LMFDB - Embedded newform 26.8.e.a.17.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [26,8,Mod(17,26)] 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("26.17"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(26, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	26.e (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:	$8.12201066259$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 22180 x^{14} + 184473654 x^{12} + 707524481236 x^{10} + \cdots + 18\!\cdots\!76 $ x^16 + 22180x^14 + 184473654x^12 + 707524481236x^10 + 1235305573179121x^8 + 834592841081820432x^6 + 142296444753813668448x^4 + 5907885179463590558976*x^2 + 18970385728293762437376
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{34}\cdot 13^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.2
Root			$12.8548i$ of defining polynomial
Character	$\chi$	$=$	26.17
Dual form			26.8.e.a.23.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.92820 - 4.00000i) q^{2} +(-6.42739 + 11.1326i) q^{3} +(32.0000 + 55.4256i) q^{4} -260.039i q^{5} +(89.0605 - 51.4191i) q^{6} +(-850.835 + 491.230i) q^{7} -512.000i q^{8} +(1010.88 + 1750.89i) q^{9} +(-1040.15 + 1801.60i) q^{10} +(4092.11 + 2362.58i) q^{11} -822.706 q^{12} +(7791.18 + 1430.41i) q^{13} +7859.68 q^{14} +(2894.90 + 1671.37i) q^{15} +(-2048.00 + 3547.24i) q^{16} +(17075.0 + 29574.7i) q^{17} -16174.0i q^{18} +(-38627.6 + 22301.7i) q^{19} +(14412.8 - 8321.24i) q^{20} -12629.3i q^{21} +(-18900.6 - 32736.9i) q^{22} +(9156.93 - 15860.3i) q^{23} +(5699.87 + 3290.82i) q^{24} +10504.9 q^{25} +(-48257.2 - 41074.9i) q^{26} -54102.6 q^{27} +(-54453.5 - 31438.7i) q^{28} +(-43909.2 + 76052.9i) q^{29} +(-13371.0 - 23159.2i) q^{30} -212598. i q^{31} +(28377.9 - 16384.0i) q^{32} +(-52603.2 + 30370.5i) q^{33} -273200. i q^{34} +(127739. + 221250. i) q^{35} +(-64696.1 + 112057. i) q^{36} +(288740. + 166704. i) q^{37} +356827. q^{38} +(-66001.1 + 77542.0i) q^{39} -133140. q^{40} +(-553137. - 319354. i) q^{41} +(-50517.2 + 87498.4i) q^{42} +(129052. + 223524. i) q^{43} +302410. i q^{44} +(455299. - 262867. i) q^{45} +(-126882. + 73255.4i) q^{46} +774821. i q^{47} +(-26326.6 - 45599.0i) q^{48} +(70842.3 - 122702. i) q^{49} +(-72780.2 - 42019.6i) q^{50} -438990. q^{51} +(170036. + 477604. i) q^{52} +872928. q^{53} +(374834. + 216410. i) q^{54} +(614362. - 1.06411e6i) q^{55} +(251510. + 435628. i) q^{56} -573366. i q^{57} +(608423. - 351273. i) q^{58} +(-987288. + 570011. i) q^{59} +213935. i q^{60} +(141624. + 245299. i) q^{61} +(-850394. + 1.47293e6i) q^{62} +(-1.72018e6 - 993146. i) q^{63} -262144. q^{64} +(371963. - 2.02601e6i) q^{65} +485927. q^{66} +(-1.89067e6 - 1.09158e6i) q^{67} +(-1.09280e6 + 1.89278e6i) q^{68} +(117710. + 203880. i) q^{69} -2.04382e6i q^{70} +(2.31512e6 - 1.33663e6i) q^{71} +(896456. - 517569. i) q^{72} -1.80356e6i q^{73} +(-1.33363e6 - 2.30992e6i) q^{74} +(-67519.2 + 116947. i) q^{75} +(-2.47217e6 - 1.42731e6i) q^{76} -4.64228e6 q^{77} +(767437. - 273222. i) q^{78} -557628. q^{79} +(922419. + 532559. i) q^{80} +(-1.86305e6 + 3.22690e6i) q^{81} +(2.55483e6 + 4.42510e6i) q^{82} +9.45510e6i q^{83} +(699987. - 404138. i) q^{84} +(7.69057e6 - 4.44015e6i) q^{85} -2.06483e6i q^{86} +(-564443. - 977644. i) q^{87} +(1.20964e6 - 2.09516e6i) q^{88} +(7.84469e6 + 4.52914e6i) q^{89} -4.20587e6 q^{90} +(-7.33167e6 + 2.61021e6i) q^{91} +1.17209e6 q^{92} +(2.36677e6 + 1.36645e6i) q^{93} +(3.09928e6 - 5.36811e6i) q^{94} +(5.79929e6 + 1.00447e7i) q^{95} +421226. i q^{96} +(1.18308e7 - 6.83053e6i) q^{97} +(-981620. + 566738. i) q^{98} +9.55312e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 512 q^{4} + 2520 q^{7} - 4684 q^{9} + 2432 q^{10} - 8496 q^{11} - 3620 q^{13} + 34560 q^{14} + 51648 q^{15} - 32768 q^{16} + 41520 q^{17} - 54432 q^{19} - 16128 q^{20} - 17280 q^{22} - 7560 q^{23}+ \cdots + 19031040 q^{98}+O(q^{100}) $ 16 * q + 512 * q^4 + 2520 * q^7 - 4684 * q^9 + 2432 * q^10 - 8496 * q^11 - 3620 * q^13 + 34560 * q^14 + 51648 * q^15 - 32768 * q^16 + 41520 * q^17 - 54432 * q^19 - 16128 * q^20 - 17280 * q^22 - 7560 * q^23 - 273960 * q^25 + 51072 * q^26 + 133920 * q^27 + 161280 * q^28 - 346056 * q^29 + 170368 * q^30 + 486300 * q^33 - 283248 * q^35 + 299776 * q^36 - 68280 * q^37 - 1059840 * q^38 - 1122680 * q^39 + 311296 * q^40 - 1288008 * q^41 + 408320 * q^42 + 285360 * q^43 + 5743980 * q^45 - 188928 * q^46 - 2131660 * q^49 + 85248 * q^50 + 957280 * q^51 + 354560 * q^52 + 3666600 * q^53 - 4074624 * q^54 - 1091472 * q^55 + 1105920 * q^56 + 3504000 * q^58 + 1799280 * q^59 - 4626000 * q^61 - 2770560 * q^62 - 8609760 * q^63 - 4194304 * q^64 - 11518020 * q^65 + 7941120 * q^66 - 7094400 * q^67 - 2657280 * q^68 + 18027316 * q^69 + 25958520 * q^71 + 4423680 * q^72 - 1142400 * q^74 - 10898032 * q^75 - 3483648 * q^76 - 20577480 * q^77 - 22023040 * q^78 + 34143488 * q^79 - 1032192 * q^80 - 15745864 * q^81 + 12202240 * q^82 + 17311488 * q^84 + 7123932 * q^85 - 10460440 * q^87 + 1105920 * q^88 + 10609452 * q^89 + 4070656 * q^90 - 38683952 * q^91 - 967680 * q^92 - 52747080 * q^93 - 14303616 * q^94 + 33837504 * q^95 + 83706300 * q^97 + 19031040 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−6.92820	−	4.00000i	−0.612372	−	0.353553i
$2$	−6.92820	−	4.00000i	−0.612372	−	0.353553i
$3$	−6.42739	+	11.1326i	−0.137439	+	0.238052i	−0.926527	−	0.376229i	$-0.877220\pi$
$3$	−6.42739	+	11.1326i	−0.137439	+	0.238052i	0.789087	+	0.614281i	$0.210554\pi$
$4$	32.0000	+	55.4256i	0.250000	+	0.433013i
$5$		−	260.039i		−	0.930342i	−0.885221	−	0.465171i	$-0.845993\pi$
$5$		−	260.039i		−	0.930342i	0.885221	−	0.465171i	$-0.154007\pi$
$6$	89.0605	−	51.4191i	0.168328	−	0.0971841i
$7$	−850.835	+	491.230i	−0.937567	+	0.541305i	−0.889197	−	0.457525i	$-0.848736\pi$
$7$	−850.835	+	491.230i	−0.937567	+	0.541305i	−0.0483703	+	0.998829i	$0.515403\pi$
$8$		−	512.000i		−	0.353553i
$9$	1010.88	+	1750.89i	0.462221	+	0.800590i
$10$	−1040.15	+	1801.60i	−0.328926	+	0.569716i
$11$	4092.11	+	2362.58i	0.926985	+	0.535195i	0.885857	−	0.463959i	$-0.153571\pi$
$11$	4092.11	+	2362.58i	0.926985	+	0.535195i	0.0411285	+	0.999154i	$0.486905\pi$
$12$	−822.706			−0.137439
$13$	7791.18	+	1430.41i	0.983561	+	0.180576i
$13$	7791.18	+	1430.41i	0.983561	+	0.180576i
$14$	7859.68			0.765520
$15$	2894.90	+	1671.37i	0.221469	+	0.127865i
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	17075.0	+	29574.7i	0.842925	+	1.45999i	0.887411	+	0.460979i	$0.152501\pi$
$17$	17075.0	+	29574.7i	0.842925	+	1.45999i	−0.0444865	+	0.999010i	$0.514165\pi$
$18$		−	16174.0i		−	0.653679i
$19$	−38627.6	+	22301.7i	−1.29199	+	0.745932i	−0.979007	−	0.203825i	$-0.934663\pi$
$19$	−38627.6	+	22301.7i	−1.29199	+	0.745932i	−0.312986	+	0.949758i	$0.601329\pi$
$20$	14412.8	−	8321.24i	0.402850	−	0.232586i
$21$		−	12629.3i		−	0.297586i
$22$	−18900.6	−	32736.9i	−0.378440	−	0.655478i
$23$	9156.93	−	15860.3i	0.156929	−	0.271808i	−0.776831	−	0.629709i	$-0.783174\pi$
$23$	9156.93	−	15860.3i	0.156929	−	0.271808i	0.933760	+	0.357901i	$0.116507\pi$
$24$	5699.87	+	3290.82i	0.0841639	+	0.0485921i
$25$	10504.9			0.134463
$26$	−48257.2	−	41074.9i	−0.538462	−	0.458321i
$27$	−54102.6			−0.528987
$28$	−54453.5	−	31438.7i	−0.468784	−	0.270652i
$29$	−43909.2	+	76052.9i	−0.334320	+	0.579059i	−0.983354	−	0.181700i	$-0.941840\pi$
$29$	−43909.2	+	76052.9i	−0.334320	+	0.579059i	0.649034	+	0.760759i	$0.275173\pi$
$30$	−13371.0	−	23159.2i	−0.0904145	−	0.156603i
$31$		−	212598.i		−	1.28172i	−0.767656	−	0.640862i	$-0.778577\pi$
$31$		−	212598.i		−	1.28172i	0.767656	−	0.640862i	$-0.221423\pi$
$32$	28377.9	−	16384.0i	0.153093	−	0.0883883i
$33$	−52603.2	+	30370.5i	−0.254808	+	0.147114i
$34$		−	273200.i		−	1.19208i
$35$	127739.	+	221250.i	0.503599	+	0.872258i
$36$	−64696.1	+	112057.i	−0.231110	+	0.400295i
$37$	288740.	+	166704.i	0.937132	+	0.541054i	0.889060	−	0.457790i	$-0.151359\pi$
$37$	288740.	+	166704.i	0.937132	+	0.541054i	0.0480721	+	0.998844i	$0.484692\pi$
$38$	356827.			1.05491
$39$	−66001.1	+	77542.0i	−0.178166	+	0.209320i
$40$	−133140.			−0.328926
$41$	−553137.	−	319354.i	−1.25340	−	0.723650i	−0.281616	−	0.959527i	$-0.590870\pi$
$41$	−553137.	−	319354.i	−1.25340	−	0.723650i	−0.971783	+	0.235877i	$0.924204\pi$
$42$	−50517.2	+	87498.4i	−0.105212	+	0.182233i
$43$	129052.	+	223524.i	0.247528	+	0.428732i	0.962839	−	0.270075i	$-0.0870484\pi$
$43$	129052.	+	223524.i	0.247528	+	0.428732i	−0.715311	+	0.698806i	$0.753715\pi$
$44$			302410.i			0.535195i
$45$	455299.	−	262867.i	0.744823	−	0.430024i
$46$	−126882.	+	73255.4i	−0.192198	+	0.110965i
$47$			774821.i			1.08858i	0.838899	+	0.544288i	$0.183200\pi$
$47$			774821.i			1.08858i	−0.838899	+	0.544288i	$0.816800\pi$
$48$	−26326.6	−	45599.0i	−0.0343598	−	0.0595129i
$49$	70842.3	−	122702.i	0.0860214	−	0.148993i
$50$	−72780.2	−	42019.6i	−0.0823414	−	0.0475398i
$51$	−438990.			−0.463403
$52$	170036.	+	477604.i	0.167699	+	0.471038i
$53$	872928.			0.805403			0.402701	−	0.915331i	$-0.368071\pi$
$53$	872928.			0.805403			0.402701	+	0.915331i	$0.368071\pi$
$54$	374834.	+	216410.i	0.323937	+	0.187025i
$55$	614362.	−	1.06411e6i	0.497915	−	0.862414i
$56$	251510.	+	435628.i	0.191380	+	0.331480i
$57$		−	573366.i		−	0.410081i
$58$	608423.	−	351273.i	0.409457	−	0.236400i
$59$	−987288.	+	570011.i	−0.625838	+	0.361328i	−0.779138	−	0.626852i	$-0.784343\pi$
$59$	−987288.	+	570011.i	−0.625838	+	0.361328i	0.153301	+	0.988180i	$0.451010\pi$
$60$			213935.i			0.127865i
