LMFDB - Embedded newform 19.10.c.a.7.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [19,10,Mod(7,19)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(19, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("19.7"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	19.c (of order $3$, 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:	$9.78568088711$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.13
Character	$\chi$	$=$	19.7
Dual form			19.10.c.a.11.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(19.4836 + 33.7465i) q^{2} +(89.2835 + 154.644i) q^{3} +(-503.218 + 871.599i) q^{4} +(-249.322 - 431.838i) q^{5} +(-3479.12 + 6026.01i) q^{6} +698.529 q^{7} -19266.8 q^{8} +(-6101.58 + 10568.2i) q^{9} +(9715.34 - 16827.5i) q^{10} +73060.2 q^{11} -179716. q^{12} +(-10087.3 + 17471.6i) q^{13} +(13609.8 + 23572.9i) q^{14} +(44520.6 - 77111.9i) q^{15} +(-117737. - 203927. i) q^{16} +(-280086. - 485122. i) q^{17} -475522. q^{18} +(-169762. + 542097. i) q^{19} +501852. q^{20} +(62367.1 + 108023. i) q^{21} +(1.42347e6 + 2.46553e6i) q^{22} +(-919291. + 1.59226e6i) q^{23} +(-1.72020e6 - 2.97948e6i) q^{24} +(852240. - 1.47612e6i) q^{25} -786142. q^{26} +1.33565e6 q^{27} +(-351513. + 608838. i) q^{28} +(454559. - 787320. i) q^{29} +3.46968e6 q^{30} +7.56865e6 q^{31} +(-344409. + 596534. i) q^{32} +(6.52306e6 + 1.12983e7i) q^{33} +(1.09141e7 - 1.89038e7i) q^{34} +(-174158. - 301651. i) q^{35} +(-6.14085e6 - 1.06363e7i) q^{36} -9.38380e6 q^{37} +(-2.16014e7 + 4.83311e6i) q^{38} -3.60250e6 q^{39} +(4.80362e6 + 8.32011e6i) q^{40} +(-510515. - 884238. i) q^{41} +(-2.43027e6 + 4.20935e6i) q^{42} +(1.05881e7 + 1.83391e7i) q^{43} +(-3.67652e7 + 6.36792e7i) q^{44} +6.08502e6 q^{45} -7.16442e7 q^{46} +(9.01577e6 - 1.56158e7i) q^{47} +(2.10240e7 - 3.64146e7i) q^{48} -3.98657e7 q^{49} +6.64187e7 q^{50} +(5.00140e7 - 8.66268e7i) q^{51} +(-1.01522e7 - 1.75841e7i) q^{52} +(4.18253e7 - 7.24435e7i) q^{53} +(2.60233e7 + 4.50737e7i) q^{54} +(-1.82155e7 - 3.15501e7i) q^{55} -1.34584e7 q^{56} +(-9.89886e7 + 2.21477e7i) q^{57} +3.54257e7 q^{58} +(5.02267e6 + 8.69952e6i) q^{59} +(4.48071e7 + 7.76082e7i) q^{60} +(7.56822e7 - 1.31085e8i) q^{61} +(1.47464e8 + 2.55415e8i) q^{62} +(-4.26213e6 + 7.38222e6i) q^{63} -1.47404e8 q^{64} +1.00599e7 q^{65} +(-2.54185e8 + 4.40261e8i) q^{66} +(8.89000e7 - 1.53979e8i) q^{67} +5.63776e8 q^{68} -3.28310e8 q^{69} +(6.78645e6 - 1.17545e7i) q^{70} +(2.76953e7 + 4.79696e7i) q^{71} +(1.17558e8 - 2.03616e8i) q^{72} +(-1.49027e8 - 2.58122e8i) q^{73} +(-1.82830e8 - 3.16671e8i) q^{74} +3.04364e8 q^{75} +(-3.87064e8 - 4.20757e8i) q^{76} +5.10347e7 q^{77} +(-7.01895e7 - 1.21572e8i) q^{78} +(1.23202e8 + 2.13391e8i) q^{79} +(-5.87088e7 + 1.01687e8i) q^{80} +(2.39349e8 + 4.14565e8i) q^{81} +(1.98933e7 - 3.44562e7i) q^{82} +1.32993e8 q^{83} -1.25537e8 q^{84} +(-1.39663e8 + 2.41903e8i) q^{85} +(-4.12588e8 + 7.14624e8i) q^{86} +1.62339e8 q^{87} -1.40763e9 q^{88} +(1.90855e8 - 3.30570e8i) q^{89} +(1.18558e8 + 2.05348e8i) q^{90} +(-7.04624e6 + 1.22044e7i) q^{91} +(-9.25207e8 - 1.60251e9i) q^{92} +(6.75755e8 + 1.17044e9i) q^{93} +7.02637e8 q^{94} +(2.76423e8 - 6.18469e7i) q^{95} -1.23000e8 q^{96} +(-3.30367e8 - 5.72213e8i) q^{97} +(-7.76725e8 - 1.34533e9i) q^{98} +(-4.45782e8 + 7.72117e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 15 q^{2} - 74 q^{3} - 2987 q^{4} - 285 q^{5} - 535 q^{6} - 2676 q^{7} - 24270 q^{8} - 57928 q^{9} + 41180 q^{10} - 114810 q^{11} + 235458 q^{12} + 98671 q^{13} - 148290 q^{14} + 428251 q^{15} - 279203 q^{16}+ \cdots - 736622698 q^{99}+O(q^{100}) $ 28 * q + 15 * q^2 - 74 * q^3 - 2987 * q^4 - 285 * q^5 - 535 * q^6 - 2676 * q^7 - 24270 * q^8 - 57928 * q^9 + 41180 * q^10 - 114810 * q^11 + 235458 * q^12 + 98671 * q^13 - 148290 * q^14 + 428251 * q^15 - 279203 * q^16 + 466251 * q^17 + 734964 * q^18 + 387157 * q^19 - 3343620 * q^20 + 689090 * q^21 - 1689395 * q^22 - 3087747 * q^23 - 234183 * q^24 - 3260823 * q^25 + 9033144 * q^26 + 4216540 * q^27 - 703814 * q^28 + 7831383 * q^29 - 11859224 * q^30 - 9265632 * q^31 + 11470815 * q^32 + 22791973 * q^33 + 13457096 * q^34 - 13222428 * q^35 + 7355018 * q^36 + 27205020 * q^37 - 67677738 * q^38 - 20775702 * q^39 - 16500258 * q^40 + 20419440 * q^41 - 10220798 * q^42 + 27415427 * q^43 + 41775405 * q^44 - 85982588 * q^45 - 137234708 * q^46 - 90906681 * q^47 + 33057375 * q^48 + 229824892 * q^49 + 44406714 * q^50 + 134429123 * q^51 + 66195006 * q^52 + 47827863 * q^53 - 130507669 * q^54 - 157712310 * q^55 + 382459116 * q^56 - 162912873 * q^57 - 344026048 * q^58 + 255540 * q^59 + 287916794 * q^60 + 304035459 * q^61 + 693626280 * q^62 - 122148024 * q^63 - 908491514 * q^64 - 1424960190 * q^65 - 611099417 * q^66 + 165758480 * q^67 + 357518508 * q^68 + 271237278 * q^69 + 1167527028 * q^70 + 685508589 * q^71 + 142349670 * q^72 - 602867050 * q^73 - 82104492 * q^74 + 1900274774 * q^75 - 1298297525 * q^76 - 491994756 * q^77 - 911449840 * q^78 + 78162339 * q^79 + 227607150 * q^80 + 1230916118 * q^81 + 360208019 * q^82 + 413839926 * q^83 - 467304924 * q^84 - 1440537237 * q^85 + 936824310 * q^86 - 678876318 * q^87 - 1646777694 * q^88 + 1256827551 * q^89 + 1879090924 * q^90 + 537759588 * q^91 - 677003592 * q^92 - 492493440 * q^93 - 848375184 * q^94 - 2034458607 * q^95 - 6041588930 * q^96 + 2109813492 * q^97 + 2689941591 * q^98 - 736622698 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	19.4836	+	33.7465i	0.861060	+	1.49140i	0.870907	+	0.491448i	$0.163532\pi$
$2$	19.4836	+	33.7465i	0.861060	+	1.49140i	−0.00984733	+	0.999952i	$0.503135\pi$
$3$	89.2835	+	154.644i	0.636393	+	1.10227i	0.986218	+	0.165450i	$0.0529077\pi$
$3$	89.2835	+	154.644i	0.636393	+	1.10227i	−0.349825	+	0.936815i	$0.613759\pi$
$4$	−503.218	+	871.599i	−0.982848	+	1.70234i
$5$	−249.322	−	431.838i	−0.178400	−	0.308998i	0.762933	−	0.646478i	$-0.223759\pi$
$5$	−249.322	−	431.838i	−0.178400	−	0.308998i	−0.941333	+	0.337480i	$0.890425\pi$
$6$	−3479.12	+	6026.01i	−1.09594	+	1.89823i
$7$	698.529			0.109962			0.0549811	−	0.998487i	$-0.482490\pi$
$7$	698.529			0.109962			0.0549811	+	0.998487i	$0.482490\pi$
$8$	−19266.8			−1.66304
$9$	−6101.58	+	10568.2i	−0.309992	+	0.536922i
$10$	9715.34	−	16827.5i	0.307226	−	0.532131i
$11$	73060.2			1.50457			0.752287	−	0.658836i	$-0.228951\pi$
$11$	73060.2			1.50457			0.752287	+	0.658836i	$0.228951\pi$
$12$	−179716.			−2.50191
$13$	−10087.3	+	17471.6i	−0.0979553	+	0.169663i	−0.910838	−	0.412764i	$-0.864564\pi$
$13$	−10087.3	+	17471.6i	−0.0979553	+	0.169663i	0.812883	+	0.582427i	$0.197897\pi$
$14$	13609.8	+	23572.9i	0.0946840	+	0.163998i
$15$	44520.6	−	77111.9i	0.227065	−	0.393288i
$16$	−117737.	−	203927.i	−0.449132	−	0.777919i
$17$	−280086.	−	485122.i	−0.813337	−	1.40874i	−0.910516	−	0.413474i	$-0.864315\pi$
$17$	−280086.	−	485122.i	−0.813337	−	1.40874i	0.0971789	−	0.995267i	$-0.469018\pi$
$18$	−475522.			−1.06769
$19$	−169762.	+	542097.i	−0.298847	+	0.954301i
$19$	−169762.	+	542097.i	−0.298847	+	0.954301i
$20$	501852.			0.701360
$21$	62367.1	+	108023.i	0.0699792	+	0.121207i
$22$	1.42347e6	+	2.46553e6i	1.29553	+	2.24392i
$23$	−919291.	+	1.59226e6i	−0.684980	+	1.18642i	0.288464	+	0.957491i	$0.406856\pi$
$23$	−919291.	+	1.59226e6i	−0.684980	+	1.18642i	−0.973443	+	0.228929i	$0.926478\pi$
$24$	−1.72020e6	−	2.97948e6i	−1.05835	−	1.83311i
$25$	852240.	−	1.47612e6i	0.436347	−	0.755775i
$26$	−786142.			−0.337381
$27$	1.33565e6			0.483679
$28$	−351513.	+	608838.i	−0.108076	+	0.187193i
$29$	454559.	−	787320.i	0.119344	−	0.206709i	−0.800164	−	0.599781i	$-0.795254\pi$
$29$	454559.	−	787320.i	0.119344	−	0.206709i	0.919508	+	0.393072i	$0.128588\pi$
$30$	3.46968e6			0.782066
$31$	7.56865e6			1.47194			0.735971	−	0.677013i	$-0.236726\pi$
$31$	7.56865e6			1.47194			0.735971	+	0.677013i	$0.236726\pi$
$32$	−344409.	+	596534.i	−0.0580630	+	0.100568i
$33$	6.52306e6	+	1.12983e7i	0.957500	+	1.65844i
$34$	1.09141e7	−	1.89038e7i	1.40066	−	2.42602i
$35$	−174158.	−	301651.i	−0.0196173	−	0.0339781i
$36$	−6.14085e6	−	1.06363e7i	−0.609350	−	1.05543i
$37$	−9.38380e6			−0.823135			−0.411567	−	0.911379i	$-0.635019\pi$
$37$	−9.38380e6			−0.823135			−0.411567	+	0.911379i	$0.635019\pi$
$38$	−2.16014e7	+	4.83311e6i	−1.68057	+	0.376011i
$39$	−3.60250e6			−0.249352
$40$	4.80362e6	+	8.32011e6i	0.296687	+	0.513877i
$41$	−510515.	−	884238.i	−0.0282151	−	0.0488699i	0.851573	−	0.524236i	$-0.175649\pi$
$41$	−510515.	−	884238.i	−0.0282151	−	0.0488699i	−0.879788	+	0.475366i	$0.842316\pi$
$42$	−2.43027e6	+	4.20935e6i	−0.120513	+	0.208734i
$43$	1.05881e7	+	1.83391e7i	0.472292	+	0.818034i	0.999497	−	0.0317043i	$-0.0100935\pi$
$43$	1.05881e7	+	1.83391e7i	0.472292	+	0.818034i	−0.527205	+	0.849738i	$0.676760\pi$
$44$	−3.67652e7	+	6.36792e7i	−1.47877	+	2.56130i
$45$	6.08502e6			0.221210
$46$	−7.16442e7			−2.35923
$47$	9.01577e6	−	1.56158e7i	0.269502	−	0.466792i	−0.699231	−	0.714896i	$-0.746474\pi$
$47$	9.01577e6	−	1.56158e7i	0.269502	−	0.466792i	0.968733	+	0.248104i	$0.0798075\pi$
$48$	2.10240e7	−	3.64146e7i	0.571649	−	0.990124i
$49$	−3.98657e7			−0.987908
$50$	6.64187e7			1.50288
$51$	5.00140e7	−	8.66268e7i	1.03520	−	1.79303i
$52$	−1.01522e7	−	1.75841e7i	−0.192550	−	0.333507i
$53$	4.18253e7	−	7.24435e7i	0.728110	−	1.26112i	−0.229570	−	0.973292i	$-0.573732\pi$
$53$	4.18253e7	−	7.24435e7i	0.728110	−	1.26112i	0.957681	−	0.287832i	$-0.0929345\pi$
$54$	2.60233e7	+	4.50737e7i	0.416476	+	0.721358i
$55$	−1.82155e7	−	3.15501e7i	−0.268416	−	0.464910i
$56$	−1.34584e7			−0.182872
$57$	−9.89886e7	+	2.21477e7i	−1.24208	+	0.277902i
