LMFDB - Embedded newform 81.10.e.a.10.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,10,Mod(10,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("81.10");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	81.e (of order $9$, degree $6$, 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:	$41.7179027293$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			10.18
Character	$\chi$	$=$	81.10
Dual form			81.10.e.a.73.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.18108 + 18.0408i) q^{2} +(165.772 - 60.3360i) q^{4} +(1375.78 + 1154.42i) q^{5} +(2117.11 + 770.566i) q^{7} +(6305.53 + 10921.5i) q^{8} +(-16450.1 + 28492.4i) q^{10} +(-43252.3 + 36293.0i) q^{11} +(1069.11 - 6063.22i) q^{13} +(-7166.92 + 40645.6i) q^{14} +(-107783. + 90440.9i) q^{16} +(148706. - 257567. i) q^{17} +(362187. + 627326. i) q^{19} +(297718. + 108360. i) q^{20} +(-792343. - 664854. i) q^{22} +(217677. - 79228.1i) q^{23} +(220935. + 1.25299e6i) q^{25} +112786. q^{26} +397450. q^{28} +(187265. + 1.06204e6i) q^{29} +(-1.23107e6 + 448073. i) q^{31} +(2.97175e6 + 2.49360e6i) q^{32} +(5.11976e6 + 1.86344e6i) q^{34} +(2.02312e6 + 3.50415e6i) q^{35} +(6.85780e6 - 1.18781e7i) q^{37} +(-1.01653e7 + 8.52971e6i) q^{38} +(-3.93293e6 + 2.23048e7i) q^{40} +(-5.65192e6 + 3.20536e7i) q^{41} +(-1.65654e6 + 1.39000e6i) q^{43} +(-4.98023e6 + 8.62601e6i) q^{44} +(2.12179e6 + 3.67504e6i) q^{46} +(-2.89113e7 - 1.05228e7i) q^{47} +(-2.70243e7 - 2.26760e7i) q^{49} +(-2.19020e7 + 7.97169e6i) q^{50} +(-188602. - 1.06962e6i) q^{52} +9.69683e7 q^{53} -1.01403e8 q^{55} +(4.93378e6 + 2.79809e7i) q^{56} +(-1.85643e7 + 6.75684e6i) q^{58} +(-2.96299e7 - 2.48624e7i) q^{59} +(-1.84497e8 - 6.71515e7i) q^{61} +(-1.19997e7 - 2.07841e7i) q^{62} +(-7.15525e7 + 1.23933e8i) q^{64} +(8.47032e6 - 7.10745e6i) q^{65} +(-1.16980e7 + 6.63426e7i) q^{67} +(9.11076e6 - 5.16697e7i) q^{68} +(-5.67820e7 + 4.76458e7i) q^{70} +(-1.99027e8 + 3.44726e8i) q^{71} +(8.45049e7 + 1.46367e8i) q^{73} +(2.36105e8 + 8.59351e7i) q^{74} +(9.78906e7 + 8.21400e7i) q^{76} +(-1.19536e8 + 4.35076e7i) q^{77} +(-7.52500e6 - 4.26764e7i) q^{79} -2.52692e8 q^{80} -5.96252e8 q^{82} +(-5.13521e7 - 2.91232e8i) q^{83} +(5.01926e8 - 1.82686e8i) q^{85} +(-3.03464e7 - 2.54636e7i) q^{86} +(-6.69102e8 - 2.43533e8i) q^{88} +(5.24736e8 + 9.08869e8i) q^{89} +(6.93553e6 - 1.20127e7i) q^{91} +(3.13044e7 - 2.62675e7i) q^{92} +(9.78714e7 - 5.55056e8i) q^{94} +(-2.25906e8 + 1.28117e9i) q^{95} +(1.08650e9 - 9.11682e8i) q^{97} +(3.23128e8 - 5.59673e8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) $ 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	3.18108	+	18.0408i	0.140585	+	0.797298i	0.970806	+	0.239864i	$0.0771029\pi$
$2$	3.18108	+	18.0408i	0.140585	+	0.797298i	−0.830221	+	0.557434i	$0.811786\pi$
$3$		0			0
$3$		0			0
$4$	165.772	−	60.3360i	0.323773	−	0.117844i
$5$	1375.78	+	1154.42i	0.984427	+	0.826032i	0.984751	−	0.173968i	$-0.0556589\pi$
$5$	1375.78	+	1154.42i	0.984427	+	0.826032i	−0.000324567		1.00000i	$0.500103\pi$
$6$		0			0
$7$	2117.11	+	770.566i	0.333275	+	0.121302i	0.503237	−	0.864148i	$-0.332142\pi$
$7$	2117.11	+	770.566i	0.333275	+	0.121302i	−0.169962	+	0.985451i	$0.554364\pi$
$8$	6305.53	+	10921.5i	0.544273	+	0.942708i
$9$		0			0
$10$	−16450.1	+	28492.4i	−0.520198	+	0.901009i
$11$	−43252.3	+	36293.0i	−0.890721	+	0.747404i	−0.968355	−	0.249578i	$-0.919708\pi$
$11$	−43252.3	+	36293.0i	−0.890721	+	0.747404i	0.0776335	+	0.996982i	$0.475264\pi$
$12$		0			0
$13$	1069.11	−	6063.22i	0.0103819	−	0.0588787i	−0.979177	−	0.203010i	$-0.934928\pi$
$13$	1069.11	−	6063.22i	0.0103819	−	0.0588787i	0.989559	+	0.144131i	$0.0460387\pi$
$14$	−7166.92	+	40645.6i	−0.0498605	+	0.282773i
$15$		0			0
$16$	−107783.	+	90440.9i	−0.411161	+	0.345005i
$17$	148706.	−	257567.i	0.431827	−	0.747946i	−0.565204	−	0.824951i	$-0.691203\pi$
$17$	148706.	−	257567.i	0.431827	−	0.747946i	0.997031	+	0.0770054i	$0.0245359\pi$
$18$		0			0
$19$	362187.	+	627326.i	0.637590	+	1.10434i	0.985960	+	0.166981i	$0.0534018\pi$
$19$	362187.	+	627326.i	0.637590	+	1.10434i	−0.348371	+	0.937357i	$0.613265\pi$
$20$	297718.	+	108360.i	0.416073	+	0.151438i
$21$		0			0
$22$	−792343.	−	664854.i	−0.721126	−	0.605096i
$23$	217677.	−	79228.1i	0.162195	−	0.0590342i	−0.259646	−	0.965704i	$-0.583606\pi$
$23$	217677.	−	79228.1i	0.162195	−	0.0590342i	0.421842	+	0.906670i	$0.361384\pi$
$24$		0			0
$25$	220935.	+	1.25299e6i	0.113119	+	0.641529i
$26$	112786.			0.0484034
$27$		0			0
$28$	397450.			0.122200
$29$	187265.	+	1.06204e6i	0.0491662	+	0.278835i	0.999472	−	0.0324815i	$-0.0103410\pi$
$29$	187265.	+	1.06204e6i	0.0491662	+	0.278835i	−0.950306	+	0.311317i	$0.899230\pi$
$30$		0			0
$31$	−1.23107e6	+	448073.i	−0.239417	+	0.0871407i	−0.458942	−	0.888466i	$-0.651771\pi$
$31$	−1.23107e6	+	448073.i	−0.239417	+	0.0871407i	0.219525	+	0.975607i	$0.429549\pi$
$32$	2.97175e6	+	2.49360e6i	0.501000	+	0.420389i
$33$		0			0
$34$	5.11976e6	+	1.86344e6i	0.657044	+	0.239144i
$35$	2.02312e6	+	3.50415e6i	0.227885	+	0.394709i
$36$		0			0
$37$	6.85780e6	−	1.18781e7i	0.601558	−	1.04193i	−0.391028	−	0.920379i	$-0.627880\pi$
$37$	6.85780e6	−	1.18781e7i	0.601558	−	1.04193i	0.992585	−	0.121549i	$-0.0387863\pi$
$38$	−1.01653e7	+	8.52971e6i	−0.790850	+	0.663602i
$39$		0			0
$40$	−3.93293e6	+	2.23048e7i	−0.242911	+	1.37761i
$41$	−5.65192e6	+	3.20536e7i	−0.312370	+	1.77154i	0.274235	+	0.961663i	$0.411575\pi$
$41$	−5.65192e6	+	3.20536e7i	−0.312370	+	1.77154i	−0.586605	+	0.809873i	$0.699536\pi$
$42$		0			0
$43$	−1.65654e6	+	1.39000e6i	−0.0738915	+	0.0620023i	−0.678985	−	0.734152i	$-0.737580\pi$
$43$	−1.65654e6	+	1.39000e6i	−0.0738915	+	0.0620023i	0.605094	+	0.796154i	$0.293136\pi$
$44$	−4.98023e6	+	8.62601e6i	−0.200315	+	0.346955i
$45$		0			0
$46$	2.12179e6	+	3.67504e6i	0.0698701	+	0.121019i
$47$	−2.89113e7	−	1.05228e7i	−0.864225	−	0.314552i	−0.128399	−	0.991723i	$-0.540984\pi$
$47$	−2.89113e7	−	1.05228e7i	−0.864225	−	0.314552i	−0.735826	+	0.677170i	$0.763206\pi$
$48$		0			0
$49$	−2.70243e7	−	2.26760e7i	−0.669686	−	0.561934i
$50$	−2.19020e7	+	7.97169e6i	−0.495587	+	0.180379i
$51$		0			0
$52$	−188602.	−	1.06962e6i	−0.00357710	−	0.0202868i
$53$	9.69683e7			1.68806			0.844031	−	0.536294i	$-0.180176\pi$
$53$	9.69683e7			1.68806			0.844031	+	0.536294i	$0.180176\pi$
$54$		0			0
$55$	−1.01403e8			−1.49423
$56$	4.93378e6	+	2.79809e7i	0.0670400	+	0.380203i
$57$		0			0
$58$	−1.85643e7	+	6.75684e6i	−0.215403	+	0.0784002i
$59$	−2.96299e7	−	2.48624e7i	−0.318343	−	0.267122i	0.469587	−	0.882886i	$-0.344403\pi$
$59$	−2.96299e7	−	2.48624e7i	−0.318343	−	0.267122i	−0.787930	+	0.615764i	$0.788847\pi$
$60$		0			0
$61$	−1.84497e8	−	6.71515e7i	−1.70610	−	0.620971i	−0.709608	−	0.704597i	$-0.751128\pi$
$61$	−1.84497e8	−	6.71515e7i	−1.70610	−	0.620971i	−0.996497	+	0.0836257i	$0.973350\pi$
$62$	−1.19997e7	−	2.07841e7i	−0.103136	−	0.178636i
$63$		0			0
$64$	−7.15525e7	+	1.23933e8i	−0.533108	+	0.923370i
$65$	8.47032e6	−	7.10745e6i	0.0588559	−	0.0493859i
$66$		0			0
$67$	−1.16980e7	+	6.63426e7i	−0.0709210	+	0.402213i	0.928595	+	0.371095i	$0.121018\pi$
$67$	−1.16980e7	+	6.63426e7i	−0.0709210	+	0.402213i	−0.999516	+	0.0311174i	$0.990093\pi$
$68$	9.11076e6	−	5.16697e7i	0.0516731	−	0.293053i
$69$		0			0
$70$	−5.67820e7	+	4.76458e7i	−0.282663	+	0.237183i
$71$	−1.99027e8	+	3.44726e8i	−0.929502	+	1.60994i	−0.145346	+	0.989381i	$0.546430\pi$
$71$	−1.99027e8	+	3.44726e8i	−0.929502	+	1.60994i	−0.784156	+	0.620564i	$0.786904\pi$
$72$		0			0
$73$	8.45049e7	+	1.46367e8i	0.348280	+	0.603239i	0.985944	−	0.167076i	$-0.0534324\pi$
$73$	8.45049e7	+	1.46367e8i	0.348280	+	0.603239i	−0.637664	+	0.770315i	$0.720099\pi$
$74$	2.36105e8	+	8.59351e7i	0.915297	+	0.333141i
$75$		0			0
$76$	9.78906e7	+	8.21400e7i	0.336573	+	0.282419i
$77$	−1.19536e8	+	4.35076e7i	−0.387517	+	0.141045i
$78$		0			0
$79$	−7.52500e6	−	4.26764e7i	−0.0217362	−	0.123272i	0.972009	−	0.234944i	$-0.0754907\pi$
$79$	−7.52500e6	−	4.26764e7i	−0.0217362	−	0.123272i	−0.993745	+	0.111672i	$0.964380\pi$