$61$	141624.	+	245299.i	0.0798879	+	0.138370i	0.903201	−	0.429217i	$-0.141210\pi$
$61$	141624.	+	245299.i	0.0798879	+	0.138370i	−0.823314	+	0.567587i	$0.807877\pi$
$62$	−850394.	+	1.47293e6i	−0.453158	+	0.784892i
$63$	−1.72018e6	−	993146.i	−0.866726	−	0.500405i
$64$	−262144.			−0.125000
$65$	371963.	−	2.02601e6i	0.167998	−	0.915049i
$66$	485927.			0.208050
$67$	−1.89067e6	−	1.09158e6i	−0.767989	−	0.443399i	0.0641678	−	0.997939i	$-0.479561\pi$
$67$	−1.89067e6	−	1.09158e6i	−0.767989	−	0.443399i	−0.832157	+	0.554541i	$0.812894\pi$
$68$	−1.09280e6	+	1.89278e6i	−0.421462	+	0.729994i
$69$	117710.	+	203880.i	0.0431363	+	0.0747142i
$70$		−	2.04382e6i		−	0.712196i
$71$	2.31512e6	−	1.33663e6i	0.767660	−	0.443208i	−0.0643795	−	0.997925i	$-0.520507\pi$
$71$	2.31512e6	−	1.33663e6i	0.767660	−	0.443208i	0.832039	+	0.554717i	$0.187173\pi$
$72$	896456.	−	517569.i	0.283051	−	0.163420i
$73$		−	1.80356e6i		−	0.542627i	−0.962491	−	0.271313i	$-0.912542\pi$
$73$		−	1.80356e6i		−	0.542627i	0.962491	−	0.271313i	$-0.0874580\pi$
$74$	−1.33363e6	−	2.30992e6i	−0.382583	−	0.662653i
$75$	−67519.2	+	116947.i	−0.0184805	+	0.0320091i
$76$	−2.47217e6	−	1.42731e6i	−0.645996	−	0.372966i
$77$	−4.64228e6			−1.15881
$78$	767437.	−	273222.i	0.183110	−	0.0651905i
$79$	−557628.			−0.127248			−0.0636238	−	0.997974i	$-0.520266\pi$
$79$	−557628.			−0.127248			−0.0636238	+	0.997974i	$0.520266\pi$
$80$	922419.	+	532559.i	0.201425	+	0.116293i
$81$	−1.86305e6	+	3.22690e6i	−0.389517	+	0.674664i
$82$	2.55483e6	+	4.42510e6i	0.511698	+	0.886287i
$83$			9.45510e6i			1.81507i	0.419979	+	0.907534i	$0.362038\pi$
$83$			9.45510e6i			1.81507i	−0.419979	+	0.907534i	$0.637962\pi$
$84$	699987.	−	404138.i	0.128858	−	0.0743964i
$85$	7.69057e6	−	4.44015e6i	1.35829	−	0.784209i
$86$		−	2.06483e6i		−	0.350058i
$87$	−564443.	−	977644.i	−0.0918973	−	0.159171i
$88$	1.20964e6	−	2.09516e6i	0.189220	−	0.327739i
$89$	7.84469e6	+	4.52914e6i	1.17954	+	0.681005i	0.955907	−	0.293669i	$-0.0948765\pi$
$89$	7.84469e6	+	4.52914e6i	1.17954	+	0.681005i	0.223628	+	0.974675i	$0.428210\pi$
$90$	−4.20587e6			−0.608146
$91$	−7.33167e6	+	2.61021e6i	−1.01990	+	0.363104i
$92$	1.17209e6			0.156929
$93$	2.36677e6	+	1.36645e6i	0.305116	+	0.176159i
$94$	3.09928e6	−	5.36811e6i	0.384870	−	0.666614i
$95$	5.79929e6	+	1.00447e7i	0.693973	+	1.20200i
$96$			421226.i			0.0485921i
$97$	1.18308e7	−	6.83053e6i	1.31618	−	0.759895i	0.333065	−	0.942904i	$-0.391917\pi$
$97$	1.18308e7	−	6.83053e6i	1.31618	−	0.759895i	0.983111	+	0.183009i	$0.0585838\pi$
$98$	−981620.	+	566738.i	−0.105354	+	0.0608263i
$99$			9.55312e6i			0.989514i
$100$	336157.	+	582241.i	0.0336157	+	0.0582241i
$101$	−3.99278e6	+	6.91569e6i	−0.385612	+	0.667899i	−0.991854	−	0.127381i	$-0.959343\pi$
$101$	−3.99278e6	+	6.91569e6i	−0.385612	+	0.667899i	0.606242	+	0.795280i	$0.292676\pi$
$102$	3.04141e6	+	1.75596e6i	0.283775	+	0.163838i
$103$	−8.18563e6			−0.738111			−0.369056	−	0.929407i	$-0.620319\pi$
$103$	−8.18563e6			−0.738111			−0.369056	+	0.929407i	$0.620319\pi$
$104$	732372.	−	3.98908e6i	0.0638433	−	0.347741i
$105$	−3.28411e6			−0.276857
$106$	−6.04783e6	−	3.49171e6i	−0.493206	−	0.284753i
$107$	3.56350e6	−	6.17216e6i	0.281212	−	0.487073i	−0.690472	−	0.723359i	$-0.742597\pi$
$107$	3.56350e6	−	6.17216e6i	0.281212	−	0.487073i	0.971683	+	0.236286i	$0.0759303\pi$
$108$	−1.73128e6	−	2.99867e6i	−0.132247	−	0.229058i
$109$		−	1.96078e7i		−	1.45023i	−0.688628	−	0.725115i	$-0.741787\pi$
$109$		−	1.96078e7i		−	1.45023i	0.688628	−	0.725115i	$-0.258213\pi$
$110$	−8.51285e6	+	4.91490e6i	−0.609819	+	0.352079i
$111$	−3.71169e6	+	2.14295e6i	−0.257597	+	0.148724i
$112$		−	4.02416e6i		−	0.270652i
$113$	−4.35251e6	−	7.53878e6i	−0.283769	−	0.491503i	0.688541	−	0.725198i	$-0.258252\pi$
$113$	−4.35251e6	−	7.53878e6i	−0.283769	−	0.491503i	−0.972310	+	0.233695i	$0.924918\pi$
$114$	−2.29346e6	+	3.97240e6i	−0.144986	+	0.251122i
$115$	−4.12428e6	−	2.38115e6i	−0.252875	−	0.145997i
$116$	−5.62037e6			−0.334320
$117$	5.37142e6	+	1.50875e7i	0.310055	+	0.870895i
$118$	9.12017e6			0.510994
$119$	−2.90560e7	−	1.67755e7i	−1.58060	−	0.912558i
$120$	855741.	−	1.48219e6i	0.0452073	−	0.0783013i
$121$	1.41999e6	+	2.45949e6i	0.0728678	+	0.126211i
$122$		−	2.26598e6i		−	0.112979i
$123$	7.11046e6	−	4.10522e6i	0.344532	−	0.198916i
$124$	1.17834e7	−	6.80315e6i	0.555002	−	0.320431i
$125$		−	2.30472e7i		−	1.05544i
$126$	7.94517e6	+	1.37614e7i	0.353840	+	0.612868i
$127$	−9.92482e6	+	1.71903e7i	−0.429942	+	0.744681i	−0.996868	−	0.0790877i	$-0.974799\pi$
$127$	−9.92482e6	+	1.71903e7i	−0.429942	+	0.744681i	0.566926	+	0.823769i	$0.308133\pi$
$128$	1.81619e6	+	1.04858e6i	0.0765466	+	0.0441942i
$129$	−3.31787e6			−0.136080
$130$	−1.06811e7	+	1.25487e7i	−0.426396	+	0.500954i
$131$	−8.67098e6			−0.336991			−0.168496	−	0.985702i	$-0.553891\pi$
$131$	−8.67098e6			−0.336991			−0.168496	+	0.985702i	$0.553891\pi$
$132$	−3.36660e6	−	1.94371e6i	−0.127404	−	0.0735568i
$133$	2.19105e7	−	3.79501e7i	0.807553	−	1.39872i
$134$	8.73265e6	+	1.51254e7i	0.313530	+	0.543050i
$135$			1.40688e7i			0.492139i
$136$	1.51423e7	−	8.74239e6i	0.516184	−	0.298019i
$137$	2.09755e7	−	1.21102e7i	0.696932	−	0.402374i	−0.109272	−	0.994012i	$-0.534852\pi$
$137$	2.09755e7	−	1.21102e7i	0.696932	−	0.402374i	0.806204	+	0.591638i	$0.201519\pi$
$138$		−	1.88336e6i		−	0.0610039i
$139$	5.47794e6	+	9.48807e6i	0.173008	+	0.299658i	0.939470	−	0.342631i	$-0.111318\pi$
$139$	5.47794e6	+	9.48807e6i	0.173008	+	0.299658i	−0.766462	+	0.642289i	$0.777985\pi$
$140$	−8.17528e6	+	1.41600e7i	−0.251799	+	0.436129i
$141$	−8.62574e6	−	4.98007e6i	−0.259137	−	0.149613i
$142$	−2.13861e7			−0.626791
$143$	2.85029e7	+	2.42607e7i	0.815103	+	0.693789i
$144$	−8.28111e6			−0.231110
$145$	1.97767e7	+	1.14181e7i	0.538723	+	0.311032i
$146$	−7.21425e6	+	1.24955e7i	−0.191848	+	0.332290i
$147$	910662.	+	1.57731e6i	0.0236454	+	0.0409550i
$148$			2.13381e7i			0.541054i
$149$	−3.17391e6	+	1.83246e6i	−0.0786035	+	0.0453818i	−0.538787	−	0.842442i	$-0.681117\pi$
$149$	−3.17391e6	+	1.83246e6i	−0.0786035	+	0.0453818i	0.460183	+	0.887824i	$0.347784\pi$
$150$	935573.	−	540153.i	0.0226338	−	0.0130677i
$151$		−	7.24335e7i		−	1.71206i	−0.516923	−	0.856032i	$-0.672923\pi$
$151$		−	7.24335e7i		−	1.71206i	0.516923	−	0.856032i	$-0.327077\pi$
$152$	1.14184e7	+	1.97773e7i	0.263727	+	0.456788i
$153$	−3.45214e7	+	5.97928e7i	−0.779235	+	1.34967i
$154$	3.21627e7	+	1.85691e7i	0.709626	+	0.409703i
$155$	−5.52838e7			−1.19244
$156$	−6.40985e6	−	1.17681e6i	−0.135180	−	0.0248182i
$157$	2.23292e7			0.460494			0.230247	−	0.973132i	$-0.426047\pi$
$157$	2.23292e7			0.460494			0.230247	+	0.973132i	$0.426047\pi$
$158$	3.86336e6	+	2.23051e6i	0.0779230	+	0.0449888i
$159$	−5.61065e6	+	9.71794e6i	−0.110694	+	0.191727i
$160$	−4.26047e6	−	7.37936e6i	−0.0822314	−	0.142429i
$161$			1.79926e7i			0.339785i
$162$	2.58152e7	−	1.49044e7i	0.477060	−	0.275430i
$163$	891448.	−	514678.i	0.0161228	−	0.00930848i	−0.491917	−	0.870642i	$-0.663704\pi$
$163$	891448.	−	514678.i	0.0161228	−	0.00930848i	0.508040	+	0.861334i	$0.330370\pi$
$164$		−	4.08773e7i		−	0.723650i
$165$	7.89749e6	+	1.36789e7i	0.136866	+	0.237059i
$166$	3.78204e7	−	6.55069e7i	0.641723	−	1.11150i
$167$	8.28697e7	+	4.78448e7i	1.37685	+	0.794927i	0.991780	−	0.127958i	$-0.0408422\pi$
$167$	8.28697e7	+	4.78448e7i	1.37685	+	0.794927i	0.385075	+	0.922885i	$0.374176\pi$
$168$	−6.46621e6			−0.105212
$169$	5.86563e7	+	2.22892e7i	0.934785	+	0.355215i
$170$	−7.10424e7			−1.10904
$171$	−7.80955e7	−	4.50885e7i	−1.19437	−	0.689571i
$172$	−8.25932e6	+	1.43056e7i	−0.123764	+	0.214366i
$173$	−1.51502e6	−	2.62409e6i	−0.0222462	−	0.0385316i	0.854688	−	0.519142i	$-0.173748\pi$
$173$	−1.51502e6	−	2.62409e6i	−0.0222462	−	0.0385316i	−0.876934	+	0.480610i	$0.840415\pi$
$174$			9.03108e6i			0.129962i
$175$	−8.93795e6	+	5.16033e6i	−0.126068	+	0.0727854i
$176$	−1.67613e7	+	9.67713e6i	−0.231746	+	0.133799i
$177$		−	1.46547e7i		−	0.198642i
$178$	−3.62331e7	−	6.27575e7i	−0.481543	−	0.834057i
$179$	3.72709e7	−	6.45552e7i	0.485719	−	0.841289i	−0.514147	−	0.857702i	$-0.671891\pi$
$179$	3.72709e7	−	6.45552e7i	0.485719	−	0.841289i	0.999865	+	0.0164130i	$0.00522464\pi$
$180$	2.91392e7	+	1.68235e7i	0.372412	+	0.215012i
$181$	−1.43137e8			−1.79422			−0.897109	−	0.441808i	$-0.854337\pi$
$181$	−1.43137e8			−1.79422			−0.897109	+	0.441808i	$0.854337\pi$
$182$	6.12362e7	+	1.12426e7i	0.752936	+	0.138235i
$183$	−3.64108e6			−0.0439189
$184$	−8.12045e6	−	4.68835e6i	−0.0960988	−	0.0554827i
$185$	4.33495e7	−	7.50836e7i	0.503365	−	0.871854i
$186$	−1.09316e7	−	1.89341e7i	−0.124563	−	0.215750i
$187$			1.61364e8i			1.80452i
$188$	−4.29449e7	+	2.47943e7i	−0.471367	+	0.272144i
$189$	4.60324e7	−	2.65768e7i	0.495961	−	0.286343i
$190$		−	9.27887e7i		−	0.981426i
$191$	3.02178e7	+	5.23388e7i	0.313795	+	0.543509i	0.979181	−	0.202991i	$-0.0650661\pi$
$191$	3.02178e7	+	5.23388e7i	0.313795	+	0.543509i	−0.665385	+	0.746500i	$0.731733\pi$
$192$	1.68490e6	−	2.91834e6i	0.0171799	−	0.0297564i
$193$	−1.47526e8	−	8.51740e7i	−1.47713	−	0.852819i	−0.477459	−	0.878654i	$-0.658442\pi$
$193$	−1.47526e8	−	8.51740e7i	−1.47713	−	0.852819i	−0.999666	+	0.0258353i	$0.991775\pi$
$194$	−1.09289e8			−1.07465
$195$	2.01639e7	+	1.71628e7i	0.194739	+	0.165756i
$196$	9.06781e6			0.0860214
$197$	2.06833e7	+	1.19415e7i	0.192748	+	0.111283i	0.593268	−	0.805005i	$-0.297837\pi$
$197$	2.06833e7	+	1.19415e7i	0.192748	+	0.111283i	−0.400521	+	0.916288i	$0.631171\pi$
