LMFDB - Embedded newform 13.9.f.a.2.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,9,Mod(2,13)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("13.2"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	13.f (of order $12$, degree $4$, 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:	$5.29592193079$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			2.7
Character	$\chi$	$=$	13.2
Dual form			13.9.f.a.7.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(22.9875 + 6.15949i) q^{2} +(34.8819 + 60.4172i) q^{3} +(268.785 + 155.183i) q^{4} +(-80.1911 + 80.1911i) q^{5} +(429.709 + 1603.70i) q^{6} +(249.971 - 66.9796i) q^{7} +(914.868 + 914.868i) q^{8} +(847.009 - 1467.06i) q^{9} +(-2337.33 + 1349.46i) q^{10} +(-193.946 + 723.817i) q^{11} +21652.3i q^{12} +(28552.1 + 714.082i) q^{13} +6158.78 q^{14} +(-7642.13 - 2047.70i) q^{15} +(-24331.4 - 42143.2i) q^{16} +(-98542.8 - 56893.7i) q^{17} +(28507.0 - 28507.0i) q^{18} +(-32412.3 - 120964. i) q^{19} +(-33998.4 + 9109.84i) q^{20} +(12766.2 + 12766.2i) q^{21} +(-8916.69 + 15444.2i) q^{22} +(-95355.9 + 55053.8i) q^{23} +(-23361.4 + 87186.1i) q^{24} +377764. i q^{25} +(651943. + 192281. i) q^{26} +575901. q^{27} +(77582.5 + 20788.2i) q^{28} +(312345. + 540997. i) q^{29} +(-163061. - 94143.3i) q^{30} +(-826405. + 826405. i) q^{31} +(-385463. - 1.43857e6i) q^{32} +(-50496.2 + 13530.4i) q^{33} +(-1.91482e6 - 1.91482e6i) q^{34} +(-14674.3 + 25416.6i) q^{35} +(455326. - 262882. i) q^{36} +(-391225. + 1.46007e6i) q^{37} -2.98031e6i q^{38} +(952807. + 1.74994e6i) q^{39} -146728. q^{40} +(3.80624e6 + 1.01988e6i) q^{41} +(214830. + 372096. i) q^{42} +(-743021. - 428983. i) q^{43} +(-164454. + 164454. i) q^{44} +(49722.7 + 185568. i) q^{45} +(-2.53110e6 + 678206. i) q^{46} +(-2.80556e6 - 2.80556e6i) q^{47} +(1.69745e6 - 2.94007e6i) q^{48} +(-4.93446e6 + 2.84891e6i) q^{49} +(-2.32683e6 + 8.68386e6i) q^{50} -7.93824e6i q^{51} +(7.56354e6 + 4.62273e6i) q^{52} -689788. q^{53} +(1.32385e7 + 3.54726e6i) q^{54} +(-42490.9 - 73596.4i) q^{55} +(289968. + 167413. i) q^{56} +(6.17772e6 - 6.17772e6i) q^{57} +(3.84777e6 + 1.43601e7i) q^{58} +(-1.47598e7 + 3.95488e6i) q^{59} +(-1.73632e6 - 1.73632e6i) q^{60} +(9.16195e6 - 1.58690e7i) q^{61} +(-2.40872e7 + 1.39068e7i) q^{62} +(113465. - 423456. i) q^{63} -2.29857e7i q^{64} +(-2.34688e6 + 2.23236e6i) q^{65} -1.24412e6 q^{66} +(2.61536e7 + 7.00783e6i) q^{67} +(-1.76579e7 - 3.05843e7i) q^{68} +(-6.65239e6 - 3.84076e6i) q^{69} +(-493879. + 493879. i) q^{70} +(-4.29808e6 - 1.60406e7i) q^{71} +(2.11707e6 - 567267. i) q^{72} +(-5.10076e6 - 5.10076e6i) q^{73} +(-1.79866e7 + 3.11537e7i) q^{74} +(-2.28234e7 + 1.31771e7i) q^{75} +(1.00597e7 - 3.75431e7i) q^{76} +193924. i q^{77} +(1.11239e7 + 4.60957e7i) q^{78} +4.76958e7 q^{79} +(5.33067e6 + 1.42835e6i) q^{80} +(1.45313e7 + 2.51689e7i) q^{81} +(8.12141e7 + 4.68890e7i) q^{82} +(-3.73685e7 + 3.73685e7i) q^{83} +(1.45026e6 + 5.41245e6i) q^{84} +(1.24646e7 - 3.33989e6i) q^{85} +(-1.44379e7 - 1.44379e7i) q^{86} +(-2.17904e7 + 3.77420e7i) q^{87} +(-839632. + 484762. i) q^{88} +(2.46257e7 - 9.19044e7i) q^{89} +4.57201e6i q^{90} +(7.18502e6 - 1.73391e6i) q^{91} -3.41736e7 q^{92} +(-7.87556e7 - 2.11025e7i) q^{93} +(-4.72120e7 - 8.17737e7i) q^{94} +(1.22994e7 + 7.10108e6i) q^{95} +(7.34686e7 - 7.34686e7i) q^{96} +(-1.64381e7 - 6.13480e7i) q^{97} +(-1.30979e8 + 3.50957e7i) q^{98} +(897610. + 897610. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 172 q^{5} - 2726 q^{6} - 2784 q^{7} - 10470 q^{8} - 21872 q^{9} - 26886 q^{10} + 6476 q^{11} + 14794 q^{13} + 216232 q^{14} - 127934 q^{15} + 195174 q^{16} + 97644 q^{17}+ \cdots - 359343776 q^{99}+O(q^{100}) $ 32 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 172 * q^5 - 2726 * q^6 - 2784 * q^7 - 10470 * q^8 - 21872 * q^9 - 26886 * q^10 + 6476 * q^11 + 14794 * q^13 + 216232 * q^14 - 127934 * q^15 + 195174 * q^16 + 97644 * q^17 - 475646 * q^18 + 373314 * q^19 + 685798 * q^20 - 213824 * q^21 + 167756 * q^22 - 711654 * q^23 - 1396830 * q^24 - 1041274 * q^26 + 3386272 * q^27 - 491836 * q^28 - 178394 * q^29 - 6200118 * q^30 + 1793468 * q^31 + 955004 * q^32 - 369536 * q^33 + 4592250 * q^34 + 1520488 * q^35 - 11372454 * q^36 + 247730 * q^37 + 14761942 * q^39 + 15044736 * q^40 - 2285272 * q^41 - 1024084 * q^42 + 18199452 * q^43 + 5629904 * q^44 - 10428746 * q^45 - 25708302 * q^46 - 8054836 * q^47 - 19983002 * q^48 - 18234288 * q^49 - 7208294 * q^50 - 26124488 * q^52 - 26091116 * q^53 + 85261048 * q^54 - 2240524 * q^55 + 84926940 * q^56 + 57257116 * q^57 - 68659210 * q^58 - 58197100 * q^59 - 64428232 * q^60 - 38537926 * q^61 + 2935614 * q^62 - 43972436 * q^63 + 44466032 * q^65 + 209850752 * q^66 + 30462126 * q^67 + 68365716 * q^68 + 163279656 * q^69 + 256782116 * q^70 - 113836054 * q^71 - 445647780 * q^72 - 30722748 * q^73 - 156843362 * q^74 - 364524840 * q^75 - 180633890 * q^76 + 252047848 * q^78 + 364818200 * q^79 + 372146084 * q^80 - 17174000 * q^81 + 272314014 * q^82 + 389373188 * q^83 - 464450276 * q^84 - 331999758 * q^85 - 32039076 * q^86 - 337693978 * q^87 - 1180586364 * q^88 - 333088936 * q^89 + 251459988 * q^91 + 1275961956 * q^92 + 637177780 * q^93 + 171539378 * q^94 + 318589986 * q^95 + 1019148280 * q^96 - 230031796 * q^97 - 1287859636 * q^98 - 359343776 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	22.9875	+	6.15949i	1.43672	+	0.384968i	0.891384	−	0.453249i	$-0.149735\pi$
$2$	22.9875	+	6.15949i	1.43672	+	0.384968i	0.545337	+	0.838217i	$0.316402\pi$
$3$	34.8819	+	60.4172i	0.430641	+	0.745891i	0.996929	−	0.0783161i	$-0.0249544\pi$
$3$	34.8819	+	60.4172i	0.430641	+	0.745891i	−0.566288	+	0.824207i	$0.691621\pi$
$4$	268.785	+	155.183i	1.04994	+	0.606183i
$5$	−80.1911	+	80.1911i	−0.128306	+	0.128306i	−0.768343	−	0.640038i	$-0.778919\pi$
$5$	−80.1911	+	80.1911i	−0.128306	+	0.128306i	0.640038	+	0.768343i	$0.278919\pi$
$6$	429.709	+	1603.70i	0.331566	+	1.23742i
$7$	249.971	−	66.9796i	0.104111	−	0.0278965i	−0.206387	−	0.978470i	$-0.566171\pi$
$7$	249.971	−	66.9796i	0.104111	−	0.0278965i	0.310499	+	0.950574i	$0.399504\pi$
$8$	914.868	+	914.868i	0.223356	+	0.223356i
$9$	847.009	−	1467.06i	0.129097	−	0.223603i
$10$	−2337.33	+	1349.46i	−0.233733	+	0.134946i
$11$	−193.946	+	723.817i	−0.0132468	+	0.0494377i	−0.972233	−	0.234015i	$-0.924813\pi$
$11$	−193.946	+	723.817i	−0.0132468	+	0.0494377i	0.958986	+	0.283453i	$0.0914800\pi$
$12$			21652.3i			1.04419i
$13$	28552.1	+	714.082i	0.999687	+	0.0250020i
$13$	28552.1	+	714.082i	0.999687	+	0.0250020i
$14$	6158.78			0.160318
$15$	−7642.13	−	2047.70i	−0.150956	−	0.0404485i
$16$	−24331.4	−	42143.2i	−0.371267	−	0.643054i
$17$	−98542.8	−	56893.7i	−1.17986	−	0.681191i	−0.223876	−	0.974618i	$-0.571871\pi$
$17$	−98542.8	−	56893.7i	−1.17986	−	0.681191i	−0.955982	+	0.293427i	$0.905204\pi$
$18$	28507.0	−	28507.0i	0.271557	−	0.271557i
$19$	−32412.3	−	120964.i	−0.248711	−	0.928202i	−0.971482	−	0.237114i	$-0.923798\pi$
$19$	−32412.3	−	120964.i	−0.248711	−	0.928202i	0.722771	−	0.691088i	$-0.242868\pi$
$20$	−33998.4	+	9109.84i	−0.212490	+	0.0569365i
$21$	12766.2	+	12766.2i	0.0656423	+	0.0656423i
$22$	−8916.69	+	15444.2i	−0.0380639	+	0.0659285i
$23$	−95355.9	+	55053.8i	−0.340750	+	0.196732i	−0.660604	−	0.750735i	$-0.729700\pi$
$23$	−95355.9	+	55053.8i	−0.340750	+	0.196732i	0.319853	+	0.947467i	$0.396366\pi$
$24$	−23361.4	+	87186.1i	−0.0704133	+	0.262786i
$25$			377764.i			0.967075i
$26$	651943.	+	192281.i	1.42665	+	0.420769i
$27$	575901.			1.08366
$28$	77582.5	+	20788.2i	0.126221	+	0.0338208i
$29$	312345.	+	540997.i	0.441614	+	0.764897i	0.997809	−	0.0661539i	$-0.0210728\pi$
$29$	312345.	+	540997.i	0.441614	+	0.764897i	−0.556196	+	0.831051i	$0.687739\pi$
$30$	−163061.	−	94143.3i	−0.201310	−	0.116226i
$31$	−826405.	+	826405.i	−0.894841	+	0.894841i	−0.994974	−	0.100133i	$-0.968073\pi$
$31$	−826405.	+	826405.i	−0.894841	+	0.894841i	0.100133	+	0.994974i	$0.468073\pi$
$32$	−385463.	−	1.43857e6i	−0.367606	−	1.37193i
$33$	−50496.2	+	13530.4i	−0.0425797	+	0.0114092i
$34$	−1.91482e6	−	1.91482e6i	−1.43289	−	1.43289i
$35$	−14674.3	+	25416.6i	−0.00977879	+	0.0169374i
$36$	455326.	−	262882.i	0.271089	−	0.156513i
$37$	−391225.	+	1.46007e6i	−0.208747	+	0.779053i	0.779528	+	0.626367i	$0.215459\pi$
$37$	−391225.	+	1.46007e6i	−0.208747	+	0.779053i	−0.988275	+	0.152686i	$0.951208\pi$
$38$		−	2.98031e6i		−	1.42931i
$39$	952807.	+	1.74994e6i	0.411857	+	0.756425i
$40$	−146728.			−0.0573158
$41$	3.80624e6	+	1.01988e6i	1.34698	+	0.360922i	0.859019	−	0.511944i	$-0.171074\pi$
$41$	3.80624e6	+	1.01988e6i	1.34698	+	0.360922i	0.487960	+	0.872866i	$0.337741\pi$
$42$	214830.	+	372096.i	0.0690395	+	0.119580i
$43$	−743021.	−	428983.i	−0.217334	−	0.125478i	0.387381	−	0.921920i	$-0.373380\pi$
$43$	−743021.	−	428983.i	−0.217334	−	0.125478i	−0.604715	+	0.796442i	$0.706713\pi$
$44$	−164454.	+	164454.i	−0.0438766	+	0.0438766i
$45$	49722.7	+	185568.i	0.0121256	+	0.0452535i
$46$	−2.53110e6	+	678206.i	−0.565299	+	0.151471i
$47$	−2.80556e6	−	2.80556e6i	−0.574947	−	0.574947i	0.358560	−	0.933507i	$-0.383268\pi$
$47$	−2.80556e6	−	2.80556e6i	−0.574947	−	0.574947i	−0.933507	+	0.358560i	$0.883268\pi$
$48$	1.69745e6	−	2.94007e6i	0.319766	−	0.553850i
$49$	−4.93446e6	+	2.84891e6i	−0.855964	+	0.494191i
$50$	−2.32683e6	+	8.68386e6i	−0.372293	+	1.38942i
$51$		−	7.93824e6i		−	1.17339i
$52$	7.56354e6	+	4.62273e6i	1.03446	+	0.632244i
$53$	−689788.			−0.0874202			−0.0437101	−	0.999044i	$-0.513918\pi$
$53$	−689788.			−0.0874202			−0.0437101	+	0.999044i	$0.513918\pi$
$54$	1.32385e7	+	3.54726e6i	1.55692	+	0.417174i
$55$	−42490.9	−	73596.4i	−0.00464350	−	0.00804277i
$56$	289968.	+	167413.i	0.0294848	+	0.0170231i
$57$	6.17772e6	−	6.17772e6i	0.585233	−	0.585233i
$58$	3.84777e6	+	1.43601e7i	0.340014	+	1.26895i
$59$	−1.47598e7	+	3.95488e6i	−1.21807	+	0.326382i	−0.809925	−	0.586534i	$-0.800492\pi$
$59$	−1.47598e7	+	3.95488e6i	−1.21807	+	0.326382i	−0.408148	+	0.912916i	$0.633825\pi$
$60$	−1.73632e6	−	1.73632e6i	−0.133975	−	0.133975i
$61$	9.16195e6	−	1.58690e7i	0.661711	−	1.14612i	−0.318455	−	0.947938i	$-0.603164\pi$
