LMFDB - Embedded newform 13.8.e.a.10.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,8,Mod(4,13)] 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("13.4"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	13.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:	$4.06100533129$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 1279 x^{12} + 629380 x^{10} + 148562016 x^{8} + 16872573312 x^{6} + 790180980480 x^{4} + \cdots + 4669637050368 $ x^14 + 1279x^12 + 629380x^10 + 148562016x^8 + 16872573312x^6 + 790180980480x^4 + 10484997239808x^2 + 4669637050368
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{3}\cdot 13^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.1
Root			$16.7657i$ of defining polynomial
Character	$\chi$	$=$	13.10
Dual form			13.8.e.a.4.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-14.5196 + 8.38287i) q^{2} +(40.5114 + 70.1679i) q^{3} +(76.5449 - 132.580i) q^{4} +223.318i q^{5} +(-1176.42 - 679.204i) q^{6} +(-577.559 - 333.454i) q^{7} +420.649i q^{8} +(-2188.85 + 3791.20i) q^{9} +(-1872.05 - 3242.48i) q^{10} +(6573.82 - 3795.40i) q^{11} +12403.8 q^{12} +(-6519.11 + 4499.97i) q^{13} +11181.2 q^{14} +(-15669.7 + 9046.93i) q^{15} +(6271.50 + 10862.6i) q^{16} +(-7051.44 + 12213.4i) q^{17} -73395.4i q^{18} +(-7226.10 - 4171.99i) q^{19} +(29607.4 + 17093.9i) q^{20} -54034.7i q^{21} +(-63632.6 + 110215. i) q^{22} +(29072.6 + 50355.3i) q^{23} +(-29516.0 + 17041.1i) q^{24} +28254.0 q^{25} +(56931.9 - 119986. i) q^{26} -177497. q^{27} +(-88418.3 + 51048.4i) q^{28} +(16522.5 + 28617.8i) q^{29} +(151678. - 262715. i) q^{30} +91450.2i q^{31} +(-228748. - 132068. i) q^{32} +(532630. + 307514. i) q^{33} -236445. i q^{34} +(74466.2 - 128979. i) q^{35} +(335091. + 580394. i) q^{36} +(-307911. + 177773. i) q^{37} +139893. q^{38} +(-579852. - 275132. i) q^{39} -93938.5 q^{40} +(504092. - 291038. i) q^{41} +(452966. + 784560. i) q^{42} +(-52248.9 + 90497.7i) q^{43} -1.16207e6i q^{44} +(-846644. - 488810. i) q^{45} +(-844243. - 487424. i) q^{46} +398024. i q^{47} +(-508135. + 880116. i) q^{48} +(-189389. - 328031. i) q^{49} +(-410236. + 236850. i) q^{50} -1.14266e6 q^{51} +(97600.3 + 1.20875e6i) q^{52} +1.49881e6 q^{53} +(2.57718e6 - 1.48793e6i) q^{54} +(847581. + 1.46805e6i) q^{55} +(140267. - 242949. i) q^{56} -676053. i q^{57} +(-479799. - 277012. i) q^{58} +(286332. + 165314. i) q^{59} +2.76999e6i q^{60} +(721365. - 1.24944e6i) q^{61} +(-766615. - 1.32782e6i) q^{62} +(2.52838e6 - 1.45976e6i) q^{63} +2.82292e6 q^{64} +(-1.00493e6 - 1.45583e6i) q^{65} -1.03114e7 q^{66} +(2.22292e6 - 1.28340e6i) q^{67} +(1.07950e6 + 1.86975e6i) q^{68} +(-2.35555e6 + 4.07993e6i) q^{69} +2.49696e6i q^{70} +(1.12386e6 + 648863. i) q^{71} +(-1.59477e6 - 920738. i) q^{72} -2.66195e6i q^{73} +(2.98049e6 - 5.16236e6i) q^{74} +(1.14461e6 + 1.98253e6i) q^{75} +(-1.10624e6 + 638689. i) q^{76} -5.06236e6 q^{77} +(1.07256e7 - 866034. i) q^{78} +2.13906e6 q^{79} +(-2.42581e6 + 1.40054e6i) q^{80} +(-2.40364e6 - 4.16323e6i) q^{81} +(-4.87946e6 + 8.45147e6i) q^{82} +1.63158e6i q^{83} +(-7.16391e6 - 4.13608e6i) q^{84} +(-2.72748e6 - 1.57471e6i) q^{85} -1.75198e6i q^{86} +(-1.33870e6 + 2.31870e6i) q^{87} +(1.59653e6 + 2.76527e6i) q^{88} +(-347455. + 200603. i) q^{89} +1.63905e7 q^{90} +(5.26570e6 - 425178. i) q^{91} +8.90145e6 q^{92} +(-6.41686e6 + 3.70478e6i) q^{93} +(-3.33658e6 - 5.77913e6i) q^{94} +(931681. - 1.61372e6i) q^{95} -2.14010e7i q^{96} +(-9.56294e6 - 5.52117e6i) q^{97} +(5.49968e6 + 3.17524e6i) q^{98} +3.32303e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{2} + 26 q^{3} + 383 q^{4} - 264 q^{6} - 2772 q^{7} - 3491 q^{9} - 509 q^{10} + 6516 q^{11} + 38380 q^{12} + 5109 q^{13} - 47916 q^{14} - 19266 q^{15} - 633 q^{16} - 38403 q^{17} + 43254 q^{19}+ \cdots + 16173003 q^{98}+O(q^{100}) $ 14 * q - 3 * q^2 + 26 * q^3 + 383 * q^4 - 264 * q^6 - 2772 * q^7 - 3491 * q^9 - 509 * q^10 + 6516 * q^11 + 38380 * q^12 + 5109 * q^13 - 47916 * q^14 - 19266 * q^15 - 633 * q^16 - 38403 * q^17 + 43254 * q^19 + 89409 * q^20 - 125882 * q^22 - 68550 * q^23 + 224454 * q^24 + 39380 * q^25 + 361959 * q^26 - 432400 * q^27 - 234780 * q^28 + 221583 * q^29 - 157890 * q^30 - 878067 * q^32 + 219756 * q^33 + 659616 * q^35 + 635675 * q^36 - 565347 * q^37 + 953640 * q^38 + 30082 * q^39 - 77182 * q^40 + 1716057 * q^41 + 206406 * q^42 - 882692 * q^43 - 4616853 * q^45 - 3267480 * q^46 + 1133630 * q^48 + 2653979 * q^49 + 145128 * q^50 - 38964 * q^51 + 4962178 * q^52 - 1791210 * q^53 + 9597234 * q^54 + 2453536 * q^55 - 7457952 * q^56 - 14978127 * q^58 - 1189032 * q^59 + 3858525 * q^61 + 1904142 * q^62 + 7718520 * q^63 + 14570922 * q^64 + 10424661 * q^65 - 31956396 * q^66 + 4674330 * q^67 + 9569619 * q^68 - 13743840 * q^69 - 25203126 * q^71 - 6851607 * q^72 + 8640105 * q^74 + 10316152 * q^75 + 12934506 * q^76 + 19599336 * q^77 + 50085750 * q^78 - 30688440 * q^79 + 29127963 * q^80 + 13886221 * q^81 - 37359719 * q^82 - 96398508 * q^84 - 22436313 * q^85 + 12769686 * q^87 + 27045536 * q^88 + 2123160 * q^89 + 41193546 * q^90 + 37205532 * q^91 - 47685588 * q^92 + 36638964 * q^93 + 19138810 * q^94 - 43420386 * q^95 - 68556288 * q^97 + 16173003 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−14.5196	+	8.38287i	−1.28336	+	0.740948i	−0.977461	−	0.211117i	$-0.932290\pi$
$2$	−14.5196	+	8.38287i	−1.28336	+	0.740948i	−0.305898	+	0.952064i	$0.598957\pi$
$3$	40.5114	+	70.1679i	0.866270	+	1.50042i	0.865781	+	0.500423i	$0.166822\pi$
$3$	40.5114	+	70.1679i	0.866270	+	1.50042i	0.000489031		1.00000i	$0.499844\pi$
$4$	76.5449	−	132.580i	0.598007	−	1.03578i
$5$			223.318i			0.798967i	0.916740	+	0.399483i	$0.130811\pi$
$5$			223.318i			0.798967i	−0.916740	+	0.399483i	$0.869189\pi$
$6$	−1176.42	−	679.204i	−2.22347	−	1.28372i
$7$	−577.559	−	333.454i	−0.636433	−	0.367445i	0.146806	−	0.989165i	$-0.453101\pi$
$7$	−577.559	−	333.454i	−0.636433	−	0.367445i	−0.783239	+	0.621720i	$0.786434\pi$
$8$			420.649i			0.290472i
$9$	−2188.85	+	3791.20i	−1.00085	+	1.73352i
$10$	−1872.05	−	3242.48i	−0.591993	−	1.02536i
$11$	6573.82	−	3795.40i	1.48917	−	0.859771i	0.489244	−	0.872147i	$-0.337273\pi$
$11$	6573.82	−	3795.40i	1.48917	−	0.859771i	0.999923	+	0.0123755i	$0.00393934\pi$
$12$	12403.8			2.07214
$13$	−6519.11	+	4499.97i	−0.822975	+	0.568078i
$13$	−6519.11	+	4499.97i	−0.822975	+	0.568078i
$14$	11181.2			1.08903
$15$	−15669.7	+	9046.93i	−1.19879	+	0.692121i
$16$	6271.50	+	10862.6i	0.382782	+	0.662998i
$17$	−7051.44	+	12213.4i	−0.348102	+	0.602930i	−0.985912	−	0.167263i	$-0.946507\pi$
$17$	−7051.44	+	12213.4i	−0.348102	+	0.602930i	0.637810	+	0.770193i	$0.279840\pi$
$18$		−	73395.4i		−	2.96630i
$19$	−7226.10	−	4171.99i	−0.241694	−	0.139542i	0.374261	−	0.927323i	$-0.377896\pi$
$19$	−7226.10	−	4171.99i	−0.241694	−	0.139542i	−0.615955	+	0.787781i	$0.711230\pi$
$20$	29607.4	+	17093.9i	0.827553	+	0.477788i
$21$		−	54034.7i		−	1.27323i
$22$	−63632.6	+	110215.i	−1.27409	+	2.20679i
$23$	29072.6	+	50355.3i	0.498238	+	0.862974i	0.999998	−	0.00203315i	$-0.000647171\pi$
$23$	29072.6	+	50355.3i	0.498238	+	0.862974i	−0.501760	+	0.865007i	$0.667314\pi$
$24$	−29516.0	+	17041.1i	−0.435832	+	0.251627i
$25$	28254.0			0.361652
$26$	56931.9	−	119986.i	0.635256	−	1.33883i
$27$	−177497.			−1.73547
$28$	−88418.3	+	51048.4i	−0.761183	+	0.439469i
$29$	16522.5	+	28617.8i	0.125801	+	0.217893i	0.922046	−	0.387081i	$-0.126517\pi$
$29$	16522.5	+	28617.8i	0.125801	+	0.217893i	−0.796245	+	0.604974i	$0.793183\pi$
$30$	151678.	−	262715.i	1.02565	−	1.77648i
$31$			91450.2i			0.551339i	0.961252	+	0.275669i	$0.0888995\pi$
$31$			91450.2i			0.551339i	−0.961252	+	0.275669i	$0.911100\pi$
$32$	−228748.	−	132068.i	−1.23405	−	0.712479i
$33$	532630.	+	307514.i	2.58004	+	1.48959i
$34$		−	236445.i		−	1.03170i
$35$	74466.2	−	128979.i	0.293576	−	0.508489i
$36$	335091.	+	580394.i	1.19703	+	2.07331i
$37$	−307911.	+	177773.i	−0.999354	+	0.576977i	−0.908057	−	0.418846i	$-0.862435\pi$
$37$	−307911.	+	177773.i	−0.999354	+	0.576977i	−0.0912968	+	0.995824i	$0.529101\pi$
$38$	139893.			0.413574
$39$	−579852.	−	275132.i	−1.56528	−	0.742701i
$40$	−93938.5			−0.232078
$41$	504092.	−	291038.i	1.14226	−	0.659486i	0.195273	−	0.980749i	$-0.437441\pi$
$41$	504092.	−	291038.i	1.14226	−	0.659486i	0.946990	+	0.321263i	$0.104107\pi$
$42$	452966.	+	784560.i	0.943394	+	1.63401i
$43$	−52248.9	+	90497.7i	−0.100216	+	0.173579i	−0.911774	−	0.410693i	$-0.865287\pi$
$43$	−52248.9	+	90497.7i	−0.100216	+	0.173579i	0.811558	+	0.584273i	$0.198620\pi$
$44$		−	1.16207e6i		−	2.05660i
$45$	−846644.	−	488810.i	−1.38502	−	0.799644i
$46$	−844243.	−	487424.i	−1.27884	−	0.738337i
$47$			398024.i			0.559199i	0.960117	+	0.279600i	$0.0902017\pi$
$47$			398024.i			0.559199i	−0.960117	+	0.279600i	$0.909798\pi$
$48$	−508135.	+	880116.i	−0.663185	+	1.14867i
$49$	−189389.	−	328031.i	−0.229968	−	0.398317i
$50$	−410236.	+	236850.i	−0.464129	+	0.267965i
$51$	−1.14266e6			−1.20620
$52$	97600.3	+	1.20875e6i	0.0962586	+	1.19213i
$53$	1.49881e6			1.38287			0.691433	−	0.722441i	$-0.256980\pi$
$53$	1.49881e6			1.38287			0.691433	+	0.722441i	$0.256980\pi$
$54$	2.57718e6	−	1.48793e6i	2.22724	−	1.28590i
$55$	847581.	+	1.46805e6i	0.686929	+	1.18980i
$56$	140267.	−	242949.i	0.106733	−	0.184866i
$57$		−	676053.i		−	0.483525i
$58$	−479799.	−	277012.i	−0.322895	−	0.186423i
$59$	286332.	+	165314.i	0.181505	+	0.104792i	0.588000	−	0.808861i	$-0.299916\pi$
