LMFDB - Embedded newform 26.6.e.a.17.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,6,Mod(17,26)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(26, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("26.17");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.16997931514$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 2164x^{10} + 1693662x^{8} + 565924828x^{6} + 68470588153x^{4} + 28868949144x^{2} + 2602224144 $ x^12 + 2164x^10 + 1693662x^8 + 565924828x^6 + 68470588153x^4 + 28868949144*x^2 + 2602224144
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.6
Root			$-19.3520i$ of defining polynomial
Character	$\chi$	$=$	26.17
Dual form			26.6.e.a.23.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.46410 + 2.00000i) q^{2} +(9.67602 - 16.7594i) q^{3} +(8.00000 + 13.8564i) q^{4} -52.2356i q^{5} +(67.0374 - 38.7041i) q^{6} +(16.5596 - 9.56069i) q^{7} +64.0000i q^{8} +(-65.7507 - 113.884i) q^{9} +O(q^{10})$	\(q+(3.46410 + 2.00000i) q^{2} +(9.67602 - 16.7594i) q^{3} +(8.00000 + 13.8564i) q^{4} -52.2356i q^{5} +(67.0374 - 38.7041i) q^{6} +(16.5596 - 9.56069i) q^{7} +64.0000i q^{8} +(-65.7507 - 113.884i) q^{9} +(104.471 - 180.949i) q^{10} +(330.811 + 190.994i) q^{11} +309.633 q^{12} +(-45.6914 + 607.623i) q^{13} +76.4855 q^{14} +(-875.434 - 505.432i) q^{15} +(-128.000 + 221.703i) q^{16} +(-528.708 - 915.749i) q^{17} -526.006i q^{18} +(-2029.73 + 1171.86i) q^{19} +(723.797 - 417.884i) q^{20} -370.038i q^{21} +(763.976 + 1323.25i) q^{22} +(-1373.98 + 2379.80i) q^{23} +(1072.60 + 619.265i) q^{24} +396.447 q^{25} +(-1373.52 + 2013.48i) q^{26} +2157.72 q^{27} +(264.954 + 152.971i) q^{28} +(60.8591 - 105.411i) q^{29} +(-2021.73 - 3501.74i) q^{30} -5556.97i q^{31} +(-886.810 + 512.000i) q^{32} +(6401.87 - 3696.12i) q^{33} -4229.66i q^{34} +(-499.408 - 865.000i) q^{35} +(1052.01 - 1822.14i) q^{36} +(7055.04 + 4073.23i) q^{37} -9374.92 q^{38} +(9741.26 + 6645.13i) q^{39} +3343.08 q^{40} +(11678.6 + 6742.64i) q^{41} +(740.075 - 1281.85i) q^{42} +(-11009.8 - 19069.6i) q^{43} +6111.81i q^{44} +(-5948.77 + 3434.53i) q^{45} +(-9519.20 + 5495.91i) q^{46} -3489.22i q^{47} +(2477.06 + 4290.40i) q^{48} +(-8220.69 + 14238.6i) q^{49} +(1373.33 + 792.893i) q^{50} -20463.2 q^{51} +(-8785.00 + 4227.86i) q^{52} -28937.9 q^{53} +(7474.57 + 4315.45i) q^{54} +(9976.68 - 17280.1i) q^{55} +(611.884 + 1059.81i) q^{56} +45355.9i q^{57} +(421.644 - 243.436i) q^{58} +(29831.8 - 17223.4i) q^{59} -16173.8i q^{60} +(-2652.96 - 4595.07i) q^{61} +(11113.9 - 19249.9i) q^{62} +(-2177.61 - 1257.24i) q^{63} -4096.00 q^{64} +(31739.5 + 2386.71i) q^{65} +29569.0 q^{66} +(-49277.1 - 28450.2i) q^{67} +(8459.33 - 14652.0i) q^{68} +(26589.3 + 46054.0i) q^{69} -3995.26i q^{70} +(-2072.85 + 1196.76i) q^{71} +(7288.55 - 4208.05i) q^{72} -47969.6i q^{73} +(16292.9 + 28220.2i) q^{74} +(3836.03 - 6644.19i) q^{75} +(-32475.7 - 18749.8i) q^{76} +7304.14 q^{77} +(20454.4 + 42501.9i) q^{78} -79330.2 q^{79} +(11580.8 + 6686.15i) q^{80} +(36855.6 - 63835.8i) q^{81} +(26970.5 + 46714.4i) q^{82} +22090.3i q^{83} +(5127.39 - 2960.30i) q^{84} +(-47834.7 + 27617.4i) q^{85} -88078.6i q^{86} +(-1177.75 - 2039.92i) q^{87} +(-12223.6 + 21171.9i) q^{88} +(107681. + 62169.5i) q^{89} -27476.2 q^{90} +(5052.66 + 10498.8i) q^{91} -43967.3 q^{92} +(-93131.2 - 53769.3i) q^{93} +(6978.44 - 12087.0i) q^{94} +(61213.0 + 106024. i) q^{95} +19816.5i q^{96} +(81487.4 - 47046.8i) q^{97} +(-56954.6 + 32882.7i) q^{98} -50232.0i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 96 q^{4} + 360 q^{7} - 706 q^{9}+O(q^{10}) $ 12 * q + 96 * q^4 + 360 * q^7 - 706 * q^9	\( 12 q + 96 q^{4} + 360 q^{7} - 706 q^{9} - 368 q^{10} + 504 q^{11} + 3202 q^{13} - 2272 q^{14} + 2112 q^{15} - 1536 q^{16} - 1910 q^{17} - 6888 q^{19} + 1440 q^{20} + 2160 q^{22} + 5920 q^{23} - 4672 q^{25} - 2320 q^{26} - 2736 q^{27} + 5760 q^{28} + 7922 q^{29} - 11696 q^{30} - 18780 q^{33} + 16864 q^{35} + 11296 q^{36} - 882 q^{37} + 26496 q^{38} + 48304 q^{39} - 11776 q^{40} + 44346 q^{41} + 23648 q^{42} - 41920 q^{43} - 158850 q^{45} - 33408 q^{46} + 4682 q^{49} + 11040 q^{50} + 133264 q^{51} + 43520 q^{52} - 187812 q^{53} + 1296 q^{54} + 17472 q^{55} - 18176 q^{56} - 73488 q^{58} + 74832 q^{59} + 27934 q^{61} - 4336 q^{62} + 156528 q^{63} - 49152 q^{64} + 69646 q^{65} + 6336 q^{66} + 85104 q^{67} + 30560 q^{68} - 77348 q^{69} - 106320 q^{71} - 78336 q^{72} + 96208 q^{74} + 192080 q^{75} - 110208 q^{76} - 151944 q^{77} + 9392 q^{78} + 30464 q^{79} + 23040 q^{80} - 72310 q^{81} - 87040 q^{82} + 53952 q^{84} - 148986 q^{85} - 121936 q^{87} - 34560 q^{88} + 93108 q^{89} + 282016 q^{90} - 56776 q^{91} + 189440 q^{92} + 107616 q^{93} + 158256 q^{94} + 232560 q^{95} + 147156 q^{97} + 46752 q^{98}+O(q^{100}) \) 12 * q + 96 * q^4 + 360 * q^7 - 706 * q^9 - 368 * q^10 + 504 * q^11 + 3202 * q^13 - 2272 * q^14 + 2112 * q^15 - 1536 * q^16 - 1910 * q^17 - 6888 * q^19 + 1440 * q^20 + 2160 * q^22 + 5920 * q^23 - 4672 * q^25 - 2320 * q^26 - 2736 * q^27 + 5760 * q^28 + 7922 * q^29 - 11696 * q^30 - 18780 * q^33 + 16864 * q^35 + 11296 * q^36 - 882 * q^37 + 26496 * q^38 + 48304 * q^39 - 11776 * q^40 + 44346 * q^41 + 23648 * q^42 - 41920 * q^43 - 158850 * q^45 - 33408 * q^46 + 4682 * q^49 + 11040 * q^50 + 133264 * q^51 + 43520 * q^52 - 187812 * q^53 + 1296 * q^54 + 17472 * q^55 - 18176 * q^56 - 73488 * q^58 + 74832 * q^59 + 27934 * q^61 - 4336 * q^62 + 156528 * q^63 - 49152 * q^64 + 69646 * q^65 + 6336 * q^66 + 85104 * q^67 + 30560 * q^68 - 77348 * q^69 - 106320 * q^71 - 78336 * q^72 + 96208 * q^74 + 192080 * q^75 - 110208 * q^76 - 151944 * q^77 + 9392 * q^78 + 30464 * q^79 + 23040 * q^80 - 72310 * q^81 - 87040 * q^82 + 53952 * q^84 - 148986 * q^85 - 121936 * q^87 - 34560 * q^88 + 93108 * q^89 + 282016 * q^90 - 56776 * q^91 + 189440 * q^92 + 107616 * q^93 + 158256 * q^94 + 232560 * q^95 + 147156 * q^97 + 46752 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$15$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	3.46410	+	2.00000i	0.612372	+	0.353553i
$2$	3.46410	+	2.00000i	0.612372	+	0.353553i
$3$	9.67602	−	16.7594i	0.620717	−	1.07511i	−0.368635	−	0.929574i	$-0.620175\pi$
$3$	9.67602	−	16.7594i	0.620717	−	1.07511i	0.989352	−	0.145539i	$-0.0464917\pi$
$4$	8.00000	+	13.8564i	0.250000	+	0.433013i
$5$		−	52.2356i		−	0.934418i	−0.884147	−	0.467209i	$-0.845260\pi$
$5$		−	52.2356i		−	0.934418i	0.884147	−	0.467209i	$-0.154740\pi$
$6$	67.0374	−	38.7041i	0.760220	−	0.438913i
$7$	16.5596	−	9.56069i	0.127733	−	0.0737469i	−0.434772	−	0.900541i	$-0.643171\pi$
$7$	16.5596	−	9.56069i	0.127733	−	0.0737469i	0.562505	+	0.826794i	$0.309838\pi$
$8$			64.0000i			0.353553i
$9$	−65.7507	−	113.884i	−0.270579	−	0.468657i
$10$	104.471	−	180.949i	0.330367	−	0.572212i
$11$	330.811	+	190.994i	0.824325	+	0.475924i	0.851906	−	0.523695i	$-0.175447\pi$
$11$	330.811	+	190.994i	0.824325	+	0.475924i	−0.0275804	+	0.999620i	$0.508780\pi$
$12$	309.633			0.620717
$13$	−45.6914	+	607.623i	−0.0749853	+	0.997185i
$13$	−45.6914	+	607.623i	−0.0749853	+	0.997185i
$14$	76.4855			0.104294
$15$	−875.434	−	505.432i	−1.00461	−	0.580009i
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	−528.708	−	915.749i	−0.443704	−	0.768518i	0.554257	−	0.832346i	$-0.313003\pi$
$17$	−528.708	−	915.749i	−0.443704	−	0.768518i	−0.997961	+	0.0638275i	$0.979669\pi$
$18$		−	526.006i		−	0.382657i
$19$	−2029.73	+	1171.86i	−1.28989	+	0.744721i	−0.978635	−	0.205604i	$-0.934084\pi$
$19$	−2029.73	+	1171.86i	−1.28989	+	0.744721i	−0.311259	+	0.950325i	$0.600751\pi$
$20$	723.797	−	417.884i	0.404615	−	0.233605i
$21$		−	370.038i		−	0.183104i
$22$	763.976	+	1323.25i	0.336529	+	0.582886i
$23$	−1373.98	+	2379.80i	−0.541577	+	0.938039i	0.457236	+	0.889345i	$0.348839\pi$
$23$	−1373.98	+	2379.80i	−0.541577	+	0.938039i	−0.998814	+	0.0486941i	$0.984494\pi$
$24$	1072.60	+	619.265i	0.380110	+	0.219457i
$25$	396.447			0.126863
$26$	−1373.52	+	2013.48i	−0.398477	+	0.584137i
$27$	2157.72			0.569622
$28$	264.954	+	152.971i	0.0638667	+	0.0368735i
$29$	60.8591	−	105.411i	0.0134379	−	0.0232751i	−0.859228	−	0.511592i	$-0.829056\pi$
$29$	60.8591	−	105.411i	0.0134379	−	0.0232751i	0.872666	+	0.488317i	$0.162389\pi$
$30$	−2021.73	−	3501.74i	−0.410128	−	0.710363i
$31$		−	5556.97i		−	1.03856i	−0.854603	−	0.519282i	$-0.826199\pi$
$31$		−	5556.97i		−	1.03856i	0.854603	−	0.519282i	$-0.173801\pi$
$32$	−886.810	+	512.000i	−0.153093	+	0.0883883i
$33$	6401.87	−	3696.12i	1.02335	−	0.590829i
$34$		−	4229.66i		−	0.627493i
$35$	−499.408	−	865.000i	−0.0689105	−	0.119356i
$36$	1052.01	−	1822.14i	0.135290	−	0.234328i
$37$	7055.04	+	4073.23i	0.847218	+	0.489142i	0.859711	−	0.510780i	$-0.170643\pi$
$37$	7055.04	+	4073.23i	0.847218	+	0.489142i	−0.0124930	+	0.999922i	$0.503977\pi$
$38$	−9374.92			−1.05319
$39$	9741.26	+	6645.13i	1.02554	+	0.699587i
$40$	3343.08			0.330367
$41$	11678.6	+	6742.64i	1.08500	+	0.626426i	0.932241	−	0.361837i	$-0.117850\pi$
$41$	11678.6	+	6742.64i	1.08500	+	0.626426i	0.152761	+	0.988263i	$0.451184\pi$
$42$	740.075	−	1281.85i	0.0647370	−	0.112128i
$43$	−11009.8	−	19069.6i	−0.908049	−	1.57279i	−0.816771	−	0.576962i	$-0.804238\pi$
$43$	−11009.8	−	19069.6i	−0.908049	−	1.57279i	−0.0912782	−	0.995825i	$-0.529095\pi$
$44$			6111.81i			0.475924i
$45$	−5948.77	+	3434.53i	−0.437921	+	0.252834i
$46$	−9519.20	+	5495.91i	−0.663294	+	0.382953i
$47$		−	3489.22i		−	0.230401i	−0.993342	−	0.115200i	$-0.963249\pi$