$61$	9.16195e6	−	1.58690e7i	0.661711	−	1.14612i	0.980166	−	0.198179i	$-0.0635028\pi$
$62$	−2.40872e7	+	1.39068e7i	−1.63012	+	0.941152i
$63$	113465.	−	423456.i	0.00720274	−	0.0268810i
$64$		−	2.29857e7i		−	1.37006i
$65$	−2.34688e6	+	2.23236e6i	−0.131473	+	0.125058i
$66$	−1.24412e6			−0.0655674
$67$	2.61536e7	+	7.00783e6i	1.29787	+	0.347764i	0.840645	−	0.541586i	$-0.182176\pi$
$67$	2.61536e7	+	7.00783e6i	1.29787	+	0.347764i	0.457227	+	0.889350i	$0.348843\pi$
$68$	−1.76579e7	−	3.05843e7i	−0.825853	−	1.43042i
$69$	−6.65239e6	−	3.84076e6i	−0.293482	−	0.169442i
$70$	−493879.	+	493879.i	−0.0205697	+	0.0205697i
$71$	−4.29808e6	−	1.60406e7i	−0.169138	−	0.631231i	−0.997476	−	0.0710029i	$-0.977380\pi$
$71$	−4.29808e6	−	1.60406e7i	−0.169138	−	0.631231i	0.828338	−	0.560228i	$-0.189287\pi$
$72$	2.11707e6	−	567267.i	0.0787780	−	0.0211085i
$73$	−5.10076e6	−	5.10076e6i	−0.179615	−	0.179615i	0.611573	−	0.791188i	$-0.290537\pi$
$73$	−5.10076e6	−	5.10076e6i	−0.179615	−	0.179615i	−0.791188	+	0.611573i	$0.790537\pi$
$74$	−1.79866e7	+	3.11537e7i	−0.599821	+	1.03892i
$75$	−2.28234e7	+	1.31771e7i	−0.721333	+	0.416462i
$76$	1.00597e7	−	3.75431e7i	0.301529	−	1.12532i
$77$			193924.i			0.00551656i
$78$	1.11239e7	+	4.60957e7i	0.300524	+	1.24532i
$79$	4.76958e7			1.22454			0.612268	−	0.790650i	$-0.290257\pi$
$79$	4.76958e7			1.22454			0.612268	+	0.790650i	$0.290257\pi$
$80$	5.33067e6	+	1.42835e6i	0.130143	+	0.0348718i
$81$	1.45313e7	+	2.51689e7i	0.337570	+	0.584689i
$82$	8.12141e7	+	4.68890e7i	1.79629	+	1.03709i
$83$	−3.73685e7	+	3.73685e7i	−0.787396	+	0.787396i	−0.981067	−	0.193671i	$-0.937961\pi$
$83$	−3.73685e7	+	3.73685e7i	−0.787396	+	0.787396i	0.193671	+	0.981067i	$0.437961\pi$
$84$	1.45026e6	+	5.41245e6i	0.0291292	+	0.108712i
$85$	1.24646e7	−	3.33989e6i	0.238783	−	0.0639817i
$86$	−1.44379e7	−	1.44379e7i	−0.263943	−	0.263943i
$87$	−2.17904e7	+	3.77420e7i	−0.380354	+	0.658792i
$88$	−839632.	+	484762.i	−0.0140010	+	0.00808347i
$89$	2.46257e7	−	9.19044e7i	0.392490	−	1.46479i	−0.433523	−	0.901143i	$-0.642730\pi$
$89$	2.46257e7	−	9.19044e7i	0.392490	−	1.46479i	0.826013	−	0.563651i	$-0.190604\pi$
$90$			4.57201e6i			0.0696847i
$91$	7.18502e6	−	1.73391e6i	0.104776	−	0.0252848i
$92$	−3.41736e7			−0.477023
$93$	−7.87556e7	−	2.11025e7i	−1.05281	−	0.282099i
$94$	−4.72120e7	−	8.17737e7i	−0.604702	−	1.04737i
$95$	1.22994e7	+	7.10108e6i	0.151005	+	0.0871826i
$96$	7.34686e7	−	7.34686e7i	0.865001	−	0.865001i
$97$	−1.64381e7	−	6.13480e7i	−0.185680	−	0.692968i	−0.994484	−	0.104889i	$-0.966551\pi$
$97$	−1.64381e7	−	6.13480e7i	−0.185680	−	0.692968i	0.808804	−	0.588079i	$-0.200116\pi$
$98$	−1.30979e8	+	3.50957e7i	−1.42003	+	0.380496i
$99$	897610.	+	897610.i	0.00934431	+	0.00934431i
$100$	−5.86225e7	+	1.01537e8i	−0.586225	+	1.01537i
$101$	3.67577e7	−	2.12221e7i	0.353234	−	0.203940i	−0.312875	−	0.949794i	$-0.601292\pi$
$101$	3.67577e7	−	2.12221e7i	0.353234	−	0.203940i	0.666109	+	0.745855i	$0.267959\pi$
$102$	4.88955e7	−	1.82481e8i	0.451719	−	1.68584i
$103$			1.86432e8i			1.65642i	0.560416	+	0.828211i	$0.310641\pi$
$103$			1.86432e8i			1.65642i	−0.560416	+	0.828211i	$0.689359\pi$
$104$	2.54681e7	+	2.67747e7i	0.217702	+	0.228871i
$105$	−2.04747e6			−0.0168446
$106$	−1.58565e7	−	4.24874e6i	−0.125598	−	0.0336540i
$107$	−2.28280e6	−	3.95393e6i	−0.0174154	−	0.0301644i	0.857186	−	0.515006i	$-0.172210\pi$
$107$	−2.28280e6	−	3.95393e6i	−0.0174154	−	0.0301644i	−0.874602	+	0.484842i	$0.838877\pi$
$108$	1.54793e8	+	8.93700e7i	1.13778	+	0.656896i
$109$	1.45033e8	−	1.45033e8i	1.02745	−	1.02745i	0.0278391	−	0.999612i	$-0.491137\pi$
$109$	1.45033e8	−	1.45033e8i	1.02745	−	1.02745i	0.999612	−	0.0278391i	$-0.00886261\pi$
$110$	−523445.	−	1.95352e6i	−0.00357520	−	0.0133428i
$111$	−1.01860e8	+	2.72933e7i	−0.670984	+	0.179790i
$112$	−8.90488e6	−	8.90488e6i	−0.0565921	−	0.0565921i
$113$	−1.00582e8	+	1.74213e8i	−0.616890	+	1.06848i	0.373160	+	0.927767i	$0.378274\pi$
$113$	−1.00582e8	+	1.74213e8i	−0.616890	+	1.06848i	−0.990050	+	0.140717i	$0.955059\pi$
$114$	1.80062e8	−	1.03959e8i	1.06611	−	0.615520i
$115$	3.23187e6	−	1.20615e7i	0.0184783	−	0.0689621i
$116$			1.93882e8i			1.07080i
$117$	2.52315e7	−	4.12828e7i	0.134648	−	0.220306i
$118$	−3.63652e8			−1.87568
$119$	−2.84436e7	−	7.62144e6i	−0.141839	−	0.0380057i
$120$	−5.11816e6	−	8.86492e6i	−0.0246825	−	0.0427514i
$121$	1.85154e8	+	1.06899e8i	0.863757	+	0.498690i
$122$	3.08355e8	−	3.08355e8i	1.39191	−	1.39191i
$123$	7.11506e7	+	2.65538e8i	0.310855	+	1.16013i
$124$	−3.50369e8	+	9.38810e7i	−1.48197	+	0.397092i
$125$	−6.16179e7	−	6.16179e7i	−0.252387	−	0.252387i
$126$	5.21654e6	−	9.03531e6i	0.0206967	−	0.0358477i
$127$	−3.30970e7	+	1.91086e7i	−0.127226	+	0.0734537i	−0.562262	−	0.826959i	$-0.690069\pi$
$127$	−3.30970e7	+	1.91086e7i	−0.127226	+	0.0734537i	0.435037	+	0.900413i	$0.356735\pi$
$128$	4.29017e7	−	1.60111e8i	0.159821	−	0.596461i
$129$		−	5.98550e7i		−	0.216143i
$130$	−6.76992e7	+	3.68608e7i	−0.237034	+	0.129060i
$131$	−7.81218e7			−0.265269			−0.132635	−	0.991165i	$-0.542344\pi$
$131$	−7.81218e7			−0.265269			−0.132635	+	0.991165i	$0.542344\pi$
$132$	−1.56723e7	−	4.19938e6i	−0.0516222	−	0.0138321i
$133$	−1.62043e7	−	2.80666e7i	−0.0517872	−	0.0896981i
$134$	5.58042e8	+	3.22186e8i	1.73080	+	0.999279i
$135$	−4.61821e7	+	4.61821e7i	−0.139040	+	0.139040i
$136$	−3.81034e7	−	1.42204e8i	−0.111380	−	0.415677i
$137$	3.52995e8	−	9.45847e7i	1.00204	−	0.268497i	0.279742	−	0.960075i	$-0.409751\pi$
$137$	3.52995e8	−	9.45847e7i	1.00204	−	0.268497i	0.722301	+	0.691579i	$0.243084\pi$
$138$	−1.29265e8	−	1.29265e8i	−0.356422	−	0.356422i
$139$	−1.93534e8	+	3.35211e8i	−0.518440	+	0.897964i	0.481330	+	0.876539i	$0.340154\pi$
$139$	−1.93534e8	+	3.35211e8i	−0.518440	+	0.897964i	−0.999770	+	0.0214252i	$0.993180\pi$
$140$	−7.88845e6	+	4.55440e6i	−0.0205343	+	0.0118555i
$141$	7.16408e7	−	2.67367e8i	0.181252	−	0.676444i
$142$		−	3.95209e8i		−	0.972016i
$143$	−6.05443e6	+	2.05280e7i	−0.0144787	+	0.0490910i
$144$	−8.24355e7			−0.191719
$145$	−6.84304e7	−	1.83359e7i	−0.154802	−	0.0414791i
$146$	−8.58357e7	−	1.48672e8i	−0.188911	−	0.327203i
$147$	−3.44247e8	−	1.98751e8i	−0.737226	−	0.425638i
$148$	−3.31733e8	+	3.31733e8i	−0.691420	+	0.691420i
$149$	−1.43890e8	−	5.37007e8i	−0.291936	−	1.08952i	−0.943621	−	0.331029i	$-0.892604\pi$
$149$	−1.43890e8	−	5.37007e8i	−0.291936	−	1.08952i	0.651685	−	0.758490i	$-0.274062\pi$
$150$	−6.05818e8	+	1.62329e8i	−1.19668	+	0.320649i
$151$	−2.89142e8	−	2.89142e8i	−0.556164	−	0.556164i	0.372049	−	0.928213i	$-0.378655\pi$
$151$	−2.89142e8	−	2.89142e8i	−0.556164	−	0.556164i	−0.928213	+	0.372049i	$0.878655\pi$
$152$	8.10133e7	−	1.40319e8i	0.151769	−	0.262871i
$153$	−1.66933e8	+	9.63790e7i	−0.304633	+	0.175880i
$154$	−1.19447e6	+	4.45783e6i	−0.00212370	+	0.00792575i
$155$		−	1.32541e8i		−	0.229627i
$156$	−1.54615e7	+	6.18217e8i	−0.0261068	+	1.04386i
$157$	1.01088e9			1.66380			0.831900	−	0.554925i	$-0.187253\pi$
$157$	1.01088e9			1.66380			0.831900	+	0.554925i	$0.187253\pi$
$158$	1.09641e9	+	2.93782e8i	1.75932	+	0.471407i
$159$	−2.40611e7	−	4.16750e7i	−0.0376467	−	0.0652060i
$160$	1.46271e8	+	8.44496e7i	0.223192	+	0.128860i
$161$	−2.01488e7	+	2.01488e7i	−0.0299878	+	0.0299878i
$162$	1.79011e8	+	6.68077e8i	0.259907	+	0.969988i
$163$	6.82943e8	−	1.82994e8i	0.967462	−	0.259231i	0.259706	−	0.965688i	$-0.416374\pi$
$163$	6.82943e8	−	1.82994e8i	0.967462	−	0.259231i	0.707756	+	0.706457i	$0.249708\pi$
$164$	8.64791e8	+	8.64791e8i	1.19546	+	1.19546i
$165$	2.96433e6	−	5.13436e6i	0.00399936	−	0.00692709i
$166$	−1.08918e9	+	6.28838e8i	−1.43439	+	0.828145i
$167$	−5.95204e7	+	2.22133e8i	−0.0765245	+	0.285593i	−0.993575	−	0.113179i	$-0.963897\pi$
$167$	−5.95204e7	+	2.22133e8i	−0.0765245	+	0.285593i	0.917050	+	0.398772i	$0.130563\pi$
$168$			2.33587e7i			0.0293233i
$169$	8.14711e8	+	4.07770e7i	0.998750	+	0.0499884i
$170$	3.07103e8			0.367695
$171$	−2.04915e8	−	5.49069e7i	−0.239657	−	0.0642159i
$172$	−1.33142e8	−	2.30608e8i	−0.152125	−	0.263488i
$173$	−1.24660e9	−	7.19724e8i	−1.39169	−	0.803492i	−0.398187	−	0.917304i	$-0.630361\pi$
$173$	−1.24660e9	−	7.19724e8i	−1.39169	−	0.803492i	−0.993502	+	0.113812i	$0.963694\pi$
$174$	−7.33378e8	+	7.33378e8i	−0.800076	+	0.800076i
$175$	2.53025e7	+	9.44301e7i	0.0269780	+	0.100683i
$176$	3.52229e7	−	9.43796e6i	0.0367092	−	0.00983620i
$177$	−7.53794e8	−	7.53794e8i	−0.767997	−	0.767997i
$178$	1.13217e9	−	1.96097e9i	1.12780	−	1.95340i
$179$	−1.27961e9	+	7.38785e8i	−1.24643	+	0.719625i	−0.970395	−	0.241524i	$-0.922353\pi$
$179$	−1.27961e9	+	7.38785e8i	−1.24643	+	0.719625i	−0.276032	+	0.961149i	$0.589020\pi$
$180$	−1.54322e7	+	5.75939e7i	−0.0147007	+	0.0548638i
$181$		−	5.15867e8i		−	0.480644i	−0.970693	−	0.240322i	$-0.922747\pi$
$181$		−	5.15867e8i		−	0.480644i	0.970693	−	0.240322i	$-0.0772531\pi$
$182$	1.75846e8	+	4.39787e6i	0.160268	+	0.00400827i
$183$	1.27834e9			1.13984
$184$	−1.37605e8	−	3.68712e7i	−0.120050	−	0.0321674i
$185$	−8.57119e7	−	1.48457e8i	−0.0731736	−	0.126740i
$186$	−1.68042e9	−	9.70189e8i	−1.40399	−	0.810596i
$187$	6.02927e7	−	6.02927e7i	0.0493058	−	0.0493058i
$188$	−3.18716e8	−	1.18947e9i	−0.255137	−	0.952183i
$189$	1.43959e8	−	3.85736e7i	0.112821	−	0.0302303i
$190$	2.38994e8	+	2.38994e8i	0.183389	+	0.183389i
$191$	−6.93613e8	+	1.20137e9i	−0.521175	+	0.902701i	0.478522	+	0.878076i	$0.341173\pi$
$191$	−6.93613e8	+	1.20137e9i	−0.521175	+	0.902701i	−0.999697	+	0.0246257i	$0.992161\pi$
$192$	1.38873e9	−	8.01785e8i	1.02191	−	0.590001i
$193$	−3.27724e8	+	1.22308e9i	−0.236200	+	0.881509i	0.741405	+	0.671058i	$0.234160\pi$
$193$	−3.27724e8	+	1.22308e9i	−0.236200	+	0.881509i	−0.977604	+	0.210451i	$0.932507\pi$
$194$		−	1.51149e9i		−	1.06708i
$195$	−2.16737e8	−	6.39233e7i	−0.149897	−	0.0442100i
$196$	−1.76841e9			−1.19828
$197$	1.37728e9	+	3.69042e8i	0.914447	+	0.245025i	0.685210	−	0.728346i	$-0.259710\pi$
$197$	1.37728e9	+	3.69042e8i	0.914447	+	0.245025i	0.229237	+	0.973371i	$0.426377\pi$
$198$	1.51050e7	+	2.61627e7i	0.00982790	+	0.0170224i
$199$	6.77278e8	+	3.91027e8i	0.431872	+	0.249341i	0.700144	−	0.714002i	$-0.253119\pi$
