LMFDB - Embedded newform 49.7.f.a.6.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,7,Mod(6,49)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("49.6"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([9])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	49.f (of order $14$, degree $6$, 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:	$11.2726500974$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$27$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			6.12
Character	$\chi$	$=$	49.6
Dual form			49.7.f.a.41.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.24733 + 1.56411i) q^{2} +(19.3946 - 40.2732i) q^{3} +(13.3507 + 58.4935i) q^{4} +(-90.5621 + 188.054i) q^{5} +(38.8002 + 80.5694i) q^{6} +(-164.585 - 300.933i) q^{7} +(-223.500 - 107.632i) q^{8} +(-791.260 - 992.209i) q^{9} +(-181.176 - 376.215i) q^{10} +(-1500.29 + 1881.31i) q^{11} +(2614.65 + 596.777i) q^{12} +(-1321.39 - 1053.78i) q^{13} +(675.985 + 117.935i) q^{14} +(5817.14 + 7294.46i) q^{15} +(-3012.46 + 1450.73i) q^{16} +(914.015 + 208.618i) q^{17} +2538.89 q^{18} +276.749i q^{19} +(-12209.0 - 2786.63i) q^{20} +(-15311.6 + 791.915i) q^{21} +(-1071.20 - 4693.23i) q^{22} +(4862.80 + 21305.3i) q^{23} +(-8669.36 + 6913.59i) q^{24} +(-17420.8 - 21845.0i) q^{25} +(3296.44 - 752.390i) q^{26} +(-23536.4 + 5372.03i) q^{27} +(15405.3 - 13644.8i) q^{28} +(699.174 - 3063.28i) q^{29} -18665.2 q^{30} -12859.3i q^{31} +(5021.25 - 21999.5i) q^{32} +(46668.8 + 96908.7i) q^{33} +(-1466.38 + 1169.40i) q^{34} +(71496.9 - 3697.81i) q^{35} +(47473.8 - 59530.3i) q^{36} +(-8502.95 + 37253.9i) q^{37} +(-432.865 - 345.198i) q^{38} +(-68066.8 + 32779.2i) q^{39} +(40481.2 - 32282.7i) q^{40} +(18407.5 - 38223.5i) q^{41} +(17860.1 - 24936.8i) q^{42} +(-20061.0 + 9660.87i) q^{43} +(-130074. - 62640.4i) q^{44} +(258247. - 58943.2i) q^{45} +(-39389.3 - 18968.9i) q^{46} +(-5668.28 - 4520.30i) q^{47} +149458. i q^{48} +(-63472.4 + 99058.3i) q^{49} +55897.6 q^{50} +(26128.7 - 32764.3i) q^{51} +(43997.4 - 91361.5i) q^{52} +(-48505.6 - 212517. i) q^{53} +(20955.3 - 43514.2i) q^{54} +(-217918. - 452511. i) q^{55} +(4394.80 + 84973.1i) q^{56} +(11145.6 + 5367.42i) q^{57} +(3919.20 + 4914.52i) q^{58} +(39804.9 + 82655.7i) q^{59} +(-349015. + 437651. i) q^{60} +(339281. + 77438.7i) q^{61} +(20113.4 + 16039.9i) q^{62} +(-168359. + 401419. i) q^{63} +(-105274. - 132009. i) q^{64} +(317835. - 153061. i) q^{65} +(-209787. - 47882.6i) q^{66} -29303.3 q^{67} +56249.1i q^{68} +(952346. + 217367. i) q^{69} +(-83396.8 + 116441. i) q^{70} +(-83070.3 - 363955. i) q^{71} +(70053.2 + 306923. i) q^{72} +(-341860. + 272624. i) q^{73} +(-47663.0 - 59767.5i) q^{74} +(-1.21764e6 + 277918. i) q^{75} +(-16188.0 + 3694.80i) q^{76} +(813073. + 141852. i) q^{77} +(33631.8 - 147350. i) q^{78} -193636. q^{79} -697887. i q^{80} +(-34261.4 + 150109. i) q^{81} +(36825.4 + 76468.8i) q^{82} +(-312780. + 249433. i) q^{83} +(-250743. - 885056. i) q^{84} +(-122007. + 152991. i) q^{85} +(9912.14 - 43427.9i) q^{86} +(-109808. - 87569.1i) q^{87} +(537803. - 258992. i) q^{88} +(-414358. + 330439. i) q^{89} +(-229927. + 477448. i) q^{90} +(-99634.0 + 571086. i) q^{91} +(-1.18130e6 + 568884. i) q^{92} +(-517887. - 249401. i) q^{93} +(14140.5 - 3227.47i) q^{94} +(-52043.7 - 25062.9i) q^{95} +(-788607. - 628893. i) q^{96} +975693. i q^{97} +(-75766.6 - 222836. i) q^{98} +3.05377e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q - 5 q^{2} - 7 q^{3} - 837 q^{4} - 7 q^{5} - 791 q^{6} + 70 q^{7} - 843 q^{8} + 2990 q^{9} - 7 q^{10} + 1171 q^{11} - 13482 q^{12} - 7 q^{13} + 22533 q^{14} + 6181 q^{15} - 17901 q^{16} - 3143 q^{17}+ \cdots + 4449580 q^{99}+O(q^{100}) $ 162 * q - 5 * q^2 - 7 * q^3 - 837 * q^4 - 7 * q^5 - 791 * q^6 + 70 * q^7 - 843 * q^8 + 2990 * q^9 - 7 * q^10 + 1171 * q^11 - 13482 * q^12 - 7 * q^13 + 22533 * q^14 + 6181 * q^15 - 17901 * q^16 - 3143 * q^17 - 22692 * q^18 + 50169 * q^20 + 28553 * q^21 - 33057 * q^22 - 49677 * q^23 - 119077 * q^24 + 30038 * q^25 + 59577 * q^26 + 11753 * q^27 + 42994 * q^28 + 80383 * q^29 + 27328 * q^30 + 253875 * q^32 - 7 * q^33 + 54677 * q^34 - 74067 * q^35 - 193099 * q^36 + 118463 * q^37 - 121079 * q^38 - 304143 * q^39 - 702079 * q^40 - 58023 * q^41 - 1137479 * q^42 + 93963 * q^43 + 352505 * q^44 + 1333577 * q^45 + 782877 * q^46 + 408261 * q^47 - 149338 * q^49 + 1164004 * q^50 - 911743 * q^51 + 721273 * q^52 - 992325 * q^53 - 576646 * q^54 - 1502935 * q^55 + 1368514 * q^56 + 116032 * q^57 + 2610717 * q^58 + 24493 * q^59 - 1027131 * q^60 + 563101 * q^61 - 262199 * q^62 - 966154 * q^63 - 2839067 * q^64 - 140287 * q^65 - 1523319 * q^66 - 1313660 * q^67 + 2216753 * q^69 + 1806959 * q^70 + 1031011 * q^71 - 3123354 * q^72 - 846727 * q^73 + 1270357 * q^74 + 873173 * q^75 + 5463990 * q^76 + 1565235 * q^77 + 1006005 * q^78 + 82420 * q^79 + 2259538 * q^81 - 7672672 * q^82 - 3860031 * q^83 - 9104942 * q^84 + 1596833 * q^85 + 224039 * q^86 + 2590525 * q^87 + 4179421 * q^88 + 5417433 * q^89 + 6759578 * q^90 - 6163507 * q^91 - 7060306 * q^92 + 1903160 * q^93 + 4029998 * q^94 + 2115400 * q^95 + 957950 * q^96 - 1546783 * q^98 + 4449580 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{9}{14}\right)$

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 $

$2$	−1.24733	+	1.56411i	−0.155917	+	0.195513i	−0.853654	−	0.520840i	$-0.825619\pi$
$2$	−1.24733	+	1.56411i	−0.155917	+	0.195513i	0.697737	+	0.716354i	$0.254190\pi$
$3$	19.3946	−	40.2732i	0.718317	−	1.49160i	−0.146337	−	0.989235i	$-0.546748\pi$
$3$	19.3946	−	40.2732i	0.718317	−	1.49160i	0.864655	−	0.502367i	$-0.167537\pi$
$4$	13.3507	+	58.4935i	0.208605	+	0.913960i
$5$	−90.5621	+	188.054i	−0.724497	+	1.50443i	0.133650	+	0.991029i	$0.457330\pi$
$5$	−90.5621	+	188.054i	−0.724497	+	1.50443i	−0.858147	+	0.513404i	$0.828384\pi$
$6$	38.8002	+	80.5694i	0.179630	+	0.373006i
$7$	−164.585	−	300.933i	−0.479840	−	0.877356i
$7$	−164.585	−	300.933i	−0.479840	−	0.877356i
$8$	−223.500	−	107.632i	−0.436523	−	0.210218i
$9$	−791.260	−	992.209i	−1.08541	−	1.36105i
$10$	−181.176	−	376.215i	−0.181176	−	0.376215i
$11$	−1500.29	+	1881.31i	−1.12719	+	1.41345i	−0.229233	+	0.973372i	$0.573622\pi$
$11$	−1500.29	+	1881.31i	−1.12719	+	1.41345i	−0.897958	+	0.440081i	$0.854950\pi$
$12$	2614.65	+	596.777i	1.51311	+	0.345357i
$13$	−1321.39	−	1053.78i	−0.601453	−	0.479643i	0.274795	−	0.961503i	$-0.411390\pi$
$13$	−1321.39	−	1053.78i	−0.601453	−	0.479643i	−0.876248	+	0.481860i	$0.839961\pi$
$14$	675.985	+	117.935i	0.246350	+	0.0429792i
$15$	5817.14	+	7294.46i	1.72360	+	2.16132i
$16$	−3012.46	+	1450.73i	−0.735464	+	0.354181i
$17$	914.015	+	208.618i	0.186040	+	0.0424625i	0.314526	−	0.949249i	$-0.398154\pi$
$17$	914.015	+	208.618i	0.186040	+	0.0424625i	−0.128486	+	0.991711i	$0.541012\pi$
$18$	2538.89			0.435338
$19$			276.749i			0.0403482i	0.999796	+	0.0201741i	$0.00642206\pi$
$19$			276.749i			0.0403482i	−0.999796	+	0.0201741i	$0.993578\pi$
$20$	−12209.0	−	2786.63i	−1.52613	−	0.348328i
$21$	−15311.6	+	791.915i	−1.65334	+	0.0855108i
$22$	−1071.20	−	4693.23i	−0.100601	−	0.440762i
$23$	4862.80	+	21305.3i	0.399671	+	1.75107i	0.628695	+	0.777652i	$0.283590\pi$
$23$	4862.80	+	21305.3i	0.399671	+	1.75107i	−0.229024	+	0.973421i	$0.573553\pi$
$24$	−8669.36	+	6913.59i	−0.627124	+	0.500115i
$25$	−17420.8	−	21845.0i	−1.11493	−	1.39808i
$26$	3296.44	−	752.390i	0.187553	−	0.0428078i
$27$	−23536.4	+	5372.03i	−1.19577	+	0.272927i
$28$	15405.3	−	13644.8i	0.701771	−	0.621576i
$29$	699.174	−	3063.28i	0.0286676	−	0.125601i	−0.958569	−	0.284859i	$-0.908053\pi$
$29$	699.174	−	3063.28i	0.0286676	−	0.125601i	0.987237	+	0.159258i	$0.0509103\pi$
$30$	−18665.2			−0.691305
$31$		−	12859.3i		−	0.431651i	−0.976432	−	0.215826i	$-0.930756\pi$
$31$		−	12859.3i		−	0.431651i	0.976432	−	0.215826i	$-0.0692443\pi$
$32$	5021.25	−	21999.5i	0.153236	−	0.671372i
$33$	46668.8	+	96908.7i	1.29863	+	2.69663i
$34$	−1466.38	+	1169.40i	−0.0373088	+	0.0297528i
$35$	71496.9	−	3697.81i	1.66757	−	0.0862464i
$36$	47473.8	−	59530.3i	1.01753	−	1.27594i
$37$	−8502.95	+	37253.9i	−0.167867	+	0.735472i	0.818981	+	0.573820i	$0.194539\pi$
$37$	−8502.95	+	37253.9i	−0.167867	+	0.735472i	−0.986848	+	0.161652i	$0.948318\pi$
$38$	−432.865	−	345.198i	−0.00788863	−	0.00629097i
$39$	−68066.8	+	32779.2i	−1.14747	+	0.552592i
$40$	40481.2	−	32282.7i	0.632519	−	0.504417i
$41$	18407.5	−	38223.5i	0.267081	−	0.554599i	−0.723693	−	0.690122i	$-0.757557\pi$
$41$	18407.5	−	38223.5i	0.267081	−	0.554599i	0.990774	+	0.135522i	$0.0432713\pi$
$42$	17860.1	−	24936.8i	0.241065	−	0.336583i
$43$	−20061.0	+	9660.87i	−0.252318	+	0.121510i	−0.555768	−	0.831338i	$-0.687576\pi$
$43$	−20061.0	+	9660.87i	−0.252318	+	0.121510i	0.303450	+	0.952847i	$0.401861\pi$
$44$	−130074.	−	62640.4i	−1.52698	−	0.735354i
$45$	258247.	−	58943.2i	2.83399	−	0.646839i
$46$	−39389.3	−	18968.9i	−0.404674	−	0.194881i
$47$	−5668.28	−	4520.30i	−0.0545956	−	0.0435385i	0.595812	−	0.803124i	$-0.296830\pi$
$47$	−5668.28	−	4520.30i	−0.0545956	−	0.0435385i	−0.650407	+	0.759586i	$0.725402\pi$
$48$			149458.i			1.35143i
$49$	−63472.4	+	99058.3i	−0.539506	+	0.841982i
$50$	55897.6			0.447181
$51$	26128.7	−	32764.3i	0.196973	−	0.246996i
$52$	43997.4	−	91361.5i	0.312908	−	0.649760i
$53$	−48505.6	−	212517.i	−0.325810	−	1.42747i	−0.827036	−	0.562149i	$-0.809975\pi$
$53$	−48505.6	−	212517.i	−0.325810	−	1.42747i	0.501226	−	0.865316i	$-0.332882\pi$
$54$	20955.3	−	43514.2i	0.133080	−	0.276344i
$55$	−217918.	−	452511.i	−1.30980	−	2.71983i
$56$	4394.80	+	84973.1i	0.0250251	+	0.483857i
$57$	11145.6	+	5367.42i	0.0601835	+	0.0289828i
$58$	3919.20	+	4914.52i	0.0200869	+	0.0251882i
$59$	39804.9	+	82655.7i	0.193812	+	0.402454i	0.975116	−	0.221696i	$-0.0711594\pi$
$59$	39804.9	+	82655.7i	0.193812	+	0.402454i	−0.781304	+	0.624151i	$0.785445\pi$
$60$	−349015.	+	437651.i	−1.61581	+	2.02616i
$61$	339281.	+	77438.7i	1.49476	+	0.341168i	0.890264	−	0.455444i	$-0.150519\pi$
