LMFDB - Embedded newform 81.8.c.d.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,8,Mod(28,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("81.28");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	81.c (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:	$25.3031870642$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{65})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 17x^{2} + 16x + 256 $ x^4 - x^3 + 17x^2 + 16x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.1
Root			$2.26556 - 3.92407i$ of defining polynomial
Character	$\chi$	$=$	81.55
Dual form			81.8.c.d.28.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.29669 + 14.3703i) q^{2} +(-73.6702 - 127.601i) q^{4} +(-57.0934 - 98.8886i) q^{5} +(-719.202 + 1245.70i) q^{7} +320.924 q^{8} +1894.75 q^{10} +(-2964.37 + 5134.44i) q^{11} +(5723.62 + 9913.60i) q^{13} +(-11934.0 - 20670.3i) q^{14} +(6767.18 - 11721.1i) q^{16} -20235.6 q^{17} -6354.94 q^{19} +(-8412.17 + 14570.3i) q^{20} +(-49188.9 - 85197.7i) q^{22} +(-37922.8 - 65684.2i) q^{23} +(32543.2 - 56366.5i) q^{25} -189948. q^{26} +211935. q^{28} +(37392.1 - 64765.1i) q^{29} +(94681.4 + 163993. i) q^{31} +(132830. + 230068. i) q^{32} +(167889. - 290792. i) q^{34} +164247. q^{35} -33407.2 q^{37} +(52725.0 - 91322.4i) q^{38} +(-18322.6 - 31735.7i) q^{40} +(-70622.4 - 122322. i) q^{41} +(123099. - 213213. i) q^{43} +873543. q^{44} +1.25854e6 q^{46} +(-167566. + 290234. i) q^{47} +(-622733. - 1.07860e6i) q^{49} +(540002. + 935310. i) q^{50} +(843321. - 1.46067e6i) q^{52} +1.65156e6 q^{53} +676983. q^{55} +(-230809. + 399774. i) q^{56} +(620462. + 1.07467e6i) q^{58} +(-1.02411e6 - 1.77382e6i) q^{59} +(295235. - 511361. i) q^{61} -3.14217e6 q^{62} -2.67579e6 q^{64} +(653562. - 1.13200e6i) q^{65} +(-26787.7 - 46397.7i) q^{67} +(1.49076e6 + 2.58208e6i) q^{68} +(-1.36271e6 + 2.36027e6i) q^{70} -4.95678e6 q^{71} +817542. q^{73} +(277169. - 480071. i) q^{74} +(468170. + 810895. i) q^{76} +(-4.26396e6 - 7.38540e6i) q^{77} +(-3.78629e6 + 6.55804e6i) q^{79} -1.54545e6 q^{80} +2.34373e6 q^{82} +(509455. - 882402. i) q^{83} +(1.15532e6 + 2.00108e6i) q^{85} +(2.04262e6 + 3.53792e6i) q^{86} +(-951337. + 1.64776e6i) q^{88} +1.37281e6 q^{89} -1.64658e7 q^{91} +(-5.58756e6 + 9.67794e6i) q^{92} +(-2.78049e6 - 4.81596e6i) q^{94} +(362825. + 628432. i) q^{95} +(5.30114e6 - 9.18185e6i) q^{97} +2.06665e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 9 q^{2} - 77 q^{4} - 180 q^{5} - 700 q^{7} + 3654 q^{8} + 2790 q^{10} - 10890 q^{11} + 5480 q^{13} - 29475 q^{14} + 15967 q^{16} + 32832 q^{17} + 32048 q^{19} - 12195 q^{20} - 60705 q^{22} - 24372 q^{23}+ \cdots + 45559476 q^{98}+O(q^{100}) $ 4 * q - 9 * q^2 - 77 * q^4 - 180 * q^5 - 700 * q^7 + 3654 * q^8 + 2790 * q^10 - 10890 * q^11 + 5480 * q^13 - 29475 * q^14 + 15967 * q^16 + 32832 * q^17 + 32048 * q^19 - 12195 * q^20 - 60705 * q^22 - 24372 * q^23 + 138880 * q^25 - 470520 * q^26 + 527750 * q^28 + 143280 * q^29 + 38708 * q^31 + 439965 * q^32 + 614088 * q^34 + 231300 * q^35 + 911240 * q^37 + 275382 * q^38 - 135765 * q^40 - 731880 * q^41 + 1088840 * q^43 + 1049130 * q^44 + 3298788 * q^46 - 1561500 * q^47 - 967164 * q^49 + 519660 * q^50 + 2106380 * q^52 + 5220936 * q^53 + 2007000 * q^55 + 650475 * q^56 + 720810 * q^58 - 1731960 * q^59 + 620192 * q^61 - 8572302 * q^62 - 2081678 * q^64 + 914400 * q^65 - 346600 * q^67 + 5559624 * q^68 - 3094425 * q^70 - 8484480 * q^71 - 6290380 * q^73 + 4267710 * q^74 + 2510486 * q^76 - 4864500 * q^77 - 10110616 * q^79 - 3411090 * q^80 - 4282380 * q^82 - 644202 * q^83 - 101520 * q^85 - 2313270 * q^86 - 9374715 * q^88 + 12042000 * q^89 - 41744000 * q^91 - 14795802 * q^92 + 3751290 * q^94 - 747180 * q^95 - 4098670 * q^97 + 45559476 * q^98

Character values

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

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

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 $

$2$	−8.29669	+	14.3703i	−0.733331	+	1.27017i	0.222121	+	0.975019i	$0.428702\pi$
$2$	−8.29669	+	14.3703i	−0.733331	+	1.27017i	−0.955452	+	0.295147i	$0.904631\pi$
$3$		0			0
$3$		0			0
$4$	−73.6702	−	127.601i	−0.575549	−	0.996880i
$5$	−57.0934	−	98.8886i	−0.204264	−	0.353795i	0.745634	−	0.666355i	$-0.232147\pi$
$5$	−57.0934	−	98.8886i	−0.204264	−	0.353795i	−0.949898	+	0.312561i	$0.898813\pi$
$6$		0			0
$7$	−719.202	+	1245.70i	−0.792516	+	1.37268i	0.131889	+	0.991265i	$0.457896\pi$
$7$	−719.202	+	1245.70i	−0.792516	+	1.37268i	−0.924405	+	0.381413i	$0.875437\pi$
$8$	320.924			0.221609
$9$		0			0
$10$	1894.75			0.599171
$11$	−2964.37	+	5134.44i	−0.671518	+	1.16310i	0.305956	+	0.952046i	$0.401024\pi$
$11$	−2964.37	+	5134.44i	−0.671518	+	1.16310i	−0.977474	+	0.211058i	$0.932309\pi$
$12$		0			0
$13$	5723.62	+	9913.60i	0.722552	+	1.25150i	0.959974	+	0.280090i	$0.0903643\pi$
$13$	5723.62	+	9913.60i	0.722552	+	1.25150i	−0.237422	+	0.971407i	$0.576302\pi$
$14$	−11934.0	−	20670.3i	−1.16235	−	2.01325i
$15$		0			0
$16$	6767.18	−	11721.1i	0.413036	−	0.715399i
$17$	−20235.6			−0.998955			−0.499477	−	0.866327i	$-0.666475\pi$
$17$	−20235.6			−0.998955			−0.499477	+	0.866327i	$0.666475\pi$
$18$		0			0
$19$	−6354.94			−0.212556			−0.106278	−	0.994336i	$-0.533893\pi$
$19$	−6354.94			−0.212556			−0.106278	+	0.994336i	$0.533893\pi$
$20$	−8412.17	+	14570.3i	−0.235127	+	0.407252i
$21$		0			0
$22$	−49188.9	−	85197.7i	−0.984890	−	1.70588i
$23$	−37922.8	−	65684.2i	−0.649910	−	1.12568i	−0.983144	−	0.182832i	$-0.941473\pi$
$23$	−37922.8	−	65684.2i	−0.649910	−	1.12568i	0.333235	−	0.942844i	$-0.391860\pi$
$24$		0			0
$25$	32543.2	−	56366.5i	0.416553	−	0.721491i
$26$	−189948.			−2.11948
$27$		0			0
$28$	211935.			1.82453
$29$	37392.1	−	64765.1i	0.284700	−	0.493115i	−0.687836	−	0.725866i	$-0.741439\pi$
$29$	37392.1	−	64765.1i	0.284700	−	0.493115i	0.972536	+	0.232751i	$0.0747727\pi$
$30$		0			0
$31$	94681.4	+	163993.i	0.570820	+	0.988688i	0.996482	+	0.0838064i	$0.0267077\pi$
$31$	94681.4	+	163993.i	0.570820	+	0.988688i	−0.425663	+	0.904882i	$0.639959\pi$
$32$	132830.	+	230068.i	0.716589	+	1.24117i
$33$		0			0
$34$	167889.	−	290792.i	0.732565	−	1.26884i
$35$	164247.			0.647528
$36$		0			0
$37$	−33407.2			−0.108426			−0.0542130	−	0.998529i	$-0.517265\pi$
$37$	−33407.2			−0.108426			−0.0542130	+	0.998529i	$0.517265\pi$
$38$	52725.0	−	91322.4i	0.155874	−	0.269982i
$39$		0			0
$40$	−18322.6	−	31735.7i	−0.0452666	−	0.0784041i
$41$	−70622.4	−	122322.i	−0.160029	−	0.277179i	0.774850	−	0.632145i	$-0.217826\pi$
$41$	−70622.4	−	122322.i	−0.160029	−	0.277179i	−0.934879	+	0.354967i	$0.884492\pi$
$42$		0			0
$43$	123099.	−	213213.i	0.236109	−	0.408954i	−0.723485	−	0.690340i	$-0.757461\pi$
$43$	123099.	−	213213.i	0.236109	−	0.408954i	0.959595	+	0.281386i	$0.0907943\pi$
$44$	873543.			1.54597
$45$		0			0
$46$	1.25854e6			1.90640
$47$	−167566.	+	290234.i	−0.235421	+	0.407761i	−0.959395	−	0.282067i	$-0.908980\pi$
$47$	−167566.	+	290234.i	−0.235421	+	0.407761i	0.723974	+	0.689827i	$0.242313\pi$
$48$		0			0
$49$	−622733.	−	1.07860e6i	−0.756163	−	1.30971i
$50$	540002.	+	935310.i	0.610942	+	1.05818i
$51$		0			0
$52$	843321.	−	1.46067e6i	0.831728	−	1.44059i
$53$	1.65156e6			1.52381			0.761904	−	0.647691i	$-0.224265\pi$
$53$	1.65156e6			1.52381			0.761904	+	0.647691i	$0.224265\pi$
$54$		0			0
$55$	676983.			0.548667
$56$	−230809.	+	399774.i	−0.175629	+	0.304198i
$57$		0			0
$58$	620462.	+	1.07467e6i	0.417559	+	0.723233i
$59$	−1.02411e6	−	1.77382e6i	−0.649182	−	1.12442i	−0.983319	−	0.181892i	$-0.941778\pi$
$59$	−1.02411e6	−	1.77382e6i	−0.649182	−	1.12442i	0.334136	−	0.942525i	$-0.391555\pi$
$60$		0			0