$47$		−	3489.22i		−	0.230401i	0.993342	−	0.115200i	$-0.0367510\pi$
$48$	2477.06	+	4290.40i	0.155179	+	0.268778i
$49$	−8220.69	+	14238.6i	−0.489123	+	0.847186i
$50$	1373.33	+	792.893i	0.0776874	+	0.0448528i
$51$	−20463.2			−1.10166
$52$	−8785.00	+	4227.86i	−0.450540	+	0.216827i
$53$	−28937.9			−1.41507			−0.707534	−	0.706679i	$-0.750192\pi$
$53$	−28937.9			−1.41507			−0.707534	+	0.706679i	$0.750192\pi$
$54$	7474.57	+	4315.45i	0.348821	+	0.201392i
$55$	9976.68	−	17280.1i	0.444712	−	0.770264i
$56$	611.884	+	1059.81i	0.0260735	+	0.0451606i
$57$			45355.9i			1.84904i
$58$	421.644	−	243.436i	0.0164580	−	0.00950201i
$59$	29831.8	−	17223.4i	1.11570	−	0.644152i	0.175404	−	0.984497i	$-0.443877\pi$
$59$	29831.8	−	17223.4i	1.11570	−	0.644152i	0.940301	+	0.340344i	$0.110544\pi$
$60$		−	16173.8i		−	0.580009i
$61$	−2652.96	−	4595.07i	−0.0912866	−	0.158113i	0.816766	−	0.576969i	$-0.195765\pi$
$61$	−2652.96	−	4595.07i	−0.0912866	−	0.158113i	−0.908053	+	0.418856i	$0.862431\pi$
$62$	11113.9	−	19249.9i	0.367188	−	0.635988i
$63$	−2177.61	−	1257.24i	−0.0691240	−	0.0399088i
$64$	−4096.00			−0.125000
$65$	31739.5	+	2386.71i	0.931787	+	0.0700676i
$66$	29569.0			0.835558
$67$	−49277.1	−	28450.2i	−1.34109	−	0.774279i	−0.354123	−	0.935199i	$-0.615221\pi$
$67$	−49277.1	−	28450.2i	−1.34109	−	0.774279i	−0.986968	+	0.160919i	$0.948554\pi$
$68$	8459.33	−	14652.0i	0.221852	−	0.384259i
$69$	26589.3	+	46054.0i	0.672332	+	1.16451i
$70$		−	3995.26i		−	0.0974541i
$71$	−2072.85	+	1196.76i	−0.0488002	+	0.0281748i	−0.524202	−	0.851594i	$-0.675636\pi$
$71$	−2072.85	+	1196.76i	−0.0488002	+	0.0281748i	0.475401	+	0.879769i	$0.342303\pi$
$72$	7288.55	−	4208.05i	0.165695	−	0.0956642i
$73$		−	47969.6i		−	1.05356i	−0.850002	−	0.526780i	$-0.823399\pi$
$73$		−	47969.6i		−	1.05356i	0.850002	−	0.526780i	$-0.176601\pi$
$74$	16292.9	+	28220.2i	0.345875	+	0.599074i
$75$	3836.03	−	6644.19i	0.0787460	−	0.136392i
$76$	−32475.7	−	18749.8i	−0.644947	−	0.372360i
$77$	7304.14			0.140392
$78$	20454.4	+	42501.9i	0.380672	+	0.790992i
$79$	−79330.2			−1.43011			−0.715057	−	0.699066i	$-0.753599\pi$
$79$	−79330.2			−1.43011			−0.715057	+	0.699066i	$0.753599\pi$
$80$	11580.8	+	6686.15i	0.202307	+	0.116802i
$81$	36855.6	−	63835.8i	0.624153	−	1.08106i
$82$	26970.5	+	46714.4i	0.442950	+	0.767213i
$83$			22090.3i			0.351971i	0.984393	+	0.175986i	$0.0563112\pi$
$83$			22090.3i			0.351971i	−0.984393	+	0.175986i	$0.943689\pi$
$84$	5127.39	−	2960.30i	0.0792863	−	0.0457760i
$85$	−47834.7	+	27617.4i	−0.718117	+	0.414605i
$86$		−	88078.6i		−	1.28418i
$87$	−1177.75	−	2039.92i	−0.0166822	−	0.0288945i
$88$	−12223.6	+	21171.9i	−0.168265	+	0.291443i
$89$	107681.	+	62169.5i	1.44100	+	0.831960i	0.997916	−	0.0645215i	$-0.0205521\pi$
$89$	107681.	+	62169.5i	1.44100	+	0.831960i	0.443081	+	0.896482i	$0.353885\pi$
$90$	−27476.2			−0.357561
$91$	5052.66	+	10498.8i	0.0639612	+	0.132904i
$92$	−43967.3			−0.541577
$93$	−93131.2	−	53769.3i	−1.11657	−	0.644655i
$94$	6978.44	−	12087.0i	0.0814589	−	0.141091i
$95$	61213.0	+	106024.i	0.695881	+	1.20530i
$96$			19816.5i			0.219457i
$97$	81487.4	−	47046.8i	0.879349	−	0.507692i	0.00890498	−	0.999960i	$-0.497165\pi$
$97$	81487.4	−	47046.8i	0.879349	−	0.507692i	0.870444	+	0.492268i	$0.163832\pi$
$98$	−56954.6	+	32882.7i	−0.599051	+	0.345862i
$99$		−	50232.0i		−	0.515101i
$100$	3171.57	+	5493.33i	0.0317157	+	0.0549333i
$101$	−28667.7	+	49653.9i	−0.279634	+	0.484340i	−0.971294	−	0.237883i	$-0.923546\pi$
$101$	−28667.7	+	49653.9i	−0.279634	+	0.484340i	0.691660	+	0.722223i	$0.256880\pi$
$102$	−70886.5	−	40926.3i	−0.674626	−	0.389495i
$103$	−160258.			−1.48842			−0.744211	−	0.667945i	$-0.767174\pi$
$103$	−160258.			−1.48842			−0.744211	+	0.667945i	$0.767174\pi$
$104$	−38887.9	−	2924.25i	−0.352558	−	0.0265113i
$105$	−19329.1			−0.171096
$106$	−100244.	−	57875.8i	−0.866549	−	0.500302i
$107$	−9027.59	+	15636.2i	−0.0762276	+	0.132030i	−0.901619	−	0.432530i	$-0.857621\pi$
$107$	−9027.59	+	15636.2i	−0.0762276	+	0.132030i	0.825392	+	0.564560i	$0.190954\pi$
$108$	17261.8	+	29898.3i	0.142405	+	0.246653i
$109$			25954.4i			0.209240i	0.994512	+	0.104620i	$0.0333627\pi$
$109$			25954.4i			0.209240i	−0.994512	+	0.104620i	$0.966637\pi$
$110$	69120.5	−	39906.7i	0.544659	−	0.314459i
$111$	136529.	−	78825.3i	1.05177	−	0.607237i
$112$			4895.07i			0.0368735i
$113$	54786.3	+	94892.7i	0.403623	+	0.699096i	0.994160	−	0.107915i	$-0.0344174\pi$
$113$	54786.3	+	94892.7i	0.403623	+	0.699096i	−0.590537	+	0.807010i	$0.701084\pi$
$114$	−90711.9	+	157118.i	−0.653736	+	1.13230i
$115$	124310.	+	71770.5i	0.876521	+	0.506060i
$116$	1947.49			0.0134379
$117$	72202.5	−	34748.1i	0.487627	−	0.234675i
$118$	137787.			0.910969
$119$	−17510.4	−	10109.6i	−0.113352	−	0.0654437i
$120$	32347.7	−	56027.8i	0.205064	−	0.355182i
$121$	−7568.08	−	13108.3i	−0.0469918	−	0.0813922i
$122$		−	21223.7i		−	0.129099i
$123$	226005.	−	130484.i	1.34696	−	0.777667i
$124$	76999.6	−	44455.7i	0.449712	−	0.259641i
$125$		−	183945.i		−	1.05296i
$126$	−5028.98	−	8710.45i	−0.0282198	−	0.0488781i
$127$	−29176.7	+	50535.5i	−0.160519	+	0.278027i	−0.935055	−	0.354503i	$-0.884650\pi$
$127$	−29176.7	+	50535.5i	−0.160519	+	0.278027i	0.774536	+	0.632530i	$0.217984\pi$
$128$	−14189.0	−	8192.00i	−0.0765466	−	0.0441942i
$129$	−426125.			−2.25457
$130$	105175.	+	71746.8i	0.545828	+	0.372344i
$131$	29397.6			0.149670			0.0748349	−	0.997196i	$-0.476157\pi$
$131$	29397.6			0.149670			0.0748349	+	0.997196i	$0.476157\pi$
$132$	102430.	+	59138.0i	0.511673	+	0.295414i
$133$	−22407.7	+	38811.2i	−0.109842	+	0.190252i
$134$	−113801.	−	197108.i	−0.547498	−	0.948295i
$135$		−	112710.i		−	0.532265i
$136$	58607.9	−	33837.3i	0.271712	−	0.156873i
$137$	199120.	−	114962.i	0.906385	−	0.523302i	0.0271188	−	0.999632i	$-0.491367\pi$
$137$	199120.	−	114962.i	0.906385	−	0.523302i	0.879266	+	0.476331i	$0.158033\pi$
$138$			212714.i			0.950822i
$139$	−84655.6	−	146628.i	−0.371637	−	0.643694i	0.618181	−	0.786036i	$-0.287870\pi$
$139$	−84655.6	−	146628.i	−0.371637	−	0.643694i	−0.989817	+	0.142342i	$0.954537\pi$
$140$	7990.53	−	13840.0i	0.0344552	−	0.0596782i
$141$	−58477.1	−	33761.8i	−0.247707	−	0.143014i
$142$	−9574.07			−0.0398452
$143$	−131168.	+	192282.i	−0.536397	+	0.786317i
$144$	33664.4			0.135290
$145$	−5506.21	−	3179.01i	−0.0217487	−	0.0125566i
$146$	95939.2	−	166172.i	0.372489	−	0.645171i
$147$	159087.	+	275547.i	0.607214	+	1.05172i
$148$			130343.i			0.489142i
$149$	−426672.	+	246339.i	−1.57445	+	0.909007i	−0.578833	+	0.815446i	$0.696492\pi$
$149$	−426672.	+	246339.i	−1.57445	+	0.909007i	−0.995614	+	0.0935613i	$0.970175\pi$
$150$	26576.8	−	15344.1i	0.0964437	−	0.0556818i
$151$			36336.4i			0.129688i	0.997895	+	0.0648440i	$0.0206550\pi$
$151$			36336.4i			0.129688i	−0.997895	+	0.0648440i	$0.979345\pi$
$152$	−74999.3	−	129903.i	−0.263299	−	0.456046i
$153$	−69525.9	+	120422.i	−0.240114	+	0.415890i
$154$	25302.3	+	14608.3i	0.0859721	+	0.0496360i
$155$	−290271.			−0.970453
$156$	−14147.5	+	188140.i	−0.0465446	+	0.618969i
$157$	368197.			1.19215			0.596075	−	0.802929i	$-0.296726\pi$
$157$	368197.			1.19215			0.596075	+	0.802929i	$0.296726\pi$
$158$	−274808.	−	158660.i	−0.875762	−	0.505622i
$159$	−280004.	+	484981.i	−0.878357	+	1.52136i
$160$	26744.6	+	46323.0i	0.0825917	+	0.143053i
$161$			52544.7i			0.159759i
$162$	255343.	−	147422.i	0.764428	−	0.441343i
$163$	195736.	−	113008.i	0.577035	−	0.333151i	−0.182919	−	0.983128i	$-0.558555\pi$
$163$	195736.	−	113008.i	0.577035	−	0.333151i	0.759954	+	0.649977i	$0.225221\pi$
$164$			215764.i			0.626426i
$165$	−193069.	−	334405.i	−0.552081	−	0.956233i
$166$	−44180.7	+	76523.2i	−0.124441	+	0.215538i
$167$	139637.	+	80619.4i	0.387444	+	0.223691i	0.681052	−	0.732235i	$-0.261523\pi$
$167$	139637.	+	80619.4i	0.387444	+	0.223691i	−0.293608	+	0.955926i	$0.594856\pi$
$168$	23682.4			0.0647370
$169$	−367118.	−	55526.2i	−0.988754	−	0.149548i
$170$	−220939.			−0.586340
$171$	266912.	+	154102.i	0.698037	+	0.403012i
$172$	176157.	−	305113.i	0.454025	−	0.786394i
$173$	−150341.	−	260398.i	−0.381911	−	0.661489i	0.609424	−	0.792844i	$-0.291401\pi$
$173$	−150341.	−	260398.i	−0.381911	−	0.661489i	−0.991335	+	0.131355i	$0.958067\pi$
$174$		−	9421.98i		−	0.0235922i
$175$	6565.00	−	3790.30i	0.0162046	−	0.00935575i
$176$	−84687.7	+	48894.5i	−0.206081	+	0.118981i
$177$		−	666616.i		−	1.59935i
$178$	248678.	+	430723.i	0.588285	+	1.01894i
$179$	138503.	−	239895.i	0.323093	−	0.559614i	−0.658031	−	0.752990i	$-0.728611\pi$
$179$	138503.	−	239895.i	0.323093	−	0.559614i	0.981125	+	0.193377i	$0.0619440\pi$
$180$	−95180.4	−	54952.4i	−0.218961	−	0.126417i
$181$	585036.			1.32735			0.663676	−	0.748020i	$-0.268995\pi$
$181$	585036.			1.32735			0.663676	+	0.748020i	$0.268995\pi$
$182$	−3494.73	+	46474.3i	−0.00782051	+	0.104000i
$183$	−102681.			−0.226652
$184$	−152307.	−	87934.6i	−0.331647	−	0.191476i
$185$	212767.	−	368524.i	0.457063	−	0.791656i
$186$	−215077.	−	372525.i	−0.455840	−	0.789537i
$187$		−	403920.i		−	0.844679i
$188$	48348.0	−	27913.8i	0.0997664	−	0.0576002i
$189$	35731.0	−	20629.3i	0.0727597	−	0.0420079i
$190$			489704.i			0.984124i
$191$	324282.	+	561673.i	0.643190	+	1.11404i	0.984716	+	0.174166i	$0.0557228\pi$
$191$	324282.	+	561673.i	0.643190	+	1.11404i	−0.341526	+	0.939872i	$0.610944\pi$
$192$	−39633.0	+	68646.3i	−0.0775896	+	0.134389i
$193$	570240.	+	329228.i	1.10196	+	0.636215i	0.936734	−	0.350041i	$-0.113832\pi$
