LMFDB - Embedded newform 48.6.j.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,6,Mod(13,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("48.13");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	48.j (of order $4$, 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:	$7.69842335102$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	48.13
Dual form			48.6.j.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.65510 + 0.140725i) q^{2} +(-6.36396 - 6.36396i) q^{3} +(31.9604 - 1.59163i) q^{4} +(24.8890 - 24.8890i) q^{5} +(36.8844 + 35.0933i) q^{6} +146.252i q^{7} +(-180.515 + 13.4984i) q^{8} +81.0000i q^{9} +O(q^{10})$	\(q+(-5.65510 + 0.140725i) q^{2} +(-6.36396 - 6.36396i) q^{3} +(31.9604 - 1.59163i) q^{4} +(24.8890 - 24.8890i) q^{5} +(36.8844 + 35.0933i) q^{6} +146.252i q^{7} +(-180.515 + 13.4984i) q^{8} +81.0000i q^{9} +(-137.247 + 144.252i) q^{10} +(551.607 - 551.607i) q^{11} +(-213.524 - 193.266i) q^{12} +(-716.649 - 716.649i) q^{13} +(-20.5812 - 827.067i) q^{14} -316.785 q^{15} +(1018.93 - 101.738i) q^{16} -724.673 q^{17} +(-11.3987 - 458.063i) q^{18} +(-946.256 - 946.256i) q^{19} +(755.849 - 835.077i) q^{20} +(930.739 - 930.739i) q^{21} +(-3041.77 + 3197.02i) q^{22} -4844.71i q^{23} +(1234.70 + 1062.89i) q^{24} +1886.07i q^{25} +(4153.57 + 3951.87i) q^{26} +(515.481 - 515.481i) q^{27} +(232.778 + 4674.26i) q^{28} +(-846.679 - 846.679i) q^{29} +(1791.45 - 44.5796i) q^{30} +1289.78 q^{31} +(-5747.86 + 718.729i) q^{32} -7020.80 q^{33} +(4098.10 - 101.980i) q^{34} +(3640.06 + 3640.06i) q^{35} +(128.922 + 2588.79i) q^{36} +(-2065.08 + 2065.08i) q^{37} +(5484.34 + 5218.01i) q^{38} +9121.45i q^{39} +(-4156.89 + 4828.81i) q^{40} -9397.60i q^{41} +(-5132.45 + 5394.40i) q^{42} +(9676.47 - 9676.47i) q^{43} +(16751.6 - 18507.5i) q^{44} +(2016.01 + 2016.01i) q^{45} +(681.772 + 27397.4i) q^{46} +808.318 q^{47} +(-7131.91 - 5837.00i) q^{48} -4582.51 q^{49} +(-265.418 - 10665.9i) q^{50} +(4611.79 + 4611.79i) q^{51} +(-24045.0 - 21763.7i) q^{52} +(-9150.19 + 9150.19i) q^{53} +(-2842.56 + 2987.64i) q^{54} -27457.9i q^{55} +(-1974.17 - 26400.6i) q^{56} +12043.9i q^{57} +(4907.21 + 4668.91i) q^{58} +(18111.4 - 18111.4i) q^{59} +(-10124.6 + 504.205i) q^{60} +(-14346.8 - 14346.8i) q^{61} +(-7293.85 + 181.505i) q^{62} -11846.4 q^{63} +(32403.6 - 4873.35i) q^{64} -35673.4 q^{65} +(39703.4 - 988.002i) q^{66} +(42562.6 + 42562.6i) q^{67} +(-23160.8 + 1153.41i) q^{68} +(-30831.6 + 30831.6i) q^{69} +(-21097.1 - 20072.6i) q^{70} +45073.5i q^{71} +(-1093.37 - 14621.7i) q^{72} -27235.6i q^{73} +(11387.6 - 11968.8i) q^{74} +(12002.9 - 12002.9i) q^{75} +(-31748.8 - 28736.6i) q^{76} +(80673.3 + 80673.3i) q^{77} +(-1283.62 - 51582.7i) q^{78} +12637.6 q^{79} +(22828.1 - 27892.4i) q^{80} -6561.00 q^{81} +(1322.48 + 53144.4i) q^{82} +(-26850.6 - 26850.6i) q^{83} +(28265.4 - 31228.2i) q^{84} +(-18036.4 + 18036.4i) q^{85} +(-53359.7 + 56083.1i) q^{86} +10776.5i q^{87} +(-92127.6 + 107019. i) q^{88} +6477.94i q^{89} +(-11684.4 - 11117.0i) q^{90} +(104811. - 104811. i) q^{91} +(-7710.98 - 154839. i) q^{92} +(-8208.12 - 8208.12i) q^{93} +(-4571.12 + 113.750i) q^{94} -47102.8 q^{95} +(41153.1 + 32005.2i) q^{96} -1046.66 q^{97} +(25914.5 - 644.873i) q^{98} +(44680.1 + 44680.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 44 q^{4} - 492 q^{8}+O(q^{10}) $ 40 * q + 44 * q^4 - 492 * q^8	\( 40 q + 44 q^{4} - 492 q^{8} + 968 q^{10} + 1208 q^{11} - 792 q^{12} + 324 q^{14} - 1800 q^{15} - 384 q^{16} - 324 q^{18} + 2360 q^{19} - 7600 q^{20} - 1024 q^{22} + 5220 q^{24} - 12980 q^{26} + 10472 q^{28} - 8144 q^{29} - 1368 q^{30} + 23064 q^{31} + 44160 q^{32} + 4864 q^{34} - 4776 q^{35} - 1620 q^{36} + 21296 q^{37} - 72088 q^{38} - 90864 q^{40} - 14220 q^{42} + 31416 q^{43} + 43768 q^{44} + 90664 q^{46} + 44784 q^{48} - 96040 q^{49} + 106212 q^{50} + 10440 q^{51} - 116432 q^{52} - 49456 q^{53} - 14580 q^{54} - 158592 q^{56} - 111472 q^{58} + 28960 q^{59} + 49464 q^{60} + 48080 q^{61} + 191100 q^{62} + 31752 q^{63} + 369032 q^{64} - 55376 q^{65} + 63720 q^{66} + 101488 q^{67} - 122336 q^{68} - 22320 q^{69} - 460192 q^{70} - 28836 q^{72} - 94996 q^{74} - 96624 q^{75} + 211304 q^{76} - 14896 q^{77} + 200124 q^{78} - 71960 q^{79} + 623368 q^{80} - 262440 q^{81} + 33880 q^{82} - 126440 q^{83} - 116856 q^{84} + 132400 q^{85} - 581168 q^{86} - 466400 q^{88} - 46008 q^{90} + 429496 q^{91} - 12752 q^{92} + 524120 q^{94} - 76848 q^{95} + 51840 q^{96} + 477736 q^{98} + 97848 q^{99}+O(q^{100}) \) 40 * q + 44 * q^4 - 492 * q^8 + 968 * q^10 + 1208 * q^11 - 792 * q^12 + 324 * q^14 - 1800 * q^15 - 384 * q^16 - 324 * q^18 + 2360 * q^19 - 7600 * q^20 - 1024 * q^22 + 5220 * q^24 - 12980 * q^26 + 10472 * q^28 - 8144 * q^29 - 1368 * q^30 + 23064 * q^31 + 44160 * q^32 + 4864 * q^34 - 4776 * q^35 - 1620 * q^36 + 21296 * q^37 - 72088 * q^38 - 90864 * q^40 - 14220 * q^42 + 31416 * q^43 + 43768 * q^44 + 90664 * q^46 + 44784 * q^48 - 96040 * q^49 + 106212 * q^50 + 10440 * q^51 - 116432 * q^52 - 49456 * q^53 - 14580 * q^54 - 158592 * q^56 - 111472 * q^58 + 28960 * q^59 + 49464 * q^60 + 48080 * q^61 + 191100 * q^62 + 31752 * q^63 + 369032 * q^64 - 55376 * q^65 + 63720 * q^66 + 101488 * q^67 - 122336 * q^68 - 22320 * q^69 - 460192 * q^70 - 28836 * q^72 - 94996 * q^74 - 96624 * q^75 + 211304 * q^76 - 14896 * q^77 + 200124 * q^78 - 71960 * q^79 + 623368 * q^80 - 262440 * q^81 + 33880 * q^82 - 126440 * q^83 - 116856 * q^84 + 132400 * q^85 - 581168 * q^86 - 466400 * q^88 - 46008 * q^90 + 429496 * q^91 - 12752 * q^92 + 524120 * q^94 - 76848 * q^95 + 51840 * q^96 + 477736 * q^98 + 97848 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−5.65510	+	0.140725i	−0.999691	+	0.0248769i
$2$	−5.65510	+	0.140725i	−0.999691	+	0.0248769i
$3$	−6.36396	−	6.36396i	−0.408248	−	0.408248i
$3$	−6.36396	−	6.36396i	−0.408248	−	0.408248i
$4$	31.9604	−	1.59163i	0.998762	−	0.0497384i
$5$	24.8890	−	24.8890i	0.445228	−	0.445228i	−0.448536	−	0.893765i	$-0.648055\pi$
$5$	24.8890	−	24.8890i	0.445228	−	0.445228i	0.893765	+	0.448536i	$0.148055\pi$
$6$	36.8844	+	35.0933i	0.418278	+	0.397966i
$7$			146.252i			1.12812i	0.825734	+	0.564060i	$0.190761\pi$
$7$			146.252i			1.12812i	−0.825734	+	0.564060i	$0.809239\pi$
$8$	−180.515	+	13.4984i	−0.997216	+	0.0745691i
$9$			81.0000i			0.333333i
$10$	−137.247	+	144.252i	−0.434015	+	0.456166i
$11$	551.607	−	551.607i	1.37451	−	1.37451i	0.520878	−	0.853631i	$-0.325604\pi$
$11$	551.607	−	551.607i	1.37451	−	1.37451i	0.853631	−	0.520878i	$-0.174396\pi$
$12$	−213.524	−	193.266i	−0.428049	−	0.387437i
$13$	−716.649	−	716.649i	−1.17611	−	1.17611i	−0.980727	−	0.195383i	$-0.937405\pi$
$13$	−716.649	−	716.649i	−1.17611	−	1.17611i	−0.195383	−	0.980727i	$-0.562595\pi$
$14$	−20.5812	−	827.067i	−0.0280641	−	1.12777i
$15$	−316.785			−0.363527
$16$	1018.93	−	101.738i	0.995052	−	0.0993536i
$17$	−724.673			−0.608163			−0.304081	−	0.952646i	$-0.598349\pi$
$17$	−724.673			−0.608163			−0.304081	+	0.952646i	$0.598349\pi$
$18$	−11.3987	−	458.063i	−0.00829230	−	0.333230i
$19$	−946.256	−	946.256i	−0.601346	−	0.601346i	0.339323	−	0.940670i	$-0.389802\pi$
$19$	−946.256	−	946.256i	−0.601346	−	0.601346i	−0.940670	+	0.339323i	$0.889802\pi$
$20$	755.849	−	835.077i	0.422532	−	0.466822i
$21$	930.739	−	930.739i	0.460553	−	0.460553i
$22$	−3041.77	+	3197.02i	−1.33989	+	1.40828i
$23$		−	4844.71i		−	1.90963i	−0.297206	−	0.954813i	$-0.596055\pi$
$23$		−	4844.71i		−	1.90963i	0.297206	−	0.954813i	$-0.403945\pi$
$24$	1234.70	+	1062.89i	0.437554	+	0.376669i
$25$			1886.07i			0.603544i
$26$	4153.57	+	3951.87i	1.20500	+	1.14649i
$27$	515.481	−	515.481i	0.136083	−	0.136083i
$28$	232.778	+	4674.26i	0.0561109	+	1.12672i
$29$	−846.679	−	846.679i	−0.186949	−	0.186949i	0.607427	−	0.794376i	$-0.292202\pi$
$29$	−846.679	−	846.679i	−0.186949	−	0.186949i	−0.794376	+	0.607427i	$0.792202\pi$
$30$	1791.45	−	44.5796i	0.363415	−	0.00904343i
$31$	1289.78			0.241053			0.120526	−	0.992710i	$-0.461542\pi$
$31$	1289.78			0.241053			0.120526	+	0.992710i	$0.461542\pi$
$32$	−5747.86	+	718.729i	−0.992273	+	0.124077i
$33$	−7020.80			−1.12228
$34$	4098.10	−	101.980i	0.607975	−	0.0151292i
$35$	3640.06	+	3640.06i	0.502271	+	0.502271i
$36$	128.922	+	2588.79i	0.0165795	+	0.332921i
$37$	−2065.08	+	2065.08i	−0.247989	+	0.247989i	−0.820145	−	0.572156i	$-0.806107\pi$
$37$	−2065.08	+	2065.08i	−0.247989	+	0.247989i	0.572156	+	0.820145i	$0.306107\pi$
$38$	5484.34	+	5218.01i	0.616120	+	0.586201i
$39$			9121.45i			0.960290i
$40$	−4156.89	+	4828.81i	−0.410788	+	0.477189i
$41$		−	9397.60i		−	0.873086i	−0.899683	−	0.436543i	$-0.856203\pi$
$41$		−	9397.60i		−	0.873086i	0.899683	−	0.436543i	$-0.143797\pi$
$42$	−5132.45	+	5394.40i	−0.448953	+	0.471868i
$43$	9676.47	−	9676.47i	0.798079	−	0.798079i	−0.184714	−	0.982792i	$-0.559136\pi$
$43$	9676.47	−	9676.47i	0.798079	−	0.798079i	0.982792	+	0.184714i	$0.0591358\pi$
$44$	16751.6	−	18507.5i	1.30444	−	1.44117i
$45$	2016.01	+	2016.01i	0.148409	+	0.148409i
$46$	681.772	+	27397.4i	0.0475056	+	1.90904i
$47$	808.318			0.0533750			0.0266875	−	0.999644i	$-0.491504\pi$
$47$	808.318			0.0533750			0.0266875	+	0.999644i	$0.491504\pi$
$48$	−7131.91	−	5837.00i	−0.446789	−	0.365667i
$49$	−4582.51			−0.272655
$50$	−265.418	−	10665.9i	−0.0150143	−	0.603357i
$51$	4611.79	+	4611.79i	0.248281	+	0.248281i
$52$	−24045.0	−	21763.7i	−1.23315	−	1.11616i
$53$	−9150.19	+	9150.19i	−0.447446	+	0.447446i	−0.894505	−	0.447059i	$-0.852471\pi$