$61$	295235.	−	511361.i	0.166538	−	0.288452i	−0.770663	−	0.637243i	$-0.780075\pi$
$61$	295235.	−	511361.i	0.166538	−	0.288452i	0.937200	+	0.348792i	$0.113408\pi$
$62$	−3.14217e6			−1.67440
$63$		0			0
$64$	−2.67579e6			−1.27591
$65$	653562.	−	1.13200e6i	0.295182	−	0.511270i
$66$		0			0
$67$	−26787.7	−	46397.7i	−0.0108811	−	0.0188467i	0.860534	−	0.509394i	$-0.170130\pi$
$67$	−26787.7	−	46397.7i	−0.0108811	−	0.0188467i	−0.871415	+	0.490547i	$0.836797\pi$
$68$	1.49076e6	+	2.58208e6i	0.574947	+	0.995838i
$69$		0			0
$70$	−1.36271e6	+	2.36027e6i	−0.474853	+	0.822469i
$71$	−4.95678e6			−1.64360			−0.821798	−	0.569779i	$-0.807029\pi$
$71$	−4.95678e6			−1.64360			−0.821798	+	0.569779i	$0.807029\pi$
$72$		0			0
$73$	817542.			0.245969			0.122984	−	0.992409i	$-0.460753\pi$
$73$	817542.			0.245969			0.122984	+	0.992409i	$0.460753\pi$
$74$	277169.	−	480071.i	0.0795121	−	0.137719i
$75$		0			0
$76$	468170.	+	810895.i	0.122337	+	0.211893i
$77$	−4.26396e6	−	7.38540e6i	−1.06438	−	1.84356i
$78$		0			0
$79$	−3.78629e6	+	6.55804e6i	−0.864009	+	1.49651i	0.00401783	+	0.999992i	$0.498721\pi$
$79$	−3.78629e6	+	6.55804e6i	−0.864009	+	1.49651i	−0.868027	+	0.496516i	$0.834612\pi$
$80$	−1.54545e6			−0.337473
$81$		0			0
$82$	2.34373e6			0.469417
$83$	509455.	−	882402.i	0.0977986	−	0.169392i	−0.812975	−	0.582299i	$-0.802153\pi$
$83$	509455.	−	882402.i	0.0977986	−	0.169392i	0.910773	+	0.412907i	$0.135487\pi$
$84$		0			0
$85$	1.15532e6	+	2.00108e6i	0.204050	+	0.353425i
$86$	2.04262e6	+	3.53792e6i	0.346293	+	0.599797i
$87$		0			0
$88$	−951337.	+	1.64776e6i	−0.148814	+	0.257754i
$89$	1.37281e6			0.206418			0.103209	−	0.994660i	$-0.467089\pi$
$89$	1.37281e6			0.206418			0.103209	+	0.994660i	$0.467089\pi$
$90$		0			0
$91$	−1.64658e7			−2.29054
$92$	−5.58756e6	+	9.67794e6i	−0.748109	+	1.29576i
$93$		0			0
$94$	−2.78049e6	−	4.81596e6i	−0.345283	−	0.598047i
$95$	362825.	+	628432.i	0.0434175	+	0.0752013i
$96$		0			0
$97$	5.30114e6	−	9.18185e6i	0.589750	−	1.02148i	−0.404514	−	0.914532i	$-0.632559\pi$
$97$	5.30114e6	−	9.18185e6i	0.589750	−	1.02148i	0.994265	−	0.106946i	$-0.0341072\pi$
$98$	2.06665e7			2.21807
$99$		0			0
$100$	−9.58986e6			−0.958986
$101$	5.21385e6	−	9.03065e6i	0.503540	−	0.872156i	−0.496452	−	0.868064i	$-0.665364\pi$
$101$	5.21385e6	−	9.03065e6i	0.503540	−	0.872156i	0.999992	−	0.00409199i	$-0.00130252\pi$
$102$		0			0
$103$	−766574.	−	1.32775e6i	−0.0691232	−	0.119725i	0.829392	−	0.558667i	$-0.188687\pi$
$103$	−766574.	−	1.32775e6i	−0.0691232	−	0.119725i	−0.898516	+	0.438942i	$0.855353\pi$
$104$	1.83685e6	+	3.18151e6i	0.160124	+	0.277343i
$105$		0			0
$106$	−1.37025e7	+	2.37335e7i	−1.11745	+	1.93549i
$107$	9.64859e6			0.761414			0.380707	−	0.924696i	$-0.375681\pi$
$107$	9.64859e6			0.761414			0.380707	+	0.924696i	$0.375681\pi$
$108$		0			0
$109$	5.79409e6			0.428541			0.214270	−	0.976774i	$-0.431263\pi$
$109$	5.79409e6			0.428541			0.214270	+	0.976774i	$0.431263\pi$
$110$	−5.61672e6	+	9.72845e6i	−0.402354	+	0.696898i
$111$		0			0
$112$	9.73395e6	+	1.68597e7i	0.654675	+	1.13393i
$113$	7.24214e6	+	1.25438e7i	0.472164	+	0.817812i	0.999493	−	0.0318497i	$-0.0101398\pi$
$113$	7.24214e6	+	1.25438e7i	0.472164	+	0.817812i	−0.527329	+	0.849661i	$0.676806\pi$
$114$		0			0
$115$	−4.33028e6	+	7.50027e6i	−0.265506	+	0.459869i
$116$	−1.10188e7			−0.655435
$117$		0			0
$118$	3.39871e7			1.90426
$119$	1.45535e7	−	2.52074e7i	0.791688	−	1.37124i
$120$		0			0
$121$	−7.83137e6	−	1.35643e7i	−0.401873	−	0.696064i
$122$	4.89894e6	+	8.48521e6i	0.244255	+	0.423061i
$123$		0			0
$124$	1.39504e7	−	2.41628e7i	0.657069	−	1.13808i
$125$	−1.63528e7			−0.748873
$126$		0			0
$127$	−1.65775e7			−0.718136			−0.359068	−	0.933311i	$-0.616905\pi$
$127$	−1.65775e7			−0.718136			−0.359068	+	0.933311i	$0.616905\pi$
$128$	5.19800e6	−	9.00320e6i	0.219079	−	0.379456i
$129$		0			0
$130$	1.08448e7	+	1.87837e7i	0.432932	+	0.749860i
$131$	−7.23890e6	−	1.25381e7i	−0.281335	−	0.487286i	0.690379	−	0.723448i	$-0.257444\pi$
$131$	−7.23890e6	−	1.25381e7i	−0.281335	−	0.487286i	−0.971714	+	0.236162i	$0.924110\pi$
$132$		0			0
$133$	4.57049e6	−	7.91632e6i	0.168454	−	0.291771i
$134$	888999.			0.0319179
$135$		0			0
$136$	−6.49411e6			−0.221377
$137$	−2.10969e7	+	3.65409e7i	−0.700966	+	1.21411i	0.267161	+	0.963652i	$0.413914\pi$
$137$	−2.10969e7	+	3.65409e7i	−0.700966	+	1.21411i	−0.968128	+	0.250457i	$0.919419\pi$
$138$		0			0
$139$	−2.39966e7	−	4.15634e7i	−0.757877	−	1.31268i	−0.943931	−	0.330141i	$-0.892904\pi$
$139$	−2.39966e7	−	4.15634e7i	−0.757877	−	1.31268i	0.186055	−	0.982539i	$-0.440430\pi$
$140$	−1.21001e7	−	2.09580e7i	−0.372684	−	0.645508i
$141$		0			0
$142$	4.11249e7	−	7.12303e7i	1.20530	−	2.08764i
$143$	−6.78676e7			−1.94083
$144$		0			0
$145$	−8.53938e6			−0.232615
$146$	−6.78289e6	+	1.17483e7i	−0.180377	+	0.312421i
$147$		0			0
$148$	2.46111e6	+	4.26277e6i	0.0624044	+	0.108088i
$149$	−5.78338e6	−	1.00171e7i	−0.143229	−	0.248079i	0.785482	−	0.618884i	$-0.212415\pi$
$149$	−5.78338e6	−	1.00171e7i	−0.143229	−	0.248079i	−0.928711	+	0.370805i	$0.879082\pi$
$150$		0			0
$151$	−5.49667e6	+	9.52051e6i	−0.129921	+	0.225030i	−0.923646	−	0.383247i	$-0.874806\pi$
$151$	−5.49667e6	+	9.52051e6i	−0.129921	+	0.225030i	0.793725	+	0.608277i	$0.208139\pi$
$152$	−2.03945e6			−0.0471044
$153$		0			0
$154$	1.41507e8			3.12216
$155$	1.08114e7	−	1.87258e7i	0.233195	−	0.403906i
$156$		0			0
$157$	−1.24009e7	−	2.14790e7i	−0.255744	−	0.442961i	0.709354	−	0.704853i	$-0.248987\pi$
$157$	−1.24009e7	−	2.14790e7i	−0.255744	−	0.442961i	−0.965097	+	0.261892i	$0.915654\pi$
$158$	−6.28273e7	−	1.08820e8i	−1.26721	−	2.19487i
$159$		0			0
$160$	1.51674e7	−	2.62707e7i	0.292746	−	0.507051i
$161$	1.09097e8			2.06025
$162$		0			0
$163$	3.04106e6			0.0550008			0.0275004	−	0.999622i	$-0.491245\pi$
$163$	3.04106e6			0.0550008			0.0275004	+	0.999622i	$0.491245\pi$
$164$	−1.04055e7	+	1.80229e7i	−0.184209	+	0.319060i
$165$		0			0
$166$	8.45359e6	+	1.46420e7i	0.143438	+	0.248441i
$167$	5.34244e7	+	9.25337e7i	0.887629	+	1.53742i	0.842670	+	0.538430i	$0.180982\pi$
$167$	5.34244e7	+	9.25337e7i	0.887629	+	1.53742i	0.0449591	+	0.998989i	$0.485684\pi$
$168$		0			0
$169$	−3.41454e7	+	5.91415e7i	−0.544162	+	0.942517i
$170$	−3.83414e7			−0.598545
$171$		0			0
$172$	−3.62748e7			−0.543570
$173$	−4.97468e7	+	8.61640e7i	−0.730472	+	1.26521i	0.226209	+	0.974079i	$0.427367\pi$
$173$	−4.97468e7	+	8.61640e7i	−0.730472	+	1.26521i	−0.956682	+	0.291136i	$0.905967\pi$
$174$		0			0
$175$	4.68103e7	+	8.10778e7i	0.660249	+	1.14359i
$176$	4.01208e7	+	6.94913e7i	0.554722	+	0.960807i
$177$		0			0
$178$	−1.13898e7	+	1.97277e7i	−0.151372	+	0.262185i
$179$	2.29173e7			0.298661			0.149330	−	0.988787i	$-0.452288\pi$
$179$	2.29173e7			0.298661			0.149330	+	0.988787i	$0.452288\pi$
$180$		0			0
$181$	−1.35824e8			−1.70256			−0.851280	−	0.524712i	$-0.824173\pi$
$181$	−1.35824e8			−1.70256			−0.851280	+	0.524712i	$0.824173\pi$
$182$	1.36611e8	−	2.36618e8i	1.67972	−	2.90936i
$183$		0			0
$184$	−1.21703e7	−	2.10796e7i	−0.144026	−	0.249460i
$185$	1.90733e6	+	3.30359e6i	0.0221475	+	0.0383605i
$186$		0			0
$187$	5.99859e7	−	1.03899e8i	0.670816	−	1.16189i
$188$	4.93786e7			0.541984
$189$		0			0
$190$	−1.20410e7			−0.127358
$191$	−5.59594e7	+	9.69245e7i	−0.581107	+	1.00651i	0.414241	+	0.910167i	$0.364047\pi$
$191$	−5.59594e7	+	9.69245e7i	−0.581107	+	1.00651i	−0.995348	+	0.0963402i	$0.969286\pi$
$192$		0			0
$193$	−5.14492e7	−	8.91126e7i	−0.515143	−	0.892254i	−0.999846	−	0.0175746i	$-0.994406\pi$
$193$	−5.14492e7	−	8.91126e7i	−0.515143	−	0.892254i	0.484703	−	0.874679i	$-0.338928\pi$
$194$	8.79639e7	+	1.52358e8i	0.864965	+	1.49816i
$195$		0			0
