LMFDB - Embedded newform 130.4.n.a.9.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [130,4,Mod(9,130)] 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("130.9"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(130, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	130.n (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67024830075$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			9.20
Character	$\chi$	$=$	130.9
Dual form			130.4.n.a.29.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73205 + 1.00000i) q^{2} +(5.30007 + 3.06000i) q^{3} +(2.00000 + 3.46410i) q^{4} +(6.73291 + 8.92569i) q^{5} +(6.11999 + 10.6001i) q^{6} +(-12.2028 + 7.04529i) q^{7} +8.00000i q^{8} +(5.22716 + 9.05371i) q^{9} +(2.73606 + 22.1927i) q^{10} +(15.1407 - 26.2245i) q^{11} +24.4800i q^{12} +(-46.7223 + 3.74512i) q^{13} -28.1812 q^{14} +(8.37233 + 67.9095i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(102.649 - 59.2647i) q^{17} +20.9087i q^{18} +(-42.4785 - 73.5749i) q^{19} +(-17.4537 + 41.1749i) q^{20} -86.2342 q^{21} +(52.4491 - 30.2815i) q^{22} +(136.624 + 78.8802i) q^{23} +(-24.4800 + 42.4006i) q^{24} +(-34.3358 + 120.192i) q^{25} +(-84.6705 - 40.2356i) q^{26} -101.259i q^{27} +(-48.8112 - 28.1812i) q^{28} +(-78.2720 + 135.571i) q^{29} +(-53.4082 + 125.995i) q^{30} +117.160 q^{31} +(-27.7128 + 16.0000i) q^{32} +(160.494 - 92.6613i) q^{33} +237.059 q^{34} +(-145.044 - 61.4831i) q^{35} +(-20.9087 + 36.2149i) q^{36} +(10.5063 + 6.06584i) q^{37} -169.914i q^{38} +(-259.092 - 123.121i) q^{39} +(-71.4055 + 53.8633i) q^{40} +(177.062 - 306.680i) q^{41} +(-149.362 - 86.2342i) q^{42} +(-46.2035 + 26.6756i) q^{43} +121.126 q^{44} +(-45.6166 + 107.614i) q^{45} +(157.760 + 273.249i) q^{46} +371.353i q^{47} +(-84.8011 + 48.9600i) q^{48} +(-72.2278 + 125.102i) q^{49} +(-179.663 + 173.842i) q^{50} +725.399 q^{51} +(-106.418 - 154.361i) q^{52} -548.567i q^{53} +(101.259 - 175.386i) q^{54} +(336.013 - 41.4259i) q^{55} +(-56.3623 - 97.6224i) q^{56} -519.936i q^{57} +(-271.142 + 156.544i) q^{58} +(-213.384 - 369.592i) q^{59} +(-218.501 + 164.822i) q^{60} +(-136.562 - 236.532i) q^{61} +(202.927 + 117.160i) q^{62} +(-127.572 - 73.6538i) q^{63} -64.0000 q^{64} +(-348.005 - 391.813i) q^{65} +370.645 q^{66} +(-348.171 - 201.017i) q^{67} +(410.598 + 237.059i) q^{68} +(482.746 + 836.141i) q^{69} +(-189.741 - 251.536i) q^{70} +(-251.911 - 436.322i) q^{71} +(-72.4297 + 41.8173i) q^{72} -780.391i q^{73} +(12.1317 + 21.0127i) q^{74} +(-549.769 + 531.957i) q^{75} +(169.914 - 294.300i) q^{76} +426.684i q^{77} +(-325.639 - 472.343i) q^{78} +4.34901 q^{79} +(-177.541 + 21.8885i) q^{80} +(450.987 - 781.132i) q^{81} +(613.361 - 354.124i) q^{82} +405.894i q^{83} +(-172.468 - 298.724i) q^{84} +(1220.11 + 517.193i) q^{85} -106.702 q^{86} +(-829.695 + 479.024i) q^{87} +(209.796 + 121.126i) q^{88} +(-596.016 + 1032.33i) q^{89} +(-186.624 + 140.776i) q^{90} +(543.757 - 374.873i) q^{91} +631.041i q^{92} +(620.956 + 358.509i) q^{93} +(-371.353 + 643.203i) q^{94} +(370.703 - 874.523i) q^{95} -195.840 q^{96} +(-1405.30 + 811.351i) q^{97} +(-250.205 + 144.456i) q^{98} +316.573 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 88 q^{4} - 12 q^{5} + 266 q^{9} + 28 q^{10} + 2 q^{11} - 216 q^{14} - 64 q^{15} - 352 q^{16} + 14 q^{19} - 24 q^{20} - 32 q^{21} + 504 q^{25} + 336 q^{26} + 308 q^{29} + 104 q^{30} + 792 q^{31} - 352 q^{34}+ \cdots + 2916 q^{99}+O(q^{100}) $ 44 * q + 88 * q^4 - 12 * q^5 + 266 * q^9 + 28 * q^10 + 2 * q^11 - 216 * q^14 - 64 * q^15 - 352 * q^16 + 14 * q^19 - 24 * q^20 - 32 * q^21 + 504 * q^25 + 336 * q^26 + 308 * q^29 + 104 * q^30 + 792 * q^31 - 352 * q^34 + 106 * q^35 - 1064 * q^36 + 120 * q^39 + 224 * q^40 + 140 * q^41 + 16 * q^44 - 522 * q^45 - 320 * q^46 + 536 * q^49 - 96 * q^50 - 256 * q^51 + 552 * q^54 + 1188 * q^55 - 432 * q^56 - 500 * q^59 - 512 * q^60 - 2352 * q^61 - 2816 * q^64 - 2924 * q^65 + 496 * q^66 + 376 * q^69 - 1008 * q^70 - 1268 * q^71 + 436 * q^74 + 3560 * q^75 - 56 * q^76 - 264 * q^79 + 96 * q^80 - 6326 * q^81 - 64 * q^84 + 606 * q^85 + 336 * q^86 + 4730 * q^89 + 3560 * q^90 + 5866 * q^91 + 1732 * q^94 + 2224 * q^95 + 2916 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.73205	+	1.00000i	0.612372	+	0.353553i
$2$	1.73205	+	1.00000i	0.612372	+	0.353553i
$3$	5.30007	+	3.06000i	1.02000	+	0.588897i	0.914104	−	0.405481i	$-0.132896\pi$
$3$	5.30007	+	3.06000i	1.02000	+	0.588897i	0.105895	+	0.994377i	$0.466229\pi$
$4$	2.00000	+	3.46410i	0.250000	+	0.433013i
$5$	6.73291	+	8.92569i	0.602210	+	0.798338i
$5$	6.73291	+	8.92569i	0.602210	+	0.798338i
$6$	6.11999	+	10.6001i	0.416413	+	0.721248i
$7$	−12.2028	+	7.04529i	−0.658889	+	0.380410i	−0.791854	−	0.610711i	$-0.790884\pi$
$7$	−12.2028	+	7.04529i	−0.658889	+	0.380410i	0.132964	+	0.991121i	$0.457550\pi$
$8$			8.00000i			0.353553i
$9$	5.22716	+	9.05371i	0.193599	+	0.335323i
$10$	2.73606	+	22.1927i	0.0865217	+	0.701793i
$11$	15.1407	−	26.2245i	0.415010	−	0.718818i	−0.580420	−	0.814317i	$-0.697112\pi$
$11$	15.1407	−	26.2245i	0.415010	−	0.718818i	0.995429	+	0.0954996i	$0.0304449\pi$
$12$			24.4800i			0.588897i
$13$	−46.7223	+	3.74512i	−0.996803	+	0.0799007i
$13$	−46.7223	+	3.74512i	−0.996803	+	0.0799007i
$14$	−28.1812			−0.537981
$15$	8.37233	+	67.9095i	0.144115	+	1.16894i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	102.649	−	59.2647i	1.46448	−	0.845517i	0.465265	−	0.885171i	$-0.345959\pi$
$17$	102.649	−	59.2647i	1.46448	−	0.845517i	0.999213	+	0.0396542i	$0.0126256\pi$
$18$			20.9087i			0.273790i
$19$	−42.4785	−	73.5749i	−0.512907	−	0.888381i	−0.999888	−	0.0149683i	$-0.995235\pi$
$19$	−42.4785	−	73.5749i	−0.512907	−	0.888381i	0.486981	−	0.873413i	$-0.338098\pi$
$20$	−17.4537	+	41.1749i	−0.195138	+	0.460349i
$21$	−86.2342			−0.896088
$22$	52.4491	−	30.2815i	0.508281	−	0.293456i
$23$	136.624	+	78.8802i	1.23862	+	0.715115i	0.968811	−	0.247800i	$-0.0797075\pi$
$23$	136.624	+	78.8802i	1.23862	+	0.715115i	0.269805	+	0.962915i	$0.413041\pi$
$24$	−24.4800	+	42.4006i	−0.208206	+	0.360624i
$25$	−34.3358	+	120.192i	−0.274686	+	0.961534i
$26$	−84.6705	−	40.2356i	−0.638664	−	0.303494i
$27$		−	101.259i		−	0.721755i
$28$	−48.8112	−	28.1812i	−0.329445	−	0.190205i
$29$	−78.2720	+	135.571i	−0.501198	+	0.868101i	0.498801	+	0.866717i	$0.333774\pi$
$29$	−78.2720	+	135.571i	−0.501198	+	0.868101i	−0.999999	+	0.00138423i	$0.999559\pi$
$30$	−53.4082	+	125.995i	−0.325032	+	0.766781i
$31$	117.160			0.678792			0.339396	−	0.940644i	$-0.389777\pi$
$31$	117.160			0.678792			0.339396	+	0.940644i	$0.389777\pi$
$32$	−27.7128	+	16.0000i	−0.153093	+	0.0883883i
$33$	160.494	−	92.6613i	0.846619	−	0.488796i
$34$	237.059			1.19574
$35$	−145.044	−	61.4831i	−0.700485	−	0.296930i
$36$	−20.9087	+	36.2149i	−0.0967993	+	0.167661i
$37$	10.5063	+	6.06584i	0.0466819	+	0.0269518i	0.523159	−	0.852235i	$-0.324753\pi$
$37$	10.5063	+	6.06584i	0.0466819	+	0.0269518i	−0.476477	+	0.879187i	$0.658087\pi$
$38$		−	169.914i		−	0.725360i
$39$	−259.092	−	123.121i	−1.06379	−	0.505515i
$40$	−71.4055	+	53.8633i	−0.282255	+	0.212913i
$41$	177.062	−	306.680i	0.674450	−	1.16818i	−0.302180	−	0.953251i	$-0.597714\pi$
$41$	177.062	−	306.680i	0.674450	−	1.16818i	0.976629	−	0.214930i	$-0.0689524\pi$
$42$	−149.362	−	86.2342i	−0.548740	−	0.316815i
$43$	−46.2035	+	26.6756i	−0.163860	+	0.0946044i	−0.579687	−	0.814839i	$-0.696825\pi$
$43$	−46.2035	+	26.6756i	−0.163860	+	0.0946044i	0.415828	+	0.909443i	$0.363492\pi$
$44$	121.126			0.415010
$45$	−45.6166	+	107.614i	−0.151114	+	0.356492i
$46$	157.760	+	273.249i	0.505663	+	0.875834i
$47$			371.353i			1.15250i	0.817274	+	0.576249i	$0.195484\pi$
$47$			371.353i			1.15250i	−0.817274	+	0.576249i	$0.804516\pi$
$48$	−84.8011	+	48.9600i	−0.255000	+	0.147224i
$49$	−72.2278	+	125.102i	−0.210577	+	0.364730i
$50$	−179.663	+	173.842i	−0.508164	+	0.491701i
$51$	725.399			1.99169
$52$	−106.418	−	154.361i	−0.283799	−	0.411653i
$53$		−	548.567i		−	1.42173i	−0.703331	−	0.710863i	$-0.748305\pi$
$53$		−	548.567i		−	1.42173i	0.703331	−	0.710863i	$-0.251695\pi$
$54$	101.259	−	175.386i	0.255179	−	0.441983i
$55$	336.013	−	41.4259i	0.823782	−	0.101561i
$56$	−56.3623	−	97.6224i	−0.134495	−	0.232952i
$57$		−	519.936i		−	1.20820i
$58$	−271.142	+	156.544i	−0.613840	+	0.354401i
$59$	−213.384	−	369.592i	−0.470852	−	0.815539i	0.528592	−	0.848876i	$-0.322720\pi$
$59$	−213.384	−	369.592i	−0.470852	−	0.815539i	−0.999444	+	0.0333366i	$0.989387\pi$
$60$	−218.501	+	164.822i	−0.470138	+	0.354639i
$61$	−136.562	−	236.532i	−0.286639	−	0.496473i	0.686367	−	0.727256i	$-0.259205\pi$
$61$	−136.562	−	236.532i	−0.286639	−	0.496473i	−0.973005	+	0.230783i	$0.925871\pi$
$62$	202.927	+	117.160i	0.415674	+	0.239989i
$63$	−127.572	−	73.6538i	−0.255120	−	0.147294i
$64$	−64.0000			−0.125000
$65$	−348.005	−	391.813i	−0.664072	−	0.747668i
$66$	370.645			0.691261