$58$	3.54257e7			0.411048
$59$	5.02267e6	+	8.69952e6i	0.0539635	+	0.0934676i	0.891745	−	0.452538i	$-0.149481\pi$
$59$	5.02267e6	+	8.69952e6i	0.0539635	+	0.0934676i	−0.837782	+	0.546005i	$0.816148\pi$
$60$	4.48071e7	+	7.76082e7i	0.446341	+	0.773085i
$61$	7.56822e7	−	1.31085e8i	0.699858	−	1.21219i	−0.268658	−	0.963236i	$-0.586580\pi$
$61$	7.56822e7	−	1.31085e8i	0.699858	−	1.21219i	0.968516	−	0.248953i	$-0.0800865\pi$
$62$	1.47464e8	+	2.55415e8i	1.26743	+	2.19525i
$63$	−4.26213e6	+	7.38222e6i	−0.0340874	+	0.0590411i
$64$	−1.47404e8			−1.09825
$65$	1.00599e7			0.0699009
$66$	−2.54185e8	+	4.40261e8i	−1.64893	+	2.85603i
$67$	8.89000e7	−	1.53979e8i	0.538971	−	0.933525i	−0.459989	−	0.887925i	$-0.652147\pi$
$67$	8.89000e7	−	1.53979e8i	0.538971	−	0.933525i	0.998960	−	0.0456003i	$-0.0145201\pi$
$68$	5.63776e8			3.19755
$69$	−3.28310e8			−1.74366
$70$	6.78645e6	−	1.17545e7i	0.0337833	−	0.0585143i
$71$	2.76953e7	+	4.79696e7i	0.129343	+	0.224029i	0.923422	−	0.383786i	$-0.125380\pi$
$71$	2.76953e7	+	4.79696e7i	0.129343	+	0.224029i	−0.794079	+	0.607814i	$0.792047\pi$
$72$	1.17558e8	−	2.03616e8i	0.515530	−	0.892925i
$73$	−1.49027e8	−	2.58122e8i	−0.614203	−	1.06383i	−0.990524	−	0.137342i	$-0.956144\pi$
$73$	−1.49027e8	−	2.58122e8i	−0.614203	−	1.06383i	0.376320	−	0.926490i	$-0.377189\pi$
$74$	−1.82830e8	−	3.16671e8i	−0.708768	−	1.22762i
$75$	3.04364e8			1.11075
$76$	−3.87064e8	−	4.20757e8i	−1.33083	−	1.44667i
$77$	5.10347e7			0.165446
$78$	−7.01895e7	−	1.21572e8i	−0.214707	−	0.371884i
$79$	1.23202e8	+	2.13391e8i	0.355872	+	0.616389i	0.987267	−	0.159073i	$-0.0508504\pi$
$79$	1.23202e8	+	2.13391e8i	0.355872	+	0.616389i	−0.631394	+	0.775462i	$0.717517\pi$
$80$	−5.87088e7	+	1.01687e8i	−0.160250	+	0.277561i
$81$	2.39349e8	+	4.14565e8i	0.617802	+	1.07006i
$82$	1.98933e7	−	3.44562e7i	0.0485897	−	0.0841599i
$83$	1.32993e8			0.307593			0.153796	−	0.988103i	$-0.450850\pi$
$83$	1.32993e8			0.307593			0.153796	+	0.988103i	$0.450850\pi$
$84$	−1.25537e8			−0.275116
$85$	−1.39663e8	+	2.41903e8i	−0.290199	+	0.502639i
$86$	−4.12588e8	+	7.14624e8i	−0.813343	+	1.40875i
$87$	1.62339e8			0.303798
$88$	−1.40763e9			−2.50217
$89$	1.90855e8	−	3.30570e8i	0.322439	−	0.558481i	−0.658552	−	0.752536i	$-0.728831\pi$
$89$	1.90855e8	−	3.30570e8i	0.322439	−	0.558481i	0.980991	+	0.194055i	$0.0621639\pi$
$90$	1.18558e8	+	2.05348e8i	0.190475	+	0.329913i
$91$	−7.04624e6	+	1.22044e7i	−0.0107714	+	0.0186566i
$92$	−9.25207e8	−	1.60251e9i	−1.34646	−	2.33214i
$93$	6.75755e8	+	1.17044e9i	0.936734	+	1.62247i
$94$	7.02637e8			0.928230
$95$	2.76423e8	−	6.18469e7i	0.348191	−	0.0779044i
$96$	−1.23000e8			−0.147804
$97$	−3.30367e8	−	5.72213e8i	−0.378900	−	0.656273i	0.612003	−	0.790856i	$-0.290364\pi$
$97$	−3.30367e8	−	5.72213e8i	−0.378900	−	0.656273i	−0.990902	+	0.134582i	$0.957031\pi$
$98$	−7.76725e8	−	1.34533e9i	−0.850648	−	1.47337i
$99$	−4.45782e8	+	7.72117e8i	−0.466406	+	0.807839i
$100$	8.57725e8	+	1.48562e9i	0.857725	+	1.48562i
$101$	−5.63596e8	+	9.76178e8i	−0.538917	+	0.933432i	0.460045	+	0.887895i	$0.347833\pi$
$101$	−5.63596e8	+	9.76178e8i	−0.538917	+	0.933432i	−0.998963	+	0.0455367i	$0.985500\pi$
$102$	3.89780e9			3.56549
$103$	−1.42461e9			−1.24718			−0.623589	−	0.781752i	$-0.714326\pi$
$103$	−1.42461e9			−1.24718			−0.623589	+	0.781752i	$0.714326\pi$
$104$	1.94349e8	−	3.36622e8i	0.162904	−	0.282158i
$105$	3.10989e7	−	5.38649e7i	0.0249686	−	0.0432468i
$106$	3.25962e9			2.50779
$107$	1.48710e9			1.09677			0.548384	−	0.836227i	$-0.315243\pi$
$107$	1.48710e9			1.09677			0.548384	+	0.836227i	$0.315243\pi$
$108$	−6.72125e8	+	1.16415e9i	−0.475382	+	0.823387i
$109$	−5.05160e8	−	8.74963e8i	−0.342775	−	0.593704i	0.642172	−	0.766561i	$-0.278034\pi$
$109$	−5.05160e8	−	8.74963e8i	−0.342775	−	0.593704i	−0.984947	+	0.172856i	$0.944700\pi$
$110$	7.09804e8	−	1.22942e9i	0.462244	−	0.800631i
$111$	−8.37818e8	−	1.45114e9i	−0.523837	−	0.907313i
$112$	−8.22429e7	−	1.42449e8i	−0.0493875	−	0.0855417i
$113$	−2.47038e9			−1.42531			−0.712657	−	0.701512i	$-0.752508\pi$
$113$	−2.47038e9			−1.42531			−0.712657	+	0.701512i	$0.752508\pi$
$114$	−2.67606e9	−	2.90900e9i	−1.48397	−	1.61314i
$115$	9.16796e8			0.488801
$116$	4.57485e8	+	7.92387e8i	0.234593	+	0.406328i
$117$	−1.23096e8	−	2.13209e8i	−0.0607307	−	0.105189i
$118$	−1.95719e8	+	3.38995e8i	−0.0929317	+	0.160962i
$119$	−1.95648e8	−	3.38872e8i	−0.0894363	−	0.154908i
$120$	−8.57767e8	+	1.48570e9i	−0.377619	+	0.654055i
$121$	2.97984e9			1.26374
$122$	5.89824e9			2.41048
$123$	9.11611e7	−	1.57896e8i	0.0359118	−	0.0622010i
$124$	−3.80868e9	+	6.59683e9i	−1.44669	+	2.50575i
$125$	−1.82384e9			−0.668177
$126$	−3.32166e8			−0.117405
$127$	−7.52822e8	+	1.30393e9i	−0.256788	+	0.444771i	−0.965380	−	0.260848i	$-0.915998\pi$
$127$	−7.52822e8	+	1.30393e9i	−0.256788	+	0.444771i	0.708591	+	0.705619i	$0.249331\pi$
$128$	−2.69562e9	−	4.66895e9i	−0.887593	−	1.53736i
$129$	−1.89069e9	+	3.27477e9i	−0.601127	+	1.04118i
$130$	1.96002e8	+	3.39486e8i	0.0601888	+	0.104250i
$131$	−8.34509e8	−	1.44541e9i	−0.247577	−	0.428816i	0.715276	−	0.698842i	$-0.246301\pi$
$131$	−8.34509e8	−	1.44541e9i	−0.247577	−	0.428816i	−0.962853	+	0.270026i	$0.912968\pi$
$132$	−1.31301e10			−3.76431
$133$	−1.18583e8	+	3.78670e8i	−0.0328618	+	0.104937i
$134$	6.92836e9			1.85634
$135$	−3.33007e8	−	5.76785e8i	−0.0862883	−	0.149456i
$136$	5.39634e9	+	9.34673e9i	1.35261	+	2.34280i
$137$	2.61674e9	−	4.53233e9i	0.634627	−	1.09921i	−0.351967	−	0.936012i	$-0.614487\pi$
$137$	2.61674e9	−	4.53233e9i	0.634627	−	1.09921i	0.986594	−	0.163194i	$-0.0521796\pi$
$138$	−6.39664e9	−	1.10793e10i	−1.50140	−	2.60050i
$139$	−2.33328e9	+	4.04136e9i	−0.530152	+	0.918250i	0.469229	+	0.883076i	$0.344532\pi$
$139$	−2.33328e9	+	4.04136e9i	−0.530152	+	0.918250i	−0.999381	+	0.0351735i	$0.988802\pi$
$140$	3.50559e8			0.0771231
$141$	3.21984e9			0.686037
$142$	−1.07920e9	+	1.86924e9i	−0.222744	+	0.385804i
$143$	−7.36976e8	+	1.27648e9i	−0.147381	+	0.255271i
$144$	2.87353e9			0.556909
$145$	−4.53326e8			−0.0851637
$146$	5.80715e9	−	1.00583e10i	1.05773	−	1.83204i
$147$	−3.55934e9	−	6.16497e9i	−0.628698	−	1.08894i
$148$	4.72210e9	−	8.17891e9i	0.809016	−	1.40126i
$149$	4.57716e9	+	7.92787e9i	0.760778	+	1.31771i	0.942450	+	0.334347i	$0.108516\pi$
$149$	4.57716e9	+	7.92787e9i	0.760778	+	1.31771i	−0.181672	+	0.983359i	$0.558151\pi$
$150$	5.93009e9	+	1.02712e10i	0.956424	+	1.65658i
$151$	−9.78932e9			−1.53234			−0.766172	−	0.642635i	$-0.777841\pi$
$151$	−9.78932e9			−1.53234			−0.766172	+	0.642635i	$0.777841\pi$
$152$	3.27075e9	−	1.04444e10i	0.496995	−	1.58704i
$153$	6.83585e9			1.00851
$154$	9.94337e8	+	1.72224e9i	0.142459	+	0.246746i
$155$	−1.88703e9	−	3.26843e9i	−0.262594	−	0.454827i
$156$	1.81284e9	−	3.13994e9i	0.245075	−	0.424483i
$157$	4.25190e9	+	7.36450e9i	0.558514	+	0.967375i	0.997621	+	0.0689400i	$0.0219617\pi$
$157$	4.25190e9	+	7.36450e9i	0.558514	+	0.967375i	−0.439107	+	0.898435i	$0.644705\pi$
$158$	−4.80081e9	+	8.31525e9i	−0.612855	+	1.06150i
$159$	1.49372e10			1.85346
$160$	3.43474e8			0.0414338
$161$	−6.42151e8	+	1.11224e9i	−0.0753219	+	0.130461i
$162$	−9.32674e9	+	1.61544e10i	−1.06393	+	1.84278i
$163$	−9.45369e9			−1.04896			−0.524478	−	0.851424i	$-0.675739\pi$
$163$	−9.45369e9			−1.04896			−0.524478	+	0.851424i	$0.675739\pi$
$164$	1.02760e9			0.110924
$165$	3.25268e9	−	5.63381e9i	0.341636	−	0.591731i
$166$	2.59117e9	+	4.48804e9i	0.264856	+	0.458744i
$167$	8.73188e8	−	1.51241e9i	0.0868728	−	0.150468i	−0.819315	−	0.573344i	$-0.805646\pi$
$167$	8.73188e8	−	1.51241e9i	0.0868728	−	0.150468i	0.906188	+	0.422876i	$0.138979\pi$
$168$	−1.20161e9	−	2.08125e9i	−0.116378	−	0.201573i
$169$	5.09874e9	+	8.83128e9i	0.480810	+	0.832787i
$170$	−1.08845e10			−0.999513
$171$	−4.69319e9	−	5.10172e9i	−0.419745	−	0.456283i
$172$	−2.13125e10			−1.85676
$173$	−1.76826e9	−	3.06271e9i	−0.150085	−	0.259955i	0.781173	−	0.624314i	$-0.214621\pi$
$173$	−1.76826e9	−	3.06271e9i	−0.150085	−	0.259955i	−0.931259	+	0.364359i	$0.881288\pi$
$174$	3.16293e9	+	5.47836e9i	0.261588	+	0.453084i
$175$	5.95315e8	−	1.03112e9i	0.0479817	−	0.0831067i
$176$	−8.60190e9	−	1.48989e10i	−0.675752	−	1.17044i
$177$	−8.96883e8	+	1.55345e9i	−0.0686840	+	0.118964i
$178$	1.48741e10			1.11056
$179$	8.59048e9			0.625430			0.312715	−	0.949847i	$-0.398761\pi$
$179$	8.59048e9			0.625430			0.312715	+	0.949847i	$0.398761\pi$
$180$	−3.06209e9	+	5.30370e9i	−0.217416	+	0.376576i
$181$	3.01293e9	−	5.21854e9i	0.208658	−	0.361406i	−0.742634	−	0.669697i	$-0.766424\pi$
$181$	3.01293e9	−	5.21854e9i	0.208658	−	0.361406i	0.951292	+	0.308291i	$0.0997571\pi$
$182$	−5.49143e8			−0.0370992
$183$	2.70287e10			1.78154
$184$	1.77117e10	−	3.06776e10i	1.13915	−	1.97307i
$185$	2.33958e9	+	4.05228e9i	0.146847	+	0.254347i
$186$	−2.63322e10	+	4.56088e10i	−1.61317	+	2.79409i
$187$	−2.04631e10	−	3.54431e10i	−1.22373	−	2.11955i
$188$	9.07380e9	+	1.57163e10i	0.529759	+	0.917570i
$189$	9.32993e8			0.0531864
$190$	7.47282e9	+	8.12331e9i	0.416000	+	0.452212i
$191$	−2.71361e10			−1.47536			−0.737678	−	0.675153i	$-0.764078\pi$
$191$	−2.71361e10			−1.47536			−0.737678	+	0.675153i	$0.764078\pi$
$192$	−1.31608e10	−	2.27951e10i	−0.698916	−	1.21056i
$193$	−9.45718e9	−	1.63803e10i	−0.490630	−	0.849796i	0.509312	−	0.860582i	$-0.329900\pi$
$193$	−9.45718e9	−	1.63803e10i	−0.490630	−	0.849796i	−0.999942	+	0.0107862i	$0.996567\pi$
$194$	1.28735e10	−	2.22975e10i	0.652511	−	1.13018i
$195$	8.98181e8	+	1.55569e9i	0.0444844	+	0.0770493i
$196$	2.00611e10	−	3.47469e10i	0.970964	−	1.68176i
