LMFDB - Embedded newform 26.8.e.a.23.2

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			23.2
Root			$-12.8548i$ of defining polynomial
Character	$\chi$	$=$	26.23
Dual form			26.8.e.a.17.2

$q$-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 $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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	0.789087	−	0.614281i	$-0.210554\pi$
$3$	−6.42739	−	11.1326i	−0.137439	−	0.238052i	−0.926527	+	0.376229i	$0.877220\pi$
$4$	32.0000	−	55.4256i	0.250000	−	0.433013i
$5$			260.039i			0.930342i	0.885221	+	0.465171i	$0.154007\pi$
$5$			260.039i			0.930342i	−0.885221	+	0.465171i	$0.845993\pi$
$6$	89.0605	+	51.4191i	0.168328	+	0.0971841i
$7$	−850.835	−	491.230i	−0.937567	−	0.541305i	−0.0483703	−	0.998829i	$-0.515403\pi$
$7$	−850.835	−	491.230i	−0.937567	−	0.541305i	−0.889197	+	0.457525i	$0.848736\pi$
$8$			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	0.0411285	−	0.999154i	$-0.486905\pi$
$11$	4092.11	−	2362.58i	0.926985	−	0.535195i	0.885857	+	0.463959i	$0.153571\pi$
$12$	−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	−0.0444865	−	0.999010i	$-0.514165\pi$
$17$	17075.0	−	29574.7i	0.842925	−	1.45999i	0.887411	−	0.460979i	$-0.152501\pi$
$18$			16174.0i			0.653679i
$19$	−38627.6	−	22301.7i	−1.29199	−	0.745932i	−0.312986	−	0.949758i	$-0.601329\pi$
$19$	−38627.6	−	22301.7i	−1.29199	−	0.745932i	−0.979007	+	0.203825i	$0.934663\pi$
$20$	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	0.933760	−	0.357901i	$-0.116507\pi$
$23$	9156.93	+	15860.3i	0.156929	+	0.271808i	−0.776831	+	0.629709i	$0.783174\pi$
$24$	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	0.649034	−	0.760759i	$-0.275173\pi$
$29$	−43909.2	−	76052.9i	−0.334320	−	0.579059i	−0.983354	+	0.181700i	$0.941840\pi$
$30$	−13371.0	+	23159.2i	−0.0904145	+	0.156603i
$31$			212598.i			1.28172i	0.767656	+	0.640862i	$0.221423\pi$
$31$			212598.i			1.28172i	−0.767656	+	0.640862i	$0.778577\pi$
$32$	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	0.0480721	−	0.998844i	$-0.484692\pi$
$37$	288740.	−	166704.i	0.937132	−	0.541054i	0.889060	+	0.457790i	$0.151359\pi$
$38$	356827.			1.05491
$39$	−66001.1	−	77542.0i	−0.178166	−	0.209320i
$40$	−133140.			−0.328926
$41$	−553137.	+	319354.i	−1.25340	+	0.723650i	−0.971783	−	0.235877i	$-0.924204\pi$
$41$	−553137.	+	319354.i	−1.25340	+	0.723650i	−0.281616	+	0.959527i	$0.590870\pi$
$42$	−50517.2	−	87498.4i	−0.105212	−	0.182233i
$43$	129052.	−	223524.i	0.247528	−	0.428732i	−0.715311	−	0.698806i	$-0.753715\pi$
$43$	129052.	−	223524.i	0.247528	−	0.428732i	0.962839	+	0.270075i	$0.0870484\pi$
$44$		−	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	$-0.816800\pi$
$47$		−	774821.i		−	1.08858i	0.838899	−	0.544288i	$-0.183200\pi$
$48$	−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	0.153301	−	0.988180i	$-0.451010\pi$
$59$	−987288.	−	570011.i	−0.625838	−	0.361328i	−0.779138	+	0.626852i	$0.784343\pi$
$60$		−	213935.i		−	0.127865i
$61$	141624.	−	245299.i	0.0798879	−	0.138370i	−0.823314	−	0.567587i	$-0.807877\pi$
$61$	141624.	−	245299.i	0.0798879	−	0.138370i	0.903201	+	0.429217i	$0.141210\pi$
$62$	−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	−0.832157	−	0.554541i	$-0.812894\pi$
$67$	−1.89067e6	+	1.09158e6i	−0.767989	+	0.443399i	0.0641678	+	0.997939i	$0.479561\pi$
$68$	−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	0.832039	−	0.554717i	$-0.187173\pi$
