LMFDB - Embedded newform 26.6.c.a.9.1

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 = [6] 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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 314x^{4} + 24649x^{2} + 245388 $ x^6 + 314x^4 + 24649x^2 + 245388
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			9.1
Root			$13.8811i$ of defining polynomial
Character	$\chi$	$=$	26.9
Dual form			26.6.c.a.3.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00000 + 3.46410i) q^{2} +(-12.0214 + 20.8217i) q^{3} +(-8.00000 - 13.8564i) q^{4} +8.48514 q^{5} +(-48.0857 - 83.2869i) q^{6} +(-61.5791 - 106.658i) q^{7} +64.0000 q^{8} +(-167.529 - 290.169i) q^{9} +(-16.9703 + 29.3934i) q^{10} +(-176.935 + 306.461i) q^{11} +384.686 q^{12} +(-609.291 - 7.57102i) q^{13} +492.633 q^{14} +(-102.003 + 176.675i) q^{15} +(-128.000 + 221.703i) q^{16} +(-182.995 - 316.956i) q^{17} +1340.24 q^{18} +(811.468 + 1405.50i) q^{19} +(-67.8811 - 117.574i) q^{20} +2961.08 q^{21} +(-707.740 - 1225.84i) q^{22} +(-2088.78 + 3617.88i) q^{23} +(-769.371 + 1332.59i) q^{24} -3053.00 q^{25} +(1244.81 - 2095.50i) q^{26} +2213.36 q^{27} +(-985.266 + 1706.53i) q^{28} +(4283.66 - 7419.52i) q^{29} +(-408.014 - 706.701i) q^{30} -3118.00 q^{31} +(-512.000 - 886.810i) q^{32} +(-4254.02 - 7368.19i) q^{33} +1463.96 q^{34} +(-522.508 - 905.010i) q^{35} +(-2680.47 + 4642.71i) q^{36} +(-5458.91 + 9455.10i) q^{37} -6491.75 q^{38} +(7482.19 - 12595.5i) q^{39} +543.049 q^{40} +(-3173.94 + 5497.43i) q^{41} +(-5922.15 + 10257.5i) q^{42} +(7676.48 + 13296.1i) q^{43} +5661.92 q^{44} +(-1421.51 - 2462.13i) q^{45} +(-8355.14 - 14471.5i) q^{46} +22912.4 q^{47} +(-3077.49 - 5330.36i) q^{48} +(819.518 - 1419.45i) q^{49} +(6106.00 - 10575.9i) q^{50} +8799.43 q^{51} +(4769.42 + 8503.15i) q^{52} +17016.4 q^{53} +(-4426.71 + 7667.29i) q^{54} +(-1501.32 + 2600.36i) q^{55} +(-3941.07 - 6826.13i) q^{56} -39020.0 q^{57} +(17134.6 + 29678.1i) q^{58} +(-6623.03 - 11471.4i) q^{59} +3264.11 q^{60} +(15022.0 + 26018.9i) q^{61} +(6236.00 - 10801.1i) q^{62} +(-20632.6 + 35736.8i) q^{63} +4096.00 q^{64} +(-5169.92 - 64.2412i) q^{65} +34032.2 q^{66} +(-13080.1 + 22655.4i) q^{67} +(-2927.92 + 5071.30i) q^{68} +(-50220.3 - 86984.2i) q^{69} +4180.06 q^{70} +(-4503.53 - 7800.34i) q^{71} +(-10721.9 - 18570.8i) q^{72} -66973.1 q^{73} +(-21835.6 - 37820.4i) q^{74} +(36701.4 - 63568.8i) q^{75} +(12983.5 - 22488.1i) q^{76} +43582.0 q^{77} +(28667.6 + 51110.0i) q^{78} +24904.4 q^{79} +(-1086.10 + 1881.18i) q^{80} +(14101.9 - 24425.3i) q^{81} +(-12695.8 - 21989.7i) q^{82} -75793.5 q^{83} +(-23688.6 - 41029.9i) q^{84} +(-1552.74 - 2689.42i) q^{85} -61411.8 q^{86} +(102991. + 178386. i) q^{87} +(-11323.8 + 19613.5i) q^{88} +(-40021.7 + 69319.6i) q^{89} +11372.1 q^{90} +(36712.1 + 65452.1i) q^{91} +66841.1 q^{92} +(37482.8 - 64922.1i) q^{93} +(-45824.7 + 79370.7i) q^{94} +(6885.42 + 11925.9i) q^{95} +24619.9 q^{96} +(-26468.6 - 45844.9i) q^{97} +(3278.07 + 5677.79i) q^{98} +118567. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 12 q^{2} - 48 q^{4} + 2 q^{5} - 202 q^{7} + 384 q^{8} - 213 q^{9} - 4 q^{10} + 502 q^{11} - 1091 q^{13} + 1616 q^{14} - 1194 q^{15} - 768 q^{16} - 225 q^{17} + 1704 q^{18} - 1064 q^{19} - 16 q^{20}+ \cdots + 179400 q^{99}+O(q^{100}) $ 6 * q - 12 * q^2 - 48 * q^4 + 2 * q^5 - 202 * q^7 + 384 * q^8 - 213 * q^9 - 4 * q^10 + 502 * q^11 - 1091 * q^13 + 1616 * q^14 - 1194 * q^15 - 768 * q^16 - 225 * q^17 + 1704 * q^18 - 1064 * q^19 - 16 * q^20 + 876 * q^21 + 2008 * q^22 - 5140 * q^23 + 3076 * q^25 - 404 * q^26 + 15444 * q^27 - 3232 * q^28 + 5753 * q^29 - 4776 * q^30 - 15148 * q^31 - 3072 * q^32 - 22170 * q^33 + 1800 * q^34 + 18176 * q^35 - 3408 * q^36 - 3863 * q^37 + 8512 * q^38 + 18708 * q^39 + 128 * q^40 - 9441 * q^41 - 1752 * q^42 - 12586 * q^43 - 16064 * q^44 + 18339 * q^45 - 20560 * q^46 + 14692 * q^47 - 981 * q^49 - 6152 * q^50 + 54288 * q^51 + 19072 * q^52 + 112602 * q^53 - 30888 * q^54 - 46732 * q^55 - 12928 * q^56 - 130476 * q^57 + 23012 * q^58 - 92302 * q^59 + 38208 * q^60 + 11237 * q^61 + 30296 * q^62 - 74328 * q^63 + 24576 * q^64 + 156829 * q^65 + 177360 * q^66 - 79108 * q^67 - 3600 * q^68 - 121038 * q^69 - 145408 * q^70 + 3280 * q^71 - 13632 * q^72 + 25734 * q^73 - 15452 * q^74 + 135330 * q^75 - 17024 * q^76 - 122180 * q^77 - 7320 * q^78 + 189048 * q^79 - 256 * q^80 + 65889 * q^81 - 37764 * q^82 - 88440 * q^83 - 7008 * q^84 - 203667 * q^85 + 100688 * q^86 + 246540 * q^87 + 32128 * q^88 - 333396 * q^89 - 146712 * q^90 + 286194 * q^91 + 164480 * q^92 + 24996 * q^93 - 29384 * q^94 - 49254 * q^95 - 109356 * q^97 - 3924 * q^98 + 179400 * 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
$3$	−12.0214	+	20.8217i	−0.771175	+	1.33571i	0.165745	+	0.986169i	$0.446997\pi$
$3$	−12.0214	+	20.8217i	−0.771175	+	1.33571i	−0.936919	+	0.349545i	$0.886336\pi$
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	8.48514			0.151787			0.0758934	−	0.997116i	$-0.475819\pi$
$5$	8.48514			0.151787			0.0758934	+	0.997116i	$0.475819\pi$
$6$	−48.0857	−	83.2869i	−0.545303	−	0.944493i
$7$	−61.5791	−	106.658i	−0.474994	−	0.822715i	0.524595	−	0.851352i	$-0.324217\pi$
$7$	−61.5791	−	106.658i	−0.474994	−	0.822715i	−0.999590	+	0.0286371i	$0.990883\pi$
$8$	64.0000			0.353553
$9$	−167.529	−	290.169i	−0.689421	−	1.19411i
$10$	−16.9703	+	29.3934i	−0.0536647	+	0.0929500i
$11$	−176.935	+	306.461i	−0.440892	+	0.763647i	−0.997756	−	0.0669563i	$-0.978671\pi$
$11$	−176.935	+	306.461i	−0.440892	+	0.763647i	0.556864	+	0.830604i	$0.312005\pi$
$12$	384.686			0.771175
$13$	−609.291	−	7.57102i	−0.999923	−	0.0124250i
$13$	−609.291	−	7.57102i	−0.999923	−	0.0124250i
$14$	492.633			0.671744
$15$	−102.003	+	176.675i	−0.117054	+	0.202744i
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	−182.995	−	316.956i	−0.153574	−	0.265997i	0.778965	−	0.627067i	$-0.215745\pi$
$17$	−182.995	−	316.956i	−0.153574	−	0.265997i	−0.932539	+	0.361070i	$0.882412\pi$
$18$	1340.24			0.974989
$19$	811.468	+	1405.50i	0.515689	+	0.893199i	0.999834	+	0.0182113i	$0.00579717\pi$
$19$	811.468	+	1405.50i	0.515689	+	0.893199i	−0.484146	+	0.874987i	$0.660869\pi$
$20$	−67.8811	−	117.574i	−0.0379467	−	0.0657256i
$21$	2961.08			1.46522
$22$	−707.740	−	1225.84i	−0.311758	−	0.539980i
$23$	−2088.78	+	3617.88i	−0.823330	+	1.42605i	0.0798585	+	0.996806i	$0.474553\pi$
$23$	−2088.78	+	3617.88i	−0.823330	+	1.42605i	−0.903189	+	0.429244i	$0.858780\pi$
$24$	−769.371	+	1332.59i	−0.272652	+	0.472246i
$25$	−3053.00			−0.976961
$26$	1244.81	−	2095.50i	0.361135	−	0.607932i
$27$	2213.36			0.584308
$28$	−985.266	+	1706.53i	−0.237497	+	0.411357i
$29$	4283.66	−	7419.52i	0.945845	−	1.63825i	0.191796	−	0.981435i	$-0.438569\pi$
$29$	4283.66	−	7419.52i	0.945845	−	1.63825i	0.754050	−	0.656817i	$-0.228098\pi$
$30$	−408.014	−	706.701i	−0.0827698	−	0.143361i
$31$	−3118.00			−0.582736			−0.291368	−	0.956611i	$-0.594110\pi$
$31$	−3118.00			−0.582736			−0.291368	+	0.956611i	$0.594110\pi$
$32$	−512.000	−	886.810i	−0.0883883	−	0.153093i
$33$	−4254.02	−	7368.19i	−0.680010	−	1.17781i
$34$	1463.96			0.217186
$35$	−522.508	−	905.010i	−0.0720979	−	0.124877i
$36$	−2680.47	+	4642.71i	−0.344711	+	0.597057i
$37$	−5458.91	+	9455.10i	−0.655543	+	1.13543i	0.326214	+	0.945296i	$0.394227\pi$
$37$	−5458.91	+	9455.10i	−0.655543	+	1.13543i	−0.981757	+	0.190138i	$0.939106\pi$
$38$	−6491.75			−0.729294
$39$	7482.19	−	12595.5i	0.787712	−	1.32603i
$40$	543.049			0.0536647
$41$	−3173.94	+	5497.43i	−0.294876	+	0.510740i	−0.974956	−	0.222398i	$-0.928612\pi$
$41$	−3173.94	+	5497.43i	−0.294876	+	0.510740i	0.680080	+	0.733138i	$0.261945\pi$
$42$	−5922.15	+	10257.5i	−0.518032	+	0.897257i
$43$	7676.48	+	13296.1i	0.633127	+	1.09661i	0.986909	+	0.161280i	$0.0515623\pi$
$43$	7676.48	+	13296.1i	0.633127	+	1.09661i	−0.353781	+	0.935328i	$0.615104\pi$
$44$	5661.92			0.440892
$45$	−1421.51	−	2462.13i	−0.104645	−	0.181251i
$46$	−8355.14	−	14471.5i	−0.582182	−	1.00837i
$47$	22912.4			1.51295			0.756476	−	0.654022i	$-0.226920\pi$
$47$	22912.4			1.51295			0.756476	+	0.654022i	$0.226920\pi$
$48$	−3077.49	−	5330.36i	−0.192794	−	0.333929i
$49$	819.518	−	1419.45i	0.0487605	−	0.0844557i
$50$	6106.00	−	10575.9i	0.345408	−	0.598264i
$51$	8799.43			0.473728
$52$	4769.42	+	8503.15i	0.244601	+	0.436086i
$53$	17016.4			0.832105			0.416053	−	0.909341i	$-0.363413\pi$
$53$	17016.4			0.832105			0.416053	+	0.909341i	$0.363413\pi$
$54$	−4426.71	+	7667.29i	−0.206584	+	0.357814i
$55$	−1501.32	+	2600.36i	−0.0669216	+	0.115912i
$56$	−3941.07	−	6826.13i	−0.167936	−	0.290874i
$57$	−39020.0			−1.59074
$58$	17134.6	+	29678.1i	0.668814	+	1.15842i
$59$	−6623.03	−	11471.4i	−0.247701	−	0.429030i	0.715187	−	0.698933i	$-0.246342\pi$
$59$	−6623.03	−	11471.4i	−0.247701	−	0.429030i	−0.962887	+	0.269903i	$0.913008\pi$
$60$	3264.11			0.117054
$61$	15022.0	+	26018.9i	0.516896	+	0.895290i	0.999807	+	0.0196209i	$0.00624592\pi$
$61$	15022.0	+	26018.9i	0.516896	+	0.895290i	−0.482912	+	0.875669i	$0.660421\pi$
$62$	6236.00	−	10801.1i	0.206028	−	0.356851i