$53$	−9150.19	+	9150.19i	−0.447446	+	0.447446i	0.447059	+	0.894505i	$0.352471\pi$
$54$	−2842.56	+	2987.64i	−0.132655	+	0.139426i
$55$		−	27457.9i		−	1.22394i
$56$	−1974.17	−	26400.6i	−0.0841229	−	1.12498i
$57$			12043.9i			0.490997i
$58$	4907.21	+	4668.91i	0.191542	+	0.182241i
$59$	18111.4	−	18111.4i	0.677364	−	0.677364i	−0.282039	−	0.959403i	$-0.591011\pi$
$59$	18111.4	−	18111.4i	0.677364	−	0.677364i	0.959403	+	0.282039i	$0.0910106\pi$
$60$	−10124.6	+	504.205i	−0.363077	+	0.0180813i
$61$	−14346.8	−	14346.8i	−0.493662	−	0.493662i	0.415796	−	0.909458i	$-0.363503\pi$
$61$	−14346.8	−	14346.8i	−0.493662	−	0.493662i	−0.909458	+	0.415796i	$0.863503\pi$
$62$	−7293.85	+	181.505i	−0.240978	+	0.00599664i
$63$	−11846.4			−0.376040
$64$	32403.6	−	4873.35i	0.988879	−	0.148723i
$65$	−35673.4			−1.04727
$66$	39703.4	−	988.002i	1.12193	−	0.0279189i
$67$	42562.6	+	42562.6i	1.15835	+	1.15835i	0.984830	+	0.173523i	$0.0555150\pi$
$67$	42562.6	+	42562.6i	1.15835	+	1.15835i	0.173523	+	0.984830i	$0.444485\pi$
$68$	−23160.8	+	1153.41i	−0.607410	+	0.0302490i
$69$	−30831.6	+	30831.6i	−0.779602	+	0.779602i
$70$	−21097.1	−	20072.6i	−0.514610	−	0.489620i
$71$			45073.5i			1.06115i	0.847639	+	0.530574i	$0.178023\pi$
$71$			45073.5i			1.06115i	−0.847639	+	0.530574i	$0.821977\pi$
$72$	−1093.37	−	14621.7i	−0.0248564	−	0.332405i
$73$		−	27235.6i		−	0.598177i	−0.954225	−	0.299088i	$-0.903317\pi$
$73$		−	27235.6i		−	0.598177i	0.954225	−	0.299088i	$-0.0966825\pi$
$74$	11387.6	−	11968.8i	0.241743	−	0.254081i
$75$	12002.9	−	12002.9i	0.246396	−	0.246396i
$76$	−31748.8	−	28736.6i	−0.630512	−	0.570692i
$77$	80673.3	+	80673.3i	1.55061	+	1.55061i
$78$	−1283.62	−	51582.7i	−0.0238890	−	0.959993i
$79$	12637.6			0.227823			0.113911	−	0.993491i	$-0.463662\pi$
$79$	12637.6			0.227823			0.113911	+	0.993491i	$0.463662\pi$
$80$	22828.1	−	27892.4i	0.398790	−	0.487260i
$81$	−6561.00			−0.111111
$82$	1322.48	+	53144.4i	0.0217197	+	0.872816i
$83$	−26850.6	−	26850.6i	−0.427818	−	0.427818i	0.460066	−	0.887885i	$-0.347826\pi$
$83$	−26850.6	−	26850.6i	−0.427818	−	0.427818i	−0.887885	+	0.460066i	$0.847826\pi$
$84$	28265.4	−	31228.2i	0.437076	−	0.482890i
$85$	−18036.4	+	18036.4i	−0.270771	+	0.270771i
$86$	−53359.7	+	56083.1i	−0.777978	+	0.817685i
$87$			10776.5i			0.152643i
$88$	−92127.6	+	107019.i	−1.26819	+	1.47318i
$89$			6477.94i			0.0866886i	0.999060	+	0.0433443i	$0.0138013\pi$
$89$			6477.94i			0.0866886i	−0.999060	+	0.0433443i	$0.986199\pi$
$90$	−11684.4	−	11117.0i	−0.152055	−	0.144672i
$91$	104811.	−	104811.i	1.32679	−	1.32679i
$92$	−7710.98	−	154839.i	−0.0949818	−	1.90726i
$93$	−8208.12	−	8208.12i	−0.0984094	−	0.0984094i
$94$	−4571.12	+	113.750i	−0.0533584	+	0.00132780i
$95$	−47102.8			−0.535473
$96$	41153.1	+	32005.2i	0.455748	+	0.354440i
$97$	−1046.66			−0.0112947			−0.00564735	−	0.999984i	$-0.501798\pi$
$97$	−1046.66			−0.0112947			−0.00564735	+	0.999984i	$0.501798\pi$
$98$	25914.5	−	644.873i	0.272570	−	0.00678280i
$99$	44680.1	+	44680.1i	0.458170	+	0.458170i
$100$	3001.93	+	60279.7i	0.0300193	+	0.602797i
$101$	−72909.5	+	72909.5i	−0.711182	+	0.711182i	−0.966782	−	0.255601i	$-0.917727\pi$
$101$	−72909.5	+	72909.5i	−0.711182	+	0.711182i	0.255601	+	0.966782i	$0.417727\pi$
$102$	−26729.2	−	25431.2i	−0.254381	−	0.242028i
$103$			107674.i			1.00004i	0.866013	+	0.500022i	$0.166675\pi$
$103$			107674.i			1.00004i	−0.866013	+	0.500022i	$0.833325\pi$
$104$	139040.	+	119692.i	1.26054	+	1.08513i
$105$		−	46330.3i		−	0.410102i
$106$	50457.6	−	53032.9i	0.436176	−	0.458438i
$107$	−75231.5	+	75231.5i	−0.635244	+	0.635244i	−0.949378	−	0.314135i	$-0.898286\pi$
$107$	−75231.5	+	75231.5i	−0.635244	+	0.635244i	0.314135	+	0.949378i	$0.398286\pi$
$108$	15654.5	−	17295.4i	0.129146	−	0.142683i
$109$	47780.1	+	47780.1i	0.385195	+	0.385195i	0.872970	−	0.487775i	$-0.162191\pi$
$109$	47780.1	+	47780.1i	0.385195	+	0.385195i	−0.487775	+	0.872970i	$0.662191\pi$
$110$	3864.01	+	155277.i	0.0304478	+	1.22356i
$111$	26284.1			0.202482
$112$	14879.4	+	149021.i	0.112083	+	1.12254i
$113$	22066.7			0.162570			0.0812850	−	0.996691i	$-0.474098\pi$
$113$	22066.7			0.162570			0.0812850	+	0.996691i	$0.474098\pi$
$114$	−1694.87	−	68109.3i	−0.0122145	−	0.490845i
$115$	−120580.	−	120580.i	−0.850220	−	0.850220i
$116$	−28407.8	−	25712.6i	−0.196016	−	0.177419i
$117$	58048.6	−	58048.6i	0.392037	−	0.392037i
$118$	−99873.2	+	104971.i	−0.660304	+	0.694006i
$119$		−	105985.i		−	0.686081i
$120$	57184.6	−	4276.11i	0.362515	−	0.0271079i
$121$		−	447489.i		−	2.77855i
$122$	83151.4	+	79113.5i	0.505790	+	0.481228i
$123$	−59806.0	+	59806.0i	−0.356436	+	0.356436i
$124$	41221.9	−	2052.85i	0.240754	−	0.0119896i
$125$	124721.	+	124721.i	0.713943	+	0.713943i
$126$	66992.5	−	1667.08i	0.375924	−	0.00935471i
$127$	−185259.			−1.01922			−0.509612	−	0.860404i	$-0.670211\pi$
$127$	−185259.			−1.01922			−0.509612	+	0.860404i	$0.670211\pi$
$128$	−182560.	+	32119.3i	−0.984873	+	0.173277i
$129$	−123161.			−0.651629
$130$	201737.	−	5020.13i	1.04695	−	0.0260529i
$131$	14901.1	+	14901.1i	0.0758646	+	0.0758646i	0.744021	−	0.668156i	$-0.232916\pi$
$131$	14901.1	+	14901.1i	0.0758646	+	0.0758646i	−0.668156	+	0.744021i	$0.732916\pi$
$132$	−224388.	+	11174.5i	−1.12089	+	0.0558205i
$133$	138391.	−	138391.i	0.678391	−	0.678391i
$134$	−246685.	−	234706.i	−1.18681	−	1.12918i
$135$		−	25659.6i		−	0.121176i
$136$	130815.	−	9781.96i	0.606470	−	0.0453501i
$137$		−	161523.i		−	0.735244i	−0.929975	−	0.367622i	$-0.880172\pi$
$137$		−	161523.i		−	0.735244i	0.929975	−	0.367622i	$-0.119828\pi$
$138$	170017.	−	178694.i	0.759967	−	0.798755i
$139$	253073.	−	253073.i	1.11099	−	1.11099i	0.117969	−	0.993017i	$-0.462362\pi$
$139$	253073.	−	253073.i	1.11099	−	1.11099i	0.993017	−	0.117969i	$-0.0376385\pi$
$140$	122131.	+	110544.i	0.526631	+	0.476667i
$141$	−5144.10	−	5144.10i	−0.0217902	−	0.0217902i
$142$	−6342.97	−	254895.i	−0.0263980	−	1.06082i
$143$	−790616.			−3.23315
$144$	8240.79	+	82533.6i	0.0331179	+	0.331684i
$145$	−42146.0			−0.166470
$146$	3832.73	+	154020.i	0.0148808	+	0.597992i
$147$	29162.9	+	29162.9i	0.111311	+	0.111311i
$148$	−62713.9	+	69287.5i	−0.235347	+	0.260016i
$149$	148310.	−	148310.i	0.547274	−	0.547274i	−0.378378	−	0.925651i	$-0.623518\pi$
$149$	148310.	−	148310.i	0.547274	−	0.547274i	0.925651	+	0.378378i	$0.123518\pi$
$150$	−66188.5	+	69566.8i	−0.240190	+	0.252449i
$151$			199448.i			0.711847i	0.934515	+	0.355923i	$0.115834\pi$
$151$			199448.i			0.711847i	−0.934515	+	0.355923i	$0.884166\pi$
$152$	183587.	+	158041.i	0.644514	+	0.554830i
$153$		−	58698.5i		−	0.202721i
$154$	−467569.	−	444863.i	−1.58871	−	1.51156i
$155$	32101.4	−	32101.4i	0.107323	−	0.107323i
$156$	14518.0	+	291525.i	0.0477633	+	0.959101i
$157$	14542.3	+	14542.3i	0.0470851	+	0.0470851i	0.730257	−	0.683172i	$-0.239400\pi$
$157$	14542.3	+	14542.3i	0.0470851	+	0.0470851i	−0.683172	+	0.730257i	$0.739400\pi$
$158$	−71467.0	+	1778.43i	−0.227752	+	0.00566753i
$159$	116463.			0.365338
$160$	−125170.	+	160947.i	−0.386545	+	0.497030i
$161$	708547.			2.15429
$162$	37103.1	−	923.296i	0.111077	−	0.00276410i
$163$	297019.	+	297019.i	0.875618	+	0.875618i	0.993078	−	0.117460i	$-0.0374750\pi$
$163$	297019.	+	297019.i	0.875618	+	0.875618i	−0.117460	+	0.993078i	$0.537475\pi$
$164$	−14957.5	−	300351.i	−0.0434259	−	0.872006i
$165$	−174741.	+	174741.i	−0.499672	+	0.499672i
$166$	155622.	+	148065.i	0.438329	+	0.417043i
$167$		−	9483.36i		−	0.0263131i	−0.999913	−	0.0131565i	$-0.995812\pi$
$167$		−	9483.36i		−	0.0263131i	0.999913	−	0.0131565i	$-0.00418797\pi$
$168$	−155449.	+	180576.i	−0.424928	+	0.493614i
$169$			655878.i			1.76647i
$170$	99459.5	−	104536.i	0.263951	−	0.277423i
$171$	76646.7	−	76646.7i	0.200449	−	0.200449i
$172$	293862.	−	324665.i	0.757396	−	0.836786i
$173$	247131.	+	247131.i	0.627788	+	0.627788i	0.947511	−	0.319723i	$-0.103590\pi$
$173$	247131.	+	247131.i	0.627788	+	0.627788i	−0.319723	+	0.947511i	$0.603590\pi$
$174$	−1516.52	−	60942.0i	−0.00379729	−	0.152596i
$175$	−275841.			−0.680870
$176$	505931.	−	618170.i	1.23115	−	1.50427i
$177$	−230521.			−0.553066
$178$	−911.608	−	36633.4i	−0.00215654	−	0.0866618i
$179$	−87089.9	−	87089.9i	−0.203159	−	0.203159i	0.598193	−	0.801352i	$-0.295885\pi$
$179$	−87089.9	−	87089.9i	−0.203159	−	0.203159i	−0.801352	+	0.598193i	$0.795885\pi$
$180$	67641.2	+	61223.7i	0.155607	+	0.140844i
$181$	−451972.	+	451972.i	−1.02545	+	1.02545i	−0.0257847	+	0.999668i	$0.508208\pi$
$181$	−451972.	+	451972.i	−1.02545	+	1.02545i	−0.999668	+	0.0257847i	$0.991792\pi$
$182$	−577967.	+	607466.i	−1.29338	+	1.35939i
$183$			182605.i			0.403073i
$184$	65396.1	+	874545.i	0.142399	+	1.90431i
$185$			102795.i			0.220823i
$186$	47572.9	+	45262.7i	0.100827	+	0.0959308i
$187$	−399734.	+	399734.i	−0.835925	+	0.835925i
$188$	25834.2	−	1286.54i	0.0533089	−	0.00265478i
$189$	75389.9	+	75389.9i	0.153518	+	0.153518i
$190$	266371.	−	6628.53i	0.535307	−	0.0133209i
$191$	464620.			0.921541			0.460770	−	0.887519i	$-0.347573\pi$
$191$	464620.			0.921541			0.460770	+	0.887519i	$0.347573\pi$
$192$	−237229.	−	175201.i	−0.464424	−	0.342992i
$193$	−104902.			−0.202718			−0.101359	−	0.994850i	$-0.532319\pi$
$193$	−104902.			−0.202718			−0.101359	+	0.994850i	$0.532319\pi$
$194$	5918.95	−	147.291i	0.0112912	−	0.000280977i
$195$	227024.	+	227024.i	0.427548	+	0.427548i
$196$	−146459.	+	7293.65i	−0.272317	+	0.0135614i
$197$	549820.	−	549820.i	1.00938	−	1.00938i	0.00942590	−	0.999956i	$-0.497000\pi$
$197$	549820.	−	549820.i	1.00938	−	1.00938i	0.999956	−	0.00942590i	$-0.00300040\pi$