$197$	5.53715e9			0.261932			0.130966	−	0.991387i	$-0.458192\pi$
$197$	5.53715e9			0.261932			0.130966	+	0.991387i	$0.458192\pi$
$198$	−3.47417e10			−1.60641
$199$	−1.43005e10	+	2.47692e10i	−0.646417	+	1.11963i	0.337555	+	0.941306i	$0.390400\pi$
$199$	−1.43005e10	+	2.47692e10i	−0.646417	+	1.11963i	−0.983972	+	0.178322i	$0.942933\pi$
$200$	−1.64199e10	+	2.84401e10i	−0.725664	+	1.25689i
$201$	3.17492e10			1.37199
$202$	−4.39235e10			−1.85616
$203$	3.17523e8	−	5.49966e8i	0.0131233	−	0.0227302i
$204$	5.03359e10	+	8.71844e10i	2.03490	+	3.52454i
$205$	−2.54565e8	+	4.40919e8i	−0.0100671	+	0.0174368i
$206$	−2.77565e10	−	4.80756e10i	−1.07390	−	1.86004i
$207$	−1.12182e10	−	1.94306e10i	−0.424677	−	0.735561i
$208$	4.75058e9			0.175979
$209$	−1.24028e10	+	3.96057e10i	−0.449637	+	1.43582i
$210$	2.42367e9			0.0859977
$211$	5.26025e9	+	9.11102e9i	0.182699	+	0.316443i	0.942799	−	0.333363i	$-0.108183\pi$
$211$	5.26025e9	+	9.11102e9i	0.182699	+	0.316443i	−0.760100	+	0.649806i	$0.774850\pi$
$212$	4.20945e10	+	7.29097e10i	1.43124	+	2.47899i
$213$	−4.94546e9	+	8.56578e9i	−0.164626	+	0.285140i
$214$	2.89741e10	+	5.01846e10i	0.944382	+	1.63572i
$215$	5.27969e9	−	9.14469e9i	0.168514	−	0.291874i
$216$	−2.57337e10			−0.804378
$217$	5.28692e9			0.161858
$218$	1.96846e10	−	3.40948e10i	0.590300	−	1.02243i
$219$	2.66113e10	−	4.60921e10i	0.781749	−	1.35403i
$220$	3.66654e10			1.05525
$221$	1.13012e10			0.318683
$222$	3.26474e10	−	5.65469e10i	0.902110	−	1.56250i
$223$	−2.85287e10	−	4.94132e10i	−0.772521	−	1.33805i	−0.936177	−	0.351528i	$-0.885662\pi$
$223$	−2.85287e10	−	4.94132e10i	−0.772521	−	1.33805i	0.163657	−	0.986517i	$-0.447671\pi$
$224$	−2.40580e8	+	4.16696e8i	−0.00638474	+	0.0110587i
$225$	1.04000e10	+	1.80134e10i	0.270528	+	0.468569i
$226$	−4.81318e10	−	8.33667e10i	−1.22728	−	2.12571i
$227$	5.27714e10			1.31911			0.659557	−	0.751655i	$-0.270744\pi$
$227$	5.27714e10			1.31911			0.659557	+	0.751655i	$0.270744\pi$
$228$	3.05089e10	−	9.74235e10i	0.747687	−	2.38758i
$229$	−5.04301e10			−1.21180			−0.605898	−	0.795542i	$-0.707186\pi$
$229$	−5.04301e10			−1.21180			−0.605898	+	0.795542i	$0.707186\pi$
$230$	1.78624e10	+	3.09387e10i	0.420887	+	0.728998i
$231$	4.55655e9	+	7.89218e9i	0.105289	+	0.182366i
$232$	−8.75788e9	+	1.51691e10i	−0.198474	+	0.343767i
$233$	2.48496e9	+	4.30408e9i	0.0552355	+	0.0956706i	0.892321	−	0.451401i	$-0.149076\pi$
$233$	2.48496e9	+	4.30408e9i	0.0552355	+	0.0956706i	−0.837086	+	0.547072i	$0.815742\pi$
$234$	4.79671e9	−	8.30814e9i	0.104586	−	0.181148i
$235$	−8.99130e9			−0.192317
$236$	−1.01100e10			−0.212152
$237$	−2.19997e10	+	3.81046e10i	−0.452949	+	0.784531i
$238$	7.62384e9	−	1.32049e10i	0.154020	−	0.266771i
$239$	−5.47100e10			−1.08462			−0.542309	−	0.840179i	$-0.682450\pi$
$239$	−5.47100e10			−1.08462			−0.542309	+	0.840179i	$0.682450\pi$
$240$	−2.09669e10			−0.407928
$241$	9.21677e9	−	1.59639e10i	0.175996	−	0.304834i	−0.764510	−	0.644612i	$-0.777019\pi$
$241$	9.21677e9	−	1.59639e10i	0.175996	−	0.304834i	0.940505	+	0.339779i	$0.110352\pi$
$242$	5.80578e10	+	1.00559e11i	1.08816	+	1.88474i
$243$	−2.95950e10	+	5.12600e10i	−0.544490	+	0.943085i
$244$	7.61693e10	+	1.31929e11i	1.37571	+	2.38279i
$245$	9.93937e9	+	1.72155e10i	0.176243	+	0.305262i
$246$	7.10457e9			0.123689
$247$	−7.75888e9	−	8.43428e9i	−0.132636	−	0.144182i
$248$	−1.45823e11			−2.44790
$249$	1.18740e10	+	2.05665e10i	0.195750	+	0.339049i
$250$	−3.55349e10	−	6.15482e10i	−0.575340	−	0.996519i
$251$	3.47825e10	−	6.02450e10i	0.553132	−	0.958053i	−0.444914	−	0.895573i	$-0.646766\pi$
$251$	3.47825e10	−	6.02450e10i	0.553132	−	0.958053i	0.998046	−	0.0624797i	$-0.0199009\pi$
$252$	−4.28956e9	−	7.42974e9i	−0.0670055	−	0.116057i
$253$	−6.71635e10	+	1.16331e11i	−1.03060	+	1.78506i
$254$	−5.86706e10			−0.884441
$255$	−4.98783e10			−0.738721
$256$	6.73051e10	−	1.16576e11i	0.979418	−	1.69640i
$257$	2.16621e10	−	3.75199e10i	0.309743	−	0.536491i	−0.668563	−	0.743655i	$-0.733090\pi$
$257$	2.16621e10	−	3.75199e10i	0.309743	−	0.536491i	0.978306	+	0.207165i	$0.0664237\pi$
$258$	−1.47349e11			−2.07042
$259$	−6.55486e9			−0.0905137
$260$	−5.06231e9	+	8.76818e9i	−0.0687019	+	0.118995i
$261$	5.54706e9	+	9.60778e9i	0.0739912	+	0.128157i
$262$	3.25184e10	−	5.63235e10i	0.426357	−	0.738472i
$263$	6.17852e10	+	1.07015e11i	0.796313	+	1.37925i	0.922002	+	0.387185i	$0.126553\pi$
$263$	6.17852e10	+	1.07015e11i	0.796313	+	1.37925i	−0.125689	+	0.992070i	$0.540114\pi$
$264$	−1.25678e11	−	2.17681e11i	−1.59236	−	2.75806i
$265$	−4.17118e10			−0.519580
$266$	−1.50892e10	+	3.37607e9i	−0.184799	+	0.0413470i
$267$	6.81607e10			0.820792
$268$	8.94722e10	+	1.54970e11i	1.05945	+	1.83503i
$269$	6.68383e9	+	1.15767e10i	0.0778288	+	0.134803i	0.902313	−	0.431082i	$-0.141868\pi$
$269$	6.68383e9	+	1.15767e10i	0.0778288	+	0.134803i	−0.824484	+	0.565885i	$0.808535\pi$
$270$	1.29763e10	−	2.24757e10i	0.148599	−	0.257380i
$271$	2.99894e10	+	5.19432e10i	0.337759	+	0.585015i	0.984011	−	0.178109i	$-0.0569979\pi$
$271$	2.99894e10	+	5.19432e10i	0.337759	+	0.585015i	−0.646252	+	0.763124i	$0.723665\pi$
$272$	−6.59530e10	+	1.14234e11i	−0.730591	+	1.26542i
$273$	−2.51645e9			−0.0274193
$274$	2.03934e11			2.18581
$275$	6.22648e10	−	1.07846e11i	0.656516	−	1.13712i
$276$	1.65211e11	−	2.86155e11i	1.71376	−	2.96831i
$277$	1.15506e11			1.17881			0.589407	−	0.807836i	$-0.299362\pi$
$277$	1.15506e11			1.17881			0.589407	+	0.807836i	$0.299362\pi$
$278$	−1.81842e11			−1.82597
$279$	−4.61807e10	+	7.99873e10i	−0.456291	+	0.790318i
$280$	3.35547e9	+	5.81184e9i	0.0326243	+	0.0565070i
$281$	−3.42465e10	+	5.93167e10i	−0.327671	+	0.567543i	−0.982049	−	0.188625i	$-0.939597\pi$
$281$	−3.42465e10	+	5.93167e10i	−0.327671	+	0.567543i	0.654378	+	0.756167i	$0.272930\pi$
$282$	6.27339e10	+	1.08658e11i	0.590719	+	1.02316i
$283$	−7.88171e10	−	1.36515e11i	−0.730434	−	1.26515i	−0.956698	−	0.291083i	$-0.905984\pi$
$283$	−7.88171e10	−	1.36515e11i	−0.730434	−	1.26515i	0.226263	−	0.974066i	$-0.427349\pi$
$284$	−5.57470e10			−0.508498
$285$	3.42442e10	+	3.72251e10i	0.307458	+	0.334221i
$286$	−5.74357e10			−0.507615
$287$	−3.56610e8	−	6.17666e8i	−0.00310259	−	0.00537385i
$288$	−4.20288e9	−	7.27959e9i	−0.0359982	−	0.0623507i
$289$	−9.76019e10	+	1.69051e11i	−0.823034	+	1.42554i
$290$	−8.83240e9	−	1.52982e10i	−0.0733310	−	0.127013i
$291$	5.89927e10	−	1.02178e11i	0.482258	−	0.835296i
$292$	2.99972e11			2.41467
$293$	9.79877e10			0.776725			0.388363	−	0.921507i	$-0.373041\pi$
$293$	9.79877e10			0.776725			0.388363	+	0.921507i	$0.373041\pi$
$294$	1.38697e11	−	2.40231e11i	1.08269	−	1.87528i
$295$	2.50452e9	−	4.33795e9i	0.0192542	−	0.0333492i
$296$	1.80795e11			1.36891
$297$	9.75831e10			0.727730
$298$	−1.78359e11	+	3.08926e11i	−1.31015	+	2.26925i
$299$	−1.85462e10	−	3.21230e10i	−0.134195	−	0.232432i
$300$	−1.53161e11	+	2.65283e11i	−1.09170	+	1.89088i
$301$	7.39611e9	+	1.28104e10i	0.0519343	+	0.0899528i
$302$	−1.90731e11	−	3.30355e11i	−1.31944	−	2.28534i
$303$	−2.01279e11			−1.37185
$304$	1.30535e11	−	2.92060e10i	0.876591	−	0.196129i
$305$	−7.54768e10			−0.499418
$306$	1.33187e11	+	2.30686e11i	0.868389	+	1.50409i
$307$	−4.71509e9	−	8.16678e9i	−0.0302948	−	0.0524720i	0.850481	−	0.526007i	$-0.176311\pi$
$307$	−4.71509e9	−	8.16678e9i	−0.0302948	−	0.0524720i	−0.880775	+	0.473534i	$0.842978\pi$
$308$	−2.56816e10	+	4.44818e10i	−0.162608	+	0.281646i
$309$	−1.27194e11	−	2.20307e11i	−0.793696	−	1.37472i
$310$	7.35320e10	−	1.27361e11i	0.452219	−	0.783266i
$311$	−2.80188e11			−1.69835			−0.849177	−	0.528109i	$-0.822901\pi$
$311$	−2.80188e11			−1.69835			−0.849177	+	0.528109i	$0.822901\pi$
$312$	6.94084e10			0.414683
$313$	1.49014e11	−	2.58100e11i	0.877562	−	1.51998i	0.0235538	−	0.999723i	$-0.492502\pi$
$313$	1.49014e11	−	2.58100e11i	0.877562	−	1.51998i	0.854008	−	0.520259i	$-0.174165\pi$
$314$	−1.65684e11	+	2.86973e11i	−0.961828	+	1.66594i
$315$	4.25056e9			0.0243248
$316$	−2.47989e11			−1.39907
$317$	−2.85901e9	+	4.95195e9i	−0.0159019	+	0.0275429i	−0.873867	−	0.486165i	$-0.838395\pi$
$317$	−2.85901e9	+	4.95195e9i	−0.0159019	+	0.0275429i	0.857965	+	0.513708i	$0.171729\pi$
$318$	2.91030e11	+	5.04079e11i	1.59594	+	2.76425i
$319$	3.32102e10	−	5.75217e10i	0.179561	−	0.311009i
$320$	3.67510e10	+	6.36546e10i	0.195927	+	0.339356i
$321$	1.32774e11	+	2.29971e11i	0.697975	+	1.20893i
$322$	−5.00456e10			−0.259426
$323$	3.10531e11	−	6.94783e10i	1.58743	−	0.355171i
$324$	−4.81779e11			−2.42882
$325$	1.71935e10	+	2.97800e10i	0.0854849	+	0.148064i
$326$	−1.84191e11	−	3.19029e11i	−0.903213	−	1.56441i
$327$	9.02049e10	−	1.56239e11i	0.436280	−	0.755659i
$328$	9.83597e9	+	1.70364e10i	0.0469229	+	0.0812728i
$329$	6.29778e9	−	1.09081e10i	0.0296351	−	0.0513294i
$330$	2.53495e11			1.17668
$331$	−3.52488e11			−1.61406			−0.807028	−	0.590513i	$-0.798925\pi$
$331$	−3.52488e11			−1.61406			−0.807028	+	0.590513i	$0.798925\pi$
$332$	−6.69243e10	+	1.15916e11i	−0.302317	+	0.523628i
$333$	5.72560e10	−	9.91702e10i	0.255165	−	0.441959i
$334$	6.80513e10			0.299211
$335$	−8.86588e10			−0.384610
$336$	1.46859e10	−	2.54367e10i	0.0628597	−	0.108876i
$337$	−8.73275e10	−	1.51256e11i	−0.368822	−	0.638818i	0.620560	−	0.784159i	$-0.286905\pi$
$337$	−8.73275e10	−	1.51256e11i	−0.368822	−	0.638818i	−0.989382	+	0.145341i	$0.953572\pi$
$338$	−1.98683e11	+	3.44130e11i	−0.828011	+	1.43416i
$339$	−2.20564e11	−	3.82028e11i	−0.907060	−	1.57107i
$340$	−1.40562e11	−	2.43460e11i	−0.570442	−	0.988035i
$341$	5.52967e11			2.21465
$342$	8.07253e10	−	2.57779e11i	0.319075	−	1.01890i
$343$	−5.60355e10			−0.218595