$63$	−20632.6	+	35736.8i	−0.654943	+	1.13439i
$64$	4096.00			0.125000
$65$	−5169.92	−	64.2412i	−0.151775	−	0.00188595i
$66$	34032.2			0.961679
$67$	−13080.1	+	22655.4i	−0.355979	+	0.616573i	−0.987285	−	0.158960i	$-0.949186\pi$
$67$	−13080.1	+	22655.4i	−0.355979	+	0.616573i	0.631306	+	0.775534i	$0.282519\pi$
$68$	−2927.92	+	5071.30i	−0.0767868	+	0.132999i
$69$	−50220.3	−	86984.2i	−1.26986	−	2.19947i
$70$	4180.06			0.101962
$71$	−4503.53	−	7800.34i	−0.106025	−	0.183640i	0.808132	−	0.589002i	$-0.200479\pi$
$71$	−4503.53	−	7800.34i	−0.106025	−	0.183640i	−0.914156	+	0.405362i	$0.867146\pi$
$72$	−10721.9	−	18570.8i	−0.243747	−	0.422183i
$73$	−66973.1			−1.47093			−0.735467	−	0.677560i	$-0.763037\pi$
$73$	−66973.1			−1.47093			−0.735467	+	0.677560i	$0.763037\pi$
$74$	−21835.6	−	37820.4i	−0.463539	−	0.802873i
$75$	36701.4	−	63568.8i	0.753408	−	1.30494i
$76$	12983.5	−	22488.1i	0.257844	−	0.446599i
$77$	43582.0			0.837685
$78$	28667.6	+	51110.0i	0.533526	+	0.951195i
$79$	24904.4			0.448960			0.224480	−	0.974479i	$-0.427932\pi$
$79$	24904.4			0.448960			0.224480	+	0.974479i	$0.427932\pi$
$80$	−1086.10	+	1881.18i	−0.0189733	+	0.0328628i
$81$	14101.9	−	24425.3i	0.238818	−	0.413644i
$82$	−12695.8	−	21989.7i	−0.208509	−	0.361148i
$83$	−75793.5			−1.20764			−0.603819	−	0.797121i	$-0.706355\pi$
$83$	−75793.5			−1.20764			−0.603819	+	0.797121i	$0.706355\pi$
$84$	−23688.6	−	41029.9i	−0.366304	−	0.634457i
$85$	−1552.74	−	2689.42i	−0.0233104	−	0.0403749i
$86$	−61411.8			−0.895377
$87$	102991.	+	178386.i	1.45882	+	2.52676i
$88$	−11323.8	+	19613.5i	−0.155879	+	0.269990i
$89$	−40021.7	+	69319.6i	−0.535575	+	0.927643i	0.463560	+	0.886065i	$0.346572\pi$
$89$	−40021.7	+	69319.6i	−0.535575	+	0.927643i	−0.999135	+	0.0415777i	$0.986762\pi$
$90$	11372.1			0.147990
$91$	36712.1	+	65452.1i	0.464736	+	0.828553i
$92$	66841.1			0.823330
$93$	37482.8	−	64922.1i	0.449391	−	0.778368i
$94$	−45824.7	+	79370.7i	−0.534909	+	0.926490i
$95$	6885.42	+	11925.9i	0.0782747	+	0.135576i
$96$	24619.9			0.272652
$97$	−26468.6	−	45844.9i	−0.285628	−	0.494722i	0.687133	−	0.726532i	$-0.258869\pi$
$97$	−26468.6	−	45844.9i	−0.285628	−	0.494722i	−0.972761	+	0.231809i	$0.925536\pi$
$98$	3278.07	+	5677.79i	0.0344789	+	0.0597192i
$99$	118567.			1.21584
$100$	24424.0	+	42303.6i	0.244240	+	0.423036i
$101$	71258.2	−	123423.i	0.695074	−	1.20390i	−0.275081	−	0.961421i	$-0.588705\pi$
$101$	71258.2	−	123423.i	0.695074	−	1.20390i	0.970156	−	0.242483i	$-0.0779619\pi$
$102$	−17598.9	+	30482.1i	−0.167488	+	0.290098i
$103$	−101996.			−0.947306			−0.473653	−	0.880711i	$-0.657065\pi$
$103$	−101996.			−0.947306			−0.473653	+	0.880711i	$0.657065\pi$
$104$	−38994.6	−	484.545i	−0.353526	−	0.00439290i
$105$	25125.1			0.222400
$106$	−34032.8	+	58946.6i	−0.294194	+	0.509558i
$107$	−2946.09	+	5102.78i	−0.0248763	+	0.0430871i	−0.878196	−	0.478302i	$-0.841253\pi$
$107$	−2946.09	+	5102.78i	−0.0248763	+	0.0430871i	0.853319	+	0.521389i	$0.174586\pi$
$108$	−17706.9	−	30669.2i	−0.146077	−	0.253013i
$109$	86930.6			0.700820			0.350410	−	0.936596i	$-0.386042\pi$
$109$	86930.6			0.700820			0.350410	+	0.936596i	$0.386042\pi$
$110$	−6005.28	−	10401.4i	−0.0473207	−	0.0819619i
$111$	−131248.	−	227328.i	−1.01108	−	1.75124i
$112$	31528.5			0.237497
$113$	24945.3	+	43206.5i	0.183778	+	0.318312i	0.943164	−	0.332328i	$-0.107834\pi$
$113$	24945.3	+	43206.5i	0.183778	+	0.318312i	−0.759386	+	0.650640i	$0.774501\pi$
$114$	78040.0	−	135169.i	0.562413	−	0.974128i
$115$	−17723.6	+	30698.2i	−0.124971	+	0.216455i
$116$	−137077.			−0.945845
$117$	99877.3	+	178066.i	0.674531	+	1.20259i
$118$	52984.3			0.350301
$119$	−22537.3	+	39035.8i	−0.145893	+	0.252694i
$120$	−6528.22	+	11307.2i	−0.0413849	+	0.0716807i
$121$	17913.4	+	31027.0i	0.111228	+	0.192653i
$122$	−120176.			−0.731001
$123$	−76310.6	−	132174.i	−0.454802	−	0.787740i
$124$	24944.0	+	43204.3i	0.145684	+	0.252332i
$125$	−52421.2			−0.300076
$126$	−82530.5	−	142947.i	−0.463114	−	0.802138i
$127$	−13476.5	+	23342.0i	−0.0741427	+	0.128419i	−0.900713	−	0.434414i	$-0.856955\pi$
$127$	−13476.5	+	23342.0i	−0.0741427	+	0.128419i	0.826570	+	0.562833i	$0.190289\pi$
$128$	−8192.00	+	14189.0i	−0.0441942	+	0.0765466i
$129$	−369129.			−1.95301
$130$	10562.4	−	17780.6i	0.0548155	−	0.0922761i
$131$	194039.			0.987893			0.493947	−	0.869492i	$-0.335554\pi$
$131$	194039.			0.987893			0.493947	+	0.869492i	$0.335554\pi$
$132$	−68064.4	+	117891.i	−0.340005	+	0.588906i
$133$	99939.0	−	173099.i	0.489898	−	0.848529i
$134$	−52320.4	−	90621.6i	−0.251715	−	0.435983i
$135$	18780.6			0.0886903
$136$	−11711.7	−	20285.2i	−0.0542965	−	0.0940442i
$137$	87359.9	+	151312.i	0.397659	+	0.688766i	0.993437	−	0.114384i	$-0.0364894\pi$
$137$	87359.9	+	151312.i	0.397659	+	0.688766i	−0.595778	+	0.803149i	$0.703156\pi$
$138$	401763.			1.79586
$139$	−181255.	−	313944.i	−0.795709	−	1.37821i	−0.922388	−	0.386264i	$-0.873765\pi$
$139$	−181255.	−	313944.i	−0.795709	−	1.37821i	0.126680	−	0.991944i	$-0.459568\pi$
$140$	−8360.12	+	14480.2i	−0.0360489	+	0.0624386i
$141$	−275439.	+	477075.i	−1.16675	+	2.02087i
$142$	36028.2			0.149942
$143$	110125.	−	185384.i	0.450346	−	0.758110i
$144$	85775.1			0.344711
$145$	36347.5	−	62955.6i	0.143567	−	0.248665i
$146$	133946.	−	232002.i	0.520054	−	0.900760i
$147$	19703.6	+	34127.6i	0.0752058	+	0.130260i
$148$	174685.			0.655543
$149$	143079.	+	247820.i	0.527971	+	0.914473i	0.999468	+	0.0326056i	$0.0103805\pi$
$149$	143079.	+	247820.i	0.527971	+	0.914473i	−0.471497	+	0.881868i	$0.656286\pi$
$150$	146806.	+	254275.i	0.532740	+	0.922732i
$151$	−159539.			−0.569407			−0.284704	−	0.958616i	$-0.591895\pi$
$151$	−159539.			−0.569407			−0.284704	+	0.958616i	$0.591895\pi$
$152$	51934.0	+	89952.3i	0.182323	+	0.315793i
$153$	−61314.0	+	106199.i	−0.211754	+	0.366768i
$154$	−87164.1	+	150973.i	−0.296166	+	0.512975i
$155$	−26456.6			−0.0884516
$156$	−234386.	−	2912.46i	−0.771115	−	0.00958184i
$157$	48087.8			0.155699			0.0778495	−	0.996965i	$-0.475195\pi$
$157$	48087.8			0.155699			0.0778495	+	0.996965i	$0.475195\pi$
$158$	−49808.7	+	86271.2i	−0.158731	+	0.274931i
$159$	−204562.	+	354311.i	−0.641699	+	1.11145i
$160$	−4344.39	−	7524.71i	−0.0134162	−	0.0232375i
$161$	514502.			1.56431
$162$	56407.7	+	97701.1i	0.168869	+	0.292491i
$163$	−298734.	−	517423.i	−0.880675	−	1.52537i	−0.850592	−	0.525827i	$-0.823756\pi$
$163$	−298734.	−	517423.i	−0.880675	−	1.52537i	−0.0300835	−	0.999547i	$-0.509577\pi$
$164$	101566.			0.294876
$165$	−36096.0	−	62520.1i	−0.103216	−	0.178776i
$166$	151587.	−	262557.i	0.426965	−	0.739525i
$167$	−97507.0	+	168887.i	−0.270548	+	0.468603i	−0.969002	−	0.247052i	$-0.920538\pi$
$167$	−97507.0	+	168887.i	−0.270548	+	0.468603i	0.698454	+	0.715655i	$0.253872\pi$
$168$	189509.			0.518032
$169$	371178.	+	9225.91i	0.999691	+	0.0248481i
$170$	12421.9			0.0329659
$171$	271890.	−	470927.i	0.711054	−	1.23158i
$172$	122824.	−	212737.i	0.316564	−	0.548304i
$173$	19228.2	+	33304.3i	0.0488455	+	0.0846028i	0.889414	−	0.457102i	$-0.151112\pi$
$173$	19228.2	+	33304.3i	0.0488455	+	0.0846028i	−0.840569	+	0.541705i	$0.817779\pi$
$174$	−823932.			−2.06309
$175$	188001.	+	325628.i	0.464051	+	0.803760i
$176$	−45295.4	−	78453.9i	−0.110223	−	0.190912i
$177$	318473.			0.764082
$178$	−160087.	−	277278.i	−0.378709	−	0.655943i
$179$	−114374.	+	198102.i	−0.266806	+	0.462122i	−0.968035	−	0.250814i	$-0.919302\pi$
$179$	−114374.	+	198102.i	−0.266806	+	0.462122i	0.701229	+	0.712936i	$0.252635\pi$
$180$	−22744.2	+	39394.0i	−0.0523225	+	0.0906253i
$181$	−347574.			−0.788588			−0.394294	−	0.918984i	$-0.629011\pi$
$181$	−347574.			−0.788588			−0.394294	+	0.918984i	$0.629011\pi$
$182$	−300157.	−	3729.74i	−0.671692	−	0.00834641i
$183$	−722343.			−1.59447
$184$	−133682.	+	231544.i	−0.291091	+	0.504185i
$185$	−46319.6	+	80227.8i	−0.0995028	+	0.172344i
$186$	149931.	+	259688.i	0.317768	+	0.550390i
$187$	129513.			0.270837
$188$	−183299.	−	317483.i	−0.378238	−	0.655127i
$189$	−136297.	−	236073.i	−0.277543	−	0.480719i
$190$	−55083.4			−0.110697
$191$	375331.	+	650093.i	0.744443	+	1.28941i	0.950455	+	0.310863i	$0.100618\pi$
$191$	375331.	+	650093.i	0.744443	+	1.28941i	−0.206012	+	0.978549i	$0.566049\pi$
$192$	−49239.8	+	85285.8i	−0.0963969	+	0.166964i
$193$	453065.	−	784732.i	0.875523	−	1.51645i	0.0193190	−	0.999813i	$-0.493850\pi$
$193$	453065.	−	784732.i	0.875523	−	1.51645i	0.856204	−	0.516637i	$-0.172816\pi$
$194$	211749.			0.403939
$195$	63487.4	−	106874.i	0.119564	−	0.201274i
$196$	−26224.6			−0.0487605
$197$	94596.4	−	163846.i	0.173664	−	0.300794i	−0.766034	−	0.642800i	$-0.777773\pi$
$197$	94596.4	−	163846.i	0.173664	−	0.300794i	0.939698	+	0.342005i	$0.111106\pi$
$198$	−237135.	+	410729.i	−0.429865	+	0.744548i
$199$	−128776.	−	223047.i	−0.230517	−	0.399267i	0.727443	−	0.686168i	$-0.240708\pi$
$199$	−128776.	−	223047.i	−0.230517	−	0.399267i	−0.957960	+	0.286901i	$0.907375\pi$
$200$	−195392.			−0.345408
$201$	−314483.	−	544701.i	−0.549044	−	0.950972i
$202$	285033.	+	493691.i	0.491492	+	0.851289i
$203$	−1.05514e6			−1.79709
