LMFDB - Embedded newform 147.8.e.m.67.4

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			67.4
Root			$0.634077 + 10.5628i$ of defining polynomial
Character	$\chi$	$=$	147.67
Dual form			147.8.e.m.79.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(10.8306 + 18.7592i) q^{2} +(13.5000 - 23.3827i) q^{3} +(-170.605 + 295.496i) q^{4} +(258.468 + 447.680i) q^{5} +584.853 q^{6} -4618.37 q^{8} +(-364.500 - 631.333i) q^{9} +O(q^{10})$	\(q+(10.8306 + 18.7592i) q^{2} +(13.5000 - 23.3827i) q^{3} +(-170.605 + 295.496i) q^{4} +(258.468 + 447.680i) q^{5} +584.853 q^{6} -4618.37 q^{8} +(-364.500 - 631.333i) q^{9} +(-5598.75 + 9697.31i) q^{10} +(-331.291 + 573.812i) q^{11} +(4606.32 + 7978.39i) q^{12} -7851.30 q^{13} +13957.3 q^{15} +(-28182.5 - 48813.5i) q^{16} +(5816.29 - 10074.1i) q^{17} +(7895.52 - 13675.4i) q^{18} +(7492.78 + 12977.9i) q^{19} -176384. q^{20} -14352.3 q^{22} +(13092.5 + 22676.9i) q^{23} +(-62348.0 + 107990. i) q^{24} +(-94549.3 + 163764. i) q^{25} +(-85034.5 - 147284. i) q^{26} -19683.0 q^{27} +108612. q^{29} +(151166. + 261827. i) q^{30} +(-97816.2 + 169423. i) q^{31} +(314891. - 545407. i) q^{32} +(8944.85 + 15492.9i) q^{33} +251976. q^{34} +248741. q^{36} +(-163284. - 282817. i) q^{37} +(-162303. + 281117. i) q^{38} +(-105993. + 183585. i) q^{39} +(-1.19370e6 - 2.06756e6i) q^{40} +79193.0 q^{41} +638173. q^{43} +(-113039. - 195790. i) q^{44} +(188423. - 326359. i) q^{45} +(-283600. + 491209. i) q^{46} +(-388420. - 672763. i) q^{47} -1.52185e6 q^{48} -4.09611e6 q^{50} +(-157040. - 272001. i) q^{51} +(1.33947e6 - 2.32003e6i) q^{52} +(464108. - 803859. i) q^{53} +(-213179. - 369237. i) q^{54} -342513. q^{55} +404610. q^{57} +(1.17633e6 + 2.03747e6i) q^{58} +(-1.14747e6 + 1.98747e6i) q^{59} +(-2.38118e6 + 4.12432e6i) q^{60} +(1.21824e6 + 2.11006e6i) q^{61} -4.23764e6 q^{62} +6.42715e6 q^{64} +(-2.02931e6 - 3.51487e6i) q^{65} +(-193756. + 335596. i) q^{66} +(875450. - 1.51632e6i) q^{67} +(1.98457e6 + 3.43738e6i) q^{68} +706995. q^{69} -1.22315e6 q^{71} +(1.68340e6 + 2.91573e6i) q^{72} +(232080. - 401974. i) q^{73} +(3.53694e6 - 6.12616e6i) q^{74} +(2.55283e6 + 4.42164e6i) q^{75} -5.11321e6 q^{76} -4.59186e6 q^{78} +(-866218. - 1.50033e6i) q^{79} +(1.45686e7 - 2.52335e7i) q^{80} +(-265720. + 460241. i) q^{81} +(857709. + 1.48560e6i) q^{82} -3.98160e6 q^{83} +6.01330e6 q^{85} +(6.91181e6 + 1.19716e7i) q^{86} +(1.46626e6 - 2.53964e6i) q^{87} +(1.53002e6 - 2.65008e6i) q^{88} +(-3.91627e6 - 6.78318e6i) q^{89} +8.16297e6 q^{90} -8.93456e6 q^{92} +(2.64104e6 + 4.57441e6i) q^{93} +(8.41366e6 - 1.45729e7i) q^{94} +(-3.87330e6 + 6.70874e6i) q^{95} +(-8.50206e6 - 1.47260e7i) q^{96} +4.49108e6 q^{97} +483022. 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 $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	10.8306	+	18.7592i	0.957300	+	1.65809i	0.729014	+	0.684499i	$0.239979\pi$
$2$	10.8306	+	18.7592i	0.957300	+	1.65809i	0.228287	+	0.973594i	$0.426688\pi$
$3$	13.5000	−	23.3827i	0.288675	−	0.500000i
$3$	13.5000	−	23.3827i	0.288675	−	0.500000i
$4$	−170.605	+	295.496i	−1.33285	+	2.30856i
$5$	258.468	+	447.680i	0.924725	+	1.60167i	0.792003	+	0.610517i	$0.209038\pi$
$5$	258.468	+	447.680i	0.924725	+	1.60167i	0.132721	+	0.991153i	$0.457628\pi$
$6$	584.853			1.10540
$7$		0			0
$7$		0			0
$8$	−4618.37			−3.18914
$9$	−364.500	−	631.333i	−0.166667	−	0.288675i
$10$	−5598.75	+	9697.31i	−1.77048	+	3.06656i
$11$	−331.291	+	573.812i	−0.0750473	+	0.129986i	−0.901107	−	0.433597i	$-0.857244\pi$
$11$	−331.291	+	573.812i	−0.0750473	+	0.129986i	0.826060	+	0.563583i	$0.190577\pi$
$12$	4606.32	+	7978.39i	0.769520	+	1.33285i
$13$	−7851.30			−0.991151			−0.495576	−	0.868565i	$-0.665043\pi$
$13$	−7851.30			−0.991151			−0.495576	+	0.868565i	$0.665043\pi$
$14$		0			0
$15$	13957.3			1.06778
$16$	−28182.5	−	48813.5i	−1.72012	−	2.97934i
$17$	5816.29	−	10074.1i	0.287127	−	0.497319i	−0.685996	−	0.727606i	$-0.740633\pi$
$17$	5816.29	−	10074.1i	0.287127	−	0.497319i	0.973123	+	0.230287i	$0.0739664\pi$
$18$	7895.52	−	13675.4i	0.319100	−	0.552698i
$19$	7492.78	+	12977.9i	0.250614	+	0.434076i	0.963695	−	0.267005i	$-0.0860341\pi$
$19$	7492.78	+	12977.9i	0.250614	+	0.434076i	−0.713081	+	0.701082i	$0.752701\pi$
$20$	−176384.			−4.93007
$21$		0			0
$22$	−14352.3			−0.287371
$23$	13092.5	+	22676.9i	0.224375	+	0.388629i	0.956132	−	0.292937i	$-0.0946325\pi$
$23$	13092.5	+	22676.9i	0.224375	+	0.388629i	−0.731757	+	0.681566i	$0.761299\pi$
$24$	−62348.0	+	107990.i	−0.920627	+	1.59457i
$25$	−94549.3	+	163764.i	−1.21023	+	2.09618i
$26$	−85034.5	−	147284.i	−0.948830	−	1.64342i
$27$	−19683.0			−0.192450
$28$		0			0
$29$	108612.			0.826959			0.413480	−	0.910513i	$-0.364313\pi$
$29$	108612.			0.826959			0.413480	+	0.910513i	$0.364313\pi$
$30$	151166.	+	261827.i	1.02219	+	1.77048i
$31$	−97816.2	+	169423.i	−0.589719	+	1.02142i	0.404550	+	0.914516i	$0.367428\pi$
$31$	−97816.2	+	169423.i	−0.589719	+	1.02142i	−0.994269	+	0.106907i	$0.965905\pi$
$32$	314891.	−	545407.i	1.69877	−	2.94236i
$33$	8944.85	+	15492.9i	0.0433286	+	0.0750473i
$34$	251976.			1.09947
$35$		0			0
$36$	248741.			0.888566
$37$	−163284.	−	282817.i	−0.529955	−	0.917908i	−0.999389	−	0.0349412i	$-0.988876\pi$
$37$	−163284.	−	282817.i	−0.529955	−	0.917908i	0.469435	−	0.882967i	$-0.344458\pi$
$38$	−162303.	+	281117.i	−0.479826	+	0.831083i
$39$	−105993.	+	183585.i	−0.286121	+	0.495576i
$40$	−1.19370e6	−	2.06756e6i	−2.94908	−	5.10796i
$41$	79193.0			0.179450			0.0897249	−	0.995967i	$-0.471401\pi$
$41$	79193.0			0.179450			0.0897249	+	0.995967i	$0.471401\pi$
$42$		0			0
$43$	638173.			1.22405			0.612025	−	0.790838i	$-0.290355\pi$
$43$	638173.			1.22405			0.612025	+	0.790838i	$0.290355\pi$
$44$	−113039.	−	195790.i	−0.200053	−	0.346502i
$45$	188423.	−	326359.i	0.308242	−	0.533890i
$46$	−283600.	+	491209.i	−0.429589	+	0.744070i
$47$	−388420.	−	672763.i	−0.545707	−	0.945191i	−0.998562	−	0.0536075i	$-0.982928\pi$
$47$	−388420.	−	672763.i	−0.545707	−	0.945191i	0.452856	−	0.891584i	$-0.350405\pi$
$48$	−1.52185e6			−1.98622
$49$		0			0
$50$	−4.09611e6			−4.63422
$51$	−157040.	−	272001.i	−0.165773	−	0.287127i
$52$	1.33947e6	−	2.32003e6i	1.32105	−	2.28813i
$53$	464108.	−	803859.i	0.428207	−	0.741676i	−0.568507	−	0.822678i	$-0.692479\pi$
$53$	464108.	−	803859.i	0.428207	−	0.741676i	0.996714	+	0.0810022i	$0.0258121\pi$
$54$	−213179.	−	369237.i	−0.184233	−	0.319100i
$55$	−342513.			−0.277592
$56$		0			0
$57$	404610.			0.289384
$58$	1.17633e6	+	2.03747e6i	0.791648	+	1.37118i
$59$	−1.14747e6	+	1.98747e6i	−0.727374	+	1.25985i	0.230616	+	0.973045i	$0.425926\pi$
$59$	−1.14747e6	+	1.98747e6i	−0.727374	+	1.25985i	−0.957989	+	0.286803i	$0.907407\pi$
$60$	−2.38118e6	+	4.12432e6i	−1.42319	+	2.46504i
$61$	1.21824e6	+	2.11006e6i	0.687194	+	1.19026i	0.972742	+	0.231891i	$0.0744912\pi$
$61$	1.21824e6	+	2.11006e6i	0.687194	+	1.19026i	−0.285548	+	0.958365i	$0.592175\pi$
$62$	−4.23764e6			−2.25815
$63$		0			0
$64$	6.42715e6			3.06470
$65$	−2.02931e6	−	3.51487e6i	−0.916542	−	1.58750i
$66$	−193756.	+	335596.i	−0.0829569	+	0.143686i
$67$	875450.	−	1.51632e6i	0.355606	−	0.615928i	−0.631615	−	0.775282i	$-0.717608\pi$
$67$	875450.	−	1.51632e6i	0.355606	−	0.615928i	0.987222	+	0.159354i	$0.0509410\pi$
$68$	1.98457e6	+	3.43738e6i	0.765394	+	1.32570i
$69$	706995.			0.259086
$70$		0			0
$71$	−1.22315e6			−0.405581			−0.202790	−	0.979222i	$-0.565001\pi$
$71$	−1.22315e6			−0.405581			−0.202790	+	0.979222i	$0.565001\pi$
$72$	1.68340e6	+	2.91573e6i	0.531524	+	0.920627i
$73$	232080.	−	401974.i	0.0698244	−	0.120939i	−0.829000	−	0.559249i	$-0.811089\pi$
$73$	232080.	−	401974.i	0.0698244	−	0.120939i	0.898824	+	0.438310i	$0.144423\pi$
$74$	3.53694e6	−	6.12616e6i	1.01465	−	1.75743i
$75$	2.55283e6	+	4.42164e6i	0.698728	+	1.21023i
$76$	−5.11321e6			−1.33612
$77$		0			0
$78$	−4.59186e6			−1.09561
$79$	−866218.	−	1.50033e6i	−0.197666	−	0.342368i	0.750105	−	0.661319i	$-0.230003\pi$
$79$	−866218.	−	1.50033e6i	−0.197666	−	0.342368i	−0.947771	+	0.318951i	$0.896670\pi$
$80$	1.45686e7	−	2.52335e7i	3.18128	−	5.51013i
$81$	−265720.	+	460241.i	−0.0555556	+	0.0962250i
