LMFDB - Embedded newform 15.6.e.a.2.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [15,6,Mod(2,15)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(15, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("15.2"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	15.e (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.40575729719$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10768x^{12} + 16341006x^{8} + 4217167600x^{4} + 50906640625 $ x^16 + 10768x^12 + 16341006x^8 + 4217167600*x^4 + 50906640625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{10}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2.1
Root			$-6.88827 - 6.88827i$ of defining polynomial
Character	$\chi$	$=$	15.2
Dual form			15.6.e.a.8.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.77944 + 6.77944i) q^{2} +(3.70445 + 15.1419i) q^{3} -59.9217i q^{4} +(-52.1700 - 20.0821i) q^{5} +(-127.768 - 77.5396i) q^{6} +(47.9711 + 47.9711i) q^{7} +(189.294 + 189.294i) q^{8} +(-215.554 + 112.185i) q^{9} +(489.829 - 217.538i) q^{10} +234.950i q^{11} +(907.329 - 221.977i) q^{12} +(-723.818 + 723.818i) q^{13} -650.435 q^{14} +(110.820 - 864.346i) q^{15} -649.117 q^{16} +(335.918 - 335.918i) q^{17} +(700.788 - 2221.89i) q^{18} -92.0117i q^{19} +(-1203.35 + 3126.12i) q^{20} +(-548.667 + 904.080i) q^{21} +(-1592.83 - 1592.83i) q^{22} +(2142.03 + 2142.03i) q^{23} +(-2165.04 + 3567.49i) q^{24} +(2318.42 + 2095.37i) q^{25} -9814.17i q^{26} +(-2497.20 - 2848.32i) q^{27} +(2874.51 - 2874.51i) q^{28} +996.800 q^{29} +(5108.48 + 6611.08i) q^{30} +2525.76 q^{31} +(-1656.75 + 1656.75i) q^{32} +(-3557.59 + 870.360i) q^{33} +4554.67i q^{34} +(-1539.29 - 3466.01i) q^{35} +(6722.30 + 12916.4i) q^{36} +(2465.40 + 2465.40i) q^{37} +(623.788 + 623.788i) q^{38} +(-13641.3 - 8278.64i) q^{39} +(-6074.04 - 13676.9i) q^{40} -2758.58i q^{41} +(-2409.50 - 9848.82i) q^{42} +(-6545.53 + 6545.53i) q^{43} +14078.6 q^{44} +(13498.4 - 1523.89i) q^{45} -29043.5 q^{46} +(-449.067 + 449.067i) q^{47} +(-2404.62 - 9828.86i) q^{48} -12204.5i q^{49} +(-29923.0 + 1512.16i) q^{50} +(6330.82 + 3842.04i) q^{51} +(43372.4 + 43372.4i) q^{52} +(9021.16 + 9021.16i) q^{53} +(36239.6 + 2380.39i) q^{54} +(4718.30 - 12257.4i) q^{55} +18161.3i q^{56} +(1393.23 - 340.852i) q^{57} +(-6757.75 + 6757.75i) q^{58} +5804.97 q^{59} +(-51793.1 - 6640.54i) q^{60} +27112.9 q^{61} +(-17123.3 + 17123.3i) q^{62} +(-15722.0 - 4958.75i) q^{63} -43235.4i q^{64} +(52297.4 - 23225.8i) q^{65} +(18217.9 - 30019.0i) q^{66} +(-43583.6 - 43583.6i) q^{67} +(-20128.8 - 20128.8i) q^{68} +(-24499.3 + 40369.3i) q^{69} +(33933.2 + 13062.1i) q^{70} +55404.2i q^{71} +(-62038.9 - 19567.2i) q^{72} +(-26186.6 + 26186.6i) q^{73} -33428.1 q^{74} +(-23139.4 + 42867.4i) q^{75} -5513.50 q^{76} +(-11270.8 + 11270.8i) q^{77} +(148605. - 36356.1i) q^{78} +23736.6i q^{79} +(33864.4 + 13035.6i) q^{80} +(33878.2 - 48363.7i) q^{81} +(18701.6 + 18701.6i) q^{82} +(-63509.0 - 63509.0i) q^{83} +(54174.0 + 32877.1i) q^{84} +(-24270.8 + 10778.9i) q^{85} -88750.0i q^{86} +(3692.59 + 15093.5i) q^{87} +(-44474.6 + 44474.6i) q^{88} +23793.2 q^{89} +(-81180.3 + 101843. i) q^{90} -69444.7 q^{91} +(128354. - 128354. i) q^{92} +(9356.54 + 38244.8i) q^{93} -6088.84i q^{94} +(-1847.79 + 4800.25i) q^{95} +(-31223.6 - 18949.0i) q^{96} +(80721.5 + 80721.5i) q^{97} +(82740.0 + 82740.0i) q^{98} +(-26357.8 - 50644.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 84 q^{6} - 80 q^{7} + 1060 q^{10} + 420 q^{12} - 2120 q^{13} - 3000 q^{15} - 452 q^{16} + 6000 q^{18} + 1416 q^{21} + 3380 q^{22} + 9160 q^{25} - 12960 q^{27} - 10900 q^{28} - 13380 q^{30} - 21568 q^{31}+ \cdots + 440800 q^{97}+O(q^{100}) $ 16 * q - 84 * q^6 - 80 * q^7 + 1060 * q^10 + 420 * q^12 - 2120 * q^13 - 3000 * q^15 - 452 * q^16 + 6000 * q^18 + 1416 * q^21 + 3380 * q^22 + 9160 * q^25 - 12960 * q^27 - 10900 * q^28 - 13380 * q^30 - 21568 * q^31 + 5760 * q^33 + 61932 * q^36 + 55720 * q^37 + 21480 * q^40 - 103020 * q^42 - 23360 * q^43 - 21240 * q^45 - 151168 * q^46 + 74820 * q^48 + 138816 * q^51 + 204160 * q^52 + 89120 * q^55 - 163800 * q^57 - 163500 * q^58 - 217380 * q^60 - 175168 * q^61 + 143040 * q^63 + 263400 * q^66 + 140320 * q^67 + 385260 * q^70 - 328680 * q^72 - 240320 * q^73 - 199920 * q^75 - 271536 * q^76 + 429960 * q^78 + 326016 * q^81 + 431120 * q^82 + 2440 * q^85 - 331680 * q^87 - 401700 * q^88 - 348360 * q^90 - 487168 * q^91 - 22320 * q^93 + 311748 * q^96 + 440800 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−6.77944	+	6.77944i	−1.19845	+	1.19845i	−0.223816	+	0.974631i	$0.571852\pi$
$2$	−6.77944	+	6.77944i	−1.19845	+	1.19845i	−0.974631	+	0.223816i	$0.928148\pi$
$3$	3.70445	+	15.1419i	0.237640	+	0.971353i
$3$	3.70445	+	15.1419i	0.237640	+	0.971353i
$4$		−	59.9217i		−	1.87255i
$5$	−52.1700	−	20.0821i	−0.933245	−	0.359240i
$5$	−52.1700	−	20.0821i	−0.933245	−	0.359240i
$6$	−127.768	−	77.5396i	−1.44892	−	0.879317i
$7$	47.9711	+	47.9711i	0.370028	+	0.370028i	0.867487	−	0.497459i	$-0.165734\pi$
$7$	47.9711	+	47.9711i	0.370028	+	0.370028i	−0.497459	+	0.867487i	$0.665734\pi$
$8$	189.294	+	189.294i	1.04571	+	1.04571i
$9$	−215.554	+	112.185i	−0.887054	+	0.461665i
$10$	489.829	−	217.538i	1.54898	−	0.687916i
$11$			234.950i			0.585456i	0.956196	+	0.292728i	$0.0945630\pi$
$11$			234.950i			0.585456i	−0.956196	+	0.292728i	$0.905437\pi$
$12$	907.329	−	221.977i	1.81891	−	0.444994i
$13$	−723.818	+	723.818i	−1.18788	+	1.18788i	−0.210222	+	0.977654i	$0.567419\pi$
$13$	−723.818	+	723.818i	−1.18788	+	1.18788i	−0.977654	+	0.210222i	$0.932581\pi$
$14$	−650.435			−0.886919
$15$	110.820	−	864.346i	0.127172	−	0.991881i
$16$	−649.117			−0.633903
$17$	335.918	−	335.918i	0.281910	−	0.281910i	−0.551960	−	0.833870i	$-0.686120\pi$
$17$	335.918	−	335.918i	0.281910	−	0.281910i	0.833870	+	0.551960i	$0.186120\pi$
$18$	700.788	−	2221.89i	0.509806	−	1.61637i
$19$		−	92.0117i		−	0.0584735i	−0.999573	−	0.0292367i	$-0.990692\pi$
$19$		−	92.0117i		−	0.0584735i	0.999573	−	0.0292367i	$-0.00930767\pi$
$20$	−1203.35	+	3126.12i	−0.672696	+	1.74755i
$21$	−548.667	+	904.080i	−0.271494	+	0.447362i
$22$	−1592.83	−	1592.83i	−0.701638	−	0.701638i
$23$	2142.03	+	2142.03i	0.844316	+	0.844316i	0.989417	−	0.145101i	$-0.0463507\pi$
$23$	2142.03	+	2142.03i	0.844316	+	0.844316i	−0.145101	+	0.989417i	$0.546351\pi$
$24$	−2165.04	+	3567.49i	−0.767251	+	1.26426i
$25$	2318.42	+	2095.37i	0.741894	+	0.670518i
$26$		−	9814.17i		−	2.84721i
$27$	−2497.20	−	2848.32i	−0.659240	−	0.751933i
$28$	2874.51	−	2874.51i	0.692897	−	0.692897i
$29$	996.800			0.220097			0.110048	−	0.993926i	$-0.464899\pi$
$29$	996.800			0.220097			0.110048	+	0.993926i	$0.464899\pi$
$30$	5108.48	+	6611.08i	1.03631	+	1.34113i
$31$	2525.76			0.472050			0.236025	−	0.971747i	$-0.424155\pi$
$31$	2525.76			0.472050			0.236025	+	0.971747i	$0.424155\pi$
$32$	−1656.75	+	1656.75i	−0.286010	+	0.286010i
$33$	−3557.59	+	870.360i	−0.568684	+	0.139128i
$34$			4554.67i			0.675709i
$35$	−1539.29	−	3466.01i	−0.212398	−	0.478256i
$36$	6722.30	+	12916.4i	0.864493	+	1.66106i
$37$	2465.40	+	2465.40i	0.296062	+	0.296062i	0.839469	−	0.543407i	$-0.182866\pi$
$37$	2465.40	+	2465.40i	0.296062	+	0.296062i	−0.543407	+	0.839469i	$0.682866\pi$
$38$	623.788	+	623.788i	0.0700774	+	0.0700774i
$39$	−13641.3	−	8278.64i	−1.43613	−	0.871560i
$40$	−6074.04	−	13676.9i	−0.600243	−	1.35156i
$41$		−	2758.58i		−	0.256286i	−0.991756	−	0.128143i	$-0.959098\pi$
$41$		−	2758.58i		−	0.256286i	0.991756	−	0.128143i	$-0.0409017\pi$
$42$	−2409.50	−	9848.82i	−0.210768	−	0.861511i
$43$	−6545.53	+	6545.53i	−0.539850	+	0.539850i	−0.923485	−	0.383635i	$-0.874672\pi$
$43$	−6545.53	+	6545.53i	−0.539850	+	0.539850i	0.383635	+	0.923485i	$0.374672\pi$
$44$	14078.6			1.09630
$45$	13498.4	−	1523.89i	0.993688	−	0.112182i
$46$	−29043.5			−2.02374
$47$	−449.067	+	449.067i	−0.0296528	+	0.0296528i	−0.721778	−	0.692125i	$-0.756675\pi$
$47$	−449.067	+	449.067i	−0.0296528	+	0.0296528i	0.692125	+	0.721778i	$0.256675\pi$
$48$	−2404.62	−	9828.86i	−0.150641	−	0.615744i
$49$		−	12204.5i		−	0.726158i
$50$	−29923.0	+	1512.16i	−1.69270	+	0.0855405i
$51$	6330.82	+	3842.04i	0.340827	+	0.206841i
$52$	43372.4	+	43372.4i	2.22436	+	2.22436i
$53$	9021.16	+	9021.16i	0.441136	+	0.441136i	0.892394	−	0.451257i	$-0.149024\pi$
$53$	9021.16	+	9021.16i	0.441136	+	0.441136i	−0.451257	+	0.892394i	$0.649024\pi$
$54$	36239.6	+	2380.39i	1.69122	+	0.111087i
$55$	4718.30	−	12257.4i	0.210319	−	0.546374i
$56$			18161.3i			0.773884i
$57$	1393.23	−	340.852i	0.0567984	−	0.0138957i
$58$	−6757.75	+	6757.75i	−0.263774	+	0.263774i
$59$	5804.97			0.217105			0.108552	−	0.994091i	$-0.465378\pi$
$59$	5804.97			0.217105			0.108552	+	0.994091i	$0.465378\pi$
$60$	−51793.1	−	6640.54i	−1.85735	−	0.238136i
$61$	27112.9			0.932937			0.466468	−	0.884538i	$-0.345526\pi$
$61$	27112.9			0.932937			0.466468	+	0.884538i	$0.345526\pi$
$62$	−17123.3	+	17123.3i	−0.565727	+	0.565727i
$63$	−15722.0	−	4958.75i	−0.499064	−	0.157406i
$64$		−	43235.4i		−	1.31944i
$65$	52297.4	−	23225.8i	1.53531	−	0.681847i
$66$	18217.9	−	30019.0i	0.514801	−	0.848276i