$80$	−2.52692e8			−0.689743
$81$		0			0
$82$	−5.96252e8			−1.45636
$83$	−5.13521e7	−	2.91232e8i	−0.118770	−	0.673578i	−0.984814	−	0.173611i	$-0.944456\pi$
$83$	−5.13521e7	−	2.91232e8i	−0.118770	−	0.673578i	0.866044	−	0.499967i	$-0.166655\pi$
$84$		0			0
$85$	5.01926e8	−	1.82686e8i	1.04293	−	0.379595i
$86$	−3.03464e7	−	2.54636e7i	−0.0598224	−	0.0501969i
$87$		0			0
$88$	−6.69102e8	−	2.43533e8i	−1.18938	−	0.432899i
$89$	5.24736e8	+	9.08869e8i	0.886514	+	1.53549i	0.843968	+	0.536393i	$0.180213\pi$
$89$	5.24736e8	+	9.08869e8i	0.886514	+	1.53549i	0.0425457	+	0.999095i	$0.486453\pi$
$90$		0			0
$91$	6.93553e6	−	1.20127e7i	0.0106021	−	0.0183634i
$92$	3.13044e7	−	2.62675e7i	0.0455576	−	0.0382274i
$93$		0			0
$94$	9.78714e7	−	5.55056e8i	0.129295	−	0.733266i
$95$	−2.25906e8	+	1.28117e9i	−0.284558	+	1.61381i
$96$		0			0
$97$	1.08650e9	−	9.11682e8i	1.24611	−	1.04561i	0.249091	−	0.968480i	$-0.419868\pi$
$97$	1.08650e9	−	9.11682e8i	1.24611	−	1.04561i	0.997021	−	0.0771321i	$-0.0245763\pi$
$98$	3.23128e8	−	5.59673e8i	0.353881	−	0.612939i
$99$		0			0
$100$	1.12225e8	+	1.94379e8i	0.112225	+	0.194379i
$101$	−1.17960e9	−	4.29339e8i	−1.12795	−	0.410539i	−0.290401	−	0.956905i	$-0.593789\pi$
$101$	−1.17960e9	−	4.29339e8i	−1.12795	−	0.410539i	−0.837547	+	0.546366i	$0.816011\pi$
$102$		0			0
$103$	1.53524e9	+	1.28822e9i	1.34403	+	1.12777i	0.980571	+	0.196164i	$0.0628483\pi$
$103$	1.53524e9	+	1.28822e9i	1.34403	+	1.12777i	0.363458	+	0.931611i	$0.381596\pi$
$104$	7.29607e7	−	2.65555e7i	0.0611560	−	0.0222590i
$105$		0			0
$106$	3.08464e8	+	1.74939e9i	0.237316	+	1.34589i
$107$	1.33848e9			0.987151			0.493575	−	0.869703i	$-0.335690\pi$
$107$	1.33848e9			0.987151			0.493575	+	0.869703i	$0.335690\pi$
$108$		0			0
$109$	−2.51911e8			−0.170934			−0.0854669	−	0.996341i	$-0.527238\pi$
$109$	−2.51911e8			−0.170934			−0.0854669	+	0.996341i	$0.527238\pi$
$110$	−3.22570e8	−	1.82938e9i	−0.210066	−	1.19135i
$111$		0			0
$112$	−2.97880e8	+	1.08419e8i	−0.178879	+	0.0651068i
$113$	−1.64771e8	−	1.38259e8i	−0.0950664	−	0.0797701i	0.594016	−	0.804453i	$-0.297542\pi$
$113$	−1.64771e8	−	1.38259e8i	−0.0950664	−	0.0797701i	−0.689082	+	0.724683i	$0.741986\pi$
$114$		0			0
$115$	3.90938e8	+	1.42290e8i	0.208433	+	0.0758636i
$116$	9.51223e7	+	1.64757e8i	0.0487777	+	0.0844854i
$117$		0			0
$118$	3.54283e8	−	6.13636e8i	0.168221	−	0.291368i
$119$	5.13301e8	−	4.30710e8i	0.234644	−	0.196890i
$120$		0			0
$121$	1.44126e8	−	8.17380e8i	0.0611235	−	0.346649i
$122$	6.24566e8	−	3.54209e9i	0.255246	−	1.44757i
$123$		0			0
$124$	−1.77042e8	+	1.48556e8i	−0.0672478	+	0.0564276i
$125$	6.11351e8	−	1.05889e9i	0.223973	−	0.387932i
$126$		0			0
$127$	−2.27429e9	−	3.93918e9i	−0.775762	−	1.34366i	−0.934365	−	0.356317i	$-0.884032\pi$
$127$	−2.27429e9	−	3.93918e9i	−0.775762	−	1.34366i	0.158603	−	0.987342i	$-0.449301\pi$
$128$	−5.97016e8	−	2.17296e8i	−0.196581	−	0.0715496i
$129$		0			0
$130$	1.55169e8	+	1.30202e8i	0.0476496	+	0.0399827i
$131$	2.93411e9	−	1.06793e9i	0.870474	−	0.316826i	0.132115	−	0.991234i	$-0.457823\pi$
$131$	2.93411e9	−	1.06793e9i	0.870474	−	0.316826i	0.738359	+	0.674408i	$0.235601\pi$
$132$		0			0
$133$	2.83394e8	+	1.60721e9i	0.0785341	+	0.445389i
$134$	−1.23408e9			−0.330654
$135$		0			0
$136$	3.75069e9			0.940126
$137$	−1.00171e9	−	5.68098e9i	−0.242940	−	1.37778i	−0.825228	−	0.564799i	$-0.808954\pi$
$137$	−1.00171e9	−	5.68098e9i	−0.242940	−	1.37778i	0.582288	−	0.812983i	$-0.302158\pi$
$138$		0			0
$139$	5.68111e9	−	2.06775e9i	1.29082	−	0.469821i	0.396825	−	0.917894i	$-0.370112\pi$
$139$	5.68111e9	−	2.06775e9i	1.29082	−	0.469821i	0.893997	+	0.448073i	$0.147890\pi$
$140$	5.46803e8	+	4.58822e8i	0.120297	+	0.100941i
$141$		0			0
$142$	−6.85225e9	−	2.49401e9i	−1.41428	−	0.514756i
$143$	1.73811e8	+	3.01049e8i	0.0347588	+	0.0602039i
$144$		0			0
$145$	−9.68394e8	+	1.67731e9i	−0.181927	+	0.315106i
$146$	−2.37176e9	+	1.99014e9i	−0.431998	+	0.362490i
$147$		0			0
$148$	4.20155e8	−	2.38282e9i	0.0719834	−	0.408238i
$149$	6.81322e8	−	3.86397e9i	0.113244	−	0.642238i	−0.874361	−	0.485276i	$-0.838719\pi$
$149$	6.81322e8	−	3.86397e9i	0.113244	−	0.642238i	0.987605	−	0.156961i	$-0.0501698\pi$
$150$		0			0
$151$	1.79025e9	−	1.50220e9i	0.280232	−	0.235142i	−0.491828	−	0.870692i	$-0.663671\pi$
$151$	1.79025e9	−	1.50220e9i	0.280232	−	0.235142i	0.772060	+	0.635550i	$0.219227\pi$
$152$	−4.56756e9	+	7.91124e9i	−0.694046	+	1.20212i
$153$		0			0
$154$	−1.16516e9	−	2.01812e9i	−0.166934	−	0.289138i
$155$	−2.21094e9	−	8.04717e8i	−0.307670	−	0.111983i
$156$		0			0
$157$	3.55156e9	+	2.98011e9i	0.466521	+	0.391457i	0.845523	−	0.533938i	$-0.179289\pi$
$157$	3.55156e9	+	2.98011e9i	0.466521	+	0.391457i	−0.379003	+	0.925395i	$0.623733\pi$
$158$	7.45978e8	−	2.71514e8i	0.0952290	−	0.0346605i
$159$		0			0
$160$	1.20983e9	+	6.86127e9i	0.145943	+	0.827684i
$161$	5.21898e8			0.0612166
$162$		0			0
$163$	−3.94377e9			−0.437589			−0.218795	−	0.975771i	$-0.570213\pi$
$163$	−3.94377e9			−0.437589			−0.218795	+	0.975771i	$0.570213\pi$
$164$	9.97059e8	+	5.65460e9i	0.107628	+	0.610386i
$165$		0			0
$166$	5.09070e9	−	1.85286e9i	0.520345	−	0.189390i
$167$	2.15951e9	+	1.81205e9i	0.214848	+	0.180279i	0.743860	−	0.668335i	$-0.232993\pi$
$167$	2.15951e9	+	1.81205e9i	0.214848	+	0.180279i	−0.529012	+	0.848614i	$0.677437\pi$
$168$		0			0
$169$	9.92935e9	+	3.61399e9i	0.936334	+	0.340798i
$170$	4.89247e9	+	8.47401e9i	0.449271	+	0.778160i
$171$		0			0
$172$	−1.90741e8	+	3.30373e8i	−0.0166175	+	0.0287823i
$173$	−6.23242e9	+	5.22962e9i	−0.528992	+	0.443877i	−0.867753	−	0.496995i	$-0.834437\pi$
$173$	−6.23242e9	+	5.22962e9i	−0.528992	+	0.443877i	0.338761	+	0.940872i	$0.389992\pi$
$174$		0			0
$175$	−4.97763e8	+	2.82296e9i	−0.0401191	+	0.227527i
$176$	1.37950e9	−	7.82355e9i	0.108372	−	0.614606i
$177$		0			0
$178$	−1.47275e10	+	1.23578e10i	−1.09961	+	0.922683i
$179$	−7.06096e9	+	1.22299e10i	−0.514073	+	0.890401i	0.485793	+	0.874074i	$0.338531\pi$
$179$	−7.06096e9	+	1.22299e10i	−0.514073	+	0.890401i	−0.999867	+	0.0163276i	$0.994803\pi$
$180$		0			0
$181$	−8.52987e9	−	1.47742e10i	−0.590730	−	1.02317i	−0.994134	−	0.108152i	$-0.965507\pi$
$181$	−8.52987e9	−	1.47742e10i	−0.590730	−	1.02317i	0.403405	−	0.915022i	$-0.367827\pi$
$182$	2.38781e8	+	8.69091e7i	0.0161316	+	0.00587143i
$183$		0			0
$184$	2.23786e9	+	1.87779e9i	0.143931	+	0.120772i
$185$	2.31470e10	−	8.42483e9i	1.45286	−	0.528796i
$186$		0			0
$187$	2.91598e9	+	1.65374e10i	0.174380	+	0.988960i
$188$	−5.42758e9			−0.316881
$189$		0			0
$190$	−2.38320e10			−1.32669
$191$	−4.29151e8	−	2.43384e9i	−0.0233324	−	0.132325i	0.970917	−	0.239418i	$-0.0769567\pi$
$191$	−4.29151e8	−	2.43384e9i	−0.0233324	−	0.132325i	−0.994249	+	0.107093i	$0.965846\pi$
$192$		0			0
$193$	−1.80403e10	+	6.56614e9i	−0.935915	+	0.340645i	−0.764551	−	0.644563i	$-0.777039\pi$
$193$	−1.80403e10	+	6.56614e9i	−0.935915	+	0.340645i	−0.171363	+	0.985208i	$0.554817\pi$
$194$	1.99037e10	+	1.67012e10i	1.00885	+	0.846525i
$195$		0			0
$196$	−5.84804e9	−	2.12851e9i	−0.283047	−	0.103021i
$197$	−1.69840e9	−	2.94172e9i	−0.0803419	−	0.139156i	0.823055	−	0.567962i	$-0.192268\pi$
$197$	−1.69840e9	−	2.94172e9i	−0.0803419	−	0.139156i	−0.903397	+	0.428806i	$0.858935\pi$
$198$		0			0
$199$	2.03141e10	−	3.51850e10i	0.918245	−	1.59045i	0.116166	−	0.993230i	$-0.462940\pi$
$199$	2.03141e10	−	3.51850e10i	0.918245	−	1.59045i	0.802079	−	0.597217i	$-0.203727\pi$
$200$	−1.22914e10	+	1.03137e10i	−0.543207	+	0.455805i
$201$		0			0
$202$	3.99322e9	−	2.26467e10i	0.168749	−	0.957026i
$203$	−4.21906e8	+	2.39275e9i	−0.0174375	+	0.0988929i
$204$		0			0
$205$	−4.47790e10	+	3.75740e10i	−1.77085	+	1.48592i
$206$	−1.83568e10	+	3.17949e10i	−0.710222	+	1.23014i
$207$		0			0
$208$	4.33131e8	+	7.50205e8i	0.0160448	+	0.0277904i
$209$	−3.84329e10	−	1.39884e10i	−1.39330	−	0.507120i
$210$		0			0
$211$	2.19100e10	+	1.83847e10i	0.760978	+	0.638536i	0.938381	−	0.345602i	$-0.112325\pi$
$211$	2.19100e10	+	1.83847e10i	0.760978	+	0.638536i	−0.177404	+	0.984138i	$0.556770\pi$
$212$	1.60746e10	−	5.85068e9i	0.546549	−	0.198927i