$198$	−258958.	−	246383.i	−0.469426	−	0.446630i
$199$			351145.i			0.628570i	0.949329	+	0.314285i	$0.101765\pi$
$199$			351145.i			0.628570i	−0.949329	+	0.314285i	$0.898235\pi$
$200$	−25459.1	−	340465.i	−0.0450057	−	0.601863i
$201$		−	541733.i		−	0.945791i
$202$	402050.	−	422571.i	0.693269	−	0.728653i
$203$	123828.	−	123828.i	0.210901	−	0.210901i
$204$	154735.	+	140054.i	0.260323	+	0.235625i
$205$	−233897.	−	233897.i	−0.388723	−	0.388723i
$206$	−15152.5	−	608910.i	−0.0248780	−	0.999735i
$207$	392422.			0.636542
$208$	−803128.	−	657307.i	−1.28714	−	1.05344i
$209$	−1.04392e6			−1.65311
$210$	6519.84	+	262003.i	0.0102021	+	0.409975i
$211$	139309.	+	139309.i	0.215413	+	0.215413i	0.806562	−	0.591149i	$-0.201326\pi$
$211$	139309.	+	139309.i	0.215413	+	0.215413i	−0.591149	+	0.806562i	$0.701326\pi$
$212$	−277880.	+	307007.i	−0.424637	+	0.469147i
$213$	286846.	−	286846.i	0.433212	−	0.433212i
$214$	414855.	−	436029.i	0.619244	−	0.650850i
$215$		−	481675.i		−	0.710654i
$216$	−86094.0	+	100010.i	−0.125556	+	0.145851i
$217$			188633.i			0.271936i
$218$	−276925.	−	263477.i	−0.394658	−	0.375493i
$219$	−173326.	+	173326.i	−0.244205	+	0.244205i
$220$	−43702.7	−	877565.i	−0.0608768	−	1.22243i
$221$	519336.	+	519336.i	0.715266	+	0.715266i
$222$	−148640.	+	3698.84i	−0.202419	+	0.00503712i
$223$	865084.			1.16492			0.582460	−	0.812859i	$-0.302090\pi$
$223$	865084.			1.16492			0.582460	+	0.812859i	$0.302090\pi$
$224$	−105115.	−	840633.i	−0.139973	−	1.11940i
$225$	−152772.			−0.201181
$226$	−124789.	+	3105.33i	−0.162520	+	0.00404424i
$227$	−1.01276e6	−	1.01276e6i	−1.30449	−	1.30449i	−0.925330	−	0.379162i	$-0.876212\pi$
$227$	−1.01276e6	−	1.01276e6i	−1.30449	−	1.30449i	−0.379162	−	0.925330i	$-0.623788\pi$
$228$	19169.4	+	384927.i	0.0244214	+	0.490389i
$229$	−665725.	+	665725.i	−0.838892	+	0.838892i	−0.988713	−	0.149821i	$-0.952130\pi$
$229$	−665725.	+	665725.i	−0.838892	+	0.838892i	0.149821	+	0.988713i	$0.452130\pi$
$230$	698862.	+	664925.i	0.871107	+	0.828806i
$231$		−	1.02680e6i		−	1.26607i
$232$	164267.	+	141410.i	0.200369	+	0.172488i
$233$			604350.i			0.729287i	0.931147	+	0.364644i	$0.118809\pi$
$233$			604350.i			0.729287i	−0.931147	+	0.364644i	$0.881191\pi$
$234$	−320102.	+	336439.i	−0.382163	+	0.401668i
$235$	20118.2	−	20118.2i	0.0237640	−	0.0237640i
$236$	550021.	−	607675.i	0.642835	−	0.710217i
$237$	−80425.3	−	80425.3i	−0.0930083	−	0.0930083i
$238$	14914.7	+	599354.i	0.0170676	+	0.685868i
$239$	213979.			0.242313			0.121157	−	0.992633i	$-0.461340\pi$
$239$	213979.			0.242313			0.121157	+	0.992633i	$0.461340\pi$
$240$	−322783.	+	32229.2i	−0.361729	+	0.0361178i
$241$	1.38329e6			1.53416			0.767082	−	0.641549i	$-0.221708\pi$
$241$	1.38329e6			1.53416			0.767082	+	0.641549i	$0.221708\pi$
$242$	62972.8	+	2.53059e6i	0.0691217	+	2.77769i
$243$	41753.9	+	41753.9i	0.0453609	+	0.0453609i
$244$	−481363.	−	435694.i	−0.517605	−	0.468497i
$245$	−114054.	+	114054.i	−0.121394	+	0.121394i
$246$	329793.	−	346625.i	0.347459	−	0.365193i
$247$			1.35627e6i			1.41450i
$248$	−232825.	+	17410.1i	−0.240382	+	0.0179751i
$249$			341753.i			0.349312i
$250$	−722860.	−	687757.i	−0.731483	−	0.695961i
$251$	35622.5	−	35622.5i	0.0356895	−	0.0356895i	−0.689037	−	0.724726i	$-0.741966\pi$
$251$	35622.5	−	35622.5i	0.0356895	−	0.0356895i	0.724726	+	0.689037i	$0.241966\pi$
$252$	−378615.	+	18855.0i	−0.375575	+	0.0187036i
$253$	−2.67238e6	−	2.67238e6i	−2.62480	−	2.62480i
$254$	1.04766e6	−	26070.5i	1.01891	−	0.0253551i
$255$	229566.			0.221084
$256$	1.02787e6	−	207329.i	0.980258	−	0.197724i
$257$	733802.			0.693020			0.346510	−	0.938046i	$-0.387367\pi$
$257$	733802.			0.693020			0.346510	+	0.938046i	$0.387367\pi$
$258$	696490.	−	17331.9i	0.651427	−	0.0162105i
$259$	−302021.	−	302021.i	−0.279761	−	0.279761i
$260$	−1.14013e6	+	56778.7i	−1.04598	+	0.0520898i
$261$	68581.0	−	68581.0i	0.0623164	−	0.0623164i
$262$	−86364.0	−	82170.1i	−0.0777284	−	0.0739538i
$263$		−	1.41048e6i		−	1.25742i	−0.777642	−	0.628708i	$-0.783584\pi$
$263$		−	1.41048e6i		−	1.25742i	0.777642	−	0.628708i	$-0.216416\pi$
$264$	1.26736e6	−	94770.0i	1.11916	−	0.0836876i
$265$			455478.i			0.398431i
$266$	−763142.	+	802093.i	−0.661305	+	0.695057i
$267$	41225.4	−	41225.4i	0.0353905	−	0.0353905i
$268$	1.42806e6	+	1.29257e6i	1.21453	+	1.09930i
$269$	−770645.	−	770645.i	−0.649342	−	0.649342i	0.303492	−	0.952834i	$-0.401848\pi$
$269$	−770645.	−	770645.i	−0.649342	−	0.649342i	−0.952834	+	0.303492i	$0.901848\pi$
$270$	3610.95	+	145108.i	0.00301448	+	0.121138i
$271$	650112.			0.537731			0.268865	−	0.963178i	$-0.413351\pi$
$271$	650112.			0.537731			0.268865	+	0.963178i	$0.413351\pi$
$272$	−738394.	+	73726.9i	−0.605154	+	0.0604232i
$273$	−1.33403e6			−1.08332
$274$	22730.2	+	913427.i	0.0182906	+	0.735017i
$275$	1.04037e6	+	1.04037e6i	0.829576	+	0.829576i
$276$	−936317.	+	1.03446e6i	−0.739861	+	0.817413i
$277$	56782.0	−	56782.0i	0.0444643	−	0.0444643i	−0.684525	−	0.728989i	$-0.739990\pi$
$277$	56782.0	−	56782.0i	0.0444643	−	0.0444643i	0.728989	+	0.684525i	$0.239990\pi$
$278$	−1.39554e6	+	1.46677e6i	−1.08300	+	1.13828i
$279$			104472.i			0.0803509i
$280$	−706221.	−	607951.i	−0.538326	−	0.463419i
$281$		−	394434.i		−	0.297995i	−0.988838	−	0.148997i	$-0.952395\pi$
$281$		−	394434.i		−	0.297995i	0.988838	−	0.148997i	$-0.0476046\pi$
$282$	29814.3	+	28366.5i	0.0223256	+	0.0212414i
$283$	1.78581e6	−	1.78581e6i	1.32547	−	1.32547i	0.416195	−	0.909275i	$-0.363363\pi$
$283$	1.78581e6	−	1.78581e6i	1.32547	−	1.32547i	0.909275	−	0.416195i	$-0.136637\pi$
$284$	71740.3	+	1.44057e6i	0.0527797	+	1.05983i
$285$	299760.	+	299760.i	0.218606	+	0.218606i
$286$	4.47102e6	−	111259.i	3.23215	−	0.0804307i
$287$	1.37441e6			0.984946
$288$	−58217.1	−	465576.i	−0.0413589	−	0.330758i
$289$	−894706.			−0.630138
$290$	238340.	−	5931.00i	0.166419	−	0.00414126i
$291$	6660.88	+	6660.88i	0.00461104	+	0.00461104i
$292$	−43348.9	−	870460.i	−0.0297523	−	0.597436i
$293$	−1.07053e6	+	1.07053e6i	−0.728500	+	0.728500i	−0.970321	−	0.241821i	$-0.922255\pi$
$293$	−1.07053e6	+	1.07053e6i	−0.728500	+	0.728500i	0.241821	+	0.970321i	$0.422255\pi$
$294$	−169023.	−	160815.i	−0.114045	−	0.108507i
$295$		−	901551.i		−	0.603164i
$296$	344903.	−	400654.i	0.228806	−	0.265791i
$297$		−	568685.i		−	0.374094i
$298$	−817837.	+	859579.i	−0.533490	+	0.560719i
$299$	−3.47196e6	+	3.47196e6i	−2.24593	+	2.24593i
$300$	364513.	−	402722.i	0.233835	−	0.258346i
$301$	1.41520e6	+	1.41520e6i	0.900329	+	0.900329i
$302$	−28067.2	−	1.12790e6i	−0.0177085	−	0.711626i
$303$	927986.			0.580677
$304$	−1.06044e6	−	867902.i	−0.658117	−	0.538625i
$305$	−714154.			−0.439584
$306$	8260.35	+	331946.i	0.00504307	+	0.202658i
$307$	−2.03915e6	−	2.03915e6i	−1.23482	−	1.23482i	−0.962092	−	0.272725i	$-0.912075\pi$
$307$	−2.03915e6	−	2.03915e6i	−1.23482	−	1.23482i	−0.272725	−	0.962092i	$-0.587925\pi$
$308$	2.70675e6	+	2.44995e6i	1.62582	+	1.47157i
$309$	685235.	−	685235.i	0.408266	−	0.408266i
$310$	−177019.	+	186054.i	−0.104620	+	0.109960i
$311$		−	810810.i		−	0.475355i	−0.971344	−	0.237678i	$-0.923614\pi$
$311$		−	810810.i		−	0.475355i	0.971344	−	0.237678i	$-0.0763862\pi$
$312$	−123125.	−	1.64656e6i	−0.0716080	−	0.957616i
$313$			2.96600e6i			1.71124i	0.517605	+	0.855620i	$0.326824\pi$
$313$			2.96600e6i			1.71124i	−0.517605	+	0.855620i	$0.673176\pi$
$314$	−84284.6	−	80191.7i	−0.0482419	−	0.0458992i
$315$	−294845.	+	294845.i	−0.167424	+	0.167424i
$316$	403903.	−	20114.4i	0.227541	−	0.0113315i
$317$	336293.	+	336293.i	0.187962	+	0.187962i	0.794814	−	0.606852i	$-0.207568\pi$
$317$	336293.	+	336293.i	0.187962	+	0.187962i	−0.606852	+	0.794814i	$0.707568\pi$
$318$	−658610.	+	16389.2i	−0.365225	+	0.00908847i
$319$	−934067.			−0.513927
$320$	685200.	−	927786.i	0.374061	−	0.506492i
$321$	957541.			0.518674
$322$	−4.00691e6	+	99710.2i	−2.15362	+	0.0535920i
$323$	685726.	+	685726.i	0.365716	+	0.365716i
$324$	−209692.	+	10442.7i	−0.110974	+	0.00552649i
$325$	1.35165e6	−	1.35165e6i	0.709834	−	0.709834i
$326$	−1.72147e6	−	1.63787e6i	−0.897130	−	0.853564i
$327$		−	608141.i		−	0.314510i
$328$	126853.	+	1.69641e6i	0.0651053	+	0.870656i
$329$			118218.i			0.0602134i
$330$	963587.	−	1.01277e6i	0.487087	−	0.511947i
$331$	344712.	−	344712.i	0.172936	−	0.172936i	−0.615332	−	0.788268i	$-0.710978\pi$
$331$	344712.	−	344712.i	0.172936	−	0.172936i	0.788268	+	0.615332i	$0.210978\pi$
$332$	−900893.	−	815421.i	−0.448568	−	0.406010i
$333$	−167271.	−	167271.i	−0.0826629	−	0.0826629i
$334$	1334.55	+	53629.4i	0.000654587	+	0.0263049i
$335$	2.11868e6			1.03146
$336$	853669.	−	1.04305e6i	0.412517	−	0.504032i
$337$	3.46677e6			1.66284			0.831419	−	0.555647i	$-0.187529\pi$
$337$	3.46677e6			1.66284			0.831419	+	0.555647i	$0.187529\pi$
$338$	−92298.4	−	3.70906e6i	−0.0439443	−	1.76592i
$339$	−140431.	−	140431.i	−0.0663689	−	0.0663689i
$340$	−547743.	+	605158.i	−0.256968	+	0.283904i
$341$	711452.	−	711452.i	0.331329	−	0.331329i
$342$	−422659.	+	444231.i	−0.195400	+	0.205373i
$343$			1.78785e6i			0.820533i
$344$	−1.61613e6	+	1.87737e6i	−0.736345	+	0.855369i
$345$			1.53473e6i			0.694202i
$346$	−1.43233e6	−	1.36278e6i	−0.643211	−	0.611976i
$347$	101984.	−	101984.i	0.0454684	−	0.0454684i	−0.684007	−	0.729475i	$-0.739764\pi$
$347$	101984.	−	101984.i	0.0454684	−	0.0454684i	0.729475	+	0.684007i	$0.239764\pi$
$348$	17152.1	+	344420.i	0.00759224	+	0.152455i
$349$	−1.96319e6	−	1.96319e6i	−0.862778	−	0.862778i	0.128882	−	0.991660i	$-0.458861\pi$
