LMFDB - Embedded newform 147.8.e.l.79.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,8,Mod(67,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("147.67");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	147.e (of order $3$, degree $2$, not 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:	$45.9205987462$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 181x^{6} - 1656x^{5} - 6927x^{4} - 5022x^{3} - 974106x^{2} + 14431284x + 117021996 $ x^8 - 2x^7 + 181x^6 - 1656x^5 - 6927x^4 - 5022x^3 - 974106x^2 + 14431284*x + 117021996
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{5}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.3
Root			$-6.68281 - 0.882730i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.8.e.l.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.10587 - 10.5757i) q^{2} +(-13.5000 - 23.3827i) q^{3} +(-10.5634 - 18.2963i) q^{4} +(142.335 - 246.532i) q^{5} -329.717 q^{6} +1305.11 q^{8} +(-364.500 + 631.333i) q^{9} +O(q^{10})$	\(q+(6.10587 - 10.5757i) q^{2} +(-13.5000 - 23.3827i) q^{3} +(-10.5634 - 18.2963i) q^{4} +(142.335 - 246.532i) q^{5} -329.717 q^{6} +1305.11 q^{8} +(-364.500 + 631.333i) q^{9} +(-1738.16 - 3010.58i) q^{10} +(3644.47 + 6312.42i) q^{11} +(-285.211 + 494.000i) q^{12} +8519.49 q^{13} -7686.10 q^{15} +(9320.94 - 16144.3i) q^{16} +(16729.1 + 28975.6i) q^{17} +(4451.18 + 7709.67i) q^{18} +(4453.19 - 7713.15i) q^{19} -6014.15 q^{20} +89010.8 q^{22} +(-27201.7 + 47114.8i) q^{23} +(-17619.0 - 30517.0i) q^{24} +(-1456.13 - 2522.08i) q^{25} +(52018.9 - 90099.4i) q^{26} +19683.0 q^{27} -32469.4 q^{29} +(-46930.4 + 81285.8i) q^{30} +(84535.7 + 146420. i) q^{31} +(-30298.0 - 52477.6i) q^{32} +(98400.8 - 170435. i) q^{33} +408582. q^{34} +15401.4 q^{36} +(-49616.7 + 85938.7i) q^{37} +(-54381.2 - 94191.1i) q^{38} +(-115013. - 199209. i) q^{39} +(185763. - 321751. i) q^{40} +235363. q^{41} -289312. q^{43} +(76995.8 - 133361. i) q^{44} +(103762. + 179722. i) q^{45} +(332181. + 575354. i) q^{46} +(604526. - 1.04707e6i) q^{47} -503331. q^{48} -35563.7 q^{50} +(451684. - 782340. i) q^{51} +(-89994.5 - 155875. i) q^{52} +(98977.7 + 171434. i) q^{53} +(120182. - 208161. i) q^{54} +2.07495e6 q^{55} -240472. q^{57} +(-198254. + 343386. i) q^{58} +(-1.11205e6 - 1.92612e6i) q^{59} +(81191.1 + 140627. i) q^{60} +(-530377. + 918640. i) q^{61} +2.06466e6 q^{62} +1.64618e6 q^{64} +(1.21262e6 - 2.10033e6i) q^{65} +(-1.20165e6 - 2.08131e6i) q^{66} +(-1.87235e6 - 3.24300e6i) q^{67} +(353430. - 612159. i) q^{68} +1.46889e6 q^{69} -2.99969e6 q^{71} +(-475712. + 823958. i) q^{72} +(-3.28942e6 - 5.69744e6i) q^{73} +(605907. + 1.04946e6i) q^{74} +(-39315.4 + 68096.2i) q^{75} -188163. q^{76} -2.80902e6 q^{78} +(-3.54939e6 + 6.14773e6i) q^{79} +(-2.65340e6 - 4.59582e6i) q^{80} +(-265720. - 460241. i) q^{81} +(1.43709e6 - 2.48912e6i) q^{82} -441332. q^{83} +9.52453e6 q^{85} +(-1.76650e6 + 3.05967e6i) q^{86} +(438337. + 759222. i) q^{87} +(4.75644e6 + 8.23839e6i) q^{88} +(-5.92826e6 + 1.02680e7i) q^{89} +2.53424e6 q^{90} +1.14937e6 q^{92} +(2.28246e6 - 3.95334e6i) q^{93} +(-7.38231e6 - 1.27865e7i) q^{94} +(-1.26769e6 - 2.19571e6i) q^{95} +(-818045. + 1.41690e6i) q^{96} +4.49189e6 q^{97} -5.31364e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 15 q^{2} - 108 q^{3} - 437 q^{4} - 504 q^{5} - 810 q^{6} - 4290 q^{8} - 2916 q^{9}+O(q^{10}) $ 8 * q + 15 * q^2 - 108 * q^3 - 437 * q^4 - 504 * q^5 - 810 * q^6 - 4290 * q^8 - 2916 * q^9	\( 8 q + 15 q^{2} - 108 q^{3} - 437 q^{4} - 504 q^{5} - 810 q^{6} - 4290 q^{8} - 2916 q^{9} + 5724 q^{10} + 1920 q^{11} - 11799 q^{12} + 36288 q^{13} + 27216 q^{15} - 52529 q^{16} + 19584 q^{17} + 10935 q^{18} - 31320 q^{19} + 339624 q^{20} + 223880 q^{22} - 101160 q^{23} + 57915 q^{24} - 74788 q^{25} + 107820 q^{26} + 157464 q^{27} + 389664 q^{29} + 154548 q^{30} - 78840 q^{31} + 732585 q^{32} + 51840 q^{33} - 155520 q^{34} + 637146 q^{36} - 128640 q^{37} - 716292 q^{38} - 489888 q^{39} + 2649780 q^{40} + 730080 q^{41} + 899040 q^{43} - 113220 q^{44} - 367416 q^{45} - 1033664 q^{46} + 1575792 q^{47} + 2836566 q^{48} - 10783866 q^{50} + 528768 q^{51} - 5747652 q^{52} + 1448160 q^{53} + 295245 q^{54} + 6166800 q^{55} + 1691280 q^{57} + 2570950 q^{58} - 3280320 q^{59} - 4584924 q^{60} - 606960 q^{61} + 24129072 q^{62} + 5218274 q^{64} - 1318464 q^{65} - 3022380 q^{66} - 3492880 q^{67} + 1476432 q^{68} + 5462640 q^{69} + 1968 q^{71} + 1563705 q^{72} - 10981440 q^{73} + 14177022 q^{74} - 2019276 q^{75} + 37928520 q^{76} - 5822280 q^{78} - 4654544 q^{79} - 37026324 q^{80} - 2125764 q^{81} + 10402560 q^{82} + 16252992 q^{83} + 33584112 q^{85} + 6392244 q^{86} - 5260464 q^{87} + 10447140 q^{88} + 11272320 q^{89} - 8345592 q^{90} + 6578880 q^{92} - 2128680 q^{93} - 37697400 q^{94} - 11132208 q^{95} + 19779795 q^{96} + 13144896 q^{97} - 2799360 q^{99}+O(q^{100}) \) 8 * q + 15 * q^2 - 108 * q^3 - 437 * q^4 - 504 * q^5 - 810 * q^6 - 4290 * q^8 - 2916 * q^9 + 5724 * q^10 + 1920 * q^11 - 11799 * q^12 + 36288 * q^13 + 27216 * q^15 - 52529 * q^16 + 19584 * q^17 + 10935 * q^18 - 31320 * q^19 + 339624 * q^20 + 223880 * q^22 - 101160 * q^23 + 57915 * q^24 - 74788 * q^25 + 107820 * q^26 + 157464 * q^27 + 389664 * q^29 + 154548 * q^30 - 78840 * q^31 + 732585 * q^32 + 51840 * q^33 - 155520 * q^34 + 637146 * q^36 - 128640 * q^37 - 716292 * q^38 - 489888 * q^39 + 2649780 * q^40 + 730080 * q^41 + 899040 * q^43 - 113220 * q^44 - 367416 * q^45 - 1033664 * q^46 + 1575792 * q^47 + 2836566 * q^48 - 10783866 * q^50 + 528768 * q^51 - 5747652 * q^52 + 1448160 * q^53 + 295245 * q^54 + 6166800 * q^55 + 1691280 * q^57 + 2570950 * q^58 - 3280320 * q^59 - 4584924 * q^60 - 606960 * q^61 + 24129072 * q^62 + 5218274 * q^64 - 1318464 * q^65 - 3022380 * q^66 - 3492880 * q^67 + 1476432 * q^68 + 5462640 * q^69 + 1968 * q^71 + 1563705 * q^72 - 10981440 * q^73 + 14177022 * q^74 - 2019276 * q^75 + 37928520 * q^76 - 5822280 * q^78 - 4654544 * q^79 - 37026324 * q^80 - 2125764 * q^81 + 10402560 * q^82 + 16252992 * q^83 + 33584112 * q^85 + 6392244 * q^86 - 5260464 * q^87 + 10447140 * q^88 + 11272320 * q^89 - 8345592 * q^90 + 6578880 * q^92 - 2128680 * q^93 - 37697400 * q^94 - 11132208 * q^95 + 19779795 * q^96 + 13144896 * q^97 - 2799360 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	6.10587	−	10.5757i	0.539688	−	0.934767i	−0.459233	−	0.888316i	$-0.651876\pi$
$2$	6.10587	−	10.5757i	0.539688	−	0.934767i	0.998921	−	0.0464510i	$-0.0147911\pi$
$3$	−13.5000	−	23.3827i	−0.288675	−	0.500000i
$3$	−13.5000	−	23.3827i	−0.288675	−	0.500000i
$4$	−10.5634	−	18.2963i	−0.0825263	−	0.142940i
$5$	142.335	−	246.532i	0.509234	−	0.882019i	−0.490709	−	0.871324i	$-0.663262\pi$
$5$	142.335	−	246.532i	0.509234	−	0.882019i	0.999943	−	0.0106955i	$-0.00340453\pi$
$6$	−329.717			−0.623178
$7$		0			0
$7$		0			0
$8$	1305.11			0.901222
$9$	−364.500	+	631.333i	−0.166667	+	0.288675i
$10$	−1738.16	−	3010.58i	−0.549655	−	0.952030i
$11$	3644.47	+	6312.42i	0.825583	+	1.42995i	0.901473	+	0.432835i	$0.142487\pi$
$11$	3644.47	+	6312.42i	0.825583	+	1.42995i	−0.0758906	+	0.997116i	$0.524180\pi$
$12$	−285.211	+	494.000i	−0.0476466	+	0.0825263i
$13$	8519.49			1.07550			0.537752	−	0.843103i	$-0.319274\pi$
$13$	8519.49			1.07550			0.537752	+	0.843103i	$0.319274\pi$
$14$		0			0
$15$	−7686.10			−0.588013
$16$	9320.94	−	16144.3i	0.568905	−	0.985373i
$17$	16729.1	+	28975.6i	0.825848	+	1.43041i	0.901269	+	0.433259i	$0.142637\pi$
$17$	16729.1	+	28975.6i	0.825848	+	1.43041i	−0.0754212	+	0.997152i	$0.524030\pi$
$18$	4451.18	+	7709.67i	0.179896	+	0.311589i
$19$	4453.19	−	7713.15i	0.148948	−	0.257985i	−0.781891	−	0.623415i	$-0.785745\pi$
$19$	4453.19	−	7713.15i	0.148948	−	0.257985i	0.930839	+	0.365430i	$0.119078\pi$
$20$	−6014.15			−0.168101
$21$		0			0
$22$	89010.8			1.78223
$23$	−27201.7	+	47114.8i	−0.466175	+	0.807440i	−0.999254	−	0.0386264i	$-0.987702\pi$
$23$	−27201.7	+	47114.8i	−0.466175	+	0.807440i	0.533078	+	0.846066i	$0.321035\pi$
$24$	−17619.0	−	30517.0i	−0.260160	−	0.450611i
$25$	−1456.13	−	2522.08i	−0.0186384	−	0.0322827i
$26$	52018.9	−	90099.4i	0.580436	−	1.00535i
$27$	19683.0			0.192450
$28$		0			0
$29$	−32469.4			−0.247219			−0.123609	−	0.992331i	$-0.539447\pi$
$29$	−32469.4			−0.247219			−0.123609	+	0.992331i	$0.539447\pi$
$30$	−46930.4	+	81285.8i	−0.317343	+	0.549655i
$31$	84535.7	+	146420.i	0.509652	+	0.882744i	0.999937	+	0.0111818i	$0.00355935\pi$
$31$	84535.7	+	146420.i	0.509652	+	0.882744i	−0.490285	+	0.871562i	$0.663107\pi$
$32$	−30298.0	−	52477.6i	−0.163451	−	0.283106i
$33$	98400.8	−	170435.i	0.476650	−	0.825583i
$34$	408582.			1.78280
$35$		0			0
$36$	15401.4			0.0550175
$37$	−49616.7	+	85938.7i	−0.161036	+	0.278922i	−0.935240	−	0.354013i	$-0.884817\pi$
$37$	−49616.7	+	85938.7i	−0.161036	+	0.278922i	0.774205	+	0.632935i	$0.218150\pi$
$38$	−54381.2	−	94191.1i	−0.160771	−	0.278463i
$39$	−115013.	−	199209.i	−0.310471	−	0.537752i
$40$	185763.	−	321751.i	0.458933	−	0.794895i