$213$		0			0
$214$	4.25780e9	+	2.41472e10i	0.138779	+	0.787053i
$215$	−3.88368e9			−0.123957
$216$		0			0
$217$	−2.95158e9			−0.0903621
$218$	−8.01349e8	−	4.54468e9i	−0.0240308	−	0.136285i
$219$		0			0
$220$	−1.68097e10	+	6.11823e9i	−0.483791	+	0.176085i
$221$	−1.40270e9	−	1.17701e9i	−0.0395549	−	0.0331905i
$222$		0			0
$223$	4.60395e10	+	1.67570e10i	1.24669	+	0.453758i	0.879282	−	0.476302i	$-0.158023\pi$
$223$	4.60395e10	+	1.67570e10i	1.24669	+	0.453758i	0.367408	+	0.930060i	$0.380245\pi$
$224$	4.37005e9	+	7.56915e9i	0.115977	+	0.200877i
$225$		0			0
$226$	1.97015e9	−	3.41241e9i	0.0502357	−	0.0870107i
$227$	−1.96247e10	+	1.64671e10i	−0.490554	+	0.411624i	−0.854225	−	0.519904i	$-0.825968\pi$
$227$	−1.96247e10	+	1.64671e10i	−0.490554	+	0.411624i	0.363671	+	0.931528i	$0.381523\pi$
$228$		0			0
$229$	1.28706e10	−	7.29928e10i	0.309271	−	1.75396i	−0.293417	−	0.955985i	$-0.594792\pi$
$229$	1.28706e10	−	7.29928e10i	0.309271	−	1.75396i	0.602687	−	0.797977i	$-0.294097\pi$
$230$	−1.32342e9	+	7.50546e9i	−0.0311832	+	0.176849i
$231$		0			0
$232$	−1.04182e10	+	8.74192e9i	−0.236101	+	0.198112i
$233$	1.69048e10	−	2.92800e10i	0.375758	−	0.650833i	−0.614682	−	0.788775i	$-0.710716\pi$
$233$	1.69048e10	−	2.92800e10i	0.375758	−	0.650833i	0.990440	+	0.137943i	$0.0440489\pi$
$234$		0			0
$235$	−2.76278e10	−	4.78527e10i	−0.590936	−	1.02353i
$236$	−6.41189e9	−	2.33374e9i	−0.134550	−	0.0489720i
$237$		0			0
$238$	9.40320e9	+	7.89022e9i	0.189968	+	0.159402i
$239$	2.90863e10	−	1.05866e10i	0.576631	−	0.209877i	−0.0372082	−	0.999308i	$-0.511846\pi$
$239$	2.90863e10	−	1.05866e10i	0.576631	−	0.209877i	0.613839	+	0.789431i	$0.289624\pi$
$240$		0			0
$241$	−1.35007e10	−	7.65660e10i	−0.257797	−	1.46204i	−0.788789	−	0.614664i	$-0.789292\pi$
$241$	−1.35007e10	−	7.65660e10i	−0.257797	−	1.46204i	0.530992	−	0.847377i	$-0.321819\pi$
$242$	1.52047e10			0.284975
$243$		0			0
$244$	−3.46361e10			−0.625568
$245$	−1.10018e10	−	6.23944e10i	−0.195082	−	1.10637i
$246$		0			0
$247$	4.19083e9	−	1.52534e9i	0.0716413	−	0.0260753i
$248$	−1.26562e10	−	1.06198e10i	−0.212457	−	0.178272i
$249$		0			0
$250$	2.10480e10	+	7.66084e9i	0.340785	+	0.124036i
$251$	1.34873e10	+	2.33607e10i	0.214483	+	0.371496i	0.953113	−	0.302616i	$-0.0978599\pi$
$251$	1.34873e10	+	2.33607e10i	0.214483	+	0.371496i	−0.738629	+	0.674112i	$0.764527\pi$
$252$		0			0
$253$	−6.53962e9	+	1.13269e10i	−0.100348	+	0.173808i
$254$	6.38312e10	−	5.35608e10i	0.962236	−	0.807412i
$255$		0			0
$256$	−1.07021e10	+	6.06948e10i	−0.155736	+	0.883226i
$257$	1.71316e10	−	9.71579e10i	0.244961	−	1.38925i	−0.575621	−	0.817717i	$-0.695239\pi$
$257$	1.71316e10	−	9.71579e10i	0.244961	−	1.38925i	0.820582	−	0.571529i	$-0.193649\pi$
$258$		0			0
$259$	2.36716e10	−	1.98628e10i	0.326872	−	0.274278i
$260$	9.75305e8	−	1.68928e9i	0.0132361	−	0.0229256i
$261$		0			0
$262$	2.85999e10	+	4.95365e10i	0.374981	+	0.649486i
$263$	−1.56709e10	−	5.70375e9i	−0.201973	−	0.0735122i	0.239053	−	0.971007i	$-0.423163\pi$
$263$	−1.56709e10	−	5.70375e9i	−0.201973	−	0.0735122i	−0.441026	+	0.897494i	$0.645385\pi$
$264$		0			0
$265$	1.33407e11	+	1.11942e11i	1.66177	+	1.39439i
$266$	−2.80938e10	+	1.02253e10i	−0.344067	+	0.125230i
$267$		0			0
$268$	2.06365e9	+	1.17035e10i	0.0244359	+	0.138583i
$269$	−2.61530e10			−0.304534			−0.152267	−	0.988339i	$-0.548657\pi$
$269$	−2.61530e10			−0.304534			−0.152267	+	0.988339i	$0.548657\pi$
$270$		0			0
$271$	5.12755e10			0.577494			0.288747	−	0.957405i	$-0.406761\pi$
$271$	5.12755e10			0.577494			0.288747	+	0.957405i	$0.406761\pi$
$272$	7.26653e9	+	4.12106e10i	0.0804947	+	0.456508i
$273$		0			0
$274$	9.93028e10	−	3.61433e10i	1.06435	−	0.387391i
$275$	−5.50305e10	−	4.61761e10i	−0.580238	−	0.486878i
$276$		0			0
$277$	−5.29886e10	−	1.92863e10i	−0.540783	−	0.196829i	0.0571636	−	0.998365i	$-0.481794\pi$
$277$	−5.29886e10	−	1.92863e10i	−0.540783	−	0.196829i	−0.597947	+	0.801536i	$0.704017\pi$
$278$	5.53760e10	+	9.59140e10i	0.556057	+	0.963120i
$279$		0			0
$280$	−2.55137e10	+	4.41911e10i	−0.248064	+	0.429659i
$281$	5.73227e10	−	4.80995e10i	0.548464	−	0.460216i	−0.325956	−	0.945385i	$-0.605686\pi$
$281$	5.73227e10	−	4.80995e10i	0.548464	−	0.460216i	0.874421	+	0.485169i	$0.161242\pi$
$282$		0			0
$283$	2.28233e10	−	1.29438e11i	0.211514	−	1.19956i	−0.675339	−	0.737507i	$-0.736003\pi$
$283$	2.28233e10	−	1.29438e11i	0.211514	−	1.19956i	0.886853	−	0.462051i	$-0.152886\pi$
$284$	−1.21938e10	+	6.91543e10i	−0.111226	+	0.630792i
$285$		0			0
$286$	−4.87826e9	+	4.09334e9i	−0.0431139	+	0.0361769i
$287$	−3.66652e10	+	6.35060e10i	−0.318996	+	0.552518i
$288$		0			0
$289$	1.50668e10	+	2.60964e10i	0.127051	+	0.220059i
$290$	−3.33405e10	−	1.21349e10i	−0.276809	−	0.100750i
$291$		0			0
$292$	2.28397e10	+	1.91648e10i	0.183852	+	0.154270i
$293$	1.66284e10	−	6.05226e9i	0.131810	−	0.0479748i	−0.275273	−	0.961366i	$-0.588768\pi$
$293$	1.66284e10	−	6.05226e9i	0.131810	−	0.0479748i	0.407083	+	0.913391i	$0.366546\pi$
$294$		0			0
$295$	−1.20626e10	−	6.84103e10i	−0.0927345	−	0.525924i
$296$	1.72968e11			1.30965
$297$		0			0
$298$	7.18764e10			0.527975
$299$	−2.47656e8	−	1.40453e9i	−0.00179196	−	0.0101627i
$300$		0			0
$301$	−4.57818e9	+	1.66632e9i	−0.0321472	+	0.0117006i
$302$	3.27957e10	+	2.75189e10i	0.226875	+	0.190371i
$303$		0			0
$304$	−9.57736e10	−	3.48587e10i	−0.643153	−	0.234089i
$305$	−1.76307e11	−	3.05372e11i	−1.16659	−	2.02060i
$306$		0			0
$307$	−3.51307e10	+	6.08482e10i	−0.225717	+	0.390954i	−0.956534	−	0.291620i	$-0.905806\pi$
$307$	−3.51307e10	+	6.08482e10i	−0.225717	+	0.390954i	0.730817	+	0.682573i	$0.239139\pi$
$308$	−1.71906e10	+	1.44246e10i	−0.108846	+	0.0913328i
$309$		0			0
$310$	7.48456e9	−	4.24470e10i	0.0460297	−	0.261048i
$311$	−8.16527e9	+	4.63075e10i	−0.0494935	+	0.280692i	−0.999503	−	0.0315299i	$-0.989962\pi$
$311$	−8.16527e9	+	4.63075e10i	−0.0494935	+	0.280692i	0.950009	+	0.312222i	$0.101073\pi$
$312$		0			0
$313$	1.70477e11	−	1.43047e11i	1.00396	−	0.842420i	0.0164291	−	0.999865i	$-0.494770\pi$
$313$	1.70477e11	−	1.43047e11i	1.00396	−	0.842420i	0.987528	+	0.157445i	$0.0503258\pi$
$314$	−4.24658e10	+	7.35529e10i	−0.246522	+	0.426989i
$315$		0			0
$316$	−3.82235e9	−	6.62051e9i	−0.0215645	−	0.0373508i
$317$	1.03678e11	+	3.77359e10i	0.576663	+	0.209888i	0.613853	−	0.789420i	$-0.289619\pi$
$317$	1.03678e11	+	3.77359e10i	0.576663	+	0.209888i	−0.0371906	+	0.999308i	$0.511841\pi$
$318$		0			0
$319$	−4.66441e10	−	3.91390e10i	−0.252196	−	0.211618i
$320$	−2.41510e11	+	8.79025e10i	−1.28754	+	0.468626i
$321$		0			0
$322$	1.66020e9	+	9.41545e9i	0.00860614	+	0.0488079i
$323$	2.15438e11			1.10131
$324$		0			0
$325$	7.83332e9			0.0389467
$326$	−1.25454e10	−	7.11487e10i	−0.0615186	−	0.348889i
$327$		0			0
$328$	−3.85712e11	+	1.40388e11i	−1.84006	+	0.669726i
$329$	−5.30999e10	−	4.45561e10i	−0.249869	−	0.209665i
$330$		0			0
$331$	5.41688e10	+	1.97158e10i	0.248041	+	0.0902794i	0.463049	−	0.886333i	$-0.346756\pi$
$331$	5.41688e10	+	1.97158e10i	0.248041	+	0.0902794i	−0.215008	+	0.976612i	$0.568978\pi$
$332$	−2.60845e10	−	4.51797e10i	−0.117831	−	0.204090i
$333$		0			0
$334$	−2.58212e10	+	4.47235e10i	−0.113532	+	0.196642i
$335$	−9.26807e10	+	7.77684e10i	−0.402057	+	0.337366i
$336$		0			0
$337$	−1.34280e9	+	7.61541e9i	−0.00567123	+	0.0321631i	−0.987512	−	0.157543i	$-0.949643\pi$
$337$	−1.34280e9	+	7.61541e9i	−0.00567123	+	0.0321631i	0.981841	+	0.189707i	$0.0607537\pi$
$338$	−3.36132e10	+	1.90630e11i	−0.140083	+	0.794448i
$339$		0			0
$340$	7.21826e10	−	6.05684e10i	0.292939	−	0.245805i
$341$	3.69847e10	−	6.40594e10i	0.148125	−	0.256559i
$342$		0			0
$343$	−8.51980e10	−	1.47567e11i	−0.332358	−	0.575661i
$344$	−2.56263e10	−	9.32722e9i	−0.0986673	−	0.0359120i
$345$		0			0
$346$	−1.14172e11	−	9.58019e10i	−0.428271	−	0.359362i
$347$	−2.93769e10	+	1.06923e10i	−0.108774	+	0.0395904i	−0.395834	−	0.918322i	$-0.629544\pi$
$347$	−2.93769e10	+	1.06923e10i	−0.108774	+	0.0395904i	0.287060	+	0.957913i	$0.407322\pi$
$348$		0			0
