LMFDB - Embedded newform 130.4.n.a.9.6

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			9.6
Character	$\chi$	$=$	130.9
Dual form			130.4.n.a.29.6

$q$-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} +(0.162462 + 0.0937974i) q^{3} +(2.00000 + 3.46410i) q^{4} +(2.25511 + 10.9505i) q^{5} +(-0.187595 - 0.324924i) q^{6} +(-16.1121 + 9.30232i) q^{7} -8.00000i q^{8} +(-13.4824 - 23.3522i) q^{9} +(7.04459 - 21.2220i) q^{10} +(9.06526 - 15.7015i) q^{11} +0.750379i q^{12} +(-27.1045 - 38.2406i) q^{13} +37.2093 q^{14} +(-0.660764 + 1.99057i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-51.5122 + 29.7406i) q^{17} +53.9296i q^{18} +(-6.14898 - 10.6503i) q^{19} +(-33.4236 + 29.7130i) q^{20} -3.49013 q^{21} +(-31.4030 + 18.1305i) q^{22} +(-134.527 - 77.6692i) q^{23} +(0.750379 - 1.29969i) q^{24} +(-114.829 + 49.3893i) q^{25} +(8.70582 + 93.3392i) q^{26} -10.1235i q^{27} +(-64.4484 - 37.2093i) q^{28} +(-32.3294 + 55.9962i) q^{29} +(3.13504 - 2.78700i) q^{30} -111.339 q^{31} +(27.7128 - 16.0000i) q^{32} +(2.94552 - 1.70060i) q^{33} +118.962 q^{34} +(-138.200 - 155.458i) q^{35} +(53.9296 - 93.4088i) q^{36} +(176.404 + 101.847i) q^{37} +24.5959i q^{38} +(-0.816583 - 8.75497i) q^{39} +(87.6044 - 18.0409i) q^{40} +(-80.3301 + 139.136i) q^{41} +(6.04509 + 3.49013i) q^{42} +(-22.9220 + 13.2340i) q^{43} +72.5221 q^{44} +(225.315 - 200.301i) q^{45} +(155.338 + 269.054i) q^{46} -146.183i q^{47} +(-2.59939 + 1.50076i) q^{48} +(1.56631 - 2.71293i) q^{49} +(248.279 + 29.2842i) q^{50} -11.1583 q^{51} +(78.2603 - 170.374i) q^{52} -204.338i q^{53} +(-10.1235 + 17.5344i) q^{54} +(192.383 + 63.8611i) q^{55} +(74.4186 + 128.897i) q^{56} -2.30703i q^{57} +(111.992 - 64.6589i) q^{58} +(-346.709 - 600.518i) q^{59} +(-8.21706 + 1.69218i) q^{60} +(369.848 + 640.596i) q^{61} +(192.844 + 111.339i) q^{62} +(434.459 + 250.835i) q^{63} -64.0000 q^{64} +(357.632 - 383.046i) q^{65} -6.80238 q^{66} +(544.024 + 314.092i) q^{67} +(-206.049 - 118.962i) q^{68} +(-14.5703 - 25.2366i) q^{69} +(83.9109 + 407.462i) q^{70} +(103.640 + 179.510i) q^{71} +(-186.818 + 107.859i) q^{72} -604.558i q^{73} +(-203.693 - 352.807i) q^{74} +(-23.2879 - 2.74678i) q^{75} +(24.5959 - 42.6014i) q^{76} +337.312i q^{77} +(-7.34061 + 15.9806i) q^{78} -147.071 q^{79} +(-169.776 - 56.3567i) q^{80} +(-363.075 + 628.865i) q^{81} +(278.272 - 160.660i) q^{82} -617.868i q^{83} +(-6.98026 - 12.0902i) q^{84} +(-441.841 - 497.018i) q^{85} +52.9362 q^{86} +(-10.5046 + 6.06483i) q^{87} +(-125.612 - 72.5221i) q^{88} +(-9.88158 + 17.1154i) q^{89} +(-590.559 + 121.617i) q^{90} +(792.437 + 364.001i) q^{91} -621.354i q^{92} +(-18.0883 - 10.4433i) q^{93} +(-146.183 + 253.196i) q^{94} +(102.760 - 91.3523i) q^{95} +6.00303 q^{96} +(-1103.54 + 637.128i) q^{97} +(-5.42586 + 3.13262i) q^{98} -488.886 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
$3$	0.162462	+	0.0937974i	0.0312658	+	0.0180513i	0.515551	−	0.856859i	$-0.327587\pi$
$3$	0.162462	+	0.0937974i	0.0312658	+	0.0180513i	−0.484286	+	0.874910i	$0.660920\pi$
$4$	2.00000	+	3.46410i	0.250000	+	0.433013i
$5$	2.25511	+	10.9505i	0.201703	+	0.979447i
$5$	2.25511	+	10.9505i	0.201703	+	0.979447i
$6$	−0.187595	−	0.324924i	−0.0127642	−	0.0221082i
$7$	−16.1121	+	9.30232i	−0.869971	+	0.502278i	−0.867339	−	0.497718i	$-0.834171\pi$
$7$	−16.1121	+	9.30232i	−0.869971	+	0.502278i	−0.00263248	+	0.999997i	$0.500838\pi$
$8$		−	8.00000i		−	0.353553i
$9$	−13.4824	−	23.3522i	−0.499348	−	0.864897i
$10$	7.04459	−	21.2220i	0.222769	−	0.671099i
$11$	9.06526	−	15.7015i	0.248480	−	0.430380i	−0.714624	−	0.699509i	$-0.753402\pi$
$11$	9.06526	−	15.7015i	0.248480	−	0.430380i	0.963104	+	0.269129i	$0.0867356\pi$
$12$			0.750379i			0.0180513i
$13$	−27.1045	−	38.2406i	−0.578265	−	0.815849i
$13$	−27.1045	−	38.2406i	−0.578265	−	0.815849i
$14$	37.2093			0.710328
$15$	−0.660764	+	1.99057i	−0.0113739	+	0.0342642i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−51.5122	+	29.7406i	−0.734914	+	0.424303i	−0.820217	−	0.572052i	$-0.806147\pi$
$17$	−51.5122	+	29.7406i	−0.734914	+	0.424303i	0.0853033	+	0.996355i	$0.472814\pi$
$18$			53.9296i			0.706185i
$19$	−6.14898	−	10.6503i	−0.0742459	−	0.128598i	0.826512	−	0.562919i	$-0.190322\pi$
$19$	−6.14898	−	10.6503i	−0.0742459	−	0.128598i	−0.900758	+	0.434321i	$0.856988\pi$
$20$	−33.4236	+	29.7130i	−0.373687	+	0.332202i
$21$	−3.49013			−0.0362671
$22$	−31.4030	+	18.1305i	−0.304325	+	0.175702i
$23$	−134.527	−	77.6692i	−1.21960	−	0.704137i	−0.254768	−	0.967002i	$-0.581999\pi$
$23$	−134.527	−	77.6692i	−1.21960	−	0.704137i	−0.964833	+	0.262865i	$0.915333\pi$
$24$	0.750379	−	1.29969i	0.00638210	−	0.0110541i
$25$	−114.829	+	49.3893i	−0.918632	+	0.395114i
$26$	8.70582	+	93.3392i	0.0656674	+	0.704051i
$27$		−	10.1235i		−	0.0721582i
$28$	−64.4484	−	37.2093i	−0.434986	−	0.251139i
$29$	−32.3294	+	55.9962i	−0.207015	+	0.358560i	−0.950773	−	0.309889i	$-0.899708\pi$
$29$	−32.3294	+	55.9962i	−0.207015	+	0.358560i	0.743758	+	0.668449i	$0.233041\pi$
$30$	3.13504	−	2.78700i	0.0190793	−	0.0169612i
$31$	−111.339			−0.645065			−0.322532	−	0.946558i	$-0.604534\pi$
$31$	−111.339			−0.645065			−0.322532	+	0.946558i	$0.604534\pi$
$32$	27.7128	−	16.0000i	0.153093	−	0.0883883i
$33$	2.94552	−	1.70060i	0.0155378	−	0.00897078i
$34$	118.962			0.600055
$35$	−138.200	−	155.458i	−0.667430	−	0.750779i
$36$	53.9296	−	93.4088i	0.249674	−	0.432448i
$37$	176.404	+	101.847i	0.783800	+	0.452527i	0.837775	−	0.546015i	$-0.183856\pi$
$37$	176.404	+	101.847i	0.783800	+	0.452527i	−0.0539756	+	0.998542i	$0.517189\pi$
$38$			24.5959i			0.105000i
$39$	−0.816583	−	8.75497i	−0.00335277	−	0.0359466i
$40$	87.6044	−	18.0409i	0.346287	−	0.0713127i
$41$	−80.3301	+	139.136i	−0.305987	+	0.529985i	−0.977481	−	0.211026i	$-0.932320\pi$
$41$	−80.3301	+	139.136i	−0.305987	+	0.529985i	0.671494	+	0.741010i	$0.265653\pi$
$42$	6.04509	+	3.49013i	0.0222090	+	0.0128224i
$43$	−22.9220	+	13.2340i	−0.0812925	+	0.0469342i	−0.540095	−	0.841604i	$-0.681612\pi$
$43$	−22.9220	+	13.2340i	−0.0812925	+	0.0469342i	0.458803	+	0.888538i	$0.348278\pi$
$44$	72.5221			0.248480
$45$	225.315	−	200.301i	0.746400	−	0.663537i
$46$	155.338	+	269.054i	0.497900	+	0.862388i
$47$		−	146.183i		−	0.453680i	−0.973932	−	0.226840i	$-0.927161\pi$
$47$		−	146.183i		−	0.453680i	0.973932	−	0.226840i	$-0.0728395\pi$
$48$	−2.59939	+	1.50076i	−0.00781645	+	0.00451283i
$49$	1.56631	−	2.71293i	0.00456650	−	0.00790942i
$50$	248.279	+	29.2842i	0.702239	+	0.0828282i
$51$	−11.1583			−0.0306369
$52$	78.2603	−	170.374i	0.208707	−	0.454358i
$53$		−	204.338i		−	0.529585i	−0.964305	−	0.264792i	$-0.914697\pi$
$53$		−	204.338i		−	0.529585i	0.964305	−	0.264792i	$-0.0853034\pi$
$54$	−10.1235	+	17.5344i	−0.0255118	+	0.0441877i
$55$	192.383	+	63.8611i	0.471653	+	0.156564i
$56$	74.4186	+	128.897i	0.177582	+	0.307581i
$57$		−	2.30703i		−	0.00536094i
$58$	111.992	−	64.6589i	0.253540	−	0.146381i
$59$	−346.709	−	600.518i	−0.765046	−	1.32510i	−0.940222	−	0.340561i	$-0.889383\pi$
$59$	−346.709	−	600.518i	−0.765046	−	1.32510i	0.175177	−	0.984537i	$-0.443950\pi$
$60$	−8.21706	+	1.69218i	−0.0176803	+	0.00364100i
$61$	369.848	+	640.596i	0.776298	+	1.34459i	0.934062	+	0.357111i	$0.116238\pi$
$61$	369.848	+	640.596i	0.776298	+	1.34459i	−0.157764	+	0.987477i	$0.550428\pi$
$62$	192.844	+	111.339i	0.395020	+	0.228065i
$63$	434.459	+	250.835i	0.868837	+	0.501623i
$64$	−64.0000			−0.125000
$65$	357.632	−	383.046i	0.682443	−	0.730939i
$66$	−6.80238			−0.0126866
$67$	544.024	+	314.092i	0.991986	+	0.572724i	0.905867	−	0.423561i	$-0.139220\pi$
$67$	544.024	+	314.092i	0.991986	+	0.572724i	0.0861189	+	0.996285i	$0.472554\pi$
$68$	−206.049	−	118.962i	−0.367457	−	0.212151i
$69$	−14.5703	−	25.2366i	−0.0254212	−	0.0440308i
$70$	83.9109	+	407.462i	0.143275	+	0.695729i
$71$	103.640	+	179.510i	0.173237	+	0.300056i	0.939550	−	0.342412i	$-0.111244\pi$
$71$	103.640	+	179.510i	0.173237	+	0.300056i	−0.766313	+	0.642468i	$0.777911\pi$
$72$	−186.818	+	107.859i	−0.305787	+	0.176546i
$73$		−	604.558i		−	0.969290i	−0.874711	−	0.484645i	$-0.838949\pi$
$73$		−	604.558i		−	0.969290i	0.874711	−	0.484645i	$-0.161051\pi$
$74$	−203.693	−	352.807i	−0.319985	−	0.554230i
$75$	−23.2879	−	2.74678i	−0.0358541	−	0.00422895i
$76$	24.5959	−	42.6014i	0.0371230	−	0.0642988i
$77$			337.312i			0.499224i
$78$	−7.34061	+	15.9806i	−0.0106559	+	0.0231981i
$79$	−147.071			−0.209453			−0.104727	−	0.994501i	$-0.533397\pi$
$79$	−147.071			−0.209453			−0.104727	+	0.994501i	$0.533397\pi$
$80$	−169.776	−	56.3567i	−0.237269	−	0.0787609i
$81$	−363.075	+	628.865i	−0.498046	+	0.862641i
$82$	278.272	−	160.660i	0.374756	−	0.216365i