$82$	857709.	+	1.48560e6i	0.171787	+	0.297545i
$83$	−3.98160e6			−0.764337			−0.382168	−	0.924093i	$-0.624823\pi$
$83$	−3.98160e6			−0.764337			−0.382168	+	0.924093i	$0.624823\pi$
$84$		0			0
$85$	6.01330e6			1.06205
$86$	6.91181e6	+	1.19716e7i	1.17178	+	2.02959i
$87$	1.46626e6	−	2.53964e6i	0.238723	−	0.413480i
$88$	1.53002e6	−	2.65008e6i	0.239337	−	0.414543i
$89$	−3.91627e6	−	6.78318e6i	−0.588854	−	1.01992i	−0.994383	−	0.105842i	$-0.966246\pi$
$89$	−3.91627e6	−	6.78318e6i	−0.588854	−	1.01992i	0.405529	−	0.914082i	$-0.367087\pi$
$90$	8.16297e6			1.18032
$91$		0			0
$92$	−8.93456e6			−1.19623
$93$	2.64104e6	+	4.57441e6i	0.340474	+	0.589719i
$94$	8.41366e6	−	1.45729e7i	1.04481	−	1.80966i
$95$	−3.87330e6	+	6.70874e6i	−0.463498	+	0.802802i
$96$	−8.50206e6	−	1.47260e7i	−0.980787	−	1.69877i
$97$	4.49108e6			0.499632			0.249816	−	0.968293i	$-0.419630\pi$
$97$	4.49108e6			0.499632			0.249816	+	0.968293i	$0.419630\pi$
$98$		0			0
$99$	483022.			0.0500315
$100$	−3.22611e7	−	5.58779e7i	−3.22611	−	5.58779i
$101$	−6.21226e6	+	1.07600e7i	−0.599964	+	1.03917i	0.392862	+	0.919597i	$0.371485\pi$
$101$	−6.21226e6	+	1.07600e7i	−0.599964	+	1.03917i	−0.992826	+	0.119570i	$0.961848\pi$
$102$	3.40167e6	−	5.89187e6i	0.317389	−	0.549734i
$103$	1.07147e7	+	1.85583e7i	0.966157	+	1.67343i	0.706474	+	0.707739i	$0.250285\pi$
$103$	1.07147e7	+	1.85583e7i	0.966157	+	1.67343i	0.259683	+	0.965694i	$0.416382\pi$
$104$	3.62603e7			3.16092
$105$		0			0
$106$	2.01063e7			1.63969
$107$	1.11223e7	+	1.92644e7i	0.877710	+	1.52024i	0.853848	+	0.520523i	$0.174263\pi$
$107$	1.11223e7	+	1.92644e7i	0.877710	+	1.52024i	0.0238619	+	0.999715i	$0.492404\pi$
$108$	3.35801e6	−	5.81624e6i	0.256507	−	0.444283i
$109$	−4.95065e6	+	8.57478e6i	−0.366159	+	0.634206i	−0.988961	−	0.148173i	$-0.952661\pi$
$109$	−4.95065e6	+	8.57478e6i	−0.366159	+	0.634206i	0.622803	+	0.782379i	$0.285994\pi$
$110$	−3.70962e6	−	6.42526e6i	−0.265739	−	0.460274i
$111$	−8.81736e6			−0.611939
$112$		0			0
$113$	1.91928e7			1.25130			0.625652	−	0.780102i	$-0.284833\pi$
$113$	1.91928e7			1.25130			0.625652	+	0.780102i	$0.284833\pi$
$114$	4.38218e6	+	7.59016e6i	0.277028	+	0.479826i
$115$	−6.76799e6	+	1.17225e7i	−0.414971	+	0.718750i
$116$	−1.85297e7	+	3.20943e7i	−1.10221	+	1.90909i
$117$	2.86180e6	+	4.95678e6i	0.165192	+	0.286121i
$118$	−4.97110e7			−2.78526
$119$		0			0
$120$	−6.44600e7			−3.40530
$121$	9.52408e6	+	1.64962e7i	0.488736	+	0.846515i
$122$	−2.63887e7	+	4.57065e7i	−1.31570	+	2.27886i
$123$	1.06911e6	−	1.85174e6i	0.0518027	−	0.0897249i
$124$	−3.33758e7	−	5.78086e7i	−1.57201	−	2.72280i
$125$	−5.73664e7			−2.62707
$126$		0			0
$127$	−1.43563e7			−0.621912			−0.310956	−	0.950424i	$-0.600649\pi$
$127$	−1.43563e7			−0.621912			−0.310956	+	0.950424i	$0.600649\pi$
$128$	2.93039e7	+	5.07559e7i	1.23507	+	2.13920i
$129$	8.61534e6	−	1.49222e7i	0.353353	−	0.612025i
$130$	4.39574e7	−	7.61365e7i	1.75481	−	3.03942i
$131$	9.10472e6	+	1.57698e7i	0.353848	+	0.612883i	0.986920	−	0.161210i	$-0.0515396\pi$
$131$	9.10472e6	+	1.57698e7i	0.353848	+	0.612883i	−0.633072	+	0.774093i	$0.718206\pi$
$132$	−6.10413e6			−0.231002
$133$		0			0
$134$	3.79267e7			1.36169
$135$	−5.08743e6	−	8.81169e6i	−0.177963	−	0.308242i
$136$	−2.68618e7	+	4.65260e7i	−0.915690	+	1.58602i
$137$	−1.22635e7	+	2.12409e7i	−0.407466	+	0.705752i	−0.994605	−	0.103734i	$-0.966921\pi$
$137$	−1.22635e7	+	2.12409e7i	−0.407466	+	0.705752i	0.587139	+	0.809486i	$0.300254\pi$
$138$	7.65719e6	+	1.32626e7i	0.248023	+	0.429589i
$139$	−1.18402e7			−0.373946			−0.186973	−	0.982365i	$-0.559868\pi$
$139$	−1.18402e7			−0.373946			−0.186973	+	0.982365i	$0.559868\pi$
$140$		0			0
$141$	−2.09747e7			−0.630128
$142$	−1.32475e7	−	2.29454e7i	−0.388263	−	0.672490i
$143$	2.60106e6	−	4.50517e6i	0.0743832	−	0.128835i
$144$	−2.05450e7	+	3.55850e7i	−0.573374	+	0.993112i
$145$	2.80727e7	+	4.86234e7i	0.764709	+	1.32452i
$146$	1.00543e7			0.267372
$147$		0			0
$148$	1.11428e8			2.82540
$149$	−2.81606e6	−	4.87755e6i	−0.0697412	−	0.120795i	0.829046	−	0.559180i	$-0.188884\pi$
$149$	−2.81606e6	−	4.87755e6i	−0.0697412	−	0.120795i	−0.898787	+	0.438385i	$0.855551\pi$
$150$	−5.52975e7	+	9.57781e7i	−1.33778	+	2.31711i
$151$	3.03979e7	−	5.26507e7i	0.718495	−	1.24447i	−0.243101	−	0.970001i	$-0.578165\pi$
$151$	3.03979e7	−	5.26507e7i	0.718495	−	1.24447i	0.961596	−	0.274469i	$-0.0885022\pi$
$152$	−3.46045e7	−	5.99367e7i	−0.799245	−	1.38433i
$153$	−8.48014e6			−0.191418
$154$		0			0
$155$	−1.01130e8			−2.18131
$156$	−3.61656e7	−	6.26407e7i	−0.762711	−	1.32105i
$157$	−2.81674e7	+	4.87873e7i	−0.580895	+	1.00614i	0.414479	+	0.910059i	$0.363964\pi$
$157$	−2.81674e7	+	4.87873e7i	−0.580895	+	1.00614i	−0.995374	+	0.0960800i	$0.969370\pi$
$158$	1.87634e7	−	3.24991e7i	0.378452	−	0.655498i
$159$	−1.25309e7	−	2.17042e7i	−0.247225	−	0.428207i
$160$	3.25557e8			6.28359
$161$		0			0
$162$	−1.15117e7			−0.212733
$163$	−2.63360e7	−	4.56152e7i	−0.476313	−	0.824999i	0.523318	−	0.852137i	$-0.324694\pi$
$163$	−2.63360e7	−	4.56152e7i	−0.476313	−	0.824999i	−0.999632	+	0.0271383i	$0.991361\pi$
$164$	−1.35107e7	+	2.34012e7i	−0.239179	+	0.414271i
$165$	−4.62392e6	+	8.00887e6i	−0.0801340	+	0.138796i
$166$	−4.31232e7	−	7.46916e7i	−0.731700	−	1.26734i
$167$	−2.07427e7			−0.344634			−0.172317	−	0.985042i	$-0.555125\pi$
$167$	−2.07427e7			−0.344634			−0.172317	+	0.985042i	$0.555125\pi$
$168$		0			0
$169$	−1.10556e6			−0.0176189
$170$	6.51278e7	+	1.12805e8i	1.01671	+	1.76099i
$171$	5.46224e6	−	9.46088e6i	0.0835380	−	0.144692i
$172$	−1.08875e8	+	1.88578e8i	−1.63147	+	2.82579i
$173$	6.50263e7	+	1.12629e8i	0.954834	+	1.65382i	0.734747	+	0.678341i	$0.237301\pi$
$173$	6.50263e7	+	1.12629e8i	0.954834	+	1.65382i	0.220087	+	0.975480i	$0.429366\pi$
$174$	6.35220e7			0.914117
$175$		0			0
$176$	3.73463e7			0.516361
$177$	3.09816e7	+	5.36616e7i	0.419949	+	0.727374i
$178$	8.48312e7	−	1.46932e8i	1.12742	−	1.95275i
$179$	7.67270e6	−	1.32895e7i	0.0999914	−	0.173190i	−0.811689	−	0.584089i	$-0.801452\pi$
$179$	7.67270e6	−	1.32895e7i	0.0999914	−	0.173190i	0.911681	+	0.410899i	$0.134785\pi$
$180$	6.42918e7	+	1.11357e8i	0.821679	+	1.42319i
$181$	−7.02000e7			−0.879959			−0.439979	−	0.898008i	$-0.645014\pi$
$181$	−7.02000e7			−0.879959			−0.439979	+	0.898008i	$0.645014\pi$
$182$		0			0
$183$	6.57851e7			0.793504
$184$	−6.04660e7	−	1.04730e8i	−0.715565	−	1.23939i
$185$	8.44077e7	−	1.46198e8i	0.980124	−	1.69763i
$186$	−5.72082e7	+	9.90874e7i	−0.651873	+	1.12908i
$187$	3.85376e6	+	6.67491e6i	0.0430962	+	0.0746449i
$188$	2.65065e8			2.90938
$189$		0			0
$190$	−1.67801e8			−1.77483
$191$	−8.45556e7	−	1.46455e8i	−0.878063	−	1.52085i	−0.853464	−	0.521153i	$-0.825502\pi$
$191$	−8.45556e7	−	1.46455e8i	−0.878063	−	1.52085i	−0.0245996	−	0.999697i	$-0.507831\pi$
$192$	8.67665e7	−	1.50284e8i	0.884703	−	1.53235i
$193$	−4.98200e7	+	8.62907e7i	−0.498830	+	0.863999i	−0.999999	−	0.00135028i	$-0.999570\pi$
$193$	−4.98200e7	+	8.62907e7i	−0.498830	+	0.863999i	0.501169	+	0.865349i	$0.332904\pi$
$194$	4.86412e7	+	8.42490e7i	0.478298	+	0.828436i
$195$	−1.09583e8			−1.05833
$196$		0			0
$197$	1.73109e8			1.61319			0.806597	−	0.591101i	$-0.201307\pi$
$197$	1.73109e8			1.61319			0.806597	+	0.591101i	$0.201307\pi$
$198$	5.23143e6	+	9.06109e6i	0.0478952	+	0.0829569i
$199$	−4.71759e7	+	8.17111e7i	−0.424360	+	0.735013i	−0.996360	−	0.0852402i	$-0.972834\pi$
$199$	−4.71759e7	+	8.17111e7i	−0.424360	+	0.735013i	0.572000	+	0.820253i	$0.306168\pi$
$200$	4.36664e8	−	7.56325e8i	3.85960	−	6.68503i
$201$	−2.36371e7	−	4.09407e7i	−0.205309	−	0.355606i
$202$	−2.69131e8			−2.29738
$203$		0			0
$204$	1.07167e8			0.883801
$205$	2.04689e7	+	3.54531e7i	0.165942	+	0.287420i
$206$	−2.32093e8	+	4.01996e8i	−1.84981	+	3.20396i
$207$	9.54443e6	−	1.65314e7i	0.0747917	−	0.129543i
$208$	2.21269e8	+	3.83249e8i	1.70490	+	2.95297i
$209$	−9.92916e6			−0.0752316
$210$		0			0
$211$	−5.13471e6			−0.0376294			−0.0188147	−	0.999823i	$-0.505989\pi$
$211$	−5.13471e6			−0.0376294			−0.0188147	+	0.999823i	$0.505989\pi$
$212$	1.58358e8	+	2.74284e8i	1.14147	+	1.97708i
$213$	−1.65126e7	+	2.86006e7i	−0.117081	+	0.202790i
$214$	−2.40923e8	+	4.17290e8i	−1.68046	+	2.91065i