$41$	235363.			0.533328			0.266664	−	0.963790i	$-0.414079\pi$
$41$	235363.			0.533328			0.266664	+	0.963790i	$0.414079\pi$
$42$		0			0
$43$	−289312.			−0.554915			−0.277457	−	0.960738i	$-0.589492\pi$
$43$	−289312.			−0.554915			−0.277457	+	0.960738i	$0.589492\pi$
$44$	76995.8	−	133361.i	0.136265	−	0.236017i
$45$	103762.	+	179722.i	0.169745	+	0.294006i
$46$	332181.	+	575354.i	0.503179	+	0.871531i
$47$	604526.	−	1.04707e6i	0.849322	−	1.47107i	−0.0324932	−	0.999472i	$-0.510345\pi$
$47$	604526.	−	1.04707e6i	0.849322	−	1.47107i	0.881815	−	0.471596i	$-0.156322\pi$
$48$	−503331.			−0.656915
$49$		0			0
$50$	−35563.7			−0.0402357
$51$	451684.	−	782340.i	0.476804	−	0.825848i
$52$	−89994.5	−	155875.i	−0.0887573	−	0.153732i
$53$	98977.7	+	171434.i	0.0913212	+	0.158173i	0.908067	−	0.418824i	$-0.137558\pi$
$53$	98977.7	+	171434.i	0.0913212	+	0.158173i	−0.816746	+	0.576997i	$0.804224\pi$
$54$	120182.	−	208161.i	0.103863	−	0.179896i
$55$	2.07495e6			1.68166
$56$		0			0
$57$	−240472.			−0.171990
$58$	−198254.	+	343386.i	−0.133421	+	0.231092i
$59$	−1.11205e6	−	1.92612e6i	−0.704923	−	1.22096i	−0.966719	−	0.255839i	$-0.917648\pi$
$59$	−1.11205e6	−	1.92612e6i	−0.704923	−	1.22096i	0.261797	−	0.965123i	$-0.415685\pi$
$60$	81191.1	+	140627.i	0.0485265	+	0.0840504i
$61$	−530377.	+	918640.i	−0.299178	+	0.518192i	−0.975948	−	0.218003i	$-0.930046\pi$
$61$	−530377.	+	918640.i	−0.299178	+	0.518192i	0.676770	+	0.736195i	$0.263379\pi$
$62$	2.06466e6			1.10021
$63$		0			0
$64$	1.64618e6			0.784959
$65$	1.21262e6	−	2.10033e6i	0.547683	−	0.948615i
$66$	−1.20165e6	−	2.08131e6i	−0.514485	−	0.891114i
$67$	−1.87235e6	−	3.24300e6i	−0.760544	−	1.31730i	−0.942570	−	0.334007i	$-0.891599\pi$
$67$	−1.87235e6	−	3.24300e6i	−0.760544	−	1.31730i	0.182026	−	0.983294i	$-0.441734\pi$
$68$	353430.	−	612159.i	0.136308	−	0.236093i
$69$	1.46889e6			0.538293
$70$		0			0
$71$	−2.99969e6			−0.994656			−0.497328	−	0.867563i	$-0.665685\pi$
$71$	−2.99969e6			−0.994656			−0.497328	+	0.867563i	$0.665685\pi$
$72$	−475712.	+	823958.i	−0.150204	+	0.260160i
$73$	−3.28942e6	−	5.69744e6i	−0.989667	−	1.71415i	−0.619009	−	0.785384i	$-0.712465\pi$
$73$	−3.28942e6	−	5.69744e6i	−0.989667	−	1.71415i	−0.370658	−	0.928769i	$-0.620868\pi$
$74$	605907.	+	1.04946e6i	0.173818	+	0.301062i
$75$	−39315.4	+	68096.2i	−0.0107609	+	0.0186384i
$76$	−188163.			−0.0491684
$77$		0			0
$78$	−2.80902e6			−0.670230
$79$	−3.54939e6	+	6.14773e6i	−0.809952	+	1.40288i	0.102945	+	0.994687i	$0.467174\pi$
$79$	−3.54939e6	+	6.14773e6i	−0.809952	+	1.40288i	−0.912897	+	0.408191i	$0.866160\pi$
$80$	−2.65340e6	−	4.59582e6i	−0.579412	−	1.00357i
$81$	−265720.	−	460241.i	−0.0555556	−	0.0962250i
$82$	1.43709e6	−	2.48912e6i	0.287831	−	0.498537i
$83$	−441332.			−0.0847212			−0.0423606	−	0.999102i	$-0.513488\pi$
$83$	−441332.			−0.0847212			−0.0423606	+	0.999102i	$0.513488\pi$
$84$		0			0
$85$	9.52453e6			1.68220
$86$	−1.76650e6	+	3.05967e6i	−0.299481	+	0.518716i
$87$	438337.	+	759222.i	0.0713659	+	0.123609i
$88$	4.75644e6	+	8.23839e6i	0.744033	+	1.28870i
$89$	−5.92826e6	+	1.02680e7i	−0.891378	+	1.54391i	−0.0531544	+	0.998586i	$0.516928\pi$
$89$	−5.92826e6	+	1.02680e7i	−0.891378	+	1.54391i	−0.838224	+	0.545326i	$0.816406\pi$
$90$	2.53424e6			0.366437
$91$		0			0
$92$	1.14937e6			0.153887
$93$	2.28246e6	−	3.95334e6i	0.294248	−	0.509652i
$94$	−7.38231e6	−	1.27865e7i	−0.916737	−	1.58784i
$95$	−1.26769e6	−	2.19571e6i	−0.151698	−	0.262749i
$96$	−818045.	+	1.41690e6i	−0.0943687	+	0.163451i
$97$	4.49189e6			0.499722			0.249861	−	0.968282i	$-0.419615\pi$
$97$	4.49189e6			0.499722			0.249861	+	0.968282i	$0.419615\pi$
$98$		0			0
$99$	−5.31364e6			−0.550388
$100$	−30763.2	+	53283.4i	−0.00307632	+	0.00532834i
$101$	−4.69201e6	−	8.12680e6i	−0.453142	−	0.784865i	0.545437	−	0.838152i	$-0.316364\pi$
$101$	−4.69201e6	−	8.12680e6i	−0.453142	−	0.784865i	−0.998579	+	0.0532866i	$0.983030\pi$
$102$	−5.51586e6	−	9.55374e6i	−0.514650	−	0.891401i
$103$	3.53129e6	−	6.11637e6i	0.318422	−	0.551523i	−0.661737	−	0.749736i	$-0.730180\pi$
$103$	3.53129e6	−	6.11637e6i	0.318422	−	0.551523i	0.980159	+	0.198213i	$0.0635138\pi$
$104$	1.11189e7			0.969268
$105$		0			0
$106$	2.41738e6			0.197140
$107$	1.14582e7	−	1.98461e7i	0.904215	−	1.56615i	0.0822475	−	0.996612i	$-0.473790\pi$
$107$	1.14582e7	−	1.98461e7i	0.904215	−	1.56615i	0.821968	−	0.569534i	$-0.192876\pi$
$108$	−207919.	−	360126.i	−0.0158822	−	0.0275088i
$109$	7.79104e6	+	1.34945e7i	0.576239	+	0.998076i	0.995906	+	0.0903975i	$0.0288137\pi$
$109$	7.79104e6	+	1.34945e7i	0.576239	+	0.998076i	−0.419666	+	0.907678i	$0.637853\pi$
$110$	1.26694e7	−	2.19440e7i	0.907571	−	1.57196i
$111$	2.67930e6			0.185948
$112$		0			0
$113$	3.88887e6			0.253542			0.126771	−	0.991932i	$-0.459539\pi$
$113$	3.88887e6			0.253542			0.126771	+	0.991932i	$0.459539\pi$
$114$	−1.46829e6	+	2.54316e6i	−0.0928209	+	0.160771i
$115$	7.74353e6	+	1.34122e7i	0.474785	+	0.822351i
$116$	342986.	+	594069.i	0.0204020	+	0.0353374i
$117$	−3.10535e6	+	5.37863e6i	−0.179251	+	0.310471i
$118$	−2.71601e7			−1.52175
$119$		0			0
$120$	−1.00312e7			−0.529930
$121$	−1.68208e7	+	2.91345e7i	−0.863173	+	1.49506i
$122$	6.47683e6	+	1.12182e7i	0.322926	+	0.559324i
$123$	−3.17740e6	−	5.50341e6i	−0.153958	−	0.266664i
$124$	1.78596e6	−	3.09338e6i	0.0841194	−	0.145699i
$125$	2.14108e7			0.980503
$126$		0			0
$127$	2.64571e7			1.14612			0.573059	−	0.819514i	$-0.305757\pi$
$127$	2.64571e7			1.14612			0.573059	+	0.819514i	$0.305757\pi$
$128$	1.39295e7	−	2.41266e7i	0.587084	−	1.01686i
$129$	3.90571e6	+	6.76488e6i	0.160190	+	0.277457i
$130$	−1.48083e7	−	2.56486e7i	−0.591156	−	1.02391i
$131$	−3.15884e6	+	5.47127e6i	−0.122766	+	0.212637i	−0.920857	−	0.389899i	$-0.872510\pi$
$131$	−3.15884e6	+	5.47127e6i	−0.122766	+	0.212637i	0.798092	+	0.602536i	$0.205843\pi$
$132$	−4.15777e6			−0.157345
$133$		0			0
$134$	−4.57292e7			−1.64183
$135$	2.80158e6	−	4.85249e6i	0.0980021	−	0.169745i
$136$	2.18332e7	+	3.78163e7i	0.744273	+	1.28912i
$137$	384230.	+	665506.i	0.0127664	+	0.0221121i	0.872338	−	0.488903i	$-0.162603\pi$
$137$	384230.	+	665506.i	0.0127664	+	0.0221121i	−0.859572	+	0.511015i	$0.829270\pi$
$138$	8.96888e6	−	1.55346e7i	0.290510	−	0.503179i
$139$	4.86059e7			1.53510			0.767551	−	0.640988i	$-0.221475\pi$
$139$	4.86059e7			1.53510			0.767551	+	0.640988i	$0.221475\pi$
$140$		0			0
$141$	−3.26444e7			−0.980712
$142$	−1.83157e7	+	3.17238e7i	−0.536804	+	0.929771i
$143$	3.10491e7	+	5.37786e7i	0.887917	+	1.53792i
$144$	6.79497e6	+	1.17692e7i	0.189635	+	0.328458i
$145$	−4.62154e6	+	8.00474e6i	−0.125892	+	0.218052i
$146$	−8.03391e7			−2.13645
$147$		0			0
$148$	2.09648e6			0.0531587
$149$	6.83443e6	−	1.18376e7i	0.169259	−	0.293164i	−0.768901	−	0.639368i	$-0.779196\pi$
$149$	6.83443e6	−	1.18376e7i	0.169259	−	0.293164i	0.938159	+	0.346204i	$0.112529\pi$
$150$	480109.	+	831574.i	0.0116150	+	0.0201178i
$151$	−8.37244e6	−	1.45015e7i	−0.197894	−	0.342763i	0.749951	−	0.661493i	$-0.230077\pi$
$151$	−8.37244e6	−	1.45015e7i	−0.197894	−	0.342763i	−0.947845	+	0.318730i	$0.896744\pi$
$152$	5.81190e6	−	1.00665e7i	0.134235	−	0.232502i
$153$	−2.43910e7			−0.550565
$154$		0			0
$155$	4.81296e7			1.03813
$156$	−2.42985e6	+	4.20863e6i	−0.0512441	+	0.0887573i
$157$	−4.86259e6	−	8.42225e6i	−0.100281	−	0.173692i	0.811519	−	0.584325i	$-0.198641\pi$
$157$	−4.86259e6	−	8.42225e6i	−0.100281	−	0.173692i	−0.911800	+	0.410634i	$0.865308\pi$
$158$	4.33443e7	+	7.50745e7i	0.874243	+	1.51423i
$159$	2.67240e6	−	4.62873e6i	0.0527243	−	0.0913212i
$160$	−1.72499e7			−0.332940
$161$		0			0
$162$	−6.48982e6			−0.119931
$163$	−7.42421e6	+	1.28591e7i	−0.134275	+	0.232570i	−0.925320	−	0.379187i	$-0.876204\pi$
$163$	−7.42421e6	+	1.28591e7i	−0.134275	+	0.232570i	0.791046	+	0.611757i	$0.209537\pi$
$164$	−2.48622e6	−	4.30626e6i	−0.0440136	−	0.0762337i
$165$	−2.80118e7	−	4.85179e7i	−0.485453	−	0.840829i
$166$	−2.69472e6	+	4.66738e6i	−0.0457230	+	0.0791945i
$167$	−4.88199e7			−0.811128			−0.405564	−	0.914067i	$-0.632925\pi$
$167$	−4.88199e7			−0.811128			−0.405564	+	0.914067i	$0.632925\pi$
$168$		0			0
$169$	9.83322e6			0.156708
$170$	5.81556e7	−	1.00728e8i	0.907863	−	1.57246i
$171$	3.24638e6	+	5.62289e6i	0.0496492	+	0.0859950i
$172$	3.05611e6	+	5.29333e6i	0.0457951	+	0.0793194i
$173$	−5.14904e7	+	8.91841e7i	−0.756076	+	1.30956i	0.188762	+	0.982023i	$0.439553\pi$
$173$	−5.14904e7	+	8.91841e7i	−0.756076	+	1.30956i	−0.944838	+	0.327539i	$0.893781\pi$
$174$	1.07057e7			0.154061
$175$		0			0
$176$	1.35880e8			1.87871
$177$	−3.00253e7	+	5.20053e7i	−0.406987	+	0.704923i
$178$	7.23944e7	+	1.25391e8i	0.962132	+	1.66646i
$179$	1.66888e7	+	2.89059e7i	0.217491	+	0.376705i	0.954040	−	0.299679i	$-0.0968795\pi$
$179$	1.66888e7	+	2.89059e7i	0.217491	+	0.376705i	−0.736550	+	0.676384i	$0.763546\pi$
$180$	2.19216e6	−	3.79693e6i	0.0280168	−	0.0485265i
$181$	−8.05289e7			−1.00943			−0.504716	−	0.863286i	$-0.668403\pi$
$181$	−8.05289e7			−1.00943			−0.504716	+	0.863286i	$0.668403\pi$
$182$		0			0
$183$	2.86403e7			0.345461