$71$	2.31512e6	+	1.33663e6i	0.767660	+	0.443208i	−0.0643795	+	0.997925i	$0.520507\pi$
$72$	896456.	+	517569.i	0.283051	+	0.163420i
$73$			1.80356e6i			0.542627i	0.962491	+	0.271313i	$0.0874580\pi$
$73$			1.80356e6i			0.542627i	−0.962491	+	0.271313i	$0.912542\pi$
$74$	−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	$-0.637962\pi$
$83$		−	9.45510e6i		−	1.81507i	0.419979	−	0.907534i	$-0.362038\pi$
$84$	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	0.223628	−	0.974675i	$-0.428210\pi$
$89$	7.84469e6	−	4.52914e6i	1.17954	−	0.681005i	0.955907	+	0.293669i	$0.0948765\pi$
$90$	−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	0.983111	−	0.183009i	$-0.0585838\pi$
$97$	1.18308e7	+	6.83053e6i	1.31618	+	0.759895i	0.333065	+	0.942904i	$0.391917\pi$
$98$	−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	0.606242	−	0.795280i	$-0.292676\pi$
$101$	−3.99278e6	−	6.91569e6i	−0.385612	−	0.667899i	−0.991854	+	0.127381i	$0.959343\pi$
$102$	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	0.971683	−	0.236286i	$-0.0759303\pi$
$107$	3.56350e6	+	6.17216e6i	0.281212	+	0.487073i	−0.690472	+	0.723359i	$0.742597\pi$
$108$	−1.73128e6	+	2.99867e6i	−0.132247	+	0.229058i
$109$			1.96078e7i			1.45023i	0.688628	+	0.725115i	$0.258213\pi$
$109$			1.96078e7i			1.45023i	−0.688628	+	0.725115i	$0.741787\pi$
$110$	−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	−0.972310	−	0.233695i	$-0.924918\pi$
$113$	−4.35251e6	+	7.53878e6i	−0.283769	+	0.491503i	0.688541	+	0.725198i	$0.258252\pi$
$114$	−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	0.566926	−	0.823769i	$-0.308133\pi$
$127$	−9.92482e6	−	1.71903e7i	−0.429942	−	0.744681i	−0.996868	+	0.0790877i	$0.974799\pi$
$128$	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	0.806204	−	0.591638i	$-0.201519\pi$
$137$	2.09755e7	+	1.21102e7i	0.696932	+	0.402374i	−0.109272	+	0.994012i	$0.534852\pi$
$138$			1.88336e6i			0.0610039i
$139$	5.47794e6	−	9.48807e6i	0.173008	−	0.299658i	−0.766462	−	0.642289i	$-0.777985\pi$
$139$	5.47794e6	−	9.48807e6i	0.173008	−	0.299658i	0.939470	+	0.342631i	$0.111318\pi$
$140$	−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	0.460183	−	0.887824i	$-0.347784\pi$
$149$	−3.17391e6	−	1.83246e6i	−0.0786035	−	0.0453818i	−0.538787	+	0.842442i	$0.681117\pi$
$150$	935573.	+	540153.i	0.0226338	+	0.0130677i
$151$			7.24335e7i			1.71206i	0.516923	+	0.856032i	$0.327077\pi$
$151$			7.24335e7i			1.71206i	−0.516923	+	0.856032i	$0.672923\pi$
$152$	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	0.508040	−	0.861334i	$-0.330370\pi$
$163$	891448.	+	514678.i	0.0161228	+	0.00930848i	−0.491917	+	0.870642i	$0.663704\pi$
$164$			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	0.385075	−	0.922885i	$-0.374176\pi$
$167$	8.28697e7	−	4.78448e7i	1.37685	−	0.794927i	0.991780	+	0.127958i	$0.0408422\pi$
$168$	−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	−0.876934	−	0.480610i	$-0.840415\pi$
$173$	−1.51502e6	+	2.62409e6i	−0.0222462	+	0.0385316i	0.854688	+	0.519142i	$0.173748\pi$
$174$		−	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	0.999865	−	0.0164130i	$-0.00522464\pi$
$179$	3.72709e7	+	6.45552e7i	0.485719	+	0.841289i	−0.514147	+	0.857702i	$0.671891\pi$
$180$	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	−0.665385	−	0.746500i	$-0.731733\pi$
$191$	3.02178e7	−	5.23388e7i	0.313795	−	0.543509i	0.979181	+	0.202991i	$0.0650661\pi$