$198$	3.82125e7	−	6.61859e7i	0.349846	−	0.605951i
$199$	2.72320e7	+	4.71673e7i	0.244959	+	0.424282i	0.962120	−	0.272626i	$-0.0878920\pi$
$199$	2.72320e7	+	4.71673e7i	0.244959	+	0.424282i	−0.717161	+	0.696908i	$0.754559\pi$
$200$		−	5.37851e6i		−	0.0475398i
$201$	2.43042e7	−	1.40320e7i	0.211103	−	0.121881i
$202$	5.53255e7	−	3.19422e7i	0.472276	−	0.272669i
$203$		−	8.62780e7i		−	0.723876i
$204$	−1.40477e7	−	2.43313e7i	−0.115851	−	0.200660i
$205$	−8.30443e7	+	1.43837e8i	−0.673243	+	1.16609i
$206$	5.67117e7	+	3.27425e7i	0.451999	+	0.260962i
$207$	3.70261e7			0.290143
$208$	−2.10304e7	+	2.47077e7i	−0.162041	+	0.190375i
$209$	−2.10758e8			−1.59688
$210$	2.27530e7	+	1.31364e7i	0.169539	+	0.0978836i
$211$	1.22094e8	−	2.11473e8i	0.894757	−	1.54976i	0.0606511	−	0.998159i	$-0.480682\pi$
$211$	1.22094e8	−	2.11473e8i	0.894757	−	1.54976i	0.834106	−	0.551605i	$-0.185984\pi$
$212$	2.79337e7	+	4.83826e7i	0.201351	+	0.348750i
$213$			3.43643e7i			0.243657i
$214$	−4.93773e7	+	2.85080e7i	−0.344413	+	0.198847i
$215$	5.81250e7	−	3.35585e7i	0.398867	−	0.230286i
$216$			2.77005e7i			0.187025i
$217$	1.04435e8	+	1.80886e8i	0.693803	+	1.20170i
$218$	−7.84313e7	+	1.35847e8i	−0.512734	+	0.888081i
$219$	2.00783e7	+	1.15922e7i	0.129173	+	0.0745782i
$220$	7.86384e7			0.497915
$221$	9.07300e7	+	2.54846e8i	0.565429	+	1.58820i
$222$	3.42871e7			0.210327
$223$	−3.93688e7	−	2.27296e7i	−0.237731	−	0.137254i	0.376403	−	0.926456i	$-0.377161\pi$
$223$	−3.93688e7	−	2.27296e7i	−0.237731	−	0.137254i	−0.614133	+	0.789202i	$0.710494\pi$
$224$	−1.60966e7	+	2.78802e7i	−0.0956900	+	0.165740i
$225$	1.06192e7	+	1.83930e7i	0.0621516	+	0.107650i
$226$			6.96402e7i			0.401311i
$227$	1.06418e8	−	6.14402e7i	0.603842	−	0.348628i	−0.166710	−	0.986006i	$-0.553314\pi$
$227$	1.06418e8	−	6.14402e7i	0.603842	−	0.348628i	0.770551	+	0.637378i	$0.219981\pi$
$228$	3.17792e7	−	1.83477e7i	0.177570	−	0.102520i
$229$		−	1.91504e8i		−	1.05379i	−0.849930	−	0.526895i	$-0.823356\pi$
$229$		−	1.91504e8i		−	1.05379i	0.849930	−	0.526895i	$-0.176644\pi$
$230$	1.90492e7	+	3.29942e7i	0.103236	+	0.178810i
$231$	2.98378e7	−	5.16805e7i	0.159266	−	0.275858i
$232$	3.89391e7	+	2.24815e7i	0.204728	+	0.118200i
$233$	1.34176e8			0.694910			0.347455	−	0.937697i	$-0.387046\pi$
$233$	1.34176e8			0.694910			0.347455	+	0.937697i	$0.387046\pi$
$234$	2.31356e7	−	1.26015e8i	0.118039	−	0.642933i
$235$	2.01483e8			1.01275
$236$	−6.31864e7	−	3.64807e7i	−0.312919	−	0.180664i
$237$	3.58409e6	−	6.20783e6i	0.0174888	−	0.0302915i
$238$	1.34204e8	+	2.32448e8i	0.645276	+	1.11765i
$239$		−	2.42778e7i		−	0.115032i	−0.998345	−	0.0575158i	$-0.981682\pi$
$239$		−	2.42778e7i		−	0.115032i	0.998345	−	0.0575158i	$-0.0183180\pi$
$240$	−1.18575e7	+	6.84593e6i	−0.0553674	+	0.0319664i
$241$	−2.32876e8	+	1.34451e8i	−1.07168	+	0.618735i	−0.928640	−	0.370982i	$-0.879021\pi$
$241$	−2.32876e8	+	1.34451e8i	−1.07168	+	0.618735i	−0.143040	+	0.989717i	$0.545688\pi$
$242$		−	2.27198e7i		−	0.103051i
$243$	−8.31103e7	−	1.43951e8i	−0.371563	−	0.643567i
$244$	−9.06391e6	+	1.56991e7i	−0.0399440	+	0.0691850i
$245$	−3.19074e7	−	1.84217e7i	−0.138615	−	0.0800293i
$246$	−6.56836e7			−0.281309
$247$	−3.32855e8	+	1.18503e8i	−1.40545	+	0.500367i
$248$	−1.08850e8			−0.453158
$249$	−1.05260e8	−	6.07716e7i	−0.432080	−	0.249461i
$250$	−9.21888e7	+	1.59676e8i	−0.373154	+	0.646322i
$251$	−1.75162e8	−	3.03389e8i	−0.699168	−	1.21099i	−0.968755	−	0.248019i	$-0.920221\pi$
$251$	−1.75162e8	−	3.03389e8i	−0.699168	−	1.21099i	0.269587	−	0.962976i	$-0.413113\pi$
$252$		−	1.27123e8i		−	0.500405i
$253$	7.49423e7	−	4.32679e7i	0.290941	−	0.167975i
$254$	1.37522e8	−	7.93986e7i	0.526569	−	0.304015i
$255$			1.14154e8i			0.431124i
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	8.92663e7	−	1.54614e8i	0.328036	−	0.568175i	−0.654086	−	0.756420i	$-0.726947\pi$
$257$	8.92663e7	−	1.54614e8i	0.328036	−	0.568175i	0.982122	+	0.188245i	$0.0602799\pi$
$258$	2.29869e7	+	1.32715e7i	0.0833318	+	0.0481116i
$259$	−3.27560e8			−1.17150
$260$	1.24196e8	−	4.42159e7i	0.438227	−	0.156017i
$261$	−1.77547e8			−0.618119
$262$	6.00743e7	+	3.46839e7i	0.206364	+	0.119144i
$263$	2.55775e8	−	4.43016e8i	0.866989	−	1.50167i	0.00193085	−	0.999998i	$-0.499385\pi$
$263$	2.55775e8	−	4.43016e8i	0.866989	−	1.50167i	0.865058	−	0.501671i	$-0.167281\pi$
$264$	1.55497e7	+	2.69328e7i	0.0520125	+	0.0900883i
$265$		−	2.26995e8i		−	0.749300i
$266$	−3.03601e8	+	1.75284e8i	−0.989047	+	0.571026i
$267$	−1.00842e8	+	5.82211e7i	−0.324229	+	0.187193i
$268$		−	1.39722e8i		−	0.443399i
$269$	−8.74611e7	−	1.51487e8i	−0.273957	−	0.474507i	0.695915	−	0.718125i	$-0.254999\pi$
$269$	−8.74611e7	−	1.51487e8i	−0.273957	−	0.474507i	−0.969871	+	0.243618i	$0.921666\pi$
$270$	5.62751e7	−	9.74713e7i	0.173998	−	0.301373i
$271$	2.20774e8	+	1.27464e8i	0.673837	+	0.389040i	0.797529	−	0.603281i	$-0.206140\pi$
$271$	2.20774e8	+	1.27464e8i	0.673837	+	0.389040i	−0.123692	+	0.992321i	$0.539473\pi$
$272$	−1.39878e8			−0.421462
$273$	1.80652e7	−	9.83972e7i	0.0537369	−	0.292694i
$274$	−1.93763e8			−0.569042
$275$	4.29873e7	+	2.48187e7i	0.124645	+	0.0719639i
$276$	−7.53346e6	+	1.30483e7i	−0.0215681	+	0.0373571i
$277$	2.14738e8	+	3.71936e8i	0.607056	+	1.05145i	0.991723	+	0.128397i	$0.0409830\pi$
$277$	2.14738e8	+	3.71936e8i	0.607056	+	1.05145i	−0.384667	+	0.923056i	$0.625684\pi$
$278$		−	8.76470e7i		−	0.244670i
$279$	3.72237e8	−	2.14911e8i	1.02614	−	0.592439i
$280$	1.13280e8	−	6.54023e7i	0.308390	−	0.178049i
$281$			2.82277e8i			0.758933i	0.925205	+	0.379467i	$0.123892\pi$
$281$			2.82277e8i			0.758933i	−0.925205	+	0.379467i	$0.876108\pi$
$282$	3.98406e7	+	6.90059e7i	0.105792	+	0.183238i
$283$	−2.56533e8	+	4.44328e8i	−0.672808	+	1.16534i	0.304297	+	0.952577i	$0.401579\pi$
$283$	−2.56533e8	+	4.44328e8i	−0.672808	+	1.16534i	−0.977105	+	0.212760i	$0.931755\pi$
$284$	1.48167e8	+	8.55445e7i	0.383830	+	0.221604i
$285$	−1.49097e8			−0.381516
$286$	−1.00431e8	−	2.82095e8i	−0.253855	−	0.713039i
$287$	6.27505e8			1.56686
$288$	5.73732e7	+	3.31244e7i	0.141526	+	0.0817099i
$289$	−3.77940e8	+	6.54611e8i	−0.921044	+	1.59530i
$290$	−9.13446e7	−	1.58214e8i	−0.219933	−	0.380935i
$291$			1.75610e8i			0.417757i
$292$	9.99636e7	−	5.77140e7i	0.234964	−	0.135657i
$293$	1.21814e8	−	7.03295e7i	0.282919	−	0.163343i	−0.351825	−	0.936066i	$-0.614439\pi$
$293$	1.21814e8	−	7.03295e7i	0.282919	−	0.163343i	0.634744	+	0.772722i	$0.281106\pi$
$294$		−	1.45706e7i		−	0.0334396i
$295$	1.48225e8	+	2.56733e8i	0.336158	+	0.582243i
$296$	8.53525e7	−	1.47835e8i	0.191291	−	0.331326i
$297$	−2.21394e8	−	1.27822e8i	−0.490363	−	0.283111i
$298$	2.93193e7			0.0641795
$299$	9.40300e7	−	1.10472e8i	0.203431	−	0.239003i
$300$	−8.64245e6			−0.0184805
$301$	−2.19604e8	−	1.26788e8i	−0.464149	−	0.267976i
$302$	−2.89734e8	+	5.01834e8i	−0.605306	+	1.04842i
$303$	−5.13263e7	−	8.88997e7i	−0.105996	−	0.183591i
$304$		−	1.82695e8i		−	0.372966i
$305$	6.37873e7	−	3.68276e7i	0.128731	−	0.0743231i
$306$	4.78343e8	−	2.76171e8i	0.954364	−	0.551002i
$307$			5.89137e8i			1.16207i	0.813879	+	0.581034i	$0.197352\pi$
$307$			5.89137e8i			1.16207i	−0.813879	+	0.581034i	$0.802648\pi$
$308$	−1.48553e8	−	2.57301e8i	−0.289704	−	0.501781i
$309$	5.26123e7	−	9.11271e7i	0.101445	−	0.175709i
$310$	3.83018e8	+	2.21135e8i	0.730218	+	0.421592i
$311$	8.53817e8			1.60955			0.804773	−	0.593583i	$-0.202287\pi$
$311$	8.53817e8			1.60955			0.804773	+	0.593583i	$0.202287\pi$
$312$	3.97015e7	+	3.37926e7i	0.0740058	+	0.0629913i
$313$	6.79848e8			1.25316			0.626580	−	0.779357i	$-0.284454\pi$
$313$	6.79848e8			1.25316			0.626580	+	0.779357i	$0.284454\pi$
$314$	−1.54701e8	−	8.93168e7i	−0.281994	−	0.162809i
$315$	−2.58256e8	+	4.47313e8i	−0.465548	+	0.806352i
$316$	−1.78441e7	−	3.09069e7i	−0.0318119	−	0.0550999i
$317$			2.69855e8i			0.475799i	0.971290	+	0.237899i	$0.0764588\pi$
$317$			2.69855e8i			0.475799i	−0.971290	+	0.237899i	$0.923541\pi$
$318$	7.77435e7	−	4.48852e7i	0.135572	−	0.0782724i
$319$	−3.59362e8	+	2.07478e8i	−0.619819	+	0.357853i
$320$			6.81676e7i			0.116293i
$321$	4.58080e7	+	7.93418e7i	0.0772990	+	0.133886i
$322$	7.19705e7	−	1.24657e8i	0.120132	−	0.208075i
$323$	−1.31913e9	−	7.61600e8i	−2.17811	−	1.25753i
$324$	−2.38470e8			−0.389517
$325$	8.18456e7	+	1.50264e7i	0.132252	+	0.0242808i
$326$	−8.23484e6			−0.0131642
$327$	2.18286e8	+	1.26027e8i	0.345229	+	0.199318i
$328$	−1.63509e8	+	2.83206e8i	−0.255849	+	0.443143i
$329$	−3.80615e8	−	6.59245e8i	−0.589251	−	1.02061i
$330$		−	1.26360e8i		−	0.193558i
$331$	−3.24598e7	+	1.87407e7i	−0.0491981	+	0.0284045i	−0.524397	−	0.851474i	$-0.675709\pi$
$331$	−3.24598e7	+	1.87407e7i	−0.0491981	+	0.0284045i	0.475199	+	0.879878i	$0.342376\pi$
$332$	−5.24055e8	+	3.02563e8i	−0.785947	+	0.453767i
$333$			6.74070e8i			1.00035i
$334$	−3.82759e8	−	6.62958e8i	−0.562099	−	0.973583i
$335$	−2.83853e8	+	4.91648e8i	−0.412513	+	0.714493i
$336$	4.47992e7	+	2.58648e7i	0.0644292	+	0.0371982i
$337$	8.40858e8			1.19679			0.598395	−	0.801201i	$-0.295805\pi$
$337$	8.40858e8			1.19679			0.598395	+	0.801201i	$0.295805\pi$
$338$	−3.17226e8	−	3.89050e8i	−0.446849	−	0.548020i
$339$	1.11901e8			0.156004
$340$	4.92196e8	+	2.84170e8i	0.679145	+	0.392104i
$341$	5.02281e8	−	8.69976e8i	0.685972	−	1.18814i
$342$	3.60708e8	+	6.24764e8i	0.487601	+	0.844549i
$343$		−	6.69899e8i		−	0.896354i
$344$	1.14445e8	−	6.60746e7i	0.151579	−	0.0875145i
$345$	5.30167e7	−	3.06092e7i	0.0695098	−	0.0401315i