$349$	6.18876e10	+	3.50982e11i	0.223300	+	1.26640i	0.865908	+	0.500203i	$0.166741\pi$
$349$	6.18876e10	+	3.50982e11i	0.223300	+	1.26640i	−0.642608	+	0.766195i	$0.722148\pi$
$350$	−5.25118e10			−0.187047
$351$		0			0
$352$	−2.19035e11			−0.760451
$353$	4.91097e10	+	2.78515e11i	0.168338	+	0.954690i	0.945556	+	0.325459i	$0.105519\pi$
$353$	4.91097e10	+	2.78515e11i	0.168338	+	0.954690i	−0.777219	+	0.629231i	$0.783370\pi$
$354$		0			0
$355$	−6.71774e11	+	2.44506e11i	−2.24489	+	0.817074i
$356$	1.41824e11	+	1.19004e11i	0.467977	+	0.392679i
$357$		0			0
$358$	−2.43099e11	−	8.84809e10i	−0.782186	−	0.284692i
$359$	−1.18627e11	−	2.05467e11i	−0.376927	−	0.652856i	0.613687	−	0.789550i	$-0.289686\pi$
$359$	−1.18627e11	−	2.05467e11i	−0.376927	−	0.652856i	−0.990613	+	0.136694i	$0.956352\pi$
$360$		0			0
$361$	−1.01015e11	+	1.74962e11i	−0.313041	+	0.542203i
$362$	2.39403e11	−	2.00883e11i	0.732726	−	0.614830i
$363$		0			0
$364$	4.24917e8	−	2.40983e9i	0.00126867	−	0.00719498i
$365$	−5.27080e10	+	2.98922e11i	−0.155439	+	0.881536i
$366$		0			0
$367$	7.78478e10	−	6.53221e10i	0.224001	−	0.187959i	−0.523880	−	0.851792i	$-0.675516\pi$
$367$	7.78478e10	−	6.53221e10i	0.224001	−	0.187959i	0.747881	+	0.663833i	$0.231072\pi$
$368$	−1.62965e10	+	2.82264e10i	−0.0463212	+	0.0802307i
$369$		0			0
$370$	2.25623e11	+	3.90791e11i	0.625858	+	1.08402i
$371$	2.05293e11	+	7.47205e10i	0.562589	+	0.204766i
$372$		0			0
$373$	1.76640e11	+	1.48219e11i	0.472498	+	0.396473i	0.847705	−	0.530468i	$-0.177984\pi$
$373$	1.76640e11	+	1.48219e11i	0.472498	+	0.396473i	−0.375207	+	0.926941i	$0.622428\pi$
$374$	−2.89071e11	+	1.05213e11i	−0.763980	+	0.278066i
$375$		0			0
$376$	−6.73757e10	−	3.82107e11i	−0.173843	−	0.985915i
$377$	6.63956e9			0.0169279
$378$		0			0
$379$	4.34730e11			1.08229			0.541144	−	0.840930i	$-0.317991\pi$
$379$	4.34730e11			1.08229			0.541144	+	0.840930i	$0.317991\pi$
$380$	3.98521e10	+	2.26013e11i	0.0980450	+	0.556041i
$381$		0			0
$382$	4.25432e10	−	1.54844e10i	0.102222	−	0.0372058i
$383$	2.21788e11	+	1.86102e11i	0.526675	+	0.441933i	0.866952	−	0.498392i	$-0.166076\pi$
$383$	2.21788e11	+	1.86102e11i	0.526675	+	0.441933i	−0.340276	+	0.940326i	$0.610521\pi$
$384$		0			0
$385$	−2.14681e11	−	7.81374e10i	−0.497989	−	0.181253i
$386$	−1.75846e11	−	3.04574e11i	−0.403171	−	0.698313i
$387$		0			0
$388$	1.25104e11	−	2.16686e11i	0.280238	−	0.485387i
$389$	−3.46880e11	+	2.91067e11i	−0.768080	+	0.644496i	−0.940216	−	0.340577i	$-0.889377\pi$
$389$	−3.46880e11	+	2.91067e11i	−0.768080	+	0.644496i	0.172136	+	0.985073i	$0.444933\pi$
$390$		0			0
$391$	1.19635e10	−	6.78482e10i	0.0258858	−	0.146806i
$392$	7.72541e10	−	4.38130e11i	0.165247	−	0.937164i
$393$		0			0
$394$	4.76681e10	−	3.99983e10i	0.0996541	−	0.0836197i
$395$	3.89135e10	−	6.74002e10i	0.0804292	−	0.139307i
$396$		0			0
$397$	2.26479e11	+	3.92272e11i	0.457583	+	0.792557i	0.998833	−	0.0483051i	$-0.0153820\pi$
$397$	2.26479e11	+	3.92272e11i	0.457583	+	0.792557i	−0.541250	+	0.840862i	$0.682049\pi$
$398$	6.99387e11	+	2.54556e11i	1.39715	+	0.508522i
$399$		0			0
$400$	−1.37134e11	−	1.15069e11i	−0.267840	−	0.224745i
$401$	−1.70866e9	+	6.21902e8i	−0.00329994	+	0.00120108i	−0.343670	−	0.939091i	$-0.611670\pi$
$401$	−1.70866e9	+	6.21902e8i	−0.00329994	+	0.00120108i	0.340370	+	0.940292i	$0.389448\pi$
$402$		0			0
$403$	1.40062e9	+	7.94329e9i	0.00264513	+	0.0150013i
$404$	−2.21449e11			−0.413578
$405$		0			0
$406$	−4.45092e10			−0.0812985
$407$	1.34475e11	+	7.62643e11i	0.242921	+	1.37767i
$408$		0			0
$409$	−9.05323e10	+	3.29511e10i	−0.159974	+	0.0582257i	−0.420766	−	0.907169i	$-0.638239\pi$
$409$	−9.05323e10	+	3.29511e10i	−0.159974	+	0.0582257i	0.260792	+	0.965395i	$0.416016\pi$
$410$	−8.20311e11	−	6.88323e11i	−1.43368	−	1.20300i
$411$		0			0
$412$	3.32225e11	+	1.20920e11i	0.568061	+	0.206757i
$413$	−4.35716e10	−	7.54683e10i	−0.0736934	−	0.127641i
$414$		0			0
$415$	2.65554e11	−	4.59953e11i	0.439477	−	0.761196i
$416$	1.82963e10	−	1.53524e10i	0.0299533	−	0.0251338i
$417$		0			0
$418$	1.30104e11	−	7.37858e11i	0.208448	−	1.18217i
$419$	7.72259e10	−	4.37970e11i	0.122405	−	0.694194i	−0.860410	−	0.509602i	$-0.829793\pi$
$419$	7.72259e10	−	4.37970e11i	0.122405	−	0.694194i	0.982815	−	0.184592i	$-0.0590964\pi$
$420$		0			0
$421$	5.52249e11	−	4.63392e11i	0.856772	−	0.718917i	−0.104498	−	0.994525i	$-0.533324\pi$
$421$	5.52249e11	−	4.63392e11i	0.856772	−	0.718917i	0.961270	+	0.275608i	$0.0888791\pi$
$422$	−2.61977e11	+	4.53757e11i	−0.402121	+	0.696494i
$423$		0			0
$424$	6.11437e11	+	1.05904e12i	0.918767	+	1.59135i
$425$	3.55582e11	+	1.29421e11i	0.528676	+	0.192422i
$426$		0			0
$427$	−3.38857e11	−	2.84335e11i	−0.493277	−	0.413908i
$428$	2.21881e11	−	8.07582e10i	0.319613	−	0.116329i
$429$		0			0
$430$	−1.23543e10	−	7.00646e10i	−0.0174265	−	0.0988304i
$431$	2.95889e11			0.413029			0.206515	−	0.978443i	$-0.433788\pi$
$431$	2.95889e11			0.413029			0.206515	+	0.978443i	$0.433788\pi$
$432$		0			0
$433$	4.31646e11			0.590109			0.295054	−	0.955480i	$-0.404662\pi$
$433$	4.31646e11			0.590109			0.295054	+	0.955480i	$0.404662\pi$
$434$	−9.38922e9	−	5.32489e10i	−0.0127036	−	0.0720455i
$435$		0			0
$436$	−4.17597e10	+	1.51993e10i	−0.0553437	+	0.0201435i
$437$	1.28542e11	+	1.07859e11i	0.168608	+	0.141479i
$438$		0			0
$439$	6.01837e11	+	2.19051e11i	0.773373	+	0.281485i	0.698406	−	0.715701i	$-0.253893\pi$
$439$	6.01837e11	+	2.19051e11i	0.773373	+	0.281485i	0.0749663	+	0.997186i	$0.476115\pi$
$440$	−6.39398e11	−	1.10747e12i	−0.813269	−	1.40862i
$441$		0			0
$442$	1.67720e10	−	2.90500e10i	0.0209019	−	0.0362031i
$443$	−1.20640e11	+	1.01229e11i	−0.148824	+	0.124878i	−0.714160	−	0.699983i	$-0.753191\pi$
$443$	−1.20640e11	+	1.01229e11i	−0.148824	+	0.124878i	0.565336	+	0.824861i	$0.308747\pi$
$444$		0			0
$445$	−3.27292e11	+	1.85617e12i	−0.395654	+	2.24386i
$446$	−1.55854e11	+	8.83894e11i	−0.186514	+	1.05778i
$447$		0			0
$448$	−2.46983e11	+	2.07243e11i	−0.289678	+	0.243069i
$449$	1.21206e11	−	2.09934e11i	0.140739	−	0.243767i	−0.787036	−	0.616907i	$-0.788386\pi$
$449$	1.21206e11	−	2.09934e11i	0.140739	−	0.243767i	0.927775	+	0.373140i	$0.121719\pi$
$450$		0			0
$451$	−9.18863e11	−	1.59152e12i	−1.04582	−	1.81141i
$452$	−3.56563e10	−	1.29778e10i	−0.0401803	−	0.0146244i
$453$		0			0
$454$	−3.59507e11	−	3.01662e11i	−0.397152	−	0.333250i
$455$	2.34094e10	−	8.52032e9i	0.0256058	−	0.00931976i
$456$		0			0
$457$	−1.46359e11	−	8.30041e11i	−0.156962	−	0.890177i	−0.956970	−	0.290187i	$-0.906282\pi$
$457$	−1.46359e11	−	8.30041e11i	−0.156962	−	0.890177i	0.800008	−	0.599990i	$-0.204829\pi$
$458$	1.35779e12			1.44191
$459$		0			0
$460$	7.33916e10			0.0764251
$461$	−2.64210e11	−	1.49841e12i	−0.272455	−	1.54517i	−0.746931	−	0.664902i	$-0.768473\pi$
$461$	−2.64210e11	−	1.49841e12i	−0.272455	−	1.54517i	0.474476	−	0.880269i	$-0.342638\pi$
$462$		0			0
$463$	2.89751e11	−	1.05461e11i	0.293029	−	0.106654i	−0.191323	−	0.981527i	$-0.561278\pi$
$463$	2.89751e11	−	1.05461e11i	0.293029	−	0.106654i	0.484352	+	0.874873i	$0.339056\pi$
$464$	−1.16236e11	−	9.75332e10i	−0.116415	−	0.0976836i
$465$		0			0
$466$	5.82010e11	+	2.11834e11i	0.571733	+	0.208094i
$467$	−9.74341e11	−	1.68761e12i	−0.947949	−	1.64190i	−0.749735	−	0.661738i	$-0.769819\pi$
$467$	−9.74341e11	−	1.68761e12i	−0.947949	−	1.64190i	−0.198214	−	0.980159i	$-0.563514\pi$
$468$		0			0
$469$	−7.58873e10	+	1.31441e11i	−0.0724255	+	0.125445i
$470$	7.75415e11	−	6.50650e11i	0.732983	−	0.615046i
$471$		0			0
$472$	8.47028e10	−	4.80373e11i	0.0785523	−	0.445492i
$473$	2.12019e10	−	1.20242e11i	0.0194760	−	0.110454i
$474$		0			0
$475$	−7.06010e11	+	5.92413e11i	−0.636341	+	0.533953i
$476$	5.91034e10	−	1.02370e11i	0.0527693	−	0.0913990i
$477$		0			0
$478$	2.83516e11	+	4.91063e11i	0.248400	+	0.430241i
$479$	−1.38285e12	−	5.03315e11i	−1.20023	−	0.436848i	−0.336925	−	0.941531i	$-0.609387\pi$
$479$	−1.38285e12	−	5.03315e11i	−1.20023	−	0.436848i	−0.863305	+	0.504683i	$0.831609\pi$
$480$		0			0
$481$	−6.46875e10	−	5.42793e10i	−0.0551020	−	0.0462361i
$482$	1.33837e12	−	4.87125e11i	1.12944	−	0.411082i