$215$	1.64948e8	+	2.85698e8i	1.13191	+	1.96052i
$216$	9.09035e7			0.613751
$217$		0			0
$218$	−2.14474e8			−1.40210
$219$	−6.26615e6	−	1.08533e7i	−0.0403131	−	0.0698244i
$220$	5.84342e7	−	1.01211e8i	0.369988	−	0.640839i
$221$	−4.56654e7	+	7.90948e7i	−0.284587	+	0.492919i
$222$	−9.54975e7	−	1.65406e8i	−0.585809	−	1.01465i
$223$	1.73853e8			1.04982			0.524909	−	0.851158i	$-0.324099\pi$
$223$	1.73853e8			1.04982			0.524909	+	0.851158i	$0.324099\pi$
$224$		0			0
$225$	1.37853e8			0.806821
$226$	2.07870e8	+	3.60041e8i	1.19787	+	2.07478i
$227$	8.51267e7	−	1.47444e8i	0.483032	−	0.836635i	−0.516779	−	0.856119i	$-0.672869\pi$
$227$	8.51267e7	−	1.47444e8i	0.483032	−	0.836635i	0.999810	+	0.0194839i	$0.00620231\pi$
$228$	−6.90284e7	+	1.19561e8i	−0.385705	+	0.668061i
$229$	1.23849e8	+	2.14513e8i	0.681504	+	1.18040i	0.974522	+	0.224293i	$0.0720072\pi$
$229$	1.23849e8	+	2.14513e8i	0.681504	+	1.18040i	−0.293018	+	0.956107i	$0.594659\pi$
$230$	−2.93206e8			−1.58901
$231$		0			0
$232$	−5.01610e8			−2.63729
$233$	5.72057e7	+	9.90832e7i	0.296274	+	0.513162i	0.975280	−	0.220971i	$-0.0709225\pi$
$233$	5.72057e7	+	9.90832e7i	0.296274	+	0.513162i	−0.679006	+	0.734132i	$0.737589\pi$
$234$	−6.19901e7	+	1.07370e8i	−0.316277	+	0.547807i
$235$	2.00789e8	−	3.47776e8i	1.00926	−	1.74808i
$236$	−3.91526e8	−	6.78142e8i	−1.93896	−	3.35837i
$237$	−4.67758e7			−0.228245
$238$		0			0
$239$	−8.83010e7			−0.418382			−0.209191	−	0.977875i	$-0.567083\pi$
$239$	−8.83010e7			−0.418382			−0.209191	+	0.977875i	$0.567083\pi$
$240$	−3.93351e8	−	6.81304e8i	−1.83671	−	3.18128i
$241$	−7.78228e7	+	1.34793e8i	−0.358135	+	0.620308i	−0.987649	−	0.156681i	$-0.949921\pi$
$241$	−7.78228e7	+	1.34793e8i	−0.358135	+	0.620308i	0.629514	+	0.776989i	$0.283254\pi$
$242$	−2.06303e8	+	3.57328e8i	−0.935734	+	1.62074i
$243$	7.17445e6	+	1.24265e7i	0.0320750	+	0.0555556i
$244$	−8.31351e8			−3.66370
$245$		0			0
$246$	4.63163e7			0.198363
$247$	−5.88281e7	−	1.01893e8i	−0.248397	−	0.430235i
$248$	4.51752e8	−	7.82457e8i	1.88070	−	3.25747i
$249$	−5.37516e7	+	9.31006e7i	−0.220645	+	0.382168i
$250$	−6.21313e8	−	1.07615e9i	−2.51490	−	4.35593i
$251$	1.07520e8			0.429171			0.214585	−	0.976705i	$-0.431160\pi$
$251$	1.07520e8			0.429171			0.214585	+	0.976705i	$0.431160\pi$
$252$		0			0
$253$	−1.73497e7			−0.0673550
$254$	−1.55487e8	−	2.69312e8i	−0.595356	−	1.03119i
$255$	8.11796e7	−	1.40607e8i	0.306589	−	0.531027i
$256$	−2.23422e8	+	3.86978e8i	−0.832311	+	1.44160i
$257$	−2.01589e8	−	3.49162e8i	−0.740800	−	1.28310i	−0.952132	−	0.305689i	$-0.901113\pi$
$257$	−2.01589e8	−	3.49162e8i	−0.740800	−	1.28310i	0.211332	−	0.977414i	$-0.432220\pi$
$258$	3.73238e8			1.35306
$259$		0			0
$260$	1.38484e9			4.88645
$261$	−3.95890e7	−	6.85702e7i	−0.137827	−	0.238723i
$262$	−1.97219e8	+	3.41594e8i	−0.677478	+	1.17343i
$263$	1.36669e8	−	2.36718e8i	0.463260	−	0.802390i	−0.535861	−	0.844306i	$-0.680013\pi$
$263$	1.36669e8	−	2.36718e8i	0.463260	−	0.802390i	0.999121	+	0.0419165i	$0.0133463\pi$
$264$	−4.13107e7	−	7.15522e7i	−0.138181	−	0.239337i
$265$	4.79829e8			1.58389
$266$		0			0
$267$	−2.11478e8			−0.679950
$268$	2.98712e8	+	5.17384e8i	0.947939	+	1.64188i
$269$	5.18206e7	−	8.97559e7i	0.162319	−	0.281145i	−0.773381	−	0.633942i	$-0.781436\pi$
$269$	5.18206e7	−	8.97559e7i	0.162319	−	0.281145i	0.935700	+	0.352797i	$0.114769\pi$
$270$	1.10200e8	−	1.90872e8i	0.340729	−	0.590160i
$271$	−9.90620e6	−	1.71580e7i	−0.0302353	−	0.0523691i	0.850512	−	0.525956i	$-0.176292\pi$
$271$	−9.90620e6	−	1.71580e7i	−0.0302353	−	0.0523691i	−0.880747	+	0.473587i	$0.842959\pi$
$272$	−6.55669e8			−1.97557
$273$		0			0
$274$	−5.31284e8			−1.56027
$275$	−6.26466e7	−	1.08507e8i	−0.181649	−	0.314626i
$276$	−1.20617e8	+	2.08914e8i	−0.345323	+	0.598116i
$277$	1.78152e8	−	3.08569e8i	0.503630	−	0.872314i	−0.496361	−	0.868116i	$-0.665331\pi$
$277$	1.78152e8	−	3.08569e8i	0.503630	−	0.872314i	0.999991	−	0.00419715i	$-0.00133600\pi$
$278$	−1.28237e8	−	2.22113e8i	−0.357979	−	0.620037i
$279$	1.42616e8			0.393146
$280$		0			0
$281$	−1.59268e7			−0.0428210			−0.0214105	−	0.999771i	$-0.506816\pi$
$281$	−1.59268e7			−0.0428210			−0.0214105	+	0.999771i	$0.506816\pi$
$282$	−2.27169e8	−	3.93468e8i	−0.603221	−	1.04481i
$283$	2.41180e8	−	4.17737e8i	0.632542	−	1.09560i	−0.354488	−	0.935061i	$-0.615345\pi$
$283$	2.41180e8	−	4.17737e8i	0.632542	−	1.09560i	0.987030	−	0.160535i	$-0.0513218\pi$
$284$	2.08676e8	−	3.61437e8i	0.540577	−	0.936308i
$285$	1.04579e8	+	1.81136e8i	0.267601	+	0.463498i
$286$	1.12685e8			0.284828
$287$		0			0
$288$	−4.59111e8			−1.13252
$289$	1.37511e8	+	2.38176e8i	0.335116	+	0.580438i
$290$	−6.08090e8	+	1.05324e9i	−1.46411	+	2.53592i
$291$	6.06296e7	−	1.05014e8i	0.144231	−	0.249816i
$292$	7.91877e7	+	1.37157e8i	0.186131	+	0.322388i
$293$	4.43360e8			1.02972			0.514860	−	0.857274i	$-0.327844\pi$
$293$	4.43360e8			1.02972			0.514860	+	0.857274i	$0.327844\pi$
$294$		0			0
$295$	−1.18633e9			−2.69048
$296$	7.54109e8	+	1.30615e9i	1.69010	+	2.92734i
$297$	6.52079e6	−	1.12943e7i	0.0144429	−	0.0250158i
$298$	6.09993e7	−	1.05654e8i	0.133527	−	0.231275i
$299$	−1.02793e8	−	1.78043e8i	−0.222390	−	0.385190i
$300$	−1.74210e9			−3.72519
$301$		0			0
$302$	1.31691e9			2.75126
$303$	1.67731e8	+	2.90519e8i	0.346389	+	0.599964i
$304$	4.22330e8	−	7.31497e8i	0.862173	−	1.49333i
$305$	−6.29755e8	+	1.09077e9i	−1.27093	+	2.20132i
$306$	−9.18452e7	−	1.59081e8i	−0.183245	−	0.317389i
$307$	−7.75755e7			−0.153017			−0.0765086	−	0.997069i	$-0.524377\pi$
$307$	−7.75755e7			−0.153017			−0.0765086	+	0.997069i	$0.524377\pi$
$308$		0			0
$309$	5.78591e8			1.11562
$310$	−1.09530e9	−	1.89711e9i	−2.08817	−	3.61682i
$311$	−2.21318e8	+	3.83334e8i	−0.417211	+	0.722630i	−0.995658	−	0.0930898i	$-0.970326\pi$
$311$	−2.21318e8	+	3.83334e8i	−0.417211	+	0.722630i	0.578447	+	0.815720i	$0.303659\pi$
$312$	4.89513e8	−	8.47862e8i	0.912480	−	1.58046i
$313$	2.81513e8	+	4.87595e8i	0.518912	+	0.898782i	0.999758	+	0.0219770i	$0.00699605\pi$
$313$	2.81513e8	+	4.87595e8i	0.518912	+	0.898782i	−0.480847	+	0.876805i	$0.659671\pi$
$314$	−1.22028e9			−2.22436
$315$		0			0
$316$	5.91123e8			1.05384
$317$	3.81774e8	+	6.61252e8i	0.673130	+	1.16590i	0.977012	+	0.213186i	$0.0683841\pi$
$317$	3.81774e8	+	6.61252e8i	0.673130	+	1.16590i	−0.303881	+	0.952710i	$0.598283\pi$
$318$	2.71435e8	−	4.70140e8i	0.473338	−	0.819845i
$319$	−3.59821e7	+	6.23228e7i	−0.0620610	+	0.107493i
$320$	1.66121e9	+	2.87731e9i	2.83401	+	4.90864i
$321$	6.00604e8			1.01349
$322$		0			0
$323$	1.74321e8			0.287833
$324$	−9.06663e7	−	1.57039e8i	−0.148094	−	0.256507i
$325$	7.42336e8	−	1.28576e9i	1.19952	−	2.07763i
$326$	5.70470e8	−	9.88083e8i	0.911950	−	1.57954i
$327$	1.33668e8	+	2.31519e8i	0.211402	+	0.366159i
$328$	−3.65743e8			−0.572292
$329$		0			0
$330$	−2.00320e8			−0.306849
$331$	−2.14344e8	−	3.71254e8i	−0.324872	−	0.562696i	0.656614	−	0.754227i	$-0.271988\pi$
$331$	−2.14344e8	−	3.71254e8i	−0.324872	−	0.562696i	−0.981487	+	0.191531i	$0.938655\pi$
$332$	6.79280e8	−	1.17655e9i	1.01874	−	1.76452i
$333$	−1.19034e8	+	2.06174e8i	−0.176652	+	0.305969i
$334$	−2.24656e8	−	3.89116e8i	−0.329918	−	0.571435i
$335$	9.05105e8			1.31535
$336$		0			0
$337$	7.56118e8			1.07618			0.538090	−	0.842887i	$-0.319146\pi$
$337$	7.56118e8			1.07618			0.538090	+	0.842887i	$0.319146\pi$
$338$	−1.19739e7	−	2.07394e7i	−0.0168665	−	0.0292137i
$339$	2.59102e8	−	4.48779e8i	0.361221	−	0.625652i
$340$	−1.02590e9	+	1.77691e9i	−1.41556	+	2.45182i
$341$	−6.48112e7	−	1.12256e8i	−0.0885136	−	0.153310i
$342$	2.36638e8			0.319884
$343$		0			0
$344$	−2.94732e9			−3.90367
$345$	1.82736e8	+	3.16508e8i	0.239583	+	0.414971i
$346$	−1.40855e9	+	2.43968e9i	−1.82813	+	3.16641i
$347$	−5.36282e8	+	9.28868e8i	−0.689033	+	1.19344i	0.283118	+	0.959085i	$0.408631\pi$
$347$	−5.36282e8	+	9.28868e8i	−0.689033	+	1.19344i	−0.972151	+	0.234355i	$0.924702\pi$
$348$	5.00301e8	+	8.66547e8i	0.636362	+	1.10221i
$349$	8.07851e8			1.01728			0.508642	−	0.860978i	$-0.330148\pi$
$349$	8.07851e8			1.01728			0.508642	+	0.860978i	$0.330148\pi$
$350$		0			0
$351$	1.54537e8			0.190747
$352$	2.08641e8	+	3.61377e8i	0.254976	+	0.441632i