$199$	6.77278e8	+	3.91027e8i	0.431872	+	0.249341i	−0.268272	+	0.963343i	$0.586453\pi$
$200$	−3.45604e8	+	3.45604e8i	−0.216002	+	0.216002i
$201$	4.88893e8	+	1.82457e9i	0.299523	+	1.11783i
$202$	9.75686e8	−	2.61434e8i	0.586009	−	0.157021i
$203$	1.14313e8	+	1.14313e8i	0.0673150	+	0.0673150i
$204$	1.23188e9	−	2.13368e9i	0.711291	−	1.23199i
$205$	−3.87012e8	+	2.23441e8i	−0.219133	+	0.126517i
$206$	−1.14832e9	+	4.28560e9i	−0.637670	+	2.37982i
$207$			1.86524e8i			0.101591i
$208$	−6.64618e8	−	1.22065e9i	−0.355074	−	0.652135i
$209$	9.38422e7			0.0491828
$210$	−4.70662e7	−	1.26114e7i	−0.0242009	−	0.00648462i
$211$	1.86950e9	+	3.23807e9i	0.943181	+	1.63364i	0.759352	+	0.650680i	$0.225516\pi$
$211$	1.86950e9	+	3.23807e9i	0.943181	+	1.63364i	0.183829	+	0.982958i	$0.441151\pi$
$212$	−1.85404e8	−	1.07043e8i	−0.0917860	−	0.0529926i
$213$	8.19206e8	−	8.19206e8i	0.397992	−	0.397992i
$214$	−2.81218e7	−	1.04952e8i	−0.0134088	−	0.0500421i
$215$	9.39843e7	−	2.51830e7i	0.0439847	−	0.0117857i
$216$	5.26873e8	+	5.26873e8i	0.242042	+	0.242042i
$217$	−1.51225e8	+	2.61930e8i	−0.0682001	+	0.118126i
$218$	4.22728e9	−	2.44062e9i	1.87170	−	1.08062i
$219$	1.30249e8	−	4.86097e8i	0.0566238	−	0.211323i
$220$		−	2.63754e7i		−	0.0112592i
$221$	−2.77298e9	−	1.69480e9i	−1.16246	−	0.710477i
$222$	−2.50962e9			−1.03323
$223$	−1.66591e9	−	4.46378e8i	−0.673645	−	0.180503i	−0.0942490	−	0.995549i	$-0.530045\pi$
$223$	−1.66591e9	−	4.46378e8i	−0.673645	−	0.180503i	−0.579396	+	0.815046i	$0.696712\pi$
$224$	−1.92709e8	−	3.33782e8i	−0.0765439	−	0.132578i
$225$	5.54203e8	+	3.19969e8i	0.216241	+	0.124847i
$226$	−3.38520e9	+	3.38520e9i	−1.29763	+	1.29763i
$227$	−3.72538e8	−	1.39033e9i	−0.140303	−	0.523619i	−0.999920	−	0.0126787i	$-0.995964\pi$
$227$	−3.72538e8	−	1.39033e9i	−0.140303	−	0.523619i	0.859616	−	0.510940i	$-0.170703\pi$
$228$	2.61915e9	−	7.01799e8i	0.969217	−	0.259701i
$229$	−1.80081e9	−	1.80081e9i	−0.654826	−	0.654826i	0.299325	−	0.954151i	$-0.403238\pi$
$229$	−1.80081e9	−	1.80081e9i	−0.654826	−	0.654826i	−0.954151	+	0.299325i	$0.903238\pi$
$230$	1.48586e8	−	2.57358e8i	0.0530964	−	0.0919657i
$231$	−1.17163e7	+	6.76443e6i	−0.00411475	+	0.00237565i
$232$	−2.09187e8	+	7.80696e8i	−0.0722075	+	0.269482i
$233$			1.93121e9i			0.655247i	0.944808	+	0.327623i	$0.106248\pi$
$233$			1.93121e9i			0.655247i	−0.944808	+	0.327623i	$0.893752\pi$
$234$	8.34290e8	−	7.93577e8i	0.278262	−	0.264683i
$235$	4.49961e8			0.147538
$236$	−4.58094e9	−	1.22746e9i	−1.47675	−	0.395694i
$237$	1.66372e9	+	2.88164e9i	0.527335	+	0.913370i
$238$	−6.06904e8	−	3.50396e8i	−0.189152	−	0.109207i
$239$	3.78359e9	−	3.78359e9i	1.15961	−	1.15961i	0.175051	−	0.984559i	$-0.443991\pi$
$239$	3.78359e9	−	3.78359e9i	1.15961	−	1.15961i	0.984559	−	0.175051i	$-0.0560090\pi$
$240$	9.96469e7	+	3.71887e8i	0.0300344	+	0.112090i
$241$	2.84658e8	−	7.62739e7i	0.0843830	−	0.0226104i	−0.216381	−	0.976309i	$-0.569425\pi$
$241$	2.84658e8	−	7.62739e7i	0.0843830	−	0.0226104i	0.300764	+	0.953699i	$0.402759\pi$
$242$	3.59779e9	+	3.59779e9i	1.04900	+	1.04900i
$243$	8.75486e8	−	1.51639e9i	0.251087	−	0.434895i
$244$	4.92518e9	−	2.84355e9i	1.38951	−	0.802236i
$245$	1.67242e8	−	6.24157e8i	0.0464176	−	0.173233i
$246$			6.54231e9i			1.78645i
$247$	−8.39059e8	−	3.47692e9i	−0.225426	−	0.934130i
$248$	−1.51210e9			−0.399737
$249$	−3.56118e9	−	9.54216e8i	−0.926396	−	0.248227i
$250$	−1.03691e9	−	1.79598e9i	−0.265449	−	0.459770i
$251$	−6.02837e9	−	3.48048e9i	−1.51881	−	0.876888i	−0.999755	−	0.0221507i	$-0.992949\pi$
$251$	−6.02837e9	−	3.48048e9i	−1.51881	−	0.876888i	−0.519060	−	0.854738i	$-0.673718\pi$
$252$	9.62106e7	−	9.62106e7i	0.0238573	−	0.0238573i
$253$	−2.13549e7	−	7.96977e7i	−0.00521214	−	0.0194520i
$254$	−8.78518e8	+	2.35398e8i	−0.211065	+	0.0565546i
$255$	6.36576e8	+	6.36576e8i	0.150553	+	0.150553i
$256$	−9.69764e8	+	1.67968e9i	−0.225791	+	0.391081i
$257$	−4.25956e8	+	2.45926e8i	−0.0976410	+	0.0563730i	−0.548025	−	0.836462i	$-0.684620\pi$
$257$	−4.25956e8	+	2.45926e8i	−0.0976410	+	0.0563730i	0.450384	+	0.892835i	$0.351287\pi$
$258$	3.68676e8	−	1.37592e9i	0.0832082	−	0.310537i
$259$			3.91180e8i			0.0869315i
$260$	−9.77230e8	+	2.35827e8i	−0.213847	+	0.0516060i
$261$	1.05824e9			0.228045
$262$	−1.79583e9	−	4.81190e8i	−0.381118	−	0.102120i
$263$	−8.22041e8	−	1.42382e9i	−0.171819	−	0.297599i	0.767237	−	0.641364i	$-0.221631\pi$
$263$	−8.22041e8	−	1.42382e9i	−0.171819	−	0.297599i	−0.939056	+	0.343765i	$0.888298\pi$
$264$	−5.85759e7	−	3.38188e7i	−0.0120588	−	0.00696214i
$265$	5.53148e7	−	5.53148e7i	0.0112165	−	0.0112165i
$266$	−1.99620e8	−	7.44992e8i	−0.0398729	−	0.148808i
$267$	6.41160e9	−	1.71798e9i	1.26160	−	0.338044i
$268$	5.94219e9	+	5.94219e9i	1.15188	+	1.15188i
$269$	−4.10035e9	+	7.10201e9i	−0.783090	+	1.35635i	0.147044	+	0.989130i	$0.453024\pi$
$269$	−4.10035e9	+	7.10201e9i	−0.783090	+	1.35635i	−0.930134	+	0.367221i	$0.880309\pi$
$270$	−1.34607e9	+	7.77154e8i	−0.253287	+	0.146235i
$271$	7.74813e8	−	2.89164e9i	0.143655	−	0.536127i	−0.856157	−	0.516716i	$-0.827154\pi$
$271$	7.74813e8	−	2.89164e9i	0.143655	−	0.536127i	0.999812	−	0.0194108i	$-0.00617903\pi$
$272$			5.53721e9i			1.01162i
$273$	3.55385e8	+	3.73617e8i	0.0639806	+	0.0672630i
$274$	8.69708e9			1.54302
$275$	−2.73432e8	−	7.32658e7i	−0.0478100	−	0.0128106i
$276$	−1.19204e9	−	2.06467e9i	−0.205426	−	0.355807i
$277$	4.20820e9	+	2.42960e9i	0.714787	+	0.412683i	0.812831	−	0.582499i	$-0.197925\pi$
$277$	4.20820e9	+	2.42960e9i	0.714787	+	0.412683i	−0.0980437	+	0.995182i	$0.531258\pi$
$278$	−6.51360e9	+	6.51360e9i	−1.09054	+	1.09054i
$279$	5.12415e8	+	1.91236e9i	0.0845678	+	0.315611i
$280$	−3.66779e7	+	9.82781e6i	−0.00596722	+	0.00159891i
$281$	1.37760e9	+	1.37760e9i	0.220951	+	0.220951i	0.808899	−	0.587948i	$-0.200064\pi$
$281$	1.37760e9	+	1.37760e9i	0.220951	+	0.220951i	−0.587948	+	0.808899i	$0.700064\pi$
$282$	3.29369e9	−	5.70484e9i	0.520818	−	0.902084i
$283$	−4.79257e8	+	2.76699e8i	−0.0747175	+	0.0431382i	−0.536893	−	0.843650i	$-0.680402\pi$
$283$	−4.79257e8	+	2.76699e8i	−0.0747175	+	0.0431382i	0.462176	+	0.886788i	$0.347069\pi$
$284$	1.33398e9	−	4.97847e9i	0.205057	−	0.765283i
$285$			9.90795e8i			0.150177i
$286$	−2.65618e8	+	4.34595e8i	−0.0397003	+	0.0649562i
$287$	1.01976e9			0.150304
$288$	−2.43696e9	−	6.52981e8i	−0.354224	−	0.0949141i
$289$	2.98592e9	+	5.17176e9i	0.428042	+	0.741390i
$290$	−1.46011e9	−	8.42993e8i	−0.206439	−	0.119188i
$291$	3.13308e9	−	3.13308e9i	0.436917	−	0.436917i
$292$	−5.79455e8	−	2.16255e9i	−0.0797054	−	0.297465i
$293$	−1.72288e9	+	4.61645e8i	−0.233768	+	0.0626380i	−0.373801	−	0.927509i	$-0.621946\pi$
$293$	−1.72288e9	+	4.61645e8i	−0.233768	+	0.0626380i	0.140033	+	0.990147i	$0.455279\pi$
$294$	−6.68918e9	−	6.68918e9i	−0.895331	−	0.895331i
$295$	8.66460e8	−	1.50075e9i	0.114409	−	0.198162i
$296$	−1.69369e9	+	9.77853e8i	−0.220631	+	0.127382i
$297$	−1.11694e8	+	4.16847e8i	−0.0143550	+	0.0535736i
$298$		−	1.32307e10i		−	1.67772i
$299$	−2.76192e9	+	1.50381e9i	−0.345563	+	0.188151i
$300$	−8.17945e9			−1.00981
$301$	−2.14467e8	−	5.74663e7i	−0.0261273	−	0.00700079i
$302$	−4.86569e9	−	8.42761e9i	−0.584947	−	1.01316i
$303$	2.56436e9	+	1.48053e9i	0.304234	+	0.175650i
$304$	−4.30918e9	+	4.30918e9i	−0.504546	+	0.504546i
$305$	5.37842e8	+	2.00725e9i	0.0621521	+	0.231955i
$306$	−4.43103e9	+	1.18729e9i	−0.505381	+	0.135416i
$307$	−6.40334e9	−	6.40334e9i	−0.720864	−	0.720864i	0.247917	−	0.968781i	$-0.420254\pi$
$307$	−6.40334e9	−	6.40334e9i	−0.720864	−	0.720864i	−0.968781	+	0.247917i	$0.920254\pi$
$308$	−3.00937e7	+	5.21237e7i	−0.00334404	+	0.00579205i
$309$	−1.12637e10	+	6.50309e9i	−1.23551	+	0.713322i
$310$	8.16382e8	−	3.04678e9i	0.0883989	−	0.329909i
$311$		−	1.63925e10i		−	1.75228i	−0.482059	−	0.876139i	$-0.660111\pi$
$311$		−	1.63925e10i		−	1.75228i	0.482059	−	0.876139i	$-0.339889\pi$
$312$	−7.29275e8	+	2.47266e9i	−0.0769614	+	0.260943i
$313$	−8.05081e9			−0.838808			−0.419404	−	0.907800i	$-0.637761\pi$
$313$	−8.05081e9			−0.838808			−0.419404	+	0.907800i	$0.637761\pi$
$314$	2.32376e10	+	6.22651e9i	2.39042	+	0.640510i
$315$	2.48585e7	+	4.30562e7i	0.00252483	+	0.00437314i
$316$	1.28199e10	+	7.40156e9i	1.28569	+	0.742293i
$317$	9.31790e9	−	9.31790e9i	0.922743	−	0.922743i	−0.0744791	−	0.997223i	$-0.523729\pi$
$317$	9.31790e9	−	9.31790e9i	0.922743	−	0.922743i	0.997223	+	0.0744791i	$0.0237294\pi$
$318$	−2.96408e8	−	1.10621e9i	−0.0289855	−	0.108176i
$319$	−4.52161e8	+	1.21156e8i	−0.0436647	+	0.0116999i
$320$	1.84325e9	+	1.84325e9i	0.175786	+	0.175786i
$321$	1.59257e8	−	2.75841e8i	0.0149996	−	0.0259800i
$322$	−5.87276e8	+	3.39064e8i	−0.0546285	+	0.0315398i
$323$	−3.68811e9	+	1.37642e10i	−0.338839	+	1.26457i
$324$			9.02003e9i			0.818517i
$325$	−2.69754e8	+	1.07859e10i	−0.0241788	+	0.966773i
$326$	1.68263e10			1.48977
$327$	1.38215e10	+	3.70347e9i	1.20883	+	0.323905i
$328$	2.54915e9	+	4.41526e9i	0.220242	+	0.381471i
$329$	−8.89224e8	−	5.13394e8i	−0.0758975	−	0.0438194i
$330$	9.97676e7	−	9.97676e7i	0.00841266	−	0.00841266i
$331$	2.23505e9	+	8.34131e9i	0.186198	+	0.694900i	0.994371	+	0.105955i	$0.0337898\pi$
$331$	2.23505e9	+	8.34131e9i	0.186198	+	0.694900i	−0.808173	+	0.588945i	$0.799543\pi$
$332$	−1.58430e10	+	4.24512e9i	−1.30402	+	0.349412i
$333$	1.81064e9	+	1.81064e9i	0.147250	+	0.147250i
$334$	−2.73646e9	+	4.73968e9i	−0.219888	+	0.380858i
$335$	−2.65925e9	+	1.53532e9i	−0.211145	+	0.121904i
$336$	2.27389e8	−	8.48626e8i	0.0178407	−	0.0665824i
$337$		−	1.87453e10i		−	1.45336i	−0.686978	−	0.726678i	$-0.741063\pi$
$337$		−	1.87453e10i		−	1.45336i	0.686978	−	0.726678i	$-0.258937\pi$
$338$	1.84770e10	+	5.95557e9i	1.41568	+	0.456306i
$339$	−1.40340e10			−1.06263
$340$	3.86859e9	+	1.03659e9i	0.289492	+	0.0775693i
$341$	−4.37888e8	−	7.58444e8i	−0.0323851	−	0.0560927i
$342$	−4.37230e9	−	2.52435e9i	−0.319599	−	0.184521i
$343$	−2.09757e9	+	2.09757e9i	−0.151544	+	0.151544i
$344$	−2.87303e8	−	1.07223e9i	−0.0205166	−	0.0765692i
$345$	8.41457e8	−	2.25468e8i	0.0593957	−	0.0159150i
$346$	−2.42231e10	−	2.42231e10i	−1.69015	−	1.69015i
$347$	2.60502e9	−	4.51203e9i	0.179678	−	0.311211i	−0.762093	−	0.647468i	$-0.775828\pi$