$483$		0			0
$484$	−2.54254e10	−	1.44194e11i	−0.0210602	−	0.119439i
$485$	2.54724e12			2.09042
$486$		0			0
$487$	−4.38273e11			−0.353073			−0.176537	−	0.984294i	$-0.556489\pi$
$487$	−4.38273e11			−0.353073			−0.176537	+	0.984294i	$0.556489\pi$
$488$	−4.29958e11	−	2.43841e12i	−0.343192	−	1.94634i
$489$		0			0
$490$	1.09065e12	−	3.96963e11i	0.854677	−	0.311077i
$491$	5.26764e11	+	4.42008e11i	0.409025	+	0.343213i	0.823970	−	0.566634i	$-0.191755\pi$
$491$	5.26764e11	+	4.42008e11i	0.409025	+	0.343213i	−0.414945	+	0.909847i	$0.636199\pi$
$492$		0			0
$493$	3.01393e11	+	1.09698e11i	0.229785	+	0.0836349i
$494$	4.08496e10	+	7.07536e10i	0.0308615	+	0.0534537i
$495$		0			0
$496$	9.21647e10	−	1.59634e11i	0.0683750	−	0.118429i
$497$	−6.86997e11	+	5.76459e11i	−0.505070	+	0.423804i
$498$		0			0
$499$	−8.66368e10	+	4.91342e11i	−0.0625532	+	0.354757i	0.937425	+	0.348187i	$0.113203\pi$
$499$	−8.66368e10	+	4.91342e11i	−0.0625532	+	0.354757i	−0.999978	+	0.00657028i	$0.997909\pi$
$500$	3.74555e10	−	2.12421e11i	0.0268010	−	0.151996i
$501$		0			0
$502$	−3.78542e11	+	3.17634e11i	−0.266040	+	0.223234i
$503$	−1.23017e12	+	2.13072e12i	−0.856860	+	1.48413i	0.0180486	+	0.999837i	$0.494255\pi$
$503$	−1.23017e12	+	2.13072e12i	−0.856860	+	1.48413i	−0.874909	+	0.484288i	$0.839079\pi$
$504$		0			0
$505$	−1.12723e12	−	1.95242e12i	−0.771263	−	1.33587i
$506$	−2.25150e11	−	8.19480e10i	−0.152684	−	0.0555726i
$507$		0			0
$508$	−6.14687e11	−	5.15783e11i	−0.409512	−	0.343622i
$509$	−1.88778e12	+	6.87097e11i	−1.24659	+	0.453720i	−0.879247	−	0.476367i	$-0.841953\pi$
$509$	−1.88778e12	+	6.87097e11i	−1.24659	+	0.453720i	−0.367339	+	0.930087i	$0.619731\pi$
$510$		0			0
$511$	6.61211e10	+	3.74992e11i	0.0428989	+	0.243292i
$512$	−1.45432e12			−0.935285
$513$		0			0
$514$	1.80730e12			1.14208
$515$	6.25010e11	+	3.54461e12i	0.391520	+	2.22042i
$516$		0			0
$517$	1.63238e12	−	5.94139e11i	1.00488	−	0.365747i
$518$	4.33642e11	+	3.63869e11i	0.264635	+	0.222055i
$519$		0			0
$520$	1.31034e11	+	4.76924e10i	0.0785902	+	0.0286045i
$521$	1.00781e12	+	1.74559e12i	0.599254	+	1.03794i	0.992931	+	0.118690i	$0.0378694\pi$
$521$	1.00781e12	+	1.74559e12i	0.599254	+	1.03794i	−0.393677	+	0.919249i	$0.628797\pi$
$522$		0			0
$523$	−1.60874e12	+	2.78643e12i	−0.940220	+	1.62851i	−0.175169	+	0.984538i	$0.556047\pi$
$523$	−1.60874e12	+	2.78643e12i	−0.940220	+	1.62851i	−0.765051	+	0.643970i	$0.777286\pi$
$524$	4.21958e11	−	3.54065e11i	0.244500	−	0.205160i
$525$		0			0
$526$	5.30497e10	−	3.00860e11i	0.0302167	−	0.171368i
$527$	−6.76592e10	+	3.83715e11i	−0.0382102	+	0.216701i
$528$		0			0
$529$	−1.33866e12	+	1.12327e12i	−0.743222	+	0.623637i
$530$	−1.59514e12	+	2.76286e12i	−0.878126	+	1.52096i
$531$		0			0
$532$	1.43951e11	+	2.49331e11i	0.0779135	+	0.134950i
$533$	1.88306e11	+	6.85376e10i	0.101063	+	0.0367838i
$534$		0			0
$535$	1.84145e12	+	1.54516e12i	0.971778	+	0.815418i
$536$	−7.98323e11	+	2.90566e11i	−0.417770	+	0.152056i
$537$		0			0
$538$	−8.31946e10	−	4.71820e11i	−0.0428129	−	0.242804i
$539$	1.99184e12			1.01650
$540$		0			0
$541$	−2.42753e12			−1.21836			−0.609181	−	0.793031i	$-0.708502\pi$
$541$	−2.42753e12			−1.21836			−0.609181	+	0.793031i	$0.708502\pi$
$542$	1.63111e11	+	9.25050e11i	0.0811871	+	0.460435i
$543$		0			0
$544$	1.08419e12	−	3.94612e11i	0.530773	−	0.193186i
$545$	−3.46574e11	−	2.90810e11i	−0.168272	−	0.141197i
$546$		0			0
$547$	−1.09378e12	−	3.98102e11i	−0.522379	−	0.190130i	0.0673534	−	0.997729i	$-0.478544\pi$
$547$	−1.09378e12	−	3.98102e11i	−0.522379	−	0.190130i	−0.589732	+	0.807599i	$0.700767\pi$
$548$	−5.08822e11	−	8.81306e11i	−0.241020	−	0.417459i
$549$		0			0
$550$	6.57996e11	−	1.13968e12i	0.306614	−	0.531070i
$551$	−5.98417e11	+	5.02132e11i	−0.276581	+	0.232079i
$552$		0			0
$553$	1.69537e10	−	9.61492e10i	0.00770906	−	0.0437203i
$554$	1.79379e11	−	1.01731e12i	0.0809053	−	0.458837i
$555$		0			0
$556$	8.17007e11	−	6.85550e11i	0.362568	−	0.304230i
$557$	−2.13352e12	+	3.69537e12i	−0.939181	+	1.62671i	−0.172177	+	0.985066i	$0.555080\pi$
$557$	−2.13352e12	+	3.69537e12i	−0.939181	+	1.62671i	−0.767004	+	0.641643i	$0.778253\pi$
$558$		0			0
$559$	6.65687e9	+	1.15300e10i	0.00288348	+	0.00499434i
$560$	−5.34978e11	−	1.94716e11i	−0.229874	−	0.0836673i
$561$		0			0
$562$	1.05010e12	+	8.81139e11i	0.444035	+	0.372590i
$563$	2.50295e12	−	9.10998e11i	1.04994	−	0.382146i	0.241299	−	0.970451i	$-0.422427\pi$
$563$	2.50295e12	−	9.10998e11i	1.04994	−	0.382146i	0.808640	+	0.588304i	$0.200204\pi$
$564$		0			0
$565$	−6.70796e10	−	3.80427e11i	−0.0276932	−	0.157056i
$566$	2.40776e12			0.986141
$567$		0			0
$568$	−5.01990e12			−2.02361
$569$	−8.28665e11	−	4.69959e12i	−0.331416	−	1.87956i	−0.460096	−	0.887869i	$-0.652185\pi$
$569$	−8.28665e11	−	4.69959e12i	−0.331416	−	1.87956i	0.128680	−	0.991686i	$-0.458926\pi$
$570$		0			0
$571$	1.35368e12	−	4.92699e11i	0.532909	−	0.193963i	−0.0615276	−	0.998105i	$-0.519597\pi$
$571$	1.35368e12	−	4.92699e11i	0.532909	−	0.193963i	0.594437	+	0.804142i	$0.297375\pi$
$572$	4.69770e10	+	3.94184e10i	0.0183486	+	0.0153963i
$573$		0			0
$574$	−1.26233e12	−	4.59452e11i	−0.485367	−	0.176659i
$575$	1.47364e11	+	2.55242e11i	0.0562195	+	0.0973750i
$576$		0			0
$577$	−9.28577e10	+	1.60834e11i	−0.0348760	+	0.0604070i	−0.882937	−	0.469492i	$-0.844437\pi$
$577$	−9.28577e10	+	1.60834e11i	−0.0348760	+	0.0604070i	0.848061	+	0.529899i	$0.177770\pi$
$578$	−4.22871e11	+	3.54831e11i	−0.157591	+	0.132235i
$579$		0			0
$580$	−5.93303e10	+	3.36479e11i	−0.0217696	+	0.123462i
$581$	1.15695e11	−	6.56141e11i	0.0421234	−	0.238894i
$582$		0			0
$583$	−4.19410e12	+	3.51927e12i	−1.50359	+	1.26166i
$584$	−1.06570e12	+	1.84584e12i	−0.379119	+	0.656654i
$585$		0			0
$586$	1.62084e11	+	2.80738e11i	0.0567807	+	0.0983470i
$587$	−1.93706e12	−	7.05031e11i	−0.673397	−	0.245096i	−0.0173872	−	0.999849i	$-0.505535\pi$
$587$	−1.93706e12	−	7.05031e11i	−0.673397	−	0.245096i	−0.656010	+	0.754752i	$0.727757\pi$
$588$		0			0
$589$	−7.26965e11	−	6.09996e11i	−0.248883	−	0.208837i
$590$	1.19580e12	−	4.35237e11i	0.406281	−	0.147874i
$591$		0			0
$592$	3.35106e11	+	1.90048e12i	0.112133	+	0.635940i
$593$	2.75077e12			0.913499			0.456750	−	0.889595i	$-0.349014\pi$
$593$	2.75077e12			0.913499			0.456750	+	0.889595i	$0.349014\pi$
$594$		0			0
$595$	1.20341e12			0.393628
$596$	−1.20192e11	−	6.81645e11i	−0.0390184	−	0.221284i
$597$		0			0
$598$	2.45510e10	−	8.93583e9i	0.00785080	−	0.00285746i
$599$	5.33088e11	+	4.47314e11i	0.169191	+	0.141968i	0.723452	−	0.690375i	$-0.242554\pi$
$599$	5.33088e11	+	4.47314e11i	0.169191	+	0.141968i	−0.554260	+	0.832343i	$0.686999\pi$
$600$		0			0
$601$	−4.17448e12	−	1.51939e12i	−1.30517	−	0.475043i	−0.406494	−	0.913654i	$-0.633249\pi$
$601$	−4.17448e12	−	1.51939e12i	−1.30517	−	0.475043i	−0.898677	+	0.438610i	$0.855471\pi$
$602$	−4.46253e10	−	7.72932e10i	−0.0138483	−	0.0239860i
$603$		0			0
$604$	2.06136e11	−	3.57038e11i	0.0630214	−	0.109156i
$605$	1.14188e12	−	9.58152e11i	0.346515	−	0.290760i
$606$		0			0
$607$	−6.75469e11	+	3.83077e12i	−0.201956	+	1.14535i	0.700203	+	0.713944i	$0.253093\pi$
$607$	−6.75469e11	+	3.83077e12i	−0.201956	+	1.14535i	−0.902159	+	0.431404i	$0.858018\pi$
$608$	−4.87968e11	+	2.76740e12i	−0.144819	+	0.821309i
$609$		0			0
$610$	4.94831e12	−	4.15212e12i	1.44701	−	1.21419i
$611$	−9.47116e10	+	1.64045e11i	−0.0274927	+	0.0476188i
$612$		0			0
$613$	−1.18969e12	−	2.06060e12i	−0.340300	−	0.589417i	0.644188	−	0.764867i	$-0.277195\pi$
$613$	−1.18969e12	−	2.06060e12i	−0.340300	−	0.589417i	−0.984488	+	0.175450i	$0.943862\pi$
$614$	−1.20950e12	−	4.40223e11i	−0.343439	−	0.125002i
$615$		0			0
$616$	−1.22891e12	−	1.03117e12i	−0.343879	−	0.288549i
$617$	−2.63994e11	+	9.60860e10i	−0.0733349	+	0.0266917i	−0.378427	−	0.925631i	$-0.623535\pi$
$617$	−2.63994e11	+	9.60860e10i	−0.0733349	+	0.0266917i	0.305092	+	0.952323i	$0.401313\pi$
$618$		0			0
$619$	9.95985e11	+	5.64851e12i	0.272675	+	1.54642i	0.746252	+	0.665663i	$0.231851\pi$
$619$	9.95985e11	+	5.64851e12i	0.272675	+	1.54642i	−0.473578	+	0.880752i	$0.657038\pi$