$353$	1.76320e8	−	3.05395e8i	0.213349	−	0.369531i	−0.739412	−	0.673253i	$-0.764896\pi$
$353$	1.76320e8	−	3.05395e8i	0.213349	−	0.369531i	0.952760	+	0.303723i	$0.0982296\pi$
$354$	−6.71099e8	+	1.16238e9i	−0.804035	+	1.39263i
$355$	−3.16147e8	−	5.47583e8i	−0.375050	−	0.649606i
$356$	2.67253e9			3.13941
$357$		0			0
$358$	3.32400e8			0.382887
$359$	−2.36734e8	−	4.10035e8i	−0.270041	−	0.467724i	0.698831	−	0.715287i	$-0.253704\pi$
$359$	−2.36734e8	−	4.10035e8i	−0.270041	−	0.467724i	−0.968872	+	0.247562i	$0.920371\pi$
$360$	−8.70210e8	+	1.50725e9i	−0.983027	+	1.70265i
$361$	3.34652e8	−	5.79635e8i	0.374385	−	0.648454i
$362$	−7.60310e8	−	1.31689e9i	−0.842385	−	1.45905i
$363$	5.14300e8			0.564344
$364$		0			0
$365$	2.39941e8			0.258273
$366$	7.12494e8	+	1.23408e9i	0.759621	+	1.31570i
$367$	4.87256e8	−	8.43952e8i	0.514548	−	0.891223i	−0.485310	−	0.874342i	$-0.661293\pi$
$367$	4.87256e8	−	8.43952e8i	0.514548	−	0.891223i	0.999858	−	0.0168807i	$-0.00537355\pi$
$368$	7.37957e8	−	1.27818e9i	0.771905	−	1.33698i
$369$	−2.88658e7	−	4.99971e7i	−0.0299083	−	0.0518027i
$370$	3.65675e9			3.75309
$371$		0			0
$372$	−1.80229e9			−1.81520
$373$	−2.90067e8	−	5.02410e8i	−0.289412	−	0.501276i	0.684257	−	0.729241i	$-0.260126\pi$
$373$	−2.90067e8	−	5.02410e8i	−0.289412	−	0.501276i	−0.973670	+	0.227964i	$0.926793\pi$
$374$	−8.34773e7	+	1.44587e8i	−0.0825121	+	0.142915i
$375$	−7.74446e8	+	1.34138e9i	−0.758371	+	1.31354i
$376$	1.79387e9	+	3.10707e9i	1.74034	+	3.01435i
$377$	−8.52744e8			−0.819642
$378$		0			0
$379$	−5.10991e8			−0.482143			−0.241072	−	0.970507i	$-0.577499\pi$
$379$	−5.10991e8			−0.482143			−0.241072	+	0.970507i	$0.577499\pi$
$380$	−1.32160e9	−	2.28909e9i	−1.23555	−	2.14003i
$381$	−1.93810e8	+	3.35688e8i	−0.179530	+	0.310956i
$382$	1.83158e9	−	3.17239e9i	1.68114	−	2.91182i
$383$	−1.18441e6	−	2.05145e6i	−0.00107722	−	0.00186580i	0.865486	−	0.500933i	$-0.167010\pi$
$383$	−1.18441e6	−	2.05145e6i	−0.00107722	−	0.00186580i	−0.866564	+	0.499067i	$0.833676\pi$
$384$	1.58241e9			1.42613
$385$		0			0
$386$	−2.15832e9			−1.91012
$387$	−2.32614e8	−	4.02900e8i	−0.204008	−	0.353353i
$388$	−7.66199e8	+	1.32710e9i	−0.665933	+	1.15343i
$389$	6.71810e8	−	1.16361e9i	0.578660	−	1.00227i	−0.416974	−	0.908919i	$-0.636909\pi$
$389$	6.71810e8	−	1.16361e9i	0.578660	−	1.00227i	0.995633	−	0.0933494i	$-0.0297573\pi$
$390$	−1.18685e9	−	2.05569e9i	−1.01314	−	1.75481i
$391$	3.04599e8			0.257697
$392$		0			0
$393$	4.91655e8			0.408589
$394$	1.87487e9	+	3.24738e9i	1.54431	+	2.67483i
$395$	4.47780e8	−	7.75578e8i	0.365574	−	0.633192i
$396$	−8.24057e7	+	1.42731e8i	−0.0666844	+	0.115501i
$397$	−4.18044e8	−	7.24073e8i	−0.335317	−	0.580785i	0.648229	−	0.761445i	$-0.275510\pi$
$397$	−4.18044e8	−	7.24073e8i	−0.335317	−	0.580785i	−0.983546	+	0.180660i	$0.942177\pi$
$398$	−2.04378e9			−1.62496
$399$		0			0
$400$	1.06585e10			8.32698
$401$	1.20855e8	+	2.09327e8i	0.0935962	+	0.162113i	0.909022	−	0.416748i	$-0.136830\pi$
$401$	1.20855e8	+	2.09327e8i	0.0935962	+	0.162113i	−0.815426	+	0.578862i	$0.803497\pi$
$402$	5.12010e8	−	8.86827e8i	0.393086	−	0.680844i
$403$	7.67985e8	−	1.33019e9i	0.584501	−	1.01238i
$404$	−2.11968e9	−	3.67140e9i	−1.59932	−	2.77011i
$405$	−2.74721e8			−0.205494
$406$		0			0
$407$	2.16378e8			0.159087
$408$	7.25268e8	+	1.25620e9i	0.528674	+	0.915690i
$409$	1.33700e8	−	2.31575e8i	0.0966273	−	0.167363i	−0.813659	−	0.581342i	$-0.802528\pi$
$409$	1.33700e8	−	2.31575e8i	0.0966273	−	0.167363i	0.910287	+	0.413979i	$0.135861\pi$
$410$	−4.43381e8	+	7.67959e8i	−0.317712	+	0.550294i
$411$	3.31114e8	+	5.73505e8i	0.235251	+	0.407466i
$412$	−7.31187e9			−5.15096
$413$		0			0
$414$	4.13488e8			0.286393
$415$	−1.02912e9	−	1.78249e9i	−0.706801	−	1.22422i
$416$	−2.47230e9	+	4.28216e9i	−1.68374	+	2.91633i
$417$	−1.59843e8	+	2.76857e8i	−0.107949	+	0.186973i
$418$	−1.07539e8	−	1.86263e8i	−0.0720193	−	0.124741i
$419$	1.59619e9			1.06007			0.530036	−	0.847975i	$-0.322178\pi$
$419$	1.59619e9			1.06007			0.530036	+	0.847975i	$0.322178\pi$
$420$		0			0
$421$	−1.89643e9			−1.23865			−0.619327	−	0.785133i	$-0.712595\pi$
$421$	−1.89643e9			−1.23865			−0.619327	+	0.785133i	$0.712595\pi$
$422$	−5.56121e7	−	9.63230e7i	−0.0360227	−	0.0623931i
$423$	−2.83158e8	+	4.90444e8i	−0.181902	+	0.315064i
$424$	−2.14343e9	+	3.71252e9i	−1.36561	+	2.36531i
$425$	1.09985e9	+	1.90500e9i	0.694981	+	1.20374i
$426$	−7.15366e8			−0.448327
$427$		0			0
$428$	−7.59005e9			−4.67942
$429$	−7.02287e7	−	1.21640e8i	−0.0429452	−	0.0743832i
$430$	−3.57297e9	+	6.18857e9i	−2.16715	+	3.75362i
$431$	2.09961e8	−	3.63663e8i	0.126319	−	0.218790i	−0.795929	−	0.605390i	$-0.793017\pi$
$431$	2.09961e8	−	3.63663e8i	0.126319	−	0.218790i	0.922248	+	0.386600i	$0.126350\pi$
$432$	5.54715e8	+	9.60795e8i	0.331037	+	0.573374i
$433$	−2.39286e9			−1.41648			−0.708238	−	0.705974i	$-0.750509\pi$
$433$	−2.39286e9			−1.41648			−0.708238	+	0.705974i	$0.750509\pi$
$434$		0			0
$435$	1.51593e9			0.883010
$436$	−1.68921e9	−	2.92579e9i	−0.976068	−	1.69060i
$437$	−1.96198e8	+	3.39826e8i	−0.112463	+	0.194792i
$438$	1.35733e8	−	2.35096e8i	0.0771835	−	0.133686i
$439$	−2.84003e8	−	4.91908e8i	−0.160213	−	0.277497i	0.774732	−	0.632290i	$-0.217885\pi$
$439$	−2.84003e8	−	4.91908e8i	−0.160213	−	0.277497i	−0.934945	+	0.354793i	$0.884551\pi$
$440$	1.58185e9			0.885282
$441$		0			0
$442$	−1.97834e9			−1.08974
$443$	1.13170e9	+	1.96015e9i	0.618467	+	1.07122i	0.989766	+	0.142703i	$0.0455793\pi$
$443$	1.13170e9	+	1.96015e9i	0.618467	+	1.07122i	−0.371299	+	0.928514i	$0.621087\pi$
$444$	1.50428e9	−	2.60549e9i	0.815622	−	1.41270i
$445$	2.02446e9	−	3.50647e9i	1.08906	−	1.88630i
$446$	1.88293e9	+	3.26133e9i	1.00499	+	1.74070i
$447$	−1.52067e8			−0.0805302
$448$		0			0
$449$	7.86592e8			0.410098			0.205049	−	0.978752i	$-0.434265\pi$
$449$	7.86592e8			0.410098			0.205049	+	0.978752i	$0.434265\pi$
$450$	1.49303e9	+	2.58601e9i	0.772370	+	1.33778i
$451$	−2.62359e7	+	4.54419e7i	−0.0134672	+	0.0233259i
$452$	−3.27437e9	+	5.67138e9i	−1.66780	+	2.88871i
$453$	−8.20743e8	−	1.42157e9i	−0.414823	−	0.718495i
$454$	3.68790e9			1.84963
$455$		0			0
$456$	−1.86864e9			−0.922888
$457$	−5.74677e8	−	9.95370e8i	−0.281655	−	0.487841i	0.690138	−	0.723678i	$-0.257550\pi$
$457$	−5.74677e8	−	9.95370e8i	−0.281655	−	0.487841i	−0.971792	+	0.235838i	$0.924217\pi$
$458$	−2.68272e9	+	4.64661e9i	−1.30481	+	2.25999i
$459$	−1.14482e8	+	1.98289e8i	−0.0552577	+	0.0957091i
$460$	−2.30930e9	−	3.99983e9i	−1.10619	−	1.91597i
$461$	7.67125e8			0.364681			0.182340	−	0.983235i	$-0.441633\pi$
$461$	7.67125e8			0.364681			0.182340	+	0.983235i	$0.441633\pi$
$462$		0			0
$463$	2.43312e9			1.13928			0.569640	−	0.821894i	$-0.307082\pi$
$463$	2.43312e9			1.13928			0.569640	+	0.821894i	$0.307082\pi$
$464$	−3.06095e9	−	5.30172e9i	−1.42247	−	2.46379i
$465$	−1.36525e9	+	2.36468e9i	−0.629690	+	1.09066i
$466$	−1.23915e9	+	2.14626e9i	−0.567247	+	0.982500i
$467$	1.19466e9	+	2.06921e9i	0.542794	+	0.940146i	0.998742	+	0.0501403i	$0.0159668\pi$
$467$	1.19466e9	+	2.06921e9i	0.542794	+	0.940146i	−0.455948	+	0.890006i	$0.650700\pi$
$468$	−1.95294e9			−0.880703
$469$		0			0
$470$	8.69866e9			3.86465
$471$	7.60519e8	+	1.31726e9i	0.335380	+	0.580895i
$472$	5.29942e9	−	9.17887e9i	2.31970	−	4.01784i
$473$	−2.11421e8	+	3.66192e8i	−0.0918616	+	0.159109i
$474$	−5.06611e8	−	8.77475e8i	−0.218499	−	0.378452i
$475$	−2.83375e9			−1.21320
$476$		0			0
$477$	−6.76670e8			−0.285471
$478$	−9.56354e8	−	1.65645e9i	−0.400517	−	0.693716i
$479$	1.11598e9	−	1.93294e9i	0.463964	−	0.803609i	−0.535190	−	0.844731i	$-0.679760\pi$
$479$	1.11598e9	−	1.93294e9i	0.463964	−	0.803609i	0.999154	+	0.0411228i	$0.0130935\pi$
$480$	4.39503e9	−	7.61241e9i	1.81392	−	3.14179i
$481$	1.28200e9	+	2.22048e9i	0.525265	+	0.909786i
$482$	−3.37148e9			−1.37137
$483$		0			0
$484$	−6.49941e9			−2.60564
$485$	1.16080e9	+	2.01057e9i	0.462022	+	0.800245i
$486$	−1.55408e8	+	2.69174e8i	−0.0614109	+	0.106367i
$487$	−1.03913e8	+	1.79983e8i	−0.0407681	+	0.0706124i	−0.885689	−	0.464278i	$-0.846314\pi$
$487$	−1.03913e8	+	1.79983e8i	−0.0407681	+	0.0706124i	0.844921	+	0.534891i	$0.179647\pi$