$346$			2.42403e7i			0.0314609i
$347$	−1.16084e8	−	2.01063e8i	−0.149148	−	0.258332i	0.781765	−	0.623574i	$-0.214320\pi$
$347$	−1.16084e8	−	2.01063e8i	−0.149148	−	0.258332i	−0.930913	+	0.365241i	$0.880986\pi$
$348$	3.61243e7	−	6.25692e7i	0.0459486	−	0.0795854i
$349$	−1.11812e9	−	6.45546e8i	−1.40799	−	0.812902i	−0.412794	−	0.910824i	$-0.635447\pi$
$349$	−1.11812e9	−	6.45546e8i	−1.40799	−	0.812902i	−0.995194	+	0.0979218i	$0.968781\pi$
$350$	8.25652e7			0.102934
$351$	−4.21523e8	−	7.73892e7i	−0.520291	−	0.0955224i
$352$	1.54834e8			0.189220
$353$	6.50163e8	+	3.75372e8i	0.786703	+	0.454203i	0.838801	−	0.544439i	$-0.183257\pi$
$353$	6.50163e8	+	3.75372e8i	0.786703	+	0.454203i	−0.0520974	+	0.998642i	$0.516591\pi$
$354$	−5.86189e7	+	1.01531e8i	−0.0702306	+	0.121643i
$355$	−3.47576e8	−	6.02020e8i	−0.412336	−	0.714186i
$356$			5.79729e8i			0.681005i
$357$	3.73508e8	−	2.15645e8i	0.434472	−	0.250842i
$358$	−5.16441e8	+	2.98168e8i	−0.594881	+	0.343455i
$359$			4.11826e8i			0.469768i	0.972023	+	0.234884i	$0.0754710\pi$
$359$			4.11826e8i			0.469768i	−0.972023	+	0.234884i	$0.924529\pi$
$360$	−1.34588e8	−	2.33113e8i	−0.152036	−	0.263335i
$361$	5.47792e8	−	9.48803e8i	0.612831	−	1.06145i
$362$	9.91679e8	+	5.72546e8i	1.09873	+	0.634352i
$363$	−3.65073e7			−0.0400596
$364$	−3.79286e8	−	3.22836e8i	−0.412204	−	0.350854i
$365$	−4.68996e8			−0.504829
$366$	2.52261e7	+	1.45643e7i	0.0268947	+	0.0155277i
$367$	1.95572e8	−	3.38740e8i	0.206526	−	0.357714i	−0.744092	−	0.668077i	$-0.767118\pi$
$367$	1.95572e8	−	3.38740e8i	0.206526	−	0.357714i	0.950618	+	0.310364i	$0.100451\pi$
$368$	3.75068e7	+	6.49636e7i	0.0392322	+	0.0679521i
$369$		−	1.29131e9i		−	1.33795i
$370$	−6.00668e8	+	3.46796e8i	−0.616494	+	0.355933i
$371$	−7.42718e8	+	4.28809e8i	−0.755119	+	0.435968i
$372$			1.74906e8i			0.176159i
$373$	3.28201e7	+	5.68461e7i	0.0327461	+	0.0567178i	0.881934	−	0.471373i	$-0.156241\pi$
$373$	3.28201e7	+	5.68461e7i	0.0327461	+	0.0567178i	−0.849188	+	0.528091i	$0.822908\pi$
$374$	6.45456e8	−	1.11796e9i	0.637993	−	1.10504i
$375$	2.56575e8	+	1.48133e8i	0.251249	+	0.145059i
$376$	3.96708e8			0.384870
$377$	−4.50891e8	+	5.29733e8i	−0.433388	+	0.509170i
$378$	−4.25229e8			−0.404950
$379$	−8.46727e8	−	4.88858e8i	−0.798925	−	0.461260i	0.0441699	−	0.999024i	$-0.485936\pi$
$379$	−8.46727e8	−	4.88858e8i	−0.798925	−	0.461260i	−0.843095	+	0.537764i	$0.819269\pi$
$380$	−3.71155e8	+	6.42859e8i	−0.346986	+	0.600998i
$381$	−1.27581e8	−	2.20978e8i	−0.118182	−	0.204697i
$382$		−	4.83485e8i		−	0.443773i
$383$	−1.23010e9	+	7.10200e8i	−1.11878	+	0.645929i	−0.941090	−	0.338157i	$-0.890196\pi$
$383$	−1.23010e9	+	7.10200e8i	−1.11878	+	0.645929i	−0.177692	+	0.984086i	$0.556863\pi$
$384$	−2.33467e7	+	1.34792e7i	−0.0210410	+	0.0121480i
$385$			1.20717e9i			1.07809i
$386$	6.81392e8	+	1.18021e9i	0.603034	+	1.04449i
$387$	−2.60911e8	+	4.51912e8i	−0.228826	+	0.396337i
$388$	7.57173e8	+	4.37154e8i	0.658088	+	0.379947i
$389$	1.85982e9			1.60195			0.800973	−	0.598700i	$-0.204316\pi$
$389$	1.85982e9			1.60195			0.800973	+	0.598700i	$0.204316\pi$
$390$	−7.10483e7	−	1.99563e8i	−0.0606495	−	0.170355i
$391$	6.25417e8			0.529116
$392$	−6.28237e7	−	3.62713e7i	−0.0526771	−	0.0304131i
$393$	5.57318e7	−	9.65302e7i	0.0463158	−	0.0802213i
$394$	−9.55323e7	−	1.65467e8i	−0.0786889	−	0.136293i
$395$			1.45005e8i			0.118384i
$396$	−5.29487e8	+	3.05700e8i	−0.428472	+	0.247378i
$397$	780067.	−	450372.i	0.000625698	−	0.000361247i	−0.499687	−	0.866206i	$-0.666552\pi$
$397$	780067.	−	450372.i	0.000625698	−	0.000361247i	0.500313	+	0.865845i	$0.333218\pi$
$398$		−	4.35712e8i		−	0.346425i
$399$	2.81655e8	+	4.87840e8i	0.221979	+	0.384479i
$400$	−2.15141e7	+	3.72634e7i	−0.0168079	+	0.0291121i
$401$	−4.84557e8	−	2.79759e8i	−0.375266	−	0.216660i	0.300490	−	0.953785i	$-0.402850\pi$
$401$	−4.84557e8	−	2.79759e8i	−0.375266	−	0.216660i	−0.675757	+	0.737125i	$0.736183\pi$
$402$	−2.24513e8			−0.172365
$403$	3.04104e8	−	1.65639e9i	0.231449	−	1.26065i
$404$	−5.11075e8			−0.385612
$405$	8.39118e8	+	4.84465e8i	0.627669	+	0.362385i
$406$	−3.45112e8	+	5.97751e8i	−0.255929	+	0.443281i
$407$	7.87704e8	+	1.36434e9i	0.579139	+	1.00310i
$408$			2.24763e8i			0.163838i
$409$	2.90481e8	−	1.67709e8i	0.209936	−	0.121206i	−0.391346	−	0.920244i	$-0.627990\pi$
$409$	2.90481e8	−	1.67709e8i	0.209936	−	0.121206i	0.601282	+	0.799037i	$0.294657\pi$
$410$	1.15070e9	−	6.64355e8i	0.824550	−	0.476054i
$411$			3.11348e8i			0.221207i
$412$	−2.61940e8	−	4.53694e8i	−0.184528	−	0.319612i
$413$	5.60013e8	−	9.69971e8i	0.391177	−	0.677538i
$414$	−2.56524e8	−	1.48104e8i	−0.177675	−	0.102581i
$415$	2.45869e9			1.68863
$416$	2.44533e8	−	8.70584e7i	0.166537	−	0.0592904i
$417$	−1.40835e8			−0.0951121
$418$	1.46017e9	+	8.43031e8i	0.977884	+	0.564582i
$419$	−5.84233e8	+	1.01192e9i	−0.388005	+	0.672044i	−0.992181	−	0.124807i	$-0.960169\pi$
$419$	−5.84233e8	+	1.01192e9i	−0.388005	+	0.672044i	0.604176	+	0.796851i	$0.293502\pi$
$420$	−1.05091e8	−	1.82024e8i	−0.0692142	−	0.119882i
$421$			1.79478e9i			1.17226i	0.810218	+	0.586129i	$0.199349\pi$
$421$			1.79478e9i			1.17226i	−0.810218	+	0.586129i	$0.800651\pi$
$422$	−1.69178e9	+	9.76750e8i	−1.09585	+	0.632688i
$423$	−1.35663e9	+	7.83248e8i	−0.871503	+	0.503162i
$424$		−	4.46939e8i		−	0.284753i
$425$	1.79371e8	+	3.10680e8i	0.113342	+	0.196314i
$426$	1.37457e8	−	2.38083e8i	0.0861457	−	0.149209i
$427$	−2.40997e8	−	1.39139e8i	−0.149801	−	0.0864874i
$428$	4.56128e8			0.281212
$429$	−4.53283e8	+	1.61377e8i	−0.277184	+	0.0986829i
$430$	−5.36936e8			−0.325674
$431$	1.82568e9	+	1.05406e9i	1.09838	+	0.634152i	0.935796	−	0.352542i	$-0.114683\pi$
$431$	1.82568e9	+	1.05406e9i	1.09838	+	0.634152i	0.162588	+	0.986694i	$0.448016\pi$
$432$	1.10802e8	−	1.91915e8i	0.0661234	−	0.114529i
$433$	−1.54638e9	−	2.67841e9i	−0.915396	−	1.58551i	−0.806321	−	0.591478i	$-0.798545\pi$
$433$	−1.54638e9	−	2.67841e9i	−0.915396	−	1.58551i	−0.109075	−	0.994034i	$-0.534789\pi$
$434$		−	1.67096e9i		−	0.981185i
$435$	−2.54225e8	+	1.46777e8i	−0.148083	+	0.0854959i
$436$	1.08678e9	−	6.27451e8i	0.627968	−	0.362557i
$437$			8.16858e8i			0.468233i
$438$	−9.27377e7	−	1.60626e8i	−0.0527347	−	0.0913392i
$439$	−4.96775e8	+	8.60439e8i	−0.280242	+	0.485394i	−0.971444	−	0.237268i	$-0.923748\pi$
$439$	−4.96775e8	+	8.60439e8i	−0.280242	+	0.485394i	0.691202	+	0.722662i	$0.257082\pi$
$440$	−5.44823e8	−	3.14553e8i	−0.304909	−	0.176039i
$441$	2.86451e8			0.159044
$442$	3.90789e8	−	2.12855e9i	0.215260	−	1.17248i
$443$	−1.98531e9			−1.08496			−0.542481	−	0.840068i	$-0.682515\pi$
$443$	−1.98531e9			−1.08496			−0.542481	+	0.840068i	$0.682515\pi$
$444$	−2.37548e8	−	1.37148e8i	−0.128799	−	0.0743619i
$445$	1.17775e9	−	2.03992e9i	0.633568	−	1.09737i
$446$	1.81837e8	+	3.14950e8i	0.0970532	+	0.168101i
$447$		−	4.71116e7i		−	0.0249489i
$448$	2.23041e8	−	1.28773e8i	0.117196	−	0.0676631i
$449$	−1.56346e9	+	9.02662e8i	−0.815124	+	0.470612i	−0.848732	−	0.528823i	$-0.822633\pi$
$449$	−1.56346e9	+	9.02662e8i	−0.815124	+	0.470612i	0.0336083	+	0.999435i	$0.489300\pi$
$450$		−	1.69907e8i		−	0.0878956i
$451$	−1.50900e9	−	2.61366e9i	−0.774588	−	1.34163i
$452$	2.78561e8	−	4.82482e8i	0.141885	−	0.245752i
$453$	8.06370e8	+	4.65558e8i	0.407559	+	0.235305i
$454$	−9.83044e8			−0.493035
$455$	6.78756e8	+	1.90652e9i	0.337811	+	0.948857i
$456$	−2.93563e8			−0.144986
$457$	−9.07474e8	−	5.23930e8i	−0.444762	−	0.256783i	0.260854	−	0.965378i	$-0.415996\pi$
$457$	−9.07474e8	−	5.23930e8i	−0.444762	−	0.256783i	−0.705615	+	0.708595i	$0.749329\pi$
$458$	−7.66017e8	+	1.32678e9i	−0.372571	+	0.645312i
$459$	−9.23801e8	−	1.60007e9i	−0.445896	−	0.772315i
$460$		−	3.04788e8i		−	0.145997i
$461$	−1.53112e9	+	8.83993e8i	−0.727874	+	0.420238i	−0.817644	−	0.575724i	$-0.804720\pi$
$461$	−1.53112e9	+	8.83993e8i	−0.727874	+	0.420238i	0.0897697	+	0.995963i	$0.471387\pi$
$462$	−4.13444e8	+	2.38702e8i	−0.195061	+	0.112618i
$463$		−	6.76344e8i		−	0.316690i	−0.987384	−	0.158345i	$-0.949384\pi$
$463$		−	6.76344e8i		−	0.316690i	0.987384	−	0.158345i	$-0.0506158\pi$
$464$	−1.79852e8	−	3.11513e8i	−0.0835800	−	0.144765i
$465$	3.55331e8	−	6.15451e8i	0.163888	−	0.283863i
$466$	−9.29598e8	−	5.36704e8i	−0.425544	−	0.245688i
$467$	3.82747e8			0.173901			0.0869505	−	0.996213i	$-0.472288\pi$
$467$	3.82747e8			0.173901			0.0869505	+	0.996213i	$0.472288\pi$
$468$	−6.64347e8	+	7.80514e8i	−0.299595	+	0.351982i
$469$	2.14487e9			0.960055
$470$	−1.39592e9	−	8.05933e8i	−0.620179	−	0.358061i
$471$	−1.43518e8	+	2.48581e8i	−0.0632899	+	0.109621i
$472$	2.91846e8	+	5.05491e8i	0.127749	+	0.221267i
$473$			1.21958e9i			0.529904i
$474$	−4.96627e7	+	2.86728e7i	−0.0214193	+	0.0123665i
$475$	−4.05780e8	+	2.34277e8i	−0.173725	+	0.100300i
$476$		−	2.14726e9i		−	0.912558i
$477$	8.82424e8	+	1.52840e9i	0.372274	+	0.644798i
$478$	−9.71114e7	+	1.68202e8i	−0.0406698	+	0.0704422i
$479$	−2.10313e9	−	1.21424e9i	−0.874361	−	0.504813i	−0.00556629	−	0.999985i	$-0.501772\pi$
$479$	−2.10313e9	−	1.21424e9i	−0.874361	−	0.504813i	−0.868795	+	0.495172i	$0.835105\pi$
$480$	1.09535e8			0.0452073
$481$	2.01117e9	+	1.71184e9i	0.824025	+	0.701383i
$482$	2.15122e9			0.875023
$483$	−2.00304e8	−	1.15646e8i	−0.0808863	−	0.0466997i
$484$	−9.08792e7	+	1.57407e8i	−0.0364339	+	0.0631054i
$485$	−1.77620e9	−	3.07647e9i	−0.706962	−	1.22449i
$486$			1.32977e9i			0.525470i
$487$	2.64158e9	−	1.52511e9i	1.03636	−	0.598344i	0.117562	−	0.993066i	$-0.462492\pi$