$349$	−1.96319e6	−	1.96319e6i	−0.862778	−	0.862778i	−0.991660	+	0.128882i	$0.958861\pi$
$350$	1.55991e6	−	38817.7i	0.680659	−	0.0169379i
$351$	−738838.			−0.320097
$352$	−2.77410e6	+	3.56701e6i	−1.19334	+	1.53443i
$353$	−622189.			−0.265757			−0.132879	−	0.991132i	$-0.542422\pi$
$353$	−622189.			−0.265757			−0.132879	+	0.991132i	$0.542422\pi$
$354$	1.30362e6	−	32440.0i	0.552895	−	0.0137586i
$355$	1.12184e6	+	1.12184e6i	0.472453	+	0.472453i
$356$	10310.5	+	207038.i	0.00431175	+	0.0865814i
$357$	−674481.	+	674481.i	−0.280091	+	0.280091i
$358$	504758.	+	480247.i	0.208150	+	0.198042i
$359$			1.27149e6i			0.520685i	0.965516	+	0.260343i	$0.0838355\pi$
$359$			1.27149e6i			0.520685i	−0.965516	+	0.260343i	$0.916164\pi$
$360$	−391134.	−	336708.i	−0.159063	−	0.136929i
$361$		−	685298.i		−	0.276765i
$362$	2.49235e6	−	2.61955e6i	0.999625	−	1.05064i
$363$	−2.84780e6	+	2.84780e6i	−1.13434	+	1.13434i
$364$	3.18298e6	−	3.51662e6i	1.25916	−	1.39114i
$365$	−677867.	−	677867.i	−0.266325	−	0.266325i
$366$	−25697.0	−	1.03265e6i	−0.0100272	−	0.402949i
$367$	−2.85230e6			−1.10543			−0.552713	−	0.833372i	$-0.686407\pi$
$367$	−2.85230e6			−1.10543			−0.552713	+	0.833372i	$0.686407\pi$
$368$	−492892.	−	4.93644e6i	−0.189728	−	1.90018i
$369$	761205.			0.291029
$370$	−14465.9	−	581319.i	−0.00549339	−	0.220755i
$371$	−1.33823e6	−	1.33823e6i	−0.504772	−	0.504772i
$372$	−275399.	−	249271.i	−0.103182	−	0.0933929i
$373$	548455.	−	548455.i	0.204112	−	0.204112i	−0.597647	−	0.801759i	$-0.703898\pi$
$373$	548455.	−	548455.i	0.204112	−	0.204112i	0.801759	+	0.597647i	$0.203898\pi$
$374$	2.20429e6	−	2.31679e6i	0.814871	−	0.856462i
$375$		−	1.58744e6i		−	0.582932i
$376$	−145914.	+	10911.0i	−0.0532264	+	0.00398012i
$377$			1.21354e6i			0.439746i
$378$	−436947.	−	415728.i	−0.157289	−	0.149651i
$379$	208925.	−	208925.i	0.0747123	−	0.0747123i	−0.668763	−	0.743475i	$-0.733176\pi$
$379$	208925.	−	208925.i	0.0747123	−	0.0747123i	0.743475	+	0.668763i	$0.233176\pi$
$380$	−1.50542e6	+	74970.1i	−0.534810	+	0.0266335i
$381$	1.17898e6	+	1.17898e6i	0.416096	+	0.416096i
$382$	−2.62747e6	+	65383.6i	−0.921256	+	0.0229251i
$383$	−1.53611e6			−0.535089			−0.267544	−	0.963546i	$-0.586212\pi$
$383$	−1.53611e6			−0.535089			−0.267544	+	0.963546i	$0.586212\pi$
$384$	1.36621e6	+	957398.i	0.472813	+	0.331333i
$385$	4.01576e6			1.38075
$386$	593234.	−	14762.4i	0.202655	−	0.00504299i
$387$	783794.	+	783794.i	0.266026	+	0.266026i
$388$	−33451.5	+	1665.89i	−0.0112807	+	0.000561780i
$389$	4.04960e6	−	4.04960e6i	1.35687	−	1.35687i	0.479121	−	0.877749i	$-0.340956\pi$
$389$	4.04960e6	−	4.04960e6i	1.35687	−	1.35687i	0.877749	−	0.479121i	$-0.159044\pi$
$390$	−1.31579e6	−	1.25190e6i	−0.438052	−	0.416780i
$391$			3.51083e6i			1.16136i
$392$	827213.	−	61856.7i	0.271895	−	0.0203316i
$393$		−	189660.i		−	0.0619432i
$394$	−3.03192e6	+	3.18667e6i	−0.983959	+	1.03418i
$395$	314538.	−	314538.i	0.101433	−	0.101433i
$396$	1.49911e6	+	1.35688e6i	0.480391	+	0.434814i
$397$	−1.23329e6	−	1.23329e6i	−0.392724	−	0.392724i	0.482933	−	0.875657i	$-0.339571\pi$
$397$	−1.23329e6	−	1.23329e6i	−0.392724	−	0.392724i	−0.875657	+	0.482933i	$0.839571\pi$
$398$	−49414.8	−	1.98576e6i	−0.0156369	−	0.628375i
$399$	−1.76143e6			−0.553904
$400$	191886.	+	1.92178e6i	0.0599643	+	0.600557i
$401$	−4.20447e6			−1.30572			−0.652861	−	0.757478i	$-0.726431\pi$
$401$	−4.20447e6			−1.30572			−0.652861	+	0.757478i	$0.726431\pi$
$402$	76235.3	+	3.06356e6i	0.0235283	+	0.945498i
$403$	−924321.	−	924321.i	−0.283505	−	0.283505i
$404$	−2.21417e6	+	2.44626e6i	−0.674928	+	0.745674i
$405$	−163297.	+	163297.i	−0.0494698	+	0.0494698i
$406$	−682835.	+	717686.i	−0.205589	+	0.216083i
$407$			2.27822e6i			0.681726i
$408$	−894751.	−	770247.i	−0.266104	−	0.229076i
$409$		−	1.37533e6i		−	0.406535i	−0.979123	−	0.203268i	$-0.934844\pi$
$409$		−	1.37533e6i		−	0.406535i	0.979123	−	0.203268i	$-0.0651562\pi$
$410$	1.35563e6	+	1.28980e6i	0.398273	+	0.378932i
$411$	−1.02792e6	+	1.02792e6i	−0.300162	+	0.300162i
$412$	171378.	+	3.44132e6i	0.0497406	+	0.998807i
$413$	2.64882e6	+	2.64882e6i	0.764148	+	0.764148i
$414$	−2.21919e6	+	55223.5i	−0.636345	+	0.0158352i
$415$	−1.33657e6			−0.380954
$416$	4.63427e6	+	3.60412e6i	1.31295	+	1.02109i
$417$	−3.22109e6			−0.907117
$418$	5.90349e6	−	146906.i	1.65260	−	0.0411243i
$419$	3.65779e6	+	3.65779e6i	1.01785	+	1.01785i	0.999838	+	0.0180131i	$0.00573406\pi$
$419$	3.65779e6	+	3.65779e6i	1.01785	+	1.01785i	0.0180131	+	0.999838i	$0.494266\pi$
$420$	−73740.7	−	1.48074e6i	−0.0203978	−	0.409595i
$421$	466045.	−	466045.i	0.128151	−	0.128151i	−0.640122	−	0.768273i	$-0.721116\pi$
$421$	466045.	−	466045.i	0.128151	−	0.128151i	0.768273	+	0.640122i	$0.221116\pi$
$422$	−807409.	−	768201.i	−0.220705	−	0.209988i
$423$			65473.7i			0.0177917i
$424$	1.52824e6	−	1.77526e6i	0.412834	−	0.479566i
$425$		−	1.36679e6i		−	0.367053i
$426$	−1.58178e6	+	1.66251e6i	−0.422301	+	0.443854i
$427$	2.09824e6	−	2.09824e6i	0.556910	−	0.556910i
$428$	−2.28469e6	+	2.52417e6i	−0.602861	+	0.666053i
$429$	5.03145e6	+	5.03145e6i	1.31993	+	1.31993i
$430$	67783.8	+	2.72392e6i	0.0176789	+	0.710434i
$431$	2.09238e6			0.542558			0.271279	−	0.962501i	$-0.412553\pi$
$431$	2.09238e6			0.542558			0.271279	+	0.962501i	$0.412553\pi$
$432$	472797.	−	577685.i	0.121889	−	0.148930i
$433$	4.76754e6			1.22201			0.611005	−	0.791627i	$-0.290766\pi$
$433$	4.76754e6			1.22201			0.611005	+	0.791627i	$0.290766\pi$
$434$	−26545.3	−	1.06674e6i	−0.00676493	−	0.271852i
$435$	268216.	+	268216.i	0.0679612	+	0.0679612i
$436$	1.60312e6	+	1.45102e6i	0.403877	+	0.365559i
$437$	−4.58434e6	+	4.58434e6i	−1.14835	+	1.14835i
$438$	955786.	−	1.00457e6i	0.238054	−	0.250204i
$439$		−	2.78383e6i		−	0.689416i	−0.938710	−	0.344708i	$-0.887978\pi$
$439$		−	2.78383e6i		−	0.689416i	0.938710	−	0.344708i	$-0.112022\pi$
$440$	370639.	+	4.95657e6i	0.0912681	+	1.22053i
$441$		−	371183.i		−	0.0908849i
$442$	−3.00998e6	−	2.86382e6i	−0.732839	−	0.697251i
$443$	2.18772e6	−	2.18772e6i	0.529642	−	0.529642i	−0.390824	−	0.920465i	$-0.627810\pi$
$443$	2.18772e6	−	2.18772e6i	0.529642	−	0.529642i	0.920465	+	0.390824i	$0.127810\pi$
$444$	840052.	−	41834.6i	0.202231	−	0.0100711i
$445$	161230.	+	161230.i	0.0385962	+	0.0385962i
$446$	−4.89214e6	+	121739.i	−1.16456	+	0.0289796i
$447$	−1.88768e6			−0.446847
$448$	712735.	+	4.73907e6i	0.167777	+	1.11557i
$449$	−1.25760e6			−0.294391			−0.147196	−	0.989107i	$-0.547025\pi$
$449$	−1.25760e6			−0.294391			−0.147196	+	0.989107i	$0.547025\pi$
$450$	863941.	−	21498.8i	0.201119	−	0.00500476i
$451$	−5.18378e6	−	5.18378e6i	−1.20007	−	1.20007i
$452$	705259.	−	35121.9i	0.162369	−	0.00808597i
$453$	1.26928e6	−	1.26928e6i	0.290610	−	0.290610i
$454$	5.86978e6	+	5.58474e6i	1.33654	+	1.27164i
$455$		−	5.21728e6i		−	1.18145i
$456$	−162574.	−	2.17410e6i	−0.0366132	−	0.489630i
$457$		−	3.80045e6i		−	0.851225i	−0.904906	−	0.425612i	$-0.860059\pi$
$457$		−	3.80045e6i		−	0.851225i	0.904906	−	0.425612i	$-0.139941\pi$
$458$	3.67106e6	−	3.85843e6i	0.817763	−	0.859501i
$459$	−373555.	+	373555.i	−0.0827605	+	0.0827605i
$460$	−4.04571e6	−	3.66187e6i	−0.891456	−	0.806879i
$461$	−2.72349e6	−	2.72349e6i	−0.596862	−	0.596862i	0.342614	−	0.939476i	$-0.388688\pi$
$461$	−2.72349e6	−	2.72349e6i	−0.596862	−	0.596862i	−0.939476	+	0.342614i	$0.888688\pi$
$462$	144497.	+	5.80668e6i	0.0314959	+	1.26568i
$463$	−2.61243e6			−0.566359			−0.283180	−	0.959067i	$-0.591389\pi$
$463$	−2.61243e6			−0.566359			−0.283180	+	0.959067i	$0.591389\pi$
$464$	−948849.	−	776570.i	−0.204598	−	0.167450i
$465$	−408584.			−0.0876293
$466$	−85047.1	−	3.41766e6i	−0.0181424	−	0.729061i
$467$	1.63910e6	+	1.63910e6i	0.347788	+	0.347788i	0.859285	−	0.511497i	$-0.170909\pi$
$467$	1.63910e6	+	1.63910e6i	0.347788	+	0.347788i	−0.511497	+	0.859285i	$0.670909\pi$
$468$	1.76286e6	−	1.94765e6i	0.372052	−	0.411051i
$469$	−6.22484e6	+	6.22484e6i	−1.30676	+	1.30676i
$470$	−110940.	+	116602.i	−0.0231655	+	0.0243479i
$471$		−	185093.i		−	0.0384448i
$472$	−3.02491e6	+	3.51386e6i	−0.624968	+	0.725989i
$473$		−	1.06752e7i		−	2.19393i
$474$	466131.	+	443495.i	0.0952933	+	0.0906658i
$475$	1.78471e6	−	1.78471e6i	0.362939	−	0.362939i
$476$	−168688.	−	3.38731e6i	−0.0341245	−	0.685231i
$477$	−741165.	−	741165.i	−0.149149	−	0.149149i
$478$	−1.21007e6	+	30112.2i	−0.242238	+	0.00602800i
$479$	−2.98588e6			−0.594612			−0.297306	−	0.954782i	$-0.596088\pi$
$479$	−2.98588e6			−0.594612			−0.297306	+	0.954782i	$0.596088\pi$
$480$	1.82084e6	−	227683.i	0.360718	−	0.0451053i
$481$	2.95987e6			0.583324
$482$	−7.82267e6	+	194664.i	−1.53369	+	0.0381652i
$483$	−4.50916e6	−	4.50916e6i	−0.879484	−	0.879484i
$484$	−712235.	−	1.43019e7i	−0.138201	−	2.77511i
$485$	−26050.2	+	26050.2i	−0.00502872	+	0.00502872i
$486$	−241999.	−	230247.i	−0.0464753	−	0.0442184i
$487$			942765.i			0.180128i	0.995936	+	0.0900640i	$0.0287072\pi$
$487$			942765.i			0.180128i	−0.995936	+	0.0900640i	$0.971293\pi$
$488$	2.78347e6	+	2.39615e6i	0.529099	+	0.455476i
$489$		−	3.78043e6i		−	0.714939i
$490$	628937.	−	661038.i	0.118336	−	0.124376i
$491$	3.24559e6	−	3.24559e6i	0.607561	−	0.607561i	−0.334747	−	0.942308i	$-0.608651\pi$
$491$	3.24559e6	−	3.24559e6i	0.607561	−	0.607561i	0.942308	+	0.334747i	$0.108651\pi$
$492$	−1.81623e6	+	2.00661e6i	−0.338266	+	0.373723i
$493$	613566.	+	613566.i	0.113696	+	0.113696i
$494$	−190861.	−	7.66983e6i	−0.0351883	−	1.41406i
$495$	2.22409e6			0.407980
$496$	1.31420e6	−	131220.i	0.239860	−	0.0239495i
$497$	−6.59207e6			−1.19710