$204$	−70395.5	−	121929.i	−0.118432	−	0.205130i
$205$	−26931.3	+	46646.5i	−0.0447583	+	0.0775236i
$206$	203992.	−	353325.i	0.334923	−	0.580104i
$207$	1.39973e6			2.27049
$208$	79667.8	−	134112.i	0.127680	−	0.214937i
$209$	−574309.			−0.909452
$210$	−50250.3	+	87036.1i	−0.0786304	+	0.136192i
$211$	141083.	−	244362.i	0.218156	−	0.377858i	−0.736088	−	0.676886i	$-0.763329\pi$
$211$	141083.	−	244362.i	0.218156	−	0.377858i	0.954244	+	0.299028i	$0.0966624\pi$
$212$	−136131.	−	235786.i	−0.208026	−	0.360312i
$213$	216555.			0.327054
$214$	−11784.4	−	20411.1i	−0.0175902	−	0.0304672i
$215$	65136.0	+	112819.i	0.0961003	+	0.166451i
$216$	141655.			0.206584
$217$	192004.	+	332560.i	0.276796	+	0.479425i
$218$	−173861.	+	301136.i	−0.247777	+	0.429163i
$219$	805113.	−	1.39450e6i	1.13435	−	1.96475i
$220$	48042.2			0.0669216
$221$	109097.	+	194504.i	0.150257	+	0.267885i
$222$	1.04998e6			1.42988
$223$	−470330.	+	814635.i	−0.633345	+	1.09699i	0.353518	+	0.935428i	$0.384985\pi$
$223$	−470330.	+	814635.i	−0.633345	+	1.09699i	−0.986863	+	0.161558i	$0.948348\pi$
$224$	−63057.0	+	109218.i	−0.0839680	+	0.145437i
$225$	511468.	+	885888.i	0.673538	+	1.16660i
$226$	−199562.			−0.259901
$227$	530309.	+	918522.i	0.683069	+	1.18311i	0.974040	+	0.226378i	$0.0726884\pi$
$227$	530309.	+	918522.i	0.683069	+	1.18311i	−0.290971	+	0.956732i	$0.593978\pi$
$228$	312160.	+	540677.i	0.397686	+	0.688812i
$229$	−929772.			−1.17162			−0.585812	−	0.810447i	$-0.699224\pi$
$229$	−929772.			−1.17162			−0.585812	+	0.810447i	$0.699224\pi$
$230$	−70894.5	−	122793.i	−0.0883676	−	0.153057i
$231$	−523918.	+	907453.i	−0.646002	+	1.11891i
$232$	274154.	−	474849.i	0.334407	−	0.579210i
$233$	−15097.0			−0.0182179			−0.00910897	−	0.999959i	$-0.502900\pi$
$233$	−15097.0			−0.0182179			−0.00910897	+	0.999959i	$0.502900\pi$
$234$	−816594.	−	10147.0i	−0.974914	−	0.0121142i
$235$	194414.			0.229646
$236$	−105969.	+	183543.i	−0.123850	+	0.214515i
$237$	−299386.	+	518552.i	−0.346227	+	0.599682i
$238$	−90149.3	−	156143.i	−0.103162	−	0.178682i
$239$	−910661.			−1.03125			−0.515623	−	0.856816i	$-0.672439\pi$
$239$	−910661.			−1.03125			−0.515623	+	0.856816i	$0.672439\pi$
$240$	−26112.9	−	45228.8i	−0.0292635	−	0.0506859i
$241$	588607.	+	1.01950e6i	0.652804	+	1.13069i	0.982440	+	0.186581i	$0.0597408\pi$
$241$	588607.	+	1.01950e6i	0.652804	+	1.13069i	−0.329636	+	0.944108i	$0.606926\pi$
$242$	−143307.			−0.157301
$243$	607974.	+	1.05304e6i	0.660494	+	1.14401i
$244$	240352.	−	416302.i	0.258448	−	0.447645i
$245$	6953.72	−	12044.2i	0.00740120	−	0.0128193i
$246$	610485.			0.643187
$247$	−483779.	−	862505.i	−0.504551	−	0.899537i
$248$	−199552.			−0.206028
$249$	911147.	−	1.57815e6i	0.931301	−	1.61306i
$250$	104842.	−	181592.i	0.106093	−	0.183759i
$251$	−486598.	−	842813.i	−0.487513	−	0.844398i	0.512384	−	0.858757i	$-0.328763\pi$
$251$	−486598.	−	842813.i	−0.487513	−	0.844398i	−0.999897	+	0.0143591i	$0.995429\pi$
$252$	660244.			0.654943
$253$	−739159.	−	1.28026e6i	−0.726000	−	1.25747i
$254$	−53906.1	−	93368.1i	−0.0524268	−	0.0908059i
$255$	74664.4			0.0719057
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	−63368.7	+	109758.i	−0.0598470	+	0.103658i	−0.894397	−	0.447275i	$-0.852395\pi$
$257$	−63368.7	+	109758.i	−0.0598470	+	0.103658i	0.834550	+	0.550933i	$0.185728\pi$
$258$	738258.	−	1.27870e6i	0.690492	−	1.19597i
$259$	1.34462e6			1.24552
$260$	40469.2	+	72150.4i	0.0371271	+	0.0661920i
$261$	−2.87056e6			−2.60834
$262$	−388077.	+	672170.i	−0.349273	+	0.604959i
$263$	653830.	−	1.13247e6i	0.582875	−	1.00957i	−0.412262	−	0.911066i	$-0.635261\pi$
$263$	653830.	−	1.13247e6i	0.582875	−	1.00957i	0.995137	−	0.0985037i	$-0.0314056\pi$
$264$	−272258.	−	471564.i	−0.240420	−	0.416419i
$265$	144387.			0.126303
$266$	399756.	+	692398.i	0.346410	+	0.600001i
$267$	−962235.	−	1.66664e6i	−0.826044	−	1.43075i
$268$	418563.			0.355979
$269$	−499151.	−	864555.i	−0.420583	−	0.728471i	0.575414	−	0.817862i	$-0.304841\pi$
$269$	−499151.	−	864555.i	−0.420583	−	0.728471i	−0.995997	+	0.0893918i	$0.971508\pi$
$270$	−37561.3	+	65058.0i	−0.0313567	+	0.0543115i
$271$	−756604.	+	1.31048e6i	−0.625814	+	1.08394i	0.362568	+	0.931957i	$0.381900\pi$
$271$	−756604.	+	1.31048e6i	−0.625814	+	1.08394i	−0.988383	+	0.151985i	$0.951433\pi$
$272$	93693.3			0.0767868
$273$	−1.80416e6	−	22418.4i	−1.46510	−	0.0182053i
$274$	−698879.			−0.562375
$275$	540183.	−	935625.i	0.430734	−	0.746054i
$276$	−803526.	+	1.39175e6i	−0.634932	+	1.09973i
$277$	980424.	+	1.69814e6i	0.767740	+	1.32977i	0.938786	+	0.344502i	$0.111952\pi$
$277$	980424.	+	1.69814e6i	0.767740	+	1.32977i	−0.171045	+	0.985263i	$0.554714\pi$
$278$	1.45004e6			1.12530
$279$	522357.	+	904748.i	0.401751	+	0.695852i
$280$	−33440.5	−	57920.6i	−0.0254904	−	0.0441507i
$281$	−280175.			−0.211672			−0.105836	−	0.994384i	$-0.533752\pi$
$281$	−280175.			−0.211672			−0.105836	+	0.994384i	$0.533752\pi$
$282$	−1.10176e6	−	1.90830e6i	−0.825017	−	1.42897i
$283$	−1.12715e6	+	1.95228e6i	−0.836597	+	1.44903i	0.0561263	+	0.998424i	$0.482125\pi$
$283$	−1.12715e6	+	1.95228e6i	−0.836597	+	1.44903i	−0.892723	+	0.450605i	$0.851208\pi$
$284$	−72056.5	+	124805.i	−0.0530123	+	0.0918201i
$285$	−331090.			−0.241454
$286$	421939.	+	752253.i	0.305024	+	0.543812i
$287$	781795.			0.560258
$288$	−171550.	+	297134.i	−0.121874	+	0.211091i
$289$	642954.	−	1.11363e6i	0.452830	−	0.784325i
$290$	145390.	+	251823.i	0.101517	+	0.175833i
$291$	1.27276e6			0.881077
$292$	535785.	+	928007.i	0.367734	+	0.636933i
$293$	1.01502e6	+	1.75807e6i	0.690726	+	1.19637i	0.971600	+	0.236628i	$0.0760423\pi$
$293$	1.01502e6	+	1.75807e6i	0.690726	+	1.19637i	−0.280874	+	0.959745i	$0.590624\pi$
$294$	−157628.			−0.106357
$295$	−56197.4	−	97336.7i	−0.0375977	−	0.0651211i
$296$	−349370.	+	605127.i	−0.231770	+	0.401437i
$297$	−391621.	+	678307.i	−0.257617	+	0.446206i
$298$	−1.14463e6			−0.746664
$299$	1.30007e6	−	2.18853e6i	0.840985	−	1.41571i
$300$	−1.17445e6			−0.753408
$301$	945422.	−	1.63752e6i	0.601464	−	1.04177i
$302$	319077.	−	552658.i	0.201316	−	0.348689i
$303$	1.71325e6	+	2.96744e6i	1.07205	+	1.85684i
$304$	−415472.			−0.257844
$305$	127464.	+	220774.i	0.0784580	+	0.135893i
$306$	−245256.	−	424796.i	−0.149733	−	0.259344i
$307$	759319.			0.459810			0.229905	−	0.973213i	$-0.426158\pi$
$307$	759319.			0.459810			0.229905	+	0.973213i	$0.426158\pi$
$308$	−348656.	−	603891.i	−0.209421	−	0.362728i
$309$	1.22614e6	−	2.12373e6i	0.730539	−	1.26533i
$310$	52913.3	−	91648.5i	0.0312724	−	0.0541653i
$311$	−726585.			−0.425976			−0.212988	−	0.977055i	$-0.568320\pi$
$311$	−726585.			−0.425976			−0.212988	+	0.977055i	$0.568320\pi$
$312$	478860.	−	806110.i	0.278498	−	0.468822i
$313$	−668596.			−0.385747			−0.192874	−	0.981224i	$-0.561781\pi$
$313$	−668596.			−0.385747			−0.192874	+	0.981224i	$0.561781\pi$
$314$	−96175.6	+	166581.i	−0.0550479	+	0.0953458i
$315$	−175071.	+	303231.i	−0.0994116	+	0.172186i
$316$	−199235.	−	345085.i	−0.112240	−	0.194405i
$317$	108322.			0.0605437			0.0302719	−	0.999542i	$-0.490363\pi$
$317$	108322.			0.0605437			0.0302719	+	0.999542i	$0.490363\pi$
$318$	−818246.	−	1.41724e6i	−0.453749	−	0.785917i
$319$	1.51586e6	+	2.62555e6i	0.834031	+	1.44458i
$320$	34755.1			0.0189733
$321$	−70832.4	−	122685.i	−0.0383680	−	0.0664554i
$322$	−1.02900e6	+	1.78229e6i	−0.553067	+	0.957940i
$323$	296989.	−	514400.i	0.158392	−	0.274343i
$324$	−451262.			−0.238818
$325$	1.86017e6	+	23114.3i	0.976885	+	0.0121387i
$326$	2.38987e6			1.24546
$327$	−1.04503e6	+	1.81004e6i	−0.540455	+	0.936095i
$328$	−203132.	+	351836.i	−0.104254	+	0.180574i
$329$	−1.41092e6	−	2.44379e6i	−0.718644	−	1.24473i
$330$	288768.			0.145970
$331$	−119091.	−	206271.i	−0.0597459	−	0.103483i	0.834605	−	0.550848i	$-0.185696\pi$
$331$	−119091.	−	206271.i	−0.0597459	−	0.103483i	−0.894351	+	0.447365i	$0.852362\pi$
$332$	606348.	+	1.05023e6i	0.301910	+	0.522923i
$333$	3.65811e6			1.80778
$334$	−390028.	−	675548.i	−0.191306	−	0.331353i
$335$	−110986.	+	192234.i	−0.0540329	+	0.0935877i
$336$	−379018.	+	656478.i	−0.183152	+	0.317228i
$337$	−3.49103e6			−1.67447			−0.837237	−	0.546839i	$-0.815831\pi$
$337$	−3.49103e6			−1.67447			−0.837237	+	0.546839i	$0.815831\pi$
$338$	−774316.	+	1.26735e6i	−0.368660	+	0.603398i
$339$	−1.19951e6			−0.566899
$340$	−24843.8	+	43030.7i	−0.0116552	+	0.0201874i
$341$	551683.	−	955544.i	0.256924	−	0.445005i
$342$	1.08756e6	+	1.88371e6i	0.502791	+	0.870859i
$343$	−2.27178e6			−1.04263
$344$	491295.	+	850947.i	0.223844	+	0.387710i
$345$	−426127.	−	738073.i	−0.192748	−	0.333850i
$346$	−153826.			−0.0690779
$347$	−1.29472e6	−	2.24252e6i	−0.577234	−	0.999799i	−0.995795	−	0.0916101i	$-0.970799\pi$
$347$	−1.29472e6	−	2.24252e6i	−0.577234	−	0.999799i	0.418561	−	0.908189i	$-0.362535\pi$
$348$	1.64786e6	−	2.85418e6i	0.729412	−	1.26338i
$349$	−982534.	+	1.70180e6i	−0.431802	+	0.747902i	−0.997029	−	0.0770332i	$-0.975455\pi$
$349$	−982534.	+	1.70180e6i	−0.431802	+	0.747902i	0.565227	+	0.824935i	$0.308789\pi$
$350$	−1.50401e6			−0.656267
$351$	−1.34858e6	−	16757.4i	−0.584263	−	0.00726003i