$192$	1.68490e6	+	2.91834e6i	0.0171799	+	0.0297564i
$193$	−1.47526e8	+	8.51740e7i	−1.47713	+	0.852819i	−0.999666	−	0.0258353i	$-0.991775\pi$
$193$	−1.47526e8	+	8.51740e7i	−1.47713	+	0.852819i	−0.477459	+	0.878654i	$0.658442\pi$
$194$	−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	−0.400521	−	0.916288i	$-0.631171\pi$
$197$	2.06833e7	−	1.19415e7i	0.192748	−	0.111283i	0.593268	+	0.805005i	$0.297837\pi$
$198$	3.82125e7	+	6.61859e7i	0.349846	+	0.605951i
$199$	2.72320e7	−	4.71673e7i	0.244959	−	0.424282i	−0.717161	−	0.696908i	$-0.754559\pi$
$199$	2.72320e7	−	4.71673e7i	0.244959	−	0.424282i	0.962120	+	0.272626i	$0.0878920\pi$
$200$			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	0.834106	+	0.551605i	$0.185984\pi$
$211$	1.22094e8	+	2.11473e8i	0.894757	+	1.54976i	0.0606511	+	0.998159i	$0.480682\pi$
$212$	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	−0.614133	−	0.789202i	$-0.710494\pi$
$223$	−3.93688e7	+	2.27296e7i	−0.237731	+	0.137254i	0.376403	+	0.926456i	$0.377161\pi$
$224$	−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	0.770551	−	0.637378i	$-0.219981\pi$
$227$	1.06418e8	+	6.14402e7i	0.603842	+	0.348628i	−0.166710	+	0.986006i	$0.553314\pi$
$228$	3.17792e7	+	1.83477e7i	0.177570	+	0.102520i
$229$			1.91504e8i			1.05379i	0.849930	+	0.526895i	$0.176644\pi$
$229$			1.91504e8i			1.05379i	−0.849930	+	0.526895i	$0.823356\pi$
$230$	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	$0.0183180\pi$
$239$			2.42778e7i			0.115032i	−0.998345	+	0.0575158i	$0.981682\pi$
$240$	−1.18575e7	−	6.84593e6i	−0.0553674	−	0.0319664i
$241$	−2.32876e8	−	1.34451e8i	−1.07168	−	0.618735i	−0.143040	−	0.989717i	$-0.545688\pi$
$241$	−2.32876e8	−	1.34451e8i	−1.07168	−	0.618735i	−0.928640	+	0.370982i	$0.879021\pi$
$242$			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	0.269587	+	0.962976i	$0.413113\pi$
$251$	−1.75162e8	+	3.03389e8i	−0.699168	+	1.21099i	−0.968755	+	0.248019i	$0.920221\pi$
$252$			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	0.982122	−	0.188245i	$-0.0602799\pi$
$257$	8.92663e7	+	1.54614e8i	0.328036	+	0.568175i	−0.654086	+	0.756420i	$0.726947\pi$
$258$	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	0.865058	+	0.501671i	$0.167281\pi$
$263$	2.55775e8	+	4.43016e8i	0.866989	+	1.50167i	0.00193085	+	0.999998i	$0.499385\pi$
$264$	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	−0.969871	−	0.243618i	$-0.921666\pi$
$269$	−8.74611e7	+	1.51487e8i	−0.273957	+	0.474507i	0.695915	+	0.718125i	$0.254999\pi$
$270$	5.62751e7	+	9.74713e7i	0.173998	+	0.301373i
$271$	2.20774e8	−	1.27464e8i	0.673837	−	0.389040i	−0.123692	−	0.992321i	$-0.539473\pi$
$271$	2.20774e8	−	1.27464e8i	0.673837	−	0.389040i	0.797529	+	0.603281i	$0.206140\pi$
$272$	−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	−0.384667	−	0.923056i	$-0.625684\pi$
$277$	2.14738e8	−	3.71936e8i	0.607056	−	1.05145i	0.991723	−	0.128397i	$-0.0409830\pi$
$278$			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	$-0.876108\pi$
$281$		−	2.82277e8i		−	0.758933i	0.925205	−	0.379467i	$-0.123892\pi$
$282$	3.98406e7	−	6.90059e7i	0.105792	−	0.183238i
$283$	−2.56533e8	−	4.44328e8i	−0.672808	−	1.16534i	−0.977105	−	0.212760i	$-0.931755\pi$
$283$	−2.56533e8	−	4.44328e8i	−0.672808	−	1.16534i	0.304297	−	0.952577i	$-0.401579\pi$
$284$	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	0.634744	−	0.772722i	$-0.281106\pi$