$67$	−348.171	−	201.017i	−0.634864	−	0.366539i	0.147770	−	0.989022i	$-0.452791\pi$
$67$	−348.171	−	201.017i	−0.634864	−	0.366539i	−0.782633	+	0.622483i	$0.786124\pi$
$68$	410.598	+	237.059i	0.732239	+	0.422759i
$69$	482.746	+	836.141i	0.842258	+	1.45883i
$70$	−189.741	−	251.536i	−0.323977	−	0.429490i
$71$	−251.911	−	436.322i	−0.421075	−	0.729323i	0.574970	−	0.818174i	$-0.305014\pi$
$71$	−251.911	−	436.322i	−0.421075	−	0.729323i	−0.996045	+	0.0888515i	$0.971680\pi$
$72$	−72.4297	+	41.8173i	−0.118555	+	0.0684475i
$73$		−	780.391i		−	1.25120i	−0.780143	−	0.625601i	$-0.784854\pi$
$73$		−	780.391i		−	1.25120i	0.780143	−	0.625601i	$-0.215146\pi$
$74$	12.1317	+	21.0127i	0.0190578	+	0.0330091i
$75$	−549.769	+	531.957i	−0.846424	+	0.819002i
$76$	169.914	−	294.300i	0.256453	−	0.444190i
$77$			426.684i			0.631495i
$78$	−325.639	−	472.343i	−0.472710	−	0.685671i
$79$	4.34901			0.00619369			0.00309685	−	0.999995i	$-0.499014\pi$
$79$	4.34901			0.00619369			0.00309685	+	0.999995i	$0.499014\pi$
$80$	−177.541	+	21.8885i	−0.248121	+	0.0305901i
$81$	450.987	−	781.132i	0.618638	−	1.07151i
$82$	613.361	−	354.124i	0.826029	−	0.476908i
$83$			405.894i			0.536779i	0.963310	+	0.268390i	$0.0864914\pi$
$83$			405.894i			0.536779i	−0.963310	+	0.268390i	$0.913509\pi$
$84$	−172.468	−	298.724i	−0.224022	−	0.388018i
$85$	1220.11	+	517.193i	1.55693	+	0.659970i
$86$	−106.702			−0.133791
$87$	−829.695	+	479.024i	−1.02244	+	0.590308i
$88$	209.796	+	121.126i	0.254140	+	0.146728i
$89$	−596.016	+	1032.33i	−0.709861	+	1.22951i	0.255048	+	0.966928i	$0.417909\pi$
$89$	−596.016	+	1032.33i	−0.709861	+	1.22951i	−0.964909	+	0.262586i	$0.915425\pi$
$90$	−186.624	+	140.776i	−0.218577	+	0.164879i
$91$	543.757	−	374.873i	0.626388	−	0.431839i
$92$			631.041i			0.715115i
$93$	620.956	+	358.509i	0.692367	+	0.399738i
$94$	−371.353	+	643.203i	−0.407470	+	0.705758i
$95$	370.703	−	874.523i	0.400350	−	0.944465i
$96$	−195.840			−0.208206
$97$	−1405.30	+	811.351i	−1.47100	+	0.849281i	−0.999469	−	0.0325704i	$-0.989631\pi$
$97$	−1405.30	+	811.351i	−1.47100	+	0.849281i	−0.471528	+	0.881851i	$0.656297\pi$
$98$	−250.205	+	144.456i	−0.257903	+	0.148900i
$99$	316.573			0.321381
$100$	−485.028	+	121.441i	−0.485028	+	0.121441i
$101$	108.698	−	188.270i	0.107087	−	0.185481i	−0.807502	−	0.589865i	$-0.799181\pi$
$101$	108.698	−	188.270i	0.107087	−	0.185481i	0.914589	+	0.404384i	$0.132514\pi$
$102$	1256.43	+	725.399i	1.21966	+	0.704168i
$103$			370.852i			0.354768i	0.984142	+	0.177384i	$0.0567634\pi$
$103$			370.852i			0.354768i	−0.984142	+	0.177384i	$0.943237\pi$
$104$	−29.9609	−	373.778i	−0.0282492	−	0.352423i
$105$	−580.608	−	769.700i	−0.539633	−	0.715381i
$106$	548.567	−	950.146i	0.502656	−	0.870625i
$107$	1193.79	+	689.236i	1.07858	+	0.622719i	0.930513	−	0.366258i	$-0.119361\pi$
$107$	1193.79	+	689.236i	1.07858	+	0.622719i	0.148068	+	0.988977i	$0.452695\pi$
$108$	350.773	−	202.519i	0.312529	−	0.180439i
$109$	−1189.73			−1.04546			−0.522731	−	0.852498i	$-0.675087\pi$
$109$	−1189.73			−1.04546			−0.522731	+	0.852498i	$0.675087\pi$
$110$	623.418	+	264.262i	0.540369	+	0.229058i
$111$	37.1229	+	64.2987i	0.0317437	+	0.0549817i
$112$		−	225.449i		−	0.190205i
$113$	−1734.46	+	1001.39i	−1.44393	+	0.833653i	−0.998109	−	0.0614696i	$-0.980421\pi$
$113$	−1734.46	+	1001.39i	−1.44393	+	0.833653i	−0.445820	+	0.895122i	$0.647088\pi$
$114$	519.936	−	900.556i	0.427162	−	0.739866i
$115$	215.821	+	1750.56i	0.175003	+	1.41948i
$116$	−626.176			−0.501198
$117$	−278.132	−	403.434i	−0.219772	−	0.318782i
$118$		−	853.537i		−	0.665885i
$119$	−835.073	+	1446.39i	−0.643286	+	1.11420i
$120$	−543.276	+	66.9786i	−0.413284	+	0.0509524i
$121$	207.016	+	358.562i	0.155534	+	0.269393i
$122$		−	546.248i		−	0.405368i
$123$	1876.88	−	1083.62i	1.37588	−	0.794363i
$124$	234.320	+	405.854i	0.169698	+	0.293926i
$125$	−1303.97	+	502.770i	−0.933048	+	0.359753i
$126$	−147.308	−	255.144i	−0.104152	−	0.180397i
$127$	635.633	+	366.983i	0.444120	+	0.256413i	0.705344	−	0.708865i	$-0.250793\pi$
$127$	635.633	+	366.983i	0.444120	+	0.256413i	−0.261223	+	0.965278i	$0.584126\pi$
$128$	−110.851	−	64.0000i	−0.0765466	−	0.0441942i
$129$	−326.509			−0.222849
$130$	−210.949	−	1026.65i	−0.142319	−	0.692637i
$131$	1658.18			1.10592			0.552960	−	0.833208i	$-0.313498\pi$
$131$	1658.18			1.10592			0.552960	+	0.833208i	$0.313498\pi$
$132$	641.976	+	370.645i	0.423309	+	0.244398i
$133$	1036.71	+	598.546i	0.675898	+	0.390230i
$134$	−402.033	−	696.342i	−0.259182	−	0.448916i
$135$	903.810	−	681.771i	0.576204	−	0.434648i
$136$	474.117	+	821.195i	0.298935	+	0.517771i
$137$	−1537.03	+	887.407i	−0.958523	+	0.553403i	−0.895718	−	0.444622i	$-0.853338\pi$
$137$	−1537.03	+	887.407i	−0.958523	+	0.553403i	−0.0628048	+	0.998026i	$0.520005\pi$
$138$			1930.98i			1.19113i
$139$	471.744	+	817.085i	0.287862	+	0.498592i	0.973299	−	0.229540i	$-0.0737222\pi$
$139$	471.744	+	817.085i	0.287862	+	0.498592i	−0.685437	+	0.728132i	$0.740389\pi$
$140$	−77.1053	−	625.415i	−0.0465470	−	0.377551i
$141$	−1136.34	+	1968.20i	−0.678703	+	1.17555i
$142$		−	1007.64i		−	0.595490i
$143$	−609.197	+	1281.97i	−0.356249	+	0.749679i
$144$	−167.269			−0.0967993
$145$	−1737.06	+	214.157i	−0.994864	+	0.122653i
$146$	780.391	−	1351.68i	0.442367	−	0.766202i
$147$	−765.625	+	442.034i	−0.429576	+	0.248016i
$148$			48.5267i			0.0269518i
$149$	−931.702	−	1613.75i	−0.512268	−	0.887275i	−0.999899	−	0.0142245i	$-0.995472\pi$
$149$	−931.702	−	1613.75i	−0.512268	−	0.887275i	0.487631	−	0.873050i	$-0.337861\pi$
$150$	−1484.18	+	371.608i	−0.807888	+	0.202278i
$151$	3324.05			1.79144			0.895720	−	0.444619i	$-0.146661\pi$
$151$	3324.05			1.79144			0.895720	+	0.444619i	$0.146661\pi$
$152$	588.599	−	339.828i	0.314090	−	0.181340i
$153$	1073.13	+	619.572i	0.567042	+	0.327382i
$154$	−426.684	+	739.038i	−0.223267	+	0.386710i
$155$	788.828	+	1045.73i	0.408775	+	0.541905i
$156$	−91.6804	−	1143.76i	−0.0470533	−	0.587014i
$157$		−	1574.81i		−	0.800533i	−0.916399	−	0.400266i	$-0.868918\pi$
$157$		−	1574.81i		−	0.800533i	0.916399	−	0.400266i	$-0.131082\pi$
$158$	7.53270	+	4.34901i	0.00379285	+	0.00218980i
$159$	1678.61	−	2907.44i	0.837249	−	1.45016i
$160$	−329.399	−	139.629i	−0.162758	−	0.0689917i
$161$	−2222.93			−1.08815
$162$	1562.26	−	901.974i	0.757673	−	0.437443i
$163$	−1507.77	+	870.511i	−0.724525	+	0.418305i	−0.816416	−	0.577464i	$-0.804042\pi$
$163$	−1507.77	+	870.511i	−0.724525	+	0.418305i	0.0918907	+	0.995769i	$0.470709\pi$
$164$	1416.50			0.674450
$165$	1907.66	+	808.639i	0.900066	+	0.381530i
$166$	−405.894	+	703.029i	−0.189780	+	0.328709i
$167$	−1586.25	−	915.822i	−0.735016	−	0.424362i	0.0852381	−	0.996361i	$-0.472835\pi$
$167$	−1586.25	−	915.822i	−0.735016	−	0.424362i	−0.820255	+	0.571999i	$0.806168\pi$
$168$		−	689.874i		−	0.316815i
$169$	2168.95	−	349.961i	0.987232	−	0.159290i
$170$	1596.09	+	2115.91i	0.720088	+	0.954606i
$171$	444.084	−	769.176i	0.198596	−	0.343979i
$172$	−184.814	−	106.702i	−0.0819298	−	0.0473022i
$173$	−1403.72	+	810.437i	−0.616894	+	0.356164i	−0.775659	−	0.631152i	$-0.782582\pi$
$173$	−1403.72	+	810.437i	−0.616894	+	0.356164i	0.158765	+	0.987316i	$0.449249\pi$
$174$	−1916.10			−0.834822
$175$	−427.793	−	1708.58i	−0.184789	−	0.738038i
$176$	242.252	+	419.593i	0.103752	+	0.179704i
$177$		−	2611.82i		−	1.10913i
$178$	−2064.66	+	1192.03i	−0.869398	+	0.501947i
$179$	703.891	−	1219.18i	0.293918	−	0.509081i	−0.680815	−	0.732456i	$-0.738374\pi$
$179$	703.891	−	1219.18i	0.293918	−	0.509081i	0.974733	+	0.223375i	$0.0717074\pi$
$180$	−464.019	+	57.2073i	−0.192144	+	0.0236888i
$181$	−614.948			−0.252534			−0.126267	−	0.991996i	$-0.540300\pi$
$181$	−614.948			−0.252534			−0.126267	+	0.991996i	$0.540300\pi$
$182$	1316.69	−	105.542i	0.536261	−	0.0429850i
$183$		−	1671.52i		−	0.675202i
$184$	−631.041	+	1093.00i	−0.252831	+	0.437917i
$185$	16.5965	+	134.617i	0.00659566	+	0.0534986i
$186$	717.018	+	1241.91i	0.282658	+	0.489578i
$187$		−	3589.24i		−	1.40359i
$188$	−1286.41	+	742.706i	−0.499047	+	0.288125i
$189$	713.402	+	1235.65i	0.274563	+	0.475556i
$190$	1516.60	−	1144.02i	0.579082	−	0.436819i
$191$	−118.799	−	205.765i	−0.0450051	−	0.0779511i	0.842645	−	0.538469i	$-0.180997\pi$
$191$	−118.799	−	205.765i	−0.0450051	−	0.0779511i	−0.887650	+	0.460518i	$0.847664\pi$
$192$	−339.205	−	195.840i	−0.127500	−	0.0736121i
$193$	−1688.13	−	974.645i	−0.629609	−	0.363505i	0.150991	−	0.988535i	$-0.451753\pi$
$193$	−1688.13	−	974.645i	−0.629609	−	0.363505i	−0.780601	+	0.625030i	$0.785087\pi$
$194$	−3245.40			−1.20106
$195$	−645.503	−	3141.53i	−0.237054	−	1.15369i
$196$	−577.823			−0.210577
$197$	−1215.67	−	701.866i	−0.439659	−	0.253837i	0.263794	−	0.964579i	$-0.415026\pi$
$197$	−1215.67	−	701.866i	−0.439659	−	0.253837i	−0.703453	+	0.710742i	$0.748359\pi$
$198$	548.320	+	316.573i	0.196805	+	0.113625i