$193$	570240.	+	329228.i	1.10196	+	0.636215i	0.165223	+	0.986256i	$0.447166\pi$
$194$	376374.			0.717985
$195$	347112.	−	508840.i	0.653707	−	0.958285i
$196$	−263062.			−0.489123
$197$	553650.	+	319650.i	1.01641	+	0.586826i	0.913063	−	0.407819i	$-0.133711\pi$
$197$	553650.	+	319650.i	1.01641	+	0.586826i	0.103350	+	0.994645i	$0.467044\pi$
$198$	100464.	−	174009.i	0.182116	−	0.315434i
$199$	413147.	+	715592.i	0.739557	+	1.28095i	0.952695	+	0.303929i	$0.0982985\pi$
$199$	413147.	+	715592.i	0.739557	+	1.28095i	−0.213137	+	0.977022i	$0.568368\pi$
$200$			25372.6i			0.0448528i
$201$	−953613.	+	550569.i	−1.66488	+	0.961217i
$202$	−198616.	+	114671.i	−0.342480	+	0.197731i
$203$		−	2327.42i		−	0.00396401i
$204$	−163705.	−	283546.i	−0.275415	−	0.477032i
$205$	352205.	−	610038.i	0.585344	−	1.01385i
$206$	−555149.	−	320516.i	−0.911469	−	0.526237i
$207$	361360.			0.586158
$208$	−128863.	−	87905.6i	−0.206524	−	0.140883i
$209$	−895277.			−1.41772
$210$	−66958.0	−	38658.2i	−0.104774	−	0.0604914i
$211$	−224140.	+	388221.i	−0.346587	+	0.600307i	−0.985641	−	0.168855i	$-0.945993\pi$
$211$	−224140.	+	388221.i	−0.346587	+	0.600307i	0.639053	+	0.769162i	$0.279326\pi$
$212$	−231503.	−	400975.i	−0.353767	−	0.612742i
$213$			46319.4i			0.0699543i
$214$	−62545.0	+	36110.4i	−0.0933594	+	0.0539011i
$215$	−996110.	+	575104.i	−1.46964	+	0.848498i
$216$			138094.i			0.201392i
$217$	−53128.4	−	92021.1i	−0.0765910	−	0.132659i
$218$	−51908.9	+	89908.8i	−0.0739777	+	0.128133i
$219$	−803940.	−	464155.i	−1.13270	−	0.653962i
$220$	319254.			0.444712
$221$	580587.	−	279413.i	0.799626	−	0.384828i
$222$	630603.			0.858763
$223$	−168944.	−	97540.1i	−0.227500	−	0.131347i	0.381918	−	0.924196i	$-0.375264\pi$
$223$	−168944.	−	97540.1i	−0.227500	−	0.131347i	−0.609418	+	0.792849i	$0.708597\pi$
$224$	−9790.14	+	16957.0i	−0.0130367	+	0.0225803i
$225$	−26066.7	−	45148.8i	−0.0343265	−	0.0594552i
$226$			438290.i			0.570809i
$227$	488035.	−	281767.i	0.628617	−	0.362932i	−0.151599	−	0.988442i	$-0.548442\pi$
$227$	488035.	−	281767.i	0.628617	−	0.362932i	0.780216	+	0.625510i	$0.215109\pi$
$228$	−628470.	+	362848.i	−0.800659	+	0.462261i
$229$		−	27368.8i		−	0.0344879i	−0.999851	−	0.0172440i	$-0.994511\pi$
$229$		−	27368.8i		−	0.0344879i	0.999851	−	0.0172440i	$-0.00548919\pi$
$230$	287082.	+	497241.i	0.357838	+	0.619794i
$231$	70675.0	−	122413.i	0.0871436	−	0.150937i
$232$	6746.31	+	3894.98i	0.00822898	+	0.00475101i
$233$	489880.			0.591153			0.295577	−	0.955319i	$-0.404488\pi$
$233$	489880.			0.591153			0.295577	+	0.955319i	$0.404488\pi$
$234$	319613.	+	24033.9i	0.381579	+	0.0286936i
$235$	−182261.			−0.215290
$236$	477309.	+	275574.i	0.557852	+	0.322076i
$237$	−767600.	+	1.32952e6i	−0.887696	+	1.53753i
$238$	−40438.5	−	70041.5i	−0.0462757	−	0.0801518i
$239$		−	97635.3i		−	0.110564i	−0.998471	−	0.0552818i	$-0.982394\pi$
$239$		−	97635.3i		−	0.110564i	0.998471	−	0.0552818i	$-0.0176057\pi$
$240$	224111.	−	129391.i	0.251151	−	0.145002i
$241$	−964315.	+	556748.i	−1.06949	+	0.617470i	−0.928042	−	0.372476i	$-0.878509\pi$
$241$	−964315.	+	556748.i	−1.06949	+	0.617470i	−0.141448	+	0.989946i	$0.545176\pi$
$242$		−	60544.6i		−	0.0664564i
$243$	−451068.	−	781272.i	−0.490034	−	0.848764i
$244$	42447.4	−	73521.1i	0.0456433	−	0.0790565i
$245$	743764.	+	429412.i	0.791625	+	0.457045i
$246$	1.04387e6			1.09979
$247$	−619310.	−	1.28685e6i	−0.645901	−	1.34211i
$248$	355646.			0.367188
$249$	370220.	+	213747.i	0.378409	+	0.218475i
$250$	367889.	−	637203.i	0.372278	−	0.644804i
$251$	−608656.	−	1.05422e6i	−0.609800	−	1.05620i	−0.991273	−	0.131824i	$-0.957916\pi$
$251$	−608656.	−	1.05422e6i	−0.609800	−	1.05620i	0.381473	−	0.924380i	$-0.375417\pi$
$252$		−	40231.8i		−	0.0399088i
$253$	−909055.	+	524843.i	−0.892872	+	0.515500i
$254$	−202142.	+	116707.i	−0.196595	+	0.113504i
$255$			1.06890e6i			1.02941i
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	936765.	−	1.62252e6i	0.884704	−	1.53235i	0.0386508	−	0.999253i	$-0.487694\pi$
$257$	936765.	−	1.62252e6i	0.884704	−	1.53235i	0.846053	−	0.533099i	$-0.178973\pi$
$258$	−1.47614e6	−	852251.i	−1.38063	−	0.797110i
$259$	155772.			0.144291
$260$	220845.	+	458889.i	0.202607	+	0.420993i
$261$	−16006.1			−0.0145440
$262$	101836.	+	58795.3i	0.0916536	+	0.0529163i
$263$	−415561.	+	719773.i	−0.370464	+	0.641662i	−0.989637	−	0.143592i	$-0.954135\pi$
$263$	−415561.	+	719773.i	−0.370464	+	0.641662i	0.619173	+	0.785254i	$0.287468\pi$
$264$	236552.	+	409720.i	0.208890	+	0.361807i
$265$			1.51159e6i			1.32226i
$266$	−155245.	+	89630.7i	−0.134528	+	0.0776699i
$267$	2.08384e6	−	1.20311e6i	1.78890	−	1.03282i
$268$		−	910405.i		−	0.774279i
$269$	405439.	+	702241.i	0.341621	+	0.591705i	0.984734	−	0.174066i	$-0.0556907\pi$
$269$	405439.	+	702241.i	0.341621	+	0.591705i	−0.643113	+	0.765771i	$0.722357\pi$
$270$	225420.	−	390439.i	0.188184	−	0.325944i
$271$	121621.	+	70218.0i	0.100597	+	0.0580799i	0.549455	−	0.835524i	$-0.314836\pi$
$271$	121621.	+	70218.0i	0.100597	+	0.0580799i	−0.448857	+	0.893603i	$0.648169\pi$
$272$	270699.			0.221852
$273$	224843.	+	16907.5i	0.182588	+	0.0137301i
$274$	919694.			0.740060
$275$	131149.	+	75718.9i	0.104576	+	0.0603772i
$276$	−425429.	+	736864.i	−0.336166	+	0.582257i
$277$	−693039.	−	1.20038e6i	−0.542698	−	0.939981i	−0.998748	−	0.0500263i	$-0.984069\pi$
$277$	−693039.	−	1.20038e6i	−0.542698	−	0.939981i	0.456050	−	0.889954i	$-0.349264\pi$
$278$		−	677245.i		−	0.525574i
$279$	−632847.	+	365375.i	−0.486730	+	0.281014i
$280$	55360.0	−	31962.1i	0.0421989	−	0.0243635i
$281$			1.39045e6i			1.05049i	0.850953	+	0.525243i	$0.176025\pi$
$281$			1.39045e6i			1.05049i	−0.850953	+	0.525243i	$0.823975\pi$
$282$	−135047.	−	233908.i	−0.101126	−	0.175155i
$283$	456475.	−	790639.i	0.338806	−	0.586829i	−0.645402	−	0.763843i	$-0.723310\pi$
$283$	456475.	−	790639.i	0.338806	−	0.586829i	0.984208	+	0.177013i	$0.0566436\pi$
$284$	−33165.5	−	19148.1i	−0.0244001	−	0.0140874i
$285$	2.36919e6			1.72778
$286$	−838941.	+	403748.i	−0.606480	+	0.291874i
$287$	257857.			0.184788
$288$	116617.	+	67328.8i	0.0828476	+	0.0478321i
$289$	150864.	−	261304.i	0.106253	−	0.184036i
$290$	−12716.0	−	22024.8i	−0.00887885	−	0.0153786i
$291$		−	1.82090e6i		−	1.26053i
$292$	664686.	−	383757.i	0.456204	−	0.263390i
$293$	−59587.4	+	34402.8i	−0.0405495	+	0.0234112i	−0.520138	−	0.854082i	$-0.674119\pi$
$293$	−59587.4	+	34402.8i	−0.0405495	+	0.0234112i	0.479588	+	0.877494i	$0.340786\pi$
$294$			1.27270e6i			0.858730i
$295$	−899673.	−	1.55828e6i	−0.601908	−	1.04253i
$296$	−260687.	+	451523.i	−0.172938	+	0.299537i
$297$	713800.	+	412112.i	0.469554	+	0.271097i
$298$	−1.97071e6			−1.28553
$299$	−1.38324e6	−	943597.i	−0.894788	−	0.610392i
$300$	122753.			0.0787460
$301$	−364637.	−	210523.i	−0.231977	−	0.133932i
$302$	−72672.9	+	125873.i	−0.0458517	+	0.0794174i
$303$	554779.	+	960905.i	0.347147	+	0.601276i
$304$		−	599995.i		−	0.372360i
$305$	−240026.	+	138579.i	−0.147744	+	0.0852998i
$306$	−481689.	+	278104.i	−0.294079	+	0.169786i
$307$			2.66005e6i			1.61081i	0.592726	+	0.805404i	$0.298052\pi$
$307$			2.66005e6i			1.61081i	−0.592726	+	0.805404i	$0.701948\pi$
$308$	58433.1	+	101209.i	0.0350980	+	0.0607915i
$309$	−1.55066e6	+	2.68582e6i	−0.923889	+	1.60022i
$310$	−1.00553e6	−	580542.i	−0.594279	−	0.343107i
$311$	−2.21314e6			−1.29750			−0.648751	−	0.761000i	$-0.724709\pi$
$311$	−2.21314e6			−1.29750			−0.648751	+	0.761000i	$0.724709\pi$
$312$	−425288.	+	623440.i	−0.247341	+	0.362584i
$313$	−635019.			−0.366375			−0.183188	−	0.983078i	$-0.558642\pi$
$313$	−635019.			−0.366375			−0.183188	+	0.983078i	$0.558642\pi$
$314$	1.27547e6	+	736394.i	0.730040	+	0.421489i
$315$	−65672.9	+	113749.i	−0.0372915	+	0.0645907i
$316$	−634641.	−	1.09923e6i	−0.357528	−	0.619257i
$317$		−	2.29568e6i		−	1.28311i	−0.767078	−	0.641554i	$-0.778290\pi$
$317$		−	2.29568e6i		−	1.28311i	0.767078	−	0.641554i	$-0.221710\pi$
$318$	−1.93992e6	+	1.12001e6i	−1.07576	+	0.621092i
$319$	40265.8	−	23247.5i	0.0221544	−	0.0127908i
$320$			213957.i			0.116802i
$321$	174702.	+	302593.i	0.0946315	+	0.163907i
$322$	−105089.	+	182020.i	−0.0564832	+	0.0978318i
$323$	2.14627e6	+	1.23915e6i	1.14466	+	0.660872i
$324$	1.17938e6			0.624153
$325$	−18114.2	+	240890.i	−0.00951285	+	0.126506i
$326$	904067.			0.471147
$327$	434980.	+	251136.i	0.224957	+	0.129879i
$328$	−431529.	+	747430.i	−0.221475	+	0.383606i
$329$	−33359.3	−	57780.1i	−0.0169913	−	0.0294299i
$330$		−	1.54455e6i		−	0.780761i
$331$	1.66391e6	−	960657.i	0.834755	−	0.481946i	−0.0207229	−	0.999785i	$-0.506597\pi$
$331$	1.66391e6	−	960657.i	0.834755	−	0.481946i	0.855478	+	0.517839i	$0.173263\pi$
$332$	−306093.	+	176723.i	−0.152408	+	0.0879928i
$333$		−	1.07127e6i		−	0.529406i
$334$	322477.	+	558547.i	0.158173	+	0.273964i
$335$	−1.48611e6	+	2.57402e6i	−0.723500	+	1.25314i
$336$	82038.3	+	47364.8i	0.0396432	+	0.0228880i
$337$	574677.			0.275644			0.137822	−	0.990457i	$-0.455990\pi$
$337$	574677.			0.275644			0.137822	+	0.990457i	$0.455990\pi$
$338$	−1.16068e6	−	926584.i	−0.552613	−	0.441157i
$339$	2.12045e6			1.00214
$340$	−765355.	−	441878.i	−0.359059	−	0.207303i
$341$	1.06135e6	−	1.83831e6i	0.494278	−	0.856115i
$342$	616408.	+	1.06765e6i	0.284972	+	0.493587i
$343$			635755.i			0.291779i
$344$	1.22045e6	−	704629.i	0.556064	−	0.321044i
$345$	2.40566e6	−	1.38891e6i	1.08814	−	0.628240i
$346$		−	1.20273e6i		−	0.540104i
$347$	−1.31912e6	−	2.28479e6i	−0.588114	−	1.01864i	−0.994479	−	0.104933i	$-0.966537\pi$