$83$		−	617.868i		−	0.817107i	−0.912734	−	0.408553i	$-0.866033\pi$
$83$		−	617.868i		−	0.817107i	0.912734	−	0.408553i	$-0.133967\pi$
$84$	−6.98026	−	12.0902i	−0.00906678	−	0.0157041i
$85$	−441.841	−	497.018i	−0.563816	−	0.634226i
$86$	52.9362			0.0663750
$87$	−10.5046	+	6.06483i	−0.0129449	+	0.00747377i
$88$	−125.612	−	72.5221i	−0.152162	−	0.0878509i
$89$	−9.88158	+	17.1154i	−0.0117690	+	0.0203846i	−0.871850	−	0.489773i	$-0.837080\pi$
$89$	−9.88158	+	17.1154i	−0.0117690	+	0.0203846i	0.860081	+	0.510158i	$0.170413\pi$
$90$	−590.559	+	121.617i	−0.691671	+	0.142440i
$91$	792.437	+	364.001i	0.912857	+	0.419315i
$92$		−	621.354i		−	0.704137i
$93$	−18.0883	−	10.4433i	−0.0201685	−	0.0116443i
$94$	−146.183	+	253.196i	−0.160400	+	0.277821i
$95$	102.760	−	91.3523i	0.110979	−	0.0986584i
$96$	6.00303			0.00638210
$97$	−1103.54	+	637.128i	−1.15513	+	0.666913i	−0.950131	−	0.311850i	$-0.899051\pi$
$97$	−1103.54	+	637.128i	−1.15513	+	0.666913i	−0.204996	+	0.978763i	$0.565718\pi$
$98$	−5.42586	+	3.13262i	−0.00559280	+	0.00322901i
$99$	−488.886			−0.496312
$100$	−400.748	−	299.001i	−0.400748	−	0.299001i
$101$	−704.050	+	1219.45i	−0.693620	+	1.20138i	0.277024	+	0.960863i	$0.410652\pi$
$101$	−704.050	+	1219.45i	−0.693620	+	1.20138i	−0.970644	+	0.240522i	$0.922681\pi$
$102$	19.3268	+	11.1583i	0.0187612	+	0.0108318i
$103$			865.640i			0.828097i	0.910255	+	0.414049i	$0.135886\pi$
$103$			865.640i			0.828097i	−0.910255	+	0.414049i	$0.864114\pi$
$104$	−305.925	+	216.836i	−0.288446	+	0.204448i
$105$	−7.87062	−	38.2189i	−0.00731518	−	0.0355217i
$106$	−204.338	+	353.924i	−0.187236	+	0.324303i
$107$	−1850.41	−	1068.33i	−1.67183	−	0.965230i	−0.966615	−	0.256235i	$-0.917518\pi$
$107$	−1850.41	−	1068.33i	−1.67183	−	0.965230i	−0.705213	−	0.708995i	$-0.749149\pi$
$108$	35.0689	−	20.2470i	0.0312454	−	0.0180395i
$109$	1930.88			1.69674			0.848369	−	0.529406i	$-0.177585\pi$
$109$	1930.88			1.69674			0.848369	+	0.529406i	$0.177585\pi$
$110$	−269.356	−	302.994i	−0.233474	−	0.262630i
$111$	19.1059	+	33.0924i	0.0163374	+	0.0282972i
$112$		−	297.674i		−	0.251139i
$113$	−1165.89	+	673.128i	−0.970601	+	0.560377i	−0.899419	−	0.437087i	$-0.856010\pi$
$113$	−1165.89	+	673.128i	−0.970601	+	0.560377i	−0.0711816	+	0.997463i	$0.522677\pi$
$114$	−2.30703	+	3.99590i	−0.00189538	+	0.00328289i
$115$	547.148	−	1648.30i	0.443668	−	1.33656i
$116$	−258.635			−0.207015
$117$	−527.568	+	1148.53i	−0.416869	+	0.907532i
$118$			1386.84i			1.08194i
$119$	553.312	−	958.365i	0.426236	−	0.738262i
$120$	15.9245	+	5.28611i	0.0121142	+	0.00402128i
$121$	501.142	+	868.003i	0.376515	+	0.652144i
$122$		−	1479.39i		−	1.09785i
$123$	−26.1011	+	15.0695i	−0.0191338	+	0.0110469i
$124$	−222.677	−	385.688i	−0.161266	−	0.279321i
$125$	−799.792	−	1146.06i	−0.572284	−	0.820055i
$126$	−501.671	−	868.919i	−0.354701	−	0.614361i
$127$	2089.13	+	1206.16i	1.45969	+	0.842750i	0.998995	−	0.0448106i	$-0.0142684\pi$
$127$	2089.13	+	1206.16i	1.45969	+	0.842750i	0.460691	+	0.887561i	$0.347602\pi$
$128$	110.851	+	64.0000i	0.0765466	+	0.0441942i
$129$	−4.96527			−0.00338890
$130$	−1002.48	+	305.823i	−0.676335	+	0.206327i
$131$	677.449			0.451825			0.225912	−	0.974148i	$-0.427464\pi$
$131$	677.449			0.451825			0.225912	+	0.974148i	$0.427464\pi$
$132$	11.7821	+	6.80238i	0.00776892	+	0.00448539i
$133$	198.146	+	114.400i	0.129184	+	0.0745842i
$134$	−628.185	−	1088.05i	−0.404977	−	0.701440i
$135$	110.858	−	22.8296i	0.0706751	−	0.0145545i
$136$	237.925	+	412.097i	0.150014	+	0.259831i
$137$	−336.191	+	194.100i	−0.209655	+	0.121044i	−0.601151	−	0.799135i	$-0.705291\pi$
$137$	−336.191	+	194.100i	−0.209655	+	0.121044i	0.391496	+	0.920180i	$0.371958\pi$
$138$			58.2813i			0.0359510i
$139$	−1083.06	−	1875.91i	−0.660891	−	1.14470i	−0.980382	−	0.197107i	$-0.936845\pi$
$139$	−1083.06	−	1875.91i	−0.660891	−	1.14470i	0.319491	−	0.947589i	$-0.396488\pi$
$140$	262.124	−	789.656i	0.158239	−	0.476701i
$141$	13.7116	−	23.7491i	0.00818952	−	0.0141847i
$142$		−	414.561i		−	0.244995i
$143$	−846.145	+	78.9205i	−0.494812	+	0.0461515i
$144$	431.437			0.249674
$145$	−686.095	−	227.748i	−0.392946	−	0.130437i
$146$	−604.558	+	1047.13i	−0.342696	+	0.593566i
$147$	0.508931	−	0.293832i	0.000285551	−	0.000164863i
$148$			814.774i			0.452527i
$149$	1303.95	+	2258.51i	0.716939	+	1.24177i	0.962207	+	0.272319i	$0.0877907\pi$
$149$	1303.95	+	2258.51i	0.716939	+	1.24177i	−0.245268	+	0.969455i	$0.578876\pi$
$150$	37.5891	+	28.0455i	0.0204609	+	0.0152660i
$151$	469.334			0.252939			0.126470	−	0.991970i	$-0.459635\pi$
$151$	469.334			0.252939			0.126470	+	0.991970i	$0.459635\pi$
$152$	−85.2027	+	49.1918i	−0.0454662	+	0.0262499i
$153$	1389.02	+	801.949i	0.733956	+	0.423750i
$154$	337.312	−	584.241i	0.176502	−	0.305711i
$155$	−251.080	−	1219.22i	−0.130111	−	0.631807i
$156$	28.6949	−	20.3387i	0.0147271	−	0.0104384i
$157$			60.2108i			0.0306073i	0.999883	+	0.0153036i	$0.00487149\pi$
$157$			60.2108i			0.0306073i	−0.999883	+	0.0153036i	$0.995129\pi$
$158$	254.735	+	147.071i	0.128263	+	0.0740529i
$159$	19.1664	−	33.1971i	0.00955970	−	0.0165579i
$160$	237.704	+	267.389i	0.117451	+	0.132118i
$161$	2890.02			1.41469
$162$	1257.73	−	726.151i	0.609979	−	0.352172i
$163$	1129.63	−	652.194i	0.542821	−	0.313398i	−0.203401	−	0.979096i	$-0.565199\pi$
$163$	1129.63	−	652.194i	0.542821	−	0.313398i	0.746221	+	0.665698i	$0.231866\pi$
$164$	−642.641			−0.305987
$165$	25.2649	+	28.4200i	0.0119204	+	0.0134091i
$166$	−617.868	+	1070.18i	−0.288891	+	0.500374i
$167$	−593.470	−	342.640i	−0.274994	−	0.158768i	0.356161	−	0.934425i	$-0.384086\pi$
$167$	−593.470	−	342.640i	−0.274994	−	0.158768i	−0.631155	+	0.775657i	$0.717419\pi$
$168$			27.9211i			0.0128224i
$169$	−727.689	+	2072.99i	−0.331219	+	0.943554i
$170$	268.273	+	1302.70i	0.121033	+	0.587722i
$171$	−165.806	+	287.184i	−0.0741491	+	0.128430i
$172$	−91.6881	−	52.9362i	−0.0406462	−	0.0234671i
$173$	2719.04	−	1569.84i	1.19494	−	0.689899i	0.235517	−	0.971870i	$-0.424322\pi$
$173$	2719.04	−	1569.84i	1.19494	−	0.689899i	0.959423	+	0.281972i	$0.0909884\pi$
$174$	24.2593			0.0105695
$175$	1390.70	−	1863.94i	0.600726	−	0.805147i
$176$	145.044	+	251.224i	0.0621200	+	0.107595i
$177$		−	130.082i		−	0.0552403i
$178$	34.2308	−	19.7632i	0.0144141	−	0.00832197i
$179$	−505.468	+	875.496i	−0.211064	+	0.365573i	−0.952048	−	0.305949i	$-0.901026\pi$
$179$	−505.468	+	875.496i	−0.211064	+	0.365573i	0.740984	+	0.671523i	$0.234359\pi$
$180$	1144.49	+	379.912i	0.473920	+	0.157316i
$181$	−2014.89			−0.827432			−0.413716	−	0.910406i	$-0.635769\pi$
$181$	−2014.89			−0.827432			−0.413716	+	0.910406i	$0.635769\pi$
$182$	−1008.54	−	1422.91i	−0.410758	−	0.579521i
$183$			138.763i			0.0560528i
$184$	−621.354	+	1076.22i	−0.248950	+	0.431194i
$185$	−717.468	+	2161.39i	−0.285131	+	0.858966i
$186$	20.8865	+	36.1765i	0.00823374	+	0.0142613i
$187$			1078.42i			0.421723i
$188$	506.392	−	292.366i	0.196449	−	0.113420i
$189$	94.1721	+	163.111i	0.0362435	+	0.0627755i
$190$	−269.339	+	55.4664i	−0.102841	+	0.0211787i
$191$	−2512.62	−	4351.98i	−0.951867	−	1.64868i	−0.741379	−	0.671086i	$-0.765828\pi$
$191$	−2512.62	−	4351.98i	−0.951867	−	1.64868i	−0.210488	−	0.977596i	$-0.567505\pi$
$192$	−10.3976	−	6.00303i	−0.00390822	−	0.00225641i
$193$	1528.92	+	882.722i	0.570228	+	0.329221i	0.757240	−	0.653136i	$-0.226547\pi$
$193$	1528.92	+	882.722i	0.570228	+	0.329221i	−0.187013	+	0.982358i	$0.559880\pi$
$194$	2548.51			0.943157
$195$	94.0302	−	28.6854i	0.0345315	−	0.0105344i
$196$	12.5305			0.00456650
$197$	−109.842	−	63.4173i	−0.0397255	−	0.0229355i	0.480006	−	0.877265i	$-0.340635\pi$
$197$	−109.842	−	63.4173i	−0.0397255	−	0.0229355i	−0.519731	+	0.854330i	$0.673968\pi$
$198$	846.776	+	488.886i	0.303928	+	0.175473i
$199$	−2039.47	−	3532.46i	−0.726503	−	1.25834i	−0.958352	−	0.285589i	$-0.907811\pi$
$199$	−2039.47	−	3532.46i	−0.726503	−	1.25834i	0.231849	−	0.972752i	$-0.425522\pi$
$200$	395.114	+	918.632i	0.139694	+	0.324785i
$201$	58.9221	+	102.056i	0.0206768	+	0.0358133i
$202$	2438.90	−	1408.10i	0.849507	−	0.490463i
$203$		−	1202.95i		−	0.415916i
$204$	−22.3167	−	38.6536i	−0.00765922	−	0.0132662i
$205$	−1704.77	−	565.893i	−0.580810	−	0.192798i
$206$	865.640	−	1499.33i	0.292777	−	0.507104i
$207$			4188.67i			1.40644i
$208$	746.714	−	69.6465i	0.248920	−	0.0232169i
$209$	−222.968			−0.0737945
$210$	−24.5865	+	74.0676i	−0.00807920	+	0.0243388i
$211$	−2325.66	+	4028.17i	−0.758793	+	1.31427i	0.184674	+	0.982800i	$0.440877\pi$
$211$	−2325.66	+	4028.17i	−0.758793	+	1.31427i	−0.943467	+	0.331468i	$0.892456\pi$
$212$	707.848	−	408.676i	0.229317	−	0.132396i
$213$			38.8848i			0.0125086i