$199$	37.4954	+	64.9440i	0.0133567	+	0.0231345i	0.872626	−	0.488388i	$-0.162415\pi$
$199$	37.4954	+	64.9440i	0.0133567	+	0.0231345i	−0.859270	+	0.511523i	$0.829082\pi$
$200$	−961.534	−	274.686i	−0.339954	−	0.0971163i
$201$	−1230.22	−	2130.80i	−0.431707	−	0.747738i
$202$	376.540	−	217.395i	0.131155	−	0.0757222i
$203$		−	2205.80i		−	0.762643i
$204$	1450.80	+	2512.85i	0.497922	+	0.862427i
$205$	3929.48	−	484.452i	1.33876	−	0.165052i
$206$	−370.852	+	642.334i	−0.125429	+	0.217250i
$207$			1649.28i			0.553782i
$208$	321.885	−	677.364i	0.107301	−	0.225802i
$209$	−2572.62			−0.851445
$210$	−235.942	−	1913.77i	−0.0775311	−	0.628869i
$211$	2435.37	−	4218.19i	0.794588	−	1.37627i	−0.128513	−	0.991708i	$-0.541020\pi$
$211$	2435.37	−	4218.19i	0.794588	−	1.37627i	0.923101	−	0.384558i	$-0.125646\pi$
$212$	1900.29	−	1097.13i	0.615625	−	0.355431i
$213$		−	3083.39i		−	0.991878i
$214$	1378.47	+	2387.58i	0.440329	+	0.762672i
$215$	−549.182	−	232.793i	−0.174204	−	0.0738436i
$216$	810.075			0.255179
$217$	−1429.68	+	825.426i	−0.447249	+	0.258219i
$218$	−2060.67	−	1189.73i	−0.640212	−	0.369627i
$219$	2387.99	−	4136.13i	0.736829	−	1.27623i
$220$	815.530	+	1081.13i	0.249923	+	0.331318i
$221$	−4574.06	+	3153.42i	−1.39224	+	0.959827i
$222$			148.492i			0.0448924i
$223$	3450.72	+	1992.27i	1.03622	+	0.598262i	0.918760	−	0.394816i	$-0.129192\pi$
$223$	3450.72	+	1992.27i	1.03622	+	0.598262i	0.117460	+	0.993078i	$0.462525\pi$
$224$	225.449	−	390.490i	0.0672476	−	0.116476i
$225$	−1267.66	+	317.395i	−0.375603	+	0.0940431i
$226$	−4005.56			−1.17896
$227$	1669.77	−	964.042i	0.488223	−	0.281876i	−0.235614	−	0.971847i	$-0.575710\pi$
$227$	1669.77	−	964.042i	0.488223	−	0.281876i	0.723837	+	0.689971i	$0.242377\pi$
$228$	1801.11	−	1039.87i	0.523165	−	0.302049i
$229$	3432.88			0.990617			0.495308	−	0.868717i	$-0.335055\pi$
$229$	3432.88			0.990617			0.495308	+	0.868717i	$0.335055\pi$
$230$	−1376.75	+	3247.88i	−0.394696	+	0.931126i
$231$	−1305.65	+	2261.45i	−0.371885	+	0.644124i
$232$	−1084.57	−	626.176i	−0.306920	−	0.177200i
$233$			6437.17i			1.80993i	0.425488	+	0.904964i	$0.360102\pi$
$233$			6437.17i			1.80993i	−0.425488	+	0.904964i	$0.639898\pi$
$234$	−78.3054	−	976.901i	−0.0218760	−	0.272915i
$235$	−3314.58	+	2500.29i	−0.920083	+	0.694046i
$236$	853.537	−	1478.37i	0.235426	−	0.407770i
$237$	23.0501	+	13.3080i	0.00631756	+	0.00364745i
$238$	−2892.78	+	1670.15i	−0.787861	+	0.454872i
$239$	−1464.02			−0.396232			−0.198116	−	0.980179i	$-0.563482\pi$
$239$	−1464.02			−0.396232			−0.198116	+	0.980179i	$0.563482\pi$
$240$	−1007.96	−	427.265i	−0.271098	−	0.114916i
$241$	−1216.85	−	2107.65i	−0.325246	−	0.563343i	0.656316	−	0.754486i	$-0.272114\pi$
$241$	−1216.85	−	2107.65i	−0.325246	−	0.563343i	−0.981562	+	0.191143i	$0.938780\pi$
$242$			828.063i			0.219958i
$243$	2412.81	−	1393.04i	0.636962	−	0.367750i
$244$	546.248	−	946.129i	0.143319	−	0.248236i
$245$	−1602.93	+	197.619i	−0.417989	+	0.0515324i
$246$	4334.47			1.12340
$247$	2260.24	+	3278.50i	0.582249	+	0.844559i
$248$			937.280i			0.239989i
$249$	−1242.03	+	2151.27i	−0.316107	+	0.547514i
$250$	−2761.32	−	433.151i	−0.698564	−	0.109580i
$251$	2959.43	+	5125.88i	0.744213	+	1.28902i	0.950561	+	0.310537i	$0.100509\pi$
$251$	2959.43	+	5125.88i	0.744213	+	1.28902i	−0.206348	+	0.978479i	$0.566158\pi$
$252$		−	589.230i		−	0.147294i
$253$	4137.19	−	2388.61i	1.02808	−	0.593560i
$254$	733.966	+	1271.27i	0.181311	+	0.314041i
$255$	4884.05	+	6474.68i	1.19941	+	1.59004i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	2228.87	+	1286.84i	0.540984	+	0.312337i	0.745478	−	0.666530i	$-0.232221\pi$
$257$	2228.87	+	1286.84i	0.540984	+	0.312337i	−0.204493	+	0.978868i	$0.565555\pi$
$258$	−565.530	−	326.509i	−0.136467	−	0.0787890i
$259$	−170.942			−0.0410110
$260$	661.271	−	1989.15i	0.157732	−	0.474469i
$261$	−1636.56			−0.388125
$262$	2872.05	+	1658.18i	0.677235	+	0.391002i
$263$	−1344.56	−	776.282i	−0.315244	−	0.182006i	0.334027	−	0.942564i	$-0.391592\pi$
$263$	−1344.56	−	776.282i	−0.315244	−	0.182006i	−0.649271	+	0.760557i	$0.724926\pi$
$264$	741.290	+	1283.95i	0.172815	+	0.299325i
$265$	4896.34	−	3693.45i	1.13502	−	0.856177i
$266$	1197.09	+	2073.42i	0.275934	+	0.477932i
$267$	−6317.86	+	3647.62i	−1.44811	+	0.836069i
$268$		−	1608.13i		−	0.366539i
$269$	2765.84	+	4790.58i	0.626901	+	1.08582i	0.988170	+	0.153363i	$0.0490104\pi$
$269$	2765.84	+	4790.58i	0.626901	+	1.08582i	−0.361269	+	0.932462i	$0.617656\pi$
$270$	2247.22	−	277.052i	0.506523	−	0.0624475i
$271$	−2734.80	+	4736.82i	−0.613017	+	1.06178i	0.377712	+	0.925923i	$0.376711\pi$
$271$	−2734.80	+	4736.82i	−0.613017	+	1.06178i	−0.990729	+	0.135853i	$0.956623\pi$
$272$			1896.47i			0.422759i
$273$	4029.06	−	322.957i	0.893223	−	0.0715981i
$274$	−3549.63			−0.782631
$275$	2632.10	+	2720.23i	0.577170	+	0.596495i
$276$	−1930.98	+	3344.56i	−0.421129	+	0.729417i
$277$	−1524.34	+	880.077i	−0.330645	+	0.190898i	−0.656127	−	0.754650i	$-0.727807\pi$
$277$	−1524.34	+	880.077i	−0.330645	+	0.190898i	0.325483	+	0.945548i	$0.394473\pi$
$278$			1886.98i			0.407098i
$279$	612.415	+	1060.73i	0.131413	+	0.227614i
$280$	491.864	−	1160.36i	0.104980	−	0.247659i
$281$	−6545.23			−1.38952			−0.694761	−	0.719241i	$-0.744490\pi$
$281$	−6545.23			−1.38952			−0.694761	+	0.719241i	$0.744490\pi$
$282$	−3936.40	+	2272.68i	−0.831238	+	0.479915i
$283$	862.886	+	498.188i	0.181248	+	0.104644i	0.587879	−	0.808949i	$-0.299963\pi$
$283$	862.886	+	498.188i	0.181248	+	0.104644i	−0.406631	+	0.913593i	$0.633296\pi$
$284$	1007.64	−	1745.29i	0.210537	−	0.364661i
$285$	4640.79	−	3500.68i	0.964549	−	0.727588i
$286$	−2337.13	+	1611.25i	−0.483209	+	0.333130i
$287$			4989.81i			1.02627i
$288$	−289.719	−	167.269i	−0.0592773	−	0.0342237i
$289$	4568.10	−	7912.18i	0.929798	−	1.61046i
$290$	−3222.84	−	1366.13i	−0.652592	−	0.276628i
$291$	−9930.93			−2.00055
$292$	2703.35	−	1560.78i	0.541787	−	0.312801i
$293$	3838.28	−	2216.03i	0.765306	−	0.441849i	−0.0658917	−	0.997827i	$-0.520989\pi$
$293$	3838.28	−	2216.03i	0.765306	−	0.441849i	0.831197	+	0.555977i	$0.187656\pi$
$294$	−1768.14			−0.350747
$295$	1862.17	−	4393.03i	0.367524	−	0.867025i
$296$	−48.5267	+	84.0507i	−0.00952891	+	0.0165046i
$297$	−2655.48	−	1533.14i	−0.518810	−	0.299535i
$298$		−	3726.81i		−	0.724457i
$299$	−6678.83	−	3173.79i	−1.29179	−	0.613863i
$300$	−2942.29	−	840.540i	−0.566244	−	0.161762i
$301$	375.874	−	651.034i	0.0719769	−	0.124668i
$302$	5757.43	+	3324.05i	1.09703	+	0.633370i
$303$	1152.21	−	665.229i	0.218458	−	0.126127i
$304$	1359.31			0.256453
$305$	1191.75	−	2811.46i	0.223736	−	0.527815i
$306$	1239.14	+	2146.26i	0.231494	+	0.400959i
$307$			4896.49i			0.910284i	0.890419	+	0.455142i	$0.150412\pi$
$307$			4896.49i			0.910284i	−0.890419	+	0.455142i	$0.849588\pi$
$308$	−1478.08	+	853.367i	−0.273445	+	0.157874i
$309$	−1134.80	+	1965.54i	−0.208922	+	0.361863i
$310$	320.556	+	2600.09i	0.0587303	+	0.476372i
$311$	−115.563			−0.0210707			−0.0105353	−	0.999945i	$-0.503354\pi$
$311$	−115.563			−0.0210707			−0.0105353	+	0.999945i	$0.503354\pi$
$312$	984.966	−	2072.73i	0.178727	−	0.376107i
$313$		−	1047.20i		−	0.189110i	−0.995520	−	0.0945548i	$-0.969857\pi$
$313$		−	1047.20i		−	0.189110i	0.995520	−	0.0945548i	$-0.0301428\pi$
$314$	1574.81	−	2727.65i	0.283031	−	0.490224i
$315$	−201.521	−	1634.57i	−0.0360458	−	0.292374i
$316$	8.69802	+	15.0654i	0.00154842	+	0.00268195i
$317$			4305.79i			0.762894i	0.924391	+	0.381447i	$0.124574\pi$
$317$			4305.79i			0.762894i	−0.924391	+	0.381447i	$0.875426\pi$
$318$	5814.89	−	3357.23i	1.02542	−	0.592025i
$319$	2370.19	+	4105.30i	0.416004	+	0.720541i
$320$	−430.906	−	571.244i	−0.0752762	−	0.0997922i
$321$	4218.12	+	7306.00i	0.733435	+	1.27035i
$322$	−3850.24	−	2222.93i	−0.666352	−	0.384718i
$323$	−8720.78	−	5034.94i	−1.50228	−	0.867343i
$324$	3607.90			0.618638
$325$	1154.12	−	5744.23i	0.196981	−	0.980407i
$326$	−3482.04			−0.591572
$327$	−6305.65	−	3640.57i	−1.06637	−	0.615669i
$328$	2453.44	+	1416.50i	0.413014	+	0.238454i
$329$	−2616.29	−	4531.55i	−0.438422	−	0.759369i
$330$	2495.52	+	3308.26i	0.416285	+	0.551860i
$331$	−342.720	−	593.608i	−0.0569111	−	0.0985730i	0.836166	−	0.548476i	$-0.184792\pi$
$331$	−342.720	−	593.608i	−0.0569111	−	0.0985730i	−0.893077	+	0.449903i	$0.851459\pi$
$332$	−1406.06	+	811.788i	−0.232432	+	0.134195i
$333$			126.829i			0.0208714i
$334$	−1831.64	−	3172.50i	−0.300069	−	0.519735i
$335$	−549.993	−	4461.09i	−0.0896995	−	0.727569i
$336$	689.874	−	1194.90i	0.112011	−	0.194009i
$337$		−	3807.14i		−	0.615395i	−0.951484	−	0.307698i	$-0.900441\pi$
$337$		−	3807.14i		−	0.615395i	0.951484	−	0.307698i	$-0.0995585\pi$
$338$	4106.69	+	1562.80i	0.660871	+	0.251494i
$339$	−12257.0			−1.96374
$340$	648.606	+	5260.96i	0.103458	+	0.839164i
$341$	1773.89	−	3072.47i	0.281705	−	0.487928i
$342$	1538.35	−	888.168i	0.243230	−	0.140429i
$343$		−	6868.53i		−	1.08124i