$487$	2.64158e9	−	1.52511e9i	1.03636	−	0.598344i	0.918801	+	0.394722i	$0.129159\pi$
$488$	1.25593e8	−	7.25113e7i	0.0489212	−	0.0282446i
$489$			1.32321e7i			0.00511740i
$490$	1.47374e8	+	2.55259e8i	0.0565893	+	0.0980155i
$491$	1.65926e9	−	2.87392e9i	0.632599	−	1.09569i	−0.354419	−	0.935087i	$-0.615321\pi$
$491$	1.65926e9	−	2.87392e9i	0.632599	−	1.09569i	0.987018	−	0.160607i	$-0.0513453\pi$
$492$	4.55069e8	+	2.62734e8i	0.172266	+	0.0994578i
$493$	−2.99899e9			−1.12723
$494$	2.78010e9	+	5.10410e8i	1.03757	+	0.190491i
$495$	2.48418e9			0.920587
$496$	7.54138e8	+	4.35402e8i	0.277501	+	0.160215i
$497$	−1.31319e9	+	2.27451e9i	−0.479822	+	0.831075i
$498$	4.86173e8	+	8.42076e8i	0.176396	+	0.305526i
$499$			8.42737e8i			0.303627i	0.988409	+	0.151813i	$0.0485113\pi$
$499$			8.42737e8i			0.303627i	−0.988409	+	0.151813i	$0.951489\pi$
$500$	1.27741e9	−	7.37510e8i	0.457018	−	0.263860i
$501$	−1.06527e9	+	6.15035e8i	−0.378467	+	0.218508i
$502$			2.80259e9i			0.988773i
$503$	1.34123e9	+	2.32308e9i	0.469911	+	0.813911i	0.999408	−	0.0344015i	$-0.0109525\pi$
$503$	1.34123e9	+	2.32308e9i	0.469911	+	0.813911i	−0.529497	+	0.848312i	$0.677619\pi$
$504$	−5.08491e8	+	8.80732e8i	−0.176920	+	0.306434i
$505$	1.79835e9	+	1.03828e9i	0.621375	+	0.358751i
$506$	−6.92287e8			−0.237552
$507$	−6.25144e8	+	5.09734e8i	−0.213035	+	0.173706i
$508$	−1.27038e9			−0.429942
$509$	−4.39240e8	−	2.53595e8i	−0.147635	−	0.0852372i	0.424363	−	0.905492i	$-0.360498\pi$
$509$	−4.39240e8	−	2.53595e8i	−0.147635	−	0.0852372i	−0.571998	+	0.820255i	$0.693831\pi$
$510$	4.56618e8	−	7.90885e8i	0.152425	−	0.264008i
$511$	8.85964e8	+	1.53454e9i	0.293726	+	0.508749i
$512$			1.34218e8i			0.0441942i
$513$	2.08985e9	−	1.20658e9i	0.683448	−	0.394589i
$514$	−1.23691e9	+	7.14131e8i	−0.401761	+	0.231957i
$515$			2.12858e9i			0.686696i
$516$	−1.06172e8	−	1.83895e8i	−0.0340201	−	0.0589245i
$517$	−1.83058e9	+	3.17065e9i	−0.582600	+	1.00909i
$518$	2.26940e9	+	1.31024e9i	0.717394	+	0.414188i
$519$	3.89505e7			0.0122300
$520$	−1.03732e9	−	1.90445e8i	−0.323519	−	0.0593961i
$521$	−2.57587e8			−0.0797980			−0.0398990	−	0.999204i	$-0.512704\pi$
$521$	−2.57587e8			−0.0797980			−0.0398990	+	0.999204i	$0.512704\pi$
$522$	1.23008e9	+	7.10188e8i	0.378519	+	0.218538i
$523$	2.33636e9	−	4.04670e9i	0.714141	−	1.23693i	−0.249149	−	0.968465i	$-0.580151\pi$
$523$	2.33636e9	−	4.04670e9i	0.714141	−	1.23693i	0.963290	−	0.268464i	$-0.0865159\pi$
$524$	−2.77471e8	−	4.80594e8i	−0.0842478	−	0.145921i
$525$		−	1.32670e8i		−	0.0400142i
$526$	−3.54413e9	+	2.04620e9i	−1.06184	+	0.613054i
$527$	6.28754e9	−	3.63011e9i	1.87130	−	1.08040i
$528$		−	2.48795e8i		−	0.0735568i
$529$	1.53471e9	+	2.65820e9i	0.450747	+	0.780716i
$530$	−9.07980e8	+	1.57267e9i	−0.264918	+	0.458851i
$531$	−1.99605e9	−	1.15242e9i	−0.578551	−	0.334026i
$532$	2.80454e9			0.807553
$533$	−3.85278e9	−	3.27936e9i	−1.10212	−	0.938088i
$534$	9.31537e8			0.264732
$535$	−1.60500e9	−	9.26648e8i	−0.453145	−	0.261623i
$536$	−5.58890e8	+	9.68025e8i	−0.156765	+	0.271525i
$537$	4.79110e8	+	8.29843e8i	0.133513	+	0.231252i
$538$			1.39938e9i			0.387433i
$539$	5.79789e8	−	3.34741e8i	0.159481	−	0.0920764i
$540$	−7.79770e8	+	4.50201e8i	−0.213103	+	0.123035i
$541$		−	4.06728e9i		−	1.10437i	−0.833722	−	0.552184i	$-0.813794\pi$
$541$		−	4.06728e9i		−	1.10437i	0.833722	−	0.552184i	$-0.186206\pi$
$542$	−1.01971e9	−	1.76619e9i	−0.275093	−	0.476475i
$543$	9.19994e8	−	1.59348e9i	0.246596	−	0.427117i
$544$	9.69104e8	+	5.59513e8i	0.258092	+	0.149009i
$545$	−5.09879e9			−1.34921
$546$	−5.18748e8	+	6.09455e8i	−0.136390	+	0.160239i
$547$	−5.46491e9			−1.42767			−0.713835	−	0.700314i	$-0.753043\pi$
$547$	−5.46491e9			−1.42767			−0.713835	+	0.700314i	$0.753043\pi$
$548$	1.34243e9	+	7.75053e8i	0.348466	+	0.201187i
$549$	−2.86328e8	+	4.95935e8i	−0.0738517	+	0.127915i
$550$	−1.98550e8	−	3.43898e8i	−0.0508862	−	0.0881374i
$551$		−	3.91699e9i		−	0.997520i
$552$	1.04387e8	−	6.02677e7i	0.0264155	−	0.0152510i
$553$	4.74450e8	−	2.73924e8i	0.119303	−	0.0688798i
$554$		−	3.43580e9i		−	0.858507i
$555$	5.57249e8	+	9.65183e8i	0.138364	+	0.239654i
$556$	−3.50588e8	+	6.07236e8i	−0.0865038	+	0.149829i
$557$	1.21714e9	+	7.02718e8i	0.298434	+	0.172301i	0.641739	−	0.766923i	$-0.278213\pi$
$557$	1.21714e9	+	7.02718e8i	0.298434	+	0.172301i	−0.343305	+	0.939224i	$0.611546\pi$
$558$	−3.43858e9			−0.837836
$559$	6.85733e8	+	1.92612e9i	0.166040	+	0.466381i
$560$	−1.04644e9			−0.251799
$561$	−1.79640e9	−	1.03715e9i	−0.429568	−	0.248011i
$562$	1.12911e9	−	1.95567e9i	0.268323	−	0.464750i
$563$	3.21421e9	+	5.56717e9i	0.759092	+	1.31479i	0.943314	+	0.331902i	$0.107690\pi$
$563$	3.21421e9	+	5.56717e9i	0.759092	+	1.31479i	−0.184222	+	0.982885i	$0.558976\pi$
$564$		−	6.37450e8i		−	0.149613i
$565$	−1.96037e9	+	1.13182e9i	−0.457266	+	0.264003i
$566$	3.55463e9	−	2.05227e9i	0.824018	−	0.475747i
$567$		−	3.66074e9i		−	0.843390i
$568$	−6.84356e8	−	1.18534e9i	−0.156698	−	0.271409i
$569$	−2.26860e9	+	3.92932e9i	−0.516255	+	0.894180i	0.483567	+	0.875307i	$0.339341\pi$
$569$	−2.26860e9	+	3.92932e9i	−0.516255	+	0.894180i	−0.999822	+	0.0188725i	$0.993992\pi$
$570$	1.03298e9	+	5.96389e8i	0.233630	+	0.134886i
$571$	−1.08582e9			−0.244080			−0.122040	−	0.992525i	$-0.538944\pi$
$571$	−1.08582e9			−0.244080			−0.122040	+	0.992525i	$0.538944\pi$
$572$	−4.32572e8	+	2.35613e9i	−0.0966435	+	0.526397i
$573$	−7.76887e8			−0.172511
$574$	−4.34748e9	−	2.51002e9i	−0.959502	−	0.553969i
$575$	9.61927e7	−	1.66611e8i	0.0211011	−	0.0365481i
$576$	−2.64995e8	−	4.58986e8i	−0.0577776	−	0.100074i
$577$			5.44495e6i			0.00117999i	1.00000		0.000589995i	$0.000187801\pi$
$577$			5.44495e6i			0.00117999i	−1.00000		0.000589995i	$0.999812\pi$
$578$	5.23689e9	−	3.02352e9i	1.12804	−	0.651277i
$579$	1.89641e9	−	1.09489e9i	0.406030	−	0.234421i
$580$			1.46151e9i			0.311032i
$581$	−4.64463e9	−	8.04473e9i	−0.982505	−	1.70175i
$582$	7.02440e8	−	1.21666e9i	0.147699	−	0.255823i
$583$	3.57212e9	+	2.06236e9i	0.746597	+	0.431048i
$584$	−9.23424e8			−0.191848
$585$	3.92333e9	−	1.39678e9i	0.810231	−	0.288457i
$586$	−1.12527e9			−0.231002
$587$	−7.03985e9	−	4.06446e9i	−1.43658	−	0.829410i	−0.438970	−	0.898502i	$-0.644657\pi$
$587$	−7.03985e9	−	4.06446e9i	−1.43658	−	0.829410i	−0.997610	+	0.0690915i	$0.977990\pi$
$588$	−5.82824e7	+	1.00948e8i	−0.0118227	+	0.0204775i
$589$	4.74130e9	+	8.21217e9i	0.956079	+	1.65598i
$590$		−	2.37160e9i		−	0.475400i
$591$	−2.65880e8	+	1.53506e8i	−0.0529821	+	0.0305892i
$592$	−1.18268e9	+	6.82820e8i	−0.234283	+	0.135263i
$593$		−	2.87467e9i		−	0.566104i	−0.959105	−	0.283052i	$-0.908653\pi$
$593$		−	2.87467e9i		−	0.566104i	0.959105	−	0.283052i	$-0.0913469\pi$
$594$	1.02257e9	+	1.77115e9i	0.200190	+	0.346739i
$595$	−4.36227e9	+	7.55568e9i	−0.848992	+	1.47050i
$596$	−2.03130e8	−	1.17277e8i	−0.0393018	−	0.0226909i
$597$	−7.00124e8			−0.134668
$598$	−1.09335e9	+	3.89252e8i	−0.209076	+	0.0744349i
$599$	8.47330e9			1.61086			0.805431	−	0.592689i	$-0.201934\pi$
$599$	8.47330e9			1.61086			0.805431	+	0.592689i	$0.201934\pi$
$600$	5.98767e7	+	3.45698e7i	0.0113169	+	0.00653383i
$601$	5.01845e8	−	8.69221e8i	0.0942994	−	0.163331i	−0.815017	−	0.579438i	$-0.803272\pi$
$601$	5.01845e8	−	8.69221e8i	0.0942994	−	0.163331i	0.909316	+	0.416106i	$0.136606\pi$
$602$	1.01431e9	+	1.75683e9i	0.189488	+	0.328203i
$603$		−	4.41382e9i		−	0.819793i
$604$	4.01467e9	−	2.31787e9i	0.741345	−	0.428016i
$605$	6.39563e8	−	3.69252e8i	0.117419	−	0.0677920i
$606$			8.21220e8i			0.149901i
$607$	7.32899e8	+	1.26942e9i	0.133010	+	0.230380i	0.924835	−	0.380367i	$-0.124202\pi$
$607$	7.32899e8	+	1.26942e9i	0.133010	+	0.230380i	−0.791826	+	0.610747i	$0.790869\pi$
$608$	−7.30781e8	+	1.26575e9i	−0.131863	+	0.228394i
$609$	9.60496e8	+	5.54542e8i	0.172320	+	0.0994888i
$610$	−5.89241e8			−0.105109
$611$	−1.10831e9	+	6.03676e9i	−0.196571	+	1.07068i
$612$	−4.41874e9			−0.779235
$613$	7.97928e9	+	4.60684e9i	1.39911	+	0.807777i	0.994299	−	0.106624i	$-0.0340040\pi$
$613$	7.97928e9	+	4.60684e9i	1.39911	+	0.807777i	0.404811	+	0.914400i	$0.367337\pi$
$614$	2.35655e9	−	4.08166e9i	0.410853	−	0.711619i
$615$	−1.06752e9	−	1.84899e9i	−0.185060	−	0.320533i
$616$			2.37685e9i			0.409703i
$617$	−4.09033e8	+	2.36155e8i	−0.0701068	+	0.0404762i	−0.534644	−	0.845078i	$-0.679554\pi$
$617$	−4.09033e8	+	2.36155e8i	−0.0701068	+	0.0404762i	0.464537	+	0.885554i	$0.346221\pi$
$618$	−7.29017e8	+	4.20898e8i	−0.124245	+	0.0717327i
$619$		−	2.16595e9i		−	0.367055i	−0.983015	−	0.183527i	$-0.941248\pi$
$619$		−	2.16595e9i		−	0.367055i	0.983015	−	0.183527i	$-0.0587516\pi$
$620$	−1.76908e9	−	3.06414e9i	−0.298110	−	0.516342i
$621$	−4.95414e8	+	8.58082e8i	−0.0830132	+	0.143783i
$622$	−5.91541e9	−	3.41527e9i	−0.985641	−	0.569060i
$623$	−8.89939e9			−1.47452
$624$	−1.39890e8	−	3.92928e8i	−0.0230483	−	0.0647391i
$625$	−5.17247e9			−0.847457
$626$	−4.71013e9	−	2.71939e9i	−0.767401	−	0.443059i
$627$	1.35462e9	−	2.34628e9i	0.219473	−	0.380139i
$628$	7.14534e8	+	1.23761e9i	0.115124	+	0.199400i
$629$			1.13859e10i			1.82427i
$630$	3.57851e9	−	2.06605e9i	0.570177	−	0.329192i
$631$	−1.28333e9	+	7.40928e8i	−0.203345	+	0.117401i	−0.598215	−	0.801336i	$-0.704123\pi$
$631$	−1.28333e9	+	7.40928e8i	−0.203345	+	0.117401i	0.394870	+	0.918737i	$0.370790\pi$
$632$			2.85506e8i			0.0449888i
$633$	1.56949e9	+	2.71843e9i	0.245949	+	0.425996i
$634$	1.07942e9	−	1.86961e9i	0.168220	−	0.291366i
$635$	4.47014e9	+	2.58084e9i	0.692809	+	0.399993i