$196$	−9.17537e7	+	1.58922e8i	−0.870417	+	1.50761i
$197$	3.77994e7			0.352252			0.176126	−	0.984368i	$-0.443643\pi$
$197$	3.77994e7			0.352252			0.176126	+	0.984368i	$0.443643\pi$
$198$		0			0
$199$	−49088.1			−0.000441560			−0.000220780	−	1.00000i	$-0.500070\pi$
$199$	−49088.1			−0.000441560			−0.000220780		1.00000i	$0.500070\pi$
$200$	1.04439e7	−	1.80894e7i	0.0923118	−	0.159889i
$201$		0			0
$202$	8.65154e7	+	1.49849e8i	0.738522	+	1.27916i
$203$	5.37850e7	+	9.31584e7i	0.451258	+	0.781603i
$204$		0			0
$205$	−8.06415e6	+	1.39675e7i	−0.0653762	+	0.113235i
$206$	2.54401e7			0.202761
$207$		0			0
$208$	1.54931e8			1.19376
$209$	1.88384e7	−	3.26290e7i	0.142735	−	0.247225i
$210$		0			0
$211$	−9.42860e7	−	1.63308e8i	−0.690969	−	1.19679i	−0.971521	−	0.236954i	$-0.923851\pi$
$211$	−9.42860e7	−	1.63308e8i	−0.690969	−	1.19679i	0.280552	−	0.959839i	$-0.409483\pi$
$212$	−1.21671e8	−	2.10741e8i	−0.877025	−	1.51905i
$213$		0			0
$214$	−8.00514e7	+	1.38653e8i	−0.558368	+	0.967122i
$215$	−2.81125e7			−0.192914
$216$		0			0
$217$	−2.72380e8			−1.80953
$218$	−4.80718e7	+	8.32627e7i	−0.314262	+	0.544318i
$219$		0			0
$220$	−4.98735e7	−	8.63835e7i	−0.315784	−	0.546955i
$221$	−1.15821e8	−	2.00608e8i	−0.721797	−	1.25019i
$222$		0			0
$223$	−5.28378e7	+	9.15177e7i	−0.319064	+	0.552635i	−0.980293	−	0.197549i	$-0.936702\pi$
$223$	−5.28378e7	+	9.15177e7i	−0.319064	+	0.552635i	0.661229	+	0.750184i	$0.270035\pi$
$224$	−3.82125e8			−2.27163
$225$		0			0
$226$	−2.40343e8			−1.38501
$227$	2.29625e7	−	3.97723e7i	0.130295	−	0.225678i	−0.793495	−	0.608577i	$-0.791741\pi$
$227$	2.29625e7	−	3.97723e7i	0.130295	−	0.225678i	0.923790	+	0.382898i	$0.125074\pi$
$228$		0			0
$229$	6.14475e7	+	1.06430e8i	0.338127	+	0.585653i	0.984080	−	0.177724i	$-0.0568733\pi$
$229$	6.14475e7	+	1.06430e8i	0.338127	+	0.585653i	−0.645953	+	0.763377i	$0.723540\pi$
$230$	−7.18540e7	−	1.24455e8i	−0.389407	−	0.674473i
$231$		0			0
$232$	1.20000e7	−	2.07847e7i	0.0630921	−	0.109279i
$233$	1.68276e8			0.871519			0.435760	−	0.900063i	$-0.356480\pi$
$233$	1.68276e8			0.871519			0.435760	+	0.900063i	$0.356480\pi$
$234$		0			0
$235$	3.82677e7			0.192351
$236$	−1.50894e8	+	2.61355e8i	−0.747272	+	1.29431i
$237$		0			0
$238$	2.41492e8	+	4.18277e8i	1.16114	+	2.01115i
$239$	−4.01263e7	−	6.95008e7i	−0.190124	−	0.329304i	0.755167	−	0.655532i	$-0.227556\pi$
$239$	−4.01263e7	−	6.95008e7i	−0.190124	−	0.329304i	−0.945291	+	0.326228i	$0.894222\pi$
$240$		0			0
$241$	−7.46641e7	+	1.29322e8i	−0.343599	+	0.595131i	−0.985098	−	0.171993i	$-0.944980\pi$
$241$	−7.46641e7	+	1.29322e8i	−0.343599	+	0.595131i	0.641499	+	0.767124i	$0.278313\pi$
$242$	2.59898e8			1.17882
$243$		0			0
$244$	−8.70000e7			−0.383402
$245$	−7.11078e7	+	1.23162e8i	−0.308913	+	0.535053i
$246$		0			0
$247$	−3.63733e7	−	6.30004e7i	−0.153583	−	0.266014i
$248$	3.03855e7	+	5.26293e7i	0.126499	+	0.219102i
$249$		0			0
$250$	1.35675e8	−	2.34995e8i	0.549172	−	0.951194i
$251$	−4.54290e8			−1.81332			−0.906661	−	0.421861i	$-0.861377\pi$
$251$	−4.54290e8			−1.81332			−0.906661	+	0.421861i	$0.861377\pi$
$252$		0			0
$253$	4.49668e8			1.74570
$254$	1.37539e8	−	2.38224e8i	0.526631	−	0.912152i
$255$		0			0
$256$	−8.49980e7	−	1.47221e8i	−0.316642	−	0.548440i
$257$	1.46072e7	+	2.53004e7i	0.0536786	+	0.0929741i	0.891616	−	0.452792i	$-0.149572\pi$
$257$	1.46072e7	+	2.53004e7i	0.0536786	+	0.0929741i	−0.837938	+	0.545766i	$0.816239\pi$
$258$		0			0
$259$	2.40265e7	−	4.16151e7i	0.0859293	−	0.148834i
$260$	−1.92592e8			−0.679566
$261$		0			0
$262$	2.40236e8			0.825246
$263$	2.24703e8	−	3.89197e8i	0.761664	−	1.31924i	−0.180328	−	0.983607i	$-0.557716\pi$
$263$	2.24703e8	−	3.89197e8i	0.761664	−	1.31924i	0.941992	−	0.335635i	$-0.108951\pi$
$264$		0			0
$265$	−9.42934e7	−	1.63321e8i	−0.311258	−	0.539115i
$266$	7.58399e7	+	1.31359e8i	0.247066	+	0.427930i
$267$		0			0
$268$	−3.94692e6	+	6.83626e6i	−0.0125252	+	0.0216944i
$269$	−1.94325e7			−0.0608689			−0.0304345	−	0.999537i	$-0.509689\pi$
$269$	−1.94325e7			−0.0608689			−0.0304345	+	0.999537i	$0.509689\pi$
$270$		0			0
$271$	−2.13963e7			−0.0653051			−0.0326525	−	0.999467i	$-0.510395\pi$
$271$	−2.13963e7			−0.0653051			−0.0326525	+	0.999467i	$0.510395\pi$
$272$	−1.36938e8	+	2.37184e8i	−0.412604	+	0.714652i
$273$		0			0
$274$	−3.50069e8	−	6.06338e8i	−1.02808	−	1.78069i
$275$	1.92940e8	+	3.34182e8i	0.559445	+	0.968988i
$276$		0			0
$277$	9.25074e7	−	1.60228e8i	0.261515	−	0.452958i	−0.705129	−	0.709079i	$-0.749111\pi$
$277$	9.25074e7	−	1.60228e8i	0.261515	−	0.452958i	0.966645	+	0.256121i	$0.0824445\pi$
$278$	7.96371e8			2.22310
$279$		0			0
$280$	5.27107e7			0.143498
$281$	1.81176e7	−	3.13805e7i	0.0487111	−	0.0843700i	−0.840642	−	0.541591i	$-0.817822\pi$
$281$	1.81176e7	−	3.13805e7i	0.0487111	−	0.0843700i	0.889353	+	0.457221i	$0.151155\pi$
$282$		0			0
$283$	1.98050e8	+	3.43032e8i	0.519424	+	0.899668i	0.999745	+	0.0225757i	$0.00718669\pi$
$283$	1.98050e8	+	3.43032e8i	0.519424	+	0.899668i	−0.480321	+	0.877093i	$0.659480\pi$
$284$	3.65167e8	+	6.32488e8i	0.945970	+	1.63847i
$285$		0			0
$286$	5.63077e8	−	9.75278e8i	1.42327	−	2.46517i
$287$	2.03167e8			0.507303
$288$		0			0
$289$	−857331.			−0.00208932
$290$	7.08486e7	−	1.22713e8i	0.170584	−	0.295460i
$291$		0			0
$292$	−6.02285e7	−	1.04319e8i	−0.141567	−	0.245201i
$293$	−1.98234e8	−	3.43351e8i	−0.460406	−	0.797447i	0.538575	−	0.842578i	$-0.318963\pi$
$293$	−1.98234e8	−	3.43351e8i	−0.460406	−	0.797447i	−0.998981	+	0.0451308i	$0.985630\pi$
$294$		0			0
$295$	−1.16940e8	+	2.02547e8i	−0.265208	+	0.459355i
$296$	−1.07212e7			−0.0240282
$297$		0			0
$298$	1.91932e8			0.420136
$299$	4.34111e8	−	7.51903e8i	0.939187	−	1.62672i
$300$		0			0
$301$	1.77066e8	+	3.06687e8i	0.374241	+	0.648204i
$302$	−9.12083e7	−	1.57977e8i	−0.190551	−	0.330043i
$303$		0			0
$304$	−4.30051e7	+	7.44869e7i	−0.0877934	+	0.152063i
$305$	−6.74238e7			−0.136070
$306$		0			0
$307$	−3.12263e8			−0.615936			−0.307968	−	0.951397i	$-0.599649\pi$
$307$	−3.12263e8			−0.615936			−0.307968	+	0.951397i	$0.599649\pi$
$308$	−6.28254e8	+	1.08817e9i	−1.22520	+	2.12211i
$309$		0			0
$310$	1.79397e8	+	3.10725e8i	0.342019	+	0.592393i
$311$	−1.41454e8	−	2.45006e8i	−0.266658	−	0.461865i	0.701339	−	0.712828i	$-0.252586\pi$
$311$	−1.41454e8	−	2.45006e8i	−0.266658	−	0.461865i	−0.967997	+	0.250963i	$0.919253\pi$
$312$		0			0
$313$	4.77901e8	−	8.27749e8i	0.880912	−	1.52578i	0.0305838	−	0.999532i	$-0.490263\pi$
$313$	4.77901e8	−	8.27749e8i	0.880912	−	1.52578i	0.850328	−	0.526252i	$-0.176403\pi$
$314$	4.11546e8			0.750179
$315$		0			0
$316$	1.11575e9			1.98912
$317$	−2.06526e8	+	3.57713e8i	−0.364139	+	0.630707i	−0.988638	−	0.150319i	$-0.951970\pi$
$317$	−2.06526e8	+	3.57713e8i	−0.364139	+	0.630707i	0.624499	+	0.781026i	$0.285303\pi$
$318$		0			0
$319$	2.21688e8	+	3.83975e8i	0.382362	+	0.662271i
$320$	1.52770e8	+	2.64605e8i	0.260623	+	0.451412i
$321$		0			0
$322$	−9.05141e8	+	1.56775e9i	−1.51085	+	2.61687i
$323$	1.28596e8			0.212334
$324$		0			0
$325$	7.45059e8			1.20392
$326$	−2.52308e7	+	4.37010e7i	−0.0403338	+	0.0698602i
$327$		0			0
$328$	−2.26644e7	−	3.92560e7i	−0.0354639	−	0.0614253i
$329$	−2.41028e8	−	4.17473e8i	−0.373149	−	0.646313i
$330$		0			0
$331$	−1.14440e8	+	1.98216e8i	−0.173452	+	0.300428i	−0.939625	−	0.342207i	$-0.888826\pi$
$331$	−1.14440e8	+	1.98216e8i	−0.173452	+	0.300428i	0.766172	+	0.642635i	$0.222159\pi$
$332$	−1.50127e8			−0.225151
$333$		0			0
$334$	−1.77298e9			−2.60370
$335$	−3.05881e6	+	5.29801e6i	−0.00444524	+	0.00769938i
$336$		0			0
$337$	−4.89037e8	−	8.47037e8i	−0.696044	−	1.20558i	−0.969827	−	0.243793i	$-0.921608\pi$
$337$	−4.89037e8	−	8.47037e8i	−0.696044	−	1.20558i	0.273783	−	0.961792i	$-0.411725\pi$