$344$	−2.03999e11	−	3.53336e11i	−0.785442	−	1.36043i
$345$	8.18547e10	+	1.41777e11i	0.311070	+	0.538789i
$346$	6.89038e10	−	1.19345e11i	0.258465	−	0.447674i
$347$	−5.63317e10	−	9.75694e10i	−0.208579	−	0.361269i	0.742688	−	0.669637i	$-0.233550\pi$
$347$	−5.63317e10	−	9.75694e10i	−0.208579	−	0.361269i	−0.951267	+	0.308368i	$0.900217\pi$
$348$	−8.16917e10	+	1.41494e11i	−0.298587	+	0.517168i
$349$	−2.81148e10			−0.101442			−0.0507212	−	0.998713i	$-0.516152\pi$
$349$	−2.81148e10			−0.101442			−0.0507212	+	0.998713i	$0.516152\pi$
$350$	4.63954e10			0.165260
$351$	−1.34731e10	+	2.33360e10i	−0.0473789	+	0.0820626i
$352$	−2.51626e10	+	4.35829e10i	−0.0873601	+	0.151312i
$353$	3.21337e11			1.10148			0.550738	−	0.834679i	$-0.314347\pi$
$353$	3.21337e11			1.10148			0.550738	+	0.834679i	$0.314347\pi$
$354$	−6.98979e10			−0.236564
$355$	1.38100e10	−	2.39197e10i	0.0461496	−	0.0799334i
$356$	1.92083e11	+	3.32698e11i	0.633817	+	1.09780i
$357$	3.49363e10	−	6.05114e10i	0.113833	−	0.197165i
$358$	1.67373e11	+	2.89899e11i	0.538533	+	0.932766i
$359$	2.10090e11	+	3.63887e11i	0.667545	+	1.15622i	0.978589	+	0.205826i	$0.0659881\pi$
$359$	2.10090e11	+	3.63887e11i	0.667545	+	1.15622i	−0.311044	+	0.950396i	$0.600679\pi$
$360$	−1.17239e11			−0.367882
$361$	−2.65050e11	−	1.84054e11i	−0.821381	−	0.570379i
$362$	2.34810e11			0.718668
$363$	2.66050e11	+	4.60813e11i	0.804237	+	1.39298i
$364$	−7.09159e9	−	1.22830e10i	−0.0211732	−	0.0366731i
$365$	−7.43113e10	+	1.28711e11i	−0.219148	+	0.379575i
$366$	5.26615e11	+	9.12124e11i	1.53401	+	2.65698i
$367$	−1.85962e11	+	3.22096e11i	−0.535090	+	0.926803i	0.464069	+	0.885799i	$0.346389\pi$
$367$	−1.85962e11	+	3.22096e11i	−0.535090	+	0.926803i	−0.999159	+	0.0410042i	$0.986944\pi$
$368$	4.32939e11			1.23058
$369$	1.24598e10			0.0349858
$370$	−9.11668e10	+	1.57906e11i	−0.252888	+	0.438016i
$371$	2.92162e10	−	5.06039e10i	0.0800646	−	0.138676i
$372$	−1.36021e12			−3.68267
$373$	−3.28407e11			−0.878461			−0.439231	−	0.898374i	$-0.644749\pi$
$373$	−3.28407e11			−0.878461			−0.439231	+	0.898374i	$0.644749\pi$
$374$	7.97388e11	−	1.38112e12i	2.10740	−	3.65013i
$375$	−1.62839e11	−	2.82045e11i	−0.425223	−	0.736508i
$376$	−1.73705e11	+	3.00865e11i	−0.448194	+	0.776295i
$377$	9.17051e9	+	1.58838e10i	0.0233807	+	0.0404965i
$378$	1.81780e10	+	3.14853e10i	0.0457966	+	0.0793221i
$379$	−6.90698e10			−0.171954			−0.0859769	−	0.996297i	$-0.527401\pi$
$379$	−6.90698e10			−0.171954			−0.0859769	+	0.996297i	$0.527401\pi$
$380$	−8.51953e10	+	2.72052e11i	−0.209599	+	0.669309i
$381$	−2.68858e11			−0.653674
$382$	−5.28707e11	−	9.15748e11i	−1.27037	−	2.20034i
$383$	3.74149e11	+	6.48045e11i	0.888484	+	1.53890i	0.841667	+	0.539997i	$0.181574\pi$
$383$	3.74149e11	+	6.48045e11i	0.888484	+	1.53890i	0.0468172	+	0.998903i	$0.485092\pi$
$384$	4.81349e11	−	8.33720e11i	1.12972	−	1.95673i
$385$	−1.27240e10	−	2.20387e10i	−0.0295156	−	0.0511225i
$386$	3.68519e11	−	6.38294e11i	0.844923	−	1.46345i
$387$	−2.58417e11			−0.585627
$388$	6.64987e11			1.48960
$389$	−2.56055e11	+	4.43500e11i	−0.566969	+	0.982020i	0.429894	+	0.902879i	$0.358551\pi$
$389$	−2.56055e11	+	4.43500e11i	−0.566969	+	0.982020i	−0.996863	+	0.0791406i	$0.974782\pi$
$390$	−3.49995e10	+	6.06209e10i	−0.0766075	+	0.132688i
$391$	1.02992e12			2.22848
$392$	7.68082e11			1.64293
$393$	1.49016e11	−	2.58103e11i	0.315112	−	0.545791i
$394$	1.07883e11	+	1.86860e11i	0.225539	+	0.390645i
$395$	6.14336e10	−	1.06406e11i	0.126975	−	0.219928i
$396$	−4.48651e11	−	7.77087e11i	−0.916812	−	1.58797i
$397$	7.81968e10	+	1.35441e11i	0.157991	+	0.273648i	0.934144	−	0.356896i	$-0.116165\pi$
$397$	7.81968e10	+	1.35441e11i	0.157991	+	0.273648i	−0.776153	+	0.630544i	$0.782832\pi$
$398$	−1.11450e12			−2.22642
$399$	−6.91464e10	+	1.54708e10i	−0.136581	+	0.0305588i
$400$	−4.01361e11			−0.783909
$401$	2.99502e11	+	5.18752e11i	0.578429	+	1.00187i	0.995660	+	0.0930673i	$0.0296672\pi$
$401$	2.99502e11	+	5.18752e11i	0.578429	+	1.00187i	−0.417231	+	0.908800i	$0.637000\pi$
$402$	6.18588e11	+	1.07143e12i	1.18136	+	2.04618i
$403$	−7.63469e10	+	1.32237e11i	−0.144184	+	0.249735i
$404$	−5.67224e11	−	9.82461e11i	−1.05935	−	1.83484i
$405$	1.19350e11	−	2.06720e11i	0.220432	−	0.381799i
$406$	2.47459e10			0.0451998
$407$	−6.85582e11			−1.23847
$408$	−9.63608e11	+	1.66902e12i	−1.72159	+	2.98188i
$409$	1.99097e11	−	3.44847e11i	0.351812	−	0.609356i	−0.634755	−	0.772713i	$-0.718899\pi$
$409$	1.99097e11	−	3.44847e11i	0.351812	−	0.609356i	0.986567	+	0.163357i	$0.0522324\pi$
$410$	−1.98393e10			−0.0346736
$411$	9.34528e11			1.61549
$412$	7.16890e11	−	1.24169e12i	1.22579	−	2.12313i
$413$	3.50848e9	+	6.07687e9i	0.00593395	+	0.0102779i
$414$	4.37143e11	−	7.57153e11i	0.731344	−	1.26672i
$415$	−3.31579e10	−	5.74312e10i	−0.0548746	−	0.0950455i
$416$	−6.94828e9	−	1.20348e10i	−0.0113752	−	0.0197023i
$417$	−8.33293e11			−1.34954
$418$	−1.57820e12	+	3.53108e11i	−2.52854	+	0.565736i
$419$	−1.77495e11			−0.281335			−0.140667	−	0.990057i	$-0.544925\pi$
$419$	−1.77495e11			−0.281335			−0.140667	+	0.990057i	$0.544925\pi$
$420$	3.12991e10	+	5.42116e10i	0.0490806	+	0.0850101i
$421$	−5.31335e10	−	9.20299e10i	−0.0824325	−	0.142777i	0.821862	−	0.569687i	$-0.192936\pi$
$421$	−5.31335e10	−	9.20299e10i	−0.0824325	−	0.142777i	−0.904294	+	0.426910i	$0.859602\pi$
$422$	−2.04977e11	+	3.55030e11i	−0.314629	+	0.544953i
$423$	1.10021e11	+	1.90562e11i	0.167087	+	0.289403i
$424$	−8.05837e11	+	1.39575e12i	−1.21088	+	2.09730i
$425$	−9.54800e11			−1.41959
$426$	−3.85420e11			−0.567011
$427$	5.28663e10	−	9.15670e10i	0.0769579	−	0.133295i
$428$	−7.48338e11	+	1.29616e12i	−1.07796	+	1.86707i
$429$	−2.63199e11			−0.375169
$430$	4.11469e11			0.580402
$431$	5.49256e10	−	9.51339e10i	0.0766703	−	0.132797i	−0.825141	−	0.564927i	$-0.808904\pi$
$431$	5.49256e10	−	9.51339e10i	0.0766703	−	0.132797i	0.901811	+	0.432130i	$0.142238\pi$
$432$	−1.57256e11	−	2.72376e11i	−0.217235	−	0.376263i
$433$	−1.80304e11	+	3.12296e11i	−0.246496	+	0.426944i	−0.962551	−	0.271100i	$-0.912613\pi$
$433$	−1.80304e11	+	3.12296e11i	−0.246496	+	0.426944i	0.716055	+	0.698044i	$0.245946\pi$
$434$	1.03008e11	+	1.78415e11i	0.139369	+	0.241395i
$435$	−4.04745e10	−	7.01039e10i	−0.0541976	−	0.0938729i
$436$	1.01682e12			1.34758
$437$	−7.07097e11	−	7.68649e11i	−0.927498	−	1.00823i
$438$	2.07393e12			2.69253
$439$	−2.80513e10	−	4.85862e10i	−0.0360464	−	0.0624342i	0.847439	−	0.530892i	$-0.178143\pi$
$439$	−2.80513e10	−	4.85862e10i	−0.0360464	−	0.0624342i	−0.883486	+	0.468458i	$0.844810\pi$
$440$	3.50953e11	+	6.07868e11i	0.446387	+	0.773165i
$441$	2.43243e11	−	4.21310e11i	0.306244	−	0.530430i
$442$	2.20187e11	+	3.81375e11i	0.274405	+	0.475283i
$443$	7.84280e10	−	1.35841e11i	0.0967508	−	0.167577i	−0.813587	−	0.581443i	$-0.802488\pi$
$443$	7.84280e10	−	1.35841e11i	0.0967508	−	0.167577i	0.910338	+	0.413866i	$0.135822\pi$
$444$	1.68642e12			2.05941
$445$	−1.90337e11			−0.230093
$446$	1.11168e12	−	1.92549e12i	1.33037	−	2.30427i
$447$	−8.17330e11	+	1.41566e12i	−0.968308	+	1.67716i
$448$	−1.02966e11			−0.120766
$449$	−1.19354e11			−0.138589			−0.0692944	−	0.997596i	$-0.522075\pi$
$449$	−1.19354e11			−0.138589			−0.0692944	+	0.997596i	$0.522075\pi$
$450$	−4.05259e11	+	7.01928e11i	−0.465882	+	0.806931i
$451$	−3.72983e10	−	6.46026e10i	−0.0424517	−	0.0735284i
$452$	1.24314e12	−	2.15318e12i	1.40087	−	2.42637i
$453$	−8.74025e11	−	1.51386e12i	−0.975173	−	1.68905i
$454$	1.02817e12	+	1.78085e12i	1.13584	+	1.96733i
$455$	7.02712e9			0.00768645
$456$	1.90719e12	−	4.26715e11i	2.06563	−	0.462164i
$457$	−8.31358e10			−0.0891590			−0.0445795	−	0.999006i	$-0.514195\pi$
$457$	−8.31358e10			−0.0891590			−0.0445795	+	0.999006i	$0.514195\pi$
$458$	−9.82557e11	−	1.70184e12i	−1.04343	−	1.80727i
$459$	−3.74097e11	−	6.47955e11i	−0.393394	−	0.681378i
$460$	−4.61348e11	+	7.99079e11i	−0.480417	+	0.832107i
$461$	−6.01063e11	−	1.04107e12i	−0.619821	−	1.07356i	−0.989518	−	0.144409i	$-0.953872\pi$
$461$	−6.01063e11	−	1.04107e12i	−0.619821	−	1.07356i	0.369697	−	0.929152i	$-0.379461\pi$
$462$	−1.77556e11	+	3.07535e11i	−0.181320	+	0.314055i
$463$	1.04186e12			1.05365			0.526825	−	0.849974i	$-0.323382\pi$
$463$	1.04186e12			1.05365			0.526825	+	0.849974i	$0.323382\pi$
$464$	−2.14074e11			−0.214404
$465$	3.36961e11	−	5.83633e11i	0.334227	−	0.578897i
$466$	−9.68318e10	+	1.67718e11i	−0.0951221	+	0.164756i
$467$	2.01394e12			1.95939			0.979694	−	0.200499i	$-0.0642565\pi$
$467$	2.01394e12			1.95939			0.979694	+	0.200499i	$0.0642565\pi$
$468$	2.47777e11			0.238756
$469$	6.20993e10	−	1.07559e11i	0.0592664	−	0.102652i
$470$	−1.75183e11	−	3.03425e11i	−0.165596	−	0.286821i
$471$	−7.59248e11	+	1.31506e12i	−0.710869	+	1.23126i
$472$	−9.67705e10	−	1.67611e11i	−0.0897437	−	0.155441i
$473$	7.73569e11	+	1.33986e12i	0.710598	+	1.23079i
$474$	−1.71453e12			−1.56007
$475$	6.55524e11	+	7.12585e11i	0.590836	+	0.642267i
$476$	3.93814e11			0.351609
$477$	5.10400e11	+	8.84039e11i	0.451417	+	0.781877i
$478$	−1.06595e12	−	1.84627e12i	−0.933920	−	1.61760i
$479$	3.60855e11	−	6.25019e11i	0.313201	−	0.542480i	−0.665853	−	0.746083i	$-0.731932\pi$
$479$	3.60855e11	−	6.25019e11i	0.313201	−	0.542480i	0.979053	+	0.203603i	$0.0652653\pi$
$480$	3.06666e10	+	5.31161e10i	0.0263682	+	0.0456710i
$481$	9.46567e10	−	1.63950e11i	0.0806304	−	0.139656i
$482$	7.18302e11			0.606171
$483$	−2.29334e11			−0.191737
$484$	−1.49951e12	+	2.59722e12i	−1.24207	+	2.15132i
$485$	−1.64735e11	+	2.85330e11i	−0.135191	+	0.234158i
$486$	−2.30646e12			−1.87535
$487$	6.23787e11			0.502523			0.251262	−	0.967919i	$-0.419155\pi$