$488$	−5.62630e9	−	9.74504e9i	−2.19156	−	3.79590i
$489$	−1.42214e9			−0.549999
$490$		0			0
$491$	1.49013e9			0.568119			0.284060	−	0.958807i	$-0.408319\pi$
$491$	1.49013e9			0.568119			0.284060	+	0.958807i	$0.408319\pi$
$492$	3.64789e8	+	6.31832e8i	0.138090	+	0.239179i
$493$	6.31717e8	−	1.09417e9i	0.237443	−	0.411263i
$494$	1.27429e9	−	2.20713e9i	0.475580	−	0.823729i
$495$	1.24846e8	+	2.16239e8i	0.0462654	+	0.0801340i
$496$	1.10268e10			4.05755
$497$		0			0
$498$	−2.32865e9			−0.844894
$499$	−8.85786e8	−	1.53423e9i	−0.319137	−	0.552761i	0.661171	−	0.750235i	$-0.270060\pi$
$499$	−8.85786e8	−	1.53423e9i	−0.319137	−	0.552761i	−0.980308	+	0.197474i	$0.936726\pi$
$500$	9.78697e9	−	1.69515e10i	3.50149	−	6.06476i
$501$	−2.80027e8	+	4.85020e8i	−0.0994872	+	0.172317i
$502$	1.16450e9	+	2.01698e9i	0.410845	+	0.711605i
$503$	2.60286e8			0.0911933			0.0455966	−	0.998960i	$-0.485481\pi$
$503$	2.60286e8			0.0911933			0.0455966	+	0.998960i	$0.485481\pi$
$504$		0			0
$505$	−6.42270e9			−2.21921
$506$	−1.87908e8	−	3.25466e8i	−0.0644790	−	0.111681i
$507$	−1.49250e7	+	2.58509e7i	−0.00508613	+	0.00880943i
$508$	2.44925e9	−	4.24222e9i	0.828914	−	1.43572i
$509$	6.06242e8	+	1.05004e9i	0.203767	+	0.352935i	0.949739	−	0.313042i	$-0.101348\pi$
$509$	6.06242e8	+	1.05004e9i	0.203767	+	0.352935i	−0.745972	+	0.665977i	$0.768015\pi$
$510$	3.51690e9			1.17399
$511$		0			0
$512$	−2.17738e9			−0.716951
$513$	−1.47480e8	−	2.55444e8i	−0.0482307	−	0.0835380i
$514$	4.36667e9	−	7.56329e9i	1.41834	−	2.45663i
$515$	−5.53880e9	+	9.59348e9i	−1.78686	+	3.09493i
$516$	2.93963e9	+	5.09159e9i	0.941931	+	1.63147i
$517$	5.14720e8			0.163815
$518$		0			0
$519$	3.51142e9			1.10255
$520$	9.37213e9	+	1.62330e10i	2.92299	+	5.06276i
$521$	−1.28716e9	+	2.22942e9i	−0.398749	+	0.690654i	−0.993572	−	0.113203i	$-0.963889\pi$
$521$	−1.28716e9	+	2.22942e9i	−0.398749	+	0.690654i	0.594823	+	0.803857i	$0.297222\pi$
$522$	8.57547e8	−	1.48531e9i	0.263883	−	0.457058i
$523$	−1.36134e9	−	2.35791e9i	−0.416113	−	0.720729i	0.579432	−	0.815021i	$-0.303275\pi$
$523$	−1.36134e9	−	2.35791e9i	−0.416113	−	0.720729i	−0.995545	+	0.0942920i	$0.969941\pi$
$524$	−6.21323e9			−1.88650
$525$		0			0
$526$	5.92084e9			1.77392
$527$	1.13785e9	+	1.97082e9i	0.338649	+	0.586557i
$528$	5.04176e8	−	8.73258e8i	0.149061	−	0.258181i
$529$	1.35959e9	−	2.35487e9i	0.399312	−	0.691628i
$530$	5.19685e9	+	9.00120e9i	1.51626	+	2.62624i
$531$	1.67300e9			0.484916
$532$		0			0
$533$	−6.21768e8			−0.177862
$534$	−2.29044e9	−	3.96716e9i	−0.650916	−	1.12742i
$535$	−5.74952e9	+	9.95846e9i	−1.62328	+	2.81160i
$536$	−4.04316e9	+	7.00295e9i	−1.13408	+	1.96428i
$537$	−2.07163e8	−	3.58817e8i	−0.0577301	−	0.0999914i
$538$	2.24500e9			0.621552
$539$		0			0
$540$	3.47176e9			0.948793
$541$	7.70981e8	+	1.33538e9i	0.209340	+	0.362588i	0.951507	−	0.307627i	$-0.0995350\pi$
$541$	7.70981e8	+	1.33538e9i	0.209340	+	0.362588i	−0.742167	+	0.670216i	$0.766202\pi$
$542$	2.14580e8	−	3.71664e8i	0.0578885	−	0.100266i
$543$	−9.47700e8	+	1.64146e9i	−0.254022	+	0.439979i
$544$	−3.66299e9	−	6.34449e9i	−0.975528	−	1.68966i
$545$	−5.11835e9			−1.35438
$546$		0			0
$547$	−5.49200e9			−1.43475			−0.717373	−	0.696689i	$-0.754656\pi$
$547$	−5.49200e9			−1.43475			−0.717373	+	0.696689i	$0.754656\pi$
$548$	−4.18441e9	−	7.24760e9i	−1.08618	−	1.88132i
$549$	8.88099e8	−	1.53823e9i	0.229065	−	0.396752i
$550$	1.35700e9	−	2.35040e9i	0.347786	−	0.602382i
$551$	8.13805e8	+	1.40955e9i	0.207248	+	0.358963i
$552$	−3.26517e9			−0.826263
$553$		0			0
$554$	7.71799e9			1.92850
$555$	−2.27901e9	−	3.94736e9i	−0.565875	−	0.980124i
$556$	2.02000e9	−	3.49874e9i	0.498413	−	0.863277i
$557$	3.07010e9	−	5.31756e9i	0.752764	−	1.30382i	−0.193715	−	0.981058i	$-0.562054\pi$
$557$	3.07010e9	−	5.31756e9i	0.752764	−	1.30382i	0.946478	−	0.322767i	$-0.104613\pi$
$558$	1.54462e9	+	2.67536e9i	0.376359	+	0.651873i
$559$	−5.01049e9			−1.21322
$560$		0			0
$561$	2.08103e8			0.0497632
$562$	−1.72497e8	−	2.98774e8i	−0.0409925	−	0.0710012i
$563$	−1.62383e9	+	2.81256e9i	−0.383497	+	0.664236i	−0.991559	−	0.129653i	$-0.958614\pi$
$563$	−1.62383e9	+	2.81256e9i	−0.383497	+	0.664236i	0.608063	+	0.793889i	$0.291947\pi$
$564$	3.57838e9	−	6.19793e9i	0.839865	−	1.45469i
$565$	4.96072e9	+	8.59223e9i	1.15711	+	2.00418i
$566$	1.04485e10			2.42213
$567$		0			0
$568$	5.64899e9			1.29346
$569$	−1.00581e9	−	1.74211e9i	−0.228887	−	0.396444i	0.728591	−	0.684949i	$-0.240175\pi$
$569$	−1.00581e9	−	1.74211e9i	−0.228887	−	0.396444i	−0.957479	+	0.288504i	$0.906842\pi$
$570$	−2.26531e9	+	3.92363e9i	−0.512349	+	0.887414i
$571$	1.83448e9	−	3.17741e9i	0.412369	−	0.714244i	−0.582779	−	0.812631i	$-0.698035\pi$
$571$	1.83448e9	−	3.17741e9i	0.412369	−	0.714244i	0.995148	+	0.0983863i	$0.0313681\pi$
$572$	8.87507e8	+	1.53721e9i	0.198283	+	0.343436i
$573$	−4.56600e9			−1.01390
$574$		0			0
$575$	−4.95155e9			−1.08618
$576$	−2.34269e9	−	4.05767e9i	−0.510784	−	0.884703i
$577$	1.71811e9	−	2.97585e9i	0.372337	−	0.644906i	−0.617588	−	0.786502i	$-0.711890\pi$
$577$	1.71811e9	−	2.97585e9i	0.372337	−	0.644906i	0.989925	+	0.141596i	$0.0452234\pi$
$578$	−2.97866e9	+	5.15919e9i	−0.641613	+	1.11131i
$579$	1.34514e9	+	2.32985e9i	0.288000	+	0.498830i
$580$	−1.91573e10			−4.07697
$581$		0			0
$582$	2.62662e9			0.552290
$583$	3.07509e8	+	5.32622e8i	0.0642715	+	0.111322i
$584$	−1.07183e9	+	1.85646e9i	−0.222680	+	0.385693i
$585$	−1.47937e9	+	2.56234e9i	−0.305514	+	0.529166i
$586$	4.80186e9	+	8.31707e9i	0.985752	+	1.70737i
$587$	−8.47232e9			−1.72890			−0.864449	−	0.502721i	$-0.832332\pi$
$587$	−8.47232e9			−1.72890			−0.864449	+	0.502721i	$0.832332\pi$
$588$		0			0
$589$	−2.93166e9			−0.591168
$590$	−1.28487e10	−	2.22547e10i	−2.57560	−	4.46107i
$591$	2.33697e9	−	4.04774e9i	0.465689	−	0.806597i
$592$	−9.20351e9	+	1.59410e10i	−1.82317	+	3.15783i
$593$	−4.79464e9	−	8.30457e9i	−0.944202	−	1.63541i	−0.757341	−	0.653019i	$-0.773502\pi$
$593$	−4.79464e9	−	8.30457e9i	−0.944202	−	1.63541i	−0.186861	−	0.982386i	$-0.559831\pi$
$594$	2.82497e8			0.0553046
$595$		0			0
$596$	1.92173e9			0.371818
$597$	1.27375e9	+	2.20620e9i	0.245004	+	0.424360i
$598$	2.22663e9	−	3.85663e9i	0.425788	−	0.737486i
$599$	1.58317e9	−	2.74213e9i	0.300978	−	0.521308i	−0.675380	−	0.737470i	$-0.736020\pi$
$599$	1.58317e9	−	2.74213e9i	0.300978	−	0.521308i	0.976358	+	0.216161i	$0.0693538\pi$
$600$	−1.17899e10	−	2.04208e10i	−2.22834	−	3.85960i
$601$	5.32513e9			1.00062			0.500310	−	0.865846i	$-0.333219\pi$
$601$	5.32513e9			1.00062			0.500310	+	0.865846i	$0.333219\pi$
$602$		0			0
$603$	−1.27641e9			−0.237071
$604$	1.03720e10	+	1.79649e10i	1.91529	+	3.31738i
$605$	−4.92335e9	+	8.52749e9i	−0.903892	+	1.56559i
$606$	−3.63326e9	+	6.29300e9i	−0.663197	+	1.14869i
$607$	−2.66020e9	−	4.60760e9i	−0.482785	−	0.836207i	0.517020	−	0.855973i	$-0.327041\pi$
$607$	−2.66020e9	−	4.60760e9i	−0.482785	−	0.836207i	−0.999805	+	0.0197659i	$0.993708\pi$
$608$	9.43764e9			1.70295
$609$		0			0
$610$	−2.72825e10			−4.86665
$611$	3.04960e9	+	5.28207e9i	0.540878	+	0.936828i
$612$	1.44675e9	−	2.50585e9i	0.255131	−	0.441901i
$613$	3.07598e9	−	5.32775e9i	0.539351	−	0.934183i	−0.459588	−	0.888132i	$-0.652003\pi$
$613$	3.07598e9	−	5.32775e9i	0.539351	−	0.934183i	0.998939	−	0.0460509i	$-0.0146636\pi$
$614$	−8.40191e8	−	1.45525e9i	−0.146484	−	0.253717i
$615$	1.10532e9			0.191613
$616$		0			0
$617$	−4.29619e9			−0.736352			−0.368176	−	0.929756i	$-0.620018\pi$
$617$	−4.29619e9			−0.736352			−0.368176	+	0.929756i	$0.620018\pi$
$618$	6.26650e9	+	1.08539e10i	1.06799	+	1.84981i
$619$	−1.95075e9	+	3.37881e9i	−0.330587	+	0.572593i	−0.982627	−	0.185591i	$-0.940580\pi$
$619$	−1.95075e9	+	3.37881e9i	−0.330587	+	0.572593i	0.652040	+	0.758184i	$0.273913\pi$
$620$	1.72532e10	−	2.98834e10i	2.90736	−	5.03569i
$621$	−2.57700e8	−	4.46349e8i	−0.0431810	−	0.0747917i
$622$	−9.58804e9			−1.59758
$623$		0			0
$624$	1.19485e10			1.96865
$625$	−7.44073e9	−	1.28877e10i	−1.21909	−	2.11152i
$626$	−6.09792e9	+	1.05619e10i	−0.993509	+	1.72081i
$627$	−1.34044e8	+	2.32170e8i	−0.0217175	+	0.0376158i
$628$	−9.61096e9	−	1.66467e10i	−1.54849	−	2.68206i
$629$	−3.79884e9			−0.608658
$630$		0			0