$67$	−43583.6	−	43583.6i	−1.18614	−	1.18614i	−0.978126	−	0.208015i	$-0.933300\pi$
$67$	−43583.6	−	43583.6i	−1.18614	−	1.18614i	−0.208015	−	0.978126i	$-0.566700\pi$
$68$	−20128.8	−	20128.8i	−0.527892	−	0.527892i
$69$	−24499.3	+	40369.3i	−0.619486	+	1.02077i
$70$	33933.2	+	13062.1i	0.827713	+	0.318616i
$71$			55404.2i			1.30436i	0.758065	+	0.652179i	$0.226145\pi$
$71$			55404.2i			1.30436i	−0.758065	+	0.652179i	$0.773855\pi$
$72$	−62038.9	−	19567.2i	−1.41037	−	0.444833i
$73$	−26186.6	+	26186.6i	−0.575139	+	0.575139i	−0.933560	−	0.358421i	$-0.883315\pi$
$73$	−26186.6	+	26186.6i	−0.575139	+	0.575139i	0.358421	+	0.933560i	$0.383315\pi$
$74$	−33428.1			−0.709630
$75$	−23139.4	+	42867.4i	−0.475006	+	0.879983i
$76$	−5513.50			−0.109495
$77$	−11270.8	+	11270.8i	−0.216635	+	0.216635i
$78$	148605.	−	36356.1i	2.76565	−	0.676613i
$79$			23736.6i			0.427908i	0.976844	+	0.213954i	$0.0686342\pi$
$79$			23736.6i			0.427908i	−0.976844	+	0.213954i	$0.931366\pi$
$80$	33864.4	+	13035.6i	0.591587	+	0.227723i
$81$	33878.2	−	48363.7i	0.573730	−	0.819044i
$82$	18701.6	+	18701.6i	0.307146	+	0.307146i
$83$	−63509.0	−	63509.0i	−1.01191	−	1.01191i	−0.999928	−	0.0119773i	$-0.996187\pi$
$83$	−63509.0	−	63509.0i	−1.01191	−	1.01191i	−0.0119773	−	0.999928i	$-0.503813\pi$
$84$	54174.0	+	32877.1i	0.837708	+	0.508388i
$85$	−24270.8	+	10778.9i	−0.364365	+	0.161818i
$86$		−	88750.0i		−	1.29396i
$87$	3692.59	+	15093.5i	0.0523038	+	0.213791i
$88$	−44474.6	+	44474.6i	−0.612217	+	0.612217i
$89$	23793.2			0.318404			0.159202	−	0.987246i	$-0.449108\pi$
$89$	23793.2			0.318404			0.159202	+	0.987246i	$0.449108\pi$
$90$	−81180.3	+	101843.i	−1.05644	+	1.32533i
$91$	−69444.7			−0.879095
$92$	128354.	−	128354.i	1.58103	−	1.58103i
$93$	9356.54	+	38244.8i	0.112178	+	0.458527i
$94$		−	6088.84i		−	0.0710747i
$95$	−1847.79	+	4800.25i	−0.0210060	+	0.0545701i
$96$	−31223.6	−	18949.0i	−0.345784	−	0.209849i
$97$	80721.5	+	80721.5i	0.871084	+	0.871084i	0.992591	−	0.121507i	$-0.0387726\pi$
$97$	80721.5	+	80721.5i	0.871084	+	0.871084i	−0.121507	+	0.992591i	$0.538773\pi$
$98$	82740.0	+	82740.0i	0.870263	+	0.870263i
$99$	−26357.8	−	50644.5i	−0.270285	−	0.519331i
$100$	125558.	−	138924.i	1.25558	−	1.38924i
$101$			122721.i			1.19706i	0.801102	+	0.598528i	$0.204248\pi$
$101$			122721.i			1.19706i	−0.801102	+	0.598528i	$0.795752\pi$
$102$	−68966.4	+	16872.5i	−0.656352	+	0.160576i
$103$	119291.	−	119291.i	1.10794	−	1.10794i	0.114516	−	0.993421i	$-0.463468\pi$
$103$	119291.	−	119291.i	1.10794	−	1.10794i	0.993421	−	0.114516i	$-0.0365318\pi$
$104$	−274028.			−2.48435
$105$	46779.8	−	36147.5i	0.414081	−	0.319966i
$106$	−122317.			−1.05736
$107$	64584.7	−	64584.7i	0.545344	−	0.545344i	−0.379747	−	0.925091i	$-0.623989\pi$
$107$	64584.7	−	64584.7i	0.545344	−	0.545344i	0.925091	+	0.379747i	$0.123989\pi$
$108$	−170676.	+	149636.i	−1.40803	+	1.23446i
$109$			108945.i			0.878297i	0.898414	+	0.439149i	$0.144720\pi$
$109$			108945.i			0.878297i	−0.898414	+	0.439149i	$0.855280\pi$
$110$	51110.6	+	115085.i	0.402744	+	0.906857i
$111$	−28197.9	+	46463.7i	−0.217225	+	0.357937i
$112$	−31138.9	−	31138.9i	−0.234562	−	0.234562i
$113$	−73315.5	−	73315.5i	−0.540131	−	0.540131i	0.383436	−	0.923567i	$-0.374741\pi$
$113$	−73315.5	−	73315.5i	−0.540131	−	0.540131i	−0.923567	+	0.383436i	$0.874741\pi$
$114$	−7134.55	+	11756.1i	−0.0514167	+	0.0847232i
$115$	−68733.1	−	154766.i	−0.484642	−	1.09127i
$116$		−	59730.0i		−	0.412143i
$117$	74820.7	−	237223.i	0.505309	−	1.60211i
$118$	−39354.5	+	39354.5i	−0.260189	+	0.260189i
$119$	32228.7			0.208629
$120$	184593.	−	142638.i	1.17020	−	0.904234i
$121$	105849.			0.657242
$122$	−183811.	+	183811.i	−1.11808	+	1.11808i
$123$	41770.1	−	10219.0i	0.248945	−	0.0609040i
$124$		−	151348.i		−	0.883939i
$125$	−78872.5	−	155874.i	−0.451492	−	0.892275i
$126$	140204.	−	72968.8i	0.786745	−	0.409460i
$127$	101731.	+	101731.i	0.559684	+	0.559684i	0.929217	−	0.369533i	$-0.120482\pi$
$127$	101731.	+	101731.i	0.559684	+	0.559684i	−0.369533	+	0.929217i	$0.620482\pi$
$128$	240096.	+	240096.i	1.29527	+	1.29527i
$129$	−123359.	−	74864.1i	−0.652676	−	0.396095i
$130$	−197089.	+	512005.i	−1.02283	+	2.65715i
$131$			14631.0i			0.0744894i	0.999306	+	0.0372447i	$0.0118581\pi$
$131$			14631.0i			0.0744894i	−0.999306	+	0.0372447i	$0.988142\pi$
$132$	52153.5	+	213177.i	0.260524	+	1.06489i
$133$	4413.90	−	4413.90i	0.0216368	−	0.0216368i
$134$	590945.			2.84305
$135$	73078.6	+	198746.i	0.345109	+	0.938563i
$136$	127174.			0.589592
$137$	−238849.	+	238849.i	−1.08723	+	1.08723i	−0.0914178	+	0.995813i	$0.529140\pi$
$137$	−238849.	+	238849.i	−1.08723	+	1.08723i	−0.995813	+	0.0914178i	$0.970860\pi$
$138$	−107590.	−	439773.i	−0.480922	−	1.96576i
$139$			265859.i			1.16712i	0.812071	+	0.583558i	$0.198340\pi$
$139$			265859.i			1.16712i	−0.812071	+	0.583558i	$0.801660\pi$
$140$	−207689.	+	92237.0i	−0.895559	+	0.397727i
$141$	−8463.26	−	5136.18i	−0.0358501	−	0.0217567i
$142$	−375609.	−	375609.i	−1.56320	−	1.56320i
$143$	−170061.	−	170061.i	−0.695449	−	0.695449i
$144$	139920.	−	72821.0i	0.562307	−	0.292651i
$145$	−52003.1	−	20017.9i	−0.205404	−	0.0790674i
$146$		−	355062.i		−	1.37855i
$147$	184800.	−	45211.1i	0.705356	−	0.172565i
$148$	147731.	−	147731.i	0.554392	−	0.554392i
$149$	58282.4			0.215066			0.107533	−	0.994202i	$-0.465705\pi$
$149$	58282.4			0.215066			0.107533	+	0.994202i	$0.465705\pi$
$150$	−133745.	−	447489.i	−0.485344	−	1.62388i
$151$	106984.			0.381835			0.190918	−	0.981606i	$-0.438854\pi$
$151$	106984.			0.381835			0.190918	+	0.981606i	$0.438854\pi$
$152$	17417.2	−	17417.2i	0.0611463	−	0.0611463i
$153$	−34723.6	+	110093.i	−0.119921	+	0.380218i
$154$		−	152820.i		−	0.519252i
$155$	−131769.	−	50722.6i	−0.440538	−	0.169579i
$156$	−496070.	+	817412.i	−1.63204	+	2.68924i
$157$	−211942.	−	211942.i	−0.686228	−	0.686228i	0.275168	−	0.961396i	$-0.411266\pi$
$157$	−211942.	−	211942.i	−0.686228	−	0.686228i	−0.961396	+	0.275168i	$0.911266\pi$
$158$	−160921.	−	160921.i	−0.512825	−	0.512825i
$159$	−103179.	+	170016.i	−0.323667	+	0.533331i
$160$	119703.	−	53161.5i	0.369663	−	0.164171i
$161$			205511.i			0.624841i
$162$	98204.0	+	557555.i	0.293996	+	1.66917i
$163$	−213787.	+	213787.i	−0.630248	+	0.630248i	−0.948130	−	0.317882i	$-0.897028\pi$
$163$	−213787.	+	213787.i	−0.630248	+	0.630248i	0.317882	+	0.948130i	$0.397028\pi$
$164$	−165299.			−0.479910
$165$	203078.	+	26037.3i	0.580702	+	0.0744535i
$166$	861111.			2.42543
$167$	143183.	−	143183.i	0.397283	−	0.397283i	−0.479990	−	0.877274i	$-0.659360\pi$
$167$	143183.	−	143183.i	0.397283	−	0.397283i	0.877274	+	0.479990i	$0.159360\pi$
$168$	−274996.	+	67277.4i	−0.751715	+	0.183906i
$169$		−	676532.i		−	1.82210i
$170$	91467.4	−	237617.i	0.242741	−	0.630602i
$171$	10322.3	+	19833.5i	0.0269952	+	0.0518692i
$172$	392219.	+	392219.i	1.01090	+	1.01090i
$173$	386120.	+	386120.i	0.980860	+	0.980860i	0.999820	−	0.0189605i	$-0.00603568\pi$
$173$	386120.	+	386120.i	0.980860	+	0.980860i	−0.0189605	+	0.999820i	$0.506036\pi$
$174$	−127359.	−	77291.5i	−0.318901	−	0.193535i
$175$	10700.0	+	211734.i	0.0264112	+	0.522632i
$176$		−	152510.i		−	0.371122i
$177$	21504.2	+	87898.2i	0.0515929	+	0.210886i
$178$	−161305.	+	161305.i	−0.381590	+	0.381590i
$179$	377468.			0.880537			0.440269	−	0.897866i	$-0.354883\pi$
$179$	377468.			0.880537			0.440269	+	0.897866i	$0.354883\pi$
$180$	−91314.2	−	808845.i	−0.210067	−	1.86073i
$181$	−759198.			−1.72250			−0.861249	−	0.508183i	$-0.830317\pi$
$181$	−759198.			−1.72250			−0.861249	+	0.508183i	$0.830317\pi$
$182$	470797.	−	470797.i	1.05355	−	1.05355i
$183$	100438.	+	410541.i	0.221703	+	0.906211i
$184$			810944.i			1.76582i
$185$	−79109.4	−	178130.i	−0.169941	−	0.382656i
$186$	−322711.	−	195846.i	−0.683960	−	0.415081i
$187$	78923.9	+	78923.9i	0.165046	+	0.165046i
$188$	26908.8	+	26908.8i	0.0555265	+	0.0555265i
$189$	16843.6	−	256430.i	0.0342989	−	0.522173i
$190$	−20016.0	−	45070.0i	−0.0402248	−	0.0905740i
$191$		−	744634.i		−	1.47693i	−0.674293	−	0.738464i	$-0.735552\pi$
$191$		−	744634.i		−	1.47693i	0.674293	−	0.738464i	$-0.264448\pi$
$192$	654666.	−	160163.i	1.28164	−	0.313552i
$193$	387406.	−	387406.i	0.748641	−	0.748641i	−0.225583	−	0.974224i	$-0.572429\pi$
$193$	387406.	−	387406.i	0.748641	−	0.748641i	0.974224	+	0.225583i	$0.0724287\pi$
$194$	−1.09449e6			−2.08790
$195$	545415.	+	705843.i	1.02717	+	1.32930i
$196$	−731317.			−1.35977
$197$	−719280.	+	719280.i	−1.32048	+	1.32048i	−0.407096	+	0.913385i	$0.633459\pi$
$197$	−719280.	+	719280.i	−1.32048	+	1.32048i	−0.913385	+	0.407096i	$0.866541\pi$
$198$	522033.	+	164650.i	0.946313	+	0.298469i
$199$			144090.i			0.257929i	0.991649	+	0.128965i	$0.0411654\pi$
$199$			144090.i			0.257929i	−0.991649	+	0.128965i	$0.958835\pi$
$200$	42222.0	+	835502.i	0.0746387	+	1.47697i
$201$	498485.	−	821391.i	0.870286	−	1.43404i
$202$	−831979.	−	831979.i	−1.43461	−	1.43461i
$203$	47817.6	+	47817.6i	0.0814419	+	0.0814419i
$204$	230222.	−	379354.i	0.387321	−	0.638218i
$205$	−55398.0	+	143915.i	−0.0920682	+	0.239178i
$206$			1.61746e6i			2.65561i
