LMFDB - Embedded newform 26.6.c.b.9.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [26,6,Mod(3,26)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("26.3"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(26, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	26.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.16997931514$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 715x^{6} - 6060x^{5} + 441025x^{4} - 2166450x^{3} + 59373900x^{2} + 212706000x + 4928040000 $ x^8 + 715x^6 - 6060x^5 + 441025x^4 - 2166450x^3 + 59373900x^2 + 212706000x + 4928040000
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			9.3
Root			$-4.17141 + 7.22509i$ of defining polynomial
Character	$\chi$	$=$	26.9
Dual form			26.6.c.b.3.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.00000 - 3.46410i) q^{2} +(4.17141 - 7.22509i) q^{3} +(-8.00000 - 13.8564i) q^{4} +52.7082 q^{5} +(-16.6856 - 28.9003i) q^{6} +(-121.202 - 209.927i) q^{7} -64.0000 q^{8} +(86.6987 + 150.167i) q^{9} +(105.416 - 182.587i) q^{10} +(-56.1732 + 97.2949i) q^{11} -133.485 q^{12} +(457.803 - 402.131i) q^{13} -969.613 q^{14} +(219.867 - 380.822i) q^{15} +(-128.000 + 221.703i) q^{16} +(989.104 + 1713.18i) q^{17} +693.590 q^{18} +(983.557 + 1703.57i) q^{19} +(-421.666 - 730.347i) q^{20} -2022.33 q^{21} +(224.693 + 389.179i) q^{22} +(-377.996 + 654.708i) q^{23} +(-266.970 + 462.406i) q^{24} -346.840 q^{25} +(-477.415 - 2390.14i) q^{26} +3473.93 q^{27} +(-1939.23 + 3358.84i) q^{28} +(1689.57 - 2926.42i) q^{29} +(-879.470 - 1523.29i) q^{30} -6283.75 q^{31} +(512.000 + 886.810i) q^{32} +(468.643 + 811.713i) q^{33} +7912.83 q^{34} +(-6388.33 - 11064.9i) q^{35} +(1387.18 - 2402.67i) q^{36} +(2929.16 - 5073.45i) q^{37} +7868.46 q^{38} +(-995.746 - 4985.12i) q^{39} -3373.33 q^{40} +(-2445.84 + 4236.32i) q^{41} +(-4044.65 + 7005.54i) q^{42} +(-2458.74 - 4258.66i) q^{43} +1797.54 q^{44} +(4569.74 + 7915.02i) q^{45} +(1511.98 + 2618.83i) q^{46} +5461.12 q^{47} +(1067.88 + 1849.62i) q^{48} +(-20976.2 + 36331.8i) q^{49} +(-693.681 + 1201.49i) q^{50} +16503.8 q^{51} +(-9234.51 - 3126.46i) q^{52} -17869.0 q^{53} +(6947.85 - 12034.0i) q^{54} +(-2960.79 + 5128.24i) q^{55} +(7756.91 + 13435.4i) q^{56} +16411.3 q^{57} +(-6758.27 - 11705.7i) q^{58} +(-9053.99 - 15682.0i) q^{59} -7035.76 q^{60} +(18814.6 + 32587.8i) q^{61} +(-12567.5 + 21767.6i) q^{62} +(21016.1 - 36400.9i) q^{63} +4096.00 q^{64} +(24130.0 - 21195.6i) q^{65} +3749.14 q^{66} +(11862.8 - 20547.0i) q^{67} +(15825.7 - 27410.8i) q^{68} +(3153.55 + 5462.11i) q^{69} -51106.6 q^{70} +(1169.64 + 2025.87i) q^{71} +(-5548.72 - 9610.66i) q^{72} -52556.8 q^{73} +(-11716.6 - 20293.8i) q^{74} +(-1446.81 + 2505.95i) q^{75} +(15736.9 - 27257.1i) q^{76} +27233.1 q^{77} +(-19260.5 - 6520.87i) q^{78} -80150.0 q^{79} +(-6746.66 + 11685.6i) q^{80} +(-6576.64 + 11391.1i) q^{81} +(9783.36 + 16945.3i) q^{82} +86151.4 q^{83} +(16178.6 + 28022.2i) q^{84} +(52133.9 + 90298.6i) q^{85} -19669.9 q^{86} +(-14095.7 - 24414.6i) q^{87} +(3595.09 - 6226.87i) q^{88} +(55321.3 - 95819.3i) q^{89} +36557.9 q^{90} +(-139905. - 47366.6i) q^{91} +12095.9 q^{92} +(-26212.1 + 45400.7i) q^{93} +(10922.2 - 18917.9i) q^{94} +(51841.6 + 89792.3i) q^{95} +8543.04 q^{96} +(1078.06 + 1867.25i) q^{97} +(83904.7 + 145327. i) q^{98} -19480.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{2} - 64 q^{4} - 24 q^{5} + 126 q^{7} - 512 q^{8} - 458 q^{9} - 48 q^{10} + 446 q^{11} + 1384 q^{13} + 1008 q^{14} - 790 q^{15} - 1024 q^{16} - 500 q^{17} - 3664 q^{18} + 4048 q^{19} + 192 q^{20}+ \cdots - 533984 q^{99}+O(q^{100}) $ 8 * q + 16 * q^2 - 64 * q^4 - 24 * q^5 + 126 * q^7 - 512 * q^8 - 458 * q^9 - 48 * q^10 + 446 * q^11 + 1384 * q^13 + 1008 * q^14 - 790 * q^15 - 1024 * q^16 - 500 * q^17 - 3664 * q^18 + 4048 * q^19 + 192 * q^20 + 2300 * q^21 - 1784 * q^22 + 296 * q^23 + 19788 * q^25 + 1112 * q^26 - 18180 * q^27 + 2016 * q^28 - 4114 * q^29 + 3160 * q^30 - 25036 * q^31 + 4096 * q^32 - 9730 * q^33 - 4000 * q^34 + 2340 * q^35 - 7328 * q^36 + 16258 * q^37 + 32384 * q^38 + 2460 * q^39 + 1536 * q^40 - 6056 * q^41 + 4600 * q^42 + 4818 * q^43 - 14272 * q^44 + 24964 * q^45 - 1184 * q^46 - 43060 * q^47 - 95094 * q^49 + 39576 * q^50 + 129440 * q^51 - 17696 * q^52 - 30032 * q^53 - 36360 * q^54 - 3360 * q^55 - 8064 * q^56 + 37940 * q^57 + 16456 * q^58 - 6734 * q^59 + 25280 * q^60 + 6978 * q^61 - 50072 * q^62 + 175812 * q^63 + 32768 * q^64 - 149818 * q^65 - 77840 * q^66 + 24464 * q^67 - 8000 * q^68 + 115290 * q^69 + 18720 * q^70 - 18552 * q^71 + 29312 * q^72 - 84596 * q^73 - 65032 * q^74 - 218210 * q^75 + 64768 * q^76 + 358604 * q^77 - 202680 * q^78 - 529664 * q^79 + 3072 * q^80 + 64624 * q^81 + 24224 * q^82 + 139800 * q^83 - 18400 * q^84 + 171548 * q^85 + 38544 * q^86 - 39420 * q^87 - 28544 * q^88 + 154642 * q^89 + 199712 * q^90 - 65074 * q^91 - 9472 * q^92 + 331860 * q^93 - 86120 * q^94 + 284278 * q^95 + 206498 * q^97 + 380376 * q^98 - 533984 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$3$	4.17141	−	7.22509i	0.267596	−	0.463490i	−0.700645	−	0.713510i	$-0.747104\pi$
$3$	4.17141	−	7.22509i	0.267596	−	0.463490i	0.968240	+	0.250021i	$0.0804375\pi$
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	52.7082			0.942874			0.471437	−	0.881900i	$-0.343735\pi$
$5$	52.7082			0.942874			0.471437	+	0.881900i	$0.343735\pi$
$6$	−16.6856	−	28.9003i	−0.189219	−	0.327737i
$7$	−121.202	−	209.927i	−0.934896	−	1.61929i	−0.774819	−	0.632183i	$-0.782159\pi$
$7$	−121.202	−	209.927i	−0.934896	−	1.61929i	−0.160078	−	0.987104i	$-0.551174\pi$
$8$	−64.0000			−0.353553
$9$	86.6987	+	150.167i	0.356785	+	0.617970i
$10$	105.416	−	182.587i	0.333356	−	0.577390i
$11$	−56.1732	+	97.2949i	−0.139974	+	0.242442i	−0.927487	−	0.373856i	$-0.878035\pi$
$11$	−56.1732	+	97.2949i	−0.139974	+	0.242442i	0.787512	+	0.616299i	$0.211369\pi$
$12$	−133.485			−0.267596
$13$	457.803	−	402.131i	0.751312	−	0.659947i
$13$	457.803	−	402.131i	0.751312	−	0.659947i
$14$	−969.613			−1.32214
$15$	219.867	−	380.822i	0.252309	−	0.437012i
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	989.104	+	1713.18i	0.830079	+	1.43774i	0.897975	+	0.440047i	$0.145038\pi$
$17$	989.104	+	1713.18i	0.830079	+	1.43774i	−0.0678955	+	0.997692i	$0.521628\pi$
$18$	693.590			0.504570
$19$	983.557	+	1703.57i	0.625051	+	1.08262i	0.988531	+	0.151018i	$0.0482553\pi$
$19$	983.557	+	1703.57i	0.625051	+	1.08262i	−0.363480	+	0.931602i	$0.618411\pi$
$20$	−421.666	−	730.347i	−0.235718	−	0.408276i
$21$	−2022.33			−1.00070
$22$	224.693	+	389.179i	0.0989766	+	0.171433i
$23$	−377.996	+	654.708i	−0.148994	+	0.258065i	−0.930856	−	0.365387i	$-0.880937\pi$
$23$	−377.996	+	654.708i	−0.148994	+	0.258065i	0.781862	+	0.623451i	$0.214270\pi$
$24$	−266.970	+	462.406i	−0.0946094	+	0.163868i
$25$	−346.840			−0.110989
$26$	−477.415	−	2390.14i	−0.138504	−	0.693409i
$27$	3473.93			0.917088
$28$	−1939.23	+	3358.84i	−0.467448	+	0.809644i
$29$	1689.57	−	2926.42i	0.373062	−	0.646162i	−0.616973	−	0.786984i	$-0.711641\pi$
$29$	1689.57	−	2926.42i	0.373062	−	0.646162i	0.990035	+	0.140822i	$0.0449746\pi$
$30$	−879.470	−	1523.29i	−0.178409	−	0.309014i
$31$	−6283.75			−1.17440			−0.587199	−	0.809443i	$-0.699769\pi$
$31$	−6283.75			−1.17440			−0.587199	+	0.809443i	$0.699769\pi$
$32$	512.000	+	886.810i	0.0883883	+	0.153093i
$33$	468.643	+	811.713i	0.0749129	+	0.129753i
$34$	7912.83			1.17391
$35$	−6388.33	−	11064.9i	−0.881489	−	1.52678i
$36$	1387.18	−	2402.67i	0.178392	−	0.308985i
$37$	2929.16	−	5073.45i	0.351754	−	0.609255i	−0.634803	−	0.772674i	$-0.718919\pi$
$37$	2929.16	−	5073.45i	0.351754	−	0.609255i	0.986557	+	0.163419i	$0.0522521\pi$
$38$	7868.46			0.883956
$39$	−995.746	−	4985.12i	−0.104830	−	0.524824i
$40$	−3373.33			−0.333356
$41$	−2445.84	+	4236.32i	−0.227231	+	0.393576i	−0.956987	−	0.290132i	$-0.906301\pi$
$41$	−2445.84	+	4236.32i	−0.227231	+	0.393576i	0.729755	+	0.683708i	$0.239634\pi$
$42$	−4044.65	+	7005.54i	−0.353800	+	0.612799i
$43$	−2458.74	−	4258.66i	−0.202788	−	0.351239i	0.746638	−	0.665231i	$-0.231667\pi$
$43$	−2458.74	−	4258.66i	−0.202788	−	0.351239i	−0.949426	+	0.313992i	$0.898333\pi$
$44$	1797.54			0.139974
$45$	4569.74	+	7915.02i	0.336403	+	0.582667i
$46$	1511.98	+	2618.83i	0.105354	+	0.182479i
$47$	5461.12			0.360609			0.180305	−	0.983611i	$-0.442292\pi$
$47$	5461.12			0.360609			0.180305	+	0.983611i	$0.442292\pi$
$48$	1067.88	+	1849.62i	0.0668990	+	0.115872i
$49$	−20976.2	+	36331.8i	−1.24806	+	2.16171i
$50$	−693.681	+	1201.49i	−0.0392405	+	0.0679666i
$51$	16503.8			0.888503
$52$	−9234.51	−	3126.46i	−0.473593	−	0.160341i
$53$	−17869.0			−0.873795			−0.436898	−	0.899511i	$-0.643923\pi$
$53$	−17869.0			−0.873795			−0.436898	+	0.899511i	$0.643923\pi$
$54$	6947.85	−	12034.0i	0.324240	−	0.561600i
$55$	−2960.79	+	5128.24i	−0.131978	+	0.228592i
$56$	7756.91	+	13435.4i	0.330536	+	0.572505i
$57$	16411.3			0.669044
$58$	−6758.27	−	11705.7i	−0.263794	−	0.456905i
$59$	−9053.99	−	15682.0i	−0.338618	−	0.586503i	0.645555	−	0.763714i	$-0.276626\pi$
$59$	−9053.99	−	15682.0i	−0.338618	−	0.586503i	−0.984173	+	0.177210i	$0.943293\pi$