$352$	362363.			0.155879
$353$	61390.7	−	106332.i	0.0262220	−	0.0454178i	−0.852617	−	0.522537i	$-0.824986\pi$
$353$	61390.7	−	106332.i	0.0262220	−	0.0454178i	0.878839	+	0.477119i	$0.158319\pi$
$354$	−636947.	+	1.10322e6i	−0.270144	+	0.467903i
$355$	−38213.1	−	66187.0i	−0.0160931	−	0.0278741i
$356$	1.28069e6			0.535575
$357$	−541862.	−	938532.i	−0.225018	−	0.389743i
$358$	−457497.	−	792409.i	−0.188661	−	0.326770i
$359$	−897796.			−0.367656			−0.183828	−	0.982958i	$-0.558849\pi$
$359$	−897796.			−0.367656			−0.183828	+	0.982958i	$0.558849\pi$
$360$	−90976.7	−	157576.i	−0.0369976	−	0.0640817i
$361$	−78911.8	+	136679.i	−0.0318694	+	0.0551994i
$362$	695147.	−	1.20403e6i	0.278808	−	0.482910i
$363$	−861380.			−0.343106
$364$	613234.	−	1.03231e6i	0.242590	−	0.408375i
$365$	−568276.			−0.223268
$366$	1.44469e6	−	2.50227e6i	0.563730	−	0.976409i
$367$	1.02391e6	−	1.77347e6i	0.396824	−	0.687320i	−0.596508	−	0.802607i	$-0.703446\pi$
$367$	1.02391e6	−	1.77347e6i	0.396824	−	0.687320i	0.993332	+	0.115288i	$0.0367789\pi$
$368$	−534729.	−	926178.i	−0.205833	−	0.356512i
$369$	2.12692e6			0.813175
$370$	−185278.	−	320911.i	−0.0703591	−	0.121866i
$371$	−1.04786e6	−	1.81494e6i	−0.395245	−	0.684585i
$372$	−1.19945e6			−0.449391
$373$	483083.	+	836724.i	0.179783	+	0.311394i	0.941806	−	0.336156i	$-0.109127\pi$
$373$	483083.	+	836724.i	0.179783	+	0.311394i	−0.762023	+	0.647550i	$0.775794\pi$
$374$	−259026.	+	448646.i	−0.0957555	+	0.165853i
$375$	630178.	−	1.09150e6i	0.231411	−	0.400816i
$376$	1.46639e6			0.534909
$377$	−2.66617e6	+	4.48822e6i	−0.966128	+	1.62637i
$378$	1.09037e6			0.392505
$379$	−2.05093e6	+	3.55232e6i	−0.733421	+	1.27032i	0.221992	+	0.975048i	$0.428744\pi$
$379$	−2.05093e6	+	3.55232e6i	−0.733421	+	1.27032i	−0.955413	+	0.295274i	$0.904589\pi$
$380$	110167.	−	190814.i	0.0391373	−	0.0677879i
$381$	−324014.	−	561209.i	−0.114354	−	0.198067i
$382$	−3.00265e6			−1.05280
$383$	−488752.	−	846544.i	−0.170252	−	0.294885i	0.768256	−	0.640143i	$-0.221125\pi$
$383$	−488752.	−	846544.i	−0.170252	−	0.294885i	−0.938508	+	0.345258i	$0.887791\pi$
$384$	−196959.	−	341143.i	−0.0681629	−	0.118062i
$385$	369800.			0.127150
$386$	1.81226e6	+	3.13893e6i	0.619088	+	1.07229i
$387$	2.57207e6	−	4.45496e6i	0.872983	−	1.51205i
$388$	−423497.	+	733518.i	−0.142814	+	0.247361i
$389$	4.12620e6			1.38254			0.691268	−	0.722598i	$-0.257052\pi$
$389$	4.12620e6			1.38254			0.691268	+	0.722598i	$0.257052\pi$
$390$	243249.	+	433676.i	0.0809821	+	0.144379i
$391$	1.52895e6			0.505767
$392$	52449.2	−	90844.6i	0.0172394	−	0.0298596i
$393$	−2.33262e6	+	4.04022e6i	−0.761838	+	1.31954i
$394$	378386.	+	655383.i	0.122799	+	0.212694i
$395$	211317.			0.0681462
$396$	−948539.	−	1.64292e6i	−0.303960	−	0.526475i
$397$	490393.	+	849386.i	0.156159	+	0.270476i	0.933481	−	0.358628i	$-0.116755\pi$
$397$	490393.	+	849386.i	0.156159	+	0.270476i	−0.777321	+	0.629104i	$0.783422\pi$
$398$	1.03021e6			0.326000
$399$	2.40282e6	+	4.16181e6i	0.755595	+	1.30873i
$400$	390784.	−	676858.i	0.122120	−	0.211518i
$401$	−1.64903e6	+	2.85621e6i	−0.512116	+	0.887011i	0.487785	+	0.872964i	$0.337805\pi$
$401$	−1.64903e6	+	2.85621e6i	−0.512116	+	0.887011i	−0.999901	+	0.0140477i	$0.995528\pi$
$402$	2.51586e6			0.776465
$403$	1.89977e6	+	23606.4i	0.582691	+	0.00724049i
$404$	−2.28026e6			−0.695074
$405$	119657.	−	207252.i	0.0362493	−	0.0627857i
$406$	2.11027e6	−	3.65510e6i	0.635366	−	1.10049i
$407$	−1.93174e6	−	3.34588e6i	−0.578048	−	1.00121i
$408$	563164.			0.167488
$409$	−157691.	−	273129.i	−0.0466121	−	0.0807345i	0.841778	−	0.539824i	$-0.181509\pi$
$409$	−157691.	−	273129.i	−0.0466121	−	0.0807345i	−0.888390	+	0.459089i	$0.848176\pi$
$410$	−107725.	−	186586.i	−0.0316489	−	0.0548175i
$411$	−4.20076e6			−1.22666
$412$	815969.	+	1.41330e6i	0.236827	+	0.410196i
$413$	−815681.	+	1.41280e6i	−0.235313	+	0.407574i
$414$	−2.79946e6	+	4.84881e6i	−0.802738	+	1.39038i
$415$	−643119.			−0.183304
$416$	305243.	+	544202.i	0.0864793	+	0.154180i
$417$	8.71580e6			2.45452
$418$	1.14862e6	−	1.98946e6i	0.321540	−	0.556923i
$419$	−1.99735e6	+	3.45952e6i	−0.555802	+	0.962677i	0.442039	+	0.896996i	$0.354255\pi$
$419$	−1.99735e6	+	3.45952e6i	−0.555802	+	0.962677i	−0.997841	+	0.0656810i	$0.979078\pi$
$420$	−201001.	−	348144.i	−0.0556001	−	0.0963021i
$421$	2.54389e6			0.699510			0.349755	−	0.936841i	$-0.386265\pi$
$421$	2.54389e6			0.699510			0.349755	+	0.936841i	$0.386265\pi$
$422$	564331.	+	977450.i	0.154260	+	0.267186i
$423$	−3.83849e6	−	6.64846e6i	−1.04306	−	1.80664i
$424$	1.08905e6			0.294194
$425$	558684.	+	967668.i	0.150035	+	0.259869i
$426$	−433111.	+	750170.i	−0.115631	+	0.200279i
$427$	1.85008e6	−	3.20444e6i	0.491045	−	0.850516i
$428$	94274.9			0.0248763
$429$	2.53615e6	+	4.52158e6i	0.665323	+	1.18617i
$430$	−521088.			−0.135906
$431$	1.23820e6	−	2.14463e6i	0.321069	−	0.556109i	−0.659640	−	0.751582i	$-0.729291\pi$
$431$	1.23820e6	−	2.14463e6i	0.321069	−	0.556109i	0.980709	+	0.195474i	$0.0626244\pi$
$432$	−283310.	+	490707.i	−0.0730385	+	0.126506i
$433$	−2.83796e6	−	4.91550e6i	−0.727423	−	1.25993i	−0.957969	−	0.286873i	$-0.907384\pi$
$433$	−2.83796e6	−	4.91550e6i	−0.727423	−	1.25993i	0.230545	−	0.973062i	$-0.425949\pi$
$434$	−1.53603e6			−0.391449
$435$	873897.	+	1.51363e6i	0.221430	+	0.383528i
$436$	−695445.	−	1.20455e6i	−0.175205	−	0.303464i
$437$	−6.77993e6			−1.69833
$438$	3.22045e6	+	5.57798e6i	0.802105	+	1.38929i
$439$	1.06785e6	−	1.84956e6i	0.264452	−	0.458045i	−0.702968	−	0.711222i	$-0.748142\pi$
$439$	1.06785e6	−	1.84956e6i	0.264452	−	0.458045i	0.967420	+	0.253177i	$0.0814755\pi$
$440$	−96084.4	+	166423.i	−0.0236604	+	0.0409809i
$441$	−549174.			−0.134466
$442$	−891977.	−	11083.7i	−0.217169	−	0.00269853i
$443$	6.65232e6			1.61051			0.805256	−	0.592927i	$-0.202028\pi$
$443$	6.65232e6			1.61051			0.805256	+	0.592927i	$0.202028\pi$
$444$	−2.09996e6	+	3.63724e6i	−0.505538	+	0.875618i
$445$	−339589.	+	588186.i	−0.0812932	+	0.140804i
$446$	−1.88132e6	−	3.25854e6i	−0.447843	−	0.775686i
$447$	−6.88006e6			−1.62863
$448$	−252228.	−	436872.i	−0.0593743	−	0.102839i
$449$	2.54698e6	+	4.41151e6i	0.596225	+	1.03269i	0.993373	+	0.114938i	$0.0366668\pi$
$449$	2.54698e6	+	4.41151e6i	0.596225	+	1.03269i	−0.397147	+	0.917755i	$0.630000\pi$
$450$	−4.09174e6			−0.952526
$451$	−1.12316e6	−	1.94538e6i	−0.260017	−	0.450363i
$452$	399125.	−	691304.i	0.0918888	−	0.159156i
$453$	1.91788e6	−	3.32187e6i	0.439113	−	0.760566i
$454$	−4.24247e6			−0.966005
$455$	311507.	+	555370.i	0.0705407	+	0.125763i
$456$	−2.49728e6			−0.562413
$457$	−160091.	+	277286.i	−0.0358573	+	0.0621066i	−0.883397	−	0.468625i	$-0.844749\pi$
$457$	−160091.	+	277286.i	−0.0358573	+	0.0621066i	0.847540	+	0.530732i	$0.178083\pi$
$458$	1.85954e6	−	3.22083e6i	0.414231	−	0.717470i
$459$	−405033.	−	701537.i	−0.0897343	−	0.155424i
$460$	567156.			0.124971
$461$	14310.5	+	24786.5i	0.00313619	+	0.00543204i	0.867589	−	0.497282i	$-0.165668\pi$
$461$	14310.5	+	24786.5i	0.00313619	+	0.00543204i	−0.864453	+	0.502714i	$0.832335\pi$
$462$	−2.09567e6	−	3.62981e6i	−0.456792	−	0.791187i
$463$	4.30811e6			0.933972			0.466986	−	0.884265i	$-0.345340\pi$
$463$	4.30811e6			0.933972			0.466986	+	0.884265i	$0.345340\pi$
$464$	1.09662e6	+	1.89940e6i	0.236461	+	0.409563i
$465$	318047.	−	550873.i	0.0682116	−	0.118146i
$466$	30193.9	−	52297.4i	0.00644102	−	0.0111562i
$467$	2.01328e6			0.427180			0.213590	−	0.976923i	$-0.431484\pi$
$467$	2.01328e6			0.427180			0.213590	+	0.976923i	$0.431484\pi$
$468$	1.66834e6	−	2.80847e6i	0.352103	−	0.592727i
$469$	3.22185e6			0.676352
$470$	−388829.	+	673471.i	−0.0811921	+	0.140629i
$471$	−578084.	+	1.00127e6i	−0.120071	+	0.207969i
$472$	−423874.	−	734172.i	−0.0875754	−	0.151685i
$473$	−5.43295e6			−1.11656
$474$	−1.19754e6	−	2.07421e6i	−0.244819	−	0.424039i
$475$	−2.47741e6	−	4.29101e6i	−0.503807	−	0.872620i
$476$	721194.			0.145893
$477$	−2.85075e6	−	4.93764e6i	−0.573671	−	0.993628i
$478$	1.82132e6	−	3.15462e6i	0.364600	−	0.631506i
$479$	−1.44240e6	+	2.49831e6i	−0.287242	+	0.497517i	−0.973150	−	0.230170i	$-0.926072\pi$
$479$	−1.44240e6	+	2.49831e6i	−0.287242	+	0.497517i	0.685909	+	0.727688i	$0.259405\pi$
$480$	208903.			0.0413849
$481$	3.39765e6	−	5.71958e6i	0.669600	−	1.12720i
$482$	−4.70886e6			−0.923204
$483$	−6.18505e6	+	1.07128e7i	−1.20636	+	2.08947i
$484$	286615.	−	496432.i	0.0556142	−	0.0963266i
$485$	−224589.	−	389000.i	−0.0433546	−	0.0750923i
$486$	−4.86379e6			−0.934080
$487$	−382875.	−	663159.i	−0.0731534	−	0.126705i	0.827128	−	0.562013i	$-0.189973\pi$
$487$	−382875.	−	663159.i	−0.0731534	−	0.126705i	−0.900282	+	0.435308i	$0.856640\pi$
$488$	961408.	+	1.66521e6i	0.182750	+	0.316533i
$489$	1.43648e7			2.71662
$490$	27814.9	+	48176.8i	0.00523344	+	0.00906458i
$491$	1.68515e6	−	2.91877e6i	0.315454	−	0.546382i	−0.664080	−	0.747661i	$-0.731177\pi$
$491$	1.68515e6	−	2.91877e6i	0.315454	−	0.546382i	0.979534	+	0.201280i	$0.0645100\pi$
$492$	−1.22097e6	+	2.11478e6i	−0.227401	+	0.393870i
$493$	−3.13555e6			−0.581027
$494$	3.95536e6	+	49149.1i	0.729237	+	0.00906147i