$59$	286332.	+	165314.i	0.181505	+	0.104792i	−0.406495	+	0.913653i	$0.633249\pi$
$60$			2.76999e6i			1.65557i
$61$	721365.	−	1.24944e6i	0.406912	−	0.704793i	−0.587630	−	0.809130i	$-0.699939\pi$
$61$	721365.	−	1.24944e6i	0.406912	−	0.704793i	0.994542	+	0.104337i	$0.0332721\pi$
$62$	−766615.	−	1.32782e6i	−0.408513	−	0.707566i
$63$	2.52838e6	−	1.45976e6i	1.27394	−	0.735512i
$64$	2.82292e6			1.34608
$65$	−1.00493e6	−	1.45583e6i	−0.453876	−	0.657530i
$66$	−1.03114e7			−4.41483
$67$	2.22292e6	−	1.28340e6i	0.902945	−	0.521316i	0.0247906	−	0.999693i	$-0.492108\pi$
$67$	2.22292e6	−	1.28340e6i	0.902945	−	0.521316i	0.878155	+	0.478377i	$0.158775\pi$
$68$	1.07950e6	+	1.86975e6i	0.416335	+	0.721113i
$69$	−2.35555e6	+	4.07993e6i	−0.863217	+	1.49514i
$70$			2.49696e6i			0.870099i
$71$	1.12386e6	+	648863.i	0.372657	+	0.215154i	0.674619	−	0.738166i	$-0.264308\pi$
$71$	1.12386e6	+	648863.i	0.372657	+	0.215154i	−0.301962	+	0.953320i	$0.597641\pi$
$72$	−1.59477e6	−	920738.i	−0.503539	−	0.290718i
$73$		−	2.66195e6i		−	0.800885i	−0.916322	−	0.400442i	$-0.868856\pi$
$73$		−	2.66195e6i		−	0.800885i	0.916322	−	0.400442i	$-0.131144\pi$
$74$	2.98049e6	−	5.16236e6i	0.855020	−	1.48094i
$75$	1.14461e6	+	1.98253e6i	0.313288	+	0.542631i
$76$	−1.10624e6	+	638689.i	−0.289070	+	0.166895i
$77$	−5.06236e6			−1.26367
$78$	1.07256e7	−	866034.i	2.55911	−	0.206635i
$79$	2.13906e6			0.488121			0.244060	−	0.969760i	$-0.421520\pi$
$79$	2.13906e6			0.488121			0.244060	+	0.969760i	$0.421520\pi$
$80$	−2.42581e6	+	1.40054e6i	−0.529714	+	0.305830i
$81$	−2.40364e6	−	4.16323e6i	−0.502542	−	0.870428i
$82$	−4.87946e6	+	8.45147e6i	−0.977289	+	1.69271i
$83$			1.63158e6i			0.313211i	0.987661	+	0.156605i	$0.0500550\pi$
$83$			1.63158e6i			0.313211i	−0.987661	+	0.156605i	$0.949945\pi$
$84$	−7.16391e6	−	4.13608e6i	−1.31878	−	0.761398i
$85$	−2.72748e6	−	1.57471e6i	−0.481721	−	0.278122i
$86$		−	1.75198e6i		−	0.297020i
$87$	−1.33870e6	+	2.31870e6i	−0.217955	+	0.377509i
$88$	1.59653e6	+	2.76527e6i	0.249740	+	0.432562i
$89$	−347455.	+	200603.i	−0.0522436	+	0.0301629i	−0.525894	−	0.850550i	$-0.676269\pi$
$89$	−347455.	+	200603.i	−0.0522436	+	0.0301629i	0.473651	+	0.880713i	$0.342936\pi$
$90$	1.63905e7			2.36998
$91$	5.26570e6	−	425178.i	0.732506	−	0.0591460i
$92$	8.90145e6			1.19180
$93$	−6.41686e6	+	3.70478e6i	−0.827242	+	0.477608i
$94$	−3.33658e6	−	5.77913e6i	−0.414337	−	0.717653i
$95$	931681.	−	1.61372e6i	0.111490	−	0.193106i
$96$		−	2.14010e7i		−	2.46880i
$97$	−9.56294e6	−	5.52117e6i	−1.06387	−	0.614228i	−0.137373	−	0.990519i	$-0.543866\pi$
$97$	−9.56294e6	−	5.52117e6i	−1.06387	−	0.614228i	−0.926501	+	0.376291i	$0.877199\pi$
$98$	5.49968e6	+	3.17524e6i	0.590264	+	0.340789i
$99$			3.32303e7i			3.44200i
$100$	2.16270e6	−	3.74591e6i	0.216270	−	0.374591i
$101$	3.84159e6	+	6.65383e6i	0.371011	+	0.642610i	0.989721	−	0.143010i	$-0.0456779\pi$
$101$	3.84159e6	+	6.65383e6i	0.371011	+	0.642610i	−0.618711	+	0.785619i	$0.712345\pi$
$102$	1.65908e7	−	9.57873e6i	1.54799	−	0.893732i
$103$	485826.			0.0438077			0.0219039	−	0.999760i	$-0.493027\pi$
$103$	485826.			0.0438077			0.0219039	+	0.999760i	$0.493027\pi$
$104$	−1.89291e6	−	2.74226e6i	−0.165011	−	0.239051i
$105$	1.20669e7			1.01727
$106$	−2.17620e7	+	1.25643e7i	−1.77471	+	1.02463i
$107$	34987.1	+	60599.5i	0.00276099	+	0.00478218i	0.867403	−	0.497607i	$-0.165788\pi$
$107$	34987.1	+	60599.5i	0.00276099	+	0.00478218i	−0.864642	+	0.502389i	$0.832454\pi$
$108$	−1.35865e7	+	2.35325e7i	−1.03783	+	1.79757i
$109$			4.06366e6i			0.300556i	0.988644	+	0.150278i	$0.0480168\pi$
$109$			4.06366e6i			0.300556i	−0.988644	+	0.150278i	$0.951983\pi$
$110$	−2.46130e7	−	1.42103e7i	−1.76315	−	1.01796i
$111$	−2.49478e7	−	1.44036e7i	−1.73142	−	0.999636i
$112$		−	8.36502e6i		−	0.562606i
$113$	1.04977e7	−	1.81826e7i	0.684417	−	1.18544i	−0.289203	−	0.957268i	$-0.593390\pi$
$113$	1.04977e7	−	1.81826e7i	0.684417	−	1.18544i	0.973620	−	0.228177i	$-0.0732764\pi$
$114$	5.66727e6	+	9.81599e6i	0.358267	+	0.620536i
$115$	−1.12452e7	+	6.49245e6i	−0.689488	+	0.398076i
$116$	5.05885e6			0.300919
$117$	−2.79094e6	−	3.45650e7i	−0.161102	−	1.99520i
$118$	−5.54322e6			−0.310581
$119$	8.14524e6	−	4.70266e6i	0.443087	−	0.255817i
$120$	−3.80558e6	−	6.59146e6i	−0.201042	−	0.348215i
$121$	1.90665e7	−	3.30242e7i	0.978414	−	1.69466i
$122$			2.41884e7i			1.20600i
$123$	4.08430e7	+	2.35807e7i	1.97902	+	1.14259i
$124$	1.21244e7	+	7.00004e6i	0.571065	+	0.329705i
$125$			2.37564e7i			1.08791i
$126$	−2.44740e7	+	4.23902e7i	−1.08995	+	1.88785i
$127$	4.66784e6	+	8.08493e6i	0.202210	+	0.350238i	0.949240	−	0.314552i	$-0.101854\pi$
$127$	4.66784e6	+	8.08493e6i	0.202210	+	0.350238i	−0.747030	+	0.664790i	$0.768521\pi$
$128$	−1.17078e7	+	6.75951e6i	−0.493448	+	0.284892i
$129$	−8.46671e6			−0.347257
$130$	2.67951e7	+	1.27139e7i	1.06968	+	0.507548i
$131$	−4.07546e7			−1.58390			−0.791948	−	0.610588i	$-0.790933\pi$
$131$	−4.07546e7			−1.58390			−0.791948	+	0.610588i	$0.790933\pi$
$132$	8.15402e7	−	4.70773e7i	3.08577	−	1.78157i
$133$	2.78233e6	+	4.81914e6i	0.102548	+	0.177619i
$134$	−2.15172e7	+	3.72688e7i	−0.772535	+	1.33807i
$135$		−	3.96383e7i		−	1.38659i
$136$	−5.13757e6	−	2.96618e6i	−0.175135	−	0.101114i
$137$	4.21961e7	+	2.43619e7i	1.40201	+	0.809449i	0.994598	−	0.103797i	$-0.0330993\pi$
$137$	4.21961e7	+	2.43619e7i	1.40201	+	0.809449i	0.407408	+	0.913246i	$0.366433\pi$
$138$		−	7.89850e7i		−	2.55840i
$139$	2.66447e7	−	4.61501e7i	0.841511	−	1.45754i	−0.0471059	−	0.998890i	$-0.515000\pi$
$139$	2.66447e7	−	4.61501e7i	0.841511	−	1.45754i	0.888617	−	0.458650i	$-0.151667\pi$
$140$	−1.14000e7	−	1.97454e7i	−0.351122	−	0.608160i
$141$	−2.79285e7	+	1.61245e7i	−0.839036	+	0.484417i
$142$	−2.17573e7			−0.637670
$143$	−2.57763e7	+	5.43246e7i	−0.737130	+	1.55353i
$144$	−5.49096e7			−1.53243
$145$	−6.39088e6	+	3.68977e6i	−0.174089	+	0.100511i
$146$	2.23148e7	+	3.86503e7i	0.593414	+	1.02782i
$147$	1.53448e7	−	2.65780e7i	0.398429	−	0.690100i
$148$			5.44303e7i			1.38015i
$149$	−3.13839e7	−	1.81195e7i	−0.777241	−	0.448740i	0.0582108	−	0.998304i	$-0.481460\pi$
$149$	−3.13839e7	−	1.81195e7i	−0.777241	−	0.448740i	−0.835451	+	0.549564i	$0.814794\pi$
$150$	−3.32385e7	−	1.91903e7i	−0.804122	−	0.464260i
$151$			2.55676e7i			0.604326i	0.953256	+	0.302163i	$0.0977087\pi$
$151$			2.55676e7i			0.604326i	−0.953256	+	0.302163i	$0.902291\pi$
$152$	1.75494e6	−	3.03965e6i	0.0405332	−	0.0702055i
$153$	−3.08691e7	−	5.34669e7i	−0.696793	−	1.20688i
$154$	7.35032e7	−	4.24371e7i	1.62175	−	0.936317i
$155$	−2.04225e7			−0.440502
$156$	−8.08615e7	+	5.58166e7i	−1.70532	+	1.17714i
$157$	4.23295e7			0.872960			0.436480	−	0.899714i	$-0.356225\pi$
$157$	4.23295e7			0.872960			0.436480	+	0.899714i	$0.356225\pi$
$158$	−3.10581e7	+	1.79314e7i	−0.626434	+	0.361672i
$159$	6.07188e7	+	1.05168e8i	1.19793	+	2.07488i
$160$	2.94931e7	−	5.10836e7i	0.569247	−	0.985966i
$161$		−	3.87775e7i		−	0.732301i
$162$	6.97996e7	+	4.02988e7i	1.28988	+	0.744714i
$163$	−2.98690e7	−	1.72449e7i	−0.540213	−	0.311892i	0.204952	−	0.978772i	$-0.434296\pi$
$163$	−2.98690e7	−	1.72449e7i	−0.540213	−	0.311892i	−0.745165	+	0.666880i	$0.767629\pi$
$164$		−	8.91098e7i		−	1.57751i
$165$	−6.86734e7	+	1.18946e8i	−1.19013	+	2.06137i
$166$	−1.36774e7	−	2.36899e7i	−0.232073	−	0.401962i
$167$	6.93649e6	−	4.00479e6i	0.115248	−	0.0665383i	−0.441268	−	0.897375i	$-0.645471\pi$
$167$	6.93649e6	−	4.00479e6i	0.115248	−	0.0665383i	0.556516	+	0.830837i	$0.312138\pi$
$168$	2.27297e7			0.369837
$169$	2.22490e7	−	5.86716e7i	0.354574	−	0.935028i
$170$	5.28024e7			0.824295
$171$	3.16337e7	−	1.82637e7i	0.483798	−	0.279321i
$172$	7.99877e6	+	1.38543e7i	0.119860	+	0.207603i
$173$	1.86570e7	−	3.23149e7i	0.273956	−	0.474506i	−0.695915	−	0.718124i	$-0.745001\pi$
$173$	1.86570e7	−	3.23149e7i	0.273956	−	0.474506i	0.969871	+	0.243618i	$0.0783343\pi$
$174$		−	4.48886e7i		−	0.645972i
$175$	−1.63184e7	−	9.42142e6i	−0.230167	−	0.132887i
$176$	8.24555e7	+	4.76057e7i	1.14005	+	0.658210i
$177$			2.67884e7i			0.363112i
$178$	3.36326e6	−	5.82534e6i	0.0446982	−	0.0774196i
$179$	−3.42603e7	−	5.93407e7i	−0.446484	−	0.773333i	0.551670	−	0.834062i	$-0.313991\pi$
$179$	−3.42603e7	−	5.93407e7i	−0.446484	−	0.773333i	−0.998154	+	0.0607291i	$0.980657\pi$
$180$	−1.29613e8	+	7.48318e7i	−1.65651	+	0.956385i
$181$	−1.20860e8			−1.51498			−0.757489	−	0.652848i	$-0.773574\pi$
$181$	−1.20860e8			−1.51498			−0.757489	+	0.652848i	$0.773574\pi$
$182$	−7.28914e7	+	5.03150e7i	−0.896244	+	0.618654i
$183$	1.16894e8			1.40998
$184$	−2.11819e7	+	1.22294e7i	−0.250670	+	0.144724i
$185$	−3.96998e7	−	6.87621e7i	−0.460986	−	0.798451i
$186$	6.21133e7	−	1.07583e8i	0.707765	−	1.22589i
$187$			1.07052e8i			1.19715i
$188$	5.27699e7	+	3.04667e7i	0.579207	+	0.334405i
$189$	1.02515e8	+	5.91871e7i	1.10451	+	0.637691i
$190$			3.12406e7i			0.330432i
$191$	4.20222e7	−	7.27846e7i	0.436377	−	0.755828i	−0.561029	−	0.827796i	$-0.689595\pi$
$191$	4.20222e7	−	7.27846e7i	0.436377	−	0.755828i	0.997407	+	0.0719679i	$0.0229279\pi$
$192$	1.14361e8	+	1.98079e8i	1.16606	+	2.01968i
$193$	−3.85466e7	+	2.22549e7i	−0.385954	+	0.222830i	−0.680405	−	0.732836i	$-0.738196\pi$
$193$	−3.85466e7	+	2.22549e7i	−0.385954	+	0.222830i	0.294452	+	0.955666i	$0.404863\pi$
$194$	1.85133e8			1.82044
$195$	6.14418e7	−	1.29491e8i	0.593394	−	1.25060i
$196$	−5.79870e7			−0.550091
$197$	−1.09554e8	+	6.32512e7i	−1.02093	+	0.589437i	−0.914374	−	0.404870i	$-0.867317\pi$