$60$	−7035.76			−0.252309
$61$	18814.6	+	32587.8i	0.647395	+	1.12132i	0.983743	+	0.179583i	$0.0574749\pi$
$61$	18814.6	+	32587.8i	0.647395	+	1.12132i	−0.336348	+	0.941738i	$0.609192\pi$
$62$	−12567.5	+	21767.6i	−0.415212	+	0.719168i
$63$	21016.1	−	36400.9i	0.667114	−	1.15548i
$64$	4096.00			0.125000
$65$	24130.0	−	21195.6i	0.708393	−	0.622247i
$66$	3749.14			0.105943
$67$	11862.8	−	20547.0i	0.322850	−	0.559193i	−0.658225	−	0.752821i	$-0.728692\pi$
$67$	11862.8	−	20547.0i	0.322850	−	0.559193i	0.981075	+	0.193629i	$0.0620257\pi$
$68$	15825.7	−	27410.8i	0.415040	−	0.718870i
$69$	3153.55	+	5462.11i	0.0797401	+	0.138114i
$70$	−51106.6			−1.24661
$71$	1169.64	+	2025.87i	0.0275363	+	0.0476942i	0.879465	−	0.475963i	$-0.157900\pi$
$71$	1169.64	+	2025.87i	0.0275363	+	0.0476942i	−0.851929	+	0.523658i	$0.824567\pi$
$72$	−5548.72	−	9610.66i	−0.126143	−	0.218485i
$73$	−52556.8			−1.15431			−0.577154	−	0.816636i	$-0.695837\pi$
$73$	−52556.8			−1.15431			−0.577154	+	0.816636i	$0.695837\pi$
$74$	−11716.6	−	20293.8i	−0.248727	−	0.430809i
$75$	−1446.81	+	2505.95i	−0.0297002	+	0.0514422i
$76$	15736.9	−	27257.1i	0.312526	−	0.541310i
$77$	27233.1			0.523445
$78$	−19260.5	−	6520.87i	−0.358451	−	0.121358i
$79$	−80150.0			−1.44489			−0.722447	−	0.691426i	$-0.756983\pi$
$79$	−80150.0			−1.44489			−0.722447	+	0.691426i	$0.756983\pi$
$80$	−6746.66	+	11685.6i	−0.117859	+	0.204138i
$81$	−6576.64	+	11391.1i	−0.111376	+	0.192909i
$82$	9783.36	+	16945.3i	0.160677	+	0.278300i
$83$	86151.4			1.37267			0.686337	−	0.727284i	$-0.259218\pi$
$83$	86151.4			1.37267			0.686337	+	0.727284i	$0.259218\pi$
$84$	16178.6	+	28022.2i	0.250174	+	0.433315i
$85$	52133.9	+	90298.6i	0.782660	+	1.35561i
$86$	−19669.9			−0.286785
$87$	−14095.7	−	24414.6i	−0.199660	−	0.345820i
$88$	3595.09	−	6226.87i	0.0494883	−	0.0857163i
$89$	55321.3	−	95819.3i	0.740316	−	1.28227i	−0.212035	−	0.977262i	$-0.568009\pi$
$89$	55321.3	−	95819.3i	0.740316	−	1.28227i	0.952351	−	0.305003i	$-0.0986575\pi$
$90$	36557.9			0.475746
$91$	−139905.	−	47366.6i	−1.77104	−	0.599609i
$92$	12095.9			0.148994
$93$	−26212.1	+	45400.7i	−0.314264	+	0.544321i
$94$	10922.2	−	18917.9i	0.127495	−	0.220827i
$95$	51841.6	+	89792.3i	0.589344	+	1.02077i
$96$	8543.04			0.0946094
$97$	1078.06	+	1867.25i	0.0116336	+	0.0201499i	0.871784	−	0.489891i	$-0.162964\pi$
$97$	1078.06	+	1867.25i	0.0116336	+	0.0201499i	−0.860150	+	0.510041i	$0.829630\pi$
$98$	83904.7	+	145327.i	0.882513	+	1.52856i
$99$	−19480.6			−0.199763
$100$	2774.72	+	4805.96i	0.0277472	+	0.0480596i
$101$	−7806.78	+	13521.7i	−0.0761498	+	0.131895i	−0.901586	−	0.432601i	$-0.857596\pi$
$101$	−7806.78	+	13521.7i	−0.0761498	+	0.131895i	0.825436	+	0.564496i	$0.190929\pi$
$102$	33007.6	−	57170.9i	0.314133	−	0.544095i
$103$	74563.8			0.692524			0.346262	−	0.938138i	$-0.387451\pi$
$103$	74563.8			0.692524			0.346262	+	0.938138i	$0.387451\pi$
$104$	−29299.4	+	25736.4i	−0.265629	+	0.233326i
$105$	−106593.			−0.943531
$106$	−35737.9	+	61899.9i	−0.308933	+	0.535088i
$107$	−68473.9	+	118600.i	−0.578183	+	1.00144i	0.417505	+	0.908675i	$0.362905\pi$
$107$	−68473.9	+	118600.i	−0.578183	+	1.00144i	−0.995688	+	0.0927677i	$0.970429\pi$
$108$	−27791.4	−	48136.1i	−0.229272	−	0.397111i
$109$	−52626.7			−0.424267			−0.212134	−	0.977241i	$-0.568041\pi$
$109$	−52626.7			−0.424267			−0.212134	+	0.977241i	$0.568041\pi$
$110$	11843.2	+	20513.0i	0.0933225	+	0.161639i
$111$	−24437.4	−	42326.9i	−0.188256	−	0.326068i
$112$	62055.2			0.467448
$113$	−95672.3	−	165709.i	−0.704839	−	1.22082i	−0.966749	−	0.255725i	$-0.917686\pi$
$113$	−95672.3	−	165709.i	−0.704839	−	1.22082i	0.261910	−	0.965092i	$-0.415648\pi$
$114$	32822.5	−	56850.3i	0.236543	−	0.409704i
$115$	−19923.5	+	34508.5i	−0.140482	+	0.243322i
$116$	−54066.2			−0.373062
$117$	100078.	+	33882.5i	0.675884	+	0.228829i
$118$	−72431.9			−0.478878
$119$	239762.	−	415280.i	1.55208	−	2.68827i
$120$	−14071.5	+	24372.6i	−0.0892047	+	0.154507i
$121$	74214.6	+	128544.i	0.460815	+	0.798154i
$122$	150516.			0.915555
$123$	20405.2	+	35342.8i	0.121612	+	0.210639i
$124$	50270.0	+	87070.3i	0.293599	+	0.508529i
$125$	−182995.			−1.04752
$126$	−84064.3	−	145604.i	−0.471721	−	0.817044i
$127$	−79211.9	+	137199.i	−0.435794	+	0.754817i	−0.997360	−	0.0726149i	$-0.976866\pi$
$127$	−79211.9	+	137199.i	−0.435794	+	0.754817i	0.561566	+	0.827432i	$0.310199\pi$
$128$	8192.00	−	14189.0i	0.0441942	−	0.0765466i
$129$	−41025.6			−0.217061
$130$	−25163.7	−	125980.i	−0.130592	−	0.653798i
$131$	−344398.			−1.75341			−0.876703	−	0.481031i	$-0.840262\pi$
$131$	−344398.			−1.75341			−0.876703	+	0.481031i	$0.840262\pi$
$132$	7498.28	−	12987.4i	0.0374565	−	0.0648765i
$133$	238418.	−	412951.i	1.16872	−	2.02428i
$134$	−47451.3	−	82188.0i	−0.228289	−	0.395409i
$135$	183105.			0.864699
$136$	−63302.6	−	109643.i	−0.293477	−	0.508318i
$137$	112342.	+	194582.i	0.511377	+	0.885731i	0.999913	+	0.0131875i	$0.00419784\pi$
$137$	112342.	+	194582.i	0.511377	+	0.885731i	−0.488536	+	0.872544i	$0.662469\pi$
$138$	25228.4			0.112770
$139$	153094.	+	265167.i	0.672082	+	1.16408i	0.977313	+	0.211801i	$0.0679329\pi$
$139$	153094.	+	265167.i	0.672082	+	1.16408i	−0.305231	+	0.952278i	$0.598734\pi$
$140$	−102213.	+	177039.i	−0.440745	+	0.763392i
$141$	22780.5	−	39457.0i	0.0964975	−	0.167139i
$142$	9357.09			0.0389421
$143$	13409.0	+	67130.9i	0.0548347	+	0.274525i
$144$	−44389.8			−0.178392
$145$	89054.2	−	154246.i	0.351750	−	0.609249i
$146$	−105114.	+	182062.i	−0.408109	+	0.706866i
$147$	175000.	+	303109.i	0.667952	+	1.15693i
$148$	−93733.1			−0.351754
$149$	−40971.0	−	70963.8i	−0.151186	−	0.261861i	0.780478	−	0.625183i	$-0.214976\pi$
$149$	−40971.0	−	70963.8i	−0.151186	−	0.261861i	−0.931664	+	0.363322i	$0.881642\pi$
$150$	5787.25	+	10023.8i	0.0210012	+	0.0363751i
$151$	265562.			0.947816			0.473908	−	0.880574i	$-0.342843\pi$
$151$	265562.			0.947816			0.473908	+	0.880574i	$0.342843\pi$
$152$	−62947.7	−	109029.i	−0.220989	−	0.382764i
$153$	−171508.	+	297061.i	−0.592320	+	1.02593i
$154$	54466.3	−	94338.4i	0.185066	−	0.320543i
$155$	−331206.			−1.10731
$156$	−61109.9	+	53678.4i	−0.201048	+	0.176599i
$157$	−141965.			−0.459656			−0.229828	−	0.973231i	$-0.573816\pi$
$157$	−141965.			−0.459656			−0.229828	+	0.973231i	$0.573816\pi$
$158$	−160300.	+	277648.i	−0.510847	+	0.884813i
$159$	−74538.7	+	129105.i	−0.233824	+	0.404995i
$160$	26986.6	+	46742.2i	0.0833391	+	0.144347i
$161$	183255.			0.557174
$162$	26306.6	+	45564.3i	0.0787547	+	0.136407i
$163$	68564.7	+	118758.i	0.202130	+	0.350100i	0.949215	−	0.314629i	$-0.101880\pi$
$163$	68564.7	+	118758.i	0.202130	+	0.350100i	−0.747084	+	0.664729i	$0.768547\pi$
$164$	78266.8			0.227231
$165$	24701.3	+	42784.0i	0.0706335	+	0.122341i
$166$	172303.	−	298437.i	0.485313	−	0.840587i
$167$	−89964.0	+	155822.i	−0.249619	+	0.432353i	−0.963420	−	0.267996i	$-0.913639\pi$
$167$	−89964.0	+	155822.i	−0.249619	+	0.432353i	0.713801	+	0.700348i	$0.246972\pi$
$168$	129429.			0.353800
$169$	47874.7	−	368194.i	0.128940	−	0.991652i
$170$	417071.			1.10685
$171$	−170546.	+	295395.i	−0.446018	+	0.772526i
$172$	−39339.9	+	68138.6i	−0.101394	+	0.175619i
$173$	−200013.	−	346433.i	−0.508093	−	0.880042i	−0.999956	−	0.00936986i	$-0.997017\pi$
$173$	−200013.	−	346433.i	−0.508093	−	0.880042i	0.491864	−	0.870672i	$-0.336316\pi$
$174$	−112766.			−0.282361
$175$	42037.6	+	72811.3i	0.103763	+	0.179723i
$176$	−14380.3	−	24907.5i	−0.0349935	−	0.0606106i
$177$	−151071.			−0.362451
$178$	−221285.	−	383277.i	−0.523483	−	0.906698i
$179$	270578.	−	468655.i	0.631191	−	1.09325i	−0.356118	−	0.934441i	$-0.615900\pi$
$179$	270578.	−	468655.i	0.631191	−	1.09325i	0.987309	−	0.158813i	$-0.0507667\pi$
$180$	73115.8	−	126640.i	0.168202	−	0.291334i
$181$	237750.			0.539417			0.269709	−	0.962942i	$-0.413073\pi$
$181$	237750.			0.539417			0.269709	+	0.962942i	$0.413073\pi$
$182$	−443892.	+	389911.i	−0.993342	+	0.872544i
$183$	313933.			0.692961
$184$	24191.7	−	41901.3i	0.0526772	−	0.0912396i
$185$	154391.	−	267413.i	0.331659	−	0.574451i
$186$	104848.	+	181603.i	0.222218	+	0.384893i
$187$	−222245.			−0.464758
$188$	−43688.9	−	75671.4i	−0.0901523	−	0.156148i
$189$	−421046.	−	729272.i	−0.857382	−	1.48503i
$190$	414733.			0.833459
$191$	107541.	+	186266.i	0.213299	+	0.369445i	0.952745	−	0.303771i	$-0.0982458\pi$
$191$	107541.	+	186266.i	0.213299	+	0.369445i	−0.739446	+	0.673216i	$0.764912\pi$
$192$	17086.1	−	29594.0i	0.0334495	−	0.0579362i
$193$	−52073.8	+	90194.5i	−0.100630	+	0.174296i	−0.911944	−	0.410314i	$-0.865419\pi$
$193$	−52073.8	+	90194.5i	−0.100630	+	0.174296i	0.811315	+	0.584610i	$0.198752\pi$
$194$	8624.46			0.0164523
$195$	−52484.0	−	262757.i	−0.0988418	−	0.494843i
$196$	671238.			1.24806
$197$	−150213.	+	260177.i	−0.275767	+	0.477643i	−0.970328	−	0.241791i	$-0.922265\pi$
$197$	−150213.	+	260177.i	−0.275767	+	0.477643i	0.694561	+	0.719434i	$0.255599\pi$
$198$	−38961.2	+	67482.7i	−0.0706267	+	0.122329i
$199$	−200745.	−	347700.i	−0.359345	−	0.622404i	0.628507	−	0.777804i	$-0.283667\pi$