$347$	2.60502e9	−	4.51203e9i	0.179678	−	0.311211i	0.941770	+	0.336257i	$0.109161\pi$
$348$	−1.17138e10	+	6.76298e9i	−0.798697	+	0.461128i
$349$	−1.28775e9	+	4.80593e9i	−0.0868017	+	0.323948i	−0.995649	−	0.0931799i	$-0.970297\pi$
$349$	−1.28775e9	+	4.80593e9i	−0.0868017	+	0.323948i	0.908848	+	0.417128i	$0.136963\pi$
$350$			2.32656e9i			0.155040i
$351$	1.64432e10	+	4.11241e8i	1.08332	+	0.0270937i
$352$	1.11602e9			0.0726944
$353$	−8.80531e9	−	2.35938e9i	−0.567082	−	0.151949i	−0.0361241	−	0.999347i	$-0.511501\pi$
$353$	−8.80531e9	−	2.35938e9i	−0.567082	−	0.151949i	−0.530958	+	0.847398i	$0.678168\pi$
$354$	−1.26849e10	−	2.19708e10i	−0.807742	−	1.39905i
$355$	1.63098e9	+	9.41649e8i	0.102692	+	0.0592892i
$356$	2.08810e10	−	2.08810e10i	1.30002	−	1.30002i
$357$	−5.31700e8	−	1.98433e9i	−0.0327336	−	0.122163i
$358$	−3.39657e10	+	9.10108e9i	−2.06780	+	0.554065i
$359$	9.23561e9	+	9.23561e9i	0.556017	+	0.556017i	0.928171	−	0.372154i	$-0.121381\pi$
$359$	9.23561e9	+	9.23561e9i	0.556017	+	0.556017i	−0.372154	+	0.928171i	$0.621381\pi$
$360$	−1.24280e8	+	2.15260e8i	−0.00739933	+	0.0128160i
$361$	1.12641e9	−	6.50333e8i	0.0663235	−	0.0382919i
$362$	3.17748e9	−	1.18585e10i	0.185033	−	0.690551i
$363$			1.49153e10i			0.859025i
$364$	2.20030e9	+	6.48945e8i	0.125336	+	0.0369660i
$365$	8.18070e8			0.0460913
$366$	2.93860e10	+	7.87394e9i	1.63763	+	0.438801i
$367$	5.88309e9	+	1.01898e10i	0.324296	+	0.561697i	0.981370	−	0.192130i	$-0.0615394\pi$
$367$	5.88309e9	+	1.01898e10i	0.324296	+	0.561697i	−0.657074	+	0.753826i	$0.728206\pi$
$368$	4.64028e9	+	2.67907e9i	0.253019	+	0.146081i
$369$	4.72015e9	−	4.72015e9i	0.254595	−	0.254595i
$370$	−1.05588e9	−	3.94061e9i	−0.0563390	−	0.210260i
$371$	−1.72427e8	+	4.62017e7i	−0.00910143	+	0.00243872i
$372$	−1.78935e10	−	1.78935e10i	−0.934383	−	0.934383i
$373$	−1.42784e9	+	2.47309e9i	−0.0737639	+	0.127763i	−0.900548	−	0.434756i	$-0.856834\pi$
$373$	−1.42784e9	+	2.47309e9i	−0.0737639	+	0.127763i	0.826784	+	0.562519i	$0.190168\pi$
$374$	1.75735e9	−	1.01461e9i	0.0898198	−	0.0518575i
$375$	1.57343e9	−	5.87213e9i	0.0795652	−	0.296941i
$376$		−	5.13343e9i		−	0.256836i
$377$	8.53178e9	+	1.56696e10i	0.422352	+	0.775700i
$378$	3.54685e9			0.173730
$379$	−2.89048e10	−	7.74501e9i	−1.40092	−	0.375375i	−0.522244	−	0.852796i	$-0.674905\pi$
$379$	−2.89048e10	−	7.74501e9i	−1.40092	−	0.375375i	−0.878675	+	0.477421i	$0.841572\pi$
$380$	2.20393e9	+	3.81732e9i	0.105697	+	0.183073i
$381$	−2.30897e9	−	1.33309e9i	−0.109577	−	0.0632643i
$382$	−2.33443e10	+	2.33443e10i	−1.09629	+	1.09629i
$383$	−5.60108e9	−	2.09035e10i	−0.260301	−	0.971458i	−0.965064	−	0.262015i	$-0.915613\pi$
$383$	−5.60108e9	−	2.09035e10i	−0.260301	−	0.971458i	0.704762	−	0.709443i	$-0.251054\pi$
$384$	1.11700e10	−	2.99298e9i	0.513720	−	0.137651i
$385$	−1.55510e7	−	1.55510e7i	−0.000707806	−	0.000707806i
$386$	−1.50671e10	+	2.60970e10i	−0.678706	+	1.17555i
$387$	−1.25869e9	+	7.26705e8i	−0.0561145	+	0.0323977i
$388$	5.10184e9	−	1.90403e10i	0.225112	−	0.840131i
$389$		−	8.57092e8i		−	0.0374308i	−0.999825	−	0.0187154i	$-0.994042\pi$
$389$		−	8.57092e8i		−	0.0374308i	0.999825	−	0.0187154i	$-0.00595764\pi$
$390$	−4.58850e9	−	2.80442e9i	−0.198341	−	0.121223i
$391$	1.25289e10			0.536049
$392$	−7.12076e9	−	1.90800e9i	−0.301566	−	0.0808043i
$393$	−2.72503e9	−	4.71990e9i	−0.114236	−	0.197862i
$394$	2.93872e10	+	1.69667e10i	1.21948	+	0.704065i
$395$	−3.82477e9	+	3.82477e9i	−0.157115	+	0.157115i
$396$	1.01970e8	+	3.80558e8i	0.00414660	+	0.0154753i
$397$	2.06495e10	−	5.53302e9i	0.831280	−	0.222741i	0.182008	−	0.983297i	$-0.441740\pi$
$397$	2.06495e10	−	5.53302e9i	0.831280	−	0.222741i	0.649272	+	0.760556i	$0.275074\pi$
$398$	1.31604e10	+	1.31604e10i	0.524490	+	0.524490i
$399$	1.13047e9	−	1.95803e9i	0.0446034	−	0.0772553i
$400$	1.59202e10	−	9.19151e9i	0.621882	−	0.359043i
$401$	9.82411e9	−	3.66641e10i	0.379940	−	1.41796i	−0.466050	−	0.884759i	$-0.654323\pi$
$401$	9.82411e9	−	3.66641e10i	0.379940	−	1.41796i	0.845990	−	0.533199i	$-0.179010\pi$
$402$			4.49538e10i			1.72132i
$403$	−2.41857e10	+	2.30055e10i	−0.916935	+	0.872189i
$404$	1.31732e10			0.494500
$405$	−3.18360e9	−	8.53044e8i	−0.118331	−	0.0317067i
$406$	1.92366e9	+	3.33188e9i	0.0707987	+	0.122627i
$407$	−9.80948e8	−	5.66351e8i	−0.0357494	−	0.0206399i
$408$	7.26244e9	−	7.26244e9i	0.262085	−	0.262085i
$409$	−1.18217e10	−	4.41192e10i	−0.422461	−	1.57665i	−0.769406	−	0.638760i	$-0.779447\pi$
$409$	−1.18217e10	−	4.41192e10i	−0.422461	−	1.57665i	0.346945	−	0.937886i	$-0.387219\pi$
$410$	−1.02727e10	+	2.75257e9i	−0.363538	+	0.0974098i
$411$	1.80277e10	+	1.80277e10i	0.631789	+	0.631789i
$412$	−2.89310e10	+	5.01100e10i	−1.00409	+	1.73914i
$413$	−3.42464e9	+	1.97721e9i	−0.117710	+	0.0679600i
$414$	−1.14889e9	+	4.28773e9i	−0.0391091	+	0.145957i
$415$		−	5.99324e9i		−	0.202055i
$416$	−9.97852e9	−	4.13493e10i	−0.333190	−	1.38069i
$417$	−2.70033e10			−0.893045
$418$	2.15720e9	+	5.78020e8i	0.0706619	+	0.0189338i
$419$	4.44085e9	+	7.69178e9i	0.144082	+	0.249558i	0.929030	−	0.370004i	$-0.120644\pi$
$419$	4.44085e9	+	7.69178e9i	0.144082	+	0.249558i	−0.784948	+	0.619562i	$0.787310\pi$
$420$	−5.50328e8	−	3.17732e8i	−0.0176858	−	0.0102109i
$421$	3.57725e9	−	3.57725e9i	0.113873	−	0.113873i	−0.647874	−	0.761747i	$-0.724342\pi$
$421$	3.57725e9	−	3.57725e9i	0.113873	−	0.113873i	0.761747	+	0.647874i	$0.224342\pi$
$422$	2.30303e10	+	8.59503e10i	0.726189	+	2.71018i
$423$	−6.49226e9	+	1.73960e9i	−0.202784	+	0.0543359i
$424$	−6.31064e8	−	6.31064e8i	−0.0195259	−	0.0195259i
$425$	2.14924e10	−	3.72259e10i	0.658763	−	1.14101i
$426$	2.38774e10	−	1.37856e10i	0.725018	−	0.418589i
$427$	1.22733e9	−	4.58045e9i	0.0369189	−	0.137783i
$428$		−	1.41701e9i		−	0.0422277i
$429$	−1.45143e9	+	3.50263e8i	−0.0428517	+	0.0103411i
$430$	2.31558e9			0.0677308
$431$	−5.88723e10	−	1.57748e10i	−1.70609	−	0.457146i	−0.731630	−	0.681702i	$-0.761240\pi$
$431$	−5.88723e10	−	1.57748e10i	−1.70609	−	0.457146i	−0.974461	+	0.224556i	$0.927907\pi$
$432$	−1.40125e10	−	2.42703e10i	−0.402327	−	0.696851i
$433$	5.37740e10	+	3.10464e10i	1.52975	+	0.883202i	0.999372	+	0.0354411i	$0.0112836\pi$
$433$	5.37740e10	+	3.10464e10i	1.52975	+	0.883202i	0.530379	+	0.847761i	$0.322050\pi$
$434$	−5.08965e9	+	5.08965e9i	−0.143459	+	0.143459i
$435$	−1.27918e9	−	4.77397e9i	−0.0357252	−	0.133328i
$436$	6.14893e10	−	1.64760e10i	1.70159	−	0.455939i
$437$	9.75024e9	+	9.75024e9i	0.267356	+	0.267356i
$438$	5.98822e9	−	1.03719e10i	0.162705	−	0.281814i
$439$	2.05544e10	−	1.18671e10i	0.553410	−	0.319511i	−0.197086	−	0.980386i	$-0.563148\pi$
$439$	2.05544e10	−	1.18671e10i	0.553410	−	0.319511i	0.750496	+	0.660875i	$0.229815\pi$
$440$	2.84574e7	−	1.06205e8i	0.000759250	−	0.00283356i
$441$			9.65222e9i			0.255195i
$442$	−5.33047e10	−	5.60394e10i	−1.39662	−	1.46827i
$443$	−5.00688e10			−1.30003			−0.650013	−	0.759923i	$-0.725237\pi$
$443$	−5.00688e10			−1.30003			−0.650013	+	0.759923i	$0.725237\pi$
$444$	−3.16139e10	−	8.47091e9i	−0.813478	−	0.217971i
$445$	5.39515e9	+	9.34468e9i	0.137583	+	0.238300i
$446$	−3.55456e10	−	2.05223e10i	−0.898352	−	0.518664i
$447$	2.74253e10	−	2.74253e10i	0.686943	−	0.686943i
$448$	−1.53957e9	−	5.74577e9i	−0.0382198	−	0.142638i
$449$	−4.07233e10	+	1.09118e10i	−1.00198	+	0.268479i	−0.722273	−	0.691608i	$-0.756903\pi$
$449$	−4.07233e10	+	1.09118e10i	−1.00198	+	0.268479i	−0.279703	+	0.960087i	$0.590236\pi$
$450$	1.07689e10	+	1.07689e10i	0.262616	+	0.262616i
$451$	−1.47641e9	+	2.55722e9i	−0.0356863	+	0.0618105i
$452$	−5.40699e10	+	3.12173e10i	−1.29539	+	0.747896i
$453$	7.38332e9	−	2.75549e10i	0.175331	−	0.654344i
$454$		−	3.42549e10i		−	0.806306i
$455$	−4.37131e8	+	7.15218e8i	−0.0101992	+	0.0166876i
$456$	1.13036e10			0.261431
$457$	2.45307e10	+	6.57299e9i	0.562401	+	0.150695i	0.528809	−	0.848741i	$-0.322639\pi$
$457$	2.45307e10	+	6.57299e9i	0.562401	+	0.150695i	0.0335916	+	0.999436i	$0.489305\pi$
$458$	−3.03041e10	−	5.24882e10i	−0.688714	−	1.19289i
$459$	−5.67509e10	−	3.27652e10i	−1.27856	−	0.738179i
$460$	2.74042e9	−	2.74042e9i	0.0612048	−	0.0612048i
$461$	4.75122e9	+	1.77318e10i	0.105196	+	0.392599i	0.998367	−	0.0571187i	$-0.0181914\pi$
$461$	4.75122e9	+	1.77318e10i	0.105196	+	0.392599i	−0.893171	+	0.449717i	$0.851525\pi$
$462$	−3.10995e8	+	8.33308e7i	−0.00682630	+	0.00182910i
$463$	5.46142e10	+	5.46142e10i	1.18845	+	1.18845i	0.977496	+	0.210955i	$0.0676574\pi$
$463$	5.46142e10	+	5.46142e10i	1.18845	+	1.18845i	0.210955	+	0.977496i	$0.432343\pi$
$464$	1.51996e10	−	2.63264e10i	0.327914	−	0.567963i
$465$	8.00773e9	−	4.62326e9i	0.171276	−	0.0988865i
$466$	−1.18952e10	+	4.43936e10i	−0.252249	+	0.941406i
$467$			7.79373e10i			1.63862i	0.573352	+	0.819309i	$0.305643\pi$
$467$			7.79373e10i			1.63862i	−0.573352	+	0.819309i	$0.694357\pi$
$468$	1.31882e10	−	7.18070e9i	0.274918	−	0.149687i
$469$	7.00703e9			0.144825
$470$	1.03435e10	+	2.77153e9i	0.211971	+	0.0567974i
$471$	3.52614e10	+	6.10746e10i	0.716500	+	1.24101i
$472$	−1.71215e10	−	9.88510e9i	−0.344964	−	0.199165i
$473$	4.54612e8	−	4.54612e8i	0.00908230	−	0.00908230i
$474$	2.04953e10	+	7.64895e10i	0.406014	+	1.51526i
$475$	4.56959e10	−	1.22442e10i	0.897641	−	0.240522i
$476$	−6.46248e9	−	6.46248e9i	−0.125884	−	0.125884i
$477$	−5.84256e8	+	1.01196e9i	−0.0112857	+	0.0195475i
$478$	1.10280e11	−	6.36703e10i	2.11245	−	1.21962i
$479$	−1.90333e10	+	7.10334e10i	−0.361554	+	1.34934i	0.510479	+	0.859890i	$0.329468\pi$
$479$	−1.90333e10	+	7.10334e10i	−0.361554	+	1.34934i	−0.872033	+	0.489447i	$0.837199\pi$
$480$			1.17830e10i			0.221969i
$481$	−1.22129e10	+	4.14087e10i	−0.228159	+	0.773591i
$482$	7.01339e9			0.129939
$483$	−1.92016e9	−	5.14505e8i	−0.0352816	−	0.00945368i
$484$	3.31777e10	+	5.74654e10i	0.604595	+	1.04719i
$485$	6.23775e9	+	3.60137e9i	0.112736	+	0.0650879i
$486$	2.94654e10	−	2.94654e10i	0.528163	−	0.528163i
$487$	−1.62796e10	−	6.07561e10i	−0.289419	−	1.08013i	−0.945549	−	0.325479i	$-0.894475\pi$
$487$	−1.62796e10	−	6.07561e10i	−0.289419	−	1.08013i	0.656131	−	0.754647i	$-0.272192\pi$
$488$	2.29000e10	−	6.13603e9i	0.403790	−	0.108195i
$489$	3.48783e10	+	3.48783e10i	0.609986	+	0.609986i