$207$	−702025.	−	221420.i	−1.13875	−	0.359163i
$208$	469843.	−	469843.i	0.752998	−	0.752998i
$209$	21618.2			0.0342336
$210$	−72081.4	+	562201.i	−0.112791	+	0.879717i
$211$	397577.			0.614774			0.307387	−	0.951585i	$-0.400545\pi$
$211$	397577.			0.614774			0.307387	+	0.951585i	$0.400545\pi$
$212$	540564.	−	540564.i	0.826051	−	0.826051i
$213$	−838924.	+	205242.i	−1.26699	+	0.309968i
$214$			875697.i			1.30713i
$215$	472928.	−	210032.i	0.697749	−	0.309877i
$216$	66464.7	−	1.01187e6i	0.0969297	−	1.47568i
$217$	121164.	+	121164.i	0.174672	+	0.174672i
$218$	−738587.	−	738587.i	−1.05259	−	1.05259i
$219$	−493522.	−	299508.i	−0.695339	−	0.421987i
$220$	−734481.	−	282728.i	−1.02311	−	0.393833i
$221$			486287.i			0.669748i
$222$	−123832.	−	506164.i	−0.168637	−	0.689301i
$223$	519537.	−	519537.i	0.699607	−	0.699607i	−0.264718	−	0.964326i	$-0.585279\pi$
$223$	519537.	−	519537.i	0.699607	−	0.699607i	0.964326	+	0.264718i	$0.0852790\pi$
$224$	−158952.			−0.211663
$225$	−734813.	−	191574.i	−0.967655	−	0.252279i
$226$	994076.			1.29464
$227$	448406.	−	448406.i	0.577573	−	0.577573i	−0.356661	−	0.934234i	$-0.616085\pi$
$227$	448406.	−	448406.i	0.577573	−	0.577573i	0.934234	+	0.356661i	$0.116085\pi$
$228$	−20424.5	−	83484.8i	−0.0260204	−	0.106358i
$229$			492328.i			0.620392i	0.950673	+	0.310196i	$0.100395\pi$
$229$			492328.i			0.620392i	−0.950673	+	0.310196i	$0.899605\pi$
$230$	1.51520e6	+	583254.i	1.88864	+	0.727007i
$231$	−212414.	−	128909.i	−0.261910	−	0.158948i
$232$	188688.	+	188688.i	0.230157	+	0.230157i
$233$	−336239.	−	336239.i	−0.405750	−	0.405750i	0.474504	−	0.880253i	$-0.342627\pi$
$233$	−336239.	−	336239.i	−0.405750	−	0.405750i	−0.880253	+	0.474504i	$0.842627\pi$
$234$	1.10100e6	+	2.11548e6i	1.31446	+	2.52563i
$235$	32446.0	−	14409.6i	0.0383258	−	0.0170209i
$236$		−	347844.i		−	0.406541i
$237$	−359417.	+	87930.8i	−0.415650	+	0.101688i
$238$	−218493.	+	218493.i	−0.250031	+	0.250031i
$239$	−323618.			−0.366470			−0.183235	−	0.983069i	$-0.558657\pi$
$239$	−323618.			−0.366470			−0.183235	+	0.983069i	$0.558657\pi$
$240$	−71935.4	+	561062.i	−0.0806147	+	0.628756i
$241$	629170.			0.697791			0.348896	−	0.937162i	$-0.386557\pi$
$241$	629170.			0.697791			0.348896	+	0.937162i	$0.386557\pi$
$242$	−717600.	+	717600.i	−0.787670	+	0.787670i
$243$	857819.	+	333819.i	0.931923	+	0.362657i
$244$		−	1.62465e6i		−	1.74697i
$245$	−245093.	+	636711.i	−0.260865	+	0.677684i
$246$	−213899.	+	352457.i	−0.225357	+	0.371337i
$247$	66599.7	+	66599.7i	0.0694593	+	0.0694593i
$248$	478111.	+	478111.i	0.493627	+	0.493627i
$249$	726381.	−	1.19691e6i	0.742448	−	1.22339i
$250$	1.59145e6	+	522028.i	1.61043	+	0.528255i
$251$		−	801687.i		−	0.803194i	−0.915816	−	0.401597i	$-0.868455\pi$
$251$		−	801687.i		−	0.803194i	0.915816	−	0.401597i	$-0.131545\pi$
$252$	−297137.	+	942089.i	−0.294751	+	0.934524i
$253$	−503269.	+	503269.i	−0.494310	+	0.494310i
$254$	−1.37936e6			−1.34150
$255$	−253123.	−	327576.i	−0.243770	−	0.315472i
$256$	−1.87190e6			−1.78518
$257$	584340.	−	584340.i	0.551865	−	0.551865i	−0.375114	−	0.926979i	$-0.622396\pi$
$257$	584340.	−	584340.i	0.551865	−	0.551865i	0.926979	+	0.375114i	$0.122396\pi$
$258$	1.34384e6	−	328770.i	1.25690	−	0.307498i
$259$			236536.i			0.219103i
$260$	−1.39173e6	−	3.13375e6i	−1.27680	−	2.87495i
$261$	−214864.	+	111826.i	−0.195238	+	0.101611i
$262$	−99189.8	−	99189.8i	−0.0892717	−	0.0892717i
$263$	992491.	+	992491.i	0.884784	+	0.884784i	0.994016	−	0.109232i	$-0.0348392\pi$
$263$	992491.	+	992491.i	0.884784	+	0.884784i	−0.109232	+	0.994016i	$0.534839\pi$
$264$	−838183.	−	508676.i	−0.740166	−	0.449191i
$265$	−289470.	−	651798.i	−0.253215	−	0.570162i
$266$			59847.6i			0.0518612i
$267$	88140.6	+	360274.i	0.0756655	+	0.309282i
$268$	−2.61160e6	+	2.61160e6i	−2.22111	+	2.22111i
$269$	2.15952e6			1.81960			0.909800	−	0.415047i	$-0.136235\pi$
$269$	2.15952e6			1.81960			0.909800	+	0.415047i	$0.136235\pi$
$270$	−1.84282e6	−	851953.i	−1.53841	−	0.711224i
$271$	−1.97368e6			−1.63250			−0.816250	−	0.577699i	$-0.803951\pi$
$271$	−1.97368e6			−1.63250			−0.816250	+	0.577699i	$0.803951\pi$
$272$	−218050.	+	218050.i	−0.178704	+	0.178704i
$273$	−257254.	−	1.05152e6i	−0.208908	−	0.853912i
$274$		−	3.23852e6i		−	2.60598i
$275$	−492307.	+	544713.i	−0.392558	+	0.434346i
$276$	2.41900e6	+	1.46804e6i	1.91145	+	1.16002i
$277$	1.49968e6	+	1.49968e6i	1.17435	+	1.17435i	0.981161	+	0.193193i	$0.0618845\pi$
$277$	1.49968e6	+	1.49968e6i	1.17435	+	1.17435i	0.193193	+	0.981161i	$0.438116\pi$
$278$	−1.80237e6	−	1.80237e6i	−1.39873	−	1.39873i
$279$	−544438.	+	283352.i	−0.418734	+	0.217929i
$280$	364716.	−	947473.i	0.278010	−	0.722224i
$281$			1.21370e6i			0.916953i	0.888707	+	0.458476i	$0.151605\pi$
$281$			1.21370e6i			0.916953i	−0.888707	+	0.458476i	$0.848395\pi$
$282$	92196.6	−	22555.8i	0.0690386	−	0.0168902i
$283$	509824.	−	509824.i	0.378403	−	0.378403i	−0.492123	−	0.870526i	$-0.663779\pi$
$283$	509824.	−	509824.i	0.378403	−	0.378403i	0.870526	+	0.492123i	$0.163779\pi$
$284$	3.31991e6			2.44248
$285$	−79529.9	−	10196.8i	−0.0579987	−	0.00743619i
$286$	2.30584e6			1.66692
$287$	132332.	−	132332.i	0.0948331	−	0.0948331i
$288$	171257.	−	542980.i	0.121665	−	0.385747i
$289$			1.19418e6i			0.841053i
$290$	488262.	−	216842.i	0.340924	−	0.151408i
$291$	−923249.	+	1.52131e6i	−0.639126	+	1.05313i
$292$	1.56915e6	+	1.56915e6i	1.07698	+	1.07698i
$293$	210974.	+	210974.i	0.143569	+	0.143569i	0.775238	−	0.631669i	$-0.217630\pi$
$293$	210974.	+	210974.i	0.143569	+	0.143569i	−0.631669	+	0.775238i	$0.717630\pi$
$294$	−946335.	+	1.55935e6i	−0.638523	+	1.05214i
$295$	−302845.	−	116576.i	−0.202612	−	0.0779927i
$296$			933369.i			0.619190i
$297$	669213.	−	586717.i	0.440223	−	0.385956i
$298$	−395123.	+	395123.i	−0.257746	+	0.257746i
$299$	−3.10087e6			−2.00589
$300$	2.56869e6	+	1.38655e6i	1.64781	+	0.889473i
$301$	−627992.			−0.399520
$302$	−725291.	+	725291.i	−0.457610	+	0.457610i
$303$	−1.85823e6	+	454613.i	−1.16277	+	0.284469i
$304$			59726.4i			0.0370665i
$305$	−1.41448e6	−	544485.i	−0.870659	−	0.335148i
$306$	−510964.	−	981778.i	−0.311951	−	0.599390i
$307$	−772273.	−	772273.i	−0.467654	−	0.467654i	0.433500	−	0.901154i	$-0.357279\pi$
$307$	−772273.	−	772273.i	−0.467654	−	0.467654i	−0.901154	+	0.433500i	$0.857279\pi$
$308$	675367.	+	675367.i	0.405661	+	0.405661i
$309$	2.24820e6	+	1.36439e6i	1.33949	+	0.812908i
$310$	1.23719e6	−	549449.i	0.731194	−	0.324731i
$311$		−	2.69384e6i		−	1.57932i	−0.613542	−	0.789662i	$-0.710256\pi$
$311$		−	2.69384e6i		−	1.57932i	0.613542	−	0.789662i	$-0.289744\pi$
$312$	−1.01512e6	−	4.14931e6i	−0.590381	−	2.41318i
$313$	1.95406e6	−	1.95406e6i	1.12740	−	1.12740i	0.136797	−	0.990599i	$-0.456319\pi$
$313$	1.95406e6	−	1.95406e6i	1.12740	−	1.12740i	0.990599	−	0.136797i	$-0.0436808\pi$
$314$	2.87370e6			1.64482
$315$	720634.	+	574429.i	0.409203	+	0.326182i
$316$	1.42234e6			0.801280
$317$	−198194.	+	198194.i	−0.110775	+	0.110775i	−0.760322	−	0.649547i	$-0.774959\pi$
$317$	−198194.	+	198194.i	−0.110775	+	0.110775i	0.649547	+	0.760322i	$0.274959\pi$
$318$	−453116.	−	1.85211e6i	−0.251271	−	1.02707i
$319$			234198.i			0.128857i
$320$	−868258.	+	2.25559e6i	−0.473995	+	1.23136i
$321$	1.21719e6	+	738685.i	0.659317	+	0.400126i
$322$	−1.39325e6	−	1.39325e6i	−0.748840	−	0.748840i
$323$	−30908.4	−	30908.4i	−0.0164843	−	0.0164843i
$324$	−2.89804e6	−	2.03004e6i	−1.53370	−	1.07434i
$325$	−3.19478e6	+	161448.i	−1.67777	+	0.0847860i
$326$		−	2.89871e6i		−	1.51064i
$327$	−1.64964e6	+	403581.i	−0.853137	+	0.208719i
$328$	522181.	−	522181.i	0.268001	−	0.268001i
$329$	−43084.4			−0.0219448
$330$	−1.55328e6	+	1.20024e6i	−0.785170	+	0.606713i
$331$	−754878.			−0.378710			−0.189355	−	0.981909i	$-0.560640\pi$
$331$	−754878.			−0.378710			−0.189355	+	0.981909i	$0.560640\pi$
$332$	−3.80557e6	+	3.80557e6i	−1.89485	+	1.89485i
$333$	−808007.	−	254847.i	−0.399305	−	0.125941i
$334$			1.94140e6i			0.952247i
$335$	1.39851e6	+	3.14901e6i	0.680851	+	1.53307i
$336$	356149.	−	586854.i	0.172101	−	0.283584i
$337$	1.39598e6	+	1.39598e6i	0.669581	+	0.669581i	0.957619	−	0.288038i	$-0.0930029\pi$
$337$	1.39598e6	+	1.39598e6i	0.669581	+	0.669581i	−0.288038	+	0.957619i	$0.593003\pi$
$338$	4.58651e6	+	4.58651e6i	2.18369	+	2.18369i
$339$	838542.	−	1.38173e6i	0.396301	−	0.653015i
$340$	645890.	+	1.45435e6i	0.303013	+	0.682292i
$341$			593428.i			0.276364i
$342$	−204440.	−	64480.7i	−0.0945148	−	0.0298102i
$343$	1.39172e6	−	1.39172e6i	0.638727	−	0.638727i
$344$	−2.47805e6			−1.12905
$345$	2.08883e6	−	1.61407e6i	0.944834	−	0.730087i
$346$	−5.23536e6			−2.35102
$347$	1.44749e6	−	1.44749e6i	0.645344	−	0.645344i	−0.306520	−	0.951864i	$-0.599165\pi$
$347$	1.44749e6	−	1.44749e6i	0.645344	−	0.645344i	0.951864	+	0.306520i	$0.0991646\pi$
$348$	904425.	−	221267.i	0.400336	−	0.0979417i
$349$		−	1.18200e6i		−	0.519462i	−0.965681	−	0.259731i	$-0.916366\pi$
$349$		−	1.18200e6i		−	0.519462i	0.965681	−	0.259731i	$-0.0836338\pi$
$350$	−1.50798e6	−	1.36290e6i	−0.657999	−	0.594694i
$351$	3.86918e6	+	254147.i	1.67630	+	0.110107i