$495$	1.00606e6			0.184549
$496$	399104.	−	691268.i	0.0728420	−	0.126166i
$497$	−554647.	+	960676.i	−0.100722	+	0.174456i
$498$	3.64459e6	+	6.31261e6i	0.658529	+	1.14061i
$499$	5.15019e6			0.925916			0.462958	−	0.886380i	$-0.346788\pi$
$499$	5.15019e6			0.925916			0.462958	+	0.886380i	$0.346788\pi$
$500$	419370.	+	726369.i	0.0750191	+	0.129937i
$501$	−2.34435e6	−	4.06053e6i	−0.417280	−	0.722750i
$502$	3.89279e6			0.689448
$503$	−846672.	−	1.46648e6i	−0.149209	−	0.258438i	0.781726	−	0.623622i	$-0.214339\pi$
$503$	−846672.	−	1.46648e6i	−0.149209	−	0.258438i	−0.930935	+	0.365184i	$0.881006\pi$
$504$	−1.32049e6	+	2.28715e6i	−0.231557	+	0.401069i
$505$	604635.	−	1.04726e6i	0.105503	−	0.182737i
$506$	5.91327e6			1.02672
$507$	−4.65419e6	+	7.61766e6i	−0.804127	+	1.31614i
$508$	431249.			0.0741427
$509$	−2.36076e6	+	4.08896e6i	−0.403885	+	0.699549i	−0.994191	−	0.107630i	$-0.965674\pi$
$509$	−2.36076e6	+	4.08896e6i	−0.403885	+	0.699549i	0.590306	+	0.807180i	$0.299007\pi$
$510$	−149329.	+	258645.i	−0.0254225	+	0.0440331i
$511$	4.12415e6	+	7.14323e6i	0.698686	+	1.21016i
$512$	262144.			0.0441942
$513$	1.79607e6	+	3.11088e6i	0.301321	+	0.521904i
$514$	−253475.	−	439031.i	−0.0423182	−	0.0732973i
$515$	−865451.			−0.143789
$516$	2.95303e6	+	5.11480e6i	0.488252	+	0.845677i
$517$	−4.05400e6	+	7.02173e6i	−0.667048	+	1.15536i
$518$	−2.68924e6	+	4.65790e6i	−0.440357	+	0.762721i
$519$	−924603.			−0.150674
$520$	−330875.	−	4111.43i	−0.0536606	−	0.000666784i
$521$	1.63695e6			0.264204			0.132102	−	0.991236i	$-0.457827\pi$
$521$	1.63695e6			0.264204			0.132102	+	0.991236i	$0.457827\pi$
$522$	5.74111e6	−	9.94390e6i	0.922189	−	1.59728i
$523$	−3.85125e6	+	6.67056e6i	−0.615669	+	1.06637i	0.374597	+	0.927188i	$0.377781\pi$
$523$	−3.85125e6	+	6.67056e6i	−0.615669	+	1.06637i	−0.990267	+	0.139183i	$0.955552\pi$
$524$	−1.55231e6	−	2.68868e6i	−0.246973	−	0.427770i
$525$	−9.04017e6			−1.43146
$526$	2.61532e6	+	4.52987e6i	0.412155	+	0.713873i
$527$	570578.	+	988269.i	0.0894928	+	0.155006i
$528$	2.17806e6			0.340005
$529$	−5.50787e6	−	9.53991e6i	−0.855745	−	1.48219i
$530$	−288773.	+	500170.i	−0.0446547	+	0.0773442i
$531$	−2.21911e6	+	3.84360e6i	−0.341540	+	0.591565i
$532$	−3.19805e6			−0.489898
$533$	1.97548e6	−	3.32551e6i	0.301199	−	0.507037i
$534$	7.69788e6			1.16820
$535$	−24998.0	+	43297.8i	−0.00377590	+	0.00654005i
$536$	−837127.	+	1.44995e6i	−0.125858	+	0.217992i
$537$	−2.74989e6	−	4.76294e6i	−0.411509	−	0.712754i
$538$	3.99321e6			0.594794
$539$	290003.	+	502300.i	0.0429963	+	0.0744717i
$540$	−150245.	−	260232.i	−0.0221726	−	0.0384040i
$541$	5.64436e6			0.829128			0.414564	−	0.910020i	$-0.363934\pi$
$541$	5.64436e6			0.829128			0.414564	+	0.910020i	$0.363934\pi$
$542$	−3.02642e6	−	5.24191e6i	−0.442518	−	0.766463i
$543$	4.17833e6	−	7.23708e6i	0.608139	−	1.05333i
$544$	−187387.	+	324563.i	−0.0271482	+	0.0470221i
$545$	737618.			0.106375
$546$	3.68598e6	−	6.20495e6i	0.529140	−	0.890752i
$547$	3.10848e6			0.444202			0.222101	−	0.975024i	$-0.428709\pi$
$547$	3.10848e6			0.444202			0.222101	+	0.975024i	$0.428709\pi$
$548$	1.39776e6	−	2.42099e6i	0.198830	−	0.344383i
$549$	5.03325e6	−	8.71785e6i	0.712718	−	1.23446i
$550$	2.16073e6	+	3.74250e6i	0.304575	+	0.527540i
$551$	1.39042e7			1.95105
$552$	−3.21410e6	−	5.56699e6i	−0.448964	−	0.777629i
$553$	−1.53359e6	−	2.65625e6i	−0.213253	−	0.369366i
$554$	−7.84339e6			−1.08575
$555$	−1.11365e6	−	1.92891e6i	−0.153468	−	0.265815i
$556$	−2.90009e6	+	5.02310e6i	−0.397854	+	0.689104i
$557$	−3.98456e6	+	6.90146e6i	−0.544179	+	0.942547i	0.454479	+	0.890758i	$0.349826\pi$
$557$	−3.98456e6	+	6.90146e6i	−0.544179	+	0.942547i	−0.998658	+	0.0517888i	$0.983508\pi$
$558$	−4.17885e6			−0.568161
$559$	−4.57655e6	−	8.15929e6i	−0.619453	−	1.10439i
$560$	267524.			0.0360489
$561$	−1.55693e6	+	2.69668e6i	−0.208863	+	0.361761i
$562$	560350.	−	970555.i	0.0748374	−	0.129622i
$563$	299588.	+	518902.i	0.0398340	+	0.0689945i	0.885255	−	0.465106i	$-0.153984\pi$
$563$	299588.	+	518902.i	0.0398340	+	0.0689945i	−0.845421	+	0.534100i	$0.820650\pi$
$564$	8.81405e6			1.16675
$565$	211664.	+	366613.i	0.0278950	+	0.0483156i
$566$	−4.50861e6	−	7.80914e6i	−0.591563	−	1.02462i
$567$	−3.47354e6			−0.453748
$568$	−288226.	−	499222.i	−0.0374854	−	0.0649266i
$569$	−2.57475e6	+	4.45960e6i	−0.333391	+	0.577451i	−0.983174	−	0.182669i	$-0.941526\pi$
$569$	−2.57475e6	+	4.45960e6i	−0.333391	+	0.577451i	0.649783	+	0.760120i	$0.274860\pi$
$570$	662181.	−	1.14693e6i	0.0853669	−	0.147860i
$571$	−9.62204e6			−1.23503			−0.617514	−	0.786560i	$-0.711860\pi$
$571$	−9.62204e6			−1.23503			−0.617514	+	0.786560i	$0.711860\pi$
$572$	−3.44976e6	−	42866.5i	−0.440858	−	0.00547808i
$573$	−1.80481e7			−2.29638
$574$	−1.56359e6	+	2.70822e6i	−0.198081	+	0.343086i
$575$	6.37706e6	−	1.10454e7i	0.804361	−	1.39319i
$576$	−686200.	−	1.18853e6i	−0.0861777	−	0.149264i
$577$	−9.41255e6			−1.17698			−0.588488	−	0.808506i	$-0.700277\pi$
$577$	−9.41255e6			−1.17698			−0.588488	+	0.808506i	$0.700277\pi$
$578$	2.57182e6	+	4.45452e6i	0.320199	+	0.554602i
$579$	1.08930e7	+	1.88672e7i	1.35036	+	2.33890i
$580$	−1.16312e6			−0.143567
$581$	4.66730e6	+	8.08400e6i	0.573622	+	0.993542i
$582$	−2.54552e6	+	4.40897e6i	−0.311508	+	0.539547i
$583$	−3.01080e6	+	5.21486e6i	−0.366869	+	0.635435i
$584$	−4.28628e6			−0.520054
$585$	847473.	+	1.51091e6i	0.102385	+	0.182537i
$586$	−8.12017e6			−0.976834
$587$	4.76505e6	−	8.25331e6i	0.570785	−	0.988629i	−0.425701	−	0.904864i	$-0.639972\pi$
$587$	4.76505e6	−	8.25331e6i	0.570785	−	0.988629i	0.996486	−	0.0837645i	$-0.0266944\pi$
$588$	315257.	−	546041.i	0.0376029	−	0.0651301i
$589$	−2.53016e6	−	4.38236e6i	−0.300510	−	0.520499i
$590$	449579.			0.0531711
$591$	2.27437e6	+	3.93932e6i	0.267850	+	0.463930i
$592$	−1.39748e6	−	2.42051e6i	−0.163886	−	0.283859i
$593$	3.86865e6			0.451775			0.225888	−	0.974153i	$-0.427472\pi$
$593$	3.86865e6			0.451775			0.225888	+	0.974153i	$0.427472\pi$
$594$	−1.56648e6	−	2.71323e6i	−0.182163	−	0.315515i
$595$	−191232.	+	331224.i	−0.0221447	+	0.0383557i
$596$	2.28927e6	−	3.96512e6i	0.263986	−	0.457237i
$597$	6.19229e6			0.711076
$598$	4.98115e6	+	8.88063e6i	0.569608	+	1.01553i
$599$	−437926.			−0.0498694			−0.0249347	−	0.999689i	$-0.507938\pi$
$599$	−437926.			−0.0498694			−0.0249347	+	0.999689i	$0.507938\pi$
$600$	2.34889e6	−	4.06840e6i	0.266370	−	0.461366i
$601$	−4.24091e6	+	7.34548e6i	−0.478931	+	0.829534i	−0.999708	−	0.0241594i	$-0.992309\pi$
$601$	−4.24091e6	+	7.34548e6i	−0.478931	+	0.829534i	0.520777	+	0.853693i	$0.325642\pi$
$602$	3.78169e6	+	6.55008e6i	0.425299	+	0.736640i
$603$	8.76521e6			0.981678
$604$	1.27631e6	+	2.21063e6i	0.142352	+	0.246561i
$605$	151998.	+	263268.i	0.0168830	+	0.0292422i
$606$	−1.37060e7			−1.51610
$607$	−4.98018e6	−	8.62593e6i	−0.548622	−	0.950242i	−0.998369	−	0.0570859i	$-0.981819\pi$
$607$	−4.98018e6	−	8.62593e6i	−0.548622	−	0.950242i	0.449747	−	0.893156i	$-0.351514\pi$
$608$	830943.	−	1.43924e6i	0.0911617	−	0.157897i
$609$	1.26842e7	−	2.19698e7i	1.38587	−	2.40039i
$610$	−1.01971e6			−0.110956
$611$	−1.39603e7	−	173470.i	−1.51283	−	0.0187984i
$612$	1.96205e6			0.211754
$613$	1.26409e6	−	2.18946e6i	0.135871	−	0.235335i	−0.790059	−	0.613031i	$-0.789950\pi$
$613$	1.26409e6	−	2.18946e6i	0.135871	−	0.235335i	0.925930	+	0.377696i	$0.123283\pi$
$614$	−1.51864e6	+	2.63036e6i	−0.162567	+	0.281575i
$615$	−647506.	−	1.12151e6i	−0.0690329	−	0.119569i
$616$	2.78925e6			0.296166
$617$	−6.37944e6	−	1.10495e7i	−0.674636	−	1.16850i	−0.976575	−	0.215176i	$-0.930967\pi$
$617$	−6.37944e6	−	1.10495e7i	−0.674636	−	1.16850i	0.301939	−	0.953327i	$-0.402366\pi$
$618$	4.90455e6	+	8.49494e6i	0.516569	+	0.894724i
$619$	−1.18393e6			−0.124194			−0.0620971	−	0.998070i	$-0.519779\pi$
$619$	−1.18393e6			−0.124194			−0.0620971	+	0.998070i	$0.519779\pi$
$620$	211653.	+	366594.i	0.0221129	+	0.0383007i
$621$	−4.62323e6	+	8.00766e6i	−0.481079	+	0.833253i
$622$	1.45317e6	−	2.51696e6i	0.150605	−	0.260856i
$623$	9.85800e6			1.01758
$624$	1.83473e6	+	3.27104e6i	0.188630	+	0.336298i
$625$	9.09583e6			0.931413
$626$	1.33719e6	−	2.31608e6i	0.136382	−	0.236221i
$627$	6.90401e6	−	1.19581e7i	0.701347	−	1.21477i
$628$	−384702.	−	666324.i	−0.0389247	−	0.0674196i
$629$	3.99581e6			0.402696
$630$	−700283.	−	1.21293e6i	−0.0702946	−	0.121754i
$631$	5.21983e6	+	9.04101e6i	0.521895	+	0.903949i	0.999676	+	0.0254694i	$0.00810804\pi$
$631$	5.21983e6	+	9.04101e6i	0.521895	+	0.903949i	−0.477781	+	0.878479i	$0.658559\pi$
$632$	1.59388e6			0.158731
$633$	3.39203e6	+	5.87517e6i	0.336473	+	0.582789i
$634$	−216644.	+	375239.i	−0.0214054	+	0.0370753i
$635$	−114350.	+	198060.i	−0.0112539	+	0.0194923i
$636$	6.54597e6			0.641699
$637$	−510072.	+	858652.i	−0.0498061	+	0.0838433i
$638$	−1.21269e7			−1.17950
$639$	−1.50895e6	+	2.61357e6i	−0.146191	+	0.253211i
$640$	−69510.2	+	120395.i	−0.00670809	+	0.0116188i
$641$	3.52817e6	+	6.11096e6i	0.339159	+	0.587441i	0.984275	−	0.176644i	$-0.0565241\pi$
$641$	3.52817e6	+	6.11096e6i	0.339159	+	0.587441i	−0.645115	+	0.764085i	$0.723191\pi$