$197$	−1.09554e8	+	6.32512e7i	−1.02093	+	0.589437i	−0.106560	+	0.994306i	$0.533984\pi$
$198$	−2.78565e8	−	4.82488e8i	−2.55034	−	4.41732i
$199$	−4.81092e7	+	8.33276e7i	−0.432755	+	0.749554i	−0.997109	−	0.0759785i	$-0.975792\pi$
$199$	−4.81092e7	+	8.33276e7i	−0.432755	+	0.749554i	0.564354	+	0.825533i	$0.309125\pi$
$200$			1.18850e7i			0.105050i
$201$	1.80107e8	+	1.03985e8i	1.56439	+	0.903200i
$202$	−1.11556e8	−	6.44071e7i	−0.952280	−	0.549799i
$203$		−	2.20380e7i		−	0.184899i
$204$	−8.74644e7	+	1.51493e8i	−0.721317	+	1.24936i
$205$	6.49939e7	+	1.12573e8i	0.526908	+	0.912631i
$206$	−7.05398e6	+	4.07262e6i	−0.0562210	+	0.0324592i
$207$	−2.54543e8			−1.99464
$208$	−8.97658e7	−	4.25926e7i	−0.691655	−	0.328180i
$209$	−6.33375e7			−0.479898
$210$	−1.75206e8	+	1.01155e8i	−1.30552	+	0.753741i
$211$	2.51766e7	+	4.36072e7i	0.184505	+	0.319573i	0.943410	−	0.331629i	$-0.107598\pi$
$211$	2.51766e7	+	4.36072e7i	0.184505	+	0.319573i	−0.758904	+	0.651202i	$0.774265\pi$
$212$	1.14726e8	−	1.98711e8i	0.826963	−	1.43234i
$213$			1.05145e8i			0.745524i
$214$	−1.01599e6	−	586585.i	−0.00708669	−	0.00409150i
$215$	−2.02098e7	−	1.16681e7i	−0.138684	−	0.0800693i
$216$		−	7.46640e7i		−	0.504107i
$217$	3.04944e7	−	5.28178e7i	0.202587	−	0.350890i
$218$	−3.40651e7	−	5.90026e7i	−0.222696	−	0.385721i
$219$	1.86783e8	−	1.07839e8i	1.20167	−	0.693782i
$220$	2.59512e8			1.64315
$221$	−8.99109e6	−	1.11352e8i	−0.0560324	−	0.693945i
$222$	4.82975e8			2.96271
$223$	−2.12315e8	+	1.22580e8i	−1.28208	+	0.740208i	−0.977228	−	0.212192i	$-0.931940\pi$
$223$	−2.12315e8	+	1.22580e8i	−1.28208	+	0.740208i	−0.304851	+	0.952400i	$0.598607\pi$
$224$	8.80770e7	+	1.52554e8i	0.523594	+	0.906891i
$225$	−6.18439e7	+	1.07117e8i	−0.361958	+	0.626930i
$226$			3.52004e8i			2.02847i
$227$	−1.65319e6	−	954470.i	−0.00938064	−	0.00541591i	0.495302	−	0.868721i	$-0.335057\pi$
$227$	−1.65319e6	−	954470.i	−0.00938064	−	0.00541591i	−0.504683	+	0.863305i	$0.668391\pi$
$228$	−8.96309e7	−	5.17484e7i	−0.500825	−	0.289151i
$229$		−	2.07407e8i		−	1.14130i	−0.821194	−	0.570650i	$-0.806691\pi$
$229$		−	2.07407e8i		−	1.14130i	0.821194	−	0.570650i	$-0.193309\pi$
$230$	1.08851e8	−	1.88535e8i	0.589907	−	1.02175i
$231$	−2.05083e8	−	3.55215e8i	−1.09468	−	1.89605i
$232$	−1.20381e7	+	6.95018e6i	−0.0632919	+	0.0365416i
$233$	3.42955e8			1.77620			0.888099	−	0.459652i	$-0.152026\pi$
$233$	3.42955e8			1.77620			0.888099	+	0.459652i	$0.152026\pi$
$234$	3.30277e8	+	4.78473e8i	1.68509	+	2.44119i
$235$	−8.88859e7			−0.446782
$236$	4.38346e7	−	2.53079e7i	0.217082	−	0.125333i
$237$	8.66562e7	+	1.50093e8i	0.422844	+	0.732388i
$238$	−7.88435e7	+	1.36561e8i	−0.379094	+	0.656609i
$239$		−	3.94963e8i		−	1.87139i	−0.352815	−	0.935693i	$-0.614775\pi$
$239$		−	3.94963e8i		−	1.87139i	0.352815	−	0.935693i	$-0.385225\pi$
$240$	−1.96546e8	−	1.13476e8i	−0.917750	−	0.529863i
$241$	6.73226e7	+	3.88687e7i	0.309814	+	0.178871i	0.646843	−	0.762623i	$-0.276089\pi$
$241$	6.73226e7	+	3.88687e7i	0.309814	+	0.178871i	−0.337029	+	0.941494i	$0.609422\pi$
$242$			6.39328e8i			2.89981i
$243$	656866.	−	1.13773e6i	0.00293667	−	0.00508646i
$244$	−1.10434e8	−	1.91277e8i	−0.486673	−	0.842942i
$245$	7.32552e7	−	4.22939e7i	0.318242	−	0.183737i
$246$	−7.90695e8			−3.38638
$247$	6.58816e7	−	5.31959e6i	0.278179	−	0.0224615i
$248$	−3.84684e7			−0.160149
$249$	−1.14485e8	+	6.60978e7i	−0.469948	+	0.271325i
$250$	−1.99146e8	−	3.44932e8i	−0.806088	−	1.39619i
$251$	−1.75438e8	+	3.03868e8i	−0.700272	+	1.21291i	0.268099	+	0.963391i	$0.413604\pi$
$251$	−1.75438e8	+	3.03868e8i	−0.700272	+	1.21291i	−0.968371	+	0.249515i	$0.919729\pi$
$252$		−	4.46949e8i		−	1.75937i
$253$	3.82237e8	+	2.20684e8i	1.48392	+	0.856742i
$254$	−1.35550e8	−	7.82597e7i	−0.519016	−	0.299654i
$255$		−	2.55176e8i		−	0.963715i
$256$	−6.73390e7	+	1.16635e8i	−0.250857	+	0.434498i
$257$	−1.79600e8	−	3.11076e8i	−0.659995	−	1.14314i	−0.980616	−	0.195937i	$-0.937225\pi$
$257$	−1.79600e8	−	3.11076e8i	−0.659995	−	1.14314i	0.320622	−	0.947207i	$-0.396108\pi$
$258$	1.22933e8	−	7.09753e7i	0.445655	−	0.257299i
$259$	2.37116e8			0.848030
$260$	−2.69936e8	+	2.17959e7i	−0.952476	+	0.0769074i
$261$	−1.44661e8			−0.503629
$262$	5.91738e8	−	3.41640e8i	2.03271	−	1.17358i
$263$	9.97562e7	+	1.72783e8i	0.338139	+	0.585673i	0.984083	−	0.177712i	$-0.0568694\pi$
$263$	9.97562e7	+	1.72783e8i	0.338139	+	0.585673i	−0.645944	+	0.763385i	$0.723536\pi$
$264$	−1.29355e8	+	2.24050e8i	−0.432684	+	0.749431i
$265$			3.34711e8i			1.10486i
$266$	−8.07964e7	−	4.66478e7i	−0.263212	−	0.151966i
$267$	−2.81518e7	−	1.62534e7i	−0.0905142	−	0.0522584i
$268$		−	3.92951e8i		−	1.24700i
$269$	3.22428e7	−	5.58463e7i	0.100995	−	0.174929i	−0.811100	−	0.584908i	$-0.801131\pi$
$269$	3.22428e7	−	5.58463e7i	0.100995	−	0.174929i	0.912095	+	0.409979i	$0.134464\pi$
$270$	3.32283e8	+	5.75530e8i	1.02739	+	1.77949i
$271$	−4.15254e7	+	2.39747e7i	−0.126742	+	0.0731747i	−0.562031	−	0.827116i	$-0.689980\pi$
$271$	−4.15254e7	+	2.39747e7i	−0.126742	+	0.0731747i	0.435288	+	0.900291i	$0.356646\pi$
$272$	−1.76892e8			−0.532989
$273$	2.43155e8	+	3.52258e8i	0.723292	+	1.04783i
$274$	−8.16891e8			−2.39904
$275$	1.85737e8	−	1.07235e8i	0.538560	−	0.310938i
$276$	3.60610e8	+	6.24596e8i	1.03242	+	1.78820i
$277$	2.96509e8	−	5.13568e8i	0.838221	−	1.45184i	−0.0531601	−	0.998586i	$-0.516929\pi$
$277$	2.96509e8	−	5.13568e8i	0.838221	−	1.45184i	0.891381	−	0.453255i	$-0.149737\pi$
$278$			8.93438e8i			2.49406i
$279$	−3.46706e8	−	2.00171e8i	−0.955756	−	0.551806i
$280$	5.42550e7	+	3.13241e7i	0.147702	+	0.0852758i
$281$			1.74758e8i			0.469856i	0.972013	+	0.234928i	$0.0754854\pi$
$281$			1.74758e8i			0.469856i	−0.972013	+	0.234928i	$0.924515\pi$
$282$	2.70339e8	−	4.68241e8i	0.717856	−	1.24336i
$283$	3.30559e8	+	5.72544e8i	0.866954	+	1.50161i	0.865094	+	0.501609i	$0.167259\pi$
$283$	3.30559e8	+	5.72544e8i	0.866954	+	1.50161i	0.00185936	+	0.999998i	$0.499408\pi$
$284$	1.72052e8	−	9.93343e7i	0.445703	−	0.257327i
$285$	1.50975e8			0.386321
$286$	−8.11362e7	−	1.00485e9i	−0.205085	−	2.53992i
$287$	−3.88190e8			−0.969299
$288$	1.00139e9	−	5.78154e8i	2.47019	−	1.42617i
$289$	1.05724e8	+	1.83119e8i	0.257650	+	0.446263i
$290$	6.18618e7	−	1.07148e8i	0.148946	−	0.257982i
$291$		−	8.94681e8i		−	2.12835i
$292$	−3.52921e8	−	2.03759e8i	−0.829539	−	0.478935i
$293$	−4.64833e8	−	2.68372e8i	−1.07959	−	0.623304i	−0.148807	−	0.988866i	$-0.547543\pi$
$293$	−4.64833e8	−	2.68372e8i	−1.07959	−	0.623304i	−0.930787	+	0.365562i	$0.880877\pi$
$294$			5.14534e8i			1.18086i
$295$	−3.69176e7	+	6.39432e7i	−0.0837253	+	0.145016i
$296$	−7.47798e7	−	1.29522e8i	−0.167596	−	0.290285i
$297$	−1.16683e9	+	6.73672e8i	−2.58441	+	1.49211i
$298$	6.07574e8			1.32997
$299$	−4.16125e8	−	1.97445e8i	−0.900274	−	0.427167i
$300$	3.50457e8			0.749394
$301$	6.03536e7	−	3.48452e7i	0.127562	−	0.0736478i
$302$	−2.14330e8	−	3.71231e8i	−0.447774	−	0.775567i
$303$	−3.11257e8	+	5.39113e8i	−0.642791	+	1.11335i
$304$		−	1.04659e8i		−	0.213657i
$305$	2.79023e8	+	1.61094e8i	0.563106	+	0.325110i
$306$	8.96411e8	+	5.17543e8i	1.78847	+	1.03257i
$307$			3.58135e8i			0.706419i	0.935544	+	0.353209i	$0.114910\pi$
$307$			3.58135e8i			0.706419i	−0.935544	+	0.353209i	$0.885090\pi$
$308$	−3.87498e8	+	6.71166e8i	−0.755686	+	1.30889i
$309$	1.96815e7	+	3.40894e7i	0.0379493	+	0.0657301i
$310$	2.96525e8	−	1.71199e8i	0.565322	−	0.326389i
$311$	4.95093e8			0.933309			0.466655	−	0.884440i	$-0.345459\pi$
$311$	4.95093e8			0.933309			0.466655	+	0.884440i	$0.345459\pi$
$312$	1.15734e8	−	2.43914e8i	0.215734	−	0.454669i
$313$	−3.14797e8			−0.580263			−0.290131	−	0.956987i	$-0.593699\pi$
$313$	−3.14797e8			−0.580263			−0.290131	+	0.956987i	$0.593699\pi$
$314$	−6.14606e8	+	3.54843e8i	−1.12032	+	0.646818i
$315$	3.25991e8	+	5.64633e8i	0.587650	+	1.01784i
$316$	1.63734e8	−	2.83595e8i	0.291900	−	0.505585i
$317$		−	6.24177e8i		−	1.10053i	−0.834991	−	0.550263i	$-0.814527\pi$
$317$		−	6.24177e8i		−	1.10053i	0.834991	−	0.550263i	$-0.185473\pi$
$318$	−1.76322e9	−	1.01800e9i	−3.07476	−	1.77521i
$319$	2.17232e8	+	1.25419e8i	0.374677	+	0.216320i
$320$			6.30410e8i			1.07547i
$321$	−2.83476e6	+	4.90994e6i	−0.00478353	+	0.00828531i
$322$	3.25067e8	+	5.63032e8i	0.542596	+	0.939805i
$323$	1.01909e8	−	5.88371e7i	0.168269	−	0.0971499i
$324$	−7.35946e8			−1.20209
$325$	−1.84191e8	+	1.27142e8i	−0.297630	+	0.205446i
$326$	5.78247e8			0.924382
$327$	−2.85139e8	+	1.64625e8i	−0.450961	+	0.260362i
$328$	1.22425e8	+	2.12046e8i	0.191562	+	0.331796i
$329$	1.32722e8	−	2.29882e8i	0.205475	−	0.355893i
$330$		−	2.30272e9i		−	3.52730i
$331$	−4.36304e8	−	2.51900e8i	−0.661289	−	0.381795i	0.131479	−	0.991319i	$-0.458027\pi$
$331$	−4.36304e8	−	2.51900e8i	−0.661289	−	0.381795i	−0.792768	+	0.609524i	$0.791361\pi$
$332$	2.16315e8	+	1.24890e8i	0.324417	+	0.187302i
$333$		−	1.55647e9i		−	2.30986i
$334$	−6.71432e7	+	1.16295e8i	−0.0986028	+	0.170785i
$335$	2.86607e8	+	4.96417e8i	0.416514	+	0.721423i
$336$	5.86956e8	−	3.38879e8i	0.844147	−	0.487368i
$337$	−9.64189e8			−1.37233			−0.686164	−	0.727447i	$-0.740707\pi$
$337$	−9.64189e8			−1.37233			−0.686164	+	0.727447i	$0.740707\pi$
$338$	1.68791e8	+	1.03840e9i	0.237760	+	1.46270i
$339$	1.70111e9			2.37156
$340$	−4.17550e8	+	2.41073e8i	−0.576145	+	0.332638i
$341$	3.47090e8	+	6.01177e8i	0.474025	+	0.821036i
$342$	−3.06205e8	+	5.30363e8i	−0.413924	+	0.716938i
$343$			8.01836e8i			1.07289i
$344$	−3.80678e7	−	2.19784e7i	−0.0504200	−	0.0291100i