$352$	−389253.	−	389253.i	−0.167446	−	0.167446i
$353$	−1.97886e6	−	1.97886e6i	−0.845237	−	0.845237i	0.144297	−	0.989534i	$-0.453908\pi$
$353$	−1.97886e6	−	1.97886e6i	−0.845237	−	0.845237i	−0.989534	+	0.144297i	$0.953908\pi$
$354$	−741688.	−	450115.i	−0.314567	−	0.190904i
$355$	1.11263e6	−	2.89043e6i	0.468577	−	1.21729i
$356$		−	1.42573e6i		−	0.596228i
$357$	119389.	+	488004.i	0.0495787	+	0.202653i
$358$	−2.55902e6	+	2.55902e6i	−1.05528	+	1.05528i
$359$	−2.12864e6			−0.871698			−0.435849	−	0.900020i	$-0.643552\pi$
$359$	−2.12864e6			−0.871698			−0.435849	+	0.900020i	$0.643552\pi$
$360$	2.84362e6	+	2.26669e6i	1.15642	+	0.921799i
$361$	2.46763e6			0.996581
$362$	5.14694e6	−	5.14694e6i	2.06432	−	2.06432i
$363$	392113.	+	1.60276e6i	0.156187	+	0.638414i
$364$			4.16125e6i			1.64615i
$365$	1.89204e6	−	840274.i	0.743358	−	0.330133i
$366$	−3.46416e6	−	2.10233e6i	−1.35175	−	0.820347i
$367$	−2.50899e6	−	2.50899e6i	−0.972375	−	0.972375i	0.0272533	−	0.999629i	$-0.491324\pi$
$367$	−2.50899e6	−	2.50899e6i	−0.972375	−	0.972375i	−0.999629	+	0.0272533i	$0.991324\pi$
$368$	−1.39043e6	−	1.39043e6i	−0.535215	−	0.535215i
$369$	309470.	+	594623.i	0.118319	+	0.227340i
$370$	1.74394e6	+	671306.i	0.662259	+	0.254927i
$371$			865510.i			0.326466i
$372$	2.29169e6	−	560660.i	0.858617	−	0.210059i
$373$	−2.49820e6	+	2.49820e6i	−0.929727	+	0.929727i	−0.997688	−	0.0679611i	$-0.978351\pi$
$373$	−2.49820e6	+	2.49820e6i	−0.929727	+	0.929727i	0.0679611	+	0.997688i	$0.478351\pi$
$374$	−1.07012e6			−0.395598
$375$	2.06805e6	−	1.77171e6i	0.759421	−	0.650599i
$376$	−170011.			−0.0620165
$377$	−721502.	+	721502.i	−0.261447	+	0.261447i
$378$	1.62426e6	+	1.85264e6i	0.584692	+	0.666903i
$379$			2.41728e6i			0.864426i	0.901771	+	0.432213i	$0.142267\pi$
$379$			2.41728e6i			0.864426i	−0.901771	+	0.432213i	$0.857733\pi$
$380$	287639.	+	110723.i	0.102185	+	0.0393349i
$381$	−1.16354e6	+	1.91725e6i	−0.410647	+	0.676654i
$382$	5.04820e6	+	5.04820e6i	1.77002	+	1.77002i
$383$	−812455.	−	812455.i	−0.283010	−	0.283010i	0.551298	−	0.834308i	$-0.314133\pi$
$383$	−812455.	−	812455.i	−0.283010	−	0.283010i	−0.834308	+	0.551298i	$0.814133\pi$
$384$	−2.74609e6	+	4.52493e6i	−0.950355	+	1.56597i
$385$	814341.	−	361657.i	0.279998	−	0.124350i
$386$			5.25280e6i			1.79441i
$387$	676608.	−	2.14522e6i	0.229646	−	0.728107i
$388$	4.83697e6	−	4.83697e6i	1.63115	−	1.63115i
$389$	−1.24471e6			−0.417057			−0.208528	−	0.978016i	$-0.566867\pi$
$389$	−1.24471e6			−0.417057			−0.208528	+	0.978016i	$0.566867\pi$
$390$	−8.48284e6	−	1.08761e6i	−2.82410	−	0.362086i
$391$	1.43909e6			0.476042
$392$	2.31024e6	−	2.31024e6i	0.759351	−	0.759351i
$393$	−221541.	+	54199.6i	−0.0723556	+	0.0177017i
$394$		−	9.75263e6i		−	3.16506i
$395$	476680.	−	1.23834e6i	0.153721	−	0.399343i
$396$	−3.03470e6	+	1.57941e6i	−0.972475	+	0.506122i
$397$	151167.	+	151167.i	0.0481370	+	0.0481370i	0.730766	−	0.682629i	$-0.239163\pi$
$397$	151167.	+	151167.i	0.0481370	+	0.0481370i	−0.682629	+	0.730766i	$0.739163\pi$
$398$	−976849.	−	976849.i	−0.309115	−	0.309115i
$399$	83185.9	+	50483.8i	0.0261588	+	0.0158752i
$400$	−1.50492e6	−	1.36014e6i	−0.470289	−	0.425043i
$401$		−	336687.i		−	0.104560i	−0.998632	−	0.0522800i	$-0.983351\pi$
$401$		−	336687.i		−	0.104560i	0.998632	−	0.0522800i	$-0.0166488\pi$
$402$	2.18912e6	+	8.94803e6i	0.675624	+	2.76161i
$403$	−1.82819e6	+	1.82819e6i	−0.560737	+	0.560737i
$404$	7.35364e6			2.24155
$405$	−2.73867e6	+	1.84279e6i	−0.829664	+	0.558263i
$406$	−648354.			−0.195208
$407$	−579246.	+	579246.i	−0.173331	+	0.173331i
$408$	471110.	+	1.92566e6i	0.140111	+	0.572702i
$409$		−	3.05565e6i		−	0.903222i	−0.892215	−	0.451611i	$-0.850849\pi$
$409$		−	3.05565e6i		−	0.903222i	0.892215	−	0.451611i	$-0.149151\pi$
$410$	−600095.	−	1.35123e6i	−0.176303	−	0.396981i
$411$	−4.50143e6	−	2.73182e6i	−1.31445	−	0.797715i
$412$	−7.14813e6	−	7.14813e6i	−2.07467	−	2.07467i
$413$	278471.	+	278471.i	0.0803349	+	0.0803349i
$414$	6.26044e6	−	3.25823e6i	1.79516	−	0.934289i
$415$	2.03787e6	+	4.58866e6i	0.580839	+	1.30787i
$416$		−	2.39837e6i		−	0.679488i
$417$	−4.02561e6	+	984860.i	−1.13368	+	0.277354i
$418$	−146559.	+	146559.i	−0.0410272	+	0.0410272i
$419$	−5.43000e6			−1.51100			−0.755501	−	0.655147i	$-0.772607\pi$
$419$	−5.43000e6			−1.51100			−0.755501	+	0.655147i	$0.772607\pi$
$420$	−2.16602e6	−	2.80313e6i	−0.599154	−	0.775389i
$421$	1.62539e6			0.446942			0.223471	−	0.974711i	$-0.428261\pi$
$421$	1.62539e6			0.446942			0.223471	+	0.974711i	$0.428261\pi$
$422$	−2.69535e6	+	2.69535e6i	−0.736774	+	0.736774i
$423$	46419.8	−	147177.i	0.0126140	−	0.0399933i
$424$			3.41530e6i			0.922601i
$425$	1.48267e6	−	74926.6i	0.398173	−	0.0201216i
$426$	4.29601e6	−	7.07886e6i	1.14694	−	1.88990i
$427$	1.30064e6	+	1.30064e6i	0.345213	+	0.345213i
$428$	−3.87003e6	−	3.87003e6i	−1.02119	−	1.02119i
$429$	1.94507e6	−	3.20503e6i	0.510260	−	0.840793i
$430$	−1.78229e6	+	4.63009e6i	−0.464844	+	1.20759i
$431$			1.28973e6i			0.334431i	0.985920	+	0.167215i	$0.0534775\pi$
$431$			1.28973e6i			0.334431i	−0.985920	+	0.167215i	$0.946522\pi$
$432$	1.62097e6	+	1.84889e6i	0.417894	+	0.476653i
$433$	−2.09694e6	+	2.09694e6i	−0.537484	+	0.537484i	−0.922789	−	0.385305i	$-0.874096\pi$
$433$	−2.09694e6	+	2.09694e6i	−0.537484	+	0.537484i	0.385305	+	0.922789i	$0.374096\pi$
$434$	−1.64284e6			−0.418670
$435$	110466.	−	861580.i	0.0279901	−	0.218310i
$436$	6.52818e6			1.64466
$437$	197091.	−	197091.i	0.0493701	−	0.0493701i
$438$	5.37631e6	−	1.31531e6i	1.33906	−	0.327598i
$439$			5.13713e6i			1.27221i	0.771602	+	0.636106i	$0.219456\pi$
$439$			5.13713e6i			1.27221i	−0.771602	+	0.636106i	$0.780544\pi$
$440$	3.21338e6	−	1.42710e6i	0.791281	−	0.351416i
$441$	1.36916e6	+	2.63074e6i	0.335242	+	0.644142i
$442$	−3.29675e6	−	3.29675e6i	−0.802658	−	0.802658i
$443$	3.71542e6	+	3.71542e6i	0.899495	+	0.899495i	0.995391	−	0.0958967i	$-0.0305718\pi$
$443$	3.71542e6	+	3.71542e6i	0.899495	+	0.899495i	−0.0958967	+	0.995391i	$0.530572\pi$
$444$	2.78419e6	+	1.68967e6i	0.670256	+	0.406765i
$445$	−1.24129e6	−	477818.i	−0.297149	−	0.114383i
$446$			7.04434e6i			1.67689i
$447$	215904.	+	882507.i	0.0511084	+	0.208905i
$448$	2.07405e6	−	2.07405e6i	0.488229	−	0.488229i
$449$	2.30498e6			0.539575			0.269787	−	0.962920i	$-0.413047\pi$
$449$	2.30498e6			0.539575			0.269787	+	0.962920i	$0.413047\pi$
$450$	6.28039e6	−	3.68285e6i	1.46203	−	0.857340i
$451$	648128.			0.150044
$452$	−4.39319e6	+	4.39319e6i	−1.01143	+	1.01143i
$453$	396316.	+	1.61994e6i	0.0907394	+	0.370897i
$454$			6.07989e6i			1.38438i
$455$	3.62293e6	+	1.39460e6i	0.820411	+	0.315806i
$456$	328251.	+	199209.i	0.0739255	+	0.0448638i
$457$	−1.88245e6	−	1.88245e6i	−0.421632	−	0.421632i	0.464133	−	0.885765i	$-0.346366\pi$
$457$	−1.88245e6	−	1.88245e6i	−0.421632	−	0.421632i	−0.885765	+	0.464133i	$0.846366\pi$
$458$	−3.33771e6	−	3.33771e6i	−0.743507	−	0.743507i
$459$	−1.79565e6	−	117947.i	−0.397824	−	0.0261310i
$460$	−9.27384e6	+	4.11860e6i	−2.04345	+	0.907518i
$461$			2.61918e6i			0.574002i	0.957930	+	0.287001i	$0.0926583\pi$
$461$			2.61918e6i			0.574002i	−0.957930	+	0.287001i	$0.907342\pi$
$462$	2.31398e6	−	566113.i	0.504377	−	0.123395i
$463$	1.61089e6	−	1.61089e6i	0.349232	−	0.349232i	−0.510591	−	0.859824i	$-0.670573\pi$
$463$	1.61089e6	−	1.61089e6i	0.349232	−	0.349232i	0.859824	+	0.510591i	$0.170573\pi$
$464$	−647040.			−0.139520
$465$	279906.	−	2.18313e6i	0.0600315	−	0.468217i
$466$	4.55902e6			0.972539
$467$	4.17597e6	−	4.17597e6i	0.886064	−	0.886064i	−0.108078	−	0.994142i	$-0.534470\pi$
$467$	4.17597e6	−	4.17597e6i	0.886064	−	0.886064i	0.994142	+	0.108078i	$0.0344698\pi$
$468$	−1.42148e7	−	4.48339e6i	−3.00004	−	0.946218i
$469$		−	4.18151e6i		−	0.877810i
$470$	−122277.	+	317655.i	−0.0255329	+	0.0663301i
$471$	2.42408e6	−	3.99434e6i	0.503494	−	0.829645i
$472$	1.09884e6	+	1.09884e6i	0.227029	+	0.227029i
$473$	−1.53787e6	−	1.53787e6i	−0.316058	−	0.316058i
$474$	1.84052e6	−	3.03277e6i	0.376266	−	0.620002i
$475$	192798.	−	213322.i	0.0392075	−	0.0433811i
$476$		−	1.93120e6i		−	0.390669i
$477$	−2.95659e6	−	932513.i	−0.594969	−	0.187654i
$478$	2.19395e6	−	2.19395e6i	0.439195	−	0.439195i
$479$	5.52715e6			1.10068			0.550342	−	0.834940i	$-0.314498\pi$
$479$	5.52715e6			1.10068			0.550342	+	0.834940i	$0.314498\pi$
$480$	1.24840e6	+	1.61560e6i	0.247315	+	0.320060i
$481$	−3.56900e6			−0.703370
$482$	−4.26542e6	+	4.26542e6i	−0.836266	+	0.836266i
$483$	−3.11182e6	+	761303.i	−0.606942	+	0.148487i
$484$		−	6.34268e6i		−	1.23072i
$485$	−2.59018e6	−	5.83230e6i	−0.500007	−	1.12586i
$486$	−8.07864e6	+	3.55243e6i	−1.55149	+	0.682236i
$487$	1.77022e6	+	1.77022e6i	0.338224	+	0.338224i	0.855699	−	0.517475i	$-0.173128\pi$
$487$	1.77022e6	+	1.77022e6i	0.338224	+	0.338224i	−0.517475	+	0.855699i	$0.673128\pi$
$488$	5.13231e6	+	5.13231e6i	0.975581	+	0.975581i
$489$	−4.02909e6	−	2.44517e6i	−0.761965	−	0.462421i
$490$	−2.65495e6	−	5.97814e6i	−0.499536	−	1.12480i
$491$			3.33369e6i			0.624052i	0.950073	+	0.312026i	$0.101008\pi$
$491$			3.33369e6i			0.624052i	−0.950073	+	0.312026i	$0.898992\pi$