$61$	339281.	+	77438.7i	1.49476	+	0.341168i	0.604491	+	0.796612i	$0.293377\pi$
$62$	20113.4	+	16039.9i	0.0843937	+	0.0673017i
$63$	−168359.	+	401419.i	−0.673308	+	1.60538i
$64$	−105274.	−	132009.i	−0.401587	−	0.503574i
$65$	317835.	−	153061.i	1.15734	−	0.557346i
$66$	−209787.	−	47882.6i	−0.729705	−	0.166550i
$67$	−29303.3			−0.0974297			−0.0487149	−	0.998813i	$-0.515513\pi$
$67$	−29303.3			−0.0974297			−0.0487149	+	0.998813i	$0.515513\pi$
$68$			56249.1i			0.178891i
$69$	952346.	+	217367.i	2.89899	+	0.661676i
$70$	−83396.8	+	116441.i	−0.243139	+	0.339479i
$71$	−83070.3	−	363955.i	−0.232098	−	1.01689i	−0.947896	−	0.318579i	$-0.896794\pi$
$71$	−83070.3	−	363955.i	−0.232098	−	1.01689i	0.715798	−	0.698307i	$-0.246063\pi$
$72$	70053.2	+	306923.i	0.187685	+	0.822304i
$73$	−341860.	+	272624.i	−0.878779	+	0.700803i	−0.955101	−	0.296280i	$-0.904254\pi$
$73$	−341860.	+	272624.i	−0.878779	+	0.700803i	0.0763216	+	0.997083i	$0.475682\pi$
$74$	−47663.0	−	59767.5i	−0.117621	−	0.147493i
$75$	−1.21764e6	+	277918.i	−2.88626	+	0.658770i
$76$	−16188.0	+	3694.80i	−0.0368767	+	0.00841686i
$77$	813073.	+	141852.i	1.78097	+	0.310716i
$78$	33631.8	−	147350.i	0.0708706	−	0.310504i
$79$	−193636.			−0.392740			−0.196370	−	0.980530i	$-0.562915\pi$
$79$	−193636.			−0.392740			−0.196370	+	0.980530i	$0.562915\pi$
$80$		−	697887.i		−	1.36306i
$81$	−34261.4	+	150109.i	−0.0644688	+	0.282456i
$82$	36825.4	+	76468.8i	0.0667892	+	0.138689i
$83$	−312780.	+	249433.i	−0.547021	+	0.436235i	−0.857603	−	0.514312i	$-0.828047\pi$
$83$	−312780.	+	249433.i	−0.547021	+	0.436235i	0.310582	+	0.950547i	$0.399476\pi$
$84$	−250743.	−	885056.i	−0.423050	−	1.49325i
$85$	−122007.	+	152991.i	−0.198667	+	0.249121i
$86$	9912.14	−	43427.9i	0.0155838	−	0.0682769i
$87$	−109808.	−	87569.1i	−0.166754	−	0.132982i
$88$	537803.	−	258992.i	0.789179	−	0.380048i
$89$	−414358.	+	330439.i	−0.587767	+	0.468729i	−0.871649	−	0.490131i	$-0.836949\pi$
$89$	−414358.	+	330439.i	−0.587767	+	0.468729i	0.283882	+	0.958859i	$0.408378\pi$
$90$	−229927.	+	477448.i	−0.315401	+	0.654936i
$91$	−99634.0	+	571086.i	−0.132216	+	0.757840i
$92$	−1.18130e6	+	568884.i	−1.51704	+	0.730567i
$93$	−517887.	−	249401.i	−0.643852	−	0.310063i
$94$	14140.5	−	3227.47i	0.0170247	−	0.00388579i
$95$	−52043.7	−	25062.9i	−0.0607012	−	0.0292322i
$96$	−788607.	−	628893.i	−0.891348	−	0.710826i
$97$			975693.i			1.06905i	0.845153	+	0.534525i	$0.179509\pi$
$97$			975693.i			1.06905i	−0.845153	+	0.534525i	$0.820491\pi$
$98$	−75766.6	−	222836.i	−0.0805007	−	0.236760i
$99$	3.05377e6			3.14725
$100$	1.04521e6	−	1.31065e6i	1.04521	−	1.31065i
$101$	−123161.	+	255746.i	−0.119539	+	0.248225i	−0.952149	−	0.305635i	$-0.901131\pi$
$101$	−123161.	+	255746.i	−0.119539	+	0.248225i	0.832610	+	0.553860i	$0.186846\pi$
$102$	18655.7	+	81736.1i	0.0175797	+	0.0770217i
$103$	−73007.4	+	151601.i	−0.0668121	+	0.138737i	−0.931700	−	0.363227i	$-0.881675\pi$
$103$	−73007.4	+	151601.i	−0.0668121	+	0.138737i	0.864888	+	0.501964i	$0.167389\pi$
$104$	181911.	+	377742.i	0.161718	+	0.335812i
$105$	1.23773e6	−	2.95113e6i	1.06920	−	2.54930i
$106$	392902.	+	189212.i	0.329888	+	0.158866i
$107$	903998.	+	1.13358e6i	0.737931	+	0.925337i	0.999203	−	0.0399287i	$-0.0127131\pi$
$107$	903998.	+	1.13358e6i	0.737931	+	0.925337i	−0.261271	+	0.965265i	$0.584142\pi$
$108$	−628457.	−	1.30500e6i	−0.498889	−	1.03595i
$109$	154800.	−	194113.i	0.119534	−	0.149891i	−0.718464	−	0.695564i	$-0.755154\pi$
$109$	154800.	−	194113.i	0.119534	−	0.149891i	0.837998	+	0.545673i	$0.183726\pi$
$110$	979592.	+	223586.i	0.735982	+	0.167983i
$111$	1.33542e6	+	1.06496e6i	0.976449	+	0.778692i
$112$	932378.	+	667781.i	0.663648	+	0.475314i
$113$	1.40556e6	+	1.76252e6i	0.974127	+	1.22152i	0.975157	+	0.221517i	$0.0711008\pi$
$113$	1.40556e6	+	1.76252e6i	0.974127	+	1.22152i	−0.00102980	+	0.999999i	$0.500328\pi$
$114$	−22297.5	+	10737.9i	−0.0150502	+	0.00724777i
$115$	−4.44694e6	−	1.01498e6i	−2.92393	−	0.667369i
$116$	188516.			0.120775
$117$			2.14491e6i			1.33922i
$118$	−178932.	−	40840.2i	−0.108904	−	0.0248566i
$119$	−87653.4	−	309393.i	−0.0520149	−	0.183599i
$120$	−515013.	−	2.25642e6i	−0.298040	−	1.30580i
$121$	−894228.	−	3.91787e6i	−0.504768	−	2.21153i
$122$	−544319.	+	434080.i	−0.299760	+	0.239051i
$123$	−1.18238e6	−	1.48266e6i	−0.635392	−	0.796757i
$124$	752186.	−	171682.i	0.394512	−	0.0900448i
$125$	2.50617e6	−	572016.i	1.28316	−	0.292872i
$126$	−417864.	−	764035.i	−0.208893	−	0.381946i
$127$	21338.2	−	93488.8i	0.0104171	−	0.0456403i	−0.969452	−	0.245280i	$-0.921120\pi$
$127$	21338.2	−	93488.8i	0.0104171	−	0.0456403i	0.979869	+	0.199640i	$0.0639772\pi$
$128$	1.78197e6			0.849708
$129$			995290.i			0.463640i
$130$	−157042.	+	688046.i	−0.0714802	+	0.313175i
$131$	−226766.	−	470884.i	−0.100870	−	0.209459i	0.844426	−	0.535672i	$-0.179942\pi$
$131$	−226766.	−	470884.i	−0.100870	−	0.209459i	−0.945296	+	0.326213i	$0.894227\pi$
$132$	−5.04546e6	+	4.02362e6i	−2.19371	+	1.74942i
$133$	83282.8	−	45548.7i	0.0353998	−	0.0193607i
$134$	36551.0	−	45833.5i	0.0151909	−	0.0190488i
$135$	1.12127e6	−	4.91262e6i	0.455732	−	1.99669i
$136$	−181828.	−	145003.i	−0.0722844	−	0.0576449i
$137$	−3.00130e6	+	1.44535e6i	−1.16721	+	0.562097i	−0.914159	−	0.405357i	$-0.867147\pi$
$137$	−3.00130e6	+	1.44535e6i	−1.16721	+	0.562097i	−0.253048	+	0.967454i	$0.581433\pi$
$138$	−1.52788e6	+	1.21844e6i	−0.581369	+	0.463626i
$139$	−160620.	+	333530.i	−0.0598073	+	0.124191i	−0.928730	−	0.370756i	$-0.879098\pi$
$139$	−160620.	+	333530.i	−0.0598073	+	0.124191i	0.868923	+	0.494948i	$0.164813\pi$
$140$	1.17083e6	+	4.13273e6i	0.426689	+	1.50610i
$141$	−291981.	+	140611.i	−0.104159	+	0.0501604i
$142$	672881.	+	324042.i	0.235003	+	0.113171i
$143$	3.96495e6	−	904973.i	1.35590	−	0.309476i
$144$	3.82307e6	+	1.84109e6i	1.28034	+	0.616578i
$145$	512744.	+	408900.i	0.168189	+	0.134126i
$146$		−	874760.i		−	0.281080i
$147$	2.75838e6	+	4.47743e6i	0.868364	+	1.40954i
$148$	−2.29263e6			−0.707210
$149$	−2.35889e6	+	2.95795e6i	−0.713096	+	0.894195i	−0.997925	−	0.0643838i	$-0.979492\pi$
$149$	−2.35889e6	+	2.95795e6i	−0.713096	+	0.894195i	0.284829	+	0.958578i	$0.408063\pi$
$150$	1.08411e6	−	2.25118e6i	0.321218	−	0.667016i
$151$	−326489.	−	1.43044e6i	−0.0948283	−	0.415470i	0.905125	−	0.425146i	$-0.139777\pi$
$151$	−326489.	−	1.43044e6i	−0.0948283	−	0.415470i	−0.999953	+	0.00967585i	$0.996920\pi$
$152$	29787.0	−	61853.2i	0.00848194	−	0.0176129i
$153$	−516231.	−	1.07197e6i	−0.144135	−	0.299300i
$154$	−1.23605e6	+	1.09480e6i	−0.338433	+	0.299758i
$155$	2.41825e6	+	1.16457e6i	0.649391	+	0.312730i
$156$	−2.82611e6	−	3.54383e6i	−0.744416	−	0.933468i
$157$	1.32265e6	+	2.74652e6i	0.341780	+	0.709713i	0.999033	−	0.0439561i	$-0.0139962\pi$
$157$	1.32265e6	+	2.74652e6i	0.341780	+	0.709713i	−0.657253	+	0.753670i	$0.728282\pi$
$158$	241529.	−	302868.i	0.0612348	−	0.0767860i
$159$	−9.49948e6	−	2.16819e6i	−2.36324	−	0.539395i
$160$	3.68237e6	+	2.93659e6i	0.899016	+	0.716941i
$161$	5.61113e6	−	4.96992e6i	1.34454	−	1.19089i
$162$	−192051.	−	240825.i	−0.0451723	−	0.0566442i
$163$	−5.49736e6	+	2.64739e6i	−1.26938	+	0.611301i	−0.942639	−	0.333813i	$-0.891664\pi$
$163$	−5.49736e6	+	2.64739e6i	−1.26938	+	0.611301i	−0.326740	+	0.945114i	$0.605950\pi$
$164$	2.48158e6	+	566405.i	0.562596	+	0.128409i
$165$	−2.24505e7			−4.99775
$166$		−	800348.i		−	0.174966i
$167$	2.84694e6	+	649796.i	0.611264	+	0.139517i	0.516936	−	0.856024i	$-0.327072\pi$
$167$	2.84694e6	+	649796.i	0.611264	+	0.139517i	0.0943284	+	0.995541i	$0.469930\pi$
$168$	3.50738e6	+	1.47102e6i	0.739698	+	0.310236i
$169$	−438431.	−	1.92089e6i	−0.0908324	−	0.397963i
$170$	−87112.1	−	381663.i	−0.0177309	−	0.0776843i
$171$	274592.	−	218980.i	0.0549162	−	0.0437942i
$172$	−832927.	−	1.04446e6i	−0.163690	−	0.205261i
$173$	5.77401e6	−	1.31788e6i	1.11516	−	0.254529i	0.375047	−	0.927006i	$-0.377627\pi$
$173$	5.77401e6	−	1.31788e6i	1.11516	−	0.254529i	0.740118	+	0.672477i	$0.234770\pi$
$174$	273935.	−	62523.9i	0.0519996	−	0.0118686i
$175$	−3.70668e6	+	8.83788e6i	−0.691625	+	1.64905i
$176$	1.79031e6	−	7.84387e6i	0.328391	−	1.43877i
$177$	4.10081e6			0.739520
$178$		−	1.06027e6i		−	0.187999i
$179$	−1.13434e6	+	4.96985e6i	−0.197780	+	0.866532i	0.774474	+	0.632606i	$0.218015\pi$
$179$	−1.13434e6	+	4.96985e6i	−0.197780	+	0.866532i	−0.972254	+	0.233926i	$0.924843\pi$
$180$	6.89559e6	+	1.43188e7i	1.18237	+	2.45522i
$181$	−3.24505e6	+	2.58784e6i	−0.547250	+	0.436417i	−0.857684	−	0.514178i	$-0.828097\pi$
$181$	−3.24505e6	+	2.58784e6i	−0.547250	+	0.436417i	0.310434	+	0.950595i	$0.399526\pi$
$182$	−768964.	−	868174.i	−0.127553	−	0.144010i
$183$	9.69892e6	−	1.21621e7i	1.58260	−	1.98451i
$184$	1.20629e6	−	5.28512e6i	0.193642	−	0.848402i
$185$	−6.23570e6	−	4.97280e6i	−0.984849	−	0.785391i
$186$	1.03607e6	−	498944.i	0.161009	−	0.0775377i
$187$	−1.76376e6	+	1.40655e6i	−0.269721	+	0.215096i
$188$	188732.	−	391907.i	0.0284036	−	0.0589806i
$189$	5.49036e6	+	6.19872e6i	0.813234	+	0.918156i
$190$	104117.	−	50140.1i	0.0151796	−	0.00731012i
$191$	−2.92959e6	−	1.41082e6i	−0.420443	−	0.202475i	0.211686	−	0.977338i	$-0.432104\pi$
$191$	−2.92959e6	−	1.41082e6i	−0.420443	−	0.202475i	−0.632129	+	0.774863i	$0.717819\pi$
$192$	−7.35816e6	+	1.67945e6i	−1.03960	+	0.237282i
$193$	6.38400e6	+	3.07437e6i	0.888016	+	0.427646i	0.821546	−	0.570142i	$-0.193112\pi$
$193$	6.38400e6	+	3.07437e6i	0.888016	+	0.427646i	0.0664702	+	0.997788i	$0.478826\pi$
$194$	−1.52609e6	−	1.21702e6i	−0.209014	−	0.166683i
$195$		−	1.57688e7i		−	2.12664i
$196$	−6.64167e6	−	2.39022e6i	−0.882082	−	0.317445i
$197$	1.03616e7			1.35527			0.677636	−	0.735397i	$-0.263004\pi$
$197$	1.03616e7			1.35527			0.677636	+	0.735397i	$0.263004\pi$
$198$	−3.80907e6	+	4.77643e6i	−0.490709	+	0.615329i
$199$	3.15047e6	−	6.54202e6i	0.399776	−	0.830143i	−0.599775	−	0.800169i	$-0.704743\pi$
$199$	3.15047e6	−	6.54202e6i	0.399776	−	0.830143i	0.999551	−	0.0299740i	$-0.00954244\pi$