$347$	−1.31912e6	−	2.28479e6i	−0.588114	−	1.01864i	0.406365	−	0.913711i	$-0.366796\pi$
$348$	18844.0	−	32638.7i	0.00834112	−	0.0144472i
$349$	−1.07989e6	−	623472.i	−0.474585	−	0.274002i	0.243572	−	0.969883i	$-0.421681\pi$
$349$	−1.07989e6	−	623472.i	−0.474585	−	0.274002i	−0.718157	+	0.695881i	$0.755014\pi$
$350$	30322.4			0.0132310
$351$	−98589.4	+	1.31108e6i	−0.0427132	+	0.568018i
$352$	−391156.			−0.168265
$353$	1.30762e6	+	754956.i	0.558528	+	0.322467i	0.752555	−	0.658530i	$-0.228821\pi$
$353$	1.30762e6	+	754956.i	0.558528	+	0.322467i	−0.194026	+	0.980996i	$0.562155\pi$
$354$	1.33323e6	−	2.30922e6i	0.565454	−	0.979395i
$355$	62513.3	+	108276.i	0.0263270	+	0.0455997i
$356$			1.98942e6i			0.831960i
$357$	−338862.	+	195642.i	−0.140719	+	0.0812440i
$358$	959579.	−	554013.i	0.395707	−	0.228461i
$359$		−	576783.i		−	0.236198i	−0.993002	−	0.118099i	$-0.962320\pi$
$359$		−	576783.i		−	0.236198i	0.993002	−	0.118099i	$-0.0376801\pi$
$360$	−219810.	−	380722.i	−0.0893903	−	0.154829i
$361$	1.50848e6	−	2.61277e6i	0.609218	−	1.05520i
$362$	2.02662e6	+	1.17007e6i	0.812834	+	0.469290i
$363$	−292915.			−0.116674
$364$	−105055.	+	154002.i	−0.0415587	+	0.0609220i
$365$	−2.50572e6			−0.984465
$366$	−355696.	−	205361.i	−0.138796	−	0.0801337i
$367$	−1.44020e6	+	2.49449e6i	−0.558157	+	0.966756i	0.439494	+	0.898246i	$0.355158\pi$
$367$	−1.44020e6	+	2.49449e6i	−0.558157	+	0.966756i	−0.997650	+	0.0685102i	$0.978175\pi$
$368$	−351739.	−	609229.i	−0.135394	−	0.234510i
$369$		−	1.77333e6i		−	0.677992i
$370$	1.47410e6	−	851070.i	0.559785	−	0.323192i
$371$	−479200.	+	276666.i	−0.180752	+	0.104357i
$372$		−	1.72062e6i		−	0.644655i
$373$	1.35711e6	+	2.35059e6i	0.505061	+	0.874792i	0.999983	+	0.00585399i	$0.00186339\pi$
$373$	1.35711e6	+	2.35059e6i	0.505061	+	0.874792i	−0.494922	+	0.868938i	$0.664803\pi$
$374$	807841.	−	1.39922e6i	0.298639	−	0.517258i
$375$	−3.08280e6	−	1.77985e6i	−1.13205	−	0.653591i
$376$	223310.			0.0814589
$377$	61269.4	+	41795.8i	0.0222019	+	0.0151453i
$378$	165035.			0.0594081
$379$	−2.57607e6	−	1.48729e6i	−0.921211	−	0.531861i	−0.0371897	−	0.999308i	$-0.511841\pi$
$379$	−2.57607e6	−	1.48729e6i	−0.921211	−	0.531861i	−0.884021	+	0.467447i	$0.845174\pi$
$380$	−979408.	+	1.69638e6i	−0.347940	+	0.602650i
$381$	564629.	+	977965.i	0.199274	+	0.345153i
$382$			2.59425e6i			0.909608i
$383$	3.50980e6	−	2.02638e6i	1.22260	−	0.705869i	0.257130	−	0.966377i	$-0.417223\pi$
$383$	3.50980e6	−	2.02638e6i	1.22260	−	0.705869i	0.965472	+	0.260508i	$0.0838900\pi$
$384$	−274585.	+	158532.i	−0.0950275	+	0.0548641i
$385$		−	381536.i		−	0.131185i
$386$	1.31691e6	+	2.28096e6i	0.449872	+	0.779201i
$387$	−1.44781e6	+	2.50768e6i	−0.491398	+	0.851127i
$388$	1.30380e6	+	752748.i	0.439674	+	0.253846i
$389$	−4.80279e6			−1.60924			−0.804618	−	0.593793i	$-0.797630\pi$
$389$	−4.80279e6			−1.60924			−0.804618	+	0.593793i	$0.797630\pi$
$390$	2.22011e6	−	1.06845e6i	0.739117	−	0.355707i
$391$	2.90573e6			0.961201
$392$	−911273.	−	526124.i	−0.299525	−	0.172931i
$393$	284452.	−	492685.i	0.0929026	−	0.160912i
$394$	1.27860e6	+	2.21460e6i	0.414949	+	0.718712i
$395$			4.14385e6i			1.33632i
$396$	696035.	−	401856.i	0.223045	−	0.128775i
$397$	−3.99550e6	+	2.30681e6i	−1.27232	+	0.734573i	−0.975424	−	0.220338i	$-0.929284\pi$
$397$	−3.99550e6	+	2.30681e6i	−1.27232	+	0.734573i	−0.296893	+	0.954911i	$0.595951\pi$
$398$			3.30518e6i			1.04589i
$399$	433634.	+	751076.i	0.136361	+	0.236185i
$400$	−50745.2	+	87893.2i	−0.0158579	+	0.0274666i
$401$	−1.82505e6	−	1.05369e6i	−0.566780	−	0.327230i	0.189082	−	0.981961i	$-0.439449\pi$
$401$	−1.82505e6	−	1.05369e6i	−0.566780	−	0.327230i	−0.755862	+	0.654731i	$0.772782\pi$
$402$	−4.40455e6			−1.35937
$403$	3.37654e6	+	253905.i	1.03564	+	0.0778770i
$404$	−917367.			−0.279634
$405$	−3.33450e6	−	1.92517e6i	−1.01017	−	0.583220i
$406$	4654.84	−	8062.42i	0.00140149	−	0.00242745i
$407$	1.55593e6	+	2.69494e6i	0.465589	+	0.806424i
$408$		−	1.30964e6i		−	0.389495i
$409$	−1.88221e6	+	1.08669e6i	−0.556365	+	0.321217i	−0.751685	−	0.659522i	$-0.770759\pi$
$409$	−1.88221e6	+	1.08669e6i	−0.556365	+	0.321217i	0.195320	+	0.980739i	$0.437425\pi$
$410$	2.44015e6	−	1.40882e6i	0.716897	−	0.413901i
$411$		−	4.44949e6i		−	1.29929i
$412$	−1.28206e6	−	2.22060e6i	−0.372106	−	0.644506i
$413$	329335.	−	570425.i	0.0950085	−	0.164560i
$414$	1.25179e6	+	722721.i	0.358947	+	0.207238i
$415$	1.15390e6			0.328888
$416$	−270583.	−	562240.i	−0.0766598	−	0.159290i
$417$	−3.27652e6			−0.922725
$418$	−3.10133e6	−	1.79055e6i	−0.868175	−	0.501241i
$419$	921033.	−	1.59528e6i	0.256295	−	0.443916i	−0.708951	−	0.705257i	$-0.750831\pi$
$419$	921033.	−	1.59528e6i	0.256295	−	0.443916i	0.965246	+	0.261341i	$0.0841648\pi$
$420$	−154633.	−	267832.i	−0.0427739	−	0.0740866i
$421$			2.27354e6i			0.625170i	0.949890	+	0.312585i	$0.101195\pi$
$421$			2.27354e6i			0.625170i	−0.949890	+	0.312585i	$0.898805\pi$
$422$	−1.55289e6	+	896559.i	−0.424481	+	0.245074i
$423$	−397365.	+	229419.i	−0.107979	+	0.0623416i
$424$		−	1.85203e6i		−	0.500302i
$425$	−209605.	−	363046.i	−0.0562896	−	0.0974965i
$426$	−92638.9	+	160455.i	−0.0247326	+	0.0428381i
$427$	−87864.0	−	50728.3i	−0.0233207	−	0.0134642i
$428$	−288883.			−0.0762276
$429$	1.95334e6	+	4.05880e6i	0.512430	+	1.06477i
$430$	−4.60084e6			−1.19996
$431$	−310084.	−	179027.i	−0.0804057	−	0.0464222i	0.459258	−	0.888303i	$-0.348115\pi$
$431$	−310084.	−	179027.i	−0.0804057	−	0.0464222i	−0.539664	+	0.841881i	$0.681449\pi$
$432$	−276189.	+	478373.i	−0.0712027	+	0.123327i
$433$	1.92488e6	+	3.33398e6i	0.493382	+	0.854562i	0.999971	−	0.00762540i	$-0.00242726\pi$
$433$	1.92488e6	+	3.33398e6i	0.493382	+	0.854562i	−0.506589	+	0.862188i	$0.669094\pi$
$434$		−	425027.i		−	0.108316i
$435$	−106556.	+	61520.3i	−0.0269995	+	0.0155882i
$436$	−359635.	+	207636.i	−0.0906037	+	0.0523101i
$437$		−	6.44047e6i		−	1.61330i
$438$	−1.85662e6	−	3.21576e6i	−0.462421	−	0.800937i
$439$	2.53969e6	−	4.39887e6i	0.628954	−	1.08938i	−0.358808	−	0.933411i	$-0.616817\pi$
$439$	2.53969e6	−	4.39887e6i	0.628954	−	1.08938i	0.987762	−	0.155969i	$-0.0498499\pi$
$440$	1.10593e6	+	638507.i	0.272330	+	0.157230i
$441$	2.16206e6			0.529386
$442$	2.57004e6	+	193259.i	0.625726	+	0.0470527i
$443$	4.53588e6			1.09813			0.549063	−	0.835781i	$-0.314985\pi$
$443$	4.53588e6			1.09813			0.549063	+	0.835781i	$0.314985\pi$
$444$	2.18447e6	+	1.26121e6i	0.525883	+	0.303619i
$445$	3.24746e6	−	5.62476e6i	0.777399	−	1.34649i
$446$	−390161.	−	675778.i	−0.0928766	−	0.160867i
$447$			9.53432e6i			2.25694i
$448$	−67828.1	+	39160.6i	−0.0159667	+	0.00921837i
$449$	1.00080e6	−	577811.i	0.234277	−	0.135260i	−0.378266	−	0.925697i	$-0.623480\pi$
$449$	1.00080e6	−	577811.i	0.234277	−	0.135260i	0.612544	+	0.790437i	$0.290146\pi$
$450$		−	208533.i		−	0.0485450i
$451$	2.57561e6	+	4.46108e6i	0.596263	+	1.03276i
$452$	−876581.	+	1.51828e6i	−0.201812	+	0.349548i
$453$	608976.	+	351592.i	0.139429	+	0.0804996i
$454$	2.25414e6			0.513264
$455$	548412.	−	263928.i	0.124188	−	0.0597665i
$456$	−2.90278e6			−0.653736
$457$	1.32953e6	+	767605.i	0.297789	+	0.171928i	0.641449	−	0.767166i	$-0.278334\pi$
$457$	1.32953e6	+	767605.i	0.297789	+	0.171928i	−0.343660	+	0.939094i	$0.611667\pi$
$458$	54737.6	−	94808.3i	0.0121933	−	0.0211194i
$459$	−1.14081e6	−	1.97593e6i	−0.252744	−	0.437765i
$460$			2.29666e6i			0.506060i
$461$	5.55254e6	−	3.20576e6i	1.21686	−	0.702552i	0.252612	−	0.967568i	$-0.418710\pi$
$461$	5.55254e6	−	3.20576e6i	1.21686	−	0.702552i	0.964244	+	0.265016i	$0.0853772\pi$
$462$	489651.	−	282700.i	0.106729	−	0.0616199i
$463$		−	3.67970e6i		−	0.797736i	−0.917008	−	0.398868i	$-0.869403\pi$
$463$		−	3.67970e6i		−	0.797736i	0.917008	−	0.398868i	$-0.130597\pi$
$464$	15579.9	+	26985.2i	0.00335947	+	0.00581877i
$465$	−2.80867e6	+	4.86476e6i	−0.602377	+	1.04335i
$466$	1.69699e6	+	979760.i	0.362006	+	0.209004i
$467$	−5.57471e6			−1.18285			−0.591425	−	0.806360i	$-0.701435\pi$
$467$	−5.57471e6			−1.18285			−0.591425	+	0.806360i	$0.701435\pi$
$468$	1.05910e6	+	722482.i	0.223524	+	0.152480i
$469$	−1.08801e6			−0.228403
$470$	−631372.	−	364523.i	−0.131838	−	0.0761167i
$471$	3.56268e6	−	6.17074e6i	0.739988	−	1.28170i
$472$	1.10230e6	+	1.90923e6i	0.227742	+	0.394461i
$473$		−	8.41124e6i		−	1.72865i
$474$	−5.31809e6	+	3.07040e6i	−1.08720	+	0.627696i
$475$	−804679.	+	464582.i	−0.163640	+	0.0944775i
$476$		−	323508.i		−	0.0654437i
$477$	1.90269e6	+	3.29555e6i	0.382888	+	0.663181i
$478$	195271.	−	338219.i	0.0390901	−	0.0677061i
$479$	−1.31283e6	−	757965.i	−0.261439	−	0.150942i	0.363552	−	0.931574i	$-0.381564\pi$
$479$	−1.31283e6	−	757965.i	−0.261439	−	0.150942i	−0.624991	+	0.780632i	$0.714897\pi$
$480$	1.03513e6			0.205064
$481$	−2.79734e6	+	4.10069e6i	−0.551294	+	0.808155i
$482$	−4.45398e6			−0.873234
$483$	880616.	+	508424.i	0.171759	+	0.0991649i
$484$	121089.	−	209733.i	0.0234959	−	0.0406961i
$485$	−2.45751e6	−	4.25654e6i	−0.474397	−	0.821679i
$486$		−	3.60854e6i		−	0.693013i
$487$	522111.	−	301441.i	0.0997563	−	0.0575943i	−0.449292	−	0.893385i	$-0.648324\pi$
$487$	522111.	−	301441.i	0.0997563	−	0.0575943i	0.549048	+	0.835791i	$0.314990\pi$
$488$	294084.	−	169790.i	0.0559014	−	0.0322747i
$489$		−	4.37388e6i		−	0.827171i
$490$	1.71765e6	+	2.97505e6i	0.323180	+	0.559764i
$491$	−3.03369e6	+	5.25451e6i	−0.567895	+	0.983622i	0.428879	+	0.903362i	$0.358909\pi$