$345$	−9.11122e8	−	5.26036e8i	−1.19456	−	0.689682i
$346$			6.25598e8i			0.811949i
$347$	−2.30234e8	+	3.98777e8i	−0.295812	+	0.512362i	−0.975173	−	0.221442i	$-0.928924\pi$
$347$	−2.30234e8	+	3.98777e8i	−0.295812	+	0.512362i	0.679361	+	0.733804i	$0.262257\pi$
$348$	2.04941e8	+	3.54969e8i	0.260677	+	0.451506i
$349$	−2.11799e8	+	1.22282e8i	−0.266707	+	0.153984i	−0.627390	−	0.778705i	$-0.715877\pi$
$349$	−2.11799e8	+	1.22282e8i	−0.266707	+	0.153984i	0.360683	+	0.932688i	$0.382544\pi$
$350$	3.15914e8			0.393850
$351$	1.15712e9	−	7.98732e8i	1.42825	−	0.985885i
$352$	−2.00500e9			−2.45028
$353$	4.69439e8	−	2.71031e8i	0.568025	−	0.327949i	−0.188335	−	0.982105i	$-0.560309\pi$
$353$	4.69439e8	−	2.71031e8i	0.568025	−	0.327949i	0.756360	+	0.654155i	$0.226976\pi$
$354$	−2.24564e8	−	3.88956e8i	−0.269047	−	0.466003i
$355$	−1.44903e8	+	2.50979e8i	−0.171901	+	0.297741i
$356$			6.14206e7i			0.0721505i
$357$	6.59950e8	+	3.81023e8i	0.767667	+	0.443212i
$358$	9.94890e8	+	5.74400e8i	1.14600	+	0.661643i
$359$		−	5.16223e8i		−	0.588853i	−0.955674	−	0.294427i	$-0.904871\pi$
$359$		−	5.16223e8i		−	0.588853i	0.955674	−	0.294427i	$-0.0951286\pi$
$360$	2.05617e8	−	3.56140e8i	0.232274	−	0.402311i
$361$	−4.12125e8	−	7.13821e8i	−0.461056	−	0.798572i
$362$	1.75483e9	−	1.01315e9i	1.94426	−	1.12252i
$363$	3.08965e9			3.39028
$364$	3.46693e8	−	7.30670e8i	0.376782	−	0.794084i
$365$	5.94462e8			0.639880
$366$	−1.69725e9	+	9.79908e8i	−1.80952	+	1.04472i
$367$	−5.16064e8	−	8.93849e8i	−0.544969	−	0.943915i	−0.998609	−	0.0527295i	$-0.983208\pi$
$367$	−5.16064e8	−	8.93849e8i	−0.544969	−	0.943915i	0.453639	−	0.891185i	$-0.350125\pi$
$368$	−3.64658e8	+	6.31607e8i	−0.381433	+	0.660662i
$369$			2.54815e9i			2.64018i
$370$	1.15285e9	+	6.65597e8i	1.18322	+	0.683133i
$371$	−8.65649e8	−	4.99783e8i	−0.880102	−	0.508127i
$372$			1.13433e9i			1.14245i
$373$	9.00042e8	−	1.55892e9i	0.898012	−	1.55540i	0.0679796	−	0.997687i	$-0.478345\pi$
$373$	9.00042e8	−	1.55892e9i	0.898012	−	1.55540i	0.830032	−	0.557715i	$-0.188322\pi$
$374$	−8.97403e8	−	1.55435e9i	−0.887027	−	1.53638i
$375$	−1.66693e9	+	9.62404e8i	−1.63233	+	0.942428i
$376$	−1.67428e8			−0.162432
$377$	−2.36491e8	−	1.12212e8i	−0.227311	−	0.107856i
$378$	−1.98463e9			−1.88998
$379$	6.87995e8	−	3.97214e8i	0.649155	−	0.374790i	−0.138978	−	0.990296i	$-0.544382\pi$
$379$	6.87995e8	−	3.97214e8i	0.649155	−	0.374790i	0.788132	+	0.615506i	$0.211048\pi$
$380$	−1.42631e8	−	2.47044e8i	−0.133343	−	0.230957i
$381$	−3.78201e8	+	6.55064e8i	−0.350337	+	0.606801i
$382$			1.40907e9i			1.29333i
$383$	−1.63844e9	−	9.45952e8i	−1.49016	−	0.860346i	−0.490226	−	0.871595i	$-0.663086\pi$
$383$	−1.63844e9	−	9.45952e8i	−1.49016	−	0.860346i	−0.999937	+	0.0112491i	$0.996419\pi$
$384$	−9.48601e8	−	5.47675e8i	−0.854918	−	0.493587i
$385$		−	1.13052e9i		−	1.00963i
$386$	3.73119e8	−	6.46262e8i	0.330211	−	0.571943i
$387$	−2.28730e8	−	3.96172e8i	−0.200602	−	0.347453i
$388$	−1.46399e9	+	8.45234e8i	−1.27241	+	0.734626i
$389$	−9.79194e8			−0.843422			−0.421711	−	0.906730i	$-0.638570\pi$
$389$	−9.79194e8			−0.843422			−0.421711	+	0.906730i	$0.638570\pi$
$390$	1.93401e8	+	2.39522e9i	0.165095	+	2.04465i
$391$	−8.20016e8			−0.693751
$392$	1.37986e8	−	7.96662e7i	0.115700	−	0.0667994i
$393$	−1.65103e9	−	2.85966e9i	−1.37208	−	2.37651i
$394$	1.06045e9	−	1.83676e9i	0.873484	−	1.51292i
$395$			4.77690e8i			0.389993i
$396$	4.40566e9	+	2.54361e9i	3.56515	+	2.05834i
$397$	1.02057e9	+	5.89224e8i	0.818605	+	0.472622i	0.849935	−	0.526887i	$-0.176641\pi$
$397$	1.02057e9	+	5.89224e8i	0.818605	+	0.472622i	−0.0313301	+	0.999509i	$0.509974\pi$
$398$		−	1.61317e9i		−	1.28260i
$399$	−2.25433e8	+	3.90461e8i	−0.177669	+	0.307732i
$400$	1.77195e8	+	3.06911e8i	0.138434	+	0.239774i
$401$	8.16601e8	−	4.71465e8i	0.632418	−	0.365127i	−0.149270	−	0.988797i	$-0.547692\pi$
$401$	8.16601e8	−	4.71465e8i	0.632418	−	0.365127i	0.781688	+	0.623670i	$0.214359\pi$
$402$	−3.48676e9			−2.67690
$403$	−4.11523e8	−	5.96174e8i	−0.313204	−	0.453738i
$404$	1.17622e9			0.887468
$405$	9.29724e8	−	5.36777e8i	0.695443	−	0.401514i
$406$	1.84741e8	+	3.19981e8i	0.137001	+	0.237292i
$407$	−1.34944e9	+	2.33729e9i	−0.992137	+	1.71843i
$408$		−	4.80657e8i		−	0.350368i
$409$	1.70476e9	+	9.84245e8i	1.23206	+	0.711331i	0.967459	−	0.253027i	$-0.0814262\pi$
$409$	1.70476e9	+	9.84245e8i	1.23206	+	0.711331i	0.264602	+	0.964358i	$0.414760\pi$
$410$	−1.88737e9	−	1.08967e9i	−1.35242	−	0.780822i
$411$			3.94774e9i			2.80480i
$412$	3.71875e7	−	6.44107e7i	0.0261973	−	0.0453751i
$413$	−1.10249e8	−	1.90957e8i	−0.0770105	−	0.133386i
$414$	3.69585e9	−	2.13380e9i	2.55984	−	1.47792i
$415$	−3.64362e8			−0.250245
$416$	2.08554e9	−	1.68396e8i	1.42034	−	0.114685i
$417$	4.31767e9			2.91590
$418$	9.19632e8	−	5.30950e8i	0.615881	−	0.355579i
$419$	9.78364e8	+	1.69458e9i	0.649758	+	1.12541i	0.983181	+	0.182636i	$0.0584630\pi$
$419$	9.78364e8	+	1.69458e9i	0.649758	+	1.12541i	−0.333423	+	0.942777i	$0.608204\pi$
$420$	9.23662e8	−	1.59983e9i	0.608332	−	1.05366i
$421$		−	2.92602e8i		−	0.191113i	−0.995424	−	0.0955563i	$-0.969537\pi$
$421$		−	2.92602e8i		−	0.191113i	0.995424	−	0.0955563i	$-0.0304630\pi$
$422$	−7.31107e8	−	4.22105e8i	−0.473573	−	0.273418i
$423$	−1.50899e9	−	8.71215e8i	−0.969382	−	0.559673i
$424$			6.30471e8i			0.401684i
$425$	−1.99232e8	+	3.45079e8i	−0.125892	+	0.218051i
$426$	−8.81420e8	−	1.52666e9i	−0.552395	−	0.956775i
$427$	−8.33262e8	+	4.81084e8i	−0.517945	+	0.299036i
$428$	1.07123e7			0.00660437
$429$	−4.85608e9	+	3.92103e8i	−2.96951	+	0.239772i
$430$	3.91249e8			0.237309
$431$	−8.46643e7	+	4.88810e7i	−0.0509366	+	0.0294083i	−0.525252	−	0.850947i	$-0.676029\pi$
$431$	−8.46643e7	+	4.88810e7i	−0.0509366	+	0.0294083i	0.474315	+	0.880355i	$0.342696\pi$
$432$	−1.11317e9	−	1.92807e9i	−0.664308	−	1.15062i
$433$	−3.26639e8	+	5.65755e8i	−0.193357	+	0.334904i	−0.946361	−	0.323112i	$-0.895271\pi$
$433$	−3.26639e8	+	5.65755e8i	−0.193357	+	0.334904i	0.753004	+	0.658016i	$0.228604\pi$
$434$			1.02252e9i			0.600425i
$435$	−5.17807e8	−	2.98956e8i	−0.301617	−	0.174139i
$436$	5.38759e8	+	3.11053e8i	0.311309	+	0.179734i
$437$		−	4.85163e8i		−	0.278101i
$438$	−1.80801e9	+	3.13156e9i	−1.02811	+	1.78074i
$439$	7.87825e8	+	1.36455e9i	0.444431	+	0.769777i	0.998012	−	0.0630183i	$-0.0200726\pi$
$439$	7.87825e8	+	1.36455e9i	0.444431	+	0.769777i	−0.553582	+	0.832795i	$0.686739\pi$
$440$	−6.17535e8	+	3.56534e8i	−0.345603	+	0.199534i
$441$	1.65818e9			0.920652
$442$	1.06400e9	+	1.54141e9i	0.586087	+	0.849064i
$443$	2.36999e9			1.29519			0.647594	−	0.761985i	$-0.275775\pi$
$443$	2.36999e9			1.29519			0.647594	+	0.761985i	$0.275775\pi$
$444$	−3.81926e9	+	2.20505e9i	−2.07080	+	1.19558i
$445$	−4.47983e7	−	7.75930e7i	−0.0240991	−	0.0417409i
$446$	2.05515e9	−	3.55962e9i	1.09691	−	1.89991i
$447$		−	2.93619e9i		−	1.55492i
$448$	−1.63040e9	−	9.41315e8i	−0.856687	−	0.494609i
$449$	1.77974e8	+	1.02754e8i	0.0927887	+	0.0535716i	0.545676	−	0.837996i	$-0.316273\pi$
$449$	1.77974e8	+	1.02754e8i	0.0927887	+	0.0535716i	−0.452888	+	0.891568i	$0.649606\pi$
$450$		−	2.07372e9i		−	1.07277i
$451$	2.20921e9	−	3.82646e9i	1.13401	−	1.96417i
$452$	−1.60709e9	−	2.78357e9i	−0.818572	−	1.41781i
$453$	−1.79403e9	+	1.03578e9i	−0.906745	+	0.523509i
$454$	3.20048e7			0.0160516
$455$	9.49498e7	+	1.17593e9i	0.0472557	+	0.585248i
$456$	2.84381e8			0.140451
$457$	−2.33582e9	+	1.34858e9i	−1.14481	+	0.660954i	−0.947616	−	0.319411i	$-0.896515\pi$
$457$	−2.33582e9	+	1.34858e9i	−1.14481	+	0.660954i	−0.197190	+	0.980365i	$0.563182\pi$
$458$	1.73867e9	+	3.01146e9i	0.845643	+	1.46470i
$459$	1.25161e9	−	2.16785e9i	0.604122	−	1.04637i
$460$			1.98785e9i			0.952209i
$461$	1.66805e9	+	9.63051e8i	0.792970	+	0.457821i	0.841007	−	0.541024i	$-0.181963\pi$
$461$	1.66805e9	+	9.63051e8i	0.792970	+	0.457821i	−0.0480374	+	0.998846i	$0.515297\pi$
$462$	5.95544e9	+	3.43837e9i	2.80974	+	1.62221i
$463$		−	2.34776e9i		−	1.09931i	−0.835391	−	0.549655i	$-0.814759\pi$
$463$		−	2.34776e9i		−	1.09931i	0.835391	−	0.549655i	$-0.185241\pi$
$464$	−2.07242e8	+	3.58954e8i	−0.0963085	+	0.166811i
$465$	−8.27344e8	−	1.43300e9i	−0.381593	−	0.660939i
$466$	−4.97955e9	+	2.87495e9i	−2.27950	+	1.31607i
$467$	−1.71342e9			−0.778493			−0.389246	−	0.921134i	$-0.627264\pi$
$467$	−1.71342e9			−0.778493			−0.389246	+	0.921134i	$0.627264\pi$
$468$	−4.79625e9	−	2.27575e9i	−2.16293	−	1.02628i
$469$	−1.71182e9			−0.766219
$470$	1.29058e9	−	7.45119e8i	0.573381	−	0.331042i
$471$	1.71483e9	+	2.97017e9i	0.756219	+	1.30981i
$472$	−6.95392e7	+	1.20445e8i	−0.0304392	+	0.0527222i
$473$			7.93221e8i			0.344652i
$474$	−2.51642e9	−	1.45286e9i	−1.08532	−	0.626611i
$475$	−2.04167e8	−	1.17876e8i	−0.0874092	−	0.0504657i
$476$		−	1.43986e9i		−	0.611921i
$477$	−3.28067e9	+	5.68228e9i	−1.38404	+	2.39722i
$478$	3.31092e9	+	5.73468e9i	1.38660	+	2.40166i
$479$	9.86746e7	−	5.69698e7i	0.0410234	−	0.0236848i	−0.479348	−	0.877625i	$-0.659127\pi$
$479$	9.86746e7	−	5.69698e7i	0.0410234	−	0.0236848i	0.520371	+	0.853940i	$0.325794\pi$
$480$	4.77924e9			1.97249
$481$	1.20733e9	−	2.54451e9i	0.494675	−	1.04255i
$482$	−1.30332e9			−0.530137
$483$	2.72093e9	−	1.57093e9i	1.09876	−	0.634370i
$484$	−2.91889e9	−	5.05566e9i	−1.17020	−	2.02684i
$485$	1.23298e9	−	2.13558e9i	0.490748	−	0.850001i
$486$			2.20257e7i			0.00870367i
$487$	6.89579e8	+	3.98129e8i	0.270541	+	0.156197i	0.629133	−	0.777297i	$-0.283410\pi$