$338$	−5.66587e8	−	9.81358e8i	−0.798102	−	1.38235i
$339$		0			0
$340$	1.70226e8	−	2.94839e8i	0.234881	−	0.406827i
$341$	−1.12268e9			−1.53326
$342$		0			0
$343$	6.06895e8			0.812053
$344$	3.95053e7	−	6.84252e7i	0.0523240	−	0.0906278i
$345$		0			0
$346$	−8.25468e8	−	1.42975e9i	−1.07136	−	1.85564i
$347$	7.10494e7	+	1.23061e8i	0.0912867	+	0.158113i	0.908053	−	0.418856i	$-0.137569\pi$
$347$	7.10494e7	+	1.23061e8i	0.0912867	+	0.158113i	−0.816766	+	0.576969i	$0.804235\pi$
$348$		0			0
$349$	2.31667e8	−	4.01259e8i	0.291726	−	0.505284i	−0.682492	−	0.730893i	$-0.739104\pi$
$349$	2.31667e8	−	4.01259e8i	0.291726	−	0.505284i	0.974218	+	0.225609i	$0.0724372\pi$
$350$	−1.55348e9			−1.93673
$351$		0			0
$352$	−1.57502e9			−1.92481
$353$	1.10318e8	−	1.91076e8i	0.133486	−	0.231204i	−0.791532	−	0.611127i	$-0.790716\pi$
$353$	1.10318e8	−	1.91076e8i	0.133486	−	0.231204i	0.925018	+	0.379924i	$0.124050\pi$
$354$		0			0
$355$	2.82999e8	+	4.90169e8i	0.335727	+	0.581496i
$356$	−1.01136e8	−	1.75172e8i	−0.118803	−	0.205773i
$357$		0			0
$358$	−1.90138e8	+	3.29329e8i	−0.219017	+	0.379349i
$359$	2.57110e8			0.293284			0.146642	−	0.989190i	$-0.453153\pi$
$359$	2.57110e8			0.293284			0.146642	+	0.989190i	$0.453153\pi$
$360$		0			0
$361$	−8.53486e8			−0.954820
$362$	1.12689e9	−	1.95183e9i	1.24854	−	2.16253i
$363$		0			0
$364$	1.21304e9	+	2.10104e9i	1.31831	+	2.28339i
$365$	−4.66762e7	−	8.08456e7i	−0.0502425	−	0.0870225i
$366$		0			0
$367$	−3.61360e8	+	6.25893e8i	−0.381600	+	0.660951i	−0.991291	−	0.131688i	$-0.957960\pi$
$367$	−3.61360e8	+	6.25893e8i	−0.381600	+	0.660951i	0.609691	+	0.792639i	$0.291293\pi$
$368$	−1.02652e9			−1.07374
$369$		0			0
$370$	−6.32980e7			−0.0649657
$371$	−1.18781e9	+	2.05735e9i	−1.20764	+	2.09170i
$372$		0			0
$373$	2.94579e8	+	5.10226e8i	0.293915	+	0.509075i	0.974732	−	0.223378i	$-0.0717085\pi$
$373$	2.94579e8	+	5.10226e8i	0.293915	+	0.509075i	−0.680817	+	0.732453i	$0.738375\pi$
$374$	9.95369e8	+	1.72403e9i	0.983861	+	1.70410i
$375$		0			0
$376$	−5.37761e7	+	9.31429e7i	−0.0521713	+	0.0903634i
$377$	8.56073e8			0.822842
$378$		0			0
$379$	9.02541e8			0.851589			0.425794	−	0.904820i	$-0.359995\pi$
$379$	9.02541e8			0.851589			0.425794	+	0.904820i	$0.359995\pi$
$380$	5.34588e7	−	9.25934e7i	0.0499778	−	0.0865641i
$381$		0			0
$382$	−9.28556e8	−	1.60831e9i	−0.852288	−	1.47621i
$383$	−2.79688e8	−	4.84433e8i	−0.254377	−	0.440594i	0.710349	−	0.703849i	$-0.248537\pi$
$383$	−2.79688e8	−	4.84433e8i	−0.254377	−	0.440594i	−0.964726	+	0.263256i	$0.915204\pi$
$384$		0			0
$385$	−4.86888e8	+	8.43315e8i	−0.434827	+	0.753142i
$386$	1.70743e9			1.51108
$387$		0			0
$388$	−1.56215e9			−1.35772
$389$	6.70702e8	−	1.16169e9i	0.577705	−	1.00061i	−0.418037	−	0.908430i	$-0.637282\pi$
$389$	6.70702e8	−	1.16169e9i	0.577705	−	1.00061i	0.995742	−	0.0921844i	$-0.0293849\pi$
$390$		0			0
$391$	7.67392e8	+	1.32916e9i	0.649230	+	1.12450i
$392$	−1.99850e8	−	3.46150e8i	−0.167572	−	0.290244i
$393$		0			0
$394$	−3.13610e8	+	5.43189e8i	−0.258317	+	0.447419i
$395$	8.64687e8			0.705942
$396$		0			0
$397$	2.24763e9			1.80285			0.901423	−	0.432939i	$-0.142523\pi$
$397$	2.24763e9			1.80285			0.901423	+	0.432939i	$0.142523\pi$
$398$	407269.	−	705410.i	0.000323810	−	0.000560855i
$399$		0			0
$400$	−4.40451e8	−	7.62884e8i	−0.344103	−	0.596003i
$401$	1.20251e9	+	2.08281e9i	0.931289	+	1.61304i	0.781120	+	0.624380i	$0.214648\pi$
$401$	1.20251e9	+	2.08281e9i	0.931289	+	1.61304i	0.150169	+	0.988660i	$0.452018\pi$
$402$		0			0
$403$	−1.08384e9	+	1.87727e9i	−0.824893	+	1.42876i
$404$	−1.53642e9			−1.15925
$405$		0			0
$406$	−1.78495e9			−1.32369
$407$	9.90311e7	−	1.71527e8i	0.0728100	−	0.126111i
$408$		0			0
$409$	−3.81997e8	−	6.61639e8i	−0.276076	−	0.478178i	0.694330	−	0.719657i	$-0.255701\pi$
$409$	−3.81997e8	−	6.61639e8i	−0.276076	−	0.478178i	−0.970406	+	0.241479i	$0.922367\pi$
$410$	−1.33812e8	−	2.31768e8i	−0.0958849	−	0.166077i
$411$		0			0
$412$	−1.12947e8	+	1.95631e8i	−0.0795676	+	0.137815i
$413$	2.94618e9			2.05795
$414$		0			0
$415$	−1.16346e8			−0.0799068
$416$	−1.52053e9	+	2.63364e9i	−1.03554	+	1.79362i
$417$		0			0
$418$	3.12593e8	+	5.41426e8i	0.209345	+	0.362596i
$419$	−1.44306e8	−	2.49945e8i	−0.0958373	−	0.165995i	0.814120	−	0.580696i	$-0.197220\pi$
$419$	−1.44306e8	−	2.49945e8i	−0.0958373	−	0.165995i	−0.909958	+	0.414701i	$0.863886\pi$
$420$		0			0
$421$	7.79439e8	−	1.35003e9i	0.509090	−	0.881770i	−0.490855	−	0.871242i	$-0.663315\pi$
$421$	7.79439e8	−	1.35003e9i	0.509090	−	0.881770i	0.999945	−	0.0105283i	$-0.00335132\pi$
$422$	3.12905e9			2.02684
$423$		0			0
$424$	5.30027e8			0.337689
$425$	−6.58532e8	+	1.14061e9i	−0.416117	+	0.720737i
$426$		0			0
$427$	4.24667e8	+	7.35544e8i	0.263968	+	0.457205i
$428$	−7.10814e8	−	1.23117e9i	−0.438231	−	0.759038i
$429$		0			0
$430$	2.33240e8	−	4.03984e8i	0.141470	−	0.245033i
$431$	−9.87526e8			−0.594125			−0.297063	−	0.954858i	$-0.596007\pi$
$431$	−9.87526e8			−0.594125			−0.297063	+	0.954858i	$0.596007\pi$
$432$		0			0
$433$	−2.07048e9			−1.22564			−0.612820	−	0.790223i	$-0.709965\pi$
$433$	−2.07048e9			−1.22564			−0.612820	+	0.790223i	$0.709965\pi$
$434$	2.25986e9	−	3.91419e9i	1.32699	−	2.29841i
$435$		0			0
$436$	−4.26852e8	−	7.39329e8i	−0.246646	−	0.427204i
$437$	2.40997e8	+	4.17419e8i	0.138142	+	0.239270i
$438$		0			0
$439$	1.55383e9	−	2.69131e9i	0.876553	−	1.51823i	0.0214532	−	0.999770i	$-0.493171\pi$
$439$	1.55383e9	−	2.69131e9i	0.876553	−	1.51823i	0.855100	−	0.518464i	$-0.173496\pi$
$440$	2.17260e8			0.121589
$441$		0			0
$442$	3.84373e9			2.11726
$443$	−8.88643e8	+	1.53917e9i	−0.485640	+	0.841153i	−0.999864	−	0.0165031i	$-0.994747\pi$
$443$	−8.88643e8	+	1.53917e9i	−0.485640	+	0.841153i	0.514224	+	0.857656i	$0.328080\pi$
$444$		0			0
$445$	−7.83786e7	−	1.35756e8i	−0.0421636	−	0.0730294i
$446$	−8.76758e8	−	1.51859e9i	−0.467959	−	0.810528i
$447$		0			0
$448$	1.92443e9	−	3.33322e9i	1.01118	−	1.75142i
$449$	−3.38966e9			−1.76723			−0.883616	−	0.468212i	$-0.844898\pi$
$449$	−3.38966e9			−1.76723			−0.883616	+	0.468212i	$0.844898\pi$
$450$		0			0
$451$	8.37404e8			0.429850
$452$	1.06706e9	−	1.84820e9i	0.543506	−	0.941381i
$453$		0			0
$454$	3.81026e8	+	6.59957e8i	0.191099	+	0.330994i
$455$	9.40086e8	+	1.62828e9i	0.467873	+	0.810379i
$456$		0			0
$457$	1.04822e9	−	1.81557e9i	0.513744	−	0.889830i	−0.486129	−	0.873887i	$-0.661592\pi$
$457$	1.04822e9	−	1.81557e9i	0.513744	−	0.889830i	0.999873	−	0.0159431i	$-0.00507507\pi$
$458$	−2.03924e9			−0.991836
$459$		0			0
$460$	1.27605e9			0.611246
$461$	−8.92296e8	+	1.54550e9i	−0.424185	+	0.734711i	−0.996344	−	0.0854323i	$-0.972773\pi$
$461$	−8.92296e8	+	1.54550e9i	−0.424185	+	0.734711i	0.572158	+	0.820143i	$0.306106\pi$
$462$		0			0
$463$	−1.14900e9	−	1.99013e9i	−0.538005	−	0.931852i	−0.999011	−	0.0444554i	$-0.985845\pi$
$463$	−1.14900e9	−	1.99013e9i	−0.538005	−	0.931852i	0.461006	−	0.887397i	$-0.347489\pi$
$464$	−5.06079e8	−	8.76554e8i	−0.235183	−	0.407348i
$465$		0			0
$466$	−1.39614e9	+	2.41818e9i	−0.639112	+	1.10697i
$467$	−8.59979e8			−0.390732			−0.195366	−	0.980730i	$-0.562589\pi$
$467$	−8.59979e8			−0.390732			−0.195366	+	0.980730i	$0.562589\pi$
$468$		0			0
$469$	7.70632e7			0.0344939
$470$	−3.17496e8	+	5.49919e8i	−0.141057	+	0.244318i
$471$		0			0
$472$	−3.28663e8	−	5.69261e8i	−0.143865	−	0.249181i
$473$	7.29819e8	+	1.26408e9i	0.317103	+	0.549239i
$474$		0			0
$475$	−2.06810e8	+	3.58206e8i	−0.0885409	+	0.153357i
$476$	−4.28865e9			−1.82262
$477$		0			0
$478$	1.33166e9			0.557695
$479$	−1.53303e7	+	2.65529e7i	−0.00637349	+	0.0110392i	−0.869195	−	0.494470i	$-0.835362\pi$
$479$	−1.53303e7	+	2.65529e7i	−0.00637349	+	0.0110392i	0.862821	+	0.505509i	$0.168695\pi$