$631$	5.79183e9			0.917726			0.458863	−	0.888507i	$-0.348257\pi$
$631$	5.79183e9			0.917726			0.458863	+	0.888507i	$0.348257\pi$
$632$	4.00052e9	+	6.92910e9i	0.630386	+	1.09186i
$633$	−6.93186e7	+	1.20063e8i	−0.0108627	+	0.0188147i
$634$	−8.26970e9	+	1.43235e10i	−1.28878	+	2.23223i
$635$	−3.71064e9	−	6.42702e9i	−0.575097	−	0.996097i
$636$	8.55133e9			1.31806
$637$		0			0
$638$	−1.55883e9			−0.237644
$639$	4.45840e8	+	7.72217e8i	0.0675968	+	0.117081i
$640$	−1.51483e10	+	2.62376e10i	−2.28420	+	3.95634i
$641$	−1.65946e9	+	2.87426e9i	−0.248864	+	0.431046i	−0.963211	−	0.268746i	$-0.913391\pi$
$641$	−1.65946e9	+	2.87426e9i	−0.248864	+	0.431046i	0.714347	+	0.699792i	$0.246724\pi$
$642$	6.50491e9	+	1.12668e10i	0.970216	+	1.68046i
$643$	1.23513e10			1.83220			0.916100	−	0.400949i	$-0.131319\pi$
$643$	1.23513e10			1.83220			0.916100	+	0.400949i	$0.131319\pi$
$644$		0			0
$645$	8.90718e9			1.30702
$646$	1.88800e9	+	3.27011e9i	0.275542	+	0.477253i
$647$	4.33840e9	−	7.51432e9i	0.629744	−	1.09075i	−0.357858	−	0.933776i	$-0.616493\pi$
$647$	4.33840e9	−	7.51432e9i	0.629744	−	1.09075i	0.987603	−	0.156973i	$-0.0501737\pi$
$648$	1.22720e9	−	2.12557e9i	0.177175	−	0.306876i
$649$	−7.60289e8	−	1.31686e9i	−0.109175	−	0.189096i
$650$	3.21598e10			4.59321
$651$		0			0
$652$	1.79722e10			2.53941
$653$	2.54107e9	+	4.40127e9i	0.357126	+	0.618560i	0.987479	−	0.157748i	$-0.0504234\pi$
$653$	2.54107e9	+	4.40127e9i	0.357126	+	0.618560i	−0.630354	+	0.776308i	$0.717090\pi$
$654$	−2.89540e9	+	5.01499e9i	−0.404750	+	0.701048i
$655$	−4.70656e9	+	8.15201e9i	−0.654424	+	1.13350i
$656$	−2.23185e9	−	3.86568e9i	−0.308675	−	0.534642i
$657$	−3.38372e8			−0.0465496
$658$		0			0
$659$	7.83208e9			1.06605			0.533026	−	0.846099i	$-0.321055\pi$
$659$	7.83208e9			1.06605			0.533026	+	0.846099i	$0.321055\pi$
$660$	−1.57772e9	−	2.73270e9i	−0.213613	−	0.369988i
$661$	−3.18338e9	+	5.51377e9i	−0.428729	+	0.742581i	−0.996761	−	0.0804261i	$-0.974372\pi$
$661$	−3.18338e9	+	5.51377e9i	−0.428729	+	0.742581i	0.568031	+	0.823007i	$0.307705\pi$
$662$	4.64295e9	−	8.04183e9i	0.622001	−	1.07734i
$663$	1.23297e9	+	2.13556e9i	0.164306	+	0.284587i
$664$	1.83885e10			2.43758
$665$		0			0
$666$	−5.15686e9			−0.676434
$667$	1.42200e9	+	2.46297e9i	0.185549	+	0.321381i
$668$	3.53880e9	−	6.12938e9i	0.459345	−	0.795608i
$669$	2.34701e9	−	4.06514e9i	0.303056	−	0.524909i
$670$	9.80284e9	+	1.69790e10i	1.25919	+	2.18098i
$671$	−1.61437e9			−0.206288
$672$		0			0
$673$	1.11438e10			1.40923			0.704615	−	0.709590i	$-0.251120\pi$
$673$	1.11438e10			1.40923			0.704615	+	0.709590i	$0.251120\pi$
$674$	8.18923e9	+	1.41842e10i	1.03023	+	1.78441i
$675$	1.86101e9	−	3.22337e9i	0.232909	−	0.403411i
$676$	1.88613e8	−	3.26688e8i	0.0234833	−	0.0406742i
$677$	−3.86595e9	−	6.69603e9i	−0.478846	−	0.829386i	0.520859	−	0.853642i	$-0.325612\pi$
$677$	−3.86595e9	−	6.69603e9i	−0.478846	−	0.829386i	−0.999706	+	0.0242563i	$0.992278\pi$
$678$	1.12250e10			1.38319
$679$		0			0
$680$	−2.77717e10			−3.38705
$681$	−2.29842e9	−	3.98098e9i	−0.278878	−	0.483032i
$682$	1.40389e9	−	2.43161e9i	0.169468	−	0.293527i
$683$	−1.63295e9	+	2.82835e9i	−0.196110	+	0.339673i	−0.947264	−	0.320455i	$-0.896164\pi$
$683$	−1.63295e9	+	2.82835e9i	−0.196110	+	0.339673i	0.751154	+	0.660127i	$0.229498\pi$
$684$	1.86377e9	+	3.22814e9i	0.222687	+	0.385705i
$685$	−1.26789e10			−1.50717
$686$		0			0
$687$	6.68785e9			0.786933
$688$	−1.79853e10	−	3.11514e10i	−2.10551	−	3.64686i
$689$	−3.64385e9	+	6.31134e9i	−0.424418	+	0.735113i
$690$	−3.95828e9	+	6.85595e9i	−0.458707	+	0.794503i
$691$	−7.20996e9	−	1.24880e10i	−0.831303	−	1.43986i	−0.897005	−	0.442020i	$-0.854262\pi$
$691$	−7.20996e9	−	1.24880e10i	−0.831303	−	1.43986i	0.0657020	−	0.997839i	$-0.479071\pi$
$692$	−4.43752e10			−5.09060
$693$		0			0
$694$	−2.32331e10			−2.63845
$695$	−3.06033e9	−	5.30065e9i	−0.345797	−	0.598938i
$696$	−6.77173e9	+	1.17290e10i	−0.761321	+	1.31865i
$697$	4.60609e8	−	7.97798e8i	0.0515250	−	0.0892439i
$698$	8.74952e9	+	1.51546e10i	0.973846	+	1.68675i
$699$	3.08911e9			0.342108
$700$		0			0
$701$	1.37465e9			0.150723			0.0753615	−	0.997156i	$-0.475989\pi$
$701$	1.37465e9			0.150723			0.0753615	+	0.997156i	$0.475989\pi$
$702$	1.67373e9	+	2.89899e9i	0.182602	+	0.316277i
$703$	2.44691e9	−	4.23817e9i	0.265628	−	0.460082i
$704$	−2.12925e9	+	3.68798e9i	−0.229997	+	0.398367i
$705$	−5.42129e9	−	9.38996e9i	−0.582695	−	1.00926i
$706$	7.63862e9			0.816955
$707$		0			0
$708$	−2.11424e10			−2.23892
$709$	7.07713e9	+	1.22579e10i	0.745753	+	1.29168i	0.949842	+	0.312730i	$0.101244\pi$
$709$	7.07713e9	+	1.22579e10i	0.745753	+	1.29168i	−0.204089	+	0.978952i	$0.565423\pi$
$710$	6.84813e9	−	1.18613e10i	0.718072	−	1.24374i
$711$	−6.31473e8	+	1.09374e9i	−0.0658887	+	0.114123i
$712$	1.80868e10	+	3.13272e10i	1.87794	+	3.25269i
$713$	−5.12263e9			−0.529273
$714$		0			0
$715$	2.68917e9			0.275136
$716$	2.61800e9	+	4.53450e9i	0.266547	+	0.461673i
$717$	−1.19206e9	+	2.06471e9i	−0.120776	+	0.209191i
$718$	5.12794e9	−	8.88186e9i	0.517020	−	0.895505i
$719$	−3.32111e9	−	5.75234e9i	−0.333221	−	0.577156i	0.649920	−	0.760002i	$-0.274802\pi$
$719$	−3.32111e9	−	5.75234e9i	−0.333221	−	0.577156i	−0.983141	+	0.182846i	$0.941469\pi$
$720$	−2.12409e10			−2.12085
$721$		0			0
$722$	1.44980e10			1.43360
$723$	2.10122e9	+	3.63941e9i	0.206769	+	0.358135i
$724$	1.19764e10	−	2.07438e10i	1.17285	−	2.03144i
$725$	−1.02692e10	+	1.77867e10i	−1.00081	+	1.73346i
$726$	5.57019e9	+	9.64785e9i	0.540246	+	0.935734i
$727$	7.79081e9			0.751990			0.375995	−	0.926622i	$-0.377301\pi$
$727$	7.79081e9			0.751990			0.375995	+	0.926622i	$0.377301\pi$
$728$		0			0
$729$	3.87420e8			0.0370370
$730$	2.59871e9	+	4.50110e9i	0.247245	+	0.428241i
$731$	3.71180e9	−	6.42902e9i	0.351458	−	0.608743i
$732$	−1.12232e10	+	1.94392e10i	−1.05762	+	1.83185i
$733$	9.60758e9	+	1.66408e10i	0.901052	+	1.56067i	0.826131	+	0.563479i	$0.190537\pi$
$733$	9.60758e9	+	1.66408e10i	0.901052	+	1.56067i	0.0749215	+	0.997189i	$0.476129\pi$
$734$	2.11091e10			1.97031
$735$		0			0
$736$	1.64908e10			1.52465
$737$	5.80057e8	+	1.00469e9i	0.0533746	+	0.0924475i
$738$	6.25270e8	−	1.08300e9i	0.0572625	−	0.0991815i
$739$	5.66298e9	−	9.80857e9i	0.516166	−	0.894026i	−0.483658	−	0.875257i	$-0.660692\pi$
$739$	5.66298e9	−	9.80857e9i	0.516166	−	0.894026i	0.999824	−	0.0187685i	$-0.00597455\pi$
$740$	2.88007e10	+	4.98843e10i	2.61271	+	4.52535i
$741$	−3.17672e9			−0.286824
$742$		0			0
$743$	−9.10743e9			−0.814582			−0.407291	−	0.913298i	$-0.633527\pi$
$743$	−9.10743e9			−0.814582			−0.407291	+	0.913298i	$0.633527\pi$
$744$	−1.21973e10	−	2.11263e10i	−1.08582	−	1.88070i
$745$	1.45572e9	−	2.52139e9i	0.128983	−	0.223405i
$746$	6.28320e9	−	1.08828e10i	0.554109	−	0.959744i
$747$	1.45129e9	+	2.51372e9i	0.127389	+	0.220645i
$748$	−2.62988e9			−0.229763
$749$		0			0
$750$	−3.35509e10			−2.90396
$751$	−8.26880e8	−	1.43220e9i	−0.0712365	−	0.123385i	0.828207	−	0.560422i	$-0.189361\pi$
$751$	−8.26880e8	−	1.43220e9i	−0.0712365	−	0.123385i	−0.899443	+	0.437037i	$0.856028\pi$
$752$	−2.18933e10	+	3.79202e10i	−1.87736	+	3.25169i
$753$	1.45152e9	−	2.51410e9i	0.123891	−	0.214585i
$754$	−9.23575e9	−	1.59968e10i	−0.784643	−	1.35904i
$755$	3.14276e10			2.65764
$756$		0			0
$757$	1.48318e10			1.24268			0.621338	−	0.783543i	$-0.286590\pi$
$757$	1.48318e10			1.24268			0.621338	+	0.783543i	$0.286590\pi$
$758$	−5.53435e9	−	9.58577e9i	−0.461556	−	0.799438i
$759$	−2.34221e8	+	4.05682e8i	−0.0194437	+	0.0336775i
$760$	1.78883e10	−	3.09835e10i	1.47816	−	2.56025i
$761$	1.40318e9	+	2.43039e9i	0.115417	+	0.199908i	0.917946	−	0.396705i	$-0.129846\pi$
$761$	1.40318e9	+	2.43039e9i	0.115417	+	0.199908i	−0.802530	+	0.596612i	$0.796513\pi$
$762$	−8.39631e9			−0.687458
$763$		0			0
$764$	5.77023e10			4.68130
$765$	−2.19185e9	−	3.79639e9i	−0.177009	−	0.306589i
$766$	2.56557e7	−	4.44370e7i	0.00206245	−	0.00357227i
$767$	9.00910e9	−	1.56042e10i	0.720937	−	1.24870i
$768$	6.03239e9	+	1.04484e10i	0.480535	+	0.832311i
$769$	1.56499e10			1.24099			0.620496	−	0.784210i	$-0.286932\pi$
$769$	1.56499e10			1.24099			0.620496	+	0.784210i	$0.286932\pi$
$770$		0			0