$487$	6.23787e11			0.502523			0.251262	+	0.967919i	$0.419155\pi$
$488$	−1.45815e12	+	2.52559e12i	−1.16389	+	2.01592i
$489$	−8.44058e11	−	1.46195e12i	−0.667548	−	1.15623i
$490$	−3.87309e11	+	6.70838e11i	−0.303511	+	0.525697i
$491$	1.17448e12	+	2.03426e12i	0.911967	+	1.57957i	0.811283	+	0.584654i	$0.198770\pi$
$491$	1.17448e12	+	2.03426e12i	0.911967	+	1.57957i	0.100684	+	0.994918i	$0.467897\pi$
$492$	9.17478e10	+	1.58912e11i	0.0705916	+	0.122268i
$493$	−5.09262e11			−0.388267
$494$	1.33457e11	−	4.26165e11i	0.100825	−	0.321963i
$495$	4.44572e11			0.332827
$496$	−8.91111e11	−	1.54345e12i	−0.661096	−	1.14505i
$497$	1.93459e10	+	3.35082e10i	0.0142228	+	0.0246347i
$498$	−4.62697e11	+	8.01415e11i	−0.337105	+	0.583883i
$499$	2.73673e11	+	4.74016e11i	0.197597	+	0.342248i	0.947749	−	0.319018i	$-0.103353\pi$
$499$	2.73673e11	+	4.74016e11i	0.197597	+	0.342248i	−0.750152	+	0.661266i	$0.770020\pi$
$500$	9.17789e11	−	1.58966e12i	0.656716	−	1.13747i
$501$	3.11845e11			0.221141
$502$	2.71075e12			1.90512
$503$	−1.30556e11	+	2.26130e11i	−0.0909372	+	0.157508i	−0.907906	−	0.419174i	$-0.862320\pi$
$503$	−1.30556e11	+	2.26130e11i	−0.0909372	+	0.157508i	0.816969	+	0.576682i	$0.195653\pi$
$504$	8.21174e10	−	1.42231e11i	0.0566889	−	0.0981880i
$505$	5.62067e11			0.384571
$506$	−5.23434e12			−3.54964
$507$	−9.10467e11	+	1.57698e12i	−0.611968	+	1.05996i
$508$	−7.57667e11	−	1.31232e12i	−0.504768	−	0.874284i
$509$	−4.89686e11	+	8.48161e11i	−0.323361	+	0.560078i	−0.981179	−	0.193099i	$-0.938146\pi$
$509$	−4.89686e11	+	8.48161e11i	−0.323361	+	0.560078i	0.657818	+	0.753177i	$0.271480\pi$
$510$	−9.71807e11	−	1.68322e12i	−0.636083	−	1.10173i
$511$	−1.04100e11	−	1.80306e11i	−0.0675391	−	0.116981i
$512$	2.48505e12			1.59816
$513$	−2.26743e11	+	7.24053e11i	−0.144546	+	0.461575i
$514$	1.68822e12			1.06683
$515$	3.55186e11	+	6.15200e11i	0.222497	+	0.385376i
$516$	−1.90286e12	−	3.29584e12i	−1.18163	−	2.04665i
$517$	6.58693e11	−	1.14089e12i	0.405486	−	0.702322i
$518$	−1.27712e11	−	2.21204e11i	−0.0779377	−	0.134992i
$519$	3.15752e11	−	5.46899e11i	0.191026	−	0.330867i
$520$	−1.93821e11			−0.116248
$521$	1.88855e12			1.12295			0.561474	−	0.827494i	$-0.310234\pi$
$521$	1.88855e12			1.12295			0.561474	+	0.827494i	$0.310234\pi$
$522$	−2.16153e11	+	3.74388e11i	−0.127422	+	0.220701i
$523$	1.18716e12	−	2.05621e12i	0.693825	−	1.20174i	−0.276750	−	0.960942i	$-0.589257\pi$
$523$	1.18716e12	−	2.05621e12i	0.693825	−	1.20174i	0.970575	−	0.240799i	$-0.0774093\pi$
$524$	1.67976e12			0.973321
$525$	2.12607e11			0.122141
$526$	−2.40759e12	+	4.17007e12i	−1.37135	+	2.37524i
$527$	−2.11987e12	−	3.67172e12i	−1.19718	−	2.07359i
$528$	1.53601e12	−	2.66046e12i	0.860088	−	1.48972i
$529$	−7.89615e11	−	1.36765e12i	−0.438394	−	0.759321i
$530$	−8.12693e11	−	1.40763e12i	−0.447389	−	0.774901i
$531$	−1.22585e11			−0.0669131
$532$	−2.70375e11	−	2.93911e11i	−0.146341	−	0.159079i
$533$	2.05988e10			0.0110553
$534$	1.32801e12	+	2.30018e12i	0.706751	+	1.22413i
$535$	−3.70767e11	−	6.42188e11i	−0.195663	−	0.338899i
$536$	−1.71281e12	+	2.96668e12i	−0.896332	+	1.55249i
$537$	7.66988e11	+	1.32846e12i	0.398020	+	0.689390i
$538$	−2.60450e11	+	4.51112e11i	−0.134031	+	0.232148i
$539$	−2.91259e12			−1.48638
$540$	6.70301e11			0.339233
$541$	1.28276e12	−	2.22181e12i	0.643812	−	1.11512i	−0.340763	−	0.940149i	$-0.610685\pi$
$541$	1.28276e12	−	2.22181e12i	0.643812	−	1.11512i	0.984575	−	0.174966i	$-0.0559814\pi$
$542$	−1.16860e12	+	2.02408e12i	−0.581661	+	1.00747i
$543$	1.07602e12			0.531154
$544$	3.85856e11			0.188899
$545$	−2.51895e11	+	4.36294e11i	−0.122302	+	0.211834i
$546$	−4.90294e10	−	8.49214e10i	−0.0236097	−	0.0408931i
$547$	−1.13001e12	+	1.95723e12i	−0.539682	+	0.934756i	0.459239	+	0.888313i	$0.348122\pi$
$547$	−1.13001e12	+	1.95723e12i	−0.539682	+	0.934756i	−0.998921	+	0.0464435i	$0.985211\pi$
$548$	2.63359e12	+	4.56150e12i	1.24748	+	2.16071i
$549$	9.23562e11	+	1.59966e12i	0.433901	+	0.751538i
$550$	4.85256e12			2.26120
$551$	3.49637e11	+	3.80072e11i	0.161598	+	0.175664i
$552$	6.32546e12			2.89979
$553$	8.60599e10	+	1.49060e11i	0.0391325	+	0.0677795i
$554$	2.25047e12	+	3.89792e12i	1.01503	+	1.75808i
$555$	−4.17772e11	+	7.23603e11i	−0.186905	+	0.323729i
$556$	−2.34830e12	−	4.06737e12i	−1.04212	−	1.80500i
$557$	−7.25488e11	+	1.25658e12i	−0.319361	+	0.553149i	−0.980355	−	0.197242i	$-0.936802\pi$
$557$	−7.25488e11	+	1.25658e12i	−0.319361	+	0.553149i	0.660994	+	0.750391i	$0.270135\pi$
$558$	−3.59906e12			−1.57157
$559$	−4.27220e11			−0.185054
$560$	−4.10098e10	+	7.10311e10i	−0.0176215	+	0.0305213i
$561$	3.65403e12	−	6.32897e12i	1.55754	−	2.69774i
$562$	−2.66897e12			−1.12858
$563$	−5.24786e11			−0.220138			−0.110069	−	0.993924i	$-0.535107\pi$
$563$	−5.24786e11			−0.220138			−0.110069	+	0.993924i	$0.535107\pi$
$564$	−1.62028e12	+	2.80641e12i	−0.674270	+	1.16787i
$565$	6.15919e11	+	1.06680e12i	0.254276	+	0.440419i
$566$	3.07127e12	−	5.31960e12i	1.25790	−	2.17874i
$567$	1.67192e11	+	2.89586e11i	0.0679349	+	0.117667i
$568$	−5.33598e11	−	9.24218e11i	−0.215103	−	0.372569i
$569$	−2.43113e12			−0.972305			−0.486152	−	0.873874i	$-0.661600\pi$
$569$	−2.43113e12			−0.972305			−0.486152	+	0.873874i	$0.661600\pi$
$570$	−5.89018e11	+	1.88090e12i	−0.233718	+	0.746327i
$571$	−3.88683e12			−1.53015			−0.765073	−	0.643943i	$-0.777297\pi$
$571$	−3.88683e12			−1.53015			−0.765073	+	0.643943i	$0.777297\pi$
$572$	−7.41719e11	−	1.28470e12i	−0.289706	−	0.501785i
$573$	−2.42280e12	−	4.19642e12i	−0.938906	−	1.62623i
$574$	1.38961e10	−	2.40687e10i	0.00534303	−	0.00925441i
$575$	1.56691e12	+	2.71397e12i	0.597777	+	1.03538i
$576$	8.99398e11	−	1.55780e12i	0.340448	−	0.589673i
$577$	−1.04864e11			−0.0393853			−0.0196927	−	0.999806i	$-0.506269\pi$
$577$	−1.04864e11			−0.0393853			−0.0196927	+	0.999806i	$0.506269\pi$
$578$	−7.60653e12			−2.83473
$579$	1.68874e12	−	2.92498e12i	0.624467	−	1.08161i
$580$	2.28122e11	−	3.95118e11i	0.0837029	−	0.144978i
$581$	9.28993e10			0.0338236
$582$	4.59755e12			1.66101
$583$	3.05576e12	−	5.29273e12i	1.09550	−	1.89745i
$584$	2.87127e12	+	4.97318e12i	1.02145	+	1.76920i
$585$	−6.13811e10	+	1.06315e11i	−0.0216687	+	0.0375313i
$586$	1.90915e12	+	3.30674e12i	0.668807	+	1.15841i
$587$	5.24055e11	+	9.07691e11i	0.182182	+	0.315549i	0.942623	−	0.333858i	$-0.108351\pi$
$587$	5.24055e11	+	9.07691e11i	0.182182	+	0.315549i	−0.760441	+	0.649407i	$0.775017\pi$
$588$	7.16451e12			2.47166
$589$	−1.28487e12	+	4.10294e12i	−0.439885	+	1.40468i
$590$	1.95188e11			0.0663160
$591$	4.94376e11	+	8.56285e11i	0.166692	+	0.288718i
$592$	1.10482e12	+	1.91361e12i	0.369696	+	0.640332i
$593$	1.44350e11	−	2.50022e11i	0.0479370	−	0.0830294i	−0.841061	−	0.540940i	$-0.818069\pi$
$593$	1.44350e11	−	2.50022e11i	0.0479370	−	0.0830294i	0.888998	+	0.457910i	$0.151402\pi$
$594$	1.90127e12	+	3.29309e12i	0.626619	+	1.08534i
$595$	−9.75585e10	+	1.68976e11i	−0.0319109	+	0.0552713i
$596$	−9.21324e12			−2.99092
$597$	−5.10720e12			−1.64550
$598$	7.22693e11	−	1.25174e12i	0.231099	−	0.400276i
$599$	−1.86663e12	+	3.23309e12i	−0.592430	+	1.02612i	0.401474	+	0.915870i	$0.368498\pi$
$599$	−1.86663e12	+	3.23309e12i	−0.592430	+	1.02612i	−0.993904	+	0.110248i	$0.964835\pi$
$600$	−5.86410e12			−1.84723
$601$	4.76358e12			1.48936			0.744678	−	0.667423i	$-0.232603\pi$
$601$	4.76358e12			1.48936			0.744678	+	0.667423i	$0.232603\pi$
$602$	−2.88205e11	+	4.99186e11i	−0.0894370	+	0.154909i
$603$	1.08486e12	+	1.87903e12i	0.334154	+	0.578771i
$604$	4.92616e12	−	8.53237e12i	1.50606	−	2.60857i
$605$	−7.42938e11	−	1.28681e12i	−0.225452	−	0.390494i
$606$	−3.92164e12	−	6.79248e12i	−1.18125	−	2.04598i
$607$	−1.86681e12			−0.558150			−0.279075	−	0.960269i	$-0.590028\pi$
$607$	−1.86681e12			−0.558150			−0.279075	+	0.960269i	$0.590028\pi$
$608$	−2.64912e11	−	2.87972e11i	−0.0786203	−	0.0854640i
$609$	1.13398e11			0.0334063
$610$	−1.47056e12	−	2.54708e12i	−0.430029	−	0.744832i
$611$	1.81889e11	+	3.15040e11i	0.0527983	+	0.0914494i
$612$	−3.43992e12	+	5.95812e12i	−0.991214	+	1.71683i
$613$	1.62474e12	+	2.81413e12i	0.464742	+	0.804957i	0.999190	−	0.0402446i	$-0.0128137\pi$
$613$	1.62474e12	+	2.81413e12i	0.464742	+	0.804957i	−0.534448	+	0.845201i	$0.679480\pi$
$614$	1.83734e11	−	3.18236e11i	0.0521712	−	0.0903631i
$615$	−9.09137e10			−0.0256266
$616$	−9.83272e11			−0.275144
$617$	3.46772e11	−	6.00627e11i	0.0963299	−	0.166848i	−0.813833	−	0.581099i	$-0.802623\pi$
$617$	3.46772e11	−	6.00627e11i	0.0963299	−	0.166848i	0.910163	+	0.414251i	$0.135956\pi$
$618$	4.95639e12	−	8.58472e12i	1.36684	−	2.36743i
$619$	−2.74106e12			−0.750430			−0.375215	−	0.926938i	$-0.622431\pi$
$619$	−2.74106e12			−0.750430			−0.375215	+	0.926938i	$0.622431\pi$
$620$	3.79834e12			1.03236
$621$	−1.22785e12	+	2.12671e12i	−0.331310	+	0.573846i
$622$	−5.45906e12	−	9.45537e12i	−1.46238	−	2.53292i
$623$	1.33318e11	−	2.30913e11i	0.0354561	−	0.0614118i
$624$	4.24148e11	+	7.34646e11i	0.111992	+	0.193976i
$625$	−1.20981e12	−	2.09545e12i	−0.317144	−	0.549310i
$626$	1.16133e13			3.02253
$627$	−7.23212e12	+	1.61812e12i	−1.86880	+	0.418125i
$628$	−8.55852e12			−2.19574
$629$	2.62827e12	+	4.55229e12i	0.669486	+	1.15958i
$630$	8.28161e10	+	1.43442e11i	0.0209451	+	0.0362780i
$631$	1.37336e12	−	2.37874e12i	0.344868	−	0.597330i	−0.640461	−	0.767990i	$-0.721257\pi$
$631$	1.37336e12	−	2.37874e12i	0.344868	−	0.597330i	0.985330	+	0.170661i	$0.0545902\pi$
$632$	−2.37369e12	−	4.11136e12i	−0.591831	−	1.02508i
$633$	−9.39307e11	+	1.62693e12i	−0.232536	+	0.402765i
$634$	−2.22815e11			−0.0547699
$635$	7.50779e11			0.183244