$480$		0			0
$481$	−1.91210e8	−	3.31185e8i	−0.0783434	−	0.135695i
$482$	−1.23893e9	−	2.14589e9i	−0.503944	−	0.872857i
$483$		0			0
$484$	−1.15388e9	+	1.99857e9i	−0.462595	+	0.801238i
$485$	−1.21064e9			−0.481858
$486$		0			0
$487$	−5.78717e8			−0.227047			−0.113523	−	0.993535i	$-0.536214\pi$
$487$	−5.78717e8			−0.227047			−0.113523	+	0.993535i	$0.536214\pi$
$488$	9.47479e7	−	1.64108e8i	0.0369063	−	0.0639235i
$489$		0			0
$490$	−1.17992e9	−	2.04368e9i	−0.453071	−	0.784742i
$491$	−1.64860e9	−	2.85545e9i	−0.628534	−	1.08865i	−0.987846	−	0.155436i	$-0.950322\pi$
$491$	−1.64860e9	−	2.85545e9i	−0.628534	−	1.08865i	0.359312	−	0.933218i	$-0.383011\pi$
$492$		0			0
$493$	−7.56654e8	+	1.31056e9i	−0.284402	+	0.492599i
$494$	1.20711e9			0.450509
$495$		0			0
$496$	2.56291e9			0.943076
$497$	3.56493e9	−	6.17463e9i	1.30258	−	2.25613i
$498$		0			0
$499$	2.13590e9	+	3.69949e9i	0.769537	+	1.33288i	0.937814	+	0.347138i	$0.112846\pi$
$499$	2.13590e9	+	3.69949e9i	0.769537	+	1.33288i	−0.168277	+	0.985740i	$0.553820\pi$
$500$	1.20472e9	+	2.08663e9i	0.431013	+	0.746536i
$501$		0			0
$502$	3.76910e9	−	6.52827e9i	1.32976	−	2.30322i
$503$	1.85857e9			0.651165			0.325582	−	0.945514i	$-0.394440\pi$
$503$	1.85857e9			0.651165			0.325582	+	0.945514i	$0.394440\pi$
$504$		0			0
$505$	−1.19071e9			−0.411419
$506$	−3.73076e9	+	6.46187e9i	−1.28018	+	2.21733i
$507$		0			0
$508$	1.22127e9	+	2.11530e9i	0.413322	+	0.715895i
$509$	1.06304e9	+	1.84125e9i	0.357305	+	0.618870i	0.987510	−	0.157559i	$-0.0503624\pi$
$509$	1.06304e9	+	1.84125e9i	0.357305	+	0.618870i	−0.630205	+	0.776429i	$0.717029\pi$
$510$		0			0
$511$	−5.87978e8	+	1.01841e9i	−0.194934	+	0.337636i
$512$	4.15150e9			1.36697
$513$		0			0
$514$	−4.84766e8			−0.157457
$515$	−8.75327e7	+	1.51611e8i	−0.0282387	+	0.0489109i
$516$		0			0
$517$	−9.93457e8	−	1.72072e9i	−0.316178	−	0.547637i
$518$	3.98681e8	+	6.90536e8i	0.126029	+	0.218289i
$519$		0			0
$520$	2.09744e8	−	3.63287e8i	0.0654150	−	0.113302i
$521$	−5.97837e9			−1.85204			−0.926021	−	0.377472i	$-0.876793\pi$
$521$	−5.97837e9			−1.85204			−0.926021	+	0.377472i	$0.876793\pi$
$522$		0			0
$523$	5.69436e8			0.174056			0.0870280	−	0.996206i	$-0.472263\pi$
$523$	5.69436e8			0.174056			0.0870280	+	0.996206i	$0.472263\pi$
$524$	−1.06658e9	+	1.84738e9i	−0.323844	+	0.560914i
$525$		0			0
$526$	3.72858e9	+	6.45809e9i	1.11710	+	1.93488i
$527$	−1.91594e9	−	3.31850e9i	−0.570223	−	0.987655i
$528$		0			0
$529$	−1.17386e9	+	2.03319e9i	−0.344765	+	0.597150i
$530$	3.12929e9			0.913021
$531$		0			0
$532$	−1.34684e9			−0.387815
$533$	8.08432e8	−	1.40025e9i	0.231259	−	0.400552i
$534$		0			0
$535$	−5.50871e8	−	9.54136e8i	−0.155529	−	0.269384i
$536$	−8.59683e6	−	1.48901e7i	−0.00241136	−	0.00417659i
$537$		0			0
$538$	1.61226e8	−	2.79251e8i	0.0446371	−	0.0773137i
$539$	7.38403e9			2.03111
$540$		0			0
$541$	−1.88830e9			−0.512722			−0.256361	−	0.966581i	$-0.582524\pi$
$541$	−1.88830e9			−0.512722			−0.256361	+	0.966581i	$0.582524\pi$
$542$	1.77519e8	−	3.07472e8i	0.0478902	−	0.0829483i
$543$		0			0
$544$	−2.68789e9	−	4.65557e9i	−0.715840	−	1.23987i
$545$	−3.30804e8	−	5.72969e8i	−0.0875352	−	0.151615i
$546$		0			0
$547$	−2.94314e8	+	5.09767e8i	−0.0768875	+	0.133173i	−0.901906	−	0.431933i	$-0.857832\pi$
$547$	−2.94314e8	+	5.09767e8i	−0.0768875	+	0.133173i	0.825018	+	0.565106i	$0.191165\pi$
$548$	6.21686e9			1.61376
$549$		0			0
$550$	−6.40305e9			−1.64103
$551$	−2.37625e8	+	4.11578e8i	−0.0605148	+	0.104815i
$552$		0			0
$553$	−5.44621e9	−	9.43311e9i	−1.36948	−	2.37201i
$554$	1.53501e9	+	2.65872e9i	0.383555	+	0.664336i
$555$		0			0
$556$	−3.53568e9	+	6.12397e9i	−0.872390	+	1.51102i
$557$	5.59795e9			1.37257			0.686287	−	0.727331i	$-0.259239\pi$
$557$	5.59795e9			1.37257			0.686287	+	0.727331i	$0.259239\pi$
$558$		0			0
$559$	2.81828e9			0.682405
$560$	1.11149e9	−	1.92515e9i	0.267453	−	0.463241i
$561$		0			0
$562$	3.00632e8	+	5.20709e8i	0.0714427	+	0.123742i
$563$	1.53093e9	+	2.65165e9i	0.361557	+	0.626235i	0.988217	−	0.153058i	$-0.0489121\pi$
$563$	1.53093e9	+	2.65165e9i	0.361557	+	0.626235i	−0.626661	+	0.779292i	$0.715579\pi$
$564$		0			0
$565$	8.26957e8	−	1.43233e9i	0.192892	−	0.334098i
$566$	−6.57263e9			−1.52364
$567$		0			0
$568$	−1.59075e9			−0.364236
$569$	−8.72861e8	+	1.51184e9i	−0.198633	+	0.344043i	−0.948086	−	0.318015i	$-0.896984\pi$
$569$	−8.72861e8	+	1.51184e9i	−0.198633	+	0.344043i	0.749452	+	0.662059i	$0.230317\pi$
$570$		0			0
$571$	2.64148e9	+	4.57517e9i	0.593773	+	1.02844i	0.993719	+	0.111906i	$0.0356955\pi$
$571$	2.64148e9	+	4.57517e9i	0.593773	+	1.02844i	−0.399946	+	0.916539i	$0.630971\pi$
$572$	4.99983e9	+	8.65995e9i	1.11704	+	1.93477i
$573$		0			0
$574$	−1.68562e9	+	2.91957e9i	−0.372021	+	0.644359i
$575$	−4.93651e9			−1.08289
$576$		0			0
$577$	−6.38776e9			−1.38431			−0.692155	−	0.721749i	$-0.743338\pi$
$577$	−6.38776e9			−1.38431			−0.692155	+	0.721749i	$0.743338\pi$
$578$	7.11301e6	−	1.23201e7i	0.00153217	−	0.00265379i
$579$		0			0
$580$	6.29098e8	+	1.08963e9i	0.133881	+	0.231889i
$581$	7.32803e8	+	1.26925e9i	0.155014	+	0.268492i
$582$		0			0
$583$	−4.89584e9	+	8.47985e9i	−1.02326	+	1.77235i
$584$	2.62369e8			0.0545089
$585$		0			0
$586$	6.57874e9			1.35052
$587$	2.96744e9	−	5.13976e9i	0.605548	−	1.04884i	−0.386417	−	0.922324i	$-0.626287\pi$
$587$	2.96744e9	−	5.13976e9i	0.605548	−	1.04884i	0.991965	−	0.126515i	$-0.0403793\pi$
$588$		0			0
$589$	−6.01695e8	−	1.04217e9i	−0.121331	−	0.210152i
$590$	−1.94044e9	−	3.36093e9i	−0.388971	−	0.673718i
$591$		0			0
$592$	−2.26072e8	+	3.91569e8i	−0.0447838	+	0.0775679i
$593$	−2.18286e9			−0.429867			−0.214933	−	0.976629i	$-0.568953\pi$
$593$	−2.18286e9			−0.429867			−0.214933	+	0.976629i	$0.568953\pi$
$594$		0			0
$595$	−3.32364e9			−0.646852
$596$	−8.52125e8	+	1.47592e9i	−0.164870	+	0.285563i
$597$		0			0
$598$	7.20338e9	+	1.24766e10i	1.37747	+	2.38585i
$599$	−4.25945e9	−	7.37759e9i	−0.809766	−	1.40256i	−0.913026	−	0.407902i	$-0.866260\pi$
$599$	−4.25945e9	−	7.37759e9i	−0.809766	−	1.40256i	0.103259	−	0.994654i	$-0.467073\pi$
$600$		0			0
$601$	3.29770e9	−	5.71178e9i	0.619656	−	1.07328i	−0.369893	−	0.929074i	$-0.620606\pi$
$601$	3.29770e9	−	5.71178e9i	0.619656	−	1.07328i	0.989548	−	0.144201i	$-0.0460611\pi$
$602$	−5.87623e9			−1.09777
$603$		0			0
$604$	1.61976e9			0.299104
$605$	−8.94238e8	+	1.54887e9i	−0.164176	+	0.284361i
$606$		0			0
$607$	3.30740e9	+	5.72858e9i	0.600242	+	1.03965i	0.992784	+	0.119915i	$0.0382623\pi$
$607$	3.30740e9	+	5.72858e9i	0.600242	+	1.03965i	−0.392542	+	0.919734i	$0.628404\pi$
$608$	−8.44125e8	−	1.46207e9i	−0.152315	−	0.263818i
$609$		0			0
$610$	5.59394e8	−	9.68899e8i	0.0997846	−	0.172832i
$611$	−3.83635e9			−0.680414
$612$		0			0
$613$	−6.77351e9			−1.18769			−0.593843	−	0.804581i	$-0.702390\pi$
$613$	−6.77351e9			−1.18769			−0.593843	+	0.804581i	$0.702390\pi$
$614$	2.59075e9	−	4.48731e9i	0.451685	−	0.782342i
$615$		0			0
$616$	−1.36841e9	−	2.37015e9i	−0.235876	−	0.408548i
$617$	−5.48291e9	−	9.49667e9i	−0.939751	−	1.62770i	−0.765935	−	0.642918i	$-0.777723\pi$
$617$	−5.48291e9	−	9.49667e9i	−0.939751	−	1.62770i	−0.173816	−	0.984778i	$-0.555610\pi$
$618$		0			0
$619$	−2.78882e9	+	4.83038e9i	−0.472610	+	0.818585i	−0.999509	−	0.0313431i	$-0.990022\pi$
$619$	−2.78882e9	+	4.83038e9i	−0.472610	+	0.818585i	0.526898	+	0.849928i	$0.323355\pi$
$620$	−3.18590e9			−0.536861
$621$		0			0
$622$	4.69441e9			0.782194
$623$	−9.87331e8	+	1.71011e9i	−0.163589	+	0.283345i
$624$		0			0
$625$	−1.60880e9	−	2.78652e9i	−0.263585	−	0.456543i
$626$	7.92999e9	+	1.37352e10i	1.29200	+	2.23781i
$627$		0			0
$628$	−1.82716e9	+	3.16473e9i	−0.294386	+	0.509891i