$293$	1.21814e8	+	7.03295e7i	0.282919	+	0.163343i	−0.351825	+	0.936066i	$0.614439\pi$
$294$			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	$-0.802648\pi$
$307$		−	5.89137e8i		−	1.16207i	0.813879	−	0.581034i	$-0.197352\pi$
$308$	−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	$-0.923541\pi$
$317$		−	2.69855e8i		−	0.475799i	0.971290	−	0.237899i	$-0.0764588\pi$
$318$	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	0.475199	−	0.879878i	$-0.342376\pi$
$331$	−3.24598e7	−	1.87407e7i	−0.0491981	−	0.0284045i	−0.524397	+	0.851474i	$0.675709\pi$
$332$	−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	−0.930913	−	0.365241i	$-0.880986\pi$
$347$	−1.16084e8	+	2.01063e8i	−0.149148	+	0.258332i	0.781765	+	0.623574i	$0.214320\pi$
$348$	3.61243e7	+	6.25692e7i	0.0459486	+	0.0795854i
$349$	−1.11812e9	+	6.45546e8i	−1.40799	+	0.812902i	−0.995194	−	0.0979218i	$-0.968781\pi$
$349$	−1.11812e9	+	6.45546e8i	−1.40799	+	0.812902i	−0.412794	+	0.910824i	$0.635447\pi$
$350$	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	−0.0520974	−	0.998642i	$-0.516591\pi$
$353$	6.50163e8	−	3.75372e8i	0.786703	−	0.454203i	0.838801	+	0.544439i	$0.183257\pi$
$354$	−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	$-0.924529\pi$
$359$		−	4.11826e8i		−	0.469768i	0.972023	−	0.234884i	$-0.0754710\pi$
$360$	−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	0.950618	−	0.310364i	$-0.100451\pi$
$367$	1.95572e8	+	3.38740e8i	0.206526	+	0.357714i	−0.744092	+	0.668077i	$0.767118\pi$
$368$	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	−0.849188	−	0.528091i	$-0.822908\pi$
$373$	3.28201e7	−	5.68461e7i	0.0327461	−	0.0567178i	0.881934	+	0.471373i	$0.156241\pi$
$374$	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	−0.843095	−	0.537764i	$-0.819269\pi$
$379$	−8.46727e8	+	4.88858e8i	−0.798925	+	0.461260i	0.0441699	+	0.999024i	$0.485936\pi$
$380$	−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	−0.177692	−	0.984086i	$-0.556863\pi$
$383$	−1.23010e9	−	7.10200e8i	−1.11878	−	0.645929i	−0.941090	+	0.338157i	$0.890196\pi$
$384$	−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	0.500313	−	0.865845i	$-0.333218\pi$
$397$	780067.	+	450372.i	0.000625698	+	0.000361247i	−0.499687	+	0.866206i	$0.666552\pi$
$398$			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	−0.675757	−	0.737125i	$-0.736183\pi$
$401$	−4.84557e8	+	2.79759e8i	−0.375266	+	0.216660i	0.300490	+	0.953785i	$0.402850\pi$
$402$	−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	0.601282	−	0.799037i	$-0.294657\pi$
$409$	2.90481e8	+	1.67709e8i	0.209936	+	0.121206i	−0.391346	+	0.920244i	$0.627990\pi$
$410$	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	0.604176	−	0.796851i	$-0.293502\pi$
$419$	−5.84233e8	−	1.01192e9i	−0.388005	−	0.672044i	−0.992181	+	0.124807i	$0.960169\pi$
$420$	−1.05091e8	+	1.82024e8i	−0.0692142	+	0.119882i
$421$		−	1.79478e9i		−	1.17226i	−0.810218	−	0.586129i	$-0.800651\pi$
$421$		−	1.79478e9i		−	1.17226i	0.810218	−	0.586129i	$-0.199349\pi$
$422$	−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	0.162588	−	0.986694i	$-0.448016\pi$
$431$	1.82568e9	−	1.05406e9i	1.09838	−	0.634152i	0.935796	+	0.352542i	$0.114683\pi$
$432$	1.10802e8	+	1.91915e8i	0.0661234	+	0.114529i
$433$	−1.54638e9	+	2.67841e9i	−0.915396	+	1.58551i	−0.109075	+	0.994034i	$0.534789\pi$
$433$	−1.54638e9	+	2.67841e9i	−0.915396	+	1.58551i	−0.806321	+	0.591478i	$0.798545\pi$