$214$	2136.67	+	3700.81i	0.682521	+	1.18216i
$215$	−196.612	−	221.165i	−0.0623665	−	0.0701549i
$216$	−80.9881			−0.0255118
$217$	1793.90	−	1035.71i	0.561188	−	0.324002i
$218$	−3344.38	−	1930.88i	−1.03904	−	0.599887i
$219$	56.7059	−	98.2176i	0.0174969	−	0.0303056i
$220$	163.545	+	794.157i	0.0501191	+	0.243373i
$221$	2533.51	+	1163.75i	0.771142	+	0.354219i
$222$		−	76.4236i		−	0.0231046i
$223$	145.276	+	83.8754i	0.0436252	+	0.0251870i	0.521654	−	0.853157i	$-0.325315\pi$
$223$	145.276	+	83.8754i	0.0436252	+	0.0251870i	−0.478029	+	0.878344i	$0.658649\pi$
$224$	−297.674	+	515.587i	−0.0887911	+	0.153791i
$225$	2701.52	+	2015.62i	0.800450	+	0.597222i
$226$	2692.51			0.792492
$227$	−1095.34	+	632.395i	−0.320265	+	0.184905i	−0.651511	−	0.758639i	$-0.725865\pi$
$227$	−1095.34	+	632.395i	−0.320265	+	0.184905i	0.331245	+	0.943545i	$0.392531\pi$
$228$	7.99179	−	4.61406i	0.00232136	−	0.00134024i
$229$	−4281.25			−1.23543			−0.617714	−	0.786403i	$-0.711941\pi$
$229$	−4281.25			−1.23543			−0.617714	+	0.786403i	$0.711941\pi$
$230$	−2595.98	+	2307.79i	−0.744235	+	0.661613i
$231$	−31.6390	+	54.8003i	−0.00901165	+	0.0156086i
$232$	447.970	+	258.635i	0.126770	+	0.0731907i
$233$		−	3286.61i		−	0.924089i	−0.886857	−	0.462045i	$-0.847116\pi$
$233$		−	3286.61i		−	0.924089i	0.886857	−	0.462045i	$-0.152884\pi$
$234$	2062.30	−	1461.74i	0.576140	−	0.408362i
$235$	1600.78	−	329.658i	0.444355	−	0.0915086i
$236$	1386.84	−	2402.07i	0.382523	−	0.662549i
$237$	−23.8934	−	13.7949i	−0.00654872	−	0.00378090i
$238$	−1916.73	+	1106.62i	−0.522030	+	0.301394i
$239$	6297.79			1.70448			0.852239	−	0.523152i	$-0.175244\pi$
$239$	6297.79			1.70448			0.852239	+	0.523152i	$0.175244\pi$
$240$	−22.2960	−	25.0804i	−0.00599667	−	0.00674554i
$241$	−3479.08	−	6025.95i	−0.929906	−	1.61064i	−0.783475	−	0.621424i	$-0.786555\pi$
$241$	−3479.08	−	6025.95i	−0.929906	−	1.61064i	−0.146432	−	0.989221i	$-0.546779\pi$
$242$		−	2004.57i		−	0.532473i
$243$	−354.687	+	204.778i	−0.0936344	+	0.0540598i
$244$	−1479.39	+	2562.38i	−0.388149	+	0.672294i
$245$	33.2403	+	11.0340i	0.00866793	+	0.00287730i
$246$	60.2780			0.0156227
$247$	−240.610	+	523.813i	−0.0619825	+	0.134937i
$248$			890.709i			0.228065i
$249$	57.9544	−	100.380i	0.0147498	−	0.0255475i
$250$	239.217	+	2784.83i	0.0605177	+	0.704512i
$251$	−2305.21	−	3992.74i	−0.579695	−	1.00406i	−0.995514	−	0.0946136i	$-0.969838\pi$
$251$	−2305.21	−	3992.74i	−0.579695	−	1.00406i	0.415819	−	0.909447i	$-0.363495\pi$
$252$			2006.68i			0.501623i
$253$	−2439.05	+	1408.18i	−0.606093	+	0.349928i
$254$	−2412.32	−	4178.26i	−0.595914	−	1.03215i
$255$	−25.1633	−	122.190i	−0.00617955	−	0.0300072i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	138.199	+	79.7895i	0.0335434	+	0.0193663i	0.516678	−	0.856180i	$-0.327168\pi$
$257$	138.199	+	79.7895i	0.0335434	+	0.0193663i	−0.483135	+	0.875546i	$0.660502\pi$
$258$	8.60010	+	4.96527i	0.00207527	+	0.00119816i
$259$	−3789.64			−0.909177
$260$	2042.17	+	472.781i	0.487117	+	0.112772i
$261$	1743.51			0.413490
$262$	−1173.38	−	677.449i	−0.276685	−	0.159744i
$263$	−5485.64	−	3167.14i	−1.28616	−	0.742563i	−0.308190	−	0.951325i	$-0.599723\pi$
$263$	−5485.64	−	3167.14i	−1.28616	−	0.742563i	−0.977966	+	0.208762i	$0.933057\pi$
$264$	−13.6048	−	23.5641i	−0.00317165	−	0.00549346i
$265$	2237.61	−	460.804i	0.518700	−	0.106819i
$266$	−228.799	−	396.292i	−0.0527390	−	0.0913466i
$267$	−3.21076	+	1.85373i	−0.000735937	+	0.000424893i
$268$			2512.74i			0.572724i
$269$	−1347.66	−	2334.21i	−0.305457	−	0.529067i	0.671906	−	0.740637i	$-0.265476\pi$
$269$	−1347.66	−	2334.21i	−0.305457	−	0.529067i	−0.977363	+	0.211569i	$0.932143\pi$
$270$	−214.841	−	71.3160i	−0.0484253	−	0.0160746i
$271$	3867.25	−	6698.27i	0.866858	−	1.50144i	0.00166833	−	0.999999i	$-0.499469\pi$
$271$	3867.25	−	6698.27i	0.866858	−	1.50144i	0.865190	−	0.501444i	$-0.167198\pi$
$272$		−	951.698i		−	0.212151i
$273$	94.5984	+	133.465i	0.0209720	+	0.0295885i
$274$	776.401			0.171183
$275$	−265.469	+	2250.71i	−0.0582123	+	0.493539i
$276$	58.2813	−	100.946i	0.0127106	−	0.0220154i
$277$	−7026.58	+	4056.80i	−1.52414	+	0.879961i	−0.524546	+	0.851382i	$0.675765\pi$
$277$	−7026.58	+	4056.80i	−1.52414	+	0.879961i	−0.999592	+	0.0285791i	$0.990902\pi$
$278$			4332.23i			0.934640i
$279$	1501.11	+	2600.00i	0.322112	+	0.557914i
$280$	−1243.67	+	1105.60i	−0.265441	+	0.235972i
$281$	−4505.21			−0.956435			−0.478218	−	0.878241i	$-0.658717\pi$
$281$	−4505.21			−0.956435			−0.478218	+	0.878241i	$0.658717\pi$
$282$	−47.4983	+	27.4231i	−0.0100301	+	0.00579086i
$283$	−472.098	−	272.566i	−0.0991637	−	0.0572522i	0.449598	−	0.893231i	$-0.351567\pi$
$283$	−472.098	−	272.566i	−0.0991637	−	0.0572522i	−0.548762	+	0.835979i	$0.684901\pi$
$284$	−414.561	+	718.041i	−0.0866186	+	0.150028i
$285$	25.2633	−	5.20260i	0.00525076	−	0.00108132i
$286$	1544.49	+	709.450i	0.319326	+	0.146681i
$287$		−	2989.03i		−	0.614762i
$288$	−747.271	−	431.437i	−0.152894	−	0.0882731i
$289$	−687.498	+	1190.78i	−0.139934	+	0.242373i
$290$	960.605	+	1080.57i	0.194513	+	0.218803i
$291$	−239.044			−0.0481546
$292$	2094.25	−	1209.12i	0.419715	−	0.242322i
$293$	−5448.64	+	3145.77i	−1.08639	+	0.627229i	−0.932614	−	0.360877i	$-0.882478\pi$
$293$	−5448.64	+	3145.77i	−1.08639	+	0.627229i	−0.153778	+	0.988105i	$0.549144\pi$
$294$	−1.17533			−0.000233151
$295$	5794.13	−	5150.89i	1.14355	−	1.01660i
$296$	814.774	−	1411.23i	0.159992	−	0.277115i
$297$	−158.954	−	91.7723i	−0.0310554	−	0.0179299i
$298$		−	5215.81i		−	1.01390i
$299$	676.174	+	7249.58i	0.130783	+	1.40219i
$300$	−37.0607	−	86.1652i	−0.00713233	−	0.0165825i
$301$	246.215	−	426.456i	0.0471481	−	0.0816629i
$302$	−812.910	−	469.334i	−0.154893	−	0.0894276i
$303$	−228.762	+	132.076i	−0.0433731	+	0.0250415i
$304$	196.767			0.0371230
$305$	−6180.83	+	5494.65i	−1.16037	+	1.03155i
$306$	−1603.90	−	2778.03i	−0.299636	−	0.518985i
$307$			7627.50i			1.41799i	0.705211	+	0.708997i	$0.250852\pi$
$307$			7627.50i			1.41799i	−0.705211	+	0.708997i	$0.749148\pi$
$308$	−1168.48	+	674.624i	−0.216170	+	0.124806i
$309$	−81.1947	+	140.633i	−0.0149482	+	0.0258911i
$310$	−784.335	+	2362.83i	−0.143701	+	0.432902i
$311$	568.314			0.103621			0.0518105	−	0.998657i	$-0.483501\pi$
$311$	568.314			0.103621			0.0518105	+	0.998657i	$0.483501\pi$
$312$	−70.0398	+	6.53266i	−0.0127090	+	0.00118538i
$313$		−	3520.09i		−	0.635678i	−0.948145	−	0.317839i	$-0.897043\pi$
$313$		−	3520.09i		−	0.635678i	0.948145	−	0.317839i	$-0.102957\pi$
$314$	60.2108	−	104.288i	0.0108213	−	0.0187431i
$315$	−1767.03	+	5323.23i	−0.316066	+	0.952159i
$316$	−294.142	−	509.470i	−0.0523633	−	0.0906959i
$317$		−	1550.97i		−	0.274798i	−0.990516	−	0.137399i	$-0.956126\pi$
$317$		−	1550.97i		−	0.274798i	0.990516	−	0.137399i	$-0.0438743\pi$
$318$	−66.3943	+	38.3327i	−0.0117082	+	0.00675973i
$319$	586.150	+	1015.24i	0.102878	+	0.178190i
$320$	−144.327	−	700.835i	−0.0252129	−	0.122431i
$321$	−200.414	−	347.127i	−0.0348473	−	0.0603574i
$322$	−5005.65	−	2890.02i	−0.866317	−	0.500169i
$323$	633.494	+	365.748i	0.109129	+	0.0630055i
$324$	−2904.60			−0.498046
$325$	5001.06	+	3052.46i	0.853566	+	0.520984i
$326$	−2608.78			−0.443211
$327$	313.694	+	181.111i	0.0530498	+	0.0306283i
$328$	1113.09	+	642.641i	0.187378	+	0.108183i
$329$	1359.84	+	2355.31i	0.227874	+	0.394689i
$330$	−15.3401	−	74.4898i	−0.00255892	−	0.0124258i
$331$	−2880.89	−	4989.85i	−0.478393	−	0.828602i	0.521300	−	0.853374i	$-0.325447\pi$
$331$	−2880.89	−	4989.85i	−0.478393	−	0.828602i	−0.999693	+	0.0247720i	$0.992114\pi$
$332$	2140.36	−	1235.74i	0.353818	−	0.204277i
$333$		−	5492.55i		−	0.903874i
$334$	685.280	+	1186.94i	0.112266	+	0.194450i
$335$	−2212.65	+	6665.67i	−0.360866	+	1.08712i
$336$	27.9211	−	48.3607i	0.00453339	−	0.00785206i
$337$			2027.43i			0.327719i	0.986484	+	0.163859i	$0.0523944\pi$
$337$			2027.43i			0.327719i	−0.986484	+	0.163859i	$0.947606\pi$
$338$	3333.38	−	2862.83i	0.536426	−	0.460703i
$339$	−252.551			−0.0404621
$340$	838.040	−	2524.62i	0.133674	−	0.402696i
$341$	−1009.31	+	1748.18i	−0.160286	+	0.277623i
$342$	574.369	−	331.612i	0.0908138	−	0.0524314i
$343$		−	6323.11i		−	0.995382i
$344$	105.872	+	183.376i	0.0165938	+	0.0287412i
$345$	243.496	−	216.464i	0.0379983	−	0.0337798i
$346$	−6279.35			−0.975664
$347$	6698.82	−	3867.57i	1.03634	−	0.598334i	0.117549	−	0.993067i	$-0.462496\pi$
$347$	6698.82	−	3867.57i	1.03634	−	0.598334i	0.918796	+	0.394733i	$0.129163\pi$
$348$	−42.0184	−	24.2593i	−0.00647247	−	0.00373688i
$349$	3615.12	−	6261.56i	0.554478	−	0.960383i	−0.443466	−	0.896291i	$-0.646251\pi$
$349$	3615.12	−	6261.56i	0.554478	−	0.960383i	0.997944	−	0.0640923i	$-0.0204152\pi$