$629$	6.76015e8			0.108313
$630$		0			0
$631$	−6.36080e9			−1.00788			−0.503940	−	0.863739i	$-0.668117\pi$
$631$	−6.36080e9			−1.00788			−0.503940	+	0.863739i	$0.668117\pi$
$632$	−1.21511e9	+	2.10463e9i	−0.191472	+	0.331640i
$633$		0			0
$634$	−3.42696e9	−	5.93568e9i	−0.534069	−	0.925034i
$635$	9.46467e8	+	1.63933e9i	0.146689	+	0.254073i
$636$		0			0
$637$	7.12857e9	−	1.23470e10i	1.09273	−	1.89267i
$638$	−7.35711e9			−1.12159
$639$		0			0
$640$	−1.18709e9			−0.179000
$641$	3.77408e8	−	6.53690e8i	0.0565989	−	0.0980322i	−0.836338	−	0.548215i	$-0.815308\pi$
$641$	3.77408e8	−	6.53690e8i	0.0565989	−	0.0980322i	0.892937	+	0.450182i	$0.148641\pi$
$642$		0			0
$643$	−5.21207e9	−	9.02756e9i	−0.773164	−	1.33916i	−0.935821	−	0.352476i	$-0.885340\pi$
$643$	−5.21207e9	−	9.02756e9i	−0.773164	−	1.33916i	0.162657	−	0.986683i	$-0.447994\pi$
$644$	−8.03718e9	−	1.39208e10i	−1.18578	−	2.05383i
$645$		0			0
$646$	−1.06692e9	+	1.84797e9i	−0.155711	+	0.269700i
$647$	8.26499e9			1.19971			0.599857	−	0.800107i	$-0.295224\pi$
$647$	8.26499e9			1.19971			0.599857	+	0.800107i	$0.295224\pi$
$648$		0			0
$649$	1.21434e10			1.74375
$650$	−6.18153e9	+	1.07067e10i	−0.882875	+	1.52918i
$651$		0			0
$652$	−2.24036e8	−	3.88042e8i	−0.0316556	−	0.0548292i
$653$	−4.56354e9	−	7.90429e9i	−0.641366	−	1.11088i	−0.985128	−	0.171822i	$-0.945035\pi$
$653$	−4.56354e9	−	7.90429e9i	−0.641366	−	1.11088i	0.343762	−	0.939057i	$-0.388299\pi$
$654$		0			0
$655$	−8.26587e8	+	1.43169e9i	−0.114933	+	0.199069i
$656$	−1.91166e9			−0.264391
$657$		0			0
$658$	7.99895e9			1.09457
$659$	−7.53027e8	+	1.30428e9i	−0.102497	+	0.177530i	−0.912713	−	0.408602i	$-0.866017\pi$
$659$	−7.53027e8	+	1.30428e9i	−0.102497	+	0.177530i	0.810216	+	0.586132i	$0.199350\pi$
$660$		0			0
$661$	−4.89923e9	−	8.48572e9i	−0.659816	−	1.14284i	−0.980663	−	0.195704i	$-0.937301\pi$
$661$	−4.89923e9	−	8.48572e9i	−0.659816	−	1.14284i	0.320847	−	0.947131i	$-0.396033\pi$
$662$	−1.89895e9	−	3.28907e9i	−0.254396	−	0.440627i
$663$		0			0
$664$	1.63496e8	−	2.83184e8i	0.0216730	−	0.0375388i
$665$	−1.04378e9			−0.137636
$666$		0			0
$667$	−5.67206e9			−0.740117
$668$	7.87157e9	−	1.36340e10i	1.02175	−	1.76972i
$669$		0			0
$670$	−5.07559e7	−	8.79119e7i	−0.00651966	−	0.0112924i
$671$	1.75037e9	+	3.03173e9i	0.223666	+	0.387401i
$672$		0			0
$673$	4.59414e9	−	7.95729e9i	0.580968	−	1.00627i	−0.414397	−	0.910096i	$-0.636008\pi$
$673$	4.59414e9	−	7.95729e9i	0.580968	−	1.00627i	0.995365	−	0.0961693i	$-0.0306590\pi$
$674$	1.62296e10			2.04172
$675$		0			0
$676$	1.00620e10			1.25277
$677$	−5.08073e9	+	8.80008e9i	−0.629312	+	1.09000i	0.358379	+	0.933576i	$0.383330\pi$
$677$	−5.08073e9	+	8.80008e9i	−0.629312	+	1.09000i	−0.987690	+	0.156423i	$0.950004\pi$
$678$		0			0
$679$	7.62519e9	+	1.32072e10i	0.934773	+	1.61907i
$680$	3.70770e8	+	6.42193e8i	0.0452193	+	0.0783221i
$681$		0			0
$682$	9.31455e9	−	1.61333e10i	1.12439	−	1.94750i
$683$	−9.85009e9			−1.18295			−0.591477	−	0.806322i	$-0.701455\pi$
$683$	−9.85009e9			−1.18295			−0.591477	+	0.806322i	$0.701455\pi$
$684$		0			0
$685$	4.81798e9			0.572727
$686$	−5.03522e9	+	8.72126e9i	−0.595503	+	1.03144i
$687$		0			0
$688$	−1.66606e9	−	2.88570e9i	−0.195043	−	0.337825i
$689$	9.45293e9	+	1.63729e10i	1.10103	+	1.90704i
$690$		0			0
$691$	−1.77163e9	+	3.06856e9i	−0.204268	+	0.353803i	−0.949899	−	0.312556i	$-0.898815\pi$
$691$	−1.77163e9	+	3.06856e9i	−0.204268	+	0.353803i	0.745631	+	0.666359i	$0.232148\pi$
$692$	1.46594e10			1.68169
$693$		0			0
$694$	−2.35790e9			−0.267773
$695$	−2.74010e9	+	4.74599e9i	−0.309613	+	0.536266i
$696$		0			0
$697$	1.42909e9	+	2.47526e9i	0.159862	+	0.276889i
$698$	3.84414e9	+	6.65824e9i	0.427863	+	0.741081i
$699$		0			0
$700$	6.89705e9	−	1.19460e10i	0.760012	−	1.31638i
$701$	1.22196e10			1.33982			0.669908	−	0.742444i	$-0.266334\pi$
$701$	1.22196e10			1.33982			0.669908	+	0.742444i	$0.266334\pi$
$702$		0			0
$703$	2.12301e8			0.0230466
$704$	7.93202e9	−	1.37387e10i	0.856800	−	1.48402i
$705$		0			0
$706$	1.83055e9	+	3.17060e9i	0.195778	+	0.339098i
$707$	7.49962e9	+	1.29897e10i	0.798126	+	1.38240i
$708$		0			0
$709$	−5.09117e9	+	8.81817e9i	−0.536483	+	0.929216i	0.462607	+	0.886563i	$0.346914\pi$
$709$	−5.09117e9	+	8.81817e9i	−0.536483	+	0.929216i	−0.999090	+	0.0426522i	$0.986419\pi$
$710$	−9.39183e9			−0.984795
$711$		0			0
$712$	4.40569e8			0.0457440
$713$	7.18117e9	−	1.24381e10i	0.741962	−	1.28512i
$714$		0			0
$715$	3.87479e9	+	6.71134e9i	0.396440	+	0.686654i
$716$	−1.68833e9	−	2.92427e9i	−0.171894	−	0.297729i
$717$		0			0
$718$	−2.13316e9	+	3.69474e9i	−0.215074	+	0.372519i
$719$	2.32175e9			0.232951			0.116476	−	0.993194i	$-0.462840\pi$
$719$	2.32175e9			0.232951			0.116476	+	0.993194i	$0.462840\pi$
$720$		0			0
$721$	2.20529e9			0.219125
$722$	7.08112e9	−	1.22649e10i	0.700199	−	1.21278i
$723$		0			0
$724$	1.00062e10	+	1.73313e10i	0.979906	+	1.69725i
$725$	−2.43372e9	−	4.21533e9i	−0.237185	−	0.410817i
$726$		0			0
$727$	−6.04458e9	+	1.04695e10i	−0.583439	+	1.01055i	0.411629	+	0.911352i	$0.364960\pi$
$727$	−6.04458e9	+	1.04695e10i	−0.583439	+	1.01055i	−0.995068	+	0.0991947i	$0.968373\pi$
$728$	−5.28426e9			−0.507603
$729$		0			0
$730$	1.54903e9			0.147377
$731$	−2.49098e9	+	4.31450e9i	−0.235863	+	0.408526i
$732$		0			0
$733$	−6.75924e9	−	1.17073e10i	−0.633919	−	1.09798i	−0.986743	−	0.162291i	$-0.948112\pi$
$733$	−6.75924e9	−	1.17073e10i	−0.633919	−	1.09798i	0.352824	−	0.935690i	$-0.385222\pi$
$734$	−5.99618e9	−	1.03857e10i	−0.559678	−	0.969391i
$735$		0			0
$736$	1.00745e10	−	1.74496e10i	0.931436	−	1.61329i
$737$	3.17635e8			0.0292275
$738$		0			0
$739$	9.64611e9			0.879218			0.439609	−	0.898189i	$-0.355117\pi$
$739$	9.64611e9			0.879218			0.439609	+	0.898189i	$0.355117\pi$
$740$	2.81027e8	−	4.86752e8i	0.0254939	−	0.0441567i
$741$		0			0
$742$	−1.97098e10	−	3.41383e10i	−1.77120	−	3.06781i
$743$	6.34672e9	+	1.09928e10i	0.567660	+	0.983217i	0.996797	+	0.0799770i	$0.0254847\pi$
$743$	6.34672e9	+	1.09928e10i	0.567660	+	0.983217i	−0.429136	+	0.903240i	$0.641182\pi$
$744$		0			0
$745$	−6.60385e8	+	1.14382e9i	−0.0585127	+	0.101347i
$746$	−9.77613e9			−0.862147
$747$		0			0
$748$	−1.76767e10			−1.54435
$749$	−6.93929e9	+	1.20192e10i	−0.603432	+	1.04518i
$750$		0			0
$751$	9.19331e8	+	1.59233e9i	0.0792013	+	0.137181i	0.902906	−	0.429839i	$-0.141430\pi$
$751$	9.19331e8	+	1.59233e9i	0.0792013	+	0.137181i	−0.823704	+	0.567020i	$0.808096\pi$
$752$	2.26791e9	+	3.92813e9i	0.194474	+	0.336840i
$753$		0			0
$754$	−7.10258e9	+	1.23020e10i	−0.603415	+	1.04515i
$755$	1.25529e9			0.106153
$756$		0			0
$757$	−3.69951e9			−0.309962			−0.154981	−	0.987917i	$-0.549532\pi$
$757$	−3.69951e9			−0.309962			−0.154981	+	0.987917i	$0.549532\pi$
$758$	−7.48811e9	+	1.29698e10i	−0.624496	+	1.08166i
$759$		0			0
$760$	1.16439e8	+	2.01679e8i	0.00962171	+	0.0166653i
$761$	4.55240e9	+	7.88499e9i	0.374451	+	0.648567i	0.990245	−	0.139340i	$-0.0444980\pi$
$761$	4.55240e9	+	7.88499e9i	0.374451	+	0.648567i	−0.615794	+	0.787907i	$0.711165\pi$
$762$		0			0
$763$	−4.16712e9	+	7.21766e9i	−0.339625	+	0.588248i
$764$	1.64902e10			1.33782
$765$		0			0
$766$	9.28193e9			0.746170
$767$	1.17233e10	−	2.03053e10i	0.938135	−	1.62490i
$768$		0			0
$769$	2.43749e9	+	4.22186e9i	0.193286	+	0.334782i	0.946337	−	0.323180i	$-0.104752\pi$
$769$	2.43749e9	+	4.22186e9i	0.193286	+	0.334782i	−0.753051	+	0.657962i	$0.771419\pi$
$770$	−8.07912e9	−	1.39934e10i	−0.637744	−	1.10461i
$771$		0			0
$772$	−7.58054e9	+	1.31299e10i	−0.592980	+	1.02707i
$773$	−1.86703e9			−0.145386			−0.0726930	−	0.997354i	$-0.523159\pi$
$773$	−1.86703e9			−0.145386			−0.0726930	+	0.997354i	$0.523159\pi$