$492$	−612340.	−	2.50294e6i	−0.114046	−	0.466162i
$493$	334843.	−	334843.i	0.0620474	−	0.0620474i
$494$	−903018.			−0.166487
$495$	358039.	+	3.17144e6i	0.0656776	+	0.581760i
$496$	−1.63951e6			−0.299234
$497$	−2.65780e6	+	2.65780e6i	−0.482649	+	0.482649i
$498$	3.18994e6	+	1.30389e7i	0.576380	+	2.35595i
$499$			750873.i			0.134994i	0.997719	+	0.0674971i	$0.0215013\pi$
$499$			750873.i			0.134994i	−0.997719	+	0.0674971i	$0.978499\pi$
$500$	−9.34024e6	+	4.72617e6i	−1.67083	+	0.845443i
$501$	2.69848e6	+	1.63765e6i	0.480313	+	0.291492i
$502$	5.43499e6	+	5.43499e6i	0.962586	+	0.962586i
$503$	158714.	+	158714.i	0.0279702	+	0.0279702i	0.720954	−	0.692983i	$-0.243704\pi$
$503$	158714.	+	158714.i	0.0279702	+	0.0279702i	−0.692983	+	0.720954i	$0.743704\pi$
$504$	−2.03741e6	−	3.91473e6i	−0.357275	−	0.686477i
$505$	2.46449e6	−	6.40234e6i	0.430030	−	1.11715i
$506$		−	6.82377e6i		−	1.18481i
$507$	1.02440e7	−	2.50618e6i	1.76990	−	0.433004i
$508$	6.09588e6	−	6.09588e6i	1.04804	−	1.04804i
$509$	1.45573e6			0.249050			0.124525	−	0.992216i	$-0.460259\pi$
$509$	1.45573e6			0.249050			0.124525	+	0.992216i	$0.460259\pi$
$510$	3.93681e6	+	504750.i	0.670223	+	0.0859312i
$511$	−2.51240e6			−0.425635
$512$	5.00738e6	−	5.00738e6i	0.844182	−	0.844182i
$513$	−262079.	+	229771.i	−0.0439681	+	0.0385481i
$514$			7.92300e6i			1.32276i
$515$	−8.61904e6	+	3.82780e6i	−1.43199	+	0.635962i
$516$	−4.48599e6	+	7.39190e6i	−0.741709	+	1.22217i
$517$	−105508.	−	105508.i	−0.0173604	−	0.0173604i
$518$	−1.60358e6	−	1.60358e6i	−0.262583	−	0.262583i
$519$	−4.41623e6	+	7.27695e6i	−0.719669	+	1.18585i
$520$	1.42961e7	+	5.50307e6i	2.31851	+	0.892476i
$521$		−	6.02414e6i		−	0.972302i	−0.873875	−	0.486151i	$-0.838401\pi$
$521$		−	6.02414e6i		−	0.972302i	0.873875	−	0.486151i	$-0.161599\pi$
$522$	698545.	−	2.21478e6i	0.112207	−	0.355757i
$523$	5.13865e6	−	5.13865e6i	0.821476	−	0.821476i	−0.164844	−	0.986320i	$-0.552712\pi$
$523$	5.13865e6	−	5.13865e6i	0.821476	−	0.821476i	0.986320	+	0.164844i	$0.0527121\pi$
$524$	876713.			0.139485
$525$	−3.16642e6	+	946376.i	−0.501384	+	0.149853i
$526$	−1.34571e7			−2.12073
$527$	848448.	−	848448.i	0.133076	−	0.133076i
$528$	2.30929e6	−	564966.i	0.360491	−	0.0881936i
$529$			2.74020e6i			0.425739i
$530$	6.38127e6	+	2.45638e6i	0.986774	+	0.379845i
$531$	−1.25129e6	+	651228.i	−0.192584	+	0.100230i
$532$	−264489.	−	264489.i	−0.0405161	−	0.0405161i
$533$	1.99671e6	+	1.99671e6i	0.304436	+	0.304436i
$534$	−3.04000e6	−	1.84491e6i	−0.461340	−	0.279977i
$535$	−4.66638e6	+	2.07239e6i	−0.704849	+	0.313030i
$536$		−	1.65002e7i		−	2.48072i
$537$	1.39831e6	+	5.71558e6i	0.209251	+	0.855312i
$538$	−1.46403e7	+	1.46403e7i	−2.18070	+	2.18070i
$539$	2.86746e6			0.425134
$540$	1.19092e7	−	4.37899e6i	1.75751	−	0.646234i
$541$	−301647.			−0.0443105			−0.0221552	−	0.999755i	$-0.507053\pi$
$541$	−301647.			−0.0443105			−0.0221552	+	0.999755i	$0.507053\pi$
$542$	1.33804e7	−	1.33804e7i	1.95647	−	1.95647i
$543$	−2.81241e6	−	1.14957e7i	−0.409335	−	1.67315i
$544$			1.11306e6i			0.161258i
$545$	2.18785e6	−	5.68367e6i	0.315519	−	0.819667i
$546$	8.87279e6	+	5.38471e6i	1.27373	+	0.773003i
$547$	−1.29950e6	−	1.29950e6i	−0.185698	−	0.185698i	0.608135	−	0.793833i	$-0.291918\pi$
$547$	−1.29950e6	−	1.29950e6i	−0.185698	−	0.185698i	−0.793833	+	0.608135i	$0.791918\pi$
$548$	1.43122e7	+	1.43122e7i	2.03590	+	2.03590i
$549$	−5.84431e6	+	3.04166e6i	−0.827565	+	0.430705i
$550$	−355282.	−	7.03042e6i	−0.0500802	−	0.991001i
$551$		−	91717.3i		−	0.0128698i
$552$	−1.22792e7	+	3.00410e6i	−1.71523	+	0.419630i
$553$	−1.13867e6	+	1.13867e6i	−0.158338	+	0.158338i
$554$	−2.03340e7			−2.81480
$555$	2.40417e6	−	1.85774e6i	0.331309	−	0.256007i
$556$	1.59307e7			2.18549
$557$	−3.41090e6	+	3.41090e6i	−0.465834	+	0.465834i	−0.900562	−	0.434728i	$-0.856845\pi$
$557$	−3.41090e6	+	3.41090e6i	−0.465834	+	0.465834i	0.434728	+	0.900562i	$0.356845\pi$
$558$	1.77002e6	−	5.61195e6i	0.240654	−	0.763007i
$559$		−	9.47554e6i		−	1.28255i
$560$	999180.	+	2.24985e6i	0.134640	+	0.303168i
$561$	−902689.	+	1.48743e6i	−0.121096	+	0.199539i
$562$	−8.22824e6	−	8.22824e6i	−1.09892	−	1.09892i
$563$	−3.96333e6	−	3.96333e6i	−0.526974	−	0.526974i	0.392695	−	0.919669i	$-0.371543\pi$
$563$	−3.96333e6	−	3.96333e6i	−0.526974	−	0.526974i	−0.919669	+	0.392695i	$0.871543\pi$
$564$	−307769.	+	507133.i	−0.0407405	+	0.0671312i
$565$	2.35254e6	+	5.29720e6i	0.310038	+	0.698112i
$566$			6.91265e6i			0.906992i
$567$	3.94524e6	−	694888.i	0.515366	−	0.0907731i
$568$	−1.04877e7	+	1.04877e7i	−1.36398	+	1.36398i
$569$	9.62378e6			1.24614			0.623068	−	0.782168i	$-0.285886\pi$
$569$	9.62378e6			1.24614			0.623068	+	0.782168i	$0.285886\pi$
$570$	608297.	−	470040.i	0.0784203	−	0.0605966i
$571$	3.59785e6			0.461799			0.230899	−	0.972978i	$-0.425833\pi$
$571$	3.59785e6			0.461799			0.230899	+	0.972978i	$0.425833\pi$
$572$	−1.01904e7	+	1.01904e7i	−1.30227	+	1.30227i
$573$	1.12752e7	−	2.75846e6i	1.43462	−	0.350978i
$574$			1.79427e6i			0.227305i
$575$	477780.	+	9.45444e6i	0.0602640	+	1.19252i
$576$	4.85035e6	+	9.31957e6i	0.609139	+	1.17041i
$577$	1.31621e6	+	1.31621e6i	0.164583	+	0.164583i	0.784594	−	0.620010i	$-0.212872\pi$
$577$	1.31621e6	+	1.31621e6i	0.164583	+	0.164583i	−0.620010	+	0.784594i	$0.712872\pi$
$578$	−8.09585e6	−	8.09585e6i	−1.00796	−	1.00796i
$579$	7.30120e6	+	4.43094e6i	0.905102	+	0.549288i
$580$	−1.19950e6	+	3.11611e6i	−0.148058	+	0.384630i
$581$		−	6.09319e6i		−	0.748867i
$582$	−4.05449e6	−	1.65727e7i	−0.496169	−	2.02809i
$583$	−2.11952e6	+	2.11952e6i	−0.258266	+	0.258266i
$584$	−9.91393e6			−1.20286
$585$	−8.66734e6	+	1.08734e7i	−1.04712	+	1.31364i
$586$	−2.86057e6			−0.344119
$587$	−8.58242e6	+	8.58242e6i	−1.02805	+	1.02805i	−0.0284553	+	0.999595i	$0.509059\pi$
$587$	−8.58242e6	+	8.58242e6i	−1.02805	+	1.02805i	−0.999595	+	0.0284553i	$0.990941\pi$
$588$	−2.70913e6	−	1.10735e7i	−0.323136	−	1.32082i
$589$		−	232400.i		−	0.0276024i
$590$	2.84344e6	−	1.26280e6i	0.336290	−	0.149350i
$591$	−1.35558e7	−	8.22673e6i	−1.59645	−	0.968854i
$592$	−1.60033e6	−	1.60033e6i	−0.187675	−	0.187675i
$593$	250104.	+	250104.i	0.0292068	+	0.0292068i	0.721559	−	0.692353i	$-0.243426\pi$
$593$	250104.	+	250104.i	0.0292068	+	0.0292068i	−0.692353	+	0.721559i	$0.743426\pi$
$594$	−559274.	+	8.51450e6i	−0.0650367	+	0.990132i
$595$	−1.68137e6	−	647220.i	−0.194702	−	0.0749479i
$596$		−	3.49238e6i		−	0.402723i
$597$	−2.18179e6	+	533773.i	−0.250541	+	0.0612944i
$598$	2.10222e7	−	2.10222e7i	2.40395	−	2.40395i
$599$	1.33172e7			1.51651			0.758253	−	0.651960i	$-0.226053\pi$
$599$	1.33172e7			1.51651			0.758253	+	0.651960i	$0.226053\pi$
$600$	−1.24947e7	+	3.73439e6i	−1.41692	+	0.423489i
$601$	−7.15703e6			−0.808251			−0.404126	−	0.914703i	$-0.632424\pi$
$601$	−7.15703e6			−0.808251			−0.404126	+	0.914703i	$0.632424\pi$
$602$	4.25744e6	−	4.25744e6i	0.478803	−	0.478803i
$603$	1.42840e7	+	4.50521e6i	1.59977	+	0.504571i
$604$		−	6.41066e6i		−	0.715007i
$605$	−5.52216e6	−	2.12568e6i	−0.613368	−	0.236107i
$606$	9.51572e6	−	1.56798e7i	1.05259	−	1.73443i
$607$	−6.97472e6	−	6.97472e6i	−0.768343	−	0.768343i	0.209472	−	0.977815i	$-0.432826\pi$
$607$	−6.97472e6	−	6.97472e6i	−0.768343	−	0.768343i	−0.977815	+	0.209472i	$0.932826\pi$
$608$	152440.	+	152440.i	0.0167240	+	0.0167240i
$609$	−546912.	+	901187.i	−0.0597550	+	0.0984627i
$610$	1.32807e7	−	5.89810e6i	1.44510	−	0.641782i
$611$		−	650085.i		−	0.0704477i
$612$	6.59698e6	+	2.08070e6i	0.711978	+	0.224559i
$613$	2.79030e6	−	2.79030e6i	0.299916	−	0.299916i	−0.541065	−	0.840981i	$-0.681979\pi$
$613$	2.79030e6	−	2.79030e6i	0.299916	−	0.299916i	0.840981	+	0.541065i	$0.181979\pi$
$614$	1.04712e7			1.12092
$615$	−2.38436e6	−	305706.i	−0.254205	−	0.0325924i
$616$	−4.26699e6			−0.453075
$617$	5.00630e6	−	5.00630e6i	0.529425	−	0.529425i	−0.390976	−	0.920401i	$-0.627863\pi$
$617$	5.00630e6	−	5.00630e6i	0.529425	−	0.529425i	0.920401	+	0.390976i	$0.127863\pi$
$618$	−2.44913e7	+	5.99178e6i	−2.57954	+	0.631080i
$619$			2.77818e6i			0.291430i	0.989327	+	0.145715i	$0.0465483\pi$
$619$			2.77818e6i			0.291430i	−0.989327	+	0.145715i	$0.953452\pi$
$620$	−3.03939e6	+	7.89582e6i	−0.317546	+	0.824932i
$621$	752107.	−	1.14502e7i	0.0782619	−	1.19148i
$622$	1.82628e7	+	1.82628e7i	1.89274	+	1.89274i
$623$	1.14139e6	+	1.14139e6i	0.117818	+	0.117818i
$624$	8.85482e6	+	5.37380e6i	0.910370	+	0.552485i
$625$	984496.	+	9.71587e6i	0.100812	+	0.994905i
$626$			2.64949e7i			2.70225i
$627$	80083.3	+	327340.i	0.00813529	+	0.0332530i
$628$	−1.26999e7	+	1.26999e7i	−1.28500	+	1.28500i
$629$	1.65634e6			0.166926
$630$	−8.77981e6	+	991193.i	−0.881320	+	0.0994962i
$631$	5.03294e6			0.503209			0.251604	−	0.967830i	$-0.419042\pi$
$631$	5.03294e6			0.503209			0.251604	+	0.967830i	$0.419042\pi$
$632$	−4.49318e6	+	4.49318e6i	−0.447467	+	0.447467i
$633$	1.47280e6	+	6.02007e6i	0.146095	+	0.597162i
$634$		−	2.68729e6i		−	0.265516i
$635$	−3.26433e6	−	7.35026e6i	−0.321262	−	0.723383i
$636$	1.01876e7	+	6.18267e6i	0.998691	+	0.606085i
$637$	8.83387e6	+	8.83387e6i	0.862586	+	0.862586i
$638$	−1.58774e6	−	1.58774e6i	−0.154428	−	0.154428i