$620$	−4.15065e11			−0.112812
$621$		0			0
$622$	−8.61399e11			−0.230753
$623$	4.10581e11	+	2.32852e12i	0.109195	+	0.619276i
$624$		0			0
$625$	4.39861e12	−	1.60096e12i	1.15307	−	0.419683i
$626$	3.12298e12	+	2.62049e12i	0.812801	+	0.682021i
$627$		0			0
$628$	7.68556e11	+	2.79732e11i	0.197177	+	0.0717667i
$629$	−2.03960e12	−	3.53269e12i	−0.519537	−	0.899865i
$630$		0			0
$631$	2.86459e12	−	4.96162e12i	0.719334	−	1.24592i	−0.241930	−	0.970294i	$-0.577780\pi$
$631$	2.86459e12	−	4.96162e12i	0.719334	−	1.24592i	0.961264	−	0.275629i	$-0.0888862\pi$
$632$	4.18641e11	−	3.51282e11i	0.104379	−	0.0875848i
$633$		0			0
$634$	−3.50976e11	+	1.99048e12i	−0.0862731	+	0.489279i
$635$	1.41853e12	−	8.04491e12i	0.346225	−	1.96354i
$636$		0			0
$637$	−1.66382e11	+	1.39611e11i	−0.0400385	+	0.0335963i
$638$	5.57720e11	−	9.66000e11i	0.133267	−	0.230826i
$639$		0			0
$640$	−5.70512e11	−	9.88156e11i	−0.134417	−	0.232817i
$641$	−5.18535e12	−	1.88731e12i	−1.21316	−	0.441553i	−0.345360	−	0.938470i	$-0.612243\pi$
$641$	−5.18535e12	−	1.88731e12i	−1.21316	−	0.441553i	−0.867798	+	0.496917i	$0.834465\pi$
$642$		0			0
$643$	−5.41878e12	−	4.54690e12i	−1.25012	−	1.04898i	−0.996663	−	0.0816309i	$-0.973987\pi$
$643$	−5.41878e12	−	4.54690e12i	−1.25012	−	1.04898i	−0.253459	−	0.967346i	$-0.581568\pi$
$644$	8.65159e10	−	3.14892e10i	0.0198203	−	0.00721399i
$645$		0			0
$646$	6.85325e11	+	3.88667e12i	0.154828	+	0.878074i
$647$	4.09026e11			0.0917660			0.0458830	−	0.998947i	$-0.485390\pi$
$647$	4.09026e11			0.0917660			0.0458830	+	0.998947i	$0.485390\pi$
$648$		0			0
$649$	2.18389e12			0.483203
$650$	2.49184e10	+	1.41319e11i	0.00547533	+	0.0310521i
$651$		0			0
$652$	−6.53765e11	+	2.37951e11i	−0.141680	+	0.0515672i
$653$	−5.34411e12	−	4.48424e12i	−1.15018	−	0.965116i	−0.150456	−	0.988617i	$-0.548074\pi$
$653$	−5.34411e12	−	4.48424e12i	−1.15018	−	0.965116i	−0.999724	+	0.0235012i	$0.992519\pi$
$654$		0			0
$655$	5.26952e12	+	1.91795e12i	1.11863	+	0.407147i
$656$	−2.28978e12	−	3.96601e12i	−0.482754	−	0.836155i
$657$		0			0
$658$	6.34912e11	−	1.09970e12i	0.132037	−	0.228696i
$659$	−3.77424e12	+	3.16696e12i	−0.779552	+	0.654122i	−0.943136	−	0.332408i	$-0.892139\pi$
$659$	−3.77424e12	+	3.16696e12i	−0.779552	+	0.654122i	0.163584	+	0.986529i	$0.447695\pi$
$660$		0			0
$661$	7.61963e11	−	4.32131e12i	0.155249	−	0.880458i	−0.803310	−	0.595561i	$-0.796930\pi$
$661$	7.61963e11	−	4.32131e12i	0.155249	−	0.880458i	0.958558	−	0.284897i	$-0.0919593\pi$
$662$	−1.83374e11	+	1.03996e12i	−0.0371088	+	0.210454i
$663$		0			0
$664$	2.85689e12	−	2.39722e12i	0.570344	−	0.478576i
$665$	−1.46550e12	+	2.53832e12i	−0.290595	+	0.503325i
$666$		0			0
$667$	1.24906e11	+	2.16344e11i	0.0244354	+	0.0423233i
$668$	4.67317e11	+	1.70090e11i	0.0908067	+	0.0330509i
$669$		0			0
$670$	−1.69783e12	−	1.42465e12i	−0.325504	−	0.273131i
$671$	1.04171e13	−	3.79150e12i	1.98378	−	0.722037i
$672$		0			0
$673$	1.51399e11	+	8.58629e11i	0.0284483	+	0.161338i	0.995722	−	0.0923954i	$-0.0294524\pi$
$673$	1.51399e11	+	8.58629e11i	0.0284483	+	0.161338i	−0.967274	+	0.253734i	$0.918341\pi$
$674$	−1.41660e11			−0.0264409
$675$		0			0
$676$	1.86406e12			0.343320
$677$	8.43098e11	+	4.78144e12i	0.154251	+	0.874803i	0.959467	+	0.281821i	$0.0909383\pi$
$677$	8.43098e11	+	4.78144e12i	0.154251	+	0.874803i	−0.805216	+	0.592982i	$0.797951\pi$
$678$		0			0
$679$	3.00275e12	−	1.09291e12i	0.542133	−	0.197320i
$680$	5.16012e12	+	4.32985e12i	0.925486	+	0.776575i
$681$		0			0
$682$	1.27333e12	+	4.63455e11i	0.225378	+	0.0820310i
$683$	−3.86723e11	−	6.69825e11i	−0.0679998	−	0.117779i	0.830021	−	0.557732i	$-0.188328\pi$
$683$	−3.86723e11	−	6.69825e11i	−0.0679998	−	0.117779i	−0.898021	+	0.439953i	$0.854995\pi$
$684$		0			0
$685$	5.18008e12	−	8.97215e12i	0.898935	−	1.55700i
$686$	2.39121e12	−	2.00646e12i	0.412249	−	0.345918i
$687$		0			0
$688$	5.28344e10	−	2.99639e11i	0.00899018	−	0.0509859i
$689$	1.03670e11	−	5.87940e11i	0.0175253	−	0.0993908i
$690$		0			0
$691$	−4.89965e12	+	4.11129e12i	−0.817549	+	0.686005i	−0.952397	−	0.304861i	$-0.901390\pi$
$691$	−4.89965e12	+	4.11129e12i	−0.817549	+	0.686005i	0.134848	+	0.990866i	$0.456945\pi$
$692$	−7.17624e11	+	1.24296e12i	−0.118965	+	0.206054i
$693$		0			0
$694$	−2.86348e11	−	4.95970e11i	−0.0468573	−	0.0811592i
$695$	1.02030e13	+	3.71358e12i	1.65881	+	0.603756i
$696$		0			0
$697$	7.41548e12	+	6.22233e12i	1.19012	+	0.998632i
$698$	−6.13512e12	+	2.23300e12i	−0.978304	+	0.356073i
$699$		0			0
$700$	8.78107e10	+	4.97999e11i	0.0138231	+	0.0783949i
$701$	9.18203e12			1.43618			0.718088	−	0.695953i	$-0.245018\pi$
$701$	9.18203e12			1.43618			0.718088	+	0.695953i	$0.245018\pi$
$702$		0			0
$703$	9.93522e12			1.53419
$704$	−1.40307e12	−	7.95722e12i	−0.215280	−	1.22091i
$705$		0			0
$706$	−4.86841e12	+	1.77196e12i	−0.737506	+	0.268430i
$707$	−2.16651e12	−	1.81792e12i	−0.326117	−	0.273645i
$708$		0			0
$709$	−2.82352e12	−	1.02768e12i	−0.419646	−	0.152738i	0.123562	−	0.992337i	$-0.460568\pi$
$709$	−2.82352e12	−	1.02768e12i	−0.419646	−	0.152738i	−0.543208	+	0.839598i	$0.682790\pi$
$710$	−6.54804e12	−	1.13415e13i	−0.967050	−	1.67498i
$711$		0			0
$712$	−6.61748e12	+	1.14618e13i	−0.965011	+	1.67145i
$713$	−2.32476e11	+	1.95071e11i	−0.0336880	+	0.0282676i
$714$		0			0
$715$	−1.08410e11	+	6.14826e11i	−0.0155129	+	0.0879782i
$716$	−4.32602e11	+	2.45341e12i	−0.0615149	+	0.348868i
$717$		0			0
$718$	3.32943e12	−	2.79372e12i	0.467530	−	0.392305i
$719$	−3.89833e12	+	6.75211e12i	−0.544000	+	0.942236i	0.454669	+	0.890660i	$0.349758\pi$
$719$	−3.89833e12	+	6.75211e12i	−0.544000	+	0.942236i	−0.998669	+	0.0515752i	$0.983576\pi$
$720$		0			0
$721$	2.25762e12	+	3.91031e12i	0.311130	+	0.538893i
$722$	−3.47779e12	−	1.26581e12i	−0.476306	−	0.173361i
$723$		0			0
$724$	−2.30542e12	−	1.93448e12i	−0.311837	−	0.261662i
$725$	−1.28934e12	+	4.69282e11i	−0.173319	+	0.0630831i
$726$		0			0
$727$	−8.83784e11	−	5.01219e12i	−0.117339	−	0.665461i	−0.985566	−	0.169294i	$-0.945851\pi$
$727$	−8.83784e11	−	5.01219e12i	−0.117339	−	0.665461i	0.868227	−	0.496167i	$-0.165260\pi$
$728$	1.74929e11			0.0230818
$729$		0			0
$730$	−5.56046e12			−0.724699
$731$	1.11681e11	+	6.33373e11i	0.0144661	+	0.0820411i
$732$		0			0
$733$	4.68571e12	−	1.70546e12i	0.599525	−	0.218209i	−0.0243888	−	0.999703i	$-0.507764\pi$
$733$	4.68571e12	−	1.70546e12i	0.599525	−	0.218209i	0.623914	+	0.781493i	$0.285542\pi$
$734$	1.42610e12	+	1.19664e12i	0.181350	+	0.152171i
$735$		0			0
$736$	8.44446e11	+	3.07353e11i	0.106077	+	0.0386089i
$737$	−1.90180e12	−	3.29402e12i	−0.237444	−	0.411266i
$738$		0			0
$739$	−2.74608e12	+	4.75636e12i	−0.338699	+	0.586644i	−0.984188	−	0.177125i	$-0.943320\pi$
$739$	−2.74608e12	+	4.75636e12i	−0.338699	+	0.586644i	0.645489	+	0.763769i	$0.276654\pi$
$740$	3.32880e12	−	2.79320e12i	0.408080	−	0.342420i
$741$		0			0
$742$	−6.94964e11	+	3.94134e12i	−0.0841676	+	0.477338i
$743$	−1.11559e12	+	6.32681e12i	−0.134293	+	0.761614i	0.841056	+	0.540948i	$0.181934\pi$
$743$	−1.11559e12	+	6.32681e12i	−0.134293	+	0.761614i	−0.975349	+	0.220666i	$0.929177\pi$
$744$		0			0
$745$	5.39798e12	−	4.52944e12i	0.641989	−	0.538693i
$746$	−2.11208e12	+	3.65823e12i	−0.249681	+	0.432460i
$747$		0			0
$748$	1.48118e12	+	2.56549e12i	0.173002	+	0.299649i
$749$	2.83370e12	+	1.03138e12i	0.328993	+	0.119744i
$750$		0			0
$751$	4.54149e12	+	3.81076e12i	0.520977	+	0.437151i	0.864972	−	0.501820i	$-0.167336\pi$
$751$	4.54149e12	+	3.81076e12i	0.520977	+	0.437151i	−0.343995	+	0.938971i	$0.611780\pi$
$752$	4.06785e12	−	1.48058e12i	0.463857	−	0.168830i
$753$		0			0
$754$	2.11210e10	+	1.19783e11i	0.00237981	+	0.0134966i
$755$	4.19714e12			0.470103
$756$		0			0
$757$	−5.65008e12			−0.625350			−0.312675	−	0.949860i	$-0.601225\pi$
$757$	−5.65008e12			−0.625350			−0.312675	+	0.949860i	$0.601225\pi$
$758$	1.38291e12	+	7.84287e12i	0.152154	+	0.862906i
$759$		0			0
$760$	−1.54168e13	+	5.61126e12i	−1.67623	+	0.610097i
$761$	−7.77088e12	−	6.52054e12i	−0.839922	−	0.704778i	0.117624	−	0.993058i	$-0.462472\pi$