$200$	1.54233e6	+	6.75740e6i	0.192791	+	0.844675i
$201$	−568324.	+	1.18014e6i	−0.0699855	+	0.145326i
$202$	−246392.	−	511638.i	−0.0298932	−	0.0620739i
$203$	−1.03692e6	+	293767.i	−0.123953	+	0.0351167i
$204$	2.26533e6	+	1.09093e6i	0.266834	+	0.128501i
$205$	5.52107e6	+	6.92321e6i	0.640858	+	0.803611i
$206$	−146056.	−	303289.i	−0.0167078	−	0.0346940i
$207$	1.72916e7	−	2.16830e7i	1.94950	−	2.44460i
$208$	5.50938e6	+	1.25748e6i	0.612228	+	0.139737i
$209$	−520649.	−	415204.i	−0.0570303	−	0.0454802i
$210$	3.07202e6	+	5.61699e6i	0.331716	+	0.606520i
$211$	−5.46308e6	−	6.85048e6i	−0.581554	−	0.729245i	0.400823	−	0.916155i	$-0.368724\pi$
$211$	−5.46308e6	−	6.85048e6i	−0.581554	−	0.729245i	−0.982377	+	0.186910i	$0.940153\pi$
$212$	1.17833e7	−	5.67452e6i	1.23668	−	0.595554i
$213$	−1.62688e7	−	3.71324e6i	−1.68351	−	0.384250i
$214$	−2.90062e6			−0.295972
$215$		−	4.64746e6i		−	0.467628i
$216$	5.83858e6	+	1.33262e6i	0.579356	+	0.132234i
$217$	−3.86980e6	+	2.11646e6i	−0.378712	+	0.207124i
$218$	110527.	+	484249.i	0.0106684	+	0.0467411i
$219$	4.34924e6	+	1.90552e7i	0.414077	+	1.81419i
$220$	2.35596e7	−	1.87881e7i	2.21258	−	1.76447i
$221$	−987936.	−	1.23883e6i	−0.0915276	−	0.114772i
$222$	−3.33144e6	+	760379.i	−0.304490	+	0.0694978i
$223$	−1.99435e7	+	4.55197e6i	−1.79840	+	0.410473i	−0.985185	−	0.171493i	$-0.945141\pi$
$223$	−1.99435e7	+	4.55197e6i	−1.79840	+	0.410473i	−0.813213	+	0.581966i	$0.802284\pi$
$224$	−7.44681e6	+	2.10974e6i	−0.662561	+	0.187709i
$225$	−7.89043e6	+	3.45702e7i	−0.692712	+	3.03497i
$226$	−4.50998e6			−0.390706
$227$			1.90023e7i			1.62453i	0.583285	+	0.812267i	$0.301767\pi$
$227$			1.90023e7i			1.62453i	−0.583285	+	0.812267i	$0.698233\pi$
$228$	−165157.	+	723602.i	−0.0139346	+	0.0610513i
$229$	468547.	+	972947.i	0.0390163	+	0.0810182i	0.919566	−	0.392936i	$-0.128541\pi$
$229$	468547.	+	972947.i	0.0390163	+	0.0810182i	−0.880550	+	0.473954i	$0.842826\pi$
$230$	7.13436e6	−	5.68946e6i	0.586370	−	0.467614i
$231$	2.14820e7	−	2.99939e7i	1.74277	−	2.43331i
$232$	−485972.	+	609389.i	−0.0389177	+	0.0488013i
$233$	1.04824e6	−	4.59263e6i	0.0828690	−	0.363073i	−0.916443	−	0.400166i	$-0.868953\pi$
$233$	1.04824e6	−	4.59263e6i	0.0828690	−	0.363073i	0.999312	+	0.0370929i	$0.0118098\pi$
$234$	−3.35487e6	−	2.67542e6i	−0.261835	−	0.208806i
$235$	1.36339e6	−	656575.i	0.105055	−	0.0505919i
$236$	−4.30339e6	+	3.43184e6i	−0.327397	+	0.261090i
$237$	−3.75549e6	+	7.79836e6i	−0.282112	+	0.585812i
$238$	593257.	+	248817.i	0.0440060	+	0.0184565i
$239$	6.56758e6	−	3.16278e6i	0.481074	−	0.231673i	−0.177598	−	0.984103i	$-0.556833\pi$
$239$	6.56758e6	−	3.16278e6i	0.481074	−	0.231673i	0.658672	+	0.752430i	$0.271118\pi$
$240$	−2.81062e7	−	1.35352e7i	−2.03314	−	0.979110i
$241$	−8.80755e6	+	2.01027e6i	−0.629222	+	0.143616i	−0.525227	−	0.850962i	$-0.676020\pi$
$241$	−8.80755e6	+	2.01027e6i	−0.629222	+	0.143616i	−0.103995	+	0.994578i	$0.533163\pi$
$242$	7.24337e6	+	3.48822e6i	0.511087	+	0.246126i
$243$	−8.37878e6	−	6.68186e6i	−0.583932	−	0.465670i
$244$			2.08796e7i			1.43732i
$245$	−1.28801e7	−	2.09072e7i	−0.875834	−	1.42166i
$246$	3.79386e6			0.254845
$247$	291631.	−	365693.i	0.0193527	−	0.0242676i
$248$	−1.38407e6	+	2.87406e6i	−0.0907410	+	0.188426i
$249$	3.97927e6	+	1.74343e7i	0.257754	+	1.12929i
$250$	−2.23133e6	+	4.63341e6i	−0.142805	+	0.296538i
$251$	2.90855e6	+	6.03966e6i	0.183931	+	0.381937i	0.972463	−	0.233057i	$-0.0748729\pi$
$251$	2.90855e6	+	6.03966e6i	0.183931	+	0.381937i	−0.788532	+	0.614994i	$0.789159\pi$
$252$	−2.57281e7	−	4.48863e6i	−1.60771	−	0.280487i
$253$	−4.73774e7	−	2.28158e7i	−2.92556	−	1.40888i
$254$	119611.	+	149987.i	0.00729909	+	0.00915277i
$255$	3.79520e6	+	7.88081e6i	0.228883	+	0.475281i
$256$	4.51480e6	−	5.66138e6i	0.269103	−	0.337445i
$257$	1.76473e6	+	402788.i	0.103963	+	0.0237288i	0.274186	−	0.961677i	$-0.411592\pi$
$257$	1.76473e6	+	402788.i	0.103963	+	0.0237288i	−0.170223	+	0.985406i	$0.554449\pi$
$258$	−1.55674e6	−	1.24146e6i	−0.0906478	−	0.0722892i
$259$	1.26104e7	−	3.57262e6i	0.725820	−	0.205630i
$260$	1.31964e7	+	1.65478e7i	0.750820	+	0.941498i
$261$	−3.59265e6	+	1.73013e6i	−0.202066	+	0.0973098i
$262$	1.01937e6	+	232664.i	0.0566795	+	0.0129367i
$263$	−3.56229e7			−1.95822			−0.979110	−	0.203329i	$-0.934824\pi$
$263$	−3.56229e7			−1.95822			−0.979110	+	0.203329i	$0.934824\pi$
$264$		−	2.66821e7i		−	1.45014i
$265$	4.43574e7	+	1.01243e7i	2.38357	+	0.544035i
$266$	−32638.3	+	187078.i	−0.00173414	+	0.00993979i
$267$	5.27157e6	+	2.30962e7i	0.276953	+	1.21341i
$268$	−391220.	−	1.71405e6i	−0.0203244	−	0.0890469i
$269$	−6.89831e6	+	5.50122e6i	−0.354394	+	0.282619i	−0.784462	−	0.620177i	$-0.787061\pi$
$269$	−6.89831e6	+	5.50122e6i	−0.354394	+	0.282619i	0.430068	+	0.902796i	$0.358489\pi$
$270$	6.28526e6	+	7.88147e6i	0.319324	+	0.400420i
$271$	9.85010e6	−	2.24822e6i	0.494918	−	0.112962i	0.0322253	−	0.999481i	$-0.489741\pi$
$271$	9.85010e6	−	2.24822e6i	0.494918	−	0.112962i	0.462692	+	0.886519i	$0.346883\pi$
$272$	−3.05608e6	+	697531.i	−0.151865	+	0.0346623i
$273$	2.10671e7	+	1.50886e7i	1.03542	+	0.741583i
$274$	1.48294e6	−	6.49719e6i	0.0720896	−	0.315845i
$275$	6.72335e7			3.23287
$276$			5.86080e7i			2.78759i
$277$	7.90512e6	−	3.46346e7i	0.371937	−	1.62956i	−0.349398	−	0.936974i	$-0.613614\pi$
$277$	7.90512e6	−	3.46346e7i	0.371937	−	1.62956i	0.721335	−	0.692587i	$-0.243529\pi$
$278$	−321331.	−	667250.i	−0.0149561	−	0.0310566i
$279$	−1.27591e7	+	1.01751e7i	−0.587501	+	0.468517i
$280$	−1.63775e7	−	6.86888e6i	−0.746061	−	0.312904i
$281$	−2.44822e7	+	3.06997e7i	−1.10340	+	1.38362i	−0.187471	+	0.982270i	$0.560029\pi$
$281$	−2.44822e7	+	3.06997e7i	−1.10340	+	1.38362i	−0.915926	+	0.401347i	$0.868542\pi$
$282$	144268.	−	632078.i	0.00643313	−	0.0281854i
$283$	1.98088e7	+	1.57970e7i	0.873976	+	0.696973i	0.953996	−	0.299821i	$-0.0969268\pi$
$283$	1.98088e7	+	1.57970e7i	0.873976	+	0.696973i	−0.0800195	+	0.996793i	$0.525498\pi$
$284$	2.01799e7	−	9.71814e6i	0.880977	−	0.424256i
$285$	−2.01873e6	+	1.60988e6i	−0.0872055	+	0.0695441i
$286$	−3.53014e6	+	7.33041e6i	−0.150902	+	0.313350i
$287$	−1.45323e7	+	751611.i	−0.614737	+	0.0317942i
$288$	−2.58013e7	+	1.24252e7i	−1.08010	+	0.520148i
$289$	−2.09553e7	−	1.00915e7i	−0.868161	−	0.418084i
$290$	−1.27913e6	+	291952.i	−0.0524469	+	0.0119707i
$291$	3.92943e7	+	1.89231e7i	1.59460	+	0.767917i
$292$	−2.05108e7	−	1.63568e7i	−0.823825	−	0.656978i
$293$		−	4.97876e7i		−	1.97933i	−0.143398	−	0.989665i	$-0.545803\pi$
$293$		−	4.97876e7i		−	1.97933i	0.143398	−	0.989665i	$-0.454197\pi$
$294$	−1.04438e7	−	1.27045e6i	−0.410976	−	0.0499938i
$295$	−1.91486e7			−0.745882
$296$	5.91011e6	−	7.41104e6i	0.227887	−	0.285762i
$297$	2.52050e7	−	5.23387e7i	0.962094	−	1.99781i
$298$	−1.68423e6	−	7.37911e6i	−0.0636434	−	0.278840i
$299$	1.60253e7	−	3.32770e7i	0.599506	−	1.24489i
$300$	−3.25128e7	−	6.75136e7i	−1.20418	−	2.50050i
$301$	6.20902e6	+	4.44698e6i	0.227679	+	0.163067i
$302$	2.64461e6	+	1.27358e6i	0.0960153	+	0.0462385i
$303$	7.91108e6	+	9.92018e6i	0.284386	+	0.356609i
$304$	−401486.	−	833695.i	−0.0142906	−	0.0296747i
$305$	−4.52887e7	+	5.67902e7i	−1.59621	+	2.00158i
$306$	2.32058e6	+	529658.i	0.0809903	+	0.0184855i
$307$	−5.62269e6	−	4.48395e6i	−0.194325	−	0.154969i	0.521494	−	0.853255i	$-0.325375\pi$
$307$	−5.62269e6	−	4.48395e6i	−0.194325	−	0.154969i	−0.715819	+	0.698286i	$0.753946\pi$
$308$	2.55772e6	+	4.94533e7i	0.0875388	+	1.69256i
$309$	4.68953e6	+	5.88049e6i	0.158948	+	0.199314i
$310$	−4.83787e6	+	2.32980e6i	−0.162394	+	0.0782048i
$311$	−2.56514e7	−	5.85476e6i	−0.852765	−	0.194638i	−0.226271	−	0.974064i	$-0.572654\pi$
$311$	−2.56514e7	−	5.85476e6i	−0.852765	−	0.194638i	−0.626494	+	0.779426i	$0.715511\pi$
$312$	1.87410e7			0.617062
$313$			9.66065e6i			0.315045i	0.987515	+	0.157523i	$0.0503508\pi$
$313$			9.66065e6i			0.315045i	−0.987515	+	0.157523i	$0.949649\pi$
$314$	−5.94564e6	−	1.35705e6i	−0.192048	−	0.0438337i
$315$	−6.02417e7	−	6.80139e7i	−1.92737	−	2.17604i
$316$	−2.58519e6	−	1.13265e7i	−0.0819278	−	0.358949i
$317$	4.92499e6	+	2.15778e7i	0.154606	+	0.677375i	0.991511	+	0.130026i	$0.0415060\pi$
$317$	4.92499e6	+	2.15778e7i	0.154606	+	0.677375i	−0.836904	+	0.547350i	$0.815637\pi$
$318$	1.52403e7	−	1.21538e7i	0.473928	−	0.377945i
$319$	4.71401e6	+	5.91118e6i	0.145217	+	0.182097i
$320$	3.43586e7	−	7.84213e6i	1.04854	−	0.239323i
$321$	6.31855e7	−	1.44217e7i	1.91030	−	0.436014i
$322$	774535.	+	1.49756e7i	0.0231992	+	0.448555i
$323$	−57734.8	+	252952.i	−0.00171329	+	0.00750639i
$324$	−9.23780e6			−0.271602
$325$			4.72235e7i			1.37565i
$326$	2.71624e6	−	1.19006e7i	0.0784000	−	0.343493i
$327$	−4.81529e6	−	9.99905e6i	−0.137714	−	0.285967i
$328$	−8.22814e6	+	6.56172e6i	−0.233174	+	0.185950i
$329$	−427393.	+	2.44975e6i	−0.0120016	+	0.0687913i
$330$	2.80033e7	−	3.51150e7i	0.779233	−	0.977127i
$331$	1.01610e7	−	4.45183e7i	0.280191	−	1.22759i	−0.617359	−	0.786681i	$-0.711797\pi$
$331$	1.01610e7	−	4.45183e7i	0.280191	−	1.22759i	0.897550	−	0.440913i	$-0.145345\pi$
$332$	−1.87661e7	−	1.49654e7i	−0.512813	−	0.408955i
$333$	4.36917e7	−	2.10408e7i	1.18322	−	0.569809i
$334$	−4.56744e6	+	3.64241e6i	−0.122584	+	0.0977574i
$335$	2.65376e6	−	5.51060e6i	0.0705875	−	0.146577i
$336$	4.49768e7	−	2.45986e7i	1.18569	−	0.648473i
$337$	−2.63934e6	+	1.27104e6i	−0.0689614	+	0.0332100i	−0.468047	−	0.883704i	$-0.655042\pi$
$337$	−2.63934e6	+	1.27104e6i	−0.0689614	+	0.0332100i	0.399085	+	0.916914i	$0.369328\pi$
$338$	3.55135e6	+	1.71024e6i	0.0919694	+	0.0442901i
$339$	9.82428e7	−	2.24233e7i	2.52175	−	0.575572i
$340$	−1.05779e7	−	5.09404e6i	−0.269130	−	0.129606i
$341$	2.41923e7	+	1.92927e7i	0.610119	+	0.486554i
$342$			702634.i			0.0175651i
$343$	4.02565e7	+	2.79740e6i	0.997594	+	0.0693222i
$344$	5.52345e6			0.135686
$345$	−1.27123e8	+	1.59407e8i	−3.09576	+	3.88196i
$346$	−5.14081e6	+	1.06750e7i	−0.124109	+	0.257715i