$498$	−48093.1	−	1.93265e6i	−0.00868980	−	0.349204i
$499$	2.21435e6	+	2.21435e6i	0.398102	+	0.398102i	0.877563	−	0.479461i	$-0.159168\pi$
$499$	2.21435e6	+	2.21435e6i	0.398102	+	0.398102i	−0.479461	+	0.877563i	$0.659168\pi$
$500$	4.18463e6	+	3.78761e6i	0.748570	+	0.677549i
$501$	−60351.8	+	60351.8i	−0.0107423	+	0.0107423i
$502$	−196436.	+	206462.i	−0.0347906	+	0.0365663i
$503$			5.15904e6i			0.909178i	0.890701	+	0.454589i	$0.150214\pi$
$503$			5.15904e6i			0.909178i	−0.890701	+	0.454589i	$0.849786\pi$
$504$	2.13845e6	−	159908.i	0.374993	−	0.0280410i
$505$			3.62929e6i			0.633276i
$506$	1.54886e7	+	1.47365e7i	2.68928	+	2.55869i
$507$	4.17398e6	−	4.17398e6i	0.721159	−	0.721159i
$508$	−5.92094e6	+	294863.i	−1.01796	+	0.0506945i
$509$	−755918.	−	755918.i	−0.129324	−	0.129324i	0.639482	−	0.768806i	$-0.279149\pi$
$509$	−755918.	−	755918.i	−0.129324	−	0.129324i	−0.768806	+	0.639482i	$0.779149\pi$
$510$	−1.29822e6	+	32305.6i	−0.221015	+	0.00549988i
$511$	3.98325e6			0.674815
$512$	−5.78356e6	+	1.31711e6i	−0.975036	+	0.222049i
$513$	−975554.			−0.163666
$514$	−4.14972e6	+	103264.i	−0.692806	+	0.0172402i
$515$	2.67991e6	+	2.67991e6i	0.445248	+	0.445248i
$516$	−3.93628e6	+	196027.i	−0.650822	+	0.0324110i
$517$	445873.	−	445873.i	0.0733644	−	0.0733644i
$518$	1.75046e6	+	1.66546e6i	0.286634	+	0.272715i
$519$		−	3.14547e6i		−	0.512586i
$520$	6.43959e6	−	481535.i	1.04436	−	0.0780943i
$521$		−	3.39802e6i		−	0.548443i	−0.961667	−	0.274221i	$-0.911580\pi$
$521$		−	3.39802e6i		−	0.548443i	0.961667	−	0.274221i	$-0.0884201\pi$
$522$	−378182.	+	397484.i	−0.0607469	+	0.0638474i
$523$	4.50826e6	−	4.50826e6i	0.720701	−	0.720701i	−0.248047	−	0.968748i	$-0.579789\pi$
$523$	4.50826e6	−	4.50826e6i	0.720701	−	0.720701i	0.968748	+	0.248047i	$0.0797888\pi$
$524$	499961.	+	452527.i	0.0795440	+	0.0719973i
$525$	1.75544e6	+	1.75544e6i	0.277964	+	0.277964i
$526$	198490.	+	7.97643e6i	0.0312806	+	1.25703i
$527$	−934670.			−0.146599
$528$	−7.15373e6	+	714284.i	−1.11673	+	0.111503i
$529$	−1.70349e7			−2.64668
$530$	−64097.2	−	2.57578e6i	−0.00991172	−	0.398308i
$531$	1.46702e6	+	1.46702e6i	0.225788	+	0.225788i
$532$	4.20277e6	−	4.64331e6i	0.643809	−	0.711293i
$533$	−6.73478e6	+	6.73478e6i	−1.02685	+	1.02685i
$534$	−227332.	+	238935.i	−0.0344991	+	0.0362599i
$535$			3.74488e6i			0.565657i
$536$	−8.25772e6	−	7.10867e6i	−1.24150	−	1.06875i
$537$			1.10847e6i			0.165878i
$538$	4.46653e6	+	4.24963e6i	0.665295	+	0.632988i
$539$	−2.52774e6	+	2.52774e6i	−0.374766	+	0.374766i
$540$	−40840.6	−	820092.i	−0.00602709	−	0.121026i
$541$	5.18951e6	+	5.18951e6i	0.762313	+	0.762313i	0.976740	−	0.214427i	$-0.0687885\pi$
$541$	5.18951e6	+	5.18951e6i	0.762313	+	0.762313i	−0.214427	+	0.976740i	$0.568788\pi$
$542$	−3.67645e6	+	91486.9i	−0.537564	+	0.0133771i
$543$	5.75267e6			0.837278
$544$	4.16532e6	−	520844.i	0.603463	−	0.0754588i
$545$	2.37840e6			0.342999
$546$	7.54406e6	−	187731.i	1.08299	−	0.0269497i
$547$	7.57146e6	+	7.57146e6i	1.08196	+	1.08196i	0.996327	+	0.0856330i	$0.0272912\pi$
$547$	7.57146e6	+	7.57146e6i	1.08196	+	1.08196i	0.0856330	+	0.996327i	$0.472709\pi$
$548$	−257084.	−	5.16232e6i	−0.0365699	−	0.734334i
$549$	1.16209e6	−	1.16209e6i	0.164554	−	0.164554i
$550$	−6.02981e6	−	5.73700e6i	−0.849957	−	0.808682i
$551$			1.60235e6i			0.224843i
$552$	5.14939e6	−	5.98175e6i	0.719297	−	0.835566i
$553$			1.84827e6i			0.257012i
$554$	−313117.	+	329099.i	−0.0433444	+	0.0455566i
$555$	654186.	−	654186.i	0.0901507	−	0.0901507i
$556$	7.68551e6	−	8.49111e6i	1.05435	−	1.16487i
$557$	7.81494e6	+	7.81494e6i	1.06730	+	1.06730i	0.997565	+	0.0697369i	$0.0222160\pi$
$557$	7.81494e6	+	7.81494e6i	1.06730	+	1.06730i	0.0697369	+	0.997565i	$0.477784\pi$
$558$	−14701.9	−	590802.i	−0.00199888	−	0.0803261i
$559$	−1.38693e7			−1.87726
$560$	4.07931e6	+	3.33864e6i	0.549688	+	0.449883i
$561$	5.08779e6			0.682530
$562$	55506.7	+	2.23057e6i	0.00741318	+	0.297902i
$563$	2.70886e6	+	2.70886e6i	0.360177	+	0.360177i	0.863878	−	0.503701i	$-0.168029\pi$
$563$	2.70886e6	+	2.70886e6i	0.360177	+	0.360177i	−0.503701	+	0.863878i	$0.668029\pi$
$564$	−172595.	−	156220.i	−0.0228471	−	0.0206795i
$565$	549217.	−	549217.i	0.0723808	−	0.0723808i
$566$	−9.84765e6	+	1.03503e7i	−1.29209	+	1.35803i
$567$		−	959556.i		−	0.125347i
$568$	−608423.	−	8.13646e6i	−0.0791288	−	1.05819i
$569$			1.45337e7i			1.88190i	0.338550	+	0.940948i	$0.390064\pi$
$569$			1.45337e7i			1.88190i	−0.338550	+	0.940948i	$0.609936\pi$
$570$	−1.73736e6	−	1.65299e6i	−0.223976	−	0.213100i
$571$	−4.07932e6	+	4.07932e6i	−0.523597	+	0.523597i	−0.918656	−	0.395059i	$-0.870724\pi$
$571$	−4.07932e6	+	4.07932e6i	−0.523597	+	0.523597i	0.395059	+	0.918656i	$0.370724\pi$
$572$	−2.52684e7	+	1.25837e6i	−3.22915	+	0.160812i
$573$	−2.95682e6	−	2.95682e6i	−0.376217	−	0.376217i
$574$	−7.77245e6	+	193414.i	−0.984641	+	0.0245024i
$575$	9.13749e6			1.15254
$576$	394742.	+	2.62469e6i	0.0495743	+	0.329626i
$577$	5.84909e6			0.731389			0.365695	−	0.930735i	$-0.380831\pi$
$577$	5.84909e6			0.731389			0.365695	+	0.930735i	$0.380831\pi$
$578$	5.05965e6	−	125907.i	0.629943	−	0.0156759i
$579$	667594.	+	667594.i	0.0827592	+	0.0827592i
$580$	−1.34700e6	+	67080.8i	−0.166264	+	0.00827996i
$581$	3.92695e6	−	3.92695e6i	0.482630	−	0.482630i
$582$	−38605.3	−	36730.6i	−0.00472432	−	0.00449490i
$583$			1.00946e7i			1.23004i
$584$	367638.	+	4.91644e6i	0.0446055	+	0.596511i
$585$		−	2.88954e6i		−	0.349092i
$586$	5.90330e6	−	6.20460e6i	0.710152	−	0.746397i
$587$	7.84557e6	−	7.84557e6i	0.939787	−	0.939787i	−0.0585003	−	0.998287i	$-0.518632\pi$
$587$	7.84557e6	−	7.84557e6i	0.939787	−	0.939787i	0.998287	+	0.0585003i	$0.0186319\pi$
$588$	978474.	+	885641.i	0.116709	+	0.105637i
$589$	−1.22046e6	−	1.22046e6i	−0.144956	−	0.144956i
$590$	126871.	+	5.09836e6i	0.0150048	+	0.602977i
$591$	−6.99807e6			−0.824157
$592$	−1.89408e6	+	2.31427e6i	−0.222123	+	0.271400i
$593$	−50575.8			−0.00590618			−0.00295309	−	0.999996i	$-0.500940\pi$
$593$	−50575.8			−0.00590618			−0.00295309	+	0.999996i	$0.500940\pi$
$594$	80028.2	+	3.21597e6i	0.00930630	+	0.373978i
$595$	−2.63785e6	−	2.63785e6i	−0.305462	−	0.305462i
$596$	4.50399e6	−	4.97610e6i	0.519376	−	0.573817i
$597$	2.23467e6	−	2.23467e6i	0.256613	−	0.256613i
$598$	1.91457e7	−	2.01229e7i	2.18936	−	2.30111i
$599$		−	868370.i		−	0.0988867i	−0.998777	−	0.0494433i	$-0.984255\pi$
$599$		−	868370.i		−	0.0988867i	0.998777	−	0.0494433i	$-0.0157447\pi$
$600$	−2.00469e6	+	2.32873e6i	−0.227336	+	0.264083i
$601$			1.08662e7i			1.22714i	0.789642	+	0.613568i	$0.210266\pi$
$601$			1.08662e7i			1.22714i	−0.789642	+	0.613568i	$0.789734\pi$
$602$	−8.20225e6	−	7.80394e6i	−0.922447	−	0.877653i
$603$	−3.44757e6	+	3.44757e6i	−0.386117	+	0.386117i
$604$	317446.	+	6.37442e6i	0.0354061	+	0.710965i
$605$	−1.11375e7	−	1.11375e7i	−1.23709	−	1.23709i
$606$	−5.24786e6	+	130591.i	−0.580498	+	0.0144454i
$607$	5.97402e6			0.658104			0.329052	−	0.944312i	$-0.393271\pi$
$607$	5.97402e6			0.658104			0.329052	+	0.944312i	$0.393271\pi$
$608$	6.11905e6	+	4.75884e6i	0.671313	+	0.522086i
$609$	−1.57607e6			−0.172200
$610$	4.03861e6	−	100499.i	0.439448	−	0.0109355i
$611$	−579280.	−	579280.i	−0.0627748	−	0.0627748i
$612$	−93426.2	−	1.87603e6i	−0.0100830	−	0.202470i
$613$	−6.91894e6	+	6.91894e6i	−0.743684	+	0.743684i	−0.973285	−	0.229601i	$-0.926258\pi$
$613$	−6.91894e6	+	6.91894e6i	−0.743684	+	0.743684i	0.229601	+	0.973285i	$0.426258\pi$
$614$	1.18185e7	+	1.12446e7i	1.26515	+	1.20372i
$615$			2.97702e6i			0.317391i
$616$	−1.56517e7	−	1.34738e7i	−1.66192	−	1.43067i
$617$		−	3.07128e6i		−	0.324793i	−0.986726	−	0.162396i	$-0.948078\pi$
$617$		−	3.07128e6i		−	0.324793i	0.986726	−	0.162396i	$-0.0519223\pi$
$618$	−3.77865e6	+	3.97151e6i	−0.397984	+	0.418296i
$619$	4.99436e6	−	4.99436e6i	0.523906	−	0.523906i	−0.394842	−	0.918749i	$-0.629201\pi$
$619$	4.99436e6	−	4.99436e6i	0.523906	−	0.523906i	0.918749	+	0.394842i	$0.129201\pi$
$620$	974880.	−	1.07707e6i	0.101853	−	0.112529i
$621$	−2.49736e6	−	2.49736e6i	−0.259867	−	0.259867i
$622$	114101.	+	4.58522e6i	0.0118254	+	0.475208i
$623$	−947409.			−0.0977952
$624$	927999.	+	9.29415e6i	0.0954083	+	0.955539i
$625$	314368.			0.0321913
$626$	−417391.	−	1.67731e7i	−0.0425703	−	1.71071i
$627$	6.64348e6	+	6.64348e6i	0.674880	+	0.674880i
$628$	487923.	+	441631.i	0.0493688	+	0.0446849i
$629$	1.49651e6	−	1.49651e6i	0.150818	−	0.150818i
$630$	1.62588e6	−	1.70887e6i	0.163207	−	0.171537i
$631$		−	6.40949e6i		−	0.640841i	−0.947275	−	0.320420i	$-0.896176\pi$
$631$		−	6.40949e6i		−	0.640841i	0.947275	−	0.320420i	$-0.103824\pi$
$632$	−2.28128e6	+	170588.i	−0.227189	+	0.0169885i
$633$		−	1.77311e6i		−	0.175884i
$634$	−1.94910e6	−	1.85445e6i	−0.192580	−	0.183228i
$635$	−4.61091e6	+	4.61091e6i	−0.453787	+	0.453787i
$636$	3.72220e6	−	185366.i	0.364886	−	0.0181713i
$637$	3.28405e6	+	3.28405e6i	0.320672	+	0.320672i
$638$	5.28225e6	−	131447.i	0.513768	−	0.0127849i
$639$	−3.65096e6			−0.353716
$640$	−3.74432e6	+	5.34315e6i	−0.361345	+	0.515641i
$641$	−5.63241e6			−0.541439			−0.270719	−	0.962658i	$-0.587262\pi$
$641$	−5.63241e6			−0.541439			−0.270719	+	0.962658i	$0.587262\pi$
$642$	−5.41499e6	+	134750.i	−0.518514	+	0.0129030i
$643$	−2.93713e6	−	2.93713e6i	−0.280153	−	0.280153i	0.553017	−	0.833170i	$-0.313476\pi$
$643$	−2.93713e6	−	2.93713e6i	−0.280153	−	0.280153i	−0.833170	+	0.553017i	$0.813476\pi$
$644$	2.26454e7	−	1.12774e6i	2.15162	−	0.107151i
$645$	−3.06536e6	+	3.06536e6i	−0.290123	+	0.290123i
$646$	−3.97435e6	−	3.78135e6i	−0.374701	−	0.356505i