$434$			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	0.691202	−	0.722662i	$-0.257082\pi$
$439$	−4.96775e8	−	8.60439e8i	−0.280242	−	0.485394i	−0.971444	+	0.237268i	$0.923748\pi$
$440$	−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	0.0336083	−	0.999435i	$-0.489300\pi$
$449$	−1.56346e9	−	9.02662e8i	−0.815124	−	0.470612i	−0.848732	+	0.528823i	$0.822633\pi$
$450$			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	−0.705615	−	0.708595i	$-0.749329\pi$
$457$	−9.07474e8	+	5.23930e8i	−0.444762	+	0.256783i	0.260854	+	0.965378i	$0.415996\pi$
$458$	−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	0.0897697	−	0.995963i	$-0.471387\pi$
$461$	−1.53112e9	−	8.83993e8i	−0.727874	−	0.420238i	−0.817644	+	0.575724i	$0.804720\pi$
$462$	−4.13444e8	−	2.38702e8i	−0.195061	−	0.112618i
$463$			6.76344e8i			0.316690i	0.987384	+	0.158345i	$0.0506158\pi$
$463$			6.76344e8i			0.316690i	−0.987384	+	0.158345i	$0.949384\pi$
$464$	−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	−0.868795	−	0.495172i	$-0.835105\pi$
$479$	−2.10313e9	+	1.21424e9i	−0.874361	+	0.504813i	−0.00556629	+	0.999985i	$0.501772\pi$
$480$	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	0.918801	−	0.394722i	$-0.129159\pi$
$487$	2.64158e9	+	1.52511e9i	1.03636	+	0.598344i	0.117562	+	0.993066i	$0.462492\pi$
$488$	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	0.987018	+	0.160607i	$0.0513453\pi$
$491$	1.65926e9	+	2.87392e9i	0.632599	+	1.09569i	−0.354419	+	0.935087i	$0.615321\pi$
$492$	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	$-0.951489\pi$
$499$		−	8.42737e8i		−	0.303627i	0.988409	−	0.151813i	$-0.0485113\pi$
$500$	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	−0.529497	−	0.848312i	$-0.677619\pi$
$503$	1.34123e9	−	2.32308e9i	0.469911	−	0.813911i	0.999408	+	0.0344015i	$0.0109525\pi$
$504$	−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	−0.571998	−	0.820255i	$-0.693831\pi$
$509$	−4.39240e8	+	2.53595e8i	−0.147635	+	0.0852372i	0.424363	+	0.905492i	$0.360498\pi$
$510$	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	0.963290	+	0.268464i	$0.0865159\pi$
$523$	2.33636e9	+	4.04670e9i	0.714141	+	1.23693i	−0.249149	+	0.968465i	$0.580151\pi$
$524$	−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	$0.186206\pi$
$541$			4.06728e9i			1.10437i	−0.833722	+	0.552184i	$0.813794\pi$
$542$	−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	−0.343305	−	0.939224i	$-0.611546\pi$
$557$	1.21714e9	−	7.02718e8i	0.298434	−	0.172301i	0.641739	+	0.766923i	$0.278213\pi$
$558$	−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	−0.184222	−	0.982885i	$-0.558976\pi$
$563$	3.21421e9	−	5.56717e9i	0.759092	−	1.31479i	0.943314	−	0.331902i	$-0.107690\pi$
$564$			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	−0.999822	−	0.0188725i	$-0.993992\pi$
$569$	−2.26860e9	−	3.92932e9i	−0.516255	−	0.894180i	0.483567	−	0.875307i	$-0.339341\pi$
$570$	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	$-0.999812\pi$
$577$		−	5.44495e6i		−	0.00117999i	1.00000		0.000589995i	$-0.000187801\pi$
$578$	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	−0.997610	−	0.0690915i	$-0.977990\pi$
$587$	−7.03985e9	+	4.06446e9i	−1.43658	+	0.829410i	−0.438970	+	0.898502i	$0.644657\pi$
$588$	−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	$0.0913469\pi$
$593$			2.87467e9i			0.566104i	−0.959105	+	0.283052i	$0.908653\pi$