$199$	−200745.	−	347700.i	−0.359345	−	0.622404i	−0.987852	+	0.155401i	$0.950333\pi$
$200$	22197.8			0.0392405
$201$	−98969.3	−	171420.i	−0.172787	−	0.299275i
$202$	31227.1	+	54087.0i	0.0538460	+	0.0932640i
$203$	−819114.			−1.39510
$204$	−132030.	−	228684.i	−0.222126	−	0.384733i
$205$	−128916.	+	223289.i	−0.214250	+	0.371093i
$206$	149128.	−	258296.i	0.244844	−	0.424082i
$207$	−131087.			−0.212635
$208$	30554.6	+	152969.i	0.0489686	+	0.245157i
$209$	−220998.			−0.349964
$210$	−213186.	+	369250.i	−0.333589	+	0.577793i
$211$	−81175.7	+	140600.i	−0.125522	+	0.217410i	−0.921937	−	0.387340i	$-0.873394\pi$
$211$	−81175.7	+	140600.i	−0.125522	+	0.217410i	0.796415	+	0.604751i	$0.206727\pi$
$212$	142952.	+	247600.i	0.218449	+	0.378364i
$213$	19516.1			0.0294743
$214$	273895.	+	474401.i	0.408837	+	0.708127i
$215$	−129596.	−	224467.i	−0.191203	−	0.331174i
$216$	−222331.			−0.324240
$217$	761601.	+	1.31913e6i	1.09794	+	1.90169i
$218$	−105253.	+	182304.i	−0.150001	+	0.259810i
$219$	−219236.	+	379727.i	−0.308888	+	0.535009i
$220$	94745.3			0.131978
$221$	1.14174e6	+	386549.i	1.57248	+	0.532383i
$222$	−195499.			−0.266234
$223$	400294.	−	693329.i	0.539035	−	0.933635i	−0.459922	−	0.887959i	$-0.652123\pi$
$223$	400294.	−	693329.i	0.539035	−	0.933635i	0.998956	−	0.0456758i	$-0.0145441\pi$
$224$	124110.	−	214966.i	0.165268	−	0.286252i
$225$	−30070.6	−	52083.9i	−0.0395992	−	0.0685878i
$226$	−765379.			−0.996794
$227$	212936.	+	368816.i	0.274274	+	0.475057i	0.969952	−	0.243297i	$-0.0782291\pi$
$227$	212936.	+	368816.i	0.274274	+	0.475057i	−0.695678	+	0.718354i	$0.744896\pi$
$228$	−131290.	−	227401.i	−0.167261	−	0.289705i
$229$	−146421.			−0.184507			−0.0922537	−	0.995736i	$-0.529407\pi$
$229$	−146421.			−0.184507			−0.0922537	+	0.995736i	$0.529407\pi$
$230$	79694.0	+	138034.i	0.0993359	+	0.172055i
$231$	113601.	−	196762.i	0.140072	−	0.242611i
$232$	−108132.	+	187291.i	−0.131897	+	0.228453i
$233$	838409.			1.01173			0.505867	−	0.862612i	$-0.331173\pi$
$233$	838409.			1.01173			0.505867	+	0.862612i	$0.331173\pi$
$234$	317528.	−	278914.i	0.379090	−	0.332989i
$235$	287846.			0.340009
$236$	−144864.	+	250911.i	−0.169309	+	0.293252i
$237$	−334338.	+	579091.i	−0.386648	+	0.669693i
$238$	−959048.	−	1.66112e6i	−1.09748	−	1.90090i
$239$	−313492.			−0.355002			−0.177501	−	0.984121i	$-0.556801\pi$
$239$	−313492.			−0.355002			−0.177501	+	0.984121i	$0.556801\pi$
$240$	56286.1	+	97490.3i	0.0630773	+	0.109253i
$241$	−814245.	−	1.41031e6i	−0.903051	−	1.56413i	−0.823512	−	0.567299i	$-0.807988\pi$
$241$	−814245.	−	1.41031e6i	−0.903051	−	1.56413i	−0.0795396	−	0.996832i	$-0.525345\pi$
$242$	593717.			0.651690
$243$	476950.	+	826101.i	0.518152	+	0.897465i
$244$	301033.	−	521404.i	0.323698	−	0.560661i
$245$	−1.10562e6	+	1.91499e6i	−1.17677	+	2.03822i
$246$	163241.			0.171986
$247$	1.13533e6	+	384382.i	1.18408	+	0.400886i
$248$	402160.			0.415212
$249$	359373.	−	622451.i	0.367322	−	0.636220i
$250$	−365989.	+	633912.i	−0.370355	+	0.641474i
$251$	−181425.	−	314237.i	−0.181766	−	0.314828i	0.760716	−	0.649085i	$-0.224848\pi$
$251$	−181425.	−	314237.i	−0.181766	−	0.314828i	−0.942482	+	0.334257i	$0.891515\pi$
$252$	−672514.			−0.667114
$253$	−42466.5	−	73554.1i	−0.0417105	−	0.0722447i
$254$	316847.	+	548796.i	0.308153	+	0.533736i
$255$	869887.			0.837746
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	229995.	−	398363.i	0.217213	−	0.376224i	−0.736742	−	0.676174i	$-0.763637\pi$
$257$	229995.	−	398363.i	0.217213	−	0.376224i	0.953955	+	0.299950i	$0.0969701\pi$
$258$	−82051.2	+	142117.i	−0.0767425	+	0.132922i
$259$	−1.42008e6			−1.31541
$260$	−486735.	−	164790.i	−0.446539	−	0.151181i
$261$	585934.			0.532411
$262$	−688796.	+	1.19303e6i	−0.619923	+	1.07374i
$263$	660607.	−	1.14420e6i	0.588916	−	1.02003i	−0.405459	−	0.914113i	$-0.632888\pi$
$263$	660607.	−	1.14420e6i	0.588916	−	1.02003i	0.994375	−	0.105919i	$-0.0337785\pi$
$264$	−29993.1	−	51949.6i	−0.0264857	−	0.0458746i
$265$	−941842.			−0.823879
$266$	−953670.	−	1.65181e6i	−0.826407	−	1.43138i
$267$	−461535.	−	799402.i	−0.396211	−	0.686258i
$268$	−379610.			−0.322850
$269$	−512757.	−	888122.i	−0.432047	−	0.748328i	0.565002	−	0.825089i	$-0.308875\pi$
$269$	−512757.	−	888122.i	−0.432047	−	0.748328i	−0.997049	+	0.0767616i	$0.975542\pi$
$270$	366209.	−	634293.i	0.305717	−	0.529518i
$271$	779859.	−	1.35076e6i	0.645049	−	1.11726i	−0.339241	−	0.940700i	$-0.610170\pi$
$271$	779859.	−	1.35076e6i	0.645049	−	1.11726i	0.984290	−	0.176558i	$-0.0564965\pi$
$272$	−506421.			−0.415040
$273$	−925827.	+	813239.i	−0.751836	+	0.660407i
$274$	898737.			0.723197
$275$	19483.1	−	33745.8i	0.0155356	−	0.0269084i
$276$	50456.8	−	87393.7i	0.0398701	−	0.0690570i
$277$	455403.	+	788781.i	0.356613	+	0.617671i	0.987393	−	0.158291i	$-0.0505983\pi$
$277$	455403.	+	788781.i	0.356613	+	0.617671i	−0.630780	+	0.775962i	$0.717265\pi$
$278$	1.22475e6			0.950467
$279$	−544794.	−	943610.i	−0.419007	−	0.725742i
$280$	408853.	+	708154.i	0.311654	+	0.539800i
$281$	1.73516e6			1.31091			0.655455	−	0.755235i	$-0.272477\pi$
$281$	1.73516e6			1.31091			0.655455	+	0.755235i	$0.272477\pi$
$282$	−91122.1	−	157828.i	−0.0682340	−	0.118185i
$283$	−45393.8	+	78624.4i	−0.0336923	+	0.0583568i	−0.882380	−	0.470538i	$-0.844060\pi$
$283$	−45393.8	+	78624.4i	−0.0336923	+	0.0583568i	0.848688	+	0.528895i	$0.177393\pi$
$284$	18714.2	−	32413.9i	0.0137681	−	0.0238471i
$285$	865009.			0.630824
$286$	259366.	+	87811.7i	0.187499	+	0.0634801i
$287$	1.18576e6			0.849751
$288$	−88779.5	+	153771.i	−0.0630713	+	0.109243i
$289$	−1.24672e6	+	2.15939e6i	−0.878063	+	1.52085i
$290$	−356217.	−	616985.i	−0.248725	−	0.430804i
$291$	17988.1			0.0124524
$292$	420454.	+	728248.i	0.288577	+	0.499830i
$293$	−517700.	−	896682.i	−0.352297	−	0.610196i	0.634355	−	0.773042i	$-0.281266\pi$
$293$	−517700.	−	896682.i	−0.352297	−	0.610196i	−0.986651	+	0.162846i	$0.947933\pi$
$294$	1.40000e6			0.944627
$295$	−477220.	−	826569.i	−0.319274	−	0.552998i
$296$	−187466.	+	324701.i	−0.124364	+	0.215404i
$297$	−195142.	+	337995.i	−0.128369	+	0.222341i
$298$	−327768.			−0.213809
$299$	90230.5	+	451731.i	0.0583681	+	0.292215i
$300$	46298.0			0.0297002
$301$	−596007.	+	1.03231e6i	−0.379171	+	0.656743i
$302$	531125.	−	919935.i	0.335104	−	0.580416i
$303$	65130.5	+	112809.i	0.0407547	+	0.0705892i
$304$	−503581.			−0.312526
$305$	991682.	+	1.71764e6i	0.610412	+	1.05726i
$306$	686032.	+	1.18824e6i	0.418833	+	0.725440i
$307$	−3.10579e6			−1.88073			−0.940363	−	0.340172i	$-0.889515\pi$
$307$	−3.10579e6			−1.88073			−0.940363	+	0.340172i	$0.889515\pi$
$308$	−217865.	−	377354.i	−0.130861	−	0.226658i
$309$	311036.	−	538730.i	0.185316	−	0.320978i
$310$	−662411.	+	1.14733e6i	−0.391493	+	0.678085i
$311$	−2.49096e6			−1.46038			−0.730191	−	0.683243i	$-0.760569\pi$
$311$	−2.49096e6			−1.46038			−0.730191	+	0.683243i	$0.760569\pi$
$312$	63727.8	+	319048.i	0.0370631	+	0.185553i
$313$	647621.			0.373646			0.186823	−	0.982394i	$-0.440181\pi$
$313$	647621.			0.373646			0.186823	+	0.982394i	$0.440181\pi$
$314$	−283931.	+	491782.i	−0.162513	+	0.281481i
$315$	1.10772e6	−	1.91863e6i	0.629004	−	1.08947i
$316$	641200.	+	1.11059e6i	0.361223	+	0.625657i
$317$	806778.			0.450927			0.225463	−	0.974252i	$-0.427610\pi$
$317$	806778.			0.450927			0.225463	+	0.974252i	$0.427610\pi$
$318$	298155.	+	516419.i	0.165339	+	0.286375i
$319$	189817.	+	328773.i	0.104438	+	0.180892i
$320$	215893.			0.117859
$321$	571264.	+	989459.i	0.309439	+	0.535964i
$322$	366510.	−	634814.i	0.196991	−	0.341198i
$323$	−1.94568e6	+	3.37002e6i	−1.03768	+	1.79732i
$324$	210453.			0.111376
$325$	−158785.	+	139475.i	−0.0833874	+	0.0732468i
$326$	548518.			0.285855
$327$	−219527.	+	380232.i	−0.113532	+	0.196644i
$328$	156534.	−	271124.i	0.0803384	−	0.139150i
$329$	−661896.	−	1.14644e6i	−0.337132	−	0.583930i
$330$	197611.			0.0998908
$331$	−481627.	−	834202.i	−0.241624	−	0.418506i	0.719553	−	0.694438i	$-0.244347\pi$
$331$	−481627.	−	834202.i	−0.241624	−	0.418506i	−0.961177	+	0.275932i	$0.911014\pi$
$332$	−689211.	−	1.19375e6i	−0.343168	−	0.594385i
$333$	1.01582e6			0.502002
$334$	359856.	+	623289.i	0.176507	+	0.305720i
$335$	625268.	−	1.08300e6i	0.304407	−	0.527248i
$336$	258858.	−	448355.i	0.125087	−	0.216657i
$337$	−3.16391e6			−1.51757			−0.758787	−	0.651339i	$-0.774208\pi$
$337$	−3.16391e6			−1.51757			−0.758787	+	0.651339i	$0.774208\pi$
$338$	−1.17971e6	−	902230.i	−0.561673	−	0.429562i
$339$	−1.59635e6			−0.754448
$340$	834143.	−	1.44478e6i	0.391330	−	0.677803i
$341$	352979.	−	611377.i	0.164385	−	0.284723i
$342$	682185.	+	1.18158e6i	0.315382	+	0.546258i
$343$	6.09532e6			2.79744
$344$	157359.	+	272555.i	0.0716963	+	0.124182i
$345$	166218.	+	287898.i	0.0751849	+	0.130224i
$346$	−1.60010e6			−0.718551
$347$	514401.	+	890969.i	0.229339	+	0.397227i	0.957612	−	0.288060i	$-0.0930102\pi$
$347$	514401.	+	890969.i	0.229339	+	0.397227i	−0.728273	+	0.685287i	$0.759677\pi$
$348$	−225532.	+	390633.i	−0.0998298	+	0.172910i
$349$	1.38715e6	−	2.40261e6i	0.609619	−	1.05589i	−0.381684	−	0.924293i	$-0.624656\pi$
$349$	1.38715e6	−	2.40261e6i	0.609619	−	1.05589i	0.991303	−	0.131599i	$-0.0420111\pi$