$487$	6.89579e8	+	3.98129e8i	0.270541	+	0.156197i	−0.358593	+	0.933494i	$0.616743\pi$
$488$	5.25576e8	+	3.03442e8i	0.204723	+	0.118197i
$489$		−	2.79446e9i		−	1.08073i
$490$	−7.09089e8	+	1.22818e9i	−0.272279	+	0.471601i
$491$	1.82811e9	+	3.16637e9i	0.696973	+	1.20719i	0.969511	+	0.245048i	$0.0788038\pi$
$491$	1.82811e9	+	3.16637e9i	0.696973	+	1.20719i	−0.272538	+	0.962145i	$0.587863\pi$
$492$	6.25264e9	−	3.60996e9i	2.36693	−	1.36655i
$493$	−4.66030e8			−0.175166
$494$	−9.11978e8	+	6.29515e8i	−0.340361	+	0.234942i
$495$	−7.42092e9			−2.75004
$496$	−9.93383e8	+	5.73530e8i	−0.365537	+	0.211043i
$497$	−4.32731e8	−	7.49513e8i	−0.158114	−	0.273862i
$498$	1.10818e9	−	1.91942e9i	0.402075	−	0.696414i
$499$		−	7.46131e8i		−	0.268821i	−0.990926	−	0.134411i	$-0.957086\pi$
$499$		−	7.46131e8i		−	0.268821i	0.990926	−	0.134411i	$-0.0429141\pi$
$500$	3.14961e9	+	1.81843e9i	1.12684	+	0.650581i
$501$	5.62015e8	+	3.24479e8i	0.199671	+	0.115280i
$502$		−	5.88270e9i		−	2.07546i
$503$	2.34080e8	−	4.05438e8i	0.0820117	−	0.142048i	−0.822102	−	0.569340i	$-0.807199\pi$
$503$	2.34080e8	−	4.05438e8i	0.0820117	−	0.142048i	0.904114	+	0.427291i	$0.140532\pi$
$504$	6.14047e8	+	1.06356e9i	0.213646	+	0.370046i
$505$	−1.48592e9	+	8.57897e8i	−0.513424	+	0.296425i
$506$	−7.39987e9			−2.53920
$507$	5.01820e9	−	8.15705e8i	1.71009	−	0.277975i
$508$	1.42920e9			0.483692
$509$	−5.13887e8	+	2.96693e8i	−0.172725	+	0.0997229i	−0.583870	−	0.811847i	$-0.698462\pi$
$509$	−5.13887e8	+	2.96693e8i	−0.172725	+	0.0997229i	0.411145	+	0.911570i	$0.365129\pi$
$510$	2.13910e9	+	3.70503e9i	0.714062	+	1.23679i
$511$	−8.87637e8	+	1.53743e9i	−0.294281	+	0.509710i
$512$		−	3.98841e9i		−	1.31327i
$513$	1.28261e9	+	7.40516e8i	0.419454	+	0.242172i
$514$	5.21542e9	+	3.01113e9i	1.69402	+	0.978043i
$515$			1.08494e8i			0.0350009i
$516$	−6.48083e8	+	1.12251e9i	−0.207662	+	0.359681i
$517$	1.51066e9	+	2.61654e9i	0.480783	+	0.832741i
$518$	−3.44281e9	+	1.98771e9i	−1.08833	+	0.628346i
$519$	3.02329e9			0.949280
$520$	6.12395e8	−	4.22721e8i	0.190994	−	0.131838i
$521$	2.35950e9			0.730950			0.365475	−	0.930821i	$-0.380907\pi$
$521$	2.35950e9			0.730950			0.365475	+	0.930821i	$0.380907\pi$
$522$	2.10042e9	−	1.21268e9i	0.646337	−	0.373163i
$523$	−2.74632e8	−	4.75677e8i	−0.0839451	−	0.145397i	0.820996	−	0.570934i	$-0.193419\pi$
$523$	−2.74632e8	−	4.75677e8i	−0.0839451	−	0.145397i	−0.904941	+	0.425537i	$0.860085\pi$
$524$	−3.11955e9	+	5.40323e9i	−0.947181	+	1.64057i
$525$		−	1.52670e9i		−	0.460465i
$526$	−2.89683e9	−	1.67249e9i	−0.867907	−	0.501086i
$527$	−1.11692e9	−	6.44855e8i	−0.332419	−	0.191922i
$528$			7.71430e9i			2.28075i
$529$	1.19760e7	−	2.07431e7i	0.00351737	−	0.00609227i
$530$	−2.80583e9	−	4.85985e9i	−0.818646	−	1.41794i
$531$	−1.25348e9	+	7.23696e8i	−0.363317	+	0.209761i
$532$	8.51893e8			0.245298
$533$	−1.97657e9	+	4.16570e9i	−0.565414	+	1.19164i
$534$	5.45002e8			0.154883
$535$	−1.35330e7	+	7.81326e6i	−0.00382080	+	0.00220594i
$536$	5.39861e8	+	9.35068e8i	0.151428	+	0.262281i
$537$	2.77587e9	−	4.80795e9i	0.773552	−	1.33983i
$538$			1.08115e9i			0.299328i
$539$	−2.49002e9	−	1.43761e9i	−0.684923	−	0.395440i
$540$	−5.25523e9	−	3.03411e9i	−1.43620	−	0.829188i
$541$		−	6.19192e7i		−	0.0168126i	−0.999965	−	0.00840630i	$-0.997324\pi$
$541$		−	6.19192e7i		−	0.0168126i	0.999965	−	0.00840630i	$-0.00267584\pi$
$542$	4.01954e8	−	6.96204e8i	0.108437	−	0.187819i
$543$	−4.89620e9	−	8.48047e9i	−1.31238	−	2.27311i
$544$	3.22601e9	−	1.86254e9i	0.859151	−	0.496031i
$545$	−9.07489e8			−0.240134
$546$	−6.48343e9	−	3.07630e9i	−1.70463	−	0.808824i
$547$	−4.11747e9			−1.07566			−0.537830	−	0.843053i	$-0.680756\pi$
$547$	−4.11747e9			−1.07566			−0.537830	+	0.843053i	$0.680756\pi$
$548$	6.45979e9	−	3.72956e9i	1.67682	−	0.968112i
$549$	3.15792e9	+	5.46968e9i	0.814514	+	1.41078i
$550$	−1.79788e9	+	3.11402e9i	−0.460777	+	0.798090i
$551$		−	2.75727e8i		−	0.0702181i
$552$	−1.71622e9	−	9.90859e8i	−0.434296	−	0.250741i
$553$	−1.23543e9	−	7.13276e8i	−0.310656	−	0.179358i
$554$			9.94238e9i			2.48431i
$555$	3.21659e9	−	5.57130e9i	0.798676	−	1.38335i
$556$	−4.07904e9	−	7.06510e9i	−1.00646	−	1.74324i
$557$	3.49708e9	−	2.01904e9i	0.857456	−	0.495052i	−0.00570362	−	0.999984i	$-0.501816\pi$
$557$	3.49708e9	−	2.01904e9i	0.857456	−	0.495052i	0.863160	+	0.504931i	$0.168482\pi$
$558$	6.71202e9			1.63544
$559$	−6.66211e7	−	8.25083e8i	−0.0161313	−	0.199782i
$560$	1.86806e9			0.449503
$561$	−7.51161e9	+	4.33683e9i	−1.79624	+	1.03706i
$562$	−1.46497e9	−	2.53741e9i	−0.348139	−	0.602994i
$563$	−3.26975e8	+	5.66337e8i	−0.0772209	+	0.133751i	−0.902050	−	0.431632i	$-0.857938\pi$
$563$	−3.26975e8	+	5.66337e8i	−0.0772209	+	0.133751i	0.824829	+	0.565382i	$0.191271\pi$
$564$			4.93700e9i			1.15874i
$565$	4.06050e9	+	2.34433e9i	0.947131	+	0.546826i
$566$	−9.59912e9	−	5.54206e9i	−2.22523	−	1.28473i
$567$			3.20601e9i			0.738626i
$568$	−2.72943e8	+	4.72752e8i	−0.0624962	+	0.108247i
$569$	1.89049e9	+	3.27443e9i	0.430211	+	0.745148i	0.996891	−	0.0787902i	$-0.0251057\pi$
$569$	1.89049e9	+	3.27443e9i	0.430211	+	0.745148i	−0.566680	+	0.823938i	$0.691772\pi$
$570$	−2.19209e9	+	1.26560e9i	−0.495788	+	0.286243i
$571$	−1.41244e9			−0.317499			−0.158750	−	0.987319i	$-0.550746\pi$
$571$	−1.41244e9			−0.317499			−0.158750	+	0.987319i	$0.550746\pi$
$572$	5.22930e9	+	7.57568e9i	1.16831	+	1.69253i
$573$	6.80952e9			1.51208
$574$	5.63635e9	−	3.25415e9i	1.24396	−	0.718200i
$575$	8.21420e8	+	1.42274e9i	0.180189	+	0.312096i
$576$	−6.17896e9	+	1.07023e10i	−1.34722	+	2.33345i
$577$		−	2.80901e9i		−	0.608749i	−0.952553	−	0.304374i	$-0.901553\pi$
$577$		−	2.80901e9i		−	0.608749i	0.952553	−	0.304374i	$-0.0984474\pi$
$578$	−3.07012e9	−	1.77254e9i	−0.661315	−	0.381810i
$579$	−3.12315e9	−	1.80315e9i	−0.668680	−	0.386063i
$580$			1.12973e9i			0.240424i
$581$	5.44058e8	−	9.42336e8i	0.115088	−	0.199338i
$582$	7.50000e9	+	1.29904e10i	1.57700	+	2.73144i
$583$	9.85289e9	−	5.68857e9i	2.05932	−	1.18895i
$584$	1.11975e9			0.232635
$585$	7.71900e9	−	6.23268e8i	1.59410	−	0.128715i
$586$	8.99889e9			1.84734
$587$	4.64252e9	−	2.68036e9i	0.947371	−	0.546965i	0.0551076	−	0.998480i	$-0.482450\pi$
$587$	4.64252e9	−	2.68036e9i	0.947371	−	0.546965i	0.892263	+	0.451516i	$0.149116\pi$
$588$	−2.34914e9	−	4.06882e9i	−0.476527	−	0.825369i
$589$	3.81529e8	−	6.60828e8i	0.0769351	−	0.133255i
$590$		−	1.23790e9i		−	0.248144i
$591$	−8.87641e9	−	5.12480e9i	−1.76881	−	1.02122i
$592$	−3.86213e9	−	2.22980e9i	−0.765070	−	0.441713i
$593$			2.19757e9i			0.432765i	0.976309	+	0.216382i	$0.0694258\pi$
$593$			2.19757e9i			0.432765i	−0.976309	+	0.216382i	$0.930574\pi$
$594$	1.12946e10	−	1.95628e10i	2.21115	−	3.82983i
$595$	1.05019e9	+	1.81898e9i	0.204389	+	0.354012i
$596$	−4.80456e9	+	2.77391e9i	−0.929591	+	0.536700i
$597$	−7.79589e9			−1.49953
$598$	7.69711e9	−	6.21501e8i	1.47188	−	0.118847i
$599$	−9.75825e9			−1.85515			−0.927573	−	0.373642i	$-0.878109\pi$
$599$	−9.75825e9			−1.85515			−0.927573	+	0.373642i	$0.878109\pi$
$600$	−8.33947e8	+	4.81480e8i	−0.157619	+	0.0910015i
$601$	−1.84366e9	−	3.19331e9i	−0.346434	−	0.600041i	0.639179	−	0.769058i	$-0.279274\pi$
$601$	−1.84366e9	−	3.19331e9i	−0.346434	−	0.600041i	−0.985613	+	0.169017i	$0.945941\pi$
$602$	−5.84205e8	+	1.01187e9i	−0.109138	+	0.189033i
$603$			1.12367e10i			2.08703i
$604$	3.38975e9	+	1.95707e9i	0.625948	+	0.361391i
$605$	7.37489e9	+	4.25790e9i	1.35398	+	0.781720i
$606$		−	1.04369e10i		−	1.90510i
$607$	−2.95249e9	+	5.11386e9i	−0.535831	+	0.928086i	0.463292	+	0.886206i	$0.346668\pi$
$607$	−2.95249e9	+	5.11386e9i	−0.535831	+	0.928086i	−0.999123	+	0.0418806i	$0.986665\pi$
$608$	1.10197e9	+	1.90867e9i	0.198842	+	0.344404i
$609$	1.54636e9	−	8.92789e8i	0.277427	−	0.160173i
$610$	−5.40171e9			−0.963557
$611$	−1.79110e9	−	2.59476e9i	−0.317669	−	0.460207i
$612$	−9.45149e9			−1.66675
$613$	−7.28326e9	+	4.20499e9i	−1.27707	+	0.737316i	−0.976308	−	0.216384i	$-0.930574\pi$
$613$	−7.28326e9	+	4.20499e9i	−1.27707	+	0.737316i	−0.300760	+	0.953700i	$0.597240\pi$
$614$	−3.00220e9	−	5.19996e9i	−0.523419	−	0.906589i
$615$	−5.26600e9	+	9.12097e9i	−0.912888	+	1.58117i
$616$		−	2.12948e9i		−	0.367063i
$617$	7.37210e9	+	4.25629e9i	1.26355	+	0.729512i	0.973760	−	0.227577i	$-0.0730803\pi$
$617$	7.37210e9	+	4.25629e9i	1.26355	+	0.729512i	0.289793	+	0.957089i	$0.406414\pi$
$618$	−5.71534e8	−	3.29975e8i	−0.0974052	−	0.0562369i
$619$			8.70392e9i			1.47502i	0.675337	+	0.737509i	$0.263998\pi$
$619$			8.70392e9i			1.47502i	−0.675337	+	0.737509i	$0.736002\pi$
$620$	−1.56324e9	+	2.70760e9i	−0.263423	+	0.456262i
$621$	−5.16031e9	−	8.93792e9i	−0.864679	−	1.49767i
$622$	−7.18853e9	+	4.15030e9i	−1.19777	+	0.691533i
$623$	2.67568e8			0.0443328
$624$	−6.47909e8	−	8.02416e9i	−0.106750	−	1.32207i
$625$	−3.09788e9			−0.507556
$626$	4.57071e9	−	2.63890e9i	0.744686	−	0.429945i
$627$	−2.56589e9	−	4.44426e9i	−0.415721	−	0.720050i
$628$	3.24011e9	−	5.61203e9i	0.522036	−	0.904194i
$629$		−	5.01421e9i		−	0.803388i
$630$	−9.46649e9	−	5.46548e9i	−1.50833	−	0.870836i
$631$	8.56201e9	+	4.94328e9i	1.35667	+	0.783272i	0.989173	−	0.146754i	$-0.0468826\pi$
$631$	8.56201e9	+	4.94328e9i	1.35667	+	0.783272i	0.367494	+	0.930026i	$0.380216\pi$
$632$			8.99792e8i			0.141786i
$633$	−2.03988e9	+	3.53318e9i	−0.319663	+	0.553672i
$634$	5.23239e9	+	9.06277e9i	0.815432	+	1.41237i
$635$	−1.80551e9	+	1.04241e9i	−0.279829	+	0.161559i
$636$	1.85909e10			2.86549
$637$	2.71078e9	+	1.28623e9i	0.415533	+	0.197165i