$344$	−213.405	−	369.628i	−0.0334477	−	0.0579331i
$345$	−4212.85	+	9938.50i	−0.657426	+	1.55093i
$346$	−3241.75			−0.503692
$347$	7322.08	−	4227.41i	1.13277	−	0.654003i	0.188137	−	0.982143i	$-0.439755\pi$
$347$	7322.08	−	4227.41i	1.13277	−	0.654003i	0.944629	+	0.328140i	$0.106422\pi$
$348$	−3318.78	−	1916.10i	−0.511222	−	0.295154i
$349$	663.060	−	1148.45i	0.101698	−	0.176147i	−0.810686	−	0.585481i	$-0.800906\pi$
$349$	663.060	−	1148.45i	0.101698	−	0.176147i	0.912385	+	0.409334i	$0.134239\pi$
$350$	967.623	−	3387.14i	0.147776	−	0.517287i
$351$	379.228	+	4731.07i	0.0576687	+	0.719447i
$352$			969.008i			0.146728i
$353$	−5074.08	−	2929.52i	−0.765060	−	0.441707i	0.0660497	−	0.997816i	$-0.478960\pi$
$353$	−5074.08	−	2929.52i	−0.765060	−	0.441707i	−0.831109	+	0.556109i	$0.812294\pi$
$354$	2611.82	−	4523.81i	0.392137	−	0.679202i
$355$	2198.38	−	5186.20i	0.328671	−	0.775365i
$356$	−4768.13			−0.709861
$357$	−8851.89	+	5110.64i	−1.31230	+	0.757658i
$358$	2438.35	−	1407.78i	0.359975	−	0.207831i
$359$	10970.9			1.61287			0.806435	−	0.591323i	$-0.201394\pi$
$359$	10970.9			1.61287			0.806435	+	0.591323i	$0.201394\pi$
$360$	−860.911	−	364.933i	−0.126039	−	0.0534268i
$361$	−179.342	+	310.630i	−0.0261470	+	0.0452879i
$362$	−1065.12	−	614.948i	−0.154645	−	0.0892844i
$363$			2533.87i			0.366374i
$364$	2386.11	+	1133.88i	0.343589	+	0.163274i
$365$	6965.52	−	5254.30i	0.998883	−	0.753487i
$366$	1671.52	−	2895.15i	0.238720	−	0.413475i
$367$	2600.89	+	1501.63i	0.369933	+	0.213581i	0.673429	−	0.739252i	$-0.264821\pi$
$367$	2600.89	+	1501.63i	0.369933	+	0.213581i	−0.303496	+	0.952833i	$0.598154\pi$
$368$	−2185.99	+	1262.08i	−0.309654	+	0.178779i
$369$	3702.13			0.522290
$370$	−105.871	+	249.760i	−0.0148756	+	0.0350930i
$371$	3864.81	+	6694.05i	0.540838	+	0.936759i
$372$			2868.07i			0.399738i
$373$	−5883.79	+	3397.01i	−0.816760	+	0.471556i	−0.849298	−	0.527914i	$-0.822974\pi$
$373$	−5883.79	+	3397.01i	−0.816760	+	0.471556i	0.0325382	+	0.999470i	$0.489641\pi$
$374$	3589.24	−	6216.75i	0.496244	−	0.859521i
$375$	−8449.63	−	1325.44i	−1.16356	−	0.182521i
$376$	−2970.83			−0.407470
$377$	3149.32	−	6627.33i	0.430234	−	0.905372i
$378$			2853.61i			0.388290i
$379$	−1310.01	+	2269.01i	−0.177549	+	0.307523i	−0.941040	−	0.338295i	$-0.890150\pi$
$379$	−1310.01	+	2269.01i	−0.177549	+	0.307523i	0.763492	+	0.645818i	$0.223483\pi$
$380$	3770.84	−	464.894i	0.509053	−	0.0627594i
$381$	2245.93	+	3890.07i	0.302002	+	0.523082i
$382$		−	475.195i		−	0.0636468i
$383$	−9237.18	+	5333.09i	−1.23237	+	0.711509i	−0.967523	−	0.252781i	$-0.918655\pi$
$383$	−9237.18	+	5333.09i	−1.23237	+	0.711509i	−0.264847	+	0.964290i	$0.585321\pi$
$384$	−391.680	−	678.409i	−0.0520516	−	0.0901560i
$385$	−3808.45	+	2872.82i	−0.504146	+	0.380293i
$386$	−1949.29	−	3376.27i	−0.257037	−	0.445201i
$387$	−483.026	−	278.875i	−0.0634460	−	0.0366306i
$388$	−5621.21	−	3245.40i	−0.735499	−	0.424640i
$389$	7592.68			0.989624			0.494812	−	0.869000i	$-0.335237\pi$
$389$	7592.68			0.989624			0.494812	+	0.869000i	$0.335237\pi$
$390$	2023.49	−	6086.80i	0.262726	−	0.790300i
$391$	18699.2			2.41857
$392$	−1000.82	−	577.823i	−0.128951	−	0.0744501i
$393$	8788.45	+	5074.01i	1.12804	+	0.651273i
$394$	−1403.73	−	2431.34i	−0.179490	−	0.310886i
$395$	29.2815	+	38.8179i	0.00372990	+	0.00494466i
$396$	633.145	+	1096.64i	0.0803453	+	0.139162i
$397$	158.086	−	91.2710i	0.0199852	−	0.0115384i	−0.489974	−	0.871737i	$-0.662994\pi$
$397$	158.086	−	91.2710i	0.0199852	−	0.0115384i	0.509959	+	0.860199i	$0.329660\pi$
$398$			149.982i			0.0188892i
$399$	3663.10	+	6344.67i	0.459610	+	0.796068i
$400$	−1390.74	−	1437.30i	−0.173842	−	0.179663i
$401$	5134.80	−	8893.74i	0.639451	−	1.10756i	−0.346103	−	0.938197i	$-0.612495\pi$
$401$	5134.80	−	8893.74i	0.639451	−	1.10756i	0.985553	−	0.169365i	$-0.0541716\pi$
$402$		−	4920.88i		−	0.610526i
$403$	−5473.98	+	438.778i	−0.676622	+	0.0542360i
$404$	869.581			0.107087
$405$	10008.6	−	1233.93i	1.22798	−	0.151393i
$406$	2205.80	−	3820.55i	0.269635	−	0.467022i
$407$	318.148	−	183.683i	0.0387469	−	0.0223705i
$408$			5803.19i			0.704168i
$409$	490.250	+	849.138i	0.0592697	+	0.102658i	0.894138	−	0.447792i	$-0.147789\pi$
$409$	490.250	+	849.138i	0.0592697	+	0.102658i	−0.834868	+	0.550450i	$0.814456\pi$
$410$	7290.51	+	3090.38i	0.878177	+	0.372251i
$411$	−10861.8			−1.30359
$412$	−1284.67	+	741.703i	−0.153619	+	0.0886920i
$413$	5207.77	+	3006.71i	0.620478	+	0.358233i
$414$	−1649.28	+	2856.63i	−0.195791	+	0.339121i
$415$	−3622.88	+	2732.85i	−0.428531	+	0.323254i
$416$	1234.88	−	851.345i	0.145541	−	0.100338i
$417$			5774.14i			0.678084i
$418$	−4455.91	−	2572.62i	−0.521402	−	0.301031i
$419$	−7152.52	+	12388.5i	−0.833946	+	1.44444i	0.0609403	+	0.998141i	$0.480590\pi$
$419$	−7152.52	+	12388.5i	−0.833946	+	1.44444i	−0.894886	+	0.446295i	$0.852743\pi$
$420$	1505.10	−	3550.68i	0.174861	−	0.412513i
$421$	−13678.6			−1.58350			−0.791752	−	0.610843i	$-0.790831\pi$
$421$	−13678.6			−1.58350			−0.791752	+	0.610843i	$0.790831\pi$
$422$	8436.38	−	4870.75i	0.973167	−	0.561858i
$423$	−3362.13	+	1941.12i	−0.386459	+	0.223122i
$424$	4388.53			0.502656
$425$	3598.57	+	14372.5i	0.410721	+	1.64040i
$426$	3083.39	−	5340.58i	0.350682	−	0.607399i
$427$	3332.87	+	1924.24i	0.377726	+	0.218080i
$428$			5513.89i			0.622719i
$429$	−7151.62	+	4930.42i	−0.804857	+	0.554878i
$430$	−718.418	−	952.392i	−0.0805702	−	0.106810i
$431$	3672.00	−	6360.08i	0.410380	−	0.710799i	−0.584551	−	0.811357i	$-0.698729\pi$
$431$	3672.00	−	6360.08i	0.410380	−	0.710799i	0.994931	+	0.100558i	$0.0320627\pi$
$432$	1403.09	+	810.075i	0.156265	+	0.0902194i
$433$	−1858.48	+	1072.99i	−0.206265	+	0.119087i	−0.599575	−	0.800319i	$-0.704664\pi$
$433$	−1858.48	+	1072.99i	−0.206265	+	0.119087i	0.393309	+	0.919406i	$0.371330\pi$
$434$	−3301.70			−0.365177
$435$	−9861.88	−	4180.37i	−1.08699	−	0.460766i
$436$	−2379.46	−	4121.34i	−0.261366	−	0.452699i
$437$		−	13402.8i		−	1.46715i
$438$	8272.25	−	4775.99i	0.902428	−	0.521017i
$439$	−819.026	+	1418.59i	−0.0890432	+	0.154227i	−0.907107	−	0.420900i	$-0.861714\pi$
$439$	−819.026	+	1418.59i	−0.0890432	+	0.154227i	0.818064	+	0.575128i	$0.195048\pi$
$440$	331.408	+	2688.11i	0.0359074	+	0.291251i
$441$	−1510.19			−0.163070
$442$	−11075.9	+	887.813i	−1.19192	+	0.0955406i
$443$		−	17693.5i		−	1.89762i	−0.315853	−	0.948808i	$-0.602291\pi$
$443$		−	17693.5i		−	1.89762i	0.315853	−	0.948808i	$-0.397709\pi$
$444$	−148.492	+	257.195i	−0.0158718	+	0.0274908i
$445$	−13227.2	+	1630.73i	−1.40905	+	0.173717i
$446$	3984.54	+	6901.43i	0.423035	+	0.732718i
$447$		−	11404.0i		−	1.20669i
$448$	780.979	−	450.898i	0.0823611	−	0.0475512i
$449$	−7108.66	−	12312.6i	−0.747168	−	1.29413i	−0.949175	−	0.314749i	$-0.898080\pi$
$449$	−7108.66	−	12312.6i	−0.747168	−	1.29413i	0.202007	−	0.979384i	$-0.435254\pi$
$450$	−2513.05	−	717.916i	−0.263258	−	0.0752064i
$451$	−5361.70	−	9286.74i	−0.559806	−	0.969613i
$452$	−6937.83	−	4005.56i	−0.721965	−	0.416826i
$453$	17617.7	+	10171.6i	1.82727	+	1.05497i
$454$	3856.17			0.398632
$455$	7007.07	+	2329.42i	0.721970	+	0.240011i
$456$	4159.49			0.427162
$457$	8007.40	+	4623.07i	0.819629	+	0.473213i	0.850288	−	0.526317i	$-0.176428\pi$
$457$	8007.40	+	4623.07i	0.819629	+	0.473213i	−0.0306598	+	0.999530i	$0.509761\pi$
$458$	5945.93	+	3432.88i	0.606626	+	0.350236i
$459$	−6001.10	−	10394.2i	−0.610256	−	1.05699i
$460$	−5632.48	+	4248.75i	−0.570904	+	0.430650i
$461$	−754.676	−	1307.14i	−0.0762446	−	0.132060i	0.825382	−	0.564574i	$-0.190960\pi$
$461$	−754.676	−	1307.14i	−0.0762446	−	0.132060i	−0.901627	+	0.432515i	$0.857626\pi$
$462$	−4522.91	+	2611.30i	−0.455465	+	0.262963i
$463$			15065.2i			1.51218i	0.654469	+	0.756089i	$0.272892\pi$
$463$			15065.2i			1.51218i	−0.654469	+	0.756089i	$0.727108\pi$
$464$	−1252.35	−	2169.14i	−0.125300	−	0.217025i
$465$	980.902	+	7956.27i	0.0978241	+	0.793469i
$466$	−6437.17	+	11149.5i	−0.639906	+	1.10835i
$467$		−	17082.1i		−	1.69265i	−0.532667	−	0.846325i	$-0.678810\pi$
$467$		−	17082.1i		−	1.69265i	0.532667	−	0.846325i	$-0.321190\pi$
$468$	841.272	−	1770.35i	0.0830936	−	0.174860i
$469$	5664.88			0.557740
$470$	−8241.31	+	1016.04i	−0.808816	+	0.0997162i
$471$	4818.92	−	8346.61i	0.471431	−	0.816543i
$472$	2956.74	−	1707.07i	0.288337	−	0.166471i
$473$			1615.55i			0.157047i
$474$	26.6159	+	46.1001i	0.00257913	+	0.00446719i
$475$	10301.6	−	2579.31i	0.995097	−	0.249151i
$476$	−6680.59			−0.643286
$477$	4966.57	−	2867.45i	0.476737	−	0.275244i
$478$	−2535.76	−	1464.02i	−0.242642	−	0.140089i
$479$	−5915.17	+	10245.4i	−0.564240	+	0.977292i	0.432880	+	0.901452i	$0.357497\pi$
$479$	−5915.17	+	10245.4i	−0.564240	+	0.977292i	−0.997120	+	0.0758406i	$0.975836\pi$
$480$	−1318.57	−	1748.01i	−0.125384	−	0.166219i
$481$	−513.598	−	244.062i	−0.0486862	−	0.0231357i
$482$		−	4867.41i		−	0.459967i
$483$	−11781.7	−	6802.17i	−1.10991	−	0.640807i