$594$	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	0.909316	−	0.416106i	$-0.136606\pi$
$601$	5.01845e8	+	8.69221e8i	0.0942994	+	0.163331i	−0.815017	+	0.579438i	$0.803272\pi$
$602$	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	−0.791826	−	0.610747i	$-0.790869\pi$
$607$	7.32899e8	−	1.26942e9i	0.133010	−	0.230380i	0.924835	+	0.380367i	$0.124202\pi$
$608$	−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	0.404811	−	0.914400i	$-0.367337\pi$
$613$	7.97928e9	−	4.60684e9i	1.39911	−	0.807777i	0.994299	+	0.106624i	$0.0340040\pi$
$614$	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	0.464537	−	0.885554i	$-0.346221\pi$
$617$	−4.09033e8	−	2.36155e8i	−0.0701068	−	0.0404762i	−0.534644	+	0.845078i	$0.679554\pi$
$618$	−7.29017e8	−	4.20898e8i	−0.124245	−	0.0717327i
$619$			2.16595e9i			0.367055i	0.983015	+	0.183527i	$0.0587516\pi$
$619$			2.16595e9i			0.367055i	−0.983015	+	0.183527i	$0.941248\pi$
$620$	−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	0.394870	−	0.918737i	$-0.370790\pi$
$631$	−1.28333e9	−	7.40928e8i	−0.203345	−	0.117401i	−0.598215	+	0.801336i	$0.704123\pi$
$632$		−	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	−0.248090	−	0.968737i	$-0.579803\pi$
$641$	4.76707e9	−	8.25681e9i	0.714906	−	1.23825i	0.962996	−	0.269516i	$-0.0868637\pi$
$642$			7.32928e8i			0.109317i
$643$	6.04531e9	+	3.49026e9i	0.896769	+	0.517750i	0.876150	−	0.482038i	$-0.160103\pi$
$643$	6.04531e9	+	3.49026e9i	0.896769	+	0.517750i	0.0206182	+	0.999787i	$0.493437\pi$
$644$	−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	0.989179	−	0.146712i	$-0.0468690\pi$
$647$	2.53199e9	+	4.38553e9i	0.367534	+	0.636587i	−0.621646	+	0.783298i	$0.713536\pi$
$648$	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	0.995608	−	0.0936184i	$-0.0298433\pi$
$653$	2.96517e9	+	5.13582e9i	0.416728	+	0.721794i	−0.578880	+	0.815413i	$0.696510\pi$
$654$	−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	−0.909434	−	0.415848i	$-0.863485\pi$
$659$	−6.94879e8	+	1.20357e9i	−0.0945823	+	0.163821i	0.814852	+	0.579669i	$0.196818\pi$
$660$	−5.05440e8	−	8.75447e8i	−0.0684330	−	0.118529i
$661$	−4.74362e9	+	2.73873e9i	−0.638859	+	0.368845i	−0.784175	−	0.620540i	$-0.786913\pi$
$661$	−4.74362e9	+	2.73873e9i	−0.638859	+	0.368845i	0.145316	+	0.989385i	$0.453580\pi$
$662$	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	0.928578	−	0.371136i	$-0.121032\pi$
$673$	1.12983e9	+	1.95691e9i	0.142876	+	0.247468i	−0.785703	+	0.618604i	$0.787698\pi$
$674$	−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	0.622246	−	0.782822i	$-0.286220\pi$
$683$	2.12684e9	+	1.22793e9i	0.255425	+	0.147470i	−0.366821	+	0.930292i	$0.619554\pi$
$684$			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	−0.816939	−	0.576723i	$-0.804331\pi$
$691$	−6.29624e9	+	3.63513e9i	−0.725952	+	0.419129i	0.0909875	+	0.995852i	$0.470998\pi$
$692$	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	0.502305	−	0.864690i	$-0.332485\pi$
$709$	4.37884e7	+	2.52812e7i	0.00461420	+	0.00266401i	−0.497691	+	0.867354i	$0.665819\pi$
$710$		−	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	−0.821718	−	0.569894i	$-0.806984\pi$
$719$	8.24083e8	−	1.42735e9i	0.0826837	−	0.143212i	0.904402	+	0.426682i	$0.140318\pi$
$720$		−	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	$-0.987224\pi$
$733$		−	8.55734e8i		−	0.0802555i	0.999195	−	0.0401277i	$-0.0127765\pi$
$734$	−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	0.741001	−	0.671503i	$-0.234351\pi$