$647$		−	8.76349e6i		−	0.823031i	−0.911403	−	0.411516i	$-0.865000\pi$
$647$		−	8.76349e6i		−	0.823031i	0.911403	−	0.411516i	$-0.135000\pi$
$648$	1.18436e6	−	88563.3i	0.110802	−	0.00828545i
$649$		−	1.99808e7i		−	1.86209i
$650$	−7.45353e6	+	7.83395e6i	−0.691956	+	0.727273i
$651$	1.20045e6	−	1.20045e6i	0.111018	−	0.111018i
$652$	9.96558e6	+	9.02009e6i	0.918086	+	0.830983i
$653$	1.40251e7	+	1.40251e7i	1.28713	+	1.28713i	0.936522	+	0.350609i	$0.114025\pi$
$653$	1.40251e7	+	1.40251e7i	1.28713	+	1.28713i	0.350609	+	0.936522i	$0.385975\pi$
$654$	85580.6	+	3.43910e6i	0.00782404	+	0.314413i
$655$	741745.			0.0675541
$656$	−956094.	−	9.57553e6i	−0.0867443	−	0.868767i
$657$	2.20608e6			0.199392
$658$	−16636.2	−	668533.i	−0.00149792	−	0.0601947i
$659$	−1.42602e7	−	1.42602e7i	−1.27912	−	1.27912i	−0.941159	−	0.337965i	$-0.890261\pi$
$659$	−1.42602e7	−	1.42602e7i	−1.27912	−	1.27912i	−0.337965	−	0.941159i	$-0.609739\pi$
$660$	−5.30667e6	+	5.86291e6i	−0.474200	+	0.523906i
$661$	5.74184e6	−	5.74184e6i	0.511149	−	0.511149i	−0.403730	−	0.914878i	$-0.632286\pi$
$661$	5.74184e6	−	5.74184e6i	0.511149	−	0.511149i	0.914878	+	0.403730i	$0.132286\pi$
$662$	−1.90087e6	+	1.99789e6i	−0.168581	+	0.177185i
$663$		−	6.61007e6i		−	0.584013i
$664$	5.20939e6	+	4.48451e6i	0.458529	+	0.394725i
$665$		−	6.88885e6i		−	0.604077i
$666$	969476.	+	922397.i	0.0846937	+	0.0805810i
$667$	−4.10192e6	+	4.10192e6i	−0.357003	+	0.357003i
$668$	−15094.0	−	303092.i	−0.00130877	−	0.0262805i
$669$	−5.50536e6	−	5.50536e6i	−0.475577	−	0.475577i
$670$	−1.19814e7	+	298151.i	−1.03114	+	0.0256596i
$671$	−1.58275e7			−1.35709
$672$	−4.68081e6	+	6.01870e6i	−0.399850	+	0.514138i
$673$	−846028.			−0.0720024			−0.0360012	−	0.999352i	$-0.511462\pi$
$673$	−846028.			−0.0720024			−0.0360012	+	0.999352i	$0.511462\pi$
$674$	−1.96049e7	+	487860.i	−1.66232	+	0.0413662i
$675$	972235.	+	972235.i	0.0821319	+	0.0821319i
$676$	1.04391e6	+	2.09621e7i	0.0878614	+	1.76428i
$677$	1.27193e7	−	1.27193e7i	1.06658	−	1.06658i	0.0689566	−	0.997620i	$-0.478033\pi$
$677$	1.27193e7	−	1.27193e7i	1.06658	−	1.06658i	0.997620	−	0.0689566i	$-0.0219670\pi$
$678$	813916.	+	774392.i	0.0679995	+	0.0646974i
$679$		−	153075.i		−	0.0127418i
$680$	3.01238e6	−	3.49931e6i	0.249826	−	0.290209i
$681$			1.28903e7i			1.06511i
$682$	−3.92322e6	+	4.12346e6i	−0.322984	+	0.339469i
$683$	−6.68908e6	+	6.68908e6i	−0.548674	+	0.548674i	−0.926057	−	0.377383i	$-0.876824\pi$
$683$	−6.68908e6	+	6.68908e6i	−0.548674	+	0.548674i	0.377383	+	0.926057i	$0.376824\pi$
$684$	2.32767e6	−	2.57165e6i	0.190231	−	0.210171i
$685$	−4.02014e6	−	4.02014e6i	−0.327351	−	0.327351i
$686$	−251595.	−	1.01105e7i	−0.0204123	−	0.820279i
$687$	8.47329e6			0.684952
$688$	8.87521e6	−	1.08441e7i	0.714838	−	0.873422i
$689$	1.31149e7			1.05249
$690$	−215975.	−	8.67908e6i	−0.0172696	−	0.693987i
$691$	4.41088e6	+	4.41088e6i	0.351423	+	0.351423i	0.860639	−	0.509216i	$-0.170065\pi$
$691$	4.41088e6	+	4.41088e6i	0.351423	+	0.351423i	−0.509216	+	0.860639i	$0.670065\pi$
$692$	8.29176e6	+	7.50508e6i	0.658236	+	0.595785i
$693$	−6.53454e6	+	6.53454e6i	−0.516870	+	0.516870i
$694$	−562380.	+	591084.i	−0.0443232	+	0.0465855i
$695$		−	1.25975e7i		−	0.989285i
$696$	−145466.	−	1.94532e6i	−0.0113825	−	0.152218i
$697$			6.81019e6i			0.530979i
$698$	1.13783e7	+	1.08258e7i	0.883975	+	0.841048i
$699$	3.84606e6	−	3.84606e6i	0.297730	−	0.297730i
$700$	−8.81599e6	+	439037.i	−0.680027	+	0.0338654i
$701$	−586205.	−	586205.i	−0.0450562	−	0.0450562i	0.684220	−	0.729276i	$-0.260143\pi$
$701$	−586205.	−	586205.i	−0.0450562	−	0.0450562i	−0.729276	+	0.684220i	$0.760143\pi$
$702$	4.17820e6	−	103973.i	0.319998	−	0.00796301i
$703$	3.90818e6			0.298254
$704$	1.51859e7	−	2.05622e7i	1.15480	−	1.56364i
$705$	−256063.			−0.0194033
$706$	3.51854e6	−	87557.5i	0.265675	−	0.00661122i
$707$	−1.06631e7	−	1.06631e7i	−0.802298	−	0.802298i
$708$	−7.36753e6	+	366903.i	−0.552381	+	0.0275086i
$709$	2.71020e6	−	2.71020e6i	0.202481	−	0.202481i	−0.598581	−	0.801062i	$-0.704269\pi$
$709$	2.71020e6	−	2.71020e6i	0.202481	−	0.202481i	0.801062	+	0.598581i	$0.204269\pi$
$710$	−6.50197e6	−	6.18623e6i	−0.484060	−	0.460553i
$711$			1.02365e6i			0.0759410i
$712$	−87442.2	−	1.16937e6i	−0.00646429	−	0.0864473i
$713$		−	6.24863e6i		−	0.460321i
$714$	3.71935e6	−	3.90918e6i	0.273037	−	0.286972i
$715$	−1.96777e7	+	1.96777e7i	−1.43949	+	1.43949i
$716$	−2.92204e6	−	2.64481e6i	−0.213012	−	0.192802i
$717$	−1.36176e6	−	1.36176e6i	−0.0989239	−	0.0989239i
$718$	−178930.	−	7.19038e6i	−0.0129530	−	0.520524i
$719$	1.08394e7			0.781957			0.390979	−	0.920400i	$-0.372137\pi$
$719$	1.08394e7			0.781957			0.390979	+	0.920400i	$0.372137\pi$
$720$	2.25929e6	+	1.84907e6i	0.162420	+	0.132930i
$721$	−1.57475e7			−1.12817
$722$	96438.6	+	3.87543e6i	0.00688506	+	0.276680i
$723$	−8.80323e6	−	8.80323e6i	−0.626320	−	0.626320i
$724$	−1.37258e7	+	1.51646e7i	−0.973179	+	1.07519i
$725$	1.59690e6	−	1.59690e6i	0.112832	−	0.112832i
$726$	1.57038e7	−	1.65054e7i	1.10577	−	1.16221i
$727$		−	1.53703e7i		−	1.07856i	−0.842125	−	0.539282i	$-0.818696\pi$
$727$		−	1.53703e7i		−	1.07856i	0.842125	−	0.539282i	$-0.181304\pi$
$728$	−1.75052e7	+	2.03348e7i	−1.22416	+	1.42204i
$729$		−	531441.i		−	0.0370370i
$730$	3.92880e6	+	3.73801e6i	0.272868	+	0.259617i
$731$	−7.01228e6	+	7.01228e6i	−0.485362	+	0.485362i
$732$	290639.	+	5.83611e6i	0.0200482	+	0.402574i
$733$	−1.85659e7	−	1.85659e7i	−1.27631	−	1.27631i	−0.942716	−	0.333597i	$-0.891738\pi$
$733$	−1.85659e7	−	1.85659e7i	−1.27631	−	1.27631i	−0.333597	−	0.942716i	$-0.608262\pi$
$734$	1.61300e7	−	401389.i	1.10508	−	0.0274996i
$735$	1.45167e6			0.0991174
$736$	3.48204e6	+	2.78467e7i	0.236940	+	1.89487i
$737$	4.69556e7			3.18433
$738$	−4.30470e6	+	107121.i	−0.290939	+	0.00723989i
$739$	6.82947e6	+	6.82947e6i	0.460019	+	0.460019i	0.898662	−	0.438642i	$-0.144540\pi$
$739$	6.82947e6	+	6.82947e6i	0.460019	+	0.460019i	−0.438642	+	0.898662i	$0.644540\pi$
$740$	163612.	+	3.28538e6i	0.0109834	+	0.220550i
$741$	8.63123e6	−	8.63123e6i	0.577467	−	0.577467i
$742$	7.75615e6	+	7.37950e6i	0.517173	+	0.492059i
$743$			1.67926e7i			1.11595i	0.829857	+	0.557976i	$0.188422\pi$
$743$			1.67926e7i			1.11595i	−0.829857	+	0.557976i	$0.811578\pi$
$744$	1.59249e6	+	1.37090e6i	0.105474	+	0.0907971i
$745$		−	7.38258e6i		−	0.487324i
$746$	−3.02439e6	+	3.17875e6i	−0.198971	+	0.209127i
$747$	2.17490e6	−	2.17490e6i	0.142606	−	0.142606i
$748$	−1.21394e7	+	1.34119e7i	−0.793313	+	0.876468i
$749$	−1.10027e7	−	1.10027e7i	−0.716631	−	0.716631i
$750$	223392.	+	8.97711e6i	0.0145015	+	0.582752i
$751$	2.17592e7			1.40781			0.703903	−	0.710296i	$-0.251439\pi$
$751$	2.17592e7			1.40781			0.703903	+	0.710296i	$0.251439\pi$
$752$	823622.	−	82236.7i	0.0531109	−	0.00530300i
$753$	−453401.			−0.0291403
$754$	−170776.	−	6.86271e6i	−0.0109395	−	0.439610i
$755$	4.96405e6	+	4.96405e6i	0.316934	+	0.316934i
$756$	2.52948e6	+	2.28950e6i	0.160963	+	0.145692i
$757$	1.54368e7	−	1.54368e7i	0.979081	−	0.979081i	−0.0207046	−	0.999786i	$-0.506591\pi$
$757$	1.54368e7	−	1.54368e7i	0.979081	−	0.979081i	0.999786	+	0.0207046i	$0.00659095\pi$
$758$	−1.15209e6	+	1.21089e6i	−0.0728306	+	0.0765478i
$759$			3.40138e7i			2.14314i
$760$	8.50277e6	−	635814.i	0.533982	−	0.0399297i
$761$			2.84056e7i			1.77804i	0.457868	+	0.889020i	$0.348613\pi$
$761$			2.84056e7i			1.77804i	−0.457868	+	0.889020i	$0.651387\pi$
$762$	−6.83317e6	−	6.50134e6i	−0.426319	−	0.405616i
$763$	−6.98791e6	+	6.98791e6i	−0.434546	+	0.434546i
$764$	1.48494e7	−	739502.i	0.920400	−	0.0458360i
$765$	−1.46095e6	−	1.46095e6i	−0.0902571	−	0.0902571i
$766$	8.68687e6	−	216169.i	0.534923	−	0.0133113i
$767$	−2.59591e7			−1.59331
$768$	−7.86079e6	−	5.22192e6i	−0.480909	−	0.319468i
$769$	1.05061e7			0.640657			0.320328	−	0.947307i	$-0.396207\pi$
$769$	1.05061e7			0.640657			0.320328	+	0.947307i	$0.396207\pi$
$770$	−2.27095e7	+	565117.i	−1.38032	+	0.0343488i
$771$	−4.66989e6	−	4.66989e6i	−0.282924	−	0.282924i
$772$	−3.35272e6	+	166966.i	−0.202467	+	0.0100829i
$773$	−6.12083e6	+	6.12083e6i	−0.368435	+	0.368435i	−0.866906	−	0.498471i	$-0.833895\pi$
$773$	−6.12083e6	+	6.12083e6i	−0.368435	+	0.368435i	0.498471	+	0.866906i	$0.333895\pi$
$774$	−4.54274e6	−	4.32214e6i	−0.272562	−	0.259326i
$775$			2.43262e6i			0.145486i
$776$	188937.	−	14128.2i	0.0112632	−	0.000842235i
$777$			3.84410e6i			0.228424i
$778$	−2.23310e7	+	2.34708e7i	−1.32270	+	1.39020i
$779$	−8.89253e6	+	8.89253e6i	−0.525027	+	0.525027i
$780$	7.61711e6	+	6.89444e6i	0.448285	+	0.405753i
$781$	2.48628e7	+	2.48628e7i	1.45856	+	1.45856i
$782$	−494062.	−	1.98541e7i	−0.0288911	−	1.16100i
$783$	−872894.			−0.0508812
$784$	−4.66927e6	+	466216.i	−0.271306	+	0.0270892i
$785$	723886.			0.0419272
$786$	26689.8	+	1.07254e6i	0.00154095	+	0.0619240i
$787$	−1.18146e7	−	1.18146e7i	−0.679959	−	0.679959i	0.280032	−	0.959991i	$-0.409655\pi$
$787$	−1.18146e7	−	1.18146e7i	−0.679959	−	0.679959i	−0.959991	+	0.280032i	$0.909655\pi$
$788$	1.66974e7	−	1.84476e7i	0.957927	−	1.05834i
$789$	−8.97626e6	+	8.97626e6i	−0.513338	+	0.513338i
$790$	−1.73448e6	+	1.82301e6i	−0.0988784	+	0.103925i
$791$			3.22728e6i			0.183399i
$792$	−8.66856e6	−	7.46234e6i	−0.491059	−	0.422729i
$793$			2.05632e7i			1.16120i
$794$	7.14791e6	+	6.80080e6i	0.402372	+	0.382833i
$795$	2.89865e6	−	2.89865e6i	0.162659	−	0.162659i
$796$	558892.	+	1.12227e7i	0.0312641	+	0.627792i
$797$	−1.12494e7	−	1.12494e7i	−0.627313	−	0.627313i	0.320078	−	0.947391i	$-0.396291\pi$