$484$	−828.063	+	1434.25i	−0.0777670	+	0.134696i
$485$	−16703.6	−	7080.53i	−1.56386	−	0.662908i
$486$	5572.14			0.520077
$487$	−9454.07	+	5458.31i	−0.879682	+	0.507884i	−0.870553	−	0.492074i	$-0.836239\pi$
$487$	−9454.07	+	5458.31i	−0.879682	+	0.507884i	−0.00912818	+	0.999958i	$0.502906\pi$
$488$	1892.26	−	1092.50i	0.175530	−	0.101342i
$489$	−10655.0			−0.985353
$490$	−2973.97	−	1260.64i	−0.274184	−	0.116224i
$491$	−7287.90	+	12623.0i	−0.669854	+	1.16022i	0.308090	+	0.951357i	$0.400310\pi$
$491$	−7287.90	+	12623.0i	−0.669854	+	1.16022i	−0.977945	+	0.208865i	$0.933023\pi$
$492$	7507.53	+	4334.47i	0.687938	+	0.397181i
$493$			18555.1i			1.69509i
$494$	636.348	+	7938.77i	0.0579568	+	0.723041i
$495$	2131.46	+	2825.63i	0.193539	+	0.256571i
$496$	−937.280	+	1623.42i	−0.0848490	+	0.146963i
$497$	6148.03	+	3549.57i	0.554883	+	0.320362i
$498$	−4302.53	+	2484.07i	−0.387151	+	0.223522i
$499$	14491.1			1.30002			0.650012	−	0.759924i	$-0.274764\pi$
$499$	14491.1			1.30002			0.650012	+	0.759924i	$0.274764\pi$
$500$	−4349.59	−	3511.56i	−0.389039	−	0.314083i
$501$	−5604.83	−	9707.84i	−0.499811	−	0.865698i
$502$			11837.7i			1.05248i
$503$	10521.8	−	6074.79i	0.932696	−	0.538492i	0.0450327	−	0.998986i	$-0.485661\pi$
$503$	10521.8	−	6074.79i	0.932696	−	0.538492i	0.887663	+	0.460493i	$0.152327\pi$
$504$	589.230	−	1020.58i	0.0520762	−	0.0901986i
$505$	2412.29	−	297.403i	0.212565	−	0.0262065i
$506$	9554.44			0.839420
$507$	12566.5	+	4782.16i	1.10078	+	0.418901i
$508$			2935.86i			0.256413i
$509$	−2480.72	+	4296.73i	−0.216023	+	0.374163i	−0.953589	−	0.301113i	$-0.902642\pi$
$509$	−2480.72	+	4296.73i	−0.216023	+	0.374163i	0.737565	+	0.675276i	$0.235975\pi$
$510$	1984.73	+	16098.5i	0.172324	+	1.39775i
$511$	5498.08	+	9522.95i	0.475970	+	0.824404i
$512$		−	512.000i		−	0.0441942i
$513$	−7450.15	+	4301.35i	−0.641193	+	0.370193i
$514$	2573.68	+	4457.74i	0.220856	+	0.382534i
$515$	−3310.11	+	2496.91i	−0.283225	+	0.213645i
$516$	−653.018	−	1131.06i	−0.0557122	−	0.0964964i
$517$	9738.57	+	5622.56i	0.828437	+	0.478298i
$518$	−296.081	−	170.942i	−0.0251140	−	0.0144996i
$519$	−9919.74			−0.838975
$520$	3134.51	−	2784.04i	0.264341	−	0.234785i
$521$	22462.9			1.88890			0.944452	−	0.328651i	$-0.106594\pi$
$521$	22462.9			1.88890			0.944452	+	0.328651i	$0.106594\pi$
$522$	−2834.61	−	1636.56i	−0.237677	−	0.137223i
$523$	−1089.78	−	629.185i	−0.0911143	−	0.0526049i	0.453751	−	0.891129i	$-0.350086\pi$
$523$	−1089.78	−	629.185i	−0.0911143	−	0.0526049i	−0.544865	+	0.838524i	$0.683419\pi$
$524$	3316.35	+	5744.09i	0.276480	+	0.478877i
$525$	2960.92	−	10364.6i	0.246143	−	0.861619i
$526$	−1552.56	−	2689.12i	−0.128698	−	0.222911i
$527$	12026.4	−	6943.45i	0.994076	−	0.573930i
$528$			2965.16i			0.244398i
$529$	6360.66	+	11017.0i	0.522780	+	0.905481i
$530$	12174.2	−	1500.91i	0.997758	−	0.123010i
$531$	2230.79	−	3863.84i	0.182313	−	0.315775i
$532$			4788.37i			0.390230i
$533$	−7124.19	+	14991.9i	−0.578955	+	1.21834i
$534$	−14590.5			−1.18238
$535$	1885.79	+	15296.0i	0.152392	+	1.23608i
$536$	1608.13	−	2785.37i	0.129591	−	0.224458i
$537$	7461.35	−	4307.81i	0.599592	−	0.346175i
$538$			11063.4i			0.886572i
$539$	2187.17	+	3788.28i	0.174783	+	0.302733i
$540$	4169.34	+	1767.35i	0.332259	+	0.140842i
$541$	14556.8			1.15683			0.578417	−	0.815741i	$-0.303671\pi$
$541$	14556.8			1.15683			0.578417	+	0.815741i	$0.303671\pi$
$542$	−9473.64	+	5469.61i	−0.750789	+	0.433468i
$543$	−3259.27	−	1881.74i	−0.257585	−	0.148717i
$544$	−1896.47	+	3284.78i	−0.149468	+	0.258886i
$545$	−8010.34	−	10619.2i	−0.629588	−	0.834632i
$546$	7301.50	+	3469.68i	0.572299	+	0.271957i
$547$		−	16605.5i		−	1.29799i	−0.760794	−	0.648993i	$-0.775190\pi$
$547$		−	16605.5i		−	1.29799i	0.760794	−	0.648993i	$-0.224810\pi$
$548$	−6148.13	−	3549.63i	−0.479261	−	0.276702i
$549$	1427.66	−	2472.79i	0.110986	−	0.192233i
$550$	1838.70	+	7343.69i	0.142550	+	0.569338i
$551$	13299.5			1.02827
$552$	−6689.13	+	3861.97i	−0.515776	+	0.297783i
$553$	−53.0701	+	30.6400i	−0.00408096	+	0.00235614i
$554$	−3520.31			−0.269970
$555$	−323.965	+	764.265i	−0.0247776	+	0.0584527i
$556$	−1886.98	+	3268.34i	−0.143931	+	0.249296i
$557$	−2919.60	−	1685.63i	−0.222096	−	0.128227i	0.384825	−	0.922990i	$-0.374262\pi$
$557$	−2919.60	−	1685.63i	−0.222096	−	0.128227i	−0.606920	+	0.794763i	$0.707595\pi$
$558$			2449.66i			0.185846i
$559$	2058.83	−	1419.38i	0.155777	−	0.107394i
$560$	2012.29	−	1517.93i	0.151848	−	0.114543i
$561$	10983.1	−	19023.2i	0.826570	−	1.43166i
$562$	−11336.7	−	6545.23i	−0.850904	−	0.491270i
$563$	4133.86	−	2386.69i	0.309452	−	0.178662i	−0.337229	−	0.941423i	$-0.609490\pi$
$563$	4133.86	−	2386.69i	0.309452	−	0.178662i	0.646681	+	0.762760i	$0.276156\pi$
$564$	−9090.72			−0.678703
$565$	−20616.0	−	8738.96i	−1.53509	−	0.650709i
$566$	996.376	+	1725.77i	0.0739943	+	0.128162i
$567$			12709.3i			0.941344i
$568$	3490.58	−	2015.29i	0.257855	−	0.148872i
$569$	8878.13	−	15377.4i	0.654114	−	1.13296i	−0.328001	−	0.944677i	$-0.606375\pi$
$569$	8878.13	−	15377.4i	0.654114	−	1.13296i	0.982115	−	0.188281i	$-0.0602916\pi$
$570$	11538.8	−	1422.57i	0.847905	−	0.104535i
$571$	−19264.7			−1.41191			−0.705956	−	0.708256i	$-0.749482\pi$
$571$	−19264.7			−1.41191			−0.705956	+	0.708256i	$0.749482\pi$
$572$	−5659.28	+	453.631i	−0.413683	+	0.0331596i
$573$		−	1454.09i		−	0.106013i
$574$	−4989.81	+	8642.61i	−0.362841	+	0.628459i
$575$	−14171.9	+	13712.7i	−1.02784	+	0.994539i
$576$	−334.539	−	579.438i	−0.0241998	−	0.0419153i
$577$			12737.2i			0.918991i	0.888180	+	0.459496i	$0.151970\pi$
$577$			12737.2i			0.918991i	−0.888180	+	0.459496i	$0.848030\pi$
$578$	15824.4	−	9136.20i	1.13877	−	0.657467i
$579$	−5964.82	−	10331.4i	−0.428134	−	0.741550i
$580$	−4215.99	−	5589.05i	−0.301827	−	0.400126i
$581$	−2859.64	−	4953.04i	−0.204196	−	0.353678i
$582$	−17200.9	−	9930.93i	−1.22508	−	0.707303i
$583$	−14385.9	−	8305.71i	−1.02196	−	0.590030i
$584$	6243.12			0.442367
$585$	1728.29	−	5198.81i	0.122147	−	0.367426i
$586$	8864.12			0.624870
$587$	19624.7	+	11330.3i	1.37989	+	0.796681i	0.992146	−	0.125086i	$-0.0399207\pi$
$587$	19624.7	+	11330.3i	1.37989	+	0.796681i	0.387745	+	0.921767i	$0.373254\pi$
$588$	−3062.50	−	1768.14i	−0.214788	−	0.124008i
$589$	−4976.78	−	8620.03i	−0.348157	−	0.603026i
$590$	7618.40	−	5746.79i	0.531601	−	0.401003i
$591$	−4295.42	−	7439.88i	−0.298968	−	0.517827i
$592$	−168.101	+	97.0534i	−0.0116705	+	0.00673796i
$593$		−	10966.7i		−	0.759444i	−0.925101	−	0.379722i	$-0.876020\pi$
$593$		−	10966.7i		−	0.759444i	0.925101	−	0.379722i	$-0.123980\pi$
$594$	−3066.29	−	5310.96i	−0.211803	−	0.366854i
$595$	−18532.5	+	2284.81i	−1.27690	+	0.157425i
$596$	3726.81	−	6455.02i	0.256134	−	0.443637i
$597$			458.944i			0.0314628i
$598$	−8394.28	−	12176.0i	−0.574026	−	0.832631i
$599$	−3288.67			−0.224326			−0.112163	−	0.993690i	$-0.535778\pi$
$599$	−3288.67			−0.224326			−0.112163	+	0.993690i	$0.535778\pi$
$600$	−4255.66	−	4398.15i	−0.289561	−	0.299256i
$601$	−8920.83	+	15451.3i	−0.605471	+	1.04871i	0.386506	+	0.922287i	$0.373682\pi$
$601$	−8920.83	+	15451.3i	−0.605471	+	1.04871i	−0.991977	+	0.126420i	$0.959651\pi$
$602$	1302.07	−	751.749i	0.0881533	−	0.0508953i
$603$		−	4202.99i		−	0.283846i
$604$	6648.10	+	11514.9i	0.447860	+	0.775716i
$605$	−1806.59	+	4261.92i	−0.121402	+	0.286400i
$606$	2660.92			0.178370
$607$	−22136.2	+	12780.3i	−1.48020	+	0.854592i	−0.999748	−	0.0224314i	$-0.992859\pi$
$607$	−22136.2	+	12780.3i	−1.48020	+	0.854592i	−0.480448	+	0.877023i	$0.659526\pi$
$608$	2354.40	+	1359.31i	0.157045	+	0.0906700i
$609$	6749.73	−	11690.9i	0.449118	−	0.777895i
$610$	4875.64	−	3677.84i	0.323621	−	0.244117i
$611$	−1390.76	−	17350.5i	−0.0920854	−	1.14881i
$612$			4956.58i			0.327382i
$613$	3956.20	+	2284.11i	0.260668	+	0.150497i	0.624639	−	0.780913i	$-0.285246\pi$
$613$	3956.20	+	2284.11i	0.260668	+	0.150497i	−0.363971	+	0.931410i	$0.618579\pi$
$614$	−4896.49	+	8480.97i	−0.321834	+	0.557433i
$615$	22308.9	+	9456.56i	1.46274	+	0.620041i
$616$	−3413.47			−0.223267
$617$	−9859.26	+	5692.25i	−0.643305	+	0.371412i	−0.785886	−	0.618371i	$-0.787793\pi$
$617$	−9859.26	+	5692.25i	−0.643305	+	0.371412i	0.142582	+	0.989783i	$0.454460\pi$
$618$	−3931.08	+	2269.61i	−0.255876	+	0.147730i
$619$	20545.0			1.33404			0.667021	−	0.745039i	$-0.267569\pi$
$619$	20545.0			1.33404			0.667021	+	0.745039i	$0.267569\pi$
$620$	−2044.87	+	4824.05i	−0.132458	+	0.312481i
$621$	7987.36	−	13834.5i	0.516138	−	0.893977i
$622$	−200.161	−	115.563i	−0.0129031	−	0.00744961i
$623$		−	16796.4i		−	1.08015i
$624$	3778.74	−	2605.11i	0.242421	−	0.167128i
$625$	−13267.1	−	8253.76i	−0.849095	−	0.528241i
$626$	1047.20	−	1813.81i	0.0668604	−	0.115806i
$627$	−13635.1	−	7872.22i	−0.868473	−	0.501413i
$628$	5455.31	−	3149.62i	0.346641	−	0.200133i
$629$	1437.96			0.0911529
$630$	1285.53	−	3032.68i	0.0812963	−	0.191786i