$184$	−3.55012e7	+	6.14900e7i	−0.420128	+	0.727682i
$185$	1.41244e7	+	2.44642e7i	0.164010	+	0.284073i
$186$	−2.78729e7	−	4.82772e7i	−0.317604	−	0.550107i
$187$	−1.21937e8	+	2.11201e8i	−1.36361	+	2.36184i
$188$	−2.55433e7			−0.280365
$189$		0			0
$190$	−3.09615e7			−0.327479
$191$	1.75869e7	−	3.04614e7i	0.182630	−	0.316324i	−0.760145	−	0.649753i	$-0.774872\pi$
$191$	1.75869e7	−	3.04614e7i	0.182630	−	0.316324i	0.942775	+	0.333429i	$0.108206\pi$
$192$	−2.22234e7	−	3.84921e7i	−0.226598	−	0.392480i
$193$	4.18332e7	+	7.24573e7i	0.418862	+	0.725490i	0.995825	−	0.0912801i	$-0.0290959\pi$
$193$	4.18332e7	+	7.24573e7i	0.418862	+	0.725490i	−0.576963	+	0.816770i	$0.695763\pi$
$194$	2.74269e7	−	4.75048e7i	0.269694	−	0.467123i
$195$	−6.54817e7			−0.632410
$196$		0			0
$197$	−1.57062e8			−1.46365			−0.731826	−	0.681491i	$-0.761332\pi$
$197$	−1.57062e8			−1.46365			−0.731826	+	0.681491i	$0.761332\pi$
$198$	−3.24444e7	+	5.61954e7i	−0.297038	+	0.514485i
$199$	−8.15296e7	−	1.41213e8i	−0.733381	−	1.27025i	−0.955430	−	0.295218i	$-0.904608\pi$
$199$	−8.15296e7	−	1.41213e8i	−0.733381	−	1.27025i	0.222049	−	0.975036i	$-0.428725\pi$
$200$	−1.90040e6	−	3.29159e6i	−0.0167973	−	0.0290938i
$201$	−5.05534e7	+	8.75610e7i	−0.439100	+	0.760544i
$202$	−1.14595e8			−0.978221
$203$		0			0
$204$	−1.90852e7			−0.157395
$205$	3.35004e7	−	5.80244e7i	0.271589	−	0.470405i
$206$	−4.31232e7	−	7.46916e7i	−0.343697	−	0.595301i
$207$	−1.98301e7	−	3.43467e7i	−0.155392	−	0.269147i
$208$	7.94097e7	−	1.37542e8i	0.611860	−	1.05977i
$209$	6.49182e7			0.491874
$210$		0			0
$211$	−2.27246e8			−1.66536			−0.832678	−	0.553757i	$-0.813194\pi$
$211$	−2.27246e8			−1.66536			−0.832678	+	0.553757i	$0.813194\pi$
$212$	2.09107e6	−	3.62185e6i	0.0150728	−	0.0261069i
$213$	4.04959e7	+	7.01409e7i	0.287132	+	0.497328i
$214$	−1.39924e8	−	2.42356e8i	−0.975988	−	1.69046i
$215$	−4.11792e7	+	7.13245e7i	−0.282582	+	0.489446i
$216$	2.56885e7			0.173440
$217$		0			0
$218$	1.90285e8			1.24396
$219$	−8.88143e7	+	1.53831e8i	−0.571384	+	0.989667i
$220$	−2.19184e7	−	3.79638e7i	−0.138781	−	0.240376i
$221$	1.42523e8	+	2.46857e8i	0.888203	+	1.53841i
$222$	1.63595e7	−	2.83355e7i	0.100354	−	0.173818i
$223$	1.36641e8			0.825113			0.412557	−	0.910932i	$-0.364636\pi$
$223$	1.36641e8			0.825113			0.412557	+	0.910932i	$0.364636\pi$
$224$		0			0
$225$	2.12303e6			0.0124256
$226$	2.37450e7	−	4.11275e7i	0.136833	−	0.237002i
$227$	−4.05401e7	−	7.02176e7i	−0.230035	−	0.398433i	0.727783	−	0.685808i	$-0.240551\pi$
$227$	−4.05401e7	−	7.02176e7i	−0.230035	−	0.398433i	−0.957818	+	0.287375i	$0.907218\pi$
$228$	2.54020e6	+	4.39975e6i	0.0141937	+	0.0245842i
$229$	8.39945e7	−	1.45483e8i	0.462197	−	0.800548i	−0.536873	−	0.843663i	$-0.680395\pi$
$229$	8.39945e7	−	1.45483e8i	0.462197	−	0.800548i	0.999070	+	0.0431147i	$0.0137281\pi$
$230$	1.89124e8			1.02494
$231$		0			0
$232$	−4.23761e7			−0.222799
$233$	1.35898e8	−	2.35382e8i	0.703828	−	1.21907i	−0.263284	−	0.964718i	$-0.584806\pi$
$233$	1.35898e8	−	2.35382e8i	0.703828	−	1.21907i	0.967113	−	0.254348i	$-0.0818609\pi$
$234$	3.79218e7	+	6.56825e7i	0.193479	+	0.335115i
$235$	−1.72091e8	−	2.98070e8i	−0.865007	−	1.49824i
$236$	−2.34939e7	+	4.06927e7i	−0.116349	+	0.201523i
$237$	1.91667e8			0.935252
$238$		0			0
$239$	3.22573e8			1.52839			0.764197	−	0.644983i	$-0.223136\pi$
$239$	3.22573e8			1.52839			0.764197	+	0.644983i	$0.223136\pi$
$240$	−7.16417e7	+	1.24087e8i	−0.334523	+	0.579412i
$241$	−6.50063e7	−	1.12594e8i	−0.299155	−	0.518151i	0.676788	−	0.736178i	$-0.263371\pi$
$241$	−6.50063e7	−	1.12594e8i	−0.299155	−	0.518151i	−0.975943	+	0.218027i	$0.930038\pi$
$242$	2.05411e8	+	3.55783e8i	0.931689	+	1.61373i
$243$	−7.17445e6	+	1.24265e7i	−0.0320750	+	0.0555556i
$244$	2.24103e7			0.0987603
$245$		0			0
$246$	−7.76031e7			−0.332358
$247$	3.79389e7	−	6.57121e7i	0.160194	−	0.277464i
$248$	1.10328e8	+	1.91094e8i	0.459310	+	0.795548i
$249$	5.95798e6	+	1.03195e7i	0.0244569	+	0.0423606i
$250$	1.30732e8	−	2.26434e8i	0.529166	−	0.916542i
$251$	−1.58789e8			−0.633815			−0.316907	−	0.948456i	$-0.602644\pi$
$251$	−1.58789e8			−0.633815			−0.316907	+	0.948456i	$0.602644\pi$
$252$		0			0
$253$	−3.96544e8			−1.53947
$254$	1.61544e8	−	2.79802e8i	0.618546	−	1.07135i
$255$	−1.28581e8	−	2.22709e8i	−0.485609	−	0.841100i
$256$	−6.47481e7	−	1.12147e8i	−0.241205	−	0.417780i
$257$	1.38124e8	−	2.39238e8i	0.507579	−	0.879152i	−0.492383	−	0.870379i	$-0.663874\pi$
$257$	1.38124e8	−	2.39238e8i	0.507579	−	0.879152i	0.999962	−	0.00877328i	$-0.00279266\pi$
$258$	9.53910e7			0.345811
$259$		0			0
$260$	−5.12375e7			−0.180793
$261$	1.18351e7	−	2.04990e7i	0.0412031	−	0.0713659i
$262$	3.85749e7	+	6.68137e7i	0.132511	+	0.229515i
$263$	−2.01190e7	−	3.48471e7i	−0.0681963	−	0.118119i	0.829911	−	0.557896i	$-0.188391\pi$
$263$	−2.01190e7	−	3.48471e7i	−0.0681963	−	0.118119i	−0.898107	+	0.439776i	$0.855058\pi$
$264$	1.28424e8	−	2.22437e8i	0.429568	−	0.744033i
$265$	5.63520e7			0.186015
$266$		0			0
$267$	3.20126e8			1.02928
$268$	−3.95566e7	+	6.85140e7i	−0.125530	+	0.217424i
$269$	−1.92361e8	−	3.33179e8i	−0.602537	−	1.04362i	−0.992436	−	0.122767i	$-0.960823\pi$
$269$	−1.92361e8	−	3.33179e8i	−0.602537	−	1.04362i	0.389899	−	0.920858i	$-0.372510\pi$
$270$	−3.42122e7	−	5.92573e7i	−0.105781	−	0.183218i
$271$	9.78943e7	−	1.69558e8i	0.298789	−	0.517518i	−0.677070	−	0.735919i	$-0.736751\pi$
$271$	9.78943e7	−	1.69558e8i	0.298789	−	0.517518i	0.975859	+	0.218401i	$0.0700839\pi$
$272$	6.23722e8			1.87932
$273$		0			0
$274$	9.38423e6			0.0275595
$275$	1.06136e7	−	1.83833e7i	0.0307751	−	0.0533040i
$276$	−1.55165e7	−	2.68753e7i	−0.0444233	−	0.0769435i
$277$	1.62603e8	+	2.81637e8i	0.459674	+	0.796178i	0.998944	−	0.0459547i	$-0.0146330\pi$
$277$	1.62603e8	+	2.81637e8i	0.459674	+	0.796178i	−0.539270	+	0.842133i	$0.681300\pi$
$278$	2.96781e8	−	5.14040e8i	0.828476	−	1.43496i
$279$	−1.23253e8			−0.339768
$280$		0			0
$281$	6.42019e8			1.72614			0.863069	−	0.505086i	$-0.168539\pi$
$281$	6.42019e8			1.72614			0.863069	+	0.505086i	$0.168539\pi$
$282$	−1.99322e8	+	3.45237e8i	−0.529279	+	0.916737i
$283$	−1.34726e8	−	2.33353e8i	−0.353346	−	0.612013i	0.633488	−	0.773753i	$-0.281623\pi$
$283$	−1.34726e8	−	2.33353e8i	−0.353346	−	0.612013i	−0.986833	+	0.161740i	$0.948289\pi$
$284$	3.16869e7	+	5.48833e7i	0.0820852	+	0.142176i
$285$	−3.42277e7	+	5.92841e7i	−0.0875831	+	0.151698i
$286$	7.58327e8			1.91679
$287$		0			0
$288$	4.41744e7			0.108968
$289$	−3.54553e8	+	6.14104e8i	−0.864050	+	1.49658i
$290$	5.64370e7	+	9.77518e7i	0.135885	+	0.235360i
$291$	−6.06405e7	−	1.05032e8i	−0.144257	−	0.249861i
$292$	−6.94946e7	+	1.20368e8i	−0.163347	+	0.282925i
$293$	−3.00641e7			−0.0698252			−0.0349126	−	0.999390i	$-0.511115\pi$
$293$	−3.00641e7			−0.0698252			−0.0349126	+	0.999390i	$0.511115\pi$
$294$		0			0
$295$	−6.33134e8			−1.43588
$296$	−6.47552e7	+	1.12159e8i	−0.145129	+	0.251371i
$297$	7.17342e7	+	1.24247e8i	0.158883	+	0.275194i
$298$	−8.34603e7	−	1.44558e8i	−0.182694	−	0.316435i
$299$	−2.31745e8	+	4.01394e8i	−0.501373	+	0.868404i
$300$	1.66121e6			0.00355222
$301$		0			0
$302$	−2.04484e8			−0.427204
$303$	−1.26684e8	+	2.19424e8i	−0.261622	+	0.453142i
$304$	−8.30159e7	−	1.43788e8i	−0.169474	−	0.293538i
$305$	1.50983e8	+	2.61510e8i	0.304704	+	0.527762i
$306$	−1.48928e8	+	2.57951e8i	−0.297134	+	0.514650i
$307$	−2.00137e8			−0.394769			−0.197385	−	0.980326i	$-0.563245\pi$
$307$	−2.00137e8			−0.394769			−0.197385	+	0.980326i	$0.563245\pi$
$308$		0			0
$309$	−1.90690e8			−0.367682
$310$	2.93873e8	−	5.09004e8i	0.560266	−	0.970409i
$311$	−2.66212e8	−	4.61093e8i	−0.501842	−	0.869215i	−0.999998	−	0.00212799i	$-0.999323\pi$
$311$	−2.66212e8	−	4.61093e8i	−0.501842	−	0.869215i	0.498156	−	0.867087i	$-0.334011\pi$
$312$	−1.50105e8	−	2.59989e8i	−0.279804	−	0.484634i
$313$	−2.62148e8	+	4.54053e8i	−0.483215	+	0.836953i	−0.999814	−	0.0192742i	$-0.993864\pi$
$313$	−2.62148e8	+	4.54053e8i	−0.483215	+	0.836953i	0.516599	+	0.856227i	$0.327198\pi$
$314$	−1.18761e8			−0.216482
$315$		0			0
$316$	1.49974e8			0.267369
$317$	2.47055e8	−	4.27912e8i	0.435599	−	0.754480i	−0.561745	−	0.827310i	$-0.689870\pi$
$317$	2.47055e8	−	4.27912e8i	0.435599	−	0.754480i	0.997344	+	0.0728306i	$0.0232033\pi$
$318$	−3.26346e7	−	5.65248e7i	−0.0569094	−	0.0985699i
$319$	−1.18334e8	−	2.04960e8i	−0.204099	−	0.353510i
$320$	2.34309e8	−	4.05835e8i	0.399728	−	0.692349i
$321$	−6.18741e8			−1.04410
$322$		0			0
$323$	2.97991e8			0.492033
$324$	−5.61381e6	+	9.72340e6i	−0.00916959	+	0.0158822i
$325$	−1.24054e7	−	2.14869e7i	−0.0200457	−	0.0347201i
$326$	9.06626e7	+	1.57032e8i	0.144933	+	0.251031i
$327$	2.10358e8	−	3.64351e8i	0.332692	−	0.576239i
$328$	3.07174e8			0.480647
$329$		0			0
$330$	−6.84146e8			−1.04797
$331$	1.22105e8	−	2.11491e8i	0.185069	−	0.320549i	−0.758531	−	0.651637i	$-0.774082\pi$
$331$	1.22105e8	−	2.11491e8i	0.185069	−	0.320549i	0.943600	+	0.331088i	$0.107416\pi$
$332$	4.66195e6	+	8.07473e6i	0.00699172	+	0.0121100i
$333$	−3.61706e7	−	6.26493e7i	−0.0536786	−	0.0929740i