$739$	1.85748e10	−	1.07241e10i	1.69304	−	0.977478i	0.952040	−	0.305974i	$-0.0989822\pi$
$740$	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	−0.0971933	−	0.995266i	$-0.530986\pi$
$743$	8.00674e9	−	4.62270e9i	0.716135	−	0.413461i	0.813329	+	0.581805i	$0.197653\pi$
$744$	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	0.999610	−	0.0279370i	$-0.00889379\pi$
$751$	5.52066e9	+	9.56207e9i	0.475611	+	0.823782i	−0.523999	+	0.851719i	$0.675560\pi$
$752$	−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	0.821952	−	0.569556i	$-0.192885\pi$
$757$	−9.81968e8	−	1.70082e9i	−0.0822738	−	0.142502i	−0.904226	+	0.427054i	$0.859552\pi$
$758$	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	0.907067	−	0.420986i	$-0.138316\pi$
$761$	1.21091e10	+	6.99121e9i	0.996017	+	0.575050i	0.0889494	+	0.996036i	$0.471649\pi$
$762$		−	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	0.443363	−	0.896342i	$-0.353785\pi$
$769$	1.81759e10	−	1.04939e10i	1.44130	−	0.832135i	0.997937	+	0.0642071i	$0.0204518\pi$
$770$	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	−0.238807	−	0.971067i	$-0.576756\pi$
$773$	−1.53997e10	−	8.89103e9i	−1.19918	−	0.692347i	−0.960372	+	0.278720i	$0.910090\pi$
$774$	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	0.123847	−	0.992301i	$-0.460477\pi$
$787$	−9.21097e9	−	5.31796e9i	−0.673587	−	0.388896i	−0.797434	+	0.603406i	$0.793810\pi$
$788$		−	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	0.419355	+	0.907822i	$0.362256\pi$
$797$	−8.23983e9	+	1.42718e10i	−0.576519	+	0.998561i	−0.995875	+	0.0907388i	$0.971077\pi$
$798$			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	−0.983564	−	0.180562i	$-0.942208\pi$
$809$	−9.76107e9	−	1.69067e10i	−0.648153	−	1.12263i	0.335411	−	0.942072i	$-0.391125\pi$
$810$	−3.87572e9	+	6.71294e9i	−0.256245	+	0.443829i
$811$		−	2.83592e7i		−	0.00186690i	−1.00000		0.000933451i	$-0.999703\pi$
$811$		−	2.83592e7i		−	0.00186690i	1.00000		0.000933451i	$-0.000297127\pi$
$812$	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	−0.949674	−	0.313239i	$-0.898586\pi$
$821$	−1.82861e10	+	1.05575e10i	−1.15324	+	0.665823i	−0.203565	+	0.979062i	$0.565253\pi$
$822$	1.24539e9	+	2.15708e9i	0.0782087	+	0.135461i
$823$	−7.32448e9	+	1.26864e10i	−0.458013	+	0.793301i	−0.998856	−	0.0478223i	$-0.984772\pi$
$823$	−7.32448e9	+	1.26864e10i	−0.458013	+	0.793301i	0.540843	+	0.841123i	$0.318105\pi$
$824$		−	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	$-0.909813\pi$
$827$		−	9.09426e9i		−	0.559111i	0.960130	−	0.279555i	$-0.0901871\pi$
$828$	1.18484e9	−	2.05220e9i	0.0725357	−	0.125636i
$829$	6.90809e9	+	1.19652e10i	0.421131	+	0.729421i	0.996050	−	0.0887895i	$-0.0282999\pi$
$829$	6.90809e9	+	1.19652e10i	0.421131	+	0.729421i	−0.574919	+	0.818210i	$0.694967\pi$
$830$	−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	0.509088	−	0.860715i	$-0.329983\pi$
$839$	3.11865e8	+	1.80055e8i	0.0182305	+	0.0105254i	−0.490857	+	0.871240i	$0.663316\pi$
$840$		−	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	$0.0120392\pi$
$853$			1.37086e9i			0.0756263i	−0.999285	+	0.0378132i	$0.987961\pi$
$854$	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	$0.0992962\pi$
$863$			1.15900e10i			0.613827i	−0.951737	+	0.306914i	$0.900704\pi$
$864$	−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	0.515301	−	0.857009i	$-0.327680\pi$