$490$	7.68898e9	−	1.33177e10i	0.133378	−	0.231018i
$491$	−5.89458e10	+	3.40324e10i	−1.01421	+	0.585553i	−0.912421	−	0.409253i	$-0.865789\pi$
$491$	−5.89458e10	+	3.40324e10i	−1.01421	+	0.585553i	−0.101787	+	0.994806i	$0.532456\pi$
$492$	−2.20827e10	+	8.24138e10i	−0.376870	+	1.40650i
$493$		−	7.10819e10i		−	1.20329i
$494$	2.12819e9	−	8.50941e10i	0.0357357	−	1.42887i
$495$	−1.43961e8			−0.00239786
$496$	5.49349e10	+	1.47198e10i	0.907657	+	0.243206i
$497$	−2.14879e9	−	3.72182e9i	−0.0352183	−	0.0609999i
$498$	−7.59853e10	−	4.38701e10i	−1.23541	−	0.713266i
$499$	−8.51444e10	+	8.51444e10i	−1.37326	+	1.37326i	−0.517703	+	0.855561i	$0.673213\pi$
$499$	−8.51444e10	+	8.51444e10i	−1.37326	+	1.37326i	−0.855561	+	0.517703i	$0.826787\pi$
$500$	−6.99990e9	−	2.61240e10i	−0.111998	−	0.417984i
$501$	−1.54969e10	+	4.15237e9i	−0.245976	+	0.0659091i
$502$	−1.17139e11	−	1.17139e11i	−1.84454	−	1.84454i
$503$	5.49353e10	−	9.51507e10i	0.858182	−	1.48641i	−0.0154796	−	0.999880i	$-0.504928\pi$
$503$	5.49353e10	−	9.51507e10i	0.858182	−	1.48641i	0.873661	−	0.486534i	$-0.161739\pi$
$504$	4.91211e8	−	2.83601e8i	0.00761282	−	0.00439527i
$505$	−1.24582e9	+	4.64946e9i	−0.0191553	+	0.0714886i
$506$		−	1.96359e9i		−	0.0299536i
$507$	2.59550e10	+	5.06449e10i	0.392816	+	0.766486i
$508$	−1.18613e10			−0.178105
$509$	−6.68968e10	−	1.79249e10i	−0.996631	−	0.267046i	−0.276598	−	0.960986i	$-0.589207\pi$
$509$	−6.68968e10	−	1.79249e10i	−0.996631	−	0.267046i	−0.720033	+	0.693939i	$0.755874\pi$
$510$	1.07123e10	+	1.85543e10i	0.158345	+	0.274261i
$511$	−1.61669e9	−	9.33395e8i	−0.0237106	−	0.0136893i
$512$	−6.26441e10	+	6.26441e10i	−0.911592	+	0.911592i
$513$	−1.86663e10	−	6.96634e10i	−0.269518	−	1.00585i
$514$	−1.13064e10	+	3.02955e9i	−0.161985	+	0.0434036i
$515$	−1.49502e10	−	1.49502e10i	−0.212528	−	0.212528i
$516$	9.28847e9	−	1.60881e10i	0.131022	−	0.226937i
$517$	2.57484e9	−	1.48658e9i	0.0360402	−	0.0208078i
$518$	−2.40947e9	+	8.99226e9i	−0.0334659	+	0.124896i
$519$		−	1.00421e11i		−	1.38407i
$520$	−4.18940e9	−	1.04776e8i	−0.0572979	−	0.00143301i
$521$	4.16034e10			0.564648			0.282324	−	0.959319i	$-0.408895\pi$
$521$	4.16034e10			0.564648			0.282324	+	0.959319i	$0.408895\pi$
$522$	2.43262e10	+	6.51819e9i	0.327637	+	0.0877900i
$523$	1.22714e10	+	2.12547e10i	0.164017	+	0.284085i	0.936306	−	0.351186i	$-0.114222\pi$
$523$	1.22714e10	+	2.12547e10i	0.164017	+	0.284085i	−0.772289	+	0.635271i	$0.780888\pi$
$524$	−2.09979e10	−	1.21232e10i	−0.278517	−	0.160802i
$525$	−4.82260e9	+	4.82260e9i	−0.0634811	+	0.0634811i
$526$	−1.01267e10	−	3.77934e10i	−0.132289	−	0.493711i
$527$	1.28454e11	−	3.44190e10i	1.66534	−	0.446227i
$528$	1.79886e9	+	1.79886e9i	0.0231452	+	0.0231452i
$529$	−3.30937e10	+	5.73199e10i	−0.422593	+	0.731952i
$530$	1.61226e9	−	9.30839e8i	0.0204330	−	0.0117970i
$531$	−6.69964e9	+	2.50034e10i	−0.0842701	+	0.314500i
$532$		−	1.00585e10i		−	0.125570i
$533$	1.07948e11	+	3.18376e10i	1.33753	+	0.394486i
$534$	1.57969e11			1.94270
$535$	5.00131e8	+	1.34010e8i	0.00610476	+	0.00163576i
$536$	1.75158e10	+	3.03383e10i	0.212213	+	0.367564i
$537$	−8.92707e10	−	5.15404e10i	−1.07352	−	0.619799i
$538$	−1.38002e11	+	1.38002e11i	−1.64723	+	1.64723i
$539$	−1.10507e9	−	4.12419e9i	−0.0130929	−	0.0488633i
$540$	−1.95797e10	+	5.24637e9i	−0.230267	+	0.0616998i
$541$	−5.83294e10	−	5.83294e10i	−0.680924	−	0.680924i	0.279285	−	0.960208i	$-0.409903\pi$
$541$	−5.83294e10	−	5.83294e10i	−0.680924	−	0.680924i	−0.960208	+	0.279285i	$0.909903\pi$
$542$	3.56221e10	−	6.16993e10i	0.412783	−	0.714962i
$543$	3.11673e10	−	1.79944e10i	0.358508	−	0.206985i
$544$	−4.38609e10	+	1.63691e11i	−0.500820	+	1.86909i
$545$			2.32607e10i			0.263656i
$546$	5.86813e9	+	1.07775e10i	0.0660281	+	0.121269i
$547$	−2.66453e10			−0.297626			−0.148813	−	0.988865i	$-0.547545\pi$
$547$	−2.66453e10			−0.297626			−0.148813	+	0.988865i	$0.547545\pi$
$548$	1.09558e11	+	2.93559e10i	1.21484	+	0.325516i
$549$	−1.55205e10	−	2.68823e10i	−0.170850	−	0.295922i
$550$	−5.83424e9	−	3.36840e9i	−0.0637579	−	0.0368106i
$551$	5.53175e10	−	5.53175e10i	0.600145	−	0.600145i
$552$	−2.57227e9	−	9.59984e9i	−0.0277051	−	0.103397i
$553$	1.19226e10	−	3.19464e9i	0.127488	−	0.0341603i
$554$	8.17709e10	+	8.17709e10i	0.868080	+	0.868080i
$555$	5.97959e9	−	1.03569e10i	0.0630230	−	0.109159i
$556$	−1.04038e11	+	6.00664e10i	−1.08866	+	0.628539i
$557$	9.47047e9	−	3.53443e10i	0.0983900	−	0.367196i	−0.899122	−	0.437699i	$-0.855794\pi$
$557$	9.47047e9	−	3.53443e10i	0.0983900	−	0.367196i	0.997512	+	0.0705024i	$0.0224603\pi$
$558$			4.71166e10i			0.486001i
$559$	−2.09085e10	−	1.27789e10i	−0.214129	−	0.130872i
$560$	1.42818e9			0.0145222
$561$	5.74584e9	+	1.53959e9i	0.0580098	+	0.0155437i
$562$	2.31822e10	+	4.01528e10i	0.232386	+	0.402504i
$563$	−2.65747e10	−	1.53429e10i	−0.264506	−	0.152712i	0.361882	−	0.932224i	$-0.382134\pi$
$563$	−2.65747e10	−	1.53429e10i	−0.264506	−	0.152712i	−0.626388	+	0.779511i	$0.715467\pi$
$564$	6.07467e10	−	6.07467e10i	0.600353	−	0.600353i
$565$	−5.90457e9	−	2.20362e10i	−0.0579421	−	0.216243i
$566$	−1.27212e10	+	3.40865e9i	−0.123955	+	0.0332136i
$567$	5.31821e9	+	5.31821e9i	0.0514557	+	0.0514557i
$568$	1.07429e10	−	1.86072e10i	0.103212	−	0.178768i
$569$	−8.95129e10	+	5.16803e10i	−0.853958	+	0.493033i	−0.861984	−	0.506935i	$-0.830778\pi$
$569$	−8.95129e10	+	5.16803e10i	−0.853958	+	0.493033i	0.00802652	+	0.999968i	$0.497445\pi$
$570$	−6.10279e9	+	2.27759e10i	−0.0578135	+	0.215763i
$571$		−	9.60362e10i		−	0.903422i	−0.892164	−	0.451711i	$-0.850814\pi$
$571$		−	9.60362e10i		−	0.903422i	0.892164	−	0.451711i	$-0.149186\pi$
$572$	−4.81293e9	+	4.57806e9i	−0.0449599	+	0.0427659i
$573$	−9.67780e10			−0.897756
$574$	2.34418e10	+	6.28121e9i	0.215945	+	0.0578623i
$575$	−2.07973e10	−	3.60220e10i	−0.190255	−	0.329531i
$576$	−3.37215e10	−	1.94691e10i	−0.306349	−	0.176871i
$577$	4.52673e10	−	4.52673e10i	0.408396	−	0.408396i	−0.472783	−	0.881179i	$-0.656751\pi$
$577$	4.52673e10	−	4.52673e10i	0.408396	−	0.408396i	0.881179	+	0.472783i	$0.156751\pi$
$578$	3.67834e10	+	1.37278e11i	0.329565	+	1.22995i
$579$	−8.53269e10	+	2.28633e10i	−0.759227	+	0.203434i
$580$	−1.55476e10	−	1.55476e10i	−0.137389	−	0.137389i
$581$	−6.83812e9	+	1.18440e10i	−0.0600112	+	0.103942i
$582$	9.13199e10	−	5.27236e10i	0.795928	−	0.459529i
$583$	1.33782e8	−	4.99280e8i	0.00115804	−	0.00432185i
$584$		−	9.33303e9i		−	0.0802364i
$585$	1.28718e9	+	5.33385e9i	0.0109904	+	0.0455426i
$586$	−4.24483e10			−0.359973
$587$	2.97286e10	+	7.96574e9i	0.250393	+	0.0670925i	0.381832	−	0.924232i	$-0.375293\pi$
$587$	2.97286e10	+	7.96574e9i	0.250393	+	0.0670925i	−0.131440	+	0.991324i	$0.541960\pi$
$588$	−6.16855e10	−	1.06842e11i	−0.516029	−	0.893788i
$589$	1.26751e11	+	7.31798e10i	1.05315	+	0.608037i
$590$	2.91616e10	−	2.91616e10i	0.240660	−	0.240660i
$591$	2.57458e10	+	9.60845e10i	0.211036	+	0.787595i
$592$	7.10511e10	−	1.90381e10i	0.578474	−	0.155002i
$593$	6.92710e10	+	6.92710e10i	0.560186	+	0.560186i	0.929360	−	0.369174i	$-0.120359\pi$
$593$	6.92710e10	+	6.92710e10i	0.560186	+	0.560186i	−0.369174	+	0.929360i	$0.620359\pi$
$594$	−5.13513e9	+	8.89430e9i	−0.0412483	+	0.0714441i
$595$	2.89209e9	−	1.66975e9i	0.0230751	−	0.0133224i
$596$	4.46587e10	−	1.66668e11i	0.353933	−	1.32089i
$597$			5.45590e10i			0.429506i
$598$	−7.27525e10	+	1.75568e10i	−0.568909	+	0.137290i
$599$	8.70701e10			0.676335			0.338168	−	0.941086i	$-0.390193\pi$
$599$	8.70701e10			0.676335			0.338168	+	0.941086i	$0.390193\pi$
$600$	−3.29357e10	−	8.82510e9i	−0.254134	−	0.0680949i
$601$	3.35858e10	+	5.81723e10i	0.257429	+	0.445880i	0.965552	−	0.260209i	$-0.0837913\pi$
$601$	3.35858e10	+	5.81723e10i	0.257429	+	0.445880i	−0.708123	+	0.706089i	$0.750458\pi$
$602$	−4.57610e9	−	2.64201e9i	−0.0348425	−	0.0201164i
$603$	3.24332e10	−	3.24332e10i	0.245313	−	0.245313i
$604$	−3.28470e10	−	1.22587e11i	−0.246801	−	0.921076i
$605$	−2.34200e10	+	6.27537e9i	−0.174810	+	0.0468401i
$606$	4.98289e10	+	4.98289e10i	0.369480	+	0.369480i
$607$	3.56967e10	−	6.18285e10i	0.262950	−	0.455443i	−0.704074	−	0.710126i	$-0.748638\pi$
$607$	3.56967e10	−	6.18285e10i	0.262950	−	0.455443i	0.967025	+	0.254683i	$0.0819712\pi$
$608$	−1.61522e11	+	9.32545e10i	−1.18200	+	0.682426i
$609$	−2.91902e9	+	1.08939e10i	−0.0212211	+	0.0791982i
$610$			4.94547e10i			0.357181i
$611$	−7.81011e10	−	8.21079e10i	−0.560393	−	0.589142i
$612$	−5.98255e10			−0.426462
$613$	−5.57452e10	−	1.49369e10i	−0.394789	−	0.105783i	0.0559624	−	0.998433i	$-0.482177\pi$
$613$	−5.57452e10	−	1.49369e10i	−0.394789	−	0.105783i	−0.450752	+	0.892649i	$0.648844\pi$
$614$	−1.07756e11	−	1.86638e11i	−0.758170	−	1.31319i
$615$	−2.69994e10	−	1.55881e10i	−0.188735	−	0.108966i
$616$	−1.77415e8	+	1.77415e8i	−0.00123216	+	0.00123216i
$617$	6.16188e10	+	2.29964e11i	0.425180	+	1.58679i	0.763530	+	0.645772i	$0.223464\pi$
$617$	6.16188e10	+	2.29964e11i	0.425180	+	1.58679i	−0.338350	+	0.941020i	$0.609869\pi$
$618$	−2.98980e11	+	8.01114e10i	−2.04969	+	0.549213i
$619$	−6.79287e10	−	6.79287e10i	−0.462690	−	0.462690i	0.436846	−	0.899536i	$-0.356095\pi$
$619$	−6.79287e10	−	6.79287e10i	−0.462690	−	0.462690i	−0.899536	+	0.436846i	$0.856095\pi$
$620$	2.05680e10	−	3.56249e10i	0.139196	−	0.241094i
$621$	−5.49156e10	+	3.17055e10i	−0.369257	+	0.213191i
$622$	1.00969e11	−	3.76822e11i	0.674571	−	2.51753i
$623$		−	2.46229e10i		−	0.163451i
$624$	5.05651e10	−	8.27329e10i	0.333513	−	0.545682i
$625$	−1.37682e11			−0.902310
$626$	−1.85068e11	−	4.95889e10i	−1.20513	−	0.322914i
$627$	3.27339e9	+	5.66968e9i	0.0211801	+	0.0366850i
$628$	2.71709e11	+	1.56871e11i	1.74689	+	1.00857i
$629$	1.21621e11	−	1.21621e11i	0.776975	−	0.776975i
$630$	3.06231e8	+	1.14287e9i	0.00194396	+	0.00725496i
$631$	1.63368e11	−	4.37742e10i	1.03050	−	0.276122i	0.296330	−	0.955086i	$-0.404237\pi$
$631$	1.63368e11	−	4.37742e10i	1.03050	−	0.276122i	0.734172	+	0.678964i	$0.237571\pi$
$632$	4.36353e10	+	4.36353e10i	0.273508	+	0.273508i
$633$	−1.30423e11	+	2.25900e11i	−0.812344	+	1.40702i
$634$	2.71589e11	−	1.56802e11i	1.68095	−	0.970498i
$635$	1.12175e9	−	4.18642e9i	0.00689923	−	0.0257483i
$636$		−	1.49355e10i		−	0.0912831i