$334$	−2.98088e8	+	5.16304e8i	−0.437756	+	0.758215i
$335$	−1.06600e9			−1.54918
$336$		0			0
$337$	1.19277e9			1.69766			0.848832	−	0.528663i	$-0.177307\pi$
$337$	1.19277e9			1.69766			0.848832	+	0.528663i	$0.177307\pi$
$338$	6.00404e7	−	1.03993e8i	0.0845736	−	0.146486i
$339$	−5.24998e7	−	9.09323e7i	−0.0731911	−	0.126771i
$340$	−1.00611e8	−	1.74264e8i	−0.138826	−	0.240453i
$341$	−6.16176e8	+	1.06725e9i	−0.841520	+	1.45756i
$342$	7.92878e7			0.107180
$343$		0			0
$344$	−3.77583e8			−0.500102
$345$	2.09075e8	−	3.62129e8i	0.274117	−	0.474785i
$346$	6.28788e8	+	1.08909e9i	0.816090	+	1.41351i
$347$	−3.40650e8	−	5.90022e8i	−0.437678	−	0.758080i	0.559832	−	0.828606i	$-0.310866\pi$
$347$	−3.40650e8	−	5.90022e8i	−0.437678	−	0.758080i	−0.997510	+	0.0705257i	$0.977532\pi$
$348$	9.26062e6	−	1.60399e7i	0.0117791	−	0.0204020i
$349$	−1.39362e9			−1.75491			−0.877457	−	0.479656i	$-0.840761\pi$
$349$	−1.39362e9			−1.75491			−0.877457	+	0.479656i	$0.840761\pi$
$350$		0			0
$351$	1.67689e8			0.206981
$352$	2.20840e8	−	3.82507e8i	0.269885	−	0.467455i
$353$	−5.71873e8	−	9.90512e8i	−0.691971	−	1.19853i	−0.971191	−	0.238302i	$-0.923409\pi$
$353$	−5.71873e8	−	9.90512e8i	−0.691971	−	1.19853i	0.279220	−	0.960227i	$-0.409924\pi$
$354$	3.66661e8	+	6.35076e8i	0.439292	+	0.760877i
$355$	−4.26962e8	+	7.39520e8i	−0.506512	+	0.877305i
$356$	2.50489e8			0.294249
$357$		0			0
$358$	4.07600e8			0.469508
$359$	6.57466e7	−	1.13876e8i	0.0749967	−	0.129898i	−0.826088	−	0.563541i	$-0.809439\pi$
$359$	6.57466e7	−	1.13876e8i	0.0749967	−	0.129898i	0.901085	+	0.433643i	$0.142772\pi$
$360$	1.35421e8	+	2.34556e8i	0.152978	+	0.264965i
$361$	4.07274e8	+	7.05419e8i	0.455629	+	0.789173i
$362$	−4.91699e8	+	8.51648e8i	−0.544778	+	0.943583i
$363$	9.08324e8			0.996707
$364$		0			0
$365$	−1.87280e9			−2.01589
$366$	1.74874e8	−	3.02891e8i	0.186441	−	0.322926i
$367$	−3.41381e8	−	5.91289e8i	−0.360502	−	0.624408i	0.627541	−	0.778583i	$-0.284061\pi$
$367$	−3.41381e8	−	5.91289e8i	−0.360502	−	0.624408i	−0.988044	+	0.154175i	$0.950728\pi$
$368$	5.07092e8	+	8.78309e8i	0.530419	+	0.918713i
$369$	−8.57897e7	+	1.48592e8i	−0.0888879	+	0.153958i
$370$	3.44967e8			0.354056
$371$		0			0
$372$	−9.64420e7			−0.0971328
$373$	−8.00258e8	+	1.38609e9i	−0.798452	+	1.38296i	0.122171	+	0.992509i	$0.461014\pi$
$373$	−8.00258e8	+	1.38609e9i	−0.798452	+	1.38296i	−0.920624	+	0.390451i	$0.872319\pi$
$374$	1.48907e9	+	2.57914e9i	1.47185	+	2.54932i
$375$	−2.89046e8	−	5.00643e8i	−0.283047	−	0.490251i
$376$	7.88972e8	−	1.36654e9i	0.765427	−	1.32576i
$377$	−2.76623e8			−0.265885
$378$		0			0
$379$	−5.79581e7			−0.0546861			−0.0273431	−	0.999626i	$-0.508705\pi$
$379$	−5.79581e7			−0.0546861			−0.0273431	+	0.999626i	$0.508705\pi$
$380$	−2.67822e7	+	4.63881e7i	−0.0250382	+	0.0433675i
$381$	−3.57171e8	−	6.18638e8i	−0.330856	−	0.573059i
$382$	−2.14766e8	−	3.71986e8i	−0.197126	−	0.341433i
$383$	5.13585e8	−	8.89555e8i	0.467107	−	0.809054i	−0.532187	−	0.846627i	$-0.678629\pi$
$383$	5.13585e8	−	8.89555e8i	0.467107	−	0.809054i	0.999294	+	0.0375735i	$0.0119628\pi$
$384$	−7.52193e8			−0.677907
$385$		0			0
$386$	1.02171e9			0.904219
$387$	1.05454e8	−	1.82652e8i	0.0924858	−	0.160190i
$388$	−4.74495e7	−	8.21849e7i	−0.0412402	−	0.0714301i
$389$	−7.54383e8	−	1.30663e9i	−0.649783	−	1.12546i	−0.983175	−	0.182668i	$-0.941527\pi$
$389$	−7.54383e8	−	1.30663e9i	−0.649783	−	1.12546i	0.333392	−	0.942788i	$-0.391807\pi$
$390$	−3.99823e8	+	6.92513e8i	−0.341304	+	0.591156i
$391$	−1.82024e9			−1.53996
$392$		0			0
$393$	1.70577e8			0.141758
$394$	−9.58998e8	+	1.66103e9i	−0.789916	+	1.36817i
$395$	1.01041e9	+	1.75008e9i	0.824910	+	1.42879i
$396$	5.61300e7	+	9.72199e7i	0.0454215	+	0.0786724i
$397$	−1.74588e8	+	3.02395e8i	−0.140038	+	0.242554i	−0.927511	−	0.373796i	$-0.878056\pi$
$397$	−1.74588e8	+	3.02395e8i	−0.140038	+	0.242554i	0.787472	+	0.616350i	$0.211389\pi$
$398$	−1.99124e9			−1.58319
$399$		0			0
$400$	−5.42898e7			−0.0424139
$401$	3.96179e8	−	6.86201e8i	0.306821	−	0.531430i	−0.670844	−	0.741599i	$-0.734068\pi$
$401$	3.96179e8	−	6.86201e8i	0.306821	−	0.531430i	0.977665	+	0.210168i	$0.0674012\pi$
$402$	6.17345e8	+	1.06927e9i	0.473954	+	0.820913i
$403$	7.20201e8	+	1.24742e9i	0.548133	+	0.949394i
$404$	−9.91269e7	+	1.71693e8i	−0.0747923	+	0.129544i
$405$	−1.51286e8			−0.113163
$406$		0			0
$407$	−7.23308e8			−0.531793
$408$	5.89498e8	−	1.02104e9i	0.429706	−	0.744273i
$409$	7.34109e8	+	1.27151e9i	0.530553	+	0.918945i	0.999364	+	0.0356470i	$0.0113492\pi$
$409$	7.34109e8	+	1.27151e9i	0.530553	+	0.918945i	−0.468811	+	0.883298i	$0.655317\pi$
$410$	−4.09098e8	−	7.08579e8i	−0.293146	−	0.507744i
$411$	1.03742e7	−	1.79687e7i	0.00737070	−	0.0127664i
$412$	−1.49209e8			−0.105113
$413$		0			0
$414$	−4.84320e8			−0.335452
$415$	−6.28171e7	+	1.08802e8i	−0.0431429	+	0.0747257i
$416$	−2.58123e8	−	4.47083e8i	−0.175793	−	0.304482i
$417$	−6.56180e8	−	1.13654e9i	−0.443146	−	0.767551i
$418$	3.96382e8	−	6.86554e8i	0.265459	−	0.459788i
$419$	1.76645e9			1.17315			0.586573	−	0.809897i	$-0.300477\pi$
$419$	1.76645e9			1.17315			0.586573	+	0.809897i	$0.300477\pi$
$420$		0			0
$421$	1.64598e9			1.07507			0.537537	−	0.843240i	$-0.319355\pi$
$421$	1.64598e9			1.07507			0.537537	+	0.843240i	$0.319355\pi$
$422$	−1.38753e9	+	2.40328e9i	−0.898773	+	1.55672i
$423$	4.40699e8	+	7.63313e8i	0.283107	+	0.490356i
$424$	1.29177e8	+	2.23741e8i	0.0823007	+	0.142549i
$425$	4.87192e7	−	8.43841e7i	0.0307850	−	0.0533211i
$426$	9.89050e8			0.619848
$427$		0			0
$428$	−4.84147e8			−0.298486
$429$	8.38325e8	−	1.45202e9i	0.512639	−	0.887917i
$430$	5.02870e8	+	8.70997e8i	0.305012	+	0.528296i
$431$	−5.88520e8	−	1.01935e9i	−0.354072	−	0.613270i	0.632887	−	0.774244i	$-0.281870\pi$
$431$	−5.88520e8	−	1.01935e9i	−0.354072	−	0.613270i	−0.986959	+	0.160974i	$0.948536\pi$
$432$	1.83464e8	−	3.17769e8i	0.109486	−	0.189635i
$433$	9.32782e8			0.552170			0.276085	−	0.961133i	$-0.410963\pi$
$433$	9.32782e8			0.552170			0.276085	+	0.961133i	$0.410963\pi$
$434$		0			0
$435$	2.49563e8			0.145368
$436$	1.64599e8	−	2.85094e8i	0.0951098	−	0.164735i
$437$	2.42269e8	+	4.19622e8i	0.138871	+	0.240532i
$438$	1.08458e9	+	1.87854e9i	0.616739	+	1.06822i
$439$	4.95951e8	−	8.59013e8i	0.279778	−	0.484589i	−0.691552	−	0.722327i	$-0.743073\pi$
$439$	4.95951e8	−	8.59013e8i	0.279778	−	0.484589i	0.971329	+	0.237738i	$0.0764059\pi$
$440$	2.70803e9			1.51555
$441$		0			0
$442$	3.48091e9			1.91741
$443$	−8.64720e8	+	1.49774e9i	−0.472566	+	0.818508i	−0.999507	−	0.0313936i	$-0.990005\pi$
$443$	−8.64720e8	+	1.49774e9i	−0.472566	+	0.818508i	0.526941	+	0.849902i	$0.323339\pi$
$444$	−2.83025e7	−	4.90213e7i	−0.0153456	−	0.0265793i
$445$	1.68760e9	+	2.92301e9i	0.907840	+	1.57243i
$446$	8.34312e8	−	1.44507e9i	0.445304	−	0.771289i
$447$	−3.69059e8			−0.195443
$448$		0			0
$449$	7.43406e8			0.387582			0.193791	−	0.981043i	$-0.437922\pi$
$449$	7.43406e8			0.387582			0.193791	+	0.981043i	$0.437922\pi$
$450$	1.29630e7	−	2.24525e7i	0.00670595	−	0.0116150i
$451$	8.57773e8	+	1.48571e9i	0.440306	+	0.762632i
$452$	−4.10796e7	−	7.11519e7i	−0.0209238	−	0.0362412i
$453$	−2.26056e8	+	3.91540e8i	−0.114254	+	0.197894i
$454$	−9.90131e8			−0.496589
$455$		0			0
$456$	−3.13843e8			−0.155001
$457$	1.73265e9	−	3.00103e9i	0.849187	−	1.47084i	−0.0327472	−	0.999464i	$-0.510426\pi$
$457$	1.73265e9	−	3.00103e9i	0.849187	−	1.47084i	0.881935	−	0.471372i	$-0.156241\pi$
$458$	−1.02572e9	−	1.77660e9i	−0.498884	−	0.864092i
$459$	3.29278e8	+	5.70326e8i	0.158935	+	0.275283i
$460$	1.63596e8	−	2.83356e8i	0.0783644	−	0.135731i
$461$	−4.98582e8			−0.237019			−0.118510	−	0.992953i	$-0.537812\pi$
$461$	−4.98582e8			−0.237019			−0.118510	+	0.992953i	$0.537812\pi$
$462$		0			0
$463$	−1.00802e9			−0.471994			−0.235997	−	0.971754i	$-0.575836\pi$
$463$	−1.00802e9			−0.471994			−0.235997	+	0.971754i	$0.575836\pi$
$464$	−3.02645e8	+	5.24197e8i	−0.140644	+	0.243602i
$465$	−6.49750e8	−	1.12540e9i	−0.299682	−	0.519065i
$466$	−1.65955e9	−	2.87442e9i	−0.759695	−	1.31583i
$467$	−1.95503e8	+	3.38622e8i	−0.0888270	+	0.153853i	−0.907016	−	0.421097i	$-0.861645\pi$
$467$	−1.95503e8	+	3.38622e8i	−0.0888270	+	0.153853i	0.818189	+	0.574950i	$0.194979\pi$
$468$	1.31212e8			0.0591716
$469$		0			0
$470$	−4.20305e9			−1.86733
$471$	−1.31290e8	+	2.27401e8i	−0.0578973	+	0.100281i
$472$	−1.45134e9	−	2.51380e9i	−0.635292	−	1.10036i
$473$	−1.05439e9	−	1.82626e9i	−0.458128	−	0.793501i
$474$	1.17030e9	−	2.02701e9i	0.504744	−	0.874243i
$475$	−2.59376e7			−0.0111046
$476$		0			0
$477$	−1.44309e8			−0.0608808
$478$	1.96959e9	−	3.41143e9i	0.824856	−	1.42869i
$479$	−1.36998e9	−	2.37288e9i	−0.569562	−	0.986510i	−0.996609	−	0.0822808i	$-0.973780\pi$
$479$	−1.36998e9	−	2.37288e9i	−0.569562	−	0.986510i	0.427047	−	0.904229i	$-0.359554\pi$
$480$	2.32873e8	+	4.03348e8i	0.0961115	+	0.166470i
$481$	−4.22709e8	+	7.32154e8i	−0.173194	+	0.299982i
$482$	−1.58768e9			−0.645800
$483$		0			0
$484$	7.10737e8			0.284938
$485$	6.39354e8	−	1.10739e9i	0.254475	−	0.440764i