$774$		0			0
$775$	1.23249e10			0.951106
$776$	1.70126e9	−	2.94668e9i	0.130694	−	0.226369i
$777$		0			0
$778$	1.11292e10	+	1.92764e10i	0.847298	+	1.46756i
$779$	4.48802e8	+	7.77347e8i	0.0340152	+	0.0589161i
$780$		0			0
$781$	1.46937e10	−	2.54503e10i	1.10370	−	1.91167i
$782$	−2.54673e10			−1.90440
$783$		0			0
$784$	−1.68566e10			−1.24929
$785$	−1.41602e9	+	2.45262e9i	−0.104478	+	0.180961i
$786$		0			0
$787$	3.38274e8	+	5.85908e8i	0.0247376	+	0.0428468i	0.878129	−	0.478424i	$-0.158792\pi$
$787$	3.38274e8	+	5.85908e8i	0.0247376	+	0.0428468i	−0.853392	+	0.521270i	$0.825458\pi$
$788$	−2.78469e9	−	4.82323e9i	−0.202738	−	0.351153i
$789$		0			0
$790$	−7.17405e9	+	1.24258e10i	−0.517689	+	0.896665i
$791$	−2.08343e10			−1.49679
$792$		0			0
$793$	6.75924e9			0.481329
$794$	−1.86479e10	+	3.22992e10i	−1.32208	+	2.28992i
$795$		0			0
$796$	3.61633e6	+	6.26367e6i	0.000254140	+	0.000440183i
$797$	−1.39211e10	−	2.41121e10i	−0.974025	−	1.68706i	−0.683116	−	0.730310i	$-0.739376\pi$
$797$	−1.39211e10	−	2.41121e10i	−0.974025	−	1.68706i	−0.290909	−	0.956751i	$-0.593958\pi$
$798$		0			0
$799$	3.39082e9	−	5.87306e9i	0.235175	−	0.407334i
$800$	1.72908e10			1.19399
$801$		0			0
$802$	−3.99075e10			−2.73177
$803$	−2.42349e9	+	4.19762e9i	−0.165172	+	0.286087i
$804$		0			0
$805$	−6.22870e9	−	1.07884e10i	−0.420835	−	0.728907i
$806$	−1.79846e10	−	3.11502e10i	−1.20984	−	2.09550i
$807$		0			0
$808$	1.67325e9	−	2.89815e9i	0.111589	−	0.193278i
$809$	−5.64823e9			−0.375053			−0.187527	−	0.982260i	$-0.560047\pi$
$809$	−5.64823e9			−0.375053			−0.187527	+	0.982260i	$0.560047\pi$
$810$		0			0
$811$	−7.40101e9			−0.487212			−0.243606	−	0.969874i	$-0.578330\pi$
$811$	−7.40101e9			−0.487212			−0.243606	+	0.969874i	$0.578330\pi$
$812$	7.92471e9	−	1.37260e10i	0.519442	−	0.899701i
$813$		0			0
$814$	1.64326e9	+	2.84621e9i	0.106788	+	0.184962i
$815$	−1.73625e8	−	3.00727e8i	−0.0112347	−	0.0194590i
$816$		0			0
$817$	−7.82284e8	+	1.35496e9i	−0.0501866	+	0.0869257i
$818$	1.26773e10			0.809820
$819$		0			0
$820$	2.37635e9			0.150509
$821$	−7.64324e9	+	1.32385e10i	−0.482033	+	0.834905i	−0.999787	−	0.0206240i	$-0.993435\pi$
$821$	−7.64324e9	+	1.32385e10i	−0.482033	+	0.834905i	0.517755	+	0.855529i	$0.326768\pi$
$822$		0			0
$823$	1.48998e10	+	2.58073e10i	0.931714	+	1.61378i	0.780392	+	0.625291i	$0.215020\pi$
$823$	1.48998e10	+	2.58073e10i	0.931714	+	1.61378i	0.151322	+	0.988485i	$0.451647\pi$
$824$	−2.46012e8	−	4.26106e8i	−0.0153183	−	0.0265321i
$825$		0			0
$826$	−2.44436e10	+	4.23375e10i	−1.50916	+	2.61394i
$827$	−6.76407e9			−0.415852			−0.207926	−	0.978145i	$-0.566671\pi$
$827$	−6.76407e9			−0.415852			−0.207926	+	0.978145i	$0.566671\pi$
$828$		0			0
$829$	−2.81440e10			−1.71571			−0.857857	−	0.513888i	$-0.828205\pi$
$829$	−2.81440e10			−1.71571			−0.857857	+	0.513888i	$0.828205\pi$
$830$	9.65288e8	−	1.67193e9i	0.0585981	−	0.101495i
$831$		0			0
$832$	−1.53152e10	−	2.65267e10i	−0.921915	−	1.59680i
$833$	1.26014e10	+	2.18263e10i	0.755373	+	1.30834i
$834$		0			0
$835$	6.10035e9	−	1.05661e10i	0.362621	−	0.628077i
$836$	−5.55131e9			−0.328605
$837$		0			0
$838$	4.78904e9			0.281122
$839$	4.01326e9	−	6.95116e9i	0.234601	−	0.406341i	−0.724556	−	0.689216i	$-0.757955\pi$
$839$	4.01326e9	−	6.95116e9i	0.234601	−	0.406341i	0.959157	+	0.282875i	$0.0912883\pi$
$840$		0			0
$841$	5.82859e9	+	1.00954e10i	0.337892	+	0.585246i
$842$	1.29335e10	+	2.24015e10i	0.746663	+	1.29326i
$843$		0			0
$844$	−1.38921e10	+	2.40619e10i	−0.795373	+	1.37763i
$845$	7.79790e9			0.444610
$846$		0			0
$847$	2.25294e10			1.27396
$848$	1.11764e10	−	1.93582e10i	0.629387	−	1.09013i
$849$		0			0
$850$	−1.09273e10	−	1.89266e10i	−0.610304	−	1.05708i
$851$	1.26689e9	+	2.19432e9i	0.0704671	+	0.122053i
$852$		0			0
$853$	−1.72702e10	+	2.99129e10i	−0.952743	+	1.65020i	−0.213291	+	0.976989i	$0.568418\pi$
$853$	−1.72702e10	+	2.99129e10i	−0.952743	+	1.65020i	−0.739451	+	0.673210i	$0.764915\pi$
$854$	−1.40933e10			−0.774303
$855$		0			0
$856$	3.09647e9			0.168736
$857$	−9.13008e9	+	1.58138e10i	−0.495498	+	0.858227i	−0.999987	−	0.00519114i	$-0.998348\pi$
$857$	−9.13008e9	+	1.58138e10i	−0.495498	+	0.858227i	0.504489	+	0.863418i	$0.331681\pi$
$858$		0			0
$859$	1.08974e10	+	1.88749e10i	0.586608	+	1.01604i	0.994673	+	0.103082i	$0.0328705\pi$
$859$	1.08974e10	+	1.88749e10i	0.586608	+	1.01604i	−0.408065	+	0.912953i	$0.633796\pi$
$860$	2.07105e9	+	3.58717e9i	0.111032	+	0.192312i
$861$		0			0
$862$	8.19320e9	−	1.41910e10i	0.435691	−	0.754638i
$863$	1.25884e10			0.666702			0.333351	−	0.942803i	$-0.391821\pi$
$863$	1.25884e10			0.666702			0.333351	+	0.942803i	$0.391821\pi$
$864$		0			0
$865$	1.13609e10			0.596835
$866$	1.71781e10	−	2.97534e10i	0.898800	−	1.55677i
$867$		0			0
$868$	2.00663e10	+	3.47559e10i	1.04148	+	1.80389i
$869$	−2.24479e10	−	3.88809e10i	−1.16040	−	2.00986i
$870$		0			0
$871$	3.06646e8	−	5.31126e8i	0.0157244	−	0.0272354i
$872$	1.85946e9			0.0949685
$873$		0			0
$874$	−7.99792e9			−0.405216
$875$	1.17610e10	−	2.03707e10i	0.593494	−	1.02796i
$876$		0			0
$877$	−9.17484e9	−	1.58913e10i	−0.459304	−	0.795537i	0.539621	−	0.841908i	$-0.318568\pi$
$877$	−9.17484e9	−	1.58913e10i	−0.459304	−	0.795537i	−0.998924	+	0.0463711i	$0.985234\pi$
$878$	2.57833e10	+	4.46580e10i	1.28561	+	2.22674i
$879$		0			0
$880$	4.58127e9	−	7.93499e9i	0.226619	−	0.392516i
$881$	1.25257e10			0.617146			0.308573	−	0.951201i	$-0.400149\pi$
$881$	1.25257e10			0.617146			0.308573	+	0.951201i	$0.400149\pi$
$882$		0			0
$883$	2.79816e10			1.36776			0.683880	−	0.729594i	$-0.260291\pi$
$883$	2.79816e10			1.36776			0.683880	+	0.729594i	$0.260291\pi$
$884$	−1.70651e10	+	2.95577e10i	−0.830858	+	1.43909i
$885$		0			0
$886$	−1.47456e10	−	2.55401e10i	−0.712269	−	1.23369i
$887$	1.37282e10	+	2.37780e10i	0.660515	+	1.14405i	0.980481	+	0.196616i	$0.0629952\pi$
$887$	1.37282e10	+	2.37780e10i	0.660515	+	1.14405i	−0.319966	+	0.947429i	$0.603671\pi$
$888$		0			0
$889$	1.19226e10	−	2.06505e10i	0.569134	−	0.985769i
$890$	2.60113e9			0.123679
$891$		0			0
$892$	1.55703e10			0.734547
$893$	1.06488e9	−	1.84442e9i	0.0500402	−	0.0866721i
$894$		0			0
$895$	−1.30843e9	−	2.26626e9i	−0.0610055	−	0.105665i
$896$	7.47683e9	+	1.29502e10i	0.347248	+	0.601450i
$897$		0			0
$898$	2.81230e10	−	4.87104e10i	1.29597	−	2.24468i
$899$	1.41614e10			0.650049
$900$		0			0
$901$	−3.34205e10			−1.52221
$902$	−6.94768e9	+	1.20337e10i	−0.315222	+	0.545981i
$903$		0			0
$904$	2.32418e9	+	4.02559e9i	0.104636	+	0.181234i
$905$	7.75466e9	+	1.34315e10i	0.347771	+	0.602357i
$906$		0			0
$907$	−1.58184e9	+	2.73983e9i	−0.0703944	+	0.121927i	−0.899074	−	0.437796i	$-0.855759\pi$
$907$	−1.58184e9	+	2.73983e9i	−0.0703944	+	0.121927i	0.828680	+	0.559723i	$0.189092\pi$
$908$	−6.76662e9			−0.299966
$909$		0			0
$910$	−3.11984e10			−1.37242
$911$	8.63699e9	−	1.49597e10i	0.378485	−	0.655555i	−0.612357	−	0.790581i	$-0.709779\pi$
$911$	8.63699e9	−	1.49597e10i	0.378485	−	0.655555i	0.990842	+	0.135027i	$0.0431120\pi$
$912$		0			0
$913$	3.02043e9	+	5.23153e9i	0.131347	+	0.227500i
$914$	1.73935e10	+	3.01265e10i	0.753488	+	1.30508i
$915$		0			0
$916$	9.05370e9	−	1.56815e10i	0.389217	−	0.674144i
$917$	2.08249e10			0.891849
$918$		0			0
$919$	9.42182e9			0.400434			0.200217	−	0.979752i	$-0.435835\pi$
$919$	9.42182e9			0.400434			0.200217	+	0.979752i	$0.435835\pi$
$920$	−1.38969e9	+	2.40702e9i	−0.0588384	+	0.101911i
$921$		0			0
$922$	−1.48062e10	−	2.56451e10i	−0.622137	−	1.07757i
$923$	−2.83707e10	−	4.91395e10i	−1.18758	−	2.05696i
$924$		0			0
$925$	−1.08718e9	+	1.88304e9i	−0.0451652	+	0.0782283i
$926$	3.81316e10			1.57814
$927$		0			0
$928$	1.98671e10			0.816051