$350$	336301.			0.146743
$351$	1.59037e6	−	1.39697e6i	0.689020	−	0.605229i
$352$	−115043.			−0.0494883
$353$	1.74114e6	−	3.01575e6i	0.743700	−	1.28813i	−0.207100	−	0.978320i	$-0.566403\pi$
$353$	1.74114e6	−	3.01575e6i	0.743700	−	1.28813i	0.950800	−	0.309806i	$-0.100264\pi$
$354$	−302143.	+	523327.i	−0.128146	+	0.221955i
$355$	61649.5	+	106780.i	0.0259632	+	0.0449696i
$356$	−1.77028e6			−0.740316
$357$	−2.00029e6	−	3.46460e6i	−0.830658	−	1.43874i
$358$	−1.08231e6	−	1.87462e6i	−0.446319	−	0.773047i
$359$	−1.46407e6			−0.599552			−0.299776	−	0.954010i	$-0.596912\pi$
$359$	−1.46407e6			−0.599552			−0.299776	+	0.954010i	$0.596912\pi$
$360$	−292463.	−	506561.i	−0.118936	−	0.206004i
$361$	−696720.	+	1.20675e6i	−0.281378	+	0.487361i
$362$	475501.	−	823591.i	0.190713	−	0.330324i
$363$	1.23832e6			0.493248
$364$	462908.	+	2.31751e6i	0.183122	+	0.916786i
$365$	−2.77017e6			−1.08837
$366$	627865.	−	1.08749e6i	0.244999	−	0.424350i
$367$	11422.5	−	19784.3i	0.00442686	−	0.00766755i	−0.863803	−	0.503829i	$-0.831924\pi$
$367$	11422.5	−	19784.3i	0.00442686	−	0.00766755i	0.868230	+	0.496161i	$0.165258\pi$
$368$	−96767.0	−	167605.i	−0.0372484	−	0.0645161i
$369$	−848205.			−0.324291
$370$	−617563.	−	1.06965e6i	−0.234519	−	0.406198i
$371$	2.16575e6	+	3.75119e6i	0.816908	+	1.41493i
$372$	838787.			0.314264
$373$	−397329.	−	688195.i	−0.147870	−	0.256117i	0.782570	−	0.622562i	$-0.213908\pi$
$373$	−397329.	−	688195.i	−0.147870	−	0.256117i	−0.930440	+	0.366445i	$0.880575\pi$
$374$	−444489.	+	769878.i	−0.164317	+	0.284605i
$375$	−763345.	+	1.32215e6i	−0.280313	+	0.485516i
$376$	−349511.			−0.127495
$377$	−403313.	−	2.01915e6i	−0.146147	−	0.731670i
$378$	−3.36836e6			−1.21252
$379$	−704181.	+	1.21968e6i	−0.251818	+	0.436161i	−0.964026	−	0.265807i	$-0.914362\pi$
$379$	−704181.	+	1.21968e6i	−0.251818	+	0.436161i	0.712209	+	0.701968i	$0.247695\pi$
$380$	829465.	−	1.43668e6i	0.294672	−	0.510387i
$381$	660850.	+	1.14463e6i	0.233233	+	0.403972i
$382$	860325.			0.301650
$383$	2.38948e6	+	4.13871e6i	0.832352	+	1.44168i	0.896168	+	0.443715i	$0.146340\pi$
$383$	2.38948e6	+	4.13871e6i	0.832352	+	1.44168i	−0.0638155	+	0.997962i	$0.520327\pi$
$384$	−68344.3	−	118376.i	−0.0236524	−	0.0409671i
$385$	1.43541e6			0.493543
$386$	208295.	+	360778.i	0.0711559	+	0.123246i
$387$	426340.	−	738442.i	0.144703	−	0.250633i
$388$	17248.9	−	29876.0i	0.00581678	−	0.0100750i
$389$	5.44144e6			1.82322			0.911611	−	0.411054i	$-0.134839\pi$
$389$	5.44144e6			1.82322			0.911611	+	0.411054i	$0.134839\pi$
$390$	−1.01518e6	−	343704.i	−0.337974	−	0.114425i
$391$	−1.49551e6			−0.494706
$392$	1.34248e6	−	2.32524e6i	0.441257	−	0.764279i
$393$	−1.43662e6	+	2.48831e6i	−0.469204	+	0.812686i
$394$	600853.	+	1.04071e6i	0.194997	+	0.337744i
$395$	−4.22457e6			−1.36235
$396$	155845.	+	269931.i	0.0499406	+	0.0864997i
$397$	2.51957e6	+	4.36403e6i	0.802325	+	1.38967i	0.918082	+	0.396391i	$0.129737\pi$
$397$	2.51957e6	+	4.36403e6i	0.802325	+	1.38967i	−0.115757	+	0.993278i	$0.536929\pi$
$398$	−1.60596e6			−0.508190
$399$	−1.98907e6	−	3.44517e6i	−0.625487	−	1.08338i
$400$	44395.6	−	76895.4i	0.0138736	−	0.0240298i
$401$	2.23695e6	−	3.87451e6i	0.694697	−	1.20325i	−0.275585	−	0.961277i	$-0.588872\pi$
$401$	2.23695e6	−	3.87451e6i	0.694697	−	1.20325i	0.970283	−	0.241974i	$-0.0777950\pi$
$402$	−791754.			−0.244357
$403$	−2.87672e6	+	2.52689e6i	−0.882339	+	0.775040i
$404$	249817.			0.0761498
$405$	−346643.	+	600404.i	−0.105014	+	0.181889i
$406$	−1.63823e6	+	2.83749e6i	−0.493241	+	0.854318i
$407$	329081.	+	569984.i	0.0984728	+	0.170560i
$408$	−1.05624e6			−0.314133
$409$	141328.	+	244787.i	0.0417752	+	0.0723568i	0.886157	−	0.463385i	$-0.153365\pi$
$409$	141328.	+	244787.i	0.0417752	+	0.0723568i	−0.844382	+	0.535742i	$0.820032\pi$
$410$	515664.	+	893155.i	0.151498	+	0.262402i
$411$	1.87450e6			0.547370
$412$	−596510.	−	1.03319e6i	−0.173131	−	0.299872i
$413$	−2.19472e6	+	3.80136e6i	−0.633145	+	1.09664i
$414$	−262174.	+	454099.i	−0.0751777	+	0.130212i
$415$	4.54089e6			1.29426
$416$	591009.	+	200094.i	0.167441	+	0.0566891i
$417$	2.55447e6			0.719385
$418$	−441997.	+	765561.i	−0.123731	+	0.214308i
$419$	−707235.	+	1.22497e6i	−0.196802	+	0.340870i	−0.947490	−	0.319786i	$-0.896389\pi$
$419$	−707235.	+	1.22497e6i	−0.196802	+	0.340870i	0.750688	+	0.660657i	$0.229722\pi$
$420$	852746.	+	1.47700e6i	0.235883	+	0.408561i
$421$	−4.25092e6			−1.16890			−0.584450	−	0.811430i	$-0.698690\pi$
$421$	−4.25092e6			−1.16890			−0.584450	+	0.811430i	$0.698690\pi$
$422$	324703.	+	562402.i	0.0887574	+	0.153732i
$423$	473472.	+	820077.i	0.128660	+	0.222846i
$424$	1.14361e6			0.308933
$425$	−343061.	−	594199.i	−0.0921296	−	0.159573i
$426$	39032.2	−	67605.8i	0.0104208	−	0.0180493i
$427$	4.56071e6	−	7.89938e6i	1.21049	−	2.09664i
$428$	2.19116e6			0.578183
$429$	540961.	+	183149.i	0.141913	+	0.0480465i
$430$	−1.03677e6			−0.270402
$431$	−2.98289e6	+	5.16651e6i	−0.773470	+	1.33969i	0.162180	+	0.986761i	$0.448148\pi$
$431$	−2.98289e6	+	5.16651e6i	−0.773470	+	1.33969i	−0.935650	+	0.352929i	$0.885186\pi$
$432$	−444663.	+	770178.i	−0.114636	+	0.198555i
$433$	−2.59557e6	−	4.49567e6i	−0.665294	−	1.15232i	−0.979206	−	0.202871i	$-0.934973\pi$
$433$	−2.59557e6	−	4.49567e6i	−0.665294	−	1.15232i	0.313911	−	0.949452i	$-0.398360\pi$
$434$	6.09281e6			1.55272
$435$	−742962.	−	1.28685e6i	−0.188254	−	0.326065i
$436$	421013.	+	729217.i	0.106067	+	0.183713i
$437$	−1.48712e6			−0.372515
$438$	876942.	+	1.51891e6i	0.218417	+	0.378309i
$439$	352761.	−	611000.i	0.0873614	−	0.151314i	−0.819034	−	0.573745i	$-0.805490\pi$
$439$	352761.	−	611000.i	0.0873614	−	0.151314i	0.906395	+	0.422431i	$0.138823\pi$
$440$	189491.	−	328207.i	0.0466612	−	0.0808196i
$441$	−7.27443e6			−1.78116
$442$	3.62252e6	−	3.18199e6i	0.881973	−	0.774718i
$443$	630026.			0.152528			0.0762639	−	0.997088i	$-0.475701\pi$
$443$	630026.			0.152528			0.0762639	+	0.997088i	$0.475701\pi$
$444$	−390999.	+	677230.i	−0.0941278	+	0.163034i
$445$	2.91589e6	−	5.05047e6i	0.698025	−	1.20901i
$446$	−1.60117e6	−	2.77332e6i	−0.381155	−	0.660180i
$447$	−683626.			−0.161827
$448$	−496442.	−	859863.i	−0.116862	−	0.202411i
$449$	−171636.	−	297283.i	−0.0401784	−	0.0695911i	0.845237	−	0.534392i	$-0.179459\pi$
$449$	−171636.	−	297283.i	−0.0401784	−	0.0695911i	−0.885415	+	0.464801i	$0.846126\pi$
$450$	−240565.			−0.0560017
$451$	−274781.	−	475935.i	−0.0636130	−	0.110181i
$452$	−1.53076e6	+	2.65135e6i	−0.352420	+	0.610409i
$453$	1.10777e6	−	1.91871e6i	0.253632	−	0.439303i
$454$	1.70349e6			0.387882
$455$	−7.37414e6	−	2.49661e6i	−1.66987	−	0.565356i
$456$	−1.05032e6			−0.236543
$457$	3.03986e6	−	5.26518e6i	0.680867	−	1.17930i	−0.293849	−	0.955852i	$-0.594936\pi$
$457$	3.03986e6	−	5.26518e6i	0.680867	−	1.17930i	0.974717	−	0.223445i	$-0.0717302\pi$
$458$	−292841.	+	507216.i	−0.0652332	+	0.112987i
$459$	3.43607e6	+	5.95145e6i	0.761256	+	1.31853i
$460$	637552.			0.140482
$461$	604298.	+	1.04667e6i	0.132434	+	0.229382i	0.924614	−	0.380905i	$-0.124387\pi$
$461$	604298.	+	1.04667e6i	0.132434	+	0.229382i	−0.792180	+	0.610287i	$0.791054\pi$
$462$	−454402.	−	787047.i	−0.0990456	−	0.171552i
$463$	−3.31679e6			−0.719061			−0.359530	−	0.933133i	$-0.617063\pi$
$463$	−3.31679e6			−0.719061			−0.359530	+	0.933133i	$0.617063\pi$
$464$	432529.	+	749163.i	0.0932654	+	0.161540i
$465$	−1.38159e6	+	2.39299e6i	−0.296311	+	0.513226i
$466$	1.67682e6	−	2.90433e6i	0.357702	−	0.619558i
$467$	7.69798e6			1.63337			0.816685	−	0.577084i	$-0.195810\pi$
$467$	7.69798e6			1.63337			0.816685	+	0.577084i	$0.195810\pi$
$468$	−331130.	−	1.65778e6i	−0.0698851	−	0.349874i
$469$	−5.75117e6			−1.20733
$470$	575692.	−	997127.i	0.120211	−	0.208212i
$471$	−592195.	+	1.02571e6i	−0.123002	+	0.213046i
$472$	579455.	+	1.00365e6i	0.119719	+	0.207360i
$473$	552462.			0.113540
$474$	1.33735e6	+	2.31636e6i	0.273401	+	0.473545i
$475$	−341137.	−	590867.i	−0.0693738	−	0.120159i
$476$	−7.67238e6			−1.55208
$477$	−1.54922e6	−	2.68332e6i	−0.311757	−	0.539979i
$478$	−626983.	+	1.08597e6i	−0.125512	+	0.217394i
$479$	−1.41391e6	+	2.44896e6i	−0.281568	+	0.487689i	−0.971771	−	0.235926i	$-0.924188\pi$
$479$	−1.41391e6	+	2.44896e6i	−0.281568	+	0.487689i	0.690203	+	0.723615i	$0.257521\pi$
$480$	450289.			0.0892047
$481$	−699213.	−	3.50055e6i	−0.137799	−	0.689880i
$482$	−6.51396e6			−1.27711
$483$	764431.	−	1.32403e6i	0.149098	−	0.258244i
$484$	1.18743e6	−	2.05670e6i	0.230407	−	0.399077i
$485$	56822.5	+	98419.5i	0.0109690	+	0.0189988i
$486$	3.81560e6			0.732777
$487$	199352.	+	345287.i	0.0380888	+	0.0659718i	0.884441	−	0.466651i	$-0.154540\pi$
$487$	199352.	+	345287.i	0.0380888	+	0.0659718i	−0.846353	+	0.532623i	$0.821206\pi$
$488$	−1.20413e6	−	2.08562e6i	−0.228889	−	0.396447i
$489$	1.14404e6			0.216357
$490$	4.42247e6	+	7.65994e6i	0.832099	+	1.44124i
$491$	−1.06018e6	+	1.83628e6i	−0.198461	+	0.343744i	−0.948029	−	0.318182i	$-0.896928\pi$
$491$	−1.06018e6	+	1.83628e6i	−0.198461	+	0.343744i	0.749569	+	0.661926i	$0.230261\pi$
$492$	326483.	−	565485.i	0.0608061	−	0.105319i
$493$	6.68463e6			1.23868