$771$	−1.08858e10			−0.855402
$772$	−1.69990e10	−	2.94432e10i	−1.32973	−	2.30316i
$773$	2.04453e9	−	3.54122e9i	0.159208	−	0.275756i	−0.775375	−	0.631501i	$-0.782439\pi$
$773$	2.04453e9	−	3.54122e9i	0.159208	−	0.275756i	0.934583	+	0.355745i	$0.115773\pi$
$774$	5.03871e9	−	8.72730e9i	0.390595	−	0.676530i
$775$	−1.84969e10	−	3.20376e10i	−1.42739	−	2.47232i
$776$	−2.07415e10			−1.59340
$777$		0			0
$778$	2.91045e10			2.21580
$779$	5.93376e8	+	1.02776e9i	0.0449727	+	0.0778950i
$780$	1.86954e10	−	3.23813e10i	1.41060	−	2.44322i
$781$	4.05220e8	−	7.01861e8i	0.0304377	−	0.0527197i
$782$	3.29899e9	+	5.71402e9i	0.246693	+	0.427286i
$783$	−2.13781e9			−0.159148
$784$		0			0
$785$	−2.91215e10			−2.14867
$786$	5.32493e9	+	9.22304e9i	0.391142	+	0.677478i
$787$	−1.26027e10	+	2.18286e10i	−0.921623	+	1.59630i	−0.124719	+	0.992192i	$0.539803\pi$
$787$	−1.26027e10	+	2.18286e10i	−0.921623	+	1.59630i	−0.796904	+	0.604106i	$0.793530\pi$
$788$	−2.95331e10	+	5.11529e10i	−2.15014	+	3.72416i
$789$	−3.69006e9	−	6.39137e9i	−0.267463	−	0.463260i
$790$	1.93989e10			1.39986
$791$		0			0
$792$	−2.23078e9			−0.159558
$793$	−9.56480e9	−	1.65667e10i	−0.681114	−	1.17972i
$794$	9.05534e9	−	1.56843e10i	0.641997	−	1.11197i
$795$	6.47770e9	−	1.12197e10i	0.457231	−	0.791947i
$796$	−1.60969e10	−	2.78806e10i	−1.13122	−	1.95932i
$797$	6.07194e9			0.424838			0.212419	−	0.977179i	$-0.431866\pi$
$797$	6.07194e9			0.424838			0.212419	+	0.977179i	$0.431866\pi$
$798$		0			0
$799$	−9.03665e9			−0.626749
$800$	5.95455e10	+	1.03136e11i	4.11182	+	7.12188i
$801$	−2.85496e9	+	4.94494e9i	−0.196285	+	0.339975i
$802$	−2.61786e9	+	4.53427e9i	−0.179199	+	0.310383i
$803$	1.53772e8	+	2.66340e8i	0.0104803	+	0.0181523i
$804$	1.61304e10			1.09459
$805$		0			0
$806$	3.32710e10			2.23817
$807$	−1.39916e9	−	2.42341e9i	−0.0937149	−	0.162319i
$808$	2.86906e10	−	4.96935e10i	1.91337	−	3.31406i
$809$	−1.13125e10	+	1.95937e10i	−0.751168	+	1.30106i	0.196089	+	0.980586i	$0.437176\pi$
$809$	−1.13125e10	+	1.95937e10i	−0.751168	+	1.30106i	−0.947257	+	0.320475i	$0.896158\pi$
$810$	−2.97540e9	−	5.15355e9i	−0.196720	−	0.340729i
$811$	−1.70292e10			−1.12104			−0.560520	−	0.828141i	$-0.689399\pi$
$811$	−1.70292e10			−1.12104			−0.560520	+	0.828141i	$0.689399\pi$
$812$		0			0
$813$	−5.34935e8			−0.0349127
$814$	2.34351e9	+	4.05908e9i	0.152294	+	0.263780i
$815$	1.36140e10	−	2.35802e10i	0.880918	−	1.52579i
$816$	−8.85153e9	+	1.53313e10i	−0.570299	+	0.987787i
$817$	4.78170e9	+	8.28214e9i	0.306764	+	0.531331i
$818$	5.79222e9			0.370006
$819$		0			0
$820$	−1.39683e10			−0.884701
$821$	1.49757e10	+	2.59386e10i	0.944463	+	1.63586i	0.756822	+	0.653621i	$0.226751\pi$
$821$	1.49757e10	+	2.59386e10i	0.944463	+	1.63586i	0.187641	+	0.982238i	$0.439916\pi$
$822$	−7.17233e9	+	1.24228e10i	−0.450411	+	0.780134i
$823$	5.50746e9	−	9.53920e9i	0.344391	−	0.596503i	−0.640852	−	0.767665i	$-0.721419\pi$
$823$	5.50746e9	−	9.53920e9i	0.344391	−	0.596503i	0.985243	+	0.171162i	$0.0547521\pi$
$824$	−4.94843e10	−	8.57093e10i	−3.08121	−	5.33682i
$825$	−3.38292e9			−0.209750
$826$		0			0
$827$	−1.67625e10			−1.03055			−0.515276	−	0.857024i	$-0.672311\pi$
$827$	−1.67625e10			−1.03055			−0.515276	+	0.857024i	$0.672311\pi$
$828$	3.25665e9	+	5.64068e9i	0.199372	+	0.345323i
$829$	1.50012e10	−	2.59829e10i	0.914504	−	1.58397i	0.106878	−	0.994272i	$-0.465915\pi$
$829$	1.50012e10	−	2.59829e10i	0.914504	−	1.58397i	0.807626	−	0.589695i	$-0.200752\pi$
$830$	2.22920e10	−	3.86108e10i	1.35324	−	2.34388i
$831$	−4.81011e9	−	8.33135e9i	−0.290771	−	0.503630i
$832$	−5.04615e10			−3.03758
$833$		0			0
$834$	−6.92481e9			−0.413358
$835$	−5.36134e9	−	9.28610e9i	−0.318691	−	0.551990i
$836$	1.69396e9	−	2.93402e9i	0.100272	−	0.173677i
$837$	1.92532e9	−	3.33475e9i	0.113491	−	0.196573i
$838$	1.72877e10	+	2.99432e10i	1.01481	+	1.75770i
$839$	2.30538e10			1.34764			0.673821	−	0.738894i	$-0.264652\pi$
$839$	2.30538e10			1.34764			0.673821	+	0.738894i	$0.264652\pi$
$840$		0			0
$841$	−5.45335e9			−0.316139
$842$	−2.05395e10	−	3.55755e10i	−1.18576	−	2.05380i
$843$	−2.15012e8	+	3.72412e8i	−0.0123614	+	0.0214105i
$844$	8.76006e8	−	1.51729e9i	0.0501543	−	0.0868698i
$845$	−2.85752e8	−	4.94937e8i	−0.0162926	−	0.0282196i
$846$	−1.22671e10			−0.696540
$847$		0			0
$848$	−5.23188e10			−2.94627
$849$	−6.51187e9	−	1.12789e10i	−0.365198	−	0.632542i
$850$	−2.38242e10	+	4.12646e10i	−1.33061	+	2.30469i
$851$	4.27560e9	−	7.40556e9i	0.237817	−	0.411912i
$852$	−5.63425e9	−	9.75880e9i	−0.312103	−	0.540577i
$853$	5.09026e9			0.280814			0.140407	−	0.990094i	$-0.455159\pi$
$853$	5.09026e9			0.280814			0.140407	+	0.990094i	$0.455159\pi$
$854$		0			0
$855$	5.64726e9			0.308999
$856$	−5.13669e10	−	8.89701e10i	−2.79914	−	4.84826i
$857$	−6.98397e9	+	1.20966e10i	−0.379026	+	0.656493i	−0.990921	−	0.134447i	$-0.957074\pi$
$857$	−6.98397e9	+	1.20966e10i	−0.379026	+	0.656493i	0.611895	+	0.790939i	$0.290408\pi$
$858$	1.52124e9	−	2.63487e9i	0.0822228	−	0.142414i
$859$	−1.11721e10	−	1.93507e10i	−0.601396	−	1.04165i	−0.992610	−	0.121348i	$-0.961278\pi$
$859$	−1.11721e10	−	1.93507e10i	−0.601396	−	1.04165i	0.391214	−	0.920300i	$-0.372055\pi$
$860$	−1.12563e11			−6.03465
$861$		0			0
$862$	9.09602e9			0.483700
$863$	3.33117e9	+	5.76976e9i	0.176425	+	0.305576i	0.940653	−	0.339369i	$-0.110213\pi$
$863$	3.33117e9	+	5.76976e9i	0.176425	+	0.305576i	−0.764229	+	0.644945i	$0.776880\pi$
$864$	−6.19800e9	+	1.07352e10i	−0.326929	+	0.566258i
$865$	−3.36145e10	+	5.82220e10i	−1.76592	+	3.05866i
$866$	−2.59161e10	−	4.48880e10i	−1.35599	−	2.34865i
$867$	7.42559e9			0.386958
$868$		0			0
$869$	1.14788e9			0.0593372
$870$	1.64184e10	+	2.84375e10i	0.845306	+	1.46411i
$871$	−6.87342e9	+	1.19051e10i	−0.352460	+	0.610478i
$872$	2.28640e10	−	3.96015e10i	1.16773	−	2.02257i
$873$	−1.63700e9	−	2.83537e9i	−0.0832719	−	0.144231i
$874$	−8.49980e9			−0.430644
$875$		0			0
$876$	4.27614e9			0.214925
$877$	1.49491e10	+	2.58926e10i	0.748370	+	1.29621i	0.948604	+	0.316467i	$0.102497\pi$
$877$	1.49491e10	+	2.58926e10i	0.748370	+	1.29621i	−0.200234	+	0.979748i	$0.564170\pi$
$878$	6.15186e9	−	1.06553e10i	0.306744	−	0.531296i
$879$	5.98536e9	−	1.03669e10i	0.297255	−	0.514860i
$880$	9.65285e9	+	1.67192e10i	0.477492	+	0.827041i
$881$	−1.24713e10			−0.614466			−0.307233	−	0.951634i	$-0.599403\pi$
$881$	−1.24713e10			−0.614466			−0.307233	+	0.951634i	$0.599403\pi$
$882$		0			0
$883$	1.37548e10			0.672345			0.336173	−	0.941800i	$-0.390867\pi$
$883$	1.37548e10			0.672345			0.336173	+	0.941800i	$0.390867\pi$
$884$	−1.55815e10	−	2.69879e10i	−0.758622	−	1.31397i
$885$	−1.60155e10	+	2.77397e10i	−0.776675	+	1.34524i
$886$	−2.45139e10	+	4.24594e10i	−1.18412	+	2.05095i
$887$	1.56768e10	+	2.71530e10i	0.754265	+	1.30643i	0.945739	+	0.324928i	$0.105340\pi$
$887$	1.56768e10	+	2.71530e10i	0.754265	+	1.30643i	−0.191473	+	0.981498i	$0.561327\pi$
$888$	4.07219e10			1.95156
$889$		0			0
$890$	8.77048e10			4.17021
$891$	−1.76061e8	−	3.04947e8i	−0.00833858	−	0.0144429i
$892$	−2.96600e10	+	5.13727e10i	−1.39925	+	2.42357i
$893$	5.82069e9	−	1.00817e10i	0.273524	−	0.473757i
$894$	−1.64698e9	−	2.85265e9i	−0.0770916	−	0.133527i
$895$	7.93261e9			0.369858
$896$		0			0
$897$	−5.55083e9			−0.256794
$898$	8.51928e9	+	1.47558e10i	0.392587	+	0.679980i
$899$	−1.06240e10	+	1.84013e10i	−0.487673	+	0.844675i
$900$	−2.35183e10	+	4.07350e10i	−1.07537	+	1.86260i
$901$	−5.39877e9	−	9.35095e9i	−0.245900	−	0.425911i
$902$	−1.13660e9			−0.0515687
$903$		0			0
$904$	−8.86394e10			−3.99059
$905$	−1.81445e10	−	3.14272e10i	−0.813719	−	1.40940i
$906$	1.77783e10	−	3.07929e10i	0.794221	−	1.37563i
$907$	5.60311e8	−	9.70487e8i	0.0249347	−	0.0431881i	−0.853289	−	0.521439i	$-0.825396\pi$
$907$	5.60311e8	−	9.70487e8i	0.0249347	−	0.0431881i	0.878223	+	0.478250i	$0.158729\pi$
$908$	2.90460e10	+	5.03092e10i	1.28762	+	2.23022i
$909$	9.05748e9			0.399976
$910$		0			0
$911$	−3.97792e10			−1.74318			−0.871589	−	0.490238i	$-0.836910\pi$
$911$	−3.97792e10			−1.74318			−0.871589	+	0.490238i	$0.836910\pi$
$912$	−1.14029e10	−	1.97504e10i	−0.497776	−	0.862173i
$913$	1.31907e9	−	2.28469e9i	0.0573614	−	0.0993528i
$914$	1.24482e10	−	2.15609e10i	0.539257	−	0.934020i