$350$	−4272.70	+	1837.74i	−0.652530	+	0.280661i
$351$	−387.129	+	274.393i	−0.0588702	+	0.0417265i
$352$		−	580.177i		−	0.0878509i
$353$	8400.04	+	4849.76i	1.26654	+	0.731238i	0.974332	−	0.225117i	$-0.0722764\pi$
$353$	8400.04	+	4849.76i	1.26654	+	0.731238i	0.292209	+	0.956355i	$0.405610\pi$
$354$	−130.082	+	225.308i	−0.0195304	+	0.0338276i
$355$	−1732.02	+	1539.73i	−0.258946	+	0.230199i
$356$	−79.0526			−0.0117690
$357$	179.784	−	103.798i	0.0266532	−	0.0153882i
$358$	1750.99	−	1010.94i	0.258499	−	0.149245i
$359$	11939.8			1.75531			0.877655	−	0.479293i	$-0.159107\pi$
$359$	11939.8			1.75531			0.877655	+	0.479293i	$0.159107\pi$
$360$	−1602.41	−	1802.52i	−0.234596	−	0.263892i
$361$	3353.88	−	5809.09i	0.488975	−	0.846930i
$362$	3489.88	+	2014.89i	0.506697	+	0.292542i
$363$			188.023i			0.0271864i
$364$	323.937	+	3473.08i	0.0466454	+	0.500107i
$365$	6620.24	−	1363.34i	0.949368	−	0.195509i
$366$	138.763	−	240.345i	0.0198177	−	0.0343252i
$367$	1411.14	+	814.724i	0.200711	+	0.115881i	0.596987	−	0.802251i	$-0.296364\pi$
$367$	1411.14	+	814.724i	0.200711	+	0.115881i	−0.396276	+	0.918131i	$0.629698\pi$
$368$	2152.43	−	1242.71i	0.304900	−	0.176034i
$369$	4332.17			0.611176
$370$	3404.08	−	3026.17i	0.478297	−	0.425198i
$371$	1900.82	+	3292.31i	0.265999	+	0.460723i
$372$		−	83.5461i		−	0.0116443i
$373$	9566.79	−	5523.39i	1.32802	−	0.766730i	0.343023	−	0.939327i	$-0.388549\pi$
$373$	9566.79	−	5523.39i	1.32802	−	0.766730i	0.984993	+	0.172597i	$0.0552158\pi$
$374$	1078.42	−	1867.89i	0.149102	−	0.258252i
$375$	−22.4380	−	261.210i	−0.00308984	−	0.0359702i
$376$	−1169.46			−0.160400
$377$	3017.60	−	281.454i	0.412240	−	0.0384499i
$378$		−	376.689i		−	0.0512560i
$379$	−3792.00	+	6567.93i	−0.513936	+	0.890164i	0.485933	+	0.873996i	$0.338480\pi$
$379$	−3792.00	+	6567.93i	−0.513936	+	0.890164i	−0.999869	+	0.0161677i	$0.994853\pi$
$380$	521.975	+	173.268i	0.0704651	+	0.0233907i
$381$	226.269	+	391.909i	0.0304255	+	0.0526985i
$382$			10050.5i			1.34614i
$383$	−9731.99	+	5618.77i	−1.29838	+	0.749623i	−0.980125	−	0.198381i	$-0.936432\pi$
$383$	−9731.99	+	5618.77i	−1.29838	+	0.749623i	−0.318260	+	0.948004i	$0.603098\pi$
$384$	12.0061	+	20.7951i	0.00159553	+	0.00276353i
$385$	−3693.75	+	760.674i	−0.488964	+	0.100695i
$386$	−1765.44	−	3057.84i	−0.232795	−	0.403212i
$387$	618.088	+	356.853i	0.0811865	+	0.0468731i
$388$	−4414.15	−	2548.51i	−0.577563	−	0.333456i
$389$	−4469.20			−0.582512			−0.291256	−	0.956645i	$-0.594073\pi$
$389$	−4469.20			−0.582512			−0.291256	+	0.956645i	$0.594073\pi$
$390$	−191.551	−	44.3456i	−0.0248706	−	0.00575777i
$391$	9239.70			1.19507
$392$	−21.7034	−	12.5305i	−0.00279640	−	0.00161450i
$393$	110.060	+	63.5430i	0.0141267	+	0.00815603i
$394$	126.835	+	219.684i	0.0162179	+	0.0280901i
$395$	−331.661	−	1610.51i	−0.0422473	−	0.205148i
$396$	−977.772	−	1693.55i	−0.124078	−	0.214910i
$397$	6610.97	−	3816.85i	0.835756	−	0.482524i	−0.0200635	−	0.999799i	$-0.506387\pi$
$397$	6610.97	−	3816.85i	0.835756	−	0.482524i	0.855819	+	0.517275i	$0.173054\pi$
$398$			8157.88i			1.02743i
$399$	21.4607	+	37.1711i	0.00269268	+	0.00466387i
$400$	234.274	−	1986.23i	0.0292842	−	0.248279i
$401$	1239.56	−	2146.98i	0.154366	−	0.267369i	−0.778462	−	0.627692i	$-0.784000\pi$
$401$	1239.56	−	2146.98i	0.154366	−	0.267369i	0.932828	+	0.360322i	$0.117333\pi$
$402$		−	235.688i		−	0.0292414i
$403$	3017.78	+	4257.66i	0.373018	+	0.526275i
$404$	−5632.40			−0.693620
$405$	−7705.19	−	2557.72i	−0.945368	−	0.313812i
$406$	−1202.95	+	2083.58i	−0.147048	+	0.254695i
$407$	3198.29	−	1846.53i	0.389517	−	0.224888i
$408$			89.2668i			0.0108318i
$409$	1074.24	+	1860.63i	0.129872	+	0.224945i	0.923627	−	0.383293i	$-0.125210\pi$
$409$	1074.24	+	1860.63i	0.129872	+	0.224945i	−0.793755	+	0.608238i	$0.791877\pi$
$410$	2386.85	+	2684.92i	0.287508	+	0.323412i
$411$	−72.8243			−0.00874005
$412$	−2998.66	+	1731.28i	−0.358577	+	0.207024i
$413$	11172.4	+	6450.40i	1.33114	+	0.768531i
$414$	4188.67	−	7254.99i	0.497251	−	0.861264i
$415$	6765.99	−	1393.36i	0.800312	−	0.164813i
$416$	−1362.99	−	626.082i	−0.160640	−	0.0737890i
$417$		−	406.352i		−	0.0477198i
$418$	386.193	+	222.968i	0.0451897	+	0.0260903i
$419$	−2181.80	+	3778.99i	−0.254387	+	0.440611i	−0.964729	−	0.263246i	$-0.915207\pi$
$419$	−2181.80	+	3778.99i	−0.254387	+	0.440611i	0.710342	+	0.703857i	$0.248540\pi$
$420$	116.653	−	103.702i	0.0135526	−	0.0120480i
$421$	2412.54			0.279287			0.139644	−	0.990202i	$-0.455404\pi$
$421$	2412.54			0.279287			0.139644	+	0.990202i	$0.455404\pi$
$422$	8056.33	−	4651.33i	0.929327	−	0.536547i
$423$	−3413.69	+	1970.90i	−0.392386	+	0.226544i
$424$	−1634.70			−0.187236
$425$	4446.22	−	5959.23i	0.507467	−	0.680153i
$426$	38.8848	−	67.3504i	0.00442247	−	0.00765995i
$427$	−11918.1	−	6880.89i	−1.35071	−	0.779835i
$428$		−	8546.66i		−	0.965230i
$429$	−144.869	−	66.5446i	−0.0163038	−	0.00748905i
$430$	119.377	+	579.680i	0.0133880	+	0.0650108i
$431$	−1851.89	+	3207.57i	−0.206967	+	0.358477i	−0.950758	−	0.309936i	$-0.899692\pi$
$431$	−1851.89	+	3207.57i	−0.206967	+	0.358477i	0.743791	+	0.668412i	$0.233026\pi$
$432$	140.275	+	80.9881i	0.0156227	+	0.00901977i
$433$	−934.336	+	539.439i	−0.103698	+	0.0598702i	−0.550952	−	0.834537i	$-0.685735\pi$
$433$	−934.336	+	539.439i	−0.103698	+	0.0598702i	0.447254	+	0.894407i	$0.352402\pi$
$434$	−4142.83			−0.458208
$435$	−90.1022	−	101.354i	−0.00993119	−	0.0111714i
$436$	3861.75	+	6688.75i	0.424184	+	0.734709i
$437$			1910.35i			0.209117i
$438$	−196.435	+	113.412i	−0.0214293	+	0.0123722i
$439$	−560.400	+	970.641i	−0.0609258	+	0.105527i	−0.894879	−	0.446308i	$-0.852739\pi$
$439$	−560.400	+	970.641i	−0.0609258	+	0.105527i	0.833954	+	0.551834i	$0.186072\pi$
$440$	510.888	−	1539.07i	0.0553538	−	0.166755i
$441$	−84.4705			−0.00912110
$442$	−3224.42	−	4549.19i	−0.346991	−	0.489554i
$443$			9267.16i			0.993896i	0.867780	+	0.496948i	$0.165546\pi$
$443$			9267.16i			0.993896i	−0.867780	+	0.496948i	$0.834454\pi$
$444$	−76.4236	+	132.370i	−0.00816870	+	0.0141486i
$445$	−209.707	−	69.6117i	−0.0223395	−	0.00741553i
$446$	−167.751	−	290.553i	−0.0178099	−	0.0308477i
$447$			489.229i			0.0517667i
$448$	1031.17	−	595.348i	0.108746	−	0.0627848i
$449$	−6712.19	−	11625.9i	−0.705496	−	1.22196i	−0.966512	−	0.256621i	$-0.917391\pi$
$449$	−6712.19	−	11625.9i	−0.705496	−	1.22196i	0.261016	−	0.965335i	$-0.415943\pi$
$450$	−2663.55	−	6192.68i	−0.279024	−	0.648724i
$451$	1456.43	+	2522.61i	0.152063	+	0.263381i
$452$	−4663.57	−	2692.51i	−0.485300	−	0.280188i
$453$	76.2488	+	44.0223i	0.00790835	+	0.00456589i
$454$	2529.58			0.261496
$455$	−2198.98	+	9498.48i	−0.226571	+	0.978672i
$456$	−18.4563			−0.00189538
$457$	−7642.44	−	4412.36i	−0.782272	−	0.451645i	0.0549631	−	0.998488i	$-0.482496\pi$
$457$	−7642.44	−	4412.36i	−0.782272	−	0.451645i	−0.837235	+	0.546844i	$0.815829\pi$
$458$	7415.34	+	4281.25i	0.756542	+	0.436790i
$459$	301.079	+	521.484i	0.0306169	+	0.0530300i
$460$	6804.16	−	1401.22i	0.689665	−	0.142026i
$461$	2034.18	+	3523.30i	0.205512	+	0.355957i	0.950296	−	0.311349i	$-0.100781\pi$
$461$	2034.18	+	3523.30i	0.205512	+	0.355957i	−0.744784	+	0.667306i	$0.767447\pi$
$462$	109.601	−	63.2779i	0.0110370	−	0.00637220i
$463$			8511.92i			0.854390i	0.904159	+	0.427195i	$0.140498\pi$
$463$			8511.92i			0.854390i	−0.904159	+	0.427195i	$0.859502\pi$
$464$	−517.271	−	895.939i	−0.0517537	−	0.0896400i
$465$	73.5685	−	221.627i	0.00733690	−	0.0221026i
$466$	−3286.61	+	5692.57i	−0.326715	+	0.565887i
$467$		−	7999.89i		−	0.792699i	−0.918100	−	0.396350i	$-0.870277\pi$
$467$		−	7999.89i		−	0.792699i	0.918100	−	0.396350i	$-0.129723\pi$
$468$	−5033.75	+	469.501i	−0.497190	+	0.0463733i
$469$	−11687.1			−1.15067
$470$	−3102.29	−	1029.80i	−0.304464	−	0.101066i
$471$	−5.64761	+	9.78195i	−0.000552502	+	0.000956961i
$472$	−4804.14	+	2773.67i	−0.468493	+	0.270484i
$473$			479.880i			0.0466489i
$474$	27.5898	+	47.7869i	0.00267350	+	0.00463064i
$475$	1232.09	+	919.274i	0.119015	+	0.0887983i
$476$	4426.50			0.426236
$477$	−4771.75	+	2754.97i	−0.458036	+	0.264447i
$478$	−10908.1	−	6297.79i	−1.04378	−	0.602624i
$479$	5715.00	−	9898.67i	0.545146	−	0.944221i	−0.453451	−	0.891281i	$-0.649807\pi$
$479$	5715.00	−	9898.67i	0.545146	−	0.944221i	0.998598	−	0.0529402i	$-0.0168593\pi$
$480$	13.5375	+	65.7365i	0.00128729	+	0.00625093i
$481$	−886.659	−	9506.29i	−0.0840502	−	0.901143i
$482$			13916.3i			1.31509i
$483$	469.517	+	271.076i	0.0442314	+	0.0255370i
$484$	−2004.57	+	3472.01i	−0.188258	+	0.326072i
$485$	−9465.50	−	10647.6i	−0.886198	−	0.996867i
$486$	819.114			0.0764522