$636$	−7.18164e8			−0.110694
$637$	7.27460e8	−	8.54663e8i	0.111512	−	0.131011i
$638$	3.31965e9			0.506080
$639$	4.68060e9	+	2.70234e9i	0.709657	+	0.409721i
$640$	2.72670e8	−	4.72279e8i	0.0411157	−	0.0712145i
$641$	4.76707e9	+	8.25681e9i	0.714906	+	1.23825i	0.962996	+	0.269516i	$0.0868637\pi$
$641$	4.76707e9	+	8.25681e9i	0.714906	+	1.23825i	−0.248090	+	0.968737i	$0.579803\pi$
$642$		−	7.32928e8i		−	0.109317i
$643$	6.04531e9	−	3.49026e9i	0.896769	−	0.517750i	0.0206182	−	0.999787i	$-0.493437\pi$
$643$	6.04531e9	−	3.49026e9i	0.896769	−	0.517750i	0.876150	+	0.482038i	$0.160103\pi$
$644$	−9.97253e8	+	5.75764e8i	−0.147131	+	0.0849462i
$645$			8.62774e8i			0.126601i
$646$	6.09280e9	+	1.05530e10i	0.889208	+	1.54015i
$647$	2.53199e9	−	4.38553e9i	0.367534	−	0.636587i	−0.621646	−	0.783298i	$-0.713536\pi$
$647$	2.53199e9	−	4.38553e9i	0.367534	−	0.636587i	0.989179	+	0.146712i	$0.0468690\pi$
$648$	1.65217e9	+	9.53882e8i	0.238530	+	0.137715i
$649$	−5.38679e9			−0.773523
$650$	−5.06938e8	−	4.31488e8i	−0.0724032	−	0.0616272i
$651$	−2.68497e9			−0.381422
$652$	5.70527e7	+	3.29394e7i	0.00806138	+	0.00465424i
$653$	2.96517e9	−	5.13582e9i	0.416728	−	0.721794i	−0.578880	−	0.815413i	$-0.696510\pi$
$653$	2.96517e9	−	5.13582e9i	0.416728	−	0.721794i	0.995608	+	0.0936184i	$0.0298433\pi$
$654$	−1.00822e9	−	1.74628e9i	−0.140939	−	0.244114i
$655$			2.25479e9i			0.313517i
$656$	2.26565e9	−	1.30807e9i	0.313350	−	0.180913i
$657$	3.15784e9	−	1.82318e9i	0.434422	−	0.250814i
$658$			6.08984e9i			0.833327i
$659$	−6.94879e8	−	1.20357e9i	−0.0945823	−	0.163821i	0.814852	−	0.579669i	$-0.196818\pi$
$659$	−6.94879e8	−	1.20357e9i	−0.0945823	−	0.163821i	−0.909434	+	0.415848i	$0.863485\pi$
$660$	−5.05440e8	+	8.75447e8i	−0.0684330	+	0.118529i
$661$	−4.74362e9	−	2.73873e9i	−0.638859	−	0.368845i	0.145316	−	0.989385i	$-0.453580\pi$
$661$	−4.74362e9	−	2.73873e9i	−0.638859	−	0.368845i	−0.784175	+	0.620540i	$0.786913\pi$
$662$	2.99851e8			0.0401701
$663$	−3.42025e9	−	6.27938e8i	−0.455785	−	0.0836796i
$664$	4.84101e9			0.641723
$665$	−9.86848e9	−	5.69757e9i	−1.30129	−	0.751301i
$666$	2.69628e9	−	4.67009e9i	0.353675	−	0.612584i
$667$	8.04146e8	+	1.39282e9i	0.104929	+	0.181742i
$668$			6.12414e9i			0.794927i
$669$	5.06078e8	−	2.92184e8i	0.0653470	−	0.0377281i
$670$	3.93319e9	−	2.27083e9i	0.505223	−	0.291690i
$671$			1.33839e9i			0.171023i
$672$	−2.06919e8	−	3.58394e8i	−0.0263031	−	0.0455583i
$673$	1.12983e9	−	1.95691e9i	0.142876	−	0.247468i	−0.785703	−	0.618604i	$-0.787698\pi$
$673$	1.12983e9	−	1.95691e9i	0.142876	−	0.247468i	0.928578	+	0.371136i	$0.121032\pi$
$674$	−5.82563e9	−	3.36343e9i	−0.732881	−	0.423129i
$675$	−5.68343e8			−0.0711291
$676$	6.41608e8	+	3.96432e9i	0.0798834	+	0.493577i
$677$	1.09058e10			1.35082			0.675411	−	0.737441i	$-0.263966\pi$
$677$	1.09058e10			1.35082			0.675411	+	0.737441i	$0.263966\pi$
$678$	−7.75275e8	−	4.47605e8i	−0.0955326	−	0.0551558i
$679$	−6.71072e9	+	1.16233e10i	−0.822669	+	1.42490i
$680$	−2.27336e9	−	3.93757e9i	−0.277260	−	0.480228i
$681$			1.57960e9i			0.191661i
$682$	−6.95981e9	+	4.01825e9i	−0.840141	+	0.485056i
$683$	2.12684e9	−	1.22793e9i	0.255425	−	0.147470i	−0.366821	−	0.930292i	$-0.619554\pi$
$683$	2.12684e9	−	1.22793e9i	0.255425	−	0.147470i	0.622246	+	0.782822i	$0.286220\pi$
$684$		−	5.77132e9i		−	0.689571i
$685$	−3.14912e9	−	5.45444e9i	−0.374345	−	0.648385i
$686$	−2.67959e9	+	4.64119e9i	−0.316909	+	0.548903i
$687$	2.13193e9	+	1.23087e9i	0.250856	+	0.144832i
$688$	−1.05719e9			−0.123764
$689$	6.80114e9	+	1.24865e9i	0.792163	+	0.145436i
$690$	−4.89748e8			−0.0567545
$691$	−6.29624e9	−	3.63513e9i	−0.725952	−	0.419129i	0.0909875	−	0.995852i	$-0.470998\pi$
$691$	−6.29624e9	−	3.63513e9i	−0.725952	−	0.419129i	−0.816939	+	0.576723i	$0.804331\pi$
$692$	9.69611e7	−	1.67942e8i	0.0111231	−	0.0192658i
$693$	−4.69278e9	−	8.12813e9i	−0.535628	−	0.927736i
$694$			1.85734e9i			0.210927i
$695$	2.46726e9	−	1.42448e9i	0.278785	−	0.160956i
$696$	−5.00553e8	+	2.88995e8i	−0.0562753	+	0.0324906i
$697$		−	2.18118e10i		−	2.43993i
$698$	5.16437e9	+	8.94495e9i	0.574809	+	0.995598i
$699$	−8.62401e8	+	1.49372e9i	−0.0955079	+	0.165424i
$700$	−5.72029e8	−	3.30261e8i	−0.0630340	−	0.0363927i
$701$	4.48759e9			0.492040			0.246020	−	0.969265i	$-0.420877\pi$
$701$	4.48759e9			0.492040			0.246020	+	0.969265i	$0.420877\pi$
$702$	2.61084e9	+	2.22226e9i	0.284840	+	0.242446i
$703$	−1.48711e10			−1.61436
$704$	−1.07272e9	−	6.19336e8i	−0.115873	−	0.0668994i
$705$	−1.29501e9	+	2.24303e9i	−0.139191	+	0.241086i
$706$	−3.00298e9	−	5.20131e9i	−0.321170	−	0.556283i
$707$		−	7.84549e9i		−	0.834934i
$708$	8.12248e8	−	4.68951e8i	0.0860146	−	0.0496605i
$709$	4.37884e7	−	2.52812e7i	0.00461420	−	0.00266401i	−0.497691	−	0.867354i	$-0.665819\pi$
$709$	4.37884e7	−	2.52812e7i	0.00461420	−	0.00266401i	0.502305	+	0.864690i	$0.332485\pi$
$710$			5.56122e9i			0.583131i
$711$	−5.63694e8	−	9.76346e8i	−0.0588165	−	0.101873i
$712$	2.31892e9	−	4.01648e9i	0.240772	−	0.417029i
$713$	−3.37187e9	−	1.94675e9i	−0.348383	−	0.201139i
$714$	−3.45032e9			−0.354745
$715$	6.30872e9	−	7.41185e9i	0.645461	−	0.758325i
$716$	4.77068e9			0.485719
$717$	2.70275e8	+	1.56043e8i	0.0273835	+	0.0158099i
$718$	1.64731e9	−	2.85322e9i	0.166088	−	0.287673i
$719$	8.24083e8	+	1.42735e9i	0.0826837	+	0.143212i	0.904402	−	0.426682i	$-0.140318\pi$
$719$	8.24083e8	+	1.42735e9i	0.0826837	+	0.143212i	−0.821718	+	0.569894i	$0.806984\pi$
$720$			2.15341e9i			0.215012i
$721$	6.96463e9	−	4.02103e9i	0.692029	−	0.399543i
$722$	−7.59043e9	+	4.38234e9i	−0.750561	+	0.433337i
$723$		−	3.45668e9i		−	0.340154i
$724$	−4.58037e9	−	7.93343e9i	−0.448555	−	0.776920i
$725$	−4.61262e8	+	7.98929e8i	−0.0449536	+	0.0778619i
$726$	2.52930e8	+	1.46029e8i	0.0245314	+	0.0141632i
$727$	−1.74960e10			−1.68877			−0.844383	−	0.535740i	$-0.820033\pi$
$727$	−1.74960e10			−1.68877			−0.844383	+	0.535740i	$0.820033\pi$
$728$	1.33643e9	+	3.75382e9i	0.128377	+	0.360589i
$729$	−6.01225e9			−0.574765
$730$	3.24930e9	+	1.87598e9i	0.309143	+	0.178484i
$731$	−4.40712e9	+	7.63335e9i	−0.417295	+	0.722777i
$732$	−1.16515e8	−	2.01809e8i	−0.0109797	−	0.0190174i
$733$			8.55734e8i			0.0802555i	0.999195	+	0.0401277i	$0.0127765\pi$
$733$			8.55734e8i			0.0802555i	−0.999195	+	0.0401277i	$0.987224\pi$
$734$	−2.70992e9	+	1.56457e9i	−0.252942	+	0.146036i
$735$	4.10162e8	−	2.36807e8i	0.0381022	−	0.0219983i
$736$		−	6.00108e8i		−	0.0554827i
$737$	−5.15790e9	−	8.93374e9i	−0.474610	−	0.822048i
$738$	−5.16524e9	+	8.94646e9i	−0.473035	+	0.819321i
$739$	1.85748e10	+	1.07241e10i	1.69304	+	0.977478i	0.952040	+	0.305974i	$0.0989822\pi$
$739$	1.85748e10	+	1.07241e10i	1.69304	+	0.977478i	0.741001	+	0.671503i	$0.234351\pi$
$740$	5.54874e9			0.503365
$741$	8.20151e8	−	4.46719e9i	0.0740509	−	0.403340i
$742$	6.86094e9			0.616552
$743$	8.00674e9	+	4.62270e9i	0.716135	+	0.413461i	0.813329	−	0.581805i	$-0.197653\pi$
$743$	8.00674e9	+	4.62270e9i	0.716135	+	0.413461i	−0.0971933	+	0.995266i	$0.530986\pi$
$744$	6.99624e8	−	1.21178e9i	0.0622816	−	0.107875i
$745$	4.76509e8	+	8.25338e8i	0.0422206	+	0.0731282i
$746$		−	5.25122e8i		−	0.0463099i
$747$	−1.65549e10	+	9.55795e9i	−1.45313	+	0.838962i
$748$	−8.94370e9	+	5.16365e9i	−0.781379	+	0.451129i
$749$			7.00199e9i			0.608885i
$750$	−1.18507e9	−	2.05260e9i	−0.102572	−	0.177660i
$751$	5.52066e9	−	9.56207e9i	0.475611	−	0.823782i	−0.523999	−	0.851719i	$-0.675560\pi$
$751$	5.52066e9	−	9.56207e9i	0.475611	−	0.823782i	0.999610	+	0.0279370i	$0.00889379\pi$
$752$	−2.74847e9	−	1.58683e9i	−0.235684	−	0.136072i
$753$	4.50334e9			0.384372
$754$	5.24280e9	−	1.86653e9i	0.445414	−	0.158576i
$755$	−1.88355e10			−1.59281
$756$	2.94607e9	+	1.70092e9i	0.247980	+	0.143172i
$757$	−9.81968e8	+	1.70082e9i	−0.0822738	+	0.142502i	−0.904226	−	0.427054i	$-0.859552\pi$
$757$	−9.81968e8	+	1.70082e9i	−0.0822738	+	0.142502i	0.821952	+	0.569556i	$0.192885\pi$
$758$	3.91086e9	+	6.77382e9i	0.326160	+	0.564926i
$759$			1.11240e9i			0.0923453i
$760$	5.14287e9	−	2.96924e9i	0.424970	−	0.245356i
$761$	1.21091e10	−	6.99121e9i	0.996017	−	0.575050i	0.0889494	−	0.996036i	$-0.471649\pi$
$761$	1.21091e10	−	6.99121e9i	0.996017	−	0.575050i	0.907067	+	0.420986i	$0.138316\pi$
$762$			2.04130e9i			0.167134i
$763$	9.63196e9	+	1.66830e10i	0.785016	+	1.35969i
$764$	−1.93394e9	+	3.34968e9i	−0.156898	+	0.271755i
$765$	1.55484e10	+	8.97690e9i	1.25566	+	0.724955i
$766$	1.13632e10			0.913482
$767$	−8.50749e9	+	3.02882e9i	−0.680797	+	0.242376i
$768$	2.15667e8			0.0171799
$769$	1.81759e10	+	1.04939e10i	1.44130	+	0.832135i	0.997937	−	0.0642071i	$-0.0204518\pi$
$769$	1.81759e10	+	1.04939e10i	1.44130	+	0.832135i	0.443363	+	0.896342i	$0.353785\pi$
$770$	4.82869e9	−	8.36354e9i	0.381164	−	0.660195i
$771$	1.14750e9	+	1.98753e9i	0.0901700	+	0.156179i
$772$		−	1.09023e10i		−	0.852819i
$773$	−1.53997e10	+	8.89103e9i	−1.19918	+	0.692347i	−0.960372	−	0.278720i	$-0.910090\pi$
$773$	−1.53997e10	+	8.89103e9i	−1.19918	+	0.692347i	−0.238807	+	0.971067i	$0.576756\pi$
$774$	3.61529e9	−	2.08729e9i	0.280253	−	0.161804i
$775$		−	2.23333e9i		−	0.172344i
$776$	−3.49723e9	−	6.05738e9i	−0.268663	−	0.465339i
$777$	2.10536e9	−	3.64659e9i	0.161010	−	0.278877i
$778$	−1.28852e10	−	7.43929e9i	−0.980988	−	0.566374i
$779$	2.84885e10			2.15918
$780$	−3.06016e8	+	1.66681e9i	−0.0230894	+	0.125763i
$781$	1.26316e10			0.948812
$782$	−4.33302e9	−	2.50167e9i	−0.324016	−	0.187071i
$783$	2.37560e9	−	4.11466e9i	0.176851	−	0.306315i