$638$	−4.20548e9			−0.641126
$639$	−4.91994e9	+	2.84053e9i	−0.745945	+	0.430672i
$640$	−1.50952e9	−	2.61457e9i	−0.227619	−	0.394248i
$641$	−3.38085e9	+	5.85580e9i	−0.507017	+	0.878179i	0.492950	+	0.870058i	$0.335918\pi$
$641$	−3.38085e9	+	5.85580e9i	−0.507017	+	0.878179i	−0.999967	+	0.00812132i	$0.997415\pi$
$642$		−	9.50536e7i		−	0.0141774i
$643$	2.43813e9	+	1.40766e9i	0.361676	+	0.208814i	0.669816	−	0.742528i	$-0.266373\pi$
$643$	2.43813e9	+	1.40766e9i	0.361676	+	0.208814i	−0.308140	+	0.951341i	$0.599706\pi$
$644$	−5.14111e9	−	2.96822e9i	−0.758501	−	0.437921i
$645$		−	1.89077e9i		−	0.277447i
$646$	−9.86447e8	+	1.70858e9i	−0.143966	+	0.249356i
$647$	−5.96746e9	−	1.03360e10i	−0.866213	−	1.50033i	−0.865837	−	0.500326i	$-0.833214\pi$
$647$	−5.96746e9	−	1.03360e10i	−0.866213	−	1.50033i	−0.000375912	−	1.00000i	$-0.500120\pi$
$648$	1.75126e9	−	1.01109e9i	0.252835	−	0.145975i
$649$	2.50973e9			0.360388
$650$	1.60856e9	−	3.39010e9i	0.229741	−	0.484190i
$651$	4.94149e9			0.701979
$652$	−4.57265e9	+	2.64002e9i	−0.646102	+	0.373027i
$653$	−6.41202e8	−	1.11059e9i	−0.0901153	−	0.156084i	0.817444	−	0.576008i	$-0.195390\pi$
$653$	−6.41202e8	−	1.11059e9i	−0.0901153	−	0.156084i	−0.907559	+	0.419924i	$0.862057\pi$
$654$	2.76006e9	−	4.78056e9i	0.385830	−	0.668277i
$655$		−	9.10123e9i		−	1.26548i
$656$	6.32283e9	+	3.65049e9i	0.874476	+	0.504879i
$657$	1.00920e10	+	5.82662e9i	1.38835	+	0.801563i
$658$			4.45038e9i			0.608985i
$659$	2.42623e9	−	4.20235e9i	0.330242	−	0.571996i	−0.652317	−	0.757946i	$-0.726203\pi$
$659$	2.42623e9	−	4.20235e9i	0.330242	−	0.571996i	0.982559	+	0.185950i	$0.0595363\pi$
$660$	1.05132e10	+	1.82094e10i	1.42341	+	2.46543i
$661$	−4.12321e9	+	2.38054e9i	−0.555304	+	0.320605i	−0.751258	−	0.660008i	$-0.770553\pi$
$661$	−4.12321e9	+	2.38054e9i	−0.555304	+	0.320605i	0.195955	+	0.980613i	$0.437219\pi$
$662$	8.44658e9			1.13156
$663$	7.44909e9	−	5.14192e9i	0.992673	−	0.685216i
$664$	−6.86325e8			−0.0909790
$665$	−1.07620e9	+	6.21345e8i	−0.141912	+	0.0819327i
$666$	1.30477e10	+	2.25993e10i	1.71149	+	2.96438i
$667$	−9.60706e8	+	1.66399e9i	−0.125357	+	0.217125i
$668$		−	1.22618e9i		−	0.159162i
$669$	−1.72024e10	−	9.93181e9i	−2.22125	−	1.28244i
$670$	−8.32280e9	−	4.80517e9i	−1.06907	−	0.617230i
$671$		−	1.09515e10i		−	1.39941i
$672$	−7.13625e9	+	1.23604e10i	−0.907147	+	1.57123i
$673$	−5.17406e9	−	8.96173e9i	−0.654303	−	1.13329i	−0.982068	−	0.188526i	$-0.939629\pi$
$673$	−5.17406e9	−	8.96173e9i	−0.654303	−	1.13329i	0.327766	−	0.944759i	$-0.393704\pi$
$674$	1.39996e10	−	8.08267e9i	1.76119	−	1.01682i
$675$	−5.01501e9			−0.627637
$676$	−6.07561e9	−	7.44078e9i	−0.756444	−	0.926414i
$677$	−1.09230e9			−0.135295			−0.0676477	−	0.997709i	$-0.521549\pi$
$677$	−1.09230e9			−0.135295			−0.0676477	+	0.997709i	$0.521549\pi$
$678$	−2.46994e10	+	1.42602e10i	−3.04356	+	1.75720i
$679$	3.68211e9	+	6.37760e9i	0.451390	+	0.781831i
$680$	6.62401e8	−	1.14731e9i	0.0807867	−	0.139927i
$681$		−	1.54668e8i		−	0.0187666i
$682$	−1.00792e10	−	5.81922e9i	−1.21669	−	0.702456i
$683$	6.69361e9	+	3.86456e9i	0.803875	+	0.464117i	0.844824	−	0.535044i	$-0.179705\pi$
$683$	6.69361e9	+	3.86456e9i	0.803875	+	0.464117i	−0.0409497	+	0.999161i	$0.513038\pi$
$684$		−	5.59199e9i		−	0.668144i
$685$	−5.44046e9	+	9.42314e9i	−0.646723	+	1.12016i
$686$	−6.72169e9	−	1.16423e10i	−0.794958	−	1.37691i
$687$	1.45533e10	−	8.40236e9i	1.71243	−	0.988673i
$688$	−1.31072e9			−0.153444
$689$	−9.77088e9	+	6.74459e9i	−1.13806	+	0.785576i
$690$	1.76388e10			2.04407
$691$	7.44583e9	−	4.29885e9i	0.858500	−	0.495655i	−0.00500987	−	0.999987i	$-0.501595\pi$
$691$	7.44583e9	−	4.29885e9i	0.858500	−	0.495655i	0.863510	+	0.504332i	$0.168261\pi$
$692$	−2.85620e9	−	4.94709e9i	−0.327656	−	0.567516i
$693$	1.10808e10	−	1.91924e10i	1.26474	−	2.19060i
$694$		−	7.72008e9i		−	0.876725i
$695$	1.03061e10	+	5.95025e9i	1.16453	+	0.672340i
$696$	−9.75358e8	−	5.63123e8i	−0.109656	−	0.0633098i
$697$			8.20893e9i			0.918273i
$698$	2.05015e9	−	3.55097e9i	0.228188	−	0.395232i
$699$	1.38936e10	+	2.40644e10i	1.53867	+	2.66505i
$700$	−2.49818e9	+	1.44232e9i	−0.275283	+	0.158935i
$701$	4.34708e9			0.476633			0.238317	−	0.971188i	$-0.423404\pi$
$701$	4.34708e9			0.476633			0.238317	+	0.971188i	$0.423404\pi$
$702$	−1.01052e10	+	2.12972e10i	−1.10247	+	2.32350i
$703$	2.96666e9			0.322051
$704$	1.85574e10	−	1.07141e10i	2.00453	−	1.15732i
$705$	−3.60089e9	−	6.23693e9i	−0.387033	−	0.670362i
$706$	−4.54403e9	+	7.87048e9i	−0.485987	+	0.841754i
$707$		−	5.12397e9i		−	0.545304i
$708$	3.55160e9	+	2.05052e9i	0.376104	+	0.217144i
$709$	−1.06035e10	−	6.12194e9i	−1.11735	−	0.645100i	−0.176624	−	0.984278i	$-0.556518\pi$
$709$	−1.06035e10	−	6.12194e9i	−1.11735	−	0.645100i	−0.940722	+	0.339178i	$0.889851\pi$
$710$		−	4.85880e9i		−	0.509477i
$711$	−4.68208e9	+	8.10960e9i	−0.488534	+	0.846166i
$712$	−8.43835e7	−	1.46157e8i	−0.00876149	−	0.0151753i
$713$	−4.60500e9	+	2.65870e9i	−0.475791	+	0.274698i
$714$	−1.27762e10			−1.31359
$715$	−1.21317e10	−	5.75631e9i	−1.24122	−	0.588942i
$716$	−1.04898e10			−1.06800
$717$	2.77137e10	−	1.60005e10i	2.80787	−	1.62113i
$718$	4.32743e9	+	7.49533e9i	0.436309	+	0.755710i
$719$	−1.14736e9	+	1.98729e9i	−0.115119	+	0.199393i	−0.917828	−	0.396979i	$-0.870058\pi$
$719$	−1.14736e9	+	1.98729e9i	−0.115119	+	0.199393i	0.802708	+	0.596372i	$0.203392\pi$
$720$		−	1.22623e10i		−	1.22436i
$721$	−2.80593e8	−	1.62001e8i	−0.0278807	−	0.0160969i
$722$	1.19677e10	+	6.90957e9i	1.18340	+	0.683237i
$723$			6.29851e9i			0.619803i
$724$	−9.25119e9	+	1.60235e10i	−0.905968	+	1.56918i
$725$	4.66828e8	+	8.08569e8i	0.0454960	+	0.0788015i
$726$	−4.48603e10	+	2.59001e10i	−4.35095	+	2.51202i
$727$	−5.74619e9			−0.554638			−0.277319	−	0.960778i	$-0.589446\pi$
$727$	−5.74619e9			−0.554638			−0.277319	+	0.960778i	$0.589446\pi$
$728$	1.78851e8	+	2.21501e9i	0.0171803	+	0.212773i
$729$	−1.04071e10			−0.994908
$730$	−8.63132e9	+	4.98329e9i	−0.821196	+	0.474118i
$731$	−7.36860e8	−	1.27628e9i	−0.0697708	−	0.120847i
$732$	8.94765e9	−	1.54978e10i	0.843180	−	1.46043i
$733$		−	1.26955e9i		−	0.119065i	−0.998226	−	0.0595326i	$-0.981039\pi$
$733$		−	1.26955e9i		−	0.119065i	0.998226	−	0.0595326i	$-0.0189610\pi$
$734$	1.49860e10	+	8.65219e9i	1.39878	+	0.807588i
$735$	5.93535e9	+	3.42678e9i	0.551367	+	0.318332i
$736$		−	1.53582e10i		−	1.41994i
$737$	9.74204e9	−	1.68737e10i	0.896424	−	1.55265i
$738$	−2.13608e10	−	3.69980e10i	−1.95623	−	3.38830i
$739$	2.22921e9	−	1.28703e9i	0.203187	−	0.117310i	−0.394954	−	0.918701i	$-0.629240\pi$
$739$	2.22921e9	−	1.28703e9i	0.203187	−	0.117310i	0.598141	+	0.801391i	$0.295906\pi$
$740$	−1.21553e10			−1.10269
$741$	3.04222e9	+	4.40727e9i	0.274680	+	0.397929i
$742$	1.67584e10			1.50598
$743$	−4.19446e9	+	2.42167e9i	−0.375159	+	0.216598i	−0.675710	−	0.737168i	$-0.736163\pi$
$743$	−4.19446e9	+	2.42167e9i	−0.375159	+	0.216598i	0.300551	+	0.953766i	$0.402829\pi$
$744$	−1.55841e9	−	2.69925e9i	−0.138732	−	0.240291i
$745$	4.04642e9	−	7.00860e9i	0.358529	−	0.620990i
$746$			3.01797e10i			2.66152i
$747$	−6.18567e9	−	3.57130e9i	−0.542956	−	0.313476i
$748$	1.41929e10	+	8.19429e9i	1.23998	+	0.715905i
$749$		−	4.66664e7i		−	0.00405805i
$750$	1.61354e10	−	2.79474e10i	1.39658	−	2.41895i
$751$	1.03699e10	+	1.79612e10i	0.893378	+	1.54738i	0.835800	+	0.549034i	$0.185004\pi$
$751$	1.03699e10	+	1.79612e10i	0.893378	+	1.54738i	0.0575779	+	0.998341i	$0.481662\pi$
$752$	−4.32356e9	+	2.49621e9i	−0.370748	+	0.214051i
$753$	−2.84290e10			−2.42650
$754$	4.37441e9	−	3.53210e8i	0.371637	−	0.0300078i
$755$	−5.70971e9			−0.482836
$756$	1.56940e10	−	9.06093e9i	1.32101	−	0.762688i
$757$	−1.49204e9	−	2.58429e9i	−0.125010	−	0.216524i	0.796727	−	0.604340i	$-0.206563\pi$
$757$	−1.49204e9	−	2.58429e9i	−0.125010	−	0.216524i	−0.921737	+	0.387816i	$0.873230\pi$
$758$	−6.65959e9	+	1.15347e10i	−0.555399	+	0.961979i
$759$			3.57610e10i			2.96868i
$760$	6.78809e8	+	3.91911e8i	0.0560919	+	0.0323847i
$761$	−1.83097e10	−	1.05711e10i	−1.50603	−	0.869507i	−0.999975	−	0.00700633i	$-0.997770\pi$
$761$	−1.83097e10	−	1.05711e10i	−1.50603	−	0.869507i	−0.506055	−	0.862501i	$-0.668897\pi$
$762$		−	1.26816e10i		−	1.03832i
$763$	1.35504e9	−	2.34700e9i	0.110438	−	0.191284i
$764$	−6.43317e9	−	1.11426e10i	−0.521914	−	0.903981i
$765$	1.19401e10	−	6.89363e9i	0.964258	−	0.556715i
$766$	3.17191e10			2.54989
$767$	−2.61054e9	+	2.10787e8i	−0.208904	+	0.0168679i
$768$	−1.09120e10			−0.869240
$769$	1.19184e8	−	6.88110e7i	0.00945097	−	0.00545652i	−0.495267	−	0.868741i	$-0.664930\pi$
$769$	1.19184e8	−	6.88110e7i	0.00945097	−	0.00545652i	0.504718	+	0.863284i	$0.331596\pi$
$770$	9.47696e9	+	1.64146e10i	0.748086	+	1.29572i
$771$	1.45517e10	−	2.52043e10i	1.14347	−	1.98054i
$772$			6.81399e9i			0.533017i
$773$	3.53984e9	+	2.04373e9i	0.275649	+	0.159146i	0.631452	−	0.775415i	$-0.282459\pi$
$773$	3.53984e9	+	2.04373e9i	0.275649	+	0.159146i	−0.355803	+	0.934561i	$0.615793\pi$
$774$	6.64212e9	+	3.83483e9i	0.514889	+	0.297271i
$775$			2.58384e9i			0.199393i
$776$	2.32247e9	−	4.02264e9i	0.178416	−	0.309026i
$777$	9.60589e9	+	1.66379e10i	0.734622	+	1.27240i
$778$	1.42175e10	−	8.20845e9i	1.08241	−	0.624932i
$779$	−4.85683e9			−0.368105
$780$	−1.24649e10	−	1.80578e10i	−0.940495	−	1.36249i
$781$	9.85077e9			0.739932
$782$	1.19063e10	−	6.87408e9i	0.890331	−	0.514033i
$783$	−2.93270e9	−	5.07958e9i	−0.218324	−	0.378148i
$784$	2.37551e9	−	4.11450e9i	0.176056	−	0.304937i