$486$	8.76126e7	+	1.51749e8i	0.0346210	+	0.0599653i
$487$	1.29302e9	+	2.23957e9i	0.507286	+	0.878646i	0.999964	+	0.00843401i	$0.00268466\pi$
$487$	1.29302e9	+	2.23957e9i	0.507286	+	0.878646i	−0.492678	+	0.870212i	$0.663982\pi$
$488$	−6.92200e8	+	1.19893e9i	−0.269626	+	0.467006i
$489$	4.00908e8			0.155047
$490$		0			0
$491$	−2.60025e9			−0.991357			−0.495678	−	0.868506i	$-0.665081\pi$
$491$	−2.60025e9			−0.991357			−0.495678	+	0.868506i	$0.665081\pi$
$492$	−6.71280e7	+	1.16269e8i	−0.0254112	+	0.0440136i
$493$	−5.43182e8	−	9.40819e8i	−0.204165	−	0.353624i
$494$	−4.63300e8	−	8.02460e8i	−0.172909	−	0.299488i
$495$	−7.56319e8	+	1.30998e9i	−0.280276	+	0.485453i
$496$	3.15181e9			1.15978
$497$		0			0
$498$	1.45515e8			0.0527964
$499$	−1.80658e9	+	3.12909e9i	−0.650886	+	1.12737i	0.332022	+	0.943272i	$0.392269\pi$
$499$	−1.80658e9	+	3.12909e9i	−0.650886	+	1.12737i	−0.982908	+	0.184096i	$0.941064\pi$
$500$	−2.26171e8	−	3.91739e8i	−0.0809172	−	0.140153i
$501$	6.59069e8	+	1.14154e9i	0.234152	+	0.405564i
$502$	−9.69546e8	+	1.67930e9i	−0.342062	+	0.592469i
$503$	−1.19103e9			−0.417286			−0.208643	−	0.977992i	$-0.566905\pi$
$503$	−1.19103e9			−0.417286			−0.208643	+	0.977992i	$0.566905\pi$
$504$		0			0
$505$	−2.67135e9			−0.923021
$506$	−2.42125e9	+	4.19373e9i	−0.830831	+	1.43904i
$507$	−1.32748e8	−	2.29927e8i	−0.0452378	−	0.0783542i
$508$	−2.79476e8	−	4.84067e8i	−0.0945849	−	0.163826i
$509$	5.34378e8	−	9.25570e8i	0.179612	−	0.311098i	−0.762135	−	0.647418i	$-0.775849\pi$
$509$	5.34378e8	−	9.25570e8i	0.179612	−	0.311098i	0.941748	+	0.336320i	$0.109182\pi$
$510$	−3.14040e9			−1.04831
$511$		0			0
$512$	1.98458e9			0.653466
$513$	8.76522e7	−	1.51818e8i	0.0286650	−	0.0496492i
$514$	−1.68674e9	−	2.92151e9i	−0.547868	−	0.948936i
$515$	−1.00525e9	−	1.74115e9i	−0.324303	−	0.561708i
$516$	8.25148e7	−	1.42920e8i	0.0264398	−	0.0457951i
$517$	8.81271e9			2.80474
$518$		0			0
$519$	2.78048e9			0.873041
$520$	1.58261e9	−	2.74115e9i	0.493584	−	0.854913i
$521$	−2.15780e8	−	3.73742e8i	−0.0668466	−	0.115782i	0.830665	−	0.556773i	$-0.187960\pi$
$521$	−2.15780e8	−	3.73742e8i	−0.0668466	−	0.115782i	−0.897512	+	0.440991i	$0.854627\pi$
$522$	−1.44527e8	−	2.50328e8i	−0.0444736	−	0.0770306i
$523$	−1.53697e9	+	2.66211e9i	−0.469796	+	0.813711i	−0.999404	−	0.0345319i	$-0.989006\pi$
$523$	−1.53697e9	+	2.66211e9i	−0.469796	+	0.813711i	0.529607	+	0.848243i	$0.322339\pi$
$524$	1.33472e8			0.0405257
$525$		0			0
$526$	−4.91376e8			−0.147219
$527$	−2.82840e9	+	4.89894e9i	−0.841791	+	1.45802i
$528$	−1.83438e9	−	3.17723e9i	−0.542338	−	0.939356i
$529$	2.22543e8	+	3.85455e8i	0.0653610	+	0.113209i
$530$	3.44078e8	−	5.95961e8i	0.100390	−	0.173881i
$531$	1.62137e9			0.469948
$532$		0			0
$533$	2.00517e9			0.573596
$534$	1.95465e9	−	3.38555e9i	0.555487	−	0.962132i
$535$	−3.26180e9	−	5.64960e9i	−0.920914	−	1.59507i
$536$	−2.44362e9	−	4.23247e9i	−0.685419	−	1.18718i
$537$	4.50598e8	−	7.80459e8i	0.125568	−	0.217491i
$538$	−4.69812e9			−1.30073
$539$		0			0
$540$	−1.18377e8			−0.0323510
$541$	−4.76287e8	+	8.24953e8i	−0.129324	+	0.223995i	−0.923415	−	0.383804i	$-0.874614\pi$
$541$	−4.76287e8	+	8.24953e8i	−0.129324	+	0.223995i	0.794091	+	0.607799i	$0.207947\pi$
$542$	−1.19546e9	−	2.07060e9i	−0.322506	−	0.558596i
$543$	1.08714e9	+	1.88298e9i	0.291398	+	0.504716i
$544$	1.01371e9	−	1.75580e9i	0.269972	−	0.467605i
$545$	4.43576e9			1.17376
$546$		0			0
$547$	−5.06010e9			−1.32192			−0.660958	−	0.750423i	$-0.729850\pi$
$547$	−5.06010e9			−1.32192			−0.660958	+	0.750423i	$0.729850\pi$
$548$	8.11752e6	−	1.40600e7i	0.00210713	−	0.00364966i
$549$	−3.86645e8	−	6.69688e8i	−0.0997261	−	0.172731i
$550$	−1.29611e8	−	2.24493e8i	−0.0332179	−	0.0575351i
$551$	−1.44592e8	+	2.50441e8i	−0.0368226	+	0.0637787i
$552$	1.91707e9			0.485122
$553$		0			0
$554$	3.97134e9			0.992322
$555$	3.81359e8	−	6.60533e8i	0.0946910	−	0.164010i
$556$	−5.13442e8	−	8.89307e8i	−0.126686	−	0.219427i
$557$	−7.16651e8	−	1.24128e9i	−0.175717	−	0.304351i	0.764692	−	0.644396i	$-0.222891\pi$
$557$	−7.16651e8	−	1.24128e9i	−0.175717	−	0.304351i	−0.940409	+	0.340045i	$0.889558\pi$
$558$	−7.52567e8	+	1.30348e9i	−0.183369	+	0.317604i
$559$	−2.46479e9			−0.596813
$560$		0			0
$561$	6.58461e9			1.57456
$562$	3.92008e9	−	6.78978e9i	0.931576	−	1.61354i
$563$	−5.13648e8	−	8.89664e8i	−0.121307	−	0.210110i	0.798976	−	0.601363i	$-0.205375\pi$
$563$	−5.13648e8	−	8.89664e8i	−0.121307	−	0.210110i	−0.920283	+	0.391253i	$0.872042\pi$
$564$	3.44834e8	+	5.97271e8i	0.0809345	+	0.140183i
$565$	5.53523e8	−	9.58731e8i	0.129112	−	0.223628i
$566$	−3.29049e9			−0.762786
$567$		0			0
$568$	−3.91493e9			−0.896406
$569$	2.68919e8	−	4.65781e8i	0.0611967	−	0.105996i	−0.833804	−	0.552061i	$-0.813842\pi$
$569$	2.68919e8	−	4.65781e8i	0.0611967	−	0.105996i	0.895001	+	0.446065i	$0.147175\pi$
$570$	4.17980e8	+	7.23962e8i	0.0945351	+	0.163740i
$571$	8.79021e7	+	1.52251e8i	0.0197594	+	0.0342242i	0.875736	−	0.482790i	$-0.160377\pi$
$571$	8.79021e7	+	1.52251e8i	0.0197594	+	0.0342242i	−0.855977	+	0.517014i	$0.827043\pi$
$572$	6.55965e8	−	1.13617e9i	0.146553	−	0.253837i
$573$	−9.49691e8			−0.210883
$574$		0			0
$575$	1.58437e8			0.0347551
$576$	−6.00032e8	+	1.03929e9i	−0.130827	+	0.226598i
$577$	3.94062e9	+	6.82535e9i	0.853983	+	1.47914i	0.877586	+	0.479420i	$0.159153\pi$
$577$	3.94062e9	+	6.82535e9i	0.853983	+	1.47914i	−0.0236030	+	0.999721i	$0.507514\pi$
$578$	4.32971e9	+	7.49928e9i	0.932635	+	1.61537i
$579$	1.12950e9	−	1.95635e9i	0.241830	−	0.418862i
$580$	1.95276e8			0.0415576
$581$		0			0
$582$	−1.48105e9			−0.311416
$583$	−7.21443e8	+	1.24958e9i	−0.150786	+	0.261170i
$584$	−4.29305e9	−	7.43578e9i	−0.891910	−	1.54483i
$585$	8.84003e8	+	1.53114e9i	0.182561	+	0.316205i
$586$	−1.83568e8	+	3.17949e8i	−0.0376838	+	0.0652703i
$587$	7.45016e9			1.52031			0.760155	−	0.649742i	$-0.225123\pi$
$587$	7.45016e9			1.52031			0.760155	+	0.649742i	$0.225123\pi$
$588$		0			0
$589$	1.50581e9			0.303646
$590$	−3.86584e9	+	6.69583e9i	−0.774928	+	1.34222i
$591$	2.12033e9	+	3.67252e9i	0.422520	+	0.731826i
$592$	9.24949e8	+	1.60206e9i	0.183228	+	0.317360i
$593$	−8.85364e8	+	1.53350e9i	−0.174353	+	0.301989i	−0.939937	−	0.341347i	$-0.889117\pi$
$593$	−8.85364e8	+	1.53350e9i	−0.174353	+	0.301989i	0.765584	+	0.643336i	$0.222450\pi$
$594$	1.75200e9			0.342990
$595$		0			0
$596$	−2.88778e8			−0.0558731
$597$	−2.20130e9	+	3.81276e9i	−0.423418	+	0.733381i
$598$	2.83001e9	+	4.90172e9i	0.541170	+	0.937335i
$599$	6.86667e8	+	1.18934e9i	0.130543	+	0.226107i	0.923886	−	0.382668i	$-0.124995\pi$
$599$	6.86667e8	+	1.18934e9i	0.130543	+	0.226107i	−0.793343	+	0.608775i	$0.791661\pi$
$600$	−5.13109e7	+	8.88730e7i	−0.00969795	+	0.0167973i
$601$	2.69227e9			0.505892			0.252946	−	0.967480i	$-0.418601\pi$
$601$	2.69227e9			0.505892			0.252946	+	0.967480i	$0.418601\pi$
$602$		0			0
$603$	2.72988e9			0.507029
$604$	−1.76882e8	+	3.06369e8i	−0.0326629	+	0.0565738i
$605$	4.78839e9	+	8.29373e9i	0.879114	+	1.52267i
$606$	1.54704e9	+	2.67955e9i	0.282388	+	0.489111i
$607$	2.85285e9	−	4.94128e9i	0.517748	−	0.896766i	−0.482039	−	0.876150i	$-0.660104\pi$
$607$	2.85285e9	−	4.94128e9i	0.517748	−	0.896766i	0.999787	−	0.0206167i	$-0.00656297\pi$
$608$	−5.39691e8			−0.0973828
$609$		0			0
$610$	3.68752e9			0.657779
$611$	5.15025e9	−	8.92049e9i	0.913448	−	1.58214i
$612$	2.57651e8	+	4.46264e8i	0.0454361	+	0.0786977i
$613$	−2.63593e9	−	4.56556e9i	−0.462191	−	0.800539i	0.536879	−	0.843659i	$-0.319603\pi$
$613$	−2.63593e9	−	4.56556e9i	−0.462191	−	0.800539i	−0.999070	+	0.0431209i	$0.986270\pi$
$614$	−1.22201e9	+	2.11659e9i	−0.213052	+	0.369017i
$615$	−1.80902e9			−0.313603
$616$		0			0
$617$	−2.13431e9			−0.365812			−0.182906	−	0.983130i	$-0.558550\pi$
$617$	−2.13431e9			−0.365812			−0.182906	+	0.983130i	$0.558550\pi$
$618$	−1.16433e9	+	2.01667e9i	−0.198434	+	0.343697i
$619$	5.55040e8	+	9.61357e8i	0.0940604	+	0.162917i	0.909216	−	0.416325i	$-0.136682\pi$
$619$	5.55040e8	+	9.61357e8i	0.0940604	+	0.162917i	−0.815156	+	0.579242i	$0.803349\pi$
$620$	−5.08411e8	−	8.80593e8i	−0.0856730	−	0.148390i
$621$	−5.35412e8	+	9.27361e8i	−0.0897155	+	0.155392i
$622$	−6.50183e9			−1.08335
$623$		0			0
$624$	−4.28812e9			−0.706515
$625$	3.16128e9	−	5.47549e9i	0.517944	−	0.897105i
$626$	3.20128e9	+	5.54478e9i	0.521571	+	0.903387i
$627$	−8.76395e8	−	1.51796e9i	−0.141992	−	0.245937i
$628$	−1.02731e8	+	1.77935e8i	−0.0165516	+	0.0286683i
$629$	−3.32016e9			−0.531964
$630$		0			0
$631$	−4.46562e8			−0.0707585			−0.0353793	−	0.999374i	$-0.511264\pi$
$631$	−4.46562e8			−0.0707585			−0.0353793	+	0.999374i	$0.511264\pi$
$632$	−4.63235e9	+	8.02346e9i	−0.729947	+	1.26430i
$633$	3.06782e9	+	5.31362e9i	0.480747	+	0.832678i
$634$	−3.01698e9	−	5.22556e9i	−0.470175	−	0.814367i
$635$	3.76578e9	−	6.52252e9i	0.583642	−	1.01090i
$636$	−1.12918e8			−0.0174046
$637$		0			0
$638$	−2.89013e9			−0.440600
$639$	1.09339e9	−	1.89380e9i	0.165776	−	0.287132i
$640$	−3.96532e9	−	6.86813e9i	−0.597927	−	1.03564i