$491$	−3.03369e6	+	5.25451e6i	−0.567895	+	0.983622i	−0.996774	+	0.0802605i	$0.974425\pi$
$492$	3.61607e6	+	2.08774e6i	0.673479	+	0.388834i
$493$	−128707.			−0.0238498
$494$	428353.	−	5.69641e6i	0.0789740	−	1.05023i
$495$	−2.62390e6			−0.481320
$496$	1.23199e6	+	711292.i	0.224856	+	0.129821i
$497$	−22883.7	+	39635.7i	−0.00415561	+	0.00719772i
$498$	854986.	+	1.48088e6i	0.154485	+	0.267576i
$499$		−	294588.i		−	0.0529618i	−0.999649	−	0.0264809i	$-0.991570\pi$
$499$		−	294588.i		−	0.0529618i	0.999649	−	0.0264809i	$-0.00843012\pi$
$500$	2.54881e6	−	1.47156e6i	0.455946	−	0.263240i
$501$	2.70226e6	−	1.56015e6i	0.480986	−	0.277697i
$502$		−	4.86924e6i		−	0.862387i
$503$	2.24771e6	+	3.89314e6i	0.396113	+	0.686088i	0.993243	−	0.116057i	$-0.0370254\pi$
$503$	2.24771e6	+	3.89314e6i	0.396113	+	0.686088i	−0.597129	+	0.802145i	$0.703692\pi$
$504$	80463.7	−	139367.i	0.0141099	−	0.0244390i
$505$	2.59370e6	+	1.49747e6i	0.452576	+	0.261295i
$506$	−4.19875e6			−0.729027
$507$	−4.48282e6	+	5.61538e6i	−0.774518	+	0.970196i
$508$	−933654.			−0.160519
$509$	825529.	+	476619.i	0.141234	+	0.0815412i	0.568952	−	0.822371i	$-0.307349\pi$
$509$	825529.	+	476619.i	0.141234	+	0.0815412i	−0.427718	+	0.903912i	$0.640682\pi$
$510$	−2.13781e6	+	3.70279e6i	−0.363951	+	0.630382i
$511$	−458622.	−	794357.i	−0.0776968	−	0.134575i
$512$		−	262144.i		−	0.0441942i
$513$	−4.37960e6	+	2.52856e6i	−0.734752	+	0.424209i
$514$	6.49010e6	−	3.74706e6i	1.08354	−	0.625580i
$515$			8.37116e6i			1.39081i
$516$	−3.40900e6	−	5.90456e6i	−0.563642	−	0.976256i
$517$	666420.	−	1.15427e6i	0.109653	−	0.189925i
$518$	539608.	+	311543.i	0.0883597	+	0.0510145i
$519$	−5.81881e6			−0.948235
$520$	−152750.	+	2.03133e6i	−0.0247726	+	0.329437i
$521$	3.66026e6			0.590769			0.295384	−	0.955378i	$-0.404552\pi$
$521$	3.66026e6			0.590769			0.295384	+	0.955378i	$0.404552\pi$
$522$	−55446.8	−	32012.3i	−0.00890637	−	0.00514209i
$523$	2.11090e6	−	3.65619e6i	0.337454	−	0.584487i	−0.646499	−	0.762915i	$-0.723768\pi$
$523$	2.11090e6	−	3.65619e6i	0.337454	−	0.584487i	0.983953	+	0.178427i	$0.0571010\pi$
$524$	235181.	+	407346.i	0.0374174	+	0.0648089i
$525$		−	146700.i		−	0.0232291i
$526$	−2.87909e6	+	1.66225e6i	−0.453724	+	0.261957i
$527$	−5.08879e6	+	2.93801e6i	−0.798156	+	0.460816i
$528$			1.89242e6i			0.295414i
$529$	−557463.	−	965555.i	−0.0866118	−	0.150016i
$530$	−3.02317e6	+	5.23629e6i	−0.467491	+	0.809719i
$531$	−3.92292e6	−	2.26490e6i	−0.603773	−	0.348588i
$532$	−717045.			−0.109842
$533$	−4.63059e6	+	6.78809e6i	−0.706022	+	1.03498i
$534$	9.62486e6			1.46063
$535$	816768.	+	471561.i	0.123371	+	0.0712285i
$536$	1.82081e6	−	3.15374e6i	0.273749	−	0.474147i
$537$	−2.68032e6	−	4.64245e6i	−0.401099	−	0.694723i
$538$			3.24351e6i			0.483125i
$539$	−5.43899e6	+	3.14020e6i	−0.806393	+	0.465571i
$540$	1.56175e6	−	901679.i	0.230477	−	0.133066i
$541$			1.03047e7i			1.51371i	0.653582	+	0.756856i	$0.273266\pi$
$541$			1.03047e7i			1.51371i	−0.653582	+	0.756856i	$0.726734\pi$
$542$	280872.	+	486485.i	0.0410687	+	0.0711330i
$543$	5.66082e6	−	9.80482e6i	0.823910	−	1.42705i
$544$	937727.	+	541397.i	0.135856	+	0.0784366i
$545$	1.35574e6			0.195518
$546$	745065.	+	508256.i	0.106958	+	0.0729627i
$547$	−5.03080e6			−0.718901			−0.359450	−	0.933164i	$-0.617036\pi$
$547$	−5.03080e6			−0.718901			−0.359450	+	0.933164i	$0.617036\pi$
$548$	3.18591e6	+	1.83939e6i	0.453193	+	0.261651i
$549$	−348869.	+	604258.i	−0.0494005	+	0.0855641i
$550$	302876.	+	524596.i	0.0426931	+	0.0739466i
$551$			285275.i			0.0400299i
$552$	−2.94746e6	+	1.70171e6i	−0.411718	+	0.237705i
$553$	−1.31368e6	+	758451.i	−0.182673	+	0.105467i
$554$		−	5.54431e6i		−	0.767491i
$555$	−4.11748e6	−	7.13169e6i	−0.567413	−	0.982789i
$556$	1.35449e6	−	2.34604e6i	0.185818	−	0.321847i
$557$	2.73734e6	+	1.58040e6i	0.373844	+	0.215839i	0.675137	−	0.737693i	$-0.264085\pi$
$557$	2.73734e6	+	1.58040e6i	0.373844	+	0.215839i	−0.301292	+	0.953532i	$0.597418\pi$
$558$	−2.92300e6			−0.397414
$559$	1.20902e7	−	5.81851e6i	1.63645	−	0.787557i
$560$	255697.			0.0344552
$561$	−6.76944e6	−	3.90834e6i	−0.908126	−	0.524307i
$562$	−2.78090e6	+	4.81666e6i	−0.371403	+	0.643288i
$563$	−6.29451e6	−	1.09024e7i	−0.836933	−	1.44961i	−0.892447	−	0.451152i	$-0.851013\pi$
$563$	−6.29451e6	−	1.09024e7i	−0.836933	−	1.44961i	0.0555140	−	0.998458i	$-0.482320\pi$
$564$		−	1.08038e6i		−	0.143014i
$565$	4.95677e6	−	2.86179e6i	0.653248	−	0.377153i
$566$	3.16255e6	−	1.82590e6i	0.414951	−	0.239572i
$567$		−	1.40946e6i		−	0.184117i
$568$	−76592.5	−	132662.i	−0.00996129	−	0.0172535i
$569$	−5.53329e6	+	9.58395e6i	−0.716478	+	1.24098i	0.245908	+	0.969293i	$0.420914\pi$
$569$	−5.53329e6	+	9.58395e6i	−0.716478	+	1.24098i	−0.962387	+	0.271684i	$0.912419\pi$
$570$	8.20713e6	+	4.73839e6i	1.05804	+	0.610862i
$571$	409116.			0.0525117			0.0262559	−	0.999655i	$-0.491642\pi$
$571$	409116.			0.0525117			0.0262559	+	0.999655i	$0.491642\pi$
$572$	−3.71367e6	−	279257.i	−0.474585	−	0.0356873i
$573$	1.25510e7			1.59696
$574$	893243.	+	515714.i	0.113159	+	0.0653325i
$575$	−544709.	+	943464.i	−0.0687061	+	0.119002i
$576$	269315.	+	466467.i	0.0338224	+	0.0585821i
$577$		−	1.63753e6i		−	0.204762i	−0.994745	−	0.102381i	$-0.967354\pi$
$577$		−	1.63753e6i		−	0.204762i	0.994745	−	0.102381i	$-0.0326461\pi$
$578$	1.04522e6	−	603457.i	0.130133	−	0.0751322i
$579$	1.10353e7	−	6.37124e6i	1.36801	−	0.789819i
$580$		−	101728.i		−	0.0125566i
$581$	211199.	+	365807.i	0.0259568	+	0.0449585i
$582$	3.64180e6	−	6.30779e6i	0.445666	−	0.771915i
$583$	−9.57298e6	−	5.52697e6i	−1.16648	−	0.673465i
$584$	3.07005e6			0.372489
$585$	−1.81509e6	−	3.77154e6i	−0.219285	−	0.455647i
$586$	−275222.			−0.0331085
$587$	9.74809e6	+	5.62806e6i	1.16768	+	0.674161i	0.953133	−	0.302552i	$-0.0978387\pi$
$587$	9.74809e6	+	5.62806e6i	1.16768	+	0.674161i	0.214548	+	0.976713i	$0.431172\pi$
$588$	−2.54539e6	+	4.40875e6i	−0.303607	+	0.525862i
$589$	6.51201e6	+	1.12791e7i	0.773441	+	1.33964i
$590$		−	7.19739e6i		−	0.851226i
$591$	1.07143e7	−	6.18588e6i	1.26181	−	0.728506i
$592$	−1.80609e6	+	1.04275e6i	−0.211805	+	0.122285i
$593$			7.47990e6i			0.873492i	0.899585	+	0.436746i	$0.143869\pi$
$593$			7.47990e6i			0.873492i	−0.899585	+	0.436746i	$0.856131\pi$
$594$	1.64845e6	+	2.85520e6i	0.191694	+	0.332024i
$595$	−528082.	+	914665.i	−0.0611517	+	0.105918i
$596$	−6.82674e6	−	3.94142e6i	−0.787223	−	0.454504i
$597$	1.59905e7			1.83622
$598$	−2.90450e6	−	6.03520e6i	−0.332138	−	0.690142i
$599$	7.02078e6			0.799499			0.399750	−	0.916624i	$-0.369097\pi$
$599$	7.02078e6			0.799499			0.399750	+	0.916624i	$0.369097\pi$
$600$	425228.	+	245506.i	0.0482219	+	0.0278409i
$601$	−3.88725e6	+	6.73292e6i	−0.438992	+	0.760357i	−0.997612	−	0.0690671i	$-0.977998\pi$
$601$	−3.88725e6	+	6.73292e6i	−0.438992	+	0.760357i	0.558620	+	0.829424i	$0.311331\pi$
$602$	−842092.	−	1.45855e6i	−0.0947040	−	0.164032i
$603$			7.48247e6i			0.838015i
$604$	−503493.	+	290692.i	−0.0561566	+	0.0324220i
$605$	−684719.	+	395323.i	−0.0760543	+	0.0439100i
$606$			4.43823e6i			0.490940i
$607$	−7.33673e6	−	1.27076e7i	−0.808222	−	1.39988i	−0.914094	−	0.405501i	$-0.867097\pi$
$607$	−7.33673e6	−	1.27076e7i	−0.808222	−	1.39988i	0.105873	−	0.994380i	$-0.466236\pi$
$608$	1.19999e6	−	2.07844e6i	0.131649	−	0.228023i
$609$	−39006.1	−	22520.2i	−0.00426176	−	0.00246053i
$610$	−1.10863e6			−0.120632
$611$	2.12013e6	+	159427.i	0.229752	+	0.0172767i
$612$	−2.22483e6			−0.240114
$613$	−1.17606e7	−	6.78996e6i	−1.26409	−	0.729820i	−0.290223	−	0.956959i	$-0.593730\pi$
$613$	−1.17606e7	−	6.78996e6i	−1.26409	−	0.729820i	−0.973862	+	0.227139i	$0.927063\pi$
$614$	−5.32010e6	+	9.21468e6i	−0.569507	+	0.986415i
$615$	−6.81589e6	−	1.18055e7i	−0.726666	−	1.25862i
$616$			467465.i			0.0496360i
$617$	4.82515e6	−	2.78580e6i	0.510268	−	0.294603i	−0.222676	−	0.974892i	$-0.571479\pi$
$617$	4.82515e6	−	2.78580e6i	0.510268	−	0.294603i	0.732944	+	0.680289i	$0.238146\pi$
$618$	−1.07433e7	+	6.20263e6i	−1.13153	+	0.653288i
$619$			2.82758e6i			0.296611i	0.988942	+	0.148306i	$0.0473820\pi$
$619$			2.82758e6i			0.296611i	−0.988942	+	0.148306i	$0.952618\pi$
$620$	−2.32217e6	−	4.02212e6i	−0.242613	−	0.420219i
$621$	−2.96467e6	+	5.13495e6i	−0.308494	+	0.534327i
$622$	−7.66655e6	−	4.42628e6i	−0.794555	−	0.458737i
$623$	2.37753e6			0.245418
$624$	−2.72012e6	+	1.30908e6i	−0.279658	+	0.134588i
$625$	−8.36956e6			−0.857043
$626$	−2.19977e6	−	1.27004e6i	−0.224358	−	0.129533i
$627$	−8.66271e6	+	1.50043e7i	−0.880005	+	1.52421i
$628$	2.94558e6	+	5.10189e6i	0.298038	+	0.516216i
$629$		−	8.61420e6i		−	0.868137i
$630$	−454995.	+	262691.i	−0.0456725	+	0.0263691i
$631$	−7.38560e6	+	4.26408e6i	−0.738435	+	0.426336i	−0.821500	−	0.570209i	$-0.806862\pi$
$631$	−7.38560e6	+	4.26408e6i	−0.738435	+	0.426336i	0.0830651	+	0.996544i	$0.473529\pi$
$632$		−	5.07713e6i		−	0.505622i
$633$	4.33756e6	+	7.51288e6i	0.430265	+	0.745241i
$634$	4.59136e6	−	7.95247e6i	0.453647	−	0.785740i
$635$	2.63975e6	+	1.52406e6i	0.259794	+	0.149992i
$636$	−8.96012e6			−0.878357
$637$	−8.27611e6	−	5.64566e6i	−0.808123	−	0.551272i
$638$	185980.			0.0180890
$639$	272582.	+	157375.i	0.0264086	+	0.0152470i
$640$	−427914.	+	741168.i	−0.0412958	+	0.0715265i
$641$	8.69681e6	+	1.50633e7i	0.836016	+	1.44802i	0.893200	+	0.449659i	$0.148455\pi$
$641$	8.69681e6	+	1.50633e7i	0.836016	+	1.44802i	−0.0571837	+	0.998364i	$0.518212\pi$
$642$			1.39762e6i			0.133829i
$643$	−2.63671e6	+	1.52230e6i	−0.251498	+	0.145203i	−0.620450	−	0.784246i	$-0.713050\pi$