$642$	566659.			0.0542606
$643$	1.21288e6	+	2.10076e6i	0.115688	+	0.200378i	0.918055	−	0.396454i	$-0.129759\pi$
$643$	1.21288e6	+	2.10076e6i	0.115688	+	0.200378i	−0.802366	+	0.596832i	$0.796426\pi$
$644$	−4.11602e6	−	7.12915e6i	−0.391077	−	0.677366i
$645$	−3.13211e6			−0.296441
$646$	1.18796e6	+	2.05760e6i	0.112000	+	0.193990i
$647$	8.90613e6	−	1.54259e7i	0.836428	−	1.44874i	−0.0564348	−	0.998406i	$-0.517973\pi$
$647$	8.90613e6	−	1.54259e7i	0.836428	−	1.44874i	0.892863	−	0.450329i	$-0.148693\pi$
$648$	902524.	−	1.56322e6i	0.0844347	−	0.146245i
$649$	4.68739e6			0.436837
$650$	−3.80041e6	+	6.39758e6i	−0.352815	+	0.593926i
$651$	−9.23263e6			−0.853833
$652$	−4.77975e6	+	8.27876e6i	−0.440338	+	0.762687i
$653$	−5.28384e6	+	9.15187e6i	−0.484916	+	0.839899i	−0.999850	−	0.0173310i	$-0.994483\pi$
$653$	−5.28384e6	+	9.15187e6i	−0.484916	+	0.839899i	0.514934	+	0.857230i	$0.327816\pi$
$654$	−4.18012e6	−	7.24018e6i	−0.382159	−	0.661919i
$655$	1.64644e6			0.149949
$656$	−812529.	−	1.40734e6i	−0.0737190	−	0.127685i
$657$	1.12200e7	+	1.94336e7i	1.01409	+	1.75646i
$658$	1.12874e7			1.01632
$659$	7.12109e6	+	1.23341e7i	0.638753	+	1.10635i	0.985707	+	0.168470i	$0.0538828\pi$
$659$	7.12109e6	+	1.23341e7i	0.638753	+	1.10635i	−0.346954	+	0.937882i	$0.612784\pi$
$660$	−577536.	+	1.00032e6i	−0.0516082	+	0.0893881i
$661$	−880634.	+	1.52530e6i	−0.0783956	+	0.135785i	−0.902558	−	0.430569i	$-0.858313\pi$
$661$	−880634.	+	1.52530e6i	−0.0783956	+	0.135785i	0.824162	+	0.566354i	$0.191646\pi$
$662$	952726.			0.0844934
$663$	−5.36142e6	−	66620.7i	−0.473692	−	0.00588607i
$664$	−4.85079e6			−0.426965
$665$	847996.	−	1.46877e6i	0.0743601	−	0.128795i
$666$	−7.31622e6	+	1.26721e7i	−0.639147	+	1.10704i
$667$	1.78953e7	+	3.09956e7i	1.55749	+	2.69765i
$668$	3.12022e6			0.270548
$669$	−1.13081e7	−	1.95862e7i	−0.976840	−	1.69194i
$670$	−443946.	−	768937.i	−0.0382070	−	0.0661765i
$671$	−1.06317e7			−0.911581
$672$	−1.51607e6	−	2.62591e6i	−0.129508	−	0.224314i
$673$	2.27159e6	−	3.93451e6i	0.193327	−	0.334852i	−0.753024	−	0.657993i	$-0.771406\pi$
$673$	2.27159e6	−	3.93451e6i	0.193327	−	0.334852i	0.946351	+	0.323141i	$0.104739\pi$
$674$	6.98206e6	−	1.20933e7i	0.592016	−	1.02540i
$675$	−6.75738e6			−0.570846
$676$	−2.84159e6	−	5.21701e6i	−0.239163	−	0.439091i
$677$	587872.			0.0492959			0.0246480	−	0.999696i	$-0.492154\pi$
$677$	587872.			0.0492959			0.0246480	+	0.999696i	$0.492154\pi$
$678$	2.39902e6	−	4.15523e6i	0.200429	−	0.347153i
$679$	−3.25982e6	+	5.64618e6i	−0.271344	+	0.469981i
$680$	−99375.1	−	172123.i	−0.00824148	−	0.0142747i
$681$	−2.55003e7			−2.10706
$682$	2.20673e6	+	3.82218e6i	0.181672	+	0.314666i
$683$	3.86034e6	+	6.68631e6i	0.316646	+	0.548447i	0.979786	−	0.200048i	$-0.0641099\pi$
$683$	3.86034e6	+	6.68631e6i	0.316646	+	0.548447i	−0.663140	+	0.748495i	$0.730777\pi$
$684$	−8.70047e6			−0.711054
$685$	741261.	+	1.28390e6i	0.0603594	+	0.104546i
$686$	4.54356e6	−	7.86968e6i	0.368626	−	0.638480i
$687$	1.11772e7	−	1.93595e7i	0.903526	−	1.56495i
$688$	−3.93036e6			−0.316564
$689$	−1.03679e7	−	128832.i	−0.832041	−	0.0103389i
$690$	3.40901e6			0.272587
$691$	5.41487e6	−	9.37882e6i	0.431412	−	0.747228i	−0.565583	−	0.824692i	$-0.691349\pi$
$691$	5.41487e6	−	9.37882e6i	0.431412	−	0.747228i	0.996995	+	0.0774633i	$0.0246821\pi$
$692$	307652.	−	532869.i	0.0244227	−	0.0423014i
$693$	−7.30128e6	−	1.26462e7i	−0.577518	−	1.00029i
$694$	1.03578e7			0.816332
$695$	−1.53798e6	−	2.66386e6i	−0.120778	−	0.209194i
$696$	6.59145e6	+	1.14167e7i	0.515772	+	0.893344i
$697$	2.32326e6			0.181141
$698$	−3.93014e6	−	6.80720e6i	−0.305330	−	0.528847i
$699$	181487.	−	314345.i	0.0140492	−	0.0243340i
$700$	3.00802e6	−	5.21004e6i	0.232025	−	0.401880i
$701$	2.48674e7			1.91133			0.955663	−	0.294462i	$-0.0951404\pi$
$701$	2.48674e7			1.91133			0.955663	+	0.294462i	$0.0951404\pi$
$702$	2.75521e6	−	4.63810e6i	0.211014	−	0.355220i
$703$	−1.77189e7			−1.35222
$704$	−724726.	+	1.25526e6i	−0.0551115	+	0.0954559i
$705$	−2.33714e6	+	4.04804e6i	−0.177097	+	0.306741i
$706$	245563.	+	425327.i	0.0185417	+	0.0321152i
$707$	−1.75521e7			−1.32063
$708$	−2.54779e6	−	4.41289e6i	−0.191020	−	0.330857i
$709$	−5.63352e6	−	9.75755e6i	−0.420886	−	0.728996i	0.575140	−	0.818055i	$-0.304947\pi$
$709$	−5.63352e6	−	9.75755e6i	−0.420886	−	0.728996i	−0.996026	+	0.0890589i	$0.971614\pi$
$710$	305704.			0.0227591
$711$	−4.17221e6	−	7.22648e6i	−0.309523	−	0.536109i
$712$	−2.56139e6	+	4.43645e6i	−0.189354	+	0.327971i
$713$	6.51283e6	−	1.12805e7i	0.479784	−	0.831010i
$714$	4.33489e6			0.318224
$715$	934428.	−	1.57301e6i	0.0683566	−	0.115071i
$716$	3.65998e6			0.266806
$717$	1.09474e7	−	1.89615e7i	0.795271	−	1.37745i
$718$	1.79559e6	−	3.11006e6i	0.129986	−	0.225142i
$719$	−7.09197e6	−	1.22836e7i	−0.511616	−	0.886146i	−0.999909	−	0.0134658i	$-0.995714\pi$
$719$	−7.09197e6	−	1.22836e7i	−0.511616	−	0.886146i	0.488293	−	0.872680i	$-0.337620\pi$
$720$	727813.			0.0523225
$721$	6.28083e6	+	1.08787e7i	0.449965	+	0.779363i
$722$	−315647.	−	546717.i	−0.0225351	−	0.0390319i
$723$	−2.83036e7			−2.01370
$724$	2.78059e6	+	4.81612e6i	0.197147	+	0.341469i
$725$	−1.30780e7	+	2.26518e7i	−0.924054	+	1.60051i
$726$	1.72276e6	−	2.98391e6i	0.121306	−	0.210109i
$727$	−1.95108e7			−1.36911			−0.684556	−	0.728960i	$-0.740004\pi$
$727$	−1.95108e7			−1.36911			−0.684556	+	0.728960i	$0.740004\pi$
$728$	2.34958e6	+	4.18894e6i	0.164309	+	0.292938i
$729$	−2.23813e7			−1.55979
$730$	1.13655e6	−	1.96857e6i	0.0789373	−	0.136723i
$731$	2.80951e6	−	4.86622e6i	0.194463	−	0.336820i
$732$	5.77875e6	+	1.00091e7i	0.398617	+	0.690425i
$733$	1.50302e7			1.03325			0.516624	−	0.856212i	$-0.327188\pi$
$733$	1.50302e7			1.03325			0.516624	+	0.856212i	$0.327188\pi$
$734$	4.09565e6	+	7.09388e6i	0.280597	+	0.486008i
$735$	167187.	+	289577.i	0.0114152	+	0.0197718i
$736$	4.27783e6			0.291091
$737$	−4.62866e6	−	8.01707e6i	−0.313896	−	0.543685i
$738$	−4.25383e6	+	7.36785e6i	−0.287501	+	0.497966i
$739$	−1.04075e7	+	1.80263e7i	−0.701028	+	1.21422i	0.267078	+	0.963675i	$0.413942\pi$
$739$	−1.04075e7	+	1.80263e7i	−0.701028	+	1.21422i	−0.968106	+	0.250541i	$0.919391\pi$
$740$	1.48223e6			0.0995028
$741$	2.37746e7	+	295421.i	1.59062	+	0.0197650i
$742$	8.38285e6			0.558961
$743$	−6.71143e6	+	1.16245e7i	−0.446009	+	0.772509i	−0.998122	−	0.0612596i	$-0.980488\pi$
$743$	−6.71143e6	+	1.16245e7i	−0.446009	+	0.772509i	0.552113	+	0.833769i	$0.313822\pi$
$744$	2.39890e6	−	4.15501e6i	0.158884	−	0.275195i
$745$	1.21405e6	+	2.10279e6i	0.0801391	+	0.138805i
$746$	−3.86466e6			−0.254252
$747$	1.26976e7	+	2.19930e7i	0.832572	+	1.44206i
$748$	−1.03610e6	−	1.79458e6i	−0.0677094	−	0.117276i
$749$	725671.			0.0472645
$750$	2.52071e6	+	4.36600e6i	0.163633	+	0.283420i
$751$	585205.	−	1.01361e6i	0.0378624	−	0.0655796i	−0.846473	−	0.532431i	$-0.821278\pi$
$751$	585205.	−	1.01361e6i	0.0378624	−	0.0655796i	0.884336	+	0.466852i	$0.154612\pi$
$752$	−2.93278e6	+	5.07973e6i	−0.189119	+	0.327564i
$753$	2.33984e7			1.50383
$754$	−1.02153e7	−	1.82123e7i	−0.654369	−	1.16664i
$755$	−1.35371e6			−0.0864285
$756$	−2.18075e6	+	3.77716e6i	−0.138772	+	0.240359i
$757$	8.56483e6	−	1.48347e7i	0.543224	−	0.940891i	−0.455492	−	0.890240i	$-0.650537\pi$
$757$	8.56483e6	−	1.48347e7i	0.543224	−	0.940891i	0.998716	−	0.0506518i	$-0.0161299\pi$
$758$	−8.20373e6	−	1.42093e7i	−0.518607	−	0.898253i
$759$	3.55430e7			2.23949
$760$	440667.	+	763257.i	0.0276743	+	0.0479333i
$761$	−2.06941e6	−	3.58432e6i	−0.129534	−	0.224360i	0.793962	−	0.607967i	$-0.208015\pi$
$761$	−2.06941e6	−	3.58432e6i	−0.129534	−	0.224360i	−0.923496	+	0.383608i	$0.874682\pi$
$762$	2.59211e6			0.161721
$763$	−5.35311e6	−	9.27186e6i	−0.332886	−	0.576575i
$764$	6.00530e6	−	1.04015e7i	0.372221	−	0.644706i
$765$	−520258.	+	901113.i	−0.0321414	+	0.0556706i
$766$	3.91002e6			0.240772
$767$	3.94851e6	+	7.03958e6i	0.242351	+	0.432074i
$768$	1.57567e6			0.0963969
$769$	−6.37289e6	+	1.10382e7i	−0.388616	+	0.673103i	−0.992264	−	0.124148i	$-0.960380\pi$
$769$	−6.37289e6	+	1.10382e7i	−0.388616	+	0.673103i	0.603647	+	0.797251i	$0.293713\pi$
$770$	−739599.	+	1.28102e6i	−0.0449541	+	0.0778629i
$771$	−1.52356e6	−	2.63889e6i	−0.0923050	−	0.159877i
$772$	−1.44981e7			−0.875523
$773$	1.04801e7	+	1.81521e7i	0.630838	+	1.09264i	0.987381	+	0.158365i	$0.0506222\pi$
$773$	1.04801e7	+	1.81521e7i	0.630838	+	1.09264i	−0.356542	+	0.934279i	$0.616044\pi$
$774$	1.02883e7	+	1.78198e7i	0.617292	+	1.06918i
$775$	9.51926e6			0.569310
$776$	−1.69399e6	−	2.93407e6i	−0.100985	−	0.174911i
$777$	−1.61642e7	+	2.79973e7i	−0.960512	+	1.66366i
$778$	−8.25241e6	+	1.42936e7i	−0.488801	+	0.846627i
$779$	−1.03022e7			−0.608257
$780$	−1.98879e6	−	24712.7i	−0.117045	−	0.00145440i
$781$	3.18733e6			0.186982
$782$	−3.05789e6	+	5.29643e6i	−0.178816	+	0.309718i
$783$	9.48127e6	−	1.64220e7i	0.552665	−	0.957244i
$784$	209797.	+	363378.i	0.0121901	+	0.0211139i
$785$	408032.			0.0236330
$786$	−9.33048e6	−	1.61609e7i	−0.538701	−	0.933058i
$787$	−1.32480e7	−	2.29462e7i	−0.762454	−	1.32061i	−0.941582	−	0.336784i	$-0.890661\pi$