$347$	−2.29394e6	−	1.00504e7i	−0.0549026	−	0.240544i	0.940029	−	0.341093i	$-0.110797\pi$
$347$	−2.29394e6	−	1.00504e7i	−0.0549026	−	0.240544i	−0.994932	+	0.100549i	$0.967940\pi$
$348$	3.65620e6	−	7.59217e6i	0.0867544	−	0.180147i
$349$	2.40793e7	+	5.00011e7i	0.566457	+	1.17626i	0.965759	+	0.259441i	$0.0835384\pi$
$349$	2.40793e7	+	5.00011e7i	0.566457	+	1.17626i	−0.399301	+	0.916820i	$0.630747\pi$
$350$	−9.19992e6	−	1.68214e7i	−0.214575	−	0.392337i
$351$	3.67617e7	+	1.77035e7i	0.850108	+	0.409391i
$352$	3.38545e7	+	4.24522e7i	0.776227	+	0.973357i
$353$	2.98137e7	+	6.19087e7i	0.677784	+	1.40743i	0.901501	+	0.432778i	$0.142467\pi$
$353$	2.98137e7	+	6.19087e7i	0.677784	+	1.40743i	−0.223717	+	0.974654i	$0.571819\pi$
$354$	−5.11508e6	+	6.41411e6i	−0.115304	+	0.144586i
$355$	7.59662e7	+	1.73388e7i	1.69799	+	0.387555i
$356$	−2.48605e7	−	1.98256e7i	−0.551011	−	0.439416i
$357$	−1.41603e7	−	2.47046e6i	−0.311219	−	0.0542966i
$358$	−6.35849e6	−	7.97329e6i	−0.138581	−	0.173776i
$359$	−4.92099e7	+	2.36982e7i	−1.06358	+	0.512192i	−0.882032	−	0.471190i	$-0.843824\pi$
$359$	−4.92099e7	+	2.36982e7i	−1.06358	+	0.512192i	−0.181546	+	0.983382i	$0.558110\pi$
$360$	−6.40624e7	−	1.46218e7i	−1.37308	−	0.313396i
$361$	4.69693e7			0.998372
$362$		−	8.30351e6i		−	0.175039i
$363$	−1.75128e8	−	3.99719e7i	−3.66131	−	0.835671i
$364$	−3.47350e7	+	1.79649e6i	−0.720217	+	0.0372496i
$365$	−2.03086e7	−	8.89777e7i	−0.417639	−	1.82979i
$366$	6.92498e6	+	3.03403e7i	0.141246	+	0.618838i
$367$	5.29748e7	−	4.22460e7i	1.07170	−	0.854648i	0.0818283	−	0.996646i	$-0.473924\pi$
$367$	5.29748e7	−	4.22460e7i	1.07170	−	0.854648i	0.989867	+	0.141998i	$0.0453526\pi$
$368$	−4.55571e7	−	5.71269e7i	−0.914141	−	1.14630i
$369$	−5.24909e7	+	1.19807e7i	−1.04473	+	0.238453i
$370$	1.55560e7	−	3.55056e6i	0.307109	−	0.0700957i
$371$	−5.59700e7	+	4.95740e7i	−1.09606	+	0.970806i
$372$	7.67416e6	−	3.36227e7i	0.149074	−	0.653136i
$373$	2.09043e7			0.402818			0.201409	−	0.979507i	$-0.435448\pi$
$373$	2.09043e7			0.402818			0.201409	+	0.979507i	$0.435448\pi$
$374$		−	4.51316e6i		−	0.0862712i
$375$	2.55691e7	−	1.12025e8i	0.484866	−	2.12434i
$376$	780331.	+	1.62037e6i	0.0146796	+	0.0304826i
$377$	−4.15189e6	+	3.31102e6i	−0.0774858	+	0.0617929i
$378$	−1.65438e7	+	855644.i	−0.306309	+	0.0158423i
$379$	−2.39402e7	+	3.00200e7i	−0.439754	+	0.551434i	−0.951478	−	0.307716i	$-0.900435\pi$
$379$	−2.39402e7	+	3.00200e7i	−0.439754	+	0.551434i	0.511725	+	0.859150i	$0.329007\pi$
$380$	771195.	−	3.37883e6i	0.0140544	−	0.0615765i
$381$	−3.35125e6	−	2.67253e6i	−0.0605943	−	0.0483224i
$382$	5.86085e6	−	2.82244e6i	0.105141	−	0.0506330i
$383$	−9.51793e6	+	7.59030e6i	−0.169413	+	0.135102i	−0.704526	−	0.709678i	$-0.748840\pi$
$383$	−9.51793e6	+	7.59030e6i	−0.169413	+	0.135102i	0.535113	+	0.844780i	$0.320269\pi$
$384$	3.45605e7	−	7.17655e7i	0.610360	−	1.26743i
$385$	−1.00309e8	+	1.40055e8i	−1.75776	+	2.45424i
$386$	−1.27716e7	+	6.15049e6i	−0.222067	+	0.106942i
$387$	2.54591e7	+	1.22604e7i	0.439248	+	0.211531i
$388$	−5.70717e7	+	1.30262e7i	−0.977069	+	0.223010i
$389$	2.90468e6	+	1.39882e6i	0.0493458	+	0.0237637i	0.458394	−	0.888749i	$-0.348425\pi$
$389$	2.90468e6	+	1.39882e6i	0.0493458	+	0.0237637i	−0.409048	+	0.912513i	$0.634139\pi$
$390$	2.46641e7	+	1.96690e7i	0.415787	+	0.331579i
$391$			2.04878e7i			0.342741i
$392$	2.48479e7	−	1.53079e7i	0.412507	−	0.254130i
$393$	−2.33620e7			−0.384887
$394$	−1.29243e7	+	1.62066e7i	−0.211310	+	0.264974i
$395$	1.75361e7	−	3.64141e7i	0.284539	−	0.590851i
$396$	4.07701e7	+	1.78626e8i	0.656533	+	2.87646i
$397$	1.82923e7	−	3.79844e7i	0.292346	−	0.607063i	−0.702127	−	0.712052i	$-0.747766\pi$
$397$	1.82923e7	−	3.79844e7i	0.292346	−	0.607063i	0.994473	+	0.104988i	$0.0334805\pi$
$398$	6.30274e6	+	1.30878e7i	0.0999723	+	0.207595i
$399$	−219161.	−	4.23747e6i	−0.00345021	−	0.0667095i
$400$	8.41708e7	+	4.05345e7i	1.31517	+	0.633352i
$401$	−2.46341e7	−	3.08902e7i	−0.382035	−	0.479057i	0.553218	−	0.833037i	$-0.313400\pi$
$401$	−2.46341e7	−	3.08902e7i	−0.382035	−	0.479057i	−0.935253	+	0.353980i	$0.884828\pi$
$402$	−1.13697e6	−	2.36095e6i	−0.0175013	−	0.0363419i
$403$	−1.35508e7	+	1.69922e7i	−0.207038	+	0.259618i
$404$	−1.66038e7	−	3.78971e6i	−0.251804	−	0.0574727i
$405$	−2.51258e7	−	2.00372e7i	−0.378229	−	0.301628i
$406$	833899.	−	1.98827e6i	0.0124605	−	0.0297097i
$407$	−5.73290e7	−	7.18883e7i	−0.850337	−	1.06629i
$408$	−9.36623e6	+	4.51054e6i	−0.137906	+	0.0664122i
$409$	−6.84513e6	−	1.56236e6i	−0.100049	−	0.0228355i	0.172203	−	0.985061i	$-0.444911\pi$
$409$	−6.84513e6	−	1.56236e6i	−0.100049	−	0.0228355i	−0.272252	+	0.962226i	$0.587769\pi$
$410$	−1.77153e7			−0.257037
$411$			1.48904e8i			2.14477i
$412$	−9.84239e6	−	2.24646e6i	−0.140737	−	0.0321223i
$413$	1.83225e7	−	2.55825e7i	0.260097	−	0.363156i
$414$	1.23461e7	+	5.40918e7i	0.173992	+	0.762308i
$415$	−1.85810e7	−	8.14087e7i	−0.259971	−	1.13901i
$416$	−2.98176e7	+	2.37787e7i	−0.414183	+	0.330300i
$417$	1.03172e7	+	1.29373e7i	0.142283	+	0.178417i
$418$	1.29885e6	−	296453.i	0.0177840	−	0.00405908i
$419$	3.93639e7	−	8.98455e6i	0.535126	−	0.122139i	0.0535860	−	0.998563i	$-0.482935\pi$
$419$	3.93639e7	−	8.98455e6i	0.535126	−	0.122139i	0.481540	+	0.876424i	$0.340078\pi$
$420$	1.89146e8	+	3.29992e7i	2.55300	+	0.445406i
$421$	−4.88637e6	+	2.14086e7i	−0.0654848	+	0.286908i	−0.997058	−	0.0766450i	$-0.975579\pi$
$421$	−4.88637e6	+	2.14086e7i	−0.0654848	+	0.286908i	0.931574	+	0.363553i	$0.118436\pi$
$422$	1.75292e7			0.233251
$423$			9.20086e6i			0.121565i
$424$	−1.20326e7	+	5.27182e7i	−0.157856	+	0.691613i
$425$	−1.13656e7	−	2.36010e7i	−0.148056	−	0.307442i
$426$	2.61005e7	−	2.08144e7i	0.337613	−	0.269238i
$427$	−3.25368e7	−	1.14846e8i	−0.417918	−	1.47514i
$428$	−5.42378e7	+	6.80121e7i	−0.691784	+	0.867470i
$429$	4.04522e7	−	1.77233e8i	0.512354	−	2.24477i
$430$	7.26914e6	+	5.79694e6i	0.0914276	+	0.0729111i
$431$	−5.81326e7	+	2.79952e7i	−0.726086	+	0.349665i	−0.760144	−	0.649755i	$-0.774871\pi$
$431$	−5.81326e7	+	2.79952e7i	−0.726086	+	0.349665i	0.0340573	+	0.999420i	$0.489157\pi$
$432$	6.31091e7	−	5.03279e7i	0.782782	−	0.624248i
$433$	4.57789e7	−	9.50609e7i	0.563900	−	1.17095i	−0.402860	−	0.915262i	$-0.631984\pi$
$433$	4.57789e7	−	9.50609e7i	0.563900	−	1.17095i	0.966759	−	0.255688i	$-0.0823020\pi$
$434$	1.51656e6	−	8.69271e6i	0.0185520	−	0.106337i
$435$	2.64122e7	−	1.27194e7i	0.320875	−	0.154525i
$436$	1.34211e7	+	6.46324e6i	0.161930	+	0.0779814i
$437$	−5.89621e6	+	1.34577e6i	−0.0706527	+	0.0161260i
$438$	−3.52294e7	−	1.69656e7i	−0.419260	−	0.201905i
$439$	−9.00929e7	−	7.18467e7i	−1.06487	−	0.849206i	−0.0758705	−	0.997118i	$-0.524174\pi$
$439$	−9.00929e7	−	7.18467e7i	−1.06487	−	0.849206i	−0.989001	+	0.147911i	$0.952745\pi$
$440$			1.24591e8i			1.46261i
$441$	1.48510e8	−	1.54030e7i	1.73157	−	0.179593i
$442$	3.16996e6			0.0367102
$443$	2.85550e7	−	3.58068e7i	0.328451	−	0.411865i	−0.589997	−	0.807405i	$-0.700871\pi$
$443$	2.85550e7	−	3.58068e7i	0.328451	−	0.411865i	0.918449	+	0.395540i	$0.129443\pi$
$444$	−4.44645e7	+	9.23315e7i	−0.508001	+	1.05488i
$445$	−2.46154e7	−	1.07847e8i	−0.279335	−	1.22385i
$446$	1.77564e7	−	3.68716e7i	0.200148	−	0.415611i
$447$	7.33766e7	+	1.52368e8i	0.821552	+	1.70597i
$448$	−2.23994e7	+	5.34070e7i	−0.249116	+	0.593970i
$449$	9.23843e7	+	4.44899e7i	1.02061	+	0.491499i	0.867882	−	0.496770i	$-0.165481\pi$
$449$	9.23843e7	+	4.44899e7i	1.02061	+	0.491499i	0.152726	+	0.988269i	$0.451195\pi$
$450$	−4.42296e7	−	5.54621e7i	−0.485372	−	0.608638i
$451$	4.42936e7	+	9.19765e7i	0.482849	+	1.00265i
$452$	−8.43307e7	+	1.05747e8i	−0.913209	+	1.14513i
$453$	−6.39407e7	−	1.45940e7i	−0.687832	−	0.156993i
$454$	−2.97217e7	−	2.37022e7i	−0.317618	−	0.253292i
$455$	−9.83721e7	−	7.04554e7i	−1.04433	−	0.747963i
$456$	−1.91333e6	−	2.39923e6i	−0.0201788	−	0.0253034i
$457$	8.57844e7	−	4.13116e7i	0.898793	−	0.432836i	0.0733401	−	0.997307i	$-0.476634\pi$
$457$	8.57844e7	−	4.13116e7i	0.898793	−	0.432836i	0.825453	+	0.564471i	$0.190920\pi$
$458$	−2.10623e6	−	480733.i	−0.0219235	−	0.00500389i
$459$	−2.26333e7			−0.234051
$460$		−	2.73667e8i		−	2.81157i
$461$	1.04871e8	+	2.39361e7i	1.07042	+	0.244316i	0.721200	−	0.692726i	$-0.243591\pi$
$461$	1.04871e8	+	2.39361e7i	1.07042	+	0.244316i	0.349216	+	0.937042i	$0.386448\pi$
$462$	2.01184e7	+	7.10127e7i	0.204018	+	0.720128i
$463$	−1.18633e7	−	5.19764e7i	−0.119526	−	0.523677i	−0.998872	−	0.0474929i	$-0.984877\pi$
$463$	−1.18633e7	−	5.19764e7i	−0.119526	−	0.523677i	0.879346	−	0.476184i	$-0.157980\pi$
$464$	2.33775e6	+	1.02423e7i	0.0234015	+	0.102529i
$465$	9.38018e7	−	7.48044e7i	0.932937	−	0.743992i
$466$	5.87586e6	+	7.36810e6i	0.0580649	+	0.0728111i
$467$	3.38113e7	−	7.71720e6i	0.331979	−	0.0757720i	−0.0532825	−	0.998579i	$-0.516968\pi$
$467$	3.38113e7	−	7.71720e6i	0.331979	−	0.0757720i	0.385262	+	0.922807i	$0.374111\pi$
$468$	−1.25463e8	+	2.86361e7i	−1.22399	+	0.279368i
$469$	4.82288e6	+	8.81832e6i	0.0467507	+	0.0854805i
$470$	−673652.	+	2.95146e6i	−0.00648847	+	0.0284278i
$471$	1.36263e8			1.30412
$472$		−	2.27578e7i		−	0.216423i
$473$	1.19223e7	−	5.22350e7i	0.112662	−	0.493604i
$474$	−7.51312e6	−	1.56012e7i	−0.0705481	−	0.146495i
$475$	6.04558e6	−	4.82119e6i	0.0564102	−	0.0449856i
$476$	1.69272e7	−	9.25778e6i	0.156951	−	0.0858392i
$477$	−1.72481e8	+	2.16284e8i	−1.58922	+	1.99282i
$478$	−3.24504e6	+	1.42174e7i	−0.0297123	+	0.130178i
$479$	−1.02645e8	−	8.18568e7i	−0.933968	−	0.744815i	0.0330684	−	0.999453i	$-0.489472\pi$
$479$	−1.02645e8	−	8.18568e7i	−0.933968	−	0.744815i	−0.967036	+	0.254639i	$0.918044\pi$
$480$	1.89684e8	−	9.13470e7i	1.71517	−	0.825982i
$481$	5.04929e7	−	4.02668e7i	0.453728	−	0.361836i
$482$	7.84169e6	−	1.62834e7i	0.0700275	−	0.145413i
$483$	−9.13292e7	−	3.22368e8i	−0.810529	−	2.86095i
$484$	2.17231e8	−	1.04613e8i	1.91596	−	0.922676i
$485$	−1.83483e8	−	8.83608e7i	−1.60831	−	0.774523i
$486$	2.09023e7	−	4.77081e6i	0.182090	−	0.0415607i