$784$	2.90170e8	+	5.02589e8i	0.0215053	+	0.0372483i
$785$		−	5.80645e9i		−	0.428417i
$786$	−7.72242e8	+	4.45854e8i	−0.0567250	+	0.0327502i
$787$	−9.21097e9	+	5.31796e9i	−0.673587	+	0.388896i	−0.797434	−	0.603406i	$-0.793810\pi$
$787$	−9.21097e9	+	5.31796e9i	−0.673587	+	0.388896i	0.123847	+	0.992301i	$0.460477\pi$
$788$			1.52852e9i			0.111283i
$789$	3.28794e9	+	5.69487e9i	0.238316	+	0.412776i
$790$	5.80019e8	−	1.00462e9i	0.0418550	−	0.0724950i
$791$	7.40655e9	+	4.27617e9i	0.532106	+	0.307211i
$792$	4.89120e9			0.349846
$793$	7.52534e8	+	2.11375e9i	0.0535883	+	0.150521i
$794$	−7.20595e6			−0.000510881
$795$	2.52704e9	+	1.45899e9i	0.178372	+	0.102983i
$796$	−1.74285e9	+	3.01870e9i	−0.122480	+	0.212141i
$797$	−8.23983e9	−	1.42718e10i	−0.576519	−	0.998561i	−0.995875	−	0.0907388i	$-0.971077\pi$
$797$	−8.23983e9	−	1.42718e10i	−0.576519	−	0.998561i	0.419355	−	0.907822i	$-0.362256\pi$
$798$		−	4.50647e9i		−	0.313925i
$799$	−2.29151e10	+	1.32300e10i	−1.58931	+	0.917587i
$800$	2.98108e8	−	1.72112e8i	0.0205853	−	0.0118850i
$801$			1.83136e10i			1.25910i
$802$	2.23807e9	+	3.87646e9i	0.153202	+	0.265353i
$803$	4.26106e9	−	7.38038e9i	0.290411	−	0.503007i
$804$	1.55547e9	+	8.98051e8i	0.105552	+	0.0609403i
$805$	4.67878e9			0.316116
$806$	−8.73246e9	+	1.02594e10i	−0.587441	+	0.690160i
$807$	2.24859e9			0.150609
$808$	3.54083e9	+	2.04430e9i	0.236138	+	0.136334i
$809$	−9.76107e9	+	1.69067e10i	−0.648153	+	1.12263i	0.335411	+	0.942072i	$0.391125\pi$
$809$	−9.76107e9	+	1.69067e10i	−0.648153	+	1.12263i	−0.983564	+	0.180562i	$0.942208\pi$
$810$	−3.87572e9	−	6.71294e9i	−0.256245	−	0.443829i
$811$			2.83592e7i			0.00186690i	1.00000		0.000933451i	$0.000297127\pi$
$811$			2.83592e7i			0.00186690i	−1.00000		0.000933451i	$0.999703\pi$
$812$	4.78201e9	−	2.76090e9i	0.313447	−	0.180969i
$813$	−2.83800e9	+	1.63852e9i	−0.185223	+	0.106939i
$814$		−	1.26033e10i		−	0.819026i
$815$	−1.33836e8	−	2.31811e8i	−0.00866007	−	0.0149997i
$816$	8.99052e8	−	1.55720e9i	0.0579254	−	0.100330i
$817$	−9.96993e9	−	5.75614e9i	−0.639610	−	0.369279i
$818$	−2.68335e9			−0.171412
$819$	−1.19816e10	−	1.01984e10i	−0.762117	−	0.648689i
$820$	−1.06297e10			−0.673243
$821$	−1.82861e10	−	1.05575e10i	−1.15324	−	0.665823i	−0.203565	−	0.979062i	$-0.565253\pi$
$821$	−1.82861e10	−	1.05575e10i	−1.15324	−	0.665823i	−0.949674	+	0.313239i	$0.898586\pi$
$822$	1.24539e9	−	2.15708e9i	0.0782087	−	0.135461i
$823$	−7.32448e9	−	1.26864e10i	−0.458013	−	0.793301i	0.540843	−	0.841123i	$-0.318105\pi$
$823$	−7.32448e9	−	1.26864e10i	−0.458013	−	0.793301i	−0.998856	+	0.0478223i	$0.984772\pi$
$824$			4.19104e9i			0.260962i
$825$	−5.52592e8	+	3.19039e8i	−0.0342622	+	0.0197813i
$826$	−7.75977e9	+	4.48010e9i	−0.479092	+	0.276604i
$827$			9.09426e9i			0.559111i	0.960130	+	0.279555i	$0.0901871\pi$
$827$			9.09426e9i			0.559111i	−0.960130	+	0.279555i	$0.909813\pi$
$828$	1.18484e9	+	2.05220e9i	0.0725357	+	0.125636i
$829$	6.90809e9	−	1.19652e10i	0.421131	−	0.729421i	−0.574919	−	0.818210i	$-0.694967\pi$
$829$	6.90809e9	−	1.19652e10i	0.421131	−	0.729421i	0.996050	+	0.0887895i	$0.0282999\pi$
$830$	−1.70343e10	−	9.83477e9i	−1.03407	−	0.597023i
$831$	−5.52081e9			−0.333733
$832$	−2.04241e9	−	3.74975e8i	−0.122945	−	0.0225720i
$833$	4.83852e9			0.290038
$834$	9.75737e8	+	5.63342e8i	0.0582440	+	0.0336272i
$835$	1.24415e10	−	2.15493e10i	0.739555	−	1.28095i
$836$	−6.74425e9	−	1.16814e10i	−0.399219	−	0.691468i
$837$			1.15021e10i			0.678015i
$838$	8.09537e9	−	4.67387e9i	0.475207	−	0.274361i
$839$	3.11865e8	−	1.80055e8i	0.0182305	−	0.0105254i	−0.490857	−	0.871240i	$-0.663316\pi$
$839$	3.11865e8	−	1.80055e8i	0.0182305	−	0.0105254i	0.509088	+	0.860715i	$0.329983\pi$
$840$			1.68146e9i			0.0978836i
$841$	4.76891e9	+	8.25999e9i	0.276460	+	0.478844i
$842$	7.17911e9	−	1.24346e10i	0.414456	−	0.717859i
$843$	−3.14247e9	−	1.81431e9i	−0.180665	−	0.104307i
$844$	1.56280e10			0.894757
$845$	5.79606e9	−	1.52529e10i	0.330472	−	0.869670i
$846$	1.25320e10			0.711579
$847$	−2.41635e9	−	1.39508e9i	−0.136637	−	0.0788874i
$848$	−1.78776e9	+	3.09649e9i	−0.100675	+	0.174375i
$849$	−3.29768e9	−	5.71175e9i	−0.184940	−	0.320326i
$850$		−	2.86994e9i		−	0.160290i
$851$	5.28794e9	−	3.05299e9i	0.294126	−	0.169814i
$852$	−1.90466e9	+	1.09966e9i	−0.105506	+	0.0609142i
$853$		−	1.37086e9i		−	0.0756263i	−0.999285	−	0.0378132i	$-0.987961\pi$
$853$		−	1.37086e9i		−	0.0756263i	0.999285	−	0.0378132i	$-0.0120392\pi$
$854$	1.11312e9	+	1.92797e9i	0.0611558	+	0.105925i
$855$	−1.17247e10	+	2.03079e10i	−0.641537	+	1.11118i
$856$	−3.16015e9	−	1.82451e9i	−0.172206	−	0.0994234i
$857$	−1.13418e10			−0.615529			−0.307765	−	0.951463i	$-0.599581\pi$
$857$	−1.13418e10			−0.615529			−0.307765	+	0.951463i	$0.599581\pi$
$858$	3.78595e9	+	6.95078e8i	0.204630	+	0.0375688i
$859$	−2.65647e9			−0.142997			−0.0714987	−	0.997441i	$-0.522778\pi$
$859$	−2.65647e9			−0.142997			−0.0714987	+	0.997441i	$0.522778\pi$
$860$	3.72000e9	+	2.14774e9i	0.199434	+	0.115143i
$861$	−4.03322e9	+	6.98574e9i	−0.215348	+	0.372994i
$862$	−8.43245e9	−	1.46054e10i	−0.448413	−	0.776675i
$863$		−	1.15900e10i		−	0.613827i	−0.951737	−	0.306914i	$-0.900704\pi$
$863$		−	1.15900e10i		−	0.613827i	0.951737	−	0.306914i	$-0.0992962\pi$
$864$	−1.53532e9	+	8.86417e8i	−0.0809843	+	0.0467563i
$865$	−6.82364e8	+	3.93963e8i	−0.0358476	+	0.0206966i
$866$			2.47421e10i			1.29457i
$867$	−4.85834e9	−	8.41489e9i	−0.253175	−	0.438512i
$868$	−6.68382e9	+	1.15767e10i	−0.346901	+	0.600851i
$869$	−2.28188e9	−	1.31744e9i	−0.117957	−	0.0681023i
$870$	2.34843e9			0.120909
$871$	−1.31692e10	−	1.12092e10i	−0.675297	−	0.574790i
$872$	−1.00392e10			−0.512734
$873$	2.39190e10	+	1.38097e10i	1.21673	+	0.702479i
$874$	3.26743e9	−	5.65936e9i	0.165545	−	0.286733i
$875$	1.13215e10	+	1.96094e10i	0.571314	+	0.989545i
$876$			1.48380e9i			0.0745782i
$877$	6.14451e8	−	3.54754e8i	0.0307602	−	0.0177594i	−0.484541	−	0.874769i	$-0.661013\pi$
$877$	6.14451e8	−	3.54754e8i	0.0307602	−	0.0177594i	0.515301	+	0.857009i	$0.327680\pi$
$878$	6.88351e9	−	3.97420e9i	0.343225	−	0.198161i
$879$			1.80814e9i			0.0897990i
$880$	2.51643e9	+	4.35858e9i	0.124479	+	0.215603i
$881$	1.62798e10	−	2.81974e10i	0.802109	−	1.38929i	−0.116117	−	0.993236i	$-0.537045\pi$
$881$	1.62798e10	−	2.81974e10i	0.802109	−	1.38929i	0.918226	−	0.396058i	$-0.129622\pi$
$882$	−1.98459e9	−	1.14581e9i	−0.0973939	−	0.0562304i
$883$	3.63549e10			1.77705			0.888526	−	0.458827i	$-0.151730\pi$
$883$	3.63549e10			1.77705			0.888526	+	0.458827i	$0.151730\pi$
$884$	−1.12216e10	+	1.31838e10i	−0.546353	+	0.641888i
$885$	−3.81080e9			−0.184805
$886$	1.37546e10	+	7.94123e9i	0.664401	+	0.383592i
$887$	−1.33122e9	+	2.30574e9i	−0.0640497	+	0.110937i	−0.896272	−	0.443505i	$-0.853735\pi$
$887$	−1.33122e9	+	2.30574e9i	−0.0640497	+	0.110937i	0.832222	+	0.554442i	$0.187068\pi$
$888$	1.09719e9	+	1.90039e9i	0.0525818	+	0.0910744i
$889$		−	1.95015e10i		−	0.930918i
$890$	−1.63194e10	+	9.42200e9i	−0.775959	+	0.448000i
$891$	−1.52476e10	+	8.80321e9i	−0.722154	+	0.416936i
$892$		−	2.90939e9i		−	0.137254i
$893$	−1.72798e10	−	2.99295e10i	−0.812004	−	1.40643i
$894$	−1.88446e8	+	3.26399e8i	−0.00882078	+	0.0152780i
$895$	−1.67868e10	−	9.69188e9i	−0.782687	−	0.451885i
$896$	−2.06037e9			−0.0956900
$897$	6.25468e8	+	1.75684e9i	0.0289356	+	0.0812754i
$898$	1.44426e10			0.665546
$899$	1.61687e10	+	9.33502e9i	0.742193	+	0.428506i
$900$	−6.79627e8	+	1.17715e9i	−0.0310758	+	0.0538248i
$901$	1.49052e10	+	2.58166e10i	0.678894	+	1.17588i
$902$			2.41440e10i			1.09543i
$903$	2.82296e9	−	1.62984e9i	0.127584	−	0.0736609i
$904$	−3.85985e9	+	2.22849e9i	−0.173773	+	0.100328i
$905$			3.72210e10i			1.66924i
$906$	−3.72447e9	−	6.45096e9i	−0.166385	−	0.288188i
$907$	9.57186e9	−	1.65789e10i	0.425962	−	0.737788i	−0.570548	−	0.821264i	$-0.693269\pi$
$907$	9.57186e9	−	1.65789e10i	0.425962	−	0.737788i	0.996510	+	0.0834767i	$0.0266024\pi$
$908$	6.81073e9	+	3.93217e9i	0.301921	+	0.174314i
$909$	−1.61448e10			−0.712951
$910$	2.92351e9	−	1.59238e10i	0.128606	−	0.700488i
$911$	2.89170e10			1.26718			0.633590	−	0.773669i	$-0.281580\pi$
$911$	2.89170e10			1.26718			0.633590	+	0.773669i	$0.281580\pi$
$912$	2.03387e9	+	1.17425e9i	0.0887852	+	0.0512601i
$913$	−2.23384e10	+	3.86913e10i	−0.971416	+	1.68254i
$914$	4.19144e9	+	7.25979e9i	0.181573	+	0.314494i
$915$			9.46821e8i			0.0408596i
$916$	1.06142e10	−	6.12814e9i	0.456305	−	0.263448i
$917$	7.37757e9	−	4.25944e9i	0.315952	−	0.182415i
$918$			1.47808e10i			0.630593i
$919$	−1.67964e10	−	2.90922e10i	−0.713857	−	1.23644i	−0.963399	−	0.268072i	$-0.913613\pi$
$919$	−1.67964e10	−	2.90922e10i	−0.713857	−	1.23644i	0.249542	−	0.968364i	$-0.419720\pi$
$920$	−1.21915e9	+	2.11163e9i	−0.0516179	+	0.0894048i
$921$	−6.55861e9	−	3.78661e9i	−0.276632	−	0.159714i
$922$	1.41439e10			0.594307
$923$	1.99494e10	−	7.10237e9i	0.835073	−	0.297302i
$924$	3.81923e9			0.159266
$925$	3.03319e9	+	1.75121e9i	0.126010	+	0.0727516i
$926$	−2.70537e9	+	4.68585e9i	−0.111967	+	0.193932i
$927$	−8.27467e9	−	1.43321e10i	−0.341171	−	0.590925i
$928$			2.87763e9i			0.118200i
$929$	−1.49543e10	+	8.63388e9i	−0.611944	+	0.353306i	−0.773726	−	0.633520i	$-0.781609\pi$
$929$	−1.49543e10	+	8.63388e9i	−0.611944	+	0.353306i	0.161782	+	0.986827i	$0.448276\pi$
$930$	−4.92361e9	+	2.84265e9i	−0.200721	+	0.115886i
$931$			6.31960e9i			0.256665i
$932$	4.29363e9	+	7.43678e9i	0.173728	+	0.300905i