$787$	−1.32480e7	−	2.29462e7i	−0.762454	−	1.32061i	0.179128	−	0.983826i	$-0.442672\pi$
$788$	−3.02709e6			−0.173664
$789$	1.57199e7	+	2.72277e7i	0.898997	+	1.55711i
$790$	−422634.	+	732023.i	−0.0240933	+	0.0417308i
$791$	3.07222e6	−	5.32124e6i	0.174587	−	0.302393i
$792$	7.58831e6			0.429865
$793$	−8.95578e6	−	1.59668e7i	−0.505732	−	0.901643i
$794$	−3.92314e6			−0.220843
$795$	−1.73573e6	+	3.00638e6i	−0.0974014	+	0.168704i
$796$	−2.06042e6	+	3.56875e6i	−0.115258	+	0.199634i
$797$	1.15992e7	+	2.00904e7i	0.646819	+	1.12032i	0.983878	+	0.178840i	$0.0572345\pi$
$797$	1.15992e7	+	2.00904e7i	0.646819	+	1.12032i	−0.337059	+	0.941484i	$0.609432\pi$
$798$	−1.92226e7			−1.06857
$799$	−4.19284e6	−	7.26221e6i	−0.232349	−	0.402441i
$800$	1.56314e6	+	2.70743e6i	0.0863519	+	0.149566i
$801$	2.68192e7			1.47695
$802$	−6.59613e6	−	1.14248e7i	−0.362121	−	0.627212i
$803$	1.18499e7	−	2.05246e7i	0.648523	−	1.12328i
$804$	−5.03173e6	+	8.71521e6i	−0.274522	+	0.475486i
$805$	4.36562e6			0.237441
$806$	−3.88131e6	+	6.53378e6i	−0.210446	+	0.354264i
$807$	2.40020e7			1.29737
$808$	4.56052e6	−	7.89906e6i	0.245746	−	0.425644i
$809$	−1.72204e7	+	2.98265e7i	−0.925062	+	1.60225i	−0.133601	+	0.991035i	$0.542654\pi$
$809$	−1.72204e7	+	2.98265e7i	−0.925062	+	1.60225i	−0.791461	+	0.611220i	$0.790679\pi$
$810$	478628.	+	829007.i	0.0256322	+	0.0443962i
$811$	1.40426e7			0.749711			0.374856	−	0.927083i	$-0.377692\pi$
$811$	1.40426e7			0.749711			0.374856	+	0.927083i	$0.377692\pi$
$812$	8.44109e6	+	1.46204e7i	0.449271	+	0.778161i
$813$	−1.81909e7	−	3.15076e7i	−0.965225	−	1.67182i
$814$	1.54540e7			0.817483
$815$	−2.53480e6	−	4.39040e6i	−0.133675	−	0.231532i
$816$	−1.12633e6	+	1.95086e6i	−0.0592160	+	0.102565i
$817$	−1.24584e7	+	2.15786e7i	−0.652993	+	1.13102i
$818$	1.26153e6			0.0659194
$819$	1.28418e7	−	2.16179e7i	0.668987	−	1.12617i
$820$	861803.			0.0447583
$821$	1.15291e7	−	1.99689e7i	0.596947	−	1.03394i	−0.396322	−	0.918112i	$-0.629714\pi$
$821$	1.15291e7	−	1.99689e7i	0.596947	−	1.03394i	0.993269	−	0.115831i	$-0.0369531\pi$
$822$	8.40153e6	−	1.45519e7i	0.433689	−	0.751172i
$823$	1.03616e7	+	1.79468e7i	0.533246	+	0.923609i	0.999246	+	0.0388243i	$0.0123613\pi$
$823$	1.03616e7	+	1.79468e7i	0.533246	+	0.923609i	−0.466000	+	0.884785i	$0.654305\pi$
$824$	−6.52775e6			−0.334923
$825$	1.29875e7	+	2.24951e7i	0.664343	+	1.15068i
$826$	−3.26273e6	−	5.65121e6i	−0.166391	−	0.288198i
$827$	−7.89216e6			−0.401266			−0.200633	−	0.979667i	$-0.564300\pi$
$827$	−7.89216e6			−0.401266			−0.200633	+	0.979667i	$0.564300\pi$
$828$	−1.11979e7	−	1.93952e7i	−0.567622	−	0.983149i
$829$	−1.31721e7	+	2.28147e7i	−0.665685	+	1.15300i	0.313414	+	0.949616i	$0.398527\pi$
$829$	−1.31721e7	+	2.28147e7i	−0.665685	+	1.15300i	−0.979099	+	0.203383i	$0.934806\pi$
$830$	1.28624e6	−	2.22783e6i	0.0648076	−	0.112250i
$831$	−4.71444e7			−2.36825
$832$	−2.49566e6	−	31010.9i	−0.124990	−	0.00155312i
$833$	−599870.			−0.0299533
$834$	−1.74316e7	+	3.01924e7i	−0.867805	+	1.50308i
$835$	−827360.	+	1.43303e6i	−0.0410656	+	0.0711278i
$836$	4.59447e6	+	7.95786e6i	0.227363	+	0.393804i
$837$	−6.90125e6			−0.340497
$838$	−7.98941e6	−	1.38381e7i	−0.393011	−	0.680715i
$839$	−8.36408e6	−	1.44870e7i	−0.410217	−	0.710516i	0.584696	−	0.811252i	$-0.301214\pi$
$839$	−8.36408e6	−	1.44870e7i	−0.410217	−	0.710516i	−0.994913	+	0.100736i	$0.967880\pi$
$840$	1.60801e6			0.0786304
$841$	−2.64439e7	−	4.58022e7i	−1.28925	−	2.23304i
$842$	−5.08779e6	+	8.81231e6i	−0.247314	+	0.428360i
$843$	3.36810e6	−	5.83373e6i	0.163236	−	0.282733i
$844$	−4.51465e6			−0.218156
$845$	3.14950e6	+	78283.1i	0.151740	+	0.00377161i
$846$	3.07079e7			1.47511
$847$	2.20619e6	−	3.82123e6i	0.105666	−	0.183018i
$848$	−2.17810e6	+	3.77258e6i	−0.104013	+	0.180156i
$849$	−2.70999e7	−	4.69385e7i	−1.29033	−	2.23491i
$850$	−4.46947e6			−0.212182
$851$	−2.28050e7	−	3.94993e7i	−1.07946	−	1.86967i
$852$	−1.73244e6	−	3.00068e6i	−0.0817636	−	0.141619i
$853$	4.03546e7			1.89898			0.949490	−	0.313798i	$-0.101602\pi$
$853$	4.03546e7			1.89898			0.949490	+	0.313798i	$0.101602\pi$
$854$	7.40033e6	+	1.28178e7i	0.347222	+	0.601405i
$855$	2.30702e6	−	3.99588e6i	0.107929	−	0.186938i
$856$	−188550.	+	326578.i	−0.00879512	+	0.0152336i
$857$	1.95923e7			0.911240			0.455620	−	0.890174i	$-0.349418\pi$
$857$	1.95923e7			0.911240			0.455620	+	0.890174i	$0.349418\pi$
$858$	−2.07355e7	−	257659.i	−0.961605	−	0.0119489i
$859$	3.41788e6			0.158042			0.0790212	−	0.996873i	$-0.474821\pi$
$859$	3.41788e6			0.158042			0.0790212	+	0.996873i	$0.474821\pi$
$860$	1.04218e6	−	1.80510e6i	0.0480502	−	0.0832253i
$861$	−9.39829e6	+	1.62783e7i	−0.432057	+	0.748344i
$862$	4.95282e6	+	8.57853e6i	0.227030	+	0.393228i
$863$	5.81597e6			0.265825			0.132912	−	0.991128i	$-0.457567\pi$
$863$	5.81597e6			0.265825			0.132912	+	0.991128i	$0.457567\pi$
$864$	−1.13324e6	−	1.96283e6i	−0.0516460	−	0.0894536i
$865$	163154.	+	282591.i	0.00741409	+	0.0128416i
$866$	2.27037e7			1.02873
$867$	1.54585e7	+	2.67748e7i	0.698423	+	1.20970i
$868$	3.07206e6	−	5.32096e6i	0.138398	−	0.239713i
$869$	−4.40645e6	+	7.63220e6i	−0.197943	+	0.342847i
$870$	−6.99117e6			−0.313150
$871$	8.14111e6	−	1.37047e7i	0.363612	−	0.612103i
$872$	5.56356e6			0.247777
$873$	−8.86853e6	+	1.53607e7i	−0.393836	+	0.682145i
$874$	1.35599e7	−	2.34864e7i	0.600450	−	1.04001i
$875$	3.22805e6	+	5.59115e6i	0.142535	+	0.246877i
$876$	−2.57636e7			−1.13435
$877$	−9.42738e6	−	1.63287e7i	−0.413897	−	0.716890i	0.581415	−	0.813607i	$-0.302499\pi$
$877$	−9.42738e6	−	1.63287e7i	−0.413897	−	0.716890i	−0.995312	+	0.0967168i	$0.969166\pi$
$878$	4.27139e6	+	7.39826e6i	0.186996	+	0.323887i
$879$	−4.88080e7			−2.13068
$880$	−384338.	−	665692.i	−0.0167304	−	0.0289779i
$881$	7.01846e6	−	1.21563e7i	0.304651	−	0.527671i	−0.672533	−	0.740067i	$-0.734794\pi$
$881$	7.01846e6	−	1.21563e7i	0.304651	−	0.527671i	0.977184	+	0.212397i	$0.0681269\pi$
$882$	1.09835e6	−	1.90239e6i	0.0475410	−	0.0823434i
$883$	6.36913e6			0.274902			0.137451	−	0.990509i	$-0.456109\pi$
$883$	6.36913e6			0.274902			0.137451	+	0.990509i	$0.456109\pi$
$884$	1.82235e6	−	3.06773e6i	0.0784334	−	0.132034i
$885$	2.70229e6			0.115977
$886$	−1.33046e7	+	2.30443e7i	−0.569402	+	0.986233i
$887$	−1.19713e7	+	2.07349e7i	−0.510895	+	0.884897i	0.489025	+	0.872270i	$0.337353\pi$
$887$	−1.19713e7	+	2.07349e7i	−0.510895	+	0.884897i	−0.999920	+	0.0126269i	$0.995981\pi$
$888$	−8.39985e6	−	1.45490e7i	−0.357470	−	0.619156i
$889$	3.31949e6			0.140870
$890$	−1.35836e6	−	2.35274e6i	−0.0574830	−	0.0995634i
$891$	4.99026e6	+	8.64338e6i	0.210586	+	0.364745i
$892$	1.50506e7			0.633345
$893$	1.85926e7	+	3.22034e7i	0.780212	+	1.35137i
$894$	1.37601e7	−	2.38332e7i	0.575809	−	0.997330i
$895$	−970482.	+	1.68092e6i	−0.0404977	+	0.0701440i
$896$	2.01783e6			0.0839680
$897$	2.99403e7	+	5.33789e7i	1.24244	+	2.21508i
$898$	−2.03759e7			−0.843190
$899$	−1.33565e7	+	2.31341e7i	−0.551178	+	0.954668i
$900$	8.18348e6	−	1.41742e7i	0.336769	−	0.583301i
$901$	−3.11391e6	−	5.39346e6i	−0.127789	−	0.221338i
$902$	8.98531e6			0.367720
$903$	2.27306e7	+	3.93706e7i	0.927668	+	1.60677i
$904$	1.59650e6	+	2.76522e6i	0.0649752	+	0.112540i
$905$	−2.94921e6			−0.119697
$906$	7.67152e6	+	1.32875e7i	0.310500	+	0.537801i
$907$	−3.72786e6	+	6.45684e6i	−0.150467	+	0.260616i	−0.931399	−	0.363999i	$-0.881411\pi$
$907$	−3.72786e6	+	6.45684e6i	−0.150467	+	0.260616i	0.780932	+	0.624616i	$0.214744\pi$
$908$	8.48494e6	−	1.46964e7i	0.341534	−	0.591555i
$909$	−4.77514e7			−1.91680
$910$	−2.54687e6	−	31647.3i	−0.101954	−	0.00126687i
$911$	1.48610e7			0.593272			0.296636	−	0.954991i	$-0.404135\pi$
$911$	1.48610e7			0.593272			0.296636	+	0.954991i	$0.404135\pi$
$912$	4.99456e6	−	8.65084e6i	0.198843	−	0.344406i
$913$	1.34105e7	−	2.32277e7i	0.532438	−	0.922210i
$914$	−640365.	−	1.10914e6i	−0.0253549	−	0.0439160i
$915$	−6.12918e6			−0.242019
$916$	7.43818e6	+	1.28833e7i	0.292906	+	0.507328i
$917$	−1.19487e7	−	2.06958e7i	−0.469244	−	0.812754i
$918$	3.24026e6			0.126903
$919$	9.75500e6	+	1.68962e7i	0.381012	+	0.659932i	0.991207	−	0.132319i	$-0.0422423\pi$
$919$	9.75500e6	+	1.68962e7i	0.381012	+	0.659932i	−0.610195	+	0.792251i	$0.708909\pi$
$920$	−1.13431e6	+	1.96469e6i	−0.0441838	+	0.0765286i
$921$	−9.12810e6	+	1.58103e7i	−0.354594	+	0.614174i
$922$	−114484.			−0.00443524
$923$	2.68490e6	+	4.78677e6i	0.103735	+	0.184943i
$924$	1.67654e7			0.646002
$925$	1.66661e7	−	2.88664e7i	0.640440	−	1.10927i
$926$	−8.61621e6	+	1.49237e7i	−0.330209	+	0.571939i
$927$	1.70873e7	+	2.95961e7i	0.653093	+	1.13119i
$928$	−8.77294e6			−0.334407
$929$	−2.05373e7	−	3.55716e7i	−0.780735	−	1.35227i	−0.931514	−	0.363705i	$-0.881512\pi$
$929$	−2.05373e7	−	3.55716e7i	−0.780735	−	1.35227i	0.150779	−	0.988567i	$-0.451822\pi$
$930$	1.27219e6	+	2.20349e6i	0.0482329	+	0.0835419i
$931$	2.66005e6			0.100581
$932$	120776.	+	209189.i	0.00455449	+	0.00788860i
$933$	8.73459e6	−	1.51288e7i	0.328502	−	0.568983i
$934$	−4.02655e6	+	6.97419e6i	−0.151031	+	0.261593i
$935$	1.09893e6			0.0411095