$631$	−4127.61	−	7149.23i	−0.260408	−	0.451040i	0.705942	−	0.708269i	$-0.250524\pi$
$631$	−4127.61	−	7149.23i	−0.260408	−	0.451040i	−0.966350	+	0.257229i	$0.917191\pi$
$632$			34.7921i			0.00218980i
$633$	25815.3	−	14904.5i	1.62096	−	0.935860i
$634$	−4305.79	+	7457.85i	−0.269724	+	0.467175i
$635$	1004.09	+	8144.32i	0.0627495	+	0.508973i
$636$	13428.9			0.837249
$637$	2906.13	−	6115.57i	0.180761	−	0.380389i
$638$			9480.77i			0.588319i
$639$	2633.56	−	4561.46i	0.163039	−	0.282392i
$640$	−175.108	−	1420.33i	−0.0108152	−	0.0877242i
$641$	14296.8	+	24762.8i	0.880952	+	1.52585i	0.850285	+	0.526323i	$0.176430\pi$
$641$	14296.8	+	24762.8i	0.880952	+	1.52585i	0.0306669	+	0.999530i	$0.490237\pi$
$642$			16872.5i			1.03723i
$643$	22449.0	−	12960.9i	1.37683	−	0.794912i	0.385052	−	0.922895i	$-0.374183\pi$
$643$	22449.0	−	12960.9i	1.37683	−	0.794912i	0.991776	+	0.127982i	$0.0408501\pi$
$644$	−4445.87	−	7700.47i	−0.272037	−	0.471182i
$645$	−2198.36	−	2914.32i	−0.134202	−	0.177909i
$646$	−10069.9	−	17441.6i	−0.613304	−	1.06227i
$647$	24519.6	+	14156.4i	1.48990	+	0.860194i	0.999933	−	0.0115477i	$-0.00367584\pi$
$647$	24519.6	+	14156.4i	1.48990	+	0.860194i	0.489966	+	0.871742i	$0.337009\pi$
$648$	6249.06	+	3607.90i	0.378837	+	0.218721i
$649$	−12923.2			−0.781632
$650$	7743.21	−	8795.18i	0.467252	−	0.530731i
$651$	−10103.2			−0.608258
$652$	−6031.08	−	3482.04i	−0.362263	−	0.209152i
$653$	−21040.3	−	12147.6i	−1.26090	−	0.727983i	−0.287654	−	0.957734i	$-0.592875\pi$
$653$	−21040.3	−	12147.6i	−1.26090	−	0.727983i	−0.973249	+	0.229751i	$0.926209\pi$
$654$	−7281.14	−	12611.3i	−0.435344	−	0.754038i
$655$	11164.4	+	14800.4i	0.665996	+	0.882898i
$656$	2832.99	+	4906.89i	0.168612	+	0.292045i
$657$	7065.43	−	4079.23i	0.419557	−	0.242231i
$658$		−	10465.2i		−	0.620022i
$659$	−10429.5	−	18064.3i	−0.616501	−	1.06781i	−0.990119	−	0.140228i	$-0.955216\pi$
$659$	−10429.5	−	18064.3i	−0.616501	−	1.06781i	0.373619	−	0.927582i	$-0.378117\pi$
$660$	1014.11	+	8225.60i	0.0598091	+	0.485123i
$661$	10275.4	−	17797.5i	0.604641	−	1.04727i	−0.387468	−	0.921883i	$-0.626650\pi$
$661$	10275.4	−	17797.5i	0.604641	−	1.04727i	0.992108	−	0.125385i	$-0.0400166\pi$
$662$		−	1370.88i		−	0.0804845i
$663$	−33892.3	+	2716.70i	−1.98532	+	0.159137i
$664$	−3247.15			−0.189780
$665$	1637.66	+	13283.3i	0.0954972	+	0.774595i
$666$	−126.829	+	219.673i	−0.00737914	+	0.0127810i
$667$	−21387.7	+	12348.2i	−1.24158	+	0.716829i
$668$		−	7326.58i		−	0.424362i
$669$	12192.7	+	21118.4i	0.704629	+	1.22045i
$670$	3508.48	−	8276.83i	0.202305	−	0.477257i
$671$	−8270.60			−0.475831
$672$	2389.79	−	1379.75i	0.137185	−	0.0792038i
$673$	14125.0	+	8155.06i	0.809031	+	0.467094i	0.846619	−	0.532199i	$-0.178634\pi$
$673$	14125.0	+	8155.06i	0.809031	+	0.467094i	−0.0375880	+	0.999293i	$0.511967\pi$
$674$	3807.14	−	6594.16i	0.217575	−	0.376851i
$675$	12170.5	+	3476.82i	0.693992	+	0.198256i
$676$	5550.20	+	6813.53i	0.315783	+	0.387661i
$677$			2737.95i			0.155433i	0.996976	+	0.0777165i	$0.0247629\pi$
$677$			2737.95i			0.155433i	−0.996976	+	0.0777165i	$0.975237\pi$
$678$	−21229.7	−	12257.0i	−1.20254	−	0.694288i
$679$	11432.4	−	19801.5i	0.646149	−	1.11916i
$680$	−4137.54	+	9760.86i	−0.233335	+	0.550459i
$681$	11799.9			0.663982
$682$	6144.93	−	3547.78i	0.345017	−	0.199196i
$683$	−8153.76	+	4707.58i	−0.456801	+	0.263734i	−0.710698	−	0.703497i	$-0.751621\pi$
$683$	−8153.76	+	4707.58i	−0.456801	+	0.263734i	0.253897	+	0.967231i	$0.418287\pi$
$684$	3552.67			0.198596
$685$	−18269.4	−	7744.25i	−1.01903	−	0.431960i
$686$	6868.53	−	11896.6i	0.382277	−	0.662122i
$687$	18194.5	+	10504.6i	1.01043	+	0.583371i
$688$		−	853.619i		−	0.0473022i
$689$	2054.45	+	25630.3i	0.113597	+	1.41718i
$690$	−17235.4	+	13001.1i	−0.950926	+	0.717312i
$691$	2787.02	−	4827.25i	0.153434	−	0.265756i	−0.779054	−	0.626957i	$-0.784300\pi$
$691$	2787.02	−	4827.25i	0.153434	−	0.265756i	0.932488	+	0.361201i	$0.117633\pi$
$692$	−5614.87	−	3241.75i	−0.308447	−	0.178082i
$693$	−3863.07	+	2230.35i	−0.211755	+	0.122257i
$694$	16909.6			0.924900
$695$	−4116.83	+	9712.00i	−0.224691	+	0.530068i
$696$	−3832.19	−	6637.56i	−0.208705	−	0.361488i
$697$		−	41974.1i		−	2.28104i
$698$	2296.91	−	1326.12i	0.124555	−	0.0719117i
$699$	−19697.7	+	34117.5i	−1.06586	+	1.84612i
$700$	5063.11	−	4899.08i	0.273382	−	0.264525i
$701$	18389.3			0.990804			0.495402	−	0.868664i	$-0.335021\pi$
$701$	18389.3			0.990804			0.495402	+	0.868664i	$0.335021\pi$
$702$	−4074.23	+	8573.69i	−0.219048	+	0.460959i
$703$		−	1030.67i		−	0.0552951i
$704$	−969.008	+	1678.37i	−0.0518762	+	0.0898522i
$705$	−25218.4	+	3109.09i	−1.34721	+	0.166092i
$706$	−5859.04	−	10148.2i	−0.312334	−	0.540979i
$707$			3063.23i			0.162948i
$708$	9047.61	−	5223.64i	0.480268	−	0.277283i
$709$	8328.23	+	14424.9i	0.441147	+	0.764089i	0.997775	−	0.0666732i	$-0.0212385\pi$
$709$	8328.23	+	14424.9i	0.441147	+	0.764089i	−0.556628	+	0.830762i	$0.687905\pi$
$710$	8993.91	−	6784.37i	0.475402	−	0.358610i
$711$	22.7330	+	39.3747i	0.00119909	+	0.00207689i
$712$	−8258.64	−	4768.13i	−0.434699	−	0.250974i
$713$	16006.9	+	9241.60i	0.840763	+	0.485415i
$714$	−20442.6			−1.07149
$715$	−15544.2	+	3193.93i	−0.813034	+	0.167057i
$716$	5631.13			0.293918
$717$	−7759.41	−	4479.90i	−0.404157	−	0.233340i
$718$	19002.1	+	10970.9i	0.987677	+	0.570235i
$719$	−8882.63	−	15385.2i	−0.460732	−	0.798011i	0.538266	−	0.842775i	$-0.319080\pi$
$719$	−8882.63	−	15385.2i	−0.460732	−	0.798011i	−0.998998	+	0.0447641i	$0.985746\pi$
$720$	−1126.21	−	1492.99i	−0.0582935	−	0.0772786i
$721$	−2612.76	−	4525.43i	−0.134957	−	0.233753i
$722$	−621.259	+	358.684i	−0.0320234	+	0.0184887i
$723$		−	14894.2i		−	0.766145i
$724$	−1229.90	−	2130.24i	−0.0631336	−	0.109351i
$725$	−13607.0	−	14062.6i	−0.697036	−	0.720375i
$726$	−2533.87	+	4388.79i	−0.129533	+	0.224357i
$727$		−	3627.50i		−	0.185057i	−0.995710	−	0.0925286i	$-0.970505\pi$
$727$		−	3627.50i		−	0.185057i	0.995710	−	0.0925286i	$-0.0294950\pi$
$728$	2998.98	+	4350.06i	0.152678	+	0.221461i
$729$	−7302.56			−0.371008
$730$	17318.9	−	2135.19i	0.878086	−	0.108256i
$731$	−3161.84	+	5476.47i	−0.159979	+	0.277092i
$732$	5790.30	−	3343.03i	0.292371	−	0.168801i
$733$			7709.23i			0.388468i	0.980955	+	0.194234i	$0.0622221\pi$
$733$			7709.23i			0.388468i	−0.980955	+	0.194234i	$0.937778\pi$
$734$	3003.25	+	5201.79i	0.151025	+	0.261582i
$735$	−9100.34	−	3857.56i	−0.456696	−	0.193589i
$736$	−5048.33			−0.252831
$737$	−10543.1	+	6087.08i	−0.526949	+	0.304234i
$738$	6412.28	+	3702.13i	0.319836	+	0.184658i
$739$	9859.44	−	17077.1i	0.490779	−	0.850054i	−0.509165	−	0.860669i	$-0.670046\pi$
$739$	9859.44	−	17077.1i	0.490779	−	0.850054i	0.999944	+	0.0106154i	$0.00337905\pi$
$740$	−433.134	+	326.726i	−0.0215167	+	0.0162307i
$741$	1947.22	+	24292.6i	0.0965358	+	1.20433i
$742$			15459.2i			0.764861i
$743$	−22231.6	−	12835.4i	−1.09771	−	0.633762i	−0.162090	−	0.986776i	$-0.551824\pi$
$743$	−22231.6	−	12835.4i	−1.09771	−	0.633762i	−0.935618	+	0.353014i	$0.885157\pi$
$744$	−2868.07	+	4967.65i	−0.141329	+	0.244789i
$745$	8130.80	−	19181.3i	0.399852	−	0.943289i
$746$	−13588.0			−0.666881
$747$	−3674.85	+	2121.68i	−0.179994	+	0.103920i
$748$	12433.5	−	7178.49i	0.607773	−	0.350898i
$749$	−19423.5			−0.947554
$750$	−13309.7	−	10745.4i	−0.648004	−	0.523153i
$751$	−16493.0	+	28566.8i	−0.801384	+	1.38804i	0.117322	+	0.993094i	$0.462569\pi$
$751$	−16493.0	+	28566.8i	−0.801384	+	1.38804i	−0.918705	+	0.394943i	$0.870764\pi$
$752$	−5145.62	−	2970.83i	−0.249523	−	0.144062i
$753$			36223.4i			1.75306i
$754$	12082.1	−	8329.56i	0.583561	−	0.402314i
$755$	22380.5	+	29669.4i	1.07882	+	1.43017i
$756$	−2853.61	+	4942.59i	−0.137281	+	0.237778i
$757$	−13455.5	−	7768.56i	−0.646037	−	0.372990i	0.140899	−	0.990024i	$-0.455001\pi$
$757$	−13455.5	−	7768.56i	−0.646037	−	0.372990i	−0.786936	+	0.617034i	$0.788334\pi$
$758$	−4538.02	+	2620.03i	−0.217452	+	0.125546i
$759$	29236.5			1.39818
$760$	6996.18	+	2965.62i	0.333919	+	0.141545i
$761$	5126.51	+	8879.38i	0.244200	+	0.422966i	0.961906	−	0.273379i	$-0.0881414\pi$
$761$	5126.51	+	8879.38i	0.244200	+	0.422966i	−0.717707	+	0.696346i	$0.754808\pi$
$762$			8983.73i			0.427095i
$763$	14518.0	−	8381.99i	0.688844	−	0.397704i
$764$	475.195	−	823.062i	0.0225025	−	0.0389755i
$765$	1695.19	+	13750.0i	0.0801171	+	0.649844i
$766$	−21332.4			−1.00623
$767$	11354.0	+	16469.1i	0.534509	+	0.775310i
$768$		−	1566.72i		−	0.0736121i
$769$	−6397.89	+	11081.5i	−0.300018	+	0.519646i	−0.976140	−	0.217144i	$-0.930326\pi$
$769$	−6397.89	+	11081.5i	−0.300018	+	0.519646i	0.676122	+	0.736790i	$0.263659\pi$
$770$	−9469.24	+	1167.43i	−0.443179	+	0.0546380i
$771$	7875.44	+	13640.7i	0.367869	+	0.637168i
$772$		−	7797.16i		−	0.363505i
$773$	26543.3	−	15324.8i	1.23505	−	0.713058i	0.266973	−	0.963704i	$-0.413976\pi$
$773$	26543.3	−	15324.8i	1.23505	−	0.713058i	0.968079	+	0.250646i	$0.0806431\pi$