$643$	−2.63671e6	+	1.52230e6i	−0.251498	+	0.145203i	0.368952	+	0.929448i	$0.379717\pi$
$644$	−728081.	+	420358.i	−0.0691775	+	0.0399397i
$645$			2.22589e7i			2.10671i
$646$	4.95659e6	+	8.58507e6i	0.467307	+	0.809399i
$647$	−436205.	+	755529.i	−0.0409666	+	0.0709562i	−0.885782	−	0.464102i	$-0.846377\pi$
$647$	−436205.	+	755529.i	−0.0409666	+	0.0709562i	0.844815	+	0.535058i	$0.179710\pi$
$648$	4.08549e6	+	2.35876e6i	0.382214	+	0.220671i
$649$	1.31583e7			1.22627
$650$	−544529.	+	798239.i	−0.0505520	+	0.0741054i
$651$	−2.05629e6			−0.190165
$652$	3.13178e6	+	1.80813e6i	0.288517	+	0.166576i
$653$	9.82192e6	−	1.70121e7i	0.901391	−	1.56126i	0.0757021	−	0.997130i	$-0.475880\pi$
$653$	9.82192e6	−	1.70121e7i	0.901391	−	1.56126i	0.825689	−	0.564125i	$-0.190786\pi$
$654$	1.00454e6	+	1.73992e6i	0.0918384	+	0.159069i
$655$		−	1.53560e6i		−	0.139854i
$656$	−2.98972e6	+	1.72611e6i	−0.271251	+	0.156607i
$657$	−5.46295e6	+	3.15404e6i	−0.493758	+	0.285071i
$658$		−	266875.i		−	0.0240294i
$659$	4.81181e6	+	8.33430e6i	0.431613	+	0.747576i	0.997012	−	0.0772411i	$-0.0246111\pi$
$659$	4.81181e6	+	8.33430e6i	0.431613	+	0.747576i	−0.565399	+	0.824818i	$0.691278\pi$
$660$	3.08911e6	−	5.35049e6i	0.276041	−	0.478116i
$661$	−1.38540e7	−	7.99863e6i	−1.23331	−	0.712052i	−0.265592	−	0.964085i	$-0.585567\pi$
$661$	−1.38540e7	−	7.99863e6i	−1.23331	−	0.712052i	−0.967719	+	0.252033i	$0.918901\pi$
$662$	7.68526e6			0.681575
$663$	934990.	−	1.24339e7i	0.0826082	−	1.09856i
$664$	−1.41378e6			−0.124441
$665$	2.02733e6	+	1.17048e6i	0.177774	+	0.102638i
$666$	2.14254e6	−	3.71099e6i	0.187173	−	0.324194i
$667$	167238.	+	289665.i	0.0145553	+	0.0252105i
$668$			2.57982e6i			0.223691i
$669$	−3.26942e6	+	1.88760e6i	−0.282427	+	0.163059i
$670$	−1.02961e7	+	5.94444e6i	−0.886103	+	0.511592i
$671$		−	2.02680e6i		−	0.173782i
$672$	189459.	+	328153.i	0.0161843	+	0.0280319i
$673$	2.54875e6	−	4.41457e6i	0.216915	−	0.375708i	−0.736948	−	0.675949i	$-0.763734\pi$
$673$	2.54875e6	−	4.41457e6i	0.216915	−	0.375708i	0.953863	+	0.300241i	$0.0970671\pi$
$674$	1.99074e6	+	1.14935e6i	0.168797	+	0.0974550i
$675$	855423.			0.0722639
$676$	−2.16755e6	−	5.53114e6i	−0.182432	−	0.465530i
$677$	2.72355e6			0.228383			0.114191	−	0.993459i	$-0.463572\pi$
$677$	2.72355e6			0.228383			0.114191	+	0.993459i	$0.463572\pi$
$678$	7.34547e6	+	4.24091e6i	0.613685	+	0.354311i
$679$	899599.	−	1.55815e6i	0.0748815	−	0.129699i
$680$	−1.76751e6	−	3.06142e6i	−0.146585	−	0.253893i
$681$		−	1.09055e7i		−	0.901113i
$682$	7.35323e6	−	4.24539e6i	0.605365	−	0.349508i
$683$	−1.06956e7	+	6.17513e6i	−0.877314	+	0.506518i	−0.869772	−	0.493454i	$-0.835734\pi$
$683$	−1.06956e7	+	6.17513e6i	−0.877314	+	0.506518i	−0.00754239	+	0.999972i	$0.502401\pi$
$684$			4.93126e6i			0.403012i
$685$	−6.00509e6	−	1.04011e7i	−0.488983	−	0.846943i
$686$	−1.27151e6	+	2.20232e6i	−0.103159	+	0.178677i
$687$	−458683.	−	264821.i	−0.0370784	−	0.0214072i
$688$	5.63703e6			0.454025
$689$	1.32221e6	−	1.75833e7i	0.106109	−	1.41108i
$690$	1.11113e7			0.888465
$691$	5.82080e6	+	3.36064e6i	0.463754	+	0.267749i	0.713621	−	0.700531i	$-0.247054\pi$
$691$	5.82080e6	+	3.36064e6i	0.463754	+	0.267749i	−0.249867	+	0.968280i	$0.580387\pi$
$692$	2.40546e6	−	4.16637e6i	0.190956	−	0.330745i
$693$	−480252.	−	831821.i	−0.0379871	−	0.0657956i
$694$		−	1.05530e7i		−	0.831719i
$695$	−7.65918e6	+	4.42203e6i	−0.601479	+	0.347264i
$696$	130555.	−	75375.9i	0.0102157	−	0.00589806i
$697$		−	1.42595e7i		−	1.11179i
$698$	−2.49389e6	−	4.31954e6i	−0.193749	−	0.335582i
$699$	4.74009e6	−	8.21008e6i	0.366939	−	0.635557i
$700$	105040.	+	60644.8i	0.00810232	+	0.00467788i
$701$	1.81950e7			1.39848			0.699241	−	0.714886i	$-0.253521\pi$
$701$	1.81950e7			1.39848			0.699241	+	0.714886i	$0.253521\pi$
$702$	−2.96369e6	+	4.34454e6i	−0.226981	+	0.332737i
$703$	−1.90931e7			−1.45710
$704$	−1.35500e6	−	782311.i	−0.103041	−	0.0594906i
$705$	−1.76356e6	+	3.05458e6i	−0.133634	+	0.231462i
$706$	3.01982e6	+	5.23049e6i	0.228018	+	0.394939i
$707$			1.09633e6i			0.0824885i
$708$	9.23690e6	−	5.33292e6i	0.692537	−	0.399836i
$709$	−1.50923e7	+	8.71354e6i	−1.12756	+	0.650997i	−0.943320	−	0.331884i	$-0.892316\pi$
$709$	−1.50923e7	+	8.71354e6i	−1.12756	+	0.650997i	−0.184240	+	0.982881i	$0.558982\pi$
$710$			500107.i			0.0372320i
$711$	5.21602e6	+	9.03441e6i	0.386959	+	0.670233i
$712$	−3.97885e6	+	6.89157e6i	−0.294142	+	0.509469i
$713$	1.32245e7	+	7.63515e6i	0.974214	+	0.562463i
$714$	−1.56513e6			−0.114896
$715$	1.00439e7	+	6.85161e6i	0.734749	+	0.501219i
$716$	4.43211e6			0.323093
$717$	−1.63631e6	−	944721.i	−0.118868	−	0.0686287i
$718$	1.15357e6	−	1.99804e6i	0.0835087	−	0.144641i
$719$	−2.30109e6	−	3.98561e6i	−0.166001	−	0.287523i	0.771009	−	0.636824i	$-0.219752\pi$
$719$	−2.30109e6	−	3.98561e6i	−0.166001	−	0.287523i	−0.937010	+	0.349301i	$0.886419\pi$
$720$		−	1.75848e6i		−	0.126417i
$721$	−2.65380e6	+	1.53217e6i	−0.190121	+	0.109767i
$722$	1.04511e7	−	6.03394e6i	0.746137	−	0.430782i
$723$			2.15484e7i			1.53310i
$724$	4.68029e6	+	8.10649e6i	0.331838	+	0.574760i
$725$	24127.4	−	41789.9i	0.00170477	−	0.00295275i
$726$	−1.01469e6	−	585831.i	−0.0714482	−	0.0412506i
$727$	2.47173e7			1.73446			0.867231	−	0.497905i	$-0.165897\pi$
$727$	2.47173e7			1.73446			0.867231	+	0.497905i	$0.165897\pi$
$728$	−671925.	+	323370.i	−0.0469886	+	0.0226137i
$729$	453661.			0.0316164
$730$	−8.68006e6	−	5.01144e6i	−0.602859	−	0.348061i
$731$	−1.16420e7	+	2.01645e7i	−0.805811	+	1.39570i
$732$	−821444.	−	1.42278e6i	−0.0566631	−	0.0981434i
$733$		−	6.19827e6i		−	0.426099i	−0.977041	−	0.213050i	$-0.931660\pi$
$733$		−	6.19827e6i		−	0.426099i	0.977041	−	0.213050i	$-0.0683396\pi$
$734$	−9.97797e6	+	5.76078e6i	−0.683600	+	0.394676i
$735$	1.43933e7	−	8.31000e6i	0.982751	−	0.567391i
$736$		−	2.81391e6i		−	0.191476i
$737$	−1.08676e7	−	1.88233e7i	−0.736997	−	1.27652i
$738$	3.54667e6	−	6.14301e6i	0.239706	−	0.415184i
$739$	−1.71679e7	−	9.91188e6i	−1.15639	−	0.667644i	−0.205957	−	0.978561i	$-0.566031\pi$
$739$	−1.71679e7	−	9.91188e6i	−1.15639	−	0.667644i	−0.950437	+	0.310917i	$0.899364\pi$
$740$	6.80856e6			0.457063
$741$	−2.75593e7	−	2.07238e6i	−1.84384	−	0.138651i
$742$	−2.21333e6			−0.147583
$743$	1.57575e7	+	9.09760e6i	1.04717	+	0.604581i	0.921855	−	0.387536i	$-0.126674\pi$
$743$	1.57575e7	+	9.09760e6i	1.04717	+	0.604581i	0.125311	+	0.992117i	$0.460007\pi$
$744$	3.44124e6	−	5.96040e6i	0.227920	−	0.394769i
$745$	1.28676e7	+	2.22874e7i	0.849393	+	1.47119i
$746$			1.08569e7i			0.714264i
$747$	2.51573e6	−	1.45246e6i	0.164954	−	0.0952361i
$748$	5.59688e6	−	3.23136e6i	0.365757	−	0.211170i
$749$			345240.i			0.0224862i
$750$	−7.11941e6	−	1.23312e7i	−0.462159	−	0.800482i
$751$	7.60897e6	−	1.31791e7i	0.492296	−	0.852681i	−0.507665	−	0.861555i	$-0.669491\pi$
$751$	7.60897e6	−	1.31791e7i	0.492296	−	0.852681i	0.999961	+	0.00887332i	$0.00282450\pi$
$752$	773569.	+	446620.i	0.0498832	+	0.0288001i
$753$	−2.35575e7			−1.51405
$754$	128652.	+	267324.i	0.00824116	+	0.0171241i
$755$	1.89805e6			0.121183
$756$	571697.	+	330069.i	0.0363799	+	0.0210039i
$757$	1.67971e6	−	2.90934e6i	0.106535	−	0.184525i	−0.807829	−	0.589417i	$-0.799358\pi$
$757$	1.67971e6	−	2.90934e6i	0.106535	−	0.184525i	0.914364	+	0.404892i	$0.132691\pi$
$758$	−5.94917e6	−	1.03043e7i	−0.376083	−	0.651394i
$759$			2.03136e7i			1.27992i
$760$	−6.78554e6	+	3.91763e6i	−0.426138	+	0.246031i
$761$	1.58560e7	−	9.15447e6i	0.992504	−	0.573023i	0.0864823	−	0.996253i	$-0.472437\pi$
$761$	1.58560e7	−	9.15447e6i	0.992504	−	0.573023i	0.906022	+	0.423231i	$0.139104\pi$
$762$			4.51703e6i			0.281816i
$763$	248142.	+	429795.i	0.0154308	+	0.0267270i
$764$	−5.18851e6	+	8.98676e6i	−0.321595	+	0.557019i
$765$	6.29033e6	+	3.63172e6i	0.388615	+	0.224367i
$766$	1.62111e7			0.998250
$767$	9.10227e6	+	1.89134e7i	0.558677	+	1.16087i
$768$	−1.26826e6			−0.0775896
$769$	−1.51071e7	−	8.72210e6i	−0.921225	−	0.531869i	−0.0371993	−	0.999308i	$-0.511844\pi$
$769$	−1.51071e7	−	8.72210e6i	−0.921225	−	0.531869i	−0.884026	+	0.467438i	$0.845177\pi$
$770$	763071.	−	1.32168e6i	0.0463808	−	0.0803339i
$771$	−1.81283e7	−	3.13992e7i	−1.09830	−	1.90231i
$772$			1.05353e7i			0.636215i
$773$	−2.50721e7	+	1.44754e7i	−1.50918	+	0.871327i	−0.509240	+	0.860624i	$0.670074\pi$
$773$	−2.50721e7	+	1.44754e7i	−1.50918	+	0.871327i	−0.999943	+	0.0107031i	$0.996593\pi$
$774$	−1.00307e7	+	5.79123e6i	−0.601838	+	0.347471i
$775$		−	2.20304e6i		−	0.131755i
$776$	3.01099e6	+	5.21519e6i	0.179496	+	0.310897i
$777$	1.50725e6	−	2.61063e6i	0.0895638	−	0.155129i
$778$	−1.66374e7	−	9.60558e6i	−0.985452	−	0.568951i
$779$	−3.16058e7			−1.86605
$780$	9.82759e6	+	739005.i	0.578376	+	0.0434921i
$781$	−914295.			−0.0536363
$782$	1.00658e7	+	5.81147e6i	0.588613	+	0.339836i
$783$	131317.	−	227448.i	0.00765450	−	0.0132580i
$784$	−2.10450e6	−	3.64509e6i	−0.122281	−	0.211796i
$785$		−	1.92330e7i		−	1.11397i
$786$	1.97074e6	−	1.13781e6i	0.113782	−	0.0656920i
$787$	4.87944e6	−	2.81715e6i	0.280823	−	0.162133i	−0.352973	−	0.935634i	$-0.614829\pi$
$787$	4.87944e6	−	2.81715e6i	0.280823	−	0.162133i	0.633796	+	0.773500i	$0.281496\pi$
$788$			1.02288e7i			0.586826i
$789$	8.04196e6	+	1.39291e7i	0.459906	+	0.796581i
$790$	−8.28771e6	+	1.43547e7i	−0.472462	+	0.818328i
$791$	1.81448e6	+	1.04759e6i	0.103112	+	0.0595319i
$792$	3.21485e6			0.182116
$793$	2.91329e6	−	1.40205e6i	0.164513	−	0.0791734i
$794$	−1.84544e7			−1.03884