$636$	−7.51668e12	+	1.30193e13i	−1.82167	+	3.15522i
$637$	4.02135e11	−	6.96518e11i	0.0967708	−	0.167612i
$638$	2.58821e12			0.618452
$639$	−6.75939e11			−0.160381
$640$	−1.34415e12	+	2.32814e12i	−0.316693	+	0.548528i
$641$	3.20550e12	+	5.55209e12i	0.749954	+	1.29896i	0.947844	+	0.318734i	$0.103258\pi$
$641$	3.20550e12	+	5.55209e12i	0.749954	+	1.29896i	−0.197890	+	0.980224i	$0.563409\pi$
$642$	−5.17382e12	+	8.96131e12i	−1.20200	+	2.08192i
$643$	5.68589e11	+	9.84825e11i	0.131174	+	0.227201i	0.924130	−	0.382079i	$-0.124792\pi$
$643$	5.68589e11	+	9.84825e11i	0.131174	+	0.227201i	−0.792955	+	0.609280i	$0.791459\pi$
$644$	−6.46284e11	−	1.11940e12i	−0.148060	−	0.256447i
$645$	1.88556e12			0.428964
$646$	8.39490e12	+	9.12565e12i	1.89657	+	2.06166i
$647$	6.67594e12			1.49776			0.748882	−	0.662703i	$-0.230591\pi$
$647$	6.67594e12			1.49776			0.748882	+	0.662703i	$0.230591\pi$
$648$	−4.61148e12	−	7.98732e12i	−1.02743	−	1.77956i
$649$	3.66957e11	+	6.35588e11i	0.0811921	+	0.140629i
$650$	−6.69982e11	+	1.16044e12i	−0.147215	+	0.254984i
$651$	4.72035e11	+	8.17588e11i	0.103005	+	0.178410i
$652$	4.75727e12	−	8.23983e12i	1.03096	−	1.78568i
$653$	−4.52898e12			−0.974746			−0.487373	−	0.873194i	$-0.662045\pi$
$653$	−4.52898e12			−0.974746			−0.487373	+	0.873194i	$0.662045\pi$
$654$	7.03005e12			1.50265
$655$	−4.16122e11	+	7.20744e11i	−0.0883354	+	0.153001i
$656$	−1.20213e11	+	2.08215e11i	−0.0253446	+	0.0438981i
$657$	3.63720e12			0.761593
$658$	4.90813e11			0.102070
$659$	−9.28952e11	+	1.60899e12i	−0.191871	+	0.332330i	−0.945870	−	0.324545i	$-0.894789\pi$
$659$	−9.28952e11	+	1.60899e12i	−0.191871	+	0.332330i	0.753999	+	0.656875i	$0.228122\pi$
$660$	3.27362e12	+	5.67007e12i	0.671552	+	1.16316i
$661$	−4.51460e12	+	7.81952e12i	−0.919841	+	1.59321i	−0.120186	+	0.992751i	$0.538349\pi$
$661$	−4.51460e12	+	7.81952e12i	−0.919841	+	1.59321i	−0.799655	+	0.600460i	$0.794984\pi$
$662$	−6.86772e12	−	1.18952e13i	−1.38980	−	2.40720i
$663$	1.00901e12	+	1.74765e12i	0.202807	+	0.351273i
$664$	−2.56234e12			−0.511540
$665$	1.93089e11	−	4.32019e10i	0.0382879	−	0.00856654i
$666$	4.46220e12			0.878850
$667$	8.35744e11	+	1.44755e12i	0.163496	+	0.283183i
$668$	8.78808e11	+	1.52214e12i	0.170765	+	0.295774i
$669$	5.09428e12	−	8.82356e12i	0.983254	−	1.70305i
$670$	−1.72739e12	−	2.99192e12i	−0.331172	−	0.573606i
$671$	5.52936e12	−	9.57712e12i	1.05299	−	1.82383i
$672$	−8.59192e10			−0.0162528
$673$	−1.14876e12			−0.215854			−0.107927	−	0.994159i	$-0.534421\pi$
$673$	−1.14876e12			−0.215854			−0.107927	+	0.994159i	$0.534421\pi$
$674$	3.40290e12	−	5.89400e12i	0.635155	−	1.10012i
$675$	1.13830e12	−	1.97159e12i	0.211052	−	0.365552i
$676$	−1.02631e13			−1.89025
$677$	−7.22371e12			−1.32163			−0.660817	−	0.750547i	$-0.729790\pi$
$677$	−7.22371e12			−1.32163			−0.660817	+	0.750547i	$0.729790\pi$
$678$	8.59474e12	−	1.48865e13i	1.56207	−	2.70558i
$679$	−2.30771e11	−	3.99707e11i	−0.0416646	−	0.0721653i
$680$	2.69085e12	−	4.66068e12i	0.482613	−	0.835910i
$681$	4.71161e12	+	8.16076e12i	0.839475	+	1.45401i
$682$	1.07738e13	+	1.86607e13i	1.90694	+	3.30292i
$683$	−1.91334e12			−0.336433			−0.168217	−	0.985750i	$-0.553801\pi$
$683$	−1.91334e12			−0.336433			−0.168217	+	0.985750i	$0.553801\pi$
$684$	6.80836e12	−	1.52330e12i	1.18930	−	0.266093i
$685$	−2.60964e12			−0.452870
$686$	−1.09177e12	−	1.89100e12i	−0.188223	−	0.326012i
$687$	−4.50257e12	−	7.79868e12i	−0.771179	−	1.33572i
$688$	2.49323e12	−	4.31840e12i	0.424243	−	0.734810i
$689$	8.43804e11	+	1.46151e12i	0.142644	+	0.247067i
$690$	−3.18964e12	+	5.52462e12i	−0.535699	+	0.927858i
$691$	−3.46118e12			−0.577528			−0.288764	−	0.957400i	$-0.593244\pi$
$691$	−3.46118e12			−0.577528			−0.288764	+	0.957400i	$0.593244\pi$
$692$	3.55927e12			0.590043
$693$	−3.11392e11	+	5.39346e11i	−0.0512870	+	0.0888318i
$694$	2.19508e12	−	3.80200e12i	0.359198	−	0.622149i
$695$	2.32695e12			0.378316
$696$	−3.12774e12			−0.505229
$697$	−2.85976e11	+	4.95325e11i	−0.0458967	+	0.0794955i
$698$	−5.47775e11	−	9.48775e11i	−0.0873480	−	0.151291i
$699$	−4.43732e11	+	7.68566e11i	−0.0703029	+	0.121768i
$700$	5.99146e11	+	1.03775e12i	0.0943173	+	0.163362i
$701$	1.85327e12	+	3.20996e12i	0.289873	+	0.502074i	0.973779	−	0.227495i	$-0.0730537\pi$
$701$	1.85327e12	+	3.20996e12i	0.289873	+	0.502074i	−0.683906	+	0.729570i	$0.739720\pi$
$702$	−1.05001e12			−0.163184
$703$	1.59301e12	−	5.08693e12i	0.245991	−	0.785519i
$704$	−1.07694e13			−1.65239
$705$	−8.02775e11	−	1.39045e12i	−0.122389	−	0.211984i
$706$	6.26079e12	+	1.08440e13i	0.948436	+	1.64274i
$707$	−3.93689e11	+	6.81889e11i	−0.0592605	+	0.102642i
$708$	−9.02655e11	−	1.56344e12i	−0.135012	−	0.233848i
$709$	1.36686e12	−	2.36748e12i	0.203150	−	0.351866i	−0.746392	−	0.665507i	$-0.768215\pi$
$709$	1.36686e12	−	2.36748e12i	0.203150	−	0.351866i	0.949542	+	0.313641i	$0.101549\pi$
$710$	1.07628e12			0.158950
$711$	−3.00689e12			−0.441271
$712$	−3.67715e12	+	6.36901e12i	−0.536230	+	0.928778i
$713$	−6.95779e12	+	1.20512e13i	−1.00825	+	1.74634i
$714$	2.72273e12			0.392069
$715$	7.34976e11			0.105171
$716$	−4.32289e12	+	7.48746e12i	−0.614703	+	1.06470i
$717$	−4.88470e12	−	8.46055e12i	−0.690243	−	1.19554i
$718$	−8.18660e12	+	1.41796e13i	−1.14959	+	1.99115i
$719$	−2.18306e12	−	3.78117e12i	−0.304639	−	0.527650i	0.672542	−	0.740059i	$-0.265203\pi$
$719$	−2.18306e12	−	3.78117e12i	−0.304639	−	0.527650i	−0.977181	+	0.212409i	$0.931869\pi$
$720$	−7.16433e11	−	1.24090e12i	−0.0993526	−	0.172084i
$721$	−9.95132e11			−0.137143
$722$	1.04708e12	−	1.25305e13i	0.143405	−	1.71614i
$723$	3.29162e12			0.448010
$724$	3.03232e12	+	5.25213e12i	0.410158	+	0.710414i
$725$	−7.74787e11	−	1.34197e12i	−0.104151	−	0.180394i
$726$	−1.03672e13	+	1.79565e13i	−1.38499	+	2.39888i
$727$	−2.04181e12	−	3.53653e12i	−0.271089	−	0.469540i	0.698052	−	0.716047i	$-0.254050\pi$
$727$	−2.04181e12	−	3.53653e12i	−0.271089	−	0.469540i	−0.969141	+	0.246507i	$0.920717\pi$
$728$	1.35758e11	−	2.35140e11i	0.0179133	−	0.0310267i
$729$	−1.14716e12			−0.150436
$730$	−5.79139e12			−0.754797
$731$	5.93115e12	−	1.02731e13i	0.768265	−	1.33067i
$732$	−1.36013e13	+	2.35582e13i	−1.75098	+	3.03279i
$733$	2.99131e12			0.382731			0.191365	−	0.981519i	$-0.438708\pi$
$733$	2.99131e12			0.382731			0.191365	+	0.981519i	$0.438708\pi$
$734$	−1.44928e13			−1.84298
$735$	−1.77484e12	+	3.07412e12i	−0.224319	+	0.388533i
$736$	−6.33224e11	−	1.09678e12i	−0.0795440	−	0.137774i
$737$	6.49505e12	−	1.12498e13i	0.810921	−	1.40456i
$738$	2.42761e11	+	4.20474e11i	0.0301249	+	0.0521778i
$739$	2.72600e12	+	4.72157e12i	0.336222	+	0.582353i	0.983719	−	0.179715i	$-0.0575175\pi$
$739$	2.72600e12	+	4.72157e12i	0.336222	+	0.582353i	−0.647497	+	0.762068i	$0.724184\pi$
$740$	−4.70928e12			−0.577314
$741$	6.11566e11	−	1.95290e12i	0.0745180	−	0.237957i
$742$	2.27694e12			0.275762
$743$	3.70870e12	+	6.42366e12i	0.446449	+	0.773273i	0.998152	−	0.0607679i	$-0.0193549\pi$
$743$	3.70870e12	+	6.42366e12i	0.446449	+	0.773273i	−0.551702	+	0.834041i	$0.686022\pi$
$744$	−1.30196e13	−	2.25506e13i	−1.55783	−	2.69824i
$745$	2.28237e12	−	3.95318e12i	0.271446	−	0.470157i
$746$	−6.39853e12	−	1.10826e13i	−0.756407	−	1.31014i
$747$	−8.11465e11	+	1.40550e12i	−0.0953514	+	0.165153i
$748$	4.11896e13			4.81094
$749$	1.03879e12			0.120603
$750$	6.34536e12	−	1.09905e13i	0.732285	−	1.26836i
$751$	3.34945e12	−	5.80141e12i	0.384232	−	0.665509i	−0.607430	−	0.794373i	$-0.707800\pi$
$751$	3.34945e12	−	5.80141e12i	0.384232	−	0.665509i	0.991662	+	0.128864i	$0.0411330\pi$
$752$	−4.24597e12			−0.484168
$753$	1.24220e13			1.40804
$754$	−3.57348e11	+	6.18945e11i	−0.0402643	+	0.0697399i
$755$	2.44069e12	+	4.22740e12i	0.273370	+	0.473491i
$756$	−4.69499e11	+	8.13196e11i	−0.0522741	+	0.0905414i
$757$	−1.94692e12	−	3.37217e12i	−0.215485	−	0.373231i	0.737937	−	0.674869i	$-0.235800\pi$
$757$	−1.94692e12	−	3.37217e12i	−0.215485	−	0.373231i	−0.953423	+	0.301638i	$0.902467\pi$
$758$	−1.34573e12	−	2.33087e12i	−0.148063	−	0.256452i
$759$	−2.39864e13			−2.62347
$760$	−5.32577e12	+	1.19159e12i	−0.579057	+	0.129558i
$761$	1.13176e13			1.22327			0.611636	−	0.791139i	$-0.290512\pi$
$761$	1.13176e13			1.22327			0.611636	+	0.791139i	$0.290512\pi$
$762$	−5.23831e12	−	9.07303e12i	−0.562852	−	0.974888i
$763$	−3.52869e11	−	6.11187e11i	−0.0376923	−	0.0652850i
$764$	1.36554e13	−	2.36518e13i	1.45005	−	2.51156i
$765$	−1.70433e12	−	2.95198e12i	−0.179919	−	0.311628i
$766$	−1.45795e13	+	2.52524e13i	−1.53008	+	2.65017i
$767$	−2.02660e11			−0.0211441
$768$	2.40369e13			2.49318
$769$	−2.62956e12	+	4.55453e12i	−0.271153	+	0.469651i	−0.969157	−	0.246443i	$-0.920738\pi$
$769$	−2.62956e12	+	4.55453e12i	−0.271153	+	0.469651i	0.698004	+	0.716094i	$0.254072\pi$
$770$	4.95819e11	−	8.58784e11i	0.0508294	−	0.0880391i
$771$	7.73627e12			0.788473
$772$	1.90361e13			1.92886
$773$	−3.34960e11	+	5.80167e11i	−0.0337431	+	0.0584448i	−0.882404	−	0.470493i	$-0.844076\pi$
$773$	−3.34960e11	+	5.80167e11i	−0.0337431	+	0.0584448i	0.848661	+	0.528938i	$0.177409\pi$
$774$	−5.03488e12	−	8.72066e12i	−0.504260	−	0.873404i
$775$	6.45031e12	−	1.11723e13i	0.642277	−	1.11246i
$776$	6.36510e12	+	1.10247e13i	0.630127	+	1.09141i
$777$	−5.85241e11	−	1.01367e12i	−0.0576023	−	0.0997701i
$778$	−1.99554e13			−1.95278
$779$	5.66008e11	−	1.26639e11i	0.0550686	−	0.0123211i
$780$	−1.80792e12			−0.174886
$781$	2.02342e12	+	3.50467e12i	0.194606	+	0.337068i
$782$	2.00665e13	+	3.47562e13i	1.91885	+	3.32355i
$783$	6.07134e11	−	1.05159e12i	0.0577240	−	0.0999809i
$784$	4.69367e12	+	8.12968e12i	0.443701	+	0.768513i