$494$	3.60221e6	−	3.16415e6i	0.664127	−	0.583364i
$495$	−1.02679e6			−0.188351
$496$	804321.	−	1.39312e6i	0.146800	−	0.254264i
$497$	283524.	−	491077.i	0.0514871	−	0.0891783i
$498$	−1.43749e6	−	2.48981e6i	−0.259736	−	0.449875i
$499$	663616.			0.119307			0.0596534	−	0.998219i	$-0.481000\pi$
$499$	663616.			0.119307			0.0596534	+	0.998219i	$0.481000\pi$
$500$	1.46396e6	+	2.53565e6i	0.261881	+	0.453591i
$501$	750553.	+	1.30000e6i	0.133594	+	0.231392i
$502$	−1.45140e6			−0.257056
$503$	−1.47643e6	−	2.55725e6i	−0.260191	−	0.450664i	0.706101	−	0.708111i	$-0.250452\pi$
$503$	−1.47643e6	−	2.55725e6i	−0.260191	−	0.450664i	−0.966293	+	0.257446i	$0.917119\pi$
$504$	−1.34503e6	+	2.32966e6i	−0.235860	+	0.408522i
$505$	−411482.	+	712707.i	−0.0717996	+	0.124361i
$506$	−339732.			−0.0589875
$507$	−2.46053e6	−	1.88178e6i	−0.425117	−	0.325125i
$508$	2.53478e6			0.435794
$509$	−2.72732e6	+	4.72385e6i	−0.466596	+	0.808168i	−0.999272	−	0.0381513i	$-0.987853\pi$
$509$	−2.72732e6	+	4.72385e6i	−0.466596	+	0.808168i	0.532676	+	0.846319i	$0.321186\pi$
$510$	1.73977e6	−	3.01338e6i	0.296188	−	0.513013i
$511$	6.36997e6	+	1.10331e7i	1.07916	+	1.86916i
$512$	−262144.			−0.0441942
$513$	3.41680e6	+	5.91808e6i	0.573227	+	0.992859i
$514$	−919980.	−	1.59345e6i	−0.153593	−	0.266030i
$515$	3.93012e6			0.652963
$516$	328205.	+	568468.i	0.0542651	+	0.0939900i
$517$	−306768.	+	531339.i	−0.0504759	+	0.0874269i
$518$	−2.84015e6	+	4.91929e6i	−0.465069	+	0.805523i
$519$	−3.33734e6			−0.543854
$520$	−1.54432e6	+	1.35652e6i	−0.250455	+	0.219997i
$521$	8.03623e6			1.29705			0.648527	−	0.761192i	$-0.275385\pi$
$521$	8.03623e6			1.29705			0.648527	+	0.761192i	$0.275385\pi$
$522$	1.17187e6	−	2.02973e6i	0.188236	−	0.326034i
$523$	−542554.	+	939732.i	−0.0867339	+	0.150228i	−0.906129	−	0.423002i	$-0.860976\pi$
$523$	−542554.	+	939732.i	−0.0867339	+	0.150228i	0.819395	+	0.573230i	$0.194310\pi$
$524$	2.75519e6	+	4.77212e6i	0.438352	+	0.759247i
$525$	701424.			0.111066
$526$	−2.64243e6	−	4.57682e6i	−0.416427	−	0.721272i
$527$	−6.21528e6	−	1.07652e7i	−0.974843	−	1.68848i
$528$	−239945.			−0.0374565
$529$	2.93241e6	+	5.07908e6i	0.455602	+	0.789125i
$530$	−1.88368e6	+	3.26264e6i	−0.291285	+	0.504521i
$531$	1.56994e6	−	2.71921e6i	0.241627	−	0.418511i
$532$	−7.62936e6			−1.16872
$533$	583840.	+	2.92295e6i	0.0890176	+	0.445659i
$534$	−3.69228e6			−0.560327
$535$	−3.60914e6	+	6.25121e6i	−0.545154	+	0.944234i
$536$	−759220.	+	1.31501e6i	−0.114145	+	0.197704i
$537$	−2.25738e6	−	3.90990e6i	−0.337808	−	0.585100i
$538$	−4.10206e6			−0.611007
$539$	−2.35660e6	−	4.08175e6i	−0.349393	−	0.605166i
$540$	−1.46484e6	−	2.53717e6i	−0.216175	−	0.374425i
$541$	5.89345e6			0.865718			0.432859	−	0.901462i	$-0.357505\pi$
$541$	5.89345e6			0.865718			0.432859	+	0.901462i	$0.357505\pi$
$542$	−3.11944e6	−	5.40302e6i	−0.456119	−	0.790021i
$543$	991753.	−	1.71777e6i	0.144346	−	0.250014i
$544$	−1.01284e6	+	1.75429e6i	−0.146739	+	0.254159i
$545$	−2.77386e6			−0.400031
$546$	965489.	+	4.83364e6i	0.138601	+	0.693893i
$547$	1.95350e6			0.279154			0.139577	−	0.990211i	$-0.455426\pi$
$547$	1.95350e6			0.279154			0.139577	+	0.990211i	$0.455426\pi$
$548$	1.79747e6	−	3.11332e6i	0.255689	−	0.442866i
$549$	−3.26240e6	+	5.65064e6i	−0.461962	+	0.800141i
$550$	−77932.6	−	134983.i	−0.0109853	−	0.0190271i
$551$	6.64715e6			0.932731
$552$	−201827.	−	349575.i	−0.0281924	−	0.0488307i
$553$	9.71432e6	+	1.68257e7i	1.35083	+	2.33970i
$554$	3.64322e6			0.504326
$555$	−1.28805e6	−	2.23097e6i	−0.177501	−	0.307441i
$556$	2.44951e6	−	4.24267e6i	0.336041	−	0.582040i
$557$	246140.	−	426327.i	0.0336159	−	0.0582244i	−0.848728	−	0.528830i	$-0.822631\pi$
$557$	246140.	−	426327.i	0.0336159	−	0.0582244i	0.882344	+	0.470605i	$0.155964\pi$
$558$	−4.35835e6			−0.592566
$559$	−2.83816e6	−	960895.i	−0.384156	−	0.130061i
$560$	3.27082e6			0.440745
$561$	−927072.	+	1.60574e6i	−0.124367	+	0.215411i
$562$	3.47031e6	−	6.01075e6i	0.463476	−	0.802765i
$563$	−6.83723e6	−	1.18424e7i	−0.909096	−	1.57460i	−0.815323	−	0.579006i	$-0.803441\pi$
$563$	−6.83723e6	−	1.18424e7i	−0.909096	−	1.57460i	−0.0937722	−	0.995594i	$-0.529893\pi$
$564$	−728977.			−0.0964975
$565$	−5.04272e6	−	8.73425e6i	−0.664575	−	1.15108i
$566$	181575.	+	314498.i	0.0238241	+	0.0412645i
$567$	3.18840e6			0.416500
$568$	−74856.7	−	129656.i	−0.00973554	−	0.0168624i
$569$	−3.28061e6	+	5.68218e6i	−0.424789	+	0.735757i	−0.996401	−	0.0847678i	$-0.972985\pi$
$569$	−3.28061e6	+	5.68218e6i	−0.424789	+	0.735757i	0.571611	+	0.820524i	$0.306318\pi$
$570$	1.73002e6	−	2.99648e6i	0.223030	−	0.386300i
$571$	5.00673e6			0.642635			0.321317	−	0.946972i	$-0.395874\pi$
$571$	5.00673e6			0.642635			0.321317	+	0.946972i	$0.395874\pi$
$572$	822921.	−	722847.i	0.105164	−	0.0923754i
$573$	1.79438e6			0.228312
$574$	2.37152e6	−	4.10759e6i	0.300432	−	0.520364i
$575$	131104.	−	227079.i	0.0165366	−	0.0286423i
$576$	355118.	+	615083.i	0.0445981	+	0.0772462i
$577$	−1.15472e7			−1.44390			−0.721949	−	0.691946i	$-0.756754\pi$
$577$	−1.15472e7			−1.44390			−0.721949	+	0.691946i	$0.756754\pi$
$578$	4.98690e6	+	8.63756e6i	0.620884	+	1.07540i
$579$	434442.	+	752476.i	0.0538562	+	0.0932816i
$580$	−2.84973e6			−0.351750
$581$	−1.04417e7	−	1.80855e7i	−1.28331	−	2.22275i
$582$	35976.1	−	62312.5i	0.00440258	−	0.00762548i
$583$	1.00376e6	−	1.73856e6i	0.122309	−	0.211845i
$584$	3.36363e6			0.408109
$585$	5.27491e6	+	1.78589e6i	0.637273	+	0.215757i
$586$	−4.14160e6			−0.498223
$587$	157807.	−	273330.i	0.0189030	−	0.0327410i	−0.856419	−	0.516281i	$-0.827316\pi$
$587$	157807.	−	273330.i	0.0189030	−	0.0327410i	0.875322	+	0.483540i	$0.160649\pi$
$588$	2.80001e6	−	4.84975e6i	0.333976	−	0.578464i
$589$	−6.18043e6	−	1.07048e7i	−0.734058	−	1.27143i
$590$	−3.81776e6			−0.451521
$591$	1.25320e6	+	2.17061e6i	0.147588	+	0.255630i
$592$	749865.	+	1.29880e6i	0.0879384	+	0.152314i
$593$	1.09534e7			1.27912			0.639562	−	0.768740i	$-0.279116\pi$
$593$	1.09534e7			1.27912			0.639562	+	0.768740i	$0.279116\pi$
$594$	780566.	+	1.35198e6i	0.0907703	+	0.157219i
$595$	1.26374e7	−	2.18887e7i	1.46341	−	2.53470i
$596$	−655536.	+	1.13542e6i	−0.0755928	+	0.130931i
$597$	−3.34955e6			−0.384637
$598$	1.74530e6	+	590895.i	0.199581	+	0.0675706i
$599$	4.90735e6			0.558830			0.279415	−	0.960170i	$-0.409859\pi$
$599$	4.90735e6			0.558830			0.279415	+	0.960170i	$0.409859\pi$
$600$	92596.0	−	160381.i	0.0105006	−	0.0181876i
$601$	−3.96846e6	+	6.87358e6i	−0.448163	+	0.776242i	−0.998267	−	0.0588551i	$-0.981255\pi$
$601$	−3.96846e6	+	6.87358e6i	−0.448163	+	0.776242i	0.550103	+	0.835097i	$0.314588\pi$
$602$	2.38403e6	+	4.12926e6i	0.268114	+	0.464388i
$603$	4.11397e6			0.460752
$604$	−2.12450e6	−	3.67974e6i	−0.236954	−	0.410416i
$605$	3.91172e6	+	6.77530e6i	0.434490	+	0.752559i
$606$	521044.			0.0576359
$607$	1.86890e6	+	3.23704e6i	0.205880	+	0.356595i	0.950413	−	0.310991i	$-0.100661\pi$
$607$	1.86890e6	+	3.23704e6i	0.205880	+	0.356595i	−0.744532	+	0.667586i	$0.767328\pi$
$608$	−1.00716e6	+	1.74446e6i	−0.110494	+	0.191382i
$609$	−3.41686e6	+	5.91817e6i	−0.373322	+	0.646612i
$610$	7.93346e6			0.863253
$611$	2.50012e6	−	2.19608e6i	0.270930	−	0.237983i
$612$	5.48826e6			0.592320
$613$	−4.91617e6	+	8.51505e6i	−0.528416	+	0.915243i	0.471036	+	0.882114i	$0.343880\pi$
$613$	−4.91617e6	+	8.51505e6i	−0.528416	+	0.915243i	−0.999451	+	0.0331283i	$0.989453\pi$
$614$	−6.21157e6	+	1.07588e7i	−0.664937	+	1.15171i
$615$	1.07552e6	+	1.86286e6i	0.114665	+	0.198606i
$616$	−1.74292e6			−0.185066
$617$	−683692.	−	1.18419e6i	−0.0723016	−	0.125230i	0.827608	−	0.561306i	$-0.189701\pi$
$617$	−683692.	−	1.18419e6i	−0.0723016	−	0.125230i	−0.899910	+	0.436076i	$0.856368\pi$
$618$	−1.24414e6	−	2.15492e6i	−0.131039	−	0.226965i
$619$	−1.27231e7			−1.33465			−0.667323	−	0.744768i	$-0.732560\pi$
$619$	−1.27231e7			−1.33465			−0.667323	+	0.744768i	$0.732560\pi$
$620$	2.64965e6	+	4.58932e6i	0.276827	+	0.479479i
$621$	−1.31313e6	+	2.27441e6i	−0.136640	+	0.236668i
$622$	−4.98193e6	+	8.62895e6i	−0.516323	+	0.894298i
$623$	−2.68201e7			−2.76848
$624$	1.23267e6	+	417336.i	0.126732	+	0.0429066i
$625$	−8.56145e6			−0.876693
$626$	1.29524e6	−	2.24343e6i	0.132104	−	0.228811i
$627$	−921874.	+	1.59673e6i	−0.0936489	+	0.162205i
$628$	1.13572e6	+	1.96713e6i	0.114914	+	0.199037i
$629$	1.15890e7			1.16793
$630$	−4.43088e6	−	7.67451e6i	−0.444773	−	0.770370i
$631$	−3.63055e6	−	6.28830e6i	−0.362994	−	0.628723i	0.625458	−	0.780258i	$-0.284912\pi$
$631$	−3.63055e6	−	6.28830e6i	−0.362994	−	0.628723i	−0.988452	+	0.151534i	$0.951579\pi$
$632$	5.12960e6			0.510847
$633$	677233.	+	1.17300e6i	0.0671783	+	0.116356i
$634$	1.61356e6	−	2.79476e6i	0.159427	−	0.276135i
$635$	−4.17512e6	+	7.23152e6i	−0.410898	+	0.711697i
$636$	2.38524e6			0.233824
$637$	5.00717e6	+	2.50680e7i	0.488927	+	2.44777i
$638$	1.51854e6			0.147698
$639$	−202812.	+	351281.i	−0.0196490	+	0.0340331i
$640$	431786.	−	747875.i	0.0416695	−	0.0721737i
$641$	−1.43164e6	−	2.47967e6i	−0.137622	−	0.238368i	0.788974	−	0.614426i	$-0.210613\pi$
$641$	−1.43164e6	−	2.47967e6i	−0.137622	−	0.238368i	−0.926596	+	0.376058i	$0.877279\pi$