$795$	2.53332e7	+	1.46261e7i	1.42158	+	0.820752i
$796$	−6.61035e6	+	1.14495e7i	−0.369779	+	0.640476i
$797$	−1.38018e7	−	2.39055e7i	−0.769646	−	1.33307i	−0.937755	−	0.347298i	$-0.887099\pi$
$797$	−1.38018e7	−	2.39055e7i	−0.769646	−	1.33307i	0.168109	−	0.985768i	$-0.446234\pi$
$798$			3.46907e6i			0.192844i
$799$	−3.19525e6	+	1.84478e6i	−0.177067	+	0.102230i
$800$	−351573.	+	202981.i	−0.0194218	+	0.0112132i
$801$		−	1.63508e7i		−	0.900444i
$802$	−4.21478e6	−	7.30021e6i	−0.231387	−	0.400774i
$803$	9.16190e6	−	1.58689e7i	0.501415	−	0.868475i
$804$	−1.52578e7	−	8.80910e6i	−0.832438	−	0.480608i
$805$	2.74470e6			0.149281
$806$	1.11889e7	+	7.63263e6i	0.606664	+	0.413844i
$807$	1.56921e7			0.848200
$808$	−3.17785e6	−	1.83473e6i	−0.171240	−	0.0988654i
$809$	−7.09257e6	+	1.22847e7i	−0.381007	+	0.659923i	−0.991206	−	0.132325i	$-0.957756\pi$
$809$	−7.09257e6	+	1.22847e7i	−0.381007	+	0.659923i	0.610200	+	0.792248i	$0.291089\pi$
$810$	−7.70069e6	−	1.33380e7i	−0.412399	−	0.714295i
$811$			2.59109e7i			1.38334i	0.722212	+	0.691671i	$0.243125\pi$
$811$			2.59109e7i			1.38334i	−0.722212	+	0.691671i	$0.756875\pi$
$812$	32249.7	−	18619.4i	0.00171647	−	0.000991002i
$813$	2.35362e6	−	1.35886e6i	0.124885	−	0.0721023i
$814$			1.24474e7i			0.658442i
$815$	−5.90305e6	−	1.02244e7i	−0.311303	−	0.539192i
$816$	2.61928e6	−	4.53673e6i	0.137707	−	0.238516i
$817$	4.46939e7	+	2.58041e7i	2.34257	+	1.35249i
$818$	−8.69355e6			−0.454270
$819$	863428.	−	1.26572e6i	0.0449797	−	0.0659368i
$820$	1.12706e7			0.585344
$821$	7.83145e6	+	4.52149e6i	0.405494	+	0.234112i	0.688852	−	0.724902i	$-0.258115\pi$
$821$	7.83145e6	+	4.52149e6i	0.405494	+	0.234112i	−0.283358	+	0.959014i	$0.591448\pi$
$822$	8.89898e6	−	1.54135e7i	0.459368	−	0.795649i
$823$	1.51844e7	+	2.63002e7i	0.781446	+	1.35350i	0.931099	+	0.364766i	$0.118851\pi$
$823$	1.51844e7	+	2.63002e7i	0.781446	+	1.35350i	−0.149653	+	0.988739i	$0.547816\pi$
$824$		−	1.02565e7i		−	0.526237i
$825$	2.53800e6	−	1.46532e6i	0.129825	−	0.0749543i
$826$	2.28170e6	−	1.31734e6i	0.116361	−	0.0671812i
$827$		−	2.58958e7i		−	1.31664i	−0.752740	−	0.658318i	$-0.771268\pi$
$827$		−	2.58958e7i		−	1.31664i	0.752740	−	0.658318i	$-0.228732\pi$
$828$	2.89088e6	+	5.00716e6i	0.146540	+	0.253814i
$829$	−6.94503e6	+	1.20291e7i	−0.350984	+	0.607923i	−0.986422	−	0.164229i	$-0.947486\pi$
$829$	−6.94503e6	+	1.20291e7i	−0.350984	+	0.607923i	0.635438	+	0.772152i	$0.280820\pi$
$830$	3.99723e6	+	2.30780e6i	0.201402	+	0.116280i
$831$	−2.68234e7			−1.34745
$832$	187152.	−	2.48882e6i	0.00937316	−	0.124648i
$833$	1.73854e7			0.868103
$834$	−1.13502e7	−	6.55303e6i	−0.565051	−	0.326233i
$835$	4.21120e6	−	7.29401e6i	0.209021	−	0.362035i
$836$	−7.16221e6	−	1.24053e7i	−0.354431	−	0.613892i
$837$		−	1.19904e7i		−	0.591589i
$838$	6.38110e6	−	3.68413e6i	0.313896	−	0.181228i
$839$	3.26871e6	−	1.88719e6i	0.160314	−	0.0925574i	−0.417697	−	0.908587i	$-0.637162\pi$
$839$	3.26871e6	−	1.88719e6i	0.160314	−	0.0925574i	0.578011	+	0.816029i	$0.303829\pi$
$840$		−	1.23706e6i		−	0.0604914i
$841$	1.02482e7	+	1.77503e7i	0.499639	+	0.865400i
$842$	−4.54708e6	+	7.87578e6i	−0.221031	+	0.382837i
$843$	2.33031e7	+	1.34540e7i	1.12939	+	0.652054i
$844$	−7.17247e6			−0.346587
$845$	−2.90044e6	+	1.91766e7i	−0.139741	+	0.923910i
$846$	−1.83535e6			−0.0881643
$847$	−250649.	−	144712.i	−0.0120048	−	0.00693100i
$848$	3.70405e6	−	6.41560e6i	0.176883	−	0.306371i
$849$	−8.83373e6	−	1.53005e7i	−0.420605	−	0.728510i
$850$		−	1.67684e6i		−	0.0796056i
$851$	−1.93870e7	+	1.11931e7i	−0.917668	+	0.529816i
$852$	−641821.	+	370555.i	−0.0302911	+	0.0174886i
$853$		−	2.15044e7i		−	1.01194i	−0.862551	−	0.505970i	$-0.831134\pi$
$853$		−	2.15044e7i		−	1.01194i	0.862551	−	0.505970i	$-0.168866\pi$
$854$	−202913.	−	351456.i	−0.00952063	−	0.0164902i
$855$	8.04960e6	−	1.39423e7i	0.376582	−	0.652258i
$856$	−1.00072e6	−	577766.i	−0.0466797	−	0.0269505i
$857$	3.57752e6			0.166391			0.0831954	−	0.996533i	$-0.473487\pi$
$857$	3.57752e6			0.166391			0.0831954	+	0.996533i	$0.473487\pi$
$858$	−1.35105e6	+	1.79668e7i	−0.0626545	+	0.833206i
$859$	3.10648e7			1.43643			0.718217	−	0.695819i	$-0.244959\pi$
$859$	3.10648e7			1.43643			0.718217	+	0.695819i	$0.244959\pi$
$860$	−1.59378e7	−	9.20167e6i	−0.734820	−	0.424249i
$861$	2.49503e6	−	4.32152e6i	0.114701	−	0.198668i
$862$	−716109.	−	1.24034e6i	−0.0328255	−	0.0568554i
$863$		−	2.54355e6i		−	0.116255i	−0.998309	−	0.0581277i	$-0.981487\pi$
$863$		−	2.54355e6i		−	0.116255i	0.998309	−	0.0581277i	$-0.0185131\pi$
$864$	−1.91349e6	+	1.10475e6i	−0.0872051	+	0.0503479i
$865$	−1.36021e7	+	7.85315e6i	−0.618108	+	0.356865i
$866$			1.53990e7i			0.697747i
$867$	−2.91953e6	−	5.05677e6i	−0.131906	−	0.228468i
$868$	850055.	−	1.47234e6i	0.0382955	−	0.0663297i
$869$	−2.62433e7	−	1.51516e7i	−1.17888	−	0.680626i
$870$	−492163.			−0.0220450
$871$	1.95385e7	−	2.86420e7i	0.872661	−	1.27926i
$872$	−1.66108e6			−0.0739777
$873$	−1.07157e7	−	6.18672e6i	−0.475867	−	0.274742i
$874$	1.28809e7	−	2.23104e7i	0.570386	−	0.987938i
$875$	−1.75864e6	−	3.04605e6i	−0.0776527	−	0.134498i
$876$		−	1.48530e7i		−	0.653962i
$877$	3.74382e7	−	2.16150e7i	1.64368	−	0.948977i	0.664166	−	0.747586i	$-0.268787\pi$
$877$	3.74382e7	−	2.16150e7i	1.64368	−	0.948977i	0.979511	−	0.201391i	$-0.0645463\pi$
$878$	1.75955e7	−	1.01587e7i	0.770308	−	0.444738i
$879$			1.33153e6i			0.0581270i
$880$	2.55403e6	+	4.42371e6i	0.111178	+	0.192566i
$881$	−1.87151e6	+	3.24156e6i	−0.0812369	+	0.140706i	−0.903781	−	0.427994i	$-0.859220\pi$
$881$	−1.87151e6	+	3.24156e6i	−0.0812369	+	0.140706i	0.822545	+	0.568701i	$0.192554\pi$
$882$	7.48961e6	+	4.32413e6i	0.324181	+	0.187166i
$883$	−2.87001e7			−1.23874			−0.619371	−	0.785098i	$-0.712612\pi$
$883$	−2.87001e7			−1.23874			−0.619371	+	0.785098i	$0.712612\pi$
$884$	8.51636e6	+	5.80955e6i	0.366542	+	0.250041i
$885$	−3.48210e7			−1.49446
$886$	1.57127e7	+	9.07176e6i	0.672462	+	0.388246i
$887$	−5.43141e6	+	9.40748e6i	−0.231795	+	0.401480i	−0.958336	−	0.285642i	$-0.907793\pi$
$887$	−5.43141e6	+	9.40748e6i	−0.231795	+	0.401480i	0.726542	+	0.687123i	$0.241126\pi$
$888$	5.04482e6	+	8.73789e6i	0.214691	+	0.371855i
$889$			1.11580e6i			0.0473512i
$890$	2.24991e7	−	1.29898e7i	0.952115	−	0.549704i
$891$	2.43845e7	−	1.40784e7i	1.02901	−	0.594099i
$892$		−	3.12128e6i		−	0.131347i
$893$	4.08889e6	+	7.08217e6i	0.171584	+	0.297192i
$894$	−1.90686e7	+	3.30279e7i	−0.797951	+	1.38209i
$895$	−1.25310e7	−	7.23480e6i	−0.522913	−	0.301904i
$896$	−313285.			−0.0130367
$897$	−2.91984e7	+	1.40520e7i	−1.21165	+	0.583118i
$898$	4.62249e6			0.191287
$899$	−585766.	−	338192.i	−0.0241727	−	0.0139561i
$900$	417067.	−	722381.i	0.0171632	−	0.0297276i
$901$	1.52997e7	+	2.64999e7i	0.627872	+	1.08751i
$902$			2.06049e7i			0.843244i
$903$	−7.05646e6	+	4.07405e6i	−0.287984	+	0.166267i
$904$	−6.07313e6	+	3.50632e6i	−0.247168	+	0.142702i
$905$		−	3.05597e7i		−	1.24030i
$906$	1.40637e6	+	2.43590e6i	0.0569218	+	0.0985915i
$907$	−1.29232e7	+	2.23836e7i	−0.521615	+	0.903464i	0.478069	+	0.878322i	$0.341337\pi$
$907$	−1.29232e7	+	2.23836e7i	−0.521615	+	0.903464i	−0.999684	+	0.0251416i	$0.991996\pi$
$908$	7.80855e6	+	4.50827e6i	0.314308	+	0.181466i
$909$	7.53969e6			0.302652
$910$	2.42761e6	+	182549.i	0.0971798	+	0.00730762i
$911$	−4.52408e7			−1.80607			−0.903034	−	0.429569i	$-0.858666\pi$
$911$	−4.52408e7			−1.80607			−0.903034	+	0.429569i	$0.858666\pi$
$912$	−1.00555e7	−	5.80556e6i	−0.400330	−	0.231130i
$913$	−4.21912e6	+	7.30774e6i	−0.167512	+	0.290139i
$914$	3.07042e6	+	5.31812e6i	0.121572	+	0.210568i
$915$			5.36358e6i			0.211788i
$916$	379233.	−	218950.i	0.0149337	−	0.00862198i
$917$	486813.	−	281062.i	0.0191178	−	0.0110377i
$918$		−	9.12645e6i		−	0.357433i
$919$	5.97780e6	+	1.03538e7i	0.233481	+	0.404402i	0.958830	−	0.283980i	$-0.0916549\pi$
$919$	5.97780e6	+	1.03538e7i	0.233481	+	0.404402i	−0.725349	+	0.688381i	$0.758322\pi$
$920$	−4.59331e6	+	7.95585e6i	−0.178919	+	0.309897i
$921$	4.45807e7	+	2.57387e7i	1.73180	+	0.999856i
$922$	2.56461e7			0.993559
$923$	−632466.	−	1.31419e6i	−0.0244362	−	0.0507755i
$924$	2.26160e6			0.0871436
$925$	2.79695e6	+	1.61482e6i	0.107481	+	0.0620540i
$926$	7.35939e6	−	1.27468e7i	0.282042	−	0.488512i
$927$	1.05371e7	+	1.82507e7i	0.402736	+	0.697559i
$928$			124639.i			0.00475101i
$929$	−3.86170e7	+	2.22955e7i	−1.46805	+	0.847576i	−0.999359	−	0.0357884i	$-0.988606\pi$
$929$	−3.86170e7	+	2.22955e7i	−1.46805	+	0.847576i	−0.468686	+	0.883365i	$0.655272\pi$
$930$	−1.94590e7	+	1.12347e7i	−0.737758	+	0.425945i
$931$		−	3.85341e7i		−	1.45704i
$932$	3.91904e6	+	6.78798e6i	0.147788	+	0.255977i
$933$	−2.14144e7	+	3.70908e7i	−0.805382	+	1.39496i
$934$	−1.93114e7	−	1.11494e7i	−0.724345	−	0.418201i
$935$	−2.10990e7			−0.789283
$936$	2.22388e6	+	4.62096e6i	0.0829702	+	0.172402i
$937$	−4.58884e7			−1.70747			−0.853737	−	0.520705i	$-0.825669\pi$
$937$	−4.58884e7			−1.70747			−0.853737	+	0.520705i	$0.825669\pi$
$938$	−3.76898e6	−	2.17602e6i	−0.139868	−	0.0807526i
$939$	−6.14446e6	+	1.06425e7i	−0.227415	+	0.393895i
$940$	−1.45809e6	−	2.52549e6i	−0.0538226	−	0.0932235i
$941$		−	2.52187e7i		−	0.928430i	−0.885723	−	0.464215i	$-0.846337\pi$
$941$		−	2.52187e7i		−	0.928430i	0.885723	−	0.464215i	$-0.153663\pi$
$942$	2.46830e7	−	1.42507e7i	0.906296	−	0.523250i
$943$	−3.20923e7	+	1.85285e7i	−1.17523	+	0.678517i
$944$			8.81838e6i			0.322076i
$945$	−1.07758e6	−	1.86643e6i	−0.0392529	−	0.0679880i