$487$	542.697	−	313.326i	0.0504968	−	0.0291543i	−0.474539	−	0.880234i	$-0.657385\pi$
$487$	542.697	−	313.326i	0.0504968	−	0.0291543i	0.525036	+	0.851080i	$0.324052\pi$
$488$	5124.76	−	2958.78i	0.475384	−	0.274463i
$489$	244.696			0.0226289
$490$	−46.5398	−	52.3517i	−0.00429072	−	0.00482655i
$491$	−9791.12	+	16958.7i	−0.899933	+	1.55873i	−0.0723552	+	0.997379i	$0.523052\pi$
$491$	−9791.12	+	16958.7i	−0.899933	+	1.55873i	−0.827578	+	0.561351i	$0.810282\pi$
$492$	−104.405	−	60.2780i	−0.00956691	−	0.00552346i
$493$		−	3845.98i		−	0.351347i
$494$	940.563	−	666.661i	0.0856638	−	0.0607176i
$495$	−1102.49	−	5353.57i	−0.100108	−	0.486111i
$496$	890.709	−	1542.75i	0.0806331	−	0.139661i
$497$	−3339.73	−	1928.19i	−0.301423	−	0.174027i
$498$	−200.760	+	115.909i	−0.0180648	+	0.0104297i
$499$	−12782.2			−1.14671			−0.573355	−	0.819307i	$-0.694358\pi$
$499$	−12782.2			−1.14671			−0.573355	+	0.819307i	$0.694358\pi$
$500$	2370.49	−	5062.68i	0.212023	−	0.452820i
$501$	−64.2774	−	111.332i	−0.00573194	−	0.00992802i
$502$			9220.83i			0.819812i
$503$	−15048.8	+	8688.42i	−1.33398	+	0.770174i	−0.985907	−	0.167294i	$-0.946497\pi$
$503$	−15048.8	+	8688.42i	−1.33398	+	0.770174i	−0.348073	+	0.937467i	$0.613164\pi$
$504$	2006.68	−	3475.68i	0.177351	−	0.307180i
$505$	−14941.4	−	4959.74i	−1.31660	−	0.437041i
$506$	5632.74			0.494873
$507$	−312.662	+	268.526i	−0.0273882	+	0.0235220i
$508$			9649.27i			0.842750i
$509$	1444.78	−	2502.43i	0.125813	−	0.217914i	−0.796238	−	0.604984i	$-0.793179\pi$
$509$	1444.78	−	2502.43i	0.125813	−	0.217914i	0.922050	+	0.387070i	$0.126513\pi$
$510$	−78.6059	+	236.803i	−0.00682496	+	0.0205604i
$511$	5623.79	+	9740.69i	0.486853	+	0.843254i
$512$			512.000i			0.0441942i
$513$	−107.819	+	62.2493i	−0.00927938	+	0.00535745i
$514$	−159.579	−	276.399i	−0.0136940	−	0.0237187i
$515$	−9479.23	+	1952.11i	−0.811077	+	0.167030i
$516$	−9.93054	−	17.2002i	−0.000847224	−	0.00146744i
$517$	−2295.29	−	1325.19i	−0.195255	−	0.112730i
$518$	6563.85	+	3789.64i	0.556755	+	0.321443i
$519$	588.986			0.0498143
$520$	−3064.37	−	2861.06i	−0.258426	−	0.241280i
$521$	−7655.58			−0.643756			−0.321878	−	0.946781i	$-0.604314\pi$
$521$	−7655.58			−0.643756			−0.321878	+	0.946781i	$0.604314\pi$
$522$	−3019.85	−	1743.51i	−0.253210	−	0.146191i
$523$	−13318.1	−	7689.20i	−1.11350	−	0.642878i	−0.173764	−	0.984787i	$-0.555593\pi$
$523$	−13318.1	−	7689.20i	−1.11350	−	0.642878i	−0.939733	+	0.341909i	$0.888926\pi$
$524$	1354.90	+	2346.75i	0.112956	+	0.195646i
$525$	400.768	−	172.375i	0.0333161	−	0.0143297i
$526$	6334.27	+	10971.3i	0.525071	+	0.909450i
$527$	5735.29	−	3311.27i	0.474067	−	0.273703i
$528$			54.4191i			0.00448539i
$529$	5981.51	+	10360.3i	0.491618	+	0.851507i
$530$	−4336.47	−	1439.48i	−0.355404	−	0.117975i
$531$	−9348.95	+	16192.9i	−0.764048	+	1.32337i
$532$			915.196i			0.0745842i
$533$	7497.95	−	699.339i	0.609329	−	0.0568325i
$534$	7.41493			0.000600890
$535$	7525.97	−	22672.2i	0.608179	−	1.83216i
$536$	2512.74	−	4352.19i	0.202488	−	0.350720i
$537$	−164.238	+	94.8231i	−0.0131982	+	0.00761996i
$538$			5390.62i			0.431982i
$539$	−28.3980	−	49.1868i	−0.00226937	−	0.00393066i
$540$	300.800	+	338.364i	0.0239711	+	0.0269646i
$541$	−6283.50			−0.499351			−0.249675	−	0.968330i	$-0.580324\pi$
$541$	−6283.50			−0.499351			−0.249675	+	0.968330i	$0.580324\pi$
$542$	−13396.5	+	7734.50i	−1.06168	+	0.612961i
$543$	−327.342	−	188.991i	−0.0258703	−	0.0149362i
$544$	−951.698	+	1648.39i	−0.0750068	+	0.129916i
$545$	4354.33	+	21144.1i	0.342237	+	1.66186i
$546$	−30.3845	−	325.766i	−0.00238157	−	0.0255339i
$547$		−	6659.22i		−	0.520526i	−0.965538	−	0.260263i	$-0.916191\pi$
$547$		−	6659.22i		−	0.520526i	0.965538	−	0.260263i	$-0.0838092\pi$
$548$	−1344.77	−	776.401i	−0.104828	−	0.0605222i
$549$	9972.88	−	17273.5i	0.775286	−	1.34284i
$550$	2710.52	−	3632.88i	0.210140	−	0.281648i
$551$	795.172			0.0614800
$552$	−201.892	+	116.563i	−0.0155672	+	0.00898775i
$553$	2369.62	−	1368.10i	0.182218	−	0.105204i
$554$	16227.2			1.24445
$555$	−319.294	+	283.847i	−0.0244203	+	0.0217092i
$556$	4332.23	−	7503.65i	0.330445	−	0.572348i
$557$	7913.85	+	4569.06i	0.602012	+	0.347572i	0.769833	−	0.638246i	$-0.220340\pi$
$557$	7913.85	+	4569.06i	0.602012	+	0.347572i	−0.167821	+	0.985818i	$0.553673\pi$
$558$		−	6004.45i		−	0.455535i
$559$	1127.37	+	517.850i	0.0852998	+	0.0391820i
$560$	3259.70	−	671.287i	0.245977	−	0.0506555i
$561$	−101.153	+	175.203i	−0.00761265	+	0.0131855i
$562$	7803.25	+	4505.21i	0.585695	+	0.338151i
$563$	8532.78	−	4926.40i	0.638746	−	0.368780i	−0.145386	−	0.989375i	$-0.546442\pi$
$563$	8532.78	−	4926.40i	0.638746	−	0.368780i	0.784131	+	0.620595i	$0.213109\pi$
$564$	109.693			0.00818952
$565$	−10000.3	−	11249.2i	−0.744632	−	0.837622i
$566$	545.132	+	944.196i	0.0404834	+	0.0701193i
$567$		−	13509.8i		−	1.00063i
$568$	1436.08	−	829.123i	0.106086	−	0.0612486i
$569$	7020.92	−	12160.6i	0.517280	−	0.895955i	−0.482519	−	0.875886i	$-0.660278\pi$
$569$	7020.92	−	12160.6i	0.517280	−	0.895955i	0.999799	−	0.0200695i	$-0.00638874\pi$
$570$	−48.9598	−	16.2521i	−0.00359772	−	0.00119425i
$571$	2935.30			0.215129			0.107564	−	0.994198i	$-0.465695\pi$
$571$	2935.30			0.215129			0.107564	+	0.994198i	$0.465695\pi$
$572$	−1965.68	−	2773.29i	−0.143687	−	0.202722i
$573$		−	942.708i		−	0.0687298i
$574$	−2989.03	+	5177.14i	−0.217351	+	0.376463i
$575$	19283.6	+	2274.48i	1.39858	+	0.164961i
$576$	862.874	+	1494.54i	0.0624185	+	0.108112i
$577$		−	874.237i		−	0.0630762i	−0.999503	−	0.0315381i	$-0.989959\pi$
$577$		−	874.237i		−	0.0630762i	0.999503	−	0.0315381i	$-0.0100405\pi$
$578$	2381.56	−	1375.00i	0.171384	−	0.0989486i
$579$	165.594	+	286.817i	0.0118857	+	0.0205867i
$580$	−583.250	−	2832.20i	−0.0417554	−	0.202760i
$581$	5747.61	+	9955.15i	0.410415	+	0.710859i
$582$	414.036	+	239.044i	0.0294885	+	0.0170252i
$583$	−3208.41	−	1852.38i	−0.227923	−	0.131591i
$584$	−4836.46			−0.342696
$585$	−13766.7	−	3187.11i	−0.972963	−	0.225250i
$586$	12583.1			0.887035
$587$	8031.92	+	4637.23i	0.564758	+	0.326063i	0.755053	−	0.655664i	$-0.227611\pi$
$587$	8031.92	+	4637.23i	0.564758	+	0.326063i	−0.190295	+	0.981727i	$0.560945\pi$
$588$	2.03572	+	1.17533i	0.000142775	+	8.24314e-5i
$589$	684.619	+	1185.79i	0.0478934	+	0.0829538i
$590$	−15186.6	+	3127.46i	−1.05970	+	0.218230i
$591$	−11.8967	−	20.6058i	−0.000828032	−	0.00143419i
$592$	−2822.46	+	1629.55i	−0.195950	+	0.113132i
$593$		−	5655.80i		−	0.391662i	−0.980638	−	0.195831i	$-0.937260\pi$
$593$		−	5655.80i		−	0.391662i	0.980638	−	0.195831i	$-0.0627405\pi$
$594$	183.545	+	317.909i	0.0126783	+	0.0219595i
$595$	11742.4	+	3897.86i	0.809062	+	0.268566i
$596$	−5215.81	+	9034.04i	−0.358469	+	0.620887i
$597$		−	765.187i		−	0.0524573i
$598$	6078.42	−	13232.8i	0.415660	−	0.904900i
$599$	−21245.2			−1.44918			−0.724588	−	0.689182i	$-0.757970\pi$
$599$	−21245.2			−1.44918			−0.724588	+	0.689182i	$0.757970\pi$
$600$	−21.9742	+	186.303i	−0.00149516	+	0.0126763i
$601$	3222.20	−	5581.02i	0.218696	−	0.378793i	−0.735713	−	0.677293i	$-0.763153\pi$
$601$	3222.20	−	5581.02i	0.218696	−	0.378793i	0.954410	+	0.298500i	$0.0964863\pi$
$602$	−852.912	+	492.429i	−0.0577444	+	0.0333387i
$603$		−	16938.9i		−	1.14395i
$604$	938.667	+	1625.82i	0.0632348	+	0.109526i
$605$	−8374.98	+	7445.22i	−0.562796	+	0.500316i
$606$	528.304			0.0354140
$607$	16894.0	−	9753.74i	1.12966	−	0.652211i	0.185813	−	0.982585i	$-0.440508\pi$
$607$	16894.0	−	9753.74i	1.12966	−	0.652211i	0.943850	+	0.330374i	$0.107175\pi$
$608$	−340.811	−	196.767i	−0.0227331	−	0.0131249i
$609$	112.834	−	195.434i	0.00750782	−	0.0130039i
$610$	16200.2	−	3336.19i	1.07529	−	0.221440i
$611$	−5590.12	+	3962.22i	−0.370134	+	0.262347i
$612$			6415.59i			0.423750i
$613$	24422.4	+	14100.3i	1.60916	+	0.929047i	0.989559	+	0.144126i	$0.0460370\pi$
$613$	24422.4	+	14100.3i	1.60916	+	0.929047i	0.619596	+	0.784921i	$0.287296\pi$
$614$	7627.50	−	13211.2i	0.501337	−	0.868341i
$615$	−223.880	−	251.838i	−0.0146792	−	0.0165124i
$616$	2698.50			0.176502
$617$	1904.61	−	1099.63i	0.124273	−	0.0717492i	−0.436575	−	0.899668i	$-0.643809\pi$
$617$	1904.61	−	1099.63i	0.124273	−	0.0717492i	0.560848	+	0.827919i	$0.310475\pi$
$618$	281.267	−	162.389i	0.0183078	−	0.0105700i
$619$	2986.69			0.193934			0.0969671	−	0.995288i	$-0.469086\pi$
$619$	2986.69			0.193934			0.0969671	+	0.995288i	$0.469086\pi$
$620$	3721.34	−	3308.21i	0.241052	−	0.214292i
$621$	−786.285	+	1361.89i	−0.0508092	+	0.0880042i
$622$	−984.349	−	568.314i	−0.0634547	−	0.0366356i
$623$		−	367.686i		−	0.0236453i
$624$	127.845	+	58.7249i	0.00820176	+	0.00376743i
$625$	10746.4	−	11342.6i	0.687769	−	0.725929i
$626$	−3520.09	+	6096.97i	−0.224746	+	0.389271i