$642$	4.57012e6			0.437612
$643$	3.43693e6	+	5.95294e6i	0.327826	+	0.567811i	0.982080	−	0.188463i	$-0.0603507\pi$
$643$	3.43693e6	+	5.95294e6i	0.327826	+	0.567811i	−0.654254	+	0.756275i	$0.727017\pi$
$644$	−1.46604e6	−	2.53926e6i	−0.139294	−	0.241264i
$645$	−2.16239e6			−0.204661
$646$	7.78272e6	+	1.34801e7i	0.733754	+	1.27090i
$647$	1.05613e6	−	1.82928e6i	0.0991879	−	0.171798i	−0.812161	−	0.583434i	$-0.801709\pi$
$647$	1.05613e6	−	1.82928e6i	0.0991879	−	0.171798i	0.911349	+	0.411635i	$0.135042\pi$
$648$	420905.	−	729029.i	0.0393774	−	0.0682036i
$649$	2.03437e6			0.189591
$650$	165587.	+	828997.i	0.0153724	+	0.0769608i
$651$	1.27078e7			1.17522
$652$	1.09704e6	−	1.90012e6i	0.101065	−	0.175050i
$653$	8.03197e6	−	1.39118e7i	0.737122	−	1.27673i	−0.216664	−	0.976246i	$-0.569518\pi$
$653$	8.03197e6	−	1.39118e7i	0.737122	−	1.27673i	0.953786	−	0.300486i	$-0.0971490\pi$
$654$	878109.	+	1.52093e6i	0.0802794	+	0.139048i
$655$	−1.81526e7			−1.65324
$656$	−626135.	−	1.08450e6i	−0.0568078	−	0.0983940i
$657$	−4.55660e6	−	7.89227e6i	−0.411839	−	0.713327i
$658$	−5.29517e6			−0.476777
$659$	9.86910e6	+	1.70938e7i	0.885246	+	1.53329i	0.845432	+	0.534083i	$0.179343\pi$
$659$	9.86910e6	+	1.70938e7i	0.885246	+	1.53329i	0.0398140	+	0.999207i	$0.487323\pi$
$660$	395221.	−	684543.i	0.0353167	−	0.0611704i
$661$	−7.25233e6	+	1.25614e7i	−0.645615	+	1.11824i	0.338544	+	0.940951i	$0.390066\pi$
$661$	−7.25233e6	+	1.25614e7i	−0.645615	+	1.11824i	−0.984159	+	0.177287i	$0.943268\pi$
$662$	−3.85302e6			−0.341708
$663$	7.55550e6	−	6.63669e6i	0.667543	−	0.586365i
$664$	−5.51369e6			−0.485313
$665$	1.25666e7	−	2.17659e7i	1.10195	−	1.90864i
$666$	2.03164e6	−	3.51890e6i	0.177484	−	0.307412i
$667$	1.27730e6	+	2.21235e6i	0.111168	+	0.192548i
$668$	2.87885e6			0.249619
$669$	−3.33957e6	−	5.78431e6i	−0.288487	−	0.499674i
$670$	−2.50107e6	−	4.33199e6i	−0.215248	−	0.372821i
$671$	−4.22750e6			−0.362474
$672$	−1.03543e6	−	1.79342e6i	−0.0884500	−	0.153200i
$673$	5.38629e6	−	9.32933e6i	0.458408	−	0.793986i	−0.540469	−	0.841364i	$-0.681753\pi$
$673$	5.38629e6	−	9.32933e6i	0.458408	−	0.793986i	0.998877	+	0.0473777i	$0.0150864\pi$
$674$	−6.32782e6	+	1.09601e7i	−0.536543	+	0.929320i
$675$	−1.20490e6			−0.101787
$676$	−5.48484e6	+	2.28218e6i	−0.461633	+	0.192080i
$677$	8.05322e6			0.675302			0.337651	−	0.941271i	$-0.390368\pi$
$677$	8.05322e6			0.675302			0.337651	+	0.941271i	$0.390368\pi$
$678$	−3.19270e6	+	5.52993e6i	−0.266738	+	0.462003i
$679$	261325.	−	452628.i	0.0217523	−	0.0376762i
$680$	−3.33657e6	−	5.77911e6i	−0.276712	−	0.479279i
$681$	3.55297e6			0.293579
$682$	−1.41191e6	−	2.44551e6i	−0.116238	−	0.201330i
$683$	−4.65782e6	−	8.06757e6i	−0.382059	−	0.661746i	0.609297	−	0.792942i	$-0.291452\pi$
$683$	−4.65782e6	−	8.06757e6i	−0.382059	−	0.661746i	−0.991356	+	0.131196i	$0.958118\pi$
$684$	5.45748e6			0.446018
$685$	5.92136e6	+	1.02561e7i	0.482164	+	0.835133i
$686$	1.21906e7	−	2.11148e7i	0.989045	−	1.71308i
$687$	−610780.	+	1.05790e6i	−0.0493734	+	0.0855172i
$688$	1.25888e6			0.101394
$689$	−8.18047e6	+	7.18566e6i	−0.656493	+	0.576658i
$690$	1.32974e6			0.106327
$691$	−2.59769e6	+	4.49934e6i	−0.206963	+	0.358471i	−0.950756	−	0.309939i	$-0.899691\pi$
$691$	−2.59769e6	+	4.49934e6i	−0.206963	+	0.358471i	0.743793	+	0.668410i	$0.233025\pi$
$692$	−3.20021e6	+	5.54292e6i	−0.254046	+	0.440021i
$693$	2.36108e6	+	4.08951e6i	0.186757	+	0.323473i
$694$	4.11521e6			0.324334
$695$	8.06933e6	+	1.39765e7i	0.633688	+	1.09758i
$696$	902128.	+	1.56253e6i	0.0705903	+	0.122266i
$697$	−9.67675e6			−0.754480
$698$	−5.54859e6	−	9.61043e6i	−0.431066	−	0.746628i
$699$	3.49734e6	−	6.05758e6i	0.270736	−	0.468928i
$700$	672602.	−	1.16498e6i	0.0518816	−	0.0898615i
$701$	7.84176e6			0.602724			0.301362	−	0.953510i	$-0.402559\pi$
$701$	7.84176e6			0.602724			0.301362	+	0.953510i	$0.402559\pi$
$702$	−1.65851e6	−	8.30316e6i	−0.127021	−	0.635918i
$703$	1.15240e7			0.879456
$704$	−230086.	+	398520.i	−0.0174968	+	0.0303053i
$705$	1.20072e6	−	2.07971e6i	0.0909850	−	0.157591i
$706$	−6.96457e6	−	1.20630e7i	−0.525875	−	0.910843i
$707$	3.78478e6			0.284768
$708$	1.20857e6	+	2.09331e6i	0.0906127	+	0.156946i
$709$	−9.96878e6	−	1.72664e7i	−0.744778	−	1.28999i	−0.950299	−	0.311340i	$-0.899222\pi$
$709$	−9.96878e6	−	1.72664e7i	−0.744778	−	1.28999i	0.205521	−	0.978653i	$-0.434111\pi$
$710$	493196.			0.0367175
$711$	−6.94891e6	−	1.20359e7i	−0.515516	−	0.892901i
$712$	−3.54056e6	+	6.13243e6i	−0.261741	+	0.453349i
$713$	2.37523e6	−	4.11403e6i	0.174978	−	0.303070i
$714$	−1.60023e7			−1.17473
$715$	706764.	+	3.53835e6i	0.0517022	+	0.258843i
$716$	−8.65851e6			−0.631191
$717$	−1.30770e6	+	2.26500e6i	−0.0949971	+	0.164540i
$718$	−2.92815e6	+	5.07170e6i	−0.211974	+	0.367149i
$719$	−204812.	−	354745.i	−0.0147752	−	0.0255914i	0.858543	−	0.512741i	$-0.171370\pi$
$719$	−204812.	−	354745.i	−0.0147752	−	0.0255914i	−0.873318	+	0.487150i	$0.838037\pi$
$720$	−2.33971e6			−0.168202
$721$	−9.03725e6	−	1.56530e7i	−0.647438	−	1.12140i
$722$	2.78688e6	+	4.82702e6i	0.198964	+	0.344617i
$723$	−1.35862e7			−0.966611
$724$	−1.90200e6	−	3.29436e6i	−0.134854	−	0.233574i
$725$	−586011.	+	1.01500e6i	−0.0414057	+	0.0717168i
$726$	2.47663e6	−	4.28966e6i	0.174390	−	0.302052i
$727$	2.85707e6			0.200486			0.100243	−	0.994963i	$-0.468038\pi$
$727$	2.85707e6			0.200486			0.100243	+	0.994963i	$0.468038\pi$
$728$	8.95391e6	+	3.03146e6i	0.626158	+	0.211994i
$729$	4.76195e6			0.331869
$730$	−5.54035e6	+	9.59617e6i	−0.384795	+	0.666485i
$731$	4.86390e6	−	8.42452e6i	0.336660	−	0.583112i
$732$	−2.51146e6	−	4.34998e6i	−0.173240	−	0.300061i
$733$	−8.04109e6			−0.552783			−0.276392	−	0.961045i	$-0.589139\pi$
$733$	−8.04109e6			−0.552783			−0.276392	+	0.961045i	$0.589139\pi$
$734$	−45690.0	−	79137.4i	−0.00313026	−	0.00542177i
$735$	9.22396e6	+	1.59764e7i	0.629795	+	1.09084i
$736$	−774136.			−0.0526772
$737$	1.33275e6	+	2.30838e6i	0.0903813	+	0.156545i
$738$	−1.69641e6	+	2.93827e6i	−0.114654	+	0.198587i
$739$	1.26396e7	−	2.18925e7i	0.851380	−	1.47463i	−0.0285822	−	0.999591i	$-0.509099\pi$
$739$	1.26396e7	−	2.18925e7i	0.851380	−	1.47463i	0.879963	−	0.475043i	$-0.157567\pi$
$740$	−4.94051e6			−0.331659
$741$	7.51313e6	−	6.59947e6i	0.502661	−	0.441534i
$742$	1.73260e7			1.15528
$743$	−1.40649e7	+	2.43611e7i	−0.934682	+	1.61892i	−0.159481	+	0.987201i	$0.550982\pi$
$743$	−1.40649e7	+	2.43611e7i	−0.934682	+	1.61892i	−0.775201	+	0.631715i	$0.782351\pi$
$744$	1.67757e6	−	2.90564e6i	0.111109	−	0.192446i
$745$	−2.15951e6	−	3.74038e6i	−0.142549	−	0.246902i
$746$	−3.17864e6			−0.209119
$747$	7.46922e6	+	1.29371e7i	0.489749	+	0.848271i
$748$	1.77796e6	+	3.07951e6i	0.116190	+	0.201246i
$749$	3.31966e7			2.16216
$750$	3.05338e6	+	5.28861e6i	0.198211	+	0.343311i
$751$	−7.96651e6	+	1.37984e7i	−0.515428	+	0.892748i	0.484411	+	0.874840i	$0.339034\pi$
$751$	−7.96651e6	+	1.37984e7i	−0.515428	+	0.892748i	−0.999840	+	0.0179078i	$0.994299\pi$
$752$	−699023.	+	1.21074e6i	−0.0450761	+	0.0780742i
$753$	−3.02719e6			−0.194559
$754$	−7.80117e6	−	2.64119e6i	−0.499725	−	0.169188i
$755$	1.39973e7			0.893671
$756$	−6.73673e6	+	1.16684e7i	−0.428691	+	0.742515i
$757$	−1.36866e7	+	2.37059e7i	−0.868073	+	1.50355i	−0.00410944	+	0.999992i	$0.501308\pi$
$757$	−1.36866e7	+	2.37059e7i	−0.868073	+	1.50355i	−0.863963	+	0.503555i	$0.832025\pi$
$758$	2.81672e6	+	4.87871e6i	0.178062	+	0.308412i
$759$	−708580.			−0.0446462
$760$	−3.31786e6	−	5.74670e6i	−0.208365	−	0.360898i
$761$	−3.35057e6	−	5.80336e6i	−0.209728	−	0.363260i	0.741901	−	0.670510i	$-0.233925\pi$
$761$	−3.35057e6	−	5.80336e6i	−0.209728	−	0.363260i	−0.951629	+	0.307250i	$0.900591\pi$
$762$	5.28680e6			0.329841
$763$	6.37844e6	+	1.10478e7i	0.396646	+	0.687011i
$764$	1.72065e6	−	2.98025e6i	0.106650	−	0.184722i
$765$	−9.03989e6	+	1.56576e7i	−0.558483	+	0.967320i
$766$	1.91159e7			1.17712
$767$	−1.04511e7	−	3.53837e6i	−0.641469	−	0.217177i
$768$	−546754.			−0.0334495
$769$	5.69416e6	−	9.86257e6i	0.347227	−	0.601415i	−0.638529	−	0.769598i	$-0.720457\pi$
$769$	5.69416e6	−	9.86257e6i	0.347227	−	0.601415i	0.985756	+	0.168183i	$0.0537899\pi$
$770$	2.87082e6	−	4.97241e6i	0.174494	−	0.302232i
$771$	−1.91881e6	−	3.32347e6i	−0.116251	−	0.201352i
$772$	1.66636e6			0.100630
$773$	−1.49555e7	−	2.59037e7i	−0.900228	−	1.55924i	−0.827198	−	0.561911i	$-0.810066\pi$
$773$	−1.49555e7	−	2.59037e7i	−0.900228	−	1.55924i	−0.0730303	−	0.997330i	$-0.523267\pi$
$774$	−1.70536e6	−	2.95377e6i	−0.102321	−	0.177225i
$775$	2.17946e6			0.130345
$776$	−68995.7	−	119504.i	−0.00411308	−	0.00712407i
$777$	−5.92371e6	+	1.02602e7i	−0.351999	+	0.609680i
$778$	1.08829e7	−	1.88497e7i	0.644606	−	1.11649i
$779$	−9.62249e6			−0.568125
$780$	−3.22099e6	+	2.82930e6i	−0.189563	+	0.166511i
$781$	−262809.			−0.0154174
$782$	−2.99102e6	+	5.18060e6i	−0.174905	+	0.302944i
$783$	5.86943e6	−	1.01662e7i	0.342131	−	0.592587i
$784$	−5.36990e6	−	9.30094e6i	−0.312016	−	0.540427i
$785$	−7.48275e6			−0.433398
$786$	5.74650e6	+	9.95323e6i	0.331778	+	0.574656i
$787$	−3.24262e6	−	5.61639e6i	−0.186621	−	0.323236i	0.757501	−	0.652834i	$-0.226420\pi$