$761$	−7.77088e12	−	6.52054e12i	−0.839922	−	0.704778i	−0.957546	+	0.288280i	$0.906917\pi$
$762$		0			0
$763$	−5.33324e11	−	1.94114e11i	−0.0569680	−	0.0207346i
$764$	−2.17989e11	−	3.77568e11i	−0.0231480	−	0.0400936i
$765$		0			0
$766$	−2.65190e12	+	4.59323e12i	−0.278310	+	0.482046i
$767$	−1.82424e11	+	1.53072e11i	−0.0190328	+	0.0159704i
$768$		0			0
$769$	1.59520e12	−	9.04681e12i	0.164492	−	0.932882i	−0.785094	−	0.619377i	$-0.787385\pi$
$769$	1.59520e12	−	9.04681e12i	0.164492	−	0.932882i	0.949586	−	0.313506i	$-0.101503\pi$
$770$	7.26745e11	−	4.12157e12i	0.0745030	−	0.422527i
$771$		0			0
$772$	−2.59440e12	+	2.17696e12i	−0.262881	+	0.220583i
$773$	2.81840e12	−	4.88161e12i	0.283919	−	0.491763i	−0.688427	−	0.725305i	$-0.741699\pi$
$773$	2.81840e12	−	4.88161e12i	0.283919	−	0.491763i	0.972347	+	0.233543i	$0.0750319\pi$
$774$		0			0
$775$	−8.33416e11	−	1.44352e12i	−0.0829859	−	0.143736i
$776$	1.68079e13	+	6.11757e12i	1.66393	+	0.605622i
$777$		0			0
$778$	−6.35454e12	−	5.33209e12i	−0.621836	−	0.521782i
$779$	−2.21551e13	+	8.06381e12i	−2.15554	+	0.784552i
$780$		0			0
$781$	−3.90273e12	−	2.21335e13i	−0.375352	−	2.12873i
$782$	1.26209e12			0.120687
$783$		0			0
$784$	4.96361e12			0.469218
$785$	1.44587e12	+	8.19995e12i	0.135899	+	0.770722i
$786$		0			0
$787$	−1.58091e13	+	5.75405e12i	−1.46900	+	0.534672i	−0.947828	−	0.318782i	$-0.896726\pi$
$787$	−1.58091e13	+	5.75405e12i	−1.46900	+	0.534672i	−0.521170	+	0.853453i	$0.674504\pi$
$788$	−4.59038e11	−	3.85179e11i	−0.0424112	−	0.0355872i
$789$		0			0
$790$	1.33974e12	+	4.87626e11i	0.122377	+	0.0445415i
$791$	−2.42300e11	−	4.19676e11i	−0.0220069	−	0.0381172i
$792$		0			0
$793$	−6.04402e11	+	1.04685e12i	−0.0542746	+	0.0940063i
$794$	−6.35646e12	+	5.33370e12i	−0.567575	+	0.476252i
$795$		0			0
$796$	1.24458e12	−	7.05836e12i	0.109879	−	0.623153i
$797$	−3.65633e11	+	2.07361e12i	−0.0320984	+	0.182039i	−0.996642	−	0.0818855i	$-0.973906\pi$
$797$	−3.65633e11	+	2.07361e12i	−0.0320984	+	0.182039i	0.964543	+	0.263924i	$0.0850169\pi$
$798$		0			0
$799$	−7.00963e12	+	5.88178e12i	−0.608464	+	0.510562i
$800$	−2.46787e12	+	4.27448e12i	−0.213019	+	0.368960i
$801$		0			0
$802$	−1.66550e10	−	2.88473e10i	−0.00142154	−	0.00246218i
$803$	−8.96711e12	−	3.26376e12i	−0.761084	−	0.277012i
$804$		0			0
$805$	7.18016e11	+	6.02487e11i	0.0602632	+	0.0505669i
$806$	−1.38848e11	+	5.05364e10i	−0.0115886	+	0.00421791i
$807$		0			0
$808$	−2.74898e12	−	1.55902e13i	−0.226892	−	1.28677i
$809$	−2.25794e12			−0.185329			−0.0926647	−	0.995697i	$-0.529538\pi$
$809$	−2.25794e12			−0.185329			−0.0926647	+	0.995697i	$0.529538\pi$
$810$		0			0
$811$	4.94641e12			0.401510			0.200755	−	0.979642i	$-0.435661\pi$
$811$	4.94641e12			0.401510			0.200755	+	0.979642i	$0.435661\pi$
$812$	7.44287e10	+	4.22106e11i	0.00600812	+	0.0340737i
$813$		0			0
$814$	−1.33309e13	+	4.85205e12i	−1.06427	+	0.387361i
$815$	−5.42575e12	−	4.55274e12i	−0.430775	−	0.361463i
$816$		0			0
$817$	−1.47196e12	−	5.35751e11i	−0.115584	−	0.0420691i
$818$	−8.82454e11	−	1.52846e12i	−0.0689132	−	0.119361i
$819$		0			0
$820$	−5.15602e12	+	8.93050e12i	−0.398247	+	0.689784i
$821$	6.83054e12	−	5.73150e12i	0.524699	−	0.440275i	−0.341567	−	0.939857i	$-0.610958\pi$
$821$	6.83054e12	−	5.73150e12i	0.524699	−	0.440275i	0.866266	+	0.499582i	$0.166513\pi$
$822$		0			0
$823$	−7.78590e11	+	4.41560e12i	−0.0591575	+	0.335499i	−0.999994	−	0.00336111i	$-0.998930\pi$
$823$	−7.78590e11	+	4.41560e12i	−0.0591575	+	0.335499i	0.940837	+	0.338860i	$0.110041\pi$
$824$	−4.38878e12	+	2.48900e13i	−0.331644	+	1.88084i
$825$		0			0
$826$	1.22290e12	−	1.02614e12i	0.0914075	−	0.0767000i
$827$	1.05330e13	−	1.82437e13i	0.783028	−	1.35624i	−0.147143	−	0.989115i	$-0.547008\pi$
$827$	1.05330e13	−	1.82437e13i	0.783028	−	1.35624i	0.930170	−	0.367128i	$-0.119659\pi$
$828$		0			0
$829$	4.76625e12	+	8.25539e12i	0.350495	+	0.607075i	0.986336	−	0.164745i	$-0.0526802\pi$
$829$	4.76625e12	+	8.25539e12i	0.350495	+	0.607075i	−0.635842	+	0.771820i	$0.719347\pi$
$830$	9.14266e12	+	3.32765e12i	0.668684	+	0.243381i
$831$		0			0
$832$	6.74933e11	+	5.66336e11i	0.0488321	+	0.0409750i
$833$	−9.85928e12	+	3.58849e12i	−0.709484	+	0.258231i
$834$		0			0
$835$	8.79156e11	+	4.98594e12i	0.0625860	+	0.354943i
$836$	−7.21509e12			−0.510874
$837$		0			0
$838$	8.14698e12			0.570688
$839$	−2.05496e12	−	1.16542e13i	−0.143177	−	0.811998i	−0.968813	−	0.247794i	$-0.920294\pi$
$839$	−2.05496e12	−	1.16542e13i	−0.143177	−	0.811998i	0.825636	−	0.564204i	$-0.190817\pi$
$840$		0			0
$841$	1.25394e13	−	4.56397e12i	0.864361	−	0.314602i
$842$	1.01167e13	+	8.48892e12i	0.693641	+	0.582034i
$843$		0			0
$844$	4.74132e12	+	1.72570e12i	0.321631	+	0.117064i
$845$	9.48854e12	+	1.64346e13i	0.640242	+	1.10893i
$846$		0			0
$847$	9.34976e11	−	1.61943e12i	0.0624202	−	0.108115i
$848$	−1.04516e13	+	8.76990e12i	−0.694065	+	0.582389i
$849$		0			0
$850$	−1.20373e12	+	6.82668e12i	−0.0790940	+	0.448564i
$851$	5.51712e11	−	3.12892e12i	0.0360603	−	0.204508i
$852$		0			0
$853$	−2.38008e12	+	1.99712e12i	−0.153929	+	0.129162i	−0.716500	−	0.697587i	$-0.754257\pi$
$853$	−2.38008e12	+	1.99712e12i	−0.153929	+	0.129162i	0.562571	+	0.826749i	$0.309812\pi$
$854$	4.05169e12	−	7.01774e12i	0.260661	−	0.451478i
$855$		0			0
$856$	8.43980e12	+	1.46182e13i	0.537279	+	0.930595i
$857$	−1.00108e13	−	3.64363e12i	−0.633950	−	0.230739i	0.00499983	−	0.999988i	$-0.498408\pi$
$857$	−1.00108e13	−	3.64363e12i	−0.633950	−	0.230739i	−0.638949	+	0.769249i	$0.720631\pi$
$858$		0			0
$859$	8.96564e12	+	7.52307e12i	0.561839	+	0.471439i	0.878927	−	0.476957i	$-0.158260\pi$
$859$	8.96564e12	+	7.52307e12i	0.561839	+	0.471439i	−0.317087	+	0.948396i	$0.602705\pi$
$860$	−6.43804e11	+	2.34325e11i	−0.0401338	+	0.0146075i
$861$		0			0
$862$	9.41246e11	+	5.33807e12i	0.0580658	+	0.329308i
$863$	3.00625e13			1.84492			0.922459	−	0.386095i	$-0.126176\pi$
$863$	3.00625e13			1.84492			0.922459	+	0.386095i	$0.126176\pi$
$864$		0			0
$865$	−1.46116e13			−0.887410
$866$	1.37310e12	+	7.78724e12i	0.0829605	+	0.470493i
$867$		0			0
$868$	−4.89289e11	+	1.78087e11i	−0.0292568	+	0.0106486i
$869$	1.87433e12	+	1.57275e12i	0.111495	+	0.0935556i
$870$		0			0
$871$	3.89743e11	+	1.41855e11i	0.0229455	+	0.00835146i
$872$	−1.58843e12	−	2.75125e12i	−0.0930347	−	0.161141i
$873$		0			0
$874$	−1.53697e12	+	2.66210e12i	−0.0890969	+	0.154320i
$875$	2.11024e12	−	1.77070e12i	0.121702	−	0.102120i
$876$		0			0
$877$	−5.36016e11	+	3.03990e12i	−0.0305971	+	0.173525i	−0.996277	−	0.0862107i	$-0.972524\pi$
$877$	−5.36016e11	+	3.03990e12i	−0.0305971	+	0.173525i	0.965680	+	0.259735i	$0.0836353\pi$
$878$	−2.03736e12	+	1.15544e13i	−0.115702	+	0.656181i
$879$		0			0
$880$	1.09295e13	−	9.17095e12i	0.614368	−	0.515516i
$881$	1.03812e13	−	1.79808e13i	0.580573	−	1.00558i	−0.414838	−	0.909895i	$-0.636162\pi$
$881$	1.03812e13	−	1.79808e13i	0.580573	−	1.00558i	0.995411	−	0.0956870i	$-0.0305048\pi$
$882$		0			0
$883$	−5.36537e12	−	9.29310e12i	−0.297014	−	0.514443i	0.678438	−	0.734658i	$-0.262657\pi$
$883$	−5.36537e12	−	9.29310e12i	−0.297014	−	0.514443i	−0.975451	+	0.220215i	$0.929324\pi$
$884$	−3.03544e11	−	1.10481e11i	−0.0167181	−	0.00608488i
$885$		0			0
$886$	−2.21001e12	−	1.85442e12i	−0.120488	−	0.101101i
$887$	−1.66700e13	+	6.06737e12i	−0.904229	+	0.329112i	−0.751946	−	0.659225i	$-0.770885\pi$
$887$	−1.66700e13	+	6.06737e12i	−0.904229	+	0.329112i	−0.152283	+	0.988337i	$0.548662\pi$
$888$		0			0
$889$	−1.77952e12	−	1.00922e13i	−0.0955533	−	0.541910i
$890$	−3.45278e13			−1.84465
$891$		0			0
$892$	8.64309e12			0.457117
$893$	−3.87003e12	−	2.19480e13i	−0.203649	−	1.15495i
$894$		0			0
$895$	−2.38327e13	+	8.67441e12i	−1.24157	+	0.451894i
$896$	−1.09651e12	−	9.20081e11i	−0.0568364	−	0.0476914i
$897$		0			0
$898$	4.17294e12	+	1.51883e12i	0.214140	+	0.0779408i
$899$	−7.06407e11	−	1.22353e12i	−0.0360692	−	0.0624736i
$900$		0			0
$901$	1.44198e13	−	2.49758e13i	0.728950	−	1.26258i
$902$	2.57893e13	−	2.16398e13i	1.29721	−	1.08849i
$903$		0			0
$904$	4.71029e11	−	2.67134e12i	0.0234579	−	0.133037i