$785$	2.12018e12	−	3.67226e12i	0.199278	−	0.345159i
$786$	1.16134e13			1.08532
$787$	4.03096e11			0.0374561			0.0187280	−	0.999825i	$-0.494038\pi$
$787$	4.03096e11			0.0374561			0.0187280	+	0.999825i	$0.494038\pi$
$788$	−2.78640e12	+	4.82618e12i	−0.257439	+	0.445898i
$789$	−1.10328e13	+	1.91094e13i	−1.01354	+	1.75550i
$790$	4.78778e12			0.437333
$791$	−1.72563e12			−0.156731
$792$	8.58877e12	−	1.48762e13i	0.775653	−	1.34347i
$793$	1.52685e12	+	2.64458e12i	0.137109	+	0.237481i
$794$	−3.04710e12	+	5.27774e12i	−0.272079	+	0.471255i
$795$	−3.72417e12	−	6.45045e12i	−0.330657	−	0.572714i
$796$	−1.43926e13	−	2.49286e13i	−1.27066	−	2.20085i
$797$	−4.64460e12			−0.407743			−0.203871	−	0.978998i	$-0.565352\pi$
$797$	−4.64460e12			−0.407743			−0.203871	+	0.978998i	$0.565352\pi$
$798$	−1.86931e12	−	2.03202e12i	−0.163180	−	0.177385i
$799$	−1.01007e13			−0.876785
$800$	5.87038e11	+	1.01678e12i	0.0506712	+	0.0877652i
$801$	2.32903e12	+	4.03400e12i	0.199907	+	0.346249i
$802$	−1.16707e13	+	2.02143e13i	−0.996123	+	1.72534i
$803$	−1.08879e13	−	1.88585e13i	−0.924114	−	1.60061i
$804$	−1.59768e13	+	2.76726e13i	−1.34846	+	2.33560i
$805$	6.40409e11			0.0537497
$806$	−5.95003e12			−0.496606
$807$	−1.19351e12	+	2.06722e12i	−0.0990594	+	0.171576i
$808$	1.08587e13	−	1.88078e13i	0.896243	−	1.55234i
$809$	5.35072e12			0.439182			0.219591	−	0.975592i	$-0.429528\pi$
$809$	5.35072e12			0.439182			0.219591	+	0.975592i	$0.429528\pi$
$810$	9.30143e12			0.759219
$811$	−7.67759e10	+	1.32980e11i	−0.00623205	+	0.0107942i	−0.869125	−	0.494593i	$-0.835317\pi$
$811$	−7.67759e10	+	1.32980e11i	−0.00623205	+	0.0107942i	0.862893	+	0.505387i	$0.168650\pi$
$812$	3.19567e11	+	5.53506e11i	0.0257964	+	0.0446807i
$813$	−5.35512e12	+	9.27534e12i	−0.429894	+	0.744599i
$814$	−1.33576e13	−	2.31360e13i	−1.06639	−	1.84705i
$815$	2.35701e12	+	4.08246e12i	0.187134	+	0.324125i
$816$	−2.35540e13			−1.85977
$817$	−1.17390e13	+	2.62650e12i	−0.921793	+	0.206242i
$818$	1.55165e13			1.21172
$819$	−8.59863e10	−	1.48933e11i	−0.00667808	−	0.0115668i
$820$	−2.56203e11	−	4.43757e11i	−0.0197889	−	0.0342754i
$821$	1.39774e12	−	2.42096e12i	0.107370	−	0.185971i	−0.807334	−	0.590095i	$-0.799090\pi$
$821$	1.39774e12	−	2.42096e12i	0.107370	−	0.185971i	0.914704	+	0.404124i	$0.132424\pi$
$822$	1.82079e13	+	3.15371e13i	1.39103	+	2.40934i
$823$	1.26805e12	−	2.19633e12i	0.0963469	−	0.166878i	−0.813823	−	0.581113i	$-0.802618\pi$
$823$	1.26805e12	−	2.19633e12i	0.0963469	−	0.166878i	0.910170	+	0.414235i	$0.135951\pi$
$824$	2.74476e13			2.07411
$825$	2.22369e13			1.67121
$826$	−1.36715e11	+	2.36798e11i	−0.0102190	+	0.0176998i
$827$	1.00920e12	−	1.74799e12i	0.0750245	−	0.129946i	−0.826072	−	0.563564i	$-0.809430\pi$
$827$	1.00920e12	−	1.74799e12i	0.0750245	−	0.129946i	0.901097	+	0.433618i	$0.142763\pi$
$828$	2.25809e13			1.66957
$829$	−1.99176e13			−1.46468			−0.732338	−	0.680942i	$-0.761571\pi$
$829$	−1.99176e13			−1.46468			−0.732338	+	0.680942i	$0.761571\pi$
$830$	1.29207e12	−	2.23793e12i	0.0945006	−	0.163680i
$831$	1.03128e13	+	1.78622e13i	0.750189	+	1.29936i
$832$	1.48690e12	−	2.57539e12i	0.107579	−	0.186332i
$833$	1.11658e13	+	1.93397e13i	0.803502	+	1.39171i
$834$	−1.62355e13	−	2.81207e13i	−1.16203	−	2.01270i
$835$	−8.70819e11			−0.0619924
$836$	−2.82789e13	−	3.07406e13i	−2.00233	−	2.17662i
$837$	1.01091e13			0.711947
$838$	−3.45824e12	−	5.98985e12i	−0.242246	−	0.419583i
$839$	8.81493e12	+	1.52679e13i	0.614172	+	1.06378i	0.990529	+	0.137302i	$0.0438432\pi$
$839$	8.81493e12	+	1.52679e13i	0.614172	+	1.06378i	−0.376357	+	0.926475i	$0.622823\pi$
$840$	−5.99175e11	+	1.03780e12i	−0.0415238	+	0.0719213i
$841$	6.84032e12	+	1.18478e13i	0.471514	+	0.816686i
$842$	2.07046e12	−	3.58614e12i	0.141959	−	0.245880i
$843$	−1.22306e13			−0.834110
$844$	−1.05882e13			−0.718260
$845$	2.54245e12	−	4.40366e12i	0.171553	−	0.297138i
$846$	−4.28719e12	+	7.42564e12i	−0.287744	+	0.498387i
$847$	2.08150e12			0.138964
$848$	−1.96976e13			−1.30807
$849$	1.40741e13	−	2.43771e13i	0.929687	−	1.61026i
$850$	−1.86029e13	−	3.22212e13i	−1.22235	−	2.11717i
$851$	8.62644e12	−	1.49414e13i	0.563831	−	0.976583i
$852$	−4.97729e12	−	8.62091e12i	−0.323604	−	0.560499i
$853$	−1.69111e12	−	2.92909e12i	−0.109371	−	0.189436i	0.806145	−	0.591718i	$-0.201550\pi$
$853$	−1.69111e12	−	2.92909e12i	−0.109371	−	0.189436i	−0.915516	+	0.402283i	$0.868217\pi$
$854$	4.12009e12			0.265061
$855$	−1.03300e12	+	3.29867e12i	−0.0661080	+	0.211101i
$856$	−2.86517e13			−1.82397
$857$	−3.66805e11	−	6.35324e11i	−0.0232285	−	0.0402329i	0.854177	−	0.519982i	$-0.174061\pi$
$857$	−3.66805e11	−	6.35324e11i	−0.0232285	−	0.0402329i	−0.877406	+	0.479749i	$0.840728\pi$
$858$	−5.12806e12	−	8.88205e12i	−0.323043	−	0.559526i
$859$	4.68311e12	−	8.11138e12i	0.293471	−	0.508306i	−0.681157	−	0.732137i	$-0.738523\pi$
$859$	4.68311e12	−	8.11138e12i	0.293471	−	0.508306i	0.974628	+	0.223831i	$0.0718563\pi$
$860$	5.31367e12	+	9.20355e12i	0.331247	+	0.573736i
$861$	6.36787e10	−	1.10295e11i	0.00394894	−	0.00683976i
$862$	4.28058e12			0.264071
$863$	−2.30669e13			−1.41560			−0.707800	−	0.706413i	$-0.750312\pi$
$863$	−2.30669e13			−1.41560			−0.707800	+	0.706413i	$0.750312\pi$
$864$	−4.60011e11	+	7.96763e11i	−0.0280838	+	0.0486426i
$865$	−8.81729e11	+	1.52720e12i	−0.0535504	+	0.0927520i
$866$	−1.40519e13			−0.848991
$867$	−3.48569e13			−2.09509
$868$	−2.66047e12	+	4.60808e12i	−0.159082	+	0.275538i
$869$	9.00112e12	+	1.55904e13i	0.535436	+	0.927403i
$870$	1.57717e12	−	2.73175e12i	0.0933347	−	0.161660i
$871$	1.79351e12	+	3.10646e12i	0.105590	+	0.182887i
$872$	9.73279e12	+	1.68577e13i	0.570050	+	0.987356i
$873$	8.06304e12			0.469824
$874$	1.21624e13	−	3.88381e13i	0.705049	−	2.25142i
$875$	−1.27401e12			−0.0734742
$876$	2.67826e13	+	4.63888e13i	1.53668	+	2.66161i
$877$	−7.83740e12	−	1.35748e13i	−0.447377	−	0.774880i	0.550837	−	0.834613i	$-0.314308\pi$
$877$	−7.83740e12	−	1.35748e13i	−0.447377	−	0.774880i	−0.998214	+	0.0597328i	$0.980975\pi$
$878$	1.09308e12	−	1.89326e12i	0.0620762	−	0.107519i
$879$	8.74869e12	+	1.51532e13i	0.494303	+	0.856157i
$880$	−4.28928e12	+	7.42925e12i	−0.241108	+	0.417612i
$881$	−1.87703e12			−0.104974			−0.0524868	−	0.998622i	$-0.516715\pi$
$881$	−1.87703e12			−0.104974			−0.0524868	+	0.998622i	$0.516715\pi$
$882$	1.89570e13			1.05478
$883$	−1.27762e13	+	2.21291e13i	−0.707260	+	1.22501i	0.258609	+	0.965982i	$0.416736\pi$
$883$	−1.27762e13	+	2.21291e13i	−0.707260	+	1.22501i	−0.965870	+	0.259029i	$0.916598\pi$
$884$	−5.68695e12	+	9.85009e12i	−0.313216	+	0.542507i
$885$	8.94449e11			0.0490129
$886$	6.11223e12			0.333233
$887$	−2.85582e12	+	4.94643e12i	−0.154908	+	0.268309i	−0.933026	−	0.359810i	$-0.882842\pi$
$887$	−2.85582e12	+	4.94643e12i	−0.154908	+	0.268309i	0.778117	+	0.628119i	$0.216175\pi$
$888$	1.61420e13	+	2.79588e13i	0.871164	+	1.50890i
$889$	−5.25868e11	+	9.10830e11i	−0.0282370	+	0.0489080i
$890$	−3.70844e12	−	6.42320e12i	−0.198123	−	0.343160i
$891$	1.74869e13	+	3.02882e13i	0.929528	+	1.60999i
$892$	5.74246e13			3.03708
$893$	6.93472e12	+	7.53838e12i	0.364920	+	0.396685i
$894$	−6.36980e13			−3.33508
$895$	−2.14179e12	−	3.70969e12i	−0.111577	−	0.193257i
$896$	−1.88297e12	−	3.26140e12i	−0.0976017	−	0.169051i
$897$	3.31174e12	−	5.73611e12i	0.170801	−	0.295836i
$898$	−2.32544e12	−	4.02778e12i	−0.119333	−	0.206691i
$899$	3.44040e12	−	5.95895e12i	0.175667	−	0.304264i
$900$	−2.09339e13			−1.06355
$901$	−4.68586e13			−2.36880
$902$	1.45341e12	−	2.51738e12i	0.0731068	−	0.126625i
$903$	−1.32070e12	+	2.28752e12i	−0.0661012	+	0.114491i
$904$	4.75962e13			2.37036
$905$	−3.00475e12			−0.148898
$906$	3.40582e13	−	5.89906e13i	1.67936	−	2.90875i
$907$	7.43959e12	+	1.28857e13i	0.365020	+	0.632233i	0.988779	−	0.149384i	$-0.0477289\pi$
$907$	7.43959e12	+	1.28857e13i	0.365020	+	0.632233i	−0.623760	+	0.781616i	$0.714396\pi$
$908$	−2.65555e13	+	4.59955e13i	−1.29649	+	2.24558i
$909$	−6.87765e12	−	1.19124e13i	−0.334120	−	0.578713i
$910$	1.36913e11	+	2.37141e11i	0.00661849	+	0.0114636i
$911$	−4.10897e12			−0.197652			−0.0988258	−	0.995105i	$-0.531509\pi$
$911$	−4.10897e12			−0.197652			−0.0988258	+	0.995105i	$0.531509\pi$
$912$	1.61712e13	+	1.75788e13i	0.774042	+	0.841420i
$913$	9.71646e12			0.462796
$914$	−1.61978e12	−	2.80554e12i	−0.0767712	−	0.132972i
$915$	−6.73883e12	−	1.16720e13i	−0.317826	−	0.550491i
$916$	2.53773e13	−	4.39548e13i	1.19101	−	2.06289i
$917$	−5.82929e11	−	1.00966e12i	−0.0272241	−	0.0471535i
$918$	1.45775e13	−	2.52490e13i	0.677471	−	1.17341i
$919$	−1.25468e12			−0.0580248			−0.0290124	−	0.999579i	$-0.509236\pi$
$919$	−1.25468e12			−0.0580248			−0.0290124	+	0.999579i	$0.509236\pi$
$920$	−1.76637e13			−0.812898
$921$	8.41959e11	−	1.45832e12i	0.0385587	−	0.0667857i
$922$	2.34217e13	−	4.05676e13i	1.06741	−	1.84880i
$923$	−1.11748e12			−0.0506793
$924$	−9.17176e12			−0.413932
$925$	−7.99725e12	+	1.38516e13i	−0.359172	+	0.622105i
$926$	2.02992e13	+	3.51593e13i	0.907256	+	1.57141i
$927$	8.69237e12	−	1.50556e13i	0.386616	−	0.669638i
$928$	3.13109e11	+	5.42320e11i	0.0138589	+	0.0240043i
$929$	−1.77214e13	−	3.06943e13i	−0.780596	−	1.35203i	−0.931595	−	0.363498i	$-0.881582\pi$
$929$	−1.77214e13	−	3.06943e13i	−0.780596	−	1.35203i	0.150999	−	0.988534i	$-0.451751\pi$
$930$	2.62608e13			1.15116
$931$	6.76766e12	−	2.16110e13i	0.295233	−	0.942762i
$932$	−5.00191e12			−0.217152
$933$	−2.50162e13	−	4.33293e13i	−1.08082	−	1.87204i
$934$	3.92387e13	+	6.79634e13i	1.68715	+	2.92223i
$935$	−1.02038e13	+	1.76735e13i	−0.436625	+	0.756257i
$936$	2.37166e12	+	4.10784e12i	0.100998	+	0.174933i