$627$	−36.2239	−	20.9139i	−0.00230724	−	0.00133209i
$628$	−208.576	+	120.422i	−0.0132533	+	0.00765182i
$629$	−12115.9			−0.768034
$630$	8383.82	−	7453.07i	0.530189	−	0.471329i
$631$	6781.46	+	11745.8i	0.427838	+	0.741037i	0.996681	−	0.0814092i	$-0.0259421\pi$
$631$	6781.46	+	11745.8i	0.427838	+	0.741037i	−0.568843	+	0.822446i	$0.692609\pi$
$632$			1176.57i			0.0740529i
$633$	−755.663	+	436.282i	−0.0474485	+	0.0273944i
$634$	−1550.97	+	2686.36i	−0.0971559	+	0.168279i
$635$	−8496.89	+	25597.1i	−0.531006	+	1.59967i
$636$	153.331			0.00955970
$637$	−146.198	+	13.6360i	−0.00909354	+	0.000848161i
$638$		−	2344.60i		−	0.145491i
$639$	2794.64	−	4840.46i	0.173011	−	0.299665i
$640$	−450.854	+	1358.21i	−0.0278462	+	0.0838874i
$641$	4703.70	+	8147.04i	0.289836	+	0.502011i	0.973770	−	0.227533i	$-0.0730659\pi$
$641$	4703.70	+	8147.04i	0.289836	+	0.502011i	−0.683934	+	0.729543i	$0.739733\pi$
$642$			801.654i			0.0492816i
$643$	−22171.3	+	12800.6i	−1.35980	+	0.785082i	−0.989597	−	0.143868i	$-0.954046\pi$
$643$	−22171.3	+	12800.6i	−1.35980	+	0.785082i	−0.370205	+	0.928950i	$0.620713\pi$
$644$	5780.03	+	10011.3i	0.353673	+	0.612579i
$645$	−11.1972	−	54.3724i	−0.000683550	−	0.00331924i
$646$	−731.496	−	1266.99i	−0.0445516	−	0.0771656i
$647$	17398.6	+	10045.1i	1.05720	+	0.610374i	0.924656	−	0.380803i	$-0.124352\pi$
$647$	17398.6	+	10045.1i	1.05720	+	0.610374i	0.132543	+	0.991177i	$0.457686\pi$
$648$	5030.92	+	2904.60i	0.304989	+	0.176086i
$649$	−12572.0			−0.760394
$650$	−5609.64	−	10288.1i	−0.338505	−	0.620818i
$651$	388.586			0.0233946
$652$	4518.54	+	2608.78i	0.271410	+	0.156699i
$653$	−12689.1	−	7326.04i	−0.760432	−	0.439035i	0.0690191	−	0.997615i	$-0.478013\pi$
$653$	−12689.1	−	7326.04i	−0.760432	−	0.439035i	−0.829451	+	0.558580i	$0.811346\pi$
$654$	−362.222	−	627.387i	−0.0216575	−	0.0375119i
$655$	1527.72	+	7418.44i	0.0911343	+	0.442538i
$656$	−1285.28	−	2226.17i	−0.0764967	−	0.132496i
$657$	−14117.8	+	8150.89i	−0.838335	+	0.484013i
$658$		−	5439.36i		−	0.322262i
$659$	9738.87	+	16868.2i	0.575679	+	0.997105i	0.995968	+	0.0897146i	$0.0285955\pi$
$659$	9738.87	+	16868.2i	0.575679	+	0.997105i	−0.420289	+	0.907390i	$0.638071\pi$
$660$	−47.9200	+	144.360i	−0.00282619	+	0.00851396i
$661$	−7865.73	+	13623.9i	−0.462847	+	0.801674i	−0.999101	−	0.0423822i	$-0.986505\pi$
$661$	−7865.73	+	13623.9i	−0.462847	+	0.801674i	0.536255	+	0.844056i	$0.319839\pi$
$662$			11523.6i			0.676550i
$663$	302.442	+	426.702i	0.0177162	+	0.0249951i
$664$	−4942.95			−0.288891
$665$	−805.898	+	2427.79i	−0.0469945	+	0.141572i
$666$	−5492.55	+	9513.38i	−0.319568	+	0.553508i
$667$	8698.36	−	5022.00i	0.504950	−	0.291533i
$668$		−	2741.12i		−	0.158768i
$669$	15.7346	+	27.2531i	0.000909318	+	0.00157499i
$670$	10498.1	−	9332.63i	0.605338	−	0.538136i
$671$	13411.1			0.771578
$672$	−96.7214	+	55.8421i	−0.00555224	+	0.00320559i
$673$	13400.0	+	7736.50i	0.767507	+	0.443121i	0.831985	−	0.554799i	$-0.187205\pi$
$673$	13400.0	+	7736.50i	0.767507	+	0.443121i	−0.0644773	+	0.997919i	$0.520538\pi$
$674$	2027.43	−	3511.62i	0.115866	−	0.200686i
$675$	499.993	+	1162.47i	0.0285107	+	0.0662868i
$676$	−8636.42	+	1625.19i	−0.491376	+	0.0924663i
$677$		−	24473.0i		−	1.38933i	−0.719335	−	0.694663i	$-0.755553\pi$
$677$		−	24473.0i		−	1.38933i	0.719335	−	0.694663i	$-0.244447\pi$
$678$	437.430	+	252.551i	0.0247779	+	0.0143055i
$679$	11853.5	−	20530.9i	0.669951	−	1.16039i
$680$	−3976.15	+	3534.73i	−0.224233	+	0.199339i
$681$	−237.268			−0.0133511
$682$	3496.37	−	2018.63i	0.196309	−	0.113339i
$683$	−15982.4	+	9227.45i	−0.895388	+	0.516952i	−0.875701	−	0.482854i	$-0.839600\pi$
$683$	−15982.4	+	9227.45i	−0.895388	+	0.516952i	−0.0196867	+	0.999806i	$0.506267\pi$
$684$	−1326.45			−0.0741491
$685$	−2883.65	−	3243.76i	−0.160845	−	0.180931i
$686$	−6323.11	+	10951.9i	−0.351921	+	0.609544i
$687$	−695.540	−	401.570i	−0.0386266	−	0.0223011i
$688$		−	423.489i		−	0.0234671i
$689$	−7814.01	+	5538.49i	−0.432061	+	0.306240i
$690$	−638.212	+	131.431i	−0.0352121	+	0.00725142i
$691$	1509.37	−	2614.31i	0.0830958	−	0.143926i	−0.821482	−	0.570234i	$-0.806853\pi$
$691$	1509.37	−	2614.31i	0.0830958	−	0.143926i	0.904578	+	0.426308i	$0.140186\pi$
$692$	10876.1	+	6279.35i	0.597470	+	0.344949i
$693$	7876.98	−	4547.78i	0.431777	−	0.249287i
$694$	−15470.3			−0.846172
$695$	18099.8	−	16090.5i	0.987865	−	0.878196i
$696$	48.5186	+	84.0367i	0.00264238	+	0.00457673i
$697$		−	9556.25i		−	0.519324i
$698$	−12523.1	+	7230.23i	−0.679094	+	0.392075i
$699$	308.275	−	533.948i	0.0166810	−	0.0288924i
$700$	9238.28	+	1089.64i	0.498820	+	0.0588353i
$701$	3095.36			0.166776			0.0833880	−	0.996517i	$-0.473426\pi$
$701$	3095.36			0.166776			0.0833880	+	0.996517i	$0.473426\pi$
$702$	944.921	−	88.1335i	0.0508030	−	0.00473844i
$703$		−	2505.01i		−	0.134393i
$704$	−580.177	+	1004.90i	−0.0310600	+	0.0537975i
$705$	290.987	+	96.5923i	0.0155450	+	0.00516011i
$706$	−9699.53	−	16800.1i	−0.517063	−	0.895580i
$707$		−	26197.2i		−	1.39356i
$708$	450.616	−	260.163i	0.0239198	−	0.0138101i
$709$	7967.58	+	13800.3i	0.422043	+	0.731001i	0.996139	−	0.0877876i	$-0.0279797\pi$
$709$	7967.58	+	13800.3i	0.422043	+	0.731001i	−0.574096	+	0.818788i	$0.694646\pi$
$710$	4539.67	−	934.880i	0.239959	−	0.0494161i
$711$	1982.87	+	3434.44i	0.104590	+	0.181155i
$712$	136.923	+	79.0526i	0.00720704	+	0.00416099i
$713$	14978.1	+	8647.58i	0.786722	+	0.454214i
$714$	−415.194			−0.0217622
$715$	−2772.37	−	9087.77i	−0.145008	−	0.475333i
$716$	−4043.74			−0.211064
$717$	1023.15	+	590.716i	0.0532919	+	0.0307681i
$718$	−20680.3	−	11939.8i	−1.07490	−	0.620596i
$719$	−5451.36	−	9442.03i	−0.282756	−	0.489747i	0.689307	−	0.724470i	$-0.257915\pi$
$719$	−5451.36	−	9442.03i	−0.282756	−	0.489747i	−0.972062	+	0.234722i	$0.924582\pi$
$720$	972.936	+	4724.47i	0.0503600	+	0.244543i
$721$	−8052.46	−	13947.3i	−0.415935	−	0.720421i
$722$	−11618.2	+	6707.76i	−0.598870	+	0.345758i
$723$		−	1305.31i		−	0.0671441i
$724$	−4029.77	−	6979.77i	−0.206858	−	0.358289i
$725$	946.742	−	8026.72i	0.0484981	−	0.411179i
$726$	188.023	−	325.666i	0.00961184	−	0.0166482i
$727$			29675.2i			1.51388i	0.653482	+	0.756942i	$0.273308\pi$
$727$			29675.2i			1.51388i	−0.653482	+	0.756942i	$0.726692\pi$
$728$	2912.01	−	6339.50i	0.148250	−	0.322744i
$729$	19529.2			0.992188
$730$	−12829.9	−	4258.86i	−0.650489	−	0.215928i
$731$	787.176	−	1363.43i	0.0398286	−	0.0689852i
$732$	−480.689	+	277.526i	−0.0242716	+	0.0140132i
$733$		−	18298.1i		−	0.922041i	−0.887390	−	0.461020i	$-0.847483\pi$
$733$		−	18298.1i		−	0.922041i	0.887390	−	0.461020i	$-0.152517\pi$
$734$	−1629.45	−	2822.29i	−0.0819401	−	0.141924i
$735$	4.36531	+	4.91045i	0.000219071	+	0.000246428i
$736$	−4970.83			−0.248950
$737$	9863.44	−	5694.66i	0.492978	−	0.284621i
$738$	−7503.54	−	4332.17i	−0.374267	−	0.216083i
$739$	−8833.01	+	15299.2i	−0.439686	+	0.761558i	−0.997665	−	0.0682971i	$-0.978243\pi$
$739$	−8833.01	+	15299.2i	−0.439686	+	0.761558i	0.557980	+	0.829855i	$0.311577\pi$
$740$	−8922.22	+	1837.40i	−0.443226	+	0.0912760i
$741$	−88.2223	+	62.5310i	−0.00437372	+	0.00310005i
$742$		−	7603.27i		−	0.376179i
$743$	−3722.94	−	2149.44i	−0.183824	−	0.106131i	0.405264	−	0.914200i	$-0.367180\pi$
$743$	−3722.94	−	2149.44i	−0.183824	−	0.106131i	−0.589088	+	0.808069i	$0.700513\pi$
$744$	−83.5461	+	144.706i	−0.00411687	+	0.00713063i
$745$	−21791.4	+	19372.2i	−1.07164	+	0.952673i
$746$	−22093.6			−1.08432
$747$	−14428.6	+	8330.35i	−0.706713	+	0.408021i
$748$	−3735.77	+	2156.85i	−0.182611	+	0.105431i
$749$	39751.9			1.93926
$750$	−222.346	+	474.866i	−0.0108252	+	0.0231196i
$751$	17605.6	−	30493.8i	0.855443	−	1.48167i	−0.0207900	−	0.999784i	$-0.506618\pi$
$751$	17605.6	−	30493.8i	0.855443	−	1.48167i	0.876233	−	0.481887i	$-0.160049\pi$
$752$	2025.57	+	1169.46i	0.0982246	+	0.0567100i
$753$		−	864.889i		−	0.0418570i
$754$	−5508.10	−	2530.11i	−0.266039	−	0.122203i
$755$	1058.40	+	5139.46i	0.0510186	+	0.247741i
$756$	−376.689	+	652.444i	−0.0181217	+	0.0313878i
$757$	−7520.57	−	4342.00i	−0.361083	−	0.208471i	0.308473	−	0.951233i	$-0.400182\pi$
$757$	−7520.57	−	4342.00i	−0.361083	−	0.208471i	−0.669556	+	0.742762i	$0.733515\pi$
$758$	13135.9	−	7584.00i	0.629441	−	0.363408i
$759$	−528.336			−0.0252666
$760$	−730.819	−	822.084i	−0.0348810	−	0.0392370i
$761$	8222.34	+	14241.5i	0.391668	+	0.678389i	0.992670	−	0.120859i	$-0.0385648\pi$
$761$	8222.34	+	14241.5i	0.391668	+	0.678389i	−0.601002	+	0.799248i	$0.705231\pi$
$762$		−	905.076i		−	0.0430281i
$763$	−31110.4	+	17961.6i	−1.47611	+	0.852234i
$764$	10050.5	−	17407.9i	0.475934	−	0.824341i
$765$	−5649.40	+	17019.0i	−0.266999	+	0.804342i