$639$	−6.21550e6	−	1.19426e7i	−0.602176	−	1.15704i
$640$	−7.70417e6	−	1.73474e7i	−0.743492	−	1.67412i
$641$			1.33865e7i			1.28684i	0.765515	+	0.643418i	$0.222484\pi$
$641$			1.33865e7i			1.28684i	−0.765515	+	0.643418i	$0.777516\pi$
$642$	−1.32597e7	+	3.24397e6i	−1.26969	+	0.310627i
$643$	−4.89566e6	+	4.89566e6i	−0.466964	+	0.466964i	−0.900930	−	0.433965i	$-0.857114\pi$
$643$	−4.89566e6	+	4.89566e6i	−0.466964	+	0.466964i	0.433965	+	0.900930i	$0.357114\pi$
$644$	1.23146e7			1.17005
$645$	4.93222e6	+	6.38298e6i	0.466813	+	0.604121i
$646$	419083.			0.0395111
$647$	−6.88725e6	+	6.88725e6i	−0.646823	+	0.646823i	−0.952224	−	0.305401i	$-0.901210\pi$
$647$	−6.88725e6	+	6.88725e6i	−0.646823	+	0.646823i	0.305401	+	0.952224i	$0.401210\pi$
$648$	1.55679e7	−	2.74202e6i	1.45644	−	0.256527i
$649$			1.36388e6i			0.127105i
$650$	2.05643e7	−	2.27533e7i	1.90911	−	2.11233i
$651$	−1.38580e6	+	2.28349e6i	−0.128159	+	0.211177i
$652$	1.28105e7	+	1.28105e7i	1.18017	+	1.18017i
$653$	−7.00901e6	−	7.00901e6i	−0.643241	−	0.643241i	0.308110	−	0.951351i	$-0.400304\pi$
$653$	−7.00901e6	−	7.00901e6i	−0.643241	−	0.643241i	−0.951351	+	0.308110i	$0.900304\pi$
$654$	8.44756e6	−	1.39197e7i	0.772301	−	1.27258i
$655$	293821.	−	763297.i	0.0267596	−	0.0695169i
$656$			1.79064e6i			0.162461i
$657$	2.70690e6	−	8.58238e6i	0.244658	−	0.775701i
$658$	292089.	−	292089.i	0.0262996	−	0.0262996i
$659$	−1.90743e7			−1.71094			−0.855469	−	0.517854i	$-0.826731\pi$
$659$	−1.90743e7			−1.71094			−0.855469	+	0.517854i	$0.826731\pi$
$660$	1.56020e6	−	1.21688e7i	0.139418	−	1.08740i
$661$	−68430.6			−0.00609182			−0.00304591	−	0.999995i	$-0.500970\pi$
$661$	−68430.6			−0.00609182			−0.00304591	+	0.999995i	$0.500970\pi$
$662$	5.11765e6	−	5.11765e6i	0.453864	−	0.453864i
$663$	−7.36330e6	+	1.80142e6i	−0.650562	+	0.159159i
$664$		−	2.40437e7i		−	2.11632i
$665$	−318914.	+	141633.i	−0.0279653	+	0.0124197i
$666$	7.20556e6	−	3.75012e6i	0.629480	−	0.327611i
$667$	2.13517e6	+	2.13517e6i	0.185831	+	0.185831i
$668$	−8.57977e6	−	8.57977e6i	−0.743934	−	0.743934i
$669$	9.79137e6	+	5.94218e6i	0.845821	+	0.513311i
$670$	−3.08296e7	−	1.18674e7i	−2.65327	−	1.02134i
$671$			6.37019e6i			0.546193i
$672$	−588829.	−	2.40683e6i	−0.0502997	−	0.205600i
$673$	−1.18130e7	+	1.18130e7i	−1.00536	+	1.00536i	−0.00537862	+	0.999986i	$0.501712\pi$
$673$	−1.18130e7	+	1.18130e7i	−1.00536	+	1.00536i	−0.999986	+	0.00537862i	$0.998288\pi$
$674$	−1.89279e7			−1.60492
$675$	178724.	−	1.18361e7i	0.0150981	−	0.999886i
$676$	−4.05390e7			−3.41198
$677$	3.43887e6	−	3.43887e6i	0.288366	−	0.288366i	−0.548068	−	0.836434i	$-0.684637\pi$
$677$	3.43887e6	−	3.43887e6i	0.288366	−	0.288366i	0.836434	+	0.548068i	$0.184637\pi$
$678$	3.68250e6	+	1.50522e7i	0.307658	+	1.25755i
$679$			7.74460e6i			0.644651i
$680$	−6.63468e6	−	2.55393e6i	−0.550234	−	0.211805i
$681$	8.45082e6	+	5.12863e6i	0.698282	+	0.423773i
$682$	−4.02311e6	−	4.02311e6i	−0.331208	−	0.331208i
$683$	1.02568e6	+	1.02568e6i	0.0841315	+	0.0841315i	0.747920	−	0.663789i	$-0.231053\pi$
$683$	1.02568e6	+	1.02568e6i	0.0841315	+	0.0841315i	−0.663789	+	0.747920i	$0.731053\pi$
$684$	1.18846e6	−	618530.i	0.0971278	−	0.0505499i
$685$	1.72573e7	−	7.66415e6i	1.40523	−	0.624076i
$686$			1.88701e7i			1.53096i
$687$	−7.45479e6	+	1.82380e6i	−0.602620	+	0.147430i
$688$	4.24881e6	−	4.24881e6i	0.342213	−	0.342213i
$689$	−1.30594e7			−1.04803
$690$	−3.21861e6	+	2.51036e7i	−0.257363	+	2.00731i
$691$	599071.			0.0477291			0.0238645	−	0.999715i	$-0.492403\pi$
$691$	599071.			0.0477291			0.0238645	+	0.999715i	$0.492403\pi$
$692$	2.31370e7	−	2.31370e7i	1.83671	−	1.83671i
$693$	1.16506e6	−	3.69389e6i	0.0921541	−	0.292180i
$694$			1.96263e7i			1.54682i
$695$	5.33901e6	−	1.38699e7i	0.419274	−	1.08921i
$696$	−2.15811e6	+	3.55608e6i	−0.168869	+	0.278258i
$697$	−926655.	−	926655.i	−0.0722497	−	0.0722497i
$698$	8.01330e6	+	8.01330e6i	0.622548	+	0.622548i
$699$	3.84572e6	−	6.33687e6i	0.297704	−	0.490549i
$700$	1.26875e7	−	641161.i	0.978656	−	0.0494563i
$701$		−	2.25223e7i		−	1.73108i	−0.500839	−	0.865541i	$-0.666975\pi$
$701$		−	2.25223e7i		−	1.73108i	0.500839	−	0.865541i	$-0.333025\pi$
$702$	−2.79539e7	+	2.45079e7i	−2.14091	+	1.87700i
$703$	226845.	−	226845.i	0.0173118	−	0.0173118i
$704$	1.01582e7			0.772473
$705$	338383.	+	437915.i	0.0256411	+	0.0331831i
$706$	2.68311e7			2.02594
$707$	−5.88705e6	+	5.88705e6i	−0.442945	+	0.442945i
$708$	5.26701e6	−	1.28857e6i	0.394895	−	0.0966105i
$709$		−	2.46524e7i		−	1.84181i	−0.389792	−	0.920903i	$-0.627453\pi$
$709$		−	2.46524e7i		−	1.84181i	0.389792	−	0.920903i	$-0.372547\pi$
$710$	1.20525e7	+	2.71386e7i	0.897288	+	2.02042i
$711$	−2.66288e6	−	5.11651e6i	−0.197550	−	0.379577i
$712$	4.50390e6	+	4.50390e6i	0.332958	+	0.332958i
$713$	5.41024e6	+	5.41024e6i	0.398559	+	0.398559i
$714$	−4.11779e6	−	2.49900e6i	−0.302286	−	0.183451i
$715$	5.45690e6	+	1.22873e7i	0.399191	+	0.898857i
$716$		−	2.26185e7i		−	1.64885i
$717$	−1.19883e6	−	4.90019e6i	−0.0870879	−	0.355971i
$718$	1.44310e7	−	1.44310e7i	1.04468	−	1.04468i
$719$	3.34973e6			0.241651			0.120825	−	0.992674i	$-0.461446\pi$
$719$	3.34973e6			0.241651			0.120825	+	0.992674i	$0.461446\pi$
$720$	−8.76202e6	+	989184.i	−0.629902	+	0.0711125i
$721$	1.14451e7			0.819936
$722$	−1.67292e7	+	1.67292e7i	−1.19435	+	1.19435i
$723$	2.33073e6	+	9.52683e6i	0.165823	+	0.677802i
$724$			4.54925e7i			3.22547i
$725$	2.31100e6	+	2.08866e6i	0.163288	+	0.147579i
$726$	−1.35241e7	−	8.20752e6i	−0.952288	−	0.577923i
$727$	−1.38078e7	−	1.38078e7i	−0.968921	−	0.968921i	0.0306102	−	0.999531i	$-0.490255\pi$
$727$	−1.38078e7	−	1.38078e7i	−0.968921	−	0.968921i	−0.999531	+	0.0306102i	$0.990255\pi$
$728$	−1.31454e7	−	1.31454e7i	−0.919278	−	0.919278i
$729$	−1.87691e6	+	1.42256e7i	−0.130805	+	0.991408i
$730$	−7.13039e6	+	1.85236e7i	−0.495229	+	1.28652i
$731$			4.39752e6i			0.304379i
$732$	2.46003e7	−	6.01844e6i	1.69693	−	0.415151i
$733$	5.56274e6	−	5.56274e6i	0.382410	−	0.382410i	−0.489560	−	0.871970i	$-0.662843\pi$
$733$	5.56274e6	−	5.56274e6i	0.382410	−	0.382410i	0.871970	+	0.489560i	$0.162843\pi$
$734$	3.40191e7			2.33068
$735$	−1.05489e7	−	1.35251e6i	−0.720263	−	0.0923470i
$736$	−7.09758e6			−0.482965
$737$	1.02400e7	−	1.02400e7i	0.694433	−	0.694433i
$738$	−6.12925e6	−	1.93318e6i	−0.414253	−	0.130656i
$739$		−	2.07306e7i		−	1.39637i	−0.715918	−	0.698185i	$-0.753991\pi$
$739$		−	2.07306e7i		−	1.39637i	0.715918	−	0.698185i	$-0.246009\pi$
$740$	−1.06739e7	+	4.74037e6i	−0.716543	+	0.318224i
$741$	−761731.	+	1.25516e6i	−0.0509632	+	0.0839758i
$742$	−5.86768e6	−	5.86768e6i	−0.391252	−	0.391252i
$743$	474382.	+	474382.i	0.0315251	+	0.0315251i	0.722694	−	0.691169i	$-0.242904\pi$
$743$	474382.	+	474382.i	0.0315251	+	0.0315251i	−0.691169	+	0.722694i	$0.742904\pi$
$744$	−5.46837e6	+	9.01064e6i	−0.362181	+	0.596792i
$745$	−3.04060e6	−	1.17043e6i	−0.200709	−	0.0772603i
$746$		−	3.38728e7i		−	2.22846i
$747$	2.08144e7	+	6.56489e6i	1.36478	+	0.430453i
$748$	4.72926e6	−	4.72926e6i	0.309057	−	0.309057i
$749$	6.19640e6			0.403585
$750$	−2.00905e6	+	2.60314e7i	−0.130418	+	1.68984i
$751$	1.47738e7			0.955856			0.477928	−	0.878399i	$-0.341388\pi$
$751$	1.47738e7			0.955856			0.477928	+	0.878399i	$0.341388\pi$
$752$	291497.	−	291497.i	0.0187970	−	0.0187970i
$753$	1.21391e7	−	2.96981e6i	0.780185	−	0.190871i
$754$		−	9.78277e6i		−	0.626662i
$755$	−5.58135e6	−	2.14846e6i	−0.356346	−	0.137170i
$756$	−1.53657e7	−	1.00930e6i	−0.977798	−	0.0642265i
$757$	−519919.	−	519919.i	−0.0329759	−	0.0329759i	0.690427	−	0.723402i	$-0.257423\pi$
$757$	−519919.	−	519919.i	−0.0329759	−	0.0329759i	−0.723402	+	0.690427i	$0.757423\pi$
$758$	−1.63878e7	−	1.63878e7i	−1.03597	−	1.03597i
$759$	−9.48479e6	−	5.75612e6i	−0.597617	−	0.362681i
$760$	−1.25843e6	+	558882.i	−0.0790307	+	0.0350983i
$761$			1.95212e7i			1.22192i	0.791660	+	0.610961i	$0.209217\pi$
$761$			1.95212e7i			1.22192i	−0.791660	+	0.610961i	$0.790783\pi$
$762$	−5.10975e6	−	2.08861e7i	−0.318795	−	1.30307i
$763$	−5.22622e6	+	5.22622e6i	−0.324995	+	0.324995i
$764$	−4.46197e7			−2.76563
$765$	4.02244e6	−	5.04624e6i	0.248505	−	0.311756i
$766$	1.10160e7			0.678346
$767$	−4.20174e6	+	4.20174e6i	−0.257894	+	0.257894i
$768$	−6.93436e6	−	2.83441e7i	−0.424232	−	1.73404i
$769$			8.84626e6i			0.539441i	0.962939	+	0.269720i	$0.0869312\pi$
$769$			8.84626e6i			0.539441i	−0.962939	+	0.269720i	$0.913069\pi$
$770$	−3.06894e6	+	7.97261e6i	−0.186536	+	0.484589i
$771$	1.10127e7	+	6.68336e6i	0.667201	+	0.404910i
$772$	−2.32141e7	−	2.32141e7i	−1.40187	−	1.40187i
$773$	4.97544e6	+	4.97544e6i	0.299490	+	0.299490i	0.840814	−	0.541324i	$-0.182077\pi$
$773$	4.97544e6	+	4.97544e6i	0.299490	+	0.299490i	−0.541324	+	0.840814i	$0.682077\pi$
$774$	9.95640e6	+	1.91304e7i	0.597379	+	1.14782i
$775$	5.85577e6	+	5.29240e6i	0.350211	+	0.316518i
$776$			3.05602e7i			1.82180i
$777$	−3.58160e6	+	876234.i	−0.212826	+	0.0520676i
$778$	8.43846e6	−	8.43846e6i	0.499821	−	0.499821i
$779$	−253821.			−0.0149860
$780$	4.22953e7	−	3.26822e7i	2.48918	−	1.92342i
$781$	−1.30172e7			−0.763643