$877$	6.14451e8	+	3.54754e8i	0.0307602	+	0.0177594i	−0.484541	+	0.874769i	$0.661013\pi$
$878$	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	0.918226	+	0.396058i	$0.129622\pi$
$881$	1.62798e10	+	2.81974e10i	0.802109	+	1.38929i	−0.116117	+	0.993236i	$0.537045\pi$
$882$	−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	0.832222	−	0.554442i	$-0.187068\pi$
$887$	−1.33122e9	−	2.30574e9i	−0.0640497	−	0.110937i	−0.896272	+	0.443505i	$0.853735\pi$
$888$	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	0.996510	−	0.0834767i	$-0.0266024\pi$
$907$	9.57186e9	+	1.65789e10i	0.425962	+	0.737788i	−0.570548	+	0.821264i	$0.693269\pi$
$908$	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	0.249542	+	0.968364i	$0.419720\pi$
$919$	−1.67964e10	+	2.90922e10i	−0.713857	+	1.23644i	−0.963399	+	0.268072i	$0.913613\pi$
$920$	−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	0.161782	−	0.986827i	$-0.448276\pi$
$929$	−1.49543e10	−	8.63388e9i	−0.611944	−	0.353306i	−0.773726	+	0.633520i	$0.781609\pi$
$930$	−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	$-0.954807\pi$
$941$		−	7.23360e9i		−	0.283003i	0.989938	−	0.141501i	$-0.0451930\pi$
$942$	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	−0.120031	−	0.992770i	$-0.538299\pi$
$947$	1.77645e10	−	1.02564e10i	0.679718	−	0.392436i	0.799749	+	0.600335i	$0.204966\pi$
$948$	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	0.0666215	+	0.997778i	$0.478778\pi$
$953$	−2.21981e10	+	3.84483e10i	−0.830791	+	1.43897i	−0.897412	+	0.441193i	$0.854555\pi$
$954$			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	$0.209044\pi$
$967$			3.43345e10i			1.22106i	−0.791992	+	0.610531i	$0.790956\pi$
$968$	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	−0.610781	−	0.791799i	$-0.709145\pi$
$971$	1.08499e10	−	1.87925e10i	0.380327	−	0.658747i	0.991109	+	0.133053i	$0.0424780\pi$
$972$	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	−0.141791	−	0.989897i	$-0.545286\pi$
$977$	1.87894e10	−	1.08481e10i	0.644589	−	0.372154i	0.786380	+	0.617743i	$0.211953\pi$
$978$	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	$0.300579\pi$
$983$			4.82500e10i			1.62017i	−0.586314	+	0.810084i	$0.699421\pi$
$984$	−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	0.926402	−	0.376536i	$-0.122885\pi$
$991$	4.20077e9	+	7.27595e9i	0.137111	+	0.237483i	−0.789291	+	0.614019i	$0.789552\pi$
$992$	−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	−0.409213	−	0.912439i	$-0.634197\pi$
$997$	1.83242e10	−	3.17385e10i	0.585588	−	1.01427i	0.994802	−	0.101830i	$-0.0324698\pi$
$998$	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.23.2	yes	16
3.2	odd	2		234.8.l.c.127.5		16
4.3	odd	2		208.8.w.b.49.6		16
13.2	odd	12		338.8.a.m.1.6		8
13.3	even	3		338.8.b.i.337.6		16
13.4	even	6	inner	26.8.e.a.17.2	✓	16
13.10	even	6		338.8.b.i.337.14		16
13.11	odd	12		338.8.a.n.1.6		8
39.17	odd	6		234.8.l.c.199.8		16
52.43	odd	6		208.8.w.b.17.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.8.e.a.17.2	✓	16	13.4	even	6	inner
26.8.e.a.23.2	yes	16	1.1	even	1	trivial
208.8.w.b.17.6		16	52.43	odd	6
208.8.w.b.49.6		16	4.3	odd	2
234.8.l.c.127.5		16	3.2	odd	2
234.8.l.c.199.8		16	39.17	odd	6
338.8.a.m.1.6		8	13.2	odd	12
338.8.a.n.1.6		8	13.11	odd	12
338.8.b.i.337.6		16	13.3	even	3
338.8.b.i.337.14		16	13.10	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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