$487$	−3.07081e7	−	1.47882e7i	−0.265868	−	0.128035i	0.296201	−	0.955126i	$-0.404280\pi$
$487$	−3.07081e7	−	1.47882e7i	−0.265868	−	0.128035i	−0.562069	+	0.827090i	$0.689994\pi$
$488$	−6.74944e7	−	5.38250e7i	−0.580775	−	0.463153i
$489$			2.72742e8i			2.33252i
$490$	4.87669e7	+	5.93232e6i	0.414512	+	0.0504239i
$491$	−1.16368e8			−0.983078			−0.491539	−	0.870856i	$-0.663565\pi$
$491$	−1.16368e8			−0.983078			−0.491539	+	0.870856i	$0.663565\pi$
$492$	7.09401e7	−	8.89561e7i	0.595658	−	0.746931i
$493$	1.27811e6	−	2.65403e6i	0.0106667	−	0.0221495i
$494$	208223.	+	912284.i	0.00172722	+	0.00756744i
$495$	−2.76556e8	+	5.74274e8i	−2.28017	+	4.73482i
$496$	1.86554e7	+	3.87382e7i	0.152883	+	0.317464i
$497$	−9.58539e7	+	8.49002e7i	−0.780801	+	0.691575i
$498$	−3.22326e7	−	1.55224e7i	−0.260980	−	0.125681i
$499$	1.35232e8	+	1.69575e8i	1.08837	+	1.36478i	0.925772	+	0.378083i	$0.123417\pi$
$499$	1.35232e8	+	1.69575e8i	1.08837	+	1.36478i	0.162600	+	0.986692i	$0.448012\pi$
$500$	6.69184e7	+	1.38958e8i	0.535347	+	1.11166i
$501$	8.13846e7	−	1.02053e8i	0.647186	−	0.811545i
$502$	−1.30746e7	−	2.98419e6i	−0.103352	−	0.0235893i
$503$	1.04212e8	+	8.31067e7i	0.818872	+	0.653028i	0.940593	−	0.339536i	$-0.110270\pi$
$503$	1.04212e8	+	8.31067e7i	0.818872	+	0.653028i	−0.121721	+	0.992564i	$0.538841\pi$
$504$	8.08336e7	−	7.15964e7i	0.631394	−	0.559242i
$505$	−3.69405e7	−	4.63219e7i	−0.286832	−	0.359676i
$506$	9.47818e7	−	4.56445e7i	0.731599	−	0.352320i
$507$	−8.58637e7	−	1.95978e7i	−0.658849	−	0.150378i
$508$	5.75336e6			0.0438865
$509$		−	2.98604e7i		−	0.226435i	−0.993570	−	0.113217i	$-0.963884\pi$
$509$		−	2.98604e7i		−	0.226435i	0.993570	−	0.113217i	$-0.0361156\pi$
$510$	−1.70603e7	−	3.89390e6i	−0.128610	−	0.0293545i
$511$	1.38307e8	+	5.80071e7i	1.03653	+	0.434729i
$512$	2.86011e7	+	1.25310e8i	0.213095	+	0.933630i
$513$	−1.48670e6	−	6.51366e6i	−0.0110121	−	0.0482473i
$514$	−2.83121e6	+	2.25781e6i	−0.0208489	+	0.0166264i
$515$	−2.18976e7	−	2.74587e7i	−0.160315	−	0.201029i
$516$	−5.82180e7	+	1.32879e7i	−0.423748	+	0.0967178i
$517$	1.70081e7	−	3.88200e6i	0.123079	−	0.0280921i
$518$	−1.01414e7	+	2.41802e7i	−0.0729640	+	0.173969i
$519$	5.89091e7	−	2.58098e8i	0.421386	−	1.84621i
$520$	−8.75103e7			−0.622370
$521$		−	1.43767e8i		−	1.01659i	−0.861183	−	0.508295i	$-0.830276\pi$
$521$		−	1.43767e8i		−	1.01659i	0.861183	−	0.508295i	$-0.169724\pi$
$522$	1.77513e6	−	7.77733e6i	0.0124801	−	0.0546788i
$523$	7.61724e7	+	1.58174e8i	0.532467	+	1.10568i	0.977650	+	0.210240i	$0.0674244\pi$
$523$	7.61724e7	+	1.58174e8i	0.532467	+	1.10568i	−0.445183	+	0.895440i	$0.646861\pi$
$524$	2.45161e7	−	1.95510e7i	0.170395	−	0.135886i
$525$	2.84040e8	+	3.20687e8i	1.96292	+	2.21617i
$526$	4.44336e7	−	5.57180e7i	0.305320	−	0.382859i
$527$	2.68269e6	−	1.17536e7i	0.0183290	−	0.0803045i
$528$	−2.81176e8	−	2.24230e8i	−1.91019	−	1.52332i
$529$	−2.96894e8	+	1.42976e8i	−2.00555	+	0.965823i
$530$	−7.11640e7	+	5.67514e7i	−0.478005	+	0.381197i
$531$	5.05157e7	−	1.04897e8i	0.337398	−	0.700615i
$532$	3.77619e6	+	4.26339e6i	0.0250795	+	0.0283152i
$533$	−6.46025e7	+	3.11109e7i	−0.426646	+	0.205462i
$534$	−4.27004e7	−	2.05634e7i	−0.280420	−	0.135043i
$535$	−2.95042e8	+	6.73414e7i	−1.92674	+	0.439765i
$536$	6.54927e6	+	3.15396e6i	0.0425303	+	0.0204815i
$537$	1.78152e8	+	1.42072e8i	1.15045	+	0.917454i
$538$		−	1.76516e7i		−	0.113354i
$539$	−9.11319e7	−	2.68027e8i	−0.581975	−	1.71164i
$540$	3.02326e8			1.91997
$541$	−4.90487e6	+	6.15052e6i	−0.0309768	+	0.0388436i	−0.797079	−	0.603876i	$-0.793622\pi$
$541$	−4.90487e6	+	6.15052e6i	−0.0309768	+	0.0388436i	0.766102	+	0.642719i	$0.222194\pi$
$542$	−8.76991e6	+	1.82109e7i	−0.0550804	+	0.114376i
$543$	4.12844e7	+	1.80879e8i	0.257861	+	1.12976i
$544$	9.17900e6	−	1.90604e7i	0.0570162	−	0.118395i
$545$	2.24848e7	+	4.66901e7i	0.138899	+	0.288427i
$546$	−4.98779e7	+	1.41308e7i	−0.306429	+	0.0868138i
$547$	3.79643e7	+	1.82826e7i	0.231960	+	0.111706i	0.546254	−	0.837620i	$-0.316053\pi$
$547$	3.79643e7	+	1.82826e7i	0.231960	+	0.111706i	−0.314294	+	0.949326i	$0.601768\pi$
$548$	−1.24613e8	−	1.56260e8i	−0.757220	−	0.949524i
$549$	−1.91624e8	−	3.97912e8i	−1.15807	−	2.40475i
$550$	−8.38627e7	+	1.05160e8i	−0.504058	+	0.632069i
$551$	847759.	+	193495.i	0.00506778	+	0.00115669i
$552$	−1.89453e8	−	1.51084e8i	−1.12638	−	0.898259i
$553$	3.18697e7	+	5.82715e7i	0.188453	+	0.344573i
$554$	4.43119e7	+	5.55654e7i	0.260610	+	0.326795i
$555$	−3.21210e8	+	1.54686e8i	−1.87892	+	0.904843i
$556$	−2.16537e7	−	4.94232e6i	−0.125982	−	0.0287545i
$557$	1.29923e8			0.751830			0.375915	−	0.926654i	$-0.377329\pi$
$557$	1.29923e8			0.751830			0.375915	+	0.926654i	$0.377329\pi$
$558$		−	3.26484e7i		−	0.187914i
$559$	3.66888e7	+	8.37399e6i	0.210038	+	0.0479399i
$560$	−2.10017e8	+	1.14862e8i	−1.19589	+	0.654051i
$561$	2.24391e7	+	9.83120e7i	0.127091	+	0.556824i
$562$	−1.74802e7	−	7.65857e7i	−0.0984775	−	0.431458i
$563$	−6.69623e7	+	5.34007e7i	−0.375237	+	0.299241i	−0.792890	−	0.609365i	$-0.791424\pi$
$563$	−6.69623e7	+	5.34007e7i	−0.375237	+	0.299241i	0.417653	+	0.908607i	$0.362853\pi$
$564$	−1.21230e7	−	1.52017e7i	−0.0675728	−	0.0847336i
$565$	−4.58740e8	+	1.04705e8i	−2.54344	+	0.580524i
$566$	−4.94165e7	+	1.12790e7i	−0.272535	+	0.0622044i
$567$	5.08116e7	−	1.43953e7i	0.278750	−	0.0789719i
$568$	−2.06069e7	+	9.02848e7i	−0.112452	+	0.492685i
$569$	1.40663e8			0.763560			0.381780	−	0.924253i	$-0.375311\pi$
$569$	1.40663e8			0.763560			0.381780	+	0.924253i	$0.375311\pi$
$570$		−	5.16558e6i		−	0.0278929i
$571$	7.11474e6	−	3.11717e7i	0.0382165	−	0.167437i	−0.952219	−	0.305418i	$-0.901204\pi$
$571$	7.11474e6	−	3.11717e7i	0.0382165	−	0.167437i	0.990435	+	0.137980i	$0.0440611\pi$
$572$	1.05870e8	+	2.19841e8i	0.565698	+	1.17468i
$573$	−1.13636e8	+	9.06219e7i	−0.604023	+	0.481692i
$574$	1.69511e7	−	2.36676e7i	0.0896317	−	0.125147i
$575$	3.80701e8	−	4.77384e8i	2.00254	−	2.51110i
$576$	−4.76816e7	+	2.08907e8i	−0.249508	+	1.09316i
$577$	2.01726e8	+	1.60871e8i	1.05011	+	0.837434i	0.987024	−	0.160574i	$-0.0513346\pi$
$577$	2.01726e8	+	1.60871e8i	1.05011	+	0.837434i	0.0630852	+	0.998008i	$0.479906\pi$
$578$	4.19225e7	−	2.01888e7i	0.217102	−	0.104551i
$579$	2.47630e8	−	1.97478e8i	1.27575	−	1.01738i
$580$	−1.70724e7	+	3.54513e7i	−0.0875008	+	0.181697i
$581$	1.26542e8	+	5.30727e7i	0.645216	+	0.270609i
$582$	−7.86110e7	+	3.78571e7i	−0.398763	+	0.192034i
$583$	4.72581e8	+	2.27583e8i	2.38490	+	1.14851i
$584$	1.05749e8	−	2.41365e7i	0.530929	−	0.121181i
$585$	−4.03359e8	−	1.94247e8i	−2.01476	−	0.970259i
$586$	7.78732e7	+	6.21018e7i	0.386986	+	0.308611i
$587$			1.40372e8i			0.694011i	0.937863	+	0.347005i	$0.112801\pi$
$587$			1.40372e8i			0.694011i	−0.937863	+	0.347005i	$0.887199\pi$
$588$	−2.25074e8	+	2.21124e8i	−1.10712	+	1.08769i
$589$	3.55880e6			0.0174164
$590$	2.38847e7	−	2.99504e7i	0.116295	−	0.145830i
$591$	2.00958e8	−	4.17294e8i	0.973516	−	2.02153i
$592$	−2.84303e7	−	1.24561e8i	−0.137030	−	0.600369i
$593$	1.39457e8	−	2.89586e8i	0.668771	−	1.38872i	−0.239733	−	0.970839i	$-0.577060\pi$
$593$	1.39457e8	−	2.89586e8i	0.668771	−	1.38872i	0.908503	−	0.417878i	$-0.137226\pi$
$594$	5.04244e7	+	1.04707e8i	0.240592	+	0.499594i
$595$	6.61207e7	+	1.15357e7i	0.313896	+	0.0547637i
$596$	−2.04514e8	−	9.84886e7i	−0.966014	−	0.465208i
$597$	−2.02366e8	−	2.53759e8i	−0.951076	−	1.19261i
$598$	3.20598e7	+	6.65729e7i	0.149919	+	0.311310i
$599$	−8.41775e7	+	1.05555e8i	−0.391665	+	0.491133i	−0.938098	−	0.346370i	$-0.887414\pi$
$599$	−8.41775e7	+	1.05555e8i	−0.391665	+	0.491133i	0.546432	+	0.837503i	$0.315986\pi$
$600$	3.02055e8	+	6.89421e7i	1.39840	+	0.319176i
$601$	−9.02068e7	−	7.19375e7i	−0.415543	−	0.331384i	0.393299	−	0.919411i	$-0.371334\pi$
$601$	−9.02068e7	−	7.19375e7i	−0.415543	−	0.331384i	−0.808842	+	0.588026i	$0.799905\pi$
$602$	−1.47003e7	+	4.16471e6i	−0.0673808	+	0.0190895i
$603$	2.31865e7	+	2.90750e7i	0.105751	+	0.132607i
$604$	7.93127e7	−	3.81950e7i	0.359941	−	0.173339i
$605$	8.17755e8	+	1.86647e8i	3.69281	+	0.842860i
$606$	−2.53840e7			−0.114062
$607$			3.12713e8i			1.39823i	0.715007	+	0.699117i	$0.246423\pi$
$607$			3.12713e8i			1.39823i	−0.715007	+	0.699117i	$0.753577\pi$
$608$	6.08834e6	+	1.38962e6i	0.0270887	+	0.00618282i
$609$	−8.27962e6	+	4.74575e7i	−0.0366571	+	0.210113i
$610$	−3.23359e7	−	1.41673e8i	−0.142461	−	0.624161i
$611$	2.72664e6	+	1.19462e7i	0.0119537	+	0.0523728i
$612$	5.58109e7	−	4.45077e7i	0.243481	−	0.194169i
$613$	−1.08539e8	−	1.36104e8i	−0.471201	−	0.590867i	0.488264	−	0.872696i	$-0.337630\pi$
$613$	−1.08539e8	−	1.36104e8i	−0.471201	−	0.590867i	−0.959465	+	0.281829i	$0.909059\pi$
$614$	1.40268e7	−	3.20151e6i	0.0605971	−	0.0138309i
$615$	3.85899e8	−	8.80789e7i	1.65901	−	0.378657i
$616$	−1.66454e8	−	1.19216e8i	−0.712117	−	0.510028i
$617$	−1.32438e7	+	5.80249e7i	−0.0563842	+	0.247035i	−0.995264	−	0.0972103i	$-0.969008\pi$
$617$	−1.32438e7	+	5.80249e7i	−0.0563842	+	0.247035i	0.938880	+	0.344245i	$0.111865\pi$
$618$	−1.50471e7			−0.0637512
$619$			7.56621e7i			0.319012i	0.987197	+	0.159506i	$0.0509901\pi$
$619$			7.56621e7i			0.319012i	−0.987197	+	0.159506i	$0.949010\pi$
$620$	−3.58341e7	+	1.57000e8i	−0.150356	+	0.658754i
$621$	−2.28905e8	−	4.75327e8i	−0.955831	−	1.98480i
$622$	4.11533e7	−	3.28187e7i	0.171015	−	0.136380i
$623$	1.67637e8	+	7.03085e7i	0.693276	+	0.290766i
$624$	1.57495e8	−	1.97492e8i	0.648206	−	0.812824i
$625$	−2.22465e7	+	9.74682e7i	−0.0911216	+	0.399230i
$626$	−1.51103e7	−	1.20501e7i	−0.0615956	−	0.0491209i
$627$	−2.68193e7	+	1.29155e7i	−0.108804	+	0.0523973i
$628$	−1.42995e8	+	1.14035e8i	−0.577353	+	0.460423i
$629$	−1.55437e7	+	3.22767e7i	−0.0624599	+	0.129699i
$630$	1.81523e8	−	9.38834e6i	0.725954	−	0.0375463i
$631$	3.08408e7	−	1.48521e7i	0.122754	−	0.0591154i	−0.371499	−	0.928434i	$-0.621156\pi$
$631$	3.08408e7	−	1.48521e7i	0.122754	−	0.0591154i	0.494253	+	0.869318i	$0.335442\pi$
$632$	4.32777e7	+	2.08414e7i	0.171440	+	0.0825612i
$633$	−3.81845e8	+	8.71537e7i	−1.50548	+	0.343617i