$774$	−557.751	−	966.053i	−0.0259017	−	0.0448631i
$775$	−4022.78	+	14081.7i	−0.186455	+	0.652682i
$776$	−6490.81	−	11242.4i	−0.300266	−	0.520076i
$777$	−906.006	−	523.083i	−0.0418311	−	0.0241512i
$778$	13150.9	+	7592.68i	0.606019	+	0.349885i
$779$	−30085.3			−1.38372
$780$	9591.58	−	8519.15i	0.440299	−	0.391070i
$781$	−15256.5			−0.699000
$782$	32388.0	+	18699.2i	1.48107	+	0.855093i
$783$	13727.9	+	7925.78i	0.626556	+	0.361742i
$784$	−1155.65	−	2001.64i	−0.0526442	−	0.0911824i
$785$	14056.3	−	10603.1i	0.639096	−	0.482089i
$786$	10148.0	+	17576.9i	0.460519	+	0.797643i
$787$	18433.6	−	10642.7i	0.834928	−	0.482046i	−0.0206092	−	0.999788i	$-0.506561\pi$
$787$	18433.6	−	10642.7i	0.834928	−	0.482046i	0.855537	+	0.517742i	$0.173227\pi$
$788$		−	5614.93i		−	0.253837i
$789$	−4750.84	−	8228.70i	−0.214366	−	0.371292i
$790$	11.8991	+	96.5161i	0.000535889	+	0.00434669i
$791$	14110.2	−	24439.5i	0.634260	−	1.09857i
$792$			2532.58i			0.113625i
$793$	7266.33	+	10539.9i	0.325391	+	0.471983i
$794$	365.084			0.0163178
$795$	37252.9	−	4592.78i	1.66192	−	0.204892i
$796$	−149.982	+	259.776i	−0.00667834	+	0.0115672i
$797$	12059.8	−	6962.76i	0.535987	−	0.309452i	−0.207464	−	0.978243i	$-0.566521\pi$
$797$	12059.8	−	6962.76i	0.535987	−	0.309452i	0.743451	+	0.668790i	$0.233188\pi$
$798$			14652.4i			0.649987i
$799$	22008.1	+	38119.2i	0.974457	+	1.68781i
$800$	−971.526	−	3880.22i	−0.0429358	−	0.171483i
$801$	−12461.9			−0.549712
$802$	17787.5	−	10269.6i	0.783164	−	0.452160i
$803$	−20465.4	−	11815.7i	−0.899387	−	0.519261i
$804$	4920.88	−	8523.22i	0.215853	−	0.373869i
$805$	−14966.8	−	19841.2i	−0.655293	−	0.868709i
$806$	−9920.00	−	4714.00i	−0.433520	−	0.206009i
$807$			33853.9i			1.47672i
$808$	1506.16	+	869.581i	0.0655773	+	0.0378611i
$809$	6479.90	−	11223.5i	0.281609	−	0.487760i	−0.690173	−	0.723645i	$-0.742465\pi$
$809$	6479.90	−	11223.5i	0.281609	−	0.487760i	0.971781	+	0.235885i	$0.0757987\pi$
$810$	18569.3	+	7871.38i	0.805506	+	0.341447i
$811$	−954.838			−0.0413426			−0.0206713	−	0.999786i	$-0.506580\pi$
$811$	−954.838			−0.0413426			−0.0206713	+	0.999786i	$0.506580\pi$
$812$	7641.10	−	4411.59i	0.330234	−	0.190661i
$813$	−28989.3	+	16737.0i	−1.25055	+	0.722007i
$814$	734.731			0.0316367
$815$	−17921.6	−	7596.81i	−0.770265	−	0.326509i
$816$	−5803.19	+	10051.4i	−0.248961	+	0.431213i
$817$	3925.31	+	2266.28i	0.168089	+	0.0970465i
$818$			1961.00i			0.0838200i
$819$	6236.30	+	2963.50i	0.266073	+	0.126438i
$820$	9537.14	+	12643.2i	0.406160	+	0.538439i
$821$	−18762.5	+	32497.6i	−0.797583	+	1.38145i	0.123603	+	0.992332i	$0.460555\pi$
$821$	−18762.5	+	32497.6i	−0.797583	+	1.38145i	−0.921186	+	0.389122i	$0.872778\pi$
$822$	−18813.3	−	10861.8i	−0.798282	−	0.460889i
$823$	−9569.53	+	5524.97i	−0.405313	+	0.234008i	−0.688774	−	0.724976i	$-0.741851\pi$
$823$	−9569.53	+	5524.97i	−0.405313	+	0.234008i	0.283461	+	0.958984i	$0.408517\pi$
$824$	−2966.81			−0.125429
$825$	5626.43	+	22471.7i	0.237439	+	0.948318i
$826$	6013.41	+	10415.5i	0.253309	+	0.438744i
$827$		−	32252.9i		−	1.35616i	−0.734989	−	0.678079i	$-0.762813\pi$
$827$		−	32252.9i		−	1.35616i	0.734989	−	0.678079i	$-0.237187\pi$
$828$	−5713.27	+	3298.56i	−0.239794	+	0.138445i
$829$	−2801.12	+	4851.68i	−0.117355	+	0.203264i	−0.918719	−	0.394913i	$-0.870775\pi$
$829$	−2801.12	+	4851.68i	−0.117355	+	0.203264i	0.801364	+	0.598177i	$0.204108\pi$
$830$	−9007.87	+	1110.55i	−0.376708	+	0.0464431i
$831$	−10772.1			−0.449677
$832$	2990.23	−	239.688i	0.124600	−	0.00998759i
$833$			17122.2i			0.712185i
$834$	−5774.14	+	10001.1i	−0.239739	+	0.415240i
$835$	−2505.74	−	20324.5i	−0.103850	−	0.842346i
$836$	−5145.25	−	8911.83i	−0.212861	−	0.368687i
$837$		−	11863.6i		−	0.489921i
$838$	−24777.0	+	14305.0i	−1.02137	+	0.589689i
$839$	−7344.98	−	12721.9i	−0.302237	−	0.523490i	0.674405	−	0.738361i	$-0.264400\pi$
$839$	−7344.98	−	12721.9i	−0.302237	−	0.523490i	−0.976642	+	0.214872i	$0.931067\pi$
$840$	6157.60	−	4644.86i	0.252925	−	0.190789i
$841$	−58.5205	−	101.361i	−0.00239946	−	0.00415599i
$842$	−23692.1	−	13678.6i	−0.969694	−	0.559853i
$843$	−34690.2	−	20028.4i	−1.41731	−	0.818284i
$844$	19483.0			0.794588
$845$	17727.0	+	17003.1i	0.721688	+	0.692218i
$846$	−7764.50			−0.315542
$847$	−5052.34	−	2916.97i	−0.204959	−	0.118333i
$848$	7601.16	+	4388.53i	0.307813	+	0.177716i
$849$	3048.91	+	5280.86i	0.123249	+	0.213473i
$850$	−8139.60	+	28492.5i	−0.328454	+	1.14975i
$851$	956.949	+	1657.48i	0.0385473	+	0.0667659i
$852$	10681.2	−	6166.77i	0.429496	−	0.247970i
$853$		−	18742.9i		−	0.752337i	−0.926551	−	0.376168i	$-0.877241\pi$
$853$		−	18742.9i		−	0.752337i	0.926551	−	0.376168i	$-0.122759\pi$
$854$	3848.47	+	6665.75i	0.154206	+	0.267093i
$855$	9855.40	−	1215.04i	0.394208	−	0.0486005i
$856$	−5513.89	+	9550.33i	−0.220164	+	0.381336i
$857$			30896.6i			1.23151i	0.787936	+	0.615757i	$0.211150\pi$
$857$			30896.6i			1.23151i	−0.787936	+	0.615757i	$0.788850\pi$
$858$	−17317.4	+	1388.11i	−0.689051	+	0.0552323i
$859$	2963.39			0.117706			0.0588530	−	0.998267i	$-0.481256\pi$
$859$	2963.39			0.117706			0.0588530	+	0.998267i	$0.481256\pi$
$860$	−291.944	−	2368.01i	−0.0115758	−	0.0938935i
$861$	−15268.8	+	26446.4i	−0.604367	+	1.04679i
$862$	12720.2	−	7343.99i	0.502611	−	0.290183i
$863$			44141.4i			1.74112i	0.492059	+	0.870562i	$0.336244\pi$
$863$			44141.4i			1.74112i	−0.492059	+	0.870562i	$0.663756\pi$
$864$	1620.15	+	2806.18i	0.0637947	+	0.110496i
$865$	−16684.8	−	7072.55i	−0.655839	−	0.278004i
$866$	−4291.98			−0.168415
$867$	48422.5	−	27956.7i	1.89679	−	1.09511i
$868$	−5718.72	−	3301.70i	−0.223624	−	0.129110i
$869$	65.8472	−	114.051i	0.00257044	−	0.00445214i
$870$	−12900.9	−	17102.5i	−0.502738	−	0.666470i
$871$	17020.2	+	8088.02i	0.662120	+	0.314641i
$872$		−	9517.84i		−	0.369627i
$873$	−14691.5	−	8482.13i	−0.569566	−	0.328839i
$874$	13402.8	−	23214.4i	0.518716	−	0.898442i
$875$	12370.0	−	15322.1i	0.477922	−	0.591978i
$876$	19103.9			0.736829
$877$	−3825.93	+	2208.90i	−0.147312	+	0.0850506i	−0.571844	−	0.820362i	$-0.693772\pi$
$877$	−3825.93	+	2208.90i	−0.147312	+	0.0850506i	0.424532	+	0.905413i	$0.360439\pi$
$878$	−2837.19	+	1638.05i	−0.109055	+	0.0629631i
$879$	27124.2			1.04081
$880$	−2114.09	+	4987.35i	−0.0809841	+	0.191049i
$881$	−8678.25	+	15031.2i	−0.331870	+	0.574816i	−0.982879	−	0.184255i	$-0.941013\pi$
$881$	−8678.25	+	15031.2i	−0.331870	+	0.574816i	0.651008	+	0.759070i	$0.274346\pi$
$882$	−2615.72	−	1510.19i	−0.0998593	−	0.0576538i
$883$			41393.0i			1.57756i	0.614675	+	0.788780i	$0.289287\pi$
$883$			41393.0i			1.57756i	−0.614675	+	0.788780i	$0.710713\pi$
$884$	−20071.9	−	9538.19i	−0.763677	−	0.362901i
$885$	23312.3	−	17585.2i	0.885462	−	0.667930i
$886$	17693.5	−	30646.1i	0.670909	−	1.16205i
$887$	−19724.6	−	11388.0i	−0.746658	−	0.431083i	0.0778268	−	0.996967i	$-0.475202\pi$
$887$	−19724.6	−	11388.0i	−0.746658	−	0.431083i	−0.824485	+	0.565883i	$0.808535\pi$
$888$	−514.390	+	296.983i	−0.0194390	+	0.0112231i
$889$	−10342.0			−0.390168
$890$	−24540.9	−	10402.7i	−0.924284	−	0.391796i
$891$	−13656.6	−	23653.9i	−0.513481	−	0.889376i
$892$			15938.2i			0.598262i
$893$	27322.3	−	15774.5i	1.02386	−	0.591124i
$894$	11404.0	−	19752.3i	0.426630	−	0.738945i
$895$	15621.2	−	1925.89i	0.583419	−	0.0719277i
$896$	1803.59			0.0672476
$897$	−25686.5	−	37258.5i	−0.956127	−	1.38687i
$898$		−	28434.6i		−	1.05665i
$899$	−9170.35	+	15883.5i	−0.340209	+	0.589260i
$900$	−3634.81	−	3756.51i	−0.134623	−	0.139130i
$901$	−32510.6	−	56310.1i	−1.20209	−	2.08209i
$902$		−	21446.8i		−	0.791686i
$903$	3984.32	−	2300.35i	0.146833	−	0.0847739i
$904$	−8011.11	−	13875.7i	−0.294741	−	0.510506i
$905$	−4140.39	−	5488.83i	−0.152079	−	0.201608i
$906$	20343.2	+	35235.4i	0.745979	+	1.29207i
$907$	35198.5	+	20321.8i	1.28858	+	0.743964i	0.978402	−	0.206713i	$-0.0662766\pi$
$907$	35198.5	+	20321.8i	1.28858	+	0.743964i	0.310182	+	0.950677i	$0.399610\pi$
$908$	6679.08	+	3856.17i	0.244111	+	0.140938i
$909$	2272.72			0.0829279
$910$	9807.18	+	11041.7i	0.357258	+	0.402231i
$911$	−25652.9			−0.932953			−0.466476	−	0.884534i	$-0.654477\pi$
$911$	−25652.9			−0.932953			−0.466476	+	0.884534i	$0.654477\pi$
$912$	7204.45	+	4159.49i	0.261582	+	0.151025i
$913$	10644.4	+	6145.54i	0.385846	+	0.222769i
$914$	9246.15	+	16014.8i	0.334612	+	0.579565i
$915$	14919.4	−	11254.2i	0.539040	−	0.406614i
$916$	6865.76	+	11891.9i	0.247654	+	0.428950i
$917$	−20234.4	+	11682.3i	−0.728679	+	0.420703i
$918$		−	24004.4i		−	0.863033i
$919$	−4392.17	−	7607.46i	−0.157654	−	0.273065i	0.776368	−	0.630280i	$-0.217060\pi$
$919$	−4392.17	−	7607.46i	−0.157654	−	0.273065i	−0.934022	+	0.357215i	$0.883726\pi$
$920$	−14004.5	+	1726.57i	−0.501863	+	0.0618730i
$921$	−14983.2	+	25951.7i	−0.536063	+	0.928489i
$922$		−	3018.70i		−	0.107826i
$923$	13403.9	+	19442.5i	0.478002	+	0.693347i
$924$	−10445.2			−0.371885