$641$	−2.16534e9	−	3.75048e9i	−0.324731	−	0.562450i	0.656727	−	0.754128i	$-0.271940\pi$
$641$	−2.16534e9	−	3.75048e9i	−0.324731	−	0.562450i	−0.981458	+	0.191678i	$0.938607\pi$
$642$	−3.77795e9	+	6.54360e9i	−0.563487	+	0.975988i
$643$	−5.12208e9			−0.759814			−0.379907	−	0.925025i	$-0.624044\pi$
$643$	−5.12208e9			−0.759814			−0.379907	+	0.925025i	$0.624044\pi$
$644$		0			0
$645$	2.22368e9			0.326297
$646$	1.81949e9	−	3.15146e9i	0.265544	−	0.459936i
$647$	5.39045e9	+	9.33654e9i	0.782457	+	1.35525i	0.930507	+	0.366275i	$0.119367\pi$
$647$	5.39045e9	+	9.33654e9i	0.782457	+	1.35525i	−0.148050	+	0.988980i	$0.547300\pi$
$648$	−3.46794e8	−	6.00665e8i	−0.0500679	−	0.0867201i
$649$	8.10566e9	−	1.40394e10i	1.16394	−	2.01601i
$650$	−3.02984e8			−0.0432736
$651$		0			0
$652$	3.13699e8			0.0443247
$653$	−5.55180e9	+	9.61601e9i	−0.780258	+	1.35145i	0.151534	+	0.988452i	$0.451579\pi$
$653$	−5.55180e9	+	9.61601e9i	−0.780258	+	1.35145i	−0.931792	+	0.362994i	$0.881755\pi$
$654$	−2.56884e9	−	4.44936e9i	−0.359100	−	0.621979i
$655$	8.99228e8	+	1.55751e9i	0.125033	+	0.216564i
$656$	2.19380e9	−	3.79978e9i	0.303413	−	0.525526i
$657$	4.79597e9			0.659778
$658$		0			0
$659$	−5.33302e9			−0.725896			−0.362948	−	0.931809i	$-0.618230\pi$
$659$	−5.33302e9			−0.725896			−0.362948	+	0.931809i	$0.618230\pi$
$660$	−5.91798e8	+	1.02502e9i	−0.0801253	+	0.138781i
$661$	1.49409e9	+	2.58784e9i	0.201221	+	0.348524i	0.948922	−	0.315511i	$-0.102176\pi$
$661$	1.49409e9	+	2.58784e9i	0.201221	+	0.348524i	−0.747701	+	0.664035i	$0.768843\pi$
$662$	−1.49111e9	−	2.58268e9i	−0.199759	−	0.345993i
$663$	3.84812e9	−	6.66514e9i	0.512804	−	0.888203i
$664$	−5.75986e8			−0.0763526
$665$		0			0
$666$	−8.83412e8			−0.115879
$667$	8.83224e8	−	1.52979e9i	0.115247	−	0.199614i
$668$	5.15702e8	+	8.93223e8i	0.0669394	+	0.115942i
$669$	−1.84465e9	−	3.19503e9i	−0.238190	−	0.412557i
$670$	−6.50888e9	+	1.12737e10i	−0.836074	+	1.44812i
$671$	−7.73178e9			−0.987986
$672$		0			0
$673$	−1.02787e10			−1.29982			−0.649910	−	0.760011i	$-0.725194\pi$
$673$	−1.02787e10			−1.29982			−0.649910	+	0.760011i	$0.725194\pi$
$674$	7.28289e9	−	1.26143e10i	0.916209	−	1.58692i
$675$	−2.86609e7	−	4.96422e7i	−0.00358696	−	0.00621280i
$676$	−1.03872e8	−	1.79911e8i	−0.0129326	−	0.0223999i
$677$	−4.78417e9	+	8.28642e9i	−0.592578	+	1.02638i	0.401305	+	0.915944i	$0.368557\pi$
$677$	−4.78417e9	+	8.28642e9i	−0.592578	+	1.02638i	−0.993884	+	0.110432i	$0.964777\pi$
$678$	−1.28223e9			−0.158001
$679$		0			0
$680$	1.24306e10			1.51604
$681$	−1.09458e9	+	1.89587e9i	−0.132811	+	0.230035i
$682$	7.52459e9	+	1.30330e10i	0.908317	+	1.57325i
$683$	1.77947e9	+	3.08213e9i	0.213706	+	0.370150i	0.952872	−	0.303374i	$-0.0981131\pi$
$683$	1.77947e9	+	3.08213e9i	0.213706	+	0.370150i	−0.739165	+	0.673524i	$0.764780\pi$
$684$	6.85853e7	−	1.18793e8i	0.00819473	−	0.0141937i
$685$	2.18758e8			0.0260044
$686$		0			0
$687$	−4.53570e9			−0.533699
$688$	−2.69666e9	+	4.67075e9i	−0.315694	+	0.546798i
$689$	8.43239e8	+	1.46053e9i	0.0982163	+	0.170116i
$690$	−2.55318e9	−	4.42223e9i	−0.295875	−	0.512471i
$691$	−4.72251e9	+	8.17963e9i	−0.544502	+	0.943106i	0.454136	+	0.890932i	$0.349948\pi$
$691$	−4.72251e9	+	8.17963e9i	−0.544502	+	0.943106i	−0.998638	+	0.0521731i	$0.983385\pi$
$692$	2.17565e9			0.249584
$693$		0			0
$694$	−8.31985e9			−0.944838
$695$	6.91833e9	−	1.19829e10i	0.781726	−	1.35399i
$696$	5.72077e8	+	9.90867e8i	0.0643165	+	0.111399i
$697$	3.93740e9	+	6.81977e9i	0.440448	+	0.762878i
$698$	−8.50927e9	+	1.47385e10i	−0.947106	+	1.64043i
$699$	−7.33848e9			−0.812711
$700$		0			0
$701$	1.11584e9			0.122345			0.0611726	−	0.998127i	$-0.480516\pi$
$701$	1.11584e9			0.122345			0.0611726	+	0.998127i	$0.480516\pi$
$702$	1.02389e9	−	1.77343e9i	0.111705	−	0.193479i
$703$	4.41906e8	+	7.65403e8i	0.0479718	+	0.0830896i
$704$	5.99946e9	+	1.03914e10i	0.648049	+	1.12245i
$705$	−4.64644e9	+	8.04788e9i	−0.499412	+	0.865007i
$706$	−1.39671e10			−1.49379
$707$		0			0
$708$	1.26867e9			0.134349
$709$	−3.57825e9	+	6.19771e9i	−0.377058	+	0.653084i	−0.990633	−	0.136553i	$-0.956398\pi$
$709$	−3.57825e9	+	6.19771e9i	−0.377058	+	0.653084i	0.613574	+	0.789637i	$0.289731\pi$
$710$	5.21395e9	+	9.03083e9i	0.546717	+	0.946942i
$711$	−2.58751e9	−	4.48169e9i	−0.269984	−	0.467626i
$712$	−7.73702e9	+	1.34009e10i	−0.803330	+	1.39141i
$713$	−9.19807e9			−0.950350
$714$		0			0
$715$	1.76775e10			1.80863
$716$	3.52580e8	−	6.10687e8i	0.0358974	−	0.0621761i
$717$	−4.35473e9	−	7.54262e9i	−0.441209	−	0.764197i
$718$	−8.02880e8	−	1.39063e9i	−0.0809497	−	0.140209i
$719$	5.93490e9	−	1.02796e10i	0.595474	−	1.03139i	−0.398006	−	0.917383i	$-0.630298\pi$
$719$	5.93490e9	−	1.02796e10i	0.595474	−	1.03139i	0.993480	−	0.114008i	$-0.0363689\pi$
$720$	3.86865e9			0.386274
$721$		0			0
$722$	9.94705e9			0.983590
$723$	−1.75517e9	+	3.04004e9i	−0.172717	+	0.299155i
$724$	8.50656e8	+	1.47338e9i	0.0833046	+	0.144288i
$725$	4.72795e7	+	8.18905e7i	0.00460776	+	0.00798087i
$726$	5.54611e9	−	9.60614e9i	0.537911	−	0.931689i
$727$	1.03634e10			1.00031			0.500153	−	0.865937i	$-0.333277\pi$
$727$	1.03634e10			1.00031			0.500153	+	0.865937i	$0.333277\pi$
$728$		0			0
$729$	3.87420e8			0.0370370
$730$	−1.14351e10	+	1.98061e10i	−1.08795	+	1.88439i
$731$	−4.83991e9	−	8.38297e9i	−0.458275	−	0.793756i
$732$	−3.02538e8	−	5.24012e8i	−0.0285096	−	0.0493802i
$733$	2.30469e9	−	3.99183e9i	0.216146	−	0.374376i	−0.737480	−	0.675369i	$-0.763985\pi$
$733$	2.30469e9	−	3.99183e9i	0.216146	−	0.374376i	0.953627	+	0.300992i	$0.0973179\pi$
$734$	−8.33771e9			−0.778235
$735$		0			0
$736$	3.29663e9			0.304788
$737$	1.36474e10	−	2.36381e10i	1.25578	−	2.17508i
$738$	1.04764e9	+	1.81457e9i	0.0959435	+	0.166179i
$739$	4.02461e9	+	6.97083e9i	0.366833	+	0.635373i	0.989068	−	0.147457i	$-0.0471088\pi$
$739$	4.02461e9	+	6.97083e9i	0.366833	+	0.635373i	−0.622236	+	0.782830i	$0.713775\pi$
$740$	2.98403e8	−	5.16849e8i	0.0270702	−	0.0468870i
$741$	−2.04870e9			−0.184976
$742$		0			0
$743$	−1.41059e10			−1.26165			−0.630827	−	0.775924i	$-0.717284\pi$
$743$	−1.41059e10			−1.26165			−0.630827	+	0.775924i	$0.717284\pi$
$744$	2.97886e9	−	5.15954e9i	0.265183	−	0.459310i
$745$	−1.94556e9	−	3.36981e9i	−0.172384	−	0.298578i
$746$	9.77255e9	+	1.69265e10i	0.861830	+	1.49273i
$747$	1.60865e8	−	2.78627e8i	0.0141202	−	0.0244569i
$748$	5.15227e9			0.450135
$749$		0			0
$750$	−7.05952e9			−0.611028
$751$	−6.68971e9	+	1.15869e10i	−0.576325	+	0.998225i	0.419571	+	0.907722i	$0.362180\pi$
$751$	−6.68971e9	+	1.15869e10i	−0.576325	+	0.998225i	−0.995896	+	0.0905020i	$0.971153\pi$
$752$	−1.12695e10	−	1.95193e10i	−0.966367	−	1.67380i
$753$	2.14365e9	+	3.71291e9i	0.182967	+	0.316907i
$754$	−1.68902e9	+	2.92547e9i	−0.143495	+	0.248540i
$755$	−4.76677e9			−0.403097
$756$		0			0
$757$	1.36103e10			1.14034			0.570169	−	0.821528i	$-0.306878\pi$
$757$	1.36103e10			1.14034			0.570169	+	0.821528i	$0.306878\pi$
$758$	−3.53885e8	+	6.12947e8i	−0.0295135	+	0.0511188i
$759$	5.35335e9	+	9.27227e9i	0.444405	+	0.769733i
$760$	−1.65448e9	−	2.86564e9i	−0.136714	−	0.236796i
$761$	−5.18088e9	+	8.97356e9i	−0.426145	+	0.738105i	−0.996527	−	0.0832748i	$-0.973462\pi$
$761$	−5.18088e9	+	8.97356e9i	−0.426145	+	0.738105i	0.570381	+	0.821380i	$0.306795\pi$
$762$	−8.72336e9			−0.714236
$763$		0			0
$764$	−7.43106e8			−0.0602871
$765$	−3.47169e9	+	6.01315e9i	−0.280367	+	0.485609i
$766$	−6.27177e9	−	1.08630e10i	−0.504184	−	0.873273i
$767$	−9.47408e9	−	1.64096e10i	−0.758147	−	1.31315i
$768$	−1.74820e9	+	3.02797e9i	−0.139260	+	0.241205i
$769$	−1.58529e8			−0.0125709			−0.00628543	−	0.999980i	$-0.502001\pi$
$769$	−1.58529e8			−0.0125709			−0.00628543	+	0.999980i	$0.502001\pi$
$770$		0			0
$771$	−7.45870e9			−0.586101
$772$	8.83799e8	−	1.53078e9i	0.0691342	−	0.119744i
$773$	−5.35045e9	−	9.26725e9i	−0.416641	−	0.721643i	0.578958	−	0.815357i	$-0.303459\pi$
$773$	−5.35045e9	−	9.26725e9i	−0.416641	−	0.721643i	−0.995599	+	0.0937140i	$0.970126\pi$
$774$	−1.28778e9	−	2.23050e9i	−0.0998270	−	0.172905i
$775$	2.46189e8	−	4.26412e8i	0.0189982	−	0.0329059i
$776$	5.86241e9			0.450360
$777$		0			0
$778$	−1.84247e10			−1.40272
$779$	1.04812e9	−	1.81539e9i	0.0794379	−	0.137591i
$780$	6.91707e8	+	1.19807e9i	0.0521904	+	0.0903965i
$781$	−1.09323e10	−	1.89353e10i	−0.821170	−	1.42231i
$782$	−1.11141e10	+	1.92503e10i	−0.831098	+	1.43950i
$783$	−6.39095e8			−0.0475772
$784$		0			0
$785$	−2.76847e9			−0.204266
$786$	1.04152e9	−	1.80397e9i	0.0765050	−	0.132511i
$787$	5.40652e8	+	9.36436e8i	0.0395372	+	0.0684804i	0.885117	−	0.465369i	$-0.154078\pi$
$787$	5.40652e8	+	9.36436e8i	0.0395372	+	0.0684804i	−0.845580	+	0.533849i	$0.820745\pi$
$788$	1.65910e9	+	2.87364e9i	0.120790	+	0.209214i
$789$	−5.43213e8	+	9.40872e8i	−0.0393732	+	0.0681963i
$790$	2.46777e10			1.78078
$791$		0			0
$792$	−6.93489e9			−0.496022
$793$	−4.51854e9	+	7.82634e9i	−0.321767	+	0.557318i
$794$	2.13202e9	+	3.69277e9i	0.151154	+	0.261807i
$795$	−7.60752e8	−	1.31766e9i	−0.0536980	−	0.0930077i
$796$	−1.72245e9	+	2.98338e9i	−0.121046	+	0.209659i