$787$	−3.24262e6	−	5.61639e6i	−0.186621	−	0.323236i	−0.944121	+	0.329598i	$0.893087\pi$
$788$	4.80682e6			0.275767
$789$	−5.51132e6	−	9.54588e6i	−0.315183	−	0.545913i
$790$	−8.44913e6	+	1.46343e7i	−0.481664	+	0.834267i
$791$	−2.31913e7	+	4.01685e7i	−1.31790	+	2.28268i
$792$	1.24676e6			0.0706267
$793$	2.17179e7	+	7.35288e6i	1.22641	+	0.415216i
$794$	2.01566e7			1.13466
$795$	−3.92880e6	+	6.80489e6i	−0.220466	+	0.381859i
$796$	−3.21192e6	+	5.56320e6i	−0.179672	+	0.311202i
$797$	3.57395e6	+	6.19026e6i	0.199298	+	0.345194i	0.948301	−	0.317373i	$-0.102801\pi$
$797$	3.57395e6	+	6.19026e6i	0.199298	+	0.345194i	−0.749003	+	0.662566i	$0.769467\pi$
$798$	−1.59126e7			−0.884572
$799$	5.40161e6	+	9.35586e6i	0.299334	+	0.518462i
$800$	−177582.	−	307582.i	−0.00981013	−	0.0169916i
$801$	1.91851e7			1.05653
$802$	−8.94781e6	−	1.54981e7i	−0.491225	−	0.850827i
$803$	2.95228e6	−	5.11350e6i	0.161573	−	0.279853i
$804$	−1.58351e6	+	2.74272e6i	−0.0863933	+	0.149638i
$805$	9.65905e6			0.525345
$806$	2.99996e6	+	1.50190e7i	0.162659	+	0.814338i
$807$	−8.55568e6			−0.462456
$808$	499634.	−	865391.i	0.0269230	−	0.0466320i
$809$	−3.28552e6	+	5.69068e6i	−0.176495	+	0.305698i	−0.940678	−	0.339302i	$-0.889809\pi$
$809$	−3.28552e6	+	5.69068e6i	−0.176495	+	0.305698i	0.764183	+	0.645000i	$0.223143\pi$
$810$	1.38657e6	+	2.40162e6i	0.0742558	+	0.128615i
$811$	1.65638e7			0.884316			0.442158	−	0.896937i	$-0.354213\pi$
$811$	1.65638e7			0.884316			0.442158	+	0.896937i	$0.354213\pi$
$812$	6.55291e6	+	1.13500e7i	0.348774	+	0.604094i
$813$	−6.50622e6	−	1.12691e7i	−0.345225	−	0.597947i
$814$	2.63265e6			0.139262
$815$	3.61393e6	+	6.25950e6i	0.190583	+	0.330100i
$816$	−2.11249e6	+	3.65894e6i	−0.111063	+	0.192367i
$817$	4.83662e6	−	8.37728e6i	0.253505	−	0.439084i
$818$	1.13062e6			0.0590791
$819$	−5.01669e6	−	2.51157e7i	−0.261341	−	1.30838i
$820$	4.12531e6			0.214250
$821$	1.51810e7	−	2.62943e7i	0.786036	−	1.36145i	−0.142342	−	0.989817i	$-0.545463\pi$
$821$	1.51810e7	−	2.62943e7i	0.786036	−	1.36145i	0.928378	−	0.371637i	$-0.121203\pi$
$822$	3.74900e6	−	6.49346e6i	0.193524	−	0.335194i
$823$	−3.25857e6	−	5.64400e6i	−0.167698	−	0.290461i	0.769912	−	0.638150i	$-0.220300\pi$
$823$	−3.25857e6	−	5.64400e6i	−0.167698	−	0.290461i	−0.937610	+	0.347689i	$0.886967\pi$
$824$	−4.77208e6			−0.244844
$825$	−162544.	−	281535.i	−0.00831451	−	0.0144012i
$826$	8.77886e6	+	1.52054e7i	0.447701	+	0.775441i
$827$	−2.40119e7			−1.22085			−0.610425	−	0.792074i	$-0.709001\pi$
$827$	−2.40119e7			−1.22085			−0.610425	+	0.792074i	$0.709001\pi$
$828$	1.04870e6	+	1.81640e6i	0.0531587	+	0.0920735i
$829$	2.50611e6	−	4.34071e6i	0.126653	−	0.219369i	−0.795725	−	0.605658i	$-0.792910\pi$
$829$	2.50611e6	−	4.34071e6i	0.126653	−	0.219369i	0.922378	+	0.386289i	$0.126243\pi$
$830$	9.08178e6	−	1.57301e7i	0.457589	−	0.792568i
$831$	7.59868e6			0.381712
$832$	1.87516e6	−	1.64713e6i	0.0939140	−	0.0824933i
$833$	−8.29905e7			−4.14396
$834$	5.10895e6	−	8.84896e6i	0.254341	−	0.440531i
$835$	−4.74185e6	+	8.21312e6i	−0.235359	+	0.407654i
$836$	1.76799e6	+	3.06224e6i	0.0874910	+	0.151539i
$837$	−2.18293e7			−1.07703
$838$	2.82894e6	+	4.89987e6i	0.139160	+	0.241032i
$839$	−5.65067e6	−	9.78725e6i	−0.277137	−	0.480016i	0.693535	−	0.720423i	$-0.256052\pi$
$839$	−5.65067e6	−	9.78725e6i	−0.277137	−	0.480016i	−0.970672	+	0.240407i	$0.922719\pi$
$840$	6.82197e6			0.333589
$841$	4.54629e6	+	7.87441e6i	0.221650	+	0.383909i
$842$	−8.50184e6	+	1.47256e7i	−0.413269	+	0.715802i
$843$	7.23804e6	−	1.25366e7i	0.350794	−	0.607593i
$844$	2.59762e6			0.125522
$845$	2.52339e6	−	1.94068e7i	0.121575	−	0.935003i
$846$	3.78778e6			0.181953
$847$	1.79899e7	−	3.11594e7i	0.861628	−	1.49238i
$848$	2.28723e6	−	3.96159e6i	0.109224	−	0.189182i
$849$	378712.	+	655949.i	0.0180318	+	0.0312321i
$850$	−2.74449e6			−0.130291
$851$	2.21442e6	+	3.83549e6i	0.104818	+	0.181550i
$852$	−156129.	−	270423.i	−0.00736859	−	0.0127628i
$853$	2.15583e6			0.101448			0.0507239	−	0.998713i	$-0.483847\pi$
$853$	2.15583e6			0.101448			0.0507239	+	0.998713i	$0.483847\pi$
$854$	−1.82428e7	−	3.15975e7i	−0.855949	−	1.48255i
$855$	−8.98920e6	+	1.55698e7i	−0.420539	+	0.728394i
$856$	4.38233e6	−	7.59041e6i	0.204419	−	0.354063i
$857$	2.28849e7			1.06438			0.532190	−	0.846625i	$-0.321369\pi$
$857$	2.28849e7			1.06438			0.532190	+	0.846625i	$0.321369\pi$
$858$	1.71637e6	−	1.50764e6i	0.0795962	−	0.0699167i
$859$	−3.14203e6			−0.145287			−0.0726437	−	0.997358i	$-0.523144\pi$
$859$	−3.14203e6			−0.145287			−0.0726437	+	0.997358i	$0.523144\pi$
$860$	−2.07353e6	+	3.59147e6i	−0.0956016	+	0.165587i
$861$	4.94628e6	−	8.56721e6i	0.227390	−	0.393851i
$862$	1.19316e7	+	2.06661e7i	0.546926	+	0.947304i
$863$	5.29393e6			0.241964			0.120982	−	0.992655i	$-0.461396\pi$
$863$	5.29393e6			0.241964			0.120982	+	0.992655i	$0.461396\pi$
$864$	1.77865e6	+	3.08071e6i	0.0810599	+	0.140400i
$865$	−1.05423e7	−	1.82599e7i	−0.479067	−	0.829769i
$866$	−2.07646e7			−0.940868
$867$	1.04012e7	+	1.80154e7i	0.469932	+	0.813946i
$868$	1.21856e7	−	2.11061e7i	0.548970	−	0.950843i
$869$	4.50228e6	−	7.79819e6i	0.202248	−	0.350303i
$870$	−5.94370e6			−0.266231
$871$	−2.83175e6	−	1.41769e7i	−0.126476	−	0.633192i
$872$	3.36811e6			0.150001
$873$	−186932.	+	323776.i	−0.00830136	+	0.0143784i
$874$	−2.97425e6	+	5.15155e6i	−0.131704	+	0.228118i
$875$	2.21793e7	+	3.84156e7i	0.979325	+	1.69624i
$876$	7.01554e6			0.308888
$877$	9.04101e6	+	1.56595e7i	0.396933	+	0.687509i	0.993346	−	0.115169i	$-0.0367410\pi$
$877$	9.04101e6	+	1.56595e7i	0.396933	+	0.687509i	−0.596412	+	0.802678i	$0.703408\pi$
$878$	−1.41104e6	−	2.44400e6i	−0.0617738	−	0.106995i
$879$	−8.63814e6			−0.377093
$880$	−757963.	−	1.31283e6i	−0.0329945	−	0.0571481i
$881$	−1.73939e7	+	3.01270e7i	−0.755016	+	1.30773i	0.190350	+	0.981716i	$0.439038\pi$
$881$	−1.73939e7	+	3.01270e7i	−0.755016	+	1.30773i	−0.945366	+	0.326010i	$0.894296\pi$
$882$	−1.45489e7	+	2.51994e7i	−0.629735	+	1.09073i
$883$	7.86729e6			0.339565			0.169783	−	0.985482i	$-0.445693\pi$
$883$	7.86729e6			0.339565			0.169783	+	0.985482i	$0.445693\pi$
$884$	−3.77771e6	−	1.89128e7i	−0.162591	−	0.814000i
$885$	−7.96271e6			−0.341745
$886$	1.26005e6	−	2.18247e6i	0.0539267	−	0.0934038i
$887$	1.49144e7	−	2.58325e7i	0.636498	−	1.10245i	−0.349698	−	0.936863i	$-0.613716\pi$
$887$	1.49144e7	−	2.58325e7i	0.636498	−	1.10245i	0.986196	−	0.165584i	$-0.0529509\pi$
$888$	1.56400e6	+	2.70892e6i	0.0665584	+	0.115283i
$889$	3.84024e7			1.62969
$890$	−1.16636e7	−	2.02019e7i	−0.493578	−	0.854902i
$891$	−738862.	−	1.27975e6i	−0.0311795	−	0.0540045i
$892$	−1.28094e7			−0.539035
$893$	5.37132e6	+	9.30340e6i	0.225399	+	0.390403i
$894$	−1.36725e6	+	2.36815e6i	−0.0572143	+	0.0990981i
$895$	1.42617e7	−	2.47020e7i	0.595133	−	1.03080i
$896$	−3.97154e6			−0.165268
$897$	3.64019e6	+	1.23243e6i	0.151058	+	0.0511425i
$898$	−1.37309e6			−0.0568209
$899$	−1.06168e7	+	1.83889e7i	−0.438123	+	0.758851i
$900$	−481130.	+	833342.i	−0.0197996	+	0.0342939i
$901$	−1.76743e7	−	3.06127e7i	−0.725319	−	1.25629i
$902$	−2.19825e6			−0.0899623
$903$	4.97237e6	+	8.61240e6i	0.202929	+	0.351484i
$904$	6.12303e6	+	1.06054e7i	0.249198	+	0.431624i
$905$	1.25314e7			0.508602
$906$	−4.43107e6	−	7.67484e6i	−0.179345	−	0.310634i
$907$	6.69786e6	−	1.16010e7i	0.270345	−	0.468251i	−0.698605	−	0.715507i	$-0.746196\pi$
$907$	6.69786e6	−	1.16010e7i	0.270345	−	0.468251i	0.968950	+	0.247256i	$0.0795290\pi$
$908$	3.40698e6	−	5.90106e6i	0.137137	−	0.237528i
$909$	−2.70735e6			−0.108676
$910$	−2.33968e7	+	2.05515e7i	−0.936597	+	0.822699i
$911$	−1.30417e7			−0.520641			−0.260320	−	0.965522i	$-0.583828\pi$
$911$	−1.30417e7			−0.520641			−0.260320	+	0.965522i	$0.583828\pi$
$912$	−2.10064e6	+	3.63842e6i	−0.0836305	+	0.144852i
$913$	−4.83940e6	+	8.38209e6i	−0.192139	+	0.332794i
$914$	−1.21594e7	−	2.10607e7i	−0.481446	−	0.833889i
$915$	1.65468e7			0.653375
$916$	1.17137e6	+	2.02886e6i	0.0461268	+	0.0798940i
$917$	4.17416e7	+	7.22986e7i	1.63925	+	2.83927i
$918$	2.74886e7			1.07658
$919$	1.15432e7	+	1.99934e7i	0.450855	+	0.780904i	0.998439	−	0.0558468i	$-0.0177858\pi$
$919$	1.15432e7	+	1.99934e7i	0.450855	+	0.780904i	−0.547584	+	0.836750i	$0.684453\pi$
$920$	1.27510e6	−	2.20855e6i	0.0496680	−	0.0860274i
$921$	−1.29555e7	+	2.24396e7i	−0.503275	+	0.871697i
$922$	4.83438e6			0.187290
$923$	1.35013e6	+	457103.i	0.0521640	+	0.0176608i
$924$	−3.63522e6			−0.140072
$925$	−1.01595e6	+	1.75968e6i	−0.0390408	+	0.0676206i
$926$	−6.63358e6	+	1.14897e7i	−0.254226	+	0.440333i
$927$	6.46458e6	+	1.11970e7i	0.247082	+	0.427959i
$928$	3.46024e6			0.131897
$929$	3.26726e6	+	5.65905e6i	0.124206	+	0.215132i	0.921422	−	0.388562i	$-0.127028\pi$
$929$	3.26726e6	+	5.65905e6i	0.124206	+	0.215132i	−0.797216	+	0.603694i	$0.793695\pi$
$930$	5.52637e6	+	9.57196e6i	0.209524	+	0.362905i
$931$	−8.25251e7			−3.12041
$932$	−6.70727e6	−	1.16173e7i	−0.252933	−	0.438094i
$933$	−1.03908e7	+	1.79974e7i	−0.390792	+	0.676872i
$934$	1.53960e7	−	2.66666e7i	0.577483	−	1.00023i
$935$	−1.17141e7			−0.438208
$936$	−6.40497e6	−	2.16848e6i	−0.238961	−	0.0809033i