$925$	−1089.81	+	1054.50i	−0.0387380	+	0.0374830i
$926$	−15065.2	+	26093.7i	−0.534636	+	0.926016i
$927$	−3357.58	+	1938.50i	−0.118962	+	0.0686826i
$928$		−	5009.41i		−	0.177200i
$929$	−21569.0	−	37358.6i	−0.761740	−	1.31937i	−0.941953	−	0.335744i	$-0.891012\pi$
$929$	−21569.0	−	37358.6i	−0.761740	−	1.31937i	0.180214	−	0.983628i	$-0.442321\pi$
$930$	−6257.30	+	14761.6i	−0.220629	+	0.520485i
$931$	12272.5			0.432025
$932$	−22299.0	+	12874.3i	−0.783722	+	0.452482i
$933$	−612.493	−	353.623i	−0.0214921	−	0.0124085i
$934$	17082.1	−	29587.1i	0.598442	−	1.03653i
$935$	32036.5	−	24166.1i	1.12054	−	0.845257i
$936$	3227.47	−	2225.06i	0.112706	−	0.0777012i
$937$		−	36881.7i		−	1.28588i	−0.765915	−	0.642942i	$-0.777714\pi$
$937$		−	36881.7i		−	1.28588i	0.765915	−	0.642942i	$-0.222286\pi$
$938$	9811.86	+	5664.88i	0.341544	+	0.197191i
$939$	3204.43	−	5550.24i	0.111366	−	0.192892i
$940$	−15290.4	−	6481.47i	−0.530552	−	0.224896i
$941$	34086.5			1.18086			0.590429	−	0.807090i	$-0.298959\pi$
$941$	34086.5			1.18086			0.590429	+	0.807090i	$0.298959\pi$
$942$	16693.2	−	9637.84i	0.577383	−	0.333352i
$943$	48382.0	−	27933.4i	1.67077	−	0.964619i
$944$	6828.29			0.235426
$945$	−6225.74	+	14687.1i	−0.214310	+	0.505579i
$946$	−1615.55	+	2798.22i	−0.0555245	+	0.0961712i
$947$	−20608.0	−	11898.1i	−0.707150	−	0.408273i	0.102855	−	0.994696i	$-0.467202\pi$
$947$	−20608.0	−	11898.1i	−0.707150	−	0.408273i	−0.810005	+	0.586423i	$0.800536\pi$
$948$			106.464i			0.00364745i
$949$	2922.66	+	36461.7i	0.0999720	+	1.24720i
$950$	20422.2	+	5834.13i	0.697458	+	0.199247i
$951$	−13175.7	+	22821.0i	−0.449266	+	0.778151i
$952$	−11571.1	−	6680.59i	−0.393931	−	0.227436i
$953$	−8898.46	+	5137.53i	−0.302465	+	0.174628i	−0.643550	−	0.765404i	$-0.722539\pi$
$953$	−8898.46	+	5137.53i	−0.302465	+	0.174628i	0.341085	+	0.940033i	$0.389206\pi$
$954$	11469.8			0.389254
$955$	1036.74	−	2445.76i	0.0351288	−	0.0828722i
$956$	−2928.04	−	5071.51i	−0.0990581	−	0.171574i
$957$			29011.1i			0.979934i
$958$	−20490.7	+	11830.3i	−0.691050	+	0.398978i
$959$	12504.1	−	21657.7i	0.421040	−	0.729263i
$960$	−535.829	−	4346.21i	−0.0180144	−	0.146118i
$961$	−16064.5			−0.539241
$962$	−645.515	−	936.326i	−0.0216343	−	0.0313808i
$963$			14411.0i			0.482230i
$964$	4867.41	−	8430.59i	0.162623	−	0.281671i
$965$	−2666.68	−	21630.0i	−0.0889571	−	0.721547i
$966$	−13604.3	−	23563.4i	−0.453119	−	0.784825i
$967$			15526.5i			0.516339i	0.966100	+	0.258169i	$0.0831192\pi$
$967$			15526.5i			0.516339i	−0.966100	+	0.258169i	$0.916881\pi$
$968$	−2868.49	+	1656.13i	−0.0952447	+	0.0549895i
$969$	−30813.8	−	53371.1i	−1.02155	−	1.76938i
$970$	−21851.0	−	28967.5i	−0.723293	−	0.958855i
$971$	−16328.2	−	28281.3i	−0.539648	−	0.934698i	−0.998923	−	0.0464035i	$-0.985224\pi$
$971$	−16328.2	−	28281.3i	−0.539648	−	0.934698i	0.459275	−	0.888294i	$-0.348109\pi$
$972$	9651.23	+	5572.14i	0.318481	+	0.183875i
$973$	−11513.2	−	6647.15i	−0.379338	−	0.219011i
$974$	−21833.2			−0.718257
$975$	23694.2	−	26913.2i	0.778279	−	0.884013i
$976$	4369.98			0.143319
$977$	−9450.39	−	5456.18i	−0.309462	−	0.178668i	0.337224	−	0.941425i	$-0.390512\pi$
$977$	−9450.39	−	5456.18i	−0.309462	−	0.178668i	−0.646686	+	0.762756i	$0.723846\pi$
$978$	−18455.1	−	10655.0i	−0.603403	−	0.348375i
$979$	18048.3	+	31260.5i	0.589198	+	1.02052i
$980$	−3890.43	−	5157.46i	−0.126811	−	0.168111i
$981$	−6218.91	−	10771.5i	−0.202400	−	0.350567i
$982$	−25246.0	+	14575.8i	−0.820401	+	0.473659i
$983$		−	33727.1i		−	1.09433i	−0.837024	−	0.547166i	$-0.815707\pi$
$983$		−	33727.1i		−	1.09433i	0.837024	−	0.547166i	$-0.184293\pi$
$984$	8668.95	+	15015.1i	0.280850	+	0.486446i
$985$	−1920.35	−	15576.3i	−0.0621191	−	0.503859i
$986$	−18555.1	+	32138.3i	−0.599304	+	1.03802i
$987$		−	32023.4i		−	1.03274i
$988$	−6836.58	+	14386.7i	−0.220142	+	0.463261i
$989$	−8416.70			−0.270612
$990$	866.161	+	7025.59i	0.0278065	+	0.225543i
$991$	1956.24	−	3388.31i	0.0627064	−	0.108611i	−0.832968	−	0.553321i	$-0.813360\pi$
$991$	1956.24	−	3388.31i	0.0627064	−	0.108611i	0.895674	+	0.444711i	$0.146693\pi$
$992$	−3246.83	+	1874.56i	−0.103918	+	0.0599973i
$993$		−	4194.89i		−	0.134059i
$994$	7099.14	+	12296.1i	0.226530	+	0.392362i
$995$	−327.216	+	771.935i	−0.0104256	+	0.0245949i
$996$	−9936.28			−0.316107
$997$	−2812.97	+	1624.07i	−0.0893557	+	0.0515895i	−0.544012	−	0.839077i	$-0.683095\pi$
$997$	−2812.97	+	1624.07i	−0.0893557	+	0.0515895i	0.454656	+	0.890667i	$0.349762\pi$
$998$	25099.4	+	14491.1i	0.796099	+	0.459628i
$999$	614.223	−	1063.87i	0.0194526	−	0.0336929i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.4.n.a.9.20	yes	44
5.4	even	2	inner	130.4.n.a.9.3	✓	44
13.3	even	3	inner	130.4.n.a.29.3	yes	44
65.29	even	6	inner	130.4.n.a.29.20	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.4.n.a.9.3	✓	44	5.4	even	2	inner
130.4.n.a.9.20	yes	44	1.1	even	1	trivial
130.4.n.a.29.3	yes	44	13.3	even	3	inner
130.4.n.a.29.20	yes	44	65.29	even	6	inner

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:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	130.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 + 1.00000i) q^{2} +(5.30007 + 3.06000i) q^{3} +(2.00000 + 3.46410i) q^{4} +(6.73291 + 8.92569i) q^{5} +(6.11999 + 10.6001i) q^{6} +(-12.2028 + 7.04529i) q^{7} +8.00000i q^{8} +(5.22716 + 9.05371i) q^{9} +(2.73606 + 22.1927i) q^{10} +(15.1407 - 26.2245i) q^{11} +24.4800i q^{12} +(-46.7223 + 3.74512i) q^{13} -28.1812 q^{14} +(8.37233 + 67.9095i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(102.649 - 59.2647i) q^{17} +20.9087i q^{18} +(-42.4785 - 73.5749i) q^{19} +(-17.4537 + 41.1749i) q^{20} -86.2342 q^{21} +(52.4491 - 30.2815i) q^{22} +(136.624 + 78.8802i) q^{23} +(-24.4800 + 42.4006i) q^{24} +(-34.3358 + 120.192i) q^{25} +(-84.6705 - 40.2356i) q^{26} -101.259i q^{27} +(-48.8112 - 28.1812i) q^{28} +(-78.2720 + 135.571i) q^{29} +(-53.4082 + 125.995i) q^{30} +117.160 q^{31} +(-27.7128 + 16.0000i) q^{32} +(160.494 - 92.6613i) q^{33} +237.059 q^{34} +(-145.044 - 61.4831i) q^{35} +(-20.9087 + 36.2149i) q^{36} +(10.5063 + 6.06584i) q^{37} -169.914i q^{38} +(-259.092 - 123.121i) q^{39} +(-71.4055 + 53.8633i) q^{40} +(177.062 - 306.680i) q^{41} +(-149.362 - 86.2342i) q^{42} +(-46.2035 + 26.6756i) q^{43} +121.126 q^{44} +(-45.6166 + 107.614i) q^{45} +(157.760 + 273.249i) q^{46} +371.353i q^{47} +(-84.8011 + 48.9600i) q^{48} +(-72.2278 + 125.102i) q^{49} +(-179.663 + 173.842i) q^{50} +725.399 q^{51} +(-106.418 - 154.361i) q^{52} -548.567i q^{53} +(101.259 - 175.386i) q^{54} +(336.013 - 41.4259i) q^{55} +(-56.3623 - 97.6224i) q^{56} -519.936i q^{57} +(-271.142 + 156.544i) q^{58} +(-213.384 - 369.592i) q^{59} +(-218.501 + 164.822i) q^{60} +(-136.562 - 236.532i) q^{61} +(202.927 + 117.160i) q^{62} +(-127.572 - 73.6538i) q^{63} -64.0000 q^{64} +(-348.005 - 391.813i) q^{65} +370.645 q^{66} +(-348.171 - 201.017i) q^{67} +(410.598 + 237.059i) q^{68} +(482.746 + 836.141i) q^{69} +(-189.741 - 251.536i) q^{70} +(-251.911 - 436.322i) q^{71} +(-72.4297 + 41.8173i) q^{72} -780.391i q^{73} +(12.1317 + 21.0127i) q^{74} +(-549.769 + 531.957i) q^{75} +(169.914 - 294.300i) q^{76} +426.684i q^{77} +(-325.639 - 472.343i) q^{78} +4.34901 q^{79} +(-177.541 + 21.8885i) q^{80} +(450.987 - 781.132i) q^{81} +(613.361 - 354.124i) q^{82} +405.894i q^{83} +(-172.468 - 298.724i) q^{84} +(1220.11 + 517.193i) q^{85} -106.702 q^{86} +(-829.695 + 479.024i) q^{87} +(209.796 + 121.126i) q^{88} +(-596.016 + 1032.33i) q^{89} +(-186.624 + 140.776i) q^{90} +(543.757 - 374.873i) q^{91} +631.041i q^{92} +(620.956 + 358.509i) q^{93} +(-371.353 + 643.203i) q^{94} +(370.703 - 874.523i) q^{95} -195.840 q^{96} +(-1405.30 + 811.351i) q^{97} +(-250.205 + 144.456i) q^{98} +316.573 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 88 q^{4} - 12 q^{5} + 266 q^{9} + 28 q^{10} + 2 q^{11} - 216 q^{14} - 64 q^{15} - 352 q^{16} + 14 q^{19} - 24 q^{20} - 32 q^{21} + 504 q^{25} + 336 q^{26} + 308 q^{29} + 104 q^{30} + 792 q^{31} - 352 q^{34}+ \cdots + 2916 q^{99}+O(q^{100}) \) 44 * q + 88 * q^4 - 12 * q^5 + 266 * q^9 + 28 * q^10 + 2 * q^11 - 216 * q^14 - 64 * q^15 - 352 * q^16 + 14 * q^19 - 24 * q^20 - 32 * q^21 + 504 * q^25 + 336 * q^26 + 308 * q^29 + 104 * q^30 + 792 * q^31 - 352 * q^34 + 106 * q^35 - 1064 * q^36 + 120 * q^39 + 224 * q^40 + 140 * q^41 + 16 * q^44 - 522 * q^45 - 320 * q^46 + 536 * q^49 - 96 * q^50 - 256 * q^51 + 552 * q^54 + 1188 * q^55 - 432 * q^56 - 500 * q^59 - 512 * q^60 - 2352 * q^61 - 2816 * q^64 - 2924 * q^65 + 496 * q^66 + 376 * q^69 - 1008 * q^70 - 1268 * q^71 + 436 * q^74 + 3560 * q^75 - 56 * q^76 - 264 * q^79 + 96 * q^80 - 6326 * q^81 - 64 * q^84 + 606 * q^85 + 336 * q^86 + 4730 * q^89 + 3560 * q^90 + 5866 * q^91 + 1732 * q^94 + 2224 * q^95 + 2916 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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