$797$	−1.12494e7	−	1.12494e7i	−0.627313	−	0.627313i	−0.947391	+	0.320078i	$0.896291\pi$
$798$	9.96109e6	−	247878.i	0.553732	−	0.0137794i
$799$	−585766.			−0.0324607
$800$	−1.35558e6	−	1.08409e7i	−0.0748857	−	0.598880i
$801$	−524714.			−0.0288962
$802$	2.37767e7	−	591674.i	1.30532	−	0.0324823i
$803$	−1.50233e7	−	1.50233e7i	−0.822200	−	0.822200i
$804$	−862237.	−	1.73140e7i	−0.0470421	−	0.944620i
$805$	1.76350e7	−	1.76350e7i	0.959150	−	0.959150i
$806$	5.35721e6	+	5.09706e6i	0.290470	+	0.276364i
$807$			9.80871e6i			0.530186i
$808$	1.21771e7	−	1.41454e7i	0.656169	−	0.762234i
$809$			2.15883e7i			1.15970i	0.814722	+	0.579852i	$0.196890\pi$
$809$			2.15883e7i			1.15970i	−0.814722	+	0.579852i	$0.803110\pi$
$810$	900480.	−	946440.i	0.0482238	−	0.0506851i
$811$	−4.57772e6	+	4.57772e6i	−0.244398	+	0.244398i	−0.818667	−	0.574269i	$-0.805286\pi$
$811$	−4.57772e6	+	4.57772e6i	−0.244398	+	0.244398i	0.574269	+	0.818667i	$0.305286\pi$
$812$	3.76051e6	−	4.15468e6i	0.200150	−	0.221130i
$813$	−4.13729e6	−	4.13729e6i	−0.219528	−	0.219528i
$814$	−320602.	−	1.28836e7i	−0.0169592	−	0.681515i
$815$	1.47850e7			0.779700
$816$	5.16830e6	+	4.22991e6i	0.271721	+	0.222385i
$817$	−1.83128e7			−0.959843
$818$	193543.	+	7.77763e6i	0.0101133	+	0.406409i
$819$	8.48969e6	+	8.48969e6i	0.442264	+	0.442264i
$820$	−7.84772e6	−	7.10316e6i	−0.407576	−	0.368907i
$821$	−1.52456e7	+	1.52456e7i	−0.789383	+	0.789383i	−0.981393	−	0.192010i	$-0.938499\pi$
$821$	−1.52456e7	+	1.52456e7i	−0.789383	+	0.789383i	0.192010	+	0.981393i	$0.438499\pi$
$822$	5.66836e6	−	5.95767e6i	0.292602	−	0.307536i
$823$		−	3.54479e7i		−	1.82428i	−0.409883	−	0.912138i	$-0.634431\pi$
$823$		−	3.54479e7i		−	1.82428i	0.409883	−	0.912138i	$-0.365569\pi$
$824$	−1.45344e6	−	1.94369e7i	−0.0745724	−	0.997260i
$825$		−	1.32418e7i		−	0.677346i
$826$	−1.53521e7	−	1.46066e7i	−0.782922	−	0.744902i
$827$	1.70780e7	−	1.70780e7i	0.868305	−	0.868305i	−0.123980	−	0.992285i	$-0.539566\pi$
$827$	1.70780e7	−	1.70780e7i	0.868305	−	0.868305i	0.992285	+	0.123980i	$0.0395658\pi$
$828$	1.25420e7	−	624590.i	0.635754	−	0.0316606i
$829$	−3.50303e6	−	3.50303e6i	−0.177035	−	0.177035i	0.613027	−	0.790062i	$-0.289952\pi$
$829$	−3.50303e6	−	3.50303e6i	−0.177035	−	0.177035i	−0.790062	+	0.613027i	$0.789952\pi$
$830$	7.55845e6	−	188089.i	0.380836	−	0.00947694i
$831$	−722717.			−0.0363049
$832$	−2.67145e7	−	1.97295e7i	−1.33795	−	0.988116i
$833$	3.32082e6			0.165818
$834$	1.82156e7	−	453288.i	0.906836	−	0.0225662i
$835$	−236032.	−	236032.i	−0.0117153	−	0.0117153i
$836$	−3.33642e7	+	1.66154e6i	−1.65107	+	0.0822231i
$837$	664858.	−	664858.i	0.0328031	−	0.0328031i
$838$	−2.11999e7	−	2.01705e7i	−1.04286	−	0.992215i
$839$			1.35430e7i			0.664218i	0.943241	+	0.332109i	$0.107760\pi$
$839$			1.35430e7i			0.664218i	−0.943241	+	0.332109i	$0.892240\pi$
$840$	625388.	+	8.36334e6i	0.0305810	+	0.408961i
$841$		−	1.90774e7i		−	0.930100i
$842$	−2.56995e6	+	2.70112e6i	−0.124923	+	0.131299i
$843$	−2.51016e6	+	2.51016e6i	−0.121656	+	0.121656i
$844$	4.67409e6	+	4.23063e6i	0.225861	+	0.204432i
$845$	1.63242e7	+	1.63242e7i	0.786483	+	0.786483i
$846$	−9213.79	−	370261.i	−0.000442601	−	0.0177861i
$847$	6.54459e7			3.13454
$848$	−8.39251e6	+	1.02544e7i	−0.400777	+	0.489687i
$849$	−2.27297e7			−1.08224
$850$	192341.	+	7.72932e6i	0.00913113	+	0.366939i
$851$	1.00047e7	+	1.00047e7i	0.473566	+	0.473566i
$852$	8.71116e6	−	9.62427e6i	0.411128	−	0.454223i
$853$	−2.27067e7	+	2.27067e7i	−1.06852	+	1.06852i	−0.0710439	+	0.997473i	$0.522633\pi$
$853$	−2.27067e7	+	2.27067e7i	−1.06852	+	1.06852i	−0.997473	+	0.0710439i	$0.977367\pi$
$854$	−1.15705e7	+	1.21610e7i	−0.542883	+	0.570592i
$855$		−	3.81532e6i		−	0.178491i
$856$	1.25649e7	−	1.45959e7i	0.586105	−	0.680845i
$857$			7.70351e6i			0.358291i	0.983823	+	0.179146i	$0.0573334\pi$
$857$			7.70351e6i			0.358291i	−0.983823	+	0.179146i	$0.942667\pi$
$858$	−2.91614e7	−	2.77453e7i	−1.35235	−	1.28668i
$859$	−1.64136e7	+	1.64136e7i	−0.758965	+	0.758965i	−0.976134	−	0.217169i	$-0.930318\pi$
$859$	−1.64136e7	+	1.64136e7i	−0.758965	+	0.758965i	0.217169	+	0.976134i	$0.430318\pi$
$860$	−766648.	−	1.53945e7i	−0.0353468	−	0.709775i
$861$	−8.74671e6	−	8.74671e6i	−0.402103	−	0.402103i
$862$	−1.18326e7	+	294449.i	−0.542391	+	0.0134972i
$863$	6.50680e6			0.297400			0.148700	−	0.988882i	$-0.452491\pi$
$863$	6.50680e6			0.297400			0.148700	+	0.988882i	$0.452491\pi$
$864$	−2.59242e6	+	3.33340e6i	−0.118147	+	0.151916i
$865$	1.23017e7			0.559018
$866$	−2.69609e7	+	670912.i	−1.22163	+	0.0303998i
$867$	5.69387e6	+	5.69387e6i	0.257253	+	0.257253i
$868$	300233.	+	6.02877e6i	0.0135257	+	0.271600i
$869$	6.97099e6	−	6.97099e6i	0.313145	−	0.313145i
$870$	−1.55453e6	−	1.47904e6i	−0.0696308	−	0.0662495i
$871$		−	6.10048e7i		−	2.72470i
$872$	−9.26999e6	−	7.98008e6i	−0.412846	−	0.355399i
$873$		−	84779.1i		−	0.00376490i
$874$	2.52798e7	−	2.65700e7i	1.11942	−	1.17656i
$875$	−1.82406e7	+	1.82406e7i	−0.805413	+	0.805413i
$876$	−5.26370e6	+	5.81544e6i	−0.231756	+	0.256049i
$877$	−2.88045e6	−	2.88045e6i	−0.126462	−	0.126462i	0.641043	−	0.767505i	$-0.278502\pi$
$877$	−2.88045e6	−	2.88045e6i	−0.126462	−	0.126462i	−0.767505	+	0.641043i	$0.778502\pi$
$878$	391754.	+	1.57428e7i	0.0171505	+	0.689202i
$879$	1.36256e7			0.594818
$880$	−2.79351e6	−	2.79778e7i	−0.121603	−	1.21788i
$881$	−3.73147e7			−1.61972			−0.809860	−	0.586623i	$-0.800457\pi$
$881$	−3.73147e7			−1.61972			−0.809860	+	0.586623i	$0.800457\pi$
$882$	52234.7	+	2.09908e6i	0.00226093	+	0.0908567i
$883$	2.13757e7	+	2.13757e7i	0.922612	+	0.922612i	0.997213	−	0.0746019i	$-0.0237686\pi$
$883$	2.13757e7	+	2.13757e7i	0.922612	+	0.922612i	−0.0746019	+	0.997213i	$0.523769\pi$
$884$	1.74248e7	+	1.57716e7i	0.749957	+	0.678805i
$885$	−5.73743e6	+	5.73743e6i	−0.246240	+	0.246240i
$886$	−1.20639e7	+	1.26796e7i	−0.516302	+	0.542653i
$887$			8.98890e6i			0.383617i	0.981432	+	0.191808i	$0.0614352\pi$
$887$			8.98890e6i			0.383617i	−0.981432	+	0.191808i	$0.938565\pi$
$888$	−4.74469e6	+	354795.i	−0.201918	+	0.0150989i
$889$		−	2.70944e7i		−	1.14981i
$890$	−934459.	−	889081.i	−0.0395444	−	0.0376241i
$891$	−3.61909e6	+	3.61909e6i	−0.152723	+	0.152723i
$892$	2.76484e7	−	1.37689e6i	1.16348	−	0.0579413i
$893$	−764876.	−	764876.i	−0.0320968	−	0.0320968i
$894$	1.06750e7	−	265643.i	0.446709	−	0.0111162i
$895$	−4.33516e6			−0.180904
$896$	−4.69750e6	−	2.66997e7i	−0.195477	−	1.11105i
$897$	4.41908e7			1.83380
$898$	7.11183e6	−	176975.i	0.294300	−	0.00732354i
$899$	−1.09203e6	−	1.09203e6i	−0.0450646	−	0.0450646i
$900$	−4.88265e6	+	243156.i	−0.200932	+	0.0100064i
$901$	6.63090e6	−	6.63090e6i	0.272120	−	0.272120i
$902$	3.00443e7	+	2.85853e7i	1.22955	+	1.16984i
$903$		−	1.80125e7i		−	0.735115i
$904$	−3.98337e6	+	297866.i	−0.162117	+	0.0121227i
$905$			2.24983e7i			0.913120i
$906$	−6.99927e6	+	7.35651e6i	−0.283291	+	0.297750i
$907$	2.51954e7	−	2.51954e7i	1.01696	−	1.01696i	0.0171060	−	0.999854i	$-0.494555\pi$
$907$	2.51954e7	−	2.51954e7i	1.01696	−	1.01696i	0.999854	−	0.0171060i	$-0.00544526\pi$
$908$	−3.39801e7	−	3.07562e7i	−1.36776	−	1.23799i
$909$	−5.90567e6	−	5.90567e6i	−0.237061	−	0.237061i
$910$	734202.	+	2.95043e7i	0.0293908	+	1.18109i
$911$	−4.50098e7			−1.79685			−0.898424	−	0.439128i	$-0.855287\pi$
$911$	−4.50098e7			−1.79685			−0.898424	+	0.439128i	$0.855287\pi$
$912$	1.22532e6	+	1.22719e7i	0.0487824	+	0.488568i
$913$	−2.96220e7			−1.17608
$914$	534818.	+	2.14919e7i	0.0211758	+	0.850961i
$915$	4.54485e6	+	4.54485e6i	0.179460	+	0.179460i
$916$	−2.02172e7	+	2.23364e7i	−0.796129	+	0.879579i
$917$	−2.17930e6	+	2.17930e6i	−0.0855843	+	0.0855843i
$918$	2.05992e6	−	2.16506e6i	0.0806760	−	0.0847937i
$919$			3.94424e7i			1.54054i	0.637716	+	0.770272i	$0.279880\pi$
$919$			3.94424e7i			1.54054i	−0.637716	+	0.770272i	$0.720120\pi$
$920$	2.33942e7	+	2.01389e7i	0.911253	+	0.784453i
$921$			2.59541e7i			1.00822i
$922$	1.57849e7	+	1.50184e7i	0.611525	+	0.581829i
$923$	3.23019e7	−	3.23019e7i	1.24803	−	1.24803i
$924$	−1.63429e6	−	3.28170e7i	−0.0629722	−	1.26450i
$925$	−3.89489e6	−	3.89489e6i	−0.149672	−	0.149672i
$926$	1.47736e7	−	367634.i	0.566184	−	0.0140893i
$927$	−8.72162e6			−0.333348
$928$	5.47512e6	+	4.25806e6i	0.208701	+	0.162309i
$929$	−9.53118e6			−0.362332			−0.181166	−	0.983452i	$-0.557987\pi$
$929$	−9.53118e6			−0.362332			−0.181166	+	0.983452i	$0.557987\pi$
$930$	2.31059e6	−	57498.0i	0.0876021	−	0.00217994i
$931$	4.33622e6	+	4.33622e6i	0.163960	+	0.163960i
$932$	961900.	+	1.93153e7i	0.0362736	+	0.728385i
$933$	−5.15996e6	+	5.15996e6i	−0.194063	+	0.194063i
$934$	−9.49996e6	−	9.03864e6i	−0.356332	−	0.339028i
$935$			1.98980e7i			0.744355i
$936$	−9.69509e6	+	1.12622e7i	−0.361711	+	0.420179i
$937$			6.66158e6i			0.247872i	0.992290	+	0.123936i	$0.0395518\pi$
$937$			6.66158e6i			0.247872i	−0.992290	+	0.123936i	$0.960448\pi$
$938$	3.43261e7	−	3.60781e7i	1.27385	−	1.33886i
$939$	1.88755e7	−	1.88755e7i	0.698610	−	0.698610i
$940$	610966.	−	675007.i	0.0225526	−	0.0249166i
$941$	−4.64177e6	−	4.64177e6i	−0.170887	−	0.170887i	0.616482	−	0.787369i	$-0.288557\pi$
$941$	−4.64177e6	−	4.64177e6i	−0.170887	−	0.170887i	−0.787369	+	0.616482i	$0.788557\pi$
$942$	26047.2	+	1.04672e6i	0.000956388	+	0.0384329i
$943$	−4.55287e7			−1.66727
$944$	1.66117e7	−	2.02970e7i	0.606714	−	0.741312i
$945$	3.75276e6			0.136701
$946$	1.50227e6	+	6.03694e7i	0.0545782	+	2.19325i
$947$	−2.85229e6	−	2.85229e6i	−0.103352	−	0.103352i	0.653540	−	0.756892i	$-0.273283\pi$