$766$	22475.1			1.06013
$767$	−13566.8	+	29535.1i	−0.638681	+	1.39042i
$768$		−	48.0242i		−	0.00225641i
$769$	−17571.4	+	30434.6i	−0.823981	+	1.42718i	0.0787138	+	0.996897i	$0.474919\pi$
$769$	−17571.4	+	30434.6i	−0.823981	+	1.42718i	−0.902695	+	0.430280i	$0.858415\pi$
$770$	7158.44	+	2376.22i	0.335029	+	0.111212i
$771$	14.9681	+	25.9255i	0.000699173	+	0.00121100i
$772$			7061.77i			0.329221i
$773$	−17426.4	+	10061.1i	−0.810845	+	0.468141i	−0.847249	−	0.531196i	$-0.821743\pi$
$773$	−17426.4	+	10061.1i	−0.810845	+	0.468141i	0.0364044	+	0.999337i	$0.488410\pi$
$774$	−713.707	−	1236.18i	−0.0331443	−	0.0574075i
$775$	12784.9	−	5498.94i	0.592577	−	0.254874i
$776$	5097.02	+	8828.30i	0.235789	+	0.408399i
$777$	−615.672	−	355.458i	−0.0284261	−	0.0164118i
$778$	7740.87	+	4469.20i	0.356714	+	0.205949i
$779$	1975.79			0.0908730
$780$	287.430	+	268.359i	0.0131944	+	0.0123190i
$781$	3758.11			0.172184
$782$	−16003.6	−	9239.70i	−0.731827	−	0.422521i
$783$	566.878	+	327.287i	0.0258730	+	0.0149378i
$784$	25.0610	+	43.4069i	0.00114163	+	0.00197735i
$785$	−659.341	+	135.782i	−0.0299782	+	0.00617358i
$786$	−127.086	−	220.119i	−0.00576718	−	0.00998905i
$787$	−7057.57	+	4074.69i	−0.319663	+	0.184558i	−0.651243	−	0.758870i	$-0.725752\pi$
$787$	−7057.57	+	4074.69i	−0.319663	+	0.184558i	0.331579	+	0.943427i	$0.392419\pi$
$788$		−	507.338i		−	0.0229355i
$789$	−594.138	−	1029.08i	−0.0268085	−	0.0464336i
$790$	−1036.06	+	3121.15i	−0.0466598	+	0.140564i
$791$	12523.3	−	21691.0i	0.562930	−	0.975023i
$792$			3911.09i			0.175473i
$793$	14472.2	−	31506.3i	0.648075	−	1.41087i
$794$	−15267.4			−0.682392
$795$	406.749	+	135.019i	0.0181458	+	0.00602344i
$796$	8157.88	−	14129.9i	0.363252	−	0.629170i
$797$	−18697.5	+	10795.0i	−0.830992	+	0.479774i	−0.854192	−	0.519957i	$-0.825948\pi$
$797$	−18697.5	+	10795.0i	−0.830992	+	0.479774i	0.0232000	+	0.999731i	$0.492615\pi$
$798$		−	85.8430i		−	0.00380803i
$799$	4347.56	+	7530.20i	0.192498	+	0.333416i
$800$	−2392.01	+	3205.98i	−0.105713	+	0.141686i
$801$	532.910			0.0235074
$802$	−4293.96	+	2479.12i	−0.189059	+	0.109153i
$803$	−9492.47	−	5480.48i	−0.417163	−	0.240849i
$804$	−235.688	+	408.224i	−0.0103384	+	0.0179067i
$805$	6517.29	+	31647.3i	0.285347	+	1.38561i
$806$	−969.294	−	10392.3i	−0.0423597	−	0.454158i
$807$		−	505.626i		−	0.0220556i
$808$	9755.61	+	5632.40i	0.424754	+	0.245232i
$809$	16808.7	−	29113.6i	0.730486	−	1.26524i	−0.226189	−	0.974083i	$-0.572627\pi$
$809$	16808.7	−	29113.6i	0.730486	−	1.26524i	0.956676	−	0.291156i	$-0.0940398\pi$
$810$	10788.1	+	12135.3i	0.467968	+	0.526408i
$811$	−27642.1			−1.19685			−0.598426	−	0.801178i	$-0.704207\pi$
$811$	−27642.1			−1.19685			−0.598426	+	0.801178i	$0.704207\pi$
$812$	4167.16	−	2405.91i	0.180097	−	0.103979i
$813$	1256.56	−	725.475i	0.0542060	−	0.0312959i
$814$	−7386.14			−0.318039
$815$	9689.33	+	10899.3i	0.416445	+	0.468451i
$816$	89.2668	−	154.615i	0.00382961	−	0.00663308i
$817$	281.894	+	162.752i	0.0120713	+	0.00696935i
$818$		−	4296.95i		−	0.183667i
$819$	−2183.73	−	23412.8i	−0.0931692	−	0.998911i
$820$	−1449.22	−	7037.27i	−0.0617184	−	0.299698i
$821$	7860.45	−	13614.7i	0.334143	−	0.578753i	−0.649177	−	0.760638i	$-0.724886\pi$
$821$	7860.45	−	13614.7i	0.334143	−	0.578753i	0.983320	+	0.181885i	$0.0582198\pi$
$822$	126.135	+	72.8243i	0.00535216	+	0.00309007i
$823$	−8116.30	+	4685.95i	−0.343762	+	0.198471i	−0.661934	−	0.749562i	$-0.730264\pi$
$823$	−8116.30	+	4685.95i	−0.343762	+	0.198471i	0.318172	+	0.948033i	$0.396931\pi$
$824$	6925.12			0.292777
$825$	−254.240	+	340.755i	−0.0107291	+	0.0143801i
$826$	−12900.8	−	22344.8i	−0.543434	−	0.941255i
$827$		−	33117.9i		−	1.39253i	−0.717784	−	0.696266i	$-0.754844\pi$
$827$		−	33117.9i		−	1.39253i	0.717784	−	0.696266i	$-0.245156\pi$
$828$	−14510.0	+	8377.34i	−0.609006	+	0.351610i
$829$	−14199.5	+	24594.2i	−0.594894	+	1.03039i	0.398667	+	0.917096i	$0.369473\pi$
$829$	−14199.5	+	24594.2i	−0.594894	+	1.03039i	−0.993562	+	0.113292i	$0.963861\pi$
$830$	−13112.4	−	4352.63i	−0.548359	−	0.182026i
$831$	−1522.07			−0.0635378
$832$	1734.69	+	2447.40i	0.0722831	+	0.101981i
$833$			186.332i			0.00775032i
$834$	−406.352	+	703.822i	−0.0168715	+	0.0292223i
$835$	2413.76	−	7271.51i	0.100038	−	0.301366i
$836$	−445.937	−	772.385i	−0.0184486	−	0.0319540i
$837$			1127.14i			0.0465467i
$838$	7557.98	−	4363.60i	0.311559	−	0.179879i
$839$	−11413.2	−	19768.3i	−0.469640	−	0.813441i	0.529757	−	0.848149i	$-0.322283\pi$
$839$	−11413.2	−	19768.3i	−0.469640	−	0.813441i	−0.999397	+	0.0347086i	$0.988950\pi$
$840$	−305.751	+	62.9650i	−0.0125588	+	0.00258631i
$841$	10104.1	+	17500.8i	0.414290	+	0.717571i
$842$	−4178.64	−	2412.54i	−0.171028	−	0.0987429i
$843$	−731.924	−	422.577i	−0.0299037	−	0.0172649i
$844$	−18605.3			−0.758793
$845$	−24341.4	−	3293.78i	−0.990969	−	0.134094i
$846$	7883.59			0.320382
$847$	−16148.9	−	9323.57i	−0.655115	−	0.378231i
$848$	2831.39	+	1634.70i	0.114658	+	0.0661981i
$849$	−51.1319	−	88.5631i	−0.00206695	−	0.00358007i
$850$	−13660.3	+	5875.46i	−0.551229	+	0.237090i
$851$	−15820.7	−	27402.3i	−0.637282	−	1.10380i
$852$	−134.701	+	77.7695i	−0.00541640	+	0.00312716i
$853$			34222.4i			1.37368i	0.726807	+	0.686842i	$0.241004\pi$
$853$			34222.4i			1.37368i	−0.726807	+	0.686842i	$0.758996\pi$
$854$	13761.8	+	23836.1i	0.551427	+	0.955099i
$855$	−3518.74	−	1168.04i	−0.140747	−	0.0467204i
$856$	−8546.66	+	14803.3i	−0.341260	+	0.591080i
$857$			16219.2i			0.646486i	0.946316	+	0.323243i	$0.104773\pi$
$857$			16219.2i			0.646486i	−0.946316	+	0.323243i	$0.895227\pi$
$858$	184.375	+	260.127i	0.00733621	+	0.0103503i
$859$	−26749.3			−1.06248			−0.531242	−	0.847220i	$-0.678275\pi$
$859$	−26749.3			−1.06248			−0.531242	+	0.847220i	$0.678275\pi$
$860$	372.913	−	1123.41i	0.0147863	−	0.0445442i
$861$	280.363	−	485.602i	0.0110973	−	0.0192210i
$862$	6415.15	−	3703.79i	0.253481	−	0.146347i
$863$			4627.12i			0.182513i	0.995827	+	0.0912566i	$0.0290883\pi$
$863$			4627.12i			0.182513i	−0.995827	+	0.0912566i	$0.970912\pi$
$864$	−161.976	−	280.551i	−0.00637794	−	0.0110469i
$865$	23322.3	+	26234.8i	0.916742	+	1.03123i
$866$	2157.76			0.0846692
$867$	−223.384	+	128.971i	−0.00875032	+	0.00505200i
$868$	7175.59	+	4142.83i	0.280594	+	0.162001i
$869$	−1333.24	+	2309.24i	−0.0520449	+	0.0901445i
$870$	54.7073	+	265.653i	0.00213190	+	0.0103523i
$871$	−2734.43	−	29317.1i	−0.106375	−	1.14050i
$872$		−	15447.0i		−	0.599887i
$873$	29756.7	+	17180.0i	1.15362	+	0.666044i
$874$	1910.35	−	3308.81i	0.0739341	−	0.128058i
$875$	23547.4	+	11025.5i	0.909767	+	0.425979i
$876$	453.647			0.0174969
$877$	22840.7	−	13187.1i	0.879446	−	0.507748i	0.00897043	−	0.999960i	$-0.497145\pi$
$877$	22840.7	−	13187.1i	0.879446	−	0.507748i	0.870476	+	0.492211i	$0.163811\pi$
$878$	1941.28	−	1120.80i	0.0746186	−	0.0430811i
$879$	−1180.26			−0.0452892
$880$	−2423.95	+	2154.85i	−0.0928538	+	0.0825455i
$881$	711.813	−	1232.90i	0.0272209	−	0.0471479i	−0.852094	−	0.523389i	$-0.824668\pi$
$881$	711.813	−	1232.90i	0.0272209	−	0.0471479i	0.879315	+	0.476241i	$0.158001\pi$
$882$	146.307	+	84.4705i	0.00558551	+	0.00322480i
$883$		−	51374.6i		−	1.95798i	−0.203919	−	0.978988i	$-0.565368\pi$
$883$		−	51374.6i		−	1.95798i	0.203919	−	0.978988i	$-0.434632\pi$
$884$	1035.66	+	11103.8i	0.0394040	+	0.422469i
$885$	1424.46	−	293.348i	0.0541049	−	0.0111421i
$886$	9267.16	−	16051.2i	0.351395	−	0.608634i
$887$	33952.4	+	19602.4i	1.28524	+	0.742035i	0.977802	−	0.209533i	$-0.0671943\pi$
$887$	33952.4	+	19602.4i	1.28524	+	0.742035i	0.307440	+	0.951567i	$0.400528\pi$
$888$	264.739	−	152.847i	0.0100046	−	0.00577615i
$889$	−44880.3			−1.69318
$890$	293.612	+	330.278i	0.0110583	+	0.0124393i
$891$	6582.75	+	11401.7i	0.247509	+	0.428698i
$892$			671.003i			0.0251870i
$893$	−1556.90	+	898.875i	−0.0583422	+	0.0336839i
$894$	489.229	−	847.369i	0.0183023	−	0.0317005i
$895$	−10727.0	−	3560.81i	−0.400632	−	0.132989i
$896$	−2381.39			−0.0887911
$897$	−570.139	+	1241.20i	−0.0212223	+	0.0462013i
$898$			26848.8i			0.997722i
$899$	3599.51	−	6234.54i	0.133538	−	0.231294i
$900$	−1579.29	+	13389.6i	−0.0584921	+	0.495911i
$901$	6077.13	+	10525.9i	0.224704	+	0.389199i
$902$		−	5825.71i		−	0.215050i
$903$	80.0009	−	46.1885i	0.00294824	−	0.00170217i
$904$	5385.03	+	9327.14i	0.198123	+	0.343159i
$905$	−4543.78	−	22064.1i	−0.166895	−	0.810426i
$906$	−88.0445	−	152.498i	−0.00322857	−	0.00559205i
$907$	31299.7	+	18070.9i	1.14585	+	0.661559i	0.947874	−	0.318646i	$-0.103228\pi$
$907$	31299.7	+	18070.9i	1.14585	+	0.661559i	0.197981	+	0.980206i	$0.436562\pi$
$908$	−4381.36	−	2529.58i	−0.160133	−	0.0924527i