$937$	−7.98947e12	+	1.38382e13i	−0.338602	+	0.586476i	−0.984170	−	0.177227i	$-0.943287\pi$
$937$	−7.98947e12	+	1.38382e13i	−0.338602	+	0.586476i	0.645568	+	0.763703i	$0.276621\pi$
$938$	4.83966e12			0.204128
$939$	5.32180e13			2.23390
$940$	4.52459e12	−	7.83681e12i	0.189018	−	0.327389i
$941$	1.15328e13	−	1.99754e13i	0.479492	−	0.830505i	−0.520231	−	0.854025i	$-0.674154\pi$
$941$	1.15328e13	−	1.99754e13i	0.479492	−	0.830505i	0.999723	+	0.0235208i	$0.00748758\pi$
$942$	−5.91714e13			−2.44840
$943$	1.87725e12			0.0773070
$944$	1.18271e12	−	2.04851e12i	0.0484735	−	0.0839585i
$945$	−2.32615e11	−	4.02902e11i	−0.00948845	−	0.0164345i
$946$	−3.01438e13	+	5.22105e13i	−1.22373	+	2.11957i
$947$	−3.52107e12	−	6.09867e12i	−0.142266	−	0.246411i	0.786084	−	0.618120i	$-0.212105\pi$
$947$	−3.52107e12	−	6.09867e12i	−0.142266	−	0.246411i	−0.928349	+	0.371709i	$0.878772\pi$
$948$	−2.21413e13	−	3.83499e13i	−0.890361	−	1.54215i
$949$	6.01309e12			0.240658
$950$	−1.12753e13	+	3.60053e13i	−0.449131	+	1.43420i
$951$	−1.02105e12			−0.0404794
$952$	3.76950e12	+	6.52897e12i	0.148736	+	0.257619i
$953$	−1.47315e13	−	2.55157e13i	−0.578533	−	1.00205i	−0.995648	−	0.0931953i	$-0.970292\pi$
$953$	−1.47315e13	−	2.55157e13i	−0.578533	−	1.00205i	0.417114	−	0.908854i	$-0.363041\pi$
$954$	−1.98888e13	+	3.44484e13i	−0.777394	+	1.34649i
$955$	6.76561e12	+	1.17184e13i	0.263203	+	0.455882i
$956$	2.75311e13	−	4.76852e13i	1.06601	−	1.84639i
$957$	1.18605e13			0.457087
$958$	2.81230e13			1.07874
$959$	1.82787e12	−	3.16597e12i	0.0697850	−	0.120871i
$960$	−6.56252e12	+	1.13666e13i	−0.249373	+	0.431927i
$961$	3.08448e13			1.16661
$962$	7.37700e12			0.277710
$963$	−9.07368e12	+	1.57161e13i	−0.339989	+	0.588879i
$964$	9.27609e12	+	1.60667e13i	0.345954	+	0.599210i
$965$	−4.71576e12	+	8.16793e12i	−0.175057	+	0.303207i
$966$	−4.46824e12	−	7.73922e12i	−0.165097	−	0.285957i
$967$	−6.00434e12	−	1.03998e13i	−0.220824	−	0.382478i	0.734235	−	0.678896i	$-0.237541\pi$
$967$	−6.00434e12	−	1.03998e13i	−0.220824	−	0.382478i	−0.955058	+	0.296418i	$0.904208\pi$
$968$	−5.74118e13			−2.10166
$969$	3.84696e13	+	4.18183e13i	1.40172	+	1.52374i
$970$	−1.28385e13			−0.465631
$971$	−1.05661e13	−	1.83010e13i	−0.381441	−	0.660674i	0.609828	−	0.792534i	$-0.291239\pi$
$971$	−1.05661e13	−	1.83010e13i	−0.381441	−	0.660674i	−0.991268	+	0.131859i	$0.957905\pi$
$972$	−2.97855e13	−	5.15900e13i	−1.07030	−	1.85382i
$973$	−1.62986e12	+	2.82301e12i	−0.0582967	+	0.100973i
$974$	1.21536e13	+	2.10506e13i	0.432702	+	0.749462i
$975$	−3.07019e12	+	5.31773e12i	−0.108804	+	0.188454i
$976$	−3.56425e13			−1.25731
$977$	−3.03696e13			−1.06638			−0.533192	−	0.845994i	$-0.679008\pi$
$977$	−3.03696e13			−1.06638			−0.533192	+	0.845994i	$0.679008\pi$
$978$	3.28905e13	−	5.69680e13i	1.14960	−	1.99116i
$979$	1.39439e13	−	2.41515e13i	0.485133	−	0.840276i
$980$	−2.00067e13			−0.692879
$981$	1.23291e13			0.425031
$982$	−4.57661e13	+	7.92692e13i	−1.57052	+	2.72021i
$983$	1.63388e12	+	2.82996e12i	0.0558121	+	0.0966693i	0.892582	−	0.450886i	$-0.148892\pi$
$983$	1.63388e12	+	2.82996e12i	0.0558121	+	0.0966693i	−0.836769	+	0.547555i	$0.815559\pi$
$984$	−1.75638e12	+	3.04214e12i	−0.0597228	+	0.103443i
$985$	−1.38053e12	−	2.39115e12i	−0.0467287	−	0.0809364i
$986$	−9.92223e12	−	1.71858e13i	−0.334321	−	0.579061i
$987$	2.24915e12			0.0754382
$988$	1.12557e13	−	2.51836e12i	0.375809	−	0.0840835i
$989$	−3.89342e13			−1.29404
$990$	8.66185e12	+	1.50028e13i	0.286584	+	0.496378i
$991$	2.10866e12	+	3.65230e12i	0.0694503	+	0.120291i	0.898659	−	0.438647i	$-0.144542\pi$
$991$	2.10866e12	+	3.65230e12i	0.0694503	+	0.120291i	−0.829209	+	0.558938i	$0.811209\pi$
$992$	−2.60671e12	+	4.51496e12i	−0.0854654	+	0.148030i
$993$	−3.14714e13	−	5.45100e13i	−1.02717	−	1.77912i
$994$	−7.53856e11	+	1.30572e12i	−0.0244934	+	0.0424239i
$995$	1.42617e13			0.461283
$996$	−2.39009e13			−0.769570
$997$	−1.99132e13	+	3.44907e13i	−0.638282	+	1.10554i	0.347527	+	0.937670i	$0.387021\pi$
$997$	−1.99132e13	+	3.44907e13i	−0.638282	+	1.10554i	−0.985810	+	0.167867i	$0.946312\pi$
$998$	−1.06643e13	+	1.84710e13i	−0.340285	+	0.589392i
$999$	−1.25335e13			−0.398133

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.10.c.a.7.13	✓	28
19.7	even	3		361.10.a.e.1.2		14
19.11	even	3	inner	19.10.c.a.11.13	yes	28
19.12	odd	6		361.10.a.f.1.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.10.c.a.7.13	✓	28	1.1	even	1	trivial
19.10.c.a.11.13	yes	28	19.11	even	3	inner
361.10.a.e.1.2		14	19.7	even	3
361.10.a.f.1.13		14	19.12	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	19.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(19.4836 + 33.7465i) q^{2} +(89.2835 + 154.644i) q^{3} +(-503.218 + 871.599i) q^{4} +(-249.322 - 431.838i) q^{5} +(-3479.12 + 6026.01i) q^{6} +698.529 q^{7} -19266.8 q^{8} +(-6101.58 + 10568.2i) q^{9} +(9715.34 - 16827.5i) q^{10} +73060.2 q^{11} -179716. q^{12} +(-10087.3 + 17471.6i) q^{13} +(13609.8 + 23572.9i) q^{14} +(44520.6 - 77111.9i) q^{15} +(-117737. - 203927. i) q^{16} +(-280086. - 485122. i) q^{17} -475522. q^{18} +(-169762. + 542097. i) q^{19} +501852. q^{20} +(62367.1 + 108023. i) q^{21} +(1.42347e6 + 2.46553e6i) q^{22} +(-919291. + 1.59226e6i) q^{23} +(-1.72020e6 - 2.97948e6i) q^{24} +(852240. - 1.47612e6i) q^{25} -786142. q^{26} +1.33565e6 q^{27} +(-351513. + 608838. i) q^{28} +(454559. - 787320. i) q^{29} +3.46968e6 q^{30} +7.56865e6 q^{31} +(-344409. + 596534. i) q^{32} +(6.52306e6 + 1.12983e7i) q^{33} +(1.09141e7 - 1.89038e7i) q^{34} +(-174158. - 301651. i) q^{35} +(-6.14085e6 - 1.06363e7i) q^{36} -9.38380e6 q^{37} +(-2.16014e7 + 4.83311e6i) q^{38} -3.60250e6 q^{39} +(4.80362e6 + 8.32011e6i) q^{40} +(-510515. - 884238. i) q^{41} +(-2.43027e6 + 4.20935e6i) q^{42} +(1.05881e7 + 1.83391e7i) q^{43} +(-3.67652e7 + 6.36792e7i) q^{44} +6.08502e6 q^{45} -7.16442e7 q^{46} +(9.01577e6 - 1.56158e7i) q^{47} +(2.10240e7 - 3.64146e7i) q^{48} -3.98657e7 q^{49} +6.64187e7 q^{50} +(5.00140e7 - 8.66268e7i) q^{51} +(-1.01522e7 - 1.75841e7i) q^{52} +(4.18253e7 - 7.24435e7i) q^{53} +(2.60233e7 + 4.50737e7i) q^{54} +(-1.82155e7 - 3.15501e7i) q^{55} -1.34584e7 q^{56} +(-9.89886e7 + 2.21477e7i) q^{57} +3.54257e7 q^{58} +(5.02267e6 + 8.69952e6i) q^{59} +(4.48071e7 + 7.76082e7i) q^{60} +(7.56822e7 - 1.31085e8i) q^{61} +(1.47464e8 + 2.55415e8i) q^{62} +(-4.26213e6 + 7.38222e6i) q^{63} -1.47404e8 q^{64} +1.00599e7 q^{65} +(-2.54185e8 + 4.40261e8i) q^{66} +(8.89000e7 - 1.53979e8i) q^{67} +5.63776e8 q^{68} -3.28310e8 q^{69} +(6.78645e6 - 1.17545e7i) q^{70} +(2.76953e7 + 4.79696e7i) q^{71} +(1.17558e8 - 2.03616e8i) q^{72} +(-1.49027e8 - 2.58122e8i) q^{73} +(-1.82830e8 - 3.16671e8i) q^{74} +3.04364e8 q^{75} +(-3.87064e8 - 4.20757e8i) q^{76} +5.10347e7 q^{77} +(-7.01895e7 - 1.21572e8i) q^{78} +(1.23202e8 + 2.13391e8i) q^{79} +(-5.87088e7 + 1.01687e8i) q^{80} +(2.39349e8 + 4.14565e8i) q^{81} +(1.98933e7 - 3.44562e7i) q^{82} +1.32993e8 q^{83} -1.25537e8 q^{84} +(-1.39663e8 + 2.41903e8i) q^{85} +(-4.12588e8 + 7.14624e8i) q^{86} +1.62339e8 q^{87} -1.40763e9 q^{88} +(1.90855e8 - 3.30570e8i) q^{89} +(1.18558e8 + 2.05348e8i) q^{90} +(-7.04624e6 + 1.22044e7i) q^{91} +(-9.25207e8 - 1.60251e9i) q^{92} +(6.75755e8 + 1.17044e9i) q^{93} +7.02637e8 q^{94} +(2.76423e8 - 6.18469e7i) q^{95} -1.23000e8 q^{96} +(-3.30367e8 - 5.72213e8i) q^{97} +(-7.76725e8 - 1.34533e9i) q^{98} +(-4.45782e8 + 7.72117e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 15 q^{2} - 74 q^{3} - 2987 q^{4} - 285 q^{5} - 535 q^{6} - 2676 q^{7} - 24270 q^{8} - 57928 q^{9} + 41180 q^{10} - 114810 q^{11} + 235458 q^{12} + 98671 q^{13} - 148290 q^{14} + 428251 q^{15} - 279203 q^{16}+ \cdots - 736622698 q^{99}+O(q^{100}) \) 28 * q + 15 * q^2 - 74 * q^3 - 2987 * q^4 - 285 * q^5 - 535 * q^6 - 2676 * q^7 - 24270 * q^8 - 57928 * q^9 + 41180 * q^10 - 114810 * q^11 + 235458 * q^12 + 98671 * q^13 - 148290 * q^14 + 428251 * q^15 - 279203 * q^16 + 466251 * q^17 + 734964 * q^18 + 387157 * q^19 - 3343620 * q^20 + 689090 * q^21 - 1689395 * q^22 - 3087747 * q^23 - 234183 * q^24 - 3260823 * q^25 + 9033144 * q^26 + 4216540 * q^27 - 703814 * q^28 + 7831383 * q^29 - 11859224 * q^30 - 9265632 * q^31 + 11470815 * q^32 + 22791973 * q^33 + 13457096 * q^34 - 13222428 * q^35 + 7355018 * q^36 + 27205020 * q^37 - 67677738 * q^38 - 20775702 * q^39 - 16500258 * q^40 + 20419440 * q^41 - 10220798 * q^42 + 27415427 * q^43 + 41775405 * q^44 - 85982588 * q^45 - 137234708 * q^46 - 90906681 * q^47 + 33057375 * q^48 + 229824892 * q^49 + 44406714 * q^50 + 134429123 * q^51 + 66195006 * q^52 + 47827863 * q^53 - 130507669 * q^54 - 157712310 * q^55 + 382459116 * q^56 - 162912873 * q^57 - 344026048 * q^58 + 255540 * q^59 + 287916794 * q^60 + 304035459 * q^61 + 693626280 * q^62 - 122148024 * q^63 - 908491514 * q^64 - 1424960190 * q^65 - 611099417 * q^66 + 165758480 * q^67 + 357518508 * q^68 + 271237278 * q^69 + 1167527028 * q^70 + 685508589 * q^71 + 142349670 * q^72 - 602867050 * q^73 - 82104492 * q^74 + 1900274774 * q^75 - 1298297525 * q^76 - 491994756 * q^77 - 911449840 * q^78 + 78162339 * q^79 + 227607150 * q^80 + 1230916118 * q^81 + 360208019 * q^82 + 413839926 * q^83 - 467304924 * q^84 - 1440537237 * q^85 + 936824310 * q^86 - 678876318 * q^87 - 1646777694 * q^88 + 1256827551 * q^89 + 1879090924 * q^90 + 537759588 * q^91 - 677003592 * q^92 - 492493440 * q^93 - 848375184 * q^94 - 2034458607 * q^95 - 6041588930 * q^96 + 2109813492 * q^97 + 2689941591 * q^98 - 736622698 * q^99

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