$933$	−5.48781e9	+	9.50517e9i	−0.221214	+	0.383155i
$934$	−2.65175e9	−	1.53099e9i	−0.106492	−	0.0614833i
$935$	4.19609e10			1.67882
$936$	7.72479e9	−	2.75017e9i	0.307908	−	0.109621i
$937$	−2.62551e10			−1.04262			−0.521309	−	0.853368i	$-0.674556\pi$
$937$	−2.62551e10			−1.04262			−0.521309	+	0.853368i	$0.674556\pi$
$938$	−1.48601e10	−	8.57948e9i	−0.587911	−	0.339431i
$939$	−4.36965e9	+	7.56846e9i	−0.172233	+	0.298317i
$940$	6.44746e9	+	1.11673e10i	0.253187	+	0.438533i
$941$			7.23360e9i			0.283003i	0.989938	+	0.141501i	$0.0451930\pi$
$941$			7.23360e9i			0.283003i	−0.989938	+	0.141501i	$0.954807\pi$
$942$	1.98865e9	−	1.14815e9i	0.0775140	−	0.0447527i
$943$	−1.01301e10	+	5.84860e9i	−0.393388	+	0.227123i
$944$		−	4.66953e9i		−	0.180664i
$945$	−6.91100e9	−	1.19702e10i	−0.266397	−	0.461414i
$946$	4.87833e9	−	8.44951e9i	0.187349	−	0.324498i
$947$	1.77645e10	+	1.02564e10i	0.679718	+	0.392436i	0.799749	−	0.600335i	$-0.204966\pi$
$947$	1.77645e10	+	1.02564e10i	0.679718	+	0.392436i	−0.120031	+	0.992770i	$0.538299\pi$
$948$	4.58764e8			0.0174888
$949$	2.57984e9	−	1.40519e10i	0.0979855	−	0.533707i
$950$	3.74843e9			0.141846
$951$	−3.00418e9	−	1.73446e9i	−0.113265	−	0.0653933i
$952$	−8.58904e9	+	1.48767e10i	−0.322638	+	0.558825i
$953$	−2.21981e10	−	3.84483e10i	−0.830791	−	1.43897i	−0.897412	−	0.441193i	$-0.854555\pi$
$953$	−2.21981e10	−	3.84483e10i	−0.830791	−	1.43897i	0.0666215	−	0.997778i	$-0.478778\pi$
$954$		−	1.41188e10i		−	0.526475i
$955$	1.36101e10	−	7.85780e9i	0.505650	−	0.291937i
$956$	1.34561e9	−	7.76891e8i	0.0498102	−	0.0287579i
$957$		−	5.33417e9i		−	0.196732i
$958$	9.71392e9	+	1.68250e10i	0.356957	+	0.618267i
$959$	−1.18978e10	+	2.06076e10i	−0.435613	+	0.754505i
$960$	−7.58880e8	−	4.38140e8i	−0.0276837	−	0.0159832i
$961$	−1.76855e10			−0.642814
$962$	−7.08643e9	−	1.99046e10i	−0.256634	−	0.720845i
$963$	1.44090e10			0.519928
$964$	−1.49041e10	−	8.60487e9i	−0.535840	−	0.309368i
$965$	−2.21485e10	+	3.83624e10i	−0.793413	+	1.37423i
$966$	9.25165e8	+	1.60243e9i	0.0330217	+	0.0571952i
$967$		−	3.43345e10i		−	1.22106i	−0.791992	−	0.610531i	$-0.790956\pi$
$967$		−	3.43345e10i		−	1.22106i	0.791992	−	0.610531i	$-0.209044\pi$
$968$	1.25926e9	−	7.27034e8i	0.0446223	−	0.0257627i
$969$	1.69571e10	−	9.79021e9i	0.598714	−	0.345668i
$970$			2.84192e10i			0.999796i
$971$	1.08499e10	+	1.87925e10i	0.380327	+	0.658747i	0.991109	−	0.133053i	$-0.0424780\pi$
$971$	1.08499e10	+	1.87925e10i	0.380327	+	0.658747i	−0.610781	+	0.791799i	$0.709145\pi$
$972$	5.31906e9	−	9.21288e9i	0.185782	−	0.321783i
$973$	−9.32165e9	−	5.38186e9i	−0.324413	−	0.187300i
$974$	−2.44018e10			−0.846186
$975$	−6.93336e8	+	8.14572e8i	−0.0239567	+	0.0281458i
$976$	−1.16018e9			−0.0399440
$977$	1.87894e10	+	1.08481e10i	0.644589	+	0.372154i	0.786380	−	0.617743i	$-0.211953\pi$
$977$	1.87894e10	+	1.08481e10i	0.644589	+	0.372154i	−0.141791	+	0.989897i	$0.545286\pi$
$978$	5.29286e7	−	9.16750e7i	0.00180927	−	0.00313375i
$979$	2.14009e10	+	3.70674e10i	0.728941	+	1.26256i
$980$		−	2.35798e9i		−	0.0800293i
$981$	3.43312e10	−	1.98211e10i	1.16104	−	0.670327i
$982$	−2.29914e10	+	1.32741e10i	−0.774773	+	0.447315i
$983$		−	4.82500e10i		−	1.62017i	−0.586314	−	0.810084i	$-0.699421\pi$
$983$		−	4.82500e10i		−	1.62017i	0.586314	−	0.810084i	$-0.300579\pi$
$984$	−2.10188e9	−	3.64055e9i	−0.0703273	−	0.121810i
$985$	3.10526e9	−	5.37847e9i	0.103531	−	0.179321i
$986$	2.07776e10	+	1.19960e10i	0.690282	+	0.398535i
$987$	9.78545e9			0.323945
$988$	−1.72194e10	−	1.46566e10i	−0.568028	−	0.483487i
$989$	4.72687e9			0.155377
$990$	−1.72109e10	−	9.93672e9i	−0.563742	−	0.325477i
$991$	4.20077e9	−	7.27595e9i	0.137111	−	0.237483i	−0.789291	−	0.614019i	$-0.789552\pi$
$991$	4.20077e9	−	7.27595e9i	0.137111	−	0.237483i	0.926402	+	0.376536i	$0.122885\pi$
$992$	−3.48321e9	−	6.03310e9i	−0.113289	−	0.196223i
$993$		−	4.81815e8i		−	0.0156156i
$994$	1.81961e10	−	1.05055e10i	0.587659	−	0.339285i
$995$	1.22653e10	−	7.08138e9i	0.394728	−	0.227896i
$996$		−	7.77877e9i		−	0.249461i
$997$	1.83242e10	+	3.17385e10i	0.585588	+	1.01427i	0.994802	+	0.101830i	$0.0324698\pi$
$997$	1.83242e10	+	3.17385e10i	0.585588	+	1.01427i	−0.409213	+	0.912439i	$0.634197\pi$
$998$	3.37095e9	−	5.83865e9i	0.107348	−	0.185933i
$999$	−1.56216e10	−	9.01913e9i	−0.495731	−	0.286210i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.8.e.a.17.2	✓	16
3.2	odd	2		234.8.l.c.199.8		16
4.3	odd	2		208.8.w.b.17.6		16
13.4	even	6		338.8.b.i.337.6		16
13.6	odd	12		338.8.a.n.1.6		8
13.7	odd	12		338.8.a.m.1.6		8
13.9	even	3		338.8.b.i.337.14		16
13.10	even	6	inner	26.8.e.a.23.2	yes	16
39.23	odd	6		234.8.l.c.127.5		16
52.23	odd	6		208.8.w.b.49.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.8.e.a.17.2	✓	16	1.1	even	1	trivial
26.8.e.a.23.2	yes	16	13.10	even	6	inner
208.8.w.b.17.6		16	4.3	odd	2
208.8.w.b.49.6		16	52.23	odd	6
234.8.l.c.127.5		16	39.23	odd	6
234.8.l.c.199.8		16	3.2	odd	2
338.8.a.m.1.6		8	13.7	odd	12
338.8.a.n.1.6		8	13.6	odd	12
338.8.b.i.337.6		16	13.4	even	6
338.8.b.i.337.14		16	13.9	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	26.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.92820 - 4.00000i) q^{2} +(-6.42739 + 11.1326i) q^{3} +(32.0000 + 55.4256i) q^{4} -260.039i q^{5} +(89.0605 - 51.4191i) q^{6} +(-850.835 + 491.230i) q^{7} -512.000i q^{8} +(1010.88 + 1750.89i) q^{9} +(-1040.15 + 1801.60i) q^{10} +(4092.11 + 2362.58i) q^{11} -822.706 q^{12} +(7791.18 + 1430.41i) q^{13} +7859.68 q^{14} +(2894.90 + 1671.37i) q^{15} +(-2048.00 + 3547.24i) q^{16} +(17075.0 + 29574.7i) q^{17} -16174.0i q^{18} +(-38627.6 + 22301.7i) q^{19} +(14412.8 - 8321.24i) q^{20} -12629.3i q^{21} +(-18900.6 - 32736.9i) q^{22} +(9156.93 - 15860.3i) q^{23} +(5699.87 + 3290.82i) q^{24} +10504.9 q^{25} +(-48257.2 - 41074.9i) q^{26} -54102.6 q^{27} +(-54453.5 - 31438.7i) q^{28} +(-43909.2 + 76052.9i) q^{29} +(-13371.0 - 23159.2i) q^{30} -212598. i q^{31} +(28377.9 - 16384.0i) q^{32} +(-52603.2 + 30370.5i) q^{33} -273200. i q^{34} +(127739. + 221250. i) q^{35} +(-64696.1 + 112057. i) q^{36} +(288740. + 166704. i) q^{37} +356827. q^{38} +(-66001.1 + 77542.0i) q^{39} -133140. q^{40} +(-553137. - 319354. i) q^{41} +(-50517.2 + 87498.4i) q^{42} +(129052. + 223524. i) q^{43} +302410. i q^{44} +(455299. - 262867. i) q^{45} +(-126882. + 73255.4i) q^{46} +774821. i q^{47} +(-26326.6 - 45599.0i) q^{48} +(70842.3 - 122702. i) q^{49} +(-72780.2 - 42019.6i) q^{50} -438990. q^{51} +(170036. + 477604. i) q^{52} +872928. q^{53} +(374834. + 216410. i) q^{54} +(614362. - 1.06411e6i) q^{55} +(251510. + 435628. i) q^{56} -573366. i q^{57} +(608423. - 351273. i) q^{58} +(-987288. + 570011. i) q^{59} +213935. i q^{60} +(141624. + 245299. i) q^{61} +(-850394. + 1.47293e6i) q^{62} +(-1.72018e6 - 993146. i) q^{63} -262144. q^{64} +(371963. - 2.02601e6i) q^{65} +485927. q^{66} +(-1.89067e6 - 1.09158e6i) q^{67} +(-1.09280e6 + 1.89278e6i) q^{68} +(117710. + 203880. i) q^{69} -2.04382e6i q^{70} +(2.31512e6 - 1.33663e6i) q^{71} +(896456. - 517569. i) q^{72} -1.80356e6i q^{73} +(-1.33363e6 - 2.30992e6i) q^{74} +(-67519.2 + 116947. i) q^{75} +(-2.47217e6 - 1.42731e6i) q^{76} -4.64228e6 q^{77} +(767437. - 273222. i) q^{78} -557628. q^{79} +(922419. + 532559. i) q^{80} +(-1.86305e6 + 3.22690e6i) q^{81} +(2.55483e6 + 4.42510e6i) q^{82} +9.45510e6i q^{83} +(699987. - 404138. i) q^{84} +(7.69057e6 - 4.44015e6i) q^{85} -2.06483e6i q^{86} +(-564443. - 977644. i) q^{87} +(1.20964e6 - 2.09516e6i) q^{88} +(7.84469e6 + 4.52914e6i) q^{89} -4.20587e6 q^{90} +(-7.33167e6 + 2.61021e6i) q^{91} +1.17209e6 q^{92} +(2.36677e6 + 1.36645e6i) q^{93} +(3.09928e6 - 5.36811e6i) q^{94} +(5.79929e6 + 1.00447e7i) q^{95} +421226. i q^{96} +(1.18308e7 - 6.83053e6i) q^{97} +(-981620. + 566738. i) q^{98} +9.55312e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 512 q^{4} + 2520 q^{7} - 4684 q^{9} + 2432 q^{10} - 8496 q^{11} - 3620 q^{13} + 34560 q^{14} + 51648 q^{15} - 32768 q^{16} + 41520 q^{17} - 54432 q^{19} - 16128 q^{20} - 17280 q^{22} - 7560 q^{23}+ \cdots + 19031040 q^{98}+O(q^{100}) \) 16 * q + 512 * q^4 + 2520 * q^7 - 4684 * q^9 + 2432 * q^10 - 8496 * q^11 - 3620 * q^13 + 34560 * q^14 + 51648 * q^15 - 32768 * q^16 + 41520 * q^17 - 54432 * q^19 - 16128 * q^20 - 17280 * q^22 - 7560 * q^23 - 273960 * q^25 + 51072 * q^26 + 133920 * q^27 + 161280 * q^28 - 346056 * q^29 + 170368 * q^30 + 486300 * q^33 - 283248 * q^35 + 299776 * q^36 - 68280 * q^37 - 1059840 * q^38 - 1122680 * q^39 + 311296 * q^40 - 1288008 * q^41 + 408320 * q^42 + 285360 * q^43 + 5743980 * q^45 - 188928 * q^46 - 2131660 * q^49 + 85248 * q^50 + 957280 * q^51 + 354560 * q^52 + 3666600 * q^53 - 4074624 * q^54 - 1091472 * q^55 + 1105920 * q^56 + 3504000 * q^58 + 1799280 * q^59 - 4626000 * q^61 - 2770560 * q^62 - 8609760 * q^63 - 4194304 * q^64 - 11518020 * q^65 + 7941120 * q^66 - 7094400 * q^67 - 2657280 * q^68 + 18027316 * q^69 + 25958520 * q^71 + 4423680 * q^72 - 1142400 * q^74 - 10898032 * q^75 - 3483648 * q^76 - 20577480 * q^77 - 22023040 * q^78 + 34143488 * q^79 - 1032192 * q^80 - 15745864 * q^81 + 12202240 * q^82 + 17311488 * q^84 + 7123932 * q^85 - 10460440 * q^87 + 1105920 * q^88 + 10609452 * q^89 + 4070656 * q^90 - 38683952 * q^91 - 967680 * q^92 - 52747080 * q^93 - 14303616 * q^94 + 33837504 * q^95 + 83706300 * q^97 + 19031040 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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