + 1132 * q^45 + 1356 * q^46 + 622 * q^47 + 3448 * q^48 - 712 * q^49 - 2852 * q^50 + 668 * q^51 + 877 * q^52 + 412 * q^53 + 1814 * q^54 + 2228 * q^55 - 1321 * q^56 - 8164 * q^57 + 1309 * q^58 + 620 * q^59 + 3724 * q^60 - 774 * q^61 + 3330 * q^62 - 2550 * q^63 - 6570 * q^64 + 1036 * q^65 + 1056 * q^66 + 2972 * q^67 + 1525 * q^68 + 6608 * q^69 - 365 * q^70 - 7080 * q^71 + 821 * q^72 + 60 * q^73 + 2043 * q^74 - 450 * q^75 + 4342 * q^76 - 4846 * q^77 - 2272 * q^78 + 5190 * q^79 + 1564 * q^80 - 284 * q^81 + 205 * q^82 + 3312 * q^83 - 8326 * q^84 - 10128 * q^85 + 782 * q^86 + 1940 * q^87 + 4232 * q^88 + 1196 * q^89 + 16060 * q^90 - 4788 * q^91 - 9236 * q^92 - 698 * q^93 + 35 * q^94 + 1968 * q^95 + 7926 * q^96 + 7724 * q^97 - 11646 * q^98 - 11928 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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