$797$	1.82163e10			1.27454			0.637272	−	0.770639i	$-0.280063\pi$
$797$	1.82163e10			1.27454			0.637272	+	0.770639i	$0.280063\pi$
$798$		0			0
$799$	4.04526e10			2.80564
$800$	−8.82353e7	+	1.52828e8i	−0.00609295	+	0.0105533i
$801$	−4.32170e9	−	7.48540e9i	−0.297126	−	0.514638i
$802$	−4.83803e9	−	8.37972e9i	−0.331176	−	0.573613i
$803$	2.39764e10	−	4.15283e10i	1.63410	−	2.83035i
$804$	2.13605e9			0.144949
$805$		0			0
$806$	1.75898e10			1.18328
$807$	−5.19374e9	+	8.99582e9i	−0.347875	+	0.602537i
$808$	−6.12359e9	−	1.06064e10i	−0.408382	−	0.707338i
$809$	1.24301e10	+	2.15296e10i	0.825383	+	1.42960i	0.901627	+	0.432515i	$0.142374\pi$
$809$	1.24301e10	+	2.15296e10i	0.825383	+	1.42960i	−0.0762441	+	0.997089i	$0.524293\pi$
$810$	−9.23730e8	+	1.59995e9i	−0.0610728	+	0.105781i
$811$	−2.15538e10			−1.41890			−0.709449	−	0.704757i	$-0.751056\pi$
$811$	−2.15538e10			−1.41890			−0.709449	+	0.704757i	$0.751056\pi$
$812$		0			0
$813$	−5.28629e9			−0.345012
$814$	−4.41642e9	+	7.64947e9i	−0.287002	+	0.497103i
$815$	2.11345e9	+	3.66061e9i	0.136754	+	0.236866i
$816$	−8.42025e9	−	1.45843e10i	−0.542512	−	0.939658i
$817$	−1.28836e9	+	2.23151e9i	−0.0826533	+	0.143160i
$818$	1.79295e10			1.14533
$819$		0			0
$820$	−1.41551e9			−0.0896528
$821$	5.24010e9	−	9.07612e9i	0.330475	−	0.572399i	−0.652130	−	0.758107i	$-0.726124\pi$
$821$	5.24010e9	−	9.07612e9i	0.330475	−	0.572399i	0.982605	+	0.185708i	$0.0594578\pi$
$822$	−1.26687e8	−	2.19429e8i	−0.00795575	−	0.0137798i
$823$	1.89782e9	+	3.28711e9i	0.118674	+	0.205549i	0.919242	−	0.393692i	$-0.128802\pi$
$823$	1.89782e9	+	3.28711e9i	0.118674	+	0.205549i	−0.800569	+	0.599241i	$0.795469\pi$
$824$	4.60872e9	−	7.98253e9i	0.286969	−	0.497045i
$825$	−5.73136e8			−0.0355360
$826$		0			0
$827$	5.11868e9			0.314694			0.157347	−	0.987543i	$-0.449706\pi$
$827$	5.11868e9			0.314694			0.157347	+	0.987543i	$0.449706\pi$
$828$	−4.18945e8	+	7.25633e8i	−0.0256478	+	0.0444233i
$829$	7.69243e9	+	1.33237e10i	0.468946	+	0.812238i	0.999370	−	0.0354942i	$-0.0113005\pi$
$829$	7.69243e9	+	1.33237e10i	0.468946	+	0.812238i	−0.530424	+	0.847733i	$0.677967\pi$
$830$	7.67106e8	+	1.32867e9i	0.0465674	+	0.0806571i
$831$	4.39029e9	−	7.60420e9i	0.265393	−	0.459674i
$832$	1.40246e10			0.844227
$833$		0			0
$834$	−1.60262e10			−0.956642
$835$	−6.94879e9	+	1.20357e10i	−0.413054	+	0.715430i
$836$	−6.85754e8	−	1.18776e9i	−0.0405926	−	0.0703084i
$837$	1.66392e9	+	2.88199e9i	0.0980827	+	0.169884i
$838$	1.07857e10	−	1.86814e10i	0.633132	−	1.09662i
$839$	−1.39438e10			−0.815104			−0.407552	−	0.913182i	$-0.633618\pi$
$839$	−1.39438e10			−0.815104			−0.407552	+	0.913182i	$0.633618\pi$
$840$		0			0
$841$	−1.61956e10			−0.938883
$842$	1.00502e10	−	1.74074e10i	0.580204	−	1.00494i
$843$	−8.66725e9	−	1.50121e10i	−0.498293	−	0.863069i
$844$	2.40048e9	+	4.15775e9i	0.137436	+	0.238046i
$845$	1.39961e9	−	2.42420e9i	0.0798012	−	0.138220i
$846$	1.07634e10			0.611158
$847$		0			0
$848$	3.69026e9			0.207812
$849$	−3.63761e9	+	6.30053e9i	−0.204004	+	0.353346i
$850$	−5.94946e8	−	1.03048e9i	−0.0332286	−	0.0575536i
$851$	−2.69932e9	−	4.67536e9i	−0.150142	−	0.260053i
$852$	8.55545e8	−	1.48185e9i	0.0473919	−	0.0820852i
$853$	−2.36230e9			−0.130321			−0.0651604	−	0.997875i	$-0.520756\pi$
$853$	−2.36230e9			−0.130321			−0.0651604	+	0.997875i	$0.520756\pi$
$854$		0			0
$855$	1.84829e9			0.101132
$856$	1.49542e10	−	2.59013e10i	0.814899	−	1.41145i
$857$	6.43636e9	+	1.11481e10i	0.349307	+	0.605018i	0.986127	−	0.165995i	$-0.0530837\pi$
$857$	6.43636e9	+	1.11481e10i	0.349307	+	0.605018i	−0.636820	+	0.771013i	$0.719750\pi$
$858$	−1.02374e10	−	1.77317e10i	−0.553331	−	0.958397i
$859$	1.02329e10	−	1.77238e10i	0.550835	−	0.954074i	−0.447380	−	0.894344i	$-0.647643\pi$
$859$	1.02329e10	−	1.77238e10i	0.550835	−	0.954074i	0.998215	−	0.0597298i	$-0.0190239\pi$
$860$	1.73997e9			0.0932816
$861$		0			0
$862$	−1.43737e10			−0.764353
$863$	1.64337e10	−	2.84640e10i	0.870357	−	1.50750i	0.00872890	−	0.999962i	$-0.497221\pi$
$863$	1.64337e10	−	2.84640e10i	0.870357	−	1.50750i	0.861628	−	0.507540i	$-0.169445\pi$
$864$	−5.96355e8	−	1.03292e9i	−0.0314562	−	0.0544838i
$865$	1.46578e10	+	2.53881e10i	0.770039	+	1.33375i
$866$	5.69545e9	−	9.86480e9i	0.297999	−	0.516150i
$867$	1.91459e10			0.997719
$868$		0			0
$869$	−5.17427e10			−2.67473
$870$	1.52380e9	−	2.63930e9i	0.0784532	−	0.135885i
$871$	−1.59514e10	−	2.76287e10i	−0.817968	−	1.41676i
$872$	1.01682e10	+	1.76118e10i	0.519320	+	0.899488i
$873$	−1.63729e9	+	2.83588e9i	−0.0832869	+	0.144257i
$874$	5.91706e9			0.299789
$875$		0			0
$876$	3.75271e9			0.188617
$877$	−1.14094e10	+	1.97617e10i	−0.571168	+	0.989293i	0.425278	+	0.905063i	$0.360176\pi$
$877$	−1.14094e10	+	1.97617e10i	−0.571168	+	0.989293i	−0.996446	+	0.0842300i	$0.973157\pi$
$878$	−6.05643e9	−	1.04900e10i	−0.301985	−	0.523054i
$879$	4.05866e8	+	7.02980e8i	0.0201568	+	0.0349126i
$880$	1.93405e10	−	3.34987e10i	0.956704	−	1.65706i
$881$	3.68607e10			1.81613			0.908067	−	0.418826i	$-0.137558\pi$
$881$	3.68607e10			1.81613			0.908067	+	0.418826i	$0.137558\pi$
$882$		0			0
$883$	−5.64136e8			−0.0275754			−0.0137877	−	0.999905i	$-0.504389\pi$
$883$	−5.64136e8			−0.0275754			−0.0137877	+	0.999905i	$0.504389\pi$
$884$	3.01105e9	−	5.21528e9i	0.146600	−	0.253919i
$885$	8.54731e9	+	1.48044e10i	0.414503	+	0.717941i
$886$	1.05597e10	+	1.82900e10i	0.510076	+	0.883478i
$887$	−1.26134e10	+	2.18470e10i	−0.606874	+	1.05114i	0.384879	+	0.922967i	$0.374243\pi$
$887$	−1.26134e10	+	2.18470e10i	−0.606874	+	1.05114i	−0.991752	+	0.128169i	$0.959090\pi$
$888$	3.49678e9			0.167580
$889$		0			0
$890$	4.12171e10			1.95980
$891$	1.93682e9	−	3.35468e9i	0.0917314	−	0.158883i
$892$	−1.44339e9	−	2.50002e9i	−0.0680935	−	0.117941i
$893$	−5.38414e9	−	9.32560e9i	−0.253009	−	0.438224i
$894$	−2.25343e9	+	3.90305e9i	−0.105478	+	0.182694i
$895$	9.50163e9			0.443014
$896$		0			0
$897$	1.25142e10			0.578936
$898$	4.53914e9	−	7.86202e9i	0.209173	−	0.362299i
$899$	−2.74482e9	−	4.75417e9i	−0.125996	−	0.218231i
$900$	−2.24263e7	−	3.88436e7i	−0.00102544	−	0.00177611i
$901$	−3.31161e9	+	5.73587e9i	−0.150835	+	0.261254i
$902$	2.09498e10			0.950512
$903$		0			0
$904$	5.07540e9			0.228497
$905$	−1.14621e10	+	1.98529e10i	−0.514037	+	0.890337i
$906$	2.76054e9	+	4.78139e9i	0.123323	+	0.213602i
$907$	−1.53724e10	−	2.66257e10i	−0.684092	−	1.18488i	−0.973721	−	0.227744i	$-0.926865\pi$
$907$	−1.53724e10	−	2.66257e10i	−0.684092	−	1.18488i	0.289629	−	0.957139i	$-0.406468\pi$
$908$	−8.56480e8	+	1.48347e9i	−0.0379679	+	0.0657624i
$909$	6.84095e9			0.302095
$910$		0			0
$911$	6.02571e9			0.264055			0.132027	−	0.991246i	$-0.457851\pi$
$911$	6.02571e9			0.264055			0.132027	+	0.991246i	$0.457851\pi$
$912$	−2.24143e9	+	3.88227e9i	−0.0978460	+	0.169474i
$913$	−1.60842e9	−	2.78587e9i	−0.0699443	−	0.121147i
$914$	−2.11587e10	−	3.66479e10i	−0.916592	−	1.58758i
$915$	4.07653e9	−	7.06076e9i	0.175921	−	0.304704i
$916$	−3.54906e9			−0.152574
$917$		0			0
$918$	8.04212e9			0.343100
$919$	3.86485e9	−	6.69411e9i	0.164259	−	0.284504i	−0.772133	−	0.635461i	$-0.780810\pi$
$919$	3.86485e9	−	6.69411e9i	0.164259	−	0.284504i	0.936392	+	0.350956i	$0.114143\pi$
$920$	1.01062e10	+	1.75044e10i	0.427887	+	0.741121i
$921$	2.70185e9	+	4.67974e9i	0.113960	+	0.197385i
$922$	−3.04428e9	+	5.27284e9i	−0.127916	+	0.221558i
$923$	−2.55559e10			−1.06976
$924$		0			0
$925$	2.88993e8			0.0120058
$926$	−6.15486e9	+	1.06605e10i	−0.254730	+	0.441205i
$927$	2.57431e9	+	4.45884e9i	0.106141	+	0.183841i
$928$	9.83757e8	+	1.70392e9i	0.0404082	+	0.0699891i
$929$	3.00620e9	−	5.20690e9i	0.123016	−	0.213071i	−0.797939	−	0.602738i	$-0.794077\pi$
$929$	3.00620e9	−	5.20690e9i	0.123016	−	0.213071i	0.920956	+	0.389667i	$0.127410\pi$
$930$	−1.58692e10			−0.646939
$931$		0			0
$932$	−5.74215e9			−0.232337
$933$	−7.18773e9	+	1.24495e10i	−0.289738	+	0.501842i
$934$	2.38744e9	+	4.13516e9i	0.0958778	+	0.166065i
$935$	3.47119e10	+	6.01228e10i	1.38879	+	2.40546i
$936$	−4.05283e9	+	7.01970e9i	−0.161545	+	0.279804i
$937$	2.80399e10			1.11349			0.556746	−	0.830683i	$-0.312050\pi$
$937$	2.80399e10			1.11349			0.556746	+	0.830683i	$0.312050\pi$
$938$		0			0
$939$	1.41560e10			0.557969
$940$	−3.63571e9	+	6.29723e9i	−0.142772	+	0.247288i
$941$	−1.50297e10	−	2.60322e10i	−0.588013	−	1.01847i	−0.994492	−	0.104808i	$-0.966577\pi$
$941$	−1.50297e10	−	2.60322e10i	−0.588013	−	1.01847i	0.406480	−	0.913660i	$-0.366756\pi$
$942$	1.60328e9	+	2.77696e9i	0.0624929	+	0.108241i
$943$	−6.40228e9	+	1.10891e10i	−0.248624	+	0.430630i
$944$	−4.14613e10			−1.60414
$945$		0			0
$946$	−2.57519e10			−0.988985
$947$	5.66131e9	−	9.80568e9i	0.216617	−	0.375191i	−0.737155	−	0.675724i	$-0.763831\pi$
$947$	5.66131e9	−	9.80568e9i	0.216617	−	0.375191i	0.953772	+	0.300533i	$0.0971644\pi$
$948$	−2.02465e9	−	3.50680e9i	−0.0771829	−	0.133685i
$949$	−2.80242e10	−	4.85393e10i	−1.06439	−	1.84358i
$950$	−1.58372e8	+	2.74308e8i	−0.00599301	+	0.0103802i
$951$	−1.33410e10			−0.502986
$952$		0			0