$634$	−3.98931e7	−	1.92115e7i	−0.156542	−	0.0753865i
$635$	1.56485e7	+	1.24793e7i	0.0611156	+	0.0487381i
$636$		−	5.84605e8i		−	2.27243i
$637$	1.88257e8	−	6.40092e7i	0.728338	−	0.247642i
$638$	−1.51257e7			−0.0582441
$639$	−2.95389e8	+	3.70406e8i	−1.13212	+	1.41963i
$640$	−1.61379e8	+	3.35106e8i	−0.615611	+	1.27833i
$641$	−9.10465e7	−	3.98901e8i	−0.345692	−	1.51458i	−0.786849	−	0.617146i	$-0.788289\pi$
$641$	−9.10465e7	−	3.98901e8i	−0.345692	−	1.51458i	0.441157	−	0.897430i	$-0.354568\pi$
$642$	−5.62564e7	+	1.16818e8i	−0.212602	+	0.441472i
$643$	−9.64766e7	−	2.00336e8i	−0.362902	−	0.753573i	0.636948	−	0.770907i	$-0.280197\pi$
$643$	−9.64766e7	−	2.00336e8i	−0.362902	−	0.753573i	−0.999850	+	0.0173335i	$0.994482\pi$
$644$	3.65620e8	+	2.61862e8i	1.36890	+	0.980426i
$645$	−1.87168e8	−	9.01356e7i	−0.697515	−	0.335905i
$646$	−323630.	−	405820.i	−0.00120047	−	0.00150534i
$647$	−1.45655e8	−	3.02455e8i	−0.537788	−	1.11673i	−0.975983	−	0.217848i	$-0.930096\pi$
$647$	−1.45655e8	−	3.02455e8i	−0.537788	−	1.11673i	0.438195	−	0.898880i	$-0.355618\pi$
$648$	2.38139e7	−	2.98617e7i	0.0875197	−	0.109746i
$649$	−2.15219e8	−	4.91224e7i	−0.787313	−	0.179699i
$650$	−7.38627e7	−	5.89035e7i	−0.268958	−	0.214487i
$651$	1.01835e7	+	1.96897e8i	0.0369108	+	0.713668i
$652$	−2.28249e8	−	2.86215e8i	−0.823504	−	1.03264i
$653$	−1.78133e8	+	8.57842e7i	−0.639741	+	0.308083i	−0.725489	−	0.688234i	$-0.758386\pi$
$653$	−1.78133e8	+	8.57842e7i	−0.639741	+	0.308083i	0.0857478	+	0.996317i	$0.472672\pi$
$654$	2.16459e7	+	4.94053e6i	0.0773824	+	0.0176620i
$655$	1.09088e8			0.388198
$656$			1.41851e8i			0.502483i
$657$	5.41001e8	+	1.23480e8i	1.90766	+	0.435412i
$658$	−3.29857e6	−	3.72414e6i	−0.0115784	−	0.0130722i
$659$	−3.46863e6	−	1.51971e7i	−0.0121200	−	0.0531012i	0.968506	−	0.248989i	$-0.0800983\pi$
$659$	−3.46863e6	−	1.51971e7i	−0.0121200	−	0.0531012i	−0.980626	+	0.195888i	$0.937241\pi$
$660$	−2.99731e8	−	1.31321e9i	−1.04256	−	4.56774i
$661$	1.84871e8	−	1.47430e8i	0.640124	−	0.510482i	−0.248789	−	0.968558i	$-0.580033\pi$
$661$	1.84871e8	−	1.47430e8i	0.640124	−	0.510482i	0.888913	+	0.458076i	$0.151461\pi$
$662$	5.69573e7	+	7.14222e7i	0.196325	+	0.246184i
$663$	−6.90524e7	+	1.57608e7i	−0.236940	+	0.0540800i
$664$	9.67532e7	−	2.20833e7i	0.330492	−	0.0754326i
$665$	1.02336e6	+	1.97867e7i	0.00347989	+	0.0672834i
$666$	−2.15880e7	+	9.45834e7i	−0.0730787	+	0.320178i
$667$	6.86641e7			0.231394
$668$			1.75203e8i			0.587775i
$669$	−2.03473e8	+	8.91471e8i	−0.679559	+	2.97734i
$670$	5.30904e6	+	1.10243e7i	0.0176519	+	0.0366546i
$671$	−6.54706e8	+	5.22111e8i	−2.16710	+	1.72820i
$672$	−5.94616e7	+	3.40825e8i	−0.195943	+	1.12311i
$673$	−3.33596e8	+	4.18316e8i	−1.09440	+	1.37233i	−0.172449	+	0.985018i	$0.555168\pi$
$673$	−3.33596e8	+	4.18316e8i	−1.09440	+	1.37233i	−0.921948	+	0.387313i	$0.873403\pi$
$674$	1.30410e6	−	5.71363e6i	0.00425922	−	0.0186609i
$675$	5.27376e8	+	4.20568e8i	1.71478	+	1.36749i
$676$	1.06506e8	−	5.12907e7i	0.344774	−	0.166034i
$677$	2.82134e8	−	2.24994e8i	0.909263	−	0.725113i	−0.0526082	−	0.998615i	$-0.516753\pi$
$677$	2.82134e8	−	2.24994e8i	0.909263	−	0.725113i	0.961871	+	0.273502i	$0.0881820\pi$
$678$	−8.74692e7	+	1.81632e8i	−0.280651	+	0.582777i
$679$	2.93618e8	−	1.60585e8i	0.937937	−	0.512973i
$680$	4.37352e7	−	2.10618e7i	0.139093	−	0.0669835i
$681$	7.65285e8	+	3.68542e8i	2.42316	+	1.16693i
$682$	−6.03518e7	+	1.37749e7i	−0.190256	+	0.0434246i
$683$	4.47867e7	+	2.15682e7i	0.140568	+	0.0676941i	0.502846	−	0.864376i	$-0.332286\pi$
$683$	4.47867e7	+	2.15682e7i	0.140568	+	0.0676941i	−0.362277	+	0.932070i	$0.618001\pi$
$684$	1.64749e7	+	1.31383e7i	0.0514820	+	0.0410555i
$685$		−	6.95301e8i		−	2.16322i
$686$	−5.45888e7	+	5.94763e7i	−0.169095	+	0.184235i
$687$	4.82710e7			0.148873
$688$	4.64178e7	−	5.82060e7i	0.142534	−	0.178732i
$689$	−1.59850e8	+	3.31932e8i	−0.488714	+	1.01483i
$690$	−9.07652e7	−	3.97669e8i	−0.276295	−	1.21053i
$691$	1.83641e8	−	3.81335e8i	0.556590	−	1.15577i	−0.412930	−	0.910763i	$-0.635495\pi$
$691$	1.83641e8	−	3.81335e8i	0.556590	−	1.15577i	0.969521	−	0.245009i	$-0.0787910\pi$
$692$	1.54175e8	+	3.20147e8i	0.465259	+	0.966120i
$693$	−5.02605e8	−	9.18980e8i	−1.51018	−	2.76125i
$694$	1.85812e7	+	8.94823e6i	0.0555898	+	0.0267707i
$695$	−4.81756e7	−	6.04103e7i	−0.143507	−	0.179952i
$696$	1.51169e7	+	3.13905e7i	0.0448368	+	0.0931045i
$697$	2.47988e7	−	3.10968e7i	0.0732374	−	0.0918368i
$698$	−1.08242e8	−	2.47056e7i	−0.318295	−	0.0726488i
$699$	−1.64630e8	−	1.31288e8i	−0.482033	−	0.384409i
$700$	−5.66445e8	−	9.88243e7i	−1.65144	−	0.288117i
$701$	2.59019e8	+	3.24800e8i	0.751932	+	0.942893i	0.999664	−	0.0259361i	$-0.00825665\pi$
$701$	2.59019e8	+	3.24800e8i	0.751932	+	0.942893i	−0.247732	+	0.968829i	$0.579685\pi$
$702$	−7.35443e7	+	3.54171e7i	−0.212588	+	0.102377i
$703$	−1.03100e7	−	2.35318e6i	−0.0296750	−	0.00677312i
$704$	4.06290e8			1.16444
$705$		−	6.76422e7i		−	0.193041i
$706$	−1.34019e8	−	3.05891e7i	−0.380850	−	0.0869265i
$707$	9.72330e7	−	5.02889e6i	0.275141	−	0.0142303i
$708$	5.47489e7	+	2.39871e8i	0.154268	+	0.675892i
$709$	2.23821e7	+	9.80623e7i	0.0628003	+	0.275146i	0.996573	−	0.0827213i	$-0.0263611\pi$
$709$	2.23821e7	+	9.80623e7i	0.0628003	+	0.275146i	−0.933772	+	0.357867i	$0.883504\pi$
$710$	−1.21875e8	+	9.71921e7i	−0.340518	+	0.271554i
$711$	1.53217e8	+	1.92128e8i	0.426282	+	0.534541i
$712$	1.28175e8	−	2.92550e7i	0.355109	−	0.0810514i
$713$	2.73972e8	−	6.25323e7i	0.755853	−	0.172519i
$714$	2.15266e7	−	1.90667e7i	0.0591400	−	0.0523818i
$715$	−1.88890e8	+	8.27581e8i	−0.516762	+	2.26408i
$716$	−3.05848e8			−0.833234
$717$		−	3.25838e8i		−	0.883985i
$718$	2.43146e7	−	1.06529e8i	0.0656892	−	0.287803i
$719$	2.02854e8	+	4.21231e8i	0.545754	+	1.13327i	0.973355	+	0.229302i	$0.0736443\pi$
$719$	2.02854e8	+	4.21231e8i	0.545754	+	1.13327i	−0.427602	+	0.903967i	$0.640641\pi$
$720$	−6.92450e8	+	5.52210e8i	−1.85520	+	1.47947i
$721$	5.76378e7	−	2.98102e6i	0.153781	−	0.00795352i
$722$	−5.85864e7	+	7.34650e7i	−0.155663	+	0.195195i
$723$	−8.98587e7	+	3.93697e8i	−0.237764	+	1.04171i
$724$	−1.94696e8	−	1.55265e8i	−0.513027	−	0.409126i
$725$	−7.90977e7	+	3.80915e7i	−0.207563	+	0.0999571i
$726$	2.80964e8	−	2.24061e8i	0.734245	−	0.585541i
$727$	−1.42386e8	+	2.95668e8i	−0.370566	+	0.769488i	−0.999971	−	0.00758939i	$-0.997584\pi$
$727$	−1.42386e8	+	2.95668e8i	−0.370566	+	0.769488i	0.629405	+	0.777077i	$0.283298\pi$
$728$	8.37352e7	−	1.16914e8i	0.217027	−	0.303020i
$729$	−5.32731e8	+	2.56550e8i	−1.37507	+	0.662199i
$730$	1.64502e8	+	7.92201e7i	0.422866	+	0.203642i
$731$	−2.03515e7	+	4.64510e6i	−0.0521008	+	0.0118917i
$732$	8.40888e8	+	4.04951e8i	2.14390	+	1.03245i
$733$	−5.79526e8	−	4.62156e8i	−1.47150	−	1.17348i	−0.946639	−	0.322296i	$-0.895545\pi$
$733$	−5.79526e8	−	4.62156e8i	−1.47150	−	1.17348i	−0.524863	−	0.851187i	$-0.675883\pi$
$734$			1.35553e8i			0.342785i
$735$	−1.09180e9	+	1.13239e8i	−2.74968	+	0.285190i
$736$	4.93124e8			1.23687
$737$	4.39634e7	−	5.51284e7i	0.109822	−	0.137712i
$738$	4.67345e7	−	9.70453e7i	0.116270	−	0.241438i
$739$	−1.36714e8	−	5.98984e8i	−0.338751	−	1.48416i	−0.801672	−	0.597764i	$-0.796056\pi$
$739$	−1.36714e8	−	5.98984e8i	−0.338751	−	1.48416i	0.462921	−	0.886399i	$-0.346801\pi$
$740$	2.07625e8	−	4.31138e8i	0.512371	−	1.06395i
$741$	−9.07161e6	−	1.88374e7i	−0.0222961	−	0.0462984i
$742$	−7.72585e6	−	1.49379e8i	−0.0189119	−	0.365659i
$743$	2.25086e8	+	1.08396e8i	0.548759	+	0.264268i	0.687654	−	0.726039i	$-0.258641\pi$
$743$	2.25086e8	+	1.08396e8i	0.548759	+	0.264268i	−0.138895	+	0.990307i	$0.544355\pi$
$744$	8.89041e7	+	1.11482e8i	0.215875	+	0.270699i
$745$	−3.42629e8	−	7.11477e8i	−0.828620	−	1.72065i
$746$	−2.60746e7	+	3.26966e7i	−0.0628061	+	0.0787564i
$747$	4.94980e8	+	1.12976e8i	1.18748	+	0.271034i
$748$	−1.05822e8	−	8.43901e7i	−0.252854	−	0.201645i
$749$	1.92346e8	−	4.58613e8i	0.457760	−	1.09144i
$750$	1.43327e8	+	1.79726e8i	0.339737	+	0.426017i
$751$	−1.72450e6	+	830474.i	−0.00407139	+	0.00196068i	−0.435918	−	0.899986i	$-0.643576\pi$
$751$	−1.72450e6	+	830474.i	−0.00407139	+	0.00196068i	0.431847	+	0.901947i	$0.357862\pi$
$752$	2.36332e7	+	5.39412e6i	0.0555737	+	0.0126843i
$753$	2.99647e8			0.701818
$754$		−	1.06240e7i		−	0.0247841i
$755$	2.98568e8	+	6.81462e7i	0.693750	+	0.158344i
$756$	−2.89284e8	+	4.03908e8i	−0.669513	+	0.934796i
$757$	−1.55887e8	−	6.82985e8i	−0.359353	−	1.57443i	−0.754809	−	0.655945i	$-0.772270\pi$
$757$	−1.55887e8	−	6.82985e8i	−0.359353	−	1.57443i	0.395456	−	0.918485i	$-0.370587\pi$
$758$	−1.70932e7	−	7.48900e7i	−0.0392477	−	0.171956i
$759$	−1.83773e9	+	1.46554e9i	−4.20297	+	3.35176i
$760$	8.93419e6	+	1.12031e7i	0.0203523	+	0.0255210i
$761$	−1.46806e8	+	3.35075e7i	−0.333111	+	0.0760305i	−0.385805	−	0.922580i	$-0.626076\pi$
$761$	−1.46806e8	+	3.35075e7i	−0.333111	+	0.0760305i	0.0526941	+	0.998611i	$0.483219\pi$
$762$	8.36026e6	−	1.90818e6i	0.0188954	−	0.00431274i
$763$	−8.38930e7	−	1.46363e7i	−0.188865	−	0.0329502i
$764$	4.34113e7	−	1.90197e8i	0.0973470	−	0.426505i
$765$	2.48339e8			0.554702
$766$		−	2.43547e7i		−	0.0541872i
$767$	3.45026e7	−	1.51166e8i	0.0764656	−	0.335018i
$768$	−1.40440e8	−	2.91626e8i	−0.310032	−	0.643787i
$769$	3.60924e8	−	2.87827e8i	0.793664	−	0.632926i	−0.140374	−	0.990099i	$-0.544831\pi$
$769$	3.60924e8	−	2.87827e8i	0.793664	−	0.632926i	0.934038	+	0.357172i	$0.116259\pi$
$770$	−9.39422e7	−	3.31591e8i	−0.205773	−	0.726323i
$771$	5.04477e7	−	6.32594e7i	0.110072	−	0.138026i
$772$	−9.45994e7	+	4.14467e8i	−0.205606	+	0.900821i
$773$	4.41444e8	+	3.52040e8i	0.955735	+	0.762173i	0.971337	−	0.237705i	$-0.0763952\pi$
$773$	4.41444e8	+	3.52040e8i	0.955735	+	0.762173i	−0.0156024	+	0.999878i	$0.504967\pi$
$774$	−5.09327e7	+	2.45279e7i	−0.109843	+	0.0528977i
$775$	−2.80912e8	+	2.24020e8i	−0.603484	+	0.481263i
$776$	1.05016e8	−	2.18067e8i	0.224734	−	0.466665i
$777$	1.00692e8	−	5.77150e8i	0.214650	−	1.23034i