$909$	37969.2			1.38543
$910$	13307.2	−	14252.9i	0.484759	−	0.519207i
$911$	−26416.9			−0.960735			−0.480368	−	0.877067i	$-0.659497\pi$
$911$	−26416.9			−0.960735			−0.480368	+	0.877067i	$0.659497\pi$
$912$	31.9672	+	18.4563i	0.00116068	+	0.000670118i
$913$	−9701.46	−	5601.14i	−0.351666	−	0.203035i
$914$	8824.73	+	15284.9i	0.319361	+	0.553150i
$915$	−1519.53	+	312.926i	−0.0549007	+	0.0113060i
$916$	−8562.50	−	14830.7i	−0.308857	−	0.534956i
$917$	−10915.1	+	6301.85i	−0.393074	+	0.226942i
$918$		−	1204.32i		−	0.0432989i
$919$	14119.0	+	24454.8i	0.506793	+	0.877790i	0.999969	+	0.00786115i	$0.00250231\pi$
$919$	14119.0	+	24454.8i	0.506793	+	0.877790i	−0.493177	+	0.869929i	$0.664164\pi$
$920$	−13186.4	−	4377.18i	−0.472546	−	0.156860i
$921$	−715.439	+	1239.18i	−0.0255967	+	0.0443347i
$922$		−	8136.71i		−	0.290638i
$923$	4055.46	−	8828.81i	0.144623	−	0.314847i
$924$	−253.112			−0.00901165
$925$	−25286.4	−	2982.50i	−0.898823	−	0.106015i
$926$	8511.92	−	14743.1i	0.302073	−	0.523205i
$927$	20214.6	−	11670.9i	0.716219	−	0.413509i
$928$			2069.08i			0.0731907i
$929$	21785.8	+	37734.2i	0.769397	+	1.33264i	0.937890	+	0.346933i	$0.112777\pi$
$929$	21785.8	+	37734.2i	0.769397	+	1.33264i	−0.168493	+	0.985703i	$0.553890\pi$
$930$	−349.052	+	310.301i	−0.0123074	+	0.0109410i
$931$	−38.5248			−0.00135618
$932$	11385.1	−	6573.21i	0.400142	−	0.231022i
$933$	92.3293	+	53.3064i	0.00323979	+	0.00187050i
$934$	−7999.89	+	13856.2i	−0.280262	+	0.485427i
$935$	−11809.3	+	2431.96i	−0.413055	+	0.0850627i
$936$	9188.21	+	4220.55i	0.320861	+	0.147386i
$937$			7402.81i			0.258100i	0.991638	+	0.129050i	$0.0411927\pi$
$937$			7402.81i			0.258100i	−0.991638	+	0.129050i	$0.958807\pi$
$938$	20242.7	+	11687.1i	0.704636	+	0.406822i
$939$	330.175	−	571.880i	0.0114748	−	0.0198750i
$940$	4343.53	+	4885.96i	0.150713	+	0.169534i
$941$	−36843.9			−1.27638			−0.638192	−	0.769878i	$-0.720317\pi$
$941$	−36843.9			−1.27638			−0.638192	+	0.769878i	$0.720317\pi$
$942$	19.5639	−	11.2952i	0.000676674	−	0.000390678i
$943$	21613.1	−	12478.4i	0.746363	−	0.430913i
$944$	11094.7			0.382523
$945$	−1573.79	+	1399.07i	−0.0541749	+	0.0481606i
$946$	479.880	−	831.177i	0.0164929	−	0.0285665i
$947$	−22079.4	−	12747.5i	−0.757638	−	0.437423i	0.0708088	−	0.997490i	$-0.477442\pi$
$947$	−22079.4	−	12747.5i	−0.757638	−	0.437423i	−0.828447	+	0.560067i	$0.810775\pi$
$948$		−	110.359i		−	0.00378090i
$949$	−23118.7	+	16386.3i	−0.790794	+	0.560506i
$950$	−1214.78	−	2824.32i	−0.0414868	−	0.0964560i
$951$	145.477	−	251.973i	0.00496047	−	0.00859179i
$952$	−7666.92	−	4426.50i	−0.261015	−	0.150697i
$953$	28283.5	−	16329.5i	0.961378	−	0.555052i	0.0647813	−	0.997899i	$-0.479365\pi$
$953$	28283.5	−	16329.5i	0.961378	−	0.555052i	0.896597	+	0.442848i	$0.146032\pi$
$954$	11019.9			0.373985
$955$	41990.4	−	37328.7i	1.42280	−	1.26485i
$956$	12595.6	+	21816.2i	0.426120	+	0.738061i
$957$			219.917i			0.00742833i
$958$	−19797.3	+	11430.0i	−0.667665	+	0.385477i
$959$	3611.16	−	6254.72i	0.121596	−	0.210610i
$960$	42.2889	−	127.396i	0.00142174	−	0.00428302i
$961$	−17394.7			−0.583892
$962$	−7970.55	+	17352.0i	−0.267132	+	0.581551i
$963$			57614.8i			1.92794i
$964$	13916.3	−	24103.8i	0.464953	−	0.805322i
$965$	−6218.41	+	18733.1i	−0.207438	+	0.624913i
$966$	−542.152	−	939.034i	−0.0180574	−	0.0312763i
$967$		−	9956.75i		−	0.331114i	−0.986200	−	0.165557i	$-0.947058\pi$
$967$		−	9956.75i		−	0.331114i	0.986200	−	0.165557i	$-0.0529422\pi$
$968$	6944.03	−	4009.14i	0.230568	−	0.133118i
$969$	68.6124	+	118.840i	0.00227466	+	0.00393983i
$970$	5747.17	+	27907.6i	0.190237	+	0.923772i
$971$	−16846.6	−	29179.2i	−0.556780	−	0.964371i	−0.997763	−	0.0668552i	$-0.978703\pi$
$971$	−16846.6	−	29179.2i	−0.556780	−	0.964371i	0.440983	−	0.897515i	$-0.354630\pi$
$972$	−1418.75	−	819.114i	−0.0468172	−	0.0270299i
$973$	34900.7	+	20149.9i	1.14991	+	0.663902i
$974$	−1253.30			−0.0412305
$975$	526.169	+	964.994i	0.0172830	+	0.0316970i
$976$	−11835.1			−0.388149
$977$	−35738.9	−	20633.9i	−1.17031	−	0.675677i	−0.216554	−	0.976271i	$-0.569482\pi$
$977$	−35738.9	−	20633.9i	−1.17031	−	0.675677i	−0.953752	+	0.300594i	$0.902815\pi$
$978$	−423.827	−	244.696i	−0.0138573	−	0.00800054i
$979$	179.158	+	310.311i	0.00584875	+	0.0101303i
$980$	28.2576	+	137.216i	0.000921077	+	0.00447265i
$981$	−26032.8	−	45090.2i	−0.847263	−	1.46750i
$982$	33917.4	−	19582.2i	1.10219	−	0.636349i
$983$			37742.0i			1.22460i	0.790625	+	0.612301i	$0.209756\pi$
$983$			37742.0i			1.22460i	−0.790625	+	0.612301i	$0.790244\pi$
$984$	120.556	+	208.809i	0.00390568	+	0.00676483i
$985$	446.749	−	1345.84i	0.0144514	−	0.0435351i
$986$	−3845.98	+	6661.44i	−0.124220	+	0.215155i
$987$			510.197i			0.0164537i
$988$	−2295.76	+	214.128i	−0.0739251	+	0.00689505i
$989$	4111.51			0.132193
$990$	−3444.00	+	10375.1i	−0.110563	+	0.333075i
$991$	17333.5	−	30022.4i	0.555616	−	0.962356i	−0.442239	−	0.896897i	$-0.645816\pi$
$991$	17333.5	−	30022.4i	0.555616	−	0.962356i	0.997855	−	0.0654583i	$-0.0208509\pi$
$992$	−3085.51	+	1781.42i	−0.0987550	+	0.0570162i
$993$		−	1080.88i		−	0.0345425i
$994$	3856.38	+	6679.45i	0.123055	+	0.213138i
$995$	34083.2	−	30299.4i	1.08594	−	0.965382i
$996$	463.635			0.0147498
$997$	−19143.0	+	11052.2i	−0.608090	+	0.351081i	−0.772218	−	0.635358i	$-0.780852\pi$
$997$	−19143.0	+	11052.2i	−0.608090	+	0.351081i	0.164128	+	0.986439i	$0.447519\pi$
$998$	22139.3	+	12782.2i	0.702213	+	0.405423i
$999$	1031.05	−	1785.82i	0.0326535	−	0.0565576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.4.n.a.9.6	✓	44
5.4	even	2	inner	130.4.n.a.9.17	yes	44
13.3	even	3	inner	130.4.n.a.29.17	yes	44
65.29	even	6	inner	130.4.n.a.29.6	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.4.n.a.9.6	✓	44	1.1	even	1	trivial
130.4.n.a.9.17	yes	44	5.4	even	2	inner
130.4.n.a.29.6	yes	44	65.29	even	6	inner
130.4.n.a.29.17	yes	44	13.3	even	3	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} +(0.162462 + 0.0937974i) q^{3} +(2.00000 + 3.46410i) q^{4} +(2.25511 + 10.9505i) q^{5} +(-0.187595 - 0.324924i) q^{6} +(-16.1121 + 9.30232i) q^{7} -8.00000i q^{8} +(-13.4824 - 23.3522i) q^{9} +(7.04459 - 21.2220i) q^{10} +(9.06526 - 15.7015i) q^{11} +0.750379i q^{12} +(-27.1045 - 38.2406i) q^{13} +37.2093 q^{14} +(-0.660764 + 1.99057i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-51.5122 + 29.7406i) q^{17} +53.9296i q^{18} +(-6.14898 - 10.6503i) q^{19} +(-33.4236 + 29.7130i) q^{20} -3.49013 q^{21} +(-31.4030 + 18.1305i) q^{22} +(-134.527 - 77.6692i) q^{23} +(0.750379 - 1.29969i) q^{24} +(-114.829 + 49.3893i) q^{25} +(8.70582 + 93.3392i) q^{26} -10.1235i q^{27} +(-64.4484 - 37.2093i) q^{28} +(-32.3294 + 55.9962i) q^{29} +(3.13504 - 2.78700i) q^{30} -111.339 q^{31} +(27.7128 - 16.0000i) q^{32} +(2.94552 - 1.70060i) q^{33} +118.962 q^{34} +(-138.200 - 155.458i) q^{35} +(53.9296 - 93.4088i) q^{36} +(176.404 + 101.847i) q^{37} +24.5959i q^{38} +(-0.816583 - 8.75497i) q^{39} +(87.6044 - 18.0409i) q^{40} +(-80.3301 + 139.136i) q^{41} +(6.04509 + 3.49013i) q^{42} +(-22.9220 + 13.2340i) q^{43} +72.5221 q^{44} +(225.315 - 200.301i) q^{45} +(155.338 + 269.054i) q^{46} -146.183i q^{47} +(-2.59939 + 1.50076i) q^{48} +(1.56631 - 2.71293i) q^{49} +(248.279 + 29.2842i) q^{50} -11.1583 q^{51} +(78.2603 - 170.374i) q^{52} -204.338i q^{53} +(-10.1235 + 17.5344i) q^{54} +(192.383 + 63.8611i) q^{55} +(74.4186 + 128.897i) q^{56} -2.30703i q^{57} +(111.992 - 64.6589i) q^{58} +(-346.709 - 600.518i) q^{59} +(-8.21706 + 1.69218i) q^{60} +(369.848 + 640.596i) q^{61} +(192.844 + 111.339i) q^{62} +(434.459 + 250.835i) q^{63} -64.0000 q^{64} +(357.632 - 383.046i) q^{65} -6.80238 q^{66} +(544.024 + 314.092i) q^{67} +(-206.049 - 118.962i) q^{68} +(-14.5703 - 25.2366i) q^{69} +(83.9109 + 407.462i) q^{70} +(103.640 + 179.510i) q^{71} +(-186.818 + 107.859i) q^{72} -604.558i q^{73} +(-203.693 - 352.807i) q^{74} +(-23.2879 - 2.74678i) q^{75} +(24.5959 - 42.6014i) q^{76} +337.312i q^{77} +(-7.34061 + 15.9806i) q^{78} -147.071 q^{79} +(-169.776 - 56.3567i) q^{80} +(-363.075 + 628.865i) q^{81} +(278.272 - 160.660i) q^{82} -617.868i q^{83} +(-6.98026 - 12.0902i) q^{84} +(-441.841 - 497.018i) q^{85} +52.9362 q^{86} +(-10.5046 + 6.06483i) q^{87} +(-125.612 - 72.5221i) q^{88} +(-9.88158 + 17.1154i) q^{89} +(-590.559 + 121.617i) q^{90} +(792.437 + 364.001i) q^{91} -621.354i q^{92} +(-18.0883 - 10.4433i) q^{93} +(-146.183 + 253.196i) q^{94} +(102.760 - 91.3523i) q^{95} +6.00303 q^{96} +(-1103.54 + 637.128i) q^{97} +(-5.42586 + 3.13262i) q^{98} -488.886 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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