$953$	2.35412e10			0.881057			0.440529	−	0.897739i	$-0.354791\pi$
$953$	2.35412e10			0.881057			0.440529	+	0.897739i	$0.354791\pi$
$954$	−8.81135e8	+	1.52617e9i	−0.0328566	+	0.0569094i
$955$	−5.00646e9	−	8.67145e9i	−0.186003	−	0.322166i
$956$	−3.40745e9	−	5.90188e9i	−0.126133	−	0.218468i
$957$	−3.19501e9	+	5.53393e9i	−0.117837	+	0.204099i
$958$	−3.34598e10			−1.22954
$959$		0			0
$960$	−1.26527e10			−0.461566
$961$	−5.36255e8	+	9.28822e8i	−0.0194913	+	0.0337598i
$962$	5.16202e9	+	8.94088e9i	0.186942	+	0.323793i
$963$	8.35300e9	+	1.44678e10i	0.301405	+	0.522049i
$964$	−1.37337e9	+	2.37875e9i	−0.0493762	+	0.0855221i
$965$	2.38174e10			0.853194
$966$		0			0
$967$	−1.02470e10			−0.364420			−0.182210	−	0.983260i	$-0.558325\pi$
$967$	−1.02470e10			−0.364420			−0.182210	+	0.983260i	$0.558325\pi$
$968$	−2.19530e10	+	3.80237e10i	−0.777911	+	1.34738i
$969$	−4.02287e9	−	6.96782e9i	−0.142038	−	0.246016i
$970$	−7.80763e9	−	1.35232e10i	−0.274674	−	0.475750i
$971$	−1.26563e10	+	2.19214e10i	−0.443651	+	0.768425i	−0.997957	−	0.0638872i	$-0.979650\pi$
$971$	−1.26563e10	+	2.19214e10i	−0.443651	+	0.768425i	0.554307	+	0.832313i	$0.312984\pi$
$972$	3.03145e8			0.0105881
$973$		0			0
$974$	3.15800e10			1.09511
$975$	−3.34947e8	+	5.80145e8i	−0.0115734	+	0.0200457i
$976$	9.88722e9	+	1.71252e10i	0.340408	+	0.589604i
$977$	−1.70251e9	−	2.94883e9i	−0.0584060	−	0.101162i	0.835344	−	0.549728i	$-0.185268\pi$
$977$	−1.70251e9	−	2.94883e9i	−0.0584060	−	0.101162i	−0.893750	+	0.448565i	$0.851935\pi$
$978$	2.44789e9	−	4.23987e9i	0.0836770	−	0.144933i
$979$	−8.64215e10			−2.94363
$980$		0			0
$981$	−1.13593e10			−0.384160
$982$	−1.58768e10	+	2.74994e10i	−0.535023	+	0.926688i
$983$	−8.46380e9	−	1.46597e10i	−0.284203	−	0.492253i	0.688213	−	0.725509i	$-0.258395\pi$
$983$	−8.46380e9	−	1.46597e10i	−0.284203	−	0.492253i	−0.972415	+	0.233256i	$0.925062\pi$
$984$	−4.14685e9	−	7.18255e9i	−0.138751	−	0.240323i
$985$	−2.23554e10	+	3.87207e10i	−0.745342	+	1.29097i
$986$	−1.32664e10			−0.440742
$987$		0			0
$988$	−1.60305e9			−0.0528808
$989$	7.86978e9	−	1.36309e10i	0.258688	−	0.448060i
$990$	9.23597e9	+	1.59972e10i	0.302524	+	0.523986i
$991$	−9.35993e9	−	1.62119e10i	−0.305503	−	0.529146i	0.671871	−	0.740669i	$-0.265491\pi$
$991$	−9.35993e9	−	1.62119e10i	−0.305503	−	0.529146i	−0.977373	+	0.211523i	$0.932158\pi$
$992$	5.12252e9	−	8.87246e9i	0.166607	−	0.288571i
$993$	−6.59365e9			−0.213699
$994$		0			0
$995$	−4.64181e10			−1.49385
$996$	1.25873e8	−	2.18018e8i	0.00403667	−	0.00699172i
$997$	2.71939e10	+	4.71012e10i	0.869037	+	1.50522i	0.862982	+	0.505235i	$0.168594\pi$
$997$	2.71939e10	+	4.71012e10i	0.869037	+	1.50522i	0.00605595	+	0.999982i	$0.498072\pi$
$998$	2.20615e10	+	3.82116e10i	0.702551	+	1.21685i
$999$	−9.76606e8	+	1.69153e9i	−0.0309913	+	0.0536786i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.8.e.l.79.3		8
7.2	even	3		147.8.a.g.1.2	yes	4
7.3	odd	6		147.8.e.m.67.3		8
7.4	even	3	inner	147.8.e.l.67.3		8
7.5	odd	6		147.8.a.f.1.2	✓	4
7.6	odd	2		147.8.e.m.79.3		8
21.2	odd	6		441.8.a.u.1.3		4
21.5	even	6		441.8.a.v.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.8.a.f.1.2	✓	4	7.5	odd	6
147.8.a.g.1.2	yes	4	7.2	even	3
147.8.e.l.67.3		8	7.4	even	3	inner
147.8.e.l.79.3		8	1.1	even	1	trivial
147.8.e.m.67.3		8	7.3	odd	6
147.8.e.m.79.3		8	7.6	odd	2
441.8.a.u.1.3		4	21.2	odd	6
441.8.a.v.1.3		4	21.5	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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(6.10587 - 10.5757i) q^{2} +(-13.5000 - 23.3827i) q^{3} +(-10.5634 - 18.2963i) q^{4} +(142.335 - 246.532i) q^{5} -329.717 q^{6} +1305.11 q^{8} +(-364.500 + 631.333i) q^{9} +O(q^{10})\)	\(q+(6.10587 - 10.5757i) q^{2} +(-13.5000 - 23.3827i) q^{3} +(-10.5634 - 18.2963i) q^{4} +(142.335 - 246.532i) q^{5} -329.717 q^{6} +1305.11 q^{8} +(-364.500 + 631.333i) q^{9} +(-1738.16 - 3010.58i) q^{10} +(3644.47 + 6312.42i) q^{11} +(-285.211 + 494.000i) q^{12} +8519.49 q^{13} -7686.10 q^{15} +(9320.94 - 16144.3i) q^{16} +(16729.1 + 28975.6i) q^{17} +(4451.18 + 7709.67i) q^{18} +(4453.19 - 7713.15i) q^{19} -6014.15 q^{20} +89010.8 q^{22} +(-27201.7 + 47114.8i) q^{23} +(-17619.0 - 30517.0i) q^{24} +(-1456.13 - 2522.08i) q^{25} +(52018.9 - 90099.4i) q^{26} +19683.0 q^{27} -32469.4 q^{29} +(-46930.4 + 81285.8i) q^{30} +(84535.7 + 146420. i) q^{31} +(-30298.0 - 52477.6i) q^{32} +(98400.8 - 170435. i) q^{33} +408582. q^{34} +15401.4 q^{36} +(-49616.7 + 85938.7i) q^{37} +(-54381.2 - 94191.1i) q^{38} +(-115013. - 199209. i) q^{39} +(185763. - 321751. i) q^{40} +235363. q^{41} -289312. q^{43} +(76995.8 - 133361. i) q^{44} +(103762. + 179722. i) q^{45} +(332181. + 575354. i) q^{46} +(604526. - 1.04707e6i) q^{47} -503331. q^{48} -35563.7 q^{50} +(451684. - 782340. i) q^{51} +(-89994.5 - 155875. i) q^{52} +(98977.7 + 171434. i) q^{53} +(120182. - 208161. i) q^{54} +2.07495e6 q^{55} -240472. q^{57} +(-198254. + 343386. i) q^{58} +(-1.11205e6 - 1.92612e6i) q^{59} +(81191.1 + 140627. i) q^{60} +(-530377. + 918640. i) q^{61} +2.06466e6 q^{62} +1.64618e6 q^{64} +(1.21262e6 - 2.10033e6i) q^{65} +(-1.20165e6 - 2.08131e6i) q^{66} +(-1.87235e6 - 3.24300e6i) q^{67} +(353430. - 612159. i) q^{68} +1.46889e6 q^{69} -2.99969e6 q^{71} +(-475712. + 823958. i) q^{72} +(-3.28942e6 - 5.69744e6i) q^{73} +(605907. + 1.04946e6i) q^{74} +(-39315.4 + 68096.2i) q^{75} -188163. q^{76} -2.80902e6 q^{78} +(-3.54939e6 + 6.14773e6i) q^{79} +(-2.65340e6 - 4.59582e6i) q^{80} +(-265720. - 460241. i) q^{81} +(1.43709e6 - 2.48912e6i) q^{82} -441332. q^{83} +9.52453e6 q^{85} +(-1.76650e6 + 3.05967e6i) q^{86} +(438337. + 759222. i) q^{87} +(4.75644e6 + 8.23839e6i) q^{88} +(-5.92826e6 + 1.02680e7i) q^{89} +2.53424e6 q^{90} +1.14937e6 q^{92} +(2.28246e6 - 3.95334e6i) q^{93} +(-7.38231e6 - 1.27865e7i) q^{94} +(-1.26769e6 - 2.19571e6i) q^{95} +(-818045. + 1.41690e6i) q^{96} +4.49189e6 q^{97} -5.31364e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 15 q^{2} - 108 q^{3} - 437 q^{4} - 504 q^{5} - 810 q^{6} - 4290 q^{8} - 2916 q^{9}+O(q^{10}) \) 8 * q + 15 * q^2 - 108 * q^3 - 437 * q^4 - 504 * q^5 - 810 * q^6 - 4290 * q^8 - 2916 * q^9	\( 8 q + 15 q^{2} - 108 q^{3} - 437 q^{4} - 504 q^{5} - 810 q^{6} - 4290 q^{8} - 2916 q^{9} + 5724 q^{10} + 1920 q^{11} - 11799 q^{12} + 36288 q^{13} + 27216 q^{15} - 52529 q^{16} + 19584 q^{17} + 10935 q^{18} - 31320 q^{19} + 339624 q^{20} + 223880 q^{22} - 101160 q^{23} + 57915 q^{24} - 74788 q^{25} + 107820 q^{26} + 157464 q^{27} + 389664 q^{29} + 154548 q^{30} - 78840 q^{31} + 732585 q^{32} + 51840 q^{33} - 155520 q^{34} + 637146 q^{36} - 128640 q^{37} - 716292 q^{38} - 489888 q^{39} + 2649780 q^{40} + 730080 q^{41} + 899040 q^{43} - 113220 q^{44} - 367416 q^{45} - 1033664 q^{46} + 1575792 q^{47} + 2836566 q^{48} - 10783866 q^{50} + 528768 q^{51} - 5747652 q^{52} + 1448160 q^{53} + 295245 q^{54} + 6166800 q^{55} + 1691280 q^{57} + 2570950 q^{58} - 3280320 q^{59} - 4584924 q^{60} - 606960 q^{61} + 24129072 q^{62} + 5218274 q^{64} - 1318464 q^{65} - 3022380 q^{66} - 3492880 q^{67} + 1476432 q^{68} + 5462640 q^{69} + 1968 q^{71} + 1563705 q^{72} - 10981440 q^{73} + 14177022 q^{74} - 2019276 q^{75} + 37928520 q^{76} - 5822280 q^{78} - 4654544 q^{79} - 37026324 q^{80} - 2125764 q^{81} + 10402560 q^{82} + 16252992 q^{83} + 33584112 q^{85} + 6392244 q^{86} - 5260464 q^{87} + 10447140 q^{88} + 11272320 q^{89} - 8345592 q^{90} + 6578880 q^{92} - 2128680 q^{93} - 37697400 q^{94} - 11132208 q^{95} + 19779795 q^{96} + 13144896 q^{97} - 2799360 q^{99}+O(q^{100}) \) 8 * q + 15 * q^2 - 108 * q^3 - 437 * q^4 - 504 * q^5 - 810 * q^6 - 4290 * q^8 - 2916 * q^9 + 5724 * q^10 + 1920 * q^11 - 11799 * q^12 + 36288 * q^13 + 27216 * q^15 - 52529 * q^16 + 19584 * q^17 + 10935 * q^18 - 31320 * q^19 + 339624 * q^20 + 223880 * q^22 - 101160 * q^23 + 57915 * q^24 - 74788 * q^25 + 107820 * q^26 + 157464 * q^27 + 389664 * q^29 + 154548 * q^30 - 78840 * q^31 + 732585 * q^32 + 51840 * q^33 - 155520 * q^34 + 637146 * q^36 - 128640 * q^37 - 716292 * q^38 - 489888 * q^39 + 2649780 * q^40 + 730080 * q^41 + 899040 * q^43 - 113220 * q^44 - 367416 * q^45 - 1033664 * q^46 + 1575792 * q^47 + 2836566 * q^48 - 10783866 * q^50 + 528768 * q^51 - 5747652 * q^52 + 1448160 * q^53 + 295245 * q^54 + 6166800 * q^55 + 1691280 * q^57 + 2570950 * q^58 - 3280320 * q^59 - 4584924 * q^60 - 606960 * q^61 + 24129072 * q^62 + 5218274 * q^64 - 1318464 * q^65 - 3022380 * q^66 - 3492880 * q^67 + 1476432 * q^68 + 5462640 * q^69 + 1968 * q^71 + 1563705 * q^72 - 10981440 * q^73 + 14177022 * q^74 - 2019276 * q^75 + 37928520 * q^76 - 5822280 * q^78 - 4654544 * q^79 - 37026324 * q^80 - 2125764 * q^81 + 10402560 * q^82 + 16252992 * q^83 + 33584112 * q^85 + 6392244 * q^86 - 5260464 * q^87 + 10447140 * q^88 + 11272320 * q^89 - 8345592 * q^90 + 6578880 * q^92 - 2128680 * q^93 - 37697400 * q^94 - 11132208 * q^95 + 19779795 * q^96 + 13144896 * q^97 - 2799360 * q^99

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