$778$	−5.81102e6	+	2.79844e6i	−0.0123400	+	0.00594261i
$779$	1.05783e7	+	5.09425e6i	0.0223771	+	0.0107762i
$780$	9.22371e8	−	2.10525e8i	1.94367	−	0.443629i
$781$	8.09340e8	+	3.89758e8i	1.69894	+	0.818166i
$782$	−3.20452e7	−	2.55552e7i	−0.0670105	−	0.0534391i
$783$			7.58546e7i			0.158014i
$784$	4.75018e7	−	3.90490e8i	0.0985738	−	0.810330i
$785$	−6.36276e8			−1.31533
$786$	2.91403e7	−	3.65407e7i	0.0600103	−	0.0752506i
$787$	−6.94918e7	+	1.44301e8i	−0.142564	+	0.296037i	−0.960009	−	0.279970i	$-0.909675\pi$
$787$	−6.94918e7	+	1.44301e8i	−0.142564	+	0.296037i	0.817445	+	0.576007i	$0.195390\pi$
$788$	1.38335e8	+	6.06084e8i	0.282717	+	1.23867i
$789$	−6.90890e8	+	1.43465e9i	−1.40662	+	2.92089i
$790$	3.50822e7	+	7.28489e7i	0.0711550	+	0.147755i
$791$	2.99066e8	−	7.13066e8i	0.604279	−	1.44079i
$792$	−6.82517e8	−	3.28683e8i	−1.37385	−	0.661609i
$793$	−3.66720e8	−	4.59853e8i	−0.735386	−	0.922145i
$794$	3.65951e7	+	7.59905e7i	0.0731074	+	0.151809i
$795$	1.26803e9	−	1.59006e9i	2.52365	−	3.16455i
$796$	4.24727e8	+	9.69411e7i	0.842113	+	0.192207i
$797$	5.24622e7	+	4.18372e7i	0.103627	+	0.0826395i	0.673932	−	0.738793i	$-0.264604\pi$
$797$	5.24622e7	+	4.18372e7i	0.103627	+	0.0826395i	−0.570306	+	0.821432i	$0.693175\pi$
$798$	6.90122e6	+	4.94275e6i	0.0135805	+	0.00972657i
$799$	−4.23788e6	−	5.31413e6i	−0.00830822	−	0.0104182i
$800$	−5.68055e8	+	2.73561e8i	−1.10948	+	0.534299i
$801$	6.55729e8	+	1.49666e8i	1.27593	+	0.291223i
$802$	7.90425e7			0.153228
$803$		−	1.05216e9i		−	2.03205i
$804$	−7.66178e7	−	1.74875e7i	−0.147422	−	0.0336481i
$805$	4.26458e8	+	1.50528e9i	0.817501	+	2.88556i
$806$	−9.67523e6	−	4.23899e7i	−0.0184780	−	0.0809576i
$807$	8.77621e7	+	3.84511e8i	0.166989	+	0.731625i
$808$	5.50529e7	−	4.39032e7i	0.104363	−	0.0832266i
$809$	−1.44922e8	−	1.81726e8i	−0.273708	−	0.343219i	0.625911	−	0.779894i	$-0.284727\pi$
$809$	−1.44922e8	−	1.81726e8i	−0.273708	−	0.343219i	−0.899619	+	0.436675i	$0.856156\pi$
$810$	6.26806e7	−	1.43064e7i	0.117945	−	0.0269201i
$811$	−7.87603e8	+	1.79765e8i	−1.47654	+	0.337010i	−0.883602	−	0.468239i	$-0.844889\pi$
$811$	−7.87603e8	+	1.79765e8i	−1.47654	+	0.337010i	−0.592937	+	0.805249i	$0.702032\pi$
$812$	−3.10270e7	−	5.67308e7i	−0.0579525	−	0.105962i
$813$	1.00495e8	−	4.40299e8i	0.187014	−	0.819362i
$814$	1.83949e8			0.341056
$815$		−	1.27355e9i		−	2.35258i
$816$	−3.11796e7	+	1.36607e8i	−0.0573852	+	0.251421i
$817$	−2.67363e6	−	5.55186e6i	−0.00490270	−	0.0101806i
$818$	1.09819e7	−	8.75775e6i	0.0200639	−	0.0160005i
$819$	6.45474e8	−	3.53020e8i	1.17497	−	0.642611i
$820$	−3.31252e8	+	4.15377e8i	−0.600782	+	0.753357i
$821$	−2.22909e8	+	9.76630e8i	−0.402809	+	1.76482i	0.213128	+	0.977024i	$0.431635\pi$
$821$	−2.22909e8	+	9.76630e8i	−0.402809	+	1.76482i	−0.615936	+	0.787796i	$0.711222\pi$
$822$	−2.32902e8	−	1.85733e8i	−0.419332	−	0.334406i
$823$	−2.88282e8	+	1.38829e8i	−0.517152	+	0.249047i	−0.674207	−	0.738543i	$-0.735514\pi$
$823$	−2.88282e8	+	1.38829e8i	−0.517152	+	0.249047i	0.157055	+	0.987590i	$0.449800\pi$
$824$	3.26343e7	−	2.60250e7i	0.0583300	−	0.0465166i
$825$	1.30397e9	−	2.70771e9i	2.32222	−	4.82215i
$826$	1.71595e7	+	6.05684e7i	0.0304484	+	0.107475i
$827$	7.82817e6	−	3.76985e6i	0.0138402	−	0.00666511i	−0.426951	−	0.904275i	$-0.640412\pi$
$827$	7.82817e6	−	3.76985e6i	0.0138402	−	0.00666511i	0.440791	+	0.897610i	$0.354698\pi$
$828$	1.49917e9	+	7.21961e8i	2.64094	+	1.27181i
$829$	5.15741e8	−	1.17715e8i	0.905249	−	0.206617i	0.255539	−	0.966799i	$-0.417747\pi$
$829$	5.15741e8	−	1.17715e8i	0.905249	−	0.206617i	0.649711	+	0.760182i	$0.274890\pi$
$830$	1.50509e8	+	7.24812e7i	0.263225	+	0.126763i
$831$	−1.24153e9	−	9.90088e8i	−2.16349	−	1.72532i
$832$			2.85370e8i			0.495494i
$833$	−7.86801e7	+	7.72993e7i	−0.136122	+	0.133734i
$834$	−3.31044e7			−0.0570673
$835$	−3.80022e8	+	4.76532e8i	−0.652753	+	0.818527i
$836$	1.73356e7	−	3.59978e7i	0.0296702	−	0.0616109i
$837$	6.90806e7	+	3.02662e8i	0.117809	+	0.516157i
$838$	−3.50471e7	+	7.27761e7i	−0.0595553	+	0.123668i
$839$	−2.60778e8	−	5.41511e8i	−0.441555	−	0.916899i	−0.996386	−	0.0849363i	$-0.972931\pi$
$839$	−2.60778e8	−	5.41511e8i	−0.441555	−	0.916899i	0.554831	−	0.831963i	$-0.312783\pi$
$840$	−5.94267e8	+	5.26358e8i	−1.00264	+	0.888062i
$841$	5.27022e8	+	2.53801e8i	0.886015	+	0.426682i
$842$	−2.73904e7	−	3.43465e7i	−0.0458841	−	0.0575369i
$843$	7.61556e8	+	1.58139e9i	1.27122	+	2.63971i
$844$	3.27772e8	−	4.11013e8i	0.545186	−	0.683642i
$845$	4.00937e8	+	9.15112e7i	0.664516	+	0.151672i
$846$	−1.43911e7	−	1.14765e7i	−0.0237675	−	0.0189540i
$847$	−1.03184e9	+	9.13926e8i	−1.69809	+	1.50405i
$848$	4.54425e8	+	5.69830e8i	0.745202	+	0.934454i
$849$	1.02038e9	−	4.91390e8i	1.66740	−	0.802976i
$850$	5.10913e7	+	1.16612e7i	0.0831936	+	0.0189884i
$851$	−8.35053e8			−1.35496
$852$		−	1.00119e9i		−	1.61882i
$853$	6.23065e8	+	1.42210e8i	1.00389	+	0.229131i	0.692707	−	0.721219i	$-0.256418\pi$
$853$	6.23065e8	+	1.42210e8i	1.00389	+	0.229131i	0.311183	+	0.950350i	$0.399275\pi$
$854$	2.20216e8	+	9.23605e7i	0.353570	+	0.148290i
$855$	1.63125e7	+	7.14696e7i	0.0260988	+	0.114346i
$856$	−8.00343e7	−	3.50653e8i	−0.127601	−	0.559058i
$857$	5.47085e8	−	4.36286e8i	0.869186	−	0.693152i	−0.0836971	−	0.996491i	$-0.526673\pi$
$857$	5.47085e8	−	4.36286e8i	0.869186	−	0.693152i	0.952883	+	0.303339i	$0.0981014\pi$
$858$	2.26754e8	+	2.84340e8i	0.358998	+	0.450170i
$859$	6.08220e8	−	1.38822e8i	0.959580	−	0.219018i	0.286080	−	0.958206i	$-0.407648\pi$
$859$	6.08220e8	−	1.38822e8i	0.959580	−	0.219018i	0.673499	+	0.739188i	$0.264790\pi$
$860$	2.71846e8	−	6.20471e7i	0.427394	−	0.0975498i
$861$	−2.51578e8	+	5.99841e8i	−0.394152	+	0.939781i
$862$	2.87233e7	−	1.25845e8i	0.0448449	−	0.196478i
$863$	−7.00239e8			−1.08947			−0.544733	−	0.838609i	$-0.683369\pi$
$863$	−7.00239e8			−1.08947			−0.544733	+	0.838609i	$0.683369\pi$
$864$			5.44764e8i			0.844631i
$865$	−2.75074e8	+	1.20518e9i	−0.425011	+	1.86210i
$866$	9.15839e7	+	1.90176e8i	0.141015	+	0.292821i
$867$	−8.12838e8	+	6.48217e8i	−1.24723	+	0.994633i
$868$	−1.75463e8	−	1.98101e8i	−0.268304	−	0.302920i
$869$	2.90511e8	−	3.64289e8i	0.442693	−	0.555120i
$870$	−1.30503e7	+	5.71769e7i	−0.0198181	+	0.0868286i
$871$	3.87211e7	+	3.08790e7i	0.0585994	+	0.0467315i
$872$	−5.54906e7	+	2.67229e7i	−0.0836893	+	0.0403026i
$873$	9.68092e8	−	7.72027e8i	1.45504	−	1.16035i
$874$	5.24962e6	−	1.09009e7i	0.00786309	−	0.0163279i
$875$	−5.84617e8	−	6.60043e8i	−0.872664	−	0.985254i
$876$	−1.05654e9	+	5.08804e8i	−1.57172	+	0.756899i
$877$	−7.28855e8	−	3.50998e8i	−1.08054	−	0.520363i	−0.193054	−	0.981188i	$-0.561839\pi$
$877$	−7.28855e8	−	3.50998e8i	−1.08054	−	0.520363i	−0.887491	+	0.460826i	$0.847553\pi$
$878$	2.24752e8	−	5.12982e7i	0.332063	−	0.0757911i
$879$	−2.00511e9	−	9.65609e8i	−2.95237	−	1.42179i
$880$	1.31294e9	+	1.04703e9i	1.92662	+	1.53643i
$881$			4.92280e8i			0.719920i	0.932968	+	0.359960i	$0.117210\pi$
$881$			4.92280e8i			0.719920i	−0.932968	+	0.359960i	$0.882790\pi$
$882$	−1.61149e8	+	2.51498e8i	−0.234867	+	0.366546i
$883$	−2.83296e8			−0.411489			−0.205745	−	0.978606i	$-0.565962\pi$
$883$	−2.83296e8			−0.411489			−0.205745	+	0.978606i	$0.565962\pi$
$884$	5.92739e7	−	7.43271e7i	0.0858039	−	0.107595i
$885$	−3.71378e8	+	7.71174e8i	−0.535780	+	1.11256i
$886$	2.03881e7	+	8.93262e7i	0.0293141	+	0.128433i
$887$	6.17722e7	−	1.28271e8i	0.0885161	−	0.183806i	−0.852011	−	0.523523i	$-0.824617\pi$
$887$	6.17722e7	−	1.28271e8i	0.0885161	−	0.183806i	0.940527	+	0.339718i	$0.110332\pi$
$888$	−1.83843e8	−	3.81753e8i	−0.262547	−	0.545185i
$889$	−3.16458e7	+	8.96551e6i	−0.0450413	+	0.0127606i
$890$	1.99388e8	+	9.60201e7i	0.282832	+	0.136205i
$891$	−2.30999e8	−	2.89663e8i	−0.326570	−	0.409506i
$892$	−5.32520e8	−	1.10579e9i	−0.750312	−	1.55804i
$893$	1.25099e6	−	1.56869e6i	0.00175670	−	0.00220284i
$894$	−3.29845e8	−	7.52851e7i	−0.461634	−	0.105365i
$895$	−8.31874e8	−	6.63397e8i	−1.16035	−	0.925347i
$896$	−2.93285e8	−	5.36252e8i	−0.407724	−	0.745496i
$897$	−1.02937e9	−	1.29078e9i	−1.42624	−	1.78845i
$898$	−1.84821e8	+	8.90052e7i	−0.255225	+	0.122910i
$899$	−3.93917e7	−	8.99091e6i	−0.0542158	−	0.0123744i
$900$	−2.12747e9			−2.91835
$901$		−	2.04363e8i		−	0.279401i
$902$	−1.99110e8	−	4.54456e7i	−0.271315	−	0.0619259i
$903$	2.99516e8	−	1.63810e8i	0.406777	−	0.222473i
$904$	−1.24440e8	−	5.45207e8i	−0.168444	−	0.737999i
$905$	−1.92776e8	−	8.44605e8i	−0.260080	−	1.13948i
$906$	1.02582e8	−	8.18065e7i	0.137939	−	0.110003i
$907$	7.68349e8	+	9.63479e8i	1.02976	+	1.29128i	0.955799	+	0.294019i	$0.0949930\pi$
$907$	7.68349e8	+	9.63479e8i	1.02976	+	1.29128i	0.0739623	+	0.997261i	$0.476436\pi$
$908$	−1.11151e9	+	2.53695e8i	−1.48476	+	0.338887i
$909$	3.51206e8	−	8.01606e7i	0.467596	−	0.106726i
$910$	2.32903e8	−	6.59831e7i	0.309065	−	0.0875606i
$911$	−1.37045e8	+	6.00434e8i	−0.181263	+	0.794164i	0.799768	+	0.600310i	$0.204956\pi$
$911$	−1.37045e8	+	6.00434e8i	−0.181263	+	0.794164i	−0.981030	+	0.193854i	$0.937901\pi$
$912$	−4.13622e7			−0.0545280
$913$		−	9.62657e8i		−	1.26491i
$914$	−4.23860e7	+	1.85705e8i	−0.0555117	+	0.243213i
$915$	1.40877e9	+	2.92534e9i	1.83898	+	3.81868i
$916$	−5.06556e7	+	4.03965e7i	−0.0659084	+	0.0525602i
$917$	−1.04382e8	+	1.45742e8i	−0.135369	+	0.189006i
$918$	2.82313e7	−	3.54010e7i	0.0364925	−	0.0457601i
$919$	1.66897e8	−	7.31222e8i	0.215031	−	0.942112i	−0.746060	−	0.665879i	$-0.768057\pi$
$919$	1.66897e8	−	7.31222e8i	0.215031	−	0.942112i	0.961091	−	0.276233i	$-0.0890862\pi$
$920$	8.84645e8	+	7.05481e8i	1.13607	+	0.905986i
$921$	−2.89633e8	+	1.39480e8i	−0.370739	+	0.178539i
$922$	−1.68248e8	+	1.34173e8i	−0.214663	+	0.171188i
$923$	−2.73758e8	+	5.68464e8i	−0.348146	+	0.722933i
$924$	2.04125e9	+	8.56117e8i	2.58750	+	1.08522i
$925$	9.61940e8	−	4.63246e8i	1.21541	−	0.585311i
$926$	9.60942e7	+	4.62765e7i	0.121022	+	0.0582811i
$927$	2.08188e8	−	4.75176e7i	0.261346	−	0.0596506i
$928$	−6.38800e7	−	3.07630e7i	−0.0799321	−	0.0384933i