$929$	1.16296e10	−	2.01431e10i	0.475894	−	0.824272i	−0.523725	−	0.851888i	$-0.675458\pi$
$929$	1.16296e10	−	2.01431e10i	0.475894	−	0.824272i	0.999619	+	0.0276152i	$0.00879131\pi$
$930$		0			0
$931$	3.95743e9	+	6.85447e9i	0.160727	+	0.278388i
$932$	−1.23969e10	−	2.14721e10i	−0.501602	−	0.868800i
$933$		0			0
$934$	7.13498e9	−	1.23582e10i	0.286536	−	0.496295i
$935$	−1.36992e10			−0.548093
$936$		0			0
$937$	2.57549e10			1.02275			0.511377	−	0.859357i	$-0.329136\pi$
$937$	2.57549e10			1.02275			0.511377	+	0.859357i	$0.329136\pi$
$938$	−6.39370e8	+	1.10742e9i	−0.0252954	+	0.0438130i
$939$		0			0
$940$	−2.81919e9	−	4.88299e9i	−0.110708	−	0.191751i
$941$	1.06913e10	+	1.85178e10i	0.418278	+	0.724479i	0.995766	−	0.0919198i	$-0.0293004\pi$
$941$	1.06913e10	+	1.85178e10i	0.418278	+	0.724479i	−0.577488	+	0.816399i	$0.695967\pi$
$942$		0			0
$943$	−5.35640e9	+	9.27756e9i	−0.208009	+	0.360282i
$944$	−2.77215e10			−1.07254
$945$		0			0
$946$	−2.42203e10			−0.930167
$947$	−1.95339e10	+	3.38338e10i	−0.747420	+	1.29457i	0.201635	+	0.979461i	$0.435375\pi$
$947$	−1.95339e10	+	3.38338e10i	−0.747420	+	1.29457i	−0.949055	+	0.315109i	$0.897959\pi$
$948$		0			0
$949$	4.67930e9	+	8.10478e9i	0.177725	+	0.307829i
$950$	−3.43168e9	−	5.94384e9i	−0.129860	−	0.224924i
$951$		0			0
$952$	4.67058e9	−	8.08968e9i	0.175445	−	0.303880i
$953$	−1.44692e10			−0.541527			−0.270763	−	0.962646i	$-0.587276\pi$
$953$	−1.44692e10			−0.541527			−0.270763	+	0.962646i	$0.587276\pi$
$954$		0			0
$955$	1.27796e10			0.474796
$956$	−5.91223e9	+	1.02403e10i	−0.218851	+	0.379061i
$957$		0			0
$958$	−2.54382e8	−	4.40603e8i	−0.00934775	−	0.0161908i
$959$	−3.03459e10	−	5.25607e10i	−1.11105	−	1.92440i
$960$		0			0
$961$	−4.17283e9	+	7.22756e9i	−0.151670	+	0.262700i
$962$	6.34564e9			0.229807
$963$		0			0
$964$	2.20021e10			0.791032
$965$	−5.87481e9	+	1.01755e10i	−0.210450	+	0.364510i
$966$		0			0
$967$	−1.84269e10	−	3.19163e10i	−0.655329	−	1.13506i	−0.981811	−	0.189860i	$-0.939197\pi$
$967$	−1.84269e10	−	3.19163e10i	−0.655329	−	1.13506i	0.326482	−	0.945203i	$-0.394137\pi$
$968$	−2.51327e9	−	4.35312e9i	−0.0890586	−	0.154254i
$969$		0			0
$970$	1.00443e10	−	1.73973e10i	0.353361	−	0.612040i
$971$	−1.36704e10			−0.479198			−0.239599	−	0.970872i	$-0.577016\pi$
$971$	−1.36704e10			−0.479198			−0.239599	+	0.970872i	$0.577016\pi$
$972$		0			0
$973$	6.90337e10			2.40252
$974$	4.80144e9	−	8.31634e9i	0.166500	−	0.288387i
$975$		0			0
$976$	−3.99581e9	−	6.92095e9i	−0.137572	−	0.238282i
$977$	−1.75709e10	−	3.04336e10i	−0.602785	−	1.04405i	−0.992397	−	0.123075i	$-0.960725\pi$
$977$	−1.75709e10	−	3.04336e10i	−0.602785	−	1.04405i	0.389613	−	0.920979i	$-0.372609\pi$
$978$		0			0
$979$	−4.06952e9	+	7.04862e9i	−0.138613	+	0.240085i
$980$	2.09541e10			0.711178
$981$		0			0
$982$	5.47116e10			1.84369
$983$	−1.64952e10	+	2.85705e10i	−0.553885	+	0.959356i	0.444105	+	0.895975i	$0.353522\pi$
$983$	−1.64952e10	+	2.85705e10i	−0.553885	+	0.959356i	−0.997989	+	0.0633816i	$0.979811\pi$
$984$		0			0
$985$	−2.15810e9	−	3.73794e9i	−0.0719523	−	0.124625i
$986$	−1.25555e10	−	2.17467e10i	−0.417122	−	0.722477i
$987$		0			0
$988$	−5.35926e9	+	9.28250e9i	−0.176789	+	0.306207i
$989$	−1.86730e10			−0.613799
$990$		0			0
$991$	−2.08796e10			−0.681496			−0.340748	−	0.940155i	$-0.610680\pi$
$991$	−2.08796e10			−0.681496			−0.340748	+	0.940155i	$0.610680\pi$
$992$	−2.51530e10	+	4.35663e10i	−0.818086	+	1.41697i
$993$		0			0
$994$	5.91542e10	+	1.02458e11i	1.91044	+	3.30898i
$995$	2.80260e6	+	4.85425e6i	9.01947e−5	+	0.000156222i
$996$		0			0
$997$	1.64943e10	−	2.85690e10i	0.527111	−	0.912982i	−0.472390	−	0.881389i	$-0.656609\pi$
$997$	1.64943e10	−	2.85690e10i	0.527111	−	0.912982i	0.999501	−	0.0315927i	$-0.0100580\pi$
$998$	−7.08837e10			−2.25730
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.8.c.d.55.1		4
3.2	odd	2		81.8.c.h.55.2		4
9.2	odd	6		27.8.a.b.1.1	✓	2
9.4	even	3	inner	81.8.c.d.28.1		4
9.5	odd	6		81.8.c.h.28.2		4
9.7	even	3		27.8.a.e.1.2	yes	2
36.7	odd	6		432.8.a.q.1.2		2
36.11	even	6		432.8.a.j.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.8.a.b.1.1	✓	2	9.2	odd	6
27.8.a.e.1.2	yes	2	9.7	even	3
81.8.c.d.28.1		4	9.4	even	3	inner
81.8.c.d.55.1		4	1.1	even	1	trivial
81.8.c.h.28.2		4	9.5	odd	6
81.8.c.h.55.2		4	3.2	odd	2
432.8.a.j.1.1		2	36.11	even	6
432.8.a.q.1.2		2	36.7	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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	81.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-8.29669 + 14.3703i) q^{2} +(-73.6702 - 127.601i) q^{4} +(-57.0934 - 98.8886i) q^{5} +(-719.202 + 1245.70i) q^{7} +320.924 q^{8} +1894.75 q^{10} +(-2964.37 + 5134.44i) q^{11} +(5723.62 + 9913.60i) q^{13} +(-11934.0 - 20670.3i) q^{14} +(6767.18 - 11721.1i) q^{16} -20235.6 q^{17} -6354.94 q^{19} +(-8412.17 + 14570.3i) q^{20} +(-49188.9 - 85197.7i) q^{22} +(-37922.8 - 65684.2i) q^{23} +(32543.2 - 56366.5i) q^{25} -189948. q^{26} +211935. q^{28} +(37392.1 - 64765.1i) q^{29} +(94681.4 + 163993. i) q^{31} +(132830. + 230068. i) q^{32} +(167889. - 290792. i) q^{34} +164247. q^{35} -33407.2 q^{37} +(52725.0 - 91322.4i) q^{38} +(-18322.6 - 31735.7i) q^{40} +(-70622.4 - 122322. i) q^{41} +(123099. - 213213. i) q^{43} +873543. q^{44} +1.25854e6 q^{46} +(-167566. + 290234. i) q^{47} +(-622733. - 1.07860e6i) q^{49} +(540002. + 935310. i) q^{50} +(843321. - 1.46067e6i) q^{52} +1.65156e6 q^{53} +676983. q^{55} +(-230809. + 399774. i) q^{56} +(620462. + 1.07467e6i) q^{58} +(-1.02411e6 - 1.77382e6i) q^{59} +(295235. - 511361. i) q^{61} -3.14217e6 q^{62} -2.67579e6 q^{64} +(653562. - 1.13200e6i) q^{65} +(-26787.7 - 46397.7i) q^{67} +(1.49076e6 + 2.58208e6i) q^{68} +(-1.36271e6 + 2.36027e6i) q^{70} -4.95678e6 q^{71} +817542. q^{73} +(277169. - 480071. i) q^{74} +(468170. + 810895. i) q^{76} +(-4.26396e6 - 7.38540e6i) q^{77} +(-3.78629e6 + 6.55804e6i) q^{79} -1.54545e6 q^{80} +2.34373e6 q^{82} +(509455. - 882402. i) q^{83} +(1.15532e6 + 2.00108e6i) q^{85} +(2.04262e6 + 3.53792e6i) q^{86} +(-951337. + 1.64776e6i) q^{88} +1.37281e6 q^{89} -1.64658e7 q^{91} +(-5.58756e6 + 9.67794e6i) q^{92} +(-2.78049e6 - 4.81596e6i) q^{94} +(362825. + 628432. i) q^{95} +(5.30114e6 - 9.18185e6i) q^{97} +2.06665e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 9 q^{2} - 77 q^{4} - 180 q^{5} - 700 q^{7} + 3654 q^{8} + 2790 q^{10} - 10890 q^{11} + 5480 q^{13} - 29475 q^{14} + 15967 q^{16} + 32832 q^{17} + 32048 q^{19} - 12195 q^{20} - 60705 q^{22} - 24372 q^{23}+ \cdots + 45559476 q^{98}+O(q^{100}) \) 4 * q - 9 * q^2 - 77 * q^4 - 180 * q^5 - 700 * q^7 + 3654 * q^8 + 2790 * q^10 - 10890 * q^11 + 5480 * q^13 - 29475 * q^14 + 15967 * q^16 + 32832 * q^17 + 32048 * q^19 - 12195 * q^20 - 60705 * q^22 - 24372 * q^23 + 138880 * q^25 - 470520 * q^26 + 527750 * q^28 + 143280 * q^29 + 38708 * q^31 + 439965 * q^32 + 614088 * q^34 + 231300 * q^35 + 911240 * q^37 + 275382 * q^38 - 135765 * q^40 - 731880 * q^41 + 1088840 * q^43 + 1049130 * q^44 + 3298788 * q^46 - 1561500 * q^47 - 967164 * q^49 + 519660 * q^50 + 2106380 * q^52 + 5220936 * q^53 + 2007000 * q^55 + 650475 * q^56 + 720810 * q^58 - 1731960 * q^59 + 620192 * q^61 - 8572302 * q^62 - 2081678 * q^64 + 914400 * q^65 - 346600 * q^67 + 5559624 * q^68 - 3094425 * q^70 - 8484480 * q^71 - 6290380 * q^73 + 4267710 * q^74 + 2510486 * q^76 - 4864500 * q^77 - 10110616 * q^79 - 3411090 * q^80 - 4282380 * q^82 - 644202 * q^83 - 101520 * q^85 - 2313270 * q^86 - 9374715 * q^88 + 12042000 * q^89 - 41744000 * q^91 - 14795802 * q^92 + 3751290 * q^94 - 747180 * q^95 - 4098670 * q^97 + 45559476 * q^98

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