$937$	2.63991e7			0.982291			0.491145	−	0.871078i	$-0.336578\pi$
$937$	2.63991e7			0.982291			0.491145	+	0.871078i	$0.336578\pi$
$938$	−1.15023e7	+	1.99226e7i	−0.426854	+	0.739333i
$939$	2.70149e6	−	4.67912e6i	0.0999861	−	0.173181i
$940$	−2.30277e6	−	3.98851e6i	−0.0850022	−	0.147228i
$941$	−1.31486e7			−0.484067			−0.242034	−	0.970268i	$-0.577814\pi$
$941$	−1.31486e7			−0.484067			−0.242034	+	0.970268i	$0.577814\pi$
$942$	2.36878e6	+	4.10285e6i	0.0869756	+	0.150646i
$943$	−1.84903e6	−	3.20262e6i	−0.0677120	−	0.117281i
$944$	4.63564e6			0.169309
$945$	−2.21926e7	−	3.84387e7i	−0.808403	−	1.40020i
$946$	1.10492e6	−	1.91378e6i	0.0401425	−	0.0695288i
$947$	−1.65015e6	+	2.85814e6i	−0.0597927	+	0.103564i	−0.894372	−	0.447323i	$-0.852377\pi$
$947$	−1.65015e6	+	2.85814e6i	−0.0597927	+	0.103564i	0.834580	+	0.550887i	$0.185711\pi$
$948$	1.06988e7			0.386648
$949$	−2.40607e7	+	2.11347e7i	−0.867245	+	0.761781i
$950$	−2.72910e6			−0.0981093
$951$	3.36540e6	−	5.82904e6i	0.120666	−	0.209000i
$952$	−1.53448e7	+	2.65779e7i	−0.548742	+	0.950449i
$953$	2.63312e7	+	4.56070e7i	0.939159	+	1.62667i	0.767045	+	0.641594i	$0.221727\pi$
$953$	2.63312e7	+	4.56070e7i	0.939159	+	1.62667i	0.172114	+	0.985077i	$0.444940\pi$
$954$	−1.23937e7			−0.440891
$955$	5.66828e6	+	9.81774e6i	0.201114	+	0.348340i
$956$	2.50793e6	+	4.34387e6i	0.0887506	+	0.153721i
$957$	3.16721e6			0.111789
$958$	5.65564e6	+	9.79585e6i	0.199098	+	0.344848i
$959$	2.72321e7	−	4.71674e7i	0.956169	−	1.65613i
$960$	900577.	−	1.55985e6i	0.0315386	−	0.0546265i
$961$	1.08564e7			0.379208
$962$	−1.35247e7	−	4.57895e6i	−0.471183	−	0.159525i
$963$	−2.37464e7			−0.825148
$964$	−1.30279e7	+	2.25650e7i	−0.451526	+	0.782065i
$965$	−2.74472e6	+	4.75399e6i	−0.0948811	+	0.164339i
$966$	−3.05772e6	−	5.29613e6i	−0.105428	−	0.182606i
$967$	1.14943e7			0.395291			0.197646	−	0.980274i	$-0.436670\pi$
$967$	1.14943e7			0.395291			0.197646	+	0.980274i	$0.436670\pi$
$968$	−4.74974e6	−	8.22679e6i	−0.162923	−	0.282190i
$969$	1.62324e7	+	2.81154e7i	0.555360	+	0.961911i
$970$	454580.			0.0155125
$971$	−2.38756e7	−	4.13538e7i	−0.812655	−	1.40756i	−0.910999	−	0.412408i	$-0.864688\pi$
$971$	−2.38756e7	−	4.13538e7i	−0.812655	−	1.40756i	0.0983438	−	0.995152i	$-0.468646\pi$
$972$	7.63119e6	−	1.32176e7i	0.259076	−	0.448732i
$973$	3.71106e7	−	6.42774e7i	1.25665	−	2.17659i
$974$	1.59481e6			0.0538658
$975$	345365.	+	1.72904e6i	0.0116350	+	0.0582497i
$976$	−9.63305e6			−0.323698
$977$	1.10965e7	−	1.92197e7i	0.371920	−	0.644185i	−0.617941	−	0.786225i	$-0.712033\pi$
$977$	1.10965e7	−	1.92197e7i	0.371920	−	0.644185i	0.989861	+	0.142040i	$0.0453661\pi$
$978$	2.28809e6	−	3.96309e6i	0.0764937	−	0.132491i
$979$	6.21515e6	+	1.07650e7i	0.207250	+	0.358968i
$980$	3.53798e7			1.17677
$981$	−4.56267e6	−	7.90277e6i	−0.151372	−	0.262184i
$982$	4.24071e6	+	7.34512e6i	0.140333	+	0.243064i
$983$	3.73443e7			1.23265			0.616327	−	0.787491i	$-0.288620\pi$
$983$	3.73443e7			1.23265			0.616327	+	0.787491i	$0.288620\pi$
$984$	−1.30593e6	−	2.26194e6i	−0.0429964	−	0.0744720i
$985$	−7.91747e6	+	1.37135e7i	−0.260014	+	0.450357i
$986$	1.33693e7	−	2.31562e7i	0.437941	−	0.758535i
$987$	−1.10442e7			−0.360861
$988$	−3.75652e6	−	1.88067e7i	−0.122432	−	0.612943i
$989$	3.71758e6			0.120856
$990$	−2.05358e6	+	3.55690e6i	−0.0665921	+	0.115341i
$991$	1.31161e7	−	2.27177e7i	0.424248	−	0.734819i	−0.572102	−	0.820183i	$-0.693872\pi$
$991$	1.31161e7	−	2.27177e7i	0.424248	−	0.734819i	0.996350	+	0.0853634i	$0.0272051\pi$
$992$	−3.21728e6	−	5.57250e6i	−0.103803	−	0.179792i
$993$	−8.03624e6			−0.258631
$994$	−1.13409e6	−	1.96431e6i	−0.0364069	−	0.0630586i
$995$	−1.05809e7	−	1.83267e7i	−0.338817	−	0.586848i
$996$	−1.14999e7			−0.367322
$997$	1.30594e7	+	2.26195e7i	0.416088	+	0.720686i	0.995542	−	0.0943192i	$-0.0300674\pi$
$997$	1.30594e7	+	2.26195e7i	0.416088	+	0.720686i	−0.579454	+	0.815005i	$0.696734\pi$
$998$	1.32723e6	−	2.29883e6i	0.0421813	−	0.0730602i
$999$	1.01757e7	−	1.76248e7i	0.322589	−	0.558741i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.6.c.b.9.3	yes	8
3.2	odd	2		234.6.h.f.217.2		8
4.3	odd	2		208.6.i.c.113.2		8
13.3	even	3	inner	26.6.c.b.3.3	✓	8
13.4	even	6		338.6.a.k.1.2		4
13.6	odd	12		338.6.b.e.337.6		8
13.7	odd	12		338.6.b.e.337.2		8
13.9	even	3		338.6.a.j.1.2		4
39.29	odd	6		234.6.h.f.55.2		8
52.3	odd	6		208.6.i.c.81.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.6.c.b.3.3	✓	8	13.3	even	3	inner
26.6.c.b.9.3	yes	8	1.1	even	1	trivial
208.6.i.c.81.2		8	52.3	odd	6
208.6.i.c.113.2		8	4.3	odd	2
234.6.h.f.55.2		8	39.29	odd	6
234.6.h.f.217.2		8	3.2	odd	2
338.6.a.j.1.2		4	13.9	even	3
338.6.a.k.1.2		4	13.4	even	6
338.6.b.e.337.2		8	13.7	odd	12
338.6.b.e.337.6		8	13.6	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	26.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 - 3.46410i) q^{2} +(4.17141 - 7.22509i) q^{3} +(-8.00000 - 13.8564i) q^{4} +52.7082 q^{5} +(-16.6856 - 28.9003i) q^{6} +(-121.202 - 209.927i) q^{7} -64.0000 q^{8} +(86.6987 + 150.167i) q^{9} +(105.416 - 182.587i) q^{10} +(-56.1732 + 97.2949i) q^{11} -133.485 q^{12} +(457.803 - 402.131i) q^{13} -969.613 q^{14} +(219.867 - 380.822i) q^{15} +(-128.000 + 221.703i) q^{16} +(989.104 + 1713.18i) q^{17} +693.590 q^{18} +(983.557 + 1703.57i) q^{19} +(-421.666 - 730.347i) q^{20} -2022.33 q^{21} +(224.693 + 389.179i) q^{22} +(-377.996 + 654.708i) q^{23} +(-266.970 + 462.406i) q^{24} -346.840 q^{25} +(-477.415 - 2390.14i) q^{26} +3473.93 q^{27} +(-1939.23 + 3358.84i) q^{28} +(1689.57 - 2926.42i) q^{29} +(-879.470 - 1523.29i) q^{30} -6283.75 q^{31} +(512.000 + 886.810i) q^{32} +(468.643 + 811.713i) q^{33} +7912.83 q^{34} +(-6388.33 - 11064.9i) q^{35} +(1387.18 - 2402.67i) q^{36} +(2929.16 - 5073.45i) q^{37} +7868.46 q^{38} +(-995.746 - 4985.12i) q^{39} -3373.33 q^{40} +(-2445.84 + 4236.32i) q^{41} +(-4044.65 + 7005.54i) q^{42} +(-2458.74 - 4258.66i) q^{43} +1797.54 q^{44} +(4569.74 + 7915.02i) q^{45} +(1511.98 + 2618.83i) q^{46} +5461.12 q^{47} +(1067.88 + 1849.62i) q^{48} +(-20976.2 + 36331.8i) q^{49} +(-693.681 + 1201.49i) q^{50} +16503.8 q^{51} +(-9234.51 - 3126.46i) q^{52} -17869.0 q^{53} +(6947.85 - 12034.0i) q^{54} +(-2960.79 + 5128.24i) q^{55} +(7756.91 + 13435.4i) q^{56} +16411.3 q^{57} +(-6758.27 - 11705.7i) q^{58} +(-9053.99 - 15682.0i) q^{59} -7035.76 q^{60} +(18814.6 + 32587.8i) q^{61} +(-12567.5 + 21767.6i) q^{62} +(21016.1 - 36400.9i) q^{63} +4096.00 q^{64} +(24130.0 - 21195.6i) q^{65} +3749.14 q^{66} +(11862.8 - 20547.0i) q^{67} +(15825.7 - 27410.8i) q^{68} +(3153.55 + 5462.11i) q^{69} -51106.6 q^{70} +(1169.64 + 2025.87i) q^{71} +(-5548.72 - 9610.66i) q^{72} -52556.8 q^{73} +(-11716.6 - 20293.8i) q^{74} +(-1446.81 + 2505.95i) q^{75} +(15736.9 - 27257.1i) q^{76} +27233.1 q^{77} +(-19260.5 - 6520.87i) q^{78} -80150.0 q^{79} +(-6746.66 + 11685.6i) q^{80} +(-6576.64 + 11391.1i) q^{81} +(9783.36 + 16945.3i) q^{82} +86151.4 q^{83} +(16178.6 + 28022.2i) q^{84} +(52133.9 + 90298.6i) q^{85} -19669.9 q^{86} +(-14095.7 - 24414.6i) q^{87} +(3595.09 - 6226.87i) q^{88} +(55321.3 - 95819.3i) q^{89} +36557.9 q^{90} +(-139905. - 47366.6i) q^{91} +12095.9 q^{92} +(-26212.1 + 45400.7i) q^{93} +(10922.2 - 18917.9i) q^{94} +(51841.6 + 89792.3i) q^{95} +8543.04 q^{96} +(1078.06 + 1867.25i) q^{97} +(83904.7 + 145327. i) q^{98} -19480.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{2} - 64 q^{4} - 24 q^{5} + 126 q^{7} - 512 q^{8} - 458 q^{9} - 48 q^{10} + 446 q^{11} + 1384 q^{13} + 1008 q^{14} - 790 q^{15} - 1024 q^{16} - 500 q^{17} - 3664 q^{18} + 4048 q^{19} + 192 q^{20}+ \cdots - 533984 q^{99}+O(q^{100}) \) 8 * q + 16 * q^2 - 64 * q^4 - 24 * q^5 + 126 * q^7 - 512 * q^8 - 458 * q^9 - 48 * q^10 + 446 * q^11 + 1384 * q^13 + 1008 * q^14 - 790 * q^15 - 1024 * q^16 - 500 * q^17 - 3664 * q^18 + 4048 * q^19 + 192 * q^20 + 2300 * q^21 - 1784 * q^22 + 296 * q^23 + 19788 * q^25 + 1112 * q^26 - 18180 * q^27 + 2016 * q^28 - 4114 * q^29 + 3160 * q^30 - 25036 * q^31 + 4096 * q^32 - 9730 * q^33 - 4000 * q^34 + 2340 * q^35 - 7328 * q^36 + 16258 * q^37 + 32384 * q^38 + 2460 * q^39 + 1536 * q^40 - 6056 * q^41 + 4600 * q^42 + 4818 * q^43 - 14272 * q^44 + 24964 * q^45 - 1184 * q^46 - 43060 * q^47 - 95094 * q^49 + 39576 * q^50 + 129440 * q^51 - 17696 * q^52 - 30032 * q^53 - 36360 * q^54 - 3360 * q^55 - 8064 * q^56 + 37940 * q^57 + 16456 * q^58 - 6734 * q^59 + 25280 * q^60 + 6978 * q^61 - 50072 * q^62 + 175812 * q^63 + 32768 * q^64 - 149818 * q^65 - 77840 * q^66 + 24464 * q^67 - 8000 * q^68 + 115290 * q^69 + 18720 * q^70 - 18552 * q^71 + 29312 * q^72 - 84596 * q^73 - 65032 * q^74 - 218210 * q^75 + 64768 * q^76 + 358604 * q^77 - 202680 * q^78 - 529664 * q^79 + 3072 * q^80 + 64624 * q^81 + 24224 * q^82 + 139800 * q^83 - 18400 * q^84 + 171548 * q^85 + 38544 * q^86 - 39420 * q^87 - 28544 * q^88 + 154642 * q^89 + 199712 * q^90 - 65074 * q^91 - 9472 * q^92 + 331860 * q^93 - 86120 * q^94 + 284278 * q^95 + 206498 * q^97 + 380376 * q^98 - 533984 * q^99

Introduction

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