$637$	−1.42924e11	+	7.78188e10i	−0.868053	+	0.472636i
$638$	−1.11403e10			−0.0672381
$639$	−2.71731e10	−	7.28102e9i	−0.162981	−	0.0436706i
$640$	9.39916e9	+	1.62798e10i	0.0560233	+	0.0970353i
$641$	1.42174e11	+	8.20843e10i	0.842148	+	0.486215i	0.857994	−	0.513660i	$-0.171711\pi$
$641$	1.42174e11	+	8.20843e10i	0.842148	+	0.486215i	−0.0158456	+	0.999874i	$0.505044\pi$
$642$	5.35997e9	−	5.35997e9i	0.0315516	−	0.0315516i
$643$	6.34060e9	+	2.36634e10i	0.0370925	+	0.138431i	0.981989	−	0.188938i	$-0.0605046\pi$
$643$	6.34060e9	+	2.36634e10i	0.0370925	+	0.138431i	−0.944896	+	0.327369i	$0.893838\pi$
$644$	−8.54242e9	+	2.28893e9i	−0.0496635	+	0.0133073i
$645$	4.79984e9	+	4.79984e9i	0.0277324	+	0.0277324i
$646$	−1.69561e11	+	2.93688e11i	−0.973635	+	1.68638i
$647$	1.53965e11	−	8.88916e10i	0.878626	−	0.507275i	0.00842096	−	0.999965i	$-0.497319\pi$
$647$	1.53965e11	−	8.88916e10i	0.878626	−	0.507275i	0.870205	+	0.492690i	$0.163986\pi$
$648$	−9.73204e9	+	3.63205e10i	−0.0551955	+	0.205992i
$649$		−	1.14505e10i		−	0.0645422i
$650$	−7.26369e10	+	2.46281e11i	−0.406915	+	1.37967i
$651$	−2.11001e10			−0.117479
$652$	2.11962e11	+	5.67950e10i	1.17292	+	0.314282i
$653$	5.94428e10	+	1.02958e11i	0.326924	+	0.566249i	0.981900	−	0.189401i	$-0.0606546\pi$
$653$	5.94428e10	+	1.02958e11i	0.326924	+	0.566249i	−0.654976	+	0.755650i	$0.727321\pi$
$654$	2.94911e11	+	1.70267e11i	1.61206	+	0.930721i
$655$	6.26467e9	−	6.26467e9i	0.0340356	−	0.0340356i
$656$	−4.96301e10	−	1.85222e11i	−0.267997	−	1.00018i
$657$	−1.18035e10	+	3.16274e9i	−0.0633504	+	0.0169747i
$658$	−1.72788e10	−	1.72788e10i	−0.0921744	−	0.0921744i
$659$	−8.74152e10	+	1.51408e11i	−0.463495	+	0.802798i	−0.999132	−	0.0416509i	$-0.986738\pi$
$659$	−8.74152e10	+	1.51408e11i	−0.463495	+	0.802798i	0.535637	+	0.844448i	$0.320072\pi$
$660$	1.59353e9	−	9.20025e8i	0.00839817	−	0.00484868i
$661$	−3.15797e9	+	1.17857e10i	−0.0165425	+	0.0617376i	−0.973704	−	0.227818i	$-0.926841\pi$
$661$	−3.15797e9	+	1.17857e10i	−0.0165425	+	0.0617376i	0.957161	+	0.289556i	$0.0935075\pi$
$662$			2.05513e11i			1.07006i
$663$	5.66856e9	−	2.26653e11i	0.0293372	−	1.17303i
$664$	−6.83744e10			−0.351740
$665$	3.55013e9	+	9.51254e8i	0.0181534	+	0.00486418i
$666$	3.04696e10	+	5.27749e10i	0.154871	+	0.268244i
$667$	−5.95679e10	−	3.43915e10i	−0.300960	−	0.173759i
$668$	−5.04695e10	+	5.04695e10i	−0.253468	+	0.253468i
$669$	−3.11410e10	−	1.16220e11i	−0.155464	−	0.580198i
$670$	−7.05864e10	+	1.89136e10i	−0.350285	+	0.0938586i
$671$	9.70930e9	+	9.70930e9i	0.0478958	+	0.0478958i
$672$	1.34441e10	−	2.32859e10i	0.0659258	−	0.114187i
$673$	−3.66698e8	+	2.11713e8i	−0.00178751	+	0.00103202i	−0.500893	−	0.865509i	$-0.666995\pi$
$673$	−3.66698e8	+	2.11713e8i	−0.00178751	+	0.00103202i	0.499106	+	0.866541i	$0.333662\pi$
$674$	1.15461e11	−	4.30907e11i	0.559496	−	2.08807i
$675$			2.17555e11i			1.04798i
$676$	2.12654e11	+	1.37389e11i	1.01832	+	0.657910i
$677$	1.27209e11			0.605568			0.302784	−	0.953059i	$-0.402084\pi$
$677$	1.27209e11			0.605568			0.302784	+	0.953059i	$0.402084\pi$
$678$	−3.22607e11	−	8.64422e10i	−1.52670	−	0.409079i
$679$	−8.21812e9	−	1.42342e10i	−0.0386628	−	0.0669660i
$680$	1.44590e10	+	8.34793e9i	0.0676245	+	0.0390430i
$681$	7.10051e10	−	7.10051e10i	0.330142	−	0.330142i
$682$	−5.39433e9	−	2.01319e10i	−0.0249345	−	0.0930567i
$683$	2.61438e10	−	7.00522e9i	0.120140	−	0.0321913i	−0.198248	−	0.980152i	$-0.563525\pi$
$683$	2.61438e10	−	7.00522e9i	0.120140	−	0.0321913i	0.318388	+	0.947961i	$0.396859\pi$
$684$	−4.65575e10	−	4.65575e10i	−0.212699	−	0.212699i
$685$	−2.07222e10	+	3.58919e10i	−0.0941182	+	0.163017i
$686$	−6.11378e10	+	3.52979e10i	−0.276066	+	0.159387i
$687$	4.59842e10	−	1.71615e11i	0.206434	−	0.770423i
$688$			4.17510e10i			0.186343i
$689$	−1.96949e10	−	4.92565e8i	−0.0873929	−	0.00218568i
$690$	2.07318e10			0.0914619
$691$	−1.94505e11	−	5.21175e10i	−0.853137	−	0.228597i	−0.194355	−	0.980931i	$-0.562261\pi$
$691$	−1.94505e11	−	5.21175e10i	−0.853137	−	0.228597i	−0.658782	+	0.752334i	$0.728928\pi$
$692$	−2.23378e11	−	3.86902e11i	−0.974127	−	1.68724i
$693$	2.84498e8	+	1.64255e8i	0.00123352	+	0.000712174i
$694$	8.76749e10	−	8.76749e10i	0.377953	−	0.377953i
$695$	−1.13612e10	−	4.24006e10i	−0.0486951	−	0.181733i
$696$	−5.44643e10	+	1.45937e10i	−0.232100	+	0.0621909i
$697$	−3.17053e11	−	3.17053e11i	−1.34339	−	1.34339i
$698$	−5.92042e10	+	1.02545e11i	−0.249420	+	0.432008i
$699$	−1.16678e11	+	6.73641e10i	−0.488743	+	0.282176i
$700$	−7.85302e9	+	2.93079e10i	−0.0327073	+	0.122065i
$701$			6.67895e10i			0.276590i	0.990391	+	0.138295i	$0.0441622\pi$
$701$			6.67895e10i			0.276590i	−0.990391	+	0.138295i	$0.955838\pi$
$702$	3.75455e11	+	1.10735e11i	1.54600	+	0.455970i
$703$	1.89297e11			0.775036
$704$	1.66374e10	+	4.45799e9i	0.0677323	+	0.0181488i
$705$	1.56955e10	+	2.71854e10i	0.0635358	+	0.110047i
$706$	−1.87880e11	−	1.08472e11i	−0.756243	−	0.436617i
$707$	7.76692e9	−	7.76692e9i	0.0310865	−	0.0310865i
$708$	−8.56323e10	−	3.19584e11i	−0.340804	−	1.27190i
$709$	−4.24652e11	+	1.13785e11i	−1.68054	+	0.450299i	−0.967921	−	0.251254i	$-0.919157\pi$
$709$	−4.24652e11	+	1.13785e11i	−1.68054	+	0.450299i	−0.712617	+	0.701553i	$0.752490\pi$
$710$	3.16922e10	+	3.16922e10i	0.124715	+	0.124715i
$711$	4.03987e10	−	6.99726e10i	0.158084	−	0.273810i
$712$	1.06610e11	−	6.15511e10i	0.414836	−	0.239506i
$713$	3.33059e10	−	1.24299e11i	0.128873	−	0.480962i
$714$		−	4.88899e10i		−	0.188116i
$715$	−1.16065e9	−	2.13167e9i	−0.00444096	−	0.00815636i
$716$	−4.58587e11			−1.74490
$717$	3.60572e11	+	9.66150e10i	1.36432	+	0.365568i
$718$	1.55417e11	+	2.69190e11i	0.584792	+	1.01289i
$719$	−7.53769e10	−	4.35189e10i	−0.282048	−	0.162840i	0.352302	−	0.935886i	$-0.385399\pi$
$719$	−7.53769e10	−	4.35189e10i	−0.282048	−	0.162840i	−0.634350	+	0.773046i	$0.718732\pi$
$720$	6.61059e9	−	6.61059e9i	0.0245986	−	0.0245986i
$721$	1.24871e10	+	4.66026e10i	0.0462084	+	0.172452i
$722$	2.98991e10	−	8.01144e9i	0.110030	−	0.0294823i
$723$	1.45377e10	+	1.45377e10i	0.0532036	+	0.0532036i
$724$	8.00538e10	−	1.38657e11i	0.291358	−	0.504648i
$725$	−2.04369e11	+	1.17993e11i	−0.739713	+	0.427074i
$726$	−9.18707e10	+	3.42866e11i	−0.330697	+	1.23418i
$727$			2.43759e11i			0.872616i	0.899797	+	0.436308i	$0.143714\pi$
$727$			2.43759e11i			0.872616i	−0.899797	+	0.436308i	$0.856286\pi$
$728$	8.15964e9	+	4.98705e9i	0.0290500	+	0.0177549i
$729$	3.12834e11			1.10765
$730$	1.88054e10	+	5.03889e9i	0.0662203	+	0.0177437i
$731$	4.88129e10	+	8.45465e10i	0.170949	+	0.296092i
$732$	3.43599e11	+	1.98377e11i	1.19676	+	0.690951i
$733$	1.24375e11	−	1.24375e11i	0.430841	−	0.430841i	−0.458073	−	0.888915i	$-0.651460\pi$
$733$	1.24375e11	−	1.24375e11i	0.430841	−	0.430841i	0.888915	+	0.458073i	$0.151460\pi$
$734$	7.24737e10	+	2.70475e11i	0.249687	+	0.931845i
$735$	4.35436e10	−	1.16675e10i	0.149202	−	0.0399786i
$736$	1.15955e11	+	1.15955e11i	0.395164	+	0.395164i
$737$	−1.01448e10	+	1.75713e10i	−0.0343853	+	0.0595571i
$738$	1.37578e11	−	7.94308e10i	0.463793	−	0.267771i
$739$	−1.01258e11	+	3.77901e11i	−0.339511	+	1.26707i	0.559385	+	0.828908i	$0.311037\pi$
$739$	−1.01258e11	+	3.77901e11i	−0.339511	+	1.26707i	−0.898896	+	0.438163i	$0.855629\pi$
$740$		−	5.32041e10i		−	0.177426i
$741$	1.80798e11	−	1.71975e11i	0.599682	−	0.570418i
$742$	−4.24825e9			−0.0140150
$743$	4.93293e11	+	1.32178e11i	1.61864	+	0.433713i	0.950601	−	0.310415i	$-0.100468\pi$
$743$	4.93293e11	+	1.32178e11i	1.61864	+	0.433713i	0.668037	+	0.744128i	$0.267135\pi$
$744$	−5.27450e10	−	9.13570e10i	−0.172143	−	0.298160i
$745$	5.46019e10	+	3.15244e10i	0.177248	+	0.102334i
$746$	−4.80554e10	+	4.80554e10i	−0.155163	+	0.155163i
$747$	2.31704e10	+	8.64733e10i	0.0744135	+	0.277715i
$748$	2.55621e10	−	6.84935e9i	0.0816565	−	0.0218798i
$749$	−8.35468e8	−	8.35468e8i	−0.00265462	−	0.00265462i
$750$	7.23386e10	−	1.25294e11i	0.228626	−	0.395992i
$751$	−4.82108e10	+	2.78345e10i	−0.151560	+	0.0875032i	−0.573862	−	0.818952i	$-0.694555\pi$
$751$	−4.82108e10	+	2.78345e10i	−0.151560	+	0.0875032i	0.422302	+	0.906455i	$0.361222\pi$
$752$	−4.99721e10	+	1.86498e11i	−0.156263	+	0.583181i
$753$		−	4.85623e11i		−	1.51049i
$754$	9.96076e10	+	4.12758e11i	0.308182	+	1.27706i
$755$	4.63731e10			0.142718
$756$	4.46798e10	+	1.19719e10i	0.136781	+	0.0366502i
$757$	−1.48857e11	−	2.57828e11i	−0.453300	−	0.785138i	0.545289	−	0.838248i	$-0.316420\pi$
$757$	−1.48857e11	−	2.57828e11i	−0.453300	−	0.785138i	−0.998589	+	0.0531101i	$0.983087\pi$
$758$	−6.16744e11	−	3.56077e11i	−1.86822	−	1.07862i
$759$	4.07021e9	−	4.07021e9i	0.0122645	−	0.0122645i
$760$	4.75580e9	+	1.77489e10i	0.0142551	+	0.0532006i
$761$	−1.02010e11	+	2.73336e10i	−0.304162	+	0.0815001i	−0.407672	−	0.913128i	$-0.633659\pi$
$761$	−1.02010e11	+	2.73336e10i	−0.304162	+	0.0815001i	0.103510	+	0.994628i	$0.466993\pi$
$762$	−4.48665e10	−	4.48665e10i	−0.133077	−	0.133077i
$763$	2.65399e10	−	4.59684e10i	0.0783070	−	0.135632i
$764$	−3.72865e11	+	2.15274e11i	−1.09440	+	0.631855i
$765$	5.65782e9	−	2.11153e10i	0.0165198	−	0.0616526i
$766$		−	5.15020e11i		−	1.49592i
$767$	−4.24248e11	+	1.02380e11i	−1.22585	+	0.295825i
$768$	−1.35309e11			−0.388939
$769$	−1.24279e10	−	3.33004e9i	−0.0355379	−	0.00952234i	0.241006	−	0.970524i	$-0.422523\pi$
$769$	−1.24279e10	−	3.33004e9i	−0.0355379	−	0.00952234i	−0.276544	+	0.961001i	$0.589189\pi$
$770$	−2.61692e8	−	4.53264e8i	−0.000744437	−	0.00128940i
$771$	−2.97163e10	−	1.71567e10i	−0.0840963	−	0.0485530i
$772$	−2.77889e11	+	2.77889e11i	−0.782351	+	0.782351i
$773$	2.30754e10	+	8.61186e10i	0.0646296	+	0.241201i	0.990682	−	0.136193i	$-0.0434868\pi$
$773$	2.30754e10	+	8.61186e10i	0.0646296	+	0.241201i	−0.926053	+	0.377394i	$0.876820\pi$
$774$	−3.34103e10	+	8.95227e9i	−0.0930929	+	0.0249442i
$775$	−3.12186e11	−	3.12186e11i	−0.865379	−	0.865379i
$776$	4.10866e10	−	7.11640e10i	0.113306	−	0.196252i
$777$	−2.36340e10	+	1.36451e10i	−0.0648415	+	0.0374362i
$778$	5.27925e9	−	1.97024e10i	0.0144097	−	0.0537776i
$779$		−	4.93476e11i		−	1.34003i
$780$	−4.83356e10	−	5.08154e10i	−0.130584	−	0.137283i
$781$	1.24441e10			0.0334471