$915$	1.70034e10	+	2.94507e10i	0.733772	+	1.27093i
$916$	−8.45169e10			−3.63337
$917$		0			0
$918$	−4.95964e9			−0.211593
$919$	7.21452e9	+	1.24959e10i	0.306622	+	0.531085i	0.977621	−	0.210373i	$-0.0674680\pi$
$919$	7.21452e9	+	1.24959e10i	0.306622	+	0.531085i	−0.670999	+	0.741458i	$0.734135\pi$
$920$	3.12571e10	−	5.41389e10i	1.32340	−	2.29220i
$921$	−1.04727e9	+	1.81392e9i	−0.0441723	+	0.0765086i
$922$	8.30844e9	+	1.43906e10i	0.349109	+	0.604675i
$923$	9.60336e9			0.401992
$924$		0			0
$925$	6.17537e10			2.56547
$926$	2.63522e10	+	4.56434e10i	1.09063	+	1.88903i
$927$	7.81098e9	−	1.35290e10i	0.322052	−	0.557811i
$928$	3.42009e10	−	5.92377e10i	1.40482	−	2.43321i
$929$	1.33031e10	+	2.30416e10i	0.544374	+	0.942884i	0.998646	+	0.0520206i	$0.0165662\pi$
$929$	1.33031e10	+	2.30416e10i	0.544374	+	0.942884i	−0.454272	+	0.890863i	$0.650101\pi$
$930$	−5.91460e10			−2.41121
$931$		0			0
$932$	−3.90382e10			−1.57955
$933$	5.97559e9	+	1.03500e10i	0.240877	+	0.417211i
$934$	−2.58778e10	+	4.48217e10i	−1.03923	+	1.80001i
$935$	−1.99215e9	+	3.45051e9i	−0.0797043	+	0.138052i
$936$	−1.32169e10	−	2.28923e10i	−0.526821	−	0.912480i
$937$	−4.46208e10			−1.77194			−0.885970	−	0.463742i	$-0.846506\pi$
$937$	−4.46208e10			−1.77194			−0.885970	+	0.463742i	$0.846506\pi$
$938$		0			0
$939$	1.52017e10			0.599188
$940$	6.85109e10	+	1.18664e11i	2.69037	+	4.65986i
$941$	2.14179e9	−	3.70970e9i	0.0837942	−	0.145136i	−0.821083	−	0.570809i	$-0.806629\pi$
$941$	2.14179e9	−	3.70970e9i	0.0837942	−	0.145136i	0.904877	+	0.425674i	$0.139963\pi$
$942$	−1.64738e10	+	2.85334e10i	−0.642118	+	1.11218i
$943$	1.03683e9	+	1.79585e9i	0.0402641	+	0.0697395i
$944$	1.29354e11			5.00468
$945$		0			0
$946$	−9.15928e9			−0.351757
$947$	−8.93776e8	−	1.54807e9i	−0.0341982	−	0.0592331i	0.848420	−	0.529324i	$-0.177554\pi$
$947$	−8.93776e8	−	1.54807e9i	−0.0341982	−	0.0592331i	−0.882618	+	0.470091i	$0.844221\pi$
$948$	7.98016e9	−	1.38220e10i	0.304216	−	0.526918i
$949$	−1.82213e9	+	3.15602e9i	−0.0692065	+	0.119869i
$950$	−3.06913e10	−	5.31588e10i	−1.16140	−	2.01161i
$951$	2.06158e10			0.777264
$952$		0			0
$953$	−1.13652e10			−0.425356			−0.212678	−	0.977122i	$-0.568219\pi$
$953$	−1.13652e10			−0.425356			−0.212678	+	0.977122i	$0.568219\pi$
$954$	−7.32875e9	−	1.26938e10i	−0.273282	−	0.473338i
$955$	4.37099e10	−	7.57078e10i	1.62393	−	2.81274i
$956$	1.50645e10	−	2.60926e10i	0.557639	−	0.965860i
$957$	9.71516e8	+	1.68272e9i	0.0358309	+	0.0620610i
$958$	4.83472e10			1.77661
$959$		0			0
$960$	8.97056e10			3.27243
$961$	−5.37973e9	−	9.31796e9i	−0.195537	−	0.338680i
$962$	−2.77696e10	+	4.80984e10i	−1.00567	+	1.74188i
$963$	8.10815e9	−	1.40437e10i	0.292570	−	0.506746i
$964$	−2.65538e10	−	4.59926e10i	−0.954680	−	1.65355i
$965$	−5.15075e10			−1.84512
$966$		0			0
$967$	4.31418e10			1.53428			0.767141	−	0.641478i	$-0.221678\pi$
$967$	4.31418e10			1.53428			0.767141	+	0.641478i	$0.221678\pi$
$968$	−4.39858e10	−	7.61856e10i	−1.55865	−	2.69966i
$969$	2.35333e9	−	4.07609e9i	0.0830901	−	0.143916i
$970$	−2.51444e10	+	4.35514e10i	−0.884587	+	1.53215i
$971$	−9.40111e9	−	1.62832e10i	−0.329543	−	0.570785i	0.652878	−	0.757463i	$-0.273561\pi$
$971$	−9.40111e9	−	1.62832e10i	−0.329543	−	0.570785i	−0.982421	+	0.186678i	$0.940228\pi$
$972$	−4.89598e9			−0.171005
$973$		0			0
$974$	−4.50179e9			−0.156109
$975$	−2.00431e10	−	3.47156e10i	−0.692545	−	1.19952i
$976$	6.86662e10	−	1.18933e11i	2.36411	−	4.09477i
$977$	1.16023e9	−	2.00958e9i	0.0398028	−	0.0689405i	−0.845438	−	0.534074i	$-0.820660\pi$
$977$	1.16023e9	−	2.00958e9i	0.0398028	−	0.0689405i	0.885241	+	0.465134i	$0.153994\pi$
$978$	−1.54027e10	−	2.66782e10i	−0.526515	−	0.911950i
$979$	5.18969e9			0.176767
$980$		0			0
$981$	7.21805e9			0.244106
$982$	1.61390e10	+	2.79536e10i	0.543861	+	0.941994i
$983$	−1.21690e10	+	2.10772e10i	−0.408616	+	0.707744i	−0.994735	−	0.102481i	$-0.967322\pi$
$983$	−1.21690e10	+	2.10772e10i	−0.408616	+	0.707744i	0.586119	+	0.810225i	$0.300655\pi$
$984$	−4.93753e9	+	8.55205e9i	−0.165206	+	0.286146i
$985$	4.47431e10	+	7.74973e10i	1.49176	+	2.58381i
$986$	2.73676e10			0.909215
$987$		0			0
$988$	4.01454e10			1.32430
$989$	8.35528e9	+	1.44718e10i	0.274646	+	0.475702i
$990$	−2.70432e9	+	4.68401e9i	−0.0885797	+	0.153425i
$991$	1.36427e10	−	2.36299e10i	0.445291	−	0.771267i	−0.552782	−	0.833326i	$-0.686434\pi$
$991$	1.36427e10	−	2.36299e10i	0.445291	−	0.771267i	0.998072	+	0.0620597i	$0.0197669\pi$
$992$	6.16029e10	+	1.06699e11i	2.00360	+	3.47033i
$993$	−1.15746e10			−0.375130
$994$		0			0
$995$	−4.87739e10			−1.56966
$996$	−1.83406e10	−	3.17668e10i	−0.588173	−	1.01874i
$997$	−9.09819e8	+	1.57585e9i	−0.0290751	+	0.0503596i	−0.880197	−	0.474609i	$-0.842590\pi$
$997$	−9.09819e8	+	1.57585e9i	−0.0290751	+	0.0503596i	0.851122	+	0.524968i	$0.175923\pi$
$998$	1.91872e10	−	3.32332e10i	0.611020	−	1.05832i
$999$	3.21393e9	+	5.56669e9i	0.101990	+	0.176652i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.8.e.m.67.4		8
7.2	even	3	inner	147.8.e.m.79.4		8
7.3	odd	6		147.8.a.g.1.1	yes	4
7.4	even	3		147.8.a.f.1.1	✓	4
7.5	odd	6		147.8.e.l.79.4		8
7.6	odd	2		147.8.e.l.67.4		8
21.11	odd	6		441.8.a.v.1.4		4
21.17	even	6		441.8.a.u.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.8.a.f.1.1	✓	4	7.4	even	3
147.8.a.g.1.1	yes	4	7.3	odd	6
147.8.e.l.67.4		8	7.6	odd	2
147.8.e.l.79.4		8	7.5	odd	6
147.8.e.m.67.4		8	1.1	even	1	trivial
147.8.e.m.79.4		8	7.2	even	3	inner
441.8.a.u.1.4		4	21.17	even	6
441.8.a.v.1.4		4	21.11	odd	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)

\(f(q)\)	\(=\)	\(q+(10.8306 + 18.7592i) q^{2} +(13.5000 - 23.3827i) q^{3} +(-170.605 + 295.496i) q^{4} +(258.468 + 447.680i) q^{5} +584.853 q^{6} -4618.37 q^{8} +(-364.500 - 631.333i) q^{9} +O(q^{10})\)	\(q+(10.8306 + 18.7592i) q^{2} +(13.5000 - 23.3827i) q^{3} +(-170.605 + 295.496i) q^{4} +(258.468 + 447.680i) q^{5} +584.853 q^{6} -4618.37 q^{8} +(-364.500 - 631.333i) q^{9} +(-5598.75 + 9697.31i) q^{10} +(-331.291 + 573.812i) q^{11} +(4606.32 + 7978.39i) q^{12} -7851.30 q^{13} +13957.3 q^{15} +(-28182.5 - 48813.5i) q^{16} +(5816.29 - 10074.1i) q^{17} +(7895.52 - 13675.4i) q^{18} +(7492.78 + 12977.9i) q^{19} -176384. q^{20} -14352.3 q^{22} +(13092.5 + 22676.9i) q^{23} +(-62348.0 + 107990. i) q^{24} +(-94549.3 + 163764. i) q^{25} +(-85034.5 - 147284. i) q^{26} -19683.0 q^{27} +108612. q^{29} +(151166. + 261827. i) q^{30} +(-97816.2 + 169423. i) q^{31} +(314891. - 545407. i) q^{32} +(8944.85 + 15492.9i) q^{33} +251976. q^{34} +248741. q^{36} +(-163284. - 282817. i) q^{37} +(-162303. + 281117. i) q^{38} +(-105993. + 183585. i) q^{39} +(-1.19370e6 - 2.06756e6i) q^{40} +79193.0 q^{41} +638173. q^{43} +(-113039. - 195790. i) q^{44} +(188423. - 326359. i) q^{45} +(-283600. + 491209. i) q^{46} +(-388420. - 672763. i) q^{47} -1.52185e6 q^{48} -4.09611e6 q^{50} +(-157040. - 272001. i) q^{51} +(1.33947e6 - 2.32003e6i) q^{52} +(464108. - 803859. i) q^{53} +(-213179. - 369237. i) q^{54} -342513. q^{55} +404610. q^{57} +(1.17633e6 + 2.03747e6i) q^{58} +(-1.14747e6 + 1.98747e6i) q^{59} +(-2.38118e6 + 4.12432e6i) q^{60} +(1.21824e6 + 2.11006e6i) q^{61} -4.23764e6 q^{62} +6.42715e6 q^{64} +(-2.02931e6 - 3.51487e6i) q^{65} +(-193756. + 335596. i) q^{66} +(875450. - 1.51632e6i) q^{67} +(1.98457e6 + 3.43738e6i) q^{68} +706995. q^{69} -1.22315e6 q^{71} +(1.68340e6 + 2.91573e6i) q^{72} +(232080. - 401974. i) q^{73} +(3.53694e6 - 6.12616e6i) q^{74} +(2.55283e6 + 4.42164e6i) q^{75} -5.11321e6 q^{76} -4.59186e6 q^{78} +(-866218. - 1.50033e6i) q^{79} +(1.45686e7 - 2.52335e7i) q^{80} +(-265720. + 460241. i) q^{81} +(857709. + 1.48560e6i) q^{82} -3.98160e6 q^{83} +6.01330e6 q^{85} +(6.91181e6 + 1.19716e7i) q^{86} +(1.46626e6 - 2.53964e6i) q^{87} +(1.53002e6 - 2.65008e6i) q^{88} +(-3.91627e6 - 6.78318e6i) q^{89} +8.16297e6 q^{90} -8.93456e6 q^{92} +(2.64104e6 + 4.57441e6i) q^{93} +(8.41366e6 - 1.45729e7i) q^{94} +(-3.87330e6 + 6.70874e6i) q^{95} +(-8.50206e6 - 1.47260e7i) q^{96} +4.49108e6 q^{97} +483022. 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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