$782$	−9.75622e6	+	9.75622e6i	−0.570512	+	0.570512i
$783$	−2.48921e6	−	2.83920e6i	−0.145096	−	0.165498i
$784$			7.92218e6i			0.460314i
$785$	6.80078e6	+	1.53133e7i	0.393899	+	0.886939i
$786$	1.13448e6	−	1.86937e6i	0.0654998	−	0.107929i
$787$	−1.51555e7	−	1.51555e7i	−0.872237	−	0.872237i	0.120479	−	0.992716i	$-0.461557\pi$
$787$	−1.51555e7	−	1.51555e7i	−0.872237	−	0.872237i	−0.992716	+	0.120479i	$0.961557\pi$
$788$	4.31005e7	+	4.31005e7i	2.47267	+	2.47267i
$789$	−1.13516e7	+	1.87048e7i	−0.649178	+	1.06970i
$790$	5.16361e6	+	1.16269e7i	0.294364	+	0.662819i
$791$		−	7.03405e6i		−	0.399728i
$792$	4.59732e6	−	1.45760e7i	0.260430	−	0.825709i
$793$	−1.96248e7	+	1.96248e7i	−1.10821	+	1.10821i
$794$	−2.04965e6			−0.115379
$795$	8.79713e6	−	6.79768e6i	0.493655	−	0.381454i
$796$	8.63411e6			0.482987
$797$	−1.20255e6	+	1.20255e6i	−0.0670591	+	0.0670591i	−0.739841	−	0.672782i	$-0.765099\pi$
$797$	−1.20255e6	+	1.20255e6i	−0.0670591	+	0.0670591i	0.672782	+	0.739841i	$0.265099\pi$
$798$	−906207.	+	221702.i	−0.0503756	+	0.0123243i
$799$			301699.i			0.0167189i
$800$	−7.31252e6	+	369538.i	−0.403963	+	0.0204143i
$801$	−5.12872e6	+	2.66923e6i	−0.282441	+	0.146996i
$802$	2.28255e6	+	2.28255e6i	0.125310	+	0.125310i
$803$	−6.15256e6	−	6.15256e6i	−0.336718	−	0.336718i
$804$	−4.92192e7	−	2.98701e7i	−2.68531	−	1.62966i
$805$	4.12709e6	−	1.07215e7i	0.224468	−	0.583130i
$806$		−	2.47882e7i		−	1.34403i
$807$	7.99982e6	+	3.26992e7i	0.432410	+	1.76747i
$808$	−2.32303e7	+	2.32303e7i	−1.25177	+	1.25177i
$809$	−2.61496e7			−1.40473			−0.702367	−	0.711815i	$-0.747873\pi$
$809$	−2.61496e7			−1.40473			−0.702367	+	0.711815i	$0.747873\pi$
$810$	6.07357e6	−	3.10598e7i	0.325261	−	1.66336i
$811$	−1.69246e7			−0.903580			−0.451790	−	0.892124i	$-0.649214\pi$
$811$	−1.69246e7			−0.903580			−0.451790	+	0.892124i	$0.649214\pi$
$812$	2.86531e6	−	2.86531e6i	0.152504	−	0.152504i
$813$	−7.31138e6	−	2.98852e7i	−0.387948	−	1.58573i
$814$		−	7.85393e6i		−	0.415457i
$815$	1.54465e7	−	6.85996e6i	0.814586	−	0.361766i
$816$	−4.10944e6	−	2.49394e6i	−0.216052	−	0.131117i
$817$	602265.	+	602265.i	0.0315669	+	0.0315669i
$818$	2.07156e7	+	2.07156e7i	1.08246	+	1.08246i
$819$	1.49691e7	−	7.79063e6i	0.779805	−	0.405848i
$820$	8.62363e6	+	3.31955e6i	0.447874	+	0.172403i
$821$		−	2.09092e7i		−	1.08263i	−0.840821	−	0.541314i	$-0.817927\pi$
$821$		−	2.09092e7i		−	1.08263i	0.840821	−	0.541314i	$-0.182073\pi$
$822$	4.90374e7	−	1.19969e7i	2.53132	−	0.619285i
$823$	−2.54512e6	+	2.54512e6i	−0.130981	+	0.130981i	−0.769558	−	0.638577i	$-0.779523\pi$
$823$	−2.54512e6	+	2.54512e6i	−0.130981	+	0.130981i	0.638577	+	0.769558i	$0.279523\pi$
$824$	4.51621e7			2.31716
$825$	−1.00717e7	−	5.43660e6i	−0.515191	−	0.278095i
$826$	−3.77575e6			−0.192554
$827$	1.42123e7	−	1.42123e7i	0.722607	−	0.722607i	−0.246529	−	0.969135i	$-0.579290\pi$
$827$	1.42123e7	−	1.42123e7i	0.722607	−	0.722607i	0.969135	+	0.246529i	$0.0792900\pi$
$828$	−1.32679e7	+	4.20665e7i	−0.672551	+	2.13236i
$829$			2.23790e7i			1.13098i	0.824756	+	0.565489i	$0.191313\pi$
$829$			2.23790e7i			1.13098i	−0.824756	+	0.565489i	$0.808687\pi$
$830$	−4.49242e7	−	1.72929e7i	−2.26352	−	0.871311i
$831$	−1.71525e7	+	2.82635e7i	−0.861639	+	1.41979i
$832$	3.12945e7	+	3.12945e7i	1.56733	+	1.56733i
$833$	−4.09972e6	−	4.09972e6i	−0.204711	−	0.204711i
$834$	2.06146e7	−	3.39682e7i	1.02626	−	1.69105i
$835$	−1.03453e7	+	4.59444e6i	−0.513483	+	0.228043i
$836$		−	1.29540e6i		−	0.0641043i
$837$	−6.30732e6	−	7.19417e6i	−0.311194	−	0.354950i
$838$	3.68124e7	−	3.68124e7i	1.81086	−	1.81086i
$839$	2.35677e7			1.15588			0.577940	−	0.816079i	$-0.303857\pi$
$839$	2.35677e7			1.15588			0.577940	+	0.816079i	$0.303857\pi$
$840$	1.56976e7	+	2.01264e6i	0.767601	+	0.0984163i
$841$	−1.95175e7			−0.951558
$842$	−1.10192e7	+	1.10192e7i	−0.535637	+	0.535637i
$843$	−1.83778e7	+	4.49610e6i	−0.890685	+	0.217905i
$844$		−	2.38235e7i		−	1.15120i
$845$	−1.35862e7	+	3.52947e7i	−0.654570	+	1.70046i
$846$	683075.	+	1.31248e6i	0.0328127	+	0.0630471i
$847$	5.07771e6	+	5.07771e6i	0.243198	+	0.243198i
$848$	−5.85579e6	−	5.85579e6i	−0.279638	−	0.279638i
$849$	9.60832e6	+	5.83109e6i	0.457487	+	0.277639i
$850$	−9.54371e6	+	1.05596e7i	−0.453075	+	0.501304i
$851$			1.05619e7i			0.499940i
$852$	1.22984e7	+	5.02698e7i	0.580431	+	2.37251i
$853$	1.06645e7	−	1.06645e7i	0.501844	−	0.501844i	−0.410167	−	0.912010i	$-0.634530\pi$
$853$	1.06645e7	−	1.06645e7i	0.501844	−	0.501844i	0.912010	+	0.410167i	$0.134530\pi$
$854$	−1.76352e7			−0.827439
$855$	−140216.	−	1.24201e6i	−0.00655967	−	0.0581044i
$856$	2.44510e7			1.14054
$857$	−2.47847e6	+	2.47847e6i	−0.115274	+	0.115274i	−0.762391	−	0.647117i	$-0.775975\pi$
$857$	−2.47847e6	+	2.47847e6i	−0.115274	+	0.115274i	0.647117	+	0.762391i	$0.275975\pi$
$858$	8.54186e6	+	3.49148e7i	0.396127	+	1.61917i
$859$			5.76055e6i			0.266368i	0.991091	+	0.133184i	$0.0425200\pi$
$859$			5.76055e6i			0.266368i	−0.991091	+	0.133184i	$0.957480\pi$
$860$	−1.25855e7	−	2.83387e7i	−0.580262	−	1.30657i
$861$	2.49397e6	+	1.51354e6i	0.114653	+	0.0695803i
$862$	−8.74367e6	−	8.74367e6i	−0.400798	−	0.400798i
$863$	2.09029e7	+	2.09029e7i	0.955386	+	0.955386i	0.999046	−	0.0436609i	$-0.0139021\pi$
$863$	2.09029e7	+	2.09029e7i	0.955386	+	0.955386i	−0.0436609	+	0.999046i	$0.513902\pi$
$864$	8.85616e6	+	581716.i	0.403609	+	0.0265110i
$865$	−1.23898e7	−	2.78980e7i	−0.563019	−	1.26775i
$866$		−	2.84321e7i		−	1.28829i
$867$	−1.80821e7	+	4.42376e6i	−0.816960	+	0.199868i
$868$	7.26033e6	−	7.26033e6i	0.327082	−	0.327082i
$869$	−5.57691e6			−0.250521
$870$	5.09214e6	+	6.58993e6i	0.228088	+	0.295177i
$871$	6.30932e7			2.81797
$872$	−2.06226e7	+	2.06226e7i	−0.918444	+	0.918444i
$873$	−2.64556e7	−	8.34414e6i	−1.17485	−	0.370549i
$874$			2.67234e6i			0.118335i
$875$	3.69385e6	−	1.12610e7i	0.163102	−	0.497232i
$876$	−1.79471e7	+	2.95727e7i	−0.790193	+	1.30206i
$877$	9.76036e6	+	9.76036e6i	0.428516	+	0.428516i	0.888122	−	0.459607i	$-0.152010\pi$
$877$	9.76036e6	+	9.76036e6i	0.428516	+	0.428516i	−0.459607	+	0.888122i	$0.652010\pi$
$878$	−3.48269e7	−	3.48269e7i	−1.52468	−	1.52468i
$879$	−2.41300e6	+	3.97609e6i	−0.105338	+	0.173574i
$880$	−3.06273e6	+	7.95645e6i	−0.133322	+	0.346348i
$881$			1.89297e7i			0.821681i	0.911707	+	0.410840i	$0.134765\pi$
$881$			1.89297e7i			0.821681i	−0.911707	+	0.410840i	$0.865235\pi$
$882$	−2.71171e7	−	8.55279e6i	−1.17374	−	0.370200i
$883$	1.37478e7	−	1.37478e7i	0.593377	−	0.593377i	−0.345165	−	0.938542i	$-0.612177\pi$
$883$	1.37478e7	−	1.37478e7i	0.593377	−	0.593377i	0.938542	+	0.345165i	$0.112177\pi$
$884$	2.91391e7			1.25414
$885$	643309.	−	5.01750e6i	0.0276097	−	0.215342i
$886$	−5.03770e7			−2.15599
$887$	2.78970e7	−	2.78970e7i	1.19055	−	1.19055i	0.213637	−	0.976913i	$-0.431469\pi$
$887$	2.78970e7	−	2.78970e7i	1.19055	−	1.19055i	0.976913	−	0.213637i	$-0.0685311\pi$
$888$	−1.41330e7	+	3.45761e6i	−0.601452	+	0.147144i
$889$			9.76027e6i			0.414198i
$890$	1.16546e7	−	5.17593e6i	0.493199	−	0.219035i
$891$	1.13631e7	+	7.95969e6i	0.479514	+	0.335894i
$892$	−3.11315e7	−	3.11315e7i	−1.31005	−	1.31005i
$893$	41319.4	+	41319.4i	0.00173390	+	0.00173390i
$894$	−7.44662e6	−	4.51920e6i	−0.311613	−	0.189111i
$895$	−1.96925e7	−	7.58035e6i	−0.821757	−	0.316324i
$896$			2.30353e7i			0.958572i
$897$	−1.14870e7	−	4.69531e7i	−0.476679	−	1.94842i
$898$	−1.56265e7	+	1.56265e7i	−0.646652	+	0.646652i
$899$	2.51768e6			0.103897
$900$	−1.14795e7	+	4.40312e7i	−0.472406	+	1.81199i
$901$	6.06074e6			0.248722
$902$	−4.39395e6	+	4.39395e6i	−0.179820	+	0.179820i
$903$	−2.32636e6	−	9.50899e6i	−0.0949420	−	0.388075i
$904$		−	2.77563e7i		−	1.12964i
$905$	3.96074e7	+	1.52463e7i	1.60751	+	0.618790i
$906$	−1.36691e7	−	8.29548e6i	−0.553247	−	0.335754i
$907$	1.35201e7	+	1.35201e7i	0.545709	+	0.545709i	0.925197	−	0.379488i	$-0.123900\pi$
$907$	1.35201e7	+	1.35201e7i	0.545709	+	0.545709i	−0.379488	+	0.925197i	$0.623900\pi$
$908$	−2.68693e7	−	2.68693e7i	−1.08154	−	1.08154i
$909$	−1.37674e7	−	2.64530e7i	−0.552640	−	1.06185i
$910$	−3.40160e7	+	1.51069e7i	−1.36170	+	0.604743i
$911$		−	1.16244e7i		−	0.464059i	−0.972709	−	0.232029i	$-0.925463\pi$
$911$		−	1.16244e7i		−	0.464059i	0.972709	−	0.232029i	$-0.0745365\pi$
$912$	−904371.	+	221253.i	−0.0360047	+	0.00880850i
$913$	1.49214e7	−	1.49214e7i	0.592426	−	0.592426i
$914$	2.55240e7			1.01061
$915$	3.00467e6	−	2.34350e7i	0.118643	−	0.925362i
$916$	2.95012e7			1.16172
$917$	−701864.	+	701864.i	−0.0275632	+	0.0275632i
$918$	1.29731e7	−	1.13739e7i	0.508088	−	0.445454i
$919$			3.03569e7i			1.18569i	0.805318	+	0.592843i	$0.201994\pi$
$919$			3.03569e7i			1.18569i	−0.805318	+	0.592843i	$0.798006\pi$
$920$	1.62855e7	−	4.23069e7i	0.634352	−	1.64794i
$921$	8.83283e6	−	1.45545e7i	0.343124	−	0.565391i
$922$	−1.77566e7	−	1.77566e7i	−0.687911	−	0.687911i
$923$	−4.01025e7	−	4.01025e7i	−1.54941	−	1.54941i
$924$	−7.72448e6	+	1.27282e7i	−0.297639	+	0.490441i
$925$	549908.	+	1.08817e7i	0.0211318	+	0.418161i
$926$			2.18419e7i			0.837073i
$927$	−1.23311e7	+	3.90964e7i	−0.471304	+	1.49430i
$928$	−1.65145e6	+	1.65145e6i	−0.0629498	+	0.0629498i