$905$	5.32031e12	−	3.01730e13i	0.263644	−	1.49520i
$906$		0			0
$907$	1.83588e11	−	1.54048e11i	0.00900764	−	0.00755830i	−0.638273	−	0.769810i	$-0.720351\pi$
$907$	1.83588e11	−	1.54048e11i	0.00900764	−	0.00755830i	0.647280	+	0.762252i	$0.275906\pi$
$908$	−2.25967e12	+	3.91385e12i	−0.110321	+	0.191081i
$909$		0			0
$910$	2.28180e11	+	3.95220e11i	0.0110304	+	0.0191052i
$911$	2.67117e13	+	9.72225e12i	1.28490	+	0.467664i	0.892049	−	0.451940i	$-0.149268\pi$
$911$	2.67117e13	+	9.72225e12i	1.28490	+	0.467664i	0.392848	+	0.919604i	$0.371490\pi$
$912$		0			0
$913$	1.27908e13	+	1.07327e13i	0.609226	+	0.511201i
$914$	1.45090e13	−	5.28085e12i	0.687670	−	0.250291i
$915$		0			0
$916$	−2.27051e12	−	1.28767e13i	−0.106560	−	0.604331i
$917$	7.03475e12			0.328539
$918$		0			0
$919$	−2.26056e13			−1.04543			−0.522717	−	0.852506i	$-0.675082\pi$
$919$	−2.26056e13			−1.04543			−0.522717	+	0.852506i	$0.675082\pi$
$920$	9.11053e11	+	5.16684e12i	0.0419275	+	0.237782i
$921$		0			0
$922$	2.61920e13	−	9.53312e12i	1.19366	−	0.434456i
$923$	1.87736e12	+	1.57530e12i	0.0851414	+	0.0714421i
$924$		0			0
$925$	1.63982e13	+	5.96845e12i	0.736474	+	0.268055i
$926$	2.82431e12	+	4.89186e12i	0.126230	+	0.218637i
$927$		0			0
$928$	−2.09178e12	+	3.62307e12i	−0.0925870	+	0.160365i
$929$	−1.24111e13	+	1.04142e13i	−0.546689	+	0.458727i	−0.873818	−	0.486253i	$-0.838363\pi$
$929$	−1.24111e13	+	1.04142e13i	−0.546689	+	0.458727i	0.327129	+	0.944980i	$0.393919\pi$
$930$		0			0
$931$	4.43744e12	−	2.51660e13i	0.193579	−	1.09784i
$932$	1.03570e12	−	5.87376e12i	0.0449639	−	0.255003i
$933$		0			0
$934$	2.73463e13	−	2.29463e13i	1.17581	−	0.986624i
$935$	−1.50792e13	+	2.61180e13i	−0.645248	+	1.11760i
$936$		0			0
$937$	1.77481e13	+	3.07406e13i	0.752182	+	1.30282i	0.946763	+	0.321931i	$0.104332\pi$
$937$	1.77481e13	+	3.07406e13i	0.752182	+	1.30282i	−0.194581	+	0.980886i	$0.562335\pi$
$938$	−2.61270e12	−	9.50944e11i	−0.110199	−	0.0401090i
$939$		0			0
$940$	−7.46715e12	−	6.26568e12i	−0.311946	−	0.261754i
$941$	1.03843e12	−	3.77957e11i	0.0431741	−	0.0157141i	−0.320343	−	0.947302i	$-0.603798\pi$
$941$	1.03843e12	−	3.77957e11i	0.0431741	−	0.0157141i	0.363517	+	0.931588i	$0.381576\pi$
$942$		0			0
$943$	1.30925e12	+	7.42514e12i	0.0539164	+	0.305775i
$944$	5.44219e12			0.223049
$945$		0			0
$946$	2.23670e12			0.0908025
$947$	3.52640e12	+	1.99992e13i	0.142481	+	0.808049i	0.969355	+	0.245662i	$0.0790055\pi$
$947$	3.52640e12	+	1.99992e13i	0.142481	+	0.808049i	−0.826875	+	0.562386i	$0.809883\pi$
$948$		0			0
$949$	9.77798e11	−	3.55889e11i	0.0391337	−	0.0142435i
$950$	−1.29335e13	−	1.08525e13i	−0.515180	−	0.432287i
$951$		0			0
$952$	7.94063e12	+	2.89015e12i	0.313321	+	0.114039i
$953$	−1.46728e13	−	2.54140e13i	−0.576227	−	0.998055i	−0.995907	−	0.0903827i	$-0.971191\pi$
$953$	−1.46728e13	−	2.54140e13i	−0.576227	−	0.998055i	0.419680	−	0.907672i	$-0.362142\pi$
$954$		0			0
$955$	2.21924e12	−	3.84384e12i	0.0863355	−	0.149537i
$956$	4.18294e12	−	3.50990e12i	0.161965	−	0.135905i
$957$		0			0
$958$	4.68126e12	−	2.65487e13i	0.179563	−	1.01836i
$959$	2.25684e12	−	1.27992e13i	0.0861621	−	0.488649i
$960$		0			0
$961$	−1.89392e13	+	1.58918e13i	−0.716317	+	0.601062i
$962$	7.73465e11	−	1.33968e12i	0.0291174	−	0.0504328i
$963$		0			0
$964$	−6.85771e12	−	1.18779e13i	−0.255760	−	0.442989i
$965$	−3.23995e13	−	1.17925e13i	−1.20272	−	0.437755i
$966$		0			0
$967$	2.73518e13	+	2.29509e13i	1.00593	+	0.844074i	0.987795	−	0.155761i	$-0.0497831\pi$
$967$	2.73518e13	+	2.29509e13i	1.00593	+	0.844074i	0.0181337	+	0.999836i	$0.494228\pi$
$968$	9.83580e12	−	3.57994e12i	0.360057	−	0.131050i
$969$		0			0
$970$	8.10298e12	+	4.59543e13i	0.293881	+	1.66668i
$971$	−3.73550e13			−1.34853			−0.674267	−	0.738488i	$-0.735540\pi$
$971$	−3.73550e13			−1.34853			−0.674267	+	0.738488i	$0.735540\pi$
$972$		0			0
$973$	1.36209e13			0.487189
$974$	−1.39418e12	−	7.90680e12i	−0.0496368	−	0.281504i
$975$		0			0
$976$	2.59590e13	−	9.44829e12i	0.915721	−	0.333295i
$977$	−1.16521e13	−	9.77725e12i	−0.409145	−	0.343314i	0.414870	−	0.909880i	$-0.363827\pi$
$977$	−1.16521e13	−	9.77725e12i	−0.409145	−	0.343314i	−0.824016	+	0.566567i	$0.808271\pi$
$978$		0			0
$979$	−5.56816e13	−	2.02664e13i	−1.93727	−	0.705107i
$980$	−5.58842e12	−	9.67943e12i	−0.193540	−	0.335222i
$981$		0			0
$982$	−6.29849e12	+	1.09093e13i	−0.216140	+	0.374365i
$983$	−7.23845e12	+	6.07378e12i	−0.247261	+	0.207476i	−0.757992	−	0.652264i	$-0.773819\pi$
$983$	−7.23845e12	+	6.07378e12i	−0.247261	+	0.207476i	0.510731	+	0.859741i	$0.329375\pi$
$984$		0			0
$985$	1.05934e12	−	6.00781e12i	0.0358568	−	0.203354i
$986$	−1.02029e12	+	5.78632e12i	−0.0343776	+	0.194965i
$987$		0			0
$988$	6.02688e11	−	5.05715e11i	0.0201227	−	0.0168850i
$989$	−2.50464e11	+	4.33817e11i	−0.00832459	+	0.0144186i
$990$		0			0
$991$	−1.17808e13	−	2.04049e13i	−0.388009	−	0.672051i	0.604173	−	0.796853i	$-0.293504\pi$
$991$	−1.17808e13	−	2.04049e13i	−0.388009	−	0.672051i	−0.992182	+	0.124802i	$0.960170\pi$
$992$	−4.77575e12	−	1.73823e12i	−0.156581	−	0.0569908i
$993$		0			0
$994$	−1.25852e13	−	1.05602e13i	−0.408903	−	0.343110i
$995$	6.85658e13	−	2.49559e13i	2.21771	−	0.807179i
$996$		0			0
$997$	5.44626e12	+	3.08873e13i	0.174570	+	0.990037i	0.938639	+	0.344902i	$0.112088\pi$
$997$	5.44626e12	+	3.08873e13i	0.174570	+	0.990037i	−0.764069	+	0.645135i	$0.776801\pi$
$998$	−9.13979e12			−0.291641
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.e.a.10.18		156
3.2	odd	2		27.10.e.a.13.9	✓	156
27.2	odd	18		27.10.e.a.25.9	yes	156
27.25	even	9	inner	81.10.e.a.73.18		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.13.9	✓	156	3.2	odd	2
27.10.e.a.25.9	yes	156	27.2	odd	18
81.10.e.a.10.18		156	1.1	even	1	trivial
81.10.e.a.73.18		156	27.25	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.18108 + 18.0408i) q^{2} +(165.772 - 60.3360i) q^{4} +(1375.78 + 1154.42i) q^{5} +(2117.11 + 770.566i) q^{7} +(6305.53 + 10921.5i) q^{8} +(-16450.1 + 28492.4i) q^{10} +(-43252.3 + 36293.0i) q^{11} +(1069.11 - 6063.22i) q^{13} +(-7166.92 + 40645.6i) q^{14} +(-107783. + 90440.9i) q^{16} +(148706. - 257567. i) q^{17} +(362187. + 627326. i) q^{19} +(297718. + 108360. i) q^{20} +(-792343. - 664854. i) q^{22} +(217677. - 79228.1i) q^{23} +(220935. + 1.25299e6i) q^{25} +112786. q^{26} +397450. q^{28} +(187265. + 1.06204e6i) q^{29} +(-1.23107e6 + 448073. i) q^{31} +(2.97175e6 + 2.49360e6i) q^{32} +(5.11976e6 + 1.86344e6i) q^{34} +(2.02312e6 + 3.50415e6i) q^{35} +(6.85780e6 - 1.18781e7i) q^{37} +(-1.01653e7 + 8.52971e6i) q^{38} +(-3.93293e6 + 2.23048e7i) q^{40} +(-5.65192e6 + 3.20536e7i) q^{41} +(-1.65654e6 + 1.39000e6i) q^{43} +(-4.98023e6 + 8.62601e6i) q^{44} +(2.12179e6 + 3.67504e6i) q^{46} +(-2.89113e7 - 1.05228e7i) q^{47} +(-2.70243e7 - 2.26760e7i) q^{49} +(-2.19020e7 + 7.97169e6i) q^{50} +(-188602. - 1.06962e6i) q^{52} +9.69683e7 q^{53} -1.01403e8 q^{55} +(4.93378e6 + 2.79809e7i) q^{56} +(-1.85643e7 + 6.75684e6i) q^{58} +(-2.96299e7 - 2.48624e7i) q^{59} +(-1.84497e8 - 6.71515e7i) q^{61} +(-1.19997e7 - 2.07841e7i) q^{62} +(-7.15525e7 + 1.23933e8i) q^{64} +(8.47032e6 - 7.10745e6i) q^{65} +(-1.16980e7 + 6.63426e7i) q^{67} +(9.11076e6 - 5.16697e7i) q^{68} +(-5.67820e7 + 4.76458e7i) q^{70} +(-1.99027e8 + 3.44726e8i) q^{71} +(8.45049e7 + 1.46367e8i) q^{73} +(2.36105e8 + 8.59351e7i) q^{74} +(9.78906e7 + 8.21400e7i) q^{76} +(-1.19536e8 + 4.35076e7i) q^{77} +(-7.52500e6 - 4.26764e7i) q^{79} -2.52692e8 q^{80} -5.96252e8 q^{82} +(-5.13521e7 - 2.91232e8i) q^{83} +(5.01926e8 - 1.82686e8i) q^{85} +(-3.03464e7 - 2.54636e7i) q^{86} +(-6.69102e8 - 2.43533e8i) q^{88} +(5.24736e8 + 9.08869e8i) q^{89} +(6.93553e6 - 1.20127e7i) q^{91} +(3.13044e7 - 2.62675e7i) q^{92} +(9.78714e7 - 5.55056e8i) q^{94} +(-2.25906e8 + 1.28117e9i) q^{95} +(1.08650e9 - 9.11682e8i) q^{97} +(3.23128e8 - 5.59673e8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) \) 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Introduction

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