$782$	2.88008e11	+	7.71714e10i	0.770153	+	0.206362i
$783$	1.79880e11	+	3.11561e11i	0.478559	+	0.828888i
$784$	2.40125e11	+	1.38636e11i	0.635583	+	0.366954i
$785$	−8.10636e10	+	8.10636e10i	−0.213475	+	0.213475i
$786$	−3.35696e10	−	1.25284e11i	−0.0879542	−	0.328250i
$787$	1.98939e11	−	5.33056e10i	0.518587	−	0.138955i	0.00997392	−	0.999950i	$-0.496825\pi$
$787$	1.98939e11	−	5.33056e10i	0.518587	−	0.138955i	0.508613	+	0.860995i	$0.330158\pi$
$788$	3.12923e11	+	3.12923e11i	0.811584	+	0.811584i
$789$	5.73486e10	−	9.93308e10i	0.147984	−	0.256316i
$790$	−1.11481e11	+	6.43634e10i	−0.286214	+	0.165246i
$791$	−1.34739e10	+	5.02853e10i	−0.0344182	+	0.128450i
$792$			1.64239e9i			0.00417422i
$793$	2.72924e11	−	4.46549e11i	0.690159	−	1.12921i
$794$	5.08762e11			1.28007
$795$	5.27145e9	+	1.41248e9i	0.0131966	+	0.00353601i
$796$	1.21361e11	+	2.10204e11i	0.302293	+	0.523586i
$797$	−1.45136e11	−	8.37941e10i	−0.359700	−	0.207673i	0.309249	−	0.950981i	$-0.399922\pi$
$797$	−1.45136e11	−	8.37941e10i	−0.359700	−	0.207673i	−0.668949	+	0.743308i	$0.733256\pi$
$798$	3.80472e10	−	3.80472e10i	0.0938234	−	0.0938234i
$799$	1.16849e11	+	4.36086e11i	0.286707	+	1.07000i
$800$	5.43439e11	−	1.45614e11i	1.32676	−	0.355503i
$801$	−1.13971e11	−	1.13971e11i	−0.276863	−	0.276863i
$802$	4.51664e11	−	7.82305e11i	1.09174	−	1.89094i
$803$	4.68129e9	−	2.70274e9i	0.0112591	−	0.00650043i
$804$	−1.51736e11	+	5.66285e11i	−0.363131	+	1.35522i
$805$		−	3.23150e9i		−	0.00769521i
$806$	−6.97671e11	+	3.79867e11i	−1.65314	+	0.900101i
$807$	−5.72111e11			−1.34892
$808$	5.30438e10	+	1.42131e10i	0.124448	+	0.0333459i
$809$	−3.32962e11	−	5.76707e11i	−0.777321	−	1.34636i	−0.933481	−	0.358628i	$-0.883245\pi$
$809$	−3.32962e11	−	5.76707e11i	−0.777321	−	1.34636i	0.156160	−	0.987732i	$-0.450089\pi$
$810$	−6.79288e10	−	3.92187e10i	−0.157803	−	0.0911074i
$811$	−2.56515e11	+	2.56515e11i	−0.592966	+	0.592966i	−0.938431	−	0.345466i	$-0.887721\pi$
$811$	−2.56515e11	+	2.56515e11i	−0.592966	+	0.592966i	0.345466	+	0.938431i	$0.387721\pi$
$812$	1.29862e10	+	4.84650e10i	0.0298715	+	0.111482i
$813$	2.01732e11	−	5.40539e10i	0.461756	−	0.123727i
$814$	−1.90611e10	−	1.90611e10i	−0.0434161	−	0.0434161i
$815$	−4.00914e10	+	6.94404e10i	−0.0908701	+	0.157392i
$816$	−3.34543e11	+	1.93148e11i	−0.754555	+	0.435643i
$817$	−2.78087e10	+	1.03783e11i	−0.0624154	+	0.232937i
$818$		−	1.08701e12i		−	2.42783i
$819$	3.54203e9	−	1.20095e10i	0.00787257	−	0.0266925i
$820$	−1.38697e11			−0.306769
$821$	1.20215e11	+	3.22116e10i	0.264599	+	0.0708990i	0.388679	−	0.921373i	$-0.372931\pi$
$821$	1.20215e11	+	3.22116e10i	0.264599	+	0.0708990i	−0.124080	+	0.992272i	$0.539598\pi$
$822$	3.03370e11	+	5.25453e11i	0.664486	+	1.15092i
$823$	−2.41530e11	−	1.39448e11i	−0.526469	−	0.303957i	0.213109	−	0.977029i	$-0.431641\pi$
$823$	−2.41530e11	−	1.39448e11i	−0.526469	−	0.303957i	−0.739577	+	0.673072i	$0.764975\pi$
$824$	−1.70560e11	+	1.70560e11i	−0.369972	+	0.369972i
$825$	−5.11130e9	−	1.90756e10i	−0.0110336	−	0.0411778i
$826$	−9.09025e10	+	2.43573e10i	−0.195279	+	0.0523249i
$827$	3.32070e10	+	3.32070e10i	0.0709916	+	0.0709916i	0.741711	−	0.670719i	$-0.234015\pi$
$827$	3.32070e10	+	3.32070e10i	0.0709916	+	0.0709916i	−0.670719	+	0.741711i	$0.734015\pi$
$828$	−2.89453e10	+	5.01348e10i	−0.0615825	+	0.106664i
$829$	3.65352e11	−	2.10936e11i	0.773560	−	0.446615i	−0.0605833	−	0.998163i	$-0.519296\pi$
$829$	3.65352e11	−	2.10936e11i	0.773560	−	0.446615i	0.834143	+	0.551548i	$0.185963\pi$
$830$	3.69153e10	−	1.37770e11i	0.0777846	−	0.290296i
$831$			3.38997e11i			0.710872i
$832$	1.64137e10	−	6.56290e11i	0.0342541	−	1.36963i
$833$	6.48342e11			1.34655
$834$	−6.20740e11	−	1.66327e11i	−1.28306	−	0.343794i
$835$	−1.30401e10	−	2.25861e10i	−0.0268247	−	0.0464618i
$836$	2.52233e10	+	1.45627e10i	0.0516389	+	0.0298138i
$837$	−4.75927e11	+	4.75927e11i	−0.969703	+	0.969703i
$838$	5.47067e10	+	2.04168e11i	0.110934	+	0.414011i
$839$	−1.73418e8	+	4.64671e7i	−0.000349982	+	9.37773e-5i	−0.258994	−	0.965879i	$-0.583391\pi$
$839$	−1.73418e8	+	4.64671e7i	−0.000349982	+	9.37773e-5i	0.258644	+	0.965973i	$0.416724\pi$
$840$	−1.87316e9	−	1.87316e9i	−0.00376234	−	0.00376234i
$841$	5.50044e10	−	9.52704e10i	0.109955	−	0.190447i
$842$	1.04266e11	−	6.01981e10i	0.207441	−	0.119766i
$843$	−3.51773e10	+	1.31284e11i	−0.0696550	+	0.259956i
$844$			1.16046e12i			2.28696i
$845$	−6.86025e10	+	6.20626e10i	−0.134559	+	0.121731i
$846$	−1.59956e11			−0.312262
$847$	5.34432e10	+	1.43201e10i	0.103839	+	0.0278235i
$848$	1.67835e10	+	2.90698e10i	0.0324563	+	0.0562159i
$849$	−3.34347e10	−	1.93036e10i	−0.0643528	−	0.0371541i
$850$	7.23350e11	−	7.23350e11i	1.38571	−	1.38571i
$851$	−4.30768e10	−	1.60765e11i	−0.0821345	−	0.306530i
$852$	3.47317e11	−	9.30632e10i	0.659124	−	0.176612i
$853$	4.84048e11	+	4.84048e11i	0.914307	+	0.914307i	0.996608	−	0.0823002i	$-0.0262266\pi$
$853$	4.84048e11	+	4.84048e11i	0.914307	+	0.914307i	−0.0823002	+	0.996608i	$0.526227\pi$
$854$	5.64264e10	−	9.77334e10i	0.106084	−	0.183743i
$855$	2.08354e10	−	1.20293e10i	0.0389886	−	0.0225101i
$856$	1.52886e9	−	5.70579e9i	0.00284756	−	0.0106272i
$857$			8.12048e11i			1.50542i	0.658351	+	0.752711i	$0.271254\pi$
$857$			8.12048e11i			1.50542i	−0.658351	+	0.752711i	$0.728746\pi$
$858$	−3.55223e10	−	8.88406e8i	−0.0655469	−	0.00163931i
$859$	6.07481e11			1.11573			0.557866	−	0.829931i	$-0.311620\pi$
$859$	6.07481e11			1.11573			0.557866	+	0.829931i	$0.311620\pi$
$860$	2.91695e10	+	7.81594e9i	0.0533255	+	0.0142885i
$861$	3.55712e10	+	6.16111e10i	0.0647271	+	0.112111i
$862$	−1.25616e12	−	7.25247e11i	−2.27519	−	1.31358i
$863$	−4.14610e11	+	4.14610e11i	−0.747475	+	0.747475i	−0.974004	−	0.226530i	$-0.927262\pi$
$863$	−4.14610e11	+	4.14610e11i	−0.747475	+	0.747475i	0.226530	+	0.974004i	$0.427262\pi$
$864$	−2.21989e11	−	8.28473e11i	−0.398360	−	1.48670i
$865$	1.57682e11	−	4.22506e10i	0.281654	−	0.0754691i
$866$	1.04490e12	+	1.04490e12i	1.85782	+	1.85782i
$867$	−2.08309e11	+	3.60801e11i	−0.368664	+	0.638545i
$868$	−8.12940e10	+	4.69351e10i	−0.143212	+	0.0826835i
$869$	−9.25041e9	+	3.45230e10i	−0.0162212	+	0.0605382i
$870$		−	1.17621e11i		−	0.205308i
$871$	7.41735e11	+	2.18764e11i	1.28877	+	0.380105i
$872$	2.65372e11			0.458976
$873$	−1.03925e11	−	2.78465e10i	−0.178921	−	0.0479417i
$874$	1.64077e11	+	2.84190e11i	0.281192	+	0.487039i
$875$	−1.95298e10	−	1.12756e10i	−0.0333171	−	0.0192356i
$876$	1.10443e11	−	1.10443e11i	0.187552	−	0.187552i
$877$	−3.83451e9	−	1.43106e10i	−0.00648204	−	0.0241913i	0.962609	−	0.270894i	$-0.0873194\pi$
$877$	−3.83451e9	−	1.43106e10i	−0.00648204	−	0.0241913i	−0.969091	+	0.246703i	$0.920653\pi$
$878$	5.45591e11	−	1.46191e11i	0.918097	−	0.246003i
$879$	−8.79887e10	−	8.79887e10i	−0.147391	−	0.147391i
$880$	−2.06772e9	+	3.58140e9i	−0.00344796	+	0.00597204i
$881$	3.44620e11	−	1.98967e11i	0.572054	−	0.330276i	−0.185915	−	0.982566i	$-0.559525\pi$
$881$	3.44620e11	−	1.98967e11i	0.572054	−	0.330276i	0.757969	+	0.652290i	$0.226192\pi$
$882$	−5.94527e10	+	2.21881e11i	−0.0982421	+	0.366644i
$883$			8.37707e11i			1.37800i	0.724761	+	0.689000i	$0.241950\pi$
$883$			8.37707e11i			1.37800i	−0.724761	+	0.689000i	$0.758050\pi$
$884$	−4.82329e11	−	8.85855e11i	−0.789831	−	1.45062i
$885$	1.20895e11			0.197077
$886$	−1.15096e12	−	3.08398e11i	−1.86777	−	0.500469i
$887$	−3.35824e11	−	5.81664e11i	−0.542522	−	0.939675i	−0.998758	−	0.0498165i	$-0.984136\pi$
$887$	−3.35824e11	−	5.81664e11i	−0.542522	−	0.939675i	0.456237	−	0.889858i	$-0.349197\pi$
$888$	−1.18158e11	−	6.82187e10i	−0.190026	−	0.109711i
$889$	−6.99342e9	+	6.99342e9i	−0.0111965	+	0.0111965i
$890$	6.64628e10	+	2.48042e11i	0.105930	+	0.395336i
$891$	−2.10360e10	+	5.63658e9i	−0.0333774	+	0.00894344i
$892$	−3.78500e11	−	3.78500e11i	−0.597869	−	0.597869i
$893$	−2.48438e11	+	4.30307e11i	−0.390671	+	0.676663i
$894$	7.99364e11	−	4.61513e11i	1.25140	−	0.722494i
$895$	4.33696e10	−	1.61858e11i	0.0675917	−	0.252256i
$896$		−	4.28967e10i		−	0.0665568i
$897$	−1.87197e11	−	1.14412e11i	−0.289154	−	0.176727i
$898$	−1.00334e12			−1.54291
$899$	−7.05206e11	−	1.88959e11i	−1.07964	−	0.289288i
$900$	9.93075e10	+	1.72006e11i	0.151360	+	0.262164i
$901$	6.79736e10	+	3.92446e10i	0.103143	+	0.0595498i
$902$	−4.96902e10	+	4.96902e10i	−0.0750663	+	0.0750663i
$903$	−4.00906e9	−	1.49620e10i	−0.00602965	−	0.0225029i
$904$	−2.51402e11	+	6.73629e10i	−0.376439	+	0.100867i
$905$	4.13680e10	+	4.13680e10i	0.0616694	+	0.0616694i
$906$	3.39449e11	−	5.87942e11i	0.503803	−	0.872613i
$907$	4.23905e11	−	2.44742e11i	0.626382	−	0.361642i	−0.152967	−	0.988231i	$-0.548883\pi$
$907$	4.23905e11	−	2.44742e11i	0.626382	−	0.361642i	0.779350	+	0.626589i	$0.215550\pi$
$908$	1.15623e11	−	4.31511e11i	0.170099	−	0.634817i
$909$		−	7.19011e10i		−	0.105313i
$910$	−1.44539e10	+	1.37486e10i	−0.0210776	+	0.0200490i
$911$	−5.90205e11			−0.856898			−0.428449	−	0.903566i	$-0.640940\pi$
$911$	−5.90205e11			−0.856898			−0.428449	+	0.903566i	$0.640940\pi$
$912$	−4.10661e11	−	1.10036e11i	−0.593614	−	0.159058i
$913$	−1.98005e10	−	3.42954e10i	−0.0284965	−	0.0493575i
$914$	5.23415e11	+	3.02194e11i	0.750000	+	0.433013i
$915$	−1.02512e11	+	1.02512e11i	−0.146248	+	0.146248i
$916$	−2.04575e11	−	7.63484e11i	−0.290583	−	1.08447i
$917$	−1.95282e10	+	5.23256e9i	−0.0276175	+	0.00740009i
$918$	−1.10275e12	−	1.10275e12i	−1.55276	−	1.55276i
$919$	1.08271e11	−	1.87531e11i	0.151792	−	0.262912i	−0.780094	−	0.625662i	$-0.784829\pi$
$919$	1.08271e11	−	1.87531e11i	0.151792	−	0.262912i	0.931886	+	0.362750i	$0.118162\pi$
$920$	1.39914e10	−	8.07795e9i	0.0195304	−	0.0112759i
$921$	1.63511e11	−	6.10233e11i	0.227253	−	0.848119i
$922$			4.36875e11i			0.604552i
$923$	−1.11265e11	−	4.61063e11i	−0.153303	−	0.635263i
$924$	−4.19889e9			−0.00576032
$925$	−5.51562e11	−	1.47791e11i	−0.753403	−	0.201874i
$926$	9.19049e11	+	1.59184e12i	1.24996	+	2.16499i
$927$	2.73507e11	+	1.57909e11i	0.370382	+	0.213840i
$928$	6.57864e11	−	6.57864e11i	0.887042	−	0.887042i
$929$	−9.87431e10	−	3.68514e11i	−0.132570	−	0.494756i	0.867427	−	0.497565i	$-0.165773\pi$
$929$	−9.87431e10	−	3.68514e11i	−0.132570	−	0.494756i	−0.999996	+	0.00280908i	$0.999106\pi$