$946$	1.68225e7	−	2.91374e7i	0.611171	−	1.05858i
$947$	−1.72805e7	−	9.97692e6i	−0.626155	−	0.361511i	0.153106	−	0.988210i	$-0.451072\pi$
$947$	−1.72805e7	−	9.97692e6i	−0.626155	−	0.361511i	−0.779262	+	0.626699i	$0.784406\pi$
$948$	−2.45632e7			−0.887696
$949$	2.91474e7	+	2.19180e6i	1.05059	+	0.0790014i
$950$	−3.71666e6			−0.133611
$951$	−3.84741e7	−	2.22131e7i	−1.37949	−	0.796447i
$952$	647016.	−	1.12066e6i	0.0231378	−	0.0400759i
$953$	2.01711e7	+	3.49373e7i	0.719443	+	1.24611i	0.961221	+	0.275780i	$0.0889362\pi$
$953$	2.01711e7	+	3.49373e7i	0.719443	+	1.24611i	−0.241778	+	0.970332i	$0.577731\pi$
$954$			1.52215e7i			0.541485i
$955$	2.93393e7	−	1.69390e7i	1.04098	−	0.601008i
$956$	1.35287e6	−	781083.i	0.0478754	−	0.0276409i
$957$		−	899771.i		−	0.0317579i
$958$	−3.03186e6	−	5.25134e6i	−0.106732	−	0.184866i
$959$	2.19823e6	−	3.80744e6i	0.0771838	−	0.133686i
$960$	3.58578e6	+	2.07025e6i	0.125576	+	0.0725011i
$961$	−2.25072e6			−0.0786163
$962$	−1.78917e7	+	8.61053e6i	−0.623323	+	0.299980i
$963$	2.37428e6			0.0825024
$964$	−1.54290e7	−	8.90796e6i	−0.534745	−	0.308735i
$965$	1.71974e7	−	2.97868e7i	0.594491	−	1.02969i
$966$	2.03370e6	+	3.52246e6i	0.0701202	+	0.121452i
$967$			3.93424e7i			1.35299i	0.736447	+	0.676496i	$0.236502\pi$
$967$			3.93424e7i			1.35299i	−0.736447	+	0.676496i	$0.763498\pi$
$968$	838931.	−	484357.i	0.0287765	−	0.0166141i
$969$	4.15347e7	−	2.39801e7i	1.42102	−	0.820428i
$970$		−	1.96601e7i		−	0.670898i
$971$	−1.27614e7	−	2.21033e7i	−0.434359	−	0.752332i	0.562884	−	0.826536i	$-0.309692\pi$
$971$	−1.27614e7	−	2.21033e7i	−0.434359	−	0.752332i	−0.997243	+	0.0742036i	$0.976359\pi$
$972$	7.21709e6	−	1.25004e7i	0.245017	−	0.424382i
$973$	−2.80372e6	−	1.61873e6i	−0.0949409	−	0.0548141i
$974$	2.41153e6			0.0814507
$975$	3.86189e6	+	2.63444e6i	0.130103	+	0.0887517i
$976$	1.35832e6			0.0456433
$977$	−1.33197e7	−	7.69015e6i	−0.446436	−	0.257750i	0.259888	−	0.965639i	$-0.416314\pi$
$977$	−1.33197e7	−	7.69015e6i	−0.446436	−	0.257750i	−0.706324	+	0.707889i	$0.749648\pi$
$978$	8.74777e6	−	1.51516e7i	0.292449	−	0.506537i
$979$	2.37480e7	+	4.11328e7i	0.791900	+	1.37161i
$980$			1.37412e7i			0.457045i
$981$	2.95579e6	−	1.70652e6i	0.0980620	−	0.0566161i
$982$	−2.10180e7	+	1.21348e7i	−0.695526	+	0.401562i
$983$			1.23631e7i			0.408077i	0.978963	+	0.204038i	$0.0654067\pi$
$983$			1.23631e7i			0.408077i	−0.978963	+	0.204038i	$0.934593\pi$
$984$	8.35096e6	+	1.44643e7i	0.274947	+	0.476222i
$985$	1.66971e7	−	2.89202e7i	0.548341	−	0.949754i
$986$	−445853.	−	257414.i	−0.0146049	−	0.00843217i
$987$	−1.29114e6			−0.0421873
$988$	1.28767e7	−	1.88762e7i	0.419674	−	0.615210i
$989$	6.05091e7			1.96712
$990$	−9.08944e6	−	5.24779e6i	−0.294747	−	0.170172i
$991$	1.36660e6	−	2.36701e6i	0.0442034	−	0.0765626i	−0.843077	−	0.537793i	$-0.819258\pi$
$991$	1.36660e6	−	2.36701e6i	0.0442034	−	0.0765626i	0.887281	+	0.461230i	$0.152592\pi$
$992$	2.84517e6	+	4.92797e6i	0.0917970	+	0.158997i
$993$		−	3.71814e7i		−	1.19661i
$994$	−158543.	+	91534.6i	−0.00508956	+	0.00293846i
$995$	3.73793e7	−	2.15810e7i	1.19694	−	0.691056i
$996$			6.83989e6i			0.218475i
$997$	−4.21532e6	−	7.30116e6i	−0.134305	−	0.232624i	0.791027	−	0.611782i	$-0.209547\pi$
$997$	−4.21532e6	−	7.30116e6i	−0.134305	−	0.232624i	−0.925332	+	0.379158i	$0.876214\pi$
$998$	589175.	−	1.02048e6i	0.0187248	−	0.0324324i
$999$	1.52228e7	+	8.78891e6i	0.482594	+	0.278626i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.6.e.a.17.6	✓	12
3.2	odd	2		234.6.l.c.199.3		12
4.3	odd	2		208.6.w.c.17.2		12
13.4	even	6		338.6.b.g.337.8		12
13.6	odd	12		338.6.a.m.1.2		6
13.7	odd	12		338.6.a.o.1.2		6
13.9	even	3		338.6.b.g.337.2		12
13.10	even	6	inner	26.6.e.a.23.6	yes	12
39.23	odd	6		234.6.l.c.127.1		12
52.23	odd	6		208.6.w.c.49.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.6.e.a.17.6	✓	12	1.1	even	1	trivial
26.6.e.a.23.6	yes	12	13.10	even	6	inner
208.6.w.c.17.2		12	4.3	odd	2
208.6.w.c.49.2		12	52.23	odd	6
234.6.l.c.127.1		12	39.23	odd	6
234.6.l.c.199.3		12	3.2	odd	2
338.6.a.m.1.2		6	13.6	odd	12
338.6.a.o.1.2		6	13.7	odd	12
338.6.b.g.337.2		12	13.9	even	3
338.6.b.g.337.8		12	13.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(3.46410 + 2.00000i) q^{2} +(9.67602 - 16.7594i) q^{3} +(8.00000 + 13.8564i) q^{4} -52.2356i q^{5} +(67.0374 - 38.7041i) q^{6} +(16.5596 - 9.56069i) q^{7} +64.0000i q^{8} +(-65.7507 - 113.884i) q^{9} +O(q^{10})\)	\(q+(3.46410 + 2.00000i) q^{2} +(9.67602 - 16.7594i) q^{3} +(8.00000 + 13.8564i) q^{4} -52.2356i q^{5} +(67.0374 - 38.7041i) q^{6} +(16.5596 - 9.56069i) q^{7} +64.0000i q^{8} +(-65.7507 - 113.884i) q^{9} +(104.471 - 180.949i) q^{10} +(330.811 + 190.994i) q^{11} +309.633 q^{12} +(-45.6914 + 607.623i) q^{13} +76.4855 q^{14} +(-875.434 - 505.432i) q^{15} +(-128.000 + 221.703i) q^{16} +(-528.708 - 915.749i) q^{17} -526.006i q^{18} +(-2029.73 + 1171.86i) q^{19} +(723.797 - 417.884i) q^{20} -370.038i q^{21} +(763.976 + 1323.25i) q^{22} +(-1373.98 + 2379.80i) q^{23} +(1072.60 + 619.265i) q^{24} +396.447 q^{25} +(-1373.52 + 2013.48i) q^{26} +2157.72 q^{27} +(264.954 + 152.971i) q^{28} +(60.8591 - 105.411i) q^{29} +(-2021.73 - 3501.74i) q^{30} -5556.97i q^{31} +(-886.810 + 512.000i) q^{32} +(6401.87 - 3696.12i) q^{33} -4229.66i q^{34} +(-499.408 - 865.000i) q^{35} +(1052.01 - 1822.14i) q^{36} +(7055.04 + 4073.23i) q^{37} -9374.92 q^{38} +(9741.26 + 6645.13i) q^{39} +3343.08 q^{40} +(11678.6 + 6742.64i) q^{41} +(740.075 - 1281.85i) q^{42} +(-11009.8 - 19069.6i) q^{43} +6111.81i q^{44} +(-5948.77 + 3434.53i) q^{45} +(-9519.20 + 5495.91i) q^{46} -3489.22i q^{47} +(2477.06 + 4290.40i) q^{48} +(-8220.69 + 14238.6i) q^{49} +(1373.33 + 792.893i) q^{50} -20463.2 q^{51} +(-8785.00 + 4227.86i) q^{52} -28937.9 q^{53} +(7474.57 + 4315.45i) q^{54} +(9976.68 - 17280.1i) q^{55} +(611.884 + 1059.81i) q^{56} +45355.9i q^{57} +(421.644 - 243.436i) q^{58} +(29831.8 - 17223.4i) q^{59} -16173.8i q^{60} +(-2652.96 - 4595.07i) q^{61} +(11113.9 - 19249.9i) q^{62} +(-2177.61 - 1257.24i) q^{63} -4096.00 q^{64} +(31739.5 + 2386.71i) q^{65} +29569.0 q^{66} +(-49277.1 - 28450.2i) q^{67} +(8459.33 - 14652.0i) q^{68} +(26589.3 + 46054.0i) q^{69} -3995.26i q^{70} +(-2072.85 + 1196.76i) q^{71} +(7288.55 - 4208.05i) q^{72} -47969.6i q^{73} +(16292.9 + 28220.2i) q^{74} +(3836.03 - 6644.19i) q^{75} +(-32475.7 - 18749.8i) q^{76} +7304.14 q^{77} +(20454.4 + 42501.9i) q^{78} -79330.2 q^{79} +(11580.8 + 6686.15i) q^{80} +(36855.6 - 63835.8i) q^{81} +(26970.5 + 46714.4i) q^{82} +22090.3i q^{83} +(5127.39 - 2960.30i) q^{84} +(-47834.7 + 27617.4i) q^{85} -88078.6i q^{86} +(-1177.75 - 2039.92i) q^{87} +(-12223.6 + 21171.9i) q^{88} +(107681. + 62169.5i) q^{89} -27476.2 q^{90} +(5052.66 + 10498.8i) q^{91} -43967.3 q^{92} +(-93131.2 - 53769.3i) q^{93} +(6978.44 - 12087.0i) q^{94} +(61213.0 + 106024. i) q^{95} +19816.5i q^{96} +(81487.4 - 47046.8i) q^{97} +(-56954.6 + 32882.7i) q^{98} -50232.0i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 96 q^{4} + 360 q^{7} - 706 q^{9}+O(q^{10}) \) 12 * q + 96 * q^4 + 360 * q^7 - 706 * q^9	\( 12 q + 96 q^{4} + 360 q^{7} - 706 q^{9} - 368 q^{10} + 504 q^{11} + 3202 q^{13} - 2272 q^{14} + 2112 q^{15} - 1536 q^{16} - 1910 q^{17} - 6888 q^{19} + 1440 q^{20} + 2160 q^{22} + 5920 q^{23} - 4672 q^{25} - 2320 q^{26} - 2736 q^{27} + 5760 q^{28} + 7922 q^{29} - 11696 q^{30} - 18780 q^{33} + 16864 q^{35} + 11296 q^{36} - 882 q^{37} + 26496 q^{38} + 48304 q^{39} - 11776 q^{40} + 44346 q^{41} + 23648 q^{42} - 41920 q^{43} - 158850 q^{45} - 33408 q^{46} + 4682 q^{49} + 11040 q^{50} + 133264 q^{51} + 43520 q^{52} - 187812 q^{53} + 1296 q^{54} + 17472 q^{55} - 18176 q^{56} - 73488 q^{58} + 74832 q^{59} + 27934 q^{61} - 4336 q^{62} + 156528 q^{63} - 49152 q^{64} + 69646 q^{65} + 6336 q^{66} + 85104 q^{67} + 30560 q^{68} - 77348 q^{69} - 106320 q^{71} - 78336 q^{72} + 96208 q^{74} + 192080 q^{75} - 110208 q^{76} - 151944 q^{77} + 9392 q^{78} + 30464 q^{79} + 23040 q^{80} - 72310 q^{81} - 87040 q^{82} + 53952 q^{84} - 148986 q^{85} - 121936 q^{87} - 34560 q^{88} + 93108 q^{89} + 282016 q^{90} - 56776 q^{91} + 189440 q^{92} + 107616 q^{93} + 158256 q^{94} + 232560 q^{95} + 147156 q^{97} + 46752 q^{98}+O(q^{100}) \) 12 * q + 96 * q^4 + 360 * q^7 - 706 * q^9 - 368 * q^10 + 504 * q^11 + 3202 * q^13 - 2272 * q^14 + 2112 * q^15 - 1536 * q^16 - 1910 * q^17 - 6888 * q^19 + 1440 * q^20 + 2160 * q^22 + 5920 * q^23 - 4672 * q^25 - 2320 * q^26 - 2736 * q^27 + 5760 * q^28 + 7922 * q^29 - 11696 * q^30 - 18780 * q^33 + 16864 * q^35 + 11296 * q^36 - 882 * q^37 + 26496 * q^38 + 48304 * q^39 - 11776 * q^40 + 44346 * q^41 + 23648 * q^42 - 41920 * q^43 - 158850 * q^45 - 33408 * q^46 + 4682 * q^49 + 11040 * q^50 + 133264 * q^51 + 43520 * q^52 - 187812 * q^53 + 1296 * q^54 + 17472 * q^55 - 18176 * q^56 - 73488 * q^58 + 74832 * q^59 + 27934 * q^61 - 4336 * q^62 + 156528 * q^63 - 49152 * q^64 + 69646 * q^65 + 6336 * q^66 + 85104 * q^67 + 30560 * q^68 - 77348 * q^69 - 106320 * q^71 - 78336 * q^72 + 96208 * q^74 + 192080 * q^75 - 110208 * q^76 - 151944 * q^77 + 9392 * q^78 + 30464 * q^79 + 23040 * q^80 - 72310 * q^81 - 87040 * q^82 + 53952 * q^84 - 148986 * q^85 - 121936 * q^87 - 34560 * q^88 + 93108 * q^89 + 282016 * q^90 - 56776 * q^91 + 189440 * q^92 + 107616 * q^93 + 158256 * q^94 + 232560 * q^95 + 147156 * q^97 + 46752 * q^98

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