$785$			9.45295e9i			0.697466i
$786$	4.79443e10	+	2.76807e10i	3.52175	+	2.03328i
$787$	−1.59259e10	−	9.19480e9i	−1.16464	−	0.672404i	−0.212227	−	0.977220i	$-0.568072\pi$
$787$	−1.59259e10	−	9.19480e9i	−1.16464	−	0.672404i	−0.952411	+	0.304816i	$0.901405\pi$
$788$			1.93662e10i			1.40995i
$789$	−8.08253e9	+	1.39994e10i	−0.585839	+	1.01470i
$790$	−4.00441e9	−	6.93584e9i	−0.288964	−	0.500500i
$791$	−1.21261e10	+	7.00101e9i	−0.871171	+	0.502971i
$792$	−1.39783e10			−0.999805
$793$	9.19793e8	+	1.13914e10i	0.0654989	+	0.811185i
$794$	−1.97576e10			−1.40075
$795$	−2.34859e10	+	1.35596e10i	−1.65776	+	0.957110i
$796$	7.36503e9	+	1.27566e10i	0.517582	+	0.896478i
$797$	−5.37705e9	+	9.31332e9i	−0.376218	+	0.651629i	−0.990509	−	0.137451i	$-0.956109\pi$
$797$	−5.37705e9	+	9.31332e9i	−0.376218	+	0.651629i	0.614290	+	0.789080i	$0.289442\pi$
$798$		−	7.55908e9i		−	0.526573i
$799$	−4.86124e9	−	2.80664e9i	−0.337158	−	0.194658i
$800$	−6.46306e9	−	3.73145e9i	−0.446297	−	0.257669i
$801$		−	1.75636e9i		−	0.120754i
$802$	−7.90445e9	+	1.36909e10i	−0.541080	+	0.937178i
$803$	−1.01032e10	−	1.74992e10i	−0.688578	−	1.19265i
$804$	2.75726e10	−	1.59190e10i	1.87103	−	1.08024i
$805$	8.65972e9			0.585084
$806$	1.09728e10	+	5.20643e9i	0.738149	+	0.350241i
$807$	5.22482e9			0.349956
$808$	−2.79893e9	+	1.61596e9i	−0.186660	+	0.107768i
$809$	−3.96695e9	−	6.87096e9i	−0.263413	−	0.456245i	0.703734	−	0.710464i	$-0.251515\pi$
$809$	−3.96695e9	−	6.87096e9i	−0.263413	−	0.456245i	−0.967147	+	0.254219i	$0.918182\pi$
$810$	−8.99945e9	+	1.55875e10i	−0.595002	+	1.03057i
$811$		−	2.50497e10i		−	1.64903i	−0.565837	−	0.824517i	$-0.691447\pi$
$811$		−	2.50497e10i		−	1.64903i	0.565837	−	0.824517i	$-0.308553\pi$
$812$	−2.92179e9	−	1.68689e9i	−0.191515	−	0.110571i
$813$	−3.36451e9	−	1.94250e9i	−0.219586	−	0.126778i
$814$		−	4.52485e10i		−	2.94049i
$815$	3.85110e9	−	6.67030e9i	0.249191	−	0.431612i
$816$	−7.16617e9	−	1.24122e10i	−0.461712	−	0.799709i
$817$	7.55112e8	−	4.35964e8i	0.0484433	−	0.0279688i
$818$	−3.30032e10			−2.10824
$819$	−9.91390e9	+	2.08940e10i	−0.630596	+	1.32901i
$820$	1.98998e10			1.26038
$821$	4.79566e9	−	2.76877e9i	0.302445	−	0.174617i	−0.341095	−	0.940029i	$-0.610798\pi$
$821$	4.79566e9	−	2.76877e9i	0.302445	−	0.174617i	0.643541	+	0.765412i	$0.277465\pi$
$822$	−3.30934e10	−	5.73195e10i	−2.07821	−	3.59957i
$823$	1.47330e10	−	2.55183e10i	0.921282	−	1.59571i	0.123847	−	0.992301i	$-0.460477\pi$
$823$	1.47330e10	−	2.55183e10i	0.921282	−	1.59571i	0.797435	−	0.603405i	$-0.206190\pi$
$824$			2.04362e8i			0.0127249i
$825$	1.50490e10	+	8.68852e9i	0.933077	+	0.538712i
$826$	3.20154e9	+	1.84841e9i	0.197664	+	0.114122i
$827$			2.47966e10i			1.52448i	0.647294	+	0.762241i	$0.275901\pi$
$827$			2.47966e10i			1.52448i	−0.647294	+	0.762241i	$0.724099\pi$
$828$	−1.94840e10	+	3.37472e10i	−1.19281	+	2.06601i
$829$	−5.43179e9	−	9.40814e9i	−0.331133	−	0.573539i	0.651601	−	0.758562i	$-0.274098\pi$
$829$	−5.43179e9	−	9.40814e9i	−0.331133	−	0.573539i	−0.982734	+	0.185022i	$0.940764\pi$
$830$	5.29038e9	−	3.05440e9i	0.321154	−	0.185418i
$831$	4.80480e10			2.90450
$832$	−1.84030e10	+	1.27031e10i	−1.10779	+	0.764676i
$833$	5.34185e9			0.320210
$834$	−6.26906e10	+	3.61944e10i	−3.74215	+	2.16053i
$835$	8.94341e8	+	1.54904e9i	0.0531619	+	0.0920791i
$836$	−4.84816e9	+	8.39726e9i	−0.286982	+	0.497068i
$837$		−	1.62321e10i		−	0.956834i
$838$	−2.84108e10	−	1.64030e10i	−1.66775	−	0.962873i
$839$	1.24298e10	+	7.17633e9i	0.726602	+	0.419504i	0.817178	−	0.576386i	$-0.195537\pi$
$839$	1.24298e10	+	7.17633e9i	0.726602	+	0.419504i	−0.0905759	+	0.995890i	$0.528871\pi$
$840$			5.07594e9i			0.295488i
$841$	8.07895e9	−	1.39932e10i	0.468348	−	0.811203i
$842$	2.45284e9	+	4.24844e9i	0.141604	+	0.245266i
$843$	−1.22624e10	+	7.07969e9i	−0.704982	+	0.407022i
$844$	7.70857e9			0.441342
$845$	1.31024e10	+	4.96861e9i	0.747056	+	0.283293i
$846$	2.92131e10			1.65875
$847$	−2.20241e10	+	1.27156e10i	−1.24539	+	0.719026i
$848$	9.39977e9	+	1.62809e10i	0.529336	+	0.916837i
$849$	−2.67828e10	+	4.63892e10i	−1.50203	+	2.60159i
$850$		−	6.68053e9i		−	0.373117i
$851$	−1.79036e10	−	1.03366e10i	−0.995833	−	0.574944i
$852$	1.39401e10	+	8.04835e9i	0.772198	+	0.445829i
$853$			2.42734e10i			1.33909i	0.742774	+	0.669543i	$0.233510\pi$
$853$			2.42734e10i			1.33909i	−0.742774	+	0.669543i	$0.766490\pi$
$854$	8.06572e9	−	1.39702e10i	0.443140	−	0.767541i
$855$	4.07862e9	+	7.06438e9i	0.223168	+	0.386539i
$856$	−2.54911e7	+	1.47173e7i	−0.00138909	+	0.000801992i
$857$	9.63070e9			0.522667			0.261334	−	0.965249i	$-0.415838\pi$
$857$	9.63070e9			0.522667			0.261334	+	0.965249i	$0.415838\pi$
$858$	6.72211e10	−	4.64010e10i	3.63329	−	2.50797i
$859$	2.19480e10			1.18146			0.590729	−	0.806870i	$-0.298840\pi$
$859$	2.19480e10			1.18146			0.590729	+	0.806870i	$0.298840\pi$
$860$	−3.09391e9	+	1.78627e9i	−0.165868	+	0.0957641i
$861$	−1.57261e10	−	2.72385e10i	−0.839675	−	1.45436i
$862$	8.19525e8	−	1.41946e9i	0.0435800	−	0.0754827i
$863$			1.90983e10i			1.01148i	0.862686	+	0.505740i	$0.168780\pi$
$863$			1.90983e10i			1.01148i	−0.862686	+	0.505740i	$0.831220\pi$
$864$	4.06022e10	+	2.34417e10i	2.14166	+	1.23649i
$865$	7.21651e9	+	4.16645e9i	0.379115	+	0.218882i
$866$		−	1.09527e10i		−	0.573070i
$867$	−8.56604e9	+	1.48368e10i	−0.446389	+	0.773168i
$868$	−4.66838e9	−	8.08587e9i	−0.242297	−	0.419670i
$869$	1.40618e10	−	8.11857e9i	0.726894	−	0.419672i
$870$	1.00244e10			0.516110
$871$	−8.71616e9	+	1.83697e10i	−0.446953	+	0.941973i
$872$	−1.70938e9			−0.0873031
$873$	4.18637e10	−	2.41700e10i	2.12955	−	1.22950i
$874$	4.06706e9	+	7.04435e9i	0.206058	+	0.356904i
$875$	7.92165e9	−	1.37207e10i	0.399749	−	0.692385i
$876$		−	3.30182e10i		−	1.65955i
$877$	−2.41084e10	−	1.39190e10i	−1.20690	−	0.696802i	−0.244817	−	0.969569i	$-0.578728\pi$
$877$	−2.41084e10	−	1.39190e10i	−1.20690	−	0.696802i	−0.962080	+	0.272767i	$0.912061\pi$
$878$	−2.28777e10	−	1.32085e10i	−1.14073	−	0.658600i
$879$		−	4.34885e10i		−	2.15980i
$880$	−1.06312e10	+	1.84138e10i	−0.525888	+	0.910865i
$881$	1.12237e10	+	1.94400e10i	0.552992	+	0.957811i	0.998057	+	0.0623123i	$0.0198475\pi$
$881$	1.12237e10	+	1.94400e10i	0.552992	+	0.957811i	−0.445064	+	0.895499i	$0.646819\pi$
$882$	−2.40760e10	+	1.39003e10i	−1.18153	+	0.682155i
$883$	1.41508e10			0.691700			0.345850	−	0.938290i	$-0.387591\pi$
$883$	1.41508e10			0.691700			0.345850	+	0.938290i	$0.387591\pi$
$884$	−1.54512e10	−	7.33140e9i	−0.752282	−	0.356947i
$885$	−5.98234e9			−0.290115
$886$	−3.44112e10	+	1.98673e10i	−1.66219	+	0.959667i
$887$	−1.63692e10	−	2.83523e10i	−0.787582	−	1.36413i	−0.927445	−	0.373961i	$-0.878000\pi$
$887$	−1.63692e10	−	2.83523e10i	−0.787582	−	1.36413i	0.139863	−	0.990171i	$-0.455334\pi$
$888$	6.05888e9	−	1.04943e10i	0.290367	−	0.502930i
$889$		−	6.22603e9i		−	0.297204i
$890$	1.30090e9	+	7.51077e8i	0.0618557	+	0.0357124i
$891$	−3.16022e10	−	1.82456e10i	−1.49674	−	0.864142i
$892$			3.75316e10i			1.77060i
$893$	1.66055e9	−	2.87616e9i	0.0780319	−	0.135155i
$894$	2.46137e10	+	4.26322e10i	1.15211	+	1.99552i
$895$	1.32518e10	−	7.65095e9i	0.617868	−	0.356726i
$896$	9.01594e9			0.418729
$897$	−3.00349e9	−	3.71974e10i	−0.138948	−	1.72083i
$898$	−3.44548e9			−0.158775
$899$	−2.61710e9	+	1.51099e9i	−0.120133	+	0.0693588i
$900$	9.46767e9	+	1.63985e10i	0.432907	+	0.749817i
$901$	−1.05687e10	+	1.83056e10i	−0.481378	+	0.833772i
$902$			7.40780e10i			3.36098i
$903$	4.89002e9	+	2.82326e9i	0.221006	+	0.127598i
$904$	7.64849e9	+	4.41586e9i	0.344339	+	0.198804i
$905$		−	2.69902e10i		−	1.21042i
$906$	1.73656e10	−	3.00782e10i	0.775786	−	1.34370i
$907$	2.32474e9	+	4.02657e9i	0.103454	+	0.179188i	0.913106	−	0.407723i	$-0.133677\pi$
$907$	2.32474e9	+	4.02657e9i	0.103454	+	0.179188i	−0.809651	+	0.586911i	$0.800344\pi$
$908$	−2.53087e8	+	1.46120e8i	−0.0112194	+	0.00647751i
$909$	−3.36347e10			−1.48530
$910$	−1.12363e10	−	1.62780e10i	−0.494284	−	0.716069i
$911$	−1.91286e9			−0.0838242			−0.0419121	−	0.999121i	$-0.513345\pi$
$911$	−1.91286e9			−0.0838242			−0.0419121	+	0.999121i	$0.513345\pi$
$912$	7.34367e9	−	4.23987e9i	0.320576	−	0.185085i
$913$	6.19251e9	+	1.07258e10i	0.269289	+	0.466423i
$914$	2.26100e10	−	3.91617e10i	0.979465	−	1.69648i
$915$			2.61046e10i			1.12653i
$916$	−2.74980e10	−	1.58760e10i	−1.18213	−	0.682505i
$917$	2.35382e10	+	1.35898e10i	1.00804	+	0.581995i
$918$			4.19683e10i			1.79049i
$919$	2.25653e10	−	3.90842e10i	0.959039	−	1.66110i	0.234196	−	0.972189i	$-0.424754\pi$
$919$	2.25653e10	−	3.90842e10i	0.959039	−	1.66110i	0.724843	−	0.688914i	$-0.241912\pi$
$920$	−2.73104e9	−	4.73030e9i	−0.115630	−	0.200277i
$921$	−2.51296e10	+	1.45086e10i	−1.05993	+	0.611949i
$922$	−3.22925e10			−1.35689
$923$	−1.02464e10	+	8.27347e8i	−0.428911	+	0.0346323i
$924$	−6.27923e10			−2.61851
$925$	−8.69973e9	+	5.02279e9i	−0.361418	+	0.208665i
$926$	1.96810e10	+	3.40884e10i	0.814532	+	1.41081i
$927$	−1.06340e9	+	1.84187e9i	−0.0438448	+	0.0759415i
$928$		−	8.72837e9i		−	0.358522i
$929$	−5.68298e9	−	3.28107e9i	−0.232553	−	0.134264i	0.379196	−	0.925316i	$-0.376200\pi$
$929$	−5.68298e9	−	3.28107e9i	−0.232553	−	0.134264i	−0.611749	+	0.791052i	$0.709534\pi$
$930$	2.40253e10	+	1.38710e10i	0.979442	+	0.565481i
$931$			3.16051e9i			0.128361i
$932$	2.62515e10	−	4.54689e10i	1.06218	−	1.83975i
$933$	2.00569e10	+	3.47396e10i	0.808498	+	1.40036i
$934$	2.48781e10	−	1.43634e10i	0.999086	−	0.576822i
$935$	−2.39067e10			−0.956485