$930$	2.12555e11	−	5.69539e10i	0.284144	−	0.0761363i
$931$	5.04554e11	+	5.04554e11i	0.671597	+	0.671597i
$932$	−2.99690e11	+	5.19078e11i	−0.397199	+	0.687969i
$933$	9.90387e11	−	5.71800e11i	1.30701	−	0.754602i
$934$	−4.80054e11	+	1.79159e12i	−0.630816	+	2.35424i
$935$			9.66987e9i			0.0126524i
$936$	6.08518e10	−	1.46849e10i	0.0792811	−	0.0191323i
$937$	−7.93522e11			−1.02944			−0.514720	−	0.857358i	$-0.672104\pi$
$937$	−7.93522e11			−1.02944			−0.514720	+	0.857358i	$0.672104\pi$
$938$	1.61074e11	+	4.31597e10i	0.208072	+	0.0557529i
$939$	−2.80828e11	−	4.86408e11i	−0.361225	−	0.625659i
$940$	1.20943e11	+	6.98263e10i	0.154906	+	0.0894350i
$941$	−1.82469e11	+	1.82469e11i	−0.232719	+	0.232719i	−0.813827	−	0.581108i	$-0.802619\pi$
$941$	−1.82469e11	+	1.82469e11i	−0.232719	+	0.232719i	0.581108	+	0.813827i	$0.302619\pi$
$942$	4.34385e11	+	1.62115e12i	0.551659	+	2.05882i
$943$	−4.19096e11	+	1.12296e11i	−0.529989	+	0.142010i
$944$	5.25798e11	+	5.25798e11i	0.662112	+	0.662112i
$945$	−8.45094e9	+	1.46375e10i	−0.0105969	+	0.0183543i
$946$	1.32506e10	−	7.65022e9i	0.0165451	−	0.00955233i
$947$	1.91541e11	−	7.14839e11i	0.238156	−	0.888809i	−0.738545	−	0.674204i	$-0.764487\pi$
$947$	1.91541e11	−	7.14839e11i	0.238156	−	0.888809i	0.976701	−	0.214605i	$-0.0688464\pi$
$948$			1.03272e12i			1.27865i
$949$	−1.41995e11	−	1.49279e11i	−0.175068	−	0.184050i
$950$	1.12585e12			1.38225
$951$	8.87987e11	+	2.37935e11i	1.08564	+	0.290896i
$952$	−1.90495e10	−	3.29947e10i	−0.0231919	−	0.0401695i
$953$	4.39522e11	+	2.53758e11i	0.532855	+	0.307644i	0.742178	−	0.670203i	$-0.233793\pi$
$953$	4.39522e11	+	2.53758e11i	0.532855	+	0.307644i	−0.209323	+	0.977846i	$0.567126\pi$
$954$	−1.96638e10	+	1.96638e10i	−0.0237396	+	0.0237396i
$955$	−4.07178e10	−	1.51961e11i	−0.0489520	−	0.182691i
$956$	1.60412e12	−	4.29822e11i	1.92046	−	0.514585i
$957$	−2.30922e10	−	2.30922e10i	−0.0275307	−	0.0275307i
$958$	−8.75059e11	+	1.51565e12i	−1.03890	+	1.79943i
$959$	8.19033e10	−	4.72869e10i	0.0968338	−	0.0559070i
$960$	−4.70679e10	+	1.75660e11i	−0.0554166	+	0.206818i
$961$		−	5.12999e11i		−	0.601482i
$962$	−5.35801e11	+	8.76658e11i	−0.625609	+	1.02360i
$963$	−7.73422e9			−0.00899314
$964$	8.83480e10	+	2.36728e10i	0.102303	+	0.0274120i
$965$	−7.17998e10	−	1.24361e11i	−0.0827969	−	0.143408i
$966$	−4.09706e10	−	2.36544e10i	−0.0470504	−	0.0271646i
$967$	−5.59315e10	+	5.59315e10i	−0.0639662	+	0.0639662i	−0.738366	−	0.674400i	$-0.764402\pi$
$967$	−5.59315e10	+	5.59315e10i	−0.0639662	+	0.0639662i	0.674400	+	0.738366i	$0.264402\pi$
$968$	7.15932e10	+	2.67190e11i	0.0815400	+	0.304311i
$969$	−9.60243e11	+	2.57296e11i	−1.08915	+	0.291836i
$970$	1.21208e11	+	1.21208e11i	0.136913	+	0.136913i
$971$	6.75482e11	−	1.16997e12i	0.759866	−	1.31613i	−0.183053	−	0.983103i	$-0.558598\pi$
$971$	6.75482e11	−	1.16997e12i	0.759866	−	1.31613i	0.942919	−	0.333023i	$-0.108069\pi$
$972$	4.70634e11	−	2.71721e11i	0.527252	−	0.304409i
$973$	−2.59257e10	+	9.67559e10i	−0.0289254	+	0.107951i
$974$		−	1.49691e12i		−	1.66326i
$975$	−6.61066e11	+	3.59936e11i	−0.731520	+	0.398297i
$976$	−8.91691e11			−0.982687
$977$	1.45549e11	+	3.89997e10i	0.159746	+	0.0428039i	0.337806	−	0.941216i	$-0.390315\pi$
$977$	1.45549e11	+	3.89997e10i	0.159746	+	0.0428039i	−0.178060	+	0.984020i	$0.556982\pi$
$978$	5.86934e11	+	1.01660e12i	0.641554	+	1.11120i
$979$	6.17459e10	+	3.56490e10i	0.0672168	+	0.0388076i
$980$	1.41811e11	−	1.41811e11i	0.153746	−	0.153746i
$981$	−8.99283e10	−	3.35617e11i	−0.0971003	−	0.362383i
$982$	−1.56464e12	+	4.19244e11i	−1.68255	+	0.450839i
$983$	−7.12914e11	−	7.12914e11i	−0.763524	−	0.763524i	0.213433	−	0.976958i	$-0.431535\pi$
$983$	−7.12914e11	−	7.12914e11i	−0.763524	−	0.763524i	−0.976958	+	0.213433i	$0.931535\pi$
$984$	−1.77839e11	+	3.08025e11i	−0.189690	+	0.328553i
$985$	−1.40040e11	+	8.08519e10i	−0.148767	+	0.0858906i
$986$	4.37828e11	−	1.63400e12i	0.463229	−	1.72880i
$987$		−	7.16325e10i		−	0.0754817i
$988$	3.14033e11	−	1.06475e12i	0.329570	−	1.11743i
$989$	9.44686e10			0.0987421
$990$	−3.30930e9	−	8.86724e8i	−0.00344505	−	0.000923098i
$991$	−4.43570e11	−	7.68285e11i	−0.459904	−	0.796577i	0.539052	−	0.842273i	$-0.318783\pi$
$991$	−4.43570e11	−	7.68285e11i	−0.459904	−	0.796577i	−0.998955	+	0.0456959i	$0.985449\pi$
$992$	1.50739e12	+	8.70291e11i	1.55660	+	0.898706i
$993$	−4.25996e11	+	4.25996e11i	−0.438135	+	0.438135i
$994$	−2.64709e10	−	9.87908e10i	−0.0271159	−	0.101198i
$995$	−8.56685e10	+	2.29548e10i	−0.0874035	+	0.0234197i
$996$	−8.09113e11	−	8.09113e11i	−0.822189	−	0.822189i
$997$	3.54039e11	−	6.13213e11i	0.358319	−	0.620627i	−0.629361	−	0.777113i	$-0.716683\pi$
$997$	3.54039e11	−	6.13213e11i	0.358319	−	0.620627i	0.987680	+	0.156486i	$0.0500165\pi$
$998$	−2.48170e12	+	1.43281e12i	−2.50166	+	1.44433i
$999$	−2.25307e11	+	8.40857e11i	−0.226210	+	0.844228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.9.f.a.2.7	✓	32
13.7	odd	12	inner	13.9.f.a.7.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.9.f.a.2.7	✓	32	1.1	even	1	trivial
13.9.f.a.7.7	yes	32	13.7	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	13.f (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(22.9875 + 6.15949i) q^{2} +(34.8819 + 60.4172i) q^{3} +(268.785 + 155.183i) q^{4} +(-80.1911 + 80.1911i) q^{5} +(429.709 + 1603.70i) q^{6} +(249.971 - 66.9796i) q^{7} +(914.868 + 914.868i) q^{8} +(847.009 - 1467.06i) q^{9} +(-2337.33 + 1349.46i) q^{10} +(-193.946 + 723.817i) q^{11} +21652.3i q^{12} +(28552.1 + 714.082i) q^{13} +6158.78 q^{14} +(-7642.13 - 2047.70i) q^{15} +(-24331.4 - 42143.2i) q^{16} +(-98542.8 - 56893.7i) q^{17} +(28507.0 - 28507.0i) q^{18} +(-32412.3 - 120964. i) q^{19} +(-33998.4 + 9109.84i) q^{20} +(12766.2 + 12766.2i) q^{21} +(-8916.69 + 15444.2i) q^{22} +(-95355.9 + 55053.8i) q^{23} +(-23361.4 + 87186.1i) q^{24} +377764. i q^{25} +(651943. + 192281. i) q^{26} +575901. q^{27} +(77582.5 + 20788.2i) q^{28} +(312345. + 540997. i) q^{29} +(-163061. - 94143.3i) q^{30} +(-826405. + 826405. i) q^{31} +(-385463. - 1.43857e6i) q^{32} +(-50496.2 + 13530.4i) q^{33} +(-1.91482e6 - 1.91482e6i) q^{34} +(-14674.3 + 25416.6i) q^{35} +(455326. - 262882. i) q^{36} +(-391225. + 1.46007e6i) q^{37} -2.98031e6i q^{38} +(952807. + 1.74994e6i) q^{39} -146728. q^{40} +(3.80624e6 + 1.01988e6i) q^{41} +(214830. + 372096. i) q^{42} +(-743021. - 428983. i) q^{43} +(-164454. + 164454. i) q^{44} +(49722.7 + 185568. i) q^{45} +(-2.53110e6 + 678206. i) q^{46} +(-2.80556e6 - 2.80556e6i) q^{47} +(1.69745e6 - 2.94007e6i) q^{48} +(-4.93446e6 + 2.84891e6i) q^{49} +(-2.32683e6 + 8.68386e6i) q^{50} -7.93824e6i q^{51} +(7.56354e6 + 4.62273e6i) q^{52} -689788. q^{53} +(1.32385e7 + 3.54726e6i) q^{54} +(-42490.9 - 73596.4i) q^{55} +(289968. + 167413. i) q^{56} +(6.17772e6 - 6.17772e6i) q^{57} +(3.84777e6 + 1.43601e7i) q^{58} +(-1.47598e7 + 3.95488e6i) q^{59} +(-1.73632e6 - 1.73632e6i) q^{60} +(9.16195e6 - 1.58690e7i) q^{61} +(-2.40872e7 + 1.39068e7i) q^{62} +(113465. - 423456. i) q^{63} -2.29857e7i q^{64} +(-2.34688e6 + 2.23236e6i) q^{65} -1.24412e6 q^{66} +(2.61536e7 + 7.00783e6i) q^{67} +(-1.76579e7 - 3.05843e7i) q^{68} +(-6.65239e6 - 3.84076e6i) q^{69} +(-493879. + 493879. i) q^{70} +(-4.29808e6 - 1.60406e7i) q^{71} +(2.11707e6 - 567267. i) q^{72} +(-5.10076e6 - 5.10076e6i) q^{73} +(-1.79866e7 + 3.11537e7i) q^{74} +(-2.28234e7 + 1.31771e7i) q^{75} +(1.00597e7 - 3.75431e7i) q^{76} +193924. i q^{77} +(1.11239e7 + 4.60957e7i) q^{78} +4.76958e7 q^{79} +(5.33067e6 + 1.42835e6i) q^{80} +(1.45313e7 + 2.51689e7i) q^{81} +(8.12141e7 + 4.68890e7i) q^{82} +(-3.73685e7 + 3.73685e7i) q^{83} +(1.45026e6 + 5.41245e6i) q^{84} +(1.24646e7 - 3.33989e6i) q^{85} +(-1.44379e7 - 1.44379e7i) q^{86} +(-2.17904e7 + 3.77420e7i) q^{87} +(-839632. + 484762. i) q^{88} +(2.46257e7 - 9.19044e7i) q^{89} +4.57201e6i q^{90} +(7.18502e6 - 1.73391e6i) q^{91} -3.41736e7 q^{92} +(-7.87556e7 - 2.11025e7i) q^{93} +(-4.72120e7 - 8.17737e7i) q^{94} +(1.22994e7 + 7.10108e6i) q^{95} +(7.34686e7 - 7.34686e7i) q^{96} +(-1.64381e7 - 6.13480e7i) q^{97} +(-1.30979e8 + 3.50957e7i) q^{98} +(897610. + 897610. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 172 q^{5} - 2726 q^{6} - 2784 q^{7} - 10470 q^{8} - 21872 q^{9} - 26886 q^{10} + 6476 q^{11} + 14794 q^{13} + 216232 q^{14} - 127934 q^{15} + 195174 q^{16} + 97644 q^{17}+ \cdots - 359343776 q^{99}+O(q^{100}) \) 32 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 172 * q^5 - 2726 * q^6 - 2784 * q^7 - 10470 * q^8 - 21872 * q^9 - 26886 * q^10 + 6476 * q^11 + 14794 * q^13 + 216232 * q^14 - 127934 * q^15 + 195174 * q^16 + 97644 * q^17 - 475646 * q^18 + 373314 * q^19 + 685798 * q^20 - 213824 * q^21 + 167756 * q^22 - 711654 * q^23 - 1396830 * q^24 - 1041274 * q^26 + 3386272 * q^27 - 491836 * q^28 - 178394 * q^29 - 6200118 * q^30 + 1793468 * q^31 + 955004 * q^32 - 369536 * q^33 + 4592250 * q^34 + 1520488 * q^35 - 11372454 * q^36 + 247730 * q^37 + 14761942 * q^39 + 15044736 * q^40 - 2285272 * q^41 - 1024084 * q^42 + 18199452 * q^43 + 5629904 * q^44 - 10428746 * q^45 - 25708302 * q^46 - 8054836 * q^47 - 19983002 * q^48 - 18234288 * q^49 - 7208294 * q^50 - 26124488 * q^52 - 26091116 * q^53 + 85261048 * q^54 - 2240524 * q^55 + 84926940 * q^56 + 57257116 * q^57 - 68659210 * q^58 - 58197100 * q^59 - 64428232 * q^60 - 38537926 * q^61 + 2935614 * q^62 - 43972436 * q^63 + 44466032 * q^65 + 209850752 * q^66 + 30462126 * q^67 + 68365716 * q^68 + 163279656 * q^69 + 256782116 * q^70 - 113836054 * q^71 - 445647780 * q^72 - 30722748 * q^73 - 156843362 * q^74 - 364524840 * q^75 - 180633890 * q^76 + 252047848 * q^78 + 364818200 * q^79 + 372146084 * q^80 - 17174000 * q^81 + 272314014 * q^82 + 389373188 * q^83 - 464450276 * q^84 - 331999758 * q^85 - 32039076 * q^86 - 337693978 * q^87 - 1180586364 * q^88 - 333088936 * q^89 + 251459988 * q^91 + 1275961956 * q^92 + 637177780 * q^93 + 171539378 * q^94 + 318589986 * q^95 + 1019148280 * q^96 - 230031796 * q^97 - 1287859636 * q^98 - 359343776 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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