$929$	−1.67254e6			−0.0635824			−0.0317912	−	0.999495i	$-0.510121\pi$
$929$	−1.67254e6			−0.0635824			−0.0317912	+	0.999495i	$0.510121\pi$
$930$	1.29028e7	+	1.66980e7i	0.489189	+	0.633078i
$931$	−1.12296e6			−0.0424610
$932$	−2.01480e7	+	2.01480e7i	−0.759788	+	0.759788i
$933$	4.07899e7	−	9.97919e6i	1.53408	−	0.375311i
$934$			5.66215e7i			2.12380i
$935$	−2.53250e6	−	5.70242e6i	−0.0947372	−	0.213319i
$936$	5.90680e7	−	3.07418e7i	2.20375	−	1.14694i
$937$	−7.43506e6	−	7.43506e6i	−0.276653	−	0.276653i	0.555118	−	0.831771i	$-0.312673\pi$
$937$	−7.43506e6	−	7.43506e6i	−0.276653	−	0.276653i	−0.831771	+	0.555118i	$0.812673\pi$
$938$	2.83483e7	+	2.83483e7i	1.05201	+	1.05201i
$939$	3.68268e7	+	2.23494e7i	1.36301	+	0.827185i
$940$	−863448.	−	1.94422e6i	−0.0318725	−	0.0717672i
$941$			2.57735e7i			0.948853i	0.880295	+	0.474427i	$0.157345\pi$
$941$			2.57735e7i			0.948853i	−0.880295	+	0.474427i	$0.842655\pi$
$942$	1.06455e7	+	4.35133e7i	0.390875	+	1.59770i
$943$	5.90894e6	−	5.90894e6i	0.216387	−	0.216387i
$944$	−3.76810e6			−0.137624
$945$	−6.02839e6	+	1.30397e7i	−0.219595	+	0.474994i
$946$	2.08518e7			0.757559
$947$	−1.59306e7	+	1.59306e7i	−0.577240	+	0.577240i	−0.934142	−	0.356902i	$-0.883833\pi$
$947$	−1.59306e7	+	1.59306e7i	−0.577240	+	0.577240i	0.356902	+	0.934142i	$0.383833\pi$
$948$	5.26896e6	+	2.15369e7i	0.190416	+	0.778326i
$949$		−	3.79087e7i		−	1.36639i
$950$	139136.	+	2.75327e6i	0.00500185	+	0.0989781i
$951$	−3.73523e6	−	2.26683e6i	−0.133926	−	0.0812770i
$952$	6.10069e6	+	6.10069e6i	0.218166	+	0.218166i
$953$	−3.79784e6	−	3.79784e6i	−0.135458	−	0.135458i	0.636127	−	0.771585i	$-0.280536\pi$
$953$	−3.79784e6	−	3.79784e6i	−0.135458	−	0.135458i	−0.771585	+	0.636127i	$0.780536\pi$
$954$	2.63659e7	−	1.37221e7i	0.937934	−	0.488145i
$955$	−1.49538e7	+	3.88475e7i	−0.530571	+	1.37834i
$956$			1.93917e7i			0.686234i
$957$	−3.54621e6	+	867575.i	−0.125165	+	0.0306216i
$958$	−3.74710e7	+	3.74710e7i	−1.31911	+	1.31911i
$959$	−2.29157e7			−0.804612
$960$	−3.73703e7	−	4.79136e6i	−1.30873	−	0.167796i
$961$	−2.22497e7			−0.777169
$962$	2.41958e7	−	2.41958e7i	0.842952	−	0.842952i
$963$	−6.67609e6	+	2.11669e7i	−0.231983	+	0.735516i
$964$		−	3.77009e7i		−	1.30665i
$965$	−2.79909e7	+	1.24311e7i	−0.967607	+	0.429724i
$966$	1.59352e7	−	2.62576e7i	0.549433	−	0.905342i
$967$	2.08823e7	+	2.08823e7i	0.718145	+	0.718145i	0.968225	−	0.250080i	$-0.0804570\pi$
$967$	2.08823e7	+	2.08823e7i	0.718145	+	0.718145i	−0.250080	+	0.968225i	$0.580457\pi$
$968$	2.00366e7	+	2.00366e7i	0.687284	+	0.687284i
$969$	353513.	−	582510.i	0.0120947	−	0.0199294i
$970$	5.70998e7	+	2.19798e7i	1.94852	+	0.750056i
$971$		−	4.07167e7i		−	1.38588i	−0.720997	−	0.692938i	$-0.756316\pi$
$971$		−	4.07167e7i		−	1.38588i	0.720997	−	0.692938i	$-0.243684\pi$
$972$	2.00030e7	−	5.14020e7i	0.679094	−	1.74508i
$973$	−1.27535e7	+	1.27535e7i	−0.431866	+	0.431866i
$974$	−2.40022e7			−0.810687
$975$	−1.42795e7	−	4.77769e7i	−0.481063	−	1.60956i
$976$	−1.75995e7			−0.591392
$977$	1.49430e7	−	1.49430e7i	0.500841	−	0.500841i	−0.410858	−	0.911699i	$-0.634771\pi$
$977$	1.49430e7	−	1.49430e7i	0.500841	−	0.500841i	0.911699	+	0.410858i	$0.134771\pi$
$978$	4.38919e7	−	1.07381e7i	1.46736	−	0.358988i
$979$			5.59022e6i			0.186411i
$980$	3.81528e7	+	1.46864e7i	1.26900	+	0.488484i
$981$	−1.22220e7	−	2.34836e7i	−0.405479	−	0.779097i
$982$	−2.26005e7	−	2.26005e7i	−0.747894	−	0.747894i
$983$	9.41115e6	+	9.41115e6i	0.310641	+	0.310641i	0.845158	−	0.534517i	$-0.179506\pi$
$983$	9.41115e6	+	9.41115e6i	0.310641	+	0.310641i	−0.534517	+	0.845158i	$0.679506\pi$
$984$	9.84121e6	+	5.97242e6i	0.324012	+	0.196636i
$985$	5.19695e7	−	2.30802e7i	1.70670	−	0.757964i
$986$			4.54010e6i			0.148721i
$987$	−159604.	−	652380.i	−0.00521496	−	0.0213161i
$988$	3.99077e6	−	3.99077e6i	0.130066	−	0.130066i
$989$	−2.80414e7			−0.911609
$990$	−2.39279e7	−	1.90733e7i	−0.775920	−	0.618498i
$991$	−3.18226e7			−1.02932			−0.514661	−	0.857394i	$-0.672082\pi$
$991$	−3.18226e7			−1.02932			−0.514661	+	0.857394i	$0.672082\pi$
$992$	−4.18454e6	+	4.18454e6i	−0.135011	+	0.135011i
$993$	−2.79640e6	−	1.14303e7i	−0.0899967	−	0.367861i
$994$		−	3.60368e7i		−	1.15686i
$995$	2.89363e6	−	7.51717e6i	0.0926585	−	0.240711i
$996$	−7.17210e7	−	4.35260e7i	−2.29086	−	1.39027i
$997$	559652.	+	559652.i	0.0178312	+	0.0178312i	0.715966	−	0.698135i	$-0.245986\pi$
$997$	559652.	+	559652.i	0.0178312	+	0.0178312i	−0.698135	+	0.715966i	$0.745986\pi$
$998$	−5.09050e6	−	5.09050e6i	−0.161783	−	0.161783i
$999$	865649.	−	1.31788e7i	0.0274428	−	0.417795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.6.e.a.2.1	✓	16
3.2	odd	2	inner	15.6.e.a.2.8	yes	16
5.2	odd	4		75.6.e.e.68.1		16
5.3	odd	4	inner	15.6.e.a.8.8	yes	16
5.4	even	2		75.6.e.e.32.8		16
15.2	even	4		75.6.e.e.68.8		16
15.8	even	4	inner	15.6.e.a.8.1	yes	16
15.14	odd	2		75.6.e.e.32.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.6.e.a.2.1	✓	16	1.1	even	1	trivial
15.6.e.a.2.8	yes	16	3.2	odd	2	inner
15.6.e.a.8.1	yes	16	15.8	even	4	inner
15.6.e.a.8.8	yes	16	5.3	odd	4	inner
75.6.e.e.32.1		16	15.14	odd	2
75.6.e.e.32.8		16	5.4	even	2
75.6.e.e.68.1		16	5.2	odd	4
75.6.e.e.68.8		16	15.2	even	4

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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	15.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.77944 + 6.77944i) q^{2} +(3.70445 + 15.1419i) q^{3} -59.9217i q^{4} +(-52.1700 - 20.0821i) q^{5} +(-127.768 - 77.5396i) q^{6} +(47.9711 + 47.9711i) q^{7} +(189.294 + 189.294i) q^{8} +(-215.554 + 112.185i) q^{9} +(489.829 - 217.538i) q^{10} +234.950i q^{11} +(907.329 - 221.977i) q^{12} +(-723.818 + 723.818i) q^{13} -650.435 q^{14} +(110.820 - 864.346i) q^{15} -649.117 q^{16} +(335.918 - 335.918i) q^{17} +(700.788 - 2221.89i) q^{18} -92.0117i q^{19} +(-1203.35 + 3126.12i) q^{20} +(-548.667 + 904.080i) q^{21} +(-1592.83 - 1592.83i) q^{22} +(2142.03 + 2142.03i) q^{23} +(-2165.04 + 3567.49i) q^{24} +(2318.42 + 2095.37i) q^{25} -9814.17i q^{26} +(-2497.20 - 2848.32i) q^{27} +(2874.51 - 2874.51i) q^{28} +996.800 q^{29} +(5108.48 + 6611.08i) q^{30} +2525.76 q^{31} +(-1656.75 + 1656.75i) q^{32} +(-3557.59 + 870.360i) q^{33} +4554.67i q^{34} +(-1539.29 - 3466.01i) q^{35} +(6722.30 + 12916.4i) q^{36} +(2465.40 + 2465.40i) q^{37} +(623.788 + 623.788i) q^{38} +(-13641.3 - 8278.64i) q^{39} +(-6074.04 - 13676.9i) q^{40} -2758.58i q^{41} +(-2409.50 - 9848.82i) q^{42} +(-6545.53 + 6545.53i) q^{43} +14078.6 q^{44} +(13498.4 - 1523.89i) q^{45} -29043.5 q^{46} +(-449.067 + 449.067i) q^{47} +(-2404.62 - 9828.86i) q^{48} -12204.5i q^{49} +(-29923.0 + 1512.16i) q^{50} +(6330.82 + 3842.04i) q^{51} +(43372.4 + 43372.4i) q^{52} +(9021.16 + 9021.16i) q^{53} +(36239.6 + 2380.39i) q^{54} +(4718.30 - 12257.4i) q^{55} +18161.3i q^{56} +(1393.23 - 340.852i) q^{57} +(-6757.75 + 6757.75i) q^{58} +5804.97 q^{59} +(-51793.1 - 6640.54i) q^{60} +27112.9 q^{61} +(-17123.3 + 17123.3i) q^{62} +(-15722.0 - 4958.75i) q^{63} -43235.4i q^{64} +(52297.4 - 23225.8i) q^{65} +(18217.9 - 30019.0i) q^{66} +(-43583.6 - 43583.6i) q^{67} +(-20128.8 - 20128.8i) q^{68} +(-24499.3 + 40369.3i) q^{69} +(33933.2 + 13062.1i) q^{70} +55404.2i q^{71} +(-62038.9 - 19567.2i) q^{72} +(-26186.6 + 26186.6i) q^{73} -33428.1 q^{74} +(-23139.4 + 42867.4i) q^{75} -5513.50 q^{76} +(-11270.8 + 11270.8i) q^{77} +(148605. - 36356.1i) q^{78} +23736.6i q^{79} +(33864.4 + 13035.6i) q^{80} +(33878.2 - 48363.7i) q^{81} +(18701.6 + 18701.6i) q^{82} +(-63509.0 - 63509.0i) q^{83} +(54174.0 + 32877.1i) q^{84} +(-24270.8 + 10778.9i) q^{85} -88750.0i q^{86} +(3692.59 + 15093.5i) q^{87} +(-44474.6 + 44474.6i) q^{88} +23793.2 q^{89} +(-81180.3 + 101843. i) q^{90} -69444.7 q^{91} +(128354. - 128354. i) q^{92} +(9356.54 + 38244.8i) q^{93} -6088.84i q^{94} +(-1847.79 + 4800.25i) q^{95} +(-31223.6 - 18949.0i) q^{96} +(80721.5 + 80721.5i) q^{97} +(82740.0 + 82740.0i) q^{98} +(-26357.8 - 50644.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 84 q^{6} - 80 q^{7} + 1060 q^{10} + 420 q^{12} - 2120 q^{13} - 3000 q^{15} - 452 q^{16} + 6000 q^{18} + 1416 q^{21} + 3380 q^{22} + 9160 q^{25} - 12960 q^{27} - 10900 q^{28} - 13380 q^{30} - 21568 q^{31}+ \cdots + 440800 q^{97}+O(q^{100}) \) 16 * q - 84 * q^6 - 80 * q^7 + 1060 * q^10 + 420 * q^12 - 2120 * q^13 - 3000 * q^15 - 452 * q^16 + 6000 * q^18 + 1416 * q^21 + 3380 * q^22 + 9160 * q^25 - 12960 * q^27 - 10900 * q^28 - 13380 * q^30 - 21568 * q^31 + 5760 * q^33 + 61932 * q^36 + 55720 * q^37 + 21480 * q^40 - 103020 * q^42 - 23360 * q^43 - 21240 * q^45 - 151168 * q^46 + 74820 * q^48 + 138816 * q^51 + 204160 * q^52 + 89120 * q^55 - 163800 * q^57 - 163500 * q^58 - 217380 * q^60 - 175168 * q^61 + 143040 * q^63 + 263400 * q^66 + 140320 * q^67 + 385260 * q^70 - 328680 * q^72 - 240320 * q^73 - 199920 * q^75 - 271536 * q^76 + 429960 * q^78 + 326016 * q^81 + 431120 * q^82 + 2440 * q^85 - 331680 * q^87 - 401700 * q^88 - 348360 * q^90 - 487168 * q^91 - 22320 * q^93 + 311748 * q^96 + 440800 * q^97

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