$947$	−2.85229e6	−	2.85229e6i	−0.103352	−	0.103352i	−0.756892	+	0.653540i	$0.773283\pi$
$948$	−2.69843e6	−	2.44242e6i	−0.0975193	−	0.0882671i
$949$	−1.95184e7	+	1.95184e7i	−0.703522	+	0.703522i
$950$	−9.84156e6	+	1.03439e7i	−0.353798	+	0.371855i
$951$		−	4.28031e6i		−	0.153470i
$952$	1.43063e6	+	1.91318e7i	0.0511604	+	0.684170i
$953$			3.22240e7i			1.14934i	0.818386	+	0.574669i	$0.194869\pi$
$953$			3.22240e7i			1.14934i	−0.818386	+	0.574669i	$0.805131\pi$
$954$	4.29567e6	+	4.08707e6i	0.152813	+	0.145392i
$955$	1.15639e7	−	1.15639e7i	0.410296	−	0.410296i
$956$	6.83886e6	−	340575.i	0.242013	−	0.0120523i
$957$	5.94437e6	+	5.94437e6i	0.209810	+	0.209810i
$958$	1.68855e7	−	420188.i	0.594428	−	0.0147921i
$959$	2.36229e7			0.829444
$960$	−1.02650e7	+	1.54381e6i	−0.359484	+	0.0540649i
$961$	−2.69656e7			−0.941894
$962$	−1.67384e7	+	416528.i	−0.583144	+	0.0145113i
$963$	−6.09375e6	−	6.09375e6i	−0.211748	−	0.211748i
$964$	4.42106e7	−	2.20169e6i	1.53227	−	0.0763068i
$965$	−2.61092e6	+	2.61092e6i	−0.0902557	+	0.0902557i
$966$	2.61343e7	+	2.48652e7i	0.901091	+	0.857333i
$967$			3.62100e7i			1.24527i	0.782514	+	0.622633i	$0.213937\pi$
$967$			3.62100e7i			1.24527i	−0.782514	+	0.622633i	$0.786063\pi$
$968$	6.04040e6	+	8.07785e7i	0.207194	+	2.77082i
$969$		−	8.72787e6i		−	0.298606i
$970$	143651.	−	150983.i	0.00490206	−	0.00515226i
$971$	2.77031e7	−	2.77031e7i	0.942933	−	0.942933i	−0.0555240	−	0.998457i	$-0.517683\pi$
$971$	2.77031e7	−	2.77031e7i	0.942933	−	0.942933i	0.998457	+	0.0555240i	$0.0176829\pi$
$972$	1.40093e6	+	1.26802e6i	0.0475610	+	0.0430486i
$973$	3.70123e7	+	3.70123e7i	1.25333	+	1.25333i
$974$	−132671.	−	5.33144e6i	−0.00448102	−	0.180072i
$975$	−1.72037e7			−0.579577
$976$	−1.60780e7	−	1.31588e7i	−0.540266	−	0.442172i
$977$	2.77033e7			0.928527			0.464263	−	0.885697i	$-0.346319\pi$
$977$	2.77033e7			0.928527			0.464263	+	0.885697i	$0.346319\pi$
$978$	532001.	+	2.13787e7i	0.0177855	+	0.714718i
$979$	3.57328e6	+	3.57328e6i	0.119154	+	0.119154i
$980$	−3.46368e6	+	3.82674e6i	−0.115205	+	0.127281i
$981$	−3.87019e6	+	3.87019e6i	−0.128398	+	0.128398i
$982$	−1.78974e7	+	1.88109e7i	−0.592258	+	0.622487i
$983$		−	4.40745e7i		−	1.45480i	−0.686212	−	0.727401i	$-0.740728\pi$
$983$		−	4.40745e7i		−	1.45480i	0.686212	−	0.727401i	$-0.259272\pi$
$984$	9.98860e6	−	1.16032e7i	0.328865	−	0.382023i
$985$		−	2.73690e7i		−	0.898810i
$986$	−3.55612e6	−	3.38343e6i	−0.116489	−	0.110832i
$987$	752333.	−	752333.i	0.0245820	−	0.0245820i
$988$	2.15867e6	+	4.33468e7i	0.0703549	+	1.41275i
$989$	−4.68797e7	−	4.68797e7i	−1.52403	−	1.52403i
$990$	−1.25775e7	+	312985.i	−0.407854	+	0.0101493i
$991$	−5.74278e6			−0.185754			−0.0928770	−	0.995678i	$-0.529606\pi$
$991$	−5.74278e6			−0.185754			−0.0928770	+	0.995678i	$0.529606\pi$
$992$	−7.41348e6	+	927004.i	−0.239190	+	0.0299090i
$993$	−4.38746e6			−0.141202
$994$	3.72788e7	−	927669.i	1.19673	−	0.0297802i
$995$	8.73965e6	+	8.73965e6i	0.279857	+	0.279857i
$996$	543943.	+	1.09226e7i	0.0173742	+	0.348880i
$997$	2.29046e7	−	2.29046e7i	0.729769	−	0.729769i	−0.240804	−	0.970574i	$-0.577411\pi$
$997$	2.29046e7	−	2.29046e7i	0.729769	−	0.729769i	0.970574	+	0.240804i	$0.0774112\pi$
$998$	−1.28340e7	−	1.22107e7i	−0.407882	−	0.388075i
$999$			2.12902e6i			0.0674940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.6.j.a.13.1	✓	40
3.2	odd	2		144.6.k.c.109.20		40
4.3	odd	2		192.6.j.a.145.19		40
8.3	odd	2		384.6.j.b.289.2		40
8.5	even	2		384.6.j.a.289.19		40
12.11	even	2		576.6.k.c.145.8		40
16.3	odd	4		384.6.j.b.97.2		40
16.5	even	4	inner	48.6.j.a.37.1	yes	40
16.11	odd	4		192.6.j.a.49.19		40
16.13	even	4		384.6.j.a.97.19		40
48.5	odd	4		144.6.k.c.37.20		40
48.11	even	4		576.6.k.c.433.8		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.6.j.a.13.1	✓	40	1.1	even	1	trivial
48.6.j.a.37.1	yes	40	16.5	even	4	inner
144.6.k.c.37.20		40	48.5	odd	4
144.6.k.c.109.20		40	3.2	odd	2
192.6.j.a.49.19		40	16.11	odd	4
192.6.j.a.145.19		40	4.3	odd	2
384.6.j.a.97.19		40	16.13	even	4
384.6.j.a.289.19		40	8.5	even	2
384.6.j.b.97.2		40	16.3	odd	4
384.6.j.b.289.2		40	8.3	odd	2
576.6.k.c.145.8		40	12.11	even	2
576.6.k.c.433.8		40	48.11	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	48.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.65510 + 0.140725i) q^{2} +(-6.36396 - 6.36396i) q^{3} +(31.9604 - 1.59163i) q^{4} +(24.8890 - 24.8890i) q^{5} +(36.8844 + 35.0933i) q^{6} +146.252i q^{7} +(-180.515 + 13.4984i) q^{8} +81.0000i q^{9} +O(q^{10})\)	\(q+(-5.65510 + 0.140725i) q^{2} +(-6.36396 - 6.36396i) q^{3} +(31.9604 - 1.59163i) q^{4} +(24.8890 - 24.8890i) q^{5} +(36.8844 + 35.0933i) q^{6} +146.252i q^{7} +(-180.515 + 13.4984i) q^{8} +81.0000i q^{9} +(-137.247 + 144.252i) q^{10} +(551.607 - 551.607i) q^{11} +(-213.524 - 193.266i) q^{12} +(-716.649 - 716.649i) q^{13} +(-20.5812 - 827.067i) q^{14} -316.785 q^{15} +(1018.93 - 101.738i) q^{16} -724.673 q^{17} +(-11.3987 - 458.063i) q^{18} +(-946.256 - 946.256i) q^{19} +(755.849 - 835.077i) q^{20} +(930.739 - 930.739i) q^{21} +(-3041.77 + 3197.02i) q^{22} -4844.71i q^{23} +(1234.70 + 1062.89i) q^{24} +1886.07i q^{25} +(4153.57 + 3951.87i) q^{26} +(515.481 - 515.481i) q^{27} +(232.778 + 4674.26i) q^{28} +(-846.679 - 846.679i) q^{29} +(1791.45 - 44.5796i) q^{30} +1289.78 q^{31} +(-5747.86 + 718.729i) q^{32} -7020.80 q^{33} +(4098.10 - 101.980i) q^{34} +(3640.06 + 3640.06i) q^{35} +(128.922 + 2588.79i) q^{36} +(-2065.08 + 2065.08i) q^{37} +(5484.34 + 5218.01i) q^{38} +9121.45i q^{39} +(-4156.89 + 4828.81i) q^{40} -9397.60i q^{41} +(-5132.45 + 5394.40i) q^{42} +(9676.47 - 9676.47i) q^{43} +(16751.6 - 18507.5i) q^{44} +(2016.01 + 2016.01i) q^{45} +(681.772 + 27397.4i) q^{46} +808.318 q^{47} +(-7131.91 - 5837.00i) q^{48} -4582.51 q^{49} +(-265.418 - 10665.9i) q^{50} +(4611.79 + 4611.79i) q^{51} +(-24045.0 - 21763.7i) q^{52} +(-9150.19 + 9150.19i) q^{53} +(-2842.56 + 2987.64i) q^{54} -27457.9i q^{55} +(-1974.17 - 26400.6i) q^{56} +12043.9i q^{57} +(4907.21 + 4668.91i) q^{58} +(18111.4 - 18111.4i) q^{59} +(-10124.6 + 504.205i) q^{60} +(-14346.8 - 14346.8i) q^{61} +(-7293.85 + 181.505i) q^{62} -11846.4 q^{63} +(32403.6 - 4873.35i) q^{64} -35673.4 q^{65} +(39703.4 - 988.002i) q^{66} +(42562.6 + 42562.6i) q^{67} +(-23160.8 + 1153.41i) q^{68} +(-30831.6 + 30831.6i) q^{69} +(-21097.1 - 20072.6i) q^{70} +45073.5i q^{71} +(-1093.37 - 14621.7i) q^{72} -27235.6i q^{73} +(11387.6 - 11968.8i) q^{74} +(12002.9 - 12002.9i) q^{75} +(-31748.8 - 28736.6i) q^{76} +(80673.3 + 80673.3i) q^{77} +(-1283.62 - 51582.7i) q^{78} +12637.6 q^{79} +(22828.1 - 27892.4i) q^{80} -6561.00 q^{81} +(1322.48 + 53144.4i) q^{82} +(-26850.6 - 26850.6i) q^{83} +(28265.4 - 31228.2i) q^{84} +(-18036.4 + 18036.4i) q^{85} +(-53359.7 + 56083.1i) q^{86} +10776.5i q^{87} +(-92127.6 + 107019. i) q^{88} +6477.94i q^{89} +(-11684.4 - 11117.0i) q^{90} +(104811. - 104811. i) q^{91} +(-7710.98 - 154839. i) q^{92} +(-8208.12 - 8208.12i) q^{93} +(-4571.12 + 113.750i) q^{94} -47102.8 q^{95} +(41153.1 + 32005.2i) q^{96} -1046.66 q^{97} +(25914.5 - 644.873i) q^{98} +(44680.1 + 44680.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 44 q^{4} - 492 q^{8}+O(q^{10}) \) 40 * q + 44 * q^4 - 492 * q^8	\( 40 q + 44 q^{4} - 492 q^{8} + 968 q^{10} + 1208 q^{11} - 792 q^{12} + 324 q^{14} - 1800 q^{15} - 384 q^{16} - 324 q^{18} + 2360 q^{19} - 7600 q^{20} - 1024 q^{22} + 5220 q^{24} - 12980 q^{26} + 10472 q^{28} - 8144 q^{29} - 1368 q^{30} + 23064 q^{31} + 44160 q^{32} + 4864 q^{34} - 4776 q^{35} - 1620 q^{36} + 21296 q^{37} - 72088 q^{38} - 90864 q^{40} - 14220 q^{42} + 31416 q^{43} + 43768 q^{44} + 90664 q^{46} + 44784 q^{48} - 96040 q^{49} + 106212 q^{50} + 10440 q^{51} - 116432 q^{52} - 49456 q^{53} - 14580 q^{54} - 158592 q^{56} - 111472 q^{58} + 28960 q^{59} + 49464 q^{60} + 48080 q^{61} + 191100 q^{62} + 31752 q^{63} + 369032 q^{64} - 55376 q^{65} + 63720 q^{66} + 101488 q^{67} - 122336 q^{68} - 22320 q^{69} - 460192 q^{70} - 28836 q^{72} - 94996 q^{74} - 96624 q^{75} + 211304 q^{76} - 14896 q^{77} + 200124 q^{78} - 71960 q^{79} + 623368 q^{80} - 262440 q^{81} + 33880 q^{82} - 126440 q^{83} - 116856 q^{84} + 132400 q^{85} - 581168 q^{86} - 466400 q^{88} - 46008 q^{90} + 429496 q^{91} - 12752 q^{92} + 524120 q^{94} - 76848 q^{95} + 51840 q^{96} + 477736 q^{98} + 97848 q^{99}+O(q^{100}) \) 40 * q + 44 * q^4 - 492 * q^8 + 968 * q^10 + 1208 * q^11 - 792 * q^12 + 324 * q^14 - 1800 * q^15 - 384 * q^16 - 324 * q^18 + 2360 * q^19 - 7600 * q^20 - 1024 * q^22 + 5220 * q^24 - 12980 * q^26 + 10472 * q^28 - 8144 * q^29 - 1368 * q^30 + 23064 * q^31 + 44160 * q^32 + 4864 * q^34 - 4776 * q^35 - 1620 * q^36 + 21296 * q^37 - 72088 * q^38 - 90864 * q^40 - 14220 * q^42 + 31416 * q^43 + 43768 * q^44 + 90664 * q^46 + 44784 * q^48 - 96040 * q^49 + 106212 * q^50 + 10440 * q^51 - 116432 * q^52 - 49456 * q^53 - 14580 * q^54 - 158592 * q^56 - 111472 * q^58 + 28960 * q^59 + 49464 * q^60 + 48080 * q^61 + 191100 * q^62 + 31752 * q^63 + 369032 * q^64 - 55376 * q^65 + 63720 * q^66 + 101488 * q^67 - 122336 * q^68 - 22320 * q^69 - 460192 * q^70 - 28836 * q^72 - 94996 * q^74 - 96624 * q^75 + 211304 * q^76 - 14896 * q^77 + 200124 * q^78 - 71960 * q^79 + 623368 * q^80 - 262440 * q^81 + 33880 * q^82 - 126440 * q^83 - 116856 * q^84 + 132400 * q^85 - 581168 * q^86 - 466400 * q^88 - 46008 * q^90 + 429496 * q^91 - 12752 * q^92 + 524120 * q^94 - 76848 * q^95 + 51840 * q^96 + 477736 * q^98 + 97848 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more