$936$	1.45397e10	−	1.17401e9i	0.579551	−	0.0467957i
$937$	−1.55199e10			−0.616314			−0.308157	−	0.951336i	$-0.599712\pi$
$937$	−1.55199e10			−0.616314			−0.308157	+	0.951336i	$0.599712\pi$
$938$	2.48549e10	−	1.43500e10i	0.983334	−	0.567728i
$939$	−1.27529e10	−	2.20886e10i	−0.502664	−	0.870640i
$940$	−6.80376e9	+	1.17845e10i	−0.267179	+	0.462767i
$941$			1.49766e10i			0.585933i	0.956123	+	0.292967i	$0.0946425\pi$
$941$			1.49766e10i			0.585933i	−0.956123	+	0.292967i	$0.905358\pi$
$942$	−4.97971e10	−	2.87504e10i	−1.94100	−	1.12064i
$943$	2.93106e10	+	1.69225e10i	1.13824	+	0.657162i
$944$			4.14707e9i			0.160450i
$945$	−1.32175e10	+	2.28934e10i	−0.509494	+	0.882470i
$946$	−6.64947e9	−	1.15172e10i	−0.255369	−	0.442312i
$947$	1.03810e10	−	5.99345e9i	0.397203	−	0.229325i	−0.288073	−	0.957608i	$-0.593015\pi$
$947$	1.03810e10	−	5.99345e9i	0.397203	−	0.229325i	0.685276	+	0.728283i	$0.259681\pi$
$948$	2.65324e10			1.01146
$949$	1.19787e10	+	1.73535e10i	0.454965	+	0.659108i
$950$	3.95254e9			0.149570
$951$	4.37972e10	−	2.52863e10i	1.65126	−	0.953353i
$952$	1.97817e9	+	3.42629e9i	0.0743077	+	0.128705i
$953$	−3.02214e9	+	5.23451e9i	−0.113107	+	0.195907i	−0.917022	−	0.398838i	$-0.869414\pi$
$953$	−3.02214e9	+	5.23451e9i	−0.113107	+	0.195907i	0.803914	+	0.594745i	$0.202747\pi$
$954$		−	1.10006e11i		−	4.10200i
$955$	1.62541e10	+	9.38432e9i	0.603882	+	0.348651i
$956$	−5.23640e10	−	3.02324e10i	−1.93834	−	1.11910i
$957$			2.03236e10i			0.749565i
$958$	−9.55141e8	+	1.65435e9i	−0.0350985	+	0.0607923i
$959$	−1.62471e10	−	2.81409e10i	−0.594856	−	1.03032i
$960$	−4.42345e10	+	2.55388e10i	−1.61366	+	0.931647i
$961$	1.91495e10			0.696025
$962$	3.80034e9	+	4.70661e10i	0.137629	+	1.70449i
$963$	−3.06327e8			−0.0110533
$964$	1.03064e10	−	5.95040e9i	0.370542	−	0.213932i
$965$	−4.96991e9	−	8.60815e9i	−0.178034	−	0.308364i
$966$	−2.63378e10	+	4.56185e10i	−0.940070	+	1.62825i
$967$		−	4.09241e9i		−	0.145541i	−0.997349	−	0.0727706i	$-0.976816\pi$
$967$		−	4.09241e9i		−	0.145541i	0.997349	−	0.0727706i	$-0.0231841\pi$
$968$	1.38916e10	+	8.02031e9i	0.492253	+	0.284202i
$969$	8.25694e9	+	4.76715e9i	0.291532	+	0.168316i
$970$			4.13435e10i			1.45447i
$971$	−2.47218e10	+	4.28194e10i	−0.866587	+	1.50097i	−0.00112478	+	0.999999i	$0.500358\pi$
$971$	−2.47218e10	+	4.28194e10i	−0.866587	+	1.50097i	−0.865462	+	0.500974i	$0.832975\pi$
$972$	−1.00560e8	−	1.74174e8i	−0.00351230	−	0.00608348i
$973$	−3.07778e10	+	1.77696e10i	−1.07113	+	0.618418i
$974$	−1.33498e10			−0.462935
$975$	−1.63832e10	−	7.77358e9i	−0.566085	−	0.268599i
$976$	1.80962e10			0.623035
$977$	4.23697e10	−	2.44622e10i	1.45353	−	0.839197i	0.454852	−	0.890567i	$-0.349692\pi$
$977$	4.23697e10	−	2.44622e10i	1.45353	−	0.839197i	0.998680	+	0.0513706i	$0.0163590\pi$
$978$	2.34256e10	+	4.05743e10i	0.800765	+	1.38696i
$979$	−1.52274e9	+	2.63746e9i	−0.0518664	+	0.0898352i
$980$		−	1.29495e10i		−	0.439504i
$981$	−1.54062e10	−	8.89476e9i	−0.521019	−	0.300810i
$982$	−5.30866e10	−	3.06495e10i	−1.78893	−	1.03284i
$983$		−	1.74370e10i		−	0.585511i	−0.956187	−	0.292755i	$-0.905428\pi$
$983$		−	1.74370e10i		−	0.585511i	0.956187	−	0.292755i	$-0.0945722\pi$
$984$	−9.91920e9	+	1.71806e10i	−0.331890	+	0.574850i
$985$	−1.41251e10	−	2.44655e10i	−0.470940	−	0.815693i
$986$	6.76654e9	−	3.90666e9i	0.224801	−	0.129789i
$987$	2.15071e10			0.711987
$988$	4.33763e9	−	9.14175e9i	0.143088	−	0.301564i
$989$	−6.07605e9			−0.199726
$990$	1.07748e11	−	6.22086e10i	3.52929	−	2.03764i
$991$	2.42425e10	+	4.19893e10i	0.791262	+	1.37051i	0.925186	+	0.379514i	$0.123909\pi$
$991$	2.42425e10	+	4.19893e10i	0.791262	+	1.37051i	−0.133924	+	0.990992i	$0.542758\pi$
$992$	1.20776e10	−	2.09191e10i	0.392818	−	0.680380i
$993$		−	4.08193e10i		−	1.32295i
$994$	1.25661e10	+	7.25506e9i	0.405835	+	0.234309i
$995$	−1.86086e10	−	1.07437e10i	−0.598869	−	0.345757i
$996$			2.02378e10i			0.649017i
$997$	−1.09796e10	+	1.90172e10i	−0.350876	+	0.607735i	−0.986403	−	0.164343i	$-0.947450\pi$
$997$	−1.09796e10	+	1.90172e10i	−0.350876	+	0.607735i	0.635527	+	0.772079i	$0.280783\pi$
$998$	6.25472e9	+	1.08335e10i	0.199182	+	0.344994i
$999$	5.46533e10	−	3.15541e10i	1.73435	−	1.00133i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.8.e.a.10.1	yes	14
3.2	odd	2		117.8.q.b.10.7		14
4.3	odd	2		208.8.w.a.49.1		14
13.2	odd	12		169.8.a.g.1.2		14
13.3	even	3		169.8.b.d.168.2		14
13.4	even	6	inner	13.8.e.a.4.1	✓	14
13.10	even	6		169.8.b.d.168.13		14
13.11	odd	12		169.8.a.g.1.13		14
39.17	odd	6		117.8.q.b.82.7		14
52.43	odd	6		208.8.w.a.17.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.8.e.a.4.1	✓	14	13.4	even	6	inner
13.8.e.a.10.1	yes	14	1.1	even	1	trivial
117.8.q.b.10.7		14	3.2	odd	2
117.8.q.b.82.7		14	39.17	odd	6
169.8.a.g.1.2		14	13.2	odd	12
169.8.a.g.1.13		14	13.11	odd	12
169.8.b.d.168.2		14	13.3	even	3
169.8.b.d.168.13		14	13.10	even	6
208.8.w.a.17.1		14	52.43	odd	6
208.8.w.a.49.1		14	4.3	odd	2

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

\(f(q)\)	\(=\)	\(q+(-14.5196 + 8.38287i) q^{2} +(40.5114 + 70.1679i) q^{3} +(76.5449 - 132.580i) q^{4} +223.318i q^{5} +(-1176.42 - 679.204i) q^{6} +(-577.559 - 333.454i) q^{7} +420.649i q^{8} +(-2188.85 + 3791.20i) q^{9} +(-1872.05 - 3242.48i) q^{10} +(6573.82 - 3795.40i) q^{11} +12403.8 q^{12} +(-6519.11 + 4499.97i) q^{13} +11181.2 q^{14} +(-15669.7 + 9046.93i) q^{15} +(6271.50 + 10862.6i) q^{16} +(-7051.44 + 12213.4i) q^{17} -73395.4i q^{18} +(-7226.10 - 4171.99i) q^{19} +(29607.4 + 17093.9i) q^{20} -54034.7i q^{21} +(-63632.6 + 110215. i) q^{22} +(29072.6 + 50355.3i) q^{23} +(-29516.0 + 17041.1i) q^{24} +28254.0 q^{25} +(56931.9 - 119986. i) q^{26} -177497. q^{27} +(-88418.3 + 51048.4i) q^{28} +(16522.5 + 28617.8i) q^{29} +(151678. - 262715. i) q^{30} +91450.2i q^{31} +(-228748. - 132068. i) q^{32} +(532630. + 307514. i) q^{33} -236445. i q^{34} +(74466.2 - 128979. i) q^{35} +(335091. + 580394. i) q^{36} +(-307911. + 177773. i) q^{37} +139893. q^{38} +(-579852. - 275132. i) q^{39} -93938.5 q^{40} +(504092. - 291038. i) q^{41} +(452966. + 784560. i) q^{42} +(-52248.9 + 90497.7i) q^{43} -1.16207e6i q^{44} +(-846644. - 488810. i) q^{45} +(-844243. - 487424. i) q^{46} +398024. i q^{47} +(-508135. + 880116. i) q^{48} +(-189389. - 328031. i) q^{49} +(-410236. + 236850. i) q^{50} -1.14266e6 q^{51} +(97600.3 + 1.20875e6i) q^{52} +1.49881e6 q^{53} +(2.57718e6 - 1.48793e6i) q^{54} +(847581. + 1.46805e6i) q^{55} +(140267. - 242949. i) q^{56} -676053. i q^{57} +(-479799. - 277012. i) q^{58} +(286332. + 165314. i) q^{59} +2.76999e6i q^{60} +(721365. - 1.24944e6i) q^{61} +(-766615. - 1.32782e6i) q^{62} +(2.52838e6 - 1.45976e6i) q^{63} +2.82292e6 q^{64} +(-1.00493e6 - 1.45583e6i) q^{65} -1.03114e7 q^{66} +(2.22292e6 - 1.28340e6i) q^{67} +(1.07950e6 + 1.86975e6i) q^{68} +(-2.35555e6 + 4.07993e6i) q^{69} +2.49696e6i q^{70} +(1.12386e6 + 648863. i) q^{71} +(-1.59477e6 - 920738. i) q^{72} -2.66195e6i q^{73} +(2.98049e6 - 5.16236e6i) q^{74} +(1.14461e6 + 1.98253e6i) q^{75} +(-1.10624e6 + 638689. i) q^{76} -5.06236e6 q^{77} +(1.07256e7 - 866034. i) q^{78} +2.13906e6 q^{79} +(-2.42581e6 + 1.40054e6i) q^{80} +(-2.40364e6 - 4.16323e6i) q^{81} +(-4.87946e6 + 8.45147e6i) q^{82} +1.63158e6i q^{83} +(-7.16391e6 - 4.13608e6i) q^{84} +(-2.72748e6 - 1.57471e6i) q^{85} -1.75198e6i q^{86} +(-1.33870e6 + 2.31870e6i) q^{87} +(1.59653e6 + 2.76527e6i) q^{88} +(-347455. + 200603. i) q^{89} +1.63905e7 q^{90} +(5.26570e6 - 425178. i) q^{91} +8.90145e6 q^{92} +(-6.41686e6 + 3.70478e6i) q^{93} +(-3.33658e6 - 5.77913e6i) q^{94} +(931681. - 1.61372e6i) q^{95} -2.14010e7i q^{96} +(-9.56294e6 - 5.52117e6i) q^{97} +(5.49968e6 + 3.17524e6i) q^{98} +3.32303e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{2} + 26 q^{3} + 383 q^{4} - 264 q^{6} - 2772 q^{7} - 3491 q^{9} - 509 q^{10} + 6516 q^{11} + 38380 q^{12} + 5109 q^{13} - 47916 q^{14} - 19266 q^{15} - 633 q^{16} - 38403 q^{17} + 43254 q^{19}+ \cdots + 16173003 q^{98}+O(q^{100}) \) 14 * q - 3 * q^2 + 26 * q^3 + 383 * q^4 - 264 * q^6 - 2772 * q^7 - 3491 * q^9 - 509 * q^10 + 6516 * q^11 + 38380 * q^12 + 5109 * q^13 - 47916 * q^14 - 19266 * q^15 - 633 * q^16 - 38403 * q^17 + 43254 * q^19 + 89409 * q^20 - 125882 * q^22 - 68550 * q^23 + 224454 * q^24 + 39380 * q^25 + 361959 * q^26 - 432400 * q^27 - 234780 * q^28 + 221583 * q^29 - 157890 * q^30 - 878067 * q^32 + 219756 * q^33 + 659616 * q^35 + 635675 * q^36 - 565347 * q^37 + 953640 * q^38 + 30082 * q^39 - 77182 * q^40 + 1716057 * q^41 + 206406 * q^42 - 882692 * q^43 - 4616853 * q^45 - 3267480 * q^46 + 1133630 * q^48 + 2653979 * q^49 + 145128 * q^50 - 38964 * q^51 + 4962178 * q^52 - 1791210 * q^53 + 9597234 * q^54 + 2453536 * q^55 - 7457952 * q^56 - 14978127 * q^58 - 1189032 * q^59 + 3858525 * q^61 + 1904142 * q^62 + 7718520 * q^63 + 14570922 * q^64 + 10424661 * q^65 - 31956396 * q^66 + 4674330 * q^67 + 9569619 * q^68 - 13743840 * q^69 - 25203126 * q^71 - 6851607 * q^72 + 8640105 * q^74 + 10316152 * q^75 + 12934506 * q^76 + 19599336 * q^77 + 50085750 * q^78 - 30688440 * q^79 + 29127963 * q^80 + 13886221 * q^81 - 37359719 * q^82 - 96398508 * q^84 - 22436313 * q^85 + 12769686 * q^87 + 27045536 * q^88 + 2123160 * q^89 + 41193546 * q^90 + 37205532 * q^91 - 47685588 * q^92 + 36638964 * q^93 + 19138810 * q^94 - 43420386 * q^95 - 68556288 * q^97 + 16173003 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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