$936$	6.39215e6	+	1.13962e7i	0.238483	+	0.425179i
$937$	2.95075e7			1.09795			0.548976	−	0.835838i	$-0.315018\pi$
$937$	2.95075e7			1.09795			0.548976	+	0.835838i	$0.315018\pi$
$938$	−6.44369e6	+	1.11608e7i	−0.239126	+	0.414179i
$939$	8.03748e6	−	1.39213e7i	0.297479	−	0.515248i
$940$	−1.55532e6	−	2.69389e6i	−0.0574115	−	0.0994396i
$941$	−6.00024e6			−0.220900			−0.110450	−	0.993882i	$-0.535229\pi$
$941$	−6.00024e6			−0.220900			−0.110450	+	0.993882i	$0.535229\pi$
$942$	−2.31234e6	−	4.00508e6i	−0.0849031	−	0.147057i
$943$	−1.32594e7	−	2.29659e7i	−0.485561	−	0.841016i
$944$	3.39099e6			0.123850
$945$	−1.15650e6	−	2.00311e6i	−0.0421274	−	0.0729668i
$946$	1.08659e7	−	1.88203e7i	0.394765	−	0.683752i
$947$	−584865.	+	1.01302e6i	−0.0211924	+	0.0367063i	−0.876427	−	0.481535i	$-0.840080\pi$
$947$	−584865.	+	1.01302e6i	−0.0211924	+	0.0367063i	0.855235	+	0.518241i	$0.173413\pi$
$948$	9.58035e6			0.346227
$949$	4.08061e7	+	507055.i	1.47082	+	0.0182764i
$950$	1.98193e7			0.712491
$951$	−1.30219e6	+	2.25545e6i	−0.0466898	+	0.0808691i
$952$	−1.44239e6	+	2.49829e6i	−0.0515810	+	0.0893410i
$953$	−1.84044e7	−	3.18773e7i	−0.656430	−	1.13697i	−0.981533	−	0.191291i	$-0.938732\pi$
$953$	−1.84044e7	−	3.18773e7i	−0.656430	−	1.13697i	0.325103	−	0.945678i	$-0.394601\pi$
$954$	2.28060e7			0.811294
$955$	3.18474e6	+	5.51613e6i	0.112997	+	0.195716i
$956$	7.28529e6	+	1.26185e7i	0.257811	+	0.446542i
$957$	−7.28912e7			−2.57274
$958$	−5.76961e6	−	9.99325e6i	−0.203111	−	0.351798i
$959$	1.07591e7	−	1.86353e7i	0.377772	−	0.654320i
$960$	−417806.	+	723662.i	−0.0146318	+	0.0253430i
$961$	−1.89072e7			−0.660419
$962$	1.30179e7	+	2.32090e7i	0.453528	+	0.808571i
$963$	1.97423e6			0.0686011
$964$	9.41771e6	−	1.63120e7i	0.326402	−	0.565345i
$965$	3.84432e6	−	6.65856e6i	0.132893	−	0.230177i
$966$	−2.47402e7	−	4.28513e7i	−0.853023	−	1.47748i
$967$	−1.91028e6			−0.0656948			−0.0328474	−	0.999460i	$-0.510458\pi$
$967$	−1.91028e6			−0.0656948			−0.0328474	+	0.999460i	$0.510458\pi$
$968$	1.14646e6	+	1.98573e6i	0.0393252	+	0.0681132i
$969$	7.14046e6	+	1.23676e7i	0.244296	+	0.423134i
$970$	1.79672e6			0.0613126
$971$	2.26115e7	+	3.91642e7i	0.769627	+	1.33303i	0.937765	+	0.347270i	$0.112891\pi$
$971$	2.26115e7	+	3.91642e7i	0.769627	+	1.33303i	−0.168138	+	0.985764i	$0.553775\pi$
$972$	9.72758e6	−	1.68487e7i	0.330247	−	0.572005i
$973$	−2.23231e7	+	3.86648e7i	−0.755914	+	1.30928i
$974$	3.06300e6			0.103455
$975$	−2.28431e7	+	3.84540e7i	−0.769563	+	1.29548i
$976$	−7.69126e6			−0.258448
$977$	2.26858e7	−	3.92929e7i	0.760357	−	1.31698i	−0.182310	−	0.983241i	$-0.558357\pi$
$977$	2.26858e7	−	3.92929e7i	0.760357	−	1.31698i	0.942667	−	0.333735i	$-0.108309\pi$
$978$	−2.87297e7	+	4.97613e7i	−0.960470	+	1.66358i
$979$	−1.41625e7	−	2.45301e7i	−0.472262	−	0.817981i
$980$	−222519.			−0.00740120
$981$	−1.45634e7	−	2.52246e7i	−0.483160	−	0.836858i
$982$	6.74061e6	+	1.16751e7i	0.223059	+	0.386350i
$983$	−1.24747e7			−0.411763			−0.205881	−	0.978577i	$-0.566006\pi$
$983$	−1.24747e7			−0.411763			−0.205881	+	0.978577i	$0.566006\pi$
$984$	−4.88388e6	−	8.45913e6i	−0.160797	−	0.278508i
$985$	802664.	−	1.39025e6i	0.0263599	−	0.0456566i
$986$	6.27110e6	−	1.08619e7i	0.205424	−	0.355805i
$987$	6.78452e7			2.21680
$988$	−8.08098e6	+	1.36035e7i	−0.263373	+	0.443361i
$989$	−6.41380e7			−2.08509
$990$	−2.01212e6	+	3.48509e6i	−0.0652478	+	0.113013i
$991$	−9.61269e6	+	1.66497e7i	−0.310929	+	0.538544i	−0.978564	−	0.205945i	$-0.933973\pi$
$991$	−9.61269e6	+	1.66497e7i	−0.310929	+	0.538544i	0.667635	+	0.744489i	$0.267307\pi$
$992$	1.59642e6	+	2.76507e6i	0.0515071	+	0.0892128i
$993$	5.72656e6			0.184298
$994$	−2.21859e6	−	3.84271e6i	−0.0712214	−	0.123359i
$995$	−1.09268e6	−	1.89258e6i	−0.0349894	−	0.0606035i
$996$	−2.91567e7			−0.931301
$997$	3.16907e6	+	5.48899e6i	0.100970	+	0.174886i	0.912085	−	0.410002i	$-0.134472\pi$
$997$	3.16907e6	+	5.48899e6i	0.100970	+	0.174886i	−0.811114	+	0.584888i	$0.801139\pi$
$998$	−1.03004e7	+	1.78408e7i	−0.327361	+	0.567006i
$999$	−1.20825e7	+	2.09275e7i	−0.383039	+	0.663444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.6.c.a.9.1	yes	6
3.2	odd	2		234.6.h.d.217.2		6
4.3	odd	2		208.6.i.a.113.3		6
13.3	even	3	inner	26.6.c.a.3.1	✓	6
13.4	even	6		338.6.a.h.1.3		3
13.6	odd	12		338.6.b.d.337.3		6
13.7	odd	12		338.6.b.d.337.6		6
13.9	even	3		338.6.a.i.1.3		3
39.29	odd	6		234.6.h.d.55.2		6
52.3	odd	6		208.6.i.a.81.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.6.c.a.3.1	✓	6	13.3	even	3	inner
26.6.c.a.9.1	yes	6	1.1	even	1	trivial
208.6.i.a.81.3		6	52.3	odd	6
208.6.i.a.113.3		6	4.3	odd	2
234.6.h.d.55.2		6	39.29	odd	6
234.6.h.d.217.2		6	3.2	odd	2
338.6.a.h.1.3		3	13.4	even	6
338.6.a.i.1.3		3	13.9	even	3
338.6.b.d.337.3		6	13.6	odd	12
338.6.b.d.337.6		6	13.7	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} +(-12.0214 + 20.8217i) q^{3} +(-8.00000 - 13.8564i) q^{4} +8.48514 q^{5} +(-48.0857 - 83.2869i) q^{6} +(-61.5791 - 106.658i) q^{7} +64.0000 q^{8} +(-167.529 - 290.169i) q^{9} +(-16.9703 + 29.3934i) q^{10} +(-176.935 + 306.461i) q^{11} +384.686 q^{12} +(-609.291 - 7.57102i) q^{13} +492.633 q^{14} +(-102.003 + 176.675i) q^{15} +(-128.000 + 221.703i) q^{16} +(-182.995 - 316.956i) q^{17} +1340.24 q^{18} +(811.468 + 1405.50i) q^{19} +(-67.8811 - 117.574i) q^{20} +2961.08 q^{21} +(-707.740 - 1225.84i) q^{22} +(-2088.78 + 3617.88i) q^{23} +(-769.371 + 1332.59i) q^{24} -3053.00 q^{25} +(1244.81 - 2095.50i) q^{26} +2213.36 q^{27} +(-985.266 + 1706.53i) q^{28} +(4283.66 - 7419.52i) q^{29} +(-408.014 - 706.701i) q^{30} -3118.00 q^{31} +(-512.000 - 886.810i) q^{32} +(-4254.02 - 7368.19i) q^{33} +1463.96 q^{34} +(-522.508 - 905.010i) q^{35} +(-2680.47 + 4642.71i) q^{36} +(-5458.91 + 9455.10i) q^{37} -6491.75 q^{38} +(7482.19 - 12595.5i) q^{39} +543.049 q^{40} +(-3173.94 + 5497.43i) q^{41} +(-5922.15 + 10257.5i) q^{42} +(7676.48 + 13296.1i) q^{43} +5661.92 q^{44} +(-1421.51 - 2462.13i) q^{45} +(-8355.14 - 14471.5i) q^{46} +22912.4 q^{47} +(-3077.49 - 5330.36i) q^{48} +(819.518 - 1419.45i) q^{49} +(6106.00 - 10575.9i) q^{50} +8799.43 q^{51} +(4769.42 + 8503.15i) q^{52} +17016.4 q^{53} +(-4426.71 + 7667.29i) q^{54} +(-1501.32 + 2600.36i) q^{55} +(-3941.07 - 6826.13i) q^{56} -39020.0 q^{57} +(17134.6 + 29678.1i) q^{58} +(-6623.03 - 11471.4i) q^{59} +3264.11 q^{60} +(15022.0 + 26018.9i) q^{61} +(6236.00 - 10801.1i) q^{62} +(-20632.6 + 35736.8i) q^{63} +4096.00 q^{64} +(-5169.92 - 64.2412i) q^{65} +34032.2 q^{66} +(-13080.1 + 22655.4i) q^{67} +(-2927.92 + 5071.30i) q^{68} +(-50220.3 - 86984.2i) q^{69} +4180.06 q^{70} +(-4503.53 - 7800.34i) q^{71} +(-10721.9 - 18570.8i) q^{72} -66973.1 q^{73} +(-21835.6 - 37820.4i) q^{74} +(36701.4 - 63568.8i) q^{75} +(12983.5 - 22488.1i) q^{76} +43582.0 q^{77} +(28667.6 + 51110.0i) q^{78} +24904.4 q^{79} +(-1086.10 + 1881.18i) q^{80} +(14101.9 - 24425.3i) q^{81} +(-12695.8 - 21989.7i) q^{82} -75793.5 q^{83} +(-23688.6 - 41029.9i) q^{84} +(-1552.74 - 2689.42i) q^{85} -61411.8 q^{86} +(102991. + 178386. i) q^{87} +(-11323.8 + 19613.5i) q^{88} +(-40021.7 + 69319.6i) q^{89} +11372.1 q^{90} +(36712.1 + 65452.1i) q^{91} +66841.1 q^{92} +(37482.8 - 64922.1i) q^{93} +(-45824.7 + 79370.7i) q^{94} +(6885.42 + 11925.9i) q^{95} +24619.9 q^{96} +(-26468.6 - 45844.9i) q^{97} +(3278.07 + 5677.79i) q^{98} +118567. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 12 q^{2} - 48 q^{4} + 2 q^{5} - 202 q^{7} + 384 q^{8} - 213 q^{9} - 4 q^{10} + 502 q^{11} - 1091 q^{13} + 1616 q^{14} - 1194 q^{15} - 768 q^{16} - 225 q^{17} + 1704 q^{18} - 1064 q^{19} - 16 q^{20}+ \cdots + 179400 q^{99}+O(q^{100}) \) 6 * q - 12 * q^2 - 48 * q^4 + 2 * q^5 - 202 * q^7 + 384 * q^8 - 213 * q^9 - 4 * q^10 + 502 * q^11 - 1091 * q^13 + 1616 * q^14 - 1194 * q^15 - 768 * q^16 - 225 * q^17 + 1704 * q^18 - 1064 * q^19 - 16 * q^20 + 876 * q^21 + 2008 * q^22 - 5140 * q^23 + 3076 * q^25 - 404 * q^26 + 15444 * q^27 - 3232 * q^28 + 5753 * q^29 - 4776 * q^30 - 15148 * q^31 - 3072 * q^32 - 22170 * q^33 + 1800 * q^34 + 18176 * q^35 - 3408 * q^36 - 3863 * q^37 + 8512 * q^38 + 18708 * q^39 + 128 * q^40 - 9441 * q^41 - 1752 * q^42 - 12586 * q^43 - 16064 * q^44 + 18339 * q^45 - 20560 * q^46 + 14692 * q^47 - 981 * q^49 - 6152 * q^50 + 54288 * q^51 + 19072 * q^52 + 112602 * q^53 - 30888 * q^54 - 46732 * q^55 - 12928 * q^56 - 130476 * q^57 + 23012 * q^58 - 92302 * q^59 + 38208 * q^60 + 11237 * q^61 + 30296 * q^62 - 74328 * q^63 + 24576 * q^64 + 156829 * q^65 + 177360 * q^66 - 79108 * q^67 - 3600 * q^68 - 121038 * q^69 - 145408 * q^70 + 3280 * q^71 - 13632 * q^72 + 25734 * q^73 - 15452 * q^74 + 135330 * q^75 - 17024 * q^76 - 122180 * q^77 - 7320 * q^78 + 189048 * q^79 - 256 * q^80 + 65889 * q^81 - 37764 * q^82 - 88440 * q^83 - 7008 * q^84 - 203667 * q^85 + 100688 * q^86 + 246540 * q^87 + 32128 * q^88 - 333396 * q^89 - 146712 * q^90 + 286194 * q^91 + 164480 * q^92 + 24996 * q^93 - 29384 * q^94 - 49254 * q^95 - 109356 * q^97 - 3924 * q^98 + 179400 * q^99

Introduction

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