$929$	−5.74872e8	−	4.58445e8i	−0.717008	−	0.571795i	0.195574	−	0.980689i	$-0.437343\pi$
$929$	−5.74872e8	−	4.58445e8i	−0.717008	−	0.571795i	−0.912582	+	0.408894i	$0.865915\pi$
$930$			2.40022e8i			0.298403i
$931$	−2.74142e7	−	1.75659e7i	−0.0339725	−	0.0217681i
$932$	2.82633e8			0.349121
$933$	−7.33287e8	+	9.19513e8i	−0.902878	+	1.13217i
$934$	−3.01034e7	+	6.25104e7i	−0.0369467	+	0.0767205i
$935$	−1.04778e8	−	4.59064e8i	−0.128185	−	0.561614i
$936$	2.30860e8	−	4.79386e8i	0.281528	−	0.584599i
$937$	4.21781e8	+	8.75836e8i	0.512705	+	1.06464i	0.983249	+	0.182267i	$0.0583435\pi$
$937$	4.21781e8	+	8.75836e8i	0.512705	+	1.06464i	−0.470544	+	0.882377i	$0.655942\pi$
$938$	−1.98086e7	−	3.45588e6i	−0.0240018	−	0.00418745i
$939$	3.89066e8	+	1.87364e8i	0.469922	+	0.226303i
$940$	5.66077e7	+	7.09838e7i	0.0681541	+	0.0854625i
$941$	4.72949e8	+	9.82089e8i	0.567604	+	1.17864i	0.965304	+	0.261127i	$0.0840941\pi$
$941$	4.72949e8	+	9.82089e8i	0.567604	+	1.17864i	−0.397700	+	0.917515i	$0.630192\pi$
$942$	−1.69966e8	+	2.13131e8i	−0.203334	+	0.254972i
$943$	9.03876e8	+	2.06304e8i	1.07789	+	0.246021i
$944$	−2.39821e8	−	1.91251e8i	−0.285083	−	0.227346i
$945$	−1.66291e9	+	4.71116e8i	−1.97049	+	0.558255i
$946$	6.68301e7	+	8.38023e7i	0.0789403	+	0.0989880i
$947$	−1.36704e9	+	6.58332e8i	−1.60965	+	0.775166i	−0.999849	−	0.0173892i	$-0.994465\pi$
$947$	−1.36704e9	+	6.58332e8i	−1.60965	+	0.775166i	−0.609800	+	0.792555i	$0.708750\pi$
$948$	−5.06292e8	−	1.15558e8i	−0.594259	−	0.135636i
$949$	7.39016e8			0.864680
$950$			1.54696e7i			0.0180430i
$951$	9.64526e8	+	2.20147e8i	1.12143	+	0.255959i
$952$	−1.37100e7	+	7.85835e7i	−0.0158901	+	0.0910795i
$953$	7.90664e7	+	3.46412e8i	0.0913510	+	0.400235i	0.999844	−	0.0176654i	$-0.00562335\pi$
$953$	7.90664e7	+	3.46412e8i	0.0913510	+	0.400235i	−0.908493	+	0.417900i	$0.862766\pi$
$954$	−1.23150e8	−	5.39556e8i	−0.141837	−	0.621429i
$955$	5.30620e8	−	4.23155e8i	0.609219	−	0.485836i
$956$	2.72684e8	+	3.41935e8i	0.312094	+	0.391354i
$957$	3.29488e8	−	7.52036e7i	0.375928	−	0.0858030i
$958$	2.56066e8	−	5.84453e7i	0.291243	−	0.0664742i
$959$	9.28923e8	+	6.65307e8i	1.05323	+	0.754339i
$960$	3.50543e8	−	1.53583e9i	0.396212	−	1.73592i
$961$	7.22141e8			0.813677
$962$			1.29202e8i			0.145126i
$963$	4.09448e8	−	1.79391e9i	0.458480	−	2.00873i
$964$	−2.35175e8	−	4.88345e8i	−0.262518	−	0.545125i
$965$	−1.15630e9	+	9.22116e8i	−1.28673	+	1.02613i
$966$	6.18136e8	+	2.59251e8i	0.685729	+	0.287601i
$967$	−8.08889e8	+	1.01431e9i	−0.894560	+	1.12174i	0.0974066	+	0.995245i	$0.468945\pi$
$967$	−8.08889e8	+	1.01431e9i	−0.894560	+	1.12174i	−0.991967	+	0.126498i	$0.959626\pi$
$968$	−2.21828e8	+	9.71890e8i	−0.244562	+	1.07150i
$969$	9.06748e6	+	7.23107e6i	0.00996587	+	0.00794751i
$970$	3.67071e8	−	1.76772e8i	0.402193	−	0.193686i
$971$	−6.30268e8	+	5.02622e8i	−0.688442	+	0.549014i	−0.904029	−	0.427470i	$-0.859405\pi$
$971$	−6.30268e8	+	5.02622e8i	−0.688442	+	0.549014i	0.215587	+	0.976485i	$0.430833\pi$
$972$	2.78982e8	−	5.79312e8i	0.303793	−	0.630832i
$973$	1.26806e8	−	6.55839e6i	0.137658	−	0.00711965i
$974$	6.14337e7	−	2.95849e7i	0.0664859	−	0.0320179i
$975$	1.90184e9	+	9.15879e8i	2.05192	+	0.988154i
$976$	−1.13441e9	+	2.58923e8i	−1.22017	+	0.278497i
$977$	−4.09684e8	−	1.97294e8i	−0.439304	−	0.211558i	0.201140	−	0.979563i	$-0.435535\pi$
$977$	−4.09684e8	−	1.97294e8i	−0.439304	−	0.211558i	−0.640444	+	0.768005i	$0.721250\pi$
$978$	−4.26597e8	−	3.40200e8i	−0.456038	−	0.363678i
$979$		−	1.27529e9i		−	1.35913i
$980$	1.05097e9	−	1.03253e9i	1.11664	−	1.09704i
$981$	−3.15088e8			−0.333753
$982$	1.45149e8	−	1.82012e8i	0.153278	−	0.192205i
$983$	5.94731e8	−	1.23497e9i	0.626123	−	1.30016i	−0.310751	−	0.950491i	$-0.600580\pi$
$983$	5.94731e8	−	1.23497e9i	0.626123	−	1.30016i	0.936874	−	0.349667i	$-0.113705\pi$
$984$	1.04681e8	+	4.58635e8i	0.109870	+	0.481374i
$985$	−9.38365e8	+	1.94853e9i	−0.981891	+	2.03892i
$986$	2.55695e6	+	5.30956e6i	0.00266742	+	0.00553896i
$987$	9.03702e7	+	6.47243e7i	0.0939883	+	0.0673156i
$988$	2.52842e7	+	1.21762e7i	0.0262167	+	0.0126253i
$989$	−3.03380e8	−	3.80427e8i	−0.313616	−	0.393263i
$990$	−5.53269e8	−	1.14887e9i	−0.570205	−	1.18404i
$991$	5.70984e8	−	7.15991e8i	0.586682	−	0.735676i	−0.396555	−	0.918011i	$-0.629794\pi$
$991$	5.70984e8	−	7.15991e8i	0.586682	−	0.735676i	0.983236	+	0.182335i	$0.0583657\pi$
$992$	−2.82899e8	−	6.45699e7i	−0.289799	−	0.0661447i
$993$	−1.59583e9	−	1.27263e9i	−1.62982	−	1.29974i
$994$	−1.32312e7	−	2.55825e8i	−0.0134723	−	0.260485i
$995$	9.44941e8	+	1.18492e9i	0.959258	+	1.20287i
$996$	−9.66667e8	+	4.65522e8i	−0.978360	+	0.471153i
$997$	2.13284e8	+	4.86808e7i	0.215216	+	0.0491216i	0.328769	−	0.944410i	$-0.393366\pi$
$997$	2.13284e8	+	4.86808e7i	0.215216	+	0.0491216i	−0.113554	+	0.993532i	$0.536223\pi$
$998$	−4.33913e8			−0.436527
$999$		−	9.22499e8i		−	0.925272i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.7.f.a.6.12	✓	162
49.41	odd	14	inner	49.7.f.a.41.12	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.7.f.a.6.12	✓	162	1.1	even	1	trivial
49.7.f.a.41.12	yes	162	49.41	odd	14	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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	49.f (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24733 + 1.56411i) q^{2} +(19.3946 - 40.2732i) q^{3} +(13.3507 + 58.4935i) q^{4} +(-90.5621 + 188.054i) q^{5} +(38.8002 + 80.5694i) q^{6} +(-164.585 - 300.933i) q^{7} +(-223.500 - 107.632i) q^{8} +(-791.260 - 992.209i) q^{9} +(-181.176 - 376.215i) q^{10} +(-1500.29 + 1881.31i) q^{11} +(2614.65 + 596.777i) q^{12} +(-1321.39 - 1053.78i) q^{13} +(675.985 + 117.935i) q^{14} +(5817.14 + 7294.46i) q^{15} +(-3012.46 + 1450.73i) q^{16} +(914.015 + 208.618i) q^{17} +2538.89 q^{18} +276.749i q^{19} +(-12209.0 - 2786.63i) q^{20} +(-15311.6 + 791.915i) q^{21} +(-1071.20 - 4693.23i) q^{22} +(4862.80 + 21305.3i) q^{23} +(-8669.36 + 6913.59i) q^{24} +(-17420.8 - 21845.0i) q^{25} +(3296.44 - 752.390i) q^{26} +(-23536.4 + 5372.03i) q^{27} +(15405.3 - 13644.8i) q^{28} +(699.174 - 3063.28i) q^{29} -18665.2 q^{30} -12859.3i q^{31} +(5021.25 - 21999.5i) q^{32} +(46668.8 + 96908.7i) q^{33} +(-1466.38 + 1169.40i) q^{34} +(71496.9 - 3697.81i) q^{35} +(47473.8 - 59530.3i) q^{36} +(-8502.95 + 37253.9i) q^{37} +(-432.865 - 345.198i) q^{38} +(-68066.8 + 32779.2i) q^{39} +(40481.2 - 32282.7i) q^{40} +(18407.5 - 38223.5i) q^{41} +(17860.1 - 24936.8i) q^{42} +(-20061.0 + 9660.87i) q^{43} +(-130074. - 62640.4i) q^{44} +(258247. - 58943.2i) q^{45} +(-39389.3 - 18968.9i) q^{46} +(-5668.28 - 4520.30i) q^{47} +149458. i q^{48} +(-63472.4 + 99058.3i) q^{49} +55897.6 q^{50} +(26128.7 - 32764.3i) q^{51} +(43997.4 - 91361.5i) q^{52} +(-48505.6 - 212517. i) q^{53} +(20955.3 - 43514.2i) q^{54} +(-217918. - 452511. i) q^{55} +(4394.80 + 84973.1i) q^{56} +(11145.6 + 5367.42i) q^{57} +(3919.20 + 4914.52i) q^{58} +(39804.9 + 82655.7i) q^{59} +(-349015. + 437651. i) q^{60} +(339281. + 77438.7i) q^{61} +(20113.4 + 16039.9i) q^{62} +(-168359. + 401419. i) q^{63} +(-105274. - 132009. i) q^{64} +(317835. - 153061. i) q^{65} +(-209787. - 47882.6i) q^{66} -29303.3 q^{67} +56249.1i q^{68} +(952346. + 217367. i) q^{69} +(-83396.8 + 116441. i) q^{70} +(-83070.3 - 363955. i) q^{71} +(70053.2 + 306923. i) q^{72} +(-341860. + 272624. i) q^{73} +(-47663.0 - 59767.5i) q^{74} +(-1.21764e6 + 277918. i) q^{75} +(-16188.0 + 3694.80i) q^{76} +(813073. + 141852. i) q^{77} +(33631.8 - 147350. i) q^{78} -193636. q^{79} -697887. i q^{80} +(-34261.4 + 150109. i) q^{81} +(36825.4 + 76468.8i) q^{82} +(-312780. + 249433. i) q^{83} +(-250743. - 885056. i) q^{84} +(-122007. + 152991. i) q^{85} +(9912.14 - 43427.9i) q^{86} +(-109808. - 87569.1i) q^{87} +(537803. - 258992. i) q^{88} +(-414358. + 330439. i) q^{89} +(-229927. + 477448. i) q^{90} +(-99634.0 + 571086. i) q^{91} +(-1.18130e6 + 568884. i) q^{92} +(-517887. - 249401. i) q^{93} +(14140.5 - 3227.47i) q^{94} +(-52043.7 - 25062.9i) q^{95} +(-788607. - 628893. i) q^{96} +975693. i q^{97} +(-75766.6 - 222836. i) q^{98} +3.05377e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q - 5 q^{2} - 7 q^{3} - 837 q^{4} - 7 q^{5} - 791 q^{6} + 70 q^{7} - 843 q^{8} + 2990 q^{9} - 7 q^{10} + 1171 q^{11} - 13482 q^{12} - 7 q^{13} + 22533 q^{14} + 6181 q^{15} - 17901 q^{16} - 3143 q^{17}+ \cdots + 4449580 q^{99}+O(q^{100}) \) 162 * q - 5 * q^2 - 7 * q^3 - 837 * q^4 - 7 * q^5 - 791 * q^6 + 70 * q^7 - 843 * q^8 + 2990 * q^9 - 7 * q^10 + 1171 * q^11 - 13482 * q^12 - 7 * q^13 + 22533 * q^14 + 6181 * q^15 - 17901 * q^16 - 3143 * q^17 - 22692 * q^18 + 50169 * q^20 + 28553 * q^21 - 33057 * q^22 - 49677 * q^23 - 119077 * q^24 + 30038 * q^25 + 59577 * q^26 + 11753 * q^27 + 42994 * q^28 + 80383 * q^29 + 27328 * q^30 + 253875 * q^32 - 7 * q^33 + 54677 * q^34 - 74067 * q^35 - 193099 * q^36 + 118463 * q^37 - 121079 * q^38 - 304143 * q^39 - 702079 * q^40 - 58023 * q^41 - 1137479 * q^42 + 93963 * q^43 + 352505 * q^44 + 1333577 * q^45 + 782877 * q^46 + 408261 * q^47 - 149338 * q^49 + 1164004 * q^50 - 911743 * q^51 + 721273 * q^52 - 992325 * q^53 - 576646 * q^54 - 1502935 * q^55 + 1368514 * q^56 + 116032 * q^57 + 2610717 * q^58 + 24493 * q^59 - 1027131 * q^60 + 563101 * q^61 - 262199 * q^62 - 966154 * q^63 - 2839067 * q^64 - 140287 * q^65 - 1523319 * q^66 - 1313660 * q^67 + 2216753 * q^69 + 1806959 * q^70 + 1031011 * q^71 - 3123354 * q^72 - 846727 * q^73 + 1270357 * q^74 + 873173 * q^75 + 5463990 * q^76 + 1565235 * q^77 + 1006005 * q^78 + 82420 * q^79 + 2259538 * q^81 - 7672672 * q^82 - 3860031 * q^83 - 9104942 * q^84 + 1596833 * q^85 + 224039 * q^86 + 2590525 * q^87 + 4179421 * q^88 + 5417433 * q^89 + 6759578 * q^90 - 6163507 * q^91 - 7060306 * q^92 + 1903160 * q^93 + 4029998 * q^94 + 2115400 * q^95 + 957950 * q^96 - 1546783 * q^98 + 4449580 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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